/* 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([-39, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([11, 11, -3*w - 17]) primes_array = [ [3, 3, w + 6],\ [3, 3, -w + 7],\ [4, 2, 2],\ [11, 11, -3*w - 17],\ [11, 11, 3*w - 20],\ [13, 13, 2*w - 13],\ [13, 13, 2*w + 11],\ [17, 17, w + 7],\ [17, 17, -w + 8],\ [19, 19, -w - 4],\ [19, 19, -w + 5],\ [25, 5, 5],\ [31, 31, -6*w - 35],\ [31, 31, -6*w + 41],\ [37, 37, -w - 1],\ [37, 37, w - 2],\ [47, 47, 3*w + 16],\ [47, 47, -3*w + 19],\ [49, 7, -7],\ [67, 67, 3*w - 22],\ [67, 67, -3*w - 19],\ [71, 71, -w - 10],\ [71, 71, w - 11],\ [89, 89, -8*w - 47],\ [89, 89, 8*w - 55],\ [101, 101, 4*w - 29],\ [101, 101, -4*w - 25],\ [109, 109, -3*w - 20],\ [109, 109, 3*w - 23],\ [113, 113, 3*w - 17],\ [113, 113, -3*w - 14],\ [127, 127, -9*w - 53],\ [127, 127, 9*w - 62],\ [157, 157, 2*w - 1],\ [167, 167, 2*w - 19],\ [167, 167, -2*w - 17],\ [173, 173, 13*w - 89],\ [173, 173, -13*w - 76],\ [193, 193, 11*w - 73],\ [193, 193, -11*w - 62],\ [197, 197, 3*w - 14],\ [197, 197, -3*w - 11],\ [199, 199, 3*w - 25],\ [199, 199, -3*w - 22],\ [233, 233, -w - 16],\ [233, 233, w - 17],\ [239, 239, 7*w - 50],\ [239, 239, -7*w - 43],\ [257, 257, 6*w + 31],\ [257, 257, -6*w + 37],\ [263, 263, 3*w - 11],\ [263, 263, -3*w - 8],\ [277, 277, -12*w - 71],\ [277, 277, 12*w - 83],\ [281, 281, -3*w - 7],\ [281, 281, 3*w - 10],\ [283, 283, -7*w + 44],\ [283, 283, 7*w + 37],\ [311, 311, 3*w - 8],\ [311, 311, -3*w - 5],\ [313, 313, -13*w - 73],\ [313, 313, 13*w - 86],\ [317, 317, -9*w + 58],\ [317, 317, 9*w + 49],\ [331, 331, -5*w - 23],\ [331, 331, 5*w - 28],\ [347, 347, -3*w - 1],\ [347, 347, 3*w - 4],\ [349, 349, 3*w - 28],\ [349, 349, -3*w - 25],\ [353, 353, 3*w - 2],\ [353, 353, 3*w - 1],\ [389, 389, 6*w - 35],\ [389, 389, 6*w + 29],\ [419, 419, 2*w - 25],\ [419, 419, -2*w - 23],\ [431, 431, 10*w - 71],\ [431, 431, -10*w - 61],\ [457, 457, 27*w + 157],\ [457, 457, 27*w - 184],\ [461, 461, -4*w - 31],\ [461, 461, 4*w - 35],\ [467, 467, -w - 22],\ [467, 467, w - 23],\ [487, 487, 8*w + 41],\ [487, 487, -8*w + 49],\ [523, 523, -6*w - 41],\ [523, 523, 6*w - 47],\ [529, 23, -23],\ [547, 547, 4*w - 11],\ [547, 547, -4*w - 7],\ [557, 557, 28*w - 191],\ [557, 557, -28*w - 163],\ [571, 571, 20*w - 133],\ [571, 571, -20*w - 113],\ [577, 577, -3*w - 29],\ [577, 577, 3*w - 32],\ [593, 593, 19*w - 131],\ [593, 593, -19*w - 112],\ [601, 601, 5*w - 22],\ [601, 601, -5*w - 17],\ [617, 617, -18*w - 101],\ [617, 617, 18*w - 119],\ [619, 619, -4*w - 1],\ [619, 619, 4*w - 5],\ [631, 631, 17*w - 112],\ [631, 631, -17*w - 95],\ [641, 641, 15*w + 83],\ [641, 641, 15*w - 98],\ [647, 647, -17*w - 101],\ [647, 647, 17*w - 118],\ [653, 