/* 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([4, 6, -7, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([13, 13, 1/2*w^3 + 1/2*w^2 - 7/2*w - 1]) primes_array = [ [3, 3, -w + 1],\ [4, 2, w],\ [4, 2, -1/2*w^3 + 1/2*w^2 + 7/2*w - 3],\ [7, 7, -1/2*w^3 + 1/2*w^2 + 5/2*w - 2],\ [13, 13, 1/2*w^3 + 1/2*w^2 - 7/2*w - 1],\ [17, 17, 1/2*w^3 - 1/2*w^2 - 5/2*w],\ [27, 3, -w^3 + 7*w + 1],\ [31, 31, w + 3],\ [31, 31, -w^2 + 5],\ [37, 37, w^2 - 3],\ [41, 41, 1/2*w^3 + 1/2*w^2 - 3/2*w - 2],\ [47, 47, w^3 - 5*w - 3],\ [53, 53, 1/2*w^3 - 1/2*w^2 - 7/2*w],\ [61, 61, w^3 - w^2 - 5*w + 3],\ [83, 83, w^3 + w^2 - 6*w - 7],\ [83, 83, -w^3 + 5*w + 1],\ [83, 83, 2*w - 1],\ [83, 83, -3/2*w^3 - 1/2*w^2 + 19/2*w + 2],\ [89, 89, 1/2*w^3 - 1/2*w^2 - 7/2*w - 2],\ [89, 89, w^3 - 5*w + 5],\ [97, 97, -1/2*w^3 + 1/2*w^2 + 7/2*w - 6],\ [97, 97, -1/2*w^3 + 1/2*w^2 + 9/2*w - 1],\ [103, 103, 3/2*w^3 + 3/2*w^2 - 19/2*w - 9],\ [109, 109, 1/2*w^3 - 1/2*w^2 - 9/2*w + 4],\ [127, 127, 1/2*w^3 + 1/2*w^2 - 3/2*w - 3],\ [127, 127, 1/2*w^3 - 1/2*w^2 - 5/2*w + 6],\ [139, 139, 1/2*w^3 + 3/2*w^2 - 9/2*w - 3],\ [139, 139, 3/2*w^3 - 1/2*w^2 - 21/2*w + 1],\ [149, 149, -1/2*w^3 + 1/2*w^2 + 9/2*w - 2],\ [151, 151, -1/2*w^3 - 1/2*w^2 + 9/2*w - 3],\ [157, 157, 3/2*w^3 - 1/2*w^2 - 21/2*w + 4],\ [163, 163, 1/2*w^3 + 3/2*w^2 - 5/2*w - 3],\ [167, 167, -1/2*w^3 + 3/2*w^2 + 9/2*w - 9],\ [179, 179, w^3 - w^2 - 5*w + 1],\ [179, 179, -1/2*w^3 + 1/2*w^2 + 3/2*w - 4],\ [181, 181, 5/2*w^3 + 3/2*w^2 - 31/2*w - 10],\ [191, 191, -1/2*w^3 + 5/2*w^2 + 7/2*w - 14],\ [191, 191, 2*w^3 - 2*w^2 - 12*w + 11],\ [193, 193, w^2 + 1],\ [193, 193, 1/2*w^3 + 3/2*w^2 - 9/2*w - 6],\ [197, 197, 1/2*w^3 + 1/2*w^2 - 11/2*w + 1],\ [197, 197, -3/2*w^3 + 3/2*w^2 + 17/2*w - 8],\ [199, 199, 3/2*w^3 - 3/2*w^2 - 19/2*w + 7],\ [227, 227, 1/2*w^3 + 1/2*w^2 - 7/2*w - 6],\ [227, 227, -2*w^3 - w^2 + 14*w + 9],\ [229, 229, w^3 - w^2 - 4*w + 3],\ [229, 229, 3/2*w^3 - 1/2*w^2 - 17/2*w + 1],\ [233, 233, -w^3 - w^2 + 7*w + 9],\ [233, 233, 1/2*w^3 + 3/2*w^2 - 5/2*w - 9],\ [251, 251, -5/2*w^3 - 1/2*w^2 + 31/2*w + 2],\ [257, 257, -3/2*w^3 - 1/2*w^2 + 19/2*w + 1],\ [257, 257, 1/2*w^3 + 1/2*w^2 - 11/2*w - 1],\ [269, 269, 2*w^3 - 2*w^2 - 13*w + 15],\ [269, 269, 1/2*w^3 + 3/2*w^2 - 9/2*w - 4],\ [271, 271, 1/2*w^3 + 3/2*w^2 - 5/2*w - 6],\ [277, 277, -1/2*w^3 + 5/2*w^2 + 5/2*w - 16],\ [281, 281, -2*w^3 + 12*w + 1],\ [281, 281, -3/2*w^3 - 1/2*w^2 + 15/2*w - 3],\ [283, 283, 5/2*w^3 + 3/2*w^2 - 29/2*w - 8],\ [283, 283, 3/2*w^3 + 1/2*w^2 - 15/2*w],\ [293, 293, -w^3 - w^2 + 6*w + 1],\ [307, 307, -3/2*w^3 + 1/2*w^2 + 13/2*w + 4],\ [307, 307, -3/2*w^3 - 1/2*w^2 + 13/2*w - 2],\ [311, 311, 2*w^2 + w - 11],\ [311, 311, 1/2*w^3 + 3/2*w^2 - 5/2*w - 5],\ [313, 313, 3/2*w^3 - 1/2*w^2 - 17/2*w + 2],\ [317, 317, w^3 + 2*w^2 - 7*w - 3],\ [331, 331, 2*w^2 + 2*w - 9],\ [343, 7, -w^3 + 2*w^2 + 5*w - 11],\ [349, 349, 5/2*w^3 + 1/2*w^2 - 35/2*w - 6],\ [353, 353, 1/2*w^3 + 3/2*w^2 - 7/2*w - 4],\ [359, 359, w - 5],\ [361, 19, -5/2*w^3 + 1/2*w^2 + 33/2*w],\ [361, 19, w^3 - w^2 - 8*w + 3],\ [367, 367, -3/2*w^3 + 3/2*w^2 + 15/2*w - 8],\ [383, 383, -1/2*w^3 + 1/2*w^2 + 1/2*w - 3],\ [397, 397, -3/2*w^3 + 5/2*w^2 + 17/2*w - 16],\ [397, 397, 1/2*w^3 - 1/2*w^2 - 5/2*w - 3],\ [401, 401, -w^3 + 3*w - 3],\ [401, 401, 3/2*w^3 + 3/2*w^2 - 21/2*w - 4],\ [409, 409, 3/2*w^3 - 1/2*w^2 - 19/2*w - 3],\ [419, 419, -5/2*w^3 - 1/2*w^2 + 29/2*w + 1],\ [421, 421, -1/2*w^3 + 3/2*w^2 + 9/2*w - 11],\ [421, 