/* 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. = PolynomialRing(QQ) g = P([5, -1, -6, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([25, 25, -w^3 + 5*w + 3]) primes_array = [ [5, 5, w],\ [5, 5, -w^2 + w + 2],\ [7, 7, -w^2 + 2],\ [13, 13, -w^2 + 3],\ [13, 13, w^2 - w - 4],\ [16, 2, 2],\ [19, 19, -w^2 + w + 1],\ [23, 23, -w^3 + 4*w + 2],\ [25, 5, -w^3 + w^2 + 3*w - 1],\ [29, 29, w^3 - w^2 - 4*w + 1],\ [29, 29, -w + 3],\ [31, 31, -w^3 + w^2 + 5*w - 2],\ [37, 37, w^3 - 4*w - 1],\ [37, 37, w^3 - 3*w + 1],\ [53, 53, -w^3 + 2*w^2 + 4*w - 6],\ [59, 59, w^2 + w - 4],\ [61, 61, -2*w^2 + w + 8],\ [73, 73, -w^3 + 5*w - 1],\ [79, 79, 2*w^2 + w - 6],\ [79, 79, 2*w^3 - w^2 - 9*w + 3],\ [81, 3, -3],\ [83, 83, -w^3 + w^2 + 3*w - 4],\ [97, 97, -w^3 + 6*w + 2],\ [97, 97, -2*w^3 + w^2 + 10*w - 1],\ [97, 97, 3*w^3 - 4*w^2 - 15*w + 13],\ [97, 97, w^3 - w^2 - 6*w + 2],\ [103, 103, -2*w^3 + 3*w^2 + 11*w - 9],\ [109, 109, w^2 + 3*w - 3],\ [137, 137, -w^2 + 7],\ [149, 149, w^3 - 2*w^2 - 5*w + 4],\ [149, 149, w^3 + 2*w^2 - 6*w - 7],\ [151, 151, w^3 + w^2 - 5*w - 3],\ [163, 163, w^3 - 3*w - 4],\ [163, 163, -w^3 + 6*w - 3],\ [167, 167, w^3 - 2*w^2 - 6*w + 4],\ [169, 13, w^2 + 2*w - 4],\ [191, 191, w^3 - w^2 - 5*w - 2],\ [191, 191, 2*w^3 - 9*w - 2],\ [197, 197, w^3 - 4*w + 4],\ [211, 211, -w^3 + 2*w^2 + 6*w - 8],\ [223, 223, -w^3 + 3*w^2 + 4*w - 6],\ [229, 229, w^3 - w^2 - 5*w - 1],\ [251, 251, 2*w^3 - 2*w^2 - 7*w + 3],\ [257, 257, 3*w^2 - 14],\ [263, 263, w^2 - 3*w - 1],\ [263, 263, w^2 - 2*w - 7],\ [269, 269, -w^3 + w^2 + 2*w - 4],\ [269, 269, 2*w^3 - 11*w - 1],\ [271, 271, -w^3 + w^2 + 4*w - 7],\ [277, 277, w^3 - w^2 - 3*w + 8],\ [311, 311, w^3 + 2*w^2 - 7*w - 11],\ [311, 311, -3*w^2 - 2*w + 8],\ [317, 317, -2*w^3 + 2*w^2 + 7*w - 4],\ [331, 331, w^2 - w - 8],\ [331, 331, 3*w^3 - 2*w^2 - 12*w + 9],\ [337, 337, -2*w^3 + 2*w^2 + 11*w - 8],\ [343, 7, w^3 - 3*w^2 - 4*w + 11],\ [347, 347, -2*w^3 + 2*w^2 + 9*w - 4],\ [349, 349, -w^3 + 2*w^2 + 2*w - 6],\ [353, 353, 2*w^2 - w - 12],\ [353, 353, 2*w^3 - w^2 - 9*w - 1],\ [367, 367, -2*w^3 + w^2 + 10*w - 6],\ [367, 367, 2*w^3 - 11*w - 3],\ [379, 379, -3*w - 1],\ [379, 379, w^3 - 2*w - 3],\ [383, 383, -w^3 + 2*w^2 + 4*w - 11],\ [383, 383, -w^3 - w^2 + 7*w + 4],\ [389, 389, 2*w^3 - w^2 - 11*w + 4],\ [401, 401, w^3 + 2*w^2 - 7*w - 