/* 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([19, 14, -13, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([16, 2, 2]) primes_array = [ [4, 2, -2/19*w^3 + 3/19*w^2 + 37/19*w - 3],\ [5, 5, 3/19*w^3 + 5/19*w^2 - 27/19*w - 1],\ [5, 5, -3/19*w^3 + 14/19*w^2 + 8/19*w - 2],\ [9, 3, -2/19*w^3 + 3/19*w^2 + 37/19*w - 4],\ [19, 19, -w],\ [19, 19, 4/19*w^3 - 6/19*w^2 - 55/19*w + 1],\ [19, 19, 4/19*w^3 - 6/19*w^2 - 55/19*w + 2],\ [19, 19, w - 1],\ [29, 29, -5/19*w^3 - 2/19*w^2 + 64/19*w + 2],\ [29, 29, 10/19*w^3 - 34/19*w^2 - 71/19*w + 9],\ [29, 29, 4/19*w^3 - 6/19*w^2 - 55/19*w + 4],\ [29, 29, -w + 3],\ [49, 7, 5/19*w^3 - 17/19*w^2 - 64/19*w + 11],\ [49, 7, 6/19*w^3 - 9/19*w^2 - 92/19*w - 1],\ [71, 71, 3/19*w^3 + 5/19*w^2 - 46/19*w - 1],\ [71, 71, 6/19*w^3 - 9/19*w^2 - 73/19*w],\ [71, 71, 6/19*w^3 - 9/19*w^2 - 73/19*w + 4],\ [71, 71, -3/19*w^3 + 14/19*w^2 + 27/19*w - 3],\ [101, 101, 7/19*w^3 - 1/19*w^2 - 63/19*w - 3],\ [101, 101, -9/19*w^3 + 23/19*w^2 + 81/19*w - 5],\ [101, 101, 9/19*w^3 - 4/19*w^2 - 100/19*w],\ [101, 101, 7/19*w^3 - 20/19*w^2 - 44/19*w + 6],\ [121, 11, 6/19*w^3 - 9/19*w^2 - 54/19*w + 1],\ [121, 11, -6/19*w^3 + 9/19*w^2 + 54/19*w - 2],\ [139, 139, 9/19*w^3 - 4/19*w^2 - 100/19*w - 2],\ [139, 139, -7/19*w^3 + 1/19*w^2 + 63/19*w + 1],\ [139, 139, 7/19*w^3 - 20/19*w^2 - 44/19*w + 4],\ [139, 139, w - 5],\ [149, 149, -1/19*w^3 + 11/19*w^2 - 10/19*w - 6],\ [149, 149, -3/19*w^3 - 5/19*w^2 + 46/19*w],\ [149, 149, -3/19*w^3 + 14/19*w^2 + 27/19*w - 2],\ [149, 149, 1/19*w^3 + 8/19*w^2 - 9/19*w - 6],\ [169, 13, 14/19*w^3 - 40/19*w^2 - 126/19*w + 13],\ [169, 13, 10/19*w^3 - 34/19*w^2 - 52/19*w + 7],\ [191, 191, -10/19*w^3 + 15/19*w^2 + 109/19*w - 6],\ [191, 191, 6/19*w^3 - 9/19*w^2 - 35/19*w - 2],\ [191, 191, -6/19*w^3 + 9/19*w^2 + 35/19*w - 4],\ [191, 191, 10/19*w^3 - 15/19*w^2 - 109/19*w],\ [211, 211, 1/19*w^3 + 8/19*w^2 - 28/19*w - 8],\ [211, 211, 1/19*w^3 - 11/19*w^2 - 9/19*w - 1],\ [211, 211, -1/19*w^3 - 8/19*w^2 + 28/19*w - 2],\ [211, 211, -1/19*w^3 + 11/19*w^2 + 9/19*w - 9],\ [239, 239, 4/19*w^3 - 25/19*w^2 - 17/19*w + 12],\ [239, 239, -1/19*w^3 - 8/19*w^2 - 29/19*w + 5],\ [239, 239, 10/19*w^3 - 15/19*w^2 - 128/19*w + 1],\ [239, 239, -4/19*w^3 - 13/19*w^2 + 55/19*w + 10],\ [241, 241, -2/19*w^3 + 3/19*w^2 + 56/19*w - 4],\ [241, 241, -6/19*w^3 + 9/19*w^2 + 92/19*w],\ [241, 241, 6/19*w^3 - 9/19*w^2 - 92/19*w + 5],\ [241, 241, -2/19*w^3 + 3/19*w^2 + 56/19*w + 1],\ [269, 269, -10/19*w^3 + 34/19*w^2 + 71/19*w - 11],\ [269, 269, 8/19*w^3 - 12/19*w^2 - 129/19*w + 11],\ [269, 269, -10/19*w^3 + 34/19*w^2 + 71/19*w - 8],\ [269, 269, -13/19*w^3 + 48/19*w^2 + 60/19*w - 8],\ [289, 17, 30/19*w^3 - 7/19*w^2 - 384/19*w - 14],\ [289, 17, 11/19*w^3 - 45/19*w^2 - 80/19*w + 17],\ [311, 311, -12/19*w^3 + 37/19*w^2 + 108/19*w - 15],\ [311, 311, -24/19*w^3 + 55/19*w^2 + 273/19*w - 22],\ [311, 311, -8/19*w^3 - 7/19*w^2 + 110/19*w + 4],\ [311, 311, 