"""
  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([55, -1, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((57, a + 55))

primes_array = [
(3,a+1),(2,),(5,a),(5,a+4),(11,a),(11,a+10),(17,a+5),(17,a+11),(19,a+1),(19,a+17),(29,a+9),(29,a+19),(37,a+7),(37,a+29),(47,a+21),(47,a+25),(7,),(53,a+14),(53,a+38),(59,a+15),(59,a+43),(a+2,),(a-3,),(a+3,),(a-4,),(73,a+36),(79,a+13),(79,a+65),(83,a+34),(83,a+48),(a+6,),(a-7,),(101,a+32),(101,a+68),(107,a+33),(107,a+73),(109,a+16),(109,a+92),(113,a+40),(113,a+72),(a+8,),(a-9,),(131,a+24),(131,a+106),(167,a+49),(167,a+117),(13,),(179,a+76),(179,a+102),(181,a+81),(181,a+99),(191,a+56),(191,a+134),(197,a+30),(197,a+166),(a+12,),(a-13,),(-2*a+3,),(-2*a-1,),(233,a+62),(233,a+170),(239,a+88),(239,a+150),(263,a+35),(263,a+227),(281,a+64),(281,a+216),(-2*a+9,),(2*a+7,),(349,a+31),(349,a+317),(367,a+95),(367,a+271),(373,a+171),(373,a+201),(a+18,),(a-19,),(431,a+193),(431,a+237),(439,a+104),(439,a+334),(443,a+161),(443,a+281),(449,a+121),(449,a+327),(457,a+182),(457,a+274),(463,a+93),(463,a+369),(467,a+210),(467,a+256),(487,a+37),(487,a+449),(491,a+85),(491,a+405),(-3*a+4,),(3*a+1,),(521,a+50),(521,a+470),(-3*a+7,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [1, 1, 0, -4, 2, 2, 4, 0, 4, 1, 0, 0, 2, -6, 6, 6, -6, 4, -12, 6, -6, -10, 6, 4, 4, -10, 0, -8, 6, 14, 10, -14, 0, 12, -14, -2, -14, -14, -4, -20, -16, -8, 14, -2, -2, 2, -6, -10, 10, 10, -14, 10, -6, -16, -4, 20, 12, -24, 16, -24, -4, -30, -6, 18, 18, -16, -8, 4, -4, 2, 2, 32, 8, -22, 10, -2, -18, 22, 2, -32, 0, 30, 22, -36, -28, 38, -10, 32, 16, 18, -14, 24, 16, -2, 14, -36, 4, 0, -16, 12]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal((3, a + 1))] = -1
AL_eigenvalues[ZF.ideal((19, a + 17))] = -1

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