/* 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([-10, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([288,72,-4*w + 32]) primes_array = [ [2, 2, w],\ [3, 3, w + 1],\ [3, 3, w + 2],\ [5, 5, w],\ [13, 13, w + 6],\ [13, 13, w + 7],\ [31, 31, -2*w + 3],\ [31, 31, 2*w + 3],\ [37, 37, w + 11],\ [37, 37, w + 26],\ [41, 41, 3*w + 7],\ [41, 41, -3*w + 7],\ [43, 43, w + 15],\ [43, 43, w + 28],\ [49, 7, -7],\ [53, 53, w + 13],\ [53, 53, w + 40],\ [67, 67, w + 12],\ [67, 67, w + 55],\ [71, 71, -w - 9],\ [71, 71, w - 9],\ [79, 79, -4*w - 9],\ [79, 79, 4*w - 9],\ [83, 83, w + 33],\ [83, 83, w + 50],\ [89, 89, -3*w - 1],\ [89, 89, 3*w - 1],\ [107, 107, w + 44],\ [107, 107, w + 63],\ [121, 11, -11],\ [151, 151, 4*w - 3],\ [151, 151, -4*w - 3],\ [157, 157, w + 18],\ [157, 157, w + 139],\ [163, 163, w + 70],\ [163, 163, w + 93],\ [173, 173, w + 23],\ [173, 173, w + 150],\ [191, 191, -6*w - 13],\ [191, 191, 6*w - 13],\ [197, 197, w + 73],\ [197, 197, w + 124],\ [199, 199, -3*w - 17],\ [199, 199, 3*w - 17],\ [227, 227, w + 64],\ [227, 227, w + 163],\ [239, 239, 6*w - 11],\ [239, 239, -6*w - 11],\ [241, 241, -5*w - 3],\ [241, 241, 5*w - 3],\ [271, 271, 3*w - 19],\ [271, 271, -3*w - 19],\ [277, 277, w + 29],\ [277, 277, w + 248],\ [281, 281, 4*w - 21],\ [281, 281, -4*w - 21],\ [283, 283, w + 24],\ [283, 283, w + 259],\ [289, 17, -17],\ [293, 293, w + 89],\ [293, 293, w + 204],\ [307, 307, w + 138],\ [307, 307, w + 169],\ [311, 311, -6*w - 7],\ [311, 311, 6*w - 7],\ [317, 317, w + 31],\ [317, 317, w + 286],\ [347, 347, w + 125],\ [347, 347, w + 222],\ [359, 359, -6*w - 1],\ [359, 359, 6*w - 1],\ [361, 19, -19],\ [373, 373, w + 82],\ [373, 373, w + 291],\ [397, 397, w + 176],\ [397, 397, w + 221],\ [401, 401, 2*w - 21],\ [401, 401, -2*w - 21],\ [409, 409, 7*w - 9],\ [409, 409, -7*w - 9],\ [431, 431, -w - 21],\ [431, 431, w - 21],\ [439, 439, -3*w - 23],\ [439, 439, 3*w - 23],\ [443, 443, w + 203],\ [443, 443, w + 240],\ [449, 449, 8*w - 33],\ [449, 449, -8*w - 33],\ [467, 467, w + 145],\ [467, 467, w + 322],\ [479, 479, -5*w - 27],\ [479, 479, 5*w - 27],\ [521, 521, 9*w - 17],\ [521, 521, -9*w - 17],\ [523, 523, w + 202],\ [523, 523, w + 321],\ [529, 23, -23],\ [547, 547, w + 253],\ [547, 547, w + 294],\ [557, 557, w + 41],\ [557, 557, w + 516],\ [563, 563, w + 130],\ [563, 563, w + 433],\ [569, 569, -4*w - 27],\ [569, 569, 4*w - 27],\ [587, 587, w + 214],\ [587, 587, w + 373],\ [599, 599, 12*w + 29],\ [599, 599, -12*w + 29],\ [601, 601, 6*w - 31],\ [601, 601, -6*w - 31],\ [613, 613, w + 43],\ [613, 613, w + 570],\ [631, 631, -8*w - 3],\ [631, 631, 8*w - 3],\ [641, 641, 9*w - 13],\ [641, 641, -9*w - 13],\ [643, 643, w + 36],\ [643, 643, w + 607],\ [653, 653, w + 140],\ [653, 653, w + 513],\ [677, 677, w + 213],\ [677, 677, w + 464],\ [683, 683, w + 159],\ [683, 683, w + 524],\ [719, 719, -w - 27],\ [719, 719, w - 27],\ [733, 733, w + 47],\ [733, 733, w + 686],\ [751, 751, -3*w - 29],\ [751, 751, 3*w - 29],\ [757, 757, w + 143],\ [757, 757, w + 614],\ [761, 761, -9*w - 7],\ [761, 761, 9*w - 7],\ [769, 769, 11*w - 21],\ [769, 769, -11*w - 21],\ [773, 773, w + 118],\ [773, 773, w + 655],\ [787, 787, w + 369],\ [787, 787, w + 418],\ [797, 797, w + 49],\ [797, 797, w + 748],\ [809, 809, -9*w - 1],\ [809, 809, 9*w - 1],\ [827, 827, w + 254],\ [827, 827, w + 573],\ [839, 839, 5*w - 33],\ [839, 839, -5*w - 33],\ [841, 29, -29],\ [853, 853, w + 160],\ [853, 853, w + 693],\ [877, 877, w + 42],\ [877, 877, w + 835],\ [881, 881, -8*w - 39],\ [881, 881, 8*w - 39],\ [883, 883, w + 234],\ [883, 883, w + 649],\ [907, 907, w + 266],\ [907, 907, w + 641],\ [911, 911, 12*w - 23],\ [911, 911, -12*w - 23],\ [919, 919, 10*w - 9],\ [919, 919, -10*w - 9],\ [929, 929, 4*w - 33],\ [929, 929, -4*w - 33],\ [947, 947, w + 111],\ [947, 947, w + 836],\ [991, 991, 10*w - 3],\ [991, 991, -10*w - 3],\ [997, 997, w + 134],\ [997, 997, w + 863],\ [1009, 1009, 6*w - 37],\ [1009, 1009, -6*w - 37],\ [1013, 1013, w + 353],\ [1013, 1013, w + 660],\ [1031, 1031, 7*w - 39],\ [1031, 1031, -7*w - 39],\ [1039, 1039, 16*w + 39],\ [1039, 1039, -16*w + 39],\ [1049, 1049, 2*w - 33],\ [1049, 1049, -2*w - 33],\ [1093, 1093, w + 292],\ [1093, 1093, w + 801],\ [1117, 1117, w + 521],\ [1117, 1117, w + 596],\ [1123, 1123, w + 75],\ [1123, 1123, w + 1048],\ [1129, 1129, -11*w - 9],\ [1129, 1129, 11*w - 9],\ [1151, 1151, -12*w - 17],\ [1151, 1151, 12*w - 17],\ [1163, 1163, w + 123],\ [1163, 1163, w + 1040],\ [1187, 1187, w + 312],\ [1187, 1187, w + 875],\ [1201, 1201, -11*w - 3],\ [1201, 1201, 11*w - 3],\ [1213, 1213, w + 181],\ [1213, 1213, w + 1032],\ [1231, 1231, 14*w - 27],\ [1231, 1231, -14*w - 27],\ [1237, 1237, w + 61],\ [1237, 1237, w + 1176],\ [1249, 1249, -13*w - 21],\ [1249, 1249, 13*w - 21],\ [1277, 1277, w + 574],\ [1277, 1277, w + 703],\ [1279, 1279, 3*w - 37],\ [1279, 1279, -3*w - 37],\ [1283, 1283, w + 152],\ [1283, 1283, w + 1131],\ [1289, 1289, -15*w - 31],\ [1289, 1289, 15*w - 31],\ [1307, 1307, w + 453],\ [1307, 1307, w + 854],\ [1319, 1319, 12*w - 11],\ [1319, 1319, -12*w - 11],\ [1321, 1321, -6*w - 41],\ [1321, 1321, 6*w - 41],\ [1361, 1361, -4*w - 39],\ [1361, 1361, 4*w - 39],\ [1373, 1373, w + 243],\ [1373, 1373, w + 1130],\ [1399, 1399, -9*w - 47],\ [1399, 1399, 9*w - 47],\ [1409, 1409, 15*w - 29],\ [1409, 1409, -15*w - 29],\ [1427, 1427, w + 504],\ [1427, 1427, w + 923],\ [1439, 1439, -12*w - 1],\ [1439, 1439, 12*w - 1],\ [1453, 1453, w + 54],\ [1453, 1453, w + 1399],\ [1471, 1471, -16*w - 33],\ [1471, 1471, 16*w - 33],\ [1481, 1481, 2*w - 39],\ [1481, 1481, -2*w - 39],\ [1483, 1483, w + 708],\ [1483, 1483, w + 775],\ [1489, 1489, 6*w - 43],\ [1489, 1489, -6*w - 43],\ [1493, 1493, w + 67],\ [1493, 1493, w + 1426],\ [1511, 1511, -w - 39],\ [1511, 1511, w - 39],\ [1523, 1523, w + 489],\ [1523, 1523, w + 1034],\ [1559, 1559, -13*w - 57],\ [1559, 1559, 13*w - 57],\ [1597, 1597, w + 653],\ [1597, 1597, w + 944],\ [1601, 1601, 10*w - 51],\ [1601, 1601, -10*w - 51],\ [1609, 1609, -13*w - 9],\ [1609, 1609, 13*w - 9],\ [1613, 1613, w + 220],\ [1613, 1613, w + 1393],\ [1627, 1627, w + 389],\ [1627, 1627, w + 1238],\ [1637, 1637, w + 565],\ [1637, 1637, w + 1072],\ [1667, 1667, w + 798],\ [1667, 1667, w + 869],\ [1693, 1693, w + 324],\ [1693, 1693, w + 1369],\ [1721, 1721, -15*w - 