/*
  This code can be loaded, or copied and pasted, into Magma.
  It will load the data associated to the HMF, including
  the field, level, and Hecke and Atkin-Lehner eigenvalue data.
  At the *bottom* of the file, there is code to recreate the
  Hilbert modular form in Magma, by creating the HMF space
  and cutting out the corresponding Hecke irreducible subspace.
  From there, you can ask for more eigenvalues or modify as desired.
  It is commented out, as this computation may be lengthy.
*/

P<x> := PolynomialRing(Rationals());
g := P![3, 2, -5, -2, 1];
F<w> := NumberField(g);
ZF := Integers(F);

NN := ideal<ZF | {23, 23, w^2 - 2*w - 1}>;

primesArray := [
[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 := [ideal<ZF | {F!x : x in I}> : I in primesArray];

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);

heckeEigenvaluesArray := [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 - 8983348/3427*e^2 - 2762310/3427*e + 868966/3427, 2633/3427*e^10 + 10345/3427*e^9 - 30102/3427*e^8 - 147875/3427*e^7 + 46358/3427*e^6 + 594526/3427*e^5 + 192604/3427*e^4 - 758858/3427*e^3 - 323643/3427*e^2 + 200214/3427*e - 15412/3427, -216/3427*e^10 - 4644/3427*e^9 - 9432/3427*e^8 + 63428/3427*e^7 + 166386/3427*e^6 - 221830/3427*e^5 - 695346/3427*e^4 + 150814/3427*e^3 + 828234/3427*e^2 + 153668/3427*e - 66552/3427, -19231/3427*e^10 - 120458/3427*e^9 + 50124/3427*e^8 + 1606778/3427*e^7 + 2091675/3427*e^6 - 5258450/3427*e^5 - 11157219/3427*e^4 + 2221456/3427*e^3 + 14238665/3427*e^2 + 5152454/3427*e - 1572614/3427, 137/3427*e^10 + 4659/3427*e^9 + 11694/3427*e^8 - 59586/3427*e^7 - 181973/3427*e^6 + 164655/3427*e^5 + 705575/3427*e^4 + 74965/3427*e^3 - 759779/3427*e^2 - 390220/3427*e + 42592/3427, 14815/3427*e^10 + 94054/3427*e^9 - 33909/3427*e^8 - 1252072/3427*e^7 - 1676065/3427*e^6 + 4072961/3427*e^5 + 8835231/3427*e^4 - 1625388/3427*e^3 - 11229782/3427*e^2 - 4130587/3427*e + 1249234/3427, -8632/3427*e^10 - 48508/3427*e^9 + 43448/3427*e^8 + 654744/3427*e^7 + 637558/3427*e^6 - 2227012/3427*e^5 - 3789567/3427*e^4 + 1318784/3427*e^3 + 4888763/3427*e^2 + 1597842/3427*e - 485374/3427, -19948/3427*e^10 - 117025/3427*e^9 + 80501/3427*e^8 + 1569247/3427*e^7 + 1761246/3427*e^6 - 5229915/3427*e^5 - 9935857/3427*e^4 + 2655153/3427*e^3 + 12792437/3427*e^2 + 4394366/3427*e - 1369724/3427, 2057/3427*e^10 + 11669/3427*e^9 - 7276/3427*e^8 - 151226/3427*e^7 - 198773/3427*e^6 + 447347/3427*e^5 + 1114218/3427*e^4 + 24852/3427*e^3 - 1483760/3427*e^2 - 761947/3427*e + 204648/3427, 6920/3427*e^10 + 35689/3427*e^9 - 45096/3427*e^8 - 485072/3427*e^7 - 368980/3427*e^6 + 1688562/3427*e^5 + 2502274/3427*e^4 - 1174517/3427*e^3 - 3315096/3427*e^2 - 943305/3427*e + 296780/3427, 5689/3427*e^10 + 31498/3427*e^9 - 31452/3427*e^8 - 429673/3427*e^7 - 381341/3427*e^6 + 1508379/3427*e^5 + 2350936/3427*e^4 - 1084537/3427*e^3 - 3044603/3427*e^2 - 811516/3427*e + 274284/3427, 65/149*e^10 + 280/149*e^9 - 688/149*e^8 - 4074/149*e^7 + 288/149*e^6 + 17056/149*e^5 + 8913/149*e^4 - 24012/149*e^3 - 15543/149*e^2 + 8570/149*e + 2528/149, -7517/3427*e^10 - 43384/3427*e^9 + 36162/3427*e^8 + 590888/3427*e^7 + 578967/3427*e^6 - 2066450/3427*e^5 - 3394034/3427*e^4 + 1466931/3427*e^3 + 4369666/3427*e^2 + 1126042/3427*e - 438456/3427, 5528/3427*e^10 + 33177/3427*e^9 - 20205/3427*e^8 - 446049/3427*e^7 - 517869/3427*e^6 + 1497661/3427*e^5 + 2869218/3427*e^4 - 794714/3427*e^3 - 3666408/3427*e^2 - 1243456/3427*e + 356808/3427, -3643/3427*e^10 - 28633/3427*e^9 - 12859/3427*e^8 + 371858/3427*e^7 + 714706/3427*e^6 - 1109423/3427*e^5 - 3375260/3427*e^4 + 10307/3427*e^3 + 4200402/3427*e^2 + 1726661/3427*e - 539478/3427, 102/149*e^10 + 852/149*e^9 + 282/149*e^8 - 