/* 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([-14, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([200, 20, 10*w + 40]) primes_array = [ [2, 2, -w - 4],\ [5, 5, -w + 3],\ [5, 5, w + 3],\ [7, 7, -2*w - 7],\ [9, 3, 3],\ [11, 11, w + 5],\ [11, 11, -w + 5],\ [13, 13, -w - 1],\ [13, 13, -w + 1],\ [31, 31, 2*w - 5],\ [31, 31, -2*w - 5],\ [43, 43, 7*w + 27],\ [43, 43, 3*w + 13],\ [47, 47, 2*w - 3],\ [47, 47, -2*w - 3],\ [61, 61, 7*w + 25],\ [61, 61, -5*w - 17],\ [67, 67, -w - 9],\ [67, 67, w - 9],\ [101, 101, 3*w - 5],\ [101, 101, -3*w - 5],\ [103, 103, 4*w - 11],\ [103, 103, -4*w - 11],\ [107, 107, -w - 11],\ [107, 107, w - 11],\ [113, 113, 2*w - 13],\ [113, 113, -2*w - 13],\ [137, 137, 4*w + 19],\ [137, 137, 16*w + 61],\ [157, 157, 13*w + 47],\ [157, 157, -7*w - 23],\ [163, 163, -3*w - 17],\ [163, 163, 3*w - 17],\ [167, 167, -8*w - 27],\ [167, 167, 12*w + 43],\ [173, 173, 11*w + 39],\ [173, 173, -9*w - 31],\ [179, 179, 17*w + 65],\ [179, 179, 5*w + 23],\ [181, 181, -5*w - 13],\ [181, 181, 5*w - 13],\ [193, 193, 12*w + 47],\ [193, 193, 8*w + 33],\ [199, 199, -4*w - 5],\ [199, 199, 4*w - 5],\ [211, 211, -w - 15],\ [211, 211, w - 15],\ [223, 223, -4*w - 1],\ [223, 223, 4*w - 1],\ [229, 229, -5*w - 11],\ [229, 229, 5*w - 11],\ [233, 233, 2*w - 17],\ [233, 233, -2*w - 17],\ [269, 269, 5*w - 9],\ [269, 269, -5*w - 9],\ [271, 271, -8*w - 25],\ [271, 271, 20*w + 73],\ [281, 281, 14*w + 55],\ [281, 281, 10*w + 41],\ [289, 17, -17],\ [293, 293, 19*w + 69],\ [293, 293, -9*w - 29],\ [311, 311, 18*w + 65],\ [311, 311, -10*w - 33],\ [331, 331, 15*w + 59],\ [331, 331, 11*w + 45],\ [337, 337, 6*w + 29],\ [337, 337, 26*w + 99],\ [347, 347, -w - 19],\ [347, 347, w - 19],\ [349, 349, -5*w - 1],\ [349, 349, 5*w - 1],\ [361, 19, -19],\ [367, 367, 8*w - 23],\ [367, 367, -8*w - 23],\ [379, 379, -5*w - 27],\ [379, 379, 5*w - 27],\ [383, 383, 6*w - 11],\ [383, 383, -6*w - 11],\ [397, 397, 7*w - 17],\ [397, 397, -7*w - 17],\ [401, 401, 4*w - 25],\ [401, 401, -4*w - 25],\ [439, 439, -10*w - 31],\ [439, 439, 26*w + 95],\ [443, 443, 17*w + 67],\ [443, 443, 13*w + 53],\ [449, 449, 10*w + 43],\ [449, 449, 22*w + 85],\ [457, 457, 6*w - 31],\ [457, 457, -6*w - 31],\ [461, 461, -7*w - 15],\ [461, 461, 7*w - 15],\ [479, 479, 6*w - 5],\ [479, 479, -6*w - 5],\ [491, 491, -5*w - 29],\ [491, 491, 5*w - 29],\ [499, 499, 3*w - 25],\ [499, 499, -3*w - 25],\ [503, 503, -6*w - 1],\ [503, 503, 6*w - 1],\ [509, 509, -9*w - 25],\ [509, 509, 9*w - 25],\ [529, 23, -23],\ [547, 547, 29*w + 111],\ [547, 547, 9*w + 41],\ [569, 569, 2*w - 25],\ [569, 569, -2*w - 25],\ [571, 571, 19*w + 75],\ [571, 571, 15*w + 61],\ [607, 607, -8*w - 17],\ [607, 607, 8*w - 17],\ [617, 617, 4*w - 29],\ [617, 617, -4*w - 29],\ [641, 641, 20*w + 79],\ [641, 641, 16*w + 65],\ [647, 647, -12*w - 37],\ [647, 647, 32*w + 117],\ [659, 659, 13*w + 55],\ [659, 659, 25*w + 97],\ [661, 661, -7*w - 5],\ [661, 661, 7*w - 5],\ [673, 673, 2*w - 27],\ [673, 673, -2*w - 27],\ [677, 677, 7*w - 3],\ [677, 677, -7*w - 3],\ [683, 683, -7*w - 37],\ [683, 683, 7*w - 37],\ [719, 719, -14*w - 45],\ [719, 719, 30*w + 109],\ [727, 727, 8*w - 13],\ [727, 727, -8*w - 13],\ [733, 733, -11*w - 31],\ [733, 733, 11*w - 31],\ [739, 739, 5*w - 33],\ [739, 739, -5*w - 33],\ [773, 773, -9*w - 19],\ [773, 773, 9*w - 19],\ [797, 797, -17*w - 57],\ [797, 797, 27*w + 97],\ [809, 809, 38*w + 145],\ [809, 809, 10*w + 47],\ [827, 827, -w - 29],\ [827, 827, w - 29],\ [829, 829, 25*w + 89],\ [829, 829, -19*w - 65],\ [839, 839, -20*w - 69],\ [839, 839, 24*w + 85],\ [841, 29, -29],\ [853, 853, 11*w - 29],\ [853, 853, -11*w - 29],\ [883, 883, 13*w + 57],\ [883, 883, 33*w + 127],\ [887, 887, -8*w - 3],\ [887, 887, 8*w - 3],\ [907, 907, 11*w + 51],\ [907, 907, 39*w + 149],\ [941, 941, 37*w + 135],\ [941, 941, -15*w - 47],\ [947, 947, -w - 31],\ [947, 947, w - 31],\ [953, 953, 8*w - 43],\ [953, 953, -8*w - 43],\ [977, 977, 34*w + 131],\ [977, 977, 14*w + 61],\ [983, 983, 36*w + 131],\ [983, 983, -16*w - 51],\ [997, 997, -13*w - 37],\ [997, 997, 13*w - 37],\ [1009, 1009, 12*w + 55],\ [1009, 1009, 40*w + 153],\ [1013, 1013, 9*w - 11],\ [1013, 1013, -9*w - 11],\ [1019, 1019, -5*w - 37],\ [1019, 1019, 5*w - 37],\ [1021, 1021, 35*w + 127],\ [1021, 1021, -17*w - 55],\ [1033, 1033, 2*w - 33],\ [1033, 1033, -2*w - 33],\ [1039, 1039, 10*w - 19],\ [1039, 1039, -10*w - 19],\ [1051, 1051, 25*w + 99],\ [1051, 1051, 21*w + 85],\ [1063, 1063, -14*w + 41],\ [1063, 1063, 14*w + 41],\ [1069, 1069, -11*w - 25],\ [1069, 1069, 11*w - 25],\ [1109, 1109, -9*w - 5],\ [1109, 1109, 9*w - 5],\ [1129, 1129, -8*w - 45],\ [1129, 1129, 8*w - 45],\ [1151, 1151, -22*w - 75],\ [1151, 1151, 30*w + 107],\ [1163, 1163, 7*w - 43],\ [1163, 1163, -7*w - 43],\ [1171, 1171, -5*w - 39],\ [1171, 1171, 5*w - 39],\ [1181, 1181, 27*w + 95],\ [1181, 1181, -25*w - 87],\ [1187, 1187, 19*w + 79],\ [1187, 1187, 31*w + 121],\ [1201, 1201, 10*w - 51],\ [1201, 1201, -10*w - 51],\ [1223, 1223, 14*w - 39],\ [1223, 1223, -14*w - 39],\ [1231, 1231, 10*w - 13],\ [1231, 1231, -10*w - 13],\ [1237, 1237, 43*w + 157],\ [1237, 1237, -17*w - 53],\ [1277, 1277, -13*w - 33],\ [1277, 1277, 13*w - 33],\ [1279, 1279, -10*w - 11],\ [1279, 1279, 10*w - 11],\ [1283, 1283, 37*w + 143],\ [1283, 1283, 17*w + 73],\ [1289, 1289, 32*w + 125],\ [1289, 1289, 20*w + 83],\ [1297, 1297, -4*w - 39],\ [1297, 1297, 4*w - 39],\ [1301, 1301, -15*w - 43],\ [1301, 1301, 15*w - 43],\ [1319, 1319, 10*w - 9],\ [1319, 1319, -10*w - 9],\ [1369, 37, -37],\ [1399, 1399, -10*w - 1],\ [1399, 1399, 10*w - 1],\ [1409, 1409, -10*w - 53],\ [1409, 1409, 10*w - 53],\ [1447, 1447, 38*w + 137],\ [1447, 1447, -22*w - 73],\ [1451, 1451, 29*w + 115],\ [1451, 1451, 25*w + 101],\ [1481, 1481, 14*w + 65],\ [1481, 1481, 50*w + 191],\ [1487, 1487, 12*w - 23],\ [1487, 1487, -12*w - 23],\ [1499, 1499, 5*w - 43],\ [1499, 1499, -5*w - 43],\ [1511, 1511, -18*w - 55],\ [1511, 1511, 