"""
  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([2, -1, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((44, 2*a + 30))

primes_array = [
(a,),(-a+1,),(-2*a+1,),(3,),(-2*a+3,),(2*a+1,),(-2*a+5,),(2*a+3,),(5,),(-4*a+1,),(4*a-3,),(-4*a+5,),(4*a+1,),(-2*a+7,),(2*a+5,),(-4*a-3,),(4*a-7,),(-6*a+1,),(6*a-5,),(-2*a+9,),(2*a+7,),(-6*a+7,),(6*a+1,),(-2*a+11,),(2*a+9,),(-4*a-7,),(4*a-11,),(-8*a+3,),(-8*a+5,),(-6*a-5,),(6*a-11,),(-8*a+9,),(8*a+1,),(-4*a+13,),(4*a+9,),(-2*a+13,),(2*a+11,),(-6*a+13,),(6*a+7,),(13,),(10*a-7,),(10*a-3,),(-10*a+1,),(10*a-9,),(-8*a-5,),(-8*a+13,),(-4*a-11,),(4*a-15,),(-10*a+11,),(10*a+1,),(-8*a-7,),(8*a-15,),(10*a+3,),(10*a-13,),(-2*a+17,),(2*a+15,),(-12*a+1,),(12*a-11,),(-8*a+17,),(8*a+9,),(17,),(-4*a-15,),(4*a-19,),(-2*a+19,),(2*a+17,),(-8*a+19,),(-8*a-11,),(-14*a+5,),(-14*a+9,),(-14*a+3,),(-14*a+11,),(19,),(-12*a+17,),(12*a+5,),(-14*a+1,),(14*a-13,),(-4*a+21,),(4*a+17,),(-8*a-13,),(-8*a+21,),(12*a+7,),(-12*a+19,),(-10*a+21,),(10*a+11,),(-14*a+17,),(-14*a-3,),(16*a-7,),(-16*a+9,),(16*a-11,),(16*a-5,),(-6*a-17,),(6*a-23,),(-14*a+19,),(-14*a-5,),(-2*a+23,),(2*a+21,),(10*a+13,),(10*a-23,),(-12*a-11,),(12*a-23,),(-6*a+25,),(6*a+19,),(-4*a+25,),(4*a+21,),(16*a+3,),(16*a-19,),(18*a-11,),(-18*a+7,),(-14*a-9,),(-14*a+23,),(-12*a+25,),(12*a+13,),(16*a+5,),(16*a-21,),(-18*a+1,),(18*a-17,),(-8*a+27,),(-8*a-19,),(-4*a-23,),(4*a-27,),(10*a-27,),(10*a+17,),(-16*a+23,),(16*a+7,),(-2*a+27,),(2*a+25,),(20*a-9,),(-20*a+11,),(-20*a+7,),(-20*a+13,),(-6*a-23,),(6*a-29,),(-14*a-13,),(14*a-27,),(-10*a-19,),(10*a-29,),(-4*a+29,),(4*a+25,),(16*a-27,),(16*a+11,),(-20*a+21,),(20*a+1,),(-18*a-7,),(18*a-25,),(-14*a+29,),(14*a+15,),(22*a-15,),(22*a-7,),(12*a+19,),(-12*a+31,),(-22*a+5,),(22*a-17,),(-2*a+31,),(2*a+29,),(22*a-19,),(22*a-3,),(-14*a+31,),(-14*a-17,),(-22*a+1,),(22*a-21,),(-8*a+33,),(8*a+25,),(31,),(18*a-29,),(-18*a-11,),(-16*a-15,),(16*a-31,),(-22*a+23,),(22*a+1,),(24*a-11,),(-24*a+13,),(-14*a+33,),(-14*a-19,),(-2*a+33,),(2*a+31,),(-24*a+7,),(24*a-17,),(-18*a+31,),(18*a+13,),(-20*a+29,),(20*a+9,),(-6*a-29,),(6*a-35,),(-12*a-23,),(12*a-35,),(-22*a+27,),(22*a+5,),(-4*a-31,),(4*a-35,),(-24*a+1,),(24*a-23,),(-2*a+35,),(2*a+33,),(22*a+7,),(22*a-29,),(26*a-15,),(-26*a+11,),(-8*a-29,),(-8*a+37,),(-12*a+37,),(12*a+25,),(-20*a-13