/* 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([29, 8, -12, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([9, 3, 2/5*w^3 - 19/5*w - 3/5]) primes_array = [ [5, 5, -w + 2],\ [5, 5, -3/5*w^3 - w^2 + 26/5*w + 42/5],\ [9, 3, 2/5*w^3 - 19/5*w - 3/5],\ [9, 3, -1/5*w^3 + 2/5*w + 4/5],\ [11, 11, -2/5*w^3 - w^2 + 14/5*w + 28/5],\ [11, 11, 1/5*w^3 - w^2 - 7/5*w + 36/5],\ [16, 2, 2],\ [29, 29, -w],\ [29, 29, 1/5*w^3 - 12/5*w + 1/5],\ [41, 41, -2/5*w^3 - w^2 + 14/5*w + 38/5],\ [41, 41, -w^2 + 10],\ [41, 41, 11/5*w^3 + 3*w^2 - 102/5*w - 149/5],\ [41, 41, -1/5*w^3 + w^2 + 7/5*w - 26/5],\ [49, 7, 1/5*w^3 + w^2 - 12/5*w - 19/5],\ [49, 7, 1/5*w^3 + w^2 - 12/5*w - 44/5],\ [59, 59, -4/5*w^3 - w^2 + 33/5*w + 36/5],\ [59, 59, -2*w^3 - 3*w^2 + 17*w + 26],\ [61, 61, -1/5*w^3 + w^2 + 12/5*w - 51/5],\ [61, 61, 4/5*w^3 + w^2 - 28/5*w - 41/5],\ [71, 71, 1/5*w^3 + w^2 - 7/5*w - 49/5],\ [71, 71, -2*w^3 - 3*w^2 + 18*w + 28],\ [89, 89, -3/5*w^3 + 16/5*w + 7/5],\ [89, 89, 3/5*w^3 + w^2 - 26/5*w - 57/5],\ [121, 11, -3/5*w^3 + 21/5*w + 2/5],\ [131, 131, w^2 - w - 8],\ [131, 131, 2/5*w^3 + w^2 - 19/5*w - 23/5],\ [149, 149, 2/5*w^3 - w^2 - 14/5*w + 22/5],\ [149, 149, 3/5*w^3 + w^2 - 21/5*w - 42/5],\ [179, 179, -6/5*w^3 - w^2 + 57/5*w + 69/5],\ [179, 179, -2/5*w^3 - 2*w^2 + 14/5*w + 73/5],\ [179, 179, 2*w^2 - 11],\ [179, 179, -3/5*w^3 + 2*w^2 + 16/5*w - 48/5],\ [181, 181, -7/5*w^3 - 2*w^2 + 59/5*w + 78/5],\ [181, 181, -2/5*w^3 + 24/5*w - 27/5],\ [191, 191, -3/5*w^3 + 2*w^2 + 21/5*w - 78/5],\ [191, 191, 2/5*w^3 - 2*w^2 - 9/5*w + 57/5],\ [199, 199, -1/5*w^3 + 17/5*w - 16/5],\ [199, 199, 1/5*w^3 - 17/5*w - 14/5],\ [211, 211, 2/5*w^3 - w^2 + 1/5*w + 7/5],\ [211, 211, -1/5*w^3 + w^2 - 3/5*w - 26/5],\ [211, 211, 4/5*w^3 + w^2 - 38/5*w - 36/5],\ [211, 211, -1/5*w^3 - 2*w^2 + 7/5*w + 44/5],\ [239, 239, 3/5*w^3 + w^2 - 16/5*w - 37/5],\ [239, 239, 2/5*w^3 + w^2 - 14/5*w - 53/5],\ [251, 251, 2/5*w^3 - 24/5*w - 13/5],\ [251, 251, 2*w - 3],\ [251, 251, w^2 + w - 10],\ [251, 251, -4/5*w^3 - w^2 + 28/5*w + 46/5],\ [269, 269, 1/5*w^3 - 12/5*w - 24/5],\ [269, 269, w - 5],\ [271, 271, -3/5*w^3 + 31/5*w - 33/5],\ [271, 271, -8/5*w^3 - 2*w^2 + 66/5*w + 77/5],\ [281, 281, 4/5*w^3 - w^2 - 38/5*w + 39/5],\ [281, 281, -14/5*w^3 - 3*w^2 + 128/5*w + 161/5],\ [311, 311, 1/5*w^3 - 2*w^2 - 2/5*w + 51/5],\ [311, 311, 1/5*w^3 - w^2 - 17/5*w + 21/5],\ [331, 331, 1/5*w^3 + 3/5*w - 4/5],\ [331, 331, 