"""
  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([41, -1, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((122, 2*a + 112))

primes_array = [
(2,),(3,),(5,),(-a,),(a-1,),(a+1,),(a-2,),(a+2,),(a-3,),(7,),(a+3,),(a-4,),(a+4,),(a-5,),(a+5,),(a-6,),(a+6,),(a-7,),(a+7,),(a-8,),(a+8,),(a-9,),(11,),(a+9,),(a-10,),(a+10,),(a-11,),(-2*a+1,),(-2*a+3,),(-2*a-1,),(13,),(a+11,),(a-12,),(-2*a+5,),(2*a+3,),(a+12,),(a-13,),(-2*a+7,),(2*a+5,),(a+13,),(a-14,),(-2*a+9,),(2*a+7,),(a+14,),(a-15,),(-2*a+11,),(2*a+9,),(a+15,),(a-16,),(17,),(-2*a+13,),(2*a+11,),(a+16,),(a-17,),(a+17,),(a-18,),(-2*a+15,),(2*a+13,),(19,),(-3*a+1,),(3*a-2,),(-3*a+4,),(3*a+1,),(-3*a-2,),(3*a-5,),(a+18,),(a-19,),(-3*a+7,),(3*a+4,),(-3*a-5,),(3*a-8,),(-2*a+17,),(2*a+15,),(a+19,),(a-20,),(-3*a+10,),(3*a+7,),(-3*a-8,),(3*a-11,),(a+20,),(a-21,),(-2*a+19,),(2*a+17,),(-3*a+13,),(3*a+10,),(a+21,),(a-22,),(-3*a-11,),(3*a-14,),(23,),(a+22,),(a-23,),(-2*a+21,),(2*a+19,),(-3*a+16,),(3*a+13,),(a+23,),(a-24,),(-3*a-14,),(3*a-17,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [-1, -2, 1, -7, -3, -5, -5, -6, -12, 1, -6, 12, 8, -1, 0, 0, 1, 15, 5, -3, -2, 14, -14, 20, 12, 12, 10, -4, 14, 6, -3, 6, 0, -9, 9, -12, 8, 22, -16, -16, 28, -1, -5, 9, -7, 6, -4, 27, -15, 18, 9, 29, -17, 9, -3, 19, 28, -26, -2, -18, -36, 18, 34, 17, -29, -8, -18, -4, -36, -10, -10, 37, -27, -28, 8, -8, 22, 27, -7, -32, -12, -2, 32, -24, -4, 4, -14, -7, -11, 13, -16, 12, 11, -31, 43, -3, -3, 19, -28, 22]
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((a - 5,))] = 1

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