/* 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([-11, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([121, 11, 11]) primes_array = [ [2, 2, -w + 3],\ [5, 5, w - 4],\ [5, 5, -w - 4],\ [7, 7, w + 2],\ [7, 7, w - 2],\ [9, 3, 3],\ [11, 11, -w],\ [19, 19, 2*w - 5],\ [19, 19, -2*w - 5],\ [37, 37, 2*w - 9],\ [37, 37, -2*w - 9],\ [43, 43, 2*w - 1],\ [43, 43, -2*w - 1],\ [53, 53, -w - 8],\ [53, 53, w - 8],\ [79, 79, 5*w - 14],\ [79, 79, 8*w - 25],\ [83, 83, -3*w - 4],\ [83, 83, 3*w - 4],\ [89, 89, -w - 10],\ [89, 89, w - 10],\ [97, 97, -3*w - 14],\ [97, 97, 3*w - 14],\ [107, 107, 6*w - 17],\ [107, 107, 9*w - 28],\ [113, 113, -4*w + 17],\ [113, 113, 11*w - 38],\ [127, 127, 4*w - 7],\ [127, 127, -4*w - 7],\ [131, 131, 5*w - 12],\ [131, 131, 14*w - 45],\ [137, 137, -7*w + 26],\ [137, 137, 8*w - 29],\ [139, 139, 7*w - 20],\ [139, 139, 10*w - 31],\ [151, 151, -4*w - 5],\ [151, 151, 4*w - 5],\ [157, 157, 3*w - 16],\ [157, 157, -3*w - 16],\ [167, 167, 4*w - 3],\ [167, 167, -4*w - 3],\ [169, 13, -13],\ [181, 181, 2*w - 15],\ [181, 181, -2*w - 15],\ [211, 211, -5*w - 8],\ [211, 211, 5*w - 8],\ [227, 227, -6*w - 13],\ [227, 227, 6*w - 13],\ [229, 229, -6*w + 25],\ [229, 229, 15*w - 52],\ [239, 239, -5*w - 6],\ [239, 239, 5*w - 6],\ [257, 257, 13*w - 46],\ [257, 257, -8*w + 31],\ [263, 263, 8*w - 21],\ [263, 263, 17*w - 54],\ [269, 269, -10*w + 37],\ [269, 269, 11*w - 40],\ [271, 271, 5*w - 2],\ [271, 271, -5*w - 2],\ [283, 283, 7*w - 16],\ [283, 283, -7*w - 16],\ [289, 17, -17],\ [307, 307, 11*w - 32],\ [307, 307, 14*w - 43],\ [313, 313, -w - 18],\ [313, 313, w - 18],\ [317, 317, 2*w - 19],\ [317, 317, -2*w - 19],\ [347, 347, -6*w - 7],\ [347, 347, 6*w - 7],\ [353, 353, -4*w - 23],\ [353, 353, 4*w - 23],\ [359, 359, 12*w - 35],\ [359, 359, 15*w - 46],\ [389, 389, -w - 20],\ [389, 389, w - 20],\ [397, 397, 2*w - 21],\ [397, 397, -2*w - 21],\ [401, 401, 5*w - 26],\ [401, 401, -5*w - 26],\ [421, 421, 17*w - 60],\ [421, 421, -10*w + 39],\ [431, 431, 11*w - 30],\ [431, 431, 20*w - 63],\ [433, 433, -11*w + 42],\ [433, 433, 16*w - 57],\ [439, 439, 7*w - 10],\ [439, 439, -7*w - 10],\ [449, 449, 4*w - 25],\ [449, 449, -4*w - 25],\ [479, 479, 8*w - 15],\ [479, 479, -8*w - 15],\ [491, 491, 9*w - 20],\ [491, 491, -9*w - 20],\ [503, 503, 7*w - 6],\ [503, 503, -7*w - 6],\ [509, 509, 5*w - 28],\ [509, 509, -5*w - 28],\ [521, 521, 8*w - 35],\ [521, 521, -8*w - 35],\ [523, 523, -7*w - 4],\ [523, 523, 7*w - 4],\ [529, 23, -23],\ [547, 547, 11*w + 28],\ [547, 547, -11*w + 28],\ [563, 563, 22*w - 69],\ [563, 563, 13*w - 36],\ [571, 571, 10*w - 23],\ [571, 571, -10*w - 23],\ [577, 577, -3*w - 26],\ [577, 577, 3*w - 26],\ [607, 607, 16*w - 47],\ [607, 607, 19*w - 58],\ [617, 617, -7*w - 34],\ [617, 617, 7*w - 34],\ [641, 641, -13*w + 50],\ [641, 641, 20*w - 71],\ [653, 653, 19*w - 68],\ [653, 653, -14*w + 53],\ [659, 659, -10*w - 21],\ [659, 659, 10*w - 21],\ [661, 661, 18*w - 65],\ [661, 661, -15*w + 56],\ [709, 709, -9*w - 40],\ [709, 709, 9*w - 40],\ [739, 739, 10*w - 19],\ [739, 739, -10*w - 19],\ [743, 743, 33*w - 106],\ [743, 743, 12*w - 29],\ [757, 757, 7*w - 36],\ [757, 757, -7*w - 36],\ [773, 773, -w - 28],\ [773, 773, w - 28],\ [787, 787, 14*w - 37],\ [787, 787, 29*w - 92],\ [797, 797, 2*w - 29],\ [797, 797, -2*w - 29],\ [811, 811, -10*w - 17],\ [811, 811, 10*w - 17],\ [827, 827, 9*w - 8],\ [827, 827, -9*w - 8],\ [829, 829, -6*w - 35],\ [829, 829, 6*w - 35],\ [841, 29, -29],\ [881, 881, -5*w - 34],\ [881, 881, 5*w - 34],\ [887, 887, 9*w - 2],\ [887, 887, -9*w - 2],\ [919, 919, 20*w - 59],\ [919, 919, 23*w - 70],\ [929, 929, -19*w + 70],\ [929, 929, 20*w - 73],\ [961, 31, -31],\ [967, 967, 31*w - 98],\ [967, 967, 16*w - 43],\ [977, 977, 8*w - 41],\ [977, 977, -8*w - 41],\ [1013, 1013, -w - 32],\ [1013, 1013, w - 32],\ [1019, 1019, 10*w - 9],\ [1019, 1019, -10*w - 9],\ [1021, 1021, 5*w - 36],\ [1021, 1021, -5*w - 36],\ [1031, 1031, 15*w + 38],\ [1031, 1031, -15*w + 38],\ [1049, 1049, -4*w - 35],\ [1049, 1049, 4*w - 35],\ [1051, 1051, -10*w - 7],\ [1051, 1051, 10*w - 7],\ [1061, 1061, 7*w - 40],\ [1061, 1061, -7*w - 40],\ [1063, 1063, 17*w - 46],\ [1063, 1063, 32*w - 101],\ [1091, 1091, 10*w - 3],\ [1091, 1091, -10*w - 3],\ [1093, 1093, -14*w + 57],\ [1093, 1093, 31*w - 108],\ [1109, 1109, 10*w - 47],\ [1109, 1109, -41*w + 140],\ [1151, 1151, 20*w - 57],\ [1151, 1151, 29*w - 90],\ [1153, 1153, 29*w - 102],\ [1153, 1153, -16*w + 63],\ [1163, 1163, 33*w - 104],\ [1163, 1163, 18*w - 49],\ [1181, 1181, 2*w - 35],\ [1181, 1181, -2*w - 35],\ [1187, 1187, -11*w - 12],\ [1187, 1187, 11*w - 12],\ [1193, 1193, 4*w - 37],\ [1193, 1193, -4*w - 37],\ [1213, 1213, 26*w - 93],\ [1213, 1213, -19*w + 72],\ [1223, 1223, 12*w - 19],\ [1223, 1223, -12*w - 19],\ [1231, 1231, 11*w - 10],\ [1231, 1231, -11*w - 10],\ [1237, 1237, -22*w + 81],\ [1237, 1237, 23*w - 84],\ [1277, 1277, 38*w - 131],\ [1277, 1277, -13*w + 56],\ [1283, 1283, -13*w - 24],\ [1283, 1283, 13*w - 24],\ [1301, 1301, -10*w - 49],\ [1301, 1301, 10*w - 49],\ [1319, 1319, -15*w - 34],\ [1319, 1319, 15*w - 34],\ [1321, 1321, -8*w - 45],\ [1321, 1321, 8*w - 45],\ [1327, 1327, 11*w - 2],\ [1327, 1327, -11*w - 2],\ [1373, 1373, -46*w + 157],\ [1373, 1373, 11*w - 52],\ [1399, 1399, 25*w - 74],\ [1399, 1399, 28*w - 85],\ [1409, 1409, -16*w + 65],\ [1409, 1409, 35*w - 122],\ [1427, 1427, 14*w - 27],\ [1427, 1427, -14*w - 27],\ [1433, 1433, -w - 38],\ [1433, 1433, w - 38],\ [1447, 1447, 16*w - 37],\ [1447, 1447, 49*w - 158],\ [1451, 1451, 15*w - 32],\ [1451, 1451, -15*w - 32],\ [1453, 1453, 6*w - 43],\ [1453, 1453, -6*w - 43],\ [1459, 1459, -13*w - 20],\ [1459, 1459, 13*w - 20],\ [1471, 1471, 40*w - 127],\ [1471, 1471, 19*w - 50],\ [1487, 1487, 36*w - 113],\ [1487, 1487, 21*w - 58],\ [1489, 1489, -5*w - 42],\ [1489, 1489, 5*w - 42],\ [1531, 1531, 14*w - 25],\ [1531, 1531, -14*w - 25],\ [1549, 1549, -21*w + 80],\ [1549, 1549, 30*w - 107],\ [1559, 1559, -12*w - 5],\ [1559, 1559, 12*w - 5],\ [1579, 1579, 50*w - 161],\ [1579, 1579, 17*w - 40],\ [1583, 1583, -12*w - 1],\ [1583, 1583, 12*w - 1],\ [1609, 1609, 9*w - 50],\ [1609, 1609, -9*w - 50],\ [1619, 1619, 27*w - 80],\ [1619, 1619, 30*w - 91],\ [1621, 1621, -15*w + 64],\ [1621, 1621, 42*w - 145],\ [1627, 1627, 14*w - 23],\ [1627, 1627, -14*w - 23],\ [1637, 1637, 2*w - 41],\ [1637, 1637, -2*w - 41],\ [1663, 1663, -13*w - 14],\ [1663, 1663, 13*w - 14],\ [1667, 1667, 19*w + 48],\ [1667, 1667, -19*w + 48],\ [1681, 41, -41],\ [1697, 1697, 8*w - 49],\ [1697, 1697, -8*w - 49],\ [1709, 1709, -10*w - 53],\ [1709, 1709, 10*w - 53],\ [1721, 1721, 40*w - 139],\ [1721, 1721, -17*w + 70],\ [1723, 1723, 38*w - 119],\ [1723, 1723, 23*w - 64],\ [1741, 1741, 13*w - 60],\ [1741, 1741, -50*w + 171],\ [1753, 1753, -w - 42],\ [1753, 1753, w - 42],\ [1759, 1759, -13*w - 10],\ [1759, 1759, 13*w - 10],\ [1811, 1811, 26*w - 75],\ [1811, 1811, 35*w - 108],\ [1823, 1823, 13*w - 6],\ [1823, 1823, -13*w - 6],\ [1847, 1847, 24*w - 67],\ [1847, 1847, 39*w - 122],\ [1867, 1867, -14*w - 17],\ [1867, 1867, 14*w - 17],\ [1873, 1873, -21*w + 82],\ [1873, 1873, 36*w - 127],\ [1901, 1901, -22*w + 85],\ [1901, 1901, 35*w - 124],\ [1931, 1931, -14*w - 15],\ [1931, 1931, 14*w - 15],\ [1973, 1973, -26*w + 97],\ [1973, 1973, 31*w - 112],\ [1979, 1979, 30*w - 89],\ [1979, 1979, 33*w - 100],\ [1987, 1987, 14*w - 13],\ [1987, 1987, -14*w - 13],\ [1999, 1999, 20*w + 49],\ [1999, 1999, -20*w + 49],\ [2017, 2017, 3*w - 46],\ [2017, 2017, -3*w - 46],\ [2029, 2029, 5*w - 48],\ [2029, 2029, -5*w - 48],\ [2063, 2063, 37*w - 114],\ [2063, 2063, 28*w - 81],\ [2069, 2069, -55*w + 188],\ [2069, 2069, 14*w - 65],\ [2087, 2087, -16*w - 27],\ [2087, 2087, 16*w - 27],\ [2111, 2111, 24*w - 65],\ [2111, 2111, 45*w - 142],\ [2113, 2113, 44*w - 153],\ [2113, 2113, -19*w + 78],\ [2131, 2131, -14*w - 5],\ [2131, 2131, 14*w - 5],\ [2137, 2137, 12*w - 61],\ [2137, 2137, -12*w - 61],\ [2161, 2161, -20*w + 81],\ [2161, 2161, 43*w - 150],\ [2207, 2207, -19*w - 42],\ [2207, 2207, 19*w - 42],\ [2209, 47, -47],\ [2237, 2237, -13*w - 64],\ [2237, 2237, 13*w - 64],\ [2239, 2239, 32*w - 95],\ [2239, 2239, 35*w - 106],\ [2243, 2243, 27*w - 76],\ [2243, 2243, 42*w - 131],\ [2251, 2251, 46*w - 145],\ [2251, 2251, 25*w - 68],\ [2269, 2269, -11*w - 60],\ [2269, 2269, 11*w - 60],\ [2281, 2281, -23*w + 90],\ [2281, 2281, 40*w - 141],\ [2287, 2287, -16*w - 23],\ [2287, 2287, 16*w - 23],\ [2293, 2293, -w - 48],\ [2293, 2293, w - 48],\ [2297, 2297, 17*w - 74],\ [2297, 2297, -17*w - 74],\ [2333, 2333, -61*w + 208],\ [2333, 2333, 14*w - 67],\ [2339, 2339, 18*w - 35],\ [2339, 2339, -18*w - 35],\ [2341, 2341, -25*w + 96],\ [2341, 2341, 38*w - 135],\ [2351, 2351, 60*w - 193],\ [2351, 2351, 21*w - 50],\ [2357, 2357, 2*w - 49],\ [2357, 2357, -2*w - 49],\ [2371, 2371, 19*w - 40],\ [2371, 2371, -19*w - 40],\ [2377, 2377, 7*w - 54],\ [2377, 2377, -7*w - 54],\ [2381, 2381, -10*w - 59],\ [2381, 2381, 10*w - 59],\ [2383, 2383, 43*w - 134],\ [2383, 2383, 28*w - 79],\ [2411, 2411, -15*w - 8],\ [2411, 2411, 15*w - 8],\ [2459, 2459, -15*w - 4],\ [2459, 2459, 15*w - 4],\ [2473, 2473, -9*w - 58],\ [2473, 2473, 9*w - 58],\ [2503, 2503, -17*w - 26],\ [2503, 2503, 17*w - 26],\ [2543, 2543, 27*w - 74],\ [2543, 2543, 48*w - 151],\ [2551, 2551, -20*w - 43],\ [2551, 2551, 20*w - 43],\ [2557, 2557, 2*w - 51],\ [2557, 2557, -2*w - 51],\ [2591, 2591, 16*w - 15],\ [2591, 2591, -16*w - 15],\ [2621, 2621, 10*w - 61],\ [2621, 2621, -10*w - 61],\ [2633, 2633, 4*w - 53],\ [2633, 2633, -4*w - 53],\ [2647, 2647, -16*w - 13],\ [2647, 2647, 16*w - 13],\ [2659, 2659, 35*w - 104],\ [2659, 2659, 38*w - 115],\ [2677, 2677, -18*w - 79],\ [2677, 2677, 18*w - 79],\ [2683, 2683, 62*w - 199],\ [2683, 2683, 23*w - 56],\ [2689, 2689, 45*w - 158],\ [2689, 2689, -24*w + 95],\ [2693, 2693, -w - 52],\ [2693, 2693, w - 52],\ [2719, 2719, -20*w - 41],\ [2719, 2719, 20*w - 41],\ [2729, 2729, -25*w + 98],\ [2729, 2729, 44*w - 155],\ [2753, 2753, -19*w - 82],\ [2753, 2753, 19*w - 82],\ [2767, 2767, -16*w - 7],\ [2767, 2767, 16*w - 7],\ [2777, 2777, 8*w - 59],\ [2777, 2777, -8*w - 59],\ [2791, 2791, 16*w - 5],\ [2791, 2791, -16*w - 5],\ [2797, 2797, 42*w - 149],\ [2797, 2797, -27*w + 104],\ [2851, 2851, 50*w - 157],\ [2851, 2851, 29*w - 80],\ [2861, 2861, 5*w - 56],\ [2861, 2861, -5*w - 56],\ [2879, 2879, 20*w - 39],\ [2879, 2879, -20*w - 39],\ [2897, 2897, -32*w + 119],\ [2897, 2897, 37*w - 134],\ [2903, 2903, 68*w - 219],\ [2903, 2903, 23*w - 54],\ [2909, 2909, -34*w + 125],\ [2909, 2909, 35*w - 128],\ [2939, 2939, 18*w - 25],\ [2939, 2939, -18*w - 25],\ [2953, 2953, -9*w - 62],\ [2953, 2953, 9*w - 62],\ [2957, 2957, 53*w - 184],\ [2957, 2957, -22*w + 91],\ [2999, 2999, 55*w - 174],\ [2999, 2999, 28*w - 75],\ [3001, 3001, -15*w - 74],\ [3001, 3001, 15*w - 74],\ [3011, 3011, 30*w - 83],\ [3011, 3011, 51*w - 160],\ [3037, 3037, -3*w - 56],\ [3037, 3037, 3*w - 56],\ [3041, 3041, -13*w - 70],\ [3041, 3041, 13*w - 70],\ [3061, 3061, 7*w - 60],\ [3061, 3061, -7*w - 60],\ [3079, 3079, 17*w - 10],\ [3079, 3079, -17*w - 10],\ [3089, 3089, 5*w - 58],\ [3089, 3089, -5*w - 58],\ [3119, 3119, 27*w - 70],\ [3119, 3119, 60*w - 191],\ [3163, 3163, 17*w - 4],\ [3163, 3163, -17*w - 4],\ [3167, 3167, 29*w - 78],\ [3167, 3167, 56*w - 177],\ [3169, 3169, 20*w - 87],\ [3169, 3169, -20*w - 87],\ [3187, 3187, 19*w - 28],\ [3187, 3187, -19*w - 28],\ [3203, 3203, -18*w - 19],\ [3203, 3203, 18*w - 