/* 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, -5, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([49, 7, w^3 - w^2 - 6*w - 1]) primes_array = [ [5, 5, -w^3 + w^2 + 5*w],\ [7, 7, -w^3 + 2*w^2 + 3*w - 3],\ [7, 7, w^3 - 2*w^2 - 3*w],\ [13, 13, -w^2 + w + 3],\ [13, 13, -w^2 + w + 2],\ [16, 2, 2],\ [23, 23, -w^2 + 3*w + 1],\ [23, 23, -2*w^3 + 3*w^2 + 9*w - 2],\ [25, 5, w^3 - 2*w^2 - 2*w + 2],\ [49, 7, w^3 - w^2 - 6*w - 1],\ [53, 53, 2*w^3 - 2*w^2 - 8*w - 3],\ [53, 53, 2*w^3 - 2*w^2 - 8*w - 1],\ [67, 67, 2*w^3 - 4*w^2 - 7*w + 2],\ [67, 67, -2*w^3 + 4*w^2 + 6*w - 1],\ [81, 3, -3],\ [83, 83, 2*w^3 - 3*w^2 - 6*w - 1],\ [83, 83, 3*w^3 - 4*w^2 - 12*w + 1],\ [103, 103, 3*w^3 - 4*w^2 - 12*w - 1],\ [103, 103, 2*w^3 - 3*w^2 - 6*w + 1],\ [107, 107, w^3 - w^2 - 3*w - 3],\ [107, 107, 2*w^3 - 2*w^2 - 9*w],\ [109, 109, -3*w^3 + 5*w^2 + 10*w - 5],\ [109, 109, -2*w^3 + 3*w^2 + 9*w + 1],\ [109, 109, -2*w^3 + 2*w^2 + 7*w],\ [109, 109, w^2 - 3*w - 4],\ [121, 11, 3*w^3 - 4*w^2 - 12*w],\ [121, 11, 2*w^2 - 3*w - 6],\ [139, 139, w^3 - 7*w - 1],\ [139, 139, -w^3 + 2*w^2 + 5*w - 4],\ [139, 139, 3*w^3 - 3*w^2 - 14*w - 2],\ [139, 139, -3*w^3 + 5*w^2 + 13*w - 2],\ [149, 149, -w^2 + 4*w + 1],\ [149, 149, -3*w^3 + 4*w^2 + 14*w - 1],\ [149, 149, 2*w^2 - 3*w - 5],\ [149, 149, -w^3 + 3*w^2 + 3*w - 4],\ [167, 167, -w^3 - w^2 + 7*w + 4],\ [167, 167, -4*w^3 + 6*w^2 + 15*w - 4],\ [169, 13, w^3 - w^2 - 6*w + 4],\ [173, 173, w^2 - 3*w - 5],\ [173, 173, 2*w^3 - 2*w^2 - 11*w],\ [179, 179, 2*w^3 - 2*w^2 - 9*w + 1],\ [179, 179, w^3 - w^2 - 3*w - 4],\ [179, 179, w^2 - 5],\ [179, 179, w^3 - 6*w - 1],\ [197, 197, w^3 + w^2 - 7*w - 6],\ [197, 197, 2*w^3 - 2*w^2 - 9*w + 2],\ [223, 223, -w^2 + 7],\ [223, 223, 2*w^2 - w - 4],\ [227, 227, 2*w^3 - 2*w^2 - 11*w - 2],\ [227, 227, w^3 - w^2 - 7*w - 1],\ [233, 233, w^3 - w^2 - 7*w],\ [233, 233, -2*w^3 + 2*w^2 + 11*w + 1],\ [257, 257, -2*w^3 + 4*w^2 + 8*w - 1],\ [257, 257, 2*w^2 - 4*w - 7],\ [277, 277, -4*w^3 + 6*w^2 + 15*w - 3],\ [277, 277, -3*w^3 + 5*w^2 + 9*w],\ [281, 281, -2*w^3 + 5*w^2 + 3*w - 5],\ [281, 281, -2*w^3 + 5*w^2 + 5*w - 7],\ [281, 281, 2*w^3 - 5*w^2 - 5*w + 4],\ [281, 281, -4*w^3 + 7*w^2 + 15*w - 4],\ [283, 283, 3*w^3 - 4*w^2 - 13*w - 3],\ [283, 283, -w^3 + 2*w^2 + w - 4],\ [313, 313, -2*w^3 + 4*w^2 + 5*w - 5],\ [313, 313, 3*w^3 - 5*w^2 - 11*w],\ [347, 347, -w^3 + 2*w^2 + w - 5],\ [347, 347, 3*w^3 - 4*w^2 - 13*w - 4],\ [353, 353, 3*w^3 - 5*w^2 - 12*w + 1],\ [353, 353, -w^3 + 3*w^2 - 5],\ [361, 19, 3*w^3 - 3*w^2 - 13*w - 9],\ [361, 19, 2*w^3 - 2*w^2 - 7*w + 4],\ [373, 373, -3*w^3 + 4*w^2 + 11*w + 1],\ [373, 373, -3*w^3 + 4*w^2 + 11*w],\ [383, 383, 3*w^3 - 5*w^2 - 13*w + 1],\ [383, 383, 2*w^2 - 5*w - 6],\ [397, 397, 4*w^3 - 5*w^2 - 19*w - 1],\ [397, 397, 2*w^3 - 2*w^2 - 9*w - 7],\ [431, 431, 2*w^3 - 2*w^2 - 7*w - 5],\ [431, 431, 3*w^3 - 6*w^2 - 11*w + 3],\ [431, 431, 3*w^3 - 3*w^2 - 13*w],\ [431, 431, w^3 - 4*w^2 + w + 8],\ [457, 457, 4*w^3 - 7*w^2 - 13*w],\ [457, 457, -3*w^2 + 4*w + 5],\ [463, 463, -3*w^3 + 5*w^2 + 11*w + 1],\ [463, 463, 2*w^3 - 4*w^2 - 5*w + 6],\ [487, 487, -w^3 + 4*w^2 - 7],\ [487, 487, -2*w^3 + 5*w^2 + 6*w - 5],\ [499, 499, -6*w^3 + 8*w^2 + 25*w - 1],\ [499, 499, -w^3 + 4*w^2 - 5],\ [499, 499, -2*w^3 + 5*w^2 + 6*w - 7],\ [499, 499, 3*w^3 - 5*w^2 - 7*w],\ [509, 509, -4*w^3 + 8*w^2 + 15*w - 8],\ [509, 509, 3*w^3 - 4*w^2 - 10*w - 2],\ [509, 509, -3*w^3 + 3*w^2 + 11*w + 6],\ [509, 509, 4*w^3 - 5*w^2 - 16*w],\ [521, 521, -4*w^3 + 5*w^2 + 15*w - 2],\ [521, 521, w^3 - w^2 - 8*w + 1],\ [521, 521, -4*w^3 + 7*w^2 + 12*w - 6],\ [521, 521, 3*w^3 - 3*w^2 - 16*w - 1],\ [523, 523, 3*w^3 - w^2 - 17*w - 8],\ [523, 523, -5*w^3 + 5*w^2 + 23*w + 4],\ [529, 23, 3*w^3 - 6*w^2 - 10*w + 2],\ [547, 547, -2*w^3 + 5*w^2 + 6*w - 6],\ [547, 547, -w^3 + 4*w^2 - 6],\ [557, 557, -3*w^3 + 6*w^2 + 9*w - 10],\ [557, 557, 3*w^3 - 6*w^2 - 9*w - 1],\ [571, 571, 4*w^3 - 4*w^2 - 17*w - 6],\ [571, 571, -2*w^3 + 6*w^2 + 3*w - 10],\ [571, 571, 4*w^3 - 5*w^2 - 18*w + 3],\ [571, 571, -3*w^3 + 7*w^2 + 9*w - 5],\ [587, 587, 3*w^3 - 3*w^2 - 14*w],\ [587, 587, w^3 - w^2 - 2*w - 4],\ [593, 593, -w^3 + 3*w^2 + 2*w - 10],\ [593, 593, -5*w^3 + 7*w^2 + 19*w - 4],\ [613, 613, 3*w^3 - 5*w^2 - 12*w - 4],\ [613, 613, -w^3 + 3*w^2 - 10],\ [631, 631, 4*w^3 - 8*w^2 - 13*w + 4],\ [631, 631, 3*w^3 - 4*w^2 - 15*w + 2],\ [631, 631, w^3 - 9*w - 1],\ [631, 631, 3*w^3 - 7*w^2 - 7*w + 9],\ [643, 643, 3*w^3 - 3*w^2 - 16*w - 2],\ [643, 643, w^3 - w^2 - 8*w],\ [647, 647, -w^3 + 4*w^2 + 2*w - 4],\ [647, 647, -3*w^2 + 4*w + 10],\ [673, 673, w^3 + 2*w^2 - 9*w - 8],\ [673, 673, -w^3 + 4*w^2 + 3*w - 7],\ [683, 683, 3*w^3 - 3*w^2 - 11*w - 2],\ [683, 683, 4*w^3 - 4*w^2 - 17*w - 5],\ [709, 709, -5*w^3 + 7*w^2 + 21*w + 1],\ [709, 709, -3*w^3 + 2*w^2 + 16*w + 4],\ [709, 709, 4*w^3 - 4*w^2 - 19*w - 2],\ [709, 709, -2*w^3 + 4*w^2 + 3*w - 4],\ [787, 787, 2*w^2 - w - 9],\ [787, 787, w^3 + w^2 - 7*w - 2],\ [811, 811, 4*w^3 - 7*w^2 - 11*w],\ [811, 811, 3*w^3 - 4*w^2 - 9*w - 1],\ [811, 811, -6*w^3 + 9*w^2 + 23*w - 5],\ [811, 811, 5*w^3 - 6*w^2 - 21*w - 2],\ [821, 821, -3*w^3 + 6*w^2 + 11*w - 2],\ [821, 821, 2*w^3 - 13*w - 5],\ [821, 821, -w^3 + 4*w^2 - w - 9],\ [821, 821, -w^3 + 3*w^2 + 5*w - 6],\ [841, 29, 2*w^3 - 2*w^2 - 12*w - 1],\ [857, 857, w^3 - 4*w^2 + 3*w + 6],\ [857, 857, -5*w^3 + 8*w^2 + 21*w - 3],\ [863, 863, -w^3 + 4*w^2 + w - 7],\ [863, 863, -w^3 + 4*w^2 + w - 6],\ [877, 877, -w^3 - w^2 + 8*w + 2],\ [877, 877, -w^3 + 3*w^2 + 4*w - 8],\ [883, 883, 4*w^3 - 7*w^2 - 14*w + 1],\ [883, 883, 3*w^3 - 6*w^2 - 8*w + 7],\ [929, 929, 3*w^3 - 5*w^2 - 12*w - 3],\ [929, 929, -w^3 + 3*w^2 - 9],\ [929, 929, 3*w - 5],\ [929, 929, 3*w^3 - 3*w^2 - 15*w + 2],\ [937, 937, w^3 - 2*w^2 - 6*w + 6],\ [937, 937, 2*w^3 - w^2 - 12*w],\ [941, 941, -w^3 + 4*w^2 + 2*w - 7],\ [941, 941, -4*w^3 + 6*w^2 + 13*w - 3],\ [941, 941, -5*w^3 + 7*w^2 + 19*w + 2],\ [941, 941, 3*w^2 - 4*w - 7],\ [953, 953, 3*w^3 - 5*w^2 - 12*w - 2],\ [953, 953, -w^3 + 3*w^2 - 8],\ [961, 31, 4*w^3 - 6*w^2 - 13*w - 2],\ [961, 31, 5*w^3 - 7*w^2 - 19*w + 3],\ [977, 977, -4*w^3 + 7*w^2 + 19*w - 6],\ [977, 977, -3*w^3 + 7*w^2 + 10*w - 6]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^6 - 23*x^4 - 2*x^3 + 112*x^2 - 40*x - 8 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, 1/12*e^5 - 19/12*e^3 - 5/6*e^2 + 5*e + 2, 1/12*e^5 - 19/12*e^3 - 5/6*e^2 + 5*e + 2, -1/6*e^5 + 23/6*e^3 + 2/3*e^2 - 56/3*e + 10/3, -1/6*e^5 + 23/6*e^3 + 2/3*e^2 - 56/3*e + 10/3, 1/6*e^5 + 1/6*e^4 - 23/6*e^3 - 17/6*e^2 + 17*e - 1/3, -1/3*e^3 + 13/3*e + 10/3, -1/3*e^3 + 13/3*e + 10/3, 1/6*e^5 - 23/6*e^3 - 2/3*e^2 + 50/3*e - 4/3, -1, -1/6*e^5 - 1/3*e^4 + 9/2*e^3 + 5*e^2 - 26*e + 8/3, -1/6*e^5 - 1/3*e^4 + 9/2*e^3 + 5*e^2 - 26*e + 8/3, -1/6*e^5 + 19/6*e^3 + 5/3*e^2 - 12*e - 8, -1/6*e^5 + 19/6*e^3 + 5/3*e^2 - 12*e - 8, 1/6*e^4 - 13/6*e^2 - 5/3*e + 4, 1/3*e^5 - 1/3*e^4 - 19/3*e^3 + 3*e^2 + 70/3*e - 6, 1/3*e^5 - 1/3*e^4 - 19/3*e^3 + 3*e^2 + 70/3*e - 6, -1/6*e^4 + 19/6*e^2 + 5/3*e - 4, -1/6*e^4 + 19/6*e^2 + 5/3*e - 4, -1/3*e^4 + 4/3*e^3 + 13/3*e^2 - 14*e - 10/3, -1/3*e^4 + 4/3*e^3 + 13/3*e^2 - 14*e - 10/3, -1/3*e^4 + 2/3*e^3 + 13/3*e^2 - 13/3*e + 4/3, -1/3*e^5 + 1/3*e^4 + 6*e^3 - 3*e^2 - 16*e + 34/3, -1/3*e^4 + 2/3*e^3 + 13/3*e^2 - 13/3*e + 4/3, -1/3*e^5 + 1/3*e^4 + 6*e^3 - 3*e^2 - 16*e + 34/3, 1/6*e^5 + 1/3*e^4 - 31/6*e^3 - 5*e^2 + 98/3*e - 6, 1/6*e^5 + 1/3*e^4 - 31/6*e^3 - 5*e^2 + 98/3*e - 6, 1/12*e^5 + 2/3*e^4 - 13/4*e^3 - 