/* 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([-1, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([1280, 80, -32*w + 16]) primes_array = [ [4, 2, 2],\ [5, 5, -2*w + 1],\ [9, 3, 3],\ [11, 11, -3*w + 2],\ [11, 11, -3*w + 1],\ [19, 19, -4*w + 3],\ [19, 19, -4*w + 1],\ [29, 29, w + 5],\ [29, 29, -w + 6],\ [31, 31, -5*w + 2],\ [31, 31, -5*w + 3],\ [41, 41, -6*w + 5],\ [41, 41, w - 7],\ [49, 7, -7],\ [59, 59, 2*w - 9],\ [59, 59, 7*w - 5],\ [61, 61, 3*w - 10],\ [61, 61, -3*w - 7],\ [71, 71, -8*w + 7],\ [71, 71, w - 9],\ [79, 79, 8*w - 5],\ [79, 79, 3*w - 11],\ [89, 89, -10*w - 1],\ [89, 89, 10*w - 11],\ [101, 101, 4*w - 13],\ [101, 101, 5*w - 14],\ [109, 109, -11*w - 1],\ [109, 109, 11*w - 12],\ [131, 131, -12*w - 1],\ [131, 131, 12*w - 13],\ [139, 139, 2*w - 13],\ [139, 139, -11*w + 9],\ [149, 149, 7*w - 18],\ [149, 149, 4*w - 15],\ [151, 151, 5*w - 16],\ [151, 151, 6*w - 17],\ [169, 13, -13],\ [179, 179, 7*w - 19],\ [179, 179, 5*w - 17],\ [181, 181, -14*w - 1],\ [181, 181, 14*w - 15],\ [191, 191, 2*w - 15],\ [191, 191, -13*w + 11],\ [199, 199, 3*w - 16],\ [199, 199, -13*w + 10],\ [211, 211, 6*w - 19],\ [211, 211, 7*w - 20],\ [229, 229, -14*w + 11],\ [229, 229, 3*w - 17],\ [239, 239, -16*w - 1],\ [239, 239, 16*w - 17],\ [241, 241, 9*w - 23],\ [241, 241, 5*w - 19],\ [251, 251, 2*w - 17],\ [251, 251, -15*w + 13],\ [269, 269, 15*w - 11],\ [269, 269, 4*w - 19],\ [271, 271, -17*w - 1],\ [271, 271, 17*w - 18],\ [281, 281, 7*w - 22],\ [281, 281, 8*w - 23],\ [289, 17, -17],\ [311, 311, 5*w - 21],\ [311, 311, 16*w - 11],\ [331, 331, -17*w + 14],\ [331, 331, 3*w - 20],\ [349, 349, 17*w - 12],\ [349, 349, 5*w - 22],\ [359, 359, 10*w - 27],\ [359, 359, 7*w - 24],\ [379, 379, -20*w - 1],\ [379, 379, 20*w - 21],\ [389, 389, 5*w - 23],\ [389, 389, 18*w - 13],\ [401, 401, 7*w - 25],\ [401, 401, 11*w - 29],\ [409, 409, 3*w - 22],\ [409, 409, -19*w + 16],\ [419, 419, -21*w - 1],\ [419, 419, 21*w - 22],\ [421, 421, -19*w + 15],\ [421, 421, 4*w - 23],\ [431, 431, 19*w - 14],\ [431, 431, 5*w - 24],\ [439, 439, 6*w - 25],\ [439, 439, 19*w - 13],\ [449, 449, 8*w - 27],\ [449, 449, 11*w - 30],\ [461, 461, -22*w - 1],\ [461, 461, 22*w - 23],\ [479, 479, 23*w - 25],\ [479, 479, -23*w - 2],\ [491, 491, 13*w - 33],\ [491, 491, 7*w - 27],\ [499, 499, 11*w - 31],\ [499, 499, 9*w - 29],\ [509, 509, 4*w - 25],\ [509, 509, -21*w + 17],\ [521, 521, 5*w - 26],\ [521, 521, 21*w - 16],\ [529, 23, -23],\ [541, 541, 25*w - 28],\ [541, 541, -25*w - 3],\ [569, 569, -22*w + 17],\ [569, 569, 5*w - 27],\ [571, 571, 25*w - 27],\ [571, 571, -25*w - 2],\ [599, 599, -25*w - 1],\ [599, 599, 25*w - 26],\ [601, 601, 13*w - 35],\ [601, 601, 9*w - 31],\ [619, 619, 5*w - 28],\ [619, 619, -23*w + 18],\ [631, 631, 23*w - 17],\ [631, 631, 6*w - 29],\ [641, 641, 23*w - 16],\ [641, 641, 7*w - 30],\ [659, 659, 13*w - 36],\ [659, 659, 10*w - 33],\ [661, 661, 11*w - 34],\ [661, 661, 12*w - 35],\ [691, 691, 28*w - 31],\ [691, 691, -28*w - 3],\ [701, 701, -27*w - 1],\ [701, 701, 27*w - 28],\ [709, 709, 4*w - 29],\ [709, 709, -25*w + 21],\ [719, 719, 13*w - 37],\ [719, 719, 11*w - 35],\ [739, 739, 6*w - 31],\ [739, 739, 25*w - 19],\ [751, 751, 7*w - 32],\ [751, 751, 25*w - 18],\ [761, 761, 8*w - 33],\ [761, 761, 25*w - 17],\ [769, 769, 9*w - 34],\ [769, 769, 16*w - 41],\ [809, 809, 7*w - 33],\ [809, 809, 26*w - 19],\ [811, 811, -29*w - 1],\ [811, 811, 29*w - 30],\ [821, 821, -27*w + 23],\ [821, 821, 4*w - 31],\ [829, 829, 17*w - 43],\ [829, 829, 9*w - 35],\ [839, 839, -27*w + 22],\ [839, 839, 5*w - 32],\ [859, 859, 31*w - 34],\ [859, 859, -31*w - 3],\ [881, 881, 8*w - 35],\ [881, 881, 27*w - 19],\ [911, 911, 13*w - 40],\ [911, 911, 14*w - 41],\ [919, 919, -32*w - 3],\ [919, 919, 32*w - 35],\ [929, 929, -31*w - 1],\ [929, 929, 31*w - 32],\ [941, 941, 33*w - 37],\ [941, 941, -33*w - 4],\ [971, 971, 11*w - 39],\ [971, 971, 17*w - 45],\ [991, 991, -32*w - 1],\ [991, 991, 32*w - 33],\ [1009, 1009, 29*w - 21],\ [1009, 1009, 8*w - 37],\ [1019, 1019, 33*w - 35],\ [1019, 1019, -33*w - 2],\ [1021, 1021, 29*w - 20],\ [1021, 1021, 9*w - 38],\ [1031, 1031, 19*w - 48],\ [1031, 1031, 10*w - 39],\ [1039, 1039, 18*w - 47],\ [1039, 1039, 11*w - 40],\ [1049, 1049, 16*w - 45],\ [1049, 1049, 13*w - 42],\ [1051, 1051, 14*w - 43],\ [1051, 1051, 15*w - 44],\ [1061, 1061, -30*w + 23],\ [1061, 1061, 7*w - 37],\ [1069, 1069, -35*w - 4],\ [1069, 1069, 35*w - 39],\ [1091, 1091, 36*w - 41],\ [1091, 1091, -36*w - 5],\ [1109, 1109, 19*w - 49],\ [1109, 1109, 11*w - 41],\ [1129, 1129, -31*w + 24],\ [1129, 1129, 7*w - 38],\ [1151, 1151, 35*w - 37],\ [1151, 1151, -35*w - 2],\ [1171, 1171, 10*w - 41],\ [1171, 1171, 21*w - 52],\ [1181, 1181, 11*w - 42],\ [1181, 1181, 20*w - 51],\ [1201, 1201, 15*w - 46],\ [1201, 1201, 16*w - 47],\ [1229, 1229, 38*w - 43],\ [1229, 1229, -38*w - 5],\ [1231, 1231, 9*w - 41],\ [1231, 1231, 32*w - 23],\ [1249, 1249, 37*w - 40],\ [1249, 1249, -37*w - 3],\ [1259, 1259, -36*w - 1],\ [1259, 1259, 36*w - 37],\ [1279, 1279, 17*w - 49],\ [1279, 1279, 15*w - 47],\ [1289, 1289, 8*w - 41],\ [1289, 1289, 33*w - 25],\ [1291, 1291, 37*w - 39],\ [1291, 1291, -37*w - 2],\ [1301, 1301, -39*w - 5],\ [1301, 1301, 39*w - 44],\ [1319, 1319, 33*w - 23],\ [1319, 1319, 10*w - 43],\ [1321, 1321, -38*w - 3],\ [1321, 1321, 38*w - 41],\ [1361, 1361, 16*w - 49],\ [1361, 1361, 17*w - 50],\ [1369, 37, -37],\ [1381, 1381, 9*w - 43],\ [1381, 1381, 34*w - 25],\ [1399, 1399, -35*w + 29],\ [1399, 1399, 6*w - 41],\ [1409, 1409, 11*w - 45],\ [1409, 1409, 23*w - 57],\ [1429, 1429, 13*w - 47],\ [1429, 1429, 21*w - 55],\ [1439, 1439, 39*w - 41],\ [1439, 1439, -39*w - 2],\ [1451, 1451, 41*w - 46],\ [1451, 1451, -41*w - 5],\ [1459, 1459, 35*w - 26],\ [1459, 1459, 9*w - 44],\ [1471, 1471, 40*w - 43],\ [1471, 1471, -40*w - 3],\ [1481, 1481, -39*w - 1],\ [1481, 1481, 39*w - 40],\ [1489, 1489, 35*w - 24],\ [1489, 1489, 11*w - 46],\ [1499, 1499, 7*w - 43],\ [1499, 1499, -36*w + 29],\ [1511, 1511, 13*w - 48],\ [1511, 1511, 22*w - 57],\ [1531, 1531, 17*w - 52],\ [1531, 1531, 18*w - 53],\ [1549, 1549, -41*w - 3],\ [1549, 1549, 41*w - 44],\ [1559, 1559, -40*w - 1],\ [1559, 1559, 40*w - 41],\ [1571, 1571, 11*w - 47],\ [1571, 1571, 36*w - 25],\ [1579, 1579, -37*w + 30],\ [1579, 1579, 7*w - 44],\ [1601, 1601, -37*w + 29],\ [1601, 1601, 8*w - 45],\ [1609, 1609, 43*w - 48],\ [1609, 1609, -43*w - 5],\ [1619, 1619, 19*w - 55],\ [1619, 1619, 17*w - 53],\ [1621, 1621, 9*w - 46],\ [1621, 1621, 37*w - 28],\ [1669, 1669, 12*w - 49],\ [1669, 1669, 37*w - 25],\ [1699, 1699, 22*w - 59],\ [1699, 1699, 15*w - 52],\ [1709, 1709, 17*w - 54],\ [1709, 1709, 20*w - 57],\ [1721, 1721, -42*w - 1],\ [1721, 1721, 42*w - 43],\ [1741, 1741, 38*w - 27],\ [1741, 1741, 11*w - 49],\ [1759, 1759, 43*w - 45],\ [1759, 1759, -43*w - 2],\ [1789, 1789, 15*w - 53],\ [1789, 1789, 23*w - 61],\ [1801, 1801, 21*w - 59],\ [1801, 1801, 17*w - 55],\ [1811, 1811, 39*w - 29],\ [1811, 1811, 10*w - 49],\ [1831, 1831, 7*w - 47],\ [1831, 1831, -40*w + 33],\ [1849, 43, -43],\ [1861, 1861, 46*w - 51],\ [1861, 1861, -46*w - 5],\ [1871, 1871, 25*w - 64],\ [1871, 1871, 14*w - 53],\ [1879, 1879, -40*w + 31],\ [1879, 1879, 9*w - 49],\ [1889, 1889, 16*w - 55],\ [1889, 1889, 23*w - 62],\ [1901, 1901, 19*w - 58],\ [1901, 1901, 20*w - 59],\ [1931, 1931, 45*w - 47],\ [1931, 1931, -45*w - 2],\ [1949, 1949, -47*w - 5],\ [1949, 1949, 47*w - 52],\ [1951, 1951, 13*w - 53],\ [1951, 1951, 27*w - 67],\ [1979, 1979, -45*w - 1],\ [1979, 1979, 45*w - 46],\ [1999, 1999, 21*w - 61],\ [1999, 1999, 19*w - 59],\ [2011, 2011, 41*w - 30],\ [2011, 2011, 11*w - 52],\ [2029, 2029, 12*w - 53],\ [2029, 2029, 41*w - 29],\ [2039, 2039, 48*w - 53],\ [2039, 2039, -48*w - 5],\ [2069, 2069, -46*w - 1],\ [2069, 2069, 46*w - 47],\ [2081, 2081, 25*w - 66],\ [2081, 2081, 16*w - 57],\ [2089, 2089, 17*w - 58],\ [2089, 2089, 24*w - 65],\ [2099, 2099, 22*w - 63],\ [2099, 2099, 19*w - 60],\ [2111, 2111, 47*w - 49],\ [2111, 2111, -47*w - 2],\ [2129, 2129, 8*w - 51],\ [2129, 2129, -43*w + 35],\ [2131, 2131, -49*w - 5],\ [2131, 2131, 49*w - 54],\ [2141, 2141, 42*w - 29],\ [2141, 2141, 13*w - 55],\ [2161, 2161, -47*w - 1],\ [2161, 2161, 47*w - 48],\ [2179, 2179, -43*w + 33],\ [2179, 2179, 10*w - 53],\ [2209, 47, -47],\ [2221, 2221, 43*w - 31],\ [2221, 2221, 12*w - 55],\ [2239, 2239, 43*w - 30],\ [2239, 2239, 13*w - 56],\ [2251, 2251, -44*w + 35],\ [2251, 2251, 9*w - 53],\ [2269, 2269, 15*w - 58],\ [2269, 2269, 28*w - 71],\ [2281, 2281, 16*w - 59],\ [2281, 2281, 27*w - 70],\ [2309, 2309, 20*w - 63],\ [2309, 2309, 23*w - 66],\ [2311, 2311, 21*w - 64],\ [2311, 2311, 22*w - 65],\ [2339, 2339, 44*w - 31],\ [2339, 2339, 13*w - 57],\ [2341, 2341, -50*w - 3],\ [2341, 2341, 50*w - 53],\ [2351, 2351, -49*w - 1],\ [2351, 2351, 49*w - 50],\ [2371, 2371, 29*w - 73],\ [2371, 2371, 15*w - 59],\ [2381, 2381, -51*w - 4],\ [2381, 2381, 51*w - 55],\ [2389, 2389, 7*w - 53],\ [2389, 2389, -46*w + 39],\ [2399, 2399, 11*w - 56],\ [2399, 2399, 45*w - 34],\ [2411, 2411, 25*w - 69],\ [2411, 2411, 19*w - 63],\ [2441, 2441, 45*w - 32],\ [2441, 2441, 13*w - 58],\ [2459, 2459, 14*w - 59],\ [2459, 2459, 45*w - 31],\ [2521, 2521, -47*w + 39],\ [2521, 2521, 8*w - 55],\ [2531, 2531, 22*w - 67],\ [2531, 2531, 23*w - 68],\ [2539, 2539, 52*w - 55],\ [2539, 2539, -52*w - 3],\ [2549, 2549, -51*w - 1],\ [2549, 2549, 51*w - 52],\ [2551, 2551, -47*w + 38],\ [2551, 2551, 9*w - 56],\ [2579, 2579, 10*w - 57],\ [2579, 2579, -47*w + 37],\ [2591, 2591, -55*w - 7],\ [2591, 2591, 55*w - 62],\ [2609, 2609, 29*w - 75],\ [2609, 2609, 17*w - 