,),(-20*a+33,),(-26*a+3,),(-26*a+23,),(16*a+21,),(16*a-37,),(-24*a+29,),(-24*a-5,),(-2*a+37,),(2*a+35,),(-26*a+1,),(26*a-25,),(-14*a-25,),(-14*a+39,),(28*a-13,),(-28*a+15,),(28*a-17,),(-28*a+11,),(-16*a+39,),(16*a+23,),(22*a+13,),(-22*a+35,),(-20*a-17,),(-20*a+37,),(-26*a+29,),(-26*a-3,),(-2*a+39,),(2*a+37,),(-28*a+23,),(28*a-5,),(-10*a+41,),(10*a+31,),(-8*a+41,),(8*a+33,),(28*a-25,),(28*a-3,),(-14*a-27,),(14*a-41,),(22*a-37,),(22*a+15,),(-4*a+41,),(4*a+37,),(30*a-13,),(-30*a+17,),(26*a+7,),(-26*a+33,),(-28*a+29,),(28*a+1,),(-2*a+41,),(2*a+39,),(10*a+33,),(10*a-43,),(12*a+31,),(-12*a+43,),(-6*a+43,),(6*a+37,),(-26*a+35,),(-26*a-9,),(41,),(-4*a-39,),(4*a-43,),(-18*a-25,),(18*a-43,),(-28*a-5,),(28*a-33,),(22*a-41,),(22*a+19,),(-26*a-11,),(26*a-37,),(-14*a+45,),(-14*a-31,),(-20*a+43,),(-20*a-23,),(32*a-13,),(-32*a+19,),(-30*a+31,),(30*a+1,),(-22*a-21,),(22*a-43,),(-32*a+25,),(32*a-7,),(-4*a+45,),(4*a+41,),(28*a+9,),(28*a-37,),(-32*a+5,),(32*a-27,),(-12*a-35,),(12*a-47,),(-28*a-11,),(28*a-39,),(-6*a-41,),(6*a-47,),(-22*a+45,),(22*a+23,),(18*a-47,),(-18*a-29,),(-32*a+1,),(32*a-31,),(34*a-19,),(-34*a+15,),(34*a-21,),(34*a-13,),(-4*a-43,),(4*a-47,),(-20*a+47,),(-20*a-27,),(-32*a+33,),(32*a+1,),(-26*a-17,),(-26*a+43,),(34*a-25,),(-34*a+9,),(-10*a-39,),(10*a-49,),(-16*a+49,),(16*a+33,),(-8*a+49,),(8*a+41,),(22*a+25,),(22*a-47,),(-32*a+35,),(-32*a-3,),(-6*a+49,),(6*a+43,),(26*a-45,),(-26*a-19,),(47,),(28*a+15,),(-28*a+43,),(-20*a+49,),(20*a+29,),(-4*a+49,),(4*a+45,),(30*a-41,),(-30*a-11,),(36*a-17,),(-36*a+19,),(36*a-23,),(-36*a+13,),(16*a+35,),(16*a-51,),(-2*a+49,),(2*a+47,),(28*a-45,),(-28*a-17,),(26*a-47,),(26*a+21,),(-34*a+35,),(34*a+1,),(-24*a+49,),(24*a+25,),(20*a+31,),(-20*a+51,),(36*a-29,),(36*a-7,),(-32*a-9,),(32*a-41,),(34*a+3,),(34*a-37,),(36*a-31,),(36*a-5,),(22*a+29,),(22*a-51,),(-14*a-39,),(-14*a+53,),(16*a+37,),(16*a-53,),(-18*a-35,),(18*a-53,),(-32*a+43,),(-32*a-11,),(38*a-17,),(-38*a+21,),(38*a-23,),(-38*a+15,),(-20*a-33,),(-20*a+53,),(-36*a+1,),(36*a-35,),(-38*a+11,),(38*a-27,),(-32*a+45,),(32*a+13,),(-14*a-41,),(14*a-55,),(-16*a+55,),(16*a+39,),(-38*a+7,),(38*a-31,),(-18*a+55,),(18*a+37,),(-24*a+53,),(-24*a-29,),(34*a+9,),(-34*a+43,),(-2*a+53,),(-2*a-51,),(-8*a-47,),(8*a-55,),(30*a+19,),(-30*a+49,),(-28*a+51,),(28*a+23,),(-32*a+47