/* 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([-41, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([15, 15, -w - 7]) primes_array = [ [3, 3, w + 1],\ [4, 2, 2],\ [5, 5, w + 2],\ [7, 7, w + 2],\ [7, 7, w + 4],\ [11, 11, w + 5],\ [13, 13, w + 1],\ [13, 13, w + 11],\ [23, 23, w + 10],\ [23, 23, w + 12],\ [29, 29, -w - 3],\ [29, 29, w - 4],\ [31, 31, -w - 8],\ [31, 31, w - 9],\ [41, 41, -w],\ [41, 41, w - 1],\ [43, 43, w + 18],\ [43, 43, w + 24],\ [47, 47, w + 13],\ [47, 47, w + 33],\ [53, 53, w + 17],\ [53, 53, w + 35],\ [73, 73, w + 23],\ [73, 73, w + 49],\ [101, 101, 2*w - 9],\ [101, 101, -2*w - 7],\ [113, 113, w + 19],\ [113, 113, w + 93],\ [127, 127, w + 30],\ [127, 127, w + 96],\ [131, 131, 3*w - 17],\ [131, 131, -3*w - 14],\ [137, 137, w + 56],\ [137, 137, w + 80],\ [149, 149, 2*w - 5],\ [149, 149, -2*w - 3],\ [181, 181, 3*w - 25],\ [181, 181, -3*w - 22],\ [193, 193, w + 50],\ [193, 193, w + 142],\ [199, 199, -w - 15],\ [199, 199, w - 16],\ [229, 229, -3*w - 23],\ [229, 229, 3*w - 26],\ [239, 239, -3*w - 10],\ [239, 239, 3*w - 13],\ [257, 257, w + 28],\ [257, 257, w + 228],\ [277, 277, w + 44],\ [277, 277, w + 232],\ [281, 281, 3*w - 11],\ [281, 281, -3*w - 8],\ [283, 283, w + 110],\ [283, 283, w + 172],\ [289, 17, -17],\ [307, 307, w + 63],\ [307, 307, w + 243],\ [317, 317, w + 31],\ [317, 317, w + 285],\ [331, 331, 3*w - 28],\ [331, 331, -3*w - 25],\ [337, 337, w + 66],\ [337, 337, w + 270],\ [353, 353, w + 42],\ [353, 353, w + 310],\ [359, 359, 3*w - 5],\ [359, 359, -3*w - 2],\ [361, 19, -19],\ [373, 373, w + 51],\ [373, 373, w + 321],\ [379, 379, -w - 20],\ [379, 379, w - 21],\ [383, 383, w + 34],\ [383, 383, w + 348],\ [421, 421, -w - 21],\ [421, 421, w - 22],\ [431, 431, 5*w - 27],\ [431, 431, -5*w - 22],\ [443, 443, w + 47],\ [443, 443, w + 395],\ [457, 457, w + 199],\ [457, 457, w + 257],\ [461, 461, 6*w - 35],\ [461, 461, -6*w - 29],\ [467, 467, w + 208],\ [467, 467, w + 258],\ [479, 479, -5*w - 21],\ [479, 479, 5*w - 26],\ [491, 491, 4*w - 15],\ [491, 491, -4*w - 11],\ [499, 499, 3*w - 31],\ [499, 499, -3*w - 28],\ [523, 523, w + 195],\ [523, 523, w + 327],\ [547, 547, w + 153],\ [547, 547, w + 393],\ [569, 569, 5*w - 24],\ [569, 569, -5*w - 19],\ [587, 587, w + 176],\ [587, 587, w + 410],\ [607, 607, w + 65],\ [607, 607, w + 541],\ [613, 613, w + 89],\ [613, 613, w + 523],\ [617, 617, w + 43],\ [617, 617, w + 573],\ [619, 619, 2*w - 29],\ [619, 619, -2*w - 27],\ [631, 631, 7*w + 48],\ [631, 