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

NN = ZF.ideal((24, 12*a))

primes_array = [
(2,a),(3,a+1),(3,a+2),(5,a+1),(5,a+4),(7,a),(13,a+5),(13,a+8),(19,a+9),(19,a+10),(a+3,),(a-3,),(59,a+24),(59,a+35),(61,a+13),(61,a+48),(71,a+25),(71,a+46),(79,a+12),(79,a+67),(83,a+22),(83,a+61),(101,a+17),(101,a+84),(113,a+41),(113,a+72),(11,),(-3*a+1,),(3*a+1,),(131,a+36),(131,a+95),(-2*a+9,),(2*a+9,),(139,a+60),(139,a+79),(-3*a-5,),(3*a-5,),(157,a+65),(157,a+92),(173,a+32),(173,a+141),(181,a+23),(181,a+158),(191,a+69),(191,a+122),(193,a+76),(193,a+117),(227,a+101),(227,a+126),(229,a+98),(229,a+131),(-4*a-3,),(4*a-3,),(a+15,),(a-15,),(251,a+57),(251,a+194),(263,a+81),(263,a+182),(269,a+40),(269,a+229),(-2*a+15,),(2*a+15,),(283,a+77),(283,a+206),(17,),(293,a+54),(293,a+239),(307,a+39),(307,a+268),(337,a+71),(337,a+266),(349,a+97),(349,a+252),(-5*a+3,),(-5*a-3,),(397,a+153),(397,a+244),(401,a+125),(401,a+276),(419,a+50),(419,a+369),(-5*a-9,),(5*a-9,),(-4*a-15,),(4*a-15,),(457,a+30),(457,a+427),(461,a+37),(461,a+424),(463,a+190),(463,a+273),(467,a+140),(467,a+327),(-3*a+19,),(3*a+19,),(509,a+214),(509,a+295),(523,a+51),(523,a+472)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [0, -1, -1, 2, 2, 4, -2, -2, 4, 4, 0, 0, 4, 4, 6, 6, 16, 16, -4, -4, -12, -12, -6, -6, 2, 2, -6, 20, 20, -4, -4, 18, 18, 20, 20, -12, -12, -10, -10, -6, -6, -10, -10, 0, 0, 18, 18, -12, -12, -10, -10, -6, -6, 0, 0, 12, 12, 24, 24, 18, 18, -6, -6, -28, -28, 2, -6, -6, 12, 12, 2, 2, -26, -26, -16, -16, 22, 22, 10, 10, 20, 20, -24, -24, 10, 10, 26, 26, -6, -6, 20, 20, -28, -28, 4, 4, 18, 18, 12, 12]
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((3, a + 1))] = 1
AL_eigenvalues[ZF.ideal((3, a + 2))] = 1

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