63],\ [2621, 2621, -54*w - 5],\ [2621, 2621, 54*w - 59],\ [2659, 2659, 55*w - 61],\ [2659, 2659, -55*w - 6],\ [2671, 2671, 14*w - 61],\ [2671, 2671, 47*w - 33],\ [2689, 2689, 47*w - 32],\ [2689, 2689, 15*w - 62],\ [2699, 2699, 53*w - 55],\ [2699, 2699, -53*w - 2],\ [2711, 2711, 11*w - 59],\ [2711, 2711, -48*w + 37],\ [2719, 2719, 17*w - 64],\ [2719, 2719, 30*w - 77],\ [2729, 2729, 57*w - 65],\ [2729, 2729, -57*w - 8],\ [2731, 2731, 18*w - 65],\ [2731, 2731, 29*w - 76],\ [2741, 2741, 28*w - 75],\ [2741, 2741, 19*w - 66],\ [2749, 2749, 20*w - 67],\ [2749, 2749, 27*w - 74],\ [2789, 2789, -55*w - 4],\ [2789, 2789, 55*w - 59],\ [2791, 2791, -49*w + 39],\ [2791, 2791, 10*w - 59],\ [2801, 2801, 57*w - 64],\ [2801, 2801, -57*w - 7],\ [2809, 53, -53],\ [2819, 2819, -49*w + 38],\ [2819, 2819, 11*w - 60],\ [2851, 2851, 55*w - 58],\ [2851, 2851, -55*w - 3],\ [2861, 2861, -54*w - 1],\ [2861, 2861, 54*w - 55],\ [2879, 2879, 25*w - 73],\ [2879, 2879, 23*w - 71],\ [2909, 2909, -58*w - 7],\ [2909, 2909, 58*w - 65],\ [2939, 2939, -57*w - 5],\ [2939, 2939, 57*w - 62],\ [2969, 2969, -55*w - 1],\ [2969, 2969, 55*w - 56],\ [2971, 2971, 19*w - 68],\ [2971, 2971, 30*w - 79],\ [2999, 2999, 23*w - 72],\ [2999, 2999, 26*w - 75],\ [3001, 3001, 24*w - 73],\ [3001, 3001, 25*w - 74],\ [3011, 3011, 10*w - 61],\ [3011, 3011, -51*w + 41],\ [3019, 3019, -59*w - 7],\ [3019, 3019, 59*w - 66],\ [3041, 3041, -51*w + 40],\ [3041, 3041, 11*w - 62],\ [3049, 3049, 58*w - 63],\ [3049, 3049, -58*w - 5],\ [3061, 3061, 33*w - 83],\ [3061, 3061, 17*w - 67],\ [3079, 3079, -56*w - 1],\ [3079, 3079, 56*w - 57],\ [3089, 3089, 19*w - 69],\ [3089, 3089, 31*w - 81],\ [3109, 3109, 21*w - 71],\ [3109, 3109, 29*w - 79],\ [3119, 3119, 51*w - 37],\ [3119, 3119, 14*w - 65],\ [3121, 3121, 23*w - 73],\ [3121, 3121, 27*w - 77],\ [3169, 3169, -61*w - 8],\ [3169, 3169, 61*w - 69],\ [3181, 3181, 58*w - 61],\ [3181, 3181, -58*w - 3],\ [3191, 3191, -57*w - 1],\ [3191, 3191, 57*w - 58],\ [3209, 3209, 19*w - 70],\ [3209, 3209, 32*w - 83],\ [3221, 3221, 31*w - 82],\ [3221, 3221, 20*w - 71],\ [3229, 3229, -59*w - 4],\ [3229, 3229, 59*w - 63],\ [3251, 3251, 25*w - 76],\ [3251, 3251, 26*w - 77],\ [3259, 3259, 52*w - 37],\ [3259, 3259, 15*w - 67],\ [3271, 3271, 11*w - 64],\ [3271, 3271, -53*w + 42],\ [3299, 3299, 17*w - 69],\ [3299, 3299, 35*w - 87],\ [3301, 3301, 12*w - 65],\ [3301, 3301, -53*w + 41],\ [3319, 3319, 61*w - 67],\ [3319, 3319, -61*w - 6],\ [3329, 3329, 13*w - 66],\ [3329, 3329, 53*w - 40],\ [3331, 3331, 33*w - 85],\ [3331, 3331, 19*w - 71],\ [3359, 3359, 59*w - 61],\ [3359, 3359, -59*w - 2],\ [3361, 3361, -62*w - 7],\ [3361, 3361, 62*w - 69],\ [3371, 3371, 23*w - 75],\ [3371, 3371, 29*w - 81],\ [3389, 3389, -54*w + 43],\ [3389, 3389, 11*w - 65],\ [3391, 3391, 61*w - 66],\ [3391, 3391, -61*w - 5],\ [3449, 3449, 54*w - 41],\ [3449, 3449, 13*w - 67],\ [3461, 3461, 61*w - 65],\ [3461, 3461, -61*w - 4],\ [3469, 3469, 33*w - 86],\ [3469, 3469, 20*w - 73],\ [3491, 3491, 22*w - 75],\ [3491, 3491, 31*w - 84],\ [3499, 3499, 23*w - 76],\ [3499, 3499, 30*w - 83],\ [3511, 3511, 26*w - 79],\ [3511, 3511, 27*w - 80],\ [3529, 3529, 61*w - 64],\ [3529, 3529, -61*w - 3],\ [3539, 3539, -60*w - 1],\ [3539, 3539, 60*w - 61],\ [3541, 3541, -55*w + 43],\ [3541, 3541, 12*w - 67],\ [3559, 3559, -56*w + 47],\ [3559, 3559, 9*w - 65],\ [3571, 3571, 55*w - 42],\ [3571, 3571, 13*w - 68],\ [3581, 3581, 19*w - 73],\ [3581, 3581, 35*w - 89],\ [3631, 3631, 11*w - 67],\ [3631, 3631, -56*w + 45],\ [3659, 3659, -61*w - 1],\ [3659, 3659, 61*w - 62],\ [3671, 3671, 55*w - 38],\ [3671, 3671, 17*w - 72],\ [3691, 3691, 18*w - 73],\ [3691, 3691, 37*w - 92],\ [3701, 3701, -63*w - 4],\ [3701, 3701, 63*w - 67],\ [3709, 3709, 19*w - 74],\ [3709, 3709, 36*w - 91],\ [3719, 3719, 10*w - 67],\ [3719, 3719, -57*w + 47],\ [3739, 3739, 34*w - 89],\ [3739, 3739, 21*w - 76],\ [3761, 3761, 32*w - 87],\ [3761, 3761, 23*w - 78],\ [3769, 3769, 24*w - 79],\ [3769, 3769, 31*w - 86],\ [3779, 3779, 26*w - 81],\ [3779, 3779, 29*w - 84],\ [3821, 3821, -57*w + 44],\ [3821, 3821, 13*w - 70],\ [3851, 3851, 14*w - 71],\ [3851, 3851, 57*w - 43],\ [3881, 3881, 11*w - 69],\ [3881, 3881, -58*w + 47],\ [3889, 3889, 67*w - 75],\ [3889, 3889, -67*w - 8],\ [3911, 3911, 31*w - 87],\ [3911, 3911, 25*w - 81],\ [3919, 3919, 29*w - 85],\ [3919, 3919, 27*w - 83],\ [3929, 3929, 17*w - 74],\ [3929, 3929, 57*w - 40],\ [3931, 3931, 68*w - 77],\ [3931, 3931, -68*w - 9],\ [3989, 3989, 37*w - 94],\ [3989, 3989, 20*w - 77],\ [4001, 4001, 66*w - 71],\ [4001, 4001, -66*w - 5],\ [4019, 4019, 35*w - 92],\ [4019, 4019, 22*w - 79],\ [4021, 4021, -65*w - 3],\ [4021, 4021, 65*w - 68],\ [4049, 4049, 32*w - 89],\ [4049, 4049, 25*w - 82],\ [4051, 4051, 67*w - 73],\ [4051, 4051, -67*w - 6],\ [4079, 4079, 