/* 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^9 + 2*x^8 - 17*x^7 - 30*x^6 + 86*x^5 + 104*x^4 - 163*x^3 - 66*x^2 + 44*x + 16 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -1, -1, e^8 + 3/2*e^7 - 18*e^6 - 43/2*e^5 + 100*e^4 + 61*e^3 - 202*e^2 + 33/2*e + 42, -3/4*e^8 - e^7 + 51/4*e^6 + 14*e^5 - 129/2*e^4 - 36*e^3 + 469/4*e^2 - 12*e - 22, -e^8 - 3/2*e^7 + 17*e^6 + 43/2*e^5 - 86*e^4 - 61*e^3 + 158*e^2 - 7/2*e - 32, -1/2*e^8 - e^7 + 17/2*e^6 + 14*e^5 - 43*e^4 - 39*e^3 + 165/2*e^2 - 3*e - 16, 7/4*e^8 + 3*e^7 - 123/4*e^6 - 43*e^5 + 331/2*e^4 + 124*e^3 - 1337/4*e^2 + 17*e + 72, -1/2*e^8 - e^7 + 17/2*e^6 + 14*e^5 - 43*e^4 - 39*e^3 + 165/2*e^2 - 2*e - 16, -2*e^8 - 3*e^7 + 35*e^6 + 43*e^5 - 186*e^4 - 122*e^3 + 359*e^2 - 20*e - 70, e^8 + 2*e^7 - 18*e^6 - 29*e^5 + 100*e^4 + 90*e^3 - 207*e^2 - 7*e + 42, e^8 + 3/2*e^7 - 17*e^6 - 43/2*e^5 + 85*e^4 + 62*e^3 - 149*e^2 - 3/2*e + 26, -5/2*e^8 - 4*e^7 + 87/2*e^6 + 57*e^5 - 229*e^4 - 161*e^3 + 883/2*e^2 - 26*e - 86, 3/4*e^8 + e^7 - 55/4*e^6 - 14*e^5 + 157/2*e^4 + 36*e^3 - 649/4*e^2 + 25*e + 38, 1/2*e^7 - e^6 - 15/2*e^5 + 14*e^4 + 27*e^3 - 48*e^2 + 11/2*e + 2, -5/2*e^8 - 4*e^7 + 87/2*e^6 + 57*e^5 - 230*e^4 - 160*e^3 + 905/2*e^2 - 27*e - 96, -11/4*e^8 - 4*e^7 + 195/4*e^6 + 57*e^5 - 531/2*e^4 - 156*e^3 + 2125/4*e^2 - 59*e - 116, -1/2*e^8 - e^7 + 19/2*e^6 + 14*e^5 - 57*e^4 - 39*e^3 + 255/2*e^2 - 14*e - 28, -5/2*e^8 - 4*e^7 + 87/2*e^6 + 58*e^5 - 229*e^4 - 172*e^3 + 879/2*e^2 - 5*e - 82, -5/2*e^8 - 4*e^7 + 87/2*e^6 + 57*e^5 - 229*e^4 - 160*e^3 + 883/2*e^2 - 29*e - 82, 3/2*e^8 + 3*e^7 - 53/2*e^6 - 44*e^5 + 144*e^4 + 139*e^3 - 593/2*e^2 - 19*e + 62, -e^6 + 14*e^4 - 44*e^2 + 11*e + 10, 7/4*e^8 + 2*e^7 - 123/4*e^6 - 28*e^5 + 329/2*e^4 + 69*e^3 - 1265/4*e^2 + 43*e + 72, e^8 + 2*e^7 - 17*e^6 - 29*e^5 + 87*e^4 + 90*e^3 - 172*e^2 - 20*e + 34, -2*e^8 - 3*e^7 + 35*e^6 + 43*e^5 - 186*e^4 - 122*e^3 + 359*e^2 - 22*e - 72, -3/2*e^8 - 5/2*e^7 + 53/2*e^6 + 73/2*e^5 - 144*e^4 - 110*e^3 + 579/2*e^2 - 13/2*e - 50, 3/2*e^8 + 3*e^7 - 51/2*e^6 - 43*e^5 + 130*e^4 + 128*e^3 - 509/2*e^2 - 11*e + 48, e^8 + 2*e^7 - 18*e^6 - 29*e^5 + 101*e^4 + 86*e^3 - 214*e^2 + 21*e + 40, 7/4*e^8 + 3*e^7 - 127/4*e^6 - 43*e^5 + 359/2*e^4 + 126*e^3 - 1517/4*e^2 + 14*e + 86, -3*e^8 - 5*e^7 + 53*e^6 + 71*e^5 - 287*e^4 - 199*e^3 + 577*e^2 - 46*e - 112, 5/2*e^8 + 4*e^7 - 91/2*e^6 - 57*e^5 + 258*e^4 + 158*e^3 - 1083/2*e^2 + 71*e + 118, -3*e^8 - 5*e^7 + 53*e^6 + 72*e^5 - 286*e^4 - 210*e^3 + 566*e^2 - 25*e - 104, 1/2*e^8 + 1/2*e^7 - 19/2*e^6 - 15/2*e^5 + 58*e^4 + 19*e^3 - 255/2*e^2 + 67/2*e + 22, 5*e^8 + 8*e^7 - 89*e^6 - 114*e^5 + 487*e^4 + 322*e^3 - 983*e^2 + 68*e + 204, -e^8 - 3/2*e^7 + 16*e^6 + 45/2*e^5 - 72*e^4 - 74*e^3 + 112*e^2 + 89/2*e - 26, -3/4*e^8 - e^7 + 55/4*e^6 + 15*e^5 - 157/2*e^4 - 47*e^3 + 645/4*e^2 - 6*e - 34, 7/4*e^8 + 2*e^7 - 123/4*e^6 - 29*e^5 + 333/2*e^4 + 80*e^3 - 1325/4*e^2 + 24*e + 84, 3*e^8 + 4*e^7 - 54*e^6 - 57*e^5 + 301*e^4 + 154*e^3 - 611*e^2 + 71*e + 140, 4*e^8 + 13/2*e^7 - 70*e^6 - 187/2*e^5 + 372*e^4 + 273*e^3 - 725*e^2 + 33/2*e + 148, 5/2*e^8 + 4*e^7 - 89/2*e^6 - 58*e^5 + 244*e^4 + 173*e^3 - 985/2*e^2 + 7*e + 98, -4*e^8 - 7*e^7 + 70*e^6 + 101*e^5 - 373*e^4 - 301*e^3 + 738*e^2 - 2*e - 142, -e^5 - e^4 + 14*e^3 + 11*e^2 - 38*e - 2, -15/4*e^8 - 6*e^7 + 267/4*e^6 + 86*e^5 - 733/2*e^4 - 245*e^3 + 2985/4*e^2 - 61*e - 160, e^4 - 2*e^3 - 6*e^2 + 12*e - 12, 3/2*e^8 + 5/2*e^7 - 51/2*e^6 - 69/2*e^5 + 130*e^4 + 88*e^3 - 505/2*e^2 + 73/2*e + 62, -e^8 - 2*e^7 + 18*e^6 + 28*e^5 - 101*e^4 - 75*e^3 + 218*e^2 - 44*e - 42, -23/4*e^8 - 9*e^7 + 403/4*e^6 + 129*e^5 - 1073/2*e^4 - 371*e^3 + 4177/4*e^2 - 36*e - 206, -e^7 + e^6 + 15*e^5 - 15*e^4 - 54*e^3 + 63*e^2 + 6*e - 14, 5*e^8 + 15/2*e^7 - 89*e^6 - 215/2*e^5 + 486*e^4 + 307*e^3 - 967*e^2 + 113/2*e + 200, 3*e^8 + 5*e^7 - 55*e^6 - 72*e^5 + 316*e^4 + 208*e^3 - 674*e^2 + 61*e + 144, -13/2*e^8 - 11*e^7 + 229/2*e^6 + 158*e^5 - 616*e^4 - 460*e^3 + 2449/2*e^2 - 52*e - 246, 15/2*e^8 + 13*e^7 - 265/2*e^6 - 186*e^5 + 