/* 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([21, 21, 1/2*w^3 + 1/2*w^2 - 9/2*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^6 + 6*x^5 + x^4 - 45*x^3 - 47*x^2 + 85*x + 107 K. = NumberField(heckePol) hecke_eigenvalues_array = [1, e, e^3 + 3*e^2 - 4*e - 11, -1, -e^5 - 4*e^4 + 5*e^3 + 24*e^2 - 7*e - 29, e^4 + 5*e^3 + 2*e^2 - 18*e - 22, e^5 + 4*e^4 - 6*e^3 - 29*e^2 + 9*e + 49, 2*e^5 + 8*e^4 - 11*e^3 - 52*e^2 + 17*e + 76, -e^5 - 5*e^4 + e^3 + 27*e^2 + 8*e - 30, -2*e^4 - 11*e^3 - 6*e^2 + 42*e + 45, -2*e^2 - 4*e + 4, -2*e^5 - 7*e^4 + 16*e^3 + 54*e^2 - 36*e - 101, -2*e^5 - 8*e^4 + 9*e^3 + 45*e^2 - 10*e - 50, e^5 + 5*e^4 - e^3 - 27*e^2 - 11*e + 29, e^5 + 4*e^4 - 8*e^3 - 35*e^2 + 17*e + 69, -3*e^4 - 11*e^3 + 8*e^2 + 41*e + 13, 2*e^5 + 9*e^4 - 5*e^3 - 46*e^2 - 5*e + 33, e^5 + 4*e^4 - 4*e^3 - 22*e^2 + 3*e + 22, -3*e - 5, 2*e^5 + 8*e^4 - 12*e^3 - 54*e^2 + 21*e + 79, e^5 + 4*e^4 - 9*e^3 - 35*e^2 + 25*e + 70, 2*e^5 + 9*e^4 - 6*e^3 - 52*e^2 - 4*e + 65, e^5 + 2*e^4 - 13*e^3 - 21*e^2 + 40*e + 47, -e^5 - 4*e^4 + 2*e^3 + 19*e^2 + 10*e - 22, 2*e^5 + 5*e^4 - 24*e^3 - 48*e^2 + 68*e + 97, -3*e^4 - 18*e^3 - 14*e^2 + 68*e + 91, -5*e^5 - 20*e^4 + 27*e^3 + 133*e^2 - 36*e - 203, e^5 + 4*e^4 - 7*e^3 - 33*e^2 + 10*e + 61, -e^5 - 4*e^4 + 8*e^3 + 36*e^2 - 11*e - 74, -e^5 - e^4 + 21*e^3 + 29*e^2 - 70*e - 78, 3*e^5 + 10*e^4 - 28*e^3 - 88*e^2 + 68*e + 175, e^5 + 6*e^4 + 5*e^3 - 21*e^2 - 32*e - 15, -2*e^5 - 6*e^4 + 19*e^3 + 50*e^2 - 47*e - 106, 2*e^4 + 9*e^3 - 2*e^2 - 33*e - 12, -e^4 - 3*e^3 + 6*e^2 + 15*e - 13, 2*e^5 + 6*e^4 - 18*e^3 - 43*e^2 + 46*e + 61, 3*e^5 + 9*e^4 - 31*e^3 - 83*e^2 + 78*e + 172, e^4 + 3*e^3 - 9*e^2 - 13*e + 22, 4*e^5 + 16*e^4 - 22*e^3 - 100*e^2 + 38*e + 138, e^5 + 4*e^4 - 3*e^3 - 14*e^2 - 10, -2*e^5 - 9*e^4 + 6*e^3 + 52*e^2 + 3*e - 70, -2*e^4 - 7*e^3 + 10*e^2 + 29*e - 12, e^5 + 3*e^4 - 11*e^3 - 28*e^2 + 28*e + 59, 2*e^5 + 8*e^4 - 11*e^3 - 53*e^2 + 15*e + 79, 3*e^5 + 9*e^4 - 28*e^3 - 72*e^2 + 71*e + 137, 3*e^5 + 14*e^4 - 2*e^3 - 60*e^2 - 33*e + 20, -2*e^3 - 7*e^2 + 15*e + 38, -3*e^5 - 10*e^4 + 30*e^3 + 90*e^2 - 74*e - 177, -3*e^5 - 12*e^4 + 14*e^3 + 74*e^2 - 14*e - 111, -4*e^5 - 14*e^4 + 34*e^3 + 112*e^2 - 84*e - 212, -4*e^5 - 13*e^4 + 41*e^3 + 119*e^2 - 108*e - 251, 2*e^5 + 12*e^4 + 6*e^3 - 53*e^2 - 42*e + 21, -4*e^5 - 17*e^4 + 10*e^3 + 85*e^2 + 17*e - 75, 4*e^5 + 19*e^4 - 7*e^3 - 100*e^2 - 26*e + 98, 5*e^5 + 18*e^4 - 36*e^3 - 129*e^2 + 75*e + 219, e^5 + 5*e^4 - 5*e^3 - 39*e^2 + 4*e + 72, -3*e^4 - 9*e^3 + 16*e^2 + 39*e - 5, -3*e^5 - 8*e^4 + 38*e^3 + 88*e^2 - 108*e - 211, 2*e^5 + 10*e^4 + 2*e^3 - 43*e^2 - 36*e + 13, -3*e^5 - 6*e^4 + 45*e^3 + 77*e^2 - 138*e - 187, -2*e^5 - 3*e^4 + 37*e^3 + 63*e^2 - 111*e - 178, -2*e^4 - 5*e^3 + 13*e^2 + 13*e - 23, 2*e^5 + 9*e^4 - 8*e^3 - 55*e^2 + 6*e + 74, 2*e^5 + 12*e^4 + 12*e^3 - 34*e^2 - 66*e - 46, -3*e^5 - 11*e^4 + 27*e^3 + 101*e^2 - 66*e - 212, -4*e^5 - 17*e^4 + 10*e^3 + 82*e^2 + 11*e - 66, -e^5 - 2*e^4 + 14*e^3 + 32*e^2 - 28*e - 91, e^5 + 2*e^4 - 20*e^3 - 41*e^2 + 67*e + 115, 7*e^5 + 22*e^4 - 69*e^3 - 198*e^2 + 168*e + 402, 2*e^4 + 7*e^3 - 10*e^2 - 33*e, 3*e^5 + 11*e^4 - 19*e^3 - 73*e^2 + 31*e + 95, -2*e^5 - 9*e^4 + 5*e^3 + 49*e^2 + 11*e - 42, e^5 + 2*e^4 - 17*e^3 - 34*e^2 + 51*e + 101, 2*e^5 + 2*e^4 - 42*e^3 - 59*e^2 + 141*e + 168, -3*e^5 - 9*e^4 + 28*e^3 + 70*e^2 - 75*e - 119, 4*e^5 + 17*e^4 - 16*e^3 - 102*e^2 + 12*e + 133, 5*e^5 + 14*e^4 - 56*e^3 - 135*e^2 + 153*e + 285, 2*e^5 + 6*e^4 - 23*e^3 - 65*e^2 + 56*e + 152, 4*e^5 + 16*e^4 - 15*e^3 - 81*e^2 + 6*e + 58, -6*e^5 - 19*e^4 + 54*e^3 + 149*e^2 - 130*e - 258, -2*e^5 - 3*e^4 + 36*e^3 + 54*e^2 - 111*e - 134, -4*e^5 - 16*e^4 + 23*e^3 + 107*e^2 - 33*e - 157, e^4 - 3*e^3 - 26*e^2 + 12*e + 80, -3*e^5 - 7*e^4 + 40*e^3 + 85*e^2 - 111*e - 206, -4*e^5 - 19*e^4 + 2*e^3 + 85*e^2 + 44*e - 40, -e^5 - 7*e^4 - 7*e^3 + 27*e^2 + 28*e, -4*e^5 - 20*e^4 + 95*e^2 + 46*e - 