"""
  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([5, 0, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((69, a + 8))

primes_array = [
(2,a+1),(3,a+1),(3,a+2),(a,),(7,a+3),(7,a+4),(23,a+8),(23,a+15),(-2*a+3,),(2*a+3,),(a+6,),(a-6,),(43,a+9),(43,a+34),(47,a+18),(47,a+29),(-3*a+4,),(3*a+4,),(67,a+14),(67,a+53),(83,a+24),(83,a+59),(-4*a-3,),(4*a-3,),(-2*a+9,),(2*a+9,),(103,a+43),(103,a+60),(107,a+40),(107,a+67),(-3*a-8,),(3*a-8,),(11,),(127,a+54),(127,a+73),(a+12,),(a-12,),(163,a+22),(163,a+141),(167,a+50),(167,a+117),(13,),(-6*a+1,),(6*a+1,),(223,a+21),(223,a+202),(227,a+26),(227,a+201),(-6*a+7,),(6*a+7,),(-3*a-14,),(3*a-14,),(263,a+28),(263,a+235),(5*a+12,),(5*a-12,),(-7*a-6,),(7*a-6,),(283,a+109),(283,a+174),(17,),(307,a+84),(307,a+223),(347,a+79),(347,a+268),(-6*a+13,),(6*a+13,),(19,),(367,a+27),(367,a+340),(383,a+83),(383,a+300),(7*a-12,),(7*a+12,),(-8*a+9,),(8*a+9,),(9*a+2,),(9*a-2,),(9*a+4,),(9*a-4,),(443,a+138),(443,a+305),(-5*a+18,),(-5*a-18,),(-2*a+21,),(2*a+21,),(463,a+213),(463,a+250),(467,a+205),(467,a+262),(487,a+143),(487,a+344),(503,a+178),(503,a+325),(10*a+3,),(10*a-3,),(-4*a+21,),(4*a+21,),(523,a+97),(523,a+426)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [1, 1, 1, -4, -2, -1, 1, -7, 1, -6, 9, -6, -2, -5, 11, 4, -8, -1, 10, -11, 14, 0, 6, -10, 0, -2, 0, -4, 7, 17, -11, -10, 7, -15, 0, -7, -6, 16, -22, -14, 9, -19, 4, -7, 8, -19, 1, -13, -6, -9, -23, 0, 9, 12, -4, -15, -22, 31, -20, 20, 23, -16, 2, -18, 7, 1, -1, -20, 19, 0, 0, 16, 23, -9, -21, -21, 26, 24, -2, 12, -6, -13, 24, -6, -21, 14, 24, 22, -12, 12, -22, -40, -38, 8, -17, 18, -18, -15, 10, 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 + 2))] = -1
AL_eigenvalues[ZF.ideal((23, a + 8))] = -1

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