/*
  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, 2, -5, -2, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([13, 13, w^3 - 2*w^2 - 4*w + 2])

primes_array = [
[3, 3, w],\
[4, 2, -w^3 + 3*w^2 + w - 2],\
[11, 11, -w^3 + 3*w^2 + 2*w - 5],\
[13, 13, w^3 - 2*w^2 - 4*w + 2],\
[13, 13, -w + 2],\
[17, 17, w^3 - 3*w^2 - 2*w + 2],\
[19, 19, -w^2 + w + 4],\
[19, 19, w^3 - 2*w^2 - 3*w + 2],\
[23, 23, w^2 - 2*w - 1],\
[27, 3, w^3 - 2*w^2 - 5*w - 1],\
[29, 29, -w^3 + 2*w^2 + 5*w - 1],\
[37, 37, -w^3 + 2*w^2 + 5*w - 4],\
[41, 41, 2*w^3 - 5*w^2 - 6*w + 4],\
[53, 53, w^3 - 2*w^2 - 3*w - 2],\
[59, 59, w - 4],\
[67, 67, 2*w^2 - 3*w - 8],\
[73, 73, 2*w^3 - 5*w^2 - 6*w + 5],\
[89, 89, -2*w^3 + 6*w^2 + 5*w - 7],\
[97, 97, -2*w^3 + 6*w^2 + 3*w - 7],\
[97, 97, -w^3 + 3*w^2 + 3*w - 1],\
[103, 103, w^2 - 4*w - 4],\
[113, 113, 2*w^3 - 5*w^2 - 4*w + 1],\
[113, 113, -w^3 + 3*w^2 + w - 5],\
[139, 139, 2*w^2 - 3*w - 4],\
[139, 139, w^3 - w^2 - 6*w - 1],\
[149, 149, 2*w^3 - 5*w^2 - 5*w + 2],\
[149, 149, w^3 - 4*w^2 + 10],\
[151, 151, -3*w - 1],\
[157, 157, w^2 - w - 8],\
[157, 157, w^3 - 7*w - 8],\
[163, 163, -3*w^3 + 8*w^2 + 8*w - 10],\
[163, 163, w^3 - 3*w^2 - 4*w + 7],\
[163, 163, -w^3 + 4*w^2 + w - 8],\
[163, 163, -2*w^3 + 5*w^2 + 7*w - 4],\
[167, 167, -2*w^3 + 5*w^2 + 8*w - 4],\
[169, 13, -2*w^3 + 4*w^2 + 7*w - 5],\
[173, 173, 2*w^3 - 4*w^2 - 9*w + 4],\
[173, 173, -w^3 + 5*w^2 - 2*w - 5],\
[181, 181, 3*w^3 - 7*w^2 - 12*w + 7],\
[191, 191, w^3 - 3*w^2 - 3*w - 1],\
[199, 199, 2*w^3 - 3*w^2 - 10*w - 1],\
[199, 199, 2*w^3 - 6*w^2 - 6*w + 13],\
[223, 223, -2*w^3 + 6*w^2 + 4*w - 11],\
[223, 223, 3*w^3 - 7*w^2 - 12*w + 8],\
[223, 223, -2*w^3 + 5*w^2 + 6*w - 1],\
[229, 229, -w^3 + 3*w^2 + 2*w + 1],\
[229, 229, 3*w^3 - 4*w^2 - 15*w - 5],\
[233, 233, -3*w^3 + 7*w^2 + 11*w - 5],\
[233, 233, 2*w^3 - 5*w^2 - 4*w + 5],\
[241, 241, w^3 - 3*w^2 - 5*w + 7],\
[257, 257, w^3 - 3*w^2 - 4*w + 8],\
[263, 263, w^2 - 4*w - 5],\
[271, 271, -2*w^3 + 6*w^2 + 5*w - 13],\
[277, 277, -2*w^3 + 6*w^2 + 3*w - 8],\
[277, 277, w^3 - 2*w^2 - 2*w - 2],\
[281, 281, 2*w^3 - 5*w^2 - 4*w + 2],\
[283, 283, -3*w^2 + 7*w + 10],\
[283, 283, -w^3 + 4*w^2 - w - 7],\
[293, 293, 2*w^3 - 5*w^2 - 3*w + 4],\
[293, 293, w^3 - 8*w - 4],\
[307, 307, -w^3 + 2*w^2 + 6*w - 2],\
[311, 311, w^2 - 5],\
[317, 317, -w^3 + 5*w^2 - 2*w - 11],\
[331, 331, -w^3 + 3*w^2 - 5],\
[349, 349, -2*w^2 + 5*w + 2],\
[353, 353, -2*w^3 + 5*w^2 + 4*w - 4],\
[353, 353, 3*w^3 - 7*w^2 - 10*w + 2],\
[353, 353, -2*w^3 + 7*w^2 + 2*w - 10],\
[353, 353, w^3 + w^2 - 9*w - 13],\
[361, 19, -w^3 + w^2 + 5*w - 1],\
[373, 373, -w^3 + 3*w^2 + 4*w - 11],\
[373, 373, 2*w^3 - 5*w^2 - 5*w - 2],\
[383, 383, w^3 - 5*w^2 + w + 13],\
[389, 389, 3*w^3 - 10*w^2 - 4*w + 16],\
[397, 397, -w^3 + 2*w^2 + 3*w + 5],\
[397, 397, -3*w^3 + 7*w^2 + 10*w - 7],\
[419, 419, -w^3 + 2*w^2 + 4*w + 4],\
[419, 419, 3*w^3 - 7*w^2 - 12*w + 5],\
[421, 421, -w^2 + 5*w - 2],\
[421, 421, 3*w^3 - 7*w^2 - 10*w + 5],\
[431, 431, w^2 - 10],\
[439, 439, w^3 - w^2 - 7*w - 7],\
[461, 461, -2*w^3 + 7*w^2 + 5*w - 10],\
[467, 467, -3*w^3 + 6*w^2 + 14*w - 4],\
[479, 479, 3*w^2 - 6*w - 5],\
[479, 479, -4*w^3 + 11*w^2 + 10*w - 10],\
[491, 491, -w^3 + w^2 + 6*w - 1],\
[499, 499, -4*w^3 + 9*w^2 + 15*w - 10],\