13*w - 72],\ [4079, 4079, -59*w + 46],\ [4091, 4091, 65*w - 67],\ [4091, 4091, -65*w - 2],\ [4099, 4099, 68*w - 75],\ [4099, 4099, -68*w - 7],\ [4111, 4111, 14*w - 73],\ [4111, 4111, 59*w - 45],\ [4129, 4129, -67*w - 5],\ [4129, 4129, 67*w - 72],\ [4139, 4139, -60*w + 49],\ [4139, 4139, 11*w - 71],\ [4159, 4159, -65*w - 1],\ [4159, 4159, 65*w - 66],\ [4201, 4201, 27*w - 85],\ [4201, 4201, 31*w - 89],\ [4211, 4211, 13*w - 73],\ [4211, 4211, -60*w + 47],\ [4219, 4219, 59*w - 41],\ [4219, 4219, 18*w - 77],\ [4229, 4229, -69*w - 7],\ [4229, 4229, 69*w - 76],\ [4231, 4231, 71*w - 81],\ [4231, 4231, -71*w - 10],\ [4241, 4241, 40*w - 99],\ [4241, 4241, 19*w - 78],\ [4259, 4259, 68*w - 73],\ [4259, 4259, -68*w - 5],\ [4261, 4261, 39*w - 98],\ [4261, 4261, 20*w - 79],\ [4271, 4271, 11*w - 72],\ [4271, 4271, -61*w + 50],\ [4289, 4289, -66*w - 1],\ [4289, 4289, 66*w - 67],\ [4339, 4339, 33*w - 92],\ [4339, 4339, 26*w - 85],\ [4349, 4349, 31*w - 90],\ [4349, 4349, 28*w - 87],\ [4391, 4391, -69*w - 5],\ [4391, 4391, 69*w - 74],\ [4409, 4409, -71*w - 8],\ [4409, 4409, 71*w - 79],\ [4421, 4421, -67*w - 1],\ [4421, 4421, 67*w - 68],\ [4441, 4441, 16*w - 77],\ [4441, 4441, 61*w - 45],\ [4451, 4451, 23*w - 83],\ [4451, 4451, 37*w - 97],\ [4481, 4481, 13*w - 75],\ [4481, 4481, -62*w + 49],\ [4489, 67, -67],\ [4519, 4519, 19*w - 80],\ [4519, 4519, 42*w - 103],\ [4549, 4549, 62*w - 47],\ [4549, 4549, 15*w - 77],\ [4561, 4561, 21*w - 82],\ [4561, 4561, 40*w - 101],\ [4591, 4591, 73*w - 82],\ [4591, 4591, -73*w - 9],\ [4621, 4621, 36*w - 97],\ [4621, 4621, 25*w - 86],\ [4639, 4639, 27*w - 88],\ [4639, 4639, 34*w - 95],\ [4649, 4649, 29*w - 90],\ [4649, 4649, 32*w - 93],\ [4651, 4651, 30*w - 91],\ [4651, 4651, 31*w - 92],\ [4679, 4679, 11*w - 75],\ [4679, 4679, -64*w + 53],\ [4691, 4691, -69*w - 1],\ [4691, 4691, 69*w - 70],\ [4721, 4721, 63*w - 47],\ [4721, 4721, 16*w - 79],\ [4729, 4729, -74*w - 9],\ [4729, 4729, 74*w - 83],\ [4751, 4751, 63*w - 46],\ [4751, 4751, 17*w - 80],\ [4759, 4759, -64*w + 51],\ [4759, 4759, 13*w - 77],\ [4789, 4789, 35*w - 97],\ [4789, 4789, 27*w - 89],\ [4799, 4799, -72*w - 5],\ [4799, 4799, 72*w - 77],\ [4801, 4801, 33*w - 95],\ [4801, 4801, 29*w - 91],\ [4831, 4831, 15*w - 79],\ [4831, 4831, -64*w + 49],\ [4861, 4861, 12*w - 77],\ [4861, 4861, -65*w + 53],\ [4871, 4871, 22*w - 85],\ [4871, 4871, 41*w - 104],\ [4889, 4889, 40*w - 103],\ [4889, 4889, 23*w - 86],\ [4909, 4909, 74*w - 81],\ [4909, 4909, -74*w - 7],\ [4919, 4919, 25*w - 88],\ [4919, 4919, 38*w - 101],\ [4931, 4931, 37*w - 100],\ [4931, 4931, 26*w - 89],\ [4951, 4951, 64*w - 45],\ [4951, 4951, 19*w - 83],\ [4969, 4969, -71*w - 1],\ [4969, 4969, 71*w - 72],\ [4999, 4999, 21*w - 85],\ [4999, 4999, 43*w - 107],\ [5009, 5009, 16*w - 81],\ [5009, 5009, 65*w - 49],\ [5011, 5011, -76*w - 9],\ [5011, 5011, 76*w - 85],\ [5021, 5021, 73*w - 77],\ [5021, 5021, -73*w - 4],\ [5039, 5039, 23*w - 87],\ [5039, 5039, 41*w - 105],\ [5051, 5051, 75*w - 82],\ [5051, 5051, -75*w - 7],\ [5059, 5059, 77*w - 87],\ [5059, 5059, -77*w - 10],\ [5081, 5081, -74*w - 5],\ [5081, 5081, 74*w - 79],\ [5099, 5099, 65*w - 46],\ [5099, 5099, 19*w - 84],\ [5101, 5101, 73*w - 76],\ [5101, 5101, -73*w - 3],\ [5119, 5119, 33*w - 97],\ [5119, 5119, 31*w - 95],\ [5171, 5171, 43*w - 108],\ [5171, 5171, 22*w - 87],\ [5179, 5179, 73*w - 75],\ [5179, 5179, -73*w - 2],\ [5189, 5189, 17*w - 83],\ [5189, 5189, 66*w - 49],\ [5209, 5209, 41*w - 106],\ [5209, 5209, 24*w - 89],\ [5231, 5231, -67*w + 53],\ [5231, 5231, 14*w - 81],\ [5261, 5261, 37*w - 102],\ [5261, 5261, 28*w - 93],\ [5279, 5279, 34*w - 99],\ [5279, 5279, 31*w - 96],\ [5281, 5281, 32*w - 97],\ [5281, 5281, 33*w - 98],\ [5309, 5309, -75*w - 4],\ [5309, 5309, 75*w - 79],\ [5329, 73, -73],\ [5351, 5351, -79*w - 10],\ [5351, 5351, 79*w - 89],\ [5381, 5381, 25*w - 91],\ [5381, 5381, 41*w - 107],\ [5399, 5399, 80*w - 91],\ [5399, 5399, -80*w - 11],\ [5419, 5419, 15*w - 83],\ [5419, 5419, -68*w + 53],\ [5431, 5431, -77*w - 6],\ [5431, 5431, 77*w - 83],\ [5441, 5441, 31*w - 97],\ [5441, 5441, 35*w - 101],\ [5449, 5449, 79*w - 88],\ [5449, 5449, -79*w - 9],\ [5471, 5471, 75*w - 77],\ [5471, 5471, -75*w - 2],\ [5479, 5479, 22*w - 89],\ [5479, 5479, 45*w - 112],\ [5501, 5501, 23*w - 90],\ [5501, 5501, 44*w - 111],\ [5519, 5519, -77*w - 5],\ [5519, 5519, 77*w - 82],\ [5521, 5521, 43*w - 110],\ [5521, 5521, 24*w - 91],\ [5531, 5531, -69*w + 55],\ [5531, 5531, 14*w - 83],\ [5569, 5569, 40*w - 107],\ [5569, 5569, 27*w - 94],\ [5581, 5581, 39*w - 106],\ [5581, 5581, 28*w - 95],\ [5591, 5591, 29*w - 96],\ [5591, 5591, 38*w - 105],\ [5639, 5639, -79*w - 7],\ [5639, 5639, 79*w - 86],\ [5641, 5641, -70*w + 57],\ [5641, 5641, 13*w - 83],\ [5651, 5651, 81*w - 91],\ [5651, 