/*
  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, 3, -4, -2, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([31, 31, w^3 - 2*w^2 - 4*w + 2])

primes_array = [
[3, 3, w],\
[7, 7, w^2 - w - 2],\
[9, 3, w^2 - 2*w - 1],\
[13, 13, w^3 - 3*w^2 - w + 5],\
[13, 13, w^3 - 3*w^2 - w + 2],\
[16, 2, 2],\
[17, 17, -w^3 + 2*w^2 + 2*w - 2],\
[19, 19, -w^3 + 2*w^2 + 2*w - 1],\
[29, 29, -2*w^3 + 5*w^2 + 4*w - 7],\
[31, 31, w^3 - 2*w^2 - 4*w + 2],\
[47, 47, -w^3 + 4*w^2 - w - 5],\
[53, 53, -w^3 + 4*w^2 - w - 7],\
[67, 67, 2*w^3 - 3*w^2 - 8*w + 1],\
[67, 67, 2*w^3 - 5*w^2 - 4*w + 4],\
[71, 71, w^3 - 3*w^2 - 2*w + 2],\
[79, 79, w^2 - 3*w - 4],\
[83, 83, 2*w^2 - 3*w - 4],\
[89, 89, -3*w^3 + 7*w^2 + 8*w - 11],\
[101, 101, w^3 - 2*w^2 - 3*w - 2],\
[103, 103, -2*w^3 + 4*w^2 + 5*w - 1],\
[107, 107, w^3 - 2*w^2 - w - 1],\
[107, 107, 2*w^2 - 3*w - 5],\
[109, 109, w^3 - 4*w^2 + 7],\
[109, 109, -w^3 + w^2 + 4*w - 1],\
[113, 113, -w^3 + 3*w^2 - 5],\
[113, 113, 2*w^2 - 2*w - 5],\
[127, 127, -2*w^3 + 5*w^2 + 3*w - 5],\
[137, 137, w^3 - 2*w^2 - 5*w + 5],\
[137, 137, -w^3 + w^2 + 5*w - 1],\
[151, 151, 3*w^3 - 6*w^2 - 9*w + 5],\
[151, 151, -2*w^3 + 4*w^2 + 5*w - 4],\
[157, 157, -w^3 + 4*w^2 - w - 8],\
[163, 163, 2*w^3 - 5*w^2 - 5*w + 5],\
[163, 163, w^3 - 4*w^2 - w + 11],\
[167, 167, 2*w^3 - 3*w^2 - 6*w - 1],\
[167, 167, w^3 - 2*w^2 - w - 4],\
[169, 13, 3*w^3 - 8*w^2 - 6*w + 10],\
[173, 173, -2*w^3 + 7*w^2 - 8],\
[181, 181, -w^3 + w^2 + 4*w - 2],\
[181, 181, w^2 - 5],\
[197, 197, w^3 - 2*w^2 - w - 2],\
[211, 211, 2*w^3 - 3*w^2 - 9*w + 1],\
[211, 211, w^3 - 7*w - 2],\
[227, 227, -w^2 + w + 7],\
[229, 229, w^3 - 2*w^2 - 5*w + 4],\
[229, 229, w^3 - w^2 - 5*w - 5],\
[229, 229, -2*w^3 + 6*w^2 + 5*w - 8],\
[229, 229, -w^3 + 3*w^2 + 4*w - 8],\
[233, 233, -w^3 + 5*w^2 - 3*w - 7],\
[239, 239, w^2 - 4*w - 1],\
[241, 241, -w^3 + 3*w^2 - 2*w - 4],\
[251, 251, -w^3 + 2*w^2 + 5*w - 2],\
[263, 263, -w^3 + 4*w^2 - w - 10],\
[263, 263, 3*w^3 - 7*w^2 - 7*w + 5],\
[271, 271, -w^2 + 7],\
[283, 283, 3*w - 1],\
[293, 293, w - 5],\
[311, 311, -w - 4],\
[311, 311, w^3 - 5*w - 1],\
[313, 313, 2*w^3 - 6*w^2 - 2*w + 11],\
[313, 313, 2*w^3 - 5*w^2 - 5*w + 4],\
[317, 317, 2*w^2 - 3*w - 10],\
[317, 317, -w^3 + 3*w^2 - w - 5],\
[317, 317, -2*w^3 + 4*w^2 + 3*w - 2],\
[317, 317, -3*w^3 + 8*w^2 + 4*w - 4],\
[337, 337, -w^3 + 4*w^2 - 4*w - 1],\
[343, 7, 2*w^3 - 7*w^2 - w + 11],\
[347, 347, -w^3 + w^2 + 5*w - 4],\
[353, 353, 5*w^3 - 13*w^2 - 10*w + 19],\
[353, 353, -2*w^3 + 6*w^2 + 4*w - 7],\
[379, 379, 2*w^3 - 6*w^2 - 5*w + 13],\
[379, 379, -w^3 + 5*w^2 - 2*w - 10],\
[383, 383, w^3 - w^2 - 6*w + 4],\
[383, 383, w^2 + w - 5],\
[389, 389, 3*w^2 - 5*w - 8],\
[389, 389, -2*w^3 + 7*w^2 + w - 10],\
[397, 397, -2*w^3 + 7*w^2 + 2*w - 10],\
[401, 401, 2*w^2 - w - 7],\