,),(32*a+15,),(-6*a+55,),(6*a+49,),(36*a+5,),(36*a-41,),(40*a-19,),(-40*a+21,),(-4*a-51,),(4*a-55,),(-14*a+57,),(14*a+43,),(-38*a+1,),(38*a-37,),(-24*a+55,),(24*a+31,),(10*a-57,),(10*a+47,),(-20*a-37,),(-20*a+57,),(-38*a+39,),(38*a+1,),(22*a+35,),(-22*a+57,),(40*a-33,),(-40*a+7,),(-38*a+41,),(-38*a-3,),(-30*a-23,),(30*a-53,),(16*a-59,),(16*a+43,),(-12*a-47,),(12*a-59,),(-18*a-41,),(18*a-59,),(40*a-37,),(40*a-3,),(-36*a-11,),(36*a-47,),(26*a+31,),(26*a-57,),(-8*a+59,),(-8*a-51,),(42*a-31,),(-42*a+11,),(-38*a+45,),(38*a+7,),(-24*a+59,),(24*a+35,),(-28*a+57,),(28*a+29,),(36*a+13,),(-36*a+49,),(16*a-61,),(16*a+45,),(-14*a+61,),(-14*a-47,),(-18*a-43,),(18*a-61,),(26*a+33,),(-26*a+59,),(-20*a+61,),(20*a+41,),(-32*a+55,),(32*a+23,),(34*a-53,),(-34*a-19,),(40*a+3,),(40*a-43,),(-42*a+5,),(42*a-37,),(-22*a-39,),(22*a-61,),(-8*a-53,),(-8*a+61,),(-2*a+59,),(-2*a-57,),(44*a-21,),(-44*a+23,),(-44*a+17,),(-44*a+27,),(34*a-55,),(34*a+21,),(-44*a+13,),(-44*a+31,),(59,),(-30*a-29,),(30*a-59,),(40*a+7,),(-40*a+47,),(10*a+53,),(10*a-63,),(-44*a+9,),(-44*a+35,),(-42*a+43,),(42*a+1,),(-28*a-33,),(28*a-61,),(-8*a-55,),(8*a-63,),(-2*a+61,),(-2*a-59,),(-44*a+7,),(44*a-37,),(34*a-57,),(34*a+23,),(36*a+19,),(-36*a+55,),(-44*a+5,),(-44*a+39,),(-30*a+61,),(30*a+31,),(-16*a+65,),(16*a+49,),(46*a-19,),(46*a-27,),(61,),(-12*a+65,),(12*a+53,),(-46*a+17,),(-46*a+29,),(40*a-51,),(-40*a-11,),(46*a-31,),(46*a-15,),(-46*a+33,),(46*a-13,),(-38*a+55,),(38*a+17,),(-8*a+65,),(8*a+57,),(-46*a+11,),(46*a-35,),(-2*a+63,),(-2*a-61,),(40*a+13,),(40*a-53,),(-6*a-59,),(6*a-65,),(-44*a+45,),(44*a+1,),(16*a+51,),(16*a-67,),(-18*a+67,),(18*a+49,),(-14*a-53,),(-14*a+67,),(-32*a-31,),(32*a-63,),(-44*a+47,),(-44*a-3,),(10*a-67,),(10*a+57,),(46*a-41,),(46*a-5,),(48*a-29,),(-48*a+19,),(26*a-67,),(-26*a-41,),(42*a+11,),(-42*a+53,),(38*a+21,),(-38*a+59,),(-34*a-29,),(-34*a+63,),(48*a-35,),(-48*a+13,),(-6*a+67,),(6*a+61,),(-48*a+37,),(48*a-11,),(22*a+47,),(22*a-69,),(-44*a+51,),(44*a+7,),(-42*a+55,),(42*a+13,),(-4*a-63,),(4*a-67,),(-10*a-59,),(10*a-69,),(34*a-65,),(34*a+31,),(-8*a-61,),(-8*a+69,),(-44*a+53,),(-44*a-9,),(-2*a+67,),(-2*a-65,),(50*a-29,),(50*a-21,),(-28*a+69,),(28*a+41,),(20*a+51,),(-20*a+71,),(-22*a+71,),(22*a+49,),(-38*a-25,),(-38*a+63,),(40*a+21,),(-40*a+61,),(-4*a+69,),(4*a+65,),