/* This code can be loaded, or copied and pasted, into Magma. It will load the data associated to the HMF, including the field, level, and Hecke and Atkin-Lehner eigenvalue data. At the *bottom* of the file, there is code to recreate the Hilbert modular form in Magma, by creating the HMF space and cutting out the corresponding Hecke irreducible subspace. From there, you can ask for more eigenvalues or modify as desired. It is commented out, as this computation may be lengthy. */ P := PolynomialRing(Rationals()); g := P![-21, -1, 1]; F := NumberField(g); ZF := Integers(F); NN := ideal; primesArray := [ [3, 3, w], [3, 3, w + 2], [4, 2, 2], [5, 5, w + 2], [7, 7, w], [7, 7, w + 6], [17, 17, w + 8], [19, 19, w + 1], [19, 19, w - 2], [23, 23, w + 9], [23, 23, w + 13], [37, 37, w + 11], [37, 37, w + 25], [59, 59, 3*w + 10], [59, 59, 3*w - 13], [73, 73, w + 15], [73, 73, w + 57], [89, 89, -w - 10], [89, 89, w - 11], [97, 97, w + 22], [97, 97, w + 74], [101, 101, 3*w - 11], [101, 101, -3*w - 8], [107, 107, w + 18], [107, 107, w + 88], [113, 113, w + 28], [113, 113, w + 84], [121, 11, -11], [149, 149, 3*w - 8], [149, 149, -3*w - 5], [151, 151, -3*w - 17], [151, 151, 3*w - 20], [163, 163, w + 66], [163, 163, w + 96], [167, 167, w + 34], [167, 167, w + 132], [169, 13, -13], [173, 173, w + 68], [173, 173, w + 104], [179, 179, 3*w - 5], [179, 179, -3*w - 2], [191, 191, 3*w - 2], [191, 191, 3*w - 1], [193, 193, w + 24], [193, 193, w + 168], [197, 197, w + 85], [197, 197, w + 111], [227, 227, w + 26], [227, 227, w + 200], [229, 229, 3*w - 22], [229, 229, -3*w - 19], [233, 233, w + 102], [233, 233, w + 130], [239, 239, 2*w - 19], [239, 239, -2*w - 17], [251, 251, -w - 16], [251, 251, w - 17], [271, 271, -3*w - 20], [271, 271, 3*w - 23], [277, 277, w + 37], [277, 277, w + 239], [281, 281, 5*w - 31], [281, 281, -5*w - 26], [283, 283, w + 29], [283, 283, w + 253], [313, 313, w + 140], [313, 313, w + 172], [317, 317, w + 134], [317, 317, w + 182], [331, 331, -4*w - 1], [331, 331, 4*w - 5], [337, 337, w + 95], [337, 337, w + 241], [347, 347, w + 49], [347, 347, w + 297], [349, 349, -5*w - 11], [349, 349, 5*w - 16], [359, 359, -w - 19], [359, 359, w - 20], [367, 367, w + 33], [367, 367, w + 333], [389, 389, 4*w - 29], [389, 389, -4*w - 25], [397, 397, w + 150], [397, 397, w + 246], [409, 409, -3*w - 23], [409, 409, 3*w - 26], [421, 421, -5*w - 8], [421, 421, 5*w - 13], [461, 461, -5*w - 29], [461, 461, 5*w - 34], [487, 487, w + 38], [487, 487, w + 448], [491, 491, 2*w - 25], [491, 491, -2*w - 23], [503, 503, w + 136], [503, 503, w + 366], [509, 509, -6*w - 13], [509, 509, 6*w - 19], [547, 547, w + 52], [547, 547, w + 494], [569, 569, 6*w - 17], [569, 569, -6*w - 11], [599, 599, 9*w - 38], [599, 599, 9*w + 29], [607, 607, w + 252], [607, 607, w + 354], [617, 617, w + 286], [617, 617, w + 330], [631, 631, 8*w - 31], [631, 631, -8*w - 23], [643, 643, w + 191], [643, 643, w + 451], [653, 653, w + 44], [653, 653, w + 608], [659, 659, -5*w - 32], [659, 659, 5*w - 37], [661, 661, 7*w - 23], [661, 661, -7*w - 16], [673, 673, w + 124], [673, 673, w + 548], [677, 677, w + 315], [677, 677, w + 361], [683, 683, w + 45], [683, 683, w + 637], [701, 701, 6*w - 11], [701, 701, -6*w - 5], [739, 739, -3*w - 29], [739, 739, 3*w - 32], [743, 743, w + 268], [743, 743, w + 474], [761, 761, 6*w - 5], [761, 761, 6*w - 1], [769, 769, 7*w - 20], [769, 769, -7*w - 13], [787, 787, w + 287], [787, 787, w + 499], [823, 823, w + 192], [823, 823, w + 630], [827, 827, w + 149], [827, 827, w + 677], [829, 829, -9*w + 55], [829, 829, -9*w - 46], [841, 29, -29], [853, 853, w + 310], [853, 853, w + 542], [857, 857, w + 389], [857, 857, w + 467], [859, 859, 7*w - 17], [859, 859, -7*w - 10], [877, 877, w + 51], [877, 877, w + 825], [887, 887, w + 343], [887, 887, w + 543], [907, 907, w + 67], [907, 907, w + 839], [919, 919, -8*w - 17], [919, 919, 8*w - 25], [947, 947, w + 53], [947, 947, w + 893], [961, 31, -31], [971, 971, -w - 31], [971, 971, w - 32], [983, 983, w + 54], [983, 983, w + 928], [997, 997, w + 151], [997, 997, w + 845], [1013, 1013, w + 313], [1013, 1013, w + 699], [1019, 1019, 9*w - 31], [1019, 1019, -9*w - 22], [1021, 1021, -7*w - 1], [1021, 1021, 7*w - 8], [1039, 1039, 7*w - 2], [1039, 1039, 7*w - 5], [1069, 1069, 3*w - 37], [1069, 1069, -3*w - 34], [1093, 1093, w + 517], [1093, 1093, w + 575], [1109, 1109, 5*w - 43], [1109, 1109, -5*w - 38], [1117, 1117, w + 342], [1117, 1117, w + 774], [1153, 1153, w + 176], [1153, 1153, w + 976], [1163, 1163, w + 413], [1163, 1163, w + 749], [1171, 1171, -6*w - 41], [1171, 1171, 6*w - 47], [1181, 1181, 4*w - 41], [1181, 1181, -4*w - 37], [1187, 1187, w + 273], [1187, 1187, w + 913], [1193, 1193, w + 91], [1193, 1193, w + 1101], [1213, 1213, w + 60], [1213, 1213, w + 1152], [1217, 1217, w + 357], [1217, 1217, w + 859], [1249, 1249, 9*w - 59], [1249, 1249, -9*w - 50], [1259, 1259, 9*w - 26], [1259, 1259, -9*w - 17], [1279, 1279, 8*w - 13], [1279, 1279, -8*w - 5], [1291, 1291, 3*w - 40], [1291, 1291, -3*w - 37], [1297, 1297, w + 505], [1297, 1297, w + 791], [1301, 1301, -9*w - 16], [1301, 1301, 9*w - 25], [1303, 1303, w + 466], [1303, 1303, w + 836], [1361, 1361, 5*w - 46], [1361, 1361, -5*w - 41], [1367, 1367, w + 293], [1367, 1367, w + 1073], [1381, 1381, 11*w - 40], [1381, 1381, -11*w - 29], [1409, 1409, 7*w - 53], [1409, 1409, -7*w - 46], [1423, 1423, w + 65], [1423, 1423, w + 1357], [1429, 1429, -12*w + 73], [1429, 1429, -12*w - 61], [1433, 1433, w + 300], [1433, 1433, w + 1132], [1471, 1471, 9*w - 61], [1471, 1471, -9*w - 52], [1481, 1481, 9*w - 20], [1481, 1481, -9*w - 11], [1493, 1493, w + 468], [1493, 1493, w + 1024], [1511, 1511, -9*w - 10], [1511, 1511, 9*w - 19], [1523, 1523, w + 561], [1523, 1523, w + 961], [1531, 1531, 3*w - 43], [1531, 1531, -3*w - 40], [1549, 1549, 10*w - 29], [1549, 1549, -10*w - 19], [1553, 1553, w + 454], [1553, 1553, w + 1098], [1567, 1567, w + 409], [1567, 1567, w + 1157], [1579, 1579, -11*w - 26], [1579, 1579, 11*w - 37], [1619, 1619, -w - 40], [1619, 1619, w - 41], [1627, 1627, w + 193], [1627, 1627, w + 1433], [1637, 1637, w + 305], [1637, 1637, w + 1331], [1663, 1663, w + 397], [1663, 1663, w + 1265], [1681, 41, -41], [1693, 1693, w + 739], [1693, 1693, w + 953], [1697, 1697, w + 71], [1697, 1697, w + 1625], [1699, 1699, -13*w - 37], [1699, 1699, 13*w - 50], [1709, 1709, 9*w - 8], [1709, 1709, 9*w - 1], [1721, 1721, 9*w - 4], [1721, 1721, 9*w - 5], [1723, 1723, w + 329], [1723, 1723, w + 1393], [1759, 1759, -11*w - 23], [1759, 1759, 11*w - 34], [1789, 1789, 3*w - 46], [1789, 1789, -3*w - 43], [1801, 1801, 10*w - 23], [1801, 1801, -10*w - 13], [1811, 1811, -13*w - 67], [1811, 1811, 13*w - 80], [1847, 1847, w + 324], [1847, 1847, w + 1522], [1849, 43, -43], [1861, 1861, 14*w - 55], [1861, 1861, -14*w - 41], [1867, 1867, w + 788], [1867, 1867, w + 1078], [1871, 1871, -w - 43], [1871, 1871, w - 44], [1873, 1873, w + 178], [1873, 1873, w + 1694], [1877, 1877, w + 766], [1877, 1877, w + 1110], [1879, 1879, -3*w - 44], [1879, 1879, 3*w - 47], [1889, 1889, -8*w - 53], [1889, 1889, 8*w - 61], [1907, 1907, w + 447], [1907, 1907, w + 1459], [1933, 1933, w + 228], [1933, 1933, w + 1704], [1951, 1951, -13*w - 34], [1951, 1951, 13*w - 47], [2003, 2003, w + 118], [2003, 2003, w + 1884], [2017, 2017, w + 356], [2017, 2017, w + 1660], [2039, 2039, -7*w - 52], [2039, 2039, 7*w - 59], [2063, 2063, w + 653], [2063, 2063, w + 1409], [2089, 2089, -10*w - 1], [2089, 2089, 10*w - 11], [2099, 2099, -12*w - 25], [2099, 2099, 12*w - 37], [2113, 2113, w + 220], [2113, 2113, w + 1892], [2129, 2129, 15*w - 59], [2129, 2129, -15*w - 44], [2137, 2137, w + 560], [2137, 2137, w + 1576], [2141, 2141, -w - 46], [2141, 2141, w - 47], [2153, 2153, w + 80], [2153, 2153, w + 2072], [2161, 2161, -3*w - 47], [2161, 2161, 3*w - 50], [2203, 2203, w + 