11592/149*e^7 - 18698/149*e^6 + 40145/149*e^5 + 87996/149*e^4 - 25781/149*e^3 - 107638/149*e^2 - 27435/149*e + 11362/149, 12506/3427*e^10 + 80394/3427*e^9 - 20502/3427*e^8 - 1058832/3427*e^7 - 1533346/3427*e^6 + 3324546/3427*e^5 + 7948157/3427*e^4 - 815164/3427*e^3 - 10109425/3427*e^2 - 4064388/3427*e + 1172562/3427, -16590/3427*e^10 - 92806/3427*e^9 + 84342/3427*e^8 + 1252330/3427*e^7 + 1216100/3427*e^6 - 4254876/3427*e^5 - 7269306/3427*e^4 + 2485620/3427*e^3 + 9433816/3427*e^2 + 3127296/3427*e - 974032/3427, 20917/3427*e^10 + 132718/3427*e^9 - 45042/3427*e^8 - 1758788/3427*e^7 - 2409717/3427*e^6 + 5632674/3427*e^5 + 12671718/3427*e^4 - 1847164/3427*e^3 - 16171284/3427*e^2 - 6257866/3427*e + 1875046/3427, 13722/3427*e^10 + 79122/3427*e^9 - 58790/3427*e^8 - 1059754/3427*e^7 - 1167016/3427*e^6 + 3519120/3427*e^5 + 6692116/3427*e^4 - 1730954/3427*e^3 - 8707428/3427*e^2 - 3013662/3427*e + 983674/3427, 1885/3427*e^10 + 14825/3427*e^9 + 4633/3427*e^8 - 197563/3427*e^7 - 341202/3427*e^6 + 638409/3427*e^5 + 1632406/3427*e^4 - 201817/3427*e^3 - 2008840/3427*e^2 - 767650/3427*e + 180592/3427, 26891/3427*e^10 + 168630/3427*e^9 - 70903/3427*e^8 - 2250256/3427*e^7 - 2909213/3427*e^6 + 7371393/3427*e^5 + 15515462/3427*e^4 - 3132310/3427*e^3 - 19800643/3427*e^2 - 7196554/3427*e + 2197160/3427, -1340/3427*e^10 - 8248/3427*e^9 + 888/3427*e^8 + 103082/3427*e^7 + 186502/3427*e^6 - 263408/3427*e^5 - 968207/3427*e^4 - 215232/3427*e^3 + 1288455/3427*e^2 + 742106/3427*e - 201918/3427, 13120/3427*e^10 + 79887/3427*e^9 - 46238/3427*e^8 - 1076286/3427*e^7 - 1252564/3427*e^6 + 3632663/3427*e^5 + 6901938/3427*e^4 - 1998251/3427*e^3 - 8852270/3427*e^2 - 2887975/3427*e + 954310/3427, -7132/3427*e^10 - 47101/3427*e^9 + 12992/3427*e^8 + 631985/3427*e^7 + 854042/3427*e^6 - 2099973/3427*e^5 - 4439406/3427*e^4 + 983519/3427*e^3 + 5621022/3427*e^2 + 1947958/3427*e - 608082/3427, 10244/3427*e^10 + 59177/3427*e^9 - 43882/3427*e^8 - 793655/3427*e^7 - 870991/3427*e^6 + 2642074/3427*e^5 + 4990642/3427*e^4 - 1286485/3427*e^3 - 6471951/3427*e^2 - 2396122/3427*e + 699512/3427, 15787/3427*e^10 + 94390/3427*e^9 - 53151/3427*e^8 - 1256484/3427*e^7 - 1550917/3427*e^6 + 4091074/3427*e^5 + 8537288/3427*e^4 - 1663202/3427*e^3 - 11036347/3427*e^2 - 4071580/3427*e + 1288266/3427, -2236/3427*e^10 - 20658/3427*e^9 - 16533/3427*e^8 + 271504/3427*e^7 + 561031/3427*e^6 - 840384/3427*e^5 - 2557580/3427*e^4 + 117041/3427*e^3 + 3187654/3427*e^2 + 1245256/3427*e - 442954/3427, 7081/3427*e^10 + 40864/3427*e^9 - 32354/3427*e^8 - 550944/3427*e^7 - 568298/3427*e^6 + 1870630/3427*e^5 + 3279398/3427*e^4 - 1121640/3427*e^3 - 4211452/3427*e^2 - 1275586/3427*e + 426730/3427, -7762/3427*e^10 - 40084/3427*e^9 + 54022/3427*e^8 + 551962/3427*e^7 + 364353/3427*e^6 - 1985612/3427*e^5 - 2610410/3427*e^4 + 1580464/3427*e^3 + 3497643/3427*e^2 + 907696/3427*e - 301850/3427, 7025/3427*e^10 + 39660/3427*e^9 - 37084/3427*e^8 - 540846/3427*e^7 - 492414/3427*e^6 + 1896255/3427*e^5 + 2963947/3427*e^4 - 1349973/3427*e^3 - 3795674/3427*e^2 - 1047515/3427*e + 330274/3427, 13817/3427*e^10 + 76024/3427*e^9 - 72919/3427*e^8 - 1024378/3427*e^7 - 976792/3427*e^6 + 3472528/3427*e^5 + 5929953/3427*e^4 - 2038856/3427*e^3 - 7772579/3427*e^2 - 2498594/3427*e + 864822/3427, -23067/3427*e^10 - 141246/3427*e^9 + 68819/3427*e^8 + 1880397/3427*e^7 + 2385692/3427*e^6 - 6119652/3427*e^5 - 12901007/3427*e^4 + 2463077/3427*e^3 + 16526897/3427*e^2 + 6112898/3427*e - 1826192/3427, -221/149*e^10 - 1846/149*e^9 - 1207/149*e^8 + 23775/149*e^7 + 49353/149*e^6 - 68778/149*e^5 - 227908/149*e^4 - 9577/149*e^3 + 280846/149*e^2 + 122097/149*e - 34700/149, 7663/3427*e^10 + 43096/3427*e^9 - 41210/3427*e^8 - 588575/3427*e^7 - 