/* 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([12, 6, 1/2*w^3 + 1/2*w^2 - 5/2*w]) 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^5 + 5*x^4 - 5*x^3 - 51*x^2 - 54*x - 4 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1, e, -1, -e^4 - 2*e^3 + 10*e^2 + 19*e + 4, 1/2*e^4 + 1/2*e^3 - 11/2*e^2 - 11/2*e + 2, -e^4 - e^3 + 11*e^2 + 9*e - 4, 1/2*e^4 + 3/2*e^3 - 7/2*e^2 - 29/2*e - 10, -3/2*e^4 - 5/2*e^3 + 31/2*e^2 + 47/2*e + 3, -1/2*e^4 - 3/2*e^3 + 11/2*e^2 + 31/2*e + 1, -e^4 - 2*e^3 + 9*e^2 + 18*e + 10, 1/2*e^4 + 1/2*e^3 - 9/2*e^2 - 7/2*e - 5, -5/2*e^4 - 9/2*e^3 + 53/2*e^2 + 91/2*e + 5, -e^3 + 11*e + 4, 5/2*e^4 + 11/2*e^3 - 51/2*e^2 - 113/2*e - 10, 3/2*e^4 + 3/2*e^3 - 35/2*e^2 - 31/2*e + 6, -3*e^4 - 6*e^3 + 30*e^2 + 59*e + 18, e^3 - 9*e - 4, -3/2*e^4 - 3/2*e^3 + 31/2*e^2 + 29/2*e + 7, -e^4 - e^3 + 12*e^2 + 10*e - 12, -5/2*e^4 - 5/2*e^3 + 57/2*e^2 + 51/2*e - 13, -e^4 + 11*e^2 - 2*e - 10, -5/2*e^4 - 7/2*e^3 + 55/2*e^2 + 65/2*e - 10, -e^4 + 11*e^2 + 2*e, 2*e^4 + 3*e^3 - 21*e^2 - 30*e - 2, -3*e^4 - 6*e^3 + 31*e^2 + 60*e + 10, 2*e^3 + 3*e^2 - 19*e - 16, e^4 + 3*e^3 - 9*e^2 - 33*e - 10, -2*e^4 - 3*e^3 + 22*e^2 + 27*e, -5/2*e^4 - 9/2*e^3 + 49/2*e^2 + 91/2*e + 17, e^4 + e^3 - 11*e^2 - 9*e + 10, 3/2*e^4 + 5/2*e^3 - 35/2*e^2 - 49/2*e + 12, -5/2*e^4 - 11/2*e^3 + 51/2*e^2 + 105/2*e + 16, -1/2*e^4 - 1/2*e^3 + 9/2*e^2 + 11/2*e - 3, -1/2*e^4 - 3/2*e^3 + 11/2*e^2 + 29/2*e + 8, 5/2*e^4 + 5/2*e^3 - 55/2*e^2 - 47/2*e + 12, 7/2*e^4 + 13/2*e^3 - 73/2*e^2 - 127/2*e - 2, -3*e^3 - 2*e^2 + 29*e + 12, 7/2*e^4 + 9/2*e^3 - 75/2*e^2 - 79/2*e + 11, e^4 + 3*e^3 - 11*e^2 - 29*e + 10, -3/2*e^4 - 7/2*e^3 + 31/2*e^2 + 57/2*e - 3, -9/2*e^4 - 21/2*e^3 + 91/2*e^2 + 213/2*e + 25, 4*e^4 + 6*e^3 - 44*e^2 - 62*e + 6, -7/2*e^4 - 13/2*e^3 + 73/2*e^2 + 131/2*e + 14, -1/2*e^4 - 7/2*e^3 + 5/2*e^2 + 65/2*e + 11, 3/2*e^4 + 5/2*e^3 - 33/2*e^2 - 55/2*e + 6, 2*e^4 + 4*e^3 - 20*e^2 - 36*e - 8, 7/2*e^4 + 9/2*e^3 - 77/2*e^2 - 75/2*e + 20, -2*e^4 - 3*e^3 + 21*e^2 + 32*e + 8, 