4/19*w^3 + 13/19*w^2 - 36/19*w - 7],\ [331, 331, -1/19*w^3 - 8/19*w^2 + 66/19*w - 2],\ [331, 331, -6/19*w^3 + 28/19*w^2 + 35/19*w - 9],\ [331, 331, 20/19*w^3 - 68/19*w^2 - 161/19*w + 22],\ [331, 331, 16/19*w^3 - 62/19*w^2 - 87/19*w + 15],\ [359, 359, 13/19*w^3 - 48/19*w^2 - 79/19*w + 11],\ [359, 359, -7/19*w^3 + 20/19*w^2 + 101/19*w - 13],\ [359, 359, -15/19*w^3 + 51/19*w^2 + 116/19*w - 17],\ [359, 359, 3/19*w^3 + 5/19*w^2 - 84/19*w + 5],\ [379, 379, 3/19*w^3 + 5/19*w^2 - 65/19*w - 9],\ [379, 379, 25/19*w^3 - 9/19*w^2 - 339/19*w - 11],\ [379, 379, -25/19*w^3 + 66/19*w^2 + 282/19*w - 28],\ [379, 379, 3/19*w^3 - 14/19*w^2 - 46/19*w + 12],\ [389, 389, -13/19*w^3 + 48/19*w^2 + 136/19*w - 24],\ [389, 389, 11/19*w^3 - 7/19*w^2 - 118/19*w + 2],\ [389, 389, -3/19*w^3 + 14/19*w^2 + 46/19*w - 10],\ [389, 389, -13/19*w^3 - 9/19*w^2 + 193/19*w + 15],\ [409, 409, 2/19*w^3 - 3/19*w^2 - 56/19*w],\ [409, 409, 6/19*w^3 - 9/19*w^2 - 92/19*w + 4],\ [409, 409, -6/19*w^3 + 9/19*w^2 + 92/19*w - 1],\ [409, 409, -2/19*w^3 + 3/19*w^2 + 56/19*w - 3],\ [431, 431, -6/19*w^3 + 9/19*w^2 + 130/19*w - 13],\ [431, 431, 12/19*w^3 - 37/19*w^2 - 108/19*w + 11],\ [431, 431, 10/19*w^3 - 15/19*w^2 - 166/19*w + 14],\ [431, 431, -8/19*w^3 + 31/19*w^2 + 34/19*w - 8],\ [461, 461, 5/19*w^3 - 17/19*w^2 - 45/19*w + 1],\ [461, 461, -3/19*w^3 + 14/19*w^2 + 8/19*w - 8],\ [461, 461, 3/19*w^3 + 5/19*w^2 - 27/19*w - 7],\ [461, 461, 5/19*w^3 + 2/19*w^2 - 64/19*w + 2],\ [479, 479, 5/19*w^3 - 17/19*w^2 - 26/19*w + 7],\ [479, 479, 1/19*w^3 - 11/19*w^2 - 28/19*w + 7],\ [479, 479, 7/19*w^3 - 1/19*w^2 - 82/19*w + 1],\ [479, 479, -5/19*w^3 + 17/19*w^2 + 64/19*w - 3],\ [499, 499, -11/19*w^3 + 7/19*w^2 + 118/19*w + 2],\ [499, 499, 9/19*w^3 - 23/19*w^2 - 62/19*w + 4],\ [499, 499, -9/19*w^3 + 4/19*w^2 + 81/19*w],\ [499, 499, -11/19*w^3 + 26/19*w^2 + 99/19*w - 8],\ [509, 509, -6/19*w^3 - 10/19*w^2 + 73/19*w + 9],\ [509, 509, -1/19*w^3 + 11/19*w^2 + 47/19*w - 7],\ [509, 509, -6/19*w^3 - 10/19*w^2 + 73/19*w + 2],\ [509, 509, -9/19*w^3 + 4/19*w^2 + 138/19*w - 2],\ [529, 23, -4/19*w^3 + 6/19*w^2 + 74/19*w - 1],\ [529, 23, 4/19*w^3 - 6/19*w^2 - 74/19*w + 3],\ [571, 571, 1/19*w^3 + 8/19*w^2 - 66/19*w + 6],\ [571, 571, -9/19*w^3 + 23/19*w^2 + 119/19*w - 15],\ [571, 571, -11/19*w^3 + 26/19*w^2 + 156/19*w - 18],\ [571, 571, 3/19*w^3 + 5/19*w^2 - 103/19*w + 9],\ [599, 599, 6/19*w^3 - 9/19*w^2 - 16/19*w - 2],\ [599, 599, -14/19*w^3 + 21/19*w^2 + 164/19*w - 7],\ [599, 599, -2/19*w^3 + 22/19*w^2 + 18/19*w - 13],\ [599, 599, -6/19*w^3 + 9/19*w^2 + 16/19*w - 3],\ [601, 601, 23/19*w^3 - 63/19*w^2 - 264/19*w + 31],\ [601, 601, -36/19*w^3 - 3/19*w^2 + 476/19*w + 23],\ [601, 601, 36/19*w^3 - 111/19*w^2 - 362/19*w + 46],\ [601, 601, -16/19*w^3 + 43/19*w^2 + 125/19*w - 8],\ [619, 619, -5/19*w^3 + 17/19*w^2 + 45/19*w - 11],\ [619, 619, 5/19*w^3 - 17/19*w^2 - 26/19*w - 2],\ [619, 619, -5/19*w^3 - 2/19*w^2 + 45/19*w - 4],\ [619, 