"""
  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([6, -1, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((78, a + 21))

primes_array = [
(2,a),(2,a+1),(3,a),(3,a+2),(13,a+4),(13,a+8),(-2*a+1,),(5,),(29,a+10),(29,a+18),(31,a+7),(31,a+23),(41,a+15),(41,a+25),(47,a+13),(47,a+33),(7,),(-2*a+7,),(2*a+5,),(71,a+20),(71,a+50),(73,a+29),(73,a+43),(-4*a+5,),(4*a+1,),(11,),(127,a+27),(127,a+99),(131,a+48),(131,a+82),(139,a+16),(139,a+122),(151,a+42),(151,a+108),(163,a+62),(163,a+100),(-2*a+13,),(2*a+11,),(-4*a-7,),(4*a-11,),(179,a+65),(179,a+113),(193,a+19),(193,a+173),(197,a+59),(197,a+137),(-6*a+1,),(6*a-5,),(-6*a+7,),(6*a+1,),(233,a+103),(233,a+129),(239,a+53),(239,a+185),(257,a+78),(257,a+178),(269,a+120),(269,a+148),(-6*a-5,),(6*a-11,),(277,a+81),(277,a+195),(17,),(-6*a+13,),(6*a+7,),(311,a+70),(311,a+240),(-4*a+17,),(4*a+13,),(331,a+44),(331,a+286),(-2*a+19,),(2*a+17,),(349,a+158),(349,a+190),(353,a+37),(353,a+315),(19,),(397,a+84),(397,a+312),(409,a+28),(409,a+380),(439,a+118),(439,a+320),(443,a+51),(443,a+391),(-8*a-5,),(-8*a+13,),(461,a+163),(461,a+297),(-6*a+19,),(6*a+13,),(487,a+112),(487,a+374),(491,a+153),(491,a+337),(499,a+31),(499,a+467),(509,a+110),(509,a+398)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [0, -1, -1, 3, 0, 1, 1, 4, 10, 2, -5, 1, -11, -3, 6, -11, -9, 12, 7, 13, -2, 2, 7, 7, 9, 2, 2, 17, 17, 4, -14, -2, -20, 6, -1, -14, 12, -4, -18, 11, -8, 3, 10, -9, -22, -24, -22, -14, -22, -24, -14, -4, -16, 0, -28, 22, 0, -30, -15, -13, -1, 18, -12, 29, 34, 0, -4, 7, 10, 16, 18, 26, 7, -10, 1, -6, -12, -12, 12, -18, 26, 8, -24, -7, 20, 8, 2, -12, -12, -35, 8, -20, -21, -12, 15, 36, -10, -23, -9, 6]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal((2, a + 1))] = 1
AL_eigenvalues[ZF.ideal((3, a))] = 1
AL_eigenvalues[ZF.ideal((13, a + 8))] = -1

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