[499, 499, 2*w^3 - 5*w^2 - 7*w + 2],\
[503, 503, -2*w^3 + 7*w^2 - 8],\
[521, 521, 2*w^2 - w - 7],\
[521, 521, -3*w^3 + 7*w^2 + 11*w - 11],\
[569, 569, 2*w^2 - 5*w - 1],\
[569, 569, -4*w - 1],\
[571, 571, -w^3 + 3*w^2 - 7],\
[577, 577, -w^3 + w^2 + 8*w - 4],\
[587, 587, -3*w^3 + 8*w^2 + 7*w - 8],\
[593, 593, 3*w^2 - 4*w - 11],\
[593, 593, -3*w^3 + 9*w^2 + 6*w - 14],\
[601, 601, -3*w^3 + 9*w^2 + 4*w - 10],\
[601, 601, 5*w^3 - 9*w^2 - 24*w - 2],\
[607, 607, 2*w^2 - 7*w - 5],\
[613, 613, w^3 - 6*w - 2],\
[613, 613, -w^2 + 3*w + 8],\
[617, 617, -w^2 + 4*w - 5],\
[619, 619, 3*w^3 - 6*w^2 - 13*w + 5],\
[625, 5, -5],\
[631, 631, -2*w^3 + 4*w^2 + 8*w - 7],\
[647, 647, -2*w^3 + 4*w^2 + 5*w - 1],\
[647, 647, w^3 - 3*w^2 - 2*w - 2],\
[653, 653, w^3 - 4*w^2 - w + 13],\
[653, 653, w^3 - 2*w^2 - 7*w + 5],\
[659, 659, -4*w^3 + 10*w^2 + 15*w - 14],\
[659, 659, 5*w^3 - 12*w^2 - 17*w + 14],\
[661, 661, w^2 - 5*w - 2],\
[661, 661, -w^3 + 5*w^2 - 2*w - 7],\
[673, 673, -w^3 + w^2 + 6*w - 2],\
[683, 683, 2*w^3 - 8*w^2 + w + 8],\
[683, 683, 5*w^3 - 12*w^2 - 19*w + 14],\
[701, 701, -2*w^3 + 6*w^2 + 5*w - 4],\
[709, 709, -w^2 + 3*w - 4],\
[709, 709, -2*w^3 + 5*w^2 + 9*w - 8],\
[719, 719, w^2 - 7],\
[719, 719, -2*w^3 + 3*w^2 + 8*w + 5],\
[733, 733, -2*w^3 + 7*w^2 + 3*w - 10],\
[739, 739, 4*w^3 - 11*w^2 - 13*w + 14],\
[739, 739, -5*w^3 + 10*w^2 + 21*w - 4],\
[739, 739, 3*w^3 - 8*w^2 - 6*w + 8],\
[739, 739, -w^3 + w^2 + 8*w - 5],\
[743, 743, -w - 5],\
[743, 743, w^3 - w^2 - 8*w - 8],\
[751, 751, -2*w^3 + 5*w^2 + 8*w - 2],\
[751, 751, -2*w^3 + 6*w^2 - 1],\
[757, 757, -2*w^3 + 6*w^2 + 3*w - 10],\
[757, 757, 5*w^2 - 9*w - 22],\
[761, 761, -2*w^3 + 4*w^2 + 9*w - 7],\
[761, 761, 2*w^3 - 3*w^2 - 12*w - 1],\
[769, 769, 5*w^3 - 13*w^2 - 14*w + 10],\
[773, 773, -3*w^3 + 5*w^2 + 16*w + 1],\
[773, 773, w^3 - 11*w + 2],\
[787, 787, -w^3 + 4*w^2 - w - 11],\
[797, 797, -5*w^3 + 12*w^2 + 17*w - 11],\
[809, 809, -2*w^3 + 7*w^2 + 4*w - 11],\
[809, 809, 4*w^3 - 9*w^2 - 14*w + 4],\
[821, 821, -w^3 + 5*w^2 - 2*w - 17],\
[827, 827, -3*w^3 + 8*w^2 + 9*w - 7],\
[829, 829, 2*w^3 - 6*w^2 - 5*w + 2],\
[829, 829, -w^3 + 4*w^2 - w - 10],\
[839, 839, w^2 - 8],\
[853, 853, -5*w^3 + 12*w^2 + 18*w - 16],\
[853, 853, w^3 - 6*w - 8],\
[863, 863, 5*w^3 - 11*w^2 - 19*w + 7],\
[881, 881, -3*w^3 + 9*w^2 + 9*w - 11],\
[907, 907, -w^3 + 2*w^2 + 7*w - 4],\
[907, 907, -2*w^3 + 3*w^2 + 7*w + 4],\
[929, 929, -w^3 + 5*w^2 - 3*w - 11],\
[937, 937, 2*w^3 - 5*w^2 - 6*w + 11],\
[937, 937, -2*w^3 + 6*w^2 + 3*w - 11],\
[941, 941, -3*w^3 + 8*w^2 + 11*w - 8],\
[953, 953, -4*w^3 + 10*w^2 + 10*w - 13],\
[953, 953, w^3 - 5*w^2 - w + 13],\
[967, 967, 3*w^3 - 7*w^2 - 9*w + 7],\
[967, 967, -2*w^3 + 5*w^2 + 8*w + 1],\
[967, 967, 4*w^3 - 13*w^2 - 6*w + 20],\
[967, 967, -2*w^2 + 3*w + 13],\
[971, 971, -6*w^3 + 13*w^2 + 25*w - 8],\
[977, 977, w^3 - w^2 - 4*w - 10],\
[977, 977, 2*w^3 - 6*w^2 - 7*w + 13],\
[983, 983, -4*w^3 + 10*w^2 + 11*w - 13],\
[983, 983, -w^3 + 5*w^2 - w - 7],\
[983, 983, 3*w^3 - 9*w^2 - 7*w + 19],\
[983, 983, -2*w^3 + 3*w^2 + 10*w - 1],\
[997, 997, 5*w^3 - 12*w^2 - 17*w + 13],\
[997, 997, -2*w^3 + 3*w^2 + 13*w - 4],\
[997, 997, w^3 - 7*w - 2],\
