/* Generated by Cython 3.1.6 */

/* BEGIN: Cython Metadata
{
    "distutils": {
        "depends": [],
        "extra_compile_args": [
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            "-ffast-math"
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        "include_dirs": [
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            "pyRing"
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        "language": "c",
        "libraries": [
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        "name": "pyRing.eob_utils",
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}
END: Cython Metadata */

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  #undef CYTHON_METH_FASTCALL
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  #define CYTHON_COMPILING_IN_PYPY 0
  #define CYTHON_COMPILING_IN_CPYTHON 1
  #define CYTHON_COMPILING_IN_LIMITED_API 0
  #define CYTHON_COMPILING_IN_GRAAL 0
  #ifdef Py_GIL_DISABLED
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#if CYTHON_COMPILING_IN_LIMITED_API
#define CYTHON_VECTORCALL  (__PYX_LIMITED_VERSION_HEX >= 0x030C0000)
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#define CYTHON_VECTORCALL  (CYTHON_FAST_PYCCALL && PY_VERSION_HEX >= 0x030800B1)
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      #if __has_cpp_attribute(maybe_unused)
        #define CYTHON_UNUSED [[maybe_unused]]
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# if defined(__GNUC__)
#   if !(defined(__cplusplus)) || (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4))
#     define CYTHON_UNUSED __attribute__ ((__unused__))
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#     define CYTHON_UNUSED
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# elif defined(__ICC) || (defined(__INTEL_COMPILER) && !defined(_MSC_VER))
#   define CYTHON_UNUSED __attribute__ ((__unused__))
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# if CYTHON_COMPILING_IN_CPYTHON && !CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
#  define CYTHON_NCP_UNUSED
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#define __Pyx_void_to_None(void_result) ((void)(void_result), Py_INCREF(Py_None), Py_None)
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      #define CYTHON_FALLTHROUGH
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#ifndef Py_UNREACHABLE
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#ifdef __cplusplus
  template <typename T>
  struct __PYX_IS_UNSIGNED_IMPL {static const bool value = T(0) < T(-1);};
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#if CYTHON_COMPILING_IN_PYPY == 1
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#else
  #define __PYX_NEED_TP_PRINT_SLOT  (PY_VERSION_HEX >= 0x030800b4 && PY_VERSION_HEX < 0x03090000)
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#define __PYX_REINTERPRET_FUNCION(func_pointer, other_pointer) ((func_pointer)(void(*)(void))(other_pointer))

/* CInitCode */
#ifndef CYTHON_INLINE
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    #define CYTHON_INLINE __inline__ __attribute__ ((__unused__))
  #elif defined(__GNUC__)
    #define CYTHON_INLINE __inline__
  #elif defined(_MSC_VER)
    #define CYTHON_INLINE __inline
  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
    #define CYTHON_INLINE inline
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    #define CYTHON_INLINE
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/* PythonCompatibility */
#define __PYX_BUILD_PY_SSIZE_T "n"
#define CYTHON_FORMAT_SSIZE_T "z"
#define __Pyx_BUILTIN_MODULE_NAME "builtins"
#define __Pyx_DefaultClassType PyType_Type
#if CYTHON_COMPILING_IN_LIMITED_API
    #ifndef CO_OPTIMIZED
    static int CO_OPTIMIZED;
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    #ifndef CO_NEWLOCALS
    static int CO_NEWLOCALS;
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    #ifndef CO_VARARGS
    static int CO_VARARGS;
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    #ifndef CO_VARKEYWORDS
    static int CO_VARKEYWORDS;
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    #ifndef CO_ASYNC_GENERATOR
    static int CO_ASYNC_GENERATOR;
    #endif
    #ifndef CO_GENERATOR
    static int CO_GENERATOR;
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    #ifndef CO_COROUTINE
    static int CO_COROUTINE;
    #endif
#else
    #ifndef CO_COROUTINE
      #define CO_COROUTINE 0x80
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    #ifndef CO_ASYNC_GENERATOR
      #define CO_ASYNC_GENERATOR 0x200
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static int __Pyx_init_co_variables(void);
#if PY_VERSION_HEX >= 0x030900A4 || defined(Py_IS_TYPE)
  #define __Pyx_IS_TYPE(ob, type) Py_IS_TYPE(ob, type)
#else
  #define __Pyx_IS_TYPE(ob, type) (((const PyObject*)ob)->ob_type == (type))
#endif
#if PY_VERSION_HEX >= 0x030A00B1 || defined(Py_Is)
  #define __Pyx_Py_Is(x, y)  Py_Is(x, y)
#else
  #define __Pyx_Py_Is(x, y) ((x) == (y))
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#if PY_VERSION_HEX >= 0x030A00B1 || defined(Py_IsNone)
  #define __Pyx_Py_IsNone(ob) Py_IsNone(ob)
#else
  #define __Pyx_Py_IsNone(ob) __Pyx_Py_Is((ob), Py_None)
#endif
#if PY_VERSION_HEX >= 0x030A00B1 || defined(Py_IsTrue)
  #define __Pyx_Py_IsTrue(ob) Py_IsTrue(ob)
#else
  #define __Pyx_Py_IsTrue(ob) __Pyx_Py_Is((ob), Py_True)
#endif
#if PY_VERSION_HEX >= 0x030A00B1 || defined(Py_IsFalse)
  #define __Pyx_Py_IsFalse(ob) Py_IsFalse(ob)
#else
  #define __Pyx_Py_IsFalse(ob) __Pyx_Py_Is((ob), Py_False)
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#define __Pyx_NoneAsNull(obj)  (__Pyx_Py_IsNone(obj) ? NULL : (obj))
#if PY_VERSION_HEX >= 0x030900F0 && !CYTHON_COMPILING_IN_PYPY
  #define __Pyx_PyObject_GC_IsFinalized(o) PyObject_GC_IsFinalized(o)
#else
  #define __Pyx_PyObject_GC_IsFinalized(o) _PyGC_FINALIZED(o)
#endif
#ifndef Py_TPFLAGS_CHECKTYPES
  #define Py_TPFLAGS_CHECKTYPES 0
#endif
#ifndef Py_TPFLAGS_HAVE_INDEX
  #define Py_TPFLAGS_HAVE_INDEX 0
#endif
#ifndef Py_TPFLAGS_HAVE_NEWBUFFER
  #define Py_TPFLAGS_HAVE_NEWBUFFER 0
#endif
#ifndef Py_TPFLAGS_HAVE_FINALIZE
  #define Py_TPFLAGS_HAVE_FINALIZE 0
#endif
#ifndef Py_TPFLAGS_SEQUENCE
  #define Py_TPFLAGS_SEQUENCE 0
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#ifndef Py_TPFLAGS_MAPPING
  #define Py_TPFLAGS_MAPPING 0
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#ifndef METH_STACKLESS
  #define METH_STACKLESS 0
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#ifndef METH_FASTCALL
  #ifndef METH_FASTCALL
     #define METH_FASTCALL 0x80
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  typedef PyObject *(*__Pyx_PyCFunctionFast) (PyObject *self, PyObject *const *args, Py_ssize_t nargs);
  typedef PyObject *(*__Pyx_PyCFunctionFastWithKeywords) (PyObject *self, PyObject *const *args,
                                                          Py_ssize_t nargs, PyObject *kwnames);
#else
  #if PY_VERSION_HEX >= 0x030d00A4
  #  define __Pyx_PyCFunctionFast PyCFunctionFast
  #  define __Pyx_PyCFunctionFastWithKeywords PyCFunctionFastWithKeywords
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  #  define __Pyx_PyCFunctionFast _PyCFunctionFast
  #  define __Pyx_PyCFunctionFastWithKeywords _PyCFunctionFastWithKeywords
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#endif
#if CYTHON_METH_FASTCALL
  #define __Pyx_METH_FASTCALL METH_FASTCALL
  #define __Pyx_PyCFunction_FastCall __Pyx_PyCFunctionFast
  #define __Pyx_PyCFunction_FastCallWithKeywords __Pyx_PyCFunctionFastWithKeywords
#else
  #define __Pyx_METH_FASTCALL METH_VARARGS
  #define __Pyx_PyCFunction_FastCall PyCFunction
  #define __Pyx_PyCFunction_FastCallWithKeywords PyCFunctionWithKeywords
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#if CYTHON_VECTORCALL
  #define __pyx_vectorcallfunc vectorcallfunc
  #define __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET  PY_VECTORCALL_ARGUMENTS_OFFSET
  #define __Pyx_PyVectorcall_NARGS(n)  PyVectorcall_NARGS((size_t)(n))
#elif CYTHON_BACKPORT_VECTORCALL
  typedef PyObject *(*__pyx_vectorcallfunc)(PyObject *callable, PyObject *const *args,
                                            size_t nargsf, PyObject *kwnames);
  #define __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET  ((size_t)1 << (8 * sizeof(size_t) - 1))
  #define __Pyx_PyVectorcall_NARGS(n)  ((Py_ssize_t)(((size_t)(n)) & ~__Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET))
#else
  #define __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET  0
  #define __Pyx_PyVectorcall_NARGS(n)  ((Py_ssize_t)(n))
#endif
#if PY_VERSION_HEX >= 0x030900B1
#define __Pyx_PyCFunction_CheckExact(func)  PyCFunction_CheckExact(func)
#else
#define __Pyx_PyCFunction_CheckExact(func)  PyCFunction_Check(func)
#endif
#define __Pyx_CyOrPyCFunction_Check(func)  PyCFunction_Check(func)
#if CYTHON_COMPILING_IN_CPYTHON
#define __Pyx_CyOrPyCFunction_GET_FUNCTION(func)  (((PyCFunctionObject*)(func))->m_ml->ml_meth)
#elif !CYTHON_COMPILING_IN_LIMITED_API
#define __Pyx_CyOrPyCFunction_GET_FUNCTION(func)  PyCFunction_GET_FUNCTION(func)
#endif
#if CYTHON_COMPILING_IN_CPYTHON
#define __Pyx_CyOrPyCFunction_GET_FLAGS(func)  (((PyCFunctionObject*)(func))->m_ml->ml_flags)
static CYTHON_INLINE PyObject* __Pyx_CyOrPyCFunction_GET_SELF(PyObject *func) {
    return (__Pyx_CyOrPyCFunction_GET_FLAGS(func) & METH_STATIC) ? NULL : ((PyCFunctionObject*)func)->m_self;
}
#endif
static CYTHON_INLINE int __Pyx__IsSameCFunction(PyObject *func, void (*cfunc)(void)) {
#if CYTHON_COMPILING_IN_LIMITED_API
    return PyCFunction_Check(func) && PyCFunction_GetFunction(func) == (PyCFunction) cfunc;
#else
    return PyCFunction_Check(func) && PyCFunction_GET_FUNCTION(func) == (PyCFunction) cfunc;
#endif
}
#define __Pyx_IsSameCFunction(func, cfunc)   __Pyx__IsSameCFunction(func, cfunc)
#if __PYX_LIMITED_VERSION_HEX < 0x03090000
  #define __Pyx_PyType_FromModuleAndSpec(m, s, b)  ((void)m, PyType_FromSpecWithBases(s, b))
  typedef PyObject *(*__Pyx_PyCMethod)(PyObject *, PyTypeObject *, PyObject *const *, size_t, PyObject *);
#else
  #define __Pyx_PyType_FromModuleAndSpec(m, s, b)  PyType_FromModuleAndSpec(m, s, b)
  #define __Pyx_PyCMethod  PyCMethod
#endif
#ifndef METH_METHOD
  #define METH_METHOD 0x200
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#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Malloc)
  #define PyObject_Malloc(s)   PyMem_Malloc(s)
  #define PyObject_Free(p)     PyMem_Free(p)
  #define PyObject_Realloc(p)  PyMem_Realloc(p)
#endif
#if CYTHON_COMPILING_IN_LIMITED_API
  #define __Pyx_PyFrame_SetLineNumber(frame, lineno)
#elif CYTHON_COMPILING_IN_GRAAL
  #define __Pyx_PyCode_HasFreeVars(co)  (PyCode_GetNumFree(co) > 0)
  #define __Pyx_PyFrame_SetLineNumber(frame, lineno) _PyFrame_SetLineNumber((frame), (lineno))
#else
  #define __Pyx_PyCode_HasFreeVars(co)  (PyCode_GetNumFree(co) > 0)
  #define __Pyx_PyFrame_SetLineNumber(frame, lineno)  (frame)->f_lineno = (lineno)
#endif
#if CYTHON_COMPILING_IN_LIMITED_API
  #define __Pyx_PyThreadState_Current PyThreadState_Get()
#elif !CYTHON_FAST_THREAD_STATE
  #define __Pyx_PyThreadState_Current PyThreadState_GET()
#elif PY_VERSION_HEX >= 0x030d00A1
  #define __Pyx_PyThreadState_Current PyThreadState_GetUnchecked()
#else
  #define __Pyx_PyThreadState_Current _PyThreadState_UncheckedGet()
#endif
#if CYTHON_USE_MODULE_STATE
static CYTHON_INLINE void *__Pyx__PyModule_GetState(PyObject *op)
{
    void *result;
    result = PyModule_GetState(op);
    if (!result)
        Py_FatalError("Couldn't find the module state");
    return result;
}
#define __Pyx_PyModule_GetState(o) (__pyx_mstatetype *)__Pyx__PyModule_GetState(o)
#else
#define __Pyx_PyModule_GetState(op) ((void)op,__pyx_mstate_global)
#endif
#define __Pyx_PyObject_GetSlot(obj, name, func_ctype)  __Pyx_PyType_GetSlot(Py_TYPE((PyObject *) obj), name, func_ctype)
#define __Pyx_PyObject_TryGetSlot(obj, name, func_ctype) __Pyx_PyType_TryGetSlot(Py_TYPE(obj), name, func_ctype)
#define __Pyx_PyObject_GetSubSlot(obj, sub, name, func_ctype) __Pyx_PyType_GetSubSlot(Py_TYPE(obj), sub, name, func_ctype)
#define __Pyx_PyObject_TryGetSubSlot(obj, sub, name, func_ctype) __Pyx_PyType_TryGetSubSlot(Py_TYPE(obj), sub, name, func_ctype)
#if CYTHON_USE_TYPE_SLOTS
  #define __Pyx_PyType_GetSlot(type, name, func_ctype)  ((type)->name)
  #define __Pyx_PyType_TryGetSlot(type, name, func_ctype) __Pyx_PyType_GetSlot(type, name, func_ctype)
  #define __Pyx_PyType_GetSubSlot(type, sub, name, func_ctype) (((type)->sub) ? ((type)->sub->name) : NULL)
  #define __Pyx_PyType_TryGetSubSlot(type, sub, name, func_ctype) __Pyx_PyType_GetSubSlot(type, sub, name, func_ctype)
#else
  #define __Pyx_PyType_GetSlot(type, name, func_ctype)  ((func_ctype) PyType_GetSlot((type), Py_##name))
  #define __Pyx_PyType_TryGetSlot(type, name, func_ctype)\
    ((__PYX_LIMITED_VERSION_HEX >= 0x030A0000 ||\
     (PyType_GetFlags(type) & Py_TPFLAGS_HEAPTYPE) || __Pyx_get_runtime_version() >= 0x030A0000) ?\
     __Pyx_PyType_GetSlot(type, name, func_ctype) : NULL)
  #define __Pyx_PyType_GetSubSlot(obj, sub, name, func_ctype) __Pyx_PyType_GetSlot(obj, name, func_ctype)
  #define __Pyx_PyType_TryGetSubSlot(obj, sub, name, func_ctype) __Pyx_PyType_TryGetSlot(obj, name, func_ctype)
#endif
#if CYTHON_COMPILING_IN_CPYTHON || defined(_PyDict_NewPresized)
#define __Pyx_PyDict_NewPresized(n)  ((n <= 8) ? PyDict_New() : _PyDict_NewPresized(n))
#else
#define __Pyx_PyDict_NewPresized(n)  PyDict_New()
#endif
#define __Pyx_PyNumber_Divide(x,y)         PyNumber_TrueDivide(x,y)
#define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceTrueDivide(x,y)
#if CYTHON_COMPILING_IN_CPYTHON && CYTHON_USE_UNICODE_INTERNALS
#define __Pyx_PyDict_GetItemStrWithError(dict, name)  _PyDict_GetItem_KnownHash(dict, name, ((PyASCIIObject *) name)->hash)
static CYTHON_INLINE PyObject * __Pyx_PyDict_GetItemStr(PyObject *dict, PyObject *name) {
    PyObject *res = __Pyx_PyDict_GetItemStrWithError(dict, name);
    if (res == NULL) PyErr_Clear();
    return res;
}
#elif !CYTHON_COMPILING_IN_PYPY || PYPY_VERSION_NUM >= 0x07020000
#define __Pyx_PyDict_GetItemStrWithError  PyDict_GetItemWithError
#define __Pyx_PyDict_GetItemStr           PyDict_GetItem
#else
static CYTHON_INLINE PyObject * __Pyx_PyDict_GetItemStrWithError(PyObject *dict, PyObject *name) {
#if CYTHON_COMPILING_IN_PYPY
    return PyDict_GetItem(dict, name);
#else
    PyDictEntry *ep;
    PyDictObject *mp = (PyDictObject*) dict;
    long hash = ((PyStringObject *) name)->ob_shash;
    assert(hash != -1);
    ep = (mp->ma_lookup)(mp, name, hash);
    if (ep == NULL) {
        return NULL;
    }
    return ep->me_value;
#endif
}
#define __Pyx_PyDict_GetItemStr           PyDict_GetItem
#endif
#if CYTHON_USE_TYPE_SLOTS
  #define __Pyx_PyType_GetFlags(tp)   (((PyTypeObject *)tp)->tp_flags)
  #define __Pyx_PyType_HasFeature(type, feature)  ((__Pyx_PyType_GetFlags(type) & (feature)) != 0)
#else
  #define __Pyx_PyType_GetFlags(tp)   (PyType_GetFlags((PyTypeObject *)tp))
  #define __Pyx_PyType_HasFeature(type, feature)  PyType_HasFeature(type, feature)
#endif
#define __Pyx_PyObject_GetIterNextFunc(iterator)  __Pyx_PyObject_GetSlot(iterator, tp_iternext, iternextfunc)
#if CYTHON_USE_TYPE_SPECS && PY_VERSION_HEX >= 0x03080000
#define __Pyx_PyHeapTypeObject_GC_Del(obj)  {\
    PyTypeObject *type = Py_TYPE((PyObject*)obj);\
    assert(__Pyx_PyType_HasFeature(type, Py_TPFLAGS_HEAPTYPE));\
    PyObject_GC_Del(obj);\
    Py_DECREF(type);\
}
#else
#define __Pyx_PyHeapTypeObject_GC_Del(obj)  PyObject_GC_Del(obj)
#endif
#if CYTHON_COMPILING_IN_LIMITED_API
  #define __Pyx_PyUnicode_READY(op)       (0)
  #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_ReadChar(u, i)
  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u)   ((void)u, 1114111U)
  #define __Pyx_PyUnicode_KIND(u)         ((void)u, (0))
  #define __Pyx_PyUnicode_DATA(u)         ((void*)u)
  #define __Pyx_PyUnicode_READ(k, d, i)   ((void)k, PyUnicode_ReadChar((PyObject*)(d), i))
  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != PyUnicode_GetLength(u))
#else
  #if PY_VERSION_HEX >= 0x030C0000
    #define __Pyx_PyUnicode_READY(op)       (0)
  #else
    #define __Pyx_PyUnicode_READY(op)       (likely(PyUnicode_IS_READY(op)) ?\
                                                0 : _PyUnicode_Ready((PyObject *)(op)))
  #endif
  #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_READ_CHAR(u, i)
  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u)   PyUnicode_MAX_CHAR_VALUE(u)
  #define __Pyx_PyUnicode_KIND(u)         ((int)PyUnicode_KIND(u))
  #define __Pyx_PyUnicode_DATA(u)         PyUnicode_DATA(u)
  #define __Pyx_PyUnicode_READ(k, d, i)   PyUnicode_READ(k, d, i)
  #define __Pyx_PyUnicode_WRITE(k, d, i, ch)  PyUnicode_WRITE(k, d, i, (Py_UCS4) ch)
  #if PY_VERSION_HEX >= 0x030C0000
    #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != PyUnicode_GET_LENGTH(u))
  #else
    #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03090000
    #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : ((PyCompactUnicodeObject *)(u))->wstr_length))
    #else
    #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : PyUnicode_GET_SIZE(u)))
    #endif
  #endif
#endif
#if CYTHON_COMPILING_IN_PYPY
  #define __Pyx_PyUnicode_Concat(a, b)      PyNumber_Add(a, b)
  #define __Pyx_PyUnicode_ConcatSafe(a, b)  PyNumber_Add(a, b)
#else
  #define __Pyx_PyUnicode_Concat(a, b)      PyUnicode_Concat(a, b)
  #define __Pyx_PyUnicode_ConcatSafe(a, b)  ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ?\
      PyNumber_Add(a, b) : __Pyx_PyUnicode_Concat(a, b))
#endif
#if CYTHON_COMPILING_IN_PYPY
  #if !defined(PyUnicode_DecodeUnicodeEscape)
    #define PyUnicode_DecodeUnicodeEscape(s, size, errors)  PyUnicode_Decode(s, size, "unicode_escape", errors)
  #endif
  #if !defined(PyUnicode_Contains)
    #define PyUnicode_Contains(u, s)  PySequence_Contains(u, s)
  #endif
  #if !defined(PyByteArray_Check)
    #define PyByteArray_Check(obj)  PyObject_TypeCheck(obj, &PyByteArray_Type)
  #endif
  #if !defined(PyObject_Format)
    #define PyObject_Format(obj, fmt)  PyObject_CallMethod(obj, "__format__", "O", fmt)
  #endif
#endif
#define __Pyx_PyUnicode_FormatSafe(a, b)  ((unlikely((a) == Py_None || (PyUnicode_Check(b) && !PyUnicode_CheckExact(b)))) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b))
#if CYTHON_COMPILING_IN_CPYTHON
  #define __Pyx_PySequence_ListKeepNew(obj)\
    (likely(PyList_CheckExact(obj) && Py_REFCNT(obj) == 1) ? __Pyx_NewRef(obj) : PySequence_List(obj))
#else
  #define __Pyx_PySequence_ListKeepNew(obj)  PySequence_List(obj)
#endif
#ifndef PySet_CheckExact
  #define PySet_CheckExact(obj)        __Pyx_IS_TYPE(obj, &PySet_Type)
#endif
#if PY_VERSION_HEX >= 0x030900A4
  #define __Pyx_SET_REFCNT(obj, refcnt) Py_SET_REFCNT(obj, refcnt)
  #define __Pyx_SET_SIZE(obj, size) Py_SET_SIZE(obj, size)
#else
  #define __Pyx_SET_REFCNT(obj, refcnt) Py_REFCNT(obj) = (refcnt)
  #define __Pyx_SET_SIZE(obj, size) Py_SIZE(obj) = (size)
#endif
#if CYTHON_AVOID_BORROWED_REFS || CYTHON_AVOID_THREAD_UNSAFE_BORROWED_REFS
  #if __PYX_LIMITED_VERSION_HEX >= 0x030d0000
    #define __Pyx_PyList_GetItemRef(o, i) PyList_GetItemRef(o, i)
  #elif CYTHON_COMPILING_IN_LIMITED_API || !CYTHON_ASSUME_SAFE_MACROS
    #define __Pyx_PyList_GetItemRef(o, i) (likely((i) >= 0) ? PySequence_GetItem(o, i) : (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL))
  #else
    #define __Pyx_PyList_GetItemRef(o, i) PySequence_ITEM(o, i)
  #endif
#elif CYTHON_COMPILING_IN_LIMITED_API || !CYTHON_ASSUME_SAFE_MACROS
  #if __PYX_LIMITED_VERSION_HEX >= 0x030d0000
    #define __Pyx_PyList_GetItemRef(o, i) PyList_GetItemRef(o, i)
  #else
    #define __Pyx_PyList_GetItemRef(o, i) __Pyx_XNewRef(PyList_GetItem(o, i))
  #endif
#else
  #define __Pyx_PyList_GetItemRef(o, i) __Pyx_NewRef(PyList_GET_ITEM(o, i))
#endif
#if __PYX_LIMITED_VERSION_HEX >= 0x030d0000
#define __Pyx_PyDict_GetItemRef(dict, key, result) PyDict_GetItemRef(dict, key, result)
#elif CYTHON_AVOID_BORROWED_REFS || CYTHON_AVOID_THREAD_UNSAFE_BORROWED_REFS
static CYTHON_INLINE int __Pyx_PyDict_GetItemRef(PyObject *dict, PyObject *key, PyObject **result) {
  *result = PyObject_GetItem(dict, key);
  if (*result == NULL) {
    if (PyErr_ExceptionMatches(PyExc_KeyError)) {
      PyErr_Clear();
      return 0;
    }
    return -1;
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  return 1;
}
#else
static CYTHON_INLINE int __Pyx_PyDict_GetItemRef(PyObject *dict, PyObject *key, PyObject **result) {
  *result = PyDict_GetItemWithError(dict, key);
  if (*result == NULL) {
    return PyErr_Occurred() ? -1 : 0;
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  Py_INCREF(*result);
  return 1;
}
#endif
#if defined(CYTHON_DEBUG_VISIT_CONST) && CYTHON_DEBUG_VISIT_CONST
  #define __Pyx_VISIT_CONST(obj)  Py_VISIT(obj)
#else
  #define __Pyx_VISIT_CONST(obj)
#endif
#if CYTHON_ASSUME_SAFE_MACROS
  #define __Pyx_PySequence_ITEM(o, i) PySequence_ITEM(o, i)
  #define __Pyx_PySequence_SIZE(seq)  Py_SIZE(seq)
  #define __Pyx_PyTuple_SET_ITEM(o, i, v) (PyTuple_SET_ITEM(o, i, v), (0))
  #define __Pyx_PyTuple_GET_ITEM(o, i) PyTuple_GET_ITEM(o, i)
  #define __Pyx_PyList_SET_ITEM(o, i, v) (PyList_SET_ITEM(o, i, v), (0))
  #define __Pyx_PyList_GET_ITEM(o, i) PyList_GET_ITEM(o, i)
#else
  #define __Pyx_PySequence_ITEM(o, i) PySequence_GetItem(o, i)
  #define __Pyx_PySequence_SIZE(seq)  PySequence_Size(seq)
  #define __Pyx_PyTuple_SET_ITEM(o, i, v) PyTuple_SetItem(o, i, v)
  #define __Pyx_PyTuple_GET_ITEM(o, i) PyTuple_GetItem(o, i)
  #define __Pyx_PyList_SET_ITEM(o, i, v) PyList_SetItem(o, i, v)
  #define __Pyx_PyList_GET_ITEM(o, i) PyList_GetItem(o, i)
#endif
#if CYTHON_ASSUME_SAFE_SIZE
  #define __Pyx_PyTuple_GET_SIZE(o) PyTuple_GET_SIZE(o)
  #define __Pyx_PyList_GET_SIZE(o) PyList_GET_SIZE(o)
  #define __Pyx_PySet_GET_SIZE(o) PySet_GET_SIZE(o)
  #define __Pyx_PyBytes_GET_SIZE(o) PyBytes_GET_SIZE(o)
  #define __Pyx_PyByteArray_GET_SIZE(o) PyByteArray_GET_SIZE(o)
  #define __Pyx_PyUnicode_GET_LENGTH(o) PyUnicode_GET_LENGTH(o)
#else
  #define __Pyx_PyTuple_GET_SIZE(o) PyTuple_Size(o)
  #define __Pyx_PyList_GET_SIZE(o) PyList_Size(o)
  #define __Pyx_PySet_GET_SIZE(o) PySet_Size(o)
  #define __Pyx_PyBytes_GET_SIZE(o) PyBytes_Size(o)
  #define __Pyx_PyByteArray_GET_SIZE(o) PyByteArray_Size(o)
  #define __Pyx_PyUnicode_GET_LENGTH(o) PyUnicode_GetLength(o)
#endif
#if __PYX_LIMITED_VERSION_HEX >= 0x030d0000
  #define __Pyx_PyImport_AddModuleRef(name) PyImport_AddModuleRef(name)
#else
  static CYTHON_INLINE PyObject *__Pyx_PyImport_AddModuleRef(const char *name) {
      PyObject *module = PyImport_AddModule(name);
      Py_XINCREF(module);
      return module;
  }
#endif
#if CYTHON_COMPILING_IN_PYPY && !defined(PyUnicode_InternFromString)
  #define PyUnicode_InternFromString(s) PyUnicode_FromString(s)
#endif
#define __Pyx_PyLong_FromHash_t PyLong_FromSsize_t
#define __Pyx_PyLong_AsHash_t   __Pyx_PyIndex_AsSsize_t
#if __PYX_LIMITED_VERSION_HEX >= 0x030A0000
    #define __Pyx_PySendResult PySendResult
#else
    typedef enum {
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        PYGEN_ERROR = -1,
        PYGEN_NEXT = 1,
    } __Pyx_PySendResult;
#endif
#if CYTHON_COMPILING_IN_LIMITED_API || PY_VERSION_HEX < 0x030A00A3
  typedef __Pyx_PySendResult (*__Pyx_pyiter_sendfunc)(PyObject *iter, PyObject *value, PyObject **result);
#else
  #define __Pyx_pyiter_sendfunc sendfunc
#endif
#if !CYTHON_USE_AM_SEND
#define __PYX_HAS_PY_AM_SEND 0
#elif __PYX_LIMITED_VERSION_HEX >= 0x030A0000
#define __PYX_HAS_PY_AM_SEND 1
#else
#define __PYX_HAS_PY_AM_SEND 2  // our own backported implementation
#endif
#if __PYX_HAS_PY_AM_SEND < 2
    #define __Pyx_PyAsyncMethodsStruct PyAsyncMethods
#else
    typedef struct {
        unaryfunc am_await;
        unaryfunc am_aiter;
        unaryfunc am_anext;
        __Pyx_pyiter_sendfunc am_send;
    } __Pyx_PyAsyncMethodsStruct;
    #define __Pyx_SlotTpAsAsync(s) ((PyAsyncMethods*)(s))
#endif
#if CYTHON_USE_AM_SEND && PY_VERSION_HEX < 0x030A00F0
    #define __Pyx_TPFLAGS_HAVE_AM_SEND (1UL << 21)
#else
    #define __Pyx_TPFLAGS_HAVE_AM_SEND (0)
#endif
#if PY_VERSION_HEX >= 0x03090000
#define __Pyx_PyInterpreterState_Get() PyInterpreterState_Get()
#else
#define __Pyx_PyInterpreterState_Get() PyThreadState_Get()->interp
#endif
#if CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX < 0x030A0000
#ifdef __cplusplus
extern "C"
#endif
PyAPI_FUNC(void *) PyMem_Calloc(size_t nelem, size_t elsize);
#endif
#if CYTHON_COMPILING_IN_LIMITED_API
static int __Pyx_init_co_variable(PyObject *inspect, const char* name, int *write_to) {
    int value;
    PyObject *py_value = PyObject_GetAttrString(inspect, name);
    if (!py_value) return 0;
    value = (int) PyLong_AsLong(py_value);
    Py_DECREF(py_value);
    *write_to = value;
    return value != -1 || !PyErr_Occurred();
}
static int __Pyx_init_co_variables(void) {
    PyObject *inspect;
    int result;
    inspect = PyImport_ImportModule("inspect");
    result =
#if !defined(CO_OPTIMIZED)
        __Pyx_init_co_variable(inspect, "CO_OPTIMIZED", &CO_OPTIMIZED) &&
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#if !defined(CO_NEWLOCALS)
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#if !defined(CO_VARARGS)
        __Pyx_init_co_variable(inspect, "CO_VARARGS", &CO_VARARGS) &&
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#if !defined(CO_VARKEYWORDS)
        __Pyx_init_co_variable(inspect, "CO_VARKEYWORDS", &CO_VARKEYWORDS) &&
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#if !defined(CO_ASYNC_GENERATOR)
        __Pyx_init_co_variable(inspect, "CO_ASYNC_GENERATOR", &CO_ASYNC_GENERATOR) &&
#endif
#if !defined(CO_GENERATOR)
        __Pyx_init_co_variable(inspect, "CO_GENERATOR", &CO_GENERATOR) &&
#endif
#if !defined(CO_COROUTINE)
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#endif
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}
#else
static int __Pyx_init_co_variables(void) {
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}
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/* MathInitCode */
#if defined(_WIN32) || defined(WIN32) || defined(MS_WINDOWS)
  #ifndef _USE_MATH_DEFINES
    #define _USE_MATH_DEFINES
  #endif
#endif
#include <math.h>
#ifdef NAN
#define __PYX_NAN() ((float) NAN)
#else
static CYTHON_INLINE float __PYX_NAN() {
  float value;
  memset(&value, 0xFF, sizeof(value));
  return value;
}
#endif
#if defined(__CYGWIN__) && defined(_LDBL_EQ_DBL)
#define __Pyx_truncl trunc
#else
#define __Pyx_truncl truncl
#endif

#ifndef CYTHON_CLINE_IN_TRACEBACK_RUNTIME
#define CYTHON_CLINE_IN_TRACEBACK_RUNTIME 0
#endif
#ifndef CYTHON_CLINE_IN_TRACEBACK
#define CYTHON_CLINE_IN_TRACEBACK CYTHON_CLINE_IN_TRACEBACK_RUNTIME
#endif
#if CYTHON_CLINE_IN_TRACEBACK
#define __PYX_MARK_ERR_POS(f_index, lineno)  { __pyx_filename = __pyx_f[f_index]; (void) __pyx_filename; __pyx_lineno = lineno; (void) __pyx_lineno; __pyx_clineno = __LINE__; (void) __pyx_clineno; }
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#define __PYX_MARK_ERR_POS(f_index, lineno)  { __pyx_filename = __pyx_f[f_index]; (void) __pyx_filename; __pyx_lineno = lineno; (void) __pyx_lineno; (void) __pyx_clineno; }
#endif
#define __PYX_ERR(f_index, lineno, Ln_error) \
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#ifdef CYTHON_EXTERN_C
    #undef __PYX_EXTERN_C
    #define __PYX_EXTERN_C CYTHON_EXTERN_C
#elif defined(__PYX_EXTERN_C)
    #ifdef _MSC_VER
    #pragma message ("Please do not define the '__PYX_EXTERN_C' macro externally. Use 'CYTHON_EXTERN_C' instead.")
    #else
    #warning Please do not define the '__PYX_EXTERN_C' macro externally. Use 'CYTHON_EXTERN_C' instead.
    #endif
#else
  #ifdef __cplusplus
    #define __PYX_EXTERN_C extern "C"
  #else
    #define __PYX_EXTERN_C extern
  #endif
#endif

#define __PYX_HAVE__pyRing__eob_utils
#define __PYX_HAVE_API__pyRing__eob_utils
/* Early includes */
#include <math.h>
#ifdef _OPENMP
#include <omp.h>
#endif /* _OPENMP */

#if defined(PYREX_WITHOUT_ASSERTIONS) && !defined(CYTHON_WITHOUT_ASSERTIONS)
#define CYTHON_WITHOUT_ASSERTIONS
#endif

#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0
#define __PYX_DEFAULT_STRING_ENCODING_IS_UTF8 0
#define __PYX_DEFAULT_STRING_ENCODING ""
#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
#define __Pyx_uchar_cast(c) ((unsigned char)c)
#define __Pyx_long_cast(x) ((long)x)
#define __Pyx_fits_Py_ssize_t(v, type, is_signed)  (\
    (sizeof(type) < sizeof(Py_ssize_t))  ||\
    (sizeof(type) > sizeof(Py_ssize_t) &&\
          likely(v < (type)PY_SSIZE_T_MAX ||\
                 v == (type)PY_SSIZE_T_MAX)  &&\
          (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\
                                v == (type)PY_SSIZE_T_MIN)))  ||\
    (sizeof(type) == sizeof(Py_ssize_t) &&\
          (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||\
                               v == (type)PY_SSIZE_T_MAX)))  )
static CYTHON_INLINE int __Pyx_is_valid_index(Py_ssize_t i, Py_ssize_t limit) {
    return (size_t) i < (size_t) limit;
}
#if defined (__cplusplus) && __cplusplus >= 201103L
    #include <cstdlib>
    #define __Pyx_sst_abs(value) std::abs(value)
#elif SIZEOF_INT >= SIZEOF_SIZE_T
    #define __Pyx_sst_abs(value) abs(value)
#elif SIZEOF_LONG >= SIZEOF_SIZE_T
    #define __Pyx_sst_abs(value) labs(value)
#elif defined (_MSC_VER)
    #define __Pyx_sst_abs(value) ((Py_ssize_t)_abs64(value))
#elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
    #define __Pyx_sst_abs(value) llabs(value)
#elif defined (__GNUC__)
    #define __Pyx_sst_abs(value) __builtin_llabs(value)
#else
    #define __Pyx_sst_abs(value) ((value<0) ? -value : value)
#endif
static CYTHON_INLINE Py_ssize_t __Pyx_ssize_strlen(const char *s);
static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*);
static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
static CYTHON_INLINE PyObject* __Pyx_PyByteArray_FromString(const char*);
#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)
#define __Pyx_PyBytes_FromString        PyBytes_FromString
#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize
static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);
#if CYTHON_ASSUME_SAFE_MACROS
    #define __Pyx_PyBytes_AsWritableString(s)     ((char*) PyBytes_AS_STRING(s))
    #define __Pyx_PyBytes_AsWritableSString(s)    ((signed char*) PyBytes_AS_STRING(s))
    #define __Pyx_PyBytes_AsWritableUString(s)    ((unsigned char*) PyBytes_AS_STRING(s))
    #define __Pyx_PyBytes_AsString(s)     ((const char*) PyBytes_AS_STRING(s))
    #define __Pyx_PyBytes_AsSString(s)    ((const signed char*) PyBytes_AS_STRING(s))
    #define __Pyx_PyBytes_AsUString(s)    ((const unsigned char*) PyBytes_AS_STRING(s))
    #define __Pyx_PyByteArray_AsString(s) PyByteArray_AS_STRING(s)
#else
    #define __Pyx_PyBytes_AsWritableString(s)     ((char*) PyBytes_AsString(s))
    #define __Pyx_PyBytes_AsWritableSString(s)    ((signed char*) PyBytes_AsString(s))
    #define __Pyx_PyBytes_AsWritableUString(s)    ((unsigned char*) PyBytes_AsString(s))
    #define __Pyx_PyBytes_AsString(s)     ((const char*) PyBytes_AsString(s))
    #define __Pyx_PyBytes_AsSString(s)    ((const signed char*) PyBytes_AsString(s))
    #define __Pyx_PyBytes_AsUString(s)    ((const unsigned char*) PyBytes_AsString(s))
    #define __Pyx_PyByteArray_AsString(s) PyByteArray_AsString(s)
#endif
#define __Pyx_PyObject_AsWritableString(s)    ((char*)(__pyx_uintptr_t) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsWritableSString(s)    ((signed char*)(__pyx_uintptr_t) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsWritableUString(s)    ((unsigned char*)(__pyx_uintptr_t) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsSString(s)    ((const signed char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsUString(s)    ((const unsigned char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_FromCString(s)  __Pyx_PyObject_FromString((const char*)s)
#define __Pyx_PyBytes_FromCString(s)   __Pyx_PyBytes_FromString((const char*)s)
#define __Pyx_PyByteArray_FromCString(s)   __Pyx_PyByteArray_FromString((const char*)s)
#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s)
#define __Pyx_PyUnicode_FromOrdinal(o)       PyUnicode_FromOrdinal((int)o)
#define __Pyx_PyUnicode_AsUnicode            PyUnicode_AsUnicode
static CYTHON_INLINE PyObject *__Pyx_NewRef(PyObject *obj) {
#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030a0000 || defined(Py_NewRef)
    return Py_NewRef(obj);
#else
    Py_INCREF(obj);
    return obj;
#endif
}
static CYTHON_INLINE PyObject *__Pyx_XNewRef(PyObject *obj) {
#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030a0000 || defined(Py_XNewRef)
    return Py_XNewRef(obj);
#else
    Py_XINCREF(obj);
    return obj;
#endif
}
static CYTHON_INLINE PyObject *__Pyx_Owned_Py_None(int b);
static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b);
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject*);
static CYTHON_INLINE PyObject* __Pyx_PyNumber_Long(PyObject* x);
#define __Pyx_PySequence_Tuple(obj)\
    (likely(PyTuple_CheckExact(obj)) ? __Pyx_NewRef(obj) : PySequence_Tuple(obj))
static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
static CYTHON_INLINE PyObject * __Pyx_PyLong_FromSize_t(size_t);
static CYTHON_INLINE Py_hash_t __Pyx_PyIndex_AsHash_t(PyObject*);
#if CYTHON_ASSUME_SAFE_MACROS
#define __Pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))
#define __Pyx_PyFloat_AS_DOUBLE(x) PyFloat_AS_DOUBLE(x)
#else
#define __Pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)
#define __Pyx_PyFloat_AS_DOUBLE(x) PyFloat_AsDouble(x)
#endif
#define __Pyx_PyFloat_AsFloat(x) ((float) __Pyx_PyFloat_AsDouble(x))
#define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x))
#if CYTHON_USE_PYLONG_INTERNALS
  #if PY_VERSION_HEX >= 0x030C00A7
  #ifndef _PyLong_SIGN_MASK
    #define _PyLong_SIGN_MASK 3
  #endif
  #ifndef _PyLong_NON_SIZE_BITS
    #define _PyLong_NON_SIZE_BITS 3
  #endif
  #define __Pyx_PyLong_Sign(x)  (((PyLongObject*)x)->long_value.lv_tag & _PyLong_SIGN_MASK)
  #define __Pyx_PyLong_IsNeg(x)  ((__Pyx_PyLong_Sign(x) & 2) != 0)
  #define __Pyx_PyLong_IsNonNeg(x)  (!__Pyx_PyLong_IsNeg(x))
  #define __Pyx_PyLong_IsZero(x)  (__Pyx_PyLong_Sign(x) & 1)
  #define __Pyx_PyLong_IsPos(x)  (__Pyx_PyLong_Sign(x) == 0)
  #define __Pyx_PyLong_CompactValueUnsigned(x)  (__Pyx_PyLong_Digits(x)[0])
  #define __Pyx_PyLong_DigitCount(x)  ((Py_ssize_t) (((PyLongObject*)x)->long_value.lv_tag >> _PyLong_NON_SIZE_BITS))
  #define __Pyx_PyLong_SignedDigitCount(x)\
        ((1 - (Py_ssize_t) __Pyx_PyLong_Sign(x)) * __Pyx_PyLong_DigitCount(x))
  #if defined(PyUnstable_Long_IsCompact) && defined(PyUnstable_Long_CompactValue)
    #define __Pyx_PyLong_IsCompact(x)     PyUnstable_Long_IsCompact((PyLongObject*) x)
    #define __Pyx_PyLong_CompactValue(x)  PyUnstable_Long_CompactValue((PyLongObject*) x)
  #else
    #define __Pyx_PyLong_IsCompact(x)     (((PyLongObject*)x)->long_value.lv_tag < (2 << _PyLong_NON_SIZE_BITS))
    #define __Pyx_PyLong_CompactValue(x)  ((1 - (Py_ssize_t) __Pyx_PyLong_Sign(x)) * (Py_ssize_t) __Pyx_PyLong_Digits(x)[0])
  #endif
  typedef Py_ssize_t  __Pyx_compact_pylong;
  typedef size_t  __Pyx_compact_upylong;
  #else
  #define __Pyx_PyLong_IsNeg(x)  (Py_SIZE(x) < 0)
  #define __Pyx_PyLong_IsNonNeg(x)  (Py_SIZE(x) >= 0)
  #define __Pyx_PyLong_IsZero(x)  (Py_SIZE(x) == 0)
  #define __Pyx_PyLong_IsPos(x)  (Py_SIZE(x) > 0)
  #define __Pyx_PyLong_CompactValueUnsigned(x)  ((Py_SIZE(x) == 0) ? 0 : __Pyx_PyLong_Digits(x)[0])
  #define __Pyx_PyLong_DigitCount(x)  __Pyx_sst_abs(Py_SIZE(x))
  #define __Pyx_PyLong_SignedDigitCount(x)  Py_SIZE(x)
  #define __Pyx_PyLong_IsCompact(x)  (Py_SIZE(x) == 0 || Py_SIZE(x) == 1 || Py_SIZE(x) == -1)
  #define __Pyx_PyLong_CompactValue(x)\
        ((Py_SIZE(x) == 0) ? (sdigit) 0 : ((Py_SIZE(x) < 0) ? -(sdigit)__Pyx_PyLong_Digits(x)[0] : (sdigit)__Pyx_PyLong_Digits(x)[0]))
  typedef sdigit  __Pyx_compact_pylong;
  typedef digit  __Pyx_compact_upylong;
  #endif
  static CYTHON_INLINE int __Pyx_PyLong_CompactAsLong(PyObject *x, long *return_value);
  #if PY_VERSION_HEX >= 0x030C00A5
  #define __Pyx_PyLong_Digits(x)  (((PyLongObject*)x)->long_value.ob_digit)
  #else
  #define __Pyx_PyLong_Digits(x)  (((PyLongObject*)x)->ob_digit)
  #endif
#endif
#if __PYX_DEFAULT_STRING_ENCODING_IS_UTF8
  #define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)
#elif __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
  #define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeASCII(c_str, size, NULL)
#else
  #define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)
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/* Test for GCC > 2.95 */
#if defined(__GNUC__)     && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95)))
  #define likely(x)   __builtin_expect(!!(x), 1)
  #define unlikely(x) __builtin_expect(!!(x), 0)
#else /* !__GNUC__ or GCC < 2.95 */
  #define likely(x)   (x)
  #define unlikely(x) (x)
#endif /* __GNUC__ */
/* PretendToInitialize */
#ifdef __cplusplus
#if __cplusplus > 201103L
#include <type_traits>
#endif
template <typename T>
static void __Pyx_pretend_to_initialize(T* ptr) {
#if __cplusplus > 201103L
    if ((std::is_trivially_default_constructible<T>::value))
#endif
        *ptr = T();
    (void)ptr;
}
#else
static CYTHON_INLINE void __Pyx_pretend_to_initialize(void* ptr) { (void)ptr; }
#endif


#if !CYTHON_USE_MODULE_STATE
static PyObject *__pyx_m = NULL;
#endif
static int __pyx_lineno;
static int __pyx_clineno = 0;
static const char * const __pyx_cfilenm = __FILE__;
static const char *__pyx_filename;

/* #### Code section: filename_table ### */

static const char* const __pyx_f[] = {
  "pyRing/eob_utils.pyx",
};
/* #### Code section: utility_code_proto_before_types ### */
/* Atomics.proto */
#include <pythread.h>
#ifndef CYTHON_ATOMICS
    #define CYTHON_ATOMICS 1
#endif
#define __PYX_CYTHON_ATOMICS_ENABLED() CYTHON_ATOMICS
#define __PYX_GET_CYTHON_COMPILING_IN_CPYTHON_FREETHREADING() CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
#define __pyx_atomic_int_type int
#define __pyx_nonatomic_int_type int
#if CYTHON_ATOMICS && (defined(__STDC_VERSION__) &&\
                        (__STDC_VERSION__ >= 201112L) &&\
                        !defined(__STDC_NO_ATOMICS__))
    #include <stdatomic.h>
#elif CYTHON_ATOMICS && (defined(__cplusplus) && (\
                    (__cplusplus >= 201103L) ||\
                    (defined(_MSC_VER) && _MSC_VER >= 1700)))
    #include <atomic>
#endif
#if CYTHON_ATOMICS && (defined(__STDC_VERSION__) &&\
                        (__STDC_VERSION__ >= 201112L) &&\
                        !defined(__STDC_NO_ATOMICS__) &&\
                       ATOMIC_INT_LOCK_FREE == 2)
    #undef __pyx_atomic_int_type
    #define __pyx_atomic_int_type atomic_int
    #define __pyx_atomic_ptr_type atomic_uintptr_t
    #define __pyx_nonatomic_ptr_type uintptr_t
    #define __pyx_atomic_incr_relaxed(value) atomic_fetch_add_explicit(value, 1, memory_order_relaxed)
    #define __pyx_atomic_incr_acq_rel(value) atomic_fetch_add_explicit(value, 1, memory_order_acq_rel)
    #define __pyx_atomic_decr_acq_rel(value) atomic_fetch_sub_explicit(value, 1, memory_order_acq_rel)
    #define __pyx_atomic_sub(value, arg) atomic_fetch_sub(value, arg)
    #define __pyx_atomic_int_cmp_exchange(value, expected, desired) atomic_compare_exchange_strong(value, expected, desired)
    #define __pyx_atomic_load(value) atomic_load(value)
    #define __pyx_atomic_store(value, new_value) atomic_store(value, new_value)
    #define __pyx_atomic_pointer_load_relaxed(value) atomic_load_explicit(value, memory_order_relaxed)
    #define __pyx_atomic_pointer_load_acquire(value) atomic_load_explicit(value, memory_order_acquire)
    #define __pyx_atomic_pointer_exchange(value, new_value) atomic_exchange(value, (__pyx_nonatomic_ptr_type)new_value)
    #if defined(__PYX_DEBUG_ATOMICS) && defined(_MSC_VER)
        #pragma message ("Using standard C atomics")
    #elif defined(__PYX_DEBUG_ATOMICS)
        #warning "Using standard C atomics"
    #endif
#elif CYTHON_ATOMICS && (defined(__cplusplus) && (\
                    (__cplusplus >= 201103L) ||\
\
                    (defined(_MSC_VER) && _MSC_VER >= 1700)) &&\
                    ATOMIC_INT_LOCK_FREE == 2)
    #undef __pyx_atomic_int_type
    #define __pyx_atomic_int_type std::atomic_int
    #define __pyx_atomic_ptr_type std::atomic_uintptr_t
    #define __pyx_nonatomic_ptr_type uintptr_t
    #define __pyx_atomic_incr_relaxed(value) std::atomic_fetch_add_explicit(value, 1, std::memory_order_relaxed)
    #define __pyx_atomic_incr_acq_rel(value) std::atomic_fetch_add_explicit(value, 1, std::memory_order_acq_rel)
    #define __pyx_atomic_decr_acq_rel(value) std::atomic_fetch_sub_explicit(value, 1, std::memory_order_acq_rel)
    #define __pyx_atomic_sub(value, arg) std::atomic_fetch_sub(value, arg)
    #define __pyx_atomic_int_cmp_exchange(value, expected, desired) std::atomic_compare_exchange_strong(value, expected, desired)
    #define __pyx_atomic_load(value) std::atomic_load(value)
    #define __pyx_atomic_store(value, new_value) std::atomic_store(value, new_value)
    #define __pyx_atomic_pointer_load_relaxed(value) std::atomic_load_explicit(value, std::memory_order_relaxed)
    #define __pyx_atomic_pointer_load_acquire(value) std::atomic_load_explicit(value, std::memory_order_acquire)
    #define __pyx_atomic_pointer_exchange(value, new_value) std::atomic_exchange(value, (__pyx_nonatomic_ptr_type)new_value)
    #if defined(__PYX_DEBUG_ATOMICS) && defined(_MSC_VER)
        #pragma message ("Using standard C++ atomics")
    #elif defined(__PYX_DEBUG_ATOMICS)
        #warning "Using standard C++ atomics"
    #endif
#elif CYTHON_ATOMICS && (__GNUC__ >= 5 || (__GNUC__ == 4 &&\
                    (__GNUC_MINOR__ > 1 ||\
                    (__GNUC_MINOR__ == 1 && __GNUC_PATCHLEVEL__ >= 2))))
    #define __pyx_atomic_ptr_type void*
    #define __pyx_atomic_incr_relaxed(value) __sync_fetch_and_add(value, 1)
    #define __pyx_atomic_incr_acq_rel(value) __sync_fetch_and_add(value, 1)
    #define __pyx_atomic_decr_acq_rel(value) __sync_fetch_and_sub(value, 1)
    #define __pyx_atomic_sub(value, arg) __sync_fetch_and_sub(value, arg)
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    #define __pyx_atomic_load(value) __sync_fetch_and_add(value, 0)
    #define __pyx_atomic_store(value, new_value) __sync_lock_test_and_set(value, new_value)
    #define __pyx_atomic_pointer_load_relaxed(value) __sync_fetch_and_add(value, 0)
    #define __pyx_atomic_pointer_load_acquire(value) __sync_fetch_and_add(value, 0)
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    #include <intrin.h>
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    #define __pyx_atomic_int_type long
    #define __pyx_atomic_ptr_type void*
    #undef __pyx_nonatomic_int_type
    #define __pyx_nonatomic_int_type long
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    #define __pyx_atomic_decr_acq_rel(value) _InterlockedExchangeAdd(value, -1)
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    #define __pyx_atomic_store(value, new_value) _InterlockedExchange(value, new_value)
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        #pragma message ("Using MSVC atomics")
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    #ifdef __PYX_DEBUG_ATOMICS
        #warning "Not using atomics"
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#if CYTHON_ATOMICS
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/* ForceInitThreads.proto */
#ifndef __PYX_FORCE_INIT_THREADS
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/* NoFastGil.proto */
#define __Pyx_PyGILState_Ensure PyGILState_Ensure
#define __Pyx_PyGILState_Release PyGILState_Release
#define __Pyx_FastGIL_Remember()
#define __Pyx_FastGIL_Forget()
#define __Pyx_FastGilFuncInit()

/* IncludeStructmemberH.proto */
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/* CriticalSections.proto */
#if !CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
#define __Pyx_PyCriticalSection void*
#define __Pyx_PyCriticalSection2 void*
#define __Pyx_PyCriticalSection_Begin1(cs, arg) (void)cs
#define __Pyx_PyCriticalSection_Begin2(cs, arg1, arg2) (void)cs
#define __Pyx_PyCriticalSection_End1(cs)
#define __Pyx_PyCriticalSection_End2(cs)
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#define __Pyx_PyCriticalSection PyCriticalSection
#define __Pyx_PyCriticalSection2 PyCriticalSection2
#define __Pyx_PyCriticalSection_Begin1 PyCriticalSection_Begin
#define __Pyx_PyCriticalSection_Begin2 PyCriticalSection2_Begin
#define __Pyx_PyCriticalSection_End1 PyCriticalSection_End
#define __Pyx_PyCriticalSection_End2 PyCriticalSection2_End
#endif
#if PY_VERSION_HEX < 0x030d0000 || CYTHON_COMPILING_IN_LIMITED_API
#define __Pyx_BEGIN_CRITICAL_SECTION(o) {
#define __Pyx_END_CRITICAL_SECTION() }
#else
#define __Pyx_BEGIN_CRITICAL_SECTION Py_BEGIN_CRITICAL_SECTION
#define __Pyx_END_CRITICAL_SECTION Py_END_CRITICAL_SECTION
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/* #### Code section: numeric_typedefs ### */
/* #### Code section: complex_type_declarations ### */
/* #### Code section: type_declarations ### */

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  #define __Pyx_XGOTREF(r)  do { if((r) == NULL); else {__Pyx_GOTREF(r); }} while(0)
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  #define __Pyx_GOTREF(r)
  #define __Pyx_GIVEREF(r)
  #define __Pyx_XINCREF(r) Py_XINCREF(r)
  #define __Pyx_XDECREF(r) Py_XDECREF(r)
  #define __Pyx_XGOTREF(r)
  #define __Pyx_XGIVEREF(r)
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#define __Pyx_Py_XDECREF_SET(r, v) do {\
        PyObject *tmp = (PyObject *) r;\
        r = v; Py_XDECREF(tmp);\
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#define __Pyx_XDECREF_SET(r, v) do {\
        PyObject *tmp = (PyObject *) r;\
        r = v; __Pyx_XDECREF(tmp);\
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#define __Pyx_DECREF_SET(r, v) do {\
        PyObject *tmp = (PyObject *) r;\
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#define __Pyx_CLEAR(r)    do { PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);} while(0)
#define __Pyx_XCLEAR(r)   do { if((r) != NULL) {PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);}} while(0)

/* TupleAndListFromArray.proto */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyList_FromArray(PyObject *const *src, Py_ssize_t n);
#endif
#if CYTHON_COMPILING_IN_CPYTHON || CYTHON_METH_FASTCALL
static CYTHON_INLINE PyObject* __Pyx_PyTuple_FromArray(PyObject *const *src, Py_ssize_t n);
#endif

/* IncludeStringH.proto */
#include <string.h>

/* BytesEquals.proto */
static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals);

/* UnicodeEquals.proto */
static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals);

/* fastcall.proto */
#if CYTHON_AVOID_BORROWED_REFS
    #define __Pyx_ArgRef_VARARGS(args, i) __Pyx_PySequence_ITEM(args, i)
#elif CYTHON_ASSUME_SAFE_MACROS
    #define __Pyx_ArgRef_VARARGS(args, i) __Pyx_NewRef(__Pyx_PyTuple_GET_ITEM(args, i))
#else
    #define __Pyx_ArgRef_VARARGS(args, i) __Pyx_XNewRef(PyTuple_GetItem(args, i))
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#define __Pyx_NumKwargs_VARARGS(kwds) PyDict_Size(kwds)
#define __Pyx_KwValues_VARARGS(args, nargs) NULL
#define __Pyx_GetKwValue_VARARGS(kw, kwvalues, s) __Pyx_PyDict_GetItemStrWithError(kw, s)
#define __Pyx_KwargsAsDict_VARARGS(kw, kwvalues) PyDict_Copy(kw)
#if CYTHON_METH_FASTCALL
    #define __Pyx_ArgRef_FASTCALL(args, i) __Pyx_NewRef(args[i])
    #define __Pyx_NumKwargs_FASTCALL(kwds) __Pyx_PyTuple_GET_SIZE(kwds)
    #define __Pyx_KwValues_FASTCALL(args, nargs) ((args) + (nargs))
    static CYTHON_INLINE PyObject * __Pyx_GetKwValue_FASTCALL(PyObject *kwnames, PyObject *const *kwvalues, PyObject *s);
  #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030d0000 || CYTHON_COMPILING_IN_LIMITED_API
    CYTHON_UNUSED static PyObject *__Pyx_KwargsAsDict_FASTCALL(PyObject *kwnames, PyObject *const *kwvalues);
  #else
    #define __Pyx_KwargsAsDict_FASTCALL(kw, kwvalues) _PyStack_AsDict(kwvalues, kw)
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    #define __Pyx_ArgRef_FASTCALL __Pyx_ArgRef_VARARGS
    #define __Pyx_NumKwargs_FASTCALL __Pyx_NumKwargs_VARARGS
    #define __Pyx_KwValues_FASTCALL __Pyx_KwValues_VARARGS
    #define __Pyx_GetKwValue_FASTCALL __Pyx_GetKwValue_VARARGS
    #define __Pyx_KwargsAsDict_FASTCALL __Pyx_KwargsAsDict_VARARGS
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#define __Pyx_ArgsSlice_VARARGS(args, start, stop) PyTuple_GetSlice(args, start, stop)
#if CYTHON_METH_FASTCALL || (CYTHON_COMPILING_IN_CPYTHON && CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS)
#define __Pyx_ArgsSlice_FASTCALL(args, start, stop) __Pyx_PyTuple_FromArray(args + start, stop - start)
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#define __Pyx_ArgsSlice_FASTCALL(args, start, stop) PyTuple_GetSlice(args, start, stop)
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/* RaiseDoubleKeywords.proto */
static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name);

/* ParseKeywords.proto */
static CYTHON_INLINE int __Pyx_ParseKeywords(
    PyObject *kwds, PyObject *const *kwvalues, PyObject ** const argnames[],
    PyObject *kwds2, PyObject *values[],
    Py_ssize_t num_pos_args, Py_ssize_t num_kwargs,
    const char* function_name,
    int ignore_unknown_kwargs
);

/* CallCFunction.proto */
#define __Pyx_CallCFunction(cfunc, self, args)\
    ((PyCFunction)(void(*)(void))(cfunc)->func)(self, args)
#define __Pyx_CallCFunctionWithKeywords(cfunc, self, args, kwargs)\
    ((PyCFunctionWithKeywords)(void(*)(void))(cfunc)->func)(self, args, kwargs)
#define __Pyx_CallCFunctionFast(cfunc, self, args, nargs)\
    ((__Pyx_PyCFunctionFast)(void(*)(void))(PyCFunction)(cfunc)->func)(self, args, nargs)
#define __Pyx_CallCFunctionFastWithKeywords(cfunc, self, args, nargs, kwnames)\
    ((__Pyx_PyCFunctionFastWithKeywords)(void(*)(void))(PyCFunction)(cfunc)->func)(self, args, nargs, kwnames)

/* PyFunctionFastCall.proto */
#if CYTHON_FAST_PYCALL
#if !CYTHON_VECTORCALL
#define __Pyx_PyFunction_FastCall(func, args, nargs)\
    __Pyx_PyFunction_FastCallDict((func), (args), (nargs), NULL)
static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject *const *args, Py_ssize_t nargs, PyObject *kwargs);
#endif
#define __Pyx_BUILD_ASSERT_EXPR(cond)\
    (sizeof(char [1 - 2*!(cond)]) - 1)
#ifndef Py_MEMBER_SIZE
#define Py_MEMBER_SIZE(type, member) sizeof(((type *)0)->member)
#endif
#if !CYTHON_VECTORCALL
#if PY_VERSION_HEX >= 0x03080000
  #include "frameobject.h"
  #define __Pxy_PyFrame_Initialize_Offsets()
  #define __Pyx_PyFrame_GetLocalsplus(frame)  ((frame)->f_localsplus)
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  static size_t __pyx_pyframe_localsplus_offset = 0;
  #include "frameobject.h"
  #define __Pxy_PyFrame_Initialize_Offsets()\
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  #define __Pyx_PyFrame_GetLocalsplus(frame)\
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/* PyObjectCall.proto */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw);
#else
#define __Pyx_PyObject_Call(func, arg, kw) PyObject_Call(func, arg, kw)
#endif

/* PyObjectCallMethO.proto */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg);
#endif

/* PyObjectFastCall.proto */
#define __Pyx_PyObject_FastCall(func, args, nargs)  __Pyx_PyObject_FastCallDict(func, args, (size_t)(nargs), NULL)
static CYTHON_INLINE PyObject* __Pyx_PyObject_FastCallDict(PyObject *func, PyObject * const*args, size_t nargs, PyObject *kwargs);

/* PyObjectGetAttrStr.proto */
#if CYTHON_USE_TYPE_SLOTS
static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name);
#else
#define __Pyx_PyObject_GetAttrStr(o,n) PyObject_GetAttr(o,n)
#endif

/* UnpackUnboundCMethod.proto */
typedef struct {
    PyObject *type;
    PyObject **method_name;
#if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING && CYTHON_ATOMICS
    __pyx_atomic_int_type initialized;
#endif
    PyCFunction func;
    PyObject *method;
    int flag;
} __Pyx_CachedCFunction;
#if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
static CYTHON_INLINE int __Pyx_CachedCFunction_GetAndSetInitializing(__Pyx_CachedCFunction *cfunc) {
#if !CYTHON_ATOMICS
    return 1;
#else
    __pyx_nonatomic_int_type expected = 0;
    if (__pyx_atomic_int_cmp_exchange(&cfunc->initialized, &expected, 1)) {
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    return expected;
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}
static CYTHON_INLINE void __Pyx_CachedCFunction_SetFinishedInitializing(__Pyx_CachedCFunction *cfunc) {
#if CYTHON_ATOMICS
    __pyx_atomic_store(&cfunc->initialized, 2);
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}
#else
#define __Pyx_CachedCFunction_GetAndSetInitializing(cfunc) 2
#define __Pyx_CachedCFunction_SetFinishedInitializing(cfunc)
#endif

/* CallUnboundCMethod2.proto */
CYTHON_UNUSED
static PyObject* __Pyx__CallUnboundCMethod2(__Pyx_CachedCFunction* cfunc, PyObject* self, PyObject* arg1, PyObject* arg2);
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject *__Pyx_CallUnboundCMethod2(__Pyx_CachedCFunction *cfunc, PyObject *self, PyObject *arg1, PyObject *arg2);
#else
#define __Pyx_CallUnboundCMethod2(cfunc, self, arg1, arg2)  __Pyx__CallUnboundCMethod2(cfunc, self, arg1, arg2)
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/* RaiseArgTupleInvalid.proto */
static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact,
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/* ErrOccurredWithGIL.proto */
static CYTHON_INLINE int __Pyx_ErrOccurredWithGIL(void);

/* LimitedApiGetTypeDict.proto */
#if CYTHON_COMPILING_IN_LIMITED_API
static PyObject *__Pyx_GetTypeDict(PyTypeObject *tp);
#endif

/* SetItemOnTypeDict.proto */
static int __Pyx__SetItemOnTypeDict(PyTypeObject *tp, PyObject *k, PyObject *v);
#define __Pyx_SetItemOnTypeDict(tp, k, v) __Pyx__SetItemOnTypeDict((PyTypeObject*)tp, k, v)

/* FixUpExtensionType.proto */
static CYTHON_INLINE int __Pyx_fix_up_extension_type_from_spec(PyType_Spec *spec, PyTypeObject *type);

/* FetchSharedCythonModule.proto */
static PyObject *__Pyx_FetchSharedCythonABIModule(void);

/* dict_setdefault.proto */
static CYTHON_INLINE PyObject *__Pyx_PyDict_SetDefault(PyObject *d, PyObject *key, PyObject *default_value, int is_safe_type);

/* FetchCommonType.proto */
static PyTypeObject* __Pyx_FetchCommonTypeFromSpec(PyTypeObject *metaclass, PyObject *module, PyType_Spec *spec, PyObject *bases);

/* CommonTypesMetaclass.proto */
static int __pyx_CommonTypesMetaclass_init(PyObject *module);
#define __Pyx_CommonTypesMetaclass_USED

/* CallTypeTraverse.proto */
#if !CYTHON_USE_TYPE_SPECS || (!CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX < 0x03090000)
#define __Pyx_call_type_traverse(o, always_call, visit, arg) 0
#else
static int __Pyx_call_type_traverse(PyObject *o, int always_call, visitproc visit, void *arg);
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/* PyMethodNew.proto */
static PyObject *__Pyx_PyMethod_New(PyObject *func, PyObject *self, PyObject *typ);

/* PyVectorcallFastCallDict.proto */
#if CYTHON_METH_FASTCALL && (CYTHON_VECTORCALL || CYTHON_BACKPORT_VECTORCALL)
static CYTHON_INLINE PyObject *__Pyx_PyVectorcall_FastCallDict(PyObject *func, __pyx_vectorcallfunc vc, PyObject *const *args, size_t nargs, PyObject *kw);
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/* CythonFunctionShared.proto */
#define __Pyx_CyFunction_USED
#define __Pyx_CYFUNCTION_STATICMETHOD  0x01
#define __Pyx_CYFUNCTION_CLASSMETHOD   0x02
#define __Pyx_CYFUNCTION_CCLASS        0x04
#define __Pyx_CYFUNCTION_COROUTINE     0x08
#define __Pyx_CyFunction_GetClosure(f)\
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#if PY_VERSION_HEX < 0x030900B1 || CYTHON_COMPILING_IN_LIMITED_API
  #define __Pyx_CyFunction_GetClassObj(f)\
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  #define __Pyx_CyFunction_GetClassObj(f)\
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#define __Pyx_CyFunction_SetClassObj(f, classobj)\
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#define __Pyx_CyFunction_Defaults(type, f)\
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#define __Pyx_CyFunction_SetDefaultsGetter(f, g)\
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#if CYTHON_COMPILING_IN_LIMITED_API
    PyObject_HEAD
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#elif PY_VERSION_HEX < 0x030900B1
    PyCFunctionObject func;
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    PyCMethodObject func;
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#if CYTHON_BACKPORT_VECTORCALL ||\
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    __pyx_vectorcallfunc func_vectorcall;
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#if CYTHON_COMPILING_IN_LIMITED_API
    PyObject *func_weakreflist;
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    PyObject *func_dict;
    PyObject *func_name;
    PyObject *func_qualname;
    PyObject *func_doc;
    PyObject *func_globals;
    PyObject *func_code;
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#if PY_VERSION_HEX < 0x030900B1 || CYTHON_COMPILING_IN_LIMITED_API
    PyObject *func_classobj;
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    PyObject *defaults;
    int flags;
    PyObject *defaults_tuple;
    PyObject *defaults_kwdict;
    PyObject *(*defaults_getter)(PyObject *);
    PyObject *func_annotations;
    PyObject *func_is_coroutine;
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#undef __Pyx_CyOrPyCFunction_Check
#define __Pyx_CyFunction_Check(obj)  __Pyx_TypeCheck(obj, __pyx_mstate_global->__pyx_CyFunctionType)
#define __Pyx_CyOrPyCFunction_Check(obj)  __Pyx_TypeCheck2(obj, __pyx_mstate_global->__pyx_CyFunctionType, &PyCFunction_Type)
#define __Pyx_CyFunction_CheckExact(obj)  __Pyx_IS_TYPE(obj, __pyx_mstate_global->__pyx_CyFunctionType)
static CYTHON_INLINE int __Pyx__IsSameCyOrCFunction(PyObject *func, void (*cfunc)(void));
#undef __Pyx_IsSameCFunction
#define __Pyx_IsSameCFunction(func, cfunc)   __Pyx__IsSameCyOrCFunction(func, cfunc)
static PyObject *__Pyx_CyFunction_Init(__pyx_CyFunctionObject* op, PyMethodDef *ml,
                                      int flags, PyObject* qualname,
                                      PyObject *closure,
                                      PyObject *module, PyObject *globals,
                                      PyObject* code);
static CYTHON_INLINE void __Pyx__CyFunction_SetClassObj(__pyx_CyFunctionObject* f, PyObject* classobj);
static CYTHON_INLINE PyObject *__Pyx_CyFunction_InitDefaults(PyObject *func,
                                                         PyTypeObject *defaults_type);
static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsTuple(PyObject *m,
                                                            PyObject *tuple);
static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsKwDict(PyObject *m,
                                                             PyObject *dict);
static CYTHON_INLINE void __Pyx_CyFunction_SetAnnotationsDict(PyObject *m,
                                                              PyObject *dict);
static int __pyx_CyFunction_init(PyObject *module);
#if CYTHON_METH_FASTCALL
static PyObject * __Pyx_CyFunction_Vectorcall_NOARGS(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames);
static PyObject * __Pyx_CyFunction_Vectorcall_O(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames);
static PyObject * __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames);
static PyObject * __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS_METHOD(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames);
#if CYTHON_BACKPORT_VECTORCALL || CYTHON_COMPILING_IN_LIMITED_API
#define __Pyx_CyFunction_func_vectorcall(f) (((__pyx_CyFunctionObject*)f)->func_vectorcall)
#else
#define __Pyx_CyFunction_func_vectorcall(f) (((PyCFunctionObject*)f)->vectorcall)
#endif
#endif

/* CythonFunction.proto */
static PyObject *__Pyx_CyFunction_New(PyMethodDef *ml,
                                      int flags, PyObject* qualname,
                                      PyObject *closure,
                                      PyObject *module, PyObject *globals,
                                      PyObject* code);

/* PyDictVersioning.proto */
#if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS
#define __PYX_DICT_VERSION_INIT  ((PY_UINT64_T) -1)
#define __PYX_GET_DICT_VERSION(dict)  (((PyDictObject*)(dict))->ma_version_tag)
#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)\
    (version_var) = __PYX_GET_DICT_VERSION(dict);\
    (cache_var) = (value);
#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP) {\
    static PY_UINT64_T __pyx_dict_version = 0;\
    static PyObject *__pyx_dict_cached_value = NULL;\
    if (likely(__PYX_GET_DICT_VERSION(DICT) == __pyx_dict_version)) {\
        (VAR) = __pyx_dict_cached_value;\
    } else {\
        (VAR) = __pyx_dict_cached_value = (LOOKUP);\
        __pyx_dict_version = __PYX_GET_DICT_VERSION(DICT);\
    }\
}
static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj);
static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj);
static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version);
#else
#define __PYX_GET_DICT_VERSION(dict)  (0)
#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)
#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP)  (VAR) = (LOOKUP);
#endif

/* PyErrExceptionMatches.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_PyErr_ExceptionMatches(err) __Pyx_PyErr_ExceptionMatchesInState(__pyx_tstate, err)
static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err);
#else
#define __Pyx_PyErr_ExceptionMatches(err)  PyErr_ExceptionMatches(err)
#endif

/* PyThreadStateGet.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_PyThreadState_declare  PyThreadState *__pyx_tstate;
#define __Pyx_PyThreadState_assign  __pyx_tstate = __Pyx_PyThreadState_Current;
#if PY_VERSION_HEX >= 0x030C00A6
#define __Pyx_PyErr_Occurred()  (__pyx_tstate->current_exception != NULL)
#define __Pyx_PyErr_CurrentExceptionType()  (__pyx_tstate->current_exception ? (PyObject*) Py_TYPE(__pyx_tstate->current_exception) : (PyObject*) NULL)
#else
#define __Pyx_PyErr_Occurred()  (__pyx_tstate->curexc_type != NULL)
#define __Pyx_PyErr_CurrentExceptionType()  (__pyx_tstate->curexc_type)
#endif
#else
#define __Pyx_PyThreadState_declare
#define __Pyx_PyThreadState_assign
#define __Pyx_PyErr_Occurred()  (PyErr_Occurred() != NULL)
#define __Pyx_PyErr_CurrentExceptionType()  PyErr_Occurred()
#endif

/* PyErrFetchRestore.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_PyErr_Clear() __Pyx_ErrRestore(NULL, NULL, NULL)
#define __Pyx_ErrRestoreWithState(type, value, tb)  __Pyx_ErrRestoreInState(PyThreadState_GET(), type, value, tb)
#define __Pyx_ErrFetchWithState(type, value, tb)    __Pyx_ErrFetchInState(PyThreadState_GET(), type, value, tb)
#define __Pyx_ErrRestore(type, value, tb)  __Pyx_ErrRestoreInState(__pyx_tstate, type, value, tb)
#define __Pyx_ErrFetch(type, value, tb)    __Pyx_ErrFetchInState(__pyx_tstate, type, value, tb)
static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030C00A6
#define __Pyx_PyErr_SetNone(exc) (Py_INCREF(exc), __Pyx_ErrRestore((exc), NULL, NULL))
#else
#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
#endif
#else
#define __Pyx_PyErr_Clear() PyErr_Clear()
#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
#define __Pyx_ErrRestoreWithState(type, value, tb)  PyErr_Restore(type, value, tb)
#define __Pyx_ErrFetchWithState(type, value, tb)  PyErr_Fetch(type, value, tb)
#define __Pyx_ErrRestoreInState(tstate, type, value, tb)  PyErr_Restore(type, value, tb)
#define __Pyx_ErrFetchInState(tstate, type, value, tb)  PyErr_Fetch(type, value, tb)
#define __Pyx_ErrRestore(type, value, tb)  PyErr_Restore(type, value, tb)
#define __Pyx_ErrFetch(type, value, tb)  PyErr_Fetch(type, value, tb)
#endif

/* PyObjectGetAttrStrNoError.proto */
static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStrNoError(PyObject* obj, PyObject* attr_name);

/* CLineInTraceback.proto */
#if CYTHON_CLINE_IN_TRACEBACK && CYTHON_CLINE_IN_TRACEBACK_RUNTIME
static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line);
#else
#define __Pyx_CLineForTraceback(tstate, c_line)  (((CYTHON_CLINE_IN_TRACEBACK)) ? c_line : 0)
#endif

/* CodeObjectCache.proto */
#if CYTHON_COMPILING_IN_LIMITED_API
typedef PyObject __Pyx_CachedCodeObjectType;
#else
typedef PyCodeObject __Pyx_CachedCodeObjectType;
#endif
typedef struct {
    __Pyx_CachedCodeObjectType* code_object;
    int code_line;
} __Pyx_CodeObjectCacheEntry;
struct __Pyx_CodeObjectCache {
    int count;
    int max_count;
    __Pyx_CodeObjectCacheEntry* entries;
  #if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
    __pyx_atomic_int_type accessor_count;
  #endif
};
static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);
static __Pyx_CachedCodeObjectType *__pyx_find_code_object(int code_line);
static void __pyx_insert_code_object(int code_line, __Pyx_CachedCodeObjectType* code_object);

/* AddTraceback.proto */
static void __Pyx_AddTraceback(const char *funcname, int c_line,
                               int py_line, const char *filename);

/* FormatTypeName.proto */
#if CYTHON_COMPILING_IN_LIMITED_API
typedef PyObject *__Pyx_TypeName;
#define __Pyx_FMT_TYPENAME "%U"
#define __Pyx_DECREF_TypeName(obj) Py_XDECREF(obj)
#if __PYX_LIMITED_VERSION_HEX >= 0x030d0000
#define __Pyx_PyType_GetFullyQualifiedName PyType_GetFullyQualifiedName
#else
static __Pyx_TypeName __Pyx_PyType_GetFullyQualifiedName(PyTypeObject* tp);
#endif
#else  // !LIMITED_API
typedef const char *__Pyx_TypeName;
#define __Pyx_FMT_TYPENAME "%.200s"
#define __Pyx_PyType_GetFullyQualifiedName(tp) ((tp)->tp_name)
#define __Pyx_DECREF_TypeName(obj)
#endif

/* GCCDiagnostics.proto */
#if !defined(__INTEL_COMPILER) && defined(__GNUC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6))
#define __Pyx_HAS_GCC_DIAGNOSTIC
#endif

/* PyObjectVectorCallKwBuilder.proto */
CYTHON_UNUSED static int __Pyx_VectorcallBuilder_AddArg_Check(PyObject *key, PyObject *value, PyObject *builder, PyObject **args, int n);
#if CYTHON_VECTORCALL
#if PY_VERSION_HEX >= 0x03090000
#define __Pyx_Object_Vectorcall_CallFromBuilder PyObject_Vectorcall
#else
#define __Pyx_Object_Vectorcall_CallFromBuilder _PyObject_Vectorcall
#endif
#define __Pyx_MakeVectorcallBuilderKwds(n) PyTuple_New(n)
static int __Pyx_VectorcallBuilder_AddArg(PyObject *key, PyObject *value, PyObject *builder, PyObject **args, int n);
static int __Pyx_VectorcallBuilder_AddArgStr(const char *key, PyObject *value, PyObject *builder, PyObject **args, int n);
#else
#define __Pyx_Object_Vectorcall_CallFromBuilder __Pyx_PyObject_FastCallDict
#define __Pyx_MakeVectorcallBuilderKwds(n) __Pyx_PyDict_NewPresized(n)
#define __Pyx_VectorcallBuilder_AddArg(key, value, builder, args, n) PyDict_SetItem(builder, key, value)
#define __Pyx_VectorcallBuilder_AddArgStr(key, value, builder, args, n) PyDict_SetItemString(builder, key, value)
#endif

/* CIntToPy.proto */
static CYTHON_INLINE PyObject* __Pyx_PyLong_From_long(long value);

/* CIntFromPy.proto */
static CYTHON_INLINE long __Pyx_PyLong_As_long(PyObject *);

/* CIntFromPy.proto */
static CYTHON_INLINE int __Pyx_PyLong_As_int(PyObject *);

/* FastTypeChecks.proto */
#if CYTHON_COMPILING_IN_CPYTHON
#define __Pyx_TypeCheck(obj, type) __Pyx_IsSubtype(Py_TYPE(obj), (PyTypeObject *)type)
#define __Pyx_TypeCheck2(obj, type1, type2) __Pyx_IsAnySubtype2(Py_TYPE(obj), (PyTypeObject *)type1, (PyTypeObject *)type2)
static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b);
static CYTHON_INLINE int __Pyx_IsAnySubtype2(PyTypeObject *cls, PyTypeObject *a, PyTypeObject *b);
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject *type);
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2);
#else
#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
#define __Pyx_TypeCheck2(obj, type1, type2) (PyObject_TypeCheck(obj, (PyTypeObject *)type1) || PyObject_TypeCheck(obj, (PyTypeObject *)type2))
#define __Pyx_PyErr_GivenExceptionMatches(err, type) PyErr_GivenExceptionMatches(err, type)
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2) {
    return PyErr_GivenExceptionMatches(err, type1) || PyErr_GivenExceptionMatches(err, type2);
}
#endif
#define __Pyx_PyErr_ExceptionMatches2(err1, err2)  __Pyx_PyErr_GivenExceptionMatches2(__Pyx_PyErr_CurrentExceptionType(), err1, err2)
#define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception)
#ifdef PyExceptionInstance_Check
  #define __Pyx_PyBaseException_Check(obj) PyExceptionInstance_Check(obj)
#else
  #define __Pyx_PyBaseException_Check(obj) __Pyx_TypeCheck(obj, PyExc_BaseException)
#endif

/* GetRuntimeVersion.proto */
static unsigned long __Pyx_get_runtime_version(void);

/* CheckBinaryVersion.proto */
static int __Pyx_check_binary_version(unsigned long ct_version, unsigned long rt_version, int allow_newer);

/* FunctionExport.proto */
static int __Pyx_ExportFunction(const char *name, void (*f)(void), const char *sig);

/* MultiPhaseInitModuleState.proto */
#if CYTHON_PEP489_MULTI_PHASE_INIT && CYTHON_USE_MODULE_STATE
static PyObject *__Pyx_State_FindModule(void*);
static int __Pyx_State_AddModule(PyObject* module, void*);
static int __Pyx_State_RemoveModule(void*);
#elif CYTHON_USE_MODULE_STATE
#define __Pyx_State_FindModule PyState_FindModule
#define __Pyx_State_AddModule PyState_AddModule
#define __Pyx_State_RemoveModule PyState_RemoveModule
#endif

/* #### Code section: module_declarations ### */
/* CythonABIVersion.proto */
#if CYTHON_COMPILING_IN_LIMITED_API
    #if CYTHON_METH_FASTCALL
        #define __PYX_FASTCALL_ABI_SUFFIX  "_fastcall"
    #else
        #define __PYX_FASTCALL_ABI_SUFFIX
    #endif
    #define __PYX_LIMITED_ABI_SUFFIX "limited" __PYX_FASTCALL_ABI_SUFFIX __PYX_AM_SEND_ABI_SUFFIX
#else
    #define __PYX_LIMITED_ABI_SUFFIX
#endif
#if __PYX_HAS_PY_AM_SEND == 1
    #define __PYX_AM_SEND_ABI_SUFFIX
#elif __PYX_HAS_PY_AM_SEND == 2
    #define __PYX_AM_SEND_ABI_SUFFIX "amsendbackport"
#else
    #define __PYX_AM_SEND_ABI_SUFFIX "noamsend"
#endif
#ifndef __PYX_MONITORING_ABI_SUFFIX
    #define __PYX_MONITORING_ABI_SUFFIX
#endif
#if CYTHON_USE_TP_FINALIZE
    #define __PYX_TP_FINALIZE_ABI_SUFFIX
#else
    #define __PYX_TP_FINALIZE_ABI_SUFFIX "nofinalize"
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#if CYTHON_USE_FREELISTS || !defined(__Pyx_AsyncGen_USED)
    #define __PYX_FREELISTS_ABI_SUFFIX
#else
    #define __PYX_FREELISTS_ABI_SUFFIX "nofreelists"
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#define CYTHON_ABI  __PYX_ABI_VERSION __PYX_LIMITED_ABI_SUFFIX __PYX_MONITORING_ABI_SUFFIX __PYX_TP_FINALIZE_ABI_SUFFIX __PYX_FREELISTS_ABI_SUFFIX __PYX_AM_SEND_ABI_SUFFIX
#define __PYX_ABI_MODULE_NAME "_cython_" CYTHON_ABI
#define __PYX_TYPE_MODULE_PREFIX __PYX_ABI_MODULE_NAME "."


/* Module declarations from "libc.math" */

/* Module declarations from "pyRing.eob_utils" */
static double __pyx_f_6pyRing_9eob_utils__Y(double, double, double, double, double, double, double, double, double, double); /*proto*/
/* #### Code section: typeinfo ### */
/* #### Code section: before_global_var ### */
#define __Pyx_MODULE_NAME "pyRing.eob_utils"
extern int __pyx_module_is_main_pyRing__eob_utils;
int __pyx_module_is_main_pyRing__eob_utils = 0;

/* Implementation of "pyRing.eob_utils" */
/* #### Code section: global_var ### */
/* #### Code section: string_decls ### */
static const char __pyx_k_[] = "?";
static const char __pyx_k_Y[] = "Y";
static const char __pyx_k_af[] = "af";
static const char __pyx_k_Y_0[] = "Y_0";
static const char __pyx_k_af2[] = "af2";
static const char __pyx_k_af3[] = "af3";
static const char __pyx_k_b_1[] = "b_1";
static const char __pyx_k_b_2[] = "b_2";
static const char __pyx_k_b_3[] = "b_3";
static const char __pyx_k_c_1[] = "c_1";
static const char __pyx_k_c_2[] = "c_2";
static const char __pyx_k_c_3[] = "c_3";
static const char __pyx_k_pop[] = "pop";
static const char __pyx_k_func[] = "__func__";
static const char __pyx_k_main[] = "__main__";
static const char __pyx_k_name[] = "__name__";
static const char __pyx_k_test[] = "__test__";
static const char __pyx_k_module[] = "__module__";
static const char __pyx_k_qualname[] = "__qualname__";
static const char __pyx_k_set_name[] = "__set_name__";
static const char __pyx_k_2Qe5_U_uE_U[] = "\200\001\330\004\013\2102\210Q\210e\2205\230\005\230U\240%\240u\250E\260\024\260U\270!";
static const char __pyx_k_is_coroutine[] = "_is_coroutine";
static const char __pyx_k_pyRing_eob_utils[] = "pyRing.eob_utils";
static const char __pyx_k_asyncio_coroutines[] = "asyncio.coroutines";
static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback";
static const char __pyx_k_pyRing_eob_utils_pyx[] = "pyRing/eob_utils.pyx";
/* #### Code section: decls ### */
static PyObject *__pyx_pf_6pyRing_9eob_utils_Y(CYTHON_UNUSED PyObject *__pyx_self, double __pyx_v_Y_0, double __pyx_v_b_1, double __pyx_v_b_2, double __pyx_v_b_3, double __pyx_v_c_1, double __pyx_v_c_2, double __pyx_v_c_3, double __pyx_v_af, double __pyx_v_af2, double __pyx_v_af3); /* proto */
/* #### Code section: late_includes ### */
/* #### Code section: module_state ### */
/* SmallCodeConfig */
#ifndef CYTHON_SMALL_CODE
#if defined(__clang__)
    #define CYTHON_SMALL_CODE
#elif defined(__GNUC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 3))
    #define CYTHON_SMALL_CODE __attribute__((cold))
#else
    #define CYTHON_SMALL_CODE
#endif
#endif

typedef struct {
  PyObject *__pyx_d;
  PyObject *__pyx_b;
  PyObject *__pyx_cython_runtime;
  PyObject *__pyx_empty_tuple;
  PyObject *__pyx_empty_bytes;
  PyObject *__pyx_empty_unicode;
  #ifdef __Pyx_CyFunction_USED
  PyTypeObject *__pyx_CyFunctionType;
  #endif
  #ifdef __Pyx_FusedFunction_USED
  PyTypeObject *__pyx_FusedFunctionType;
  #endif
  #ifdef __Pyx_Generator_USED
  PyTypeObject *__pyx_GeneratorType;
  #endif
  #ifdef __Pyx_IterableCoroutine_USED
  PyTypeObject *__pyx_IterableCoroutineType;
  #endif
  #ifdef __Pyx_Coroutine_USED
  PyTypeObject *__pyx_CoroutineAwaitType;
  #endif
  #ifdef __Pyx_Coroutine_USED
  PyTypeObject *__pyx_CoroutineType;
  #endif
  __Pyx_CachedCFunction __pyx_umethod_PyDict_Type_pop;
  PyObject *__pyx_codeobj_tab[1];
  PyObject *__pyx_string_tab[25];
/* #### Code section: module_state_contents ### */
/* CommonTypesMetaclass.module_state_decls */
PyTypeObject *__pyx_CommonTypesMetaclassType;

/* CachedMethodType.module_state_decls */
#if CYTHON_COMPILING_IN_LIMITED_API
PyObject *__Pyx_CachedMethodType;
#endif

/* CodeObjectCache.module_state_decls */
struct __Pyx_CodeObjectCache __pyx_code_cache;

/* #### Code section: module_state_end ### */
} __pyx_mstatetype;

#if CYTHON_USE_MODULE_STATE
#ifdef __cplusplus
namespace {
extern struct PyModuleDef __pyx_moduledef;
} /* anonymous namespace */
#else
static struct PyModuleDef __pyx_moduledef;
#endif

#define __pyx_mstate_global (__Pyx_PyModule_GetState(__Pyx_State_FindModule(&__pyx_moduledef)))

#define __pyx_m (__Pyx_State_FindModule(&__pyx_moduledef))
#else
static __pyx_mstatetype __pyx_mstate_global_static =
#ifdef __cplusplus
    {};
#else
    {0};
#endif
static __pyx_mstatetype * const __pyx_mstate_global = &__pyx_mstate_global_static;
#endif
/* #### Code section: constant_name_defines ### */
#define __pyx_kp_u_ __pyx_string_tab[0]
#define __pyx_n_u_Y __pyx_string_tab[1]
#define __pyx_n_u_Y_0 __pyx_string_tab[2]
#define __pyx_n_u_af __pyx_string_tab[3]
#define __pyx_n_u_af2 __pyx_string_tab[4]
#define __pyx_n_u_af3 __pyx_string_tab[5]
#define __pyx_n_u_asyncio_coroutines __pyx_string_tab[6]
#define __pyx_n_u_b_1 __pyx_string_tab[7]
#define __pyx_n_u_b_2 __pyx_string_tab[8]
#define __pyx_n_u_b_3 __pyx_string_tab[9]
#define __pyx_n_u_c_1 __pyx_string_tab[10]
#define __pyx_n_u_c_2 __pyx_string_tab[11]
#define __pyx_n_u_c_3 __pyx_string_tab[12]
#define __pyx_n_u_cline_in_traceback __pyx_string_tab[13]
#define __pyx_n_u_func __pyx_string_tab[14]
#define __pyx_n_u_is_coroutine __pyx_string_tab[15]
#define __pyx_n_u_main __pyx_string_tab[16]
#define __pyx_n_u_module __pyx_string_tab[17]
#define __pyx_n_u_name __pyx_string_tab[18]
#define __pyx_n_u_pop __pyx_string_tab[19]
#define __pyx_n_u_pyRing_eob_utils __pyx_string_tab[20]
#define __pyx_kp_u_pyRing_eob_utils_pyx __pyx_string_tab[21]
#define __pyx_n_u_qualname __pyx_string_tab[22]
#define __pyx_n_u_set_name __pyx_string_tab[23]
#define __pyx_n_u_test __pyx_string_tab[24]
/* #### Code section: module_state_clear ### */
#if CYTHON_USE_MODULE_STATE
static CYTHON_SMALL_CODE int __pyx_m_clear(PyObject *m) {
  __pyx_mstatetype *clear_module_state = __Pyx_PyModule_GetState(m);
  if (!clear_module_state) return 0;
  Py_CLEAR(clear_module_state->__pyx_d);
  Py_CLEAR(clear_module_state->__pyx_b);
  Py_CLEAR(clear_module_state->__pyx_cython_runtime);
  Py_CLEAR(clear_module_state->__pyx_empty_tuple);
  Py_CLEAR(clear_module_state->__pyx_empty_bytes);
  Py_CLEAR(clear_module_state->__pyx_empty_unicode);
  #ifdef __Pyx_CyFunction_USED
  Py_CLEAR(clear_module_state->__pyx_CyFunctionType);
  #endif
  #ifdef __Pyx_FusedFunction_USED
  Py_CLEAR(clear_module_state->__pyx_FusedFunctionType);
  #endif
  #if CYTHON_PEP489_MULTI_PHASE_INIT
  __Pyx_State_RemoveModule(NULL);
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/* "pyRing/eob_utils.pyx":33
 *     their definitions are summarized at the end of section I of arXiv:2001.09082v2.
 * """
 * cdef inline double _sym_mass_ratio(double m1, double m2) nogil:             # <<<<<<<<<<<<<<
 *     cdef double q  = m1/m2
 *     cdef double Q  = 1.0 + q
*/

static CYTHON_INLINE double __pyx_f_6pyRing_9eob_utils__sym_mass_ratio(double __pyx_v_m1, double __pyx_v_m2) {
  double __pyx_v_q;
  double __pyx_v_Q;
  double __pyx_v_Q2;
  double __pyx_r;

  /* "pyRing/eob_utils.pyx":34
 * """
 * cdef inline double _sym_mass_ratio(double m1, double m2) nogil:
 *     cdef double q  = m1/m2             # <<<<<<<<<<<<<<
 *     cdef double Q  = 1.0 + q
 *     cdef double Q2 = Q * Q
*/
  __pyx_v_q = (__pyx_v_m1 / __pyx_v_m2);

  /* "pyRing/eob_utils.pyx":35
 * cdef inline double _sym_mass_ratio(double m1, double m2) nogil:
 *     cdef double q  = m1/m2
 *     cdef double Q  = 1.0 + q             # <<<<<<<<<<<<<<
 *     cdef double Q2 = Q * Q
 *     return q / Q2
*/
  __pyx_v_Q = (1.0 + __pyx_v_q);

  /* "pyRing/eob_utils.pyx":36
 *     cdef double q  = m1/m2
 *     cdef double Q  = 1.0 + q
 *     cdef double Q2 = Q * Q             # <<<<<<<<<<<<<<
 *     return q / Q2
 * 
*/
  __pyx_v_Q2 = (__pyx_v_Q * __pyx_v_Q);

  /* "pyRing/eob_utils.pyx":37
 *     cdef double Q  = 1.0 + q
 *     cdef double Q2 = Q * Q
 *     return q / Q2             # <<<<<<<<<<<<<<
 * 
 * cdef inline double _X_1(double m1, double m2) nogil:
*/
  __pyx_r = (__pyx_v_q / __pyx_v_Q2);
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":33
 *     their definitions are summarized at the end of section I of arXiv:2001.09082v2.
 * """
 * cdef inline double _sym_mass_ratio(double m1, double m2) nogil:             # <<<<<<<<<<<<<<
 *     cdef double q  = m1/m2
 *     cdef double Q  = 1.0 + q
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "pyRing/eob_utils.pyx":39
 *     return q / Q2
 * 
 * cdef inline double _X_1(double m1, double m2) nogil:             # <<<<<<<<<<<<<<
 *     cdef double M = m1 + m2
 *     return m1 / M
*/

static CYTHON_INLINE double __pyx_f_6pyRing_9eob_utils__X_1(double __pyx_v_m1, double __pyx_v_m2) {
  double __pyx_v_M;
  double __pyx_r;

  /* "pyRing/eob_utils.pyx":40
 * 
 * cdef inline double _X_1(double m1, double m2) nogil:
 *     cdef double M = m1 + m2             # <<<<<<<<<<<<<<
 *     return m1 / M
 * 
*/
  __pyx_v_M = (__pyx_v_m1 + __pyx_v_m2);

  /* "pyRing/eob_utils.pyx":41
 * cdef inline double _X_1(double m1, double m2) nogil:
 *     cdef double M = m1 + m2
 *     return m1 / M             # <<<<<<<<<<<<<<
 * 
 * cdef inline double _X_2(double m1, double m2) nogil:
*/
  __pyx_r = (__pyx_v_m1 / __pyx_v_M);
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":39
 *     return q / Q2
 * 
 * cdef inline double _X_1(double m1, double m2) nogil:             # <<<<<<<<<<<<<<
 *     cdef double M = m1 + m2
 *     return m1 / M
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "pyRing/eob_utils.pyx":43
 *     return m1 / M
 * 
 * cdef inline double _X_2(double m1, double m2) nogil:             # <<<<<<<<<<<<<<
 *     cdef double M = m1 + m2
 *     return m2 / M
*/

static CYTHON_INLINE double __pyx_f_6pyRing_9eob_utils__X_2(double __pyx_v_m1, double __pyx_v_m2) {
  double __pyx_v_M;
  double __pyx_r;

  /* "pyRing/eob_utils.pyx":44
 * 
 * cdef inline double _X_2(double m1, double m2) nogil:
 *     cdef double M = m1 + m2             # <<<<<<<<<<<<<<
 *     return m2 / M
 * 
*/
  __pyx_v_M = (__pyx_v_m1 + __pyx_v_m2);

  /* "pyRing/eob_utils.pyx":45
 * cdef inline double _X_2(double m1, double m2) nogil:
 *     cdef double M = m1 + m2
 *     return m2 / M             # <<<<<<<<<<<<<<
 * 
 * cdef inline double _X_12(double X1, double X2) nogil:
*/
  __pyx_r = (__pyx_v_m2 / __pyx_v_M);
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":43
 *     return m1 / M
 * 
 * cdef inline double _X_2(double m1, double m2) nogil:             # <<<<<<<<<<<<<<
 *     cdef double M = m1 + m2
 *     return m2 / M
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "pyRing/eob_utils.pyx":47
 *     return m2 / M
 * 
 * cdef inline double _X_12(double X1, double X2) nogil:             # <<<<<<<<<<<<<<
 *     return X1 - X2
 * 
*/

static CYTHON_INLINE double __pyx_f_6pyRing_9eob_utils__X_12(double __pyx_v_X1, double __pyx_v_X2) {
  double __pyx_r;

  /* "pyRing/eob_utils.pyx":48
 * 
 * cdef inline double _X_12(double X1, double X2) nogil:
 *     return X1 - X2             # <<<<<<<<<<<<<<
 * 
 * cdef inline double _a_0(double X1, double X2, double chi1, double chi2) nogil:
*/
  __pyx_r = (__pyx_v_X1 - __pyx_v_X2);
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":47
 *     return m2 / M
 * 
 * cdef inline double _X_12(double X1, double X2) nogil:             # <<<<<<<<<<<<<<
 *     return X1 - X2
 * 
*/

  /* function exit code */
  __pyx_L0:;
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}

/* "pyRing/eob_utils.pyx":50
 *     return X1 - X2
 * 
 * cdef inline double _a_0(double X1, double X2, double chi1, double chi2) nogil:             # <<<<<<<<<<<<<<
 *     return X1 * chi1 + X2 * chi2
 * 
*/

static CYTHON_INLINE double __pyx_f_6pyRing_9eob_utils__a_0(double __pyx_v_X1, double __pyx_v_X2, double __pyx_v_chi1, double __pyx_v_chi2) {
  double __pyx_r;

  /* "pyRing/eob_utils.pyx":51
 * 
 * cdef inline double _a_0(double X1, double X2, double chi1, double chi2) nogil:
 *     return X1 * chi1 + X2 * chi2             # <<<<<<<<<<<<<<
 * 
 * cdef inline double _a_12(double X1, double X2, double chi1, double chi2) nogil:
*/
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  /* "pyRing/eob_utils.pyx":50
 *     return X1 - X2
 * 
 * cdef inline double _a_0(double X1, double X2, double chi1, double chi2) nogil:             # <<<<<<<<<<<<<<
 *     return X1 * chi1 + X2 * chi2
 * 
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "pyRing/eob_utils.pyx":53
 *     return X1 * chi1 + X2 * chi2
 * 
 * cdef inline double _a_12(double X1, double X2, double chi1, double chi2) nogil:             # <<<<<<<<<<<<<<
 *     return X1 * chi1 - X2 * chi2
 * 
*/

static CYTHON_INLINE double __pyx_f_6pyRing_9eob_utils__a_12(double __pyx_v_X1, double __pyx_v_X2, double __pyx_v_chi1, double __pyx_v_chi2) {
  double __pyx_r;

  /* "pyRing/eob_utils.pyx":54
 * 
 * cdef inline double _a_12(double X1, double X2, double chi1, double chi2) nogil:
 *     return X1 * chi1 - X2 * chi2             # <<<<<<<<<<<<<<
 * 
 * cdef inline double _S_hat(double X12, double a0, double a12) nogil:
*/
  __pyx_r = ((__pyx_v_X1 * __pyx_v_chi1) - (__pyx_v_X2 * __pyx_v_chi2));
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":53
 *     return X1 * chi1 + X2 * chi2
 * 
 * cdef inline double _a_12(double X1, double X2, double chi1, double chi2) nogil:             # <<<<<<<<<<<<<<
 *     return X1 * chi1 - X2 * chi2
 * 
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "pyRing/eob_utils.pyx":56
 *     return X1 * chi1 - X2 * chi2
 * 
 * cdef inline double _S_hat(double X12, double a0, double a12) nogil:             # <<<<<<<<<<<<<<
 *     cdef double s = a0 + X12 * a12
 *     return 0.5 * s
*/

static CYTHON_INLINE double __pyx_f_6pyRing_9eob_utils__S_hat(double __pyx_v_X12, double __pyx_v_a0, double __pyx_v_a12) {
  double __pyx_v_s;
  double __pyx_r;

