/*
  This code can be loaded, or copied and paste using cpaste, into Sage.
  It will load the data associated to the HMF, including
  the field, level, and Hecke and Atkin-Lehner eigenvalue data.
*/

P.<x> = PolynomialRing(QQ)
g = P([1, 7, 11, -2, -7, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([45, 15, 2*w^5 - 14*w^3 - 3*w^2 + 23*w + 9])

primes_array = [
[5, 5, -2*w^5 + w^4 + 13*w^3 - 2*w^2 - 19*w - 5],\
[9, 3, 2*w^5 - w^4 - 14*w^3 + 2*w^2 + 23*w + 6],\
[11, 11, w - 1],\
[25, 5, w^3 + w^2 - 4*w - 3],\
[29, 29, w^5 - w^4 - 7*w^3 + 4*w^2 + 11*w],\
[41, 41, w^4 - w^3 - 5*w^2 + 3*w + 3],\
[49, 7, w^5 - w^4 - 7*w^3 + 4*w^2 + 11*w + 1],\
[59, 59, 2*w^5 - w^4 - 14*w^3 + 2*w^2 + 24*w + 7],\
[59, 59, -w^5 + 8*w^3 + 2*w^2 - 15*w - 8],\
[61, 61, w^5 - 7*w^3 - 2*w^2 + 12*w + 4],\
[61, 61, -w^5 + 7*w^3 - 11*w - 1],\
[64, 2, 2],\
[71, 71, w^3 + w^2 - 5*w - 3],\
[71, 71, -3*w^5 + w^4 + 21*w^3 - w^2 - 33*w - 9],\
[79, 79, -2*w^5 + w^4 + 13*w^3 - 3*w^2 - 19*w - 5],\
[81, 3, 2*w^5 - w^4 - 13*w^3 + w^2 + 19*w + 8],\
[89, 89, 2*w^5 - w^4 - 13*w^3 + 2*w^2 + 20*w + 7],\
[89, 89, -w^5 + 8*w^3 + w^2 - 16*w - 5],\
[89, 89, -3*w^5 + w^4 + 20*w^3 - 30*w - 11],\
[89, 89, -w^5 + 7*w^3 + 2*w^2 - 11*w - 4],\
[89, 89, -2*w^5 + 14*w^3 + 3*w^2 - 22*w - 8],\
[89, 89, 2*w^5 - w^4 - 14*w^3 + 3*w^2 + 22*w + 6],\
[101, 101, 3*w^5 - 2*w^4 - 18*w^3 + 6*w^2 + 22*w + 6],\
[101, 101, w^2 - w - 4],\
[101, 101, -3*w^5 + w^4 + 20*w^3 - 2*w^2 - 29*w - 7],\
[109, 109, w^4 - w^3 - 5*w^2 + 4*w + 5],\
[121, 11, w^5 - 7*w^3 - 2*w^2 + 10*w + 6],\
[131, 131, w^5 - 2*w^4 - 5*w^3 + 9*w^2 + 4*w - 3],\
[131, 131, -2*w^5 + w^4 + 13*w^3 - 3*w^2 - 20*w - 6],\
[131, 131, 3*w^5 - w^4 - 21*w^3 + w^2 + 35*w + 11],\
[131, 131, -w^5 + w^4 + 6*w^3 - 4*w^2 - 7*w + 2],\
[139, 139, -w^5 + 6*w^3 + w^2 - 8*w - 1],\
[151, 151, -w^3 + w^2 + 4*w - 2],\
[179, 179, w^4 - 6*w^2 + 6],\
[181, 181, w^3 + w^2 - 3*w],\
[191, 191, 3*w^5 - w^4 - 20*w^3 + 2*w^2 + 28*w + 5],\
[199, 199, -2*w^5 + w^4 + 12*w^3 - 3*w^2 - 15*w - 2],\
[199, 199, 5*w^5 - w^4 - 34*w^3 - w^2 + 52*w + 15],\
[211, 211, 3*w^5 - w^4 - 19*w^3 + w^2 + 26*w + 9],\
[229, 229, -w^5 + w^4 + 7*w^3 - 3*w^2 - 11*w],\
[229, 229, -w^4 + 2*w^3 + 6*w^2 - 7*w - 6],\
[239, 239, -w^5 + w^4 + 7*w^3 - 3*w^2 - 13*w - 6],\
[239, 239, 3*w^5 - w^4 - 21*w^3 + w^2 + 35*w + 10],\
[239, 239, w^3 - w^2 - 4*w + 1],\
[239, 239, 5*w^5 - 2*w^4 - 34*w^3 + 2*w^2 + 53*w + 17],\
[241, 241, -w^5 + 7*w^3 + w^2 - 13*w - 4],\
[241, 241, -3*w^5 + w^4 + 21*w^3 - 35*w - 10],\
[241, 241, -w^5 + 7*w^3 - 11*w],\
