/*
  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![31, 0, -12, 0, 1];
F<w> := NumberField(g);
ZF := Integers(F);

NN := ideal<ZF | {25, 5, w^2 - 6}>;

primesArray := [
[4, 2, -1/2*w^3 - 1/2*w^2 + 7/2*w + 11/2],
[5, 5, -1/2*w^3 + w^2 + 5/2*w - 4],
[5, 5, -1/2*w^2 - w + 3/2],
[9, 3, -1/2*w^3 + 1/2*w^2 + 7/2*w - 9/2],
[9, 3, -1/2*w^3 - 1/2*w^2 + 7/2*w + 9/2],
[19, 19, -1/2*w^2 + w + 5/2],
[19, 19, 1/2*w^2 + w - 5/2],
[29, 29, -3/2*w^2 - w + 17/2],
[29, 29, -3/2*w^2 + w + 17/2],
[31, 31, 1/2*w^3 - 7/2*w],
[59, 59, 1/2*w^2 + w - 11/2],
[59, 59, 1/2*w^2 - w - 11/2],
[61, 61, -1/2*w^3 + w^2 + 7/2*w - 5],
[61, 61, 1/2*w^3 + w^2 - 7/2*w - 5],
[71, 71, -1/2*w^3 - 2*w^2 + 11/2*w + 13],
[71, 71, 3/2*w^3 + 2*w^2 - 23/2*w - 18],
[79, 79, 1/2*w^3 + 1/2*w^2 - 7/2*w - 1/2],
[79, 79, -2*w^2 + w + 10],
[79, 79, 2*w^2 + w - 10],
[79, 79, 1/2*w^3 - 1/2*w^2 - 7/2*w + 1/2],
[89, 89, 1/2*w^3 - 2*w^2 - 5/2*w + 11],
[89, 89, -1/2*w^2 + w + 15/2],
[109, 109, -w^3 + 7*w + 3],
[109, 109, 1/2*w^3 - 2*w^2 - 9/2*w + 12],
[109, 109, w^3 + w^2 - 8*w - 11],
[109, 109, w^3 - 7*w + 3],
[121, 11, 3/2*w^2 - 19/2],
[121, 11, -1/2*w^2 + 13/2],
[131, 131, -1/2*w^3 + 3/2*w^2 + 7/2*w - 15/2],
[131, 131, -1/2*w^3 + 9/2*w + 3],
[179, 179, -w^3 - 5/2*w^2 + 9*w + 35/2],
[179, 179, 1/2*w^3 + 2*w^2 - 7/2*w - 13],
[179, 179, -1/2*w^3 + 2*w^2 + 7/2*w - 13],
[179, 179, 3/2*w^3 + 4*w^2 - 27/2*w - 29],
[181, 181, -1/2*w^3 + w^2 + 5/2*w - 7],
[181, 181, 1/2*w^3 + w^2 - 5/2*w - 7],
[191, 191, 2*w^2 + w - 12],
[191, 191, 2*w^2 - w - 12],
[211, 211, w^3 - w^2 - 7*w + 4],
[211, 211, -w^3 - w^2 + 7*w + 4],
[229, 229, 3/2*w^2 + w - 23/2],
[229, 229, 3/2*w^2 - w - 23/2],
[241, 241, 1/2*w^3 + 3/2*w^2 - 9/2*w - 17/2],
[241, 241, -1/2*w^3 + 3/2*w^2 + 9/2*w - 17/2],
[251, 251, w^3 - 5*w + 3],
[251, 251, 3/2*w^3 - 23/2*w + 2],
[251, 251, 5/2*w^2 + 3*w - 23/2],
[251, 251, w^3 + 3*w^2 - 9*w - 24],
[269, 269, 1/2*w^2 + 2*w - 9/2],
[269, 269, 1/2*w^2 - 2*w - 9/2],
[271, 271, 1/2*w^3 - 1/2*w^2 - 3/2*w - 3/2],
[271, 271, w^3 + 3/2*w^2 - 6*w - 15/2],
[271, 271, 1/2*w^3 + 3*w^2 - 9/2*w - 16],
[271, 271, -1/2*w^3 - 2*w^2 + 5/2*w + 13],
[281, 281, w^3 - 5/2*w^2 - 8*w + 33/2],
[281, 281, w^2 + 2*w - 6],
[281, 281, w^2 - 2*w - 6],
[281, 281, w^3 + 5/2*w^2 - 8*w - 33/2],
[311, 311, -5/2*w^3 - 3*w^2 + 37/2*w + 30],
[311, 311, 2*w^2 - 2*w - 13],
[331, 331, -1/2*w^3 + 7/2*w - 5],
[331, 331, -w^3 + 5/2*w^2 + 7*w - 29/2],
[331, 331, w^3 + 5/2*w^2 - 7*w - 29/2],
[331, 331, 1/2*w^3 - 7/2*w - 5],
[349, 349, 1/2*w^3 - 2*w^2 - 11/2*w + 16],
[349, 349, w^3 + 3*w^2 - 6*w - 19],
[349, 349, 1/2*w^3 - w^2 - 1/2*w - 1],
[349, 349, 1/2*w^3 + 2*w^2 - 11/2*w - 16],
[359, 359, 1/2*w^3 + 3/2*w^2 - 11/2*w - 15/2],
[359, 359, w^3 - 4*w^2 - 2*w + 16],
[361, 19, -1/2*w^2 + 15/2],
[379, 379, 1/2*w^3 + 5/2*w^2 - 11/2*w - 37/2],
[379, 379, -w^3 + 1/2*w^2 + 6*w - 15/2],
[389, 389, w^3 - 1/2*w^2 - 7*w + 5/2],
[389, 389, w^3 + 1/2*w^2 - 7*w - 5/2],
[401, 401, 1/2*w^3 + 3/2*w^2 - 5/2*w - 21/2],
[401, 401, -1/2*w^3 + 3/2*w^2 + 5/2*w - 21/2],
[409, 409, -2*w^3 - 5*w^2 + 18*w + 38],
[409, 409, 1/2*w^3 - w^2 - 13/2*w + 1],
[419, 419, -1/2*w^3 + 1/2*w^2 + 5/2*w - 19/2],
[419, 419, 1/2*w^3 + 1/2*w^2 - 5/2*w - 19/2],
[431, 431, 1/2*w^3 - 3/2*w^2 - 7/2*w + 11/2],
[431, 431, 1/2*w^3 + 3/2*w^2 - 7/2*w - 11/2],
[439, 439, -1/2*w^3 + 5/2*w^2 + 5/2*w - 27/2],
[439, 439, -1/2*w^3 - 5/2*w^2 + 5/2*w + 27/2],
[449, 449, w^3 - 1/2*w^2 - 7*w + 7/2],
[449, 449, w^3 + 1/2*w^2 - 7*w - 7/2],
[461, 461, w^3 - 7/2*w^2 - 5*w + 37/2],
[461, 461, -1/2*w^2 + 2*w + 21/2],
