/*
  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([23, 23, w^2 - 2*w - 1])

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^11 - 6*x^10 - 4*x^9 + 82*x^8 - 90*x^7 - 290*x^6 + 517*x^5 + 222*x^4 - 707*x^3 + 124*x^2 + 134*x + 16
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -2432/3427*e^10 + 14591/3427*e^9 + 8036/3427*e^8 - 193756/3427*e^7 + 240608/3427*e^6 + 625611/3427*e^5 - 1319304/3427*e^4 - 231171/3427*e^3 + 1705938/3427*e^2 - 653856/3427*e - 197960/3427, -3003/3427*e^10 + 18300/3427*e^9 + 9376/3427*e^8 - 244213/3427*e^7 + 304720/3427*e^6 + 801576/3427*e^5 - 1656914/3427*e^4 - 354580/3427*e^3 + 2125630/3427*e^2 - 756283/3427*e - 227292/3427, -1320/3427*e^10 + 7818/3427*e^9 + 4046/3427*e^8 - 102413/3427*e^7 + 134922/3427*e^6 + 316866/3427*e^5 - 730950/3427*e^4 - 63368/3427*e^3 + 935322/3427*e^2 - 397997/3427*e - 102846/3427, 97/3427*e^10 - 3799/3427*e^9 + 12232/3427*e^8 + 44540/3427*e^7 - 188477/3427*e^6 - 79659/3427*e^5 + 762246/3427*e^4 - 254570/3427*e^3 - 913690/3427*e^2 + 500493/3427*e + 125462/3427, -3575/3427*e^10 + 20317/3427*e^9 + 16384/3427*e^8 - 272942/3427*e^7 + 289163/3427*e^6 + 915581/3427*e^5 - 1685791/3427*e^4 - 491475/3427*e^3 + 2196461/3427*e^2 - 730782/3427*e - 231420/3427, -4166/3427*e^10 + 24456/3427*e^9 + 17993/3427*e^8 - 330922/3427*e^7 + 350023/3427*e^6 + 1134044/3427*e^5 - 1996779/3427*e^4 - 706400/3427*e^3 + 2558046/3427*e^2 - 766078/3427*e - 257014/3427, -1452/3427*e^10 + 10656/3427*e^9 - 1718/3427*e^8 - 140413/3427*e^7 + 235460/3427*e^6 + 441767/3427*e^5 - 1143318/3427*e^4 - 116312/3427*e^3 + 1420903/3427*e^2 - 526556/3427*e - 154940/3427, -1, -20/23*e^10 + 108/23*e^9 + 108/23*e^8 - 1451/23*e^7 + 1394/23*e^6 + 4870/23*e^5 - 8614/23*e^4 - 2621/23*e^3 + 11468/23*e^2 - 3893/23*e - 1276/23, 254/149*e^10 - 1587/149*e^9 - 630/149*e^8 + 21057/149*e^7 - 28074/149*e^6 - 67782/149*e^5 + 149071/149*e^4 + 24072/149*e^3 - 190326/149*e^2 + 72622/149*e + 22468/149, -5214/3427*e^10 + 36707/3427*e^9 - 1496/3427*e^8 - 483181/3427*e^7 + 780714/3427*e^6 + 1511730/3427*e^5 - 3862234/3427*e^4 - 336664/3427*e^3 + 4840168/3427*e^2 - 1923527/3427*e - 546406/3427, 198/149*e^10 - 1128/149*e^9 - 890/149*e^8 + 15131/149*e^7 - 16260/149*e^6 - 50495/149*e^5 + 94370/149*e^4 + 25776/149*e^3 - 123208/149*e^2 + 42870/149*e + 13922/149, -7473/3427*e^10 + 42438/3427*e^9 + 33514/3427*e^8 - 566798/3427*e^7 + 612852/3427*e^6 + 