/*
  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([3, -3, -6, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([13, 13, -w^3 + w^2 + 3*w - 1])

primes_array = [
[3, 3, w],\
[5, 5, w - 1],\
[7, 7, w^3 - w^2 - 4*w + 1],\
[11, 11, -w^2 + w + 2],\
[13, 13, -w^3 + w^2 + 3*w - 1],\
[16, 2, 2],\
[17, 17, -w^3 + 5*w + 2],\
[29, 29, -w^2 + w + 1],\
[37, 37, -w^3 + 2*w^2 + 4*w - 4],\
[41, 41, -w^3 + w^2 + 5*w + 1],\
[41, 41, w^2 - 5],\
[47, 47, w^3 - w^2 - 5*w - 2],\
[47, 47, -w^3 + 2*w^2 + 4*w - 1],\
[53, 53, w^3 - 4*w - 4],\
[53, 53, 2*w^3 - 2*w^2 - 9*w + 1],\
[61, 61, -w^3 + w^2 + 6*w - 2],\
[71, 71, w^3 - w^2 - 6*w - 2],\
[103, 103, 2*w^3 - 2*w^2 - 8*w + 1],\
[103, 103, -3*w^3 + 3*w^2 + 13*w - 5],\
[109, 109, 2*w^3 - w^2 - 8*w - 4],\
[109, 109, 2*w^3 - w^2 - 9*w - 1],\
[113, 113, -2*w^3 + w^2 + 11*w - 1],\
[113, 113, 2*w^3 - w^2 - 10*w - 4],\
[125, 5, 2*w^3 - 3*w^2 - 10*w + 4],\
[131, 131, -2*w^3 + w^2 + 9*w - 1],\
[139, 139, 2*w^3 - 4*w^2 - 7*w + 5],\
[139, 139, 3*w^3 - w^2 - 16*w - 5],\
[149, 149, w^2 + w - 4],\
[149, 149, 3*w^3 - 3*w^2 - 13*w + 1],\
[151, 151, w^2 - 2*w - 8],\
[157, 157, w^3 - w^2 - 7*w - 2],\
[157, 157, -2*w^2 + w + 7],\
[167, 167, 2*w^3 - 2*w^2 - 7*w + 5],\
[173, 173, -w^3 + 6*w - 2],\
[173, 173, -w^3 + 2*w^2 + 5*w - 7],\
[181, 181, -3*w^3 + 2*w^2 + 14*w + 1],\
[191, 191, -w^3 + 2*w^2 + 2*w - 5],\
[191, 191, -w^3 + 2*w^2 + 6*w - 5],\
[193, 193, -w^3 + 3*w^2 + 4*w - 4],\
[193, 193, 2*w^3 + 3*w^2 - 13*w - 20],\
[197, 197, w^3 - 2*w - 2],\
[199, 199, 2*w^3 - w^2 - 11*w - 2],\
[211, 211, -2*w^3 + 9*w + 5],\
[223, 223, -w^3 + w^2 + 4*w - 5],\
[223, 223, w^2 - 3*w - 2],\
[229, 229, 2*w^3 - 2*w^2 - 7*w + 1],\
[241, 241, 3*w^2 - 2*w - 13],\
[241, 241, -w^3 + w^2 + 5*w + 4],\
[257, 257, -3*w^3 + w^2 + 15*w + 8],\
[263, 263, -3*w^3 + 5*w^2 + 9*w - 7],\
[263, 263, 2*w^3 - w^2 - 9*w + 2],\
[263, 263, -w^3 + 4*w^2 + 2*w - 16],\
[263, 263, w^3 - w^2 - 2*w - 2],\
[271, 271, -3*w - 1],\