527126/3427*e^6 + 2074424/3427*e^5 + 3205862/3427*e^4 - 1527048/3427*e^3 - 4162414/3427*e^2 - 1081153/3427*e + 405000/3427, -33771/3427*e^10 - 196605/3427*e^9 + 139450/3427*e^8 + 2634607/3427*e^7 + 2941997/3427*e^6 - 8759058/3427*e^5 - 16703607/3427*e^4 + 4315707/3427*e^3 + 21583566/3427*e^2 + 7653834/3427*e - 2336920/3427, -10618/3427*e^10 - 74072/3427*e^9 - 9004/3427*e^8 + 957296/3427*e^7 + 1681322/3427*e^6 - 2806904/3427*e^5 - 8276904/3427*e^4 - 218748/3427*e^3 + 10456282/3427*e^2 + 4766881/3427*e - 1300618/3427, 7448/3427*e^10 + 47041/3427*e^9 - 18613/3427*e^8 - 626791/3427*e^7 - 819110/3427*e^6 + 2040805/3427*e^5 + 4340231/3427*e^4 - 803703/3427*e^3 - 5500737/3427*e^2 - 2064120/3427*e + 559988/3427, 12321/3427*e^10 + 78130/3427*e^9 - 27438/3427*e^8 - 1038079/3427*e^7 - 1405785/3427*e^6 + 3354674/3427*e^5 + 7404487/3427*e^4 - 1240058/3427*e^3 - 9446608/3427*e^2 - 3529594/3427*e + 1099188/3427, 1223/3427*e^10 + 592/3427*e^9 - 29986/3427*e^8 - 20176/3427*e^7 + 248894/3427*e^6 + 202937/3427*e^5 - 809225/3427*e^4 - 712043/3427*e^3 + 931074/3427*e^2 + 763907/3427*e - 152842/3427, -24286/3427*e^10 - 152033/3427*e^9 + 58998/3427*e^8 + 2014901/3427*e^7 + 2702218/3427*e^6 - 6453911/3427*e^5 - 14330825/3427*e^4 + 2113638/3427*e^3 + 18303808/3427*e^2 + 7162963/3427*e - 2082596/3427, 32571/3427*e^10 + 208502/3427*e^9 - 68478/3427*e^8 - 2772671/3427*e^7 - 3771112/3427*e^6 + 8981621/3427*e^5 + 19767683/3427*e^4 - 3392938/3427*e^3 - 25117964/3427*e^2 - 9330772/3427*e + 2835360/3427, -10397/3427*e^10 - 57326/3427*e^9 + 54336/3427*e^8 + 772899/3427*e^7 + 744674/3427*e^6 - 2624141/3427*e^5 - 4512481/3427*e^4 + 1550668/3427*e^3 + 5899434/3427*e^2 + 1870404/3427*e - 626708/3427, -6868/3427*e^10 - 44852/3427*e^9 + 10812/3427*e^8 + 593682/3427*e^7 + 844878/3427*e^6 - 1898149/3427*e^5 - 4348048/3427*e^4 + 637741/3427*e^3 + 5465486/3427*e^2 + 2060956/3427*e - 572434/3427, 2910/3427*e^10 + 4306/3427*e^9 - 61415/3427*e^8 - 81918/3427*e^7 + 452604/3427*e^6 + 532336/3427*e^5 - 1385499/3427*e^4 - 1389618/3427*e^3 + 1595428/3427*e^2 + 1236044/3427*e - 369102/3427, -7823/3427*e^10 - 43109/3427*e^9 + 46789/3427*e^8 + 593927/3427*e^7 + 470267/3427*e^6 - 2147102/3427*e^5 - 2992886/3427*e^4 + 1799958/3427*e^3 + 3868908/3427*e^2 + 766860/3427*e - 381950/3427, -31308/3427*e^10 - 200196/3427*e^9 + 65370/3427*e^8 + 2658628/3427*e^7 + 3628978/3427*e^6 - 8577170/3427*e^5 - 18998900/3427*e^4 + 3111296/3427*e^3 + 24115906/3427*e^2 + 9080896/3427*e - 2748934/3427, 12054/3427*e^10 + 70676/3427*e^9 - 49378/3427*e^8 - 948442/3427*e^7 - 1056465/3427*e^6 + 3160526/3427*e^5 + 6001497/3427*e^4 - 1552930/3427*e^3 - 7832518/3427*e^2 - 2802937/3427*e + 926678/3427, 2359/3427*e^10 + 11308/3427*e^9 - 19220/3427*e^8 - 155502/3427*e^7 - 69476/3427*e^6 + 559938/3427*e^5 + 621753/3427*e^4 - 456424/3427*e^3 - 860285/3427*e^2 - 266774/3427*e + 84462/3427, -8526/3427*e^10 - 56510/3427*e^9 + 8095/3427*e^8 + 744070/3427*e^7 + 1131832/3427*e^6 - 2331450/3427*e^5 - 5785356/3427*e^4 + 533544/3427*e^3 + 7388982/3427*e^2 + 2944382/3427*e - 908886/3427, 4173/3427*e^10 + 19466/3427*e^9 - 37107/3427*e^8 - 271355/3427*e^7 - 76781/3427*e^6 + 1015608/3427*e^5 + 898018/3427*e^4 - 1002995/3427*e^3 - 1202378/3427*e^2 - 86483/3427*e + 25754/3427, -8370/3427*e^10 - 46302/3427*e^9 + 38896/3427*e^8 + 614109/3427*e^7 + 671249/3427*e^6 - 1980089/3427*e^5 - 3934066/3427*e^4 + 749807/3427*e^3 + 5135572/3427*e^2 + 1965607/3427*e - 563814/3427, 19085/3427*e^10 + 103611/3427*e^9 - 103335/3427*e^8 - 1393190/3427*e^7 - 1317609/3427*e^6 + 4688448/3427*e^5 + 8103449/3427*e^4 - 2582860/3427*e^3 - 10652228/3427*e^2 - 3624350/3427*e + 1064604/3427, 1379/3427*e^10 + 10800/3427*e^9 + 11096/3427*e^8 - 126148/3427*e^7 - 365904/3427*e^6 + 221879/3427*e^5 + 1700049/3427*e^4 + 741367/3427*e^3 - 2151670/3427*e^2 - 1445161/3427*e + 267624/3427, 7311/3427*e^10 + 45809/3427*e^9 - 16599/3427*e^8 - 604902/3427*e^7 - 832476/3427*e^6 + 1910420/3427*e^5 + 4409158/3427*e^4 - 484563/3427*e^3 - 5662821/3427*e^2 - 2352446/3427*e + 654476/3427, 18830/3427*e^10 + 110123/3427*e^9 - 76773/3427*e^8 - 1478046/3427*e^7 - 1653794/3427*e^6 + 4943376/3427*e^5 + 9363029/3427*e^4 - 2588065/3427*e^3 - 12082776/3427*e^2 - 4080168/3427*e + 1281900/3427, -4479/3427*e^10 - 26045/3427*e^9 + 13464/3427*e^8 + 336080/3427*e^7 + 464996/3427*e^6 - 983169/3427*e^5 - 2539362/3427*e^4 - 69048/3427*e^3 + 3347264/3427*e^2 + 1608724/3427*e - 490152/3427, 12610/3427*e^10 + 75776/3427*e^9 - 44519/3427*e^8 - 1012962/3427*e^7 - 1201837/3427*e^6 + 3337174/3427*e^5 + 6610958/3427*e^4 - 1491184/3427*e^3 - 8413165/3427*e^2 - 3151908/3427*e + 867998/3427, 3937/3427*e^10 + 34954/3427*e^9 + 32551/3427*e^8 - 440294/3427*e^7 - 1037703/3427*e^6 + 1169374/3427*e^5 + 4691248/3427*e^4 + 640978/3427*e^3 - 5737247/3427*e^2 - 2720984/3427*e + 682610/3427, 33664/3427*e^10 + 209726/3427*e^9 - 91575/3427*e^8 - 2797066/3427*e^7 - 3605042/3427*e^6 + 9151638/3427*e^5 + 19295997/3427*e^4 - 3873389/3427*e^3 - 24631412/3427*e^2 - 8898693/3427*e + 2669118/3427, 1594/3427*e^10 + 13709/3427*e^9 + 5634/3427*e^8 - 187315/3427*e^7 - 313810/3427*e^6 + 649603/3427*e^5 + 1490970/3427*e^4 - 372656/3427*e^3 - 1851728/3427*e^2 - 575285/3427*e + 194884/3427, -16700/3427*e^10 - 102025/3427*e^9 + 49838/3427*e^8 + 1357106/3427*e^7 + 1725972/3427*e^6 - 4409794/3427*e^5 - 9333300/3427*e^4 + 1775800/3427*e^3 + 11998048/3427*e^2 + 4367052/3427*e - 1381848/3427, -17392/3427*e^10 - 116903/3427*e^9 + 17336/3427*e^8 + 1550918/3427*e^7 + 2290628/3427*e^6 - 4977553/3427*e^5 - 11683593/3427*e^4 + 1635884/3427*e^3 + 14838807/3427*e^2 + 5607714/3427*e - 1761080/3427, 31690/3427*e^10 + 204982/3427*e^9 - 57828/3427*e^8 - 2720412/3427*e^7 - 3791676/3427*e^6 + 8756943/3427*e^5 + 19691926/3427*e^4 - 3081324/3427*e^3 - 24908390/3427*e^2 - 9448109/3427*e + 2778292/3427, 3124/3427*e^10 + 8907/3427*e^9 - 50928/3427*e^8 - 140824/3427*e^7 + 270814/3427*e^6 + 689601/3427*e^5 - 617580/3427*e^4 - 1239300/3427*e^3 + 610938/3427*e^2 + 631181/3427*e - 231580/3427, 3896/3427*e^10 + 25505/3427*e^9 - 9221/3427*e^8 - 344166/3427*e^7 - 435049/3427*e^6 + 1160046/3427*e^5 + 2294490/3427*e^4 - 594990/3427*e^3 - 2922683/3427*e^2 - 1016076/3427*e + 352028/3427, 26154/3427*e^10 + 161352/3427*e^9 - 84808/3427*e^8 - 2170600/3427*e^7 - 2598618/3427*e^6 + 7295744/3427*e^5 + 14131510/3427*e^4 - 3905930/3427*e^3 - 17980788/3427*e^2 - 5934730/3427*e + 1848614/3427, 17956/3427*e^10 + 111894/3427*e^9 - 57821/3427*e^8 - 1510154/3427*e^7 - 1781513/3427*e^6 + 5128020/3427*e^5 + 9624424/3427*e^4 - 2977432/3427*e^3 - 12097381/3427*e^2 - 3785216/3427*e + 1137506/3427, -12977/3427*e^10 - 57964/3427*e^9 + 123307/3427*e^8 + 814649/3427*e^7 + 133254/3427*e^6 - 3120098/3427*e^5 - 2428481/3427*e^4 + 3339111/3427*e^3 + 3441321/3427*e^2 + 33662/3427*e - 192484/3427, 16976/3427*e^10 + 107959/3427*e^9 - 37786/3427*e^8 - 1436249/3427*e^7 - 1937434/3427*e^6 + 4659735/3427*e^5 + 10202378/3427*e^4 - 1786495/3427*e^3 - 12984380/3427*e^2 - 4843658/3427*e + 1519434/3427, 38680/3427*e^10 + 238749/3427*e^9 - 115860/3427*e^8 - 3192404/3427*e^7 - 3984778/3427*e^6 + 10535989/3427*e^5 + 21497871/3427*e^4 - 4874296/3427*e^3 - 27384403/3427*e^2 - 9613276/3427*e + 2955752/3427, 25656/3427*e^10 + 160926/3427*e^9 - 62003/3427*e^8 - 2134408/3427*e^7 - 2856426/3427*e^6 + 6863314/3427*e^5 + 15125446/3427*e^4 - 2426358/3427*e^3 - 19294342/3427*e^2 - 7292036/3427*e + 