67, 2*e^5 + 7*e^4 - 15*e^3 - 52*e^2 + 31*e + 97, -e^5 - 6*e^4 - 12*e^3 - e^2 + 63*e + 77, 7*e^5 + 27*e^4 - 46*e^3 - 194*e^2 + 89*e + 329, -3*e^5 - 12*e^4 + 18*e^3 + 82*e^2 - 39*e - 142, -2*e^5 - 6*e^4 + 19*e^3 + 53*e^2 - 45*e - 115, 2*e^5 + 9*e^4 - 5*e^3 - 45*e^2 - 5*e + 32, -6*e^5 - 24*e^4 + 28*e^3 + 139*e^2 - 30*e - 151, 3*e^5 + 7*e^4 - 40*e^3 - 78*e^2 + 116*e + 192, -2*e^5 - 2*e^4 + 36*e^3 + 42*e^2 - 117*e - 125, -e^5 + 26*e^3 + 27*e^2 - 97*e - 103, e^5 + 4*e^4 - 9*e^3 - 37*e^2 + 24*e + 83, -4*e^5 - 8*e^4 + 55*e^3 + 95*e^2 - 161*e - 233, -3*e^5 - 14*e^4 + 5*e^3 + 71*e^2 + 18*e - 73, -3*e^5 - 5*e^4 + 53*e^3 + 95*e^2 - 160*e - 284, -3*e^4 - 10*e^3 + 7*e^2 + 30*e + 12, -e^5 - 3*e^4 + 20*e^3 + 51*e^2 - 72*e - 131, e^5 - 2*e^4 - 35*e^3 - 27*e^2 + 120*e + 119, 5*e^5 + 18*e^4 - 30*e^3 - 115*e^2 + 46*e + 168, 4*e^5 + 15*e^4 - 29*e^3 - 107*e^2 + 61*e + 164, -7*e^4 - 33*e^3 - 7*e^2 + 123*e + 116, 8*e^5 + 25*e^4 - 80*e^3 - 225*e^2 + 200*e + 456, -2*e^5 - 6*e^4 + 16*e^3 + 43*e^2 - 38*e - 85, -2*e^5 - 10*e^4 - e^3 + 39*e^2 + 23*e - 15, -2*e^5 - 15*e^4 - 31*e^3 + 26*e^2 + 151*e + 97, -5*e^5 - 18*e^4 + 44*e^3 + 150*e^2 - 99*e - 266, -4*e^5 - 20*e^4 + e^3 + 91*e^2 + 47*e - 41, -7*e^5 - 25*e^4 + 47*e^3 + 169*e^2 - 83*e - 253, 5*e^5 + 23*e^4 - 2*e^3 - 92*e^2 - 59*e + 11, -3*e^5 - 2*e^4 + 61*e^3 + 78*e^2 - 186*e - 240, -4*e^5 - 8*e^4 + 67*e^3 + 131*e^2 - 203*e - 353, 3*e^5 + 6*e^4 - 57*e^3 - 124*e^2 + 176*e + 346, 6*e^5 + 25*e^4 - 26*e^3 - 156*e^2 + 17*e + 230, 4*e^5 + 14*e^4 - 26*e^3 - 90*e^2 + 48*e + 106, 2*e^5 + 12*e^4 + 11*e^3 - 42*e^2 - 65*e - 2, 5*e^5 + 10*e^4 - 78*e^3 - 141*e^2 + 237*e + 355, -4*e^5 - 14*e^4 + 26*e^3 + 85*e^2 - 48*e - 117, 2*e^5 + 8*e^4 - 6*e^3 - 40*e^2 + 4*e + 50, -e^4 - 10*e^3 - 10*e^2 + 49*e + 28, -e^5 - 6*e^4 - e^3 + 32*e^2 + 8*e - 20, -4*e^5 - 14*e^4 + 32*e^3 + 101*e^2 - 74*e - 141, 8*e^5 + 29*e^4 - 59*e^3 - 218*e^2 + 109*e + 373, -4*e^4 - 12*e^3 + 20*e^2 + 36*e - 38, -7*e^5 - 26*e^4 + 47*e^3 + 177*e^2 - 105*e - 286, -7*e^5 - 24*e^4 + 65*e^3 + 213*e^2 - 155*e - 440, e^5 + 6*e^4 - 5*e^3 - 53*e^2 + 6*e + 101, 3*e^5 + 8*e^4 - 40*e^3 - 95*e^2 + 113*e + 211, -3*e^5 - 7*e^4 + 54*e^3 + 124*e^2 - 165*e - 327, -4*e^5 - 19*e^4 - 4*e^3 + 73*e^2 + 72*e - 14, -2*e^5 - 8*e^4 + 13*e^3 + 62*e^2 - 31*e - 138, -6*e^5 - 17*e^4 + 68*e^3 + 161*e^2 - 183*e - 327, 4*e^5 + 7*e^4 - 67*e^3 - 122*e^2 + 202*e + 340, -5*e^5 - 20*e^4 + 19*e^3 + 99*e^2 - 10*e - 55, -5*e^5 - 18*e^4 + 33*e^3 + 124*e^2 - 58*e - 212, -5*e^5 - 23*e^4 + 6*e^3 + 103*e^2 + 37*e - 44, -2*e^5 - 9*e^4 + 11*e^3 + 69*e^2 - 10*e - 135, -5*e^5 - 15*e^4 + 63*e^3 + 173*e^2 - 174*e - 412, -e^5 + 8*e^4 + 61*e^3 + 28*e^2 - 218*e - 200, -4*e^5 - 10*e^4 + 47*e^3 + 100*e^2 - 121*e - 224, 6*e^5 + 19*e^4 - 58*e^3 - 166*e^2 + 144*e + 311, 4*e^4 + 9*e^3 - 22*e^2 - 26*e + 15, 2*e^5 + 8*e^4 - 3*e^3 - 24*e^2 - 22*e - 33, 7*e^5 + 23*e^4 - 59*e^3 - 181*e^2 + 137*e + 349, 12*e^5 + 49*e^4 - 57*e^3 - 293*e^2 + 73*e + 378, -e^5 - 3*e^4 + 4*e^3 + 3*e^2 - 4*e + 33, -5*e^5 - 23*e^4 + 20*e^3 + 153*e^2 - 17*e - 238, -7*e^5 - 26*e^4 + 57*e^3 + 213*e^2 - 135*e - 422, 4*e^5 + 16*e^4 - 17*e^3 - 100*e^2 - e + 156, -4*e^5 - 12*e^4 + 37*e^3 + 96*e^2 - 87*e - 166, -7*e^5 - 21*e^4 + 76*e^3 + 198*e^2 - 197*e - 393, -e^5 + 6*e^4 + 46*e^3 + 9*e^2 - 167*e - 107, -5*e^5 - 6*e^4 + 94*e^3 + 132*e^2 - 300*e - 359, e^5 + 7*e^4 - 52*e^2 - 21*e + 77, -3*e^5 - 6*e^4 + 44*e^3 + 87*e^2 - 117*e - 237, -e^5 - 5*e^4 - 2*e^3 + 17*e^2 + 17*e - 12, -7*e^5 - 21*e^4 + 80*e^3 + 212*e^2 - 213*e - 461, -9*e^5 - 32*e^4 + 66*e^3 + 223*e^2 - 141*e - 351, e^5 + 4*e^4 + e^3 - 7*e^2 - 22*e - 29, 6*e^5 + 24*e^4 - 31*e^3 - 141*e^2 + 49*e + 153, -9*e^5 - 34*e^4 + 54*e^3 + 207*e^2 - 109*e - 273, -9*e^5 - 40*e^4 + 27*e^3 + 228*e^2 + 12*e - 296, e^5 + 5*e^4 - 7*e^3 - 48*e^2 + 4*e + 95, 6*e^5 + 26*e^4 - 26*e^3 - 167*e^2 + 18*e + 233, -e^5 - 11*e^4 - 27*e^3 + 28*e^2 + 