/* 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, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([121, 11, -11]) primes_array = [ [2, 2, -w + 4],\ [2, 2, -w - 3],\ [3, 3, -4*w - 13],\ [7, 7, -2*w - 7],\ [7, 7, -2*w + 9],\ [19, 19, 10*w + 33],\ [25, 5, 5],\ [29, 29, -6*w - 19],\ [29, 29, -6*w + 25],\ [41, 41, 2*w - 5],\ [41, 41, -2*w - 3],\ [43, 43, 2*w - 11],\ [43, 43, 2*w + 9],\ [53, 53, 2*w - 3],\ [53, 53, -2*w - 1],\ [59, 59, 4*w - 15],\ [59, 59, 4*w + 11],\ [61, 61, -4*w - 15],\ [61, 61, -4*w + 19],\ [71, 71, 8*w + 25],\ [71, 71, 8*w - 33],\ [73, 73, -16*w - 53],\ [73, 73, 24*w + 79],\ [89, 89, 14*w + 45],\ [89, 89, 14*w - 59],\ [107, 107, -4*w - 9],\ [107, 107, 4*w - 13],\ [113, 113, 6*w - 23],\ [113, 113, 6*w + 17],\ [121, 11, -11],\ [139, 139, 2*w - 15],\ [139, 139, -2*w - 13],\ [157, 157, 12*w - 53],\ [157, 157, 12*w + 41],\ [163, 163, -6*w - 23],\ [163, 163, -6*w + 29],\ [167, 167, 56*w + 183],\ [167, 167, 16*w + 51],\ [169, 13, -13],\ [173, 173, 22*w + 71],\ [173, 173, 42*w + 137],\ [179, 179, -4*w - 5],\ [179, 179, 4*w - 9],\ [199, 199, 2*w - 17],\ [199, 199, -2*w - 15],\ [227, 227, 4*w - 3],\ [227, 227, 4*w - 1],\ [229, 229, 20*w - 87],\ [229, 229, -20*w - 67],\ [257, 257, -6*w - 13],\ [257, 257, 6*w - 19],\ [269, 269, 10*w - 39],\ [269, 269, 10*w + 29],\ [271, 271, -6*w + 31],\ [271, 271, -6*w - 25],\ [277, 277, -28*w - 93],\ [277, 277, 52*w + 171],\ [281, 281, 30*w + 97],\ [281, 281, 50*w + 163],\ [283, 283, 18*w + 61],\ [283, 283, 18*w - 79],\ [289, 17, -17],\ [293, 293, 14*w + 43],\ [293, 293, 14*w - 57],\ [313, 313, -8*w - 31],\ [313, 313, -8*w + 39],\ [317, 317, 6*w - 17],\ [317, 317, -6*w - 11],\ [349, 349, -12*w - 43],\ [349, 349, 12*w - 55],\ [367, 367, 26*w - 113],\ [367, 367, -26*w - 87],\ [383, 383, -8*w - 19],\ [383, 383, 8*w - 27],\ [397, 397, -4*w - 23],\ [397, 397, 4*w - 27],\ [401, 401, 10*w + 27],\ [401, 401, 10*w - 37],\ [431, 431, 32*w - 135],\ [431, 431, 32*w + 103],\ [449, 449, 6*w - 11],\ [449, 449, -6*w - 5],\ [457, 457, -8*w + 41],\ [457, 457, -8*w - 33],\ [463, 463, 58*w + 191],\ [463, 463, -42*w - 139],\ [499, 499, 22*w - 97],\ [499, 499, 22*w + 75],\ [509, 509, 6*w - 5],\ [509, 509, 6*w - 1],\ [521, 521, 18*w + 55],\ [521, 521, 18*w - 73],\ [529, 23, -23],\ [541, 541, 20*w - 89],\ [541, 541, 20*w + 69],\ [563, 563, 28*w - 117],\ [563, 563, 28*w + 89],\ [569, 569, 46*w + 149],\ [569, 569, 66*w + 215],\ [571, 571, -14*w - 51],\ [571, 571, 14*w - 65],\ [577, 577, -16*w - 57],\ [577, 577, 16*w - 73],\ [599, 599, 40*w + 129],\ [599, 599, 80*w + 261],\ [613, 613, -4*w - 27],\ [613, 613, 4*w - 31],\ [619, 619, 2*w - 27],\ [619, 619, -2*w - 25],\ [631, 631, 30*w - 131],\ [631, 631, 30*w + 101],\ [641, 641, 10*w - 33],\ [641, 641, -10*w - 23],\ [643, 643, 6*w - 37],\ [643, 643, -6*w - 31],\ [659, 659, 20*w + 61],\ [659, 659, 20*w - 81],\ [677, 677, 14*w - 53],\ [677, 677, 14*w + 39],\ [683, 683, 12*w - 43],\ [683, 683, 12*w + 31],\ [691, 691, -10*w + 51],\ [691, 691, -10*w - 41],\ [709, 709, 28*w + 95],\ [709, 709, 28*w - 123],\ [727, 727, 2*w - 29],\ [727, 727, -2*w - 27],\ [733, 733, 4*w - 33],\ [733, 733, -4*w - 29],\ [739, 739, 38*w - 165],\ [739, 739, -38*w - 127],\ [743, 743, -8*w - 9],\ [743, 