23],\ [1721, 1721, 15*w - 23],\ [1723, 1723, w + 449],\ [1723, 1723, w + 1274],\ [1733, 1733, w + 273],\ [1733, 1733, w + 1460],\ [1747, 1747, w + 532],\ [1747, 1747, w + 1215],\ [1759, 1759, 3*w - 43],\ [1759, 1759, -3*w - 43],\ [1787, 1787, w + 564],\ [1787, 1787, w + 1223],\ [1801, 1801, 17*w - 33],\ [1801, 1801, -17*w - 33],\ [1831, 1831, -16*w - 27],\ [1831, 1831, 16*w - 27],\ [1867, 1867, w + 710],\ [1867, 1867, w + 1157],\ [1871, 1871, -18*w - 37],\ [1871, 1871, 18*w - 37],\ [1877, 1877, w + 605],\ [1877, 1877, w + 1272],\ [1879, 1879, 14*w - 9],\ [1879, 1879, -14*w - 9],\ [1889, 1889, -15*w - 19],\ [1889, 1889, 15*w - 19],\ [1907, 1907, w + 840],\ [1907, 1907, w + 1067],\ [1933, 1933, w + 819],\ [1933, 1933, w + 1114],\ [1951, 1951, -14*w - 3],\ [1951, 1951, 14*w - 3],\ [1973, 1973, w + 77],\ [1973, 1973, w + 1896],\ [1987, 1987, w + 716],\ [1987, 1987, w + 1271],\ [1997, 1997, w + 783],\ [1997, 1997, w + 1214],\ [1999, 1999, -9*w - 53],\ [1999, 1999, 9*w - 53],\ [2003, 2003, w + 689],\ [2003, 2003, w + 1314],\ [2027, 2027, w + 487],\ [2027, 2027, w + 1540],\ [2039, 2039, -11*w - 57],\ [2039, 2039, 11*w - 57],\ [2053, 2053, w + 808],\ [2053, 2053, w + 1245],\ [2081, 2081, -15*w - 13],\ [2081, 2081, 15*w - 13],\ [2083, 2083, w + 250],\ [2083, 2083, w + 1833],\ [2089, 2089, -19*w - 39],\ [2089, 2089, 19*w - 39],\ [2111, 2111, -7*w - 51],\ [2111, 2111, 7*w - 51],\ [2129, 2129, 15*w - 11],\ [2129, 2129, -15*w - 11],\ [2161, 2161, 17*w - 27],\ [2161, 2161, -17*w - 27],\ [2203, 2203, w + 105],\ [2203, 2203, w + 2098],\ [2209, 47, -47],\ [2213, 2213, w + 426],\ [2213, 2213, w + 1787],\ [2237, 2237, w + 602],\ [2237, 2237, w + 1635],\ [2239, 2239, -22*w + 51],\ [2239, 2239, 22*w + 51],\ [2243, 2243, w + 540],\ [2243, 2243, w + 1703],\ [2267, 2267, w + 733],\ [2267, 2267, w + 1534],\ [2281, 2281, 12*w - 61],\ [2281, 2281, -12*w - 61],\ [2293, 2293, w + 83],\ [2293, 2293, w + 2210],\ [2311, 2311, 3*w - 49],\ [2311, 2311, -3*w - 49],\ [2333, 2333, w + 251],\ [2333, 2333, w + 2082],\ [2347, 2347, w + 325],\ [2347, 2347, w + 2022],\ [2351, 2351, 5*w - 51],\ [2351, 2351, -5*w - 51],\ [2357, 2357, w + 206],\ [2357, 2357, w + 2151],\ [2399, 2399, -18*w - 29],\ [2399, 2399, 18*w - 29],\ [2437, 2437, w + 436],\ [2437, 2437, w + 2001],\ [2441, 2441, -4*w - 51],\ [2441, 2441, 4*w - 51],\ [2467, 2467, w + 479],\ [2467, 2467, w + 1988],\ [2477, 2477, w + 695],\ [2477, 2477, w + 1782],\ [2521, 2521, 19*w - 33],\ [2521, 2521, -19*w - 33],\ [2551, 2551, 16*w - 3],\ [2551, 2551, -16*w - 3],\ [2557, 2557, w + 1005],\ [2557, 2557, w + 1552],\ [2591, 2591, -w - 51],\ [2591, 2591, w - 51],\ [2609, 2609, 8*w - 57],\ [2609, 2609, -8*w - 57],\ [2671, 2671, 9*w - 59],\ [2671, 2671, -9*w - 59],\ [2677, 2677, w + 1089],\ [2677, 2677, w + 1588],\ [2683, 2683, w + 832],\ [2683, 2683, w + 1851],\ [2689, 2689, -18*w - 77],\ [2689, 2689, 18*w - 77],\ [2693, 2693, w + 873],\ [2693, 2693, w + 1820],\ [2707, 2707, w + 654],\ [2707, 2707, w + 2053],\ [2711, 2711, 18*w - 23],\ [2711, 2711, -18*w - 23],\ [2719, 2719, -3*w - 53],\ [2719, 2719, 3*w - 53],\ [2729, 2729, 21*w - 41],\ [2729, 2729, -21*w - 41],\ [2791, 2791, -26*w + 63],\ [2791, 2791, 26*w + 63],\ [2797, 2797, w + 788],\ [2797, 2797, w + 2009],\ [2801, 2801, -14*w - 69],\ [2801, 2801, 14*w - 69],\ [2803, 2803, w + 290],\ [2803, 2803, w + 2513],\ [2837, 2837, w + 226],\ [2837, 2837, w + 2611],\ [2843, 2843, w + 973],\ [2843, 2843, w + 1870],\ [2879, 2879, -18*w - 19],\ [2879, 2879, 18*w - 19],\ [2917, 2917, w + 599],\ [2917, 2917, w + 2318],\ [2957, 2957, w + 648],\ [2957, 2957, w + 2309],\ [2963, 2963, w + 1303],\ [2963, 2963, w + 1660],\ [2969, 2969, -10*w - 63],\ [2969, 2969, 10*w - 63],\ [2999, 2999, -5*w - 57],\ [2999, 2999, 5*w - 57],\ [3001, 3001, -25*w + 57],\ [3001, 3001, 25*w + 57],\ [3037, 3037, w + 78],\ [3037, 3037, w + 2959],\ [3041, 3041, -21*w - 37],\ [3041, 3041, 21*w - 37],\ [3049, 3049, -12*w - 67],\ [3049, 3049, 12*w - 67],\ [3067, 3067, w + 910],\ [3067, 3067, w + 2157],\ [3079, 3079, 15*w - 73],\ [3079, 3079, -15*w - 73],\ [3083, 3083, w + 795],\ [3083, 3083, w + 2288],\ [3089, 3089, 4*w - 57],\ [3089, 3089, -4*w - 57],\ [3119, 3119, -18*w - 11],\ [3119, 3119, 18*w - 11],\ [3121, 3121, -6*w - 59],\ [3121, 3121, 6*w - 59],\ [3163, 3163, w + 1122],\ [3163, 3163, w + 2041],\ [3169, 3169, 19*w - 21],\ [3169, 3169, -19*w - 21],\ [3187, 3187, w + 411],\ [3187, 3187, w + 2776],\ [3191, 3191, 18*w - 7],\ [3191, 3191, -18*w - 7],\ [3203, 3203, w + 310],\ [3203, 3203, w + 2893],\ [3209, 3209, 2*w - 57],\ [3209, 3209, -2*w - 57],\ [3253, 3253, w + 242],\ [3253, 3253, w + 3011],\ [3271, 3271, -20*w - 27],\ [3271, 3271, 20*w - 27],\ [3307, 3307, w + 244],\ [3307, 3307, w + 3063],\ [3319, 3319, 22*w - 39],\ [3319, 3319, -22*w - 39],\ [3323, 3323, w + 1259],\ [3323, 3323, w + 2064],\ [3329, 3329, -8*w - 63],\ [3329, 3329, 8*w - 63],\ [3347, 3347, w + 862],\ [3347, 3347, w + 2485],\ [3359, 3359, -24*w - 49],\ [3359, 3359, 24*w - 49],\ [3361, 3361, 6*w - 61],\ [3361, 3361, -6*w - 61],\ [3373, 3373, w + 949],\ [3373, 3373, w + 2424],\ [3391, 3391, -3*w - 59],\ [3391, 3391, 3*w - 59],\ [3413, 3413, w + 320],\ [3413, 3413, w + 3093],\ [3449, 3449, 21*w - 31],\ [3449, 3449, -21*w - 31],\ [3467, 3467, w + 395],\ [3467, 3467, w + 3072],\ [3481, 59, -59],\ [3511, 3511, -21*w - 89],\ [3511, 3511, 21*w - 89],\ [3517, 3517, w + 1302],\ [3517, 3517, w + 2215],\ [3529, 3529, 19*w - 9],\ [3529, 3529, -19*w - 9],\ [3533, 3533, w + 103],\ [3533, 3533, w + 3430],\ [3547, 3547, w + 526],\ [3547, 3547, w + 3021],\ [3557, 3557, w + 980],\ [3557, 3557, w + 2577],\ [3559, 3559, -20*w - 21],\ [3559, 3559, 20*w - 21],\ [3613, 3613, w + 937],\ [3613, 3613, w + 2676],\ [3631, 3631, 3*w - 61],\ [3631, 3631, -3*w - 61],\ [3637, 3637, w + 1751],\ [3637, 3637, w + 1886],\ [3643, 3643, w + 135],\ [3643, 3643, w + 3508],\ [3671, 3671, 30*w + 73],\ [3671, 3671, -30*w + 73],\ [3677, 3677, w + 974],\ [3677, 3677, w + 2703],\ [3719, 3719, 5*w - 63],\ [3719, 3719, -5*w - 63],\ [3721, 61, -61],\ [3733, 3733, w + 768],\ [3733, 3733, w + 2965],\ [3761, 3761, -10*w - 69],\ [3761, 3761, 10*w - 69],\ [3769, 3769, 23*w - 39],\ [3769, 3769, -23*w - 39],\ [3797, 3797, w + 558],\ [3797, 3797, w + 3239],\ [3803, 3803, w + 1848],\ [3803, 3803, w + 1955],\ [3853, 3853, w + 340],\ [3853, 3853, w + 3513],\ [3877, 3877, w + 1529],\ [3877, 3877, w + 2348],\ [3881, 3881, 21*w - 23],\ [3881, 3881, -21*w - 23],\ [3889, 3889, 12*w - 73],\ [3889, 3889, -12*w - 73],\ [3907, 3907, w + 1004],\ [3907, 3907, w + 2903],\ [3911, 3911, 24*w - 43],\ [3911, 3911, -24*w - 43],\ [3917, 3917, w + 1620],\ [3917, 3917, w + 2297],\ [3919, 3919, -20*w - 9],\ [3919, 3919, 20*w - 9],\ [3923, 3923, w + 381],\ [3923, 3923, w + 3542],\ [3929, 3929, 2*w - 63],\ [3929, 3929, -2*w - 63],\ [3947, 3947, w + 1919],\ [3947, 3947, w + 2028],\ [4001, 4001, 16*w - 81],\ [4001, 4001, -16*w - 81],\ [4003, 4003, w + 1083],\ [4003, 4003, w + 2920],\ [4013, 4013, w + 1794],\ [4013, 4013, w + 2219],\ [4027, 4027, w + 1266],\ [4027, 4027, w + 2761],\ [4049, 4049, -21*w - 19],\ [4049, 4049, 21*w - 19],\ [4079, 4079, 24*w - 41],\ [4079, 4079, -24*w - 41],\ [4093, 4093, w + 1738],\ [4093, 4093, w + 2355],\ [4111, 4111, -22*w - 27],\ [4111, 4111, 22*w - 27],\ [4129, 4129, 6*w - 67],\ [4129, 4129, -6*w - 67],\ [4133, 4133, w + 713],\ [4133, 4133, w + 3420],\ [4157, 4157, w + 1608],\ [4157, 4157, w + 2549],\ [4159, 4159, 26*w - 51],\ [4159, 4159, -26*w - 51],\ [4201, 4201, -23*w - 33],\ [4201, 4201, 23*w - 33],\ [4231, 4231, -9*w - 71],\ [4231, 4231, 9*w - 71],\ [4241, 4241, 21*w - 13],\ [4241, 4241, -21*w - 13],\ [4243, 4243, w + 2065],\ [4243, 4243, w + 2178],\ [4253, 4253, w + 113],\ [4253, 4253, w + 4140],\ [4271, 4271, -7*w - 69],\ [4271, 4271, 7*w - 69],\ [4283, 4283, w + 578],\ [4283, 4283, w + 3705],\ [4289, 4289, -21*w - 11],\ [4289, 4289, 21*w - 11],\ [4357, 4357, w + 343],\ [4357, 4357, w + 4014],\ [4363, 4363, w + 637],\ [4363, 4363, w + 3726],\ [4373, 4373, w + 1489],\ [4373, 4373, w + 2884],\ [4391, 4391, 24*w - 37],\ [4391, 4391, -24*w - 37],\ [4397, 4397, w + 988],\ [4397, 4397, w + 3409],\ [4409, 4409, -21*w - 1],\ [4409, 4409, 21*w - 1],\ [4441, 4441, 24*w - 101],\ [4441, 4441, -24*w - 101],\ [4481, 4481, 27*w - 53],\ [4481, 4481, -27*w - 53],\ [4483, 4483, w + 1774],\ [4483, 4483, w + 2709],\ [4493, 4493, w + 592],\ [4493, 4493, w + 3901],\ [4507, 4507, w + 1705],\ [4507, 4507, w + 2802],\ [4517, 4517, w + 1895],\ [4517, 4517, w + 2622],\ [4519, 4519, 9*w - 73],\ [4519, 4519, -9*w - 73],\ [4523, 4523, w + 856],\ [4523, 4523, w + 3667],\ [4547, 4547, w + 1352],\ [4547, 4547, w + 3195],\ [4561, 4561, -23*w - 27],\ [4561, 4561, 23*w - 27],\ [4591, 4591, -28*w - 57],\ [4591, 4591, 28*w - 57],\ [4597, 4597, w + 1263],\ [4597, 4597, w + 3334],\ [4603, 4603, w + 96],\ [4603, 4603, w + 4507],\ [4637, 4637, w + 1831],\ [4637, 4637, w + 2806],\ [4639, 4639, 15*w - 83],\ [4639, 4639, -15*w - 83],\ [4643, 4643, w + 1049],\ [4643, 4643, w + 3594],\ [4649, 4649, -33*w + 79],\ [4649, 4649, 33*w + 79],\ [4679, 4679, -17*w - 87],\ [4679, 4679, 17*w - 87],\ [4721, 4721, 2*w - 69],\ [4721, 4721, -2*w - 69],\ [4723, 4723, w + 1003],\ [4723, 4723, w + 3720],\ [4729, 4729, -25*w - 39],\ [4729, 4729, 25*w - 39],\ [4733, 4733, w + 763],\ [4733, 4733, w + 3970],\ [4751, 4751, -w - 69],\ [4751, 4751, w - 69],\ [4759, 4759, -22*w - 9],\ [4759, 4759, 22*w - 9],\ [4787, 4787, w + 