/*
  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([2, 0, -6, -2, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([13, 13, -w^3 + 3*w^2 + 3*w - 1])

primes_array = [
[2, 2, w],\
[5, 5, -w^3 + 3*w^2 + 2*w - 1],\
[5, 5, w - 1],\
[11, 11, w^3 - 2*w^2 - 5*w - 1],\
[13, 13, -w^3 + 3*w^2 + 3*w - 1],\
[17, 17, 2*w^3 - 5*w^2 - 9*w + 5],\
[23, 23, -w^3 + 3*w^2 + 4*w - 5],\
[25, 5, -w^2 + 3*w + 1],\
[29, 29, -2*w^3 + 6*w^2 + 5*w - 1],\
[31, 31, -w^2 + 2*w + 1],\
[43, 43, -w^3 + 3*w^2 + 2*w - 3],\
[43, 43, -w^3 + 2*w^2 + 6*w - 3],\
[59, 59, 2*w^3 - 6*w^2 - 7*w + 7],\
[73, 73, 3*w^3 - 6*w^2 - 16*w - 5],\
[79, 79, -5*w^3 + 14*w^2 + 20*w - 17],\
[81, 3, -3],\
[83, 83, -w - 3],\
[83, 83, w^2 - 3*w - 7],\
[89, 89, w^2 - 2*w - 7],\
[101, 101, -2*w^3 + 5*w^2 + 8*w - 3],\
[101, 101, 5*w^3 - 14*w^2 - 19*w + 17],\
[103, 103, -w^3 + w^2 + 8*w + 3],\
[103, 103, 2*w^3 - 5*w^2 - 7*w - 1],\
[109, 109, 3*w^3 - 7*w^2 - 14*w + 1],\
[109, 109, -w^2 + 4*w + 1],\
[127, 127, -3*w^3 + 8*w^2 + 11*w - 7],\
[127, 127, -w^3 + 2*w^2 + 7*w + 1],\
[137, 137, -2*w^3 + 5*w^2 + 9*w - 1],\
[139, 139, -w^3 + 3*w^2 + 2*w - 5],\
[149, 149, w^3 - 3*w^2 - w - 1],\
[149, 149, -2*w^3 + 4*w^2 + 10*w + 1],\
[163, 163, w^3 - 4*w^2 - w + 11],\
[163, 163, 2*w^3 - 4*w^2 - 10*w + 1],\
[173, 173, -4*w^3 + 11*w^2 + 15*w - 13],\
[179, 179, 2*w^2 - 6*w - 3],\
[179, 179, -w^3 + 2*w^2 + 7*w - 1],\
[181, 181, w^3 - 10*w - 9],\
[181, 181, -3*w^3 + 8*w^2 + 14*w - 7],\
[199, 199, w^3 - 8*w - 9],\
[211, 211, 2*w - 3],\
[223, 223, -w^3 + 4*w^2 + w - 5],\
[227, 227, w^3 - 2*w^2 - 5*w - 5],\
[227, 227, -3*w^3 + 7*w^2 + 14*w - 5],\
[227, 227, -4*w^3 + 10*w^2 + 19*w - 7],\
[227, 227, w^2 - 4*w - 5],\
[239, 239, -2*w^3 + 5*w^2 + 7*w - 3],\
[251, 251, -w^3 + 4*w^2 + 2*w - 11],\
[251, 251, 2*w^3 - 6*w^2 - 6*w + 1],\
[257, 257, -3*w^3 + 6*w^2 + 16*w + 3],\
[263, 263, -w^3 + 3*w^2 + 3*w - 7],\
[263, 263, w^3 - 4*w^2 + 7],\
[269, 269, -2*w^3 + 6*w^2 + 6*w - 11],\
[269, 269, -w^3 + 4*w^2 - w - 5],\
[271, 271, -3*w^3 + 9*w^2 + 11*w - 11],\
[271, 271, w^2 - 5*w - 3],\
[277, 277, w^3 - 4*w^2 - 2*w + 7],\
[277, 277, -2*w^3 + 7*w^2 + 8*w - 9],\
[281, 281, 2*w^2 - 4*w - 5],\
[281, 281, 2*w^3 - 4*w^2 - 11*w + 1],\
[283, 283, -3*w^3 + 8*w^2 + 14*w - 11],\
[293, 293, w^3 - 2*w^2 - 6*w + 5],\
[307, 307, -2*w^3 + 5*w^2 + 7*w - 1],\
[313, 313, 2*w^3 - 4*w^2 - 9*w + 3],\
[313, 313, -2*w^3 + 5*w^2 + 6*w - 3],\
[317, 317, -2*w^3 + 5*w^2 + 9*w + 1],\
