/* 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([7, 7, -1/2*w^3 + 1/2*w^2 + 5/2*w - 2]) 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^12 - 29*x^10 + 308*x^8 - 1435*x^6 + 2617*x^4 - 820*x^2 + 64 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, 283/9456*e^11 - 2765/3152*e^9 + 22085/2364*e^7 - 134835/3152*e^5 + 679579/9456*e^3 - 17621/2364*e, 305/9456*e^11 - 2863/3152*e^9 + 21985/2364*e^7 - 130537/3152*e^5 + 672281/9456*e^3 - 42493/2364*e, -1, -109/2364*e^10 + 987/788*e^8 - 7295/591*e^6 + 41817/788*e^4 - 206689/2364*e^2 + 7286/591, 167/1576*e^11 - 4739/1576*e^9 + 12225/394*e^7 - 218469/1576*e^5 + 367471/1576*e^3 - 15459/394*e, e^3 - 9*e, 103/2364*e^10 - 817/788*e^8 + 5012/591*e^6 - 22143/788*e^4 + 79519/2364*e^2 - 3404/591, -275/4728*e^11 + 2801/1576*e^9 - 11786/591*e^7 + 154307/1576*e^5 - 873287/4728*e^3 + 27794/591*e, 113/1576*e^11 - 3301/1576*e^9 + 8817/394*e^7 - 164011/1576*e^5 + 289105/1576*e^3 - 15193/394*e, 49/788*e^11 - 1407/788*e^9 + 7345/394*e^7 - 66343/788*e^5 + 111867/788*e^3 - 6867/394*e, 73/1576*e^11 - 2265/1576*e^9 + 3201/197*e^7 - 125131/1576*e^5 + 231669/1576*e^3 - 7954/197*e, -8/591*e^11 + 125/394*e^9 - 2879/1182*e^7 + 1213/197*e^5 + 1493/1182*e^3 - 11191/1182*e, 3/197*e^10 - 58/197*e^8 + 232/197*e^6 + 1024/197*e^4 - 5956/197*e^2 + 2086/197, -527/4728*e^11 + 5213/1576*e^9 - 21314/591*e^7 + 271415/1576*e^5 - 1486427/4728*e^3 + 40169/591*e, -28/197*e^10 + 804/197*e^8 - 8338/197*e^6 + 37066/197*e^4 - 61363/197*e^2 + 10212/197, 437/2364*e^11 - 4239/788*e^9 + 33796/591*e^7 - 207977/788*e^5 + 1077653/2364*e^3 - 38065/591*e, -65/2364*e^10 + 791/788*e^8 - 7495/591*e^6 + 51989/788*e^4 - 292205/2364*e^2 + 17824/591, 115/2364*e^10 - 1157/788*e^8 + 9578/591*e^6 - 61491/788*e^4 + 338587/2364*e^2 - 17078/591, -23/197*e^10 + 576/197*e^8 - 5062/197*e^6 + 18613/197*e^4 - 25323/197*e^2 + 3970/197, 11/197*e^10 - 344/197*e^8 + 3937/197*e^6 - 19557/197*e^4 + 36145/197*e^2 - 5222/197, 359/1576*e^11 - 10027/1576*e^9 + 25393/394*e^7 - 444493/1576*e^5 + 728583/1576*e^3 - 27787/394*e, 599/4728*e^11 - 5677/1576*e^9 + 22010/591*e^7 - 261647/1576*e^5 + 1282019/4728*e^3 - 12044/591*e, -283/4728*e^11 + 2765/1576*e^9 - 22085/1182*e^7 + 134835/1576*e^5 - 689035/4728*e^3 + 34169/1182*e, 17/1182*e^11 - 219/394*e^9 + 4466/591*e^7 - 17131/394*e^5 + 112883/1182*e^3 - 23180/591*e, 95/1182*e^10 - 853/394*e^8 + 