/* 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([44, 2, -15, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([11,11,w + 3]) primes_array = [ [4, 2, w + 2],\ [4, 2, -1/2*w^3 + 3/2*w^2 + 9/2*w - 10],\ [9, 3, 1/2*w^3 - 5/2*w^2 - 5/2*w + 17],\ [9, 3, 3/2*w^3 - 11/2*w^2 - 19/2*w + 28],\ [11, 11, 1/2*w^3 - 3/2*w^2 - 9/2*w + 11],\ [11, 11, -w - 3],\ [25, 5, w^3 - 3*w^2 - 7*w + 15],\ [29, 29, w + 1],\ [29, 29, 1/2*w^3 - 3/2*w^2 - 9/2*w + 9],\ [31, 31, -1/2*w^3 + 5/2*w^2 + 5/2*w - 16],\ [31, 31, 1/2*w^3 - 3/2*w^2 - 9/2*w + 5],\ [31, 31, -w + 3],\ [31, 31, 3/2*w^3 - 11/2*w^2 - 19/2*w + 29],\ [59, 59, 2*w^2 - w - 13],\ [59, 59, 9/2*w^3 - 31/2*w^2 - 61/2*w + 85],\ [61, 61, 2*w^3 - 6*w^2 - 15*w + 31],\ [61, 61, -3/2*w^3 + 11/2*w^2 + 21/2*w - 34],\ [71, 71, 3/2*w^3 - 11/2*w^2 - 19/2*w + 32],\ [71, 71, -1/2*w^3 + 5/2*w^2 + 5/2*w - 13],\ [79, 79, -3*w^3 + 10*w^2 + 19*w - 51],\ [79, 79, 15/2*w^3 - 51/2*w^2 - 103/2*w + 139],\ [101, 101, -2*w^3 + 7*w^2 + 14*w - 37],\ [101, 101, -1/2*w^3 + 5/2*w^2 + 7/2*w - 16],\ [109, 109, w^3 - 3*w^2 - 6*w + 19],\ [109, 109, -w^3 + 4*w^2 + 5*w - 19],\ [121, 11, -3/2*w^3 + 9/2*w^2 + 21/2*w - 23],\ [139, 139, -w^3 + 4*w^2 + 7*w - 25],\ [139, 139, -5/2*w^3 + 17/2*w^2 + 33/2*w - 41],\ [149, 149, 1/2*w^3 + 1/2*w^2 - 11/2*w - 8],\ [149, 149, 5/2*w^3 - 19/2*w^2 - 35/2*w + 50],\ [149, 149, -9/2*w^3 + 31/2*w^2 + 59/2*w - 82],\ [149, 149, -5/2*w^3 + 19/2*w^2 + 35/2*w - 56],\ [151, 151, -1/2*w^3 + 3/2*w^2 + 3/2*w - 12],\ [151, 151, 3/2*w^3 - 9/2*w^2 - 25/2*w + 28],\ [179, 179, -1/2*w^3 + 3/2*w^2 + 9/2*w - 3],\ [179, 179, w - 5],\ [229, 229, -15/2*w^3 + 51/2*w^2 + 105/2*w - 142],\ [229, 229, 1/2*w^3 - 7/2*w^2 - 7/2*w + 19],\ [229, 229, -17/2*w^3 + 57/2*w^2 + 119/2*w - 156],\ [229, 229, -9/2*w^3 + 33/2*w^2 + 55/2*w - 82],\ [239, 239, -9*w^3 + 31*w^2 + 59*w - 161],\ [239, 239, w^3 + w^2 - 11*w - 19],\ [241, 241, 5/2*w^3 - 15/2*w^2 - 37/2*w + 37],\ [241, 241, -2*w^3 + 6*w^2 + 13*w - 29],\ [251, 251, -7/2*w^3 + 25/2*w^2 + 45/2*w - 67],\ [251, 251, 1/2*w^3 - 5/2*w^2 - 13/2*w + 7],\ [251, 251, -1/2*w^3 + 1/2*w^2 + 13/2*w + 4],\ [251, 251, -1/2*w^3 + 7/2*w^2 + 3/2*w - 23],\ [271, 271, -w^3 + 4*w^2 + 5*w - 25],\ [271, 271, -5/2*w^3 + 17/2*w^2 + 33/2*w - 47],\ [281, 281, 5/2*w^3 - 15/2*w^2 - 39/2*w + 41],\ [281, 281, 3/2*w^3 - 7/2*w^2 - 27/2*w + 14],\ [289, 17, -7/2*w^3 + 25/2*w^2 + 45/2*w - 62],\ [289, 17, 5/2*w^3 - 15/2*w^2 - 39/2*w + 37],\ [311, 311, -19/2*w^3 + 65/2*w^2 + 129/2*w - 175],\ [311, 311, -7/2*w^3 + 25/2*w^2 + 47/2*w - 71],\ [311, 311, 7/2*w^3 - 25/2*w^2 - 49/2*w + 67],\ [311, 311, -3/2*w^3 + 11/2*w^2 + 15/2*w - 31],\ [331, 331, 19/2*w^3 - 65/2*w^2 - 127/2*w + 173],\ [331, 331, -w^3 - w^2 + 10*w + 15],\ [349, 349, -5/2*w^3 + 15/2*w^2 + 33/2*w - 35],\ [349, 349, 3/2*w^3 - 11/2*w^2 - 21/2*w + 36],\ [361, 19, 2*w^3 - 6*w^2 - 14*w + 29],\ [361, 19, 2*w^3 - 6*w^2 - 14*w + 31],\ [379, 379, 1/2*w^3 - 5/2*w^2 - 1/2*w + 20],\ [379, 379, -1/2*w^3 + 5/2*w^2 + 1/2*w - 9],\ [401, 401, -7/2*w^3 + 25/2*w^2 + 45/2*w - 69],\ [401, 401, w^3 - 3*w^2 - 5*w + 19],\ [409, 409, 3/2*w^3 - 7/2*w^2 - 23/2*w + 13],\ [409, 409, -11/2*w^3 + 37/2*w^2 + 77/2*w - 100],\ [409, 409, 7/2*w^3 - 