[401, 401, -3*w^3 + 6*w^2 + 9*w - 8],\
[409, 409, 3*w^2 - 5*w - 7],\
[421, 421, 3*w^3 - 9*w^2 - 4*w + 17],\
[449, 449, 2*w^3 - 2*w^2 - 11*w - 2],\
[449, 449, 3*w^3 - 7*w^2 - 6*w + 5],\
[457, 457, w^3 - 2*w^2 - 2],\
[457, 457, -2*w^3 + 6*w^2 + 3*w - 5],\
[461, 461, 4*w^3 - 8*w^2 - 12*w + 7],\
[461, 461, -4*w^3 + 10*w^2 + 7*w - 14],\
[461, 461, 4*w^3 - 10*w^2 - 8*w + 11],\
[461, 461, 2*w^3 - 7*w^2 - 2*w + 7],\
[467, 467, -w^3 + 5*w^2 - 7],\
[479, 479, w^3 - 6*w - 1],\
[479, 479, -w^3 + 2*w^2 + 2*w + 4],\
[487, 487, 2*w^3 - 7*w^2 - 2*w + 11],\
[491, 491, 3*w^2 - 6*w - 10],\
[499, 499, -2*w^3 + 6*w^2 + 5*w - 14],\
[509, 509, w^3 + w^2 - 9*w - 4],\
[521, 521, 3*w^2 - 7*w - 8],\
[521, 521, 2*w^3 - 7*w^2 - 3*w + 16],\
[523, 523, -2*w^3 + 4*w^2 + 8*w - 5],\
[541, 541, w^3 + w^2 - 8*w - 4],\
[547, 547, -2*w^3 + 3*w^2 + 6*w - 5],\
[563, 563, 2*w^3 - 8*w^2 + w + 8],\
[569, 569, -3*w^3 + 9*w^2 + w - 10],\
[569, 569, -w^3 + w^2 + 7*w - 2],\
[569, 569, -3*w^3 + 8*w^2 + 7*w - 17],\
[569, 569, -4*w^3 + 11*w^2 + 6*w - 11],\
[571, 571, 5*w^3 - 12*w^2 - 12*w + 16],\
[577, 577, -w^3 + 5*w^2 - w - 7],\
[577, 577, -2*w^3 + 5*w^2 + 5*w - 2],\
[593, 593, 3*w^3 - 7*w^2 - 6*w + 8],\
[593, 593, -3*w^2 + 3*w + 11],\
[601, 601, -2*w^3 + 5*w^2 + 7*w - 8],\
[601, 601, w^3 - 3*w^2 - 3*w + 11],\
[607, 607, -w^3 + 3*w^2 + 4*w - 10],\
[613, 613, 3*w^2 - 8*w - 4],\
[613, 613, -3*w^3 + 5*w^2 + 12*w - 5],\
[619, 619, 2*w^3 - 7*w^2 - 3*w + 17],\
[625, 5, -5],\
[643, 643, 2*w^3 - 8*w^2 + 2*w + 11],\
[643, 643, -w^3 + 4*w^2 - 2*w - 8],\
[643, 643, -3*w^3 + 6*w^2 + 8*w - 5],\
[643, 643, -w^2 + w + 8],\
[653, 653, 3*w^3 - 6*w^2 - 8*w + 4],\
[653, 653, -3*w^3 + 7*w^2 + 6*w - 7],\
[653, 653, 3*w^3 - 9*w^2 - 3*w + 14],\
[653, 653, 2*w^3 - w^2 - 13*w - 5],\
[677, 677, -3*w^3 + 6*w^2 + 11*w - 7],\
[683, 683, w^3 - w^2 - 7*w + 1],\
[683, 683, -w^3 + 2*w^2 + 6*w - 1],\
[701, 701, -w^3 + 5*w^2 - w - 8],\
[727, 727, w^3 - w^2 - 2*w - 4],\
[739, 739, -2*w^3 + 3*w^2 + 10*w - 4],\
[757, 757, 3*w^3 - 7*w^2 - 5*w + 8],\
[757, 757, w^3 + 2*w^2 - 9*w - 8],\
[773, 773, -3*w^3 + 7*w^2 + 5*w - 4],\
[787, 787, -w^3 + 4*w^2 + 2*w - 11],\
[787, 787, -w^3 + 2*w^2 + 2*w - 7],\
[787, 787, -3*w^3 + 8*w^2 + 6*w - 8],\
[787, 787, w^3 - 3*w^2 - 5*w + 5],\
[821, 821, 5*w^3 - 14*w^2 - 7*w + 20],\
[821, 821, -w^3 + 5*w^2 - 14],\
[823, 823, -2*w^3 + 3*w^2 + 8*w - 4],\
[827, 827, w^3 - 3*w^2 - w - 2],\
[839, 839, 2*w^3 - 4*w^2 - 3*w - 2],\
[859, 859, w^3 - 2*w^2 - 3*w - 4],\
[877, 877, -w^3 + 2*w^2 + 6*w - 2],\
[881, 881, w^3 + 2*w^2 - 8*w - 5],\
[883, 883, -3*w^3 + 5*w^2 + 10*w - 5],\
[887, 887, 4*w^3 - 8*w^2 - 13*w + 10],\
[887, 887, -w^3 + 4*w^2 - 3*w - 7],\
[911, 911, -3*w^3 + 6*w^2 + 7*w - 2],\
[929, 929, 2*w^3 - 3*w^2 - 5*w + 8],\
[937, 937, w^3 - 2*w^2 - 4*w - 4],\
[941, 941, -w^3 + 6*w^2 - 4*w - 17],\
