"""
  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((442, i + 47))

primes_array = [
(i+1,),(-i-2,),(2*i+1,),(3,),(-2*i+3,),(2*i+3,),(i+4,),(i-4,),(-2*i+5,),(2*i+5,),(i+6,),(i-6,),(-4*i+5,),(4*i+5,),(7,),(-2*i+7,),(2*i+7,),(-6*i-5,),(6*i-5,),(-3*i-8,),(3*i-8,),(-5*i+8,),(-5*i-8,),(-4*i+9,),(4*i+9,),(i+10,),(i-10,),(-3*i+10,),(3*i+10,),(-8*i-7,),(8*i-7,),(11,),(-4*i-11,),(4*i-11,),(7*i+10,),(7*i-10,),(-6*i-11,),(6*i-11,),(-2*i+13,),(2*i+13,),(-10*i-9,),(10*i-9,),(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,),(13*i+10,),(-9*i+14,),(-9*i-14,),(-5*i+16,),(5*i+16,),(-2*i+17,),(2*i+17,),(-12*i+13,),(12*i+13,),(-11*i+14,),(-11*i-14,),(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,),(-14*i+15,),(14*i+15,),(-12*i+17,),(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,),(-19*i-14,),(-19*i+14,),(-13*i+20,),(-13*i-20,),(i+24,),(i-24,),(-8*i-23,),(8*i-23,),(-5*i-24,),(5*i-24,),(-18*i-17,),(18*i-17,),(19*i-16,),(19*i+16,),(-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,),(15*i+22,),(15*i-22,),(-2*i+27,),(2*i+27,),(-9*i-26,),(9*i-26,),(-20*i-19,),(20*i-19,),(-12*i+25,),(12*i+25,),(-22*i-17,),(22*i-17,),(-11*i+26,),(-11*i-26,),(-5*i+28,),(-5*i-28,),(-14*i-25,),(-14*i+25,),(10*i-27,),(10*i+27,),(-23*i+18,),(23*i+18,),(-4*i+29,),(4*i+29,),(-6*i-29,),(6*i-29,),(16*i+25,),(-16*i+25,),(-23*i-20,),(-23*i+20,),(-19*i+24,),(-19*i-24,),(-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,),(-22*i+23,),(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,),(25*i+22,),(21*i+26,),(21*i-26,),(-27*i-20,),(-27*i+20,),(-8*i+33,),(8*i+33,),(-5*i-34,),(5*i-34,),(13*i+32,),(13*i-32,),(-24*i+25,),(24*i+25,),(-22*i+27,),(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,),(26*i-25,),(-5*i+36,),(5*i+36,),(20*i+31,),(-20*i+31,),(-2*i+37,),(2*i+37,),(-15*i+34,),(-15*i-34,),(25*i+28,),(25*i-28,),(-30*i-23,),(30*i-23,),(-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,),(23*i-32,),(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,),(31*i+26,),(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,),(-22*i+35,),(-11*i-40,),(-11*i+40,),(17*i+38,),(17*i-38,),(-30*i-29,),(30*i-29,),(-32*i-27,),(32*i-27,),(-16*i+39,),(16*i+39,),(5*i+42,),(5*i-42,),(-24*i+35,),(24*i+35,),(43,),(-30*i+31,),(30*i+31,),(-33*i+28,),(33*i+28,),(-14*i-41,),(14*i-41,),(-17*i+40,),(-17*i-40,),(-35*i-26,),(-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,),(-29*i-34,),(-9*i-44,),(9*i-44,),(-2*i+45,),(2*i+45,),(17*i+42,),(17*i-42,),(-25*i+38,),(-25*i-38,),(-20*i+41,),(20*i+41,),(-8*i-45,),(-8*i+45,),(-32*i+33,),(32*i+33,),(-23*i-40,),