126*e + 49, -8*e^5 - 38*e^4 + 21*e^3 + 222*e^2 + 19*e - 280, -3*e^5 - 14*e^4 + 2*e^3 + 71*e^2 + 46*e - 78, -7*e^5 - 27*e^4 + 39*e^3 + 170*e^2 - 58*e - 231, -3*e^4 - 15*e^3 - 8*e^2 + 49*e + 77, 2*e^5 + 6*e^4 - 25*e^3 - 64*e^2 + 81*e + 142, -e^5 + 2*e^4 + 31*e^3 + 16*e^2 - 107*e - 73, 8*e^5 + 29*e^4 - 53*e^3 - 191*e^2 + 93*e + 264, 2*e^5 + 10*e^4 + 12*e^3 - 12*e^2 - 78*e - 82, -3*e^5 - 10*e^4 + 23*e^3 + 74*e^2 - 48*e - 120, 6*e^5 + 23*e^4 - 34*e^3 - 147*e^2 + 54*e + 204, 7*e^5 + 37*e^4 + 11*e^3 - 161*e^2 - 138*e + 94, 3*e^5 + 7*e^4 - 37*e^3 - 62*e^2 + 108*e + 109, -7*e^5 - 25*e^4 + 63*e^3 + 211*e^2 - 149*e - 393, -3*e^5 - 11*e^4 + 31*e^3 + 116*e^2 - 77*e - 272, -5*e^5 - 20*e^4 + 27*e^3 + 125*e^2 - 46*e - 145, 4*e^5 + 12*e^4 - 33*e^3 - 84*e^2 + 67*e + 126, -6*e^5 - 24*e^4 + 23*e^3 + 118*e^2 - 29*e - 94, -3*e^5 - 9*e^4 + 37*e^3 + 98*e^2 - 107*e - 200, -e^5 - e^4 + 23*e^3 + 35*e^2 - 76*e - 112, 7*e^5 + 38*e^4 + 8*e^3 - 179*e^2 - 119*e + 125, -3*e^5 - 4*e^4 + 47*e^3 + 54*e^2 - 150*e - 140, 4*e^5 + 11*e^4 - 50*e^3 - 118*e^2 + 144*e + 261, 2*e^5 + 7*e^4 - 8*e^3 - 27*e^2 + 11*e - 21, e^5 - 4*e^4 - 51*e^3 - 49*e^2 + 192*e + 211, 2*e^5 + 10*e^4 + 2*e^3 - 34*e^2 - 28*e - 48, 4*e^5 + 15*e^4 - 25*e^3 - 91*e^2 + 42*e + 91, -7*e^5 - 23*e^4 + 50*e^3 + 147*e^2 - 95*e - 188, -4*e^5 - 16*e^4 + 25*e^3 + 116*e^2 - 49*e - 204, -3*e^5 - 5*e^4 + 55*e^3 + 101*e^2 - 175*e - 265, e^4 + 13*e^3 + 25*e^2 - 49*e - 96, 3*e^5 + 15*e^4 - 9*e^3 - 94*e^2 + 13*e + 132, 8*e^5 + 38*e^4 - 17*e^3 - 216*e^2 - 41*e + 242, -8*e^5 - 25*e^4 + 93*e^3 + 264*e^2 - 249*e - 599, -3*e^5 - 19*e^4 - 7*e^3 + 110*e^2 + 51*e - 156, -e^5 - 5*e^4 + 32*e^2 + 28*e - 50, 3*e^5 + 18*e^4 + 11*e^3 - 80*e^2 - 88*e + 50, -5*e^5 - 11*e^4 + 74*e^3 + 152*e^2 - 221*e - 407, -2*e^5 - 8*e^4 + 15*e^3 + 58*e^2 - 27*e - 62, e^5 + 6*e^4 + 9*e^3 - 21*e^2 - 67*e + 4, -6*e^5 - 19*e^4 + 46*e^3 + 120*e^2 - 106*e - 167, -3*e^5 - 5*e^4 + 54*e^3 + 102*e^2 - 