/*
  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, -7, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([8, 2, 2])

primes_array = [
[3, 3, w],\
[3, 3, w + 1],\
[3, 3, w + 2],\
[8, 2, 2],\
[11, 11, -w^2 + 5],\
[13, 13, w^2 - w - 7],\
[17, 17, -w^2 + w + 4],\
[19, 19, -w^2 - w + 4],\
[29, 29, 2*w^2 - 2*w - 11],\
[31, 31, w^2 - 2*w - 4],\
[37, 37, -2*w^2 + 3*w + 7],\
[41, 41, w^2 - 2],\
[59, 59, 2*w^2 - 13],\
[61, 61, w^2 + w - 10],\
[67, 67, 2*w^2 - w - 11],\
[73, 73, -w^2 - 1],\
[83, 83, w^2 - w - 10],\
[89, 89, -w^2 + 4*w - 2],\
[97, 97, w^2 - 2*w - 7],\
[97, 97, -w^2 - 4*w - 5],\
[97, 97, 2*w^2 + w - 8],\
[101, 101, -4*w^2 + 2*w + 25],\
[103, 103, w^2 + w - 7],\
[107, 107, -3*w - 4],\
[109, 109, 5*w^2 - 3*w - 31],\
[121, 11, 2*w^2 - 3*w - 4],\
[125, 5, -5],\
[137, 137, -5*w^2 + 3*w + 34],\
[139, 139, w^2 + 2*w - 4],\
[151, 151, 3*w^2 - 23],\
[151, 151, w^2 - 3*w - 5],\
[151, 151, 3*w^2 - 3*w - 17],\
[157, 157, 4*w^2 - 9*w - 8],\
[157, 157, w^2 + 3*w - 2],\
[157, 157, 2*w^2 - w - 2],\
[167, 167, 2*w^2 + w - 11],\
[167, 167, -w^2 + 11],\
[167, 167, -3*w^2 + 19],\
[169, 13, w^2 - 4*w - 4],\
[173, 173, 2*w^2 - 3*w - 10],\
[179, 179, -3*w + 7],\
[191, 191, -w^2 + 5*w - 5],\
[193, 193, -w^2 + w - 2],\
[199, 199, 3*w - 2],\
[211, 211, w^2 - 3*w - 11],\
[223, 223, 3*w^2 - 20],\
[223, 223, w^2 - 5*w - 4],\
[223, 223, 2*w^2 - w - 8],\
[229, 229, 4*w^2 - 3*w - 26],\
[229, 229, 2*w^2 + w - 20],\
[229, 229, 2*w^2 - 2*w - 5],\
[239, 239, -6*w^2 + 3*w + 38],\
[241, 241, -w^2 + 4*w - 5],\
[257, 257, -2*w^2 + 5*w - 1],\
[263, 263, -2*w^2 - w + 17],\
[269, 269, -w^2 - w + 13],\
[269, 269, 3*w - 4],\
[269, 269, -4*w^2 + w + 31],\
[271, 271, 2*w^2 - 7],\
[271, 271, 3*w - 5],\
[271, 271, w^2 - 3*w - 8],\
[289, 17, 2*w^2 + w - 5],\
[307, 307, 2*w^2 - w - 5],\
[311, 311, 3*w^2 - 3*w - 19],\
[311, 311, -7*w^2 + 13*w + 19],\
[311, 311, w^2 - 2*w - 13],\
[313, 313, w^2 + 2*w - 7],\
[317, 317, -5*w^2 + w + 35],\
[331, 331, -w^2 + 3*w - 4],\
[337, 337, 3*w^2 - 3*w - 13],\
[343, 7, -7],\
[347, 347, 2*w^2 - 3*w - 13],\
[349, 349, 3*w^2 - 3*w - 20],\
[359, 359, -w^2 + 5*w - 2],\
[361, 19, -2*w^2 + 7*w - 1],\
[389, 389, -2*w^2 + w - 1],\
[397, 397, w^2 - 6*w + 10],\
[401, 401, 6*w^2 - 3*w - 44],\
[419, 419, -3*w^2 + 6*w + 10],\
[419, 419, 4*w^2 - 2*w - 31],\
[419, 419, -4*w^2 + 4*w + 19],\
[421, 421, 6*w^2 - 12*w - 13],\
[431, 431, 4*w^2 - 7*w - 10],\
[433, 433, w^2 - 4*w - 7],\
[443, 443, 2*w^2 + 4*w - 5],\
[443, 443, 5*w^2 - 11*w - 11],\
[443, 443, 3*w^2 - 14],\
[449, 449, -2*w^2 + 2*w - 1],\
[457, 457, w^2 - 6*w - 5],\
[457, 457, w^2 + 3*w - 5],\
[457, 457, 6*w^2 - 3*w - 37],\
[463, 463, w^2 + 5*w - 1],\
[467, 467, w^2 - w - 13],\
[479, 479, 5*w^2 - 9*w - 16],\
[487, 487, -6*w - 5],\
[499, 499, 3*w^2 - 3*w - 4],\
[499, 499, 3*w^2 + 3*w - 1],\
[499, 499, w^2 - 5*w + 8],\
[503, 503, 4*w^2 - 5*w - 16],\
[509, 509, 2*w^2 - 5*w - 8],\
[521, 521, 4*w^2 - w - 22],\
[523, 523, w^2 - 5*w - 16],\
