/* 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, 14, -13, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([11,11,-1/2*w^3 - 1/2*w^2 + 5*w + 7]) primes_array = [ [4, 2, w^2 - 2*w - 6],\ [4, 2, -w^2 + 7],\ [5, 5, -1/2*w^3 + 2*w^2 + 7/2*w - 14],\ [5, 5, 1/2*w^3 + 1/2*w^2 - 6*w - 9],\ [11, 11, 1/2*w^3 - 2*w^2 - 5/2*w + 11],\ [11, 11, 1/2*w^3 + 1/2*w^2 - 5*w - 7],\ [31, 31, 1/2*w^2 + 1/2*w - 4],\ [31, 31, -1/2*w^2 + 3/2*w + 3],\ [41, 41, 1/2*w^2 + 1/2*w - 6],\ [41, 41, 2*w^3 - 15/2*w^2 - 25/2*w + 50],\ [41, 41, 5/2*w^2 - 1/2*w - 17],\ [41, 41, 1/2*w^2 - 3/2*w - 5],\ [61, 61, -1/2*w^3 + w^2 + 7/2*w - 1],\ [61, 61, -1/2*w^3 + 1/2*w^2 + 4*w - 3],\ [71, 71, 1/2*w^3 + w^2 - 11/2*w - 13],\ [71, 71, -1/2*w^3 + 5/2*w^2 + 2*w - 17],\ [81, 3, -3],\ [89, 89, -w^3 + 3/2*w^2 + 13/2*w - 9],\ [89, 89, w^3 - 7/2*w^2 - 11/2*w + 20],\ [89, 89, -w^3 - 1/2*w^2 + 19/2*w + 12],\ [89, 89, 1/2*w^3 + 2*w^2 - 17/2*w - 19],\ [109, 109, 1/2*w^3 + 3/2*w^2 - 7*w - 15],\ [109, 109, -1/2*w^3 + 1/2*w^2 + 4*w - 5],\ [121, 11, -3/2*w^2 + 3/2*w + 10],\ [131, 131, 3/2*w^3 - 13/2*w^2 - 9*w + 43],\ [131, 131, -3/2*w^3 - 2*w^2 + 35/2*w + 29],\ [139, 139, -3/2*w^3 + 11/2*w^2 + 10*w - 39],\ [139, 139, 1/2*w^3 + w^2 - 11/2*w - 9],\ [139, 139, -1/2*w^3 + 5/2*w^2 + 2*w - 13],\ [139, 139, -3/2*w^3 - w^2 + 33/2*w + 25],\ [151, 151, -1/2*w^3 + 3/2*w^2 + 3*w - 5],\ [151, 151, -1/2*w^3 + 9/2*w + 1],\ [179, 179, 5/2*w^2 - 3/2*w - 20],\ [179, 179, -w^3 + 5/2*w^2 + 11/2*w - 5],\ [179, 179, -w^3 + 1/2*w^2 + 15/2*w - 2],\ [179, 179, w^3 + 1/2*w^2 - 19/2*w - 10],\ [181, 181, 1/2*w^2 - 3/2*w - 8],\ [181, 181, 3/2*w^2 - 1/2*w - 13],\ [181, 181, -3/2*w^2 + 5/2*w + 12],\ [181, 181, 1/2*w^2 + 1/2*w - 9],\ [191, 191, w^3 + 1/2*w^2 - 17/2*w - 9],\ [191, 191, 1/2*w^3 - w^2 - 5/2*w + 8],\ [199, 199, -1/2*w^3 + 7/2*w^2 + 3*w - 23],\ [199, 199, -1/2*w^3 - 2*w^2 + 17/2*w + 17],\ [211, 211, w^3 - 5/2*w^2 - 9/2*w + 3],\ [211, 211, -w^3 + 1/2*w^2 + 13/2*w - 3],\ [229, 229, 3/2*w^3 - 2*w^2 - 21/2*w - 6],\ [229, 229, -w^3 + 3*w^2 + 8*w - 23],\ [239, 239, -w^3 + 3*w^2 + 4*w - 9],\ [239, 239, w^3 - 9*w - 7],\ [239, 239, 1/2*w^3 - 3/2*w^2 - 2*w + 13],\ [239, 239, -w^3 + 7*w + 3],\ [241, 241, 1/2*w^3 + 2*w^2 - 15/2*w - 16],\ [241, 241, -1/2*w^3 + 7/2*w^2 + 2*w - 21],\ [251, 251, w^3 - 5/2*w^2 - 9/2*w + 10],\ [251, 251, w^3 - 9*w - 9],\ [269, 269, w^3 - 1/2*w^2 - 17/2*w - 10],\ [269, 269, w^3 - 5/2*w^2 - 13/2*w + 18],\ [281, 281, -1/2*w^3 + 3*w^2 + 3/2*w - 19],\ [281, 281, 1/2*w^3 + 3/2*w^2 - 6*w - 15],\ [289, 17, w^3 - 3/2*w^2 - 15/2*w - 1],\ [289, 17, -w^3 + 3/2*w^2 + 15/2*w - 9],\ [331, 331, 3/2*w^2 - 1/2*w - 14],\ [331, 331, -3/2*w^2 + 5/2*w + 13],\ [349, 349, -w^3 + 3/2*w^2 + 11/2*w - 1],\ [349, 349, w^3 - 5/2*w^2 - 13/2*w + 14],\ [359, 359, -w^3 + 5/2*w^2 + 11/2*w - 14],\ [359, 359, w^3 - 1/2*w^2 - 15/2*w - 7],\ [361, 19, 2*w^2 - 2*w - 15],\ [361, 19, -2*w^2 + 2*w + 13],\ [379, 379, 5/2*w^2 - 3/2*w - 16],\ [379, 379, 5/2*w^2 - 7/2*w - 15],\ [389, 389, 7/2*w^2 - 1/2*w - 26],\ [389, 389, 1/2*w^3 - 3/2*w^2 - 5*w + 5],\ [389, 389, 1/2*w^3 + 2*w^2 - 11/2*w - 18],\ [389, 389, 3/2*w^3 - 1/2*w^2 - 13*w - 15],\ [409, 409, -w^3 + 7/2*w^2 + 9/2*w - 19],\ [409, 409, w^3 + 1/2*w^2 - 