457], [2203, 2203, w + 1745], [2207, 2207, w + 81], [2207, 2207, w + 2125], [2209, 47, -47], [2213, 2213, w + 1065], [2213, 2213, w + 1147], [2237, 2237, w + 680], [2237, 2237, w + 1556], [2267, 2267, w + 359], [2267, 2267, w + 1907], [2269, 2269, -12*w - 67], [2269, 2269, 12*w - 79], [2273, 2273, w + 793], [2273, 2273, w + 1479], [2311, 2311, 9*w - 68], [2311, 2311, -9*w - 59], [2357, 2357, w + 497], [2357, 2357, w + 1859], [2371, 2371, -6*w - 53], [2371, 2371, 6*w - 59], [2377, 2377, w + 1071], [2377, 2377, w + 1305], [2381, 2381, -7*w - 55], [2381, 2381, 7*w - 62], [2383, 2383, w + 327], [2383, 2383, w + 2055], [2389, 2389, 11*w - 19], [2389, 2389, -11*w - 8], [2399, 2399, -11*w - 65], [2399, 2399, 11*w - 76], [2417, 2417, w + 255], [2417, 2417, w + 2161], [2437, 2437, w + 1175], [2437, 2437, w + 1261], [2477, 2477, w + 1172], [2477, 2477, w + 1304], [2531, 2531, -12*w - 17], [2531, 2531, 12*w - 29], [2543, 2543, w + 133], [2543, 2543, w + 2409], [2549, 2549, 5*w - 58], [2549, 2549, -5*w - 53], [2551, 2551, 11*w - 10], [2551, 2551, 11*w - 1], [2557, 2557, w + 807], [2557, 2557, w + 1749], [2609, 2609, 8*w - 67], [2609, 2609, -8*w - 59], [2647, 2647, w + 684], [2647, 2647, w + 1962], [2657, 2657, w + 1194], [2657, 2657, w + 1462], [2663, 2663, w + 89], [2663, 2663, w + 2573], [2671, 2671, 3*w - 55], [2671, 2671, -3*w - 52], [2683, 2683, w + 347], [2683, 2683, w + 2335], [2693, 2693, w + 1140], [2693, 2693, w + 1552], [2699, 2699, -12*w - 13], [2699, 2699, 12*w - 25], [2711, 2711, -15*w - 38], [2711, 2711, 15*w - 53], [2713, 2713, w + 950], [2713, 2713, w + 1762], [2719, 2719, 17*w - 67], [2719, 2719, -17*w - 50], [2729, 2729, 13*w - 86], [2729, 2729, -13*w - 73], [2741, 2741, -7*w - 58], [2741, 2741, 7*w - 65], [2777, 2777, w + 139], [2777, 2777, w + 2637], [2789, 2789, -17*w + 103], [2789, 2789, -17*w - 86], [2801, 2801, 15*w - 52], [2801, 2801, -15*w - 37], [2809, 53, -53], [2833, 2833, w + 991], [2833, 2833, w + 1841], [2887, 2887, w + 426], [2887, 2887, w + 2460], [2897, 2897, w + 879], [2897, 2897, w + 2017], [2909, 2909, -4*w - 55], [2909, 2909, 4*w - 59], [2917, 2917, w + 1411], [2917, 2917, w + 1505], [2927, 2927, w + 1151], [2927, 2927, w + 1775], [2939, 2939, -12*w - 5], [2939, 2939, 12*w - 17], [2953, 2953, w + 829], [2953, 2953, w + 2123], [2963, 2963, w + 1028], [2963, 2963, w + 1934], [2971, 2971, 9*w - 73], [2971, 2971, -9*w - 64], [3001, 3001, 3*w - 58], [3001, 3001, -3*w - 55], [3011, 3011, -12*w - 1], [3011, 3011, 12*w - 13], [3023, 3023, w + 731], [3023, 3023, w + 2291], [3037, 3037, w + 900], [3037, 3037, w + 2136], [3041, 3041, 18*w - 71], [3041, 3041, -18*w - 53], [3061, 3061, -17*w - 47], [3061, 3061, 17*w - 64], [3067, 3067, w + 567], [3067, 3067, w + 2499], [3079, 3079, -6*w - 59], [3079, 3079, 6*w - 65], [3083, 3083, w + 372], [3083, 3083, w + 2710], [3109, 3109, -9*w - 65], [3109, 3109, 9*w - 74], [3119, 3119, 7*w - 68], [3119, 3119, -7*w - 61], [3167, 3167, w + 718], [3167, 3167, w + 2448], [3181, 3181, 12*w - 85], [3181, 3181, -12*w - 73], [3203, 3203, w + 1311], [3203, 3203, w + 1891], [3209, 3209, 21*w - 89], [3209, 3209, 21*w + 68], [3221, 3221, 15*w - 47], [3221, 3221, -15*w - 32], [3229, 3229, 22*w - 95], [3229, 3229, 22*w + 73], [3251, 3251, -5*w - 59], [3251, 3251, 5*w - 64], [3253, 3253, w + 705], [3253, 3253, w + 2547], [3257, 3257, w + 1282], [3257, 3257, w + 1974], [3299, 3299, -15*w - 31], [3299, 3299, 15*w - 46], [3319, 3319, -13*w - 10], [3319, 3319, 13*w - 23], [3331, 3331, 6*w - 67], [3331, 3331, -6*w - 61], [3343, 3343, w + 760], [3343, 3343, w + 2582], [3373, 3373, w + 438], [3373, 3373, w + 2934], [3391, 3391, -9*w - 67], [3391, 3391, 9*w - 76], [3407, 3407, w + 154], [3407, 3407, w + 3252], [3449, 3449, 15*w - 44], [3449, 3449, -15*w - 29], [3457, 3457, w + 602], [3457, 3457, w + 2854], [3463, 3463, w + 713], [3463, 3463, w + 2749], [3469, 3469, -3*w - 59], [3469, 3469, 3*w - 62], [3511, 3511, -19*w - 55], [3511, 3511, 19*w - 74], [3533, 3533, w + 685], [3533, 3533, w + 2847], [3547, 3547, w + 309], [3547, 3547, w + 3237], [3571, 3571, 13*w - 2], [3571, 3571, 13*w - 11], [3593, 3593, w + 311], [3593, 3593, w + 3281], [3607, 3607, w + 1255], [3607, 3607, w + 2351], [3643, 3643, w + 289], [3643, 3643, w + 3353], [3659, 3659, 15*w - 41], [3659, 3659, -15*w - 26], [3671, 3671, -19*w - 97], [3671, 3671, -19*w + 116], [3677, 3677, w + 160], [3677, 3677, w + 3516], [3691, 3691, -17*w - 41], [3691, 3691, 17*w - 58], [3719, 3719, 13*w - 92], [3719, 3719, -13*w - 79], [3721, 61, -61], [3733, 3733, w + 649], [3733, 3733, w + 3083], [3739, 3739, 20*w - 79], [3739, 3739, -20*w - 59], [3761, 3761, -w - 61], [3761, 3761, w - 62], [3767, 3767, w + 604], [3767, 3767, w + 3162], [3797, 3797, w + 526], [3797, 3797, w + 3270], [3803, 3803, w + 489], [3803, 3803, w + 3313], [3821, 3821, -20*w + 121], [3821, 3821, -20*w - 101], [3847, 3847, w + 934], [3847, 3847, w + 2912], [3851, 3851, -15*w - 23], [3851, 3851, 15*w - 38], [3853, 3853, w + 1080], [3853, 3853, w + 2772], [3889, 3889, 19*w - 71], [3889, 3889, -19*w - 52], [3907, 3907, w + 1717], [3907, 3907, w + 2189], [3911, 3911, 15*w - 37], [3911, 3911, -15*w - 22], [3917, 3917, w + 108], [3917, 3917, w + 3808], [3919, 3919, 16*w - 47], [3919, 3919, -16*w - 31], [3929, 3929, 7*w - 74], [3929, 3929, -7*w - 67], [3931, 3931, 23*w - 97], [3931, 3931, 23*w + 74], [3947, 3947, w + 1111], [3947, 3947, w + 2835], [3967, 3967, w + 1564], [3967, 3967, w + 2402], [4007, 4007, w + 1764], [4007, 4007, w + 2242], [4021, 4021, -14*w - 5], [4021, 4021, 14*w - 19], [4057, 4057, w + 142], [4057, 4057, w + 3914], [4073, 4073, w + 1445], [4073, 4073, w + 2627], [4079, 4079, -15*w - 19], [4079, 4079, 15*w - 34], [4099, 4099, 3*w - 67], [4099, 4099, -3*w - 64], [4129, 4129, 14*w - 13], [4129, 4129, 14*w - 1], [4139, 4139, -w - 64], [4139, 4139, w - 65], [4153, 4153, w + 2020], [4153, 4153, w + 2132], [4177, 4177, w + 1773], [4177, 4177, w + 2403], [4201, 4201, -22*w - 67], [4201, 4201, 22*w - 89], [4229, 4229, -15*w - 16], [4229, 4229, 15*w - 31], [4231, 4231, -3*w - 65], [4231, 4231, 3*w - 68], [4241, 4241, -13*w - 82], [4241, 4241, 13*w - 95], [4243, 4243, w + 338], [4243, 4243, w + 3904], [4253, 4253, w + 437], [4253, 4253, w + 3815], [4259, 4259, -21*w - 61], [4259, 4259, 21*w - 82], [4271, 4271, 2*w - 67], [4271, 4271, -2*w - 65], [4273, 4273, w + 1366], [4273, 4273, w + 2906], [4339, 4339, 15*w - 103], [4339, 4339, -15*w - 88], [4357, 4357, w + 1916], [4357, 4357, w + 2440], [4363, 4363, w + 114], [4363, 4363, w + 4248], [4397, 4397, w + 175], [4397, 4397, w + 4221], [4421, 4421, -4*w - 67], [4421, 4421, 4*w - 71], [4423, 4423, w + 1415], [4423, 4423, w + 3007], [4441, 4441, -9*w - 74], [4441, 4441, 9*w - 83], [4447, 4447, w + 1198], [4447, 4447, w + 3248], [4457, 4457, w + 2170], [4457, 4457, w + 2286], [4483, 4483, w + 2166], [4483, 4483, w + 2316], [4489, 67, -67], [4493, 4493, w + 1266], [4493, 4493, w + 3226], [4517, 4517, w + 116], [4517, 4517, w + 4400], [4567, 4567, w + 692], [4567, 4567, w + 3874], [4583, 4583, w + 940], [4583, 4583, w + 3642], [4591, 4591, 19*w - 65], [4591, 4591, -19*w - 46], [4597, 4597, w + 975], [4597, 4597, w + 3621], [4639, 4639, -3*w - 68], [4639, 4639, 3*w - 71], [4649, 4649, -15*w - 4], [4649, 4649, 15*w - 19], [4663, 4663, w + 908], [4663, 4663, w + 3754], [4679, 4679, -21*w - 58], [4679, 4679, 21*w - 79], [4691, 4691, 15*w - 17], [4691, 4691, -15*w - 2], [4703, 4703, w + 181], [4703, 4703, w + 4521], [4723, 4723, w + 545], [4723, 4723, w + 4177], [4733, 4733, w + 418], [4733, 4733, w + 4314], [4751, 4751, 15*w - 2], [4751, 4751, 15*w - 13], [4759, 4759, -9*w - 76], [4759, 4759, 9*w - 85], [4783, 4783, w + 1655], [4783, 4783, w + 3127], [4787, 4787, w + 920], [4787, 4787, w + 3866], [4817, 4817, w + 858], [4817, 4817, w + 3958], [4861, 