(-23*i+40,),(29*i+36,),(29*i-36,),(-5*i+46,),(5*i+46,),(37*i-28,),(37*i+28,),(-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,),(-30*i+37,),(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,),(26*i-41,),(-26*i-41,),(21*i+44,),(21*i-44,),(-34*i+35,),(34*i+35,),(25*i-42,),(25*i+42,),(-32*i+37,),(32*i+37,),(-4*i+49,),(4*i+49,),(-6*i+49,),(6*i+49,),(40*i+29,),(-40*i+29,),(13*i-48,),(13*i+48,),(-19*i-46,),(19*i-46,),(-36*i-35,),(36*i-35,),(-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,),(-28*i+43,),(-16*i+49,),(16*i+49,),(-39*i-34,),(-39*i+34,),(40*i-33,),(-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,),(-30*i+43,),(30*i+43,),(7*i+52,),(7*i-52,),(-29*i+44,),(-29*i-44,),(-17*i-50,),(17*i-50,),(-14*i-51,),(-14*i+51,),(-20*i+49,),(20*i+49,),(23*i+48,),(23*i-48,),(-41*i-34,),(-41*i+34,),(16*i+51,),(16*i-51,),(19*i-50,),(-19*i-50,),(-31*i+44,),(-31*i-44,),(10*i+53,),(10*i-53,),(i+54,),(i-54,),(-12*i+53,),(12*i+53,),(-29*i+46,),(-29*i-46,),(37*i+40,),(37*i-40,),(20*i+51,),(-20*i+51,),(-11*i-54,),(11*i-54,),(-4*i-55,),(4*i-55,),(-32*i+45,),(32*i+45,),(-6*i+55,),(6*i+55,),(-8*i-55,),(8*i-55,),(30*i+47,),(-30*i+47,),(-40*i-39,),(40*i-39,),(i+56,),(i-56,),(12*i+55,),(-12*i+55,),(45*i-34,),(45*i+34,),(-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,),(43*i+40,),(-39*i+44,),(-39*i-44,),(-31*i-50,),(-31*i+50,),(-45*i-38,),(45*i-38,),(59,),(-6*i-59,),(6*i-59,),(48*i-35,),(-48*i-35,),(13*i+58,),(13*i-58,),(25*i+54,),(25*i-54,),(-34*i-49,),(34*i-49,),(-10*i-59,),(10*i-59,),(28*i-53,),(28*i+53,),(-42*i+43,),(42*i+43,),(-41*i+44,),(-41*i-44,),(-46*i+39,),(46*i+39,),(-48*i+37,),(48*i+37,),(-14*i+59,),(-14*i-59,),(49*i-36,),(-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,),(33*i-52,),(-33*i-52,),(41*i+46,),(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,),(35*i+52,),(35*i-52,),(25*i+58,),(25*i-58,),(-40*i+49,),(40*i+49,),(13*i-62,),(13*i+62,),(-50*i+39,),(50*i+39,),(-32*i+55,),(32*i+55,),(-24*i+59,),(24*i+59,),(-37*i+52,),(37*i+52,),(-27*i+58,),(-27*i-58,),(23*i-60,),(-23*i-60,),(-17*i-62,),(-17*i+62,),(-43*i-48,),(43*i-48,),(26*i+59,),(-26*i+59,),(-9*i+64,),(9*i+64,),(40*i-51,),(-40*i-51,),(11*i-64,),(11*i+64,),(-2*i+65,),(-2*i-65,),(-4*i+65,),(4*i+65,),(-38*i-53,),(38*i-53,),(-6*i-65,),(6*i-65,),(-32*i+57,),(32*i+57,),(-8*i+65,),(8*i+65,),(24*i+61,),(-24*i+61,),(-49*i-44,),(-49*i+44,),(43*i+50,),(43*i-50,),(i+66,),(i-66,),(-23*i-62,),(23*i-62,),(-26*i+61,),(-26*i-61,),(53*i-40,),(53*i+40,),(-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,),(48*i-47,),(49*i-46,),(49*i+46,),(18*i-65,),(-18*i