17/2*w - 12],\ [439, 439, -1/2*w^3 + 5/2*w^2 + w - 15],\ [439, 439, 1/2*w^3 + w^2 - 9/2*w - 12],\ [461, 461, 1/2*w^3 + 2*w^2 - 15/2*w - 18],\ [461, 461, -1/2*w^3 + 7/2*w^2 + 2*w - 23],\ [479, 479, -1/2*w^3 + 2*w^2 + 7/2*w - 10],\ [479, 479, 1/2*w^3 - 2*w^2 - 5/2*w + 7],\ [491, 491, -2*w^3 + 1/2*w^2 + 29/2*w - 1],\ [491, 491, 2*w^3 - 11/2*w^2 - 19/2*w + 12],\ [499, 499, -w^3 + 5/2*w^2 + 13/2*w - 13],\ [499, 499, w^3 - 1/2*w^2 - 17/2*w - 5],\ [509, 509, -w^3 + 3/2*w^2 + 15/2*w - 2],\ [509, 509, w^3 - 3/2*w^2 - 15/2*w + 6],\ [521, 521, -1/2*w^3 + 2*w^2 + 9/2*w - 15],\ [521, 521, 1/2*w^3 + 1/2*w^2 - 7*w - 9],\ [529, 23, -w^3 + 2*w^2 + 5*w - 9],\ [529, 23, -3/2*w^2 + 7/2*w + 12],\ [541, 541, 3/2*w^3 + 1/2*w^2 - 14*w - 17],\ [541, 541, -3/2*w^3 + 5*w^2 + 17/2*w - 29],\ [569, 569, -2*w^3 + 1/2*w^2 + 35/2*w + 18],\ [569, 569, -w^3 - 5/2*w^2 + 27/2*w + 27],\ [571, 571, -w^3 + w^2 + 8*w + 7],\ [571, 571, -1/2*w^3 + 2*w^2 + 3/2*w - 4],\ [571, 571, 1/2*w^3 + 1/2*w^2 - 4*w - 1],\ [571, 571, -4*w^3 - 7/2*w^2 + 91/2*w + 68],\ [599, 599, -1/2*w^3 - 5/2*w^2 + 10*w + 21],\ [599, 599, 2*w^3 + 5/2*w^2 - 47/2*w - 37],\ [599, 599, 2*w^3 - 17/2*w^2 - 25/2*w + 56],\ [599, 599, -1/2*w^3 + 4*w^2 + 7/2*w - 28],\ [601, 601, -w^3 - 3/2*w^2 + 23/2*w + 18],\ [601, 601, 1/2*w^3 + 7/2*w^2 - 5*w - 27],\ [601, 601, 1/2*w^3 - 5*w^2 + 7/2*w + 28],\ [601, 601, 2*w^3 - 3*w^2 - 13*w + 21],\ [619, 619, -w^3 + 5/2*w^2 + 9/2*w - 8],\ [619, 619, w^3 - 1/2*w^2 - 13/2*w - 2],\ [631, 631, -5/2*w^3 + 1/2*w^2 + 18*w - 1],\ [631, 631, -5/2*w^3 + 7*w^2 + 23/2*w - 15],\ [641, 641, 5/2*w^2 - 1/2*w - 20],\ [641, 641, -5/2*w^2 + 9/2*w + 18],\ [659, 659, w^3 - 7/2*w^2 - 15/2*w + 28],\ [659, 659, w^3 + 2*w^2 - 11*w - 21],\ [661, 661, -w^3 + 15/2*w^2 + 11/2*w - 52],\ [661, 661, -3/2*w^3 + 1/2*w^2 + 13*w + 5],\ [661, 661, 3/2*w^3 - 4*w^2 - 19/2*w + 17],\ [661, 661, -w^3 - 9/2*w^2 + 35/2*w + 40],\ [691, 691, 2*w^3 - 9/2*w^2 - 21/2*w + 5],\ [691, 691, -5/2*w^3 - w^2 + 55/2*w + 37],\ [701, 701, w^3 - 2*w^2 - 7*w + 3],\ [701, 701, w^3 - w^2 - 8*w + 5],\ [709, 709, -11/2*w^2 + 3/2*w + 40],\ [709, 709, -3/2*w^3 - 3/2*w^2 + 16*w + 23],\ [739, 739, 1/2*w^3 - 9/2*w^2 + 3*w + 25],\ [739, 739, 1/2*w^3 + 3*w^2 - 9/2*w - 24],\ [751, 751, -7/2*w^3 + 12*w^2 + 47/2*w - 83],\ [751, 751, -3/2*w^3 + 23/2*w + 3],\ [751, 751, -3/2*w^3 + 9/2*w^2 + 7*w - 13],\ [751, 751, 7/2*w^3 + 3/2*w^2 - 37*w - 51],\ [761, 761, -3/2*w^3 - 1/2*w^2 + 14*w + 19],\ [761, 761, -w^3 + 3/2*w^2 + 15/2*w - 4],\ [761, 761, -3/2*w^3 + 5*w^2 + 17/2*w - 31],\ [769, 769, -3*w^3 - 5/2*w^2 + 69/2*w + 51],\ [769, 769, -1/2*w^3 - 4*w^2 + 9/2*w + 27],\ [769, 769, -w^3 - 5/2*w^2 + 29/2*w + 25],\ [769, 769, 3*w^3 - 23/2*w^2 - 41/2*w + 80],\ [809, 809, 1/2*w^3 + 2*w^2 - 13/2*w - 17],\ [809, 809, 1/2*w^3 - 7/2*w^2 - w + 21],\ [821, 821, 1/2*w^3 - 1/2*w^2 - 6*w + 3],\ [821, 821, -1/2*w^3 + w^2 + 11/2*w - 3],\ [829, 829, -3/2*w^3 + 3*w^2 + 23/2*w - 10],\ [829, 829, -w^3 + 2*w^2 + 5*w + 1],\ [829, 829, 7/2*w^2 - 3/2*w - 28],\ [829, 829, 3/2*w^3 - 3/2*w^2 - 13*w + 3],\ [839, 839, -w^3 - 7/2*w^2 + 17/2*w + 27],\ [839, 839, 2*w^3 + 1/2*w^2 - 43/2*w - 27],\ [839, 839, 2*w^3 - 13/2*w^2 - 29/2*w + 46],\ [839, 839, -w^3 - 3/2*w^2 + 19/2*w + 14],\ [841, 29, 5/2*w^2 - 5/2*w - 19],\ [841, 29, 5/2*w^2 - 5/2*w - 16],\ [859, 859, 1/2*w^3 + w^2 - 5/2*w - 12],\ [859, 859, w^3 + 3/2*w^2 - 19/2*w - 19],\ [859, 859, -w^3 + 9/2*w^2 + 7/2*w - 26],\ [859, 859, 1/2*w^3 - 5/2*w^2 + w + 13],\ [881, 881, -1/2*w^3 + 1/2*w^2 + 6*w + 1],\ [881, 881, 1/2*w^3 - w^2 - 11/2*w + 7],\ [911, 911, -1/2*w^3 + 5/2*w^2 + 3*w - 13],\ [911, 911, 1/2*w^3 + w^2 - 13/2*w - 8],\ [941, 941, -2*w^3 + 7/2*w^2 + 27/2*w - 21],\ [941, 941, 3/2*w^3 - 7*w^2 - 21/2*w + 51],\ [941, 941, 3/2*w^3 + 5/2*w^2 - 20*w - 35],\ [941, 941, -2*w^3 + 13/2*w^2 + 29/2*w - 48],\ [961, 31, -w^2 + w + 13],\ [1009, 1009, -5/2*w^2 - 1/2*w + 18],\ [1009, 1009, 3/2*w^3 - 3/2*w^2 - 12*w - 5],\ [1021, 1021, w^3 + w^2 - 10*w - 19],\ [1021, 1021, w^3 - 5/2*w^2 - 9/2*w + 12],\ [1031, 1031, -1/2*w^3 + 3/2*w^2 + 5*w - 9],\ [1031, 1031, -w^3 + 3/2*w^2 + 13/2*w - 2],\ [1049, 1049, -3/2*w^3 - 1/2*w^2 + 16*w + 23],\ [1049, 1049, -2*w^3 + 9/2*w^2 + 23/2*w - 6],\ [1049, 1049, -2*w^3 + 3/2*w^2 + 29/2*w - 8],\ [1049, 1049, 3/2*w^3 - 5*w^2 - 21/2*w + 37],\ [1051, 1051, -2*w^3 + 11/2*w^2 + 17/2*w - 10],\ [1051, 1051, -3*w^3 - 1/2*w^2 + 59/2*w + 36],\ [1051, 1051, -3*w^3 + 19/2*w^2 + 39/2*w - 62],\ [1051, 1051, 2*w^3 - 1/2*w^2 - 27/2*w + 2],\ [1061, 1061, 11/2*w^2 - 3/2*w - 38],\ [1061, 1061, 11/2*w^2 - 19/2*w - 34],\ [1069, 1069, 1/2*w^3 - 4*w^2 - 5/2*w + 25],\ [1069, 1069, 2*w^3 - 20*w - 25],\ [1069, 1069, -2*w^3 + 6*w^2 + 14*w - 43],\ [1069, 1069, 1/2*w^3 + 5/2*w^2 - 9*w - 19],\ [1109, 1109, -5/2*w^3 + 13/2*w^2 + 12*w - 13],\ [1109, 1109, -5/2*w^3 + w^2 + 35/2*w - 3],\ [1151, 1151, 13/2*w^2 - 3/2*w - 46],\ [1151, 1151, 1/2*w^3 + 3/2*w^2 - 5*w - 17],\ [1151, 1151, 1/2*w^3 - 3*w^2 - 1/2*w + 20],\ [1151, 1151, 13/2*w^2 - 23/2*w - 41],\ [1171, 1171, w^3 - 3/2*w^2 - 13/2*w + 12],\ [1171, 1171, 1/2*w^3 - 1/2*w^2 - 6*w + 1],\ [1171, 1171, -1/2*w^3 + w^2 + 11/2*w - 5],\ [1171, 1171, -1/2*w^3 + 5*w^2 - 7/2*w - 26],\ [1201, 1201, 1/2*w^3 + 1/2*w^2 - 6*w - 3],\ [1201, 1201, -1/2*w^3 + 2*w^2 + 7/2*w - 8],\ [1229, 1229, 1/2*w^3 + 5/2*w^2 - 8*w - 21],\ [1229, 1229, -1/2*w^3 + 4*w^2 + 3/2*w - 26],\ [1249, 1249, -w^3 + 7/2*w^2 + 9/2*w - 12],\ [1249, 1249, w^3 + 1/2*w^2 - 17/2*w - 5],\ [1279, 1279, 1/2*w^3 + 3/2*w^2 - 3*w - 15],\ [1279, 1279, -1/2*w^3 + 3*w^2 - 3/2*w - 16],\ [1289, 1289, 5/2*w^2 - 9/2*w - 19],\ [1289, 1289, w^3 - 9/2*w^2 - 15/2*w + 32],\ [1289, 1289, -w^3 - 3/2*w^2 + 27/2*w + 21],\ [1289, 1289, 5/2*w^2 - 1/2*w - 21],\ [1291, 1291, -1/2*w^3 + 5*w^2 - 9/2*w - 23],\ [1291, 1291, 1/2*w^3 + 7/2*w^2 - 4*w - 23],\ [1301, 1301, -3/2*w^3 + 2*w^2 + 21/2*w - 10],\ [1301, 1301, -3/2*w^3 + 5/2*w^2 + 10*w - 1],\ [1319, 1319, 4*w^3 - 29/2*w^2 - 49/2*w + 93],\ [1319, 1319, -4*w^3 - 5/2*w^2 + 83/2*w + 58],\ [1321, 1321, -17/2*w^2 + 31/2*w + 52],\ [1321, 1321, 17/2*w^2 - 3/2*w - 59],\ [1361, 1361, -3*w^3 - 7/2*w^2 + 71/2*w + 58],\ [1361, 1361, -3/2*w^3 - 3*w^2 + 39/2*w + 34],\ [1369, 37, 3/2*w^3 - 1/2*w^2 - 13*w - 17],\ [1369, 37, 3/2*w^3 + 1/2*w^2 - 11*w - 3],\ [1381, 1381, w^3 - 5*w^2 - 2*w + 27],\ [1381, 1381, w^3 + 2*w^2 - 9*w - 21],\ [1399, 1399, w^3 + 5/2*w^2 - 19/2*w - 25],\ [1399, 1399, w^3 - 11/2*w^2 - 3/2*w + 31],\ [1439, 1439, -2*w^3 + 13/2*w^2 + 23/2*w - 40],\ [1439, 1439, 4*w^3 + 3*w^2 - 43*w - 65],\ [1451, 1451, 1/2*w^3 + 9/2*w^2 - 5*w - 35],\ [1451, 1451, -1/2*w^3 + 6*w^2 - 11/2*w - 35],\ [1459, 1459, -3/2*w^3 + 9/2*w^2 + 9*w - 25],\ [1459, 1459, -3/2*w^3 + 1/2*w^2 + 10*w + 7],\ [1471, 1471, 3/2*w^3 - 11/2*w^2 - 7*w + 31],\ [1471, 1471, -3/2*w^3 - w^2 + 27/2*w + 20],\ [1489, 1489, -3*w^3 - 3*w^2 + 34*w + 51],\ [1489, 1489, 1/2*w^3 + 5/2*w^2 - 6*w - 25],\ [1489, 1489, -1/2*w^3 + 4*w^2 - 1/2*w - 28],\ [1489, 1489, 3*w^3 - 12*w^2 - 19*w + 79],\ [1499, 1499, 1/2*w^3 - 7/2*w^2 + 2*w + 19],\ [1499, 1499, 1/2*w^3 + 5/2*w^2 - 6*w - 21],\ [1499, 1499, -1/2*w^3 + 4*w^2 - 1/2*w - 24],\ [1499, 1499, -w^3 + 5/2*w^2 + 11/2*w - 17],\ [1511, 1511, -2*w^3 + 15/2*w^2 + 17/2*w - 37],\ [1511, 1511, -2*w^3 - 3/2*w^2 + 35/2*w + 23],\ [1531, 1531, 1/2*w^3 - 3*w^2 - 9/2*w + 16],\ [1531, 1531, -2*w^3 + 9/2*w^2 + 23/2*w - 8],\ [1531, 1531, -2*w^3 + 3/2*w^2 + 29/2*w - 6],\ [1531, 1531, w^3 + 5/2*w^2 - 21/2*w - 25],\ [1549, 1549, -1/2*w^3 + 1/2*w^2 + 3*w - 7],\ [1549, 1549, 1/2*w^3 - w^2 - 5/2*w - 4],\ [1579, 1579, w^3 + 3/2*w^2 - 19/2*w - 13],\ [1579, 1579, -w^3 + 9/2*w^2 + 7/2*w - 20],\ [1609, 1609, -11/2*w^2 + 1/2*w + 37],\ [1609, 1609, 11/2*w^2 - 21/2*w - 32],\ [1619, 1619, 1/2*w^3 - 3/2*w^2 - w + 15],\ [1619, 1619, w^3 - 3/2*w^2 - 21/2*w + 1],\ [1621, 1621, -2*w^3 + 15/2*w^2 + 23/2*w - 49],\ [1621, 1621, 1/2*w^3 + 3/2*w^2 - 9*w - 19],\ [1669, 1669, 1/2*w^3 + 5/2*w^2 - 7*w - 23],\ [1669, 1669, 1/2*w^3 - 4*w^2 - 1/2*w + 27],\ [1699, 1699, -w^3 + 1/2*w^2 + 17/2*w - 2],\ [1699, 1699, -w^3 + 5/2*w^2 + 13/2*w - 6],\ [1709, 1709, 1/2*w^3 + 3/2*w^2 - 2*w - 15],\ [1709, 1709, -1/2*w^3 + 3*w^2 - 5/2*w - 15],\ [1721, 1721, 5/2*w^3 - w^2 - 45/2*w - 20],\ [1721, 1721, -5/2*w^3 + 13/2*w^2 + 17*w - 41],\ [1741, 1741, -w^3 + 5/2*w^2 + 13/2*w - 3],\ [1741, 1741, -5/2*w^3 - 3*w^2 + 61/2*w + 48],\ [1741, 1741, -5*w^3 + 35/2*w^2 + 65/2*w - 116],\ [1741, 1741, -w^3 + 5*w^2 + 6*w - 31],\ [1759, 1759, 4*w^3 - 16*w^2 - 26*w + 111],\ [1759, 1759, 3*w^3 + 3/2*w^2 - 61/2*w - 43],\ [1789, 1789, w^3 + 1/2*w^2 - 17/2*w - 14],\ [1789, 1789, -w^3 + 7/2*w^2 + 9/2*w - 21],\ [1801, 1801, w^3 + 5/2*w^2 - 23/2*w - 24],\ [1801, 1801, w^3 + 11/2*w^2 - 15/2*w - 38],\ [1831, 1831, 13/2*w^2 - 1/2*w - 46],\ [1831, 1831, -3/2*w^3 + 8*w^2 + 19/2*w - 53],\ [1831, 1831, 9/2*w^3 - 33/2*w^2 - 28*w + 109],\ [1831, 1831, -13/2*w^2 + 25/2*w + 40],\ [1861, 1861, 5/2*w^2 - 9/2*w - 8],\ [1861, 1861, 5/2*w^2 - 1/2*w - 10],\ [1871, 1871, -1/2*w^3 - 1/2*w^2 + 7*w + 15],\ [1871, 1871, -1/2*w^3 - 4*w^2 + 7/2*w + 26],\ [1879, 1879, 1/2*w^3 - 9/2*w^2 - w + 25],\ [1879, 1879, -w^3 - 5/2*w^2 + 23/2*w + 27],\ [1879, 1879, w^3 - 11/2*w^2 - 7/2*w + 35],\ [1879, 1879, 1/2*w^3 + 3*w^2 - 17/2*w - 20],\ [1889, 1889, w^3 + 5/2*w^2 - 25/2*w - 27],\ [1889, 1889, -w^3 + 11/2*w^2 + 9/2*w - 36],\ [1901, 1901, -3*w^3 - w^2 + 32*w + 41],\ [1901, 1901, 3*w^3 - 10*w^2 - 21*w + 69],\ [1931, 1931, 2*w^3 - 15/2*w^2 - 13/2*w + 26],\ [1931, 1931, -w^3 + 11/2*w^2 + 5/2*w - 31],\ [1951, 1951, -w^3 + 1/2*w^2 + 13/2*w + 7],\ [1951, 1951, 2*w^2 - 19],\ [1979, 1979, -1/2*w^3 + 4*w^2 + 1/2*w - 25],\ [1979, 1979, 7/2*w^3 + w^2 - 73/2*w - 47],\ [1979, 1979, 7/2*w^3 - 23/2*w^2 - 24*w + 79],\ [1979, 1979, 1/2*w^3 + 5/2*w^2 - 7*w - 21],\ [1999, 1999, -w^3 + 15/2*w^2 + 11/2*w - 54],\ [1999, 1999, -w^3 + 15/2*w^2 - 9/2*w - 37]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^8 - x^7 - 19*x^6 + 23*x^5 + 78*x^4 - 105*x^3 - 57*x^2 + 95*x - 23 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, 217/1951*e^7 - 116/1951*e^6 - 4168/1951*e^5 + 3105/1951*e^4 + 18551/1951*e^3 - 14798/1951*e^2 - 22718/1951*e + 12172/1951, -273/3902*e^7 + 83/3902*e^6 + 2433/1951*e^5 - 1607/1951*e^4 - 8428/1951*e^3 + 19435/3902*e^2 + 5861/3902*e - 8223/1951, 505/3902*e^7 - 225/3902*e^6 - 4715/1951*e^5 + 3087/1951*e^4 + 18992/1951*e^3 - 28333/3902*e^2 - 30509/3902*e + 9551/1951, -856/1951*e^7 + 53/1951*e^6 + 15965/1951*e^5 - 4732/1951*e^4 - 65509/1951*e^3 + 26843/1951*e^2 + 60063/1951*e - 21573/1951, 1, 505/1951*e^7 - 225/1951*e^6 - 9430/1951*e^5 + 6174/1951*e^4 + 37984/1951*e^3 - 28333/1951*e^2 - 34411/1951*e + 19102/1951, -173/3902*e^7 + 280/1951*e^6 + 4177/3902*e^5 - 5342/1951*e^4 - 13495/1951*e^3 + 44461/3902*e^2 + 19584/1951*e - 46719/3902, 2419/3902*e^7 - 421/3902*e^6 - 22566/1951*e^5 + 9444/1951*e^4 + 92488/1951*e^3 - 106619/3902*e^2 - 171423/3902*e + 45870/1951, -173/1951*e^7 + 560/1951*e^6 + 4177/1951*e^5 - 10684/1951*e^4 - 26990/1951*e^3 + 42510/1951*e^2 + 45021/1951*e - 35013/1951, -1107/3902*e^7 + 179/1951*e^6 + 21811/3902*e^5 - 5380/1951*e^4 - 51584/1951*e^3 + 50379/3902*e^2 + 67315/1951*e - 50415/3902, 473/1951*e^7 - 209/3902*e^6 - 18341/3902*e^5 + 3882/1951*e^4 + 41461/1951*e^3 - 20109/1951*e^2 - 79447/3902*e + 30811/3902, -137/3902*e^7 + 639/1951*e^6 + 4007/3902*e^5 - 11369/1951*e^4 - 15085/1951*e^3 + 82033/3902*e^2 + 27023/1951*e - 57071/3902, 2033/3902*e^7 + 59/1951*e^6 - 37673/3902*e^5 + 4156/1951*e^4 + 75719/1951*e^3 - 69849/3902*e^2 - 61204/1951*e + 80257/3902, 2141/3902*e^7 - 815/1951*e^6 - 42085/3902*e^5 + 19242/1951*e^4 + 96312/1951*e^3 - 167841/3902*e^2 - 101319/1951*e + 127241/3902, -1477/1951*e^7 + 349/1951*e^6 + 27677/1951*e^5 - 12386/1951*e^4 - 114057/1951*e^3 + 57674/1951*e^2 + 104847/1951*e - 42003/1951, 3669/3902*e^7 + 332/1951*e^6 - 68377/3902*e^5 + 2752/1951*e^4 + 141333/1951*e^3 - 80591/3902*e^2 - 130685/1951*e + 81091/3902, 415/3902*e^7 - 69/3902*e^6 - 3527/1951*e^5 + 1571/1951*e^4 + 11261/1951*e^3 - 13007/3902*e^2 - 15027/3902*e - 4823/1951, -4317/3902*e^7 + 1010/1951*e^6 + 83143/3902*e^5 - 26934/1951*e^4 - 182949/1951*e^3 + 243225/3902*e^2 + 187981/1951*e - 206915/3902, 1095/3902*e^7 - 949/1951*e^6 - 23055/3902*e^5 + 19095/1951*e^4 + 59918/1951*e^3 - 152649/3902*e^2 - 78249/1951*e + 111095/3902, 271/1951*e^7 - 29/3902*e^6 - 10797/3902*e^5 + 632/1951*e^4 + 25487/1951*e^3 + 4491/1951*e^2 - 41773/3902*e - 39879/3902, 1025/1951*e^7 + 999/3902*e^6 - 36561/3902*e^5 - 3405/1951*e^4 + 66839/1951*e^3 - 7844/1951*e^2 - 88827/3902*e + 20307/3902, 844/1951*e^7 - 1235/3902*e^6 - 32467/3902*e^5 + 14603/1951*e^4 + 70471/1951*e^3 - 62779/1951*e^2 - 142401/3902*e + 80613/3902, -75/1951*e^7 - 1691/3902*e^6 + 2009/3902*e^5 + 14382/1951*e^4 - 3130/1951*e^3 - 47059/1951*e^2 + 5643/3902*e + 34679/3902, -333/3902*e^7 - 882/1951*e^6 + 4499/3902*e^5 + 14291/1951*e^4 - 