1866032/3427*e^5 - 3541019/3427*e^4 - 849558/3427*e^3 + 4582491/3427*e^2 - 1717184/3427*e - 498770/3427, -17056/3427*e^10 + 106252/3427*e^9 + 45716/3427*e^8 - 1414936/3427*e^7 + 1835324/3427*e^6 + 4606972/3427*e^5 - 9804595/3427*e^4 - 1854410/3427*e^3 + 12512062/3427*e^2 - 4609404/3427*e - 1394818/3427, 3815/3427*e^10 - 18623/3427*e^9 - 29893/3427*e^8 + 256981/3427*e^7 - 130194/3427*e^6 - 935496/3427*e^5 + 1078459/3427*e^4 + 818592/3427*e^3 - 1454626/3427*e^2 + 285045/3427*e + 118024/3427, -7686/3427*e^10 + 45304/3427*e^9 + 31067/3427*e^8 - 609735/3427*e^7 + 678972/3427*e^6 + 2054414/3427*e^5 - 3839742/3427*e^4 - 1127837/3427*e^3 + 4969990/3427*e^2 - 1630922/3427*e - 538124/3427, 13268/3427*e^10 - 86496/3427*e^9 - 21498/3427*e^8 + 1147035/3427*e^7 - 1627402/3427*e^6 - 3684640/3427*e^5 + 8412952/3427*e^4 + 1276568/3427*e^3 - 10647772/3427*e^2 + 3971738/3427*e + 1199438/3427, -13011/3427*e^10 + 86111/3427*e^9 + 14443/3427*e^8 - 1134840/3427*e^7 + 1691123/3427*e^6 + 3566573/3427*e^5 - 8634757/3427*e^4 - 870977/3427*e^3 + 10932316/3427*e^2 - 4402398/3427*e - 1275230/3427, 5195/3427*e^10 - 34585/3427*e^9 - 3903/3427*e^8 + 453930/3427*e^7 - 704297/3427*e^6 - 1407272/3427*e^5 + 3580123/3427*e^4 + 258634/3427*e^3 - 4542560/3427*e^2 + 1855876/3427*e + 524940/3427, 2773/3427*e^10 - 16782/3427*e^9 - 7996/3427*e^8 + 221098/3427*e^7 - 290713/3427*e^6 - 696673/3427*e^5 + 1568962/3427*e^4 + 189739/3427*e^3 - 2034780/3427*e^2 + 820614/3427*e + 280560/3427, -1200/3427*e^10 + 12092/3427*e^9 - 11276/3427*e^8 - 160085/3427*e^7 + 332638/3427*e^6 + 507388/3427*e^5 - 1473272/3427*e^4 - 131132/3427*e^3 + 1756890/3427*e^2 - 632860/3427*e - 180106/3427, -18846/3427*e^10 + 110467/3427*e^9 + 74932/3427*e^8 - 1479952/3427*e^7 + 1684777/3427*e^6 + 4918430/3427*e^5 - 9508969/3427*e^4 - 2433725/3427*e^3 + 12313192/3427*e^2 - 4247162/3427*e - 1337854/3427, 16118/3427*e^10 - 89512/3427*e^9 - 85533/3427*e^8 + 1213238/3427*e^7 - 1133149/3427*e^6 - 4178584/3427*e^5 + 6891418/3427*e^4 + 2672652/3427*e^3 - 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1281886/3427*e^6 - 3588938/3427*e^5 + 6987801/3427*e^4 + 1753477/3427*e^3 - 8867516/3427*e^2 + 3198983/3427*e + 893310/3427, -626/3427*e^10 + 20313/3427*e^9 - 63890/3427*e^8 - 236498/3427*e^7 + 1004448/3427*e^6 + 407639/3427*e^5 - 4107780/3427*e^4 + 1400108/3427*e^3 + 5032852/3427*e^2 - 2672268/3427*e - 767852/3427, 23274/3427*e^10 - 