3/5*w^3 - 31/5*w - 2/5],\ [359, 359, -w^3 + 6*w - 1],\ [359, 359, -6/5*w^3 + 47/5*w - 6/5],\ [359, 359, 3/5*w^3 + w^2 - 31/5*w - 27/5],\ [359, 359, 3/5*w^3 + w^2 - 26/5*w - 22/5],\ [361, 19, 4/5*w^3 - 28/5*w - 11/5],\ [361, 19, 1/5*w^3 - 7/5*w - 24/5],\ [379, 379, 9/5*w^3 + 3*w^2 - 78/5*w - 121/5],\ [379, 379, -4/5*w^3 + 3*w^2 + 28/5*w - 99/5],\ [389, 389, -3/5*w^3 - 2*w^2 + 26/5*w + 42/5],\ [389, 389, -2*w^2 + w + 17],\ [401, 401, 4/5*w^3 - w^2 - 23/5*w + 24/5],\ [401, 401, 3/5*w^3 + w^2 - 26/5*w - 7/5],\ [401, 401, -4/5*w^3 - w^2 + 38/5*w + 66/5],\ [401, 401, 6/5*w^3 + w^2 - 52/5*w - 39/5],\ [409, 409, -6/5*w^3 + 52/5*w + 19/5],\ [409, 409, 1/5*w^3 + 2*w^2 - 7/5*w - 39/5],\ [421, 421, -1/5*w^3 - w^2 + 17/5*w + 44/5],\ [421, 421, 2/5*w^3 + w^2 - 24/5*w - 18/5],\ [431, 431, -3/5*w^3 - w^2 + 36/5*w + 47/5],\ [431, 431, -13/5*w^3 - 4*w^2 + 116/5*w + 182/5],\ [431, 431, -2/5*w^3 + w^2 + 24/5*w - 47/5],\ [431, 431, 2/5*w^3 - w^2 + 6/5*w - 8/5],\ [439, 439, 6/5*w^3 + w^2 - 47/5*w - 49/5],\ [439, 439, -2/5*w^3 + 2*w^2 + 9/5*w - 42/5],\ [439, 439, 4/5*w^3 - w^2 - 23/5*w + 14/5],\ [439, 439, -w^3 - 2*w^2 + 8*w + 17],\ [461, 461, w^3 + w^2 - 10*w - 9],\ [461, 461, -2*w^3 - 3*w^2 + 17*w + 27],\ [461, 461, -1/5*w^3 + w^2 - 8/5*w - 16/5],\ [461, 461, -3*w^3 - 4*w^2 + 26*w + 35],\ [479, 479, 2*w - 1],\ [479, 479, 2/5*w^3 - 24/5*w - 3/5],\ [491, 491, w^3 - 2*w^2 - 6*w + 11],\ [491, 491, w^3 + w^2 - 10*w - 15],\ [499, 499, -1/5*w^3 + 2*w^2 + 2/5*w - 36/5],\ [499, 499, 4/5*w^3 + 2*w^2 - 33/5*w - 91/5],\ [509, 509, 8/5*w^3 + w^2 - 66/5*w - 42/5],\ [509, 509, 1/5*w^3 - 2*w^2 + 8/5*w + 16/5],\ [521, 521, w^3 - 9*w - 4],\ [521, 521, 3/5*w^3 + w^2 - 16/5*w - 42/5],\ [521, 521, 3/5*w^3 - w^2 - 26/5*w + 23/5],\ [521, 521, -3/5*w^3 + 11/5*w + 22/5],\ [529, 23, 3/5*w^3 + w^2 - 36/5*w - 62/5],\ [529, 23, -4/5*w^3 + 2*w^2 + 23/5*w - 64/5],\ [541, 541, -w^3 - w^2 + 9*w + 7],\ [541, 541, 1/5*w^3 + 2*w^2 - 7/5*w - 64/5],\ [541, 541, 3/5*w^3 + w^2 - 26/5*w - 12/5],\ [571, 571, -w^3 - w^2 + 6*w + 9],\ [571, 571, -w^3 + w^2 + 8*w - 4],\ [619, 619, -w^3 - 2*w^2 + 8*w + 11],\ [619, 619, -2/5*w^3 + 2*w^2 + 9/5*w - 72/5],\ [619, 619, 2/5*w^3 - 2*w^2 - 4/5*w + 57/5],\ [619, 619, -6/5*w^3 - 2*w^2 + 52/5*w + 69/5],\ [631, 631, 1/5*w^3 + w^2 + 3/5*w - 24/5],\ [631, 631, 2/5*w^3 - w^2 - 24/5*w + 42/5],\ [659, 659, -13/5*w^3 - 4*w^2 + 111/5*w + 177/5],\ [659, 659, -11/5*w^3 - 3*w^2 + 92/5*w + 