/* 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([11,11,12*w + 53]) 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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797],\ [8447, 8447, 782*w + 3461],\ [8447, 8447, -782*w + 4243],\ [8461, 8461, 562*w + 2485],\ [8461, 8461, -562*w + 3047],\ [8501, 8501, 100*w + 451],\ [8501, 8501, 100*w - 551],\ [8527, 8527, 18*w - 137],\ [8527, 8527, -18*w - 119],\ [8537, 8537, 512*w + 2267],\ [8537, 8537, -512*w + 2779],\ [8539, 8539, 380*w - 2059],\ [8539, 8539, -380*w - 1679],\ [8563, 8563, 548*w + 2423],\ [8563, 8563, -548*w + 2971],\ [8597, 8597, 268*w + 1189],\ [8597, 8597, -268*w + 1457],\ [8609, 8609, 640*w + 2833],\ [8609, 8609, -640*w + 3473],\ [8627, 8627, -36*w - 133],\ [8627, 8627, -36*w + 169],\ [8629, 8629, 394*w - 2135],\ [8629, 8629, -394*w - 1741],\ [8641, 8641, 50*w + 203],\ [8641, 8641, 50*w - 253],\ [8669, 8669, 412*w + 1825],\ [8669, 8669, -412*w + 2237],\ [8677, 8677, 58*w + 241],\ [8677, 8677, -58*w + 299],\ [8681, 8681, 224*w - 1219],\ [8681, 8681, 224*w + 995],\ [8699, 8699, -84*w - 361],\ [8699, 8699, -84*w + 445],\ [8719, 8719, 520*w + 2299],\ [8719, 8719, -520*w + 2819],\ [8731, 8731, -6*w - 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^10 - x^9 - 14*x^8 + 13*x^7 + 61*x^6 - 51*x^5 - 92*x^4 + 76*x^3 + 36*x^2 - 31*x + 1 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, 25/91*e^9 + 5/91*e^8 - 365/91*e^7 - 92/91*e^6 + 1696/91*e^5 + 74/13*e^4 - 2776/91*e^3 - 713/91*e^2 + 1296/91*e + 132/91, 120/91*e^9 - 25/91*e^8 - 131/7*e^7 + 215/91*e^6 + 7515/91*e^5 - 28/13*e^4 - 11194/91*e^3 + 226/91*e^2 + 4405/91*e - 128/91, -113/91*e^9 + 25/91*e^8 + 1584/91*e^7 - 222/91*e^6 - 6850/91*e^5 + 40/13*e^4 + 9864/91*e^3 - 506/91*e^2 - 3782/91*e + 268/91, 222/91*e^9 - 62/91*e^8 - 3153/91*e^7 + 627/91*e^6 + 13985/91*e^5 - 198/13*e^4 - 21285/91*e^3 + 1921/91*e^2 + 8837/91*e - 843/91, 1, -53/91*e^9 + 23/91*e^8 + 722/91*e^7 - 237/91*e^6 - 3026/91*e^5 + 68/13*e^4 + 4372/91*e^3 - 36/91*e^2 - 1947/91*e - 405/91, 8/91*e^9 - 32/91*e^8 - 5/7*e^7 + 348/91*e^6 - 45/91*e^5 - 118/13*e^4 + 825/91*e^3 - 173/91*e^2 - 1132/91*e + 586/91, 58/91*e^9 + 6/91*e^8 - 823/91*e^7 - 102/91*e^6 + 3585/91*e^5 + 64/13*e^4 - 4993/91*e^3 + 172/91*e^2 + 1663/91*e - 592/91, -296/91*e^9 + 36/91*e^8 + 4190/91*e^7 - 150/91*e^6 - 18467/91*e^5 - 174/13*e^4 + 27701/91*e^3 + 1494/91*e^2 - 11484/91*e + 10/7, -75/91*e^9 + 27/91*e^8 + 81/7*e^7 - 305/91*e^6 - 4549/91*e^5 + 141/13*e^4 + 6382/91*e^3 - 1893/91*e^2 - 1809/91*e + 626/91, -222/91*e^9 + 62/91*e^8 + 3153/91*e^7 - 627/91*e^6 - 13985/91*e^5 + 198/13*e^4 + 21376/91*e^3 - 2012/91*e^2 - 9474/91*e + 661/91, 53/13*e^9 - 14/13*e^8 - 744/13*e^7 + 132/13*e^6 + 3226/13*e^5 - 237/13*e^4 - 4685/13*e^3 + 394/13*e^2 + 1814/13*e - 14, -141/91*e^9 + 3/7*e^8 + 2046/91*e^7 - 418/91*e^6 - 9391/91*e^5 + 152/13*e^4 + 15051/91*e^3 - 1458/91*e^2 - 6400/91*e + 716/91, -433/91*e^9 + 73/91*e^8 + 6144/91*e^7 - 618/91*e^6 - 2083/7*e^5 + 92/13*e^4 + 40165/91*e^3 - 2441/91*e^2 - 16028/91*e + 1328/91, 2/13*e^9 + 2/13*e^8 - 36/13*e^7 - 21/13*e^6 + 220/13*e^5 + 41/13*e^4 - 503/13*e^3 + 66/13*e^2 + 329/13*e - 89/13, -233/91*e^9 + 43/91*e^8 + 3294/91*e^7 - 25/7*e^6 - 14470/91*e^5 + 1/13*e^4 + 21625/91*e^3 - 424/91*e^2 - 9125/91*e + 74/91, 15/91*e^9 + 4/7*e^8 - 177/91*e^7 - 730/91*e^6 + 515/91*e^5 + 438/13*e^4 - 120/91*e^3 - 3512/91*e^2 + 464/91*e + 495/91, -12/7*e^9 + 85/91*e^8 + 2216/91*e^7 - 983/91*e^6 - 9983/91*e^5 + 431/13*e^4 + 16242/91*e^3 - 3441/91*e^2 - 7655/91*e + 725/91, -125/91*e^9 + 45/91*e^8 + 135/7*e^7 - 387/91*e^6 - 7703/91*e^5 + 40/13*e^4 + 11941/91*e^3 + 576/91*e^2 - 5927/91*e + 103/91, 6*e^9 - 21/13*e^8 - 1097/13*e^7 + 193/13*e^6 + 4768/13*e^5 - 289/13*e^4 - 6931/13*e^3 + 313/13*e^2 + 2672/13*e - 30/13, -88/91*e^9 - 47/91*e^8 + 1296/91*e^7 + 645/91*e^6 - 6036/91*e^5 - 376/13*e^4 + 745/7*e^3 + 2624/91*e^2 - 4614/91*e - 776/91, -453/91*e^9 + 118/91*e^8 + 6387/91*e^7 - 1019/91*e^6 - 27901/91*e^5 + 9*e^4 + 41074/91*e^3 + 578/91*e^2 - 1250/7*e - 655/91, 710/91*e^9 - 103/91*e^8 - 10030/91*e^7 + 652/91*e^6 + 43909/91*e^5 + 196/13*e^4 - 64599/91*e^3 - 104/7*e^2 + 25962/91*e + 141/91, 744/91*e^9 - 204/91*e^8 - 10455/91*e^7 + 1935/91*e^6 + 45494/91*e^5 - 458/13*e^4 - 66726/91*e^3 + 3266/91*e^2 + 26387/91*e - 809/91, 359/91*e^9 - 36/91*e^8 - 5079/91*e^7 + 178/91*e^6 + 22359/91*e^5 + 126/13*e^4 - 33483/91*e^3 - 10/91*e^2 + 14543/91*e - 963/91, -33/7*e^9 + 29/91*e^8 + 6094/91*e^7 + 4/91*e^6 - 26930/91*e^5 - 300/13*e^4 + 40161/91*e^3 + 1662/91*e^2 - 16524/91*e + 424/91, -258/91*e^9 + 3/91*e^8 + 3694/91*e^7 + 145/91*e^6 - 16418/91*e^5 - 213/13*e^4 + 24051/91*e^3 + 919/91*e^2 - 8559/91*e - 667/91, -46/13*e^9 - 1/13*e^8 + 653/13*e^7 + 62/13*e^6 - 2877/13*e^5 - 515/13*e^4 + 4245/13*e^3 + 636/13*e^2 - 1732/13*e - 147/13, -229/91*e^9 + 62/91*e^8 + 3272/91*e^7 - 620/91*e^6 - 14559/91*e^5 + 199/13*e^4 + 21887/91*e^3 - 2187/91*e^2 - 8732/91*e + 885/91, 173/91*e^9 - 125/91*e^8 - 2439/91*e^7 + 1502/91*e^6 + 820/7*e^5 - 729/13*e^4 - 15790/91*e^3 + 6471/91*e^2 + 6044/91*e - 2082/91, -106/91*e^9 + 53/91*e^8 + 1437/91*e^7 - 586/91*e^6 - 5856/91*e^5 + 216/13*e^4 + 580/7*e^3 - 1017/91*e^2 - 2046/91*e + 58/91, -44/13*e^9 + 14/13*e^8 + 630/13*e^7 - 141/13*e^6 - 2826/13*e^5 + 293/13*e^4 + 4379/13*e^3 - 21*e^2 - 1923/13*e + 102/13, 37/13*e^9 - 17/13*e^8 - 508/13*e^7 + 183/13*e^6 + 2116/13*e^5 - 487/13*e^4 - 2845/13*e^3 + 633/13*e^2 + 950/13*e - 302/13, -7/13*e^9 + 18/13*e^8 + 101/13*e^7 - 242/13*e^6 - 460/13*e^5 + 966/13*e^4 + 717/13*e^3 - 1188/13*e^2 - 122/13*e + 259/13, 485/91*e^9 - 29/91*e^8 - 528/7*e^7 - 60/91*e^6 + 30157/91*e^5 + 396/13*e^4 - 44522/91*e^3 - 3174/91*e^2 + 17595/91*e + 423/91, -191/91*e^9 + 92/91*e^8 + 2622/91*e^7 - 969/91*e^6 - 11019/91*e^5 + 321/13*e^4 + 15409/91*e^3 - 1348/91*e^2 - 5100/91*e - 199/91, -95/91*e^9 + 37/91*e^8 + 1513/91*e^7 - 510/91*e^6 - 7989/91*e^5 + 22*e^4 + 15586/91*e^3 - 2248/91*e^2 - 629/7*e + 36/91, 354/91*e^9 - 58/91*e^8 - 4985/91*e^7 + 405/91*e^6 + 1671/7*e^5 + 48/13*e^4 - 31700/91*e^3 + 1/91*e^2 + 12307/91*e - 463/91, -116/91*e^9 + 79/91*e^8 + 1737/91*e^7 - 979/91*e^6 - 8535/91*e^5 + 509/13*e^4 + 15992/91*e^3 - 4985/91*e^2 - 9150/91*e + 1730/91, 736/91*e^9 - 25/91*e^8 - 10446/91*e^7 - 492/91*e^6 + 46106/91*e^5 + 937/13*e^4 - 68811/91*e^3 - 646/7*e^2 + 28653/91*e + 1181/91, 473/91*e^9 - 212/91*e^8 - 6672/91*e^7 + 2386/91*e^6 + 29262/91*e^5 - 75*e^4 - 43565/91*e^3 + 7568/91*e^2 + 1273/7*e - 1891/91, -4/91*e^9 - 5/91*e^8 + 8/91*e^7 + 71/91*e^6 + 23/7*e^5 - 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129680/91*e + 418/91, 233/91*e^9 - 106/91*e^8 - 2776/91*e^7 + 787/91*e^6 + 8156/91*e^5 + 46/13*e^4 - 1416/91*e^3 - 2173/91*e^2 - 136/91*e - 2153/91, 2941/91*e^9 - 1796/91*e^8 - 41246/91*e^7 + 20452/91*e^6 + 179876/91*e^5 - 8568/13*e^4 - 269599/91*e^3 + 57311/91*e^2 + 104792/91*e - 3516/91, 485/91*e^9 - 1030/91*e^8 - 521/7*e^7 + 13772/91*e^6 + 30703/91*e^5 - 7703/13*e^4 - 55715/91*e^3 + 63711/91*e^2 + 30972/91*e - 10861/91, 2330/91*e^9 - 591/91*e^8 - 32051/91*e^7 + 5371/91*e^6 + 10203/7*e^5 - 1291/13*e^4 - 169084/91*e^3 + 18968/91*e^2 + 46198/91*e - 7873/91, 7480/91*e^9 - 1486/91*e^8 - 105953/91*e^7 + 12669/91*e^6 + 466699/91*e^5 - 113*e^4 - 695489/91*e^3 + 14484/91*e^2 + 21048/7*e - 6987/91, -354/91*e^9 + 219/91*e^8 + 5643/91*e^7 - 3072/91*e^6 - 30319/91*e^5 + 1935/13*e^4 + 63886/91*e^3 - 1847/7*e^2 - 39145/91*e + 15604/91, 4705/91*e^9 - 634/91*e^8 - 66299/91*e^7 + 3827/91*e^6 + 288901/91*e^5 + 1288/13*e^4 - 420330/91*e^3 + 1416/91*e^2 + 163424/91*e - 9788/91, 537/91*e^9 - 1/7*e^8 - 7374/91*e^7 - 290/91*e^6 + 30540/91*e^5 + 447/13*e^4 - 40150/91*e^3 - 1551/91*e^2 + 16047/91*e + 2069/91, 5074/91*e^9 - 360/91*e^8 - 72651/91*e^7 + 296/91*e^6 + 325258/91*e^5 + 3440/13*e^4 - 495032/91*e^3 - 27792/91*e^2 + 198882/91*e + 6855/91, -3949/91*e^9 + 620/91*e^8 + 56191/91*e^7 - 4996/91*e^6 - 249960/91*e^5 + 368/13*e^4 + 381564/91*e^3 - 13932/91*e^2 - 160715/91*e + 9613/91, 97/13*e^9 + 42/13*e^8 - 1418/13*e^7 - 691/13*e^6 + 6478/13*e^5 + 276*e^4 - 9911/13*e^3 - 5260/13*e^2 + 324*e + 882/13, 374/91*e^9 + 1094/91*e^8 - 5697/91*e^7 - 14888/91*e^6 + 26304/91*e^5 + 8503/13*e^4 - 33197/91*e^3 - 65514/91*e^2 + 7944/91*e + 11446/91, -687/91*e^9 + 634/91*e^8 + 9641/91*e^7 - 7845/91*e^6 - 42417/91*e^5 + 4105/13*e^4 + 66683/91*e^3 - 3057/7*e^2 - 30683/91*e + 3061/91, 1562/91*e^9 - 340/91*e^8 - 22171/91*e^7 + 2812/91*e^6 + 98375/91*e^5 - 51/13*e^4 - 150459/91*e^3 - 8195/91*e^2 + 64416/91*e + 471/7, -3553/91*e^9 + 863/91*e^8 + 50737/91*e^7 - 8266/91*e^6 - 227012/91*e^5 + 2303/13*e^4 + 350900/91*e^3 - 31130/91*e^2 - 152657/91*e + 14190/91, 4317/91*e^9 - 811/91*e^8 - 61190/91*e^7 + 6423/91*e^6 + 271109/91*e^5 - 165/13*e^4 - 414797/91*e^3 + 3027/91*e^2 + 182472/91*e - 9180/91, -1203/91*e^9 + 801/91*e^8 + 16959/91*e^7 - 10040/91*e^6 - 74385/91*e^5 + 5220/13*e^4 + 111208/91*e^3 - 49446/91*e^2 - 40332/91*e + 9315/91, -1745/91*e^9 - 167/91*e^8 + 24567/91*e^7 + 4274/91*e^6 - 107206/91*e^5 - 4120/13*e^4 + 156200/91*e^3 + 39266/91*e^2 - 59539/91*e - 12708/91, 255/91*e^9 - 404/91*e^8 - 4360/91*e^7 + 6014/91*e^6 + 