/* 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([15, 15, 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 - 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 = [ZF.ideal(I) for I in primes_array] heckePol = x^2 + 3*x - 1 K. = NumberField(heckePol) hecke_eigenvalues_array = [1, 1, e, -1, -e - 2, e, -2*e + 1, -1, -3*e - 7, -3*e - 3, 2*e - 1, -4, 6*e + 8, -e - 10, 3*e - 3, 5, e + 3, -3*e - 6, 6*e + 9, 10*e + 15, -3*e - 4, e + 13, -15, -4*e - 1, -6, 4*e + 1, 4*e + 4, 5*e + 7, 6*e + 9, -6*e - 9, -4*e + 7, -10, -e - 11, -1, 5*e + 11, -2*e + 7, -2*e + 3, -2*e + 1, 5*e + 8, -2*e - 14, 2*e - 19, 6*e + 3, 5*e - 1, -e - 11, -3*e + 11, -6*e - 15, -11*e - 14, 4*e + 10, -21, 8, 5*e + 10, -3*e + 12, -9*e, -8*e - 20, -7*e - 22, 6*e - 6, e + 13, 2*e - 20, 3*e + 5, 7*e + 30, -4*e + 7, 2*e - 4, 9*e + 9, -2*e - 9, -8*e - 18, -e + 4, 12*e + 17, -4*e - 10, 9*e + 21, 4*e - 6, -10*e + 1, -9*e - 16, -6*e - 28, 3*e - 3, 5*e + 32, 10*e + 18, -3*e - 13, 10*e + 13, 15, -5*e - 27, -8*e - 12, 3*e + 6, 12*e + 30, -5*e - 12, -11*e - 12, -9*e - 31, 14*e + 25, -10*e - 35, -4*e - 5, -4*e - 7, -6*e - 9, 4*e + 21, -e - 23, -4*e + 14, -9*e - 21, 8*e + 20, 3*e + 27, 4*e - 2, -2*e - 5, -4*e - 5, 4*e - 3, -2*e + 19, -2*e - 5, -10*e - 40, -6*e, -1, -6*e - 22, 17*e + 26, 39, -5*e - 6, -6*e - 16, -15*e - 40, 19*e + 36, -10*e + 11, -4*e - 37, -21*e - 24, 5*e + 17, -2*e - 6, -17*e - 39, -12*e - 22, -8*e - 12, 21*e + 24, -3*e + 3, 12*e + 39, 3*e - 21, 24*e + 30, -6*e + 3, -10*e - 23, -3*e + 35, -6*e - 6, -18, 6*e + 36, -2*e + 4, 10*e + 21, -4*e + 16, -24*e - 40, -22*e - 35, -8*e - 36, 17*e + 10, -4*e + 23, 9*e + 27, 12*e - 7, 15*e + 35, -13*e - 29, -10, -5*e + 9, -6*e - 15, 26*e + 47, 4*e + 30, -15*e - 34, 16*e + 3, -4*e + 22, -18*e - 51, 24, -12*e - 19, -10*e + 1, 28*e + 42, -13*e - 20, -2*e + 25, e - 44, -6*e - 34, -15*e + 6, 18*e + 21, -19*e - 43, -6*e - 39, -20*e - 51, 26, 15*e + 15, 5*e + 11, -20*e - 35, 12*e - 6, 19*e + 39, -25*e - 44, 18*e + 5, 25*e + 54, -13*e - 11, 5*e - 2, e - 21, 16*e + 39, -16*e + 2, 9*e + 48, -12*e - 31, -2*e - 42, -7*e - 23, -4*e - 17, -15*e - 18, -9*e - 12, 30*e + 44, 11*e + 16, -12*e + 6, 15*e + 45, -16*e - 13, 18, -3*e - 39, 24*e + 18, 21*e + 47, 6*e - 43, -13*e - 31, -6*e - 45, -11*e + 12, -9*e + 17, -3, -27*e - 45, 24*e + 53, -2*e - 3, 21*e + 20, 10*e - 