  /* "pyRing/eob_utils.pyx":57
 * 
 * cdef inline double _S_hat(double X12, double a0, double a12) nogil:
 *     cdef double s = a0 + X12 * a12             # <<<<<<<<<<<<<<
 *     return 0.5 * s
 * 
*/
  __pyx_v_s = (__pyx_v_a0 + (__pyx_v_X12 * __pyx_v_a12));

  /* "pyRing/eob_utils.pyx":58
 * cdef inline double _S_hat(double X12, double a0, double a12) nogil:
 *     cdef double s = a0 + X12 * a12
 *     return 0.5 * s             # <<<<<<<<<<<<<<
 * 
 * cdef inline double _S_bar(double X12, double a0, double a12) nogil:
*/
  __pyx_r = (0.5 * __pyx_v_s);
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":56
 *     return X1 * chi1 - X2 * chi2
 * 
 * cdef inline double _S_hat(double X12, double a0, double a12) nogil:             # <<<<<<<<<<<<<<
 *     cdef double s = a0 + X12 * a12
 *     return 0.5 * s
*/

  /* function exit code */
  __pyx_L0:;
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}

/* "pyRing/eob_utils.pyx":60
 *     return 0.5 * s
 * 
 * cdef inline double _S_bar(double X12, double a0, double a12) nogil:             # <<<<<<<<<<<<<<
 *     cdef double s = X12 * a0 + a12
 *     return 0.5 * s
*/

static CYTHON_INLINE double __pyx_f_6pyRing_9eob_utils__S_bar(double __pyx_v_X12, double __pyx_v_a0, double __pyx_v_a12) {
  double __pyx_v_s;
  double __pyx_r;

  /* "pyRing/eob_utils.pyx":61
 * 
 * cdef inline double _S_bar(double X12, double a0, double a12) nogil:
 *     cdef double s = X12 * a0 + a12             # <<<<<<<<<<<<<<
 *     return 0.5 * s
 * 
*/
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  /* "pyRing/eob_utils.pyx":62
 * cdef inline double _S_bar(double X12, double a0, double a12) nogil:
 *     cdef double s = X12 * a0 + a12
 *     return 0.5 * s             # <<<<<<<<<<<<<<
 * 
 * 
*/
  __pyx_r = (0.5 * __pyx_v_s);
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  /* "pyRing/eob_utils.pyx":60
 *     return 0.5 * s
 * 
 * cdef inline double _S_bar(double X12, double a0, double a12) nogil:             # <<<<<<<<<<<<<<
 *     cdef double s = X12 * a0 + a12
 *     return 0.5 * s
*/

  /* function exit code */
  __pyx_L0:;
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}

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  goto __pyx_L6_skip;
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  /* function exit code */
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  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
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 * 
 * def Y(double Y_0, double b_1, double b_2, double b_3, double c_1, double c_2, double c_3, double af, double af2, double af3):
 *     return _Y(Y_0, b_1, b_2, b_3, c_1, c_2, c_3, af, af2, af3)             # <<<<<<<<<<<<<<
 * 
 * # eq. 5.21 of arXiv:1904.09550v2
*/
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 * #############################################################
 * 
 * def Y(double Y_0, double b_1, double b_2, double b_3, double c_1, double c_2, double c_3, double af, double af2, double af3):             # <<<<<<<<<<<<<<
 *     return _Y(Y_0, b_1, b_2, b_3, c_1, c_2, c_3, af, af2, af3)
 * 
*/

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/* "pyRing/eob_utils.pyx":104
 * 
 * # eq. 5.21 of arXiv:1904.09550v2
 * cdef double _Y(double Y_0, double b_1, double b_2, double b_3, double c_1, double c_2, double c_3, double af, double af2, double af3) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function implementing eq. 5.21 of arXiv:1904.09550v2.
*/

static double __pyx_f_6pyRing_9eob_utils__Y(double __pyx_v_Y_0, double __pyx_v_b_1, double __pyx_v_b_2, double __pyx_v_b_3, double __pyx_v_c_1, double __pyx_v_c_2, double __pyx_v_c_3, double __pyx_v_af, double __pyx_v_af2, double __pyx_v_af3) {
  double __pyx_v_num;
  double __pyx_v_den;
  double __pyx_v_res;
  double __pyx_r;

  /* "pyRing/eob_utils.pyx":109
 *     It is the same fitting equation for the three coefficients alpha1, alpha21, omega1.
 *     """
 *     cdef double num, den , res = 0.             # <<<<<<<<<<<<<<
 * 
 *     num = 1 + b_1*af + b_2*af2 + b_3*af3
*/
  __pyx_v_res = 0.;

  /* "pyRing/eob_utils.pyx":111
 *     cdef double num, den , res = 0.
 * 
 *     num = 1 + b_1*af + b_2*af2 + b_3*af3             # <<<<<<<<<<<<<<
 *     den = 1 + c_1*af + c_2*af2 + c_3*af3
 *     res = Y_0 * num/den
*/
  __pyx_v_num = (((1.0 + (__pyx_v_b_1 * __pyx_v_af)) + (__pyx_v_b_2 * __pyx_v_af2)) + (__pyx_v_b_3 * __pyx_v_af3));

  /* "pyRing/eob_utils.pyx":112
 * 
 *     num = 1 + b_1*af + b_2*af2 + b_3*af3
 *     den = 1 + c_1*af + c_2*af2 + c_3*af3             # <<<<<<<<<<<<<<
 *     res = Y_0 * num/den
 * 
*/
  __pyx_v_den = (((1.0 + (__pyx_v_c_1 * __pyx_v_af)) + (__pyx_v_c_2 * __pyx_v_af2)) + (__pyx_v_c_3 * __pyx_v_af3));

  /* "pyRing/eob_utils.pyx":113
 *     num = 1 + b_1*af + b_2*af2 + b_3*af3
 *     den = 1 + c_1*af + c_2*af2 + c_3*af3
 *     res = Y_0 * num/den             # <<<<<<<<<<<<<<
 * 
 *     return res
*/
  __pyx_v_res = ((__pyx_v_Y_0 * __pyx_v_num) / __pyx_v_den);

  /* "pyRing/eob_utils.pyx":115
 *     res = Y_0 * num/den
 * 
 *     return res             # <<<<<<<<<<<<<<
 * 
 * 
*/
  __pyx_r = __pyx_v_res;
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":104
 * 
 * # eq. 5.21 of arXiv:1904.09550v2
 * cdef double _Y(double Y_0, double b_1, double b_2, double b_3, double c_1, double c_2, double c_3, double af, double af2, double af3) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function implementing eq. 5.21 of arXiv:1904.09550v2.
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "pyRing/eob_utils.pyx":118
 * 
 * 
 * cdef double _alpha1(double af, int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function returning the value of alpha1 for each mode, following appendix C.2 of arXiv:2001.09082v2.
*/

static double __pyx_f_6pyRing_9eob_utils__alpha1(double __pyx_v_af, int __pyx_v_l, int __pyx_v_m) {
  double __pyx_v_res;
  double __pyx_v_alpha1_22;
  double __pyx_v_alpha1_21;
  double __pyx_v_alpha1_33;
  double __pyx_v_alpha1_32;
  double __pyx_v_alpha1_31;
  double __pyx_v_alpha1_44;
  double __pyx_v_alpha1_43;
  double __pyx_v_alpha1_42;
  double __pyx_v_alpha1_41;
  double __pyx_v_alpha1_55;
  double __pyx_v_af2;
  double __pyx_v_af3;
  double __pyx_v_alp1_22_0;
  double __pyx_v_b_1_22;
  double __pyx_v_b_2_22;
  double __pyx_v_b_3_22;
  double __pyx_v_c_1_22;
  double __pyx_v_c_2_22;
  double __pyx_v_c_3_22;
  double __pyx_v_alp1_21_0;
  double __pyx_v_b_1_21;
  double __pyx_v_b_2_21;
  double __pyx_v_b_3_21;
  double __pyx_v_c_1_21;
  double __pyx_v_c_2_21;
  double __pyx_v_c_3_21;
  double __pyx_v_alp1_33_0;
  double __pyx_v_b_1_33;
  double __pyx_v_b_2_33;
  double __pyx_v_b_3_33;
  double __pyx_v_c_1_33;
  double __pyx_v_c_2_33;
  double __pyx_v_c_3_33;
  double __pyx_v_alp1_32_0;
  double __pyx_v_b_1_32;
  double __pyx_v_b_2_32;
  double __pyx_v_b_3_32;
  double __pyx_v_c_1_32;
  double __pyx_v_c_2_32;
  double __pyx_v_c_3_32;
  double __pyx_v_alp1_31_0;
  double __pyx_v_b_1_31;
  double __pyx_v_b_2_31;
  double __pyx_v_b_3_31;
  double __pyx_v_c_1_31;
  double __pyx_v_c_2_31;
  double __pyx_v_c_3_31;
  double __pyx_v_alp1_44_0;
  double __pyx_v_b_1_44;
  double __pyx_v_b_2_44;
  double __pyx_v_b_3_44;
  double __pyx_v_c_1_44;
  double __pyx_v_c_2_44;
  double __pyx_v_c_3_44;
  double __pyx_v_alp1_43_0;
  double __pyx_v_b_1_43;
  double __pyx_v_b_2_43;
  double __pyx_v_b_3_43;
  double __pyx_v_c_1_43;
  double __pyx_v_c_2_43;
  double __pyx_v_c_3_43;
  double __pyx_v_alp1_42_0;
  double __pyx_v_b_1_42;
  double __pyx_v_b_2_42;
  double __pyx_v_b_3_42;
  double __pyx_v_c_1_42;
  double __pyx_v_c_2_42;
  double __pyx_v_c_3_42;
  double __pyx_v_alp1_41_0;
  double __pyx_v_b_1_41;
  double __pyx_v_b_2_41;
  double __pyx_v_b_3_41;
  double __pyx_v_c_1_41;
  double __pyx_v_c_2_41;
  double __pyx_v_c_3_41;
  double __pyx_v_alp1_55_0;
  double __pyx_v_b_1_55;
  double __pyx_v_b_2_55;
  double __pyx_v_b_3_55;
  double __pyx_v_c_1_55;
  double __pyx_v_c_2_55;
  double __pyx_v_c_3_55;
  double __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;
  double __pyx_t_3;
  int __pyx_lineno = 0;
  const char *__pyx_filename = NULL;
  int __pyx_clineno = 0;
  PyGILState_STATE __pyx_gilstate_save;

  /* "pyRing/eob_utils.pyx":130
 *     """
 * 
 *     cdef double res = 0.             # <<<<<<<<<<<<<<
 *     cdef double num_alp, den_alp
 *     cdef double alpha1_22, alpha1_21, alpha1_33, alpha1_32, alpha1_31, alpha1_44, alpha1_43, alpha1_42, alpha1_41, alpha1_55
*/
  __pyx_v_res = 0.;

  /* "pyRing/eob_utils.pyx":133
 *     cdef double num_alp, den_alp
 *     cdef double alpha1_22, alpha1_21, alpha1_33, alpha1_32, alpha1_31, alpha1_44, alpha1_43, alpha1_42, alpha1_41, alpha1_55
 *     cdef double af2 = af*af, af3 = af2*af             # <<<<<<<<<<<<<<
 * 
 *     # -------------------------------------------------------------------------------- #
*/
  __pyx_v_af2 = (__pyx_v_af * __pyx_v_af);
  __pyx_v_af3 = (__pyx_v_af2 * __pyx_v_af);

  /* "pyRing/eob_utils.pyx":137
 *     # -------------------------------------------------------------------------------- #
 *     # (2,2) - TEOBResumSFits.c, line 2803
 *     cdef double alp1_22_0 = 0.08896             # <<<<<<<<<<<<<<
 *     cdef double b_1_22    = -1.90036, b_2_22 = 0.86200, b_3_22 = 0.0384893
 *     cdef double c_1_22    = -1.87933, c_2_22 = 0.88062, c_3_22 = 0.
*/
  __pyx_v_alp1_22_0 = 0.08896;

  /* "pyRing/eob_utils.pyx":138
 *     # (2,2) - TEOBResumSFits.c, line 2803
 *     cdef double alp1_22_0 = 0.08896
 *     cdef double b_1_22    = -1.90036, b_2_22 = 0.86200, b_3_22 = 0.0384893             # <<<<<<<<<<<<<<
 *     cdef double c_1_22    = -1.87933, c_2_22 = 0.88062, c_3_22 = 0.
 * 
*/
  __pyx_v_b_1_22 = -1.90036;
  __pyx_v_b_2_22 = 0.86200;
  __pyx_v_b_3_22 = 0.0384893;

  /* "pyRing/eob_utils.pyx":139
 *     cdef double alp1_22_0 = 0.08896
 *     cdef double b_1_22    = -1.90036, b_2_22 = 0.86200, b_3_22 = 0.0384893
 *     cdef double c_1_22    = -1.87933, c_2_22 = 0.88062, c_3_22 = 0.             # <<<<<<<<<<<<<<
 * 
 *     # (2,1) - TEOBResumSFits.c, line 2798
*/
  __pyx_v_c_1_22 = -1.87933;
  __pyx_v_c_2_22 = 0.88062;
  __pyx_v_c_3_22 = 0.;

  /* "pyRing/eob_utils.pyx":142
 * 
 *     # (2,1) - TEOBResumSFits.c, line 2798
 *     cdef double alp1_21_0 = 0.0889623             # <<<<<<<<<<<<<<
 *     cdef double b_1_21    = -1.31253, b_2_21 = -0.21033, b_3_21 = 0.52502
 *     cdef double c_1_21    = -1.30041, c_2_21 = -0.1566,  c_3_21 = 0.46204
*/
  __pyx_v_alp1_21_0 = 0.0889623;

  /* "pyRing/eob_utils.pyx":143
 *     # (2,1) - TEOBResumSFits.c, line 2798
 *     cdef double alp1_21_0 = 0.0889623
 *     cdef double b_1_21    = -1.31253, b_2_21 = -0.21033, b_3_21 = 0.52502             # <<<<<<<<<<<<<<
 *     cdef double c_1_21    = -1.30041, c_2_21 = -0.1566,  c_3_21 = 0.46204
 * 
*/
  __pyx_v_b_1_21 = -1.31253;
  __pyx_v_b_2_21 = -0.21033;
  __pyx_v_b_3_21 = 0.52502;

  /* "pyRing/eob_utils.pyx":144
 *     cdef double alp1_21_0 = 0.0889623
 *     cdef double b_1_21    = -1.31253, b_2_21 = -0.21033, b_3_21 = 0.52502
 *     cdef double c_1_21    = -1.30041, c_2_21 = -0.1566,  c_3_21 = 0.46204             # <<<<<<<<<<<<<<
 * 
 *     # (3,3) - TEOBResumSFits.c, line 2832
*/
  __pyx_v_c_1_21 = -1.30041;
  __pyx_v_c_2_21 = -0.1566;
  __pyx_v_c_3_21 = 0.46204;

  /* "pyRing/eob_utils.pyx":147
 * 
 *     # (3,3) - TEOBResumSFits.c, line 2832
 *     cdef double alp1_33_0 = 0.0927030             # <<<<<<<<<<<<<<
 *     cdef double b_1_33    = -1.8310, b_2_33 = 0.7568, b_3_33 = 0.0745
 *     cdef double c_1_33    = -1.8098, c_2_33 = 0.7926, c_3_33 = 0.0196
*/
  __pyx_v_alp1_33_0 = 0.0927030;

  /* "pyRing/eob_utils.pyx":148
 *     # (3,3) - TEOBResumSFits.c, line 2832
 *     cdef double alp1_33_0 = 0.0927030
 *     cdef double b_1_33    = -1.8310, b_2_33 = 0.7568, b_3_33 = 0.0745             # <<<<<<<<<<<<<<
 *     cdef double c_1_33    = -1.8098, c_2_33 = 0.7926, c_3_33 = 0.0196
 * 
*/
  __pyx_v_b_1_33 = -1.8310;
  __pyx_v_b_2_33 = 0.7568;
  __pyx_v_b_3_33 = 0.0745;

  /* "pyRing/eob_utils.pyx":149
 *     cdef double alp1_33_0 = 0.0927030
 *     cdef double b_1_33    = -1.8310, b_2_33 = 0.7568, b_3_33 = 0.0745
 *     cdef double c_1_33    = -1.8098, c_2_33 = 0.7926, c_3_33 = 0.0196             # <<<<<<<<<<<<<<
 * 
 *     # (3,2) - TEOBResumSFits.c, line 2827
*/
  __pyx_v_c_1_33 = -1.8098;
  __pyx_v_c_2_33 = 0.7926;
  __pyx_v_c_3_33 = 0.0196;

  /* "pyRing/eob_utils.pyx":152
 * 
 *     # (3,2) - TEOBResumSFits.c, line 2827
 *     cdef double alp1_32_0 = 0.0927030             # <<<<<<<<<<<<<<
 *     cdef double b_1_32    = -1.58277, b_2_32 = 0.2783, b_3_32 = 0.30503
 *     cdef double c_1_32    = -1.56797, c_2_32 = 0.3290, c_3_32 = 0.24155
*/
  __pyx_v_alp1_32_0 = 0.0927030;

  /* "pyRing/eob_utils.pyx":153
 *     # (3,2) - TEOBResumSFits.c, line 2827
 *     cdef double alp1_32_0 = 0.0927030
 *     cdef double b_1_32    = -1.58277, b_2_32 = 0.2783, b_3_32 = 0.30503             # <<<<<<<<<<<<<<
 *     cdef double c_1_32    = -1.56797, c_2_32 = 0.3290, c_3_32 = 0.24155
 * 
*/
  __pyx_v_b_1_32 = -1.58277;
  __pyx_v_b_2_32 = 0.2783;
  __pyx_v_b_3_32 = 0.30503;

  /* "pyRing/eob_utils.pyx":154
 *     cdef double alp1_32_0 = 0.0927030
 *     cdef double b_1_32    = -1.58277, b_2_32 = 0.2783, b_3_32 = 0.30503
 *     cdef double c_1_32    = -1.56797, c_2_32 = 0.3290, c_3_32 = 0.24155             # <<<<<<<<<<<<<<
 * 
 *     # (3,1) - TEOBResumSFits.c, line 2822
*/
  __pyx_v_c_1_32 = -1.56797;
  __pyx_v_c_2_32 = 0.3290;
  __pyx_v_c_3_32 = 0.24155;

  /* "pyRing/eob_utils.pyx":157
 * 
 *     # (3,1) - TEOBResumSFits.c, line 2822
 *     cdef double alp1_31_0 = 0.0927030             # <<<<<<<<<<<<<<
 *     cdef double b_1_31    = -1.2345, b_2_31 = -0.30447, b_3_31 = 0.5446
 *     cdef double c_1_31    = -1.2263, c_2_31 = -0.24223, c_3_31 = 0.47738
*/
  __pyx_v_alp1_31_0 = 0.0927030;

  /* "pyRing/eob_utils.pyx":158
 *     # (3,1) - TEOBResumSFits.c, line 2822
 *     cdef double alp1_31_0 = 0.0927030
 *     cdef double b_1_31    = -1.2345, b_2_31 = -0.30447, b_3_31 = 0.5446             # <<<<<<<<<<<<<<
 *     cdef double c_1_31    = -1.2263, c_2_31 = -0.24223, c_3_31 = 0.47738
 * 
*/
  __pyx_v_b_1_31 = -1.2345;
  __pyx_v_b_2_31 = -0.30447;
  __pyx_v_b_3_31 = 0.5446;

  /* "pyRing/eob_utils.pyx":159
 *     cdef double alp1_31_0 = 0.0927030
 *     cdef double b_1_31    = -1.2345, b_2_31 = -0.30447, b_3_31 = 0.5446
 *     cdef double c_1_31    = -1.2263, c_2_31 = -0.24223, c_3_31 = 0.47738             # <<<<<<<<<<<<<<
 * 
 *     # (4,4) - TEOBResumSFits.c, line 2852
*/
  __pyx_v_c_1_31 = -1.2263;
  __pyx_v_c_2_31 = -0.24223;
  __pyx_v_c_3_31 = 0.47738;

  /* "pyRing/eob_utils.pyx":162
 * 
 *     # (4,4) - TEOBResumSFits.c, line 2852
 *     cdef double alp1_44_0 = 0.0941640             # <<<<<<<<<<<<<<
 *     cdef double b_1_44    = -1.8662, b_2_44 = 0.8248, b_3_44 = 0.0417
 *     cdef double c_1_44    = -1.8514, c_2_44 = 0.8736, c_3_44 = -0.0198
*/
  __pyx_v_alp1_44_0 = 0.0941640;

  /* "pyRing/eob_utils.pyx":163
 *     # (4,4) - TEOBResumSFits.c, line 2852
 *     cdef double alp1_44_0 = 0.0941640
 *     cdef double b_1_44    = -1.8662, b_2_44 = 0.8248, b_3_44 = 0.0417             # <<<<<<<<<<<<<<
 *     cdef double c_1_44    = -1.8514, c_2_44 = 0.8736, c_3_44 = -0.0198
 * 
*/
  __pyx_v_b_1_44 = -1.8662;
  __pyx_v_b_2_44 = 0.8248;
  __pyx_v_b_3_44 = 0.0417;

  /* "pyRing/eob_utils.pyx":164
 *     cdef double alp1_44_0 = 0.0941640
 *     cdef double b_1_44    = -1.8662, b_2_44 = 0.8248, b_3_44 = 0.0417
 *     cdef double c_1_44    = -1.8514, c_2_44 = 0.8736, c_3_44 = -0.0198             # <<<<<<<<<<<<<<
 * 
 *     # (4,3) - TEOBResumSFits.c, line 2847
*/
  __pyx_v_c_1_44 = -1.8514;
  __pyx_v_c_2_44 = 0.8736;
  __pyx_v_c_3_44 = -0.0198;

  /* "pyRing/eob_utils.pyx":167
 * 
 *     # (4,3) - TEOBResumSFits.c, line 2847
 *     cdef double alp1_43_0 = 0.0941640             # <<<<<<<<<<<<<<
 *     cdef double b_1_43    = -1.7177, b_2_43 = 0.5320, b_3_43 = 0.1860
 *     cdef double c_1_43    = -1.7065, c_2_43 = 0.5876, c_3_43 = 0.120939
*/
  __pyx_v_alp1_43_0 = 0.0941640;

  /* "pyRing/eob_utils.pyx":168
 *     # (4,3) - TEOBResumSFits.c, line 2847
 *     cdef double alp1_43_0 = 0.0941640
 *     cdef double b_1_43    = -1.7177, b_2_43 = 0.5320, b_3_43 = 0.1860             # <<<<<<<<<<<<<<
 *     cdef double c_1_43    = -1.7065, c_2_43 = 0.5876, c_3_43 = 0.120939
 * 
*/
  __pyx_v_b_1_43 = -1.7177;
  __pyx_v_b_2_43 = 0.5320;
  __pyx_v_b_3_43 = 0.1860;

  /* "pyRing/eob_utils.pyx":169
 *     cdef double alp1_43_0 = 0.0941640
 *     cdef double b_1_43    = -1.7177, b_2_43 = 0.5320, b_3_43 = 0.1860
 *     cdef double c_1_43    = -1.7065, c_2_43 = 0.5876, c_3_43 = 0.120939             # <<<<<<<<<<<<<<
 * 
 *     # (4,2) - TEOBResumSFits.c, line 2842
*/
  __pyx_v_c_1_43 = -1.7065;
  __pyx_v_c_2_43 = 0.5876;
  __pyx_v_c_3_43 = 0.120939;

  /* "pyRing/eob_utils.pyx":172
 * 
 *     # (4,2) - TEOBResumSFits.c, line 2842
 *     cdef double alp1_42_0 = 0.0941640             # <<<<<<<<<<<<<<
 *     cdef double b_1_42    = -1.44152, b_2_42 = 0.0542, b_3_42 = 0.39020
 *     cdef double c_1_42    = -1.43312, c_2_42 = 0.1167, c_3_42 = 0.32253
*/
  __pyx_v_alp1_42_0 = 0.0941640;

  /* "pyRing/eob_utils.pyx":173
 *     # (4,2) - TEOBResumSFits.c, line 2842
 *     cdef double alp1_42_0 = 0.0941640
 *     cdef double b_1_42    = -1.44152, b_2_42 = 0.0542, b_3_42 = 0.39020             # <<<<<<<<<<<<<<
 *     cdef double c_1_42    = -1.43312, c_2_42 = 0.1167, c_3_42 = 0.32253
 * 
*/
  __pyx_v_b_1_42 = -1.44152;
  __pyx_v_b_2_42 = 0.0542;
  __pyx_v_b_3_42 = 0.39020;

  /* "pyRing/eob_utils.pyx":174
 *     cdef double alp1_42_0 = 0.0941640
 *     cdef double b_1_42    = -1.44152, b_2_42 = 0.0542, b_3_42 = 0.39020
 *     cdef double c_1_42    = -1.43312, c_2_42 = 0.1167, c_3_42 = 0.32253             # <<<<<<<<<<<<<<
 * 
 *     # (4,1) - TEOBResumSFits.c, line 2837
*/
  __pyx_v_c_1_42 = -1.43312;
  __pyx_v_c_2_42 = 0.1167;
  __pyx_v_c_3_42 = 0.32253;

  /* "pyRing/eob_utils.pyx":177
 * 
 *     # (4,1) - TEOBResumSFits.c, line 2837
 *     cdef double alp1_41_0 = 0.0941640             # <<<<<<<<<<<<<<
 *     cdef double b_1_41    = 1.1018882, b_2_41 = -0.88643, b_3_41 = -0.78266
 *     cdef double c_1_41    = 1.1065495, c_2_41 = -0.80961, c_3_41 = -0.68905
*/
  __pyx_v_alp1_41_0 = 0.0941640;

  /* "pyRing/eob_utils.pyx":178
 *     # (4,1) - TEOBResumSFits.c, line 2837
 *     cdef double alp1_41_0 = 0.0941640
 *     cdef double b_1_41    = 1.1018882, b_2_41 = -0.88643, b_3_41 = -0.78266             # <<<<<<<<<<<<<<
 *     cdef double c_1_41    = 1.1065495, c_2_41 = -0.80961, c_3_41 = -0.68905
 * 
*/
  __pyx_v_b_1_41 = 1.1018882;
  __pyx_v_b_2_41 = -0.88643;
  __pyx_v_b_3_41 = -0.78266;

  /* "pyRing/eob_utils.pyx":179
 *     cdef double alp1_41_0 = 0.0941640
 *     cdef double b_1_41    = 1.1018882, b_2_41 = -0.88643, b_3_41 = -0.78266
 *     cdef double c_1_41    = 1.1065495, c_2_41 = -0.80961, c_3_41 = -0.68905             # <<<<<<<<<<<<<<
 * 
 *     # (5,5) - TEOBResumSFits.c, line 2857
*/
  __pyx_v_c_1_41 = 1.1065495;
  __pyx_v_c_2_41 = -0.80961;
  __pyx_v_c_3_41 = -0.68905;

  /* "pyRing/eob_utils.pyx":182
 * 
 *     # (5,5) - TEOBResumSFits.c, line 2857
 *     cdef double alp1_55_0 = 0.0948705             # <<<<<<<<<<<<<<
 *     cdef double b_1_55    = -1.8845, b_2_55 = 0.8585, b_3_55 = 0.0263
 *     cdef double c_1_55    = -1.8740, c_2_55 = 0.9147, c_3_55 = -0.0384
*/
  __pyx_v_alp1_55_0 = 0.0948705;

  /* "pyRing/eob_utils.pyx":183
 *     # (5,5) - TEOBResumSFits.c, line 2857
 *     cdef double alp1_55_0 = 0.0948705
 *     cdef double b_1_55    = -1.8845, b_2_55 = 0.8585, b_3_55 = 0.0263             # <<<<<<<<<<<<<<
 *     cdef double c_1_55    = -1.8740, c_2_55 = 0.9147, c_3_55 = -0.0384
 *     # -------------------------------------------------------------------------------- #
*/
  __pyx_v_b_1_55 = -1.8845;
  __pyx_v_b_2_55 = 0.8585;
  __pyx_v_b_3_55 = 0.0263;

  /* "pyRing/eob_utils.pyx":184
 *     cdef double alp1_55_0 = 0.0948705
 *     cdef double b_1_55    = -1.8845, b_2_55 = 0.8585, b_3_55 = 0.0263
 *     cdef double c_1_55    = -1.8740, c_2_55 = 0.9147, c_3_55 = -0.0384             # <<<<<<<<<<<<<<
 *     # -------------------------------------------------------------------------------- #
 * 
*/
  __pyx_v_c_1_55 = -1.8740;
  __pyx_v_c_2_55 = 0.9147;
  __pyx_v_c_3_55 = -0.0384;

  /* "pyRing/eob_utils.pyx":187
 *     # -------------------------------------------------------------------------------- #
 * 
 *     if ((l==2) and (m==2)):             # <<<<<<<<<<<<<<
 *         alpha1_22 = _Y(alp1_22_0, b_1_22, b_2_22, b_3_22, c_1_22, c_2_22, c_3_22, af, af2, af3)
 *         res = alpha1_22
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L4_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":188
 * 
 *     if ((l==2) and (m==2)):
 *         alpha1_22 = _Y(alp1_22_0, b_1_22, b_2_22, b_3_22, c_1_22, c_2_22, c_3_22, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha1_22
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp1_22_0, __pyx_v_b_1_22, __pyx_v_b_2_22, __pyx_v_b_3_22, __pyx_v_c_1_22, __pyx_v_c_2_22, __pyx_v_c_3_22, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 188, __pyx_L1_error)
    __pyx_v_alpha1_22 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":189
 *     if ((l==2) and (m==2)):
 *         alpha1_22 = _Y(alp1_22_0, b_1_22, b_2_22, b_3_22, c_1_22, c_2_22, c_3_22, af, af2, af3)
 *         res = alpha1_22             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==2) and (m==1)):
*/
    __pyx_v_res = __pyx_v_alpha1_22;

    /* "pyRing/eob_utils.pyx":187
 *     # -------------------------------------------------------------------------------- #
 * 
 *     if ((l==2) and (m==2)):             # <<<<<<<<<<<<<<
 *         alpha1_22 = _Y(alp1_22_0, b_1_22, b_2_22, b_3_22, c_1_22, c_2_22, c_3_22, af, af2, af3)
 *         res = alpha1_22
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":191
 *         res = alpha1_22
 * 
 *     elif ((l==2) and (m==1)):             # <<<<<<<<<<<<<<
 *         alpha1_21 = _Y(alp1_21_0, b_1_21, b_2_21, b_3_21, c_1_21, c_2_21, c_3_21, af, af2, af3)
 *         res = alpha1_21
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L6_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L6_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":192
 * 
 *     elif ((l==2) and (m==1)):
 *         alpha1_21 = _Y(alp1_21_0, b_1_21, b_2_21, b_3_21, c_1_21, c_2_21, c_3_21, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha1_21
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp1_21_0, __pyx_v_b_1_21, __pyx_v_b_2_21, __pyx_v_b_3_21, __pyx_v_c_1_21, __pyx_v_c_2_21, __pyx_v_c_3_21, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 192, __pyx_L1_error)
    __pyx_v_alpha1_21 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":193
 *     elif ((l==2) and (m==1)):
 *         alpha1_21 = _Y(alp1_21_0, b_1_21, b_2_21, b_3_21, c_1_21, c_2_21, c_3_21, af, af2, af3)
 *         res = alpha1_21             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==3) and (m==3)):
*/
    __pyx_v_res = __pyx_v_alpha1_21;

    /* "pyRing/eob_utils.pyx":191
 *         res = alpha1_22
 * 
 *     elif ((l==2) and (m==1)):             # <<<<<<<<<<<<<<
 *         alpha1_21 = _Y(alp1_21_0, b_1_21, b_2_21, b_3_21, c_1_21, c_2_21, c_3_21, af, af2, af3)
 *         res = alpha1_21
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":195
 *         res = alpha1_21
 * 
 *     elif ((l==3) and (m==3)):             # <<<<<<<<<<<<<<
 *         alpha1_33 = _Y(alp1_33_0, b_1_33, b_2_33, b_3_33, c_1_33, c_2_33, c_3_33, af, af2, af3)
 *         res = alpha1_33
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L8_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L8_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":196
 * 
 *     elif ((l==3) and (m==3)):
 *         alpha1_33 = _Y(alp1_33_0, b_1_33, b_2_33, b_3_33, c_1_33, c_2_33, c_3_33, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha1_33
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp1_33_0, __pyx_v_b_1_33, __pyx_v_b_2_33, __pyx_v_b_3_33, __pyx_v_c_1_33, __pyx_v_c_2_33, __pyx_v_c_3_33, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 196, __pyx_L1_error)
    __pyx_v_alpha1_33 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":197
 *     elif ((l==3) and (m==3)):
 *         alpha1_33 = _Y(alp1_33_0, b_1_33, b_2_33, b_3_33, c_1_33, c_2_33, c_3_33, af, af2, af3)
 *         res = alpha1_33             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==3) and (m==2)):
*/
    __pyx_v_res = __pyx_v_alpha1_33;

    /* "pyRing/eob_utils.pyx":195
 *         res = alpha1_21
 * 
 *     elif ((l==3) and (m==3)):             # <<<<<<<<<<<<<<
 *         alpha1_33 = _Y(alp1_33_0, b_1_33, b_2_33, b_3_33, c_1_33, c_2_33, c_3_33, af, af2, af3)
 *         res = alpha1_33
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":199
 *         res = alpha1_33
 * 
 *     elif ((l==3) and (m==2)):             # <<<<<<<<<<<<<<
 *         alpha1_32 = _Y(alp1_32_0, b_1_32, b_2_32, b_3_32, c_1_32, c_2_32, c_3_32, af, af2, af3)
 *         res = alpha1_32
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L10_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L10_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":200
 * 
 *     elif ((l==3) and (m==2)):
 *         alpha1_32 = _Y(alp1_32_0, b_1_32, b_2_32, b_3_32, c_1_32, c_2_32, c_3_32, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha1_32
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp1_32_0, __pyx_v_b_1_32, __pyx_v_b_2_32, __pyx_v_b_3_32, __pyx_v_c_1_32, __pyx_v_c_2_32, __pyx_v_c_3_32, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 200, __pyx_L1_error)
    __pyx_v_alpha1_32 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":201
 *     elif ((l==3) and (m==2)):
 *         alpha1_32 = _Y(alp1_32_0, b_1_32, b_2_32, b_3_32, c_1_32, c_2_32, c_3_32, af, af2, af3)
 *         res = alpha1_32             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==3) and (m==1)):
*/
    __pyx_v_res = __pyx_v_alpha1_32;

    /* "pyRing/eob_utils.pyx":199
 *         res = alpha1_33
 * 
 *     elif ((l==3) and (m==2)):             # <<<<<<<<<<<<<<
 *         alpha1_32 = _Y(alp1_32_0, b_1_32, b_2_32, b_3_32, c_1_32, c_2_32, c_3_32, af, af2, af3)
 *         res = alpha1_32
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":203
 *         res = alpha1_32
 * 
 *     elif ((l==3) and (m==1)):             # <<<<<<<<<<<<<<
 *         alpha1_31 = _Y(alp1_31_0, b_1_31, b_2_31, b_3_31, c_1_31, c_2_31, c_3_31, af, af2, af3)
 *         res = alpha1_31
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L12_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L12_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":204
 * 
 *     elif ((l==3) and (m==1)):
 *         alpha1_31 = _Y(alp1_31_0, b_1_31, b_2_31, b_3_31, c_1_31, c_2_31, c_3_31, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha1_31
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp1_31_0, __pyx_v_b_1_31, __pyx_v_b_2_31, __pyx_v_b_3_31, __pyx_v_c_1_31, __pyx_v_c_2_31, __pyx_v_c_3_31, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 204, __pyx_L1_error)
    __pyx_v_alpha1_31 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":205
 *     elif ((l==3) and (m==1)):
 *         alpha1_31 = _Y(alp1_31_0, b_1_31, b_2_31, b_3_31, c_1_31, c_2_31, c_3_31, af, af2, af3)
 *         res = alpha1_31             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==4)):
*/
    __pyx_v_res = __pyx_v_alpha1_31;

    /* "pyRing/eob_utils.pyx":203
 *         res = alpha1_32
 * 
 *     elif ((l==3) and (m==1)):             # <<<<<<<<<<<<<<
 *         alpha1_31 = _Y(alp1_31_0, b_1_31, b_2_31, b_3_31, c_1_31, c_2_31, c_3_31, af, af2, af3)
 *         res = alpha1_31
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":207
 *         res = alpha1_31
 * 
 *     elif ((l==4) and (m==4)):             # <<<<<<<<<<<<<<
 *         alpha1_44 = _Y(alp1_44_0, b_1_44, b_2_44, b_3_44, c_1_44, c_2_44, c_3_44, af, af2, af3)
 *         res = alpha1_44
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L14_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 4);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L14_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":208
 * 
 *     elif ((l==4) and (m==4)):
 *         alpha1_44 = _Y(alp1_44_0, b_1_44, b_2_44, b_3_44, c_1_44, c_2_44, c_3_44, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha1_44
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp1_44_0, __pyx_v_b_1_44, __pyx_v_b_2_44, __pyx_v_b_3_44, __pyx_v_c_1_44, __pyx_v_c_2_44, __pyx_v_c_3_44, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 208, __pyx_L1_error)
    __pyx_v_alpha1_44 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":209
 *     elif ((l==4) and (m==4)):
 *         alpha1_44 = _Y(alp1_44_0, b_1_44, b_2_44, b_3_44, c_1_44, c_2_44, c_3_44, af, af2, af3)
 *         res = alpha1_44             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==3)):
*/
    __pyx_v_res = __pyx_v_alpha1_44;

    /* "pyRing/eob_utils.pyx":207
 *         res = alpha1_31
 * 
 *     elif ((l==4) and (m==4)):             # <<<<<<<<<<<<<<
 *         alpha1_44 = _Y(alp1_44_0, b_1_44, b_2_44, b_3_44, c_1_44, c_2_44, c_3_44, af, af2, af3)
 *         res = alpha1_44
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":211
 *         res = alpha1_44
 * 
 *     elif ((l==4) and (m==3)):             # <<<<<<<<<<<<<<
 *         alpha1_43 = _Y(alp1_43_0, b_1_43, b_2_43, b_3_43, c_1_43, c_2_43, c_3_43, af, af2, af3)
 *         res = alpha1_43
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L16_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L16_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":212
 * 
 *     elif ((l==4) and (m==3)):
 *         alpha1_43 = _Y(alp1_43_0, b_1_43, b_2_43, b_3_43, c_1_43, c_2_43, c_3_43, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha1_43
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp1_43_0, __pyx_v_b_1_43, __pyx_v_b_2_43, __pyx_v_b_3_43, __pyx_v_c_1_43, __pyx_v_c_2_43, __pyx_v_c_3_43, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 212, __pyx_L1_error)
    __pyx_v_alpha1_43 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":213
 *     elif ((l==4) and (m==3)):
 *         alpha1_43 = _Y(alp1_43_0, b_1_43, b_2_43, b_3_43, c_1_43, c_2_43, c_3_43, af, af2, af3)
 *         res = alpha1_43             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==2)):
*/
    __pyx_v_res = __pyx_v_alpha1_43;

    /* "pyRing/eob_utils.pyx":211
 *         res = alpha1_44
 * 
 *     elif ((l==4) and (m==3)):             # <<<<<<<<<<<<<<
 *         alpha1_43 = _Y(alp1_43_0, b_1_43, b_2_43, b_3_43, c_1_43, c_2_43, c_3_43, af, af2, af3)
 *         res = alpha1_43
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":215
 *         res = alpha1_43
 * 
 *     elif ((l==4) and (m==2)):             # <<<<<<<<<<<<<<
 *         alpha1_42 = _Y(alp1_42_0, b_1_42, b_2_42, b_3_42, c_1_42, c_2_42, c_3_42, af, af2, af3)
 *         res = alpha1_42
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L18_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L18_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":216
 * 
 *     elif ((l==4) and (m==2)):
 *         alpha1_42 = _Y(alp1_42_0, b_1_42, b_2_42, b_3_42, c_1_42, c_2_42, c_3_42, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha1_42
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp1_42_0, __pyx_v_b_1_42, __pyx_v_b_2_42, __pyx_v_b_3_42, __pyx_v_c_1_42, __pyx_v_c_2_42, __pyx_v_c_3_42, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 216, __pyx_L1_error)
    __pyx_v_alpha1_42 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":217
 *     elif ((l==4) and (m==2)):
 *         alpha1_42 = _Y(alp1_42_0, b_1_42, b_2_42, b_3_42, c_1_42, c_2_42, c_3_42, af, af2, af3)
 *         res = alpha1_42             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==1)):
*/
    __pyx_v_res = __pyx_v_alpha1_42;

    /* "pyRing/eob_utils.pyx":215
 *         res = alpha1_43
 * 
 *     elif ((l==4) and (m==2)):             # <<<<<<<<<<<<<<
 *         alpha1_42 = _Y(alp1_42_0, b_1_42, b_2_42, b_3_42, c_1_42, c_2_42, c_3_42, af, af2, af3)
 *         res = alpha1_42
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":219
 *         res = alpha1_42
 * 
 *     elif ((l==4) and (m==1)):             # <<<<<<<<<<<<<<
 *         alpha1_41 = _Y(alp1_41_0, b_1_41, b_2_41, b_3_41, c_1_41, c_2_41, c_3_41, af, af2, af3)
 *         res = alpha1_41
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L20_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L20_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":220
 * 
 *     elif ((l==4) and (m==1)):
 *         alpha1_41 = _Y(alp1_41_0, b_1_41, b_2_41, b_3_41, c_1_41, c_2_41, c_3_41, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha1_41
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp1_41_0, __pyx_v_b_1_41, __pyx_v_b_2_41, __pyx_v_b_3_41, __pyx_v_c_1_41, __pyx_v_c_2_41, __pyx_v_c_3_41, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 220, __pyx_L1_error)
    __pyx_v_alpha1_41 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":221
 *     elif ((l==4) and (m==1)):
 *         alpha1_41 = _Y(alp1_41_0, b_1_41, b_2_41, b_3_41, c_1_41, c_2_41, c_3_41, af, af2, af3)
 *         res = alpha1_41             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==5) and (m==5)):
*/
    __pyx_v_res = __pyx_v_alpha1_41;

    /* "pyRing/eob_utils.pyx":219
 *         res = alpha1_42
 * 
 *     elif ((l==4) and (m==1)):             # <<<<<<<<<<<<<<
 *         alpha1_41 = _Y(alp1_41_0, b_1_41, b_2_41, b_3_41, c_1_41, c_2_41, c_3_41, af, af2, af3)
 *         res = alpha1_41
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":223
 *         res = alpha1_41
 * 
 *     elif ((l==5) and (m==5)):             # <<<<<<<<<<<<<<
 *         alpha1_55 = _Y(alp1_55_0, b_1_55, b_2_55, b_3_55, c_1_55, c_2_55, c_3_55, af, af2, af3)
 *         res = alpha1_55
*/
  __pyx_t_2 = (__pyx_v_l == 5);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L22_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 5);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L22_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":224
 * 
 *     elif ((l==5) and (m==5)):
 *         alpha1_55 = _Y(alp1_55_0, b_1_55, b_2_55, b_3_55, c_1_55, c_2_55, c_3_55, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha1_55
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp1_55_0, __pyx_v_b_1_55, __pyx_v_b_2_55, __pyx_v_b_3_55, __pyx_v_c_1_55, __pyx_v_c_2_55, __pyx_v_c_3_55, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 224, __pyx_L1_error)
    __pyx_v_alpha1_55 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":225
 *     elif ((l==5) and (m==5)):
 *         alpha1_55 = _Y(alp1_55_0, b_1_55, b_2_55, b_3_55, c_1_55, c_2_55, c_3_55, af, af2, af3)
 *         res = alpha1_55             # <<<<<<<<<<<<<<
 * 
 *     return res
*/
    __pyx_v_res = __pyx_v_alpha1_55;

    /* "pyRing/eob_utils.pyx":223
 *         res = alpha1_41
 * 
 *     elif ((l==5) and (m==5)):             # <<<<<<<<<<<<<<
 *         alpha1_55 = _Y(alp1_55_0, b_1_55, b_2_55, b_3_55, c_1_55, c_2_55, c_3_55, af, af2, af3)
 *         res = alpha1_55
*/
  }
  __pyx_L3:;

  /* "pyRing/eob_utils.pyx":227
 *         res = alpha1_55
 * 
 *     return res             # <<<<<<<<<<<<<<
 * 
 * 
*/
  __pyx_r = __pyx_v_res;
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":118
 * 
 * 
 * cdef double _alpha1(double af, int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function returning the value of alpha1 for each mode, following appendix C.2 of arXiv:2001.09082v2.
*/

  /* function exit code */
  __pyx_L1_error:;
  __pyx_gilstate_save = __Pyx_PyGILState_Ensure();
  __Pyx_AddTraceback("pyRing.eob_utils._alpha1", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = -1;
  __Pyx_PyGILState_Release(__pyx_gilstate_save);
  __pyx_L0:;
  return __pyx_r;
}

/* "pyRing/eob_utils.pyx":230
 * 
 * 
 * cdef double _alpha21(double af, int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function returning the value of alpha21 for each mode, following appendix C.2 of arXiv:2001.09082v2.
*/

static double __pyx_f_6pyRing_9eob_utils__alpha21(double __pyx_v_af, int __pyx_v_l, int __pyx_v_m) {
  double __pyx_v_res;
  double __pyx_v_alpha21_22;
  double __pyx_v_alpha21_21;
  double __pyx_v_alpha21_33;
  double __pyx_v_alpha21_32;
  double __pyx_v_alpha21_31;
  double __pyx_v_alpha21_44;
  double __pyx_v_alpha21_43;
  double __pyx_v_alpha21_42;
  double __pyx_v_alpha21_41;
  double __pyx_v_alpha21_55;
  double __pyx_v_af2;
  double __pyx_v_af3;
  double __pyx_v_alp21_22_0;
  double __pyx_v_b_1_22;
  double __pyx_v_b_2_22;
  double __pyx_v_b_3_22;
  double __pyx_v_c_1_22;
  double __pyx_v_c_2_22;
  double __pyx_v_c_3_22;
  double __pyx_v_alp21_21_0;
  double __pyx_v_b_1_21;
  double __pyx_v_b_2_21;
  double __pyx_v_b_3_21;
  double __pyx_v_c_1_21;
  double __pyx_v_c_2_21;
  double __pyx_v_c_3_21;
  double __pyx_v_alp21_33_0;
  double __pyx_v_b_1_33;
  double __pyx_v_b_2_33;
  double __pyx_v_b_3_33;
  double __pyx_v_c_1_33;
  double __pyx_v_c_2_33;
  double __pyx_v_c_3_33;
  double __pyx_v_alp21_32_0;
  double __pyx_v_b_1_32;
  double __pyx_v_b_2_32;
  double __pyx_v_b_3_32;
  double __pyx_v_c_1_32;
  double __pyx_v_c_2_32;
  double __pyx_v_c_3_32;
  double __pyx_v_alp21_31_0;
  double __pyx_v_b_1_31;
  double __pyx_v_b_2_31;
  double __pyx_v_b_3_31;
  double __pyx_v_c_1_31;
  double __pyx_v_c_2_31;
  double __pyx_v_c_3_31;
  double __pyx_v_alp21_44_0;
  double __pyx_v_b_1_44;
  double __pyx_v_b_2_44;
  double __pyx_v_b_3_44;
  double __pyx_v_c_1_44;
  double __pyx_v_c_2_44;
  double __pyx_v_c_3_44;
  double __pyx_v_alp21_43_0;
  double __pyx_v_b_1_43;
  double __pyx_v_b_2_43;
  double __pyx_v_b_3_43;
  double __pyx_v_c_1_43;
  double __pyx_v_c_2_43;
  double __pyx_v_c_3_43;
  double __pyx_v_alp21_42_0;
  double __pyx_v_b_1_42;
  double __pyx_v_b_2_42;
  double __pyx_v_b_3_42;
  double __pyx_v_c_1_42;
  double __pyx_v_c_2_42;
  double __pyx_v_c_3_42;
  double __pyx_v_alp21_41_0;
  double __pyx_v_b_1_41;
  double __pyx_v_b_2_41;
  double __pyx_v_b_3_41;
  double __pyx_v_c_1_41;
  double __pyx_v_c_2_41;
  double __pyx_v_c_3_41;
  double __pyx_v_alp21_55_0;
  double __pyx_v_b_1_55;
  double __pyx_v_b_2_55;
  double __pyx_v_b_3_55;
  double __pyx_v_c_1_55;
  double __pyx_v_c_2_55;
  double __pyx_v_c_3_55;
  double __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;
  double __pyx_t_3;
  int __pyx_lineno = 0;
  const char *__pyx_filename = NULL;
  int __pyx_clineno = 0;
  PyGILState_STATE __pyx_gilstate_save;

  /* "pyRing/eob_utils.pyx":242
 *     """
 * 
 *     cdef double res = 0.             # <<<<<<<<<<<<<<
 *     cdef double num_alp, den_alp
 *     cdef double alpha21_22, alpha21_21, alpha21_33, alpha21_32, alpha21_31, alpha21_44, alpha21_43, alpha21_42, alpha21_41, alpha21_55
*/
  __pyx_v_res = 0.;

  /* "pyRing/eob_utils.pyx":245
 *     cdef double num_alp, den_alp
 *     cdef double alpha21_22, alpha21_21, alpha21_33, alpha21_32, alpha21_31, alpha21_44, alpha21_43, alpha21_42, alpha21_41, alpha21_55
 *     cdef double af2 = af*af, af3 = af2*af             # <<<<<<<<<<<<<<
 * 
 *     # -------------------------------------------------------------------------------- #
*/
  __pyx_v_af2 = (__pyx_v_af * __pyx_v_af);
  __pyx_v_af3 = (__pyx_v_af2 * __pyx_v_af);

  /* "pyRing/eob_utils.pyx":249
 *     # -------------------------------------------------------------------------------- #
 *     # (2,2) - TEOBResumSFits.c, line 2804
 *     cdef double alp21_22_0 = 0.184953             # <<<<<<<<<<<<<<
 *     cdef double b_1_22     = -1.89397, b_2_22 = 0.88126, b_3_22 = 0.0130256
 *     cdef double c_1_22     = -1.83901, c_2_22 = 0.84162, c_3_22 = 0.
*/
  __pyx_v_alp21_22_0 = 0.184953;

  /* "pyRing/eob_utils.pyx":250
 *     # (2,2) - TEOBResumSFits.c, line 2804
 *     cdef double alp21_22_0 = 0.184953
 *     cdef double b_1_22     = -1.89397, b_2_22 = 0.88126, b_3_22 = 0.0130256             # <<<<<<<<<<<<<<
 *     cdef double c_1_22     = -1.83901, c_2_22 = 0.84162, c_3_22 = 0.
 * 
*/
  __pyx_v_b_1_22 = -1.89397;
  __pyx_v_b_2_22 = 0.88126;
  __pyx_v_b_3_22 = 0.0130256;

  /* "pyRing/eob_utils.pyx":251
 *     cdef double alp21_22_0 = 0.184953
 *     cdef double b_1_22     = -1.89397, b_2_22 = 0.88126, b_3_22 = 0.0130256
 *     cdef double c_1_22     = -1.83901, c_2_22 = 0.84162, c_3_22 = 0.             # <<<<<<<<<<<<<<
 * 
 *     # (2,1) - TEOBResumSFits.c, line 2799
*/
  __pyx_v_c_1_22 = -1.83901;
  __pyx_v_c_2_22 = 0.84162;
  __pyx_v_c_3_22 = 0.;

  /* "pyRing/eob_utils.pyx":254
 * 
 *     # (2,1) - TEOBResumSFits.c, line 2799
 *     cdef double alp21_21_0 = 0.184952             # <<<<<<<<<<<<<<
 *     cdef double b_1_21     = -1.1329,  b_2_21 = -0.3520, b_3_21 = 0.4924
 *     cdef double c_1_21     = -1.10334, c_2_21 = -0.3037, c_3_21 = 0.4262
*/
  __pyx_v_alp21_21_0 = 0.184952;

  /* "pyRing/eob_utils.pyx":255
 *     # (2,1) - TEOBResumSFits.c, line 2799
 *     cdef double alp21_21_0 = 0.184952
 *     cdef double b_1_21     = -1.1329,  b_2_21 = -0.3520, b_3_21 = 0.4924             # <<<<<<<<<<<<<<
 *     cdef double c_1_21     = -1.10334, c_2_21 = -0.3037, c_3_21 = 0.4262
 * 
*/
  __pyx_v_b_1_21 = -1.1329;
  __pyx_v_b_2_21 = -0.3520;
  __pyx_v_b_3_21 = 0.4924;

  /* "pyRing/eob_utils.pyx":256
 *     cdef double alp21_21_0 = 0.184952
 *     cdef double b_1_21     = -1.1329,  b_2_21 = -0.3520, b_3_21 = 0.4924
 *     cdef double c_1_21     = -1.10334, c_2_21 = -0.3037, c_3_21 = 0.4262             # <<<<<<<<<<<<<<
 * 
 *     # (3,3) - TEOBResumSFits.c, line 2833
*/
  __pyx_v_c_1_21 = -1.10334;
  __pyx_v_c_2_21 = -0.3037;
  __pyx_v_c_3_21 = 0.4262;

  /* "pyRing/eob_utils.pyx":259
 * 
 *     # (3,3) - TEOBResumSFits.c, line 2833
 *     cdef double alp21_33_0 = 0.188595             # <<<<<<<<<<<<<<
 *     cdef double b_1_33     = -1.8011, b_2_33 = 0.7046, b_3_33 = 0.0968
 *     cdef double c_1_33     = -1.7653, c_2_33 = 0.7176, c_3_33 = 0.0504
*/
  __pyx_v_alp21_33_0 = 0.188595;

  /* "pyRing/eob_utils.pyx":260
 *     # (3,3) - TEOBResumSFits.c, line 2833
 *     cdef double alp21_33_0 = 0.188595
 *     cdef double b_1_33     = -1.8011, b_2_33 = 0.7046, b_3_33 = 0.0968             # <<<<<<<<<<<<<<
 *     cdef double c_1_33     = -1.7653, c_2_33 = 0.7176, c_3_33 = 0.0504
 * 
*/
  __pyx_v_b_1_33 = -1.8011;
  __pyx_v_b_2_33 = 0.7046;
  __pyx_v_b_3_33 = 0.0968;

  /* "pyRing/eob_utils.pyx":261
 *     cdef double alp21_33_0 = 0.188595
 *     cdef double b_1_33     = -1.8011, b_2_33 = 0.7046, b_3_33 = 0.0968
 *     cdef double c_1_33     = -1.7653, c_2_33 = 0.7176, c_3_33 = 0.0504             # <<<<<<<<<<<<<<
 * 
 *     # (3,2) - TEOBResumSFits.c, line 2828
*/
  __pyx_v_c_1_33 = -1.7653;
  __pyx_v_c_2_33 = 0.7176;
  __pyx_v_c_3_33 = 0.0504;

  /* "pyRing/eob_utils.pyx":264
 * 
 *     # (3,2) - TEOBResumSFits.c, line 2828
 *     cdef double alp21_32_0 = 0.188595             # <<<<<<<<<<<<<<
 *     cdef double b_1_32     = -1.5212, b_2_32 = 0.1563, b_3_32 = 0.3652
 *     cdef double c_1_32     = -1.4968, c_2_32 = 0.1968, c_3_32 = 0.3021
*/
  __pyx_v_alp21_32_0 = 0.188595;

  /* "pyRing/eob_utils.pyx":265
 *     # (3,2) - TEOBResumSFits.c, line 2828
 *     cdef double alp21_32_0 = 0.188595
 *     cdef double b_1_32     = -1.5212, b_2_32 = 0.1563, b_3_32 = 0.3652             # <<<<<<<<<<<<<<
 *     cdef double c_1_32     = -1.4968, c_2_32 = 0.1968, c_3_32 = 0.3021
 * 
*/
  __pyx_v_b_1_32 = -1.5212;
  __pyx_v_b_2_32 = 0.1563;
  __pyx_v_b_3_32 = 0.3652;

  /* "pyRing/eob_utils.pyx":266
 *     cdef double alp21_32_0 = 0.188595
 *     cdef double b_1_32     = -1.5212, b_2_32 = 0.1563, b_3_32 = 0.3652
 *     cdef double c_1_32     = -1.4968, c_2_32 = 0.1968, c_3_32 = 0.3021             # <<<<<<<<<<<<<<
 * 
 *     # (3,1) - TEOBResumSFits.c, line 2823
*/
  __pyx_v_c_1_32 = -1.4968;
  __pyx_v_c_2_32 = 0.1968;
  __pyx_v_c_3_32 = 0.3021;

  /* "pyRing/eob_utils.pyx":269
 * 
 *     # (3,1) - TEOBResumSFits.c, line 2823
 *     cdef double alp21_31_0 = 0.188595             # <<<<<<<<<<<<<<
 *     cdef double b_1_31     = -1.035, b_2_31 = -0.3816, b_3_31 = 0.4486
 *     cdef double c_1_31     = -1.023, c_2_31 = -0.3170, c_3_31 = 0.3898
*/
  __pyx_v_alp21_31_0 = 0.188595;

  /* "pyRing/eob_utils.pyx":270
 *     # (3,1) - TEOBResumSFits.c, line 2823
 *     cdef double alp21_31_0 = 0.188595
 *     cdef double b_1_31     = -1.035, b_2_31 = -0.3816, b_3_31 = 0.4486             # <<<<<<<<<<<<<<
 *     cdef double c_1_31     = -1.023, c_2_31 = -0.3170, c_3_31 = 0.3898
 * 
*/
  __pyx_v_b_1_31 = -1.035;
  __pyx_v_b_2_31 = -0.3816;
  __pyx_v_b_3_31 = 0.4486;

  /* "pyRing/eob_utils.pyx":271
 *     cdef double alp21_31_0 = 0.188595
 *     cdef double b_1_31     = -1.035, b_2_31 = -0.3816, b_3_31 = 0.4486
 *     cdef double c_1_31     = -1.023, c_2_31 = -0.3170, c_3_31 = 0.3898             # <<<<<<<<<<<<<<
 * 
 *     # (4,4) - TEOBResumSFits.c, line 2853
*/
  __pyx_v_c_1_31 = -1.023;
  __pyx_v_c_2_31 = -0.3170;
  __pyx_v_c_3_31 = 0.3898;

  /* "pyRing/eob_utils.pyx":274
 * 
 *     # (4,4) - TEOBResumSFits.c, line 2853
 *     cdef double alp21_44_0 = 0.190170             # <<<<<<<<<<<<<<
 *     cdef double b_1_44     = -1.8546, b_2_44 = 0.8041, b_3_44 = 0.0507
 *     cdef double c_1_44     = -1.8315, c_2_44 = 0.8391, c_3_44 = -0.0051
*/
  __pyx_v_alp21_44_0 = 0.190170;

  /* "pyRing/eob_utils.pyx":275
 *     # (4,4) - TEOBResumSFits.c, line 2853
 *     cdef double alp21_44_0 = 0.190170
 *     cdef double b_1_44     = -1.8546, b_2_44 = 0.8041, b_3_44 = 0.0507             # <<<<<<<<<<<<<<
 *     cdef double c_1_44     = -1.8315, c_2_44 = 0.8391, c_3_44 = -0.0051
 * 
*/
  __pyx_v_b_1_44 = -1.8546;
  __pyx_v_b_2_44 = 0.8041;
  __pyx_v_b_3_44 = 0.0507;

  /* "pyRing/eob_utils.pyx":276
 *     cdef double alp21_44_0 = 0.190170
 *     cdef double b_1_44     = -1.8546, b_2_44 = 0.8041, b_3_44 = 0.0507
 *     cdef double c_1_44     = -1.8315, c_2_44 = 0.8391, c_3_44 = -0.0051             # <<<<<<<<<<<<<<
 * 
 *     # (4,3) - TEOBResumSFits.c, line 2848
*/
  __pyx_v_c_1_44 = -1.8315;
  __pyx_v_c_2_44 = 0.8391;
  __pyx_v_c_3_44 = -0.0051;

  /* "pyRing/eob_utils.pyx":279
 * 
 *     # (4,3) - TEOBResumSFits.c, line 2848
 *     cdef double alp21_43_0 = 0.190170             # <<<<<<<<<<<<<<
 *     cdef double b_1_43     = -1.6860, b_2_43 = 0.4724, b_3_43 = 0.2139
 *     cdef double c_1_43     = -1.6684, c_2_43 = 0.5198, c_3_43 = 0.1508
*/
  __pyx_v_alp21_43_0 = 0.190170;

  /* "pyRing/eob_utils.pyx":280
 *     # (4,3) - TEOBResumSFits.c, line 2848
 *     cdef double alp21_43_0 = 0.190170
 *     cdef double b_1_43     = -1.6860, b_2_43 = 0.4724, b_3_43 = 0.2139             # <<<<<<<<<<<<<<
 *     cdef double c_1_43     = -1.6684, c_2_43 = 0.5198, c_3_43 = 0.1508
 * 
*/
  __pyx_v_b_1_43 = -1.6860;
  __pyx_v_b_2_43 = 0.4724;
  __pyx_v_b_3_43 = 0.2139;

  /* "pyRing/eob_utils.pyx":281
 *     cdef double alp21_43_0 = 0.190170
 *     cdef double b_1_43     = -1.6860, b_2_43 = 0.4724, b_3_43 = 0.2139
 *     cdef double c_1_43     = -1.6684, c_2_43 = 0.5198, c_3_43 = 0.1508             # <<<<<<<<<<<<<<
 * 
 *     # (4,2) - TEOBResumSFits.c, line 2843
*/
  __pyx_v_c_1_43 = -1.6684;
  __pyx_v_c_2_43 = 0.5198;
  __pyx_v_c_3_43 = 0.1508;

  /* "pyRing/eob_utils.pyx":284
 * 
 *     # (4,2) - TEOBResumSFits.c, line 2843
 *     cdef double alp21_42_0 = 0.190170             # <<<<<<<<<<<<<<
 *     cdef double b_1_42     = -1.38840, b_2_42 = 0.,        b_3_42 = 0.39333
 *     cdef double c_1_42     = -1.37584, c_2_42 = 0.0600017, c_3_42 = 0.32632
*/
  __pyx_v_alp21_42_0 = 0.190170;

  /* "pyRing/eob_utils.pyx":285
 *     # (4,2) - TEOBResumSFits.c, line 2843
 *     cdef double alp21_42_0 = 0.190170
 *     cdef double b_1_42     = -1.38840, b_2_42 = 0.,        b_3_42 = 0.39333             # <<<<<<<<<<<<<<
 *     cdef double c_1_42     = -1.37584, c_2_42 = 0.0600017, c_3_42 = 0.32632
 * 
*/
  __pyx_v_b_1_42 = -1.38840;
  __pyx_v_b_2_42 = 0.;
  __pyx_v_b_3_42 = 0.39333;

  /* "pyRing/eob_utils.pyx":286
 *     cdef double alp21_42_0 = 0.190170
 *     cdef double b_1_42     = -1.38840, b_2_42 = 0.,        b_3_42 = 0.39333
 *     cdef double c_1_42     = -1.37584, c_2_42 = 0.0600017, c_3_42 = 0.32632             # <<<<<<<<<<<<<<
 * 
 *     # (4,1) - TEOBResumSFits.c, line 2838
*/
  __pyx_v_c_1_42 = -1.37584;
  __pyx_v_c_2_42 = 0.0600017;
  __pyx_v_c_3_42 = 0.32632;

  /* "pyRing/eob_utils.pyx":289
 * 
 *     # (4,1) - TEOBResumSFits.c, line 2838
 *     cdef double alp21_41_0 = 0.190170             # <<<<<<<<<<<<<<
 *     cdef double b_1_41     = 1.0590157, b_2_41 = -0.8650630, b_3_41 = -0.75222
 *     cdef double c_1_41     = 1.0654880, c_2_41 = -0.7830051, c_3_41 = -0.65814
*/
  __pyx_v_alp21_41_0 = 0.190170;

  /* "pyRing/eob_utils.pyx":290
 *     # (4,1) - TEOBResumSFits.c, line 2838
 *     cdef double alp21_41_0 = 0.190170
 *     cdef double b_1_41     = 1.0590157, b_2_41 = -0.8650630, b_3_41 = -0.75222             # <<<<<<<<<<<<<<
 *     cdef double c_1_41     = 1.0654880, c_2_41 = -0.7830051, c_3_41 = -0.65814
 * 
*/
  __pyx_v_b_1_41 = 1.0590157;
  __pyx_v_b_2_41 = -0.8650630;
  __pyx_v_b_3_41 = -0.75222;

  /* "pyRing/eob_utils.pyx":291
 *     cdef double alp21_41_0 = 0.190170
 *     cdef double b_1_41     = 1.0590157, b_2_41 = -0.8650630, b_3_41 = -0.75222
 *     cdef double c_1_41     = 1.0654880, c_2_41 = -0.7830051, c_3_41 = -0.65814             # <<<<<<<<<<<<<<
 * 
 *     # (5,5) - TEOBResumSFits.c, line 2858
*/
  __pyx_v_c_1_41 = 1.0654880;
  __pyx_v_c_2_41 = -0.7830051;
  __pyx_v_c_3_41 = -0.65814;

  /* "pyRing/eob_utils.pyx":294
 * 
 *     # (5,5) - TEOBResumSFits.c, line 2858
 *     cdef double alp21_55_0 = 0.190947             # <<<<<<<<<<<<<<
 *     cdef double b_1_55     = -1.8780, b_2_55 = 0.8467, b_3_55 = 0.0315
 *     cdef double c_1_55     = -1.8619, c_2_55 = 0.8936, c_3_55 = -0.0293
*/
  __pyx_v_alp21_55_0 = 0.190947;

  /* "pyRing/eob_utils.pyx":295
 *     # (5,5) - TEOBResumSFits.c, line 2858
 *     cdef double alp21_55_0 = 0.190947
 *     cdef double b_1_55     = -1.8780, b_2_55 = 0.8467, b_3_55 = 0.0315             # <<<<<<<<<<<<<<
 *     cdef double c_1_55     = -1.8619, c_2_55 = 0.8936, c_3_55 = -0.0293
 *     # -------------------------------------------------------------------------------- #
*/
  __pyx_v_b_1_55 = -1.8780;
  __pyx_v_b_2_55 = 0.8467;
  __pyx_v_b_3_55 = 0.0315;

  /* "pyRing/eob_utils.pyx":296
 *     cdef double alp21_55_0 = 0.190947
 *     cdef double b_1_55     = -1.8780, b_2_55 = 0.8467, b_3_55 = 0.0315
 *     cdef double c_1_55     = -1.8619, c_2_55 = 0.8936, c_3_55 = -0.0293             # <<<<<<<<<<<<<<
 *     # -------------------------------------------------------------------------------- #
 * 
*/
  __pyx_v_c_1_55 = -1.8619;
  __pyx_v_c_2_55 = 0.8936;
  __pyx_v_c_3_55 = -0.0293;

  /* "pyRing/eob_utils.pyx":299
 *     # -------------------------------------------------------------------------------- #
 * 
 *     if ((l==2) and (m==2)):             # <<<<<<<<<<<<<<
 *         alpha21_22 = _Y(alp21_22_0, b_1_22, b_2_22, b_3_22, c_1_22, c_2_22, c_3_22, af, af2, af3)
 *         res = alpha21_22
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L4_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":300
 * 
 *     if ((l==2) and (m==2)):
 *         alpha21_22 = _Y(alp21_22_0, b_1_22, b_2_22, b_3_22, c_1_22, c_2_22, c_3_22, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha21_22
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp21_22_0, __pyx_v_b_1_22, __pyx_v_b_2_22, __pyx_v_b_3_22, __pyx_v_c_1_22, __pyx_v_c_2_22, __pyx_v_c_3_22, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 300, __pyx_L1_error)
    __pyx_v_alpha21_22 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":301
 *     if ((l==2) and (m==2)):
 *         alpha21_22 = _Y(alp21_22_0, b_1_22, b_2_22, b_3_22, c_1_22, c_2_22, c_3_22, af, af2, af3)
 *         res = alpha21_22             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==2) and (m==1)):
*/
    __pyx_v_res = __pyx_v_alpha21_22;

    /* "pyRing/eob_utils.pyx":299
 *     # -------------------------------------------------------------------------------- #
 * 
 *     if ((l==2) and (m==2)):             # <<<<<<<<<<<<<<
 *         alpha21_22 = _Y(alp21_22_0, b_1_22, b_2_22, b_3_22, c_1_22, c_2_22, c_3_22, af, af2, af3)
 *         res = alpha21_22
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":303
 *         res = alpha21_22
 * 
 *     elif ((l==2) and (m==1)):             # <<<<<<<<<<<<<<
 *         alpha21_21 = _Y(alp21_21_0, b_1_21, b_2_21, b_3_21, c_1_21, c_2_21, c_3_21, af, af2, af3)
 *         res = alpha21_21
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L6_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L6_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":304
 * 
 *     elif ((l==2) and (m==1)):
 *         alpha21_21 = _Y(alp21_21_0, b_1_21, b_2_21, b_3_21, c_1_21, c_2_21, c_3_21, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha21_21
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp21_21_0, __pyx_v_b_1_21, __pyx_v_b_2_21, __pyx_v_b_3_21, __pyx_v_c_1_21, __pyx_v_c_2_21, __pyx_v_c_3_21, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 304, __pyx_L1_error)
    __pyx_v_alpha21_21 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":305
 *     elif ((l==2) and (m==1)):
 *         alpha21_21 = _Y(alp21_21_0, b_1_21, b_2_21, b_3_21, c_1_21, c_2_21, c_3_21, af, af2, af3)
 *         res = alpha21_21             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==3) and (m==3)):
*/
    __pyx_v_res = __pyx_v_alpha21_21;

    /* "pyRing/eob_utils.pyx":303
 *         res = alpha21_22
 * 
 *     elif ((l==2) and (m==1)):             # <<<<<<<<<<<<<<
 *         alpha21_21 = _Y(alp21_21_0, b_1_21, b_2_21, b_3_21, c_1_21, c_2_21, c_3_21, af, af2, af3)
 *         res = alpha21_21
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":307
 *         res = alpha21_21
 * 
 *     elif ((l==3) and (m==3)):             # <<<<<<<<<<<<<<
 *         alpha21_33 = _Y(alp21_33_0, b_1_33, b_2_33, b_3_33, c_1_33, c_2_33, c_3_33, af, af2, af3)
 *         res = alpha21_33
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L8_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L8_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":308
 * 
 *     elif ((l==3) and (m==3)):
 *         alpha21_33 = _Y(alp21_33_0, b_1_33, b_2_33, b_3_33, c_1_33, c_2_33, c_3_33, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha21_33
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp21_33_0, __pyx_v_b_1_33, __pyx_v_b_2_33, __pyx_v_b_3_33, __pyx_v_c_1_33, __pyx_v_c_2_33, __pyx_v_c_3_33, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 308, __pyx_L1_error)
    __pyx_v_alpha21_33 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":309
 *     elif ((l==3) and (m==3)):
 *         alpha21_33 = _Y(alp21_33_0, b_1_33, b_2_33, b_3_33, c_1_33, c_2_33, c_3_33, af, af2, af3)
 *         res = alpha21_33             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==3) and (m==2)):
*/
    __pyx_v_res = __pyx_v_alpha21_33;

    /* "pyRing/eob_utils.pyx":307
 *         res = alpha21_21
 * 
 *     elif ((l==3) and (m==3)):             # <<<<<<<<<<<<<<
 *         alpha21_33 = _Y(alp21_33_0, b_1_33, b_2_33, b_3_33, c_1_33, c_2_33, c_3_33, af, af2, af3)
 *         res = alpha21_33
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":311
 *         res = alpha21_33
 * 
 *     elif ((l==3) and (m==2)):             # <<<<<<<<<<<<<<
 *         alpha21_32 = _Y(alp21_32_0, b_1_32, b_2_32, b_3_32, c_1_32, c_2_32, c_3_32, af, af2, af3)
 *         res = alpha21_32
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L10_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L10_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":312
 * 
 *     elif ((l==3) and (m==2)):
 *         alpha21_32 = _Y(alp21_32_0, b_1_32, b_2_32, b_3_32, c_1_32, c_2_32, c_3_32, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha21_32
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp21_32_0, __pyx_v_b_1_32, __pyx_v_b_2_32, __pyx_v_b_3_32, __pyx_v_c_1_32, __pyx_v_c_2_32, __pyx_v_c_3_32, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 312, __pyx_L1_error)
    __pyx_v_alpha21_32 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":313
 *     elif ((l==3) and (m==2)):
 *         alpha21_32 = _Y(alp21_32_0, b_1_32, b_2_32, b_3_32, c_1_32, c_2_32, c_3_32, af, af2, af3)
 *         res = alpha21_32             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==3) and (m==1)):
*/
    __pyx_v_res = __pyx_v_alpha21_32;

    /* "pyRing/eob_utils.pyx":311
 *         res = alpha21_33
 * 
 *     elif ((l==3) and (m==2)):             # <<<<<<<<<<<<<<
 *         alpha21_32 = _Y(alp21_32_0, b_1_32, b_2_32, b_3_32, c_1_32, c_2_32, c_3_32, af, af2, af3)
 *         res = alpha21_32
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":315
 *         res = alpha21_32
 * 
 *     elif ((l==3) and (m==1)):             # <<<<<<<<<<<<<<
 *         alpha21_31 = _Y(alp21_31_0, b_1_31, b_2_31, b_3_31, c_1_31, c_2_31, c_3_31, af, af2, af3)
 *         res = alpha21_31
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L12_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L12_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":316
 * 
 *     elif ((l==3) and (m==1)):
 *         alpha21_31 = _Y(alp21_31_0, b_1_31, b_2_31, b_3_31, c_1_31, c_2_31, c_3_31, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha21_31
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp21_31_0, __pyx_v_b_1_31, __pyx_v_b_2_31, __pyx_v_b_3_31, __pyx_v_c_1_31, __pyx_v_c_2_31, __pyx_v_c_3_31, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 316, __pyx_L1_error)
    __pyx_v_alpha21_31 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":317
 *     elif ((l==3) and (m==1)):
 *         alpha21_31 = _Y(alp21_31_0, b_1_31, b_2_31, b_3_31, c_1_31, c_2_31, c_3_31, af, af2, af3)
 *         res = alpha21_31             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==4)):
*/
    __pyx_v_res = __pyx_v_alpha21_31;

    /* "pyRing/eob_utils.pyx":315
 *         res = alpha21_32
 * 
 *     elif ((l==3) and (m==1)):             # <<<<<<<<<<<<<<
 *         alpha21_31 = _Y(alp21_31_0, b_1_31, b_2_31, b_3_31, c_1_31, c_2_31, c_3_31, af, af2, af3)
 *         res = alpha21_31
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":319
 *         res = alpha21_31
 * 
 *     elif ((l==4) and (m==4)):             # <<<<<<<<<<<<<<
 *         alpha21_44 = _Y(alp21_44_0, b_1_44, b_2_44, b_3_44, c_1_44, c_2_44, c_3_44, af, af2, af3)
 *         res = alpha21_44
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L14_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 4);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L14_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":320
 * 
 *     elif ((l==4) and (m==4)):
 *         alpha21_44 = _Y(alp21_44_0, b_1_44, b_2_44, b_3_44, c_1_44, c_2_44, c_3_44, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha21_44
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp21_44_0, __pyx_v_b_1_44, __pyx_v_b_2_44, __pyx_v_b_3_44, __pyx_v_c_1_44, __pyx_v_c_2_44, __pyx_v_c_3_44, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 320, __pyx_L1_error)
    __pyx_v_alpha21_44 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":321
 *     elif ((l==4) and (m==4)):
 *         alpha21_44 = _Y(alp21_44_0, b_1_44, b_2_44, b_3_44, c_1_44, c_2_44, c_3_44, af, af2, af3)
 *         res = alpha21_44             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==3)):
*/
    __pyx_v_res = __pyx_v_alpha21_44;

    /* "pyRing/eob_utils.pyx":319
 *         res = alpha21_31
 * 
 *     elif ((l==4) and (m==4)):             # <<<<<<<<<<<<<<
 *         alpha21_44 = _Y(alp21_44_0, b_1_44, b_2_44, b_3_44, c_1_44, c_2_44, c_3_44, af, af2, af3)
 *         res = alpha21_44
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":323
 *         res = alpha21_44
 * 
 *     elif ((l==4) and (m==3)):             # <<<<<<<<<<<<<<
 *         alpha21_43 = _Y(alp21_43_0, b_1_43, b_2_43, b_3_43, c_1_43, c_2_43, c_3_43, af, af2, af3)
 *         res = alpha21_43
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L16_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L16_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":324
 * 
 *     elif ((l==4) and (m==3)):
 *         alpha21_43 = _Y(alp21_43_0, b_1_43, b_2_43, b_3_43, c_1_43, c_2_43, c_3_43, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha21_43
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp21_43_0, __pyx_v_b_1_43, __pyx_v_b_2_43, __pyx_v_b_3_43, __pyx_v_c_1_43, __pyx_v_c_2_43, __pyx_v_c_3_43, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 324, __pyx_L1_error)
    __pyx_v_alpha21_43 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":325
 *     elif ((l==4) and (m==3)):
 *         alpha21_43 = _Y(alp21_43_0, b_1_43, b_2_43, b_3_43, c_1_43, c_2_43, c_3_43, af, af2, af3)
 *         res = alpha21_43             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==2)):
*/
    __pyx_v_res = __pyx_v_alpha21_43;

    /* "pyRing/eob_utils.pyx":323
 *         res = alpha21_44
 * 
 *     elif ((l==4) and (m==3)):             # <<<<<<<<<<<<<<
 *         alpha21_43 = _Y(alp21_43_0, b_1_43, b_2_43, b_3_43, c_1_43, c_2_43, c_3_43, af, af2, af3)
 *         res = alpha21_43
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":327
 *         res = alpha21_43
 * 
 *     elif ((l==4) and (m==2)):             # <<<<<<<<<<<<<<
 *         alpha21_42 = _Y(alp21_42_0, b_1_42, b_2_42, b_3_42, c_1_42, c_2_42, c_3_42, af, af2, af3)
 *         res = alpha21_42
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L18_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L18_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":328
 * 
 *     elif ((l==4) and (m==2)):
 *         alpha21_42 = _Y(alp21_42_0, b_1_42, b_2_42, b_3_42, c_1_42, c_2_42, c_3_42, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha21_42
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp21_42_0, __pyx_v_b_1_42, __pyx_v_b_2_42, __pyx_v_b_3_42, __pyx_v_c_1_42, __pyx_v_c_2_42, __pyx_v_c_3_42, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 328, __pyx_L1_error)
    __pyx_v_alpha21_42 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":329
 *     elif ((l==4) and (m==2)):
 *         alpha21_42 = _Y(alp21_42_0, b_1_42, b_2_42, b_3_42, c_1_42, c_2_42, c_3_42, af, af2, af3)
 *         res = alpha21_42             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==1)):
*/
    __pyx_v_res = __pyx_v_alpha21_42;

    /* "pyRing/eob_utils.pyx":327
 *         res = alpha21_43
 * 
 *     elif ((l==4) and (m==2)):             # <<<<<<<<<<<<<<
 *         alpha21_42 = _Y(alp21_42_0, b_1_42, b_2_42, b_3_42, c_1_42, c_2_42, c_3_42, af, af2, af3)
 *         res = alpha21_42
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":331
 *         res = alpha21_42
 * 
 *     elif ((l==4) and (m==1)):             # <<<<<<<<<<<<<<
 *         alpha21_41 = _Y(alp21_41_0, b_1_41, b_2_41, b_3_41, c_1_41, c_2_41, c_3_41, af, af2, af3)
 *         res = alpha21_41
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L20_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L20_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":332
 * 
 *     elif ((l==4) and (m==1)):
 *         alpha21_41 = _Y(alp21_41_0, b_1_41, b_2_41, b_3_41, c_1_41, c_2_41, c_3_41, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha21_41
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp21_41_0, __pyx_v_b_1_41, __pyx_v_b_2_41, __pyx_v_b_3_41, __pyx_v_c_1_41, __pyx_v_c_2_41, __pyx_v_c_3_41, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 332, __pyx_L1_error)
    __pyx_v_alpha21_41 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":333
 *     elif ((l==4) and (m==1)):
 *         alpha21_41 = _Y(alp21_41_0, b_1_41, b_2_41, b_3_41, c_1_41, c_2_41, c_3_41, af, af2, af3)
 *         res = alpha21_41             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==5) and (m==5)):
*/
    __pyx_v_res = __pyx_v_alpha21_41;

    /* "pyRing/eob_utils.pyx":331
 *         res = alpha21_42
 * 
 *     elif ((l==4) and (m==1)):             # <<<<<<<<<<<<<<
 *         alpha21_41 = _Y(alp21_41_0, b_1_41, b_2_41, b_3_41, c_1_41, c_2_41, c_3_41, af, af2, af3)
 *         res = alpha21_41
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":335
 *         res = alpha21_41
 * 
 *     elif ((l==5) and (m==5)):             # <<<<<<<<<<<<<<
 *         alpha21_55 = _Y(alp21_55_0, b_1_55, b_2_55, b_3_55, c_1_55, c_2_55, c_3_55, af, af2, af3)
 *         res = alpha21_55
*/
  __pyx_t_2 = (__pyx_v_l == 5);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L22_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 5);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L22_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":336
 * 
 *     elif ((l==5) and (m==5)):
 *         alpha21_55 = _Y(alp21_55_0, b_1_55, b_2_55, b_3_55, c_1_55, c_2_55, c_3_55, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = alpha21_55
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_alp21_55_0, __pyx_v_b_1_55, __pyx_v_b_2_55, __pyx_v_b_3_55, __pyx_v_c_1_55, __pyx_v_c_2_55, __pyx_v_c_3_55, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 336, __pyx_L1_error)
    __pyx_v_alpha21_55 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":337
 *     elif ((l==5) and (m==5)):
 *         alpha21_55 = _Y(alp21_55_0, b_1_55, b_2_55, b_3_55, c_1_55, c_2_55, c_3_55, af, af2, af3)
 *         res = alpha21_55             # <<<<<<<<<<<<<<
 * 
 *     return res
*/
    __pyx_v_res = __pyx_v_alpha21_55;

    /* "pyRing/eob_utils.pyx":335
 *         res = alpha21_41
 * 
 *     elif ((l==5) and (m==5)):             # <<<<<<<<<<<<<<
 *         alpha21_55 = _Y(alp21_55_0, b_1_55, b_2_55, b_3_55, c_1_55, c_2_55, c_3_55, af, af2, af3)
 *         res = alpha21_55
*/
  }
  __pyx_L3:;

  /* "pyRing/eob_utils.pyx":339
 *         res = alpha21_55
 * 
 *     return res             # <<<<<<<<<<<<<<
 * 
 * 
*/
  __pyx_r = __pyx_v_res;
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":230
 * 
 * 
 * cdef double _alpha21(double af, int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function returning the value of alpha21 for each mode, following appendix C.2 of arXiv:2001.09082v2.
*/

  /* function exit code */
  __pyx_L1_error:;
  __pyx_gilstate_save = __Pyx_PyGILState_Ensure();
  __Pyx_AddTraceback("pyRing.eob_utils._alpha21", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = -1;
  __Pyx_PyGILState_Release(__pyx_gilstate_save);
  __pyx_L0:;
  return __pyx_r;
}

/* "pyRing/eob_utils.pyx":342
 * 
 * 
 * cdef double _omega1(double af, int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function returning the value of omega1 for each mode, following appendix C.2 of arXiv:2001.09082v2.
*/

static double __pyx_f_6pyRing_9eob_utils__omega1(double __pyx_v_af, int __pyx_v_l, int __pyx_v_m) {
  double __pyx_v_res;
  double __pyx_v_omega1_22;
  double __pyx_v_omega1_21;
  double __pyx_v_omega1_33;
  double __pyx_v_omega1_32;
  double __pyx_v_omega1_31;
  double __pyx_v_omega1_44;
  double __pyx_v_omega1_43;
  double __pyx_v_omega1_42;
  double __pyx_v_omega1_41;
  double __pyx_v_omega1_55;
  double __pyx_v_af2;
  double __pyx_v_af3;
  double __pyx_v_omg1_22_0;
  double __pyx_v_b_1_22;
  double __pyx_v_b_2_22;
  double __pyx_v_b_3_22;
  double __pyx_v_c_1_22;
  double __pyx_v_c_2_22;
  double __pyx_v_c_3_22;
  double __pyx_v_omg1_21_0;
  double __pyx_v_b_1_21;
  double __pyx_v_b_2_21;
  double __pyx_v_b_3_21;
  double __pyx_v_c_1_21;
  double __pyx_v_c_2_21;
  double __pyx_v_c_3_21;
  double __pyx_v_omg1_33_0;
  double __pyx_v_b_1_33;
  double __pyx_v_b_2_33;
  double __pyx_v_b_3_33;
  double __pyx_v_c_1_33;
  double __pyx_v_c_2_33;
  double __pyx_v_c_3_33;
  double __pyx_v_omg1_32_0;
  double __pyx_v_b_1_32;
  double __pyx_v_b_2_32;
  double __pyx_v_b_3_32;
  double __pyx_v_c_1_32;
  double __pyx_v_c_2_32;
  double __pyx_v_c_3_32;
  double __pyx_v_omg1_31_0;
  double __pyx_v_b_1_31;
  double __pyx_v_b_2_31;
  double __pyx_v_b_3_31;
  double __pyx_v_c_1_31;
  double __pyx_v_c_2_31;
  double __pyx_v_c_3_31;
  double __pyx_v_omg1_44_0;
  double __pyx_v_b_1_44;
  double __pyx_v_b_2_44;
  double __pyx_v_b_3_44;
  double __pyx_v_c_1_44;
  double __pyx_v_c_2_44;
  double __pyx_v_c_3_44;
  double __pyx_v_omg1_43_0;
  double __pyx_v_b_1_43;
  double __pyx_v_b_2_43;
  double __pyx_v_b_3_43;
  double __pyx_v_c_1_43;
  double __pyx_v_c_2_43;
  double __pyx_v_c_3_43;
  double __pyx_v_omg1_42_0;
  double __pyx_v_b_1_42;
  double __pyx_v_b_2_42;
  double __pyx_v_b_3_42;
  double __pyx_v_c_1_42;
  double __pyx_v_c_2_42;
  double __pyx_v_c_3_42;
  double __pyx_v_omg1_41_0;
  double __pyx_v_b_1_41;
  double __pyx_v_b_2_41;
  double __pyx_v_b_3_41;
  double __pyx_v_c_1_41;
  double __pyx_v_c_2_41;
  double __pyx_v_c_3_41;
  double __pyx_v_omg1_55_0;
  double __pyx_v_b_1_55;
  double __pyx_v_b_2_55;
  double __pyx_v_b_3_55;
  double __pyx_v_c_1_55;
  double __pyx_v_c_2_55;
  double __pyx_v_c_3_55;
  double __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;
  double __pyx_t_3;
  int __pyx_lineno = 0;
  const char *__pyx_filename = NULL;
  int __pyx_clineno = 0;
  PyGILState_STATE __pyx_gilstate_save;

  /* "pyRing/eob_utils.pyx":354
 *     """
 * 
 *     cdef double res = 0.             # <<<<<<<<<<<<<<
 *     cdef double num_omg, den_omg
 *     cdef double omega1_22, omega1_21, omega1_33, omega1_32, omega1_31, omega1_44, omega1_43, omega1_42, omega1_41, omega1_55
*/
  __pyx_v_res = 0.;

  /* "pyRing/eob_utils.pyx":357
 *     cdef double num_omg, den_omg
 *     cdef double omega1_22, omega1_21, omega1_33, omega1_32, omega1_31, omega1_44, omega1_43, omega1_42, omega1_41, omega1_55
 *     cdef double af2 = af*af, af3 = af2*af             # <<<<<<<<<<<<<<
 * 
 *     # -------------------------------------------------------------------------------- #
*/
  __pyx_v_af2 = (__pyx_v_af * __pyx_v_af);
  __pyx_v_af3 = (__pyx_v_af2 * __pyx_v_af);

  /* "pyRing/eob_utils.pyx":361
 *     # -------------------------------------------------------------------------------- #
 *     # (2,2) - TEOBResumSFits.c, line 2802
 *     cdef double omg1_22_0 = 0.373672             # <<<<<<<<<<<<<<
 *     cdef double b_1_22    = -1.5367, b_2_22 = 0.5503, b_3_22 = 0.
 *     cdef double c_1_22    = -1.8700, c_2_22 = 0.9848, c_3_22 = -0.10943
*/
  __pyx_v_omg1_22_0 = 0.373672;

  /* "pyRing/eob_utils.pyx":362
 *     # (2,2) - TEOBResumSFits.c, line 2802
 *     cdef double omg1_22_0 = 0.373672
 *     cdef double b_1_22    = -1.5367, b_2_22 = 0.5503, b_3_22 = 0.             # <<<<<<<<<<<<<<
 *     cdef double c_1_22    = -1.8700, c_2_22 = 0.9848, c_3_22 = -0.10943
 * 
*/
  __pyx_v_b_1_22 = -1.5367;
  __pyx_v_b_2_22 = 0.5503;
  __pyx_v_b_3_22 = 0.;

  /* "pyRing/eob_utils.pyx":363
 *     cdef double omg1_22_0 = 0.373672
 *     cdef double b_1_22    = -1.5367, b_2_22 = 0.5503, b_3_22 = 0.
 *     cdef double c_1_22    = -1.8700, c_2_22 = 0.9848, c_3_22 = -0.10943             # <<<<<<<<<<<<<<
 * 
 *     # (2,1) - TEOBResumSFits.c, line 2797
*/
  __pyx_v_c_1_22 = -1.8700;
  __pyx_v_c_2_22 = 0.9848;
  __pyx_v_c_3_22 = -0.10943;

  /* "pyRing/eob_utils.pyx":366
 * 
 *     # (2,1) - TEOBResumSFits.c, line 2797
 *     cdef double omg1_21_0 = 0.373672             # <<<<<<<<<<<<<<
 *     cdef double b_1_21    = -0.79546, b_2_21 = -0.1908, b_3_21 = 0.11460
 *     cdef double c_1_21    = -0.96337, c_2_21 = -0.1495, c_3_21 = 0.19522
*/
  __pyx_v_omg1_21_0 = 0.373672;

  /* "pyRing/eob_utils.pyx":367
 *     # (2,1) - TEOBResumSFits.c, line 2797
 *     cdef double omg1_21_0 = 0.373672
 *     cdef double b_1_21    = -0.79546, b_2_21 = -0.1908, b_3_21 = 0.11460             # <<<<<<<<<<<<<<
 *     cdef double c_1_21    = -0.96337, c_2_21 = -0.1495, c_3_21 = 0.19522
 * 
*/
  __pyx_v_b_1_21 = -0.79546;
  __pyx_v_b_2_21 = -0.1908;
  __pyx_v_b_3_21 = 0.11460;

  /* "pyRing/eob_utils.pyx":368
 *     cdef double omg1_21_0 = 0.373672
 *     cdef double b_1_21    = -0.79546, b_2_21 = -0.1908, b_3_21 = 0.11460
 *     cdef double c_1_21    = -0.96337, c_2_21 = -0.1495, c_3_21 = 0.19522             # <<<<<<<<<<<<<<
 * 
 *     # (3,3) - TEOBResumSFits.c, line 2831
*/
  __pyx_v_c_1_21 = -0.96337;
  __pyx_v_c_2_21 = -0.1495;
  __pyx_v_c_3_21 = 0.19522;

  /* "pyRing/eob_utils.pyx":371
 * 
 *     # (3,3) - TEOBResumSFits.c, line 2831
 *     cdef double omg1_33_0 = 0.599443             # <<<<<<<<<<<<<<
 *     cdef double b_1_33    = -1.84922, b_2_33 = 0.9294, b_3_33 = -0.07613
 *     cdef double c_1_33    = -2.18719, c_2_33 = 1.4903, c_3_33 = -0.3014
*/
  __pyx_v_omg1_33_0 = 0.599443;

  /* "pyRing/eob_utils.pyx":372
 *     # (3,3) - TEOBResumSFits.c, line 2831
 *     cdef double omg1_33_0 = 0.599443
 *     cdef double b_1_33    = -1.84922, b_2_33 = 0.9294, b_3_33 = -0.07613             # <<<<<<<<<<<<<<
 *     cdef double c_1_33    = -2.18719, c_2_33 = 1.4903, c_3_33 = -0.3014
 * 
*/
  __pyx_v_b_1_33 = -1.84922;
  __pyx_v_b_2_33 = 0.9294;
  __pyx_v_b_3_33 = -0.07613;

  /* "pyRing/eob_utils.pyx":373
 *     cdef double omg1_33_0 = 0.599443
 *     cdef double b_1_33    = -1.84922, b_2_33 = 0.9294, b_3_33 = -0.07613
 *     cdef double c_1_33    = -2.18719, c_2_33 = 1.4903, c_3_33 = -0.3014             # <<<<<<<<<<<<<<
 * 
 *     # (3,2) - TEOBResumSFits.c, line 2826
*/
  __pyx_v_c_1_33 = -2.18719;
  __pyx_v_c_2_33 = 1.4903;
  __pyx_v_c_3_33 = -0.3014;

  /* "pyRing/eob_utils.pyx":376
 * 
 *     # (3,2) - TEOBResumSFits.c, line 2826
 *     cdef double omg1_32_0 = 0.599443             # <<<<<<<<<<<<<<
 *     cdef double b_1_32    = -0.251, b_2_32 = -0.891, b_3_32 = 0.2706
 *     cdef double c_1_32    = -0.475, c_2_32 = -0.911, c_3_32 = 0.4609
*/
  __pyx_v_omg1_32_0 = 0.599443;

  /* "pyRing/eob_utils.pyx":377
 *     # (3,2) - TEOBResumSFits.c, line 2826
 *     cdef double omg1_32_0 = 0.599443
 *     cdef double b_1_32    = -0.251, b_2_32 = -0.891, b_3_32 = 0.2706             # <<<<<<<<<<<<<<
 *     cdef double c_1_32    = -0.475, c_2_32 = -0.911, c_3_32 = 0.4609
 * 
*/
  __pyx_v_b_1_32 = -0.251;
  __pyx_v_b_2_32 = -0.891;
  __pyx_v_b_3_32 = 0.2706;

  /* "pyRing/eob_utils.pyx":378
 *     cdef double omg1_32_0 = 0.599443
 *     cdef double b_1_32    = -0.251, b_2_32 = -0.891, b_3_32 = 0.2706
 *     cdef double c_1_32    = -0.475, c_2_32 = -0.911, c_3_32 = 0.4609             # <<<<<<<<<<<<<<
 * 
 *     # (3,1) - TEOBResumSFits.c, line 2821
*/
  __pyx_v_c_1_32 = -0.475;
  __pyx_v_c_2_32 = -0.911;
  __pyx_v_c_3_32 = 0.4609;

  /* "pyRing/eob_utils.pyx":381
 * 
 *     # (3,1) - TEOBResumSFits.c, line 2821
 *     cdef double omg1_31_0 = 0.599443             # <<<<<<<<<<<<<<
 *     cdef double b_1_31    = -0.70941, b_2_31 = -0.16975, b_3_31 = 0.08559
 *     cdef double c_1_31    = -0.82174, c_2_31 = -0.16792, c_3_31 = 0.14524
*/
  __pyx_v_omg1_31_0 = 0.599443;

  /* "pyRing/eob_utils.pyx":382
 *     # (3,1) - TEOBResumSFits.c, line 2821
 *     cdef double omg1_31_0 = 0.599443
 *     cdef double b_1_31    = -0.70941, b_2_31 = -0.16975, b_3_31 = 0.08559             # <<<<<<<<<<<<<<
 *     cdef double c_1_31    = -0.82174, c_2_31 = -0.16792, c_3_31 = 0.14524
 * 
*/
  __pyx_v_b_1_31 = -0.70941;
  __pyx_v_b_2_31 = -0.16975;
  __pyx_v_b_3_31 = 0.08559;

  /* "pyRing/eob_utils.pyx":383
 *     cdef double omg1_31_0 = 0.599443
 *     cdef double b_1_31    = -0.70941, b_2_31 = -0.16975, b_3_31 = 0.08559
 *     cdef double c_1_31    = -0.82174, c_2_31 = -0.16792, c_3_31 = 0.14524             # <<<<<<<<<<<<<<
 * 
 *     # (4,4) - TEOBResumSFits.c, line 2851
*/
  __pyx_v_c_1_31 = -0.82174;
  __pyx_v_c_2_31 = -0.16792;
  __pyx_v_c_3_31 = 0.14524;

  /* "pyRing/eob_utils.pyx":386
 * 
 *     # (4,4) - TEOBResumSFits.c, line 2851
 *     cdef double omg1_44_0 = 0.809178             # <<<<<<<<<<<<<<
 *     cdef double b_1_44    = -1.83156, b_2_44 = 0.9016, b_3_44 = -0.06579
 *     cdef double c_1_44    = -2.17745, c_2_44 = 1.4753, c_3_44 = -0.2961
*/
  __pyx_v_omg1_44_0 = 0.809178;

  /* "pyRing/eob_utils.pyx":387
 *     # (4,4) - TEOBResumSFits.c, line 2851
 *     cdef double omg1_44_0 = 0.809178
 *     cdef double b_1_44    = -1.83156, b_2_44 = 0.9016, b_3_44 = -0.06579             # <<<<<<<<<<<<<<
 *     cdef double c_1_44    = -2.17745, c_2_44 = 1.4753, c_3_44 = -0.2961
 * 
*/
  __pyx_v_b_1_44 = -1.83156;
  __pyx_v_b_2_44 = 0.9016;
  __pyx_v_b_3_44 = -0.06579;

  /* "pyRing/eob_utils.pyx":388
 *     cdef double omg1_44_0 = 0.809178
 *     cdef double b_1_44    = -1.83156, b_2_44 = 0.9016, b_3_44 = -0.06579
 *     cdef double c_1_44    = -2.17745, c_2_44 = 1.4753, c_3_44 = -0.2961             # <<<<<<<<<<<<<<
 * 
 *     # (4,3) - TEOBResumSFits.c, line 2846
*/
  __pyx_v_c_1_44 = -2.17745;
  __pyx_v_c_2_44 = 1.4753;
  __pyx_v_c_3_44 = -0.2961;

  /* "pyRing/eob_utils.pyx":391
 * 
 *     # (4,3) - TEOBResumSFits.c, line 2846
 *     cdef double omg1_43_0 = 0.809178             # <<<<<<<<<<<<<<
 *     cdef double b_1_43    = -1.8397, b_2_43 = 0.9616, b_3_43 = -0.11339
 *     cdef double c_1_43    = -2.0979, c_2_43 = 1.3701, c_3_43 = -0.2675
*/
  __pyx_v_omg1_43_0 = 0.809178;

  /* "pyRing/eob_utils.pyx":392
 *     # (4,3) - TEOBResumSFits.c, line 2846
 *     cdef double omg1_43_0 = 0.809178
 *     cdef double b_1_43    = -1.8397, b_2_43 = 0.9616, b_3_43 = -0.11339             # <<<<<<<<<<<<<<
 *     cdef double c_1_43    = -2.0979, c_2_43 = 1.3701, c_3_43 = -0.2675
 * 
*/
  __pyx_v_b_1_43 = -1.8397;
  __pyx_v_b_2_43 = 0.9616;
  __pyx_v_b_3_43 = -0.11339;

  /* "pyRing/eob_utils.pyx":393
 *     cdef double omg1_43_0 = 0.809178
 *     cdef double b_1_43    = -1.8397, b_2_43 = 0.9616, b_3_43 = -0.11339
 *     cdef double c_1_43    = -2.0979, c_2_43 = 1.3701, c_3_43 = -0.2675             # <<<<<<<<<<<<<<
 * 
 *     # (4,2) - TEOBResumSFits.c, line 2841
*/
  __pyx_v_c_1_43 = -2.0979;
  __pyx_v_c_2_43 = 1.3701;
  __pyx_v_c_3_43 = -0.2675;