[941, 941, 3*w^3 - 10*w^2 - 3*w + 17],\
[947, 947, -2*w^3 + 7*w^2 - 13],\
[947, 947, -w^3 + 4*w^2 + 3*w - 10],\
[953, 953, -3*w^3 + 5*w^2 + 9*w - 1],\
[953, 953, 4*w^3 - 12*w^2 - 5*w + 20],\
[967, 967, 4*w^3 - 11*w^2 - 4*w + 10],\
[971, 971, w^3 - 2*w^2 - 4],\
[983, 983, 5*w^3 - 15*w^2 - 8*w + 25],\
[991, 991, -w^2 + 2*w - 4],\
[997, 997, -w^3 + 4*w^2 - 2*w - 10]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^11 - 3*x^10 - 18*x^9 + 51*x^8 + 117*x^7 - 291*x^6 - 358*x^5 + 634*x^4 + 556*x^3 - 352*x^2 - 390*x - 82
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 1/29*e^10 - 23/29*e^9 + 7/29*e^8 + 433/29*e^7 - 220/29*e^6 - 2764/29*e^5 + 924/29*e^4 + 6833/29*e^3 - 384/29*e^2 - 4707/29*e - 1428/29, 26/1421*e^10 + 127/1421*e^9 - 17/29*e^8 - 1908/1421*e^7 + 7127/1421*e^6 + 1255/203*e^5 - 18142/1421*e^4 - 15830/1421*e^3 + 2776/1421*e^2 + 1835/203*e + 8228/1421, 445/1421*e^10 - 2144/1421*e^9 - 127/29*e^8 + 36317/1421*e^7 + 25408/1421*e^6 - 29278/203*e^5 - 31882/1421*e^4 + 442952/1421*e^3 + 26088/1421*e^2 - 37746/203*e - 77790/1421, 88/1421*e^10 - 226/1421*e^9 - 33/29*e^8 + 4145/1421*e^7 + 9147/1421*e^6 - 3560/203*e^5 - 13199/1421*e^4 + 49608/1421*e^3 - 14652/1421*e^2 - 1066/203*e + 7736/1421, -1195/1421*e^10 + 3618/1421*e^9 + 401/29*e^8 - 58887/1421*e^7 - 106821/1421*e^6 + 45372/203*e^5 + 230893/1421*e^4 - 651564/1421*e^3 - 201044/1421*e^2 + 52912/203*e + 142461/1421, 450/1421*e^10 - 316/1421*e^9 - 176/29*e^8 + 2174/1421*e^7 + 56237/1421*e^6 + 1468/203*e^5 - 144132/1421*e^4 - 84004/1421*e^3 + 102700/1421*e^2 + 14286/203*e + 21732/1421, 877/1421*e^10 - 2220/1421*e^9 - 318/29*e^8 + 36642/1421*e^7 + 93435/1421*e^6 - 28632/203*e^5 - 220950/1421*e^4 + 409258/1421*e^3 + 181520/1421*e^2 - 30836/203*e - 91486/1421, 97/1421*e^10 - 1767/1421*e^9 + 18/29*e^8 + 31358/1421*e^7 - 25168/1421*e^6 - 26900/203*e^5 + 113002/1421*e^4 + 443648/1421*e^3 - 103542/1421*e^2 - 42850/203*e - 71178/1421, -1, 547/1421*e^10 - 2083/1421*e^9 - 158/29*e^8 + 33532/1421*e^7 + 31069/1421*e^6 - 25432/203*e^5 - 31130/1421*e^4 + 359644/1421*e^3 - 842/1421*e^2 - 28564/203*e - 49446/1421, 94/203*e^10 - 103/203*e^9 - 254/29*e^8 + 1175/203*e^7 + 11510/203*e^6 - 386/29*e^5 - 29550/203*e^4 - 4108/203*e^3 + 21904/203*e^2 + 1238/29*e + 1546/203, 332/1421*e^10 - 1111/1421*e^9 - 110/29*e^8 + 18157/1421*e^7 + 28373/1421*e^6 - 13800/203*e^5 - 52832/1421*e^4 + 186124/1421*e^3 + 18614/1421*e^2 - 11422/203*e - 23262/1421, -75/1421*e^10 - 421/1421*e^9 + 39/29*e^8 + 9111/1421*e^7 - 14820/1421*e^6 - 9718/203*e^5 + 35390/1421*e^4 + 202520/1421*e^3 + 16040/1421*e^2 - 26132/203*e - 68988/1421, -985/1421*e^10 + 2239/1421*e^9 + 373/29*e^8 - 37789/1421*e^7 - 115060/1421*e^6 + 30399/203*e^5 + 283848/1421*e^4 - 445596/1421*e^3 - 234588/1421*e^2 + 33879/203*e + 