"""
  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([1, 0, 1])
F = NumberField(g, "i")
i = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((11767, 7*i + 2646))

primes_array = [
(i+1,),(-i-2,),(2*i+1,),(3,),(-2*i+3,),(2*i+3,),(i+4,),(i-4,),(-2*i+5,),(2*i+5,),(i+6,),(i-6,),(-4*i+5,),(4*i+5,),(7,),(-2*i+7,),(2*i+7,),(-6*i-5,),(6*i-5,),(-3*i-8,),(3*i-8,),(-5*i+8,),(-5*i-8,),(-4*i+9,),(4*i+9,),(i+10,),(i-10,),(-3*i+10,),(3*i+10,),(-8*i-7,),(8*i-7,),(11,),(-4*i-11,),(4*i-11,),(7*i+10,),(7*i-10,),(-6*i-11,),(6*i-11,),(-2*i+13,),(2*i+13,),(-10*i-9,),(10*i-9,),(7*i-12,),(7*i+12,),(i+14,),(i-14,),(-2*i+15,),(2*i+15,),(-8*i-13,),(-8*i+13,),(-4*i-15,),(4*i-15,),(i+16,),(i-16,),(13*i-10,),(13*i+10,),(-9*i+14,),(-9*i-14,),(-5*i+16,),(5*i+16,),(-2*i+17,),(2*i+17,),(-12*i+13,),(12*i+13,),(-11*i+14,),(-11*i-14,),(9*i-16,),(9*i+16,),(-5*i+18,),(-5*i-18,),(-8*i+17,),(8*i+17,),(19,),(-7*i+18,),(-7*i-18,),(10*i-17,),(10*i+17,),(-6*i+19,),(6*i+19,),(i+20,),(i-20,),(-3*i-20,),(3*i-20,),(-14*i+15,),(14*i+15,),(-12*i+17,),(12*i+17,),(-7*i-20,),(7*i-20,),(-4*i+21,),(4*i+21,),(-10*i-19,),(10*i-19,),(5*i+22,),(5*i-22,),(11*i-20,),(11*i+20,),(23,),(-10*i+21,),(10*i+21,),(-19*i-14,),(-19*i+14,),(-13*i+20,),(-13*i-20,),(i+24,),(i-24,),(-8*i-23,),(8*i-23,),(-5*i-24,),(5*i-24,),(-18*i-17,),(18*i-17,),(19*i-16,),(19*i+16,),(-4*i+25,),(4*i+25,),(13*i-22,),(13*i+22,),(-6*i+25,),(6*i+25,),(-12*i-23,),(12*i-23,),(i+26,),(i-26,),(-5*i+26,),(5*i+26,),(15*i+22,),(15*i-22,),(-2*i+27,),(2*i+27,),(-9*i-26,),(9*i-26,),(-20*i-19,),(20*i-19,),(-12*i+25,),(12*i+25,),(-22*i-17,),(22*i-17,),(-11*i+26,),(-11*i-26,),(-5*i+28,),(-5*i-28,),(-14*i-25,),(-14*i+25,),(10*i-27,),(10*i+27,),(-23*i+18,),(23*i+18,),(-4*i+29,),(4*i+29,),(-6*i-29,),(6*i-29,),(16*i+25,),(-16*i+25,),(-23*i-20,),(-23*i+20,),(-19*i+24,),(-19*i-24,),(-10*i-29,),(10*i-29,),(13*i+28,),(13*i-28,),(31,),(-4*i-31,),(4*i-31,),(-6*i+31,),(6*i+31,),(15*i-28,),(15*i+28,),(-22*i+23,),(22*i+23,),(-11*i-30,),(-11*i+30,),(-3*i-32,),(3*i-32,),(5*i+32,),(5*i-32,),(-10*i+31,),(10*i+31,),(13*i+30,),(13*i-30,),(-2*i+33,),(2*i+33,),(16*i-29,),(16*i+29,),(25*i-22,),(25*i+22,),(21*i+26,),(21*i-26,),(-27*i-20,),(-27*i+20,),(-8*i+33,),(8*i+33,),(-5*i-34,),(5*i-34,),(13*i+32,),(13*i-32,),(-24*i+25,),(24*i+25,),(-22*i+27,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [1, 1, 3, -3, -1, 1, 0, -4, 6, 8, -2, -2, 0, -12, 1, 4, -6, 7, -3, 4, 6, -8, -2, 8, -14, 9, 6, -6, -4, -1, -13, 5, -1, 3, 2, -24, -2, 13, -15, -22, 10, 3, -13, -1, -2, 6, 25, -22, 15, -21, 22, -18, 2, 6, 23, 22, -4, 2, 3, 3, -6, 23, -4, -18, -18, -10, -18, -23, 35, -26, 8, -18, -26, -34, 16, -32, -18, 5, 23, 34, -6, 8, -2, 4, 16, -30, -30, -9, -42, 29, 13, 6, 35, 31, -19, 0, -18, -26, 4, 34, 12, -26, -13, -18, 30, -32, -16, -8, 0, -8, 26, -40, -33, -18, -15, -19, -38, 12, -46, -43, 37, 29, -22, -43, 0, -20, 48, 36, 17, 19, 48, 22, 18, 12, -42, 34, 30, 39, -30, 50, -23, 33, 36, -20, -31, -18, -45, -51, 32, -26, 2, -48, -34, 12, -36, 30, 22, 2, -11, 31, 45, -30, 27, -2, 33, 49, 2, 47, -34, 27, 33, 38, -6, -6, -34, -54, 16, -30, 30, 37, -17, -46, 26, -42, 6, 10, -18, -26, 44, -50, -6, -60, 56, -19, 30, -14, 20, -66, 2, 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((-4*i + 5,))] = -1
AL_eigenvalues[ZF.ideal((7,))] = -1

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