[347, 347, 4*w^3 - 9*w^2 - 21*w + 3],\
[347, 347, 4*w^3 - 10*w^2 - 18*w + 5],\
[349, 349, -2*w^3 + 6*w^2 + 7*w - 3],\
[353, 353, -w^3 + 12*w + 5],\
[353, 353, w^2 - w - 7],\
[359, 359, -2*w^3 + 5*w^2 + 6*w - 7],\
[359, 359, -w^3 + 4*w^2 - 11],\
[373, 373, -w^3 + 2*w^2 + 6*w + 5],\
[379, 379, -3*w^3 + 8*w^2 + 14*w - 5],\
[397, 397, 6*w^3 - 14*w^2 - 30*w + 7],\
[401, 401, 3*w^3 - 5*w^2 - 20*w - 7],\
[409, 409, 3*w^3 - 7*w^2 - 12*w - 3],\
[409, 409, 2*w^2 - 4*w - 7],\
[421, 421, w^3 - 11*w - 11],\
[421, 421, -w^3 + 3*w^2 + w - 7],\
[431, 431, 2*w^3 - 3*w^2 - 14*w - 3],\
[431, 431, -4*w^3 + 11*w^2 + 15*w - 15],\
[433, 433, 2*w^3 - 5*w^2 - 6*w + 1],\
[439, 439, -4*w^3 + 11*w^2 + 13*w - 9],\
[439, 439, -2*w^3 + 6*w^2 + 8*w - 11],\
[443, 443, 2*w - 5],\
[443, 443, -6*w^3 + 17*w^2 + 24*w - 21],\
[449, 449, w^3 - 2*w^2 - 8*w + 3],\
[449, 449, 4*w^3 - 12*w^2 - 15*w + 17],\
[457, 457, -2*w^3 + 4*w^2 + 9*w + 5],\
[461, 461, -3*w^3 + 6*w^2 + 15*w - 1],\
[461, 461, -3*w^3 + 7*w^2 + 17*w + 1],\
[463, 463, -4*w^3 + 10*w^2 + 17*w - 7],\
[463, 463, -3*w^3 + 10*w^2 + 9*w - 17],\
[467, 467, 4*w^3 - 8*w^2 - 21*w - 7],\
[467, 467, w^3 - 6*w^2 + 3*w + 19],\
[479, 479, -w^3 + w^2 + 8*w + 1],\
[487, 487, -4*w^3 + 11*w^2 + 14*w - 15],\
[487, 487, 3*w^3 - 6*w^2 - 15*w - 5],\
[491, 491, w^2 - 5],\
[503, 503, 2*w^3 - 5*w^2 - 11*w + 3],\
[523, 523, -3*w^3 + 7*w^2 + 13*w + 1],\
[547, 547, 2*w^3 - 3*w^2 - 12*w - 3],\
[547, 547, 2*w^3 - 3*w^2 - 12*w - 9],\
[557, 557, -3*w^3 + 9*w^2 + 9*w - 11],\
[557, 557, -6*w^3 + 15*w^2 + 27*w - 13],\
[563, 563, -3*w^3 + 7*w^2 + 14*w - 7],\
[571, 571, -5*w^3 + 11*w^2 + 26*w - 3],\
[593, 593, -6*w^3 + 15*w^2 + 26*w - 7],\
[599, 599, 7*w^3 - 18*w^2 - 29*w + 17],\
[599, 599, -2*w^3 + 6*w^2 + 8*w - 3],\
[601, 601, -7*w^3 + 20*w^2 + 28*w - 23],\
[601, 601, 3*w^3 - 7*w^2 - 12*w + 5],\
[607, 607, 5*w^3 - 12*w^2 - 24*w + 9],\
[607, 607, w^3 - 5*w^2 + 15],\
[613, 613, -w^3 + 5*w^2 - 2*w - 9],\
[617, 617, w^3 + w^2 - 13*w - 15],\
[617, 617, 2*w^3 - 4*w^2 - 8*w - 1],\
[619, 619, 5*w^3 - 10*w^2 - 27*w - 7],\
[619, 619, 2*w^3 - 4*w^2 - 10*w + 3],\
[643, 643, w^3 - 5*w^2 + 5*w + 5],\
[643, 643, 4*w^3 - 9*w^2 - 20*w - 1],\
[643, 643, 3*w^3 - 7*w^2 - 14*w - 3],\
[643, 643, -3*w^3 + 7*w^2 + 13*w - 3],\
[647, 647, -3*w^3 + 8*w^2 + 12*w - 3],\
[653, 653, -w^3 + 9*w + 13],\
[653, 653, -w^3 + 4*w^2 + 3*w - 9],\
[653, 653, -2*w^3 + 7*w^2 + 4*w - 7],\
[653, 653, w^2 - 4*w - 9],\
[673, 673, -w^3 + 5*w^2 + w - 13],\