717*e^4 + 537*e^3 - 2887/2*e^2 + 77*e + 298, -2*e^8 - 4*e^7 + 35*e^6 + 57*e^5 - 188*e^4 - 165*e^3 + 388*e^2 - 14*e - 74, 3*e^8 + 5*e^7 - 53*e^6 - 71*e^5 + 288*e^4 + 198*e^3 - 585*e^2 + 51*e + 110, 5/2*e^8 + 9/2*e^7 - 89/2*e^6 - 131/2*e^5 + 243*e^4 + 200*e^3 - 973/2*e^2 - 1/2*e + 86, 2*e^8 + 4*e^7 - 35*e^6 - 57*e^5 + 187*e^4 + 164*e^3 - 380*e^2 + 29*e + 74, 1/4*e^8 + e^7 - 17/4*e^6 - 15*e^5 + 45/2*e^4 + 54*e^3 - 219/4*e^2 - 29*e + 18, -5/2*e^8 - 4*e^7 + 87/2*e^6 + 57*e^5 - 228*e^4 - 162*e^3 + 867/2*e^2 - 12*e - 78, -2*e^8 - 4*e^7 + 38*e^6 + 58*e^5 - 229*e^4 - 177*e^3 + 514*e^2 - 28*e - 108, -5/4*e^8 - 3*e^7 + 89/4*e^6 + 42*e^5 - 247/2*e^4 - 116*e^3 + 1107/4*e^2 - 37*e - 68, 3*e^8 + 4*e^7 - 55*e^6 - 57*e^5 + 314*e^4 + 155*e^3 - 648*e^2 + 77*e + 154, -7/4*e^8 - 3*e^7 + 123/4*e^6 + 43*e^5 - 329/2*e^4 - 125*e^3 + 1289/4*e^2 - 7*e - 52, -4*e^8 - 6*e^7 + 71*e^6 + 86*e^5 - 386*e^4 - 246*e^3 + 765*e^2 - 32*e - 156, -21/4*e^8 - 8*e^7 + 373/4*e^6 + 115*e^5 - 1019/2*e^4 - 328*e^3 + 4091/4*e^2 - 77*e - 216, 5*e^8 + 9*e^7 - 88*e^6 - 129*e^5 + 474*e^4 + 376*e^3 - 958*e^2 + 40*e + 200, 7/2*e^8 + 5*e^7 - 123/2*e^6 - 72*e^5 + 328*e^4 + 206*e^3 - 1261/2*e^2 + 33*e + 134, -4*e^8 - 6*e^7 + 71*e^6 + 86*e^5 - 385*e^4 - 245*e^3 + 755*e^2 - 50*e - 154, -3/4*e^8 - 2*e^7 + 59/4*e^6 + 29*e^5 - 189/2*e^4 - 90*e^3 + 941/4*e^2 - 14*e - 56, -21/4*e^8 - 8*e^7 + 369/4*e^6 + 114*e^5 - 991/2*e^4 - 315*e^3 + 3931/4*e^2 - 95*e - 208, 1/2*e^8 + 3/2*e^7 - 19/2*e^6 - 41/2*e^5 + 58*e^4 + 55*e^3 - 283/2*e^2 + 49/2*e + 28, 29/4*e^8 + 11*e^7 - 521/4*e^6 - 157*e^5 + 1449/2*e^4 + 438*e^3 - 5931/4*e^2 + 148*e + 314, 3/4*e^8 + e^7 - 47/4*e^6 - 15*e^5 + 101/2*e^4 + 49*e^3 - 285/4*e^2 - 36*e + 12, -e^8 - e^7 + 15*e^6 + 15*e^5 - 56*e^4 - 47*e^3 + 41*e^2 + 38*e - 2, 1/2*e^8 - 1/2*e^7 - 17/2*e^6 + 15/2*e^5 + 42*e^4 - 32*e^3 - 113/2*e^2 + 37/2*e + 8, 6*e^8 + 9*e^7 - 108*e^6 - 128*e^5 + 602*e^4 + 351*e^3 - 1233*e^2 + 146*e + 264, 3/2*e^8 + 2*e^7 - 51/2*e^6 - 27*e^5 + 129*e^4 + 63*e^3 - 