/* 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([11, 9, -9, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([49, 7, 2*w^3 + 3*w^2 - 13*w - 15]) primes_array = [ [5, 5, -2*w^3 - 2*w^2 + 13*w + 8],\ [11, 11, 2*w^3 + 3*w^2 - 12*w - 11],\ [11, 11, -w^3 - 2*w^2 + 6*w + 9],\ [11, 11, w^3 + w^2 - 7*w - 4],\ [11, 11, w - 1],\ [16, 2, 2],\ [19, 19, -w^2 + 4],\ [19, 19, 2*w^3 + 2*w^2 - 13*w - 6],\ [19, 19, 3*w^3 + 4*w^2 - 18*w - 16],\ [19, 19, -w^3 - w^2 + 5*w + 3],\ [49, 7, 2*w^3 + 3*w^2 - 13*w - 15],\ [59, 59, -3*w^3 - 4*w^2 + 19*w + 14],\ [59, 59, 3*w^3 + 4*w^2 - 18*w - 17],\ [59, 59, 2*w^3 + 3*w^2 - 11*w - 13],\ [59, 59, -w^3 - 2*w^2 + 7*w + 9],\ [71, 71, 3*w^3 + 3*w^2 - 17*w - 10],\ [71, 71, -2*w^3 - w^2 + 14*w + 2],\ [71, 71, 5*w^3 + 7*w^2 - 30*w - 25],\ [71, 71, -3*w^3 - 4*w^2 + 16*w + 16],\ [81, 3, -3],\ [89, 89, -2*w^3 - 2*w^2 + 13*w + 4],\ [89, 89, 3*w^3 + 4*w^2 - 17*w - 16],\ [89, 89, 3*w^3 + 4*w^2 - 18*w - 18],\ [89, 89, -4*w^3 - 5*w^2 + 25*w + 18],\ [139, 139, -w^3 + 6*w + 1],\ [139, 139, -3*w^3 - 3*w^2 + 19*w + 8],\ [139, 139, 4*w^3 + 5*w^2 - 24*w - 21],\ [139, 139, -2*w^3 - 2*w^2 + 11*w + 5],\ [151, 151, -6*w^3 - 7*w^2 + 37*w + 27],\ [151, 151, 3*w^3 + 5*w^2 - 19*w - 17],\ [151, 151, -6*w^3 - 8*w^2 + 37*w + 31],\ [151, 151, 4*w^3 + 6*w^2 - 25*w - 26],\ [191, 191, 5*w^3 + 7*w^2 - 31*w - 26],\ [191, 191, -2*w^3 - 3*w^2 + 10*w + 13],\ [191, 191, -5*w^3 - 7*w^2 + 31*w + 29],\ [191, 191, 2*w^3 + 4*w^2 - 13*w - 17],\ [199, 199, 2*w^3 + 4*w^2 - 11*w - 20],\ [199, 199, -2*w^3 - 2*w^2 + 11*w + 3],\ [199, 199, 3*w^3 + 5*w^2 - 17*w - 17],\ [199, 199, 3*w^3 + 3*w^2 - 19*w - 6],\ [211, 211, 3*w^3 + 5*w^2 - 18*w - 19],\ [211, 211, -3*w^3 - 5*w^2 + 18*w + 21],\ [211, 211, 2*w^3 + 4*w^2 - 12*w - 17],\ [211, 211, -4*w^3 - 6*w^2 + 24*w + 23],\ [229, 229, 2*w^3 + 4*w^2 - 13*w - 19],\ [229, 229, -2*w^3 - 3*w^2 + 10*w + 15],\ [229, 229, -5*w^3 - 7*w^2 + 31*w + 24],\ [229, 229, 2*w^3 + 2*w^2 - 14*w - 3],\ [269, 269, 2*w^3 + w^2 - 11*w - 1],\ [269, 269, -6*w^3 - 7*w^2 + 37*w + 24],\ [269, 269, 5*w^3 + 6*w^2 - 29*w - 24],\ [269, 269, 3*w^3 + 2*w^2 - 19*w - 7],\ [281, 281, -4*w^3 - 6*w^2 + 25*w + 25],\ [281, 