"""
  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([17, -1, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((174, 6*a + 18))

primes_array = [
(2,),(3,),(-a,),(a-1,),(a+1,),(a-2,),(a+2,),(a-3,),(5,),(a+3,),(a-4,),(a+4,),(a-5,),(a+5,),(a-6,),(7,),(a+6,),(a-7,),(-2*a+1,),(-2*a+3,),(2*a+1,),(a+7,),(a-8,),(-2*a+5,),(2*a+3,),(a+8,),(a-9,),(-2*a+7,),(2*a+5,),(a+9,),(a-10,),(11,),(a+10,),(a-11,),(-2*a+9,),(2*a+7,),(a+11,),(a-12,),(-3*a+1,),(3*a-2,),(-3*a+4,),(3*a+1,),(-3*a-2,),(3*a-5,),(-2*a+11,),(2*a+9,),(13,),(a+12,),(a-13,),(-3*a+7,),(3*a+4,),(-3*a-5,),(3*a-8,),(a+13,),(a-14,),(-2*a+13,),(2*a+11,),(-3*a+10,),(3*a+7,),(a+14,),(a-15,),(-3*a-8,),(3*a-11,),(a+15,),(a-16,),(-2*a+15,),(2*a+13,),(-4*a+1,),(4*a-3,),(-4*a+5,),(4*a+1,),(-3*a+13,),(3*a+10,),(-4*a-3,),(4*a-7,),(-3*a-11,),(3*a-14,),(-4*a+9,),(4*a+5,),(-4*a-7,),(4*a-11,),(a+18,),(a-19,),(-4*a+13,),(4*a+9,),(a+19,),(a-20,),(-5*a+3,),(-5*a+2,),(-5*a+1,),(5*a-4,),(-5*a+6,),(5*a+1,),(5*a+2,),(5*a-7,),(-5*a+8,),(-5*a-3,),(-3*a+19,),(3*a+16,),(-5*a-4,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [1, 1, 3, 0, -4, -4, 0, 6, -1, -1, -6, 5, -4, -3, -6, -1, -12, 3, -4, 0, -6, -7, 2, 9, 3, 0, 3, -4, -13, 18, 0, -4, 17, 8, -9, 18, -21, -6, -10, 8, 11, -10, 20, 14, -3, 24, -1, 0, 18, -7, 17, 23, 14, -4, -10, 20, -13, -10, 2, -21, 9, 23, -7, -18, 15, -9, 0, -18, 15, -16, -16, -25, -28, 6, -15, -16, -16, 6, -12, 2, 17, 12, 24, -6, -30, 29, 17, 27, -9, 35, -22, -3, 12, 35, -37, -36, 15, 23, -13, -9]
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,))] = -1
AL_eigenvalues[ZF.ideal((3,))] = -1
AL_eigenvalues[ZF.ideal((a + 3,))] = 1

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