1544],\ [4787, 4787, w + 3243],\ [4799, 4799, -24*w - 31],\ [4799, 4799, 24*w - 31],\ [4801, 4801, -12*w - 79],\ [4801, 4801, 12*w - 79],\ [4813, 4813, w + 380],\ [4813, 4813, w + 4433],\ [4831, 4831, 22*w - 3],\ [4831, 4831, -22*w - 3],\ [4871, 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79],\ [8999, 8999, -30*w - 1],\ [8999, 8999, 30*w - 1],\ [9001, 9001, -35*w - 57],\ [9001, 9001, 35*w - 57],\ [9013, 9013, w + 520],\ [9013, 9013, w + 8493],\ [9041, 9041, -33*w - 43],\ [9041, 9041, 33*w - 43],\ [9043, 9043, w + 2900],\ [9043, 9043, w + 6143],\ [9049, 9049, 6*w - 97],\ [9049, 9049, -6*w - 97],\ [9067, 9067, w + 404],\ [9067, 9067, w + 8663],\ [9133, 9133, w + 3938],\ [9133, 9133, w + 5195],\ [9151, 9151, -32*w - 33],\ [9151, 9151, 32*w - 33],\ [9157, 9157, w + 406],\ [9157, 9157, w + 8751],\ [9161, 9161, 8*w - 99],\ [9161, 9161, -8*w - 99],\ [9173, 9173, w + 1493],\ [9173, 9173, w + 7680],\ [9187, 9187, w + 2773],\ [9187, 9187, w + 6414],\ [9199, 9199, -15*w - 107],\ [9199, 9199, 15*w - 107],\ [9203, 9203, w + 3113],\ [9203, 9203, w + 6090],\ [9209, 9209, 33*w - 41],\ [9209, 9209, -33*w - 41],\ [9227, 9227, w + 3004],\ [9227, 9227, w + 6223],\ [9239, 9239, -36*w - 61],\ [9239, 9239, 36*w - 61],\ [9241, 9241, -36*w - 149],\ [9241, 9241, 36*w - 149],\ [9277, 9277, w + 1345],\ [9277, 9277, w + 7932],\ [9281, 9281, 39*w - 77],\ [9281, 9281, -39*w - 77],\ [9283, 9283, w + 4558],\ [9283, 9283, w + 4725],\ [9293, 9293, w + 167],\ [9293, 9293, w + 9126],\ [9311, 9311, 7*w - 99],\ [9311, 9311, -7*w - 99],\ [9319, 9319, 3*w - 97],\ [9319, 9319, -3*w - 97],\ [9323, 9323, w + 3342],\ [9323, 9323, w + 5981],\ [9391, 9391, -9*w - 101],\ [9391, 9391, 9*w - 101],\ [9397, 9397, w + 1907],\ [9397, 9397, w + 7490],\ [9403, 9403, w + 3971],\ [9403, 9403, w + 5432],\ [9409, 97, -97],\ [9413, 9413, w + 2883],\ [9413, 9413, w + 6530],\ [9431, 9431, 17*w - 111],\ [9431, 9431, -17*w - 111],\ [9437, 9437, w + 3741],\ [9437, 9437, w + 5696],\ [9439, 9439, -40*w - 81],\ [9439, 9439, 40*w - 81],\ [9467, 9467, w + 2409],\ [9467, 9467, w + 7058],\ [9479, 9479, -36*w - 59],\ [9479, 9479, 36*w - 59],\ [9511, 9511, 32*w - 27],\ [9511, 9511, -32*w - 27],\ [9521, 9521, 33*w - 37],\ [9521, 9521, -33*w - 37],\ [9533, 9533, w + 4439],\ [9533, 9533, w + 5094],\ [9547, 9547, w + 1698],\ [9547, 9547, w + 7849],\ [9551, 9551, -5*w - 99],\ [9551, 9551, 5*w - 99],\ [9587, 9587, w + 1429],\ [9587, 9587, w + 8158],\ [9601, 9601, 31*w - 3],\ [9601, 9601, -31*w - 3],\ [9613, 9613, w + 2990],\ [9613, 9613, w + 6623],\ [9631, 9631, 15*w - 109],\ [9631, 9631, -15*w - 109],\ [9643, 9643, w + 947],\ [9643, 9643, w + 8696],\ [9649, 9649, -35*w - 51],\ [9649, 9649, 35*w - 51],\ [9677, 9677, w + 1091],\ [9677, 9677, w + 8586],\ [9679, 9679, 38*w - 69],\ [9679, 9679, -38*w - 69],\ [9689, 9689, -20*w - 117],\ [9689, 9689, 20*w - 117],\ [9719, 9719, 37*w - 153],\ [9719, 9719, -37*w - 153],\ [9721, 9721, -37*w - 63],\ [9721, 9721, 37*w - 63],\ [9733, 9733, w + 3460],\ [9733, 9733, w + 6273],\ [9769, 9769, -47*w + 111],\ [9769, 9769, 47*w + 111],\ [9787, 9787, w + 1523],\ [9787, 9787, w + 8264],\ [9791, 9791, -w - 99],\ [9791, 9791, w - 99],\ [9803, 9803, w + 357],\ [9803, 9803, w + 9446],\ [9839, 9839, 23*w - 123],\ [9839, 9839, -23*w - 123],\ [9871, 9871, -27*w - 131],\ [9871, 9871, 27*w - 131],\ [9883, 9883, w + 878],\ [9883, 9883, w + 9005],\ [9907, 9907, w + 3422],\ [9907, 9907, w + 6485],\ [9923, 9923, w + 2524],\ [9923, 9923, w + 7399],\ [9929, 9929, -33*w - 31],\ [9929, 9929, 33*w - 31],\ [9973, 9973, w + 173],\ [9973, 9973, w + 9800]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, 0, 3, 1, 6, 3, 3, 6, -2, -2, -2, -5, 9, -9, 4, -10, 11, -6, -12, 15, 3, -15, -12, -15, 6, 4, -5, -9, 0, 14, 0, -9, 13, -14, -6, -12, 4, 10, 12, -21, -8, 16, -6, 24, 12, -21, -24, -12, -18, 0, 15, 12, 15, 30, -8, -23, 24, -6, 18, -22, -16, -3, 12, -3, -24, 22, -8, -12, 30, -6, 24, 7, -4, 23, 2, 2, 14, -34, -21, 30, -18, -36, -24, 15, 6, -24, 34, 37, -36, -36, -3, 3, -10, -16, 24, 12, -19, 9, 9, -28, -34, 42, 21, 8, -22, -15, 6, 30, -30, 46, -8, 38, 11, -18, 0, 2, -16, 12, 6, -17, 46, -23, 1, -27, 18, 42, 30, 36, -27, -27, 36, 48, 15, 43, 4, -31, 23, 14, 32, -42, 6, -26, -8, 7, 28, 24, 48, 30, -30, 9, 10, 37, 14, 14, -4, 14, 18, 0, -21, 12, 54, -36, 24, -51, -43, 38, -12, -6, -30, 3, 26, -28, 24, -42, 16, 22, 24, -60, 30, -48, 34, 49, 12, -21, -42, 42, -54, 36, -60, -30, -24, 51, -57, 48, -24, -48, 5, 5, 60, 3, -33, -66, 42, -6, 3, 33, -56, 10, 15, 12, -9, 0, -34, -43, 21, 42, 9, 0, 28, -26, -65, -20, 46, 10, 45, 0, -67, 56, 54, 63, 6, -60, 12, 6, 12, -66, -22, 2, 66, 6, -15, -75, -13, 23, -60, -39, 33, -6, 48, 51, 0, -54, -1, -70, -24, -30, -53, -59, 18, 18, -7, -37, -48, -33, -2, 79, -46, 68, -6, -48, 11, -22, -33, 15, -48, 48, -27, 0, 47, 74, 48, -12, 36, 27, -57, -51, 2, -49, 33, 66, -5, 22, 33, -42, -8, 73, 30, -3, -11, -74, 36, -36, 29, 17, -48, 39, -12, -60, 33, 84, 9, -45, 74, 47, 1, -50, 3, -12, -42, 69, -15, -12, -37, 26, 30, 24, -93, 84, -13, -8, 34, 58, -92, -54, 63, 36, -9, 45, -18, 6, -42, 10, 64, 24, 84, 26, 41, 69, -15, 57, -12, -37, -43, 30, -66, 73, -62, 58, -35, 84, -66, 77, -1, 65, -97, 36, -27, -3, 48, 24, -24, -22, -22, 36, -54, -30, -51, 75, -84, -54, 27, -98, -68, -60, 24, -60, -30, -69, -66, 58, 46, 90, -27, -33, 42, -4, 35, -12, -78, -34, 29, 3, 78, 72, -54, 70, 43, 68, 56, 33, -24, -25, -10, 18, 54, 60, -24, 58, -23, 10, 34, 57, -21, 78, -42, 48, -48, 36, -90, -53, 76, 33, -15, 30, -30, -69, -12, 70, -92, -60, 24, 105, 57, 36, -36, 40, 106, 0, -81, -48, -69, -63, 9, -45, 0, -36, -54, -52, -10, -84, -33, 60, 30, 18, 90, 66, -12, -12, 102, -55, 5, -38, -47, 45, -72, 44, 0, -90, 37, -44, -97, 38, -74, -14, 0, -72, 85, 19, -45, -54, -85, -112, -69, -48, 51, 66, 36, -36, 18, 18, 73, -62, -6, 42, -40, 18, 90, -85, 68, -64, -64, -64, -52, -51, 60, -18, 9, 35, -100, -37, 14, -83, 79, -39, -51, 60, -60, 1, 103, 30, 69, -72, 9, 5, 38, -114, 33, 110, -112, -72, 36, 25, -53, -6, -66, 58, -122, 15, 93, -96, 51, 9, 18, 53, -109, 62, -67, 40, 94, 60, 84, 18, -54, 72, 108, 67, -80, -69, 69, 14, -52, 108, 63, 45, 54, -47, 4, 34, 34, 87, 21, 70, -44, -39, 93, -53, 19, 49, -68, 94, -95, -89, -74, -48, -42, -46, -40, 6, 30, 28, -38, -72, 0, 0, 45, -12, -24, -17, -98, -108, 18, 8, 