2227502/3427, 13493/3427*e^10 + 75912/3427*e^9 - 69932/3427*e^8 - 1032046/3427*e^7 - 970530/3427*e^6 + 3588720/3427*e^5 + 5836213/3427*e^4 - 2446630/3427*e^3 - 7534339/3427*e^2 - 2158428/3427*e + 717016/3427, -19329/3427*e^10 - 125992/3427*e^9 + 29852/3427*e^8 + 1667287/3427*e^7 + 2392395/3427*e^6 - 5317273/3427*e^5 - 12344110/3427*e^4 + 1661661/3427*e^3 + 15608839/3427*e^2 + 6049350/3427*e - 1713996/3427, -30379/3427*e^10 - 202498/3427*e^9 + 32827/3427*e^8 + 2679472/3427*e^7 + 3960979/3427*e^6 - 8536994/3427*e^5 - 20209104/3427*e^4 + 2604718/3427*e^3 + 25559152/3427*e^2 + 9790464/3427*e - 2914682/3427, -38459/3427*e^10 - 235711/3427*e^9 + 120941/3427*e^8 + 3151941/3427*e^7 + 3887745/3427*e^6 - 10387496/3427*e^5 - 21146740/3427*e^4 + 4635490/3427*e^3 + 27135294/3427*e^2 + 9859358/3427*e - 3022074/3427, -11348/3427*e^10 - 52070/3427*e^9 + 98484/3427*e^8 + 719549/3427*e^7 + 253510/3427*e^6 - 2630873/3427*e^5 - 2692459/3427*e^4 + 2336803/3427*e^3 + 3710640/3427*e^2 + 779590/3427*e - 201194/3427, -43070/3427*e^10 - 254313/3427*e^9 + 173192/3427*e^8 + 3419784/3427*e^7 + 3805576/3427*e^6 - 11498993/3427*e^5 - 21418556/3427*e^4 + 6278054/3427*e^3 + 27482880/3427*e^2 + 9029818/3427*e - 2872066/3427, 26718/3427*e^10 + 166624/3427*e^9 - 73888/3427*e^8 - 2222365/3427*e^7 - 2833162/3427*e^6 + 7274861/3427*e^5 + 15118944/3427*e^4 - 3115884/3427*e^3 - 19159850/3427*e^2 - 7004620/3427*e + 2047520/3427, -16651/3427*e^10 - 95831/3427*e^9 + 80536/3427*e^8 + 1301149/3427*e^7 + 1277463/3427*e^6 - 4498614/3427*e^5 - 7511275/3427*e^4 + 2921015/3427*e^3 + 9691990/3427*e^2 + 2945336/3427*e - 917052/3427, 13647/3427*e^10 + 68942/3427*e^9 - 96335/3427*e^8 - 941584/3427*e^7 - 620610/3427*e^6 + 3313488/3427*e^5 + 4504426/3427*e^4 - 2371318/3427*e^3 - 6044079/3427*e^2 - 1854336/3427*e + 543614/3427, 318/3427*e^10 + 17118/3427*e^9 + 58437/3427*e^8 - 201521/3427*e^7 - 885235/3427*e^6 + 368659/3427*e^5 + 3608233/3427*e^4 + 1126112/3427*e^3 - 4394460/3427*e^2 - 2252352/3427*e + 559482/3427, 29806/3427*e^10 + 171330/3427*e^9 - 133242/3427*e^8 - 2302355/3427*e^7 - 2448942/3427*e^6 + 7724155/3427*e^5 + 14135302/3427*e^4 - 4116432/3427*e^3 - 18270366/3427*e^2 - 6249587/3427*e + 1859680/3427, -477/3427*e^10 + 5166/3427*e^9 + 27149/3427*e^8 - 69548/3427*e^7 - 322248/3427*e^6 + 223227/3427*e^5 + 1251452/3427*e^4 - 30500/3427*e^3 - 1571424/3427*e^2 - 322632/3427*e + 253990/3427, -13083/3427*e^10 - 73951/3427*e^9 + 59277/3427*e^8 + 989202/3427*e^7 + 1064612/3427*e^6 - 3282966/3427*e^5 - 6169490/3427*e^4 + 1663765/3427*e^3 + 8011003/3427*e^2 + 2724128/3427*e - 934152/3427, 1258/3427*e^10 - 3796/3427*e^9 - 43308/3427*e^8 + 37769/3427*e^7 + 422508/3427*e^6 + 15143/3427*e^5 - 1402420/3427*e^4 - 594609/3427*e^3 + 1438004/3427*e^2 + 830838/3427*e - 191940/3427, -21164/3427*e^10 - 126034/3427*e^9 + 77665/3427*e^8 + 1683260/3427*e^7 + 1974079/3427*e^6 - 5537580/3427*e^5 - 10921074/3427*e^4 + 2501719/3427*e^3 + 13953836/3427*e^2 + 5125680/3427*e - 1523536/3427, 410/3427*e^10 - 15174/3427*e^9 - 72341/3427*e^8 + 162776/3427*e^7 + 971394/3427*e^6 - 105486/3427*e^5 - 3794547/3427*e^4 - 1828100/3427*e^3 + 4489681/3427*e^2 + 2854936/3427*e - 594106/3427, 34022/3427*e^10 + 210569/3427*e^9 - 102216/3427*e^8 - 2821721/3427*e^7 - 3500224/3427*e^6 + 9379111/3427*e^5 + 18889374/3427*e^4 - 4630101/3427*e^3 - 24077588/3427*e^2 - 8158665/3427*e + 2597410/3427, 39232/3427*e^10 + 243763/3427*e^9 - 105464/3427*e^8 - 3244453/3427*e^7 - 4215790/3427*e^6 + 10559518/3427*e^5 + 22512930/3427*e^4 - 4306242/3427*e^3 - 28668240/3427*e^2 - 10419127/3427*e + 3176092/3427, 8754/3427*e^10 + 51131/3427*e^9 - 28982/3427*e^8 - 670134/3427*e^7 - 869948/3427*e^6 + 2073639/3427*e^5 + 