19/2*e^2 + 22*e + 20/3, 1/12*e^5 + 2/3*e^4 - 13/4*e^3 - 19/2*e^2 + 22*e + 20/3, -1/2*e^5 - 1/6*e^4 + 23/2*e^3 + 25/6*e^2 - 175/3*e + 10, -1/2*e^5 - 1/6*e^4 + 23/2*e^3 + 25/6*e^2 - 175/3*e + 10, -1/12*e^5 - 1/3*e^4 + 31/12*e^3 + 31/6*e^2 - 53/3*e - 8, -1/12*e^5 - 1/3*e^4 + 31/12*e^3 + 31/6*e^2 - 53/3*e - 8, 1/12*e^5 + 1/3*e^4 - 35/12*e^3 - 31/6*e^2 + 20*e - 2/3, 1/12*e^5 + 1/3*e^4 - 35/12*e^3 - 31/6*e^2 + 20*e - 2/3, 1/6*e^5 - 1/6*e^4 - 19/6*e^3 + 3/2*e^2 + 35/3*e - 2, 1/6*e^5 - 1/6*e^4 - 19/6*e^3 + 3/2*e^2 + 35/3*e - 2, 1/3*e^5 - 1/6*e^4 - 7*e^3 + 5/6*e^2 + 91/3*e + 32/3, 1/12*e^5 - 5/4*e^3 - 5/6*e^2 - 4/3*e + 2/3, 1/12*e^5 - 5/4*e^3 - 5/6*e^2 - 4/3*e + 2/3, -1/6*e^5 + 1/3*e^4 + 7/2*e^3 - 14/3*e^2 - 41/3*e + 14/3, -1/6*e^5 + 1/3*e^4 + 7/2*e^3 - 14/3*e^2 - 41/3*e + 14/3, -1/12*e^5 - 1/3*e^4 + 23/12*e^3 + 43/6*e^2 - 4*e - 64/3, -1/12*e^5 - 1/3*e^4 + 23/12*e^3 + 43/6*e^2 - 4*e - 64/3, -1/3*e^5 + 1/3*e^4 + 6*e^3 - 3*e^2 - 17*e + 16/3, -1/3*e^5 + 1/3*e^4 + 6*e^3 - 3*e^2 - 17*e + 16/3, 1/3*e^4 - 5/3*e^3 - 7/3*e^2 + 61/3*e - 58/3, 1/3*e^4 - 5/3*e^3 - 7/3*e^2 + 61/3*e - 58/3, -1/3*e^5 - 1/3*e^4 + 23/3*e^3 + 23/3*e^2 - 34*e - 28/3, -1/3*e^5 - 1/3*e^4 + 23/3*e^3 + 23/3*e^2 - 34*e - 28/3, -1/2*e^5 - 1/6*e^4 + 65/6*e^3 + 19/6*e^2 - 131/3*e + 38/3, -1/2*e^5 - 1/6*e^4 + 65/6*e^3 + 19/6*e^2 - 131/3*e + 38/3, 5/12*e^5 - 2/3*e^4 - 33/4*e^3 + 17/2*e^2 + 35*e - 56/3, 5/12*e^5 - 2/3*e^4 - 33/4*e^3 + 17/2*e^2 + 35*e - 56/3, -1/4*e^5 + 1/3*e^4 + 61/12*e^3 - 23/6*e^2 - 62/3*e + 62/3, -1/4*e^5 + 1/3*e^4 + 61/12*e^3 - 23/6*e^2 - 62/3*e + 62/3, -2/3*e^5 - 2/3*e^4 + 16*e^3 + 40/3*e^2 - 221/3*e + 8/3, 1/3*e^5 - 7*e^3 + 2/3*e^2 + 83/3*e - 64/3, 1/3*e^5 - 7*e^3 + 2/3*e^2 + 83/3*e - 64/3, -2/3*e^5 - 2/3*e^4 + 16*e^3 + 40/3*e^2 - 221/3*e + 8/3, -1/6*e^5 - 2/3*e^4 + 29/6*e^3 + 31/3*e^2 - 23*e - 2/3, -1/6*e^5 - 2/3*e^4 + 29/6*e^3 + 31/3*e^2 - 23*e - 2/3, e^4 - 2*e^3 - 14*e^2 + 16*e + 8, e^4 - 2*e^3 - 14*e^2 + 16*e + 8, -1/6*e^5 + 1/3*e^4 + 11/6*e^3 - 14/3*e^2 + 8*e + 58/3, -1/6*e^5 + 1/3*e^4 + 11/6*e^3 - 14/3*e^2 + 8*e + 58/3, -2/3*e^3 + 2*e^2 + 26/3*e - 28/3, -2/3*e^3 + 2*e^2 + 26/3*e - 28/3, -1/12*e^5 - 1/3*e^4 + 35/12*e^3 + 19/6*e^2 - 23*e + 8/3, -1/12*e^5 - 1/3*e^4 + 35/12*e^3 + 19/6*e^2 - 23*e + 8/3, 1/2*e^5 - e^4 - 59/6*e^3 + 12*e^2 + 112/3*e - 50/3, 1/2*e^5 - e^4 - 59/6*e^3 + 12*e^2 + 112/3*e - 50/3, 5/12*e^5 - 103/12*e^3 - 1/6*e^2 + 89/3*e - 22/3, 5/12*e^5 - 103/12*e^3 - 1/6*e^2 + 89/3*e - 22/3, 1/3*e^4 - 1/3*e^3 - 19/3*e^2 - 2*e + 34/3, 1/3*e^4 - 1/3*e^3 - 19/3*e^2 - 2*e + 34/3, 1/6*e^5 - 1/6*e^4 - 19/6*e^3 + 7/2*e^2 + 35/3*e - 10, -1/2*e^5 - 1/3*e^4 + 19/2*e^3 + 34/3*e^2 - 92/3*e - 24, 1/6*e^5 - 1/6*e^4 - 19/6*e^3 + 7/2*e^2 + 35/3*e - 10, -1/2*e^5 - 1/3*e^4 + 19/2*e^3 + 34/3*e^2 - 92/3*e - 24, 1/2*e^5 - 23/2*e^3 - e^2 + 52*e - 22, 1/2*e^5 - 23/2*e^3 - e^2 + 52*e - 22, -5/6*e^5 + 115/6*e^3 + 13/3*e^2 - 268/3*e + 2/3, -5/6*e^5 + 115/6*e^3 + 13/3*e^2 - 268/3*e + 2/3, -2/3*e^4 + 2/3*e^3 + 32/3*e^2 - 6*e - 20/3, -2/3*e^4 + 2/3*e^3 + 32/3*e^2 - 6*e - 20/3, 1/3*e^5 - 19/3*e^3 - 10/3*e^2 + 24*e + 2, -1/6*e^5 + 2/3*e^4 + 11/6*e^3 - 7*e^2 - 10/3*e - 26/3, -1/6*e^5 + 2/3*e^4 + 11/6*e^3 - 7*e^2 - 10/3*e - 26/3, 1/3*e^5 - 19/3*e^3 - 10/3*e^2 + 24*e + 2, 5/12*e^5 - 37/4*e^3 - 13/6*e^2 + 130/3*e + 58/3, -2/3*e^5 - 2/3*e^4 + 46/3*e^3 + 37/3*e^2 - 72*e + 52/3, 5/12*e^5 - 37/4*e^3 - 13/6*e^2 + 130/3*e + 58/3, -2/3*e^5 - 2/3*e^4 + 46/3*e^3 + 37/3*e^2 - 72*e + 52/3, 5/12*e^5 + 2/3*e^4 - 119/12*e^3 - 89/6*e^2 + 136/3*e + 22, -1/3*e^5 - e^4 + 25/3*e^3 + 46/3*e^2 - 38*e - 14, 5/12*e^5 + 2/3*e^4 - 119/12*e^3 - 89/6*e^2 + 136/3*e + 22, -1/3*e^5 - e^4 + 25/3*e^3 + 46/3*e^2 - 38*e - 14, -1/3*e^4 + 2/3*e^3 + 7/3*e^2 - 34/3*e + 88/3, -1/3*e^4 + 2/3*e^3 + 