6],\ [401, 401, 2*w^3 - 11*w - 6],\ [419, 419, -2*w^3 + w^2 + 8*w - 1],\ [421, 421, -w^3 + 3*w^2 + 3*w - 12],\ [421, 421, -w^3 - 2*w^2 + 2*w + 6],\ [433, 433, w^3 - 2*w^2 - 6*w + 11],\ [433, 433, w^2 - 8],\ [439, 439, -w^3 + 3*w^2 + 3*w - 7],\ [443, 443, w^3 - w^2 - 2*w - 4],\ [443, 443, 2*w^3 + w^2 - 7*w - 2],\ [443, 443, 2*w^3 - w^2 - 8*w + 2],\ [443, 443, -w^2 - 2],\ [467, 467, 3*w^3 - 5*w^2 - 15*w + 19],\ [467, 467, 2*w^3 - 3*w^2 - 8*w + 13],\ [467, 467, -w^3 + 2*w^2 + 3*w - 9],\ [467, 467, -w^3 + 3*w^2 + 3*w - 8],\ [479, 479, -w^3 - 3*w^2 + 5*w + 13],\ [479, 479, -w^3 + w^2 + w - 4],\ [487, 487, 3*w^3 - w^2 - 13*w - 2],\ [491, 491, w^2 + w - 9],\ [499, 499, -3*w^3 + 3*w^2 + 13*w - 7],\ [503, 503, 2*w^2 + w - 9],\ [509, 509, -2*w^2 - 3*w + 6],\ [509, 509, -w^3 + w^2 - 4],\ [521, 521, -3*w^2 + w + 12],\ [523, 523, 2*w^3 - 8*w - 3],\ [529, 23, 2*w^3 - w^2 - 6*w - 1],\ [541, 541, -w^3 + w^2 + 7*w - 4],\ [547, 547, 2*w^3 - 3*w^2 - 9*w + 7],\ [557, 557, 3*w^2 - 2*w - 9],\ [557, 557, w^3 - 6*w - 7],\ [563, 563, -2*w^3 + w^2 + 6*w - 6],\ [577, 577, -w^3 + 4*w^2 + 2*w - 13],\ [587, 587, w^2 - 2*w + 3],\ [587, 587, w^2 + 2*w - 6],\ [593, 593, -2*w^3 + 2*w^2 + 11*w - 3],\ [599, 599, w^3 + 3*w^2 - 6*w - 12],\ [601, 601, -2*w^3 + w^2 + 9*w + 2],\ [607, 607, -w^3 + 3*w^2 + 4*w - 9],\ [617, 617, -2*w^3 + w^2 + 7*w - 3],\ [619, 619, -2*w^3 + 4*w^2 + 9*w - 11],\ [631, 631, 3*w^2 - w - 7],\ [631, 631, -w^3 - w^2 + 6*w + 1],\ [641, 641, -w^3 + 2*w^2 + 5*w - 1],\ [641, 641, -w^3 + 2*w^2 + 2*w - 7],\ [643, 643, -3*w^3 + w^2 + 14*w - 4],\ [647, 647, -3*w^3 + 5*w^2 + 14*w - 18],\ [647, 647, -w^3 + 7*w + 2],\ [647, 647, -2*w^3 + 7*w - 1],\ [647, 647, 2*w^3 - w^2 - 10*w - 1],\ [653, 653, -2*w^3 - w^2 + 11*w + 4],\ [659, 659, -w^3 - w^2 + 5*w - 1],\ [673, 673, -w^3 + w^2 + 7*w - 2],\ [673, 673, -w^3 + w^2 + 2*w - 8],\ [683, 683, 2*w^3 - 11*w - 8],\ [683, 683, 2*w^3 - 7*w - 3],\ [701, 701, 2*w^3 - 4*w^2 - 10*w + 17],\ [727, 727, -w^3 + w^2 + 4*w - 8],\ [727, 727, 3*w^2 - 11],\ [739, 739, 2*w^3 + 3*w^2 - 8*w - 13],\ [743, 743, 2*w^2 + w - 12],\ [743, 743, 3*w^2 - 2*w - 14],\ [751, 751, w^3 + w^2 - 3*w - 7],\ [757, 757, -2*w^3 + 10*w - 1],\ [761, 761, -2*w^3 + w^2 + 7*w - 1],\ [761, 761, 3*w^2 + w - 7],\ [773, 773, -2*w^3 + 2*w^2 + 8*w - 1],\ [797, 797, -2*w^3 + w^2 + 9*w + 3],\ [797, 