(50*a-37,),(-50*a+13,),(-34*a-33,),(34*a-67,),(26*a-71,),(-26*a-45,),(-48*a+1,),(48*a-47,),(-46*a-7,),(46*a-53,),(28*a+43,),(-28*a+71,),(-38*a-27,),(38*a-65,),(40*a-63,),(-40*a-23,),(-48*a+49,),(48*a+1,),(-18*a+73,),(18*a+55,),(16*a+57,),(-16*a+73,),(22*a+51,),(22*a-73,),(-24*a+73,),(24*a+49,),(52*a-25,),(-52*a+27,),(26*a-73,),(26*a+47,),(-4*a-67,),(4*a-71,),(10*a+63,),(10*a-73,),(52*a-35,),(52*a-17,),(-32*a-39,),(32*a-71,),(-38*a-29,),(38*a-67,),(44*a-61,),(44*a+17,),(16*a-75,),(16*a+59,),(-22*a+75,),(22*a+53,),(-50*a+1,),(50*a-49,),(52*a-11,),(-52*a+41,),(-14*a+75,),(-14*a-61,),(-48*a+55,),(-48*a-7,),(-46*a-13,),(46*a-59,),(40*a-67,),(40*a+27,),(52*a-43,),(-52*a+9,),(42*a-65,),(-42*a-23,),(-50*a+51,),(50*a+1,),(-36*a-35,),(36*a-71,),(54*a-25,),(-54*a+29,),(54*a-31,),(-54*a+23,),(46*a+15,),(46*a-61,),(-8*a+75,),(-8*a-67,),(54*a-35,),(-54*a+19,),(-20*a-57,),(-20*a+77,),(16*a-77,),(16*a+61,),(-38*a+71,),(38*a+33,),(-24*a+77,),(-24*a-53,),(-44*a+65,),(44*a+21,),(52*a-49,),(52*a-3,),(-32*a+75,),(-32*a-43,),(-26*a-51,),(26*a-77,),(-46*a+63,),(-46*a-17,),(73,),(-34*a+75,),(-34*a-41,),(50*a+7,),(50*a-57,),(44*a+23,),(-44*a+67,),(30*a+47,),(-30*a+77,),(-8*a-69,),(-8*a+77,),(-38*a-35,),(-38*a+73,),(22*a+57,),(-22*a+79,),(-2*a+75,),(-2*a-73,),(54*a-47,),(-54*a+7,),(-14*a-65,),(-14*a+79,),(-50*a-9,),(50*a-59,),(-56*a+19,),(-56*a+37,),(52*a+3,),(52*a-55,),(12*a+67,),(-12*a+79,),(34*a+43,),(-34*a+77,),(-46*a+67,),(46*a+21,),(-10*a-69,),(10*a-79,),(-4*a+77,),(4*a+73,),(56*a-15,),(-56*a+41,),(-52*a+57,),(52*a+5,),(-8*a-71,),(8*a-79,),(-20*a+81,),(20*a+61,),(36*a+41,),(36*a-77,),(-54*a+1,),(54*a-53,),(-2*a+77,),(-2*a-75,),(42*a-73,),(-42*a-31,),(-26*a+81,),(-26*a-55,),(-52*a+59,),(52*a+7,),(-6*a+79,),(6*a+73,),(-56*a+9,),(56*a-47,),(28*a-81,),(28*a+53,),(34*a+45,),(34*a-79,),(-48*a-19,),(48*a-67,),(58*a-25,),(-58*a+33,),(58*a-35,),(-58*a+23,),(58*a-39,),(58*a-19,),(46*a+25,),(-46*a+71,),(-20*a+83,),(-20*a-63,),(18*a-83,),(-18*a-65,),(16*a+67,),(16*a-83,),(-2*a+79,),(-2*a-77,),(52*a-63,),(-52*a-11,),(-56*a+3,),(-56*a+53,),(-28*a-55,),(28*a-83,),(-58*a+13,),(58*a-45,),(-44*a-31,),(-44*a+75,),(-30*a-53,),(30*a-83,),(46*a+27,),(46*a-73,),(-58*a+47,),(58*a-11,),(-56*a+1,),(56*a-55,),(-4*a+81,),(4*a+77,),(-58*a+9,),(58*a-49,),(60*a-29,),(-60*a+31,),(-50*a-19,),