5651, -81*w - 10],\ [5659, 5659, 45*w - 113],\ [5659, 5659, 23*w - 91],\ [5669, 5669, 78*w - 83],\ [5669, 5669, -78*w - 5],\ [5689, 5689, -77*w - 3],\ [5689, 5689, 77*w - 80],\ [5701, 5701, -82*w - 11],\ [5701, 5701, 82*w - 93],\ [5711, 5711, 19*w - 88],\ [5711, 5711, 69*w - 50],\ [5741, 5741, 20*w - 89],\ [5741, 5741, 69*w - 49],\ [5749, 5749, -71*w + 59],\ [5749, 5749, 12*w - 83],\ [5779, 5779, 35*w - 103],\ [5779, 5779, 33*w - 101],\ [5791, 5791, -80*w - 7],\ [5791, 5791, 80*w - 87],\ [5801, 5801, 70*w - 53],\ [5801, 5801, 17*w - 87],\ [5821, 5821, -79*w - 5],\ [5821, 5821, 79*w - 84],\ [5839, 5839, 14*w - 85],\ [5839, 5839, -71*w + 57],\ [5849, 5849, 81*w - 89],\ [5849, 5849, -81*w - 8],\ [5851, 5851, -77*w - 1],\ [5851, 5851, 77*w - 78],\ [5861, 5861, 25*w - 94],\ [5861, 5861, 44*w - 113],\ [5869, 5869, 19*w - 89],\ [5869, 5869, 70*w - 51],\ [5879, 5879, 43*w - 112],\ [5879, 5879, 26*w - 95],\ [5881, 5881, -71*w + 56],\ [5881, 5881, 15*w - 86],\ [5939, 5939, 31*w - 100],\ [5939, 5939, 38*w - 107],\ [5981, 5981, 23*w - 93],\ [5981, 5981, 47*w - 117],\ [6011, 6011, -84*w - 11],\ [6011, 6011, 84*w - 95],\ [6029, 6029, 71*w - 52],\ [6029, 6029, 19*w - 90],\ [6079, 6079, 79*w - 81],\ [6079, 6079, -79*w - 2],\ [6089, 6089, 41*w - 111],\ [6089, 6089, 29*w - 99],\ [6091, 6091, 21*w - 92],\ [6091, 6091, 71*w - 50],\ [6101, 6101, 82*w - 89],\ [6101, 6101, -82*w - 7],\ [6121, 6121, 37*w - 107],\ [6121, 6121, 33*w - 103],\ [6131, 6131, 81*w - 86],\ [6131, 6131, -81*w - 5],\ [6151, 6151, -80*w - 3],\ [6151, 6151, 80*w - 83],\ [6199, 6199, 15*w - 88],\ [6199, 6199, -73*w + 58],\ [6211, 6211, 26*w - 97],\ [6211, 6211, 45*w - 116],\ [6221, 6221, 81*w - 85],\ [6221, 6221, -81*w - 4],\ [6229, 6229, 27*w - 98],\ [6229, 6229, 44*w - 115],\ [6269, 6269, 13*w - 87],\ [6269, 6269, -74*w + 61],\ [6271, 6271, 30*w - 101],\ [6271, 6271, 41*w - 112],\ [6299, 6299, 37*w - 108],\ [6299, 6299, 34*w - 105],\ [6301, 6301, 35*w - 106],\ [6301, 6301, 36*w - 107],\ [6311, 6311, 23*w - 95],\ [6311, 6311, 49*w - 121],\ [6329, 6329, 86*w - 97],\ [6329, 6329, -86*w - 11],\ [6359, 6359, 25*w - 97],\ [6359, 6359, 47*w - 119],\ [6361, 6361, -74*w + 59],\ [6361, 6361, 15*w - 89],\ [6379, 6379, -85*w - 9],\ [6379, 6379, 85*w - 94],\ [6389, 6389, 73*w - 53],\ [6389, 6389, 20*w - 93],\ [6421, 6421, 73*w - 52],\ [6421, 6421, 21*w - 94],\ [6449, 6449, 83*w - 88],\ [6449, 6449, -83*w - 5],\ [6451, 6451, 73*w - 51],\ [6451, 6451, 22*w - 95],\ [6469, 6469, 82*w - 85],\ [6469, 6469, -82*w - 3],\ [6481, 6481, -85*w - 8],\ [6481, 6481, 85*w - 93],\ [6491, 6491, -87*w - 11],\ [6491, 6491, 87*w - 98],\ [6521, 6521, 19*w - 93],\ [6521, 6521, 74*w - 55],\ [6529, 6529, 25*w - 98],\ [6529, 6529, 48*w - 121],\ [6551, 6551, 26*w - 99],\ [6551, 6551, 47*w - 120],\ [6569, 6569, 16*w - 91],\ [6569, 6569, -75*w + 59],\ [6571, 6571, 27*w - 100],\ [6571, 6571, 46*w - 119],\ [6581, 6581, 85*w - 92],\ [6581, 6581, -85*w - 7],\ [6599, 6599, 87*w - 97],\ [6599, 6599, -87*w - 10],\ [6619, 6619, 30*w - 103],\ [6619, 6619, 43*w - 116],\ [6659, 6659, 35*w - 108],\ [6659, 6659, 38*w - 111],\ [6661, 6661, 36*w - 109],\ [6661, 6661, 37*w - 110],\ [6679, 6679, 85*w - 91],\ [6679, 6679, -85*w - 6],\ [6689, 6689, 75*w - 56],\ [6689, 6689, 19*w - 94],\ [6691, 6691, 15*w - 91],\ [6691, 6691, -76*w + 61],\ [6701, 6701, 49*w - 123],\ [6701, 6701, 25*w - 99],\ [6709, 6709, 89*w - 101],\ [6709, 6709, -89*w - 12],\ [6719, 6719, 83*w - 85],\ [6719, 6719, -83*w - 2],\ [6761, 6761, -77*w + 64],\ [6761, 6761, 13*w - 90],\ [6779, 6779, -76*w + 59],\ [6779, 6779, 17*w - 93],\ [6781, 6781, 45*w - 119],\ [6781, 6781, 29*w - 103],\ [6791, 6791, 22*w - 97],\ [6791, 6791, 75*w - 53],\ [6829, 6829, 41*w - 115],\ [6829, 6829, 33*w - 107],\ [6841, 6841, 35*w - 109],\ [6841, 6841, 39*w - 113],\ [6869, 6869, 85*w - 89],\ [6869, 6869, -85*w - 4],\ [6871, 6871, 88*w - 97],\ [6871, 6871, -88*w - 9],\ [6889, 83, -83],\ [6899, 6899, 49*w - 124],\ [6899, 6899, 26*w - 101],\ [6911, 6911, -87*w - 7],\ [6911, 6911, 87*w - 94],\ [6949, 6949, 17*w - 94],\ [6949, 6949, -77*w + 60],\ [6959, 6959, 29*w - 104],\ [6959, 6959, 46*w - 121],\ [6961, 6961, 85*w - 88],\ [6961, 6961, -85*w - 3],\ [6971, 6971, -84*w - 1],\ [6971, 6971, 84*w - 85],\ [6991, 6991, -77*w + 59],\ [6991, 6991, 18*w - 95],\ [7001, 7001, 32*w - 107],\ [7001, 7001, 43*w - 118],\ [7019, 7019, 34*w - 109],\ [7019, 7019, 41*w - 116],\ [7039, 7039, -89*w - 9],\ [7039, 7039, 89*w - 98],\ [7069, 7069, 77*w - 57],\ [7069, 7069, 20*w - 97],\ [7079, 7079, 88*w - 95],\ [7079, 7079, -88*w - 7],\ [7109, 7109, -87*w - 5],\ [7109, 7109, 87*w - 92],\ [7121, 7121, -78*w + 61],\ [7121, 7121, 17*w - 95],\ [7129, 7129, -86*w - 3],\ [7129, 7129, 86*w - 89],\ [7151, 7151, -79*w + 65],\ [7151, 7151, 14*w - 93],\ [7159, 7159, 91*w - 102],\ [7159, 7159, -91*w - 11],\ [7211, 7211, 35*w - 111],\ [7211, 7211, 41*w - 117],\ [7219, 7219, 39*w - 115],\ [7219, 7219, 37*w - 113],\ [7229, 7229, 52*w - 129],\ [7229, 7229, 25*w - 102],\ [7309, 7309, -86*w - 1],\ [7309, 7309, 86*w - 87],\ [7321, 7321, 48*w - 125],\ [7321, 7321, 29*w - 106],\ [7331, 7331, 92*w - 103],\ [7331, 7331, -92*w - 11],\ [7349, 7349, 78*w - 55],\ [7349, 7349, 23*w - 101],\ [7351, 7351, -89*w - 6],\ [7351, 7351, 89*w - 95],\ [7369, 7369, 32*w - 109],\ [7369, 7369, 45*w - 122],\ [7411, 7411, 38*w - 115],\ [7411, 7411, 39*w - 116],\ [7451, 7451, -89*w - 5],\ [7451, 7451, 89*w - 94],\ [7459, 7459, 21*w - 100],\ [7459, 7459, 79*w - 58],\ [7481, 7481, -87*w - 1],\ [7481, 7481, 87*w - 88],\ [7489, 7489, 91*w - 99],\ [7489, 7489, -91*w - 8],\ [7499, 7499, -81*w + 67],\ [7499, 7499, 14*w - 95],\ [7529, 7529, 23*w - 102],\ [7529, 7529, 79*w - 56],\ [7541, 7541, 31*w - 109],\ [7541, 7541, 47*w - 125],\ [7549, 7549, 89*w - 93],\ [7549, 7549, -89*w - 4],\ [7559, 7559, 19*w - 99],\ [7559, 7559, 80*w - 61],\ [7561, 7561, 24*w - 103],\ [7561, 7561, 79*w - 55],\ [7589, 7589, 43*w - 121],\ [7589, 7589, 35*w - 113],\ [7591, 7591, 54*w - 133],\ [7591, 7591, 25*w - 104],\ [7621, 7621, -95*w - 13],\ [7621, 7621, 95*w - 108],\ [7639, 7639, 21*w - 101],\ [7639, 7639, 80*w - 59],\ [7649, 7649, 17*w - 98],\ [7649, 7649, -81*w + 64],\ [7669, 7669, 28*w - 107],\ [7669, 7669, 51*w - 130],\ [7681, 7681, 94*w - 105],\ [7681, 7681, -94*w - 11],\ [7691, 7691, 50*w - 129],\ [7691, 7691, 29*w - 108],\ [7699, 7699, 91*w - 97],\ [7699, 7699, -91*w - 6],\ [7741, 7741, -95*w - 12],\ [7741, 7741, 95*w - 107],\ [7759, 7759, 46*w - 125],\ [7759, 7759, 33*w - 112],\ [7789, 7789, 43*w - 122],\ [7789, 7789, 36*w - 115],\ [7829, 7829, -82*w + 65],\ [7829, 7829, 17*w - 99],\ [7841, 7841, -93*w - 8],\ [7841, 7841, 93*w - 101],\ [7879, 7879, 29*w - 109],\ [7879, 7879, 51*w - 131],\ [7901, 7901, -91*w - 4],\ [7901, 7901, 91*w - 95],\ [7919, 7919, 49*w - 129],\ [7919, 7919, 31*w - 111],\ [7949, 7949, -93*w - 7],\ [7949, 7949, 93*w - 100],\ [7951, 7951, 47*w - 127],\ [7951, 7951, 33*w - 113],\ [8009, 8009, -90*w - 1],\ [8009, 8009, 90*w - 91],\ [8011, 8011, 17*w - 100],\ [8011, 8011, -83*w + 66],\ [8039, 8039, -96*w - 11],\ [8039, 8039, 96*w - 107],\ [8059, 8059, 18*w - 101],\ [8059, 8059, -83*w + 65],\ [8069, 8069, 52*w - 133],\ [8069, 8069, 29*w - 110],\ [8081, 8081, 82*w - 59],\ [8081, 8081, 23*w - 105],\ [8089, 8089, 95*w - 104],\ [8089, 8089, -95*w - 9],\ [8101, 8101, 97*w - 109],\ [8101, 8101, -97*w - 12],\ [8111, 8111, 50*w - 131],\ [8111, 8111, 31*w - 112],\ [8161, 8161, 98*w - 111],\ [8161, 8161, -98*w - 13],\ [8171, 8171, 35*w - 116],\ [8171, 8171, 46*w - 127],\ [8179, 8179, -92*w - 3],\ [8179, 8179, 92*w - 95],\ [8191, 8191, 83*w - 62],\ [8191, 8191, 21*w - 104],\ [8209, 8209, 27*w - 109],\ [8209, 8209, 55*w - 137],\ [8219, 8219, 14*w - 99],\ [8219, 8219, -85*w + 71],\ [8221, 8221, 97*w - 108],\ [8221, 8221, -97*w - 11],\ [8231, 8231, 83*w - 61],\ [8231, 8231, 22*w - 105],\ [8269, 8269, 23*w - 106],\ [8269, 8269, 83*w - 60],\ [8291, 8291, -84*w + 65],\ [8291, 8291, 19*w - 103],\ [8311, 8311, 95*w - 102],\ [8311, 8311, -95*w - 7],\ [8329, 8329, -85*w + 69],\ [8329, 8329, 16*w - 101],\ [8369, 8369, 35*w - 117],\ [8369, 8369, 47*w - 129],\ [8389, 8389, 37*w - 119],\ [8389, 8389, 45*w - 127],\ [8419, 8419, -95*w - 6],\ [8419, 8419, 95*w - 101],\ [8429, 8429, 55*w - 138],\ [8429, 8429, 28*w - 111],\ [8431, 8431, 18*w - 103],\ [8431, 8431, -85*w + 67],\ [8461, 8461, -86*w + 71],\ [8461, 8461, 15*w - 101],\ [8501, 8501, 31*w - 114],\ [8501, 8501, 52*w - 135],\ [8521, 8521, 51*w - 134],\ [8521, 8521, 32*w - 115],\ [8539, 8539, 33*w - 116],\ [8539, 8539, 50*w - 133],\ [8581, 8581, 47*w - 130],\ [8581, 8581, 36*w - 119],\ [8599, 8599, 38*w - 121],\ [8599, 8599, 45*w - 128],\ [8609, 8609, 43*w - 126],\ [8609, 8609, 40*w - 123],\ [8629, 8629, -95*w - 4],\ [8629, 8629, 95*w - 99],\ [8641, 8641, -98*w - 9],\ [8641, 8641, 98*w - 107],\ [8669, 8669, 19*w - 105],\ [8669, 8669, -86*w + 67],\ [8681, 8681, -97*w - 7],\ [8681, 8681, 97*w - 104],\ [8689, 8689, 85*w - 61],\ [8689, 8689, 24*w - 109],\ [8699, 8699, 53*w - 137],\ [8699, 8699, 31*w - 115],\ [8719, 8719, 101*w - 114],\ [8719, 8719, -101*w - 13],\ [8731, 8731, -95*w - 3],\ [8731, 8731, 95*w - 98],\ [8741, 8741, -94*w - 1],\ [8741, 8741, 94*w - 95],\ [8761, 8761, 86*w - 65],\ [8761, 8761, 21*w - 107],\ [8779, 8779, 100*w - 111],\ [8779, 8779, -100*w - 11],\ [8819, 8819, 43*w - 127],\ [8819, 8819, 41*w - 125],\ [8821, 8821, 28*w - 113],\ [8821, 8821, 57*w - 142],\ [8831, 8831, 95*w - 97],\ [8831, 8831, -95*w - 2],\ [8839, 8839, 15*w - 103],\ [8839, 8839, -88*w + 73],\ [8849, 8849, 29*w - 