[683, 683, w^3 - 3*w^2 - 3*w - 3],\
[701, 701, 5*w^3 - 13*w^2 - 23*w + 9],\
[709, 709, 2*w^3 - w^2 - 19*w - 15],\
[719, 719, -5*w^3 + 15*w^2 + 20*w - 19],\
[727, 727, -w - 5],\
[751, 751, -4*w^3 + 10*w^2 + 15*w - 9],\
[751, 751, 6*w^3 - 17*w^2 - 22*w + 21],\
[757, 757, 3*w^3 - 6*w^2 - 18*w - 1],\
[757, 757, -w^3 + 4*w^2 + 2*w + 1],\
[769, 769, w^2 - 2*w + 3],\
[773, 773, 5*w^3 - 12*w^2 - 23*w + 9],\
[787, 787, 2*w^3 - 4*w^2 - 5*w + 1],\
[797, 797, -3*w^3 + 8*w^2 + 10*w - 3],\
[809, 809, 2*w^2 - 5*w - 1],\
[809, 809, 4*w^3 - 6*w^2 - 28*w - 11],\
[827, 827, 4*w^3 - 8*w^2 - 22*w - 1],\
[827, 827, 2*w^2 - 6*w - 9],\
[829, 829, -w^3 + w^2 + 10*w + 1],\
[839, 839, -2*w^3 + 2*w^2 + 16*w + 7],\
[877, 877, 6*w^3 - 16*w^2 - 25*w + 13],\
[877, 877, w^3 - w^2 - 7*w + 1],\
[881, 881, 2*w^3 - 2*w^2 - 15*w - 7],\
[881, 881, -4*w^3 + 7*w^2 + 26*w + 9],\
[887, 887, 2*w^3 - 4*w^2 - 13*w - 1],\
[907, 907, 5*w^3 - 11*w^2 - 26*w - 1],\
[907, 907, 5*w^3 - 13*w^2 - 22*w + 9],\
[907, 907, w^3 - 5*w^2 + 2*w + 13],\
[907, 907, -2*w^3 + 7*w^2 + 5*w - 7],\
[911, 911, -3*w^3 + 8*w^2 + 9*w - 5],\
[919, 919, -2*w^3 + 7*w^2 + 6*w - 3],\
[919, 919, -3*w^3 + 8*w^2 + 15*w - 7],\
[947, 947, -2*w^3 + 5*w^2 + 12*w - 9],\
[947, 947, -w^2 + w - 3],\
[947, 947, 3*w^3 - 6*w^2 - 14*w - 7],\
[947, 947, -w^3 + 5*w^2 - w - 17],\
[953, 953, 3*w^3 - 9*w^2 - 9*w + 13],\
[953, 953, -4*w^3 + 13*w^2 + 11*w - 23],\
[967, 967, 8*w^3 - 20*w^2 - 33*w + 19]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^13 - 8*x^12 + 11*x^11 + 66*x^10 - 202*x^9 - 64*x^8 + 804*x^7 - 565*x^6 - 985*x^5 + 1282*x^4 + 21*x^3 - 452*x^2 + 83*x + 1
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -336/97*e^12 + 2218/97*e^11 - 620/97*e^10 - 22907/97*e^9 + 35964/97*e^8 + 70238/97*e^7 - 171078/97*e^6 - 43455/97*e^5 + 264062/97*e^4 - 69501/97*e^3 - 93499/97*e^2 + 22665/97*e - 38/97, -92/97*e^12 + 605/97*e^11 - 179/97*e^10 - 6174/97*e^9 + 9875/97*e^8 + 18375/97*e^7 - 46531/97*e^6 - 9172/97*e^5 + 70947/97*e^4 - 22283/97*e^3 - 24251/97*e^2 + 7214/97*e - 179/97, -312/97*e^12 + 2115/97*e^11 - 839/97*e^10 - 21638/97*e^9 + 36416/97*e^8 + 64833/97*e^7 - 170609/97*e^6 - 34344/97*e^5 + 262993/97*e^4 - 74105/97*e^3 - 94823/97*e^2 + 22702/97*e + 325/97, -1, -1102/97*e^12 + 7405/97*e^11 - 2627/97*e^10 - 76189/97*e^9 + 125069/97*e^8 + 231633/97*e^7 - 590642/97*e^6 - 136780/97*e^5 + 915594/97*e^4 - 237063/97*e^3 - 333770/97*e^2 + 70364/97*e + 1059/97, 