[479, 479, -w^3 + 4*w^2 + 4*w - 20],
[479, 479, 1/2*w^3 - 3/2*w + 8],
[491, 491, 1/2*w^3 - 5/2*w^2 - 3/2*w + 29/2],
[491, 491, 1/2*w^3 + 1/2*w^2 - 1/2*w - 7/2],
[491, 491, 1/2*w^3 + w^2 - 11/2*w - 8],
[491, 491, -1/2*w^3 + w^2 + 5/2*w - 12],
[499, 499, 3*w^2 - w - 21],
[499, 499, 1/2*w^3 + 5/2*w^2 - 11/2*w - 29/2],
[499, 499, w^3 + 5*w^2 - 11*w - 32],
[499, 499, 3*w^2 + w - 21],
[509, 509, -w^3 + 3/2*w^2 + 4*w - 3/2],
[509, 509, 1/2*w^3 + 3*w^2 - 3/2*w - 18],
[529, 23, 1/2*w^3 - 2*w^2 - 11/2*w + 11],
[529, 23, 1/2*w^3 + 2*w^2 - 11/2*w - 11],
[569, 569, 1/2*w^3 + w^2 - 11/2*w - 3],
[569, 569, -1/2*w^3 + w^2 + 11/2*w - 3],
[571, 571, 5/2*w^2 + 2*w - 33/2],
[571, 571, 2*w^3 - 5/2*w^2 - 16*w + 49/2],
[571, 571, 2*w^3 + 5/2*w^2 - 16*w - 49/2],
[571, 571, 5/2*w^2 - 2*w - 33/2],
[599, 599, 1/2*w^3 - 1/2*w^2 - 11/2*w - 3/2],
[599, 599, -1/2*w^3 - 1/2*w^2 + 11/2*w - 3/2],
[601, 601, 2*w^3 + 3/2*w^2 - 15*w - 35/2],
[601, 601, 5/2*w^3 + 3*w^2 - 39/2*w - 29],
[619, 619, 5/2*w^3 + 5/2*w^2 - 37/2*w - 51/2],
[619, 619, w^3 - 1/2*w^2 - 5*w + 11/2],
[619, 619, 3/2*w^2 - 2*w - 23/2],
[619, 619, w^3 + 3*w^2 - 10*w - 21],
[631, 631, -5/2*w^3 + 33/2*w + 13],
[631, 631, 3/2*w^3 - 5*w^2 - 13/2*w + 22],
[631, 631, -2*w^3 - 2*w^2 + 14*w + 23],
[631, 631, -5/2*w^2 - 5*w + 13/2],
[641, 641, -1/2*w^3 + 1/2*w^2 + 11/2*w - 5/2],
[641, 641, 1/2*w^3 + 1/2*w^2 - 11/2*w - 5/2],
[659, 659, -3/2*w^3 - w^2 + 23/2*w + 14],
[659, 659, 3/2*w^3 + 5/2*w^2 - 19/2*w - 27/2],
[661, 661, -1/2*w^3 + 1/2*w^2 + 11/2*w - 9/2],
[661, 661, w^3 + w^2 - 8*w - 5],
[661, 661, -1/2*w^3 + 2*w^2 + 7/2*w - 8],
[661, 661, -1/2*w^3 - 1/2*w^2 + 11/2*w + 9/2],
[691, 691, 1/2*w^3 - 3/2*w^2 - 3/2*w + 19/2],
[691, 691, 1/2*w^3 + 3/2*w^2 - 3/2*w - 19/2],
[709, 709, 1/2*w^3 - 2*w^2 - 3/2*w + 12],
[709, 709, 1/2*w^3 + 2*w^2 - 3/2*w - 12],
[751, 751, 3/2*w^3 - w^2 - 21/2*w + 11],
[751, 751, 3/2*w^3 + w^2 - 21/2*w - 11],
[761, 761, 2*w^3 + 11/2*w^2 - 17*w - 85/2],
[761, 761, -3/2*w^3 - 4*w^2 + 17/2*w + 23],
[769, 769, w^3 - 7/2*w^2 - 8*w + 45/2],
[769, 769, -1/2*w^3 - 5/2*w^2 + 5/2*w + 35/2],
[769, 769, -1/2*w^3 + 5/2*w^2 + 5/2*w - 35/2],
[769, 769, w^3 + 7/2*w^2 - 8*w - 45/2],
[809, 809, w^3 - 7/2*w^2 - 7*w + 41/2],
[809, 809, w^3 + 7/2*w^2 - 7*w - 41/2],
[811, 811, -1/2*w^3 - 9/2*w^2 + 13/2*w + 59/2],
[811, 811, 3*w^3 + 5*w^2 - 24*w - 45],
[821, 821, -2*w^3 - 7/2*w^2 + 12*w + 33/2],
[821, 821, w^3 - 4*w^2 - w + 13],
[829, 829, -w^3 + 1/2*w^2 + 8*w - 1/2],
[829, 829, w^3 + 1/2*w^2 - 8*w - 1/2],
[839, 839, w^3 - 3/2*w^2 - 7*w + 13/2],
[839, 839, w^3 + 3/2*w^2 - 7*w - 13/2],
[841, 29, 5/2*w^2 - 27/2],
[859, 859, 1/2*w^3 - 7/2*w - 6],
[859, 859, -3/2*w^3 + 2*w^2 + 21/2*w - 15],
[859, 859, 3/2*w^3 + 2*w^2 - 21/2*w - 15],
[859, 859, 1/2*w^3 - 7/2*w + 6],
[881, 881, -3/2*w^3 + 21/2*w + 8],
[881, 881, -2*w^3 + 1/2*w^2 + 13*w + 15/2],
[919, 919, -3/2*w^3 + 5/2*w^2 + 15/2*w - 19/2],
[919, 919, 3/2*w^3 + w^2 - 21/2*w - 4],
[929, 929, 1/2*w^3 + w^2 - 9/2*w - 1],
[929, 929, 1/2*w^3 - w^2 - 9/2*w + 1],
[941, 941, 2*w^3 + 7*w^2 - 19*w - 51],
[941, 941, 5/2*w^2 - 3*w - 33/2],
[961, 31, -w^2 + 12],
[971, 971, 3/2*w^2 - 3*w - 25/2],
[971, 971, w^3 + 7/2*w^2 - 6*w - 39/2],
[991, 991, 1/2*w^3 - 3/2*w^2 - 13/2*w + 13/2],
[991, 991, w^3 + 5/2*w^2 - 5*w - 29/2],
[991, 991, w^3 - 5/2*w^2 - 5*w + 29/2],
[991, 991, -3/2*w^3 + 2*w^2 + 17/2*w - 7]];
primes := [ideal<ZF | {F!x : x in I}> : I in primesArray];

heckePol := x^9 + 2*x^8 - 30*x^7 - 50*x^6 + 293*x^5 + 364*x^4 - 1076*x^3 - 896*x^2 + 1232*x + 448;
K<e> := NumberField(heckePol);

