/* 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([-21, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([7, 7, w]) primes_array = [ [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 - 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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 = [ZF.ideal(I) for I in primes_array] heckePol = x^5 - 2*x^4 - 12*x^3 + 13*x^2 + 37*x + 16 K. = NumberField(heckePol) hecke_eigenvalues_array = [e^3 - 9*e - 4, e, -e^4 + 3*e^3 + 10*e^2 - 23*e - 23, 2*e^3 + e^2 - 18*e - 14, -1, -e^4 + e^3 + 10*e^2 - 6*e - 12, -2*e^3 - e^2 + 18*e + 18, 3*e^4 - 6*e^3 - 28*e^2 + 41*e + 44, 2*e^3 + e^2 - 17*e - 20, -2*e^4 + 17*e^2 + 8*e, -2*e^3 + 16*e + 12, e^4 + e^3 - 9*e^2 - 11*e - 2, 3*e^4 - 8*e^3 - 28*e^2 + 56*e + 54, -5*e^3 - e^2 + 42*e + 28, e^4 - 4*e^3 - 11*e^2 + 33*e + 36, -2*e^3 - e^2 + 20*e + 14, -e^4 + 9*e^2 + 4*e + 6, -4*e^4 + 9*e^3 + 38*e^2 - 63*e - 70, -5*e^4 + 3*e^3 + 46*e^2 - 10*e - 30, 11*e^3 + 3*e^2 - 95*e - 70, e^4 - 2*e^3 - 11*e^2 + 14*e + 26, -3*e^4 + 9*e^3 + 28*e^2 - 67*e - 58, -3*e^4 + 7*e^3 + 28*e^2 - 47*e - 50, -3*e^4 + 24*e^2 + 15*e + 8, 4*e^4 - 14*e^3 - 39*e^2 + 104*e + 92, -3*e^4 + 3*e^3 + 28*e^2 - 17*e - 34, 5*e^4 - 14*e^3 - 50*e^2 + 106*e + 110, -3*e^4 + 3*e^3 + 27*e^2 - 16*e - 30, 7*e^4 - 11*e^3 - 67*e^2 + 70*e + 94, -3*e^4 + 26*e^2 + 13*e - 2, -e^4 + 5*e^3 + 10*e^2 - 34*e - 32, -2*e^4 + 8*e^3 + 20*e^2 - 65*e - 56, e^4 + 3*e^3 - 9*e^2 - 29*e, -e^3 + e^2 + 10*e + 4, -7*e^4 + 18*e^3 + 66*e^2 - 131*e - 128, -e^4 + 5*e^3 + 13*e^2 - 43*e - 36, -e^4 - 7*e^3 + 9*e^2 + 61*e + 26, 6*e^4 - 8*e^3 - 58*e^2 + 52*e + 78, 5*e^4 - 9*e^3 - 48*e^2 + 61*e + 70, -3*e^4 + 11*e^3 + 30*e^2 - 90*e - 76, e^4 - e^3 - 9*e^2 + 4*e + 4, e^4 - 3*e^3 - 12*e^2 + 30*e + 32, e^4 - 6*e^3 - 9*e^2 + 46*e + 24, e^4 + 3*e^3 - 9*e^2 - 24*e - 10, 2*e^4 - 4*e^3 - 18*e^2 + 27*e + 38, -e^4 + 8*e^3 + 8*e^2 - 65*e - 34, -7*e^4 + 12*e^3 + 67*e^2 - 81*e - 106, -5*e^4 + 11*e^3 + 47*e^2 - 79*e - 76, e^4 + 7*e^3 - 7*e^2 - 66*e - 40, -e^4 + 13*e^3 + 14*e^2 - 108*e - 98, -6*e^3 - 2*e^2 + 50*e + 38, 3*e^4 - e^3 - 23*e^2 - 6*e - 6, 2*e^4 - 17*e^3 - 25*e^2 + 143*e + 122, 6*e^4 - 15*e^3 - 59*e^2 + 108*e + 112, -e^4 - 2*e^3 + 7*e^2 + 20*e + 24, 7*e^4 - 9*e^3 - 67*e^2 + 58*e + 84, e^4 + 12*e^3 - 6*e^2 - 112*e - 60, 6*e^4 - 21*e^3 - 62*e^2 + 166*e + 160, 4*e^4 - 2*e^3 - 41*e^2 + 10*e + 48, -4*e^4 + 7*e^3 + 37*e^2 - 44*e - 62, -7*e^4 + 18*e^3 + 69*e^2 - 136*e - 134, -e^3 - e^2 + 2*e + 18, 3*e^4 - 6*e^3 - 31*e^2 + 45*e + 50, -8*e^4 + 11*e^3 + 73*e^2 - 67*e - 80, -e^4 + 15*e^3 + 19*e^2 - 134*e - 124, 13*e^4 - 24*e^3 - 125*e^2 + 163*e + 190, -10*e^4 + 14*e^3 + 95*e^2 - 87*e - 122, 11*e^4 - 19*e^3 - 105*e^2 + 125*e + 162, 4*e^4 - 9*e^3 - 39*e^2 + 62*e + 74, e^4 + 13*e^3 - 4*e^2 - 119*e - 76, -e^4 + 4*e^3 + 11*e^2 - 28*e - 28, -2*e^3 + e^2 + 9*e + 10, -2*e^4 + 14*e^3 + 24*e^2 - 111*e - 118, 3*e^4 - 5*e^3 - 30*e^2 + 38*e + 52, 3*e^4 - 15*e^3 - 32*e^2 + 122*e + 96, -3*e^4 - 4*e^3 + 31*e^2 + 39*e - 18, -2*e^4 + e^3 + 18*e^2 - e - 18, -5*e^4 + 29*e^3 + 54*e^2 - 230*e - 208, 11*e^4 - 24*e^3 - 105*e^2 + 159*e + 184, 12*e^4 - 27*e^3 - 117*e^2 + 197*e + 208, 12*e^3 - e^2 - 95*e - 52, 4*e^4 - 22*e^3 - 41*e^2 + 174*e + 134, 7*e^4 - 20*e^3 - 68*e^2 + 153*e + 166, 8*e^4 - 26*e^3 - 76*e^2 + 196*e + 178, e^4 + 11*e^3 - 2*e^2 - 98*e - 94, 4*e^4 - 15*e^3 - 36*e^2 + 107*e + 74, 6*e^4 - e^3 - 57*e^2 - 11*e + 34, -3*e^4 + 10*e^3 + 32*e^2 - 74*e - 90, -3*e^4 + 13*e^3 + 32*e^2 - 99*e - 90, 3*e^4 - 8*e^3 - 30*e^2 + 58*e + 46, -8*e^4 + 8*e^3 + 70*e^2 - 31*e - 50, -6*e^4 + 22*e^3 + 56*e^2 - 156*e - 128, 3*e^4 + 4*e^3 - 26*e^2 - 45*e + 4, 9*e^4 - 21*e^3 - 84*e^2 + 148*e + 140, 17*e^3 + 5*e^2 - 145*e - 100, 6*e^4 - 57*e^2 - 24*e + 36, -8*e^4 + 19*e^3 + 77*e^2 - 129*e - 152, 2*e^4 - 15*e^3 - 23*e^2 + 123*e + 110, 9*e^4 + e^3 - 83*e^2 - 41*e + 46, 9*e^4 - 20*e^3 - 83*e^2 + 129*e + 132, 14*e^4 - 35*e^3 - 134*e^2 + 248*e + 264, -8*e^4 + 14*e^3 + 75*e^2 - 94*e - 118, -10*e^4 + 17*e^3 + 95*e^2 - 111*e - 118, 8*e^4 - 2*e^3 - 70*e^2 - 19*e + 32, 3*e^4 - 16*e^3 - 38*e^2 + 134*e + 144, -12*e^4 + 11*e^3 + 114*e^2 - 60*e - 120, 9*e^4 - 18*e^3 - 84*e^2 + 119*e + 140, -5*e^4 + 5*e^3 + 48*e^2 - 25*e - 58, 7*e^4 - e^3 - 60*e^2 - 19*e + 6, -2*e^4 - 2*e^3 + 12*e^2 + 29*e + 48, -5*e^4 - 3*e^3 + 44*e^2 + 47*e, -3*e^4 + 10*e^3 + 31*e^2 - 74*e - 96, -3*e^4 + 3*e^3 + 32*e^2 - 24*e - 