"""
  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((65, i + 47))

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,),(-10*i-59,),(10*i-59,),(28*i-53,),(28*i+53,),(-43*i-42,),(42*i+43,),(-41*i+44,),(-44*i+41,),(-39*i-46,),(46*i+39,),(-37*i-48,),(48*i+37,),(-14*i+59,),(-14*i-59,),(36*i+49,),(-49*i-36,),(-26*i+55,),(-26*i-55,),(-30*i-53,),(30*i-53,),(22*i+57,),(-22*i+57,),(25*i+56,),(25*i-56,),(13*i-60,),(-13*i-60,),(52*i+33,),(-33*i-52,),(46*i-41,),(41*i-46,),(-10*i+61,),(10*i+61,),(-32*i-53,),(-32*i+53,),(-3*i-62,),(3*i-62,),(-31*i-54,),(-31*i+54,),(-20*i-59,),(20*i-59,),(-17*i+60,),(-17*i-60,),(-14*i+61,),(-14*i-61,),(52*i-35,),(35*i-52,),(25*i+58,),(25*i-58,),(-49*i-40,),(40*i+49,),(13*i-62,),(13*i+62,),(-39*i-50,),(50*i+39,),(-32*i+55,),(32*i+55,),(-24*i+59,),(24*i+59,),(-52*i-37,),(37*i+52,),(-27*i+58,),(-27*i-58,),(23*i-60,),(-23*i-60,),(-17*i-62,),(-17*i+62,),(-43*i-48,),(48*i+43,),(26*i+59,),(-26*i+59,),(-9*i+64,),(9*i+64,),(51*i+40,),(-40*i-51,),(11*i-64,),(11*i+64,),(-2*i+65,),(-2*i-65,),(-4*i+65,),(4*i+65,),(-38*i-53,),(53*i+38,),(-6*i-65,),(6*i-65,),(-32*i+57,),(32*i+57,),(-8*i+65,),(8*i+65,),(24*i+61,),(-24*i+61,),(-44*i+49,),(-49*i+44,),(50*i-43,),(43*i-50,),(i+66,),(i-66,),(-23*i-62,),(23*i-62,),(-26*i+61,),(-26*i-61,),(53*i-40,),(40*i-53,),(-14*i-65,),(-14*i+65,),(29*i+60,),(29*i-60,),(19*i+64,),(-19*i+64,),(-16*i+65,),(16*i+65,),(67,),(-2*i+67,),(-2*i-67,),(-48*i-47,),(47*i+48,),(49*i-46,),(46*i-49,),(18*i-65,),(-18*i-65,),(31*i-60,),(31*i+60,),(-54*i-41,),(41*i+54,),(-30*i+61,),(30*i+61,),(34*i-59,),(-34*i-59,),(-5*i+68,),(-5*i-68,),(56*i-39,),(39*i-56,),(7*i-68,),(7*i+68,),(25*i-64,),(-25*i-64,),(-52*i-45,),(45*i+52,),(37*i+58,),(-58*i-37,),(-55*i-42,),(42*i+55,),(13*i+68,),(13*i-68,),(-24*i-65,),(24*i-65,),(-18*i+67,),(18*i+67,),(56*i+41,),(-41*i-56,),(-10*i-69,),(10*i-69,),(-34*i-61,),(-34*i+61,),(-20*i+67,),(-20*i-67,),(-3*i+70,),(3*i+70,),(33*i-62,),(33*i+62,),(-29*i+64,),(-29*i-64,),(-14*i-69,),(14*i-69,),(37*i+60,),(-37*i+60,),(-22*i+67,),(22*i+67,),(-32*i-63,),(32*i-63,),(28*i+65,),(28*i-65,),(-11*i+70,),(-11*i-70,),(71,),(-6*i-71,),(6*i-71,),(-59*i-40,),(40*i+59,),(-51*i-50,),(50*i+51,),(-48*i-53,),(53*i+48,),(-23*i-68,),(23*i-68,),(17*i+70,),(17*i-70,),(29*i-66,),(-29*i-66,),(5*i+72,),(5*i-72,),(7*i+72,),(7*i-72,),(-14*i+71,),(14*i+71,),(19*i-70,),(19*i+70,),(-28*i-67,),(28*i-67,),(-60*i-41,),(41*i+60,),(-16*i+71,),(16*i+71,),(-50*i+53,),(-53*i+50,),(-2*i+73,),(-2*i-73,),(34*i-65,),(34*i+65,),(-8*i+73,),(8*i+73,),(-38*i-63,),(-38*i+63,),(-44*i+59,),(-59*i+44,),(-26*i-69,),(-26*i+69,),(20*i+71,),(-20*i+71,),(-43*i-