/* 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, -6, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([15, 15, -w^3 + 6*w - 1]) primes_array = [ [3, 3, w + 1],\ [5, 5, -w^3 + 5*w + 2],\ [5, 5, w - 1],\ [11, 11, -w^3 + 5*w],\ [13, 13, -w^3 + w^2 + 6*w - 3],\ [16, 2, 2],\ [19, 19, 2*w^3 - w^2 - 11*w + 2],\ [25, 5, -w^2 + w + 3],\ [27, 3, w^3 - w^2 - 5*w + 4],\ [31, 31, -w - 3],\ [37, 37, -w^3 - w^2 + 6*w + 4],\ [41, 41, w^3 + w^2 - 6*w - 5],\ [43, 43, w^3 - 7*w - 2],\ [47, 47, -2*w^3 + 11*w + 2],\ [61, 61, w^2 - 3],\ [67, 67, w^2 + w - 4],\ [79, 79, -4*w^3 + 2*w^2 + 22*w - 9],\ [97, 97, -3*w^3 + 2*w^2 + 19*w - 6],\ [97, 97, -w^3 + 6*w - 3],\ [97, 97, -3*w^3 + 16*w],\ [97, 97, -w^3 + w^2 + 4*w - 3],\ [101, 101, -2*w^3 + w^2 + 11*w - 6],\ [103, 103, w^3 - w^2 - 7*w],\ [109, 109, -w^3 - w^2 + 6*w + 2],\ [121, 11, 2*w^3 - 11*w + 1],\ [127, 127, -2*w^3 + w^2 + 13*w - 1],\ [127, 127, w^3 - w^2 - 6*w - 2],\ [157, 157, -2*w^3 + 2*w^2 + 10*w - 7],\ [157, 157, w - 4],\ [163, 163, 2*w^3 - w^2 - 13*w + 3],\ [173, 173, -2*w^3 + w^2 + 13*w - 6],\ [173, 173, 2*w^3 - 12*w + 1],\ [173, 173, 2*w^3 - 11*w + 2],\ [173, 173, w^2 + w - 5],\ [179, 179, -2*w^3 + 10*w + 3],\ [181, 181, -w^3 - w^2 + 7*w + 8],\ [191, 191, w^3 - 5*w - 5],\ [191, 191, 2*w^3 - w^2 - 9*w - 1],\ [193, 193, -3*w^3 + 3*w^2 + 19*w - 7],\ [197, 197, -w^3 + w^2 + 6*w - 7],\ [223, 223, w^3 + w^2 - 6*w + 1],\ [227, 227, 6*w^3 - 3*w^2 - 34*w + 9],\ [227, 227, w^3 + w^2 - 8*w],\ [233, 233, 2*w^3 - 13*w - 3],\ [233, 233, -w^3 + 2*w^2 + 4*w - 6],\ [239, 239, -2*w^3 + 10*w + 1],\ [239, 239, w^3 - 8*w - 2],\ [251, 251, -3*w^3 + w^2 + 18*w],\ [251, 251, -5*w^3 + 2*w^2 + 30*w - 11],\ [263, 263, -2*w^3 + w^2 + 10*w + 2],\ [269, 269, 3*w^3 - 18*w - 8],\ [271, 271, 2*w^3 + w^2 - 10*w - 2],\ [271, 271, -3*w^3 + 19*w],\ [277, 277, -w^3 + w^2 + 4*w - 8],\ [277, 277, 2*w^3 + w^2 - 14*w - 8],\ [281, 281, w^3 - 8*w],\ [307, 307, 3*w^3 - w^2 - 16*w + 2],\ [307, 307, 2*w^3 - w^2 - 9*w + 1],\ [307, 307, -2*w^3 + 2*w^2 + 13*w - 7],\ [307, 307, -w^3 + w^2 + 7*w - 6],\ [313, 313, -3*w^3 + w^2 + 15*w + 4],\ [317, 317, -4*w^3 + w^2 + 22*w - 3],\ [317, 317, 2*w^3 - w^2 - 10*w - 3],\ [337, 337, w^3 + w^2 - 4*w - 5],\ [349, 349, -2*w^3 - w^2 + 11*w + 3],\ [349, 349, -4*w^3 + 2*w^2 + 24*w - 11],\ [353, 353, 3*w^3 - w^2 - 17*w + 7],\ [353, 353, -3*w^3 - 2*w^2 + 17*w + 11],\ [367, 367, 2*w^3 - 11*w - 7],\ [373, 373, -w^3 + w^2 + 4*w - 5],\ [383, 383, -4*w^3 + 3*w^2 + 23*w - 9],\ [383, 383, 4*w^3 - w^2 - 22*w],\ [389, 389, w^2 - 2*w - 5],\ [401, 401, -3*w^3 + 2*w^2 + 16*w - 9],\ [401, 401, 2*w^3 - w^2 - 14*w - 1],\ [409, 409, 2*w^3 + 2*w^2 - 13*w - 9],\ [419, 419, -4*w^3 + 24*w + 7],\ [419, 419, 2*w^2 + 2*w - 7],\ [419, 419, -w^3 + 2*w^2 + 8*w - 6],\ [419, 419, 6*w^3 - 3*w^2 - 33*w + 13],\ [431, 431, 2*w^3 - w^2 - 12*w - 5],\ [439, 439, -3*w^3 + 2*w^2 + 18*w - 4],\ [439, 439, w^3 + 2*w^2 - 7*w - 3],\ [443, 443, 6*w^3 - 3*w^2 - 33*w + 7],\ [449, 449, -3*w^3 + w^2 + 14*w - 4],\ [457, 457, 2*w^3 - 9*w],\ [457, 457, 3*w^3 - w^2 - 16*w - 2],\ [479, 479, 3*w^3 - w^2 - 19*w + 4],\ [487, 487, -w^3 + w^2 + 4*w - 6],\ [491, 491, 3*w^3 + w^2 - 17*w - 5],\ [499, 499, 5*w^3 - 3*w^2 - 28*w + 8],\ [499, 499, 2*w^3 - w^2 - 12*w - 1],\ [503, 503, -2*w^3 - w^2 + 12*w + 3],\ [503, 503, w^3 - 3*w - 4],\ [509, 509, -3*w - 5],\ [509, 509, -4*w^3 + 3*w^2 + 25*w - 10],\ [523, 523, -2*w^3 + w^2 + 14*w - 6],\ [529, 23, 4*w^3 - 2*w^2 - 21*w + 5],\ [529, 23, -3*w^3 - w^2 + 15*w + 6],\ [557, 557, -2*w^3 + w^2 + 13*w + 2],\ [557, 557, 3*w^3 - 2*w^2 - 16*w + 3],\ [569, 569, 2*w^2 - w - 8],\ [587, 587, w^3 + 2*w^2 - 5*w - 16],\ [587, 587, -4*w^3 + w^2 + 25*w - 5],\ [599, 599, w^3 + 2*w^2 - 6*w - 5],\ [599, 599, -5*w^3 + 3*w^2 + 30*w - 15],\ [601, 601, w^3 - 6*w - 6],\ [607, 607, -w^3 + w^2 + 3*w - 4],\ [607, 607, -w^3 + 2*w - 3],\ [613, 613, 6*w^3 - 2*w^2 - 31*w + 11],\ [613, 613, w^3 + w^2 - 4*w - 6],\ [617, 617, 5*w^3 - w^2 - 30*w + 2],\ [617, 617, -2*w^3 + 2*w^2 + 9*w + 3],\ [619, 619, -w^3 + 2*w^2 + 6*w - 5],\ [619, 619, 2*w^3 - w^2 - 11*w - 3],\ [631, 631, -w^3 + 2*w^2 + 5*w - 5],\ [631, 631, -3*w^3 - w^2 + 18*w + 5],\ [647, 647, 6*w^3 - w^2 - 36*w + 2],\ [659, 659, 4*w^3 + w^2 - 24*w - 14],\ [661, 661, 2*w^2 - w - 4],\ [673, 673, 2*w^3 + w^2 - 14*w - 12],\ [677, 677, 3*w^3 + 2*w^2 - 16*w - 7],\ [677, 677, -3*w^3 + w^2 + 15*w + 1],\ [683, 683, 2*w^2 - 2*w - 9],\ [683, 683, 2*w^3 - 14*w + 1],\ [691, 691, 5*w^3 - 2*w^2 - 30*w + 6],\ [701, 701, -2*w^3 + w^2 + 12*w + 2],\ [701, 701, -5*w^3 + 2*w^2 + 26*w],\ [719, 719, 3*w^3 - 18*w + 1],\ [719, 719, 3*w^3 - w^2 - 19*w + 1],\ [727, 727, -3*w^2 - 2*w + 11],\ [727, 727, 2*w^3 + w^2 - 13*w - 2],\ [733, 733, 2*w^3 - 3*w^2 - 8*w + 5],\ [739, 739, -3*w^3 + 16*w - 6],\ [743, 743, -4*w^3 - w^2 + 25*w + 8],\ [751, 751, w^2 - 2*w - 7],\ [751, 751, -3*w^3 + 15*w + 5],\ [757, 757, 3*w^3 - 19*w - 2],\ [761, 761, 2*w^2 + w - 5],\ [769, 769, -2*w^3 + w^2 + 14*w - 9],\ [769, 769, 2*w^2 - w - 7],\ [773, 773, w^3 - w^2 - 5*w - 4],\ [773, 773, w^3 - 3*w - 6],\ [787, 787, 3*w^3 - 19*w - 3],\ [797, 797, 8*w^3 - 3*w^2 - 47*w + 10],\ [809, 809, 4*w^3 - 25*w - 1],\ [811, 811, w^3 - 9*w - 1],\ [821, 821, 6*w^3 - 3*w^2 - 35*w + 8],\ [823, 823, 2*w^3 + w^2 - 10*w + 1],\ [823, 823, -2*w^3 + 2*w^2 + 7*w - 4],\ [829, 829, -5*w^3 + w^2 + 27*w - 4],\ [829, 829, 5*w^3 - 2*w^2 - 26*w + 10],\ [839, 839, w^3 + 2*w^2 - 5*w - 7],\ [839, 839, 3*w^3 - w^2 - 15*w + 2],\ [841, 29, 3*w^3 + w^2 - 14*w - 2],\ [841, 29, 4*w^3 - 2*w^2 - 21*w + 10],\ [857, 857, -8*w^3 + 4*w^2 + 44*w - 11],\ [857, 857, -3*w^3 + 3*w^2 + 20*w - 9],\ [859, 859, w^3 + 2*w^2 - 6*w - 6],\ [877, 877, w^3 - 3*w^2 - 4*w + 14],\ [883, 883, 2*w^3 + w^2 - 10*w - 11],\ [887, 887, 3*w^3 + w^2 - 20*w - 2],\ [919, 919, 7*w^3 - 3*w^2 - 39*w + 9],\ [929, 929, 3*w^3 - 17*w + 2],\ [929, 929, -6*w^3 + 2*w^2 + 35*w - 10],\ [937, 937, w^3 + w^2 - 3*w - 5],\ [937, 937, -2*w^3 + 3*w^2 + 12*w - 12],\ [937, 937, -3*w^3 - 2*w^2 + 19*w + 8],\ [937, 937, 3*w^3 - 2*w^2 - 13*w + 3],\ [941, 941, w^3 + 2*w^2 - 6*w - 8],\ [941, 941, 5*w^3 - w^2 - 28*w - 3],\ [947, 947, -4*w^3 + 2*w^2 + 25*w - 6],\ [953, 953, w^3 - 7*w - 7],\ [953, 953, -3*w^3 + 2*w^2 + 18*w - 3],\ [967, 967, w^3 - 2*w^2 - 5*w - 3],\ [971, 971, w^2 + 2*w - 6],\ [977, 977, 2*w^3 - 11*w - 8],\ [997, 997, -3*w^3 + w^2 + 17*w + 2],\ [997, 997, -2*w^3 + 2*w^2 + 14*w - 7]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^7 - 8*x^6 + 8*x^5 + 68*x^4 - 140*x^3 - 64*x^2 + 176*x + 48 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1, -1, e, -1/8*e^6 + 3/4*e^5 + 1/4*e^4 - 13/2*e^3 + 5*e^2 + 5*e, 1/4*e^5 - e^4 - 2*e^3 + 8*e^2 + e - 4, -1/8*e^6 + 5/8*e^5 + 3/4*e^4 - 23/4*e^3 + 1/2*e^2 + 9*e + 4, -1/4*e^6 + 3/2*e^5 + 1/2*e^4 - 27/2*e^3 + 10*e^2 + 16*e - 2, -1/2*e^4 + 3/2*e^3 + 5*e^2 - 9*e - 10, 1/2*e^3 - e^2 - 4*e + 2, 1/2*e^3 - e^2 - 3*e + 4, 1/8*e^6 - 3/4*e^5 - 1/4*e^4 + 13/2*e^3 - 5*e^2 - 5*e + 2, 1/2*e^4 - e^3 - 6*e^2 + 8*e + 6, -1/4*e^6 + 7/4*e^5 - 1/2*e^4 - 31/2*e^3 + 19*e^2 + 16*e - 10, -1/4*e^6 + 5/4*e^5 + 2*e^4 - 13*e^3 - 2*e^2 + 25*e + 6, -1/4*e^5 + 1/2*e^4 + 4*e^3 - 5*e^2 - 13*e + 4, -1/2*e^4 + 2*e^3 + 5*e^2 - 16*e - 8, 1/4*e^6 - 5/4*e^5 - 2*e^4 + 25/2*e^3 + 3*e^2 - 20*e - 14, 1/4*e^6 - 3/2*e^5 - 1/2*e^4 + 27/2*e^3 - 9*e^2 - 17*e - 2, 1/4*e^5 - 1/2*e^4 - 7/2*e^3 + 4*e^2 + 12*e - 8, -1/8*e^6 + e^5 - 5/4*e^4 - 8*e^3 + 20*e^2 + 5*e - 16, -1/4*e^5 + e^4 + 5/2*e^3 - 8*e^2 - 8*e + 8, 1/4*e^5 - 1/2*e^4 - 5/2*e^3 + 6*e + 12, 3/8*e^6 - 7/4*e^5 - 15/4*e^4 + 39/2*e^3 + 9*e^2 - 41*e - 16, -1/4*e^6 + e^5 + 7/2*e^4 - 13*e^3 - 15*e^2 + 40*e + 22, -1/8*e^6 + 1/2*e^5 + 5/4*e^4 - 5*e^3 - 5*e^2 + 13*e + 16, 3/8*e^6 - 2*e^5 - 7/4*e^4 + 18*e^3 - 7*e^2 - 19*e - 2, -1/2*e^5 + 5/2*e^4 + 2*e^3 - 21*e^2 + 16*e + 20, -1/2*e^6 + 11/4*e^5 + 2*e^4 - 26*e^3 + 15*e^2 + 38*e - 14, -1/8*e^6 + 1/2*e^5 + 5/4*e^4 - 5*e^3 - 3*e^2 + 9*e + 4, 1/2*e^4 - 5/2*e^3 - 4*e^2 + 19*e + 8, 3/4*e^5 - 3*e^4 - 13/2*e^3 + 27*e^2 + 2*e - 24, 1/4*e^6 - 5/4*e^5 - 2*e^4 + 13*e^3 + e^2 - 26*e + 6, -1/4*e^6 + e^5 + 7/2*e^4 - 13*e^3 - 16*e^2 + 38*e + 30, -1/4*e^6 + 5/4*e^5 + e^4 - 11*e^3 + 9*e^2 + 11*e, 1/4*e^6 - 7/4*e^5 + 1/2*e^4 + 31/2*e^3 - 19*e^2 - 12*e + 6, 1/4*e^6 - 3/2*e^5 - 2*e^4 + 17*e^3 + 7*e^2 - 40*e - 26, 1/2*e^6 - 2*e^5 - 