15, -8*e + 6, 7*e - 12, 16*e + 10, -6*e - 51, 4*e + 33, 7*e + 36, -14*e - 35, -5*e - 50, 2*e + 44, 31*e + 46, 16*e + 63, 22*e + 6, 13*e + 28, 15*e + 6, -8*e - 45, 25*e + 60, 27*e + 35, 5*e + 28, 12*e + 27, -4*e - 70, 12*e - 19, 13*e - 9, 2*e + 74, 10*e + 19, 33*e + 57, -15*e - 57, -21*e - 60, -6, 23*e + 59, 4*e - 26, -16*e - 44, -19*e - 56, -6*e - 31, 27*e + 38, -4*e - 19, 12*e - 15, 9*e + 2, -11*e - 9, -2*e - 21, 4*e - 21, 3*e - 9, -20*e - 20, 17, -8*e - 24, -20*e + 13, -21*e - 72, 6*e - 4, -20*e - 24, 7*e + 9, -35*e - 66, -11*e - 39, -5*e - 14, -3*e - 33, -4*e + 43, -20*e - 51, 25*e + 34, 11*e - 1, 9*e - 18, 7*e + 43, 9*e + 5, -2*e + 9, -11*e - 18, -49, -11*e - 45, 21*e + 23, -20*e - 6, -14*e + 3, -e + 20, 29*e + 29, 18*e + 39, -12*e - 15, -14*e - 30, -28*e - 62, -16*e - 14, 21*e + 62, -2*e - 54, -15*e - 6, -e - 1, 6*e - 37, 5*e + 40, -7*e + 2, 18*e + 3, e - 6, 5*e - 23, -4*e - 34, -39*e - 45, 21*e + 48, -16*e - 16, 16*e + 72, 2*e + 28, -18*e - 55, -7*e - 53, 12*e + 51, 4*e + 46, 10*e + 36, e + 3, -4*e - 19, 2*e + 11, 18, 4*e + 25, -38*e - 63, 16*e + 24, -13*e - 43, 20*e + 71, -13*e - 2, -27*e - 46, 16*e + 28, 16*e - 11, -9*e + 23, -6*e - 46, -10*e + 50, 27*e + 63, -30*e - 51, 6*e + 54, -5*e + 15, -3*e + 17, -35*e - 54, 13*e - 15, 16*e + 64, -2*e + 55, -11*e, -8*e - 35, -3*e + 57, 27*e + 36, -24*e - 72, 18*e + 18, -11*e - 41, 36*e + 47, -22*e - 8, 28*e + 85, 3*e + 66, -36*e - 37, 22*e + 54, 3, -10*e + 38, -23*e - 30, -2*e - 27, -32*e - 66, 2*e - 56, -13*e - 58, -12*e - 51, 13*e - 18, -4*e + 7, -6*e - 64, 4*e - 39, -9*e + 39, -27*e - 33, 16*e + 10, -6*e - 15, -8*e - 3, 22*e + 81, e - 26, -2*e + 49, -8*e + 49, -23*e - 86, e + 10, -8*e + 7, -31*e - 40, -33*e - 69, 7*e - 54, 4*e + 51, -9*e - 16, -9*e + 20, -36*e - 39, 2*e + 2, 101, 4*e - 12, -22*e + 26, 12*e - 6, 27*e + 60, -8*e - 50, 7*e + 75, 35*e + 37, 39*e + 50, 14*e + 19, -19*e + 2, -3*e - 78, 15*e - 27, -3*e + 18, -18*e - 57, -10*e + 20, -44*e - 60, -18*e - 49, -15*e - 34, 2*e - 17, 10*e + 7, 6*e + 27, -14*e - 74, -40*e - 43, 21*e + 72, -42*e - 39, -6*e + 24, -15*e - 93, 7*e - 47, 31*e + 70, 10*e + 3, -28*e - 35, 4*e - 15, 14*e + 61, -2*e + 72, -27*e - 87, 15*e + 72, 20*e - 1, 20*e + 77, -25*e - 29, 47*e + 67, -29*e - 17, 3*e + 102, 3*e - 51, 2*e + 32, -e + 34, 34*e + 39, 6*e - 12, -8*e + 55, 14*e + 28, -23*e - 51, -28*e - 62, -33*e - 70, 6*e - 57, -11*e - 80, -6*e + 69, -15*e - 81, 15*e - 1, 39*e + 29, 69, -6*e + 33, -12*e - 73, -7*e + 64, -3*e + 8, -12*e - 28, 24*e + 71, -23*e - 96, -27*e - 24, -18*e - 24, -32*e - 39, -28*e - 11, 23*e + 47, -9*e - 75, -2*e - 47, 33*e + 54, 15*e + 44, 42*e + 71, -11*e + 7, -3*e - 93, 42*e + 36, 10*e + 76, 4*e + 73, -27*e - 96, 40*e + 72, 6*e - 13, 15*e + 6, -19*e - 70, 9*e + 5, 14*e + 76, 28*e + 10, -18*e - 6, -e + 5, 31*e - 8, -27*e - 46, 20*e + 67, -15*e + 56, -2*e - 30, 33*e + 2, 14*e + 4, 23*e + 13, 12*e + 44, 2*e + 4, 28*e + 15, 30*e + 60, 28*e + 16, 15*e - 21, -30*e - 15, -5*e - 33, 28*e + 21, 6*e - 61, e + 18, -10*e + 43, 23*e + 37, -26*e - 6, 14*e - 17, -34*e - 61, -21*e - 60, -3*e + 8, e + 63, 37*e + 9, 10*e + 60, 36*e + 18, -9*e - 33, 35*e + 82, -20*e - 87, -11*e - 93, 43*e + 90, -22*e + 35, 4*e + 49, 10*e + 40, -33*e - 78, 13*e + 82, 6*e + 57, -4*e - 92, -8*e - 24, -33*e - 99, -24*e - 96, 40*e + 78, -6*e + 47, -32*e - 45, 44*e + 70, 4*e + 15, -15, -27*e - 3, 31*e + 82, -37*e - 46, -18*e - 51, 22*e - 8, 18*e + 12, 8*e - 13, 21*e + 6, 41*e + 77, -26*e - 99, -34*e - 47, 16*e - 20, 10*e + 70, 6*e - 73, 24*e - 28, -22*e - 2, -15*e - 70, -7*e + 31, 3*e - 52, -28*e - 73, -12*e - 105, -27*e + 9, 11*e - 37, -4*e - 59, e - 36, -26*e - 11, -41*e - 35, -26*e - 45, 30*e + 35, 14*e + 113, -6*e + 36, 40*e + 27, 28*e + 60, 18*e + 33, -10*e + 83, 22*e + 54, -8*e + 9, 22*e + 9, 32*e + 7, -15*e - 69, 21*e - 39, -47*e - 62, -26*e + 7, 12*e + 71, -42*e - 55, -24*e + 2, -44*e - 39, -28*e - 97, 59*e + 107, 43*e + 72, 27*e + 95, 6*e + 44, 2*e - 92, -6*e - 7, -7*e - 113, 14*e + 23, 20*e + 20, -38*e - 111, 24*e + 35, -27*e + 3, -51*e - 75, 26*e + 97, -14*e - 30, -25*e + 5, 5*e - 43, -5*e + 19, -11*e + 16, -3*e + 33, 6*e - 6, 4*e + 9, -28*e - 80, 18*e + 50, 13*e + 60, -10*e - 122, -13*e - 26, -2*e + 27, -3*e + 62, 4*e + 118, -10*e + 59, 18*e + 27, -2*e + 55, -47*e - 72, 48*e + 50, 20*e + 64, -30*e - 43, 60*e + 89, 13*e - 33, 17*e - 22, 24*e + 72, 28*e + 42, -37*e - 26, 41*e + 43, 21*e + 48, -2*e - 95, -5*e - 14, 38*e + 119, -16*e - 20, 31*e + 9, -14*e - 29, -3*e - 108, 42*e + 32, 26*e - 47, -5*e - 54, 52*e + 111, 4*e - 66, -56*e - 57, 18*e + 114, -49*e - 76, -26*e - 45, -7*e + 10, 27*e, 12*e + 66, -8*e - 20, 3*e + 36, 47*e + 62, -21*e - 114, -54*e - 