[251, 251, 3*w^5 - w^4 - 21*w^3 + 35*w + 11],\
[251, 251, w^5 - 2*w^4 - 6*w^3 + 9*w^2 + 8*w - 3],\
[269, 269, -w^5 + 8*w^3 + 3*w^2 - 16*w - 8],\
[269, 269, -2*w^5 + w^4 + 13*w^3 - w^2 - 21*w - 9],\
[269, 269, 3*w^5 - 21*w^3 - 3*w^2 + 32*w + 12],\
[271, 271, -5*w^5 + 3*w^4 + 34*w^3 - 8*w^2 - 53*w - 14],\
[281, 281, -w^5 + 8*w^3 + 3*w^2 - 16*w - 11],\
[281, 281, 4*w^5 - w^4 - 29*w^3 + 49*w + 13],\
[281, 281, w^5 - w^4 - 7*w^3 + 3*w^2 + 11*w + 5],\
[281, 281, -5*w^5 + 3*w^4 + 33*w^3 - 8*w^2 - 50*w - 12],\
[311, 311, 2*w^5 - w^4 - 14*w^3 + w^2 + 21*w + 9],\
[311, 311, -3*w^5 + 20*w^3 + 3*w^2 - 30*w - 10],\
[311, 311, 5*w^5 - 2*w^4 - 35*w^3 + 2*w^2 + 57*w + 19],\
[331, 331, -w^5 - w^4 + 7*w^3 + 6*w^2 - 11*w - 7],\
[349, 349, -6*w^5 + 3*w^4 + 41*w^3 - 7*w^2 - 64*w - 17],\
[349, 349, 4*w^5 - w^4 - 29*w^3 - w^2 + 50*w + 17],\
[349, 349, 5*w^5 - w^4 - 34*w^3 - w^2 + 52*w + 17],\
[359, 359, w^5 - 6*w^3 - w^2 + 5*w + 3],\
[379, 379, -w^5 + w^4 + 8*w^3 - 3*w^2 - 17*w - 3],\
[379, 379, 2*w^5 - 14*w^3 - 4*w^2 + 22*w + 11],\
[379, 379, -5*w^5 + 3*w^4 + 34*w^3 - 8*w^2 - 53*w - 13],\
[379, 379, 4*w^5 - 2*w^4 - 27*w^3 + 3*w^2 + 43*w + 14],\
[389, 389, 4*w^5 - 2*w^4 - 28*w^3 + 4*w^2 + 44*w + 13],\
[401, 401, -2*w^5 + 2*w^4 + 13*w^3 - 6*w^2 - 20*w - 6],\
[409, 409, -w^5 + 2*w^4 + 6*w^3 - 8*w^2 - 9*w],\
[419, 419, -5*w^5 + w^4 + 34*w^3 + 2*w^2 - 53*w - 19],\
[419, 419, 2*w^5 - w^4 - 14*w^3 + 4*w^2 + 23*w + 3],\
[421, 421, -w^5 - w^4 + 8*w^3 + 6*w^2 - 13*w - 7],\
[421, 421, 2*w^5 - 2*w^4 - 13*w^3 + 8*w^2 + 18*w + 2],\
[421, 421, 4*w^5 - w^4 - 26*w^3 + 37*w + 11],\
[431, 431, 2*w^5 - w^4 - 13*w^3 + 2*w^2 + 20*w + 9],\
[431, 431, w^5 - 8*w^3 - w^2 + 14*w + 2],\
[449, 449, 4*w^5 - 2*w^4 - 26*w^3 + 4*w^2 + 38*w + 9],\
[449, 449, -3*w^5 + w^4 + 20*w^3 - 31*w - 14],\
[461, 461, 3*w^5 - 2*w^4 - 18*w^3 + 6*w^2 + 23*w + 4],\
[461, 461, -4*w^5 + 2*w^4 + 26*w^3 - 5*w^2 - 36*w - 9],\
[461, 461, -4*w^5 + 2*w^4 + 27*w^3 - 3*w^2 - 42*w - 15],\
[491, 491, -3*w^5 + w^4 + 20*w^3 - 29*w - 10],\
[491, 491, -5*w^5 + w^4 + 35*w^3 + 2*w^2 - 56*w - 18],\
[491, 491, 2*w^5 - 14*w^3 - 4*w^2 + 24*w + 13],\
[491, 491, -3*w^5 + w^4 + 21*w^3 - 2*w^2 - 33*w - 10],\
[499, 499, 6*w^5 - 3*w^4 - 40*w^3 + 6*w^2 + 61*w + 18],\
[499, 499, -4*w^5 + w^4 + 29*w^3 + w^2 - 49*w - 17],\
[499, 499, -w^5 - w^4 + 8*w^3 + 5*w^2 - 14*w - 4],\
[499, 499, -3*w^5 + w^4 + 19*w^3 - 2*w^2 - 26*w - 8],\
[509, 509, -4*w^5 + 2*w^4 + 27*w^3 - 5*w^2 - 43*w - 11],\
[509, 509, -2*w^5 + 16*w^3 + 2*w^2 - 30*w - 9],\
[521, 521, 3*w^5 - 21*w^3 - 3*w^2 + 34*w + 10],\