653, -11*w - 68],\ [653, 653, 11*w - 79],\ [659, 659, 5*w - 43],\ [659, 659, -5*w - 38],\ [661, 661, -25*w - 142],\ [661, 661, 25*w - 167],\ [677, 677, 13*w - 92],\ [677, 677, -13*w - 79],\ [709, 709, 5*w - 19],\ [709, 709, -5*w - 14],\ [727, 727, -9*w - 58],\ [727, 727, 9*w - 67],\ [733, 733, 7*w - 38],\ [733, 733, -7*w - 31],\ [739, 739, -18*w - 107],\ [739, 739, 18*w - 125],\ [743, 743, 2*w - 31],\ [743, 743, -2*w - 29],\ [769, 769, -3*w - 32],\ [769, 769, 3*w - 35],\ [773, 773, -w - 28],\ [773, 773, w - 29],\ [797, 797, 21*w - 139],\ [797, 797, -21*w - 118],\ [821, 821, -15*w + 97],\ [821, 821, 15*w + 82],\ [827, 827, 9*w - 53],\ [827, 827, -9*w - 44],\ [829, 829, -19*w - 106],\ [829, 829, 19*w - 125],\ [841, 29, -29],\ [853, 853, 9*w - 68],\ [853, 853, -9*w - 59],\ [907, 907, 3*w - 37],\ [907, 907, -3*w - 34],\ [911, 911, 5*w - 46],\ [911, 911, -5*w - 41],\ [929, 929, -6*w - 19],\ [929, 929, 6*w - 25],\ [941, 941, -20*w - 119],\ [941, 941, 20*w - 139],\ [953, 953, -w - 31],\ [953, 953, w - 32],\ [967, 967, 11*w + 56],\ [967, 967, -11*w + 67],\ [977, 977, 16*w - 113],\ [977, 977, -16*w - 97],\ [991, 991, -8*w - 35],\ [991, 991, 8*w - 43]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^13 - 16*x^11 - 6*x^10 + 90*x^9 + 57*x^8 - 209*x^7 - 159*x^6 + 201*x^5 + 166*x^4 - 58*x^3 - 54*x^2 - 5*x + 1 K. = NumberField(heckePol) hecke_eigenvalues_array = [-47/53*e^12 + 26/53*e^11 + 741/53*e^10 - 111/53*e^9 - 4234/53*e^8 - 586/53*e^7 + 10499/53*e^6 + 2866/53*e^5 - 11585/53*e^4 - 3396/53*e^3 + 4811/53*e^2 + 949/53*e - 246/53, e, 28/53*e^12 - 20/53*e^11 - 411/53*e^10 + 118/53*e^9 + 2095/53*e^8 + 92/53*e^7 - 4199/53*e^6 - 1006/53*e^5 + 3106/53*e^4 + 1430/53*e^3 - 480/53*e^2 - 677/53*e - 35/53, 1, 93/53*e^12 - 21/53*e^11 - 1473/53*e^10 - 210/53*e^9 + 8255/53*e^8 + 3160/53*e^7 - 19347/53*e^6 - 8895/53*e^5 + 19421/53*e^4 + 8312/53*e^3 - 6758/53*e^2 - 2065/53*e + 56/53, 34/53*e^12 + 6/53*e^11 - 571/53*e^10 - 258/53*e^9 + 3373/53*e^8 + 2103/53*e^7 - 8381/53*e^6 - 5613/53*e^5 + 8958/53*e^4 + 5507/53*e^3 - 3354/53*e^2 - 1265/53*e + 37/53, -34/53*e^12 - 6/53*e^11 + 571/53*e^10 + 258/53*e^9 - 3373/53*e^8 - 2103/53*e^7 + 8381/53*e^6 + 5613/53*e^5 - 8958/53*e^4 - 5560/53*e^3 + 3460/53*e^2 + 1530/53*e - 249/53, 3/53*e^12 + 66/53*e^11 - 133/53*e^10 - 930/53*e^9 + 1063/53*e^8 + 4583/53*e^7 - 2992/53*e^6 - 8849/53*e^5 + 3880/53*e^4 + 6093/53*e^3 - 2285/53*e^2 - 665/53*e + 301/53, -91/53*e^12 + 12/53*e^11 + 1455/53*e^10 + 332/53*e^9 - 8253/53*e^8 - 3744/53*e^7 + 19755/53*e^6 + 10080/53*e^5 - 20827/53*e^4 - 9285/53*e^3 + 8344/53*e^2 + 2134/53*e - 562/53, 216/53*e^12 - 124/53*e^11 - 3375/53*e^10 + 562/53*e^9 + 19031/53*e^8 + 2436/53*e^7 - 