4861, -12*w - 83], [4861, 4861, 12*w - 95], [4871, 4871, 5*w - 76], [4871, 4871, -5*w - 71], [4903, 4903, w + 682], [4903, 4903, w + 4220], [4909, 4909, -21*w - 109], [4909, 4909, 21*w - 130], [4931, 4931, -10*w - 79], [4931, 4931, 10*w - 89], [4933, 4933, w + 2405], [4933, 4933, w + 2527], [4937, 4937, w + 530], [4937, 4937, w + 4406], [4951, 4951, -17*w - 26], [4951, 4951, 17*w - 43], [4957, 4957, w + 157], [4957, 4957, w + 4799], [4967, 4967, w + 854], [4967, 4967, w + 4112], [4987, 4987, w + 730], [4987, 4987, w + 4256], [4993, 4993, w + 533], [4993, 4993, w + 4459], [4999, 4999, -16*w - 13], [4999, 4999, 16*w - 29], [5003, 5003, w + 1554], [5003, 5003, w + 3448], [5011, 5011, 6*w - 79], [5011, 5011, -6*w - 73], [5041, 71, -71], [5051, 5051, 14*w - 103], [5051, 5051, -14*w - 89], [5077, 5077, w + 123], [5077, 5077, w + 4953], [5081, 5081, 21*w - 76], [5081, 5081, -21*w - 55], [5099, 5099, 2*w - 73], [5099, 5099, -2*w - 71], [5101, 5101, 22*w - 83], [5101, 5101, -22*w - 61], [5107, 5107, w + 2111], [5107, 5107, w + 2995], [5119, 5119, -15*w - 92], [5119, 5119, 15*w - 107], [5189, 5189, 27*w + 88], [5189, 5189, 27*w - 115], [5197, 5197, w + 2009], [5197, 5197, w + 3187], [5233, 5233, w + 2428], [5233, 5233, w + 2804], [5261, 5261, 11*w - 94], [5261, 5261, -11*w - 83], [5273, 5273, w + 2070], [5273, 5273, w + 3202], [5279, 5279, -7*w - 76], [5279, 5279, 7*w - 83], [5297, 5297, w + 549], [5297, 5297, w + 4747], [5333, 5333, w + 1894], [5333, 5333, w + 3438], [5351, 5351, 24*w - 95], [5351, 5351, -24*w - 71], [5381, 5381, -w - 73], [5381, 5381, w - 74], [5413, 5413, w + 1108], [5413, 5413, w + 4304], [5417, 5417, w + 1566], [5417, 5417, w + 3850], [5419, 5419, -9*w - 80], [5419, 5419, 9*w - 89], [5431, 5431, 16*w - 5], [5431, 5431, 16*w - 11], [5437, 5437, w + 1498], [5437, 5437, w + 3938], [5441, 5441, -18*w - 29], [5441, 5441, 18*w - 47], [5443, 5443, w + 2024], [5443, 5443, w + 3418], [5449, 5449, -25*w - 76], [5449, 5449, 25*w - 101], [5477, 5477, w + 853], [5477, 5477, w + 4623], [5503, 5503, w + 2598], [5503, 5503, w + 2904], [5521, 5521, 15*w - 109], [5521, 5521, -15*w - 94], [5573, 5573, w + 1913], [5573, 5573, w + 3659], [5591, 5591, 22*w - 137], [5591, 5591, -22*w - 115], [5647, 5647, w + 390], [5647, 5647, w + 5256], [5659, 5659, 18*w - 121], [5659, 5659, -18*w - 103], [5669, 5669, 19*w - 125], [5669, 5669, -19*w - 106], [5683, 5683, w + 1604], [5683, 5683, w + 4078], [5711, 5711, -21*w - 50], [5711, 5711, 21*w - 71], [5717, 5717, w + 1235], [5717, 5717, w + 4481], [5743, 5743, w + 1665], [5743, 5743, w + 4077], [5779, 5779, 19*w - 53], [5779, 5779, -19*w - 34], [5783, 5783, w + 1412], [5783, 5783, w + 4370], [5801, 5801, 11*w - 97], [5801, 5801, -11*w - 86], [5807, 5807, w + 2040], [5807, 5807, w + 3766], [5839, 5839, 23*w - 85], [5839, 5839, -23*w - 62], [5843, 5843, w + 1612], [5843, 5843, w + 4230], [5849, 5849, -17*w - 101], [5849, 5849, 17*w - 118], [5861, 5861, 18*w - 41], [5861, 5861, -18*w - 23], [5869, 5869, 17*w - 25], [5869, 5869, -17*w - 8], [5881, 5881, 29*w + 95], [5881, 5881, 29*w - 124], [5923, 5923, w + 2485], [5923, 5923, w + 3437], [5927, 5927, w + 2248], [5927, 5927, w + 3678], [5953, 5953, w + 1026], [5953, 5953, w + 4926], [5987, 5987, w + 2262], [5987, 5987, w + 3724], [6007, 6007, w + 2743], [6007, 6007, w + 3263], [6047, 6047, w + 1747], [6047, 6047, w + 4299], [6101, 6101, -18*w - 19], [6101, 6101, 18*w - 37], [6113, 6113, w + 135], [6113, 6113, w + 5977], [6121, 6121, 17*w - 4], [6121, 6121, 17*w - 13], [6143, 6143, w + 1501], [6143, 6143, w + 4641], [6217, 6217, w + 2514], [6217, 6217, w + 3702], [6221, 6221, -4*w - 79], [6221, 6221, 4*w - 83], [6241, 79, -79], [6263, 6263, w + 2028], [6263, 6263, w + 4234], [6269, 6269, 7*w - 89], [6269, 6269, -7*w - 82], [6271, 6271, 23*w - 82], [6271, 6271, -23*w - 59], [6287, 6287, w + 812], [6287, 6287, w + 5474], [6299, 6299, -w - 79], [6299, 6299, w - 80], [6311, 6311, 24*w - 89], [6311, 6311, -24*w - 65], [6317, 6317, w + 1383], [6317, 6317, w + 4933], [6353, 6353, w + 1454], [6353, 6353, w + 4898], [6359, 6359, 11*w - 100], [6359, 6359, -11*w - 89], [6379, 6379, 31*w - 134], [6379, 6379, 31*w + 103], [6397, 6397, w + 1904], [6397, 6397, w + 4492], [6451, 6451, -3*w - 80], [6451, 6451, 3*w - 83], [6469, 6469, 9*w - 95], [6469, 6469, -9*w - 86], [6481, 6481, 19*w - 44], [6481, 6481, -19*w - 25], [6529, 6529, 24*w - 149], [6529, 6529, -24*w - 125], [6571, 6571, -18*w - 107], [6571, 6571, 18*w - 125], [6581, 6581, 30*w + 97], [6581, 6581, 30*w - 127], [6607, 6607, w + 2130], [6607, 6607, w + 4476], [6637, 6637, w + 1450], [6637, 6637, w + 5186], [6653, 6653, w + 3218], [6653, 6653, w + 3434], [6679, 6679, 19*w - 41], [6679, 6679, -19*w - 22], [6689, 6689, 18*w - 23], [6689, 6689, -18*w - 5], [6703, 6703, w + 1711], [6703, 6703, w + 4991], [6719, 6719, 21*w - 62], [6719, 6719, -21*w - 41], [6737, 6737, w + 651], [6737, 6737, w + 6085], [6763, 6763, w + 1527], [6763, 6763, w + 5235], [6779, 6779, 5*w - 88], [6779, 6779, -5*w - 83], [6781, 6781, 3*w - 85], [6781, 6781, -3*w - 82], [6791, 6791, 7*w - 92], [6791, 6791, -7*w - 85], [6793, 6793, w + 2191], [6793, 6793, w + 4601], [6803, 6803, w + 1755], [6803, 6803, w + 5047], [6823, 6823, w + 1001], [6823, 6823, w + 5821], [6827, 6827, w + 2143], [6827, 6827, w + 4683], [6857, 6857, w + 143], [6857, 6857, w + 6713], [6863, 6863, w + 3179], [6863, 6863, w + 3683], [6869, 6869, 18*w - 5], [6869, 6869, 18*w - 13], [6889, 83, -83], [6907, 6907, w + 1826], [6907, 6907, w + 5080], [6911, 6911, 24*w - 85], [6911, 6911, -24*w - 61], [6947, 6947, w + 2586], [6947, 6947, w + 4360], [6949, 6949, -3*w - 83], [6949, 6949, 3*w - 86], [6961, 6961, -25*w - 67], [6961, 6961, 25*w - 92], [6967, 6967, w + 3203], [6967, 6967, w + 3763], [6971, 6971, 2*w - 85], [6971, 6971, -2*w - 83], [6977, 6977, w + 2761], [6977, 6977, w + 4215], [6991, 6991, -15*w - 101], [6991, 6991, 15*w - 116], [6997, 6997, w + 3166], [6997, 6997, w + 3830], [7019, 7019, -21*w - 38], [7019, 7019, 21*w - 59], [7027, 7027, w + 187], [7027, 7027, w + 6839], [7039, 7039, 18*w - 127], [7039, 7039, -18*w - 109], [7043, 7043, w + 3091], [7043, 7043, w + 3951], [7103, 7103, w + 3065], [7103, 7103, w + 4037], [7121, 7121, -13*w - 97], [7121, 7121, 13*w - 110], [7159, 7159, -27*w - 137], [7159, 7159, -27*w + 164], [7177, 7177, w + 2220], [7177, 7177, w + 4956], [7213, 7213, w + 1577], [7213, 7213, w + 5635], [7229, 7229, 4*w - 89], [7229, 7229, -4*w - 85], [7237, 7237, w + 2487], [7237, 7237, w + 4749], [7247, 7247, w + 2279], [7247, 7247, w + 4967], [7253, 7253, w + 2946], [7253, 7253, w + 4306], [7283, 7283, w + 572], [7283, 7283, w + 6710], [7307, 7307, w + 678], [7307, 7307, w + 6628], [7309, 7309, -26*w - 71], [7309, 7309, 26*w - 97], [7331, 7331, 7*w - 95], [7331, 7331, -7*w - 88], [7333, 7333, w + 2725], [7333, 7333, w + 4607], [7369, 7369, 22*w - 65], [7369, 7369, -22*w - 43], [7411, 7411, -20*w - 23], [7411, 7411, 20*w - 43], [7417, 7417, w + 882], [7417, 7417, w + 6534], [7457, 7457, w + 850], [7457, 7457, w + 6606], [7459, 7459, -23*w - 50], [7459, 7459, 23*w - 73], [7477, 7477, w + 1958], [7477, 7477, w + 5518], [7481, 7481, 27*w - 103], [7481, 7481, -27*w - 76], [7487, 7487, w + 1909], [7487, 7487, w + 5577], [7489, 7489, -19*w - 4], [7489, 7489, 19*w - 23], [7499, 7499, 14*w - 115], [7499, 7499, -14*w - 101], [7507, 7507, w + 1050], [7507, 7507, w + 6456], [7517, 7517, w + 2064], [7517, 7517, w + 5452], [7529, 7529, -11*w - 95], [7529, 7529, 11*w - 106], [7537, 7537, w + 1835], [7537, 7537, w + 5701], [7549, 7549, 12*w - 109], [7549, 7549, -12*w - 97], [7561, 7561, -19*w - 1], [7561, 7561, 19*w - 20], [7577, 7577, w + 529], [7577, 7577, w + 7047], [7591, 7591, -9*w - 92], [7591, 7591, 9*w - 101], [7643, 7643, w + 2687], [7643, 7643, w + 4955], [7649, 7649, 21*w - 52], [7649, 7649, -21*w - 31], [7669, 7669, 19*w - 8], [7669, 7669, 19*w - 11], [7673, 7673, w + 3760], [7673, 7673, w + 3912], [7687, 7687, w + 3512], [7687, 7687, w + 4174], [7699, 7699, -6*w - 89], [7699, 7699, 6*w - 95], [7723, 7723, w + 663], [7723, 7723, w + 7059], [7757, 7757, w + 902], [7757, 7757, w + 6854], [7793, 7793, w + 666], [7793, 7793, w + 7126], [7817, 7817, w + 3372], [7817, 7817, w + 4444], [7823, 7823, w + 3021], [7823, 7823, w + 4801], [7829, 7829, 19*w - 134], [7829, 7829, -19*w - 115], [7841, 7841, -5*w - 89], [7841, 7841, 5*w - 94], [7877, 7877, w + 3861], [7877, 7877, w + 4015], [7879, 7879, 25*w - 86], [7879, 7879, -25*w - 61], [7883, 7883, w + 1545], [7883, 7883, w + 6337], [7901, 7901, -17*w - 110], [7901, 7901, 17*w - 127], [7927, 7927, w + 2097], [7927, 7927, w + 5829], [7933, 7933, w + 597], [7933, 7933, w + 7335], [7963, 7963, w + 2575], [7963, 7963, w + 5387], [7993, 7993, w + 3454], [7993, 7993, w + 4538], [8009, 8009, -27*w - 73], [8009, 8009, 27*w - 100], [8011, 8011, -28*w - 79], [8011, 8011, 28*w - 107], [8017, 8017, w + 917], [8017, 8017, w + 7099], [8039, 8039, 21*w - 47], [8039, 8039, -21*w - 26], [8053, 8053, w + 155], [8053, 8053, w + 7897], [8059, 8059, 20*w - 31], [8059, 8059, -20*w - 11], [8087, 8087, w + 2839], [8087, 8087, w + 5247], [8101, 8101, 15*w - 121], [8101, 8101, -15*w - 106], [8111, 8111, 21*w - 46], [8111, 8111, -21*w - 25], [8123, 8123, w + 238], [8123, 8123, w + 7884], [8161, 8161, -23*w - 44], [8161, 8161, 23*w - 67], [8167, 8167, w + 2642], [8167, 8167, w + 5524], [8179, 8179, 9*w - 104], [8179, 8179, -9*w - 95], [8209, 8209, 35*w + 116], [8209, 8209, 35*w - 151], [8219, 8219, -23*w - 128], [8219, 8219, 23*w - 151], [8233, 8233, w + 471], [8233, 8233, w + 7761], [8273, 8273, w + 3775], [8273, 8273, w + 4497], [8293, 8293, w + 4067], [8293, 8293, w + 4225], [8311, 8311, 25*w - 83], [8311, 8311, -25*w - 58], [8329, 8329, -15*w - 107], [8329, 8329, 15*w - 122], [8353, 8353, w + 1130], [8353, 8353, w + 7222], [8387, 8387, w + 2157], [8387, 8387, w + 6229], [8389, 8389, 12*w - 113], [8389, 8389, -12*w - 101], [8419, 8419, 20*w - 19], [8419, 8419, 20*w - 1], [8431, 8431, -31*w - 94], [8431, 8431, 31*w - 125], [8443, 8443, w + 2895], [8443, 8443, w + 5547], [8501, 8501, -21*w - 19], [8501, 8501, 21*w - 40], [8521, 8521, -22*w - 31], [8521, 8521, 22*w - 53], [8527, 8527, w + 2091], [8527, 8527, w + 6435], [8537, 8537, w + 244], [8537, 8537, w + 8292], [8563, 8563, w + 734], [8563, 8563, w + 7828], [8573, 8573, w + 2788], [8573, 8573, w + 5784], [8581, 8581, 9*w - 106], [8581, 8581, -9*w - 97], [8597, 8597, w + 3930], [8597, 8597, w + 4666], [8647, 8647, w + 988], [8647, 8647, w + 7658], [8663, 8663, w + 3217], [8663, 8663, w + 5445], [8669, 8669, -21*w - 16], [8669, 8669, 21*w - 37], [8677, 8677, w + 1487], [8677, 8677, w + 7189], [8689, 8689, 34*w + 109], [8689, 8689, 34*w - 143], [8693, 8693, w + 1523], [8693, 8693, w + 7169], [8707, 8707, w + 704], [8707, 8707, w + 8002], [8719, 8719, 21*w - 145], [8719, 8719, -21*w - 124], [8783, 8783, w + 3740], [8783, 8783, w + 5042], [8803, 8803, w + 4296], [8803, 8803, w + 4506], [8819, 8819, 21*w - 34], [8819, 8819, -21*w - 13], [8821, 8821, -12*w - 103], [8821, 8821, 12*w - 115], [8831, 8831, -14*w - 107], [8831, 8831, 14*w - 121], [8837, 8837, w + 3385], [8837, 8837, w + 5451], [8839, 8839, -6*w - 95], [8839, 8839, 6*w - 101], [8849, 8849, -27*w - 68], [8849, 8849, 27*w - 95], [8861, 8861, -29*w - 149], [8861, 8861, 29*w - 178], [8863, 8863, w + 1164], [8863, 8863, w + 7698], [8867, 8867, w + 3890], [8867, 8867, w + 4976], [8929, 8929, 3*w - 97], [8929, 8929, -3*w - 94], [8941, 8941, -29*w - 80], [8941, 8941, 29*w - 109], [8951, 8951, 21*w - 31], [8951, 8951, -21*w - 10], [9001, 9001, 35*w - 148], [9001, 9001, 35*w + 113], [9007, 9007, w + 972], [9007, 9007, w + 8034], [9011, 9011, 27*w - 94], [9011, 9011, -27*w - 67], [9013, 9013, w + 164], [9013, 9013, w + 8848], [9029, 9029, -21*w - 8], [9029, 9029, 21*w - 29], [9059, 9059, -7*w - 97], [9059, 9059, 7*w - 104], [9067, 9067, w + 1154], [9067, 9067, w + 7912], [9091, 9091, -28*w - 73], [9091, 9091, 28*w - 101], [9157, 9157, w + 4495], [9157, 9157, w + 4661], [9161, 9161, 21*w - 25], [9161, 9161, -21*w - 4], [9173, 9173, w + 642], [9173, 9173, w + 8530], [9181, 9181, 26*w - 85], [9181, 9181, -26*w - 59], [9187, 9187, w + 2106], [9187, 9187, w + 7080], [9199, 9199, 9*w - 109], [9199, 9199, -9*w - 100], [9203, 9203, w + 498], [9203, 9203, w + 8704], [9239, 9239, -21*w - 1], [9239, 9239, 21*w - 22], [9277, 9277, w + 500], [9277, 9277, w + 8776], [9281, 9281, 21*w - 20], [9281, 9281, 21*w - 1], [9293, 9293, w + 1705], [9293, 9293, w + 7587], [9323, 9323, w + 3780], [9323, 9323, w + 5542], [9341, 9341, 21*w - 5], [9341, 9341, 21*w - 16], [9343, 9343, w + 4028], [9343, 9343, w + 5314], [9349, 9349, 23*w - 55], [9349, 9349, -23*w - 32], [9371, 9371, 21*w - 10], [9371, 9371, 21*w - 11], [9377, 9377, w + 2992], [9377, 9377, w + 6384], [9413, 9413, w + 2982], [9413, 9413, w + 6430], [9419, 9419, -11*w - 104], [9419, 9419, 11*w - 115], [9431, 9431, 24*w - 65], [9431, 9431, -24*w - 41], [9439, 9439, 32*w - 127], [9439, 9439, -32*w - 95], [9461, 9461, 4*w - 101], [9461, 9461, -4*w - 97], [9463, 9463, w + 1279], [9463, 9463, w + 8183], [9497, 9497, w + 4619], [9497, 9497, w + 4877], [9511, 9511, 3*w - 100], [9511, 9511, -3*w - 97], [9521, 9521, 30*w - 113], [9521, 9521, -30*w - 83], [9539, 9539, -10*w - 103], [9539, 9539, 10*w - 113], [9547, 9547, w + 3380], [9547, 9547, w + 6166], [9601, 9601, -23*w - 29], [9601, 9601, 23*w - 52], [9631, 9631, 37*w - 158], [9631, 9631, 37*w + 121], [9689, 9689, -16*w - 115], [9689, 9689, 16*w - 131], [9697, 9697, w + 1572], [9697, 9697, w + 8124], [9739, 9739, 15*w - 128], [9739, 9739, -15*w - 113], [9749, 9749, -13*w - 109], [9749, 9749, 13*w - 122], [9787, 9787, w + 4689], [9787, 9787, w + 5097], [9791, 9791, 27*w - 89], [9791, 9791, -27*w - 62], [9803, 9803, w + 1375], [9803, 9803, w + 8427], [9811, 9811, -21*w - 128], [9811, 9811, 21*w - 149], [9833, 9833, w + 4830], [9833, 9833, w + 5002], [9839, 9839, 24*w - 61], [9839, 9839, -24*w - 37], [9851, 9851, -29*w - 152], [9851, 9851, 29*w - 181], [9857, 9857, w + 3977], [9857, 9857, w + 5879], [9859, 9859, -25*w - 46], [9859, 9859, 25*w - 71], [9883, 9883, w + 3577], [9883, 9883, w + 6305], [9887, 9887, w + 2342], [9887, 9887, w + 7544], [9923, 9923, w + 4658], [9923, 9923, w + 5264], [9929, 9929, -23*w - 134], [9929, 9929, 23*w - 157], [9941, 9941, -27*w - 61], [9941, 9941, 27*w - 88], [9949, 9949, 38*w + 125], [9949, 9949, 38*w - 163], [9967, 9967, w + 3410], [9967, 9967, w + 6556], [9973, 9973, w + 2029], [9973, 9973, w + 7943]]; primes := [ideal : I in primesArray]; heckePol := x^6 + 12*x^4 + 32*x^2 + 16; K := NumberField(heckePol); heckeEigenvaluesArray := [e, 1/8*e^5 + 5/4*e^3 + 2*e, -1, -3/8*e^5 - 4*e^3 - 6*e, -1/8*e^5 - 2*e^3 - 7*e, -1/8*e^5 - 3/2*e^3 - 4*e, -1/2*e^5 - 5*e^3 - 9*e, 3/4*e^4 + 7*e^2 + 10, -3/4*e^4 - 6*e^2 - 4, -1/8*e^5 - 3/2*e^3 - e, 5/8*e^5 + 13/2*e^3 + 10*e, -9/8*e^5 - 12*e^3 - 21*e, 1/8*e^5 + 5/2*e^3 + 11*e, -e^4 - 9*e^2 - 8, -e^4 - 9*e^2 - 8, 1/2*e^5 + 7*e^3 + 20*e, -3/4*e^5 - 8*e^3 - 10*e, 1/4*e^4 + 3*e^2 + 4, 1/4*e^4 + 3*e^2 + 4, 3/4*e^5 + 9*e^3 + 25*e, 3*e, -e^4 - 12*e^2 - 24, -1/2*e^4 - 2*e^2 + 8, -1/4*e^5 - 3*e^3 - 6*e, 3*e, 6*e, -1/2*e^5 - 7*e^3 - 28*e, -1/2*e^4 - 5*e^2 - 10, -3/2*e^4 - 16*e^2 - 32, 1/2*e^4 + 6*e^2 - 2, 2*e^4 + 22*e^2 + 32, 2, e^5 + 11*e^3 + 26*e, -3/4*e^5 - 11*e^3 - 33*e, 7/8*e^5 + 7*e^3 + e, -9/8*e^5 - 11*e^3 - 20*e, e^4 + 10*e^2 + 14, -3/8*e^5 - 2*e^3 + 5*e, 1/8*e^5 - 11*e, 5/4*e^4 + 12*e^2 + 12, -3/4*e^4 - 9*e^2 - 2, 2*e^4 + 22*e^2 + 32, -1/2*e^4 - 9*e^2 - 14, 1/4*e^5 + 5*e^3 + 22*e, 3*e^5 + 30*e^3 + 48*e, -13/8*e^5 - 37/2*e^3 - 37*e, 3/8*e^5 + 9/2*e^3 + 19*e, 7/4*e^5 + 17*e^3 + 27*e, -1/4*e^5 - 2*e^3, e^4 + 10*e^2 + 14, -e^4 - 12*e^2 - 16, 5/4*e^5 + 15*e^3 + 31*e, -5/4*e^5 - 12*e^3 - 21*e, -3*e^4 - 27*e^2 - 34, 2*e^4 + 22*e^2 + 40, -5/4*e^4 - 17*e^2 - 30, 3/4*e^4 + 6*e^2 + 16, 2*e^4 + 19*e^2 + 14, -3/2*e^4 - 14*e^2 + 2, 5/8*e^5 + 7*e^3 + 10*e, 5/8*e^5 + 23/2*e^3 + 42*e, 3/4*e^4 + 9*e^2 + 4, -1/4*e^4 - 9*e^2 - 28, -2*e^5 - 23*e^3 - 50*e, 3/4*e^5 + 9*e^3 + 13*e, -2*e^5 - 20*e^3 - 32*e, 7/4*e^5 + 19*e^3 + 42*e, -15/8*e^5 - 19*e^3 - 36*e, 5/8*e^5 + 3*e^3 - 14*e, 3*e^4 + 33*e^2 + 52, 5/2*e^4 + 24*e^2 + 36, -3*e^3 - 15*e, 1/2*e^5 + 7*e^3 + 27*e, 3*e^5 + 30*e^3 + 45*e, 9/4*e^5 + 25*e^3 + 42*e, -3*e^4 - 25*e^2 - 12, -1/2*e^4 - 9*e^2 - 16, 2*e^4 + 10*e^2 - 22, -2*e^4 - 18*e^2 - 16, -3/8*e^5 - 4*e^3 - 5*e, 13/8*e^5 + 27/2*e^3 + 8*e, 1/2*e^4 - 18, -2*e^4 - 18*e^2 - 46, -3/8*e^5 - 6*e^3 - 22*e, 9/8*e^5 + 27/2*e^3 + 26*e, -11/4*e^4 - 23*e^2 - 24, 13/4*e^4 + 29*e^2 + 32, 1/2*e^4 + 4*e^2 + 18, 5/2*e^4 + 25*e^2 + 32, -2*e^4 - 14*e^2 - 10, -1/2*e^4 + e^2 + 36, -1/8*e^5 + 5/2*e^3 + 25*e, 1/8*e^5 - 4*e, 11/4*e^4 + 31*e^2 + 54, -9/4*e^4 - 17*e^2 - 4, 25/8*e^5 + 71/2*e^3 + 74*e, -21/8*e^5 - 61/2*e^3 - 65*e, 9/2*e^4 + 40*e^2 + 38, 3*e^2 + 28, -13/4*e^5 - 31*e^3 - 41*e, 13/4*e^5 + 34*e^3 + 70*e, -1/2*e^4 - 3*e^2 + 30, 6*e^2 + 46, -e^4 - 16*e^2 - 20, -1/2*e^4 - 8*e^2 - 20, -7/8*e^5 - 15/2*e^3 - 13*e, -21/8*e^5 - 27*e^3 - 42*e, 2*e^5 + 23*e^3 + 44*e, -3/4*e^5 - 4*e^3 + 16*e, -3/2*e^4 - 16*e^2 - 40, -e^4 - 6*e^2 - 8, 4*e^5 + 41*e^3 + 78*e, -9*e, -7/8*e^5 - 15/2*e^3 - 5*e, 17/8*e^5 + 37/2*e^3 + 13*e, -e^4 - 8*e^2 + 8, -1/2*e^4 - 2*e^2 - 24, -3/2*e^4 - 24*e^2 - 48, -4*e^4 - 40*e^2 - 44, -2*e^5 - 26*e^3 - 78*e, 3*e^5 + 30*e^3 + 38*e, -21/8*e^5 - 59/2*e^3 - 62*e, -5/8*e^5 - 19/2*e^3 - 34*e, -2*e^5 - 25*e^3 - 57*e, -1/4*e^5 - 9*e^3 - 44*e, 5/2*e^4 + 30*e^2 + 42, -3/2*e^4 - 16*e^2 - 50, 23/4*e^4 + 55*e^2 + 68, 5/4*e^4 + 17*e^2 + 42, 27/8*e^5 + 71/2*e^3 + 60*e, -11/8*e^5 - 39/2*e^3 - 69*e, -2*e^4 - 18*e^2 - 34, -3/2*e^4 - 7*e^2 + 14, -e^4 - 10*e^2 - 14, -e^4 - 8*e^2 + 18, -3/2*e^5 - 14*e^3 - 12*e, -4*e^5 - 43*e^3 - 81*e, -23/8*e^5 - 33*e^3 - 61*e, -7/8*e^5 - 29/2*e^3 - 62*e, 13/4*e^5 + 34*e^3 + 60*e, 4*e^5 + 44*e^3 + 73*e, 9/2*e^4 + 40*e^2 + 48, 2*e^4 + 22*e^2 + 20, -9/4*e^4 - 32*e^2 - 74, 13/8*e^5 + 11*e^3 - 9*e, -37/8*e^5 - 101/2*e^3 - 83*e, -1/2*e^5 - 8*e^3 - 22*e, 5/2*e^5 + 25*e^3 + 48*e, 9/2*e^4 + 35*e^2 + 8, e^4 + 3*e^2 + 12, 19/8*e^5 + 23*e^3 + 28*e, 15/8*e^5 + 41/2*e^3 + 36*e, -11/8*e^5 - 17*e^3 - 47*e, 21/8*e^5 + 26*e^3 + 42*e, -17/4*e^5 - 45*e^3 - 79*e, -11/4*e^5 - 25*e^3 - 28*e, 3/2*e^4 + 20*e^2 + 56, -5/2*e^4 - 28*e^2 - 68, -15/4*e^5 - 38*e^3 - 50*e, -7/2*e^5 - 37*e^3 - 73*e, -7/4*e^4 - 7*e^2 + 28, -e^4 - e^2 + 32, 2*e^4 + 24*e^2 + 44, 29/8*e^5 + 38*e^3 + 66*e, -11/8*e^5 - 15*e^3 - 27*e, -3/8*e^5 - e^3 + 13*e, 39/8*e^5 + 101/2*e^3 + 83*e, 23/8*e^5 + 61/2*e^3 + 63*e, -9/8*e^5 - 17/2*e^3 - 7*e, -3*e^4 - 29*e^2 - 36, 4*e^4 + 42*e^2 + 68, 3*e^4 + 24*e^2 + 28, -3/2*e^4 - 18*e^2 - 62, -e^4 - 20*e^2 - 44, -2*e^4 - 25*e^2 - 58, -e^4 - 6*e^2 + 30, 1/2*e^4 + 7*e^2 + 44, 3/8*e^5 + 4*e^3 - 6*e, 39/8*e^5 + 105/2*e^3 + 98*e, 3*e^4 + 32*e^2 + 24, 2*e^4 + 14*e^2 - 8, 15/8*e^5 + 39/2*e^3 + 50*e, 19/8*e^5 + 25*e^3 + 30*e, -3*e^5 - 33*e^3 - 59*e, -11/4*e^5 - 29*e^3 - 69*e, -9/4*e^5 - 22*e^3 - 30*e, -9/4*e^5 - 22*e^3 - 35*e, 27/4*e^4 + 75*e^2 + 114, -11/4*e^4 - 26*e^2 - 20, -17/2*e^4 - 76*e^2 - 98, 1/2*e^4 + 4*e^2 + 18, -5/4*e^5 - 18*e^3 - 55*e, 9/4*e^5 + 20*e^3 + 2*e, 7*e^5 + 72*e^3 + 116*e, 21/4*e^5 + 56*e^3 + 88*e, 25/8*e^5 + 27*e^3 + 18*e, 21/8*e^5 + 45/2*e^3 + 24*e, -e^5 - 2*e^3 + 42*e, e^5 + 14*e^3 + 36*e, 15/2*e^4 + 71*e^2 + 86, -13/2*e^4 - 69*e^2 - 90, -5/2*e^4 - 21*e^2 - 16, e^4 + 16*e^2 + 60, -7/2*e^4 - 41*e^2 - 70, -9/2*e^4 - 44*e^2 - 52, 3*e^4 + 14*e^2 - 32, 4*e^4 + 37*e^2 + 80, -19/4*e^5 - 50*e^3 - 91*e, 9/4*e^5 + 28*e^3 + 75*e, 3/2*e^4 + 17*e^2, -2*e^4 - 15*e^2 + 4, -7/8*e^5 - 23/2*e^3 - 19*e, -5/8*e^5 - 6*e^3 - 10*e, -5*e^4 - 52*e^2 - 50, -4*e^4 - 36*e^2 - 50, -29/8*e^5 - 46*e^3 - 110*e, 7/8*e^5 + 10*e^3 + 29*e, -9/2*e^4 - 36*e^2 - 2, e^4 - 74, 11/4*e^4 + 36*e^2 + 82, -5/4*e^4 - 9*e^2 + 6, -17/8*e^5 - 19*e^3 - 14*e, -15/8*e^5 - 27/2*e^3 + 5*e, 3/2*e^4 + 5*e^2 - 4, 2*e^4 + 30*e^2 + 78, 5*e^5 + 57*e^3 + 103*e, -5/4*e^5 - 13*e^3 - 17*e, 11/2*e^4 + 46*e^2 + 40, -e^4 - 16*e^2 - 48, 7/4*e^4 + 23*e^2 + 62, 3/4*e^4 - e^2 - 66, 7/8*e^5 + 12*e^3 + 54*e, -9/8*e^5 - 10*e^3 + 4*e, -15/2*e^4 - 74*e^2 - 112, -5/2*e^4 - 24*e^2 - 22, 17/4*e^5 + 46*e^3 + 79*e, 5/4*e^5 + 7*e^3 - 12*e, -3*e^4 - 23*e^2 - 8, 5/2*e^4 + 16*e^2 - 32, e^4 + 6*e^2 - 10, 7/2*e^4 + 40*e^2 + 84, -7/2*e^5 - 37*e^3 - 75*e, -5/4*e^5 - 22*e^3 - 71*e, -27/8*e^5 - 69/2*e^3 - 55*e, 15/8*e^5 + 23*e^3 + 46*e, -2*e^4 - 14*e^2 - 32, -3*e^4 - 31*e^2 - 48, 1/4*e^4 - e^2 - 30, 9/4*e^4 + 23*e^2 + 32, 31/4*e^5 + 79*e^3 + 123*e, 3*e^5 + 37*e^3 + 102*e, -61/8*e^5 - 77*e^3 - 127*e, 15/8*e^5 + 22*e^3 + 35*e, 15/8*e^5 + 22*e^3 + 68*e, -43/8*e^5 - 121/2*e^3 - 111*e, 4*e^4 + 47*e^2 + 90, -5/8*e^5 - 13*e^3 - 72*e, -49/8*e^5 - 139/2*e^3 - 128*e, e^5 + 17*e^3 + 59*e, 23/4*e^5 + 60*e^3 + 91*e, 17/4*e^4 + 49*e^2 + 86, 19/4*e^4 + 43*e^2 + 52, -4*e^4 - 34*e^2 - 70, -1/2*e^4 - 11*e^2 - 28, 13/4*e^4 + 38*e^2 + 78, -3/4*e^4 - 5*e^2 + 34, 4*e^5 + 46*e^3 + 103*e, 9/4*e^5 + 27*e^3 + 92*e, 9/2*e^4 + 39*e^2 + 22, 5*e^4 + 52*e^2 + 102, 11/2*e^4 + 48*e^2 + 50, 13/2*e^4 + 50*e^2 + 16, -13/4*e^4 - 43*e^2 - 54, 7/4*e^4 + 18*e^2 + 22, 7*e^4 + 63*e^2 + 48, -6*e^4 - 57*e^2 - 64, -41/8*e^5 - 51*e^3 - 61*e, 71/8*e^5 + 94*e^3 + 150*e, -e^4 - 12*e^2 - 46, 2*e^4 + 22*e^2 + 22, -9/2*e^4 - 38*e^2 - 34, -3/4*e^5 - 12*e^3 - 32*e, -7/2*e^5 - 37*e^3 - 63*e, -3*e^4 - 38*e^2 - 38, 3/2*e^4 + 9*e^2 - 58, -3/4*e^5 - 8*e^3 - 20*e, 1/2*e^5 + 9*e^3 + 62*e, -43/8*e^5 - 60*e^3 - 111*e, -27/8*e^5 - 39*e^3 - 107*e, 9/2*e^4 + 52*e^2 + 100, 8*e^4 + 70*e^2 + 62, -13/4*e^4 - 46*e^2 - 94, -5/4*e^4 - 10*e^2 - 30, 7/4*e^5 + 16*e^3 + 36*e, -1/4*e^5 + e^3 + 23*e, 19/8*e^5 + 23*e^3 + 36*e, 3/8*e^5 + 7/2*e^3 + 26*e, -e^4 - 9*e^2 + 14, 7/2*e^4 + 30*e^2 + 56, -23/4*e^5 - 57*e^3 - 99*e, -1/2*e^5 - 6*e^3 - 12*e, -9/4*e^5 - 19*e^3 + 5*e, 7/2*e^5 + 38*e^3 + 55*e, 2*e^4 + 10*e^2 - 52, 5*e^4 + 40*e^2 + 40, -21/8*e^5 - 53/2*e^3 - 31*e, -35/8*e^5 - 99/2*e^3 - 96*e, 29/4*e^4 + 61*e^2 + 50, -3/4*e^4 - e^2 - 34, 27/4*e^4 + 73*e^2 + 110, 27/4*e^4 + 60*e^2 + 92, 17/2*e^5 + 90*e^3 + 155*e, 3/4*e^5 + 13*e^3 + 37*e, 3/4*e^4 + 21*e^2 + 64, 7/4*e^4 + 9*e^2 - 4, -1/4*e^5 - 11*e^3 - 59*e, 1/4*e^5 + 5*e^3 + 39*e, -7*e^4 - 72*e^2 - 78, -9/2*e^4 - 42*e^2 - 48, -21/4*e^5 - 58*e^3 - 103*e, -2*e^5 - 13*e^3 + 25*e, e^4 + 6*e^2 - 38, 6*e^4 + 72*e^2 + 118, -1/4*e^5 - 3*e^3 - 3*e, 2*e^5 + 16*e^3 + 10*e, -9/8*e^5 - 11/2*e^3 + 13*e, 29/8*e^5 + 81/2*e^3 + 78*e, 3*e^4 + 14*e^2 - 14, 35/8*e^5 + 81/2*e^3 + 44*e, -13/8*e^5 - 33/2*e^3 - 22*e, -25/8*e^5 - 45/2*e^3 + 3*e, 51/8*e^5 + 131/2*e^3 + 119*e, 3/2*e^5 + 20*e^3 + 39*e, 9/4*e^5 + 22*e^3 + 34*e, -13/2*e^4 - 64*e^2 - 40, -9/2*e^4 - 32*e^2 - 40, 31/4*e^5 + 83*e^3 + 150*e, e^5 + 9*e^3 - 6*e, 3*e^4 + 29*e^2 + 38, 9/2*e^4 + 44*e^2 + 84, 7/8*e^5 + 3/2*e^3 - 37*e, 63/8*e^5 + 159/2*e^3 + 119*e, 3*e^4 + 25*e^2 + 84, 3/2*e^4 + 24*e^2 + 72, -11/2*e^5 - 59*e^3 - 123*e, 13/4*e^5 + 41*e^3 + 107*e, 2*e^4 + 12*e^2 - 48, -3/2*e^4 - 2*e^2 + 54, 35/8*e^5 + 41*e^3 + 47*e, 35/8*e^5 + 85/2*e^3 + 56*e, 6*e^4 + 66*e^2 + 130, e^4 + 14*e^2 + 8, 5/2*e^4 + 24*e^2 + 4, 2*e^4 + 28*e^2 + 6, -5*e^3 - 52*e, -11/4*e^5 - 24*e^3 - 12*e, -33/8*e^5 - 85/2*e^3 - 41*e, 53/8*e^5 + 71*e^3 + 123*e, -35/8*e^5 - 97/2*e^3 - 68*e, -19/8*e^5 - 43/2*e^3 - 8*e, 3*e^4 + 34*e^2 + 68, -17/2*e^4 - 89*e^2 - 96, -11/8*e^5 - 8*e^3 + 15*e, 65/8*e^5 + 87*e^3 + 148*e, 5/2*e^4 + 34*e^2 + 34, 1/2*e^4 - 4*e^2 - 62, -9/2*e^4 - 38*e^2 - 44, 1/2*e^4 - 4*e^2 - 20, -3/8*e^5 + 7/2*e^3 + 35*e, -41/8*e^5 - 52*e^3 - 87*e, 5/4*e^4 + 21*e^2 + 36, -3/4*e^4 - 19*e^2 - 92, 9/8*e^5 - 1/2*e^3 - 58*e, -15/8*e^5 - 