483/2*e^2 + 27*e + 68, -11/2*e^8 - 8*e^7 + 195/2*e^6 + 115*e^5 - 530*e^4 - 326*e^3 + 2103/2*e^2 - 76*e - 218, 2*e^8 + 3*e^7 - 35*e^6 - 43*e^5 + 186*e^4 + 122*e^3 - 361*e^2 + 20*e + 78, -1/2*e^8 - e^7 + 15/2*e^6 + 15*e^5 - 30*e^4 - 51*e^3 + 93/2*e^2 + 42*e - 14, -9/4*e^8 - 4*e^7 + 165/4*e^6 + 57*e^5 - 469/2*e^4 - 163*e^3 + 1947/4*e^2 - 50*e - 98, 5/4*e^8 + 3*e^7 - 89/4*e^6 - 42*e^5 + 249/2*e^4 + 115*e^3 - 1143/4*e^2 + 42*e + 74, 5/4*e^8 + 2*e^7 - 93/4*e^6 - 28*e^5 + 275/2*e^4 + 72*e^3 - 1231/4*e^2 + 59*e + 76, -19/2*e^8 - 14*e^7 + 335/2*e^6 + 200*e^5 - 904*e^4 - 557*e^3 + 3581/2*e^2 - 147*e - 378, 3*e^8 + 11/2*e^7 - 51*e^6 - 159/2*e^5 + 258*e^4 + 239*e^3 - 483*e^2 - 53/2*e + 96, -7*e^8 - 21/2*e^7 + 122*e^6 + 301/2*e^5 - 643*e^4 - 428*e^3 + 1226*e^2 - 125/2*e - 234, 2*e^8 + 7/2*e^7 - 37*e^6 - 101/2*e^5 + 217*e^4 + 145*e^3 - 482*e^2 + 113/2*e + 114, 5/2*e^8 + 4*e^7 - 85/2*e^6 - 57*e^5 + 218*e^4 + 158*e^3 - 849/2*e^2 + 35*e + 98, 1/2*e^8 + 1/2*e^7 - 17/2*e^6 - 13/2*e^5 + 41*e^4 + 14*e^3 - 123/2*e^2 + 7/2*e + 24, -e^8 - e^7 + 17*e^6 + 15*e^5 - 86*e^4 - 41*e^3 + 149*e^2 - 22*e - 20, -e^7 + e^6 + 13*e^5 - 17*e^4 - 29*e^3 + 87*e^2 - 53*e - 28, 9*e^8 + 29/2*e^7 - 157*e^6 - 417/2*e^5 + 831*e^4 + 606*e^3 - 1617*e^2 + 87/2*e + 326, 3*e^8 + 4*e^7 - 53*e^6 - 57*e^5 + 287*e^4 + 154*e^3 - 568*e^2 + 62*e + 128, 7/4*e^8 + 2*e^7 - 119/4*e^6 - 28*e^5 + 299/2*e^4 + 70*e^3 - 1049/4*e^2 + 25*e + 60, 2*e^8 + 4*e^7 - 35*e^6 - 56*e^5 + 185*e^4 + 157*e^3 - 364*e^2 + 16*e + 52, -5*e^8 - 17/2*e^7 + 85*e^6 + 241/2*e^5 - 430*e^4 - 339*e^3 + 799*e^2 - 41/2*e - 132, e^8 + 2*e^7 - 21*e^6 - 28*e^5 + 142*e^4 + 74*e^3 - 341*e^2 + 92*e + 66, 41/4*e^8 + 16*e^7 - 713/4*e^6 - 229*e^5 + 1881/2*e^4 + 651*e^3 - 7307/4*e^2 + 86*e + 360, e^6 + e^5 - 14*e^4 - 13*e^3 + 48*e^2 + 22*e - 22, -1/2*e^8 + 25/2*e^6 - 100*e^4 + 8*e^3 + 515/2*e^2 - 88*e - 68, -1/2*e^7 + 17/2*e^5 - e^4 - 38*e^3 + 14*e^2 + 71/2*e - 6, -6*e^8 - 10*e^7 + 107*e^6 + 144*e^5 - 587*e^4 - 423*e^3 + 1188*e^2 - 