50*w + 183],\ [1523, 1523, 7*w - 47],\ [1523, 1523, -7*w - 47],\ [1543, 1543, 34*w + 121],\ [1543, 1543, -26*w - 89],\ [1559, 1559, -16*w - 45],\ [1559, 1559, 16*w - 45],\ [1567, 1567, -28*w - 97],\ [1567, 1567, 32*w + 113],\ [1579, 1579, 45*w + 173],\ [1579, 1579, 17*w + 75],\ [1613, 1613, -11*w - 9],\ [1613, 1613, 11*w - 9],\ [1619, 1619, 35*w + 137],\ [1619, 1619, 23*w + 95],\ [1637, 1637, -13*w - 27],\ [1637, 1637, 13*w - 27],\ [1667, 1667, -w - 41],\ [1667, 1667, w - 41],\ [1669, 1669, 11*w - 5],\ [1669, 1669, -11*w - 5],\ [1681, 41, -41],\ [1693, 1693, -11*w - 1],\ [1693, 1693, 11*w - 1],\ [1723, 1723, 3*w - 43],\ [1723, 1723, -3*w - 43],\ [1741, 1741, 13*w - 25],\ [1741, 1741, -13*w - 25],\ [1747, 1747, 21*w + 89],\ [1747, 1747, 41*w + 159],\ [1783, 1783, -14*w - 31],\ [1783, 1783, 14*w - 31],\ [1787, 1787, 11*w - 59],\ [1787, 1787, -11*w - 59],\ [1801, 1801, 4*w - 45],\ [1801, 1801, -4*w - 45],\ [1823, 1823, -24*w - 79],\ [1823, 1823, 44*w + 159],\ [1847, 1847, -12*w - 13],\ [1847, 1847, 12*w - 13],\ [1861, 1861, 43*w + 155],\ [1861, 1861, -25*w - 83],\ [1873, 1873, 42*w + 163],\ [1873, 1873, 22*w + 93],\ [1879, 1879, -20*w - 61],\ [1879, 1879, 56*w + 205],\ [1913, 1913, -8*w - 53],\ [1913, 1913, 8*w - 53],\ [1949, 1949, 55*w + 201],\ [1949, 1949, -21*w - 65],\ [1951, 1951, 40*w + 143],\ [1951, 1951, -28*w - 95],\ [1973, 1973, 39*w + 139],\ [1973, 1973, -29*w - 99],\ [2003, 2003, 23*w + 97],\ [2003, 2003, 43*w + 167],\ [2011, 2011, -w - 45],\ [2011, 2011, w - 45],\ [2017, 2017, -14*w - 69],\ [2017, 2017, 14*w - 69],\ [2027, 2027, 11*w - 61],\ [2027, 2027, -11*w - 61],\ [2029, 2029, -19*w - 55],\ [2029, 2029, 19*w - 55],\ [2063, 2063, -16*w - 39],\ [2063, 2063, 16*w - 39],\ [2081, 2081, -10*w - 59],\ [2081, 2081, 10*w - 59],\ [2083, 2083, -3*w - 47],\ [2083, 2083, 3*w - 47],\ [2129, 2129, -8*w - 55],\ [2129, 2129, 8*w - 55],\ [2137, 2137, 44*w + 171],\ [2137, 2137, 24*w + 101],\ [2141, 2141, 13*w - 15],\ [2141, 2141, -13*w - 15],\ [2153, 2153, 2*w - 47],\ [2153, 2153, -2*w - 47],\ [2179, 2179, 67*w + 255],\ [2179, 2179, 15*w + 73],\ [2239, 2239, 50*w + 181],\ [2239, 2239, -26*w - 85],\ [2251, 2251, 5*w - 51],\ [2251, 2251, -5*w - 51],\ [2287, 2287, -22*w - 67],\ [2287, 2287, 62*w + 227],\ [2297, 2297, 14*w - 71],\ [2297, 2297, -14*w - 71],\ [2309, 2309, 15*w - 29],\ [2309, 2309, -15*w - 29],\ [2339, 2339, -7*w - 55],\ [2339, 2339, 7*w - 55],\ [2341, 2341, 13*w - 5],\ [2341, 2341, -13*w - 5],\ [2347, 2347, 9*w - 59],\ [2347, 2347, -9*w - 59],\ [2351, 2351, 20*w - 57],\ [2351, 2351, -20*w - 57],\ [2357, 2357, 13*w - 3],\ [2357, 2357, -13*w - 3],\ [2377, 2377, -4*w - 51],\ [2377, 2377, 4*w - 51],\ [2383, 2383, -14*w - 19],\ [2383, 2383, 14*w - 19],\ [2399, 2399, -30*w - 101],\ [2399, 2399, 46*w + 165],\ [2417, 2417, 26*w + 109],\ [2417, 2417, 46*w + 179],\ [2459, 2459, 5*w - 53],\ [2459, 2459, -5*w - 53],\ [2473, 2473, -12*w - 67],\ [2473, 2473, 12*w - 67],\ [2477, 2477, 43*w + 153],\ [2477, 2477, -33*w - 113],\ [2521, 2521, 6*w - 55],\ [2521, 2521, -6*w - 55],\ [2531, 2531, -11*w - 65],\ [2531, 2531, 11*w - 65],\ [2551, 2551, 70*w + 257],\ [2551, 2551, -22*w - 65],\ [2621, 2621, -15*w - 23],\ [2621, 2621, 15*w - 23],\ [2633, 2633, 58*w + 223],\ [2633, 2633, 22*w + 97],\ [2657, 2657, -16*w - 79],\ [2657, 2657, 16*w - 79],\ [2663, 2663, 14*w - 9],\ [2663, 2663, -14*w - 9],\ [2677, 2677, -17*w - 37],\ [2677, 2677, 17*w - 37],\ [2683, 2683, -3*w - 53],\ [2683, 2683, 3*w - 53],\ [2687, 2687, 18*w - 43],\ [2687, 2687, -18*w - 43],\ [2689, 2689, 70*w + 267],\ [2689, 2689, 18*w + 85],\ [2693, 2693, -21*w - 59],\ [2693, 2693, 21*w - 59],\ [2699, 2699, 25*w + 107],\ [2699, 2699, 53*w + 205],\ [2713, 2713, 28*w + 117],\ [2713, 2713, 48*w + 187],\ [2719, 2719, -14*w - 5],\ [2719, 2719, 14*w - 5],\ [2731, 2731, 39*w + 155],\ [2731, 2731, 35*w + 141],\ [2749, 2749, -29*w - 95],\ [2749, 2749, 55*w + 199],\ [2753, 2753, 2*w - 53],\ [2753, 2753, -2*w - 53],\ [2789, 2789, -15*w - 19],\ [2789, 2789, 15*w - 19],\ [2791, 2791, 20*w - 53],\ [2791, 2791, -20*w - 53],\ [2801, 2801, -4*w - 55],\ [2801, 2801, 4*w - 55],\ [2809, 53, -53],\ [2843, 2843, 17*w - 83],\ [2843, 2843, -17*w - 83],\ [2851, 2851, 65*w + 249],\ [2851, 2851, 21*w + 95],\ [2857, 2857, 26*w + 111],\ [2857, 2857, 54*w + 209],\ [2861, 2861, 15*w - 17],\ [2861, 2861, -15*w - 17],\ [2887, 2887, -32*w - 107],\ [2887, 2887, 52*w + 187],\ [2903, 2903, -26*w - 81],\ [2903, 2903, 66*w + 241],\ [2917, 2917, 23*w + 67],\ [2917, 2917, -23*w + 67],\ [2957, 2957, 17*w - 33],\ [2957, 2957, -17*w - 33],\ [2963, 2963, 13*w - 73],\ [2963, 2963, -13*w - 73],\ [2969, 2969, 2*w - 55],\ [2969, 2969, -2*w - 55],\ [2999, 2999, 20*w - 51],\ [2999, 2999, -20*w - 51],\ [3011, 3011, -w - 55],\ [3011, 3011, w - 55],\ [3019, 3019, 55*w + 213],\ [3019, 3019, 27*w + 115],\ [3023, 3023, 76*w + 279],\ [3023, 3023, -24*w - 71],\ [3037, 3037, -37*w - 127],\ [3037, 3037, 47*w + 167],\ [3049, 3049, 20*w + 93],\ [3049, 3049, 72*w + 275],\ [3067, 3067, 11*w - 69],\ [3067, 3067, -11*w - 69],\ [3079, 3079, -40*w - 139],\ [3079, 3079, 44*w + 155],\ [3089, 3089, 10*w - 67],\ [3089, 3089, -10*w - 67],\ [3137, 3137, 34*w + 139],\ [3137, 3137, 46*w + 181],\ [3167, 3167, -18*w - 37],\ [3167, 3167, 18*w - 37],\ [3181, 3181, 23*w - 65],\ [3181, 3181, -23*w - 65],\ [3187, 3187, 31*w + 129],\ [3187, 3187, 51*w + 199],\ [3191, 3191, -30*w - 97],\ [3191, 3191, 62*w + 225],\ [3203, 3203, 23*w + 103],\ [3203, 3203, 67*w + 257],\ [3217, 3217, 6*w - 61],\ [3217, 3217, -6*w - 61],\ [3253, 3253, -31*w - 101],\ [3253, 3253, 61*w + 221],\ [3257, 3257, -4*w - 59],\ [3257, 3257, 4*w - 59],\ [3259, 3259, 13*w - 75],\ [3259, 3259, -13*w - 75],\ [3299, 3299, 47*w + 185],\ [3299, 3299, 35*w + 143],\ [3313, 3313, 12*w - 73],\ [3313, 3313, -12*w - 73],\ [3329, 3329, 8*w - 65],\ [3329, 3329, -8*w - 65],\ [3347, 3347, -11*w - 71],\ [3347, 3347, 11*w - 71],\ [3359, 3359, 16*w - 15],\ [3359, 3359, -16*w - 15],\ [3361, 3361, -10*w - 69],\ [3361, 3361, 10*w - 69],\ [3371, 3371, 5*w - 61],\ [3371, 3371, -5*w - 61],\ [3373, 3373, 19*w - 41],\ [3373, 3373, -19*w - 41],\ [3391, 3391, -20*w - 47],\ [3391, 3391, 20*w - 47],\ [3407, 3407, 72*w + 263],\ [3407, 3407, -28*w - 87],\ [3461, 3461, -35*w - 117],\ [3461, 3461, 57*w + 205],\ [3463, 3463, -16*w - 11],\ [3463, 3463, 16*w - 11],\ [3467, 3467, -w - 59],\ [3467, 3467, w - 59],\ [3481, 59, -59],\ [3517, 3517, -17*w - 23],\ [3517, 3517, 17*w - 23],\ [3527, 3527, 22*w - 57],\ [3527, 3527, -22*w - 57],\ [3529, 3529, 58*w + 225],\ [3529, 3529, 30*w + 127],\ [3533, 3533, -19*w - 39],\ [3533, 3533, 19*w - 39],\ [3539, 3539, -7*w - 65],\ [3539, 3539, 7*w - 65],\ [3541, 3541, -37*w - 125],\ [3541, 3541, 55*w + 197],\ [3559, 3559, 16*w - 5],\ [3559, 3559, -16*w - 5],\ [3571, 3571, 25*w + 111],\ [3571, 3571, 69*w + 265],\ [3583, 3583, -16*w - 1],\ [3583, 3583, 16*w - 1],\ [3593, 3593, 8*w - 67],\ [3593, 3593, -8*w - 67],\ [3631, 3631, 52*w + 185],\ [3631, 3631, -40*w - 137],\ [3671, 3671, 50*w + 177],\ [3671, 3671, -42*w - 145],\ [3691, 3691, 45*w + 179],\ [3691, 3691, 41*w + 165],\ [3697, 3697, 54*w + 211],\ [3697, 3697, 34*w + 141],\ [3701, 3701, 47*w + 165],\ [3701, 3701, -45*w - 157],\ [3709, 3709, -25*w - 71],\ [3709, 3709, 25*w - 71],\ [3727, 3727, 68*w + 247],\ [3727, 3727, -32*w - 103],\ [3739, 3739, 15*w - 83],\ [3739, 3739, -15*w - 83],\ [3761, 3761, 26*w + 115],\ [3761, 3761, 70*w + 269],\ [3797, 3797, 67*w + 243],\ [3797, 3797, -33*w - 107],\ [3803, 3803, 7*w - 67],\ [3803, 3803, -7*w - 67],\ [3821, 3821, -17*w - 15],\ [3821, 3821, 17*w - 15],\ [3833, 3833, 82*w + 313],\ [3833, 3833, 22*w + 103],\ [3851, 3851, 65*w + 251],\ [3851, 3851, 29*w + 125],\ [3853, 3853, 79*w + 289],\ [3853, 3853, -29*w - 89],\ [3863, 3863, 66*w + 239],\ [3863, 3863, -34*w - 111],\ [3877, 3877, -17*w - 13],\ [3877, 3877, 17*w - 13],\ [3889, 3889, 32*w + 135],\ [3889, 3889, 60*w + 233],\ [3907, 3907, -9*w - 71],\ [3907, 3907, 9*w - 71],\ [3911, 3911, 18*w - 25],\ [3911, 3911, -18*w - 25],\ [3919, 3919, -20*w - 41],\ [3919, 3919, 20*w - 41],\ [3929, 3929, -10*w - 73],\ 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37],\ [8839, 8839, 26*w - 25],\ [8839, 8839, -26*w - 25],\ [8849, 8849, 22*w - 125],\ [8849, 8849, -22*w - 125],\ [8861, 8861, 93*w + 335],\ [8861, 8861, -55*w - 183],\ [8893, 8893, -41*w - 121],\ [8893, 8893, 131*w + 481],\ [8929, 8929, 40*w + 177],\ [8929, 8929, 108*w + 415],\ [8951, 8951, -28*w - 45],\ [8951, 8951, 28*w - 45],\ [8969, 8969, 2*w - 95],\ [8969, 8969, -2*w - 95],\ [8971, 8971, 69*w + 275],\ [8971, 8971, 65*w + 261],\ [9007, 9007, 32*w - 73],\ [9007, 9007, -32*w - 73],\ [9011, 9011, -w - 95],\ [9011, 9011, w - 95],\ [9029, 9029, 119*w + 435],\ [9029, 9029, -45*w - 139],\ [9041, 9041, 20*w - 121],\ [9041, 9041, -20*w - 121],\ [9059, 9059, -5*w - 97],\ [9059, 9059, 5*w - 97],\ [9067, 9067, -9*w - 101],\ [9067, 9067, 9*w - 101],\ [9103, 9103, -26*w - 19],\ [9103, 9103, 26*w - 19],\ [9127, 9127, 28*w - 43],\ [9127, 9127, -28*w - 43],\ [9133, 9133, 89*w + 319],\ [9133, 9133, -59*w - 199],\ [9137, 9137, -14*w - 109],\ [9137, 9137, 14*w - 109],\ [9173, 9173, -29*w - 51],\ [9173, 9173, 29*w - 51],\ [9209, 9209, -10*w - 103],\ [9209, 9209, 10*w - 103],\ [9227, 9227, 41*w + 181],\ [9227, 9227, 109*w + 419],\ [9239, 9239, -26*w - 15],\ [9239, 9239, 26*w - 15],\ [9241, 9241, 70*w + 279],\ [9241, 9241, 66*w + 265],\ [9283, 9283, 3*w - 97],\ [9283, 9283, -3*w - 97],\ [9341, 9341, -63*w - 215],\ [9341, 9341, 85*w + 303],\ [9343, 9343, 26*w - 11],\ [9343, 9343, -26*w - 11],\ [9377, 9377, 104*w + 401],\ [9377, 9377, 44*w + 191],\ [9397, 9397, -53*w - 173],\ [9397, 9397, 103*w + 373],\ [9403, 9403, 133*w + 507],\ [9403, 9403, 33*w + 157],\ [9409, 97, -97],\ [9413, 9413, 39*w - 109],\ [9413, 9413, -39*w - 109],\ [9419, 9419, 35*w + 163],\ [9419, 9419, 127*w + 485],\ [9421, 9421, -65*w - 223],\ [9421, 9421, 83*w + 295],\ [9433, 9433, -12*w - 107],\ [9433, 9433, 12*w - 107],\ [9439, 9439, 26*w - 5],\ [9439, 9439, -26*w - 5],\ [9463, 9463, -26*w - 1],\ [9463, 9463, 26*w - 1],\ [9473, 9473, -28*w - 143],\ [9473, 9473, 28*w - 143],\ [9511, 9511, -68*w - 235],\ [9511, 9511, 80*w + 283],\ [9521, 9521, 50*w + 211],\ [9521, 9521, 94*w + 365],\ [9533, 9533, 79*w + 279],\ [9533, 9533, -69*w - 239],\ [9551, 9551, -70*w - 243],\ [9551, 9551, 78*w + 275],\ [9587, 9587, -19*w - 121],\ [9587, 9587, 19*w - 121],\ [9601, 9601, -30*w - 149],\ [9601, 9601, 30*w - 149],\ [9619, 9619, 15*w - 113],\ [9619, 9619, -15*w - 113],\ [9623, 9623, 34*w - 81],\ [9623, 9623, -34*w - 81],\ [9631, 9631, -40*w - 113],\ [9631, 9631, 40*w - 113],\ [9643, 9643, 17*w - 117],\ [9643, 9643, -17*w - 117],\ [9677, 9677, 27*w - 23],\ [9677, 9677, -27*w - 23],\ [9679, 9679, 100*w + 361],\ [9679, 9679, -56*w - 185],\ [9689, 9689, -32*w - 155],\ [9689, 9689, 32*w - 155],\ [9697, 9697, -6*w - 101],\ [9697, 9697, 6*w - 101],\ [9719, 9719, 114*w + 415],\ [9719, 9719, -50*w - 159],\ [9733, 9733, 31*w - 61],\ [9733, 9733, -31*w - 61],\ [9739, 9739, 57*w + 235],\ [9739, 9739, 85*w + 333],\ [9743, 9743, 126*w + 461],\ [9743, 9743, -46*w - 141],\ [9749, 9749, 29*w - 45],\ [9749, 9749, -29*w - 45],\ [9769, 9769, 48*w + 205],\ [9769, 9769, 100*w + 387],\ [9787, 9787, -w - 99],\ [9787, 9787, w - 99],\ [9791, 9791, 30*w - 53],\ [9791, 9791, -30*w - 53],\ [9811, 9811, 95*w + 369],\ [9811, 9811, 51*w + 215],\ [9851, 9851, 5*w - 101],\ [9851, 9851, -5*w - 101],\ [9857, 9857, 26*w - 139],\ [9857, 9857, -26*w - 139],\ [9887, 9887, 28*w - 33],\ [9887, 9887, -28*w - 33],\ [9901, 9901, -47*w - 145],\ [9901, 9901, 125*w + 457],\ [9907, 9907, 61*w + 249],\ [9907, 9907, 81*w + 319],\ [9923, 9923, 7*w - 103],\ [9923, 9923, -7*w - 103],\ [9967, 9967, -52*w - 167],\ [9967, 9967, 112*w + 407],\ [9973, 9973, -31*w - 59],\ [9973, 9973, 31*w - 