(-50*a+69,),(22*a-85,),(22*a+63,),(-56*a+57,),(56*a+1,),(24*a+61,),(-24*a+85,),(-18*a+85,),(18*a+67,),(-8*a+83,),(-8*a-75,),(26*a+59,),(-26*a+85,),(-34*a-49,),(34*a-83,),(-60*a+19,),(60*a-41,),(-14*a+85,),(14*a+71,),(-56*a+59,),(-56*a-3,),(-42*a-37,),(42*a-79,),(-60*a+43,),(60*a-17,),(-50*a-21,),(-50*a+71,),(-40*a+81,),(40*a+41,),(-54*a+65,),(-54*a-11,),(-32*a-53,),(-32*a+85,),(58*a-55,),(58*a-3,),(56*a+5,),(56*a-61,),(52*a+17,),(52*a-69,),(46*a-77,),(46*a+31,),(-44*a-35,),(-44*a+79,),(-26*a+87,),(-26*a-61,),(-60*a+11,),(60*a-49,),(-8*a-77,),(-8*a+85,),(-50*a-23,),(50*a-73,),(-16*a+87,),(16*a+71,),(28*a+59,),(28*a-87,),(-54*a+67,),(54*a+13,),(62*a-25,),(-62*a+37,),(-62*a+23,),(-62*a+39,),(-62*a+21,),(-62*a+41,),(-60*a+53,),(60*a-7,),(-32*a+87,),(32*a+55,),(48*a-77,),(-48*a-29,),(-56*a+65,),(56*a+9,),(-44*a-37,),(44*a-81,),(-62*a+43,),(62*a-19,),(-38*a+85,),(38*a+47,),(83,),(10*a-87,),(10*a+77,),(58*a+3,),(58*a-61,),(-4*a+85,),(4*a+81,),(-26*a-63,),(26*a-89,),(-18*a-71,),(18*a-89,),(-62*a+15,),(62*a-47,),(-28*a-61,),(28*a-89,),(-8*a-79,),(8*a-87,),(-54*a-17,),(54*a-71,),(-58*a-5,),(58*a-63,),(48*a+31,),(-48*a+79,),(50*a-77,),(-50*a-27,),(-44*a-39,),(-44*a+83,),(-32*a+89,),(32*a+57,),(62*a-11,),(-62*a+51,),(-38*a+87,),(38*a+49,),(64*a-35,),(-64*a+29,),(-64*a+27,),(-64*a+37,),(34*a-89,),(34*a+55,),(-62*a+9,),(-62*a+53,),(54*a+19,),(-54*a+73,),(22*a+69,),(22*a-91,),(-4*a-83,),(4*a-87,),(-36*a+89,),(36*a+53,),(-58*a+67,),(58*a+9,),(-52*a+77,),(52*a+25,),(-30*a+91,),(30*a+61,),(64*a-47,),(-64*a+17,),(-32*a-59,),(32*a-91,),(-64*a+49,),(64*a-15,),(-6*a-83,),(6*a-89,),(12*a+79,),(-12*a+91,),(-58*a-11,),(58*a-69,),(34*a-91,),(34*a+57,),(-64*a+13,),(-64*a+51,),(52*a+27,),(-52*a+79,),(-46*a+85,),(46*a+39,),(-40*a+89,),(40*a+49,),(26*a-93,),(-26*a-67,),(-20*a-73,),(-20*a+93,),(-54*a-23,),(54*a-77,),(66*a-37,),(66*a-29,),(-60*a-7,),(60*a-67,),(16*a-93,),(16*a+77,),(-8*a+91,),(-8*a-83,),(-66*a+41,),(-66*a+25,),(66*a-23,),(-66*a+43,),(-48*a+85,),(48*a+37,),(52*a-81,),(-52*a-29,),(64*a-57,),(64*a-7,),(58*a+15,),(-58*a+73,),(40*a-91,),(-40*a-51,),(-44*a+89,),(44*a+45,),(66*a-49,),(-66*a+17,),(-62*a+65,),(-62*a-3,),(-26*a-69,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [-1, 0, 2, 4, -1, -6, 0, 0, 2, 6, -6, -4, 2, -4, -4, 0, -6, 2, -4, -12, -6, -4, 