[281, 281, 2*w^3 - 3*w^2 - 8*w + 2],\
[281, 281, 3*w^3 - 4*w^2 - 12*w + 4],\
[283, 283, w^3 - 5*w - 7],\
[293, 293, -2*w^3 + w^2 + 10*w - 1],\
[307, 307, w^3 - 3*w^2 - 3*w + 8],\
[307, 307, 3*w^3 - 15*w - 10],\
[311, 311, 2*w^3 - 3*w^2 - 7*w + 7],\
[313, 313, -w^3 + 7*w + 2],\
[337, 337, 3*w^3 - 17*w - 10],\
[337, 337, 2*w^3 - 2*w^2 - 9*w - 5],\
[343, 7, -2*w^3 + w^2 + 8*w + 2],\
[347, 347, -3*w^3 + 17*w + 14],\
[347, 347, -3*w^3 - w^2 + 17*w + 13],\
[349, 349, 2*w^3 - w^2 - 8*w - 1],\
[349, 349, -w^3 + 3*w^2 + 4*w - 8],\
[353, 353, -w^3 - w^2 + 7*w + 4],\
[359, 359, -2*w^3 + 9*w + 10],\
[367, 367, 3*w^3 - 4*w^2 - 9*w + 4],\
[367, 367, -w^3 + w^2 + 4*w + 4],\
[367, 367, -w^3 + 3*w^2 + 3*w - 7],\
[373, 373, -w^2 + w - 2],\
[373, 373, -2*w^3 + 2*w^2 + 11*w - 2],\
[379, 379, -2*w^3 + 4*w^2 + 7*w - 8],\
[379, 379, -w^2 - 2],\
[389, 389, -w^3 - 2*w^2 + 5*w + 11],\
[397, 397, -2*w^3 + 4*w^2 + 7*w - 7],\
[401, 401, w^3 - 3*w^2 - 2*w + 10],\
[401, 401, -2*w^3 + 11*w + 4],\
[401, 401, 3*w^3 - 2*w^2 - 14*w - 4],\
[401, 401, -3*w^3 + 4*w^2 + 15*w - 5],\
[421, 421, -w^3 + w^2 + 7*w - 1],\
[421, 421, -2*w^3 + 2*w^2 + 9*w - 7],\
[433, 433, w^2 - w - 8],\
[439, 439, -w^3 + 3*w^2 + 4*w - 7],\
[443, 443, -2*w^3 + w^2 + 10*w - 2],\
[449, 449, w^2 + 2*w - 4],\
[449, 449, 2*w^3 - 2*w^2 - 10*w - 1],\
[461, 461, 2*w^3 - 2*w^2 - 6*w + 5],\
[461, 461, -2*w^3 + 4*w^2 + 7*w - 13],\
[463, 463, -3*w^3 + 3*w^2 + 12*w - 4],\
[463, 463, w - 5],\
[467, 467, -3*w^3 + w^2 + 16*w + 8],\
[467, 467, 2*w^2 - 3*w - 10],\
[479, 479, 2*w^2 - 4*w - 1],\
[479, 479, -w^3 + 2*w^2 + 2*w - 7],\
[487, 487, -3*w^3 + 5*w^2 + 12*w - 10],\
[503, 503, w^3 + 2*w^2 - 8*w - 8],\
[509, 509, -3*w^3 + 5*w^2 + 11*w - 5],\
[521, 521, 2*w^2 - 3*w - 11],\
[523, 523, -2*w^3 - w^2 + 13*w + 11],\
[523, 523, -2*w^3 + 4*w^2 + 8*w - 7],\
[541, 541, 3*w^3 - 2*w^2 - 13*w + 1],\
[563, 563, w^3 - 3*w - 5],\
[563, 563, -w^3 + 3*w^2 + 2*w - 11],\
[569, 569, -2*w^3 + 4*w^2 + 9*w - 4],\