421, -3*w + 1],\ [431, 431, 1/2*w^3 - 1/2*w^2 + 1/2*w + 2],\ [431, 431, w^3 - 7*w - 5],\ [433, 433, 1/2*w^3 + 1/2*w^2 - 3/2*w - 6],\ [433, 433, w^3 + w^2 - 6*w + 3],\ [467, 467, 1/2*w^3 + 3/2*w^2 - 11/2*w - 6],\ [487, 487, -2*w^3 + w^2 + 12*w - 9],\ [503, 503, 3/2*w^3 - 3/2*w^2 - 19/2*w + 6],\ [503, 503, w^2 + 2*w - 7],\ [523, 523, w^3 - w^2 - 6*w + 1],\ [523, 523, -w^3 + 3*w^2 + 7*w - 19],\ [541, 541, -3/2*w^3 + 3/2*w^2 + 15/2*w - 7],\ [541, 541, w^3 - w^2 - 8*w + 7],\ [547, 547, -1/2*w^3 + 3/2*w^2 + 3/2*w - 8],\ [557, 557, 2*w^2 - w - 9],\ [563, 563, -3*w^3 - w^2 + 19*w + 5],\ [563, 563, 7/2*w^3 + 5/2*w^2 - 45/2*w - 16],\ [563, 563, -w^3 + 3*w + 3],\ [563, 563, -w^2 + 2*w - 3],\ [569, 569, w^3 - w^2 - 6*w - 1],\ [571, 571, -5/2*w^3 + 3/2*w^2 + 31/2*w - 11],\ [577, 577, 2*w^2 - 2*w - 5],\ [587, 587, 3/2*w^3 + 1/2*w^2 - 23/2*w - 3],\ [587, 587, -2*w^3 + 14*w + 1],\ [599, 599, -3/2*w^3 - 1/2*w^2 + 13/2*w + 4],\ [607, 607, -3/2*w^3 - 3/2*w^2 + 21/2*w + 13],\ [613, 613, -1/2*w^3 + 3/2*w^2 + 11/2*w - 6],\ [613, 613, w^3 + w^2 - 8*w - 7],\ [617, 617, 2*w^2 - w - 5],\ [625, 5, -5],\ [653, 653, -1/2*w^3 + 3/2*w^2 + 9/2*w - 3],\ [653, 653, -2*w^3 - w^2 + 14*w + 3],\ [659, 659, -7/2*w^3 - 1/2*w^2 + 43/2*w + 6],\ [661, 661, 5/2*w^3 + 1/2*w^2 - 25/2*w - 5],\ [661, 661, w^3 + w^2 - 5*w - 7],\ [677, 677, -11/2*w^3 - 3/2*w^2 + 73/2*w + 13],\ [683, 683, -7/2*w^3 + 5/2*w^2 + 45/2*w - 16],\ [683, 683, -w^3 + 3*w^2 + 5*w - 11],\ [691, 691, 2*w^2 - 15],\ [691, 691, w^3 + w^2 - 4*w - 5],\ [701, 701, -7/2*w^3 - 1/2*w^2 + 47/2*w + 5],\ [701, 701, -w^3 + w^2 + 3*w - 5],\ [719, 719, 5/2*w^3 + 1/2*w^2 - 27/2*w - 5],\ [727, 727, -1/2*w^3 - 1/2*w^2 + 3/2*w - 4],\ [733, 733, 3/2*w^3 - 1/2*w^2 - 15/2*w + 1],\ [733, 733, -w^3 - 2*w^2 + 5*w + 5],\ [733, 733, 1/2*w^3 - 1/2*w^2 + 3/2*w + 2],\ [733, 733, 1/2*w^3 + 5/2*w^2 - 5/2*w - 13],\ [739, 739, 2*w^2 - 7],\ [743, 743, 3/2*w^3 - 1/2*w^2 - 9/2*w + 4],\ [743, 743, 2*w^3 - 12*w + 3],\ [751, 751, 1/2*w^3 + 1/2*w^2 - 11/2*w - 5],\ [751, 751, -1/2*w^3 + 1/2*w^2 + 11/2*w - 2],\ [761, 761, -3/2*w^3 + 3/2*w^2 + 23/2*w - 5],\ [769, 769, w^3 - 2*w^2 - 5*w + 13],\ [787, 787, -3/2*w^3 + 1/2*w^2 + 15/2*w - 3],\ [787, 787, 2*w^3 - 10*w - 3],\ [797, 797, 3/2*w^3 - 1/2*w^2 - 21/2*w + 7],\ [797, 797, -2*w^3 + 2*w^2 + 14*w - 13],\ [809, 809, -4*w^3 - 2*w^2 + 25*w + 15],\ [821, 821, 2*w^3 + 2*w^2 - 13*w - 11],\ [839, 839, -1/2*w^3 + 3/2*w^2 + 3/2*w - 9],\ [839, 839, -7/2*w^3 - 5/2*w^2 + 47/2*w + 18],\ [841, 29, 3/2*w^3 - 1/2*w^2 - 17/2*w + 10],\ [841, 29, 2*w^3 - 15*w + 5],\ [853, 853, 2*w^3 - 9*w - 3],\ [853, 853, -1/2*w^3 - 3/2*w^2 - 3/2*w + 7],\ [857, 857, 3/2*w^3 + 3/2*w^2 - 9/2*w - 4],\ [857, 857, w^3 - 3*w^2 - 5*w + 9],\ [857, 857, -w^3 + 3*w^2 + 6*w - 13],\ [857, 857, 1/2*w^3 + 5/2*w^2 - 7/2*w - 14],\ [859, 859, -5/2*w^3 - 1/2*w^2 + 35/2*w + 3],\ [863, 863, 2*w^3 - 2*w^2 - 13*w + 9],\ [881, 881, 2*w^2 + w - 13],\ [881, 881, 5/2*w^3 - 1/2*w^2 - 33/2*w - 1],\ [907, 907, -w^3 + 3*w^2 + 6*w - 15],\ [919, 919, 3/2*w^3 + 5/2*w^2 - 19/2*w - 4],\ [929, 929, 3/2*w^3 + 1/2*w^2 - 19/2*w + 1],\ [941, 941, 3/2*w^3 - 1/2*w^2 - 13/2*w],\ [947, 947, -1/2*w^3 + 5/2*w^2 + 13/2*w - 11],\ [947, 947, -7/2*w^3 - 1/2*w^2 + 43/2*w + 4],\ [947, 947, 1/2*w^3 + 1/2*w^2 - 13/2*w - 1],\ [947, 947, -4*w - 3],\ [953, 953, 3/2*w^3 - 7/2*w^2 - 21/2*w + 22],\ [953, 953, 1/2*w^3 + 5/2*w^2 - 3/2*w - 10],\ [961, 31, 3/2*w^3 + 3/2*w^2 - 17/2*w - 10],\ [967, 967, w^3 - 2*w^2 - 7*w + 7],\ [967, 967, 1/2*w^3 - 1/2*w^2 - 5/2*w - 4],\ [977, 977, -2*w^3 + 11*w + 1],\ [977, 977, 3/2*w^3 + 1/2*w^2 - 25/2*w + 4],\ [991, 991, -1/2*w^3 + 1/2*w^2 + 5/2*w - 8],\ [997, 997, 1/2*w^3 + 3/2*w^2 - 1/2*w - 7],\ [1013, 1013, 2*w^3 - w^2 - 14*w + 5],\ [1013, 1013, 3/2*w^3 + 3/2*w^2 - 23/2*w - 3],\ [1019, 1019, -1/2*w^3 + 3/2*w^2 + 3/2*w - 12],\ [1019, 1019, -3/2*w^3 + 7/2*w^2 + 17/2*w - 22],\ [1049, 1049, -5/2*w^3 - 5/2*w^2 + 33/2*w + 15],\ [1049, 1049, -3*w^3 - w^2 + 18*w + 3],\ [1051, 1051, 3*w^3 - 3*w^2 - 18*w + 17],\ [1061, 1061, 3/2*w^3 + 1/2*w^2 - 15/2*w - 7],\ [1061, 1061, -3*w - 5],\ [1087, 1087, w^2 - 2*w - 7],\ [1087, 1087, -w^3 - w^2 + 7*w - 1],\ [1091, 1091, 3/2*w^3 - 3/2*w^2 - 23/2*w + 3],\ [1093, 1093, 2*w^2 + w + 1],\ [1103, 1103, -2*w^3 + w^2 + 12*w - 1],\ [1103, 1103, 11/2*w^3 + 3/2*w^2 - 69/2*w - 11],\ [1103, 1103, -3/2*w^3 - 3/2*w^2 + 23/2*w + 9],\ [1103, 1103, 3/2*w^3 - 3/2*w^2 - 15/2*w + 1],\ [1109, 1109, -9/2*w^3 - 1/2*w^2 + 57/2*w + 3],\ [1151, 1151, 5/2*w^3 + 5/2*w^2 - 31/2*w - 14],\ [1151, 1151, -1/2*w^3 - 1/2*w^2 + 7/2*w - 5],\ [1153, 1153, -1/2*w^3 + 5/2*w^2 + 9/2*w - 15],\ [1163, 1163, -1/2*w^3 + 3/2*w^2 + 5/2*w - 13],\ [1163, 1163, -5/2*w^3 - 1/2*w^2 + 33/2*w + 1],\ [1181, 1181, -5/2*w^3 + 1/2*w^2 + 33/2*w - 5],\ [1181, 1181, -w^3 + w^2 + 4*w - 9],\ [1181, 1181, -5/2*w^3 + 1/2*w^2 + 35/2*w],\ [1181, 1181, -3/2*w^3 - 3/2*w^2 + 13/2*w + 6],\ [1187, 1187, 7/2*w^3 - 5/2*w^2 - 43/2*w + 15],\ [1193, 1193, -3/2*w^3 + 1/2*w^2 + 13/2*w - 2],\ [1201, 1201, -2*w^3 - 2*w^2 + 13*w + 5],\ [1201, 1201, 3/2*w^3 + 1/2*w^2 - 25/2*w + 2],\ [1213, 1213, 3*w^3 - w^2 - 18*w + 3],\ [1213, 1213, 3/2*w^3 + 5/2*w^2 - 21/2*w - 6],\ [1217, 1217, -1/2*w^3 - 1/2*w^2 + 11/2*w - 7],\ [1223, 1223, -1/2*w^3 - 1/2*w^2 - 5/2*w],\ [1237, 1237, -w^3 - 2*w^2 + 7*w + 9],\ [1259, 1259, -1/2*w^3 + 3/2*w^2 + 11/2*w - 12],\ [1279, 1279, 1/2*w^3 + 5/2*w^2 - 3/2*w - 13],\ [1279, 1279, 3/2*w^3 - 1/2*w^2 - 11/2*w + 1],\ [1297, 1297, -4*w^3 + 25*w - 1],\ [1301, 1301, 5/2*w^3 - 1/2*w^2 - 29/2*w + 4],\ [1303, 1303, -3/2*w^3 - 1/2*w^2 + 25/2*w + 4],\ [1303, 1303, w^3 + w^2 - 7*w + 3],\ [1319, 1319, 9/2*w^3 - 9/2*w^2 - 57/2*w + 29],\ [1321, 1321, 1/2*w^3 + 5/2*w^2 - 3/2*w - 8],\ [1321, 1321, w^2 - 2*w - 9],\ [1381, 1381, 1/2*w^3 + 1/2*w^2 - 1/2*w - 7],\ [1399, 1399, -1/2*w^3 + 1/2*w^2 + 1/2*w - 7],\ [1399, 1399, -w^2 - 3],\ [1409, 1409, -5/2*w^3 - 3/2*w^2 + 25/2*w],\ [1423, 1423, 5/2*w^3 - 3/2*w^2 - 31/2*w + 5],\ [1423, 1423, -w^3 + 9*w - 3],\ [1439, 1439, w^3 + 2*w^2 - 7*w - 7],\ [1439, 1439, -5/2*w^3 - 5/2*w^2 + 33/2*w + 7],\ [1447, 1447, 3/2*w^3 - 5/2*w^2 - 17/2*w + 9],\ [1451, 1451, 1/2*w^3 + 5/2*w^2 - 7/2*w - 5],\ [1459, 1459, -1/2*w^3 + 1/2*w^2 + 13/2*w],\ [1459, 1459, 1/2*w^3 + 3/2*w^2 - 17/2*w - 3],\ [1481, 1481, 3/2*w^3 - 3/2*w^2 - 21/2*w + 4],\ [1487, 1487, 7/2*w^3 - 1/2*w^2 - 43/2*w + 1],\ [1499, 1499, -3/2*w^3 - 5/2*w^2 + 11/2*w + 8],\ [1523, 1523, -5/2*w^3 + 1/2*w^2 + 29/2*w - 1],\ [1523, 1523, -3/2*w^3 + 1/2*w^2 + 11/2*w + 5],\ [1543, 1543, -2*w^3 + 10*w - 3],\ [1567, 1567, -1/2*w^3 - 5/2*w^2 + 9/2*w + 5],\ [1567, 1567, 2*w^3 - 15*w - 3],\ [1579, 1579, 1/2*w^3 + 3/2*w^2 - 3/2*w - 10],\ [1579, 1579, -3/2*w^3 + 3/2*w^2 + 13/2*w - 10],\ [1597, 1597, -1/2*w^3 - 3/2*w^2 + 11/2*w + 8],\ [1601, 1601, 2*w^3 - w^2 - 10*w + 1],\ [1601, 1601, 3/2*w^3 + 1/2*w^2 - 21/2*w + 2],\ [1613, 1613, -1/2*w^3 - 1/2*w^2 + 5/2*w - 5],\ [1619, 1619, 5/2*w^3 - 1/2*w^2 - 29/2*w + 3],\ [1619, 1619, 3*w^3 - 3*w^2 - 17*w + 19],\ [1621, 1621, w^3 + w^2 - w - 5],\ [1621, 1621, 3/2*w^3 + 5/2*w^2 - 23/2*w - 7],\ [1637, 1637, -7/2*w^3 + 1/2*w^2 + 45/2*w - 4],\ [1657, 1657, -7/2*w^3 - 5/2*w^2 + 45/2*w + 14],\ [1669, 1669, -w^3 - w^2 + 2*w + 5],\ [1693, 1693, 11/2*w^3 + 1/2*w^2 - 71/2*w - 4],\ [1699, 1699, 7/2*w^3 - 9/2*w^2 - 47/2*w + 27],\ [1699, 1699, -1/2*w^3 + 5/2*w^2 + 11/2*w - 14],\ [1733, 1733, w^3 - 9*w + 1],\ [1741, 1741, 5/2*w^3 - 1/2*w^2 - 31/2*w - 4],\ [1747, 1747, 7/2*w^3 - 5/2*w^2 - 45/2*w + 12],\ [1777, 1777, -3/2*w^3 - 1/2*w^2 + 23/2*w - 3],\ [1777, 1777, -1/2*w^3 - 1/2*w^2 - 3/2*w - 3],\ [1787, 1787, -2*w^3 - 2*w^2 + 15*w + 5],\ [1801, 1801, -1/2*w^3 - 5/2*w^2 + 11/2*w + 6],\ [1801, 1801, 1/2*w^3 - 1/2*w^2 - 9/2*w - 5],\ [1823, 1823, w^3 + 3*w^2 - 7*w - 17],\ [1823, 1823, 5/2*w^3 + 5/2*w^2 - 33/2*w - 9],\ [1847, 1847, -w^3 - 3*w^2 + 7*w + 5],\ [1861, 1861, -1/2*w^3 + 1/2*w^2 + 9/2*w - 10],\ [1861, 1861, -3/2*w^3 + 3/2*w^2 + 17/2*w - 2],\ [1871, 1871, -w^3 + w^2 + 10*w - 11],\ [1873, 1873, -5*w^3 - w^2 + 31*w + 7],\ [1879, 1879, -2*w^3 - w^2 + 8*w + 5],\ [1889, 1889, w^3 + w^2 - 7*w - 11],\ [1889, 1889, -3/2*w^3 - 1/2*w^2 + 9/2*w + 4],\ [1901, 1901, 4*w^3 - 4*w^2 - 26*w + 27],\ [1901, 1901, 3/2*w^3 + 3/2*w^2 - 21/2*w - 2],\ [1901, 1901, -1/2*w^3 + 1/2*w^2 + 13/2*w - 1],\ [1901, 1901, w^2 + 4*w - 3],\ [1907, 1907, 1/2*w^3 - 5/2*w^2 - 5/2*w + 19],\ [1913, 1913, -2*w^3 + 2*w^2 + 12*w - 7],\ [1931, 1931, -w^3 - 3*w^2 + 6*w + 5],\ [1973, 1973, 4*w^3 - 4*w^2 - 25*w + 21],\ [1973, 1973, 1/2*w^3 + 3/2*w^2 - 3/2*w - 12],\ [1979, 1979, -w^3 + 2*w^2 + 9*w - 9],\ [1979, 1979, -3/2*w^3 + 3/2*w^2 + 23/2*w - 8],\ [1987, 1987, 1/2*w^3 + 5/2*w^2 - 5/2*w - 7],\ [1993, 1993, -3*w^3 + 17*w - 3],\ [1993, 1993, -1/2*w^3 - 5/2*w^2 + 9/2*w + 11],\ [1999, 1999, -2*w^3 + 12*w - 5]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^18 - 36*x^16 + 533*x^14 - 4195*x^12 + 18957*x^10 - 49667*x^8 + 72711*x^6 - 53660*x^4 + 14928*x^2 - 64 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, 28809/2094208*e^17 - 104645/261776*e^15 + 9406877/2094208*e^13 - 51669935/2094208*e^11 + 145556401/2094208*e^9 - 205121247/2094208*e^7 + 127482939/2094208*e^5 - 1047981/261776*e^3 - 1378597/130888*e, -5733/523552*e^17 + 11805/32722*e^15 - 2492841/523552*e^13 + 16805675/523552*e^11 - 60867317/523552*e^9 + 112681611/523552*e^7 - 86803703/523552*e^5 + 217223/16361*e^3 + 259597/16361*e, 41121/1047104*e^16 - 161051/130888*e^14 + 16063957/1047104*e^12 - 102060295/1047104*e^10 + 352029849/1047104*e^8 - 649056887/1047104*e^6 + 577893587/1047104*e^4 - 22998255/130888*e^2 + 33339/65444, -1, 2429/130888*e^17 - 8505/16361*e^15 + 725849/130888*e^13 - 3715667/130888*e^11 + 9785701/130888*e^9 - 15331899/130888*e^7 + 20821607/130888*e^5 - 2835733/16361*e^3 + 1239258/16361*e, 6281/261776*e^17 - 104897/130888*e^15 + 2841533/261776*e^13 - 20116185/261776*e^11 + 80083679/261776*e^9 - 179959801/261776*e^7 + 218049145/261776*e^5 - 63783483/130888*e^3 + 3337961/32722*e, -25245/523552*e^16 + 24232/16361*e^14 - 9422481/523552*e^12 + 57887555/523552*e^10 - 191035501/523552*e^8 + 331528275/523552*e^6 - 266743967/523552*e^4 + 2014577/16361*e^2 + 263159/32722, -515/523552*e^17 - 395/32722*e^15 + 477697/523552*e^13 - 6783011/523552*e^11 + 43486909/523552*e^9 - 142731891/523552*e^7 + 240120207/523552*e^5 - 5879031/16361*e^3 + 3075799/32722*e, -69275/2094208*e^17 + 249069/261776*e^15 - 21823895/2094208*e^13 + 111909373/2094208*e^11 - 253030435/2094208*e^9 + 87879757/2094208*e^7 + 553658431/2094208*e^5 - 97158439/261776*e^3 + 17377855/130888*e, -97149/2094208*e^17 + 367697/261776*e^15 - 35041121/2094208*e^13 + 209364571/2094208*e^11 - 664315973/2094208*e^9 + 1088170251/2094208*e^7 - 778697239/2094208*e^5 + 9923649/261776*e^3 + 4224197/130888*e, 41813/2094208*e^17 - 129809/261776*e^15 + 8643353/2094208*e^13 - 20755331/2094208*e^11 - 68648675/2094208*e^9 + 405454157/2094208*e^7 - 601274785/2094208*e^5 + 33998799/261776*e^3 - 741349/130888*e, 2429/130888*e^17 - 8505/16361*e^15 + 725849/130888*e^13 - 3715667/130888*e^11 + 9785701/130888*e^9 - 15331899/130888*e^7 + 20821607/130888*e^5 - 2819372/16361*e^3 + 1124731/16361*e, 18865/1047104*e^16 - 60491/130888*e^14 + 4363557/1047104*e^12 - 14820535/1047104*e^10 + 589481/1047104*e^8 + 90247961/1047104*e^6 - 142641725/1047104*e^4 + 6554833/130888*e^2 - 70541/65444, -49681/1047104*e^17 + 202245/130888*e^15 - 21289029/1047104*e^13 + 146024679/1047104*e^11 - 562973305/1047104*e^9 + 1226775255/1047104*e^7 - 1436225683/1047104*e^5 + 100027813/130888*e^3 - 10353035/65444*e, 159047/1047104*e^16 - 613945/130888*e^14 + 60132275/1047104*e^12 - 373560369/1047104*e^10 + 1255007407/1047104*e^8 - 2249175681/1047104*e^6 + 1940701253/1047104*e^4 - 73030765/130888*e^2 - 54555/65444, 131923/1047104*e^17 - 524347/130888*e^15 + 53416943/1047104*e^13 - 350145269/1047104*e^11 + 1267033003/1047104*e^9 - 2524889029/1047104*e^7 + 2590965753/1047104*e^5 - 144715443/130888*e^3 + 9241721/65444*e, -39701/523552*e^16 + 39338/16361*e^14 - 15962937/523552*e^12 + 103947035/523552*e^10 - 371806181/523552*e^8 + 723174827/523552*e^6 - 695459463/523552*e^4 + 15352553/32722*e^2 - 22665/32722, 1597/130888*e^16 - 7515/65444*e^14 - 362931/130888*e^12 + 6612667/130888*e^10 - 40003649/130888*e^8 + 105642571/130888*e^6 - 115627487/130888*e^4 + 18565589/65444*e^2 + 255183/16361, -2189/32722*e^16 + 128151/65444*e^14 - 727671/32722*e^12 + 8122797/65444*e^10 - 23470611/65444*e^8 + 34641325/65444*e^6 - 24804919/65444*e^4 + 7816233/65444*e^2 - 96287/16361, 18457/130888*e^16 - 268453/65444*e^14 + 6045293/130888*e^12 - 33347297/130888*e^10 + 94876695/130888*e^8 - 137312177/130888*e^6 + 94330233/130888*e^4 - 12095155/65444*e^2 - 4299/16361, 567/32722*e^17 - 61597/130888*e^15 + 75358/16361*e^13 - 2306621/130888*e^11 - 90853/130888*e^9 + 25189739/130888*e^7 - 69158501/130888*e^5 + 72347989/130888*e^3 - 6321215/32722*e, -52197/2094208*e^17 + 219353/261776*e^15 - 23658089/2094208*e^13 + 162866099/2094208*e^11 - 600673901/2094208*e^9 + 1124978019/2094208*e^7 - 867222095/2094208*e^5 + 8954121/261776*e^3 + 3437013/130888*e, 5619/261776*e^17 - 18543/32722*e^15 + 1422879/261776*e^13 - 5812309/261776*e^11 + 7955259/261776*e^9 + 4600971/261776*e^7 - 11065607/261776*e^5 - 121191/32722*e^3 - 131120/16361*e, -7413/1047104*e^17 + 18141/65444*e^15 - 4345241/1047104*e^13 + 30689291/1047104*e^11 - 96229461/1047104*e^9 + 47918459/1047104*e^7 + 368856617/1047104*e^5 - 10146285/16361*e^3 + 16584359/65444*e, -27625/261776*e^16 + 98519/32722*e^14 - 8599997/261776*e^12 + 44899455/261776*e^10 - 114803137/261776*e^8 + 131361583/261776*e^6 - 46240331/261776*e^4 - 955673/32722*e^2 + 120833/16361, 12939/130888*e^17 - 396059/130888*e^15 + 4819479/130888*e^13 - 3759952/16361*e^11 + 26194171/32722*e^9 - 26355736/16361*e^7 + 122141357/65444*e^5 - 150337681/130888*e^3 + 9233617/32722*e, 34971/1047104*e^17 - 67849/65444*e^15 + 13218839/1047104*e^13 - 79241701/1047104*e^11 + 234831195/1047104*e^9 - 260248565/1047104*e^7 - 182583495/1047104*e^5 + 8582515/16361*e^3 - 15492009/65444*e, 114683/1047104*e^17 - 116691/32722*e^15 + 49004919/1047104*e^13 - 333661973/1047104*e^11 + 1265612843/1047104*e^9 - 2671346597/1047104*e^7 + 2950421769/1047104*e^5 - 91823187/65444*e^3 + 14149935/65444*e, 3839/261776*e^16 - 31269/65444*e^14 + 1635451/261776*e^12 - 10978565/261776*e^10 + 40002219/261776*e^8 - 75719141/261776*e^6 + 60155617/261776*e^4 - 790803/65444*e^2 - 264788/16361, -3911/65444*e^17 + 120539/65444*e^15 - 1481111/65444*e^13 + 2344249/16361*e^11 - 8350554/16361*e^9 + 17480133/16361*e^7 - 43928425/32722*e^5 + 63879933/65444*e^3 - 5089541/16361*e, -19871/261776*e^17 + 271849/130888*e^15 - 5532003/261776*e^13 + 25288219/261776*e^11 - 46916357/261776*e^9 + 6347147/261776*e^7 + 66096181/261776*e^5 - 26491497/130888*e^3 + 1757311/32722*e, 136469/1047104*e^17 - 524045/130888*e^15 + 50934553/1047104*e^13 - 312788707/1047104*e^11 + 1032535421/1047104*e^9 - 1802610963/1047104*e^7 + 1502273087/1047104*e^5 - 56584637/130888*e^3 + 1323479/65444*e, -81603/2094208*e^17 + 247631/261776*e^15 - 15459679/2094208*e^13 + 23264357/2094208*e^11 + 241417349/2094208*e^9 - 1156877643/2094208*e^7 + 1847039063/2094208*e^5 - 140911185/261776*e^3 + 12792963/130888*e, 122289/523552*e^16 - 463833/65444*e^14 + 44380549/523552*e^12 - 267415143/523552*e^10 + 865526617/523552*e^8 - 1494033079/523552*e^6 + 1261138899/523552*e^4 - 47614093/65444*e^2 - 559777/32722, 4909/261776*e^17 - 12437/16361*e^15 + 3204801/261776*e^13 - 26192547/261776*e^11 + 114896877/261776*e^9 - 263409875/261776*e^7 + 286391599/261776*e^5 - 7464153/16361*e^3 + 648871/16361*e, -3761/130888*e^17 + 139535/130888*e^15 - 2091697/130888*e^13 + 8095837/65444*e^11 - 34323243/65444*e^9 + 78155633/65444*e^7 - 22034107/16361*e^5 + 83044657/130888*e^3 - 2626733/32722*e, 4851/32722*e^16 - 71101/16361*e^14 + 1618497/32722*e^12 - 9065213/32722*e^10 + 26327311/32722*e^8 - 38948353/32722*e^6 + 26946291/32722*e^4 - 3440505/16361*e^2 + 150320/16361, 1345/523552*e^16 - 17157/65444*e^14 + 3220405/523552*e^12 - 32410167/523552*e^10 + 160375977/523552*e^8 - 389293351/523552*e^6 + 418061123/523552*e^4 - 18273769/65444*e^2 + 422707/32722, 10965/130888*e^17 - 322753/130888*e^15 + 3690013/130888*e^13 - 2589565/16361*e^11 + 7435346/16361*e^9 - 10149150/16361*e^7 + 16254721/65444*e^5 + 25776369/130888*e^3 - 4255767/32722*e, 8141/1047104*e^17 - 38501/130888*e^15 + 4537137/1047104*e^13 - 32360043/1047104*e^11 + 109441397/1047104*e^9 - 114451547/1047104*e^7 - 201219161/1047104*e^5 + 59333835/130888*e^3 - 13704789/65444*e, 135785/523552*e^16 - 526365/65444*e^14 + 51844509/523552*e^12 - 324575983/523552*e^10 + 1102753329/523552*e^8 - 2012251935/523552*e^6 + 1800645435/523552*e^4 - 75429217/65444*e^2 + 641499/32722, -5611/1047104*e^17 + 47465/130888*e^15 - 8195303/1047104*e^13 + 82659725/1047104*e^11 - 436163347/1047104*e^9 + 1228482909/1047104*e^7 - 1792752593/1047104*e^5 + 156530973/130888*e^3 - 21629549/65444*e, -40869/1047104*e^16 + 172239/130888*e^14 - 18796521/1047104*e^12 + 133131683/1047104*e^10 - 521683517/1047104*e^8 + 1110910867/1047104*e^6 - 1166456991/1047104*e^4 + 58343691/130888*e^2 - 794743/65444, -91061/1047104*e^16 + 355433/130888*e^14 - 35271673/1047104*e^12 + 222316771/1047104*e^10 - 757245117/1047104*e^8 + 1369241299/1047104*e^6 - 