119/5],\ [659, 659, -8/5*w^3 - w^2 + 61/5*w + 27/5],\ [659, 659, -8/5*w^3 + 71/5*w + 2/5],\ [661, 661, -w^3 - w^2 + 7*w + 11],\ [661, 661, 4/5*w^3 - w^2 - 28/5*w + 9/5],\ [691, 691, 1/5*w^3 - w^2 - 17/5*w + 41/5],\ [691, 691, 3/5*w^3 + 2*w^2 - 26/5*w - 67/5],\ [701, 701, 12/5*w^3 + 4*w^2 - 99/5*w - 158/5],\ [701, 701, -17/5*w^3 - 4*w^2 + 149/5*w + 193/5],\ [709, 709, -1/5*w^3 + w^2 + 12/5*w - 6/5],\ [709, 709, 1/5*w^3 + w^2 - 2/5*w - 59/5],\ [719, 719, 2/5*w^3 + w^2 - 29/5*w - 8/5],\ [719, 719, -w^3 + w^2 + 7*w - 4],\ [719, 719, 6/5*w^3 + w^2 - 42/5*w - 44/5],\ [719, 719, -2/5*w^3 - w^2 + 29/5*w + 53/5],\ [739, 739, 14/5*w^3 + 4*w^2 - 123/5*w - 171/5],\ [739, 739, -1/5*w^3 + 2*w^2 + 12/5*w - 56/5],\ [739, 739, -6/5*w^3 + 3*w^2 + 37/5*w - 96/5],\ [739, 739, 2/5*w^3 + 2*w^2 - 9/5*w - 73/5],\ [751, 751, -9/5*w^3 - 2*w^2 + 73/5*w + 86/5],\ [751, 751, -w^3 + 2*w^2 + 5*w - 8],\ [761, 761, 1/5*w^3 + w^2 - 22/5*w + 16/5],\ [761, 761, -16/5*w^3 - 4*w^2 + 147/5*w + 214/5],\ [769, 769, 13/5*w^3 + 3*w^2 - 121/5*w - 172/5],\ [769, 769, 3/5*w^3 - w^2 - 41/5*w + 78/5],\ [769, 769, -12/5*w^3 - 4*w^2 + 99/5*w + 153/5],\ [769, 769, -6/5*w^3 + 3*w^2 + 27/5*w - 61/5],\ [809, 809, 1/5*w^3 + 3*w^2 - 22/5*w - 104/5],\ [809, 809, w^3 + 3*w^2 - 10*w - 17],\ [811, 811, -5*w + 11],\ [811, 811, -16/5*w^3 - 5*w^2 + 137/5*w + 214/5],\ [821, 821, -1/5*w^3 + w^2 + 17/5*w - 36/5],\ [821, 821, w^2 + 2*w - 6],\ [829, 829, 3*w^2 + w - 17],\ [829, 829, 2/5*w^3 + 3*w^2 - 9/5*w - 108/5],\ [841, 29, w^3 - 7*w - 3],\ [859, 859, 6/5*w^3 + w^2 - 37/5*w - 34/5],\ [859, 859, 2/5*w^3 + w^2 - 14/5*w - 68/5],\ [881, 881, 1/5*w^3 + 2*w^2 - 17/5*w - 79/5],\ [881, 881, 3/5*w^3 + 2*w^2 - 31/5*w - 47/5],\ [911, 911, 4/5*w^3 - 3*w^2 - 28/5*w + 89/5],\ [911, 911, 1/5*w^3 - w^2 - 7/5*w + 61/5],\ [911, 911, w^3 - 6*w - 3],\ [911, 911, -11/5*w^3 - 3*w^2 + 92/5*w + 139/5],\ [919, 919, 7/5*w^3 + 2*w^2 - 54/5*w - 88/5],\ [919, 919, 4/5*w^3 - 2*w^2 - 23/5*w + 39/5],\ [929, 929, -7/5*w^3 + w^2 + 54/5*w - 17/5],\ [929, 929, -1/5*w^3 + w^2 + 22/5*w - 71/5],\ [941, 941, 9/5*w^3 + w^2 - 73/5*w - 31/5],\ [941, 941, 1/5*w^3 - w^2 - 2/5*w + 66/5],\ [941, 941, 2/5*w^3 + 2*w^2 - 19/5*w - 103/5],\ [941, 941, -w^3 + w^2 + 5*w - 3],\ [961, 31, w^3 - 7*w - 2],\ [961, 31, 2/5*w^3 - 14/5*w - 33/5],\ [971, 971, -2/5*w^3 - 2*w^2 + 24/5*w + 93/5],\ [971, 971, 2/5*w^3 + 2*w^2 - 24/5*w - 33/5],\ [991, 991, -w^3 + 2*w^2 + 7*w - 10],\ [991, 991, -7/5*w^3 - 2*w^2 + 49/5*w + 78/5]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^6 - 6*x^5 - 7*x^4 + 88*x^3 - 80*x^2 - 192*x + 224 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -1/8*e^5 + 1/2*e^4 + 15/8*e^3 - 29/4*e^2 - 9/2*e + 16, -1, -19/104*e^5 + 27/52*e^4 + 309/104*e^3 - 185/26*e^2 - 111/13*e + 178/13, 1/13*e^5 - 23/52*e^4 - 25/26*e^3 + 333/52*e^2 + 5/13*e - 142/13, -1/8*e^5 + 1/2*e^4 + 15/8*e^3 - 29/4*e^2 - 7/2*e + 16, -5/52*e^5 + 19/52*e^4 + 69/52*e^3 - 231/52*e^2 - 29/13*e + 41/13, 31/104*e^5 - 55/52*e^4 - 433/104*e^3 + 373/26*e^2 + 73/13*e - 326/13, -5/26*e^5 + 19/26*e^4 + 69/26*e^3 - 257/26*e^2 - 58/13*e + 264/13, -2/13*e^5 + 33/52*e^4 + 25/13*e^3 - 471/52*e^2 - 59/26*e + 284/13, 1/52*e^5 - 9/52*e^4 + 7/52*e^3 + 145/52*e^2 - 67/13*e - 42/13, 9/26*e^5 - 29/26*e^4 - 145/26*e^3 + 421/26*e^2 + 185/13*e - 418/13, -5/13*e^5 + 19/13*e^4 + 69/13*e^3 - 257/13*e^2 - 103/13*e + 502/13, -5/26*e^5 + 19/26*e^4 + 69/26*e^3 - 283/26*e^2 - 19/13*e + 290/13, 1/8*e^5 - 1/4*e^4 - 15/8*e^3 + 7/2*e^2 + 3*e - 10, 1/4*e^5 - 5/4*e^4 - 13/4*e^3 + 73/4*e^2 + 4*e - 36, 2/13*e^5 - 33/52*e^4 - 25/13*e^3 + 419/52*e^2 + 7/26*e - 128/13, -5/26*e^5 + 25/52*e^4 + 95/26*e^3 - 371/52*e^2 - 389/26*e + 238/13, -5/26*e^5 + 51/52*e^4 + 69/26*e^3 - 761/52*e^2 - 129/26*e + 420/13, 17/52*e^5 - 9/13*e^4 - 323/52*e^3 + 251/26*e^2 + 317/13*e - 246/13, 3/104*e^5 - 7/52*e^4 - 5/104*e^3 + 21/26*e^2 - 42/13*e + 80/13, 1/26*e^5 + 2/13*e^4 - 19/26*e^3 - 51/13*e^2 + 22/13*e + 280/13, 49/104*e^5 - 21/13*e^4 - 775/104*e^3 + 1271/52*e^2 + 461/26*e - 756/13, 4/13*e^5 - 53/52*e^4 - 63/13*e^3 + 643/52*e^2 + 339/26*e - 230/13, -33/52*e^5 + 51/26*e^4 + 523/52*e^3 - 335/13*e^2 - 324/13*e + 554/13, -2/13*e^5 + 5/13*e^4 + 38/13*e^3 - 82/13*e^2 - 101/13*e + 284/13, 7/26*e^5 - 12/13*e^4 - 107/26*e^3 + 137/13*e^2 + 154/13*e - 94/13, -5/52*e^5 + 45/52*e^4 + 69/52*e^3 - 725/52*e^2 - 55/13*e + 470/13, -1/104*e^5 + 6/13*e^4 - 33/104*e^3 - 391/52*e^2 + 119/26*e + 242/13, 21/104*e^5 - 23/52*e^4 - 451/104*e^3 + 80/13*e^2 + 265/13*e - 12/13, 31/52*e^5 - 21/13*e^4 - 537/52*e^3 + 629/26*e^2 + 432/13*e - 730/13, -3/52*e^5 - 3/13*e^4 + 109/52*e^3 + 127/26*e^2 - 202/13*e - 160/13, 29/104*e^5 - 59/52*e^4 - 395/104*e^3 + 186/13*e^2 + 49/13*e - 154/13, 1/8*e^5 - 3/4*e^4 - 15/8*e^3 + 13*e^2 + 6*e - 46, -2/13*e^5 + 23/26*e^4 + 25/13*e^3 - 359/26*e^2 + 3/13*e + 518/13, -3/104*e^5 - 19/52*e^4 + 