"""
  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, 0, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((38, 19*a))

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

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [-1, 1, 1, -6, -6, 3, 3, 1, 1, -10, 0, 0, 8, 8, -13, 9, 9, 5, 5, -7, -7, -6, -6, -12, -12, -10, -10, -9, -9, 6, 6, 0, 0, -9, -9, -4, -4, 20, 20, -1, 0, 0, 14, 14, 5, 5, -15, -15, -6, -6, 8, 8, 6, 6, 12, 12, 0, 0, -22, -22, 20, 20, -19, -19, -1, -1, -4, -4, 18, 18, -15, -15, -7, -7, 0, 0, 32, 32, -12, -12, 2, 2, -18, -18, -18, -18, 17, 17, 18, 18, -36, -36, -4, -4, -36, -36, 11, 11, -37, 44, 44, -12, -12, -24, -24, -4, -4, 11, 11, -12, -12, -30, -30, -28, -28, -6, -6, -10, -10, 6, 6, -22, -22, -45, -45, 44, 44, 36, 36, -10, -10, -16, -16, -21, -21, 5, 5, -31, -31, 9, 9, 11, 11, 33, 33, 23, -12, -12, 14, 14, -18, -18, -34, -34, -37, -37, 33, 33, -7, -7, -48, -48, 30, 30, -46, 12, 12, -12, -12, 20, 20, 39, 39, -1, -1, 30, 30, 8, 8, -33, -33, 48, 48, 8, 8, -58, -58, -34, -34, -36, -36, 56, 56, -12, -12, 12, 12, 41, 41, 3, 3, -28, -28, -6, -6, -15, -15, -3, -3, -67, -67, 29, 29, 27, 27, -46, -46, 30, 30, -70, 18, 18, 27, 27, 66, 66, 66, 66, 29, 29, -30, -30, 26, 26, -58, -58, 18, 18, -12, -12, 74, 74, 36, 36, -60, -60, -4, -4, -69, -69, 62, 62, -30, -30, -28, -28, 38, 38, 60, 60, 66, 66, 17, 17, 3, 3, -13, -13, 47, 47, -55, -55, 14, 14, 6, 6, 20, 20, 0, 0, -4, -4, -79, -79, -18, -18, 36, 36, 66, 66, 60, 60, 3, 3, -46, -46, 14, 14, 69, 69, -4, -4, -34, -34, 81, 81, 90, 90, -4, -4, -16, -16, -54, -54, -37, -37, 78, 78, -37, -37, 23, 23, -9, -9, 2, 2, -7, -7, -73, -73, -94, 30, 30, 74, 74, -48, -48, 24, 24, -49, -49, -57, -57, 84, 84, -37, -37, -40, -40, 2, 2, 72, 72, 48, 48, -33, -33, -90, -90, -15, -15, 74, 74, 44, 44, 38, 38, 90, 90, -61, -61, -45, -45, 38, 38, -3, -3, 44, 44, -30, -30, -66, -66, 5, 5, -34, -34, -82, -82, -54, -54, -10, -10, 14, 14, 48, 48, 68, 68, 66, 66, -72, -72, 84, 84, 23, 23, -97, -24, -24, -64, -64, -27, -27, 62, 62, 77, 77, 51, 51, -69, -69, 2, 2, 21, 21, 3, 3, -88, -88, 50, 50, -42, -42, -94, -94, -63, -63, -46, -46, 44, 44, 54, 54, 21, 21, 35, 35, -18, -18, -4, -4, -16, -16, 29, 29, 0, 0, -54, -54, -58, -58, -75, -75, -108, -108, -79, -79, 51, 51, 68, 68, -43, -43, 24, 24, -21, -21, -70, -70, -33, -33, 23, 23, 60, 60, -76, -76, 0, 0, 56, 56, -90, -90, -15, -15, 116, 116, 20, 20, 96, 96, 92, 92, -55, -55, 24, 24, -63, -63, 53, 