619, -7/19*w^3 + 20/19*w^2 + 63/19*w - 12],\ [691, 691, 7/19*w^3 - 1/19*w^2 - 120/19*w],\ [691, 691, 3/19*w^3 - 14/19*w^2 - 65/19*w + 6],\ [691, 691, -3/19*w^3 - 5/19*w^2 + 84/19*w + 2],\ [691, 691, 7/19*w^3 - 20/19*w^2 - 101/19*w + 6],\ [701, 701, -7/19*w^3 + 20/19*w^2 + 63/19*w - 2],\ [701, 701, 5/19*w^3 - 17/19*w^2 - 26/19*w + 8],\ [701, 701, -7/19*w^3 + 20/19*w^2 + 82/19*w - 4],\ [701, 701, -7/19*w^3 + 1/19*w^2 + 82/19*w - 2],\ [719, 719, -8/19*w^3 + 31/19*w^2 + 53/19*w - 12],\ [719, 719, 8/19*w^3 - 31/19*w^2 - 53/19*w + 6],\ [719, 719, -8/19*w^3 - 7/19*w^2 + 91/19*w + 2],\ [719, 719, 8/19*w^3 + 7/19*w^2 - 91/19*w - 8],\ [739, 739, 9/19*w^3 - 23/19*w^2 - 43/19*w + 3],\ [739, 739, -16/19*w^3 + 24/19*w^2 + 163/19*w - 9],\ [739, 739, 16/19*w^3 - 24/19*w^2 - 163/19*w],\ [739, 739, -9/19*w^3 + 4/19*w^2 + 62/19*w],\ [769, 769, 24/19*w^3 - 74/19*w^2 - 254/19*w + 35],\ [769, 769, -3/19*w^3 + 33/19*w^2 - 30/19*w - 11],\ [769, 769, 3/19*w^3 + 24/19*w^2 - 27/19*w - 11],\ [769, 769, 24/19*w^3 + 2/19*w^2 - 330/19*w - 19],\ [811, 811, 5/19*w^3 + 2/19*w^2 - 102/19*w],\ [811, 811, -5/19*w^3 + 17/19*w^2 + 83/19*w - 7],\ [811, 811, 5/19*w^3 + 2/19*w^2 - 102/19*w - 2],\ [811, 811, -5/19*w^3 + 17/19*w^2 + 83/19*w - 5],\ [821, 821, -6/19*w^3 - 10/19*w^2 + 111/19*w + 13],\ [821, 821, 1/19*w^3 + 8/19*w^2 + 10/19*w - 12],\ [821, 821, -1/19*w^3 + 11/19*w^2 - 29/19*w - 11],\ [821, 821, -6/19*w^3 + 28/19*w^2 + 73/19*w - 18],\ [839, 839, -2*w^3 + 26*w + 23],\ [839, 839, 18/19*w^3 - 65/19*w^2 - 143/19*w + 24],\ [839, 839, -18/19*w^3 - 11/19*w^2 + 219/19*w + 14],\ [839, 839, 2*w^3 - 6*w^2 - 20*w + 47],\ [859, 859, 10/19*w^3 - 34/19*w^2 - 109/19*w + 19],\ [859, 859, 3/19*w^3 + 24/19*w^2 - 46/19*w - 14],\ [859, 859, -17/19*w^3 + 35/19*w^2 + 210/19*w - 14],\ [859, 859, -10/19*w^3 - 4/19*w^2 + 147/19*w + 12],\ [911, 911, -1/19*w^3 + 11/19*w^2 + 28/19*w - 9],\ [911, 911, -5/19*w^3 + 17/19*w^2 + 64/19*w - 1],\ [911, 911, 5/19*w^3 + 2/19*w^2 - 83/19*w + 3],\ [911, 911, 1/19*w^3 + 8/19*w^2 - 47/19*w - 7],\ [941, 941, 11/19*w^3 - 7/19*w^2 - 99/19*w - 5],\ [941, 941, -1/19*w^3 + 11/19*w^2 + 28/19*w - 10],\ [941, 941, -13/19*w^3 + 10/19*w^2 + 136/19*w - 4],\ [941, 941, -6/19*w^3 + 28/19*w^2 - 3/19*w - 6],\ [961, 31, 10/19*w^3 - 15/19*w^2 - 90/19*w + 2],\ [961, 31, -10/19*w^3 + 15/19*w^2 + 90/19*w - 3]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^8 - 8*x^7 - 112*x^6 + 720*x^5 + 2888*x^4 - 17184*x^3 - 16192*x^2 + 116800*x - 85616 K. = NumberField(heckePol) hecke_eigenvalues_array = [0, -10739/587681136*e^7 + 24817/195893712*e^6 + 1170301/293840568*e^5 - 1467049/73460142*e^4 - 37459127/146920284*e^3 + 15067991/20988612*e^2 + 92356465/24486714*e - 216059303/36730071, -10739/587681136*e^7 + 24817/195893712*e^6 + 1170301/293840568*e^5 - 1467049/73460142*e^4 - 37459127/146920284*e^3 + 15067991/20988612*e^2 + 92356465/24486714*e - 216059303/36730071, 175/677052*e^7 - 709/451368*e^6 - 20221/677052*e^5 + 19348/169263*e^4 + 127444/169263*e^3 - 679367/338526*e^2 - 279997/56421*e + 1149262/169263, 10739/587681136*e^7 - 24817/195893712*e^6 - 1170301/293840568*e^5 + 1467049/73460142*e^4 + 37459127/146920284*e^3 - 15067991/20988612*e^2 - 67869751/24486714*e + 216059303/36730071, -314539/587681136*e^7 + 640229/195893712*e^6 + 18722129/293840568*e^5 - 18261113/73460142*e^4 - 258701911/146920284*e^3 + 99309499/20988612*e^2 + 310907147/24486714*e - 788299153/36730071, 10739/587681136*e^7 - 24817/195893712*e^6 - 1170301/293840568*e^5 + 1467049/73460142*e^4 + 37459127/146920284*e^3 - 15067991/20988612*e^2 - 67869751/24486714*e + 216059303/36730071, -314539/587681136*e^7 + 640229/195893712*e^6 + 18722129/293840568*e^5 - 18261113/73460142*e^4 - 258701911/146920284*e^3 + 99309499/20988612*e^2 + 310907147/24486714*e - 788299153/36730071, 150499/587681136*e^7 - 92977/97946856*e^6 - 9348005/293840568*e^5 + 11145509/293840568*e^4 + 127636165/146920284*e^3 - 7733308/36730071*e^2 - 24609053/3498102*e + 168303287/73460142, -128501/587681136*e^7 + 53161/48973428*e^6 + 9269665/293840568*e^5 - 29558359/293840568*e^4 - 182487959/146920284*e^3 + 224576335/73460142*e^2 + 359600095/24486714*e - 253894879/10494306, 150499/587681136*e^7 - 92977/97946856*e^6 - 9348005/293840568*e^5 + 11145509/293840568*e^4 + 127636165/146920284*e^3 - 7733308/36730071*e^2 - 24609053/3498102*e + 168303287/73460142, -128501/587681136*e^7 + 53161/48973428*e^6 + 9269665/293840568*e^5 - 29558359/293840568*e^4 - 182487959/146920284*e^3 + 224576335/73460142*e^2 + 359600095/24486714*e - 253894879/10494306, -175/677052*e^7 + 709/451368*e^6 + 20221/677052*e^5 - 19348/169263*e^4 - 127444/169263*e^3 + 679367/338526*e^2 + 279997/56421*e - 1487788/169263, -175/677052*e^7 + 709/451368*e^6 + 20221/677052*e^5 - 19348/169263*e^4 - 127444/169263*e^3 + 679367/338526*e^2 + 279997/56421*e - 1487788/169263, 68707/587681136*e^7 - 62437/48973428*e^6 - 3229523/293840568*e^5 + 17722687/146920284*e^4 + 33897523/146920284*e^3 - 102888292/36730071*e^2 - 9140383/3498102*e + 539298769/36730071, -133661/587681136*e^7 + 17907/10882984*e^6 + 7989067/293840568*e^5 - 10126327/73460142*e^4 - 128882237/146920284*e^3 + 207618739/73460142*e^2 + 27341313/2720746*e - 85579364/5247153, 68707/587681136*e^7 - 62437/48973428*e^6 - 3229523/293840568*e^5 + 17722687/146920284*e^4 + 33897523/146920284*e^3 - 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97685797/73460142*e^3 + 321124448/36730071*e^2 + 151245233/8162238*e - 459891253/10494306, 8783/293840568*e^7 - 305933/97946856*e^6 + 4490107/293840568*e^5 + 97739399/293840568*e^4 - 82250401/73460142*e^3 - 265623247/36730071*e^2 + 39606377/3498102*e + 1996460885/73460142, 8783/293840568*e^7 - 305933/97946856*e^6 + 4490107/293840568*e^5 + 97739399/293840568*e^4 - 82250401/73460142*e^3 - 265623247/36730071*e^2 + 39606377/3498102*e + 1996460885/73460142, 175/677052*e^7 - 709/451368*e^6 - 20221/677052*e^5 + 19348/169263*e^4 + 127444/169263*e^3 - 679367/338526*e^2 - 279997/56421*e + 2503366/169263, 175/677052*e^7 - 709/451368*e^6 - 20221/677052*e^5 + 19348/169263*e^4 + 127444/169263*e^3 - 679367/338526*e^2 - 279997/56421*e + 2503366/169263, -9419/83954448*e^7 + 69071/27984816*e^6 + 6457/41977224*e^5 - 4604915/20988612*e^4 + 11278393/20988612*e^3 + 53382563/20988612*e^2 - 23822365/3498102*e + 77685694/5247153, -77381/83954448*e^7 + 35587/9328272*e^6 + 5008351/41977224*e^5 - 4991693/20988612*e^4 - 74490617/20988612*e^3 + 115100453/20988612*e^2 + 31087207/1166034*e - 272665712/5247153, -9419/83954448*e^7 + 69071/27984816*e^6 + 6457/41977224*e^5 - 4604915/20988612*e^4 + 11278393/20988612*e^3 + 53382563/20988612*e^2 - 23822365/3498102*e + 77685694/5247153, -77381/83954448*e^7 + 35587/9328272*e^6 + 5008351/41977224*e^5 - 4991693/20988612*e^4 - 74490617/20988612*e^3 + 115100453/20988612*e^2 + 31087207/1166034*e - 272665712/5247153, 4225/9328272*e^7 - 336989/97946856*e^6 - 1216465/24486714*e^5 + 1581009/5441492*e^4 + 61799327/48973428*e^3 - 53204075/8162238*e^2 - 150770315/12243357*e + 449643365/12243357, -139187/195893712*e^7 + 54298/12243357*e^6 + 629935/6996204*e^5 - 2553113/6996204*e^4 - 150095221/48973428*e^3 + 97999487/12243357*e^2 + 425215916/12243357*e - 633520753/12243357, 4225/9328272*e^7 - 336989/97946856*e^6 - 1216465/24486714*e^5 + 1581009/5441492*e^4 + 61799327/48973428*e^3 - 53204075/8162238*e^2 - 150770315/12243357*e + 449643365/12243357, -139187/195893712*e^7 + 54298/12243357*e^6 + 629935/6996204*e^5 - 2553113/6996204*e^4 - 150095221/48973428*e^3 + 97999487/12243357*e^2 + 425215916/12243357*e - 633520753/12243357, -23047/12243357*e^7 + 375535/32648952*e^6 + 11018767/48973428*e^5 - 10774570/12243357*e^4 - 77015521/12243357*e^3 + 59186207/3498102*e^2 + 187018315/4081119*e - 1090369156/12243357, -23047/12243357*e^7 + 375535/32648952*e^6 + 11018767/48973428*e^5 - 10774570/12243357*e^4 - 77015521/12243357*e^3 + 59186207/3498102*e^2 + 187018315/4081119*e - 1090369156/12243357, 8119/24486714*e^7 - 67829/32648952*e^6 - 2242853/48973428*e^5 + 2377538/12243357*e^4 + 21704825/12243357*e^3 - 17065453/3498102*e^2 - 65499617/4081119*e + 248775452/12243357, 8119/24486714*e^7 - 67829/32648952*e^6 - 2242853/48973428*e^5 + 2377538/12243357*e^4 + 21704825/12243357*e^3 - 17065453/3498102*e^2 - 65499617/4081119*e + 248775452/12243357, -137563/195893712*e^7 + 1198177/195893712*e^6 + 2475359/32648952*e^5 - 25852975/48973428*e^4 - 32458949/16324476*e^3 + 65965345/6996204*e^2 + 347759845/24486714*e - 50212928/4081119, -137563/195893712*e^7 + 1198177/195893712*e^6 + 2475359/32648952*e^5 - 25852975/48973428*e^4 - 32458949/16324476*e^3 + 65965345/6996204*e^2 + 347759845/24486714*e - 50212928/4081119, 137563/195893712*e^7 - 1198177/195893712*e^6 - 2475359/32648952*e^5 + 25852975/48973428*e^4 + 32458949/16324476*e^3 - 