743, 8*w - 17],\ [757, 757, -12*w - 47],\ [757, 757, -12*w + 59],\ [769, 769, -8*w - 37],\ [769, 769, 8*w - 45],\ [773, 773, 18*w - 71],\ [773, 773, 18*w + 53],\ [797, 797, 26*w + 81],\ [797, 797, 26*w - 107],\ [823, 823, -46*w - 153],\ [823, 823, 94*w + 309],\ [827, 827, 12*w + 29],\ [827, 827, 12*w - 41],\ [839, 839, 16*w + 45],\ [839, 839, 16*w - 61],\ [853, 853, 36*w + 121],\ [853, 853, 36*w - 157],\ [857, 857, 14*w - 51],\ [857, 857, 14*w + 37],\ [859, 859, 18*w - 83],\ [859, 859, -18*w - 65],\ [863, 863, -8*w - 3],\ [863, 863, 8*w - 11],\ [883, 883, -54*w - 179],\ [883, 883, 86*w + 283],\ [887, 887, -8*w - 1],\ [887, 887, 8*w - 9],\ [911, 911, 8*w - 5],\ [911, 911, 8*w - 3],\ [919, 919, -62*w - 205],\ [919, 919, -78*w - 257],\ [937, 937, -8*w - 39],\ [937, 937, 8*w - 47],\ [941, 941, -10*w - 17],\ [941, 941, 10*w - 27],\ [953, 953, 62*w + 201],\ [953, 953, 82*w + 267],\ [961, 31, -31],\ [967, 967, 2*w - 33],\ [967, 967, -2*w - 31],\ [971, 971, 28*w - 115],\ [971, 971, 28*w + 87],\ [977, 977, 38*w + 121],\ [977, 977, 38*w - 159],\ [983, 983, 24*w + 73],\ [983, 983, 24*w - 97],\ [997, 997, 4*w - 37],\ [997, 997, -4*w - 33],\ [1019, 1019, 44*w + 141],\ [1019, 1019, 44*w - 185],\ [1033, 1033, 32*w - 141],\ [1033, 1033, 32*w + 109],\ [1051, 1051, -14*w - 55],\ [1051, 1051, -14*w + 69],\ [1069, 1069, -52*w - 173],\ [1069, 1069, 108*w + 355],\ [1087, 1087, 6*w - 43],\ [1087, 1087, -6*w - 37],\ [1091, 1091, -12*w - 25],\ [1091, 1091, 12*w - 37],\ [1097, 1097, 34*w + 107],\ [1097, 1097, 34*w - 141],\ [1181, 1181, 70*w + 227],\ [1181, 1181, 90*w + 293],\ [1193, 1193, -14*w - 33],\ [1193, 1193, 14*w - 47],\ [1201, 1201, -24*w - 85],\ [1201, 1201, 24*w - 109],\ [1213, 1213, -76*w - 251],\ [1213, 1213, -84*w - 277],\ [1229, 1229, 10*w - 19],\ [1229, 1229, -10*w - 9],\ [1279, 1279, 10*w - 57],\ [1279, 1279, -10*w - 47],\ [1283, 1283, 52*w + 167],\ [1283, 1283, 52*w - 219],\ [1297, 1297, 8*w - 51],\ [1297, 1297, -8*w - 43],\ [1303, 1303, -14*w + 71],\ [1303, 1303, -14*w - 57],\ [1307, 1307, 36*w - 149],\ [1307, 1307, 36*w + 113],\ [1319, 1319, 24*w - 95],\ [1319, 1319, 24*w + 71],\ [1327, 1327, 38*w + 129],\ [1327, 1327, 38*w - 167],\ [1361, 1361, 10*w - 13],\ [1361, 1361, -10*w - 3],\ [1367, 1367, 32*w + 99],\ [1367, 1367, 32*w - 131],\ [1369, 37, -37],\ [1409, 1409, 10*w - 9],\ [1409, 1409, 10*w - 1],\ [1423, 1423, -6*w - 41],\ [1423, 1423, 6*w - 47],\ [1427, 1427, 12*w - 31],\ [1427, 1427, -12*w - 19],\ [1429, 1429, -12*w + 65],\ [1429, 1429, -12*w - 53],\ [1433, 1433, 78*w + 253],\ [1433, 1433, 98*w + 319],\ [1439, 1439, 16*w + 39],\ [1439, 1439, 16*w - 55],\ [1453, 1453, -4*w - 39],\ [1453, 1453, 4*w - 43],\ [1481, 1481, 18*w + 47],\ [1481, 1481, 18*w - 65],\ [1483, 1483, 34*w + 117],\ [1483, 1483, 34*w - 151],\ [1489, 1489, -8*w - 45],\ [1489, 1489, 8*w - 53],\ [1511, 1511, 72*w + 233],\ [1511, 1511, 112*w + 365],\ [1523, 1523, -12*w - 17],\ [1523, 1523, 12*w - 29],\ [1531, 1531, 46*w - 201],\ [1531, 1531, 46*w + 155],\ [1543, 1543, 2*w - 41],\ [1543, 1543, -2*w - 39],\ [1553, 1553, 54*w + 173],\ [1553, 1553, 54*w - 227],\ [1567, 1567, -22*w + 103],\ [1567, 1567, -22*w - 81],\ [1571, 1571, 60*w - 253],\ [1571, 1571, 60*w + 193],\ [1597, 1597, -28*w - 99],\ [1597, 1597, 28*w - 127],\ [1621, 1621, 4*w - 45],\ [1621, 1621, -4*w - 41],\ [1637, 1637, 14*w - 41],\ [1637, 1637, -14*w - 27],\ [1657, 1657, -64*w - 213],\ [1657, 1657, 64*w - 277],\ [1667, 1667, 44*w + 139],\ [1667, 1667, 44*w - 183],\ [1669, 1669, -12*w - 55],\ [1669, 1669, 12*w - 67],\ [1709, 1709, 86*w + 279],\ [1709, 1709, 106*w + 345],\ [1753, 1753, -72*w - 239],\ [1753, 1753, 128*w + 421],\ [1759, 1759, 42*w - 185],\ [1759, 1759, 42*w + 143],\ [1783, 1783, -18*w - 71],\ [1783, 1783, -18*w + 89],\ [1823, 1823, 32*w + 97],\ [1823, 1823, 32*w - 129],\ [1831, 1831, -14*w + 75],\ [1831, 1831, -14*w - 61],\ [1867, 1867, 62*w - 269],\ [1867, 1867, -62*w - 207],\ [1873, 1873, -88*w - 291],\ [1873, 1873, -112*w - 369],\ [1877, 1877, 62*w - 261],\ [1877, 1877, 62*w + 199],\ [1879, 1879, 2*w - 45],\ [1879, 1879, -2*w - 43],\ [1889, 1889, 26*w - 101],\ [1889, 1889, 26*w + 75],\ [1913, 1913, -18*w + 61],\ [1913, 1913, 18*w + 43],\ [1931, 1931, -12*w - 5],\ [1931, 1931, 12*w - 17],\ [1979, 1979, 20*w - 71],\ [1979, 1979, 20*w + 51],\ [1987, 1987, -6*w - 47],\ [1987, 1987, 6*w - 53],\ [1993, 1993, -24*w - 89],\ [1993, 1993, -24*w + 113],\ [1997, 1997, 22*w + 59],\ [1997, 1997, 22*w - 81],\ [1999, 1999, -70*w - 233],\ [1999, 1999, 70*w - 303],\ [2003, 2003, -12*w - 1],\ [2003, 2003, 12*w - 13],\ [2011, 2011, 50*w + 169],\ [2011, 2011, 50*w - 219],\ [2027, 2027, 12*w - 11],\ [2027, 2027, 12*w - 1],\ [2053, 2053, 28*w - 129],\ [2053, 2053, -28*w - 101],\ [2081, 2081, 38*w + 117],\ [2081, 2081, 38*w - 155],\ [2111, 2111, 88*w + 285],\ [2111, 2111, 128*w + 417],\ [2113, 2113, 8*w - 59],\ [2113, 2113, -8*w - 51],\ [2137, 2137, 48*w + 163],\ [2137, 2137, 48*w - 211],\ [2141, 2141, 58*w - 243],\ [2141, 2141, 58*w + 185],\ [2207, 2207, 48*w + 151],\ [2207, 2207, 48*w - 199],\ [2209, 47, -47],\ [2221, 2221, -20*w - 79],\ [2221, 2221, -20*w + 99],\ [2237, 2237, 26*w + 73],\ [2237, 2237, 26*w - 99],\ [2239, 2239, 58*w + 195],\ [2239, 2239, 58*w - 253],\ [2251, 2251, 126*w + 415],\ [2251, 2251, -94*w - 311],\ [2273, 2273, 22*w - 79],\ [2273, 2273, 22*w + 57],\ [2281, 2281, -16*w - 69],\ [2281, 2281, -16*w + 85],\ [2287, 2287, -102*w - 337],\ [2287, 2287, -118*w - 389],\ [2309, 2309, -14*w - 15],\ [2309, 2309, 14*w - 29],\ [2333, 2333, 102*w + 331],\ [2333, 2333, 122*w + 397],\ [2339, 2339, 36*w + 109],\ [2339, 2339, 36*w - 145],\ [2341, 2341, 44*w - 195],\ [2341, 2341, 44*w + 151],\ [2351, 2351, 40*w - 163],\ [2351, 2351, 40*w + 123],\ [2393, 2393, 14*w - 27],\ [2393, 2393, -14*w - 13],\ [2423, 2423, -16*w - 27],\ [2423, 2423, 16*w - 43],\ [2437, 2437, 12*w - 73],\ [2437, 2437, -12*w - 61],\ [2447, 2447, 136*w + 443],\ [2447, 2447, 96*w + 311],\ [2459, 2459, 60*w + 191],\ [2459, 2459, 60*w - 251],\ [2467, 2467, -26*w + 123],\ [2467, 2467, -26*w - 97],\ [2549, 2549, 34*w - 135],\ [2549, 2549, 34*w + 101],\ [2551, 2551, -30*w - 109],\ [2551, 2551, 30*w - 139],\ [2557, 2557, -36*w - 127],\ [2557, 2557, 36*w - 163],\ [2579, 2579, 84*w + 271],\ [2579, 2579, 164*w + 535],\ [2593, 2593, 16*w - 87],\ [2593, 2593, 16*w + 71],\ [2621, 2621, 38*w + 115],\ [2621, 2621, 38*w - 153],\ [2647, 2647, 2*w - 53],\ [2647, 2647, -2*w - 51],\ [2663, 2663, 56*w + 177],\ [2663, 2663, 56*w - 233],\ [2671, 2671, -10*w - 59],\ [2671, 2671, 10*w - 69],\ [2677, 2677, 52*w - 229],\ [2677, 2677, 52*w + 177],\ [2683, 2683, -14*w - 67],\ [2683, 2683, 14*w - 81],\ [2687, 2687, -16*w - 23],\ [2687, 2687, 16*w - 39],\ [2693, 2693, -14*w - 3],\ [2693, 2693, 14*w - 17],\ [2707, 2707, -22*w - 87],\ [2707, 2707, -22*w + 109],\ [2711, 2711, 32*w - 125],\ [2711, 2711, 32*w + 93],\ [2729, 2729, -14*w - 1],\ [2729, 2729, 14*w - 15],\ [2777, 2777, 14*w - 11],\ [2777, 2777, 14*w - 3],\ [2789, 2789, 14*w - 9],\ [2789, 2789, 14*w - 5],\ [2791, 2791, 50*w + 171],\ [2791, 2791, 50*w - 221],\ [2797, 2797, 4*w - 57],\ [2797, 2797, -4*w - 53],\ [2801, 2801, 22*w + 53],\ [2801, 2801, 22*w - 75],\ [2843, 2843, 36*w - 143],\ [2843, 2843, 36*w + 107],\ [2851, 2851, 6*w - 61],\ [2851, 2851, -6*w - 55],\ [2857, 2857, -72*w - 241],\ [2857, 2857, 72*w - 313],\ [2879, 2879, 24*w - 85],\ [2879, 2879, 24*w + 61],\ [2903, 2903, 48*w - 197],\ [2903, 2903, 48*w + 149],\ [2909, 2909, 26*w - 95],\ [2909, 2909, 26*w + 69],\ [2939, 2939, 44*w + 135],\ [2939, 2939, 44*w - 179],\ [2957, 2957, 74*w + 237],\ [2957, 2957, 74*w - 311],\ [2963, 2963, 172*w + 561],\ [2963, 2963, 92*w + 297],\ [2971, 2971, 46*w - 205],\ [2971, 2971, 46*w + 159],\ [3019, 3019, 162*w + 533],\ [3019, 3019, -98*w - 325],\ [3023, 3023, -16*w - 17],\ [3023, 3023, 16*w - 33],\ [3037, 3037, 44*w - 197],\ [3037, 3037, 44*w + 153],\ [3049, 3049, 80*w - 347],\ [3049, 3049, -80*w - 267],\ [3079, 3079, 2*w - 57],\ [3079, 3079, -2*w - 55],\ [3119, 3119, 16*w - 31],\ [3119, 3119, -16*w - 15],\ [3121, 3121, -40*w - 141],\ [3121, 3121, 40*w - 181],\ [3137, 3137, 54*w - 223],\ [3137, 3137, 54*w + 169],\ [3163, 3163, -114*w - 377],\ [3163, 3163, -146*w - 481],\ [3167, 3167, 24*w + 59],\ [3167, 3167, 24*w - 83],\ [3191, 3191, 152*w + 495],\ [3191, 3191, 112*w + 363],\ [3217, 3217, -88*w - 293],\ [3217, 3217, 88*w - 381],\ [3221, 3221, 30*w - 113],\ [3221, 3221, 30*w + 83],\ [3251, 3251, 28*w + 75],\ [3251, 3251, 28*w - 103],\ [3253, 3253, 4*w - 61],\ [3253, 3253, -4*w - 57],\ [3257, 3257, 46*w - 187],\ [3257, 3257, 46*w + 141],\ [3299, 3299, 20*w - 59],\ [3299, 3299, -20*w - 39],\ [3307, 3307, 2*w - 59],\ [3307, 3307, -2*w - 57],\ [3313, 3313, -8*w - 61],\ [3313, 3313, 8*w - 69],\ [3331, 3331, -6*w - 59],\ [3331, 3331, 6*w - 65],\ [3347, 3347, 236*w + 771],\ [3347, 3347, 76*w + 243],\ [3359, 3359, 16*w - 25],\ [3359, 3359, -16*w - 9],\ [3361, 3361, 184*w + 605],\ [3361, 3361, -96*w - 319],\ [3371, 3371, 180*w + 587],\ [3371, 3371, 100*w + 323],\ [3391, 3391, 54*w + 185],\ [3391, 3391, 54*w - 239],\ [3413, 3413, 94*w + 303],\ [3413, 3413, 194*w + 633],\ [3449, 3449, 126*w + 409],\ [3449, 3449, 146*w + 475],\ [3461, 3461, 18*w - 43],\ [3461, 3461, -18*w - 25],\ [3463, 3463, 66*w + 223],\ [3463, 3463, 66*w - 289],\ [3469, 3469, -28*w + 135],\ [3469, 3469, -28*w - 107],\ [3491, 3491, 20*w - 57],\ [3491, 3491, -20*w - 37],\ [3527, 3527, 16*w - 19],\ [3527, 3527, -16*w - 3],\ [3533, 3533, 22*w - 69],\ [3533, 3533, -22*w - 47],\ [3541, 3541, 76*w - 331],\ [3541, 3541, 76*w + 255],\ [3559, 3559, -30*w - 113],\ [3559, 3559, -30*w + 143],\ [3583, 3583, 6*w - 67],\ [3583, 3583, -6*w - 61],\ [3593, 3593, 18*w - 41],\ [3593, 3593, -18*w - 23],\ [3607, 3607, 14*w - 87],\ [3607, 3607, -14*w - 73],\ [3623, 3623, 16*w - 3],\ [3623, 3623, 16*w - 13],\ [3673, 3673, -24*w + 121],\ [3673, 3673, -24*w - 97],\ [3677, 3677, 38*w - 149],\ [3677, 3677, 38*w + 111],\ [3691, 3691, -34*w + 159],\ [3691, 3691, -34*w - 125],\ [3697, 3697, -152*w - 501],\ [3697, 3697, -128*w - 423],\ [3701, 3701, 62*w + 195],\ [3701, 3701, 62*w - 257],\ [3709, 3709, -20*w + 107],\ [3709, 3709, -20*w - 87],\ [3719, 3719, -24*w - 55],\ [3719, 3719, 24*w - 79],\ [3733, 3733, 36*w - 167],\ [3733, 3733, -36*w - 131],\ [3761, 3761, -22*w - 45],\ [3761, 3761, 22*w - 67],\ [3769, 3769, 40*w - 183],\ [3769, 3769, -40*w - 143],\ [3803, 3803, 108*w + 349],\ [3803, 3803, 188*w + 613],\ [3821, 3821, 42*w - 167],\ [3821, 3821, 42*w + 125],\ [3823, 3823, -26*w - 103],\ [3823, 3823, -26*w + 129],\ [3833, 3833, -18*w - 19],\ [3833, 3833, 18*w - 37],\ [3847, 3847, 18*w - 101],\ [3847, 3847, -18*w - 83],\ [3851, 3851, 20*w - 53],\ [3851, 3851, -20*w - 33],\ [3877, 3877, -12*w - 71],\ [3877, 3877, 12*w - 83],\ 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18*w - 29],\ [4219, 4219, 18*w - 103],\ [4219, 4219, -18*w - 85],\ [4243, 4243, 54*w - 241],\ [4243, 4243, 54*w + 187],\ [4259, 4259, 116*w + 375],\ [4259, 4259, 196*w + 639],\ [4261, 4261, 4*w - 69],\ [4261, 4261, -4*w - 65],\ [4271, 4271, 48*w + 145],\ [4271, 4271, 48*w - 193],\ [4273, 4273, 16*w - 97],\ [4273, 4273, -16*w - 81],\ [4283, 4283, 28*w + 69],\ [4283, 4283, 28*w - 97],\ [4289, 4289, 70*w - 291],\ [4289, 4289, 70*w + 221],\ [4339, 4339, -22*w - 95],\ [4339, 4339, -22*w + 117],\ [4357, 4357, -108*w - 359],\ [4357, 4357, 212*w + 697],\ [4373, 4373, 34*w + 93],\ [4373, 4373, 34*w - 127],\ [4391, 4391, 32*w - 117],\ [4391, 4391, 32*w + 85],\ [4397, 4397, 22*w - 61],\ [4397, 4397, -22*w - 39],\ [4421, 4421, 18*w - 23],\ [4421, 4421, -18*w - 5],\ [4447, 4447, -42*w - 151],\ [4447, 4447, 42*w - 193],\ [4489, 67, -67],\ [4507, 4507, 78*w - 341],\ [4507, 4507, 78*w + 263],\ [4517, 4517, -18*w - 1],\ [4517, 4517, 18*w - 19],\ [4519, 4519, 98*w - 425],\ [4519, 4519, -98*w - 327],\ 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109],\ [8501, 8501, 130*w + 417],\ [8501, 8501, 130*w - 547],\ [8521, 8521, -160*w - 531],\ [8521, 8521, 280*w + 921],\ [8543, 8543, 136*w + 437],\ [8543, 8543, 136*w - 573],\ [8599, 8599, -142*w - 473],\ [8599, 8599, 142*w - 615],\ [8609, 8609, -26*w - 19],\ [8609, 8609, 26*w - 45],\ [8623, 8623, 54*w - 251],\ [8623, 8623, -54*w - 197],\ [8663, 8663, 32*w - 93],\ [8663, 8663, -32*w - 61],\ [8689, 8689, -168*w - 557],\ [8689, 8689, 272*w + 895],\ [8693, 8693, 98*w - 407],\ [8693, 8693, 98*w + 309],\ [8707, 8707, 58*w - 267],\ [8707, 8707, -58*w - 209],\ [8713, 8713, 64*w - 291],\ [8713, 8713, -64*w - 227],\ [8719, 8719, -42*w - 163],\ [8719, 8719, -42*w + 205],\ [8737, 8737, 112*w - 489],\ [8737, 8737, 112*w + 377],\ [8753, 8753, 42*w + 107],\ [8753, 8753, 42*w - 149],\ [8779, 8779, 2*w - 95],\ [8779, 8779, -2*w - 93],\ [8803, 8803, -122*w - 409],\ [8803, 8803, 122*w - 531],\ [8807, 8807, 48*w + 131],\ [8807, 8807, 48*w - 179],\ [8819, 8819, 44*w - 159],\ [8819, 8819, 44*w + 115],\ [8821, 8821, 100*w + 339],\ [8821, 8821, 