35, -120, -78, -74, 43, -12, -33, 120, -12, -26, 37, 0, 0, 122, 2, 9, 27, -108, -108, -110, -26, -12, 12, -48, -24, 120, 60, 99, 0, 94, 40, 98, 44, 30, 69, 45, -45, -2, -26, -17, 76, 48, -102, -6, -21, -54, -27, 18, -18, 38, -70, -22, -16, 33, 57, -114, 51, -108, 54, -116, 73, -111, -51, 43, 124, 122, -25, 18, 18, 120, 6, -102, 12, 68, -121, -26, 28, -84, 84, -126, 108, -68, -32, 9, -63, -35, 127, 105, 129, -83, 13, 61, 57, 60, 75, -21, -30, -24, 72, 18, -42, 15, 24, 120, -3, -78, 116, -55, -12, -114, 58, -104, -48, -33, 22, 142, -24, -30, 102, -129, 51, 120, -9, -81, -95, -41, -54, 144, 60, 129, -99, -45, -14, -26, -69, -57, 93, 51, -81, -90, 16, -11, 9, -45, 114, 84, 134, 26, 0, 63, 79, -38, -27, 36, -89, -44, -122, 58, -24, 60, -63, 108, 78, -51, 122, -58, -147, 30, 21, -21, -120, -78, 135, 27, -12, -51, -10, 17, 12, 60, -122, 16, 6, -42, -54, 99, 28, 10, 114, 102, -85, 50, 84, -21, -6, -156, 110, 89, -50, -128, 39, 6, 87, -60, -126, -144, -94, 68, -66, 120, 107, -142, -6, 33, 106, 61, -45, 144, 102, -147, -25, 56, -62, 46, -48, 138, 46, -152, 6, 12, 80, -1, 4, 58, 84, 96, 72, 0, -114, 96, 110, -91, -12, 12, 4, -77, 62, -94, -18, -72, 118, 58, -117, 72, -18, -18, -74, -38, -120, 66, 24, -60, 6, 84, 129, 42, 99, 81, 93, -102, 84, -39, 48, 132, 93, 33, 92, 122, 72, -90, 24, 66, 117, 18, -84, -105, -36, 54, -46, 20, -118, 86, -108, -27, 162, -27, 54, -117, 102, 150, -164, 106, -150, -30, -24, -102, 117, -36, 93, 60, 31, -104, -72, -45, 144, 36, 154, 16, 51, -6, -3, 84, -31, -58, -42, -39, 105, -150, 80, -82, -123, -12, 50, -145, 18, -90, -12, 84, -146, -65, -96, -66, -86, 160, 168, -150, -57, 120, -72, -18, 12, -39, -60, -156, -12, -78, 51, -60, -36, 0, 127, -146, 122, 14, 6, 12, -108, -18, -10, -106, 102, 159, -20, 43, -34, -4, -63, -153, 52, -56, -141, 96, 30, 33, 120, 87, 66, -30, 158, 131, -3, 156, 108, 0, 62, 155, -117, -171, -126, -54, -101, 82, 73, -89, -137, 97, -72, -90, 56, -28, 159, 66, -63, -72, 150, 30, 15, 66, -110, 52, -132, 60, 80, 32, 108, -9, 22, 22, 168, -132, -97, 92, 21, -39, -48, 93, 92, 89, -48, 156, -108, -72, 78, -60, -135, 36, -10, 125, 90, 90, 86, 56, 65, -106, -51, 42, 95, -34, 180, 36, -16, -124, -30, 129, 97, -104, 114, 66, -80, -20, -84, 138, -30, 12, -93, 12, -57, -51, 30, -12, -72, -9, 118, 70, -18, 108, -35, -50, 39, -84, -169, 182, -156, -51, -34, -115, 103, -155, 105, 111, -84, 39, -70, -121, 102, -30, -24, -66, 84, -75, 164, 5, 54, 36, 3, 15, -27, 27, -57, 156, 150, 48, 158, -4, -154, -106, 154, -59, -150, -66, 15, -114, 36, 36, -110, -182, -153, -72, -45, 180, 73, -143, 147, 42, -61, 110, -12, 120, -166, -106, 123, 48, 102, 168, 75, 6, -18, -9, 7, 142, -138, 48, -41, 115, -125, 6, 138, 98, 53, 87, -24, 3, -66, -21, 48, -63, -54, 1, -38, -22, 26, -54, 126, 75, -93, 102, -3, -10, -10, -57, 102, 0, -180, 132, 174, 30, 105, -157, -10, -150, 141, 68, 155, -87, -165, 6, 66, -14, 13, -30, 48, -93, 12, -84, -6, -33, -156, -162, 144, -51, -30, 183, 195, 132, 192, 96, 84, 23, -100, 51, -96] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([2,2,-w])] = 1 AL_eigenvalues[ZF.ideal([3,3,-w + 2])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]