50*e - 252, 7/2*e^8 + 11/2*e^7 - 127/2*e^6 - 155/2*e^5 + 357*e^4 + 213*e^3 - 1477/2*e^2 + 131/2*e + 162, 3/2*e^8 + 5/2*e^7 - 57/2*e^6 - 73/2*e^5 + 170*e^4 + 112*e^3 - 725/2*e^2 + 29/2*e + 72, -3*e^8 - 5*e^7 + 55*e^6 + 71*e^5 - 316*e^4 - 198*e^3 + 676*e^2 - 67*e - 144, e^8 + 2*e^7 - 16*e^6 - 28*e^5 + 72*e^4 + 78*e^3 - 126*e^2 - 6*e + 38, 9*e^8 + 12*e^7 - 159*e^6 - 171*e^5 + 859*e^4 + 466*e^3 - 1677*e^2 + 150*e + 348, 23/4*e^8 + 9*e^7 - 411/4*e^6 - 127*e^5 + 1133/2*e^4 + 343*e^3 - 4629/4*e^2 + 138*e + 240, -3*e^8 - 6*e^7 + 53*e^6 + 86*e^5 - 287*e^4 - 255*e^3 + 587*e^2 - 11*e - 116, -5*e^8 - 7*e^7 + 91*e^6 + 100*e^5 - 515*e^4 - 274*e^3 + 1060*e^2 - 129*e - 228, -2*e^7 + 3*e^6 + 29*e^5 - 44*e^4 - 99*e^3 + 176*e^2 - 38, 7/2*e^8 + 6*e^7 - 127/2*e^6 - 87*e^5 + 356*e^4 + 262*e^3 - 1451/2*e^2 + 20*e + 142, 3/2*e^8 + 3*e^7 - 51/2*e^6 - 45*e^5 + 129*e^4 + 152*e^3 - 485/2*e^2 - 65*e + 58, 13/2*e^8 + 23/2*e^7 - 227/2*e^6 - 331/2*e^5 + 603*e^4 + 489*e^3 - 2389/2*e^2 + 11/2*e + 240, -10*e^8 - 17*e^7 + 177*e^6 + 244*e^5 - 959*e^4 - 712*e^3 + 1918*e^2 - 78*e - 390, 5*e^8 + 7*e^7 - 89*e^6 - 100*e^5 + 488*e^4 + 279*e^3 - 984*e^2 + 70*e + 230, -5*e^8 - 9*e^7 + 90*e^6 + 131*e^5 - 501*e^4 - 401*e^3 + 1031*e^2 - 11*e - 200, -5*e^8 - 9*e^7 + 87*e^6 + 130*e^5 - 460*e^4 - 389*e^3 + 916*e^2 + 10*e - 194, 4*e^8 + 13/2*e^7 - 71*e^6 - 187/2*e^5 + 386*e^4 + 270*e^3 - 772*e^2 + 121/2*e + 156, 2*e^8 + 3*e^7 - 35*e^6 - 44*e^5 + 185*e^4 + 136*e^3 - 346*e^2 - 24*e + 58, -23/4*e^8 - 8*e^7 + 403/4*e^6 + 114*e^5 - 1077/2*e^4 - 311*e^3 + 4205/4*e^2 - 103*e - 228, -e^8 - 2*e^7 + 17*e^6 + 30*e^5 - 86*e^4 - 106*e^3 + 161*e^2 + 72*e - 28, e^8 + 3*e^7 - 18*e^6 - 44*e^5 + 102*e^4 + 144*e^3 - 231*e^2 - 36*e + 20, -31/4*e^8 - 12*e^7 + 547/4*e^6 + 171*e^5 - 1481/2*e^4 - 476*e^3 + 5961/4*e^2 - 126*e - 336, 13/2*e^8 + 21/2*e^7 - 229/2*e^6 - 299/2*e^5 + 618*e^4 + 417*e^3 - 2469/2*e^2 + 229/2*e + 244, 2*e^8 + 5/2*e^7 - 37*e^6 - 69/2*e^5 + 215*e^4 + 80*e^3 - 457*e^2 + 225/2*e + 