100*w - 439],\ [8831, 8831, 80*w + 247],\ [8831, 8831, 80*w - 327],\ [8837, 8837, 46*w + 123],\ [8837, 8837, 46*w - 169],\ [8839, 8839, -18*w - 107],\ [8839, 8839, 18*w - 125],\ [8849, 8849, -26*w - 15],\ [8849, 8849, 26*w - 41],\ [8863, 8863, 26*w - 149],\ [8863, 8863, -26*w - 123],\ [8867, 8867, 76*w - 309],\ [8867, 8867, 76*w + 233],\ [8893, 8893, -44*w - 169],\ [8893, 8893, -44*w + 213],\ [8933, 8933, 174*w + 563],\ [8933, 8933, 274*w + 893],\ [8941, 8941, -20*w - 111],\ [8941, 8941, 20*w - 131],\ [8951, 8951, 120*w + 383],\ [8951, 8951, 120*w - 503],\ [8963, 8963, 28*w - 61],\ [8963, 8963, -28*w - 33],\ [8999, 8999, 200*w + 649],\ [8999, 8999, 240*w + 781],\ [9007, 9007, -38*w + 191],\ [9007, 9007, -38*w - 153],\ [9013, 9013, 84*w - 373],\ [9013, 9013, 84*w + 289],\ [9049, 9049, -192*w - 635],\ [9049, 9049, -248*w - 817],\ [9059, 9059, 36*w - 115],\ [9059, 9059, -36*w - 79],\ [9067, 9067, 98*w + 333],\ [9067, 9067, 98*w - 431],\ [9091, 9091, -6*w - 95],\ [9091, 9091, 6*w - 101],\ [9127, 9127, -34*w + 177],\ [9127, 9127, -34*w - 143],\ [9161, 9161, 302*w + 985],\ [9161, 9161, 162*w + 523],\ [9173, 9173, 66*w - 263],\ [9173, 9173, 66*w + 197],\ [9181, 9181, -4*w - 95],\ [9181, 9181, 4*w - 99],\ [9209, 9209, 110*w + 349],\ [9209, 9209, 110*w - 459],\ [9227, 9227, 316*w + 1031],\ [9227, 9227, 156*w + 503],\ [9241, 9241, -40*w - 159],\ [9241, 9241, -40*w + 199],\ [9277, 9277, 28*w - 157],\ [9277, 9277, -28*w - 129],\ [9283, 9283, 294*w + 967],\ [9283, 9283, -166*w - 551],\ [9293, 9293, 86*w - 353],\ [9293, 9293, 86*w + 267],\ [9319, 9319, -50*w + 237],\ [9319, 9319, -50*w - 187],\ [9323, 9323, -28*w - 29],\ [9323, 9323, 28*w - 57],\ [9341, 9341, -38*w - 87],\ [9341, 9341, 38*w - 125],\ [9349, 9349, 108*w - 473],\ [9349, 9349, 108*w + 365],\ [9377, 9377, -26*w - 3],\ [9377, 9377, 26*w - 29],\ [9391, 9391, -10*w - 99],\ [9391, 9391, 10*w - 109],\ [9397, 9397, 12*w - 113],\ [9397, 9397, -12*w - 101],\ [9403, 9403, 78*w - 349],\ [9403, 9403, 78*w + 271],\ [9409, 97, -97],\ [9413, 9413, 78*w - 317],\ [9413, 9413, 78*w + 239],\ [9419, 9419, 116*w - 485],\ [9419, 9419, 116*w + 369],\ [9421, 9421, -36*w - 149],\ [9421, 9421, -36*w + 185],\ [9433, 9433, -32*w + 171],\ [9433, 9433, -32*w - 139],\ [9437, 9437, -26*w - 1],\ [9437, 9437, 26*w - 27],\ [9461, 9461, -30*w - 43],\ [9461, 9461, 30*w - 73],\ [9463, 9463, 286*w + 941],\ [9463, 9463, -174*w - 577],\ [9491, 9491, 28*w - 55],\ [9491, 9491, -28*w - 27],\ [9511, 9511, 94*w - 415],\ [9511, 9511, 94*w + 321],\ [9521, 9521, 58*w - 225],\ [9521, 9521, 58*w + 167],\ [9533, 9533, 26*w - 23],\ [9533, 9533, 26*w - 3],\ [9547, 9547, 2*w - 99],\ [9547, 9547, -2*w - 97],\ [9551, 9551, -32*w - 55],\ [9551, 9551, 32*w - 87],\ [9601, 9601, -56*w - 205],\ [9601, 9601, 56*w - 261],\ [9619, 9619, -182*w - 603],\ [9619, 9619, 278*w + 915],\ [9629, 9629, 26*w - 11],\ [9629, 9629, 26*w - 15],\ [9631, 9631, 106*w + 359],\ [9631, 9631, 106*w - 465],\ [9649, 9649, -72*w - 253],\ [9649, 9649, 72*w - 325],\ [9661, 9661, -44*w - 171],\ [9661, 9661, -44*w + 215],\ [9689, 9689, -30*w - 41],\ [9689, 9689, 30*w - 71],\ [9697, 9697, 8*w - 107],\ [9697, 9697, -8*w - 99],\ [9719, 9719, 56*w - 215],\ [9719, 9719, 56*w + 159],\ [9733, 