13*e^3 + 15*e, -19/4*e^5 - 52*e^3 - 73*e, 7/2*e^5 + 41*e^3 + 103*e, -5/8*e^5 + 13/2*e^3 + 80*e, 65/8*e^5 + 175/2*e^3 + 131*e, 8*e^4 + 70*e^2 + 74, -5/2*e^4 - 24*e^2 - 72, -17/4*e^5 - 47*e^3 - 93*e, -3/4*e^5 - 10*e^3 - 52*e, 21/8*e^5 + 29*e^3 + 58*e, 49/8*e^5 + 66*e^3 + 134*e, 2*e^4 + 6*e^2 - 96, -5/2*e^4 - 13*e^2 - 8, 7/2*e^4 + 32*e^2 + 88, -e^4 - 26*e^2 - 68, -2*e^5 - 25*e^3 - 92*e, -11/4*e^5 - 36*e^3 - 86*e, 7*e^4 + 58*e^2 + 66, 7*e^4 + 55*e^2 + 18, -33/4*e^4 - 87*e^2 - 110, -5/4*e^4 - 20*e^2 - 70, 3/2*e^4 + 9*e^2 + 12, -5/2*e^4 - 35*e^2 - 48, -21/4*e^5 - 63*e^3 - 141*e, 15/4*e^5 + 42*e^3 + 75*e, -5/2*e^4 - 24*e^2 + 6, -15/2*e^4 - 72*e^2 - 52, -3/2*e^4 - 15*e^2 - 114, -4*e^4 - 56*e^2 - 130, 6*e^4 + 47*e^2 + 46, -25/4*e^5 - 58*e^3 - 57*e, 3/4*e^5 + 3*e^3 - 23*e, 55/8*e^5 + 66*e^3 + 99*e, -33/8*e^5 - 85/2*e^3 - 66*e, 31/4*e^5 + 74*e^3 + 93*e, -10*e^5 - 109*e^3 - 191*e, 5/2*e^4 + 36*e^2 + 86, -4*e^4 - 42*e^2 - 68, 19/8*e^5 + 49/2*e^3 + 52*e, 11/8*e^5 + 10*e^3 - 4*e, 77/8*e^5 + 201/2*e^3 + 152*e, -41/8*e^5 - 125/2*e^3 - 145*e, 11/4*e^4 + 29*e^2 + 50, -9/4*e^4 - 16*e^2 + 40, -9/4*e^5 - 11*e^3 + 41*e, 11/2*e^5 + 62*e^3 + 95*e, -7/2*e^5 - 42*e^3 - 100*e, 7/4*e^5 + 16*e^3 - e, 1/4*e^4 + 19*e^2 + 92, -25/4*e^4 - 61*e^2 - 94, -33/4*e^4 - 85*e^2 - 76, -41/4*e^4 - 95*e^2 - 104, -29/4*e^4 - 69*e^2 - 66, -17/4*e^4 - 26*e^2 + 44, -33/8*e^5 - 45*e^3 - 98*e, -9/8*e^5 - 17*e^3 - 63*e, 51/8*e^5 + 69*e^3 + 105*e, 29/8*e^5 + 71/2*e^3 + 33*e, -11/4*e^4 - 28*e^2 - 42, 21/4*e^4 + 28*e^2 - 54, 5/2*e^4 + 31*e^2 + 8, -11*e^4 - 110*e^2 - 122, -13/4*e^5 - 39*e^3 - 109*e, 3/2*e^5 + 22*e^3 + 76*e, -5/2*e^4 - 26*e^2 + 4, -e^4 - 16*e^2 - 30, 15/4*e^5 + 34*e^3 + 45*e, -e^5 - 17*e^3 - 40*e, 10*e^4 + 87*e^2 + 112, -5*e^4 - 60*e^2 - 110, 3*e^4 + 32*e^2 - 6, -1/2*e^4 - 16*e^2 - 68, 31/8*e^5 + 39*e^3 + 85*e, 59/8*e^5 + 71*e^3 + 106*e, 5*e^4 + 49*e^2 + 96, -11/2*e^4 - 40*e^2 + 30, 15/2*e^5 + 75*e^3 + 136*e, 2*e^5 + 26*e^3 + 55*e, -51/4*e^4 - 130*e^2 - 186, -35/4*e^4 - 88*e^2 - 158, 3*e^4 + 34*e^2 + 118, 8*e^4 + 80*e^2 + 144, 8*e^4 + 64*e^2 + 46, -17/2*e^4 - 79*e^2 - 108, 2*e^4 + 22*e^2 + 72, -21/2*e^4 - 93*e^2 - 88, -3/8*e^5 - 29/2*e^3 - 75*e, 35/8*e^5 + 48*e^3 + 119*e, 2*e^5 + 31*e^3 + 92*e, -3/2*e^5 - 8*e^3 + 34*e, -49/4*e^4 - 111*e^2 - 120, 7/4*e^4 + 13*e^2 - 10, -7*e^4 - 53*e^2 + 14, -5*e^4 - 38*e^2 - 68, 13/2*e^4 + 65*e^2 + 48, -2*e^4 - 27*e^2 - 8, -19/8*e^5 - 23*e^3 - 64*e, 11/8*e^5 + 21/2*e^3 - 13*e, -25/8*e^5 - 95/2*e^3 - 159*e, -63/8*e^5 - 86*e^3 - 149*e, 9/2*e^4 + 42*e^2 + 52, 6*e^4 + 55*e^2 + 66, -17/8*e^5 - 20*e^3 - 8*e, -29/8*e^5 - 45*e^3 - 149*e, 7*e^4 + 62*e^2 + 30, 11/2*e^4 + 33*e^2 - 50, -23/4*e^5 - 52*e^3 - 42*e, -9/2*e^5 - 37*e^3 - 12*e, 37/8*e^5 + 51*e^3 + 88*e, 39/8*e^5 + 93/2*e^3 + 47*e, 7/2*e^4 + 34*e^2 + 78, -15/2*e^4 - 66*e^2 - 36, 9/2*e^4 + 52*e^2 + 32, 19/2*e^4 + 88*e^2 + 88, 47/8*e^5 + 68*e^3 + 155*e, -1/8*e^5 - 7*e, -5/4*e^5 - 4*e^3 + 59*e, 9/4*e^5 + 29*e^3 + 66*e, -27/4*e^4 - 49*e^2 + 16, -17/4*e^4 - 51*e^2 - 86, -5/4*e^5 - 14*e^3 - 33*e, 19/4*e^5 + 52*e^3 + 87*e, -11/8*e^5 - 21*e^3 - 66*e, 55/8*e^5 + 125/2*e^3 + 63*e, 3*e^3 + 14*e, -8*e^5 - 86*e^3 - 187*e, -3*e^4 - 39*e^2 - 76, -e^4 + e^2 + 52, -21/2*e^4 - 85*e^2 - 90, -5/2*e^4 - 24*e^2 - 22, -9/8*e^5 - 29/2*e^3 - 11*e, 11/8*e^5 + 37/2*e^3 + 87*e, -2*e^4 - 24*e^2 - 20, -5*e^4 - 53*e^2 - 96, -13/2*e^4 - 75*e^2 - 86, 17/2*e^4 + 68*e^2 + 72, -25/4*e^4 - 68*e^2 - 66, -1/8*e^5 - 15/2*e^3 - 42*e, 63/8*e^5 + 79*e^3 + 114*e, -17/4*e^4 - 43*e^2 - 50, 53/4*e^4 + 116*e^2 + 104, -4*e^4 - 40*e^2 - 74, 10*e^4 + 105*e^2 + 182, -1/8*e^5 - 2*e^3 - 12*e, 23/8*e^5 + 42*e^3 + 119*e, -47/8*e^5 - 113/2*e^3 - 67*e, 5/8*e^5 + 31/2*e^3 + 71*e, -5*e^5 - 50*e^3 - 84*e, -39/4*e^5 - 99*e^3 - 177*e, -13/2*e^4 - 66*e^2 - 50, -6*e^4 - 47*e^2 - 64, -5/8*e^5 - 9/2*e^3 - 4*e, -37/8*e^5 - 51*e^3 - 129*e, 25/4*e^4 + 43*e^2 + 40, -3/4*e^4 - 13*e^2 - 14, 21/8*e^5 + 36*e^3 + 75*e, -45/8*e^5 - 115/2*e^3 - 69*e, -47/4*e^4 - 115*e^2 - 152, 49/4*e^4 + 123*e^2 + 172, 7/4*e^5 + 22*e^3 + 82*e, 11/2*e^5 + 59*e^3 + 99*e, -1/2*e^4 + e^2 - 34, -10*e^4 - 94*e^2 - 72, 27/8*e^5 + 65/2*e^3 + 24*e, 31/8*e^5 + 71/2*e^3 + 44*e, 7*e^4 + 46*e^2 - 26, 11*e^4 + 123*e^2 + 182, 13/2*e^4 + 61*e^2 + 102, -11*e^4 - 116*e^2 - 150, 37/4*e^4 + 68*e^2 + 12, -5/4*e^4 - 15*e^2 + 42, -7/4*e^5 - 16*e^3 - 35*e, -7/2*e^5 - 41*e^3 - 122*e, -27/8*e^5 - 42*e^3 - 125*e, -11/8*e^5 - 49/2*e^3 - 122*e, -67/8*e^5 - 91*e^3 - 164*e, -47/8*e^5 - 58*e^3 - 111*e, -10*e^4 - 112*e^2 - 170, -7/2*e^4 - 20*e^2 + 18, -15/2*e^5 - 77*e^3 - 109*e, 21/4*e^5 + 59*e^3 + 93*e, -3/2*e^5 - 12*e^3 + 23*e, 5/4*e^5 + 13*e^3 + 19*e, -5/2*e^4 - 16*e^2 - 56, -7*e^4 - 78*e^2 - 86, -7*e^4 - 61*e^2 - 44, 11/2*e^4 + 54*e^2 + 116, -7*e^4 - 60*e^2 - 58, -7*e^4 - 90*e^2 - 158, 4*e^4 + 57*e^2 + 128, -6*e^4 - 65*e^2 - 24, 2*e^5 + 13*e^3 - 13*e, -11/2*e^5 - 66*e^3 - 167*e, -23/4*e^5 - 52*e^3 - 72*e, -9/2*e^5 - 38*e^3 + 2*e, -23/2*e^4 - 111*e^2 - 170, -1/2*e^4 + 11*e^2 + 106, 5/2*e^4 + 10*e^2 - 10, -6*e^2 - 6, -e^4 - e^2 - 38, 5/2*e^4 + 4*e^2 - 94, -3/2*e^4 + 15*e^2 + 106, -4*e^4 - 40*e^2 - 134, -4*e^5 - 50*e^3 - 145*e, 7*e^5 + 86*e^3 + 200*e, 15/8*e^5 + 49/2*e^3 + 48*e, 47/8*e^5 + 127/2*e^3 + 98*e, -11*e^2 - 96, -3*e^4 - 26*e^2 + 52, -3/2*e^4 - 19*e^2 - 138, -e^4 + 38, -7*e^5 - 73*e^3 - 110*e, -1/4*e^5 + e^3 + 16*e, 3*e^4 + 18*e^2 - 60, 11*e^4 + 112*e^2 + 156, 15/8*e^5 + 59/2*e^3 + 120*e, 39/8*e^5 + 50*e^3 + 70*e, -39/4*e^5 - 105*e^3 - 168*e, -21/2*e^5 - 115*e^3 - 201*e, 43/8*e^5 + 62*e^3 + 124*e, -21/8*e^5 - 36*e^3 - 146*e, 2*e^4 + 22*e^2 - 28, -5/2*e^4 - 16*e^2 - 54, -13/8*e^5 - 17/2*e^3 + 41*e, -35/8*e^5 - 45*e^3 - 64*e, -21/4*e^4 - 69*e^2 - 148, 3/4*e^4 + 9*e^2 - 56, -25/8*e^5 - 38*e^3 - 115*e, 35/8*e^5 + 93/2*e^3 + 102*e, -33/4*e^5 - 81*e^3 - 136*e, -1/4*e^5 - 13*e^3 - 66*e, 25/4*e^5 + 68*e^3 + 144*e, 2*e^5 + 24*e^3 + 33*e, -29/2*e^4 - 129*e^2 - 162, 69/8*e^5 + 83*e^3 + 121*e, -15/8*e^5 - 31*e^3 - 105*e, 31/8*e^5 + 83/2*e^3 + 65*e, 19/8*e^5 + 43/2*e^3 - 11*e, -71/8*e^5 - 99*e^3 - 199*e, 21/8*e^5 + 45/2*e^3 - 14*e, 41/8*e^5 + 68*e^3 + 177*e, -59/8*e^5 - 82*e^3 - 148*e, 17/2*e^4 + 101*e^2 + 142, -3/2*e^4 + 8*e^2 + 74, 63/8*e^5 + 167/2*e^3 + 178*e, -89/8*e^5 - 118*e^3 - 202*e, 13/2*e^4 + 58*e^2 + 84, -4*e^4 - 36*e^2 - 62, 27/4*e^4 + 37*e^2 - 76, 31/4*e^4 + 59*e^2 + 20, -39/8*e^5 - 48*e^3 - 34*e, -25/8*e^5 - 57/2*e^3 - 35*e, -7/2*e^4 - 19*e^2 + 2, -9/2*e^4 - 34*e^2 + 18, 7*e^2 + 24, 2*e^4 + 11*e^2 - 44, -11/8*e^5 - 21*e^3 - 98*e, -75/8*e^5 - 102*e^3 - 201*e, 11/2*e^5 + 62*e^3 + 90*e, 3/2*e^5 + 18*e^3 + 25*e, 95/8*e^5 + 125*e^3 + 196*e, 39/8*e^5 + 59*e^3 + 132*e, 15/2*e^4 + 76*e^2 + 128, -4*e^4 - 16*e^2 + 80, -1/2*e^4 - 6*e^2 + 2, -3/2*e^4 - 8*e^2 + 36, 11/8*e^5 + 9/2*e^3 - 39*e, -35/8*e^5 - 37*e^3 - 36*e, 21/2*e^5 + 112*e^3 + 177*e, -21/4*e^5 - 57*e^3 - 90*e, -7/4*e^5 - 26*e^3 - 60*e, -5/2*e^5 - 31*e^3 - 68*e, 21/2*e^4 + 106*e^2 + 150, 5/2*e^4 + 2*e^2 - 36, -31/2*e^4 - 133*e^2 - 138, -11/2*e^4 - 32*e^2 + 58, -73/8*e^5 - 207/2*e^3 - 209*e, -7/8*e^5 - e^3 + 14*e, -9/2*e^4 - 28*e^2 + 34, -21*e^2 - 56, 57/4*e^4 + 155*e^2 + 224, 5/4*e^4 - 17*e^2 - 150, -51/8*e^5 - 157/2*e^3 - 183*e, -1/8*e^5 + 5*e^3 + 63*e, 45/4*e^5 + 119*e^3 + 217*e, -1/4*e^5 + 13*e^3 + 105*e, -12*e^4 - 115*e^2 - 146, -e^4 - 14*e^2 - 16, 89/8*e^5 + 239/2*e^3 + 222*e, 69/8*e^5 + 81*e^3 + 96*e, -49/8*e^5 - 77*e^3 - 181*e, 55/8*e^5 + 79*e^3 + 192*e, -5/2*e^5 - 10*e^3 + 68*e, e^3 + 29*e, -37/4*e^5 - 85*e^3 - 91*e, 5*e^5 + 53*e^3 + 59*e, -8*e^4 - 100*e^2 - 182, -5/2*e^4 - 21*e^2 + 54, -31/4*e^5 - 77*e^3 - 107*e, 7*e^5 + 77*e^3 + 166*e, -11/4*e^4 - 15*e^2 + 56, -45/4*e^4 - 101*e^2 - 94, -15/4*e^4 - 23*e^2 - 16, -13/4*e^4 - 32*e^2 - 68, 55/4*e^4 + 121*e^2 + 118, 43/8*e^5 + 123/2*e^3 + 166*e, 47/8*e^5 + 57*e^3 + 66*e, -9*e^4 - 79*e^2 - 158, 9*e^4 + 83*e^2 + 106, -11/4*e^4 - 25*e^2 + 34, -39/4*e^4 - 84*e^2 - 68, -15/2*e^4 - 81*e^2 - 144, 1/2*e^4 + 9*e^2 + 