53, -30, -30, -79, -79, -34, -34, -55, -55, -22, -49, -49, -72, -72, -10, -10, 12, 12, 32, 32, -99, -99, 30, 30, -84, -84, 6, 6, -52, -52, -43, -43, 24, 24, 102, 102, 98, 98, 81, 81, -93, -93, 44, 44, -87, -87, -31, -31, 66, 66, -106, -106, 26, 26, 69, 69, 84, 84, -76, -76, 35, 35, 84, 84, 95, 95, 110, 110, -46, -46, -63, -63, -102, -102, 8, 8, 18, 18, 86, 86, -57, -57, 53, 53, 108, 108, 18, 18, -40, -40, -33, -33, 92, 92, -64, -64, 117, 117, 86, 86, -36, -36, 66, 66, 75, 75, 29, 29, 98, 98, -76, -76, -12, -12, -18, -18, -55, -55, 104, 104, -36, -36, 48, 48, 125, 125, 50, 50, -132, -132, -12, -12, 75, 75, -64, -64, -67, -67, 36, 36, 9, 9, 68, 68, 18, 18, -54, -54, -21, -21, -45, -45, -16, -16, -52, -52, 8, 8, 96, 96, -48, -48, -64, -64, -106, 60, 60, -70, -70, -12, -12, -12, -12, 131, 131, -16, -16, 30, 30, 57, 57, 108, 108, -58, -58, 98, 98, -73, -73, -4, -4, -30, -30, -100, -100, -96, -96, -121, -121, -61, -61, 39, 39, -111, -111, -132, -132, 20, 20, -129, -129, -82, -82, 50, 50, -96, -96, 102, 102, -22, -22, -27, -27, -124, -124, 134, 134, -10, -10, 45, 45, -18, -18, 116, 116, -49, -49, 38, 38, 140, 140, -124, -124, -123, -123, -4, -4, -36, -36, -69, -69, 20, 20, -118, -118, 87, 87, -148, -148, -51, -51, -61, -61, -72, -72, -49, -49, 69, 69, 90, 90, 14, 14, 20, 20, -10, -10, 93, 93, 62, 62, 78, 78, -88, -88, 135, 135, 80, 80, -54, -54, 2, 2, 125, 125, -58, -63, -63, -111, -111, 12, 12, -156, -156, -34, -34, 135, 135, 80, 80, -55, -55, -106, -106, -48, -48, -145, -145, 126, 126, 110, 110, -105, -105, -87, -87, -58, -58, -22, -22, 101, 101, 93, 93, -42, -42, 92, 92, -64, -64, -58, -58, -48, -48, 23, 23, -33, -33, -67, -67, -3, -3, -39, -39, -76, -76, -9, -9, 80, 80, 54, 54, -42, -42, 156, 156, 38, 38, -69, -69, 44, 44, -36, -36, 68, 68, -108, -108, -121, -121, -126, -126, -27, -27, 105, 105, -45, -45, -82, -82, -15, -15, 56, 56, -18, -18, 65, 65, 14, 14, 108, 108, 102, 102, 9, 9, -52, -52, -28, -28, 72, 72, 26, 26, -54, -54, 86, 86, 0, 0, -55, -55, 32, 32, 122, 122, -97, -97, 33, 33, 129, 129, -78, -78, 26, 26, -66, -66, -70, -70, -63, -63, 56, 56, -9, -9, -90, -90, 50, 50, 48, 48, 20, 20, -12, -12, 89, 89, -174, -174, -117, -117, 126, 126, 50, 50, -159, -159, 86, 86, 56, 56, -103, -103, 66, 66, 78, 78, 36, 36, -106, -106, 62, 62, -42, -42, 63, 63, 84]
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((-3*a + 1,))] = -1
AL_eigenvalues[ZF.ideal((3*a + 1,))] = -1

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