60,),(60*i+43,),(i+74,),(i-74,),(-5*i-74,),(5*i-74,),(36*i-65,),(36*i+65,),(9*i+74,),(9*i-74,),(63*i+40,),(-40*i-63,),(-47*i-58,),(58*i+47,),(-35*i-66,),(-35*i+66,),(-4*i-75,),(4*i-75,),(-18*i+73,),(18*i+73,),(44*i-61,),(61*i-44,),(-38*i-65,),(38*i-65,),(-8*i+75,),(-8*i-75,),(-43*i-62,),(62*i+43,),(-15*i-74,),(15*i-74,),(26*i-71,),(-26*i-71,),(56*i-51,),(51*i-56,),(29*i+70,),(29*i-70,),(57*i-50,),(50*i-57,),(-5*i+76,),(5*i+76,),(22*i+73,),(22*i-73,),(-14*i+75,),(-14*i-75,),(35*i-68,),(35*i+68,),(9*i+76,),(9*i-76,),(-31*i+70,),(-31*i-70,),(62*i+45,),(-45*i-62,),(16*i-75,),(16*i+75,),(-11*i-76,),(11*i-76,),(-57*i-52,),(52*i+57,),(-50*i-59,),(59*i+50,),(10*i-77,),(10*i+77,),(-66*i+41,),(-41*i+66,),(-62*i-47,),(47*i+62,),(-12*i+77,),(12*i+77,),(40*i-67,),(40*i+67,),(-25*i-74,),(25*i-74,),(28*i-73,),(-28*i-73,),(45*i-64,),(64*i-45,),(-7*i+78,),(7*i+78,),(-53*i-58,),(58*i+53,),(34*i+71,),(34*i-71,),(21*i+76,),(-21*i+76,),(-50*i-61,),(61*i+50,),(-30*i+73,),(30*i+73,),(79,),(-4*i-79,),(4*i-79,),(37*i-70,),(37*i+70,),(-6*i+79,),(6*i+79,),(-26*i-75,),(-26*i+75,),(29*i+74,),(-29*i+74,),(-20*i-77,),(-20*i+77,),(-36*i-71,),(36*i-71,),(-32*i-73,),(32*i-73,),(40*i+69,),(-40*i+69,),(17*i+78,),(-17*i+78,),(58*i-55,),(55*i-58,),(-54*i+59,),(-59*i+54,),(-39*i-70,),(-39*i+70,),(7*i+80,),(7*i-80,),(50*i+63,),(-63*i-50,),(68*i-43,),(43*i-68,),(-9*i-80,),(9*i-80,),(-11*i+80,),(-11*i-80,),(65*i+48,),(-48*i-65,),(37*i-72,),(37*i+72,),(13*i+80,),(13*i-80,),(-4*i+81,),(4*i+81,),(41*i-70,),(41*i+70,),(54*i+61,),(-61*i-54,),(-53*i+62,),(-62*i+53,),(-10*i+81,),(10*i+81,),(63*i+52,),(-52*i-63,),(-17*i-80,),(17*i-80,),(-35*i+74,),(-35*i-74,),(25*i+78,),(25*i-78,),(-3*i+82,),(3*i+82,),(-31*i-76,),(31*i-76,),(-19*i+80,),(-19*i-80,),(-34*i+75,),(-34*i-75,),(-48*i-67,),(67*i+48,),(30*i+77,),(-30*i+77,),(-68*i-47,),(47*i+68,),(21*i-80,),(21*i+80,),(61*i-56,),(56*i-61,),(-55*i+62,),(-62*i+55,),(83,),(-26*i+79,),(26*i+79,),(15*i+82,),(15*i-82,),(-20*i+81,),(20*i+81,),(-71*i+44,),(-44*i+71,),(-39*i-74,),(-39*i+74,),(-35*i+76,),(-35*i-76,),(-17*i-82,),(-17*i+82,),(i+84,),(i-84,),(-38*i-75,),(38*i-75,),(70*i-47,),(47*i-70,),(64*i-55,),(55*i-64,),(-27*i-80,),(27*i-80,),(-11*i-84,),(-11*i+84,),(-67*i-52,),(52*i+67,),(18*i-83,),(-18*i-83,),(-2*i+85,),(-2*i-85,),(-26*i+81,),(-26*i-81,),(23*i+82,),(-23*i+82,),(39*i-76,),(39*i+76,),(-35*i-78,),(35*i-78,),(-61*i-60,),(60*i+61,),(-58*i-63,),(63*i+58,),(-25*i-82,),(25*i-82,),(-12*i+85,),(12*i+85,),(47*i+72,),(-72*i-47,),(-19*i-84,),(19*i-84,),(-53*i-68,),(68*i+53,),(-41*i-76,),(-41*i+76,),(-9*i+86,),(-9*i-86,),(16*i+85,),(16*i-85,),(-33*i-80,),(33*i-80,