112, -11/2*e^8 - 19/2*e^7 + 193/2*e^6 + 273/2*e^5 - 518*e^4 - 395*e^3 + 2073/2*e^2 - 133/2*e - 194, 10*e^8 + 18*e^7 - 176*e^6 - 257*e^5 + 949*e^4 + 738*e^3 - 1927*e^2 + 114*e + 400, 4*e^8 + 6*e^7 - 70*e^6 - 85*e^5 + 372*e^4 + 231*e^3 - 717*e^2 + 71*e + 138, -6*e^8 - 23/2*e^7 + 106*e^6 + 329/2*e^5 - 573*e^4 - 481*e^3 + 1159*e^2 - 99/2*e - 212, -9*e^8 - 27/2*e^7 + 159*e^6 + 387/2*e^5 - 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72, -29/4*e^8 - 12*e^7 + 521/4*e^6 + 174*e^5 - 1453/2*e^4 - 516*e^3 + 6027/4*e^2 - 64*e - 316, -2*e^8 - 3*e^7 + 33*e^6 + 43*e^5 - 158*e^4 - 124*e^3 + 269*e^2 + 22*e - 24, -13/4*e^8 - 3*e^7 + 229/4*e^6 + 44*e^5 - 613/2*e^4 - 125*e^3 + 2291/4*e^2 - 5*e - 128, 1/2*e^8 + 5/2*e^7 - 23/2*e^6 - 75/2*e^5 + 87*e^4 + 130*e^3 - 495/2*e^2 - 7/2*e + 66, -14*e^8 - 23*e^7 + 247*e^6 + 328*e^5 - 1334*e^4 - 929*e^3 + 2674*e^2 - 172*e - 572, 9*e^8 + 29/2*e^7 - 160*e^6 - 417/2*e^5 + 875*e^4 + 598*e^3 - 1768*e^2 + 267/2*e + 354, 4*e^8 + 7*e^7 - 72*e^6 - 98*e^5 + 401*e^4 + 265*e^3 - 831*e^2 + 104*e + 156, -5*e^8 - 8*e^7 + 87*e^6 + 114*e^5 - 456*e^4 - 322*e^3 + 866*e^2 - 60*e - 186, 9*e^8 + 15*e^7 - 163*e^6 - 213*e^5 + 920*e^4 + 594*e^3 - 1937*e^2 + 207*e + 412, 13/2*e^8 + 19/2*e^7 - 229/2*e^6 - 269/2*e^5 + 618*e^4 + 359*e^3 - 2465/2*e^2 + 337/2*e + 270, -3*e^8 - 4*e^7 + 55*e^6 + 60*e^5 - 314*e^4 - 190*e^3 + 635*e^2 - 11*e - 104, -21/2*e^8 - 17*e^7 + 367/2*e^6 + 243*e^5 - 976*e^4 - 687*e^3 + 3843/2*e^2 - 141*e - 384, e^7 - 6*e^6 - 14*e^5 + 86*e^4 + 41*e^3 - 297*e^2 + 90*e + 64, 8*e^8 + 13*e^7 - 138*e^6 - 187*e^5 + 711*e^4 + 547*e^3 - 1312*e^2 + 14*e + 216, 3/2*e^8 + 1/2*e^7 - 49/2*e^6 - 9/2*e^5 + 114*e^4 - 18*e^3 - 335/2*e^2 + 97/2*e + 26, 19/2*e^8 + 13*e^7 - 339/2*e^6 - 185*e^5 + 935*e^4 + 500*e^3 - 3795/2*e^2 + 209*e + 432, -25/2*e^8 - 21*e^7 + 441/2*e^6 + 298*e^5 - 1191*e^4 - 831*e^3 + 4793/2*e^2 - 199*e - 504, -23/2*e^8 - 17*e^7 + 405/2*e^6 + 241*e^5 - 1088*e^4 - 655*e^3 + 4279/2*e^2 - 229*e - 462, 7/2*e^8 + 13/2*e^7 - 