8, 12, 18, 14, -16, 6, -6, 8, 20, 18, -18, 0, 18, 8, -16, 8, -16, 8, 0, 0, 12, 6, -4, -22, -18, 18, -4, -10, 6, 6, -12, 12, -6, 18, 26, 20, 6, 30, -10, -18, 6, -28, -10, 14, 8, -12, 36, 0, -24, -10, 14, -22, 8, 20, -6, -6, 18, 6, -34, -4, -24, 0, 0, -36, -30, 6, 8, -10, 14, 32, -40, 8, -24, -36, 20, 14, -10, 38, 26, 8, -6, -6, 12, -42, -16, 14, 36, 42, -10, 2, -12, -24, -16, -10, -48, 36, -18, -6, -12, 0, 50, -10, -24, 36, 42, -12, 26, -34, -34, 20, 0, 36, -16, -4, 38, 2, -36, 18, -48, -42, -4, 26, 12, 12, 24, 6, 32, -10, 56, -40, -46, -52, 36, 24, -22, 26, 18, 36, 6, -54, -10, 8, 32, -6, -42, 20, 2, 38, -16, 6, 0, 36, 36, -46, -10, 8, -28, -24, 6, -64, 8, 14, 50, 48, 24, 2, 50, -34, -10, 12, 30, -34, 20, -60, -36, -40, 50, -16, -10, 12, -18, 12, 18, -54, -12, 38, -52, -64, 56, -28, -40, 0, -18, 54, 30, -10, -58, -6, -42, 56, -4, -10, 44, 0, 24, -24, 36, 38, -64, -22, -10, 18, 30, 6, -12, -60, 6, 24, 48, 26, -28, 56, 2, -6, -66, 74, -58, 30, -12, -42, 24, -10, -52, 32, -16, 48, 6, -10, 30, 24, -28, -4, 78, 18, 80, 8, -4, -64, -60, 66, 2, -70, -58, 8, -34, 32, 48, -24, -70, 38, -48, 6, 66, -60, 30, 60, -16, 74, -36, -30, -16, -16, 24, 0, -40, -4, -34, 2, -84, 6, -48, 0, 56, -58, 30, -6, -54, 66, -22, -4, -12, -48, 18, -42, 54, 42, 86, -58, 74, -16, 12, 54, 68, -4, -24, 48, -10, -30, 12, 74, 2, 54, 84, -88, -52, 50, 68, 74, -46, -12, 48, 8, -22, -18, 30, -42, 24, 44, 20, 2, 38, 18, 30, -4, 74, 42, -78, -48, -24, -10, 56, -48, 12, 36, -36, -88, -28, 20, 44, 14, -52, -18, -84, -6, -18, -18, 54, -82, 56, 48, -72, -72, 60, 44, -52, 18, 66, 80, -82, 26, 92, 32, 20, -30, 12, -72, 72, 86, -58, 68, -58, 96, 54, -90, -18, -22, 86, 50, -46, 48, -30, 42, -90, -54, -36, 56, 44, 26, -58, 6, 30, -54, 30, -48, -78, -72, -12, -18, -30, -48, 60, 50, 68, -46, -88, 50, -10, 92, -28, 60, -72, 38, -22, 72, -36, -96, 78, -16, -76, 12, -12, 56, -64, 30, -30, -94, -82, -18, -30, -76, 86, -40, -76, -36, -60, 38, -22, 62, -70, -64, 8, -66, 0, 8, -40, 78, -12, -4, 50, 108, -78, 84, 30, -18, 12, -12, 108, 44, 50, -88, -16, -16, 38, 62, 36, -36, -6, 18, -52, 62, 66, -60, 102, 6, 32, 8, -58, 26, -24, 42, -34, 2, 30, -6, -88, 38, -82, 74, -24, 12, 56, -106, -46, 74, 20, -102, 48, 30, 36, -24, -36, 92, 92, 6, 6, 44, -76, -72, -60, 20, 86, -4, -118, -102, -54, 120, 102, 8, 