[997, 997, w^3 - 9*w - 2]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^9 + 3*x^8 - 13*x^7 - 36*x^6 + 47*x^5 + 110*x^4 - 44*x^3 - 100*x^2 + 10*x + 25
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 4/35*e^8 + 16/105*e^7 - 206/105*e^6 - 26/15*e^5 + 1124/105*e^4 + 97/21*e^3 - 671/35*e^2 - 29/7*e + 169/21, 34/105*e^8 + 19/35*e^7 - 179/35*e^6 - 77/15*e^5 + 871/35*e^4 + 122/21*e^3 - 1207/35*e^2 + 58/21*e + 263/21, 1, -4/35*e^8 - 16/105*e^7 + 206/105*e^6 + 26/15*e^5 - 1124/105*e^4 - 97/21*e^3 + 671/35*e^2 + 22/7*e - 211/21, -46/105*e^8 - 73/105*e^7 + 743/105*e^6 + 103/15*e^5 - 3737/105*e^4 - 73/7*e^3 + 1843/35*e^2 + 8/21*e - 137/7, 16/105*e^8 + 11/35*e^7 - 76/35*e^6 - 53/15*e^5 + 309/35*e^4 + 176/21*e^3 - 323/35*e^2 - 11/21*e + 41/21, -16/105*e^8 - 11/35*e^7 + 76/35*e^6 + 53/15*e^5 - 309/35*e^4 - 197/21*e^3 + 288/35*e^2 + 116/21*e - 41/21, 88/105*e^8 + 199/105*e^7 - 1289/105*e^6 - 319/15*e^5 + 5711/105*e^4 + 374/7*e^3 - 2494/35*e^2 - 638/21*e + 165/7, -53/105*e^8 - 43/35*e^7 + 243/35*e^6 + 199/15*e^5 - 982/35*e^4 - 625/21*e^3 + 1164/35*e^2 + 253/21*e - 292/21, -94/105*e^8 - 242/105*e^7 + 1252/105*e^6 + 129/5*e^5 - 4663/105*e^4 - 1363/21*e^3 + 1447/35*e^2 + 734/21*e - 268/21, -6/35*e^8 - 8/35*e^7 + 103/35*e^6 + 13/5*e^5 - 562/35*e^4 - 45/7*e^3 + 1024/35*e^2 + 12/7*e - 116/7, 8/15*e^8 + 14/15*e^7 - 124/15*e^6 - 143/15*e^5 + 601/15*e^4 + 18*e^3 - 309/5*e^2 - 22/3*e + 26, 22/105*e^8 + 37/35*e^7 - 52/35*e^6 - 191/15*e^5 - 157/35*e^4 + 809/21*e^3 + 1074/35*e^2 - 506/21*e - 361/21, -62/105*e^8 - 47/35*e^7 + 312/35*e^6 + 226/15*e^5 - 1473/35*e^4 - 766/21*e^3 + 2271/35*e^2 + 292/21*e - 613/21, -118/105*e^8 - 169/105*e^7 + 1979/105*e^6 + 244/15*e^5 - 10376/105*e^4 - 197/7*e^3 + 5414/35*e^2 + 278/21*e - 405/7, -13/21*e^8 - 12/7*e^7 + 60/7*e^6 + 59/3*e^5 - 241/7*e^4 - 1093/21*e^3 + 241/7*e^2 + 739/21*e - 181/21, 89/105*e^8 + 212/105*e^7 - 1207/105*e^6 - 317/15*e^5 + 4603/105*e^4 + 296/7*e^3 - 1357/35*e^2 - 283/21*e + 75/7, 11/105*e^8 + 73/105*e^7 - 8/105*e^6 - 41/5*e^5 - 988/105*e^4 + 485/21*e^3 + 992/35*e^2 - 169/21*e - 205/21, -1/15*e^8 - 1/5*e^7 + 1/5*e^6 + 26/15*e^5 + 31/5*e^4 - 2/3*e^3 - 147/5*e^2 - 13/3*e + 46/3, -12/35*e^8 - 118/105*e^7 + 443/105*e^6 + 188/15*e^5 - 1412/105*e^4 - 634/21*e^3 + 228/35*e^2 + 101/7*e - 10/21, -17/35*e^8 - 103/105*e^7 + 788/105*e^6 + 158/15*e^5 - 3902/105*e^4 - 505/21*e^3 + 2213/35*e^2 + 111/7*e - 706/21, -8/105*e^8 - 34/105*e^7 + 44/105*e^6 + 18/5*e^5 + 499/105*e^4 - 158/21*e^3 - 1011/35*e^2 - 68/21*e + 361/21, -68/105*e^8 - 184/105*e^7 + 899/105*e^6 + 103/5*e^5 - 3371/105*e^4 - 1280/21*e^3 + 1154/35*e^2 + 1039/21*e - 113/21, -29/21*e^8 - 55/21*e^7 + 443/21*e^6 + 27*e^5 - 2042/21*e^4 - 1063/21*e^3 + 851/7*e^2 + 437/21*e - 757/21, 302/105*e^8 + 706/105*e^7 - 4286/105*e^6 - 367/5*e^5 + 17939/105*e^4 + 3539/21*e^3 - 6906/35*e^2 - 1654/21*e + 1340/21, 17/15*e^8 + 31/15*e^7 - 266/15*e^6 - 109/5*e^5 + 1244/15*e^4 + 131/3*e^3 - 481/5*e^2 - 70/3*e + 53/3, 13/21*e^8 + 29/21*e^7 - 187/21*e^6 - 16*e^5 + 793/21*e^4 + 953/21*e^3 - 318/7*e^2 - 802/21*e + 209/21, -13/105*e^8 - 134/105*e^7 + 19/105*e^6 + 83/5*e^5 + 1034/105*e^4 - 1144/21*e^3 - 1236/35*e^2 + 614/21*e + 416/21, -28/15*e^8 - 23/5*e^7 + 128/5*e^6 + 758/15*e^5 - 507/5*e^4 - 359/3*e^3 + 529/5*e^2 + 173/3*e - 68/3, -17/21*e^8 - 25/21*e^7 + 