631, 7*w - 55],\ [647, 647, w + 174],\ [647, 647, w + 472],\ [653, 653, w + 57],\ [653, 653, w + 595],\ [659, 659, 4*w - 3],\ [659, 659, 4*w - 1],\ [661, 661, -w - 26],\ [661, 661, w - 27],\ [673, 673, w + 192],\ [673, 673, w + 480],\ [683, 683, w + 125],\ [683, 683, w + 557],\ [691, 691, -5*w - 39],\ [691, 691, 5*w - 44],\ [701, 701, -6*w - 25],\ [701, 701, 6*w - 31],\ [709, 709, -4*w - 35],\ [709, 709, 4*w - 39],\ [733, 733, w + 277],\ [733, 733, w + 455],\ [751, 751, -3*w - 32],\ [751, 751, 3*w - 35],\ [761, 761, -7*w - 32],\ [761, 761, 7*w - 39],\ [773, 773, w + 62],\ [773, 773, w + 710],\ [787, 787, w + 74],\ [787, 787, w + 712],\ [797, 797, w + 330],\ [797, 797, w + 466],\ [809, 809, 6*w - 29],\ [809, 809, -6*w - 23],\ [821, 821, 5*w - 17],\ [821, 821, -5*w - 12],\ [829, 829, -w - 29],\ [829, 829, w - 30],\ [853, 853, w + 105],\ [853, 853, w + 747],\ [859, 859, 2*w - 33],\ [859, 859, -2*w - 31],\ [863, 863, w + 201],\ [863, 863, w + 661],\ [877, 877, w + 328],\ [877, 877, w + 548],\ [937, 937, w + 427],\ [937, 937, w + 509],\ [941, 941, 5*w - 12],\ [941, 941, -5*w - 7],\ [947, 947, w + 438],\ [947, 947, w + 508],\ [967, 967, w + 350],\ [967, 967, w + 616],\ [977, 977, w + 301],\ [977, 977, w + 675],\ [983, 983, w + 150],\ [983, 983, w + 832],\ [991, 991, 2*w - 35],\ [991, 991, -2*w - 33],\ [997, 997, w + 181],\ [997, 997, w + 815],\ [1013, 1013, w + 55],\ [1013, 1013, w + 957],\ [1019, 1019, -5*w - 1],\ [1019, 1019, 5*w - 6],\ [1021, 1021, -4*w - 39],\ [1021, 1021, 4*w - 43],\ [1031, 1031, 5*w - 2],\ [1031, 1031, 5*w - 3],\ [1033, 1033, w + 473],\ [1033, 1033, w + 559],\ [1039, 1039, 5*w - 48],\ [1039, 1039, -5*w - 43],\ [1063, 1063, w + 86],\ [1063, 1063, w + 976],\ [1091, 1091, 7*w - 34],\ [1091, 1091, -7*w - 27],\ [1103, 1103, w + 291],\ [1103, 1103, w + 811],\ [1117, 1117, w + 402],\ [1117, 1117, w + 714],\ [1151, 1151, -7*w - 26],\ [1151, 1151, 7*w - 33],\ [1171, 1171, 7*w - 60],\ [1171, 1171, -7*w - 53],\ [1193, 1193, w + 77],\ [1193, 1193, w + 1115],\ [1229, 1229, -6*w - 13],\ [1229, 1229, 6*w - 19],\ [1277, 1277, w + 171],\ [1277, 1277, w + 1105],\ [1279, 1279, 2*w - 39],\ [1279, 1279, -2*w - 37],\ [1289, 1289, 6*w - 17],\ [1289, 1289, -6*w - 11],\ [1291, 1291, -w - 36],\ [1291, 1291, w - 37],\ [1297, 1297, w + 95],\ [1297, 1297, w + 1201],\ [1307, 1307, w + 173],\ [1307, 1307, w + 1133],\ [1319, 1319, 7*w - 30],\ [1319, 1319, -7*w - 23],\ [1321, 1321, 5*w - 51],\ [1321, 1321, -5*w - 46],\ [1327, 1327, w + 131],\ [1327, 1327, w + 1195],\ [1361, 1361, 9*w - 49],\ [1361, 1361, -9*w - 40],\ [1367, 1367, w + 324],\ [1367, 1367, w + 1042],\ [1369, 37, -37],\ [1373, 1373, w + 64],\ [1373, 1373, w + 1308],\ [1433, 1433, w + 625],\ [1433, 1433, w + 807],\ [1447, 1447, w + 528],\ [1447, 1447, w + 918],\ [1451, 1451, 12*w + 61],\ [1451, 1451, 12*w - 73],\ [1481, 1481, 6*w - 5],\ [1481, 1481, 6*w - 1],\ [1489, 1489, 11*w - 86],\ [1489, 1489, -11*w - 75],\ [1523, 1523, w + 87],\ [1523, 1523, w + 1435],\ [1549, 1549, 4*w - 49],\ [1549, 1549, -4*w - 45],\ [1559, 1559, -7*w - 18],\ [1559, 1559, 7*w - 25],\ [1597, 1597, w + 341],\ [1597, 1597, w + 1255],\ [1601, 1601, 7*w - 24],\ [1601, 1601, -7*w - 17],\ [1607, 1607, w + 627],\ [1607, 1607, w + 979],\ [1609, 1609, 3*w - 46],\ [1609, 1609, -3*w - 43],\ [1619, 1619, -9*w - 37],\ [1619, 1619, 9*w - 46],\ [1621, 1621, -5*w - 49],\ [1621, 1621, 5*w - 54],\ [1627, 1627, w + 740],\ [1627, 1627, w + 886],\ [1637, 1637, w + 576],\ [1637, 1637, w + 1060],\ [1657, 1657, w + 451],\ [1657, 1657, w + 1205],\ [1663, 1663, w + 302],\ [1663, 1663, w + 1360],\ [1693, 1693, w + 654],\ [1693, 1693, w + 1038],\ [1697, 1697, w + 499],\ [1697, 1697, w + 1197],\ [1699, 1699, -3*w - 44],\ [1699, 1699, 3*w - 47],\ [1723, 1723, w + 611],\ [1723, 1723, w + 1111],\ [1741, 1741, -4*w - 47],\ [1741, 1741, 4*w - 51],\ [1777, 1777, w + 276],\ [1777, 1777, w + 1500],\ [1787, 1787, w + 73],\ [1787, 1787, w + 1713],\ [1811, 1811, -7*w - 11],\ [1811, 1811, 7*w - 18],\ [1831, 1831, 5*w - 56],\ [1831, 1831, -5*w - 51],\ [1867, 1867, w + 114],\ [1867, 1867, w + 1752],\ [1879, 1879, 6*w - 61],\ [1879, 1879, -6*w - 55],\ [1889, 1889, -7*w - 8],\ [1889, 1889, 7*w - 15],\ [1907, 1907, w + 529],\ [1907, 1907, w + 1377],\ [1931, 1931, 7*w - 13],\ [1931, 1931, -7*w - 6],\ [1933, 1933, w + 116],\ [1933, 1933, w + 1816],\ [1949, 1949, -7*w - 5],\ [1949, 1949, 7*w - 12],\ [1951, 1951, 2*w - 47],\ [1951, 1951, -2*w - 45],\ [1973, 1973, w + 947],\ [1973, 1973, w + 1025],\ [1979, 1979, 7*w - 10],\ [1979, 1979, -7*w - 3],\ [1987, 1987, w + 622],\ [1987, 1987, w + 1364],\ [1993, 1993, w + 457],\ [1993, 1993, w + 1535],\ [2003, 2003, w + 739],\ [2003, 2003, w + 1263],\ [2011, 2011, 7*w - 67],\ [2011, 2011, -7*w - 60],\ [2027, 2027, w + 641],\ [2027, 2027, w + 1385],\ [2029, 2029, -w - 45],\ [2029, 2029, w - 46],\ [2053, 2053, w + 629],\ [2053, 2053, w + 1423],\ [2081, 2081, 9*w - 40],\ [2081, 2081, -9*w - 31],\ [2111, 2111, -8*w - 19],\ [2111, 2111, 8*w - 27],\ [2129, 2129, -11*w - 48],\ [2129, 2129, 11*w - 59],\ [2141, 2141, 15*w - 92],\ [2141, 2141, -15*w - 77],\ [2161, 2161, -5*w - 54],\ [2161, 2161, 5*w - 59],\ [2179, 2179, 3*w - 52],\ [2179, 2179, -3*w - 49],\ [2237, 2237, w + 781],\ [2237, 2237, w + 1455],\ [2267, 2267, w + 924],\ [2267, 2267, w + 1342],\ [2269, 2269, -7*w - 62],\ [2269, 2269, 7*w - 69],\ [2281, 2281, -3*w - 50],\ [2281, 2281, 3*w - 53],\ [2287, 2287, w + 704],\ [2287, 2287, w + 1582],\ [2297, 2297, w + 1106],\ [2297, 2297, w + 1190],\ [2309, 2309, 15*w + 76],\ [2309, 2309, 15*w - 91],\ [2311, 2311, -w - 48],\ [2311, 2311, w - 49],\ [2333, 2333, w + 1050],\ [2333, 2333, w + 1282],\ [2339, 2339, 11*w - 57],\ [2339, 2339, -11*w - 46],\ [2341, 2341, 13*w + 90],\ [2341, 2341, 13*w - 103],\ [2351, 2351, 8*w - 21],\ [2351, 2351, -8*w - 13],\ [2357, 2357, w + 353],\ [2357, 2357, w + 2003],\ [2383, 2383, w + 280],\ [2383, 2383, w + 2102],\ [2411, 2411, 9*w - 35],\ [2411, 2411, -9*w - 26],\ [2423, 2423, w + 85],\ [2423, 2423, w + 2337],\ [2437, 2437, w + 460],\ [2437, 2437, w + 1976],\ [2441, 2441, -11*w - 45],\ [2441, 2441, 11*w - 56],\ [2447, 2447, w + 960],\ [2447, 2447, w + 1486],\ [2459, 2459, -12*w - 53],\ [2459, 2459, 12*w - 65],\ [2503, 2503, w + 180],\ [2503, 2503, w + 2322],\ [2539, 2539, 2*w - 53],\ [2539, 2539, -2*w - 51],\ [2549, 2549, -13*w - 60],\ [2549, 2549, 13*w - 73],\ [2591, 2591, -8*w - 3],\ [2591, 2591, 8*w - 11],\ [2593, 2593, w + 1009],\ [2593, 2593, w + 1583],\ [2609, 2609, 14*w - 81],\ [2609, 2609, -14*w - 67],\ [2617, 2617, w + 135],\ [2617, 2617, w + 2481],\ [2633, 2633, w + 545],\ [2633, 2633, w + 2087],\ [2647, 2647, w + 944],\ [2647, 2647, w + 1702],\ [2663, 2663, w + 642],\ [2663, 2663, w + 2020],\ [2671, 2671, -7*w - 65],\ [2671, 2671, 7*w - 72],\ [2683, 2683, w + 574],\ [2683, 2683, w + 2108],\ [2687, 2687, w + 856],\ [2687, 2687, w + 1830],\ [2689, 2689, -8*w - 69],\ [2689, 2689, 8*w - 77],\ [2693, 2693, w + 1168],\ [2693, 2693, w + 1524],\ [2713, 2713, w + 1113],\ [2713, 2713, w + 1599],\ [2731, 2731, 14*w + 97],\ [2731, 2731, 14*w - 111],\ [2741, 2741, 9*w - 29],\ [2741, 2741, -9*w - 20],\ [2753, 2753, w + 117],\ [2753, 2753, w + 2635],\ [2767, 2767, w + 875],\ [2767, 2767, w + 1891],\ [2777, 2777, w + 91],\ [2777, 2777, w + 2685],\ [2789, 2789, -9*w - 19],\ [2789, 2789, 9*w - 28],\ [2801, 2801, 17*w - 104],\ [2801, 2801, 17*w + 87],\ [2833, 2833, w + 496],\ [2833, 2833, w + 2336],\ [2843, 2843, w + 