/* 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([19,19,-w + 2]) 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^10 + 27*x^8 + 253*x^6 + 968*x^4 + 1324*x^2 + 256 K. = NumberField(heckePol) hecke_eigenvalues_array = [27/2384*e^9 + 661/2384*e^7 + 5387/2384*e^5 + 4279/596*e^3 + 4639/596*e, e, 17/596*e^8 + 361/596*e^6 + 2255/596*e^4 + 1851/298*e^2 - 313/149, 27/2384*e^9 + 661/2384*e^7 + 5387/2384*e^5 + 4279/596*e^3 + 5235/596*e, -39/2384*e^9 - 1021/2384*e^7 - 8907/2384*e^5 - 3645/298*e^3 - 7661/596*e, -3/596*e^9 - 45/298*e^7 - 220/149*e^5 - 3011/596*e^3 - 915/298*e, -3/298*e^9 - 45/149*e^7 - 440/149*e^5 - 3011/298*e^3 - 1064/149*e, -1/298*e^8 - 15/149*e^6 - 97/149*e^4 + 387/298*e^2 + 1036/149, 1, -11/2384*e^9 - 181/2384*e^7 + 101/2384*e^5 + 2517/596*e^3 + 5549/596*e, 27/1192*e^9 + 661/1192*e^7 + 5387/1192*e^5 + 3981/298*e^3 + 2255/298*e, -13/1192*e^9 - 241/1192*e^7 - 883/1192*e^5 + 1845/596*e^3 + 2175/149*e, -19/1192*e^9 - 421/1192*e^7 - 2643/1192*e^5 - 583/298*e^3 + 2541/298*e, 17/298*e^8 + 361/298*e^6 + 2255/298*e^4 + 1702/149*e^2 - 1520/149, -21/298*e^8 - 481/298*e^6 - 3329/298*e^4 - 3610/149*e^2 - 2084/149, -93/2384*e^9 - 2343/2384*e^7 - 19681/2384*e^5 - 3962/149*e^3 - 15747/596*e, 93/2384*e^9 + 2343/2384*e^7 + 19681/2384*e^5 + 3962/149*e^3 + 15747/596*e, 69/596*e^8 + 1623/596*e^6 + 12045/596*e^4 + 7293/149*e^2 + 3594/149, -19/298*e^8 - 421/298*e^6 - 2941/298*e^4 - 3103/149*e^2 + 910/149, 11/1192*e^9 + 181/1192*e^7 - 101/1192*e^5 - 2517/298*e^3 - 6145/298*e, -3/149*e^9 - 211/596*e^7 - 391/596*e^5 + 7475/596*e^3 + 11985/298*e, -10/149*e^8 - 451/298*e^6 - 3135/298*e^4 - 6713/298*e^2 - 1034/149, 1/149*e^8 + 30/149*e^6 + 194/149*e^4 + 60/149*e^2 + 1206/149, 3/149*e^9 + 90/149*e^7 + 880/149*e^5 + 3011/149*e^3 + 2128/149*e, -69/2384*e^9 - 1623/2384*e^7 - 12641/2384*e^5 - 4913/298*e^3 - 10895/596*e, 27/2384*e^9 + 661/2384*e^7 + 5387/2384*e^5 + 4279/596*e^3 + 3447/596*e, 185/2384*e^9 + 4507/2384*e^7 + 35741/2384*e^5 + 6244/149*e^3 + 15175/596*e, 17/298*e^8 + 361/298*e^6 + 2255/298*e^4 + 2000/149*e^2 - 626/149, 21/298*e^8 + 481/298*e^6 + 3329/298*e^4 + 3610/149*e^2 + 1190/149, -17/298*e^8 - 361/298*e^6 - 2255/298*e^4 - 2149/149*e^2 - 1162/149, 65/596*e^8 + 1503/596*e^6 + 11269/596*e^4 + 7531/149*e^2 + 4176/149, 7/149*e^8 + 271/298*e^6 + 1375/298*e^4 + 691/298*e^2 - 