"""
  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([8, -1, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((2480, a + 263))

primes_array = [
(2,a),(2,a+1),(5,a+1),(5,a+3),(7,a+2),(7,a+4),(3,),(19,a+5),(19,a+13),(-2*a+1,),(41,a+12),(41,a+28),(-2*a+5,),(2*a+3,),(59,a+10),(59,a+48),(-2*a+7,),(2*a+5,),(71,a+26),(71,a+44),(97,a+19),(97,a+77),(101,a+37),(101,a+63),(103,a+40),(103,a+62),(107,a+20),(107,a+86),(109,a+14),(109,a+94),(113,a+33),(113,a+79),(11,),(-2*a+11,),(2*a+9,),(-4*a-3,),(4*a-7,),(157,a+17),(157,a+139),(163,a+67),(163,a+95),(13,),(-4*a+9,),(4*a+5,),(191,a+27),(191,a+163),(193,a+55),(193,a+137),(211,a+89),(211,a+121),(-2*a+15,),(2*a+13,),(233,a+96),(233,a+136),(257,a+22),(257,a+234),(281,a+118),(281,a+162),(-6*a+1,),(6*a-5,),(17,),(-4*a-11,),(4*a-15,),(307,a+65),(307,a+241),(311,a+111),(311,a+199),(317,a+35),(317,a+281),(-4*a+17,),(4*a+13,),(359,a+158),(359,a+200),(373,a+144),(373,a+228),(-6*a+13,),(6*a+7,),(397,a+74),(397,a+322),(419,a+91),(419,a+327),(421,a+183),(421,a+237),(-2*a+21,),(2*a+19,),(439,a+29),(439,a+409),(443,a+66),(443,a+376),(467,a+209),(467,a+257),(479,a+87),(479,a+391),(503,a+195),(503,a+307),(-8*a+9,),(8*a+1,),(23,),(541,a+73),(541,a+467)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [1, 0, 0, -1, -4, 2, 2, -8, 8, 1, -6, 2, -4, -2, 14, -4, -8, 8, 0, 12, -4, 0, -12, 10, -12, 16, 18, 12, 2, 14, 8, 0, -10, -12, -12, 6, -4, 10, 22, -2, 4, -16, -22, -14, -16, 10, 6, -14, 26, -12, 10, 12, 8, -24, -30, -6, 26, 2, 6, -28, -10, 6, -2, 28, 34, -12, -32, 6, -16, -36, 14, -6, 20, -2, 26, 20, 14, -2, 8, -20, 26, 10, -32, -40, -30, 24, 6, 4, 20, -12, -6, 12, 16, 0, -20, -42, -10, 2, 30, -14]
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((5, a + 3))] = 1
AL_eigenvalues[ZF.ideal((-2*a + 1,))] = -1

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