[547, 547, 5*w^2 - 2*w - 38],\
[547, 547, 8*w^2 - 3*w - 58],\
[547, 547, 4*w^2 - 29],\
[557, 557, 7*w^2 - 4*w - 43],\
[557, 557, 3*w - 11],\
[557, 557, 2*w^2 - 4*w - 11],\
[569, 569, 5*w^2 - 4*w - 32],\
[569, 569, 3*w^2 - 3*w - 11],\
[569, 569, w^2 + 2*w - 16],\
[571, 571, w^2 - 4*w - 10],\
[593, 593, 2*w^2 - 6*w - 7],\
[601, 601, -w^2 - 3*w + 14],\
[607, 607, 3*w^2 + 3*w - 7],\
[619, 619, 3*w^2 - 6*w - 11],\
[631, 631, -w^2 - w - 5],\
[641, 641, 3*w^2 - 3*w - 5],\
[647, 647, -w^2 + 6*w - 1],\
[653, 653, -5*w^2 + 4*w + 35],\
[661, 661, 3*w^2 - 3*w - 10],\
[673, 673, w^2 + 4*w - 4],\
[677, 677, 5*w^2 - 6*w - 25],\
[677, 677, w^2 - 14],\
[677, 677, 4*w^2 - 3*w - 20],\
[691, 691, 5*w^2 - 2*w - 29],\
[701, 701, 5*w^2 - 10*w - 14],\
[719, 719, -3*w - 11],\
[727, 727, -2*w^2 + 9*w - 8],\
[733, 733, -w^2 - 4*w - 8],\
[739, 739, w^2 + 3*w - 8],\
[743, 743, 2*w^2 - 4*w - 17],\
[757, 757, -w^2 + w - 5],\
[769, 769, 3*w^2 - 3*w - 7],\
[769, 769, -w^2 - 3*w - 7],\
[769, 769, 5*w^2 - 3*w - 28],\
[773, 773, 7*w^2 - 6*w - 38],\
[787, 787, 2*w^2 - w - 20],\
[797, 797, -5*w^2 + 14*w - 1],\
[821, 821, -w^2 + 6*w - 4],\
[823, 823, 7*w^2 - 6*w - 41],\
[839, 839, 4*w^2 - 6*w - 11],\
[841, 29, 5*w^2 - 4*w - 26],\
[857, 857, 3*w^2 - 11],\
[863, 863, 2*w^2 + 2*w - 17],\
[881, 881, 5*w^2 - 5*w - 29],\
[883, 883, -4*w^2 + 8*w + 13],\
[907, 907, 4*w^2 - 9*w - 11],\
[911, 911, 2*w^2 + 3*w - 10],\
[947, 947, 2*w^2 + 5*w - 5],\
[953, 953, 2*w^2 - 5*w - 11],\
[961, 31, w^2 - 5*w - 13],\
[967, 967, 2*w^2 - 3*w - 22],\
[967, 967, 5*w^2 - 9*w - 10],\
[967, 967, 3*w^2 - 10],\
[977, 977, 5*w^2 - 37],\
[983, 983, 7*w^2 - 5*w - 40],\
[997, 997, -7*w^2 + 5*w + 49]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^14 - 31*x^12 + 380*x^10 - 2329*x^8 + 7373*x^6 - 10939*x^4 + 5378*x^2 - 676
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [-50/631*e^12 + 1340/631*e^10 - 13372/631*e^8 + 60540/631*e^6 - 118799/631*e^4 + 73108/631*e^2 - 12074/631, e, 589/16406*e^13 - 15659/16406*e^11 + 77070/8203*e^9 - 676437/16406*e^7 + 1211023/16406*e^5 - 478801/16406*e^3 + 19336/8203*e, 1, 122/8203*e^13 - 3522/8203*e^11 + 39392/8203*e^9 - 212963/8203*e^7 + 560089/8203*e^5 - 615086/8203*e^3 + 179159/8203*e, -402/8203*e^13 + 10395/8203*e^11 - 99005/8203*e^9 + 417584/8203*e^7 - 708953/8203*e^5 + 218199/8203*e^3 + 95481/8203*e, -264/8203*e^13 + 6949/8203*e^11 - 67222/8203*e^9 + 282927/8203*e^7 - 434728/8203*e^5 - 45619/8203*e^3 + 162854/8203*e, 50/631*e^12 - 1340/631*e^10 + 13372/631*e^8 - 59909/631*e^6 + 110596/631*e^4 - 47237/631*e^2 + 3240/631, -93/16406*e^13 + 1609/16406*e^11 - 2239/8203*e^9 - 62435/16406*e^7 + 459845/16406*e^5 - 969203/16406*e^3 + 175686/8203*e, 1889/16406*e^13 - 50499/16406*e^11 + 250906/8203*e^9 - 2250477/16406*e^7 + 4299797/16406*e^5 - 2363203/16406*e^3 + 135283/8203*e, 463/8203*e^13 - 12156/8203*e^11 + 118701/8203*e^9 - 528167/8203*e^7 + 1050520/8203*e^5 - 788238/8203*e^3 + 