/* 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([256, 16, 16]) 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, 2, 2, -2, -2, -2, 0, 0, -10, -10, -6, -6, 6, 6, 2, 6, 6, 10, 10, -12, -12, 8, 8, -6, -6, -2, -2, -2, -2, -18, -4, -4, -18, -18, 2, 2, -18, -18, 16, 16, 14, 14, 4, 4, 18, 18, 24, 24, -2, -2, -8, -8, 6, 6, -18, -18, 6, 6, -30, 14, 14, 18, 18, 28, 28, 6, 6, -18, -18, 4, 4, -34, -10, -10, 6, 6, 30, 30, 10, 10, -40, -40, -36, -36, 6, 6, -34, -34, -14, -14, 0, 0, -22, -22, 14, 14, -30, -38, -38, -2, -2, 18, 18, 26, 26, -34, -34, 12, 12, 30, 30, -34, -34, 44, 44, 30, 30, 42, 42, -42, -42, 22, 22, -42, -42, -24, -24, 6, 6, -8, -8, 46, 46, 10, 10, -34, -34, 54, 54, -22, -22, -18, -18, -6, -6, 22, 22, 36, 36, -22, -26, -26, 22, 22, -46, -46, 34, 34, 38, 38, 24, 24, -36, -36, 30, 30, -14, -14, -16, -16, 54, 54, -34, -34, -34, -34, 20, 20, -40, -40, -18, -18, 30, 30, 46, 46, 2, 2, -38, -38, -64, -64, 54, 54, 34, 34, 50, 50, 14, 14, 40, 40, -10, -10, -14, -14, -42, -42, -64, -64, -14, -14, 14, 14, 22, 22, -12, -12, 10, 10, -2, -2, 6, 6, 12, 12, 30, 30, -62, -62, 16, 16, -74, -74, -32, -32, -2, -2, 38, 38, -34, -34, -2, -2, -12, -12, -54, -54, -52, -52, -42, -42, -14, -14, 46, 46, 38, 38, 30, 30, -42, -42, 2, 2, 22, 22, 30, 30, -50, -50, -26, -26, 50, 50, 16, 16, -10, -10, -18, -18, 4, 4, 22, 22, -40, -40, 6, 6, -4, -4, 34, 34, 18, 18, -10, -10, -64, -64, 14, 14, 58, 58, 30, 30, 24, 24, -6, -6, -50, -50, 60, 60, -10, -10, 30, 30, -86, -86, -18, -18, -64, -64, -46, -46, 62, 62, -10, -10, -30, -82, -82, 6, 6, 64, 64, 42, 42, 30, 30, 30, 30, -34, -34, 20, 20, 30, 30, -18, -18, 24, 24, -82, -82, -48, -48, 38, 38, 78, 78, -14, -14, 94, 94, -70, -70, -52, -52, 38, 38, 0, 0, -66, -66, 8, 8, -58, -58, -82, -82, -62, -62, -42, -42, 58, 58, 76, 76, 80, 80, -86, -86, -60, -60, -2, -2, 30, 30, 74, 74, -42, -42, 94, 94, 32, 32, -90, -90, -18, -18, -14, -14, 30, 30, -36, -36, 26, 26, -34, -34, -34, -34, -2, -2, -74, -74, -76, -76, 14, 14, 34, 34, 72, 72, -62, -62, 102, 102, 62, 62, -38, -38, -36, -36, -86, -86, 42, 42, -58, -58, -60, -60, 22, 22, -52, -52, 94, 94, -2, -2, 10, 10, 16, 16, 82, 82, -10, -10, 48, 48, 30, 30, -34, -34, -58, -58, 78, -20, -20, -2, -2, -34, -34, 6, 6, -74, -74, 78, 78, 116, 116, -34, -34, -24, -24, 22, 22, -10, -10, 44, 44, 22, 22, 36, 36, -118, 14, 14, -78, -78, -86, -86, -90, -90, 6, 6, 94, 94, -26, -26, -38, -38, -66, -66, 58, 58, -76, -76, -18, -18, 56, 56, -46, -46, 90, 90, 14, 14, 34, 34, 2, 2, -18, -18, 102, 102, -14, -14, 104, 104, -34, -34, -104, -104, 30, 30, -18, -18, -34, -34, 112, 112, -82, -82, -44, -44, 126, 126, -62, -62, -114, -114, -8, -8, -2, -2, -78, -78, -98, -98, -26, -26, -42, -42, -92, -92, -42, -42, 30, 30, -86, -86, 2, 2, -70, -70, 94, 94, -82, -82, 62, 62, 84, 84, 78, 78, 2, 2, -34, -34, -8, -8, 62, 62, 14, 14, 70, 70, -112, -112, 114, 114, 10, 10, 132, 132, 2, 2, -38, -38, 90, 90, 30, 30, -8, -8, 60, 60, 66, 66, -112, -112, -62, -62, 