9733, -68*w - 241],\ [9733, 9733, 68*w - 309],\ [9739, 9739, -62*w - 223],\ [9739, 9739, 62*w - 285],\ [9743, 9743, 128*w + 409],\ [9743, 9743, 128*w - 537],\ [9749, 9749, -34*w - 65],\ [9749, 9749, 34*w - 99],\ [9803, 9803, -28*w - 23],\ [9803, 9803, 28*w - 51],\ [9811, 9811, 10*w - 111],\ [9811, 9811, -10*w - 101],\ [9829, 9829, -12*w - 103],\ [9829, 9829, 12*w - 115],\ [9833, 9833, 62*w - 243],\ [9833, 9833, 62*w + 181],\ [9857, 9857, 134*w + 429],\ [9857, 9857, 134*w - 563],\ [9859, 9859, 262*w + 863],\ [9859, 9859, -198*w - 655],\ [9967, 9967, -26*w - 127],\ [9967, 9967, 26*w - 153],\ [9973, 9973, -4*w - 99],\ [9973, 9973, 4*w - 103]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-2, -2, -1, -2, -2, 0, -9, 0, 0, -8, -8, -6, -6, -6, -6, 5, 5, 12, 12, -3, -3, 4, 4, 15, 15, 18, 18, 9, 9, 1, 10, 10, -7, -7, 4, 4, -12, -12, -10, -6, -6, -15, -15, 0, 0, 18, 18, 15, 15, -2, -2, 10, 10, -28, -28, -2, -2, -18, -18, 4, 4, -30, 24, 24, -1, -1, 13, 13, 30, 30, -17, -17, -1, -1, -2, -2, 2, 2, -18, -18, 35, 35, -12, -12, -11, -11, 20, 20, 15, 15, -3, -3, -45, -8, -8, 4, 4, 0, 0, -28, -28, 33, 33, 40, 40, -16, -16, -25, -25, 7, 7, -33, -33, 29, 29, 10, 10, -42, -42, -16, -16, 17, 17, -25, -25, 3, 3, -36, -36, 50, 50, 4, 4, -22, -22, 20, 20, -6, -6, 53, 53, 39, 39, -52, -52, -5, -5, 14, 14, 8, 8, -15, -15, 24, 24, 4, 4, -22, -22, 12, 12, 10, 10, 8, 8, 42, 42, 34, 34, -13, -32, -32, 47, 47, -27, -27, 39, 39, 38, 38, -10, -10, -16, -16, 2, 2, -20, -20, 8, 8, -58, -58, -42, -42, -18, -18, -21, -21, 2, 2, -41, -41, 60, 60, -15, -15, -36, -36, 48, 48, 39, 39, 28, 28, -30, -30, 68, 68, 12, 12, -72, -72, -65, -15, -15, 29, 29, -12, -12, -70, -70, 54, 54, 0, 0, -71, -71, 32, 32, 49, 49, -15, -15, 37, 37, -41, -41, 32, 32, -36, -36, -56, -56, -52, -52, -28, -28, -32, -32, 22, 22, 33, 33, -2, -2, 48, 48, 50, 50, -45, -45, 34, 34, -40, -40, 59, 59, -56, -56, -43, -43, 28, 28, -6, -6, 18, 18, -35, -35, 70, 70, -36, -36, -18, -18, 30, 30, -22, -22, -66, -66, -72, -72, -20, -20, 4, 4, -13, -13, 63, 63, 84, 84, -18, -18, -38, -38, -86, -86, 73, 73, -58, -58, 48, 48, -30, 22, 22, 78, 78, -70, -70, -48, -48, 4, 4, 7, 7, 38, 38, 60, 60, 59, 59, 10, 10, 67, 67, -48, -48, 54, 54, -31, -31, -82, -82, 3, 3, -50, -50, 3, 3, -20, -20, -98, -98, 13, 13, 20, 20, 14, 14, 22, 22, 38, 38, 39, 39, 72, 72, -7, -7, -16, -16, 23, 23, -41, -41, -17, -17, 87, 87, 30, 30, -42, -42, -20, -20, 42, 42, -42, -42, 52, 52, 4, 4, 2, 2, -82, -82, -40, -40, 54, 54, -25, -25, -50, -50, 3, 3, -81, -81, -53, -53, 85, 85, 39, 39, 13, 13, -40, -40, -20, -20, -90, -90, 22, 22, 8, 8, -26, -26, 18, 18, -8, -8, 23, 23, -103, -103, -48, -48, 74, 74, 58, 58, 100, 100, 98, 98, 4, 4, -43, -43, -17, -17, -45, -45, -88, -88, -103, -103, 92, 92, 9, 9, 40, 40, -38, -38, -96, -96, -85, -85, 17, 17, 18, 18, 24, 24, 42, 42, 0, 0, -96, -96, -26, -26, 58, 58, 4, 4, -76, -76, -62, -62, 92, 92, 23, 23, 102, 102, 20, 20, -55, -55, 114, 114, -88, -88, 40, 40, 74, 74, -3, -3, 84, 84, 19, 19, -42, -42, -73, -73, 58, 58, -57, -57, 0, 0, -60, -60, 107, 107, -107, -107, -90, -90, 15, 15, 25, 25, -123, -123, -60, -60, 62, 62, -25, -25, 4, 4, -36, -36, -42, -42, 85, 85, 88, 88, -63, -63, 33, 33, 10, 10, 64, 64, 70, 