1876/1951*e^3 - 78303/3902*e^2 - 9793/1951*e - 23255/3902, -197/3902*e^7 + 691/1951*e^6 + 5591/3902*e^5 - 11079/1951*e^4 - 20239/1951*e^3 + 50629/3902*e^2 + 34785/1951*e + 20013/3902, -1173/3902*e^7 - 154/1951*e^6 + 22773/3902*e^5 + 792/1951*e^4 - 52571/1951*e^3 - 6797/3902*e^2 + 59855/1951*e + 10185/3902, -242/1951*e^7 - 491/1951*e^6 + 2877/1951*e^5 + 5591/1951*e^4 + 6419/1951*e^3 - 2189/1951*e^2 - 51455/1951*e - 11920/1951, 2895/3902*e^7 - 558/1951*e^6 - 54967/3902*e^5 + 16248/1951*e^4 + 115037/1951*e^3 - 150911/3902*e^2 - 92597/1951*e + 92951/3902, -2254/1951*e^7 + 135/1951*e^6 + 42727/1951*e^5 - 12679/1951*e^4 - 183943/1951*e^3 + 77871/1951*e^2 + 187262/1951*e - 73503/1951, -1369/3902*e^7 + 276/1951*e^6 + 23265/3902*e^5 - 8666/1951*e^4 - 33509/1951*e^3 + 86497/3902*e^2 - 2324/1951*e - 57451/3902, 349/3902*e^7 + 608/1951*e^6 - 4141/3902*e^5 - 9816/1951*e^4 - 3383/1951*e^3 + 66387/3902*e^2 + 26973/1951*e - 64155/3902, 535/1951*e^7 - 277/1951*e^6 - 10222/1951*e^5 + 7835/1951*e^4 + 47040/1951*e^3 - 39945/1951*e^2 - 77291/1951*e + 48845/1951, -1421/1951*e^7 + 382/1951*e^6 + 26979/1951*e^5 - 12277/1951*e^4 - 115752/1951*e^3 + 53037/1951*e^2 + 113900/1951*e - 24072/1951, -251/3902*e^7 - 823/1951*e^6 + 3895/3902*e^5 + 14545/1951*e^4 - 6148/1951*e^3 - 107181/3902*e^2 + 8994/1951*e + 58953/3902, 1574/1951*e^7 - 257/1951*e^6 - 30628/1951*e^5 + 10798/1951*e^4 + 139306/1951*e^3 - 57240/1951*e^2 - 149194/1951*e + 44459/1951, -2111/1951*e^7 + 1205/3902*e^6 + 80635/3902*e^5 - 21215/1951*e^4 - 175764/1951*e^3 + 117209/1951*e^2 + 372193/3902*e - 235967/3902, -329/3902*e^7 + 2001/3902*e^6 + 2782/1951*e^5 - 18245/1951*e^4 - 4654/1951*e^3 + 123573/3902*e^2 - 20751/3902*e - 25968/1951, -1721/3902*e^7 - 1049/3902*e^6 + 14523/1951*e^5 + 6042/1951*e^4 - 42675/1951*e^3 - 45453/3902*e^2 - 1629/3902*e + 28496/1951, 1355/1951*e^7 - 145/3902*e^6 - 50083/3902*e^5 + 9013/1951*e^4 + 100121/1951*e^3 - 67291/1951*e^2 - 169845/3902*e + 136177/3902, -1647/3902*e^7 + 647/1951*e^6 + 32165/3902*e^5 - 14476/1951*e^4 - 70656/1951*e^3 + 118923/3902*e^2 + 63035/1951*e - 101941/3902, -3889/3902*e^7 + 509/1951*e^6 + 74185/3902*e^5 - 17947/1951*e^4 - 160231/1951*e^3 + 191759/3902*e^2 + 151992/1951*e - 140525/3902, -3331/3902*e^7 + 1196/1951*e^6 + 65697/3902*e^5 - 28448/1951*e^4 - 153660/1951*e^3 + 247355/3902*e^2 + 182428/1951*e - 199529/3902, 28/1951*e^7 - 959/1951*e^6 - 349/1951*e^5 + 16638/1951*e^4 - 5725/1951*e^3 - 54020/1951*e^2 + 28914/1951*e + 17745/1951, 661/3902*e^7 - 833/1951*e^6 - 14719/3902*e^5 + 15990/1951*e^4 + 41367/1951*e^3 - 126955/3902*e^2 - 53580/1951*e + 106261/3902, 220/1951*e^7 + 269/1951*e^6 - 3857/1951*e^5 - 2777/1951*e^4 + 14384/1951*e^3 - 3863/1951*e^2 - 9447/1951*e + 26267/1951, 1514/1951*e^7 - 2257/3902*e^6 - 60039/3902*e^5 + 25035/1951*e^4 + 138753/1951*e^3 - 96448/1951*e^2 - 292703/3902*e + 116271/3902, -2481/1951*e^7 + 5089/3902*e^6 + 96269/3902*e^5 - 54057/1951*e^4 - 210065/1951*e^3 + 206446/1951*e^2 + 406275/3902*e - 258163/3902, 1535/3902*e^7 + 1271/1951*e^6 - 26867/3902*e^5 - 18800/1951*e^4 + 50890/1951*e^3 + 112765/3902*e^2 - 48676/1951*e - 70491/3902, -1017/3902*e^7 + 2052/1951*e^6 + 23337/3902*e^5 - 37031/1951*e^4 - 65314/1951*e^3 + 249663/3902*e^2 + 84937/1951*e - 107511/3902, -6231/3902*e^7 + 1108/1951*e^6 + 118845/3902*e^5 - 33291/1951*e^4 - 254494/1951*e^3 + 313707/3902*e^2 + 236977/1951*e - 248337/3902, -3695/1951*e^7 + 1202/1951*e^6 + 70234/1951*e^5 - 37119/1951*e^4 - 299229/1951*e^3 + 175068/1951*e^2 + 283575/1951*e - 133662/1951, 2299/3902*e^7 - 213/3902*e^6 - 20982/1951*e^5 + 6122/1951*e^4 + 80229/1951*e^3 - 52367/3902*e^2 - 128669/3902*e - 5812/1951, -3645/3902*e^7 + 4367/3902*e^6 + 36408/1951*e^5 - 45790/1951*e^4 - 169707/1951*e^3 + 359269/3902*e^2 + 369489/3902*e - 117809/1951, -1353/1951*e^7 + 4/1951*e^6 + 25574/1951*e^5 - 6431/1951*e^4 - 106801/1951*e^3 + 47267/1951*e^2 + 84340/1951*e - 53164/1951, 1284/1951*e^7 - 1055/1951*e^6 - 24923/1951*e^5 + 22706/1951*e^4 + 108994/1951*e^3 - 82211/1951*e^2 - 102776/1951*e + 41139/1951, -3961/1951*e^7 + 1533/1951*e^6 + 74525/1951*e^5 - 44953/1951*e^4 - 308249/1951*e^3 + 210263/1951*e^2 + 272277/1951*e - 158841/1951, 8271/3902*e^7 - 925/1951*e^6 - 157093/3902*e^5 + 35137/1951*e^4 + 336082/1951*e^3 - 377551/3902*e^2 - 333099/1951*e + 347175/3902, 1661/1951*e^7 - 798/1951*e^6 - 31364/1951*e^5 + 21663/1951*e^4 + 129670/1951*e^3 - 101060/1951*e^2 - 111613/1951*e + 84475/1951, 2525/3902*e^7 + 413/1951*e^6 - 49101/3902*e^5 - 2124/1951*e^4 + 114470/1951*e^3 - 16801/3902*e^2 - 135778/1951*e + 62343/3902, 2495/3902*e^7 - 1073/3902*e^6 - 25130/1951*e^5 + 15580/1951*e^4 + 123599/1951*e^3 - 161269/3902*e^2 - 300863/3902*e + 78732/1951, -979/1951*e^7 + 1703/3902*e^6 + 39595/3902*e^5 - 21102/1951*e^4 - 97566/1951*e^3 + 109180/1951*e^2 + 259083/3902*e - 209779/3902, -7945/3902*e^7 - 268/1951*e^6 + 149267/3902*e^5 - 13951/1951*e^4 - 316663/1951*e^3 + 239141/3902*e^2 + 330986/1951*e - 307383/3902, 2800/1951*e^7 - 2252/1951*e^6 - 54410/1951*e^5 + 50323/1951*e^4 + 239116/1951*e^3 - 198683/1951*e^2 - 230200/1951*e + 123954/1951, 4264/1951*e^7 - 1385/3902*e^6 - 162317/3902*e^5 + 32269/1951*e^4 + 351720/1951*e^3 - 184731/1951*e^2 - 733733/3902*e + 326167/3902, 2368/1951*e^7 - 4177/3902*e^6 - 91083/3902*e^5 + 46695/1951*e^4 + 195334/1951*e^3 - 189111/1951*e^2 - 374595/3902*e + 295403/3902, 2468/1951*e^7 - 636/1951*e^6 - 47206/1951*e^5 + 19715/1951*e^4 + 202759/1951*e^3 - 78241/1951*e^2 - 184231/1951*e + 32560/1951, 387/3902*e^7 + 445/1951*e^6 - 6705/3902*e^5 - 8699/1951*e^4 + 11197/1951*e^3 + 95641/3902*e^2 - 7338/1951*e - 124941/3902, -6425/3902*e^7 + 81/3902*e^6 + 59447/1951*e^5 - 16095/1951*e^4 - 238772/1951*e^3 + 223093/3902*e^2 + 420225/3902*e - 113943/1951, 6241/3902*e^7 + 2319/3902*e^6 - 58579/1951*e^5 - 7078/1951*e^4 + 249500/1951*e^3 - 35333/3902*e^2 - 503205/3902*e + 43932/1951, 1978/1951*e^7 - 437/1951*e^6 - 36221/1951*e^5 + 17298/1951*e^4 + 140038/1951*e^3 - 90832/1951*e^2 - 108828/1951*e + 66374/1951, -3387/1951*e^7 + 408/1951*e^6 + 64444/1951*e^5 - 21887/1951*e^4 - 278311/1951*e^3 + 119324/1951*e^2 + 271910/1951*e - 102351/1951, -4571/3902*e^7 - 11/3902*e^6 + 42388/1951*e^5 - 11399/1951*e^4 - 174332/1951*e^3 + 175835/3902*e^2 + 353365/3902*e - 124926/1951, 2251/3902*e^7 - 2211/1951*e^6 - 44989/3902*e^5 + 43423/1951*e^4 + 103810/1951*e^3 - 320975/3902*e^2 - 109046/1951*e + 