1392/149, 1/298*e^9 + 15/149*e^7 + 97/149*e^5 - 89/298*e^3 + 7/149*e, 81/2384*e^9 + 1983/2384*e^7 + 16161/2384*e^5 + 12241/596*e^3 + 7361/596*e, 155/2384*e^9 + 3905/2384*e^7 + 32007/2384*e^5 + 5610/149*e^3 + 10749/596*e, 39/1192*e^9 + 1021/1192*e^7 + 8907/1192*e^5 + 3645/149*e^3 + 8257/298*e, -5/149*e^8 - 150/149*e^6 - 1417/149*e^4 - 3876/149*e^2 + 526/149, 173/1192*e^9 + 4147/1192*e^7 + 32221/1192*e^5 + 22263/298*e^3 + 16027/298*e, -2/149*e^9 - 60/149*e^7 - 537/149*e^5 - 1312/149*e^3 + 568/149*e, 23/596*e^8 + 541/596*e^6 + 4015/596*e^4 + 1835/149*e^2 - 2676/149, 57/596*e^8 + 1263/596*e^6 + 8525/596*e^4 + 4431/149*e^2 + 1168/149, 15/298*e^8 + 301/298*e^6 + 1867/298*e^4 + 2089/149*e^2 - 44/149, -39/596*e^8 - 1021/596*e^6 - 8907/596*e^4 - 6992/149*e^2 - 3936/149, 125/2384*e^9 + 3303/2384*e^7 + 30657/2384*e^5 + 7360/149*e^3 + 36123/596*e, 199/2384*e^9 + 5225/2384*e^7 + 46503/2384*e^5 + 39639/596*e^3 + 38319/596*e, 10/149*e^9 + 451/298*e^7 + 3135/298*e^5 + 7011/298*e^3 + 1630/149*e, -3/596*e^9 - 45/298*e^7 - 220/149*e^5 - 3607/596*e^3 - 4491/298*e, 139/2384*e^9 + 3425/2384*e^7 + 26519/2384*e^5 + 4209/149*e^3 + 11885/596*e, -23/596*e^9 - 541/596*e^7 - 4015/596*e^5 - 2580/149*e^3 - 2539/149*e, -2/149*e^8 - 60/149*e^6 - 388/149*e^4 + 327/149*e^2 + 3250/149, -49/298*e^8 - 1023/298*e^6 - 6377/298*e^4 - 5940/149*e^2 - 1982/149, 9/149*e^9 + 391/298*e^7 + 2449/298*e^5 + 3315/298*e^3 - 2109/149*e, -55/596*e^9 - 1203/596*e^7 - 8137/596*e^5 - 8951/298*e^3 - 2204/149*e, -37/149*e^8 - 812/149*e^6 - 5390/149*e^4 - 10564/149*e^2 - 816/149, 1/298*e^8 + 15/149*e^6 + 246/149*e^4 + 3189/298*e^2 + 1348/149, -145/596*e^8 - 3307/596*e^6 - 23809/596*e^4 - 14393/149*e^2 - 6244/149, 11/298*e^8 + 181/298*e^6 + 793/298*e^4 + 628/149*e^2 + 1716/149, 21/298*e^8 + 481/298*e^6 + 3329/298*e^4 + 3014/149*e^2 + 296/149, -2/149*e^8 - 60/149*e^6 - 537/149*e^4 - 1610/149*e^2 - 1816/149, -143/2384*e^9 - 3545/2384*e^7 - 28487/2384*e^5 - 20621/596*e^3 - 15475/596*e, 29/2384*e^9 + 1019/2384*e^7 + 12629/2384*e^5 + 15335/596*e^3 + 21781/596*e, 26/149*e^8 + 631/149*e^6 + 4746/149*e^4 + 11096/149*e^2 + 3046/149, -1/298*e^8 - 179/298*e^6 - 3025/298*e^4 - 6884/149*e^2 - 5222/149, -109/1192*e^9 - 2823/1192*e^7 - 23977/1192*e^5 - 9236/149*e^3 - 15207/298*e, 257/2384*e^9 + 6667/2384*e^7 + 56861/2384*e^5 + 21521/298*e^3 + 30327/596*e, 