[569, 569, 3*w^2 - w - 14],\
[571, 571, -w^3 + 8*w - 1],\
[577, 577, 3*w^3 - 2*w^2 - 16*w + 1],\
[587, 587, -4*w^3 + 5*w^2 + 18*w - 7],\
[587, 587, 2*w^3 + w^2 - 10*w - 7],\
[599, 599, 2*w^3 + w^2 - 11*w - 8],\
[607, 607, w^3 - 3*w + 4],\
[613, 613, 3*w^3 - w^2 - 14*w - 5],\
[613, 613, 3*w^2 - w - 11],\
[619, 619, 2*w^2 - 5*w - 8],\
[631, 631, -2*w^3 - 2*w^2 + 12*w + 19],\
[647, 647, 2*w^3 - 2*w^2 - 11*w - 2],\
[653, 653, 3*w^3 - 5*w^2 - 8*w + 7],\
[677, 677, -2*w^3 + 4*w^2 + 5*w - 8],\
[683, 683, 2*w^3 + w^2 - 12*w - 8],\
[683, 683, -w^3 + 3*w^2 - 8],\
[683, 683, -2*w^3 + 3*w^2 + 11*w - 8],\
[683, 683, -2*w^3 + 3*w^2 + 10*w - 2],\
[691, 691, w^2 - 4*w - 1],\
[709, 709, 3*w^3 - 2*w^2 - 13*w - 2],\
[709, 709, w^3 - 2*w^2 - 3*w - 2],\
[727, 727, -w^3 + 4*w^2 + 2*w - 7],\
[727, 727, -w^3 + 8*w + 5],\
[733, 733, 3*w^2 - 2*w - 10],\
[733, 733, -w^3 + 5*w + 8],\
[757, 757, 3*w^3 - 14*w - 8],\
[761, 761, -w^3 + 3*w^2 + 5*w - 10],\
[773, 773, -2*w^3 + 3*w^2 + 9*w - 1],\
[787, 787, -w^3 + 4*w - 4],\
[797, 797, w^2 + 2*w - 5],\
[797, 797, w^3 + w^2 - 5*w - 1],\
[809, 809, w^3 + 3*w^2 - 9*w - 17],\
[811, 811, -4*w^2 + 3*w + 17],\
[811, 811, w^3 - 2*w^2 - 8*w + 2],\
[823, 823, -4*w^3 + 4*w^2 + 17*w - 4],\
[857, 857, 3*w^2 - w - 16],\
[881, 881, -2*w^3 + 9*w + 1],\
[883, 883, w^3 - w^2 - 4*w - 5],\
[887, 887, 3*w^2 + w - 10],\
[911, 911, w^3 - 3*w - 7],\
[919, 919, -w^3 + w^2 + 3*w - 7],\
[919, 919, 3*w^3 - 2*w^2 - 12*w + 2],\
[929, 929, 3*w^3 - w^2 - 16*w - 2],\
[929, 929, w^3 + w^2 - 6*w - 2],\
[941, 941, -3*w^3 + 5*w^2 + 14*w - 14],\
[941, 941, -w^3 + 2*w^2 + 6*w - 8],\
[947, 947, 3*w^3 - 3*w^2 - 13*w - 5],\
[947, 947, 3*w^3 - 4*w^2 - 12*w + 2],\
[953, 953, -3*w^3 + 5*w^2 + 10*w - 10],\
[961, 31, -w^3 + 4*w^2 + 3*w - 13],\
[961, 31, -4*w^3 + 3*w^2 + 17*w - 4],\
[967, 967, -w^3 - 4*w^2 + 9*w + 19],\
[967, 967, w^3 + 5*w^2 - 9*w - 26],\
[971, 971, -3*w^3 + 6*w^2 + 13*w - 7],\
[971, 971, w^3 + 2*w^2 - 7*w - 7],\
