"""
  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((4644, 6*a + 3000))

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, 0, -5, 2, -4, 6, -4, -4, 6, 9, -2, -8, -1, -5, -13, -10, 12, -5, 7, 6, 10, 9, -2, -1, 0, -2, 0, 7, 16, -21, 4, 3, 10, 12, -12, -7, 7, 17, -9, -23, -23, -3, 26, 2, -4, -10, -24, -9, 4, -15, -14, -20, 18, 3, -24, -2, 27, 14, 7, -28, -24, -4, -3, -18, -4, 30, 22, -7, -12, 17, -21, 23, -34, -19, -18, 4, -25, 21, -24, -13, 8, 20, -32, -20, 1, 7, -34, 24, -34, -10, -18, 29, 7, -5, -24, 26, 24, -32, -17, -12, -36, -36, -9, -45, -2, -40, -47, 30, 48, -36, -6, -8, -32, -42, 6, -6, 17, -32, 18, 21, 50, -45, -45, -6, 32, 5, 21, 24, 19, 25, -13, 9, 8, -6, 5, -35, 14, 27, -24, -44, -4, 50, 27, 44, 22, 30, 48, 47, 29, 18, -51, -6, 12, -5, 10, 23, -16, 16, -25, -24, 3, 6, -14, -2, -20, 56, -12, 12, 46, 43, 10, 54, -27, -26, -30, -27, 0, -30, -62, 43, 27, -36, 12, 4, 10, 22, 25, -58, 27, -44, 0, -20, -53, -59, -29, -18, -8, -40, -18]
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
AL_eigenvalues[ZF.ideal((3*a - 5,))] = 1

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