23/2*w^2 - 47/2*w + 58],\ [409, 409, -w^3 + 3*w^2 + 9*w - 9],\ [419, 419, 3/2*w^3 - 13/2*w^2 - 17/2*w + 36],\ [419, 419, -5/2*w^3 + 19/2*w^2 + 31/2*w - 54],\ [421, 421, -w^3 + 4*w^2 + 5*w - 27],\ [421, 421, 7/2*w^3 - 23/2*w^2 - 47/2*w + 63],\ [439, 439, 2*w^3 - 7*w^2 - 14*w + 35],\ [439, 439, -1/2*w^3 + 5/2*w^2 + 7/2*w - 18],\ [461, 461, -5/2*w^3 + 17/2*w^2 + 33/2*w - 48],\ [461, 461, -13/2*w^3 + 45/2*w^2 + 85/2*w - 119],\ [461, 461, -1/2*w^3 + 3/2*w^2 + 1/2*w - 15],\ [461, 461, 3/2*w^3 - 11/2*w^2 - 17/2*w + 32],\ [479, 479, -3*w^3 + 10*w^2 + 19*w - 53],\ [479, 479, 5/2*w^3 - 17/2*w^2 - 33/2*w + 51],\ [491, 491, 3*w^2 - 2*w - 23],\ [491, 491, 13/2*w^3 - 45/2*w^2 - 87/2*w + 120],\ [499, 499, -3*w^3 + 11*w^2 + 21*w - 63],\ [499, 499, -5/2*w^3 + 19/2*w^2 + 31/2*w - 50],\ [499, 499, 11/2*w^3 - 37/2*w^2 - 75/2*w + 101],\ [499, 499, 9*w^3 - 31*w^2 - 58*w + 159],\ [509, 509, 3/2*w^3 - 9/2*w^2 - 23/2*w + 29],\ [509, 509, w^3 - 3*w^2 - 6*w + 21],\ [521, 521, 2*w^3 - 8*w^2 - 12*w + 43],\ [521, 521, -3/2*w^3 + 11/2*w^2 + 19/2*w - 36],\ [521, 521, 2*w^3 - 8*w^2 - 12*w + 47],\ [521, 521, -7/2*w^3 + 23/2*w^2 + 45/2*w - 58],\ [541, 541, -1/2*w^3 + 5/2*w^2 + 13/2*w - 6],\ [541, 541, 9/2*w^3 - 33/2*w^2 - 55/2*w + 80],\ [541, 541, -15/2*w^3 + 51/2*w^2 + 101/2*w - 134],\ [541, 541, w^3 - w^2 - 7*w + 1],\ [571, 571, 13/2*w^3 - 47/2*w^2 - 79/2*w + 116],\ [571, 571, -5/2*w^3 + 11/2*w^2 + 43/2*w - 21],\ [599, 599, -3*w^3 + 9*w^2 + 19*w - 47],\ [599, 599, -15/2*w^3 + 51/2*w^2 + 103/2*w - 137],\ [599, 599, -w^3 + 2*w^2 + 11*w + 1],\ [599, 599, 5/2*w^3 - 17/2*w^2 - 35/2*w + 38],\ [601, 601, -1/2*w^3 + 11/2*w^2 - 5/2*w - 47],\ [601, 601, -3/2*w^3 + 13/2*w^2 + 17/2*w - 30],\ [619, 619, -w^3 + 5*w^2 + 5*w - 27],\ [619, 619, -1/2*w^3 + 1/2*w^2 + 11/2*w - 2],\ [619, 619, -2*w^3 + 7*w^2 + 12*w - 39],\ [619, 619, -3*w^3 + 11*w^2 + 19*w - 63],\ [631, 631, -3/2*w^3 + 13/2*w^2 + 17/2*w - 37],\ [631, 631, 5/2*w^3 - 19/2*w^2 - 31/2*w + 53],\ [641, 641, 5*w^3 - 16*w^2 - 35*w + 79],\ [641, 641, -2*w^3 + 8*w^2 + 12*w - 53],\ [641, 641, 3/2*w^3 - 11/2*w^2 - 23/2*w + 34],\ [641, 641, 3/2*w^3 - 11/2*w^2 - 23/2*w + 27],\ [659, 659, -5/2*w^3 + 19/2*w^2 + 31/2*w - 51],\ [659, 659, -3/2*w^3 + 13/2*w^2 + 17/2*w - 39],\ [661, 661, -5/2*w^3 + 17/2*w^2 + 33/2*w - 50],\ [661, 661, 5*w^3 - 17*w^2 - 30*w + 83],\ [661, 661, 5/2*w^3 - 17/2*w^2 - 31/2*w + 46],\ [661, 661, 3/2*w^3 - 5/2*w^2 - 21/2*w + 9],\ [691, 691, -3/2*w^3 + 13/2*w^2 + 19/2*w - 35],\ [691, 691, 3*w^3 - 11*w^2 - 20*w + 63],\ [709, 709, 19/2*w^3 - 65/2*w^2 - 127/2*w + 171],\ [709, 709, 4*w^3 - 14*w^2 - 28*w + 75],\ [709, 709, 1/2*w^3 - 5/2*w^2 - 15/2*w + 4],\ [709, 709, -w^3 + 5*w^2 + 7*w - 31],\ [739, 739, 11/2*w^3 - 37/2*w^2 - 73/2*w + 95],\ [739, 739, -3/2*w^3 + 5/2*w^2 + 25/2*w - 5],\ [739, 739, 27/2*w^3 - 91/2*w^2 - 187/2*w + 247],\ [739, 739, 4*w^3 - 15*w^2 - 24*w + 73],\ [751, 751, -5/2*w^3 + 19/2*w^2 + 35/2*w - 49],\ [751, 751, -2*w^2 + 2*w + 21],\ [751, 751, -9*w^3 + 31*w^2 + 61*w - 169],\ [751, 751, 17/2*w^3 - 57/2*w^2 - 117/2*w + 152],\ [761, 761, 5/2*w^3 - 15/2*w^2 - 33/2*w + 39],\ [761, 761, -3*w^3 + 9*w^2 + 22*w - 47],\ [761, 761, 9/2*w^3 - 29/2*w^2 - 61/2*w + 