[521, 521, -3*w^5 + w^4 + 19*w^3 - 26*w - 9],\
[521, 521, 4*w^5 - w^4 - 27*w^3 + 40*w + 15],\
[521, 521, -3*w^5 + 22*w^3 + 3*w^2 - 37*w - 11],\
[541, 541, -4*w^5 + w^4 + 29*w^3 + w^2 - 49*w - 18],\
[569, 569, -6*w^5 + 2*w^4 + 40*w^3 - 2*w^2 - 60*w - 19],\
[569, 569, -w^5 + w^4 + 7*w^3 - 2*w^2 - 12*w - 6],\
[571, 571, 4*w^5 - w^4 - 28*w^3 + 43*w + 14],\
[571, 571, -4*w^5 + 2*w^4 + 28*w^3 - 4*w^2 - 45*w - 14],\
[599, 599, -w^5 + w^4 + 7*w^3 - 2*w^2 - 13*w - 7],\
[601, 601, 4*w^5 - w^4 - 26*w^3 + 38*w + 13],\
[601, 601, 4*w^5 - 2*w^4 - 28*w^3 + 5*w^2 + 44*w + 11],\
[601, 601, 3*w^5 - w^4 - 21*w^3 + 2*w^2 + 35*w + 9],\
[619, 619, 4*w^5 - 2*w^4 - 27*w^3 + 4*w^2 + 40*w + 13],\
[619, 619, -4*w^5 + w^4 + 26*w^3 - 36*w - 12],\
[619, 619, w^4 - w^3 - 6*w^2 + 4*w + 4],\
[631, 631, -3*w^5 + w^4 + 20*w^3 - 30*w - 9],\
[631, 631, -5*w^5 + 2*w^4 + 35*w^3 - 3*w^2 - 57*w - 15],\
[641, 641, 5*w^5 - w^4 - 34*w^3 - w^2 + 52*w + 16],\
[641, 641, -5*w^5 + 2*w^4 + 34*w^3 - 2*w^2 - 52*w - 18],\
[659, 659, 3*w^5 - w^4 - 20*w^3 + w^2 + 32*w + 9],\
[659, 659, -4*w^5 + w^4 + 27*w^3 - w^2 - 40*w - 11],\
[661, 661, 4*w^5 - w^4 - 26*w^3 + 38*w + 12],\
[661, 661, -w^5 + 6*w^3 - 8*w + 1],\
[691, 691, 3*w^5 - 20*w^3 - 3*w^2 + 29*w + 9],\
[691, 691, w^5 + w^4 - 8*w^3 - 7*w^2 + 14*w + 9],\
[691, 691, -w^5 + w^4 + 6*w^3 - 3*w^2 - 7*w + 2],\
[701, 701, -2*w^5 + w^4 + 13*w^3 - 2*w^2 - 19*w - 9],\
[701, 701, 5*w^5 - 2*w^4 - 33*w^3 + 3*w^2 + 48*w + 14],\
[701, 701, w^4 + 3*w^3 - 3*w^2 - 10*w - 1],\
[701, 701, -2*w^5 + w^4 + 14*w^3 - 3*w^2 - 24*w - 3],\
[709, 709, -2*w^5 + 2*w^4 + 14*w^3 - 7*w^2 - 22*w - 5],\
[709, 709, -3*w^5 + 21*w^3 + 4*w^2 - 34*w - 11],\
[719, 719, 5*w^5 - 2*w^4 - 35*w^3 + 3*w^2 + 58*w + 17],\
[719, 719, 4*w^5 - 2*w^4 - 26*w^3 + 4*w^2 + 37*w + 11],\
[719, 719, 4*w^5 - 2*w^4 - 27*w^3 + 4*w^2 + 40*w + 12],\
[719, 719, 2*w^5 - 16*w^3 - 3*w^2 + 30*w + 10],\
[739, 739, -5*w^5 + w^4 + 34*w^3 + w^2 - 51*w - 17],\
[751, 751, -w^5 - w^4 + 9*w^3 + 7*w^2 - 18*w - 10],\
[761, 761, 4*w^5 - 2*w^4 - 28*w^3 + 3*w^2 + 46*w + 16],\
[761, 761, -4*w^5 + 2*w^4 + 27*w^3 - 5*w^2 - 43*w - 12],\
[769, 769, -4*w^5 + w^4 + 28*w^3 - 44*w - 12],\
[769, 769, -w^4 + w^3 + 3*w^2 - 3*w + 1],\
[809, 809, 2*w^5 - 2*w^4 - 13*w^3 + 7*w^2 + 20*w + 1],\
[811, 811, -2*w^5 + 15*w^3 + 2*w^2 - 24*w - 8],\
[811, 811, -w^5 + 9*w^3 + w^2 - 18*w - 6],\
[821, 821, -w^5 + 8*w^3 + 3*w^2 - 17*w - 9],\
[821, 821, w^5 + w^4 - 7*w^3 - 6*w^2 + 11*w + 8],\
[821, 821, 4*w^5 - 2*w^4 - 28*w^3 + 4*w^2 + 46*w + 11],\
[821, 821, 5*w^5 - 2*w^4 - 34*w^3 + 4*w^2 + 51*w + 13],\