797, 3*w^3 - 14*w - 8],\ [809, 809, 5*w^3 - 5*w^2 - 24*w + 16],\ [821, 821, -4*w^3 + 3*w^2 + 18*w - 9],\ [821, 821, w^3 - w - 3],\ [823, 823, 3*w^2 + w - 8],\ [829, 829, -2*w^3 + 3*w^2 + 10*w - 7],\ [829, 829, 3*w^2 - 2*w - 16],\ [841, 29, 2*w^2 + w - 11],\ [853, 853, 3*w^3 - 2*w^2 - 14*w + 3],\ [853, 853, 3*w^3 - 5*w^2 - 14*w + 17],\ [857, 857, 3*w^2 - w - 8],\ [857, 857, 3*w^3 - w^2 - 13*w + 3],\ [859, 859, w^3 - 3*w^2 - 6*w + 12],\ [877, 877, w^3 + 2*w^2 - 5*w - 4],\ [877, 877, w^2 - w - 9],\ [881, 881, w^3 + 2*w^2 - 4*w - 12],\ [881, 881, w^2 - 4*w - 4],\ [883, 883, -3*w^3 + 2*w^2 + 11*w - 8],\ [887, 887, -2*w^3 + w^2 + 6*w - 1],\ [911, 911, 3*w^2 - w - 17],\ [911, 911, 2*w^3 - 2*w^2 - 12*w + 3],\ [919, 919, 5*w^3 - 6*w^2 - 22*w + 24],\ [919, 919, -2*w^3 + w^2 + 6*w - 7],\ [929, 929, 2*w^3 - 7*w - 1],\ [937, 937, -w^3 - w^2 + 8*w - 2],\ [947, 947, 3*w^3 + w^2 - 15*w - 6],\ [947, 947, -2*w^3 + 9*w + 9],\ [953, 953, w^3 - 2*w^2 - 6*w + 1],\ [977, 977, w^3 - w^2 - 3*w + 9],\ [977, 977, w^3 + w^2 - 3*w - 8],\ [983, 983, w^3 - 5*w - 7],\ [991, 991, -w^3 + 2*w^2 + 2*w - 8],\ [991, 991, w^2 + 4*w - 1],\ [997, 997, 2*w^3 + w^2 - 12*w - 8]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^8 - 19*x^6 + 84*x^4 - 116*x^2 + 36 K. = NumberField(heckePol) hecke_eigenvalues_array = [3/17*e^6 - 49/17*e^4 + 127/17*e^2 - 49/17, 0, e, -3/34*e^6 + 49/34*e^4 - 72/17*e^2 + 67/17, 23/102*e^7 - 202/51*e^5 + 453/34*e^3 - 389/51*e, -4/51*e^7 + 125/102*e^5 - 77/34*e^3 - 133/51*e, -5/102*e^7 + 59/102*e^5 + 28/17*e^3 - 421/51*e, -4/17*e^6 + 71/17*e^4 - 243/17*e^2 + 88/17, -2/17*e^7 + 71/34*e^5 - 243/34*e^3 + 44/17*e, 1/17*e^6 - 22/17*e^4 + 116/17*e^2 - 124/17, -3/34*e^6 + 49/34*e^4 - 55/17*e^2 - 69/17, 3/34*e^7 - 49/34*e^5 + 55/17*e^3 + 35/17*e, -8/51*e^7 + 301/102*e^5 - 443/34*e^3 + 1009/51*e, -7/34*e^6 + 137/34*e^4 - 321/17*e^2 + 281/17, -49/102*e^7 + 437/51*e^5 - 1039/34*e^3 + 1168/51*e, 2/51*e^7 - 44/51*e^5 + 83/17*e^3 - 367/51*e, -67/102*e^7 + 1219/102*e^5 - 774/17*e^3 + 1978/51*e, 13/17*e^7 - 453/34*e^5 + 1503/34*e^3 - 609/17*e, -8/17*e^6 + 142/17*e^4 - 486/17*e^2 + 244/17, -1/34*e^6 + 5/34*e^4 + 78/17*e^2 - 278/17, -61/102*e^7 + 518/51*e^5 - 1027/34*e^3 + 841/51*e, 13/51*e^7 - 184/51*e^5 + 21/17*e^3 + 1057/51*e, 19/51*e^7 - 683/102*e^5 + 829/34*e^3 - 962/51*e, 9/34*e^6 - 