/* 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([-24, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([6, 6, 5*w + 22]) primes_array = [ [2, 2, 7*w - 38],\ [2, 2, -7*w - 31],\ [3, 3, 2*w + 9],\ [3, 3, 2*w - 11],\ [11, 11, -12*w + 65],\ [11, 11, -12*w - 53],\ [25, 5, 5],\ [31, 31, 8*w - 43],\ [31, 31, 8*w + 35],\ [43, 43, 54*w + 239],\ [43, 43, -54*w + 293],\ [47, 47, 2*w - 13],\ [47, 47, -2*w - 11],\ [49, 7, -7],\ [53, 53, 4*w + 19],\ [53, 53, 4*w - 23],\ [61, 61, 2*w - 7],\ [61, 61, -2*w - 5],\ [73, 73, 22*w + 97],\ [73, 73, -22*w + 119],\ [79, 79, -30*w + 163],\ [79, 79, 30*w + 133],\ [89, 89, 6*w + 25],\ [89, 89, -6*w + 31],\ [97, 97, 2*w - 1],\ [101, 101, 20*w - 109],\ [101, 101, 20*w + 89],\ [103, 103, 64*w + 283],\ [103, 103, -64*w + 347],\ [109, 109, -50*w + 271],\ [109, 109, -50*w - 221],\ [113, 113, -18*w + 97],\ [113, 113, 18*w + 79],\ [151, 151, 6*w + 29],\ [151, 151, 6*w - 35],\ [163, 163, -4*w - 13],\ [163, 163, 4*w - 17],\ [167, 167, 144*w - 781],\ [167, 167, 134*w - 727],\ [169, 13, -13],\ [191, 191, 34*w + 151],\ [191, 191, 34*w - 185],\ [193, 193, 24*w - 131],\ [193, 193, -24*w - 107],\ [197, 197, 6*w - 29],\ [197, 197, -6*w - 23],\ [227, 227, 2*w - 19],\ [227, 227, -2*w - 17],\ [229, 229, 12*w + 55],\ [229, 229, 12*w - 67],\ [241, 241, 96*w + 425],\ [241, 241, -96*w + 521],\ [269, 269, -148*w + 803],\ [269, 269, 148*w + 655],\ [283, 283, 6*w - 37],\ [283, 283, 6*w + 31],\ [289, 17, -17],\ [293, 293, 102*w + 451],\ [293, 293, -102*w + 553],\ [307, 307, 4*w - 11],\ [307, 307, -4*w - 7],\ [313, 313, -72*w + 391],\ [313, 313, 72*w + 319],\ [353, 353, 16*w + 73],\ [353, 353, 16*w - 89],\ [361, 19, -19],\ [379, 379, -4*w - 1],\ [379, 379, 4*w - 5],\ [389, 389, -6*w - 19],\ [389, 389, 6*w - 25],\ [397, 397, 14*w + 59],\ [397, 397, -14*w + 73],\ [419, 419, -62*w + 337],\ [419, 419, 62*w + 275],\ [421, 421, -38*w + 205],\ [421, 421, 38*w + 167],\ [431, 431, 14*w + 65],\ [431, 431, -14*w + 79],\ [449, 449, 32*w - 175],\ [449, 449, 32*w + 143],\ [461, 461, -18*w + 95],\ [461, 461, -18*w - 77],\ [463, 463, -8*w + 37],\ [463, 463, -8*w - 29],\ [467, 467, 12*w + 49],\ [467, 467, 12*w - 61],\ [479, 479, 2*w - 25],\ [479, 479, -2*w - 23],\ [487, 487, 42*w + 187],\ [487, 487, 42*w - 229],\ [491, 491, 10*w + 49],\ [491, 491, 10*w - 59],\ [503, 503, 168*w + 743],\ [503, 503, -168*w + 911],\ [509, 509, 30*w + 131],\ [509, 509, 30*w - 161],\ [521, 521, 176*w + 779],\ [521, 521, -176*w + 955],\ [529, 23, -23],\ [547, 547, -52*w - 229],\ [547, 547, -52*w + 281],\ [557, 557, 76*w + 337],\ [557, 557, -76*w + 413],\ [571, 571, -6*w - 35],\ [571, 571, 6*w - 41],\ [593, 593, -126*w + 683],\ [593, 593, -126*w - 557],\ [607, 607, 18*w - 101],\ [607, 607, 18*w + 83],\ [613, 613, 36*w - 197],\ [613, 613, 36*w + 161],\ [617, 617, -6*w - 13],\ [617, 617, 6*w - 19],\ [631, 631, 294*w + 1301],\ [631, 631, -294*w + 1595],\ [643, 643, 66*w + 293],\ [643, 643, -66*w + 359],\ [647, 647, -48*w + 259],\ [647, 647, 48*w + 211],\ [661, 661, -10*w - 37],\ [661, 661, -10*w + 47],\ [673, 673, 24*w + 109],\ [673, 673, 24*w - 133],\ [677, 677, 6*w - 17],\ [677, 677, -6*w - 11],\ [683, 683, 12*w - 59],\ [683, 683, -12*w - 47],\ [691, 691, -114*w + 619],\ [691, 691, 114*w + 505],\ [701, 701, -4*w - 31],\ [701, 701, 4*w - 35],\ [727, 727, 6*w - 43],\ [727, 727, -6*w - 37],\ [733, 733, 12*w + 59],\ [733, 733, 12*w - 71],\ [743, 743, -24*w - 103],\ [743, 743, -24*w + 127],\ [751, 751, -80*w - 353],\ [751, 751, 80*w - 433],\ [773, 773, -6*w - 7],\ [773, 773, 6*w - 13],\ [787, 787, -28*w + 149],\ [787, 787, -28*w - 121],\ [809, 809, 6*w - 11],\ [809, 809, -6*w - 5],\ [811, 811, 220*w + 973],\ [811, 811, -220*w + 1193],\ [823, 823, 8*w - 31],\ [823, 823, -8*w - 23],\ [829, 829, -94*w - 415],\ [829, 829, 94*w - 509],\ [841, 29, -29],\ [857, 857, -6*w - 1],\ [857, 857, 6*w - 7],\ [877, 877, 206*w + 911],\ [877, 877, -206*w + 1117],\ [881, 881, -104*w + 565],\ [881, 881, 104*w + 461],\ [937, 937, 122*w - 661],\ [937, 937, -122*w - 539],\ [967, 967, 136*w - 737],\ [967, 967, -136*w - 601],\ [971, 971, 374*w + 1655],\ [971, 971, -374*w + 