12407/591*e^6 - 34523/394*e^4 + 165665/1182*e^2 - 15368/591, -667/4728*e^11 + 6553/1576*e^9 - 26476/591*e^7 + 330171/1576*e^5 - 1733551/4728*e^3 + 33451/591*e, 563/2364*e^11 - 5445/788*e^9 + 43324/591*e^7 - 267319/788*e^5 + 1417319/2364*e^3 - 74671/591*e, 1039/4728*e^11 - 10001/1576*e^9 + 79253/1182*e^7 - 487735/1576*e^5 + 2580463/4728*e^3 - 132059/1182*e, 14/591*e^10 - 134/197*e^8 + 4366/591*e^6 - 7294/197*e^4 + 44570/591*e^2 - 7864/591, 227/4728*e^11 - 2229/1576*e^9 + 17719/1182*e^7 - 105659/1576*e^5 + 491843/4728*e^3 + 10337/1182*e, -113/788*e^11 + 3301/788*e^9 - 8817/197*e^7 + 164799/788*e^5 - 298561/788*e^3 + 19921/197*e, -161/591*e^11 + 1541/197*e^9 - 48436/591*e^7 + 73637/197*e^5 - 383717/591*e^3 + 77434/591*e, -11/2364*e^11 + 49/788*e^9 + 50/591*e^7 - 2937/788*e^5 + 34381/2364*e^3 - 8249/591*e, -76/591*e^10 + 643/197*e^8 - 17369/591*e^6 + 22063/197*e^4 - 92344/591*e^2 + 9932/591, -79/1576*e^11 + 1987/1576*e^9 - 4351/394*e^7 + 62013/1576*e^5 - 76735/1576*e^3 + 5015/394*e, 505/4728*e^11 - 5115/1576*e^9 + 21364/591*e^7 - 275713/1576*e^5 + 1488997/4728*e^3 - 22414/591*e, 47/197*e^10 - 1237/197*e^8 + 11646/197*e^6 - 46669/197*e^4 + 69280/197*e^2 - 10528/197, 397/2364*e^10 - 3631/788*e^8 + 27047/591*e^6 - 154041/788*e^4 + 731809/2364*e^2 - 32870/591, -361/4728*e^11 + 3399/1576*e^9 - 26351/1182*e^7 + 159713/1576*e^5 - 850561/4728*e^3 + 49175/1182*e, 167/1576*e^11 - 4739/1576*e^9 + 12225/394*e^7 - 218469/1576*e^5 + 370623/1576*e^3 - 21369/394*e, 245/2364*e^10 - 1951/788*e^8 + 12157/591*e^6 - 56725/788*e^4 + 237437/2364*e^2 - 12538/591, 739/4728*e^11 - 7017/1576*e^9 + 27172/591*e^7 - 321979/1576*e^5 + 1595335/4728*e^3 - 30148/591*e, -169/2364*e^10 + 1111/788*e^8 - 4712/591*e^6 + 7673/788*e^4 + 13295/2364*e^2 + 14192/591, -175/788*e^10 + 4631/788*e^8 - 10935/197*e^6 + 175025/788*e^4 - 255715/788*e^2 + 8224/197, -68/591*e^10 + 679/197*e^8 - 22135/591*e^6 + 34246/197*e^4 - 172580/591*e^2 + 18778/591, -127/1182*e^10 + 1103/394*e^8 - 15286/591*e^6 + 39769/394*e^4 - 173317/1182*e^2 + 13042/591, -16/591*e^10 + 125/197*e^8 - 2879/591*e^6 + 2623/197*e^4 - 4417/591*e^2 + 38/591, 669/1576*e^11 - 19041/1576*e^9 + 49379/394*e^7 - 889623/1576*e^5 + 1509597/1576*e^3 - 60119/394*e, 122/591*e^10 - 1027/197*e^8 + 27493/591*e^6 - 34603/197*e^4 + 147521/591*e^2 - 20236/591, -23/591*e^10 + 192/197*e^8 - 5062/591*e^6 + 6270/197*e^4 - 