181/34*e^4 + 420/17*e^2 - 371/17, -26/51*e^7 + 889/102*e^5 - 917/34*e^3 + 844/51*e, -2/17*e^7 + 27/17*e^5 + 23/17*e^3 - 330/17*e, -2*e, 15/17*e^6 - 245/17*e^4 + 601/17*e^2 - 109/17, 23/102*e^7 - 202/51*e^5 + 487/34*e^3 - 950/51*e, -7/34*e^7 + 137/34*e^5 - 304/17*e^3 + 230/17*e, 19/34*e^6 - 333/34*e^4 + 592/17*e^2 - 549/17, 1/6*e^7 - 19/6*e^5 + 14*e^3 - 46/3*e, -1/34*e^7 + 39/34*e^5 - 194/17*e^3 + 368/17*e, 28/51*e^7 - 463/51*e^5 + 414/17*e^3 - 599/51*e, 3/34*e^6 - 83/34*e^4 + 293/17*e^2 - 152/17, 13/17*e^6 - 235/17*e^4 + 862/17*e^2 - 677/17, -27/34*e^6 + 441/34*e^4 - 563/17*e^2 + 8/17, 1/6*e^7 - 13/6*e^5 - 2*e^3 + 53/3*e, 4/17*e^6 - 71/17*e^4 + 209/17*e^2 + 31/17, 5/34*e^6 - 93/34*e^4 + 239/17*e^2 - 514/17, -e^6 + 17*e^4 - 52*e^2 + 32, -14/17*e^6 + 223/17*e^4 - 519/17*e^2 + 19/17, -15/34*e^6 + 279/34*e^4 - 564/17*e^2 + 318/17, 79/102*e^7 - 716/51*e^5 + 1825/34*e^3 - 2569/51*e, 11/34*e^6 - 225/34*e^4 + 570/17*e^2 - 648/17, 64/51*e^7 - 1102/51*e^5 + 1160/17*e^3 - 2207/51*e, 9/17*e^6 - 147/17*e^4 + 381/17*e^2 - 487/17, -61/34*e^6 + 1053/34*e^4 - 1634/17*e^2 + 909/17, 35/102*e^7 - 617/102*e^5 + 348/17*e^3 - 980/51*e, -13/17*e^6 + 235/17*e^4 - 828/17*e^2 + 269/17, -7/34*e^6 + 103/34*e^4 - 66/17*e^2 - 110/17, 70/51*e^7 - 1234/51*e^5 + 1426/17*e^3 - 3563/51*e, -18/17*e^6 + 311/17*e^4 - 1034/17*e^2 + 804/17, -9/34*e^6 + 147/34*e^4 - 182/17*e^2 - 88/17, 21/34*e^7 - 377/34*e^5 + 691/17*e^3 - 656/17*e, -22/17*e^7 + 815/34*e^5 - 3285/34*e^3 + 1572/17*e, -10/17*e^6 + 152/17*e^4 - 208/17*e^2 - 154/17, -22/51*e^7 + 382/51*e^5 - 403/17*e^3 + 620/51*e, 7/17*e^7 - 120/17*e^5 + 336/17*e^3 + 152/17*e, 19/17*e^6 - 333/17*e^4 + 1150/17*e^2 - 826/17, -31/17*e^6 + 512/17*e^4 - 1403/17*e^2 + 716/17, 59/34*e^6 - 1009/34*e^4 + 1552/17*e^2 - 870/17, 61/102*e^7 - 1189/102*e^5 + 913/17*e^3 - 2779/51*e, -10/17*e^6 + 152/17*e^4 - 259/17*e^2 + 118/17, 23/34*e^6 - 353/34*e^4 + 348/17*e^2 + 36/17, -2/3*e^7 + 38/3*e^5 - 57*e^3 + 238/3*e, -4/3*e^7 + 70/3*e^5 - 78*e^3 + 182/3*e, -3/34*e^7 + 83/34*e^5 - 327/17*e^3 + 594/17*e, -1/2*e^7 + 9*e^5 - 65/2*e^3 + 13*e, -7/34*e^6 + 137/34*e^4 - 355/17*e^2 + 417/17, 3/2*e^6 - 51/2*e^4 + 78*e^2 - 40, -26/51*e^7 + 521/51*e^5 - 841/17*e^3 + 2986/51*e, 9/34*e^6 - 147/34*e^4 + 199/17*e^2 - 167/17, -13/34*e^6 + 235/34*e^4 - 431/17*e^2 + 75/17, -31/34*e^6 + 495/34*e^4 - 523/17*e^2 + 69/17, -29/17*e^7 + 502/17*e^5 - 1613/17*e^3 + 1114/17*e, -3/17*e^6 + 49/17*e^4 - 93/17*e^2 - 342/17, -76/51*e^7 + 1366/51*e^5 - 1692/17*e^3 + 4868/51*e, 3/17*e^6 - 32/17*e^4 - 111/17*e^2 + 274/17, -1/34*e^6 + 39/34*e^4 - 262/17*e^2 + 810/17, 137/102*e^7 - 2555/102*e^5 + 1742/17*e^3 - 5213/51*e, 21/34*e^6 - 343/34*e^4 + 453/17*e^2 - 180/17, 22/17*e^7 - 365/17*e^5 + 971/17*e^3 - 246/17*e, -57/34*e^7 + 999/34*e^5 - 1691/17*e^3 + 1188/17*e, -37/51*e^7 + 610/51*e^5 - 524/17*e^3 + 593/51*e, -49/34*e^6 + 823/34*e^4 - 1159/17*e^2 + 454/17, 25/17*e^6 - 414/17*e^4 + 1115/17*e^2 - 244/17, 95/51*e^7 - 1682/51*e^5 + 1962/17*e^3 - 4861/51*e, -15/34*e^6 + 245/34*e^4 - 309/17*e^2 - 22/17, 35/17*e^6 - 617/17*e^4 + 2088/17*e^2 - 1416/17, 10/51*e^7 - 287/102*e^5 + 65/34*e^3 + 664/51*e, 50/51*e^7 - 1741/102*e^5 + 1889/34*e^3 - 1984/51*e, -1/102*e^7 - 40/51*e^5 + 579/34*e^3 - 2879/51*e, 55/34*e^6 - 921/34*e^4 + 1303/17*e^2 - 520/17, -6/17*e^7 + 179/34*e^5 - 219/34*e^3 - 293/17*e, -21/34*e^7 + 411/34*e^5 - 963/17*e^3 + 1132/17*e, -38/17*e^6 + 649/17*e^4 - 2045/17*e^2 + 1346/17, 20/17*e^6 - 355/17*e^4 + 1198/17*e^2 - 678/17, -79/34*e^6 + 1347/34*e^4 - 1998/17*e^2 + 1005/17, 49/34*e^6 - 891/34*e^4 + 1703/17*e^2 - 1236/17, 20/17*e^6 - 338/17*e^4 + 994/17*e^2 - 542/17, 113/102*e^7 - 2129/102*e^5 + 1499/17*e^3 - 5000/51*e, 1/2*e^7 - 15/2*e^5 + 10*e^3 + 8*e, 31/102*e^7 - 290/51*e^5 + 819/34*e^3 - 1633/51*e, 5/34*e^6 - 59/34*e^4 - 84/17*e^2 - 140/17, -36/17*e^6 + 605/17*e^4 - 1711/17*e^2 + 656/17, -23/34*e^7 + 421/34*e^5 - 807/17*e^3 + 508/17*e, -19/34*e^7 + 175/17*e^5 - 1439/34*e^3 + 872/17*e, -24/17*e^7 + 409/17*e^5 - 1237/17*e^3 + 698/17*e, 26/17*e^7 - 470/17*e^5 + 1758/17*e^3 - 1388/17*e, -41/34*e^7 + 749/34*e^5 - 1409/17*e^3 + 1012/17*e, 49/102*e^7 - 488/51*e^5 + 1651/34*e^3 - 3718/51*e, -35/102*e^7 + 283/51*e^5 - 441/34*e^3 + 674/51*e, 22/17*e^7 - 382/17*e^5 + 1243/17*e^3 - 637/17*e, 2*e^4 - 31*e^2 + 54, -9/17*e^6 + 164/17*e^4 - 636/17*e^2 + 470/17, 8/17*e^6 - 125/17*e^4 + 265/17*e^2 + 62/17, 121/102*e^7 - 2203/102*e^5 + 1376/17*e^3 - 3133/51*e, 19/51*e^7 - 581/102*e^5 + 251/34*e^3 + 1282/51*e, 29/34*e^6 - 485/34*e^4 + 628/17*e^2 - 132/17, -2*e^6 + 36*e^4 - 128*e^2 + 88, -61/51*e^7 + 2123/102*e^5 - 2343/34*e^3 + 3212/51*e, -5/17*e^7 + 110/17*e^5 - 699/17*e^3 + 1538/17*e, 