59]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, -1, 1, 0, 5, 5, 5, 7, -7, -10, 10, -2, -2, -7, 7, -12, 12, -2, -2, 10, -10, -1, 1, 2, 2, 12, 12, -12, -12, -2, 2, -8, -8, 11, -11, 9, -9, 12, 12, -10, 10, 0, 0, -10, 10, -19, -19, -11, 11, -10, 10, -8, -8, 0, 0, -20, 20, -11, -11, 25, -5, 5, -30, 30, -28, -28, -16, -16, -28, -28, -26, 26, 34, 7, -7, 16, 16, 0, 0, 13, -13, -3, -3, 28, -28, 10, 10, 15, 15, 6, 6, -12, 12, 12, -12, -27, -27, -17, -17, -9, 9, -8, 8, 18, -28, -28, 18, 18, 12, 12, 29, -29, -12, -12, -26, -26, -12, 12, -23, -23, -4, 4, 32, 32, 11, -11, -12, -12, 0, 0, 32, -32, 5, -5, 25, 25, 49, -49, 1, -1, -13, -13, -24, -24, -2, 2, 4, -4, -33, -38, 38, -36, -36, 48, -48, 28, 28, -44, 44, 2, 2, -42, -42, 42, 42, -3, 3, -39, 39, 39, 39, -14, 14, -20, -20, 34, -34, 24, 24, -38, 38, -13, -13, 52, -52, 16, -16, 56, -56, 27, 27, 0, 0, 66, 66, -15, -15, -18, 18, 48, 48, -37, -37, 43, -43, -58, 58, 38, -38, -25, 25, 36, -36, -48, -48, 54, 54, 50, 50, 4, -4, 34, -34, -58, -46, 46, -39, -39, -19, 19, -16, -16, 41, 41, 27, -27, -63, -63, 0, 0, 68, 68, -39, 39, 6, -6, 72, -72, 47, 47, -6, 6, 3, 3, -3, 3, -60, -60, 10, -10, 46, 39, -39, 30, 30, 22, -22, -74, -74, -57, 57, -16, -16, -53, -53, 85, -85, 56, -56, 28, -28, 46, 46, -50, 50, 22, 22, -74, 74, -48, 48, -63, 63, 36, 36, 19, 19, 8, 8, -26, -26, 4, -4, 44, -44, 78, 78, -54, -54, 15, 15, 14, 14, 72, -72, -22, -22, -73, -73, 52, -52, 4, 4, 33, -33, 26, 26, 24, -24, 84, 84, -80, 80, 32, 32, -56, 56, 17, -17, 88, 88, 35, -35, 90, -90, -62, -62, 27, 27, -90, -90, -1, 1, -65, -65, 7, 7, 34, -34, 18, -18, -100, -100, -52, -52, 31, -31, -73, 73, 16, 16, -7, 7, -55, -55, 87, -87, -27, -27, 96, 96, 8, -8, 79, 79, -72, 72, 18, 18, -4, 4, 42, -42, -39, -39, -6, 24, 24, 52, 52, 4, 4, 0, 0, -24, 24, 89, -89, 22, -22, -15, 15, -42, -42, -42, -42, -80, 80, -20, -20, 4, 4, 9, -9, -29, 29, -29, -29, -6, -6, -28, 28, 91, 91, 22, 22, 96, -96, 16, -16, -20, -20, -24, 24, -24, -24, -86, -86, 67, -67, 42, 42, 77, 77, 15, 15, -22, -22, 66, 66, -48, -48, -6, 6, -25, -25, 21, 21, -55, 55, 40, -40, 48, -48, 26, -26, -53, 53, -24, -24, 18, -105, 105, 45, -45, 33, 33, 31, -31, -13, -13, 30, -30, 112, -112, -33, -33, -85, 85, 6, 6, 22, -22, 70, -70, 107, 107, -88, -88, -18, 18, 10, -10, -80, 80, 7, 7, 70, 70, -49, 49, -94, -94, -72, 72, -6, -6, 15, 15, 7, -7, 89, -89, 55, -55, -55, -55, 48, 48, -54, 54, 64, -64, 15, 15, 23, 23, 107, -107, -28, 28, -37, -37, -97, 97, 52, 52, -112, 112, 86, 86, -14, -14, 50, -50, -2, 2, 57, 57, -106, 106, 1, 1, -16, -16, 18, -18, -43, -43, -95, -95, 88, -88, 56, 56, -106, 106, 70, 70, 89, -89, 114, 114, 51, -51, -8, 8, -37, -37, -81, 81, 72, 72, 80, 80, 72, -72, 59, 59, 119, -119, -63, 63, -76, 76, 95, -95, -40, -40, -30, 30, 110, -110, 28, 28, 77, 77, -18, -18, -76, -76, -24, 24, -85, -85, 7, -7, -31, -31, 126, -126, -28, 28, 120, 120, 112, -112, -34, 34, -18, 18, 56, -56, -96, 96, -27, 27, 84, 84, -69, 69, 38, 38, -73, -73, 22, -22, -142, 55, 