285305/8203*e, -991/8203*e^13 + 26054/8203*e^11 - 253145/8203*e^9 + 1094021/8203*e^7 - 1919976/8203*e^5 + 705203/8203*e^3 - 612/8203*e, -59/631*e^12 + 1455/631*e^10 - 13154/631*e^8 + 52381/631*e^6 - 83885/631*e^4 + 28064/631*e^2 + 720/631, -90/631*e^12 + 2412/631*e^10 - 24322/631*e^8 + 112758/631*e^6 - 230118/631*e^4 + 150272/631*e^2 - 20976/631, -1142/8203*e^13 + 31489/8203*e^11 - 327451/8203*e^9 + 1582382/8203*e^7 - 3499999/8203*e^5 + 2896375/8203*e^3 - 669287/8203*e, 139/631*e^12 - 3599/631*e^10 + 34423/631*e^8 - 146721/631*e^6 + 257305/631*e^4 - 107303/631*e^2 + 9512/631, 159/631*e^12 - 4135/631*e^10 + 39898/631*e^8 - 173461/631*e^6 + 321483/631*e^4 - 174280/631*e^2 + 22166/631, -15/631*e^12 + 402/631*e^10 - 4264/631*e^8 + 21948/631*e^6 - 52235/631*e^4 + 44396/631*e^2 - 9806/631, -215/16406*e^13 + 5131/16406*e^11 - 21935/8203*e^9 + 158731/16406*e^7 - 206883/16406*e^5 - 9591/16406*e^3 + 16381/8203*e, 110/631*e^12 - 2948/631*e^10 + 29166/631*e^8 - 128771/631*e^6 + 236244/631*e^4 - 111241/631*e^2 + 19748/631, -154/8203*e^13 + 3370/8203*e^11 - 24174/8203*e^9 + 48148/8203*e^7 + 118278/8203*e^5 - 415570/8203*e^3 + 101834/8203*e, -747/8203*e^13 + 19010/8203*e^11 - 174361/8203*e^9 + 668095/8203*e^7 - 799798/8203*e^5 - 516766/8203*e^3 + 300285/8203*e, 59/631*e^12 - 1455/631*e^10 + 13154/631*e^8 - 52381/631*e^6 + 83885/631*e^4 - 27433/631*e^2 - 4506/631, 1942/8203*e^13 - 52298/8203*e^11 + 529414/8203*e^9 - 2474040/8203*e^7 + 5210852/8203*e^5 - 3937379/8203*e^3 + 871305/8203*e, -747/8203*e^13 + 19010/8203*e^11 - 174361/8203*e^9 + 668095/8203*e^7 - 799798/8203*e^5 - 516766/8203*e^3 + 316691/8203*e, -625/8203*e^13 + 15488/8203*e^11 - 134969/8203*e^9 + 455132/8203*e^7 - 239709/8203*e^5 - 1131852/8203*e^3 + 495850/8203*e, -90/631*e^12 + 2412/631*e^10 - 24322/631*e^8 + 112758/631*e^6 - 231380/631*e^4 + 161630/631*e^2 - 33596/631, 1467/16406*e^13 - 40199/16406*e^11 + 211286/8203*e^9 - 2131749/16406*e^7 + 5252451/16406*e^5 - 5586387/16406*e^3 + 857861/8203*e, 130/631*e^12 - 3484/631*e^10 + 34641/631*e^8 - 154880/631*e^6 + 291588/631*e^4 - 147930/631*e^2 + 22306/631, -300/631*e^12 + 8040/631*e^10 - 80232/631*e^8 + 361978/631*e^6 - 696388/631*e^4 + 388168/631*e^2 - 61086/631, -223/16406*e^13 + 5093/16406*e^11 - 17982/8203*e^9 + 45751/16406*e^7 + 362605/16406*e^5 - 989119/16406*e^3 + 48429/8203*e, 1942/8203*e^13 - 52298/8203*e^11 + 529414/8203*e^9 - 2474040/8203*e^7 + 5210852/8203*e^5 - 3929176/8203*e^3 + 830290/8203*e, -121/1262*e^13 + 3369/1262*e^11 - 17745/631*e^9 + 174397/1262*e^7 - 394019/1262*e^5 + 334949/1262*e^3 - 37742/631*e, 29/631*e^12 - 651/631*e^10 + 4626/631*e^8 - 7223/631*e^6 - 36991/631*e^4 + 111839/631*e^2 - 34214/631, -1296/8203*e^13 + 34859/8203*e^11 - 351625/8203*e^9 + 1630530/8203*e^7 - 3381721/8203*e^5 + 2480805/8203*e^3 - 583859/8203*e, -209/631*e^12 + 5475/631*e^10 - 53270/631*e^8 + 232739/631*e^6 - 423245/631*e^4 + 191229/631*e^2 - 17834/631, 150/631*e^12 - 