8, -11/4*e^5 - 36*e^3 - 64*e, -25/4*e^5 - 54*e^3 - 41*e, 13/2*e^4 + 53*e^2 + 74, 4*e^4 + 36*e^2 + 62, -5*e^4 - 36*e^2 + 4, 7*e^4 + 52*e^2 + 50, -27/8*e^5 - 49/2*e^3 + 20*e, -23/8*e^5 - 39*e^3 - 120*e, -9/2*e^5 - 54*e^3 - 131*e, -5/4*e^5 - 11*e^3 - 45*e, 21/2*e^4 + 84*e^2 + 48, 9*e^4 + 90*e^2 + 148, 15/4*e^5 + 60*e^3 + 211*e, 23/4*e^5 + 67*e^3 + 111*e, 2*e^4 + 17*e^2 + 10, -15/2*e^4 - 80*e^2 - 60, -11/4*e^5 - 36*e^3 - 139*e, 35/4*e^5 + 95*e^3 + 193*e, 11/8*e^5 + 49/2*e^3 + 121*e, -9/8*e^5 - 17/2*e^3 + 33*e, -17/2*e^4 - 112*e^2 - 214, -7/2*e^4 - 36*e^2 - 88, 6*e^4 + 62*e^2 + 78, 5/2*e^4 + 32*e^2 + 114, -31/8*e^5 - 77/2*e^3 - 33*e, 83/8*e^5 + 109*e^3 + 219*e, -5*e^5 - 45*e^3 - 22*e, 1/2*e^5 + e^3 - 24*e, -35/4*e^4 - 83*e^2 - 58, 51/4*e^4 + 122*e^2 + 188, 6*e^4 + 53*e^2 + 34, 3/2*e^4 + 22*e^2 + 120, -5/8*e^5 - 6*e^3 + 27*e, -15/8*e^5 - 21/2*e^3 + 45*e, 23/4*e^4 + 29*e^2 - 26, -37/4*e^4 - 100*e^2 - 150, 5/4*e^5 + 15*e^3 + 46*e, 13/2*e^5 + 66*e^3 + 83*e, 2*e^4 + 17*e^2 - 70, -9*e^4 - 88*e^2 - 74, 9/8*e^5 + 19*e^3 + 94*e, 13/8*e^5 + 10*e^3 - 68*e, -11/8*e^5 + 3/2*e^3 + 77*e, -5/8*e^5 - 12*e^3 - 56*e, -13*e^4 - 120*e^2 - 110, -8*e^4 - 93*e^2 - 198, 5/8*e^5 + 27/2*e^3 + 82*e, -7/8*e^5 - 23/2*e^3 - 24*e, 8*e^4 + 60*e^2 - 6, 13*e^4 + 112*e^2 + 116, 11/8*e^5 + 25/2*e^3 - 34*e, 3/8*e^5 - 43*e, -6*e^4 - 62*e^2 - 116, 10*e^4 + 114*e^2 + 124, -4*e^4 - 49*e^2 - 20, 13/2*e^4 + 62*e^2 + 18, e^5 + e^3 - 64*e, -27/4*e^5 - 76*e^3 - 177*e, -29/2*e^4 - 157*e^2 - 218, 10*e^2 + 72, 57/8*e^5 + 165/2*e^3 + 184*e, -23/8*e^5 - 79/2*e^3 - 128*e, -11/8*e^5 + 68*e, 27/8*e^5 + 69/2*e^3 + 29*e, -10*e^4 - 104*e^2 - 204, e^4 - 14*e^2 - 60, -7/8*e^5 - 5*e^3 - 10*e, 41/8*e^5 + 52*e^3 + 111*e, 9*e^4 + 111*e^2 + 194, -3*e^4 - 24*e^2 - 34, 69/8*e^5 + 181/2*e^3 + 143*e, 15/8*e^5 + 45/2*e^3 + 98*e, -4*e^4 - 53*e^2 - 154, -7*e^4 - 70*e^2 - 38, -7/2*e^5 - 51*e^3 - 144*e, 27/4*e^5 + 77*e^3 + 165*e, -33/4*e^4 - 67*e^2 + 10, -49/4*e^4 - 118*e^2 - 162, -11/2*e^4 - 56*e^2 - 46, 13*e^4 + 136*e^2 + 190, 9/2*e^4 + 16*e^2 - 46, e^4 + 8*e^2 - 38, 27/4*e^4 + 72*e^2 + 86, -5/4*e^4 - 17*e^2 - 50, 2*e^5 + 21*e^3 + 50*e, 27/2*e^5 + 147*e^3 + 247*e, -89/8*e^5 - 247/2*e^3 - 230*e, 33/8*e^5 + 113/2*e^3 + 171*e, -5/4*e^5 - 25*e^3 - 129*e, 13/4*e^5 + 52*e^3 + 201*e, -29/4*e^5 - 91*e^3 - 212*e, 5/4*e^5 + 6*e^3 - 11*e, 93/8*e^5 + 118*e^3 + 165*e, -31/8*e^5 - 99/2*e^3 - 122*e, -33/8*e^5 - 54*e^3 - 120*e, 27/8*e^5 + 38*e^3 + 37*e, -e^4 - 4*e^2 - 16, 19/2*e^4 + 88*e^2 + 98, 2*e^5 + 22*e^3 + 66*e, -13/2*e^5 - 74*e^3 - 164*e, -e^4 - 12*e^2 - 14, -13*e^4 - 145*e^2 - 210, 15/8*e^5 + 24*e^3 + 75*e, -65/8*e^5 - 86*e^3 - 170*e, 1/2*e^5 - 4*e^3 - 39*e, 2*e^5 + 8*e^3 - 81*e, -9/2*e^4 - 74*e^2 - 180, -17/2*e^4 - 88*e^2 - 140, 25/4*e^4 + 49*e^2 - 4, 35/8*e^5 + 62*e^3 + 173*e, -69/8*e^5 - 100*e^3 - 206*e, 5*e^4 + 67*e^2 + 152, 6*e^4 + 85*e^2 + 184, -9*e^4 - 70*e^2 - 44, 8*e^4 + 94*e^2 + 128, 15/8*e^5 + 53/2*e^3 + 62*e, -51/8*e^5 - 127/2*e^3 - 91*e, 13/4*e^4 + 53*e^2 + 106, -11/4*e^4 - 19*e^2 - 80, 3/2*e^4 + 19*e^2 - 78, 5/2*e^4 + 38*e^2 + 160, 61/8*e^5 + 81*e^3 + 117*e, 37/8*e^5 + 35*e^3 + 9*e, -5*e^5 - 42*e^3 - 16*e, 6*e^5 + 63*e^3 + 58*e, 9/2*e^4 + 38*e^2 + 106, -11/2*e^4 - 33*e^2 + 10, 39/4*e^4 + 81*e^2 + 130, -35/4*e^4 - 69*e^2 - 4, -5/8*e^5 - 39/2*e^3 - 94*e, -37/8*e^5 - 42*e^3 - 40*e, 41/4*e^4 + 106*e^2 + 144, 39/4*e^4 + 79*e^2 + 30, -8*e^4 - 64*e^2 - 46, 12*e^4 + 96*e^2 + 54, 41/4*e^4 + 91*e^2 + 124, -35/4*e^4 - 89*e^2 - 172, -7/4*e^4 - 39*e^2 - 66, -35/4*e^4 - 85*e^2 - 150, 5/4*e^4 - 4*e^2 - 52, -25/4*e^4 - 71*e^2 - 154, 31/2*e^4 + 145*e^2 + 204, -5/2*e^4 - 24*e^2 + 18, 89/8*e^5 + 241/2*e^3 + 233*e, 23/8*e^5 + 25*e^3 + 12*e, 77/8*e^5 + 112*e^3 + 261*e, -13/8*e^5 - 45/2*e^3 - 41*e, -7/8*e^5 - 23*e^3 - 98*e, 49/8*e^5 + 63*e^3 + 116*e, -8*e^4 - 74*e^2 - 116, -17*e^4 - 164*e^2 - 202, -4*e^4 - 35*e^2 - 26, -11*e^4 - 104*e^2 - 98, 11/8*e^5 + 1/2*e^3 - 63*e, -23/8*e^5 - 38*e^3 - 96*e, -4*e^4 - 30*e^2 - 36, -11*e^4 - 114*e^2 - 158, -19/2*e^5 - 105*e^3 - 220*e, -5/4*e^5 - 19*e^3 - 76*e, -5*e^5 - 52*e^3 - 121*e, 7*e^5 + 67*e^3 + 96*e, 12*e^4 + 137*e^2 + 160, -9*e^4 - 101*e^2 - 172, -13/2*e^4 - 51*e^2 - 40, -9/2*e^4 - 26*e^2 + 38, -8*e^4 - 74*e^2 - 124, -6*e^4 - 62*e^2 - 64, -3/4*e^5 + 63*e, 9*e^5 + 89*e^3 + 161*e, 9/2*e^5 + 50*e^3 + 99*e, 7/2*e^5 + 32*e^3 - 18*e, 1/8*e^5 - 11/2*e^3 - 74*e, 81/8*e^5 + 102*e^3 + 191*e, -9/2*e^5 - 56*e^3 - 151*e, 5*e^5 + 67*e^3 + 180*e, -5*e^5 - 51*e^3 - 53*e, -10*e^5 - 99*e^3 - 141*e, -75/8*e^5 - 92*e^3 - 126*e, -31/8*e^5 - 63*e^3 - 235*e, -7*e^4 - 42*e^2 + 10, -10*e^4 - 102*e^2 - 182, 23/2*e^4 + 125*e^2 + 166, -6*e^5 - 54*e^3 - 20*e, 25/2*e^5 + 138*e^3 + 251*e, 17/2*e^4 + 89*e^2 + 110, 5*e^4 + 42*e^2 + 64, 11/4*e^5 + 23*e^3 + 17*e, 5/2*e^5 + 28*e^3 + 6*e, 7*e^4 + 90*e^2 + 168, -17*e^4 - 164*e^2 - 222, 27/4*e^4 + 28*e^2 - 118, -49/4*e^4 - 112*e^2 - 154, -39/8*e^5 - 45*e^3 + e, -55/8*e^5 - 161/2*e^3 - 160*e, 9*e^4 + 80*e^2 + 8, 9/2*e^4 + 59*e^2 + 64, -5*e^5 - 63*e^3 - 190*e, -21/2*e^5 - 104*e^3 - 148*e, 11/2*e^4 + 57*e^2 + 166, -7/2*e^4 - 60*e^2 - 162, -3/8*e^5 + 15*e^3 + 104*e, 25/8*e^5 + 33/2*e^3 - 38*e, 47/4*e^4 + 115*e^2 + 132, 11/4*e^4 + 25*e^2 + 46, -8*e^5 - 88*e^3 - 127*e, -51/4*e^5 - 135*e^3 - 238*e, -2*e^4 - 20*e^2 - 48, -9/2*e^4 - 54*e^2 - 142, 21/2*e^5 + 122*e^3 + 235*e, 13/4*e^5 + 30*e^3 + 64*e, -69/8*e^5 - 97*e^3 - 228*e, 15/8*e^5 + 26*e^3 + 117*e, -e^4 + 5*e^2 + 118, -9*e^4 - 56*e^2 + 50, -8*e^4 - 63*e^2 + 30, -11/2*e^4 - 42*e^2 - 84, -9/4*e^5 - 32*e^3 - 103*e, 41/4*e^5 + 114*e^3 + 203*e, 59/8*e^5 + 80*e^3 + 178*e, -65/8*e^5 - 173/2*e^3 - 128*e, -37/2*e^4 - 181*e^2 - 220, 11*e^4 + 78*e^2 - 18, -49/8*e^5 - 93/2*e^3 + 7*e, 77/8*e^5 + 115*e^3 + 269*e, 1/8*e^5 + 12*e^3 + 128*e, -23/8*e^5 - 21*e^3 + 33*e, -19/8*e^5 - 39/2*e^3 - 38*e, -143/8*e^5 - 387/2*e^3 - 314*e, 33/2*e^5 + 173*e^3 + 295*e, 15/4*e^5 + 36*e^3 + 12*e, -4*e^5 - 57*e^3 - 195*e, -2*e^5 - 15*e^3 - 10*e, 8*e^4 + 66*e^2 + 78, -9/2*e^4 - 38*e^2 - 96, -1/4*e^4 - 29*e^2 - 78, -13/4*e^4 - 40*e^2 - 56, -73/8*e^5 - 201/2*e^3 - 201*e, 1/8*e^5 + 10*e^3 + 69*e, 1/2*e^4 + 25*e^2 + 162, 13/2*e^4 + 65*e^2 + 26, -21/2*e^4 - 90*e^2 - 60, -19*e^4 - 191*e^2 - 260, -e^5 - 26*e^3 - 117*e, 9/2*e^5 + 49*e^3 + 45*e, 6*e^5 + 66*e^3 + 138*e, -9/4*e^5 - 30*e^3 - 66*e, 13/4*e^4 + 29*e^2 - 58, 27/4*e^4 + 56*e^2 + 48, -41/8*e^5 - 121/2*e^3 - 148*e, 99/8*e^5 + 133*e^3 + 288*e, 11/4*e^4 + 17*e^2 - 80, 19/4*e^4 + 59*e^2 + 80, 5/8*e^5 + 13*e^3 + 76*e, 5/8*e^5 + 19*e^3 + 97*e, 31/4*e^4 + 71*e^2 + 52, -53/4*e^4 - 137*e^2 - 180, 25/4*e^4 + 45*e^2 - 40, 1/4*e^4 + 7*e^2 - 62, 19/4*e^5 + 58*e^3 + 160*e, e^5 + 9*e^3 - 9*e, -61/8*e^5 - 159/2*e^3 - 137*e, -1/8*e^5 + 13/2*e^3 + 79*e, 3/4*e^4 - 15*e^2 - 72, -49/4*e^4 - 135*e^2 - 184, -25/4*e^5 - 62*e^3 - 44*e, 31/4*e^5 + 91*e^3 + 200*e, 29/2*e^4 + 110*e^2 + 58, 15/2*e^4 + 76*e^2 + 166, 13/4*e^4 + 45*e^2 + 100, 45/4*e^4 + 131*e^2 + 188, -3/4*e^5 - 27*e^3 - 147*e, 5/2*e^5 + 37*e^3 + 125*e, -17/2*e^4 - 70*e^2 - 72, -9*e^2 + 58, 11/2*e^5 + 55*e^3 + 53*e, 21/4*e^5 + 52*e^3 + 104*e, 71/4*e^4 + 167*e^2 + 238, -65/4*e^4 - 168*e^2 - 218, 7/2*e^4 + 36*e^2 + 40, -7/2*e^4 + 2*e^2 + 148, -9/2*e^5 - 39*e^3 + 14*e, -11/4*e^5 - 12*e^3 + 38*e, -45/8*e^5 - 54*e^3 - 106*e, 1/8*e^5 + 29/2*e^3 + 103*e, 19*e^4 + 182*e^2 + 268, e^2 - 44, 11/4*e^5 + 27*e^3 + 54*e, 5/4*e^5 + 34*e^3 + 145*e, -9/8*e^5 - 12*e^3 - 31*e, 31/8*e^5 + 40*e^3 + 41*e, 63/4*e^5 + 156*e^3 + 235*e, -7*e^5 - 79*e^3 - 141*e, -1/2*e^5 + 3*e^3 + 59*e, 57/4*e^5 + 151*e^3 + 291*e, 19/8*e^5 + 19/2*e^3 - 45*e, 77/8*e^5 + 211/2*e^3 + 200*e, 2*e^4 + 26*e^2 + 134, -5*e^4 - 72*e^2 - 212, -23/4*e^4 - 86*e^2 - 182, 21/4*e^4 + 61*e^2 + 114, 119/8*e^5 + 148*e^3 + 238*e, -41/8*e^5 - 45*e^3 - 60*e, 19*e^4 + 166*e^2 + 172, 20*e^2 + 40, 27/2*e^5 + 146*e^3 + 226*e, 51/4*e^5 + 129*e^3 + 171*e, -21/2*e^4 - 118*e^2 - 118, 11/2*e^4 + 44*e^2 + 88, -65/8*e^5 - 78*e^3 - 80*e, 21/8*e^5 + 53/2*e^3 + 