2029],\ [997, 997, 12*w - 73],\ [997, 997, 12*w + 61],\ [1013, 1013, 44*w - 241],\ [1013, 1013, 44*w + 197],\ [1019, 1019, 218*w + 965],\ [1019, 1019, -218*w + 1183],\ [1031, 1031, 26*w - 145],\ [1031, 1031, 26*w + 119],\ [1049, 1049, -8*w - 47],\ [1049, 1049, 8*w - 55],\ [1051, 1051, 20*w + 83],\ [1051, 1051, -20*w + 103],\ [1061, 1061, 90*w - 487],\ [1061, 1061, -90*w - 397],\ [1063, 1063, -6*w - 41],\ [1063, 1063, 6*w - 47],\ [1069, 1069, 180*w + 797],\ [1069, 1069, -180*w + 977],\ [1091, 1091, -12*w + 55],\ [1091, 1091, 12*w + 43],\ [1103, 1103, -72*w - 317],\ [1103, 1103, -72*w + 389],\ [1117, 1117, 84*w - 457],\ [1117, 1117, 84*w + 373],\ [1129, 1129, -10*w - 31],\ [1129, 1129, 10*w - 41],\ [1153, 1153, -14*w + 67],\ [1153, 1153, -14*w - 53],\ [1163, 1163, 74*w - 403],\ [1163, 1163, 74*w + 329],\ [1213, 1213, -156*w + 847],\ [1213, 1213, 156*w + 691],\ [1217, 1217, -232*w + 1259],\ [1217, 1217, 232*w + 1027],\ [1229, 1229, 388*w + 1717],\ [1229, 1229, -388*w + 2105],\ [1237, 1237, -108*w + 587],\ [1237, 1237, 108*w + 479],\ [1249, 1249, 48*w - 263],\ [1249, 1249, 48*w + 215],\ [1259, 1259, 22*w - 125],\ [1259, 1259, 22*w + 103],\ [1277, 1277, -258*w + 1399],\ [1277, 1277, 258*w + 1141],\ [1279, 1279, -30*w - 137],\ [1279, 1279, 30*w - 167],\ [1283, 1283, -12*w - 41],\ [1283, 1283, -12*w + 53],\ [1297, 1297, -336*w + 1823],\ [1297, 1297, 336*w + 1487],\ [1327, 1327, -8*w - 11],\ [1327, 1327, 8*w - 19],\ [1361, 1361, 16*w + 79],\ [1361, 1361, 16*w - 95],\ [1367, 1367, 58*w + 259],\ [1367, 1367, 58*w - 317],\ [1369, 37, -37],\ [1423, 1423, -32*w + 169],\ [1423, 1423, -32*w - 137],\ [1433, 1433, 88*w + 391],\ [1433, 1433, 88*w - 479],\ [1439, 1439, 216*w + 955],\ [1439, 1439, -216*w + 1171],\ [1447, 1447, -16*w - 61],\ [1447, 1447, 16*w - 77],\ [1451, 1451, 60*w - 323],\ [1451, 1451, 60*w + 263],\ [1453, 1453, 82*w + 361],\ [1453, 1453, -82*w + 443],\ [1459, 1459, 78*w - 425],\ [1459, 1459, 78*w + 347],\ [1471, 1471, 8*w - 13],\ [1471, 1471, -8*w - 5],\ [1487, 1487, -146*w + 793],\ [1487, 1487, 146*w + 647],\ [1499, 1499, -36*w + 191],\ [1499, 1499, -36*w - 155],\ [1543, 1543, 8*w - 7],\ [1543, 1543, 8*w - 1],\ [1549, 1549, 12*w - 77],\ [1549, 1549, 12*w + 65],\ [1553, 1553, -114*w - 503],\ [1553, 1553, 114*w - 617],\ [1579, 1579, -44*w - 191],\ [1579, 1579, 44*w - 235],\ [1583, 1583, -48*w - 209],\ [1583, 1583, 48*w - 257],\ [1601, 1601, 40*w + 181],\ [1601, 1601, 40*w - 221],\ [1613, 1613, -78*w + 421],\ [1613, 1613, 78*w + 343],\ [1627, 1627, -6*w - 47],\ [1627, 1627, 6*w - 53],\ [1637, 1637, -4*w - 43],\ [1637, 1637, 4*w - 47],\ [1657, 1657, 24*w + 113],\ [1657, 1657, 24*w - 137],\ [1667, 1667, 2*w - 43],\ [1667, 1667, -2*w - 41],\ [1681, 41, -41],\ [1693, 1693, -468*w + 2539],\ [1693, 1693, 468*w + 2071],\ [1697, 1697, -8*w - 53],\ [1697, 1697, 8*w - 61],\ [1699, 1699, 222*w + 983],\ [1699, 1699, -222*w + 1205],\ [1721, 1721, 160*w + 709],\ [1721, 1721, -160*w + 869],\ [1747, 1747, 18*w + 89],\ [1747, 1747, 18*w - 107],\ [1777, 1777, -312*w + 1693],\ [1777, 1777, 312*w + 1381],\ [1789, 1789, -34*w + 179],\ [1789, 1789, -34*w - 145],\ [1811, 1811, 12*w - 47],\ [1811, 1811, -12*w - 35],\ [1831, 1831, 6*w - 55],\ [1831, 1831, -6*w - 49],\ [1847, 1847, 38*w + 173],\ [1847, 1847, 38*w - 211],\ [1861, 1861, 70*w + 307],\ [1861, 1861, 70*w - 377],\ [1867, 1867, -404*w + 2191],\ [1867, 1867, 404*w + 1787],\ [1879, 1879, -198*w + 1075],\ [1879, 1879, 198*w + 877],\ [1907, 1907, -274*w + 1487],\ [1907, 1907, 274*w + 1213],\ [1913, 1913, -282*w + 1529],\ [1913, 1913, 282*w + 1247],\ [1931, 1931, 10*w - 71],\ [1931, 1931, -10*w - 61],\ [1949, 1949, 66*w - 355],\ [1949, 1949, 66*w + 289],\ [1951, 1951, 66*w + 295],\ [1951, 1951, 66*w - 361],\ [1973, 1973, -42*w - 181],\ [1973, 1973, -42*w + 223],\ [1987, 1987, 124*w - 671],\ [1987, 1987, -124*w - 547],\ [1993, 1993, 26*w + 107],\ [1993, 1993, -26*w + 133],\ [2029, 2029, -46*w + 245],\ [2029, 2029, -46*w - 199],\ [2039, 2039, -240*w + 1301],\ [2039, 2039, -240*w - 1061],\ [2053, 2053, 58*w - 311],\ [2053, 2053, -58*w - 253],\ [2069, 2069, 54*w - 289],\ [2069, 2069, -54*w - 235],\ [2081, 2081, -18*w - 67],\ [2081, 2081, -18*w + 85],\ [2087, 2087, 24*w + 97],\ [2087, 2087, 24*w - 121],\ [2099, 2099, -564*w - 2495],\ [2099, 2099, -564*w + 3059],\ [2131, 2131, 20*w - 97],\ [2131, 2131, -20*w - 77],\ [2137, 2137, 96*w + 427],\ [2137, 2137, 96*w - 523],\ [2143, 2143, 18*w - 109],\ [2143, 2143, 18*w + 91],\ [2161, 2161, 24*w + 115],\ [2161, 2161, 24*w - 139],\ [2207, 2207, 2*w - 49],\ [2207, 2207, -2*w - 47],\ [2213, 2213, 4*w - 53],\ [2213, 2213, -4*w - 49],\ [2237, 2237, -188*w + 1021],\ [2237, 2237, 188*w + 833],\ [2239, 2239, 16*w + 55],\ [2239, 2239, -16*w + 71],\ [2243, 2243, 34*w - 191],\ [2243, 2243, 34*w + 157],\ [2267, 2267, -12*w - 29],\ [2267, 2267, 12*w - 41],\ [2281, 2281, -10*w - 7],\ [2281, 2281, 10*w - 17],\ [2293, 2293, -362*w + 1963],\ [2293, 2293, 362*w + 1601],\ [2297, 2297, 102*w + 449],\ [2297, 2297, -102*w + 551],\ [2339, 2339, 130*w + 577],\ [2339, 2339, -130*w + 707],\ [2371, 2371, 28*w - 143],\ [2371, 2371, 28*w + 115],\ [2377, 2377, -166*w - 733],\ [2377, 2377, 166*w - 899],\ [2381, 2381, 18*w + 65],\ [2381, 2381, -18*w + 83],\ [2389, 2389, -10*w - 1],\ [2389, 2389, 10*w - 11],\ [2393, 2393, 32*w + 149],\ [2393, 2393, 32*w - 181],\ [2417, 2417, 8*w - 67],\ [2417, 2417, -8*w - 59],\ [2423, 2423, -456*w + 2473],\ [2423, 2423, 456*w + 2017],\ [2437, 2437, -12*w - 71],\ [2437, 2437, 12*w - 83],\ [2441, 2441, 16*w + 85],\ [2441, 2441, 16*w - 101],\ [2447, 2447, 302*w + 1337],\ [2447, 2447, -302*w + 1639],\ [2473, 2473, 264*w + 1169],\ [2473, 2473, -264*w + 1433],\ [2521, 2521, -22*w - 85],\ [2521, 2521, 22*w - 107],\ [2531, 2531, -12*w - 25],\ [2531, 2531, 12*w - 37],\ [2549, 2549, 52*w + 235],\ [2549, 2549, 52*w - 287],\ [2557, 2557, 194*w - 1051],\ [2557, 2557, -194*w - 857],\ [2617, 2617, -38*w - 161],\ [2617, 2617, -38*w + 199],\ [2621, 2621, 20*w - 121],\ [2621, 2621, 20*w + 101],\ [2663, 2663, 22*w + 109],\ [2663, 2663, 22*w - 131],\ [2683, 2683, 292*w + 1291],\ [2683, 2683, -292*w + 1583],\ [2689, 2689, -240*w + 1303],\ [2689, 2689, 240*w + 1063],\ [2707, 2707, -236*w - 1043],\ [2707, 2707, -236*w + 1279],\ [2713, 2713, -278*w + 1507],\ [2713, 2713, -278*w - 1229],\ [2719, 2719, 616*w - 3341],\ [2719, 2719, -616*w - 2725],\ [2741, 2741, -316*w + 1715],\ [2741, 2741, 316*w + 1399],\ [2749, 2749, 12*w - 85],\ [2749, 2749, -12*w - 73],\ [2777, 2777, -42*w + 221],\ [2777, 2777, -42*w - 179],\ [2789, 2789, 68*w - 373],\ [2789, 2789, 68*w + 305],\ [2791, 2791, 112*w + 493],\ [2791, 2791, -112*w + 605],\ [2797, 2797, -36*w + 203],\ [2797, 2797, 36*w + 167],\ [2801, 2801, 162*w - 877],\ [2801, 2801, -162*w - 715],\ [2819, 2819, 2*w - 55],\ [2819, 2819, -2*w - 53],\ [2837, 2837, -628*w + 3407],\ [2837, 2837, 628*w + 2779],\ [2857, 2857, 192*w + 851],\ [2857, 2857, -192*w + 1043],\ [2861, 2861, -4*w - 55],\ [2861, 2861, 4*w - 59],\ [2879, 2879, 50*w - 277],\ [2879, 2879, 50*w + 227],\ [2909, 2909, 414*w + 1831],\ [2909, 2909, -414*w + 2245],\ [2953, 2953, 86*w - 463],\ [2953, 2953, 86*w + 377],\ [2957, 2957, -18*w + 79],\ [2957, 2957, -18*w - 61],\ [2963, 2963, -12*w - 17],\ [2963, 2963, 12*w - 29],\ [2971, 2971, -6*w - 59],\ [2971, 2971, 6*w - 65],\ [2999, 2999, 144*w - 779],\ [2999, 2999, -144*w - 635],\ [3001, 3001, 576*w - 3125],\ [3001, 3001, 602*w - 3265],\ [3011, 3011, -108*w + 583],\ [3011, 3011, 108*w + 475],\ [3019, 3019, -42*w - 193],\ [3019, 3019, 42*w - 235],\ [3023, 3023, -158*w + 859],\ [3023, 3023, 158*w + 701],\ [3061, 3061, 420*w + 1859],\ [3061, 3061, -420*w + 2279],\ [3079, 3079, 40*w + 169],\ [3079, 3079, -40*w + 209],\ [3137, 3137, 78*w + 341],\ [3137, 3137, 78*w - 419],\ [3169, 3169, 72*w - 395],\ [3169, 3169, 72*w + 323],\ [3203, 3203, 12*w - 23],\ [3203, 3203, -12*w - 11],\ [3209, 3209, 8*w - 73],\ [3209, 3209, -8*w - 65],\ [3217, 3217, -62*w - 269],\ [3217, 3217, 62*w - 331],\ [3251, 3251, 372*w + 1645],\ [3251, 3251, -372*w + 2017],\ [3271, 3271, 54*w + 245],\ [3271, 3271, 54*w - 299],\ [3299, 3299, -98*w - 437],\ [3299, 3299, 98*w - 535],\ [3301, 3301, 60*w + 271],\ [3301, 3301, 60*w - 331],\ [3307, 3307, 138*w - 751],\ [3307, 3307, 138*w + 613],\ [3323, 3323, 12*w - 19],\ [3323, 3323, -12*w - 7],\ [3329, 3329, 30*w + 121],\ [3329, 3329, 30*w - 151],\ [3331, 3331, -140*w + 757],\ [3331, 3331, -140*w - 617],\ [3347, 3347, -14*w - 83],\ [3347, 3347, 14*w - 97],\ [3359, 3359, -24*w + 115],\ [3359, 3359, -24*w - 91],\ [3371, 3371, -12*w - 5],\ [3371, 3371, 12*w - 17],\ [3373, 3373, 108*w + 481],\ [3373, 3373, -108*w + 589],\ [3389, 3389, -172*w + 935],\ [3389, 3389, 172*w + 763],\ [3391, 3391, 306*w + 1355],\ [3391, 3391, -306*w + 1661],\ [3407, 3407, 82*w + 367],\ [3407, 3407, 82*w - 449],\ [3413, 3413, -246*w - 1087],\ [3413, 3413, 246*w - 1333],\ [3449, 3449, 330*w + 1459],\ [3449, 3449, -330*w + 1789],\ [3457, 3457, -14*w - 29],\ [3457, 3457, 14*w - 43],\ [3461, 3461, 244*w + 1081],\ [3461, 3461, -244*w + 1325],\ [3467, 3467, 12*w - 11],\ [3467, 3467, 12*w - 1],\ [3481, 59, -59],\ [3491, 3491, 12*w - 7],\ [3491, 3491, 12*w - 5],\ [3517, 3517, 708*w + 3133],\ [3517, 3517, -708*w + 3841],\ [3527, 3527, 96*w + 421],\ [3527, 3527, 96*w - 517],\ [3539, 3539, -36*w + 185],\ [3539, 3539, 36*w + 149],\ [3541, 3541, 36*w - 205],\ [3541, 3541, 36*w + 169],\ [3557, 3557, -186*w - 821],\ [3557, 3557, 186*w - 1007],\ [3571, 3571, -52*w - 223],\ [3571, 3571, -52*w + 275],\ [3581, 3581, 4*w - 65],\ [3581, 3581, -4*w - 61],\ [3583, 3583, 162*w + 719],\ [3583, 3583, -162*w + 881],\ [3593, 3593, 16*w - 107],\ [3593, 3593, -16*w - 91],\ [3607, 3607, -16*w - 43],\ [3607, 3607, 16*w - 59],\ [3613, 3613, -396*w + 2149],\ [3613, 3613, 396*w + 1753],\ [3637, 3637, -22*w + 101],\ [3637, 3637, 22*w + 79],\ [3643, 3643, -282*w + 1531],\ [3643, 3643, 282*w + 1249],\ [3659, 3659, -10*w - 73],\ [3659, 3659, 10*w - 83],\ [3677, 3677, 44*w + 203],\ [3677, 3677, 44*w - 247],\ [3697, 3697, 34*w - 173],\ [3697, 3697, 34*w + 139],\ [3719, 3719, -358*w + 1943],\ [3719, 3719, 358*w + 1585],\ [3733, 3733, -12*w - 79],\ [3733, 3733, 12*w - 91],\ [3739, 3739, 102*w + 455],\ [3739, 3739, 102*w - 557],\ [3761, 3761, -18*w - 55],\ [3761, 3761, 18*w - 73],\ [3767, 3767, -24*w + 113],\ [3767, 3767, -24*w - 89],\ [3779, 3779, -60*w - 259],\ [3779, 3779, -60*w + 319],\ [3833, 3833, -112*w + 611],\ [3833, 3833, 112*w + 499],\ [3847, 3847, -64*w + 341],\ [3847, 3847, -64*w - 277],\ [3853, 3853, 14*w - 37],\ [3853, 3853, -14*w - 23],\ [3877, 3877, 132*w - 719],\ [3877, 3877, 132*w + 587],\ [3881, 3881, 438*w + 1937],\ [3881, 3881, -438*w + 2375],\ [3889, 3889, 552*w + 2443],\ [3889, 3889, -552*w + 2995],\ [3907, 3907, -76*w - 331],\ [3907, 3907, 76*w - 407],\ [3911, 3911, 72*w - 385],\ [3911, 3911, -72*w - 313],\ [3923, 3923, 132*w + 581],\ [3923, 3923, -132*w + 713],\ [3929, 3929, -150*w + 811],\ [3929, 3929, -150*w - 661],\ [3989, 3989, 20*w - 127],\ [3989, 3989, 20*w + 107],\ [4001, 4001, 80*w - 439],\ [4001, 4001, 80*w + 359],\ [4013, 4013, 18*w - 71],\ [4013, 4013, -18*w - 53],\ [4021, 4021, -182*w - 803],\ [4021, 4021, 182*w - 985],\ [4027, 4027, 6*w - 73],\ [4027, 4027, -6*w - 67],\ [4049, 4049, 40*w - 227],\ [4049, 4049, 40*w + 187],\ [4073, 4073, -8*w - 71],\ [4073, 4073, 8*w - 79],\ [4099, 4099, 44*w + 185],\ [4099, 4099, -44*w + 229],\ [4127, 4127, 62*w + 281],\ [4127, 4127, 62*w - 343],\ [4139, 4139, 22*w - 137],\ [4139, 4139, 22*w + 115],\ [4153, 4153, 48*w - 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95],\ [8731, 8731, 6*w - 101],\ [8741, 8741, 164*w - 895],\ [8741, 8741, -164*w - 731],\ [8761, 8761, -422*w - 1865],\ [8761, 8761, -422*w + 2287],\ [8779, 8779, 138*w - 755],\ [8779, 8779, 138*w + 617],\ [8783, 8783, 48*w + 193],\ [8783, 8783, 48*w - 241],\ [8803, 8803, -436*w + 2363],\ [8803, 8803, -436*w - 1927],\ [8819, 8819, -684*w + 3709],\ [8819, 8819, 684*w + 3025],\ [8821, 8821, 22*w - 65],\ [8821, 8821, -22*w - 43],\ [8831, 8831, 34*w - 209],\ [8831, 8831, 34*w + 175],\ [8839, 8839, -464*w + 2515],\ [8839, 8839, -464*w - 2051],\ [8849, 8849, -1074*w - 4751],\ [8849, 8849, 1074*w - 5825],\ [8863, 8863, -88*w + 467],\ [8863, 8863, -88*w - 379],\ [8893, 8893, 204*w + 907],\ [8893, 8893, 204*w - 1111],\ [8923, 8923, 44*w - 217],\ [8923, 8923, -44*w - 173],\ [8933, 8933, 