[977, 977, 2*w^3 - 3*w^2 - 4*w - 2],\
[983, 983, 3*w^3 - 5*w^2 - 7*w + 7],\
[991, 991, 2*w^2 - w - 13],\
[991, 991, w^3 - 8*w - 4]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^6 - 15*x^4 - 2*x^3 + 45*x^2 + 38*x + 8
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 1/2*e^5 - 15/2*e^3 + 45/2*e + 10, -1/2*e^5 + 15/2*e^3 - 45/2*e - 10, 3/2*e^5 - e^4 - 45/2*e^3 + 10*e^2 + 133/2*e + 26, -1, 2*e^5 - e^4 - 29*e^3 + 11*e^2 + 80*e + 33, 3/2*e^5 - e^4 - 43/2*e^3 + 12*e^2 + 113/2*e + 18, e^2 + 2*e - 8, -1/2*e^5 + e^4 + 15/2*e^3 - 10*e^2 - 39/2*e - 4, 3/2*e^5 - e^4 - 41/2*e^3 + 12*e^2 + 95/2*e + 14, -3/2*e^5 + e^4 + 41/2*e^3 - 12*e^2 - 95/2*e - 14, -1/2*e^5 + 15/2*e^3 - 49/2*e - 18, -1/2*e^5 + e^4 + 15/2*e^3 - 12*e^2 - 37/2*e + 6, -2*e^3 - 2*e^2 + 19*e + 12, e^3 - 7*e + 4, -e^5 + 14*e^3 - 38*e - 22, -e^5 + 15*e^3 - 45*e - 20, e^5 - 16*e^3 - 2*e^2 + 54*e + 32, 2*e^5 - e^4 - 28*e^3 + 12*e^2 + 70*e + 24, -4*e^5 + 2*e^4 + 56*e^3 - 24*e^2 - 144*e - 50, 2*e^3 + 2*e^2 - 16*e - 14, 5*e^5 - 2*e^4 - 72*e^3 + 24*e^2 + 196*e + 80, 2*e + 8, e^5 - 15*e^3 + 47*e + 28, 3/2*e^5 - e^4 - 45/2*e^3 + 12*e^2 + 127/2*e + 14, 2*e^5 - 2*e^4 - 30*e^3 + 20*e^2 + 84*e + 36, e^5 - 17*e^3 - 3*e^2 + 67*e + 40, 9/2*e^5 - 3*e^4 - 131/2*e^3 + 32*e^2 + 361/2*e + 66, 3*e^5 - 2*e^4 - 43*e^3 + 24*e^2 + 115*e + 44, e^5 - 13*e^3 + 25*e + 28, 7/2*e^5 - 3*e^4 - 105/2*e^3 + 32*e^2 + 307/2*e + 52, 11/2*e^5 - 3*e^4 - 165/2*e^3 + 32*e^2 + 487/2*e + 96, -2*e^5 + 30*e^3 - 94*e - 56, e^5 - 13*e^3 + 29*e + 20, -11/2*e^5 + 3*e^4 + 161/2*e^3 - 32*e^2 - 451/2*e - 86, 9/2*e^5 - 3*e^4 - 127/2*e^3 + 36*e^2 + 313/2*e + 44, 1/2*e^5 - e^4 - 19/2*e^3 + 7*e^2 + 77/2*e + 26, e^5 - 13*e^3 + 4*e^2 + 25*e + 4, 3/2*e^5 - e^4 - 37/2*e^3 + 14*e^2 + 63/2*e, -1/2*e^5 + e^4 + 11/2*e^3 - 12*e^2 - 1/2*e + 12, 6*e^5 - 4*e^4 - 88*e^3 + 43*e^2 + 244*e + 96, 3*e^5 - 43*e^3 + 123*e + 60, -9/2*e^5 + e^4 + 129/2*e^3 - 14*e^2 - 351/2*e - 66, 1/2*e^5 + e^4 - 19/2*e^3 - 