114],\ [8849, 8849, 56*w - 141],\ [8861, 8861, 19*w - 106],\ [8861, 8861, -87*w + 68],\ [8929, 8929, -95*w - 1],\ [8929, 8929, 95*w - 96],\ [8941, 8941, 33*w - 118],\ [8941, 8941, 52*w - 137],\ [8951, 8951, 17*w - 105],\ [8951, 8951, -88*w + 71],\ [8969, 8969, -101*w - 11],\ [8969, 8969, 101*w - 112],\ [8971, 8971, 103*w - 117],\ [8971, 8971, -103*w - 14],\ [8999, 8999, 87*w - 65],\ [8999, 8999, 22*w - 109],\ [9001, 9001, 48*w - 133],\ [9001, 9001, 37*w - 122],\ [9011, 9011, 38*w - 123],\ [9011, 9011, 47*w - 132],\ [9029, 9029, 41*w - 126],\ [9029, 9029, 44*w - 129],\ [9041, 9041, 23*w - 110],\ [9041, 9041, 87*w - 64],\ [9049, 9049, 57*w - 143],\ [9049, 9049, 29*w - 115],\ [9059, 9059, 99*w - 106],\ [9059, 9059, -99*w - 7],\ [9091, 9091, 101*w - 111],\ [9091, 9091, -101*w - 10],\ [9109, 9109, 97*w - 100],\ [9109, 9109, -97*w - 3],\ [9151, 9151, 88*w - 67],\ [9151, 9151, 21*w - 109],\ [9161, 9161, 102*w - 113],\ [9161, 9161, -102*w - 11],\ [9181, 9181, 35*w - 121],\ [9181, 9181, 51*w - 137],\ [9199, 9199, -89*w + 71],\ [9199, 9199, 18*w - 107],\ [9209, 9209, 49*w - 135],\ [9209, 9209, 37*w - 123],\ [9221, 9221, 59*w - 146],\ [9221, 9221, 28*w - 115],\ [9239, 9239, 88*w - 65],\ [9239, 9239, 23*w - 111],\ [9241, 9241, 45*w - 131],\ [9241, 9241, 41*w - 127],\ [9281, 9281, -99*w - 5],\ [9281, 9281, 99*w - 104],\ [9311, 9311, -97*w - 1],\ [9311, 9311, 97*w - 98],\ [9319, 9319, 25*w - 113],\ [9319, 9319, 88*w - 63],\ [9341, 9341, 17*w - 107],\ [9341, 9341, -90*w + 73],\ [9349, 9349, -89*w + 68],\ [9349, 9349, 21*w - 110],\ [9371, 9371, 34*w - 121],\ [9371, 9371, 53*w - 140],\ [9391, 9391, 27*w - 115],\ [9391, 9391, 88*w - 61],\ [9409, 97, -97],\ [9419, 9419, 50*w - 137],\ [9419, 9419, 37*w - 124],\ [9421, 9421, 106*w - 121],\ [9421, 9421, -106*w - 15],\ [9431, 9431, 38*w - 125],\ [9431, 9431, 49*w - 136],\ [9439, 9439, 89*w - 66],\ [9439, 9439, 23*w - 112],\ [9461, 9461, 43*w - 130],\ [9461, 9461, 44*w - 131],\ [9479, 9479, -103*w - 10],\ [9479, 9479, 103*w - 113],\ [9491, 9491, 105*w - 118],\ [9491, 9491, -105*w - 13],\ [9511, 9511, 31*w - 119],\ [9511, 9511, 57*w - 145],\ [9521, 9521, 25*w - 114],\ [9521, 9521, 89*w - 64],\ [9539, 9539, 17*w - 108],\ [9539, 9539, -91*w + 74],\ [9551, 9551, -104*w - 11],\ [9551, 9551, 104*w - 115],\ [9601, 9601, -103*w - 9],\ [9601, 9601, 103*w - 112],\ [9619, 9619, -107*w - 15],\ [9619, 9619, 107*w - 122],\ [9629, 9629, 61*w - 150],\ [9629, 9629, 28*w - 117],\ [9631, 9631, 37*w - 125],\ [9631, 9631, 51*w - 139],\ [9649, 9649, -91*w + 72],\ [9649, 9649, 19*w - 110],\ [9661, 9661, 60*w - 149],\ [9661, 9661, 29*w - 118],\ [9679, 9679, 45*w - 133],\ [9679, 9679, 43*w - 131],\ [9689, 9689, -106*w - 13],\ [9689, 9689, 106*w - 119],\ [9719, 9719, 58*w - 147],\ [9719, 9719, 31*w - 120],\ [9721, 9721, -103*w - 8],\ [9721, 9721, 103*w - 111],\ [9739, 9739, 17*w - 109],\ [9739, 9739, -92*w + 75],\ [9749, 9749, 105*w - 116],\ [9749, 9749, -105*w - 11],\ [9769, 9769, 56*w - 145],\ [9769, 9769, 33*w - 122],\ [9781, 9781, 101*w - 105],\ [9781, 9781, -101*w - 4],\ [9791, 9791, 34*w - 123],\ [9791, 9791, 55*w - 144],\ [9811, 9811, 54*w - 143],\ [9811, 9811, 35*w - 124],\ [9829, 9829, 36*w - 125],\ [9829, 9829, 53*w - 142],\ [9839, 9839, 103*w - 110],\ [9839, 9839, -103*w - 7],\ [9851, 9851, 19*w - 111],\ [9851, 9851, -92*w + 73],\ [9859, 9859, 38*w - 127],\ [9859, 9859, 51*w - 140],\ [9871, 9871, 50*w - 139],\ [9871, 9871, 39*w - 128],\ [9901, 9901, 44*w - 133],\ [9901, 9901, 45*w - 134],\ [9929, 9929, 31*w - 121],\ [9929, 9929, 59*w - 149],\ [9931, 9931, 25*w - 116],\ [9931, 9931, 91*w - 66],\ [9941, 9941, -93*w + 76],\ [9941, 9941, 17*w - 110],\ [9949, 9949, -106*w - 11],\ [9949, 9949, 106*w - 117]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, -1, 6, -4, 4, -4, 4, -2, -2, -8, 8, 6, 6, -2, 4, -4, 2, 2, 0, 0, 0, 0, -6, -6, 6, 6, -14, -14, -12, 12, -12, 12, 10, 10, -16, 16, -22, -20, 20, -10, -10, 8, -8, -8, 8, -4, 4, -26, -26, 0, 0, -2, -2, 12, -12, -14, -14, -24, 24, -10, -10, -30, 32, -32, -12, 12, 30, 30, -24, 24, 20, -20, -6, -6, 18, 18, -10, -10, -36, 36, -6, -6, 40, -40, 8, -8, -18, -18, -18, -18, 16, -16, 36, -36, 28, -28, -2, -2, 10, 10, 30, -2, -2, 22, 22, -4, 4, 24, -24, -10, -10, -4, 4, 16, -16, -18, -18, -12, 12, 42, 42, -44, 44, 34, 34, 38, 38, -32, 32, 36, -36, 24, -24, -6, -6, 34, 34, 42, 42, 28, -28, -22, -22, 2, 2, 40, -40, 4, -4, 30, 30, 40, -40, 8, -8, 14, 14, 46, 46, -20, 20, 40, -40, -46, -46, -44, 44, -2, -2, 16, -16, -16, 16, -6, -6, 4, -4, 38, 38, -46, -46, 12, -12, -10, -10, -26, -26, -8, 8, 52, -52, 34, 34, 30, 30, -18, -18, -8, 8, -30, -30, -12, 12, 64, -64, 42, 42, -20, 20, 10, 10, 8, -8, 6, 6, -46, -46, -38, -38, -38, -56, 56, 34, 34, -22, -22, -64, 64, 20, -20, -36, 36, -8, 8, -58, -58, 30, 30, 