114804/1421, 330/1421*e^10 - 137/1421*e^9 - 160/29*e^8 + 3110/1421*e^7 + 62366/1421*e^6 - 3200/203*e^5 - 189820/1421*e^4 + 49614/1421*e^3 + 182362/1421*e^2 - 2678/203*e - 36356/1421, -811/1421*e^10 + 4182/1421*e^9 + 228/29*e^8 - 71545/1421*e^7 - 47142/1421*e^6 + 58848/203*e^5 + 90621/1421*e^4 - 929084/1421*e^3 - 182562/1421*e^2 + 88602/203*e + 233704/1421, -185/1421*e^10 - 849/1421*e^9 + 102/29*e^8 + 17074/1421*e^7 - 42240/1421*e^6 - 16636/203*e^5 + 128978/1421*e^4 + 311030/1421*e^3 - 93535/1421*e^2 - 34036/203*e - 55922/1421, -48/29*e^10 + 118/29*e^9 + 824/29*e^8 - 1847/29*e^7 - 4723/29*e^6 + 9364/29*e^5 + 10574/29*e^4 - 17220/29*e^3 - 7726/29*e^2 + 7624/29*e + 3004/29, 13/1421*e^10 - 647/1421*e^9 + 6/29*e^8 + 13256/1421*e^7 - 7094/1421*e^6 - 12872/203*e^5 + 40664/1421*e^4 + 223708/1421*e^3 - 59715/1421*e^2 - 19078/203*e - 29990/1421, 1020/1421*e^10 - 2232/1421*e^9 - 368/29*e^8 + 34674/1421*e^7 + 109187/1421*e^6 - 25282/203*e^5 - 276680/1421*e^4 + 340666/1421*e^3 + 279206/1421*e^2 - 25514/203*e - 111598/1421, -955/1421*e^10 + 1839/1421*e^9 + 369/29*e^8 - 29497/1421*e^7 - 117658/1421*e^6 + 22228/203*e^5 + 306638/1421*e^4 - 304928/1421*e^3 - 266582/1421*e^2 + 23098/203*e + 81012/1421, -136/1421*e^10 + 2287/1421*e^9 - 7/29*e^8 - 41285/1421*e^7 + 20872/1421*e^6 + 36081/203*e^5 - 84368/1421*e^4 - 607475/1421*e^3 + 14118/1421*e^2 + 60905/203*e + 135570/1421, 93/203*e^10 + 181/203*e^9 - 313/29*e^8 - 4014/203*e^7 + 17240/203*e^6 + 4218/29*e^5 - 52166/203*e^4 - 83122/203*e^3 + 43690/203*e^2 + 9235/29*e + 13066/203, 1142/1421*e^10 - 1964/1421*e^9 - 421/29*e^8 + 27470/1421*e^7 + 125905/1421*e^6 - 16192/203*e^5 - 298628/1421*e^4 + 130408/1421*e^3 + 194948/1421*e^2 + 2194/203*e - 6312/1421, 1142/1421*e^10 - 3385/1421*e^9 - 392/29*e^8 + 55890/1421*e^7 + 107432/1421*e^6 - 43800/203*e^5 - 236104/1421*e^4 + 633442/1421*e^3 + 192106/1421*e^2 - 48150/203*e - 122834/1421, -1416/1421*e^10 + 6091/1421*e^9 + 444/29*e^8 - 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39/1421*e^9 - 351/29*e^8 - 3554/1421*e^7 + 122244/1421*e^6 + 6929/203*e^5 - 336722/1421*e^4 - 185978/1421*e^3 + 261350/1421*e^2 + 26533/203*e + 31264/1421, 1440/1421*e^10 - 3569/1421*e^9 - 511/29*e^8 + 56976/1421*e^7 + 146707/1421*e^6 - 42642/203*e^5 - 344132/1421*e^4 + 582082/1421*e^3 + 288852/1421*e^2 - 43686/203*e - 118598/1421, -1340/1421*e^10 + 4604/1421*e^9 + 430/29*e^8 - 74808/1421*e^7 - 108474/1421*e^6 + 57494/203*e^5 + 227790/1421*e^4 - 833162/1421*e^3 - 228768/1421*e^2 + 72168/203*e + 202056/1421, 995/1421*e^10 - 1425/1421*e^9 - 384/29*e^8 + 19238/1421*e^7 + 122720/1421*e^6 - 10522/203*e^5 - 323618/1421*e^4 + 68080/1421*e^3 + 275553/1421*e^2 + 1774/203*e - 37966/1421, 316/1421*e^10 - 1845/1421*e^9 - 104/29*e^8 + 34197/1421*e^7 + 28906/1421*e^6 - 30500/203*e^5 - 