46142/53*e^6 - 12576/53*e^5 + 49022/53*e^4 + 15597/53*e^3 - 18823/53*e^2 - 5056/53*e + 631/53, -168/53*e^12 + 67/53*e^11 + 2625/53*e^10 - 19/53*e^9 - 14584/53*e^8 - 3838/53*e^7 + 34045/53*e^6 + 12767/53*e^5 - 34059/53*e^4 - 13138/53*e^3 + 11678/53*e^2 + 3532/53*e - 55/53, 274/53*e^12 - 173/53*e^11 - 4268/53*e^10 + 973/53*e^9 + 23965/53*e^8 + 1559/53*e^7 - 57577/53*e^6 - 12131/53*e^5 + 59605/53*e^4 + 15788/53*e^3 - 21430/53*e^2 - 5175/53*e + 585/53, 5/53*e^12 + 57/53*e^11 - 151/53*e^10 - 861/53*e^9 + 1171/53*e^8 + 4635/53*e^7 - 3538/53*e^6 - 10473/53*e^5 + 5071/53*e^4 + 10155/53*e^3 - 2819/53*e^2 - 3246/53*e - 99/53, -84/53*e^12 + 60/53*e^11 + 1286/53*e^10 - 354/53*e^9 - 7080/53*e^8 - 541/53*e^7 + 16519/53*e^6 + 5085/53*e^5 - 16102/53*e^4 - 7682/53*e^3 + 4885/53*e^2 + 2985/53*e - 1/53, 325/53*e^12 - 164/53*e^11 - 5045/53*e^10 + 480/53*e^9 + 28044/53*e^8 + 5482/53*e^7 - 66094/53*e^6 - 21637/53*e^5 + 67371/53*e^4 + 23651/53*e^3 - 24606/53*e^2 - 6410/53*e + 879/53, -119/53*e^12 + 85/53*e^11 + 1760/53*e^10 - 528/53*e^9 - 9129/53*e^8 + 33/53*e^7 + 19078/53*e^6 + 2235/53*e^5 - 15824/53*e^4 - 2606/53*e^3 + 3842/53*e^2 + 1009/53*e + 3/53, -71/53*e^12 + 28/53*e^11 + 1063/53*e^10 + 15/53*e^9 - 5477/53*e^8 - 1687/53*e^7 + 11009/53*e^6 + 4970/53*e^5 - 8334/53*e^4 - 4970/53*e^3 + 1202/53*e^2 + 1923/53*e + 367/53, -142/53*e^12 + 56/53*e^11 + 2232/53*e^10 + 30/53*e^9 - 12597/53*e^8 - 3745/53*e^7 + 30339/53*e^6 + 12802/53*e^5 - 32038/53*e^4 - 13756/53*e^3 + 12792/53*e^2 + 3846/53*e - 697/53, -325/53*e^12 + 111/53*e^11 + 5151/53*e^10 + 156/53*e^9 - 29051/53*e^8 - 8185/53*e^7 + 69115/53*e^6 + 26354/53*e^5 - 70657/53*e^4 - 27520/53*e^3 + 25136/53*e^2 + 8106/53*e - 561/53, -302/53*e^12 + 140/53*e^11 + 4732/53*e^10 - 349/53*e^9 - 26537/53*e^8 - 5202/53*e^7 + 63366/53*e^6 + 19550/53*e^5 - 66262/53*e^4 - 21405/53*e^3 + 24931/53*e^2 + 6382/53*e - 497/53, -16/53*e^12 - 34/53*e^11 + 250/53*e^10 + 614/53*e^9 - 1129/53*e^8 - 3596/53*e^7 + 923/53*e^6 + 7904/53*e^5 + 2397/53*e^4 - 7003/53*e^3 - 3254/53*e^2 + 2416/53*e + 550/53, -164/53*e^12 + 102/53*e^11 + 2536/53*e^10 - 570/53*e^9 - 14050/53*e^8 - 819/53*e^7 + 33059/53*e^6 + 6074/53*e^5 - 33691/53*e^4 - 7028/53*e^3 + 12253/53*e^2 + 1762/53*e - 272/53, -40/53*e^12 + 21/53*e^11 + 625/53*e^10 - 55/53*e^9 - 3538/53*e^8 - 828/53*e^7 + 8641/53*e^6 + 3383/53*e^5 - 9192/53*e^4 - 3542/53*e^3 + 3472/53*e^2 + 263/53*e - 268/53, -20/53*e^12 - 122/53*e^11 + 498/53*e^10 + 1854/53*e^9 - 3624/53*e^8 - 10060/53*e^7 + 10336/53*e^6 + 22706/53*e^5 - 12599/53*e^4 - 21010/53*e^3 + 5075/53*e^2 + 5564/53*e + 343/53, -133/53*e^12 + 95/53*e^11 + 1992/53*e^10 - 587/53*e^9 - 10574/53*e^8 - 172/53*e^7 + 23218/53*e^6 + 4010/53*e^5 - 