125/2*e^6 - 185/2*e^5 + 341*e^4 + 269*e^3 - 1359/2*e^2 + 69/2*e + 132, -21/2*e^8 - 16*e^7 + 371/2*e^6 + 229*e^5 - 1003*e^4 - 650*e^3 + 3975/2*e^2 - 121*e - 378, -3/2*e^8 - 5/2*e^7 + 49/2*e^6 + 75/2*e^5 - 118*e^4 - 125*e^3 + 445/2*e^2 + 153/2*e - 72, 2*e^8 + e^7 - 31*e^6 - 13*e^5 + 129*e^4 + 12*e^3 - 153*e^2 + 12*e + 20, 33/2*e^8 + 23*e^7 - 587/2*e^6 - 331*e^5 + 1601*e^4 + 940*e^3 - 6317/2*e^2 + 215*e + 664, 3/4*e^8 + 3*e^7 - 47/4*e^6 - 41*e^5 + 95/2*e^4 + 114*e^3 - 253/4*e^2 + 13*e - 46, -14*e^8 - 22*e^7 + 245*e^6 + 314*e^5 - 1305*e^4 - 883*e^3 + 2557*e^2 - 176*e - 518, -6*e^8 - 10*e^7 + 110*e^6 + 141*e^5 - 631*e^4 - 380*e^3 + 1347*e^2 - 214*e - 290, 6*e^8 + 10*e^7 - 105*e^6 - 143*e^5 + 557*e^4 + 410*e^3 - 1078*e^2 + 52*e + 182, 8*e^8 + 15*e^7 - 138*e^6 - 213*e^5 + 718*e^4 + 606*e^3 - 1404*e^2 + 69*e + 238, -17/2*e^8 - 13*e^7 + 305/2*e^6 + 187*e^5 - 844*e^4 - 537*e^3 + 3423/2*e^2 - 120*e - 378, -11/2*e^8 - 10*e^7 + 199/2*e^6 + 142*e^5 - 563*e^4 - 396*e^3 + 2421/2*e^2 - 142*e - 260, 17/2*e^8 + 16*e^7 - 301/2*e^6 - 230*e^5 + 819*e^4 + 686*e^3 - 3355/2*e^2 + 4*e + 324, -25/2*e^8 - 39/2*e^7 + 441/2*e^6 + 555/2*e^5 - 1188*e^4 - 776*e^3 + 4691/2*e^2 - 373/2*e - 456, -7*e^8 - 10*e^7 + 125*e^6 + 144*e^5 - 684*e^4 - 412*e^3 + 1341*e^2 - 92*e - 238, -6*e^8 - 19/2*e^7 + 104*e^6 + 275/2*e^5 - 548*e^4 - 407*e^3 + 1070*e^2 + 17/2*e - 210, -41/2*e^8 - 34*e^7 + 723/2*e^6 + 487*e^5 - 1949*e^4 - 1405*e^3 + 7769/2*e^2 - 178*e - 766, 8*e^8 + 23/2*e^7 - 147*e^6 - 329/2*e^5 + 844*e^4 + 454*e^3 - 1758*e^2 + 465/2*e + 372, 15/2*e^8 + 12*e^7 - 261/2*e^6 - 171*e^5 + 690*e^4 + 478*e^3 - 2707/2*e^2 + 103*e + 304, 10*e^8 + 16*e^7 - 181*e^6 - 230*e^5 + 1013*e^4 + 667*e^3 - 2067*e^2 + 143*e + 418, -5/2*e^8 - 7/2*e^7 + 89/2*e^6 + 103/2*e^5 - 243*e^4 - 157*e^3 + 951/2*e^2 + 19/2*e - 72, 4*e^8 + 6*e^7 - 70*e^6 - 84*e^5 + 372*e^4 + 222*e^3 - 730*e^2 + 80*e + 192, 2*e^8 + 4*e^7 - 37*e^6 - 56*e^5 + 210*e^4 + 156*e^3 - 425*e^2 + 49*e + 52, 23/4*e^8 + 9*e^7 - 403/4*e^6 - 