82, -25*e - 83, -5*e - 65, -24*e - 9, 18*e - 54, -16*e + 29, -9*e + 92, 13*e + 87, -2*e - 105, 21*e + 20, 4*e + 49, -26*e - 86, -14*e + 64, -49*e - 58, 12*e - 40, -55*e - 65, 6*e - 51, 4*e - 5, -11*e + 21, 10*e + 6, -2*e - 135, -20*e + 15, -24*e - 12, 39*e + 66, -28*e + 22, -41*e - 33, -21*e - 36, 11*e - 70, 5*e - 71, -2*e - 93, 28*e - 27, -60*e - 85, -24*e - 69, 35*e + 107, 63*e + 110, e + 105, -29*e + 33, -12*e + 89, 8*e + 7, 9*e - 76, 66, -24*e + 9, -7*e - 41, -2*e + 84, -13*e - 35, 32*e + 89, -36*e - 45, 28*e + 81, 36*e - 7, 18*e + 96, 26*e - 43, 12*e + 54, -19*e - 55, 53*e + 103, 55*e + 51, 37*e + 48, 13*e - 78, 12*e - 67, 3*e - 91, 10*e - 65, -19*e - 43, 24*e + 47, 30*e - 19, 14*e - 65, -51*e - 70, -9*e + 18, 32*e + 83, -18*e - 117, -5*e + 37, 25*e + 4, -24*e - 87, -81, 17*e - 13, 53*e + 89, 48*e + 129, -9*e - 30, 51*e + 57, 53*e + 95, -9*e + 54, 77, -24*e - 52, -132, 39*e + 69, -17*e + 27, 52*e + 117, 36*e + 86, 41*e + 49, 17, -39*e - 37, 26*e + 101, 15*e + 90, -24*e + 56, -19*e - 17, 12*e - 28, -10*e + 97, -45*e - 108, 16*e - 11, -10*e + 61, -24*e - 97, 13*e + 27, -29*e - 96, 11*e + 83, -50*e - 131, -4*e - 31, 12*e - 48, -5*e - 15, 45*e + 5, -19*e - 17, 58*e + 99, -20*e - 29, -29*e - 134, 55*e + 129, -53*e - 51, 34*e + 7, -34*e - 118, 39*e + 108, 6*e + 36, 28*e + 63, 35*e + 97, -30*e - 139, 9*e - 43, -7*e + 8, -9*e - 66, -51*e - 48, 27*e + 120, -57*e - 93, -17*e - 5, 15*e - 7, 10*e + 48, 14*e + 41, 48*e + 90, -56*e - 86, -24*e - 36, 2*e - 97, 2*e + 8, -3*e - 64, -2*e + 84, 24*e + 5, -7*e + 64, -27*e - 79, 22*e + 93, -24*e + 12, -52*e - 40, -40*e - 137, -85, -9*e - 126, 27*e + 48, 47*e + 91, -8*e - 45, -44*e - 68, -64*e - 97, -14*e - 23, -18*e - 84, 23*e + 5, -4*e - 4, -18*e + 65, 15*e + 29, -87, 24*e + 96, -20*e - 48, -46*e - 110, -47*e - 116, 7*e + 106, -20*e - 45, -32*e - 83, 45, 10*e + 4, 18*e + 57, -20*e, -53*e - 24, 15*e + 72, -47*e - 56, -69, -10*e - 46, 15*e, 42*e + 27, 25*e - 11, 19*e + 49, -60*e - 63, 20*e - 22, 3*e, 48*e + 87, 37*e + 24, 40*e + 117, -36*e - 100, 12*e + 86, -12*e - 121, -35*e - 114, -13*e + 7, 49*e + 111, 58*e + 57, -60*e - 85, 9*e - 34, -68*e - 138, 34*e + 51, -33*e + 23, 27*e + 42, 28*e + 40, 29*e - 56, 64*e + 111, 40*e + 87, -32*e - 84, -15*e - 102, -9*e + 12, 13*e + 27, 5, -16*e + 26, -10*e - 127, -29*e + 45, 11*e - 89, -56*e - 65, 60*e + 102, 15*e + 42, -5*e - 107, 20*e + 91, -12*e - 70, 63*e + 129, 3*e + 27, -17*e - 9, 18*e + 140, 8*e - 67, 12*e + 15, 15*e - 79, 32*e + 127, -2*e - 2, -68*e - 80, -39*e - 19, 32*e + 40, -12*e + 69, 60*e + 105, 24*e + 84, 48*e + 87, -15, 24*e + 135, e - 47, -24*e + 3, -2*e - 99, 41*e + 49, -28*e - 20, -23*e + 76, 60*e + 75, -28*e - 19, 20*e + 68, -20*e - 93, -28*e - 77, 4*e - 87, -17*e - 21, -20*e + 96, 10*e - 63, 22*e + 121, -35*e - 14, 38*e + 128, 68*e + 125, 30*e - 58, -27*e + 29, 55*e + 120, -63*e - 85, -44*e - 11, 16*e - 65, -24*e - 61, 7*e - 87, -33*e + 11, 18*e + 65, 36*e + 36, 34*e + 49, 18*e + 42, -8*e + 112, -34*e - 49, 76*e + 124, -10*e + 16, -65*e - 72, -6*e - 100, -62*e - 123, -62*e - 60, 41*e + 31, -41*e - 71, -53*e - 71, -26*e - 81, 10*e + 54, 30*e + 129, 42*e + 90, -63*e - 123, -29*e - 8, -15*e + 105, 9*e + 69, 6*e + 69, -19*e - 49, -16*e - 89, -20*e - 42, -7*e + 8, 30*e - 27, 48*e + 68, -24*e - 118, 68*e + 58, -60*e - 118, -26*e, 10*e - 33, 62*e + 40, 24*e - 1, 13*e + 22, 20*e + 89, -e - 74, 5*e + 43, 54*e + 104, 74*e + 97, -44*e - 89, -51*e - 42, 34*e - 11, -19*e - 100, 22*e + 45, -54*e - 103, -32*e - 47, -14*e + 46, -36*e - 124, 16*e + 42, -27*e - 141, 18*e + 54, 56*e + 107, 30*e - 66, 53*e + 91, 37*e - 15, 31*e + 66, -58*e - 38, 33*e - 28, -57*e - 145, -37*e - 79, 78*e + 141, 40*e + 54, 45*e + 80, 51, 56*e + 89, 38*e + 155, 7*e + 37, 46*e + 27, -e + 58, 18*e + 99, -42*e - 69, 12*e - 19, -3*e + 65, -26*e - 48, 20*e + 82, 47*e + 64, 42*e + 107, 39*e + 48, 22*e + 10, 8*e + 140, -20*e + 100, 73*e + 121, -51*e - 126, 32*e + 2, 84, 8*e + 14, 5*e - 121, -66*e - 90, 18*e + 27, -6*e - 48, 18*e - 108, 67*e + 147, 14*e - 29, 16*e + 82, -5*e - 86, 30*e + 75, -16*e + 14, -23*e - 108, -17*e - 159, 47*e + 1, -20*e - 63, -e + 82, -30*e - 49, -12*e + 5, -25*e - 83, 44*e - 13, -14*e + 73, 47*e + 127, -64*e - 92, 5*e + 43, 34*e + 96, 12*e + 51, 39*e + 51, -3*e + 95, 7*e + 111, 9*e + 32, -3*e + 14, 40*e + 82, 6*e - 57, -e - 62, 61*e + 42, 36*e + 123, 27*e - 51, 3*e - 42, -12, -53*e - 114, -30*e - 97, 39*e + 8, -16*e - 77, -4*e + 100, 76*e + 81, 18*e + 146, 4*e - 21, 10*e + 163, 21*e + 123, -18*e - 94, 24*e + 47, -42*e - 159, 60*e + 123, 68*e + 88, 57*e + 44, -17*e - 51, -45*e - 58, -5*e - 39, 27*e + 164, 55*e + 63, -20*e - 135, 25*e + 4, 7*e + 