4020/631*e^10 + 40116/631*e^8 - 181620/631*e^6 + 357028/631*e^4 - 221848/631*e^2 + 28650/631, -51/631*e^12 + 1493/631*e^10 - 16012/631*e^8 + 75759/631*e^6 - 144787/631*e^4 + 62985/631*e^2 - 11634/631, -1817/16406*e^13 + 50841/16406*e^11 - 270077/8203*e^9 + 2693087/16406*e^7 - 6242425/16406*e^5 + 5584509/16406*e^3 - 620587/8203*e, -747/8203*e^13 + 19010/8203*e^11 - 174361/8203*e^9 + 668095/8203*e^7 - 799798/8203*e^5 - 500360/8203*e^3 + 185443/8203*e, -359/631*e^12 + 9495/631*e^10 - 93386/631*e^8 + 414359/631*e^6 - 779642/631*e^4 + 410553/631*e^2 - 54056/631, 409/631*e^12 - 10835/631*e^10 + 106758/631*e^8 - 474899/631*e^6 + 898441/631*e^4 - 479875/631*e^2 + 48462/631, 44/631*e^12 - 1053/631*e^10 + 8890/631*e^8 - 29171/631*e^6 + 15244/631*e^4 + 66181/631*e^2 - 21884/631, -59/631*e^12 + 1455/631*e^10 - 13154/631*e^8 + 52381/631*e^6 - 83885/631*e^4 + 27433/631*e^2 + 1982/631, 1767/16406*e^13 - 46977/16406*e^11 + 231210/8203*e^9 - 2029311/16406*e^7 + 3616663/16406*e^5 - 1255937/16406*e^3 - 138864/8203*e, 401/631*e^12 - 10873/631*e^10 + 109616/631*e^8 - 498277/631*e^6 + 959343/631*e^4 - 515427/631*e^2 + 62078/631, 2521/16406*e^13 - 63903/16406*e^11 + 291348/8203*e^9 - 2184297/16406*e^7 + 2228341/16406*e^5 + 2931545/16406*e^3 - 690285/8203*e, -223/16406*e^13 + 5093/16406*e^11 - 17982/8203*e^9 + 45751/16406*e^7 + 362605/16406*e^5 - 956307/16406*e^3 - 66413/8203*e, 330/8203*e^13 - 10737/8203*e^11 + 137347/8203*e^9 - 860194/8203*e^7 + 2651581/8203*e^5 - 3439505/8203*e^3 + 940751/8203*e, 159/631*e^12 - 4135/631*e^10 + 39898/631*e^8 - 173461/631*e^6 + 321483/631*e^4 - 174911/631*e^2 + 27214/631, 79/1262*e^13 - 1991/1262*e^11 + 8999/631*e^9 - 67763/1262*e^7 + 81177/1262*e^5 + 45041/1262*e^3 - 17380/631*e, -1451/8203*e^13 + 40275/8203*e^11 - 421978/8203*e^9 + 2062401/8203*e^7 - 4668797/8203*e^5 + 4100183/8203*e^3 - 1056426/8203*e, 78/631*e^12 - 1838/631*e^10 + 15358/631*e^8 - 52544/631*e^6 + 56451/631*e^4 + 21036/631*e^2 - 12866/631, 534/631*e^12 - 14185/631*e^10 + 140188/631*e^8 - 626249/631*e^6 + 1195754/631*e^4 - 668955/631*e^2 + 98208/631, -39/631*e^12 + 919/631*e^10 - 7048/631*e^8 + 15545/631*e^6 + 29511/631*e^4 - 115895/631*e^2 + 39876/631, -100/631*e^12 + 2680/631*e^10 - 26744/631*e^8 + 121080/631*e^6 - 237598/631*e^4 + 143692/631*e^2 - 12790/631, -240/631*e^12 + 6432/631*e^10 - 64438/631*e^8 + 294378/631*e^6 - 587146/631*e^4 + 375906/631*e^2 - 67294/631, 190/631*e^12 - 5092/631*e^10 + 51066/631*e^8 - 233838/631*e^6 + 467716/631*e^4 - 295226/631*e^2 + 45124/631, 4855/16406*e^13 - 130745/16406*e^11 + 657666/8203*e^9 - 6029243/16406*e^7 + 12034567/16406*e^5 - 7485085/16406*e^3 + 410333/8203*e, 150/631*e^12 - 4020/631*e^10 + 40116/631*e^8 - 181620/631*e^6 + 357028/631*e^4 - 224372/631*e^2 + 37484/631, 3038/8203*e^13 - 79904/8203*e^11 + 775178/8203*e^9 - 3336156/8203*e^7 + 5808548/8203*e^5 - 2064636/8203*e^3 - 92388/8203*e, -914/8203*e^13 + 24369/8203*e^11 - 241058/8203*e^9 + 