  /* "pyRing/eob_utils.pyx":396
 * 
 *     # (4,2) - TEOBResumSFits.c, line 2841
 *     cdef double omg1_42_0 = 0.809178             # <<<<<<<<<<<<<<
 *     cdef double b_1_42    = -0.6644, b_2_42 = -0.3357, b_3_42 = 0.1425
 *     cdef double c_1_42    = -0.8366, c_2_42 = -0.2921, c_3_42 = 0.2254
*/
  __pyx_v_omg1_42_0 = 0.809178;

  /* "pyRing/eob_utils.pyx":397
 *     # (4,2) - TEOBResumSFits.c, line 2841
 *     cdef double omg1_42_0 = 0.809178
 *     cdef double b_1_42    = -0.6644, b_2_42 = -0.3357, b_3_42 = 0.1425             # <<<<<<<<<<<<<<
 *     cdef double c_1_42    = -0.8366, c_2_42 = -0.2921, c_3_42 = 0.2254
 * 
*/
  __pyx_v_b_1_42 = -0.6644;
  __pyx_v_b_2_42 = -0.3357;
  __pyx_v_b_3_42 = 0.1425;

  /* "pyRing/eob_utils.pyx":398
 *     cdef double omg1_42_0 = 0.809178
 *     cdef double b_1_42    = -0.6644, b_2_42 = -0.3357, b_3_42 = 0.1425
 *     cdef double c_1_42    = -0.8366, c_2_42 = -0.2921, c_3_42 = 0.2254             # <<<<<<<<<<<<<<
 * 
 *     # (4,1) - TEOBResumSFits.c, line 2836
*/
  __pyx_v_c_1_42 = -0.8366;
  __pyx_v_c_2_42 = -0.2921;
  __pyx_v_c_3_42 = 0.2254;

  /* "pyRing/eob_utils.pyx":401
 * 
 *     # (4,1) - TEOBResumSFits.c, line 2836
 *     cdef double omg1_41_0 = 0.809178             # <<<<<<<<<<<<<<
 *     cdef double b_1_41    = -0.68647, b_2_41 = -0.1852590, b_3_41 = 0.0934997
 *     cdef double c_1_41    = -0.77272, c_2_41 = -0.1986852, c_3_41 = 0.1485093
*/
  __pyx_v_omg1_41_0 = 0.809178;

  /* "pyRing/eob_utils.pyx":402
 *     # (4,1) - TEOBResumSFits.c, line 2836
 *     cdef double omg1_41_0 = 0.809178
 *     cdef double b_1_41    = -0.68647, b_2_41 = -0.1852590, b_3_41 = 0.0934997             # <<<<<<<<<<<<<<
 *     cdef double c_1_41    = -0.77272, c_2_41 = -0.1986852, c_3_41 = 0.1485093
 * 
*/
  __pyx_v_b_1_41 = -0.68647;
  __pyx_v_b_2_41 = -0.1852590;
  __pyx_v_b_3_41 = 0.0934997;

  /* "pyRing/eob_utils.pyx":403
 *     cdef double omg1_41_0 = 0.809178
 *     cdef double b_1_41    = -0.68647, b_2_41 = -0.1852590, b_3_41 = 0.0934997
 *     cdef double c_1_41    = -0.77272, c_2_41 = -0.1986852, c_3_41 = 0.1485093             # <<<<<<<<<<<<<<
 * 
 *     # (5,5) - TEOBResumSFits.c, line 2856
*/
  __pyx_v_c_1_41 = -0.77272;
  __pyx_v_c_2_41 = -0.1986852;
  __pyx_v_c_3_41 = 0.1485093;

  /* "pyRing/eob_utils.pyx":406
 * 
 *     # (5,5) - TEOBResumSFits.c, line 2856
 *     cdef double omg1_55_0 = 1.012295             # <<<<<<<<<<<<<<
 *     cdef double b_1_55    = -1.5659, b_2_55 = 0.5783, b_3_55 = 0.
 *     cdef double c_1_55    = -1.9149, c_2_55 = 1.0668, c_3_55 = 0.14663
*/
  __pyx_v_omg1_55_0 = 1.012295;

  /* "pyRing/eob_utils.pyx":407
 *     # (5,5) - TEOBResumSFits.c, line 2856
 *     cdef double omg1_55_0 = 1.012295
 *     cdef double b_1_55    = -1.5659, b_2_55 = 0.5783, b_3_55 = 0.             # <<<<<<<<<<<<<<
 *     cdef double c_1_55    = -1.9149, c_2_55 = 1.0668, c_3_55 = 0.14663
 *     # -------------------------------------------------------------------------------- #
*/
  __pyx_v_b_1_55 = -1.5659;
  __pyx_v_b_2_55 = 0.5783;
  __pyx_v_b_3_55 = 0.;

  /* "pyRing/eob_utils.pyx":408
 *     cdef double omg1_55_0 = 1.012295
 *     cdef double b_1_55    = -1.5659, b_2_55 = 0.5783, b_3_55 = 0.
 *     cdef double c_1_55    = -1.9149, c_2_55 = 1.0668, c_3_55 = 0.14663             # <<<<<<<<<<<<<<
 *     # -------------------------------------------------------------------------------- #
 * 
*/
  __pyx_v_c_1_55 = -1.9149;
  __pyx_v_c_2_55 = 1.0668;
  __pyx_v_c_3_55 = 0.14663;

  /* "pyRing/eob_utils.pyx":411
 *     # -------------------------------------------------------------------------------- #
 * 
 *     if ((l==2) and (m==2)):             # <<<<<<<<<<<<<<
 *         omega1_22 = _Y(omg1_22_0, b_1_22, b_2_22, b_3_22, c_1_22, c_2_22, c_3_22, af, af2, af3)
 *         res = omega1_22
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L4_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":412
 * 
 *     if ((l==2) and (m==2)):
 *         omega1_22 = _Y(omg1_22_0, b_1_22, b_2_22, b_3_22, c_1_22, c_2_22, c_3_22, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = omega1_22
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_omg1_22_0, __pyx_v_b_1_22, __pyx_v_b_2_22, __pyx_v_b_3_22, __pyx_v_c_1_22, __pyx_v_c_2_22, __pyx_v_c_3_22, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 412, __pyx_L1_error)
    __pyx_v_omega1_22 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":413
 *     if ((l==2) and (m==2)):
 *         omega1_22 = _Y(omg1_22_0, b_1_22, b_2_22, b_3_22, c_1_22, c_2_22, c_3_22, af, af2, af3)
 *         res = omega1_22             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==2) and (m==1)):
*/
    __pyx_v_res = __pyx_v_omega1_22;

    /* "pyRing/eob_utils.pyx":411
 *     # -------------------------------------------------------------------------------- #
 * 
 *     if ((l==2) and (m==2)):             # <<<<<<<<<<<<<<
 *         omega1_22 = _Y(omg1_22_0, b_1_22, b_2_22, b_3_22, c_1_22, c_2_22, c_3_22, af, af2, af3)
 *         res = omega1_22
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":415
 *         res = omega1_22
 * 
 *     elif ((l==2) and (m==1)):             # <<<<<<<<<<<<<<
 *         omega1_21 = _Y(omg1_21_0, b_1_21, b_2_21, b_3_21, c_1_21, c_2_21, c_3_21, af, af2, af3)
 *         res = omega1_21
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L6_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L6_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":416
 * 
 *     elif ((l==2) and (m==1)):
 *         omega1_21 = _Y(omg1_21_0, b_1_21, b_2_21, b_3_21, c_1_21, c_2_21, c_3_21, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = omega1_21
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_omg1_21_0, __pyx_v_b_1_21, __pyx_v_b_2_21, __pyx_v_b_3_21, __pyx_v_c_1_21, __pyx_v_c_2_21, __pyx_v_c_3_21, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 416, __pyx_L1_error)
    __pyx_v_omega1_21 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":417
 *     elif ((l==2) and (m==1)):
 *         omega1_21 = _Y(omg1_21_0, b_1_21, b_2_21, b_3_21, c_1_21, c_2_21, c_3_21, af, af2, af3)
 *         res = omega1_21             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==3) and (m==3)):
*/
    __pyx_v_res = __pyx_v_omega1_21;

    /* "pyRing/eob_utils.pyx":415
 *         res = omega1_22
 * 
 *     elif ((l==2) and (m==1)):             # <<<<<<<<<<<<<<
 *         omega1_21 = _Y(omg1_21_0, b_1_21, b_2_21, b_3_21, c_1_21, c_2_21, c_3_21, af, af2, af3)
 *         res = omega1_21
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":419
 *         res = omega1_21
 * 
 *     elif ((l==3) and (m==3)):             # <<<<<<<<<<<<<<
 *         omega1_33 = _Y(omg1_33_0, b_1_33, b_2_33, b_3_33, c_1_33, c_2_33, c_3_33, af, af2, af3)
 *         res = omega1_33
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L8_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L8_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":420
 * 
 *     elif ((l==3) and (m==3)):
 *         omega1_33 = _Y(omg1_33_0, b_1_33, b_2_33, b_3_33, c_1_33, c_2_33, c_3_33, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = omega1_33
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_omg1_33_0, __pyx_v_b_1_33, __pyx_v_b_2_33, __pyx_v_b_3_33, __pyx_v_c_1_33, __pyx_v_c_2_33, __pyx_v_c_3_33, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 420, __pyx_L1_error)
    __pyx_v_omega1_33 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":421
 *     elif ((l==3) and (m==3)):
 *         omega1_33 = _Y(omg1_33_0, b_1_33, b_2_33, b_3_33, c_1_33, c_2_33, c_3_33, af, af2, af3)
 *         res = omega1_33             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==3) and (m==2)):
*/
    __pyx_v_res = __pyx_v_omega1_33;

    /* "pyRing/eob_utils.pyx":419
 *         res = omega1_21
 * 
 *     elif ((l==3) and (m==3)):             # <<<<<<<<<<<<<<
 *         omega1_33 = _Y(omg1_33_0, b_1_33, b_2_33, b_3_33, c_1_33, c_2_33, c_3_33, af, af2, af3)
 *         res = omega1_33
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":423
 *         res = omega1_33
 * 
 *     elif ((l==3) and (m==2)):             # <<<<<<<<<<<<<<
 *         omega1_32 = _Y(omg1_32_0, b_1_32, b_2_32, b_3_32, c_1_32, c_2_32, c_3_32, af, af2, af3)
 *         res = omega1_32
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L10_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L10_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":424
 * 
 *     elif ((l==3) and (m==2)):
 *         omega1_32 = _Y(omg1_32_0, b_1_32, b_2_32, b_3_32, c_1_32, c_2_32, c_3_32, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = omega1_32
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_omg1_32_0, __pyx_v_b_1_32, __pyx_v_b_2_32, __pyx_v_b_3_32, __pyx_v_c_1_32, __pyx_v_c_2_32, __pyx_v_c_3_32, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 424, __pyx_L1_error)
    __pyx_v_omega1_32 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":425
 *     elif ((l==3) and (m==2)):
 *         omega1_32 = _Y(omg1_32_0, b_1_32, b_2_32, b_3_32, c_1_32, c_2_32, c_3_32, af, af2, af3)
 *         res = omega1_32             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==3) and (m==1)):
*/
    __pyx_v_res = __pyx_v_omega1_32;

    /* "pyRing/eob_utils.pyx":423
 *         res = omega1_33
 * 
 *     elif ((l==3) and (m==2)):             # <<<<<<<<<<<<<<
 *         omega1_32 = _Y(omg1_32_0, b_1_32, b_2_32, b_3_32, c_1_32, c_2_32, c_3_32, af, af2, af3)
 *         res = omega1_32
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":427
 *         res = omega1_32
 * 
 *     elif ((l==3) and (m==1)):             # <<<<<<<<<<<<<<
 *         omega1_31 = _Y(omg1_31_0, b_1_31, b_2_31, b_3_31, c_1_31, c_2_31, c_3_31, af, af2, af3)
 *         res = omega1_31
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L12_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L12_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":428
 * 
 *     elif ((l==3) and (m==1)):
 *         omega1_31 = _Y(omg1_31_0, b_1_31, b_2_31, b_3_31, c_1_31, c_2_31, c_3_31, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = omega1_31
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_omg1_31_0, __pyx_v_b_1_31, __pyx_v_b_2_31, __pyx_v_b_3_31, __pyx_v_c_1_31, __pyx_v_c_2_31, __pyx_v_c_3_31, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 428, __pyx_L1_error)
    __pyx_v_omega1_31 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":429
 *     elif ((l==3) and (m==1)):
 *         omega1_31 = _Y(omg1_31_0, b_1_31, b_2_31, b_3_31, c_1_31, c_2_31, c_3_31, af, af2, af3)
 *         res = omega1_31             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==4)):
*/
    __pyx_v_res = __pyx_v_omega1_31;

    /* "pyRing/eob_utils.pyx":427
 *         res = omega1_32
 * 
 *     elif ((l==3) and (m==1)):             # <<<<<<<<<<<<<<
 *         omega1_31 = _Y(omg1_31_0, b_1_31, b_2_31, b_3_31, c_1_31, c_2_31, c_3_31, af, af2, af3)
 *         res = omega1_31
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":431
 *         res = omega1_31
 * 
 *     elif ((l==4) and (m==4)):             # <<<<<<<<<<<<<<
 *         omega1_44 = _Y(omg1_44_0, b_1_44, b_2_44, b_3_44, c_1_44, c_2_44, c_3_44, af, af2, af3)
 *         res = omega1_44
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L14_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 4);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L14_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":432
 * 
 *     elif ((l==4) and (m==4)):
 *         omega1_44 = _Y(omg1_44_0, b_1_44, b_2_44, b_3_44, c_1_44, c_2_44, c_3_44, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = omega1_44
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_omg1_44_0, __pyx_v_b_1_44, __pyx_v_b_2_44, __pyx_v_b_3_44, __pyx_v_c_1_44, __pyx_v_c_2_44, __pyx_v_c_3_44, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 432, __pyx_L1_error)
    __pyx_v_omega1_44 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":433
 *     elif ((l==4) and (m==4)):
 *         omega1_44 = _Y(omg1_44_0, b_1_44, b_2_44, b_3_44, c_1_44, c_2_44, c_3_44, af, af2, af3)
 *         res = omega1_44             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==3)):
*/
    __pyx_v_res = __pyx_v_omega1_44;

    /* "pyRing/eob_utils.pyx":431
 *         res = omega1_31
 * 
 *     elif ((l==4) and (m==4)):             # <<<<<<<<<<<<<<
 *         omega1_44 = _Y(omg1_44_0, b_1_44, b_2_44, b_3_44, c_1_44, c_2_44, c_3_44, af, af2, af3)
 *         res = omega1_44
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":435
 *         res = omega1_44
 * 
 *     elif ((l==4) and (m==3)):             # <<<<<<<<<<<<<<
 *         omega1_43 = _Y(omg1_43_0, b_1_43, b_2_43, b_3_43, c_1_43, c_2_43, c_3_43, af, af2, af3)
 *         res = omega1_43
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L16_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L16_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":436
 * 
 *     elif ((l==4) and (m==3)):
 *         omega1_43 = _Y(omg1_43_0, b_1_43, b_2_43, b_3_43, c_1_43, c_2_43, c_3_43, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = omega1_43
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_omg1_43_0, __pyx_v_b_1_43, __pyx_v_b_2_43, __pyx_v_b_3_43, __pyx_v_c_1_43, __pyx_v_c_2_43, __pyx_v_c_3_43, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 436, __pyx_L1_error)
    __pyx_v_omega1_43 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":437
 *     elif ((l==4) and (m==3)):
 *         omega1_43 = _Y(omg1_43_0, b_1_43, b_2_43, b_3_43, c_1_43, c_2_43, c_3_43, af, af2, af3)
 *         res = omega1_43             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==2)):
*/
    __pyx_v_res = __pyx_v_omega1_43;

    /* "pyRing/eob_utils.pyx":435
 *         res = omega1_44
 * 
 *     elif ((l==4) and (m==3)):             # <<<<<<<<<<<<<<
 *         omega1_43 = _Y(omg1_43_0, b_1_43, b_2_43, b_3_43, c_1_43, c_2_43, c_3_43, af, af2, af3)
 *         res = omega1_43
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":439
 *         res = omega1_43
 * 
 *     elif ((l==4) and (m==2)):             # <<<<<<<<<<<<<<
 *         omega1_42 = _Y(omg1_42_0, b_1_42, b_2_42, b_3_42, c_1_42, c_2_42, c_3_42, af, af2, af3)
 *         res = omega1_42
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L18_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L18_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":440
 * 
 *     elif ((l==4) and (m==2)):
 *         omega1_42 = _Y(omg1_42_0, b_1_42, b_2_42, b_3_42, c_1_42, c_2_42, c_3_42, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = omega1_42
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_omg1_42_0, __pyx_v_b_1_42, __pyx_v_b_2_42, __pyx_v_b_3_42, __pyx_v_c_1_42, __pyx_v_c_2_42, __pyx_v_c_3_42, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 440, __pyx_L1_error)
    __pyx_v_omega1_42 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":441
 *     elif ((l==4) and (m==2)):
 *         omega1_42 = _Y(omg1_42_0, b_1_42, b_2_42, b_3_42, c_1_42, c_2_42, c_3_42, af, af2, af3)
 *         res = omega1_42             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==1)):
*/
    __pyx_v_res = __pyx_v_omega1_42;

    /* "pyRing/eob_utils.pyx":439
 *         res = omega1_43
 * 
 *     elif ((l==4) and (m==2)):             # <<<<<<<<<<<<<<
 *         omega1_42 = _Y(omg1_42_0, b_1_42, b_2_42, b_3_42, c_1_42, c_2_42, c_3_42, af, af2, af3)
 *         res = omega1_42
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":443
 *         res = omega1_42
 * 
 *     elif ((l==4) and (m==1)):             # <<<<<<<<<<<<<<
 *         omega1_41 = _Y(omg1_41_0, b_1_41, b_2_41, b_3_41, c_1_41, c_2_41, c_3_41, af, af2, af3)
 *         res = omega1_41
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L20_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L20_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":444
 * 
 *     elif ((l==4) and (m==1)):
 *         omega1_41 = _Y(omg1_41_0, b_1_41, b_2_41, b_3_41, c_1_41, c_2_41, c_3_41, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = omega1_41
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_omg1_41_0, __pyx_v_b_1_41, __pyx_v_b_2_41, __pyx_v_b_3_41, __pyx_v_c_1_41, __pyx_v_c_2_41, __pyx_v_c_3_41, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 444, __pyx_L1_error)
    __pyx_v_omega1_41 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":445
 *     elif ((l==4) and (m==1)):
 *         omega1_41 = _Y(omg1_41_0, b_1_41, b_2_41, b_3_41, c_1_41, c_2_41, c_3_41, af, af2, af3)
 *         res = omega1_41             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==5) and (m==5)):
*/
    __pyx_v_res = __pyx_v_omega1_41;

    /* "pyRing/eob_utils.pyx":443
 *         res = omega1_42
 * 
 *     elif ((l==4) and (m==1)):             # <<<<<<<<<<<<<<
 *         omega1_41 = _Y(omg1_41_0, b_1_41, b_2_41, b_3_41, c_1_41, c_2_41, c_3_41, af, af2, af3)
 *         res = omega1_41
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":447
 *         res = omega1_41
 * 
 *     elif ((l==5) and (m==5)):             # <<<<<<<<<<<<<<
 *         omega1_55 = _Y(omg1_55_0, b_1_55, b_2_55, b_3_55, c_1_55, c_2_55, c_3_55, af, af2, af3)
 *         res = omega1_55
*/
  __pyx_t_2 = (__pyx_v_l == 5);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L22_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 5);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L22_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":448
 * 
 *     elif ((l==5) and (m==5)):
 *         omega1_55 = _Y(omg1_55_0, b_1_55, b_2_55, b_3_55, c_1_55, c_2_55, c_3_55, af, af2, af3)             # <<<<<<<<<<<<<<
 *         res = omega1_55
 * 
*/
    __pyx_t_3 = __pyx_f_6pyRing_9eob_utils__Y(__pyx_v_omg1_55_0, __pyx_v_b_1_55, __pyx_v_b_2_55, __pyx_v_b_3_55, __pyx_v_c_1_55, __pyx_v_c_2_55, __pyx_v_c_3_55, __pyx_v_af, __pyx_v_af2, __pyx_v_af3); if (unlikely(__pyx_t_3 == ((double)-1) && __Pyx_ErrOccurredWithGIL())) __PYX_ERR(0, 448, __pyx_L1_error)
    __pyx_v_omega1_55 = __pyx_t_3;

    /* "pyRing/eob_utils.pyx":449
 *     elif ((l==5) and (m==5)):
 *         omega1_55 = _Y(omg1_55_0, b_1_55, b_2_55, b_3_55, c_1_55, c_2_55, c_3_55, af, af2, af3)
 *         res = omega1_55             # <<<<<<<<<<<<<<
 * 
 *     return res
*/
    __pyx_v_res = __pyx_v_omega1_55;

    /* "pyRing/eob_utils.pyx":447
 *         res = omega1_41
 * 
 *     elif ((l==5) and (m==5)):             # <<<<<<<<<<<<<<
 *         omega1_55 = _Y(omg1_55_0, b_1_55, b_2_55, b_3_55, c_1_55, c_2_55, c_3_55, af, af2, af3)
 *         res = omega1_55
*/
  }
  __pyx_L3:;

  /* "pyRing/eob_utils.pyx":451
 *         res = omega1_55
 * 
 *     return res             # <<<<<<<<<<<<<<
 * 
 * 
*/
  __pyx_r = __pyx_v_res;
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":342
 * 
 * 
 * cdef double _omega1(double af, int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function returning the value of omega1 for each mode, following appendix C.2 of arXiv:2001.09082v2.
*/

  /* function exit code */
  __pyx_L1_error:;
  __pyx_gilstate_save = __Pyx_PyGILState_Ensure();
  __Pyx_AddTraceback("pyRing.eob_utils._omega1", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = -1;
  __Pyx_PyGILState_Release(__pyx_gilstate_save);
  __pyx_L0:;
  return __pyx_r;
}

/* "pyRing/eob_utils.pyx":460
 * #############################################################
 * 
 * cdef double _c3_A(double nu, double X12, double S_hat, double a12, int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function returning the coefficient c3_A of the ringdown model in section V.A of arXiv:1904.09550v2.
*/

static double __pyx_f_6pyRing_9eob_utils__c3_A(double __pyx_v_nu, double __pyx_v_X12, double __pyx_v_S_hat, double __pyx_v_a12, int __pyx_v_l, int __pyx_v_m) {
  double __pyx_v_res;
  double __pyx_v_c_3_A22;
  double __pyx_v_c_3_A21;
  double __pyx_v_c_3_A33;
  double __pyx_v_c_3_A32;
  double __pyx_v_c_3_A31;
  double __pyx_v_c_3_A44;
  double __pyx_v_c_3_A43;
  double __pyx_v_c_3_A42;
  double __pyx_v_c_3_A55;
  double __pyx_v_exp_A32;
  double __pyx_v_nu2;
  double __pyx_v_nu3;
  double __pyx_v_S_hat2;
  double __pyx_v_S_hat3;
  CYTHON_UNUSED double __pyx_v_S_hat4;
  double __pyx_v_X12_2;
  double __pyx_v_a12_2;
  double __pyx_v_b_0_A22;
  double __pyx_v_b_1_A22;
  double __pyx_v_b_2_A22;
  double __pyx_v_b_3_A22;
  double __pyx_v_c_3_A21_num;
  double __pyx_v_c_3_A21_den;
  double __pyx_v_b_0_A33;
  double __pyx_v_b_1_A33;
  double __pyx_v_c_3_A32_num;
  double __pyx_v_c_3_A32_den;
  double __pyx_v_c_3_A32_exp;
  double __pyx_v_c_3_A31_num;
  double __pyx_v_c_3_A31_den;
  double __pyx_v_b_0_A44;
  double __pyx_v_b_1_A44;
  double __pyx_v_b_2_A44;
  double __pyx_v_c_3_A43_num;
  double __pyx_v_c_3_A43_den;
  double __pyx_v_c_3_A42_num;
  double __pyx_v_c_3_A42_den;
  double __pyx_v_c_3_A41;
  double __pyx_v_b_0_A55;
  double __pyx_v_b_1_A55;
  double __pyx_v_b_2_A55;
  double __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;

  /* "pyRing/eob_utils.pyx":472
 *     """
 * 
 *     cdef double res = 0., c_3_A22, c_3_A21, c_3_A33, c_3_A32, c_3_A31, c_3_A44, c_3_A43, c_3_A42, c_3_A55, exp_A32             # <<<<<<<<<<<<<<
 *     cdef double nu2 = nu*nu, nu3 = nu2*nu, S_hat2 = S_hat*S_hat, S_hat3 = S_hat2*S_hat, S_hat4 = S_hat3*S_hat, X12_2 = X12*X12, a12_2 = a12*a12
 * 
*/
  __pyx_v_res = 0.;

  /* "pyRing/eob_utils.pyx":473
 * 
 *     cdef double res = 0., c_3_A22, c_3_A21, c_3_A33, c_3_A32, c_3_A31, c_3_A44, c_3_A43, c_3_A42, c_3_A55, exp_A32
 *     cdef double nu2 = nu*nu, nu3 = nu2*nu, S_hat2 = S_hat*S_hat, S_hat3 = S_hat2*S_hat, S_hat4 = S_hat3*S_hat, X12_2 = X12*X12, a12_2 = a12*a12             # <<<<<<<<<<<<<<
 * 
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
*/
  __pyx_v_nu2 = (__pyx_v_nu * __pyx_v_nu);
  __pyx_v_nu3 = (__pyx_v_nu2 * __pyx_v_nu);
  __pyx_v_S_hat2 = (__pyx_v_S_hat * __pyx_v_S_hat);
  __pyx_v_S_hat3 = (__pyx_v_S_hat2 * __pyx_v_S_hat);
  __pyx_v_S_hat4 = (__pyx_v_S_hat3 * __pyx_v_S_hat);
  __pyx_v_X12_2 = (__pyx_v_X12 * __pyx_v_X12);
  __pyx_v_a12_2 = (__pyx_v_a12 * __pyx_v_a12);

  /* "pyRing/eob_utils.pyx":477
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
 *     # (2,2) - TEOBResumSFits.c, line 2577-2580
 *     cdef double b_0_A22 = -0.5585 + 0.81196*nu, b_1_A22 = -0.398576 + 0.1659421*X12, b_2_A22 = 0.099805 -0.2560047*X12, b_3_A22 = 0.72125 -0.9418946*X12             # <<<<<<<<<<<<<<
 * 
 *     # (2,1) - TEOBResumSFits.c, line 2700
*/
  __pyx_v_b_0_A22 = (-0.5585 + (0.81196 * __pyx_v_nu));
  __pyx_v_b_1_A22 = (-0.398576 + (0.1659421 * __pyx_v_X12));
  __pyx_v_b_2_A22 = (0.099805 - (0.2560047 * __pyx_v_X12));
  __pyx_v_b_3_A22 = (0.72125 - (0.9418946 * __pyx_v_X12));

  /* "pyRing/eob_utils.pyx":480
 * 
 *     # (2,1) - TEOBResumSFits.c, line 2700
 *     cdef double c_3_A21_num = 0.23882 -2.2982*nu + 5.7022*nu2             # <<<<<<<<<<<<<<
 *     cdef double c_3_A21_den = 1 - 7.7463*nu + 27.266*nu2
 * 
*/
  __pyx_v_c_3_A21_num = ((0.23882 - (2.2982 * __pyx_v_nu)) + (5.7022 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":481
 *     # (2,1) - TEOBResumSFits.c, line 2700
 *     cdef double c_3_A21_num = 0.23882 -2.2982*nu + 5.7022*nu2
 *     cdef double c_3_A21_den = 1 - 7.7463*nu + 27.266*nu2             # <<<<<<<<<<<<<<
 * 
 *     # (3,3) - TEOBResumSFits.c, line 2591-2594
*/
  __pyx_v_c_3_A21_den = ((1.0 - (7.7463 * __pyx_v_nu)) + (27.266 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":484
 * 
 *     # (3,3) - TEOBResumSFits.c, line 2591-2594
 *     cdef double b_0_A33 = -0.41455 + 1.3225*nu, b_1_A33 = -0.3502608 + 1.587606*X12 -1.555325*X12_2             # <<<<<<<<<<<<<<
 * 
 *     # (3,2) - TEOBResumSFits.c, line 2716
*/
  __pyx_v_b_0_A33 = (-0.41455 + (1.3225 * __pyx_v_nu));
  __pyx_v_b_1_A33 = ((-0.3502608 + (1.587606 * __pyx_v_X12)) - (1.555325 * __pyx_v_X12_2));

  /* "pyRing/eob_utils.pyx":487
 * 
 *     # (3,2) - TEOBResumSFits.c, line 2716
 *     cdef double c_3_A32_num = 0.1877 -3.0017*nu + 19.501*nu2             # <<<<<<<<<<<<<<
 *     cdef double c_3_A32_den = 1 -1.8199*nu
 *     cdef double c_3_A32_exp = -703.67
*/
  __pyx_v_c_3_A32_num = ((0.1877 - (3.0017 * __pyx_v_nu)) + (19.501 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":488
 *     # (3,2) - TEOBResumSFits.c, line 2716
 *     cdef double c_3_A32_num = 0.1877 -3.0017*nu + 19.501*nu2
 *     cdef double c_3_A32_den = 1 -1.8199*nu             # <<<<<<<<<<<<<<
 *     cdef double c_3_A32_exp = -703.67
 * 
*/
  __pyx_v_c_3_A32_den = (1.0 - (1.8199 * __pyx_v_nu));

  /* "pyRing/eob_utils.pyx":489
 *     cdef double c_3_A32_num = 0.1877 -3.0017*nu + 19.501*nu2
 *     cdef double c_3_A32_den = 1 -1.8199*nu
 *     cdef double c_3_A32_exp = -703.67             # <<<<<<<<<<<<<<
 * 
 *     # (3,1) - TEOBResumSFits.c, line 2705
*/
  __pyx_v_c_3_A32_exp = -703.67;

  /* "pyRing/eob_utils.pyx":492
 * 
 *     # (3,1) - TEOBResumSFits.c, line 2705
 *     cdef double c_3_A31_num = 3.5042 -55.171*nu + 217*nu2             # <<<<<<<<<<<<<<
 *     cdef double c_3_A31_den = 1 -15.749*nu + 605.17*nu3
 * 
*/
  __pyx_v_c_3_A31_num = ((3.5042 - (55.171 * __pyx_v_nu)) + (217.0 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":493
 *     # (3,1) - TEOBResumSFits.c, line 2705
 *     cdef double c_3_A31_num = 3.5042 -55.171*nu + 217*nu2
 *     cdef double c_3_A31_den = 1 -15.749*nu + 605.17*nu3             # <<<<<<<<<<<<<<
 * 
 *     # (4,4) - TEOBResumSFits.c, line 2597-2599
*/
  __pyx_v_c_3_A31_den = ((1.0 - (15.749 * __pyx_v_nu)) + (605.17 * __pyx_v_nu3));

  /* "pyRing/eob_utils.pyx":496
 * 
 *     # (4,4) - TEOBResumSFits.c, line 2597-2599
 *     cdef double b_0_A44 = -0.41591 + 3.2099*nu, b_1_A44 = -9.614738*nu, b_2_A44 = 122.461125*nu             # <<<<<<<<<<<<<<
 * 
 *     # (4,3) - TEOBResumSFits.c, line 2741
*/
  __pyx_v_b_0_A44 = (-0.41591 + (3.2099 * __pyx_v_nu));
  __pyx_v_b_1_A44 = (-9.614738 * __pyx_v_nu);
  __pyx_v_b_2_A44 = (122.461125 * __pyx_v_nu);

  /* "pyRing/eob_utils.pyx":499
 * 
 *     # (4,3) - TEOBResumSFits.c, line 2741
 *     cdef double c_3_A43_num = -0.02833 + 2.8738*nu -31.503*nu2 + 93.513*nu3             # <<<<<<<<<<<<<<
 *     cdef double c_3_A43_den = 1 - 10.051*nu + 156.14*nu3
 * 
*/
  __pyx_v_c_3_A43_num = (((-0.02833 + (2.8738 * __pyx_v_nu)) - (31.503 * __pyx_v_nu2)) + (93.513 * __pyx_v_nu3));

  /* "pyRing/eob_utils.pyx":500
 *     # (4,3) - TEOBResumSFits.c, line 2741
 *     cdef double c_3_A43_num = -0.02833 + 2.8738*nu -31.503*nu2 + 93.513*nu3
 *     cdef double c_3_A43_den = 1 - 10.051*nu + 156.14*nu3             # <<<<<<<<<<<<<<
 * 
 *     # (4,2) - TEOBResumSFits.c, line 2731
*/
  __pyx_v_c_3_A43_den = ((1.0 - (10.051 * __pyx_v_nu)) + (156.14 * __pyx_v_nu3));

  /* "pyRing/eob_utils.pyx":503
 * 
 *     # (4,2) - TEOBResumSFits.c, line 2731
 *     cdef double c_3_A42_num = 0.27143 -2.2629*nu + 4.6249*nu2             # <<<<<<<<<<<<<<
 *     cdef double c_3_A42_den = 1 -7.6762*nu + 15.117*nu2
 * 
*/
  __pyx_v_c_3_A42_num = ((0.27143 - (2.2629 * __pyx_v_nu)) + (4.6249 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":504
 *     # (4,2) - TEOBResumSFits.c, line 2731
 *     cdef double c_3_A42_num = 0.27143 -2.2629*nu + 4.6249*nu2
 *     cdef double c_3_A42_den = 1 -7.6762*nu + 15.117*nu2             # <<<<<<<<<<<<<<
 * 
 *     # (4,1) - TEOBResumSFits.c, line 2721
*/
  __pyx_v_c_3_A42_den = ((1.0 - (7.6762 * __pyx_v_nu)) + (15.117 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":507
 * 
 *     # (4,1) - TEOBResumSFits.c, line 2721
 *     cdef double c_3_A41 = 11.47 + 10.936*nu             # <<<<<<<<<<<<<<
 * 
 *     # (5,5) - TEOBResumSFits.c, line 2604-2609
*/
  __pyx_v_c_3_A41 = (11.47 + (10.936 * __pyx_v_nu));

  /* "pyRing/eob_utils.pyx":510
 * 
 *     # (5,5) - TEOBResumSFits.c, line 2604-2609
 *     cdef double b_0_A55 = -0.5970347579708830 + 9.1187519178640084*nu, b_1_A55 = -2.055335 -0.585373*X12, b_2_A55 = -12.631409 + 19.271346*X12             # <<<<<<<<<<<<<<
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
 * 
*/
  __pyx_v_b_0_A55 = (-0.5970347579708830 + (9.1187519178640084 * __pyx_v_nu));
  __pyx_v_b_1_A55 = (-2.055335 - (0.585373 * __pyx_v_X12));
  __pyx_v_b_2_A55 = (-12.631409 + (19.271346 * __pyx_v_X12));

  /* "pyRing/eob_utils.pyx":514
 * 
 * 
 *     if ((l==2) and (m==2)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_A22 = b_0_A22 + b_1_A22*S_hat + b_2_A22*S_hat2 + b_3_A22*S_hat3    # eq. C107 of arXiv:2001.09082v2
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L4_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":516
 *     if ((l==2) and (m==2)):
 * 
 *         c_3_A22 = b_0_A22 + b_1_A22*S_hat + b_2_A22*S_hat2 + b_3_A22*S_hat3    # eq. C107 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 *         res     = c_3_A22
 * 
*/
    __pyx_v_c_3_A22 = (((__pyx_v_b_0_A22 + (__pyx_v_b_1_A22 * __pyx_v_S_hat)) + (__pyx_v_b_2_A22 * __pyx_v_S_hat2)) + (__pyx_v_b_3_A22 * __pyx_v_S_hat3));

    /* "pyRing/eob_utils.pyx":517
 * 
 *         c_3_A22 = b_0_A22 + b_1_A22*S_hat + b_2_A22*S_hat2 + b_3_A22*S_hat3    # eq. C107 of arXiv:2001.09082v2
 *         res     = c_3_A22             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==2) and (m==1)):
*/
    __pyx_v_res = __pyx_v_c_3_A22;

    /* "pyRing/eob_utils.pyx":514
 * 
 * 
 *     if ((l==2) and (m==2)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_A22 = b_0_A22 + b_1_A22*S_hat + b_2_A22*S_hat2 + b_3_A22*S_hat3    # eq. C107 of arXiv:2001.09082v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":519
 *         res     = c_3_A22
 * 
 *     elif ((l==2) and (m==1)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_A21 = c_3_A21_num/c_3_A21_den   # table IV of arXiv:1904.09550v2
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L6_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L6_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":521
 *     elif ((l==2) and (m==1)):
 * 
 *         c_3_A21 = c_3_A21_num/c_3_A21_den   # table IV of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 *         res     = c_3_A21
 * 
*/
    __pyx_v_c_3_A21 = (__pyx_v_c_3_A21_num / __pyx_v_c_3_A21_den);

    /* "pyRing/eob_utils.pyx":522
 * 
 *         c_3_A21 = c_3_A21_num/c_3_A21_den   # table IV of arXiv:1904.09550v2
 *         res     = c_3_A21             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==3) and (m==3)):
*/
    __pyx_v_res = __pyx_v_c_3_A21;

    /* "pyRing/eob_utils.pyx":519
 *         res     = c_3_A22
 * 
 *     elif ((l==2) and (m==1)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_A21 = c_3_A21_num/c_3_A21_den   # table IV of arXiv:1904.09550v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":524
 *         res     = c_3_A21
 * 
 *     elif ((l==3) and (m==3)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_A33 = b_0_A33 + b_1_A33*a12    # eq. C108 of arXiv:2001.09082v2
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L8_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L8_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":526
 *     elif ((l==3) and (m==3)):
 * 
 *         c_3_A33 = b_0_A33 + b_1_A33*a12    # eq. C108 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 *         res     = c_3_A33
 * 
*/
    __pyx_v_c_3_A33 = (__pyx_v_b_0_A33 + (__pyx_v_b_1_A33 * __pyx_v_a12));

    /* "pyRing/eob_utils.pyx":527
 * 
 *         c_3_A33 = b_0_A33 + b_1_A33*a12    # eq. C108 of arXiv:2001.09082v2
 *         res     = c_3_A33             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==3) and (m==2)):
*/
    __pyx_v_res = __pyx_v_c_3_A33;

    /* "pyRing/eob_utils.pyx":524
 *         res     = c_3_A21
 * 
 *     elif ((l==3) and (m==3)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_A33 = b_0_A33 + b_1_A33*a12    # eq. C108 of arXiv:2001.09082v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":529
 *         res     = c_3_A33
 * 
 *     elif ((l==3) and (m==2)):             # <<<<<<<<<<<<<<
 * 
 *         exp_A32 = exp(c_3_A32_exp * (nu-2./9.)*(nu-2./9.))   # table IV of arXiv:1904.09550v2
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L10_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L10_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":531
 *     elif ((l==3) and (m==2)):
 * 
 *         exp_A32 = exp(c_3_A32_exp * (nu-2./9.)*(nu-2./9.))   # table IV of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 *         c_3_A32 = c_3_A32_num/c_3_A32_den - exp_A32
 *         res     = c_3_A32
*/
    __pyx_v_exp_A32 = exp(((__pyx_v_c_3_A32_exp * (__pyx_v_nu - (2. / 9.))) * (__pyx_v_nu - (2. / 9.))));

    /* "pyRing/eob_utils.pyx":532
 * 
 *         exp_A32 = exp(c_3_A32_exp * (nu-2./9.)*(nu-2./9.))   # table IV of arXiv:1904.09550v2
 *         c_3_A32 = c_3_A32_num/c_3_A32_den - exp_A32             # <<<<<<<<<<<<<<
 *         res     = c_3_A32
 * 
*/
    __pyx_v_c_3_A32 = ((__pyx_v_c_3_A32_num / __pyx_v_c_3_A32_den) - __pyx_v_exp_A32);

    /* "pyRing/eob_utils.pyx":533
 *         exp_A32 = exp(c_3_A32_exp * (nu-2./9.)*(nu-2./9.))   # table IV of arXiv:1904.09550v2
 *         c_3_A32 = c_3_A32_num/c_3_A32_den - exp_A32
 *         res     = c_3_A32             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==3) and (m==1)):
*/
    __pyx_v_res = __pyx_v_c_3_A32;

    /* "pyRing/eob_utils.pyx":529
 *         res     = c_3_A33
 * 
 *     elif ((l==3) and (m==2)):             # <<<<<<<<<<<<<<
 * 
 *         exp_A32 = exp(c_3_A32_exp * (nu-2./9.)*(nu-2./9.))   # table IV of arXiv:1904.09550v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":535
 *         res     = c_3_A32
 * 
 *     elif ((l==3) and (m==1)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_A31 = c_3_A31_num/c_3_A31_den   # table IV of arXiv:1904.09550v2
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L12_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L12_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":537
 *     elif ((l==3) and (m==1)):
 * 
 *         c_3_A31 = c_3_A31_num/c_3_A31_den   # table IV of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 *         res     = c_3_A31
 * 
*/
    __pyx_v_c_3_A31 = (__pyx_v_c_3_A31_num / __pyx_v_c_3_A31_den);

    /* "pyRing/eob_utils.pyx":538
 * 
 *         c_3_A31 = c_3_A31_num/c_3_A31_den   # table IV of arXiv:1904.09550v2
 *         res     = c_3_A31             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==4)):
*/
    __pyx_v_res = __pyx_v_c_3_A31;

    /* "pyRing/eob_utils.pyx":535
 *         res     = c_3_A32
 * 
 *     elif ((l==3) and (m==1)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_A31 = c_3_A31_num/c_3_A31_den   # table IV of arXiv:1904.09550v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":540
 *         res     = c_3_A31
 * 
 *     elif ((l==4) and (m==4)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_A44 = b_0_A44 + b_1_A44*S_hat + b_2_A44*S_hat2    # eq. C110 of arXiv:2001.09082v2
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L14_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 4);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L14_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":542
 *     elif ((l==4) and (m==4)):
 * 
 *         c_3_A44 = b_0_A44 + b_1_A44*S_hat + b_2_A44*S_hat2    # eq. C110 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 *         res     = c_3_A44
 * 
*/
    __pyx_v_c_3_A44 = ((__pyx_v_b_0_A44 + (__pyx_v_b_1_A44 * __pyx_v_S_hat)) + (__pyx_v_b_2_A44 * __pyx_v_S_hat2));

    /* "pyRing/eob_utils.pyx":543
 * 
 *         c_3_A44 = b_0_A44 + b_1_A44*S_hat + b_2_A44*S_hat2    # eq. C110 of arXiv:2001.09082v2
 *         res     = c_3_A44             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==3)):
*/
    __pyx_v_res = __pyx_v_c_3_A44;

    /* "pyRing/eob_utils.pyx":540
 *         res     = c_3_A31
 * 
 *     elif ((l==4) and (m==4)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_A44 = b_0_A44 + b_1_A44*S_hat + b_2_A44*S_hat2    # eq. C110 of arXiv:2001.09082v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":545
 *         res     = c_3_A44
 * 
 *     elif ((l==4) and (m==3)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_A43 = c_3_A43_num/c_3_A43_den   # table IV of arXiv:1904.09550v2
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L16_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L16_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":547
 *     elif ((l==4) and (m==3)):
 * 
 *         c_3_A43 = c_3_A43_num/c_3_A43_den   # table IV of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 *         res     = c_3_A43
 * 
*/
    __pyx_v_c_3_A43 = (__pyx_v_c_3_A43_num / __pyx_v_c_3_A43_den);

    /* "pyRing/eob_utils.pyx":548
 * 
 *         c_3_A43 = c_3_A43_num/c_3_A43_den   # table IV of arXiv:1904.09550v2
 *         res     = c_3_A43             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==2)):
*/
    __pyx_v_res = __pyx_v_c_3_A43;

    /* "pyRing/eob_utils.pyx":545
 *         res     = c_3_A44
 * 
 *     elif ((l==4) and (m==3)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_A43 = c_3_A43_num/c_3_A43_den   # table IV of arXiv:1904.09550v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":550
 *         res     = c_3_A43
 * 
 *     elif ((l==4) and (m==2)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_A42 = c_3_A42_num/c_3_A42_den   # table IV of arXiv:1904.09550v2
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L18_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L18_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":552
 *     elif ((l==4) and (m==2)):
 * 
 *         c_3_A42 = c_3_A42_num/c_3_A42_den   # table IV of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 *         res     = c_3_A42
 * 
*/
    __pyx_v_c_3_A42 = (__pyx_v_c_3_A42_num / __pyx_v_c_3_A42_den);

    /* "pyRing/eob_utils.pyx":553
 * 
 *         c_3_A42 = c_3_A42_num/c_3_A42_den   # table IV of arXiv:1904.09550v2
 *         res     = c_3_A42             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==1)):
*/
    __pyx_v_res = __pyx_v_c_3_A42;

    /* "pyRing/eob_utils.pyx":550
 *         res     = c_3_A43
 * 
 *     elif ((l==4) and (m==2)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_A42 = c_3_A42_num/c_3_A42_den   # table IV of arXiv:1904.09550v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":555
 *         res     = c_3_A42
 * 
 *     elif ((l==4) and (m==1)):             # <<<<<<<<<<<<<<
 * 
 *         res = c_3_A41   # table IV of arXiv:1904.09550v2
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L20_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L20_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":557
 *     elif ((l==4) and (m==1)):
 * 
 *         res = c_3_A41   # table IV of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==5) and (m==5)):
*/
    __pyx_v_res = __pyx_v_c_3_A41;

    /* "pyRing/eob_utils.pyx":555
 *         res     = c_3_A42
 * 
 *     elif ((l==4) and (m==1)):             # <<<<<<<<<<<<<<
 * 
 *         res = c_3_A41   # table IV of arXiv:1904.09550v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":559
 *         res = c_3_A41   # table IV of arXiv:1904.09550v2
 * 
 *     elif ((l==5) and (m==5)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_A55 = b_0_A55 + b_1_A55*a12 + b_2_A55*a12_2    # eq. C111 of arXiv:2001.09082v2
*/
  __pyx_t_2 = (__pyx_v_l == 5);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L22_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 5);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L22_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":561
 *     elif ((l==5) and (m==5)):
 * 
 *         c_3_A55 = b_0_A55 + b_1_A55*a12 + b_2_A55*a12_2    # eq. C111 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 *         res     = c_3_A55
 * 
*/
    __pyx_v_c_3_A55 = ((__pyx_v_b_0_A55 + (__pyx_v_b_1_A55 * __pyx_v_a12)) + (__pyx_v_b_2_A55 * __pyx_v_a12_2));

    /* "pyRing/eob_utils.pyx":562
 * 
 *         c_3_A55 = b_0_A55 + b_1_A55*a12 + b_2_A55*a12_2    # eq. C111 of arXiv:2001.09082v2
 *         res     = c_3_A55             # <<<<<<<<<<<<<<
 * 
 *     return res
*/
    __pyx_v_res = __pyx_v_c_3_A55;

    /* "pyRing/eob_utils.pyx":559
 *         res = c_3_A41   # table IV of arXiv:1904.09550v2
 * 
 *     elif ((l==5) and (m==5)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_A55 = b_0_A55 + b_1_A55*a12 + b_2_A55*a12_2    # eq. C111 of arXiv:2001.09082v2
*/
  }
  __pyx_L3:;

  /* "pyRing/eob_utils.pyx":564
 *         res     = c_3_A55
 * 
 *     return res             # <<<<<<<<<<<<<<
 * 
 * 
*/
  __pyx_r = __pyx_v_res;
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":460
 * #############################################################
 * 
 * cdef double _c3_A(double nu, double X12, double S_hat, double a12, int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function returning the coefficient c3_A of the ringdown model in section V.A of arXiv:1904.09550v2.
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "pyRing/eob_utils.pyx":567
 * 
 * 
 * cdef double _c3_phi(double nu, double X12, double S_hat, int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function returning the coefficient c3_phi of the ringdown model in section V.A of arXiv:1904.09550v2.
*/

static double __pyx_f_6pyRing_9eob_utils__c3_phi(double __pyx_v_nu, double __pyx_v_X12, double __pyx_v_S_hat, int __pyx_v_l, int __pyx_v_m) {
  double __pyx_v_res;
  double __pyx_v_c_3_phi22;
  double __pyx_v_c_3_phi21;
  double __pyx_v_c_3_phi33;
  double __pyx_v_c_3_phi32;
  double __pyx_v_c_3_phi44;
  double __pyx_v_c_3_phi43;
  double __pyx_v_c_3_phi42;
  double __pyx_v_c_3_phi55;
  double __pyx_v_nu2;
  CYTHON_UNUSED double __pyx_v_nu3;
  double __pyx_v_S_hat2;
  double __pyx_v_S_hat3;
  double __pyx_v_S_hat4;
  CYTHON_UNUSED double __pyx_v_X12_2;
  double __pyx_v_nu_d;
  double __pyx_v_nu_d2;
  double __pyx_v_b_0_phi22;
  double __pyx_v_b_1_phi22;
  double __pyx_v_b_2_phi22;
  double __pyx_v_b_3_phi22;
  double __pyx_v_b_4_phi22;
  double __pyx_v_c_3_phi21_num;
  double __pyx_v_c_3_phi21_den;
  double __pyx_v_b_0_phi33;
  double __pyx_v_c_3_phi32_num;
  double __pyx_v_c_3_phi32_den;
  double __pyx_v_c_3_phi31_num;
  double __pyx_v_c_3_phi31_den;
  double __pyx_v_c_3_phi31_num_nu;
  double __pyx_v_c_3_phi31_den_nu;
  double __pyx_v_b_0_phi44;
  double __pyx_v_c_3_phi43_num;
  double __pyx_v_c_3_phi43_den;
  double __pyx_v_c_3_phi42_num;
  double __pyx_v_c_3_phi42_den;
  double __pyx_v_c_3_phi41;
  double __pyx_v_c_3_phi41_nu;
  double __pyx_v_b_0_phi55;
  double __pyx_v_b_1_phi55;
  double __pyx_v_b_2_phi55;
  double __pyx_v_c_3_phi31;
  double __pyx_v_c_3_phi31_nu;
  double __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;

  /* "pyRing/eob_utils.pyx":579
 *     """
 * 
 *     cdef double res = 0., c_3_phi22, c_3_phi21, c_3_phi33, c_3_phi32, c_3_phi44, c_3_phi43, c_3_phi42, c_3_phi55             # <<<<<<<<<<<<<<
 *     cdef double nu2 = nu*nu, nu3 = nu2*nu, S_hat2 = S_hat*S_hat, S_hat3 = S_hat2*S_hat, S_hat4 = S_hat3*S_hat, X12_2 = X12*X12
 *     cdef double nu_d = 0.08271, nu_d2 = nu_d*nu_d   # TEOBResumSFits.c, line 2711
*/
  __pyx_v_res = 0.;

  /* "pyRing/eob_utils.pyx":580
 * 
 *     cdef double res = 0., c_3_phi22, c_3_phi21, c_3_phi33, c_3_phi32, c_3_phi44, c_3_phi43, c_3_phi42, c_3_phi55
 *     cdef double nu2 = nu*nu, nu3 = nu2*nu, S_hat2 = S_hat*S_hat, S_hat3 = S_hat2*S_hat, S_hat4 = S_hat3*S_hat, X12_2 = X12*X12             # <<<<<<<<<<<<<<
 *     cdef double nu_d = 0.08271, nu_d2 = nu_d*nu_d   # TEOBResumSFits.c, line 2711
 * 
*/
  __pyx_v_nu2 = (__pyx_v_nu * __pyx_v_nu);
  __pyx_v_nu3 = (__pyx_v_nu2 * __pyx_v_nu);
  __pyx_v_S_hat2 = (__pyx_v_S_hat * __pyx_v_S_hat);
  __pyx_v_S_hat3 = (__pyx_v_S_hat2 * __pyx_v_S_hat);
  __pyx_v_S_hat4 = (__pyx_v_S_hat3 * __pyx_v_S_hat);
  __pyx_v_X12_2 = (__pyx_v_X12 * __pyx_v_X12);

  /* "pyRing/eob_utils.pyx":581
 *     cdef double res = 0., c_3_phi22, c_3_phi21, c_3_phi33, c_3_phi32, c_3_phi44, c_3_phi43, c_3_phi42, c_3_phi55
 *     cdef double nu2 = nu*nu, nu3 = nu2*nu, S_hat2 = S_hat*S_hat, S_hat3 = S_hat2*S_hat, S_hat4 = S_hat3*S_hat, X12_2 = X12*X12
 *     cdef double nu_d = 0.08271, nu_d2 = nu_d*nu_d   # TEOBResumSFits.c, line 2711             # <<<<<<<<<<<<<<
 * 
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
*/
  __pyx_v_nu_d = 0.08271;
  __pyx_v_nu_d2 = (__pyx_v_nu_d * __pyx_v_nu_d);

  /* "pyRing/eob_utils.pyx":585
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
 *     # (2,2) - TEOBResumSFits.c, line 2613-2617
 *     cdef double b_0_phi22 = 3.8436 + 0.71565*nu, b_1_phi22 = 5.12794 -1.323643*X12, b_2_phi22 = 9.9136 -3.555007*X12, b_3_phi22 = -4.1075 + 7.011267*X12, b_4_phi22 = -31.5562 + 32.737824*X12             # <<<<<<<<<<<<<<
 * 
 *     # (2,1) - TEOBResumSFits.c, line 2701
*/
  __pyx_v_b_0_phi22 = (3.8436 + (0.71565 * __pyx_v_nu));
  __pyx_v_b_1_phi22 = (5.12794 - (1.323643 * __pyx_v_X12));
  __pyx_v_b_2_phi22 = (9.9136 - (3.555007 * __pyx_v_X12));
  __pyx_v_b_3_phi22 = (-4.1075 + (7.011267 * __pyx_v_X12));
  __pyx_v_b_4_phi22 = (-31.5562 + (32.737824 * __pyx_v_X12));

  /* "pyRing/eob_utils.pyx":588
 * 
 *     # (2,1) - TEOBResumSFits.c, line 2701
 *     cdef double c_3_phi21_num = 2.6269 - 37.677*nu + 181.61*nu2             # <<<<<<<<<<<<<<
 *     cdef double c_3_phi21_den = 1 - 16.082*nu + 89.836*nu2
 * 
*/
  __pyx_v_c_3_phi21_num = ((2.6269 - (37.677 * __pyx_v_nu)) + (181.61 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":589
 *     # (2,1) - TEOBResumSFits.c, line 2701
 *     cdef double c_3_phi21_num = 2.6269 - 37.677*nu + 181.61*nu2
 *     cdef double c_3_phi21_den = 1 - 16.082*nu + 89.836*nu2             # <<<<<<<<<<<<<<
 * 
 *     # (3,3) - TEOBResumSFits.c, line 2632
*/
  __pyx_v_c_3_phi21_den = ((1.0 - (16.082 * __pyx_v_nu)) + (89.836 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":592
 * 
 *     # (3,3) - TEOBResumSFits.c, line 2632
 *     cdef double b_0_phi33 = 3.0611 -6.1597*nu             # <<<<<<<<<<<<<<
 * 
 *     # (3,2) - TEOBResumSFits.c, line 2717
*/
  __pyx_v_b_0_phi33 = (3.0611 - (6.1597 * __pyx_v_nu));

  /* "pyRing/eob_utils.pyx":595
 * 
 *     # (3,2) - TEOBResumSFits.c, line 2717
 *     cdef double c_3_phi32_num = 0.90944 - 1.8924*nu + 3.6848*nu2             # <<<<<<<<<<<<<<
 *     cdef double c_3_phi32_den = 1 - 8.9739*nu + 21.024*nu2
 * 
*/
  __pyx_v_c_3_phi32_num = ((0.90944 - (1.8924 * __pyx_v_nu)) + (3.6848 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":596
 *     # (3,2) - TEOBResumSFits.c, line 2717
 *     cdef double c_3_phi32_num = 0.90944 - 1.8924*nu + 3.6848*nu2
 *     cdef double c_3_phi32_den = 1 - 8.9739*nu + 21.024*nu2             # <<<<<<<<<<<<<<
 * 
 *     # (3,1) - TEOBResumSFits.c, line 2708-2712
*/
  __pyx_v_c_3_phi32_den = ((1.0 - (8.9739 * __pyx_v_nu)) + (21.024 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":599
 * 
 *     # (3,1) - TEOBResumSFits.c, line 2708-2712
 *     cdef double c_3_phi31_num = -6.1719 + 29.617*nu + 254.24*nu2             # <<<<<<<<<<<<<<
 *     cdef double c_3_phi31_den = 1 - 1.5435*nu
 *     cdef double c_3_phi31_num_nu = -6.1719 + 29.617*nu_d + 254.24*nu_d2
*/
  __pyx_v_c_3_phi31_num = ((-6.1719 + (29.617 * __pyx_v_nu)) + (254.24 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":600
 *     # (3,1) - TEOBResumSFits.c, line 2708-2712
 *     cdef double c_3_phi31_num = -6.1719 + 29.617*nu + 254.24*nu2
 *     cdef double c_3_phi31_den = 1 - 1.5435*nu             # <<<<<<<<<<<<<<
 *     cdef double c_3_phi31_num_nu = -6.1719 + 29.617*nu_d + 254.24*nu_d2
 *     cdef double c_3_phi31_den_nu = 1 - 1.5435*nu_d
*/
  __pyx_v_c_3_phi31_den = (1.0 - (1.5435 * __pyx_v_nu));

  /* "pyRing/eob_utils.pyx":601
 *     cdef double c_3_phi31_num = -6.1719 + 29.617*nu + 254.24*nu2
 *     cdef double c_3_phi31_den = 1 - 1.5435*nu
 *     cdef double c_3_phi31_num_nu = -6.1719 + 29.617*nu_d + 254.24*nu_d2             # <<<<<<<<<<<<<<
 *     cdef double c_3_phi31_den_nu = 1 - 1.5435*nu_d
 * 
*/
  __pyx_v_c_3_phi31_num_nu = ((-6.1719 + (29.617 * __pyx_v_nu_d)) + (254.24 * __pyx_v_nu_d2));

  /* "pyRing/eob_utils.pyx":602
 *     cdef double c_3_phi31_den = 1 - 1.5435*nu
 *     cdef double c_3_phi31_num_nu = -6.1719 + 29.617*nu_d + 254.24*nu_d2
 *     cdef double c_3_phi31_den_nu = 1 - 1.5435*nu_d             # <<<<<<<<<<<<<<
 * 
 *     # (4,4) - TEOBResumSFits.c, line 2637
*/
  __pyx_v_c_3_phi31_den_nu = (1.0 - (1.5435 * __pyx_v_nu_d));

  /* "pyRing/eob_utils.pyx":605
 * 
 *     # (4,4) - TEOBResumSFits.c, line 2637
 *     cdef double b_0_phi44 = (3.6662-30.072*nu + 76.371*nu2)/(1 - 3.5522*nu)             # <<<<<<<<<<<<<<
 * 
 *     # (4,3) - TEOBResumSFits.c, line 2742
*/
  __pyx_v_b_0_phi44 = (((3.6662 - (30.072 * __pyx_v_nu)) + (76.371 * __pyx_v_nu2)) / (1.0 - (3.5522 * __pyx_v_nu)));

  /* "pyRing/eob_utils.pyx":608
 * 
 *     # (4,3) - TEOBResumSFits.c, line 2742
 *     cdef double c_3_phi43_num = 2.284 - 23.817*nu + 70.952*nu2             # <<<<<<<<<<<<<<
 *     cdef double c_3_phi43_den = 1 - 10.909*nu + 30.723*nu2
 * 
*/
  __pyx_v_c_3_phi43_num = ((2.284 - (23.817 * __pyx_v_nu)) + (70.952 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":609
 *     # (4,3) - TEOBResumSFits.c, line 2742
 *     cdef double c_3_phi43_num = 2.284 - 23.817*nu + 70.952*nu2
 *     cdef double c_3_phi43_den = 1 - 10.909*nu + 30.723*nu2             # <<<<<<<<<<<<<<
 * 
 *     # (4,2) - TEOBResumSFits.c, line 2732
*/
  __pyx_v_c_3_phi43_den = ((1.0 - (10.909 * __pyx_v_nu)) + (30.723 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":612
 * 
 *     # (4,2) - TEOBResumSFits.c, line 2732
 *     cdef double c_3_phi42_num = 2.2065 - 17.629*nu + 65.372*nu2             # <<<<<<<<<<<<<<
 *     cdef double c_3_phi42_den = 1 - 4.7744*nu + 3.1876*nu2
 * 
*/
  __pyx_v_c_3_phi42_num = ((2.2065 - (17.629 * __pyx_v_nu)) + (65.372 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":613
 *     # (4,2) - TEOBResumSFits.c, line 2732
 *     cdef double c_3_phi42_num = 2.2065 - 17.629*nu + 65.372*nu2
 *     cdef double c_3_phi42_den = 1 - 4.7744*nu + 3.1876*nu2             # <<<<<<<<<<<<<<
 * 
 *     # (4,1) - TEOBResumSFits.c, line 2721-2727
*/
  __pyx_v_c_3_phi42_den = ((1.0 - (4.7744 * __pyx_v_nu)) + (3.1876 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":616
 * 
 *     # (4,1) - TEOBResumSFits.c, line 2721-2727
 *     cdef double c_3_phi41    = -6.0286 + 46.632*nu             # <<<<<<<<<<<<<<
 *     cdef double c_3_phi41_nu = -2.1747
 * 
*/
  __pyx_v_c_3_phi41 = (-6.0286 + (46.632 * __pyx_v_nu));

  /* "pyRing/eob_utils.pyx":617
 *     # (4,1) - TEOBResumSFits.c, line 2721-2727
 *     cdef double c_3_phi41    = -6.0286 + 46.632*nu
 *     cdef double c_3_phi41_nu = -2.1747             # <<<<<<<<<<<<<<
 * 
 *     # (5,5) - TEOBResumSFits.c, line 2642-2647
*/
  __pyx_v_c_3_phi41_nu = -2.1747;

  /* "pyRing/eob_utils.pyx":620
 * 
 *     # (5,5) - TEOBResumSFits.c, line 2642-2647
 *     cdef double b_0_phi55 = 4.226238 -59.69284*nu + 373.312597*nu2, b_1_phi55 = -2.687133 + 4.873750*X12, b_2_phi55 = -14.629684 + 19.696954*X12             # <<<<<<<<<<<<<<
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
 * 
*/
  __pyx_v_b_0_phi55 = ((4.226238 - (59.69284 * __pyx_v_nu)) + (373.312597 * __pyx_v_nu2));
  __pyx_v_b_1_phi55 = (-2.687133 + (4.873750 * __pyx_v_X12));
  __pyx_v_b_2_phi55 = (-14.629684 + (19.696954 * __pyx_v_X12));

  /* "pyRing/eob_utils.pyx":624
 * 
 * 
 *     if ((l==2) and (m==2)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_phi22 = b_0_phi22 + b_1_phi22*S_hat + b_2_phi22*S_hat2 + b_3_phi22*S_hat3 + b_4_phi22*S_hat4    # eq. C107 of arXiv:2001.09082v2
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L4_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":626
 *     if ((l==2) and (m==2)):
 * 
 *         c_3_phi22 = b_0_phi22 + b_1_phi22*S_hat + b_2_phi22*S_hat2 + b_3_phi22*S_hat3 + b_4_phi22*S_hat4    # eq. C107 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 *         res       = c_3_phi22
 * 
*/
    __pyx_v_c_3_phi22 = ((((__pyx_v_b_0_phi22 + (__pyx_v_b_1_phi22 * __pyx_v_S_hat)) + (__pyx_v_b_2_phi22 * __pyx_v_S_hat2)) + (__pyx_v_b_3_phi22 * __pyx_v_S_hat3)) + (__pyx_v_b_4_phi22 * __pyx_v_S_hat4));

    /* "pyRing/eob_utils.pyx":627
 * 
 *         c_3_phi22 = b_0_phi22 + b_1_phi22*S_hat + b_2_phi22*S_hat2 + b_3_phi22*S_hat3 + b_4_phi22*S_hat4    # eq. C107 of arXiv:2001.09082v2
 *         res       = c_3_phi22             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==2) and (m==1)):
*/
    __pyx_v_res = __pyx_v_c_3_phi22;

    /* "pyRing/eob_utils.pyx":624
 * 
 * 
 *     if ((l==2) and (m==2)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_phi22 = b_0_phi22 + b_1_phi22*S_hat + b_2_phi22*S_hat2 + b_3_phi22*S_hat3 + b_4_phi22*S_hat4    # eq. C107 of arXiv:2001.09082v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":629
 *         res       = c_3_phi22
 * 
 *     elif ((l==2) and (m==1)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_phi21 = c_3_phi21_num/c_3_phi21_den   # table IV of arXiv:1904.09550v2
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L6_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L6_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":631
 *     elif ((l==2) and (m==1)):
 * 
 *         c_3_phi21 = c_3_phi21_num/c_3_phi21_den   # table IV of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 *         res       = c_3_phi21
 * 
*/
    __pyx_v_c_3_phi21 = (__pyx_v_c_3_phi21_num / __pyx_v_c_3_phi21_den);

    /* "pyRing/eob_utils.pyx":632
 * 
 *         c_3_phi21 = c_3_phi21_num/c_3_phi21_den   # table IV of arXiv:1904.09550v2
 *         res       = c_3_phi21             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==3) and (m==3)):
*/
    __pyx_v_res = __pyx_v_c_3_phi21;

    /* "pyRing/eob_utils.pyx":629
 *         res       = c_3_phi22
 * 
 *     elif ((l==2) and (m==1)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_phi21 = c_3_phi21_num/c_3_phi21_den   # table IV of arXiv:1904.09550v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":634
 *         res       = c_3_phi21
 * 
 *     elif ((l==3) and (m==3)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_phi33 = b_0_phi33    # TEOBResumSFits.c, line 2632
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L8_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L8_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":636
 *     elif ((l==3) and (m==3)):
 * 
 *         c_3_phi33 = b_0_phi33    # TEOBResumSFits.c, line 2632             # <<<<<<<<<<<<<<
 *         res       = c_3_phi33
 * 
*/
    __pyx_v_c_3_phi33 = __pyx_v_b_0_phi33;

    /* "pyRing/eob_utils.pyx":637
 * 
 *         c_3_phi33 = b_0_phi33    # TEOBResumSFits.c, line 2632
 *         res       = c_3_phi33             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==3) and (m==2)):
*/
    __pyx_v_res = __pyx_v_c_3_phi33;

    /* "pyRing/eob_utils.pyx":634
 *         res       = c_3_phi21
 * 
 *     elif ((l==3) and (m==3)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_phi33 = b_0_phi33    # TEOBResumSFits.c, line 2632
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":639
 *         res       = c_3_phi33
 * 
 *     elif ((l==3) and (m==2)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_phi32 = c_3_phi32_num/c_3_phi32_den   # table IV of arXiv:1904.09550v2
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L10_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L10_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":641
 *     elif ((l==3) and (m==2)):
 * 
 *         c_3_phi32 = c_3_phi32_num/c_3_phi32_den   # table IV of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 *         res       = c_3_phi32
 * 
*/
    __pyx_v_c_3_phi32 = (__pyx_v_c_3_phi32_num / __pyx_v_c_3_phi32_den);

    /* "pyRing/eob_utils.pyx":642
 * 
 *         c_3_phi32 = c_3_phi32_num/c_3_phi32_den   # table IV of arXiv:1904.09550v2
 *         res       = c_3_phi32             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==3) and (m==1)):
*/
    __pyx_v_res = __pyx_v_c_3_phi32;

    /* "pyRing/eob_utils.pyx":639
 *         res       = c_3_phi33
 * 
 *     elif ((l==3) and (m==2)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_phi32 = c_3_phi32_num/c_3_phi32_den   # table IV of arXiv:1904.09550v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":644
 *         res       = c_3_phi32
 * 
 *     elif ((l==3) and (m==1)):             # <<<<<<<<<<<<<<
 * 
 *         if (nu>0.08271):
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L12_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L12_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":646
 *     elif ((l==3) and (m==1)):
 * 
 *         if (nu>0.08271):             # <<<<<<<<<<<<<<
 *             c_3_phi31 = c_3_phi31_num/c_3_phi31_den   # table IV of arXiv:1904.09550v2
 *             res       = c_3_phi31
*/
    __pyx_t_1 = (__pyx_v_nu > 0.08271);
    if (__pyx_t_1) {

      /* "pyRing/eob_utils.pyx":647
 * 
 *         if (nu>0.08271):
 *             c_3_phi31 = c_3_phi31_num/c_3_phi31_den   # table IV of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 *             res       = c_3_phi31
 * 
*/
      __pyx_v_c_3_phi31 = (__pyx_v_c_3_phi31_num / __pyx_v_c_3_phi31_den);

      /* "pyRing/eob_utils.pyx":648
 *         if (nu>0.08271):
 *             c_3_phi31 = c_3_phi31_num/c_3_phi31_den   # table IV of arXiv:1904.09550v2
 *             res       = c_3_phi31             # <<<<<<<<<<<<<<
 * 
 *         else:
*/
      __pyx_v_res = __pyx_v_c_3_phi31;

      /* "pyRing/eob_utils.pyx":646
 *     elif ((l==3) and (m==1)):
 * 
 *         if (nu>0.08271):             # <<<<<<<<<<<<<<
 *             c_3_phi31 = c_3_phi31_num/c_3_phi31_den   # table IV of arXiv:1904.09550v2
 *             res       = c_3_phi31
*/
      goto __pyx_L14;
    }

    /* "pyRing/eob_utils.pyx":651
 * 
 *         else:
 *             c_3_phi31_nu = c_3_phi31_num_nu/c_3_phi31_den_nu             # <<<<<<<<<<<<<<
 *             res          = c_3_phi31_nu
 * 
*/
    /*else*/ {
      __pyx_v_c_3_phi31_nu = (__pyx_v_c_3_phi31_num_nu / __pyx_v_c_3_phi31_den_nu);

      /* "pyRing/eob_utils.pyx":652
 *         else:
 *             c_3_phi31_nu = c_3_phi31_num_nu/c_3_phi31_den_nu
 *             res          = c_3_phi31_nu             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==4)):
*/
      __pyx_v_res = __pyx_v_c_3_phi31_nu;
    }
    __pyx_L14:;

    /* "pyRing/eob_utils.pyx":644
 *         res       = c_3_phi32
 * 
 *     elif ((l==3) and (m==1)):             # <<<<<<<<<<<<<<
 * 
 *         if (nu>0.08271):
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":654
 *             res          = c_3_phi31_nu
 * 
 *     elif ((l==4) and (m==4)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_phi44 = b_0_phi44    # TEOBResumSFits.c, line 2637
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L15_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 4);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L15_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":656
 *     elif ((l==4) and (m==4)):
 * 
 *         c_3_phi44 = b_0_phi44    # TEOBResumSFits.c, line 2637             # <<<<<<<<<<<<<<
 *         res       = c_3_phi44
 * 
*/
    __pyx_v_c_3_phi44 = __pyx_v_b_0_phi44;

    /* "pyRing/eob_utils.pyx":657
 * 
 *         c_3_phi44 = b_0_phi44    # TEOBResumSFits.c, line 2637
 *         res       = c_3_phi44             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==3)):
*/
    __pyx_v_res = __pyx_v_c_3_phi44;

    /* "pyRing/eob_utils.pyx":654
 *             res          = c_3_phi31_nu
 * 
 *     elif ((l==4) and (m==4)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_phi44 = b_0_phi44    # TEOBResumSFits.c, line 2637
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":659
 *         res       = c_3_phi44
 * 
 *     elif ((l==4) and (m==3)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_phi43 = c_3_phi43_num/c_3_phi43_den   # table IV of arXiv:1904.09550v2
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L17_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L17_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":661
 *     elif ((l==4) and (m==3)):
 * 
 *         c_3_phi43 = c_3_phi43_num/c_3_phi43_den   # table IV of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 *         res       = c_3_phi43
 * 
*/
    __pyx_v_c_3_phi43 = (__pyx_v_c_3_phi43_num / __pyx_v_c_3_phi43_den);

    /* "pyRing/eob_utils.pyx":662
 * 
 *         c_3_phi43 = c_3_phi43_num/c_3_phi43_den   # table IV of arXiv:1904.09550v2
 *         res       = c_3_phi43             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==2)):
*/
    __pyx_v_res = __pyx_v_c_3_phi43;

    /* "pyRing/eob_utils.pyx":659
 *         res       = c_3_phi44
 * 
 *     elif ((l==4) and (m==3)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_phi43 = c_3_phi43_num/c_3_phi43_den   # table IV of arXiv:1904.09550v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":664
 *         res       = c_3_phi43
 * 
 *     elif ((l==4) and (m==2)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_phi42 = c_3_phi42_num/c_3_phi42_den   # table IV of arXiv:1904.09550v2
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L19_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L19_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":666
 *     elif ((l==4) and (m==2)):
 * 
 *         c_3_phi42 = c_3_phi42_num/c_3_phi42_den   # table IV of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 *         res       = c_3_phi42
 * 
*/
    __pyx_v_c_3_phi42 = (__pyx_v_c_3_phi42_num / __pyx_v_c_3_phi42_den);

    /* "pyRing/eob_utils.pyx":667
 * 
 *         c_3_phi42 = c_3_phi42_num/c_3_phi42_den   # table IV of arXiv:1904.09550v2
 *         res       = c_3_phi42             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==1)):
*/
    __pyx_v_res = __pyx_v_c_3_phi42;

    /* "pyRing/eob_utils.pyx":664
 *         res       = c_3_phi43
 * 
 *     elif ((l==4) and (m==2)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_phi42 = c_3_phi42_num/c_3_phi42_den   # table IV of arXiv:1904.09550v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":669
 *         res       = c_3_phi42
 * 
 *     elif ((l==4) and (m==1)):             # <<<<<<<<<<<<<<
 * 
 *         if (nu>=10./121.):
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L21_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L21_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":671
 *     elif ((l==4) and (m==1)):
 * 
 *         if (nu>=10./121.):             # <<<<<<<<<<<<<<
 *             res = c_3_phi41   # table IV of arXiv:1904.09550v2
 * 
*/
    __pyx_t_1 = (__pyx_v_nu >= (10. / 121.));
    if (__pyx_t_1) {

      /* "pyRing/eob_utils.pyx":672
 * 
 *         if (nu>=10./121.):
 *             res = c_3_phi41   # table IV of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 * 
 *         else:   res = c_3_phi41_nu
*/
      __pyx_v_res = __pyx_v_c_3_phi41;

      /* "pyRing/eob_utils.pyx":671
 *     elif ((l==4) and (m==1)):
 * 
 *         if (nu>=10./121.):             # <<<<<<<<<<<<<<
 *             res = c_3_phi41   # table IV of arXiv:1904.09550v2
 * 
*/
      goto __pyx_L23;
    }

    /* "pyRing/eob_utils.pyx":674
 *             res = c_3_phi41   # table IV of arXiv:1904.09550v2
 * 
 *         else:   res = c_3_phi41_nu             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==5) and (m==5)):
*/
    /*else*/ {
      __pyx_v_res = __pyx_v_c_3_phi41_nu;
    }
    __pyx_L23:;

    /* "pyRing/eob_utils.pyx":669
 *         res       = c_3_phi42
 * 
 *     elif ((l==4) and (m==1)):             # <<<<<<<<<<<<<<
 * 
 *         if (nu>=10./121.):
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":676
 *         else:   res = c_3_phi41_nu
 * 
 *     elif ((l==5) and (m==5)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_phi55 = b_0_phi55 + b_1_phi55*S_hat + b_2_phi55*S_hat2    # eq. C111 of arXiv:2001.09082v2
*/
  __pyx_t_2 = (__pyx_v_l == 5);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L24_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 5);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L24_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":678
 *     elif ((l==5) and (m==5)):
 * 
 *         c_3_phi55 = b_0_phi55 + b_1_phi55*S_hat + b_2_phi55*S_hat2    # eq. C111 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 *         res     = c_3_phi55
 * 
*/
    __pyx_v_c_3_phi55 = ((__pyx_v_b_0_phi55 + (__pyx_v_b_1_phi55 * __pyx_v_S_hat)) + (__pyx_v_b_2_phi55 * __pyx_v_S_hat2));

    /* "pyRing/eob_utils.pyx":679
 * 
 *         c_3_phi55 = b_0_phi55 + b_1_phi55*S_hat + b_2_phi55*S_hat2    # eq. C111 of arXiv:2001.09082v2
 *         res     = c_3_phi55             # <<<<<<<<<<<<<<
 * 
 *     return res
*/
    __pyx_v_res = __pyx_v_c_3_phi55;

    /* "pyRing/eob_utils.pyx":676
 *         else:   res = c_3_phi41_nu
 * 
 *     elif ((l==5) and (m==5)):             # <<<<<<<<<<<<<<
 * 
 *         c_3_phi55 = b_0_phi55 + b_1_phi55*S_hat + b_2_phi55*S_hat2    # eq. C111 of arXiv:2001.09082v2
*/
  }
  __pyx_L3:;

  /* "pyRing/eob_utils.pyx":681
 *         res     = c_3_phi55
 * 
 *     return res             # <<<<<<<<<<<<<<
 * 
 * 
*/
  __pyx_r = __pyx_v_res;
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":567
 * 
 * 
 * cdef double _c3_phi(double nu, double X12, double S_hat, int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function returning the coefficient c3_phi of the ringdown model in section V.A of arXiv:1904.09550v2.
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "pyRing/eob_utils.pyx":684
 * 
 * 
 * cdef double _c4_phi(double nu, double X12, double S_hat, int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function returning the coefficient c4_phi of the ringdown model in section V.A of arXiv:1904.09550v2.
*/

static double __pyx_f_6pyRing_9eob_utils__c4_phi(double __pyx_v_nu, double __pyx_v_X12, double __pyx_v_S_hat, int __pyx_v_l, int __pyx_v_m) {
  double __pyx_v_res;
  double __pyx_v_c_4_phi22;
  double __pyx_v_c_4_phi21;
  double __pyx_v_c_4_phi33;
  double __pyx_v_c_4_phi32;
  double __pyx_v_c_4_phi44;
  double __pyx_v_c_4_phi43;
  double __pyx_v_c_4_phi42;
  double __pyx_v_c_4_phi55;
  double __pyx_v_nu2;
  double __pyx_v_nu4;
  double __pyx_v_S_hat2;
  double __pyx_v_S_hat3;
  CYTHON_UNUSED double __pyx_v_S_hat4;
  CYTHON_UNUSED double __pyx_v_X12_2;
  double __pyx_v_b_0_phi22;
  double __pyx_v_b_1_phi22;
  double __pyx_v_b_2_phi22;
  double __pyx_v_c_4_phi21_num;
  double __pyx_v_c_4_phi21_den;
  double __pyx_v_b_0_phi33;
  double __pyx_v_c_4_phi32_num;
  double __pyx_v_c_4_phi32_den;
  double __pyx_v_c_4_phi31;
  double __pyx_v_b_0_phi44;
  double __pyx_v_c_4_phi43_num;
  double __pyx_v_c_4_phi43_den;
  double __pyx_v_c_4_phi42_num_nu_a;
  double __pyx_v_c_4_phi42_den_nu_a;
  double __pyx_v_c_4_phi42_num_nu_b;
  double __pyx_v_c_4_phi42_den_nu_b;
  double __pyx_v_c_4_phi41;
  double __pyx_v_b_0_phi55;
  double __pyx_v_b_1_phi55;
  double __pyx_v_b_2_phi55;
  double __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;

  /* "pyRing/eob_utils.pyx":696
 *     """
 * 
 *     cdef double res = 0., c_4_phi22, c_4_phi21, c_4_phi33, c_4_phi32, c_4_phi44, c_4_phi43, c_4_phi42, c_4_phi55             # <<<<<<<<<<<<<<
 *     cdef double nu2 = nu*nu, nu4 = nu2*nu2, S_hat2 = S_hat*S_hat, S_hat3 = S_hat2*S_hat, S_hat4 = S_hat3*S_hat, X12_2 = X12*X12
 * 
*/
  __pyx_v_res = 0.;

  /* "pyRing/eob_utils.pyx":697
 * 
 *     cdef double res = 0., c_4_phi22, c_4_phi21, c_4_phi33, c_4_phi32, c_4_phi44, c_4_phi43, c_4_phi42, c_4_phi55
 *     cdef double nu2 = nu*nu, nu4 = nu2*nu2, S_hat2 = S_hat*S_hat, S_hat3 = S_hat2*S_hat, S_hat4 = S_hat3*S_hat, X12_2 = X12*X12             # <<<<<<<<<<<<<<
 * 
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
*/
  __pyx_v_nu2 = (__pyx_v_nu * __pyx_v_nu);
  __pyx_v_nu4 = (__pyx_v_nu2 * __pyx_v_nu2);
  __pyx_v_S_hat2 = (__pyx_v_S_hat * __pyx_v_S_hat);
  __pyx_v_S_hat3 = (__pyx_v_S_hat2 * __pyx_v_S_hat);
  __pyx_v_S_hat4 = (__pyx_v_S_hat3 * __pyx_v_S_hat);
  __pyx_v_X12_2 = (__pyx_v_X12 * __pyx_v_X12);

  /* "pyRing/eob_utils.pyx":701
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
 *     # (2,2) - TEOBResumSFits.c, line 2651-2653
 *     cdef double b_0_phi22 = 1.4736 + 2.2337*nu, b_1_phi22 = 8.26539 + 0.779683*X12, b_2_phi22 = 14.2053 -0.069638*X12             # <<<<<<<<<<<<<<
 * 
 *     # (2,1) - TEOBResumSFits.c, line 2702
*/
  __pyx_v_b_0_phi22 = (1.4736 + (2.2337 * __pyx_v_nu));
  __pyx_v_b_1_phi22 = (8.26539 + (0.779683 * __pyx_v_X12));
  __pyx_v_b_2_phi22 = (14.2053 - (0.069638 * __pyx_v_X12));

  /* "pyRing/eob_utils.pyx":704
 * 
 *     # (2,1) - TEOBResumSFits.c, line 2702
 *     cdef double c_4_phi21_num = 4.355 - 53.763*nu + 188.06*nu2             # <<<<<<<<<<<<<<
 *     cdef double c_4_phi21_den = 1 - 18.427*nu + 147.16*nu2
 * 
*/
  __pyx_v_c_4_phi21_num = ((4.355 - (53.763 * __pyx_v_nu)) + (188.06 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":705
 *     # (2,1) - TEOBResumSFits.c, line 2702
 *     cdef double c_4_phi21_num = 4.355 - 53.763*nu + 188.06*nu2
 *     cdef double c_4_phi21_den = 1 - 18.427*nu + 147.16*nu2             # <<<<<<<<<<<<<<
 * 
 *     # (3,3) - TEOBResumSFits.c, line 2666
*/
  __pyx_v_c_4_phi21_den = ((1.0 - (18.427 * __pyx_v_nu)) + (147.16 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":708
 * 
 *     # (3,3) - TEOBResumSFits.c, line 2666
 *     cdef double b_0_phi33 = 1.789 -5.6684*nu             # <<<<<<<<<<<<<<
 * 
 *     # (3,2) - TEOBResumSFits.c, line 2718
*/
  __pyx_v_b_0_phi33 = (1.789 - (5.6684 * __pyx_v_nu));

  /* "pyRing/eob_utils.pyx":711
 * 
 *     # (3,2) - TEOBResumSFits.c, line 2718
 *     cdef double c_4_phi32_num = 2.3038 - 50.79*nu + 334.41*nu2             # <<<<<<<<<<<<<<
 *     cdef double c_4_phi32_den = 1 - 18.326*nu + 99.54*nu2
 * 
*/
  __pyx_v_c_4_phi32_num = ((2.3038 - (50.79 * __pyx_v_nu)) + (334.41 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":712
 *     # (3,2) - TEOBResumSFits.c, line 2718
 *     cdef double c_4_phi32_num = 2.3038 - 50.79*nu + 334.41*nu2
 *     cdef double c_4_phi32_den = 1 - 18.326*nu + 99.54*nu2             # <<<<<<<<<<<<<<
 * 
 *     # (3,1) - TEOBResumSFits.c, line 2706
*/
  __pyx_v_c_4_phi32_den = ((1.0 - (18.326 * __pyx_v_nu)) + (99.54 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":715
 * 
 *     # (3,1) - TEOBResumSFits.c, line 2706
 *     cdef double c_4_phi31 = 3.6485 + 5.4536*nu             # <<<<<<<<<<<<<<
 * 
 *     # (4,4) - TEOBResumSFits.c, line 2671
*/
  __pyx_v_c_4_phi31 = (3.6485 + (5.4536 * __pyx_v_nu));

  /* "pyRing/eob_utils.pyx":718
 * 
 *     # (4,4) - TEOBResumSFits.c, line 2671
 *     cdef double b_0_phi44 = 0.21595 + 23.216*nu             # <<<<<<<<<<<<<<
 * 
 *     # (4,3) - TEOBResumSFits.c, line 2743
*/
  __pyx_v_b_0_phi44 = (0.21595 + (23.216 * __pyx_v_nu));

  /* "pyRing/eob_utils.pyx":721
 * 
 *     # (4,3) - TEOBResumSFits.c, line 2743
 *     cdef double c_4_phi43_num = 2.4966 - 6.2043*nu             # <<<<<<<<<<<<<<
 *     cdef double c_4_phi43_den = 1 - 252.47*nu4
 * 
*/
  __pyx_v_c_4_phi43_num = (2.4966 - (6.2043 * __pyx_v_nu));

  /* "pyRing/eob_utils.pyx":722
 *     # (4,3) - TEOBResumSFits.c, line 2743
 *     cdef double c_4_phi43_num = 2.4966 - 6.2043*nu
 *     cdef double c_4_phi43_den = 1 - 252.47*nu4             # <<<<<<<<<<<<<<
 * 
 *     # (4,2) - TEOBResumSFits.c, line 2734-2737
*/
  __pyx_v_c_4_phi43_den = (1.0 - (252.47 * __pyx_v_nu4));

  /* "pyRing/eob_utils.pyx":725
 * 
 *     # (4,2) - TEOBResumSFits.c, line 2734-2737
 *     cdef double c_4_phi42_num_nu_a = 132.56 - 1155.5*nu + 2516.8*nu2             # <<<<<<<<<<<<<<
 *     cdef double c_4_phi42_den_nu_a = 1 - 3.8231*nu
 *     cdef double c_4_phi42_num_nu_b = -0.58736 + 16.401*nu
*/
  __pyx_v_c_4_phi42_num_nu_a = ((132.56 - (1155.5 * __pyx_v_nu)) + (2516.8 * __pyx_v_nu2));

  /* "pyRing/eob_utils.pyx":726
 *     # (4,2) - TEOBResumSFits.c, line 2734-2737
 *     cdef double c_4_phi42_num_nu_a = 132.56 - 1155.5*nu + 2516.8*nu2
 *     cdef double c_4_phi42_den_nu_a = 1 - 3.8231*nu             # <<<<<<<<<<<<<<
 *     cdef double c_4_phi42_num_nu_b = -0.58736 + 16.401*nu
 *     cdef double c_4_phi42_den_nu_b = 1 - 4.5202*nu
*/
  __pyx_v_c_4_phi42_den_nu_a = (1.0 - (3.8231 * __pyx_v_nu));

  /* "pyRing/eob_utils.pyx":727
 *     cdef double c_4_phi42_num_nu_a = 132.56 - 1155.5*nu + 2516.8*nu2
 *     cdef double c_4_phi42_den_nu_a = 1 - 3.8231*nu
 *     cdef double c_4_phi42_num_nu_b = -0.58736 + 16.401*nu             # <<<<<<<<<<<<<<
 *     cdef double c_4_phi42_den_nu_b = 1 - 4.5202*nu
 * 
*/
  __pyx_v_c_4_phi42_num_nu_b = (-0.58736 + (16.401 * __pyx_v_nu));

  /* "pyRing/eob_utils.pyx":728
 *     cdef double c_4_phi42_den_nu_a = 1 - 3.8231*nu
 *     cdef double c_4_phi42_num_nu_b = -0.58736 + 16.401*nu
 *     cdef double c_4_phi42_den_nu_b = 1 - 4.5202*nu             # <<<<<<<<<<<<<<
 * 
 *     # (4,1) - TEOBResumSFits.c, line 2722
*/
  __pyx_v_c_4_phi42_den_nu_b = (1.0 - (4.5202 * __pyx_v_nu));

  /* "pyRing/eob_utils.pyx":731
 * 
 *     # (4,1) - TEOBResumSFits.c, line 2722
 *     cdef double c_4_phi41 = 1.6629 + 11.497*nu             # <<<<<<<<<<<<<<
 * 
 *     # (5,5) - TEOBResumSFits.c, line 2676-2681
*/
  __pyx_v_c_4_phi41 = (1.6629 + (11.497 * __pyx_v_nu));

  /* "pyRing/eob_utils.pyx":734
 * 
 *     # (5,5) - TEOBResumSFits.c, line 2676-2681
 *     cdef double b_0_phi55 = 1.3639723340485870 + 14.9111373110275380*nu, b_1_phi55 = 7.198729 -3.870998*X12, b_2_phi55 = -25.992190 + 36.882645*X12             # <<<<<<<<<<<<<<
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
 * 
*/
  __pyx_v_b_0_phi55 = (1.3639723340485870 + (14.9111373110275380 * __pyx_v_nu));
  __pyx_v_b_1_phi55 = (7.198729 - (3.870998 * __pyx_v_X12));
  __pyx_v_b_2_phi55 = (-25.992190 + (36.882645 * __pyx_v_X12));

  /* "pyRing/eob_utils.pyx":738
 * 
 * 
 *     if ((l==2) and (m==2)):             # <<<<<<<<<<<<<<
 * 
 *         c_4_phi22 = b_0_phi22 + b_1_phi22*S_hat + b_2_phi22*S_hat2    # eq. C107 of arXiv:2001.09082v2
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L4_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":740
 *     if ((l==2) and (m==2)):
 * 
 *         c_4_phi22 = b_0_phi22 + b_1_phi22*S_hat + b_2_phi22*S_hat2    # eq. C107 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 *         res       = c_4_phi22
 * 
*/
    __pyx_v_c_4_phi22 = ((__pyx_v_b_0_phi22 + (__pyx_v_b_1_phi22 * __pyx_v_S_hat)) + (__pyx_v_b_2_phi22 * __pyx_v_S_hat2));

    /* "pyRing/eob_utils.pyx":741
 * 
 *         c_4_phi22 = b_0_phi22 + b_1_phi22*S_hat + b_2_phi22*S_hat2    # eq. C107 of arXiv:2001.09082v2
 *         res       = c_4_phi22             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==2) and (m==1)):
*/
    __pyx_v_res = __pyx_v_c_4_phi22;

    /* "pyRing/eob_utils.pyx":738
 * 
 * 
 *     if ((l==2) and (m==2)):             # <<<<<<<<<<<<<<
 * 
 *         c_4_phi22 = b_0_phi22 + b_1_phi22*S_hat + b_2_phi22*S_hat2    # eq. C107 of arXiv:2001.09082v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":743
 *         res       = c_4_phi22
 * 
 *     elif ((l==2) and (m==1)):             # <<<<<<<<<<<<<<
 * 
 *         c_4_phi21 = c_4_phi21_num/c_4_phi21_den   # table IV of arXiv:1904.09550v2
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L6_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L6_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":745
 *     elif ((l==2) and (m==1)):
 * 
 *         c_4_phi21 = c_4_phi21_num/c_4_phi21_den   # table IV of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 *         res       = c_4_phi21
 * 
*/
    __pyx_v_c_4_phi21 = (__pyx_v_c_4_phi21_num / __pyx_v_c_4_phi21_den);

    /* "pyRing/eob_utils.pyx":746
 * 
 *         c_4_phi21 = c_4_phi21_num/c_4_phi21_den   # table IV of arXiv:1904.09550v2
 *         res       = c_4_phi21             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==3) and (m==3)):
*/
    __pyx_v_res = __pyx_v_c_4_phi21;

    /* "pyRing/eob_utils.pyx":743
 *         res       = c_4_phi22
 * 
 *     elif ((l==2) and (m==1)):             # <<<<<<<<<<<<<<
 * 
 *         c_4_phi21 = c_4_phi21_num/c_4_phi21_den   # table IV of arXiv:1904.09550v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":748
 *         res       = c_4_phi21
 * 
 *     elif ((l==3) and (m==3)):             # <<<<<<<<<<<<<<
 * 
 *         c_4_phi33 = b_0_phi33    # TEOBResumSFits.c, line 2666
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L8_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L8_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":750
 *     elif ((l==3) and (m==3)):
 * 
 *         c_4_phi33 = b_0_phi33    # TEOBResumSFits.c, line 2666             # <<<<<<<<<<<<<<
 *         res       = c_4_phi33
 * 
*/
    __pyx_v_c_4_phi33 = __pyx_v_b_0_phi33;

    /* "pyRing/eob_utils.pyx":751
 * 
 *         c_4_phi33 = b_0_phi33    # TEOBResumSFits.c, line 2666
 *         res       = c_4_phi33             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==3) and (m==2)):
*/
    __pyx_v_res = __pyx_v_c_4_phi33;

    /* "pyRing/eob_utils.pyx":748
 *         res       = c_4_phi21
 * 
 *     elif ((l==3) and (m==3)):             # <<<<<<<<<<<<<<
 * 
 *         c_4_phi33 = b_0_phi33    # TEOBResumSFits.c, line 2666
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":753
 *         res       = c_4_phi33
 * 
 *     elif ((l==3) and (m==2)):             # <<<<<<<<<<<<<<
 * 
 *         c_4_phi32 = c_4_phi32_num/c_4_phi32_den   # table IV of arXiv:1904.09550v2
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L10_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L10_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":755
 *     elif ((l==3) and (m==2)):
 * 
 *         c_4_phi32 = c_4_phi32_num/c_4_phi32_den   # table IV of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 *         res       = c_4_phi32
 * 
*/
    __pyx_v_c_4_phi32 = (__pyx_v_c_4_phi32_num / __pyx_v_c_4_phi32_den);

    /* "pyRing/eob_utils.pyx":756
 * 
 *         c_4_phi32 = c_4_phi32_num/c_4_phi32_den   # table IV of arXiv:1904.09550v2
 *         res       = c_4_phi32             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==3) and (m==1)):
*/
    __pyx_v_res = __pyx_v_c_4_phi32;

    /* "pyRing/eob_utils.pyx":753
 *         res       = c_4_phi33
 * 
 *     elif ((l==3) and (m==2)):             # <<<<<<<<<<<<<<
 * 
 *         c_4_phi32 = c_4_phi32_num/c_4_phi32_den   # table IV of arXiv:1904.09550v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":758
 *         res       = c_4_phi32
 * 
 *     elif ((l==3) and (m==1)):             # <<<<<<<<<<<<<<
 * 
 *         res = c_4_phi31   # table IV of arXiv:1904.09550v2
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L12_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L12_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":760
 *     elif ((l==3) and (m==1)):
 * 
 *         res = c_4_phi31   # table IV of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==4)):
*/
    __pyx_v_res = __pyx_v_c_4_phi31;

    /* "pyRing/eob_utils.pyx":758
 *         res       = c_4_phi32
 * 
 *     elif ((l==3) and (m==1)):             # <<<<<<<<<<<<<<
 * 
 *         res = c_4_phi31   # table IV of arXiv:1904.09550v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":762
 *         res = c_4_phi31   # table IV of arXiv:1904.09550v2
 * 
 *     elif ((l==4) and (m==4)):             # <<<<<<<<<<<<<<
 * 
 *         c_4_phi44 = b_0_phi44    # TEOBResumSFits.c, line 2671
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L14_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 4);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L14_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":764
 *     elif ((l==4) and (m==4)):
 * 
 *         c_4_phi44 = b_0_phi44    # TEOBResumSFits.c, line 2671             # <<<<<<<<<<<<<<
 *         res       = c_4_phi44
 * 
*/
    __pyx_v_c_4_phi44 = __pyx_v_b_0_phi44;

    /* "pyRing/eob_utils.pyx":765
 * 
 *         c_4_phi44 = b_0_phi44    # TEOBResumSFits.c, line 2671
 *         res       = c_4_phi44             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==3)):
*/
    __pyx_v_res = __pyx_v_c_4_phi44;

    /* "pyRing/eob_utils.pyx":762
 *         res = c_4_phi31   # table IV of arXiv:1904.09550v2
 * 
 *     elif ((l==4) and (m==4)):             # <<<<<<<<<<<<<<
 * 
 *         c_4_phi44 = b_0_phi44    # TEOBResumSFits.c, line 2671
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":767
 *         res       = c_4_phi44
 * 
 *     elif ((l==4) and (m==3)):             # <<<<<<<<<<<<<<
 * 
 *         c_4_phi43 = c_4_phi43_num/c_4_phi43_den   # table IV of arXiv:1904.09550v2
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L16_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L16_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":769
 *     elif ((l==4) and (m==3)):
 * 
 *         c_4_phi43 = c_4_phi43_num/c_4_phi43_den   # table IV of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 *         res       = c_4_phi43
 * 
*/
    __pyx_v_c_4_phi43 = (__pyx_v_c_4_phi43_num / __pyx_v_c_4_phi43_den);

    /* "pyRing/eob_utils.pyx":770
 * 
 *         c_4_phi43 = c_4_phi43_num/c_4_phi43_den   # table IV of arXiv:1904.09550v2
 *         res       = c_4_phi43             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==2)):   # eq. 5.20 of arXiv:1904.09550v2
*/
    __pyx_v_res = __pyx_v_c_4_phi43;

    /* "pyRing/eob_utils.pyx":767
 *         res       = c_4_phi44
 * 
 *     elif ((l==4) and (m==3)):             # <<<<<<<<<<<<<<
 * 
 *         c_4_phi43 = c_4_phi43_num/c_4_phi43_den   # table IV of arXiv:1904.09550v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":772
 *         res       = c_4_phi43
 * 
 *     elif ((l==4) and (m==2)):   # eq. 5.20 of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 * 
 *         if   (nu>=2.5/12.25):
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L18_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L18_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":774
 *     elif ((l==4) and (m==2)):   # eq. 5.20 of arXiv:1904.09550v2
 * 
 *         if   (nu>=2.5/12.25):             # <<<<<<<<<<<<<<
 *             c_4_phi42 = c_4_phi42_num_nu_a/c_4_phi42_den_nu_a
 *             res       = c_4_phi42
*/
    __pyx_t_1 = (__pyx_v_nu >= (2.5 / 12.25));
    if (__pyx_t_1) {

      /* "pyRing/eob_utils.pyx":775
 * 
 *         if   (nu>=2.5/12.25):
 *             c_4_phi42 = c_4_phi42_num_nu_a/c_4_phi42_den_nu_a             # <<<<<<<<<<<<<<
 *             res       = c_4_phi42
 * 
*/
      __pyx_v_c_4_phi42 = (__pyx_v_c_4_phi42_num_nu_a / __pyx_v_c_4_phi42_den_nu_a);

      /* "pyRing/eob_utils.pyx":776
 *         if   (nu>=2.5/12.25):
 *             c_4_phi42 = c_4_phi42_num_nu_a/c_4_phi42_den_nu_a
 *             res       = c_4_phi42             # <<<<<<<<<<<<<<
 * 
 *         else:
*/
      __pyx_v_res = __pyx_v_c_4_phi42;

      /* "pyRing/eob_utils.pyx":774
 *     elif ((l==4) and (m==2)):   # eq. 5.20 of arXiv:1904.09550v2
 * 
 *         if   (nu>=2.5/12.25):             # <<<<<<<<<<<<<<
 *             c_4_phi42 = c_4_phi42_num_nu_a/c_4_phi42_den_nu_a
 *             res       = c_4_phi42
*/
      goto __pyx_L20;
    }

    /* "pyRing/eob_utils.pyx":779
 * 
 *         else:
 *             c_4_phi42 = c_4_phi42_num_nu_b/c_4_phi42_den_nu_b             # <<<<<<<<<<<<<<
 *             res       = c_4_phi42
 * 
*/
    /*else*/ {
      __pyx_v_c_4_phi42 = (__pyx_v_c_4_phi42_num_nu_b / __pyx_v_c_4_phi42_den_nu_b);

      /* "pyRing/eob_utils.pyx":780
 *         else:
 *             c_4_phi42 = c_4_phi42_num_nu_b/c_4_phi42_den_nu_b
 *             res       = c_4_phi42             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==1)):
*/
      __pyx_v_res = __pyx_v_c_4_phi42;
    }
    __pyx_L20:;