150837/3427*e^9 - 39218/3427*e^8 + 1995443/3427*e^7 - 2833870/3427*e^6 - 6354229/3427*e^5 + 14682012/3427*e^4 + 1930489/3427*e^3 - 18623738/3427*e^2 + 7267130/3427*e + 2126434/3427, -31553/3427*e^10 + 190042/3427*e^9 + 110646/3427*e^8 - 2544308/3427*e^7 + 3023686/3427*e^6 + 8434646/3427*e^5 - 16662845/3427*e^4 - 4085006/3427*e^3 + 21379595/3427*e^2 - 7409502/3427*e - 2351876/3427, 36617/3427*e^10 - 223524/3427*e^9 - 115700/3427*e^8 + 2986488/3427*e^7 - 3698564/3427*e^6 - 9822980/3427*e^5 + 20155862/3427*e^4 + 4338452/3427*e^3 - 25920474/3427*e^2 + 9361872/3427*e + 2922890/3427, 24149/3427*e^10 - 147374/3427*e^9 - 74119/3427*e^8 + 1962169/3427*e^7 - 2468840/3427*e^6 - 6385212/3427*e^5 + 13402495/3427*e^4 + 2551865/3427*e^3 - 17232172/3427*e^2 + 6385492/3427*e + 2005734/3427, 31814/3427*e^10 - 190513/3427*e^9 - 116384/3427*e^8 + 2555266/3427*e^7 - 2983989/3427*e^6 - 8507066/3427*e^5 + 16573481/3427*e^4 + 4181279/3427*e^3 - 21320578/3427*e^2 + 7495230/3427*e + 2319202/3427, 29248/3427*e^10 - 166187/3427*e^9 - 133619/3427*e^8 + 2229886/3427*e^7 - 2366952/3427*e^6 - 7455526/3427*e^5 + 13759483/3427*e^4 + 3925024/3427*e^3 - 17863110/3427*e^2 + 6019392/3427*e + 1907082/3427, 2365/3427*e^10 + 9125/3427*e^9 - 90925/3427*e^8 - 94811/3427*e^7 + 943150/3427*e^6 + 14015/3427*e^5 - 3331396/3427*e^4 + 1301561/3427*e^3 + 3710602/3427*e^2 - 1946988/3427*e - 416316/3427, 311/149*e^10 - 1397/149*e^9 - 2611/149*e^8 + 19112/149*e^7 - 8793/149*e^6 - 67958/149*e^5 + 85759/149*e^4 + 53436/149*e^3 - 126570/149*e^2 + 27788/149*e + 15048/149, -11429/3427*e^10 + 93222/3427*e^9 - 52414/3427*e^8 - 1204266/3427*e^7 + 2412372/3427*e^6 + 3509980/3427*e^5 - 11259405/3427*e^4 + 446768/3427*e^3 + 13982660/3427*e^2 - 6298140/3427*e - 1696334/3427, -8212/3427*e^10 + 39478/3427*e^9 + 68642/3427*e^8 - 551593/3427*e^7 + 219216/3427*e^6 + 2078213/3427*e^5 - 2076528/3427*e^4 - 2104278/3427*e^3 + 2822517/3427*e^2 - 152902/3427*e - 207464/3427, -3098/3427*e^10 + 11775/3427*e^9 + 47494/3427*e^8 - 191702/3427*e^7 - 235058/3427*e^6 + 991447/3427*e^5 + 561724/3427*e^4 - 1978450/3427*e^3 - 779744/3427*e^2 + 1276946/3427*e + 426172/3427, -17236/3427*e^10 + 110122/3427*e^9 + 27575/3427*e^8 - 1444946/3427*e^7 + 2124767/3427*e^6 + 4489112/3427*e^5 - 11014618/3427*e^4 - 943992/3427*e^3 + 14059007/3427*e^2 - 5667320/3427*e - 1710730/3427, 28298/3427*e^10 - 176605/3427*e^9 - 71150/3427*e^8 + 