11/2*e^4 + 41/2*e^3 + 16*e^2 - 37*e - 12, -1/4*e^6 + 5/4*e^5 + 3/2*e^4 - 11*e^3 + 3*e^2 + 9*e - 6, -1/4*e^6 + 3/2*e^5 + 1/2*e^4 - 13*e^3 + 10*e^2 + 8*e - 2, -1/4*e^6 + 7/4*e^5 - e^4 - 27/2*e^3 + 24*e^2 - 2*e - 24, -1/2*e^6 + 11/4*e^5 + 5/2*e^4 - 53/2*e^3 + 5*e^2 + 44*e + 22, 1/4*e^6 - 5/4*e^5 - 2*e^4 + 12*e^3 + 3*e^2 - 15*e - 6, 1/4*e^6 - 2*e^5 + 1/2*e^4 + 21*e^3 - 19*e^2 - 40*e + 12, 3/8*e^6 - 5/2*e^5 - 3/4*e^4 + 49/2*e^3 - 12*e^2 - 36*e - 12, 1/2*e^4 - 3/2*e^3 - 7*e^2 + 11*e + 18, 1/8*e^6 - 13/4*e^4 + 2*e^3 + 17*e^2 - 15*e - 6, 1/2*e^6 - 5/2*e^5 - 7/2*e^4 + 24*e^3 - e^2 - 34*e, -1/4*e^6 + 5/4*e^5 + 3/2*e^4 - 27/2*e^3 + 6*e^2 + 32*e - 6, -1/2*e^6 + 5/2*e^5 + 7/2*e^4 - 47/2*e^3 - 4*e^2 + 32*e + 30, 3/4*e^6 - 17/4*e^5 - 5/2*e^4 + 77/2*e^3 - 24*e^2 - 46*e + 18, -1/4*e^5 + 3*e^4 - 4*e^3 - 27*e^2 + 36*e + 30, -1/2*e^6 + 13/4*e^5 - 59/2*e^3 + 30*e^2 + 38*e - 14, 1/4*e^6 - 5/4*e^5 - 3/2*e^4 + 27/2*e^3 - 5*e^2 - 35*e + 8, 1/4*e^6 - 3/4*e^5 - 9/2*e^4 + 10*e^3 + 25*e^2 - 31*e - 32, 1/2*e^6 - 13/4*e^5 + 1/2*e^4 + 28*e^3 - 37*e^2 - 22*e + 22, -1/4*e^6 + 2*e^5 - 1/2*e^4 - 20*e^3 + 14*e^2 + 38*e + 6, 1/4*e^6 - 5/4*e^5 - 3/2*e^4 + 19/2*e^3 + 3*e^2 - 4*e - 26, -3/4*e^5 + 7/2*e^4 + 7/2*e^3 - 29*e^2 + 22*e + 26, 1/8*e^6 - 1/2*e^5 - 5/4*e^4 + 11/2*e^3 - 16*e + 10, 1/2*e^4 - 3/2*e^3 - 4*e^2 + 7*e + 8, 1/2*e^6 - 13/4*e^5 + 1/2*e^4 + 27*e^3 - 33*e^2 - 15*e + 16, 1/4*e^6 - 5/4*e^5 - 5/2*e^4 + 14*e^3 + 10*e^2 - 30*e - 42, 1/2*e^6 - 9/4*e^5 - 7/2*e^4 + 19*e^3 - e^2 - 11*e, 9/8*e^6 - 13/2*e^5 - 17/4*e^4 + 123/2*e^3 - 28*e^2 - 92*e + 4, -3/8*e^6 + 5/2*e^5 - 9/4*e^4 - 35/2*e^3 + 44*e^2 - 2*e - 32, -1/4*e^6 + e^5 + 9/2*e^4 - 31/2*e^3 - 25*e^2 + 51*e + 34, 1/4*e^6 - 3/2*e^5 - 3/2*e^4 + 17*e^3 - e^2 - 38*e - 18, 3/4*e^6 - 5*e^5 + 46*e^3 - 44*e^2 - 52*e + 18, -3/4*e^6 + 11/2*e^5 - 2*e^4 - 49*e^3 + 57*e^2 + 50*e - 16, 1/2*e^6 - 3*e^5 + 25*e^3 - 32*e^2 - 22*e + 34, -1/8*e^6 + 1/2*e^5 - 1/4*e^4 - 2*e^3 + 14*e^2 - 9*e - 6, -1/2*e^5 + 3*e^4 + e^3 - 24*e^2 + 16*e + 12, -3/4*e^6 + 15/4*e^5 + 11/2*e^4 - 75/2*e^3 - 5*e^2 + 66*e + 36, 3/4*e^6 - 19/4*e^5 - 1/2*e^4 + 83/2*e^3 - 36*e^2 - 42*e, 1/4*e^6 - 5/2*e^5 + 3*e^4 + 24*e^3 - 42*e^2 - 32*e + 30, 3/4*e^5 - 3*e^4 - 5*e^3 + 21*e^2 + e - 8, 1/4*e^5 + 1/2*e^4 - 13/2*e^3 - 4*e^2 + 30*e - 6, 1/2*e^6 - 3*e^5 + 1/2*e^4 + 23*e^3 - 35*e^2 - 10*e + 24, 1/2*e^6 - 5/2*e^5 - 4*e^4 + 26*e^3 + 6*e^2 - 58*e - 24, 1/2*e^6 - 5/2*e^5 - 9/2*e^4 + 28*e^3 + 6*e^2 - 60*e - 12, 3/4*e^6 - 4*e^5 - 4*e^4 + 73/2*e^3 - 8*e^2 - 38*e - 30, 1/2*e^6 - 13/4*e^5 + 57/2*e^3 - 26*e^2 - 24*e - 10, 1/2*e^4 - 5/2*e^3 + 19*e - 16, -3/4*e^6 + 17/4*e^5 + 5/2*e^4 - 38*e^3 + 19*e^2 + 51*e + 18, 1/2*e^5 - 7/2*e^4 + 32*e^2 - 22*e - 42, -1/4*e^5 + e^4 + 5/2*e^3 - 10*e^2 - 8*e + 32, 3/4*e^6 - 4*e^5 - 5*e^4 + 41*e^3 - 78*e - 14, -1/4*e^6 + 9/4*e^5 - 7/2*e^4 - 31/2*e^3 + 39*e^2 - 5*e - 12, -1/2*e^6 + 11/4*e^5 + 3/2*e^4 - 23*e^3 + 16*e^2 + 9*e + 2, e^6 - 11/2*e^5 - 9/2*e^4 + 53*e^3 - 25*e^2 - 80*e + 12, 1/4*e^6 - 1/2*e^5 - 11/2*e^4 + 8*e^3 + 34*e^2 - 28*e - 32, 3/8*e^6 - 2*e^5 - 9/4*e^4 + 19*e^3 - 21*e - 22, -1/2*e^6 + 5/2*e^5 + 5/2*e^4 - 43/2*e^3 + 8*e^2 + 18*e + 18, 1/4*e^6 - 2*e^5 + 3/2*e^4 + 18*e^3 - 28*e^2 - 24*e + 24, 3/4*e^6 - 19/4*e^5 - 3/2*e^4 + 91/2*e^3 - 32*e^2 - 66*e + 12, -1/4*e^6 + 3/2*e^5 + 3/2*e^4 - 15*e^3 - 2*e^2 + 26*e + 6, 1/2*e^6 - 5/2*e^5 - 5*e^4 + 28*e^3 + 18*e^2 - 70*e - 40, e^3 - 20*e - 2, -1/2*e^6 + 9/4*e^5 + 4*e^4 - 37/2*e^3 - 11*e^2 + 12*e + 44, -3/4*e^6 + 4*e^5 + 4*e^4 - 38*e^3 + 10*e^2 + 64*e - 6, 1/8*e^6 - 3/4*e^5 - 1/4*e^4 + 15/2*e^3 - 9*e^2 - 11*e + 18, -1/4*e^6 + 7/4*e^5 + 3/2*e^4 - 21*e^3 - 4*e^2 + 58*e + 30, -3/4*e^6 + 7/2*e^5 + 13/2*e^4 - 34*e^3 - 15*e^2 + 48*e + 48, -3/4*e^6 + 19/4*e^5 + 3/2*e^4 - 91/2*e^3 + 29*e^2 + 69*e, 1/4*e^6 - 3/2*e^5 + 3/2*e^4 + 8*e^3 - 34*e^2 + 30*e + 48, 1/2*e^5 - 1/2*e^4 - 9*e^3 + 5*e^2 + 36*e, 1/4*e^6 - 3/4*e^5 - 3*e^4 + 7*e^3 + 3*e^2 - 4*e + 26, 1/4*e^6 - 9/4*e^5 + 3*e^4 + 19*e^3 - 42*e^2 - 25*e + 38, e^6 - 6*e^5 - 3*e^4 + 56*e^3 - 34*e^2 - 72*e + 16, 1/4*e^6 - 3/2*e^5 - e^4 + 16*e^3 - 5*e^2 - 40*e - 14, 1/2*e^6 - 5/2*e^5 - 3*e^4 + 23*e^3 - 2*e^2 - 34*e - 22, -1/8*e^6 + 2*e^5 - 23/4*e^4 - 14*e^3 + 53*e^2 - 7*e - 24, -1/4*e^6 + 2*e^5 - e^4 - 21*e^3 + 26*e^2 + 42*e - 18, 1/2*e^6 - 3*e^5 + 3/2*e^4 + 21*e^3 - 48*e^2 + 8*e + 40, 3/4*e^6 - 15/4*e^5 - 6*e^4 + 38*e^3 + 8*e^2 - 65*e - 22, -1/4*e^6 + 7/4*e^5 - 1/2*e^4 - 29/2*e^3 + 12*e^2 + 16*e + 26, -1/4*e^6 + 1/4*e^5 + 13/2*e^4 - 13/2*e^3 - 43*e^2 + 38*e + 50, e^6 - 6*e^5 - 5/2*e^4 + 55*e^3 - 38*e^2 - 66*e + 12, 1/8*e^6 - 3/2*e^5 + 11/4*e^4 + 25/2*e^3 - 30*e^2 - 10*e + 42, -3/8*e^6 + 7/2*e^5 - 21/4*e^4 - 29*e^3 + 71*e^2 + 13*e - 52, -7/8*e^6 + 4*e^5 + 35/4*e^4 - 44*e^3 - 25*e^2 + 105*e + 44, 1/4*e^6 - 9/4*e^5 + 4*e^4 + 13*e^3 - 47*e^2 + 27*e + 48, -3/4*e^6 + 9/2*e^5 + e^4 - 79/2*e^3 + 35*e^2 + 39*e - 6, -3/4*e^6 + 4*e^5 + 9/2*e^4 - 79/2*e^3 + 9*e^2 + 59*e, 3/4*e^6 - 7/2*e^5 - 7*e^4 + 35*e^3 + 21*e^2 - 58*e - 60, -1/2*e^6 + 2*e^5 + 7*e^4 - 25*e^3 - 34*e^2 + 78*e + 40, 1/4*e^6 - 3/4*e^5 - 7/2*e^4 + 6*e^3 + 17*e^2 + 3*e - 24, 1/2*e^6 - 3*e^5 - 3/2*e^4 + 59/2*e^3 - 19*e^2 - 53*e + 6, -1/8*e^6 + 3/2*e^5 - 11/4*e^4 - 13*e^3 + 29*e^2 + 9*e + 6, -e^6 + 6*e^5 + 1/2*e^4 - 103/2*e^3 + 58*e^2 + 53*e - 24, 1/2*e^6 - 11/4*e^5 - 3/2*e^4 + 51/2*e^3 - 21*e^2 - 34*e + 2, -7/8*e^6 + 5*e^5 + 19/4*e^4 - 101/2*e^3 + 10*e^2 + 86*e + 22, -3/4*e^6 + 15/4*e^5 + 11/2*e^4 - 38*e^3 - 6*e^2 + 70*e + 46, 1/2*e^6 - 5/2*e^5 - 5*e^4 + 28*e^3 + 12*e^2 - 54*e - 16, 1/2*e^6 - 2*e^5 - 9/2*e^4 + 15*e^3 + 11*e^2, 1/2*e^5 - 2*e^4 - 2*e^3 + 16*e^2 - 26*e - 8, 1/4*e^6 - 3/2*e^5 - 1/2*e^4 + 10*e^3 - 2*e^2 + 10*e - 16, 1/4*e^6 - e^5 - 1/2*e^4 + 3*e^3 - 12*e^2 + 32*e + 22, -1/2*e^6 + 5/2*e^5 + 9/2*e^4 - 27*e^3 - 9*e^2 + 50*e + 30, 1/4*e^6 - 9/4*e^5 + 3*e^4 + 17*e^3 - 43*e^2 + 11*e + 56, -1/2*e^6 + 9/4*e^5 + 7*e^4 - 57/2*e^3 - 33*e^2 + 76*e + 44, 1/4*e^6 - e^5 - 5*e^4 + 18*e^3 + 29*e^2 - 72*e - 42, -2*e^3 + 5*e^2 + 20*e - 30, -5/4*e^6 + 29/4*e^5 + 11/2*e^4 - 141/2*e^3 + 23*e^2 + 119*e + 8, 1/4*e^6 - e^5 - 3*e^4 + 11*e^3 + 16*e^2 - 40*e - 42, -3/8*e^6 + 3*e^5 - 17/4*e^4 - 22*e^3 + 65*e^2 - e - 60, -1/2*e^6 + 5/2*e^5 + 5/2*e^4 - 41/2*e^3 + 8*e^2 + 9*e + 8, -1/4*e^6 + 9/4*e^5 - 