    /* "pyRing/eob_utils.pyx":772
 *         res       = c_4_phi43
 * 
 *     elif ((l==4) and (m==2)):   # eq. 5.20 of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 * 
 *         if   (nu>=2.5/12.25):
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":782
 *             res       = c_4_phi42
 * 
 *     elif ((l==4) and (m==1)):             # <<<<<<<<<<<<<<
 * 
 *         res = c_4_phi41   # table IV of arXiv:1904.09550v2
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L21_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L21_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":784
 *     elif ((l==4) and (m==1)):
 * 
 *         res = c_4_phi41   # table IV of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==5) and (m==5)):
*/
    __pyx_v_res = __pyx_v_c_4_phi41;

    /* "pyRing/eob_utils.pyx":782
 *             res       = c_4_phi42
 * 
 *     elif ((l==4) and (m==1)):             # <<<<<<<<<<<<<<
 * 
 *         res = c_4_phi41   # table IV of arXiv:1904.09550v2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":786
 *         res = c_4_phi41   # table IV of arXiv:1904.09550v2
 * 
 *     elif ((l==5) and (m==5)):             # <<<<<<<<<<<<<<
 * 
 *         c_4_phi55 = b_0_phi55 + b_1_phi55*S_hat + b_2_phi55*S_hat2    # eq. C111 of arXiv:2001.09082v2
*/
  __pyx_t_2 = (__pyx_v_l == 5);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L23_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 5);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L23_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":788
 *     elif ((l==5) and (m==5)):
 * 
 *         c_4_phi55 = b_0_phi55 + b_1_phi55*S_hat + b_2_phi55*S_hat2    # eq. C111 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 *         res     = c_4_phi55
 * 
*/
    __pyx_v_c_4_phi55 = ((__pyx_v_b_0_phi55 + (__pyx_v_b_1_phi55 * __pyx_v_S_hat)) + (__pyx_v_b_2_phi55 * __pyx_v_S_hat2));

    /* "pyRing/eob_utils.pyx":789
 * 
 *         c_4_phi55 = b_0_phi55 + b_1_phi55*S_hat + b_2_phi55*S_hat2    # eq. C111 of arXiv:2001.09082v2
 *         res     = c_4_phi55             # <<<<<<<<<<<<<<
 * 
 *     return res
*/
    __pyx_v_res = __pyx_v_c_4_phi55;

    /* "pyRing/eob_utils.pyx":786
 *         res = c_4_phi41   # table IV of arXiv:1904.09550v2
 * 
 *     elif ((l==5) and (m==5)):             # <<<<<<<<<<<<<<
 * 
 *         c_4_phi55 = b_0_phi55 + b_1_phi55*S_hat + b_2_phi55*S_hat2    # eq. C111 of arXiv:2001.09082v2
*/
  }
  __pyx_L3:;

  /* "pyRing/eob_utils.pyx":791
 *         res     = c_4_phi55
 * 
 *     return res             # <<<<<<<<<<<<<<
 * 
 * 
*/
  __pyx_r = __pyx_v_res;
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":684
 * 
 * 
 * cdef double _c4_phi(double nu, double X12, double S_hat, int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function returning the coefficient c4_phi of the ringdown model in section V.A of arXiv:1904.09550v2.
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "pyRing/eob_utils.pyx":800
 * #################################################
 * 
 * cdef inline double _dOmega(double omega1, double Mf, double omega_peak) nogil:             # <<<<<<<<<<<<<<
 *     """ In the papers is referred to as Delta_omega, e.g. see in section V.A of arXiv:1904.09550v2 """
 *     return omega1 - Mf * omega_peak
*/

static CYTHON_INLINE double __pyx_f_6pyRing_9eob_utils__dOmega(double __pyx_v_omega1, double __pyx_v_Mf, double __pyx_v_omega_peak) {
  double __pyx_r;

  /* "pyRing/eob_utils.pyx":802
 * cdef inline double _dOmega(double omega1, double Mf, double omega_peak) nogil:
 *     """ In the papers is referred to as Delta_omega, e.g. see in section V.A of arXiv:1904.09550v2 """
 *     return omega1 - Mf * omega_peak             # <<<<<<<<<<<<<<
 * 
 * 
*/
  __pyx_r = (__pyx_v_omega1 - (__pyx_v_Mf * __pyx_v_omega_peak));
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":800
 * #################################################
 * 
 * cdef inline double _dOmega(double omega1, double Mf, double omega_peak) nogil:             # <<<<<<<<<<<<<<
 *     """ In the papers is referred to as Delta_omega, e.g. see in section V.A of arXiv:1904.09550v2 """
 *     return omega1 - Mf * omega_peak
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "pyRing/eob_utils.pyx":805
 * 
 * 
 * cdef double _amplitude_peak(double nu, double X12, double S_hat, double a12, double S_bar, double a0, double omega_peak, int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function returning the value of A at the peak, following appendix C.2 of arXiv:2001.09082v2.
*/

static double __pyx_f_6pyRing_9eob_utils__amplitude_peak(double __pyx_v_nu, double __pyx_v_X12, double __pyx_v_S_hat, double __pyx_v_a12, double __pyx_v_S_bar, double __pyx_v_a0, double __pyx_v_omega_peak, int __pyx_v_l, int __pyx_v_m) {
  double __pyx_v_res;
  double __pyx_v_scale;
  double __pyx_v_b1_A;
  double __pyx_v_b2_A;
  double __pyx_v_b3_A;
  double __pyx_v_b4_A;
  double __pyx_v_num_orb;
  double __pyx_v_den_orb;
  double __pyx_v_num_spin;
  double __pyx_v_den_spin;
  double __pyx_v_A22_orb;
  double __pyx_v_A22_spin;
  double __pyx_v_A21_orb;
  double __pyx_v_A21_spin;
  double __pyx_v_A33_orb;
  double __pyx_v_A33_spin;
  double __pyx_v_A32_orb;
  double __pyx_v_A32_spin;
  double __pyx_v_A44_orb;
  double __pyx_v_A44_spin;
  double __pyx_v_A43_orb;
  double __pyx_v_A43_spin;
  double __pyx_v_A42_orb;
  double __pyx_v_A42_spin;
  double __pyx_v_A55_orb;
  double __pyx_v_A55_spin;
  double __pyx_v_nu2;
  CYTHON_UNUSED double __pyx_v_X12_2;
  double __pyx_v_S_hat2;
  CYTHON_UNUSED double __pyx_v_S_hat3;
  double __pyx_v_S_bar2;
  double __pyx_v_a0_2;
  double __pyx_v_a12_2;
  double __pyx_v_S_bar_21;
  double __pyx_v_a12_33;
  double __pyx_v_A22_0;
  double __pyx_v_a_1_A22;
  double __pyx_v_a_2_A22;
  double __pyx_v_b_1_A22;
  double __pyx_v_b_2_A22;
  double __pyx_v_b_3_A22;
  double __pyx_v_c_11_A22;
  double __pyx_v_c_12_A22;
  double __pyx_v_c_31_A22;
  double __pyx_v_c_32_A22;
  double __pyx_v_A21_0;
  double __pyx_v_a_1_A21;
  double __pyx_v_a_2_A21;
  double __pyx_v_a_3_A21;
  double __pyx_v_b_1_A21;
  double __pyx_v_b_2_A21;
  double __pyx_v_b_3_A21;
  double __pyx_v_c_11_A21;
  double __pyx_v_c_12_A21;
  double __pyx_v_c_21_A21;
  double __pyx_v_c_22_A21;
  double __pyx_v_c_31_A21;
  double __pyx_v_c_32_A21;
  double __pyx_v_A33_0;
  double __pyx_v_a_1_A33;
  double __pyx_v_a_2_A33;
  double __pyx_v_a_3_A33;
  double __pyx_v_b_1_A33;
  double __pyx_v_b_2_A33;
  double __pyx_v_c_11_A33;
  double __pyx_v_c_12_A33;
  double __pyx_v_c_13_A33;
  double __pyx_v_c_21_A33;
  double __pyx_v_c_22_A33;
  double __pyx_v_c_23_A33;
  double __pyx_v_A32_0;
  double __pyx_v_a_1_A32;
  double __pyx_v_a_2_A32;
  double __pyx_v_a_3_A32;
  double __pyx_v_b_1_A32;
  double __pyx_v_b_2_A32;
  double __pyx_v_c_11_A32;
  double __pyx_v_c_12_A32;
  double __pyx_v_c_13_A32;
  double __pyx_v_c_14_A32;
  double __pyx_v_c_21_A32;
  double __pyx_v_c_22_A32;
  double __pyx_v_c_23_A32;
  double __pyx_v_c_24_A32;
  CYTHON_UNUSED double __pyx_v_A31_0;
  CYTHON_UNUSED double __pyx_v_n_1_A31;
  CYTHON_UNUSED double __pyx_v_n_2_A31;
  double __pyx_v_A44_0;
  double __pyx_v_a_1_A44;
  double __pyx_v_a_2_A44;
  double __pyx_v_a_3_A44;
  double __pyx_v_b_1_A44;
  double __pyx_v_b_2_A44;
  double __pyx_v_b_3_A44;
  double __pyx_v_c_11_A44;
  double __pyx_v_c_12_A44;
  double __pyx_v_c_13_A44;
  double __pyx_v_c_14_A44;
  double __pyx_v_c_21_A44;
  double __pyx_v_c_22_A44;
  double __pyx_v_c_23_A44;
  double __pyx_v_c_24_A44;
  double __pyx_v_c_31_A44;
  double __pyx_v_c_32_A44;
  double __pyx_v_c_33_A44;
  double __pyx_v_c_34_A44;
  double __pyx_v_A43_0;
  double __pyx_v_a_1_A43;
  double __pyx_v_a_2_A43;
  double __pyx_v_a_3_A43;
  double __pyx_v_b_1_A43;
  double __pyx_v_b_2_A43;
  double __pyx_v_b_3_A43;
  double __pyx_v_b_1_A43_nu;
  double __pyx_v_b_2_A43_nu;
  double __pyx_v_b_3_A43_nu;
  double __pyx_v_b_4_A43_nu;
  double __pyx_v_c_11_A43;
  double __pyx_v_c_12_A43;
  double __pyx_v_c_13_A43;
  double __pyx_v_c_21_A43;
  double __pyx_v_c_22_A43;
  double __pyx_v_c_23_A43;
  double __pyx_v_c_31_A43;
  double __pyx_v_c_32_A43;
  double __pyx_v_c_33_A43;
  double __pyx_v_A42_0;
  double __pyx_v_a_1_A42;
  double __pyx_v_a_2_A42;
  double __pyx_v_b_1_A42;
  double __pyx_v_b_2_A42;
  double __pyx_v_b_3_A42;
  double __pyx_v_b_4_A42;
  double __pyx_v_c_11_A42;
  double __pyx_v_c_12_A42;
  double __pyx_v_c_21_A42;
  double __pyx_v_c_22_A42;
  double __pyx_v_c_31_A42;
  double __pyx_v_c_32_A42;
  double __pyx_v_c_41_A42;
  double __pyx_v_c_42_A42;
  CYTHON_UNUSED double __pyx_v_A41_0;
  CYTHON_UNUSED double __pyx_v_n_1_A41;
  CYTHON_UNUSED double __pyx_v_n_2_A41;
  CYTHON_UNUSED double __pyx_v_d_1_A41;
  double __pyx_v_A55_0;
  double __pyx_v_a_1_A55;
  double __pyx_v_a_2_A55;
  double __pyx_v_b_1_A55;
  double __pyx_v_b_2_A55;
  double __pyx_v_c_11_A55;
  double __pyx_v_c_12_A55;
  double __pyx_v_c_21_A55;
  double __pyx_v_c_22_A55;
  double __pyx_v_num_peak;
  double __pyx_v_den_peak;
  double __pyx_v_A43_peak;
  double __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;

  /* "pyRing/eob_utils.pyx":820
 *     """
 * 
 *     cdef double res = 0., scale             # <<<<<<<<<<<<<<
 *     cdef double b1_A, b2_A, b3_A, b4_A, num_orb, den_orb, num_spin, den_spin,
 *     cdef double A22_orb, A22_spin, A21_orb, A21_spin
*/
  __pyx_v_res = 0.;

  /* "pyRing/eob_utils.pyx":826
 *     cdef double A44_orb, A44_spin, A43_orb, A43_spin, A42_orb, A42_spin, A41_orb
 *     cdef double A55_orb, A55_spin
 *     cdef double nu2 = nu*nu, X12_2 = X12*X12, S_hat2 = S_hat*S_hat, S_hat3 = S_hat2*S_hat, S_bar2 = S_bar*S_bar, a0_2 = a0*a0, a12_2 = a12*a12, S_bar_21 = -fabs(S_bar), a12_33 = fabs(a12)             # <<<<<<<<<<<<<<
 * 
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
*/
  __pyx_v_nu2 = (__pyx_v_nu * __pyx_v_nu);
  __pyx_v_X12_2 = (__pyx_v_X12 * __pyx_v_X12);
  __pyx_v_S_hat2 = (__pyx_v_S_hat * __pyx_v_S_hat);
  __pyx_v_S_hat3 = (__pyx_v_S_hat2 * __pyx_v_S_hat);
  __pyx_v_S_bar2 = (__pyx_v_S_bar * __pyx_v_S_bar);
  __pyx_v_a0_2 = (__pyx_v_a0 * __pyx_v_a0);
  __pyx_v_a12_2 = (__pyx_v_a12 * __pyx_v_a12);
  __pyx_v_S_bar_21 = (-fabs(__pyx_v_S_bar));
  __pyx_v_a12_33 = fabs(__pyx_v_a12);

  /* "pyRing/eob_utils.pyx":830
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
 *     # (2,2) - TEOBResumSFits.c, line 2423-2431
 *     cdef double A22_0    = 1.44959     # TEOBResumSFits.c, line 1993             # <<<<<<<<<<<<<<
 *     cdef double a_1_A22  = -0.041285, a_2_A22  = 1.5971
 *     cdef double b_1_A22  = -0.741,    b_2_A22  = -0.0887,     b_3_A22  = -1.094
*/
  __pyx_v_A22_0 = 1.44959;

  /* "pyRing/eob_utils.pyx":831
 *     # (2,2) - TEOBResumSFits.c, line 2423-2431
 *     cdef double A22_0    = 1.44959     # TEOBResumSFits.c, line 1993
 *     cdef double a_1_A22  = -0.041285, a_2_A22  = 1.5971             # <<<<<<<<<<<<<<
 *     cdef double b_1_A22  = -0.741,    b_2_A22  = -0.0887,     b_3_A22  = -1.094
 *     cdef double c_11_A22 = 0.4446696, c_12_A22 = -0.3254310, c_31_A22 = 0.4582812, c_32_A22 = -0.2124477
*/
  __pyx_v_a_1_A22 = -0.041285;
  __pyx_v_a_2_A22 = 1.5971;

  /* "pyRing/eob_utils.pyx":832
 *     cdef double A22_0    = 1.44959     # TEOBResumSFits.c, line 1993
 *     cdef double a_1_A22  = -0.041285, a_2_A22  = 1.5971
 *     cdef double b_1_A22  = -0.741,    b_2_A22  = -0.0887,     b_3_A22  = -1.094             # <<<<<<<<<<<<<<
 *     cdef double c_11_A22 = 0.4446696, c_12_A22 = -0.3254310, c_31_A22 = 0.4582812, c_32_A22 = -0.2124477
 * 
*/
  __pyx_v_b_1_A22 = -0.741;
  __pyx_v_b_2_A22 = -0.0887;
  __pyx_v_b_3_A22 = -1.094;

  /* "pyRing/eob_utils.pyx":833
 *     cdef double a_1_A22  = -0.041285, a_2_A22  = 1.5971
 *     cdef double b_1_A22  = -0.741,    b_2_A22  = -0.0887,     b_3_A22  = -1.094
 *     cdef double c_11_A22 = 0.4446696, c_12_A22 = -0.3254310, c_31_A22 = 0.4582812, c_32_A22 = -0.2124477             # <<<<<<<<<<<<<<
 * 
 *     # (2,1) - TEOBResumSFits.c, line 2375-2389
*/
  __pyx_v_c_11_A22 = 0.4446696;
  __pyx_v_c_12_A22 = -0.3254310;
  __pyx_v_c_31_A22 = 0.4582812;
  __pyx_v_c_32_A22 = -0.2124477;

  /* "pyRing/eob_utils.pyx":836
 * 
 *     # (2,1) - TEOBResumSFits.c, line 2375-2389
 *     cdef double A21_0    = 0.5238781992     # TEOBResumSFits.c, line 1992             # <<<<<<<<<<<<<<
 *     cdef double a_1_A21  = 3.3362232268, a_2_A21  = 3.4708521429, a_3_A21  = 4.7623643259
 *     cdef double b_1_A21  = -0.4281863,   b_2_A21  = -0.335659,    b_3_A21  = 0.828923
*/
  __pyx_v_A21_0 = 0.5238781992;

  /* "pyRing/eob_utils.pyx":837
 *     # (2,1) - TEOBResumSFits.c, line 2375-2389
 *     cdef double A21_0    = 0.5238781992     # TEOBResumSFits.c, line 1992
 *     cdef double a_1_A21  = 3.3362232268, a_2_A21  = 3.4708521429, a_3_A21  = 4.7623643259             # <<<<<<<<<<<<<<
 *     cdef double b_1_A21  = -0.4281863,   b_2_A21  = -0.335659,    b_3_A21  = 0.828923
 *     cdef double c_11_A21 = 0.891139,     c_12_A21 = -5.191702,    c_21_A21 = 3.480139,   c_22_A21 = 10.237782, c_31_A21 = -13.867475, c_32_A21 = 10.525510
*/
  __pyx_v_a_1_A21 = 3.3362232268;
  __pyx_v_a_2_A21 = 3.4708521429;
  __pyx_v_a_3_A21 = 4.7623643259;

  /* "pyRing/eob_utils.pyx":838
 *     cdef double A21_0    = 0.5238781992     # TEOBResumSFits.c, line 1992
 *     cdef double a_1_A21  = 3.3362232268, a_2_A21  = 3.4708521429, a_3_A21  = 4.7623643259
 *     cdef double b_1_A21  = -0.4281863,   b_2_A21  = -0.335659,    b_3_A21  = 0.828923             # <<<<<<<<<<<<<<
 *     cdef double c_11_A21 = 0.891139,     c_12_A21 = -5.191702,    c_21_A21 = 3.480139,   c_22_A21 = 10.237782, c_31_A21 = -13.867475, c_32_A21 = 10.525510
 * 
*/
  __pyx_v_b_1_A21 = -0.4281863;
  __pyx_v_b_2_A21 = -0.335659;
  __pyx_v_b_3_A21 = 0.828923;

  /* "pyRing/eob_utils.pyx":839
 *     cdef double a_1_A21  = 3.3362232268, a_2_A21  = 3.4708521429, a_3_A21  = 4.7623643259
 *     cdef double b_1_A21  = -0.4281863,   b_2_A21  = -0.335659,    b_3_A21  = 0.828923
 *     cdef double c_11_A21 = 0.891139,     c_12_A21 = -5.191702,    c_21_A21 = 3.480139,   c_22_A21 = 10.237782, c_31_A21 = -13.867475, c_32_A21 = 10.525510             # <<<<<<<<<<<<<<
 * 
 *     # (3,3) - TEOBResumSFits.c, line 2458-2468
*/
  __pyx_v_c_11_A21 = 0.891139;
  __pyx_v_c_12_A21 = -5.191702;
  __pyx_v_c_21_A21 = 3.480139;
  __pyx_v_c_22_A21 = 10.237782;
  __pyx_v_c_31_A21 = -13.867475;
  __pyx_v_c_32_A21 = 10.525510;

  /* "pyRing/eob_utils.pyx":842
 * 
 *     # (3,3) - TEOBResumSFits.c, line 2458-2468
 *     cdef double A33_0    = 0.5660165890     # TEOBResumSFits.c, line 1996             # <<<<<<<<<<<<<<
 *     cdef double a_1_A33  = -0.22523,   a_2_A33  = 3.0569,    a_3_A33  = -0.396851
 *     cdef double b_1_A33  = 0.100069,   b_2_A33  = -0.455859
*/
  __pyx_v_A33_0 = 0.5660165890;

  /* "pyRing/eob_utils.pyx":843
 *     # (3,3) - TEOBResumSFits.c, line 2458-2468
 *     cdef double A33_0    = 0.5660165890     # TEOBResumSFits.c, line 1996
 *     cdef double a_1_A33  = -0.22523,   a_2_A33  = 3.0569,    a_3_A33  = -0.396851             # <<<<<<<<<<<<<<
 *     cdef double b_1_A33  = 0.100069,   b_2_A33  = -0.455859
 *     cdef double c_11_A33 = -0.401156,  c_12_A33 = -0.141551, c_13_A33 = -15.4949, c_21_A33 = 1.84962, c_22_A33 = -2.03512, c_23_A33 = -4.92334
*/
  __pyx_v_a_1_A33 = -0.22523;
  __pyx_v_a_2_A33 = 3.0569;
  __pyx_v_a_3_A33 = -0.396851;

  /* "pyRing/eob_utils.pyx":844
 *     cdef double A33_0    = 0.5660165890     # TEOBResumSFits.c, line 1996
 *     cdef double a_1_A33  = -0.22523,   a_2_A33  = 3.0569,    a_3_A33  = -0.396851
 *     cdef double b_1_A33  = 0.100069,   b_2_A33  = -0.455859             # <<<<<<<<<<<<<<
 *     cdef double c_11_A33 = -0.401156,  c_12_A33 = -0.141551, c_13_A33 = -15.4949, c_21_A33 = 1.84962, c_22_A33 = -2.03512, c_23_A33 = -4.92334
 * 
*/
  __pyx_v_b_1_A33 = 0.100069;
  __pyx_v_b_2_A33 = -0.455859;

  /* "pyRing/eob_utils.pyx":845
 *     cdef double a_1_A33  = -0.22523,   a_2_A33  = 3.0569,    a_3_A33  = -0.396851
 *     cdef double b_1_A33  = 0.100069,   b_2_A33  = -0.455859
 *     cdef double c_11_A33 = -0.401156,  c_12_A33 = -0.141551, c_13_A33 = -15.4949, c_21_A33 = 1.84962, c_22_A33 = -2.03512, c_23_A33 = -4.92334             # <<<<<<<<<<<<<<
 * 
 *     # (3,2) - TEOBResumSFits.c, line 2435-2447
*/
  __pyx_v_c_11_A33 = -0.401156;
  __pyx_v_c_12_A33 = -0.141551;
  __pyx_v_c_13_A33 = -15.4949;
  __pyx_v_c_21_A33 = 1.84962;
  __pyx_v_c_22_A33 = -2.03512;
  __pyx_v_c_23_A33 = -4.92334;

  /* "pyRing/eob_utils.pyx":848
 * 
 *     # (3,2) - TEOBResumSFits.c, line 2435-2447
 *     cdef double A32_0    = 0.1990192432     # TEOBResumSFits.c, line 1995             # <<<<<<<<<<<<<<
 *     cdef double a_1_A32  = -6.06831,   a_2_A32  = 10.7505,  a_3_A32  = -3.68883
 *     cdef double b_1_A32  = -0.258378,  b_2_A32  = 0.679163
*/
  __pyx_v_A32_0 = 0.1990192432;

  /* "pyRing/eob_utils.pyx":849
 *     # (3,2) - TEOBResumSFits.c, line 2435-2447
 *     cdef double A32_0    = 0.1990192432     # TEOBResumSFits.c, line 1995
 *     cdef double a_1_A32  = -6.06831,   a_2_A32  = 10.7505,  a_3_A32  = -3.68883             # <<<<<<<<<<<<<<
 *     cdef double b_1_A32  = -0.258378,  b_2_A32  = 0.679163
 *     cdef double c_11_A32 = 4.36263,    c_12_A32 = -12.5897, c_13_A32 = -7.73233, c_14_A32 = 16.2082, c_21_A32 = 3.04724, c_22_A32 = 46.5711, c_23_A32 = 2.10475, c_24_A32 = 56.9136
*/
  __pyx_v_a_1_A32 = -6.06831;
  __pyx_v_a_2_A32 = 10.7505;
  __pyx_v_a_3_A32 = -3.68883;

  /* "pyRing/eob_utils.pyx":850
 *     cdef double A32_0    = 0.1990192432     # TEOBResumSFits.c, line 1995
 *     cdef double a_1_A32  = -6.06831,   a_2_A32  = 10.7505,  a_3_A32  = -3.68883
 *     cdef double b_1_A32  = -0.258378,  b_2_A32  = 0.679163             # <<<<<<<<<<<<<<
 *     cdef double c_11_A32 = 4.36263,    c_12_A32 = -12.5897, c_13_A32 = -7.73233, c_14_A32 = 16.2082, c_21_A32 = 3.04724, c_22_A32 = 46.5711, c_23_A32 = 2.10475, c_24_A32 = 56.9136
 * 
*/
  __pyx_v_b_1_A32 = -0.258378;
  __pyx_v_b_2_A32 = 0.679163;

  /* "pyRing/eob_utils.pyx":851
 *     cdef double a_1_A32  = -6.06831,   a_2_A32  = 10.7505,  a_3_A32  = -3.68883
 *     cdef double b_1_A32  = -0.258378,  b_2_A32  = 0.679163
 *     cdef double c_11_A32 = 4.36263,    c_12_A32 = -12.5897, c_13_A32 = -7.73233, c_14_A32 = 16.2082, c_21_A32 = 3.04724, c_22_A32 = 46.5711, c_23_A32 = 2.10475, c_24_A32 = 56.9136             # <<<<<<<<<<<<<<
 * 
 *     # (3,1) - TEOBResumSFits.c, line 2690
*/
  __pyx_v_c_11_A32 = 4.36263;
  __pyx_v_c_12_A32 = -12.5897;
  __pyx_v_c_13_A32 = -7.73233;
  __pyx_v_c_14_A32 = 16.2082;
  __pyx_v_c_21_A32 = 3.04724;
  __pyx_v_c_22_A32 = 46.5711;
  __pyx_v_c_23_A32 = 2.10475;
  __pyx_v_c_24_A32 = 56.9136;

  /* "pyRing/eob_utils.pyx":854
 * 
 *     # (3,1) - TEOBResumSFits.c, line 2690
 *     cdef double A31_0   = 0.0623783     # TEOBResumSFits.c, line 1994             # <<<<<<<<<<<<<<
 *     cdef double n_1_A31 = -5.49,   n_2_A31 = 10.915
 * 
*/
  __pyx_v_A31_0 = 0.0623783;

  /* "pyRing/eob_utils.pyx":855
 *     # (3,1) - TEOBResumSFits.c, line 2690
 *     cdef double A31_0   = 0.0623783     # TEOBResumSFits.c, line 1994
 *     cdef double n_1_A31 = -5.49,   n_2_A31 = 10.915             # <<<<<<<<<<<<<<
 * 
 *     # (4,4) - TEOBResumSFits.c, line 2536-2553
*/
  __pyx_v_n_1_A31 = -5.49;
  __pyx_v_n_2_A31 = 10.915;

  /* "pyRing/eob_utils.pyx":858
 * 
 *     # (4,4) - TEOBResumSFits.c, line 2536-2553
 *     cdef double A44_0    = 0.2766182761     # TEOBResumSFits.c, line 2000             # <<<<<<<<<<<<<<
 *     cdef double a_1_A44  = -3.7082,   a_2_A44  = 0.280906,  a_3_A44  = -3.71276
 *     cdef double b_1_A44  = -0.316647, b_2_A44  = -0.062423, b_3_A44  = -0.852876
*/
  __pyx_v_A44_0 = 0.2766182761;

  /* "pyRing/eob_utils.pyx":859
 *     # (4,4) - TEOBResumSFits.c, line 2536-2553
 *     cdef double A44_0    = 0.2766182761     # TEOBResumSFits.c, line 2000
 *     cdef double a_1_A44  = -3.7082,   a_2_A44  = 0.280906,  a_3_A44  = -3.71276             # <<<<<<<<<<<<<<
 *     cdef double b_1_A44  = -0.316647, b_2_A44  = -0.062423, b_3_A44  = -0.852876
 *     cdef double c_11_A44 = 1.2436,    c_12_A44 = -1.60555,  c_13_A44 = -4.05685, c_14_A44 = 1.59143, c_21_A44 = 0.837418, c_22_A44 = -2.93528, c_23_A44 = -11.5591, c_24_A44 = 34.1863, c_31_A44 = 0.950035, c_32_A44 = 7.95168, c_33_A44 = -1.26899, c_34_A44 = -9.72147
*/
  __pyx_v_a_1_A44 = -3.7082;
  __pyx_v_a_2_A44 = 0.280906;
  __pyx_v_a_3_A44 = -3.71276;

  /* "pyRing/eob_utils.pyx":860
 *     cdef double A44_0    = 0.2766182761     # TEOBResumSFits.c, line 2000
 *     cdef double a_1_A44  = -3.7082,   a_2_A44  = 0.280906,  a_3_A44  = -3.71276
 *     cdef double b_1_A44  = -0.316647, b_2_A44  = -0.062423, b_3_A44  = -0.852876             # <<<<<<<<<<<<<<
 *     cdef double c_11_A44 = 1.2436,    c_12_A44 = -1.60555,  c_13_A44 = -4.05685, c_14_A44 = 1.59143, c_21_A44 = 0.837418, c_22_A44 = -2.93528, c_23_A44 = -11.5591, c_24_A44 = 34.1863, c_31_A44 = 0.950035, c_32_A44 = 7.95168, c_33_A44 = -1.26899, c_34_A44 = -9.72147
 * 
*/
  __pyx_v_b_1_A44 = -0.316647;
  __pyx_v_b_2_A44 = -0.062423;
  __pyx_v_b_3_A44 = -0.852876;

  /* "pyRing/eob_utils.pyx":861
 *     cdef double a_1_A44  = -3.7082,   a_2_A44  = 0.280906,  a_3_A44  = -3.71276
 *     cdef double b_1_A44  = -0.316647, b_2_A44  = -0.062423, b_3_A44  = -0.852876
 *     cdef double c_11_A44 = 1.2436,    c_12_A44 = -1.60555,  c_13_A44 = -4.05685, c_14_A44 = 1.59143, c_21_A44 = 0.837418, c_22_A44 = -2.93528, c_23_A44 = -11.5591, c_24_A44 = 34.1863, c_31_A44 = 0.950035, c_32_A44 = 7.95168, c_33_A44 = -1.26899, c_34_A44 = -9.72147             # <<<<<<<<<<<<<<
 * 
 *     # (4,3) - TEOBResumSFits.c, line 2510-2531
*/
  __pyx_v_c_11_A44 = 1.2436;
  __pyx_v_c_12_A44 = -1.60555;
  __pyx_v_c_13_A44 = -4.05685;
  __pyx_v_c_14_A44 = 1.59143;
  __pyx_v_c_21_A44 = 0.837418;
  __pyx_v_c_22_A44 = -2.93528;
  __pyx_v_c_23_A44 = -11.5591;
  __pyx_v_c_24_A44 = 34.1863;
  __pyx_v_c_31_A44 = 0.950035;
  __pyx_v_c_32_A44 = 7.95168;
  __pyx_v_c_33_A44 = -1.26899;
  __pyx_v_c_34_A44 = -9.72147;

  /* "pyRing/eob_utils.pyx":864
 * 
 *     # (4,3) - TEOBResumSFits.c, line 2510-2531
 *     cdef double A43_0      = 0.0941569508     # TEOBResumSFits.c, line 1999             # <<<<<<<<<<<<<<
 *     cdef double a_1_A43    = -5.74386,    a_2_A43    = 12.6016,     a_3_A43    = -3.27435
 *     cdef double b_1_A43    = -0.02132252, b_2_A43    = 0.02592749,  b_3_A43    = -0.826977
*/
  __pyx_v_A43_0 = 0.0941569508;

  /* "pyRing/eob_utils.pyx":865
 *     # (4,3) - TEOBResumSFits.c, line 2510-2531
 *     cdef double A43_0      = 0.0941569508     # TEOBResumSFits.c, line 1999
 *     cdef double a_1_A43    = -5.74386,    a_2_A43    = 12.6016,     a_3_A43    = -3.27435             # <<<<<<<<<<<<<<
 *     cdef double b_1_A43    = -0.02132252, b_2_A43    = 0.02592749,  b_3_A43    = -0.826977
 *     cdef double b_1_A43_nu = 0.00452129,  b_2_A43_nu = -0.00471163, b_3_A43_nu = 0.0291409,  b_4_A43_nu = -0.351031
*/
  __pyx_v_a_1_A43 = -5.74386;
  __pyx_v_a_2_A43 = 12.6016;
  __pyx_v_a_3_A43 = -3.27435;

  /* "pyRing/eob_utils.pyx":866
 *     cdef double A43_0      = 0.0941569508     # TEOBResumSFits.c, line 1999
 *     cdef double a_1_A43    = -5.74386,    a_2_A43    = 12.6016,     a_3_A43    = -3.27435
 *     cdef double b_1_A43    = -0.02132252, b_2_A43    = 0.02592749,  b_3_A43    = -0.826977             # <<<<<<<<<<<<<<
 *     cdef double b_1_A43_nu = 0.00452129,  b_2_A43_nu = -0.00471163, b_3_A43_nu = 0.0291409,  b_4_A43_nu = -0.351031
 *     cdef double c_11_A43   = 0.249099,    c_12_A43   = -7.345984,   c_13_A43   = 108.923746, c_21_A43 = -0.104206, c_22_A43 = 7.073534, c_23_A43 = -44.374738, c_31_A43 = 3.545134, c_32_A43 = 1.341375, c_33_A43 = -19.552083
*/
  __pyx_v_b_1_A43 = -0.02132252;
  __pyx_v_b_2_A43 = 0.02592749;
  __pyx_v_b_3_A43 = -0.826977;

  /* "pyRing/eob_utils.pyx":867
 *     cdef double a_1_A43    = -5.74386,    a_2_A43    = 12.6016,     a_3_A43    = -3.27435
 *     cdef double b_1_A43    = -0.02132252, b_2_A43    = 0.02592749,  b_3_A43    = -0.826977
 *     cdef double b_1_A43_nu = 0.00452129,  b_2_A43_nu = -0.00471163, b_3_A43_nu = 0.0291409,  b_4_A43_nu = -0.351031             # <<<<<<<<<<<<<<
 *     cdef double c_11_A43   = 0.249099,    c_12_A43   = -7.345984,   c_13_A43   = 108.923746, c_21_A43 = -0.104206, c_22_A43 = 7.073534, c_23_A43 = -44.374738, c_31_A43 = 3.545134, c_32_A43 = 1.341375, c_33_A43 = -19.552083
 * 
*/
  __pyx_v_b_1_A43_nu = 0.00452129;
  __pyx_v_b_2_A43_nu = -0.00471163;
  __pyx_v_b_3_A43_nu = 0.0291409;
  __pyx_v_b_4_A43_nu = -0.351031;

  /* "pyRing/eob_utils.pyx":868
 *     cdef double b_1_A43    = -0.02132252, b_2_A43    = 0.02592749,  b_3_A43    = -0.826977
 *     cdef double b_1_A43_nu = 0.00452129,  b_2_A43_nu = -0.00471163, b_3_A43_nu = 0.0291409,  b_4_A43_nu = -0.351031
 *     cdef double c_11_A43   = 0.249099,    c_12_A43   = -7.345984,   c_13_A43   = 108.923746, c_21_A43 = -0.104206, c_22_A43 = 7.073534, c_23_A43 = -44.374738, c_31_A43 = 3.545134, c_32_A43 = 1.341375, c_33_A43 = -19.552083             # <<<<<<<<<<<<<<
 * 
 *     # (4,2) - TEOBResumSFits.c, line 2483-2498
*/
  __pyx_v_c_11_A43 = 0.249099;
  __pyx_v_c_12_A43 = -7.345984;
  __pyx_v_c_13_A43 = 108.923746;
  __pyx_v_c_21_A43 = -0.104206;
  __pyx_v_c_22_A43 = 7.073534;
  __pyx_v_c_23_A43 = -44.374738;
  __pyx_v_c_31_A43 = 3.545134;
  __pyx_v_c_32_A43 = 1.341375;
  __pyx_v_c_33_A43 = -19.552083;

  /* "pyRing/eob_utils.pyx":871
 * 
 *     # (4,2) - TEOBResumSFits.c, line 2483-2498
 *     cdef double A42_0    = 0.0314363901     # TEOBResumSFits.c, line 1998             # <<<<<<<<<<<<<<
 *     cdef double a_1_A42  = -4.56243,   a_2_A42  = 6.4522
 *     cdef double b_1_A42  = -1.63682,   b_2_A42  = 0.854459, b_3_A42  = 0.120537,  b_4_A42  = -0.399718
*/
  __pyx_v_A42_0 = 0.0314363901;

  /* "pyRing/eob_utils.pyx":872
 *     # (4,2) - TEOBResumSFits.c, line 2483-2498
 *     cdef double A42_0    = 0.0314363901     # TEOBResumSFits.c, line 1998
 *     cdef double a_1_A42  = -4.56243,   a_2_A42  = 6.4522             # <<<<<<<<<<<<<<
 *     cdef double b_1_A42  = -1.63682,   b_2_A42  = 0.854459, b_3_A42  = 0.120537,  b_4_A42  = -0.399718
 *     cdef double c_11_A42 = 6.53943,    c_12_A42 = -4.00073, c_21_A42 = -0.638688, c_22_A42 = -3.94066, c_31_A42 = -0.482148, c_32_A42 = -3.9999999923319502, c_41_A42 = 1.25617, c_42_A42 = -4.04848
*/
  __pyx_v_a_1_A42 = -4.56243;
  __pyx_v_a_2_A42 = 6.4522;

  /* "pyRing/eob_utils.pyx":873
 *     cdef double A42_0    = 0.0314363901     # TEOBResumSFits.c, line 1998
 *     cdef double a_1_A42  = -4.56243,   a_2_A42  = 6.4522
 *     cdef double b_1_A42  = -1.63682,   b_2_A42  = 0.854459, b_3_A42  = 0.120537,  b_4_A42  = -0.399718             # <<<<<<<<<<<<<<
 *     cdef double c_11_A42 = 6.53943,    c_12_A42 = -4.00073, c_21_A42 = -0.638688, c_22_A42 = -3.94066, c_31_A42 = -0.482148, c_32_A42 = -3.9999999923319502, c_41_A42 = 1.25617, c_42_A42 = -4.04848
 * 
*/
  __pyx_v_b_1_A42 = -1.63682;
  __pyx_v_b_2_A42 = 0.854459;
  __pyx_v_b_3_A42 = 0.120537;
  __pyx_v_b_4_A42 = -0.399718;

  /* "pyRing/eob_utils.pyx":874
 *     cdef double a_1_A42  = -4.56243,   a_2_A42  = 6.4522
 *     cdef double b_1_A42  = -1.63682,   b_2_A42  = 0.854459, b_3_A42  = 0.120537,  b_4_A42  = -0.399718
 *     cdef double c_11_A42 = 6.53943,    c_12_A42 = -4.00073, c_21_A42 = -0.638688, c_22_A42 = -3.94066, c_31_A42 = -0.482148, c_32_A42 = -3.9999999923319502, c_41_A42 = 1.25617, c_42_A42 = -4.04848             # <<<<<<<<<<<<<<
 * 
 *     # (4,1) - TEOBResumSFits.c, line 2695
*/
  __pyx_v_c_11_A42 = 6.53943;
  __pyx_v_c_12_A42 = -4.00073;
  __pyx_v_c_21_A42 = -0.638688;
  __pyx_v_c_22_A42 = -3.94066;
  __pyx_v_c_31_A42 = -0.482148;
  __pyx_v_c_32_A42 = -3.9999999923319502;
  __pyx_v_c_41_A42 = 1.25617;
  __pyx_v_c_42_A42 = -4.04848;

  /* "pyRing/eob_utils.pyx":877
 * 
 *     # (4,1) - TEOBResumSFits.c, line 2695
 *     cdef double A41_0   = 0.00925061     # TEOBResumSFits.c, line 1997             # <<<<<<<<<<<<<<
 *     cdef double n_1_A41 = -8.4449,  n_2_A41 = 26.825
 *     cdef double d_1_A41 = -1.2565
*/
  __pyx_v_A41_0 = 0.00925061;

  /* "pyRing/eob_utils.pyx":878
 *     # (4,1) - TEOBResumSFits.c, line 2695
 *     cdef double A41_0   = 0.00925061     # TEOBResumSFits.c, line 1997
 *     cdef double n_1_A41 = -8.4449,  n_2_A41 = 26.825             # <<<<<<<<<<<<<<
 *     cdef double d_1_A41 = -1.2565
 * 
*/
  __pyx_v_n_1_A41 = -8.4449;
  __pyx_v_n_2_A41 = 26.825;

  /* "pyRing/eob_utils.pyx":879
 *     cdef double A41_0   = 0.00925061     # TEOBResumSFits.c, line 1997
 *     cdef double n_1_A41 = -8.4449,  n_2_A41 = 26.825
 *     cdef double d_1_A41 = -1.2565             # <<<<<<<<<<<<<<
 * 
 *     # (5,5) - TEOBResumSFits.c, line 2565-2572
*/
  __pyx_v_d_1_A41 = -1.2565;

  /* "pyRing/eob_utils.pyx":882
 * 
 *     # (5,5) - TEOBResumSFits.c, line 2565-2572
 *     cdef double A55_0    = 0.151492     # TEOBResumSFits.c, line 2001             # <<<<<<<<<<<<<<
 *     cdef double a_1_A55  = -0.9750925916632546, a_2_A55  = 11.2008774621215608
 *     cdef double b_1_A55  = 0.04360530,          b_2_A55  = -0.5769451
*/
  __pyx_v_A55_0 = 0.151492;

  /* "pyRing/eob_utils.pyx":883
 *     # (5,5) - TEOBResumSFits.c, line 2565-2572
 *     cdef double A55_0    = 0.151492     # TEOBResumSFits.c, line 2001
 *     cdef double a_1_A55  = -0.9750925916632546, a_2_A55  = 11.2008774621215608             # <<<<<<<<<<<<<<
 *     cdef double b_1_A55  = 0.04360530,          b_2_A55  = -0.5769451
 *     cdef double c_11_A55 = 5.720690,            c_12_A55 = 44.868515,         c_21_A55 = 12.777090, c_22_A55 = -42.548247
*/
  __pyx_v_a_1_A55 = -0.9750925916632546;
  __pyx_v_a_2_A55 = 11.2008774621215608;

  /* "pyRing/eob_utils.pyx":884
 *     cdef double A55_0    = 0.151492     # TEOBResumSFits.c, line 2001
 *     cdef double a_1_A55  = -0.9750925916632546, a_2_A55  = 11.2008774621215608
 *     cdef double b_1_A55  = 0.04360530,          b_2_A55  = -0.5769451             # <<<<<<<<<<<<<<
 *     cdef double c_11_A55 = 5.720690,            c_12_A55 = 44.868515,         c_21_A55 = 12.777090, c_22_A55 = -42.548247
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
*/
  __pyx_v_b_1_A55 = 0.04360530;
  __pyx_v_b_2_A55 = -0.5769451;

  /* "pyRing/eob_utils.pyx":885
 *     cdef double a_1_A55  = -0.9750925916632546, a_2_A55  = 11.2008774621215608
 *     cdef double b_1_A55  = 0.04360530,          b_2_A55  = -0.5769451
 *     cdef double c_11_A55 = 5.720690,            c_12_A55 = 44.868515,         c_21_A55 = 12.777090, c_22_A55 = -42.548247             # <<<<<<<<<<<<<<
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
 * 
*/
  __pyx_v_c_11_A55 = 5.720690;
  __pyx_v_c_12_A55 = 44.868515;
  __pyx_v_c_21_A55 = 12.777090;
  __pyx_v_c_22_A55 = -42.548247;

  /* "pyRing/eob_utils.pyx":889
 * 
 * 
 *     if ((l==2) and (m==2)): # eqs. C17-C20 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_A = (b_1_A22 + c_11_A22*X12)/(1 + c_12_A22*X12)
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L4_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":891
 *     if ((l==2) and (m==2)): # eqs. C17-C20 of arXiv:2001.09082v2
 * 
 *         b1_A = (b_1_A22 + c_11_A22*X12)/(1 + c_12_A22*X12)             # <<<<<<<<<<<<<<
 *         b2_A =  b_2_A22
 *         b3_A = (b_3_A22 + c_31_A22*X12)/(1 + c_32_A22*X12)
*/
    __pyx_v_b1_A = ((__pyx_v_b_1_A22 + (__pyx_v_c_11_A22 * __pyx_v_X12)) / (1.0 + (__pyx_v_c_12_A22 * __pyx_v_X12)));

    /* "pyRing/eob_utils.pyx":892
 * 
 *         b1_A = (b_1_A22 + c_11_A22*X12)/(1 + c_12_A22*X12)
 *         b2_A =  b_2_A22             # <<<<<<<<<<<<<<
 *         b3_A = (b_3_A22 + c_31_A22*X12)/(1 + c_32_A22*X12)
 * 
*/
    __pyx_v_b2_A = __pyx_v_b_2_A22;

    /* "pyRing/eob_utils.pyx":893
 *         b1_A = (b_1_A22 + c_11_A22*X12)/(1 + c_12_A22*X12)
 *         b2_A =  b_2_A22
 *         b3_A = (b_3_A22 + c_31_A22*X12)/(1 + c_32_A22*X12)             # <<<<<<<<<<<<<<
 * 
 *         A22_orb  = 1 + a_1_A22*nu + a_2_A22*nu2
*/
    __pyx_v_b3_A = ((__pyx_v_b_3_A22 + (__pyx_v_c_31_A22 * __pyx_v_X12)) / (1.0 + (__pyx_v_c_32_A22 * __pyx_v_X12)));

    /* "pyRing/eob_utils.pyx":895
 *         b3_A = (b_3_A22 + c_31_A22*X12)/(1 + c_32_A22*X12)
 * 
 *         A22_orb  = 1 + a_1_A22*nu + a_2_A22*nu2             # <<<<<<<<<<<<<<
 *         num_spin = 1 + b1_A*S_hat + b2_A*S_hat2
 *         den_spin = 1 + b3_A*S_hat
*/
    __pyx_v_A22_orb = ((1.0 + (__pyx_v_a_1_A22 * __pyx_v_nu)) + (__pyx_v_a_2_A22 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":896
 * 
 *         A22_orb  = 1 + a_1_A22*nu + a_2_A22*nu2
 *         num_spin = 1 + b1_A*S_hat + b2_A*S_hat2             # <<<<<<<<<<<<<<
 *         den_spin = 1 + b3_A*S_hat
 * 
*/
    __pyx_v_num_spin = ((1.0 + (__pyx_v_b1_A * __pyx_v_S_hat)) + (__pyx_v_b2_A * __pyx_v_S_hat2));

    /* "pyRing/eob_utils.pyx":897
 *         A22_orb  = 1 + a_1_A22*nu + a_2_A22*nu2
 *         num_spin = 1 + b1_A*S_hat + b2_A*S_hat2
 *         den_spin = 1 + b3_A*S_hat             # <<<<<<<<<<<<<<
 * 
 *         A22_spin = num_spin/den_spin
*/
    __pyx_v_den_spin = (1.0 + (__pyx_v_b3_A * __pyx_v_S_hat));

    /* "pyRing/eob_utils.pyx":899
 *         den_spin = 1 + b3_A*S_hat
 * 
 *         A22_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *         res = A22_0 * A22_orb * A22_spin
*/
    __pyx_v_A22_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

    /* "pyRing/eob_utils.pyx":901
 *         A22_spin = num_spin/den_spin
 * 
 *         res = A22_0 * A22_orb * A22_spin             # <<<<<<<<<<<<<<
 * 
 *         scale = 1 - S_hat*omega_peak # eq. C6 of arXiv:2001.09082v2
*/
    __pyx_v_res = ((__pyx_v_A22_0 * __pyx_v_A22_orb) * __pyx_v_A22_spin);

    /* "pyRing/eob_utils.pyx":903
 *         res = A22_0 * A22_orb * A22_spin
 * 
 *         scale = 1 - S_hat*omega_peak # eq. C6 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 *         res = res * scale
 * 
*/
    __pyx_v_scale = (1.0 - (__pyx_v_S_hat * __pyx_v_omega_peak));

    /* "pyRing/eob_utils.pyx":904
 * 
 *         scale = 1 - S_hat*omega_peak # eq. C6 of arXiv:2001.09082v2
 *         res = res * scale             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = (__pyx_v_res * __pyx_v_scale);

    /* "pyRing/eob_utils.pyx":889
 * 
 * 
 *     if ((l==2) and (m==2)): # eqs. C17-C20 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_A = (b_1_A22 + c_11_A22*X12)/(1 + c_12_A22*X12)
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":907
 * 
 * 
 *     elif ((l==2) and (m==1)):   # eqs. C21-C24 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_A = b_1_A21 + c_11_A21*nu + c_12_A21*nu2
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L6_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L6_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":909
 *     elif ((l==2) and (m==1)):   # eqs. C21-C24 of arXiv:2001.09082v2
 * 
 *         b1_A = b_1_A21 + c_11_A21*nu + c_12_A21*nu2             # <<<<<<<<<<<<<<
 *         b2_A = b_2_A21 + c_21_A21*nu + c_22_A21*nu2
 *         b3_A = b_3_A21 + c_31_A21*nu + c_32_A21*nu2
*/
    __pyx_v_b1_A = ((__pyx_v_b_1_A21 + (__pyx_v_c_11_A21 * __pyx_v_nu)) + (__pyx_v_c_12_A21 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":910
 * 
 *         b1_A = b_1_A21 + c_11_A21*nu + c_12_A21*nu2
 *         b2_A = b_2_A21 + c_21_A21*nu + c_22_A21*nu2             # <<<<<<<<<<<<<<
 *         b3_A = b_3_A21 + c_31_A21*nu + c_32_A21*nu2
 * 
*/
    __pyx_v_b2_A = ((__pyx_v_b_2_A21 + (__pyx_v_c_21_A21 * __pyx_v_nu)) + (__pyx_v_c_22_A21 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":911
 *         b1_A = b_1_A21 + c_11_A21*nu + c_12_A21*nu2
 *         b2_A = b_2_A21 + c_21_A21*nu + c_22_A21*nu2
 *         b3_A = b_3_A21 + c_31_A21*nu + c_32_A21*nu2             # <<<<<<<<<<<<<<
 * 
 *         num_orb = 1 + a_1_A21*nu + a_2_A21*nu2
*/
    __pyx_v_b3_A = ((__pyx_v_b_3_A21 + (__pyx_v_c_31_A21 * __pyx_v_nu)) + (__pyx_v_c_32_A21 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":913
 *         b3_A = b_3_A21 + c_31_A21*nu + c_32_A21*nu2
 * 
 *         num_orb = 1 + a_1_A21*nu + a_2_A21*nu2             # <<<<<<<<<<<<<<
 *         den_orb = 1 + a_3_A21*nu
 * 
*/
    __pyx_v_num_orb = ((1.0 + (__pyx_v_a_1_A21 * __pyx_v_nu)) + (__pyx_v_a_2_A21 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":914
 * 
 *         num_orb = 1 + a_1_A21*nu + a_2_A21*nu2
 *         den_orb = 1 + a_3_A21*nu             # <<<<<<<<<<<<<<
 * 
 *         if (nu==0.25):    # TEOBResumSFits.c, line 2382
*/
    __pyx_v_den_orb = (1.0 + (__pyx_v_a_3_A21 * __pyx_v_nu));

    /* "pyRing/eob_utils.pyx":916
 *         den_orb = 1 + a_3_A21*nu
 * 
 *         if (nu==0.25):    # TEOBResumSFits.c, line 2382             # <<<<<<<<<<<<<<
 *             num_spin = b1_A*S_bar_21 + b2_A*S_bar_21*S_bar_21
 *             den_spin = 1 + b3_A*S_bar_21
*/
    __pyx_t_1 = (__pyx_v_nu == 0.25);
    if (__pyx_t_1) {

      /* "pyRing/eob_utils.pyx":917
 * 
 *         if (nu==0.25):    # TEOBResumSFits.c, line 2382
 *             num_spin = b1_A*S_bar_21 + b2_A*S_bar_21*S_bar_21             # <<<<<<<<<<<<<<
 *             den_spin = 1 + b3_A*S_bar_21
 * 
*/
      __pyx_v_num_spin = ((__pyx_v_b1_A * __pyx_v_S_bar_21) + ((__pyx_v_b2_A * __pyx_v_S_bar_21) * __pyx_v_S_bar_21));

      /* "pyRing/eob_utils.pyx":918
 *         if (nu==0.25):    # TEOBResumSFits.c, line 2382
 *             num_spin = b1_A*S_bar_21 + b2_A*S_bar_21*S_bar_21
 *             den_spin = 1 + b3_A*S_bar_21             # <<<<<<<<<<<<<<
 * 
 *         else:
*/
      __pyx_v_den_spin = (1.0 + (__pyx_v_b3_A * __pyx_v_S_bar_21));

      /* "pyRing/eob_utils.pyx":916
 *         den_orb = 1 + a_3_A21*nu
 * 
 *         if (nu==0.25):    # TEOBResumSFits.c, line 2382             # <<<<<<<<<<<<<<
 *             num_spin = b1_A*S_bar_21 + b2_A*S_bar_21*S_bar_21
 *             den_spin = 1 + b3_A*S_bar_21
*/
      goto __pyx_L8;
    }

    /* "pyRing/eob_utils.pyx":921
 * 
 *         else:
 *             num_spin = b1_A*S_bar + b2_A*S_bar2             # <<<<<<<<<<<<<<
 *             den_spin = 1 + b3_A*S_bar
 * 
*/
    /*else*/ {
      __pyx_v_num_spin = ((__pyx_v_b1_A * __pyx_v_S_bar) + (__pyx_v_b2_A * __pyx_v_S_bar2));

      /* "pyRing/eob_utils.pyx":922
 *         else:
 *             num_spin = b1_A*S_bar + b2_A*S_bar2
 *             den_spin = 1 + b3_A*S_bar             # <<<<<<<<<<<<<<
 * 
 *         A21_orb  = num_orb/den_orb
*/
      __pyx_v_den_spin = (1.0 + (__pyx_v_b3_A * __pyx_v_S_bar));
    }
    __pyx_L8:;

    /* "pyRing/eob_utils.pyx":924
 *             den_spin = 1 + b3_A*S_bar
 * 
 *         A21_orb  = num_orb/den_orb             # <<<<<<<<<<<<<<
 *         A21_spin = num_spin/den_spin
 * 
*/
    __pyx_v_A21_orb = (__pyx_v_num_orb / __pyx_v_den_orb);

    /* "pyRing/eob_utils.pyx":925
 * 
 *         A21_orb  = num_orb/den_orb
 *         A21_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *         res = A21_0 * X12 * A21_orb + A21_spin
*/
    __pyx_v_A21_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

    /* "pyRing/eob_utils.pyx":927
 *         A21_spin = num_spin/den_spin
 * 
 *         res = A21_0 * X12 * A21_orb + A21_spin             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = (((__pyx_v_A21_0 * __pyx_v_X12) * __pyx_v_A21_orb) + __pyx_v_A21_spin);

    /* "pyRing/eob_utils.pyx":907
 * 
 * 
 *     elif ((l==2) and (m==1)):   # eqs. C21-C24 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_A = b_1_A21 + c_11_A21*nu + c_12_A21*nu2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":930
 * 
 * 
 *     elif ((l==3) and (m==3)):   # eqs. C33-C37 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_A = (b_1_A33 + c_11_A33*nu)/(1 + c_12_A33*nu + c_13_A33*nu2)
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L9_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L9_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":932
 *     elif ((l==3) and (m==3)):   # eqs. C33-C37 of arXiv:2001.09082v2
 * 
 *         b1_A = (b_1_A33 + c_11_A33*nu)/(1 + c_12_A33*nu + c_13_A33*nu2)             # <<<<<<<<<<<<<<
 *         b2_A = (b_2_A33 + c_21_A33*nu)/(1 + c_22_A33*nu + c_23_A33*nu2)
 * 
*/
    __pyx_v_b1_A = ((__pyx_v_b_1_A33 + (__pyx_v_c_11_A33 * __pyx_v_nu)) / ((1.0 + (__pyx_v_c_12_A33 * __pyx_v_nu)) + (__pyx_v_c_13_A33 * __pyx_v_nu2)));

    /* "pyRing/eob_utils.pyx":933
 * 
 *         b1_A = (b_1_A33 + c_11_A33*nu)/(1 + c_12_A33*nu + c_13_A33*nu2)
 *         b2_A = (b_2_A33 + c_21_A33*nu)/(1 + c_22_A33*nu + c_23_A33*nu2)             # <<<<<<<<<<<<<<
 * 
 *         num_orb  = 1 + a_1_A33*nu + a_2_A33*nu2
*/
    __pyx_v_b2_A = ((__pyx_v_b_2_A33 + (__pyx_v_c_21_A33 * __pyx_v_nu)) / ((1.0 + (__pyx_v_c_22_A33 * __pyx_v_nu)) + (__pyx_v_c_23_A33 * __pyx_v_nu2)));

    /* "pyRing/eob_utils.pyx":935
 *         b2_A = (b_2_A33 + c_21_A33*nu)/(1 + c_22_A33*nu + c_23_A33*nu2)
 * 
 *         num_orb  = 1 + a_1_A33*nu + a_2_A33*nu2             # <<<<<<<<<<<<<<
 *         den_orb  = 1 + a_3_A33*nu
 * 
*/
    __pyx_v_num_orb = ((1.0 + (__pyx_v_a_1_A33 * __pyx_v_nu)) + (__pyx_v_a_2_A33 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":936
 * 
 *         num_orb  = 1 + a_1_A33*nu + a_2_A33*nu2
 *         den_orb  = 1 + a_3_A33*nu             # <<<<<<<<<<<<<<
 * 
 *         if (nu==0.25):    # TEOBResumSFits.c, line 2472
*/
    __pyx_v_den_orb = (1.0 + (__pyx_v_a_3_A33 * __pyx_v_nu));

    /* "pyRing/eob_utils.pyx":938
 *         den_orb  = 1 + a_3_A33*nu
 * 
 *         if (nu==0.25):    # TEOBResumSFits.c, line 2472             # <<<<<<<<<<<<<<
 *             num_spin = b1_A*a12_33
 *             den_spin = 1 + b2_A*a12_33
*/
    __pyx_t_1 = (__pyx_v_nu == 0.25);
    if (__pyx_t_1) {

      /* "pyRing/eob_utils.pyx":939
 * 
 *         if (nu==0.25):    # TEOBResumSFits.c, line 2472
 *             num_spin = b1_A*a12_33             # <<<<<<<<<<<<<<
 *             den_spin = 1 + b2_A*a12_33
 * 
*/
      __pyx_v_num_spin = (__pyx_v_b1_A * __pyx_v_a12_33);

      /* "pyRing/eob_utils.pyx":940
 *         if (nu==0.25):    # TEOBResumSFits.c, line 2472
 *             num_spin = b1_A*a12_33
 *             den_spin = 1 + b2_A*a12_33             # <<<<<<<<<<<<<<
 * 
 *         else:
*/
      __pyx_v_den_spin = (1.0 + (__pyx_v_b2_A * __pyx_v_a12_33));

      /* "pyRing/eob_utils.pyx":938
 *         den_orb  = 1 + a_3_A33*nu
 * 
 *         if (nu==0.25):    # TEOBResumSFits.c, line 2472             # <<<<<<<<<<<<<<
 *             num_spin = b1_A*a12_33
 *             den_spin = 1 + b2_A*a12_33
*/
      goto __pyx_L11;
    }

    /* "pyRing/eob_utils.pyx":943
 * 
 *         else:
 *             num_spin = b1_A*a12             # <<<<<<<<<<<<<<
 *             den_spin = 1 + b2_A*a12
 * 
*/
    /*else*/ {
      __pyx_v_num_spin = (__pyx_v_b1_A * __pyx_v_a12);

      /* "pyRing/eob_utils.pyx":944
 *         else:
 *             num_spin = b1_A*a12
 *             den_spin = 1 + b2_A*a12             # <<<<<<<<<<<<<<
 * 
 *         A33_orb  = num_orb/den_orb
*/
      __pyx_v_den_spin = (1.0 + (__pyx_v_b2_A * __pyx_v_a12));
    }
    __pyx_L11:;

    /* "pyRing/eob_utils.pyx":946
 *             den_spin = 1 + b2_A*a12
 * 
 *         A33_orb  = num_orb/den_orb             # <<<<<<<<<<<<<<
 *         A33_spin = num_spin/den_spin
 * 
*/
    __pyx_v_A33_orb = (__pyx_v_num_orb / __pyx_v_den_orb);

    /* "pyRing/eob_utils.pyx":947
 * 
 *         A33_orb  = num_orb/den_orb
 *         A33_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *         res = A33_0 * X12 * A33_orb + A33_spin
*/
    __pyx_v_A33_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

    /* "pyRing/eob_utils.pyx":949
 *         A33_spin = num_spin/den_spin
 * 
 *         res = A33_0 * X12 * A33_orb + A33_spin             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = (((__pyx_v_A33_0 * __pyx_v_X12) * __pyx_v_A33_orb) + __pyx_v_A33_spin);

    /* "pyRing/eob_utils.pyx":930
 * 
 * 
 *     elif ((l==3) and (m==3)):   # eqs. C33-C37 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_A = (b_1_A33 + c_11_A33*nu)/(1 + c_12_A33*nu + c_13_A33*nu2)
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":952
 * 
 * 
 *     elif ((l==3) and (m==2)):   # eqs. C46-C49 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_A = (b_1_A32 + c_11_A32*nu + c_12_A32*nu2)/(1 + c_13_A32*nu + c_14_A32*nu2)
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L12_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L12_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":954
 *     elif ((l==3) and (m==2)):   # eqs. C46-C49 of arXiv:2001.09082v2
 * 
 *         b1_A = (b_1_A32 + c_11_A32*nu + c_12_A32*nu2)/(1 + c_13_A32*nu + c_14_A32*nu2)             # <<<<<<<<<<<<<<
 *         b2_A = (b_2_A32 + c_21_A32*nu + c_22_A32*nu2)/(1 + c_23_A32*nu + c_24_A32*nu2)
 * 
*/
    __pyx_v_b1_A = (((__pyx_v_b_1_A32 + (__pyx_v_c_11_A32 * __pyx_v_nu)) + (__pyx_v_c_12_A32 * __pyx_v_nu2)) / ((1.0 + (__pyx_v_c_13_A32 * __pyx_v_nu)) + (__pyx_v_c_14_A32 * __pyx_v_nu2)));

    /* "pyRing/eob_utils.pyx":955
 * 
 *         b1_A = (b_1_A32 + c_11_A32*nu + c_12_A32*nu2)/(1 + c_13_A32*nu + c_14_A32*nu2)
 *         b2_A = (b_2_A32 + c_21_A32*nu + c_22_A32*nu2)/(1 + c_23_A32*nu + c_24_A32*nu2)             # <<<<<<<<<<<<<<
 * 
 *         num_orb  = 1 + a_1_A32*nu + a_2_A32*nu2
*/
    __pyx_v_b2_A = (((__pyx_v_b_2_A32 + (__pyx_v_c_21_A32 * __pyx_v_nu)) + (__pyx_v_c_22_A32 * __pyx_v_nu2)) / ((1.0 + (__pyx_v_c_23_A32 * __pyx_v_nu)) + (__pyx_v_c_24_A32 * __pyx_v_nu2)));

    /* "pyRing/eob_utils.pyx":957
 *         b2_A = (b_2_A32 + c_21_A32*nu + c_22_A32*nu2)/(1 + c_23_A32*nu + c_24_A32*nu2)
 * 
 *         num_orb  = 1 + a_1_A32*nu + a_2_A32*nu2             # <<<<<<<<<<<<<<
 *         den_orb  = 1 + a_3_A32*nu
 *         num_spin = 1 + b1_A*a0
*/
    __pyx_v_num_orb = ((1.0 + (__pyx_v_a_1_A32 * __pyx_v_nu)) + (__pyx_v_a_2_A32 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":958
 * 
 *         num_orb  = 1 + a_1_A32*nu + a_2_A32*nu2
 *         den_orb  = 1 + a_3_A32*nu             # <<<<<<<<<<<<<<
 *         num_spin = 1 + b1_A*a0
 *         den_spin = 1 + b2_A*a0
*/
    __pyx_v_den_orb = (1.0 + (__pyx_v_a_3_A32 * __pyx_v_nu));

    /* "pyRing/eob_utils.pyx":959
 *         num_orb  = 1 + a_1_A32*nu + a_2_A32*nu2
 *         den_orb  = 1 + a_3_A32*nu
 *         num_spin = 1 + b1_A*a0             # <<<<<<<<<<<<<<
 *         den_spin = 1 + b2_A*a0
 * 
*/
    __pyx_v_num_spin = (1.0 + (__pyx_v_b1_A * __pyx_v_a0));

    /* "pyRing/eob_utils.pyx":960
 *         den_orb  = 1 + a_3_A32*nu
 *         num_spin = 1 + b1_A*a0
 *         den_spin = 1 + b2_A*a0             # <<<<<<<<<<<<<<
 * 
 *         A32_orb  = num_orb/den_orb
*/
    __pyx_v_den_spin = (1.0 + (__pyx_v_b2_A * __pyx_v_a0));

    /* "pyRing/eob_utils.pyx":962
 *         den_spin = 1 + b2_A*a0
 * 
 *         A32_orb  = num_orb/den_orb             # <<<<<<<<<<<<<<
 *         A32_spin = num_spin/den_spin
 * 
*/
    __pyx_v_A32_orb = (__pyx_v_num_orb / __pyx_v_den_orb);

    /* "pyRing/eob_utils.pyx":963
 * 
 *         A32_orb  = num_orb/den_orb
 *         A32_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *         res = A32_0 * (1-3*nu) * A32_orb * A32_spin
*/
    __pyx_v_A32_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

    /* "pyRing/eob_utils.pyx":965
 *         A32_spin = num_spin/den_spin
 * 
 *         res = A32_0 * (1-3*nu) * A32_orb * A32_spin             # <<<<<<<<<<<<<<
 * 
 *         scale = 1 + a0*cbrt(omega_peak/2)  # TEOBResumSFits.c, line 2451
*/
    __pyx_v_res = (((__pyx_v_A32_0 * (1.0 - (3.0 * __pyx_v_nu))) * __pyx_v_A32_orb) * __pyx_v_A32_spin);

    /* "pyRing/eob_utils.pyx":967
 *         res = A32_0 * (1-3*nu) * A32_orb * A32_spin
 * 
 *         scale = 1 + a0*cbrt(omega_peak/2)  # TEOBResumSFits.c, line 2451             # <<<<<<<<<<<<<<
 *         res = res * scale
 * 
*/
    __pyx_v_scale = (1.0 + (__pyx_v_a0 * cbrt((__pyx_v_omega_peak / 2.0))));

    /* "pyRing/eob_utils.pyx":968
 * 
 *         scale = 1 + a0*cbrt(omega_peak/2)  # TEOBResumSFits.c, line 2451
 *         res = res * scale             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = (__pyx_v_res * __pyx_v_scale);

    /* "pyRing/eob_utils.pyx":952
 * 
 * 
 *     elif ((l==3) and (m==2)):   # eqs. C46-C49 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_A = (b_1_A32 + c_11_A32*nu + c_12_A32*nu2)/(1 + c_13_A32*nu + c_14_A32*nu2)
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":971
 * 
 * 
 *     elif ((l==3) and (m==1)):   # eq. 5.19 of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 *         '''
 *         if (nu==0.25):    # TEOBResumSFits.c, line 2685
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L14_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L14_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":981
 *             res = A31_0 * X12 * A31_orb'''
 * 
 *         res = 0     # not implemented in TEOBResumSFits.c, line 2452             # <<<<<<<<<<<<<<
 * 
 *     elif ((l==4) and (m==4)):   # eqs. C61-C64 of arXiv:2001.09082v2
*/
    __pyx_v_res = 0.0;

    /* "pyRing/eob_utils.pyx":971
 * 
 * 
 *     elif ((l==3) and (m==1)):   # eq. 5.19 of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 *         '''
 *         if (nu==0.25):    # TEOBResumSFits.c, line 2685
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":983
 *         res = 0     # not implemented in TEOBResumSFits.c, line 2452
 * 
 *     elif ((l==4) and (m==4)):   # eqs. C61-C64 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_A = (b_1_A44 + c_11_A44*nu + c_12_A44*nu2)/(1 + c_13_A44*nu + c_14_A44*nu2)
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L16_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 4);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L16_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":985
 *     elif ((l==4) and (m==4)):   # eqs. C61-C64 of arXiv:2001.09082v2
 * 
 *         b1_A = (b_1_A44 + c_11_A44*nu + c_12_A44*nu2)/(1 + c_13_A44*nu + c_14_A44*nu2)             # <<<<<<<<<<<<<<
 *         b2_A = (b_2_A44 + c_21_A44*nu + c_22_A44*nu2)/(1 + c_23_A44*nu + c_24_A44*nu2)
 *         b3_A = (b_3_A44 + c_31_A44*nu + c_32_A44*nu2)/(1 + c_33_A44*nu + c_34_A44*nu2)
*/
    __pyx_v_b1_A = (((__pyx_v_b_1_A44 + (__pyx_v_c_11_A44 * __pyx_v_nu)) + (__pyx_v_c_12_A44 * __pyx_v_nu2)) / ((1.0 + (__pyx_v_c_13_A44 * __pyx_v_nu)) + (__pyx_v_c_14_A44 * __pyx_v_nu2)));

    /* "pyRing/eob_utils.pyx":986
 * 
 *         b1_A = (b_1_A44 + c_11_A44*nu + c_12_A44*nu2)/(1 + c_13_A44*nu + c_14_A44*nu2)
 *         b2_A = (b_2_A44 + c_21_A44*nu + c_22_A44*nu2)/(1 + c_23_A44*nu + c_24_A44*nu2)             # <<<<<<<<<<<<<<
 *         b3_A = (b_3_A44 + c_31_A44*nu + c_32_A44*nu2)/(1 + c_33_A44*nu + c_34_A44*nu2)
 * 
*/
    __pyx_v_b2_A = (((__pyx_v_b_2_A44 + (__pyx_v_c_21_A44 * __pyx_v_nu)) + (__pyx_v_c_22_A44 * __pyx_v_nu2)) / ((1.0 + (__pyx_v_c_23_A44 * __pyx_v_nu)) + (__pyx_v_c_24_A44 * __pyx_v_nu2)));

    /* "pyRing/eob_utils.pyx":987
 *         b1_A = (b_1_A44 + c_11_A44*nu + c_12_A44*nu2)/(1 + c_13_A44*nu + c_14_A44*nu2)
 *         b2_A = (b_2_A44 + c_21_A44*nu + c_22_A44*nu2)/(1 + c_23_A44*nu + c_24_A44*nu2)
 *         b3_A = (b_3_A44 + c_31_A44*nu + c_32_A44*nu2)/(1 + c_33_A44*nu + c_34_A44*nu2)             # <<<<<<<<<<<<<<
 * 
 *         num_orb  = 1 + a_1_A44*nu + a_2_A44*nu2
*/
    __pyx_v_b3_A = (((__pyx_v_b_3_A44 + (__pyx_v_c_31_A44 * __pyx_v_nu)) + (__pyx_v_c_32_A44 * __pyx_v_nu2)) / ((1.0 + (__pyx_v_c_33_A44 * __pyx_v_nu)) + (__pyx_v_c_34_A44 * __pyx_v_nu2)));

    /* "pyRing/eob_utils.pyx":989
 *         b3_A = (b_3_A44 + c_31_A44*nu + c_32_A44*nu2)/(1 + c_33_A44*nu + c_34_A44*nu2)
 * 
 *         num_orb  = 1 + a_1_A44*nu + a_2_A44*nu2             # <<<<<<<<<<<<<<
 *         den_orb  = 1 + a_3_A44*nu
 *         num_spin = 1 + b1_A*S_hat + b2_A*S_hat2
*/
    __pyx_v_num_orb = ((1.0 + (__pyx_v_a_1_A44 * __pyx_v_nu)) + (__pyx_v_a_2_A44 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":990
 * 
 *         num_orb  = 1 + a_1_A44*nu + a_2_A44*nu2
 *         den_orb  = 1 + a_3_A44*nu             # <<<<<<<<<<<<<<
 *         num_spin = 1 + b1_A*S_hat + b2_A*S_hat2
 *         den_spin = 1 + b3_A*S_hat
*/
    __pyx_v_den_orb = (1.0 + (__pyx_v_a_3_A44 * __pyx_v_nu));

    /* "pyRing/eob_utils.pyx":991
 *         num_orb  = 1 + a_1_A44*nu + a_2_A44*nu2
 *         den_orb  = 1 + a_3_A44*nu
 *         num_spin = 1 + b1_A*S_hat + b2_A*S_hat2             # <<<<<<<<<<<<<<
 *         den_spin = 1 + b3_A*S_hat
 * 
*/
    __pyx_v_num_spin = ((1.0 + (__pyx_v_b1_A * __pyx_v_S_hat)) + (__pyx_v_b2_A * __pyx_v_S_hat2));

    /* "pyRing/eob_utils.pyx":992
 *         den_orb  = 1 + a_3_A44*nu
 *         num_spin = 1 + b1_A*S_hat + b2_A*S_hat2
 *         den_spin = 1 + b3_A*S_hat             # <<<<<<<<<<<<<<
 * 
 *         A44_orb  = num_orb/den_orb
*/
    __pyx_v_den_spin = (1.0 + (__pyx_v_b3_A * __pyx_v_S_hat));

    /* "pyRing/eob_utils.pyx":994
 *         den_spin = 1 + b3_A*S_hat
 * 
 *         A44_orb  = num_orb/den_orb             # <<<<<<<<<<<<<<
 *         A44_spin = num_spin/den_spin
 * 
*/
    __pyx_v_A44_orb = (__pyx_v_num_orb / __pyx_v_den_orb);

    /* "pyRing/eob_utils.pyx":995
 * 
 *         A44_orb  = num_orb/den_orb
 *         A44_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *         res = A44_0 * (1-3*nu) * A44_orb * A44_spin
*/
    __pyx_v_A44_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

    /* "pyRing/eob_utils.pyx":997
 *         A44_spin = num_spin/den_spin
 * 
 *         res = A44_0 * (1-3*nu) * A44_orb * A44_spin             # <<<<<<<<<<<<<<
 * 
 *         scale = 1 - 0.5*S_hat*omega_peak  # eq. C10 of arXiv:2001.09082v2
*/
    __pyx_v_res = (((__pyx_v_A44_0 * (1.0 - (3.0 * __pyx_v_nu))) * __pyx_v_A44_orb) * __pyx_v_A44_spin);

    /* "pyRing/eob_utils.pyx":999
 *         res = A44_0 * (1-3*nu) * A44_orb * A44_spin
 * 
 *         scale = 1 - 0.5*S_hat*omega_peak  # eq. C10 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 *         res = res * scale
 * 
*/
    __pyx_v_scale = (1.0 - ((0.5 * __pyx_v_S_hat) * __pyx_v_omega_peak));

    /* "pyRing/eob_utils.pyx":1000
 * 
 *         scale = 1 - 0.5*S_hat*omega_peak  # eq. C10 of arXiv:2001.09082v2
 *         res = res * scale             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = (__pyx_v_res * __pyx_v_scale);

    /* "pyRing/eob_utils.pyx":983
 *         res = 0     # not implemented in TEOBResumSFits.c, line 2452
 * 
 *     elif ((l==4) and (m==4)):   # eqs. C61-C64 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_A = (b_1_A44 + c_11_A44*nu + c_12_A44*nu2)/(1 + c_13_A44*nu + c_14_A44*nu2)
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1003
 * 
 * 
 *     elif ((l==4) and (m==3)):   # eqs. C73-C77 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         if (nu==0.25):  # TEOBResumSFits.c, line 2515
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L18_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L18_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1005
 *     elif ((l==4) and (m==3)):   # eqs. C73-C77 of arXiv:2001.09082v2
 * 
 *         if (nu==0.25):  # TEOBResumSFits.c, line 2515             # <<<<<<<<<<<<<<
 *             num_peak = b_1_A43_nu + b_2_A43_nu*a12 + b_3_A43_nu*a12_2
 *             den_peak = 1 + b_4_A43_nu*a12
*/
    __pyx_t_1 = (__pyx_v_nu == 0.25);
    if (__pyx_t_1) {

      /* "pyRing/eob_utils.pyx":1006
 * 
 *         if (nu==0.25):  # TEOBResumSFits.c, line 2515
 *             num_peak = b_1_A43_nu + b_2_A43_nu*a12 + b_3_A43_nu*a12_2             # <<<<<<<<<<<<<<
 *             den_peak = 1 + b_4_A43_nu*a12
 *             A43_peak = num_peak/den_peak
*/
      __pyx_v_num_peak = ((__pyx_v_b_1_A43_nu + (__pyx_v_b_2_A43_nu * __pyx_v_a12)) + (__pyx_v_b_3_A43_nu * __pyx_v_a12_2));

      /* "pyRing/eob_utils.pyx":1007
 *         if (nu==0.25):  # TEOBResumSFits.c, line 2515
 *             num_peak = b_1_A43_nu + b_2_A43_nu*a12 + b_3_A43_nu*a12_2
 *             den_peak = 1 + b_4_A43_nu*a12             # <<<<<<<<<<<<<<
 *             A43_peak = num_peak/den_peak
 * 
*/
      __pyx_v_den_peak = (1.0 + (__pyx_v_b_4_A43_nu * __pyx_v_a12));

      /* "pyRing/eob_utils.pyx":1008
 *             num_peak = b_1_A43_nu + b_2_A43_nu*a12 + b_3_A43_nu*a12_2
 *             den_peak = 1 + b_4_A43_nu*a12
 *             A43_peak = num_peak/den_peak             # <<<<<<<<<<<<<<
 * 
 *             res = A43_peak
*/
      __pyx_v_A43_peak = (__pyx_v_num_peak / __pyx_v_den_peak);

      /* "pyRing/eob_utils.pyx":1010
 *             A43_peak = num_peak/den_peak
 * 
 *             res = A43_peak             # <<<<<<<<<<<<<<
 * 
 *         else:
*/
      __pyx_v_res = __pyx_v_A43_peak;

      /* "pyRing/eob_utils.pyx":1005
 *     elif ((l==4) and (m==3)):   # eqs. C73-C77 of arXiv:2001.09082v2
 * 
 *         if (nu==0.25):  # TEOBResumSFits.c, line 2515             # <<<<<<<<<<<<<<
 *             num_peak = b_1_A43_nu + b_2_A43_nu*a12 + b_3_A43_nu*a12_2
 *             den_peak = 1 + b_4_A43_nu*a12
*/
      goto __pyx_L20;
    }

    /* "pyRing/eob_utils.pyx":1013
 * 
 *         else:
 *             b1_A = (b_1_A43 + c_11_A43*nu)/(1 + c_12_A43*nu + c_13_A43*nu2)             # <<<<<<<<<<<<<<
 *             b2_A = (b_2_A43 + c_21_A43*nu)/(1 + c_22_A43*nu + c_23_A43*nu2)
 *             b3_A = (b_3_A43 + c_31_A43*nu)/(1 + c_32_A43*nu + c_33_A43*nu2)
*/
    /*else*/ {
      __pyx_v_b1_A = ((__pyx_v_b_1_A43 + (__pyx_v_c_11_A43 * __pyx_v_nu)) / ((1.0 + (__pyx_v_c_12_A43 * __pyx_v_nu)) + (__pyx_v_c_13_A43 * __pyx_v_nu2)));

      /* "pyRing/eob_utils.pyx":1014
 *         else:
 *             b1_A = (b_1_A43 + c_11_A43*nu)/(1 + c_12_A43*nu + c_13_A43*nu2)
 *             b2_A = (b_2_A43 + c_21_A43*nu)/(1 + c_22_A43*nu + c_23_A43*nu2)             # <<<<<<<<<<<<<<
 *             b3_A = (b_3_A43 + c_31_A43*nu)/(1 + c_32_A43*nu + c_33_A43*nu2)
 * 
*/
      __pyx_v_b2_A = ((__pyx_v_b_2_A43 + (__pyx_v_c_21_A43 * __pyx_v_nu)) / ((1.0 + (__pyx_v_c_22_A43 * __pyx_v_nu)) + (__pyx_v_c_23_A43 * __pyx_v_nu2)));

      /* "pyRing/eob_utils.pyx":1015
 *             b1_A = (b_1_A43 + c_11_A43*nu)/(1 + c_12_A43*nu + c_13_A43*nu2)
 *             b2_A = (b_2_A43 + c_21_A43*nu)/(1 + c_22_A43*nu + c_23_A43*nu2)
 *             b3_A = (b_3_A43 + c_31_A43*nu)/(1 + c_32_A43*nu + c_33_A43*nu2)             # <<<<<<<<<<<<<<
 * 
 *             num_orb  = 1 + a_1_A43*nu + a_2_A43*nu2
*/
      __pyx_v_b3_A = ((__pyx_v_b_3_A43 + (__pyx_v_c_31_A43 * __pyx_v_nu)) / ((1.0 + (__pyx_v_c_32_A43 * __pyx_v_nu)) + (__pyx_v_c_33_A43 * __pyx_v_nu2)));

      /* "pyRing/eob_utils.pyx":1017
 *             b3_A = (b_3_A43 + c_31_A43*nu)/(1 + c_32_A43*nu + c_33_A43*nu2)
 * 
 *             num_orb  = 1 + a_1_A43*nu + a_2_A43*nu2             # <<<<<<<<<<<<<<
 *             den_orb  = 1 + a_3_A43*nu
 *             num_spin = b1_A*a0 + b2_A*a0_2
*/
      __pyx_v_num_orb = ((1.0 + (__pyx_v_a_1_A43 * __pyx_v_nu)) + (__pyx_v_a_2_A43 * __pyx_v_nu2));

      /* "pyRing/eob_utils.pyx":1018
 * 
 *             num_orb  = 1 + a_1_A43*nu + a_2_A43*nu2
 *             den_orb  = 1 + a_3_A43*nu             # <<<<<<<<<<<<<<
 *             num_spin = b1_A*a0 + b2_A*a0_2
 *             den_spin = 1 + b3_A*a0
*/
      __pyx_v_den_orb = (1.0 + (__pyx_v_a_3_A43 * __pyx_v_nu));

      /* "pyRing/eob_utils.pyx":1019
 *             num_orb  = 1 + a_1_A43*nu + a_2_A43*nu2
 *             den_orb  = 1 + a_3_A43*nu
 *             num_spin = b1_A*a0 + b2_A*a0_2             # <<<<<<<<<<<<<<
 *             den_spin = 1 + b3_A*a0
 * 
*/
      __pyx_v_num_spin = ((__pyx_v_b1_A * __pyx_v_a0) + (__pyx_v_b2_A * __pyx_v_a0_2));

      /* "pyRing/eob_utils.pyx":1020
 *             den_orb  = 1 + a_3_A43*nu
 *             num_spin = b1_A*a0 + b2_A*a0_2
 *             den_spin = 1 + b3_A*a0             # <<<<<<<<<<<<<<
 * 
 *             A43_orb  = num_orb/den_orb
*/
      __pyx_v_den_spin = (1.0 + (__pyx_v_b3_A * __pyx_v_a0));

      /* "pyRing/eob_utils.pyx":1022
 *             den_spin = 1 + b3_A*a0
 * 
 *             A43_orb  = num_orb/den_orb             # <<<<<<<<<<<<<<
 *             A43_spin = num_spin/den_spin
 * 
*/
      __pyx_v_A43_orb = (__pyx_v_num_orb / __pyx_v_den_orb);

      /* "pyRing/eob_utils.pyx":1023
 * 
 *             A43_orb  = num_orb/den_orb
 *             A43_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *             res = A43_0 * X12 * (1-2*nu) * A43_orb + A43_spin
*/
      __pyx_v_A43_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

      /* "pyRing/eob_utils.pyx":1025
 *             A43_spin = num_spin/den_spin
 * 
 *             res = A43_0 * X12 * (1-2*nu) * A43_orb + A43_spin             # <<<<<<<<<<<<<<
 * 
 * 
*/
      __pyx_v_res = ((((__pyx_v_A43_0 * __pyx_v_X12) * (1.0 - (2.0 * __pyx_v_nu))) * __pyx_v_A43_orb) + __pyx_v_A43_spin);
    }
    __pyx_L20:;

    /* "pyRing/eob_utils.pyx":1003
 * 
 * 
 *     elif ((l==4) and (m==3)):   # eqs. C73-C77 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         if (nu==0.25):  # TEOBResumSFits.c, line 2515
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1028
 * 
 * 
 *     elif ((l==4) and (m==2)):   # eqs. C86-C89 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_A = (b_1_A42 + c_11_A42*nu)/(1 + c_12_A42*nu)
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L21_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L21_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1030
 *     elif ((l==4) and (m==2)):   # eqs. C86-C89 of arXiv:2001.09082v2
 * 
 *         b1_A = (b_1_A42 + c_11_A42*nu)/(1 + c_12_A42*nu)             # <<<<<<<<<<<<<<
 *         b2_A = (b_2_A42 + c_21_A42*nu)/(1 + c_22_A42*nu)
 *         b3_A = (b_3_A42 + c_31_A42*nu)/(1 + c_32_A42*nu)
*/
    __pyx_v_b1_A = ((__pyx_v_b_1_A42 + (__pyx_v_c_11_A42 * __pyx_v_nu)) / (1.0 + (__pyx_v_c_12_A42 * __pyx_v_nu)));

    /* "pyRing/eob_utils.pyx":1031
 * 
 *         b1_A = (b_1_A42 + c_11_A42*nu)/(1 + c_12_A42*nu)
 *         b2_A = (b_2_A42 + c_21_A42*nu)/(1 + c_22_A42*nu)             # <<<<<<<<<<<<<<
 *         b3_A = (b_3_A42 + c_31_A42*nu)/(1 + c_32_A42*nu)
 *         b4_A = (b_4_A42 + c_41_A42*nu)/(1 + c_42_A42*nu)
*/
    __pyx_v_b2_A = ((__pyx_v_b_2_A42 + (__pyx_v_c_21_A42 * __pyx_v_nu)) / (1.0 + (__pyx_v_c_22_A42 * __pyx_v_nu)));

    /* "pyRing/eob_utils.pyx":1032
 *         b1_A = (b_1_A42 + c_11_A42*nu)/(1 + c_12_A42*nu)
 *         b2_A = (b_2_A42 + c_21_A42*nu)/(1 + c_22_A42*nu)
 *         b3_A = (b_3_A42 + c_31_A42*nu)/(1 + c_32_A42*nu)             # <<<<<<<<<<<<<<
 *         b4_A = (b_4_A42 + c_41_A42*nu)/(1 + c_42_A42*nu)
 * 
*/
    __pyx_v_b3_A = ((__pyx_v_b_3_A42 + (__pyx_v_c_31_A42 * __pyx_v_nu)) / (1.0 + (__pyx_v_c_32_A42 * __pyx_v_nu)));

    /* "pyRing/eob_utils.pyx":1033
 *         b2_A = (b_2_A42 + c_21_A42*nu)/(1 + c_22_A42*nu)
 *         b3_A = (b_3_A42 + c_31_A42*nu)/(1 + c_32_A42*nu)
 *         b4_A = (b_4_A42 + c_41_A42*nu)/(1 + c_42_A42*nu)             # <<<<<<<<<<<<<<
 * 
 *         A42_orb  = 1 + a_1_A42*nu + a_2_A42*nu2
*/
    __pyx_v_b4_A = ((__pyx_v_b_4_A42 + (__pyx_v_c_41_A42 * __pyx_v_nu)) / (1.0 + (__pyx_v_c_42_A42 * __pyx_v_nu)));

    /* "pyRing/eob_utils.pyx":1035
 *         b4_A = (b_4_A42 + c_41_A42*nu)/(1 + c_42_A42*nu)
 * 
 *         A42_orb  = 1 + a_1_A42*nu + a_2_A42*nu2             # <<<<<<<<<<<<<<
 *         num_spin = 1 + b1_A*S_hat + b2_A*S_hat2
 *         den_spin = 1 + b3_A*S_hat + b4_A*S_hat2
*/
    __pyx_v_A42_orb = ((1.0 + (__pyx_v_a_1_A42 * __pyx_v_nu)) + (__pyx_v_a_2_A42 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1036
 * 
 *         A42_orb  = 1 + a_1_A42*nu + a_2_A42*nu2
 *         num_spin = 1 + b1_A*S_hat + b2_A*S_hat2             # <<<<<<<<<<<<<<
 *         den_spin = 1 + b3_A*S_hat + b4_A*S_hat2
 * 
*/
    __pyx_v_num_spin = ((1.0 + (__pyx_v_b1_A * __pyx_v_S_hat)) + (__pyx_v_b2_A * __pyx_v_S_hat2));

    /* "pyRing/eob_utils.pyx":1037
 *         A42_orb  = 1 + a_1_A42*nu + a_2_A42*nu2
 *         num_spin = 1 + b1_A*S_hat + b2_A*S_hat2
 *         den_spin = 1 + b3_A*S_hat + b4_A*S_hat2             # <<<<<<<<<<<<<<
 * 
 *         A42_spin = num_spin/den_spin
*/
    __pyx_v_den_spin = ((1.0 + (__pyx_v_b3_A * __pyx_v_S_hat)) + (__pyx_v_b4_A * __pyx_v_S_hat2));

    /* "pyRing/eob_utils.pyx":1039
 *         den_spin = 1 + b3_A*S_hat + b4_A*S_hat2
 * 
 *         A42_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *         res = A42_0 * (1-3*nu) * A42_orb * A42_spin
*/
    __pyx_v_A42_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

    /* "pyRing/eob_utils.pyx":1041
 *         A42_spin = num_spin/den_spin
 * 
 *         res = A42_0 * (1-3*nu) * A42_orb * A42_spin             # <<<<<<<<<<<<<<
 * 
 *         scale = 1 + a0*cbrt(omega_peak/2)  # TEOBResumSFits.c, line 2506
*/
    __pyx_v_res = (((__pyx_v_A42_0 * (1.0 - (3.0 * __pyx_v_nu))) * __pyx_v_A42_orb) * __pyx_v_A42_spin);

    /* "pyRing/eob_utils.pyx":1043
 *         res = A42_0 * (1-3*nu) * A42_orb * A42_spin
 * 
 *         scale = 1 + a0*cbrt(omega_peak/2)  # TEOBResumSFits.c, line 2506             # <<<<<<<<<<<<<<
 *         res = res * scale
 * 
*/
    __pyx_v_scale = (1.0 + (__pyx_v_a0 * cbrt((__pyx_v_omega_peak / 2.0))));

    /* "pyRing/eob_utils.pyx":1044
 * 
 *         scale = 1 + a0*cbrt(omega_peak/2)  # TEOBResumSFits.c, line 2506
 *         res = res * scale             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = (__pyx_v_res * __pyx_v_scale);

    /* "pyRing/eob_utils.pyx":1028
 * 
 * 
 *     elif ((l==4) and (m==2)):   # eqs. C86-C89 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_A = (b_1_A42 + c_11_A42*nu)/(1 + c_12_A42*nu)
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1047
 * 
 * 
 *     elif ((l==4) and (m==1)):   # eq. 5.19 of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 * 
 *         '''num_orb = 1 + n_1_A41*nu + n_2_A41*nu2
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L23_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L23_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1056
 *         res = A41_0 * A41_orb'''
 * 
 *         res = 0     # TEOBResumSFits.c, line 2695             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = 0.0;

    /* "pyRing/eob_utils.pyx":1047
 * 
 * 
 *     elif ((l==4) and (m==1)):   # eq. 5.19 of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 * 
 *         '''num_orb = 1 + n_1_A41*nu + n_2_A41*nu2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1059
 * 
 * 
 *     elif ((l==5) and (m==5)):   # eqs. C98-C102 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_A = b_1_A55/(1 + c_11_A55*nu + c_12_A55*nu2)
*/
  __pyx_t_2 = (__pyx_v_l == 5);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L25_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 5);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L25_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1061
 *     elif ((l==5) and (m==5)):   # eqs. C98-C102 of arXiv:2001.09082v2
 * 
 *         b1_A = b_1_A55/(1 + c_11_A55*nu + c_12_A55*nu2)             # <<<<<<<<<<<<<<
 *         b2_A = b_2_A55/(1 + c_21_A55*nu + c_22_A55*nu2)
 * 
*/
    __pyx_v_b1_A = (__pyx_v_b_1_A55 / ((1.0 + (__pyx_v_c_11_A55 * __pyx_v_nu)) + (__pyx_v_c_12_A55 * __pyx_v_nu2)));

    /* "pyRing/eob_utils.pyx":1062
 * 
 *         b1_A = b_1_A55/(1 + c_11_A55*nu + c_12_A55*nu2)
 *         b2_A = b_2_A55/(1 + c_21_A55*nu + c_22_A55*nu2)             # <<<<<<<<<<<<<<
 * 
 *         A55_orb  = 1 + a_1_A55*nu + a_2_A55*nu2
*/
    __pyx_v_b2_A = (__pyx_v_b_2_A55 / ((1.0 + (__pyx_v_c_21_A55 * __pyx_v_nu)) + (__pyx_v_c_22_A55 * __pyx_v_nu2)));

    /* "pyRing/eob_utils.pyx":1064
 *         b2_A = b_2_A55/(1 + c_21_A55*nu + c_22_A55*nu2)
 * 
 *         A55_orb  = 1 + a_1_A55*nu + a_2_A55*nu2             # <<<<<<<<<<<<<<
 *         num_spin = b1_A*a12
 *         den_spin = 1 + b2_A*a12
*/
    __pyx_v_A55_orb = ((1.0 + (__pyx_v_a_1_A55 * __pyx_v_nu)) + (__pyx_v_a_2_A55 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1065
 * 
 *         A55_orb  = 1 + a_1_A55*nu + a_2_A55*nu2
 *         num_spin = b1_A*a12             # <<<<<<<<<<<<<<
 *         den_spin = 1 + b2_A*a12
 * 
*/
    __pyx_v_num_spin = (__pyx_v_b1_A * __pyx_v_a12);

    /* "pyRing/eob_utils.pyx":1066
 *         A55_orb  = 1 + a_1_A55*nu + a_2_A55*nu2
 *         num_spin = b1_A*a12
 *         den_spin = 1 + b2_A*a12             # <<<<<<<<<<<<<<
 * 
 *         A55_spin = num_spin/den_spin
*/
    __pyx_v_den_spin = (1.0 + (__pyx_v_b2_A * __pyx_v_a12));

    /* "pyRing/eob_utils.pyx":1068
 *         den_spin = 1 + b2_A*a12
 * 
 *         A55_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *         res = A55_0 * X12 * (1-2*nu) * A55_orb + A55_spin
*/
    __pyx_v_A55_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

    /* "pyRing/eob_utils.pyx":1070
 *         A55_spin = num_spin/den_spin
 * 
 *         res = A55_0 * X12 * (1-2*nu) * A55_orb + A55_spin             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = ((((__pyx_v_A55_0 * __pyx_v_X12) * (1.0 - (2.0 * __pyx_v_nu))) * __pyx_v_A55_orb) + __pyx_v_A55_spin);

    /* "pyRing/eob_utils.pyx":1059
 * 
 * 
 *     elif ((l==5) and (m==5)):   # eqs. C98-C102 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_A = b_1_A55/(1 + c_11_A55*nu + c_12_A55*nu2)
*/
  }
  __pyx_L3:;

  /* "pyRing/eob_utils.pyx":1073
 * 
 * 
 *     return res             # <<<<<<<<<<<<<<
 * 
 * 
*/
  __pyx_r = __pyx_v_res;
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":805
 * 
 * 
 * cdef double _amplitude_peak(double nu, double X12, double S_hat, double a12, double S_bar, double a0, double omega_peak, int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function returning the value of A at the peak, following appendix C.2 of arXiv:2001.09082v2.
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "pyRing/eob_utils.pyx":1076
 * 
 * 
 * cdef double _omega_peak(double nu, double X12, double S_hat, double a0, int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function returning the value of Omega at the peak of the strain, following appendix C.2 of arXiv:2001.09082v2.
*/

static double __pyx_f_6pyRing_9eob_utils__omega_peak(double __pyx_v_nu, double __pyx_v_X12, double __pyx_v_S_hat, double __pyx_v_a0, int __pyx_v_l, int __pyx_v_m) {
  double __pyx_v_res;
  double __pyx_v_b1_omg;
  double __pyx_v_b2_omg;
  double __pyx_v_b3_omg;
  double __pyx_v_b4_omg;
  double __pyx_v_num_orb;
  double __pyx_v_den_orb;
  double __pyx_v_num_spin;
  double __pyx_v_den_spin;
  double __pyx_v_omg22_orb;
  double __pyx_v_omg22_spin;
  double __pyx_v_omg21_orb;
  double __pyx_v_omg21_spin;
  double __pyx_v_omg33_orb;
  double __pyx_v_omg33_spin;
  double __pyx_v_omg32_orb;
  double __pyx_v_omg32_spin;
  double __pyx_v_omg31_orb;
  double __pyx_v_omg44_orb;
  double __pyx_v_omg44_spin;
  double __pyx_v_omg43_orb;
  double __pyx_v_omg43_spin;
  double __pyx_v_omg42_orb;
  double __pyx_v_omg42_spin;
  double __pyx_v_omg55_orb;
  double __pyx_v_omg55_spin;
  double __pyx_v_nu2;
  double __pyx_v_X12_2;
  double __pyx_v_S_hat2;
  double __pyx_v_S_hat3;
  double __pyx_v_a0_2;
  double __pyx_v_omg22_0;
  double __pyx_v_a_1_omg22;
  double __pyx_v_a_2_omg22;
  double __pyx_v_b_1_omg22;
  double __pyx_v_b_2_omg22;
  double __pyx_v_b_3_omg22;
  double __pyx_v_c_11_omg22;
  double __pyx_v_c_12_omg22;
  double __pyx_v_c_31_omg22;
  double __pyx_v_c_32_omg22;
  double __pyx_v_omg21_0;
  double __pyx_v_a_1_omg21;
  double __pyx_v_a_2_omg21;
  double __pyx_v_b_1_omg21;
  double __pyx_v_b_2_omg21;
  double __pyx_v_c_1_omg21;
  double __pyx_v_c_2_omg21;
  double __pyx_v_omg33_0;
  double __pyx_v_a_1_omg33;
  double __pyx_v_a_2_omg33;
  double __pyx_v_b_1_omg33;
  double __pyx_v_b_2_omg33;
  double __pyx_v_b_3_omg33;
  double __pyx_v_c_11_omg33;
  double __pyx_v_c_12_omg33;
  double __pyx_v_c_31_omg33;
  double __pyx_v_c_32_omg33;
  double __pyx_v_omg32_0;
  double __pyx_v_a_1_omg32;
  double __pyx_v_a_2_omg32;
  double __pyx_v_a_3_omg32;
  double __pyx_v_a_4_omg32;
  double __pyx_v_b_1_omg32;
  double __pyx_v_b_2_omg32;
  double __pyx_v_b_3_omg32;
  double __pyx_v_c_11_omg32;
  double __pyx_v_c_12_omg32;
  double __pyx_v_c_13_omg32;
  double __pyx_v_c_21_omg32;
  double __pyx_v_c_22_omg32;
  double __pyx_v_c_23_omg32;
  double __pyx_v_omg31_0;
  double __pyx_v_n_2_omg31;
  double __pyx_v_d_1_omg31;
  double __pyx_v_d_2_omg31;
  double __pyx_v_omg44_0;
  double __pyx_v_a_1_omg44;
  double __pyx_v_a_2_omg44;
  double __pyx_v_a_3_omg44;
  double __pyx_v_a_4_omg44;
  double __pyx_v_b_1_omg44;
  double __pyx_v_b_2_omg44;
  double __pyx_v_b_3_omg44;
  double __pyx_v_b_4_omg44;
  double __pyx_v_c_11_omg44;
  double __pyx_v_c_12_omg44;
  double __pyx_v_c_13_omg44;
  double __pyx_v_c_14_omg44;
  double __pyx_v_c_21_omg44;
  double __pyx_v_c_22_omg44;
  double __pyx_v_c_23_omg44;
  double __pyx_v_c_24_omg44;
  double __pyx_v_c_41_omg44;
  double __pyx_v_c_42_omg44;
  double __pyx_v_c_43_omg44;
  double __pyx_v_c_44_omg44;
  double __pyx_v_omg43_0;
  double __pyx_v_a_1_omg43;
  double __pyx_v_a_2_omg43;
  double __pyx_v_a_3_omg43;
  double __pyx_v_a_4_omg43;
  double __pyx_v_b_1_omg43;
  double __pyx_v_b_2_omg43;
  double __pyx_v_b_3_omg43;
  double __pyx_v_c_11_omg43;
  double __pyx_v_c_12_omg43;
  double __pyx_v_c_13_omg43;
  double __pyx_v_c_21_omg43;
  double __pyx_v_c_22_omg43;
  double __pyx_v_c_23_omg43;
  double __pyx_v_c_31_omg43;
  double __pyx_v_c_32_omg43;
  double __pyx_v_c_33_omg43;
  double __pyx_v_omg42_0;
  double __pyx_v_a_1_omg42;
  double __pyx_v_a_2_omg42;
  double __pyx_v_a_3_omg42;
  double __pyx_v_a_4_omg42;
  double __pyx_v_b_1_omg42;
  double __pyx_v_b_2_omg42;
  double __pyx_v_b_3_omg42;
  double __pyx_v_b_4_omg42;
  double __pyx_v_c_11_omg42;
  double __pyx_v_c_12_omg42;
  double __pyx_v_c_13_omg42;
  double __pyx_v_c_21_omg42;
  double __pyx_v_c_22_omg42;
  double __pyx_v_c_23_omg42;
  double __pyx_v_c_31_omg42;
  double __pyx_v_c_32_omg42;
  double __pyx_v_c_33_omg42;
  double __pyx_v_c_41_omg42;
  double __pyx_v_c_42_omg42;
  double __pyx_v_c_43_omg42;
  CYTHON_UNUSED double __pyx_v_omg41_0;
  CYTHON_UNUSED double __pyx_v_n_1_omg41;
  CYTHON_UNUSED double __pyx_v_n_2_omg41;
  CYTHON_UNUSED double __pyx_v_d_1_omg41;
  CYTHON_UNUSED double __pyx_v_d_2_omg41;
  double __pyx_v_omg55_0;
  double __pyx_v_a_1_omg55;
  double __pyx_v_a_2_omg55;
  double __pyx_v_a_3_omg55;
  double __pyx_v_b_1_omg55;
  double __pyx_v_b_2_omg55;
  double __pyx_v_c_11_omg55;
  double __pyx_v_c_12_omg55;
  double __pyx_v_c_21_omg55;
  double __pyx_v_c_22_omg55;
  double __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;