46, 46, -16, -16, 52, 52, -34, -34, 90, 90, -68, -68, -98, -98, -52, -52, -74, -74, 10, 10, -26, -26, 70, 70, 4, 4, 102, 102, 62, 62, -88, -88, -34, -34, -2, -2, -94, -94, 64, 64, -106, -106, -66, -66, 30, 30, 38, 38, -104, -104, -42, -42, 0, 0, -98, -98, -138, -138, 50, 54, 54, -38, -38, 20, 20, 78, 78, -36, -36, 54, 54, 92, 92, -66, -66, -34, -34, -14, -14, 138, 138, -96, -96, 70, 70, 68, 68, -26, -26, -126, -126, -104, -104, -130, -130, -98, -98, -34, -34, 114, 114, -26, -26, 12, 12, 132, 132, 74, 74, 70, 70, 2, 2, -2, -2, 118, 118, -8, -8, -66, -66, -16, -16, 42, 42, 30, 30, 74, 74, -56, -56, 50, 50, 42, 42, 54, 54, 12, 12, 110, 110, 74, 74, -150, -150, 118, 118, -82, -82, -18, -18, 26, 26, 48, 48, -82, -82, -98, -98, -42, -42, 132, 132, 66, 66, -114, -114, -154, -154, 76, 76, 102, 102, -48, -48, 38, 38, -12, -12, 38, 38, -22, -22, -54, -54, -52, -52, 30, 30, 94, 94, 110, 110, -18, -18, 130, 130, 34, 34, -114, -114, -110, -110, -86, -86, 44, 44, -14, -14, -66, -66, -60, -60, -26, -26, -42, -42, 156, 156, 34, 34, 80, 80, 14, 14, 158, 158, -98, -98, -92, -92, 114, 114, 110, 110, -50, -50, 28, 28, -70, -70, -2, -2, 48, 48, 134, 134, -54, -54, 72, 72, 30, 30, 56, 56, 78, 78, 26, 26, -66, -66, 58, 58, -80, -80, -102, -102, 4, 4, -78, -78, 14, 14, -40, -40, -52, -52, -14, -14, 30, 30, -26, -26, -74, -74, -58, -58, -14, -14, 54, 54, -150, -150, 150, 150, 92, 92, 90, 90, 62, 62, 142, 142, -46, -46, -38, -38, -98, -98, 154, 154, 78, 78, -26, -26, 4, 4, -38, -38, 22, 22, -92, -92, -142, -142, -36, -36, 30, 30, 126, 126, 62, 62, -82, -82, 126, 126, -42, -42, 56, 56, 98, 98, 150, 150, -42, -42, 150, 150, 4, 4, 54, 54, 26, 26, 72, 72, -58, -58, -56, -56, 150, 150, -70, -70, -76, -76, -130, -130, 162, 162, 122, 122, 22, 22, 120, 120, -42, -42, -138, -138, 26, 26, 34, 34, 0, 0, 34, 34, 4, 4, 102, 102, 114, 114, -34, -34, 92, 92, -2, -2, -86, -86, 86, 86, 66, 66, 66, 66, 136, 136, -74, -74, -38, -38, 122, 122, 74, 74, 102, 102, -98, -98, 140, 140, -30, -30, 90, 90, -34, -34, 62, 62, -102, -102, -98, -98, -146, -146, 18, 18, 168, 168, 126, 126, -66, -66, -22, -22, -48, -48, -66, -66, 20, 20, -98, -98, 74, 74, 38, 38, 46, 46, -34, -34, 94, 94, -180, -180, 10, 10, -18, -18, 164, 164, -2, -2, 14, 14, -66, -66, -126, -126, -182, -182, 78, 78, -154, -154, -32, -32, 118, 118, -150, -150, -10, -10, 98, 98, -136, -136, -14, -14, -114, -114, 30, 30, 44, 44, 14, 14, -138, -138, -62, -62, -110, -110, 134, 134, -160, -160, 20, 20, 54, 54, -152, -152, 38, 38, 6, 6, -190, -66, -66, -4, -4, 6, 6, 144, 144, 94, 94, -124, -124, 116, 116, 114, 114, -186, -186, -122, -122, 8, 8, 34, 34, 2, 2, -130, -130, -96, -96, 118, 118, 66, 66, 30, 30, 8, 8, -86, -86, 108, 108, 78, 78, -82, -82, 14, 14, 6, 6, 48, 48, -130, -130, 152, 152, -8, -8, -194, -194, -158, -158, 114, 114, -86, -86, -74, -74] 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 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]