65/2384*e^9 + 1503/2384*e^7 + 10673/2384*e^5 + 4849/596*e^3 - 4019/596*e, -215/2384*e^9 - 5109/2384*e^7 - 39475/2384*e^5 - 7027/149*e^3 - 24965/596*e, 199/2384*e^9 + 4629/2384*e^7 + 33987/2384*e^5 + 5030/149*e^3 + 4645/596*e, 137/2384*e^9 + 3067/2384*e^7 + 19277/2384*e^5 + 1147/149*e^3 - 13601/596*e, 6/149*e^8 + 180/149*e^6 + 1760/149*e^4 + 5724/149*e^2 + 4256/149, -17/149*e^8 - 361/149*e^6 - 2404/149*e^4 - 5639/149*e^2 - 5900/149, -31/596*e^9 - 158/149*e^7 - 1815/298*e^5 - 3797/596*e^3 + 3955/298*e, -93/1192*e^9 - 2343/1192*e^7 - 19681/1192*e^5 - 7775/149*e^3 - 13363/298*e, 351/2384*e^9 + 8593/2384*e^7 + 70031/2384*e^5 + 53839/596*e^3 + 46599/596*e, -123/1192*e^9 - 2945/1192*e^7 - 22223/1192*e^5 - 6957/149*e^3 - 6465/298*e, 1/149*e^8 + 30/149*e^6 + 343/149*e^4 + 2146/149*e^2 + 2398/149, 1/149*e^8 + 30/149*e^6 + 343/149*e^4 + 1252/149*e^2 - 1178/149, 25/596*e^8 + 303/596*e^6 - 663/596*e^4 - 2754/149*e^2 - 1924/149, 57/298*e^8 + 1263/298*e^6 + 8525/298*e^4 + 8862/149*e^2 + 2336/149, -71/2384*e^9 - 1981/2384*e^7 - 17499/2384*e^5 - 6269/298*e^3 - 8369/596*e, -29/298*e^9 - 721/298*e^7 - 6073/298*e^5 - 9959/149*e^3 - 10484/149*e, -1/298*e^8 - 179/298*e^6 - 2727/298*e^4 - 5096/149*e^2 - 2242/149, 14/149*e^8 + 271/149*e^6 + 1524/149*e^4 + 3224/149*e^2 + 4666/149, -3/2384*e^9 - 537/2384*e^7 - 10863/2384*e^5 - 4742/149*e^3 - 46573/596*e, -99/2384*e^9 - 2225/2384*e^7 - 16375/2384*e^5 - 6181/298*e^3 - 16513/596*e, 43/596*e^8 + 1141/596*e^6 + 10875/596*e^4 + 10032/149*e^2 + 7526/149, 11/298*e^8 + 181/298*e^6 + 793/298*e^4 + 926/149*e^2 + 2610/149, 22/149*e^8 + 511/149*e^6 + 3672/149*e^4 + 7578/149*e^2 + 1202/149, -31/596*e^8 - 781/596*e^6 - 6759/596*e^4 - 5233/149*e^2 - 1226/149, 12/149*e^8 + 571/298*e^6 + 3911/298*e^4 + 5165/298*e^2 - 3706/149, 57/298*e^8 + 706/149*e^6 + 5529/149*e^4 + 27409/298*e^2 + 4422/149, -103/2384*e^9 - 2345/2384*e^7 - 13575/2384*e^5 + 1137/596*e^3 + 24597/596*e, 77/596*e^9 + 1863/596*e^7 + 14789/596*e^5 + 11138/149*e^3 + 11370/149*e, 69/298*e^8 + 1623/298*e^6 + 12045/298*e^4 + 14586/149*e^2 + 5400/149, -3/298*e^8 - 239/298*e^6 - 3115/298*e^4 - 5603/149*e^2 - 5236/149, 16/149*e^9 + 1473/596*e^7 + 10181/596*e^5 + 19187/596*e^3 - 893/298*e, -31/2384*e^9 - 781/2384*e^7 - 4971/2384*e^5 + 219/149*e^3 + 15015/596*e, -69/596*e^8 - 1623/596*e^6 - 11449/596*e^4 - 