77302/1421*e^4 + 509360/1421*e^3 + 130695/1421*e^2 - 47842/203*e - 142224/1421, 2481/1421*e^10 - 4660/1421*e^9 - 905/29*e^8 + 68466/1421*e^7 + 266296/1421*e^6 - 44635/203*e^5 - 620490/1421*e^4 + 466173/1421*e^3 + 426014/1421*e^2 - 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128806/203*e^4 + 410818/203*e^3 + 92038/203*e^2 - 32878/29*e - 75756/203, -297/1421*e^10 + 3960/1421*e^9 - 1/29*e^8 - 69586/1421*e^7 + 42488/1421*e^6 + 58096/203*e^5 - 231305/1421*e^4 - 896400/1421*e^3 + 295994/1421*e^2 + 69928/203*e + 57730/1421, 2125/1421*e^10 - 7492/1421*e^9 - 670/29*e^8 + 122683/1421*e^7 + 164120/1421*e^6 - 95673/203*e^5 - 338636/1421*e^4 + 1412879/1421*e^3 + 380134/1421*e^2 - 121193/203*e - 338834/1421, 2948/1421*e^10 - 7571/1421*e^9 - 1033/29*e^8 + 121095/1421*e^7 + 290083/1421*e^6 - 90840/203*e^5 - 646080/1421*e^4 + 1238410/1421*e^3 + 458386/1421*e^2 - 86258/203*e - 198406/1421, 1277/1421*e^10 - 922/1421*e^9 - 468/29*e^8 + 2260/1421*e^7 + 138371/1421*e^6 + 11694/203*e^5 - 322542/1421*e^4 - 413174/1421*e^3 + 160392/1421*e^2 + 56296/203*e + 142876/1421, -2000/1421*e^10 + 2036/1421*e^9 + 750/29*e^8 - 18504/1421*e^7 - 230364/1421*e^6 - 1066/203*e^5 + 576168/1421*e^4 + 298196/1421*e^3 - 408762/1421*e^2 - 50772/203*e - 86166/1421, -4/7*e^10 + 9/7*e^9 + 10*e^8 - 141/7*e^7 - 425/7*e^6 + 106*e^5 + 1152/7*e^4 - 1553/7*e^3 - 1490/7*e^2 + 143*e + 776/7, 538/1421*e^10 - 3384/1421*e^9 - 180/29*e^8 + 64580/1421*e^7 + 49753/1421*e^6 - 59338/203*e^5 - 121806/1421*e^4 + 1014302/1421*e^3 + 183255/1421*e^2 - 94776/203*e - 234838/1421, -531/1421*e^10 + 2817/1421*e^9 + 123/29*e^8 - 43888/1421*e^7 - 13129/1421*e^6 + 31170/203*e^5 - 18292/1421*e^4 - 398680/1421*e^3 + 26598/1421*e^2 + 28241/203*e + 31992/1421, -893/203*e^10 + 2907/203*e^9 + 2094/29*e^8 - 48616/203*e^7 - 78895/203*e^6 + 38728/29*e^5 + 164000/203*e^4 - 575252/203*e^3 - 134196/203*e^2 + 47602/29*e + 120308/203, -2004/1421*e^10 + 9668/1421*e^9 + 592/29*e^8 - 167962/1421*e^7 - 128274/1421*e^6 + 140310/203*e^5 + 211248/1421*e^4 - 2220004/1421*e^3 - 274522/1421*e^2 + 200572/203*e + 481624/1421, 1084/1421*e^10 + 2125/1421*e^9 - 537/29*e^8 - 45117/1421*e^7 + 210788/1421*e^6 + 45984/203*e^5 - 636362/1421*e^4 - 898280/1421*e^3 + 515804/1421*e^2 + 103926/203*e + 119838/1421, -72/203*e^10 + 1163/203*e^9 + 15/29*e^8 - 21606/203*e^7 + 7575/203*e^6 + 19419/29*e^5 - 35614/203*e^4 - 331635/203*e^3 + 11176/203*e^2 + 32063/29*e + 68596/203, 9/49*e^10 - 120/49*e^9 + e^8 + 1880/49*e^7 - 1779/49*e^6 - 1332/7*e^5 + 7964/49*e^4 + 16740/49*e^3 - 8922/49*e^2 - 1072/7*e + 270/49, 582/203*e^10 - 1670/203*e^9 - 1390/29*e^8 + 26763/203*e^7 + 54225/203*e^6 - 20054/29*e^5 - 119575/203*e^4 + 273796/203*e^3 + 95338/203*e^2 - 20054/29*e - 55172/203, -2418/1421*e^10 + 3820/1421*e^9 + 914/29*e^8 - 54179/1421*e^7 - 284825/1421*e^6 + 33708/203*e^5 + 737978/1421*e^4 - 342427/1421*e^3 - 661732/1421*e^2 + 19759/203*e + 147078/1421, -419/203*e^10 + 1459/203*e^9 + 973/29*e^8 - 24421/203*e^7 - 37160/203*e^6 + 19513/29*e^5 + 86008/203*e^4 - 294149/203*e^3 - 97204/203*e^2 + 25719/29*e + 72620/203, 1438/1421*e^10 - 1174/1421*e^9 - 532/29*e^8 + 6404/1421*e^7 + 162227/1421*e^6 + 7746/203*e^5 - 418596/1421*e^4 - 321768/1421*e^3 + 353130/1421*e^2 + 39762/203*e + 47354/1421, -52/1421*e^10 - 3096/1421*e^9 + 121/29*e^8 + 54972/1421*e^7 - 69673/1421*e^6 - 47170/203*e^5 + 235224/1421*e^4 + 793316/1421*e^3 - 144810/1421*e^2 - 84464/203*e - 132978/1421, 5729/1421*e^10 - 17652/1421*e^9 - 1949/29*e^8 + 292375/1421*e^7 + 527557/1421*e^6 - 229771/203*e^5 - 1143824/1421*e^4 + 3345728/1421*e^3 + 950972/1421*e^2 - 266369/203*e - 692980/1421, 219/203*e^10 - 1296/203*e^9 - 390/29*e^8 + 22124/203*e^7 + 8805/203*e^6 - 18100/29*e^5 - 8010/203*e^4 + 284546/203*e^3 + 27786/203*e^2 - 27438/29*e - 64956/203, -5450/1421*e^10 + 15353/1421*e^9 + 1906/29*e^8 - 253058/1421*e^7 - 532677/1421*e^6 + 197040/203*e^5 + 1172462/1421*e^4 - 2806845/1421*e^3 - 864562/1421*e^2 + 210989/203*e + 523088/1421, -2092/1421*e^10 + 7052/1421*e^9 + 741/29*e^8 - 122372/1421*e^7 - 215576/1421*e^6 + 101646/203*e^5 + 529962/1421*e^4 - 1576164/1421*e^3 - 558280/1421*e^2 + 137490/203*e + 408522/1421, 3481/1421*e^10 - 12783/1421*e^9 - 1106/29*e^8 + 211292/1421*e^7 + 273482/1421*e^6 - 165699/203*e^5 - 550482/1421*e^4 + 2440049/1421*e^3 + 535188/1421*e^2 - 206473/203*e - 510030/1421, 598/1421*e^10 + 79/1421*e^9 - 275/29*e^8 - 4096/1421*e^7 + 105660/1421*e^6 + 5926/203*e^5 - 340532/1421*e^4 - 131046/1421*e^3 + 387836/1421*e^2 + 9116/203*e - 77904/1421, -4995/1421*e^10 + 18286/1421*e^9 + 1594/29*e^8 - 304921/1421*e^7 - 393034/1421*e^6 + 242246/203*e^5 + 761191/1421*e^4 - 3621008/1421*e^3 - 673882/1421*e^2 + 310802/203*e + 766548/1421, 3415/1421*e^10 - 7640/1421*e^9 - 1190/29*e^8 + 114042/1421*e^7 + 328080/1421*e^6 - 75942/203*e^5 - 688722/1421*e^4 + 826954/1421*e^3 + 345816/1421*e^2 - 31398/203*e - 29850/1421, 1523/1421*e^10 + 1482/1421*e^9 - 698/29*e^8 - 35468/1421*e^7 + 252915/1421*e^6 + 39980/203*e^5 - 678486/1421*e^4 - 876226/1421*e^3 + 362424/1421*e^2 + 121644/203*e + 247178/1421, -2490/1421*e^10 + 7622/1421*e^9 + 912/29*e^8 - 135467/1421*e^7 - 268927/1421*e^6 + 115680/203*e^5 + 617916/1421*e^4 - 1822230/1421*e^3 - 476382/1421*e^2 + 153061/203*e + 369142/1421, -4818/1421*e^10 + 11663/1421*e^9 + 1698/29*e^8 - 183243/1421*e^7 - 484812/1421*e^6 + 134822/203*e^5 + 1142906/1421*e^4 - 1820808/1421*e^3 - 989684/1421*e^2 + 133981/203*e + 394950/1421, -772/1421*e^10 - 2022/1421*e^9 + 391/29*e^8 + 39273/1421*e^7 - 148000/1421*e^6 - 37014/203*e^5 + 384554/1421*e^4 + 694110/1421*e^3 - 127242/1421*e^2 - 81906/203*e - 202990/1421, -2715/1421*e^10 + 4938/1421*e^9 + 913/29*e^8 - 61241/1421*e^7 - 238074/1421*e^6 + 26438/203*e^5 + 456938/1421*e^4 + 24442/1421*e^3 - 115642/1421*e^2 - 50383/203*e - 190230/1421, 401/1421*e^10 + 5074/1421*e^9 - 299/29*e^8 - 98619/1421*e^7 + 139488/1421*e^6 + 93084/203*e^5 - 425294/1421*e^4 - 1684932/1421*e^3 + 152778/1421*e^2 + 176952/203*e + 438428/1421, -7692/1421*e^10 + 20142/1421*e^9 + 2638/29*e^8 - 315999/1421*e^7 - 719632/1421*e^6 + 230124/203*e^5 + 1554370/1421*e^4 - 3021636/1421*e^3 - 1106562/1421*e^2 + 209737/203*e + 535012/1421, 1199/1421*e^10 + 118/1421*e^9 - 504/29*e^8 - 10489/1421*e^7 + 169567/1421*e^6 + 17470/203*e^5 - 427268/1421*e^4 - 456628/1421*e^3 + 203220/1421*e^2 + 64798/203*e + 183558/1421, -2796/1421*e^10 + 8860/1421*e^9 + 976/29*e^8 - 151269/1421*e^7 - 271700/1421*e^6 + 123224/203*e^5 + 587240/1421*e^4 - 1862190/1421*e^3 - 422591/1421*e^2 + 153732/203*e + 355160/1421, 193/1421*e^10 - 3047/1421*e^9 + 40/29*e^8 + 48798/1421*e^7 - 53944/1421*e^6 - 35508/203*e^5 + 265506/1421*e^4 + 456686/1421*e^3 - 395200/1421*e^2 - 28548/203*e + 62826/1421, 2750/1421*e^10 - 4931/1421*e^9 - 995/29*e^8 + 68073/1421*e^7 + 296146/1421*e^6 - 40200/203*e^5 - 742496/1421*e^4 + 372241/1421*e^3 + 654768/1421*e^2 - 17783/203*e - 139078/1421, 634/1421*e^10 - 1822/1421*e^9 - 187/29*e^8 + 23759/1421*e^7 + 42292/1421*e^6 - 11715/203*e^5 - 82982/1421*e^4 + 49692/1421*e^3 + 63538/1421*e^2 + 4583/203*e + 15688/1421, -3193/1421*e^10 + 10364/1421*e^9 + 1056/29*e^8 - 171761/1421*e^7 - 271708/1421*e^6 + 135206/203*e^5 + 536222/1421*e^4 - 1980319/1421*e^3 - 392726/1421*e^2 + 162495/203*e + 374904/1421, 2867/1421*e^10 - 5070/1421*e^9 - 1057/29*e^8 + 72276/1421*e^7 + 313297/1421*e^6 - 43586/203*e^5 - 711876/1421*e^4 + 346478/1421*e^3 + 368850/1421*e^2 + 14936/203*e + 25838/1421, -5192/1421*e^10 + 10492/1421*e^9 + 1889/29*e^8 - 159295/1421*e^7 - 552462/1421*e^6 + 109758/203*e^5 + 1260460/1421*e^4 - 1272828/1421*e^3 - 792418/1421*e^2 + 55180/203*e + 151764/1421, -2433/1421*e^10 - 243/1421*e^9 + 1032/29*e^8 + 21251/1421*e^7 - 354576/1421*e^6 - 34982/203*e^5 + 946838/1421*e^4 + 888875/1421*e^3 - 630104/1421*e^2 - 118473/203*e - 199802/1421, 5780/1421*e^10 - 14069/1421*e^9 - 2095/29*e^8 + 227748/1421*e^7 + 620621/1421*e^6 - 173850/203*e^5 - 1524276/1421*e^4 + 2437264/1421*e^3 + 1399332/1421*e^2 - 187886/203*e - 621968/1421, -4177/1421*e^10 + 14958/1421*e^9 + 1367/29*e^8 - 251051/1421*e^7 - 354740/1421*e^6 + 201108/203*e^5 + 766358/1421*e^4 - 3031214/1421*e^3 - 797290/1421*e^2 + 262646/203*e + 719352/1421, -5806/1421*e^10 + 15363/1421*e^9 + 1996/29*e^8 - 244313/1421*e^7 - 545330/1421*e^6 + 181730/203*e^5 + 1181484/1421*e^4 - 2455538/1421*e^3 - 867812/1421*e^2 + 173262/203*e + 403432/1421, 5881/1421*e^10 - 