167*e - 283, 3*e^4 - e^3 - 49*e^2 + 3*e + 140, -2*e^5 - 10*e^4 - 10*e^3 + 15*e^2 + 60*e + 59, -e^5 + e^4 + 27*e^3 + 9*e^2 - 96*e - 24, -8*e^5 - 31*e^4 + 50*e^3 + 212*e^2 - 95*e - 332, -8*e^5 - 25*e^4 + 76*e^3 + 217*e^2 - 178*e - 440, 3*e^5 + 19*e^4 + 18*e^3 - 68*e^2 - 93*e - 31, 2*e^5 + 6*e^4 - 25*e^3 - 67*e^2 + 75*e + 153, -e^5 - 7*e^4 - 13*e^3 + 16*e^2 + 70*e + 15, -3*e^4 - 5*e^3 + 17*e^2 - 4*e - 29, 2*e^5 - e^4 - 64*e^3 - 102*e^2 + 214*e + 393, 3*e^5 + 9*e^4 - 24*e^3 - 55*e^2 + 51*e + 54, -12*e^5 - 47*e^4 + 75*e^3 + 323*e^2 - 133*e - 490, 12*e^5 + 42*e^4 - 100*e^3 - 337*e^2 + 212*e + 611, 5*e^5 + 13*e^4 - 65*e^3 - 150*e^2 + 178*e + 337, e^5 + 4*e^4 - 24*e^3 - 88*e^2 + 79*e + 268, -3*e^5 - 11*e^4 + 20*e^3 + 78*e^2 - 39*e - 121, -13*e^5 - 41*e^4 + 124*e^3 + 356*e^2 - 295*e - 683, 3*e^5 + 6*e^4 - 46*e^3 - 89*e^2 + 139*e + 251, -6*e^5 - 21*e^4 + 51*e^3 + 169*e^2 - 127*e - 302, 8*e^5 + 34*e^4 - 39*e^3 - 222*e^2 + 41*e + 290, -3*e^5 - 5*e^4 + 53*e^3 + 92*e^2 - 172*e - 261, 7*e^5 + 23*e^4 - 50*e^3 - 148*e^2 + 91*e + 193, 11*e^4 + 50*e^3 + 5*e^2 - 183*e - 163, -13*e^5 - 50*e^4 + 84*e^3 + 358*e^2 - 141*e - 594, -9*e^5 - 42*e^4 + 8*e^3 + 196*e^2 + 87*e - 152, 7*e^5 + 28*e^4 - 57*e^3 - 245*e^2 + 124*e + 479, -8*e^5 - 23*e^4 + 87*e^3 + 212*e^2 - 227*e - 437, 4*e^5 + 14*e^4 - 40*e^3 - 135*e^2 + 116*e + 313, -5*e^5 - 12*e^4 + 69*e^3 + 148*e^2 - 188*e - 380, 9*e^5 + 39*e^4 - 35*e^3 - 226*e^2 + 24*e + 257, 5*e^5 + 17*e^4 - 45*e^3 - 132*e^2 + 112*e + 191, 5*e^5 + 13*e^4 - 57*e^3 - 125*e^2 + 138*e + 250, 5*e^5 + 25*e^4 - 117*e^2 - 59*e + 100, -4*e^5 - 10*e^4 + 61*e^3 + 145*e^2 - 169*e - 373, -3*e^5 - 9*e^4 + 41*e^3 + 107*e^2 - 131*e - 257, -8*e^5 - 28*e^4 + 60*e^3 + 203*e^2 - 107*e - 300, 8*e^5 + 13*e^4 - 131*e^3 - 203*e^2 + 407*e + 526, 3*e^5 + 13*e^4 - 11*e^3 - 75*e^2 + 4*e + 94, -6*e^5 - 26*e^4 + 8*e^3 + 110*e^2 + 50*e - 6, -e^5 - 17*e^4 - 45*e^3 + 54*e^2 + 189*e + 48, 9*e^5 + 40*e^4 - 