21352/53*e^4 - 5865/53*e^3 + 6891/53*e^2 + 2964/53*e - 536/53, 306/53*e^12 - 105/53*e^11 - 4768/53*e^10 - 255/53*e^9 + 26382/53*e^8 + 8539/53*e^7 - 61331/53*e^6 - 26402/53*e^5 + 62125/53*e^4 + 27303/53*e^3 - 22925/53*e^2 - 8629/53*e + 651/53, -365/53*e^12 + 344/53*e^11 + 5511/53*e^10 - 2867/53*e^9 - 30204/53*e^8 + 5827/53*e^7 + 71290/53*e^6 - 685/53*e^5 - 73012/53*e^4 - 6629/53*e^3 + 26912/53*e^2 + 3705/53*e - 1412/53, 117/53*e^12 - 23/53*e^11 - 1848/53*e^10 - 230/53*e^9 + 10134/53*e^8 + 3201/53*e^7 - 22507/53*e^6 - 7342/53*e^5 + 20410/53*e^4 + 4321/53*e^3 - 5640/53*e^2 - 124/53*e - 239/53, 26/53*e^12 - 64/53*e^11 - 234/53*e^10 + 685/53*e^9 + 132/53*e^8 - 2769/53*e^7 + 3820/53*e^6 + 5918/53*e^5 - 10169/53*e^4 - 5653/53*e^3 + 7580/53*e^2 + 1109/53*e - 801/53, 589/53*e^12 - 292/53*e^11 - 9117/53*e^10 + 843/53*e^9 + 50356/53*e^8 + 9484/53*e^7 - 117178/53*e^6 - 35771/53*e^5 + 117205/53*e^4 + 37149/53*e^3 - 41723/53*e^2 - 9757/53*e + 1556/53, -75/53*e^12 - 60/53*e^11 + 1311/53*e^10 + 1255/53*e^9 - 7972/53*e^8 - 8045/53*e^7 + 20210/53*e^6 + 18765/53*e^5 - 21952/53*e^4 - 16062/53*e^3 + 7994/53*e^2 + 3587/53*e + 213/53, 674/53*e^12 - 277/53*e^11 - 10677/53*e^10 + 198/53*e^9 + 60829/53*e^8 + 15351/53*e^7 - 148492/53*e^6 - 54918/53*e^5 + 158468/53*e^4 + 61013/53*e^3 - 60390/53*e^2 - 18299/53*e + 1304/53, 73/53*e^12 + 69/53*e^11 - 1293/53*e^10 - 1377/53*e^9 + 7970/53*e^8 + 8682/53*e^7 - 20724/53*e^6 - 20427/53*e^5 + 23941/53*e^4 + 18625/53*e^3 - 10057/53*e^2 - 5246/53*e - 237/53, -640/53*e^12 + 177/53*e^11 + 10159/53*e^10 + 869/53*e^9 - 57191/53*e^8 - 18442/53*e^7 + 135500/53*e^6 + 54128/53*e^5 - 139281/53*e^4 - 52326/53*e^3 + 51630/53*e^2 + 14066/53*e - 1585/53, 467/53*e^12 - 114/53*e^11 - 7383/53*e^10 - 928/53*e^9 + 41330/53*e^8 + 15110/53*e^7 - 96910/53*e^6 - 42548/53*e^5 + 97978/53*e^4 + 39421/53*e^3 - 35013/53*e^2 - 9726/53*e + 834/53, 15/53*e^12 - 94/53*e^11 - 29/53*e^10 + 1233/53*e^9 - 1098/53*e^8 - 6235/53*e^7 + 6187/53*e^6 + 14956/53*e^5 - 9379/53*e^4 - 14903/53*e^3 + 2673/53*e^2 + 4042/53*e + 763/53, -165/53*e^12 - 79/53*e^11 + 2810/53*e^10 + 1966/53*e^9 - 16754/53*e^8 - 13406/53*e^7 + 42077/53*e^6 + 31425/53*e^5 - 46874/53*e^4 - 26284/53*e^3 + 19569/53*e^2 + 4722/53*e - 708/53, 392/53*e^12 - 227/53*e^11 - 6072/53*e^10 + 1175/53*e^9 + 33623/53*e^8 + 2401/53*e^7 - 78979/53*e^6 - 13925/53*e^5 + 81167/53*e^4 + 16575/53*e^3 - 30835/53*e^2 - 6245/53*e + 1577/53, 51/53*e^12 - 97/53*e^11 - 618/53*e^10 + 938/53*e^9 + 2489/53*e^8 - 2808/53*e^7 - 3164/53*e^6 + 2737/53*e^5 - 555/53*e^4 + 496/53*e^3 + 2389/53*e^2 - 1129/53*e - 501/53, 64/53*e^12 + 189/53*e^11 - 1318/53*e^10 - 2880/53*e^9 + 8650/53*e^8 + 15179/53*e^7 - 23143/53*e^6 - 