"""
  This code can be loaded, or copied and paste using cpaste, into Sage.
  It will load the data associated to the BMF, including
  the field, level, and Hecke and Atkin-Lehner eigenvalue data (if known).
"""

P = PolynomialRing(QQ, "x")
x = P.gen()
g = P([1, 0, 1])
F = NumberField(g, "i")
i = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((34225, i + 28632))

primes_array = [
(i+1,),(-i-2,),(2*i+1,),(3,),(-3*i-2,),(2*i+3,),(i+4,),(i-4,),(-2*i+5,),(2*i+5,),(i+6,),(i-6,),(-5*i-4,),(4*i+5,),(7,),(-2*i+7,),(2*i+7,),(-6*i-5,),(5*i+6,),(-3*i-8,),(3*i-8,),(-5*i+8,),(-8*i+5,),(-4*i+9,),(4*i+9,),(i+10,),(i-10,),(-3*i+10,),(3*i+10,),(-8*i-7,),(7*i+8,),(11,),(-4*i-11,),(4*i-11,),(10*i-7,),(7*i-10,),(-6*i-11,),(6*i-11,),(-2*i+13,),(2*i+13,),(-10*i-9,),(9*i+10,),(7*i-12,),(7*i+12,),(i+14,),(i-14,),(-2*i+15,),(2*i+15,),(-8*i-13,),(-8*i+13,),(-4*i-15,),(4*i-15,),(i+16,),(i-16,),(13*i-10,),(10*i-13,),(-9*i+14,),(-14*i+9,),(-5*i+16,),(5*i+16,),(-2*i+17,),(2*i+17,),(-13*i-12,),(12*i+13,),(-11*i+14,),(-14*i+11,),(9*i-16,),(9*i+16,),(-5*i+18,),(-5*i-18,),(-8*i+17,),(8*i+17,),(19,),(-7*i+18,),(-7*i-18,),(10*i-17,),(10*i+17,),(-6*i+19,),(6*i+19,),(i+20,),(i-20,),(-3*i-20,),(3*i-20,),(-15*i-14,),(14*i+15,),(-17*i-12,),(12*i+17,),(-7*i-20,),(7*i-20,),(-4*i+21,),(4*i+21,),(-10*i-19,),(10*i-19,),(5*i+22,),(5*i-22,),(11*i-20,),(11*i+20,),(23,),(-10*i+21,),(10*i+21,),(-14*i+19,),(-19*i+14,),(-13*i+20,),(-20*i+13,),(i+24,),(i-24,),(-8*i-23,),(8*i-23,),(-5*i-24,),(5*i-24,),(-18*i-17,),(17*i+18,),(19*i-16,),(16*i-19,),(-4*i+25,),(4*i+25,),(13*i-22,),(13*i+22,),(-6*i+25,),(6*i+25,),(-12*i-23,),(12*i-23,),(i+26,),(i-26,),(-5*i+26,),(5*i+26,),(22*i-15,),(15*i-22,),(-2*i+27,),(2*i+27,),(-9*i-26,),(9*i-26,),(-20*i-19,),(19*i+20,),(-12*i+25,),(12*i+25,),(-22*i-17,),(17*i+22,),(-11*i+26,),(-11*i-26,),(-5*i+28,),(-5*i-28,),(-14*i-25,),(-14*i+25,),(10*i-27,),(10*i+27,),(-18*i-23,),(23*i+18,),(-4*i+29,),(4*i+29,),(-6*i-29,),(6*i-29,),(16*i+25,),(-25*i-16,),(-20*i+23,),(-23*i+20,),(-19*i+24,),(-24*i+19,),(-10*i-29,),(10*i-29,),(13*i+28,),(13*i-28,),(31,),(-4*i-31,),(4*i-31,),(-6*i+31,),(6*i+31,),(15*i-28,),(15*i+28,),(-23*i-22,),(22*i+23,),(-11*i-30,),(-11*i+30,),(-3*i-32,),(3*i-32,),(5*i+32,),(5*i-32,),(-10*i+31,),(10*i+31,),(13*i+30,),(13*i-30,),(-2*i+33,),(2*i+33,),(16*i-29,),(16*i+29,),(25*i-22,),(22*i-25,),(26*i-21,),(21*i-26,),(-20*i+27,),(-27*i+20,),(-8*i+33,),(8*i+33,),(-5*i-34,),(5*i-34,),(13*i+32,),(13*i-32,),(-25*i-24,),(24*i+25,),(-27*i-22,),(22*i+27,),(-16*i-31,),(16*i-31,),(-2*i+35,),(2*i+35,),(9*i-34,),(9*i+34,),(15*i+32,),(15*i-32,),(-11*i+34,),(11*i+34,),(-8*i+35,),(-8*i-35,),(i+36,),(i-36,),(-26*i-25,),(25*i+26,),(-5*i+36,),(5*i+36,),(20*i+31,),(-31*i-20,),(-2*i+37,),(2*i+37,),(-15*i+34,),(-15*i-