[829, 829, -2*w^5 + w^4 + 15*w^3 - w^2 - 28*w - 10],\
[829, 829, -6*w^5 + 3*w^4 + 42*w^3 - 7*w^2 - 68*w - 21],\
[829, 829, 4*w^5 - 2*w^4 - 26*w^3 + 5*w^2 + 38*w + 12],\
[829, 829, w^5 - 7*w^3 - 3*w^2 + 11*w + 6],\
[839, 839, 3*w^5 - 2*w^4 - 20*w^3 + 5*w^2 + 32*w + 11],\
[839, 839, -w^4 + w^3 + 6*w^2 - 3*w - 4],\
[841, 29, -3*w^5 + w^4 + 22*w^3 - 38*w - 11],\
[911, 911, 3*w^5 - w^4 - 21*w^3 + 36*w + 12],\
[919, 919, -w^5 - w^4 + 7*w^3 + 6*w^2 - 12*w - 5],\
[941, 941, -w^5 + w^4 + 7*w^3 - 5*w^2 - 11*w],\
[941, 941, 4*w^5 - w^4 - 29*w^3 + 48*w + 15],\
[971, 971, -4*w^5 + w^4 + 27*w^3 + w^2 - 41*w - 13],\
[991, 991, w^5 - w^4 - 8*w^3 + 3*w^2 + 16*w + 2],\
[991, 991, -4*w^5 + 3*w^4 + 27*w^3 - 9*w^2 - 42*w - 10]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^7 - 74*x^5 - 40*x^4 + 1744*x^3 + 2112*x^2 - 13248*x - 24192
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [-1, -1, e, -1/96*e^6 + 1/16*e^5 + 37/48*e^4 - 77/24*e^3 - 109/6*e^2 + 37*e + 142, 1/2*e^2 - 12, 1/120*e^6 + 1/40*e^5 - 5/12*e^4 - 13/12*e^3 + 151/30*e^2 + 51/5*e - 54/5, 1/480*e^6 + 3/80*e^5 - 5/48*e^4 - 47/24*e^3 + 19/30*e^2 + 114/5*e + 104/5, -1/40*e^6 + 1/20*e^5 + 3/2*e^4 - 5/2*e^3 - 261/10*e^2 + 127/5*e + 732/5, -3/160*e^6 + 3/80*e^5 + 19/16*e^4 - 17/8*e^3 - 227/10*e^2 + 129/5*e + 714/5, -1/48*e^6 + 1/8*e^5 + 37/24*e^4 - 77/12*e^3 - 215/6*e^2 + 73*e + 280, 1/80*e^6 - 1/40*e^5 - 7/8*e^4 + 5/4*e^3 + 183/10*e^2 - 66/5*e - 556/5, -1/96*e^6 + 1/8*e^5 + 49/48*e^4 - 19/3*e^3 - 89/3*e^2 + 72*e + 257, 1/8*e^5 + 1/4*e^4 - 25/4*e^3 - 25/2*e^2 + 69*e + 156, 1/60*e^6 - 3/40*e^5 - 13/12*e^4 + 43/12*e^3 + 316/15*e^2 - 178/5*e - 648/5, 1/30*e^6 - 1/40*e^5 - 23/12*e^4 + 17/12*e^3 + 919/30*e^2 - 71/5*e - 706/5, 17/480*e^6 - 9/80*e^5 - 109/48*e^4 + 137/24*e^3 + 664/15*e^2 - 302/5*e - 1412/5, -7/240*e^6 - 1/40*e^5 + 41/24*e^4 + 11/12*e^3 - 418/15*e^2 - 36/5*e + 594/5, -1/120*e^6 - 1/40*e^5 + 5/12*e^4 + 13/12*e^3 - 83/15*e^2 - 46/5*e + 114/5, -1/240*e^6 + 1/20*e^5 + 11/24*e^4 - 7/3*e^3 - 413/30*e^2 + 117/5*e + 582/5, -3/160*e^6 + 3/80*e^5 + 19/16*e^4 - 17/8*e^3 - 116/5*e^2 + 139/5*e + 744/5, -1/240*e^6 - 3/40*e^5 - 1/24*e^4 + 47/12*e^3 + 146/15*e^2 - 238/5*e - 678/5, -1/40*e^6 + 1/20*e^5 + 3/2*e^4 - 5/2*e^3 - 261/10*e^2 + 127/5*e + 732/5, 1/96*e^6 - 1/16*e^5 - 37/48*e^4 + 77/24*e^3 + 103/6*e^2 - 36*e - 120, -3/80*e^6 + 3/40*e^5 + 19/8*e^4 - 15/4*e^3 - 222/5*e^2 + 188/5*e + 1278/5, 1/48*e^6 - 31/24*e^4 + 1/6*e^3 + 70/3*e^2 - 4*e - 126, 1/80*e^6 - 1/40*e^5 - 7/8*e^4 + 5/4*e^3 + 183/10*e^2 - 61/5*e - 556/5, -1/48*e^6 + 1/8*e^5 + 