1226/97*e^12 - 8212/97*e^11 + 2805/97*e^10 + 84540/97*e^9 - 137704/97*e^8 - 257441/97*e^7 + 651055/97*e^6 + 153929/97*e^5 - 1008595/97*e^4 + 259674/97*e^3 + 366182/97*e^2 - 77173/97*e - 881/97, 466/97*e^12 - 3172/97*e^11 + 1301/97*e^10 + 32521/97*e^9 - 55179/97*e^8 - 97858/97*e^7 + 259132/97*e^6 + 53303/97*e^5 - 401635/97*e^4 + 108615/97*e^3 + 146532/97*e^2 - 31526/97*e + 137/97, 729/97*e^12 - 4911/97*e^11 + 1799/97*e^10 + 50392/97*e^9 - 83222/97*e^8 - 152064/97*e^7 + 391103/97*e^6 + 84723/97*e^5 - 601776/97*e^4 + 166140/97*e^3 + 213875/97*e^2 - 50468/97*e + 247/97, 461/97*e^12 - 3001/97*e^11 + 607/97*e^10 + 31323/97*e^9 - 46624/97*e^8 - 98870/97*e^7 + 224959/97*e^6 + 73727/97*e^5 - 351041/97*e^4 + 72795/97*e^3 + 128976/97*e^2 - 24093/97*e - 945/97, -1148/97*e^12 + 7756/97*e^11 - 2959/97*e^10 - 79567/97*e^9 + 132868/97*e^8 + 239899/97*e^7 - 625402/97*e^6 - 132636/97*e^5 + 968964/97*e^4 - 263967/97*e^3 - 353995/97*e^2 + 79694/97*e + 1309/97, 90/97*e^12 - 556/97*e^11 - 21/97*e^10 + 5947/97*e^9 - 7617/97*e^8 - 19808/97*e^7 + 38837/97*e^6 + 18719/97*e^5 - 62524/97*e^4 + 6791/97*e^3 + 24232/97*e^2 - 1389/97*e - 700/97, -1262/97*e^12 + 8415/97*e^11 - 2719/97*e^10 - 86686/97*e^9 + 139742/97*e^8 + 264142/97*e^7 - 661701/97*e^6 - 157459/97*e^5 + 1022857/97*e^4 - 269258/97*e^3 - 366524/97*e^2 + 81628/97*e + 191/97, 193/97*e^12 - 1285/97*e^11 + 385/97*e^10 + 13321/97*e^9 - 21084/97*e^8 - 41117/97*e^7 + 100331/97*e^6 + 26065/97*e^5 - 155208/97*e^4 + 39978/97*e^3 + 55135/97*e^2 - 12559/97*e - 197/97, 1586/97*e^12 - 10630/97*e^11 + 3594/97*e^10 + 109686/97*e^9 - 177969/97*e^8 - 336091/97*e^7 + 843069/97*e^6 + 209696/97*e^5 - 1310392/97*e^4 + 322437/97*e^3 + 481734/97*e^2 - 95824/97*e - 2517/97, -309/97*e^12 + 1993/97*e^11 - 248/97*e^10 - 21152/97*e^9 + 29634/97*e^8 + 69553/97*e^7 - 145876/97*e^6 - 63263/97*e^5 + 231880/97*e^4 - 28751/97*e^3 - 89508/97*e^2 + 8969/97*e + 528/97, 510/97*e^12 - 3280/97*e^11 + 560/97*e^10 + 34023/97*e^9 - 49953/97*e^8 - 105520/97*e^7 + 240317/97*e^6 + 70249/97*e^5 - 369176/97*e^4 + 95098/97*e^3 + 126677/97*e^2 - 31248/97*e + 560/97, -995/97*e^12 + 6772/97*e^11 - 2791/97*e^10 - 69234/97*e^9 + 117465/97*e^8 + 207176/97*e^7 - 549262/97*e^6 - 109243/97*e^5 + 846222/97*e^4 - 236136/97*e^3 - 304478/97*e^2 + 69854/97*e - 75/97, -916/97*e^12 + 6146/97*e^11 - 2166/97*e^10 - 63129/97*e^9 + 103546/97*e^8 + 191078/97*e^7 - 487946/97*e^6 - 109165/97*e^5 + 752667/97*e^4 - 203001/97*e^3 - 269826/97*e^2 + 60684/97*e + 841/97, -287/97*e^12 + 1842/97*e^11 - 279/97*e^10 - 19140/97*e^9 + 27591/97*e^8 + 59708/97*e^7 - 132537/97*e^6 - 41598/97*e^5 + 201889/97*e^4 - 49623/97*e^3 - 66989/97*e^2 + 16577/97*e - 85/97, 393/97*e^12 - 2596/97*e^11 + 694/97*e^10 + 26903/97*e^9 - 41729/97*e^8 - 83087/97*e^7 + 198685/97*e^6 + 53587/97*e^5 - 305510/97*e^4 + 77336/97*e^3 + 105535/97*e^2 - 22856/97*e + 597/97, -1384/97*e^12 + 9076/97*e^11 - 2212/97*e^10 - 94228/97*e^9 + 144396/97*e^8 + 293323/97*e^7 - 691916/97*e^6 - 202003/97*e^5 + 1075716/97*e^4 - 246307/97*e^3 - 391351/97*e^2 + 76404/97*e + 2250/97, -784/97*e^12 + 5240/97*e^11 - 1673/97*e^10 - 54161/97*e^9 + 86632/97*e^8 + 166734/97*e^7 - 410628/97*e^6 - 107506/97*e^5 + 636741/97*e^4 - 152954/97*e^3 - 232973/97*e^2 + 45804/97*e + 2013/97, -1511/97*e^12 + 10199/97*e^11 - 3854/97*e^10 - 104520/97*e^9 + 173998/97*e^8 + 314605/97*e^7 - 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194685/97*e - 2864/97, -6278/97*e^12 + 41873/97*e^11 - 13693/97*e^10 - 430865/97*e^9 + 696823/97*e^8 + 1308912/97*e^7 - 3296854/97*e^6 - 762440/97*e^5 + 5093686/97*e^4 - 1373413/97*e^3 - 1824944/97*e^2 + 425035/97*e + 4252/97, -5218/97*e^12 + 35206/97*e^11 - 13132/97*e^10 - 361480/97*e^9 + 599772/97*e^8 + 1092873/97*e^7 - 2823069/97*e^6 - 619658/97*e^5 + 4364772/97*e^4 - 1165832/97*e^3 - 1579940/97*e^2 + 342845/97*e + 4134/97, 4204/97*e^12 - 28211/97*e^11 + 9896/97*e^10 + 290041/97*e^9 - 475309/97*e^8 - 879571/97*e^7 + 2243394/97*e^6 + 508428/97*e^5 - 3468359/97*e^4 + 922784/97*e^3 + 1247297/97*e^2 - 273186/97*e + 1263/97, 172/97*e^12 - 916/97*e^11 - 939/97*e^10 + 11277/97*e^9 - 5232/97*e^8 - 48258/97*e^7 + 43891/97*e^6 + 84162/97*e^5 - 88834/97*e^4 - 53042/97*e^3 + 48485/97*e^2 + 13150/97*e - 1812/97, 2640/97*e^12 - 17344/97*e^11 + 4234/97*e^10 + 180524/97*e^9 - 276200/97*e^8 - 565256/97*e^7 + 1325782/97*e^6 + 401780/97*e^5 - 2065738/97*e^4 + 451338/97*e^3 + 753356/97*e^2 - 139199/97*e - 2071/97, 2002/97*e^12 - 13256/97*e^11 + 3969/97*e^10 + 136338/97*e^9 - 216856/97*e^8 - 413999/97*e^7 + 1025960/97*e^6 + 241617/97*e^5 - 1575754/97*e^4 + 432140/97*e^3 + 552034/97*e^2 - 134015/97*e + 2126/97, 6413/97*e^12 - 42804/97*e^11 + 14098/97*e^10 + 440610/97*e^9 - 713341/97*e^8 - 1340855/97*e^7 + 3376498/97*e^6 + 795417/97*e^5 - 5227824/97*e^4 + 1369971/97*e^3 + 1892041/97*e^2 - 414266/97*e - 6078/97, 3533/97*e^12 - 23654/97*e^11 + 8077/97*e^10 + 