5505/149*e^2 - 614/149, 1/149*e^8 + 30/149*e^6 + 194/149*e^4 + 60/149*e^2 - 582/149, -109/2384*e^9 - 2823/2384*e^7 - 25169/2384*e^5 - 5512/149*e^3 - 22955/596*e, -6/149*e^9 - 211/298*e^7 - 689/298*e^5 + 2409/298*e^3 + 2151/149*e, 127/596*e^8 + 3065/596*e^6 + 22403/596*e^4 + 11143/149*e^2 - 2610/149, -3/149*e^8 - 90/149*e^6 - 880/149*e^4 - 2862/149*e^2 + 2938/149, -12/149*e^8 - 211/149*e^6 - 987/149*e^4 - 869/149*e^2 - 168/149, -38/149*e^8 - 842/149*e^6 - 5733/149*e^4 - 12859/149*e^2 - 7684/149, -81/2384*e^9 - 1387/2384*e^7 - 3645/2384*e^5 + 2745/298*e^3 + 13201/596*e, -79/1192*e^9 - 1923/1192*e^7 - 15177/1192*e^5 - 21293/596*e^3 - 3677/149*e, -161/2384*e^9 - 4383/2384*e^7 - 38833/2384*e^5 - 29533/596*e^3 - 17773/596*e, 1/2384*e^9 - 417/2384*e^7 - 11279/2384*e^5 - 23527/596*e^3 - 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13991/2384*e^7 - 124169/2384*e^5 - 100493/596*e^3 - 101877/596*e, -233/596*e^9 - 2899/298*e^7 - 12567/149*e^5 - 183989/596*e^3 - 127089/298*e, 359/2384*e^9 + 10621/2384*e^7 + 104363/2384*e^5 + 47169/298*e^3 + 106525/596*e, 67/298*e^8 + 967/298*e^6 + 1227/298*e^4 - 6632/149*e^2 - 2660/149, -80/149*e^8 - 1655/149*e^6 - 10007/149*e^4 - 14485/149*e^2 + 22720/149, 37/298*e^8 + 555/149*e^6 + 5824/149*e^4 + 44685/298*e^2 + 20374/149, -85/149*e^8 - 3759/298*e^6 - 25679/298*e^4 - 54453/298*e^2 - 14898/149, 74/149*e^8 + 1773/149*e^6 + 13313/149*e^4 + 31707/149*e^2 + 4016/149, 257/298*e^8 + 5773/298*e^6 + 38981/298*e^4 + 35275/149*e^2 - 5204/149, 377/1192*e^9 + 8479/1192*e^7 + 56897/1192*e^5 + 24429/298*e^3 - 18423/298*e, -545/1192*e^9 - 15009/1192*e^7 - 137467/1192*e^5 - 228973/596*e^3 - 47479/149*e, -321/298*e^8 - 7693/298*e^6 - 57655/298*e^4 - 69528/149*e^2 - 31600/149, -131/298*e^8 - 1816/149*e^6 - 16432/149*e^4 - 104561/298*e^2 - 26992/149, 45/596*e^8 + 903/596*e^6 + 6793/596*e^4 + 4698/149*e^2 - 6622/149, 141/298*e^8 + 2889/298*e^6 + 16775/298*e^4 + 14064/149*e^2 + 9182/149, 49/298*e^8 + 437/149*e^6 + 1475/149*e^4 - 9427/298*e^2 - 3382/149, -281/596*e^8 - 6195/596*e^6 - 43041/596*e^4 - 22095/149*e^2 + 10862/149, -237/596*e^9 - 5173/596*e^7 - 34207/596*e^5 - 33483/298*e^3 - 904/149*e, -211/2384*e^9 - 5585/2384*e^7 - 52407/2384*e^5 - 24603/298*e^3 - 58029/596*e, 217/596*e^9 + 2659/298*e^7 + 10450/149*e^5 + 110913/596*e^3 + 25359/298*e, -943/2384*e^9 - 