/* 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([-30, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([15, 15, w]) primes_array = [ [2, 2, w],\ [3, 3, w],\ [5, 5, -w + 5],\ [7, 7, w + 3],\ [7, 7, w + 4],\ [13, 13, w + 2],\ [13, 13, w + 11],\ [17, 17, w + 8],\ [17, 17, w + 9],\ [19, 19, w + 7],\ [19, 19, -w + 7],\ [29, 29, -w - 1],\ [29, 29, w - 1],\ [37, 37, w + 17],\ [37, 37, w + 20],\ [71, 71, 2*w - 7],\ [71, 71, -2*w - 7],\ [83, 83, w + 14],\ [83, 83, w + 69],\ [101, 101, -7*w + 37],\ [101, 101, -3*w + 13],\ [103, 103, w + 37],\ [103, 103, w + 66],\ [107, 107, w + 43],\ [107, 107, w + 64],\ [113, 113, w + 16],\ [113, 113, w + 97],\ [121, 11, -11],\ [127, 127, w + 41],\ [127, 127, w + 86],\ [137, 137, w + 21],\ [137, 137, w + 116],\ [139, 139, -w - 13],\ [139, 139, w - 13],\ [149, 149, 3*w - 11],\ [149, 149, -3*w - 11],\ [157, 157, w + 40],\ [157, 157, w + 117],\ [191, 191, -4*w - 17],\ [191, 191, 4*w - 17],\ [211, 211, -5*w + 31],\ [211, 211, -7*w + 41],\ [223, 223, w + 91],\ [223, 223, w + 132],\ [227, 227, w + 22],\ [227, 227, w + 205],\ [233, 233, w + 27],\ [233, 233, w + 206],\ [239, 239, 6*w - 29],\ [239, 239, 8*w - 41],\ [241, 241, 2*w - 19],\ [241, 241, -2*w - 19],\ [257, 257, w + 95],\ [257, 257, w + 162],\ [269, 269, -3*w - 1],\ [269, 269, 3*w - 1],\ [277, 277, w + 108],\ [277, 277, w + 169],\ [311, 311, -4*w - 13],\ [311, 311, 4*w - 13],\ [331, 331, -w - 19],\ [331, 331, w - 19],\ [347, 347, w + 77],\ [347, 347, w + 270],\ [353, 353, w + 33],\ [353, 353, w + 320],\ [359, 359, 4*w - 11],\ [359, 359, -4*w - 11],\ [367, 367, w + 146],\ [367, 367, w + 221],\ [373, 373, w + 75],\ [373, 373, w + 298],\ [379, 379, -7*w + 43],\ [379, 379, -9*w + 53],\ [389, 389, 5*w - 19],\ [389, 389, -5*w - 19],\ [397, 397, w + 53],\ [397, 397, w + 344],\ [409, 409, 2*w - 23],\ [409, 409, -2*w - 23],\ [431, 431, 4*w - 7],\ [431, 431, -4*w - 7],\ [443, 443, w + 159],\ [443, 443, w + 284],\ [461, 461, 5*w - 17],\ [461, 461, -5*w - 17],\ [463, 463, w + 131],\ [463, 463, w + 332],\ [467, 467, w + 214],\ [467, 467, w + 253],\ [479, 479, -4*w - 1],\ [479, 479, 4*w - 1],\ [487, 487, w + 70],\ [487, 487, w + 417],\ [499, 499, -w - 23],\ [499, 499, w - 23],\ [509, 509, -7*w + 31],\ [509, 509, -15*w + 79],\ [529, 23, -23],\ [563, 563, w + 34],\ [563, 563, w + 529],\ [571, 571, -3*w - 29],\ [571, 571, 3*w - 29],\ [587, 587, w + 183],\ [587, 587, w + 404],\ [593, 593, w + 246],\ [593, 593, w + 347],\ [599, 599, 10*w - 49],\ [599, 599, 12*w - 61],\ [601, 601, -16*w + 91],\ [601, 601, 6*w - 41],\ [607, 607, w + 89],\ [607, 607, w + 518],\ [613, 613, w + 231],\ [613, 613, w + 382],\ [617, 617, w + 257],\ [617, 617, w + 360],\ [619, 619, -5*w - 37],\ [619, 619, 5*w - 37],\ [683, 683, w + 264],\ [683, 683, w + 419],\ [691, 691, 3*w - 31],\ [691, 691, -3*w - 31],\ [701, 701, 5*w - 7],\ [701, 701, -5*w - 7],\ [719, 719, -6*w - 19],\ [719, 719, 6*w - 19],\ [727, 727, w + 311],\ [727, 727, w + 416],\ [733, 733, w + 105],\ [733, 733, w + 628],\ [739, 739, -7*w + 47],\ [739, 739, 17*w - 97],\ [757, 757, w + 73],\ [757, 757, w + 684],\ [769, 769, 6*w - 43],\ [769, 769, -6*w - 43],\ [811, 811, -w - 29],\ [811, 811, w - 29],\ [821, 821, 15*w - 77],\ [821, 821, 11*w - 53],\ [823, 823, w + 186],\ [823, 823, w + 637],\ [827, 827, w + 388],\ [827, 827, w + 439],\ [839, 839, 12*w - 59],\ [839, 839, 14*w - 71],\ [853, 853, w + 258],\ [853, 853, w + 595],\ [857, 857, w + 51],\ [857, 857, w + 806],\ [859, 859, -11*w + 67],\ [859, 859, -13*w + 77],\ [877, 877, w + 192],\ [877, 877, w + 685],\ [911, 911, -6*w - 13],\ [911, 911, 6*w - 13],\ [941, 941, 7*w - 23],\ [941, 941, -7*w - 23],\ [947, 947, w + 127],\ [947, 947, w + 820],\ [953, 953, w + 44],\ [953, 953, w + 909],\ [961, 31, -31],\ [967, 967, w + 442],\ [967, 967, w + 525],\ [977, 977, w + 185],\ [977, 977, w + 792],\ [997, 997, w + 100],\ [997, 997, w + 897]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^6 + 13*x^5 + 54*x^4 + 56*x^3 - 105*x^2 - 168*x + 28 K. = NumberField(heckePol) hecke_eigenvalues_array = [-3/11*e^5 - 31/11*e^4 - 83/11*e^3 + 24/11*e^2 + 196/11*e - 4/11, -1, 1, e, -7/11*e^5 - 76/11*e^4 - 212/11*e^3 + 78/11*e^2 + 549/11*e - 112/11, 4/11*e^5 + 45/11*e^4 + 129/11*e^3 - 43/11*e^2 - 320/11*e + 20/11, 13/11*e^5 + 138/11*e^4 + 378/11*e^3 - 137/11*e^2 - 996/11*e + 76/11, -9/11*e^5 - 93/11*e^4 - 238/11*e^3 + 149/11*e^2 + 654/11*e - 188/11, 19/11*e^5 + 200/11*e^4 + 533/11*e^3 - 251/11*e^2 - 1410/11*e + 260/11, 3/11*e^5 + 31/11*e^4 + 72/11*e^3 - 90/11*e^2 - 240/11*e + 114/11, -2/11*e^5 - 17/11*e^4 - 26/11*e^3 + 60/11*e^2 + 72/11*e - 54/11, 9/11*e^5 + 93/11*e^4 + 249/11*e^3 - 83/11*e^2 - 632/11*e + 34/11, e^2 + 4*e - 2, 6/11*e^5 + 62/11*e^4 + 155/11*e^3 - 114/11*e^2 - 414/11*e + 184/11, -13/11*e^5 - 138/11*e^4 - 367/11*e^3 + 192/11*e^2 + 974/11*e - 208/11, 19/11*e^5 + 200/11*e^4 + 533/11*e^3 - 251/11*e^2 - 1388/11*e + 304/11, -23/11*e^5 - 245/11*e^4 - 662/11*e^3 + 305/11*e^2 + 1752/11*e - 368/11, 43/11*e^5 + 448/11*e^4 + 1186/11*e^3 - 542/11*e^2 - 3154/11*e + 468/11, -17/11*e^5 - 172/11*e^4 - 430/11*e^3 + 290/11*e^2 + 1250/11*e - 316/11, -6/11*e^5 - 62/11*e^4 - 155/11*e^3 + 103/11*e^2 + 392/11*e - 74/11, -10/11*e^5 - 107/11*e^4 - 306/11*e^3 + 47/11*e^2 + 756/11*e + 38/11, 23/11*e^5 + 245/11*e^4 + 651/11*e^3 - 371/11*e^2 - 1807/11*e + 412/11, -17/11*e^5 - 172/11*e^4 - 430/11*e^3 + 257/11*e^2 + 1107/11*e - 316/11, -34/11*e^5 - 366/11*e^4 - 1003/11*e^3 + 426/11*e^2 + 2654/11*e - 412/11, -15/11*e^5 - 166/11*e^4 - 481/11*e^3 + 120/11*e^2 + 1266/11*e - 20/11, 25/11*e^5 + 262/11*e^4 + 688/11*e^3 - 354/11*e^2 - 1802/11*e + 400/11, 1/11*e^5 + 14/11*e^4 + 68/11*e^3 + 102/11*e^2 - 102/11*e - 160/11, 18/11*e^5 + 186/11*e^4 + 498/11*e^3 - 144/11*e^2 - 1176/11*e + 46/11, 8/11*e^5 + 79/11*e^4 + 192/11*e^3 - 119/11*e^2 - 497/11*e - 4/11, -13/11*e^5 - 138/11*e^4 - 367/11*e^3 + 203/11*e^2 + 1029/11*e - 340/11, -29/11*e^5 - 318/11*e^4 - 894/11*e^3 + 331/11*e^2 + 2342/11*e - 332/11, -24/11*e^5 - 259/11*e^4 - 719/11*e^3 + 269/11*e^2 + 1942/11*e - 164/11, -6/11*e^5 - 73/11*e^4 - 232/11*e^3 + 26/11*e^2 + 568/11*e - 30/11, -29/11*e^5 - 307/11*e^4 - 828/11*e^3 + 364/11*e^2 + 2232/11*e - 310/11, 3/11*e^5 + 31/11*e^4 + 61/11*e^3 - 156/11*e^2 - 284/11*e + 158/11, -7/11*e^5 - 65/11*e^4 - 135/11*e^3 + 144/11*e^2 + 340/11*e - 178/11, -4*e^5 - 43*e^4 - 118*e^3 + 50*e^2 + 314*e - 56, 21/11*e^5 + 217/11*e^4 + 570/11*e^3 - 256/11*e^2 - 1438/11*e + 336/11, -30/11*e^5 - 321/11*e^4 - 874/11*e^3 + 361/11*e^2 + 2224/11*e - 524/11, -6/11*e^5 - 62/11*e^4 - 177/11*e^3 - 7/11*e^2 + 436/11*e + 