7/3*e^2 - 34/3*e + 88/3, -1/3*e^5 + 1/2*e^4 + 17/3*e^3 - 37/6*e^2 - 25/3*e + 116/3, 1/2*e^5 + 1/3*e^4 - 19/2*e^3 - 34/3*e^2 + 80/3*e + 28, 1/2*e^5 + 1/3*e^4 - 19/2*e^3 - 34/3*e^2 + 80/3*e + 28, -5/6*e^5 + e^4 + 103/6*e^3 - 26/3*e^2 - 220/3*e + 8/3, -5/6*e^5 + e^4 + 103/6*e^3 - 26/3*e^2 - 220/3*e + 8/3, 1/2*e^5 + 1/3*e^4 - 71/6*e^3 - 22/3*e^2 + 51*e - 2/3, 5/4*e^5 - 1/3*e^4 - 317/12*e^3 - 13/6*e^2 + 111*e - 94/3, 1/2*e^5 + 1/3*e^4 - 71/6*e^3 - 22/3*e^2 + 51*e - 2/3, 5/4*e^5 - 1/3*e^4 - 317/12*e^3 - 13/6*e^2 + 111*e - 94/3, -5/6*e^5 - 1/3*e^4 + 115/6*e^3 + 20/3*e^2 - 90*e + 80/3, -5/6*e^5 - 1/3*e^4 + 115/6*e^3 + 20/3*e^2 - 90*e + 80/3, 7/12*e^5 - 1/3*e^4 - 145/12*e^3 + 1/2*e^2 + 145/3*e - 8, 7/12*e^5 - 1/3*e^4 - 145/12*e^3 + 1/2*e^2 + 145/3*e - 8, -2/3*e^5 + 1/2*e^4 + 14*e^3 - 35/6*e^2 - 187/3*e + 80/3, -2/3*e^5 + 1/2*e^4 + 14*e^3 - 35/6*e^2 - 187/3*e + 80/3, -1/12*e^5 + e^4 + 19/12*e^3 - 85/6*e^2 - 11*e + 18, -1/3*e^5 - e^4 + 8*e^3 + 55/3*e^2 - 107/3*e - 62/3, -1/3*e^5 - e^4 + 8*e^3 + 55/3*e^2 - 107/3*e - 62/3, -1/12*e^5 + e^4 + 19/12*e^3 - 85/6*e^2 - 11*e + 18, -1/6*e^5 + 2/3*e^4 + 7/6*e^3 - 3*e^2 + 34/3*e - 36, -1/6*e^5 + 2/3*e^4 + 7/6*e^3 - 3*e^2 + 34/3*e - 36, -1/3*e^5 + 4/3*e^4 + 17/3*e^3 - 16*e^2 - 62/3*e + 14/3, -1/3*e^5 + 4/3*e^4 + 17/3*e^3 - 16*e^2 - 62/3*e + 14/3, 5/6*e^5 + 1/3*e^4 - 109/6*e^3 - 26/3*e^2 + 76*e - 74/3, 5/6*e^5 + 1/3*e^4 - 109/6*e^3 - 26/3*e^2 + 76*e - 74/3, 1/6*e^5 - 2/3*e^4 - 17/6*e^3 + 11*e^2 + 25/3*e - 46/3, 1/6*e^5 - 2/3*e^4 - 17/6*e^3 + 11*e^2 + 25/3*e - 46/3, -1/4*e^5 + 1/3*e^4 + 53/12*e^3 - 23/6*e^2 - 15*e + 88/3, 11/12*e^5 + 1/3*e^4 - 83/4*e^3 - 19/2*e^2 + 102*e - 14/3, 11/12*e^5 + 1/3*e^4 - 83/4*e^3 - 19/2*e^2 + 102*e - 14/3, -1/4*e^5 + 1/3*e^4 + 53/12*e^3 - 23/6*e^2 - 15*e + 88/3, -1/3*e^5 + 25/3*e^3 - 2/3*e^2 - 42*e + 6, -1/3*e^5 + 25/3*e^3 - 2/3*e^2 - 42*e + 6, e^5 - 