14*e^2 + 81/2*e + 42, -3/2*e^5 + e^4 + 45/2*e^3 - 8*e^2 - 127/2*e - 30, 2*e^3 + 4*e^2 - 20*e - 22, 4*e^5 - 2*e^4 - 58*e^3 + 22*e^2 + 154*e + 74, 6*e^5 - 5*e^4 - 88*e^3 + 56*e^2 + 240*e + 78, -3*e^5 + e^4 + 45*e^3 - 8*e^2 - 137*e - 68, 9/2*e^5 - e^4 - 135/2*e^3 + 8*e^2 + 409/2*e + 98, -4*e^5 + 2*e^4 + 56*e^3 - 25*e^2 - 144*e - 48, -2*e^5 + 2*e^4 + 30*e^3 - 22*e^2 - 92*e - 16, -3/2*e^5 + e^4 + 45/2*e^3 - 12*e^2 - 141/2*e - 10, -6*e^5 + 3*e^4 + 88*e^3 - 36*e^2 - 250*e - 88, 2*e + 8, e^5 - 2*e^4 - 17*e^3 + 18*e^2 + 55*e + 28, -9/2*e^5 + e^4 + 135/2*e^3 - 8*e^2 - 415/2*e - 98, 1/2*e^5 - e^4 - 15/2*e^3 + 14*e^2 + 49/2*e - 14, -7*e^5 + 4*e^4 + 105*e^3 - 39*e^2 - 313*e - 128, -e^5 + 2*e^4 + 12*e^3 - 28*e^2 - 8*e + 28, 3*e^5 - 45*e^3 - 2*e^2 + 131*e + 76, -13/2*e^5 + 5*e^4 + 195/2*e^3 - 50*e^2 - 573/2*e - 116, -9*e^5 + 4*e^4 + 132*e^3 - 44*e^2 - 380*e - 158, -5/2*e^5 + 3*e^4 + 71/2*e^3 - 32*e^2 - 169/2*e - 20, 5*e^5 - 2*e^4 - 75*e^3 + 20*e^2 + 225*e + 100, -2*e^5 + 2*e^4 + 26*e^3 - 24*e^2 - 50*e - 8, 4*e^5 - 2*e^4 - 56*e^3 + 23*e^2 + 140*e + 64, 4*e^5 - 2*e^4 - 62*e^3 + 18*e^2 + 192*e + 98, -e^5 + 15*e^3 + e^2 - 49*e - 22, 1/2*e^5 - e^4 - 15/2*e^3 + 14*e^2 + 35/2*e - 10, 2*e^5 - 2*e^4 - 28*e^3 + 24*e^2 + 68*e + 16, 7*e^5 - 4*e^4 - 101*e^3 + 44*e^2 + 275*e + 116, 1/2*e^5 - e^4 - 15/2*e^3 + 12*e^2 + 47/2*e - 2, e^5 - 14*e^3 + 2*e^2 + 36*e + 8, -2*e^2 + 4*e + 26, -7*e^5 + 4*e^4 + 107*e^3 - 40*e^2 - 331*e - 130, -6*e^5 + 4*e^4 + 88*e^3 - 44*e^2 - 242*e - 84, 3/2*e^5 - e^4 - 47/2*e^3 + 8*e^2 + 145/2*e + 46, -e^5 + 17*e^3 + 4*e^2 - 67*e - 44, 2*e^5 - 2*e^4 - 28*e^3 + 22*e^2 + 72*e + 14, -11/2*e^5 + 3*e^4 + 165/2*e^3 - 30*e^2 - 507/2*e - 102, -6*e^5 + 2*e^4 + 88*e^3 - 24*e^2 - 250*e - 104, -2*e^5 + 32*e^3 + 3*e^2 - 116*e - 64, e^5 - 2*e^4 - 15*e^3 + 24*e^2 + 42*e - 24, -5*e^3 - 6*e^2 + 47*e + 34, -e^5 - e^4 + 13*e^3 + 10*e^2 - 35*e - 18, 2*e^5 - 30*e^3 - 6*e^2 + 90*e + 70, 11/2*e^5 - e^4 - 161/2*e^3 + 10*e^2 + 463/2*e + 