116, 56, -16, -30, 78, 66, 0, 0, -36, 14, -4, 62, 62, -4, 50, -76, 20, 72, -108, -48, 36, 110, -52, 32, 8, -46, -112, -84, 60, 6, -90, 68, -124, -90, 90, 96, 0, 62, 8, 72, 12, 66, 18, -76, 8, 108, -12, -18, 90, -72, 42, -4, 110, -102, -54, -18, -42, 12, -90, 104, -64, -84, -36, 102, -108, 50, 26, -58, 68, 50, -46, 0, 60, -30, 18, -82, 38, 20, 56, -54, 30, -12, -48, 134, -46, -66, -96, -10, -4, 2, 110, -96, 30, -100, 122, -18, 54, -16, 8, 32, -118, -78, -6, -96, -120, 98, 92, -46, -22, -108, 36, 14, -82, -16, 104, -66, -90, 48, 66, 20, -76, 36, 60, -124, -118, -76, 68, 56, -46, -78, -96, -78, -42, -88, 8, -114, 90, 62, 104, 72, 84, -124, 50, -30, 96, -138, -90, 0, -36, 36, 0, -96, 42, 122, -24, 54, -36, 54, 74, -16, 116, 20, -78, -60, 68, -118, -96, 102, -144, 36, 122, -16, -34, 44, -132, 24, -124, -4, 108, 54, -70, -46, 104, -4, 96, -120, 132, 72, 38, -22, -90, -30, 30, 36, 74, 26, 54, -6, 50, 50, -112, -76, 120, -24, 8, 122, -42, -90, -100, 62, -64, 2, 18, 66, 18, 96, -108, -18, 32, -118, 18, 66, -100, -34, 90, 36, -148, -58, -60, -78, -4, -94, 8, -64, -82, -64, 30, 0, 18, 84, -58, 86, 60, 24, 18, -108, 80, -16, -120, 90, -64, 116, -58, 122, 114, 60, -24, -96, -34, 62, -108, -24, -108, 54, -6, 126, 74, -118, -28, 80, 132, -30, -112, -112, 62, 56, -58, 122, 92, 68, 66, 78, 92, 116, 110, 86, 12, -54, -6, -6, -76, -4, 20, -58, -144, -12, 98, 104, -90, 108, 20, -64, 2, 38, 84, 60, -40, 2, 86, 140, -46, 146, 114, 66, -42, 114, 116, -88, 2, -100, -54, 120, 108, 90, 44, 38, -114, 90, 62, -64, -102, 54, -114, -30, -40, 8, 92, 8, 62, 66, 12, 24, -48, -156, -30, 108, 0, 38, -148, -90, -120, -82, -70, -6, 6, 56, -100, 132, -84, 26, -34, 72, 120, -30, -54, 102, 126, 24, 156, 114, -12, 128, 80, -6, 24, 98, -70, 54, -12, 20, -82, -12, 120, 84, 54, 14, 20, 36, 72, 80, -10, -100, -112, -106, 50, 158, -58, 66, 138, 92, 26, -94, 14, 12, -144, -24, -150, 66, -90, 102, 138, 108, 36, 110, -118, 0, -36, -102, 24, 140, 44, 80, 152, -70, -82, 138, -84, 62, 14, 128, -22, -40, 152, -76, 68, 30, -12, -78, -18, -84, -96, 60, 120, 138, -78, 50, -100, -42, -156, -60]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal((a,))] = 1
AL_eigenvalues[ZF.ideal((-a + 1,))] = -1
AL_eigenvalues[ZF.ideal((-2*a + 3,))] = 1

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