1069947/8203*e^7 - 1987318/8203*e^5 + 1003221/8203*e^3 - 207386/8203*e, -21/16406*e^13 + 1951/16406*e^11 - 21410/8203*e^9 + 396581/16406*e^7 - 1728873/16406*e^5 + 3252869/16406*e^3 - 785392/8203*e, 5779/16406*e^13 - 150965/16406*e^11 + 730188/8203*e^9 - 6318131/16406*e^7 + 11324899/16406*e^5 - 5057289/16406*e^3 + 367327/8203*e, -4431/16406*e^13 + 116353/16406*e^11 - 563664/8203*e^9 + 4831355/16406*e^7 - 8224199/16406*e^5 + 2340001/16406*e^3 + 122339/8203*e, 60/631*e^12 - 1608/631*e^10 + 15794/631*e^8 - 66338/631*e^6 + 92836/631*e^4 + 39480/631*e^2 - 28924/631, 99/631*e^12 - 2527/631*e^10 + 23473/631*e^8 - 93241/631*e^6 + 130211/631*e^4 + 16555/631*e^2 - 13272/631, -100/631*e^12 + 2680/631*e^10 - 26744/631*e^8 + 119818/631*e^6 - 221192/631*e^4 + 96998/631*e^2 - 15314/631, 135/631*e^12 - 3618/631*e^10 + 35852/631*e^8 - 159672/631*e^6 + 304793/631*e^4 - 181238/631*e^2 + 28940/631, -1907/16406*e^13 + 54515/16406*e^11 - 297382/8203*e^9 + 3070865/16406*e^7 - 7497287/16406*e^5 + 7394311/16406*e^3 - 1014723/8203*e, -150/631*e^12 + 4020/631*e^10 - 40116/631*e^8 + 182882/631*e^6 - 373434/631*e^4 + 273590/631*e^2 - 45056/631, 3181/8203*e^13 - 85377/8203*e^11 + 857390/8203*e^9 - 3937497/8203*e^7 + 7958059/8203*e^5 - 5268148/8203*e^3 + 837255/8203*e, -6041/16406*e^13 + 162025/16406*e^11 - 807853/8203*e^9 + 7269137/16406*e^7 - 13903531/16406*e^5 + 7676437/16406*e^3 - 736874/8203*e, -19/631*e^12 + 383/631*e^10 - 2204/631*e^8 - 1099/631*e^6 + 44471/631*e^4 - 107783/631*e^2 + 38648/631, 239/631*e^12 - 6279/631*e^10 + 61798/631*e^8 - 278528/631*e^6 + 552955/631*e^4 - 361420/631*e^2 + 67734/631, 141/631*e^12 - 3905/631*e^10 + 40334/631*e^8 - 188517/631*e^6 + 374905/631*e^4 - 213257/631*e^2 + 35134/631, 170/631*e^12 - 4556/631*e^10 + 44960/631*e^8 - 197002/631*e^6 + 353058/631*e^4 - 141802/631*e^2 - 1604/631, 659/631*e^12 - 17535/631*e^10 + 173618/631*e^8 - 776968/631*e^6 + 1484233/631*e^4 - 817020/631*e^2 + 92426/631, -3661/16406*e^13 + 99503/16406*e^11 - 511432/8203*e^9 + 4902329/16406*e^7 - 10784309/16406*e^5 + 8896689/16406*e^3 - 1050982/8203*e, -100/631*e^12 + 2680/631*e^10 - 26744/631*e^8 + 121080/631*e^6 - 236967/631*e^4 + 139906/631*e^2 - 19100/631, 2361/16406*e^13 - 64663/16406*e^11 + 337596/8203*e^9 - 3361101/16406*e^7 + 8138497/16406*e^5 - 8521639/16406*e^3 + 1287764/8203*e, 6423/16406*e^13 - 172515/16406*e^11 + 859035/8203*e^9 - 7673863/16406*e^7 + 14288965/16406*e^5 - 6578279/16406*e^3 - 120772/8203*e, -3863/8203*e^13 + 102645/8203*e^11 - 1016008/8203*e^9 + 4551499/8203*e^7 - 8725643/8203*e^5 + 4966415/8203*e^3 - 1008532/8203*e, -1869/8203*e^13 + 50594/8203*e^11 - 521577/8203*e^9 + 2549333/8203*e^7 - 5961404/8203*e^5 + 5755368/8203*e^3 - 1300324/8203*e, -458/631*e^12 + 12022/631*e^10 - 116859/631*e^8 + 507600/631*e^6 - 909222/631*e^4 + 387688/631*e^2 - 28164/631, -69/16406*e^13 + 1723/16406*e^11 - 5895/8203*e^9 - 2397/16406*e^7 + 260733/16406*e^5 - 836045/16406*e^3 + 