23969/2384*e^7 - 203951/2384*e^5 - 160463/596*e^3 - 118999/596*e, -95/298*e^8 - 2105/298*e^6 - 12917/298*e^4 - 7916/149*e^2 - 6774/149, 679/596*e^8 + 15453/596*e^6 + 112207/596*e^4 + 68742/149*e^2 + 32102/149, 7/149*e^8 - 27/298*e^6 - 3393/298*e^4 - 17785/298*e^2 - 15994/149, -343/596*e^8 - 8353/596*e^6 - 63115/596*e^4 - 35392/149*e^2 - 6490/149, -65/298*e^8 - 1503/298*e^6 - 10673/298*e^4 - 10890/149*e^2 - 604/149, -139/298*e^8 - 3127/298*e^6 - 21155/298*e^4 - 21007/149*e^2 - 2016/149, -117/149*e^8 - 2765/149*e^6 - 20910/149*e^4 - 55743/149*e^2 - 35610/149, -107/149*e^8 - 2465/149*e^6 - 17331/149*e^4 - 36816/149*e^2 - 6862/149, -11/1192*e^9 - 181/1192*e^7 - 2283/1192*e^5 - 4635/298*e^3 - 12927/298*e, -831/2384*e^9 - 20609/2384*e^7 - 165535/2384*e^5 - 115871/596*e^3 - 58411/596*e, 209/298*e^8 + 4929/298*e^6 + 35331/298*e^4 + 40689/149*e^2 + 29624/149, -25/596*e^8 - 303/596*e^6 - 1721/596*e^4 - 6633/149*e^2 - 13572/149, -43/1192*e^9 - 843/1192*e^7 - 2233/1192*e^5 + 21805/596*e^3 + 25143/149*e, 2/149*e^9 + 91/596*e^7 + 1403/596*e^5 + 19105/596*e^3 + 19575/298*e, -25/298*e^8 - 303/298*e^6 + 365/298*e^4 + 7296/149*e^2 + 23218/149, -78/149*e^8 - 1595/149*e^6 - 9023/149*e^4 - 12577/149*e^2 - 8542/149, 401/596*e^8 + 8603/596*e^6 + 51421/596*e^4 + 17041/149*e^2 - 3588/149, -309/298*e^8 - 3592/149*e^6 - 25801/149*e^4 - 114943/298*e^2 - 11252/149, 853/2384*e^9 + 23951/2384*e^7 + 227913/2384*e^5 + 50916/149*e^3 + 210915/596*e, 249/1192*e^9 + 5533/1192*e^7 + 37727/1192*e^5 + 45167/596*e^3 + 11797/149*e, 243/298*e^8 + 5949/298*e^6 + 45205/298*e^4 + 51096/149*e^2 + 11684/149, -43/149*e^8 - 1290/149*e^6 - 11471/149*e^4 - 28506/149*e^2 + 292/149, -173/2384*e^9 - 4743/2384*e^7 - 42353/2384*e^5 - 7391/149*e^3 + 1257/596*e, 1949/2384*e^9 + 46103/2384*e^7 + 348753/2384*e^5 + 57708/149*e^3 + 148595/596*e, -107/149*e^8 - 2614/149*e^6 - 20013/149*e^4 - 47246/149*e^2 - 24742/149, -213/298*e^8 - 4453/298*e^6 - 26869/298*e^4 - 22780/149*e^2 - 17434/149, 139/596*e^9 + 3723/596*e^7 + 31585/596*e^5 + 41569/298*e^3 + 1008/149*e, 3/1192*e^9 - 59/1192*e^7 - 2845/1192*e^5 - 3531/298*e^3 + 12005/298*e, 21/149*e^8 + 481/149*e^6 + 3329/149*e^4 + 6624/149*e^2 - 7454/149, 45/298*e^8 + 1201/298*e^6 + 10071/298*e^4 + 13568/149*e^2 + 18642/149, 415/1192*e^9 + 10513/1192*e^7 + 94367/1192*e^5 + 92049/298*e^3 + 130859/298*e, 