646],\ [2843, 2843, w + 2196],\ [2857, 2857, w + 1357],\ [2857, 2857, w + 1499],\ [2879, 2879, 9*w - 26],\ [2879, 2879, -9*w - 17],\ [2897, 2897, w + 842],\ [2897, 2897, w + 2054],\ [2917, 2917, w + 461],\ [2917, 2917, w + 2455],\ [2927, 2927, w + 1016],\ [2927, 2927, w + 1910],\ [2939, 2939, 13*w - 70],\ [2939, 2939, -13*w - 57],\ [2957, 2957, w + 898],\ [2957, 2957, w + 2058],\ [2963, 2963, w + 94],\ [2963, 2963, w + 2868],\ [2969, 2969, 10*w - 39],\ [2969, 2969, -10*w - 29],\ [2971, 2971, 2*w - 57],\ [2971, 2971, -2*w - 55],\ [2999, 2999, -9*w - 14],\ [2999, 2999, 9*w - 23],\ [3001, 3001, 5*w - 66],\ [3001, 3001, -5*w - 61],\ [3011, 3011, -11*w - 39],\ [3011, 3011, 11*w - 50],\ [3019, 3019, -11*w - 84],\ [3019, 3019, 11*w - 95],\ [3023, 3023, w + 584],\ [3023, 3023, w + 2438],\ [3061, 3061, -4*w - 59],\ [3061, 3061, 4*w - 63],\ [3083, 3083, w + 535],\ [3083, 3083, w + 2547],\ [3119, 3119, 15*w - 86],\ [3119, 3119, -15*w - 71],\ [3163, 3163, w + 828],\ [3163, 3163, w + 2334],\ [3169, 3169, 3*w - 61],\ [3169, 3169, -3*w - 58],\ [3187, 3187, w + 149],\ [3187, 3187, w + 3037],\ [3209, 3209, -9*w - 7],\ [3209, 3209, 9*w - 16],\ [3251, 3251, -9*w - 5],\ [3251, 3251, 9*w - 14],\ [3253, 3253, w + 959],\ [3253, 3253, w + 2293],\ [3257, 3257, w + 1491],\ [3257, 3257, w + 1765],\ [3259, 3259, 5*w - 68],\ [3259, 3259, -5*w - 63],\ [3271, 3271, 10*w - 91],\ [3271, 3271, -10*w - 81],\ [3299, 3299, 9*w - 11],\ [3299, 3299, -9*w - 2],\ [3301, 3301, 9*w - 86],\ [3301, 3301, -9*w - 77],\ [3307, 3307, w + 692],\ [3307, 3307, w + 2614],\ [3313, 3313, w + 1155],\ [3313, 3313, w + 2157],\ [3323, 3323, w + 1408],\ [3323, 3323, w + 1914],\ [3329, 3329, 9*w - 8],\ [3329, 3329, 9*w - 1],\ [3331, 3331, -13*w - 95],\ [3331, 3331, 13*w - 108],\ [3343, 3343, w + 592],\ [3343, 3343, w + 2750],\ [3347, 3347, w + 1608],\ [3347, 3347, w + 1738],\ [3373, 3373, w + 209],\ [3373, 3373, w + 3163],\ [3391, 3391, -5*w - 64],\ [3391, 3391, 5*w - 69],\ [3413, 3413, w + 1655],\ [3413, 3413, w + 1757],\ [3449, 3449, -10*w - 21],\ [3449, 3449, 10*w - 31],\ [3461, 3461, -14*w - 61],\ [3461, 3461, 14*w - 75],\ [3469, 3469, -12*w - 91],\ [3469, 3469, 12*w - 103],\ [3481, 59, -59],\ [3499, 3499, -w - 59],\ [3499, 3499, w - 60],\ [3517, 3517, w + 1538],\ [3517, 3517, w + 1978],\ [3529, 3529, 7*w - 78],\ [3529, 3529, -7*w - 71],\ [3539, 3539, 12*w - 55],\ [3539, 3539, -12*w - 43],\ [3557, 3557, w + 103],\ [3557, 3557, w + 3453],\ [3581, 3581, -15*w - 68],\ [3581, 3581, 