60, -4*e^4 + 10*e^3 + 43*e^2 - 64*e - 106, e^4 - 28*e^3 - 13*e^2 + 232*e + 174, 16*e^4 - 24*e^3 - 152*e^2 + 155*e + 212, e^4 - 6*e^3 - 7*e^2 + 44*e + 36, e^4 - e^3 - 11*e^2 + 3*e + 14, e^4 + 19*e^3 - 2*e^2 - 173*e - 122, 10*e^3 - 2*e^2 - 81*e - 26, -5*e^4 + 16*e^3 + 47*e^2 - 121*e - 106, -e^2 + 5*e + 10, 4*e^4 - 14*e^3 - 45*e^2 + 117*e + 122, 4*e^4 + 15*e^3 - 34*e^2 - 139*e - 84, 9*e^4 - 14*e^3 - 89*e^2 + 98*e + 136, 4*e^4 - 8*e^3 - 42*e^2 + 62*e + 62, e^4 - 18*e^3 - 19*e^2 + 161*e + 142, 5*e^4 - 42*e^3 - 59*e^2 + 349*e + 300, e^4 + 10*e^3 - 3*e^2 - 87*e - 84, -5*e^4 - e^3 + 48*e^2 + 18*e - 12, -8*e^4 + 29*e^3 + 83*e^2 - 232*e - 224, 16*e^4 - 35*e^3 - 155*e^2 + 245*e + 258, 4*e^4 + 21*e^3 - 27*e^2 - 202*e - 134, -8*e^4 - 12*e^3 + 62*e^2 + 141*e + 90, -6*e^4 + 15*e^3 + 56*e^2 - 116*e - 110, 2*e^4 + 14*e^3 - 15*e^2 - 130*e - 64, -10*e^4 + 9*e^3 + 94*e^2 - 46*e - 76, -2*e^4 + 9*e^3 + 20*e^2 - 78*e - 80, 7*e^4 - 10*e^3 - 60*e^2 + 59*e + 52, -8*e^4 + 17*e^3 + 73*e^2 - 112*e - 104, -4*e^4 + 7*e^3 + 37*e^2 - 42*e - 28, 23*e^4 - 39*e^3 - 217*e^2 + 251*e + 310, -8*e^4 + e^3 + 74*e^2 + 20*e - 34, 2*e^4 + 5*e^3 - 12*e^2 - 63*e - 38, -6*e^4 - 2*e^3 + 48*e^2 + 45*e + 54, 3*e^4 - 24*e^3 - 35*e^2 + 201*e + 158, 3*e^4 + 10*e^3 - 26*e^2 - 94*e - 34, 3*e^4 + 12*e^3 - 34*e^2 - 107*e - 10, -4*e^4 + 36*e^3 + 47*e^2 - 305*e - 244, -e^4 - 5*e^3 + 4*e^2 + 52*e + 20, 2*e^4 - 28*e^3 - 32*e^2 + 247*e + 218, 2*e^4 + 18*e^3 - 9*e^2 - 173*e - 126, 3*e^4 + 10*e^3 - 27*e^2 - 92*e - 40, 3*e^4 - 15*e^3 - 31*e^2 + 126*e + 68, 26*e^3 + 7*e^2 - 225*e - 172, 5*e^4 - 22*e^3 - 51*e^2 + 165*e + 176, 7*e^4 - 23*e^3 - 70*e^2 + 175*e + 168, -13*e^4 + 52*e^3 + 133*e^2 - 406*e - 368, -5*e^4 - 7*e^3 + 41*e^2 + 74*e + 48, 2*e^4 - 16*e^3 - 23*e^2 + 138*e + 116, 16*e^4 - 40*e^3 - 154*e^2 + 296*e + 290, 6*e^4 - 24*e^3 - 58*e^2 + 191*e + 148, -21*e^4 + 36*e^3 + 200*e^2 - 233*e - 292, 4*e^4 - 35*e^2 - 13*e + 28, -5*e^4 - 13*e^3 + 50*e^2 + 121*e + 32, 5*e^4 - 31*e^3 - 49*e^2 + 239*e + 190, 14*e^4 - 24*e^3 - 126*e^2 + 153*e + 166, -4*e^4 + 7*e^3 + 46*e^2 - 49*e - 106, 13*e^4 - 13*e^3 - 118*e^2 + 64*e + 110, -e^4 - 2*e^3 + 6*e^2 + 28*e + 4, -2*e^4 + 6*e^3 + 16*e^2 - 48*e - 28, -e^4 - 2*e^3 + 7*e^2 + 24*e - 10, -2*e^4 + 17*e^3 + 24*e^2 - 144*e - 114, 4*e^3 + 3*e^2 - 33*e - 48, -4*e^4 + 4*e^3 + 38*e^2 - 19*e - 24, 7*e^4 - 44*e^3 - 75*e^2 + 360*e + 302, -3*e^4 + 23*e^3 + 24*e^2 - 173*e - 98, 9*e^4 - 16*e^3 - 84*e^2 + 105*e + 98, -21*e^4 + 35*e^3 + 197*e^2 - 235*e - 278, -3*e^4 + 5*e^3 + 27*e^2 - 35*e - 66, -9*e^4 + 19*e^3 + 81*e^2 - 133*e - 106, -6*e^4 + 30*e^3 + 55*e^2 - 230*e - 174, -15*e^4 + 34*e^3 + 147*e^2 - 253*e - 278, 6*e^4 - 5*e^3 - 51*e^2 + 11*e + 26, -3*e^4 - 4*e^3 + 28*e^2 + 38*e + 26, -3*e^4 + 35*e^2 - 48, -8*e^4 + 29*e^3 + 77*e^2 - 222*e - 188, 13*e^4 - 37*e^3 - 127*e^2 + 279*e + 268, -6*e^4 + 14*e^3 + 61*e^2 - 109*e - 92, 4*e^4 - 13*e^3 - 33*e^2 + 105*e + 46, 12*e^4 - 26*e^3 - 113*e^2 + 177*e + 190, -9*e^4 + 7*e^3 + 82*e^2 - 20*e - 68, 4*e^4 + 11*e^3 - 33*e^2 - 112*e - 16, 11*e^4 - 42*e^3 - 110*e^2 + 321*e + 278, -3*e^4 + e^3 + 25*e^2 + 12*e - 18, -8*e^4 + 10*e^3 + 69*e^2 - 48*e - 54, -e^4 - 3*e^3 + 9*e^2 + 22*e + 18, 11*e^4 - 92*e^2 - 47*e - 26, -21*e^4 + 51*e^3 + 209*e^2 - 379*e - 402, e^4 - 31*e^3 - 11*e^2 + 258*e + 162, -8*e^4 + 2*e^3 + 70*e^2 + 17*e - 38, 7*e^4 - 3*e^3 - 55*e^2 - 12*e - 12, -5*e^4 + 23*e^3 + 41*e^2 - 172*e - 100, -2*e^4 - 26*e^3 + 10*e^2 + 225*e + 176, 18*e^4 - 39*e^3 - 167*e^2 + 268*e + 264, -12*e^4 - 2*e^3 + 108*e^2 + 56*e - 20, 5*e^4 + 2*e^3 - 46*e^2 - 36*e - 28, 4*e^4 - 22*e^3 - 41*e^2 + 181*e + 162, 6*e^4 - 31*e^3 - 65*e^2 + 246*e + 242, -7*e^4 + 15*e^3 + 74*e^2 - 109*e - 170, 5*e^4 - 10*e^3 - 50*e^2 + 65*e + 102, -10*e^4 - 4*e^3 + 86*e^2 + 64*e + 32, -e^4 - 17*e^3 + 10*e^2 + 143*e + 60, 16*e^4 - 43*e^3 - 151*e^2 + 300*e + 290, 7*e^4 - 50*e^2 - 33*e - 46, 10*e^4 - 43*e^3 - 99*e^2 + 335*e + 268, 13*e^4 - 27*e^3 - 132*e^2 + 187*e + 248, 5*e^4 - 7*e^3 - 54*e^2 + 50*e + 86, 3*e^4 + e^3 - 24*e^2 - 18*e + 6, 3*e^4 - 34*e^3 - 43*e^2 + 290*e + 242, 3*e^4 + 11*e^3 - 23*e^2 - 106*e - 78, 9*e^4 - 26*e^3 - 86*e^2 + 198*e + 220, -15*e^4 + 16*e^3 + 135*e^2 - 76*e - 120, -10*e^4 + 27*e^3 + 99*e^2 - 201*e - 218, 4*e^4 + 5*e^3 - 28*e^2 - 53*e - 58, -8*e^4 + 4*e^3 + 65*e^2 + 5*e + 2, -8*e^4 - 21*e^3 + 69*e^2 + 211*e + 66, -10*e^4 + 9*e^3 + 88*e^2 - 31*e - 48, e^4 - 17*e^3 - 3*e^2 + 121*e + 40, -e^4 - 6*e^3 + 13*e^2 + 39*e - 6, -6*e^4 + 8*e^3 + 56*e^2 - 43*e - 54, -8*e^4 + 37*e^3 + 83*e^2 - 289*e - 262, -4*e^4 + 13*e^3 + 27*e^2 - 92*e - 46, 13*e^4 - 5*e^3 - 124*e^2 + 2*e + 80, -4*e^4 - 4*e^3 + 35*e^2 + 41*e + 32, -16*e^4 + 19*e^3 + 140*e^2 - 94*e - 140, 8*e^4 - 23*e^3 - 79*e^2 + 171*e + 136, -2*e^4 + 8*e^3 + 15*e^2 - 51*e - 28, -6*e^4 + 28*e^3 + 69*e^2 - 229*e - 236, -2*e^4 + 30*e^2 + 11*e - 66, -30*e^4 + 55*e^3 + 286*e^2 - 379*e - 434, -2*e^4 + 9*e^3 + 12*e^2 - 55*e + 2, -10*e^4 + 30*e^3 + 97*e^2 - 215*e - 222, -2*e^4 + 15*e^3 + 23*e^2 - 130*e - 96, 14*e^4 - 9*e^3 - 123*e^2 + 15*e + 92, e^4 - 10*e^3 - 11*e^2 + 84*e + 100, -7*e^4 - 6*e^3 + 64*e^2 + 85*e - 20, -5*e^4 + 32*e^3 + 61*e^2 - 277*e - 228, -10*e^4 + 27*e^3 + 102*e^2 - 195*e - 220, 6*e^4 + 10*e^3 - 44*e^2 - 109*e - 84, 24*e^4 - 37*e^3 - 224*e^2 + 237*e + 288, 10*e^4 - 27*e^3 - 106*e^2 + 212*e + 230, 3*e^4 + 12*e^3 - 26*e^2 - 120*e - 66, -11*e^4 + 25*e^3 + 108*e^2 - 196*e - 196, -19*e^4 + 34*e^3 + 183*e^2 - 225*e - 288, 5*e^4 + 21*e^3 - 35*e^2 - 199*e - 142, e^4 - 8*e^3 - 11*e^2 + 69*e + 2, -e^4 - 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224, 35*e^4 - 82*e^3 - 320*e^2 + 579*e + 552, 36*e^4 - 122*e^3 - 347*e^2 + 919*e + 872, -9*e^4 - 9*e^3 + 74*e^2 + 134*e - 36, 26*e^4 - 50*e^3 - 271*e^2 + 379*e + 518, -10*e^4 + 61*e^3 + 103*e^2 - 472*e - 410, 26*e^4 - 47*e^3 - 263*e^2 + 336*e + 482, -31*e^4 + 58*e^3 + 285*e^2 - 384*e - 462, -17*e^4 + 101*e^3 + 198*e^2 - 834*e - 728, -30*e^4 + 56*e^3 + 290*e^2 - 367*e - 444, -53*e^4 + 96*e^3 + 501*e^2 - 646*e - 710, -5*e^4 - 37*e^3 + 23*e^2 + 353*e + 218, -20*e^4 + 65*e^3 + 195*e^2 - 486*e - 388, -4*e^4 - 7*e^3 + 33*e^2 + 72*e + 16, -26*e^4 + 69*e^3 + 262*e^2 - 530*e - 574, 13*e^4 - 76*e^3 - 145*e^2 + 607*e + 530, 47*e^4 - 35*e^3 - 413*e^2 + 114*e + 230, 21*e^4 - 37*e^3 - 193*e^2 + 223*e + 278, 8*e^4 - 43*e^3 - 78*e^2 + 341*e + 342, 47*e^4 - 135*e^3 - 470*e^2 + 1031*e + 1038, -27*e^4 + 221*e^2 + 107*e + 40, -25*e^4 + 57*e^3 + 242*e^2 - 444*e - 452, -3*e^4 + 6*e^3 + 18*e^2 - 22*e - 60, 33*e^4 - 61*e^3 - 323*e^2 + 407*e + 576, -14*e^4 + 43*e^3 + 157*e^2 - 365*e - 434, -29*e^4 - 10*e^3 + 