3*e^4 + 8*e^3 - 29*e^2 - 82*e - 26, 3*e^4 + 3*e^3 - 34*e^2 - 24*e + 26, -11/2*e^4 - 23/2*e^3 + 111/2*e^2 + 221/2*e + 15, 5*e^4 + 9*e^3 - 51*e^2 - 87*e - 10, -3/2*e^4 - 3/2*e^3 + 29/2*e^2 + 25/2*e + 16, -e^4 - e^3 + 11*e^2 + 9*e, 3/2*e^4 + 3/2*e^3 - 35/2*e^2 - 13/2*e + 23, -5/2*e^4 - 9/2*e^3 + 53/2*e^2 + 91/2*e + 11, 5/2*e^4 + 7/2*e^3 - 55/2*e^2 - 61/2*e + 12, -5*e^4 - 12*e^3 + 50*e^2 + 125*e + 34, -11/2*e^4 - 19/2*e^3 + 113/2*e^2 + 183/2*e + 19, -2*e^3 - 2*e^2 + 24*e + 12, 1/2*e^4 - 3/2*e^3 - 15/2*e^2 + 41/2*e + 20, -3/2*e^4 - 1/2*e^3 + 37/2*e^2 + 13/2*e - 23, 5/2*e^4 + 9/2*e^3 - 51/2*e^2 - 91/2*e - 26, -2*e^4 - 9*e^3 + 16*e^2 + 87*e + 40, 7/2*e^4 + 13/2*e^3 - 71/2*e^2 - 133/2*e - 12, 2*e^4 + 2*e^3 - 24*e^2 - 20*e + 6, 4*e^4 + 6*e^3 - 43*e^2 - 63*e, 5*e^4 + 6*e^3 - 53*e^2 - 56*e + 2, -15/2*e^4 - 23/2*e^3 + 155/2*e^2 + 209/2*e + 3, -9/2*e^4 - 13/2*e^3 + 101/2*e^2 + 115/2*e - 29, 1/2*e^4 - 1/2*e^3 - 13/2*e^2 + 17/2*e + 20, -e^4 - 3*e^3 + 8*e^2 + 32*e + 26, 5/2*e^4 + 5/2*e^3 - 61/2*e^2 - 49/2*e + 20, 4*e^4 + 10*e^3 - 38*e^2 - 106*e - 40, -7*e^4 - 15*e^3 + 71*e^2 + 143*e + 16, 5/2*e^4 + 7/2*e^3 - 53/2*e^2 - 65/2*e + 15, 5*e^4 + 9*e^3 - 53*e^2 - 83*e + 12, 2*e^4 + 4*e^3 - 23*e^2 - 35*e + 16, -4*e^4 - 8*e^3 + 41*e^2 + 79*e + 24, -7/2*e^4 - 7/2*e^3 + 77/2*e^2 + 53/2*e - 22, 4*e^4 + 9*e^3 - 42*e^2 - 87*e - 18, 5*e^4 + 6*e^3 - 53*e^2 - 50*e + 16, e^4 - 11*e^2 - 2*e - 14, -2*e^3 + 22*e + 14, 5/2*e^4 + 11/2*e^3 - 51/2*e^2 - 113/2*e - 24, 1/2*e^4 + 13/2*e^3 - 1/2*e^2 - 139/2*e - 43, -11/2*e^4 - 19/2*e^3 + 123/2*e^2 + 193/2*e - 7, -3/2*e^4 - 7/2*e^3 + 33/2*e^2 + 77/2*e + 10, 1/2*e^4 + 3/2*e^3 - 11/2*e^2 - 37/2*e + 4, 11/2*e^4 + 21/2*e^3 - 115/2*e^2 - 207/2*e - 13, 1/2*e^4 - 1/2*e^3 - 7/2*e^2 + 27/2*e - 20, 9/2*e^4 + 11/2*e^3 - 95/2*e^2 - 103/2*e - 3, -e^4 - 3*e^3 + 11*e^2 + 29*e - 20, 4*e^4 + 7*e^3 - 44*e^2 - 73*e - 6, 2*e^4 + 5*e^3 - 17*e^2 - 44*e - 38, 4*e^3 + 2*e^2 - 34*e - 6, 2*e^3 - 4*e^2 - 20*e + 30, 11/2*e^4 + 21/2*e^3 - 109/2*e^2 - 199/2*e - 26, -15/2*e^4 - 25/2*e^3 + 159/2*e^2 + 243/2*e + 5, 3*e^4 + e^3 - 35*e^2 - e + 28, -7/2*e^4 - 17/2*e^3 + 69/2*e^2 + 151/2*e + 12, -6*e^4 - 14*e^3 + 60*e^2 + 142*e + 46, -e^3 - 4*e^2 + 9*e + 26, -e^4 + 11*e^2 - 6*e - 4, 3*e^4 + 3*e^3 - 33*e^2 - 31*e, 13/2*e^4 + 33/2*e^3 - 121/2*e^2 - 321/2*e - 54, -2*e^4 + e^3 + 22*e^2 - 15*e - 30, 5/2*e^4 + 7/2*e^3 - 53/2*e^2 - 67/2*e + 18, -e^4 - e^3 + 17*e^2 + 9*e - 40, 5*e^4 + 6*e^3 - 53*e^2 - 52*e - 4, -3*e^4 - e^3 + 35*e^2 + 7*e - 12, -2*e^4 - 6*e^3 + 18*e^2 + 54*e + 22, -e^4 + e^3 + 13*e^2 - 5*e + 2, 3*e^4 + 7*e^3 - 32*e^2 - 64*e + 10, -4*e^4 - 12*e^3 + 36*e^2 + 116*e + 54, -3*e^4 - 3*e^3 + 28*e^2 + 24*e + 12, 5*e^4 + 11*e^3 - 55*e^2 - 111*e - 12, 9*e^4 + 16*e^3 - 95*e^2 - 156*e - 4, -2*e^4 - 3*e^3 + 20*e^2 + 27*e + 24, 4*e^4 + 6*e^3 - 42*e^2 - 60*e + 4, -5*e^4 - 13*e^3 + 49*e^2 + 127*e + 34, -5*e^4 - 11*e^3 + 51*e^2 + 119*e + 34, 4*e^4 + 8*e^3 - 38*e^2 - 78*e - 32, 7*e^4 + 9*e^3 - 79*e^2 - 83*e + 40, -5*e^4 - 11*e^3 + 48*e^2 + 112*e + 52, 4*e^4 + 13*e^3 - 39*e^2 - 124*e - 24, -11*e^4 - 21*e^3 + 115*e^2 + 213*e + 32, 4*e^4 + 6*e^3 - 40*e^2 - 66*e - 26, -11/2*e^4 - 13/2*e^3 + 113/2*e^2 + 127/2*e + 28, 1/2*e^4 + 7/2*e^3 + 3/2*e^2 - 61/2*e - 35, -4*e^2 - 10*e + 20, 5/2*e^4 + 11/2*e^3 - 49/2*e^2 - 99/2*e - 2, -9*e^4 - 21*e^3 + 89*e^2 + 205*e + 48, 11/2*e^4 + 21/2*e^3 - 105/2*e^2 - 191/2*e - 34, -17/2*e^4 - 17/2*e^3 + 187/2*e^2 + 155/2*e - 20, 5*e^4 + 10*e^3 - 55*e^2 - 94*e + 6, 4*e^4 + 8*e^3 - 44*e^2 - 72*e + 14, 7*e^4 + 9*e^3 - 74*e^2 - 82*e + 16, -2*e^4 - 5*e^3 + 21*e^2 + 46*e - 2, 2*e^4 + 6*e^3 - 16*e^2 - 64*e - 16, e^4 + 3*e^3 - 11*e^2 - 27*e - 16, 4*e^4 + 8*e^3 - 42*e^2 - 70*e + 2, 7/2*e^4 + 3/2*e^3 - 83/2*e^2 - 21/2*e + 31, -4*e^4 - 12*e^3 + 34*e^2 + 120*e + 56, -1/2*e^4 + 1/2*e^3 + 13/2*e^2 - 3/2*e + 21, 4*e^4 + 10*e^3 - 36*e^2 - 110*e - 60, 7*e^4 + 14*e^3 - 68*e^2 - 127*e - 46, -13/2*e^4 - 23/2*e^3 + 129/2*e^2 + 221/2*e + 39, -4*e^4 - 8*e^3 + 45*e^2 + 77*e - 18, 15/2*e^4 + 31/2*e^3 - 