116*w - 637],\ [8933, 8933, 116*w + 521],\ [8951, 8951, 792*w + 3503],\ [8951, 8951, -792*w + 4295],\ [8971, 8971, 20*w - 37],\ [8971, 8971, -20*w - 17],\ [8999, 8999, 22*w - 155],\ [8999, 8999, -22*w - 133],\ [9013, 9013, 564*w + 2497],\ [9013, 9013, -564*w + 3061],\ [9029, 9029, 340*w + 1507],\ [9029, 9029, -340*w + 1847],\ [9043, 9043, 18*w - 139],\ [9043, 9043, -18*w - 121],\ [9091, 9091, -68*w + 355],\ [9091, 9091, 68*w + 287],\ [9109, 9109, -886*w + 4805],\ [9109, 9109, 886*w + 3919],\ [9127, 9127, 6*w - 103],\ [9127, 9127, -6*w - 97],\ [9151, 9151, 30*w - 191],\ [9151, 9151, 30*w + 161],\ [9161, 9161, 40*w + 199],\ [9161, 9161, 40*w - 239],\ [9199, 9199, 256*w - 1385],\ [9199, 9199, -256*w - 1129],\ [9203, 9203, 46*w - 269],\ [9203, 9203, 46*w + 223],\ [9209, 9209, 54*w + 221],\ [9209, 9209, 54*w - 275],\ [9221, 9221, 44*w + 215],\ [9221, 9221, 44*w - 259],\ [9227, 9227, -36*w - 131],\ [9227, 9227, -36*w + 167],\ [9239, 9239, -10*w - 103],\ [9239, 9239, 10*w - 113],\ [9277, 9277, -12*w - 107],\ [9277, 9277, 12*w - 119],\ [9281, 9281, -30*w - 97],\ [9281, 9281, 30*w - 127],\ [9311, 9311, 120*w - 643],\ [9311, 9311, -120*w - 523],\ [9323, 9323, 108*w - 577],\ [9323, 9323, -108*w - 469],\ [9337, 9337, -26*w - 71],\ [9337, 9337, 26*w - 97],\ [9343, 9343, -112*w - 487],\ [9343, 9343, 112*w - 599],\ [9377, 9377, 642*w + 2839],\ [9377, 9377, -642*w + 3481],\ [9391, 9391, 126*w - 691],\ [9391, 9391, 126*w + 565],\ [9397, 9397, 202*w + 889],\ [9397, 9397, -202*w + 1091],\ [9403, 9403, 52*w - 263],\ [9403, 9403, 52*w + 211],\ [9413, 9413, 4*w - 101],\ [9413, 9413, -4*w - 97],\ [9421, 9421, 60*w + 281],\ [9421, 9421, 60*w - 341],\ [9431, 9431, -72*w - 305],\ [9431, 9431, -72*w + 377],\ [9433, 9433, -22*w - 37],\ [9433, 9433, 22*w - 59],\ [9463, 9463, -872*w + 4729],\ [9463, 9463, 872*w + 3857],\ [9473, 9473, -8*w - 101],\ [9473, 9473, 8*w - 109],\ [9479, 9479, -24*w - 55],\ [9479, 9479, 24*w - 79],\ [9497, 9497, 1136*w + 5027],\ [9497, 9497, -1136*w + 6163],\ [9533, 9533, -66*w + 343],\ [9533, 9533, 66*w + 277],\ [9539, 9539, 180*w + 791],\ [9539, 9539, -180*w + 971],\ [9587, 9587, -178*w + 971],\ [9587, 9587, 178*w + 793],\ [9601, 9601, 120*w - 659],\ [9601, 9601, 120*w + 539],\ [9619, 9619, 20*w - 19],\ [9619, 9619, 20*w - 1],\ [9689, 9689, 208*w - 1133],\ [9689, 9689, 208*w + 925],\ [9697, 9697, -46*w - 181],\ [9697, 9697, 46*w - 227],\ [9733, 9733, 12*w - 121],\ [9733, 9733, -12*w - 109],\ [9743, 9743, -24*w - 53],\ [9743, 9743, 24*w - 77],\ [9749, 9749, 668*w + 2957],\ [9749, 9749, -668*w + 3625],\ [9781, 9781, 36*w + 185],\ [9781, 9781, 36*w - 221],\ [9791, 9791, -600*w + 3253],\ [9791, 9791, 600*w + 2653],\ [9803, 9803, 252*w + 1111],\ [9803, 9803, -252*w + 1363],\ [9829, 9829, 108*w + 487],\ [9829, 9829, 108*w - 595],\ [9833, 9833, 296*w + 1313],\ [9833, 9833, -296*w + 1609],\ [9851, 9851, 26*w - 175],\ [9851, 9851, -26*w - 149],\ [9859, 9859, 30*w - 193],\ [9859, 9859, 30*w + 163],\ [9883, 9883, -284*w - 1253],\ [9883, 9883, 284*w - 1537],\ [9929, 9929, -234*w - 1031],\ [9929, 9929, -234*w + 1265],\ [9941, 9941, -330*w - 1457],\ [9941, 9941, 330*w - 1787],\ [9967, 9967, 66*w + 307],\ [9967, 9967, 66*w - 373],\ [9973, 9973, -22*w - 31],\ [9973, 9973, 22*w - 53]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^2 + x - 3 K. = NumberField(heckePol) hecke_eigenvalues_array = [1, e, -1, -1, 2*e, -2*e - 3, -2*e - 2, -5, -4*e - 5, 4*e + 4, -4*e - 2, -2*e, 2*e - 6, -1, -12, 4*e + 3, -4*e - 2, 2*e - 5, -10, -6*e - 4, 6*e + 8, -2*e + 8, 2*e - 6, 6*e + 6, 4*e - 8, 2*e - 6, 4*e - 3, 10*e + 5, -2*e - 1, -2*e + 4, -4*e - 2, -6*e - 6, 12, 8*e + 4, 2*e + 4, -6*e - 13, 2, 10*e + 3, -9, 2*e + 8, -4*e - 15, -6*e + 9, 4*e + 4, -6*e + 4, 6*e + 3, 8*e + 12, 6*e, -6*e + 3, 4*e + 2, -2*e + 2, -4*e - 14, -2*e - 11, -18, -6*e - 3, -2*e + 14, 10*e - 7, 6*e - 5, -2*e + 21, -2*e - 24, 8*e - 4, -2*e + 26, -10, -12*e - 13, -10*e - 21, 8*e - 15, -4*e - 16, -4*e - 22, 10*e + 23, 2*e - 9, -4*e + 6, 2*e + 31, -20, -12*e - 3, 2*e - 24, 4*e - 14, -6*e + 16, -4*e, 12, 18*e + 9, 16*e - 3, 6*e - 18, -6, -4*e + 7, 16, 6*e + 12, 4*e - 12, 12*e - 9, -8*e + 12, 2*e + 26, -2*e + 26, -16*e - 3, -20*e - 18, 8*e + 6, -14*e - 18, 12*e - 3, 6*e - 18, 2*e, -8*e + 18, -6*e + 1, -22*e - 7, -6*e + 14, 2*e - 27, -18*e - 12, -20*e - 14, -4*e - 20, -8*e + 6, -15, -6*e - 26, 12*e + 4, 12*e - 2, -2*e - 11, 14*e + 3, -20*e - 15, 8*e - 2, -10*e - 2, 12*e + 4, 8*e + 25, 4*e - 24, -8*e - 12, -20*e - 7, 2*e - 4, -20*e + 2, -8*e + 20, -8*e, -12*e - 18, -16*e, 6*e - 12, -14*e + 20, 8*e + 20, -4*e + 6, 6*e + 18, 6*e + 20, -14*e - 10, 24*e + 10, -4*e - 2, 6*e + 6, 8*e + 6, 10*e + 16, 6*e + 22, -24, -8*e + 15, -28, 10*e + 2, -2*e + 21, 6, 4*e + 8, -6*e + 32, -12*e - 26, 6*e + 40, 2*e + 14, 8*e + 5, 10*e + 22, -18*e + 12, -2*e + 6, -10*e - 26, -2*e - 17, -12*e - 18, -8*e - 18, -10*e - 35, 6*e - 11, 2*e + 2, 12*e + 14, -8*e - 36, -12*e + 18, -4*e + 53, -4*e + 26, -6*e + 39, 12*e + 30, -10*e + 30, -16*e - 3, 12, -2*e - 3, -8*e - 21, 8*e - 18, 8*e - 32, 20*e - 14, 2*e - 36, -18*e - 15, 8*e + 28, -23, -22*e + 4, 24*e + 10, 30*e + 24, -12, 2*e + 33, -8*e - 3, 4*e - 31, -14*e + 8, 4*e - 28, -12*e - 4, -10*e - 47, 14*e + 1, -24*e - 24, 2*e + 21, 24*e + 14, 4*e + 14, -14*e, 6*e - 18, 24*e + 24, -16*e - 42, -16*e - 44, 14*e + 19, -14*e - 29, -4*e + 22, -6*e + 30, 15, 48, 6*e - 45, -20, -4*e + 31, -14*e - 30, -36*e - 15, 6*e + 61, -14*e - 5, 8*e + 52, 24*e + 4, 12*e + 30, 12*e - 33, -6*e + 6, 18*e + 24, -26*e - 16, 8*e - 8, -26*e - 20, -4*e - 42, -12*e + 18, 16*e + 24, -6*e - 27, -22*e + 5, 6*e - 55, -12*e - 51, 6*e - 60, 6*e - 16, 16*e + 11, -4*e + 19, -38, 20*e + 40, 12*e + 25, -12*e - 48, 14*e - 15, 2*e, -2*e - 3, -6*e - 50, 4*e - 8, -38, 14*e - 17, 18*e + 6, -8*e + 6, 24*e + 22, -4*e - 11, -30, -4*e + 12, 6*e + 18, 24*e + 24, 9, -6*e - 36, -20*e + 7, -16*e - 38, 42, -4*e - 9, 26*e + 19, -2*e - 35, -30*e - 18, 14*e + 39, 30*e + 19, -10*e + 8, -12*e + 38, 2*e + 24, -12*e + 6, -4*e + 19, 26*e + 34, 12*e + 48, 6*e - 42, 4*e - 23, 24*e - 14, -12*e - 58, 20*e - 4, -16*e - 7, 4*e + 8, -6*e - 54, -30*e - 27, 22*e + 29, 30*e + 5, -12*e + 30, 6*e + 72, -24*e - 22, 22*e - 4, -6*e - 2, -4*e + 40, -18*e + 8, 8*e - 16, -10*e - 9, 2*e - 6, 18*e - 30, -10*e - 60, -18*e + 27, -34*e - 24, 16*e + 3, 48, 2*e - 25, 14*e - 7, 2*e - 39, 16*e, -28*e - 16, -22*e - 1, 20*e + 10, -22*e + 19, -16*e - 1, 12*e + 32, -8*e - 21, -20*e - 36, -28*e - 22, 8*e + 77, 6*e + 18, -42, 42*e + 33, -12*e + 45, -6*e + 18, 6*e + 36, 8*e + 42, 12*e - 9, 14*e + 46, 64, -24*e - 40, -2*e + 38, 4*e - 58, 20, 34*e + 8, -4*e - 4, -28*e - 45, -22*e - 9, -6*e - 18, -16*e - 30, 26*e - 6, -4*e + 3, -16*e - 16, -8*e + 2, -4*e + 60, -8*e + 18, -10*e + 69, 6*e + 48, 24*e - 22, 2*e + 8, 26*e + 43, 8*e + 22, -4*e + 54, -4*e + 54, -16*e - 15, 50*e + 24, 22*e + 8, 38*e + 35, -28*e - 7, -70, 32*e + 24, 12*e - 6, 10*e + 38, 4*e - 25, -4*e + 30, 30, -14*e + 30, -20*e - 12, -28*e - 12, 42*e + 12, -2*e + 43, 10*e - 50, 44*e + 30, 32*e + 30, 10*e - 45, 16*e - 51, 8*e - 50, -4*e - 26, -16*e + 14, 8*e - 55, -4*e - 6, 12*e, 2*e + 18, 20*e - 33, -26*e + 7, -14*e - 32, -16*e + 22, 40*e + 40, -30*e + 21, 4*e - 54, -18, 8*e - 42, 30*e - 25, 30*e - 4, 4*e - 67, 12*e + 5, 16*e - 8, 14*e + 4, -14*e - 29, -6*e + 61, 14*e + 29, 6*e - 25, -2*e + 24, -10*e - 57, 14*e + 38, -61, 6*e - 9, -20*e + 15, -6*e - 72, 40*e - 6, 22*e - 43, -8*e - 40, 20*e + 46, 2*e + 49, -40*e - 33, 6*e + 3, 40*e + 33, 4*e, 20*e + 21, 18*e + 6, -38*e - 14, -30*e + 4, 14*e - 33, -22*e + 30, 20*e + 42, -12, -20*e + 30, -36*e - 18, -28*e - 68, -12*e - 20, 6*e, 6, -10*e + 66, 24*e - 12, 20*e + 76, 64, 36*e + 12, 6*e + 39, 30*e - 14, 40*e + 28, 10*e + 72, -12*e - 27, -6*e + 53, 10*e - 10, 2*e - 60, -18, 6*e - 2, 40*e + 58, 12*e - 22, 2*e - 40, -12*e - 39, 18*e + 51, 18*e - 8, -12*e + 70, -34*e - 54, 14*e - 51, 18*e + 45, -24*e - 6, 46*e + 37, -28*e + 22, -40*e + 12, 20*e + 30, 16*e + 28, -16*e + 22, 8*e - 18, 24*e + 69, 12*e + 35, -70, 30*e + 5, 24*e + 14, 34*e + 51, 8*e + 66, -8*e - 24, -16*e + 6, 4*e - 59, -18*e - 38, 26*e + 30, -4*e - 21, 60, 4*e + 45, -6*e - 63, 8*e + 96, 16*e + 29, 18*e - 4, 16*e - 57, -2*e + 84, 18*e + 40, -30*e - 20, -4*e + 24, -16*e - 24, 16*e + 54, 42, 34*e + 27, 32*e - 