4801263/3427*e^4 - 380118/3427*e^3 - 6289277/3427*e^2 - 2755510/3427*e + 762092/3427, 18734/3427*e^10 + 135475/3427*e^9 + 18418/3427*e^8 - 1778467/3427*e^7 - 2989484/3427*e^6 + 5511146/3427*e^5 + 14601157/3427*e^4 - 981552/3427*e^3 - 18273950/3427*e^2 - 7361954/3427*e + 2193604/3427, 33987/3427*e^10 + 232092/3427*e^9 - 20354/3427*e^8 - 3071578/3427*e^7 - 4657387/3427*e^6 + 9789660/3427*e^5 + 23444181/3427*e^4 - 3016900/3427*e^3 - 29447431/3427*e^2 - 11117984/3427*e + 3315054/3427, 21488/3427*e^10 + 146708/3427*e^9 - 12112/3427*e^8 - 1942898/3427*e^7 - 2963890/3427*e^6 + 6199317/3427*e^5 + 14969572/3427*e^4 - 1884898/3427*e^3 - 18941898/3427*e^2 - 7172492/3427*e + 2178538/3427, 704/149*e^10 + 4408/149*e^9 - 1989/149*e^8 - 59130/149*e^7 - 73955/149*e^6 + 197484/149*e^5 + 394608/149*e^4 - 103568/149*e^3 - 497110/149*e^2 - 160870/149*e + 50858/149, -456/3427*e^10 - 20085/3427*e^9 - 54182/3427*e^8 + 263368/3427*e^7 + 833324/3427*e^6 - 803773/3427*e^5 - 3333383/3427*e^4 + 56410/3427*e^3 + 3883515/3427*e^2 + 1219238/3427*e - 474060/3427, -38358/3427*e^10 - 252388/3427*e^9 + 52242/3427*e^8 + 3341674/3427*e^7 + 4854132/3427*e^6 - 10665341/3427*e^5 - 24984740/3427*e^4 + 3307674/3427*e^3 + 31756864/3427*e^2 + 12187229/3427*e - 3675974/3427, -16481/3427*e^10 - 126446/3427*e^9 - 39982/3427*e^8 + 1660438/3427*e^7 + 2970627/3427*e^6 - 5148346/3427*e^5 - 14211165/3427*e^4 + 933398/3427*e^3 + 17706451/3427*e^2 + 6804156/3427*e - 2110578/3427, -9963/3427*e^10 - 44568/3427*e^9 + 89280/3427*e^8 + 614105/3427*e^7 + 180562/3427*e^6 - 2235861/3427*e^5 - 2183397/3427*e^4 + 1996570/3427*e^3 + 3021568/3427*e^2 + 605766/3427*e - 132772/3427, 19193/3427*e^10 + 123068/3427*e^9 - 33506/3427*e^8 - 1623670/3427*e^7 - 2329519/3427*e^6 + 5118074/3427*e^5 + 12152282/3427*e^4 - 1284040/3427*e^3 - 15579704/3427*e^2 - 6271434/3427*e + 1844966/3427, -21787/3427*e^10 - 154850/3427*e^9 - 6656/3427*e^8 + 2046628/3427*e^7 + 3262085/3427*e^6 - 6490934/3427*e^5 - 16098987/3427*e^4 + 1832228/3427*e^3 + 20139508/3427*e^2 + 7722514/3427*e - 2373854/3427, -41/23*e^10 - 226/23*e^9 + 203/23*e^8 + 3024/23*e^7 + 3090/23*e^6 - 10064/23*e^5 - 18328/23*e^4 + 5296/23*e^3 + 23583/23*e^2 + 8152/23*e - 2142/23, -12338/3427*e^10 - 83636/3427*e^9 + 10703/3427*e^8 + 1110786/3427*e^7 + 1641540/3427*e^6 - 3586479/3427*e^5 - 8297210/3427*e^4 + 1335667/3427*e^3 + 10356263/3427*e^2 + 3719448/3427*e - 1013420/3427, -10248/3427*e^10 - 62690/3427*e^9 + 28857/3427*e^8 + 833542/3427*e^7 + 1090354/3427*e^6 - 2706091/3427*e^5 - 5901012/3427*e^4 + 1079977/3427*e^3 + 7653611/3427*e^2 + 2720598/3427*e - 886564/3427, -32656/3427*e^10 - 201762/3427*e^9 + 94467/3427*e^8 + 2690696/3427*e^7 + 3418018/3427*e^6 - 8800689/3427*e^5 - 18419106/3427*e^4 + 3706487/3427*e^3 + 23586741/3427*e^2 + 8580250/3427*e - 2557308/3427, 13732/3427*e^10 + 69056/3427*e^9 - 91481/3427*e^8 - 928149/3427*e^7 - 702745/3427*e^6 + 3125702/3427*e^5 + 4848787/3427*e^4 - 1763004/3427*e^3 - 6497089/3427*e^2 - 2289556/3427*e + 669948/3427, -18283/3427*e^10 - 113784/3427*e^9 + 50396/3427*e^8 + 1519550/3427*e^7 + 1953154/3427*e^6 - 4990444/3427*e^5 - 10498611/3427*e^4 + 2185168/3427*e^3 + 13492599/3427*e^2 + 4735428/3427*e - 1559254/3427, 5201/3427*e^10 + 24433/3427*e^9 - 44765/3427*e^8 - 340697/3427*e^7 - 123473/3427*e^6 + 1275402/3427*e^5 + 1292496/3427*e^4 - 1237424/3427*e^3 - 1921636/3427*e^2 - 231558/3427*e + 277760/3427, 16020/3427*e^10 + 90832/3427*e^9 - 74962/3427*e^8 - 1221269/3427*e^7 - 1274512/3427*e^6 + 4102626/3427*e^5 + 7483140/3427*e^4 - 2204347/3427*e^3 - 9820162/3427*e^2 - 3277338/3427*e + 1097700/3427, 20385/3427*e^10 + 138415/3427*e^9 - 18010/3427*e^8 - 1837634/3427*e^7 - 2706638/3427*e^6 + 