118, -24*e + 50, -5*e - 39, 38*e + 103, 21*e + 59, 18*e + 53, -53*e - 123, 24*e + 149, -4*e + 121, 47*e + 68, 99, 31*e + 84, 14*e - 5, 3*e - 82, -68*e - 147, -75*e - 93, 54*e + 66, 56*e + 46, -36*e - 67, -24*e - 93, 2*e + 32, 14*e - 116, -17*e - 162, 24*e + 141, -14*e + 55, -68*e - 63, 66*e + 83, 51*e + 24, 50*e + 107, 10*e + 10, 21*e - 99, -12*e - 40, 8*e + 73, -20*e + 42, -e + 82, -19*e + 11, 42*e + 108, -14*e + 60, 16*e + 180, -47*e - 114, -41*e, -27*e - 147, -18*e + 9, -9*e + 80, 26*e + 1, 26*e + 74, -18*e - 6, -36*e - 106, 58*e + 81, -22*e - 55, 72*e + 87, -8*e + 121, -15*e - 24, -24*e - 28, 10*e + 15, -45*e - 105, -24*e - 123, 48*e + 63, -20*e - 83, -30*e + 32, 12*e - 97, -44*e - 53, 54*e + 9, 7*e - 102, 41*e + 82, -23*e + 33, -44*e - 78, -19*e - 106, -63*e - 135, -10*e - 29, -61*e - 44, -8*e - 57, 62*e + 118, -32*e - 20, -25*e + 74, 16*e - 6, 78*e + 80, -54*e, 39*e + 111, -39*e + 18, 12*e - 96, -12*e - 166, 10*e + 57, -20*e - 129, 72*e + 155, -38*e - 42, -22*e - 11, -24*e - 147, 27*e + 78, 26*e + 104, 54*e + 45, -e + 85, -5*e - 87, 37*e + 3, 90*e + 164, -6*e + 131, 12*e + 107, -7*e + 50, 42*e + 84, 3*e + 63, 50*e + 65, -60*e - 73, -19*e - 110, -39*e - 18, 51*e + 111, 57*e + 75, -46*e - 85, -30*e - 102, -13*e - 55, -33*e - 87, -54*e + 12, -7*e - 11, 25*e + 15, 35*e + 109, 10*e + 132, 66*e + 51, 5*e - 139, -28*e - 10, -32*e + 4, 57*e + 27, -26*e - 155, -56*e - 41, -42*e - 99, -64*e - 109, -63*e - 159, 30*e - 34, 72*e + 107, 24*e + 174, -45*e - 36, -13*e + 124, -24*e - 19, 64*e + 97, 26*e + 20, 37*e + 15, -3*e + 50, 26*e + 77, -18*e - 144, 48, 66*e + 138, -4*e - 74, -38*e - 69, 40*e - 12, 28*e + 15, -5*e - 135, -61*e - 83, -70*e - 103, -9*e + 48, -17*e - 108, -10*e - 17, 43*e - 21, 50*e + 163, 76*e + 109, -34*e + 11, -20*e + 36, 23, -19*e - 130, -4*e - 139, -38*e - 56, 2*e - 46, -63*e - 139, 65*e + 112, 32*e + 116, 22*e + 145, 34*e + 115, -6*e - 177, -24*e + 69, 3*e - 105, -54*e - 39, -26*e - 71, 30*e + 80, -12*e - 34, -24*e - 109, -29*e - 57, 44*e + 47, 59*e + 125, -9*e - 48, 72*e + 108, -18*e + 69, 57*e + 33, -39*e, -18*e - 39, 81*e + 122, -12*e - 34, -13*e - 8, 14*e + 175, -70*e - 74, -27*e - 142] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([3, 3, w + 2])] = -1 AL_eigenvalues[ZF.ideal([5, 5, w + 2])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]