272/21*e^6 + 11*e^5 - 1352/21*e^4 - 214/21*e^3 + 684/7*e^2 - 250/21*e - 934/21, -72/35*e^8 - 201/35*e^7 + 921/35*e^6 + 326/5*e^5 - 3174/35*e^4 - 1198/7*e^3 + 2418/35*e^2 + 676/7*e - 111/7, -31/105*e^8 - 6/35*e^7 + 191/35*e^6 + 23/15*e^5 - 1104/35*e^4 - 26/21*e^3 + 1993/35*e^2 - 22/21*e - 611/21, 32/105*e^8 + 241/105*e^7 - 71/105*e^6 - 142/5*e^5 - 2206/105*e^4 + 1871/21*e^3 + 2329/35*e^2 - 1114/21*e - 562/21, -2/15*e^8 - 1/15*e^7 + 41/15*e^6 + 4/5*e^5 - 254/15*e^4 - 5/3*e^3 + 146/5*e^2 + 10/3*e - 44/3, 43/35*e^8 + 242/105*e^7 - 1987/105*e^6 - 352/15*e^5 + 9493/105*e^4 + 908/21*e^3 - 4527/35*e^2 - 135/7*e + 1010/21, 59/35*e^8 + 137/35*e^7 - 832/35*e^6 - 212/5*e^5 + 3403/35*e^4 + 663/7*e^3 - 3536/35*e^2 - 272/7*e + 149/7, -4/5*e^8 - 31/15*e^7 + 161/15*e^6 + 332/15*e^5 - 614/15*e^4 - 139/3*e^3 + 201/5*e^2 + 12*e - 37/3, 5/21*e^8 + 2/21*e^7 - 73/21*e^6 + 1/3*e^5 + 256/21*e^4 - 67/7*e^3 + 29/7*e^2 + 160/21*e - 150/7, 73/105*e^8 + 74/105*e^7 - 1294/105*e^6 - 28/5*e^5 + 7036/105*e^4 - 65/21*e^3 - 3414/35*e^2 + 148/21*e + 583/21, -64/105*e^8 - 97/105*e^7 + 1052/105*e^6 + 127/15*e^5 - 5318/105*e^4 - 34/7*e^3 + 2447/35*e^2 - 355/21*e - 162/7, 62/35*e^8 + 141/35*e^7 - 866/35*e^6 - 221/5*e^5 + 3509/35*e^4 + 752/7*e^3 - 3733/35*e^2 - 467/7*e + 193/7, -211/105*e^8 - 538/105*e^7 + 2858/105*e^6 + 868/15*e^5 - 11072/105*e^4 - 1042/7*e^3 + 3868/35*e^2 + 1808/21*e - 239/7, -34/105*e^8 - 22/105*e^7 + 572/105*e^6 + 7/15*e^5 - 2963/105*e^4 + 83/7*e^3 + 1557/35*e^2 - 352/21*e - 181/7, 1/3*e^8 + e^7 - 4*e^6 - 35/3*e^5 + 11*e^4 + 97/3*e^3 - 49/3*e - 20/3, 11/15*e^8 + 23/15*e^7 - 163/15*e^6 - 251/15*e^5 + 727/15*e^4 + 39*e^3 - 313/5*e^2 - 70/3*e + 27, 11/105*e^8 + 1/35*e^7 - 96/35*e^6 - 13/15*e^5 + 744/35*e^4 + 79/21*e^3 - 1808/35*e^2 + 125/21*e + 649/21, 37/35*e^8 + 96/35*e^7 - 501/35*e^6 - 156/5*e^5 + 1949/35*e^4 + 561/7*e^3 - 2173/35*e^2 - 270/7*e + 146/7, -1/5*e^8 + 16/15*e^7 + 109/15*e^6 - 227/15*e^5 - 901/15*e^4 + 184/3*e^3 + 589/5*e^2 - 42*e - 128/3, -1/21*e^8 + 22/21*e^7 + 79/21*e^6 - 14*e^5 - 733/21*e^4 + 1114/21*e^3 + 452/7*e^2 - 872/21*e - 428/21, -191/105*e^8 - 418/105*e^7 + 2783/105*e^6 + 211/5*e^5 - 12407/105*e^4 - 1835/21*e^3 + 5678/35*e^2 + 487/21*e - 1301/21, 124/105*e^8 + 94/35*e^7 - 589/35*e^6 - 452/15*e^5 + 2456/35*e^4 + 1595/21*e^3 - 2827/35*e^2 - 920/21*e + 638/21, 28/15*e^8 + 64/15*e^7 - 389/15*e^6 - 703/15*e^5 + 1556/15*e^4 + 113*e^3 - 549/5*e^2 - 200/3*e + 30, 72/35*e^8 + 323/105*e^7 - 3568/105*e^6 - 463/15*e^5 + 18412/105*e^4 + 1109/21*e^3 - 9453/35*e^2 - 165/7*e + 2153/21, -22/105*e^8 - 41/105*e^7 + 226/105*e^6 + 17/5*e^5 - 124/105*e^4 - 67/21*e^3 - 864/35*e^2 - 40/21*e + 473/21, -79/35*e^8 - 631/105*e^7 + 3176/105*e^6 + 1031/15*e^5 - 12014/105*e^4 - 3853/21*e^3 + 3811/35*e^2 + 767/7*e - 613/21, -46/35*e^8 - 289/105*e^7 + 2054/105*e^6 + 449/15*e^5 - 9356/105*e^4 - 1441/21*e^3 + 4374/35*e^2 + 211/7*e - 1177/21, -1/7*e^8 - 6/7*e^7 + 9/7*e^6 + 12*e^5 - 5/7*e^4 - 321/7*e^3 - 44/7*e^2 + 220/7*e + 62/7, 79/105*e^8 + 257/105*e^7 - 907/105*e^6 - 139/5*e^5 + 2383/105*e^4 + 1534/21*e^3 + 48/35*e^2 - 725/21*e - 365/21, 76/35*e^8 + 218/35*e^7 - 978/35*e^6 - 348/5*e^5 + 3362/35*e^4 + 1186/7*e^3 - 1969/35*e^2 - 516/7*e - 80/7, -1/5*e^8 - 4/15*e^7 + 59/15*e^6 + 38/15*e^5 - 386/15*e^4 - 7/3*e^3 + 279/5*e^2 - 6*e - 112/3, -233/105*e^8 - 509/105*e^7 + 3469/105*e^6 + 809/15*e^5 - 15991/105*e^4 - 915/7*e^3 + 7834/35*e^2 + 1201/21*e - 674/7, -e^8 - 11/3*e^7 + 31/3*e^6 + 127/3*e^5 - 49/3*e^4 - 346/3*e^3 - 37*e^2 + 66*e + 92/3, -3/5*e^8 - 9/5*e^7 + 34/5*e^6 + 93/5*e^5 - 71/5*e^4 - 36*e^3 - 163/5*e^2 + 9*e + 36, -3/5*e^8 - 37/15*e^7 + 92/15*e^6 + 434/15*e^5 - 143/15*e^4 - 241/3*e^3 - 128/5*e^2 + 45*e + 83/3, 23/35*e^8 + 337/105*e^7 - 467/105*e^6 - 572/15*e^5 - 1657/105*e^4 + 2299/21*e^3 + 3238/35*e^2 - 333/7*e - 1214/21, -152/35*e^8 - 331/35*e^7 + 2236/35*e^6 + 516/5*e^5 - 9909/35*e^4 - 1665/7*e^3 + 12548/35*e^2 + 850/7*e - 820/7, -58/105*e^8 - 89/105*e^7 + 1054/105*e^6 + 53/5*e^5 - 6226/105*e^4 - 715/21*e^3 + 3984/35*e^2 + 746/21*e - 832/21, 23/7*e^8 + 169/21*e^7 - 971/21*e^6 - 272/3*e^5 + 4055/21*e^4 + 4817/21*e^3 - 1662/7*e^2 - 860/7*e + 1679/21, 8/5*e^8 + 24/5*e^7 - 104/5*e^6 - 273/5*e^5 + 381/5*e^4 + 140*e^3 - 372/5*e^2 - 77*e + 20, 263/105*e^8 + 724/105*e^7 - 3284/105*e^6 - 383/5*e^5 + 10541/105*e^4 + 3950/21*e^3 - 1864/35*e^2 - 1786/21*e - 184/21, 19/15*e^8 + 17/15*e^7 - 352/15*e^6 - 48/5*e^5 + 2083/15*e^4 + 4/3*e^3 - 1307/5*e^2 + 22/3*e + 313/3, -3/35*e^8 + 23/105*e^7 + 242/105*e^6 - 73/15*e^5 - 1718/105*e^4 + 650/21*e^3 + 757/35*e^2 - 274/7*e - 76/21, 14/15*e^8 + 9/5*e^7 - 74/5*e^6 - 289/15*e^5 + 356/5*e^4 + 121/3*e^3 - 437/5*e^2 - 58/3*e + 76/3, -49/15*e^8 - 112/15*e^7 + 692/15*e^6 + 1189/15*e^5 - 2858/15*e^4 - 168*e^3 + 1012/5*e^2 + 221/3*e - 43, 188/105*e^8 + 103/35*e^7 - 998/35*e^6 - 439/15*e^5 + 4987/35*e^4 + 976/21*e^3 - 7829/35*e^2 + 2/21*e + 1915/21, 179/105*e^8 + 542/105*e^7 - 2332/105*e^6 - 887/15*e^5 + 8518/105*e^4 + 1067/7*e^3 - 2592/35*e^2 - 1450/21*e + 81/7, 148/105*e^8 + 244/105*e^7 - 2459/105*e^6 - 379/15*e^5 + 13046/105*e^4 + 412/7*e^3 - 7389/35*e^2 - 989/21*e + 561/7, -5/7*e^8 - 13/21*e^7 + 296/21*e^6 + 17/3*e^5 - 1832/21*e^4 - 83/21*e^3 + 1117/7*e^2 + 85/7*e - 1583/21, -6/35*e^8 - 199/105*e^7 - 181/105*e^6 + 344/15*e^5 + 3739/105*e^4 - 1465/21*e^3 - 3631/35*e^2 + 271/7*e + 1304/21, 87/35*e^8 + 488/105*e^7 - 4078/105*e^6 - 748/15*e^5 + 19687/105*e^4 + 2276/21*e^3 - 9283/35*e^2 - 384/7*e + 1700/21, -44/15*e^8 - 97/15*e^7 + 632/15*e^6 + 353/5*e^5 - 2648/15*e^4 - 494/3*e^3 + 937/5*e^2 + 289/3*e - 116/3, 3/5*e^8 + 22/15*e^7 - 137/15*e^6 - 239/15*e^5 + 698/15*e^4 + 112/3*e^3 - 432/5*e^2 - 28*e + 148/3, -29/105*e^8 - 62/105*e^7 + 457/105*e^6 + 122/15*e^5 - 2308/105*e^4 - 230/7*e^3 + 1432/35*e^2 + 793/21*e - 211/7, 52/21*e^8 + 95/21*e^7 - 832/21*e^6 - 48*e^5 + 4096/21*e^4 + 2048/21*e^3 - 1909/7*e^2 - 982/21*e + 2201/21, 367/105*e^8 + 991/105*e^7 - 4766/105*e^6 - 1561/15*e^5 + 16934/105*e^4 + 1747/7*e^3 - 4436/35*e^2 - 2498/21*e + 143/7, -34/105*e^8 + 118/105*e^7 + 1027/105*e^6 - 76/5*e^5 - 8143/105*e^4 + 1166/21*e^3 + 6037/35*e^2 - 499/21*e - 1978/21, -2/105*e^8 - 67/35*e^7 - 183/35*e^6 + 361/15*e^5 + 2022/35*e^4 - 1681/21*e^3 - 4269/35*e^2 + 970/21*e + 932/21, -79/35*e^8 - 152/35*e^7 + 1187/35*e^6 + 232/5*e^5 - 5463/35*e^4 - 722/7*e^3 + 7556/35*e^2 + 375/7*e - 419/7, 29/105*e^8 - 8/105*e^7 - 527/105*e^6 + 16/5*e^5 + 3113/105*e^4 - 472/21*e^3 - 2097/35*e^2 + 362/21*e + 584/21, 11/21*e^8 + 1/7*e^7 - 