80],\ [761, 761, 25/2*w^3 - 85/2*w^2 - 169/2*w + 227],\ [769, 769, 2*w^3 - 8*w^2 - 12*w + 45],\ [811, 811, 5/2*w^3 - 19/2*w^2 - 27/2*w + 45],\ [811, 811, 1/2*w^3 - 7/2*w^2 + 1/2*w + 29],\ [821, 821, 25/2*w^3 - 85/2*w^2 - 173/2*w + 233],\ [821, 821, 19/2*w^3 - 63/2*w^2 - 135/2*w + 173],\ [829, 829, -7/2*w^3 + 27/2*w^2 + 43/2*w - 79],\ [829, 829, 10*w^3 - 34*w^2 - 67*w + 179],\ [829, 829, -3/2*w^3 + 1/2*w^2 + 27/2*w + 9],\ [829, 829, 5/2*w^3 - 13/2*w^2 - 41/2*w + 31],\ [839, 839, -3/2*w^3 + 11/2*w^2 + 25/2*w - 26],\ [839, 839, 2*w^3 - 7*w^2 - 16*w + 43],\ [841, 29, 5/2*w^3 - 15/2*w^2 - 35/2*w + 39],\ [881, 881, -8*w^3 + 27*w^2 + 56*w - 151],\ [881, 881, -w^3 + 3*w^2 + 4*w - 21],\ [911, 911, 5/2*w^3 - 19/2*w^2 - 33/2*w + 51],\ [911, 911, 2*w^3 - 8*w^2 - 13*w + 47],\ [919, 919, 3/2*w^3 - 9/2*w^2 - 27/2*w + 29],\ [919, 919, -3*w - 5],\ [919, 919, 1/2*w^3 - 7/2*w^2 - 5/2*w + 17],\ [919, 919, -4*w^3 + 14*w^2 + 27*w - 81],\ [929, 929, 7/2*w^3 - 23/2*w^2 - 49/2*w + 58],\ [929, 929, 13*w^3 - 44*w^2 - 89*w + 237],\ [929, 929, 9/2*w^3 - 29/2*w^2 - 59/2*w + 78],\ [929, 929, -w^3 + 2*w^2 + 7*w - 5],\ [941, 941, 5/2*w^3 - 19/2*w^2 - 31/2*w + 59],\ [941, 941, -3/2*w^3 + 13/2*w^2 + 17/2*w - 31],\ [941, 941, w^3 - 3*w^2 - 10*w + 7],\ [941, 941, -8*w^3 + 27*w^2 + 56*w - 147],\ [971, 971, -9/2*w^3 + 29/2*w^2 + 73/2*w - 92],\ [971, 971, -1/2*w^3 + 5/2*w^2 + 17/2*w - 1],\ [991, 991, w^3 - 4*w^2 - 3*w + 15],\ [991, 991, -1/2*w^3 + 1/2*w^2 + 15/2*w + 6],\ [1019, 1019, 3*w^3 - 9*w^2 - 19*w + 45],\ [1019, 1019, 3*w^3 - 11*w^2 - 20*w + 53],\ [1019, 1019, -1/2*w^3 + 1/2*w^2 + 17/2*w + 9],\ [1019, 1019, -1/2*w^3 + 5/2*w^2 - 3/2*w - 4],\ [1021, 1021, -3/2*w^3 + 13/2*w^2 + 19/2*w - 37],\ [1021, 1021, 3*w^3 - 11*w^2 - 20*w + 61],\ [1049, 1049, w^3 - 4*w^2 - 9*w + 15],\ [1049, 1049, 5/2*w^3 - 17/2*w^2 - 39/2*w + 54],\ [1051, 1051, 3/2*w^3 - 11/2*w^2 - 15/2*w + 21],\ [1051, 1051, -1/2*w^3 + 7/2*w^2 + 7/2*w - 23],\ [1051, 1051, 9/2*w^3 - 31/2*w^2 - 63/2*w + 83],\ [1051, 1051, -1/2*w^3 + 1/2*w^2 + 13/2*w + 8],\ [1061, 1061, 2*w^3 - 5*w^2 - 14*w + 19],\ [1061, 1061, 9/2*w^3 - 29/2*w^2 - 63/2*w + 72],\ [1091, 1091, 3/2*w^3 - 5/2*w^2 - 21/2*w + 10],\ [1091, 1091, 3/2*w^3 - 3/2*w^2 - 19/2*w + 7],\ [1091, 1091, -13/2*w^3 + 43/2*w^2 + 91/2*w - 116],\ [1091, 1091, 19/2*w^3 - 63/2*w^2 - 135/2*w + 174],\ [1109, 1109, -5/2*w^3 + 17/2*w^2 + 33/2*w - 53],\ [1109, 1109, 4*w^3 - 13*w^2 - 26*w + 67],\ [1109, 1109, -3/2*w^3 + 11/2*w^2 + 23/2*w - 25],\ [1109, 1109, 4*w^3 - 13*w^2 - 28*w + 65],\ [1171, 1171, 1/2*w^3 - 1/2*w^2 + 3/2*w + 12],\ [1171, 1171, 11/2*w^3 - 35/2*w^2 - 87/2*w + 105],\ [1181, 1181, 2*w^3 - 8*w^2 - 13*w + 45],\ [1181, 1181, -5/2*w^3 + 19/2*w^2 + 33/2*w - 53],\ [1201, 1201, -5/2*w^3 + 15/2*w^2 + 39/2*w - 45],\ [1201, 1201, -1/2*w^3 + 3/2*w^2 + 13/2*w - 3],\ [1201, 1201, -w^3 + 3*w^2 + 10*w - 21],\ [1201, 1201, 3/2*w^3 - 9/2*w^2 - 17/2*w + 29],\ [1229, 1229, -5*w^3 + 17*w^2 + 35*w - 91],\ [1229, 1229, 3/2*w^3 - 9/2*w^2 - 25/2*w + 17],\ [1249, 1249, 5/2*w^3 - 17/2*w^2 - 35/2*w + 40],\ [1249, 1249, 3/2*w^3 - 3/2*w^2 - 21/2*w + 4],\ [1249, 1249, w^2 - 13],\ [1249, 1249, 9*w^3 - 30*w^2 - 63*w + 163],\ [1289, 1289, 3/2*w^3 - 