37/24*e^4 - 77/12*e^3 - 106/3*e^2 + 72*e + 266, 1/40*e^6 - 1/20*e^5 - 3/2*e^4 + 5/2*e^3 + 261/10*e^2 - 117/5*e - 702/5, -17/480*e^6 - 1/80*e^5 + 97/48*e^4 + 13/24*e^3 - 953/30*e^2 - 33/5*e + 642/5, -13/480*e^6 + 11/80*e^5 + 89/48*e^4 - 163/24*e^3 - 1177/30*e^2 + 363/5*e + 1368/5, -11/480*e^6 + 7/80*e^5 + 67/48*e^4 - 107/24*e^3 - 749/30*e^2 + 236/5*e + 756/5, 1/96*e^6 - 3/16*e^5 - 49/48*e^4 + 227/24*e^3 + 89/3*e^2 - 104*e - 278, -1/96*e^6 - 1/16*e^5 + 25/48*e^4 + 73/24*e^3 - 17/3*e^2 - 32*e - 8, -1/48*e^6 + 31/24*e^4 - 1/6*e^3 - 67/3*e^2 + 2*e + 96, 23/480*e^6 - 11/80*e^5 - 151/48*e^4 + 167/24*e^3 + 946/15*e^2 - 378/5*e - 2038/5, -37/480*e^6 + 9/80*e^5 + 221/48*e^4 - 133/24*e^3 - 1184/15*e^2 + 262/5*e + 2022/5, -1/240*e^6 + 1/20*e^5 + 5/24*e^4 - 7/3*e^3 - 83/30*e^2 + 107/5*e + 112/5, 7/480*e^6 + 1/80*e^5 - 35/48*e^4 - 17/24*e^3 + 253/30*e^2 + 48/5*e - 22/5, -1/40*e^6 - 3/40*e^5 + 5/4*e^4 + 15/4*e^3 - 68/5*e^2 - 218/5*e - 68/5, 1/96*e^6 + 1/16*e^5 - 25/48*e^4 - 73/24*e^3 + 31/6*e^2 + 35*e + 28, 1/240*e^6 - 1/20*e^5 - 11/24*e^4 + 17/6*e^3 + 413/30*e^2 - 187/5*e - 602/5, -1/80*e^6 + 1/40*e^5 + 7/8*e^4 - 5/4*e^3 - 89/5*e^2 + 71/5*e + 516/5, -1/240*e^6 - 3/40*e^5 + 5/24*e^4 + 47/12*e^3 - 23/30*e^2 - 233/5*e - 228/5, 1/20*e^6 - 1/10*e^5 - 3*e^4 + 5*e^3 + 527/10*e^2 - 249/5*e - 1464/5, -1/120*e^6 + 1/10*e^5 + 2/3*e^4 - 14/3*e^3 - 481/30*e^2 + 219/5*e + 624/5, -13/480*e^6 + 11/80*e^5 + 89/48*e^4 - 175/24*e^3 - 1177/30*e^2 + 423/5*e + 1418/5, -13/480*e^6 + 1/80*e^5 + 77/48*e^4 - 25/24*e^3 - 416/15*e^2 + 73/5*e + 758/5, 1/80*e^6 - 1/40*e^5 - 5/8*e^4 + 5/4*e^3 + 34/5*e^2 - 46/5*e - 26/5, -3/80*e^6 + 3/40*e^5 + 19/8*e^4 - 15/4*e^3 - 227/5*e^2 + 193/5*e + 1308/5, -7/480*e^6 + 9/80*e^5 + 59/48*e^4 - 133/24*e^3 - 943/30*e^2 + 287/5*e + 1242/5, -1/96*e^6 + 1/16*e^5 + 37/48*e^4 - 77/24*e^3 - 50/3*e^2 + 36*e + 120, -1/480*e^6 - 3/80*e^5 - 7/48*e^4 + 47/24*e^3 + 163/15*e^2 - 129/5*e - 594/5, 3/160*e^6 - 3/80*e^5 - 19/16*e^4 + 17/8*e^3 + 111/5*e^2 - 129/5*e - 654/5, 7/240*e^6 - 9/40*e^5 - 53/24*e^4 + 133/12*e^3 + 778/15*e^2 - 589/5*e - 1984/5, -1/40*e^6 - 3/40*e^5 + 5/4*e^4 + 15/4*e^3 - 68/5*e^2 - 223/5*e - 78/5, -1/40*e^6 + 1/20*e^5 + 7/4*e^4 - 3*e^3 - 193/5*e^2 + 207/5*e + 1362/5, -3/80*e^6 + 3/40*e^5 + 19/8*e^4 - 17/4*e^3 - 469/10*e^2 + 263/5*e + 1578/5, -1/40*e^6 + 1/20*e^5 + 3/2*e^4 - 5/2*e^3 - 261/10*e^2 + 107/5*e + 702/5, 1/80*e^6 + 1/10*e^5 - 5/8*e^4 - 5*e^3 + 63/10*e^2 + 289/5*e + 174/5, -1/15*e^6 + 7/40*e^5 + 49/12*e^4 - 109/12*e^3 - 1129/15*e^2 + 502/5*e + 2352/5, -13/240*e^6 + 1/40*e^5 + 