65965345/6996204*e^2 - 347759845/24486714*e + 123673070/4081119, 137563/195893712*e^7 - 1198177/195893712*e^6 - 2475359/32648952*e^5 + 25852975/48973428*e^4 + 32458949/16324476*e^3 - 65965345/6996204*e^2 - 347759845/24486714*e + 123673070/4081119, -4507/18957456*e^7 - 1527/702128*e^6 + 450017/9478728*e^5 + 320024/1184841*e^4 - 8605255/4739364*e^3 - 2184761/677052*e^2 + 1336707/87766*e - 56331067/1184841, -5293/18957456*e^7 + 33595/6319152*e^6 + 116171/9478728*e^5 - 590896/1184841*e^4 + 1468391/4739364*e^3 + 4902229/677052*e^2 - 4190447/789894*e + 4696169/1184841, -4507/18957456*e^7 - 1527/702128*e^6 + 450017/9478728*e^5 + 320024/1184841*e^4 - 8605255/4739364*e^3 - 2184761/677052*e^2 + 1336707/87766*e - 56331067/1184841, -5293/18957456*e^7 + 33595/6319152*e^6 + 116171/9478728*e^5 - 590896/1184841*e^4 + 1468391/4739364*e^3 + 4902229/677052*e^2 - 4190447/789894*e + 4696169/1184841, -32827/27984816*e^7 + 595157/195893712*e^6 + 15320467/97946856*e^5 - 2533903/48973428*e^4 - 231782717/48973428*e^3 - 39165293/48973428*e^2 + 1003218917/24486714*e - 129031760/12243357, 64433/65297904*e^7 - 652283/195893712*e^6 - 2062259/13992408*e^5 + 204017/777356*e^4 + 279945691/48973428*e^3 - 149381111/16324476*e^2 - 1567852883/24486714*e + 1057632802/12243357, -32827/27984816*e^7 + 595157/195893712*e^6 + 15320467/97946856*e^5 - 2533903/48973428*e^4 - 231782717/48973428*e^3 - 39165293/48973428*e^2 + 1003218917/24486714*e - 129031760/12243357, 64433/65297904*e^7 - 652283/195893712*e^6 - 2062259/13992408*e^5 + 204017/777356*e^4 + 279945691/48973428*e^3 - 149381111/16324476*e^2 - 1567852883/24486714*e + 1057632802/12243357, 242611/587681136*e^7 - 85381/48973428*e^6 - 1843613/41977224*e^5 + 624253/20988612*e^4 + 114163363/146920284*e^3 + 104379272/36730071*e^2 - 53487505/24486714*e - 950148539/36730071, 5749/83954448*e^7 + 38425/32648952*e^6 - 1686701/293840568*e^5 - 16802785/73460142*e^4 - 48616397/146920284*e^3 + 622153867/73460142*e^2 + 85522331/8162238*e - 2088502856/36730071, 242611/587681136*e^7 - 85381/48973428*e^6 - 1843613/41977224*e^5 + 624253/20988612*e^4 + 114163363/146920284*e^3 + 104379272/36730071*e^2 - 53487505/24486714*e - 950148539/36730071, 5749/83954448*e^7 + 38425/32648952*e^6 - 1686701/293840568*e^5 - 16802785/73460142*e^4 - 48616397/146920284*e^3 + 622153867/73460142*e^2 + 85522331/8162238*e - 2088502856/36730071, 161195/587681136*e^7 + 376399/195893712*e^6 - 16291129/293840568*e^5 - 8453695/36730071*e^4 + 341681159/146920284*e^3 + 37591609/20988612*e^2 - 508680755/24486714*e + 1517240405/36730071, 161195/587681136*e^7 + 376399/195893712*e^6 - 16291129/293840568*e^5 - 8453695/36730071*e^4 + 341681159/146920284*e^3 + 37591609/20988612*e^2 - 508680755/24486714*e + 1517240405/36730071, -464995/587681136*e^7 + 26557/21765968*e^6 + 33842957/293840568*e^5 + 56663/36730071*e^4 - 562923943/146920284*e^3 + 46649899/20988612*e^2 + 83524239/2720746*e - 