  /* "pyRing/eob_utils.pyx":1088
 *     """
 * 
 *     cdef double res = 0.             # <<<<<<<<<<<<<<
 *     cdef double b1_omg, b2_omg, b3_omg, b4_omg, num_orb, den_orb, num_spin, den_spin,
 *     cdef double omg22_orb, omg22_spin, omg21_orb, omg21_spin
*/
  __pyx_v_res = 0.;

  /* "pyRing/eob_utils.pyx":1094
 *     cdef double omg44_orb, omg44_spin, omg43_orb, omg43_spin, omg42_orb, omg42_spin, omg41_orb
 *     cdef double omg55_orb, omg55_spin
 *     cdef double nu2 = nu*nu, X12_2 = X12*X12, S_hat2 = S_hat*S_hat, S_hat3 = S_hat2*S_hat, a0_2 = a0*a0             # <<<<<<<<<<<<<<
 * 
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
*/
  __pyx_v_nu2 = (__pyx_v_nu * __pyx_v_nu);
  __pyx_v_X12_2 = (__pyx_v_X12 * __pyx_v_X12);
  __pyx_v_S_hat2 = (__pyx_v_S_hat * __pyx_v_S_hat);
  __pyx_v_S_hat3 = (__pyx_v_S_hat2 * __pyx_v_S_hat);
  __pyx_v_a0_2 = (__pyx_v_a0 * __pyx_v_a0);

  /* "pyRing/eob_utils.pyx":1098
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
 *     # (2,2) - TEOBResumSFits.c, line 2226-2236
 *     cdef double omg22_0    = 0.273356     # TEOBResumSFits.c, line 2003             # <<<<<<<<<<<<<<
 *     cdef double a_1_omg22  = 0.84074,  a_2_omg22  = 1.6976
 *     cdef double b_1_omg22  = -0.42311, b_2_omg22  = -0.066699, b_3_omg22  = -0.83053
*/
  __pyx_v_omg22_0 = 0.273356;

  /* "pyRing/eob_utils.pyx":1099
 *     # (2,2) - TEOBResumSFits.c, line 2226-2236
 *     cdef double omg22_0    = 0.273356     # TEOBResumSFits.c, line 2003
 *     cdef double a_1_omg22  = 0.84074,  a_2_omg22  = 1.6976             # <<<<<<<<<<<<<<
 *     cdef double b_1_omg22  = -0.42311, b_2_omg22  = -0.066699, b_3_omg22  = -0.83053
 *     cdef double c_11_omg22 = 0.066045, c_12_omg22 = -0.23876,  c_31_omg22 = 0.76819,  c_32_omg22 = -0.9201
*/
  __pyx_v_a_1_omg22 = 0.84074;
  __pyx_v_a_2_omg22 = 1.6976;

  /* "pyRing/eob_utils.pyx":1100
 *     cdef double omg22_0    = 0.273356     # TEOBResumSFits.c, line 2003
 *     cdef double a_1_omg22  = 0.84074,  a_2_omg22  = 1.6976
 *     cdef double b_1_omg22  = -0.42311, b_2_omg22  = -0.066699, b_3_omg22  = -0.83053             # <<<<<<<<<<<<<<
 *     cdef double c_11_omg22 = 0.066045, c_12_omg22 = -0.23876,  c_31_omg22 = 0.76819,  c_32_omg22 = -0.9201
 * 
*/
  __pyx_v_b_1_omg22 = -0.42311;
  __pyx_v_b_2_omg22 = -0.066699;
  __pyx_v_b_3_omg22 = -0.83053;

  /* "pyRing/eob_utils.pyx":1101
 *     cdef double a_1_omg22  = 0.84074,  a_2_omg22  = 1.6976
 *     cdef double b_1_omg22  = -0.42311, b_2_omg22  = -0.066699, b_3_omg22  = -0.83053
 *     cdef double c_11_omg22 = 0.066045, c_12_omg22 = -0.23876,  c_31_omg22 = 0.76819,  c_32_omg22 = -0.9201             # <<<<<<<<<<<<<<
 * 
 *     # (2,1) - TEOBResumSFits.c, line 2184-2189
*/
  __pyx_v_c_11_omg22 = 0.066045;
  __pyx_v_c_12_omg22 = -0.23876;
  __pyx_v_c_31_omg22 = 0.76819;
  __pyx_v_c_32_omg22 = -0.9201;

  /* "pyRing/eob_utils.pyx":1104
 * 
 *     # (2,1) - TEOBResumSFits.c, line 2184-2189
 *     cdef double omg21_0   = 0.2906425497     # TEOBResumSFits.c, line 2002             # <<<<<<<<<<<<<<
 *     cdef double a_1_omg21 = -0.563075,  a_2_omg21 = 3.28677
 *     cdef double b_1_omg21 = 0.179639,   b_2_omg21 = -0.302122
*/
  __pyx_v_omg21_0 = 0.2906425497;

  /* "pyRing/eob_utils.pyx":1105
 *     # (2,1) - TEOBResumSFits.c, line 2184-2189
 *     cdef double omg21_0   = 0.2906425497     # TEOBResumSFits.c, line 2002
 *     cdef double a_1_omg21 = -0.563075,  a_2_omg21 = 3.28677             # <<<<<<<<<<<<<<
 *     cdef double b_1_omg21 = 0.179639,   b_2_omg21 = -0.302122
 *     cdef double c_1_omg21 = -1.20684,   c_2_omg21 = 0.425645
*/
  __pyx_v_a_1_omg21 = -0.563075;
  __pyx_v_a_2_omg21 = 3.28677;

  /* "pyRing/eob_utils.pyx":1106
 *     cdef double omg21_0   = 0.2906425497     # TEOBResumSFits.c, line 2002
 *     cdef double a_1_omg21 = -0.563075,  a_2_omg21 = 3.28677
 *     cdef double b_1_omg21 = 0.179639,   b_2_omg21 = -0.302122             # <<<<<<<<<<<<<<
 *     cdef double c_1_omg21 = -1.20684,   c_2_omg21 = 0.425645
 * 
*/
  __pyx_v_b_1_omg21 = 0.179639;
  __pyx_v_b_2_omg21 = -0.302122;

  /* "pyRing/eob_utils.pyx":1107
 *     cdef double a_1_omg21 = -0.563075,  a_2_omg21 = 3.28677
 *     cdef double b_1_omg21 = 0.179639,   b_2_omg21 = -0.302122
 *     cdef double c_1_omg21 = -1.20684,   c_2_omg21 = 0.425645             # <<<<<<<<<<<<<<
 * 
 *     # (3,3) - TEOBResumSFits.c, line 2258-2266
*/
  __pyx_v_c_1_omg21 = -1.20684;
  __pyx_v_c_2_omg21 = 0.425645;

  /* "pyRing/eob_utils.pyx":1110
 * 
 *     # (3,3) - TEOBResumSFits.c, line 2258-2266
 *     cdef double omg33_0    = 0.4541278937     # TEOBResumSFits.c, line 2006             # <<<<<<<<<<<<<<
 *     cdef double a_1_omg33  = 1.08224,    a_2_omg33  = 2.59333
 *     cdef double b_1_omg33  = -0.406161,  b_2_omg33  = -0.0647944, b_3_omg33  = -0.748126
*/
  __pyx_v_omg33_0 = 0.4541278937;

  /* "pyRing/eob_utils.pyx":1111
 *     # (3,3) - TEOBResumSFits.c, line 2258-2266
 *     cdef double omg33_0    = 0.4541278937     # TEOBResumSFits.c, line 2006
 *     cdef double a_1_omg33  = 1.08224,    a_2_omg33  = 2.59333             # <<<<<<<<<<<<<<
 *     cdef double b_1_omg33  = -0.406161,  b_2_omg33  = -0.0647944, b_3_omg33  = -0.748126
 *     cdef double c_11_omg33 = 0.85777,    c_12_omg33 = -0.70066,   c_31_omg33 = 2.97025,   c_32_omg33 = -3.96242
*/
  __pyx_v_a_1_omg33 = 1.08224;
  __pyx_v_a_2_omg33 = 2.59333;

  /* "pyRing/eob_utils.pyx":1112
 *     cdef double omg33_0    = 0.4541278937     # TEOBResumSFits.c, line 2006
 *     cdef double a_1_omg33  = 1.08224,    a_2_omg33  = 2.59333
 *     cdef double b_1_omg33  = -0.406161,  b_2_omg33  = -0.0647944, b_3_omg33  = -0.748126             # <<<<<<<<<<<<<<
 *     cdef double c_11_omg33 = 0.85777,    c_12_omg33 = -0.70066,   c_31_omg33 = 2.97025,   c_32_omg33 = -3.96242
 * 
*/
  __pyx_v_b_1_omg33 = -0.406161;
  __pyx_v_b_2_omg33 = -0.0647944;
  __pyx_v_b_3_omg33 = -0.748126;

  /* "pyRing/eob_utils.pyx":1113
 *     cdef double a_1_omg33  = 1.08224,    a_2_omg33  = 2.59333
 *     cdef double b_1_omg33  = -0.406161,  b_2_omg33  = -0.0647944, b_3_omg33  = -0.748126
 *     cdef double c_11_omg33 = 0.85777,    c_12_omg33 = -0.70066,   c_31_omg33 = 2.97025,   c_32_omg33 = -3.96242             # <<<<<<<<<<<<<<
 * 
 *     # (3,2) - TEOBResumSFits.c, line 2240-2248
*/
  __pyx_v_c_11_omg33 = 0.85777;
  __pyx_v_c_12_omg33 = -0.70066;
  __pyx_v_c_31_omg33 = 2.97025;
  __pyx_v_c_32_omg33 = -3.96242;

  /* "pyRing/eob_utils.pyx":1116
 * 
 *     # (3,2) - TEOBResumSFits.c, line 2240-2248
 *     cdef double omg32_0    = 0.4516072248     # TEOBResumSFits.c, line 2005             # <<<<<<<<<<<<<<
 *     cdef double a_1_omg32  = -9.13525,   a_2_omg32  = 21.488,    a_3_omg32  = -8.81384, a_4_omg32  = 20.0595
 *     cdef double b_1_omg32  = -0.458126,  b_2_omg32  = 0.0474616, b_3_omg32  = -0.486049
*/
  __pyx_v_omg32_0 = 0.4516072248;

  /* "pyRing/eob_utils.pyx":1117
 *     # (3,2) - TEOBResumSFits.c, line 2240-2248
 *     cdef double omg32_0    = 0.4516072248     # TEOBResumSFits.c, line 2005
 *     cdef double a_1_omg32  = -9.13525,   a_2_omg32  = 21.488,    a_3_omg32  = -8.81384, a_4_omg32  = 20.0595             # <<<<<<<<<<<<<<
 *     cdef double b_1_omg32  = -0.458126,  b_2_omg32  = 0.0474616, b_3_omg32  = -0.486049
 *     cdef double c_11_omg32 = 3.25319,    c_12_omg32 = 0.535555,  c_13_omg32 = -8.07905, c_21_omg32 = 1.00066, c_22_omg32 = -1.1333, c_23_omg32 = 0.601572
*/
  __pyx_v_a_1_omg32 = -9.13525;
  __pyx_v_a_2_omg32 = 21.488;
  __pyx_v_a_3_omg32 = -8.81384;
  __pyx_v_a_4_omg32 = 20.0595;

  /* "pyRing/eob_utils.pyx":1118
 *     cdef double omg32_0    = 0.4516072248     # TEOBResumSFits.c, line 2005
 *     cdef double a_1_omg32  = -9.13525,   a_2_omg32  = 21.488,    a_3_omg32  = -8.81384, a_4_omg32  = 20.0595
 *     cdef double b_1_omg32  = -0.458126,  b_2_omg32  = 0.0474616, b_3_omg32  = -0.486049             # <<<<<<<<<<<<<<
 *     cdef double c_11_omg32 = 3.25319,    c_12_omg32 = 0.535555,  c_13_omg32 = -8.07905, c_21_omg32 = 1.00066, c_22_omg32 = -1.1333, c_23_omg32 = 0.601572
 * 
*/
  __pyx_v_b_1_omg32 = -0.458126;
  __pyx_v_b_2_omg32 = 0.0474616;
  __pyx_v_b_3_omg32 = -0.486049;

  /* "pyRing/eob_utils.pyx":1119
 *     cdef double a_1_omg32  = -9.13525,   a_2_omg32  = 21.488,    a_3_omg32  = -8.81384, a_4_omg32  = 20.0595
 *     cdef double b_1_omg32  = -0.458126,  b_2_omg32  = 0.0474616, b_3_omg32  = -0.486049
 *     cdef double c_11_omg32 = 3.25319,    c_12_omg32 = 0.535555,  c_13_omg32 = -8.07905, c_21_omg32 = 1.00066, c_22_omg32 = -1.1333, c_23_omg32 = 0.601572             # <<<<<<<<<<<<<<
 * 
 *     # (3,1) - TEOBResumSFits.c, line 2691
*/
  __pyx_v_c_11_omg32 = 3.25319;
  __pyx_v_c_12_omg32 = 0.535555;
  __pyx_v_c_13_omg32 = -8.07905;
  __pyx_v_c_21_omg32 = 1.00066;
  __pyx_v_c_22_omg32 = -1.1333;
  __pyx_v_c_23_omg32 = 0.601572;

  /* "pyRing/eob_utils.pyx":1122
 * 
 *     # (3,1) - TEOBResumSFits.c, line 2691
 *     cdef double omg31_0   = 0.411755     # TEOBResumSFits.c, line 2004             # <<<<<<<<<<<<<<
 *     cdef double n_2_omg31 = 7.5362
 *     cdef double d_1_omg31 = -2.7555, d_2_omg31 = 38.572
*/
  __pyx_v_omg31_0 = 0.411755;

  /* "pyRing/eob_utils.pyx":1123
 *     # (3,1) - TEOBResumSFits.c, line 2691
 *     cdef double omg31_0   = 0.411755     # TEOBResumSFits.c, line 2004
 *     cdef double n_2_omg31 = 7.5362             # <<<<<<<<<<<<<<
 *     cdef double d_1_omg31 = -2.7555, d_2_omg31 = 38.572
 * 
*/
  __pyx_v_n_2_omg31 = 7.5362;

  /* "pyRing/eob_utils.pyx":1124
 *     cdef double omg31_0   = 0.411755     # TEOBResumSFits.c, line 2004
 *     cdef double n_2_omg31 = 7.5362
 *     cdef double d_1_omg31 = -2.7555, d_2_omg31 = 38.572             # <<<<<<<<<<<<<<
 * 
 *     # (4,4) - TEOBResumSFits.c, line 2330-2353
*/
  __pyx_v_d_1_omg31 = -2.7555;
  __pyx_v_d_2_omg31 = 38.572;

  /* "pyRing/eob_utils.pyx":1127
 * 
 *     # (4,4) - TEOBResumSFits.c, line 2330-2353
 *     cdef double omg44_0    = 0.6356586393     # TEOBResumSFits.c, line 2010             # <<<<<<<<<<<<<<
 *     cdef double a_1_omg44  = -0.964614,  a_2_omg44  = -11.1828,   a_3_omg44  = -2.08471,   a_4_omg44  = -6.89287
 *     cdef double b_1_omg44  = -0.445192,  b_2_omg44  = -0.0985658, b_3_omg44  = -0.0307812, b_4_omg44  = -0.801552
*/
  __pyx_v_omg44_0 = 0.6356586393;

  /* "pyRing/eob_utils.pyx":1128
 *     # (4,4) - TEOBResumSFits.c, line 2330-2353
 *     cdef double omg44_0    = 0.6356586393     # TEOBResumSFits.c, line 2010
 *     cdef double a_1_omg44  = -0.964614,  a_2_omg44  = -11.1828,   a_3_omg44  = -2.08471,   a_4_omg44  = -6.89287             # <<<<<<<<<<<<<<
 *     cdef double b_1_omg44  = -0.445192,  b_2_omg44  = -0.0985658, b_3_omg44  = -0.0307812, b_4_omg44  = -0.801552
 *     cdef double c_11_omg44 = -0.92902,   c_12_omg44 = 10.86310,   c_13_omg44 = -4.44930,   c_14_omg44 = 3.01808,   c_21_omg44 = 0, c_22_omg44 = 1.62523, c_23_omg44 = -7.70486, c_24_omg44 = 15.06517, c_41_omg44 = 0.93790, c_42_omg44 = 8.36038, c_43_omg44 = -4.85774, c_44_omg44 = 4.80446
*/
  __pyx_v_a_1_omg44 = -0.964614;
  __pyx_v_a_2_omg44 = -11.1828;
  __pyx_v_a_3_omg44 = -2.08471;
  __pyx_v_a_4_omg44 = -6.89287;

  /* "pyRing/eob_utils.pyx":1129
 *     cdef double omg44_0    = 0.6356586393     # TEOBResumSFits.c, line 2010
 *     cdef double a_1_omg44  = -0.964614,  a_2_omg44  = -11.1828,   a_3_omg44  = -2.08471,   a_4_omg44  = -6.89287
 *     cdef double b_1_omg44  = -0.445192,  b_2_omg44  = -0.0985658, b_3_omg44  = -0.0307812, b_4_omg44  = -0.801552             # <<<<<<<<<<<<<<
 *     cdef double c_11_omg44 = -0.92902,   c_12_omg44 = 10.86310,   c_13_omg44 = -4.44930,   c_14_omg44 = 3.01808,   c_21_omg44 = 0, c_22_omg44 = 1.62523, c_23_omg44 = -7.70486, c_24_omg44 = 15.06517, c_41_omg44 = 0.93790, c_42_omg44 = 8.36038, c_43_omg44 = -4.85774, c_44_omg44 = 4.80446
 * 
*/
  __pyx_v_b_1_omg44 = -0.445192;
  __pyx_v_b_2_omg44 = -0.0985658;
  __pyx_v_b_3_omg44 = -0.0307812;
  __pyx_v_b_4_omg44 = -0.801552;

  /* "pyRing/eob_utils.pyx":1130
 *     cdef double a_1_omg44  = -0.964614,  a_2_omg44  = -11.1828,   a_3_omg44  = -2.08471,   a_4_omg44  = -6.89287
 *     cdef double b_1_omg44  = -0.445192,  b_2_omg44  = -0.0985658, b_3_omg44  = -0.0307812, b_4_omg44  = -0.801552
 *     cdef double c_11_omg44 = -0.92902,   c_12_omg44 = 10.86310,   c_13_omg44 = -4.44930,   c_14_omg44 = 3.01808,   c_21_omg44 = 0, c_22_omg44 = 1.62523, c_23_omg44 = -7.70486, c_24_omg44 = 15.06517, c_41_omg44 = 0.93790, c_42_omg44 = 8.36038, c_43_omg44 = -4.85774, c_44_omg44 = 4.80446             # <<<<<<<<<<<<<<
 * 
 *     # (4,3) - TEOBResumSFits.c, line 2305-2320
*/
  __pyx_v_c_11_omg44 = -0.92902;
  __pyx_v_c_12_omg44 = 10.86310;
  __pyx_v_c_13_omg44 = -4.44930;
  __pyx_v_c_14_omg44 = 3.01808;
  __pyx_v_c_21_omg44 = 0.0;
  __pyx_v_c_22_omg44 = 1.62523;
  __pyx_v_c_23_omg44 = -7.70486;
  __pyx_v_c_24_omg44 = 15.06517;
  __pyx_v_c_41_omg44 = 0.93790;
  __pyx_v_c_42_omg44 = 8.36038;
  __pyx_v_c_43_omg44 = -4.85774;
  __pyx_v_c_44_omg44 = 4.80446;

  /* "pyRing/eob_utils.pyx":1133
 * 
 *     # (4,3) - TEOBResumSFits.c, line 2305-2320
 *     cdef double omg43_0    = 0.6361300619     # TEOBResumSFits.c, line 2009             # <<<<<<<<<<<<<<
 *     cdef double a_1_omg43  = -9.02463,   a_2_omg43  = 21.9802,   a_3_omg43  = -8.75892, a_4_omg43 = 20.5624
 *     cdef double b_1_omg43  = -0.973324,  b_2_omg43  = -0.109921, b_3_omg43  = -1.08036
*/
  __pyx_v_omg43_0 = 0.6361300619;

  /* "pyRing/eob_utils.pyx":1134
 *     # (4,3) - TEOBResumSFits.c, line 2305-2320
 *     cdef double omg43_0    = 0.6361300619     # TEOBResumSFits.c, line 2009
 *     cdef double a_1_omg43  = -9.02463,   a_2_omg43  = 21.9802,   a_3_omg43  = -8.75892, a_4_omg43 = 20.5624             # <<<<<<<<<<<<<<
 *     cdef double b_1_omg43  = -0.973324,  b_2_omg43  = -0.109921, b_3_omg43  = -1.08036
 *     cdef double c_11_omg43 = 11.5224,    c_12_omg43 = -26.8421,  c_13_omg43 = -2.84285, c_21_omg43 = 3.51943, c_22_omg43 = -12.1688, c_23_omg43 = -3.96385, c_31_omg43 = 5.53433, c_32_omg43 = 3.73988, c_33_omg43 = 4.219
*/
  __pyx_v_a_1_omg43 = -9.02463;
  __pyx_v_a_2_omg43 = 21.9802;
  __pyx_v_a_3_omg43 = -8.75892;
  __pyx_v_a_4_omg43 = 20.5624;

  /* "pyRing/eob_utils.pyx":1135
 *     cdef double omg43_0    = 0.6361300619     # TEOBResumSFits.c, line 2009
 *     cdef double a_1_omg43  = -9.02463,   a_2_omg43  = 21.9802,   a_3_omg43  = -8.75892, a_4_omg43 = 20.5624
 *     cdef double b_1_omg43  = -0.973324,  b_2_omg43  = -0.109921, b_3_omg43  = -1.08036             # <<<<<<<<<<<<<<
 *     cdef double c_11_omg43 = 11.5224,    c_12_omg43 = -26.8421,  c_13_omg43 = -2.84285, c_21_omg43 = 3.51943, c_22_omg43 = -12.1688, c_23_omg43 = -3.96385, c_31_omg43 = 5.53433, c_32_omg43 = 3.73988, c_33_omg43 = 4.219
 * 
*/
  __pyx_v_b_1_omg43 = -0.973324;
  __pyx_v_b_2_omg43 = -0.109921;
  __pyx_v_b_3_omg43 = -1.08036;

  /* "pyRing/eob_utils.pyx":1136
 *     cdef double a_1_omg43  = -9.02463,   a_2_omg43  = 21.9802,   a_3_omg43  = -8.75892, a_4_omg43 = 20.5624
 *     cdef double b_1_omg43  = -0.973324,  b_2_omg43  = -0.109921, b_3_omg43  = -1.08036
 *     cdef double c_11_omg43 = 11.5224,    c_12_omg43 = -26.8421,  c_13_omg43 = -2.84285, c_21_omg43 = 3.51943, c_22_omg43 = -12.1688, c_23_omg43 = -3.96385, c_31_omg43 = 5.53433, c_32_omg43 = 3.73988, c_33_omg43 = 4.219             # <<<<<<<<<<<<<<
 * 
 *     # (4,2) - TEOBResumSFits.c, line 2275-2294
*/
  __pyx_v_c_11_omg43 = 11.5224;
  __pyx_v_c_12_omg43 = -26.8421;
  __pyx_v_c_13_omg43 = -2.84285;
  __pyx_v_c_21_omg43 = 3.51943;
  __pyx_v_c_22_omg43 = -12.1688;
  __pyx_v_c_23_omg43 = -3.96385;
  __pyx_v_c_31_omg43 = 5.53433;
  __pyx_v_c_32_omg43 = 3.73988;
  __pyx_v_c_33_omg43 = 4.219;

  /* "pyRing/eob_utils.pyx":1139
 * 
 *     # (4,2) - TEOBResumSFits.c, line 2275-2294
 *     cdef double omg42_0    = 0.6175331548     # TEOBResumSFits.c, line 2008             # <<<<<<<<<<<<<<
 *     cdef double a_1_omg42  = -7.44121,   a_2_omg42  = 14.233,   a_3_omg42  = -6.61754, a_4_omg42  = 11.4329
 *     cdef double b_1_omg42  = -2.37589,   b_2_omg42  = 1.97249,  b_3_omg42  = -2.36107, b_4_omg42  = 2.16383
*/
  __pyx_v_omg42_0 = 0.6175331548;

  /* "pyRing/eob_utils.pyx":1140
 *     # (4,2) - TEOBResumSFits.c, line 2275-2294
 *     cdef double omg42_0    = 0.6175331548     # TEOBResumSFits.c, line 2008
 *     cdef double a_1_omg42  = -7.44121,   a_2_omg42  = 14.233,   a_3_omg42  = -6.61754, a_4_omg42  = 11.4329             # <<<<<<<<<<<<<<
 *     cdef double b_1_omg42  = -2.37589,   b_2_omg42  = 1.97249,  b_3_omg42  = -2.36107, b_4_omg42  = 2.16383
 *     cdef double c_11_omg42 = 10.1045,    c_12_omg42 = -6.94127, c_13_omg42 = 12.1857,  c_21_omg42 = -1.62866, c_22_omg42 = -2.6756, c_23_omg42 = -4.7536, c_31_omg42 = 10.071, c_32_omg42 = -6.7299, c_33_omg42 = 12.0377, c_41_omg42 = -8.56139, c_42_omg42 = -5.27136, c_43_omg42 = 5.10653
*/
  __pyx_v_a_1_omg42 = -7.44121;
  __pyx_v_a_2_omg42 = 14.233;
  __pyx_v_a_3_omg42 = -6.61754;
  __pyx_v_a_4_omg42 = 11.4329;

  /* "pyRing/eob_utils.pyx":1141
 *     cdef double omg42_0    = 0.6175331548     # TEOBResumSFits.c, line 2008
 *     cdef double a_1_omg42  = -7.44121,   a_2_omg42  = 14.233,   a_3_omg42  = -6.61754, a_4_omg42  = 11.4329
 *     cdef double b_1_omg42  = -2.37589,   b_2_omg42  = 1.97249,  b_3_omg42  = -2.36107, b_4_omg42  = 2.16383             # <<<<<<<<<<<<<<
 *     cdef double c_11_omg42 = 10.1045,    c_12_omg42 = -6.94127, c_13_omg42 = 12.1857,  c_21_omg42 = -1.62866, c_22_omg42 = -2.6756, c_23_omg42 = -4.7536, c_31_omg42 = 10.071, c_32_omg42 = -6.7299, c_33_omg42 = 12.0377, c_41_omg42 = -8.56139, c_42_omg42 = -5.27136, c_43_omg42 = 5.10653
 * 
*/
  __pyx_v_b_1_omg42 = -2.37589;
  __pyx_v_b_2_omg42 = 1.97249;
  __pyx_v_b_3_omg42 = -2.36107;
  __pyx_v_b_4_omg42 = 2.16383;

  /* "pyRing/eob_utils.pyx":1142
 *     cdef double a_1_omg42  = -7.44121,   a_2_omg42  = 14.233,   a_3_omg42  = -6.61754, a_4_omg42  = 11.4329
 *     cdef double b_1_omg42  = -2.37589,   b_2_omg42  = 1.97249,  b_3_omg42  = -2.36107, b_4_omg42  = 2.16383
 *     cdef double c_11_omg42 = 10.1045,    c_12_omg42 = -6.94127, c_13_omg42 = 12.1857,  c_21_omg42 = -1.62866, c_22_omg42 = -2.6756, c_23_omg42 = -4.7536, c_31_omg42 = 10.071, c_32_omg42 = -6.7299, c_33_omg42 = 12.0377, c_41_omg42 = -8.56139, c_42_omg42 = -5.27136, c_43_omg42 = 5.10653             # <<<<<<<<<<<<<<
 * 
 *     # (4,1) - TEOBResumSFits.c, line 2696
*/
  __pyx_v_c_11_omg42 = 10.1045;
  __pyx_v_c_12_omg42 = -6.94127;
  __pyx_v_c_13_omg42 = 12.1857;
  __pyx_v_c_21_omg42 = -1.62866;
  __pyx_v_c_22_omg42 = -2.6756;
  __pyx_v_c_23_omg42 = -4.7536;
  __pyx_v_c_31_omg42 = 10.071;
  __pyx_v_c_32_omg42 = -6.7299;
  __pyx_v_c_33_omg42 = 12.0377;
  __pyx_v_c_41_omg42 = -8.56139;
  __pyx_v_c_42_omg42 = -5.27136;
  __pyx_v_c_43_omg42 = 5.10653;

  /* "pyRing/eob_utils.pyx":1145
 * 
 *     # (4,1) - TEOBResumSFits.c, line 2696
 *     cdef double omg41_0   = 0.552201     # TEOBResumSFits.c, line 2007             # <<<<<<<<<<<<<<
 *     cdef double n_1_omg41 = -10.876, n_2_omg41 = 37.904
 *     cdef double d_1_omg41 = -11.194, d_2_omg41 = 42.77
*/
  __pyx_v_omg41_0 = 0.552201;

  /* "pyRing/eob_utils.pyx":1146
 *     # (4,1) - TEOBResumSFits.c, line 2696
 *     cdef double omg41_0   = 0.552201     # TEOBResumSFits.c, line 2007
 *     cdef double n_1_omg41 = -10.876, n_2_omg41 = 37.904             # <<<<<<<<<<<<<<
 *     cdef double d_1_omg41 = -11.194, d_2_omg41 = 42.77
 * 
*/
  __pyx_v_n_1_omg41 = -10.876;
  __pyx_v_n_2_omg41 = 37.904;

  /* "pyRing/eob_utils.pyx":1147
 *     cdef double omg41_0   = 0.552201     # TEOBResumSFits.c, line 2007
 *     cdef double n_1_omg41 = -10.876, n_2_omg41 = 37.904
 *     cdef double d_1_omg41 = -11.194, d_2_omg41 = 42.77             # <<<<<<<<<<<<<<
 * 
 *     # (5,5) - TEOBResumSFits.c, line 2364-2369
*/
  __pyx_v_d_1_omg41 = -11.194;
  __pyx_v_d_2_omg41 = 42.77;

  /* "pyRing/eob_utils.pyx":1150
 * 
 *     # (5,5) - TEOBResumSFits.c, line 2364-2369
 *     cdef double omg55_0    = 0.818117     # TEOBResumSFits.c, line 2011             # <<<<<<<<<<<<<<
 *     cdef double a_1_omg55  = -2.8918,   a_2_omg55  = -3.2012,   a_3_omg55  = -3.773
 *     cdef double b_1_omg55  = -0.332703, b_2_omg55  = -0.675738
*/
  __pyx_v_omg55_0 = 0.818117;

  /* "pyRing/eob_utils.pyx":1151
 *     # (5,5) - TEOBResumSFits.c, line 2364-2369
 *     cdef double omg55_0    = 0.818117     # TEOBResumSFits.c, line 2011
 *     cdef double a_1_omg55  = -2.8918,   a_2_omg55  = -3.2012,   a_3_omg55  = -3.773             # <<<<<<<<<<<<<<
 *     cdef double b_1_omg55  = -0.332703, b_2_omg55  = -0.675738
 *     cdef double c_11_omg55 = 1.487294,  c_12_omg55 = -2.058537, c_21_omg55 = 1.454248, c_22_omg55 = -1.301284
*/
  __pyx_v_a_1_omg55 = -2.8918;
  __pyx_v_a_2_omg55 = -3.2012;
  __pyx_v_a_3_omg55 = -3.773;

  /* "pyRing/eob_utils.pyx":1152
 *     cdef double omg55_0    = 0.818117     # TEOBResumSFits.c, line 2011
 *     cdef double a_1_omg55  = -2.8918,   a_2_omg55  = -3.2012,   a_3_omg55  = -3.773
 *     cdef double b_1_omg55  = -0.332703, b_2_omg55  = -0.675738             # <<<<<<<<<<<<<<
 *     cdef double c_11_omg55 = 1.487294,  c_12_omg55 = -2.058537, c_21_omg55 = 1.454248, c_22_omg55 = -1.301284
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
*/
  __pyx_v_b_1_omg55 = -0.332703;
  __pyx_v_b_2_omg55 = -0.675738;

  /* "pyRing/eob_utils.pyx":1153
 *     cdef double a_1_omg55  = -2.8918,   a_2_omg55  = -3.2012,   a_3_omg55  = -3.773
 *     cdef double b_1_omg55  = -0.332703, b_2_omg55  = -0.675738
 *     cdef double c_11_omg55 = 1.487294,  c_12_omg55 = -2.058537, c_21_omg55 = 1.454248, c_22_omg55 = -1.301284             # <<<<<<<<<<<<<<
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
 * 
*/
  __pyx_v_c_11_omg55 = 1.487294;
  __pyx_v_c_12_omg55 = -2.058537;
  __pyx_v_c_21_omg55 = 1.454248;
  __pyx_v_c_22_omg55 = -1.301284;

  /* "pyRing/eob_utils.pyx":1157
 * 
 * 
 *     if ((l==2) and (m==2)): # eqs. C17-C20 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_omg = (b_1_omg22 + c_11_omg22*X12)/(1 + c_12_omg22*X12)
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L4_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1159
 *     if ((l==2) and (m==2)): # eqs. C17-C20 of arXiv:2001.09082v2
 * 
 *         b1_omg = (b_1_omg22 + c_11_omg22*X12)/(1 + c_12_omg22*X12)             # <<<<<<<<<<<<<<
 *         b2_omg =  b_2_omg22
 *         b3_omg = (b_3_omg22 + c_31_omg22*X12)/(1 + c_32_omg22*X12)
*/
    __pyx_v_b1_omg = ((__pyx_v_b_1_omg22 + (__pyx_v_c_11_omg22 * __pyx_v_X12)) / (1.0 + (__pyx_v_c_12_omg22 * __pyx_v_X12)));

    /* "pyRing/eob_utils.pyx":1160
 * 
 *         b1_omg = (b_1_omg22 + c_11_omg22*X12)/(1 + c_12_omg22*X12)
 *         b2_omg =  b_2_omg22             # <<<<<<<<<<<<<<
 *         b3_omg = (b_3_omg22 + c_31_omg22*X12)/(1 + c_32_omg22*X12)
 * 
*/
    __pyx_v_b2_omg = __pyx_v_b_2_omg22;

    /* "pyRing/eob_utils.pyx":1161
 *         b1_omg = (b_1_omg22 + c_11_omg22*X12)/(1 + c_12_omg22*X12)
 *         b2_omg =  b_2_omg22
 *         b3_omg = (b_3_omg22 + c_31_omg22*X12)/(1 + c_32_omg22*X12)             # <<<<<<<<<<<<<<
 * 
 *         omg22_orb = 1 + a_1_omg22*nu + a_2_omg22*nu2
*/
    __pyx_v_b3_omg = ((__pyx_v_b_3_omg22 + (__pyx_v_c_31_omg22 * __pyx_v_X12)) / (1.0 + (__pyx_v_c_32_omg22 * __pyx_v_X12)));

    /* "pyRing/eob_utils.pyx":1163
 *         b3_omg = (b_3_omg22 + c_31_omg22*X12)/(1 + c_32_omg22*X12)
 * 
 *         omg22_orb = 1 + a_1_omg22*nu + a_2_omg22*nu2             # <<<<<<<<<<<<<<
 *         num_spin  = 1 + b1_omg*S_hat + b2_omg*S_hat2
 *         den_spin  = 1 + b3_omg*S_hat
*/
    __pyx_v_omg22_orb = ((1.0 + (__pyx_v_a_1_omg22 * __pyx_v_nu)) + (__pyx_v_a_2_omg22 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1164
 * 
 *         omg22_orb = 1 + a_1_omg22*nu + a_2_omg22*nu2
 *         num_spin  = 1 + b1_omg*S_hat + b2_omg*S_hat2             # <<<<<<<<<<<<<<
 *         den_spin  = 1 + b3_omg*S_hat
 * 
*/
    __pyx_v_num_spin = ((1.0 + (__pyx_v_b1_omg * __pyx_v_S_hat)) + (__pyx_v_b2_omg * __pyx_v_S_hat2));

    /* "pyRing/eob_utils.pyx":1165
 *         omg22_orb = 1 + a_1_omg22*nu + a_2_omg22*nu2
 *         num_spin  = 1 + b1_omg*S_hat + b2_omg*S_hat2
 *         den_spin  = 1 + b3_omg*S_hat             # <<<<<<<<<<<<<<
 * 
 *         omg22_spin = num_spin/den_spin
*/
    __pyx_v_den_spin = (1.0 + (__pyx_v_b3_omg * __pyx_v_S_hat));

    /* "pyRing/eob_utils.pyx":1167
 *         den_spin  = 1 + b3_omg*S_hat
 * 
 *         omg22_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *         res = omg22_0 * omg22_orb * omg22_spin
*/
    __pyx_v_omg22_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

    /* "pyRing/eob_utils.pyx":1169
 *         omg22_spin = num_spin/den_spin
 * 
 *         res = omg22_0 * omg22_orb * omg22_spin             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = ((__pyx_v_omg22_0 * __pyx_v_omg22_orb) * __pyx_v_omg22_spin);

    /* "pyRing/eob_utils.pyx":1157
 * 
 * 
 *     if ((l==2) and (m==2)): # eqs. C17-C20 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_omg = (b_1_omg22 + c_11_omg22*X12)/(1 + c_12_omg22*X12)
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1172
 * 
 * 
 *     elif ((l==2) and (m==1)):   # eqs. C25-C28 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_omg = b_1_omg21 + c_1_omg21*nu
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L6_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L6_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1174
 *     elif ((l==2) and (m==1)):   # eqs. C25-C28 of arXiv:2001.09082v2
 * 
 *         b1_omg = b_1_omg21 + c_1_omg21*nu             # <<<<<<<<<<<<<<
 *         b2_omg = b_2_omg21 + c_2_omg21*nu
 * 
*/
    __pyx_v_b1_omg = (__pyx_v_b_1_omg21 + (__pyx_v_c_1_omg21 * __pyx_v_nu));

    /* "pyRing/eob_utils.pyx":1175
 * 
 *         b1_omg = b_1_omg21 + c_1_omg21*nu
 *         b2_omg = b_2_omg21 + c_2_omg21*nu             # <<<<<<<<<<<<<<
 * 
 *         omg21_orb  = 1 + a_1_omg21*nu + a_2_omg21*nu2
*/
    __pyx_v_b2_omg = (__pyx_v_b_2_omg21 + (__pyx_v_c_2_omg21 * __pyx_v_nu));

    /* "pyRing/eob_utils.pyx":1177
 *         b2_omg = b_2_omg21 + c_2_omg21*nu
 * 
 *         omg21_orb  = 1 + a_1_omg21*nu + a_2_omg21*nu2             # <<<<<<<<<<<<<<
 *         omg21_spin = 1 + b1_omg*S_hat + b2_omg*S_hat2
 * 
*/
    __pyx_v_omg21_orb = ((1.0 + (__pyx_v_a_1_omg21 * __pyx_v_nu)) + (__pyx_v_a_2_omg21 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1178
 * 
 *         omg21_orb  = 1 + a_1_omg21*nu + a_2_omg21*nu2
 *         omg21_spin = 1 + b1_omg*S_hat + b2_omg*S_hat2             # <<<<<<<<<<<<<<
 * 
 *         res = omg21_0 * omg21_orb * omg21_spin
*/
    __pyx_v_omg21_spin = ((1.0 + (__pyx_v_b1_omg * __pyx_v_S_hat)) + (__pyx_v_b2_omg * __pyx_v_S_hat2));

    /* "pyRing/eob_utils.pyx":1180
 *         omg21_spin = 1 + b1_omg*S_hat + b2_omg*S_hat2
 * 
 *         res = omg21_0 * omg21_orb * omg21_spin             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = ((__pyx_v_omg21_0 * __pyx_v_omg21_orb) * __pyx_v_omg21_spin);

    /* "pyRing/eob_utils.pyx":1172
 * 
 * 
 *     elif ((l==2) and (m==1)):   # eqs. C25-C28 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_omg = b_1_omg21 + c_1_omg21*nu
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1183
 * 
 * 
 *     elif ((l==3) and (m==3)):   # eqs. C38-C41 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_omg = (b_1_omg33 + c_11_omg33*nu)/(1 + c_12_omg33*nu)
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L8_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L8_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1185
 *     elif ((l==3) and (m==3)):   # eqs. C38-C41 of arXiv:2001.09082v2
 * 
 *         b1_omg = (b_1_omg33 + c_11_omg33*nu)/(1 + c_12_omg33*nu)             # <<<<<<<<<<<<<<
 *         b2_omg =  b_2_omg33
 *         b3_omg = (b_3_omg33 + c_31_omg33*nu)/(1 + c_32_omg33*nu)
*/
    __pyx_v_b1_omg = ((__pyx_v_b_1_omg33 + (__pyx_v_c_11_omg33 * __pyx_v_nu)) / (1.0 + (__pyx_v_c_12_omg33 * __pyx_v_nu)));

    /* "pyRing/eob_utils.pyx":1186
 * 
 *         b1_omg = (b_1_omg33 + c_11_omg33*nu)/(1 + c_12_omg33*nu)
 *         b2_omg =  b_2_omg33             # <<<<<<<<<<<<<<
 *         b3_omg = (b_3_omg33 + c_31_omg33*nu)/(1 + c_32_omg33*nu)
 * 
*/
    __pyx_v_b2_omg = __pyx_v_b_2_omg33;

    /* "pyRing/eob_utils.pyx":1187
 *         b1_omg = (b_1_omg33 + c_11_omg33*nu)/(1 + c_12_omg33*nu)
 *         b2_omg =  b_2_omg33
 *         b3_omg = (b_3_omg33 + c_31_omg33*nu)/(1 + c_32_omg33*nu)             # <<<<<<<<<<<<<<
 * 
 *         omg33_orb = 1 + a_1_omg33*nu + a_2_omg33*nu2
*/
    __pyx_v_b3_omg = ((__pyx_v_b_3_omg33 + (__pyx_v_c_31_omg33 * __pyx_v_nu)) / (1.0 + (__pyx_v_c_32_omg33 * __pyx_v_nu)));

    /* "pyRing/eob_utils.pyx":1189
 *         b3_omg = (b_3_omg33 + c_31_omg33*nu)/(1 + c_32_omg33*nu)
 * 
 *         omg33_orb = 1 + a_1_omg33*nu + a_2_omg33*nu2             # <<<<<<<<<<<<<<
 *         num_spin  = 1 + b1_omg*S_hat + b2_omg*S_hat2
 *         den_spin  = 1 + b3_omg*S_hat
*/
    __pyx_v_omg33_orb = ((1.0 + (__pyx_v_a_1_omg33 * __pyx_v_nu)) + (__pyx_v_a_2_omg33 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1190
 * 
 *         omg33_orb = 1 + a_1_omg33*nu + a_2_omg33*nu2
 *         num_spin  = 1 + b1_omg*S_hat + b2_omg*S_hat2             # <<<<<<<<<<<<<<
 *         den_spin  = 1 + b3_omg*S_hat
 * 
*/
    __pyx_v_num_spin = ((1.0 + (__pyx_v_b1_omg * __pyx_v_S_hat)) + (__pyx_v_b2_omg * __pyx_v_S_hat2));

    /* "pyRing/eob_utils.pyx":1191
 *         omg33_orb = 1 + a_1_omg33*nu + a_2_omg33*nu2
 *         num_spin  = 1 + b1_omg*S_hat + b2_omg*S_hat2
 *         den_spin  = 1 + b3_omg*S_hat             # <<<<<<<<<<<<<<
 * 
 *         omg33_spin = num_spin/den_spin
*/
    __pyx_v_den_spin = (1.0 + (__pyx_v_b3_omg * __pyx_v_S_hat));

    /* "pyRing/eob_utils.pyx":1193
 *         den_spin  = 1 + b3_omg*S_hat
 * 
 *         omg33_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *         res = omg33_0 * omg33_orb * omg33_spin
*/
    __pyx_v_omg33_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

    /* "pyRing/eob_utils.pyx":1195
 *         omg33_spin = num_spin/den_spin
 * 
 *         res = omg33_0 * omg33_orb * omg33_spin             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = ((__pyx_v_omg33_0 * __pyx_v_omg33_orb) * __pyx_v_omg33_spin);

    /* "pyRing/eob_utils.pyx":1183
 * 
 * 
 *     elif ((l==3) and (m==3)):   # eqs. C38-C41 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_omg = (b_1_omg33 + c_11_omg33*nu)/(1 + c_12_omg33*nu)
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1198
 * 
 * 
 *     elif ((l==3) and (m==2)):   # eqs. C50-C53 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_omg = (b_1_omg32 + c_11_omg32*X12 + c_12_omg32*X12_2)/(1 + c_13_omg32*X12)
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L10_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L10_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1200
 *     elif ((l==3) and (m==2)):   # eqs. C50-C53 of arXiv:2001.09082v2
 * 
 *         b1_omg = (b_1_omg32 + c_11_omg32*X12 + c_12_omg32*X12_2)/(1 + c_13_omg32*X12)             # <<<<<<<<<<<<<<
 *         b2_omg = (b_2_omg32 + c_21_omg32*X12 + c_22_omg32*X12_2)/(1 + c_23_omg32*X12)
 *         b3_omg =  b_3_omg32
*/
    __pyx_v_b1_omg = (((__pyx_v_b_1_omg32 + (__pyx_v_c_11_omg32 * __pyx_v_X12)) + (__pyx_v_c_12_omg32 * __pyx_v_X12_2)) / (1.0 + (__pyx_v_c_13_omg32 * __pyx_v_X12)));

    /* "pyRing/eob_utils.pyx":1201
 * 
 *         b1_omg = (b_1_omg32 + c_11_omg32*X12 + c_12_omg32*X12_2)/(1 + c_13_omg32*X12)
 *         b2_omg = (b_2_omg32 + c_21_omg32*X12 + c_22_omg32*X12_2)/(1 + c_23_omg32*X12)             # <<<<<<<<<<<<<<
 *         b3_omg =  b_3_omg32
 * 
*/
    __pyx_v_b2_omg = (((__pyx_v_b_2_omg32 + (__pyx_v_c_21_omg32 * __pyx_v_X12)) + (__pyx_v_c_22_omg32 * __pyx_v_X12_2)) / (1.0 + (__pyx_v_c_23_omg32 * __pyx_v_X12)));

    /* "pyRing/eob_utils.pyx":1202
 *         b1_omg = (b_1_omg32 + c_11_omg32*X12 + c_12_omg32*X12_2)/(1 + c_13_omg32*X12)
 *         b2_omg = (b_2_omg32 + c_21_omg32*X12 + c_22_omg32*X12_2)/(1 + c_23_omg32*X12)
 *         b3_omg =  b_3_omg32             # <<<<<<<<<<<<<<
 * 
 *         num_orb  = 1 + a_1_omg32*nu + a_2_omg32*nu2
*/
    __pyx_v_b3_omg = __pyx_v_b_3_omg32;

    /* "pyRing/eob_utils.pyx":1204
 *         b3_omg =  b_3_omg32
 * 
 *         num_orb  = 1 + a_1_omg32*nu + a_2_omg32*nu2             # <<<<<<<<<<<<<<
 *         den_orb  = 1 + a_3_omg32*nu + a_4_omg32*nu2
 *         num_spin = 1 + b1_omg*a0 + b2_omg*a0_2
*/
    __pyx_v_num_orb = ((1.0 + (__pyx_v_a_1_omg32 * __pyx_v_nu)) + (__pyx_v_a_2_omg32 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1205
 * 
 *         num_orb  = 1 + a_1_omg32*nu + a_2_omg32*nu2
 *         den_orb  = 1 + a_3_omg32*nu + a_4_omg32*nu2             # <<<<<<<<<<<<<<
 *         num_spin = 1 + b1_omg*a0 + b2_omg*a0_2
 *         den_spin = 1 + b3_omg*a0
*/
    __pyx_v_den_orb = ((1.0 + (__pyx_v_a_3_omg32 * __pyx_v_nu)) + (__pyx_v_a_4_omg32 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1206
 *         num_orb  = 1 + a_1_omg32*nu + a_2_omg32*nu2
 *         den_orb  = 1 + a_3_omg32*nu + a_4_omg32*nu2
 *         num_spin = 1 + b1_omg*a0 + b2_omg*a0_2             # <<<<<<<<<<<<<<
 *         den_spin = 1 + b3_omg*a0
 * 
*/
    __pyx_v_num_spin = ((1.0 + (__pyx_v_b1_omg * __pyx_v_a0)) + (__pyx_v_b2_omg * __pyx_v_a0_2));

    /* "pyRing/eob_utils.pyx":1207
 *         den_orb  = 1 + a_3_omg32*nu + a_4_omg32*nu2
 *         num_spin = 1 + b1_omg*a0 + b2_omg*a0_2
 *         den_spin = 1 + b3_omg*a0             # <<<<<<<<<<<<<<
 * 
 *         omg32_orb  = num_orb/den_orb
*/
    __pyx_v_den_spin = (1.0 + (__pyx_v_b3_omg * __pyx_v_a0));

    /* "pyRing/eob_utils.pyx":1209
 *         den_spin = 1 + b3_omg*a0
 * 
 *         omg32_orb  = num_orb/den_orb             # <<<<<<<<<<<<<<
 *         omg32_spin = num_spin/den_spin
 * 
*/
    __pyx_v_omg32_orb = (__pyx_v_num_orb / __pyx_v_den_orb);

    /* "pyRing/eob_utils.pyx":1210
 * 
 *         omg32_orb  = num_orb/den_orb
 *         omg32_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *         res = omg32_0 * omg32_orb * omg32_spin
*/
    __pyx_v_omg32_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

    /* "pyRing/eob_utils.pyx":1212
 *         omg32_spin = num_spin/den_spin
 * 
 *         res = omg32_0 * omg32_orb * omg32_spin             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = ((__pyx_v_omg32_0 * __pyx_v_omg32_orb) * __pyx_v_omg32_spin);

    /* "pyRing/eob_utils.pyx":1198
 * 
 * 
 *     elif ((l==3) and (m==2)):   # eqs. C50-C53 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_omg = (b_1_omg32 + c_11_omg32*X12 + c_12_omg32*X12_2)/(1 + c_13_omg32*X12)
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1215
 * 
 * 
 *     elif ((l==3) and (m==1)):   # eq. 5.19 of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 * 
 *         if (nu==0.25):    # TEOBResumSFits.c, line 2685
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L12_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L12_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1217
 *     elif ((l==3) and (m==1)):   # eq. 5.19 of arXiv:1904.09550v2
 * 
 *         if (nu==0.25):    # TEOBResumSFits.c, line 2685             # <<<<<<<<<<<<<<
 *             res = 0.
 * 
*/
    __pyx_t_1 = (__pyx_v_nu == 0.25);
    if (__pyx_t_1) {

      /* "pyRing/eob_utils.pyx":1218
 * 
 *         if (nu==0.25):    # TEOBResumSFits.c, line 2685
 *             res = 0.             # <<<<<<<<<<<<<<
 * 
 *         else:
*/
      __pyx_v_res = 0.;

      /* "pyRing/eob_utils.pyx":1217
 *     elif ((l==3) and (m==1)):   # eq. 5.19 of arXiv:1904.09550v2
 * 
 *         if (nu==0.25):    # TEOBResumSFits.c, line 2685             # <<<<<<<<<<<<<<
 *             res = 0.
 * 
*/
      goto __pyx_L14;
    }

    /* "pyRing/eob_utils.pyx":1221
 * 
 *         else:
 *             num_orb = 1 + n_2_omg31*nu2             # <<<<<<<<<<<<<<
 *             den_orb = 1 + d_1_omg31*nu + d_2_omg31*nu2
 * 
*/
    /*else*/ {
      __pyx_v_num_orb = (1.0 + (__pyx_v_n_2_omg31 * __pyx_v_nu2));

      /* "pyRing/eob_utils.pyx":1222
 *         else:
 *             num_orb = 1 + n_2_omg31*nu2
 *             den_orb = 1 + d_1_omg31*nu + d_2_omg31*nu2             # <<<<<<<<<<<<<<
 * 
 *             omg31_orb = num_orb/den_orb
*/
      __pyx_v_den_orb = ((1.0 + (__pyx_v_d_1_omg31 * __pyx_v_nu)) + (__pyx_v_d_2_omg31 * __pyx_v_nu2));

      /* "pyRing/eob_utils.pyx":1224
 *             den_orb = 1 + d_1_omg31*nu + d_2_omg31*nu2
 * 
 *             omg31_orb = num_orb/den_orb             # <<<<<<<<<<<<<<
 * 
 *             res = omg31_0 * omg31_orb
*/
      __pyx_v_omg31_orb = (__pyx_v_num_orb / __pyx_v_den_orb);

      /* "pyRing/eob_utils.pyx":1226
 *             omg31_orb = num_orb/den_orb
 * 
 *             res = omg31_0 * omg31_orb             # <<<<<<<<<<<<<<
 * 
 * 
*/
      __pyx_v_res = (__pyx_v_omg31_0 * __pyx_v_omg31_orb);
    }
    __pyx_L14:;

    /* "pyRing/eob_utils.pyx":1215
 * 
 * 
 *     elif ((l==3) and (m==1)):   # eq. 5.19 of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 * 
 *         if (nu==0.25):    # TEOBResumSFits.c, line 2685
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1229
 * 
 * 
 *     elif ((l==4) and (m==4)):   # eqs. C65-C68 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_omg = (b_1_omg44 + c_11_omg44*nu + c_12_omg44*nu2)/(1 + c_13_omg44*nu + c_14_omg44*nu2)
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L15_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 4);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L15_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1231
 *     elif ((l==4) and (m==4)):   # eqs. C65-C68 of arXiv:2001.09082v2
 * 
 *         b1_omg = (b_1_omg44 + c_11_omg44*nu + c_12_omg44*nu2)/(1 + c_13_omg44*nu + c_14_omg44*nu2)             # <<<<<<<<<<<<<<
 *         b2_omg = (b_2_omg44 + c_21_omg44*nu + c_22_omg44*nu2)/(1 + c_23_omg44*nu + c_24_omg44*nu2)
 *         b3_omg =  b_3_omg44
*/
    __pyx_v_b1_omg = (((__pyx_v_b_1_omg44 + (__pyx_v_c_11_omg44 * __pyx_v_nu)) + (__pyx_v_c_12_omg44 * __pyx_v_nu2)) / ((1.0 + (__pyx_v_c_13_omg44 * __pyx_v_nu)) + (__pyx_v_c_14_omg44 * __pyx_v_nu2)));

    /* "pyRing/eob_utils.pyx":1232
 * 
 *         b1_omg = (b_1_omg44 + c_11_omg44*nu + c_12_omg44*nu2)/(1 + c_13_omg44*nu + c_14_omg44*nu2)
 *         b2_omg = (b_2_omg44 + c_21_omg44*nu + c_22_omg44*nu2)/(1 + c_23_omg44*nu + c_24_omg44*nu2)             # <<<<<<<<<<<<<<
 *         b3_omg =  b_3_omg44
 *         b4_omg = (b_4_omg44 + c_41_omg44*nu + c_42_omg44*nu2)/(1 + c_43_omg44*nu + c_44_omg44*nu2)
*/
    __pyx_v_b2_omg = (((__pyx_v_b_2_omg44 + (__pyx_v_c_21_omg44 * __pyx_v_nu)) + (__pyx_v_c_22_omg44 * __pyx_v_nu2)) / ((1.0 + (__pyx_v_c_23_omg44 * __pyx_v_nu)) + (__pyx_v_c_24_omg44 * __pyx_v_nu2)));

    /* "pyRing/eob_utils.pyx":1233
 *         b1_omg = (b_1_omg44 + c_11_omg44*nu + c_12_omg44*nu2)/(1 + c_13_omg44*nu + c_14_omg44*nu2)
 *         b2_omg = (b_2_omg44 + c_21_omg44*nu + c_22_omg44*nu2)/(1 + c_23_omg44*nu + c_24_omg44*nu2)
 *         b3_omg =  b_3_omg44             # <<<<<<<<<<<<<<
 *         b4_omg = (b_4_omg44 + c_41_omg44*nu + c_42_omg44*nu2)/(1 + c_43_omg44*nu + c_44_omg44*nu2)
 * 
*/
    __pyx_v_b3_omg = __pyx_v_b_3_omg44;

    /* "pyRing/eob_utils.pyx":1234
 *         b2_omg = (b_2_omg44 + c_21_omg44*nu + c_22_omg44*nu2)/(1 + c_23_omg44*nu + c_24_omg44*nu2)
 *         b3_omg =  b_3_omg44
 *         b4_omg = (b_4_omg44 + c_41_omg44*nu + c_42_omg44*nu2)/(1 + c_43_omg44*nu + c_44_omg44*nu2)             # <<<<<<<<<<<<<<
 * 
 *         num_orb  = 1 + a_1_omg44*nu + a_2_omg44*nu2
*/
    __pyx_v_b4_omg = (((__pyx_v_b_4_omg44 + (__pyx_v_c_41_omg44 * __pyx_v_nu)) + (__pyx_v_c_42_omg44 * __pyx_v_nu2)) / ((1.0 + (__pyx_v_c_43_omg44 * __pyx_v_nu)) + (__pyx_v_c_44_omg44 * __pyx_v_nu2)));

    /* "pyRing/eob_utils.pyx":1236
 *         b4_omg = (b_4_omg44 + c_41_omg44*nu + c_42_omg44*nu2)/(1 + c_43_omg44*nu + c_44_omg44*nu2)
 * 
 *         num_orb  = 1 + a_1_omg44*nu + a_2_omg44*nu2             # <<<<<<<<<<<<<<
 *         den_orb  = 1 + a_3_omg44*nu + a_4_omg44*nu2
 *         num_spin = 1 + b1_omg*S_hat + b2_omg*S_hat2 + b3_omg*S_hat3
*/
    __pyx_v_num_orb = ((1.0 + (__pyx_v_a_1_omg44 * __pyx_v_nu)) + (__pyx_v_a_2_omg44 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1237
 * 
 *         num_orb  = 1 + a_1_omg44*nu + a_2_omg44*nu2
 *         den_orb  = 1 + a_3_omg44*nu + a_4_omg44*nu2             # <<<<<<<<<<<<<<
 *         num_spin = 1 + b1_omg*S_hat + b2_omg*S_hat2 + b3_omg*S_hat3
 *         den_spin = 1 + b4_omg*S_hat
*/
    __pyx_v_den_orb = ((1.0 + (__pyx_v_a_3_omg44 * __pyx_v_nu)) + (__pyx_v_a_4_omg44 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1238
 *         num_orb  = 1 + a_1_omg44*nu + a_2_omg44*nu2
 *         den_orb  = 1 + a_3_omg44*nu + a_4_omg44*nu2
 *         num_spin = 1 + b1_omg*S_hat + b2_omg*S_hat2 + b3_omg*S_hat3             # <<<<<<<<<<<<<<
 *         den_spin = 1 + b4_omg*S_hat
 * 
*/
    __pyx_v_num_spin = (((1.0 + (__pyx_v_b1_omg * __pyx_v_S_hat)) + (__pyx_v_b2_omg * __pyx_v_S_hat2)) + (__pyx_v_b3_omg * __pyx_v_S_hat3));

    /* "pyRing/eob_utils.pyx":1239
 *         den_orb  = 1 + a_3_omg44*nu + a_4_omg44*nu2
 *         num_spin = 1 + b1_omg*S_hat + b2_omg*S_hat2 + b3_omg*S_hat3
 *         den_spin = 1 + b4_omg*S_hat             # <<<<<<<<<<<<<<
 * 
 *         omg44_orb  = num_orb/den_orb
*/
    __pyx_v_den_spin = (1.0 + (__pyx_v_b4_omg * __pyx_v_S_hat));

    /* "pyRing/eob_utils.pyx":1241
 *         den_spin = 1 + b4_omg*S_hat
 * 
 *         omg44_orb  = num_orb/den_orb             # <<<<<<<<<<<<<<
 *         omg44_spin = num_spin/den_spin
 * 
*/
    __pyx_v_omg44_orb = (__pyx_v_num_orb / __pyx_v_den_orb);

    /* "pyRing/eob_utils.pyx":1242
 * 
 *         omg44_orb  = num_orb/den_orb
 *         omg44_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *         res = omg44_0 * omg44_orb * omg44_spin
*/
    __pyx_v_omg44_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

    /* "pyRing/eob_utils.pyx":1244
 *         omg44_spin = num_spin/den_spin
 * 
 *         res = omg44_0 * omg44_orb * omg44_spin             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = ((__pyx_v_omg44_0 * __pyx_v_omg44_orb) * __pyx_v_omg44_spin);

    /* "pyRing/eob_utils.pyx":1229
 * 
 * 
 *     elif ((l==4) and (m==4)):   # eqs. C65-C68 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_omg = (b_1_omg44 + c_11_omg44*nu + c_12_omg44*nu2)/(1 + c_13_omg44*nu + c_14_omg44*nu2)
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1247
 * 
 * 
 *     elif ((l==4) and (m==3)):   # eqs. C78-C81 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_omg = (b_1_omg43 + c_11_omg43*nu + c_12_omg43*nu2)/(1 + c_13_omg43*nu)
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L17_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L17_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1249
 *     elif ((l==4) and (m==3)):   # eqs. C78-C81 of arXiv:2001.09082v2
 * 
 *         b1_omg = (b_1_omg43 + c_11_omg43*nu + c_12_omg43*nu2)/(1 + c_13_omg43*nu)             # <<<<<<<<<<<<<<
 *         b2_omg = (b_2_omg43 + c_21_omg43*nu + c_22_omg43*nu2)/(1 + c_23_omg43*nu)
 *         b3_omg = (b_3_omg43 + c_31_omg43*nu + c_32_omg43*nu2)/(1 + c_33_omg43*nu)
*/
    __pyx_v_b1_omg = (((__pyx_v_b_1_omg43 + (__pyx_v_c_11_omg43 * __pyx_v_nu)) + (__pyx_v_c_12_omg43 * __pyx_v_nu2)) / (1.0 + (__pyx_v_c_13_omg43 * __pyx_v_nu)));

    /* "pyRing/eob_utils.pyx":1250
 * 
 *         b1_omg = (b_1_omg43 + c_11_omg43*nu + c_12_omg43*nu2)/(1 + c_13_omg43*nu)
 *         b2_omg = (b_2_omg43 + c_21_omg43*nu + c_22_omg43*nu2)/(1 + c_23_omg43*nu)             # <<<<<<<<<<<<<<
 *         b3_omg = (b_3_omg43 + c_31_omg43*nu + c_32_omg43*nu2)/(1 + c_33_omg43*nu)
 * 
*/
    __pyx_v_b2_omg = (((__pyx_v_b_2_omg43 + (__pyx_v_c_21_omg43 * __pyx_v_nu)) + (__pyx_v_c_22_omg43 * __pyx_v_nu2)) / (1.0 + (__pyx_v_c_23_omg43 * __pyx_v_nu)));

    /* "pyRing/eob_utils.pyx":1251
 *         b1_omg = (b_1_omg43 + c_11_omg43*nu + c_12_omg43*nu2)/(1 + c_13_omg43*nu)
 *         b2_omg = (b_2_omg43 + c_21_omg43*nu + c_22_omg43*nu2)/(1 + c_23_omg43*nu)
 *         b3_omg = (b_3_omg43 + c_31_omg43*nu + c_32_omg43*nu2)/(1 + c_33_omg43*nu)             # <<<<<<<<<<<<<<
 * 
 *         num_orb  = 1 + a_1_omg43*nu + a_2_omg43*nu2
*/
    __pyx_v_b3_omg = (((__pyx_v_b_3_omg43 + (__pyx_v_c_31_omg43 * __pyx_v_nu)) + (__pyx_v_c_32_omg43 * __pyx_v_nu2)) / (1.0 + (__pyx_v_c_33_omg43 * __pyx_v_nu)));

    /* "pyRing/eob_utils.pyx":1253
 *         b3_omg = (b_3_omg43 + c_31_omg43*nu + c_32_omg43*nu2)/(1 + c_33_omg43*nu)
 * 
 *         num_orb  = 1 + a_1_omg43*nu + a_2_omg43*nu2             # <<<<<<<<<<<<<<
 *         den_orb  = 1 + a_3_omg43*nu + a_4_omg43*nu2
 *         num_spin = 1 + b1_omg*S_hat + b2_omg*S_hat2
*/
    __pyx_v_num_orb = ((1.0 + (__pyx_v_a_1_omg43 * __pyx_v_nu)) + (__pyx_v_a_2_omg43 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1254
 * 
 *         num_orb  = 1 + a_1_omg43*nu + a_2_omg43*nu2
 *         den_orb  = 1 + a_3_omg43*nu + a_4_omg43*nu2             # <<<<<<<<<<<<<<
 *         num_spin = 1 + b1_omg*S_hat + b2_omg*S_hat2
 *         den_spin = 1 + b3_omg*S_hat
*/
    __pyx_v_den_orb = ((1.0 + (__pyx_v_a_3_omg43 * __pyx_v_nu)) + (__pyx_v_a_4_omg43 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1255
 *         num_orb  = 1 + a_1_omg43*nu + a_2_omg43*nu2
 *         den_orb  = 1 + a_3_omg43*nu + a_4_omg43*nu2
 *         num_spin = 1 + b1_omg*S_hat + b2_omg*S_hat2             # <<<<<<<<<<<<<<
 *         den_spin = 1 + b3_omg*S_hat
 * 
*/
    __pyx_v_num_spin = ((1.0 + (__pyx_v_b1_omg * __pyx_v_S_hat)) + (__pyx_v_b2_omg * __pyx_v_S_hat2));

    /* "pyRing/eob_utils.pyx":1256
 *         den_orb  = 1 + a_3_omg43*nu + a_4_omg43*nu2
 *         num_spin = 1 + b1_omg*S_hat + b2_omg*S_hat2
 *         den_spin = 1 + b3_omg*S_hat             # <<<<<<<<<<<<<<
 * 
 *         omg43_orb  = num_orb/den_orb
*/
    __pyx_v_den_spin = (1.0 + (__pyx_v_b3_omg * __pyx_v_S_hat));

    /* "pyRing/eob_utils.pyx":1258
 *         den_spin = 1 + b3_omg*S_hat
 * 
 *         omg43_orb  = num_orb/den_orb             # <<<<<<<<<<<<<<
 *         omg43_spin = num_spin/den_spin
 * 
*/
    __pyx_v_omg43_orb = (__pyx_v_num_orb / __pyx_v_den_orb);

    /* "pyRing/eob_utils.pyx":1259
 * 
 *         omg43_orb  = num_orb/den_orb
 *         omg43_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *         res = omg43_0 * omg43_orb * omg43_spin
*/
    __pyx_v_omg43_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

    /* "pyRing/eob_utils.pyx":1261
 *         omg43_spin = num_spin/den_spin
 * 
 *         res = omg43_0 * omg43_orb * omg43_spin             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = ((__pyx_v_omg43_0 * __pyx_v_omg43_orb) * __pyx_v_omg43_spin);

    /* "pyRing/eob_utils.pyx":1247
 * 
 * 
 *     elif ((l==4) and (m==3)):   # eqs. C78-C81 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_omg = (b_1_omg43 + c_11_omg43*nu + c_12_omg43*nu2)/(1 + c_13_omg43*nu)
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1264
 * 
 * 
 *     elif ((l==4) and (m==2)):   # eqs. C90-C93 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_omg = (b_1_omg42 + c_11_omg42*nu)/(1 + c_12_omg42*nu + c_13_omg42*nu2)
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L19_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L19_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1266
 *     elif ((l==4) and (m==2)):   # eqs. C90-C93 of arXiv:2001.09082v2
 * 
 *         b1_omg = (b_1_omg42 + c_11_omg42*nu)/(1 + c_12_omg42*nu + c_13_omg42*nu2)             # <<<<<<<<<<<<<<
 *         b2_omg = (b_2_omg42 + c_21_omg42*nu)/(1 + c_22_omg42*nu + c_23_omg42*nu2)
 *         b3_omg = (b_3_omg42 + c_31_omg42*nu)/(1 + c_32_omg42*nu + c_33_omg42*nu2)
*/
    __pyx_v_b1_omg = ((__pyx_v_b_1_omg42 + (__pyx_v_c_11_omg42 * __pyx_v_nu)) / ((1.0 + (__pyx_v_c_12_omg42 * __pyx_v_nu)) + (__pyx_v_c_13_omg42 * __pyx_v_nu2)));

    /* "pyRing/eob_utils.pyx":1267
 * 
 *         b1_omg = (b_1_omg42 + c_11_omg42*nu)/(1 + c_12_omg42*nu + c_13_omg42*nu2)
 *         b2_omg = (b_2_omg42 + c_21_omg42*nu)/(1 + c_22_omg42*nu + c_23_omg42*nu2)             # <<<<<<<<<<<<<<
 *         b3_omg = (b_3_omg42 + c_31_omg42*nu)/(1 + c_32_omg42*nu + c_33_omg42*nu2)
 *         b4_omg = (b_4_omg42 + c_41_omg42*nu)/(1 + c_42_omg42*nu + c_43_omg42*nu2)
*/
    __pyx_v_b2_omg = ((__pyx_v_b_2_omg42 + (__pyx_v_c_21_omg42 * __pyx_v_nu)) / ((1.0 + (__pyx_v_c_22_omg42 * __pyx_v_nu)) + (__pyx_v_c_23_omg42 * __pyx_v_nu2)));

    /* "pyRing/eob_utils.pyx":1268
 *         b1_omg = (b_1_omg42 + c_11_omg42*nu)/(1 + c_12_omg42*nu + c_13_omg42*nu2)
 *         b2_omg = (b_2_omg42 + c_21_omg42*nu)/(1 + c_22_omg42*nu + c_23_omg42*nu2)
 *         b3_omg = (b_3_omg42 + c_31_omg42*nu)/(1 + c_32_omg42*nu + c_33_omg42*nu2)             # <<<<<<<<<<<<<<
 *         b4_omg = (b_4_omg42 + c_41_omg42*nu)/(1 + c_42_omg42*nu + c_43_omg42*nu2)
 * 
*/
    __pyx_v_b3_omg = ((__pyx_v_b_3_omg42 + (__pyx_v_c_31_omg42 * __pyx_v_nu)) / ((1.0 + (__pyx_v_c_32_omg42 * __pyx_v_nu)) + (__pyx_v_c_33_omg42 * __pyx_v_nu2)));

    /* "pyRing/eob_utils.pyx":1269
 *         b2_omg = (b_2_omg42 + c_21_omg42*nu)/(1 + c_22_omg42*nu + c_23_omg42*nu2)
 *         b3_omg = (b_3_omg42 + c_31_omg42*nu)/(1 + c_32_omg42*nu + c_33_omg42*nu2)
 *         b4_omg = (b_4_omg42 + c_41_omg42*nu)/(1 + c_42_omg42*nu + c_43_omg42*nu2)             # <<<<<<<<<<<<<<
 * 
 *         num_orb  = 1 + a_1_omg42*nu + a_2_omg42*nu2
*/
    __pyx_v_b4_omg = ((__pyx_v_b_4_omg42 + (__pyx_v_c_41_omg42 * __pyx_v_nu)) / ((1.0 + (__pyx_v_c_42_omg42 * __pyx_v_nu)) + (__pyx_v_c_43_omg42 * __pyx_v_nu2)));

    /* "pyRing/eob_utils.pyx":1271
 *         b4_omg = (b_4_omg42 + c_41_omg42*nu)/(1 + c_42_omg42*nu + c_43_omg42*nu2)
 * 
 *         num_orb  = 1 + a_1_omg42*nu + a_2_omg42*nu2             # <<<<<<<<<<<<<<
 *         den_orb  = 1 + a_3_omg42*nu + a_4_omg42*nu2
 *         num_spin = 1 + b1_omg*S_hat + b2_omg*S_hat2
*/
    __pyx_v_num_orb = ((1.0 + (__pyx_v_a_1_omg42 * __pyx_v_nu)) + (__pyx_v_a_2_omg42 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1272
 * 
 *         num_orb  = 1 + a_1_omg42*nu + a_2_omg42*nu2
 *         den_orb  = 1 + a_3_omg42*nu + a_4_omg42*nu2             # <<<<<<<<<<<<<<
 *         num_spin = 1 + b1_omg*S_hat + b2_omg*S_hat2
 *         den_spin = 1 + b3_omg*S_hat + b4_omg*S_hat2
*/
    __pyx_v_den_orb = ((1.0 + (__pyx_v_a_3_omg42 * __pyx_v_nu)) + (__pyx_v_a_4_omg42 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1273
 *         num_orb  = 1 + a_1_omg42*nu + a_2_omg42*nu2
 *         den_orb  = 1 + a_3_omg42*nu + a_4_omg42*nu2
 *         num_spin = 1 + b1_omg*S_hat + b2_omg*S_hat2             # <<<<<<<<<<<<<<
 *         den_spin = 1 + b3_omg*S_hat + b4_omg*S_hat2
 * 
*/
    __pyx_v_num_spin = ((1.0 + (__pyx_v_b1_omg * __pyx_v_S_hat)) + (__pyx_v_b2_omg * __pyx_v_S_hat2));

    /* "pyRing/eob_utils.pyx":1274
 *         den_orb  = 1 + a_3_omg42*nu + a_4_omg42*nu2
 *         num_spin = 1 + b1_omg*S_hat + b2_omg*S_hat2
 *         den_spin = 1 + b3_omg*S_hat + b4_omg*S_hat2             # <<<<<<<<<<<<<<
 * 
 *         omg42_orb  = num_orb/den_orb
*/
    __pyx_v_den_spin = ((1.0 + (__pyx_v_b3_omg * __pyx_v_S_hat)) + (__pyx_v_b4_omg * __pyx_v_S_hat2));

    /* "pyRing/eob_utils.pyx":1276
 *         den_spin = 1 + b3_omg*S_hat + b4_omg*S_hat2
 * 
 *         omg42_orb  = num_orb/den_orb             # <<<<<<<<<<<<<<
 *         omg42_spin = num_spin/den_spin
 * 
*/
    __pyx_v_omg42_orb = (__pyx_v_num_orb / __pyx_v_den_orb);

    /* "pyRing/eob_utils.pyx":1277
 * 
 *         omg42_orb  = num_orb/den_orb
 *         omg42_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *         res = omg42_0 * omg42_orb * omg42_spin
*/
    __pyx_v_omg42_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

    /* "pyRing/eob_utils.pyx":1279
 *         omg42_spin = num_spin/den_spin
 * 
 *         res = omg42_0 * omg42_orb * omg42_spin             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = ((__pyx_v_omg42_0 * __pyx_v_omg42_orb) * __pyx_v_omg42_spin);

    /* "pyRing/eob_utils.pyx":1264
 * 
 * 
 *     elif ((l==4) and (m==2)):   # eqs. C90-C93 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_omg = (b_1_omg42 + c_11_omg42*nu)/(1 + c_12_omg42*nu + c_13_omg42*nu2)
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1282
 * 
 * 
 *     elif ((l==4) and (m==1)):   # eq. 5.19 of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 * 
 *         '''num_orb = 1 + n_1_omg41*nu + n_2_omg41*nu2
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L21_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L21_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1291
 *         res = omg41_0 * omg41_orb'''
 * 
 *         res = 0     # TEOBResumSFits.c, line 2696             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = 0.0;

    /* "pyRing/eob_utils.pyx":1282
 * 
 * 
 *     elif ((l==4) and (m==1)):   # eq. 5.19 of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 * 
 *         '''num_orb = 1 + n_1_omg41*nu + n_2_omg41*nu2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1294
 * 
 * 
 *     elif ((l==5) and (m==5)):   # eqs. C103-C106 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_omg = (b_1_omg55 + c_11_omg55*nu)/(1 + c_12_omg55*nu)
*/
  __pyx_t_2 = (__pyx_v_l == 5);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L23_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 5);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L23_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1296
 *     elif ((l==5) and (m==5)):   # eqs. C103-C106 of arXiv:2001.09082v2
 * 
 *         b1_omg = (b_1_omg55 + c_11_omg55*nu)/(1 + c_12_omg55*nu)             # <<<<<<<<<<<<<<
 *         b2_omg = (b_2_omg55 + c_21_omg55*nu)/(1 + c_22_omg55*nu)
 * 
*/
    __pyx_v_b1_omg = ((__pyx_v_b_1_omg55 + (__pyx_v_c_11_omg55 * __pyx_v_nu)) / (1.0 + (__pyx_v_c_12_omg55 * __pyx_v_nu)));

    /* "pyRing/eob_utils.pyx":1297
 * 
 *         b1_omg = (b_1_omg55 + c_11_omg55*nu)/(1 + c_12_omg55*nu)
 *         b2_omg = (b_2_omg55 + c_21_omg55*nu)/(1 + c_22_omg55*nu)             # <<<<<<<<<<<<<<
 * 
 *         num_orb  = 1 + a_1_omg55*nu + a_2_omg55*nu2
*/
    __pyx_v_b2_omg = ((__pyx_v_b_2_omg55 + (__pyx_v_c_21_omg55 * __pyx_v_nu)) / (1.0 + (__pyx_v_c_22_omg55 * __pyx_v_nu)));

    /* "pyRing/eob_utils.pyx":1299
 *         b2_omg = (b_2_omg55 + c_21_omg55*nu)/(1 + c_22_omg55*nu)
 * 
 *         num_orb  = 1 + a_1_omg55*nu + a_2_omg55*nu2             # <<<<<<<<<<<<<<
 *         den_orb  = 1 + a_3_omg55*nu
 *         num_spin = 1 + b1_omg*S_hat
*/
    __pyx_v_num_orb = ((1.0 + (__pyx_v_a_1_omg55 * __pyx_v_nu)) + (__pyx_v_a_2_omg55 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1300
 * 
 *         num_orb  = 1 + a_1_omg55*nu + a_2_omg55*nu2
 *         den_orb  = 1 + a_3_omg55*nu             # <<<<<<<<<<<<<<
 *         num_spin = 1 + b1_omg*S_hat
 *         den_spin = 1 + b2_omg*S_hat
*/
    __pyx_v_den_orb = (1.0 + (__pyx_v_a_3_omg55 * __pyx_v_nu));

    /* "pyRing/eob_utils.pyx":1301
 *         num_orb  = 1 + a_1_omg55*nu + a_2_omg55*nu2
 *         den_orb  = 1 + a_3_omg55*nu
 *         num_spin = 1 + b1_omg*S_hat             # <<<<<<<<<<<<<<
 *         den_spin = 1 + b2_omg*S_hat
 * 
*/
    __pyx_v_num_spin = (1.0 + (__pyx_v_b1_omg * __pyx_v_S_hat));

    /* "pyRing/eob_utils.pyx":1302
 *         den_orb  = 1 + a_3_omg55*nu
 *         num_spin = 1 + b1_omg*S_hat
 *         den_spin = 1 + b2_omg*S_hat             # <<<<<<<<<<<<<<
 * 
 *         omg55_orb  = num_orb/den_orb
*/
    __pyx_v_den_spin = (1.0 + (__pyx_v_b2_omg * __pyx_v_S_hat));

    /* "pyRing/eob_utils.pyx":1304
 *         den_spin = 1 + b2_omg*S_hat
 * 
 *         omg55_orb  = num_orb/den_orb             # <<<<<<<<<<<<<<
 *         omg55_spin = num_spin/den_spin
 * 
*/
    __pyx_v_omg55_orb = (__pyx_v_num_orb / __pyx_v_den_orb);

    /* "pyRing/eob_utils.pyx":1305
 * 
 *         omg55_orb  = num_orb/den_orb
 *         omg55_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *         res = omg55_0 * omg55_orb * omg55_spin
*/
    __pyx_v_omg55_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

    /* "pyRing/eob_utils.pyx":1307
 *         omg55_spin = num_spin/den_spin
 * 
 *         res = omg55_0 * omg55_orb * omg55_spin             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = ((__pyx_v_omg55_0 * __pyx_v_omg55_orb) * __pyx_v_omg55_spin);

    /* "pyRing/eob_utils.pyx":1294
 * 
 * 
 *     elif ((l==5) and (m==5)):   # eqs. C103-C106 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_omg = (b_1_omg55 + c_11_omg55*nu)/(1 + c_12_omg55*nu)
*/
  }
  __pyx_L3:;

  /* "pyRing/eob_utils.pyx":1310
 * 
 * 
 *     return res             # <<<<<<<<<<<<<<
 * 
 * 
*/
  __pyx_r = __pyx_v_res;
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":1076
 * 
 * 
 * cdef double _omega_peak(double nu, double X12, double S_hat, double a0, int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function returning the value of Omega at the peak of the strain, following appendix C.2 of arXiv:2001.09082v2.
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "pyRing/eob_utils.pyx":1319
 * ###################################################################
 * 
 * cdef double _JimenezFortezaRemnantMass(double nu, double X1, double X2, double chi1, double chi2, double M) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Compute the BH final mass with the aligned-spin NR fit by Xisco Jimenez Forteza,
*/

static double __pyx_f_6pyRing_9eob_utils__JimenezFortezaRemnantMass(double __pyx_v_nu, double __pyx_v_X1, double __pyx_v_X2, double __pyx_v_chi1, double __pyx_v_chi2, double __pyx_v_M) {
  double __pyx_v_X12;
  double __pyx_v_X1_2;
  double __pyx_v_X2_2;
  double __pyx_v_S;
  double __pyx_v_Dchi;
  double __pyx_v_res;
  double __pyx_v_Erad_nu_0;
  double __pyx_v_Erad_nu25_S;
  double __pyx_v_Erad_nu25_0;
  double __pyx_v_Erad_nu_S;
  double __pyx_v_Erad;
  double __pyx_v_f12;
  double __pyx_v_f22;
  double __pyx_v_f32;
  double __pyx_v_f52;
  double __pyx_v_b1_nu;
  double __pyx_v_b2_nu;
  double __pyx_v_b3_nu;
  double __pyx_v_b5_nu;
  double __pyx_v_A1;
  double __pyx_v_A2;
  double __pyx_v_A3;
  double __pyx_v_nu2;
  double __pyx_v_nu3;
  double __pyx_v_nu4;
  double __pyx_v_S_2;
  double __pyx_v_S_3;
  double __pyx_v_Dchi_2;
  double __pyx_v_a2;
  double __pyx_v_a3;
  double __pyx_v_a4;
  double __pyx_v_b1;
  double __pyx_v_b2;
  double __pyx_v_b3;
  double __pyx_v_b5;
  double __pyx_v_f20;
  double __pyx_v_f30;
  double __pyx_v_f50;
  double __pyx_v_f10;
  double __pyx_v_d10;
  double __pyx_v_d11;
  double __pyx_v_d20;
  double __pyx_v_d30;
  double __pyx_v_d31;
  double __pyx_v_f11;
  double __pyx_v_f21;
  double __pyx_v_f31;
  double __pyx_v_f51;
  double __pyx_v_DErad_nu_S_Dchi;
  double __pyx_r;

  /* "pyRing/eob_utils.pyx":1335
 *     """
 * 
 *     cdef double X12  = X1 - X2             # <<<<<<<<<<<<<<
 *     cdef double X1_2 = X1*X1, X2_2 = X2*X2
 *     cdef double S    = (X1_2*chi1 + X2_2*chi2)/(X1_2 + X2_2)
*/
  __pyx_v_X12 = (__pyx_v_X1 - __pyx_v_X2);

  /* "pyRing/eob_utils.pyx":1336
 * 
 *     cdef double X12  = X1 - X2
 *     cdef double X1_2 = X1*X1, X2_2 = X2*X2             # <<<<<<<<<<<<<<
 *     cdef double S    = (X1_2*chi1 + X2_2*chi2)/(X1_2 + X2_2)
 *     cdef double Dchi = chi1-chi2
*/
  __pyx_v_X1_2 = (__pyx_v_X1 * __pyx_v_X1);
  __pyx_v_X2_2 = (__pyx_v_X2 * __pyx_v_X2);

  /* "pyRing/eob_utils.pyx":1337
 *     cdef double X12  = X1 - X2
 *     cdef double X1_2 = X1*X1, X2_2 = X2*X2
 *     cdef double S    = (X1_2*chi1 + X2_2*chi2)/(X1_2 + X2_2)             # <<<<<<<<<<<<<<
 *     cdef double Dchi = chi1-chi2
 * 
*/
  __pyx_v_S = (((__pyx_v_X1_2 * __pyx_v_chi1) + (__pyx_v_X2_2 * __pyx_v_chi2)) / (__pyx_v_X1_2 + __pyx_v_X2_2));

  /* "pyRing/eob_utils.pyx":1338
 *     cdef double X1_2 = X1*X1, X2_2 = X2*X2
 *     cdef double S    = (X1_2*chi1 + X2_2*chi2)/(X1_2 + X2_2)
 *     cdef double Dchi = chi1-chi2             # <<<<<<<<<<<<<<
 * 
 *     cdef double res = 0.
*/
  __pyx_v_Dchi = (__pyx_v_chi1 - __pyx_v_chi2);

  /* "pyRing/eob_utils.pyx":1340
 *     cdef double Dchi = chi1-chi2
 * 
 *     cdef double res = 0.             # <<<<<<<<<<<<<<
 *     cdef double Erad_nu_0, Erad_nu25_S, Erad_nu25_0, Erad_nu_S, Erad
 *     cdef double f12, f22, f32, f52, b1_nu, b2_nu, b3_nu, b5_nu, A1, A2, A3
*/
  __pyx_v_res = 0.;

  /* "pyRing/eob_utils.pyx":1343
 *     cdef double Erad_nu_0, Erad_nu25_S, Erad_nu25_0, Erad_nu_S, Erad
 *     cdef double f12, f22, f32, f52, b1_nu, b2_nu, b3_nu, b5_nu, A1, A2, A3
 *     cdef double nu2 = nu*nu, nu3 = nu2*nu, nu4 = nu3*nu, S_2 = S*S, S_3 = S_2*S, Dchi_2 = Dchi*Dchi             # <<<<<<<<<<<<<<
 * 
 *     # 1D fits - Table VII from arXiv:1611.00332v2
*/
  __pyx_v_nu2 = (__pyx_v_nu * __pyx_v_nu);
  __pyx_v_nu3 = (__pyx_v_nu2 * __pyx_v_nu);
  __pyx_v_nu4 = (__pyx_v_nu3 * __pyx_v_nu);
  __pyx_v_S_2 = (__pyx_v_S * __pyx_v_S);
  __pyx_v_S_3 = (__pyx_v_S_2 * __pyx_v_S);
  __pyx_v_Dchi_2 = (__pyx_v_Dchi * __pyx_v_Dchi);

  /* "pyRing/eob_utils.pyx":1346
 * 
 *     # 1D fits - Table VII from arXiv:1611.00332v2
 *     cdef double a2 = 0.5610, a3 = -0.847, a4 = 3.145             # <<<<<<<<<<<<<<
 * 
 *     # 1D fits - Table VIII from arXiv:1611.00332v2
*/
  __pyx_v_a2 = 0.5610;
  __pyx_v_a3 = -0.847;
  __pyx_v_a4 = 3.145;

  /* "pyRing/eob_utils.pyx":1349
 * 
 *     # 1D fits - Table VIII from arXiv:1611.00332v2
 *     cdef double b1 = -0.209, b2 = -0.197, b3 = -0.159, b5 = 2.985             # <<<<<<<<<<<<<<
 * 
 *     # 2D fits - Table IX from arXiv:1611.00332v2
*/
  __pyx_v_b1 = -0.209;
  __pyx_v_b2 = -0.197;
  __pyx_v_b3 = -0.159;
  __pyx_v_b5 = 2.985;

  /* "pyRing/eob_utils.pyx":1352
 * 
 *     # 2D fits - Table IX from arXiv:1611.00332v2
 *     cdef double f20 = 4.27, f30 = 31.09, f50 = 1.56735             # <<<<<<<<<<<<<<
 *     cdef double f10 = -0.574752*f20 - 0.280958*f30 + 64.6408*f50 - 88.3165   # eq. 26 of arXiv:1611.00332v2
 * 
*/
  __pyx_v_f20 = 4.27;
  __pyx_v_f30 = 31.09;
  __pyx_v_f50 = 1.56735;

  /* "pyRing/eob_utils.pyx":1353
 *     # 2D fits - Table IX from arXiv:1611.00332v2
 *     cdef double f20 = 4.27, f30 = 31.09, f50 = 1.56735
 *     cdef double f10 = -0.574752*f20 - 0.280958*f30 + 64.6408*f50 - 88.3165   # eq. 26 of arXiv:1611.00332v2             # <<<<<<<<<<<<<<
 * 
 *     # 3D fits - Table X from arXiv:1611.00332v2
*/
  __pyx_v_f10 = ((((-0.574752 * __pyx_v_f20) - (0.280958 * __pyx_v_f30)) + (64.6408 * __pyx_v_f50)) - 88.3165);

  /* "pyRing/eob_utils.pyx":1356
 * 
 *     # 3D fits - Table X from arXiv:1611.00332v2
 *     cdef double d10 = -0.098, d11 = -3.23, d20 = 0.0112, d30 = -0.0198, d31 = -4.92             # <<<<<<<<<<<<<<
 *     cdef double f11 = 15.7, f21 = 0., f31 = -243.6, f51 = -0.58
 * 
*/
  __pyx_v_d10 = -0.098;
  __pyx_v_d11 = -3.23;
  __pyx_v_d20 = 0.0112;
  __pyx_v_d30 = -0.0198;
  __pyx_v_d31 = -4.92;

  /* "pyRing/eob_utils.pyx":1357
 *     # 3D fits - Table X from arXiv:1611.00332v2
 *     cdef double d10 = -0.098, d11 = -3.23, d20 = 0.0112, d30 = -0.0198, d31 = -4.92
 *     cdef double f11 = 15.7, f21 = 0., f31 = -243.6, f51 = -0.58             # <<<<<<<<<<<<<<
 * 
 *     """
*/
  __pyx_v_f11 = 15.7;
  __pyx_v_f21 = 0.;
  __pyx_v_f31 = -243.6;
  __pyx_v_f51 = -0.58;

  /* "pyRing/eob_utils.pyx":1382
 * 
 *     # 1D fits
 *     Erad_nu_0 = a4*nu4 + a3*nu3 + a2*nu2 + (1-2.*sqrt(2)/3.)*nu    # eq. 21 of arXiv:1611.00332v2             # <<<<<<<<<<<<<<
 * 
 *     # 2D fits
*/
  __pyx_v_Erad_nu_0 = ((((__pyx_v_a4 * __pyx_v_nu4) + (__pyx_v_a3 * __pyx_v_nu3)) + (__pyx_v_a2 * __pyx_v_nu2)) + ((1.0 - ((2. * sqrt(2.0)) / 3.)) * __pyx_v_nu));

  /* "pyRing/eob_utils.pyx":1385
 * 
 *     # 2D fits
 *     f12 = 16. - 16.*f10 - 4.*f11    # eq. 24 of arXiv:1611.00332v2             # <<<<<<<<<<<<<<
 *     f22 = 16. - 16.*f20 - 4.*f21
 *     f32 = 16. - 16.*f30 - 4.*f31
*/
  __pyx_v_f12 = ((16. - (16. * __pyx_v_f10)) - (4. * __pyx_v_f11));

  /* "pyRing/eob_utils.pyx":1386
 *     # 2D fits
 *     f12 = 16. - 16.*f10 - 4.*f11    # eq. 24 of arXiv:1611.00332v2
 *     f22 = 16. - 16.*f20 - 4.*f21             # <<<<<<<<<<<<<<
 *     f32 = 16. - 16.*f30 - 4.*f31
 *     f52 = 16. - 16.*f50 - 4.*f51
*/
  __pyx_v_f22 = ((16. - (16. * __pyx_v_f20)) - (4. * __pyx_v_f21));

  /* "pyRing/eob_utils.pyx":1387
 *     f12 = 16. - 16.*f10 - 4.*f11    # eq. 24 of arXiv:1611.00332v2
 *     f22 = 16. - 16.*f20 - 4.*f21
 *     f32 = 16. - 16.*f30 - 4.*f31             # <<<<<<<<<<<<<<
 *     f52 = 16. - 16.*f50 - 4.*f51
 * 
*/
  __pyx_v_f32 = ((16. - (16. * __pyx_v_f30)) - (4. * __pyx_v_f31));

  /* "pyRing/eob_utils.pyx":1388
 *     f22 = 16. - 16.*f20 - 4.*f21
 *     f32 = 16. - 16.*f30 - 4.*f31
 *     f52 = 16. - 16.*f50 - 4.*f51             # <<<<<<<<<<<<<<
 * 
 *     b1_nu = b1 * (f10 + f11*nu + f12*nu2)    # eq. 9 of arXiv:1611.00332v2
*/
  __pyx_v_f52 = ((16. - (16. * __pyx_v_f50)) - (4. * __pyx_v_f51));

  /* "pyRing/eob_utils.pyx":1390
 *     f52 = 16. - 16.*f50 - 4.*f51
 * 
 *     b1_nu = b1 * (f10 + f11*nu + f12*nu2)    # eq. 9 of arXiv:1611.00332v2             # <<<<<<<<<<<<<<
 *     b2_nu = b2 * (f20 + f21*nu + f22*nu2)
 *     b3_nu = b3 * (f30 + f31*nu + f32*nu2)
*/
  __pyx_v_b1_nu = (__pyx_v_b1 * ((__pyx_v_f10 + (__pyx_v_f11 * __pyx_v_nu)) + (__pyx_v_f12 * __pyx_v_nu2)));

  /* "pyRing/eob_utils.pyx":1391
 * 
 *     b1_nu = b1 * (f10 + f11*nu + f12*nu2)    # eq. 9 of arXiv:1611.00332v2
 *     b2_nu = b2 * (f20 + f21*nu + f22*nu2)             # <<<<<<<<<<<<<<
 *     b3_nu = b3 * (f30 + f31*nu + f32*nu2)
 *     b5_nu = b5 * (f50 + f51*nu + f52*nu2)
*/
  __pyx_v_b2_nu = (__pyx_v_b2 * ((__pyx_v_f20 + (__pyx_v_f21 * __pyx_v_nu)) + (__pyx_v_f22 * __pyx_v_nu2)));

  /* "pyRing/eob_utils.pyx":1392
 *     b1_nu = b1 * (f10 + f11*nu + f12*nu2)    # eq. 9 of arXiv:1611.00332v2
 *     b2_nu = b2 * (f20 + f21*nu + f22*nu2)
 *     b3_nu = b3 * (f30 + f31*nu + f32*nu2)             # <<<<<<<<<<<<<<
 *     b5_nu = b5 * (f50 + f51*nu + f52*nu2)
 * 
*/
  __pyx_v_b3_nu = (__pyx_v_b3 * ((__pyx_v_f30 + (__pyx_v_f31 * __pyx_v_nu)) + (__pyx_v_f32 * __pyx_v_nu2)));

  /* "pyRing/eob_utils.pyx":1393
 *     b2_nu = b2 * (f20 + f21*nu + f22*nu2)
 *     b3_nu = b3 * (f30 + f31*nu + f32*nu2)
 *     b5_nu = b5 * (f50 + f51*nu + f52*nu2)             # <<<<<<<<<<<<<<
 * 
 *     Erad_nu25_S = 0.0484161*(0.128*b3_nu*S_3 + 0.211*b2_nu*S_2 + 0.346*b1_nu*S + 1)/(1 - 0.212*b5_nu*S)    # eq. 22 of arXiv:1611.00332v2
*/
  __pyx_v_b5_nu = (__pyx_v_b5 * ((__pyx_v_f50 + (__pyx_v_f51 * __pyx_v_nu)) + (__pyx_v_f52 * __pyx_v_nu2)));

  /* "pyRing/eob_utils.pyx":1395
 *     b5_nu = b5 * (f50 + f51*nu + f52*nu2)
 * 
 *     Erad_nu25_S = 0.0484161*(0.128*b3_nu*S_3 + 0.211*b2_nu*S_2 + 0.346*b1_nu*S + 1)/(1 - 0.212*b5_nu*S)    # eq. 22 of arXiv:1611.00332v2             # <<<<<<<<<<<<<<
 *     Erad_nu25_0 = 0.0484161     # see discussion at the beginning od sec. IV.B
 * 
*/
  __pyx_v_Erad_nu25_S = ((0.0484161 * (((((0.128 * __pyx_v_b3_nu) * __pyx_v_S_3) + ((0.211 * __pyx_v_b2_nu) * __pyx_v_S_2)) + ((0.346 * __pyx_v_b1_nu) * __pyx_v_S)) + 1.0)) / (1.0 - ((0.212 * __pyx_v_b5_nu) * __pyx_v_S)));

  /* "pyRing/eob_utils.pyx":1396
 * 
 *     Erad_nu25_S = 0.0484161*(0.128*b3_nu*S_3 + 0.211*b2_nu*S_2 + 0.346*b1_nu*S + 1)/(1 - 0.212*b5_nu*S)    # eq. 22 of arXiv:1611.00332v2
 *     Erad_nu25_0 = 0.0484161     # see discussion at the beginning od sec. IV.B             # <<<<<<<<<<<<<<
 * 
 *     Erad_nu_S = Erad_nu_0 * Erad_nu25_S/Erad_nu25_0    # eq. 23 of arXiv:1611.00332v2
*/
  __pyx_v_Erad_nu25_0 = 0.0484161;

  /* "pyRing/eob_utils.pyx":1398
 *     Erad_nu25_0 = 0.0484161     # see discussion at the beginning od sec. IV.B
 * 
 *     Erad_nu_S = Erad_nu_0 * Erad_nu25_S/Erad_nu25_0    # eq. 23 of arXiv:1611.00332v2             # <<<<<<<<<<<<<<
 * 
 *     # 3D fits
*/
  __pyx_v_Erad_nu_S = ((__pyx_v_Erad_nu_0 * __pyx_v_Erad_nu25_S) / __pyx_v_Erad_nu25_0);

  /* "pyRing/eob_utils.pyx":1401
 * 
 *     # 3D fits
 *     A1 = d10 * X12 * nu2 * (d11*nu+1)    # eqs. 27(a-c) of arXiv:1611.00332v2             # <<<<<<<<<<<<<<
 *     A2 = d20 * nu3
 *     A3 = d30 * X12 * nu * (d31*nu+1)
*/
  __pyx_v_A1 = (((__pyx_v_d10 * __pyx_v_X12) * __pyx_v_nu2) * ((__pyx_v_d11 * __pyx_v_nu) + 1.0));

