"""
  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((516, 2*a + 376))

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,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [0, -1, 1, 2, -5, -3, -4, -1, 2, -9, -5, 6, -1, 4, -8, -1, 8, -8, -12, 3, -14, -12, 4, -7, -14, -8, -6, 10, 15, 6, 1, 12, -2, 12, 22, -10, -6, 5, 4, 21, 16, 4, -16, 12, -10, 20, -18, 14, 19, 3, 1, -12, -18, -20, -24, -18, 3, 28, 28, -25, -9, -25, 6, -19, 20, 0, -14, -6, -9, -19, -12, 14, -28, 5, 0, 14, 38, -32, 39, 15, 14, 5, 10, 41, -26, 34, 8, -5, 8, 30, -36, 20, 16, -16, 12, -20, -6, 5, -26, -15, 19, -6, -24, 39, -6, 35, -2, 27, -38, 33, -15, -29, -39, 0, 19, -27, 30, 37, -19, -30, 0, 30, 14, -27, -6, 17, 20, -30, -12, 16, -11, 6, 17, -6, -31, -50, 26, 24, -43, -2, 54, 17, -4, -43, -42, 19, -48, -9, -4, 23, -18, -39, -9, -15, 52, 22, 50, -40, -1, -20, -24, -3, 58, 42, 34, -34, -41, 30, 12, -47, 52, -45, -53, -11, 9, 6, 9, -33, -54, -53, -38, 0, -18, -41, 42, 10, -44, -34, -29, -20, -66, 52, -12, 28, 22, 12, 10, 38, -2, -12]
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((-3*a - 5,))] = 1

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