75*e, -87/8*e^5 - 101*e^3 - 126*e, 61/8*e^5 + 141/2*e^3 + 52*e, 15/4*e^5 + 32*e^3 + 38*e, -31/2*e^5 - 152*e^3 - 223*e, -29/4*e^5 - 88*e^3 - 191*e, -4*e^5 - 45*e^3 - 45*e, -37/4*e^4 - 83*e^2 - 140, 3/4*e^4 - 15*e^2 - 92, -2*e^4 - 34*e^2 - 100, -14*e^4 - 164*e^2 - 248, -25/2*e^5 - 124*e^3 - 171*e, 2*e^3 - 25*e, 6*e^4 + 54*e^2 - 2, 3/2*e^4 + 22*e^2 + 68, 41/8*e^5 + 91/2*e^3 + 27*e, 71/8*e^5 + 80*e^3 + 69*e, -39/4*e^4 - 109*e^2 - 158, 39/4*e^4 + 116*e^2 + 160, -73/8*e^5 - 98*e^3 - 214*e, 95/8*e^5 + 117*e^3 + 175*e, -8*e^4 - 71*e^2 - 136, -23/2*e^4 - 101*e^2 - 100, 3/2*e^4 + 40*e^2 + 88, -1/2*e^4 + 4*e^2 + 24, -37/4*e^5 - 100*e^3 - 166*e, 7/4*e^5 + 12*e^3 - 25*e, -5/2*e^4 - 9*e^2 + 18, -19/2*e^4 - 111*e^2 - 202, -115/8*e^5 - 146*e^3 - 208*e, -69/8*e^5 - 173/2*e^3 - 113*e, 14*e^4 + 154*e^2 + 260, -11*e^4 - 136*e^2 - 260, 53/4*e^4 + 109*e^2 + 72, 25/4*e^4 + 43*e^2 + 48, 51/4*e^4 + 115*e^2 + 236, 15/4*e^4 + 45*e^2 + 90, e^5 + 22*e^3 + 82*e, 33/2*e^5 + 178*e^3 + 310*e, 1/2*e^5 + 10*e^3 + 18*e, -e^5 - 17*e^3 - 40*e, 75/8*e^5 + 223/2*e^3 + 255*e, 25/8*e^5 + 45*e^3 + 151*e, 12*e^4 + 142*e^2 + 202, -37/2*e^4 - 211*e^2 - 298, 71/4*e^4 + 157*e^2 + 128, 39/4*e^4 + 103*e^2 + 172, 33/4*e^5 + 96*e^3 + 180*e, 9*e^5 + 116*e^3 + 278*e, 11*e^5 + 129*e^3 + 286*e, -15/4*e^5 - 48*e^3 - 105*e, -11*e^4 - 77*e^2 + 24, 6*e^4 + 38*e^2 - 18, -8*e^4 - 64*e^2 - 36, e^4 - 25*e^2 - 196, -1/2*e^4 + 6*e^2 + 76, 1/2*e^4 + 3*e^2 - 38, 59/4*e^5 + 161*e^3 + 296*e, -5*e^5 - 58*e^3 - 137*e, 15/2*e^4 + 78*e^2 + 110, -23/2*e^4 - 98*e^2 - 122, 25/4*e^4 + 93*e^2 + 180, -51/4*e^4 - 113*e^2 - 152, 79/8*e^5 + 213/2*e^3 + 189*e, -59/8*e^5 - 71*e^3 - 90*e, 23/4*e^5 + 54*e^3 + 45*e, -e^5 - 24*e^3 - 135*e, -18*e^5 - 183*e^3 - 279*e, 29/4*e^5 + 83*e^3 + 158*e, -35/8*e^5 - 62*e^3 - 206*e, 1/8*e^5 + 15*e^3 + 124*e, -11/2*e^4 - 35*e^2 + 40, 37/2*e^4 + 180*e^2 + 186, 35/8*e^5 + 44*e^3 + 37*e, -9/8*e^5 - 8*e^3 - 27*e, 9/8*e^5 + 22*e^3 + 87*e, -63/8*e^5 - 187/2*e^3 - 282*e, -61/8*e^5 - 63*e^3 - 20*e, -45/8*e^5 - 68*e^3 - 147*e, -7*e^4 - 69*e^2 - 152, 13*e^4 + 116*e^2 + 158, 61/8*e^5 + 191/2*e^3 + 214*e, -43/8*e^5 - 60*e^3 - 146*e, 6*e^4 + 77*e^2 + 86, 5*e^4 + 65*e^2 + 150, -71/8*e^5 - 193/2*e^3 - 156*e, 29/8*e^5 + 59/2*e^3 + 10*e, 1/2*e^5 + 3*e^3 + 38*e, -27/2*e^5 - 135*e^3 - 171*e, 1/2*e^4 - 2*e^2, -12*e^4 - 118*e^2 - 176, 91/8*e^5 + 129*e^3 + 278*e, 87/8*e^5 + 124*e^3 + 221*e, 11/4*e^5 + 41*e^3 + 108*e, 5/4*e^5 + 19*e^3 + 75*e, -25/4*e^4 - 62*e^2 - 132, -13/4*e^4 - 45*e^2 - 58, -15/2*e^4 - 44*e^2 + 58, 10*e^4 + 86*e^2 + 128, 2*e^4 - 5*e^2 - 30, 4*e^4 + 34*e^2 + 82, -51/8*e^5 - 59*e^3 - 59*e, -67/8*e^5 - 92*e^3 - 215*e, 9/2*e^4 + 34*e^2 + 132, 5/2*e^4 + 38*e^2 + 138, -49/4*e^4 - 123*e^2 - 132, 39/4*e^4 + 75*e^2 + 64, 11/2*e^4 + 23*e^2 - 108, -21/2*e^4 - 115*e^2 - 120, 37/8*e^5 + 53*e^3 + 160*e, -65/8*e^5 - 175/2*e^3 - 139*e, -9/2*e^5 - 55*e^3 - 160*e, 7/2*e^5 + 54*e^3 + 191*e, -17*e^4 - 156*e^2 - 174, 8*e^4 + 79*e^2 + 226, 7*e^4 + 39*e^2 - 76, 5*e^4 + 63*e^2 + 60, 35/2*e^4 + 188*e^2 + 250, 15*e^4 + 128*e^2 + 120, -11/4*e^4 - 15*e^2 + 116, -19/4*e^4 - 33*e^2 - 40, 9/8*e^5 + 35/2*e^3 + 10*e, 109/8*e^5 + 139*e^3 + 219*e, 9/4*e^4 + 47*e^2 + 158, 13/4*e^4 + 17*e^2 - 8, -1/8*e^5 - 11/2*e^3 - 75*e, 77/8*e^5 + 91*e^3 + 113*e, 13*e^4 + 129*e^2 + 156, -e^4 - 14*e^2 + 122, -37/2*e^4 - 175*e^2 - 184, -6*e^4 - 62*e^2 - 56, 3/4*e^5 + 12*e^3 + 93*e, -7/4*e^5 - 2*e^3 + 114*e, -33/4*e^4 - 81*e^2 - 82, 65/4*e^4 + 176*e^2 + 228, -13/8*e^5 - 17/2*e^3 - 12*e, 39/8*e^5 + 48*e^3 + 78*e, 5*e^4 + 55*e^2 + 142, 11*e^4 + 104*e^2 + 150, -9/8*e^5 - 7*e^3 + 17*e, -53/8*e^5 - 73*e^3 - 111*e, 25/2*e^4 + 90*e^2 + 42, 39/2*e^4 + 178*e^2 + 228, -27/4*e^5 - 77*e^3 - 126*e, -6*e^5 - 55*e^3 - 71*e, 9/2*e^4 + 24*e^2 - 148, 7*e^4 + 58*e^2 + 136, -5/2*e^5 - 27*e^3 - 86*e, -5*e^5 - 68*e^3 - 217*e, 27/2*e^4 + 140*e^2 + 124, 15*e^4 + 159*e^2 + 234, 55/8*e^5 + 153/2*e^3 + 127*e, 49/8*e^5 + 73*e^3 + 153*e, -53/4*e^4 - 144*e^2 - 170, 39/4*e^4 + 94*e^2 + 30, -105/8*e^5 - 287/2*e^3 - 300*e, -29/8*e^5 - 73/2*e^3 - 40*e, 2*e^5 + 5*e^3 - 51*e, -6*e^5 - 72*e^3 - 130*e, 5/2*e^4 + 40*e^2 + 82, 6*e^4 + 76*e^2 + 142, 63/8*e^5 + 74*e^3 + 89*e, 19/8*e^5 + 45/2*e^3 + 28*e, -19*e^4 - 184*e^2 - 260, -41/2*e^4 - 222*e^2 - 294, 15/4*e^4 + 46*e^2 + 148, 35/4*e^4 + 85*e^2 + 62, -47/4*e^5 - 114*e^3 - 143*e, 1/2*e^5 - 2*e^3 - 87*e, 1/8*e^5 + 13/2*e^3 + 3*e, 5/8*e^5 + 19/2*e^3 + 23*e, 37/4*e^4 + 94*e^2 + 236, 9/4*e^4 + 31*e^2 + 70, 5/2*e^4 + 42*e^2 + 144, 5*e^4 + 62*e^2 + 14, 6*e^4 + 82*e^2 + 196, 9/2*e^4 + 46*e^2 + 4, 14*e^4 + 120*e^2 + 198, 5*e^4 + 66*e^2 + 118, 93/8*e^5 + 237/2*e^3 + 226*e, 105/8*e^5 + 153*e^3 + 309*e, 11*e^5 + 97*e^3 + 89*e, -57/4*e^5 - 155*e^3 - 299*e, -27/2*e^4 - 100*e^2 - 52, -7*e^4 - 70*e^2 - 96, 33/4*e^4 + 89*e^2 + 64, 49/4*e^4 + 111*e^2 + 152, 73/4*e^4 + 204*e^2 + 312, 81/4*e^4 + 197*e^2 + 258, -17/4*e^5 - 47*e^3 - 131*e, 9/4*e^5 + 19*e^3 - 14*e, 39/4*e^4 + 83*e^2 + 104, -41/4*e^4 - 105*e^2 - 64, 5*e^4 + 36*e^2 + 8, 11*e^4 + 98*e^2 + 34, 5/2*e^4 + 41*e^2 - 14, 14*e^4 + 114*e^2 + 110, -11/2*e^5 - 63*e^3 - 77*e, 21/4*e^5 + 57*e^3 + 121*e, -20*e^4 - 189*e^2 - 304, -3/2*e^4 + 18*e^2 + 172, 7*e^4 + 71*e^2 + 64, -3/2*e^4 + 18*e^2 + 62, -27/4*e^5 - 60*e^3 - 34*e, 31/4*e^5 + 88*e^3 + 207*e, 31/2*e^4 + 157*e^2 + 166, 5*e^4 + 58*e^2 + 130, 9/2*e^5 + 65*e^3 + 179*e, -10*e^5 - 109*e^3 - 178*e, 35/4*e^4 + 89*e^2 + 66, -35/4*e^4 - 77*e^2 - 200, -11/4*e^5 - 40*e^3 - 95*e, -9*e^5 - 89*e^3 - 139*e, 1/2*e^4 + 7*e^2 + 94, -12*e^4 - 116*e^2 - 194, 6*e^4 + 83*e^2 + 224, -10*e^4 - 70*e^2 - 28, 43/4*e^5 + 123*e^3 + 294*e, -25/2*e^5 - 124*e^3 - 166*e, -15/2*e^4 - 62*e^2 - 12, e^4 + 13*e^2 + 152, 15/2*e^5 + 86*e^3 + 142*e, 14*e^5 + 131*e^3 + 163*e, -1/8*e^5 + 15*e^3 + 120*e, 79/8*e^5 + 122*e^3 + 317*e, 7*e^5 + 68*e^3 + 77*e, 15*e^3 + 86*e, -19*e^4 - 195*e^2 - 266, 16*e^4 + 157*e^2 + 206, -19/2*e^4 - 84*e^2 - 30, -17/2*e^4 - 94*e^2 - 66, -18*e^4 - 152*e^2 - 134, -13*e^4 - 133*e^2 - 160, -93/8*e^5 - 285/2*e^3 - 321*e, -51/8*e^5 - 66*e^3 - 136*e, 21/8*e^5 + 79/2*e^3 + 161*e, 51/8*e^5 + 69*e^3 + 183*e]; heckeEigenvalues := AssociativeArray(); for i := 1 to #heckeEigenvaluesArray do heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i]; end for; ALEigenvalues := AssociativeArray(); ALEigenvalues[ideal] := -1/8*e^5 - 5/4*e^3 - 2*e; ALEigenvalues[ideal] := 1; // EXAMPLE: // pp := Factorization(2*ZF)[1][1]; // heckeEigenvalues[pp]; print "To reconstruct the Hilbert newform f, type f, iso := Explode(make_newform());"; function make_newform(); M := HilbertCuspForms(F, NN); S := NewSubspace(M); // SetVerbose("ModFrmHil", 1); NFD := NewformDecomposition(S); newforms := [* Eigenform(U) : U in NFD *]; if #newforms eq 0 then; print "No Hilbert newforms at this level"; return 0; end if; print "Testing ", #newforms, " possible newforms"; newforms := [* f: f in newforms | IsIsomorphic(BaseField(f), K) *]; print #newforms, " newforms have the correct Hecke field"; if #newforms eq 0 then; print "No Hilbert newform found with the correct Hecke field"; return 0; end if; autos := Automorphisms(K); xnewforms := [* *]; for f in newforms do; if K eq RationalField() then; Append(~xnewforms, [* f, autos[1] *]); else; flag, iso := IsIsomorphic(K,BaseField(f)); for a in autos do; Append(~xnewforms, [* f, a*iso *]); end for; end if; end for; newforms := xnewforms; for P in primes do; xnewforms := [* *]; for f_iso in newforms do; f, iso := Explode(f_iso); if HeckeEigenvalue(f,P) eq iso(heckeEigenvalues[P]) then; Append(~xnewforms, f_iso); end if; end for; newforms := xnewforms; if #newforms eq 0 then; print "No Hilbert newform found which matches the Hecke eigenvalues"; return 0; else if #newforms eq 1 then; print "success: unique match"; return newforms[1]; end if; end if; end for; print #newforms, "Hilbert newforms found which match the Hecke eigenvalues"; return newforms[1]; end function;