heckeEigenvaluesArray := [e, 1, 1, -1/856*e^8 - 2/107*e^7 + 5/214*e^6 + 165/428*e^5 + 47/856*e^4 - 709/428*e^3 - 935/428*e^2 + 99/214*e + 432/107, -1/856*e^8 - 2/107*e^7 + 5/214*e^6 + 165/428*e^5 + 47/856*e^4 - 709/428*e^3 - 935/428*e^2 + 99/214*e + 432/107, -29/1712*e^8 - 9/428*e^7 + 397/856*e^6 + 291/856*e^5 - 6341/1712*e^4 - 231/856*e^3 + 3295/428*e^2 - 865/214*e + 58/107, -29/1712*e^8 - 9/428*e^7 + 397/856*e^6 + 291/856*e^5 - 6341/1712*e^4 - 231/856*e^3 + 3295/428*e^2 - 865/214*e + 58/107, 5/856*e^8 - 27/856*e^7 - 25/214*e^6 + 88/107*e^5 + 407/856*e^4 - 5429/856*e^3 - 35/107*e^2 + 1518/107*e + 194/107, 5/856*e^8 - 27/856*e^7 - 25/214*e^6 + 88/107*e^5 + 407/856*e^4 - 5429/856*e^3 - 35/107*e^2 + 1518/107*e + 194/107, -27/856*e^8 - 1/214*e^7 + 377/428*e^6 - 39/428*e^5 - 6435/856*e^4 + 1187/428*e^3 + 2115/107*e^2 - 750/107*e - 534/107, -13/856*e^8 + 3/428*e^7 + 237/428*e^6 - 209/428*e^5 - 5381/856*e^4 + 1437/214*e^3 + 4783/214*e^2 - 3635/214*e - 1874/107, -13/856*e^8 + 3/428*e^7 + 237/428*e^6 - 209/428*e^5 - 5381/856*e^4 + 1437/214*e^3 + 4783/214*e^2 - 3635/214*e - 1874/107, 3/428*e^8 - 11/856*e^7 - 15/107*e^6 + 187/428*e^5 + 45/107*e^4 - 3583/856*e^3 + 795/428*e^2 + 987/107*e - 24/107, 3/428*e^8 - 11/856*e^7 - 15/107*e^6 + 187/428*e^5 + 45/107*e^4 - 3583/856*e^3 + 795/428*e^2 + 987/107*e - 24/107, 19/856*e^8 - 17/856*e^7 - 297/428*e^6 + 91/214*e^5 + 5741/856*e^4 - 1627/856*e^3 - 8771/428*e^2 - 245/107*e + 1208/107, 19/856*e^8 - 17/856*e^7 - 297/428*e^6 + 91/214*e^5 + 5741/856*e^4 - 1627/856*e^3 - 8771/428*e^2 - 245/107*e + 1208/107, -3/214*e^8 + 11/428*e^7 + 227/428*e^6 - 187/214*e^5 - 1357/214*e^4 + 3797/428*e^3 + 10501/428*e^2 - 5125/214*e - 2306/107, -19/428*e^8 - 73/856*e^7 + 487/428*e^6 + 813/428*e^5 - 1747/214*e^4 - 9265/856*e^3 + 1550/107*e^2 + 3441/214*e + 366/107, -19/428*e^8 - 73/856*e^7 + 487/428*e^6 + 813/428*e^5 - 1747/214*e^4 - 9265/856*e^3 + 1550/107*e^2 + 3441/214*e + 366/107, -3/214*e^8 + 11/428*e^7 + 227/428*e^6 - 187/214*e^5 - 1357/214*e^4 + 3797/428*e^3 + 10501/428*e^2 - 5125/214*e - 2306/107, 9/856*e^8 - 35/428*e^7 - 197/428*e^6 + 869/428*e^5 + 5141/856*e^4 - 3069/214*e^3 - 2524/107*e^2 + 6171/214*e + 1676/107, 9/856*e^8 - 35/428*e^7 - 197/428*e^6 + 869/428*e^5 + 5141/856*e^4 - 3069/214*e^3 - 2524/107*e^2 + 6171/214*e + 1676/107, 1/856*e^8 + 2/107*e^7 - 5/214*e^6 - 165/428*e^5 + 381/856*e^4 + 709/428*e^3 - 2703/428*e^2 - 99/214*e + 1708/107, 2/107*e^8 + 21/428*e^7 - 40/107*e^6 - 125/107*e^5 + 347/214*e^4 + 2891/428*e^3 - 331/214*e^2 - 257/107*e + 150/107, 2/107*e^8 + 21/428*e^7 - 40/107*e^6 - 125/107*e^5 + 347/214*e^4 + 2891/428*e^3 - 331/214*e^2 - 257/107*e + 150/107, 1/856*e^8 + 2/107*e^7 - 5/214*e^6 - 165/428*e^5 + 381/856*e^4 + 709/428*e^3 - 2703/428*e^2 - 99/214*e + 1708/107, 4/107*e^8 + 21/214*e^7 - 427/428*e^6 - 250/107*e^5 + 1657/214*e^4 + 3105/214*e^3 - 7423/428*e^2 - 2547/107*e + 1370/107, -15/1712*e^8 - 13/856*e^7 + 257/856*e^6 + 335/856*e^5 - 5715/1712*e^4 - 599/214*e^3 + 5881/428*e^2 + 505/107*e - 398/107, 89/1712*e^8 + 35/428*e^7 - 1211/856*e^6 - 1631/856*e^5 + 19785/1712*e^4 + 9815/856*e^3 - 3147/107*e^2 - 3175/214*e + 1106/107, 89/1712*e^8 + 35/428*e^7 - 1211/856*e^6 - 1631/856*e^5 + 19785/1712*e^4 + 9815/856*e^3 - 3147/107*e^2 - 3175/214*e + 1106/107, -19/1712*e^8 + 31/428*e^7 + 297/856*e^6 - 1359/856*e^5 - 5955/1712*e^4 + 7715/856*e^3 + 1083/107*e^2 - 1643/107*e + 1108/107, 27/856*e^8 + 1/214*e^7 - 377/428*e^6 + 39/428*e^5 + 6007/856*e^4 - 1187/428*e^3 - 2625/214*e^2 + 1071/107*e - 108/107, 27/856*e^8 + 1/214*e^7 - 377/428*e^6 + 39/428*e^5 + 6007/856*e^4 - 1187/428*e^3 - 2625/214*e^2 + 1071/107*e - 108/107, -19/1712*e^8 + 31/428*e^7 + 297/856*e^6 - 1359/856*e^5 - 5955/1712*e^4 + 7715/856*e^3 + 1083/107*e^2 - 1643/107*e + 1108/107, 99/1712*e^8 + 43/856*e^7 - 1311/856*e^6 - 927/856*e^5 + 20599/1712*e^4 + 2407/428*e^3 - 3182/107*e^2 - 979/107*e + 1300/107, 99/1712*e^8 + 43/856*e^7 - 1311/856*e^6 - 927/856*e^5 + 20599/1712*e^4 + 2407/428*e^3 - 3182/107*e^2 - 979/107*e + 1300/107, -65/1712*e^8 + 15/856*e^7 + 971/856*e^6 - 403/856*e^5 - 18773/1712*e^4 + 1835/428*e^3 + 16211/428*e^2 - 1521/107*e - 3080/107, -65/1712*e^8 + 15/856*e^7 + 971/856*e^6 - 403/856*e^5 - 18773/1712*e^4 + 1835/428*e^3 + 16211/428*e^2 - 1521/107*e - 3080/107, 57/1712*e^8 + 7/214*e^7 - 891/856*e^6 - 203/856*e^5 + 17009/1712*e^4 - 4099/856*e^3 - 6177/214*e^2 + 4187/214*e + 1812/107, 57/1712*e^8 + 7/214*e^7 - 891/856*e^6 - 203/856*e^5 + 17009/1712*e^4 - 4099/856*e^3 - 6177/214*e^2 + 4187/214*e + 1812/107, 4/107*e^8 - 23/856*e^7 - 427/428*e^6 + 391/428*e^5 + 3207/428*e^4 - 7803/856*e^3 - 2267/214*e^2 + 2375/107*e - 2054/107, 4/107*e^8 - 23/856*e^7 - 427/428*e^6 + 391/428*e^5 + 3207/428*e^4 - 7803/856*e^3 - 2267/214*e^2 + 2375/107*e - 2054/107, -19/856*e^8 + 31/214*e^7 + 297/428*e^6 - 1573/428*e^5 - 5527/856*e^4 + 11353/428*e^3 + 3155/214*e^2 - 5533/107*e + 504/107, -19/856*e^8 + 31/214*e^7 + 297/428*e^6 - 1573/428*e^5 - 5527/856*e^4 + 11353/428*e^3 + 3155/214*e^2 - 5533/107*e + 504/107, 3/428*e^8 + 12/107*e^7 - 15/107*e^6 - 495/214*e^5 + 287/428*e^4 + 2127/214*e^3 - 405/214*e^2 + 345/107*e + 832/107, -25/856*e^8 - 79/856*e^7 + 357/428*e^6 + 511/214*e^5 - 6315/856*e^4 - 15013/856*e^3 + 9581/428*e^2 + 4073/107*e - 1398/107, -25/856*e^8 - 79/856*e^7 + 357/428*e^6 + 511/214*e^5 - 6315/856*e^4 - 15013/856*e^3 + 9581/428*e^2 + 4073/107*e - 1398/107, 3/428*e^8 + 12/107*e^7 - 15/107*e^6 - 495/214*e^5 + 287/428*e^4 + 2127/214*e^3 - 405/214*e^2 + 345/107*e + 832/107, -91/1712*e^8 - 43/428*e^7 + 1231/856*e^6 + 1961/856*e^5 - 19691/1712*e^4 - 10805/856*e^3 + 12081/428*e^2 + 2525/214*e - 1316/107, -91/1712*e^8 - 43/428*e^7 + 1231/856*e^6 + 1961/856*e^5 - 19691/1712*e^4 - 10805/856*e^3 + 12081/428*e^2 + 2525/214*e - 1316/107, 53/1712*e^8 + 103/856*e^7 - 637/856*e^6 - 2753/856*e^5 + 9065/1712*e^4 + 2624/107*e^3 - 1630/107*e^2 - 5137/107*e + 1178/107, 37/1712*e^8 + 41/428*e^7 - 263/856*e^6 - 2039/856*e^5 - 1739/1712*e^4 + 14891/856*e^3 + 1636/107*e^2 - 8519/214*e - 2000/107, 37/1712*e^8 + 41/428*e^7 - 263/856*e^6 - 2039/856*e^5 - 1739/1712*e^4 + 14891/856*e^3 + 1636/107*e^2 - 8519/214*e - 2000/107, 53/1712*e^8 + 103/856*e^7 - 637/856*e^6 - 2753/856*e^5 + 9065/1712*e^4 + 2624/107*e^3 - 1630/107*e^2 - 5137/107*e + 1178/107, 33/1712*e^8 + 25/428*e^7 - 651/856*e^6 - 951/856*e^5 + 14713/1712*e^4 + 3067/856*e^3 - 5367/214*e^2 + 453/214*e + 362/107, -91/1712*e^8 + 21/856*e^7 + 1445/856*e^6 - 821/856*e^5 - 28679/1712*e^4 + 4281/428*e^3 + 22139/428*e^2 - 5179/214*e - 2814/107, -91/1712*e^8 + 21/856*e^7 + 1445/856*e^6 - 821/856*e^5 - 28679/1712*e^4 + 4281/428*e^3 + 22139/428*e^2 - 5179/214*e - 2814/107, 33/1712*e^8 + 25/428*e^7 - 651/856*e^6 - 951/856*e^5 + 14713/1712*e^4 + 3067/856*e^3 - 5367/214*e^2 + 453/214*e + 362/107, 31/1712*e^8 - 73/856*e^7 - 417/856*e^6 + 1733/856*e^5 + 5819/1712*e^4 - 6077/428*e^3 - 755/428*e^2 + 3807/107*e - 1774/107, 31/1712*e^8 - 73/856*e^7 - 417/856*e^6 + 1733/856*e^5 + 5819/1712*e^4 - 6077/428*e^3 - 755/428*e^2 + 3807/107*e - 1774/107, -23/1712*e^8 - 77/856*e^7 - 91/856*e^6 + 2083/856*e^5 + 11781/1712*e^4 - 2025/107*e^3 - 16905/428*e^2 + 3913/107*e + 3898/107, 55/856*e^8 + 3/107*e^7 - 871/428*e^6 - 87/428*e^5 + 17531/856*e^4 - 1879/428*e^3 - 7233/107*e^2 + 1825/107*e + 4488/107, 55/856*e^8 + 3/107*e^7 - 871/428*e^6 - 87/428*e^5 + 17531/856*e^4 - 1879/428*e^3 - 7233/107*e^2 + 1825/107*e + 4488/107, -23/1712*e^8 - 77/856*e^7 - 91/856*e^6 + 2083/856*e^5 + 11781/1712*e^4 - 2025/107*e^3 - 16905/428*e^2 + 3913/107*e + 3898/107, 5/107*e^8 - 1/428*e^7 - 307/214*e^6 + 62/107*e^5 + 3061/214*e^4 - 4061/428*e^3 - 5523/107*e^2 + 5777/214*e + 4976/107, 35/856*e^8 + 25/856*e^7 - 141/107*e^6 - 26/107*e^5 + 11837/856*e^4 - 2693/856*e^3 - 5274/107*e^2 + 2313/214*e + 3712/107, 35/856*e^8 + 25/856*e^7 - 141/107*e^6 - 26/107*e^5 + 11837/856*e^4 - 2693/856*e^3 - 5274/107*e^2 + 2313/214*e + 3712/107, 5/107*e^8 - 1/428*e^7 - 307/214*e^6 + 62/107*e^5 + 3061/214*e^4 - 4061/428*e^3 - 5523/107*e^2 + 5777/214*e + 4976/107, 31/1712*e^8 + 17/428*e^7 - 417/856*e^6 - 1049/856*e^5 + 6247/1712*e^4 + 8925/856*e^3 - 483/107*e^2 - 1864/107*e - 1988/107, 31/1712*e^8 + 17/428*e^7 - 417/856*e^6 - 1049/856*e^5 + 6247/1712*e^4 + 8925/856*e^3 - 483/107*e^2 - 1864/107*e - 1988/107, 17/1712*e^8 + 29/856*e^7 - 491/856*e^6 - 665/856*e^5 + 14181/1712*e^4 + 2549/428*e^3 - 13399/428*e^2 - 2534/107*e + 3604/107, -7/428*e^8 - 5/428*e^7 + 35/107*e^6 + 85/214*e^5 - 955/428*e^4 - 1687/428*e^3 + 3085/214*e^2 + 1707/214*e - 2726/107, -7/428*e^8 - 5/428*e^7 + 35/107*e^6 + 85/214*e^5 - 955/428*e^4 - 1687/428*e^3 + 3085/214*e^2 + 1707/214*e - 2726/107, 159/1712*e^8 + 101/428*e^7 - 2125/856*e^6 - 4621/856*e^5 + 32759/1712*e^4 + 28201/856*e^3 - 8603/214*e^2 - 6209/107*e + 1822/107, 159/1712*e^8 + 101/428*e^7 - 2125/856*e^6 - 4621/856*e^5 + 32759/1712*e^4 + 28201/856*e^3 - 8603/214*e^2 - 6209/107*e + 1822/107, -7/1712*e^8 - 163/856*e^7 - 251/856*e^6 + 4579/856*e^5 + 11885/1712*e^4 - 19013/428*e^3 - 11351/428*e^2 + 10472/107*e + 656/107, -7/1712*e^8 - 163/856*e^7 - 251/856*e^6 + 4579/856*e^5 + 11885/1712*e^4 - 19013/428*e^3 - 11351/428*e^2 + 10472/107*e + 656/107, 135/1712*e^8 + 5/428*e^7 - 1885/856*e^6 + 195/856*e^5 + 31319/1712*e^4 - 5935/856*e^3 - 4592/107*e^2 + 1768/107*e + 158/107, 135/1712*e^8 + 5/428*e^7 - 1885/856*e^6 + 195/856*e^5 + 31319/1712*e^4 - 5935/856*e^3 - 4592/107*e^2 + 1768/107*e + 158/107, 37/856*e^8 + 57/856*e^7 - 146/107*e^6 - 217/214*e^5 + 11315/856*e^4 - 713/856*e^3 - 4218/107*e^2 + 4683/214*e + 3062/107, 37/856*e^8 + 57/856*e^7 - 146/107*e^6 - 217/214*e^5 + 11315/856*e^4 - 713/856*e^3 - 4218/107*e^2 + 4683/214*e + 3062/107, 3/214*e^8 - 11/428*e^7 - 30/107*e^6 + 187/214*e^5 + 287/214*e^4 - 4439/428*e^3 - 405/107*e^2 + 4007/107*e + 1022/107, 3/214*e^8 - 11/428*e^7 - 30/107*e^6 + 187/214*e^5 + 287/214*e^4 - 4439/428*e^3 - 405/107*e^2 + 4007/107*e + 1022/107, -11/214*e^8 - 169/856*e^7 + 547/428*e^6 + 2017/428*e^5 - 3781/428*e^4 - 25477/856*e^3 + 3505/214*e^2 + 5067/107*e - 252/107, -11/214*e^8 - 169/856*e^7 + 547/428*e^6 + 2017/428*e^5 - 3781/428*e^4 - 25477/856*e^3 + 3505/214*e^2 + 5067/107*e - 252/107, -63/1712*e^8 - 19/214*e^7 + 523/856*e^6 + 2049/856*e^5 - 463/1712*e^4 - 15991/856*e^3 - 5859/428*e^2 + 8201/214*e + 1196/107, -63/1712*e^8 - 19/214*e^7 + 523/856*e^6 + 2049/856*e^5 - 463/1712*e^4 - 15991/856*e^3 - 5859/428*e^2 + 8201/214*e + 1196/107, 179/1712*e^8 + 41/856*e^7 - 2325/856*e^6 - 431/856*e^5 + 33959/1712*e^4 - 467/107*e^3 - 14597/428*e^2 + 2498/107*e - 1856/107, 179/1712*e^8 + 41/856*e^7 - 2325/856*e^6 - 431/856*e^5 + 33959/1712*e^4 - 467/107*e^3 - 14597/428*e^2 + 2498/107*e - 1856/107, -7/214*e^8 + 87/856*e^7 + 387/428*e^6 - 1051/428*e^5 - 3301/428*e^4 + 13475/856*e^3 + 4993/214*e^2 - 2145/107*e - 2456/107, -7/214*e^8 + 87/856*e^7 + 387/428*e^6 - 1051/428*e^5 - 3301/428*e^4 + 13475/856*e^3 + 4993/214*e^2 - 2145/107*e - 2456/107, 9/428*e^8 + 37/428*e^7 - 45/107*e^6 - 261/107*e^5 + 647/428*e^4 + 8375/428*e^3 + 195/107*e^2 - 4422/107*e + 142/107, -31/1712*e^8 + 45/214*e^7 + 417/856*e^6 - 4515/856*e^5 - 6247/1712*e^4 + 32805/856*e^3 + 483/107*e^2 - 18207/214*e + 704/107, -31/1712*e^8 + 45/214*e^7 + 417/856*e^6 - 4515/856*e^5 - 6247/1712*e^4 + 32805/856*e^3 + 483/107*e^2 - 18207/214*e + 704/107, 9/428*e^8 + 37/428*e^7 - 45/107*e^6 - 261/107*e^5 + 647/428*e^4 + 8375/428*e^3 + 195/107*e^2 - 4422/107*e + 142/107, 3/428*e^8 - 11/856*e^7 + 47/428*e^6 - 27/428*e^5 - 873/214*e^4 + 3693/856*e^3 + 2805/214*e^2 - 1688/107*e + 1688/107, -5/214*e^8 + 27/214*e^7 + 521/428*e^6 - 811/214*e^5 - 3617/214*e^4 + 7141/214*e^3 + 27203/428*e^2 - 15033/214*e - 3558/107, -5/214*e^8 + 27/214*e^7 + 521/428*e^6 - 811/214*e^5 - 3617/214*e^4 + 7141/214*e^3 + 27203/428*e^2 - 15033/214*e - 3558/107, 3/428*e^8 - 11/856*e^7 + 47/428*e^6 - 27/428*e^5 - 873/214*e^4 + 3693/856*e^3 + 2805/214*e^2 - 1688/107*e + 1688/107, -63/856*e^8 - 19/107*e^7 + 737/428*e^6 + 2049/428*e^5 - 9451/856*e^4 - 15563/428*e^3 + 5055/214*e^2 + 7131/107*e - 1674/107, -63/856*e^8 - 19/107*e^7 + 737/428*e^6 + 2049/428*e^5 - 9451/856*e^4 - 15563/428*e^3 + 5055/214*e^2 + 7131/107*e - 1674/107, 5/856*e^8 + 10/107*e^7 - 157/428*e^6 - 825/428*e^5 + 4473/856*e^4 + 3759/428*e^3 - 1640/107*e^2 - 408/107*e - 1090/107, 5/856*e^8 + 10/107*e^7 - 157/428*e^6 - 825/428*e^5 + 4473/856*e^4 + 3759/428*e^3 - 1640/107*e^2 - 408/107*e - 1090/107, 10/107*e^8 - 1/214*e^7 - 307/107*e^6 + 141/214*e^5 + 5801/214*e^4 - 1228/107*e^3 - 17277/214*e^2 + 4065/107*e + 6314/107, 10/107*e^8 - 1/214*e^7 - 307/107*e^6 + 141/214*e^5 + 5801/214*e^4 - 1228/107*e^3 - 17277/214*e^2 + 4065/107*e + 6314/107, 21/1712*e^8 + 61/856*e^7 - 317/856*e^6 - 897/856*e^5 + 6289/1712*e^4 - 527/428*e^3 - 3357/214*e^2 + 2610/107*e + 2740/107, 17/214*e^8 + 125/856*e^7 - 447/214*e^6 - 1269/428*e^5 + 6641/428*e^4 + 11145/856*e^3 - 10999/428*e^2 - 691/107*e - 2412/107, 17/214*e^8 + 125/856*e^7 - 447/214*e^6 - 1269/428*e^5 + 6641/428*e^4 + 11145/856*e^3 - 10999/428*e^2 - 691/107*e - 2412/107, 21/1712*e^8 + 61/856*e^7 - 317/856*e^6 - 897/856*e^5 + 6289/1712*e^4 - 527/428*e^3 - 3357/214*e^2 + 2610/107*e + 2740/107, -9/1712*e^8 + 71/428*e^7 + 197/856*e^6 - 3865/856*e^5 - 4713/1712*e^4 + 30213/856*e^3 + 3443/428*e^2 - 15123/214*e - 1266/107, -9/1712*e^8 + 71/428*e^7 + 197/856*e^6 - 3865/856*e^5 - 4713/1712*e^4 + 30213/856*e^3 + 3443/428*e^2 - 15123/214*e - 1266/107, -145/1712*e^8 + 17/856*e^7 + 2199/856*e^6 - 899/856*e^5 - 39837/1712*e^4 + 1474/107*e^3 + 22467/428*e^2 - 8177/214*e + 1788/107, -145/1712*e^8 + 17/856*e^7 + 2199/856*e^6 - 899/856*e^5 - 39837/1712*e^4 + 1474/107*e^3 + 22467/428*e^2 - 8177/214*e + 1788/107, -51/856*e^8 + 5/107*e^7 + 617/428*e^6 - 573/428*e^5 - 8303/856*e^4 + 4715/428*e^3 + 4245/214*e^2 - 1809/107*e - 652/107, -6/107*e^8 - 19/856*e^7 + 587/428*e^6 - 105/428*e^5 - 3687/428*e^4 + 10153/856*e^3 + 1207/214*e^2 - 5007/107*e + 2760/107, -6/107*e^8 - 19/856*e^7 + 587/428*e^6 - 105/428*e^5 - 3687/428*e^4 + 10153/856*e^3 + 1207/214*e^2 - 5007/107*e + 2760/107, -51/856*e^8 + 5/107*e^7 + 617/428*e^6 - 573/428*e^5 - 8303/856*e^4 + 4715/428*e^3 + 