1/2*w^2 - 23/2*w - 3],\ [1289, 1289, 11*w^3 - 37*w^2 - 76*w + 201],\ [1291, 1291, -1/2*w^3 - 7/2*w^2 + 13/2*w + 29],\ [1291, 1291, 23/2*w^3 - 79/2*w^2 - 155/2*w + 212],\ [1301, 1301, 11*w^3 - 38*w^2 - 73*w + 201],\ [1301, 1301, 1/2*w^3 - 5/2*w^2 - 17/2*w + 3],\ [1319, 1319, 12*w^3 - 40*w^2 - 85*w + 219],\ [1319, 1319, 3/2*w^3 - 1/2*w^2 - 19/2*w - 1],\ [1321, 1321, -1/2*w^3 - 1/2*w^2 - 1/2*w - 7],\ [1321, 1321, -3*w^3 + 11*w^2 + 15*w - 45],\ [1361, 1361, -3*w^3 + 11*w^2 + 21*w - 57],\ [1361, 1361, 5/2*w^3 - 15/2*w^2 - 39/2*w + 35],\ [1381, 1381, -3*w^3 + 9*w^2 + 23*w - 43],\ [1381, 1381, 2*w^3 - 6*w^2 - 12*w + 27],\ [1381, 1381, -1/2*w^3 + 3/2*w^2 + 9/2*w - 1],\ [1381, 1381, w - 7],\ [1399, 1399, 9/2*w^3 - 33/2*w^2 - 57/2*w + 85],\ [1399, 1399, -5/2*w^3 + 15/2*w^2 + 41/2*w - 37],\ [1409, 1409, 3/2*w^3 - 1/2*w^2 - 21/2*w - 1],\ [1409, 1409, -23/2*w^3 + 77/2*w^2 + 161/2*w - 211],\ [1409, 1409, 11/2*w^3 - 39/2*w^2 - 71/2*w + 98],\ [1409, 1409, 1/2*w^3 - 9/2*w^2 - 1/2*w + 37],\ [1429, 1429, 3/2*w^3 - 5/2*w^2 - 33/2*w - 5],\ [1429, 1429, 7/2*w^3 - 25/2*w^2 - 37/2*w + 53],\ [1439, 1439, -7*w^3 + 23*w^2 + 52*w - 135],\ [1439, 1439, -1/2*w^3 - 1/2*w^2 + 1/2*w - 5],\ [1451, 1451, 1/2*w^3 + 3/2*w^2 - 13/2*w - 15],\ [1451, 1451, -13/2*w^3 + 45/2*w^2 + 85/2*w - 120],\ [1459, 1459, -7/2*w^3 + 27/2*w^2 + 43/2*w - 70],\ [1459, 1459, 5/2*w^3 - 21/2*w^2 - 29/2*w + 65],\ [1471, 1471, 5/2*w^3 - 17/2*w^2 - 37/2*w + 43],\ [1471, 1471, -3*w^3 + 10*w^2 + 21*w - 49],\ [1481, 1481, -6*w^3 + 21*w^2 + 40*w - 113],\ [1481, 1481, -16*w^3 + 54*w^2 + 112*w - 299],\ [1481, 1481, 9*w^3 - 30*w^2 - 63*w + 161],\ [1481, 1481, 1/2*w^3 - 9/2*w^2 - 3/2*w + 30],\ [1489, 1489, -8*w^3 + 26*w^2 + 60*w - 151],\ [1489, 1489, -w^3 + 5*w^2 + 6*w - 35],\ [1489, 1489, 7/2*w^3 - 25/2*w^2 - 47/2*w + 63],\ [1489, 1489, -w^3 + w^2 + 3*w - 13],\ [1499, 1499, 3*w^3 - 10*w^2 - 21*w + 45],\ [1499, 1499, 9/2*w^3 - 29/2*w^2 - 65/2*w + 75],\ [1511, 1511, -11/2*w^3 + 35/2*w^2 + 79/2*w - 91],\ [1511, 1511, -5/2*w^3 + 21/2*w^2 + 33/2*w - 54],\ [1511, 1511, 7/2*w^3 - 19/2*w^2 - 57/2*w + 42],\ [1511, 1511, 5/2*w^3 - 15/2*w^2 - 29/2*w + 41],\ [1531, 1531, -4*w^2 + 2*w + 29],\ [1531, 1531, 9*w^3 - 31*w^2 - 61*w + 167],\ [1549, 1549, -1/2*w^3 + 1/2*w^2 + 13/2*w - 5],\ [1549, 1549, -3/2*w^3 + 11/2*w^2 + 15/2*w - 34],\ [1559, 1559, 9/2*w^3 - 29/2*w^2 - 63/2*w + 76],\ [1559, 1559, 2*w^3 - 5*w^2 - 14*w + 23],\ [1571, 1571, 3*w^3 - 9*w^2 - 20*w + 43],\ [1571, 1571, 2*w^3 - 7*w^2 - 14*w + 45],\ [1601, 1601, -27/2*w^3 + 93/2*w^2 + 179/2*w - 247],\ [1601, 1601, 1/2*w^3 - 1/2*w^2 + 5/2*w + 16],\ [1609, 1609, -1/2*w^3 + 7/2*w^2 + 1/2*w - 31],\ [1609, 1609, 3/2*w^3 - 7/2*w^2 - 23/2*w + 25],\ [1621, 1621, 7/2*w^3 - 25/2*w^2 - 45/2*w + 71],\ [1621, 1621, -1/2*w^3 + 7/2*w^2 + 3/2*w - 19],\ [1681, 41, -3*w^3 + 9*w^2 + 21*w - 43],\ [1681, 41, 3*w^3 - 9*w^2 - 21*w + 47],\ [1721, 1721, -1/2*w^3 - 3/2*w^2 + 21/2*w + 25],\ [1721, 1721, -9/2*w^3 + 33/2*w^2 + 49/2*w - 78],\ [1759, 1759, 4*w^3 - 14*w^2 - 25*w + 75],\ [1759, 1759, 2*w^3 - 7*w^2 - 12*w + 43],\ [1831, 1831, -3/2*w^3 + 7/2*w^2 + 29/2*w - 6],\ [1831, 1831, 15/2*w^3 - 51/2*w^2 - 103/2*w + 136],\ [1849, 43, -1/2*w^3 + 7/2*w^2 - 3/2*w - 31],\ [1849, 43, 15/2*w^3 - 51/2*w^2 - 101/2*w + 138],\ [1871, 1871, 3*w^3 - 9*w^2 - 18*w + 43],\ [1871, 1871, -7/2*w^3 + 21/2*w^2 + 45/2*w - 51],\ [1879, 1879, 21/2*w^3 - 71/2*w^2 - 145/2*w + 195],\ [1879, 1879, -w^3 - w^2 + 8*w + 9],\ [1889, 1889, 2*w^3 - 4*w^2 - 16*w + 15],\ [1889, 1889, -6*w^3 + 20*w^2 + 40*w - 105],\ [1901, 1901, 2*w^2 - 7*w - 29],\ [1901, 1901, -19/2*w^3 + 65/2*w^2 + 133/2*w - 182],\ [1901, 1901, 1/2*w^3 - 11/2*w^2 - 7/2*w + 30],\ [1901, 1901, -1/2*w^3 + 5/2*w^2 + 1/2*w - 24],\ [1931, 1931, -1/2*w^3 + 9/2*w^2 + 3/2*w - 34],\ [1931, 1931, -5/2*w^3 + 19/2*w^2 + 35/2*w - 59],\ [1931, 1931, -5/2*w^3 + 19/2*w^2 + 35/2*w - 47],\ [1931, 1931, 6*w^3 - 21*w^2 - 40*w + 109],\ [1949, 1949, -3/2*w^3 + 15/2*w^2 + 19/2*w - 46],\ [1949, 1949, -11/2*w^3 + 39/2*w^2 + 75/2*w - 105],\ [1979, 1979, -7/2*w^3 + 21/2*w^2 + 55/2*w - 51],\ [1979, 1979, 3/2*w^3 - 5/2*w^2 - 29/2*w + 7],\ [1979, 1979, 9/2*w^3 - 31/2*w^2 - 55/2*w + 81],\ [1979, 1979, -2*w^3 + 6*w^2 + 11*w - 27]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^7 - 14*x^5 + 16*x^4 + 27*x^3 - 43*x^2 + 8*x + 3 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -2/25*e^6 - 11/25*e^5 + 1/5*e^4 + 83/25*e^3 + 3/5*e^2 - 169/25*e - 8/25, -13/25*e^6 - 34/25*e^5 + 24/5*e^4 + 152/25*e^3 - 48/5*e^2 - 136/25*e + 48/25, 4/5*e^6 + 7/5*e^5 - 9*e^4 - 16/5*e^3 + 19*e^2 - 12/5*e - 14/5, -4/25*e^6 + 3/25*e^5 + 12/5*e^4 - 109/25*e^3 - 29/5*e^2 + 287/25*e + 9/25, 1, 13/25*e^6 + 34/25*e^5 - 24/5*e^4 - 152/25*e^3 + 53/5*e^2 + 186/25*e - 198/25, 4/25*e^6 + 22/25*e^5 - 2/5*e^4 - 141/25*e^3 + 4/5*e^2 + 138/25*e - 34/25, 2/5*e^6 + 1/5*e^5 - 6*e^4 + 12/5*e^3 + 16*e^2 - 51/5*e - 22/5, 3/5*e^6 - 1/5*e^5 - 9*e^4 + 53/5*e^3 + 18*e^2 - 124/5*e + 7/5, -6/25*e^6 - 8/25*e^5 + 13/5*e^4 - 26/25*e^3 - 21/5*e^2 + 168/25*e - 24/25, 24/25*e^6 + 7/25*e^5 - 67/5*e^4 + 279/25*e^3 + 149/5*e^2 - 672/25*e - 104/25, -7/5*e^6 - 6/5*e^5 + 19*e^4 - 27/5*e^3 - 46*e^2 + 101/5*e + 47/5, 7/25*e^6 - 24/25*e^5 - 31/5*e^4 + 322/25*e^3 + 72/5*e^2 - 646/25*e + 28/25, -28/25*e^6 - 29/25*e^5 + 69/5*e^4 - 113/25*e^3 - 138/5*e^2 + 434/25*e + 63/25, -22/25*e^6 - 21/25*e^5 + 56/5*e^4 - 87/25*e^3 - 112/5*e^2 + 391/25*e - 88/25, -14/25*e^6 - 27/25*e^5 + 32/5*e^4 + 81/25*e^3 - 89/5*e^2 + 42/25*e + 194/25, 43/25*e^6 + 49/25*e^5 - 104/5*e^4 + 153/25*e^3 + 223/5*e^2 - 654/25*e - 178/25, 14/25*e^6 + 27/25*e^5 - 22/5*e^4 + 44/25*e^3 + 4/5*e^2 - 417/25*e + 306/25, -64/25*e^6 - 52/25*e^5 + 172/5*e^4 - 294/25*e^3 - 394/5*e^2 + 1017/25*e + 294/25, -36/25*e^6 - 48/25*e^5 + 83/5*e^4 - 81/25*e^3 - 166/5*e^2 + 658/25*e - 69/25, -12/5*e^6 - 6/5*e^5 + 32*e^4 - 117/5*e^3 - 64*e^2 + 341/5*e - 28/5, -29/25*e^6 + 3/25*e^5 + 97/5*e^4 - 309/25*e^3 - 274/5*e^2 + 762/25*e + 434/25, 33/25*e^6 + 69/25*e^5 - 74/5*e^4 - 332/25*e^3 + 158/5*e^2 + 451/25*e - 143/25, 69/25*e^6 + 92/25*e^5 - 152/5*e^4 + 249/25*e^3 + 274/5*e^2 - 1357/25*e - 24/25, -4/25*e^6 - 22/25*e^5 - 3/5*e^4 + 66/25*e^3 + 26/5*e^2 + 62/25*e - 166/25, -34/25*e^6 - 12/25*e^5 + 92/5*e^4 - 364/25*e^3 - 179/5*e^2 + 802/25*e - 11/25, 58/25*e^6 + 94/25*e^5 - 129/5*e^4 - 132/25*e^3 + 243/5*e^2 - 124/25*e - 18/25, -28/25*e^6 - 4/25*e^5 + 