36/11, -3/11*e^5 - 42/11*e^4 - 149/11*e^3 + 24/11*e^2 + 460/11*e - 158/11, -8/11*e^5 - 90/11*e^4 - 247/11*e^3 + 174/11*e^2 + 772/11*e - 326/11, -46/11*e^5 - 479/11*e^4 - 1247/11*e^3 + 687/11*e^2 + 3361/11*e - 780/11, 36/11*e^5 + 372/11*e^4 + 952/11*e^3 - 585/11*e^2 - 2605/11*e + 620/11, 17/11*e^5 + 194/11*e^4 + 573/11*e^3 - 180/11*e^2 - 1580/11*e + 228/11, 2*e^5 + 22*e^4 + 61*e^3 - 30*e^2 - 172*e + 36, 3/11*e^5 + 42/11*e^4 + 160/11*e^3 + 53/11*e^2 - 350/11*e + 4/11, 8/11*e^5 + 79/11*e^4 + 181/11*e^3 - 185/11*e^2 - 574/11*e + 172/11, 67/11*e^5 + 729/11*e^4 + 2037/11*e^3 - 745/11*e^2 - 5316/11*e + 720/11, 48/11*e^5 + 518/11*e^4 + 1438/11*e^3 - 527/11*e^2 - 3840/11*e + 328/11, 17/11*e^5 + 194/11*e^4 + 595/11*e^3 - 26/11*e^2 - 1404/11*e - 14/11, 50/11*e^5 + 524/11*e^4 + 1387/11*e^3 - 664/11*e^2 - 3692/11*e + 602/11, -3/11*e^5 - 31/11*e^4 - 83/11*e^3 + 2/11*e^2 + 130/11*e + 128/11, -35/11*e^5 - 369/11*e^4 - 1005/11*e^3 + 346/11*e^2 + 2558/11*e - 208/11, 13/11*e^5 + 138/11*e^4 + 356/11*e^3 - 258/11*e^2 - 952/11*e + 406/11, -53/11*e^5 - 566/11*e^4 - 1536/11*e^3 + 666/11*e^2 + 3976/11*e - 826/11, 13/11*e^5 + 138/11*e^4 + 356/11*e^3 - 302/11*e^2 - 1150/11*e + 472/11, -75/11*e^5 - 786/11*e^4 - 2108/11*e^3 + 842/11*e^2 + 5406/11*e - 760/11, -21/11*e^5 - 206/11*e^4 - 493/11*e^3 + 366/11*e^2 + 1460/11*e - 292/11, 48/11*e^5 + 496/11*e^4 + 1295/11*e^3 - 648/11*e^2 - 3532/11*e + 548/11, -58/11*e^5 - 614/11*e^4 - 1645/11*e^3 + 805/11*e^2 + 4508/11*e - 862/11, 30/11*e^5 + 299/11*e^4 + 742/11*e^3 - 427/11*e^2 - 1960/11*e + 370/11, -32/11*e^5 - 338/11*e^4 - 900/11*e^3 + 443/11*e^2 + 2384/11*e - 336/11, 15/11*e^5 + 155/11*e^4 + 393/11*e^3 - 263/11*e^2 - 1068/11*e + 504/11, -47/11*e^5 - 482/11*e^4 - 1249/11*e^3 + 596/11*e^2 + 3254/11*e - 488/11, 18/11*e^5 + 186/11*e^4 + 465/11*e^3 - 386/11*e^2 - 1462/11*e + 464/11, -e^5 - 11*e^4 - 31*e^3 + 8*e^2 + 68*e + 4, -47/11*e^5 - 493/11*e^4 - 1337/11*e^3 + 464/11*e^2 + 3452/11*e - 180/11, -4*e^5 - 41*e^4 - 107*e^3 + 49*e^2 + 283*e - 52, 64/11*e^5 + 676/11*e^4 + 1822/11*e^3 - 809/11*e^2 - 4933/11*e + 716/11, -10/11*e^5 - 118/11*e^4 - 383/11*e^3 - 63/11*e^2 + 822/11*e + 148/11, -6*e^5 - 63*e^4 - 168*e^3 + 75*e^2 + 