-65,),(31*i-60,),(31*i+60,),(-54*i-41,),(54*i-41,),(-30*i+61,),(30*i+61,),(34*i-59,),(-34*i-59,),(-5*i+68,),(-5*i-68,),(39*i+56,),(39*i-56,),(7*i-68,),(7*i+68,),(25*i-64,),(-25*i-64,),(-45*i+52,),(45*i+52,),(37*i+58,),(-37*i+58,),(-55*i-42,),(55*i-42,),(13*i+68,),(13*i-68,),(-24*i-65,),(24*i-65,),(-18*i+67,),(18*i+67,),(56*i+41,),(-56*i+41,),(-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,),(-40*i+59,),(40*i+59,),(-50*i+51,),(50*i+51,),(-53*i+48,),(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,),(-41*i+60,),(41*i+60,),(-16*i+71,),(16*i+71,),(-53*i-50,),(-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,),(-59*i-44,),(-59*i+44,),(-26*i-69,),(-26*i+69,),(20*i+71,),(-20*i+71,),(-43*i-60,),(43*i-60,),(i+74,),(i-74,),(-5*i-74,),(5*i-74,),(36*i-65,),(36*i+65,),(9*i+74,),(9*i-74,),(40*i-63,),(-40*i-63,),(-47*i-58,),(47*i-58,),(-35*i-66,),(-35*i+66,),(-4*i-75,),(4*i-75,),(-18*i+73,),(18*i+73,),(44*i-61,),(44*i+61,),(-38*i-65,),(38*i-65,),(-8*i+75,),(-8*i-75,),(-43*i-62,),(43*i-62,),(-15*i-74,),(15*i-74,),(26*i-71,),(-26*i-71,),(51*i+56,),(51*i-56,),(29*i+70,),(29*i-70,),(57*i-50,),(57*i+50,),(-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,),(-62*i+45,),(16*i-75,),(16*i+75,),(-11*i-76,),(11*i-76,),(-52*i+57,),(52*i+57,),(-59*i+50,),(59*i+50,),(10*i-77,),(10*i+77,),(-41*i-66,),(-41*i+66,),(-62*i-47,),(62*i-47,),(-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,),(45*i+64,),(-7*i+78,),(7*i+78,),(-53*i-58,),(53*i-58,),(34*i+71,),(34*i-71,),(21*i+76,),(-21*i+76,),(-50*i-61,),(50*i-61,),(-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,),(55*i+58,),(55*i-58,),(-59*i-54,),(-59*i+54,),(-39*i-70,),(-39*i+70,),(7*i+80,),(7*i-80,),(50*i+63,),(-50*i+63,),(43*i+68,),(43*i-68,),(-9*i-80,),(9*i-80,),(-11*i+80,),(-11*i-80,),(65*i+48,),(-65*i+48,),(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,),(-54*i+61,),(-53*i+62,),(-53*i-62,),(-10*i+81,),(10*i+81,),(63*i+52,),(-63*i+52,),(-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,),(48*i-67,),(30*i+77,),(-30*i+77,),(-47*i+68,),(47*i+68,),(21*i-80,),(21*i+80,),(61*i-56,),(61*i+56,),(-55*i+62,),(-55*i-62,),(83,),(-26*i+79,),(26*i+79,),(15*i+82,),(15*i-82,),(-20*i+81,),(20*i+81,),(-44*i-71,),(-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,),(47*i+70,),(47*i-70,),(55*i+64,),(55*i-64,),(-27*i-80,),(27*i-80,),(-11*i-84,),(-11*i+84,),(-67*i-52,),(67*i-52,),(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,),(-60*i+61,),(60*i+61,),(-63*i+58,),(63*i+58,),(-25*i-82,),(25*i-82,),(-12*i+85,),(12*i+85,),(47*i+72,),(-47*i+72,),(-19*i-84,),(19*i-84,),