5912095/3427*e^5 + 13686237/3427*e^4 - 2020100/3427*e^3 - 17145992/3427*e^2 - 6502086/3427*e + 1897712/3427, 13756/3427*e^10 + 90134/3427*e^9 - 18466/3427*e^8 - 1191460/3427*e^7 - 1744763/3427*e^6 + 3790818/3427*e^5 + 8971050/3427*e^4 - 1175086/3427*e^3 - 11366353/3427*e^2 - 4291244/3427*e + 1291918/3427, -32009/3427*e^10 - 203273/3427*e^9 + 70172/3427*e^8 + 2701439/3427*e^7 + 3668525/3427*e^6 - 8741504/3427*e^5 - 19300547/3427*e^4 + 3301801/3427*e^3 + 24564002/3427*e^2 + 9077677/3427*e - 2750542/3427, 36183/3427*e^10 + 221047/3427*e^9 - 106093/3427*e^8 - 2933931/3427*e^7 - 3771874/3427*e^6 + 9451835/3427*e^5 + 20383320/3427*e^4 - 3369003/3427*e^3 - 26195448/3427*e^2 - 10057478/3427*e + 3011544/3427, -13704/3427*e^10 - 89016/3427*e^9 + 25306/3427*e^8 + 1183552/3427*e^7 + 1634644/3427*e^6 - 3825628/3427*e^5 - 8493318/3427*e^4 + 1385396/3427*e^3 + 10764862/3427*e^2 + 4062084/3427*e - 1272850/3427, -24662/3427*e^10 - 136128/3427*e^9 + 127112/3427*e^8 + 1826656/3427*e^7 + 1787072/3427*e^6 - 6100716/3427*e^5 - 10759054/3427*e^4 + 3130233/3427*e^3 + 14068152/3427*e^2 + 5090072/3427*e - 1522946/3427, 17252/3427*e^10 + 117320/3427*e^9 - 8599/3427*e^8 - 1546235/3427*e^7 - 2395640/3427*e^6 + 4854844/3427*e^5 + 12078994/3427*e^4 - 1135779/3427*e^3 - 15272972/3427*e^2 - 6081058/3427*e + 1725560/3427, -33354/3427*e^10 - 199634/3427*e^9 + 119962/3427*e^8 + 2675319/3427*e^7 + 3161960/3427*e^6 - 8890451/3427*e^5 - 17535920/3427*e^4 + 4339741/3427*e^3 + 22586564/3427*e^2 + 7884737/3427*e - 2463178/3427, 27748/3427*e^10 + 164780/3427*e^9 - 103163/3427*e^8 - 2203700/3427*e^7 - 2580009/3427*e^6 + 7277082/3427*e^5 + 14378479/3427*e^4 - 3373858/3427*e^3 - 18591942/3427*e^2 - 6650522/3427*e + 2098330/3427, -8384/3427*e^10 - 53457/3427*e^9 + 8584/3427*e^8 + 690314/3427*e^7 + 1108314/3427*e^6 - 2024231/3427*e^5 - 5705010/3427*e^4 - 127186/3427*e^3 + 7407094/3427*e^2 + 3368579/3427*e - 1047146/3427, -21658/3427*e^10 - 143509/3427*e^9 + 26393/3427*e^8 + 1898893/3427*e^7 + 2778606/3427*e^6 - 6049927/3427*e^5 - 14198392/3427*e^4 + 1850585/3427*e^3 + 17867112/3427*e^2 + 6918876/3427*e - 1965134/3427, 53913/3427*e^10 + 334936/3427*e^9 - 147509/3427*e^8 - 4464284/3427*e^7 - 5765597/3427*e^6 + 14580093/3427*e^5 + 30898702/3427*e^4 - 6064188/3427*e^3 - 39479595/3427*e^2 - 14303468/3427*e + 4341392/3427, 34071/3427*e^10 + 213336/3427*e^9 - 85226/3427*e^8 - 2836554/3427*e^7 - 3756821/3427*e^6 + 9190908/3427*e^5 + 19974594/3427*e^4 - 3512302/3427*e^3 - 25530323/3427*e^2 - 9467290/3427*e + 2938834/3427, 17382/3427*e^10 + 96126/3427*e^9 - 90882/3427*e^8 - 1295272/3427*e^7 - 1243592/3427*e^6 + 4380568/3427*e^5 + 7543380/3427*e^4 - 2477719/3427*e^3 - 9941548/3427*e^2 - 3285217/3427*e + 1190640/3427, -29858/3427*e^10 - 172448/3427*e^9 + 133256/3427*e^8 + 2327398/3427*e^7 + 2459678/3427*e^6 - 7918954/3427*e^5 - 14215502/3427*e^4 + 4708040/3427*e^3 + 18450336/3427*e^2 + 5772785/3427*e - 1981558/3427, -10092/3427*e^10 - 59336/3427*e^9 + 39096/3427*e^8 + 796110/3427*e^7 + 917639/3427*e^6 - 2663160/3427*e^5 - 5156643/3427*e^4 + 1419612/3427*e^3 + 6678472/3427*e^2 + 2132501/3427*e - 753966/3427, -11972/3427*e^10 - 51778/3427*e^9 + 108933/3427*e^8 + 708208/3427*e^7 + 207565/3427*e^6 - 2518156/3427*e^5 - 2702153/3427*e^4 + 1975520/3427*e^3 + 4019700/3427*e^2 + 1103194/3427*e - 430010/3427, 11276/3427*e^10 + 57376/3427*e^9 - 84493/3427*e^8 - 800074/3427*e^7 - 441365/3427*e^6 + 2986447/3427*e^5 + 3433945/3427*e^4 - 2822286/3427*e^3 - 4675136/3427*e^2 - 737506/3427*e + 446316/3427, 13142/3427*e^10 + 80360/3427*e^9 - 44135/3427*e^8 - 1078050/3427*e^7 - 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];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

