"""
  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((1944, 24*a + 528))

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, 0, 1, -6, -6, -2, -4, 1, -5, -3, 8, -2, -11, 1, -5, -8, -4, -3, -12, 6, -3, 14, -8, -2, 2, -7, 5, -18, -6, 0, -12, -14, -4, -12, -12, 7, -5, -7, 20, -2, -4, -14, 3, -9, -8, 4, 2, 10, 20, -8, -7, 5, 0, 0, 6, -30, -6, 12, -1, -28, 27, -15, -5, 22, -7, -13, -22, -19, -16, 4, -18, -24, 35, -4, -6, -6, 34, 37, -24, 6, -17, -14, 18, -24, 36, -6, -7, 17, 26, 4, 20, -8, 3, -39, 24, 18, 9, 0, 3, 19, 28, 24, -24, -36, -24, -8, -41, 15, 18, 22, -4, 36, -42, -25, 14, -2, -28, 15, 39, 10, 26, -31, 23, 6, 42, -17, 43, 4, -34, 25, -32, 43, -41, -14, -22, 7, 55, 24, -27, 12, -30, 7, 28, 42, 0, 41, 6, 6, -20, 1, -20, -22, -4, 44, -43, 47, 50, 34, -29, 55, -18, -42, -54, -6, -41, -30, -48, -8, 2, 45, 42, 20, -8, 5, 26, -36, -12, -41, 52, 0, -18, 32, -2, 37, -20, 34, 10, -43, 5, 24, 42, -67, -40, -4, -2, -24, -18, -5, 7, 44]
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((a - 1,))] = -1

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