  /* "pyRing/eob_utils.pyx":1402
 *     # 3D fits
 *     A1 = d10 * X12 * nu2 * (d11*nu+1)    # eqs. 27(a-c) of arXiv:1611.00332v2
 *     A2 = d20 * nu3             # <<<<<<<<<<<<<<
 *     A3 = d30 * X12 * nu * (d31*nu+1)
 * 
*/
  __pyx_v_A2 = (__pyx_v_d20 * __pyx_v_nu3);

  /* "pyRing/eob_utils.pyx":1403
 *     A1 = d10 * X12 * nu2 * (d11*nu+1)    # eqs. 27(a-c) of arXiv:1611.00332v2
 *     A2 = d20 * nu3
 *     A3 = d30 * X12 * nu * (d31*nu+1)             # <<<<<<<<<<<<<<
 * 
 *     DErad_nu_S_Dchi = A1*Dchi + A2*Dchi_2 + A3*S*Dchi    # eq. 15 of arXiv:1611.00332v2
*/
  __pyx_v_A3 = (((__pyx_v_d30 * __pyx_v_X12) * __pyx_v_nu) * ((__pyx_v_d31 * __pyx_v_nu) + 1.0));

  /* "pyRing/eob_utils.pyx":1405
 *     A3 = d30 * X12 * nu * (d31*nu+1)
 * 
 *     DErad_nu_S_Dchi = A1*Dchi + A2*Dchi_2 + A3*S*Dchi    # eq. 15 of arXiv:1611.00332v2             # <<<<<<<<<<<<<<
 *     Erad = Erad_nu_S + DErad_nu_S_Dchi     # eq. 28 of arXiv:1611.00332v2
 *     res = M * (1 - Erad)      # see discussion at the beginning of sec. IV
*/
  __pyx_v_DErad_nu_S_Dchi = (((__pyx_v_A1 * __pyx_v_Dchi) + (__pyx_v_A2 * __pyx_v_Dchi_2)) + ((__pyx_v_A3 * __pyx_v_S) * __pyx_v_Dchi));

  /* "pyRing/eob_utils.pyx":1406
 * 
 *     DErad_nu_S_Dchi = A1*Dchi + A2*Dchi_2 + A3*S*Dchi    # eq. 15 of arXiv:1611.00332v2
 *     Erad = Erad_nu_S + DErad_nu_S_Dchi     # eq. 28 of arXiv:1611.00332v2             # <<<<<<<<<<<<<<
 *     res = M * (1 - Erad)      # see discussion at the beginning of sec. IV
 * 
*/
  __pyx_v_Erad = (__pyx_v_Erad_nu_S + __pyx_v_DErad_nu_S_Dchi);

  /* "pyRing/eob_utils.pyx":1407
 *     DErad_nu_S_Dchi = A1*Dchi + A2*Dchi_2 + A3*S*Dchi    # eq. 15 of arXiv:1611.00332v2
 *     Erad = Erad_nu_S + DErad_nu_S_Dchi     # eq. 28 of arXiv:1611.00332v2
 *     res = M * (1 - Erad)      # see discussion at the beginning of sec. IV             # <<<<<<<<<<<<<<
 * 
 *     return res
*/
  __pyx_v_res = (__pyx_v_M * (1.0 - __pyx_v_Erad));

  /* "pyRing/eob_utils.pyx":1409
 *     res = M * (1 - Erad)      # see discussion at the beginning of sec. IV
 * 
 *     return res             # <<<<<<<<<<<<<<
 * 
 * 
*/
  __pyx_r = __pyx_v_res;
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":1319
 * ###################################################################
 * 
 * cdef double _JimenezFortezaRemnantMass(double nu, double X1, double X2, double chi1, double chi2, double M) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Compute the BH final mass with the aligned-spin NR fit by Xisco Jimenez Forteza,
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "pyRing/eob_utils.pyx":1413
 * 
 * 
 * cdef double _JimenezFortezaRemnantSpin(double nu, double X1, double X2, double chi1, double chi2) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Compute the BH final spin with the aligned-spin NR fit by Xisco Jimenez Forteza,
*/

static double __pyx_f_6pyRing_9eob_utils__JimenezFortezaRemnantSpin(double __pyx_v_nu, double __pyx_v_X1, double __pyx_v_X2, double __pyx_v_chi1, double __pyx_v_chi2) {
  double __pyx_v_X12;
  double __pyx_v_X1_2;
  double __pyx_v_X2_2;
  double __pyx_v_S;
  double __pyx_v_Dchi;
  double __pyx_v_res;
  double __pyx_v_Lorb_nu_0;
  double __pyx_v_Lorb_nu25_S;
  double __pyx_v_Lorb_nu_S;
  double __pyx_v_Lorb_nu25_0;
  double __pyx_v_DLorb_nu_S_Dchi;
  double __pyx_v_f13;
  double __pyx_v_f23;
  double __pyx_v_f33;
  double __pyx_v_f53;
  double __pyx_v_b1_nu;
  double __pyx_v_b2_nu;
  double __pyx_v_b3_nu;
  double __pyx_v_b5_nu;
  double __pyx_v_A1;
  double __pyx_v_A2;
  double __pyx_v_A3;
  double __pyx_v_nu2;
  double __pyx_v_nu3;
  double __pyx_v_S_2;
  double __pyx_v_S_3;
  double __pyx_v_Dchi_2;
  double __pyx_v_a2;
  double __pyx_v_a3;
  double __pyx_v_a5;
  double __pyx_v_b1;
  double __pyx_v_b2;
  double __pyx_v_b3;
  double __pyx_v_b5;
  double __pyx_v_f21;
  double __pyx_v_f31;
  double __pyx_v_f50;
  double __pyx_v_f11;
  double __pyx_v_d10;
  double __pyx_v_d11;
  double __pyx_v_d20;
  double __pyx_v_d30;
  double __pyx_v_d31;
  double __pyx_v_f12;
  double __pyx_v_f22;
  double __pyx_v_f32;
  double __pyx_v_f51;
  double __pyx_v_Lorb;
  double __pyx_r;

  /* "pyRing/eob_utils.pyx":1429
 *     """
 * 
 *     cdef double X12  = X1 - X2             # <<<<<<<<<<<<<<
 *     cdef double X1_2 = X1*X1, X2_2 = X2*X2
 *     cdef double S    = (X1_2*chi1 + X2_2*chi2)/(X1_2 + X2_2)
*/
  __pyx_v_X12 = (__pyx_v_X1 - __pyx_v_X2);

  /* "pyRing/eob_utils.pyx":1430
 * 
 *     cdef double X12  = X1 - X2
 *     cdef double X1_2 = X1*X1, X2_2 = X2*X2             # <<<<<<<<<<<<<<
 *     cdef double S    = (X1_2*chi1 + X2_2*chi2)/(X1_2 + X2_2)
 *     cdef double Dchi = chi1-chi2
*/
  __pyx_v_X1_2 = (__pyx_v_X1 * __pyx_v_X1);
  __pyx_v_X2_2 = (__pyx_v_X2 * __pyx_v_X2);

  /* "pyRing/eob_utils.pyx":1431
 *     cdef double X12  = X1 - X2
 *     cdef double X1_2 = X1*X1, X2_2 = X2*X2
 *     cdef double S    = (X1_2*chi1 + X2_2*chi2)/(X1_2 + X2_2)             # <<<<<<<<<<<<<<
 *     cdef double Dchi = chi1-chi2
 * 
*/
  __pyx_v_S = (((__pyx_v_X1_2 * __pyx_v_chi1) + (__pyx_v_X2_2 * __pyx_v_chi2)) / (__pyx_v_X1_2 + __pyx_v_X2_2));

  /* "pyRing/eob_utils.pyx":1432
 *     cdef double X1_2 = X1*X1, X2_2 = X2*X2
 *     cdef double S    = (X1_2*chi1 + X2_2*chi2)/(X1_2 + X2_2)
 *     cdef double Dchi = chi1-chi2             # <<<<<<<<<<<<<<
 * 
 *     cdef double res = 0.
*/
  __pyx_v_Dchi = (__pyx_v_chi1 - __pyx_v_chi2);

  /* "pyRing/eob_utils.pyx":1434
 *     cdef double Dchi = chi1-chi2
 * 
 *     cdef double res = 0.             # <<<<<<<<<<<<<<
 *     cdef double Lorb_nu_0, Lorb_nu25_S, Lorb_nu_S, Lorb_nu25_0, DLorb_nu_S_Dchi
 *     cdef double f13, f23, f33, f53, b1_nu, b2_nu, b3_nu, b5_nu, A1, A2, A3
*/
  __pyx_v_res = 0.;

  /* "pyRing/eob_utils.pyx":1437
 *     cdef double Lorb_nu_0, Lorb_nu25_S, Lorb_nu_S, Lorb_nu25_0, DLorb_nu_S_Dchi
 *     cdef double f13, f23, f33, f53, b1_nu, b2_nu, b3_nu, b5_nu, A1, A2, A3
 *     cdef double nu2 = nu*nu, nu3 = nu2*nu, S_2 = S*S, S_3 = S_2*S, Dchi_2 = Dchi*Dchi             # <<<<<<<<<<<<<<
 * 
 *     # 1D fits - Table I from arXiv:1611.00332v2
*/
  __pyx_v_nu2 = (__pyx_v_nu * __pyx_v_nu);
  __pyx_v_nu3 = (__pyx_v_nu2 * __pyx_v_nu);
  __pyx_v_S_2 = (__pyx_v_S * __pyx_v_S);
  __pyx_v_S_3 = (__pyx_v_S_2 * __pyx_v_S);
  __pyx_v_Dchi_2 = (__pyx_v_Dchi * __pyx_v_Dchi);

  /* "pyRing/eob_utils.pyx":1440
 * 
 *     # 1D fits - Table I from arXiv:1611.00332v2
 *     cdef double a2 = 3.833, a3 = -9.49, a5 = 2.513             # <<<<<<<<<<<<<<
 * 
 *     # 1D fits - Table II from arXiv:1611.00332v2
*/
  __pyx_v_a2 = 3.833;
  __pyx_v_a3 = -9.49;
  __pyx_v_a5 = 2.513;

  /* "pyRing/eob_utils.pyx":1443
 * 
 *     # 1D fits - Table II from arXiv:1611.00332v2
 *     cdef double b1 = 1.00096, b2 = 0.788, b3 = 0.654, b5 = 0.840             # <<<<<<<<<<<<<<
 * 
 *     # 2D fits - Table III from arXiv:1611.00332v2
*/
  __pyx_v_b1 = 1.00096;
  __pyx_v_b2 = 0.788;
  __pyx_v_b3 = 0.654;
  __pyx_v_b5 = 0.840;

  /* "pyRing/eob_utils.pyx":1446
 * 
 *     # 2D fits - Table III from arXiv:1611.00332v2
 *     cdef double f21 = 8.774, f31 = 22.83, f50 = 1.8805             # <<<<<<<<<<<<<<
 *     cdef double f11 = 0.345225*f21 + 0.0321306*f31 - 3.66556*f50 + 7.5397   # eq. 13 of arXiv:1611.00332v2
 * 
*/
  __pyx_v_f21 = 8.774;
  __pyx_v_f31 = 22.83;
  __pyx_v_f50 = 1.8805;

  /* "pyRing/eob_utils.pyx":1447
 *     # 2D fits - Table III from arXiv:1611.00332v2
 *     cdef double f21 = 8.774, f31 = 22.83, f50 = 1.8805
 *     cdef double f11 = 0.345225*f21 + 0.0321306*f31 - 3.66556*f50 + 7.5397   # eq. 13 of arXiv:1611.00332v2             # <<<<<<<<<<<<<<
 * 
 *     # 3D fits - Table IV from arXiv:1611.00332v2
*/
  __pyx_v_f11 = ((((0.345225 * __pyx_v_f21) + (0.0321306 * __pyx_v_f31)) - (3.66556 * __pyx_v_f50)) + 7.5397);

  /* "pyRing/eob_utils.pyx":1450
 * 
 *     # 3D fits - Table IV from arXiv:1611.00332v2
 *     cdef double d10 = 0.322, d11 = 9.33, d20 = -0.0598, d30 = 2.32, d31 = -3.26             # <<<<<<<<<<<<<<
 *     cdef double f12 = 0.512, f22 = -32.1, f32 = -154, f51 = -4.77
 * 
*/
  __pyx_v_d10 = 0.322;
  __pyx_v_d11 = 9.33;
  __pyx_v_d20 = -0.0598;
  __pyx_v_d30 = 2.32;
  __pyx_v_d31 = -3.26;

  /* "pyRing/eob_utils.pyx":1451
 *     # 3D fits - Table IV from arXiv:1611.00332v2
 *     cdef double d10 = 0.322, d11 = 9.33, d20 = -0.0598, d30 = 2.32, d31 = -3.26
 *     cdef double f12 = 0.512, f22 = -32.1, f32 = -154, f51 = -4.77             # <<<<<<<<<<<<<<
 * 
 * 
*/
  __pyx_v_f12 = 0.512;
  __pyx_v_f22 = -32.1;
  __pyx_v_f32 = -154.0;
  __pyx_v_f51 = -4.77;

  /* "pyRing/eob_utils.pyx":1455
 * 
 *     # 1D fits
 *     Lorb_nu_0 = (1.3*a3*nu3 + 5.24*a2*nu2 + 2.*sqrt(3)*nu)/(2.88*a5*nu + 1)    # eq. 7 of arXiv:1611.00332v2             # <<<<<<<<<<<<<<
 * 
 *     # 2D fits
*/
  __pyx_v_Lorb_nu_0 = (((((1.3 * __pyx_v_a3) * __pyx_v_nu3) + ((5.24 * __pyx_v_a2) * __pyx_v_nu2)) + ((2. * sqrt(3.0)) * __pyx_v_nu)) / (((2.88 * __pyx_v_a5) * __pyx_v_nu) + 1.0));

  /* "pyRing/eob_utils.pyx":1458
 * 
 *     # 2D fits
 *     f13 = 64 - 16.*f11 - 4.*f12    # eq. 11 of arXiv:1611.00332v2             # <<<<<<<<<<<<<<
 *     f23 = 64 - 16.*f21 - 4.*f22
 *     f33 = 64 - 16.*f31 - 4.*f32
*/
  __pyx_v_f13 = ((64.0 - (16. * __pyx_v_f11)) - (4. * __pyx_v_f12));

  /* "pyRing/eob_utils.pyx":1459
 *     # 2D fits
 *     f13 = 64 - 16.*f11 - 4.*f12    # eq. 11 of arXiv:1611.00332v2
 *     f23 = 64 - 16.*f21 - 4.*f22             # <<<<<<<<<<<<<<
 *     f33 = 64 - 16.*f31 - 4.*f32
 *     f53 = 64 - 64.*f50 - 16.*f51
*/
  __pyx_v_f23 = ((64.0 - (16. * __pyx_v_f21)) - (4. * __pyx_v_f22));

  /* "pyRing/eob_utils.pyx":1460
 *     f13 = 64 - 16.*f11 - 4.*f12    # eq. 11 of arXiv:1611.00332v2
 *     f23 = 64 - 16.*f21 - 4.*f22
 *     f33 = 64 - 16.*f31 - 4.*f32             # <<<<<<<<<<<<<<
 *     f53 = 64 - 64.*f50 - 16.*f51
 * 
*/
  __pyx_v_f33 = ((64.0 - (16. * __pyx_v_f31)) - (4. * __pyx_v_f32));

  /* "pyRing/eob_utils.pyx":1461
 *     f23 = 64 - 16.*f21 - 4.*f22
 *     f33 = 64 - 16.*f31 - 4.*f32
 *     f53 = 64 - 64.*f50 - 16.*f51             # <<<<<<<<<<<<<<
 * 
 *     b1_nu = b1 * (f11*nu + f12*nu2 + f13*nu3)    # eq. 9 of arXiv:1611.00332v2
*/
  __pyx_v_f53 = ((64.0 - (64. * __pyx_v_f50)) - (16. * __pyx_v_f51));

  /* "pyRing/eob_utils.pyx":1463
 *     f53 = 64 - 64.*f50 - 16.*f51
 * 
 *     b1_nu = b1 * (f11*nu + f12*nu2 + f13*nu3)    # eq. 9 of arXiv:1611.00332v2             # <<<<<<<<<<<<<<
 *     b2_nu = b2 * (f21*nu + f22*nu2 + f23*nu3)
 *     b3_nu = b3 * (f31*nu + f32*nu2 + f33*nu3)
*/
  __pyx_v_b1_nu = (__pyx_v_b1 * (((__pyx_v_f11 * __pyx_v_nu) + (__pyx_v_f12 * __pyx_v_nu2)) + (__pyx_v_f13 * __pyx_v_nu3)));

  /* "pyRing/eob_utils.pyx":1464
 * 
 *     b1_nu = b1 * (f11*nu + f12*nu2 + f13*nu3)    # eq. 9 of arXiv:1611.00332v2
 *     b2_nu = b2 * (f21*nu + f22*nu2 + f23*nu3)             # <<<<<<<<<<<<<<
 *     b3_nu = b3 * (f31*nu + f32*nu2 + f33*nu3)
 *     b5_nu = b5 * (f50 + f51*nu + f53*nu3)
*/
  __pyx_v_b2_nu = (__pyx_v_b2 * (((__pyx_v_f21 * __pyx_v_nu) + (__pyx_v_f22 * __pyx_v_nu2)) + (__pyx_v_f23 * __pyx_v_nu3)));

  /* "pyRing/eob_utils.pyx":1465
 *     b1_nu = b1 * (f11*nu + f12*nu2 + f13*nu3)    # eq. 9 of arXiv:1611.00332v2
 *     b2_nu = b2 * (f21*nu + f22*nu2 + f23*nu3)
 *     b3_nu = b3 * (f31*nu + f32*nu2 + f33*nu3)             # <<<<<<<<<<<<<<
 *     b5_nu = b5 * (f50 + f51*nu + f53*nu3)
 * 
*/
  __pyx_v_b3_nu = (__pyx_v_b3 * (((__pyx_v_f31 * __pyx_v_nu) + (__pyx_v_f32 * __pyx_v_nu2)) + (__pyx_v_f33 * __pyx_v_nu3)));

  /* "pyRing/eob_utils.pyx":1466
 *     b2_nu = b2 * (f21*nu + f22*nu2 + f23*nu3)
 *     b3_nu = b3 * (f31*nu + f32*nu2 + f33*nu3)
 *     b5_nu = b5 * (f50 + f51*nu + f53*nu3)             # <<<<<<<<<<<<<<
 * 
 *     Lorb_nu25_S = (0.00954*b3_nu*S_3 + 0.0851*b2_nu*S_2 - 0.194*b1_nu*S)/(1 - 0.579*b5_nu*S) + 0.68637    # eq. 8 of arXiv:1611.00332v2
*/
  __pyx_v_b5_nu = (__pyx_v_b5 * ((__pyx_v_f50 + (__pyx_v_f51 * __pyx_v_nu)) + (__pyx_v_f53 * __pyx_v_nu3)));

  /* "pyRing/eob_utils.pyx":1468
 *     b5_nu = b5 * (f50 + f51*nu + f53*nu3)
 * 
 *     Lorb_nu25_S = (0.00954*b3_nu*S_3 + 0.0851*b2_nu*S_2 - 0.194*b1_nu*S)/(1 - 0.579*b5_nu*S) + 0.68637    # eq. 8 of arXiv:1611.00332v2             # <<<<<<<<<<<<<<
 *     Lorb_nu25_0 = 0.68637   # follow from eq. 8 by imposing S=0
 * 
*/
  __pyx_v_Lorb_nu25_S = ((((((0.00954 * __pyx_v_b3_nu) * __pyx_v_S_3) + ((0.0851 * __pyx_v_b2_nu) * __pyx_v_S_2)) - ((0.194 * __pyx_v_b1_nu) * __pyx_v_S)) / (1.0 - ((0.579 * __pyx_v_b5_nu) * __pyx_v_S))) + 0.68637);

  /* "pyRing/eob_utils.pyx":1469
 * 
 *     Lorb_nu25_S = (0.00954*b3_nu*S_3 + 0.0851*b2_nu*S_2 - 0.194*b1_nu*S)/(1 - 0.579*b5_nu*S) + 0.68637    # eq. 8 of arXiv:1611.00332v2
 *     Lorb_nu25_0 = 0.68637   # follow from eq. 8 by imposing S=0             # <<<<<<<<<<<<<<
 * 
 *     Lorb_nu_S = Lorb_nu_0 + Lorb_nu25_S - Lorb_nu25_0   # eq. 10 of arXiv:1611.00332v2
*/
  __pyx_v_Lorb_nu25_0 = 0.68637;

  /* "pyRing/eob_utils.pyx":1471
 *     Lorb_nu25_0 = 0.68637   # follow from eq. 8 by imposing S=0
 * 
 *     Lorb_nu_S = Lorb_nu_0 + Lorb_nu25_S - Lorb_nu25_0   # eq. 10 of arXiv:1611.00332v2             # <<<<<<<<<<<<<<
 * 
 *     # 3D fits
*/
  __pyx_v_Lorb_nu_S = ((__pyx_v_Lorb_nu_0 + __pyx_v_Lorb_nu25_S) - __pyx_v_Lorb_nu25_0);

  /* "pyRing/eob_utils.pyx":1474
 * 
 *     # 3D fits
 *     A1 = d10 * X12 * nu2 * (d11*nu+1)    # eqs. 19(a-c) of arXiv:1611.00332v2             # <<<<<<<<<<<<<<
 *     A2 = d20 * nu3
 *     A3 = d30 * X12 * nu3 * (d31*nu+1)
*/
  __pyx_v_A1 = (((__pyx_v_d10 * __pyx_v_X12) * __pyx_v_nu2) * ((__pyx_v_d11 * __pyx_v_nu) + 1.0));

  /* "pyRing/eob_utils.pyx":1475
 *     # 3D fits
 *     A1 = d10 * X12 * nu2 * (d11*nu+1)    # eqs. 19(a-c) of arXiv:1611.00332v2
 *     A2 = d20 * nu3             # <<<<<<<<<<<<<<
 *     A3 = d30 * X12 * nu3 * (d31*nu+1)
 * 
*/
  __pyx_v_A2 = (__pyx_v_d20 * __pyx_v_nu3);

  /* "pyRing/eob_utils.pyx":1476
 *     A1 = d10 * X12 * nu2 * (d11*nu+1)    # eqs. 19(a-c) of arXiv:1611.00332v2
 *     A2 = d20 * nu3
 *     A3 = d30 * X12 * nu3 * (d31*nu+1)             # <<<<<<<<<<<<<<
 * 
 *     DLorb_nu_S_Dchi = A1*Dchi + A2*Dchi_2 + A3*S*Dchi    # eq. 15 of arXiv:1611.00332v2
*/
  __pyx_v_A3 = (((__pyx_v_d30 * __pyx_v_X12) * __pyx_v_nu3) * ((__pyx_v_d31 * __pyx_v_nu) + 1.0));

  /* "pyRing/eob_utils.pyx":1478
 *     A3 = d30 * X12 * nu3 * (d31*nu+1)
 * 
 *     DLorb_nu_S_Dchi = A1*Dchi + A2*Dchi_2 + A3*S*Dchi    # eq. 15 of arXiv:1611.00332v2             # <<<<<<<<<<<<<<
 *     Lorb = Lorb_nu_S + DLorb_nu_S_Dchi     # eq. 16 of arXiv:1611.00332v2
 *     res = Lorb + X1_2*chi1 + X2_2*chi2      # see discussion in sec. III.A
*/
  __pyx_v_DLorb_nu_S_Dchi = (((__pyx_v_A1 * __pyx_v_Dchi) + (__pyx_v_A2 * __pyx_v_Dchi_2)) + ((__pyx_v_A3 * __pyx_v_S) * __pyx_v_Dchi));

  /* "pyRing/eob_utils.pyx":1479
 * 
 *     DLorb_nu_S_Dchi = A1*Dchi + A2*Dchi_2 + A3*S*Dchi    # eq. 15 of arXiv:1611.00332v2
 *     Lorb = Lorb_nu_S + DLorb_nu_S_Dchi     # eq. 16 of arXiv:1611.00332v2             # <<<<<<<<<<<<<<
 *     res = Lorb + X1_2*chi1 + X2_2*chi2      # see discussion in sec. III.A
 * 
*/
  __pyx_v_Lorb = (__pyx_v_Lorb_nu_S + __pyx_v_DLorb_nu_S_Dchi);

  /* "pyRing/eob_utils.pyx":1480
 *     DLorb_nu_S_Dchi = A1*Dchi + A2*Dchi_2 + A3*S*Dchi    # eq. 15 of arXiv:1611.00332v2
 *     Lorb = Lorb_nu_S + DLorb_nu_S_Dchi     # eq. 16 of arXiv:1611.00332v2
 *     res = Lorb + X1_2*chi1 + X2_2*chi2      # see discussion in sec. III.A             # <<<<<<<<<<<<<<
 * 
 *     return res
*/
  __pyx_v_res = ((__pyx_v_Lorb + (__pyx_v_X1_2 * __pyx_v_chi1)) + (__pyx_v_X2_2 * __pyx_v_chi2));

  /* "pyRing/eob_utils.pyx":1482
 *     res = Lorb + X1_2*chi1 + X2_2*chi2      # see discussion in sec. III.A
 * 
 *     return res             # <<<<<<<<<<<<<<
 * 
 * 
*/
  __pyx_r = __pyx_v_res;
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":1413
 * 
 * 
 * cdef double _JimenezFortezaRemnantSpin(double nu, double X1, double X2, double chi1, double chi2) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Compute the BH final spin with the aligned-spin NR fit by Xisco Jimenez Forteza,
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "pyRing/eob_utils.pyx":1491
 * ###################################################
 * 
 * cdef double _DeltaT(double nu, double X12, double S_hat, double a0, unsigned int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function returning the value of Delta_t, following appendix C.2 of arXiv:2001.09082v2.
*/

static double __pyx_f_6pyRing_9eob_utils__DeltaT(double __pyx_v_nu, double __pyx_v_X12, double __pyx_v_S_hat, double __pyx_v_a0, unsigned int __pyx_v_l, int __pyx_v_m) {
  double __pyx_v_res;
  double __pyx_v_b1_Dt;
  double __pyx_v_b2_Dt;
  double __pyx_v_b3_Dt;
  double __pyx_v_b1_Dt_nu;
  double __pyx_v_b2_Dt_nu;
  double __pyx_v_b3_Dt_nu;
  double __pyx_v_num_orb;
  double __pyx_v_den_orb;
  double __pyx_v_num_spin;
  double __pyx_v_den_spin;
  double __pyx_v_Dt21_orb;
  double __pyx_v_Dt21_spin;
  double __pyx_v_Dt33_orb;
  double __pyx_v_Dt33_spin;
  double __pyx_v_Dt32_orb;
  double __pyx_v_Dt32_spin;
  double __pyx_v_Dt31_orb;
  double __pyx_v_Dt44_orb;
  double __pyx_v_Dt44_spin;
  double __pyx_v_Dt43_orb;
  double __pyx_v_Dt43_spin;
  double __pyx_v_Dt42_orb;
  double __pyx_v_Dt42_spin;
  double __pyx_v_Dt41_orb;
  double __pyx_v_Dt55_orb;
  double __pyx_v_nu2;
  double __pyx_v_nu3;
  double __pyx_v_nu4;
  double __pyx_v_X12_2;
  double __pyx_v_X12_3;
  double __pyx_v_S_hat2;
  CYTHON_UNUSED double __pyx_v_S_hat3;
  double __pyx_v_a0_2;
  double __pyx_v_Dt21_0;
  double __pyx_v_Dt21_0_nu;
  double __pyx_v_a_1_Dt21;
  double __pyx_v_b_1_Dt21;
  double __pyx_v_b_2_Dt21;
  double __pyx_v_c_11_Dt21;
  double __pyx_v_c_12_Dt21;
  double __pyx_v_c_21_Dt21;
  double __pyx_v_c_22_Dt21;
  double __pyx_v_Dt33_0;
  double __pyx_v_a_1_Dt33;
  double __pyx_v_a_2_Dt33;
  double __pyx_v_b_1_Dt33;
  double __pyx_v_b_2_Dt33;
  double __pyx_v_b_3_Dt33;
  double __pyx_v_c_11_Dt33;
  double __pyx_v_c_12_Dt33;
  double __pyx_v_c_21_Dt33;
  double __pyx_v_c_22_Dt33;
  double __pyx_v_c_31_Dt33;
  double __pyx_v_c_32_Dt33;
  double __pyx_v_Dt32_0;
  double __pyx_v_a_1_Dt32;
  double __pyx_v_a_2_Dt32;
  double __pyx_v_a_3_Dt32;
  double __pyx_v_a_4_Dt32;
  double __pyx_v_b_1_Dt32;
  double __pyx_v_b_2_Dt32;
  double __pyx_v_b_3_Dt32;
  double __pyx_v_b_1_Dt32_nu;
  double __pyx_v_b_2_Dt32_nu;
  double __pyx_v_b_3_Dt32_nu;
  double __pyx_v_c_11_Dt32;
  double __pyx_v_c_12_Dt32;
  double __pyx_v_c_13_Dt32;
  double __pyx_v_c_14_Dt32;
  double __pyx_v_c_15_Dt32;
  double __pyx_v_c_21_Dt32;
  double __pyx_v_c_22_Dt32;
  double __pyx_v_c_23_Dt32;
  double __pyx_v_c_24_Dt32;
  double __pyx_v_c_25_Dt32;
  double __pyx_v_c_31_Dt32;
  double __pyx_v_c_32_Dt32;
  double __pyx_v_c_33_Dt32;
  double __pyx_v_c_34_Dt32;
  double __pyx_v_c_35_Dt32;
  double __pyx_v_c_11_Dt32_X;
  double __pyx_v_c_12_Dt32_X;
  double __pyx_v_c_13_Dt32_X;
  double __pyx_v_c_14_Dt32_X;
  double __pyx_v_c_15_Dt32_X;
  double __pyx_v_c_21_Dt32_X;
  double __pyx_v_c_22_Dt32_X;
  double __pyx_v_c_23_Dt32_X;
  double __pyx_v_c_24_Dt32_X;
  double __pyx_v_c_25_Dt32_X;
  double __pyx_v_c_31_Dt32_X;
  double __pyx_v_c_32_Dt32_X;
  double __pyx_v_c_33_Dt32_X;
  double __pyx_v_c_34_Dt32_X;
  double __pyx_v_c_35_Dt32_X;
  double __pyx_v_Dt31_0;
  double __pyx_v_n_2_Dt31;
  double __pyx_v_d_1_Dt31;
  double __pyx_v_d_2_Dt31;
  double __pyx_v_Dt44_0;
  double __pyx_v_a_1_Dt44;
  double __pyx_v_a_2_Dt44;
  double __pyx_v_a_3_Dt44;
  double __pyx_v_a_4_Dt44;
  double __pyx_v_b_1_Dt44_nu;
  double __pyx_v_b_2_Dt44_nu;
  double __pyx_v_c_11_Dt44;
  double __pyx_v_c_12_Dt44;
  double __pyx_v_c_21_Dt44;
  double __pyx_v_c_22_Dt44;
  double __pyx_v_Dt43_0;
  double __pyx_v_a_1_Dt43;
  double __pyx_v_a_2_Dt43;
  double __pyx_v_a_3_Dt43;
  double __pyx_v_a_4_Dt43;
  double __pyx_v_b_1_Dt43;
  double __pyx_v_b_2_Dt43;
  double __pyx_v_b_3_Dt43;
  double __pyx_v_c_11_Dt43;
  double __pyx_v_c_12_Dt43;
  double __pyx_v_c_13_Dt43;
  double __pyx_v_c_14_Dt43;
  double __pyx_v_c_21_Dt43;
  double __pyx_v_c_22_Dt43;
  double __pyx_v_c_23_Dt43;
  double __pyx_v_c_24_Dt43;
  double __pyx_v_c_31_Dt43;
  double __pyx_v_c_32_Dt43;
  double __pyx_v_c_33_Dt43;
  double __pyx_v_c_34_Dt43;
  double __pyx_v_Dt42_0;
  double __pyx_v_a_1_Dt42;
  double __pyx_v_a_2_Dt42;
  double __pyx_v_a_3_Dt42;
  double __pyx_v_a_4_Dt42;
  double __pyx_v_b_1_Dt42;
  double __pyx_v_b_2_Dt42;
  double __pyx_v_c_11_Dt42;
  double __pyx_v_c_12_Dt42;
  double __pyx_v_c_21_Dt42;
  double __pyx_v_c_22_Dt42;
  double __pyx_v_Dt41_0;
  double __pyx_v_n_1_Dt41;
  double __pyx_v_n_2_Dt41;
  double __pyx_v_d_1_Dt41;
  double __pyx_v_d_2_Dt41;
  double __pyx_v_Dt55_0;
  double __pyx_v_n_1_Dt55;
  double __pyx_v_n_2_Dt55;
  double __pyx_v_n_3_Dt55;
  double __pyx_v_n_4_Dt55;
  double __pyx_v_d_1_Dt55;
  double __pyx_v_d_2_Dt55;
  double __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;

  /* "pyRing/eob_utils.pyx":1503
 *     """
 * 
 *     cdef double res = 0.             # <<<<<<<<<<<<<<
 *     cdef double b1_Dt, b2_Dt, b3_Dt, b1_Dt_nu, b2_Dt_nu, b3_Dt_nu, num_orb, den_orb, num_spin, den_spin,
 *     cdef double Dt21_orb, Dt21_spin
*/
  __pyx_v_res = 0.;

  /* "pyRing/eob_utils.pyx":1509
 *     cdef double Dt44_orb, Dt44_spin, Dt43_orb, Dt43_spin, Dt42_orb, Dt42_spin, Dt41_orb
 *     cdef double Dt55_orb
 *     cdef double nu2 = nu*nu, nu3 = nu2*nu, nu4=nu3*nu, X12_2 = X12*X12, X12_3 = X12_2*X12, S_hat2 = S_hat*S_hat, S_hat3 = S_hat2*S_hat, a0_2 = a0*a0             # <<<<<<<<<<<<<<
 * 
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
*/
  __pyx_v_nu2 = (__pyx_v_nu * __pyx_v_nu);
  __pyx_v_nu3 = (__pyx_v_nu2 * __pyx_v_nu);
  __pyx_v_nu4 = (__pyx_v_nu3 * __pyx_v_nu);
  __pyx_v_X12_2 = (__pyx_v_X12 * __pyx_v_X12);
  __pyx_v_X12_3 = (__pyx_v_X12_2 * __pyx_v_X12);
  __pyx_v_S_hat2 = (__pyx_v_S_hat * __pyx_v_S_hat);
  __pyx_v_S_hat3 = (__pyx_v_S_hat2 * __pyx_v_S_hat);
  __pyx_v_a0_2 = (__pyx_v_a0 * __pyx_v_a0);

  /* "pyRing/eob_utils.pyx":1513
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
 *     # (2,1) - TEOBResumSFits.c, line 673-680
 *     cdef double Dt21_0    = 11.75925,  Dt21_0_nu = 6.6264     # TEOBResumSFits.c, line 640             # <<<<<<<<<<<<<<
 *     cdef double a_1_Dt21  = -2.0728
 *     cdef double b_1_Dt21  = 0.0472289, b_2_Dt21  = 0.115583
*/
  __pyx_v_Dt21_0 = 11.75925;
  __pyx_v_Dt21_0_nu = 6.6264;

  /* "pyRing/eob_utils.pyx":1514
 *     # (2,1) - TEOBResumSFits.c, line 673-680
 *     cdef double Dt21_0    = 11.75925,  Dt21_0_nu = 6.6264     # TEOBResumSFits.c, line 640
 *     cdef double a_1_Dt21  = -2.0728             # <<<<<<<<<<<<<<
 *     cdef double b_1_Dt21  = 0.0472289, b_2_Dt21  = 0.115583
 *     cdef double c_11_Dt21 = -1976.13,  c_12_Dt21 = 3719.88, c_21_Dt21 = -2545.41, c_22_Dt21 = 5277.62
*/
  __pyx_v_a_1_Dt21 = -2.0728;

  /* "pyRing/eob_utils.pyx":1515
 *     cdef double Dt21_0    = 11.75925,  Dt21_0_nu = 6.6264     # TEOBResumSFits.c, line 640
 *     cdef double a_1_Dt21  = -2.0728
 *     cdef double b_1_Dt21  = 0.0472289, b_2_Dt21  = 0.115583             # <<<<<<<<<<<<<<
 *     cdef double c_11_Dt21 = -1976.13,  c_12_Dt21 = 3719.88, c_21_Dt21 = -2545.41, c_22_Dt21 = 5277.62
 * 
*/
  __pyx_v_b_1_Dt21 = 0.0472289;
  __pyx_v_b_2_Dt21 = 0.115583;

  /* "pyRing/eob_utils.pyx":1516
 *     cdef double a_1_Dt21  = -2.0728
 *     cdef double b_1_Dt21  = 0.0472289, b_2_Dt21  = 0.115583
 *     cdef double c_11_Dt21 = -1976.13,  c_12_Dt21 = 3719.88, c_21_Dt21 = -2545.41, c_22_Dt21 = 5277.62             # <<<<<<<<<<<<<<
 * 
 *     # (3,3) - TEOBResumSFits.c, line 736-738
*/
  __pyx_v_c_11_Dt21 = -1976.13;
  __pyx_v_c_12_Dt21 = 3719.88;
  __pyx_v_c_21_Dt21 = -2545.41;
  __pyx_v_c_22_Dt21 = 5277.62;

  /* "pyRing/eob_utils.pyx":1519
 * 
 *     # (3,3) - TEOBResumSFits.c, line 736-738
 *     cdef double Dt33_0    = 3.42593     # TEOBResumSFits.c, line 643             # <<<<<<<<<<<<<<
 *     cdef double a_1_Dt33  = 0.183349, a_2_Dt33  = 4.22361
 *     cdef double b_1_Dt33  = -0.49791, b_2_Dt33  = -0.18754, b_3_Dt33  = -1.07291
*/
  __pyx_v_Dt33_0 = 3.42593;

  /* "pyRing/eob_utils.pyx":1520
 *     # (3,3) - TEOBResumSFits.c, line 736-738
 *     cdef double Dt33_0    = 3.42593     # TEOBResumSFits.c, line 643
 *     cdef double a_1_Dt33  = 0.183349, a_2_Dt33  = 4.22361             # <<<<<<<<<<<<<<
 *     cdef double b_1_Dt33  = -0.49791, b_2_Dt33  = -0.18754, b_3_Dt33  = -1.07291
 *     cdef double c_11_Dt33 = -1.9478,  c_12_Dt33 = 13.9828,  c_21_Dt33 = 1.25084, c_22_Dt33 = -3.41811, c_31_Dt33 = -1043.15, c_32_Dt33 = 1033.85
*/
  __pyx_v_a_1_Dt33 = 0.183349;
  __pyx_v_a_2_Dt33 = 4.22361;

  /* "pyRing/eob_utils.pyx":1521
 *     cdef double Dt33_0    = 3.42593     # TEOBResumSFits.c, line 643
 *     cdef double a_1_Dt33  = 0.183349, a_2_Dt33  = 4.22361
 *     cdef double b_1_Dt33  = -0.49791, b_2_Dt33  = -0.18754, b_3_Dt33  = -1.07291             # <<<<<<<<<<<<<<
 *     cdef double c_11_Dt33 = -1.9478,  c_12_Dt33 = 13.9828,  c_21_Dt33 = 1.25084, c_22_Dt33 = -3.41811, c_31_Dt33 = -1043.15, c_32_Dt33 = 1033.85
 * 
*/
  __pyx_v_b_1_Dt33 = -0.49791;
  __pyx_v_b_2_Dt33 = -0.18754;
  __pyx_v_b_3_Dt33 = -1.07291;

  /* "pyRing/eob_utils.pyx":1522
 *     cdef double a_1_Dt33  = 0.183349, a_2_Dt33  = 4.22361
 *     cdef double b_1_Dt33  = -0.49791, b_2_Dt33  = -0.18754, b_3_Dt33  = -1.07291
 *     cdef double c_11_Dt33 = -1.9478,  c_12_Dt33 = 13.9828,  c_21_Dt33 = 1.25084, c_22_Dt33 = -3.41811, c_31_Dt33 = -1043.15, c_32_Dt33 = 1033.85             # <<<<<<<<<<<<<<
 * 
 *     # (3,2) - TEOBResumSFits.c, line 686-729
*/
  __pyx_v_c_11_Dt33 = -1.9478;
  __pyx_v_c_12_Dt33 = 13.9828;
  __pyx_v_c_21_Dt33 = 1.25084;
  __pyx_v_c_22_Dt33 = -3.41811;
  __pyx_v_c_31_Dt33 = -1043.15;
  __pyx_v_c_32_Dt33 = 1033.85;

  /* "pyRing/eob_utils.pyx":1525
 * 
 *     # (3,2) - TEOBResumSFits.c, line 686-729
 *     cdef double Dt32_0      = 9.16665     # TEOBResumSFits.c, line 642             # <<<<<<<<<<<<<<
 *     cdef double a_1_Dt32    = -11.3497,  a_2_Dt32    = 32.9144,   a_3_Dt32    = -8.36579, a_4_Dt32    = 20.1017
 *     cdef double b_1_Dt32    = -0.34161,  b_2_Dt32    = -0.46107,  b_3_Dt32    = 0.34744
*/
  __pyx_v_Dt32_0 = 9.16665;

  /* "pyRing/eob_utils.pyx":1526
 *     # (3,2) - TEOBResumSFits.c, line 686-729
 *     cdef double Dt32_0      = 9.16665     # TEOBResumSFits.c, line 642
 *     cdef double a_1_Dt32    = -11.3497,  a_2_Dt32    = 32.9144,   a_3_Dt32    = -8.36579, a_4_Dt32    = 20.1017             # <<<<<<<<<<<<<<
 *     cdef double b_1_Dt32    = -0.34161,  b_2_Dt32    = -0.46107,  b_3_Dt32    = 0.34744
 *     cdef double b_1_Dt32_nu = 0.15477,   b_2_Dt32_nu = -0.755639, b_3_Dt32_nu = 0.21816
*/
  __pyx_v_a_1_Dt32 = -11.3497;
  __pyx_v_a_2_Dt32 = 32.9144;
  __pyx_v_a_3_Dt32 = -8.36579;
  __pyx_v_a_4_Dt32 = 20.1017;

  /* "pyRing/eob_utils.pyx":1527
 *     cdef double Dt32_0      = 9.16665     # TEOBResumSFits.c, line 642
 *     cdef double a_1_Dt32    = -11.3497,  a_2_Dt32    = 32.9144,   a_3_Dt32    = -8.36579, a_4_Dt32    = 20.1017
 *     cdef double b_1_Dt32    = -0.34161,  b_2_Dt32    = -0.46107,  b_3_Dt32    = 0.34744             # <<<<<<<<<<<<<<
 *     cdef double b_1_Dt32_nu = 0.15477,   b_2_Dt32_nu = -0.755639, b_3_Dt32_nu = 0.21816
 *     cdef double c_11_Dt32   = -0.037634, c_12_Dt32   = 12.456704, c_13_Dt32   = 2.670868, c_14_Dt32   = -12.255859, c_15_Dt32   = 37.843505, c_21_Dt32   = -25.058475, c_22_Dt32   = 449.470722,  c_23_Dt32   = -1413.508735, c_24_Dt32   = -11.852596, c_25_Dt32   = 41.348059, c_31_Dt32   = -5.650710, c_32_Dt32   = -9.567484, c_33_Dt32   = 173.182999, c_34_Dt32   = -10.938605, c_35_Dt32   = 35.670656
*/
  __pyx_v_b_1_Dt32 = -0.34161;
  __pyx_v_b_2_Dt32 = -0.46107;
  __pyx_v_b_3_Dt32 = 0.34744;

  /* "pyRing/eob_utils.pyx":1528
 *     cdef double a_1_Dt32    = -11.3497,  a_2_Dt32    = 32.9144,   a_3_Dt32    = -8.36579, a_4_Dt32    = 20.1017
 *     cdef double b_1_Dt32    = -0.34161,  b_2_Dt32    = -0.46107,  b_3_Dt32    = 0.34744
 *     cdef double b_1_Dt32_nu = 0.15477,   b_2_Dt32_nu = -0.755639, b_3_Dt32_nu = 0.21816             # <<<<<<<<<<<<<<
 *     cdef double c_11_Dt32   = -0.037634, c_12_Dt32   = 12.456704, c_13_Dt32   = 2.670868, c_14_Dt32   = -12.255859, c_15_Dt32   = 37.843505, c_21_Dt32   = -25.058475, c_22_Dt32   = 449.470722,  c_23_Dt32   = -1413.508735, c_24_Dt32   = -11.852596, c_25_Dt32   = 41.348059, c_31_Dt32   = -5.650710, c_32_Dt32   = -9.567484, c_33_Dt32   = 173.182999, c_34_Dt32   = -10.938605, c_35_Dt32   = 35.670656
 *     cdef double c_11_Dt32_X = 2.497188,  c_12_Dt32_X = -7.532596, c_13_Dt32_X = 4.645986, c_14_Dt32_X = -3.652524,  c_15_Dt32_X = 3.398687,  c_21_Dt32_X = 7.054185,   c_22_Dt32_X = -12.260185,  c_23_Dt32_X = 5.724802,     c_24_Dt32_X = -3.242611,  c_25_Dt32_X = 2.714232,  c_31_Dt32_X = 2.614565,  c_32_Dt32_X = -9.507583, c_33_Dt32_X = 7.321586,   c_34_Dt32_X = -3.937568,  c_35_Dt32_X = 4.584970
*/
  __pyx_v_b_1_Dt32_nu = 0.15477;
  __pyx_v_b_2_Dt32_nu = -0.755639;
  __pyx_v_b_3_Dt32_nu = 0.21816;

  /* "pyRing/eob_utils.pyx":1529
 *     cdef double b_1_Dt32    = -0.34161,  b_2_Dt32    = -0.46107,  b_3_Dt32    = 0.34744
 *     cdef double b_1_Dt32_nu = 0.15477,   b_2_Dt32_nu = -0.755639, b_3_Dt32_nu = 0.21816
 *     cdef double c_11_Dt32   = -0.037634, c_12_Dt32   = 12.456704, c_13_Dt32   = 2.670868, c_14_Dt32   = -12.255859, c_15_Dt32   = 37.843505, c_21_Dt32   = -25.058475, c_22_Dt32   = 449.470722,  c_23_Dt32   = -1413.508735, c_24_Dt32   = -11.852596, c_25_Dt32   = 41.348059, c_31_Dt32   = -5.650710, c_32_Dt32   = -9.567484, c_33_Dt32   = 173.182999, c_34_Dt32   = -10.938605, c_35_Dt32   = 35.670656             # <<<<<<<<<<<<<<
 *     cdef double c_11_Dt32_X = 2.497188,  c_12_Dt32_X = -7.532596, c_13_Dt32_X = 4.645986, c_14_Dt32_X = -3.652524,  c_15_Dt32_X = 3.398687,  c_21_Dt32_X = 7.054185,   c_22_Dt32_X = -12.260185,  c_23_Dt32_X = 5.724802,     c_24_Dt32_X = -3.242611,  c_25_Dt32_X = 2.714232,  c_31_Dt32_X = 2.614565,  c_32_Dt32_X = -9.507583, c_33_Dt32_X = 7.321586,   c_34_Dt32_X = -3.937568,  c_35_Dt32_X = 4.584970
 * 
*/
  __pyx_v_c_11_Dt32 = -0.037634;
  __pyx_v_c_12_Dt32 = 12.456704;
  __pyx_v_c_13_Dt32 = 2.670868;
  __pyx_v_c_14_Dt32 = -12.255859;
  __pyx_v_c_15_Dt32 = 37.843505;
  __pyx_v_c_21_Dt32 = -25.058475;
  __pyx_v_c_22_Dt32 = 449.470722;
  __pyx_v_c_23_Dt32 = -1413.508735;
  __pyx_v_c_24_Dt32 = -11.852596;
  __pyx_v_c_25_Dt32 = 41.348059;
  __pyx_v_c_31_Dt32 = -5.650710;
  __pyx_v_c_32_Dt32 = -9.567484;
  __pyx_v_c_33_Dt32 = 173.182999;
  __pyx_v_c_34_Dt32 = -10.938605;
  __pyx_v_c_35_Dt32 = 35.670656;

  /* "pyRing/eob_utils.pyx":1530
 *     cdef double b_1_Dt32_nu = 0.15477,   b_2_Dt32_nu = -0.755639, b_3_Dt32_nu = 0.21816
 *     cdef double c_11_Dt32   = -0.037634, c_12_Dt32   = 12.456704, c_13_Dt32   = 2.670868, c_14_Dt32   = -12.255859, c_15_Dt32   = 37.843505, c_21_Dt32   = -25.058475, c_22_Dt32   = 449.470722,  c_23_Dt32   = -1413.508735, c_24_Dt32   = -11.852596, c_25_Dt32   = 41.348059, c_31_Dt32   = -5.650710, c_32_Dt32   = -9.567484, c_33_Dt32   = 173.182999, c_34_Dt32   = -10.938605, c_35_Dt32   = 35.670656
 *     cdef double c_11_Dt32_X = 2.497188,  c_12_Dt32_X = -7.532596, c_13_Dt32_X = 4.645986, c_14_Dt32_X = -3.652524,  c_15_Dt32_X = 3.398687,  c_21_Dt32_X = 7.054185,   c_22_Dt32_X = -12.260185,  c_23_Dt32_X = 5.724802,     c_24_Dt32_X = -3.242611,  c_25_Dt32_X = 2.714232,  c_31_Dt32_X = 2.614565,  c_32_Dt32_X = -9.507583, c_33_Dt32_X = 7.321586,   c_34_Dt32_X = -3.937568,  c_35_Dt32_X = 4.584970             # <<<<<<<<<<<<<<
 * 
 *     # (3,1) - TEOBResumSFits.c, line 793
*/
  __pyx_v_c_11_Dt32_X = 2.497188;
  __pyx_v_c_12_Dt32_X = -7.532596;
  __pyx_v_c_13_Dt32_X = 4.645986;
  __pyx_v_c_14_Dt32_X = -3.652524;
  __pyx_v_c_15_Dt32_X = 3.398687;
  __pyx_v_c_21_Dt32_X = 7.054185;
  __pyx_v_c_22_Dt32_X = -12.260185;
  __pyx_v_c_23_Dt32_X = 5.724802;
  __pyx_v_c_24_Dt32_X = -3.242611;
  __pyx_v_c_25_Dt32_X = 2.714232;
  __pyx_v_c_31_Dt32_X = 2.614565;
  __pyx_v_c_32_Dt32_X = -9.507583;
  __pyx_v_c_33_Dt32_X = 7.321586;
  __pyx_v_c_34_Dt32_X = -3.937568;
  __pyx_v_c_35_Dt32_X = 4.584970;

  /* "pyRing/eob_utils.pyx":1533
 * 
 *     # (3,1) - TEOBResumSFits.c, line 793
 *     cdef double Dt31_0   = 12.9338     # TEOBResumSFits.c, line 641             # <<<<<<<<<<<<<<
 *     cdef double n_2_Dt31 = -25.615
 *     cdef double d_1_Dt31 = 0.88803, d_2_Dt31 = 16.292
*/
  __pyx_v_Dt31_0 = 12.9338;

  /* "pyRing/eob_utils.pyx":1534
 *     # (3,1) - TEOBResumSFits.c, line 793
 *     cdef double Dt31_0   = 12.9338     # TEOBResumSFits.c, line 641
 *     cdef double n_2_Dt31 = -25.615             # <<<<<<<<<<<<<<
 *     cdef double d_1_Dt31 = 0.88803, d_2_Dt31 = 16.292
 * 
*/
  __pyx_v_n_2_Dt31 = -25.615;

  /* "pyRing/eob_utils.pyx":1535
 *     cdef double Dt31_0   = 12.9338     # TEOBResumSFits.c, line 641
 *     cdef double n_2_Dt31 = -25.615
 *     cdef double d_1_Dt31 = 0.88803, d_2_Dt31 = 16.292             # <<<<<<<<<<<<<<
 * 
 *     # (4,4) - TEOBResumSFits.c, line 781-787
*/
  __pyx_v_d_1_Dt31 = 0.88803;
  __pyx_v_d_2_Dt31 = 16.292;

  /* "pyRing/eob_utils.pyx":1538
 * 
 *     # (4,4) - TEOBResumSFits.c, line 781-787
 *     cdef double Dt44_0       = 5.27778     # TEOBResumSFits.c, line 647             # <<<<<<<<<<<<<<
 *     cdef double a_1_Dt44     = -8.35574,   a_2_Dt44     = 17.5288, a_3_Dt44  = -6.50259,  a_4_Dt44  = 10.1575
 *     cdef double b_1_Dt44_nu  = 0.00159701, b_2_Dt44_nu  = -1.14134
*/
  __pyx_v_Dt44_0 = 5.27778;

  /* "pyRing/eob_utils.pyx":1539
 *     # (4,4) - TEOBResumSFits.c, line 781-787
 *     cdef double Dt44_0       = 5.27778     # TEOBResumSFits.c, line 647
 *     cdef double a_1_Dt44     = -8.35574,   a_2_Dt44     = 17.5288, a_3_Dt44  = -6.50259,  a_4_Dt44  = 10.1575             # <<<<<<<<<<<<<<
 *     cdef double b_1_Dt44_nu  = 0.00159701, b_2_Dt44_nu  = -1.14134
 *     cdef double c_11_Dt44    = -2.28656,   c_12_Dt44    = 1.66532, c_21_Dt44 = -0.589331, c_22_Dt44 = 0.708784
*/
  __pyx_v_a_1_Dt44 = -8.35574;
  __pyx_v_a_2_Dt44 = 17.5288;
  __pyx_v_a_3_Dt44 = -6.50259;
  __pyx_v_a_4_Dt44 = 10.1575;

  /* "pyRing/eob_utils.pyx":1540
 *     cdef double Dt44_0       = 5.27778     # TEOBResumSFits.c, line 647
 *     cdef double a_1_Dt44     = -8.35574,   a_2_Dt44     = 17.5288, a_3_Dt44  = -6.50259,  a_4_Dt44  = 10.1575
 *     cdef double b_1_Dt44_nu  = 0.00159701, b_2_Dt44_nu  = -1.14134             # <<<<<<<<<<<<<<
 *     cdef double c_11_Dt44    = -2.28656,   c_12_Dt44    = 1.66532, c_21_Dt44 = -0.589331, c_22_Dt44 = 0.708784
 * 
*/
  __pyx_v_b_1_Dt44_nu = 0.00159701;
  __pyx_v_b_2_Dt44_nu = -1.14134;

  /* "pyRing/eob_utils.pyx":1541
 *     cdef double a_1_Dt44     = -8.35574,   a_2_Dt44     = 17.5288, a_3_Dt44  = -6.50259,  a_4_Dt44  = 10.1575
 *     cdef double b_1_Dt44_nu  = 0.00159701, b_2_Dt44_nu  = -1.14134
 *     cdef double c_11_Dt44    = -2.28656,   c_12_Dt44    = 1.66532, c_21_Dt44 = -0.589331, c_22_Dt44 = 0.708784             # <<<<<<<<<<<<<<
 * 
 *     # (4,3) - TEOBResumSFits.c, line 759-777
*/
  __pyx_v_c_11_Dt44 = -2.28656;
  __pyx_v_c_12_Dt44 = 1.66532;
  __pyx_v_c_21_Dt44 = -0.589331;
  __pyx_v_c_22_Dt44 = 0.708784;

  /* "pyRing/eob_utils.pyx":1544
 * 
 *     # (4,3) - TEOBResumSFits.c, line 759-777
 *     cdef double Dt43_0    = 9.53705     # TEOBResumSFits.c, line 646             # <<<<<<<<<<<<<<
 *     cdef double a_1_Dt43  = -11.2377,  a_2_Dt43  = 38.3177,   a_3_Dt43  = -7.29734,  a_4_Dt43  = 21.4267
 *     cdef double b_1_Dt43  = -1.371832, b_2_Dt43  = 0.362375,  b_3_Dt43  = -1.0808402
*/
  __pyx_v_Dt43_0 = 9.53705;

  /* "pyRing/eob_utils.pyx":1545
 *     # (4,3) - TEOBResumSFits.c, line 759-777
 *     cdef double Dt43_0    = 9.53705     # TEOBResumSFits.c, line 646
 *     cdef double a_1_Dt43  = -11.2377,  a_2_Dt43  = 38.3177,   a_3_Dt43  = -7.29734,  a_4_Dt43  = 21.4267             # <<<<<<<<<<<<<<
 *     cdef double b_1_Dt43  = -1.371832, b_2_Dt43  = 0.362375,  b_3_Dt43  = -1.0808402
 *     cdef double c_11_Dt43 = 3.215984,  c_12_Dt43 = 42.133767, c_13_Dt43 = -9.440398, c_14_Dt43 = 35.160776, c_21_Dt43 = 1.133942, c_22_Dt43 = -10.356311, c_23_Dt43 = -6.701429, c_24_Dt43 = 10.726960, c_31_Dt43 = -6.036207, c_32_Dt43 = 67.730599, c_33_Dt43 = -3.082275, c_34_Dt43 = 11.547917
*/
  __pyx_v_a_1_Dt43 = -11.2377;
  __pyx_v_a_2_Dt43 = 38.3177;
  __pyx_v_a_3_Dt43 = -7.29734;
  __pyx_v_a_4_Dt43 = 21.4267;

  /* "pyRing/eob_utils.pyx":1546
 *     cdef double Dt43_0    = 9.53705     # TEOBResumSFits.c, line 646
 *     cdef double a_1_Dt43  = -11.2377,  a_2_Dt43  = 38.3177,   a_3_Dt43  = -7.29734,  a_4_Dt43  = 21.4267
 *     cdef double b_1_Dt43  = -1.371832, b_2_Dt43  = 0.362375,  b_3_Dt43  = -1.0808402             # <<<<<<<<<<<<<<
 *     cdef double c_11_Dt43 = 3.215984,  c_12_Dt43 = 42.133767, c_13_Dt43 = -9.440398, c_14_Dt43 = 35.160776, c_21_Dt43 = 1.133942, c_22_Dt43 = -10.356311, c_23_Dt43 = -6.701429, c_24_Dt43 = 10.726960, c_31_Dt43 = -6.036207, c_32_Dt43 = 67.730599, c_33_Dt43 = -3.082275, c_34_Dt43 = 11.547917
 * 
*/
  __pyx_v_b_1_Dt43 = -1.371832;
  __pyx_v_b_2_Dt43 = 0.362375;
  __pyx_v_b_3_Dt43 = -1.0808402;

  /* "pyRing/eob_utils.pyx":1547
 *     cdef double a_1_Dt43  = -11.2377,  a_2_Dt43  = 38.3177,   a_3_Dt43  = -7.29734,  a_4_Dt43  = 21.4267
 *     cdef double b_1_Dt43  = -1.371832, b_2_Dt43  = 0.362375,  b_3_Dt43  = -1.0808402
 *     cdef double c_11_Dt43 = 3.215984,  c_12_Dt43 = 42.133767, c_13_Dt43 = -9.440398, c_14_Dt43 = 35.160776, c_21_Dt43 = 1.133942, c_22_Dt43 = -10.356311, c_23_Dt43 = -6.701429, c_24_Dt43 = 10.726960, c_31_Dt43 = -6.036207, c_32_Dt43 = 67.730599, c_33_Dt43 = -3.082275, c_34_Dt43 = 11.547917             # <<<<<<<<<<<<<<
 * 
 *     # (4,2) - TEOBResumSFits.c, line 742-755
*/
  __pyx_v_c_11_Dt43 = 3.215984;
  __pyx_v_c_12_Dt43 = 42.133767;
  __pyx_v_c_13_Dt43 = -9.440398;
  __pyx_v_c_14_Dt43 = 35.160776;
  __pyx_v_c_21_Dt43 = 1.133942;
  __pyx_v_c_22_Dt43 = -10.356311;
  __pyx_v_c_23_Dt43 = -6.701429;
  __pyx_v_c_24_Dt43 = 10.726960;
  __pyx_v_c_31_Dt43 = -6.036207;
  __pyx_v_c_32_Dt43 = 67.730599;
  __pyx_v_c_33_Dt43 = -3.082275;
  __pyx_v_c_34_Dt43 = 11.547917;

  /* "pyRing/eob_utils.pyx":1550
 * 
 *     # (4,2) - TEOBResumSFits.c, line 742-755
 *     cdef double Dt42_0    = 11.66665     # TEOBResumSFits.c, line 645             # <<<<<<<<<<<<<<
 *     cdef double a_1_Dt42  = -9.8446172795, a_2_Dt42  = 23.3229430582, a_3_Dt42  = -5.7604819848, a_4_Dt42  = 7.1217930024
 *     cdef double b_1_Dt42  = -1.3002045,    b_2_Dt42  = -0.9494348
*/
  __pyx_v_Dt42_0 = 11.66665;

  /* "pyRing/eob_utils.pyx":1551
 *     # (4,2) - TEOBResumSFits.c, line 742-755
 *     cdef double Dt42_0    = 11.66665     # TEOBResumSFits.c, line 645
 *     cdef double a_1_Dt42  = -9.8446172795, a_2_Dt42  = 23.3229430582, a_3_Dt42  = -5.7604819848, a_4_Dt42  = 7.1217930024             # <<<<<<<<<<<<<<
 *     cdef double b_1_Dt42  = -1.3002045,    b_2_Dt42  = -0.9494348
 *     cdef double c_11_Dt42 = 24.604717,     c_12_Dt42 = -0.808279,     c_21_Dt42 = 62.471781,     c_22_Dt42 = 48.340961
*/
  __pyx_v_a_1_Dt42 = -9.8446172795;
  __pyx_v_a_2_Dt42 = 23.3229430582;
  __pyx_v_a_3_Dt42 = -5.7604819848;
  __pyx_v_a_4_Dt42 = 7.1217930024;

  /* "pyRing/eob_utils.pyx":1552
 *     cdef double Dt42_0    = 11.66665     # TEOBResumSFits.c, line 645
 *     cdef double a_1_Dt42  = -9.8446172795, a_2_Dt42  = 23.3229430582, a_3_Dt42  = -5.7604819848, a_4_Dt42  = 7.1217930024
 *     cdef double b_1_Dt42  = -1.3002045,    b_2_Dt42  = -0.9494348             # <<<<<<<<<<<<<<
 *     cdef double c_11_Dt42 = 24.604717,     c_12_Dt42 = -0.808279,     c_21_Dt42 = 62.471781,     c_22_Dt42 = 48.340961
 * 
*/
  __pyx_v_b_1_Dt42 = -1.3002045;
  __pyx_v_b_2_Dt42 = -0.9494348;

  /* "pyRing/eob_utils.pyx":1553
 *     cdef double a_1_Dt42  = -9.8446172795, a_2_Dt42  = 23.3229430582, a_3_Dt42  = -5.7604819848, a_4_Dt42  = 7.1217930024
 *     cdef double b_1_Dt42  = -1.3002045,    b_2_Dt42  = -0.9494348
 *     cdef double c_11_Dt42 = 24.604717,     c_12_Dt42 = -0.808279,     c_21_Dt42 = 62.471781,     c_22_Dt42 = 48.340961             # <<<<<<<<<<<<<<
 * 
 *     # (4,1) - TEOBResumSFits.c, line 795
*/
  __pyx_v_c_11_Dt42 = 24.604717;
  __pyx_v_c_12_Dt42 = -0.808279;
  __pyx_v_c_21_Dt42 = 62.471781;
  __pyx_v_c_22_Dt42 = 48.340961;

  /* "pyRing/eob_utils.pyx":1556
 * 
 *     # (4,1) - TEOBResumSFits.c, line 795
 *     cdef double Dt41_0   = 13.1116     # TEOBResumSFits.c, line 644             # <<<<<<<<<<<<<<
 *     cdef double n_1_Dt41 = -9.6225, n_2_Dt41 = 38.451
 *     cdef double d_1_Dt41 = -7.7998, d_2_Dt41 = 32.405
*/
  __pyx_v_Dt41_0 = 13.1116;

  /* "pyRing/eob_utils.pyx":1557
 *     # (4,1) - TEOBResumSFits.c, line 795
 *     cdef double Dt41_0   = 13.1116     # TEOBResumSFits.c, line 644
 *     cdef double n_1_Dt41 = -9.6225, n_2_Dt41 = 38.451             # <<<<<<<<<<<<<<
 *     cdef double d_1_Dt41 = -7.7998, d_2_Dt41 = 32.405
 * 
*/
  __pyx_v_n_1_Dt41 = -9.6225;
  __pyx_v_n_2_Dt41 = 38.451;

  /* "pyRing/eob_utils.pyx":1558
 *     cdef double Dt41_0   = 13.1116     # TEOBResumSFits.c, line 644
 *     cdef double n_1_Dt41 = -9.6225, n_2_Dt41 = 38.451
 *     cdef double d_1_Dt41 = -7.7998, d_2_Dt41 = 32.405             # <<<<<<<<<<<<<<
 * 
 *     # (5,5) - TEOBResumSFits.c, line 800
*/
  __pyx_v_d_1_Dt41 = -7.7998;
  __pyx_v_d_2_Dt41 = 32.405;

  /* "pyRing/eob_utils.pyx":1561
 * 
 *     # (5,5) - TEOBResumSFits.c, line 800
 *     cdef double Dt55_0    = 6.561811     # TEOBResumSFits.c, line 648             # <<<<<<<<<<<<<<
 *     cdef double n_1_Dt55 = -91.4401, n_2_Dt55 = 2548.5975, n_3_Dt55 = -11086.4884, n_4_Dt55 = 27137.0063
 *     cdef double d_1_Dt55 = -67.156,  d_2_Dt55 = 1773.5942
*/
  __pyx_v_Dt55_0 = 6.561811;

  /* "pyRing/eob_utils.pyx":1562
 *     # (5,5) - TEOBResumSFits.c, line 800
 *     cdef double Dt55_0    = 6.561811     # TEOBResumSFits.c, line 648
 *     cdef double n_1_Dt55 = -91.4401, n_2_Dt55 = 2548.5975, n_3_Dt55 = -11086.4884, n_4_Dt55 = 27137.0063             # <<<<<<<<<<<<<<
 *     cdef double d_1_Dt55 = -67.156,  d_2_Dt55 = 1773.5942
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
*/
  __pyx_v_n_1_Dt55 = -91.4401;
  __pyx_v_n_2_Dt55 = 2548.5975;
  __pyx_v_n_3_Dt55 = -11086.4884;
  __pyx_v_n_4_Dt55 = 27137.0063;

  /* "pyRing/eob_utils.pyx":1563
 *     cdef double Dt55_0    = 6.561811     # TEOBResumSFits.c, line 648
 *     cdef double n_1_Dt55 = -91.4401, n_2_Dt55 = 2548.5975, n_3_Dt55 = -11086.4884, n_4_Dt55 = 27137.0063
 *     cdef double d_1_Dt55 = -67.156,  d_2_Dt55 = 1773.5942             # <<<<<<<<<<<<<<
 *     # ------------------------------------------------------------------------------------------------------------------------------------------------ #
 * 
*/
  __pyx_v_d_1_Dt55 = -67.156;
  __pyx_v_d_2_Dt55 = 1773.5942;

  /* "pyRing/eob_utils.pyx":1567
 * 
 * 
 *     if ((l==2) and (m==2)):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L4_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1569
 *     if ((l==2) and (m==2)):
 * 
 *         res = 0.0             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = 0.0;

    /* "pyRing/eob_utils.pyx":1567
 * 
 * 
 *     if ((l==2) and (m==2)):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1572
 * 
 * 
 *     elif ((l==2) and (m==1)):   # eqs. C29-C32 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_Dt = (b_1_Dt21 + c_11_Dt21*X12)/(1 + c_12_Dt21*X12)
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L6_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L6_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1574
 *     elif ((l==2) and (m==1)):   # eqs. C29-C32 of arXiv:2001.09082v2
 * 
 *         b1_Dt = (b_1_Dt21 + c_11_Dt21*X12)/(1 + c_12_Dt21*X12)             # <<<<<<<<<<<<<<
 *         b2_Dt = (b_2_Dt21 + c_21_Dt21*X12)/(1 + c_22_Dt21*X12)
 * 
*/
    __pyx_v_b1_Dt = ((__pyx_v_b_1_Dt21 + (__pyx_v_c_11_Dt21 * __pyx_v_X12)) / (1.0 + (__pyx_v_c_12_Dt21 * __pyx_v_X12)));

    /* "pyRing/eob_utils.pyx":1575
 * 
 *         b1_Dt = (b_1_Dt21 + c_11_Dt21*X12)/(1 + c_12_Dt21*X12)
 *         b2_Dt = (b_2_Dt21 + c_21_Dt21*X12)/(1 + c_22_Dt21*X12)             # <<<<<<<<<<<<<<
 * 
 *         Dt21_orb  = (Dt21_0*(1-4*nu) + Dt21_0_nu*4*nu)*(1 + a_1_Dt21*nu*sqrt(1-4*nu))
*/
    __pyx_v_b2_Dt = ((__pyx_v_b_2_Dt21 + (__pyx_v_c_21_Dt21 * __pyx_v_X12)) / (1.0 + (__pyx_v_c_22_Dt21 * __pyx_v_X12)));

    /* "pyRing/eob_utils.pyx":1577
 *         b2_Dt = (b_2_Dt21 + c_21_Dt21*X12)/(1 + c_22_Dt21*X12)
 * 
 *         Dt21_orb  = (Dt21_0*(1-4*nu) + Dt21_0_nu*4*nu)*(1 + a_1_Dt21*nu*sqrt(1-4*nu))             # <<<<<<<<<<<<<<
 *         Dt21_spin = 1 + b1_Dt*a0 + b2_Dt*a0_2
 * 
*/
    __pyx_v_Dt21_orb = (((__pyx_v_Dt21_0 * (1.0 - (4.0 * __pyx_v_nu))) + ((__pyx_v_Dt21_0_nu * 4.0) * __pyx_v_nu)) * (1.0 + ((__pyx_v_a_1_Dt21 * __pyx_v_nu) * sqrt((1.0 - (4.0 * __pyx_v_nu))))));

    /* "pyRing/eob_utils.pyx":1578
 * 
 *         Dt21_orb  = (Dt21_0*(1-4*nu) + Dt21_0_nu*4*nu)*(1 + a_1_Dt21*nu*sqrt(1-4*nu))
 *         Dt21_spin = 1 + b1_Dt*a0 + b2_Dt*a0_2             # <<<<<<<<<<<<<<
 * 
 *         res = Dt21_orb * Dt21_spin
*/
    __pyx_v_Dt21_spin = ((1.0 + (__pyx_v_b1_Dt * __pyx_v_a0)) + (__pyx_v_b2_Dt * __pyx_v_a0_2));

    /* "pyRing/eob_utils.pyx":1580
 *         Dt21_spin = 1 + b1_Dt*a0 + b2_Dt*a0_2
 * 
 *         res = Dt21_orb * Dt21_spin             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = (__pyx_v_Dt21_orb * __pyx_v_Dt21_spin);

    /* "pyRing/eob_utils.pyx":1572
 * 
 * 
 *     elif ((l==2) and (m==1)):   # eqs. C29-C32 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_Dt = (b_1_Dt21 + c_11_Dt21*X12)/(1 + c_12_Dt21*X12)
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1583
 * 
 * 
 *     elif ((l==3) and (m==3)):   # eqs. C42-C45 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_Dt = (b_1_Dt33 + c_11_Dt33*nu)/(1 + c_12_Dt33*nu)
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L8_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L8_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1585
 *     elif ((l==3) and (m==3)):   # eqs. C42-C45 of arXiv:2001.09082v2
 * 
 *         b1_Dt = (b_1_Dt33 + c_11_Dt33*nu)/(1 + c_12_Dt33*nu)             # <<<<<<<<<<<<<<
 *         b2_Dt = (b_2_Dt33 + c_21_Dt33*nu)/(1 + c_22_Dt33*nu)
 *         b3_Dt = (b_3_Dt33 + c_31_Dt33*nu)/(1 + c_32_Dt33*nu)
*/
    __pyx_v_b1_Dt = ((__pyx_v_b_1_Dt33 + (__pyx_v_c_11_Dt33 * __pyx_v_nu)) / (1.0 + (__pyx_v_c_12_Dt33 * __pyx_v_nu)));

    /* "pyRing/eob_utils.pyx":1586
 * 
 *         b1_Dt = (b_1_Dt33 + c_11_Dt33*nu)/(1 + c_12_Dt33*nu)
 *         b2_Dt = (b_2_Dt33 + c_21_Dt33*nu)/(1 + c_22_Dt33*nu)             # <<<<<<<<<<<<<<
 *         b3_Dt = (b_3_Dt33 + c_31_Dt33*nu)/(1 + c_32_Dt33*nu)
 * 
*/
    __pyx_v_b2_Dt = ((__pyx_v_b_2_Dt33 + (__pyx_v_c_21_Dt33 * __pyx_v_nu)) / (1.0 + (__pyx_v_c_22_Dt33 * __pyx_v_nu)));

    /* "pyRing/eob_utils.pyx":1587
 *         b1_Dt = (b_1_Dt33 + c_11_Dt33*nu)/(1 + c_12_Dt33*nu)
 *         b2_Dt = (b_2_Dt33 + c_21_Dt33*nu)/(1 + c_22_Dt33*nu)
 *         b3_Dt = (b_3_Dt33 + c_31_Dt33*nu)/(1 + c_32_Dt33*nu)             # <<<<<<<<<<<<<<
 * 
 *         Dt33_orb = 1 + a_1_Dt33*nu + a_2_Dt33*nu2
*/
    __pyx_v_b3_Dt = ((__pyx_v_b_3_Dt33 + (__pyx_v_c_31_Dt33 * __pyx_v_nu)) / (1.0 + (__pyx_v_c_32_Dt33 * __pyx_v_nu)));

    /* "pyRing/eob_utils.pyx":1589
 *         b3_Dt = (b_3_Dt33 + c_31_Dt33*nu)/(1 + c_32_Dt33*nu)
 * 
 *         Dt33_orb = 1 + a_1_Dt33*nu + a_2_Dt33*nu2             # <<<<<<<<<<<<<<
 *         num_spin = 1 + b1_Dt*S_hat + b2_Dt*S_hat2
 *         den_spin = 1 + b3_Dt*S_hat
*/
    __pyx_v_Dt33_orb = ((1.0 + (__pyx_v_a_1_Dt33 * __pyx_v_nu)) + (__pyx_v_a_2_Dt33 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1590
 * 
 *         Dt33_orb = 1 + a_1_Dt33*nu + a_2_Dt33*nu2
 *         num_spin = 1 + b1_Dt*S_hat + b2_Dt*S_hat2             # <<<<<<<<<<<<<<
 *         den_spin = 1 + b3_Dt*S_hat
 * 
*/
    __pyx_v_num_spin = ((1.0 + (__pyx_v_b1_Dt * __pyx_v_S_hat)) + (__pyx_v_b2_Dt * __pyx_v_S_hat2));

    /* "pyRing/eob_utils.pyx":1591
 *         Dt33_orb = 1 + a_1_Dt33*nu + a_2_Dt33*nu2
 *         num_spin = 1 + b1_Dt*S_hat + b2_Dt*S_hat2
 *         den_spin = 1 + b3_Dt*S_hat             # <<<<<<<<<<<<<<
 * 
 *         Dt33_spin = num_spin/den_spin
*/
    __pyx_v_den_spin = (1.0 + (__pyx_v_b3_Dt * __pyx_v_S_hat));

    /* "pyRing/eob_utils.pyx":1593
 *         den_spin = 1 + b3_Dt*S_hat
 * 
 *         Dt33_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *         res = Dt33_0 * Dt33_orb * Dt33_spin
*/
    __pyx_v_Dt33_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

    /* "pyRing/eob_utils.pyx":1595
 *         Dt33_spin = num_spin/den_spin
 * 
 *         res = Dt33_0 * Dt33_orb * Dt33_spin             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = ((__pyx_v_Dt33_0 * __pyx_v_Dt33_orb) * __pyx_v_Dt33_spin);

    /* "pyRing/eob_utils.pyx":1583
 * 
 * 
 *     elif ((l==3) and (m==3)):   # eqs. C42-C45 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_Dt = (b_1_Dt33 + c_11_Dt33*nu)/(1 + c_12_Dt33*nu)
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1598
 * 
 * 
 *     elif ((l==3) and (m==2)):   # eqs. C54-C60 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         if (nu>=0.2):
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L10_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L10_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1600
 *     elif ((l==3) and (m==2)):   # eqs. C54-C60 of arXiv:2001.09082v2
 * 
 *         if (nu>=0.2):             # <<<<<<<<<<<<<<
 * 
 *             b1_Dt_nu = (b_1_Dt32_nu + c_11_Dt32_X*X12 + c_12_Dt32_X*X12_2 + c_13_Dt32_X*X12_3)/(1 + c_14_Dt32_X*X12 + c_15_Dt32_X*X12_2)
*/
    __pyx_t_1 = (__pyx_v_nu >= 0.2);
    if (__pyx_t_1) {

      /* "pyRing/eob_utils.pyx":1602
 *         if (nu>=0.2):
 * 
 *             b1_Dt_nu = (b_1_Dt32_nu + c_11_Dt32_X*X12 + c_12_Dt32_X*X12_2 + c_13_Dt32_X*X12_3)/(1 + c_14_Dt32_X*X12 + c_15_Dt32_X*X12_2)             # <<<<<<<<<<<<<<
 *             b2_Dt_nu = (b_2_Dt32_nu + c_21_Dt32_X*X12 + c_22_Dt32_X*X12_2 + c_23_Dt32_X*X12_3)/(1 + c_24_Dt32_X*X12 + c_25_Dt32_X*X12_2)
 *             b3_Dt_nu = (b_3_Dt32_nu + c_31_Dt32_X*X12 + c_32_Dt32_X*X12_2 + c_33_Dt32_X*X12_3)/(1 + c_34_Dt32_X*X12 + c_35_Dt32_X*X12_2)
*/
      __pyx_v_b1_Dt_nu = ((((__pyx_v_b_1_Dt32_nu + (__pyx_v_c_11_Dt32_X * __pyx_v_X12)) + (__pyx_v_c_12_Dt32_X * __pyx_v_X12_2)) + (__pyx_v_c_13_Dt32_X * __pyx_v_X12_3)) / ((1.0 + (__pyx_v_c_14_Dt32_X * __pyx_v_X12)) + (__pyx_v_c_15_Dt32_X * __pyx_v_X12_2)));

      /* "pyRing/eob_utils.pyx":1603
 * 
 *             b1_Dt_nu = (b_1_Dt32_nu + c_11_Dt32_X*X12 + c_12_Dt32_X*X12_2 + c_13_Dt32_X*X12_3)/(1 + c_14_Dt32_X*X12 + c_15_Dt32_X*X12_2)
 *             b2_Dt_nu = (b_2_Dt32_nu + c_21_Dt32_X*X12 + c_22_Dt32_X*X12_2 + c_23_Dt32_X*X12_3)/(1 + c_24_Dt32_X*X12 + c_25_Dt32_X*X12_2)             # <<<<<<<<<<<<<<
 *             b3_Dt_nu = (b_3_Dt32_nu + c_31_Dt32_X*X12 + c_32_Dt32_X*X12_2 + c_33_Dt32_X*X12_3)/(1 + c_34_Dt32_X*X12 + c_35_Dt32_X*X12_2)
 * 
*/
      __pyx_v_b2_Dt_nu = ((((__pyx_v_b_2_Dt32_nu + (__pyx_v_c_21_Dt32_X * __pyx_v_X12)) + (__pyx_v_c_22_Dt32_X * __pyx_v_X12_2)) + (__pyx_v_c_23_Dt32_X * __pyx_v_X12_3)) / ((1.0 + (__pyx_v_c_24_Dt32_X * __pyx_v_X12)) + (__pyx_v_c_25_Dt32_X * __pyx_v_X12_2)));

      /* "pyRing/eob_utils.pyx":1604
 *             b1_Dt_nu = (b_1_Dt32_nu + c_11_Dt32_X*X12 + c_12_Dt32_X*X12_2 + c_13_Dt32_X*X12_3)/(1 + c_14_Dt32_X*X12 + c_15_Dt32_X*X12_2)
 *             b2_Dt_nu = (b_2_Dt32_nu + c_21_Dt32_X*X12 + c_22_Dt32_X*X12_2 + c_23_Dt32_X*X12_3)/(1 + c_24_Dt32_X*X12 + c_25_Dt32_X*X12_2)
 *             b3_Dt_nu = (b_3_Dt32_nu + c_31_Dt32_X*X12 + c_32_Dt32_X*X12_2 + c_33_Dt32_X*X12_3)/(1 + c_34_Dt32_X*X12 + c_35_Dt32_X*X12_2)             # <<<<<<<<<<<<<<
 * 
 *             num_spin = 1 + b1_Dt_nu*S_hat + b2_Dt_nu*S_hat2
*/
      __pyx_v_b3_Dt_nu = ((((__pyx_v_b_3_Dt32_nu + (__pyx_v_c_31_Dt32_X * __pyx_v_X12)) + (__pyx_v_c_32_Dt32_X * __pyx_v_X12_2)) + (__pyx_v_c_33_Dt32_X * __pyx_v_X12_3)) / ((1.0 + (__pyx_v_c_34_Dt32_X * __pyx_v_X12)) + (__pyx_v_c_35_Dt32_X * __pyx_v_X12_2)));

      /* "pyRing/eob_utils.pyx":1606
 *             b3_Dt_nu = (b_3_Dt32_nu + c_31_Dt32_X*X12 + c_32_Dt32_X*X12_2 + c_33_Dt32_X*X12_3)/(1 + c_34_Dt32_X*X12 + c_35_Dt32_X*X12_2)
 * 
 *             num_spin = 1 + b1_Dt_nu*S_hat + b2_Dt_nu*S_hat2             # <<<<<<<<<<<<<<
 *             den_spin = 1 + b3_Dt_nu*S_hat
 * 
*/
      __pyx_v_num_spin = ((1.0 + (__pyx_v_b1_Dt_nu * __pyx_v_S_hat)) + (__pyx_v_b2_Dt_nu * __pyx_v_S_hat2));

      /* "pyRing/eob_utils.pyx":1607
 * 
 *             num_spin = 1 + b1_Dt_nu*S_hat + b2_Dt_nu*S_hat2
 *             den_spin = 1 + b3_Dt_nu*S_hat             # <<<<<<<<<<<<<<
 * 
 *         else:
*/
      __pyx_v_den_spin = (1.0 + (__pyx_v_b3_Dt_nu * __pyx_v_S_hat));

      /* "pyRing/eob_utils.pyx":1600
 *     elif ((l==3) and (m==2)):   # eqs. C54-C60 of arXiv:2001.09082v2
 * 
 *         if (nu>=0.2):             # <<<<<<<<<<<<<<
 * 
 *             b1_Dt_nu = (b_1_Dt32_nu + c_11_Dt32_X*X12 + c_12_Dt32_X*X12_2 + c_13_Dt32_X*X12_3)/(1 + c_14_Dt32_X*X12 + c_15_Dt32_X*X12_2)
*/
      goto __pyx_L12;
    }

    /* "pyRing/eob_utils.pyx":1611
 *         else:
 * 
 *             b1_Dt = (b_1_Dt32 + c_11_Dt32*nu + c_12_Dt32*nu2 + c_13_Dt32*nu3)/(1 + c_14_Dt32*nu + c_15_Dt32*nu2)             # <<<<<<<<<<<<<<
 *             b2_Dt = (b_2_Dt32 + c_21_Dt32*nu + c_22_Dt32*nu2 + c_23_Dt32*nu3)/(1 + c_24_Dt32*nu + c_25_Dt32*nu2)
 *             b3_Dt = (b_3_Dt32 + c_31_Dt32*nu + c_32_Dt32*nu2 + c_33_Dt32*nu3)/(1 + c_34_Dt32*nu + c_35_Dt32*nu2)
*/
    /*else*/ {
      __pyx_v_b1_Dt = ((((__pyx_v_b_1_Dt32 + (__pyx_v_c_11_Dt32 * __pyx_v_nu)) + (__pyx_v_c_12_Dt32 * __pyx_v_nu2)) + (__pyx_v_c_13_Dt32 * __pyx_v_nu3)) / ((1.0 + (__pyx_v_c_14_Dt32 * __pyx_v_nu)) + (__pyx_v_c_15_Dt32 * __pyx_v_nu2)));

      /* "pyRing/eob_utils.pyx":1612
 * 
 *             b1_Dt = (b_1_Dt32 + c_11_Dt32*nu + c_12_Dt32*nu2 + c_13_Dt32*nu3)/(1 + c_14_Dt32*nu + c_15_Dt32*nu2)
 *             b2_Dt = (b_2_Dt32 + c_21_Dt32*nu + c_22_Dt32*nu2 + c_23_Dt32*nu3)/(1 + c_24_Dt32*nu + c_25_Dt32*nu2)             # <<<<<<<<<<<<<<
 *             b3_Dt = (b_3_Dt32 + c_31_Dt32*nu + c_32_Dt32*nu2 + c_33_Dt32*nu3)/(1 + c_34_Dt32*nu + c_35_Dt32*nu2)
 * 
*/
      __pyx_v_b2_Dt = ((((__pyx_v_b_2_Dt32 + (__pyx_v_c_21_Dt32 * __pyx_v_nu)) + (__pyx_v_c_22_Dt32 * __pyx_v_nu2)) + (__pyx_v_c_23_Dt32 * __pyx_v_nu3)) / ((1.0 + (__pyx_v_c_24_Dt32 * __pyx_v_nu)) + (__pyx_v_c_25_Dt32 * __pyx_v_nu2)));

      /* "pyRing/eob_utils.pyx":1613
 *             b1_Dt = (b_1_Dt32 + c_11_Dt32*nu + c_12_Dt32*nu2 + c_13_Dt32*nu3)/(1 + c_14_Dt32*nu + c_15_Dt32*nu2)
 *             b2_Dt = (b_2_Dt32 + c_21_Dt32*nu + c_22_Dt32*nu2 + c_23_Dt32*nu3)/(1 + c_24_Dt32*nu + c_25_Dt32*nu2)
 *             b3_Dt = (b_3_Dt32 + c_31_Dt32*nu + c_32_Dt32*nu2 + c_33_Dt32*nu3)/(1 + c_34_Dt32*nu + c_35_Dt32*nu2)             # <<<<<<<<<<<<<<
 * 
 *             num_spin = 1 + b1_Dt*S_hat + b2_Dt*S_hat2
*/
      __pyx_v_b3_Dt = ((((__pyx_v_b_3_Dt32 + (__pyx_v_c_31_Dt32 * __pyx_v_nu)) + (__pyx_v_c_32_Dt32 * __pyx_v_nu2)) + (__pyx_v_c_33_Dt32 * __pyx_v_nu3)) / ((1.0 + (__pyx_v_c_34_Dt32 * __pyx_v_nu)) + (__pyx_v_c_35_Dt32 * __pyx_v_nu2)));

      /* "pyRing/eob_utils.pyx":1615
 *             b3_Dt = (b_3_Dt32 + c_31_Dt32*nu + c_32_Dt32*nu2 + c_33_Dt32*nu3)/(1 + c_34_Dt32*nu + c_35_Dt32*nu2)
 * 
 *             num_spin = 1 + b1_Dt*S_hat + b2_Dt*S_hat2             # <<<<<<<<<<<<<<
 *             den_spin = 1 + b3_Dt*S_hat
 * 
*/
      __pyx_v_num_spin = ((1.0 + (__pyx_v_b1_Dt * __pyx_v_S_hat)) + (__pyx_v_b2_Dt * __pyx_v_S_hat2));

      /* "pyRing/eob_utils.pyx":1616
 * 
 *             num_spin = 1 + b1_Dt*S_hat + b2_Dt*S_hat2
 *             den_spin = 1 + b3_Dt*S_hat             # <<<<<<<<<<<<<<
 * 
 *         num_orb  = 1 + a_1_Dt32*nu + a_2_Dt32*nu2
*/
      __pyx_v_den_spin = (1.0 + (__pyx_v_b3_Dt * __pyx_v_S_hat));
    }
    __pyx_L12:;

    /* "pyRing/eob_utils.pyx":1618
 *             den_spin = 1 + b3_Dt*S_hat
 * 
 *         num_orb  = 1 + a_1_Dt32*nu + a_2_Dt32*nu2             # <<<<<<<<<<<<<<
 *         den_orb  = 1 + a_3_Dt32*nu + a_4_Dt32*nu2
 * 
*/
    __pyx_v_num_orb = ((1.0 + (__pyx_v_a_1_Dt32 * __pyx_v_nu)) + (__pyx_v_a_2_Dt32 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1619
 * 
 *         num_orb  = 1 + a_1_Dt32*nu + a_2_Dt32*nu2
 *         den_orb  = 1 + a_3_Dt32*nu + a_4_Dt32*nu2             # <<<<<<<<<<<<<<
 * 
 *         Dt32_orb  = num_orb/den_orb
*/
    __pyx_v_den_orb = ((1.0 + (__pyx_v_a_3_Dt32 * __pyx_v_nu)) + (__pyx_v_a_4_Dt32 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1621
 *         den_orb  = 1 + a_3_Dt32*nu + a_4_Dt32*nu2
 * 
 *         Dt32_orb  = num_orb/den_orb             # <<<<<<<<<<<<<<
 *         Dt32_spin = num_spin/den_spin
 * 
*/
    __pyx_v_Dt32_orb = (__pyx_v_num_orb / __pyx_v_den_orb);

    /* "pyRing/eob_utils.pyx":1622
 * 
 *         Dt32_orb  = num_orb/den_orb
 *         Dt32_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *         res = Dt32_0 * Dt32_orb * Dt32_spin
*/
    __pyx_v_Dt32_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

    /* "pyRing/eob_utils.pyx":1624
 *         Dt32_spin = num_spin/den_spin
 * 
 *         res = Dt32_0 * Dt32_orb * Dt32_spin             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = ((__pyx_v_Dt32_0 * __pyx_v_Dt32_orb) * __pyx_v_Dt32_spin);

    /* "pyRing/eob_utils.pyx":1598
 * 
 * 
 *     elif ((l==3) and (m==2)):   # eqs. C54-C60 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         if (nu>=0.2):
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1627
 * 
 * 
 *     elif ((l==3) and (m==1)):   # eq. 5.23-24 of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 * 
 *         num_orb = 1 + n_2_Dt31*nu2
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L13_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L13_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1629
 *     elif ((l==3) and (m==1)):   # eq. 5.23-24 of arXiv:1904.09550v2
 * 
 *         num_orb = 1 + n_2_Dt31*nu2             # <<<<<<<<<<<<<<
 *         den_orb = 1 + d_1_Dt31*nu + d_2_Dt31*nu2
 * 
*/
    __pyx_v_num_orb = (1.0 + (__pyx_v_n_2_Dt31 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1630
 * 
 *         num_orb = 1 + n_2_Dt31*nu2
 *         den_orb = 1 + d_1_Dt31*nu + d_2_Dt31*nu2             # <<<<<<<<<<<<<<
 * 
 *         Dt31_orb = num_orb/den_orb
*/
    __pyx_v_den_orb = ((1.0 + (__pyx_v_d_1_Dt31 * __pyx_v_nu)) + (__pyx_v_d_2_Dt31 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1632
 *         den_orb = 1 + d_1_Dt31*nu + d_2_Dt31*nu2
 * 
 *         Dt31_orb = num_orb/den_orb             # <<<<<<<<<<<<<<
 * 
 *         res = Dt31_0 * Dt31_orb
*/
    __pyx_v_Dt31_orb = (__pyx_v_num_orb / __pyx_v_den_orb);

    /* "pyRing/eob_utils.pyx":1634
 *         Dt31_orb = num_orb/den_orb
 * 
 *         res = Dt31_0 * Dt31_orb             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = (__pyx_v_Dt31_0 * __pyx_v_Dt31_orb);

    /* "pyRing/eob_utils.pyx":1627
 * 
 * 
 *     elif ((l==3) and (m==1)):   # eq. 5.23-24 of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 * 
 *         num_orb = 1 + n_2_Dt31*nu2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1637
 * 
 * 
 *     elif ((l==4) and (m==4)):   # eqs. C69-C72 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_Dt = b_1_Dt44_nu + c_11_Dt44*X12 + c_12_Dt44*X12_2
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L15_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 4);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L15_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1639
 *     elif ((l==4) and (m==4)):   # eqs. C69-C72 of arXiv:2001.09082v2
 * 
 *         b1_Dt = b_1_Dt44_nu + c_11_Dt44*X12 + c_12_Dt44*X12_2             # <<<<<<<<<<<<<<
 *         b2_Dt = b_2_Dt44_nu + c_21_Dt44*X12 + c_22_Dt44*X12_2
 * 
*/
    __pyx_v_b1_Dt = ((__pyx_v_b_1_Dt44_nu + (__pyx_v_c_11_Dt44 * __pyx_v_X12)) + (__pyx_v_c_12_Dt44 * __pyx_v_X12_2));

    /* "pyRing/eob_utils.pyx":1640
 * 
 *         b1_Dt = b_1_Dt44_nu + c_11_Dt44*X12 + c_12_Dt44*X12_2
 *         b2_Dt = b_2_Dt44_nu + c_21_Dt44*X12 + c_22_Dt44*X12_2             # <<<<<<<<<<<<<<
 * 
 *         num_orb  = 1 + a_1_Dt44*nu + a_2_Dt44*nu2
*/
    __pyx_v_b2_Dt = ((__pyx_v_b_2_Dt44_nu + (__pyx_v_c_21_Dt44 * __pyx_v_X12)) + (__pyx_v_c_22_Dt44 * __pyx_v_X12_2));

    /* "pyRing/eob_utils.pyx":1642
 *         b2_Dt = b_2_Dt44_nu + c_21_Dt44*X12 + c_22_Dt44*X12_2
 * 
 *         num_orb  = 1 + a_1_Dt44*nu + a_2_Dt44*nu2             # <<<<<<<<<<<<<<
 *         den_orb  = 1 + a_3_Dt44*nu + a_4_Dt44*nu2
 *         num_spin = 1 + b1_Dt*S_hat
*/
    __pyx_v_num_orb = ((1.0 + (__pyx_v_a_1_Dt44 * __pyx_v_nu)) + (__pyx_v_a_2_Dt44 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1643
 * 
 *         num_orb  = 1 + a_1_Dt44*nu + a_2_Dt44*nu2
 *         den_orb  = 1 + a_3_Dt44*nu + a_4_Dt44*nu2             # <<<<<<<<<<<<<<
 *         num_spin = 1 + b1_Dt*S_hat
 *         den_spin = 1 + b2_Dt*S_hat
*/
    __pyx_v_den_orb = ((1.0 + (__pyx_v_a_3_Dt44 * __pyx_v_nu)) + (__pyx_v_a_4_Dt44 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1644
 *         num_orb  = 1 + a_1_Dt44*nu + a_2_Dt44*nu2
 *         den_orb  = 1 + a_3_Dt44*nu + a_4_Dt44*nu2
 *         num_spin = 1 + b1_Dt*S_hat             # <<<<<<<<<<<<<<
 *         den_spin = 1 + b2_Dt*S_hat
 * 
*/
    __pyx_v_num_spin = (1.0 + (__pyx_v_b1_Dt * __pyx_v_S_hat));

    /* "pyRing/eob_utils.pyx":1645
 *         den_orb  = 1 + a_3_Dt44*nu + a_4_Dt44*nu2
 *         num_spin = 1 + b1_Dt*S_hat
 *         den_spin = 1 + b2_Dt*S_hat             # <<<<<<<<<<<<<<
 * 
 *         Dt44_orb  = num_orb/den_orb
*/
    __pyx_v_den_spin = (1.0 + (__pyx_v_b2_Dt * __pyx_v_S_hat));

    /* "pyRing/eob_utils.pyx":1647
 *         den_spin = 1 + b2_Dt*S_hat
 * 
 *         Dt44_orb  = num_orb/den_orb             # <<<<<<<<<<<<<<
 *         Dt44_spin = num_spin/den_spin
 * 
*/
    __pyx_v_Dt44_orb = (__pyx_v_num_orb / __pyx_v_den_orb);

    /* "pyRing/eob_utils.pyx":1648
 * 
 *         Dt44_orb  = num_orb/den_orb
 *         Dt44_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *         res = Dt44_0 * Dt44_orb * Dt44_spin
*/
    __pyx_v_Dt44_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

    /* "pyRing/eob_utils.pyx":1650
 *         Dt44_spin = num_spin/den_spin
 * 
 *         res = Dt44_0 * Dt44_orb * Dt44_spin             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = ((__pyx_v_Dt44_0 * __pyx_v_Dt44_orb) * __pyx_v_Dt44_spin);

    /* "pyRing/eob_utils.pyx":1637
 * 
 * 
 *     elif ((l==4) and (m==4)):   # eqs. C69-C72 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_Dt = b_1_Dt44_nu + c_11_Dt44*X12 + c_12_Dt44*X12_2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1653
 * 
 * 
 *     elif ((l==4) and (m==3)):   # eqs. C82-C85 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_Dt = (b_1_Dt43 + c_11_Dt43*nu + c_12_Dt43*nu2)/(1 + c_13_Dt43*nu + c_14_Dt43*nu2)
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L17_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L17_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1655
 *     elif ((l==4) and (m==3)):   # eqs. C82-C85 of arXiv:2001.09082v2
 * 
 *         b1_Dt = (b_1_Dt43 + c_11_Dt43*nu + c_12_Dt43*nu2)/(1 + c_13_Dt43*nu + c_14_Dt43*nu2)             # <<<<<<<<<<<<<<
 *         b2_Dt = (b_2_Dt43 + c_21_Dt43*nu + c_22_Dt43*nu2)/(1 + c_23_Dt43*nu + c_24_Dt43*nu2)
 *         b3_Dt = (b_3_Dt43 + c_31_Dt43*nu + c_32_Dt43*nu2)/(1 + c_33_Dt43*nu + c_34_Dt43*nu2)
*/
    __pyx_v_b1_Dt = (((__pyx_v_b_1_Dt43 + (__pyx_v_c_11_Dt43 * __pyx_v_nu)) + (__pyx_v_c_12_Dt43 * __pyx_v_nu2)) / ((1.0 + (__pyx_v_c_13_Dt43 * __pyx_v_nu)) + (__pyx_v_c_14_Dt43 * __pyx_v_nu2)));

    /* "pyRing/eob_utils.pyx":1656
 * 
 *         b1_Dt = (b_1_Dt43 + c_11_Dt43*nu + c_12_Dt43*nu2)/(1 + c_13_Dt43*nu + c_14_Dt43*nu2)
 *         b2_Dt = (b_2_Dt43 + c_21_Dt43*nu + c_22_Dt43*nu2)/(1 + c_23_Dt43*nu + c_24_Dt43*nu2)             # <<<<<<<<<<<<<<
 *         b3_Dt = (b_3_Dt43 + c_31_Dt43*nu + c_32_Dt43*nu2)/(1 + c_33_Dt43*nu + c_34_Dt43*nu2)
 * 
*/
    __pyx_v_b2_Dt = (((__pyx_v_b_2_Dt43 + (__pyx_v_c_21_Dt43 * __pyx_v_nu)) + (__pyx_v_c_22_Dt43 * __pyx_v_nu2)) / ((1.0 + (__pyx_v_c_23_Dt43 * __pyx_v_nu)) + (__pyx_v_c_24_Dt43 * __pyx_v_nu2)));

    /* "pyRing/eob_utils.pyx":1657
 *         b1_Dt = (b_1_Dt43 + c_11_Dt43*nu + c_12_Dt43*nu2)/(1 + c_13_Dt43*nu + c_14_Dt43*nu2)
 *         b2_Dt = (b_2_Dt43 + c_21_Dt43*nu + c_22_Dt43*nu2)/(1 + c_23_Dt43*nu + c_24_Dt43*nu2)
 *         b3_Dt = (b_3_Dt43 + c_31_Dt43*nu + c_32_Dt43*nu2)/(1 + c_33_Dt43*nu + c_34_Dt43*nu2)             # <<<<<<<<<<<<<<
 * 
 *         num_orb  = 1 + a_1_Dt43*nu + a_2_Dt43*nu2
*/
    __pyx_v_b3_Dt = (((__pyx_v_b_3_Dt43 + (__pyx_v_c_31_Dt43 * __pyx_v_nu)) + (__pyx_v_c_32_Dt43 * __pyx_v_nu2)) / ((1.0 + (__pyx_v_c_33_Dt43 * __pyx_v_nu)) + (__pyx_v_c_34_Dt43 * __pyx_v_nu2)));

