/* 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([16, 2, 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^3 + x^2 - 2*x - 1 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -1, 1, -2*e^2 + 2, -2*e - 2, e^2 + 2*e - 2, -4*e^2 - 3*e + 6, 4*e^2 + 2*e - 10, 2*e^2 - 8, 2, -e^2 + 5*e + 3, 6*e^2 - 6, -2*e^2 - 4*e + 6, 6*e^2 + 6*e - 10, 3*e^2 - 3*e - 1, 3*e^2 - 4*e, -5*e^2 - 5*e + 7, 4*e^2 + 9*e - 12, -3*e^2, -11*e^2 + e + 21, -5*e^2 + 3*e + 11, 5*e^2 + 2*e + 4, -8*e^2 - 2*e + 8, -8*e, 2*e^2 + 8*e - 10, -2*e^2 + 4*e + 2, 5*e^2 + 3*e - 13, -11*e^2 + 2*e + 24, 6*e^2 - 4*e - 16, -4*e^2 - 6*e + 6, -12*e^2 - 14*e + 14, -13*e^2 - 5*e + 17, 4*e^2 + 2*e - 6, -11*e^2 + 3*e + 23, 7*e^2 + 6*e - 14, -4*e^2 - 8*e + 2, 18*e^2 + 16*e - 22, -8*e, -15*e^2 - 9*e + 7, 7*e^2 - 8*e - 16, 12*e^2 + 2*e - 22, 12*e^2 + 6*e - 22, 6*e^2 + 8*e - 12, 7*e^2 - 5*e - 7, 2*e^2 - 3*e - 20, 12*e^2 + 4*e - 28, 2*e^2 + 2*e - 22, -11*e^2 - 9*e + 17, -4*e^2 - e + 30, -9*e^2 - 3*e + 13, -14*e^2 - 13*e + 16, 3*e^2 - 6*e - 4, 12*e + 2, 8*e^2 + 12*e - 18, -10*e^2 - 12*e + 6, 2*e - 10, -4*e^2 - 13*e - 2, -6*e^2 - 13*e + 12, -10*e^2 - 15*e + 10, 13*e^2 + 20*e - 18, 16*e^2 + 4*e - 16, 14*e^2 + 11*e - 32, -12*e^2 - 5*e + 34, -4*e^2 - 12*e - 2, -4*e^2 + 26, 13*e^2 + 26*e - 24, -4*e^2 - 2*e - 6, 10*e^2 + 13*e - 6, -4*e^2 + 20, -10*e^2 + 2*e + 4, 4*e^2 - 11*e - 12, 8*e^2 - 14, -17*e^2 + e + 25, -e^2 + 11*e + 13, 22*e^2 - 38, 16*e^2 + 12*e - 10, -2*e^2 - 4*e - 20, 8*e^2 - 14*e - 20, -10*e^2 - 17*e + 30, -8*e^2 - 13*e - 8, 20*e^2 + 4*e - 22, -9*e^2 + 7*e + 7, -2*e^2 - 8*e - 2, 10*e^2 + 12*e - 8, 12*e^2 + 6*e - 30, 8*e^2 - 2*e - 2, -10*e^2 - 25*e + 26, e^2 - 3*e - 25, 19*e^2 + 7*e - 11, -20*e^2 - 18*e + 20, -2*e^2 + 14*e + 6, -14*e + 12, -13*e^2 - 20*e + 30, -5*e^2 - 6*e, 10*e^2 + 14*e - 28, -8*e^2 - 28*e + 14, -11*e^2 - 6*e + 22, -4*e^2 - 4*e - 8, -31*e^2 - 15*e + 39, 22*e^2 + e - 34, -17*e^2 - 6*e + 16, 8*e^2 - 4*e - 20, 27*e^2 + 8*e - 38, 3*e^2 + 10*e - 8, 8*e^2 - 5*e - 30, 13*e^2 + 22*e - 10, 17*e^2 + 10*e - 38, 18*e^2 + 18*e - 42, 6*e^2 + 12*e + 22, -6*e^2 - 6*e - 2, -2*e^2 - 32*e - 4, 8*e^2 - 12*e - 42, 28*e^2 + 13*e - 36, 10*e^2 + 4*e + 10, -12*e^2 + 2*e + 10, 29*e^2 + 28*e - 44, 18*e^2 + 10*e - 42, -6*e^2 - 2*e - 4, 8*e^2 + 6*e - 2, -17*e^2 + 4*e + 34, -12*e^2 + 8*e + 24, -13*e^2 + 11*e + 23, -25*e^2 - 14*e + 38, -24*e^2 - 8*e + 32, 2*e^2 - 12*e - 18, -2*e^2 - 14*e + 2, -16*e^2 + 12*e + 28, -2*e^2 - 22*e - 20, -6*e^2 - 16*e + 10, -24*e^2 - 16*e + 38, 6*e^2 + 4*e - 40, -14*e^2 - 21*e + 12, -16*e^2 - 28*e + 10, 26*e^2 + 30*e - 34, 8*e^2 - 14*e - 14, 14*e^2 + 38*e - 30, -20*e^2 - 4*e + 42, 18*e^2 + e - 32, 36*e^2 + 9*e - 52, -30*e^2 - 9*e + 44, 8*e^2 - 4*e - 36, 8*e^2 - 14*e - 22, 17*e^2 + 14*e - 8, 12*e^2 - 14*e - 44, -2*e^2 - 16*e - 18, 12*e^2 - 4*e - 8, 9*e^2 + 18*e - 8, 12*e^2 + 8*e + 6, -4*e^2 + 4*e + 8, 18*e^2 + 