4245/214*e^2 - 1809/107*e - 652/107, -115/1712*e^8 - 8/107*e^7 + 1257/856*e^6 + 1213/856*e^5 - 13427/1712*e^4 - 3639/856*e^3 + 1098/107*e^2 - 2707/214*e - 1482/107, -139/856*e^8 - 21/214*e^7 + 1925/428*e^6 + 679/428*e^5 - 31987/856*e^4 - 111/428*e^3 + 10175/107*e^2 - 2696/107*e - 4152/107, -139/856*e^8 - 21/214*e^7 + 1925/428*e^6 + 679/428*e^5 - 31987/856*e^4 - 111/428*e^3 + 10175/107*e^2 - 2696/107*e - 4152/107, -115/1712*e^8 - 8/107*e^7 + 1257/856*e^6 + 1213/856*e^5 - 13427/1712*e^4 - 3639/856*e^3 + 1098/107*e^2 - 2707/214*e - 1482/107, -39/1712*e^8 - 49/428*e^7 + 497/856*e^6 + 2369/856*e^5 - 7583/1712*e^4 - 15025/856*e^3 + 1153/107*e^2 + 4231/214*e - 564/107, -39/1712*e^8 - 49/428*e^7 + 497/856*e^6 + 2369/856*e^5 - 7583/1712*e^4 - 15025/856*e^3 + 1153/107*e^2 + 4231/214*e - 564/107, -7/856*e^8 - 14/107*e^7 + 35/214*e^6 + 1369/428*e^5 - 527/856*e^4 - 9029/428*e^3 + 303/428*e^2 + 7113/214*e - 1042/107, -7/856*e^8 - 14/107*e^7 + 35/214*e^6 + 1369/428*e^5 - 527/856*e^4 - 9029/428*e^3 + 303/428*e^2 + 7113/214*e - 1042/107, -151/1712*e^8 - 69/428*e^7 + 2045/856*e^6 + 3301/856*e^5 - 33135/1712*e^4 - 22101/856*e^3 + 10687/214*e^2 + 12557/214*e - 2694/107, 31/1712*e^8 - 73/856*e^7 - 417/856*e^6 + 1733/856*e^5 + 5819/1712*e^4 - 5863/428*e^3 - 1183/428*e^2 + 6865/214*e - 1560/107, 31/1712*e^8 - 73/856*e^7 - 417/856*e^6 + 1733/856*e^5 + 5819/1712*e^4 - 5863/428*e^3 - 1183/428*e^2 + 6865/214*e - 1560/107, -151/1712*e^8 - 69/428*e^7 + 2045/856*e^6 + 3301/856*e^5 - 33135/1712*e^4 - 22101/856*e^3 + 10687/214*e^2 + 12557/214*e - 2694/107, 9/1712*e^8 + 179/856*e^7 + 231/856*e^6 - 4481/856*e^5 - 12835/1712*e^4 + 7935/214*e^3 + 3981/107*e^2 - 7900/107*e - 2372/107, 9/1712*e^8 + 179/856*e^7 + 231/856*e^6 - 4481/856*e^5 - 12835/1712*e^4 + 7935/214*e^3 + 3981/107*e^2 - 7900/107*e - 2372/107, 2/107*e^8 + 21/428*e^7 - 187/214*e^6 - 143/214*e^5 + 1190/107*e^4 - 319/428*e^3 - 7393/214*e^2 + 920/107*e - 278/107, 2/107*e^8 + 21/428*e^7 - 187/214*e^6 - 143/214*e^5 + 1190/107*e^4 - 319/428*e^3 - 7393/214*e^2 + 920/107*e - 278/107, 27/428*e^8 + 1/107*e^7 - 377/214*e^6 + 39/214*e^5 + 6221/428*e^4 - 1401/214*e^3 - 6427/214*e^2 + 2784/107*e - 1928/107, 27/428*e^8 + 1/107*e^7 - 377/214*e^6 + 39/214*e^5 + 6221/428*e^4 - 1401/214*e^3 - 6427/214*e^2 + 2784/107*e - 1928/107, -69/1712*e^8 - 17/856*e^7 + 1225/856*e^6 - 171/856*e^5 - 26289/1712*e^4 + 4055/428*e^3 + 5217/107*e^2 - 3241/107*e - 3500/107, -69/1712*e^8 - 17/856*e^7 + 1225/856*e^6 - 171/856*e^5 - 26289/1712*e^4 + 4055/428*e^3 + 5217/107*e^2 - 3241/107*e - 3500/107, -71/428*e^8 - 239/856*e^7 + 1955/428*e^6 + 2351/428*e^5 - 4061/107*e^4 - 18279/856*e^3 + 20713/214*e^2 + 469/214*e - 4568/107, -8/107*e^8 - 61/856*e^7 + 961/428*e^6 + 609/428*e^5 - 8875/428*e^4 - 5473/856*e^3 + 6333/107*e^2 + 921/107*e - 3382/107, -8/107*e^8 - 61/856*e^7 + 961/428*e^6 + 609/428*e^5 - 8875/428*e^4 - 5473/856*e^3 + 6333/107*e^2 + 921/107*e - 3382/107, -71/428*e^8 - 239/856*e^7 + 1955/428*e^6 + 2351/428*e^5 - 4061/107*e^4 - 18279/856*e^3 + 20713/214*e^2 + 469/214*e - 4568/107, 77/856*e^8 + 269/856*e^7 - 246/107*e^6 - 742/107*e^5 + 13715/856*e^4 + 32467/856*e^3 - 2679/107*e^2 - 6005/107*e + 334/107, 77/856*e^8 + 269/856*e^7 - 246/107*e^6 - 742/107*e^5 + 13715/856*e^4 + 32467/856*e^3 - 2679/107*e^2 - 6005/107*e + 334/107, 73/856*e^8 + 49/428*e^7 - 1051/428*e^6 - 917/428*e^5 + 17541/856*e^4 + 1643/214*e^3 - 8833/214*e^2 - 885/107*e - 2218/107, 73/856*e^8 + 49/428*e^7 - 1051/428*e^6 - 917/428*e^5 + 17541/856*e^4 + 1643/214*e^3 - 8833/214*e^2 - 885/107*e - 2218/107, -41/1712*e^8 - 57/428*e^7 + 303/856*e^6 + 2699/856*e^5 + 2783/1712*e^4 - 17727/856*e^3 - 3120/107*e^2 + 8503/214*e + 5004/107, -41/1712*e^8 - 57/428*e^7 + 303/856*e^6 + 2699/856*e^5 + 2783/1712*e^4 - 17727/856*e^3 - 3120/107*e^2 + 8503/214*e + 5004/107, 135/1712*e^8 + 28/107*e^7 - 1457/856*e^6 - 5369/856*e^5 + 14199/1712*e^4 + 34511/856*e^3 - 89/214*e^2 - 7006/107*e - 3266/107, 135/1712*e^8 + 28/107*e^7 - 1457/856*e^6 - 5369/856*e^5 + 14199/1712*e^4 + 34511/856*e^3 - 89/214*e^2 - 7006/107*e - 3266/107, 1/214*e^8 - 75/428*e^7 - 147/428*e^6 + 1061/214*e^5 + 1237/214*e^4 - 17601/428*e^3 - 10705/428*e^2 + 20041/214*e + 1482/107, 1/214*e^8 - 75/428*e^7 - 147/428*e^6 + 1061/214*e^5 + 1237/214*e^4 - 17601/428*e^3 - 10705/428*e^2 + 20041/214*e + 1482/107, 13/214*e^8 - 3/107*e^7 - 627/428*e^6 + 97/214*e^5 + 1032/107*e^4 - 77/214*e^3 - 7555/428*e^2 - 434/107*e + 4928/107, -1/856*e^8 - 123/856*e^7 + 5/214*e^6 + 671/214*e^5 + 261/856*e^4 - 14793/856*e^3 - 849/107*e^2 + 3527/107*e + 3428/107, 111/1712*e^8 + 123/428*e^7 - 1217/856*e^6 - 5689/856*e^5 + 11903/1712*e^4 + 34401/856*e^3 + 1149/214*e^2 - 7375/107*e - 5144/107, 111/1712*e^8 + 123/428*e^7 - 1217/856*e^6 - 5689/856*e^5 + 11903/1712*e^4 + 34401/856*e^3 + 1149/214*e^2 - 7375/107*e - 5144/107, -1/856*e^8 - 123/856*e^7 + 5/214*e^6 + 671/214*e^5 + 261/856*e^4 - 14793/856*e^3 - 849/107*e^2 + 3527/107*e + 3428/107, 67/856*e^8 - 105/856*e^7 - 991/428*e^6 + 366/107*e^5 + 18037/856*e^4 - 23871/856*e^3 - 25737/428*e^2 + 6474/107*e + 2514/107, 67/856*e^8 - 105/856*e^7 - 991/428*e^6 + 366/107*e^5 + 18037/856*e^4 - 23871/856*e^3 - 25737/428*e^2 + 6474/107*e + 2514/107, 3/856*e^8 + 6/107*e^7 - 15/214*e^6 - 281/428*e^5 + 287/856*e^4 - 1939/428*e^3 - 1261/428*e^2 + 5267/214*e + 3198/107, 3/856*e^8 + 6/107*e^7 - 15/214*e^6 - 281/428*e^5 + 287/856*e^4 - 1939/428*e^3 - 1261/428*e^2 + 5267/214*e + 3198/107, 13/856*e^8 - 3/428*e^7 - 65/214*e^6 - 219/428*e^5 + 673/856*e^4 + 2415/214*e^3 + 3381/428*e^2 - 9633/214*e - 1764/107, 13/856*e^8 - 3/428*e^7 - 65/214*e^6 - 219/428*e^5 + 673/856*e^4 + 2415/214*e^3 + 3381/428*e^2 - 9633/214*e - 1764/107, 17/856*e^8 + 29/428*e^7 - 85/214*e^6 - 879/428*e^5 + 1769/856*e^4 + 1863/107*e^3 - 3365/428*e^2 - 3356/107*e + 788/107, 17/856*e^8 + 29/428*e^7 - 85/214*e^6 - 879/428*e^5 + 1769/856*e^4 + 1863/107*e^3 - 3365/428*e^2 - 3356/107*e + 788/107, 3/856*e^8 + 131/428*e^7 - 15/214*e^6 - 3277/428*e^5 - 141/856*e^4 + 5855/107*e^3 + 2805/428*e^2 - 11865/107*e + 2770/107, -57/1712*e^8 - 135/856*e^7 + 677/856*e^6 + 2985/856*e^5 - 8877/1712*e^4 - 1855/107*e^3 + 2539/214*e^2 + 1063/107*e + 114/107, -57/1712*e^8 - 135/856*e^7 + 677/856*e^6 + 2985/856*e^5 - 8877/1712*e^4 - 1855/107*e^3 + 2539/214*e^2 + 1063/107*e + 114/107, 77/1712*e^8 - 133/856*e^7 - 1091/856*e^6 + 3131/856*e^5 + 17353/1712*e^4 - 4943/214*e^3 - 7819/428*e^2 + 7477/214*e + 274/107, -5/856*e^8 + 67/428*e^7 - 57/428*e^6 - 1529/428*e^5 + 3231/856*e^4 + 2297/107*e^3 - 1321/214*e^2 - 3658/107*e - 4046/107, -5/856*e^8 + 67/428*e^7 - 57/428*e^6 - 1529/428*e^5 + 3231/856*e^4 + 2297/107*e^3 - 1321/214*e^2 - 3658/107*e - 4046/107, 77/1712*e^8 - 133/856*e^7 - 1091/856*e^6 + 3131/856*e^5 + 17353/1712*e^4 - 4943/214*e^3 - 7819/428*e^2 + 7477/214*e + 274/107];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

ALEigenvalues := AssociativeArray();
ALEigenvalues[ideal<ZF | {5,5,-1/2*w^3+w^2+5/2*w-4}>] := -1;
ALEigenvalues[ideal<ZF | {5,5,-1/2*w^2-w+3/2}>] := -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;