29066/591*e^2 + 15790/591, 245/2364*e^11 - 2345/788*e^9 + 36725/1182*e^7 - 110309/788*e^5 + 545939/2364*e^3 - 5573/1182*e, 91/591*e^10 - 871/197*e^8 + 27197/591*e^6 - 40516/197*e^4 + 200464/591*e^2 - 31022/591, -239/2364*e^11 + 2175/788*e^9 - 32159/1182*e^7 + 91423/788*e^5 - 456593/2364*e^3 + 75821/1182*e, 119/394*e^11 - 3417/394*e^9 + 17866/197*e^7 - 161963/394*e^5 + 276799/394*e^3 - 25936/197*e, -73/591*e^10 + 558/197*e^8 - 12803/591*e^6 + 12226/197*e^4 - 28759/591*e^2 + 986/591, 41/394*e^10 - 1121/394*e^8 + 5591/197*e^6 - 48717/394*e^4 + 80207/394*e^2 - 7350/197, -565/2364*e^10 + 5239/788*e^8 - 39554/591*e^6 + 228173/788*e^4 - 1096441/2364*e^2 + 39914/591, -2623/4728*e^11 + 25725/1576*e^9 - 103696/591*e^7 + 1290935/1576*e^5 - 6804283/4728*e^3 + 144955/591*e, -5/394*e^10 + 31/394*e^8 + 529/197*e^6 - 11491/394*e^4 + 29955/394*e^2 - 1804/197, -12/197*e^10 + 232/197*e^8 - 1125/197*e^6 - 747/197*e^4 + 9049/197*e^2 + 718/197, 913/1576*e^11 - 26385/1576*e^9 + 34764/197*e^7 - 1272571/1576*e^5 + 2193517/1576*e^3 - 47825/197*e, 41/1182*e^10 - 111/394*e^8 - 3274/591*e^6 + 26313/394*e^4 - 223567/1182*e^2 + 30868/591, -345/1576*e^11 + 9625/1576*e^9 - 12200/197*e^7 + 428915/1576*e^5 - 702925/1576*e^3 + 8084/197*e, -56/197*e^11 + 1608/197*e^9 - 16873/197*e^7 + 77284/197*e^5 - 135728/197*e^3 + 29486/197*e, -20/591*e^10 + 107/197*e^8 - 496/591*e^6 - 3764/197*e^4 + 43975/591*e^2 - 17978/591, -14/197*e^10 + 402/197*e^8 - 4169/197*e^6 + 18533/197*e^4 - 30189/197*e^2 + 2742/197, 223/788*e^11 - 6347/788*e^9 + 16394/197*e^7 - 292601/788*e^5 + 489803/788*e^3 - 20565/197*e, 5/2364*e^10 - 667/788*e^8 + 10669/591*e^6 - 99529/788*e^4 + 694217/2364*e^2 - 35740/591, 251/1576*e^11 - 7151/1576*e^9 + 18577/394*e^7 - 337153/1576*e^5 + 589187/1576*e^3 - 30013/394*e, -961/4728*e^11 + 9367/1576*e^9 - 74987/1182*e^7 + 462857/1576*e^5 - 2395297/4728*e^3 + 73319/1182*e, 493/2364*e^10 - 4775/788*e^8 + 38162/591*e^6 - 237941/788*e^4 + 1277209/2364*e^2 - 53612/591, 2927/4728*e^11 - 28297/1576*e^9 + 224761/1182*e^7 - 1379975/1576*e^5 + 7199663/4728*e^3 - 316981/1182*e, -1123/4728*e^11 + 10805/1576*e^9 - 85211/1182*e^7 + 515739/1576*e^5 - 2578387/4728*e^3 + 51659/1182*e, -11/2364*e^10 + 49/788*e^8 + 50/591*e^6 - 2149/788*e^4 + 15469/2364*e^2 - 11204/591, 623/2364*e^10 - 5569/788*e^8 + 40150/591*e^6 - 219779/788*e^4 + 1012943/2364*e^2 - 41980/591, -41/1182*e^10 + 505/394*e^8 - 10319/591*e^6 + 40667/394*e^4 - 270509/1182*e^2 + 36506/591, -31/394*e^10 + 665/394*e^8 - 2315/197*e^6 + 12599/394*e^4 - 17189/394*e^2 + 7806/197, 59/2364*e^10 - 621/788*e^8 + 5212/591*e^6 - 32315/788*e^4 + 160307/2364*e^2 + 242/591, -34/591*e^10 + 241/197*e^8 - 4271/591*e^6 + 575/197*e^4 + 28364/591*e^2 - 658/591, -281/1182*e^11 + 1387/197*e^9 - 89827/1182*e^7 + 139703/394*e^5 - 365776/591*e^3 + 129727/1182*e, -202/591*e^10 + 1849/197*e^8 - 55481/591*e^6 + 80814/197*e^4 - 406006/591*e^2 + 66524/591, -323/2364*e^11 + 2979/788*e^9 - 45257/1182*e^7 + 135187/788*e^5 - 726377/2364*e^3 + 106505/1182*e, -671/1576*e^11 + 19211/1576*e^9 - 49943/394*e^7 + 895901/1576*e^5 - 1492887/1576*e^3 + 52351/394*e, 33/197*e^10 - 835/197*e^8 + 7477/197*e^6 - 28530/197*e^4 + 41061/197*e^2 - 1088/197, 141/788*e^10 - 4105/788*e^8 + 10803/197*e^6 - 194379/788*e^4 + 319145/788*e^2 - 10260/197, 535/4728*e^11 - 5177/1576*e^9 + 41141/1182*e^7 - 250367/1576*e^5 + 1226527/4728*e^3 + 3727/1182*e, 21/788*e^10 - 209/788*e^8 - 579/197*e^6 + 31793/788*e^4 - 91927/788*e^2 + 3158/197, 71/591*e^10 - 567/197*e^8 + 13699/591*e^6 - 13745/197*e^4 + 29906/591*e^2 + 14828/591, 7/591*e^10 - 67/197*e^8 + 2183/591*e^6 - 3844/197*e^4 + 26422/591*e^2 + 3160/591, -1265/2364*e^11 + 11939/788*e^9 - 92356/591*e^7 + 552685/788*e^5 - 2842685/2364*e^3 + 154762/591*e, 101/1576*e^11 - 3069/1576*e^9 + 4194/197*e^7 - 154711/1576*e^5 + 253041/1576*e^3 - 3616/197*e, 157/4728*e^11 - 1559/1576*e^9 + 6574/591*e^7 - 91253/1576*e^5 + 614137/4728*e^3 - 43993/591*e, 385/1182*e^11 - 3685/394*e^9 + 57964/591*e^7 - 176551/394*e^5 + 919537/1182*e^3 - 83899/591*e, -191/2364*e^10 + 1997/788*e^8 - 17023/591*e^6 + 109755/788*e^4 - 579863/2364*e^2 + 16606/591, -415/788*e^11 + 12029/788*e^9 - 63655/394*e^7 + 586393/788*e^5 - 1025457/788*e^3 + 99079/394*e, -79/591*e^10 + 728/197*e^8 - 21344/591*e^6 + 28945/197*e^4 - 128152/591*e^2 + 20060/591, 67/788*e^11 - 2149/788*e^9 + 12375/394*e^7 - 119693/788*e^5 + 201817/788*e^3 - 609/394*e, 11/788*e^10 - 147/788*e^8 - 50/197*e^6 + 6447/788*e^4 - 5225/788*e^2 - 6920/197, -91/394*e^11 + 2613/394*e^9 - 13697/197*e^7 + 124897/394*e^5 - 214057/394*e^3 + 15117/197*e, -461/1182*e^11 + 4525/394*e^9 - 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97718/591*e^7 + 589871/788*e^5 - 2954839/2364*e^3 + 90617/591*e, 274/591*e^10 - 