(-68*i+53,),(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,),(-50*i-71,),(-50*i+71,),(-18*i+85,),(18*i+85,),(-44*i-75,),(-44*i+75,),(-2*i+87,),(-2*i-87,),(-59*i+64,),(-59*i-64,),(-58*i+65,),(58*i+65,),(-15*i-86,),(-15*i+86,),(-55*i+68,),(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,),(61*i+64,),(61*i-64,),(-50*i-73,),(50*i-73,),(-40*i-79,),(40*i-79,),(-58*i+67,),(58*i+67,),(-68*i-57,),(68*i-57,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [-1, 0, 3, -5, 5, 1, 3, -1, -6, 0, -7, 2, 3, -3, 14, -12, 3, -1, -1, 2, -16, 12, -15, -10, 8, 0, -15, 2, 11, -3, 0, -4, 3, 6, 0, 6, 14, -13, 18, -9, 2, 2, 5, 14, -24, -6, -4, -4, 18, -18, 26, 17, -12, -24, 24, -12, 26, 8, 6, 18, 0, 24, 26, 17, -18, 24, -22, -22, -1, 17, 27, 30, 29, 23, 14, -3, 18, 2, 29, 6, -24, -4, -31, 8, -10, 29, 2, -12, 6, -28, -19, -12, -24, -39, -6, -6, -12, -28, 20, -7, -27, -3, -21, 6, 11, 20, 6, 39, -10, -10, 2, 20, -21, -9, 3, -12, -18, 18, 41, -31, -28, -19, -15, -15, 18, -18, -28, 17, 14, 41, 20, -43, -42, -6, 23, -40, 42, 42, -33, 12, -30, -9, -30, -30, 2, 38, 26, -10, 15, 0, 14, 32, -27, 24, -33, -21, 2, 2, 51, 24, -30, 42, -37, -12, -33, -28, 8, 38, -16, -36, 30, -22, 50, 35, 26, 6, 27, -6, 6, -46, -10, -13, -49, -36, -9, 39, -48, 47, -61, 14, -40, -52, 65, 15, 33, 54, -45, 14, -22, 26, -28, 51, -63, 24, -45, -58, -22, -1, -55, 27, -30, 12, 18, -43, 2, 51, 6, -10, -19, 12, 60, -30, -3, -22, 32, 21, -54, 26, -10, -24, -9, -67, -4, 30, -54, -49, 41, -54, -48, 38, 20, -18, -39, 59, -22, 48, -24, 8, 35, 21, -6, 2, -43, 72, 72, 2, -43, 14, -58, -70, 56, 42, -27, 24, -66, 6, 72, 18, 42, -22, 32, 71, -28, -58, 50, -55, -19, -16, -25, 14, -10, -28, 74, -70, 45, 12, 84, 18, -39, -30, -15, 24, -19, 26, 30, 9, 9, -24, 14, -58, -6, 78, 29, 2, -49, -22, -52, 11, 21, 30, -66, -45, 47, -34, 44, 80, -12, 48, 32, -22, 72, -78, -24, 48, 74, -16, 86, 78, -90, -10, 53, 30, 18, -25, 38, -90, 36, -22, -40, -10, -73, 78, 84, 3, 72, -36, 54, -34, 56, -39, -3, -43, 11, 60, -6, 5, -40, -24, -12, 84, -18, 71, -46, -6, 18, 53, 89, 27, 90, -70, -7, 0, -21, -70, -52, 11, 38, 72, 30, -28, 26, 57, -6, -57, 90, 66, -6, 14, 86, 44, -64, 12, -9, 68, 14, 30, 12, 42, -33, -22, 14, -24, -78, -78, -36, 18, -51, -64, -82, 30, -30, -55, -28, -6, 18, 50, 50, 48, -30, 21, 30, 57, 18, -43, 92, 29, 29, 24, 72, -51, -57, -103, -40, -40, 41, -66, -6, -1, -82, -34, -34, -30, -27, 50, -22, 35, -10, -36, -12, -61, -70, 50, 32, -6, -3, -58, -4, -9, 6, 89, 35, 86, 68, 90, 48, -19, -73, 11, -106, -108, 45, -94, -49, 80, -46, 9, 6, 0, 54, 32, 32, -12, -24, 29, -34, -87, 6, 14, 23, -10, -28, -10, 