155/2*e^2 - 317/2*e - 27, 3*e^4 + 8*e^3 - 35*e^2 - 82*e + 12, -13/2*e^4 - 29/2*e^3 + 137/2*e^2 + 287/2*e + 13, -6*e^4 - 17*e^3 + 54*e^2 + 169*e + 70, 6*e^4 + 10*e^3 - 62*e^2 - 102*e - 14, -10*e^4 - 19*e^3 + 99*e^2 + 176*e + 44, 11/2*e^4 + 9/2*e^3 - 117/2*e^2 - 59/2*e + 8, -7*e^4 - 14*e^3 + 69*e^2 + 130*e + 28, 4*e^4 + 5*e^3 - 47*e^2 - 40*e + 42, 5*e^4 + 7*e^3 - 57*e^2 - 67*e + 44, -6*e^4 - 12*e^3 + 66*e^2 + 118*e - 2, 10*e^4 + 14*e^3 - 108*e^2 - 132*e + 6, 5*e^4 + 11*e^3 - 47*e^2 - 111*e - 60, -1/2*e^4 + 13/2*e^3 + 21/2*e^2 - 129/2*e - 56, -1/2*e^4 - 1/2*e^3 + 17/2*e^2 + 3/2*e - 31, 2*e^4 + 6*e^3 - 24*e^2 - 58*e + 14, 4*e^4 + 10*e^3 - 40*e^2 - 92*e - 18, -14*e^4 - 24*e^3 + 144*e^2 + 228*e + 32, 2*e^4 + 7*e^3 - 14*e^2 - 71*e - 54, 6*e^4 + 16*e^3 - 56*e^2 - 160*e - 64, -7/2*e^4 - 19/2*e^3 + 67/2*e^2 + 189/2*e + 51, -1/2*e^4 + 1/2*e^3 + 9/2*e^2 + 5/2*e + 27, 8*e^4 + 9*e^3 - 83*e^2 - 74*e - 8, 7*e^4 + 7*e^3 - 75*e^2 - 59*e + 18, 9*e^4 + 13*e^3 - 97*e^2 - 123*e + 18, 5*e^3 + 2*e^2 - 49*e - 28, -7/2*e^4 - 21/2*e^3 + 69/2*e^2 + 229/2*e + 51, 15/2*e^4 + 29/2*e^3 - 159/2*e^2 - 279/2*e + 5, -2*e^4 - 4*e^3 + 22*e^2 + 50*e - 2, -3*e^4 - 5*e^3 + 32*e^2 + 56*e - 10, 21/2*e^4 + 35/2*e^3 - 219/2*e^2 - 345/2*e - 30, -2*e^4 - 2*e^3 + 20*e^2 + 22*e - 4, -13/2*e^4 - 29/2*e^3 + 129/2*e^2 + 287/2*e + 39, -3/2*e^4 - 11/2*e^3 + 29/2*e^2 + 131/2*e + 17, -5/2*e^4 - 17/2*e^3 + 51/2*e^2 + 179/2*e + 28, 12*e^4 + 22*e^3 - 128*e^2 - 212*e + 14, -3*e^4 - 10*e^3 + 30*e^2 + 107*e + 58, 7/2*e^4 + 15/2*e^3 - 83/2*e^2 - 161/2*e + 21, 6*e^4 + 11*e^3 - 67*e^2 - 106*e + 24, e^3 - 4*e^2 - 7*e + 46, -13/2*e^4 - 21/2*e^3 + 147/2*e^2 + 199/2*e - 46, -23/2*e^4 - 41/2*e^3 + 229/2*e^2 + 387/2*e + 58, 9*e^4 + 20*e^3 - 91*e^2 - 192*e - 34, 8*e^4 + 20*e^3 - 77*e^2 - 193*e - 78, 3*e^4 + 9*e^3 - 29*e^2 - 83*e + 8, 3*e^4 + 12*e^3 - 23*e^2 - 128*e - 56, -5*e^3 - 4*e^2 + 61*e + 34, 9/2*e^4 + 13/2*e^3 - 87/2*e^2 - 139/2*e - 32, -2*e^4 - 4*e^3 + 22*e^2 + 40*e - 36, -1/2*e^4 + 9/2*e^3 + 27/2*e^2 - 91/2*e - 44, 9/2*e^4 + 15/2*e^3 - 93/2*e^2 - 169/2*e - 17, -7*e^4 - 13*e^3 + 71*e^2 + 129*e + 54, -15/2*e^4 - 33/2*e^3 + 149/2*e^2 + 331/2*e + 24, 3*e^4 + 14*e^3 - 23*e^2 - 150*e - 72, 11/2*e^4 + 29/2*e^3 - 103/2*e^2 - 295/2*e - 73, 9/2*e^4 + 23/2*e^3 - 89/2*e^2 - 237/2*e - 37, 4*e^4 + 9*e^3 - 44*e^2 - 79*e + 48, 6*e^4 + 14*e^3 - 58*e^2 - 136*e - 16, 25/2*e^4 + 43/2*e^3 - 263/2*e^2 - 429/2*e - 28, 17/2*e^4 + 31/2*e^3 - 189/2*e^2 - 301/2*e + 29, -5/2*e^4 + 3/2*e^3 + 59/2*e^2 - 71/2*e - 37, 9/2*e^4 + 7/2*e^3 - 103/2*e^2 - 81/2*e + 32, -5*e^4 - 7*e^3 + 58*e^2 + 64*e - 44, -15/2*e^4 - 33/2*e^3 + 157/2*e^2 + 335/2*e + 28, -9/2*e^4 - 9/2*e^3 + 103/2*e^2 + 79/2*e + 8, -9/2*e^4 - 11/2*e^3 + 95/2*e^2 + 109/2*e + 12, -9/2*e^4 - 21/2*e^3 + 97/2*e^2 + 215/2*e + 15, -6*e^4 - 4*e^3 + 66*e^2 + 40*e - 16, 9/2*e^4 + 19/2*e^3 - 95/2*e^2 - 189/2*e + 10, 7*e^4 + 13*e^3 - 78*e^2 - 128*e + 40, -e^4 - e^3 + 9*e^2 + 15*e + 52, -2*e^3 + 22*e + 30, -4*e^4 - 6*e^3 + 38*e^2 + 46*e + 32, 7/2*e^4 + 25/2*e^3 - 69/2*e^2 - 267/2*e - 54, 4*e^4 + 12*e^3 - 40*e^2 - 132*e - 28, -e^4 + 5*e^3 + 17*e^2 - 61*e - 54, 3/2*e^4 - 1/2*e^3 - 27/2*e^2 + 13/2*e - 38, 15/2*e^4 + 7/2*e^3 - 179/2*e^2 - 61/2*e + 59, 21/2*e^4 + 37/2*e^3 - 221/2*e^2 - 379/2*e - 35, 1/2*e^4 - 3/2*e^3 - 11/2*e^2 + 33/2*e + 8, -5*e^4 - 4*e^3 + 57*e^2 + 42*e - 38, -3/2*e^4 - 7/2*e^3 + 15/2*e^2 + 61/2*e + 37, 10*e^4 + 17*e^3 - 105*e^2 - 160*e - 16, -2*e^4 - 2*e^3 + 24*e^2 + 20*e, -3/2*e^4 - 13/2*e^3 + 35/2*e^2 + 149/2*e + 18, 31/2*e^4 + 51/2*e^3 - 329/2*e^2 - 481/2*e + 10, 3*e^4 + 6*e^3 - 33*e^2 - 58*e + 22, -5*e^4 - 11*e^3 + 48*e^2 + 110*e + 32, 12*e^4 + 23*e^3 - 128*e^2 - 233*e - 18, -11*e^4 - 15*e^3 + 123*e^2 + 147*e - 20, -e^3 + 8*e^2 + 13*e - 36, 7/2*e^4 - 7/2*e^3 - 89/2*e^2 + 77/2*e + 56, 9*e^4 + 21*e^3 - 87*e^2 - 203*e - 28, -11/2*e^4 - 31/2*e^3 + 105/2*e^2 + 293/2*e + 68, 7*e^4 + 15*e^3 - 77*e^2 - 149*e + 22, -14*e^4 - 24*e^3 + 148*e^2 + 230*e + 2, -e^4 - 7*e^3 + 12*e^2 + 62*e - 14, 3*e^4 + 6*e^3 - 