243322/97*e^9 - 396556/97*e^8 - 738815/97*e^7 + 1873075/97*e^6 + 429500/97*e^5 - 2893667/97*e^4 + 776299/97*e^3 + 1038726/97*e^2 - 241390/97*e - 1817/97, -27*e^12 + 181*e^11 - 62*e^10 - 1864*e^9 + 3034*e^8 + 5684*e^7 - 14339*e^6 - 3435*e^5 + 22216*e^4 - 5676*e^3 - 8076*e^2 + 1717*e - 20, -3441/97*e^12 + 23631/97*e^11 - 10905/97*e^10 - 240252/97*e^9 + 421213/97*e^8 + 707151/97*e^7 - 1960210/97*e^6 - 319448/97*e^5 + 3019630/97*e^4 - 911059/97*e^3 - 1090814/97*e^2 + 268611/97*e + 2190/97, -5864/97*e^12 + 39102/97*e^11 - 12451/97*e^10 - 403373/97*e^9 + 647390/97*e^8 + 1234130/97*e^7 - 3069180/97*e^6 - 758123/97*e^5 + 4753424/97*e^4 - 1214309/97*e^3 - 1716930/97*e^2 + 369874/97*e + 2778/97, -3983/97*e^12 + 26143/97*e^11 - 6614/97*e^10 - 270729/97*e^9 + 418054/97*e^8 + 836497/97*e^7 - 1998390/97*e^6 - 546278/97*e^5 + 3097647/97*e^4 - 769708/97*e^3 - 1113423/97*e^2 + 251439/97*e + 1728/97, -4172/97*e^12 + 27815/97*e^11 - 8927/97*e^10 - 286700/97*e^9 + 461200/97*e^8 + 875727/97*e^7 - 2185280/97*e^6 - 533431/97*e^5 + 3384225/97*e^4 - 869979/97*e^3 - 1224004/97*e^2 + 268741/97*e + 191/97, 518/97*e^12 - 3476/97*e^11 + 1166/97*e^10 + 35804/97*e^9 - 57627/97*e^8 - 109488/97*e^7 + 271190/97*e^6 + 67757/97*e^5 - 417418/97*e^4 + 109245/97*e^3 + 150518/97*e^2 - 39707/97*e + 196/97, -6491/97*e^12 + 43454/97*e^11 - 14817/97*e^10 - 447038/97*e^9 + 728362/97*e^8 + 1358203/97*e^7 - 3441630/97*e^6 - 795952/97*e^5 + 5322551/97*e^4 - 1407388/97*e^3 - 1917711/97*e^2 + 424452/97*e + 606/97, 3257/97*e^12 - 21354/97*e^11 + 5212/97*e^10 + 221599/97*e^9 - 339771/97*e^8 - 688928/97*e^7 + 1627267/97*e^6 + 470078/97*e^5 - 2526693/97*e^4 + 589073/97*e^3 + 913496/97*e^2 - 185313/97*e - 2742/97, 1058/97*e^12 - 7200/97*e^11 + 3174/97*e^10 + 72844/97*e^9 - 127191/97*e^8 - 210488/97*e^7 + 591512/97*e^6 + 73565/97*e^5 - 902948/97*e^4 + 321196/97*e^3 + 309490/97*e^2 - 104398/97*e + 3271/97, -1275/97*e^12 + 8588/97*e^11 - 3049/97*e^10 - 88695/97*e^9 + 145301/97*e^8 + 272239/97*e^7 - 688432/97*e^6 - 171985/97*e^5 + 1072708/97*e^4 - 253556/97*e^3 - 395214/97*e^2 + 68905/97*e - 818/97, -1829/97*e^12 + 12364/97*e^11 - 4905/97*e^10 - 126160/97*e^9 + 213599/97*e^8 + 373878/97*e^7 - 1000920/97*e^6 - 175275/97*e^5 + 1538047/97*e^4 - 477339/97*e^3 - 541224/97*e^2 + 147696/97*e - 1898/97]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([13, 13, -w^3 + 3*w^2 + 3*w - 1])] = 1

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