6*e - 52, -4*e^2 + 4*e - 14, -22*e^2 - 21*e + 10, -9*e^2 + 8*e + 14, -25*e^2 - 11*e + 31, 8*e + 32, -8*e^2 - 20*e - 20, -14*e^2 - 13*e + 24, -5*e^2 - 18*e + 18, 3*e^2 + 23*e + 3, 14*e^2 - 6*e - 10, 13*e^2 - 5*e - 29, -18*e^2 - 14*e + 36, 3*e^2 + 26*e - 14, -2*e^2 + 5*e + 22, 18*e^2 - 9*e - 52, -31*e^2 - 17*e + 33, 3*e^2 + 25*e - 21, 7*e^2 + 15*e - 1, -14*e^2 - 5*e, 18*e^2 + 24*e - 30, 20*e^2 + 20*e - 2, 19*e^2 + 20*e - 20, -20*e^2 + 17*e + 62, 2*e^2 - 2*e + 16, 2*e^2 + 14*e + 34, -6*e^2 + 14*e + 18, -18*e^2 - 12*e + 14, 12*e^2 - 52, 13*e^2 - 6*e - 32, -3*e^2 - e + 21, 8*e^2 + 35*e - 22, 10*e^2 + 17*e - 30, 26*e^2 + 16*e - 18, -12*e^2 + 2*e + 32, -32*e^2 - 12*e + 40, -10*e - 12, 33*e^2 - 2*e - 48, -20*e - 30, -4*e^2 - 2*e + 24, 12*e^2 + 2*e - 60, -10*e^2 + 30*e + 22, -28*e^2 - 12*e + 40, -2*e + 42, -24*e^2 - 6*e + 22, 16*e^2 - 14*e - 40, -5*e^2 + 10*e + 34, -24*e^2 - 12*e - 8, 13*e^2 + 29*e - 39, 2*e^2 + 4*e + 12, 2*e^2 + 32*e + 16, 12*e + 18, -24*e^2 + 4*e + 26, 40*e^2 + 15*e - 68, 6*e^2 + 37*e + 2, -28*e^2 - 32*e + 38, 21*e^2 + 28*e - 36, -28*e^2 - 18*e - 2, -44*e^2 - 28*e + 52, -14*e^2 - 23*e - 2, 30*e^2 + 44*e - 36, 2*e^2 - 12*e - 46, -18*e^2 + 11*e + 68, 36*e^2 - 8*e - 72, -8*e^2 - 30*e + 18, -4*e^2 + 16*e + 42, -38*e^2 - 28*e + 46, 14*e^2 + 36*e - 34, 18*e^2 + 4*e - 70, -28*e^2 - 18*e + 68, -16*e^2 - 21*e + 28, -15*e^2 + 10*e + 22, -16*e^2 - 22*e + 18, -16*e^2 - 6*e + 42, 16*e^2 + 10*e - 2, 25*e^2 - 6*e - 66, -10*e^2 + 32*e + 22, 24*e^2 - 24*e - 50, 14*e^2 + 28*e - 32, -16*e^2 + 30*e + 38, 14*e^2 + 10*e - 32, -36*e^2 - 17*e + 58, 14*e^2 + 17*e - 10, 9*e^2 - 15*e + 3, -9*e^2 - 2*e + 58, 30*e^2 + 26*e - 60, 2*e^2 - 29*e - 28, -40*e^2 - 31*e + 54, -7*e^2 + 6*e + 28, -20*e^2 + 8*e + 60, 16*e^2 - 24*e - 66, 16*e^2 + 16*e - 44, 15*e^2 - 4*e - 28, -24*e^2 - 3*e + 4, 8*e^2 + 18*e - 6, 28*e^2 + e - 64, 13*e^2 + 21*e - 63, -22*e^2 - 22*e + 38, 33*e^2 + 31*e - 19, -12*e^2 + 25*e + 10, 30*e^2 + 20*e - 32, -20*e^2 - 28*e + 22, -18*e^2 + 2*e + 12, 22*e^2 + 7*e - 14, -8*e^2 - 12*e + 26, 16*e^2 + 34*e - 30, -56*e^2 - 24*e + 76, 12*e^2 + 16*e - 24, -36*e^2 - 40*e + 50, -36*e^2 - 24*e + 62, 20*e^2 + 4*e + 20, -39*e^2 - 12*e + 32, -12*e^2 + 7*e - 6, 51*e^2 + 40*e - 48, -26*e^2 - 17*e + 56, 20*e^2 + e - 48, -18*e^2 - 6*e + 52, 8*e^2 - 8*e + 2, -38*e^2 - 16*e + 78, -50*e^2 - 28*e + 42, 6*e^2 - 20*e - 6, -4*e - 18, 16*e^2 - 28*e - 42, 48*e^2 + 12*e - 80, 29*e^2 + 11*e - 63, 7*e^2 + 3*e - 79, 30*e^2 - 18*e - 72, 12*e^2 - 22*e - 60, -22*e^2 + 16*e + 20, 22*e^2 + 8*e - 2, -45*e^2 - 11*e + 75, -e^2 + 15*e + 17, 7*e^2 + 6*e + 22, 18*e^2 - 14*e - 32, 6*e^2 - 34*e - 34, 23*e^2 + 12*e - 4, -29*e^2 - 41*e + 67, 47*e^2 + 48*e - 68, 10*e^2 + 3*e + 22, -3*e^2 - 14*e + 60, 16*e^2 + 10*e - 46] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([4, 2, w])] = 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]