442*e - 68, 59/11*e^5 + 606/11*e^4 + 1581/11*e^3 - 714/11*e^2 - 4148/11*e + 438/11, -10/11*e^5 - 96/11*e^4 - 207/11*e^3 + 300/11*e^2 + 844/11*e - 402/11, 31/11*e^5 + 335/11*e^4 + 920/11*e^3 - 457/11*e^2 - 2656/11*e + 430/11, -47/11*e^5 - 482/11*e^4 - 1271/11*e^3 + 475/11*e^2 + 3188/11*e - 466/11, -61/11*e^5 - 667/11*e^4 - 1871/11*e^3 + 708/11*e^2 + 4968/11*e - 624/11, -3*e^5 - 33*e^4 - 93*e^3 + 36*e^2 + 256*e - 16, 30/11*e^5 + 332/11*e^4 + 951/11*e^3 - 284/11*e^2 - 2444/11*e + 62/11, 53/11*e^5 + 566/11*e^4 + 1547/11*e^3 - 622/11*e^2 - 4108/11*e + 342/11, -32/11*e^5 - 338/11*e^4 - 933/11*e^3 + 278/11*e^2 + 2516/11*e - 28/11, -57/11*e^5 - 622/11*e^4 - 1731/11*e^3 + 676/11*e^2 + 4428/11*e - 868/11, -e^3 + 16*e - 12, 7*e^5 + 74*e^4 + 203*e^3 - 66*e^2 - 520*e + 44, -78/11*e^5 - 839/11*e^4 - 2312/11*e^3 + 910/11*e^2 + 6108/11*e - 786/11, -27/11*e^5 - 301/11*e^4 - 868/11*e^3 + 260/11*e^2 + 2292/11*e - 58/11, 47/11*e^5 + 504/11*e^4 + 1392/11*e^3 - 497/11*e^2 - 3705/11*e + 180/11, 87/11*e^5 + 943/11*e^4 + 2627/11*e^3 - 949/11*e^2 - 6795/11*e + 908/11, -27/11*e^5 - 279/11*e^4 - 758/11*e^3 + 205/11*e^2 + 1918/11*e - 168/11, 27/11*e^5 + 290/11*e^4 + 813/11*e^3 - 271/11*e^2 - 2226/11*e + 168/11, 10/11*e^5 + 107/11*e^4 + 306/11*e^3 - 36/11*e^2 - 712/11*e + 28/11, 15/11*e^5 + 155/11*e^4 + 404/11*e^3 - 186/11*e^2 - 1024/11*e + 196/11, 16/11*e^5 + 158/11*e^4 + 406/11*e^3 - 128/11*e^2 - 1027/11*e - 96/11, -13/11*e^5 - 138/11*e^4 - 378/11*e^3 + 170/11*e^2 + 1139/11*e - 208/11, -6/11*e^5 - 62/11*e^4 - 177/11*e^3 - 7/11*e^2 + 436/11*e + 58/11, -30/11*e^5 - 321/11*e^4 - 874/11*e^3 + 361/11*e^2 + 2224/11*e - 502/11, -79/11*e^5 - 842/11*e^4 - 2281/11*e^3 + 1050/11*e^2 + 6232/11*e - 934/11, 18/11*e^5 + 164/11*e^4 + 355/11*e^3 - 276/11*e^2 - 912/11*e + 354/11, 46/11*e^5 + 501/11*e^4 + 1401/11*e^3 - 522/11*e^2 - 3724/11*e + 362/11, 68/11*e^5 + 732/11*e^4 + 1984/11*e^3 - 1028/11*e^2 - 5484/11*e + 1308/11, -72/11*e^5 - 744/11*e^4 - 1948/11*e^3 + 884/11*e^2 + 4924/11*e - 932/11, -69/11*e^5 - 735/11*e^4 - 1975/11*e^3 + 1003/11*e^2 + 5476/11*e - 1038/11, 24/11*e^5 + 226/11*e^4 + 510/11*e^3 - 379/11*e^2 - 1304/11*e + 362/11, 6*e^5 + 63*e^4 + 167*e^3 - 79*e^2 - 438*e + 72, 23/11*e^5 + 256/11*e^4 + 772/11*e^3 - 19/11*e^2 - 1818/11*e - 160/11, -46/11*e^5 - 479/11*e^4 - 1258/11*e^3 + 676/11*e^2 + 3614/11*e - 648/11, 27/11*e^5 + 257/11*e^4 + 604/11*e^3 - 370/11*e^2 - 1654/11*e + 80/11, -118/11*e^5 - 1245/11*e^4 - 3338/11*e^3 + 1516/11*e^2 + 8912/11*e - 1404/11, 35/11*e^5 + 347/11*e^4 + 840/11*e^3 - 610/11*e^2 - 2360/11*e + 780/11, -54/11*e^5 - 580/11*e^4 - 1571/11*e^3 + 773/11*e^2 + 4188/11*e - 974/11, 54/11*e^5 + 569/11*e^4 + 1516/11*e^3 - 707/11*e^2 - 3880/11*e + 930/11, 36/11*e^5 + 394/11*e^4 + 1117/11*e^3 - 310/11*e^2 - 2693/11*e + 136/11, 42/11*e^5 + 434/11*e^4 + 1151/11*e^3 - 446/11*e^2 - 3019/11*e - 32/11, 31/11*e^5 + 346/11*e^4 + 986/11*e^3 - 391/11*e^2 - 2656/11*e + 452/11, 12/11*e^5 + 135/11*e^4 + 387/11*e^3 - 173/11*e^2 - 1180/11*e + 60/11, -74/11*e^5 - 783/11*e^4 - 2117/11*e^3 + 878/11*e^2 + 5458/11*e - 920/11, 70/11*e^5 + 749/11*e^4 + 2043/11*e^3 - 890/11*e^2 - 5402/11*e + 1208/11, 14/11*e^5 + 152/11*e^4 + 391/11*e^3 - 343/11*e^2 - 1252/11*e + 334/11, 36/11*e^5 + 405/11*e^4 + 1194/11*e^3 - 299/11*e^2 - 3144/11*e + 334/11, 52/11*e^5 + 519/11*e^4 + 1270/11*e^3 - 834/11*e^2 - 3390/11*e + 788/11, -79/11*e^5 - 831/11*e^4 - 2182/11*e^3 + 1248/11*e^2 + 6078/11*e - 1396/11, -8/11*e^5 - 101/11*e^4 - 313/11*e^3 + 141/11*e^2 + 860/11*e - 414/11, -7/11*e^5 - 76/11*e^4 - 212/11*e^3 + 111/11*e^2 + 736/11*e - 134/11, 75/11*e^5 + 797/11*e^4 + 2163/11*e^3 - 886/11*e^2 - 5692/11*e + 650/11, 47/11*e^5 + 515/11*e^4 + 1469/11*e^3 - 398/11*e^2 - 3716/11*e + 202/11, 5/11*e^5 + 70/11*e^4 + 274/11*e^3 + 92/11*e^2 - 664/11*e + 256/11, -49/11*e^5 - 532/11*e^4 - 1528/11*e^3 + 304/11*e^2 + 3744/11*e - 80/11, -26/11*e^5 - 276/11*e^4 - 745/11*e^3 + 285/11*e^2 + 1827/11*e - 372/11, -5*e^5 - 53*e^4 - 146*e^3 + 45*e^2 + 371*e - 44, -5*e^5 - 54*e^4 - 145*e^3 + 80*e^2 + 386*e - 112, 4/11*e^5 + 34/11*e^4 + 19/11*e^3 - 274/11*e^2 + 10/11*e + 504/11, -75/11*e^5 - 797/11*e^4 - 2207/11*e^3 + 622/11*e^2 + 5428/11*e - 386/11, -e^5 - 9*e^4 - 19*e^3 + 10*e^2 + 36*e + 26, 102/11*e^5 + 1076/11*e^4 + 2888/11*e^3 - 1234/11*e^2 - 7566/11*e + 1016/11, 78/11*e^5 + 850/11*e^4 + 2422/11*e^3 - 602/11*e^2 - 6042/11*e + 456/11, -54/11*e^5 - 