236*e^2 + 212*e + 94, 14*e^4 + 31*e^3 - 106*e^2 - 346*e - 166, e^4 - 38*e^3 - 40*e^2 + 376*e + 338, 6*e^4 + 38*e^3 - 56*e^2 - 355*e - 142, -18*e^4 + 10*e^3 + 158*e^2 - 9*e - 14, -17*e^4 + 76*e^3 + 152*e^2 - 563*e - 422, 11*e^4 - 40*e^3 - 102*e^2 + 300*e + 282, -11*e^4 - 10*e^3 + 105*e^2 + 94*e - 24, -16*e^4 + 59*e^3 + 132*e^2 - 422*e - 292, -2*e^4 + 50*e^3 + 18*e^2 - 386*e - 240, 18*e^4 - 47*e^3 - 166*e^2 + 341*e + 344, -6*e^4 + 36*e^3 + 79*e^2 - 295*e - 300, 26*e^4 - 53*e^3 - 231*e^2 + 337*e + 304, -13*e^4 - 35*e^3 + 78*e^2 + 386*e + 376, 13*e^4 - 139*e^3 - 162*e^2 + 1171*e + 932, 4*e^4 + 21*e^3 - 47*e^2 - 186*e - 100, 44*e^4 - 70*e^3 - 396*e^2 + 444*e + 516, -15*e^4 - 27*e^3 + 114*e^2 + 315*e + 166, 10*e^4 + 22*e^3 - 71*e^2 - 235*e - 154, 50*e^4 - 60*e^3 - 467*e^2 + 352*e + 536, -e^4 + 87*e^3 + 36*e^2 - 735*e - 632, 23*e^4 - 29*e^3 - 220*e^2 + 167*e + 230, -13*e^4 + 23*e^3 + 115*e^2 - 126*e - 98, -30*e^4 + 33*e^3 + 265*e^2 - 199*e - 192, -17*e^4 + 115*e^3 + 187*e^2 - 938*e - 840, 34*e^4 - 113*e^3 - 339*e^2 + 852*e + 818, 3*e^4 + 87*e^3 - 27*e^2 - 736*e - 414, 20*e^4 - 27*e^3 - 191*e^2 + 147*e + 270, 7*e^4 + 20*e^3 - 70*e^2 - 167*e - 18, 23*e^4 - 19*e^3 - 199*e^2 + 32*e + 116, -56*e^4 + 68*e^3 + 530*e^2 - 420*e - 624, -51*e^4 + 91*e^3 + 484*e^2 - 600*e - 744, -27*e^4 + 106*e^3 + 296*e^2 - 867*e - 876, 10*e^4 - 42*e^3 - 83*e^2 + 310*e + 258, 28*e^4 - 23*e^3 - 253*e^2 + 77*e + 194, -63*e^4 + 110*e^3 + 590*e^2 - 715*e - 866, -17*e^4 + 106*e^3 + 198*e^2 - 875*e - 786, -29*e^4 + 97*e^3 + 290*e^2 - 791*e - 688, 39*e^4 - 19*e^3 - 332*e^2 - 16*e + 128, 3*e^4 + 36*e^3 - 10*e^2 - 316*e - 278, e^4 + 48*e^3 - 8*e^2 - 415*e - 222, 29*e^4 - 96*e^3 - 269*e^2 + 686*e + 580, 6*e^4 + 24*e^3 - 46*e^2 - 235*e - 152, -33*e^4 - 5*e^3 + 276*e^2 + 180*e + 28, -e^4 + 47*e^3 + 19*e^2 - 434*e - 276, 6*e^4 - 6*e^3 - 85*e^2 + 56*e + 174, -13*e^4 + 63*e^3 + 135*e^2 - 479*e - 394, 31*e^4 - 74*e^3 - 296*e^2 + 531*e + 470, -23*e^4 + 86*e^3 + 226*e^2 - 664*e - 570, -16*e^4 + 51*e^3 + 172*e^2 - 365*e - 468, 13*e^4 - 69*e^3 - 114*e^2 + 525*e + 388, -16*e^4 + 48*e^3 + 159*e^2 - 313*e - 364, 66*e^4 - 153*e^3 - 622*e^2 + 1074*e + 1144, 2*e^4 + 5*e^3 - 29*e^2 + 4*e + 84, -6*e^4 - 32*e^3 + 42*e^2 + 296*e + 236, -38*e^4 + 91*e^3 + 379*e^2 - 682*e - 718, -32*e^4 + 50*e^3 + 300*e^2 - 319*e - 438, 19*e^4 - 139*e^3 - 205*e^2 + 1123*e + 954, 3*e^4 + 15*e^3 - 26*e^2 - 110*e - 22, -47*e^4 + 40*e^3 + 408*e^2 - 143*e - 274, -14*e^4 + 33*e^3 + 153*e^2 - 233*e - 282, 17*e^4 + 37*e^3 - 158*e^2 - 359*e - 130, 39*e^4 - 62*e^3 - 375*e^2 + 415*e + 590, -20*e^4 - 21*e^3 + 204*e^2 + 215*e - 120, 44*e^4 - 89*e^3 - 405*e^2 + 581*e + 668, -55*e^4 + 84*e^3 + 520*e^2 - 559*e - 688, -9*e^4 + 93*e^3 + 120*e^2 - 796*e - 672, 46*e^4 - 161*e^3 - 463*e^2 + 1209*e + 1160, 31*e^4 - 260*e^2 - 125*e - 12, -30*e^4 + 115*e^3 + 313*e^2 - 874*e - 864, -10*e^4 + 44*e^3 + 102*e^2 - 336*e - 336, 20*e^4 - 43*e^3 - 201*e^2 + 277*e + 358, -9*e^4 - 34*e^3 + 72*e^2 + 323*e + 190, -11*e^4 - 17*e^3 + 123*e^2 + 161*e - 62, 2*e^4 + 87*e^3 + 27*e^2 - 775*e - 670, -24*e^4 + 25*e^3 + 230*e^2 - 123*e - 326, -15*e^4 + 106*e^3 + 167*e^2 - 862*e - 734, -19*e^4 + 90*e^3 + 207*e^2 - 705*e - 684, -25*e^4 - 27*e^3 + 229*e^2 + 321*e + 32, 2*e^4 - 60*e^3 - 59*e^2 + 550*e + 478, 13*e^4 - 20*e^3 - 139*e^2 + 178*e + 318, 35*e^4 - 88*e^3 - 345*e^2 + 668*e + 728, 66*e^4 - 84*e^3 - 620*e^2 + 522*e + 708, 3*e^4 + 49*e^3 - 7*e^2 - 449*e - 306, -23*e^4 + 13*e^3 + 221*e^2 - 37*e - 226, 30*e^4 - 41*e^3 - 257*e^2 + 220*e + 212, 7*e^4 + 16*e^3 - 76*e^2 - 119*e + 44, -29*e^4 + 146*e^3 + 316*e^2 - 1210*e - 1062, 6*e^4 - 25*e^3 - 57*e^2 + 211*e + 138, 41*e^4 - 87*e^3 - 414*e^2 + 653*e + 774, -18*e^4 + 29*e^3 + 179*e^2 - 154*e - 322, -10*e^4 + 77*e^3 + 115*e^2 - 604*e - 524, -8*e^4 + 18*e^3 + 74*e^2 - 117*e - 148, -12*e^4 - 7*e^3 + 93*e^2 + 121*e + 96, -4*e^4 - 54*e^3 + 22*e^2 + 476*e + 280, 18*e^4 + 53*e^3 - 143*e^2 - 498*e - 400, 31*e^4 - 35*e^3 - 292*e^2 + 209*e + 296, 9*e^4 - 95*e^3 - 108*e^2 + 793*e + 646, 46*e^4 - 127*e^3 - 451*e^2 + 943*e + 998, -6*e^4 - 36*e^3 + 31*e^2 + 349*e + 284, 8*e^4 - 10*e^3 - 107*e^2 + 79*e + 248, 48*e^4 - 61*e^3 - 445*e^2 + 348*e + 514, -30*e^4 + 74*e^3 + 299*e^2 - 542*e - 606, -19*e^4 + 68*e^3 + 204*e^2 - 529*e - 488, -6*e^4 - 7*e^3 + 53*e^2 + 104*e + 24, 43*e^4 - 30*e^3 - 416*e^2 + 133*e + 402, -13*e^4 - 8*e^3 + 105*e^2 + 114*e + 82, 34*e^4 - 39*e^3 - 293*e^2 + 194*e + 212, 39*e^4 - 59*e^3 - 351*e^2 + 350*e + 404, 56*e^4 - 115*e^3 - 536*e^2 + 773*e + 900, -31*e^4 + 27*e^3 + 283*e^2 - 85*e - 312, -5*e^4 - 17*e^3 + 39*e^2 + 153*e + 18, -37*e^4 + 24*e^3 + 321*e^2 - 26*e - 174, 32*e^4 - 89*e^3 - 307*e^2 + 657*e + 624, -15*e^4 - 34*e^3 + 114*e^2 + 365*e + 144, -26*e^4 + 73*e^3 + 267*e^2 - 567*e - 630, 4*e^4 - e^3 - 18*e^2 - 65*e - 86, -7*e^4 + 57*e^3 + 105*e^2 - 484*e - 510, 62*e^4 - 77*e^3 - 571*e^2 + 439*e + 626, 18*e^4 - 87*e^3 - 217*e^2 + 728*e + 732, -43*e^4 + 58*e^3 + 391*e^2 - 348*e - 420, 13*e^4 - 25*e^3 - 110*e^2 + 184*e + 150, -29*e^4 + e^3 + 272*e^2 + 59*e - 154, -65*e^4 + 165*e^3 + 641*e^2 - 1250*e - 1288, -45*e^4 + 136*e^3 + 447*e^2 - 1029*e - 964, -37*e^4 + 50*e^3 + 341*e^2 - 280*e - 496, 8*e^4 - 39*e^3 - 97*e^2 + 314*e + 408, -70*e^4 + 137*e^3 + 658*e^2 - 913*e - 1076, 51*e^4 - 134*e^3 - 512*e^2 + 996*e + 1024, 60*e^4 - 115*e^3 - 555*e^2 + 769*e + 812, e^4 - 68*e^3 - 21*e^2 + 582*e + 380, -22*e^4 + 15*e^3 + 226*e^2 - 70*e - 334, 42*e^4 - 45*e^3 - 390*e^2 + 280*e + 338, 11*e^4 - 119*e^2 - 42*e + 152, -37*e^4 + 57*e^3 + 330*e^2 - 343*e - 392, 2*e^4 - 89*e^3 - 46*e^2 + 779*e + 476, e^4 - 23*e^3 - 14*e^2 + 233*e + 164, -42*e^4 + 97*e^3 + 400*e^2 - 704*e - 754, 82*e^4 - 104*e^3 - 768*e^2 + 633*e + 878, 4*e^4 - 40*e^3 - 49*e^2 + 340*e + 332, -6*e^4 + 6*e^3 + 51*e^2 + 13*e - 92, 36*e^4 - 40*e^3 - 326*e^2 + 186*e + 320, -3*e^4 + 44*e^3 + 66*e^2 - 398*e - 436, 14*e^4 + 31*e^3 - 94*e^2 - 329*e - 308, -38*e^4 + 46*e^3 + 344*e^2 - 230*e - 384, 21*e^4 - 48*e^3 - 222*e^2 + 362*e + 460, -25*e^4 + 85*e^3 + 245*e^2 - 656*e - 608, -9*e^4 + 73*e^3 + 95*e^2 - 577*e - 534, -29*e^4 + 37*e^3 + 258*e^2 - 223*e - 198, 12*e^4 - 26*e^3 - 131*e^2 + 214*e + 294, -44*e^4 + 63*e^3 + 391*e^2 - 367*e - 442, -28*e^4 + 13*e^3 + 270*e^2 - 57*e - 274, 31*e^4 - 12*e^3 - 283*e^2 + 4*e + 158, 27*e^4 - 44*e^3 - 247*e^2 + 286*e + 344, 27*e^4 + 49*e^3 - 231*e^2 - 515*e - 212, 13*e^4 + 2*e^3 - 123*e^2 - 36*e + 102, 3*e^4 + 60*e^3 + 7*e^2 - 553*e - 402] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([7, 7, w])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]