"""
  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([14, -1, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((80, a + 62))

primes_array = [
(2,a),(2,a+1),(5,a+2),(7,a),(7,a+6),(3,),(11,a+5),(13,a+3),(13,a+9),(17,a+4),(17,a+12),(31,a+10),(31,a+20),(43,a+8),(43,a+34),(-2*a+3,),(2*a+1,),(-2*a+5,),(2*a+3,),(73,a+11),(73,a+61),(83,a+25),(83,a+57),(89,a+18),(89,a+70),(107,a+32),(107,a+74),(127,a+15),(127,a+111),(167,a+60),(167,a+106),(173,a+69),(173,a+103),(179,a+26),(179,a+152),(181,a+68),(181,a+112),(191,a+80),(191,a+110),(193,a+78),(193,a+114),(197,a+19),(197,a+177),(-2*a+13,),(2*a+11,),(227,a+47),(227,a+179),(-4*a+5,),(4*a+1,),(233,a+71),(233,a+161),(-2*a+15,),(2*a+13,),(263,a+102),(263,a+160),(-4*a+9,),(4*a+5,),(277,a+52),(277,a+224),(283,a+23),(283,a+259),(293,a+90),(293,a+202),(307,a+24),(307,a+282),(-2*a+17,),(2*a+15,),(331,a+145),(331,a+185),(337,a+144),(337,a+192),(347,a+98),(347,a+248),(19,),(373,a+54),(373,a+318),(-2*a+19,),(2*a+17,),(-4*a-11,),(4*a-15,),(401,a+167),(401,a+233),(419,a+76),(419,a+342),(421,a+153),(421,a+267),(449,a+123),(449,a+325),(457,a+67),(457,a+389),(-6*a+1,),(6*a-5,),(503,a+31),(503,a+471),(-4*a-15,),(4*a-19,),(521,a+45),(521,a+475),(523,a+214),(523,a+308)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

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

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