2343756/3427*e^7 - 3114293/3427*e^6 - 7551330/3427*e^5 + 16562751/3427*e^4 + 2720573/3427*e^3 - 21173226/3427*e^2 + 8010378/3427*e + 2403348/3427, -7298/3427*e^10 + 47243/3427*e^9 + 21736/3427*e^8 - 647476/3427*e^7 + 747544/3427*e^6 + 2297806/3427*e^5 - 3977868/3427*e^4 - 1717742/3427*e^3 + 4831332/3427*e^2 - 1201943/3427*e - 255604/3427, -26064/3427*e^10 + 169698/3427*e^9 + 37333/3427*e^8 - 2234416/3427*e^7 + 3267809/3427*e^6 + 7005120/3427*e^5 - 16821559/3427*e^4 - 1657236/3427*e^3 + 21348845/3427*e^2 - 8681984/3427*e - 2513138/3427, 615/149*e^10 - 3314/149*e^9 - 3392/149*e^8 + 44449/149*e^7 - 41551/149*e^6 - 148562/149*e^5 + 257973/149*e^4 + 78328/149*e^3 - 344990/149*e^2 + 119950/149*e + 42326/149, 32732/3427*e^10 - 172553/3427*e^9 - 199670/3427*e^8 + 2334774/3427*e^7 - 1934792/3427*e^6 - 8012217/3427*e^5 + 12563324/3427*e^4 + 5074123/3427*e^3 - 16590070/3427*e^2 + 5245650/3427*e + 1628780/3427, -32835/3427*e^10 + 186762/3427*e^9 + 156333/3427*e^8 - 2523106/3427*e^7 + 2567118/3427*e^6 + 8607709/3427*e^5 - 15098938/3427*e^4 - 5205472/3427*e^3 + 19680636/3427*e^2 - 6058080/3427*e - 2089652/3427, 519/149*e^10 - 3485/149*e^9 - 879/149*e^8 + 46870/149*e^7 - 62465/149*e^6 - 157433/149*e^5 + 319543/149*e^4 + 84591/149*e^3 - 395576/149*e^2 + 126120/149*e + 37680/149, 1537/149*e^10 - 9876/149*e^9 - 3262/149*e^8 + 131746/149*e^7 - 177684/149*e^6 - 430844/149*e^5 + 932803/149*e^4 + 178498/149*e^3 - 1185533/149*e^2 + 429250/149*e + 130784/149, -24486/3427*e^10 + 170041/3427*e^9 - 6852/3427*e^8 - 2220357/3427*e^7 + 3670382/3427*e^6 + 6758946/3427*e^5 - 18207848/3427*e^4 - 681303/3427*e^3 + 22966048/3427*e^2 - 9719887/3427*e - 2792302/3427, 44966/3427*e^10 - 257380/3427*e^9 - 213772/3427*e^8 + 3481149/3427*e^7 - 3506882/3427*e^6 - 11915060/3427*e^5 + 20542492/3427*e^4 + 7361595/3427*e^3 - 26589820/3427*e^2 + 8140089/3427*e + 2720582/3427, 30497/3427*e^10 - 167338/3427*e^9 - 170466/3427*e^8 + 2274578/3427*e^7 - 2017189/3427*e^6 - 7908364/3427*e^5 + 12503724/3427*e^4 + 5398943/3427*e^3 - 16278362/3427*e^2 + 4694946/3427*e + 1482760/3427, 6874/3427*e^10 - 38127/3427*e^9 - 34539/3427*e^8 + 511292/3427*e^7 - 510798/3427*e^6 - 1701166/3427*e^5 + 3047397/3427*e^4 + 821467/3427*e^3 - 3954910/3427*e^2 + 1540132/3427*e + 359524/3427]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([23, 23, w^2 - 2*w - 1])] = 1

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