55, 40, -40, -8, 8, -112, -112, -18, -18, -6, -6, 57, -57, 62, 62, -44, -44, 124, 124, 4, -4, 142, 39, -39, 52, -52, -74, 74, -112, -112, -80, 80, -31, -31, -102, 102, -62, 62, -11, -11, -52, -52, 38, -38, 22, -22, -60, -60, -66, 66, -54, 54, 72, 72, 130, -130, -50, -50, 36, -36, 119, -119, -125, -125, -132, -132, 64, -64, 86, -86, -30, 30, 65, -65, 26, 26, 43, -43, -35, -35, -102, 102, -75, -75, -118, -118, 56, -56, 12, -12, 54, 54, 6, 6, 39, -39, -34, 34, -152, -152, 79, -79, 18, 18, -105, 105, 19, -19, 106, 106, 78, -78, 108, 108, -42, -42, -78, 78, -29, 29, -84, -84, 73, 73, 22, 22, 24, -24, -68, 68, -109, -147, 147, -63, 63, -18, 18, 49, -49, 49, -49, -46, -46, -105, -105, 64, 64, 70, 70, 6, -6, 29, -29, 41, 41, -14, 14, 133, -133, -90, -90, 25, 25, -87, -87, -12, -12, -145, -145, -4, -4, 70, -70, 146, 146, 86, 86, -34, -34, 114, -114, -112, 112, 3, 3, -123, 123, -81, -81, 62, 62, -73, -73, 66, -66, 82, -82, 65, -65, 74, 74, -30, 30, -76, 76, 58, 58, 96, 96, -79, -79, -68, -68, 101, -101, 20, 20, 150, 140, 140, 102, -102, -54, 54, -42, -42, 49, -49, -92, -92, 46, 46, -16, 16, 120, -120, 50, 50, 114, -114, -166, -166, -28, -28, 56, 56, 142, -142, -101, -101, -54, 54, -2, 2, -19, -19, 6, -6, -6, -6, 50, 50, 76, 76, 116, 116, -41, -41, 97, -97, -67, -67, 106, 106, 38, -38, 42, -42, -39, -39, -26, 26, 12, -12, -76, -76, 109, -109, -122, 122, -156, -156, 139, 139, 64, -64, -82, 82, -52, -52, -61, 61, -92, 92, 20, 20, -112, 112, 58, -58, -120, -120, -32, 32, 5, 5, 6, -6, 138, 138, -150, 150, 138, 138, 114, 31, -31, -36, 36, 86, 86, -129, -129, -62, -62, -130, 130, 6, -6, 52, 52, -72, 72, 7, 7, 88, -88, 41, -41, 33, 33, 12, 12, -62, 62, 106, -106, 68, 68, 122, -122, -102, -102, 43, -43, -115, 115, 74, -74, 22, 22, 40, 40, -67, -67, -102, -102, 140, -140, 126, -126, 86, 86, 85, -85, 10, -10, -132, -132, -156, 156, -48, -48, 110, 110, -46, -46, -129, 129, -14, -14, -43, 43, 98, -98, 70, -70, -9, 9, 118, -118, -56, 56, -99, -99, 17, 17, 147, -147, -143, -143, 58, 58, 174, -174, 18, 18, 130, 130, -36, -36, -97, 97, -136, -136, 30, -30, 132, -132, 165, 165, 24, -24, -119, 119, -139, -139, 174, -174, -110, -110, -5, -5, 88, -88, -27, -27, -106, 106, -154, -154, -39, -39, 166, 166, -11, 11, -79, 79, 46, -46, 132, 132, -73, 73, 30, 30, 92, 92, 156, -156, 21, 21, -26, -26, 30, -30, -47, 47, -68, -68, 130, -130, -96, -96, -95, -34, 34, -160, -160, -114, 114, 176, 176, 26, -26, -99, 99, -120, -120, -162, 162, 153, 153, -151, 151, -18, 18, 78, 78, -29, -29, -131, -131, -48, 48, -118, 118, -122, -122, 78, -78, -70, 70, 18, 18, 130, 130, -42, 42, -45, 45, 13, 13, -156, 156, -130, 130, -29, -29, 82, 82, 138, -138, -140, -140, 27, 27, -30, -30, -93, 93, 92, -92, 118, 118, 138, 138, 93, -93, 9, -9] 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 - 4])] = -1 AL_eigenvalues[ZF.ideal([5, 5, -w + 3])] = 1 AL_eigenvalues[ZF.ideal([5, 5, w + 3])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]