33*e^3 - 249*e^2 + 335, 7*e^5 + 31*e^4 - 18*e^3 - 155*e^2 - 3*e + 132, 4*e^5 + 8*e^4 - 66*e^3 - 140*e^2 + 183*e + 387, 5*e^4 + 34*e^3 + 47*e^2 - 112*e - 228, 3*e^5 + 8*e^4 - 26*e^3 - 57*e^2 + 51*e + 73, 10*e^5 + 43*e^4 - 34*e^3 - 244*e^2 + 4*e + 313, -e^5 - 7*e^4 + 3*e^3 + 66*e^2 + 4*e - 123, 5*e^5 + 14*e^4 - 54*e^3 - 131*e^2 + 142*e + 280, 3*e^5 + 6*e^4 - 59*e^3 - 120*e^2 + 186*e + 320, -6*e^5 - 25*e^4 + 34*e^3 + 175*e^2 - 65*e - 309, 2*e^5 + 7*e^4 - 4*e^3 - 18*e^2 - 14*e - 19, -3*e^5 - 5*e^4 + 55*e^3 + 89*e^2 - 174*e - 234, -2*e^5 - 16*e^4 - 25*e^3 + 55*e^2 + 135*e - 5, -3*e^5 - 13*e^4 + 9*e^3 + 72*e^2 - 91, -e^5 - 21*e^4 - 81*e^3 - 5*e^2 + 320*e + 296, -7*e^5 - 20*e^4 + 83*e^3 + 203*e^2 - 230*e - 473, -10*e^4 - 56*e^3 - 15*e^2 + 230*e + 167, -6*e^5 - 19*e^4 + 62*e^3 + 189*e^2 - 143*e - 399, 8*e^5 + 28*e^4 - 68*e^3 - 225*e^2 + 158*e + 433, -4*e^5 - 16*e^4 + 21*e^3 + 109*e^2 - 13*e - 153, 3*e^5 + 12*e^4 - 38*e^3 - 145*e^2 + 120*e + 376, 11*e^5 + 31*e^4 - 128*e^3 - 305*e^2 + 357*e + 658, -3*e^5 - 11*e^4 + 7*e^3 + 40*e^2 + 25*e - 2, 10*e^4 + 53*e^3 + 17*e^2 - 204*e - 216, 2*e^5 + 2*e^4 - 37*e^3 - 49*e^2 + 107*e + 133, -6*e^5 - 21*e^4 + 56*e^3 + 187*e^2 - 141*e - 375, -5*e^5 - 19*e^4 + 19*e^3 + 88*e^2 + 4*e - 33, 8*e^5 + 30*e^4 - 58*e^3 - 220*e^2 + 121*e + 395, 7*e^5 + 12*e^4 - 109*e^3 - 176*e^2 + 328*e + 458, 9*e^5 + 21*e^4 - 109*e^3 - 208*e^2 + 307*e + 444, -11*e^5 - 30*e^4 + 120*e^3 + 270*e^2 - 333*e - 540, -2*e^5 - 6*e^4 + 27*e^3 + 69*e^2 - 89*e - 213, 7*e^5 + 36*e^4 + 18*e^3 - 127*e^2 - 164*e - 34, 4*e^5 + 11*e^4 - 39*e^3 - 86*e^2 + 93*e + 161, 3*e^5 + 14*e^4 - 16*e^3 - 99*e^2 + 27*e + 167, 3*e^5 + 8*e^4 - 35*e^3 - 75*e^2 + 120*e + 159, -6*e^4 - 13*e^3 + 44*e^2 + 58*e - 51, -2*e^5 - 14*e^4 - 27*e^3 + 6*e^2 + 111*e + 176, -4*e^5 - 11*e^4 + 41*e^3 + 91*e^2 - 93*e - 136] 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([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]