"""
  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([17, 0, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((17, a))

primes_array = [
(2,a+1),(3,a+1),(3,a+2),(7,a+2),(7,a+5),(11,a+4),(11,a+7),(13,a+3),(13,a+10),(a,),(23,a+11),(23,a+12),(5,),(31,a+13),(31,a+18),(a+6,),(a-6,),(71,a+14),(71,a+57),(79,a+33),(79,a+46),(89,a+28),(89,a+61),(101,a+36),(101,a+65),(107,a+25),(107,a+82),(131,a+30),(131,a+101),(137,a+42),(137,a+95),(139,a+20),(139,a+119),(-2*a+9,),(2*a+9,),(-3*a-2,),(3*a-2,),(163,a+31),(163,a+132),(167,a+22),(167,a+145),(199,a+88),(199,a+111),(211,a+48),(211,a+163),(227,a+94),(227,a+133),(229,a+21),(229,a+208),(257,a+92),(257,a+165),(-4*a-3,),(4*a-3,),(283,a+41),(283,a+242),(-2*a+15,),(2*a+15,),(311,a+43),(311,a+268),(347,a+32),(347,a+315),(-3*a-14,),(3*a-14,),(-4*a+9,),(4*a+9,),(19,),(367,a+152),(367,a+215),(373,a+27),(373,a+346),(379,a+143),(379,a+236),(389,a+138),(389,a+251),(-3*a+16,),(3*a+16,),(419,a+54),(419,a+365),(421,a+180),(421,a+241),(431,a+198),(431,a+233),(433,a+169),(433,a+264),(439,a+185),(439,a+254),(457,a+64),(457,a+393),(-5*a+6,),(5*a+6,),(479,a+221),(479,a+258),(487,a+38),(487,a+449),(499,a+116),(499,a+383),(503,a+140),(503,a+363),(-2*a+21,),(2*a+21,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [-1, 0, 0, 4, 4, 0, 0, -2, -2, 1, 4, 4, -6, 4, 4, 6, 6, -4, -4, 12, 12, 10, 10, -10, -10, 8, 8, 16, 16, -6, -6, -8, -8, -10, -10, -2, -2, 24, 24, -4, -4, -20, -20, 8, 8, -24, -24, 6, 6, 18, 18, -6, -6, -16, -16, 6, 6, 28, 28, 32, 32, -18, -18, -30, -30, -22, 28, 28, 6, 6, -8, -8, 6, 6, 26, 26, 8, 8, 22, 22, 12, 12, 2, 2, -20, -20, -6, -6, -2, -2, 36, 36, 20, 20, -40, -40, -12, -12, -2, -2]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal((a,))] = -1

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