15, -42*e + 7, 28*e - 14, -30*e - 57, 66, 12*e + 33, 20*e + 12, -18*e + 64, 4*e - 12, -20*e - 15, 10*e - 46, -32*e - 49, -32*e - 75, -30*e - 39, -8*e + 12, 22*e - 21, -26*e - 82, -40*e - 34, 36*e + 6, 8*e + 54, -6*e - 82, -4, -12*e - 15, 34*e + 12, 12*e + 43, 36*e + 31, -12*e, 24*e - 48, 10*e - 61, -18*e - 13, -6*e + 74, -32*e + 11, 20*e - 37, 50, -26*e + 14, -18*e - 79, -32*e - 21, -24*e + 6, -66, 22*e + 27, -12*e + 5, -12*e + 35, -48*e - 24, -24*e + 12, 24*e + 26, 2*e + 38, -41, 12*e + 22, -10*e - 18, 26*e + 18, 34*e + 12, -2*e - 30, -40*e + 15, 12*e + 54, -24*e - 6, 24, -34*e - 13, 4*e - 16, -38*e - 5, 8*e - 62, -2*e - 77, 30*e + 82, -12*e - 30, -30*e - 18, 32*e + 14, 26*e - 40, -16*e - 76, -36*e + 20, 10*e - 66, -14*e + 6, 24*e, -2*e + 42, -6, -64*e - 30, 10*e + 81, 30*e + 18, 34*e + 15, -16*e - 42, -10*e - 102, 24*e + 3, 8*e + 58, 6*e - 86, 10*e - 25, 2*e + 44, -24, -24*e + 6, -52*e - 42, -38*e - 39, -16*e - 14, 24*e - 47, -18*e - 75, -16*e + 12, 10*e + 27, 2*e - 60, -14*e + 28, -64*e - 38, -16*e + 10, 24*e - 14, 30*e - 14, 30*e + 4, -10*e + 53, -12*e - 28, 36*e + 54, -26*e - 72, 32*e + 25, -28*e - 62, -42*e - 6, -24*e - 96, -4*e - 42, -24*e + 24, -66, -20*e + 45, 6*e - 35, -16*e + 28, -34*e - 40, 22*e + 89, 30*e + 78, -8*e + 18, 14*e + 90, -36*e - 42, -38*e + 18, -8*e + 6, 16*e + 12, -24*e - 36, -20*e - 84, -22*e - 21, 16*e - 58, -50*e - 60, -51, 12*e + 72, 16*e - 48, 10*e - 6, 28*e + 72, 64*e + 44, -22*e - 52, -5, 4*e - 71, -28*e - 36, -24*e - 96, 10*e - 8, -2*e + 22, 12*e - 89, 30*e + 58, 28*e + 23, 40*e + 20, 34*e + 80, 8*e + 116, 20*e + 72, 6*e - 54, -8*e - 66, -12*e - 60, 10*e + 30, -6*e + 72, -12*e + 58, 26*e + 52, 8*e + 102, -12*e - 42, 38*e + 34, 38*e + 58, -20*e - 73, -38*e - 58, 30*e + 4, -58*e - 56, -24*e + 27, -36*e - 78, -12*e + 34, -6*e + 64, -28*e - 18, 32*e + 36, -6*e - 13, 2*e - 7, -8*e + 60, -4*e - 84, 26*e + 75, -16*e - 15, 8*e - 47, -20*e - 11, 2*e - 80, -8*e - 68, 24*e + 6, 24, -28*e + 32, 22*e + 38, -16*e - 26, 4*e - 34, -20*e - 10, 36*e - 15, -40*e - 24, 24*e - 10, 32*e + 80, 10*e - 21, 6*e - 72, 12*e + 99, -26*e - 9, -40*e - 51, -42*e + 36, -32*e + 22, -40*e + 40, 42*e + 24, 16*e - 42, -40*e + 9, -6*e - 15, -40*e - 70, 56*e + 32, 16*e + 6, 30*e + 42, 48*e + 32, 46*e + 83, 20*e - 63, 30*e + 30, 46*e + 26, 42*e + 17, -20*e - 81, 24, -18*e - 3, 32*e + 69, 30*e + 28, -36*e - 44, -20*e - 53, 12*e - 59, 24*e, 48*e - 6, 12*e + 31, 2*e + 52, -50*e - 31, 22*e + 17, -60*e - 45, -42*e - 12, 22*e + 1, -52*e - 26, 14*e + 64, -8*e - 50, 52*e + 36, -56*e - 60, -16*e - 81, -30*e - 30, -3, 12*e - 60, 14*e - 7, 34*e - 31, -18*e + 75, -8*e - 54, 8*e + 131, -50*e + 14, 33, 8*e + 90, -32*e + 40, -10*e - 68, 36*e + 66, 8*e - 54, 26*e - 56, -22*e + 61, -14*e + 96, 20*e - 12, -48*e - 6, 10*e - 114, 6*e + 3, 4*e + 114, -28*e - 40, -12*e - 91, -26*e - 22, -18*e + 23, 36*e, 6*e + 144, 18*e + 115, -36*e + 64, 52*e + 50, 28*e - 79, 2*e + 101, -2*e + 134, 6*e - 93, 12*e + 30, -14*e - 17, 6*e - 83, -6*e + 30, -18*e - 3, -12*e + 48, 6*e + 30, 32*e - 12, 30*e - 75, 18*e + 27, 12*e - 87, -8*e - 28, 22*e + 80, 2*e + 107, -10*e + 35, 30*e + 39, 60*e - 15, -24*e - 105, 18*e + 15, 10*e - 58, 64*e + 17, 18*e + 6, 26*e, -46*e - 39, -62*e - 12, -28*e - 78, 16*e - 24, 28*e - 28, -62*e + 5, -30*e - 80, -8*e + 103, 12*e + 98, 34*e + 104, 14*e, -14*e - 54, -30, 8*e - 108, -12*e - 108, -3, 26*e + 66, -84, 62*e + 25, -26*e - 44, -82*e - 48, 4*e - 12, -22*e - 93, -6*e + 78, -64*e - 45, -12*e + 6, -24*e + 18, -48*e - 48, 4*e - 28, 18*e - 28, 28*e + 30, 74*e + 51, -16*e - 36, 38*e - 54, 32*e - 29, 36*e + 4, -36*e - 100, -42*e - 58, 12*e - 39, 2*e - 9, 2*e + 76, 8*e + 67, 22*e - 2, -4*e + 34, -30*e - 6, 8*e - 9, -54*e - 75, -48*e + 18, 56*e + 40, -42*e + 4, 16*e - 1, -20*e - 49, 4*e - 129, -24*e - 42, 16*e - 42, 14*e - 105, 16*e - 5, -34*e - 98, -36, -18*e + 3, -16*e - 26, -44*e - 14, -32*e - 46, 4*e + 155, -46*e - 84, -50*e - 72, 24*e + 74, -30*e - 31, 24*e - 54, -42*e + 6, 2*e - 53, -18*e + 28, -28*e + 42, 18*e - 78, -30*e - 49, 24*e + 116, 28*e + 75, 30, 38*e - 56, -16*e - 26, 18*e - 78, -60*e - 6, -42*e - 23, 32*e - 38, -42*e - 