182321/3902, -1223/3902*e^7 - 761/1951*e^6 + 24093/3902*e^5 + 11439/1951*e^4 - 58817/1951*e^3 - 75889/3902*e^2 + 53967/1951*e + 61415/3902, 3417/1951*e^7 - 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76715/1951*e^4 - 318284/1951*e^3 + 704663/3902*e^2 + 344866/1951*e - 487745/3902, 13187/3902*e^7 - 6096/1951*e^6 - 254879/3902*e^5 + 137541/1951*e^4 + 556633/1951*e^3 - 1153213/3902*e^2 - 536854/1951*e + 702025/3902, -2627/3902*e^7 - 3056/1951*e^6 + 42429/3902*e^5 + 47490/1951*e^4 - 57288/1951*e^3 - 304263/3902*e^2 - 25446/1951*e + 172493/3902, -2257/1951*e^7 - 4152/1951*e^6 + 42416/1951*e^5 + 61488/1951*e^4 - 197335/1951*e^3 - 171086/1951*e^2 + 261786/1951*e + 56776/1951, -5520/1951*e^7 - 187/1951*e^6 + 102806/1951*e^5 - 18827/1951*e^4 - 419615/1951*e^3 + 117323/1951*e^2 + 378570/1951*e - 72344/1951, -3/3902*e^7 + 2734/1951*e^6 - 311/3902*e^5 - 49736/1951*e^4 + 6961/1951*e^3 + 387069/3902*e^2 + 21654/1951*e - 345765/3902, 6827/1951*e^7 - 3119/1951*e^6 - 133799/1951*e^5 + 82932/1951*e^4 + 617624/1951*e^3 - 379084/1951*e^2 - 696314/1951*e + 366569/1951, -10175/3902*e^7 + 2315/1951*e^6 + 192531/3902*e^5 - 62353/1951*e^4 - 402866/1951*e^3 + 535209/3902*e^2 + 389906/1951*e - 262273/3902, -8651/3902*e^7 + 604/1951*e^6 + 167125/3902*e^5 - 34601/1951*e^4 - 382381/1951*e^3 + 467407/3902*e^2 + 453795/1951*e - 519715/3902, 7393/1951*e^7 - 68/1951*e^6 - 142108/1951*e^5 + 35189/1951*e^4 + 633311/1951*e^3 - 261161/1951*e^2 - 670939/1951*e + 304831/1951, 2331/1951*e^7 + 642/1951*e^6 - 41248/1951*e^5 - 3023/1951*e^4 + 145275/1951*e^3 + 13547/1951*e^2 - 77508/1951*e - 88894/1951, -8763/3902*e^7 + 571/1951*e^6 + 164619/3902*e^5 - 32759/1951*e^4 - 341666/1951*e^3 + 410347/3902*e^2 + 304270/1951*e - 286339/3902, -5448/1951*e^7 - 2653/1951*e^6 + 100515/1951*e^5 + 23399/1951*e^4 - 404514/1951*e^3 - 22143/1951*e^2 + 343943/1951*e + 14257/1951, 5349/3902*e^7 - 3075/1951*e^6 - 112729/3902*e^5 + 66819/1951*e^4 + 299302/1951*e^3 - 602097/3902*e^2 - 412404/1951*e + 626825/3902, -489/3902*e^7 + 2765/1951*e^6 + 11739/3902*e^5 - 51289/1951*e^4 - 35957/1951*e^3 + 391009/3902*e^2 + 74381/1951*e - 209915/3902, 6649/3902*e^7 - 2901/1951*e^6 - 123637/3902*e^5 + 65088/1951*e^4 + 241235/1951*e^3 - 522585/3902*e^2 - 183227/1951*e + 352287/3902, -3843/1951*e^7 + 4320/1951*e^6 + 77653/1951*e^5 - 91617/1951*e^4 - 372650/1951*e^3 + 361380/1951*e^2 + 422279/1951*e - 182584/1951, -2858/1951*e^7 + 3263/1951*e^6 + 55551/1951*e^5 - 70573/1951*e^4 - 246349/1951*e^3 + 297482/1951*e^2 + 294892/1951*e - 229972/1951, 6602/1951*e^7 - 2729/1951*e^6 - 123957/1951*e^5 + 77303/1951*e^4 + 512635/1951*e^3 - 346622/1951*e^2 - 464460/1951*e + 206904/1951, 865/3902*e^7 - 1400/1951*e^6 - 16983/3902*e^5 + 28661/1951*e^4 + 32357/1951*e^3 - 241815/3902*e^2 + 19140/1951*e + 143849/3902, 10537/1951*e^7 - 445/1951*e^6 - 200527/1951*e^5 + 57474/1951*e^4 + 878459/1951*e^3 - 382417/1951*e^2 - 938897/1951*e + 399018/1951, 3581/3902*e^7 - 112/1951*e^6 - 68395/3902*e^5 + 6429/1951*e^4 + 151723/1951*e^3 - 22857/3902*e^2 - 193959/1951*e - 91739/3902] 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,-1/2*w^3 - 1/2*w^2 + 5*w + 7])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]