1005/2384*e^9 + 28511/2384*e^7 + 271705/2384*e^5 + 120703/298*e^3 + 225751/596*e, -263/298*e^8 - 5953/298*e^6 - 44317/298*e^4 - 59593/149*e^2 - 27320/149, -159/298*e^8 - 3727/298*e^6 - 27419/298*e^4 - 31888/149*e^2 + 4400/149, -41/149*e^9 - 1081/149*e^7 - 9295/149*e^5 - 26598/149*e^3 - 11302/149*e, 1/16*e^9 + 23/16*e^7 + 105/16*e^5 - 97/4*e^3 - 387/4*e, -162/149*e^8 - 3966/149*e^6 - 31130/149*e^4 - 83475/149*e^2 - 42796/149, 49/298*e^8 + 586/149*e^6 + 4604/149*e^4 + 23353/298*e^2 - 6064/149, -19/1192*e^9 - 719/1192*e^7 - 14861/1192*e^5 - 65385/596*e^3 - 39779/149*e, 59/1192*e^9 + 2813/1192*e^7 + 40203/1192*e^5 + 53631/298*e^3 + 87893/298*e, 107/298*e^8 + 2167/298*e^6 + 12265/298*e^4 + 8425/149*e^2 + 14010/149, -55/149*e^8 - 1203/149*e^6 - 8435/149*e^4 - 21180/149*e^2 - 19842/149, 887/2384*e^9 + 21097/2384*e^7 + 160903/2384*e^5 + 106579/596*e^3 + 89003/596*e, 699/2384*e^9 + 16649/2384*e^7 + 129199/2384*e^5 + 42567/298*e^3 + 23977/596*e, 413/2384*e^9 + 10751/2384*e^7 + 94873/2384*e^5 + 43551/298*e^3 + 141431/596*e, -391/1192*e^9 - 9197/1192*e^7 - 64083/1192*e^5 - 13437/149*e^3 + 17927/298*e, -105/298*e^8 - 2703/298*e^6 - 20817/298*e^4 - 22371/149*e^2 - 4758/149, 92/149*e^8 + 1866/149*e^6 + 10547/149*e^4 + 11331/149*e^2 - 10930/149, -131/2384*e^9 - 2589/2384*e^7 - 12451/2384*e^5 + 1909/596*e^3 + 26585/596*e, 257/1192*e^9 + 6965/1192*e^7 + 63119/1192*e^5 + 105007/596*e^3 + 22688/149*e, -135/298*e^8 - 1280/149*e^6 - 5943/149*e^4 - 501/298*e^2 + 6654/149, 1/149*e^8 + 30/149*e^6 - 253/149*e^4 - 6347/149*e^2 - 16674/149, 92/149*e^8 + 1866/149*e^6 + 11441/149*e^4 + 24741/149*e^2 + 25724/149, -11/149*e^8 + 85/298*e^6 + 7503/298*e^4 + 45317/298*e^2 + 25772/149, -327/1192*e^9 - 10257/1192*e^7 - 108287/1192*e^5 - 107417/298*e^3 - 112671/298*e, 381/1192*e^9 + 10387/1192*e^7 + 99989/1192*e^5 + 101373/298*e^3 + 135359/298*e, 197/298*e^9 + 8989/596*e^7 + 64069/596*e^5 + 151333/596*e^3 + 42243/298*e, 205/298*e^9 + 2330/149*e^7 + 16309/149*e^5 + 69069/298*e^3 + 839/149*e, -106/149*e^8 - 1988/149*e^6 - 9985/149*e^4 - 7552/149*e^2 + 21164/149, -139/149*e^8 - 2829/149*e^6 - 16536/149*e^4 - 25773/149*e^2 - 9992/149, -95/298*e^8 - 2403/298*e^6 - 17387/298*e^4 - 13578/149*e^2 + 25112/149, 169/298*e^8 + 1939/149*e^6 + 13562/149*e^4 + 55585/298*e^2 - 5224/149, 267/298*e^8 + 5477/298*e^6 + 