77/24*e^4 - 19/12*e^3 - 832/15*e^2 + 96/5*e + 1476/5, 1/60*e^6 - 3/40*e^5 - 13/12*e^4 + 43/12*e^3 + 331/15*e^2 - 188/5*e - 788/5, -11/160*e^6 + 11/80*e^5 + 67/16*e^4 - 57/8*e^3 - 377/5*e^2 + 373/5*e + 2168/5, 1/240*e^6 + 3/40*e^5 + 1/24*e^4 - 47/12*e^3 - 307/30*e^2 + 233/5*e + 728/5, 1/120*e^6 - 1/10*e^5 - 2/3*e^4 + 31/6*e^3 + 511/30*e^2 - 299/5*e - 734/5, 1/60*e^6 - 3/40*e^5 - 13/12*e^4 + 43/12*e^3 + 316/15*e^2 - 158/5*e - 648/5, 7/120*e^6 - 3/40*e^5 - 41/12*e^4 + 47/12*e^3 + 866/15*e^2 - 198/5*e - 1508/5, 1/48*e^6 - 1/8*e^5 - 43/24*e^4 + 77/12*e^3 + 281/6*e^2 - 72*e - 350, 19/480*e^6 - 13/80*e^5 - 131/48*e^4 + 193/24*e^3 + 848/15*e^2 - 409/5*e - 1834/5, -1/16*e^6 + 29/8*e^4 - 59*e^2 - 6*e + 260, 1/30*e^6 - 3/20*e^5 - 13/6*e^4 + 43/6*e^3 + 647/15*e^2 - 356/5*e - 1446/5, 1/96*e^6 - 3/16*e^5 - 61/48*e^4 + 227/24*e^3 + 128/3*e^2 - 108*e - 402, 1/30*e^6 - 3/20*e^5 - 13/6*e^4 + 23/3*e^3 + 662/15*e^2 - 426/5*e - 1586/5, 11/240*e^6 + 3/40*e^5 - 61/24*e^4 - 43/12*e^3 + 539/15*e^2 + 203/5*e - 432/5, 17/160*e^6 - 7/80*e^5 - 101/16*e^4 + 37/8*e^3 + 1073/10*e^2 - 221/5*e - 2676/5, 11/120*e^6 - 9/40*e^5 - 35/6*e^4 + 139/12*e^3 + 1678/15*e^2 - 634/5*e - 3454/5, 1/48*e^6 - 1/8*e^5 - 37/24*e^4 + 77/12*e^3 + 106/3*e^2 - 74*e - 274, 1/96*e^6 - 3/16*e^5 - 49/48*e^4 + 227/24*e^3 + 193/6*e^2 - 107*e - 332, 1/80*e^6 - 11/40*e^5 - 11/8*e^4 + 55/4*e^3 + 433/10*e^2 - 766/5*e - 2106/5, 1/15*e^6 - 1/20*e^5 - 49/12*e^4 + 17/6*e^3 + 2213/30*e^2 - 162/5*e - 2022/5, -11/240*e^6 + 7/40*e^5 + 79/24*e^4 - 107/12*e^3 - 2143/30*e^2 + 487/5*e + 2352/5, -29/480*e^6 + 3/80*e^5 + 169/48*e^4 - 47/24*e^3 - 1781/30*e^2 + 84/5*e + 1524/5, 11/120*e^6 - 1/10*e^5 - 16/3*e^4 + 16/3*e^3 + 2681/30*e^2 - 289/5*e - 2334/5, 19/240*e^6 - 13/40*e^5 - 131/24*e^4 + 193/12*e^3 + 1726/15*e^2 - 848/5*e - 3858/5, 5/96*e^6 - 3/16*e^5 - 173/48*e^4 + 235/24*e^3 + 467/6*e^2 - 112*e - 534, 1/160*e^6 - 1/80*e^5 - 5/16*e^4 + 7/8*e^3 + 29/10*e^2 - 63/5*e + 72/5, -7/240*e^6 + 1/10*e^5 + 41/24*e^4 - 13/3*e^3 - 821/30*e^2 + 169/5*e + 594/5, -1/60*e^6 - 1/20*e^5 + 5/6*e^4 + 13/6*e^3 - 121/15*e^2 - 92/5*e - 72/5, 1/60*e^6 - 3/40*e^5 - 13/12*e^4 + 49/12*e^3 + 346/15*e^2 - 258/5*e - 828/5, -1/20*e^6 + 9/40*e^5 + 7/2*e^4 - 45/4*e^3 - 376/5*e^2 + 594/5*e + 2584/5, -1/48*e^6 + 1/4*e^5 + 43/24*e^4 - 38/3*e^3 - 293/6*e^2 + 141*e + 440, 1/30*e^6 - 1/40*e^5 - 23/12*e^4 + 17/12*e^3 + 467/15*e^2 - 76/5*e - 776/5, 1/32*e^6 - 1/16*e^5 - 29/16*e^4 + 27/8*e^3 + 61/2*e^2 - 40*e - 170, -1/30*e^6 + 11/40*e^5 + 8/3*e^4 - 167/12*e^3 - 992/15*e^2 + 776/5*e + 2706/5, 