19],\ [3217, 3217, -27*w + 106],\ [3217, 3217, 48*w - 169],\ [3221, 3221, -70*w + 239],\ [3221, 3221, 17*w - 80],\ [3251, 3251, -21*w - 40],\ [3251, 3251, 21*w - 40],\ [3257, 3257, -28*w + 109],\ [3257, 3257, 47*w - 166],\ [3299, 3299, -22*w - 45],\ [3299, 3299, 22*w - 45],\ [3301, 3301, 15*w - 76],\ [3301, 3301, -15*w - 76],\ [3307, 3307, 34*w - 97],\ [3307, 3307, 49*w - 152],\ [3319, 3319, -23*w - 50],\ [3319, 3319, 23*w - 50],\ [3343, 3343, 53*w - 166],\ [3343, 3343, 32*w - 89],\ [3389, 3389, 10*w - 67],\ [3389, 3389, -10*w - 67],\ [3407, 3407, -21*w - 38],\ [3407, 3407, 21*w - 38],\ [3413, 3413, -34*w + 127],\ [3413, 3413, 41*w - 148],\ [3433, 3433, -36*w + 133],\ [3433, 3433, 39*w - 142],\ [3457, 3457, -12*w - 71],\ [3457, 3457, 12*w - 71],\ [3467, 3467, 26*w - 63],\ [3467, 3467, 71*w - 228],\ [3469, 3469, 14*w - 75],\ [3469, 3469, -14*w - 75],\ [3481, 59, -59],\ [3511, 3511, 25*w - 58],\ [3511, 3511, 76*w - 245],\ [3527, 3527, -24*w - 53],\ [3527, 3527, 24*w - 53],\ [3529, 3529, 56*w - 195],\ [3529, 3529, -25*w + 102],\ [3539, 3539, 18*w - 5],\ [3539, 3539, -18*w - 5],\ [3557, 3557, 7*w - 64],\ [3557, 3557, -7*w - 64],\ [3559, 3559, -20*w - 29],\ [3559, 3559, 20*w - 29],\ [3571, 3571, -19*w - 20],\ [3571, 3571, 19*w - 20],\ [3583, 3583, -28*w + 71],\ [3583, 3583, 28*w + 71],\ [3607, 3607, 41*w - 122],\ [3607, 3607, 44*w - 133],\ [3613, 3613, 21*w - 92],\ [3613, 3613, -21*w - 92],\ [3617, 3617, 13*w - 74],\ [3617, 3617, -13*w - 74],\ [3643, 3643, -22*w - 41],\ [3643, 3643, 22*w - 41],\ [3659, 3659, 30*w - 79],\ [3659, 3659, 63*w - 200],\ [3671, 3671, -20*w - 27],\ [3671, 3671, 20*w - 27],\ [3677, 3677, 2*w - 61],\ [3677, 3677, -2*w - 61],\ [3691, 3691, 34*w - 95],\ [3691, 3691, 55*w - 172],\ [3697, 3697, 53*w - 186],\ [3697, 3697, -28*w + 111],\ [3701, 3701, -22*w - 95],\ [3701, 3701, 22*w - 95],\ [3721, 61, -61],\ [3733, 3733, 9*w - 68],\ [3733, 3733, -9*w - 68],\ [3739, 3739, 25*w - 56],\ [3739, 3739, -25*w - 56],\ [3779, 3779, 42*w - 125],\ [3779, 3779, 45*w - 136],\ [3793, 3793, -4*w - 63],\ [3793, 3793, 4*w - 63],\ [3803, 3803, 22*w - 39],\ [3803, 3803, -22*w - 39],\ [3821, 3821, -5*w - 64],\ [3821, 3821, 5*w - 64],\ [3823, 3823, 37*w - 106],\ [3823, 3823, 52*w - 161],\ [3833, 3833, -w - 62],\ [3833, 3833, w - 62],\ [3847, 3847, 64*w - 203],\ [3847, 3847, 31*w - 82],\ [3853, 3853, 11*w - 72],\ [3853, 3853, -11*w - 72],\ [3863, 3863, 28*w + 69],\ [3863, 3863, -28*w + 69],\ [3877, 3877, -17*w - 84],\ [3877, 3877, 17*w - 84],\ [3881, 3881, -20*w - 91],\ [3881, 3881, 20*w - 91],\ [3907, 3907, 19*w - 8],\ [3907, 3907, -19*w - 8],\ 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43*w + 106],\ [9109, 9109, 9*w - 100],\ [9109, 9109, -9*w - 100],\ [9127, 9127, -31*w - 38],\ [9127, 9127, 31*w - 38],\ [9133, 9133, 69*w - 248],\ [9133, 9133, -54*w + 203],\ [9151, 9151, -29*w - 10],\ [9151, 9151, 29*w - 10],\ [9157, 9157, -42*w + 169],\ [9157, 9157, 87*w - 304],\ [9161, 9161, 68*w - 245],\ [9161, 9161, -55*w + 206],\ [9187, 9187, -29*w - 8],\ [9187, 9187, 29*w - 8],\ [9203, 9203, 117*w - 376],\ [9203, 9203, 42*w - 101],\ [9221, 9221, -58*w + 215],\ [9221, 9221, 65*w - 236],\ [9239, 9239, -32*w - 45],\ [9239, 9239, 32*w - 45],\ [9241, 9241, 63*w - 230],\ [9241, 9241, -60*w + 221],\ [9277, 9277, -37*w + 156],\ [9277, 9277, 98*w - 339],\ [9283, 9283, 37*w - 76],\ [9283, 9283, -37*w - 76],\ [9293, 9293, -14*w - 107],\ [9293, 9293, 14*w - 107],\ [9319, 9319, -40*w - 91],\ [9319, 9319, 40*w - 91],\ [9323, 9323, 38*w - 81],\ [9323, 9323, -38*w - 81],\ [9337, 9337, -33*w - 146],\ [9337, 9337, 33*w - 146],\ [9371, 9371, 30*w - 23],\ [9371, 9371, -30*w - 23],\ [9377, 9377, -13*w - 106],\ [9377, 9377, 13*w - 106],\ [9391, 9391, 59*w - 170],\ [9391, 9391, 80*w - 247],\ [9397, 9397, -38*w + 159],\ [9397, 9397, 97*w - 336],\ [9421, 9421, -117*w + 400],\ [9421, 9421, 30*w - 139],\ [9461, 9461, -7*w - 100],\ [9461, 9461, 7*w - 100],\ [9467, 9467, -34*w - 57],\ [9467, 9467, 34*w - 57],\ [9479, 9479, -33*w - 50],\ [9479, 9479, 33*w - 50],\ [9497, 9497, -8*w - 101],\ [9497, 9497, 8*w - 101],\ [9511, 9511, 100*w - 317],\ [9511, 9511, 49*w - 130],\ [9539, 9539, 30*w - 19],\ [9539, 9539, -30*w - 19],\ [9547, 9547, -31*w - 32],\ [9547, 9547, 31*w - 32],\ [9587, 9587, -46*w + 117],\ [9587, 9587, 46*w + 117],\ [9601, 9601, 28*w - 135],\ [9601, 9601, -28*w - 135],\ [9629, 9629, 35*w - 152],\ [9629, 9629, -35*w - 152],\ [9631, 9631, -35*w - 62],\ [9631, 9631, 35*w - 62],\ [9643, 9643, -38*w - 79],\ [9643, 9643, 38*w - 79],\ [9661, 9661, -18*w - 115],\ [9661, 9661, 18*w - 115],\ [9679, 9679, -40*w - 89],\ [9679, 9679, 40*w - 89],\ [9689, 9689, -49*w + 190],\ [9689, 9689, 80*w - 283],\ [9719, 9719, 105*w - 334],\ [9719, 9719, 48*w - 125],\ [9733, 9733, 94*w - 327],\ [9733, 9733, -41*w + 168],\ [9743, 9743, 32*w - 39],\ [9743, 9743, -32*w - 39],\ [9749, 9749, -50*w + 193],\ [9749, 9749, 79*w - 280],\ [9767, 9767, -36*w - 67],\ [9767, 9767, 36*w - 67],\ [9769, 9769, -36*w - 155],\ [9769, 9769, 36*w - 155],\ [9787, 9787, -31*w - 28],\ [9787, 9787, 31*w - 28],\ [9803, 9803, 78*w - 239],\ [9803, 9803, 63*w - 184],\ [9811, 9811, 50*w - 133],\ [9811, 9811, 101*w - 320],\ [9817, 9817, -17*w - 114],\ [9817, 9817, 17*w - 114],\ [9851, 9851, -30*w - 7],\ [9851, 9851, 30*w - 7],\ [9857, 9857, -52*w + 199],\ [9857, 9857, 77*w - 274],\ [9901, 9901, 3*w - 100],\ [9901, 9901, -3*w - 100],\ [9907, 9907, -34*w - 53],\ [9907, 9907, 34*w - 53],\ [9949, 9949, 75*w - 268],\ [9949, 9949, -54*w + 205]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, 1, 1, 2, 2, -2, 0, -6, -6, -3, -3, 0, 0, 9, 9, 10, 10, -6, -6, -9, -9, -13, -13, -6, -6, -9, -9, 16, 16, 0, 0, -10, -10, 2, 2, 16, 16, 2, 