281, -5*w^3 - 7*w^2 + 31*w + 27],\ [281, 281, w^2 + 2*w - 7],\ [281, 281, 3*w^3 + 5*w^2 - 19*w - 18],\ [331, 331, -2*w^3 - 3*w^2 + 12*w + 7],\ [331, 331, w^3 + w^2 - 7*w - 8],\ [331, 331, w^3 + 2*w^2 - 6*w - 13],\ [331, 331, w - 5],\ [349, 349, 2*w^3 + 5*w^2 - 16*w - 12],\ [349, 349, 2*w^3 + 4*w^2 - 15*w - 10],\ [349, 349, 8*w^3 + 9*w^2 - 50*w - 32],\ [349, 349, 2*w^3 + 4*w^2 - 15*w - 9],\ [401, 401, 4*w^3 + 3*w^2 - 21*w - 12],\ [401, 401, 3*w^3 + 2*w^2 - 16*w - 9],\ [401, 401, -3*w^3 - 6*w^2 + 20*w + 19],\ [401, 401, -4*w^3 - 3*w^2 + 27*w + 9],\ [409, 409, -5*w^3 - 6*w^2 + 31*w + 20],\ [409, 409, 3*w^3 + 4*w^2 - 20*w - 12],\ [409, 409, -3*w^3 - 5*w^2 + 17*w + 23],\ [409, 409, 4*w^3 + 5*w^2 - 23*w - 21],\ [419, 419, -4*w^3 - 4*w^2 + 21*w + 18],\ [419, 419, -4*w^3 - 4*w^2 + 20*w + 19],\ [419, 419, -3*w^3 - 4*w^2 + 16*w + 18],\ [419, 419, -2*w^3 - w^2 + 8*w + 10],\ [421, 421, -6*w^3 - 7*w^2 + 36*w + 26],\ [421, 421, 5*w^3 + 5*w^2 - 31*w - 17],\ [421, 421, 3*w^3 + 2*w^2 - 18*w - 6],\ [421, 421, 4*w^3 + 4*w^2 - 23*w - 14],\ [431, 431, 6*w^3 + 7*w^2 - 36*w - 25],\ [431, 431, -3*w^3 - 2*w^2 + 18*w + 5],\ [431, 431, 4*w^3 + 4*w^2 - 23*w - 15],\ [431, 431, -5*w^3 - 5*w^2 + 31*w + 18],\ [439, 439, w^3 + w^2 - 4*w - 1],\ [439, 439, w^3 + 3*w^2 - 6*w - 10],\ [439, 439, 3*w^3 + 3*w^2 - 20*w - 7],\ [439, 439, 5*w^3 + 7*w^2 - 30*w - 30],\ [479, 479, -4*w^3 - 5*w^2 + 25*w + 15],\ [479, 479, -5*w^3 - 6*w^2 + 32*w + 21],\ [479, 479, 5*w^3 + 7*w^2 - 29*w - 28],\ [479, 479, 2*w^2 + w - 9],\ [491, 491, 7*w^3 + 8*w^2 - 43*w - 31],\ [491, 491, 6*w^3 + 6*w^2 - 37*w - 24],\ [491, 491, 4*w^3 + 3*w^2 - 24*w - 6],\ [491, 491, 5*w^3 + 5*w^2 - 29*w - 21],\ [509, 509, -4*w^3 - 5*w^2 + 25*w + 14],\ [509, 509, -3*w^3 - 4*w^2 + 17*w + 20],\ [509, 509, -6*w^3 - 7*w^2 + 38*w + 25],\ [509, 509, -6*w^3 - 8*w^2 + 35*w + 31],\ [541, 541, 9*w^3 + 12*w^2 - 55*w - 46],\ [541, 541, w^3 + 4*w^2 - 7*w - 17],\ [541, 541, -4*w^3 - 5*w^2 + 21*w + 19],\ [541, 541, -4*w^3 - 3*w^2 + 27*w + 8],\ [571, 571, -3*w^3 - 6*w^2 + 18*w + 23],\ [571, 571, 6*w^3 + 9*w^2 - 36*w - 37],\ [571, 571, 7*w^3 + 10*w^2 - 42*w - 36],\ [571, 571, 2*w^3 + 5*w^2 - 12*w - 24],\ [619, 619, -9*w^3 - 11*w^2 + 55*w + 39],\ [619, 619, -5*w^3 - 4*w^2 + 32*w + 14],\ [619, 619, 7*w^3 + 9*w^2 - 42*w - 36],\ [619, 619, 4*w^3 + 6*w^2 - 26*w - 27],\ [631, 631, 2*w^3 + 5*w^2 - 12*w - 21],\ [631, 631, -7*w^3 - 10*w^2 + 42*w + 39],\ [631, 631, 4*w^3 + 4*w^2 - 27*w - 13],\ [631, 631, w^3 + w^2 - 3*w - 4],\ [641, 641, -9*w^3 - 10*w^2 + 56*w + 36],\ [641, 641, -5*w^3 - 9*w^2 + 30*w + 32],\ [641, 641, -3*w^3 - 6*w^2 + 19*w + 21],\ [641, 641, 4*w^3 + 3*w^2 - 22*w - 10],\ [701, 701, -2*w^3 - 5*w^2 + 14*w + 20],\ [701, 701, -6*w^3 - 7*w^2 + 36*w + 34],\ [701, 701, 4*w^3 + 6*w^2 - 23*w - 17],\ [701, 701, -9*w^3 - 12*w^2 + 56*w + 46],\ [719, 719, 3*w^3 + 5*w^2 - 17*w - 25],\ [719, 719, -3*w^3 - 2*w^2 + 17*w + 3],\ [719, 719, 7*w^3 + 8*w^2 - 43*w - 26],\ [719, 719, -6*w^3 - 7*w^2 + 35*w + 29],\ [751, 751, 2*w^3 + 2*w^2 - 15*w - 4],\ [751, 751, 5*w^3 + 8*w^2 - 30*w - 34],\ [751, 751, w^3 + w^2 - 9*w - 5],\ [751, 751, -4*w^3 - 7*w^2 + 24*w + 26],\ [769, 769, 6*w^3 + 8*w^2 - 37*w - 27],\ [769, 769, -w^3 - 3*w^2 + 7*w + 16],\ [769, 769, 2*w^3 + w^2 - 14*w - 5],\ [769, 769, -3*w^3 - 4*w^2 + 16*w + 19],\ [821, 821, 6*w^3 + 6*w^2 - 37*w - 23],\ [821, 821, 5*w^3 + 5*w^2 - 29*w - 20],\ [821, 821, -7*w^3 - 8*w^2 + 42*w + 27],\ [821, 821, 4*w^3 + 3*w^2 - 24*w - 7],\ [829, 829, 7*w^3 + 8*w^2 - 44*w - 28],\ [829, 829, 7*w^3 + 9*w^2 - 41*w - 35],\ [829, 829, -2*w^3 - w^2 + 10*w + 2],\ [829, 829, 2*w^3 - 13*w + 2],\ [839, 839, 4*w^3 + 8*w^2 - 25*w - 26],\ [839, 839, -3*w^3 - 3*w^2 + 15*w + 16],\ [839, 839, -w^3 - 4*w^2 + 8*w + 10],\ [839, 839, -3*w^3 - 7*w^2 + 18*w + 26],\ [841, 29, -5*w^3 - 5*w^2 + 30*w + 16],\ [841, 29, -5*w^3 - 5*w^2 + 30*w + 19],\ [859, 859, 5*w^3 + 6*w^2 - 32*w - 20],\ [859, 859, -4*w^3 - 5*w^2 + 23*w + 23],\ [859, 859, -5*w^3 - 6*w^2 + 31*w + 18],\ [859, 859, -2*w^3 - w^2 + 13*w + 6],\ [911, 911, 9*w^3 + 12*w^2 - 56*w - 48],\ [911, 911, 6*w^3 + 5*w^2 - 38*w - 14],\ [911, 911, 7*w^3 + 8*w^2 - 40*w - 28],\ [911, 911, 10*w^3 + 12*w^2 - 61*w - 46],\ [929, 929, -7*w^3 - 10*w^2 + 39*w + 39],\ [929, 929, -10*w^3 - 13*w^2 + 60*w + 45],\ [929, 929, -6*w^3 - 7*w^2 + 32*w + 29],\ [929, 929, -3*w^3 - w^2 + 12*w + 12],\ [961, 31, -5*w^3 - 5*w^2 + 30*w + 17],\ [961, 31, -5*w^3 - 5*w^2 + 30*w + 18],\ [991, 991, 10*w^3 + 12*w^2 - 61*w - 45],\ [991, 991, -6*w^3 - 9*w^2 + 38*w + 38],\ [991, 991, 6*w^3 + 8*w^2 - 37*w - 38],\ [991, 991, -8*w^3 - 11*w^2 + 49*w + 43]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^4 + 7*x^3 - 6*x^2 - 92*x - 89 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1, e, 1/5*e^3 + 4/5*e^2 - 18/5*e - 53/5, -1/15*e^3 + 9/5*e + 29/15, 1/15*e^3 - 9/5*e + 31/15, 1/5*e^3 + 4/5*e^2 - 13/5*e - 38/5, 2/15*e^3 + 3/5*e^2 - 2*e - 112/15, -1/3*e^3 - e^2 + 5*e + 20/3, 1/15*e^3 + 1/5*e^2 - 3/5*e - 32/15, -4/15*e^3 - 7/5*e^2 + 14/5*e + 182/15, 1, 2/15*e^3 + e^2 - 18/5*e - 283/15, -1/15*e^3 - 2/5*e^2 + 12/5*e + 10/3, 4/15*e^3 + 6/5*e^2 - 5*e - 269/15, -1/3*e^3 - 9/5*e^2 + 31/5*e + 277/15, -1/5*e^3 - 4/5*e^2 + 13/5*e + 58/5, -3/5*e^3 - 3*e^2 + 36/5*e + 132/5, -1/5*e^3 - 4/5*e^2 + 13/5*e + 58/5, -3/5*e^3 - 9/5*e^2 + 42/5*e + 51/5, -1/5*e^3 - 4/5*e^2 + 13/5*e + 8/5, 2/15*e^3 + 4/5*e^2 - 14/5*e - 47/3, -1/15*e^3 + 1/5*e^2 + 3*e - 34/15, 4/15*e^3 + 3/5*e^2 - 28/5*e - 22/3, -2/15*e^3 - 4/5*e^2 + 14/5*e + 17/3, 2/5*e^3 + 7/5*e^2 - 42/5*e - 28, 8/15*e^3 + 8/5*e^2 - 29/5*e - 76/15, -1/5*e^3 - 3/5*e^2 + 29/5*e - 8/5, 13/15*e^3 + 4*e^2 - 62/5*e - 557/15, 1/3*e^3 + 6/5*e^2 - 44/5*e - 253/15, -8/15*e^3 - 6/5*e^2 + 46/5*e + 17/3, -8/15*e^3 - 2*e^2 + 57/5*e + 382/15, -4/15*e^3 - 2*e^2 + 6/5*e + 251/15, 1/3*e^3 + 6/5*e^2 - 29/5*e - 118/15, -2/3*e^3 - 16/5*e^2 + 69/5*e + 623/15, 7/15*e^3 + 12/5*e^2 - 56/5*e - 494/15, 1/15*e^3 + 2/5*e^2 + 3/5*e + 8/3, -8/15*e^3 - 13/5*e^2 + 34/5*e + 106/15, -1/5*e^3 - 1/5*e^2 + 11/5*e + 1, -7/15*e^3 - 7/5*e^2 + 31/5*e - 136/15, -2/5*e^3 - 11/5*e^2 + 28/5*e + 139/5, -1/3*e^3 - 2*e^2 + 3*e + 65/3, -7/15*e^3 - 6/5*e^2 + 37/5*e + 161/15, 7/15*e^3 + 4/5*e^2 - 54/5*e - 31/3, -4/15*e^3 + 41/5*e - 4/15, -2/5*e^3 - 2/5*e^2 + 52/5*e + 10, 11/15*e^3 + 9/5*e^2 - 12*e - 121/15, 2/5*e^3 + 2/5*e^2 - 52/5*e, 7/15*e^3 + 3*e^2 - 18/5*e - 368/15, -4/5*e^3 - 11/5*e^2 + 72/5*e + 82/5, -1/5*e^3 - 9/5*e^2 - 7/5*e + 58/5, -1/3*e^3 - 7/5*e^2 + 28/5*e + 1/15, -1/15*e^3 - 1/5*e^2 - 2/5*e - 238/15, 4/15*e^3 - 1/5*e^2 - 32/5*e + 82/15, 2/5*e^3 + 8/5*e^2 - 46/5*e - 121/5, -2/5*e^3 - 8/5*e^2 + 46/5*e + 91/5, -1/15*e^3 + e^2 + 19/5*e - 166/15, -16/15*e^3 - 17/5*e^2 + 97/5*e + 94/3, -4/15*e^3 - 6/5*e^2 + 8*e + 359/15, -2/15*e^3 - 7/5*e^2 - 19/5*e + 79/15, 2/3*e^3 + 14/5*e^2 - 66/5*e - 437/15, 11/15*e^3 + 4*e^2 - 19/5*e - 634/15, 5/3*e^3 + 28/5*e^2 - 137/5*e - 944/15, 2/3*e^3 + 7/5*e^2 - 78/5*e - 341/15, -7/15*e^3 - 3/5*e^2 + 13*e + 47/15, 11/15*e^3 + 11/5*e^2 - 68/5*e - 637/15, 1/15*e^3 + e^2 + 16/5*e - 404/15, -9/5*e^2 - 14/5*e + 104/5, -1/5*e^3 + e^2 + 27/5*e - 86/5, 13/15*e^3 + 16/5*e^2 - 76/5*e - 127/3, 2/15*e^3 + 4/5*e^2 + 11/5*e - 32/3, 1/5*e^3 + 14/5*e^2 + 12/5*e - 113/5, 4/5*e^3 + 6/5*e^2 - 77/5*e - 2/5, 4/15*e^3 + 13/5*e^2 + 7/5*e - 43/3, -8/15*e^3 - 8/5*e^2 + 54/5*e + 301/15, 2/15*e^3 - 28/5*e - 13/15, 14/15*e^3 + 11/5*e^2 - 17*e - 124/15, -11/15*e^3 - 11/5*e^2 + 88/5*e + 427/15, -4/15*e^3 - 3*e^2 + 11/5*e + 656/15, 11/15*e^3 + 11/5*e^2 - 88/5*e - 442/15, -2/15*e^3 + 7/5*e^2 + 3*e - 233/15, 6/5*e^3 + 6*e^2 - 72/5*e - 259/5, 6/5*e^3 + 18/5*e^2 - 84/5*e - 97/5, 2/5*e^3 + 3/5*e^2 - 21/5*e - 26/5, 4/5*e^3 + 21/5*e^2 - 57/5*e - 267/5, 2/5*e^3 + 1/5*e^2 - 28/5*e + 151/5, 2*e^2 + 7*e - 32, 3/5*e^3 + 19/5*e^2 - 37/5*e - 91/5, e^3 + 2*e^2 - 20*e - 31, 1/15*e^3 + 9/5*e^2 + 4*e - 221/15, 11/15*e^3 + 7/5*e^2 - 72/5*e - 26/3, 8/15*e^3 + 3/5*e^2 - 64/5*e + 119/15, -1/3*e^3 + 1/5*e^2 + 51/5*e + 187/15, 8/15*e^3 + 7/5*e^2 - 13*e - 283/15, -4/15*e^3 - 6/5*e^2 + 5*e + 374/15, -8/15*e^3 - 7/5*e^2 + 13*e + 268/15, 1/15*e^3 + 2/5*e^2 - 12/5*e + 11/3, 11/15*e^3 + 14/5*e^2 - 7*e - 406/15, -3/5*e^3 - 3/5*e^2 + 83/5*e + 13, 19/15*e^3 + 26/5*e^2 - 19*e - 884/15, 4/5*e^3 + 7/5*e^2 - 96/5*e - 63/5, 2/3*e^3 + 9/5*e^2 - 56/5*e + 13/15, 1/3*e^3 + 11/5*e^2 - 9/5*e - 73/15, -1/15*e^3 + 2/5*e^2 - 4/5*e - 262/15, -8/15*e^3 - 14/5*e^2 + 43/5*e + 379/15, 8/15*e^3 - 6/5*e^2 - 93/5*e + 221/15, -17/15*e^3 - 6/5*e^2 + 132/5*e + 196/15, -2/5*e^3 + 3/5*e^2 + 52/5*e - 7, 1/5*e^3 - 7/5*e^2 - 39/5*e + 103/5, -3/5*e^3 - 3*e^2 + 21/5*e + 77/5, 6/5*e^3 + 24/5*e^2 - 93/5*e - 208/5, -6/5*e^3 - 21/5*e^2 + 96/5*e + 31, 3/5*e^3 + 12/5*e^2 - 24/5*e - 49/5, 