"""
  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((28, 14*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 = [0, 0, 0, -4, -4, -6, -6, 8, 8, -6, 2, 2, -4, -4, 1, 0, 0, -4, -4, 10, 10, 8, 8, -6, -6, -6, -6, -12, -12, 2, 2, 8, 8, -6, -6, -8, -8, -12, -12, -22, -4, -4, -14, -14, 12, 12, -8, -8, -22, -22, 10, 10, 24, 24, 2, 2, -6, -6, 16, 16, -8, -8, -14, -14, -4, -4, 2, 2, 12, 12, -14, -14, -4, -4, 18, 18, -14, -14, -16, -16, 10, 10, 36, 36, 34, 34, -38, -38, -8, -8, -12, -12, -4, -4, 18, 18, -32, -32, -46, 36, 36, 32, 32, 26, 26, 28, 28, -14, -14, -24, -24, 34, 34, 26, 26, -38, -38, -32, -32, -30, -30, 16, 16, -12, -12, -14, -14, 36, 36, -8, -8, 52, 52, -30, -30, -22, -22, -40, -40, 26, 26, 16, 16, -28, -28, -22, 18, 18, -40, -40, 18, 18, -20, -20, -28, -28, 10, 10, 10, 10, 52, 52, -6, -6, 2, 48, 48, 2, 2, 2, 2, -60, -60, -22, -22, 42, 42, 4, 4, -48, -48, -6, -6, -8, -8, -38, -38, 50, 50, 4, 4, -20, -20, -36, -36, -6, -6, 2, 2, 2, 2, -30, -30, 32, 32, -28, -28, -6, -6, 24, 24, 50, 50, 48, 48, -46, -46, -6, -6, -70, -62, -62, -56, -56, -6, -6, 28, 28, 0, 0, 10, 10, 16, 16, 26, 26, -60, -60, -28, -28, -16, -16, 18, 18, -56, -56, 76, 76, 18, 18, -22, -22, -36, -36, -40, -40, 18, 18, 36, 36, 58, 58, 64, 64, -70, -70, 36, 36, -60, -60, 74, 74, 18, 18, -4, -4, 58, 58, 72, 72, 48, 48, -46, -46, 82, 82, -24, -24, 10, 10, 48, 48, -40, -40, -64, -64, 66, 66, -12, -12, -4, -4, -14, -14, -68, -68, -46, -46, 4, 4, 10, 10, 64, 64, 34, 34, 50, 50, 32, 32, -86, -86, -38, -38, -86, -86, -28, -28, 32, 32, -30, 32, 32, 52, 52, -80, -80, -78, -78, -38, -38, -6, -6, -44, -44, 12, 12, -96, -96, 42, 42, -86, -86, 48, 48, 18, 18, -22, -22, -76, -76, 88, 88, 90, 90, 42, 42, -36, -36, -40, -40, 72, 72, 66, 66, 42, 42, -14, -14, -6, -6, -30, -30, 48, 48, 4, 4, -46, -46, -12, -12, 32, 32, -54, -54, -14, -14, -44, -44, -30, -30, 82, 82, -30, -30, -32, -32, -70, -48, -48, -46, -46, -36, -36, 12, 12, 74, 74, 42, 42, 40, 40, -30, -30, -28, -28, 90, 90, -24, -24, -14, -14, -60, -60, -100, -100, 42, 42, 26, 26, 76, 76, -24, -24, -30, -30, -30, -30, 18, 18, 96, 96, -102, -102, -92, -92, -44, -44, 66, 66, -94, -94, 16, 16, 42, 42, 60, 60, 84, 84, 40, 40, 18, 18, -24, -24, 2, 2, -16, -16, 60, 60, -14, -14, 12, 12, -14, -14, -102, -102, 10, 10, 44, 44, -48, -48, -96, -96, 10, 10, 60, 60, -8, -8, 52, 52, 10, 10, -6, -6, 72, 72, -32, -32, 74, 74, 36, 36, 82, 82, -86, 60, 60, 66, 66, -14, -14, 80, 80, 74, 74, -92, -92, 90, 90, 60, 60, 2, 2, -46, -46, -4, -4, 96, 96, 42, 42, 60, 60, -8, -8, -30, -30, -8, -8, 60, 60, 108, 108, -78, -78, -48, -48, -86, -86, 2, 2, -40, -40, -68, -68, -102, -102, -44, -44, 106, 106, 50, 50, -6, -6, 76, 76, 10, 10, 120, 120, 42, 42, -76, -76, 32, 32, 82, 82, 80, 80, 114, 114, 42, 42, -30, -30, 80, 80, -92, -92, -70, -70, 2, 2, -72, -72, -70, -70, 50, 50, -80, -80, -40, -40, -94, -94, -20, -20, 92, 92, -30, -30, 4, 4, 36, 36, -6, -6, 32, 32, -14, -14, -94, -94, -36, -36, -14, -14, 120, 120, 10, 10, -24, -24, -126, -126, -14, -14, -46, -46, -126, -126, -80, -80, -70, -70, -62, -62, -16, -16, 2, 2, -40, -40, -30, -30, 72, 72, -78, -124, -124, 32, 32, 58, 58, -48, -48, -4, -4, 42, 42, -100, -100, 66, 66, 24, 24, -16, -16, 106, 106, 64, 64, 2, 2, -54, -54, 106, 106, 18, 18, 104, 104, 56, 56, 108, 108, -30, -30, -142, -142, -84, -84, -30, -30, -116, -116, 2, 2, -4, -4, 120, 120, 122, 122, -28, -28, -40, -40, -110, -110, 146, 146, -20, -20, -86, -86, 48, 48, -8, -8, -38, -38, 106, 106, -28, -28, 18, 18, 48, 48, -48, -48, -6, -6, -56, -56, -54, -54, -20, -20, -86, -86, 34, 34, -36, -36, 0, 0, -70, -70, 36, 36, -32, -32, -4, -4, -128, -128, -54, -54, 42, 42, 68, 68, -142, -142, -70, -70, 40, 40, -16, -16, -100, -100, 124, 124, -22, -22, 98, -102, -102, -72, -72, 44, 44, -102, -102, 2, 2, -62, -62, -6, -6, 84, 84, -44, -44, 2, 2, 140, 140, -78, -78, -110, -110, 36, 36, 90, 90, 130, 130, -68, -68, 106, 106, 116, 116, -38, -38, -40, -40, -46, -46, 28, 28, -20, -20, -62, -62, 34, 34, 40, 40, -22, -22, 154, 154, 76, 76, -96, -96, 154, 154, -72, -72, -12, -12, -62, -62, 42, 42, -54, -54, 20, 20, -108, -108, 56, 56, -72, -72, 122, 122, 96, 96, 122, 122, -6, -6, 120, 120, -112, -112, -44, -44, -110, -110, 82, 82, -54, -54, -70, -70, -144, -144, -70, -70, 148, 148, -108, -108, -120, -120, -72, -72, -118, -118, -136, -136, -62, -62, -68, -68, 50, 50, 66, 66, 24, 24, 106, 106, -14, -14, -80, -80, 114, 114, 84, 84, -150, -150, -158, -158, 60, 60, 8, 8, -24, -24, 90, 90, -86, -86, 156, 156, 122, 122, 74, 74, 28, 28, -72, -72, -150, -150, -86, -86, 18, 18, 120, 120, 0, 0, -124, -124, 26, 26, 114, 114, -134, -134, -142, -142, -56, -56, 106, 106, -140, -140, -108, -108, -54]
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((7,))] = -1

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