15*w - 83],\ [3583, 3583, w + 158],\ [3583, 3583, w + 3424],\ [3607, 3607, w + 1373],\ [3607, 3607, w + 2233],\ [3617, 3617, w + 288],\ [3617, 3617, w + 3328],\ [3623, 3623, w + 580],\ [3623, 3623, w + 3042],\ [3631, 3631, 9*w - 88],\ [3631, 3631, -9*w - 79],\ [3637, 3637, w + 346],\ [3637, 3637, w + 3290],\ [3643, 3643, w + 1712],\ [3643, 3643, w + 1930],\ [3659, 3659, -11*w - 31],\ [3659, 3659, 11*w - 42],\ [3671, 3671, -16*w - 75],\ [3671, 3671, 16*w - 91],\ [3673, 3673, w + 1170],\ [3673, 3673, w + 2502],\ [3677, 3677, w + 441],\ [3677, 3677, w + 3235],\ [3721, 61, -61],\ [3761, 3761, 19*w + 96],\ [3761, 3761, 19*w - 115],\ [3767, 3767, w + 106],\ [3767, 3767, w + 3660],\ [3779, 3779, -13*w - 50],\ [3779, 3779, 13*w - 63],\ [3823, 3823, w + 405],\ [3823, 3823, w + 3417],\ [3833, 3833, w + 1862],\ [3833, 3833, w + 1970],\ [3847, 3847, w + 1811],\ [3847, 3847, w + 2035],\ [3907, 3907, w + 165],\ [3907, 3907, w + 3741],\ [3911, 3911, -17*w - 81],\ [3911, 3911, 17*w - 98],\ [3917, 3917, w + 1162],\ [3917, 3917, w + 2754],\ [3919, 3919, 3*w - 67],\ [3919, 3919, -3*w - 64],\ [3929, 3929, 10*w - 19],\ [3929, 3929, -10*w - 9],\ [3931, 3931, 2*w - 65],\ [3931, 3931, -2*w - 63],\ [3947, 3947, w + 1670],\ [3947, 3947, w + 2276],\ [3967, 3967, w + 1166],\ [3967, 3967, w + 2800],\ [3989, 3989, -14*w - 57],\ [3989, 3989, 14*w - 71],\ [4001, 4001, -13*w - 48],\ [4001, 4001, 13*w - 61],\ [4003, 4003, w + 1390],\ [4003, 4003, w + 2612],\ [4007, 4007, w + 555],\ [4007, 4007, w + 3451],\ [4013, 4013, w + 741],\ [4013, 4013, w + 3271],\ [4051, 4051, -3*w - 65],\ [4051, 4051, 3*w - 68],\ [4073, 4073, w + 1054],\ [4073, 4073, w + 3018],\ [4091, 4091, -12*w - 37],\ [4091, 4091, 12*w - 49],\ [4129, 4129, -11*w - 90],\ [4129, 4129, 11*w - 101],\ [4153, 4153, w + 1626],\ [4153, 4153, w + 2526],\ [4159, 4159, 13*w - 112],\ [4159, 4159, -13*w - 99],\ [4177, 4177, w + 1876],\ [4177, 4177, w + 2300],\ [4217, 4217, w + 311],\ [4217, 4217, w + 3905],\ [4241, 4241, 14*w - 69],\ [4241, 4241, -14*w - 55],\ [4243, 4243, w + 667],\ [4243, 4243, w + 3575],\ [4259, 4259, 12*w - 47],\ [4259, 4259, -12*w - 35],\ [4261, 4261, -12*w - 95],\ [4261, 4261, 12*w - 107],\ [4283, 4283, w + 793],\ [4283, 4283, w + 3489],\ [4289, 4289, 11*w - 32],\ [4289, 4289, -11*w - 21],\ [4297, 4297, w + 1490],\ [4297, 4297, w + 2806],\ [4337, 4337, w + 1758],\ [4337, 4337, w + 2578],\ [4339, 4339, 10*w - 97],\ [4339, 4339, -10*w - 87],\ [4363, 4363, w + 379],\ [4363, 4363, w + 3983],\ [4391, 4391, 11*w - 30],\ [4391, 4391, -11*w - 19],\ [4421, 4421, 13*w - 57],\ [4421, 4421, -13*w - 44],\ [4451, 4451, 15*w - 77],\ [4451, 4451, -15*w - 62],\ [4483, 4483, w + 1165],\ [4483, 4483, w + 3317],\ [4489, 67, -67],\ [4493, 4493, w + 1301],\ [4493, 4493, w + 3191],\ [4507, 4507, w + 937],\ [4507, 4507, w + 3569],\ [4519, 4519, -5*w - 72],\ [4519, 4519, 5*w - 77],\ [4547, 4547, w + 1252],\ [4547, 4547, w + 3294],\ [4567, 4567, w + 2161],\ [4567, 4567, w + 2405],\ [4591, 4591, 18*w + 125],\ [4591, 4591, 18*w - 143],\ [4597, 4597, w + 179],\ [4597, 4597, w + 4417],\ [4621, 4621, 7*w - 85],\ [4621, 4621, -7*w - 78],\ [4643, 4643, w + 152],\ [4643, 4643, w + 4490],\ [4649, 4649, 11*w - 24],\ [4649, 4649, -11*w - 13],\ [4651, 4651, -w - 68],\ [4651, 4651, w - 69],\ [4663, 4663, w + 1828],\ [4663, 4663, w + 2834],\ [4673, 4673, w + 1129],\ [4673, 4673, w + 3543],\ [4721, 4721, 14*w - 65],\ [4721, 4721, -14*w - 51],\ [4733, 4733, w + 1467],\ [4733, 4733, w + 3265],\ [4751, 4751, 11*w - 21],\ [4751, 4751, -11*w - 10],\ [4789, 4789, -w - 69],\ [4789, 4789, w - 70],\ [4801, 4801, 13*w - 115],\ [4801, 4801, -13*w - 102],\ [4813, 4813, w + 2314],\ [4813, 4813, w + 2498],\ [4877, 4877, w + 673],\ [4877, 4877, w + 4203],\ [4903, 4903, w + 1031],\ [4903, 4903, w + 3871],\ [4909, 4909, 11*w - 105],\ [4909, 4909, -11*w - 94],\ [4919, 4919, -11*w - 3],\ [4919, 4919, 11*w - 14],\ [4937, 4937, w + 2042],\ [4937, 4937, w + 2894],\ [4943, 4943, w + 2215],\ [4943, 4943, w + 2727],\ [4951, 4951, -7*w - 80],\ [4951, 4951, 7*w - 87],\ [4957, 4957, w + 1826],\ [4957, 4957, w + 3130],\ [4973, 4973, w + 483],\ [4973, 4973, w + 4489],\ [4993, 4993, w + 1749],\ [4993, 4993, w + 3243],\ [4999, 4999, -15*w - 112],\ [4999, 4999, 15*w - 127]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, -3, -1, 0, 0, -4, 2, 2, 0, 0, -2, -2, 0, 0, 10, 10, -4, -4, -8, -8, 10, 10, -10, -10, 6, 6, -2, -2, 8, 8, -12, -12, 6, 6, 22, 22, -10, -10, -2, -2, -8, -8, 6, 6, -16, -16, -18, -18, -6, -6, -6, -6, 12, 12, -30, -28, -28, 2, 2, 12, 12, 14, 14, -18, -18, -24, -24, -22, 26, 26, -20, -20, 24, 24, -26, -26, 0, 0, 12, 12, -10, -10, -18, -18, -28, -28, 0, 0, 28, 28, 4, 4, -4, -4, 20, 20, -6, -6, 12, 12, 8, 8, -22, -22, 6, 6, -4, -4, -8, -8, -32, -32, -46, -46, 20, 20, 22, 22, 30, 30, -36, -36, -44, -44, -2, -2, -26, -26, -14, -14, 16, 16, -6, -6, -6, -6, -28, -28, 2, 2, 10, 10, 54, 54, 30, 30, -6, -6, -20, -20, 56, 56, -30, -30, 54, 54, -50, -50, 36, 