2/3*e^3 + 21/5*e^2 - 39/5*e - 428/15, 8/15*e^3 + 3/5*e^2 - 39/5*e + 299/15, -3/5*e^3 - 2*e^2 + 86/5*e + 112/5, 6/5*e^3 + 22/5*e^2 - 25*e - 311/5, 1/5*e^3 + 2/5*e^2 - 3*e - 111/5, 7/15*e^3 + 7/5*e^2 - 16/5*e + 76/15, 17/15*e^3 + 5*e^2 - 88/5*e - 643/15, 1/5*e^3 + 6/5*e^2 - 11/5*e - 33, 13/15*e^3 + 28/5*e^2 - 54/5*e - 851/15, -26/15*e^3 - 42/5*e^2 + 107/5*e + 218/3, -5/3*e^3 - 26/5*e^2 + 114/5*e + 443/15, 8/15*e^3 - 37/5*e + 278/15, -1/3*e^3 - 9/5*e^2 + 51/5*e + 307/15, 8/5*e^3 + 22/5*e^2 - 134/5*e - 209/5, 4/5*e^3 + 26/5*e^2 - 22/5*e - 267/5, 14/15*e^3 + 21/5*e^2 - 18*e - 889/15, -1/5*e^3 + 4/5*e^2 + 26/5*e - 32, 1/5*e^3 - 4/5*e^2 - 41/5*e + 22, -8/5*e^2 - 13/5*e + 3/5, -3/5*e^3 - 4/5*e^2 + 67/5*e + 106/5, 4/5*e^3 + 14/5*e^2 - 39/5*e - 24, 7/5*e^3 + 6*e^2 - 104/5*e - 333/5, -4/15*e^3 - 13/5*e^2 - 2/5*e + 82/3, -11/15*e^3 - 7/5*e^2 + 67/5*e + 32/3, 1/15*e^3 + 17/5*e^2 + 38/5*e - 85/3, 17/15*e^3 + 7/5*e^2 - 116/5*e - 4/15, 8/15*e^3 + 4/5*e^2 - 18/5*e + 326/15, 22/15*e^3 + 36/5*e^2 - 112/5*e - 956/15, 19/15*e^3 + 28/5*e^2 - 83/5*e - 205/3, 28/15*e^3 + 39/5*e^2 - 173/5*e - 1454/15, 17/15*e^3 + 4*e^2 - 73/5*e - 703/15, -4/15*e^3 - 7/5*e^2 + 69/5*e + 377/15, -4/3*e^3 - 2/5*e^2 + 153/5*e - 89/15, 1/3*e^3 - 18/5*e^2 - 88/5*e + 584/15, -23/15*e^3 - 32/5*e^2 + 17*e + 1063/15, -31/15*e^3 - 8*e^2 + 149/5*e + 1379/15, 7, 9/5*e^3 + 36/5*e^2 - 117/5*e - 247/5, 2/15*e^3 + 12/5*e^2 + 24/5*e - 289/15, 7/5*e^3 + 27/5*e^2 - 107/5*e - 31, 16/15*e^3 + 12/5*e^2 - 102/5*e - 55/3, 4/5*e^3 + 17/5*e^2 - 36/5*e - 23/5, -e^2 - 3*e + 22, 14/15*e^3 + 12/5*e^2 - 54/5*e - 202/15, 22/15*e^3 + 36/5*e^2 - 102/5*e - 1166/15, -2/5*e^3 - 3/5*e^2 + 41/5*e + 81/5, -16/15*e^3 - 27/5*e^2 + 42/5*e + 133/3, -7/5*e^3 - 6*e^2 + 124/5*e + 443/5, 2/5*e^2 - 33/5*e + 18/5, -29/15*e^3 - 33/5*e^2 + 153/5*e + 179/3, -e^3 - 4*e^2 + 13*e + 50, -2/5*e^3 - 8/5*e^2 + 26/5*e - 44/5, -3/5*e^3 - 8/5*e^2 + 78/5*e + 26, -22/15*e^3 - 8*e^2 + 88/5*e + 998/15, -4/3*e^3 - 16/5*e^2 + 94/5*e + 28/15, 4/5*e^3 + 12/5*e^2 - 91/5*e - 133/5] 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, 2*w^3 + 3*w^2 - 13*w - 15])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]