17784/1421*e^9 - 1977/29*e^8 + 289200/1421*e^7 + 523204/1421*e^6 - 221341/203*e^5 - 1077616/1421*e^4 + 3109881/1421*e^3 + 760828/1421*e^2 - 235435/203*e - 522016/1421, -1332/1421*e^10 + 10655/1421*e^9 + 282/29*e^8 - 189403/1421*e^7 - 14244/1421*e^6 + 161660/203*e^5 - 113804/1421*e^4 - 2609036/1421*e^3 - 39686/1421*e^2 + 241004/203*e + 578420/1421, -1371/1421*e^10 - 4456/1421*e^9 + 699/29*e^8 + 91975/1421*e^7 - 270057/1421*e^6 - 92450/203*e^5 + 736168/1421*e^4 + 1812704/1421*e^3 - 282578/1421*e^2 - 217382/203*e - 505356/1421, -246/1421*e^10 - 8088/1421*e^9 + 317/29*e^8 + 155671/1421*e^7 - 175647/1421*e^6 - 145417/203*e^5 + 620250/1421*e^4 + 2580342/1421*e^3 - 420866/1421*e^2 - 257995/203*e - 493656/1421, 46/29*e^10 - 159/29*e^9 - 780/29*e^8 + 2779/29*e^7 + 4467/29*e^6 - 16422/29*e^5 - 10624/29*e^4 + 37426/29*e^3 + 11916/29*e^2 - 23904/29*e - 10240/29, 132/1421*e^10 - 1760/1421*e^9 - 35/29*e^8 + 33927/1421*e^7 + 11589/1421*e^6 - 31730/203*e^5 - 73086/1421*e^4 + 571762/1421*e^3 + 239486/1421*e^2 - 63108/203*e - 198704/1421, -2530/1421*e^10 + 8629/1421*e^9 + 898/29*e^8 - 150786/1421*e^7 - 265463/1421*e^6 + 127116/203*e^5 + 691736/1421*e^4 - 2025892/1421*e^3 - 824972/1421*e^2 + 187871/203*e + 550614/1421, 1497/1421*e^10 - 1487/1421*e^9 - 594/29*e^8 + 17596/1421*e^7 + 191790/1421*e^6 - 6138/203*e^5 - 486982/1421*e^4 - 70320/1421*e^3 + 336912/1421*e^2 + 22572/203*e - 2620/1421, -907/1421*e^10 + 8304/1421*e^9 + 206/29*e^8 - 157193/1421*e^7 - 21208/1421*e^6 + 145408/203*e^5 - 780/1421*e^4 - 2579114/1421*e^3 - 285942/1421*e^2 + 269586/203*e + 670942/1421, -233/1421*e^10 + 5475/1421*e^9 - 83/29*e^8 - 95379/1421*e^7 + 84407/1421*e^6 + 79627/203*e^5 - 353680/1421*e^4 - 1278483/1421*e^3 + 327968/1421*e^2 + 124461/203*e + 161276/1421, -4266/1421*e^10 + 8566/1421*e^9 + 1549/29*e^8 - 129856/1421*e^7 - 454176/1421*e^6 + 89792/203*e^5 + 1064892/1421*e^4 - 1061628/1421*e^3 - 777498/1421*e^2 + 49250/203*e + 169352/1421, -18/29*e^10 + 66/29*e^9 + 251/29*e^8 - 1008/29*e^7 - 1028/29*e^6 + 4947/29*e^5 + 1464/29*e^4 - 9111/29*e^3 - 1324/29*e^2 + 4947/29*e + 1228/29, -904/1421*e^10 - 1683/1421*e^9 + 426/29*e^8 + 38029/1421*e^7 - 159589/1421*e^6 - 40606/203*e^5 + 454798/1421*e^4 + 814375/1421*e^3 - 301362/1421*e^2 - 94111/203*e - 163438/1421, 7671/1421*e^10 - 22704/1421*e^9 - 2583/29*e^8 + 364761/1421*e^7 + 690757/1421*e^6 - 274728/203*e^5 - 1479379/1421*e^4 + 3800778/1421*e^3 + 1169030/1421*e^2 - 291490/203*e - 767706/1421, 2258/1421*e^10 - 12581/1421*e^9 - 593/29*e^8 + 217421/1421*e^7 + 96899/1421*e^6 - 180814/203*e^5 - 73238/1421*e^4 + 2871392/1421*e^3 + 222284/1421*e^2 - 267640/203*e - 617672/1421]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([31, 31, w^3 - 2*w^2 - 4*w + 2])] = 1

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