"""
  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([13, 0, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((238, a + 223))

primes_array = [
(2,a+1),(7,a+1),(7,a+6),(3,),(11,a+3),(11,a+8),(a,),(a+2,),(a-2,),(19,a+5),(19,a+14),(5,),(a+4,),(a-4,),(31,a+7),(31,a+24),(47,a+9),(47,a+38),(-2*a+1,),(-2*a-1,),(59,a+20),(59,a+39),(-2*a+3,),(2*a+3,),(67,a+11),(67,a+56),(71,a+22),(71,a+49),(83,a+30),(83,a+53),(-2*a+7,),(2*a+7,),(a+10,),(a-10,),(151,a+17),(151,a+134),(a+12,),(a-12,),(163,a+65),(163,a+98),(167,a+34),(167,a+133),(-2*a+11,),(2*a+11,),(-3*a-8,),(3*a-8,),(223,a+87),(223,a+136),(227,a+21),(227,a+206),(-4*a+5,),(4*a+5,),(239,a+86),(239,a+153),(-4*a-7,),(4*a-7,),(a+16,),(a-16,),(271,a+23),(271,a+248),(-2*a+15,),(2*a+15,),(307,a+58),(307,a+249),(-3*a-14,),(3*a-14,),(331,a+48),(331,a+283),(a+18,),(a-18,),(359,a+50),(359,a+309),(-3*a+16,),(3*a+16,),(379,a+164),(379,a+215),(383,a+149),(383,a+234),(-5*a+8,),(-5*a-8,),(431,a+121),(431,a+310),(-4*a-15,),(4*a-15,),(463,a+196),(463,a+267),(479,a+150),(479,a+329),(487,a+31),(487,a+456),(499,a+74),(499,a+425),(-5*a-14,),(5*a-14,),(23,),(-4*a-19,),(4*a-19,),(587,a+64),(587,a+523),(-3*a+22,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [-1, 0, -1, -1, -2, 3, 4, -1, -1, 5, -2, -4, -6, 0, 0, 5, 4, 9, -4, -2, -11, 0, -10, -1, 7, -12, 7, -5, 6, 3, -14, -12, 2, 6, -19, -12, 14, -17, 14, -13, 4, -18, 19, 2, -14, 15, 14, 28, 12, -20, 21, 6, -3, -8, 15, -28, 0, 25, 2, -4, -3, -25, -22, 9, 26, 4, -22, 0, 18, -10, -8, 13, 26, 28, -8, 20, -30, 10, -13, -4, 8, 0, -5, -14, 1, 32, 17, -26, 4, -20, -22, -28, -12, -6, -45, -1, 9, -3, -10, 15]
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((7, a + 6))] = 1
AL_eigenvalues[ZF.ideal((a + 2,))] = 1

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