2510/197*e^8 + 74642/591*e^6 - 106506/197*e^4 + 522511/591*e^2 - 92108/591, 1/6*e^10 - 7/2*e^8 + 64/3*e^6 - 49/2*e^4 - 359/6*e^2 - 142/3, -64/591*e^10 + 697/197*e^8 - 25109/591*e^6 + 43785/197*e^4 - 258205/591*e^2 + 43886/591, 35/591*e^10 - 335/197*e^8 + 10324/591*e^6 - 15083/197*e^4 + 83057/591*e^2 - 44482/591, -41/394*e^10 + 1121/394*e^8 - 5591/197*e^6 + 48717/394*e^4 - 81389/394*e^2 + 5774/197, 583/2364*e^10 - 4961/788*e^8 + 32810/591*e^6 - 152447/788*e^4 + 494527/2364*e^2 + 9904/591, -145/788*e^10 + 4445/788*e^8 - 12522/197*e^6 + 247123/788*e^4 - 464601/788*e^2 + 27032/197, 1133/4728*e^11 - 10563/1576*e^9 + 80545/1182*e^7 - 475245/1576*e^5 + 2458589/4728*e^3 - 198787/1182*e, -2923/4728*e^11 + 28709/1576*e^9 - 232301/1182*e^7 + 1456691/1576*e^5 - 7808323/4728*e^3 + 397133/1182*e, -69/394*e^10 + 1531/394*e^8 - 5426/197*e^6 + 25895/394*e^4 - 9383/394*e^2 - 2122/197, -5347/4728*e^11 + 51685/1576*e^9 - 409973/1182*e^7 + 2508411/1576*e^5 - 13034995/4728*e^3 + 623891/1182*e, -3371/2364*e^11 + 32603/788*e^9 - 517319/1182*e^7 + 1581355/788*e^5 - 8169581/2364*e^3 + 698465/1182*e, -250/591*e^10 + 2027/197*e^8 - 50525/591*e^6 + 55193/197*e^4 - 172810/591*e^2 - 1918/591, 4789/4728*e^11 - 46119/1576*e^9 + 182158/591*e^7 - 2219269/1576*e^5 + 11453761/4728*e^3 - 252883/591*e, -313/4728*e^11 + 2827/1576*e^9 - 10249/591*e^7 + 112641/1576*e^5 - 521125/4728*e^3 + 1081/591*e, -1015/4728*e^11 + 9321/1576*e^9 - 70121/1182*e^7 + 412191/1576*e^5 - 2199439/4728*e^3 + 219365/1182*e, 137/1182*e^11 - 726/197*e^9 + 50323/1182*e^7 - 83985/394*e^5 + 245725/591*e^3 - 184939/1182*e, 179/4728*e^11 - 1657/1576*e^9 + 6524/591*e^7 - 86955/1576*e^5 + 635207/4728*e^3 - 83615/591*e, 167/591*e^10 - 1711/197*e^8 + 56977/591*e^6 - 89568/197*e^4 + 461834/591*e^2 - 64594/591, 203/788*e^10 - 5435/788*e^8 + 13315/197*e^6 - 231397/788*e^4 + 395287/788*e^2 - 14914/197, -1819/2364*e^10 + 16341/788*e^8 - 118958/591*e^6 + 662443/788*e^4 - 3127195/2364*e^2 + 125504/591, -4277/4728*e^11 + 41331/1576*e^9 - 327691/1182*e^7 + 2002949/1576*e^5 - 10369181/4728*e^3 + 469411/1182*e, 315/788*e^10 - 10227/788*e^8 + 30124/197*e^6 - 608969/788*e^4 + 1137967/788*e^2 - 47978/197, 571/591*e^11 - 5409/197*e^9 + 167939/591*e^7 - 251393/197*e^5 + 1277983/591*e^3 - 220100/591*e, 1071/1576*e^11 - 30359/1576*e^9 + 39115/197*e^7 - 1399749/1576*e^5 + 2392691/1576*e^3 - 69782/197*e, 