33471/298*e^4 + 33936/149*e^2 + 32712/149, -143/596*e^8 - 3545/596*e^6 - 29083/596*e^4 - 20472/149*e^2 - 22776/149, -177/298*e^8 - 1910/149*e^6 - 12997/149*e^4 - 66197/298*e^2 - 23738/149, 147/298*e^8 + 3665/298*e^6 + 28667/298*e^4 + 34061/149*e^2 + 11906/149, 351/596*e^9 + 4371/298*e^7 + 18141/149*e^5 + 231895/596*e^3 + 122551/298*e, -1251/2384*e^9 - 29633/2384*e^7 - 230327/2384*e^5 - 82765/298*e^3 - 130209/596*e, 9/149*e^9 + 931/596*e^7 + 7431/596*e^5 + 11845/596*e^3 - 15095/298*e, 113/596*e^9 + 1397/298*e^7 + 5257/149*e^5 + 41497/596*e^3 - 8447/298*e, -217/298*e^8 - 2063/149*e^6 - 10321/149*e^4 - 17639/298*e^2 - 476/149, -281/298*e^8 - 6493/298*e^6 - 46617/298*e^4 - 51640/149*e^2 - 7480/149, 401/298*e^8 + 9199/298*e^6 + 65427/298*e^4 + 74014/149*e^2 + 24710/149, 26/149*e^8 + 482/149*e^6 + 2362/149*e^4 + 2752/149*e^2 + 10794/149, 76/149*e^8 + 4113/298*e^6 + 35597/298*e^4 + 100755/298*e^2 + 33844/149, 115/149*e^8 + 2705/149*e^6 + 19628/149*e^4 + 42511/149*e^2 + 1908/149, 1499/2384*e^9 + 36477/2384*e^7 + 287379/2384*e^5 + 203669/596*e^3 + 159983/596*e, 701/1192*e^9 + 16411/1192*e^7 + 119157/1192*e^5 + 67135/298*e^3 + 19961/298*e, -38/149*e^8 - 842/149*e^6 - 5733/149*e^4 - 13902/149*e^2 + 5726/149, -171/298*e^8 - 2267/149*e^6 - 18673/149*e^4 - 91167/298*e^2 - 8498/149, 69/596*e^8 + 1027/596*e^6 + 4297/596*e^4 + 3419/149*e^2 + 8064/149, 265/298*e^8 + 5715/298*e^6 + 39043/298*e^4 + 47733/149*e^2 + 32400/149, -1/298*e^8 - 15/149*e^6 - 991/149*e^4 - 21963/298*e^2 - 6414/149, 303/298*e^8 + 7153/298*e^6 + 50885/298*e^4 + 49171/149*e^2 - 12034/149, -379/596*e^9 - 9433/596*e^7 - 79039/596*e^5 - 63348/149*e^3 - 55935/149*e, -24/149*e^9 - 1589/298*e^7 - 17805/298*e^5 - 79019/298*e^3 - 60085/149*e, 103/298*e^8 + 1098/149*e^6 + 7160/149*e^4 + 33149/298*e^2 + 27392/149, 165/149*e^8 + 3609/149*e^6 + 23666/149*e^4 + 41041/149*e^2 - 9908/149, -39/298*e^8 - 1021/298*e^6 - 9801/298*e^4 - 21136/149*e^2 - 24858/149, -15/149*e^8 - 152/149*e^6 + 517/149*e^4 + 5954/149*e^2 + 9326/149, -31/298*e^9 - 167/149*e^7 + 1314/149*e^5 + 31367/298*e^3 + 23325/149*e, 991/2384*e^9 + 24813/2384*e^7 + 205515/2384*e^5 + 38545/149*e^3 + 121849/596*e, -34/149*e^8 - 1020/149*e^6 - 8831/149*e^4 - 21261/149*e^2 - 3456/149, -31/298*e^8 - 483/298*e^6 - 2885/298*e^4 - 5400/149*e^2 - 1260/149, -631/2384*e^9 - 13417/2384*e^7 - 