2383320823/36730071, -464995/587681136*e^7 + 26557/21765968*e^6 + 33842957/293840568*e^5 + 56663/36730071*e^4 - 562923943/146920284*e^3 + 46649899/20988612*e^2 + 83524239/2720746*e - 2383320823/36730071, 411967/293840568*e^7 - 210929/24486714*e^6 - 6362672/36730071*e^5 + 25393727/36730071*e^4 + 388930861/73460142*e^3 - 75252929/5247153*e^2 - 507405998/12243357*e + 2763685514/36730071, -563867/293840568*e^7 + 575711/48973428*e^6 + 17113301/73460142*e^5 - 33790759/36730071*e^4 - 499552253/73460142*e^3 + 96313306/5247153*e^2 + 628924696/12243357*e - 3262465222/36730071, 411967/293840568*e^7 - 210929/24486714*e^6 - 6362672/36730071*e^5 + 25393727/36730071*e^4 + 388930861/73460142*e^3 - 75252929/5247153*e^2 - 507405998/12243357*e + 2763685514/36730071, -563867/293840568*e^7 + 575711/48973428*e^6 + 17113301/73460142*e^5 - 33790759/36730071*e^4 - 499552253/73460142*e^3 + 96313306/5247153*e^2 + 628924696/12243357*e - 3262465222/36730071, 599941/195893712*e^7 - 3308243/195893712*e^6 - 36648991/97946856*e^5 + 60343585/48973428*e^4 + 518747321/48973428*e^3 - 170779483/6996204*e^2 - 1896459935/24486714*e + 1687285532/12243357, 851/21765968*e^7 - 384229/195893712*e^6 + 1545335/97946856*e^5 + 2277557/16324476*e^4 - 76261753/48973428*e^3 + 255163/777356*e^2 + 438235559/24486714*e - 469345690/12243357, 599941/195893712*e^7 - 3308243/195893712*e^6 - 36648991/97946856*e^5 + 60343585/48973428*e^4 + 518747321/48973428*e^3 - 170779483/6996204*e^2 - 1896459935/24486714*e + 1687285532/12243357, 851/21765968*e^7 - 384229/195893712*e^6 + 1545335/97946856*e^5 + 2277557/16324476*e^4 - 76261753/48973428*e^3 + 255163/777356*e^2 + 438235559/24486714*e - 469345690/12243357, -80593/587681136*e^7 + 245239/195893712*e^6 + 2890189/146920284*e^5 - 9237425/73460142*e^4 - 143723143/146920284*e^3 + 389830711/146920284*e^2 + 173471075/12243357*e - 604539073/36730071, -80593/587681136*e^7 + 245239/195893712*e^6 + 2890189/146920284*e^5 - 9237425/73460142*e^4 - 143723143/146920284*e^3 + 389830711/146920284*e^2 + 173471075/12243357*e - 604539073/36730071, -157225/587681136*e^7 + 23921/65297904*e^6 + 6589729/146920284*e^5 - 851443/146920284*e^4 - 291067507/146920284*e^3 + 43125967/146920284*e^2 + 94791853/4081119*e - 438968476/36730071, -157225/587681136*e^7 + 23921/65297904*e^6 + 6589729/146920284*e^5 - 851443/146920284*e^4 - 291067507/146920284*e^3 + 43125967/146920284*e^2 + 94791853/4081119*e - 438968476/36730071, -37/1579788*e^7 + 593/3159576*e^6 + 2379/351064*e^5 - 66107/789894*e^4 - 87233/263298*e^3 + 4375535/789894*e^2 + 474931/112842*e - 5883988/131649, -37/1579788*e^7 + 593/3159576*e^6 + 2379/351064*e^5 - 66107/789894*e^4 - 87233/263298*e^3 + 4375535/789894*e^2 + 474931/112842*e - 5883988/131649, 1669/1579788*e^7 - 9467/3159576*e^6 - 152843/1053192*e^5 + 115963/1579788*e^4 + 1288381/263298*e^3 + 1077325/789894*e^2 - 38144383/789894*e + 70847/18807, 1669/1579788*e^7 - 9467/3159576*e^6 - 