107/102*e^7 - 1895/102*e^5 + 1145/17*e^3 - 3965/51*e, 113/51*e^7 - 3901/102*e^5 + 4109/34*e^3 - 3829/51*e, -22/17*e^6 + 416/17*e^4 - 1702/17*e^2 + 1232/17, 15/34*e^6 - 211/34*e^4 + 37/17*e^2 + 430/17, -25/34*e^6 + 465/34*e^4 - 923/17*e^2 + 972/17, 12/17*e^7 - 230/17*e^5 + 984/17*e^3 - 842/17*e, 32/17*e^6 - 517/17*e^4 + 1247/17*e^2 - 194/17, e^6 - 16*e^4 + 33*e^2 + 10, 13/17*e^6 - 201/17*e^4 + 369/17*e^2 + 190/17, 109/51*e^7 - 3929/102*e^5 + 4865/34*e^3 - 6665/51*e, -14/17*e^7 + 463/34*e^5 - 1293/34*e^3 + 580/17*e, 26/17*e^6 - 436/17*e^4 + 1197/17*e^2 - 691/17, 79/102*e^7 - 665/51*e^5 + 1247/34*e^3 - 121/51*e, -4/17*e^6 + 71/17*e^4 - 277/17*e^2 + 156/17, 11/34*e^6 - 225/34*e^4 + 519/17*e^2 - 495/17, 21/17*e^6 - 360/17*e^4 + 1110/17*e^2 - 989/17, -49/102*e^7 + 488/51*e^5 - 1617/34*e^3 + 4177/51*e, -e^6 + 17*e^4 - 54*e^2 + 40, 3/34*e^7 - 117/34*e^5 + 599/17*e^3 - 1240/17*e, e^7 - 39/2*e^5 + 183/2*e^3 - 112*e, -8/17*e^6 + 125/17*e^4 - 180/17*e^2 - 419/17, 175/102*e^7 - 1466/51*e^5 + 2681/34*e^3 - 1075/51*e, 50/51*e^7 - 794/51*e^5 + 528/17*e^3 + 872/51*e, 13/102*e^7 - 92/51*e^5 + 89/34*e^3 - 313/51*e, -27, -33/17*e^6 + 522/17*e^4 - 1023/17*e^2 - 362/17, -63/34*e^6 + 1131/34*e^4 - 2073/17*e^2 + 1237/17, 20/17*e^7 - 727/34*e^5 + 2753/34*e^3 - 1052/17*e, 3/17*e^6 - 66/17*e^4 + 365/17*e^2 - 763/17, 11/17*e^6 - 208/17*e^4 + 919/17*e^2 - 1228/17, -79/34*e^6 + 1381/34*e^4 - 2304/17*e^2 + 1668/17, 5/102*e^7 - 59/102*e^5 - 45/17*e^3 + 1543/51*e, -11/34*e^7 + 259/34*e^5 - 859/17*e^3 + 1447/17*e, -12/17*e^6 + 230/17*e^4 - 933/17*e^2 + 740/17, -15/17*e^6 + 262/17*e^4 - 805/17*e^2 + 228/17, -7/102*e^7 + 103/102*e^5 + 12/17*e^3 - 875/51*e, -149/102*e^7 + 1180/51*e^5 - 1619/34*e^3 - 826/51*e, -13/17*e^6 + 235/17*e^4 - 930/17*e^2 + 898/17, 6/17*e^6 - 81/17*e^4 + 50/17*e^2 - 64/17, -103/34*e^6 + 1773/34*e^4 - 2710/17*e^2 + 1388/17, -1/17*e^7 + 27/34*e^5 - 79/34*e^3 + 260/17*e, -131/51*e^7 + 4693/102*e^5 - 5671/34*e^3 + 6622/51*e, -16/17*e^7 + 619/34*e^5 - 2743/34*e^3 + 1253/17*e, -e^6 + 16*e^4 - 39*e^2 + 20, 19/17*e^6 - 333/17*e^4 + 1116/17*e^2 - 1234/17, 143/51*e^7 - 2534/51*e^5 + 2951/17*e^3 - 6937/51*e, 52/17*e^6 - 906/17*e^4 + 2955/17*e^2 - 2028/17] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([5, 5, -w^2 + w + 2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]