7, -12*e + 44, -4*e, -48*e - 12, 20*e + 66, 34*e + 60, -50*e - 12, -16*e - 81, 28*e - 88, 80, 12*e - 5, -30*e - 74, 18*e + 22, 30*e, -70*e - 15, -90, 30*e + 48, -28*e - 25, -18*e + 56, 4*e + 66, 30*e + 96, -44*e - 30, -36*e + 42, -42*e - 36, -24*e - 63, 20*e - 68, -38*e - 38, 36*e + 104, -52*e - 22, 32*e - 56, -26*e + 91, 14*e + 36, -126, 14*e - 9, 40*e + 63, 16*e + 10, -34*e - 20, 36*e - 51, 12*e + 12, 30*e - 17, -34*e - 11, 58*e + 27, -8*e + 102, -8*e + 96, 24*e - 33, -4*e - 100, -4*e - 10, -46, -58*e - 37, -28*e - 18, 30*e + 18, 12*e + 93, 28*e, 12*e - 118, 12*e - 46, -24*e + 27, 48*e + 84, 12*e + 17, 16*e - 49, -60*e - 66, 36*e + 6, 30*e + 75, -44*e - 90, 20*e + 51, 14*e - 93, -38*e - 2, -36*e - 62, 66*e + 24, -62*e - 12, 26*e + 30, -28*e + 72, 26*e - 66, 32*e - 42, -6*e + 6, 30*e - 75, -84, 32*e + 45, -72*e - 75, -50*e + 39, 48*e - 5, 16*e + 97, -30*e + 28, -30*e - 26, 2*e - 119, 14*e + 82, 14*e - 46, -14*e + 44, -44*e + 44, 10*e + 8, 28*e + 14, -26*e - 19, -30*e - 26, 76*e + 58, 30*e + 33, -12*e + 69, 48*e + 30, -28*e - 87, 2*e - 40, -60*e - 88, 68*e + 24, -6*e - 54, 56*e + 54, 52*e + 39, 34*e - 24, -54*e - 87, 44*e + 17, -20*e - 10, 32*e - 17, 64*e - 17, -12*e - 84, -64*e - 6, 42*e + 69, 16*e + 156, 28*e + 21, 8*e + 24, 30*e + 10, 6*e - 2, 44*e - 28, 12*e - 34, -24*e - 28, 28*e - 40, -60*e - 72, -6*e - 12, 56*e + 86, -8*e - 130, 56*e + 44, -24*e + 92, 6*e - 72, -4*e - 57, -50*e + 39, 20*e - 12, -10*e - 125, 2*e + 46, -30*e + 99, -54*e - 42, -10*e + 63, 12*e + 102, 45, -12*e - 72, 32*e - 107, 82*e + 16, 20*e + 10, 20*e + 100, -12*e - 20, -24*e - 8, -2*e - 116, -18*e + 133, -22*e + 103, -14*e + 67, 6*e + 87, -38*e - 18, 6*e + 66, 64*e, -26*e - 7, -54*e - 61, 26*e + 37, 52*e - 14, -74*e - 50, 32*e + 34, -6*e + 53, 2*e + 35, 44*e - 80, -12*e - 14, 12*e + 106, 34*e - 77, -24*e - 87, -24*e - 66, 74*e + 2, -88*e - 34, -60*e + 17, 2*e - 4, 120, 12*e + 69, 24*e - 100, 52*e + 110, -14*e + 8, 10*e + 119, 22*e - 6, -22*e + 102, 72*e + 14, -60*e - 82, -34*e + 60, -36*e - 27, 24*e - 32, 4*e + 28, 2*e - 18, 36*e + 54, -4*e + 145, -40*e - 50, -8*e + 124, 36*e - 95, -48*e - 102, -64*e - 39, -46*e - 9, -48*e - 15, 68*e + 45, -24*e + 84, -18*e - 130, -4*e - 67, 50*e + 7, 80*e + 34, -44*e - 54, -64*e - 84, -28*e + 68, -12*e + 101, 46*e + 84, -48*e - 30, 22*e - 42, 12*e - 108, -48*e + 56, 10*e - 25, 60*e + 19, -34*e + 28, -34*e + 99, 18*e + 150, -18*e + 58, 46*e + 22, -78*e - 32, -24*e - 59, -4*e - 36, -8*e - 66, 54*e - 61, 40*e + 116, -30*e - 81, -4*e + 18, -16*e + 32, -44*e - 103, 18*e - 15, 12*e - 69, 64*e + 100, -52*e - 53, 54*e + 78, -2*e + 48, -46*e + 17, -18*e - 133, -20*e - 64, -56*e - 73, -32*e - 44, 40*e + 85, 28*e + 60, -80*e - 21, 18*e - 48, 82*e + 30, 28*e + 13, -72*e - 44, 68*e + 36, 24*e + 126, 16*e - 142, 52*e + 98, 24*e + 60, -12*e - 21, -2*e + 14, 30*e - 61, 40*e + 4, 34*e + 10, -32*e + 35, 54*e + 74, 6*e + 107, -18*e + 47, 64*e - 20, -4*e - 11, 54*e - 51, 24*e + 30, 26*e - 88, 10*e - 100, -22*e - 96, 24*e + 72, 4*e - 57, 20*e - 90, -24*e - 21, -58*e + 6, 10*e + 93, -60, 32*e - 117, 2*e - 63, -20*e - 92, 36*e + 46, 66, -60*e - 72, 42*e - 87, -48*e + 12, -12*e + 78, -40*e - 57, 12*e - 26, -4*e - 2, 14*e - 16, -38*e - 52, 38*e + 90, 46*e + 66, -24*e + 50, -36*e + 14, -36*e - 112, -52*e - 85, -18*e - 82, 10*e - 67, 26*e - 30, -66*e - 3, -34*e + 85, 4*e - 80, -78*e - 54, -50*e, 12*e - 79, 56*e + 2, -4*e + 112, -88*e - 62, -18, 48*e + 126, 34*e - 78, -54*e - 60, -30*e + 6, 8*e - 72, 30*e + 126, 2*e + 69, -12*e - 72, 16*e - 60, 48*e - 60, 20*e + 108, -10*e - 56, 46*e - 2, 64, 20*e + 4, 2*e - 84, 48*e - 6, 28*e + 2, 40*e + 74, 4*e + 137, 22*e + 134, 56*e, 60*e + 60, 24*e - 60, -18*e + 63, 18*e + 37, -32*e - 50, -10*e - 3, 44*e + 60, -2*e + 156, -20*e + 84, 24*e + 35, 6*e + 74, -24*e - 33, -34*e - 117, 27, 38*e + 24, -26*e - 97, -26*e + 116, 72*e + 79, 60*e + 106, -72*e - 30, 20*e + 30, 70*e + 72, 6*e + 105, -52*e - 94, 14*e + 116, 12*e - 94, 56*e - 37] 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, 7*w - 38])] = -1 AL_eigenvalues[ZF.ideal([3, 3, 2*w - 11])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]