538910/8203*e, 61/8203*e^13 - 1761/8203*e^11 + 19696/8203*e^9 - 110583/8203*e^7 + 341567/8203*e^5 - 553633/8203*e^3 + 290553/8203*e, -49/631*e^12 + 1187/631*e^10 - 10732/631*e^8 + 46583/631*e^6 - 110479/631*e^4 + 148224/631*e^2 - 50374/631, 5219/16406*e^13 - 137219/16406*e^11 + 670575/8203*e^9 - 5925295/16406*e^7 + 11240449/16406*e^5 - 6425273/16406*e^3 + 412283/8203*e, 291/631*e^12 - 7925/631*e^10 + 80450/631*e^8 - 368875/631*e^6 + 714896/631*e^4 - 379577/631*e^2 + 53688/631, -3684/8203*e^13 + 97343/8203*e^11 - 952967/8203*e^9 + 4179666/8203*e^7 - 7637679/8203*e^5 + 3529413/8203*e^3 - 178652/8203*e, 229/631*e^12 - 6011/631*e^10 + 58114/631*e^8 - 248121/631*e^6 + 421799/631*e^4 - 130113/631*e^2 - 4848/631, 115/631*e^12 - 3082/631*e^10 + 31008/631*e^8 - 143028/631*e^6 + 289833/631*e^4 - 193136/631*e^2 + 42788/631, -111/16406*e^13 + 5625/16406*e^11 - 40512/8203*e^9 + 446239/16406*e^7 - 752519/16406*e^5 - 630211/16406*e^3 + 551305/8203*e, 2356/8203*e^13 - 62636/8203*e^11 + 616560/8203*e^9 - 2705748/8203*e^7 + 4827686/8203*e^5 - 1718332/8203*e^3 - 386710/8203*e, 342/8203*e^13 - 10680/8203*e^11 + 133691/8203*e^9 - 846581/8203*e^7 + 2765303/8203*e^5 - 4029166/8203*e^3 + 1369599/8203*e, -511/1262*e^13 + 13821/1262*e^11 - 70022/631*e^9 + 650395/1262*e^7 - 1336931/1262*e^5 + 923869/1262*e^3 - 81928/631*e, 160/631*e^12 - 4288/631*e^10 + 43169/631*e^8 - 200038/631*e^6 + 412464/631*e^4 - 282154/631*e^2 + 38132/631, 323/16406*e^13 - 12821/16406*e^11 + 95716/8203*e^9 - 1373303/16406*e^7 + 4856107/16406*e^5 - 7274281/16406*e^3 + 1011105/8203*e, -5781/16406*e^13 + 155057/16406*e^11 - 776367/8203*e^9 + 7085577/16406*e^7 - 14135607/16406*e^5 + 9028749/16406*e^3 - 646420/8203*e, -151/16406*e^13 + 5435/16406*e^11 - 28950/8203*e^9 + 160241/16406*e^7 + 618381/16406*e^5 - 3181793/16406*e^3 + 1072477/8203*e, 687/8203*e^13 - 19295/8203*e^11 + 209047/8203*e^9 - 1080686/8203*e^7 + 2626464/8203*e^5 - 2408277/8203*e^3 + 295277/8203*e, 389/631*e^12 - 10299/631*e^10 + 101283/631*e^8 - 449421/631*e^6 + 850669/631*e^4 - 466533/631*e^2 + 53476/631, 409/631*e^12 - 10835/631*e^10 + 106758/631*e^8 - 475530/631*e^6 + 906013/631*e^4 - 505746/631*e^2 + 69916/631, -130/631*e^12 + 3484/631*e^10 - 34010/631*e^8 + 143522/631*e^6 - 227226/631*e^4 + 31195/631*e^2 + 9244/631, 6657/16406*e^13 - 175505/16406*e^11 + 856201/8203*e^9 - 7461729/16406*e^7 + 13397607/16406*e^5 - 5620413/16406*e^3 + 57432/8203*e, -368/631*e^12 + 9610/631*e^10 - 93168/631*e^8 + 406200/631*e^6 - 744728/631*e^4 + 366140/631*e^2 - 42524/631, -1913/16406*e^13 + 50385/16406*e^11 - 239047/8203*e^9 + 1911537/16406*e^7 - 2574927/16406*e^5 - 755847/16406*e^3 + 182342/8203*e, -6561/16406*e^13 + 175961/16406*e^11 - 887231/8203*e^9 + 8259685/16406*e^7 - 17311195/16406*e^5 + 13043565/16406*e^3 - 1565819/8203*e, 1073/8203*e^13 - 29766/8203*e^11 + 315661/8203*e^9 - 1584779/8203*e^7 + 3752529/8203*e^5 - 3625781/8203*e^3 + 1312348/8203*e, -380/631*e^12 + 10184/631*e^10 - 100870/631*e^8 + 445591/631*e^6 - 811756/631*e^4 + 356351/631*e^2 - 19576/631, 3985/8203*e^13 - 106167/8203*e^11 + 1055400/8203*e^9 - 4772665/8203*e^7 + 9400574/8203*e^5 - 5999854/8203*e^3 + 1482999/8203*e, -435/8203*e^13 + 12289/8203*e^11 - 129966/8203*e^9 + 628289/8203*e^7 - 1345707/8203*e^5 + 1074837/8203*e^3 - 550656/8203*e, 290/631*e^12 - 7772/631*e^10 + 77179/631*e^8 - 343560/631*e^6 + 638428/631*e^4 - 303884/631*e^2 + 27626/631, -6155/16406*e^13 + 165585/16406*e^11 - 831502/8203*e^9 + 7603283/16406*e^7 - 15139747/16406*e^5 + 9582765/16406*e^3 - 796979/8203*e, -5253/16406*e^13 + 141159/16406*e^11 - 700942/8203*e^9 + 6208009/16406*e^7 - 11346649/16406*e^5 + 5215359/16406*e^3 - 513966/8203*e, 379/631*e^12 - 10031/631*e^10 + 98230/631*e^8 - 429741/631*e^6 + 778827/631*e^4 - 353223/631*e^2 + 43994/631, 915/16406*e^13 - 26415/16406*e^11 + 139517/8203*e^9 - 1297813/16406*e^7 + 2449327/16406*e^5 - 1249915/16406*e^3 + 394995/8203*e, -170/631*e^12 + 4556/631*e^10 - 44960/631*e^8 + 195740/631*e^6 - 336652/631*e^4 + 91322/631*e^2 + 9176/631, 2369/16406*e^13 - 64625/16406*e^11 + 333643/8203*e^9 - 3215309/16406*e^7 + 7126047/16406*e^5 - 6049165/16406*e^3 + 878378/8203*e, 1663/16406*e^13 - 47471/16406*e^11 + 266193/8203*e^9 - 2973059/16406*e^7 + 8542701/16406*e^5 - 11151563/16406*e^3 + 1705082/8203*e, 628/631*e^12 - 16578/631*e^10 + 162450/631*e^8 - 715960/631*e^6 + 1329166/631*e^4 - 668941/631*e^2 + 87136/631, 314/8203*e^13 - 10813/8203*e^11 + 136753/8203*e^9 - 790846/8203*e^7 + 2084333/8203*e^5 - 2166579/8203*e^3 + 839259/8203*e, -309/631*e^12 + 8155/631*e^10 - 80014/631*e^8 + 355081/631*e^6 - 678511/631*e^4 + 396759/631*e^2 - 57126/631, -2141/16406*e^13 + 57505/16406*e^11 - 286345/8203*e^9 + 2547017/16406*e^7 - 4620803/16406*e^5 + 1777141/16406*e^3 - 19898/8203*e, -6065/16406*e^13 + 161911/16406*e^11 - 812400/8203*e^9 + 7520813/16406*e^7 - 15623921/16406*e^5 + 11415095/16406*e^3 - 1214940/8203*e, 3482/8203*e^13 - 94201/8203*e^11 + 959823/8203*e^9 - 4530496/8203*e^7 + 9696345/8203*e^5 - 7459687/8203*e^3 + 1329505/8203*e, -341/631*e^12 + 9265/631*e^10 - 93822/631*e^8 + 429415/631*e^6 - 833695/631*e^4 + 457733/631*e^2 - 85954/631, -1057/631*e^12 + 27949/631*e^10 - 275314/631*e^8 + 1227695/631*e^6 - 2342265/631*e^4 + 1305395/631*e^2 - 182326/631, 110/631*e^12 - 2948/631*e^10 + 30428/631*e^8 - 149594/631*e^6 + 343514/631*e^4 - 296124/631*e^2 + 75276/631, -290/631*e^12 + 7772/631*e^10 - 77810/631*e^8 + 354918/631*e^6 - 706576/631*e^4 + 452800/631*e^2 - 73058/631, 1353/16406*e^13 - 36639/16406*e^11 + 179434/8203*e^9 - 1485889/16406*e^7 + 2063921/16406*e^5 + 618313/16406*e^3 + 2065/8203*e, 180/631*e^12 - 4824/631*e^10 + 47382/631*e^8 - 204062/631*e^6 + 345394/631*e^4 - 97362/631*e^2 + 5354/631, -2055/8203*e^13 + 53812/8203*e^11 - 522330/8203*e^9 + 2285012/8203*e^7 - 4295241/8203*e^5 + 2520888/8203*e^3 - 482738/8203*e, -789/631*e^12 + 21019/631*e^10 - 