    /* "pyRing/eob_utils.pyx":1659
 *         b3_Dt = (b_3_Dt43 + c_31_Dt43*nu + c_32_Dt43*nu2)/(1 + c_33_Dt43*nu + c_34_Dt43*nu2)
 * 
 *         num_orb  = 1 + a_1_Dt43*nu + a_2_Dt43*nu2             # <<<<<<<<<<<<<<
 *         den_orb  = 1 + a_3_Dt43*nu + a_4_Dt43*nu2
 *         num_spin = 1 + b1_Dt*S_hat + b2_Dt*S_hat2
*/
    __pyx_v_num_orb = ((1.0 + (__pyx_v_a_1_Dt43 * __pyx_v_nu)) + (__pyx_v_a_2_Dt43 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1660
 * 
 *         num_orb  = 1 + a_1_Dt43*nu + a_2_Dt43*nu2
 *         den_orb  = 1 + a_3_Dt43*nu + a_4_Dt43*nu2             # <<<<<<<<<<<<<<
 *         num_spin = 1 + b1_Dt*S_hat + b2_Dt*S_hat2
 *         den_spin = 1 + b3_Dt*S_hat
*/
    __pyx_v_den_orb = ((1.0 + (__pyx_v_a_3_Dt43 * __pyx_v_nu)) + (__pyx_v_a_4_Dt43 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1661
 *         num_orb  = 1 + a_1_Dt43*nu + a_2_Dt43*nu2
 *         den_orb  = 1 + a_3_Dt43*nu + a_4_Dt43*nu2
 *         num_spin = 1 + b1_Dt*S_hat + b2_Dt*S_hat2             # <<<<<<<<<<<<<<
 *         den_spin = 1 + b3_Dt*S_hat
 * 
*/
    __pyx_v_num_spin = ((1.0 + (__pyx_v_b1_Dt * __pyx_v_S_hat)) + (__pyx_v_b2_Dt * __pyx_v_S_hat2));

    /* "pyRing/eob_utils.pyx":1662
 *         den_orb  = 1 + a_3_Dt43*nu + a_4_Dt43*nu2
 *         num_spin = 1 + b1_Dt*S_hat + b2_Dt*S_hat2
 *         den_spin = 1 + b3_Dt*S_hat             # <<<<<<<<<<<<<<
 * 
 *         Dt43_orb  = num_orb/den_orb
*/
    __pyx_v_den_spin = (1.0 + (__pyx_v_b3_Dt * __pyx_v_S_hat));

    /* "pyRing/eob_utils.pyx":1664
 *         den_spin = 1 + b3_Dt*S_hat
 * 
 *         Dt43_orb  = num_orb/den_orb             # <<<<<<<<<<<<<<
 *         Dt43_spin = num_spin/den_spin
 * 
*/
    __pyx_v_Dt43_orb = (__pyx_v_num_orb / __pyx_v_den_orb);

    /* "pyRing/eob_utils.pyx":1665
 * 
 *         Dt43_orb  = num_orb/den_orb
 *         Dt43_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *         res = Dt43_0 * Dt43_orb * Dt43_spin
*/
    __pyx_v_Dt43_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

    /* "pyRing/eob_utils.pyx":1667
 *         Dt43_spin = num_spin/den_spin
 * 
 *         res = Dt43_0 * Dt43_orb * Dt43_spin             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = ((__pyx_v_Dt43_0 * __pyx_v_Dt43_orb) * __pyx_v_Dt43_spin);

    /* "pyRing/eob_utils.pyx":1653
 * 
 * 
 *     elif ((l==4) and (m==3)):   # eqs. C82-C85 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         b1_Dt = (b_1_Dt43 + c_11_Dt43*nu + c_12_Dt43*nu2)/(1 + c_13_Dt43*nu + c_14_Dt43*nu2)
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1670
 * 
 * 
 *     elif ((l==4) and (m==2)):   # eqs. C94-C97 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         if (nu<6./25.):
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L19_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L19_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1672
 *     elif ((l==4) and (m==2)):   # eqs. C94-C97 of arXiv:2001.09082v2
 * 
 *         if (nu<6./25.):             # <<<<<<<<<<<<<<
 *             b1_Dt = b_1_Dt42
 *             b2_Dt = b_2_Dt42
*/
    __pyx_t_1 = (__pyx_v_nu < (6. / 25.));
    if (__pyx_t_1) {

      /* "pyRing/eob_utils.pyx":1673
 * 
 *         if (nu<6./25.):
 *             b1_Dt = b_1_Dt42             # <<<<<<<<<<<<<<
 *             b2_Dt = b_2_Dt42
 * 
*/
      __pyx_v_b1_Dt = __pyx_v_b_1_Dt42;

      /* "pyRing/eob_utils.pyx":1674
 *         if (nu<6./25.):
 *             b1_Dt = b_1_Dt42
 *             b2_Dt = b_2_Dt42             # <<<<<<<<<<<<<<
 * 
 *         else:
*/
      __pyx_v_b2_Dt = __pyx_v_b_2_Dt42;

      /* "pyRing/eob_utils.pyx":1672
 *     elif ((l==4) and (m==2)):   # eqs. C94-C97 of arXiv:2001.09082v2
 * 
 *         if (nu<6./25.):             # <<<<<<<<<<<<<<
 *             b1_Dt = b_1_Dt42
 *             b2_Dt = b_2_Dt42
*/
      goto __pyx_L21;
    }

    /* "pyRing/eob_utils.pyx":1677
 * 
 *         else:
 *             b1_Dt = (b_1_Dt42 + c_11_Dt42*nu)/(1 + c_12_Dt42*nu)             # <<<<<<<<<<<<<<
 *             b2_Dt = (b_2_Dt42 + c_21_Dt42*nu)/(1 + c_22_Dt42*nu)
 * 
*/
    /*else*/ {
      __pyx_v_b1_Dt = ((__pyx_v_b_1_Dt42 + (__pyx_v_c_11_Dt42 * __pyx_v_nu)) / (1.0 + (__pyx_v_c_12_Dt42 * __pyx_v_nu)));

      /* "pyRing/eob_utils.pyx":1678
 *         else:
 *             b1_Dt = (b_1_Dt42 + c_11_Dt42*nu)/(1 + c_12_Dt42*nu)
 *             b2_Dt = (b_2_Dt42 + c_21_Dt42*nu)/(1 + c_22_Dt42*nu)             # <<<<<<<<<<<<<<
 * 
 *         num_orb  = 1 + a_1_Dt42*nu + a_2_Dt42*nu2
*/
      __pyx_v_b2_Dt = ((__pyx_v_b_2_Dt42 + (__pyx_v_c_21_Dt42 * __pyx_v_nu)) / (1.0 + (__pyx_v_c_22_Dt42 * __pyx_v_nu)));
    }
    __pyx_L21:;

    /* "pyRing/eob_utils.pyx":1680
 *             b2_Dt = (b_2_Dt42 + c_21_Dt42*nu)/(1 + c_22_Dt42*nu)
 * 
 *         num_orb  = 1 + a_1_Dt42*nu + a_2_Dt42*nu2             # <<<<<<<<<<<<<<
 *         den_orb  = 1 + a_3_Dt42*nu + a_4_Dt42*nu2
 *         num_spin = 1 + b1_Dt*S_hat
*/
    __pyx_v_num_orb = ((1.0 + (__pyx_v_a_1_Dt42 * __pyx_v_nu)) + (__pyx_v_a_2_Dt42 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1681
 * 
 *         num_orb  = 1 + a_1_Dt42*nu + a_2_Dt42*nu2
 *         den_orb  = 1 + a_3_Dt42*nu + a_4_Dt42*nu2             # <<<<<<<<<<<<<<
 *         num_spin = 1 + b1_Dt*S_hat
 *         den_spin = 1 + b2_Dt*S_hat
*/
    __pyx_v_den_orb = ((1.0 + (__pyx_v_a_3_Dt42 * __pyx_v_nu)) + (__pyx_v_a_4_Dt42 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1682
 *         num_orb  = 1 + a_1_Dt42*nu + a_2_Dt42*nu2
 *         den_orb  = 1 + a_3_Dt42*nu + a_4_Dt42*nu2
 *         num_spin = 1 + b1_Dt*S_hat             # <<<<<<<<<<<<<<
 *         den_spin = 1 + b2_Dt*S_hat
 * 
*/
    __pyx_v_num_spin = (1.0 + (__pyx_v_b1_Dt * __pyx_v_S_hat));

    /* "pyRing/eob_utils.pyx":1683
 *         den_orb  = 1 + a_3_Dt42*nu + a_4_Dt42*nu2
 *         num_spin = 1 + b1_Dt*S_hat
 *         den_spin = 1 + b2_Dt*S_hat             # <<<<<<<<<<<<<<
 * 
 *         Dt42_orb  = num_orb/den_orb
*/
    __pyx_v_den_spin = (1.0 + (__pyx_v_b2_Dt * __pyx_v_S_hat));

    /* "pyRing/eob_utils.pyx":1685
 *         den_spin = 1 + b2_Dt*S_hat
 * 
 *         Dt42_orb  = num_orb/den_orb             # <<<<<<<<<<<<<<
 *         Dt42_spin = num_spin/den_spin
 * 
*/
    __pyx_v_Dt42_orb = (__pyx_v_num_orb / __pyx_v_den_orb);

    /* "pyRing/eob_utils.pyx":1686
 * 
 *         Dt42_orb  = num_orb/den_orb
 *         Dt42_spin = num_spin/den_spin             # <<<<<<<<<<<<<<
 * 
 *         res = Dt42_0 * Dt42_orb * Dt42_spin
*/
    __pyx_v_Dt42_spin = (__pyx_v_num_spin / __pyx_v_den_spin);

    /* "pyRing/eob_utils.pyx":1688
 *         Dt42_spin = num_spin/den_spin
 * 
 *         res = Dt42_0 * Dt42_orb * Dt42_spin             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = ((__pyx_v_Dt42_0 * __pyx_v_Dt42_orb) * __pyx_v_Dt42_spin);

    /* "pyRing/eob_utils.pyx":1670
 * 
 * 
 *     elif ((l==4) and (m==2)):   # eqs. C94-C97 of arXiv:2001.09082v2             # <<<<<<<<<<<<<<
 * 
 *         if (nu<6./25.):
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1691
 * 
 * 
 *     elif ((l==4) and (m==1)):   # eq. 5.23-24 of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 * 
 *         num_orb = 1 + n_1_Dt41*nu + n_2_Dt41*nu2
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L22_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L22_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1693
 *     elif ((l==4) and (m==1)):   # eq. 5.23-24 of arXiv:1904.09550v2
 * 
 *         num_orb = 1 + n_1_Dt41*nu + n_2_Dt41*nu2             # <<<<<<<<<<<<<<
 *         den_orb = 1 + d_1_Dt41*nu + d_2_Dt41*nu2
 * 
*/
    __pyx_v_num_orb = ((1.0 + (__pyx_v_n_1_Dt41 * __pyx_v_nu)) + (__pyx_v_n_2_Dt41 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1694
 * 
 *         num_orb = 1 + n_1_Dt41*nu + n_2_Dt41*nu2
 *         den_orb = 1 + d_1_Dt41*nu + d_2_Dt41*nu2             # <<<<<<<<<<<<<<
 * 
 *         Dt41_orb = num_orb/den_orb
*/
    __pyx_v_den_orb = ((1.0 + (__pyx_v_d_1_Dt41 * __pyx_v_nu)) + (__pyx_v_d_2_Dt41 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1696
 *         den_orb = 1 + d_1_Dt41*nu + d_2_Dt41*nu2
 * 
 *         Dt41_orb = num_orb/den_orb             # <<<<<<<<<<<<<<
 * 
 *         res = Dt41_0 * Dt41_orb
*/
    __pyx_v_Dt41_orb = (__pyx_v_num_orb / __pyx_v_den_orb);

    /* "pyRing/eob_utils.pyx":1698
 *         Dt41_orb = num_orb/den_orb
 * 
 *         res = Dt41_0 * Dt41_orb             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = (__pyx_v_Dt41_0 * __pyx_v_Dt41_orb);

    /* "pyRing/eob_utils.pyx":1691
 * 
 * 
 *     elif ((l==4) and (m==1)):   # eq. 5.23-24 of arXiv:1904.09550v2             # <<<<<<<<<<<<<<
 * 
 *         num_orb = 1 + n_1_Dt41*nu + n_2_Dt41*nu2
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1701
 * 
 * 
 *     elif ((l==5) and (m==5)):   # TEOBResumSFits.c, line 800             # <<<<<<<<<<<<<<
 * 
 *         num_orb = 1 + n_1_Dt55*nu + n_2_Dt55*nu2 + n_3_Dt55*nu3 + n_4_Dt55*nu4
*/
  __pyx_t_2 = (__pyx_v_l == 5);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L24_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 5);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L24_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1703
 *     elif ((l==5) and (m==5)):   # TEOBResumSFits.c, line 800
 * 
 *         num_orb = 1 + n_1_Dt55*nu + n_2_Dt55*nu2 + n_3_Dt55*nu3 + n_4_Dt55*nu4             # <<<<<<<<<<<<<<
 *         den_orb = 1 + d_1_Dt55*nu + d_2_Dt55*nu2
 * 
*/
    __pyx_v_num_orb = ((((1.0 + (__pyx_v_n_1_Dt55 * __pyx_v_nu)) + (__pyx_v_n_2_Dt55 * __pyx_v_nu2)) + (__pyx_v_n_3_Dt55 * __pyx_v_nu3)) + (__pyx_v_n_4_Dt55 * __pyx_v_nu4));

    /* "pyRing/eob_utils.pyx":1704
 * 
 *         num_orb = 1 + n_1_Dt55*nu + n_2_Dt55*nu2 + n_3_Dt55*nu3 + n_4_Dt55*nu4
 *         den_orb = 1 + d_1_Dt55*nu + d_2_Dt55*nu2             # <<<<<<<<<<<<<<
 * 
 *         Dt55_orb = num_orb/den_orb
*/
    __pyx_v_den_orb = ((1.0 + (__pyx_v_d_1_Dt55 * __pyx_v_nu)) + (__pyx_v_d_2_Dt55 * __pyx_v_nu2));

    /* "pyRing/eob_utils.pyx":1706
 *         den_orb = 1 + d_1_Dt55*nu + d_2_Dt55*nu2
 * 
 *         Dt55_orb = num_orb/den_orb             # <<<<<<<<<<<<<<
 * 
 *         res = Dt55_0 * Dt55_orb
*/
    __pyx_v_Dt55_orb = (__pyx_v_num_orb / __pyx_v_den_orb);

    /* "pyRing/eob_utils.pyx":1708
 *         Dt55_orb = num_orb/den_orb
 * 
 *         res = Dt55_0 * Dt55_orb             # <<<<<<<<<<<<<<
 * 
 * 
*/
    __pyx_v_res = (__pyx_v_Dt55_0 * __pyx_v_Dt55_orb);

    /* "pyRing/eob_utils.pyx":1701
 * 
 * 
 *     elif ((l==5) and (m==5)):   # TEOBResumSFits.c, line 800             # <<<<<<<<<<<<<<
 * 
 *         num_orb = 1 + n_1_Dt55*nu + n_2_Dt55*nu2 + n_3_Dt55*nu3 + n_4_Dt55*nu4
*/
  }
  __pyx_L3:;

  /* "pyRing/eob_utils.pyx":1711
 * 
 * 
 *     return res             # <<<<<<<<<<<<<<
 * 
 * 
*/
  __pyx_r = __pyx_v_res;
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":1491
 * ###################################################
 * 
 * cdef double _DeltaT(double nu, double X12, double S_hat, double a0, unsigned int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Function returning the value of Delta_t, following appendix C.2 of arXiv:2001.09082v2.
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "pyRing/eob_utils.pyx":1714
 * 
 * 
 * cdef double _DeltaPhi(double nu, double X12, double S_hat, unsigned int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Not implemented
*/

static double __pyx_f_6pyRing_9eob_utils__DeltaPhi(CYTHON_UNUSED double __pyx_v_nu, CYTHON_UNUSED double __pyx_v_X12, CYTHON_UNUSED double __pyx_v_S_hat, unsigned int __pyx_v_l, int __pyx_v_m) {
  double __pyx_v_res;
  double __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;

  /* "pyRing/eob_utils.pyx":1719
 *     """
 * 
 *     cdef double res = 0.             # <<<<<<<<<<<<<<
 * 
 *     if(l==2 and m==2):
*/
  __pyx_v_res = 0.;

  /* "pyRing/eob_utils.pyx":1721
 *     cdef double res = 0.
 * 
 *     if(l==2 and m==2):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L4_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L4_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1723
 *     if(l==2 and m==2):
 * 
 *         res = 0.0             # <<<<<<<<<<<<<<
 * 
 *     elif(l==2 and m==1):
*/
    __pyx_v_res = 0.0;

    /* "pyRing/eob_utils.pyx":1721
 *     cdef double res = 0.
 * 
 *     if(l==2 and m==2):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1725
 *         res = 0.0
 * 
 *     elif(l==2 and m==1):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
  __pyx_t_2 = (__pyx_v_l == 2);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L6_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L6_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1727
 *     elif(l==2 and m==1):
 * 
 *         res = 0.0             # <<<<<<<<<<<<<<
 * 
 *     elif(l==3 and m==3):
*/
    __pyx_v_res = 0.0;

    /* "pyRing/eob_utils.pyx":1725
 *         res = 0.0
 * 
 *     elif(l==2 and m==1):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1729
 *         res = 0.0
 * 
 *     elif(l==3 and m==3):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L8_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L8_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1731
 *     elif(l==3 and m==3):
 * 
 *         res = 0.0             # <<<<<<<<<<<<<<
 * 
 *     elif(l==3 and m==2):
*/
    __pyx_v_res = 0.0;

    /* "pyRing/eob_utils.pyx":1729
 *         res = 0.0
 * 
 *     elif(l==3 and m==3):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1733
 *         res = 0.0
 * 
 *     elif(l==3 and m==2):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L10_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L10_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1735
 *     elif(l==3 and m==2):
 * 
 *         res = 0.0             # <<<<<<<<<<<<<<
 * 
 *     elif(l==3 and m==1):
*/
    __pyx_v_res = 0.0;

    /* "pyRing/eob_utils.pyx":1733
 *         res = 0.0
 * 
 *     elif(l==3 and m==2):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1737
 *         res = 0.0
 * 
 *     elif(l==3 and m==1):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
  __pyx_t_2 = (__pyx_v_l == 3);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L12_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L12_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1739
 *     elif(l==3 and m==1):
 * 
 *         res = 0.0             # <<<<<<<<<<<<<<
 * 
 *     elif(l==4 and m==4):
*/
    __pyx_v_res = 0.0;

    /* "pyRing/eob_utils.pyx":1737
 *         res = 0.0
 * 
 *     elif(l==3 and m==1):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1741
 *         res = 0.0
 * 
 *     elif(l==4 and m==4):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L14_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 4);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L14_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1743
 *     elif(l==4 and m==4):
 * 
 *         res = 0.0             # <<<<<<<<<<<<<<
 * 
 *     elif(l==4 and m==3):
*/
    __pyx_v_res = 0.0;

    /* "pyRing/eob_utils.pyx":1741
 *         res = 0.0
 * 
 *     elif(l==4 and m==4):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1745
 *         res = 0.0
 * 
 *     elif(l==4 and m==3):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L16_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 3);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L16_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1747
 *     elif(l==4 and m==3):
 * 
 *         res = 0.0             # <<<<<<<<<<<<<<
 * 
 *     elif(l==4 and m==2):
*/
    __pyx_v_res = 0.0;

    /* "pyRing/eob_utils.pyx":1745
 *         res = 0.0
 * 
 *     elif(l==4 and m==3):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1749
 *         res = 0.0
 * 
 *     elif(l==4 and m==2):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L18_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 2);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L18_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1751
 *     elif(l==4 and m==2):
 * 
 *         res = 0.0             # <<<<<<<<<<<<<<
 * 
 *     elif(l==4 and m==1):
*/
    __pyx_v_res = 0.0;

    /* "pyRing/eob_utils.pyx":1749
 *         res = 0.0
 * 
 *     elif(l==4 and m==2):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1753
 *         res = 0.0
 * 
 *     elif(l==4 and m==1):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
  __pyx_t_2 = (__pyx_v_l == 4);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L20_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 1);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L20_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1755
 *     elif(l==4 and m==1):
 * 
 *         res = 0.0             # <<<<<<<<<<<<<<
 * 
 *     elif(l==5 and m==5):
*/
    __pyx_v_res = 0.0;

    /* "pyRing/eob_utils.pyx":1753
 *         res = 0.0
 * 
 *     elif(l==4 and m==1):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
    goto __pyx_L3;
  }

  /* "pyRing/eob_utils.pyx":1757
 *         res = 0.0
 * 
 *     elif(l==5 and m==5):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
  __pyx_t_2 = (__pyx_v_l == 5);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L22_bool_binop_done;
  }
  __pyx_t_2 = (__pyx_v_m == 5);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L22_bool_binop_done:;
  if (__pyx_t_1) {

    /* "pyRing/eob_utils.pyx":1759
 *     elif(l==5 and m==5):
 * 
 *         res = 0.0             # <<<<<<<<<<<<<<
 * 
 *     return res
*/
    __pyx_v_res = 0.0;

    /* "pyRing/eob_utils.pyx":1757
 *         res = 0.0
 * 
 *     elif(l==5 and m==5):             # <<<<<<<<<<<<<<
 * 
 *         res = 0.0
*/
  }
  __pyx_L3:;

  /* "pyRing/eob_utils.pyx":1761
 *         res = 0.0
 * 
 *     return res             # <<<<<<<<<<<<<<
*/
  __pyx_r = __pyx_v_res;
  goto __pyx_L0;

  /* "pyRing/eob_utils.pyx":1714
 * 
 * 
 * cdef double _DeltaPhi(double nu, double X12, double S_hat, unsigned int l, int m) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Not implemented
*/

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}
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typedef struct {
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#if 20 <= 65535
    const unsigned short n;
#elif 20 / 2 < INT_MAX
    const unsigned int n;
#elif 20 / 2 < LONG_MAX
    const unsigned long n;
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    const Py_ssize_t n;
#endif
#if 1 <= 31
    const unsigned int encoding : 5;
#elif 1 <= 255
    const unsigned char encoding;
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    const unsigned short encoding;
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    const Py_ssize_t encoding;
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static const __Pyx_StringTabEntry __pyx_string_tab[] = {
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  {__pyx_k_test, sizeof(__pyx_k_test), 0, 1, 1}, /* PyObject cname: __pyx_n_u_test */
  {0, 0, 0, 0, 0}
};
/* InitStrings.proto */
static int __Pyx_InitStrings(__Pyx_StringTabEntry const *t, PyObject **target, const char* const* encoding_names);

/* #### Code section: cached_builtins ### */

static int __Pyx_InitCachedBuiltins(__pyx_mstatetype *__pyx_mstate) {
  CYTHON_UNUSED_VAR(__pyx_mstate);
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}
/* #### Code section: cached_constants ### */

static int __Pyx_InitCachedConstants(__pyx_mstatetype *__pyx_mstate) {
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static int __Pyx_InitConstants(__pyx_mstatetype *__pyx_mstate) {
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  __pyx_mstate->__pyx_umethod_PyDict_Type_pop.type = (PyObject*)&PyDict_Type;
  __pyx_mstate->__pyx_umethod_PyDict_Type_pop.method_name = &__pyx_mstate->__pyx_n_u_pop;
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/* #### Code section: init_codeobjects ### */
\
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            unsigned int argcount : 4;
            unsigned int num_posonly_args : 1;
            unsigned int num_kwonly_args : 1;
            unsigned int nlocals : 4;
            unsigned int flags : 10;
            unsigned int first_line : 7;
            unsigned int line_table_length : 10;
        } __Pyx_PyCode_New_function_description;
/* NewCodeObj.proto */
static PyObject* __Pyx_PyCode_New(
        const __Pyx_PyCode_New_function_description descr,
        PyObject * const *varnames,
        PyObject *filename,
        PyObject *funcname,
        const char *line_table,
        PyObject *tuple_dedup_map
);


static int __Pyx_CreateCodeObjects(__pyx_mstatetype *__pyx_mstate) {
  PyObject* tuple_dedup_map = PyDict_New();
  if (unlikely(!tuple_dedup_map)) return -1;
  {
    const __Pyx_PyCode_New_function_description descr = {10, 0, 0, 10, (unsigned int)(CO_OPTIMIZED|CO_NEWLOCALS), 100, 29};
    PyObject* const varnames[] = {__pyx_mstate->__pyx_n_u_Y_0, __pyx_mstate->__pyx_n_u_b_1, __pyx_mstate->__pyx_n_u_b_2, __pyx_mstate->__pyx_n_u_b_3, __pyx_mstate->__pyx_n_u_c_1, __pyx_mstate->__pyx_n_u_c_2, __pyx_mstate->__pyx_n_u_c_3, __pyx_mstate->__pyx_n_u_af, __pyx_mstate->__pyx_n_u_af2, __pyx_mstate->__pyx_n_u_af3};
    __pyx_mstate_global->__pyx_codeobj_tab[0] = __Pyx_PyCode_New(descr, varnames, __pyx_mstate->__pyx_kp_u_pyRing_eob_utils_pyx, __pyx_mstate->__pyx_n_u_Y, __pyx_k_2Qe5_U_uE_U, tuple_dedup_map); if (unlikely(!__pyx_mstate_global->__pyx_codeobj_tab[0])) goto bad;
  }
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  return 0;
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  Py_DECREF(tuple_dedup_map);
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}
/* #### Code section: init_globals ### */

static int __Pyx_InitGlobals(void) {
  /* PythonCompatibility.init */
  if (likely(__Pyx_init_co_variables() == 0)); else

if (unlikely(PyErr_Occurred())) __PYX_ERR(0, 1, __pyx_L1_error)

  /* CachedMethodType.init */
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{
    PyObject *typesModule=NULL;
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    if (typesModule) {
        __pyx_mstate_global->__Pyx_CachedMethodType = PyObject_GetAttrString(typesModule, "MethodType");
        Py_DECREF(typesModule);
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} // error handling follows
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if (unlikely(PyErr_Occurred())) __PYX_ERR(0, 1, __pyx_L1_error)

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/* #### Code section: cleanup_globals ### */
/* #### Code section: cleanup_module ### */
/* #### Code section: main_method ### */
/* #### Code section: utility_code_pragmas ### */
#ifdef _MSC_VER
#pragma warning( push )
/* Warning 4127: conditional expression is constant
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 * compile-time, so this warning is not useful
 */
#pragma warning( disable : 4127 )
#endif



/* #### Code section: utility_code_def ### */

/* --- Runtime support code --- */
/* Refnanny */
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static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname) {
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/* TupleAndListFromArray */
#if !CYTHON_COMPILING_IN_CPYTHON && CYTHON_METH_FASTCALL
static CYTHON_INLINE PyObject *
__Pyx_PyTuple_FromArray(PyObject *const *src, Py_ssize_t n)
{
    PyObject *res;
    Py_ssize_t i;
    if (n <= 0) {
        return __Pyx_NewRef(__pyx_mstate_global->__pyx_empty_tuple);
    }
    res = PyTuple_New(n);
    if (unlikely(res == NULL)) return NULL;
    for (i = 0; i < n; i++) {
        if (unlikely(__Pyx_PyTuple_SET_ITEM(res, i, src[i]) < (0))) {
            Py_DECREF(res);
            return NULL;
        }
        Py_INCREF(src[i]);
    }
    return res;
}
#elif CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE void __Pyx_copy_object_array(PyObject *const *CYTHON_RESTRICT src, PyObject** CYTHON_RESTRICT dest, Py_ssize_t length) {
    PyObject *v;
    Py_ssize_t i;
    for (i = 0; i < length; i++) {
        v = dest[i] = src[i];
        Py_INCREF(v);
    }
}
static CYTHON_INLINE PyObject *
__Pyx_PyTuple_FromArray(PyObject *const *src, Py_ssize_t n)
{
    PyObject *res;
    if (n <= 0) {
        return __Pyx_NewRef(__pyx_mstate_global->__pyx_empty_tuple);
    }
    res = PyTuple_New(n);
    if (unlikely(res == NULL)) return NULL;
    __Pyx_copy_object_array(src, ((PyTupleObject*)res)->ob_item, n);
    return res;
}
static CYTHON_INLINE PyObject *
__Pyx_PyList_FromArray(PyObject *const *src, Py_ssize_t n)
{
    PyObject *res;
    if (n <= 0) {
        return PyList_New(0);
    }
    res = PyList_New(n);
    if (unlikely(res == NULL)) return NULL;
    __Pyx_copy_object_array(src, ((PyListObject*)res)->ob_item, n);
    return res;
}
#endif

/* BytesEquals */
static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals) {
#if CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API || CYTHON_COMPILING_IN_GRAAL ||\
        !(CYTHON_ASSUME_SAFE_SIZE && CYTHON_ASSUME_SAFE_MACROS)
    return PyObject_RichCompareBool(s1, s2, equals);
#else
    if (s1 == s2) {
        return (equals == Py_EQ);
    } else if (PyBytes_CheckExact(s1) & PyBytes_CheckExact(s2)) {
        const char *ps1, *ps2;
        Py_ssize_t length = PyBytes_GET_SIZE(s1);
        if (length != PyBytes_GET_SIZE(s2))
            return (equals == Py_NE);
        ps1 = PyBytes_AS_STRING(s1);
        ps2 = PyBytes_AS_STRING(s2);
        if (ps1[0] != ps2[0]) {
            return (equals == Py_NE);
        } else if (length == 1) {
            return (equals == Py_EQ);
        } else {
            int result;
#if CYTHON_USE_UNICODE_INTERNALS && (PY_VERSION_HEX < 0x030B0000)
            Py_hash_t hash1, hash2;
            hash1 = ((PyBytesObject*)s1)->ob_shash;
            hash2 = ((PyBytesObject*)s2)->ob_shash;
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                return (equals == Py_NE);
            }
#endif
            result = memcmp(ps1, ps2, (size_t)length);
            return (equals == Py_EQ) ? (result == 0) : (result != 0);
        }
    } else if ((s1 == Py_None) & PyBytes_CheckExact(s2)) {
        return (equals == Py_NE);
    } else if ((s2 == Py_None) & PyBytes_CheckExact(s1)) {
        return (equals == Py_NE);
    } else {
        int result;
        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
        if (!py_result)
            return -1;
        result = __Pyx_PyObject_IsTrue(py_result);
        Py_DECREF(py_result);
        return result;
    }
#endif
}

/* UnicodeEquals */
static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals) {
#if CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API || CYTHON_COMPILING_IN_GRAAL
    return PyObject_RichCompareBool(s1, s2, equals);
#else
    int s1_is_unicode, s2_is_unicode;
    if (s1 == s2) {
        goto return_eq;
    }
    s1_is_unicode = PyUnicode_CheckExact(s1);
    s2_is_unicode = PyUnicode_CheckExact(s2);
    if (s1_is_unicode & s2_is_unicode) {
        Py_ssize_t length, length2;
        int kind;
        void *data1, *data2;
        #if !CYTHON_COMPILING_IN_LIMITED_API
        if (unlikely(__Pyx_PyUnicode_READY(s1) < 0) || unlikely(__Pyx_PyUnicode_READY(s2) < 0))
            return -1;
        #endif
        length = __Pyx_PyUnicode_GET_LENGTH(s1);
        #if !CYTHON_ASSUME_SAFE_SIZE
        if (unlikely(length < 0)) return -1;
        #endif
        length2 = __Pyx_PyUnicode_GET_LENGTH(s2);
        #if !CYTHON_ASSUME_SAFE_SIZE
        if (unlikely(length2 < 0)) return -1;
        #endif
        if (length != length2) {
            goto return_ne;
        }
#if CYTHON_USE_UNICODE_INTERNALS
        {
            Py_hash_t hash1, hash2;
            hash1 = ((PyASCIIObject*)s1)->hash;
            hash2 = ((PyASCIIObject*)s2)->hash;
            if (hash1 != hash2 && hash1 != -1 && hash2 != -1) {
                goto return_ne;
            }
        }
#endif
        kind = __Pyx_PyUnicode_KIND(s1);
        if (kind != __Pyx_PyUnicode_KIND(s2)) {
            goto return_ne;
        }
        data1 = __Pyx_PyUnicode_DATA(s1);
        data2 = __Pyx_PyUnicode_DATA(s2);
        if (__Pyx_PyUnicode_READ(kind, data1, 0) != __Pyx_PyUnicode_READ(kind, data2, 0)) {
            goto return_ne;
        } else if (length == 1) {
            goto return_eq;
        } else {
            int result = memcmp(data1, data2, (size_t)(length * kind));
            return (equals == Py_EQ) ? (result == 0) : (result != 0);
        }
    } else if ((s1 == Py_None) & s2_is_unicode) {
        goto return_ne;
    } else if ((s2 == Py_None) & s1_is_unicode) {
        goto return_ne;
    } else {
        int result;
        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
        if (!py_result)
            return -1;
        result = __Pyx_PyObject_IsTrue(py_result);
        Py_DECREF(py_result);
        return result;
    }
return_eq:
    return (equals == Py_EQ);
return_ne:
    return (equals == Py_NE);
#endif
}

/* fastcall */
#if CYTHON_METH_FASTCALL
static CYTHON_INLINE PyObject * __Pyx_GetKwValue_FASTCALL(PyObject *kwnames, PyObject *const *kwvalues, PyObject *s)
{
    Py_ssize_t i, n = __Pyx_PyTuple_GET_SIZE(kwnames);
    #if !CYTHON_ASSUME_SAFE_SIZE
    if (unlikely(n == -1)) return NULL;
    #endif
    for (i = 0; i < n; i++)
    {
        PyObject *namei = __Pyx_PyTuple_GET_ITEM(kwnames, i);
        #if !CYTHON_ASSUME_SAFE_MACROS
        if (unlikely(!namei)) return NULL;
        #endif
        if (s == namei) return kwvalues[i];
    }
    for (i = 0; i < n; i++)
    {
        PyObject *namei = __Pyx_PyTuple_GET_ITEM(kwnames, i);
        #if !CYTHON_ASSUME_SAFE_MACROS
        if (unlikely(!namei)) return NULL;
        #endif
        int eq = __Pyx_PyUnicode_Equals(s, namei, Py_EQ);
        if (unlikely(eq != 0)) {
            if (unlikely(eq < 0)) return NULL;
            return kwvalues[i];
        }
    }
    return NULL;
}
#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030d0000 || CYTHON_COMPILING_IN_LIMITED_API
CYTHON_UNUSED static PyObject *__Pyx_KwargsAsDict_FASTCALL(PyObject *kwnames, PyObject *const *kwvalues) {
    Py_ssize_t i, nkwargs;
    PyObject *dict;
#if !CYTHON_ASSUME_SAFE_SIZE
    nkwargs = PyTuple_Size(kwnames);
    if (unlikely(nkwargs < 0)) return NULL;
#else
    nkwargs = PyTuple_GET_SIZE(kwnames);
#endif
    dict = PyDict_New();
    if (unlikely(!dict))
        return NULL;
    for (i=0; i<nkwargs; i++) {
#if !CYTHON_ASSUME_SAFE_MACROS
        PyObject *key = PyTuple_GetItem(kwnames, i);
        if (!key) goto bad;
#else
        PyObject *key = PyTuple_GET_ITEM(kwnames, i);
#endif
        if (unlikely(PyDict_SetItem(dict, key, kwvalues[i]) < 0))
            goto bad;
    }
    return dict;
bad:
    Py_DECREF(dict);
    return NULL;
}
#endif
#endif

/* RaiseDoubleKeywords */
static void __Pyx_RaiseDoubleKeywordsError(
    const char* func_name,
    PyObject* kw_name)
{
    PyErr_Format(PyExc_TypeError,
        "%s() got multiple values for keyword argument '%U'", func_name, kw_name);
}

/* PyFunctionFastCall */
#if CYTHON_FAST_PYCALL && !CYTHON_VECTORCALL
static PyObject* __Pyx_PyFunction_FastCallNoKw(PyCodeObject *co, PyObject *const *args, Py_ssize_t na,
                                               PyObject *globals) {
    PyFrameObject *f;
    PyThreadState *tstate = __Pyx_PyThreadState_Current;
    PyObject **fastlocals;
    Py_ssize_t i;
    PyObject *result;
    assert(globals != NULL);
    /* XXX Perhaps we should create a specialized
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       take builtins without sanity checking them.
       */
    assert(tstate != NULL);
    f = PyFrame_New(tstate, co, globals, NULL);
    if (f == NULL) {
        return NULL;
    }
    fastlocals = __Pyx_PyFrame_GetLocalsplus(f);
    for (i = 0; i < na; i++) {
        Py_INCREF(*args);
        fastlocals[i] = *args++;
    }
    result = PyEval_EvalFrameEx(f,0);
    ++tstate->recursion_depth;
    Py_DECREF(f);
    --tstate->recursion_depth;
    return result;
}
static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject *const *args, Py_ssize_t nargs, PyObject *kwargs) {
    PyCodeObject *co = (PyCodeObject *)PyFunction_GET_CODE(func);
    PyObject *globals = PyFunction_GET_GLOBALS(func);
    PyObject *argdefs = PyFunction_GET_DEFAULTS(func);
    PyObject *closure;
    PyObject *kwdefs;
    PyObject *kwtuple, **k;
    PyObject **d;
    Py_ssize_t nd;
    Py_ssize_t nk;
    PyObject *result;
    assert(kwargs == NULL || PyDict_Check(kwargs));
    nk = kwargs ? PyDict_Size(kwargs) : 0;
    if (unlikely(Py_EnterRecursiveCall(" while calling a Python object"))) {
        return NULL;
    }
    if (
            co->co_kwonlyargcount == 0 &&
            likely(kwargs == NULL || nk == 0) &&
            co->co_flags == (CO_OPTIMIZED | CO_NEWLOCALS | CO_NOFREE)) {
        if (argdefs == NULL && co->co_argcount == nargs) {
            result = __Pyx_PyFunction_FastCallNoKw(co, args, nargs, globals);
            goto done;
        }
        else if (nargs == 0 && argdefs != NULL
                 && co->co_argcount == Py_SIZE(argdefs)) {
            /* function called with no arguments, but all parameters have
               a default value: use default values as arguments .*/
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            result =__Pyx_PyFunction_FastCallNoKw(co, args, Py_SIZE(argdefs), globals);
            goto done;
        }
    }
    if (kwargs != NULL) {
        Py_ssize_t pos, i;
        kwtuple = PyTuple_New(2 * nk);
        if (kwtuple == NULL) {
            result = NULL;
            goto done;
        }
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        pos = i = 0;
        while (PyDict_Next(kwargs, &pos, &k[i], &k[i+1])) {
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        nk = i / 2;
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    else {
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done:
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/* PyObjectCall */
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static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) {
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    if (unlikely(Py_EnterRecursiveCall(" while calling a Python object")))
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        PyErr_SetString(
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#endif

/* PyObjectCallMethO */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) {
    PyObject *self, *result;
    PyCFunction cfunc;
    cfunc = __Pyx_CyOrPyCFunction_GET_FUNCTION(func);
    self = __Pyx_CyOrPyCFunction_GET_SELF(func);
    if (unlikely(Py_EnterRecursiveCall(" while calling a Python object")))
        return NULL;
    result = cfunc(self, arg);
    Py_LeaveRecursiveCall();
    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
        PyErr_SetString(
            PyExc_SystemError,
            "NULL result without error in PyObject_Call");
    }
    return result;
}
#endif

/* PyObjectFastCall */
#if PY_VERSION_HEX < 0x03090000 || CYTHON_COMPILING_IN_LIMITED_API
static PyObject* __Pyx_PyObject_FastCall_fallback(PyObject *func, PyObject * const*args, size_t nargs, PyObject *kwargs) {
    PyObject *argstuple;
    PyObject *result = 0;
    size_t i;
    argstuple = PyTuple_New((Py_ssize_t)nargs);
    if (unlikely(!argstuple)) return NULL;
    for (i = 0; i < nargs; i++) {
        Py_INCREF(args[i]);
        if (__Pyx_PyTuple_SET_ITEM(argstuple, (Py_ssize_t)i, args[i]) != (0)) goto bad;
    }
    result = __Pyx_PyObject_Call(func, argstuple, kwargs);
  bad:
    Py_DECREF(argstuple);
    return result;
}
#endif
#if CYTHON_VECTORCALL && !CYTHON_COMPILING_IN_LIMITED_API
  #if PY_VERSION_HEX < 0x03090000
    #define __Pyx_PyVectorcall_Function(callable) _PyVectorcall_Function(callable)
  #elif CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE vectorcallfunc __Pyx_PyVectorcall_Function(PyObject *callable) {
    PyTypeObject *tp = Py_TYPE(callable);
    #if defined(__Pyx_CyFunction_USED)
    if (__Pyx_CyFunction_CheckExact(callable)) {
        return __Pyx_CyFunction_func_vectorcall(callable);
    }
    #endif
    if (!PyType_HasFeature(tp, Py_TPFLAGS_HAVE_VECTORCALL)) {
        return NULL;
    }
    assert(PyCallable_Check(callable));
    Py_ssize_t offset = tp->tp_vectorcall_offset;
    assert(offset > 0);
    vectorcallfunc ptr;
    memcpy(&ptr, (char *) callable + offset, sizeof(ptr));
    return ptr;
}
  #else
    #define __Pyx_PyVectorcall_Function(callable) PyVectorcall_Function(callable)
  #endif
#endif
static CYTHON_INLINE PyObject* __Pyx_PyObject_FastCallDict(PyObject *func, PyObject *const *args, size_t _nargs, PyObject *kwargs) {
    Py_ssize_t nargs = __Pyx_PyVectorcall_NARGS(_nargs);
#if CYTHON_COMPILING_IN_CPYTHON
    if (nargs == 0 && kwargs == NULL) {
        if (__Pyx_CyOrPyCFunction_Check(func) && likely( __Pyx_CyOrPyCFunction_GET_FLAGS(func) & METH_NOARGS))
            return __Pyx_PyObject_CallMethO(func, NULL);
    }
    else if (nargs == 1 && kwargs == NULL) {
        if (__Pyx_CyOrPyCFunction_Check(func) && likely( __Pyx_CyOrPyCFunction_GET_FLAGS(func) & METH_O))
            return __Pyx_PyObject_CallMethO(func, args[0]);
    }
#endif
    #if PY_VERSION_HEX < 0x030800B1
    #if CYTHON_FAST_PYCCALL
    if (PyCFunction_Check(func)) {
        if (kwargs) {
            return _PyCFunction_FastCallDict(func, args, nargs, kwargs);
        } else {
            return _PyCFunction_FastCallKeywords(func, args, nargs, NULL);
        }
    }
    if (!kwargs && __Pyx_IS_TYPE(func, &PyMethodDescr_Type)) {
        return _PyMethodDescr_FastCallKeywords(func, args, nargs, NULL);
    }
    #endif
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(func)) {
        return __Pyx_PyFunction_FastCallDict(func, args, nargs, kwargs);
    }
    #endif
    #endif
    if (kwargs == NULL) {
        #if CYTHON_VECTORCALL && !CYTHON_COMPILING_IN_LIMITED_API
        vectorcallfunc f = __Pyx_PyVectorcall_Function(func);
        if (f) {
            return f(func, args, _nargs, NULL);
        }
        #elif defined(__Pyx_CyFunction_USED) && CYTHON_BACKPORT_VECTORCALL
        if (__Pyx_CyFunction_CheckExact(func)) {
            __pyx_vectorcallfunc f = __Pyx_CyFunction_func_vectorcall(func);
            if (f) return f(func, args, _nargs, NULL);
        }
        #elif CYTHON_COMPILING_IN_LIMITED_API && CYTHON_VECTORCALL
        return PyObject_Vectorcall(func, args, _nargs, NULL);
        #endif
    }
    if (nargs == 0) {
        return __Pyx_PyObject_Call(func, __pyx_mstate_global->__pyx_empty_tuple, kwargs);
    }
    #if PY_VERSION_HEX >= 0x03090000 && !CYTHON_COMPILING_IN_LIMITED_API
    return PyObject_VectorcallDict(func, args, (size_t)nargs, kwargs);
    #else
    return __Pyx_PyObject_FastCall_fallback(func, args, (size_t)nargs, kwargs);
    #endif
}

/* PyObjectGetAttrStr */
#if CYTHON_USE_TYPE_SLOTS
static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name) {
    PyTypeObject* tp = Py_TYPE(obj);
    if (likely(tp->tp_getattro))
        return tp->tp_getattro(obj, attr_name);
    return PyObject_GetAttr(obj, attr_name);
}
#endif

/* UnpackUnboundCMethod */
#if CYTHON_COMPILING_IN_LIMITED_API && __PYX_LIMITED_VERSION_HEX < 0x030C0000
static PyObject *__Pyx_SelflessCall(PyObject *method, PyObject *args, PyObject *kwargs) {
    PyObject *result;
    PyObject *selfless_args = PyTuple_GetSlice(args, 1, PyTuple_Size(args));
    if (unlikely(!selfless_args)) return NULL;
    result = PyObject_Call(method, selfless_args, kwargs);
    Py_DECREF(selfless_args);
    return result;
}
#elif CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x03090000
static PyObject *__Pyx_SelflessCall(PyObject *method, PyObject **args, Py_ssize_t nargs, PyObject *kwnames) {
        return _PyObject_Vectorcall
            (method, args ? args+1 : NULL, nargs ? nargs-1 : 0, kwnames);
}
#else
static PyObject *__Pyx_SelflessCall(PyObject *method, PyObject *const *args, Py_ssize_t nargs, PyObject *kwnames) {
    return
#if PY_VERSION_HEX < 0x03090000
    _PyObject_Vectorcall
#else
    PyObject_Vectorcall
#endif
        (method, args ? args+1 : NULL, nargs ? (size_t) nargs-1 : 0, kwnames);
}
#endif
static PyMethodDef __Pyx_UnboundCMethod_Def = {
     "CythonUnboundCMethod",
     __PYX_REINTERPRET_FUNCION(PyCFunction, __Pyx_SelflessCall),
#if CYTHON_COMPILING_IN_LIMITED_API && __PYX_LIMITED_VERSION_HEX < 0x030C0000
     METH_VARARGS | METH_KEYWORDS,
#else
     METH_FASTCALL | METH_KEYWORDS,
#endif
     NULL
};
static int __Pyx_TryUnpackUnboundCMethod(__Pyx_CachedCFunction* target) {
    PyObject *method, *result=NULL;
    method = __Pyx_PyObject_GetAttrStr(target->type, *target->method_name);
    if (unlikely(!method))
        return -1;
    result = method;
#if CYTHON_COMPILING_IN_CPYTHON
    if (likely(__Pyx_TypeCheck(method, &PyMethodDescr_Type)))
    {
        PyMethodDescrObject *descr = (PyMethodDescrObject*) method;
        target->func = descr->d_method->ml_meth;
        target->flag = descr->d_method->ml_flags & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_STACKLESS);
    } else
#endif
#if CYTHON_COMPILING_IN_PYPY
#else
    if (PyCFunction_Check(method))
#endif
    {
        PyObject *self;
        int self_found;
#if CYTHON_COMPILING_IN_LIMITED_API || CYTHON_COMPILING_IN_PYPY
        self = PyObject_GetAttrString(method, "__self__");
        if (!self) {
            PyErr_Clear();
        }
#else
        self = PyCFunction_GET_SELF(method);
#endif
        self_found = (self && self != Py_None);
#if CYTHON_COMPILING_IN_LIMITED_API || CYTHON_COMPILING_IN_PYPY
        Py_XDECREF(self);
#endif
        if (self_found) {
            PyObject *unbound_method = PyCFunction_New(&__Pyx_UnboundCMethod_Def, method);
            if (unlikely(!unbound_method)) return -1;
            Py_DECREF(method);
            result = unbound_method;
        }
    }
#if !CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
    if (unlikely(target->method)) {
        Py_DECREF(result);
    } else
#endif
    target->method = result;
    return 0;
}

/* CallUnboundCMethod2 */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject *__Pyx_CallUnboundCMethod2(__Pyx_CachedCFunction *cfunc, PyObject *self, PyObject *arg1, PyObject *arg2) {
    int was_initialized = __Pyx_CachedCFunction_GetAndSetInitializing(cfunc);
    if (likely(was_initialized == 2 && cfunc->func)) {
        PyObject *args[2] = {arg1, arg2};
        if (cfunc->flag == METH_FASTCALL) {
            return __Pyx_CallCFunctionFast(cfunc, self, args, 2);
        }
        if (cfunc->flag == (METH_FASTCALL | METH_KEYWORDS))
            return __Pyx_CallCFunctionFastWithKeywords(cfunc, self, args, 2, NULL);
    }
#if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
    else if (unlikely(was_initialized == 1)) {
        __Pyx_CachedCFunction tmp_cfunc = {
#ifndef __cplusplus
            0
#endif
        };
        tmp_cfunc.type = cfunc->type;
        tmp_cfunc.method_name = cfunc->method_name;
        return __Pyx__CallUnboundCMethod2(&tmp_cfunc, self, arg1, arg2);
    }
#endif
    PyObject *result = __Pyx__CallUnboundCMethod2(cfunc, self, arg1, arg2);
    __Pyx_CachedCFunction_SetFinishedInitializing(cfunc);
    return result;
}
#endif
static PyObject* __Pyx__CallUnboundCMethod2(__Pyx_CachedCFunction* cfunc, PyObject* self, PyObject* arg1, PyObject* arg2){
    if (unlikely(!cfunc->func && !cfunc->method) && unlikely(__Pyx_TryUnpackUnboundCMethod(cfunc) < 0)) return NULL;
#if CYTHON_COMPILING_IN_CPYTHON
    if (cfunc->func && (cfunc->flag & METH_VARARGS)) {
        PyObject *result = NULL;
        PyObject *args = PyTuple_New(2);
        if (unlikely(!args)) return NULL;
        Py_INCREF(arg1);
        PyTuple_SET_ITEM(args, 0, arg1);
        Py_INCREF(arg2);
        PyTuple_SET_ITEM(args, 1, arg2);
        if (cfunc->flag & METH_KEYWORDS)
            result = __Pyx_CallCFunctionWithKeywords(cfunc, self, args, NULL);
        else
            result = __Pyx_CallCFunction(cfunc, self, args);
        Py_DECREF(args);
        return result;
    }
#endif
    {
        PyObject *args[4] = {NULL, self, arg1, arg2};
        return __Pyx_PyObject_FastCall(cfunc->method, args+1, 3 | __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET);
    }
}

/* ParseKeywords */
static int __Pyx_ValidateDuplicatePosArgs(
    PyObject *kwds,
    PyObject ** const argnames[],
    PyObject ** const *first_kw_arg,
    const char* function_name)
{
    PyObject ** const *name = argnames;
    while (name != first_kw_arg) {
        PyObject *key = **name;
        int found = PyDict_Contains(kwds, key);
        if (unlikely(found)) {
            if (found == 1) __Pyx_RaiseDoubleKeywordsError(function_name, key);
            goto bad;
        }
        name++;
    }
    return 0;
bad:
    return -1;
}
#if CYTHON_USE_UNICODE_INTERNALS
static CYTHON_INLINE int __Pyx_UnicodeKeywordsEqual(PyObject *s1, PyObject *s2) {
    int kind;
    Py_ssize_t len = PyUnicode_GET_LENGTH(s1);
    if (len != PyUnicode_GET_LENGTH(s2)) return 0;
    kind = PyUnicode_KIND(s1);
    if (kind != PyUnicode_KIND(s2)) return 0;
    const void *data1 = PyUnicode_DATA(s1);
    const void *data2 = PyUnicode_DATA(s2);
    return (memcmp(data1, data2, (size_t) len * (size_t) kind) == 0);
}
#endif
static int __Pyx_MatchKeywordArg_str(
    PyObject *key,
    PyObject ** const argnames[],
    PyObject ** const *first_kw_arg,
    size_t *index_found,
    const char *function_name)
{
    PyObject ** const *name;
    #if CYTHON_USE_UNICODE_INTERNALS
    Py_hash_t key_hash = ((PyASCIIObject*)key)->hash;
    if (unlikely(key_hash == -1)) {
        key_hash = PyObject_Hash(key);
        if (unlikely(key_hash == -1))
            goto bad;
    }
    #endif
    name = first_kw_arg;
    while (*name) {
        PyObject *name_str = **name;
        #if CYTHON_USE_UNICODE_INTERNALS
        if (key_hash == ((PyASCIIObject*)name_str)->hash && __Pyx_UnicodeKeywordsEqual(name_str, key)) {
            *index_found = (size_t) (name - argnames);
            return 1;
        }
        #else
        #if CYTHON_ASSUME_SAFE_SIZE
        if (PyUnicode_GET_LENGTH(name_str) == PyUnicode_GET_LENGTH(key))
        #endif
        {
            int cmp = PyUnicode_Compare(name_str, key);
            if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
            if (cmp == 0) {
                *index_found = (size_t) (name - argnames);
                return 1;
            }
        }
        #endif
        name++;
    }
    name = argnames;
    while (name != first_kw_arg) {
        PyObject *name_str = **name;
        #if CYTHON_USE_UNICODE_INTERNALS
        if (unlikely(key_hash == ((PyASCIIObject*)name_str)->hash)) {
            if (__Pyx_UnicodeKeywordsEqual(name_str, key))
                goto arg_passed_twice;
        }
        #else
        #if CYTHON_ASSUME_SAFE_SIZE
        if (PyUnicode_GET_LENGTH(name_str) == PyUnicode_GET_LENGTH(key))
        #endif
        {
            if (unlikely(name_str == key)) goto arg_passed_twice;
            int cmp = PyUnicode_Compare(name_str, key);
            if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
            if (cmp == 0) goto arg_passed_twice;
        }
        #endif
        name++;
    }
    return 0;
arg_passed_twice:
    __Pyx_RaiseDoubleKeywordsError(function_name, key);
    goto bad;
bad:
    return -1;
}
static int __Pyx_MatchKeywordArg_nostr(
    PyObject *key,
    PyObject ** const argnames[],
    PyObject ** const *first_kw_arg,
    size_t *index_found,
    const char *function_name)
{
    PyObject ** const *name;
    if (unlikely(!PyUnicode_Check(key))) goto invalid_keyword_type;
    name = first_kw_arg;
    while (*name) {
        int cmp = PyObject_RichCompareBool(**name, key, Py_EQ);
        if (cmp == 1) {
            *index_found = (size_t) (name - argnames);
            return 1;
        }
        if (unlikely(cmp == -1)) goto bad;
        name++;
    }
    name = argnames;
    while (name != first_kw_arg) {
        int cmp = PyObject_RichCompareBool(**name, key, Py_EQ);
        if (unlikely(cmp != 0)) {
            if (cmp == 1) goto arg_passed_twice;
            else goto bad;
        }
        name++;
    }
    return 0;
arg_passed_twice:
    __Pyx_RaiseDoubleKeywordsError(function_name, key);
    goto bad;
invalid_keyword_type:
    PyErr_Format(PyExc_TypeError,
        "%.200s() keywords must be strings", function_name);
    goto bad;
bad:
    return -1;
}
static CYTHON_INLINE int __Pyx_MatchKeywordArg(
    PyObject *key,
    PyObject ** const argnames[],
    PyObject ** const *first_kw_arg,
    size_t *index_found,
    const char *function_name)
{
    return likely(PyUnicode_CheckExact(key)) ?
        __Pyx_MatchKeywordArg_str(key, argnames, first_kw_arg, index_found, function_name) :
        __Pyx_MatchKeywordArg_nostr(key, argnames, first_kw_arg, index_found, function_name);
}
static void __Pyx_RejectUnknownKeyword(
    PyObject *kwds,
    PyObject ** const argnames[],
    PyObject ** const *first_kw_arg,
    const char *function_name)
{
    Py_ssize_t pos = 0;
    PyObject *key = NULL;
    __Pyx_BEGIN_CRITICAL_SECTION(kwds);
    while (PyDict_Next(kwds, &pos, &key, NULL)) {
        PyObject** const *name = first_kw_arg;
        while (*name && (**name != key)) name++;
        if (!*name) {
            #if CYTHON_AVOID_BORROWED_REFS
            Py_INCREF(key);
            #endif
            size_t index_found = 0;
            int cmp = __Pyx_MatchKeywordArg(key, argnames, first_kw_arg, &index_found, function_name);
            if (cmp != 1) {
                if (cmp == 0) {
                    PyErr_Format(PyExc_TypeError,
                        "%s() got an unexpected keyword argument '%U'",
                        function_name, key);
                }
                #if CYTHON_AVOID_BORROWED_REFS
                Py_DECREF(key);
                #endif
                break;
            }
            #if CYTHON_AVOID_BORROWED_REFS
            Py_DECREF(key);
            #endif
        }
    }
    __Pyx_END_CRITICAL_SECTION();
    assert(PyErr_Occurred());
}
static int __Pyx_ParseKeywordDict(
    PyObject *kwds,
    PyObject ** const argnames[],
    PyObject *values[],
    Py_ssize_t num_pos_args,
    Py_ssize_t num_kwargs,
    const char* function_name,
    int ignore_unknown_kwargs)
{
    PyObject** const *name;
    PyObject** const *first_kw_arg = argnames + num_pos_args;
    Py_ssize_t extracted = 0;
#if !CYTHON_COMPILING_IN_PYPY || defined(PyArg_ValidateKeywordArguments)
    if (unlikely(!PyArg_ValidateKeywordArguments(kwds))) return -1;
#endif
    name = first_kw_arg;
    while (*name && num_kwargs > extracted) {
        PyObject * key = **name;
        PyObject *value;
        int found = 0;
        #if __PYX_LIMITED_VERSION_HEX >= 0x030d0000
        found = PyDict_GetItemRef(kwds, key, &value);
        #else
        value = PyDict_GetItemWithError(kwds, key);
        if (value) {
            Py_INCREF(value);
            found = 1;
        } else {
            if (unlikely(PyErr_Occurred())) goto bad;
        }
        #endif
        if (found) {
            if (unlikely(found < 0)) goto bad;
            values[name-argnames] = value;
            extracted++;
        }
        name++;
    }
    if (num_kwargs > extracted) {
        if (ignore_unknown_kwargs) {
            if (unlikely(__Pyx_ValidateDuplicatePosArgs(kwds, argnames, first_kw_arg, function_name) == -1))
                goto bad;
        } else {
            __Pyx_RejectUnknownKeyword(kwds, argnames, first_kw_arg, function_name);
            goto bad;
        }
    }
    return 0;
bad:
    return -1;
}
static int __Pyx_ParseKeywordDictToDict(
    PyObject *kwds,
    PyObject ** const argnames[],
    PyObject *kwds2,
    PyObject *values[],
    Py_ssize_t num_pos_args,
    const char* function_name)
{
    PyObject** const *name;
    PyObject** const *first_kw_arg = argnames + num_pos_args;
    Py_ssize_t len;
#if !CYTHON_COMPILING_IN_PYPY || defined(PyArg_ValidateKeywordArguments)
    if (unlikely(!PyArg_ValidateKeywordArguments(kwds))) return -1;
#endif
    if (PyDict_Update(kwds2, kwds) < 0) goto bad;
    name = first_kw_arg;
    while (*name) {
        PyObject *key = **name;
        PyObject *value;
#if !CYTHON_COMPILING_IN_LIMITED_API && (PY_VERSION_HEX >= 0x030d00A2 || defined(PyDict_Pop))
        int found = PyDict_Pop(kwds2, key, &value);
        if (found) {
            if (unlikely(found < 0)) goto bad;
            values[name-argnames] = value;
        }
#elif __PYX_LIMITED_VERSION_HEX >= 0x030d0000
        int found = PyDict_GetItemRef(kwds2, key, &value);
        if (found) {
            if (unlikely(found < 0)) goto bad;
            values[name-argnames] = value;
            if (unlikely(PyDict_DelItem(kwds2, key) < 0)) goto bad;
        }
#else
    #if CYTHON_COMPILING_IN_CPYTHON
        value = _PyDict_Pop(kwds2, key, kwds2);
    #else
        value = __Pyx_CallUnboundCMethod2(&__pyx_mstate_global->__pyx_umethod_PyDict_Type_pop, kwds2, key, kwds2);
    #endif
        if (value == kwds2) {
            Py_DECREF(value);
        } else {
            if (unlikely(!value)) goto bad;
            values[name-argnames] = value;
        }
#endif
        name++;
    }
    len = PyDict_Size(kwds2);
    if (len > 0) {
        return __Pyx_ValidateDuplicatePosArgs(kwds, argnames, first_kw_arg, function_name);
    } else if (unlikely(len == -1)) {
        goto bad;
    }
    return 0;
bad:
    return -1;
}
static int __Pyx_ParseKeywordsTuple(
    PyObject *kwds,
    PyObject * const *kwvalues,
    PyObject ** const argnames[],
    PyObject *kwds2,
    PyObject *values[],
    Py_ssize_t num_pos_args,
    Py_ssize_t num_kwargs,
    const char* function_name,
    int ignore_unknown_kwargs)
{
    PyObject *key = NULL;
    PyObject** const * name;
    PyObject** const *first_kw_arg = argnames + num_pos_args;
    for (Py_ssize_t pos = 0; pos < num_kwargs; pos++) {
#if CYTHON_AVOID_BORROWED_REFS
        key = __Pyx_PySequence_ITEM(kwds, pos);
#else
        key = __Pyx_PyTuple_GET_ITEM(kwds, pos);
#endif
#if !CYTHON_ASSUME_SAFE_MACROS
        if (unlikely(!key)) goto bad;
#endif
        name = first_kw_arg;
        while (*name && (**name != key)) name++;
        if (*name) {
            PyObject *value = kwvalues[pos];
            values[name-argnames] = __Pyx_NewRef(value);
        } else {
            size_t index_found = 0;
            int cmp = __Pyx_MatchKeywordArg(key, argnames, first_kw_arg, &index_found, function_name);
            if (cmp == 1) {
                PyObject *value = kwvalues[pos];
                values[index_found] = __Pyx_NewRef(value);
            } else {
                if (unlikely(cmp == -1)) goto bad;
                if (kwds2) {
                    PyObject *value = kwvalues[pos];
                    if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
                } else if (!ignore_unknown_kwargs) {
                    goto invalid_keyword;
                }
            }
        }
        #if CYTHON_AVOID_BORROWED_REFS
        Py_DECREF(key);
        key = NULL;
        #endif
    }
    return 0;
invalid_keyword:
    PyErr_Format(PyExc_TypeError,
        "%s() got an unexpected keyword argument '%U'",
        function_name, key);
    goto bad;
bad:
    #if CYTHON_AVOID_BORROWED_REFS
    Py_XDECREF(key);
    #endif
    return -1;
}
static int __Pyx_ParseKeywords(
    PyObject *kwds,
    PyObject * const *kwvalues,
    PyObject ** const argnames[],
    PyObject *kwds2,
    PyObject *values[],
    Py_ssize_t num_pos_args,
    Py_ssize_t num_kwargs,
    const char* function_name,
    int ignore_unknown_kwargs)
{
    if (CYTHON_METH_FASTCALL && likely(PyTuple_Check(kwds)))
        return __Pyx_ParseKeywordsTuple(kwds, kwvalues, argnames, kwds2, values, num_pos_args, num_kwargs, function_name, ignore_unknown_kwargs);
    else if (kwds2)
        return __Pyx_ParseKeywordDictToDict(kwds, argnames, kwds2, values, num_pos_args, function_name);
    else
        return __Pyx_ParseKeywordDict(kwds, argnames, values, num_pos_args, num_kwargs, function_name, ignore_unknown_kwargs);
}

/* RaiseArgTupleInvalid */
static void __Pyx_RaiseArgtupleInvalid(
    const char* func_name,
    int exact,
    Py_ssize_t num_min,
    Py_ssize_t num_max,
    Py_ssize_t num_found)
{
    Py_ssize_t num_expected;
    const char *more_or_less;
    if (num_found < num_min) {
        num_expected = num_min;
        more_or_less = "at least";
    } else {
        num_expected = num_max;
        more_or_less = "at most";
    }
    if (exact) {
        more_or_less = "exactly";
    }
    PyErr_Format(PyExc_TypeError,
                 "%.200s() takes %.8s %" CYTHON_FORMAT_SSIZE_T "d positional argument%.1s (%" CYTHON_FORMAT_SSIZE_T "d given)",
                 func_name, more_or_less, num_expected,
                 (num_expected == 1) ? "" : "s", num_found);
}

/* ErrOccurredWithGIL */
static CYTHON_INLINE int __Pyx_ErrOccurredWithGIL(void) {
  int err;
  PyGILState_STATE _save = PyGILState_Ensure();
  err = !!PyErr_Occurred();
  PyGILState_Release(_save);
  return err;
}

/* LimitedApiGetTypeDict */
#if CYTHON_COMPILING_IN_LIMITED_API
static Py_ssize_t __Pyx_GetTypeDictOffset(void) {
    PyObject *tp_dictoffset_o;
    Py_ssize_t tp_dictoffset;
    tp_dictoffset_o = PyObject_GetAttrString((PyObject*)(&PyType_Type), "__dictoffset__");
    if (unlikely(!tp_dictoffset_o)) return -1;
    tp_dictoffset = PyLong_AsSsize_t(tp_dictoffset_o);
    Py_DECREF(tp_dictoffset_o);
    if (unlikely(tp_dictoffset == 0)) {
        PyErr_SetString(
            PyExc_TypeError,
            "'type' doesn't have a dictoffset");
        return -1;
    } else if (unlikely(tp_dictoffset < 0)) {
        PyErr_SetString(
            PyExc_TypeError,
            "'type' has an unexpected negative dictoffset. "
            "Please report this as Cython bug");
        return -1;
    }
    return tp_dictoffset;
}
static PyObject *__Pyx_GetTypeDict(PyTypeObject *tp) {
    static Py_ssize_t tp_dictoffset = 0;
    if (unlikely(tp_dictoffset == 0)) {
        tp_dictoffset = __Pyx_GetTypeDictOffset();
        if (unlikely(tp_dictoffset == -1 && PyErr_Occurred())) {
            tp_dictoffset = 0; // try again next time?
            return NULL;
        }
    }
    return *(PyObject**)((char*)tp + tp_dictoffset);
}
#endif

/* SetItemOnTypeDict */
static int __Pyx__SetItemOnTypeDict(PyTypeObject *tp, PyObject *k, PyObject *v) {
    int result;
    PyObject *tp_dict;
#if CYTHON_COMPILING_IN_LIMITED_API
    tp_dict = __Pyx_GetTypeDict(tp);
    if (unlikely(!tp_dict)) return -1;
#else
    tp_dict = tp->tp_dict;
#endif
    result = PyDict_SetItem(tp_dict, k, v);
    if (likely(!result)) {
        PyType_Modified(tp);
        if (unlikely(PyObject_HasAttr(v, __pyx_mstate_global->__pyx_n_u_set_name))) {
            PyObject *setNameResult = PyObject_CallMethodObjArgs(v, __pyx_mstate_global->__pyx_n_u_set_name,  (PyObject *) tp, k, NULL);
            if (!setNameResult) return -1;
            Py_DECREF(setNameResult);
        }
    }
    return result;
}

/* FixUpExtensionType */
static int __Pyx_fix_up_extension_type_from_spec(PyType_Spec *spec, PyTypeObject *type) {
#if __PYX_LIMITED_VERSION_HEX > 0x030900B1
    CYTHON_UNUSED_VAR(spec);
    CYTHON_UNUSED_VAR(type);
    CYTHON_UNUSED_VAR(__Pyx__SetItemOnTypeDict);
#else
    const PyType_Slot *slot = spec->slots;
    int changed = 0;
#if !CYTHON_COMPILING_IN_LIMITED_API
    while (slot && slot->slot && slot->slot != Py_tp_members)
        slot++;
    if (slot && slot->slot == Py_tp_members) {
#if !CYTHON_COMPILING_IN_CPYTHON
        const
#endif  // !CYTHON_COMPILING_IN_CPYTHON)
            PyMemberDef *memb = (PyMemberDef*) slot->pfunc;
        while (memb && memb->name) {
            if (memb->name[0] == '_' && memb->name[1] == '_') {
                if (strcmp(memb->name, "__weaklistoffset__") == 0) {
                    assert(memb->type == T_PYSSIZET);
                    assert(memb->flags == READONLY);
                    type->tp_weaklistoffset = memb->offset;
                    changed = 1;
                }
                else if (strcmp(memb->name, "__dictoffset__") == 0) {
                    assert(memb->type == T_PYSSIZET);
                    assert(memb->flags == READONLY);
                    type->tp_dictoffset = memb->offset;
                    changed = 1;
                }
#if CYTHON_METH_FASTCALL
                else if (strcmp(memb->name, "__vectorcalloffset__") == 0) {
                    assert(memb->type == T_PYSSIZET);
                    assert(memb->flags == READONLY);
#if PY_VERSION_HEX >= 0x030800b4
                    type->tp_vectorcall_offset = memb->offset;
#else
                    type->tp_print = (printfunc) memb->offset;
#endif
                    changed = 1;
                }
#endif  // CYTHON_METH_FASTCALL
#if !CYTHON_COMPILING_IN_PYPY
                else if (strcmp(memb->name, "__module__") == 0) {
                    PyObject *descr;
                    assert(memb->type == T_OBJECT);
                    assert(memb->flags == 0 || memb->flags == READONLY);
                    descr = PyDescr_NewMember(type, memb);
                    if (unlikely(!descr))
                        return -1;
                    int set_item_result = PyDict_SetItem(type->tp_dict, PyDescr_NAME(descr), descr);
                    Py_DECREF(descr);
                    if (unlikely(set_item_result < 0)) {
                        return -1;
                    }
                    changed = 1;
                }
#endif  // !CYTHON_COMPILING_IN_PYPY
            }
            memb++;
        }
    }
#endif  // !CYTHON_COMPILING_IN_LIMITED_API
#if !CYTHON_COMPILING_IN_PYPY
    slot = spec->slots;
    while (slot && slot->slot && slot->slot != Py_tp_getset)
        slot++;
    if (slot && slot->slot == Py_tp_getset) {
        PyGetSetDef *getset = (PyGetSetDef*) slot->pfunc;
        while (getset && getset->name) {
            if (getset->name[0] == '_' && getset->name[1] == '_' && strcmp(getset->name, "__module__") == 0) {
                PyObject *descr = PyDescr_NewGetSet(type, getset);
                if (unlikely(!descr))
                    return -1;
                #if CYTHON_COMPILING_IN_LIMITED_API
                PyObject *pyname = PyUnicode_FromString(getset->name);
                if (unlikely(!pyname)) {
                    Py_DECREF(descr);
                    return -1;
                }
                int set_item_result = __Pyx_SetItemOnTypeDict(type, pyname, descr);
                Py_DECREF(pyname);
                #else
                CYTHON_UNUSED_VAR(__Pyx__SetItemOnTypeDict);
                int set_item_result = PyDict_SetItem(type->tp_dict, PyDescr_NAME(descr), descr);
                #endif
                Py_DECREF(descr);
                if (unlikely(set_item_result < 0)) {
                    return -1;
                }
                changed = 1;
            }
            ++getset;
        }
    }
#endif  // !CYTHON_COMPILING_IN_PYPY
    if (changed)
        PyType_Modified(type);
#endif  // PY_VERSION_HEX > 0x030900B1
    return 0;
}

/* FetchSharedCythonModule */
static PyObject *__Pyx_FetchSharedCythonABIModule(void) {
    return __Pyx_PyImport_AddModuleRef(__PYX_ABI_MODULE_NAME);
}

/* dict_setdefault */
static CYTHON_INLINE PyObject *__Pyx_PyDict_SetDefault(PyObject *d, PyObject *key, PyObject *default_value,
                                                       int is_safe_type) {
    PyObject* value;
    CYTHON_MAYBE_UNUSED_VAR(is_safe_type);
#if CYTHON_COMPILING_IN_LIMITED_API
    value = PyObject_CallMethod(d, "setdefault", "OO", key, default_value);
#elif PY_VERSION_HEX >= 0x030d0000
    PyDict_SetDefaultRef(d, key, default_value, &value);
#else
    value = PyDict_SetDefault(d, key, default_value);
    if (unlikely(!value)) return NULL;
    Py_INCREF(value);
#endif
    return value;
}

/* FetchCommonType */
#if __PYX_LIMITED_VERSION_HEX < 0x030C0000
static PyObject* __Pyx_PyType_FromMetaclass(PyTypeObject *metaclass, PyObject *module, PyType_Spec *spec, PyObject *bases) {
    PyObject *result = __Pyx_PyType_FromModuleAndSpec(module, spec, bases);
    if (result && metaclass) {
        PyObject *old_tp = (PyObject*)Py_TYPE(result);
    Py_INCREF((PyObject*)metaclass);
#if __PYX_LIMITED_VERSION_HEX >= 0x03090000
        Py_SET_TYPE(result, metaclass);
#else
        result->ob_type = metaclass;
#endif
        Py_DECREF(old_tp);
    }
    return result;
}
#else
#define __Pyx_PyType_FromMetaclass(me, mo, s, b) PyType_FromMetaclass(me, mo, s, b)
#endif
static int __Pyx_VerifyCachedType(PyObject *cached_type,
                               const char *name,
                               Py_ssize_t expected_basicsize) {
    Py_ssize_t basicsize;
    if (!PyType_Check(cached_type)) {
        PyErr_Format(PyExc_TypeError,
            "Shared Cython type %.200s is not a type object", name);
        return -1;
    }
    if (expected_basicsize == 0) {
        return 0; // size is inherited, nothing useful to check
    }
#if CYTHON_COMPILING_IN_LIMITED_API
    PyObject *py_basicsize;
    py_basicsize = PyObject_GetAttrString(cached_type, "__basicsize__");
    if (unlikely(!py_basicsize)) return -1;
    basicsize = PyLong_AsSsize_t(py_basicsize);
    Py_DECREF(py_basicsize);
    py_basicsize = NULL;
    if (unlikely(basicsize == (Py_ssize_t)-1) && PyErr_Occurred()) return -1;
#else
    basicsize = ((PyTypeObject*) cached_type)->tp_basicsize;
#endif
    if (basicsize != expected_basicsize) {
        PyErr_Format(PyExc_TypeError,
            "Shared Cython type %.200s has the wrong size, try recompiling",
            name);
        return -1;
    }
    return 0;
}
static PyTypeObject *__Pyx_FetchCommonTypeFromSpec(PyTypeObject *metaclass, PyObject *module, PyType_Spec *spec, PyObject *bases) {
    PyObject *abi_module = NULL, *cached_type = NULL, *abi_module_dict, *new_cached_type, *py_object_name;
    int get_item_ref_result;
    const char* object_name = strrchr(spec->name, '.');
    object_name = object_name ? object_name+1 : spec->name;
    py_object_name = PyUnicode_FromString(object_name);
    if (!py_object_name) return NULL;
    abi_module = __Pyx_FetchSharedCythonABIModule();
    if (!abi_module) goto done;
    abi_module_dict = PyModule_GetDict(abi_module);
    if (!abi_module_dict) goto done;
    get_item_ref_result = __Pyx_PyDict_GetItemRef(abi_module_dict, py_object_name, &cached_type);
    if (get_item_ref_result == 1) {
        if (__Pyx_VerifyCachedType(
              cached_type,
              object_name,
              spec->basicsize) < 0) {
            goto bad;
        }
        goto done;
    } else if (unlikely(get_item_ref_result == -1)) {
        goto bad;
    }
    CYTHON_UNUSED_VAR(module);
    cached_type = __Pyx_PyType_FromMetaclass(metaclass, abi_module, spec, bases);
    if (unlikely(!cached_type)) goto bad;
    if (unlikely(__Pyx_fix_up_extension_type_from_spec(spec, (PyTypeObject *) cached_type) < 0)) goto bad;
    new_cached_type = __Pyx_PyDict_SetDefault(abi_module_dict, py_object_name, cached_type, 1);
    if (unlikely(new_cached_type != cached_type)) {
        if (unlikely(!new_cached_type)) goto bad;
        Py_DECREF(cached_type);
        cached_type = new_cached_type;
        if (__Pyx_VerifyCachedType(
                cached_type,
                object_name,
                spec->basicsize) < 0) {
            goto bad;
        }
        goto done;
    } else {
        Py_DECREF(new_cached_type);
    }
done:
    Py_XDECREF(abi_module);
    Py_DECREF(py_object_name);
    assert(cached_type == NULL || PyType_Check(cached_type));
    return (PyTypeObject *) cached_type;
bad:
    Py_XDECREF(cached_type);
    cached_type = NULL;
    goto done;
}

/* CommonTypesMetaclass */
static PyObject* __pyx_CommonTypesMetaclass_get_module(CYTHON_UNUSED PyObject *self, CYTHON_UNUSED void* context) {
    return PyUnicode_FromString(__PYX_ABI_MODULE_NAME);
}
static PyGetSetDef __pyx_CommonTypesMetaclass_getset[] = {
    {"__module__", __pyx_CommonTypesMetaclass_get_module, NULL, NULL, NULL},
    {0, 0, 0, 0, 0}
};
static PyType_Slot __pyx_CommonTypesMetaclass_slots[] = {
    {Py_tp_getset, (void *)__pyx_CommonTypesMetaclass_getset},
    {0, 0}
};
static PyType_Spec __pyx_CommonTypesMetaclass_spec = {
    __PYX_TYPE_MODULE_PREFIX "_common_types_metatype",
    0,
    0,
#if PY_VERSION_HEX >= 0x030A0000
    Py_TPFLAGS_IMMUTABLETYPE |
    Py_TPFLAGS_DISALLOW_INSTANTIATION |
#endif
    Py_TPFLAGS_DEFAULT,
    __pyx_CommonTypesMetaclass_slots
};
static int __pyx_CommonTypesMetaclass_init(PyObject *module) {
    __pyx_mstatetype *mstate = __Pyx_PyModule_GetState(module);
    PyObject *bases = PyTuple_Pack(1, &PyType_Type);
    if (unlikely(!bases)) {
        return -1;
    }
    mstate->__pyx_CommonTypesMetaclassType = __Pyx_FetchCommonTypeFromSpec(NULL, module, &__pyx_CommonTypesMetaclass_spec, bases);
    Py_DECREF(bases);
    if (unlikely(mstate->__pyx_CommonTypesMetaclassType == NULL)) {
        return -1;
    }
    return 0;
}

/* CallTypeTraverse */
#if !CYTHON_USE_TYPE_SPECS || (!CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX < 0x03090000)
#else
static int __Pyx_call_type_traverse(PyObject *o, int always_call, visitproc visit, void *arg) {
    #if CYTHON_COMPILING_IN_LIMITED_API && __PYX_LIMITED_VERSION_HEX < 0x03090000
    if (__Pyx_get_runtime_version() < 0x03090000) return 0;
    #endif
    if (!always_call) {
        PyTypeObject *base = __Pyx_PyObject_GetSlot(o, tp_base, PyTypeObject*);
        unsigned long flags = PyType_GetFlags(base);
        if (flags & Py_TPFLAGS_HEAPTYPE) {
            return 0;
        }
    }
    Py_VISIT((PyObject*)Py_TYPE(o));
    return 0;
}
#endif

/* PyMethodNew */
#if CYTHON_COMPILING_IN_LIMITED_API
static PyObject *__Pyx_PyMethod_New(PyObject *func, PyObject *self, PyObject *typ) {
    PyObject *result;
    CYTHON_UNUSED_VAR(typ);
    if (!self)
        return __Pyx_NewRef(func);
    #if __PYX_LIMITED_VERSION_HEX >= 0x030C0000
    {
        PyObject *args[] = {func, self};
        result = PyObject_Vectorcall(__pyx_mstate_global->__Pyx_CachedMethodType, args, 2, NULL);
    }
    #else
    result = PyObject_CallFunctionObjArgs(__pyx_mstate_global->__Pyx_CachedMethodType, func, self, NULL);
    #endif
    return result;
}
#else
static PyObject *__Pyx_PyMethod_New(PyObject *func, PyObject *self, PyObject *typ) {
    CYTHON_UNUSED_VAR(typ);
    if (!self)
        return __Pyx_NewRef(func);
    return PyMethod_New(func, self);
}
#endif

/* PyVectorcallFastCallDict */
#if CYTHON_METH_FASTCALL && (CYTHON_VECTORCALL || CYTHON_BACKPORT_VECTORCALL)
static PyObject *__Pyx_PyVectorcall_FastCallDict_kw(PyObject *func, __pyx_vectorcallfunc vc, PyObject *const *args, size_t nargs, PyObject *kw)
{
    PyObject *res = NULL;
    PyObject *kwnames;
    PyObject **newargs;
    PyObject **kwvalues;
    Py_ssize_t i, pos;
    size_t j;
    PyObject *key, *value;
    unsigned long keys_are_strings;
    #if !CYTHON_ASSUME_SAFE_SIZE
    Py_ssize_t nkw = PyDict_Size(kw);
    if (unlikely(nkw == -1)) return NULL;
    #else
    Py_ssize_t nkw = PyDict_GET_SIZE(kw);
    #endif
    newargs = (PyObject **)PyMem_Malloc((nargs + (size_t)nkw) * sizeof(args[0]));
    if (unlikely(newargs == NULL)) {
        PyErr_NoMemory();
        return NULL;
    }
    for (j = 0; j < nargs; j++) newargs[j] = args[j];
    kwnames = PyTuple_New(nkw);
    if (unlikely(kwnames == NULL)) {
        PyMem_Free(newargs);
        return NULL;
    }
    kwvalues = newargs + nargs;
    pos = i = 0;
    keys_are_strings = Py_TPFLAGS_UNICODE_SUBCLASS;
    while (PyDict_Next(kw, &pos, &key, &value)) {
        keys_are_strings &=
        #if CYTHON_COMPILING_IN_LIMITED_API
            PyType_GetFlags(Py_TYPE(key));
        #else
            Py_TYPE(key)->tp_flags;
        #endif
        Py_INCREF(key);
        Py_INCREF(value);
        #if !CYTHON_ASSUME_SAFE_MACROS
        if (unlikely(PyTuple_SetItem(kwnames, i, key) < 0)) goto cleanup;
        #else
        PyTuple_SET_ITEM(kwnames, i, key);
        #endif
        kwvalues[i] = value;
        i++;
    }
    if (unlikely(!keys_are_strings)) {
        PyErr_SetString(PyExc_TypeError, "keywords must be strings");
        goto cleanup;
    }
    res = vc(func, newargs, nargs, kwnames);
cleanup:
    Py_DECREF(kwnames);
    for (i = 0; i < nkw; i++)
        Py_DECREF(kwvalues[i]);
    PyMem_Free(newargs);
    return res;
}
static CYTHON_INLINE PyObject *__Pyx_PyVectorcall_FastCallDict(PyObject *func, __pyx_vectorcallfunc vc, PyObject *const *args, size_t nargs, PyObject *kw)
{
    Py_ssize_t kw_size =
        likely(kw == NULL) ?
        0 :
#if !CYTHON_ASSUME_SAFE_SIZE
        PyDict_Size(kw);
#else
        PyDict_GET_SIZE(kw);
#endif
    if (kw_size == 0) {
        return vc(func, args, nargs, NULL);
    }
#if !CYTHON_ASSUME_SAFE_SIZE
    else if (unlikely(kw_size == -1)) {
        return NULL;
    }
#endif
    return __Pyx_PyVectorcall_FastCallDict_kw(func, vc, args, nargs, kw);
}
#endif