131*e^5 + 1071/2*e^4 + 394*e^3 - 4097/4*e^2 - 3*e + 192, -3/2*e^8 - 9/2*e^7 + 55/2*e^6 + 131/2*e^5 - 159*e^4 - 208*e^3 + 719/2*e^2 + 37/2*e - 8, 11/2*e^8 + 19/2*e^7 - 199/2*e^6 - 269/2*e^5 + 560*e^4 + 371*e^3 - 2363/2*e^2 + 287/2*e + 272, -3*e^8 - 6*e^7 + 56*e^6 + 85*e^5 - 333*e^4 - 242*e^3 + 767*e^2 - 69*e - 212, -e^8 + 17*e^6 - 2*e^5 - 86*e^4 + 38*e^3 + 141*e^2 - 100*e - 46, -11*e^8 - 17*e^7 + 190*e^6 + 243*e^5 - 986*e^4 - 694*e^3 + 1866*e^2 - 38*e - 400, -7/2*e^8 - 5*e^7 + 117/2*e^6 + 69*e^5 - 287*e^4 - 173*e^3 + 1031/2*e^2 - 53*e - 138, -6*e^8 - 10*e^7 + 108*e^6 + 143*e^5 - 606*e^4 - 398*e^3 + 1273*e^2 - 168*e - 242, 15/2*e^8 + 12*e^7 - 251/2*e^6 - 171*e^5 + 618*e^4 + 482*e^3 - 2227/2*e^2 + 14*e + 190, 11/2*e^8 + 15/2*e^7 - 197/2*e^6 - 217/2*e^5 + 546*e^4 + 303*e^3 - 2197/2*e^2 + 273/2*e + 216, -9*e^8 - 23/2*e^7 + 159*e^6 + 325/2*e^5 - 860*e^4 - 422*e^3 + 1686*e^2 - 453/2*e - 344, e^7 + 5*e^6 - 18*e^5 - 71*e^4 + 96*e^3 + 226*e^2 - 210*e - 54, -14*e^8 - 39/2*e^7 + 249*e^6 + 559/2*e^5 - 1359*e^4 - 779*e^3 + 2681*e^2 - 477/2*e - 534, 1/2*e^8 - 1/2*e^7 - 21/2*e^6 + 7/2*e^5 + 73*e^4 + 11*e^3 - 329/2*e^2 - 53/2*e + 68, 7/4*e^8 + 2*e^7 - 147/4*e^6 - 29*e^5 + 505/2*e^4 + 74*e^3 - 2473/4*e^2 + 132*e + 168, -e^8 - 7/2*e^7 + 18*e^6 + 99/2*e^5 - 100*e^4 - 147*e^3 + 218*e^2 - 57/2*e - 8, 14*e^8 + 22*e^7 - 244*e^6 - 316*e^5 + 1289*e^4 + 913*e^3 - 2490*e^2 + 69*e + 478, -13*e^8 - 22*e^7 + 231*e^6 + 316*e^5 - 1256*e^4 - 922*e^3 + 2504*e^2 - 108*e - 492, -59/4*e^8 - 27*e^7 + 1035/4*e^6 + 386*e^5 - 2777/2*e^4 - 1117*e^3 + 11245/4*e^2 - 131*e - 572, -19/2*e^8 - 12*e^7 + 331/2*e^6 + 172*e^5 - 871*e^4 - 474*e^3 + 3259/2*e^2 - 106*e - 324, -31/2*e^8 - 25*e^7 + 543/2*e^6 + 361*e^5 - 1448*e^4 - 1059*e^3 + 5673/2*e^2 - 83*e - 554, -23/2*e^8 - 17*e^7 + 409/2*e^6 + 239*e^5 - 1117*e^4 - 636*e^3 + 4477/2*e^2 - 264*e - 466, 7*e^8 + 9*e^7 - 128*e^6 - 128*e^5 + 727*e^4 + 342*e^3 - 1485*e^2 + 204*e + 336] 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]