36, -32, -32, -2, -2, 0, 0, 32, 32, -54, -54, -22, -22, -36, -36, -2, -2, 24, 24, 54, 54, -32, -32, 16, 16, -44, -44, -24, -24, 18, 18, -16, -16, -12, -12, 38, 38, -18, -18, -30, -30, -16, -16, 42, 42, 44, 44, 46, 46, 28, 28, -24, -24, -22, -22, 56, 56, 18, 18, -16, -16, 26, 66, 66, 54, 54, 32, 32, -36, -36, -22, -22, 18, 18, -12, -12, -18, -18, 56, 56, 50, 50, 2, 2, 0, 0, -54, -54, -12, -12, 22, 22, 28, 28, -6, -6, -26, -26, 56, 56, 18, 18, 78, 78, 52, 52, -20, -20, 14, 14, -18, -18, -36, -36, -60, -60, -56, -56, 12, 12, 8, 8, -30, -30, -28, -28, -36, -36, 34, 34, 30, 30, 32, 32, 42, 42, 60, 60, -44, -44, -42, -42, -12, -12, 28, 28, 12, 12, 14, 14, -54, -54, -30, -30, -48, -48, 18, 18, -34, -34, -14, -14, 20, 20, -62, -62, -4, -4, 62, 62, -22, -22, -72, -72, -10, -10, 6, 6, 72, 72, -62, -62, -60, -60, 38, 38, 0, 0, 74, 74, -88, -88, -36, -36, -32, -32, -22, -22, 74, 74, 24, 24, -4, -4, 48, 48, -36, -36, 54, 54, 48, 48, -98, -98, -78, -78, -58, -58, 6, 6, -16, -16, 16, 16, -16, -16, -84, -84, 72, 72, 66, 66, 58, 58, -26, -26, -20, -20, 54, 54, -18, -18, -40, -40, -10, -10, -26, -26, -14, -14, -18, -18, -20, -20, 22, 22, 64, 64, 30, 30, 74, 74, 24, 24, -4, -4, 82, 82, 20, 20, 90, 90, -4, -4, 56, 56, 58, 58, -44, -44, 28, 28, -56, -56, -10, -10, 28, 28, -48, -48, 76, 76, -30, -30, 100, 100, 10, 10, 36, 36, 58, 58, -42, -42, 12, 12, 40, 40, -60, -60, 38, 38, -52, -52, 46, 46, 44, 44, -94, -94, -60, -60, -88, -88, 36, 36, 34, 34, -96, -96, -86, -86, 58, 58, 102, 102, -82, -82, -102, 28, 28, 82, 82, 10, 10, -44, -44, -38, -38, 30, 30, 88, 88, -112, -112, 46, 46, 16, 16, -80, -80, 26, 26, -116, -116, 12, 12, 8, 8, -58, -58, 2, 2, -118, 18, 18, 48, 48, 4, 4, 40, 40, 54, 54, 64, 64, -44, -44, 56, 56, 82, 82, 64, 64, -6, -6, 92, 92, -52, -52, 8, 8, -74, -74, -30, -30, -28, -28, 32, 32, -110, -110, -76, -76, -26, -26, -84, -84, 98, 98, -26, -26, -48, -48, -50, -50, -42, -42, -78, -78, 20, 20, 36, 36, -26, -26, 76, 76, 34, 34, 86, 86, -34, -34, -28, -28, 28, 28, 120, 120, 70, 70, 84, 84, -92, -92, 10, 18, 18, 28, 28, -40, -40, -12, -12, 112, 112, 112, 112, 58, 58, -50, -50, 36, 36, -54, -54, -20, -20, 64, 64, -82, -82, 82, 82, -30, -30, -128, -128, -106, -106, 2, 2, -30, -30, 50, 50, 16, 16, -50, -50, -72, -72, 102, 102, -120, -120, 56, 56, 82, 82, -46, -46, -34, -34, -8, -8] 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 + 1])] = -1 AL_eigenvalues[ZF.ideal([5, 5, w + 2])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]