),(11*i-86,),(11*i+86,),(40*i-77,),(40*i+77,),(36*i+79,),(36*i-79,),(-71*i+50,),(-50*i+71,),(-18*i+85,),(18*i+85,),(-44*i-75,),(-44*i+75,),(-2*i+87,),(-2*i-87,),(-59*i+64,),(-64*i+59,),(-65*i-58,),(58*i+65,),(-15*i-86,),(-15*i+86,),(-68*i-55,),(55*i+68,),(10*i-87,),(10*i+87,),(-28*i-83,),(28*i-83,),(25*i+84,),(-25*i+84,),(-34*i-81,),(-34*i+81,),(-46*i-75,),(-46*i+75,),(-3*i+88,),(3*i+88,),(-19*i+86,),(-19*i-86,),(-30*i-83,),(30*i-83,),(-7*i+88,),(-7*i-88,),(64*i-61,),(61*i-64,),(-50*i-73,),(73*i+50,),(-40*i-79,),(40*i-79,),(-67*i-58,),(58*i+67,),(-68*i-57,),(57*i+68,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [0, -1, 0, -2, -4, 1, 6, 0, -6, 6, 2, 2, 0, 6, -4, -6, 6, -10, -10, 2, 2, 6, 6, 8, -10, 6, -6, 2, -16, 6, 12, 14, 12, -18, -6, -12, 14, -4, 6, 6, 2, 2, -4, 14, 6, 24, 14, -22, 18, 18, -10, 8, 6, -18, 12, -24, -10, 26, 0, -30, 30, 6, 8, -10, -30, -18, -4, -22, -10, -10, -30, -6, 2, -22, -4, 36, -12, 2, -34, -30, 18, 32, -22, -10, 8, 2, 38, 12, 30, 26, -28, -18, 30, -30, -18, 6, -42, 26, 2, -34, 18, -6, 18, -18, -34, 38, 12, -30, -28, 44, 2, -16, -12, -6, 12, 0, -6, -24, 32, 14, 26, 8, -42, -42, 0, 36, 26, 26, 14, -4, 2, 38, 18, -18, -22, -22, -6, 30, 54, 36, 30, 18, 18, -36, 2, 38, -46, -10, 18, 6, 32, 14, -54, 30, -42, 36, 2, 38, -30, -30, -6, 30, -10, 42, -54, 26, 26, 38, 38, -42, 54, 50, -22, -46, 26, 6, 30, -30, 30, 8, -28, -22, 14, -54, 0, 30, 18, -52, 2, -40, 50, -34, -52, 18, 36, -6, -42, -22, -40, 26, 44, -54, 6, 42, -6, -22, 32, -46, -10, -18, -6, 30, 42, 2, -34, 42, -30, 26, -28, -6, -54, 42, -12, 50, -22, 18, 30, -10, 26, -42, 6, 14, -40, 0, -60, -22, -40, -18, 66, 38, -34, -24, -66, -22, 14, 6, 42, -64, -64, -6, 48, 38, 38, -18, 0, 2, -34, -58, -22, -70, 2, -66, 66, 66, 30, -18, 6, 30, 6, 50, 50, -28, 26, 14, -40, -46, -82, -52, -70, 50, 26, 26, -34, 74, 12, -18, 42, 54, 18, 18, -54, 24, -64, 26, 0, 48, 6, 12, 14, 86, -66, 12, -34, 74, 14, -22, -34, -16, 42, 6, 90, -30, -34, 2, -46, 62, -12, 36, -22, -22, 54, 6, -6, 66, 38, -34, -4, -6, 72, 62, -64, 72, -42, -70, -52, -6, -24, 14, -40, 80, -10, -36, 30, -18, -60, 42, 24, -52, -52, 48, -78, 38, -16, 60, -18, 86, -22, -30, -60, 90, 66, 62, 62, 30, 6, -64, 62, 78, 60, -88, 20, 6, 54, 74, 2, -16, 2, -54, 42, 44, 26, -42, 66, 78, -78, -6, 30, -58, -22, -28, -10, -78, -30, 86, 14, -42, -6, -12, -90, 14, -4, 78, 24, 18, -42, -18, -48, -82, 62, -78, 54, -10, -10, 102, -66, -58, 50, -30, 30, -30, 42, -78, 6, -34, 20, -16, -70, -30, -42, 24, -6, 14, -58, 14, 68, 66, -66, -82, -10, -34, 20, 54, 6, -4, -22, -46, 98, -24, -66, -34, 74, -40, 32, 54, 60, -22, -94, 72, 84, 8, -82, 14, 32, -54, 