89/5*e^4 - 238/25*e^3 - 233/5*e^2 + 634/25*e + 188/25, 9/5*e^6 + 12/5*e^5 - 20*e^4 + 24/5*e^3 + 33*e^2 - 132/5*e + 46/5, -53/25*e^6 - 79/25*e^5 + 119/5*e^4 + 12/25*e^3 - 228/5*e^2 + 384/25*e - 12/25, 14/5*e^6 + 22/5*e^5 - 33*e^4 - 36/5*e^3 + 76*e^2 - 52/5*e - 109/5, 114/25*e^6 + 127/25*e^5 - 282/5*e^4 + 344/25*e^3 + 594/5*e^2 - 1842/25*e - 94/25, 7/25*e^6 + 1/25*e^5 - 21/5*e^4 + 72/25*e^3 + 67/5*e^2 - 21/25*e - 497/25, -109/25*e^6 - 137/25*e^5 + 257/5*e^4 - 239/25*e^3 - 514/5*e^2 + 1502/25*e - 11/25, -42/25*e^6 - 81/25*e^5 + 96/5*e^4 + 268/25*e^3 - 252/5*e^2 - 74/25*e + 582/25, -186/25*e^6 - 223/25*e^5 + 453/5*e^4 - 456/25*e^3 - 981/5*e^2 + 2933/25*e + 281/25, 12/25*e^6 + 41/25*e^5 - 21/5*e^4 - 248/25*e^3 + 72/5*e^2 + 189/25*e - 377/25, 67/25*e^6 + 81/25*e^5 - 156/5*e^4 + 257/25*e^3 + 297/5*e^2 - 1426/25*e + 268/25, 84/25*e^6 + 137/25*e^5 - 192/5*e^4 - 161/25*e^3 + 429/5*e^2 - 802/25*e - 489/25, 43/25*e^6 + 49/25*e^5 - 94/5*e^4 + 253/25*e^3 + 123/5*e^2 - 904/25*e + 372/25, -24/25*e^6 - 57/25*e^5 + 42/5*e^4 + 196/25*e^3 - 39/5*e^2 - 203/25*e - 321/25, 148/25*e^6 + 289/25*e^5 - 319/5*e^4 - 842/25*e^3 + 683/5*e^2 + 31/25*e - 508/25, -3/25*e^6 + 46/25*e^5 + 24/5*e^4 - 563/25*e^3 - 43/5*e^2 + 1109/25*e - 62/25, -59/25*e^6 - 87/25*e^5 + 127/5*e^4 - 114/25*e^3 - 224/5*e^2 + 1052/25*e - 36/25, 113/25*e^6 + 84/25*e^5 - 299/5*e^4 + 748/25*e^3 + 653/5*e^2 - 2564/25*e + 2/25, -102/25*e^6 - 186/25*e^5 + 226/5*e^4 + 483/25*e^3 - 472/5*e^2 + 81/25*e + 142/25, -68/25*e^6 - 124/25*e^5 + 139/5*e^4 + 122/25*e^3 - 253/5*e^2 + 754/25*e - 222/25, 6/5*e^6 + 8/5*e^5 - 12*e^4 + 36/5*e^3 + 16*e^2 - 143/5*e + 4/5, 8/5*e^6 + 4/5*e^5 - 23*e^4 + 48/5*e^3 + 51*e^2 - 144/5*e - 28/5, 24/25*e^6 - 18/25*e^5 - 87/5*e^4 + 404/25*e^3 + 244/5*e^2 - 847/25*e - 279/25, 11/25*e^6 + 98/25*e^5 + 7/5*e^4 - 819/25*e^3 - 9/5*e^2 + 1417/25*e - 456/25, -46/25*e^6 - 3/25*e^5 + 128/5*e^4 - 716/25*e^3 - 261/5*e^2 + 1913/25*e - 109/25, 4*e^6 + 5*e^5 - 51*e^4 - e^3 + 120*e^2 - 35*e - 29, -81/25*e^6 - 133/25*e^5 + 168/5*e^4 - 26/25*e^3 - 291/5*e^2 + 968/25*e + 126/25, -26/5*e^6 - 43/5*e^5 + 59*e^4 + 64/5*e^3 - 128*e^2 + 143/5*e + 131/5, -41/25*e^6 - 63/25*e^5 + 88/5*e^4 - 86/25*e^3 - 161/5*e^2 + 923/25*e - 414/25, 139/25*e^6 + 252/25*e^5 - 302/5*e^4 - 481/25*e^3 + 649/5*e^2 - 692/25*e - 744/25, 21/5*e^6 + 38/5*e^5 - 45*e^4 - 64/5*e^3 + 92*e^2 - 118/5*e - 81/5, 34/5*e^6 + 42/5*e^5 - 82*e^4 + 74/5*e^3 + 176*e^2 - 507/5*e - 84/5, -226/25*e^6 - 318/25*e^5 + 533/5*e^4 - 46/25*e^3 - 1141/5*e^2 + 2578/25*e + 496/25, -6/5*e^6 - 13/5*e^5 + 11*e^4 + 29/5*e^3 - 15*e^2 + 68/5*e - 34/5, -94/25*e^6 - 117/25*e^5 + 227/5*e^4 - 174/25*e^3 - 479/5*e^2 + 1307/25*e + 74/25, -16/5*e^6 - 18/5*e^5 + 41*e^4 - 11/5*e^3 - 90*e^2 + 93/5*e + 76/5, -22/25*e^6 - 21/25*e^5 + 51/5*e^4 - 187/25*e^3 - 122/5*e^2 + 416/25*e + 487/25, 213/25*e^6 + 359/25*e^5 - 479/5*e^4 - 652/25*e^3 + 998/5*e^2 - 689/25*e - 798/25, -164/25*e^6 - 252/25*e^5 + 382/5*e^4 + 256/25*e^3 - 809/5*e^2 + 1442/25*e + 69/25, 98/25*e^6 + 114/25*e^5 - 244/5*e^4 + 233/25*e^3 + 568/5*e^2 - 1269/25*e - 858/25, -87/25*e^6 - 66/25*e^5 + 231/5*e^4 - 427/25*e^3 - 457/5*e^2 + 1311/25*e - 473/25, -36/5*e^6 - 53/5*e^5 + 84*e^4 + 34/5*e^3 - 175*e^2 + 233/5*e + 141/5, 61/25*e^6 + 98/25*e^5 - 123/5*e^4 + 131/25*e^3 + 181/5*e^2 - 1483/25*e + 594/25, 9/5*e^6 - 3/5*e^5 - 32*e^4 + 99/5*e^3 + 92*e^2 - 222/5*e - 119/5, -131/25*e^6 - 183/25*e^5 + 303/5*e^4 - 76/25*e^3 - 581/5*e^2 + 1543/25*e - 349/25, -112/25*e^6 - 116/25*e^5 + 281/5*e^4 - 452/25*e^3 - 617/5*e^2 + 2136/25*e + 102/25, 87/25*e^6 + 141/25*e^5 - 196/5*e^4 - 223/25*e^3 + 372/5*e^2 - 286/25*e + 23/25, -268/25*e^6 - 299/25*e^5 + 669/5*e^4 - 753/25*e^3 - 1478/5*e^2 + 4229/25*e + 553/25, 142/25*e^6 + 306/25*e^5 - 301/5*e^4 - 1218/25*e^3 + 647/5*e^2 + 974/25*e - 632/25, 24/5*e^6 + 42/5*e^5 - 53*e^4 - 71/5*e^3 + 111*e^2 - 197/5*e - 14/5, -101/25*e^6 - 118/25*e^5 + 243/5*e^4 - 321/25*e^3 - 506/5*e^2 + 1553/25*e + 471/25, -31/5*e^6 - 23/5*e^5 + 83*e^4 - 196/5*e^3 - 188*e^2 + 683/5*e + 26/5, -63/25*e^6 - 84/25*e^5 + 149/5*e^4 - 73/25*e^3 - 303/5*e^2 + 814/25*e - 177/25, -23/5*e^6 - 49/5*e^5 + 47*e^4 + 147/5*e^3 - 102*e^2 - 6/5*e + 168/5, 139/25*e^6 + 227/25*e^5 - 317/5*e^4 - 281/25*e^3 + 734/5*e^2 - 942/25*e - 1194/25, 137/25*e^6 + 166/25*e^5 - 331/5*e^4 + 227/25*e^3 + 647/5*e^2 - 1661/25*e + 273/25, 93/25*e^6 + 124/25*e^5 - 219/5*e^4 + 228/25*e^3 + 503/5*e^2 - 1804/25*e - 603/25, -8*e^6 - 12*e^5 + 92*e^4 + 8*e^3 - 184*e^2 + 54*e + 22, -159/25*e^6 - 212/25*e^5 + 377/5*e^4 - 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934/5*e^2 + 2517/25*e + 1094/25, 49/25*e^6 + 307/25*e^5 - 2/5*e^4 - 1996/25*e^3 - 11/5*e^2 + 2203/25*e - 1029/25, -441/25*e^6 - 488/25*e^5 + 1083/5*e^4 - 1336/25*e^3 - 2206/5*e^2 + 6498/25*e + 236/25, -13*e^6 - 26*e^5 + 140*e^4 + 84*e^3 - 301*e^2 - 30*e + 60, -57/25*e^6 - 276/25*e^5 + 51/5*e^4 + 2028/25*e^3 - 22/5*e^2 - 3929/25*e - 28/25, -6/5*e^6 + 2/5*e^5 + 18*e^4 - 126/5*e^3 - 45*e^2 + 358/5*e + 51/5, 89/25*e^6 + 77/25*e^5 - 232/5*e^4 + 494/25*e^3 + 539/5*e^2 - 1917/25*e + 6/25, -99/25*e^6 - 282/25*e^5 + 187/5*e^4 + 1771/25*e^3 - 324/5*e^2 - 3053/25*e + 254/25, 477/25*e^6 + 786/25*e^5 - 1056/5*e^4 - 858/25*e^3 + 2077/5*e^2 - 3406/25*e + 8/25, 187/25*e^6 + 141/25*e^5 - 501/5*e^4 + 977/25*e^3 + 1092/5*e^2 - 2786/25*e - 1002/25, -482/25*e^6 - 551/25*e^5 + 1181/5*e^4 - 1272/25*e^3 - 2467/5*e^2 + 6546/25*e + 972/25, -283/25*e^6 - 369/25*e^5 + 694/5*e^4 - 118/25*e^3 - 1553/5*e^2 + 3249/25*e + 1118/25, -e^6 - 10*e^5 - 5*e^4 + 84*e^3 + 6*e^2 - 128*e + 21, 253/25*e^6 + 429/25*e^5 - 559/5*e^4 - 562/25*e^3 + 1203/5*e^2 - 1609/25*e - 1188/25, 112/25*e^6 - 59/25*e^5 - 346/5*e^4 + 2277/25*e^3 + 762/5*e^2 - 4886/25*e - 27/25, 2/5*e^6 + 1/5*e^5 - 3*e^4 + 57/5*e^3 - 6*e^2 - 191/5*e + 63/5, -42/25*e^6 - 156/25*e^5 + 51/5*e^4 + 718/25*e^3 - 127/5*e^2 - 324/25*e + 107/25, -29/25*e^6 + 53/25*e^5 + 127/5*e^4 - 659/25*e^3 - 389/5*e^2 + 912/25*e + 459/25, -57/25*e^6 - 151/25*e^5 + 96/5*e^4 + 578/25*e^3 - 157/5*e^2 - 279/25*e + 522/25, -49/5*e^6 - 102/5*e^5 + 100*e^4 + 291/5*e^3 - 206*e^2 + 62/5*e + 169/5, -331/25*e^6 - 333/25*e^5 + 853/5*e^4 - 1026/25*e^3 - 1921/5*e^2 + 4643/25*e + 1601/25, -196/25*e^6 - 378/25*e^5 + 398/5*e^4 + 859/25*e^3 - 646/5*e^2 + 113/25*e - 309/25, 267/25*e^6 + 556/25*e^5 - 546/5*e^4 - 1693/25*e^3 + 1092/5*e^2 + 399/25*e - 1207/25, 