109/104*e^3 + 87/13*e^2 - 62/13*e - 236/13, -1/4*e^5 + e^4 + 11/4*e^3 - 25/2*e^2 + 2*e + 24, -35/104*e^5 + 15/13*e^4 + 613/104*e^3 - 893/52*e^2 - 463/26*e + 540/13, 21/104*e^5 - 49/52*e^4 - 243/104*e^3 + 355/26*e^2 - 112/13*e - 376/13, 10/13*e^5 - 63/26*e^4 - 164/13*e^3 + 911/26*e^2 + 492/13*e - 1108/13, 23/52*e^5 - 77/52*e^4 - 333/52*e^3 + 917/52*e^2 + 311/26*e - 264/13, -31/104*e^5 + 21/26*e^4 + 537/104*e^3 - 551/52*e^2 - 367/26*e + 274/13, -1/52*e^5 - 1/13*e^4 - 33/52*e^3 + 51/26*e^2 + 119/13*e + 94/13, -49/104*e^5 + 97/52*e^4 + 775/104*e^3 - 707/26*e^2 - 315/13*e + 808/13, -5/13*e^5 + 25/26*e^4 + 95/13*e^3 - 397/26*e^2 - 324/13*e + 502/13, 21/104*e^5 - 49/52*e^4 - 243/104*e^3 + 303/26*e^2 + 18/13*e - 324/13, 25/52*e^5 - 27/13*e^4 - 371/52*e^3 + 805/26*e^2 + 210/13*e - 972/13, -1/13*e^5 + 9/13*e^4 + 6/13*e^3 - 145/13*e^2 + 21/13*e + 506/13, 47/52*e^5 - 75/26*e^4 - 737/52*e^3 + 485/13*e^2 + 491/13*e - 856/13, -95/104*e^5 + 37/13*e^4 + 1441/104*e^3 - 2045/52*e^2 - 785/26*e + 1020/13, 3/13*e^5 - 43/52*e^4 - 44/13*e^3 + 453/52*e^2 + 147/26*e + 146/13, -31/104*e^5 + 55/52*e^4 + 537/104*e^3 - 503/26*e^2 - 190/13*e + 820/13, 71/104*e^5 - 59/26*e^4 - 1193/104*e^3 + 1683/52*e^2 + 859/26*e - 802/13, 25/52*e^5 - 27/13*e^4 - 371/52*e^3 + 805/26*e^2 + 249/13*e - 972/13, -25/52*e^5 + 41/26*e^4 + 371/52*e^3 - 253/13*e^2 - 171/13*e + 192/13, 77/104*e^5 - 145/52*e^4 - 1099/104*e^3 + 1033/26*e^2 + 287/13*e - 1032/13, -35/52*e^5 + 73/26*e^4 + 561/52*e^3 - 531/13*e^2 - 398/13*e + 1106/13, 19/26*e^5 - 67/26*e^4 - 283/26*e^3 + 909/26*e^2 + 275/13*e - 582/13, 6/13*e^5 - 17/26*e^4 - 114/13*e^3 + 245/26*e^2 + 420/13*e - 280/13, 85/104*e^5 - 181/52*e^4 - 1147/104*e^3 + 1297/26*e^2 + 175/13*e - 1252/13, 7/52*e^5 - 25/26*e^4 - 29/52*e^3 + 205/13*e^2 - 196/13*e - 294/13, -1/4*e^5 + 3/4*e^4 + 15/4*e^3 - 35/4*e^2 - 19/2*e, -23/52*e^5 + 19/26*e^4 + 385/52*e^3 - 83/13*e^2 - 227/13*e - 256/13, 89/52*e^5 - 80/13*e^4 - 1327/52*e^3 + 2247/26*e^2 + 641/13*e - 2204/13, -5/52*e^5 + 29/26*e^4 + 43/52*e^3 - 230/13*e^2 + 23/13*e + 548/13, 41/52*e^5 - 135/52*e^4 - 597/52*e^3 + 1811/52*e^2 + 308/13*e - 708/13, -2/13*e^5 - 3/26*e^4 + 51/13*e^3 + 57/26*e^2 - 231/13*e - 28/13, 6/13*e^5 - 99/52*e^4 - 75/13*e^3 + 1413/52*e^2 + 125/26*e - 592/13, 81/104*e^5 - 31/13*e^4 - 1175/104*e^3 + 1615/52*e^2 + 501/26*e - 622/13, 17/26*e^5 - 85/52*e^4 - 297/26*e^3 + 1199/52*e^2 + 891/26*e - 570/13, -29/26*e^5 + 