ALEigenvalues := AssociativeArray();
ALEigenvalues[ideal<ZF | {23, 23, w^2 - 2*w - 1}>] := -1;

// EXAMPLE:
// pp := Factorization(2*ZF)[1][1];
// heckeEigenvalues[pp];

print "To reconstruct the Hilbert newform f, type
  f, iso := Explode(make_newform());";

function make_newform();
 M := HilbertCuspForms(F, NN);
 S := NewSubspace(M);
 // SetVerbose("ModFrmHil", 1);
 NFD := NewformDecomposition(S);
 newforms := [* Eigenform(U) : U in NFD *];

 if #newforms eq 0 then;
  print "No Hilbert newforms at this level";
  return 0;
 end if;

 print "Testing ", #newforms, " possible newforms";
 newforms := [* f: f in newforms | IsIsomorphic(BaseField(f), K) *];
 print #newforms, " newforms have the correct Hecke field";

 if #newforms eq 0 then;
  print "No Hilbert newform found with the correct Hecke field";
  return 0;
 end if;

 autos := Automorphisms(K);
 xnewforms := [* *];
 for f in newforms do;
  if K eq RationalField() then;
   Append(~xnewforms, [* f, autos[1] *]);
  else;
   flag, iso := IsIsomorphic(K,BaseField(f));
   for a in autos do;
    Append(~xnewforms, [* f, a*iso *]);
   end for;
  end if;
 end for;
 newforms := xnewforms;

 for P in primes do;
  xnewforms := [* *];
  for f_iso in newforms do;
   f, iso := Explode(f_iso);
   if HeckeEigenvalue(f,P) eq iso(heckeEigenvalues[P]) then;
    Append(~xnewforms, f_iso);
   end if;
  end for;
  newforms := xnewforms;
  if #newforms eq 0 then;
   print "No Hilbert newform found which matches the Hecke eigenvalues";
   return 0;
  else if #newforms eq 1 then;
   print "success: unique match";
   return newforms[1];
  end if;
  end if;
 end for;
 print #newforms, "Hilbert newforms found which match the Hecke eigenvalues";
 return newforms[1];

end function;