2, -12, -12, -25, 1, 1, -12, -12, 24, 24, 9, 9, -6, -6, 19, 19, 22, 22, 1, 1, -20, -20, -28, -28, -9, 22, 22, 23, 23, -2, -2, -28, -28, -9, -9, 2, 2, -3, -3, 13, 13, 23, 23, 13, 13, -12, -12, 19, 19, -22, -22, -13, -13, 16, 16, 2, 2, 38, 38, -42, -42, 30, 30, 16, 16, -42, 16, 16, -34, -34, 22, 22, -21, -21, 10, 10, -9, -9, -9, -9, -14, -14, -22, -22, 13, 13, -10, -10, 10, 10, 38, 38, 53, 53, -42, -42, -28, -28, -10, -10, -28, -28, 10, 10, -47, -47, 23, 35, 35, 46, 46, -28, -28, -21, -21, -58, -22, -22, -57, -57, -42, -42, 46, 46, -2, -2, -50, -50, -25, -25, 16, 16, -43, -43, -20, -20, 10, 10, 30, 30, 42, 42, 46, 46, -46, -46, 38, 38, -3, -3, -66, -66, -21, -21, 46, 46, -56, -56, 0, 0, 45, 45, 46, 46, -42, -42, 57, 57, 66, 66, 35, 35, 46, 46, 9, 9, 54, 54, -9, -9, 60, 60, -9, -9, 38, 38, -22, -22, 13, 13, -64, -64, -28, -28, -34, -34, 30, 30, -56, -56, 9, 9, -6, -6, -6, -6, 44, 44, 35, 35, 32, 32, -47, -47, 0, 0, 9, 9, -34, -34, -6, -6, -57, -9, -9, 30, 30, 78, 78, 46, 46, -31, -31, 19, 19, 22, 22, -42, -42, -28, -28, 22, 22, 38, 38, -42, -42, -79, -79, -72, -72, -47, -47, 0, 0, -86, -86, 38, 38, -14, -14, 45, 45, -6, -6, 13, 13, -72, -72, 44, 44, 46, 46, -28, -28, 79, 79, -10, -10, 24, 24, -90, 30, 30, 16, 16, -22, -22, -42, -42, 13, 13, 19, 19, -44, -44, -43, -43, 42, 42, 2, 2, -64, -64, -35, -35, -72, -72, 57, 57, 82, 82, -42, -42, -87, -87, 24, 24, 76, 76, 38, 38, 31, 31, 16, 16, -34, -34, -88, -88, 1, 1, 82, 82, 46, 46, -69, -69, -20, -20, -94, -94, 41, 41, -44, -44, -10, -10, -2, -2, -56, -56, -9, -9, 79, 79, -72, -72, -54, -54, -6, -6, -75, -75, 10, 10, -75, -75, -50, -50, -58, -58, -66, -66, 89, 89, 32, 32, -65, -65, 9, 9, -64, -64, 75, 75, 16, 16, 46, 46, 78, 78, 46, 46, 110, 110, -2, -2, 60, 60, -94, -94, 0, 0, -42, -42, 38, 38, -12, -12, 23, 23, 86, 86, -6, -6, 46, 46, -22, -22, -31, -31, 112, 112, 60, 60, 88, 88, 57, 57, -72, -72, 57, 57, -9, -9, -42, -42, 10, 10, 41, 41, -54, 54, 54, -42, -42, -101, -101, 16, 16, -3, -3, -6, -6, -20, -20, -6, -6, -88, -88, 1, 1, -90, -90, 98, 98, -42, -42, -6, -6, 13, 13, 82, 82, -97, -97, -54, -54, -86, 30, 30, 66, 66, -72, -72, -2, -2, -50, -50, -3, -3, -6, -6, -65, -65, 60, 60, -31, -31, -78, -78, 1, 1, -101, -101, -122, -122, 60, 60, -75, -75, 24, 24, -64, -64, -44, -44, 9, 9, 46, 46, -101, -101, 35, 35, 88, 88, -119, -119, -20, -20, 82, 82, 54, 54, -25, -25, -102, -102, -28, -28, -43, -43, 2, 2, -28, -28, 32, 32, 85, 85, -65, -65, 46, 46, 129, 129, -42, -42, -42, -42, -12, -12, -57, -57, 24, 24, -6, -6, 19, 19, 16, 16, -130, 89, 89, 16, 16, 35, 35, 120, 120, -56, -56, 24, 24, 101, 101, -50, -50, 19, 19, 44, 44, 75, 75, -6, -6, 57, 57, 66, 66, 24, 24, -56, -56, 74, 74, 23, 23, 32, 32, -3, -3, 23, 23, 126, 126, -119, -119, -12, -12, -98, -98, 75, 75, -50, -50, 134, 134, 63, 63, -28, -28, 78, 78, -108, -108, 2, 54, 54, 44, 44, 82, 