/* CythonFunctionShared */
#if CYTHON_COMPILING_IN_LIMITED_API
static CYTHON_INLINE int __Pyx__IsSameCyOrCFunctionNoMethod(PyObject *func, void (*cfunc)(void)) {
    if (__Pyx_CyFunction_Check(func)) {
        return PyCFunction_GetFunction(((__pyx_CyFunctionObject*)func)->func) == (PyCFunction) cfunc;
    } else if (PyCFunction_Check(func)) {
        return PyCFunction_GetFunction(func) == (PyCFunction) cfunc;
    }
    return 0;
}
static CYTHON_INLINE int __Pyx__IsSameCyOrCFunction(PyObject *func, void (*cfunc)(void)) {
    if ((PyObject*)Py_TYPE(func) == __pyx_mstate_global->__Pyx_CachedMethodType) {
        int result;
        PyObject *newFunc = PyObject_GetAttr(func, __pyx_mstate_global->__pyx_n_u_func);
        if (unlikely(!newFunc)) {
            PyErr_Clear(); // It's only an optimization, so don't throw an error
            return 0;
        }
        result = __Pyx__IsSameCyOrCFunctionNoMethod(newFunc, cfunc);
        Py_DECREF(newFunc);
        return result;
    }
    return __Pyx__IsSameCyOrCFunctionNoMethod(func, cfunc);
}
#else
static CYTHON_INLINE int __Pyx__IsSameCyOrCFunction(PyObject *func, void (*cfunc)(void)) {
    if (PyMethod_Check(func)) {
        func = PyMethod_GET_FUNCTION(func);
    }
    return __Pyx_CyOrPyCFunction_Check(func) && __Pyx_CyOrPyCFunction_GET_FUNCTION(func) == (PyCFunction) cfunc;
}
#endif
static CYTHON_INLINE void __Pyx__CyFunction_SetClassObj(__pyx_CyFunctionObject* f, PyObject* classobj) {
#if PY_VERSION_HEX < 0x030900B1 || CYTHON_COMPILING_IN_LIMITED_API
    __Pyx_Py_XDECREF_SET(
        __Pyx_CyFunction_GetClassObj(f),
            ((classobj) ? __Pyx_NewRef(classobj) : NULL));
#else
    __Pyx_Py_XDECREF_SET(
        ((PyCMethodObject *) (f))->mm_class,
        (PyTypeObject*)((classobj) ? __Pyx_NewRef(classobj) : NULL));
#endif
}
static PyObject *
__Pyx_CyFunction_get_doc_locked(__pyx_CyFunctionObject *op)
{
    if (unlikely(op->func_doc == NULL)) {
#if CYTHON_COMPILING_IN_LIMITED_API
        op->func_doc = PyObject_GetAttrString(op->func, "__doc__");
        if (unlikely(!op->func_doc)) return NULL;
#else
        if (((PyCFunctionObject*)op)->m_ml->ml_doc) {
            op->func_doc = PyUnicode_FromString(((PyCFunctionObject*)op)->m_ml->ml_doc);
            if (unlikely(op->func_doc == NULL))
                return NULL;
        } else {
            Py_INCREF(Py_None);
            return Py_None;
        }
#endif
    }
    Py_INCREF(op->func_doc);
    return op->func_doc;
}
static PyObject *
__Pyx_CyFunction_get_doc(__pyx_CyFunctionObject *op, void *closure) {
    PyObject *result;
    CYTHON_UNUSED_VAR(closure);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    result = __Pyx_CyFunction_get_doc_locked(op);
    __Pyx_END_CRITICAL_SECTION();
    return result;
}
static int
__Pyx_CyFunction_set_doc(__pyx_CyFunctionObject *op, PyObject *value, void *context)
{
    CYTHON_UNUSED_VAR(context);
    if (value == NULL) {
        value = Py_None;
    }
    Py_INCREF(value);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    __Pyx_Py_XDECREF_SET(op->func_doc, value);
    __Pyx_END_CRITICAL_SECTION();
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_name_locked(__pyx_CyFunctionObject *op)
{
    if (unlikely(op->func_name == NULL)) {
#if CYTHON_COMPILING_IN_LIMITED_API
        op->func_name = PyObject_GetAttrString(op->func, "__name__");
#else
        op->func_name = PyUnicode_InternFromString(((PyCFunctionObject*)op)->m_ml->ml_name);
#endif
        if (unlikely(op->func_name == NULL))
            return NULL;
    }
    Py_INCREF(op->func_name);
    return op->func_name;
}
static PyObject *
__Pyx_CyFunction_get_name(__pyx_CyFunctionObject *op, void *context)
{
    PyObject *result = NULL;
    CYTHON_UNUSED_VAR(context);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    result = __Pyx_CyFunction_get_name_locked(op);
    __Pyx_END_CRITICAL_SECTION();
    return result;
}
static int
__Pyx_CyFunction_set_name(__pyx_CyFunctionObject *op, PyObject *value, void *context)
{
    CYTHON_UNUSED_VAR(context);
    if (unlikely(value == NULL || !PyUnicode_Check(value))) {
        PyErr_SetString(PyExc_TypeError,
                        "__name__ must be set to a string object");
        return -1;
    }
    Py_INCREF(value);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    __Pyx_Py_XDECREF_SET(op->func_name, value);
    __Pyx_END_CRITICAL_SECTION();
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_qualname(__pyx_CyFunctionObject *op, void *context)
{
    CYTHON_UNUSED_VAR(context);
    PyObject *result;
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    Py_INCREF(op->func_qualname);
    result = op->func_qualname;
    __Pyx_END_CRITICAL_SECTION();
    return result;
}
static int
__Pyx_CyFunction_set_qualname(__pyx_CyFunctionObject *op, PyObject *value, void *context)
{
    CYTHON_UNUSED_VAR(context);
    if (unlikely(value == NULL || !PyUnicode_Check(value))) {
        PyErr_SetString(PyExc_TypeError,
                        "__qualname__ must be set to a string object");
        return -1;
    }
    Py_INCREF(value);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    __Pyx_Py_XDECREF_SET(op->func_qualname, value);
    __Pyx_END_CRITICAL_SECTION();
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_dict_locked(__pyx_CyFunctionObject *op)
{
    if (unlikely(op->func_dict == NULL)) {
        op->func_dict = PyDict_New();
        if (unlikely(op->func_dict == NULL))
            return NULL;
    }
    Py_INCREF(op->func_dict);
    return op->func_dict;
}
static PyObject *
__Pyx_CyFunction_get_dict(__pyx_CyFunctionObject *op, void *context)
{
    CYTHON_UNUSED_VAR(context);
    PyObject *result;
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    result = __Pyx_CyFunction_get_dict_locked(op);
    __Pyx_END_CRITICAL_SECTION();
    return result;
}
static int
__Pyx_CyFunction_set_dict(__pyx_CyFunctionObject *op, PyObject *value, void *context)
{
    CYTHON_UNUSED_VAR(context);
    if (unlikely(value == NULL)) {
        PyErr_SetString(PyExc_TypeError,
               "function's dictionary may not be deleted");
        return -1;
    }
    if (unlikely(!PyDict_Check(value))) {
        PyErr_SetString(PyExc_TypeError,
               "setting function's dictionary to a non-dict");
        return -1;
    }
    Py_INCREF(value);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    __Pyx_Py_XDECREF_SET(op->func_dict, value);
    __Pyx_END_CRITICAL_SECTION();
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_globals(__pyx_CyFunctionObject *op, void *context)
{
    CYTHON_UNUSED_VAR(context);
    Py_INCREF(op->func_globals);
    return op->func_globals;
}
static PyObject *
__Pyx_CyFunction_get_closure(__pyx_CyFunctionObject *op, void *context)
{
    CYTHON_UNUSED_VAR(op);
    CYTHON_UNUSED_VAR(context);
    Py_INCREF(Py_None);
    return Py_None;
}
static PyObject *
__Pyx_CyFunction_get_code(__pyx_CyFunctionObject *op, void *context)
{
    PyObject* result = (op->func_code) ? op->func_code : Py_None;
    CYTHON_UNUSED_VAR(context);
    Py_INCREF(result);
    return result;
}
static int
__Pyx_CyFunction_init_defaults(__pyx_CyFunctionObject *op) {
    int result = 0;
    PyObject *res = op->defaults_getter((PyObject *) op);
    if (unlikely(!res))
        return -1;
    #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
    op->defaults_tuple = PyTuple_GET_ITEM(res, 0);
    Py_INCREF(op->defaults_tuple);
    op->defaults_kwdict = PyTuple_GET_ITEM(res, 1);
    Py_INCREF(op->defaults_kwdict);
    #else
    op->defaults_tuple = __Pyx_PySequence_ITEM(res, 0);
    if (unlikely(!op->defaults_tuple)) result = -1;
    else {
        op->defaults_kwdict = __Pyx_PySequence_ITEM(res, 1);
        if (unlikely(!op->defaults_kwdict)) result = -1;
    }
    #endif
    Py_DECREF(res);
    return result;
}
static int
__Pyx_CyFunction_set_defaults(__pyx_CyFunctionObject *op, PyObject* value, void *context) {
    CYTHON_UNUSED_VAR(context);
    if (!value) {
        value = Py_None;
    } else if (unlikely(value != Py_None && !PyTuple_Check(value))) {
        PyErr_SetString(PyExc_TypeError,
                        "__defaults__ must be set to a tuple object");
        return -1;
    }
    PyErr_WarnEx(PyExc_RuntimeWarning, "changes to cyfunction.__defaults__ will not "
                 "currently affect the values used in function calls", 1);
    Py_INCREF(value);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    __Pyx_Py_XDECREF_SET(op->defaults_tuple, value);
    __Pyx_END_CRITICAL_SECTION();
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_defaults_locked(__pyx_CyFunctionObject *op) {
    PyObject* result = op->defaults_tuple;
    if (unlikely(!result)) {
        if (op->defaults_getter) {
            if (unlikely(__Pyx_CyFunction_init_defaults(op) < 0)) return NULL;
            result = op->defaults_tuple;
        } else {
            result = Py_None;
        }
    }
    Py_INCREF(result);
    return result;
}
static PyObject *
__Pyx_CyFunction_get_defaults(__pyx_CyFunctionObject *op, void *context) {
    PyObject* result = NULL;
    CYTHON_UNUSED_VAR(context);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    result = __Pyx_CyFunction_get_defaults_locked(op);
    __Pyx_END_CRITICAL_SECTION();
    return result;
}
static int
__Pyx_CyFunction_set_kwdefaults(__pyx_CyFunctionObject *op, PyObject* value, void *context) {
    CYTHON_UNUSED_VAR(context);
    if (!value) {
        value = Py_None;
    } else if (unlikely(value != Py_None && !PyDict_Check(value))) {
        PyErr_SetString(PyExc_TypeError,
                        "__kwdefaults__ must be set to a dict object");
        return -1;
    }
    PyErr_WarnEx(PyExc_RuntimeWarning, "changes to cyfunction.__kwdefaults__ will not "
                 "currently affect the values used in function calls", 1);
    Py_INCREF(value);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    __Pyx_Py_XDECREF_SET(op->defaults_kwdict, value);
    __Pyx_END_CRITICAL_SECTION();
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_kwdefaults_locked(__pyx_CyFunctionObject *op) {
    PyObject* result = op->defaults_kwdict;
    if (unlikely(!result)) {
        if (op->defaults_getter) {
            if (unlikely(__Pyx_CyFunction_init_defaults(op) < 0)) return NULL;
            result = op->defaults_kwdict;
        } else {
            result = Py_None;
        }
    }
    Py_INCREF(result);
    return result;
}
static PyObject *
__Pyx_CyFunction_get_kwdefaults(__pyx_CyFunctionObject *op, void *context) {
    PyObject* result;
    CYTHON_UNUSED_VAR(context);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    result = __Pyx_CyFunction_get_kwdefaults_locked(op);
    __Pyx_END_CRITICAL_SECTION();
    return result;
}
static int
__Pyx_CyFunction_set_annotations(__pyx_CyFunctionObject *op, PyObject* value, void *context) {
    CYTHON_UNUSED_VAR(context);
    if (!value || value == Py_None) {
        value = NULL;
    } else if (unlikely(!PyDict_Check(value))) {
        PyErr_SetString(PyExc_TypeError,
                        "__annotations__ must be set to a dict object");
        return -1;
    }
    Py_XINCREF(value);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    __Pyx_Py_XDECREF_SET(op->func_annotations, value);
    __Pyx_END_CRITICAL_SECTION();
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_annotations_locked(__pyx_CyFunctionObject *op) {
    PyObject* result = op->func_annotations;
    if (unlikely(!result)) {
        result = PyDict_New();
        if (unlikely(!result)) return NULL;
        op->func_annotations = result;
    }
    Py_INCREF(result);
    return result;
}
static PyObject *
__Pyx_CyFunction_get_annotations(__pyx_CyFunctionObject *op, void *context) {
    PyObject *result;
    CYTHON_UNUSED_VAR(context);
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    result = __Pyx_CyFunction_get_annotations_locked(op);
    __Pyx_END_CRITICAL_SECTION();
    return result;
}
static PyObject *
__Pyx_CyFunction_get_is_coroutine_value(__pyx_CyFunctionObject *op) {
    int is_coroutine = op->flags & __Pyx_CYFUNCTION_COROUTINE;
    if (is_coroutine) {
        PyObject *is_coroutine_value, *module, *fromlist, *marker = __pyx_mstate_global->__pyx_n_u_is_coroutine;
        fromlist = PyList_New(1);
        if (unlikely(!fromlist)) return NULL;
        Py_INCREF(marker);
#if CYTHON_ASSUME_SAFE_MACROS
        PyList_SET_ITEM(fromlist, 0, marker);
#else
        if (unlikely(PyList_SetItem(fromlist, 0, marker) < 0)) {
            Py_DECREF(marker);
            Py_DECREF(fromlist);
            return NULL;
        }
#endif
        module = PyImport_ImportModuleLevelObject(__pyx_mstate_global->__pyx_n_u_asyncio_coroutines, NULL, NULL, fromlist, 0);
        Py_DECREF(fromlist);
        if (unlikely(!module)) goto ignore;
        is_coroutine_value = __Pyx_PyObject_GetAttrStr(module, marker);
        Py_DECREF(module);
        if (likely(is_coroutine_value)) {
            return is_coroutine_value;
        }
ignore:
        PyErr_Clear();
    }
    return __Pyx_PyBool_FromLong(is_coroutine);
}
static PyObject *
__Pyx_CyFunction_get_is_coroutine(__pyx_CyFunctionObject *op, void *context) {
    PyObject *result;
    CYTHON_UNUSED_VAR(context);
    if (op->func_is_coroutine) {
        return __Pyx_NewRef(op->func_is_coroutine);
    }
    result = __Pyx_CyFunction_get_is_coroutine_value(op);
    if (unlikely(!result))
        return NULL;
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    if (op->func_is_coroutine) {
        Py_DECREF(result);
        result = __Pyx_NewRef(op->func_is_coroutine);
    } else {
        op->func_is_coroutine = __Pyx_NewRef(result);
    }
    __Pyx_END_CRITICAL_SECTION();
    return result;
}
static void __Pyx_CyFunction_raise_argument_count_error(__pyx_CyFunctionObject *func, const char* message, Py_ssize_t size) {
#if CYTHON_COMPILING_IN_LIMITED_API
    PyObject *py_name = __Pyx_CyFunction_get_name(func, NULL);
    if (!py_name) return;
    PyErr_Format(PyExc_TypeError,
        "%.200S() %s (%" CYTHON_FORMAT_SSIZE_T "d given)",
        py_name, message, size);
    Py_DECREF(py_name);
#else
    const char* name = ((PyCFunctionObject*)func)->m_ml->ml_name;
    PyErr_Format(PyExc_TypeError,
        "%.200s() %s (%" CYTHON_FORMAT_SSIZE_T "d given)",
        name, message, size);
#endif
}
static void __Pyx_CyFunction_raise_type_error(__pyx_CyFunctionObject *func, const char* message) {
#if CYTHON_COMPILING_IN_LIMITED_API
    PyObject *py_name = __Pyx_CyFunction_get_name(func, NULL);
    if (!py_name) return;
    PyErr_Format(PyExc_TypeError,
        "%.200S() %s",
        py_name, message);
    Py_DECREF(py_name);
#else
    const char* name = ((PyCFunctionObject*)func)->m_ml->ml_name;
    PyErr_Format(PyExc_TypeError,
        "%.200s() %s",
        name, message);
#endif
}
#if CYTHON_COMPILING_IN_LIMITED_API
static PyObject *
__Pyx_CyFunction_get_module(__pyx_CyFunctionObject *op, void *context) {
    CYTHON_UNUSED_VAR(context);
    return PyObject_GetAttrString(op->func, "__module__");
}
static int
__Pyx_CyFunction_set_module(__pyx_CyFunctionObject *op, PyObject* value, void *context) {
    CYTHON_UNUSED_VAR(context);
    return PyObject_SetAttrString(op->func, "__module__", value);
}
#endif
static PyGetSetDef __pyx_CyFunction_getsets[] = {
    {"func_doc", (getter)__Pyx_CyFunction_get_doc, (setter)__Pyx_CyFunction_set_doc, 0, 0},
    {"__doc__",  (getter)__Pyx_CyFunction_get_doc, (setter)__Pyx_CyFunction_set_doc, 0, 0},
    {"func_name", (getter)__Pyx_CyFunction_get_name, (setter)__Pyx_CyFunction_set_name, 0, 0},
    {"__name__", (getter)__Pyx_CyFunction_get_name, (setter)__Pyx_CyFunction_set_name, 0, 0},
    {"__qualname__", (getter)__Pyx_CyFunction_get_qualname, (setter)__Pyx_CyFunction_set_qualname, 0, 0},
    {"func_dict", (getter)__Pyx_CyFunction_get_dict, (setter)__Pyx_CyFunction_set_dict, 0, 0},
    {"__dict__", (getter)__Pyx_CyFunction_get_dict, (setter)__Pyx_CyFunction_set_dict, 0, 0},
    {"func_globals", (getter)__Pyx_CyFunction_get_globals, 0, 0, 0},
    {"__globals__", (getter)__Pyx_CyFunction_get_globals, 0, 0, 0},
    {"func_closure", (getter)__Pyx_CyFunction_get_closure, 0, 0, 0},
    {"__closure__", (getter)__Pyx_CyFunction_get_closure, 0, 0, 0},
    {"func_code", (getter)__Pyx_CyFunction_get_code, 0, 0, 0},
    {"__code__", (getter)__Pyx_CyFunction_get_code, 0, 0, 0},
    {"func_defaults", (getter)__Pyx_CyFunction_get_defaults, (setter)__Pyx_CyFunction_set_defaults, 0, 0},
    {"__defaults__", (getter)__Pyx_CyFunction_get_defaults, (setter)__Pyx_CyFunction_set_defaults, 0, 0},
    {"__kwdefaults__", (getter)__Pyx_CyFunction_get_kwdefaults, (setter)__Pyx_CyFunction_set_kwdefaults, 0, 0},
    {"__annotations__", (getter)__Pyx_CyFunction_get_annotations, (setter)__Pyx_CyFunction_set_annotations, 0, 0},
    {"_is_coroutine", (getter)__Pyx_CyFunction_get_is_coroutine, 0, 0, 0},
#if CYTHON_COMPILING_IN_LIMITED_API
    {"__module__", (getter)__Pyx_CyFunction_get_module, (setter)__Pyx_CyFunction_set_module, 0, 0},
#endif
    {0, 0, 0, 0, 0}
};
static PyMemberDef __pyx_CyFunction_members[] = {
#if !CYTHON_COMPILING_IN_LIMITED_API
    {"__module__", T_OBJECT, offsetof(PyCFunctionObject, m_module), 0, 0},
#endif
    {"__dictoffset__", T_PYSSIZET, offsetof(__pyx_CyFunctionObject, func_dict), READONLY, 0},
#if CYTHON_METH_FASTCALL
#if CYTHON_BACKPORT_VECTORCALL || CYTHON_COMPILING_IN_LIMITED_API
    {"__vectorcalloffset__", T_PYSSIZET, offsetof(__pyx_CyFunctionObject, func_vectorcall), READONLY, 0},
#else
    {"__vectorcalloffset__", T_PYSSIZET, offsetof(PyCFunctionObject, vectorcall), READONLY, 0},
#endif
#if CYTHON_COMPILING_IN_LIMITED_API
    {"__weaklistoffset__", T_PYSSIZET, offsetof(__pyx_CyFunctionObject, func_weakreflist), READONLY, 0},
#else
    {"__weaklistoffset__", T_PYSSIZET, offsetof(PyCFunctionObject, m_weakreflist), READONLY, 0},
#endif
#endif
    {0, 0, 0,  0, 0}
};
static PyObject *
__Pyx_CyFunction_reduce(__pyx_CyFunctionObject *m, PyObject *args)
{
    PyObject *result = NULL;
    CYTHON_UNUSED_VAR(args);
    __Pyx_BEGIN_CRITICAL_SECTION(m);
    Py_INCREF(m->func_qualname);
    result = m->func_qualname;
    __Pyx_END_CRITICAL_SECTION();
    return result;
}
static PyMethodDef __pyx_CyFunction_methods[] = {
    {"__reduce__", (PyCFunction)__Pyx_CyFunction_reduce, METH_VARARGS, 0},
    {0, 0, 0, 0}
};
#if CYTHON_COMPILING_IN_LIMITED_API
#define __Pyx_CyFunction_weakreflist(cyfunc) ((cyfunc)->func_weakreflist)
#else
#define __Pyx_CyFunction_weakreflist(cyfunc) (((PyCFunctionObject*)cyfunc)->m_weakreflist)
#endif
static PyObject *__Pyx_CyFunction_Init(__pyx_CyFunctionObject *op, PyMethodDef *ml, int flags, PyObject* qualname,
                                       PyObject *closure, PyObject *module, PyObject* globals, PyObject* code) {
#if !CYTHON_COMPILING_IN_LIMITED_API
    PyCFunctionObject *cf = (PyCFunctionObject*) op;
#endif
    if (unlikely(op == NULL))
        return NULL;
#if CYTHON_COMPILING_IN_LIMITED_API
    op->func = PyCFunction_NewEx(ml, (PyObject*)op, module);
    if (unlikely(!op->func)) return NULL;
#endif
    op->flags = flags;
    __Pyx_CyFunction_weakreflist(op) = NULL;
#if !CYTHON_COMPILING_IN_LIMITED_API
    cf->m_ml = ml;
    cf->m_self = (PyObject *) op;
#endif
    Py_XINCREF(closure);
    op->func_closure = closure;
#if !CYTHON_COMPILING_IN_LIMITED_API
    Py_XINCREF(module);
    cf->m_module = module;
#endif
    op->func_dict = NULL;
    op->func_name = NULL;
    Py_INCREF(qualname);
    op->func_qualname = qualname;
    op->func_doc = NULL;
#if PY_VERSION_HEX < 0x030900B1 || CYTHON_COMPILING_IN_LIMITED_API
    op->func_classobj = NULL;
#else
    ((PyCMethodObject*)op)->mm_class = NULL;
#endif
    op->func_globals = globals;
    Py_INCREF(op->func_globals);
    Py_XINCREF(code);
    op->func_code = code;
    op->defaults = NULL;
    op->defaults_tuple = NULL;
    op->defaults_kwdict = NULL;
    op->defaults_getter = NULL;
    op->func_annotations = NULL;
    op->func_is_coroutine = NULL;
#if CYTHON_METH_FASTCALL
    switch (ml->ml_flags & (METH_VARARGS | METH_FASTCALL | METH_NOARGS | METH_O | METH_KEYWORDS | METH_METHOD)) {
    case METH_NOARGS:
        __Pyx_CyFunction_func_vectorcall(op) = __Pyx_CyFunction_Vectorcall_NOARGS;
        break;
    case METH_O:
        __Pyx_CyFunction_func_vectorcall(op) = __Pyx_CyFunction_Vectorcall_O;
        break;
    case METH_METHOD | METH_FASTCALL | METH_KEYWORDS:
        __Pyx_CyFunction_func_vectorcall(op) = __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS_METHOD;
        break;
    case METH_FASTCALL | METH_KEYWORDS:
        __Pyx_CyFunction_func_vectorcall(op) = __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS;
        break;
    case METH_VARARGS | METH_KEYWORDS:
        __Pyx_CyFunction_func_vectorcall(op) = NULL;
        break;
    default:
        PyErr_SetString(PyExc_SystemError, "Bad call flags for CyFunction");
        Py_DECREF(op);
        return NULL;
    }
#endif
    return (PyObject *) op;
}
static int
__Pyx_CyFunction_clear(__pyx_CyFunctionObject *m)
{
    Py_CLEAR(m->func_closure);
#if CYTHON_COMPILING_IN_LIMITED_API
    Py_CLEAR(m->func);
#else
    Py_CLEAR(((PyCFunctionObject*)m)->m_module);
#endif
    Py_CLEAR(m->func_dict);
    Py_CLEAR(m->func_name);
    Py_CLEAR(m->func_qualname);
    Py_CLEAR(m->func_doc);
    Py_CLEAR(m->func_globals);
    Py_CLEAR(m->func_code);
#if !CYTHON_COMPILING_IN_LIMITED_API
#if PY_VERSION_HEX < 0x030900B1
    Py_CLEAR(__Pyx_CyFunction_GetClassObj(m));
#else
    {
        PyObject *cls = (PyObject*) ((PyCMethodObject *) (m))->mm_class;
        ((PyCMethodObject *) (m))->mm_class = NULL;
        Py_XDECREF(cls);
    }
#endif
#endif
    Py_CLEAR(m->defaults_tuple);
    Py_CLEAR(m->defaults_kwdict);
    Py_CLEAR(m->func_annotations);
    Py_CLEAR(m->func_is_coroutine);
    Py_CLEAR(m->defaults);
    return 0;
}
static void __Pyx__CyFunction_dealloc(__pyx_CyFunctionObject *m)
{
    if (__Pyx_CyFunction_weakreflist(m) != NULL)
        PyObject_ClearWeakRefs((PyObject *) m);
    __Pyx_CyFunction_clear(m);
    __Pyx_PyHeapTypeObject_GC_Del(m);
}
static void __Pyx_CyFunction_dealloc(__pyx_CyFunctionObject *m)
{
    PyObject_GC_UnTrack(m);
    __Pyx__CyFunction_dealloc(m);
}
static int __Pyx_CyFunction_traverse(__pyx_CyFunctionObject *m, visitproc visit, void *arg)
{
    {
        int e = __Pyx_call_type_traverse((PyObject*)m, 1, visit, arg);
        if (e) return e;
    }
    Py_VISIT(m->func_closure);
#if CYTHON_COMPILING_IN_LIMITED_API
    Py_VISIT(m->func);
#else
    Py_VISIT(((PyCFunctionObject*)m)->m_module);
#endif
    Py_VISIT(m->func_dict);
    __Pyx_VISIT_CONST(m->func_name);
    __Pyx_VISIT_CONST(m->func_qualname);
    Py_VISIT(m->func_doc);
    Py_VISIT(m->func_globals);
    __Pyx_VISIT_CONST(m->func_code);
#if !CYTHON_COMPILING_IN_LIMITED_API
    Py_VISIT(__Pyx_CyFunction_GetClassObj(m));
#endif
    Py_VISIT(m->defaults_tuple);
    Py_VISIT(m->defaults_kwdict);
    Py_VISIT(m->func_is_coroutine);
    Py_VISIT(m->defaults);
    return 0;
}
static PyObject*
__Pyx_CyFunction_repr(__pyx_CyFunctionObject *op)
{
    PyObject *repr;
    __Pyx_BEGIN_CRITICAL_SECTION(op);
    repr = PyUnicode_FromFormat("<cyfunction %U at %p>",
                                op->func_qualname, (void *)op);
    __Pyx_END_CRITICAL_SECTION();
    return repr;
}
static PyObject * __Pyx_CyFunction_CallMethod(PyObject *func, PyObject *self, PyObject *arg, PyObject *kw) {
#if CYTHON_COMPILING_IN_LIMITED_API
    PyObject *f = ((__pyx_CyFunctionObject*)func)->func;
    PyCFunction meth;
    int flags;
    meth = PyCFunction_GetFunction(f);
    if (unlikely(!meth)) return NULL;
    flags = PyCFunction_GetFlags(f);
    if (unlikely(flags < 0)) return NULL;
#else
    PyCFunctionObject* f = (PyCFunctionObject*)func;
    PyCFunction meth = f->m_ml->ml_meth;
    int flags = f->m_ml->ml_flags;
#endif
    Py_ssize_t size;
    switch (flags & (METH_VARARGS | METH_KEYWORDS | METH_NOARGS | METH_O)) {
    case METH_VARARGS:
        if (likely(kw == NULL || PyDict_Size(kw) == 0))
            return (*meth)(self, arg);
        break;
    case METH_VARARGS | METH_KEYWORDS:
        return (*(PyCFunctionWithKeywords)(void(*)(void))meth)(self, arg, kw);
    case METH_NOARGS:
        if (likely(kw == NULL || PyDict_Size(kw) == 0)) {
#if CYTHON_ASSUME_SAFE_SIZE
            size = PyTuple_GET_SIZE(arg);
#else
            size = PyTuple_Size(arg);
            if (unlikely(size < 0)) return NULL;
#endif
            if (likely(size == 0))
                return (*meth)(self, NULL);
            __Pyx_CyFunction_raise_argument_count_error(
                (__pyx_CyFunctionObject*)func,
                "takes no arguments", size);
            return NULL;
        }
        break;
    case METH_O:
        if (likely(kw == NULL || PyDict_Size(kw) == 0)) {
#if CYTHON_ASSUME_SAFE_SIZE
            size = PyTuple_GET_SIZE(arg);
#else
            size = PyTuple_Size(arg);
            if (unlikely(size < 0)) return NULL;
#endif
            if (likely(size == 1)) {
                PyObject *result, *arg0;
                #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
                arg0 = PyTuple_GET_ITEM(arg, 0);
                #else
                arg0 = __Pyx_PySequence_ITEM(arg, 0); if (unlikely(!arg0)) return NULL;
                #endif
                result = (*meth)(self, arg0);
                #if !(CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS)
                Py_DECREF(arg0);
                #endif
                return result;
            }
            __Pyx_CyFunction_raise_argument_count_error(
                (__pyx_CyFunctionObject*)func,
                "takes exactly one argument", size);
            return NULL;
        }
        break;
    default:
        PyErr_SetString(PyExc_SystemError, "Bad call flags for CyFunction");
        return NULL;
    }
    __Pyx_CyFunction_raise_type_error(
        (__pyx_CyFunctionObject*)func, "takes no keyword arguments");
    return NULL;
}
static CYTHON_INLINE PyObject *__Pyx_CyFunction_Call(PyObject *func, PyObject *arg, PyObject *kw) {
    PyObject *self, *result;
#if CYTHON_COMPILING_IN_LIMITED_API
    self = PyCFunction_GetSelf(((__pyx_CyFunctionObject*)func)->func);
    if (unlikely(!self) && PyErr_Occurred()) return NULL;
#else
    self = ((PyCFunctionObject*)func)->m_self;
#endif
    result = __Pyx_CyFunction_CallMethod(func, self, arg, kw);
    return result;
}
static PyObject *__Pyx_CyFunction_CallAsMethod(PyObject *func, PyObject *args, PyObject *kw) {
    PyObject *result;
    __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *) func;
#if CYTHON_METH_FASTCALL && (CYTHON_VECTORCALL || CYTHON_BACKPORT_VECTORCALL)
     __pyx_vectorcallfunc vc = __Pyx_CyFunction_func_vectorcall(cyfunc);
    if (vc) {
#if CYTHON_ASSUME_SAFE_MACROS && CYTHON_ASSUME_SAFE_SIZE
        return __Pyx_PyVectorcall_FastCallDict(func, vc, &PyTuple_GET_ITEM(args, 0), (size_t)PyTuple_GET_SIZE(args), kw);
#else
        (void) &__Pyx_PyVectorcall_FastCallDict;
        return PyVectorcall_Call(func, args, kw);
#endif
    }
#endif
    if ((cyfunc->flags & __Pyx_CYFUNCTION_CCLASS) && !(cyfunc->flags & __Pyx_CYFUNCTION_STATICMETHOD)) {
        Py_ssize_t argc;
        PyObject *new_args;
        PyObject *self;
#if CYTHON_ASSUME_SAFE_SIZE
        argc = PyTuple_GET_SIZE(args);
#else
        argc = PyTuple_Size(args);
        if (unlikely(argc < 0)) return NULL;
#endif
        new_args = PyTuple_GetSlice(args, 1, argc);
        if (unlikely(!new_args))
            return NULL;
        self = PyTuple_GetItem(args, 0);
        if (unlikely(!self)) {
            Py_DECREF(new_args);
            PyErr_Format(PyExc_TypeError,
                         "unbound method %.200S() needs an argument",
                         cyfunc->func_qualname);
            return NULL;
        }
        result = __Pyx_CyFunction_CallMethod(func, self, new_args, kw);
        Py_DECREF(new_args);
    } else {
        result = __Pyx_CyFunction_Call(func, args, kw);
    }
    return result;
}
#if CYTHON_METH_FASTCALL && (CYTHON_VECTORCALL || CYTHON_BACKPORT_VECTORCALL)
static CYTHON_INLINE int __Pyx_CyFunction_Vectorcall_CheckArgs(__pyx_CyFunctionObject *cyfunc, Py_ssize_t nargs, PyObject *kwnames)
{
    int ret = 0;
    if ((cyfunc->flags & __Pyx_CYFUNCTION_CCLASS) && !(cyfunc->flags & __Pyx_CYFUNCTION_STATICMETHOD)) {
        if (unlikely(nargs < 1)) {
            __Pyx_CyFunction_raise_type_error(
                cyfunc, "needs an argument");
            return -1;
        }
        ret = 1;
    }
    if (unlikely(kwnames) && unlikely(__Pyx_PyTuple_GET_SIZE(kwnames))) {
        __Pyx_CyFunction_raise_type_error(
            cyfunc, "takes no keyword arguments");
        return -1;
    }
    return ret;
}
static PyObject * __Pyx_CyFunction_Vectorcall_NOARGS(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames)
{
    __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *)func;
#if CYTHON_BACKPORT_VECTORCALL
    Py_ssize_t nargs = (Py_ssize_t)nargsf;
#else
    Py_ssize_t nargs = PyVectorcall_NARGS(nargsf);
#endif
    PyObject *self;
#if CYTHON_COMPILING_IN_LIMITED_API
    PyCFunction meth = PyCFunction_GetFunction(cyfunc->func);
    if (unlikely(!meth)) return NULL;
#else
    PyCFunction meth = ((PyCFunctionObject*)cyfunc)->m_ml->ml_meth;
#endif
    switch (__Pyx_CyFunction_Vectorcall_CheckArgs(cyfunc, nargs, kwnames)) {
    case 1:
        self = args[0];
        args += 1;
        nargs -= 1;
        break;
    case 0:
#if CYTHON_COMPILING_IN_LIMITED_API
        self = PyCFunction_GetSelf(((__pyx_CyFunctionObject*)cyfunc)->func);
        if (unlikely(!self) && PyErr_Occurred()) return NULL;
#else
        self = ((PyCFunctionObject*)cyfunc)->m_self;
#endif
        break;
    default:
        return NULL;
    }
    if (unlikely(nargs != 0)) {
        __Pyx_CyFunction_raise_argument_count_error(
            cyfunc, "takes no arguments", nargs);
        return NULL;
    }
    return meth(self, NULL);
}
static PyObject * __Pyx_CyFunction_Vectorcall_O(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames)
{
    __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *)func;
#if CYTHON_BACKPORT_VECTORCALL
    Py_ssize_t nargs = (Py_ssize_t)nargsf;
#else
    Py_ssize_t nargs = PyVectorcall_NARGS(nargsf);
#endif
    PyObject *self;
#if CYTHON_COMPILING_IN_LIMITED_API
    PyCFunction meth = PyCFunction_GetFunction(cyfunc->func);
    if (unlikely(!meth)) return NULL;
#else
    PyCFunction meth = ((PyCFunctionObject*)cyfunc)->m_ml->ml_meth;
#endif
    switch (__Pyx_CyFunction_Vectorcall_CheckArgs(cyfunc, nargs, kwnames)) {
    case 1:
        self = args[0];
        args += 1;
        nargs -= 1;
        break;
    case 0:
#if CYTHON_COMPILING_IN_LIMITED_API
        self = PyCFunction_GetSelf(((__pyx_CyFunctionObject*)cyfunc)->func);
        if (unlikely(!self) && PyErr_Occurred()) return NULL;
#else
        self = ((PyCFunctionObject*)cyfunc)->m_self;
#endif
        break;
    default:
        return NULL;
    }
    if (unlikely(nargs != 1)) {
        __Pyx_CyFunction_raise_argument_count_error(
            cyfunc, "takes exactly one argument", nargs);
        return NULL;
    }
    return meth(self, args[0]);
}
static PyObject * __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames)
{
    __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *)func;
#if CYTHON_BACKPORT_VECTORCALL
    Py_ssize_t nargs = (Py_ssize_t)nargsf;
#else
    Py_ssize_t nargs = PyVectorcall_NARGS(nargsf);
#endif
    PyObject *self;
#if CYTHON_COMPILING_IN_LIMITED_API
    PyCFunction meth = PyCFunction_GetFunction(cyfunc->func);
    if (unlikely(!meth)) return NULL;
#else
    PyCFunction meth = ((PyCFunctionObject*)cyfunc)->m_ml->ml_meth;
#endif
    switch (__Pyx_CyFunction_Vectorcall_CheckArgs(cyfunc, nargs, NULL)) {
    case 1:
        self = args[0];
        args += 1;
        nargs -= 1;
        break;
    case 0:
#if CYTHON_COMPILING_IN_LIMITED_API
        self = PyCFunction_GetSelf(((__pyx_CyFunctionObject*)cyfunc)->func);
        if (unlikely(!self) && PyErr_Occurred()) return NULL;
#else
        self = ((PyCFunctionObject*)cyfunc)->m_self;
#endif
        break;
    default:
        return NULL;
    }
    return ((__Pyx_PyCFunctionFastWithKeywords)(void(*)(void))meth)(self, args, nargs, kwnames);
}
static PyObject * __Pyx_CyFunction_Vectorcall_FASTCALL_KEYWORDS_METHOD(PyObject *func, PyObject *const *args, size_t nargsf, PyObject *kwnames)
{
    __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *)func;
    PyTypeObject *cls = (PyTypeObject *) __Pyx_CyFunction_GetClassObj(cyfunc);
#if CYTHON_BACKPORT_VECTORCALL
    Py_ssize_t nargs = (Py_ssize_t)nargsf;
#else
    Py_ssize_t nargs = PyVectorcall_NARGS(nargsf);
#endif
    PyObject *self;
#if CYTHON_COMPILING_IN_LIMITED_API
    PyCFunction meth = PyCFunction_GetFunction(cyfunc->func);
    if (unlikely(!meth)) return NULL;
#else
    PyCFunction meth = ((PyCFunctionObject*)cyfunc)->m_ml->ml_meth;
#endif
    switch (__Pyx_CyFunction_Vectorcall_CheckArgs(cyfunc, nargs, NULL)) {
    case 1:
        self = args[0];
        args += 1;
        nargs -= 1;
        break;
    case 0:
#if CYTHON_COMPILING_IN_LIMITED_API
        self = PyCFunction_GetSelf(((__pyx_CyFunctionObject*)cyfunc)->func);
        if (unlikely(!self) && PyErr_Occurred()) return NULL;
#else
        self = ((PyCFunctionObject*)cyfunc)->m_self;
#endif
        break;
    default:
        return NULL;
    }
    return ((__Pyx_PyCMethod)(void(*)(void))meth)(self, cls, args, (size_t)nargs, kwnames);
}
#endif
static PyType_Slot __pyx_CyFunctionType_slots[] = {
    {Py_tp_dealloc, (void *)__Pyx_CyFunction_dealloc},
    {Py_tp_repr, (void *)__Pyx_CyFunction_repr},
    {Py_tp_call, (void *)__Pyx_CyFunction_CallAsMethod},
    {Py_tp_traverse, (void *)__Pyx_CyFunction_traverse},
    {Py_tp_clear, (void *)__Pyx_CyFunction_clear},
    {Py_tp_methods, (void *)__pyx_CyFunction_methods},
    {Py_tp_members, (void *)__pyx_CyFunction_members},
    {Py_tp_getset, (void *)__pyx_CyFunction_getsets},
    {Py_tp_descr_get, (void *)__Pyx_PyMethod_New},
    {0, 0},
};
static PyType_Spec __pyx_CyFunctionType_spec = {
    __PYX_TYPE_MODULE_PREFIX "cython_function_or_method",
    sizeof(__pyx_CyFunctionObject),
    0,
#ifdef Py_TPFLAGS_METHOD_DESCRIPTOR
    Py_TPFLAGS_METHOD_DESCRIPTOR |
#endif
#if CYTHON_METH_FASTCALL
#if defined(Py_TPFLAGS_HAVE_VECTORCALL)
    Py_TPFLAGS_HAVE_VECTORCALL |
#elif defined(_Py_TPFLAGS_HAVE_VECTORCALL)
    _Py_TPFLAGS_HAVE_VECTORCALL |
#endif
#endif // CYTHON_METH_FASTCALL
#if PY_VERSION_HEX >= 0x030A0000
    Py_TPFLAGS_IMMUTABLETYPE |
#endif
    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC | Py_TPFLAGS_BASETYPE,
    __pyx_CyFunctionType_slots
};
static int __pyx_CyFunction_init(PyObject *module) {
    __pyx_mstatetype *mstate = __Pyx_PyModule_GetState(module);
    mstate->__pyx_CyFunctionType = __Pyx_FetchCommonTypeFromSpec(
        mstate->__pyx_CommonTypesMetaclassType, module, &__pyx_CyFunctionType_spec, NULL);
    if (unlikely(mstate->__pyx_CyFunctionType == NULL)) {
        return -1;
    }
    return 0;
}
static CYTHON_INLINE PyObject *__Pyx_CyFunction_InitDefaults(PyObject *func, PyTypeObject *defaults_type) {
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    m->defaults = PyObject_CallObject((PyObject*)defaults_type, NULL); // _PyObject_New(defaults_type);
    if (unlikely(!m->defaults))
        return NULL;
    return m->defaults;
}
static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsTuple(PyObject *func, PyObject *tuple) {
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    m->defaults_tuple = tuple;
    Py_INCREF(tuple);
}
static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsKwDict(PyObject *func, PyObject *dict) {
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    m->defaults_kwdict = dict;
    Py_INCREF(dict);
}
static CYTHON_INLINE void __Pyx_CyFunction_SetAnnotationsDict(PyObject *func, PyObject *dict) {
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    m->func_annotations = dict;
    Py_INCREF(dict);
}

/* CythonFunction */
static PyObject *__Pyx_CyFunction_New(PyMethodDef *ml, int flags, PyObject* qualname,
                                      PyObject *closure, PyObject *module, PyObject* globals, PyObject* code) {
    PyObject *op = __Pyx_CyFunction_Init(
        PyObject_GC_New(__pyx_CyFunctionObject, __pyx_mstate_global->__pyx_CyFunctionType),
        ml, flags, qualname, closure, module, globals, code
    );
    if (likely(op)) {
        PyObject_GC_Track(op);
    }
    return op;
}

/* PyDictVersioning */
#if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS
static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj) {
    PyObject *dict = Py_TYPE(obj)->tp_dict;
    return likely(dict) ? __PYX_GET_DICT_VERSION(dict) : 0;
}
static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj) {
    PyObject **dictptr = NULL;
    Py_ssize_t offset = Py_TYPE(obj)->tp_dictoffset;
    if (offset) {
#if CYTHON_COMPILING_IN_CPYTHON
        dictptr = (likely(offset > 0)) ? (PyObject **) ((char *)obj + offset) : _PyObject_GetDictPtr(obj);
#else
        dictptr = _PyObject_GetDictPtr(obj);
#endif
    }
    return (dictptr && *dictptr) ? __PYX_GET_DICT_VERSION(*dictptr) : 0;
}
static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version) {
    PyObject *dict = Py_TYPE(obj)->tp_dict;
    if (unlikely(!dict) || unlikely(tp_dict_version != __PYX_GET_DICT_VERSION(dict)))
        return 0;
    return obj_dict_version == __Pyx_get_object_dict_version(obj);
}
#endif

/* PyErrExceptionMatches */
#if CYTHON_FAST_THREAD_STATE
static int __Pyx_PyErr_ExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
    Py_ssize_t i, n;
    n = PyTuple_GET_SIZE(tuple);
    for (i=0; i<n; i++) {
        if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
    }
    for (i=0; i<n; i++) {
        if (__Pyx_PyErr_GivenExceptionMatches(exc_type, PyTuple_GET_ITEM(tuple, i))) return 1;
    }
    return 0;
}
static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err) {
    int result;
    PyObject *exc_type;
#if PY_VERSION_HEX >= 0x030C00A6
    PyObject *current_exception = tstate->current_exception;
    if (unlikely(!current_exception)) return 0;
    exc_type = (PyObject*) Py_TYPE(current_exception);
    if (exc_type == err) return 1;
#else
    exc_type = tstate->curexc_type;
    if (exc_type == err) return 1;
    if (unlikely(!exc_type)) return 0;
#endif
    #if CYTHON_AVOID_BORROWED_REFS
    Py_INCREF(exc_type);
    #endif
    if (unlikely(PyTuple_Check(err))) {
        result = __Pyx_PyErr_ExceptionMatchesTuple(exc_type, err);
    } else {
        result = __Pyx_PyErr_GivenExceptionMatches(exc_type, err);
    }
    #if CYTHON_AVOID_BORROWED_REFS
    Py_DECREF(exc_type);
    #endif
    return result;
}
#endif

/* PyErrFetchRestore */
#if CYTHON_FAST_THREAD_STATE
static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
#if PY_VERSION_HEX >= 0x030C00A6
    PyObject *tmp_value;
    assert(type == NULL || (value != NULL && type == (PyObject*) Py_TYPE(value)));
    if (value) {
        #if CYTHON_COMPILING_IN_CPYTHON
        if (unlikely(((PyBaseExceptionObject*) value)->traceback != tb))
        #endif
            PyException_SetTraceback(value, tb);
    }
    tmp_value = tstate->current_exception;
    tstate->current_exception = value;
    Py_XDECREF(tmp_value);
    Py_XDECREF(type);
    Py_XDECREF(tb);
#else
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    tmp_type = tstate->curexc_type;
    tmp_value = tstate->curexc_value;
    tmp_tb = tstate->curexc_traceback;
    tstate->curexc_type = type;
    tstate->curexc_value = value;
    tstate->curexc_traceback = tb;
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
#endif
}
static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
#if PY_VERSION_HEX >= 0x030C00A6
    PyObject* exc_value;
    exc_value = tstate->current_exception;
    tstate->current_exception = 0;
    *value = exc_value;
    *type = NULL;
    *tb = NULL;
    if (exc_value) {
        *type = (PyObject*) Py_TYPE(exc_value);
        Py_INCREF(*type);
        #if CYTHON_COMPILING_IN_CPYTHON
        *tb = ((PyBaseExceptionObject*) exc_value)->traceback;
        Py_XINCREF(*tb);
        #else
        *tb = PyException_GetTraceback(exc_value);
        #endif
    }
#else
    *type = tstate->curexc_type;
    *value = tstate->curexc_value;
    *tb = tstate->curexc_traceback;
    tstate->curexc_type = 0;
    tstate->curexc_value = 0;
    tstate->curexc_traceback = 0;
#endif
}
#endif

/* PyObjectGetAttrStrNoError */
#if __PYX_LIMITED_VERSION_HEX < 0x030d0000
static void __Pyx_PyObject_GetAttrStr_ClearAttributeError(void) {
    __Pyx_PyThreadState_declare
    __Pyx_PyThreadState_assign
    if (likely(__Pyx_PyErr_ExceptionMatches(PyExc_AttributeError)))
        __Pyx_PyErr_Clear();
}
#endif
static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStrNoError(PyObject* obj, PyObject* attr_name) {
    PyObject *result;
#if __PYX_LIMITED_VERSION_HEX >= 0x030d0000
    (void) PyObject_GetOptionalAttr(obj, attr_name, &result);
    return result;
#else
#if CYTHON_COMPILING_IN_CPYTHON && CYTHON_USE_TYPE_SLOTS
    PyTypeObject* tp = Py_TYPE(obj);
    if (likely(tp->tp_getattro == PyObject_GenericGetAttr)) {
        return _PyObject_GenericGetAttrWithDict(obj, attr_name, NULL, 1);
    }
#endif
    result = __Pyx_PyObject_GetAttrStr(obj, attr_name);
    if (unlikely(!result)) {
        __Pyx_PyObject_GetAttrStr_ClearAttributeError();
    }
    return result;
#endif
}

/* CLineInTraceback */
#if CYTHON_CLINE_IN_TRACEBACK && CYTHON_CLINE_IN_TRACEBACK_RUNTIME
static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line) {
    PyObject *use_cline;
    PyObject *ptype, *pvalue, *ptraceback;
#if CYTHON_COMPILING_IN_CPYTHON
    PyObject **cython_runtime_dict;
#endif
    CYTHON_MAYBE_UNUSED_VAR(tstate);
    if (unlikely(!__pyx_mstate_global->__pyx_cython_runtime)) {
        return c_line;
    }
    __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback);
#if CYTHON_COMPILING_IN_CPYTHON
    cython_runtime_dict = _PyObject_GetDictPtr(__pyx_mstate_global->__pyx_cython_runtime);
    if (likely(cython_runtime_dict)) {
        __Pyx_BEGIN_CRITICAL_SECTION(*cython_runtime_dict);
        __PYX_PY_DICT_LOOKUP_IF_MODIFIED(
            use_cline, *cython_runtime_dict,
            __Pyx_PyDict_GetItemStr(*cython_runtime_dict, __pyx_mstate_global->__pyx_n_u_cline_in_traceback))
        Py_XINCREF(use_cline);
        __Pyx_END_CRITICAL_SECTION();
    } else
#endif
    {
      PyObject *use_cline_obj = __Pyx_PyObject_GetAttrStrNoError(__pyx_mstate_global->__pyx_cython_runtime, __pyx_mstate_global->__pyx_n_u_cline_in_traceback);
      if (use_cline_obj) {
        use_cline = PyObject_Not(use_cline_obj) ? Py_False : Py_True;
        Py_INCREF(use_cline);
        Py_DECREF(use_cline_obj);
      } else {
        PyErr_Clear();
        use_cline = NULL;
      }
    }
    if (!use_cline) {
        c_line = 0;
        (void) PyObject_SetAttr(__pyx_mstate_global->__pyx_cython_runtime, __pyx_mstate_global->__pyx_n_u_cline_in_traceback, Py_False);
    }
    else if (use_cline == Py_False || (use_cline != Py_True && PyObject_Not(use_cline) != 0)) {
        c_line = 0;
    }
    Py_XDECREF(use_cline);
    __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback);
    return c_line;
}
#endif

/* CodeObjectCache */
static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {
    int start = 0, mid = 0, end = count - 1;
    if (end >= 0 && code_line > entries[end].code_line) {
        return count;
    }
    while (start < end) {
        mid = start + (end - start) / 2;
        if (code_line < entries[mid].code_line) {
            end = mid;
        } else if (code_line > entries[mid].code_line) {
             start = mid + 1;
        } else {
            return mid;
        }
    }
    if (code_line <= entries[mid].code_line) {
        return mid;
    } else {
        return mid + 1;
    }
}
static __Pyx_CachedCodeObjectType *__pyx__find_code_object(struct __Pyx_CodeObjectCache *code_cache, int code_line) {
    __Pyx_CachedCodeObjectType* code_object;
    int pos;
    if (unlikely(!code_line) || unlikely(!code_cache->entries)) {
        return NULL;
    }
    pos = __pyx_bisect_code_objects(code_cache->entries, code_cache->count, code_line);
    if (unlikely(pos >= code_cache->count) || unlikely(code_cache->entries[pos].code_line != code_line)) {
        return NULL;
    }
    code_object = code_cache->entries[pos].code_object;
    Py_INCREF(code_object);
    return code_object;
}
static __Pyx_CachedCodeObjectType *__pyx_find_code_object(int code_line) {
#if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING && !CYTHON_ATOMICS
    (void)__pyx__find_code_object;
    return NULL; // Most implementation should have atomics. But otherwise, don't make it thread-safe, just miss.
#else
    struct __Pyx_CodeObjectCache *code_cache = &__pyx_mstate_global->__pyx_code_cache;
#if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
    __pyx_nonatomic_int_type old_count = __pyx_atomic_incr_acq_rel(&code_cache->accessor_count);
    if (old_count < 0) {
        __pyx_atomic_decr_acq_rel(&code_cache->accessor_count);
        return NULL;
    }
#endif
    __Pyx_CachedCodeObjectType *result = __pyx__find_code_object(code_cache, code_line);
#if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
    __pyx_atomic_decr_acq_rel(&code_cache->accessor_count);
#endif
    return result;
#endif
}
static void __pyx__insert_code_object(struct __Pyx_CodeObjectCache *code_cache, int code_line, __Pyx_CachedCodeObjectType* code_object)
{
    int pos, i;
    __Pyx_CodeObjectCacheEntry* entries = code_cache->entries;
    if (unlikely(!code_line)) {
        return;
    }
    if (unlikely(!entries)) {
        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));
        if (likely(entries)) {
            code_cache->entries = entries;
            code_cache->max_count = 64;
            code_cache->count = 1;
            entries[0].code_line = code_line;
            entries[0].code_object = code_object;
            Py_INCREF(code_object);
        }
        return;
    }
    pos = __pyx_bisect_code_objects(code_cache->entries, code_cache->count, code_line);
    if ((pos < code_cache->count) && unlikely(code_cache->entries[pos].code_line == code_line)) {
        __Pyx_CachedCodeObjectType* tmp = entries[pos].code_object;
        entries[pos].code_object = code_object;
        Py_INCREF(code_object);
        Py_DECREF(tmp);
        return;
    }
    if (code_cache->count == code_cache->max_count) {
        int new_max = code_cache->max_count + 64;
        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(
            code_cache->entries, ((size_t)new_max) * sizeof(__Pyx_CodeObjectCacheEntry));
        if (unlikely(!entries)) {
            return;
        }
        code_cache->entries = entries;
        code_cache->max_count = new_max;
    }
    for (i=code_cache->count; i>pos; i--) {
        entries[i] = entries[i-1];
    }
    entries[pos].code_line = code_line;
    entries[pos].code_object = code_object;
    code_cache->count++;
    Py_INCREF(code_object);
}
static void __pyx_insert_code_object(int code_line, __Pyx_CachedCodeObjectType* code_object) {
#if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING && !CYTHON_ATOMICS
    (void)__pyx__insert_code_object;
    return; // Most implementation should have atomics. But otherwise, don't make it thread-safe, just fail.
#else
    struct __Pyx_CodeObjectCache *code_cache = &__pyx_mstate_global->__pyx_code_cache;
#if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
    __pyx_nonatomic_int_type expected = 0;
    if (!__pyx_atomic_int_cmp_exchange(&code_cache->accessor_count, &expected, INT_MIN)) {
        return;
    }
#endif
    __pyx__insert_code_object(code_cache, code_line, code_object);
#if CYTHON_COMPILING_IN_CPYTHON_FREETHREADING
    __pyx_atomic_sub(&code_cache->accessor_count, INT_MIN);
#endif
#endif
}

/* AddTraceback */
#include "compile.h"
#include "frameobject.h"
#include "traceback.h"
#if PY_VERSION_HEX >= 0x030b00a6 && !CYTHON_COMPILING_IN_LIMITED_API && !defined(PYPY_VERSION)
  #ifndef Py_BUILD_CORE
    #define Py_BUILD_CORE 1
  #endif
  #include "internal/pycore_frame.h"
#endif
#if CYTHON_COMPILING_IN_LIMITED_API
static PyObject *__Pyx_PyCode_Replace_For_AddTraceback(PyObject *code, PyObject *scratch_dict,
                                                       PyObject *firstlineno, PyObject *name) {
    PyObject *replace = NULL;
    if (unlikely(PyDict_SetItemString(scratch_dict, "co_firstlineno", firstlineno))) return NULL;
    if (unlikely(PyDict_SetItemString(scratch_dict, "co_name", name))) return NULL;
    replace = PyObject_GetAttrString(code, "replace");
    if (likely(replace)) {
        PyObject *result = PyObject_Call(replace, __pyx_mstate_global->__pyx_empty_tuple, scratch_dict);
        Py_DECREF(replace);
        return result;
    }
    PyErr_Clear();
    return NULL;
}
static void __Pyx_AddTraceback(const char *funcname, int c_line,
                               int py_line, const char *filename) {
    PyObject *code_object = NULL, *py_py_line = NULL, *py_funcname = NULL, *dict = NULL;
    PyObject *replace = NULL, *getframe = NULL, *frame = NULL;
    PyObject *exc_type, *exc_value, *exc_traceback;
    int success = 0;
    if (c_line) {
        (void) __pyx_cfilenm;
        (void) __Pyx_CLineForTraceback(__Pyx_PyThreadState_Current, c_line);
    }
    PyErr_Fetch(&exc_type, &exc_value, &exc_traceback);
    code_object = __pyx_find_code_object(c_line ? -c_line : py_line);
    if (!code_object) {
        code_object = Py_CompileString("_getframe()", filename, Py_eval_input);
        if (unlikely(!code_object)) goto bad;
        py_py_line = PyLong_FromLong(py_line);
        if (unlikely(!py_py_line)) goto bad;
        py_funcname = PyUnicode_FromString(funcname);
        if (unlikely(!py_funcname)) goto bad;
        dict = PyDict_New();
        if (unlikely(!dict)) goto bad;
        {
            PyObject *old_code_object = code_object;
            code_object = __Pyx_PyCode_Replace_For_AddTraceback(code_object, dict, py_py_line, py_funcname);
            Py_DECREF(old_code_object);
        }
        if (unlikely(!code_object)) goto bad;
        __pyx_insert_code_object(c_line ? -c_line : py_line, code_object);
    } else {
        dict = PyDict_New();
    }
    getframe = PySys_GetObject("_getframe");
    if (unlikely(!getframe)) goto bad;
    if (unlikely(PyDict_SetItemString(dict, "_getframe", getframe))) goto bad;
    frame = PyEval_EvalCode(code_object, dict, dict);
    if (unlikely(!frame) || frame == Py_None) goto bad;
    success = 1;
  bad:
    PyErr_Restore(exc_type, exc_value, exc_traceback);
    Py_XDECREF(code_object);
    Py_XDECREF(py_py_line);
    Py_XDECREF(py_funcname);
    Py_XDECREF(dict);
    Py_XDECREF(replace);
    if (success) {
        PyTraceBack_Here(
            (struct _frame*)frame);
    }
    Py_XDECREF(frame);
}
#else
static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
            const char *funcname, int c_line,
            int py_line, const char *filename) {
    PyCodeObject *py_code = NULL;
    PyObject *py_funcname = NULL;
    if (c_line) {
        py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
        if (!py_funcname) goto bad;
        funcname = PyUnicode_AsUTF8(py_funcname);
        if (!funcname) goto bad;
    }
    py_code = PyCode_NewEmpty(filename, funcname, py_line);
    Py_XDECREF(py_funcname);
    return py_code;
bad:
    Py_XDECREF(py_funcname);
    return NULL;
}
static void __Pyx_AddTraceback(const char *funcname, int c_line,
                               int py_line, const char *filename) {
    PyCodeObject *py_code = 0;
    PyFrameObject *py_frame = 0;
    PyThreadState *tstate = __Pyx_PyThreadState_Current;
    PyObject *ptype, *pvalue, *ptraceback;
    if (c_line) {
        c_line = __Pyx_CLineForTraceback(tstate, c_line);
    }
    py_code = __pyx_find_code_object(c_line ? -c_line : py_line);
    if (!py_code) {
        __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback);
        py_code = __Pyx_CreateCodeObjectForTraceback(
            funcname, c_line, py_line, filename);
        if (!py_code) {
            /* If the code object creation fails, then we should clear the
               fetched exception references and propagate the new exception */
            Py_XDECREF(ptype);
            Py_XDECREF(pvalue);
            Py_XDECREF(ptraceback);
            goto bad;
        }
        __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback);
        __pyx_insert_code_object(c_line ? -c_line : py_line, py_code);
    }
    py_frame = PyFrame_New(
        tstate,            /*PyThreadState *tstate,*/
        py_code,           /*PyCodeObject *code,*/
        __pyx_mstate_global->__pyx_d,    /*PyObject *globals,*/
        0                  /*PyObject *locals*/
    );
    if (!py_frame) goto bad;
    __Pyx_PyFrame_SetLineNumber(py_frame, py_line);
    PyTraceBack_Here(py_frame);
bad:
    Py_XDECREF(py_code);
    Py_XDECREF(py_frame);
}
#endif

/* FormatTypeName */
#if CYTHON_COMPILING_IN_LIMITED_API && __PYX_LIMITED_VERSION_HEX < 0x030d0000
static __Pyx_TypeName
__Pyx_PyType_GetFullyQualifiedName(PyTypeObject* tp)
{
    PyObject *module = NULL, *name = NULL, *result = NULL;
    #if __PYX_LIMITED_VERSION_HEX < 0x030b0000
    name = __Pyx_PyObject_GetAttrStr((PyObject *)tp,
                                               __pyx_mstate_global->__pyx_n_u_qualname);
    #else
    name = PyType_GetQualName(tp);
    #endif
    if (unlikely(name == NULL) || unlikely(!PyUnicode_Check(name))) goto bad;
    module = __Pyx_PyObject_GetAttrStr((PyObject *)tp,
                                               __pyx_mstate_global->__pyx_n_u_module);
    if (unlikely(module == NULL) || unlikely(!PyUnicode_Check(module))) goto bad;
    if (PyUnicode_CompareWithASCIIString(module, "builtins") == 0) {
        result = name;
        name = NULL;
        goto done;
    }
    result = PyUnicode_FromFormat("%U.%U", module, name);
    if (unlikely(result == NULL)) goto bad;
  done:
    Py_XDECREF(name);
    Py_XDECREF(module);
    return result;
  bad:
    PyErr_Clear();
    if (name) {
        result = name;
        name = NULL;
    } else {
        result = __Pyx_NewRef(__pyx_mstate_global->__pyx_kp_u_);
    }
    goto done;
}
#endif

/* PyObjectVectorCallKwBuilder */
#if CYTHON_VECTORCALL
static int __Pyx_VectorcallBuilder_AddArg(PyObject *key, PyObject *value, PyObject *builder, PyObject **args, int n) {
    (void)__Pyx_PyObject_FastCallDict;
    if (__Pyx_PyTuple_SET_ITEM(builder, n, key) != (0)) return -1;
    Py_INCREF(key);
    args[n] = value;
    return 0;
}
CYTHON_UNUSED static int __Pyx_VectorcallBuilder_AddArg_Check(PyObject *key, PyObject *value, PyObject *builder, PyObject **args, int n) {
    (void)__Pyx_VectorcallBuilder_AddArgStr;
    if (unlikely(!PyUnicode_Check(key))) {
        PyErr_SetString(PyExc_TypeError, "keywords must be strings");
        return -1;
    }
    return __Pyx_VectorcallBuilder_AddArg(key, value, builder, args, n);
}
static int __Pyx_VectorcallBuilder_AddArgStr(const char *key, PyObject *value, PyObject *builder, PyObject **args, int n) {
    PyObject *pyKey = PyUnicode_FromString(key);
    if (!pyKey) return -1;
    return __Pyx_VectorcallBuilder_AddArg(pyKey, value, builder, args, n);
}
#else // CYTHON_VECTORCALL
CYTHON_UNUSED static int __Pyx_VectorcallBuilder_AddArg_Check(PyObject *key, PyObject *value, PyObject *builder, CYTHON_UNUSED PyObject **args, CYTHON_UNUSED int n) {
    if (unlikely(!PyUnicode_Check(key))) {
        PyErr_SetString(PyExc_TypeError, "keywords must be strings");
        return -1;
    }
    return PyDict_SetItem(builder, key, value);
}
#endif

/* CIntToPy */
static CYTHON_INLINE PyObject* __Pyx_PyLong_From_long(long value) {
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wconversion"
#endif
    const long neg_one = (long) -1, const_zero = (long) 0;
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(long) < sizeof(long)) {
            return PyLong_FromLong((long) value);
        } else if (sizeof(long) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
#if defined(HAVE_LONG_LONG) && !CYTHON_COMPILING_IN_PYPY
        } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
#endif
        }
    } else {
        if (sizeof(long) <= sizeof(long)) {
            return PyLong_FromLong((long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
#endif
        }
    }
    {
        unsigned char *bytes = (unsigned char *)&value;
#if !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX >= 0x030d00A4
        if (is_unsigned) {
            return PyLong_FromUnsignedNativeBytes(bytes, sizeof(value), -1);
        } else {
            return PyLong_FromNativeBytes(bytes, sizeof(value), -1);
        }
#elif !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX < 0x030d0000
        int one = 1; int little = (int)*(unsigned char *)&one;
        return _PyLong_FromByteArray(bytes, sizeof(long),
                                     little, !is_unsigned);
#else
        int one = 1; int little = (int)*(unsigned char *)&one;
        PyObject *from_bytes, *result = NULL, *kwds = NULL;
        PyObject *py_bytes = NULL, *order_str = NULL;
        from_bytes = PyObject_GetAttrString((PyObject*)&PyLong_Type, "from_bytes");
        if (!from_bytes) return NULL;
        py_bytes = PyBytes_FromStringAndSize((char*)bytes, sizeof(long));
        if (!py_bytes) goto limited_bad;
        order_str = PyUnicode_FromString(little ? "little" : "big");
        if (!order_str) goto limited_bad;
        {
            PyObject *args[3+(CYTHON_VECTORCALL ? 1 : 0)] = { NULL, py_bytes, order_str };
            if (!is_unsigned) {
                kwds = __Pyx_MakeVectorcallBuilderKwds(1);
                if (!kwds) goto limited_bad;
                if (__Pyx_VectorcallBuilder_AddArgStr("signed", __Pyx_NewRef(Py_True), kwds, args+3, 0) < 0) goto limited_bad;
            }
            result = __Pyx_Object_Vectorcall_CallFromBuilder(from_bytes, args+1, 2 | __Pyx_PY_VECTORCALL_ARGUMENTS_OFFSET, kwds);
        }
        limited_bad:
        Py_XDECREF(kwds);
        Py_XDECREF(order_str);
        Py_XDECREF(py_bytes);
        Py_XDECREF(from_bytes);
        return result;
#endif
    }
}

/* CIntFromPyVerify */
#define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\
    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)
#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\
    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)
#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\
    {\
        func_type value = func_value;\
        if (sizeof(target_type) < sizeof(func_type)) {\
            if (unlikely(value != (func_type) (target_type) value)) {\
                func_type zero = 0;\
                if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\
                    return (target_type) -1;\
                if (is_unsigned && unlikely(value < zero))\
                    goto raise_neg_overflow;\
                else\
                    goto raise_overflow;\
            }\
        }\
        return (target_type) value;\
    }

/* CIntFromPy */
static CYTHON_INLINE long __Pyx_PyLong_As_long(PyObject *x) {
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wconversion"
#endif
    const long neg_one = (long) -1, const_zero = (long) 0;
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
    const int is_unsigned = neg_one > const_zero;
    if (unlikely(!PyLong_Check(x))) {
        long val;
        PyObject *tmp = __Pyx_PyNumber_Long(x);
        if (!tmp) return (long) -1;
        val = __Pyx_PyLong_As_long(tmp);
        Py_DECREF(tmp);
        return val;
    }
    if (is_unsigned) {
#if CYTHON_USE_PYLONG_INTERNALS
        if (unlikely(__Pyx_PyLong_IsNeg(x))) {
            goto raise_neg_overflow;
        } else if (__Pyx_PyLong_IsCompact(x)) {
            __PYX_VERIFY_RETURN_INT(long, __Pyx_compact_upylong, __Pyx_PyLong_CompactValueUnsigned(x))
        } else {
            const digit* digits = __Pyx_PyLong_Digits(x);
            assert(__Pyx_PyLong_DigitCount(x) > 1);
            switch (__Pyx_PyLong_DigitCount(x)) {
                case 2:
                    if ((8 * sizeof(long) > 1 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(long) >= 2 * PyLong_SHIFT)) {
                            return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if ((8 * sizeof(long) > 2 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(long) >= 3 * PyLong_SHIFT)) {
                            return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if ((8 * sizeof(long) > 3 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(long) >= 4 * PyLong_SHIFT)) {
                            return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                        }
                    }
                    break;
            }
        }
#endif
#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030C00A7
        if (unlikely(Py_SIZE(x) < 0)) {
            goto raise_neg_overflow;
        }
#else
        {
            int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
            if (unlikely(result < 0))
                return (long) -1;
            if (unlikely(result == 1))
                goto raise_neg_overflow;
        }
#endif
        if ((sizeof(long) <= sizeof(unsigned long))) {
            __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x))
#ifdef HAVE_LONG_LONG
        } else if ((sizeof(long) <= sizeof(unsigned PY_LONG_LONG))) {
            __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
#endif
        }
    } else {
#if CYTHON_USE_PYLONG_INTERNALS
        if (__Pyx_PyLong_IsCompact(x)) {
            __PYX_VERIFY_RETURN_INT(long, __Pyx_compact_pylong, __Pyx_PyLong_CompactValue(x))
        } else {
            const digit* digits = __Pyx_PyLong_Digits(x);
            assert(__Pyx_PyLong_DigitCount(x) > 1);
            switch (__Pyx_PyLong_SignedDigitCount(x)) {
                case -2:
                    if ((8 * sizeof(long) - 1 > 1 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(long) - 1 > 2 * PyLong_SHIFT)) {
                            return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if ((8 * sizeof(long) > 1 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(long) - 1 > 2 * PyLong_SHIFT)) {
                            return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if ((8 * sizeof(long) - 1 > 2 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(long) - 1 > 3 * PyLong_SHIFT)) {
                            return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if ((8 * sizeof(long) > 2 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(long) - 1 > 3 * PyLong_SHIFT)) {
                            return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if ((8 * sizeof(long) - 1 > 3 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(long) - 1 > 4 * PyLong_SHIFT)) {
                            return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if ((8 * sizeof(long) > 3 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(long) - 1 > 4 * PyLong_SHIFT)) {
                            return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
            }
        }
#endif
        if ((sizeof(long) <= sizeof(long))) {
            __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x))
#ifdef HAVE_LONG_LONG
        } else if ((sizeof(long) <= sizeof(PY_LONG_LONG))) {
            __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x))
#endif
        }
    }
    {
        long val;
        int ret = -1;
#if PY_VERSION_HEX >= 0x030d00A6 && !CYTHON_COMPILING_IN_LIMITED_API
        Py_ssize_t bytes_copied = PyLong_AsNativeBytes(
            x, &val, sizeof(val), Py_ASNATIVEBYTES_NATIVE_ENDIAN | (is_unsigned ? Py_ASNATIVEBYTES_UNSIGNED_BUFFER | Py_ASNATIVEBYTES_REJECT_NEGATIVE : 0));
        if (unlikely(bytes_copied == -1)) {
        } else if (unlikely(bytes_copied > (Py_ssize_t) sizeof(val))) {
            goto raise_overflow;
        } else {
            ret = 0;
        }
#elif PY_VERSION_HEX < 0x030d0000 && !(CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API) || defined(_PyLong_AsByteArray)
        int one = 1; int is_little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&val;
        ret = _PyLong_AsByteArray((PyLongObject *)x,
                                    bytes, sizeof(val),
                                    is_little, !is_unsigned);
#else
        PyObject *v;
        PyObject *stepval = NULL, *mask = NULL, *shift = NULL;
        int bits, remaining_bits, is_negative = 0;
        int chunk_size = (sizeof(long) < 8) ? 30 : 62;
        if (likely(PyLong_CheckExact(x))) {
            v = __Pyx_NewRef(x);
        } else {
            v = PyNumber_Long(x);
            if (unlikely(!v)) return (long) -1;
            assert(PyLong_CheckExact(v));
        }
        {
            int result = PyObject_RichCompareBool(v, Py_False, Py_LT);
            if (unlikely(result < 0)) {
                Py_DECREF(v);
                return (long) -1;
            }
            is_negative = result == 1;
        }
        if (is_unsigned && unlikely(is_negative)) {
            Py_DECREF(v);
            goto raise_neg_overflow;
        } else if (is_negative) {
            stepval = PyNumber_Invert(v);
            Py_DECREF(v);
            if (unlikely(!stepval))
                return (long) -1;
        } else {
            stepval = v;
        }
        v = NULL;
        val = (long) 0;
        mask = PyLong_FromLong((1L << chunk_size) - 1); if (unlikely(!mask)) goto done;
        shift = PyLong_FromLong(chunk_size); if (unlikely(!shift)) goto done;
        for (bits = 0; bits < (int) sizeof(long) * 8 - chunk_size; bits += chunk_size) {
            PyObject *tmp, *digit;
            long idigit;
            digit = PyNumber_And(stepval, mask);
            if (unlikely(!digit)) goto done;
            idigit = PyLong_AsLong(digit);
            Py_DECREF(digit);
            if (unlikely(idigit < 0)) goto done;
            val |= ((long) idigit) << bits;
            tmp = PyNumber_Rshift(stepval, shift);
            if (unlikely(!tmp)) goto done;
            Py_DECREF(stepval); stepval = tmp;
        }
        Py_DECREF(shift); shift = NULL;
        Py_DECREF(mask); mask = NULL;
        {
            long idigit = PyLong_AsLong(stepval);
            if (unlikely(idigit < 0)) goto done;
            remaining_bits = ((int) sizeof(long) * 8) - bits - (is_unsigned ? 0 : 1);
            if (unlikely(idigit >= (1L << remaining_bits)))
                goto raise_overflow;
            val |= ((long) idigit) << bits;
        }
        if (!is_unsigned) {
            if (unlikely(val & (((long) 1) << (sizeof(long) * 8 - 1))))
                goto raise_overflow;
            if (is_negative)
                val = ~val;
        }
        ret = 0;
    done:
        Py_XDECREF(shift);
        Py_XDECREF(mask);
        Py_XDECREF(stepval);
#endif
        if (unlikely(ret))
            return (long) -1;
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to long");
    return (long) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to long");
    return (long) -1;
}

/* CIntFromPy */
static CYTHON_INLINE int __Pyx_PyLong_As_int(PyObject *x) {
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wconversion"
#endif
    const int neg_one = (int) -1, const_zero = (int) 0;
#ifdef __Pyx_HAS_GCC_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
    const int is_unsigned = neg_one > const_zero;
    if (unlikely(!PyLong_Check(x))) {
        int val;
        PyObject *tmp = __Pyx_PyNumber_Long(x);
        if (!tmp) return (int) -1;
        val = __Pyx_PyLong_As_int(tmp);
        Py_DECREF(tmp);
        return val;
    }
    if (is_unsigned) {
#if CYTHON_USE_PYLONG_INTERNALS
        if (unlikely(__Pyx_PyLong_IsNeg(x))) {
            goto raise_neg_overflow;
        } else if (__Pyx_PyLong_IsCompact(x)) {
            __PYX_VERIFY_RETURN_INT(int, __Pyx_compact_upylong, __Pyx_PyLong_CompactValueUnsigned(x))
        } else {
            const digit* digits = __Pyx_PyLong_Digits(x);
            assert(__Pyx_PyLong_DigitCount(x) > 1);
            switch (__Pyx_PyLong_DigitCount(x)) {
                case 2:
                    if ((8 * sizeof(int) > 1 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(int) >= 2 * PyLong_SHIFT)) {
                            return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if ((8 * sizeof(int) > 2 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(int) >= 3 * PyLong_SHIFT)) {
                            return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if ((8 * sizeof(int) > 3 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(int) >= 4 * PyLong_SHIFT)) {
                            return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                        }
                    }
                    break;
            }
        }
#endif
#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030C00A7
        if (unlikely(Py_SIZE(x) < 0)) {
            goto raise_neg_overflow;
        }
#else
        {
            int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
            if (unlikely(result < 0))
                return (int) -1;
            if (unlikely(result == 1))
                goto raise_neg_overflow;
        }
#endif
        if ((sizeof(int) <= sizeof(unsigned long))) {
            __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x))
#ifdef HAVE_LONG_LONG
        } else if ((sizeof(int) <= sizeof(unsigned PY_LONG_LONG))) {
            __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
#endif
        }
    } else {
#if CYTHON_USE_PYLONG_INTERNALS
        if (__Pyx_PyLong_IsCompact(x)) {
            __PYX_VERIFY_RETURN_INT(int, __Pyx_compact_pylong, __Pyx_PyLong_CompactValue(x))
        } else {
            const digit* digits = __Pyx_PyLong_Digits(x);
            assert(__Pyx_PyLong_DigitCount(x) > 1);
            switch (__Pyx_PyLong_SignedDigitCount(x)) {
                case -2:
                    if ((8 * sizeof(int) - 1 > 1 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(int) - 1 > 2 * PyLong_SHIFT)) {
                            return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if ((8 * sizeof(int) > 1 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 2 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(int) - 1 > 2 * PyLong_SHIFT)) {
                            return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if ((8 * sizeof(int) - 1 > 2 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(int) - 1 > 3 * PyLong_SHIFT)) {
                            return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if ((8 * sizeof(int) > 2 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 3 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(int) - 1 > 3 * PyLong_SHIFT)) {
                            return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if ((8 * sizeof(int) - 1 > 3 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(int) - 1 > 4 * PyLong_SHIFT)) {
                            return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if ((8 * sizeof(int) > 3 * PyLong_SHIFT)) {
                        if ((8 * sizeof(unsigned long) > 4 * PyLong_SHIFT)) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if ((8 * sizeof(int) - 1 > 4 * PyLong_SHIFT)) {
                            return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
            }
        }
#endif
        if ((sizeof(int) <= sizeof(long))) {
            __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x))
#ifdef HAVE_LONG_LONG
        } else if ((sizeof(int) <= sizeof(PY_LONG_LONG))) {
            __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x))
#endif
        }
    }
    {
        int val;
        int ret = -1;
#if PY_VERSION_HEX >= 0x030d00A6 && !CYTHON_COMPILING_IN_LIMITED_API
        Py_ssize_t bytes_copied = PyLong_AsNativeBytes(
            x, &val, sizeof(val), Py_ASNATIVEBYTES_NATIVE_ENDIAN | (is_unsigned ? Py_ASNATIVEBYTES_UNSIGNED_BUFFER | Py_ASNATIVEBYTES_REJECT_NEGATIVE : 0));
        if (unlikely(bytes_copied == -1)) {
        } else if (unlikely(bytes_copied > (Py_ssize_t) sizeof(val))) {
            goto raise_overflow;
        } else {
            ret = 0;
        }
#elif PY_VERSION_HEX < 0x030d0000 && !(CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_LIMITED_API) || defined(_PyLong_AsByteArray)
        int one = 1; int is_little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&val;
        ret = _PyLong_AsByteArray((PyLongObject *)x,
                                    bytes, sizeof(val),
                                    is_little, !is_unsigned);
#else
        PyObject *v;
        PyObject *stepval = NULL, *mask = NULL, *shift = NULL;
        int bits, remaining_bits, is_negative = 0;
        int chunk_size = (sizeof(long) < 8) ? 30 : 62;
        if (likely(PyLong_CheckExact(x))) {
            v = __Pyx_NewRef(x);
        } else {
            v = PyNumber_Long(x);
            if (unlikely(!v)) return (int) -1;
            assert(PyLong_CheckExact(v));
        }
        {
            int result = PyObject_RichCompareBool(v, Py_False, Py_LT);
            if (unlikely(result < 0)) {
                Py_DECREF(v);
                return (int) -1;
            }
            is_negative = result == 1;
        }
        if (is_unsigned && unlikely(is_negative)) {
            Py_DECREF(v);
            goto raise_neg_overflow;
        } else if (is_negative) {
            stepval = PyNumber_Invert(v);
            Py_DECREF(v);
            if (unlikely(!stepval))
                return (int) -1;
        } else {
            stepval = v;
        }
        v = NULL;
        val = (int) 0;
        mask = PyLong_FromLong((1L << chunk_size) - 1); if (unlikely(!mask)) goto done;
        shift = PyLong_FromLong(chunk_size); if (unlikely(!shift)) goto done;
        for (bits = 0; bits < (int) sizeof(int) * 8 - chunk_size; bits += chunk_size) {
            PyObject *tmp, *digit;
            long idigit;
            digit = PyNumber_And(stepval, mask);
            if (unlikely(!digit)) goto done;
            idigit = PyLong_AsLong(digit);
            Py_DECREF(digit);
            if (unlikely(idigit < 0)) goto done;
            val |= ((int) idigit) << bits;
            tmp = PyNumber_Rshift(stepval, shift);
            if (unlikely(!tmp)) goto done;
            Py_DECREF(stepval); stepval = tmp;
        }
        Py_DECREF(shift); shift = NULL;
        Py_DECREF(mask); mask = NULL;
        {
            long idigit = PyLong_AsLong(stepval);
            if (unlikely(idigit < 0)) goto done;
            remaining_bits = ((int) sizeof(int) * 8) - bits - (is_unsigned ? 0 : 1);
            if (unlikely(idigit >= (1L << remaining_bits)))
                goto raise_overflow;
            val |= ((int) idigit) << bits;
        }
        if (!is_unsigned) {
            if (unlikely(val & (((int) 1) << (sizeof(int) * 8 - 1))))
                goto raise_overflow;
            if (is_negative)
                val = ~val;
        }
        ret = 0;
    done:
        Py_XDECREF(shift);
        Py_XDECREF(mask);
        Py_XDECREF(stepval);
#endif
        if (unlikely(ret))
            return (int) -1;
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to int");
    return (int) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to int");
    return (int) -1;
}

/* FastTypeChecks */
#if CYTHON_COMPILING_IN_CPYTHON
static int __Pyx_InBases(PyTypeObject *a, PyTypeObject *b) {
    while (a) {
        a = __Pyx_PyType_GetSlot(a, tp_base, PyTypeObject*);
        if (a == b)
            return 1;
    }
    return b == &PyBaseObject_Type;
}
static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b) {
    PyObject *mro;
    if (a == b) return 1;
    mro = a->tp_mro;
    if (likely(mro)) {
        Py_ssize_t i, n;
        n = PyTuple_GET_SIZE(mro);
        for (i = 0; i < n; i++) {
            if (PyTuple_GET_ITEM(mro, i) == (PyObject *)b)
                return 1;
        }
        return 0;
    }
    return __Pyx_InBases(a, b);
}
static CYTHON_INLINE int __Pyx_IsAnySubtype2(PyTypeObject *cls, PyTypeObject *a, PyTypeObject *b) {
    PyObject *mro;
    if (cls == a || cls == b) return 1;
    mro = cls->tp_mro;
    if (likely(mro)) {
        Py_ssize_t i, n;
        n = PyTuple_GET_SIZE(mro);
        for (i = 0; i < n; i++) {
            PyObject *base = PyTuple_GET_ITEM(mro, i);
            if (base == (PyObject *)a || base == (PyObject *)b)
                return 1;
        }
        return 0;
    }
    return __Pyx_InBases(cls, a) || __Pyx_InBases(cls, b);
}
static CYTHON_INLINE int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject *exc_type2) {
    if (exc_type1) {
        return __Pyx_IsAnySubtype2((PyTypeObject*)err, (PyTypeObject*)exc_type1, (PyTypeObject*)exc_type2);
    } else {
        return __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type2);
    }
}
static int __Pyx_PyErr_GivenExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
    Py_ssize_t i, n;
    assert(PyExceptionClass_Check(exc_type));
    n = PyTuple_GET_SIZE(tuple);
    for (i=0; i<n; i++) {
        if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
    }
    for (i=0; i<n; i++) {
        PyObject *t = PyTuple_GET_ITEM(tuple, i);
        if (likely(PyExceptionClass_Check(t))) {
            if (__Pyx_inner_PyErr_GivenExceptionMatches2(exc_type, NULL, t)) return 1;
        } else {
        }
    }
    return 0;
}
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject* exc_type) {
    if (likely(err == exc_type)) return 1;
    if (likely(PyExceptionClass_Check(err))) {
        if (likely(PyExceptionClass_Check(exc_type))) {
            return __Pyx_inner_PyErr_GivenExceptionMatches2(err, NULL, exc_type);
        } else if (likely(PyTuple_Check(exc_type))) {
            return __Pyx_PyErr_GivenExceptionMatchesTuple(err, exc_type);
        } else {
        }
    }
    return PyErr_GivenExceptionMatches(err, exc_type);
}
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *exc_type1, PyObject *exc_type2) {
    assert(PyExceptionClass_Check(exc_type1));
    assert(PyExceptionClass_Check(exc_type2));
    if (likely(err == exc_type1 || err == exc_type2)) return 1;
    if (likely(PyExceptionClass_Check(err))) {
        return __Pyx_inner_PyErr_GivenExceptionMatches2(err, exc_type1, exc_type2);
    }
    return (PyErr_GivenExceptionMatches(err, exc_type1) || PyErr_GivenExceptionMatches(err, exc_type2));
}
#endif

/* GetRuntimeVersion */
static unsigned long __Pyx_get_runtime_version(void) {
#if __PYX_LIMITED_VERSION_HEX >= 0x030b0000
    return Py_Version & ~0xFFUL;
#else
    static unsigned long __Pyx_cached_runtime_version = 0;
    if (__Pyx_cached_runtime_version == 0) {
        const char* rt_version = Py_GetVersion();
        unsigned long version = 0;
        unsigned long factor = 0x01000000UL;
        unsigned int digit = 0;
        int i = 0;
        while (factor) {
            while ('0' <= rt_version[i] && rt_version[i] <= '9') {
                digit = digit * 10 + (unsigned int) (rt_version[i] - '0');
                ++i;
            }
            version += factor * digit;
            if (rt_version[i] != '.')
                break;
            digit = 0;
            factor >>= 8;
            ++i;
        }
        __Pyx_cached_runtime_version = version;
    }
    return __Pyx_cached_runtime_version;
#endif
}

/* CheckBinaryVersion */
static int __Pyx_check_binary_version(unsigned long ct_version, unsigned long rt_version, int allow_newer) {
    const unsigned long MAJOR_MINOR = 0xFFFF0000UL;
    if ((rt_version & MAJOR_MINOR) == (ct_version & MAJOR_MINOR))
        return 0;
    if (likely(allow_newer && (rt_version & MAJOR_MINOR) > (ct_version & MAJOR_MINOR)))
        return 1;
    {
        char message[200];
        PyOS_snprintf(message, sizeof(message),
                      "compile time Python version %d.%d "
                      "of module '%.100s' "
                      "%s "
                      "runtime version %d.%d",
                       (int) (ct_version >> 24), (int) ((ct_version >> 16) & 0xFF),
                       __Pyx_MODULE_NAME,
                       (allow_newer) ? "was newer than" : "does not match",
                       (int) (rt_version >> 24), (int) ((rt_version >> 16) & 0xFF)
       );
        return PyErr_WarnEx(NULL, message, 1);
    }
}

/* FunctionExport */
static int __Pyx_ExportFunction(const char *name, void (*f)(void), const char *sig) {
    PyObject *d = 0;
    PyObject *cobj = 0;
    union {
        void (*fp)(void);
        void *p;
    } tmp;
    d = PyObject_GetAttrString(__pyx_m, "__pyx_capi__");
    if (!d) {
        PyErr_Clear();
        d = PyDict_New();
        if (!d)
            goto bad;
        Py_INCREF(d);
        if (PyModule_AddObject(__pyx_m, "__pyx_capi__", d) < 0)
            goto bad;
    }
    tmp.fp = f;
    cobj = PyCapsule_New(tmp.p, sig, 0);
    if (!cobj)
        goto bad;
    if (PyDict_SetItemString(d, name, cobj) < 0)
        goto bad;
    Py_DECREF(cobj);
    Py_DECREF(d);
    return 0;
bad:
    Py_XDECREF(cobj);
    Py_XDECREF(d);
    return -1;
}

/* NewCodeObj */
#if CYTHON_COMPILING_IN_LIMITED_API
    static PyObject* __Pyx__PyCode_New(int a, int p, int k, int l, int s, int f,
                                       PyObject *code, PyObject *c, PyObject* n, PyObject *v,
                                       PyObject *fv, PyObject *cell, PyObject* fn,
                                       PyObject *name, int fline, PyObject *lnos) {
        PyObject *exception_table = NULL;
        PyObject *types_module=NULL, *code_type=NULL, *result=NULL;
        #if __PYX_LIMITED_VERSION_HEX < 0x030b0000
        PyObject *version_info;
        PyObject *py_minor_version = NULL;
        #endif
        long minor_version = 0;
        PyObject *type, *value, *traceback;
        PyErr_Fetch(&type, &value, &traceback);
        #if __PYX_LIMITED_VERSION_HEX >= 0x030b0000
        minor_version = 11;
        #else
        if (!(version_info = PySys_GetObject("version_info"))) goto end;
        if (!(py_minor_version = PySequence_GetItem(version_info, 1))) goto end;
        minor_version = PyLong_AsLong(py_minor_version);
        Py_DECREF(py_minor_version);
        if (minor_version == -1 && PyErr_Occurred()) goto end;
        #endif
        if (!(types_module = PyImport_ImportModule("types"))) goto end;
        if (!(code_type = PyObject_GetAttrString(types_module, "CodeType"))) goto end;
        if (minor_version <= 7) {
            (void)p;
            result = PyObject_CallFunction(code_type, "iiiiiOOOOOOiOOO", a, k, l, s, f, code,
                          c, n, v, fn, name, fline, lnos, fv, cell);
        } else if (minor_version <= 10) {
            result = PyObject_CallFunction(code_type, "iiiiiiOOOOOOiOOO", a,p, k, l, s, f, code,
                          c, n, v, fn, name, fline, lnos, fv, cell);
        } else {
            if (!(exception_table = PyBytes_FromStringAndSize(NULL, 0))) goto end;
            result = PyObject_CallFunction(code_type, "iiiiiiOOOOOOOiOOOO", a,p, k, l, s, f, code,
                          c, n, v, fn, name, name, fline, lnos, exception_table, fv, cell);
        }
    end:
        Py_XDECREF(code_type);
        Py_XDECREF(exception_table);
        Py_XDECREF(types_module);
        if (type) {
            PyErr_Restore(type, value, traceback);
        }
        return result;
    }
#elif PY_VERSION_HEX >= 0x030B0000
  static PyCodeObject* __Pyx__PyCode_New(int a, int p, int k, int l, int s, int f,
                                         PyObject *code, PyObject *c, PyObject* n, PyObject *v,
                                         PyObject *fv, PyObject *cell, PyObject* fn,
                                         PyObject *name, int fline, PyObject *lnos) {
    PyCodeObject *result;
    result =
      #if PY_VERSION_HEX >= 0x030C0000
        PyUnstable_Code_NewWithPosOnlyArgs
      #else
        PyCode_NewWithPosOnlyArgs
      #endif
        (a, p, k, l, s, f, code, c, n, v, fv, cell, fn, name, name, fline, lnos, __pyx_mstate_global->__pyx_empty_bytes);
    #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030c00A1
    if (likely(result))
        result->_co_firsttraceable = 0;
    #endif
    return result;
  }
#elif PY_VERSION_HEX >= 0x030800B2 && !CYTHON_COMPILING_IN_PYPY
  #define __Pyx__PyCode_New(a, p, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
          PyCode_NewWithPosOnlyArgs(a, p, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
#else
  #define __Pyx__PyCode_New(a, p, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
          PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
#endif
static PyObject* __Pyx_PyCode_New(
        const __Pyx_PyCode_New_function_description descr,
        PyObject * const *varnames,
        PyObject *filename,
        PyObject *funcname,
        const char *line_table,
        PyObject *tuple_dedup_map
) {
    PyObject *code_obj = NULL, *varnames_tuple_dedup = NULL, *code_bytes = NULL, *line_table_bytes = NULL;
    Py_ssize_t var_count = (Py_ssize_t) descr.nlocals;
    PyObject *varnames_tuple = PyTuple_New(var_count);
    if (unlikely(!varnames_tuple)) return NULL;
    for (Py_ssize_t i=0; i < var_count; i++) {
        Py_INCREF(varnames[i]);
        if (__Pyx_PyTuple_SET_ITEM(varnames_tuple, i, varnames[i]) != (0)) goto done;
    }
    #if CYTHON_COMPILING_IN_LIMITED_API
    varnames_tuple_dedup = PyDict_GetItem(tuple_dedup_map, varnames_tuple);
    if (!varnames_tuple_dedup) {
        if (unlikely(PyDict_SetItem(tuple_dedup_map, varnames_tuple, varnames_tuple) < 0)) goto done;
        varnames_tuple_dedup = varnames_tuple;
    }
    #else
    varnames_tuple_dedup = PyDict_SetDefault(tuple_dedup_map, varnames_tuple, varnames_tuple);
    if (unlikely(!varnames_tuple_dedup)) goto done;
    #endif
    #if CYTHON_AVOID_BORROWED_REFS
    Py_INCREF(varnames_tuple_dedup);
    #endif
    if (__PYX_LIMITED_VERSION_HEX >= (0x030b0000) && line_table != NULL
        && !CYTHON_COMPILING_IN_GRAAL) {
        line_table_bytes = PyBytes_FromStringAndSize(line_table, descr.line_table_length);
        if (unlikely(!line_table_bytes)) goto done;
        Py_ssize_t code_len = (descr.line_table_length * 2 + 4) & ~3;
        code_bytes = PyBytes_FromStringAndSize(NULL, code_len);
        if (unlikely(!code_bytes)) goto done;
        char* c_code_bytes = PyBytes_AsString(code_bytes);
        if (unlikely(!c_code_bytes)) goto done;
        memset(c_code_bytes, 0, (size_t) code_len);
    }
    code_obj = (PyObject*) __Pyx__PyCode_New(
        (int) descr.argcount,
        (int) descr.num_posonly_args,
        (int) descr.num_kwonly_args,
        (int) descr.nlocals,
        0,
        (int) descr.flags,
        code_bytes ? code_bytes : __pyx_mstate_global->__pyx_empty_bytes,
        __pyx_mstate_global->__pyx_empty_tuple,
        __pyx_mstate_global->__pyx_empty_tuple,
        varnames_tuple_dedup,
        __pyx_mstate_global->__pyx_empty_tuple,
        __pyx_mstate_global->__pyx_empty_tuple,
        filename,
        funcname,
        (int) descr.first_line,
        (__PYX_LIMITED_VERSION_HEX >= (0x030b0000) && line_table_bytes) ? line_table_bytes : __pyx_mstate_global->__pyx_empty_bytes
    );
done:
    Py_XDECREF(code_bytes);
    Py_XDECREF(line_table_bytes);
    #if CYTHON_AVOID_BORROWED_REFS
    Py_XDECREF(varnames_tuple_dedup);
    #endif
    Py_DECREF(varnames_tuple);
    return code_obj;
}

/* InitStrings */
static int __Pyx_InitStrings(__Pyx_StringTabEntry const *t, PyObject **target, const char* const* encoding_names) {
    while (t->s) {
        PyObject *str;
        if (t->is_unicode) {
            if (t->intern) {
                str = PyUnicode_InternFromString(t->s);
            } else if (t->encoding) {
                str = PyUnicode_Decode(t->s, t->n - 1, encoding_names[t->encoding], NULL);
            } else {
                str = PyUnicode_FromStringAndSize(t->s, t->n - 1);
            }
        } else {
            str = PyBytes_FromStringAndSize(t->s, t->n - 1);
        }
        if (!str)
            return -1;
        *target = str;
        if (PyObject_Hash(str) == -1)
            return -1;
        ++t;
        ++target;
    }
    return 0;
}

#include <string.h>
static CYTHON_INLINE Py_ssize_t __Pyx_ssize_strlen(const char *s) {
    size_t len = strlen(s);
    if (unlikely(len > (size_t) PY_SSIZE_T_MAX)) {
        PyErr_SetString(PyExc_OverflowError, "byte string is too long");
        return -1;
    }
    return (Py_ssize_t) len;
}
static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
    Py_ssize_t len = __Pyx_ssize_strlen(c_str);
    if (unlikely(len < 0)) return NULL;
    return __Pyx_PyUnicode_FromStringAndSize(c_str, len);
}
static CYTHON_INLINE PyObject* __Pyx_PyByteArray_FromString(const char* c_str) {
    Py_ssize_t len = __Pyx_ssize_strlen(c_str);
    if (unlikely(len < 0)) return NULL;
    return PyByteArray_FromStringAndSize(c_str, len);
}
static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject* o) {
    Py_ssize_t ignore;
    return __Pyx_PyObject_AsStringAndSize(o, &ignore);
}
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_UTF8
static CYTHON_INLINE const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
    if (unlikely(__Pyx_PyUnicode_READY(o) == -1)) return NULL;
#if CYTHON_COMPILING_IN_LIMITED_API
    {
        const char* result;
        Py_ssize_t unicode_length;
        CYTHON_MAYBE_UNUSED_VAR(unicode_length); // only for __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
        #if __PYX_LIMITED_VERSION_HEX < 0x030A0000
        if (unlikely(PyArg_Parse(o, "s#", &result, length) < 0)) return NULL;
        #else
        result = PyUnicode_AsUTF8AndSize(o, length);
        #endif
        #if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
        unicode_length = PyUnicode_GetLength(o);
        if (unlikely(unicode_length < 0)) return NULL;
        if (unlikely(unicode_length != *length)) {
            PyUnicode_AsASCIIString(o);
            return NULL;
        }
        #endif
        return result;
    }
#else
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
    if (likely(PyUnicode_IS_ASCII(o))) {
        *length = PyUnicode_GET_LENGTH(o);
        return PyUnicode_AsUTF8(o);
    } else {
        PyUnicode_AsASCIIString(o);
        return NULL;
    }
#else
    return PyUnicode_AsUTF8AndSize(o, length);
#endif
#endif
}
#endif
static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_UTF8
    if (PyUnicode_Check(o)) {
        return __Pyx_PyUnicode_AsStringAndSize(o, length);
    } else
#endif
    if (PyByteArray_Check(o)) {
#if (CYTHON_ASSUME_SAFE_SIZE && CYTHON_ASSUME_SAFE_MACROS) || (CYTHON_COMPILING_IN_PYPY && (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE)))
        *length = PyByteArray_GET_SIZE(o);
        return PyByteArray_AS_STRING(o);
#else
        *length = PyByteArray_Size(o);
        if (*length == -1) return NULL;
        return PyByteArray_AsString(o);
#endif
    } else
    {
        char* result;
        int r = PyBytes_AsStringAndSize(o, &result, length);
        if (unlikely(r < 0)) {
            return NULL;
        } else {
            return result;
        }
    }
}
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
   int is_true = x == Py_True;
   if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
   else return PyObject_IsTrue(x);
}
static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject* x) {
    int retval;
    if (unlikely(!x)) return -1;
    retval = __Pyx_PyObject_IsTrue(x);
    Py_DECREF(x);
    return retval;
}
static PyObject* __Pyx_PyNumber_LongWrongResultType(PyObject* result) {
    __Pyx_TypeName result_type_name = __Pyx_PyType_GetFullyQualifiedName(Py_TYPE(result));
    if (PyLong_Check(result)) {
        if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1,
                "__int__ returned non-int (type " __Pyx_FMT_TYPENAME ").  "
                "The ability to return an instance of a strict subclass of int is deprecated, "
                "and may be removed in a future version of Python.",
                result_type_name)) {
            __Pyx_DECREF_TypeName(result_type_name);
            Py_DECREF(result);
            return NULL;
        }
        __Pyx_DECREF_TypeName(result_type_name);
        return result;
    }
    PyErr_Format(PyExc_TypeError,
                 "__int__ returned non-int (type " __Pyx_FMT_TYPENAME ")",
                 result_type_name);
    __Pyx_DECREF_TypeName(result_type_name);
    Py_DECREF(result);
    return NULL;
}
static CYTHON_INLINE PyObject* __Pyx_PyNumber_Long(PyObject* x) {
#if CYTHON_USE_TYPE_SLOTS
  PyNumberMethods *m;
#endif
  PyObject *res = NULL;
  if (likely(PyLong_Check(x)))
      return __Pyx_NewRef(x);
#if CYTHON_USE_TYPE_SLOTS
  m = Py_TYPE(x)->tp_as_number;
  if (likely(m && m->nb_int)) {
      res = m->nb_int(x);
  }
#else
  if (!PyBytes_CheckExact(x) && !PyUnicode_CheckExact(x)) {
      res = PyNumber_Long(x);
  }
#endif
  if (likely(res)) {
      if (unlikely(!PyLong_CheckExact(res))) {
          return __Pyx_PyNumber_LongWrongResultType(res);
      }
  }
  else if (!PyErr_Occurred()) {
      PyErr_SetString(PyExc_TypeError,
                      "an integer is required");
  }
  return res;
}
static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
  Py_ssize_t ival;
  PyObject *x;
  if (likely(PyLong_CheckExact(b))) {
    #if CYTHON_USE_PYLONG_INTERNALS
    if (likely(__Pyx_PyLong_IsCompact(b))) {
        return __Pyx_PyLong_CompactValue(b);
    } else {
      const digit* digits = __Pyx_PyLong_Digits(b);
      const Py_ssize_t size = __Pyx_PyLong_SignedDigitCount(b);
      switch (size) {
         case 2:
           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
             return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case -2:
           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
             return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case 3:
           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
             return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case -3:
           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
             return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case 4:
           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
             return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case -4:
           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
             return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
      }
    }
    #endif
    return PyLong_AsSsize_t(b);
  }
  x = PyNumber_Index(b);
  if (!x) return -1;
  ival = PyLong_AsSsize_t(x);
  Py_DECREF(x);
  return ival;
}
static CYTHON_INLINE Py_hash_t __Pyx_PyIndex_AsHash_t(PyObject* o) {
  if (sizeof(Py_hash_t) == sizeof(Py_ssize_t)) {
    return (Py_hash_t) __Pyx_PyIndex_AsSsize_t(o);
  } else {
    Py_ssize_t ival;
    PyObject *x;
    x = PyNumber_Index(o);
    if (!x) return -1;
    ival = PyLong_AsLong(x);
    Py_DECREF(x);
    return ival;
  }
}
static CYTHON_INLINE PyObject *__Pyx_Owned_Py_None(int b) {
    CYTHON_UNUSED_VAR(b);
    return __Pyx_NewRef(Py_None);
}
static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b) {
  return b ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False);
}
static CYTHON_INLINE PyObject * __Pyx_PyLong_FromSize_t(size_t ival) {
    return PyLong_FromSize_t(ival);
}
#if CYTHON_USE_PYLONG_INTERNALS
static CYTHON_INLINE int __Pyx_PyLong_CompactAsLong(PyObject *x, long *return_value) {
    if (unlikely(!__Pyx_PyLong_IsCompact(x)))
        return 0;
    Py_ssize_t value = __Pyx_PyLong_CompactValue(x);
    if ((sizeof(long) < sizeof(Py_ssize_t)) && unlikely(value != (long) value))
        return 0;
    *return_value = (long) value;
    return 1;
}
#endif


/* MultiPhaseInitModuleState */
#if CYTHON_PEP489_MULTI_PHASE_INIT && CYTHON_USE_MODULE_STATE
#ifndef CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
#if (CYTHON_COMPILING_IN_LIMITED_API || PY_VERSION_HEX >= 0x030C0000)
  #define CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE 1
#else
  #define CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE 0
#endif
#endif
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE && !CYTHON_ATOMICS
#error "Module state with PEP489 requires atomics. Currently that's one of\
 C11, C++11, gcc atomic intrinsics or MSVC atomic intrinsics"
#endif
#if !CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
#define __Pyx_ModuleStateLookup_Lock()
#define __Pyx_ModuleStateLookup_Unlock()
#elif !CYTHON_COMPILING_IN_LIMITED_API && PY_VERSION_HEX >= 0x030d0000
static PyMutex __Pyx_ModuleStateLookup_mutex = {0};
#define __Pyx_ModuleStateLookup_Lock() PyMutex_Lock(&__Pyx_ModuleStateLookup_mutex)
#define __Pyx_ModuleStateLookup_Unlock() PyMutex_Unlock(&__Pyx_ModuleStateLookup_mutex)
#elif defined(__cplusplus) && __cplusplus >= 201103L
#include <mutex>
static std::mutex __Pyx_ModuleStateLookup_mutex;
#define __Pyx_ModuleStateLookup_Lock() __Pyx_ModuleStateLookup_mutex.lock()
#define __Pyx_ModuleStateLookup_Unlock() __Pyx_ModuleStateLookup_mutex.unlock()
#elif defined(__STDC_VERSION__) && (__STDC_VERSION__ > 201112L) && !defined(__STDC_NO_THREADS__)
#include <threads.h>
static mtx_t __Pyx_ModuleStateLookup_mutex;
static once_flag __Pyx_ModuleStateLookup_mutex_once_flag = ONCE_FLAG_INIT;
static void __Pyx_ModuleStateLookup_initialize_mutex(void) {
    mtx_init(&__Pyx_ModuleStateLookup_mutex, mtx_plain);
}
#define __Pyx_ModuleStateLookup_Lock()\
  call_once(&__Pyx_ModuleStateLookup_mutex_once_flag, __Pyx_ModuleStateLookup_initialize_mutex);\
  mtx_lock(&__Pyx_ModuleStateLookup_mutex)
#define __Pyx_ModuleStateLookup_Unlock() mtx_unlock(&__Pyx_ModuleStateLookup_mutex)
#elif defined(HAVE_PTHREAD_H)
#include <pthread.h>
static pthread_mutex_t __Pyx_ModuleStateLookup_mutex = PTHREAD_MUTEX_INITIALIZER;
#define __Pyx_ModuleStateLookup_Lock() pthread_mutex_lock(&__Pyx_ModuleStateLookup_mutex)
#define __Pyx_ModuleStateLookup_Unlock() pthread_mutex_unlock(&__Pyx_ModuleStateLookup_mutex)
#elif defined(_WIN32)
#include <Windows.h>  // synchapi.h on its own doesn't work
static SRWLOCK __Pyx_ModuleStateLookup_mutex = SRWLOCK_INIT;
#define __Pyx_ModuleStateLookup_Lock() AcquireSRWLockExclusive(&__Pyx_ModuleStateLookup_mutex)
#define __Pyx_ModuleStateLookup_Unlock() ReleaseSRWLockExclusive(&__Pyx_ModuleStateLookup_mutex)
#else
#error "No suitable lock available for CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE.\
 Requires C standard >= C11, or C++ standard >= C++11,\
 or pthreads, or the Windows 32 API, or Python >= 3.13."
#endif
typedef struct {
    int64_t id;
    PyObject *module;
} __Pyx_InterpreterIdAndModule;
typedef struct {
    char interpreter_id_as_index;
    Py_ssize_t count;
    Py_ssize_t allocated;
    __Pyx_InterpreterIdAndModule table[1];
} __Pyx_ModuleStateLookupData;
#define __PYX_MODULE_STATE_LOOKUP_SMALL_SIZE 32
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
static __pyx_atomic_int_type __Pyx_ModuleStateLookup_read_counter = 0;
#endif
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
static __pyx_atomic_ptr_type __Pyx_ModuleStateLookup_data = 0;
#else
static __Pyx_ModuleStateLookupData* __Pyx_ModuleStateLookup_data = NULL;
#endif
static __Pyx_InterpreterIdAndModule* __Pyx_State_FindModuleStateLookupTableLowerBound(
        __Pyx_InterpreterIdAndModule* table,
        Py_ssize_t count,
        int64_t interpreterId) {
    __Pyx_InterpreterIdAndModule* begin = table;
    __Pyx_InterpreterIdAndModule* end = begin + count;
    if (begin->id == interpreterId) {
        return begin;
    }
    while ((end - begin) > __PYX_MODULE_STATE_LOOKUP_SMALL_SIZE) {
        __Pyx_InterpreterIdAndModule* halfway = begin + (end - begin)/2;
        if (halfway->id == interpreterId) {
            return halfway;
        }
        if (halfway->id < interpreterId) {
            begin = halfway;
        } else {
            end = halfway;
        }
    }
    for (; begin < end; ++begin) {
        if (begin->id >= interpreterId) return begin;
    }
    return begin;
}
static PyObject *__Pyx_State_FindModule(CYTHON_UNUSED void* dummy) {
    int64_t interpreter_id = PyInterpreterState_GetID(__Pyx_PyInterpreterState_Get());
    if (interpreter_id == -1) return NULL;
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
    __Pyx_ModuleStateLookupData* data = (__Pyx_ModuleStateLookupData*)__pyx_atomic_pointer_load_relaxed(&__Pyx_ModuleStateLookup_data);
    {
        __pyx_atomic_incr_acq_rel(&__Pyx_ModuleStateLookup_read_counter);
        if (likely(data)) {
            __Pyx_ModuleStateLookupData* new_data = (__Pyx_ModuleStateLookupData*)__pyx_atomic_pointer_load_acquire(&__Pyx_ModuleStateLookup_data);
            if (likely(data == new_data)) {
                goto read_finished;
            }
        }
        __pyx_atomic_decr_acq_rel(&__Pyx_ModuleStateLookup_read_counter);
        __Pyx_ModuleStateLookup_Lock();
        __pyx_atomic_incr_relaxed(&__Pyx_ModuleStateLookup_read_counter);
        data = (__Pyx_ModuleStateLookupData*)__pyx_atomic_pointer_load_relaxed(&__Pyx_ModuleStateLookup_data);
        __Pyx_ModuleStateLookup_Unlock();
    }
  read_finished:;
#else
    __Pyx_ModuleStateLookupData* data = __Pyx_ModuleStateLookup_data;
#endif
    __Pyx_InterpreterIdAndModule* found = NULL;
    if (unlikely(!data)) goto end;
    if (data->interpreter_id_as_index) {
        if (interpreter_id < data->count) {
            found = data->table+interpreter_id;
        }
    } else {
        found = __Pyx_State_FindModuleStateLookupTableLowerBound(
            data->table, data->count, interpreter_id);
    }
  end:
    {
        PyObject *result=NULL;
        if (found && found->id == interpreter_id) {
            result = found->module;
        }
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
        __pyx_atomic_decr_acq_rel(&__Pyx_ModuleStateLookup_read_counter);
#endif
        return result;
    }
}
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
static void __Pyx_ModuleStateLookup_wait_until_no_readers(void) {
    while (__pyx_atomic_load(&__Pyx_ModuleStateLookup_read_counter) != 0);
}
#else
#define __Pyx_ModuleStateLookup_wait_until_no_readers()
#endif
static int __Pyx_State_AddModuleInterpIdAsIndex(__Pyx_ModuleStateLookupData **old_data, PyObject* module, int64_t interpreter_id) {
    Py_ssize_t to_allocate = (*old_data)->allocated;
    while (to_allocate <= interpreter_id) {
        if (to_allocate == 0) to_allocate = 1;
        else to_allocate *= 2;
    }
    __Pyx_ModuleStateLookupData *new_data = *old_data;
    if (to_allocate != (*old_data)->allocated) {
         new_data = (__Pyx_ModuleStateLookupData *)realloc(
            *old_data,
            sizeof(__Pyx_ModuleStateLookupData)+(to_allocate-1)*sizeof(__Pyx_InterpreterIdAndModule));
        if (!new_data) {
            PyErr_NoMemory();
            return -1;
        }
        for (Py_ssize_t i = new_data->allocated; i < to_allocate; ++i) {
            new_data->table[i].id = i;
            new_data->table[i].module = NULL;
        }
        new_data->allocated = to_allocate;
    }
    new_data->table[interpreter_id].module = module;
    if (new_data->count < interpreter_id+1) {
        new_data->count = interpreter_id+1;
    }
    *old_data = new_data;
    return 0;
}
static void __Pyx_State_ConvertFromInterpIdAsIndex(__Pyx_ModuleStateLookupData *data) {
    __Pyx_InterpreterIdAndModule *read = data->table;
    __Pyx_InterpreterIdAndModule *write = data->table;
    __Pyx_InterpreterIdAndModule *end = read + data->count;
    for (; read<end; ++read) {
        if (read->module) {
            write->id = read->id;
            write->module = read->module;
            ++write;
        }
    }
    data->count = write - data->table;
    for (; write<end; ++write) {
        write->id = 0;
        write->module = NULL;
    }
    data->interpreter_id_as_index = 0;
}
static int __Pyx_State_AddModule(PyObject* module, CYTHON_UNUSED void* dummy) {
    int64_t interpreter_id = PyInterpreterState_GetID(__Pyx_PyInterpreterState_Get());
    if (interpreter_id == -1) return -1;
    int result = 0;
    __Pyx_ModuleStateLookup_Lock();
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
    __Pyx_ModuleStateLookupData *old_data = (__Pyx_ModuleStateLookupData *)
            __pyx_atomic_pointer_exchange(&__Pyx_ModuleStateLookup_data, 0);
#else
    __Pyx_ModuleStateLookupData *old_data = __Pyx_ModuleStateLookup_data;
#endif
    __Pyx_ModuleStateLookupData *new_data = old_data;
    if (!new_data) {
        new_data = (__Pyx_ModuleStateLookupData *)calloc(1, sizeof(__Pyx_ModuleStateLookupData));
        if (!new_data) {
            result = -1;
            PyErr_NoMemory();
            goto end;
        }
        new_data->allocated = 1;
        new_data->interpreter_id_as_index = 1;
    }
    __Pyx_ModuleStateLookup_wait_until_no_readers();
    if (new_data->interpreter_id_as_index) {
        if (interpreter_id < __PYX_MODULE_STATE_LOOKUP_SMALL_SIZE) {
            result = __Pyx_State_AddModuleInterpIdAsIndex(&new_data, module, interpreter_id);
            goto end;
        }
        __Pyx_State_ConvertFromInterpIdAsIndex(new_data);
    }
    {
        Py_ssize_t insert_at = 0;
        {
            __Pyx_InterpreterIdAndModule* lower_bound = __Pyx_State_FindModuleStateLookupTableLowerBound(
                new_data->table, new_data->count, interpreter_id);
            assert(lower_bound);
            insert_at = lower_bound - new_data->table;
            if (unlikely(insert_at < new_data->count && lower_bound->id == interpreter_id)) {
                lower_bound->module = module;
                goto end;  // already in table, nothing more to do
            }
        }
        if (new_data->count+1 >= new_data->allocated) {
            Py_ssize_t to_allocate = (new_data->count+1)*2;
            new_data =
                (__Pyx_ModuleStateLookupData*)realloc(
                    new_data,
                    sizeof(__Pyx_ModuleStateLookupData) +
                    (to_allocate-1)*sizeof(__Pyx_InterpreterIdAndModule));
            if (!new_data) {
                result = -1;
                new_data = old_data;
                PyErr_NoMemory();
                goto end;
            }
            new_data->allocated = to_allocate;
        }
        ++new_data->count;
        int64_t last_id = interpreter_id;
        PyObject *last_module = module;
        for (Py_ssize_t i=insert_at; i<new_data->count; ++i) {
            int64_t current_id = new_data->table[i].id;
            new_data->table[i].id = last_id;
            last_id = current_id;
            PyObject *current_module = new_data->table[i].module;
            new_data->table[i].module = last_module;
            last_module = current_module;
        }
    }
  end:
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
    __pyx_atomic_pointer_exchange(&__Pyx_ModuleStateLookup_data, new_data);
#else
    __Pyx_ModuleStateLookup_data = new_data;
#endif
    __Pyx_ModuleStateLookup_Unlock();
    return result;
}
static int __Pyx_State_RemoveModule(CYTHON_UNUSED void* dummy) {
    int64_t interpreter_id = PyInterpreterState_GetID(__Pyx_PyInterpreterState_Get());
    if (interpreter_id == -1) return -1;
    __Pyx_ModuleStateLookup_Lock();
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
    __Pyx_ModuleStateLookupData *data = (__Pyx_ModuleStateLookupData *)
            __pyx_atomic_pointer_exchange(&__Pyx_ModuleStateLookup_data, 0);
#else
    __Pyx_ModuleStateLookupData *data = __Pyx_ModuleStateLookup_data;
#endif
    if (data->interpreter_id_as_index) {
        if (interpreter_id < data->count) {
            data->table[interpreter_id].module = NULL;
        }
        goto done;
    }
    {
        __Pyx_ModuleStateLookup_wait_until_no_readers();
        __Pyx_InterpreterIdAndModule* lower_bound = __Pyx_State_FindModuleStateLookupTableLowerBound(
            data->table, data->count, interpreter_id);
        if (!lower_bound) goto done;
        if (lower_bound->id != interpreter_id) goto done;
        __Pyx_InterpreterIdAndModule *end = data->table+data->count;
        for (;lower_bound<end-1; ++lower_bound) {
            lower_bound->id = (lower_bound+1)->id;
            lower_bound->module = (lower_bound+1)->module;
        }
    }
    --data->count;
    if (data->count == 0) {
        free(data);
        data = NULL;
    }
  done:
#if CYTHON_MODULE_STATE_LOOKUP_THREAD_SAFE
    __pyx_atomic_pointer_exchange(&__Pyx_ModuleStateLookup_data, data);
#else
    __Pyx_ModuleStateLookup_data = data;
#endif
    __Pyx_ModuleStateLookup_Unlock();
    return 0;
}
#endif

/* #### Code section: utility_code_pragmas_end ### */
#ifdef _MSC_VER
#pragma warning( pop )
#endif



/* #### Code section: end ### */
#endif /* Py_PYTHON_H */