34,),(28*i-25,),(25*i-28,),(-30*i-23,),(23*i+30,),(-8*i-37,),(-8*i+37,),(-3*i-38,),(3*i-38,),(16*i+35,),(16*i-35,),(-20*i-33,),(-20*i+33,),(7*i+38,),(7*i-38,),(-18*i-35,),(18*i-35,),(-23*i-32,),(32*i+23,),(21*i+34,),(-21*i+34,),(i+40,),(i-40,),(-3*i+40,),(3*i+40,),(-13*i-38,),(13*i-38,),(-10*i-39,),(10*i-39,),(31*i-26,),(26*i-31,),(19*i-36,),(19*i+36,),(-15*i+38,),(-15*i-38,),(-18*i+37,),(18*i+37,),(-4*i+41,),(4*i+41,),(22*i+35,),(-35*i-22,),(-11*i-40,),(-11*i+40,),(17*i+38,),(17*i-38,),(-30*i-29,),(29*i+30,),(-32*i-27,),(27*i+32,),(-16*i+39,),(16*i+39,),(5*i+42,),(5*i-42,),(-35*i-24,),(24*i+35,),(43,),(-31*i-30,),(30*i+31,),(-28*i-33,),(33*i+28,),(-14*i-41,),(14*i-41,),(-17*i+40,),(-17*i-40,),(-26*i+35,),(-35*i+26,),(-8*i+43,),(-8*i-43,),(13*i+42,),(13*i-42,),(10*i+43,),(10*i-43,),(-23*i-38,),(-23*i+38,),(12*i+43,),(-12*i+43,),(-29*i+34,),(-34*i+29,),(-9*i-44,),(9*i-44,),(-2*i+45,),(2*i+45,),(17*i+42,),(17*i-42,),(-25*i+38,),(-38*i+25,),(-20*i+41,),(20*i+41,),(-8*i-45,),(-8*i+45,),(-33*i-32,),(32*i+33,),(-23*i-40,),(-23*i+40,),(36*i-29,),(29*i-36,),(-5*i+46,),(5*i+46,),(37*i-28,),(28*i-37,),(-15*i-44,),(15*i-44,),(47,),(-2*i+47,),(2*i+47,),(-14*i+45,),(-14*i-45,),(11*i+46,),(11*i-46,),(-37*i-30,),(30*i+37,),(-8*i-47,),(8*i-47,),(16*i-45,),(16*i+45,),(-23*i-42,),(-23*i+42,),(19*i+44,),(19*i-44,),(10*i-47,),(10*i+47,),(-22*i-43,),(22*i-43,),(-15*i+46,),(15*i+46,),(41*i+26,),(-26*i-41,),(21*i+44,),(21*i-44,),(-35*i-34,),(34*i+35,),(25*i-42,),(25*i+42,),(-37*i-32,),(32*i+37,),(-4*i+49,),(4*i+49,),(-6*i+49,),(6*i+49,),(40*i+29,),(-29*i-40,),(13*i-48,),(13*i+48,),(-19*i-46,),(19*i-46,),(-36*i-35,),(35*i+36,),(-7*i+50,),(7*i+50,),(21*i+46,),(21*i-46,),(-17*i-48,),(-17*i+48,),(-20*i+47,),(-20*i-47,),(-4*i-51,),(4*i-51,),(-11*i+50,),(-11*i-50,),(28*i+43,),(-43*i-28,),(-16*i+49,),(16*i+49,),(-34*i+39,),(-39*i+34,),(33*i+40,),(-40*i-33,),(22*i+47,),(22*i-47,),(-3*i+52,),(3*i+52,),(5*i+52,),(5*i-52,),(25*i-46,),(25*i+46,),(-43*i-30,),(30*i+43,),(7*i+52,),(7*i-52,),(-29*i+44,),(-44*i+29,),(-17*i-50,),(17*i-50,),(-14*i-51,),(-14*i+51,),(-20*i+49,),(20*i+49,),(23*i+48,),(23*i-48,),(-34*i+41,),(-41*i+34,),(16*i+51,),(16*i-51,),(19*i-50,),(-19*i-50,),(-31*i+44,),(-44*i+31,),(10*i+53,),(10*i-53,),(i+54,),(i-54,),(-12*i+53,),(12*i+53,),(-29*i+46,),(-46*i+29,),(40*i-37,),(37*i-40,),(20*i+51,),(-20*i+51,),(-11*i-54,),(11*i-54,),(-4*i-55,),(4*i-55,),(-45*i-32,),(32*i+45,),(-6*i+55,),(6*i+55,),(-8*i-55,),(8*i-55,),(30*i+47,),(-47*i-30,),(-40*i-39,),(39*i+40,),(i+56,),(i-56,),(12*i+55,),(-12*i+55,),(45*i-34,),(34*i-45,),(-20*i-53,),(-20*i+53,),(9*i+56,),(9*i-56,),(-14*i-55,),(14*i-55,),(-27*i-50,),(-27*i+50,),(-2*i+57,),(-2*i-57,),(-11*i+56,),(11*i+56,),(30*i+49,),(-30*i+49,),(-8*i+57,),(8*i+57,),(25*i+52,),(25*i-52,),(-15*i-56,),(-15*i+56,),(-3*i+58,),(3*i+58,),(-5*i+58,),(-5*i-58,),(7*i+58,),(7*i-58,),(27*i-52,),(27*i+52,),(43*i-40,),(40*i-43,),(-39*i+44,),(-44*i+39,),(-50*i+31,),(-31*i+50,),(-45*i-38,),(38*i+45,),(59,),(-6*i-59,),(6*i-59,),(35*i+48,),(-48*i-35,),(13*i+58,),(13*i-58,),(25*i+54,),(25*i-54,),(-34*i-49,),(49*i+34,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [-2, 