15/1576*e^11 - 487/1576*e^9 + 736/197*e^7 - 32901/1576*e^5 + 85859/1576*e^3 - 11452/197*e, 286/591*e^10 - 2653/197*e^8 + 79904/591*e^6 - 114334/197*e^4 + 541633/591*e^2 - 79430/591, -2017/1576*e^11 + 57973/1576*e^9 - 151745/394*e^7 + 2753843/1576*e^5 - 4691097/1576*e^3 + 195495/394*e, 71/1576*e^11 - 2095/1576*e^9 + 2722/197*e^7 - 90485/1576*e^5 + 106539/1576*e^3 + 6286/197*e, -601/2364*e^10 + 7047/788*e^8 - 66254/591*e^6 + 465993/788*e^4 - 2670313/2364*e^2 + 122306/591, -765/1576*e^11 + 21685/1576*e^9 - 27883/197*e^7 + 987663/1576*e^5 - 1601897/1576*e^3 + 12752/197*e, 325/788*e^10 - 10289/788*e^8 + 29398/197*e^6 - 571015/788*e^4 + 1006349/788*e^2 - 42234/197, 1435/4728*e^11 - 13341/1576*e^9 + 101093/1182*e^7 - 586883/1576*e^5 + 2865163/4728*e^3 - 93953/1182*e, -221/591*e^10 + 1862/197*e^8 - 49924/591*e^6 + 62739/197*e^4 - 265976/591*e^2 + 57778/591, -3/394*e^10 + 649/394*e^8 - 6814/197*e^6 + 96097/394*e^4 - 225125/394*e^2 + 20430/197, -112/197*e^11 + 6235/394*e^9 - 63355/394*e^7 + 141172/197*e^5 - 491101/394*e^3 + 124839/394*e, -161/2364*e^11 + 1541/788*e^9 - 24809/1182*e^7 + 81517/788*e^5 - 522011/2364*e^3 + 152189/1182*e, 193/591*e^10 - 1594/197*e^8 + 41192/591*e^6 - 48151/197*e^4 + 169744/591*e^2 + 6412/591, -1255/1576*e^11 + 35755/1576*e^9 - 92491/394*e^7 + 1652669/1576*e^5 - 2748935/1576*e^3 + 87025/394*e, 97/2364*e^11 - 647/788*e^9 + 2138/591*e^7 + 11715/788*e^5 - 265139/2364*e^3 + 62533/591*e, -3049/4728*e^11 + 29127/1576*e^9 - 227645/1182*e^7 + 1366313/1576*e^5 - 6850153/4728*e^3 + 200885/1182*e, 4631/4728*e^11 - 45057/1576*e^9 + 360145/1182*e^7 - 2222055/1576*e^5 + 11614703/4728*e^3 - 512875/1182*e, -119/1182*e^11 + 1139/394*e^9 - 18260/591*e^7 + 59635/394*e^5 - 382391/1182*e^3 + 107297/591*e, -671/1182*e^11 + 6141/394*e^9 - 91415/591*e^7 + 259759/394*e^5 - 1219451/1182*e^3 + 48557/591*e, 791/2364*e^11 - 7965/788*e^9 + 65659/591*e^7 - 414475/788*e^5 + 2195519/2364*e^3 - 112261/591*e, 232/591*e^10 - 2108/197*e^8 + 62135/591*e^6 - 87185/197*e^4 + 409486/591*e^2 - 64970/591, 511/1182*e^11 - 2347/197*e^9 + 140447/1182*e^7 - 201221/394*e^5 + 486875/591*e^3 - 180065/1182*e, -287/1182*e^10 + 2747/394*e^8 - 43274/591*e^6 + 132191/394*e^4 - 698561/1182*e^2 + 65240/591] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([7, 7, -1/2*w^3 + 1/2*w^2 + 5/2*w - 2])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]