"""
  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((9, 9*a))

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, 0, -1, 1, -6, 2, -2, 0, -9, 9, -3, -3, -9, 9, -1, 1, 4, 3, -3, 3, 3, -15, -15, 7, 7, -3, -3, 7, -7, 3, -3, -18, -18, 15, -15, -6, -6, -14, 14, 9, 9, -9, -9, 26, 15, -15, -13, 13, 9, 9, -15, -15, -3, -3, -7, 7, -22, 22, 6, -6, 25, -25, 6, -6, 21, 21, -24, 24, 6, -33, 33, 15, 15, -19, 19, 15, 15, -24, 24, 6, 6, 10, -10, -1, -1, 4, -4, 27, 27, 25, 25, 36, -36, -7, 7, -9, -9, 25, -25, 9, -9]
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

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