1182567039/1047104*e^4 + 42807705/130888*e^2 + 1768893/65444, -227455/523552*e^16 + 876575/65444*e^14 - 85660747/523552*e^12 + 530528649/523552*e^10 - 1775825943/523552*e^8 + 3173883353/523552*e^6 - 2750448317/523552*e^4 + 106803227/65444*e^2 + 131547/32722, -13753/65444*e^16 + 413391/65444*e^14 - 4883379/65444*e^12 + 7239722/16361*e^10 - 45985239/32722*e^8 + 39010892/16361*e^6 - 32794240/16361*e^4 + 40891735/65444*e^2 + 66111/16361, 265295/523552*e^16 - 1017085/65444*e^14 + 98713147/523552*e^12 - 605921929/523552*e^10 + 2005409047/523552*e^8 - 3537293465/523552*e^6 + 3021756509/523552*e^4 - 115906205/65444*e^2 + 493017/32722, 292685/2094208*e^17 - 1134867/261776*e^15 + 111851697/2094208*e^13 - 701278939/2094208*e^11 + 2390706245/2094208*e^9 - 4400540043/2094208*e^7 + 4034342583/2094208*e^5 - 179891855/261776*e^3 + 1351271/130888*e, -72593/523552*e^16 + 254463/65444*e^14 - 21621189/523552*e^12 + 107857495/523552*e^10 - 253428041/523552*e^8 + 242481191/523552*e^6 - 45309091/523552*e^4 - 3648253/65444*e^2 + 745485/32722, -426305/1047104*e^16 + 1647239/130888*e^14 - 161597301/1047104*e^12 + 1006684743/1047104*e^10 - 3399183577/1047104*e^8 + 6150869367/1047104*e^6 - 5414463827/1047104*e^4 + 215325899/130888*e^2 - 979051/65444, -24939/523552*e^17 + 28797/16361*e^15 - 13825095/523552*e^13 + 107883173/523552*e^11 - 466189787/523552*e^9 + 1100724661/523552*e^7 - 1320727193/523552*e^5 + 42929709/32722*e^3 - 6420475/32722*e, -171949/523552*e^16 + 623381/65444*e^14 - 55862545/523552*e^12 + 305123339/523552*e^10 - 850151381/523552*e^8 + 1173108123/523552*e^6 - 721399655/523552*e^4 + 17899649/65444*e^2 + 657961/32722, -58001/523552*e^17 + 227605/65444*e^15 - 22883781/523552*e^13 + 148589703/523552*e^11 - 540521561/523552*e^9 + 1127705399/523552*e^7 - 1329600947/523552*e^5 + 103031589/65444*e^3 - 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186689/32722*e^15 + 1941837/32722*e^13 - 4609347/16361*e^11 + 9272964/16361*e^9 - 2904866/16361*e^7 - 11978639/16361*e^5 + 21930621/32722*e^3 - 1973392/16361*e, 26913/1047104*e^17 - 54817/130888*e^15 - 948331/1047104*e^13 + 56932937/1047104*e^11 - 405223127/1047104*e^9 + 1163007897/1047104*e^7 - 1404069981/1047104*e^5 + 74964591/130888*e^3 - 2543373/65444*e, 24125/523552*e^16 - 22120/16361*e^14 + 8100289/523552*e^12 - 46275827/523552*e^10 + 142679277/523552*e^8 - 245299107/523552*e^6 + 222006399/523552*e^4 - 4243553/32722*e^2 - 645807/32722, -66423/2094208*e^17 + 432303/261776*e^15 - 66727587/2094208*e^13 + 636052337/2094208*e^11 - 3269675375/2094208*e^9 + 9174373761/2094208*e^7 - 13550245477/2094208*e^5 + 1178230167/261776*e^3 - 139266361/130888*e, 150599/2094208*e^17 - 658673/261776*e^15 + 73704051/2094208*e^13 - 521513329/2094208*e^11 + 1930456431/2094208*e^9 - 3382069249/2094208*e^7 + 1628771589/2094208*e^5 + 206299627/261776*e^3 - 71081107/130888*e, 198143/261776*e^16 - 1540479/65444*e^14 + 76127755/261776*e^12 - 478549533/261776*e^10 + 1632809235/261776*e^8 - 2989000781/261776*e^6 + 2675054409/261776*e^4 - 222732645/65444*e^2 + 1532490/16361, -394011/2094208*e^17 + 1425153/261776*e^15 - 126983447/2094208*e^13 + 683672093/2094208*e^11 - 1830521219/2094208*e^9 + 2211879021/2094208*e^7 - 622397345/2094208*e^5 - 101496587/261776*e^3 + 31141887/130888*e, -1184623/1047104*e^16 + 4524049/130888*e^14 - 436575803/1047104*e^12 + 2656671497/1047104*e^10 - 8676735831/1047104*e^8 + 15000408089/1047104*e^6 - 12441949437/1047104*e^4 + 456456549/130888*e^2 - 1248645/65444, -975567/2094208*e^17 + 3715669/261776*e^15 - 358744411/2094208*e^13 + 2204632777/2094208*e^11 - 7454557911/2094208*e^9 + 14184003289/2094208*e^7 - 14880228797/2094208*e^5 + 968540153/261776*e^3 - 90267173/130888*e, 46323/261776*e^16 - 210573/32722*e^14 + 24726063/261776*e^12 - 186936885/261776*e^10 + 769091499/261776*e^8 - 1670141253/261776*e^6 + 1706215177/261776*e^4 - 75815933/32722*e^2 + 185955/16361, 134681/261776*e^16 - 1067395/65444*e^14 + 53992909/261776*e^12 - 348598915/261776*e^10 + 1220936093/261776*e^8 - 2265373843/261776*e^6 + 1969350295/261776*e^4 - 138420049/65444*e^2 - 511194/16361, 106865/523552*e^17 - 112700/16361*e^15 + 49462661/523552*e^13 - 355507903/523552*e^11 + 1440750881/523552*e^9 - 3301165679/523552*e^7 + 4069917659/523552*e^5 - 150364411/32722*e^3 + 32252477/32722*e, 65381/1047104*e^17 - 140467/65444*e^15 + 30591049/1047104*e^13 - 206521275/1047104*e^11 + 693123109/1047104*e^9 - 893527211/1047104*e^7 - 483412089/1047104*e^5 + 56899113/32722*e^3 - 52590235/65444*e, -63555/130888*e^16 + 512351/32722*e^14 - 26486575/130888*e^12 + 175884417/130888*e^10 - 639369879/130888*e^8 + 1250181241/130888*e^6 - 1185883037/130888*e^4 + 100942869/32722*e^2 - 307716/16361, -587891/2094208*e^17 + 2289217/261776*e^15 - 225340943/2094208*e^13 + 1389530373/2094208*e^11 - 4468303707/2094208*e^9 + 6859577685/2094208*e^7 - 3016686825/2094208*e^5 - 295813155/261776*e^3 + 87904783/130888*e, 210529/1047104*e^17 - 886337/130888*e^15 + 96251285/1047104*e^13 - 673716151/1047104*e^11 + 2578218729/1047104*e^9 - 5257135015/1047104*e^7 + 5120743843/1047104*e^5 - 223674785/130888*e^3 + 1773719/65444*e, -81865/261776*e^17 + 1308353/130888*e^15 - 33645941/261776*e^13 + 224629857/261776*e^11 - 842220671/261776*e^9 + 1800208785/261776*e^7 - 2128791417/261776*e^5 + 642096063/130888*e^3 - 40959859/32722*e, 11371/32722*e^17 - 737043/65444*e^15 + 4813931/32722*e^13 - 65332321/65444*e^11 + 248011199/65444*e^9 - 529449473/65444*e^7 + 605400499/65444*e^5 - 327619825/65444*e^3 + 15369385/16361*e, -199999/1047104*e^17 + 388263/65444*e^15 - 76628491/1047104*e^13 + 480624929/1047104*e^11 - 1634291807/1047104*e^9 + 2975089137/1047104*e^7 - 2639149669/1047104*e^5 + 27551337/32722*e^3 - 5350443/65444*e, -255659/2094208*e^17 + 1151953/261776*e^15 - 135413671/2094208*e^13 + 1042461261/2094208*e^11 - 4500832403/2094208*e^9 + 10855812765/2094208*e^7 - 13827583185/2094208*e^5 + 1018175293/261776*e^3 - 97385825/130888*e, -318671/2094208*e^17 + 945691/261776*e^15 - 54277211/2094208*e^13 + 3607545/2094208*e^11 + 1578513177/2094208*e^9 - 6986092919/2094208*e^7 + 12078661043/2094208*e^5 - 1075699013/261776*e^3 + 121556831/130888*e, -108117/523552*e^16 + 440143/65444*e^14 - 45975353/523552*e^12 + 308018835/523552*e^10 - 1123961261/523552*e^8 + 2179299747/523552*e^6 - 2004624463/523552*e^4 + 80725419/65444*e^2 + 365725/32722, 15551/2094208*e^17 - 24275/261776*e^15 - 4186357/2094208*e^13 + 106330039/2094208*e^11 - 919660265/2094208*e^9 + 3899040039/2094208*e^7 - 8298256931/2094208*e^5 + 993424013/261776*e^3 - 154241927/130888*e, 18559/130888*e^16 - 173863/32722*e^14 + 10467715/130888*e^12 - 80588157/130888*e^10 + 334054371/130888*e^8 - 718280269/130888*e^6 + 703164137/130888*e^4 - 54519457/32722*e^2 - 353444/16361] 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, 1/2*w^3 + 1/2*w^2 - 7/2*w - 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]