75479/2384*e^5 - 8571/596*e^3 + 64469/596*e, -66/149*e^9 - 6579/596*e^7 - 55239/596*e^5 - 184657/596*e^3 - 126263/298*e, 211/149*e^8 + 9829/298*e^6 + 71289/298*e^4 + 167317/298*e^2 + 37820/149, 1/298*e^8 - 417/298*e^6 - 7107/298*e^4 - 15764/149*e^2 - 5804/149, 213/1192*e^9 + 4155/1192*e^7 + 19717/1192*e^5 - 1871/298*e^3 - 18699/298*e, 341/596*e^9 + 4221/298*e^7 + 17507/149*e^5 + 229805/596*e^3 + 140957/298*e, 91/596*e^8 + 1985/596*e^6 + 11247/596*e^4 + 1216/149*e^2 - 7504/149, -40/149*e^8 - 1051/149*e^6 - 8505/149*e^4 - 21770/149*e^2 - 23804/149, 155/298*e^8 + 3607/298*e^6 + 27537/298*e^4 + 36238/149*e^2 + 14048/149, -221/596*e^8 - 4395/596*e^6 - 26633/596*e^4 - 10914/149*e^2 + 11668/149, 7/2384*e^9 - 2919/2384*e^7 - 69417/2384*e^5 - 119989/596*e^3 - 229361/596*e, 841/2384*e^9 + 21803/2384*e^7 + 191613/2384*e^5 + 40143/149*e^3 + 152167/596*e, 1141/596*e^8 + 25439/596*e^6 + 175909/596*e^4 + 96085/149*e^2 + 24332/149, -32/149*e^8 - 364/149*e^6 + 1391/149*e^4 + 20728/149*e^2 + 23392/149, 527/1192*e^9 + 13277/1192*e^7 + 113115/1192*e^5 + 47535/149*e^3 + 100259/298*e, 115/2384*e^9 + 321/2384*e^7 - 21049/2384*e^5 - 15155/298*e^3 - 12635/596*e, -85/596*e^9 - 2699/596*e^7 - 27665/596*e^5 - 23327/149*e^3 - 7375/149*e, -323/2384*e^9 - 6561/2384*e^7 - 31223/2384*e^5 + 6145/298*e^3 + 115611/596*e, 277/2384*e^9 + 11439/2384*e^7 + 144777/2384*e^5 + 40859/149*e^3 + 199363/596*e, 327/1192*e^9 + 6979/1192*e^7 + 38257/1192*e^5 - 4047/596*e^3 - 27924/149*e, -138/149*e^8 - 6343/298*e^6 - 45945/298*e^4 - 111473/298*e^2 - 31434/149, -11/149*e^8 - 213/298*e^6 + 53/298*e^4 - 5343/298*e^2 - 19226/149, 203/298*e^8 + 4749/298*e^6 + 36253/298*e^4 + 49002/149*e^2 + 21834/149, 11/149*e^8 + 181/149*e^6 + 495/149*e^4 - 5002/149*e^2 - 21302/149, -563/596*e^8 - 11377/596*e^6 - 65267/596*e^4 - 23941/149*e^2 - 5174/149, 135/149*e^8 + 3007/149*e^6 + 20528/149*e^4 + 42072/149*e^2 + 12022/149, 1065/2384*e^9 + 24351/2384*e^7 + 168913/2384*e^5 + 81535/596*e^3 - 27935/596*e, 203/1192*e^9 + 6537/1192*e^7 + 71119/1192*e^5 + 36314/149*e^3 + 81245/298*e, -279/1192*e^9 - 6433/1192*e^7 - 50103/1192*e^5 - 37561/298*e^3 - 26083/298*e, -33/298*e^9 - 197/149*e^7 + 1418/149*e^5 + 45849/298*e^3 + 56985/149*e] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([19,19,-w + 2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]