25198/91*e^5 - 3946/13*e^4 - 54869/91*e^3 + 39920/91*e^2 + 28216/91*e - 14979/91, 6374/91*e^9 - 1724/91*e^8 - 89643/91*e^7 + 16582/91*e^6 + 29993/7*e^5 - 4369/13*e^4 - 567900/91*e^3 + 43261/91*e^2 + 217918/91*e - 18670/91, 2859/91*e^9 - 768/91*e^8 - 40074/91*e^7 + 6959/91*e^6 + 173479/91*e^5 - 1354/13*e^4 - 251422/91*e^3 + 9834/91*e^2 + 91986/91*e - 6579/91, 909/91*e^9 - 220/91*e^8 - 12633/91*e^7 + 1948/91*e^6 + 52895/91*e^5 - 215/13*e^4 - 67556/91*e^3 - 5126/91*e^2 + 16217/91*e + 880/7, 652/91*e^9 - 522/91*e^8 - 9067/91*e^7 + 6179/91*e^6 + 39589/91*e^5 - 2690/13*e^4 - 61916/91*e^3 + 12917/91*e^2 + 24194/91*e + 604/7, -5735/91*e^9 + 2339/91*e^8 + 80154/91*e^7 - 24734/91*e^6 - 345654/91*e^5 + 676*e^4 + 499830/91*e^3 - 66826/91*e^2 - 14346/7*e + 16580/91, -2270/91*e^9 - 370/91*e^8 + 32421/91*e^7 + 521/7*e^6 - 142654/91*e^5 - 4961/13*e^4 + 202687/91*e^3 + 25336/91*e^2 - 71313/91*e + 578/91, -230/13*e^9 - 2/13*e^8 + 3249/13*e^7 + 314/13*e^6 - 14314/13*e^5 - 2790/13*e^4 + 1678*e^3 + 3191/13*e^2 - 10754/13*e - 77/13, 4196/91*e^9 - 999/91*e^8 - 59478/91*e^7 + 8954/91*e^6 + 262085/91*e^5 - 1728/13*e^4 - 392738/91*e^3 + 19116/91*e^2 + 167922/91*e - 12942/91, 1179/91*e^9 + 9/91*e^8 - 17205/91*e^7 - 1154/91*e^6 + 80043/91*e^5 + 1539/13*e^4 - 132569/91*e^3 - 12937/91*e^2 + 64147/91*e - 4710/91, -2063/91*e^9 + 209/91*e^8 + 29662/91*e^7 - 1684/91*e^6 - 132985/91*e^5 + 347/13*e^4 + 199281/91*e^3 - 20198/91*e^2 - 74182/91*e + 12099/91, 253/13*e^9 - 80/13*e^8 - 3597/13*e^7 + 55*e^6 + 16127/13*e^5 - 803/13*e^4 - 25756/13*e^3 - 334/13*e^2 + 12187/13*e - 219/13, -619/13*e^9 + 238/13*e^8 + 8712/13*e^7 - 2487/13*e^6 - 38114/13*e^5 + 6035/13*e^4 + 4382*e^3 - 6824/13*e^2 - 23095/13*e + 2104/13, 4600/91*e^9 - 1607/91*e^8 - 64451/91*e^7 + 1311/7*e^6 + 279619/91*e^5 - 6203/13*e^4 - 409564/91*e^3 + 56891/91*e^2 + 157922/91*e - 16333/91, -5340/91*e^9 + 1515/91*e^8 + 75108/91*e^7 - 14506/91*e^6 - 25204/7*e^5 + 3805/13*e^4 + 485141/91*e^3 - 36503/91*e^2 - 196460/91*e + 20389/91, -5/13*e^9 + 33/13*e^8 - 445/13*e^6 + 449/13*e^5 + 1839/13*e^4 - 1320/13*e^3 - 2396/13*e^2 - 248/13*e - 25/13, 86/7*e^9 - 258/91*e^8 - 16278/91*e^7 + 2594/91*e^6 + 74234/91*e^5 - 811/13*e^4 - 113223/91*e^3 + 9467/91*e^2 + 37656/91*e - 8774/91, 171/13*e^9 - 24/13*e^8 - 2454/13*e^7 + 96/13*e^6 + 10854/13*e^5 + 925/13*e^4 - 15427/13*e^3 - 2183/13*e^2 + 4697/13*e + 1237/13, 2966/91*e^9 - 356/91*e^8 - 41954/91*e^7 + 129/7*e^6 + 184169/91*e^5 + 1250/13*e^4 - 274587/91*e^3 - 445/91*e^2 + 121110/91*e - 8627/91, -200/91*e^9 + 485/91*e^8 + 2122/91*e^7 - 6299/91*e^6 - 4419/91*e^5 + 262*e^4 - 4938/91*e^3 - 28316/91*e^2 + 477/7*e + 5076/91, 2888/91*e^9 - 506/91*e^8 - 41245/91*e^7 + 4220/91*e^6 + 183479/91*e^5 - 40*e^4 - 274215/91*e^3 + 11901/91*e^2 + 8063/7*e - 11614/91, -1507/91*e^9 + 76/7*e^8 + 20731/91*e^7 - 10986/91*e^6 - 87473/91*e^5 + 4340/13*e^4 + 123804/91*e^3 - 25442/91*e^2 - 44566/91*e + 1320/91, -7372/91*e^9 + 157/7*e^8 + 104134/91*e^7 - 19850/91*e^6 - 457188/91*e^5 + 5189/13*e^4 + 681052/91*e^3 - 37907/91*e^2 - 273765/91*e + 15073/91, 419/13*e^9 - 45/13*e^8 - 6051/13*e^7 + 275/13*e^6 + 2114*e^5 + 648/13*e^4 - 42828/13*e^3 + 170/13*e^2 + 17533/13*e - 840/13, 2829/91*e^9 - 564/91*e^8 - 40119/91*e^7 + 4492/91*e^6 + 177342/91*e^5 - 75/13*e^4 - 266120/91*e^3 - 3337/91*e^2 + 100935/91*e - 2319/91, 2917/91*e^9 - 1077/91*e^8 - 40946/91*e^7 + 11351/91*e^6 + 177981/91*e^5 - 3941/13*e^4 - 262204/91*e^3 + 28871/91*e^2 + 107404/91*e - 1186/91, 326/91*e^9 - 240/91*e^8 - 3235/91*e^7 + 2708/91*e^6 + 3957/91*e^5 - 96*e^4 + 21850/91*e^3 + 16682/91*e^2 - 2178/7*e - 6301/91, 597/7*e^9 - 1700/91*e^8 - 109112/91*e^7 + 15019/91*e^6 + 473570/91*e^5 - 2484/13*e^4 - 684108/91*e^3 + 26414/91*e^2 + 261754/91*e - 9677/91, 2370/91*e^9 - 422/91*e^8 - 33706/91*e^7 + 3758/91*e^6 + 148906/91*e^5 - 825/13*e^4 - 222184/91*e^3 + 1378/7*e^2 + 95817/91*e - 8555/91, 1634/91*e^9 - 453/91*e^8 - 23022/91*e^7 + 4964/91*e^6 + 100868/91*e^5 - 2168/13*e^4 - 11701/7*e^3 + 30505/91*e^2 + 70671/91*e - 13677/91, 2322/91*e^9 + 365/91*e^8 - 33547/91*e^7 - 6667/91*e^6 + 151276/91*e^5 + 5006/13*e^4 - 228009/91*e^3 - 2320/7*e^2 + 89610/91*e - 262/91, -1866/91*e^9 - 23/7*e^8 + 26496/91*e^7 + 6273/91*e^6 - 117392/91*e^5 - 5355/13*e^4 + 177181/91*e^3 + 46430/91*e^2 - 75958/91*e - 9253/91, -1501/91*e^9 + 565/91*e^8 + 21468/91*e^7 - 5979/91*e^6 - 96290/91*e^5 + 2129/13*e^4 + 148893/91*e^3 - 14181/91*e^2 - 58659/91*e - 118/7] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([11,11,12*w + 53])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]