70, -113, -113, -53, -53, -41, -41, 39, 39, -60, -60, 55, 55, -117, -117, 84, 84, 42, 42, 108, 108, 72, 72, 83, 83, -85, -82, -82, 8, 8, 5, 5, 112, 112, -112, -112, 89, 89, 122, 122, -80, -80, 114, 114, -36, -36, -96, -96, 30, 30, 129, 129, 30, 30, 8, 8, 110, 110, -76, -76, -132, -132, -68, -68, -88, -88, 93, 93, -126, -126, 115, 115, 32, 32, -76, -76, -48, -48, 98, 98, -52, -52, -1, -1, 28, 28, -45, -45, 54, 54, 10, 10, 8, 8, 132, 132, 93, 93, 2, 2, 97, 97, -60, -60, -80, -80, 63, 63, -21, -21, -22, -22, 79, 79, -20, -20, -126, -126, 77, 77, -2, -2, -15, -15, 138, 138, 14, 14, -2, -2, -110, -110, 82, 82, 109, 109, -3, -3, -95, -95, 27, 27, 22, 22, 8, 8, -93, -93, -122, -122, 60, 60, 17, 17, 113, 113, -48, -48, -57, -57, -125, -125, -146, -146, 77, 77, -8, -8, 19, 19, -30, -30, -92, -92, -1, -1, -78, -78, 100, 100, -66, -66, -137, -137, 33, 33, 10, 10, -55, -55, -66, -66, 123, 123, 94, 94, -18, -18, 73, 73, -101, -101, 48, 48, -8, -8, -48, -48, -16, -16, 57, 57, 59, 59, 113, 113, 90, 90, -38, -38, -62, -62, -128, -128, -115, -115, -58, 19, 19, -30, -30, -53, -53, -132, -132, -30, -30, 12, 12, 89, 89, 50, 50, -76, -76, 60, 60, -37, -37, 105, 105, -55, -55, -91, -91, 117, 117, 68, 68, -98, -98, 74, 74, -56, -56, 130, 130, -28, -28, -50, -50, -122, -122, 69, 69, -38, -38, 4, 4, 102, 102, -120, -120, -91, -91, 60, 60, 7, 7, 117, 117, 24, 24, -108, -108, 85, 85, -96, -96, -130, -90, -90, -88, -88, -72, -72, 62, 62, -101, -101, 23, 23, -126, -126, 120, 120, 23, 23, -60, -60, 164, 164, -60, -60, 15, 15, -3, -3, -72, -72, -145, -145, 78, 78, 162, 162, 38, 38, -21, -21, -57, -57, 59, 59, 138, 138, 72, 72, -150, -150, -48, -48, -80, -80, -88, -88, 103, 103, -148, -148, 135, 135, -43, -43, 30, 30, -42, -42, 24, 24, -45, -45, 109, 109, -2, -2, 64, 64, 40, 40, -95, -95, 107, 107, -17, -17, 42, 42, 50, 50, -51, -51, -151, -151, 33, 33, 19, 19, 55, 55, -21, -21, 58, 58, 14, 14, 17, 17, 88, 88, -6, -6, -147, -147, 20, 20, -132, -132, 18, 18, -48, -48, 85, 85, -75, -75, -46, -46, -40, -40, -42, -42, -86, -86, 77, 77, 84, 84, -112, -112, 123, 123, -130, -130, -35, -35, 169, 169, -17, -17, -46, -46, -100, -100, -26, -26, -6, -6, -117, -117, -110, -110, 84, 84, -92, -92, 168, 168, -15, -15, 54, 54, 12, 12, -23, -23, 72, 72, -126, -126, 80, 80, 130, 130, 74, 74, 124, 124, 90, 90, -86, -86, 88, 88, -61, -61, 40, 40, -2, -2, 24, 24, 55, 55, 124, 124, 48, 48, 50, 50, -78, -78, 157, 157, 3, 3, -70, -70, 90, 90, -116, -116, -57, -57, -46, -46, 109, 109, -133, -133, 52, 52, 129, 129, 25, 25, 153, 153, 119, 119, -130, -130, 100, 100, -147, -147, 67, 67, -12, -12, -138, -138, 24, 24, 82, 82, 120, 120, -52, -52, -133, -133, 43, 43, -166, -166, -66, -66, -20, -20, 134, 134, 42, 42, -100, -100, -142, -142, 142, 142, 83, 83, 119, 119, -145, -166, -166, 0, 0, -78, -78, 94, 94, 38, 38, 62, 62, 184, 184, -108, -108, -38, -38, -78, -78, -36, -36, -2, -2, 27, 27, -173, -173, -140, -140, 25, 25, -118, -118, -90, -90, -13, -13, -175, -175, 178, 178, 110, 110, 49, 49, -115, -115, 164, 164, -170, -170, 144, 144, 62, 62, -80, -80, 134, 134, -117, -117, -85, -85, 43, 43, 4, 4] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([121, 11, -11])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]