0, -1, -3, -1, -3, -4, -5, 5, -1, -9, 0, -5, -8, -9, -11, 1, -3, 0, 0, -4, -1, 8, -7, -9, -5, -11, 4, 19, 13, -11, 4, -1, -17, -11, 11, 20, -21, -4, 1, 15, -12, -15, 17, 7, 8, 9, 0, -1, -19, -5, -7, -1, -28, 4, -16, -21, 14, 4, -1, -1, -14, -9, 16, 29, 20, -2, 3, 25, -4, -4, -11, 23, -7, 0, 20, -19, 13, -3, 22, -16, 14, -25, 23, 7, 5, -9, -23, -11, 3, -34, -13, 19, 5, -32, -7, -25, -36, -3, 21, -25, 16, 43, 25, 5, -15, -11, 35, -39, -36, -46, -27, 11, 29, -10, -31, -11, -16, 12, 9, -37, 39, 13, 13, 43, 41, 24, 12, -15, -41, -18, -1, -11, -44, 28, -20, -44, -11, -23, 43, 23, 5, -13, -37, -17, -53, -9, -16, 5, 19, 21, 1, -44, 49, -16, 1, 49, -30, 7, 16, -35, 11, -32, -61, -11, -15, 43, 33, 27, -31, -13, 37, -16, -37, 0, 37, -17, -8, 55, 63, 48, 47, 48, 7, -8, 35, 31, 5, -6, 55, -62, 27, 31, -50, 43, 52, -37, 12, -33, 24, 4, 61, 17, 22, -56, -21, -26, -6, -45, -11, -32, -25, 5, -57, -37, -25, 37, -48, 36, -25, -35, -1, 71, 35, -55, 13, 8, -51, 51, -34, -56, 57, 25, 11, -1, -41, -37, -56, -23, 13, 10, -7, -73, -45, 55, -29, -53, -5, 79, -53, -19, 39, 63, -61, -16, 9, -55, -15, -39, -3, -73, -41, 79, 41, 40, 55, -40, 28, -40, -47, 71, -61, 45, -57, 25, 65, -25, 9, 54, 18, 56, -52, 17, 57, 4, -14, -47, -74, 20, -56, 29, 41, -21, -16, -28, -35, -41, 44, 61, -60, -56, -8, 17, 36, 21, -57, 71, 24, 2, -83, -13, -25, -33, 3, -88, -69, -71, 31, -7, 12, -37, -23, 1, -17, -80, 23, 36, -91, -41, 11, -43, 52, -31, 3, 21, -11, -86, -16, -89, 69, -25, -14, 67, 23, 17, -44, 17, 65, -19, 13, 29, 45, -76, -25, -65, -17, -61, -37, -37, 73, -52, 25, -12, -82, 14, -21, -29, -77, 68, -12, 45, 100, -79, -1, 12, 3, -53, -16, 5, -92, 96, -19, 7, 26, 32, 32, 17, 11, -45, 25, 20, -76, 16, -39, -25, 92, -23, 29, 20, 48, 84, 77, 20, -41, 13, -11, -35, -29, -33, -29, -83, 40, 51, -11, -88, 48, 76, 38, 71, 8, -56, 83, 17, 100, 78, 45, -80, 59, -35, -25, -83, 12, 27, -29, -45, -47, -68, 72, 15, 39, -27, -4, 71, 111, -33, -27, 21, 5, 1, 59, 35, -100, 32, 77, -89, -6, -41, -17, -28, 16, -40, 84, 61, -62, -82, 31, -1, 19, 12, -65, -25, -49, 97, -29, -63, -71, 64, -62, 109, 44, -36, 101, 65, -9, 107, 8, 91, 63, -12, 79, 39, 32, 104, 80, -7, 95, 81, -15, 34, 13]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal((-i - 2,))] = -1
AL_eigenvalues[ZF.ideal((i - 6,))] = 1

# EXAMPLE:
# pp = ZF.ideal(2).factor()[0][0]
# hecke_eigenvalues[pp]