46/13*e^4 + 473/26*e^3 - 653/13*e^2 - 703/13*e + 1500/13, 1/4*e^5 - 1/2*e^4 - 19/4*e^3 + 9*e^2 + 16*e - 32, 9/26*e^5 - 29/26*e^4 - 145/26*e^3 + 291/26*e^2 + 250/13*e + 24/13, 6/13*e^5 - 99/52*e^4 - 163/26*e^3 + 1361/52*e^2 + 82/13*e - 540/13, 3/13*e^5 - 15/26*e^4 - 70/13*e^3 + 233/26*e^2 + 392/13*e - 218/13, -21/52*e^5 + 23/26*e^4 + 347/52*e^3 - 108/13*e^2 - 296/13*e - 106/13, 147/104*e^5 - 113/26*e^4 - 2429/104*e^3 + 3215/52*e^2 + 1695/26*e - 1748/13, 3/13*e^5 - 14/13*e^4 - 18/13*e^3 + 201/13*e^2 - 232/13*e - 400/13, 1/2*e^5 - 2*e^4 - 15/2*e^3 + 29*e^2 + 12*e - 62, -101/104*e^5 + 81/26*e^4 + 1555/104*e^3 - 2233/52*e^2 - 929/26*e + 1146/13, 77/104*e^5 - 33/13*e^4 - 1099/104*e^3 + 1871/52*e^2 + 327/26*e - 772/13, 3/52*e^5 - 10/13*e^4 - 5/52*e^3 + 315/26*e^2 - 84/13*e - 308/13, -27/104*e^5 + 37/52*e^4 + 461/104*e^3 - 127/13*e^2 - 259/13*e + 372/13, -18/13*e^5 + 103/26*e^4 + 303/13*e^3 - 1463/26*e^2 - 909/13*e + 1490/13, -47/26*e^5 + 163/26*e^4 + 711/26*e^3 - 2213/26*e^2 - 800/13*e + 2102/13, 19/52*e^5 - 20/13*e^4 - 309/52*e^3 + 617/26*e^2 + 196/13*e - 590/13, 15/26*e^5 - 57/26*e^4 - 181/26*e^3 + 745/26*e^2 + 70/13*e - 662/13, -59/52*e^5 + 193/52*e^4 + 913/52*e^3 - 2705/52*e^2 - 1077/26*e + 1490/13, -27/52*e^5 + 113/52*e^4 + 331/52*e^3 - 1549/52*e^2 - 37/13*e + 770/13, 5/8*e^5 - 5/2*e^4 - 75/8*e^3 + 145/4*e^2 + 47/2*e - 66, 7/26*e^5 - 61/52*e^4 - 60/13*e^3 + 951/52*e^2 + 167/13*e - 770/13, 45/104*e^5 - 23/13*e^4 - 699/104*e^3 + 1267/52*e^2 + 521/26*e - 490/13, -27/104*e^5 + 37/52*e^4 + 461/104*e^3 - 166/13*e^2 - 168/13*e + 684/13, -49/52*e^5 + 155/52*e^4 + 723/52*e^3 - 1879/52*e^2 - 727/26*e + 472/13, 4/13*e^5 - 33/26*e^4 - 63/13*e^3 + 445/26*e^2 + 98/13*e - 100/13, -17/104*e^5 + 31/52*e^4 + 271/104*e^3 - 144/13*e^2 - 126/13*e + 474/13, -10/13*e^5 + 63/26*e^4 + 151/13*e^3 - 833/26*e^2 - 297/13*e + 614/13, -17/26*e^5 + 111/52*e^4 + 271/26*e^3 - 1589/52*e^2 - 579/26*e + 804/13, 9/13*e^5 - 45/26*e^4 - 158/13*e^3 + 543/26*e^2 + 565/13*e - 420/13, 95/104*e^5 - 37/13*e^4 - 1545/104*e^3 + 2149/52*e^2 + 967/26*e - 942/13, -35/26*e^5 + 60/13*e^4 + 561/26*e^3 - 893/13*e^2 - 757/13*e + 1978/13, -35/52*e^5 + 47/26*e^4 + 561/52*e^3 - 323/13*e^2 - 320/13*e + 482/13, 9/52*e^5 - 29/52*e^4 - 93/52*e^3 + 317/52*e^2 - 96/13*e - 196/13, 139/104*e^5 - 121/26*e^4 - 2173/104*e^3 + 3311/52*e^2 + 1373/26*e - 1580/13, 7/52*e^5 - 37/52*e^4 - 159/52*e^3 + 625/52*e^2 + 168/13*e - 