152843/1053192*e^5 + 115963/1579788*e^4 + 1288381/263298*e^3 + 1077325/789894*e^2 - 38144383/789894*e + 70847/18807, 1723151/587681136*e^7 - 2799929/195893712*e^6 - 108731473/293840568*e^5 + 36465563/36730071*e^4 + 1597731587/146920284*e^3 - 443887895/20988612*e^2 - 1995346739/24486714*e + 5022296441/36730071, 1723151/587681136*e^7 - 2799929/195893712*e^6 - 108731473/293840568*e^5 + 36465563/36730071*e^4 + 1597731587/146920284*e^3 - 443887895/20988612*e^2 - 1995346739/24486714*e + 5022296441/36730071, -204151/587681136*e^7 - 92377/65297904*e^6 + 20972333/293840568*e^5 + 5519597/36730071*e^4 - 491517667/146920284*e^3 + 22680355/20988612*e^2 + 260053253/8162238*e - 2895698611/36730071, -204151/587681136*e^7 - 92377/65297904*e^6 + 20972333/293840568*e^5 + 5519597/36730071*e^4 - 491517667/146920284*e^3 + 22680355/20988612*e^2 + 260053253/8162238*e - 2895698611/36730071, -366787/587681136*e^7 + 219341/32648952*e^6 + 23511587/293840568*e^5 - 52596191/73460142*e^4 - 518908903/146920284*e^3 + 1321746119/73460142*e^2 + 419293999/8162238*e - 4063573492/36730071, -366787/587681136*e^7 + 219341/32648952*e^6 + 23511587/293840568*e^5 - 52596191/73460142*e^4 - 518908903/146920284*e^3 + 1321746119/73460142*e^2 + 419293999/8162238*e - 4063573492/36730071, 87053/587681136*e^7 - 93391/24486714*e^6 + 4653977/293840568*e^5 + 43980455/146920284*e^4 - 325258351/146920284*e^3 - 132572297/36730071*e^2 + 771336439/24486714*e - 317369347/36730071, 87053/587681136*e^7 - 93391/24486714*e^6 + 4653977/293840568*e^5 + 43980455/146920284*e^4 - 325258351/146920284*e^3 - 132572297/36730071*e^2 + 771336439/24486714*e - 317369347/36730071, -60863/293840568*e^7 - 40882/12243357*e^6 + 13887623/293840568*e^5 + 119198539/293840568*e^4 - 131048447/73460142*e^3 - 575558317/73460142*e^2 + 42848105/3498102*e + 1604812525/73460142, -60863/293840568*e^7 - 40882/12243357*e^6 + 13887623/293840568*e^5 + 119198539/293840568*e^4 - 131048447/73460142*e^3 - 575558317/73460142*e^2 + 42848105/3498102*e + 1604812525/73460142, 169033/293840568*e^7 + 48343/24486714*e^6 - 30506857/293840568*e^5 - 92282345/293840568*e^4 + 310984645/73460142*e^3 + 464555915/73460142*e^2 - 1030917073/24486714*e - 54576377/10494306, 169033/293840568*e^7 + 48343/24486714*e^6 - 30506857/293840568*e^5 - 92282345/293840568*e^4 + 310984645/73460142*e^3 + 464555915/73460142*e^2 - 1030917073/24486714*e - 54576377/10494306, 466439/293840568*e^7 - 947935/97946856*e^6 - 27498043/146920284*e^5 + 26658145/36730071*e^4 + 369323303/73460142*e^3 - 141430253/10494306*e^2 - 432425845/12243357*e + 3471120712/36730071, 141161/293840568*e^7 - 282889/97946856*e^6 - 7605613/146920284*e^5 + 6929983/36730071*e^4 + 73162265/73460142*e^3 - 27052763/10494306*e^2 - 53648947/12243357*e + 1462403800/36730071] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([4, 2, -2/19*w^3 + 3/19*w^2 + 37/19*w - 3])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]