68/7*e^6 - 1/3*e^5 + 394/7*e^4 - 88/21*e^3 - 688/7*e^2 - 299/21*e + 578/21, 6/5*e^8 + 19/15*e^7 - 314/15*e^6 - 143/15*e^5 + 1661/15*e^4 - 29/3*e^3 - 719/5*e^2 + 17*e + 76/3, 122/105*e^8 + 97/35*e^7 - 597/35*e^6 - 451/15*e^5 + 2518/35*e^4 + 1321/21*e^3 - 1986/35*e^2 - 370/21*e - 446/21, -4*e^8 - 32/3*e^7 + 163/3*e^6 + 358/3*e^5 - 637/3*e^4 - 886/3*e^3 + 215*e^2 + 157*e - 160/3, -316/105*e^8 - 643/105*e^7 + 4643/105*e^6 + 1003/15*e^5 - 20417/105*e^4 - 1112/7*e^3 + 8663/35*e^2 + 2123/21*e - 561/7, 229/105*e^8 + 199/35*e^7 - 1044/35*e^6 - 947/15*e^5 + 4066/35*e^4 + 3212/21*e^3 - 3632/35*e^2 - 1760/21*e + 197/21, 16/105*e^8 - 107/105*e^7 - 473/105*e^6 + 227/15*e^5 + 3062/105*e^4 - 450/7*e^3 - 813/35*e^2 + 997/21*e - 110/7, -97/105*e^8 - 316/105*e^7 + 1286/105*e^6 + 556/15*e^5 - 5084/105*e^4 - 813/7*e^3 + 2236/35*e^2 + 1937/21*e - 97/7, -163/105*e^8 - 404/105*e^7 + 2104/105*e^6 + 208/5*e^5 - 7171/105*e^4 - 1975/21*e^3 + 1639/35*e^2 + 809/21*e - 433/21, 131/105*e^8 + 101/35*e^7 - 631/35*e^6 - 463/15*e^5 + 2799/35*e^4 + 1357/21*e^3 - 4038/35*e^2 - 367/21*e + 1303/21, -2/5*e^8 - 28/15*e^7 + 53/15*e^6 + 341/15*e^5 - 2/15*e^4 - 208/3*e^3 - 117/5*e^2 + 46*e - 55/3, -263/105*e^8 - 584/105*e^7 + 3739/105*e^6 + 869/15*e^5 - 15826/105*e^4 - 787/7*e^3 + 6309/35*e^2 + 505/21*e - 438/7, 2/5*e^8 - 22/15*e^7 - 193/15*e^6 + 314/15*e^5 + 1522/15*e^4 - 265/3*e^3 - 988/5*e^2 + 63*e + 227/3, 104/105*e^8 + 92/105*e^7 - 1762/105*e^6 - 77/15*e^5 + 8983/105*e^4 - 153/7*e^3 - 3867/35*e^2 + 821/21*e + 97/7, 1/5*e^8 - 2/5*e^7 - 23/5*e^6 + 29/5*e^5 + 167/5*e^4 - 20*e^3 - 429/5*e^2 - 7*e + 58, -46/21*e^8 - 29/7*e^7 + 236/7*e^6 + 131/3*e^5 - 1101/7*e^4 - 1900/21*e^3 + 1388/7*e^2 + 1132/21*e - 760/21, 167/105*e^8 + 386/105*e^7 - 2371/105*e^6 - 611/15*e^5 + 10054/105*e^4 + 666/7*e^3 - 4336/35*e^2 - 481/21*e + 356/7, -10/21*e^8 - 32/21*e^7 + 118/21*e^6 + 17*e^5 - 316/21*e^4 - 893/21*e^3 - 2/7*e^2 + 625/21*e - 353/21, 148/105*e^8 + 349/105*e^7 - 2039/105*e^6 - 529/15*e^5 + 7796/105*e^4 + 524/7*e^3 - 1789/35*e^2 - 968/21*e - 111/7, -15/7*e^8 - 109/21*e^7 + 629/21*e^6 + 164/3*e^5 - 2570/21*e^4 - 2342/21*e^3 + 887/7*e^2 + 318/7*e - 794/21, 121/105*e^8 + 278/105*e^7 - 1768/105*e^6 - 146/5*e^5 + 8032/105*e^4 + 1471/21*e^3 - 3963/35*e^2 - 746/21*e + 664/21, 19/21*e^8 + 23/21*e^7 - 304/21*e^6 - 8*e^5 + 1453/21*e^4 - 208/21*e^3 - 531/7*e^2 + 608/21*e + 26/21, 117/35*e^8 + 226/35*e^7 - 1781/35*e^6 - 336/5*e^5 + 8229/35*e^4 + 916/7*e^3 - 10483/35*e^2 - 395/7*e + 554/7, -97/35*e^8 - 703/105*e^7 + 4208/105*e^6 + 1163/15*e^5 - 18437/105*e^4 - 4426/21*e^3 + 8178/35*e^2 + 894/7*e - 1426/21, 157/105*e^8 + 256/105*e^7 - 2351/105*e^6 - 316/15*e^5 + 10319/105*e^4 + 74/7*e^3 - 3386/35*e^2 + 505/21*e + 45/7, 56/15*e^8 + 118/15*e^7 - 833/15*e^6 - 422/5*e^5 + 3722/15*e^4 + 542/3*e^3 - 1528/5*e^2 - 202/3*e + 290/3, -127/105*e^8 - 37/35*e^7 + 717/35*e^6 + 101/15*e^5 - 3728/35*e^4 + 325/21*e^3 + 5366/35*e^2 - 271/21*e - 1004/21, 37/15*e^8 + 71/15*e^7 - 556/15*e^6 - 259/5*e^5 + 2539/15*e^4 + 367/3*e^3 - 1161/5*e^2 - 173/3*e + 244/3, -6/7*e^8 + 4/21*e^7 + 379/21*e^6 - 23/3*e^5 - 2407/21*e^4 + 1229/21*e^3 + 1374/7*e^2 - 353/7*e - 1684/21, 4*e^8 + 34/3*e^7 - 155/3*e^6 - 386/3*e^5 + 548/3*e^4 + 995/3*e^3 - 150*e^2 - 162*e + 62/3, 4/7*e^8 + 58/21*e^7 - 80/21*e^6 - 92/3*e^5 - 346/21*e^4 + 1493/21*e^3 + 785/7*e^2 - 26/7*e - 1780/21, 254/105*e^8 + 214/35*e^7 - 1189/35*e^6 - 1027/15*e^5 + 5076/35*e^4 + 3550/21*e^3 - 7162/35*e^2 - 1621/21*e + 1714/21, 77/15*e^8 + 52/5*e^7 - 387/5*e^6 - 1687/15*e^5 + 1783/5*e^4 + 760/3*e^3 - 2436/5*e^2 - 424/3*e + 505/3, 89/105*e^8 + 352/105*e^7 - 1067/105*e^6 - 194/5*e^5 + 3623/105*e^4 + 2141/21*e^3 - 1427/35*e^2 - 976/21*e + 491/21, 20/21*e^8 + 12/7*e^7 - 109/7*e^6 - 58/3*e^5 + 556/7*e^4 + 1016/21*e^3 - 843/7*e^2 - 620/21*e + 944/21, -502/105*e^8 - 1276/105*e^7 + 6821/105*e^6 + 2041/15*e^5 - 26954/105*e^4 - 2403/7*e^3 + 10331/35*e^2 + 4028/21*e - 677/7, -272/105*e^8 - 491/105*e^7 + 4366/105*e^6 + 761/15*e^5 - 22024/105*e^4 - 785/7*e^3 + 11511/35*e^2 + 1174/21*e - 867/7, -136/35*e^8 - 754/105*e^7 + 6374/105*e^6 + 1139/15*e^5 - 30971/105*e^4 - 3277/21*e^3 + 15394/35*e^2 + 391/7*e - 3646/21, -61/35*e^8 - 524/105*e^7 + 2494/105*e^6 + 844/15*e^5 - 9616/105*e^4 - 2888/21*e^3 + 2594/35*e^2 + 451/7*e - 143/21, 74/105*e^8 + 29/35*e^7 - 439/35*e^6 - 157/15*e^5 + 2571/35*e^4 + 709/21*e^3 - 5637/35*e^2 - 232/21*e + 2161/21, -e^8 - e^7 + 19*e^6 + 10*e^5 - 112*e^4 - 17*e^3 + 186*e^2 + 36*e - 69, 314/105*e^8 + 757/105*e^7 - 4562/105*e^6 - 414/5*e^5 + 19868/105*e^4 + 4637/21*e^3 - 8102/35*e^2 - 2938/21*e + 1355/21, -358/105*e^8 - 944/105*e^7 + 4804/105*e^6 + 503/5*e^5 - 18121/105*e^4 - 5275/21*e^3 + 5289/35*e^2 + 2921/21*e - 745/21, 232/105*e^8 + 177/35*e^7 - 1102/35*e^6 - 821/15*e^5 + 4708/35*e^4 + 2552/21*e^3 - 6206/35*e^2 - 821/21*e + 1529/21, 566/105*e^8 + 1093/105*e^7 - 8783/105*e^6 - 556/5*e^5 + 41792/105*e^4 + 4994/21*e^3 - 18938/35*e^2 - 2707/21*e + 3581/21, -2/15*e^8 - 2/5*e^7 + 12/5*e^6 + 82/15*e^5 - 73/5*e^4 - 73/3*e^3 + 146/5*e^2 + 142/3*e - 88/3, -6/35*e^8 - 94/105*e^7 + 134/105*e^6 + 164/15*e^5 + 484/105*e^4 - 730/21*e^3 - 1391/35*e^2 + 194/7*e + 611/21, -18/35*e^8 - 142/105*e^7 + 542/105*e^6 + 212/15*e^5 - 158/105*e^4 - 622/21*e^3 - 2213/35*e^2 + 50/7*e + 1070/21, 2/21*e^8 + 11/7*e^7 + 15/7*e^6 - 58/3*e^5 - 223/7*e^4 + 1286/21*e^3 + 531/7*e^2 - 797/21*e - 901/21, -157/105*e^8 - 132/35*e^7 + 772/35*e^6 + 626/15*e^5 - 3533/35*e^4 - 1979/21*e^3 + 5101/35*e^2 + 566/21*e - 1199/21, -244/105*e^8 - 512/105*e^7 + 3337/105*e^6 + 249/5*e^5 - 12448/105*e^4 - 1900/21*e^3 + 2747/35*e^2 + 152/21*e + 17/21, 47/105*e^8 + 121/105*e^7 - 731/105*e^6 - 77/5*e^5 + 3539/105*e^4 + 1259/21*e^3 - 1756/35*e^2 - 1585/21*e + 197/21, -197/105*e^8 - 391/105*e^7 + 2921/105*e^6 + 192/5*e^5 - 12689/105*e^4 - 1523/21*e^3 + 4351/35*e^2 + 646/21*e - 584/21, -1/5*e^8 + 11/15*e^7 + 119/15*e^6 - 142/15*e^5 - 1061/15*e^4 + 119/3*e^3 + 824/5*e^2 - 52*e - 235/3, -40/7*e^8 - 251/21*e^7 + 1801/21*e^6 + 388/3*e^5 - 8188/21*e^4 - 6082/21*e^3 + 3518/7*e^2 + 1086/7*e - 3550/21, 29/35*e^8 + 221/105*e^7 - 1441/105*e^6 - 421/15*e^5 + 7939/105*e^4 + 2147/21*e^3 - 5206/35*e^2 - 730/7*e + 1304/21, -304/105*e^8 - 872/105*e^7 + 3877/105*e^6 + 469/5*e^5 - 13273/105*e^4 - 5059/21*e^3 + 3232/35*e^2 + 2771/21*e - 667/21, -208/35*e^8 - 1532/105*e^7 + 8752/105*e^6 + 2407/15*e^5 - 35908/105*e^4 - 7928/21*e^3 + 13017/35*e^2 + 1368/7*e - 2285/21, 76/105*e^8 + 26/35*e^7 - 501/35*e^6 - 143/15*e^5 + 3209/35*e^4 + 626/21*e^3 - 6793/35*e^2 - 383/21*e + 2027/21, 62/15*e^8 + 52/5*e^7 - 287/5*e^6 - 1747/15*e^5 + 1158/5*e^4 + 877/3*e^3 - 1216/5*e^2 - 523/3*e + 229/3, -527/105*e^8 - 1076/105*e^7 + 8026/105*e^6 + 1676/15*e^5 - 37684/105*e^4 - 1797/7*e^3 + 17851/35*e^2 + 2776/21*e - 1311/7, 431/105*e^8 + 351/35*e^7 - 1986/35*e^6 - 1663/15*e^5 + 8094/35*e^4 + 5623/21*e^3 - 9718/35*e^2 - 2563/21*e + 1741/21, 61/105*e^8 + 23/105*e^7 - 1123/105*e^6 + 9/5*e^5 + 6577/105*e^4 - 659/21*e^3 - 3898/35*e^2 + 361/21*e + 1177/21, 25/21*e^8 + 73/21*e^7 - 344/21*e^6 - 115/3*e^5 + 1448/21*e^4 + 603/7*e^3 - 660/7*e^2 - 376/21*e + 174/7, 14/15*e^8 + 14/5*e^7 - 64/5*e^6 - 499/15*e^5 + 251/5*e^4 + 289/3*e^3 - 232/5*e^2 - 244/3*e + 58/3, -62/15*e^8 - 146/15*e^7 + 871/15*e^6 + 1562/15*e^5 - 3589/15*e^4 - 223*e^3 + 1291/5*e^2 + 235/3*e - 64, 10/3*e^8 + 17/3*e^7 - 163/3*e^6 - 61*e^5 + 829/3*e^4 + 392/3*e^3 - 424*e^2 - 169/3*e + 497/3, 71/105*e^8 + 433/105*e^7 - 128/105*e^6 - 246/5*e^5 - 5833/105*e^4 + 3056/21*e^3 + 7017/35*e^2 - 1465/21*e - 2335/21, 32/35*e^8 - 47/105*e^7 - 2033/105*e^6 + 172/15*e^5 + 12947/105*e^4 - 1583/21*e^3 - 7783/35*e^2 + 447/7*e + 1723/21, 113/105*e^8 + 244/105*e^7 - 1724/105*e^6 - 138/5*e^5 + 8426/105*e^4 + 1691/21*e^3 - 4904/35*e^2 - 1108/21*e + 1172/21, 13/105*e^8 - 146/105*e^7 - 614/105*e^6 + 281/15*e^5 + 5336/105*e^4 - 496/7*e^3 - 3594/35*e^2 + 1129/21*e + 230/7, 172/105*e^8 + 241/105*e^7 - 2801/105*e^6 - 346/15*e^5 + 13964/105*e^4 + 290/7*e^3 - 6386/35*e^2 - 428/21*e + 270/7, 37/105*e^8 + 172/35*e^7 + 148/35*e^6 - 926/15*e^5 - 2617/35*e^4 + 4208/21*e^3 + 6019/35*e^2 - 2699/21*e - 1198/21, 47/15*e^8 + 101/15*e^7 - 691/15*e^6 - 1082/15*e^5 + 3064/15*e^4 + 158*e^3 - 1286/5*e^2 - 217/3*e + 99, -572/105*e^8 - 507/35*e^7 + 2542/35*e^6 + 2446/15*e^5 - 9533/35*e^4 - 8644/21*e^3 + 8966/35*e^2 + 4441/21*e - 1093/21, 109/105*e^8 + 29/35*e^7 - 579/35*e^6 - 47/15*e^5 + 2851/35*e^4 - 733/21*e^3 - 4517/35*e^2 + 1441/21*e + 1391/21, -54/35*e^8 - 72/35*e^7 + 892/35*e^6 + 82/5*e^5 - 4638/35*e^4 + 43/7*e^3 + 7151/35*e^2 - 249/7*e - 519/7, -31/105*e^8 - 193/105*e^7 - 22/105*e^6 + 313/15*e^5 + 2953/105*e^4 - 396/7*e^3 - 2312/35*e^2 + 167/21*e + 137/7, 323/105*e^8 + 268/35*e^7 - 1438/35*e^6 - 1264/15*e^5 + 5177/35*e^4 + 4225/21*e^3 - 3014/35*e^2 - 2095/21*e - 326/21, -101/105*e^8 - 263/105*e^7 + 1483/105*e^6 + 458/15*e^5 - 6427/105*e^4 - 655/7*e^3 + 2378/35*e^2 + 1714/21*e + 4/7, -86/35*e^8 - 379/105*e^7 + 4184/105*e^6 + 524/15*e^5 - 21086/105*e^4 - 1039/21*e^3 + 10559/35*e^2 + 123/7*e - 2566/21, 17/105*e^8 - 43/35*e^7 - 177/35*e^6 + 269/15*e^5 + 1293/35*e^4 - 1514/21*e^3 - 1986/35*e^2 + 1247/21*e + 520/21, 199/105*e^8 + 382/105*e^7 - 3002/105*e^6 - 547/15*e^5 + 13658/105*e^4 + 438/7*e^3 - 5367/35*e^2 - 650/21*e + 136/7, 8/105*e^8 - 211/105*e^7 - 814/105*e^6 + 331/15*e^5 + 8251/105*e^4 - 358/7*e^3 - 6899/35*e^2 + 110/21*e + 736/7, -12/35*e^8 + 54/35*e^7 + 416/35*e^6 - 99/5*e^5 - 3574/35*e^4 + 470/7*e^3 + 8663/35*e^2 - 256/7*e - 820/7, 53/105*e^8 + 43/35*e^7 - 278/35*e^6 - 199/15*e^5 + 1507/35*e^4 + 646/21*e^3 - 3089/35*e^2 - 463/21*e + 1048/21]
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 - 2*w^2 - 4*w + 2])] = -1

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