9/2*e^4 - 14*e^3 + 57*e^2 - 19*e - 48, 1/2*e^6 - 7/2*e^5 + 7/2*e^4 + 23*e^3 - 61*e^2 + 16*e + 64, 3/4*e^6 - 19/4*e^5 - 3*e^4 + 49*e^3 - 13*e^2 - 95*e - 14, -1/4*e^6 + 5/2*e^5 - 5*e^4 - 31/2*e^3 + 55*e^2 - 21*e - 34, -e^6 + 11/2*e^5 + 5*e^4 - 51*e^3 + 14*e^2 + 72*e + 2, 1/4*e^6 - 7/4*e^5 - e^4 + 21*e^3 - 14*e^2 - 45*e + 42, 5/4*e^6 - 21/4*e^5 - 14*e^4 + 57*e^3 + 48*e^2 - 123*e - 78, 5/4*e^6 - 31/4*e^5 - 7/2*e^4 + 149/2*e^3 - 39*e^2 - 104*e - 28, -1/2*e^6 + 19/4*e^5 - 13/2*e^4 - 39*e^3 + 83*e^2 + 14*e - 50, -1/4*e^6 + 7/4*e^5 - 3/2*e^4 - 23/2*e^3 + 27*e^2 - 4*e - 24, -1/4*e^6 + 3/4*e^5 + 5*e^4 - 12*e^3 - 29*e^2 + 37*e + 36, -1/4*e^6 + 1/2*e^5 + 15/2*e^4 - 15*e^3 - 48*e^2 + 68*e + 40, 3/4*e^5 - 4*e^4 - 7/2*e^3 + 39*e^2 - 20*e - 52, 3/4*e^6 - 21/4*e^5 + 3/2*e^4 + 91/2*e^3 - 53*e^2 - 45*e + 8, 1/2*e^6 - 3*e^5 - 4*e^4 + 69/2*e^3 + 15*e^2 - 91*e - 48, 1/2*e^6 - 7/4*e^5 - 11/2*e^4 + 33/2*e^3 + 14*e^2 - 26*e - 14, -1/8*e^6 - 1/2*e^5 + 29/4*e^4 - e^3 - 57*e^2 + 29*e + 72, 3/4*e^6 - 17/4*e^5 - 3*e^4 + 81/2*e^3 - 16*e^2 - 64*e, 1/4*e^6 - 9/4*e^5 + 3*e^4 + 18*e^3 - 39*e^2 - 19*e + 44, -3/2*e^6 + 35/4*e^5 + 4*e^4 - 159/2*e^3 + 53*e^2 + 100*e + 8, 3/4*e^6 - 19/4*e^5 - 3/2*e^4 + 91/2*e^3 - 25*e^2 - 80*e - 8, -5/4*e^6 + 29/4*e^5 + 5/2*e^4 - 62*e^3 + 51*e^2 + 47*e - 8, 13/8*e^6 - 35/4*e^5 - 33/4*e^4 + 169/2*e^3 - 29*e^2 - 137*e + 18, -1/2*e^6 + 3/2*e^5 + 8*e^4 - 16*e^3 - 38*e^2 + 24*e + 42, e^6 - 11/2*e^5 - 7/2*e^4 + 101/2*e^3 - 34*e^2 - 64*e + 18, -1/4*e^6 + 3*e^5 - 8*e^4 - 18*e^3 + 84*e^2 - 32*e - 66, -1/4*e^6 + 1/2*e^5 + 7*e^4 - 11*e^3 - 50*e^2 + 52*e + 54, -e^6 + 13/2*e^5 + 1/2*e^4 - 58*e^3 + 54*e^2 + 58*e - 40, -1/4*e^6 + 3/2*e^5 + 1/2*e^4 - 29/2*e^3 + 17*e^2 + 27*e - 48, 5/4*e^6 - 27/4*e^5 - 8*e^4 + 133/2*e^3 + 8*e^2 - 118*e - 84, -1/4*e^6 + 3/2*e^5 + 2*e^4 - 19*e^3 - 8*e^2 + 60*e + 26, 3/4*e^6 - 3*e^5 - 8*e^4 + 29*e^3 + 24*e^2 - 32*e - 58] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([3, 3, w + 1])] = 1 AL_eigenvalues[ZF.ideal([5, 5, -w^3 + 5*w + 2])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]