7/160*e^6 - 17/80*e^5 - 47/16*e^4 + 87/8*e^3 + 304/5*e^2 - 606/5*e - 2136/5, 7/240*e^6 + 1/40*e^5 - 35/24*e^4 - 17/12*e^3 + 521/30*e^2 + 111/5*e - 234/5, 1/40*e^6 - 3/10*e^5 - 2*e^4 + 15*e^3 + 521/10*e^2 - 832/5*e - 2352/5, 1/24*e^6 - 7/3*e^4 - 1/6*e^3 + 104/3*e^2 + 12*e - 126, 1/24*e^6 + 1/8*e^5 - 25/12*e^4 - 65/12*e^3 + 71/3*e^2 + 50*e - 18, -29/480*e^6 + 13/80*e^5 + 193/48*e^4 - 209/24*e^3 - 2501/30*e^2 + 514/5*e + 2714/5, 13/240*e^6 - 1/40*e^5 - 71/24*e^4 + 19/12*e^3 + 1259/30*e^2 - 81/5*e - 786/5, 11/240*e^6 - 7/40*e^5 - 73/24*e^4 + 107/12*e^3 + 944/15*e^2 - 482/5*e - 2142/5, -19/240*e^6 - 1/20*e^5 + 107/24*e^4 + 8/3*e^3 - 1006/15*e^2 - 202/5*e + 1168/5, -7/240*e^6 + 9/40*e^5 + 53/24*e^4 - 139/12*e^3 - 808/15*e^2 + 644/5*e + 2284/5, 1/30*e^6 - 3/20*e^5 - 29/12*e^4 + 23/3*e^3 + 812/15*e^2 - 416/5*e - 1896/5, -1/240*e^6 + 7/40*e^5 + 17/24*e^4 - 103/12*e^3 - 364/15*e^2 + 452/5*e + 1102/5, 5/48*e^6 - 1/8*e^5 - 149/24*e^4 + 85/12*e^3 + 320/3*e^2 - 82*e - 574, -1/48*e^6 + 1/4*e^5 + 43/24*e^4 - 73/6*e^3 - 145/3*e^2 + 130*e + 422, 13/240*e^6 - 1/40*e^5 - 77/24*e^4 + 13/12*e^3 + 772/15*e^2 - 11/5*e - 1036/5, -1/96*e^6 - 1/16*e^5 + 13/48*e^4 + 73/24*e^3 + 22/3*e^2 - 35*e - 134, -1/240*e^6 + 1/20*e^5 + 17/24*e^4 - 7/3*e^3 - 364/15*e^2 + 112/5*e + 1012/5, -13/120*e^6 + 7/40*e^5 + 77/12*e^4 - 107/12*e^3 - 1664/15*e^2 + 462/5*e + 3052/5, 7/160*e^6 - 7/80*e^5 - 43/16*e^4 + 37/8*e^3 + 493/10*e^2 - 256/5*e - 1546/5, -1/40*e^6 + 3/10*e^5 + 2*e^4 - 15*e^3 - 258/5*e^2 + 812/5*e + 2322/5, -17/240*e^6 - 1/40*e^5 + 97/24*e^4 + 7/12*e^3 - 983/15*e^2 - 6/5*e + 1614/5, 1/30*e^6 - 1/40*e^5 - 13/6*e^4 + 17/12*e^3 + 617/15*e^2 - 106/5*e - 1116/5, 7/80*e^6 - 7/40*e^5 - 43/8*e^4 + 35/4*e^3 + 971/10*e^2 - 437/5*e - 2802/5, -1/60*e^6 - 1/20*e^5 + 7/12*e^4 + 8/3*e^3 + 73/30*e^2 - 187/5*e - 652/5, 1/15*e^6 - 1/20*e^5 - 23/6*e^4 + 17/6*e^3 + 934/15*e^2 - 167/5*e - 1522/5, 3/160*e^6 - 13/80*e^5 - 23/16*e^4 + 67/8*e^3 + 186/5*e^2 - 484/5*e - 1774/5, -19/480*e^6 + 3/80*e^5 + 107/48*e^4 - 55/24*e^3 - 533/15*e^2 + 144/5*e + 974/5, 3/80*e^6 - 1/5*e^5 - 23/8*e^4 + 21/2*e^3 + 347/5*e^2 - 618/5*e - 2648/5, -1/60*e^6 - 7/40*e^5 + 1/3*e^4 + 101/12*e^3 + 224/15*e^2 - 462/5*e - 1302/5, -1/240*e^6 + 7/40*e^5 + 11/24*e^4 - 109/12*e^3 - 473/30*e^2 + 517/5*e + 1032/5, 1/16*e^6 - 1/8*e^5 - 33/8*e^4 + 29/4*e^3 + 85*e^2 - 94*e - 570, 1/240*e^6 + 3/40*e^5 + 1/24*e^4 - 47/12*e^3 - 337/30*e^2 + 248/5*e + 768/5, -1/240*e^6 - 3/40*e^5 - 1/24*e^4 + 41/12*e^3 + 131/15*e^2 - 158/5*e - 518/5, -1/120*e^6 - 1/40*e^5 + 5/12*e^4 + 19/12*e^3 - 