82, -13, -13, 0, 0, 111, 111, -94, -94, -10, -10, 54, 54, -6, -6, 57, 57, 57, 57, 63, 63, -110, -110, -141, -141, 88, 88, -142, -123, -123, 104, 104, 79, 79, 60, 60, -31, -31, -98, -98, 134, 134, -28, -28, 145, 145, -113, -113, 57, 57, 24, 24, -6, -6, -50, -50, 35, 35, -14, -14, -100, -100, -42, -42, -13, -13, 126, 126, -42, -42, -47, -47, -42, -42, -31, -31, 120, 120, 16, 16, -69, -69, 110, 110, -10, -10, -6, -6, 120, 120, -44, -44, -65, -65, -35, -35, -42, -42, 24, 24, 44, 44, -42, -42, 42, 42, -72, -72, -119, -119, 60, 60, 46, 46, 134, 134, 38, 38, 67, 67, 32, 32, -91, -91, 60, 60, -154, -154, 2, 2, 101, 101, 0, 0, 31, 31, -138, -138, 90, 90, -35, -35, -6, -6, 57, 57, -58, -58, 35, 35, -86, -86, 123, 123, 85, 85, -88, -88, 42, 42, -9, -9, 101, 101, -109, -109, -90, -90, -122, -122, -28, -28, 68, 68, 57, 57, -22, -22, 24, 24, 38, 38, 85, 85, 141, 141, 32, 32, -9, -9, -31, -31, -65, -65, 133, 133, -42, -42, 86, 86, -157, -157, 110, 110, -98, -98, 46, 46, -6, -6, -12, -12, 66, 66, 53, 53, 60, 60, 90, 90, -13, -13, 104, 104, 2, 2, 104, 104, 101, 101, -65, -65, -132, -132, -138, -138, 60, 60, -75, -75, 30, 30, 66, 66, 35, 35, 122, 122, -12, -12, -138, -138, 41, 41, 63, 63, -43, -43, -75, -75, -141, -141, -50, -50, -53, -53, 167, 167, -108, -108, -2, -2, 126, 126, 30, 30, -132, -132, -98, -98, 57, 57, 120, 120, 30, 30, 133, 133, -101, -101, -34, -34, 148, 148, -35, -35, -58, -58, 35, 35, -144, -144, -44, -44, -2, -2, -75, -75, 78, 78, -56, -56, -145, -145, -34, -34, -119, -119, 24, 24, 13, 13, -44, -44, 24, 24, 154, 154, -53, -53, -101, -101, 134, 134, 68, 68, -78, -78, -69, -69, -43, -43, 46, 46, -50, -50, 46, 46, 46, 46, -144, -144, 30, 30, -98, -98, -167, -167, 76, 76, 46, 46, -138, -138, -141, -141, 38, 38, -75, -75, 107, 107, -2, -2, 126, 126, -42, -42, -72, -72, -22, -22, -28, -28, -2, -2, -100, -100, -53, -53, 90, 90, 85, 85, -42, -42, -116, -116, 88, 88, 1, 1, 170, 170, 101, 101, -79, -79, -119, -119, -28, -28, -97, -97, 2, 2, 38, 38, -53, -53, -100, -100, -109, -109, 90, 90, -116, -116, 129, 129, -116, -116, 111, 111, -28, -28, 44, 44, 89, 89, 54, 54, -119, -119, 53, 53, -160, -160, -102, -102, -28, -28, 79, 79, -34, -34, -91, -91, -35, -35, -160, -160, -182, -182, -86, -86, -72, -72, 46, 46, -132, -132, 177, 177, 42, 42, 164, 164, 112, 112, -31, -31, 0, 0, 35, 35, -179, -179, -44, -44, -90, -90, 164, 164, 16, 16, 86, 86, 0, 0, -109, -109, -160, -160, -130, -130, 45, 45, -31, -31, 112, 112, 192, 192, -69, -69, -64, -64, 120, 120, 110, 110, -72, -72, 31, 31, -47, -47, -50, -50, 156, 156, -163, -163, 0, 0, -13, -13, -50, -50, -35, -35, 82, 82, -86, -86, -66, -66, -86, -86, 38, 38, -12, -12, -110, -110, 78, 78, -6, -6, -42, -42, -42, -42, -130, -130, -175, -175] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([11, 11, -w])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]