20, -34, -90, -90, -49, -112, 27, -3, 18, -51, -66, 54, -85, 104, 0, 6, 11, -52, 29, -16, -60, -57, 62, -37, 54, 72, 2, 20, 26, 89, 9, 39, -55, 44, -76, -76, 120, -30, -105, 108, -36, 6, -88, -97, 98, 62, -54, 18, 29, -88, 78, -24, -72, -36, -105, 72, -30, 39, 60, 15, 26, 35, -36, 102, 125, 98, 57, -60, -10, 53, -82, -82, 60, -117, -85, -85, 12, 30, 2, 2, 62, -55, -54, -42, -48, -111, 105, -21, -108, 63, 95, 95, 26, -1, 87, -120, 32, -85, -102, 12, 93, -30, -7, 110, -63, 81, 0, -36, 111, 66, -78, 102, -67, -40, -54, 39, -120, -21, -1, -6, -123, -103, 32, 57, 18, 14, -22, 107, -73, 26, -82, 86, -31, 96, 3, 99, 48, 68, -22, -3, -114, -54, 54, -22, 59, -114, -66, -70, -70, -6, 12, 50, 14, -28, 89, 24, 12, 101, 38, -30, -72, -12, 54, -58, -31, -88, 29, -42, 6, 107, -91, -43, 56, 18, -48, 116, 89, 3, 66, 114, 27, 29, 29, -70, 75, 60, -1, -55, -70, -16, 96, 6, 15, -69, 122, 122, -109, -28, 50, 104, 117, -57, -39, -36, 135, -54, -10, -73, -108, -12, -30, 30, -114, -3, 0, -45, -30, 42, 32, -94, -90, 30, 2, 38, -114, -114, -4, -58, 51, 117, 30, 117, 50, -40, -130, 23, -19, -91, -84, 12, 83, 110, -82, -145, -7, -7, -42, 60, 54, -9, 2, -52, 135, -6, 104, -22, 6, -57, -148, -58, -123, -48, -82, -10, 42, -114, 54, 105, -19, 35, -30, -24, -64, 53, 6, 87, -88, -124, 86, -13, -96, 39, 95, 14, 120, 144, 117, 15, -19, 71, 108, -60, 116, 26, 30, -126, -24, 81, -36, -105, -106, -106, -31, -40, 96, 18, 27, -102, 35, -28, 120, -30, -88, 110, -94, 48, -138, 3, -120, 122, -49, -34, -16, -57, 30, 30, 108, 11, -142, 126, 102, 98, 98, 38, -70, 54, -78, -64, 80, 50, -112, 12, -54, -145, 71, -54, -138, 56, -43, -30, 105, 140, -40, -115, 74, 114, 42, -10, 71, 57, -36, 14, -13, -150, -90, 101, 56, -49, 131, 15, -96, -15, 120, 140, -148, -88, 65, 57, -12, 18, 123, -94, -130, -46, -46, -136, 26, 0, -57, -70, 2, -12, 6, 102, -78, -22, -102, -30, -34, -34, 41, 68, -141, 132, -22, 23, -27, -141, 126, 18, -7, 38, 59, 50, 84, -114, 102, 54, -88, -70, -4, 131, 45, 63, -13, -112, 90, -129, -124, -52, 24, -114, -55, -109, 137, 2, 104, 86, 35, -55, -57, -18, 44, 26, 158, 68, -97, -7, -27, 42, 60, 96, 125, 116, 6, -42, 83, -7, 111, -63, -90, -126, 50, 131, -69, 42, -145, -10, -142, -70, -13, 59, 87, 18, 78, -30, 134, 44, 99, 108, 11, -88, 48, -39, -112, -94, 122, -58, 2, -7, 122, 131, 111, 9, -67, -94, -72, -132, 96, -171, -30, 144, 132, -138, 30, 72, 152, -73]
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 + 1,))] = 1
AL_eigenvalues[ZF.ideal((2*i + 3,))] = -1
AL_eigenvalues[ZF.ideal((i - 4,))] = 1

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