208890/631*e^8 + 942575/631*e^6 - 1834504/631*e^4 + 1079161/631*e^2 - 142496/631, -29/16406*e^13 + 1913/16406*e^11 - 17457/8203*e^9 + 283601/16406*e^7 - 1126573/16406*e^5 + 1863191/16406*e^3 - 203743/8203*e, 3633/8203*e^13 - 99636/8203*e^11 + 1034129/8203*e^9 - 5018857/8203*e^7 + 11292774/8203*e^5 - 9823122/8203*e^3 + 2334503/8203*e, 175/631*e^12 - 4690/631*e^10 + 46802/631*e^8 - 211890/631*e^6 + 415481/631*e^4 - 252092/631*e^2 + 34056/631, 20/631*e^12 - 536/631*e^10 + 4844/631*e^8 - 15382/631*e^6 - 2708/631*e^4 + 68688/631*e^2 - 7538/631, 339/631*e^12 - 8959/631*e^10 + 88542/631*e^8 - 397715/631*e^6 + 765313/631*e^4 - 421189/631*e^2 + 43926/631, -891/8203*e^13 + 26529/8203*e^11 - 302752/8203*e^9 + 1636753/8203*e^7 - 4157791/8203*e^5 + 4204905/8203*e^3 - 1310398/8203*e, 2539/8203*e^13 - 67919/8203*e^11 + 675648/8203*e^9 - 3021091/8203*e^7 + 5622703/8203*e^5 - 2591743/8203*e^3 + 214250/8203*e, 4167/8203*e^13 - 109404/8203*e^11 + 1051903/8203*e^9 - 4400774/8203*e^7 + 6919953/8203*e^5 - 580960/8203*e^3 - 705252/8203*e, -1705/8203*e^13 + 43170/8203*e^11 - 396545/8203*e^9 + 1551411/8203*e^7 - 2091223/8203*e^5 - 569765/8203*e^3 + 650502/8203*e, -557/631*e^12 + 14549/631*e^10 - 141594/631*e^8 + 624819/631*e^6 - 1188349/631*e^4 + 690419/631*e^2 - 119638/631, 2092/8203*e^13 - 55687/8203*e^11 + 557541/8203*e^9 - 2595084/8203*e^7 + 5615205/8203*e^5 - 4971324/8203*e^3 + 1712052/8203*e, -6293/16406*e^13 + 169031/16406*e^11 - 851495/8203*e^9 + 7877391/16406*e^7 - 16176851/16406*e^5 + 11290311/16406*e^3 - 1072654/8203*e, 4271/16406*e^13 - 117113/16406*e^11 + 601709/8203*e^9 - 5663633/16406*e^7 + 11722673/16406*e^5 - 7755777/16406*e^3 + 346358/8203*e, -181/631*e^12 + 4977/631*e^10 - 51284/631*e^8 + 241997/631*e^6 - 501999/631*e^4 + 335853/631*e^2 - 47822/631, 219/631*e^12 - 5743/631*e^10 + 55692/631*e^8 - 241692/631*e^6 + 439559/631*e^4 - 216830/631*e^2 + 31102/631, 2105/8203*e^13 - 57676/8203*e^11 + 591861/8203*e^9 - 2784728/8203*e^7 + 5805395/8203*e^5 - 4011222/8203*e^3 + 459476/8203*e, 747/8203*e^13 - 19010/8203*e^11 + 174361/8203*e^9 - 659892/8203*e^7 + 693159/8203*e^5 + 861292/8203*e^3 - 456142/8203*e, -788/631*e^12 + 20866/631*e^10 - 204988/631*e^8 + 903378/631*e^6 - 1659600/631*e^4 + 772522/631*e^2 - 67216/631, 5571/16406*e^13 - 151953/16406*e^11 + 783748/8203*e^9 - 7549387/16406*e^7 + 16780167/16406*e^5 - 14119017/16406*e^3 + 1381041/8203*e, 10915/16406*e^13 - 290629/16406*e^11 + 1440750/8203*e^9 - 12927515/16406*e^7 + 24823451/16406*e^5 - 14032781/16406*e^3 + 1136717/8203*e, -2*e^6 + 30*e^4 - 113*e^2 + 64, -6702/8203*e^13 + 177342/8203*e^11 - 1731504/8203*e^9 + 7502964/8203*e^7 - 13155520/8203*e^5 + 4720654/8203*e^3 + 98022/8203*e, 1336/8203*e^13 - 34669/8203*e^11 + 328501/8203*e^9 - 1344532/8203*e^7 + 2027227/8203*e^5 - 158907/8203*e^3 + 296191/8203*e]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([8, 2, 2])] = -1

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