"""
  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([57, 0, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((12, 2*a + 6))

primes_array = [
(2,a+1),(3,a),(11,a+3),(11,a+8),(19,a),(23,a+9),(23,a+14),(5,),(29,a+1),(29,a+28),(31,a+6),(31,a+25),(41,a+5),(41,a+36),(47,a+15),(47,a+32),(7,),(53,a+7),(53,a+46),(a+2,),(a-2,),(67,a+12),(67,a+55),(a+4,),(a-4,),(79,a+38),(79,a+41),(83,a+21),(83,a+62),(89,a+11),(89,a+78),(103,a+47),(103,a+56),(113,a+13),(113,a+100),(127,a+18),(127,a+109),(131,a+27),(131,a+104),(151,a+68),(151,a+83),(a+10,),(a-10,),(13,),(173,a+17),(173,a+156),(191,a+33),(191,a+158),(211,a+24),(211,a+187),(223,a+101),(223,a+122),(-2*a+1,),(-2*a-1,),(239,a+95),(239,a+144),(251,a+52),(251,a+199),(257,a+86),(257,a+171),(263,a+39),(263,a+224),(269,a+88),(269,a+181),(-2*a+7,),(2*a+7,),(281,a+96),(281,a+185),(17,),(293,a+23),(293,a+270),(307,a+76),(307,a+231),(311,a+58),(311,a+253),(a+16,),(a-16,),(317,a+102),(317,a+215),(331,a+85),(331,a+246),(347,a+45),(347,a+302),(-2*a+11,),(2*a+11,),(359,a+149),(359,a+210),(379,a+91),(379,a+288),(-2*a+13,),(2*a+13,),(401,a+128),(401,a+273),(419,a+161),(419,a+258),(439,a+203),(439,a+236),(443,a+51),(443,a+392),(449,a+29),(449,a+420)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [0, 1, 4, 4, 4, -8, -8, -6, -6, -6, -8, -8, 6, 6, 0, 0, -14, 2, 2, -2, -2, 4, 4, 10, 10, 8, 8, -4, -4, 6, 6, -16, -16, -18, -18, 8, 8, -4, -4, 16, 16, -2, -2, -22, -6, -6, 0, 0, 20, 20, 8, 8, 22, 22, -16, -16, 20, 20, -2, -2, -8, -8, 10, 10, -26, -26, -26, -26, -30, 18, 18, -12, -12, -24, -24, -6, -6, -6, -6, -20, -20, -12, -12, 30, 30, -24, -24, -20, -20, 14, 14, 30, 30, 12, 12, 0, 0, 20, 20, 14, 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((3, a))] = -1

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