28*e^2 - 53*e - 4, e^4 + 3*e^3 - 7*e^2 - 49*e - 44, 11*e^4 + 20*e^3 - 110*e^2 - 199*e - 72, -2*e^4 - e^3 + 22*e^2 + 5*e + 2, 9/2*e^4 + 9/2*e^3 - 103/2*e^2 - 93/2*e + 31, -e^4 - e^3 + 7*e^2 + 11*e + 34, 29/2*e^4 + 51/2*e^3 - 299/2*e^2 - 501/2*e - 56, 3/2*e^4 + 13/2*e^3 - 31/2*e^2 - 149/2*e - 20, 8*e^4 + 14*e^3 - 84*e^2 - 130*e + 22, -1/2*e^4 - 13/2*e^3 + 9/2*e^2 + 147/2*e + 39, -1/2*e^4 + 3/2*e^3 + 17/2*e^2 - 21/2*e - 57, -15/2*e^4 - 9/2*e^3 + 177/2*e^2 + 79/2*e - 72, 3/2*e^4 + 11/2*e^3 - 29/2*e^2 - 87/2*e - 23, 7*e^4 + 11*e^3 - 79*e^2 - 101*e + 50, 11*e^4 + 22*e^3 - 117*e^2 - 224*e - 30, 27/2*e^4 + 49/2*e^3 - 271/2*e^2 - 475/2*e - 53, 21/2*e^4 + 51/2*e^3 - 209/2*e^2 - 481/2*e - 49, -3/2*e^4 - 19/2*e^3 + 23/2*e^2 + 185/2*e + 43, -3*e^4 - 11*e^3 + 29*e^2 + 129*e + 46, 7/2*e^4 + 17/2*e^3 - 69/2*e^2 - 171/2*e - 18, 3*e^4 + 5*e^3 - 36*e^2 - 62*e + 44, 13/2*e^4 + 17/2*e^3 - 157/2*e^2 - 155/2*e + 55, -2*e^4 + 27*e^2 - 9*e - 72, -3*e^4 + 31*e^2 - 6*e - 24, 15*e^4 + 21*e^3 - 161*e^2 - 203*e + 20, -e^4 - e^3 + 12*e^2 + 18*e - 44, -3/2*e^4 + 1/2*e^3 + 33/2*e^2 - 41/2*e - 19, 13/2*e^4 + 17/2*e^3 - 137/2*e^2 - 155/2*e - 41, 7*e^4 + 12*e^3 - 79*e^2 - 120*e + 66, 1/2*e^4 + 17/2*e^3 + 5/2*e^2 - 159/2*e - 48, -3*e^4 + 8*e^3 + 44*e^2 - 81*e - 88, 3/2*e^4 - 7/2*e^3 - 29/2*e^2 + 97/2*e + 16, 11/2*e^4 + 21/2*e^3 - 115/2*e^2 - 205/2*e + 2, 25/2*e^4 + 51/2*e^3 - 253/2*e^2 - 489/2*e - 9, 3/2*e^4 + 9/2*e^3 - 25/2*e^2 - 61/2*e - 49, 9*e^4 + 17*e^3 - 89*e^2 - 163*e - 54, 6*e^3 - 66*e - 18, 3*e^4 + 7*e^3 - 24*e^2 - 64*e - 38, -5/2*e^4 - 9/2*e^3 + 49/2*e^2 + 115/2*e + 39, 11*e^4 + 17*e^3 - 123*e^2 - 151*e + 70, 1/2*e^4 + 13/2*e^3 + 7/2*e^2 - 123/2*e - 27, -3*e^4 - 6*e^3 + 36*e^2 + 57*e - 24, 6*e^4 + 5*e^3 - 68*e^2 - 49*e + 48, -19/2*e^4 - 19/2*e^3 + 211/2*e^2 + 177/2*e - 53] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([3, 3, -w + 1])] = 1 AL_eigenvalues[ZF.ideal([4, 2, -1/2*w^3 + 1/2*w^2 + 7/2*w - 3])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]