20, -20, 48, -48, 52, -52, -50, -50, -56, 56, 4, -4, -20, 20, -62, -62, 70, 70, -36, 36, -10, -10, 6, 6, -44, 44, 46, 46, -6, -6, 14, 14, 32, -32, -34, -34, 70, 70, -36, 36, 48, -48, 22, 70, 70, 40, -40, 24, -24, 78, 78, 50, 50, -36, 36, 66, 66, 56, -56, 20, -20, 32, -32, -12, 12, -50, -50, 24, -24, -42, -42, -30, -30, 10, 10, 4, -4, 24, -24, -34, -34, -44, 44, -30, -30, -66, -66, -44, 44, 78, -14, -14, 80, -80, -4, 4, -62, -62, 38, 38, 26, 26, -64, 64, 44, -44, 26, 26, 24, -24, -20, 20, 50, 50, 86, 86, -48, 48, 52, -52, 10, 10, -36, 36, 22, 22, 12, -12, 4, -4, 42, 42, 48, -48, 60, -60, -40, 40, -66, -66, 62, 62, 84, -84, -88, 88, -82, -82, 84, -84, -80, 80, -16, 16, 42, 42, -68, 68, -54, -54, -30, -30, 90, 90, -96, 96, -78, -78, -70, 36, -36, 20, -20, 78, 78, 64, -64, -30, -30, -28, 28, 54, 54, 28, -28, -56, 56, 58, 58, 84, -84, -20, 20, 14, 14, 10, 10, 74, 74, 40, -40, 18, 18, -6, -6, 64, -64, 50, 50, 2, 2, 82, 82, 96, -96, 70, 70, -54, -54, -30, -30, 12, -12, 44, -44, 16, -16, 36, -36, -26, -26, 8, -8, 34, 34, -68, 68, -48, 48, -82, -82, 60, -60, -66, -66, 8, -8, -42, -42, -58, -58, 46, 46, -36, 36, -28, 28, 16, -16, -86, -86, 60, -60, -54, -54, 88, -88, -76, 76, 30, 30, -56, 56, 84, -84, -96, 96, 12, -12, -86, -86, 2, 2, 40, -40, -12, 12, -34, -34, 22, 22, -68, 68, -114, -114, -12, 12, 42, 42, 62, 62, 0, 0, 0, 0, -102, -102, -44, 44, 118, 118, -30, -30, -20, 20, -42, -42, -110, -110, -116, 116, 48, -48, -36, 36, -52, 52, 8, -8, 14, 14, -100, 100, 48, -48, 106, 106, -20, 20, -20, 20, -58, -58, 64, -64, -34, -34, 84, -84, 26, 26, 120, -120, 2, 2, 116, -116, 98, 98, -96, 96, -42, -42, 90, 90, -38, -38, 20, -20, -50, -50, 70, -24, 24, 102, 102, -110, -110, -56, 56, 46, 46, 32, -32, 106, 106, -44, 44, 8, -8, 20, -20, -34, -34, 58, 58, 56, -56, -40, 40, 54, 54, -16, 16, 14, 14, 72, -72, 62, 62, 80, -80, -10, -10, -78, -78, 8, -8, -68, 68, 16, -16, -90, -90, -56, 56, 50, 50, -60, 60, 30, 30, -128, 128, -132, 132, 124, -124, 26, 26, 12, -12, 46, 46, 64, -64, -108, 108, -76, 76, -6, -6, -70, -70, -24, 24, -18, -18, -96, 96, 34, 34, 2, 2, -110, 16, -16, -6, -6, -24, 24, 20, -20, 32, -32, 66, 66, -122, -122, 24, -24, -56, 56, 2, 2, 80, -80, -98, -98, 60, -60, -82, -82, 82, 82, 0, 0, 56, -56, 102, 102, -44, 44, 44, -44, -26, -26, 90, 90, 58, 58, -56, 56, -18, -18, 74, 74, -100, 100, 72, -72, 70, 70, 34, 34, -80, 80, 90, 90, 124, -124, -90, -90, 46, 46, 56, -56, -106, -106, -4, 4, 62, 62, -28, 28, 18, 18, 0, 0, 6, 6, -60, 60, -86, -86, 38, 38, -36, 36, 48, -48, 104, -104, 52, -52, -18, -18, -54, -54, 34, 34, -120, 120, -4, 4, 130, 130, -80, 80, -42, -42, -56, 56, 26, 26, -12, 12, 150, 150, 54, 54, -66, -66, 36, -36, 58, 58, 18, 18, 52, -52, 58, 58, -126, -126, -64, 64, 38, 38, -68, 68, 150, 150, 56, -56, -100, 100, 12, -12, -26, -26, 56, -56, 14, 14, 100, -100, -46, -46, -74, -74, -96, 96, -22, -22, -108, 108, 2, 2, -48, 48, 50, 50, -134, -134, -74, -74, -160, 160, -90, -60, 60, -120, 120, 38, 38, 0, 0, 50, 50, -116, 116, -40, 40, 22, 22, -140, 140, 16, -16, -2, -2, 104, -104, 90, 90, -2, -2, 54, 54, -120, 120, 40, -40, 12, -12, 44, -44, 30, 30, -82, -82, 26, 26, 36, -36, 54, 54, 96, -96, -118, -118, 124, -124, -52, 52, 100, -100, -42, -42, 110, 110, -108, 108, 38, 38, -138, -138, 126, 126, -24, 24, -26, -26, 6, 6, 128, -128, -6, -6, 136, -136, -126, -126, 42, 42, 110, 110, 76, -76, -124, 124, -126, -126, 64, -64, -14, -14, 74, 74, 162, 162, -88, 88, 66, 66, 64, -64, 46, 46, -152, 152, 74, 74, 84, -84, 152, -152, -124, 124, -90, -90, 18, 18, 54, 54, -58, -58, -136, 136, -158, -158, 140, -140, 4, -4, -88, 88, 146, 146, -36, 36, 30, 30, 64, -64, -142, -142, -180, 180, 176, -176, 10, 10, 50, 50, -134, -134, -84, 84, -142, -142, -40, 40, -18, -18, 10, 10, -90, -90, 44, -44, -102, -102, 40, -40, 78, 78, -54, -54, 130, 130, -66, -66, -22, -22, 82, 82, 76, -76, 16, -16, -92, 92, -58, -58, 22, 22, -76, 76, 124, -124, -10, -10, 168, -168, -56, 56, -78, -78, 2, 2, -50, -50, 174, 174, 160, -160, -150, -150, 164, -164, -120, 120, 106, 106, -52, 52, -58, -58, -98, -98, -74, -74, -36, 36, 84, -84, 22, 22, 24, -24, 102, 102, 30, 30, -160, 160, 150, 150, -102, -102, -40, 40, 118, 118, 78, 78, -168, 168, 136, -136, -126, -126, -26, -26, -164, 164, 8, -8, 2, 36, -36, 178, 178, -48, 48, -64, 64, -150, -150, 24, -24, -132, 132, -48, 48, -142, -142, -12, 12, 56, -56, -50, -50, -60, 60, 30, 30, 56, -56, -130, -130, -130, -130, 0, 0, 90, 90, 72, -72, 22, 22, -20, 20, -106, -106, 74, 74, -106, -106, -24, 24, -20, 20, 70, 70, -48, 48, -116, 116, -156, 156, -56, 56, 78, 78, 74, 74, -124, 124, -170, -170, -62, -62] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([4, 2, 2])] = 1 AL_eigenvalues[ZF.ideal([5, 5, -2*w + 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]