62/3*e^3 - 6*e^2 + 233/3*e + 50/3, -2/3*e^4 + 4/3*e^3 + 14/3*e^2 - 32/3*e + 152/3, e^5 - 62/3*e^3 - 6*e^2 + 233/3*e + 50/3, -2/3*e^4 + 4/3*e^3 + 14/3*e^2 - 32/3*e + 152/3, -1/3*e^4 - 4/3*e^3 + 34/3*e^2 + 56/3*e - 134/3, 1/3*e^5 - 23/3*e^3 - 1/3*e^2 + 118/3*e - 14/3, -1/3*e^4 - 4/3*e^3 + 34/3*e^2 + 56/3*e - 134/3, 1/3*e^5 - 23/3*e^3 - 1/3*e^2 + 118/3*e - 14/3, 7/6*e^4 - 14/3*e^3 - 85/6*e^2 + 57*e + 68/3, 13/12*e^5 + 2/3*e^4 - 319/12*e^3 - 27/2*e^2 + 406/3*e - 14, 13/12*e^5 + 2/3*e^4 - 319/12*e^3 - 27/2*e^2 + 406/3*e - 14, 1/2*e^5 + 1/3*e^4 - 77/6*e^3 - 22/3*e^2 + 78*e - 14/3, 1/2*e^5 + 1/3*e^4 - 77/6*e^3 - 22/3*e^2 + 78*e - 14/3, 1/6*e^5 - 1/3*e^4 - 5/2*e^3 + 5/3*e^2 - 16/3*e + 28/3, 1/6*e^5 - 1/3*e^4 - 5/2*e^3 + 5/3*e^2 - 16/3*e + 28/3, 1/12*e^5 - e^4 + 29/12*e^3 + 61/6*e^2 - 43*e + 2, 1/12*e^5 - e^4 + 29/12*e^3 + 61/6*e^2 - 43*e + 2, -11/12*e^5 + 5/3*e^4 + 205/12*e^3 - 45/2*e^2 - 196/3*e + 130/3, -11/12*e^5 + 5/3*e^4 + 205/12*e^3 - 45/2*e^2 - 196/3*e + 130/3, -1/2*e^5 + 4/3*e^4 + 61/6*e^3 - 61/3*e^2 - 48*e + 142/3, -1/2*e^5 + 4/3*e^4 + 61/6*e^3 - 61/3*e^2 - 48*e + 142/3, -5/12*e^5 - e^4 + 115/12*e^3 + 91/6*e^2 - 104/3*e - 2/3, -5/12*e^5 - e^4 + 115/12*e^3 + 91/6*e^2 - 104/3*e - 2/3, 1/6*e^5 + 2/3*e^4 - 25/6*e^3 - 31/3*e^2 + 70/3*e + 14, 2/3*e^5 - 14*e^3 - 17/3*e^2 + 148/3*e + 70/3, 2/3*e^5 - 14*e^3 - 17/3*e^2 + 148/3*e + 70/3, 1/6*e^5 + 2/3*e^4 - 25/6*e^3 - 31/3*e^2 + 70/3*e + 14, -1/2*e^5 + 17/2*e^3 + 3*e^2 - 16*e - 6, -1/2*e^5 + 17/2*e^3 + 3*e^2 - 16*e - 6, 11/12*e^5 - 1/3*e^4 - 241/12*e^3 - 17/6*e^2 + 94*e + 26/3, 11/12*e^5 - 1/3*e^4 - 241/12*e^3 - 17/6*e^2 + 94*e + 26/3, 3/4*e^5 + e^4 - 81/4*e^3 - 37/2*e^2 + 114*e + 6, 3/4*e^5 + e^4 - 81/4*e^3 - 37/2*e^2 + 114*e + 6] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([49, 7, w^3 - w^2 - 6*w - 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]