110, -5/2*e^5 + e^4 + 75/2*e^3 - 11*e^2 - 217/2*e - 50, 2*e^5 - 30*e^3 - 6*e^2 + 90*e + 72, e^5 - 13*e^3 - 2*e^2 + 25*e + 36, 7*e^5 - 4*e^4 - 103*e^3 + 44*e^2 + 289*e + 100, -5*e^5 + 2*e^4 + 75*e^3 - 18*e^2 - 228*e - 112, -19/2*e^5 + 5*e^4 + 277/2*e^3 - 52*e^2 - 779/2*e - 166, 3*e^5 - 2*e^4 - 47*e^3 + 20*e^2 + 146*e + 64, 3*e^5 - 2*e^4 - 45*e^3 + 20*e^2 + 129*e + 36, -7*e^5 + 4*e^4 + 105*e^3 - 40*e^2 - 315*e - 140, 3*e^5 - 45*e^3 - 2*e^2 + 142*e + 88, -5/2*e^5 - e^4 + 71/2*e^3 + 12*e^2 - 205/2*e - 74, e^5 - 9*e^3 + 6*e^2 - 9*e - 20, -2*e^5 + 2*e^4 + 30*e^3 - 23*e^2 - 82*e - 24, -5*e^5 + 3*e^4 + 75*e^3 - 32*e^2 - 219*e - 76, 3/2*e^5 - e^4 - 45/2*e^3 + 10*e^2 + 123/2*e + 38, 6*e^5 - 2*e^4 - 90*e^3 + 22*e^2 + 274*e + 100, 4*e^5 - 4*e^4 - 60*e^3 + 44*e^2 + 178*e + 44, 6*e^5 - 4*e^4 - 90*e^3 + 42*e^2 + 261*e + 82, -2*e^5 + 30*e^3 - 90*e - 40, 8*e^5 - 4*e^4 - 118*e^3 + 45*e^2 + 340*e + 128, -13/2*e^5 + 3*e^4 + 183/2*e^3 - 30*e^2 - 469/2*e - 122, -5*e^5 + 3*e^4 + 75*e^3 - 30*e^2 - 215*e - 92, 9*e^5 - 6*e^4 - 135*e^3 + 64*e^2 + 397*e + 152, -3*e^5 + 45*e^3 - 135*e - 62, 15/2*e^5 - 3*e^4 - 213/2*e^3 + 38*e^2 + 567/2*e + 94, -9*e^5 + 4*e^4 + 129*e^3 - 44*e^2 - 349*e - 148, -8*e^5 + 3*e^4 + 114*e^3 - 34*e^2 - 310*e - 120, -3*e^5 + 2*e^4 + 43*e^3 - 22*e^2 - 117*e - 52, 15/2*e^5 - 3*e^4 - 217/2*e^3 + 36*e^2 + 595/2*e + 112, 1/2*e^5 - e^4 - 11/2*e^3 + 13*e^2 + 13/2*e, -3*e^5 + 2*e^4 + 43*e^3 - 24*e^2 - 111*e - 32, 9/2*e^5 - 3*e^4 - 133/2*e^3 + 32*e^2 + 371/2*e + 46, -3*e^5 + 4*e^4 + 46*e^3 - 40*e^2 - 126*e - 56, -25/2*e^5 + 9*e^4 + 369/2*e^3 - 98*e^2 - 1035/2*e - 198, 2*e^5 - 4*e^4 - 32*e^3 + 42*e^2 + 102*e - 8, -11/2*e^5 + e^4 + 153/2*e^3 - 18*e^2 - 391/2*e - 62, -17/2*e^5 + 3*e^4 + 247/2*e^3 - 36*e^2 - 685/2*e - 138, -23/2*e^5 + 7*e^4 + 341/2*e^3 - 72*e^2 - 987/2*e - 198, 6*e^5 - 2*e^4 - 88*e^3 + 22*e^2 + 244*e + 112, -e^5 + 13*e^3 - 2*e^2 - 23*e, 5/2*e^5 + e^4 - 75/2*e^3 - 10*e^2 + 233/2*e + 72, -6*e^5 + 4*e^4 + 90*e^3 - 42*e^2 - 266*e - 98, -4*e^5 + 2*e^4 + 62*e^3 - 21*e^2 - 206*e - 64, -5*e^5 + 4*e^4 + 73*e^3 - 44*e^2 - 189*e - 68, 11*e^5 - 6*e^4 - 161*e^3 + 66*e^2 + 449*e + 166, 2*e^4 + 4*e^3 - 16*e^2 - 34*e - 6, 5*e^5 - 2*e^4 - 75*e^3 + 18*e^2 + 222*e + 110, -3*e^5 + 41*e^3 + 2*e^2 - 101*e - 84, -13/2*e^5 + 2*e^4 + 203/2*e^3 - 16*e^2 - 665/2*e - 162, 4*e^5 - 2*e^4 - 56*e^3 + 24*e^2 + 142*e + 60, -29/2*e^5 + 9*e^4 + 427/2*e^3 - 98*e^2 - 1205/2*e - 250, e^5 - 2*e^4 - 16*e^3 + 20*e^2 + 40*e + 32, -8*e^5 + 6*e^4 + 123*e^3 - 62*e^2 - 373*e - 148, 17/2*e^5 - 4*e^4 - 259/2*e^3 + 36*e^2 + 793/2*e + 182, 4*e^5 - 4*e^4 - 60*e^3 + 44*e^2 + 168*e + 36, 19/2*e^5 - 5*e^4 - 281/2*e^3 + 56*e^2 + 815/2*e + 158, -6*e^5 + 4*e^4 + 92*e^3 - 41*e^2 - 272*e - 112, -2*e^5 + 4*e^4 + 30*e^3 - 44*e^2 - 78*e + 8, 5/2*e^5 - e^4 - 75/2*e^3 + 4*e^2 + 237/2*e + 78, 3*e^5 - 3*e^4 - 41*e^3 + 40*e^2 + 87*e - 4, 13/2*e^5 - 5*e^4 - 187/2*e^3 + 58*e^2 + 473/2*e + 66, -12*e^5 + 6*e^4 + 178*e^3 - 64*e^2 - 516*e - 216, 9/2*e^5 - 2*e^4 - 123/2*e^3 + 28*e^2 + 297/2*e + 26, -5*e^5 + 6*e^4 + 73*e^3 - 67*e^2 - 191*e - 44, -5*e^5 + 4*e^4 + 75*e^3 - 42*e^2 - 213*e - 84, -2*e^2 + e + 4, 2*e^4 - 2*e^3 - 26*e^2 + 34*e + 40, 1/2*e^5 - e^4 - 15/2*e^3 + 8*e^2 + 57/2*e + 34, -7*e^5 + 2*e^4 + 103*e^3 - 18*e^2 - 291*e - 140, 3*e^5 + 2*e^4 - 45*e^3 - 25*e^2 + 141*e + 100, -1/2*e^5 + 3*e^4 + 19/2*e^3 - 34*e^2 - 61/2*e + 36, -14*e^5 + 8*e^4 + 199*e^3 - 94*e^2 - 521*e - 182, -2*e^4 - 2*e^3 + 24*e^2 + 6*e - 32, 12*e^5 - 8*e^4 - 174*e^3 + 92*e^2 + 476*e + 168, -3*e^5 - 2*e^4 + 44*e^3 + 22*e^2 - 142*e - 88, 14*e^5 - 9*e^4 - 206*e^3 + 96*e^2 + 586*e + 232, -e^5 + 13*e^3 - 25*e - 4, 4*e^5 - 6*e^4 - 58*e^3 + 66*e^2 + 140*e + 16, -3/2*e^5 - e^4 + 53/2*e^3 + 18*e^2 - 235/2*e - 102, -17/2*e^5 + 5*e^4 + 239/2*e^3 - 60*e^2 - 613/2*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([13, 13, -w^3 + w^2 + 3*w - 1])] = 1

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