"""
  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([623, -1, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((2, 2))

primes_array = [
(2,),(5,a+1),(5,a+3),(7,a),(7,a+6),(3,),(17,a+2),(17,a+14),(19,a+6),(19,a+12),(23,a+9),(23,a+13),(31,a+9),(31,a+21),(37,a+2),(37,a+34),(41,a+12),(41,a+28),(47,a+23),(53,a+26),(59,a+19),(59,a+39),(67,a+25),(67,a+41),(73,a+32),(73,a+40)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [-1, 1, -1, -4, -4, 2, -3, -3, -8, 8, -3, 3, 3, -3, -4, -4, 6, -6, -6, 4, -15, -15, 2, -2, -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,))] = 1

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