338/25*e^6 + 409/25*e^5 - 814/5*e^4 + 648/25*e^3 + 1573/5*e^2 - 4189/25*e + 302/25, 302/25*e^6 + 586/25*e^5 - 641/5*e^4 - 1483/25*e^3 + 1317/5*e^2 - 781/25*e + 208/25, 12/5*e^6 + 51/5*e^5 - 16*e^4 - 358/5*e^3 + 37*e^2 + 509/5*e - 7/5, 288/25*e^6 + 284/25*e^5 - 764/5*e^4 + 773/25*e^3 + 1848/5*e^2 - 3839/25*e - 2198/25, 73/25*e^6 + 64/25*e^5 - 209/5*e^4 + 108/25*e^3 + 568/5*e^2 - 944/25*e - 1208/25, 2/5*e^6 + 46/5*e^5 + 16*e^4 - 408/5*e^3 - 66*e^2 + 774/5*e - 2/5, -104/25*e^6 - 147/25*e^5 + 262/5*e^4 + 141/25*e^3 - 719/5*e^2 + 762/25*e + 1809/25, -72/5*e^6 - 76/5*e^5 + 181*e^4 - 267/5*e^3 - 402*e^2 + 1296/5*e + 117/5, 4*e^5 + 15*e^4 - 24*e^3 - 79*e^2 + 37*e + 58, -39/25*e^6 - 77/25*e^5 + 77/5*e^4 + 131/25*e^3 - 159/5*e^2 - 108/25*e + 269/25, -132/25*e^6 - 151/25*e^5 + 326/5*e^4 - 397/25*e^3 - 712/5*e^2 + 2496/25*e - 378/25, 278/25*e^6 + 354/25*e^5 - 659/5*e^4 + 388/25*e^3 + 1233/5*e^2 - 3134/25*e + 1037/25, -14/25*e^6 - 202/25*e^5 - 63/5*e^4 + 1431/25*e^3 + 211/5*e^2 - 1933/25*e + 1119/25, 28/25*e^6 + 54/25*e^5 - 84/5*e^4 - 637/25*e^3 + 233/5*e^2 + 2241/25*e - 1013/25, -59/25*e^6 + 63/25*e^5 + 177/5*e^4 - 1764/25*e^3 - 324/5*e^2 + 3627/25*e - 536/25, 276/25*e^6 + 493/25*e^5 - 613/5*e^4 - 1154/25*e^3 + 1316/5*e^2 - 603/25*e - 1721/25, -91/25*e^6 + 12/25*e^5 + 303/5*e^4 - 911/25*e^3 - 776/5*e^2 + 1648/25*e + 986/25, -4/25*e^6 + 3/25*e^5 + 42/5*e^4 + 291/25*e^3 - 239/5*e^2 - 638/25*e + 859/25, -287/25*e^6 - 166/25*e^5 + 796/5*e^4 - 2077/25*e^3 - 1802/5*e^2 + 6661/25*e + 177/25, 79/5*e^6 + 127/5*e^5 - 176*e^4 - 101/5*e^3 + 355*e^2 - 682/5*e - 154/5, -198/25*e^6 - 89/25*e^5 + 559/5*e^4 - 1683/25*e^3 - 1288/5*e^2 + 4244/25*e + 1083/25, 74/5*e^6 + 82/5*e^5 - 180*e^4 + 269/5*e^3 + 369*e^2 - 1267/5*e + 46/5, 177/25*e^6 + 111/25*e^5 - 501/5*e^4 + 992/25*e^3 + 1207/5*e^2 - 3081/25*e - 1392/25, 11*e^6 + 18*e^5 - 127*e^4 - 29*e^3 + 298*e^2 - 47*e - 100, 23/5*e^6 - 21/5*e^5 - 76*e^4 + 523/5*e^3 + 165*e^2 - 1114/5*e - 48/5, -209/25*e^6 - 312/25*e^5 + 487/5*e^4 + 136/25*e^3 - 1099/5*e^2 + 2002/25*e + 1839/25, -11/5*e^6 - 3/5*e^5 + 32*e^4 - 136/5*e^3 - 87*e^2 + 453/5*e + 226/5, 336/25*e^6 + 423/25*e^5 - 833/5*e^4 + 281/25*e^3 + 1916/5*e^2 - 3808/25*e - 1931/25, -161/25*e^6 - 298/25*e^5 + 363/5*e^4 + 1019/25*e^3 - 756/5*e^2 - 1092/25*e + 756/25, 167/25*e^6 + 181/25*e^5 - 441/5*e^4 + 107/25*e^3 + 982/5*e^2 - 1526/25*e + 168/25, 373/25*e^6 + 489/25*e^5 - 889/5*e^4 + 408/25*e^3 + 1868/5*e^2 - 4019/25*e - 858/25, -209/25*e^6 - 387/25*e^5 + 432/5*e^4 + 586/25*e^3 - 824/5*e^2 + 977/25*e + 639/25, -86/25*e^6 - 48/25*e^5 + 218/5*e^4 - 931/25*e^3 - 411/5*e^2 + 2983/25*e + 781/25, -391/25*e^6 - 538/25*e^5 + 898/5*e^4 - 486/25*e^3 - 1761/5*e^2 + 4698/25*e + 786/25, -178/25*e^6 - 79/25*e^5 + 474/5*e^4 - 1838/25*e^3 - 868/5*e^2 + 5309/25*e - 487/25, 126/25*e^6 + 318/25*e^5 - 243/5*e^4 - 1429/25*e^3 + 531/5*e^2 + 1647/25*e - 921/25, -177/25*e^6 - 161/25*e^5 + 436/5*e^4 - 992/25*e^3 - 757/5*e^2 + 3481/25*e - 1408/25, -463/25*e^6 - 459/25*e^5 + 1174/5*e^4 - 1798/25*e^3 - 2503/5*e^2 + 7614/25*e + 598/25] 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,w + 3])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]