30821/53*e^5 + 28943/53*e^4 + 23295/53*e^3 - 15339/53*e^2 - 4205/53*e + 927/53, 227/53*e^12 - 94/53*e^11 - 3474/53*e^10 + 67/53*e^9 + 18777/53*e^8 + 4471/53*e^7 - 42308/53*e^6 - 12816/53*e^5 + 42243/53*e^4 + 10537/53*e^3 - 16619/53*e^2 - 2159/53*e + 922/53, -296/53*e^12 + 7/53*e^11 + 4837/53*e^10 + 1554/53*e^9 - 28174/53*e^8 - 15169/53*e^7 + 69996/53*e^6 + 42291/53*e^5 - 76628/53*e^4 - 43351/53*e^3 + 30219/53*e^2 + 12949/53*e - 690/53, 49/53*e^12 + 71/53*e^11 - 971/53*e^10 - 1198/53*e^9 + 6515/53*e^8 + 7157/53*e^7 - 18041/53*e^6 - 17422/53*e^5 + 20090/53*e^4 + 16680/53*e^3 - 6299/53*e^2 - 4855/53*e - 366/53, -330/53*e^12 + 213/53*e^11 + 5037/53*e^10 - 1209/53*e^9 - 27307/53*e^8 - 1531/53*e^7 + 61417/53*e^6 + 12394/53*e^5 - 56595/53*e^4 - 15468/53*e^3 + 16242/53*e^2 + 5098/53*e - 409/53, 96/53*e^12 - 114/53*e^11 - 1394/53*e^10 + 1192/53*e^9 + 7092/53*e^8 - 4500/53*e^7 - 14654/53*e^6 + 9127/53*e^5 + 12330/53*e^4 - 9021/53*e^3 - 3107/53*e^2 + 3259/53*e - 120/53, -275/53*e^12 + 98/53*e^11 + 4383/53*e^10 + 26/53*e^9 - 25026/53*e^8 - 6037/53*e^7 + 61454/53*e^6 + 19144/53*e^5 - 68177/53*e^4 - 18561/53*e^3 + 29753/53*e^2 + 4531/53*e - 1763/53, 57/53*e^12 - 71/53*e^11 - 672/53*e^10 + 562/53*e^9 + 2230/53*e^8 - 1486/53*e^7 + 74/53*e^6 + 3589/53*e^5 - 7370/53*e^4 - 5391/53*e^3 + 6405/53*e^2 + 2470/53*e - 1065/53, 55/53*e^12 - 115/53*e^11 - 654/53*e^10 + 1288/53*e^9 + 2387/53*e^8 - 5354/53*e^7 - 1659/53*e^6 + 11043/53*e^5 - 3950/53*e^4 - 9983/53*e^3 + 4872/53*e^2 + 2242/53*e - 559/53, 177/53*e^12 - 134/53*e^11 - 2600/53*e^10 + 833/53*e^9 + 13321/53*e^8 + 362/53*e^7 - 26803/53*e^6 - 6878/53*e^5 + 18404/53*e^4 + 10588/53*e^3 + 600/53*e^2 - 4308/53*e - 1215/53, -500/53*e^12 + 342/53*e^11 + 7574/53*e^10 - 1986/53*e^9 - 40939/53*e^8 - 2082/53*e^7 + 92669/53*e^6 + 19789/53*e^5 - 88400/53*e^4 - 27368/53*e^3 + 28083/53*e^2 + 11529/53*e + 95/53, -387/53*e^12 + 231/53*e^11 + 6027/53*e^10 - 1082/53*e^9 - 33936/53*e^8 - 4232/53*e^7 + 82225/53*e^6 + 22691/53*e^5 - 87120/53*e^4 - 27461/53*e^3 + 33104/53*e^2 + 7716/53*e - 404/53, -465/53*e^12 + 158/53*e^11 + 7206/53*e^10 + 361/53*e^9 - 39367/53*e^8 - 12355/53*e^7 + 89050/53*e^6 + 36843/53*e^5 - 85922/53*e^4 - 36578/53*e^3 + 28967/53*e^2 + 11226/53*e + 38/53, 157/53*e^12 - 44/53*e^11 - 2473/53*e^10 - 334/53*e^9 + 13884/53*e^8 + 5990/53*e^7 - 32473/53*e^6 - 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547/53*e^11 - 9362/53*e^10 + 4176/53*e^9 + 49971/53*e^8 - 6038/53*e^7 - 112084/53*e^6 - 6012/53*e^5 + 106112/53*e^4 + 16347/53*e^3 - 33851/53*e^2 - 7113/53*e + 699/53, 1245/53*e^12 - 647/53*e^11 - 19473/53*e^10 + 2487/53*e^9 + 109312/53*e^8 + 15887/53*e^7 - 262399/53*e^6 - 68176/53*e^5 + 277674/53*e^4 + 75066/53*e^3 - 109709/53*e^2 - 20674/53*e + 5135/53, 910/53*e^12 - 597/53*e^11 - 13808/53*e^10 + 3358/53*e^9 + 74686/53*e^8 + 3891/53*e^7 - 169195/53*e^6 - 30840/53*e^5 + 163008/53*e^4 + 36405/53*e^3 - 53707/53*e^2 - 11217/53*e + 691/53, 935/53*e^12 - 365/53*e^11 - 14616/53*e^10 - 46/53*e^9 + 81283/53*e^8 + 22296/53*e^7 - 189800/53*e^6 - 73877/53*e^5 + 189476/53*e^4 + 77958/53*e^3 - 65629/53*e^2 - 23313/53*e + 779/53, -1228/53*e^12 + 544/53*e^11 + 19267/53*e^10 - 920/53*e^9 - 108288/53*e^8 - 24349/53*e^7 + 258659/53*e^6 + 87285/53*e^5 - 267312/53*e^4 - 91366/53*e^3 + 97273/53*e^2 + 23725/53*e - 3182/53, -313/53*e^12 - 102/53*e^11 + 5361/53*e^10 + 3167/53*e^9 - 32537/53*e^8 - 24144/53*e^7 + 83541/53*e^6 + 64416/53*e^5 - 90700/53*e^4 - 65423/53*e^3 + 32108/53*e^2 + 19862/53*e + 7/53, 99/53*e^12 + 482/53*e^11 - 2163/53*e^10 - 7264/53*e^9 + 14250/53*e^8 + 37607/53*e^7 - 36938/53*e^6 - 74664/53*e^5 + 45890/53*e^4 + 54206/53*e^3 - 24472/53*e^2 - 8271/53*e + 552/53, 495/53*e^12 + 78/53*e^11 - 8377/53*e^10 - 3460/53*e^9 + 50262/53*e^8 + 27498/53*e^7 - 128881/53*e^6 - 69206/53*e^5 + 146558/53*e^4 + 63535/53*e^3 - 61622/53*e^2 - 15968/53*e + 2972/53, 110/53*e^12 - 177/53*e^11 - 1732/53*e^10 + 2046/53*e^9 + 10339/53*e^8 - 7634/53*e^7 - 28016/53*e^6 + 9472/53*e^5 + 32539/53*e^4 - 1045/53*e^3 - 13523/53*e^2 - 2512/53*e + 631/53, -221/53*e^12 - 92/53*e^11 + 3738/53*e^10 + 2525/53*e^9 - 22322/53*e^8 - 17936/53*e^7 + 56835/53*e^6 + 43613/53*e^5 - 65594/53*e^4 - 38525/53*e^3 + 29804/53*e^2 + 9150/53*e - 903/53, -353/53*e^12 + 184/53*e^11 + 5403/53*e^10 - 545/53*e^9 - 29344/53*e^8 - 5945/53*e^7 + 65788/53*e^6 + 22802/53*e^5 - 59135/53*e^4 - 22802/53*e^3 + 13426/53*e^2 + 5232/53*e + 1806/53, 12*e^12 - 4*e^11 - 190*e^10 - 11*e^9 + 1076*e^8 + 352*e^7 - 2592*e^6 - 1143*e^5 + 2727*e^4 + 1205*e^3 - 1051*e^2 - 328*e + 44, 247/53*e^12 + 187/53*e^11 - 4237/53*e^10 - 3854/53*e^9 + 24839/53*e^8 + 24336/53*e^7 - 59481/53*e^6 - 55344/53*e^5 + 61414/53*e^4 + 48613/53*e^3 - 22224/53*e^2 - 12705/53*e - 163/53, 163/53*e^12 + 141/53*e^11 - 2845/53*e^10 - 2724/53*e^9 + 17070/53*e^8 + 16216/53*e^7 - 42750/53*e^6 - 33617/53*e^5 + 49022/53*e^4 + 24766/53*e^3 - 22904/53*e^2 - 4844/53*e + 896/53, -450/53*e^12 + 223/53*e^11 + 6965/53*e^10 - 420/53*e^9 - 38663/53*e^8 - 10216/53*e^7 + 90785/53*e^6 + 40139/53*e^5 - 90266/53*e^4 - 46499/53*e^3 + 29255/53*e^2 + 13254/53*e + 483/53, 329/53*e^12 - 129/53*e^11 - 5346/53*e^10 + 300/53*e^9 + 31334/53*e^8 + 4844/53*e^7 - 79747/53*e^6 - 16882/53*e^5 + 90794/53*e^4 + 16882/53*e^3 - 38447/53*e^2 - 6113/53*e + 1669/53, 1088/53*e^12 - 444/53*e^11 - 17106/53*e^10 + 171/53*e^9 + 96223/53*e^8 + 25850/53*e^7 - 229608/53*e^6 - 