42, 26, 26, 38, 2, -18, 18, -76, 14, -64, 26, -78, -102, 42, -30, 86, 86, -90, -6, 2, 38, 18, -102, 86, 14, 98, 8, 98, 2, -70, -78, -6, -40, -58, 78, -18, -18, -66, 54, -12, 68, 14, 18, 30, -70, 2, -52, -106, -108, -66, -28, 98, -30, -30, 20, 20, -100, 26, 72, 60, -46, -10, 14, 68, -48, 66, -90, 30, 54, -114, 20, -34, -82, -64, -102, 42, -16, -70, 54, -42, -42, 66, -42, 6, 6, 54, -6, -60, -10, 26, 54, 78, 98, -10, 0, -54, -46, -82, -64, -10, -18, 96, -94, -94, -48, 42, 2, -70, 62, -10, -60, 90, -42, 102, -36, -36, 30, 66, 50, -58, -10, -118, -66, -30, 86, 86, 84, 114, -78, 108, 38, 74, -90, 126, 30, 66, -84, 42, 12, 84, 86, -94, 132, 102, -60, 84, 80, 66, -114, -22, -4, 60, 18, -58, 14, -10, 62, 26, 98, -58, 14, 36, -78, -42, -54, 86, -76, -18, -60, 84, -42, 122, -58, 60, 30, -70, -70, -18, 72, 50, 14, 26, -46, -126, 48, 2, -70, -78, -126, 72, 60, -40, -58, 74, -106, -54, -84, -118, 98, 110, -106, -78, -84, 26, 44, -54, 54, 66, -18, -106, -106, 56, 18, -66, -46, 98, -52, 38, 42, 42, 60, -90, -40, 86, 134, 26, -58, 14, 90, -132, 6, 30, 54, -108, 98, -10, -6, 114, -60, 42, -144, 42, 18, -18, -90, -54, 140, -22, -108, -66, 2, 2, 126, 18, 14, -4, 42, 12, -78, -48, 104, 32, 14, 14, -100, 134, -18, -42, -106, 74, 98, -82, 74, -16, 18, -48, -54, -90, 2, 74, 12, -90, -22, 32, -72, 126, 68, -94, -138, -78, 80, 44, -120, 72, 90, 84, -64, 44, -6, -66, 26, -82, 90, 18, -34, -70, -148, -22, 48, 138, -94, -148, 90, -6, 54, -78, 26, -46, 48, -90, -10, -64, -126, -60, -48, 36, 6, 48, -70, 56, -22, -4, -42, -36, 12, 150, 116, 134, 66, -18, 110, 56, -94, -42, -36, -54, 114, 122, -76, 38, -34, 66, -102, -60, -102, 146, -88, -54, 78, -10, -10, 146, 38, -90, 78, 134, 98, -58, 86, -54, -6, 98, 44, 42, 72, -34, 38, 78, 6, -22, 158, 56, -70, -6, 30, -46, -82, -42, -138, 104, 50, 66, -66, -34, 38, -4, -94, 36, 66, 108, 90, -58, 14, -70, -70, -108, -30, -102, -90, 50, 32, -154, -82, 44, -100, 78, 108, 74, 74, -150, 156, -114, 30, -4, -102, -30, -34, -34, 50, -130, 156, -54, 32, -22, 162, -48, 6, -84, -34, 92, 14, -94, 42, 24, 120, -84, 74, 92, -22, -148, 78, 132, 158, 86, 150, 162, 38, 38, -6, 114, -154, 98, -106, 2, -94, -58, 116, 134, -30, -114, -46, -118, 158, 50, -88, -70, 54, -6, -66, 150, 26, 134, 162, 120, -34, -34, 30, -138, -60, -114, -166, 14, 78, -150, -10, -46, 110, -16, 122, -40, 30, 18, 18, 90, 26, -46, 18, 126, -88, 56, -144, -30, -40, -22, 50, -94, 56, 146, 14, -22, -120, 90, 14, 140, 54, -66, 6, -42, 12, 72, 90, -18, -36, -78, -118, -118]
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((2*i + 3,))] = -1

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