68/15*e^2 - 136/5*e + 34/5, 13/480*e^6 + 9/80*e^5 - 53/48*e^4 - 125/24*e^3 + 41/15*e^2 + 282/5*e + 642/5, 1/16*e^6 - 1/8*e^5 - 29/8*e^4 + 25/4*e^3 + 119/2*e^2 - 61*e - 300, 5/48*e^6 - 149/24*e^4 + 1/3*e^3 + 320/3*e^2 - 4*e - 516, 3/160*e^6 - 13/80*e^5 - 23/16*e^4 + 67/8*e^3 + 176/5*e^2 - 489/5*e - 1584/5, -1/30*e^6 - 1/10*e^5 + 5/3*e^4 + 13/3*e^3 - 287/15*e^2 - 204/5*e + 56/5, 1/240*e^6 - 1/20*e^5 - 11/24*e^4 + 17/6*e^3 + 214/15*e^2 - 182/5*e - 692/5, -13/240*e^6 + 1/40*e^5 + 83/24*e^4 - 19/12*e^3 - 997/15*e^2 + 116/5*e + 1866/5, -11/240*e^6 + 1/20*e^5 + 61/24*e^4 - 8/3*e^3 - 554/15*e^2 + 132/5*e + 702/5, 1/160*e^6 - 1/80*e^5 - 5/16*e^4 + 3/8*e^3 + 17/5*e^2 - 13/5*e + 2/5, 1/240*e^6 + 3/40*e^5 - 11/24*e^4 - 41/12*e^3 + 443/30*e^2 + 143/5*e - 542/5, 7/80*e^6 - 7/40*e^5 - 47/8*e^4 + 37/4*e^3 + 598/5*e^2 - 542/5*e - 3702/5, 19/480*e^6 + 7/80*e^5 - 107/48*e^4 - 95/24*e^3 + 518/15*e^2 + 191/5*e - 664/5, 1/120*e^6 + 1/40*e^5 - 1/6*e^4 - 13/12*e^3 - 82/15*e^2 + 66/5*e + 316/5, -11/240*e^6 + 1/20*e^5 + 61/24*e^4 - 8/3*e^3 - 1243/30*e^2 + 137/5*e + 1182/5, 3/80*e^6 - 1/5*e^5 - 23/8*e^4 + 21/2*e^3 + 342/5*e^2 - 613/5*e - 2538/5, 1/24*e^6 - 1/4*e^5 - 10/3*e^4 + 77/6*e^3 + 242/3*e^2 - 146*e - 594, -3/80*e^6 - 1/20*e^5 + 13/8*e^4 + 5/2*e^3 - 52/5*e^2 - 152/5*e - 342/5, 1/40*e^6 - 7/40*e^5 - 7/4*e^4 + 35/4*e^3 + 178/5*e^2 - 462/5*e - 1142/5, -7/480*e^6 - 1/80*e^5 + 23/48*e^4 + 5/24*e^3 + 107/30*e^2 - 13/5*e - 448/5, -1/48*e^6 + 31/24*e^4 + 1/3*e^3 - 67/3*e^2 - 6*e + 94, 11/120*e^6 + 1/40*e^5 - 16/3*e^4 - 5/12*e^3 + 1303/15*e^2 - 4/5*e - 2014/5, -1/48*e^6 + 1/4*e^5 + 49/24*e^4 - 38/3*e^3 - 178/3*e^2 + 140*e + 516, 1/60*e^6 - 1/5*e^5 - 13/12*e^4 + 28/3*e^3 + 617/30*e^2 - 443/5*e - 648/5, 1/16*e^6 - 1/4*e^5 - 35/8*e^4 + 25/2*e^3 + 95*e^2 - 134*e - 658, -9/160*e^6 - 1/80*e^5 + 49/16*e^4 + 7/8*e^3 - 208/5*e^2 - 128/5*e + 552/5, -1/120*e^6 - 1/40*e^5 + 2/3*e^4 + 19/12*e^3 - 203/15*e^2 - 116/5*e + 184/5, 1/96*e^6 - 5/16*e^5 - 73/48*e^4 + 389/24*e^3 + 164/3*e^2 - 194*e - 552, -1/24*e^6 + 1/4*e^5 + 37/12*e^4 - 77/6*e^3 - 421/6*e^2 + 144*e + 516, 3/160*e^6 - 3/80*e^5 - 19/16*e^4 + 17/8*e^3 + 207/10*e^2 - 109/5*e - 474/5, -17/240*e^6 + 7/20*e^5 + 121/24*e^4 - 53/3*e^3 - 1673/15*e^2 + 964/5*e + 4024/5, 1/96*e^6 + 1/16*e^5 - 37/48*e^4 - 61/24*e^3 + 50/3*e^2 + 17*e - 98]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([5, 5, -2*w^5 + w^4 + 13*w^3 - 2*w^2 - 19*w - 5])] = 1
AL_eigenvalues[ZF.ideal([9, 3, 2*w^5 - w^4 - 14*w^3 + 2*w^2 + 23*w + 6])] = 1

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