90152/53*e^5 + 236359/53*e^4 + 96300/53*e^3 - 85651/53*e^2 - 25799/53*e + 2138/53, -452/53*e^12 + 391/53*e^11 + 6877/53*e^10 - 2768/53*e^9 - 38294/53*e^8 + 1180/53*e^7 + 92391/53*e^6 + 18814/53*e^5 - 94902/53*e^4 - 31852/53*e^3 + 31591/53*e^2 + 11807/53*e + 88/53, 1299/53*e^12 - 837/53*e^11 - 19800/53*e^10 + 4509/53*e^9 + 107723/53*e^8 + 8334/53*e^7 - 245977/53*e^6 - 55685/53*e^5 + 237539/53*e^4 + 67186/53*e^3 - 77328/53*e^2 - 20454/53*e + 1490/53, -946/53*e^12 + 335/53*e^11 + 14874/53*e^10 + 435/53*e^9 - 83361/53*e^8 - 23695/53*e^7 + 197679/53*e^6 + 73905/53*e^5 - 204639/53*e^4 - 73481/53*e^3 + 76622/53*e^2 + 20098/53*e - 3031/53, -36/53*e^12 - 156/53*e^11 + 907/53*e^10 + 2150/53*e^9 - 6714/53*e^8 - 10529/53*e^7 + 20057/53*e^6 + 20434/53*e^5 - 27109/53*e^4 - 14710/53*e^3 + 15707/53*e^2 + 2945/53*e - 1439/53, -57/53*e^12 + 18/53*e^11 + 990/53*e^10 + 233/53*e^9 - 6735/53*e^8 - 3973/53*e^7 + 21073/53*e^6 + 15650/53*e^5 - 27928/53*e^4 - 20208/53*e^3 + 10396/53*e^2 + 6593/53*e + 1754/53, -644/53*e^12 + 36/53*e^11 + 10513/53*e^10 + 2798/53*e^9 - 60693/53*e^8 - 28351/53*e^7 + 147669/53*e^6 + 76880/53*e^5 - 155814/53*e^4 - 74442/53*e^3 + 59429/53*e^2 + 20235/53*e - 2428/53, 95/53*e^12 - 83/53*e^11 - 1650/53*e^10 + 1025/53*e^9 + 10589/53*e^8 - 4738/53*e^7 - 30546/53*e^6 + 10893/53*e^5 + 39427/53*e^4 - 11582/53*e^3 - 18634/53*e^2 + 3781/53*e + 1299/53, 335/53*e^12 - 50/53*e^11 - 5400/53*e^10 - 1189/53*e^9 + 31075/53*e^8 + 14487/53*e^7 - 76297/53*e^6 - 43007/53*e^5 + 82707/53*e^4 + 46823/53*e^3 - 32947/53*e^2 - 16983/53*e + 893/53, 491/53*e^12 - 328/53*e^11 - 7811/53*e^10 + 2338/53*e^9 + 45011/53*e^8 - 1756/53*e^7 - 112207/53*e^6 - 8930/53*e^5 + 121492/53*e^4 + 13170/53*e^3 - 46350/53*e^2 - 3280/53*e + 2129/53, 842/53*e^12 - 238/53*e^11 - 13302/53*e^10 - 1161/53*e^9 + 74459/53*e^8 + 24807/53*e^7 - 175064/53*e^6 - 73780/53*e^5 + 179065/53*e^4 + 74098/53*e^3 - 67457/53*e^2 - 20983/53*e + 2419/53, 644/53*e^12 - 354/53*e^11 - 10089/53*e^10 + 1389/53*e^9 + 57089/53*e^8 + 9218/53*e^7 - 139136/53*e^6 - 42695/53*e^5 + 148871/53*e^4 + 48896/53*e^3 - 58581/53*e^2 - 11384/53*e + 3011/53, -263/53*e^12 - 380/53*e^11 + 4964/53*e^10 + 6641/53*e^9 - 31904/53*e^8 - 39486/53*e^7 + 85314/53*e^6 + 91497/53*e^5 - 98078/53*e^4 - 80314/53*e^3 + 39057/53*e^2 + 17400/53*e - 294/53, -231/53*e^12 + 324/53*e^11 + 3404/53*e^10 - 3491/53*e^9 - 18304/53*e^8 + 12915/53*e^7 + 42711/53*e^6 - 20930/53*e^5 - 42717/53*e^4 + 12079/53*e^3 + 14136/53*e^2 + 1120/53*e - 493/53, 874/53*e^12 - 382/53*e^11 - 13696/53*e^10 + 579/53*e^9 + 76770/53*e^8 + 17689/53*e^7 - 182369/53*e^6 - 63194/53*e^5 + 187203/53*e^4 + 68335/53*e^3 - 68899/53*e^2 - 20727/53*e + 2538/53, 236/53*e^12 + 263/53*e^11 - 4191/53*e^10 - 5002/53*e^9 + 25517/53*e^8 + 30728/53*e^7 - 64216/53*e^6 - 70792/53*e^5 + 70154/53*e^4 + 61994/53*e^3 - 26707/53*e^2 - 14224/53*e - 1090/53, -121/53*e^12 - 12/53*e^11 + 1778/53*e^10 + 1046/53*e^9 - 8919/53*e^8 - 8128/53*e^7 + 17133/53*e^6 + 17427/53*e^5 - 13782/53*e^4 - 12975/53*e^3 + 3846/53*e^2 + 3855/53*e + 721/53, -103/53*e^12 + 331/53*e^11 + 1404/53*e^10 - 4216/53*e^9 - 7894/53*e^8 + 18946/53*e^7 + 23031/53*e^6 - 34978/53*e^5 - 32743/53*e^4 + 25067/53*e^3 + 18120/53*e^2 - 5064/53*e - 1872/53, 236/53*e^12 - 320/53*e^11 - 3661/53*e^10 + 3266/53*e^9 + 21542/53*e^8 - 9817/53*e^7 - 57644/53*e^6 + 6482/53*e^5 + 66815/53*e^4 + 6503/53*e^3 - 25541/53*e^2 - 3889/53*e - 348/53, 52/53*e^12 - 181/53*e^11 - 998/53*e^10 + 2589/53*e^9 + 7896/53*e^8 - 12110/53*e^7 - 29089/53*e^6 + 20157/53*e^5 + 42997/53*e^4 - 12896/53*e^3 - 20880/53*e^2 + 4444/53*e + 624/53, 81/53*e^12 - 285/53*e^11 - 782/53*e^10 + 3510/53*e^9 + 1883/53*e^8 - 16603/53*e^7 + 1790/53*e^6 + 38055/53*e^5 - 8342/53*e^4 - 39062/53*e^3 + 5297/53*e^2 + 12202/53*e - 35/53, -417/53*e^12 - 58/53*e^11 + 6827/53*e^10 + 3130/53*e^9 - 39372/53*e^8 - 25629/53*e^7 + 95503/53*e^6 + 65495/53*e^5 - 102017/53*e^4 - 60619/53*e^3 + 40478/53*e^2 + 14207/53*e - 1135/53, 194/53*e^12 + 134/53*e^11 - 3442/53*e^10 - 2953/53*e^9 + 21288/53*e^8 + 20520/53*e^7 - 55188/53*e^6 - 54814/53*e^5 + 59930/53*e^4 + 58259/53*e^3 - 20210/53*e^2 - 18482/53*e - 958/53, 753/53*e^12 - 235/53*e^11 - 11865/53*e^10 - 654/53*e^9 + 66155/53*e^8 + 19737/53*e^7 - 154424/53*e^6 - 58964/53*e^5 + 155295/53*e^4 + 57904/53*e^3 - 55725/53*e^2 - 16448/53*e + 2994/53, -1491/53*e^12 + 1065/53*e^11 + 22853/53*e^10 - 6840/53*e^9 - 125988/53*e^8 - 1083/53*e^7 + 295266/53*e^6 + 49038/53*e^5 - 295324/53*e^4 - 67906/53*e^3 + 100290/53*e^2 + 21038/53*e - 2098/53, 74/53*e^12 + 356/53*e^11 - 1673/53*e^10 - 5503/53*e^9 + 11575/53*e^8 + 30014/53*e^7 - 31915/53*e^6 - 66448/53*e^5 + 38979/53*e^4 + 58127/53*e^3 - 16790/53*e^2 - 13930/53*e - 1073/53, -54/53*e^12 + 190/53*e^11 + 751/53*e^10 - 2340/53*e^9 - 4506/53*e^8 + 9461/53*e^7 + 14106/53*e^6 - 13074/53*e^5 - 19808/53*e^4 + 5654/53*e^3 + 11238/53*e^2 - 2340/53*e - 1867/53, -875/53*e^12 + 572/53*e^11 + 13281/53*e^10 - 2972/53*e^9 - 72054/53*e^8 - 6850/53*e^7 + 163986/53*e^6 + 42223/53*e^5 - 157297/53*e^4 - 50385/53*e^3 + 51305/53*e^2 + 14147/53*e - 854/53, 1073/53*e^12 - 774/53*e^11 - 16600/53*e^10 + 5298/53*e^9 + 92710/53*e^8 - 2153/53*e^7 - 222545/53*e^6 - 27940/53*e^5 + 233548/53*e^4 + 43469/53*e^3 - 88801/53*e^2 - 15690/53*e + 3389/53] 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, -3*w - 17])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]