268/13, 27/104*e^5 - 11/52*e^4 - 565/104*e^3 - 19/26*e^2 + 350/13*e + 200/13, -51/52*e^5 + 147/52*e^4 + 761/52*e^3 - 1675/52*e^2 - 875/26*e + 192/13, -9/13*e^5 + 129/52*e^4 + 132/13*e^3 - 1723/52*e^2 - 415/26*e + 446/13, 89/52*e^5 - 173/26*e^4 - 1379/52*e^3 + 1247/13*e^2 + 823/13*e - 2724/13, 20/13*e^5 - 317/52*e^4 - 617/26*e^3 + 4723/52*e^2 + 724/13*e - 2632/13, -45/52*e^5 + 79/26*e^4 + 647/52*e^3 - 484/13*e^2 - 313/13*e + 512/13, -19/26*e^5 + 40/13*e^4 + 257/26*e^3 - 552/13*e^2 - 223/13*e + 790/13, 1/26*e^5 - 11/13*e^4 + 59/26*e^3 + 131/13*e^2 - 342/13*e - 188/13, -5/13*e^5 + 37/52*e^4 + 95/13*e^3 - 599/52*e^2 - 713/26*e + 164/13, 25/13*e^5 - 341/52*e^4 - 781/26*e^3 + 4971/52*e^2 + 957/13*e - 2666/13, -33/104*e^5 + 3/13*e^4 + 575/104*e^3 + 45/52*e^2 - 285/26*e - 308/13, 27/52*e^5 - 87/52*e^4 - 487/52*e^3 + 1263/52*e^2 + 479/13*e - 666/13, 95/52*e^5 - 161/26*e^4 - 1441/52*e^3 + 1107/13*e^2 + 824/13*e - 2274/13, -17/26*e^5 + 59/52*e^4 + 155/13*e^3 - 653/52*e^2 - 478/13*e - 28/13, 73/104*e^5 - 75/52*e^4 - 1335/104*e^3 + 197/13*e^2 + 655/13*e - 324/13, -2/13*e^5 + 59/52*e^4 + 25/13*e^3 - 913/52*e^2 - 33/26*e + 596/13, -19/26*e^5 + 173/52*e^4 + 135/13*e^3 - 2507/52*e^2 - 184/13*e + 1024/13, -11/104*e^5 + 43/52*e^4 + 53/104*e^3 - 233/26*e^2 + 89/13*e + 62/13, -3/26*e^5 + 1/26*e^4 + 31/26*e^3 + 163/26*e^2 - 14/13*e - 788/13, -79/52*e^5 + 269/52*e^4 + 1215/52*e^3 - 3733/52*e^2 - 648/13*e + 1628/13, -3/2*e^5 + 5*e^4 + 45/2*e^3 - 66*e^2 - 50*e + 126, 14/13*e^5 - 153/52*e^4 - 441/26*e^3 + 2023/52*e^2 + 486/13*e - 688/13, -57/52*e^5 + 201/52*e^4 + 927/52*e^3 - 2961/52*e^2 - 1163/26*e + 1718/13, -77/104*e^5 + 145/52*e^4 + 995/104*e^3 - 981/26*e^2 - 66/13*e + 772/13, 11/13*e^5 - 47/13*e^4 - 170/13*e^3 + 672/13*e^2 + 458/13*e - 1562/13, -5/104*e^5 - 49/52*e^4 + 43/104*e^3 + 249/13*e^2 + 83/13*e - 896/13, 7/52*e^5 + 15/52*e^4 - 211/52*e^3 - 155/52*e^2 + 324/13*e + 200/13, 33/26*e^5 - 191/52*e^4 - 523/26*e^3 + 2745/52*e^2 + 1179/26*e - 1446/13, 11/104*e^5 - 1/13*e^4 - 53/104*e^3 - 327/52*e^2 - 269/26*e + 692/13, 19/13*e^5 - 147/26*e^4 - 283/13*e^3 + 2143/26*e^2 + 576/13*e - 2152/13, -17/104*e^5 + 5/52*e^4 + 271/104*e^3 + 11/26*e^2 + 4/13*e - 150/13, 67/52*e^5 - 239/52*e^4 - 987/52*e^3 + 3267/52*e^2 + 451/13*e - 1566/13, -e^5 + 15/4*e^4 + 15*e^3 - 209/4*e^2 - 71/2*e + 116, -11/13*e^5 + 81/26*e^4 + 170/13*e^3 - 1175/26*e^2 - 341/13*e + 1094/13, 11/52*e^5 + 11/13*e^4 - 261/52*e^3 - 405/26*e^2 + 212/13*e + 760/13, -103/104*e^5 + 46/13*e^4 + 1489/104*e^3 - 2313/52*e^2 - 795/26*e + 590/13, 75/104*e^5 - 55/26*e^4 - 1373/104*e^3 + 1635/52*e^2 + 1189/26*e - 886/13, 3/26*e^5 - 7/13*e^4 - 57/26*e^3 + 68/13*e^2 + 170/13*e - 200/13, -51/26*e^5 + 93/13*e^4 + 761/26*e^3 - 1338/13*e^2 - 836/13*e + 2802/13, 21/52*e^5 - 18/13*e^4 - 399/52*e^3 + 619/26*e^2 + 322/13*e - 986/13, -95/52*e^5 + 87/13*e^4 + 1337/52*e^3 - 2435/26*e^2 - 512/13*e + 2430/13, 1/2*e^5 - 9/4*e^4 - 7*e^3 + 111/4*e^2 + 17*e - 38, -27/26*e^5 + 37/13*e^4 + 461/26*e^3 - 469/13*e^2 - 750/13*e + 786/13, -21/26*e^5 + 59/26*e^4 + 321/26*e^3 - 757/26*e^2 - 228/13*e + 360/13, 10/13*e^5 - 37/26*e^4 - 177/13*e^3 + 391/26*e^2 + 700/13*e - 302/13, 67/52*e^5 - 213/52*e^4 - 1065/52*e^3 + 2877/52*e^2 + 1539/26*e - 1566/13, -97/104*e^5 + 183/52*e^4 + 1583/104*e^3 - 645/13*e^2 - 488/13*e + 1036/13, 63/52*e^5 - 177/52*e^4 - 1067/52*e^3 + 2505/52*e^2 + 745/13*e - 1138/13, 7/26*e^5 - 25/13*e^4 - 55/26*e^3 + 384/13*e^2 - 93/13*e - 822/13, 5/4*e^5 - 5*e^4 - 71/4*e^3 + 145/2*e^2 + 38*e - 162, -7/52*e^5 + 25/26*e^4 - 23/52*e^3 - 192/13*e^2 + 352/13*e + 268/13, -47/26*e^5 + 365/52*e^4 + 685/26*e^3 - 4907/52*e^2 - 1457/26*e + 2154/13, 12/13*e^5 - 107/52*e^4 - 215/13*e^3 + 1409/52*e^2 + 1329/26*e - 586/13, -101/52*e^5 + 389/52*e^4 + 1451/52*e^3 - 5337/52*e^2 - 1377/26*e + 2552/13, -9/104*e^5 + 21/52*e^4 - 89/104*e^3 - 167/26*e^2 + 295/13*e + 280/13, 27/26*e^5 - 37/13*e^4 - 461/26*e^3 + 521/13*e^2 + 750/13*e - 968/13, 3/8*e^5 - 3/4*e^4 - 61/8*e^3 + 25/2*e^2 + 35*e - 34, 1/26*e^5 - 9/26*e^4 + 59/26*e^3 + 41/26*e^2 - 355/13*e + 46/13, -61/52*e^5 + 99/26*e^4 + 1055/52*e^3 - 674/13*e^2 - 879/13*e + 1262/13, 81/52*e^5 - 287/52*e^4 - 1201/52*e^3 + 3971/52*e^2 + 696/13*e - 1816/13, -15/8*e^5 + 13/2*e^4 + 233/8*e^3 - 371/4*e^2 - 153/2*e + 190, 45/52*e^5 - 33/13*e^4 - 699/52*e^3 + 825/26*e^2 + 482/13*e - 798/13, 8/13*e^5 - 79/26*e^4 - 87/13*e^3 + 1137/26*e^2 - 77/13*e - 954/13, 33/104*e^5 - 77/52*e^4 - 367/104*e^3 + 361/26*e^2 - 20/13*e + 204/13, 45/26*e^5 - 145/26*e^4 - 751/26*e^3 + 2001/26*e^2 + 1029/13*e - 1752/13, 18/13*e^5 - 58/13*e^4 - 290/13*e^3 + 777/13*e^2 + 675/13*e - 1360/13, -115/104*e^5 + 40/13*e^4 + 1821/104*e^3 - 2013/52*e^2 - 1395/26*e + 660/13] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([9, 3, 2/5*w^3 - 19/5*w - 3/5])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]