569/11*e^4 - 1527/11*e^3 + 685/11*e^2 + 4188/11*e - 314/11, -27/11*e^5 - 312/11*e^4 - 934/11*e^3 + 227/11*e^2 + 2336/11*e - 146/11, -31/11*e^5 - 302/11*e^4 - 689/11*e^3 + 666/11*e^2 + 1996/11*e - 694/11, 114/11*e^5 + 1200/11*e^4 + 3187/11*e^3 - 1572/11*e^2 - 8548/11*e + 1714/11, -54/11*e^5 - 591/11*e^4 - 1637/11*e^3 + 729/11*e^2 + 4276/11*e - 974/11, 13/11*e^5 + 138/11*e^4 + 356/11*e^3 - 225/11*e^2 - 776/11*e + 538/11, 50/11*e^5 + 535/11*e^4 + 1464/11*e^3 - 609/11*e^2 - 3901/11*e + 492/11, -17/11*e^5 - 172/11*e^4 - 441/11*e^3 + 213/11*e^2 + 1129/11*e - 404/11, -115/11*e^5 - 1214/11*e^4 - 3244/11*e^3 + 1558/11*e^2 + 8716/11*e - 1708/11, 71/11*e^5 + 730/11*e^4 + 1880/11*e^3 - 1030/11*e^2 - 5020/11*e + 1092/11, 62/11*e^5 + 637/11*e^4 + 1686/11*e^3 - 584/11*e^2 - 4168/11*e + 244/11, 21/11*e^5 + 217/11*e^4 + 592/11*e^3 - 58/11*e^2 - 1152/11*e - 148/11, -150/11*e^5 - 1594/11*e^4 - 4304/11*e^3 + 1937/11*e^2 + 11560/11*e - 1740/11, -29/11*e^5 - 351/11*e^4 - 1125/11*e^3 + 67/11*e^2 + 2804/11*e + 108/11, -49/11*e^5 - 532/11*e^4 - 1484/11*e^3 + 557/11*e^2 + 3986/11*e - 564/11, -54/11*e^5 - 591/11*e^4 - 1659/11*e^3 + 619/11*e^2 + 4386/11*e - 732/11, 15/11*e^5 + 166/11*e^4 + 448/11*e^3 - 362/11*e^2 - 1464/11*e + 438/11, -87/11*e^5 - 910/11*e^4 - 2440/11*e^3 + 938/11*e^2 + 6168/11*e - 1018/11, -2*e^5 - 22*e^4 - 64*e^3 + 9*e^2 + 146*e - 12, -45/11*e^5 - 465/11*e^4 - 1223/11*e^3 + 525/11*e^2 + 3182/11*e - 412/11, 144/11*e^5 + 1543/11*e^4 + 4226/11*e^3 - 1746/11*e^2 - 11256/11*e + 1556/11, 19/11*e^5 + 233/11*e^4 + 742/11*e^3 - 108/11*e^2 - 1960/11*e - 180/11, -76/11*e^5 - 800/11*e^4 - 2154/11*e^3 + 905/11*e^2 + 5772/11*e - 578/11, -3/11*e^5 - 53/11*e^4 - 215/11*e^3 - 53/11*e^2 + 416/11*e + 150/11, 46/11*e^5 + 490/11*e^4 + 1335/11*e^3 - 522/11*e^2 - 3592/11*e + 164/11, 125/11*e^5 + 1354/11*e^4 + 3781/11*e^3 - 1308/11*e^2 - 9736/11*e + 1340/11, 45/11*e^5 + 476/11*e^4 + 1322/11*e^3 - 283/11*e^2 - 3050/11*e - 116/11, 2*e^5 + 19*e^4 + 45*e^3 - 19*e^2 - 102*e - 36, -42/11*e^5 - 445/11*e^4 - 1217/11*e^3 + 402/11*e^2 + 3052/11*e - 430/11, 62/11*e^5 + 659/11*e^4 + 1741/11*e^3 - 1002/11*e^2 - 4751/11*e + 1080/11, -17/11*e^5 - 161/11*e^4 - 331/11*e^3 + 444/11*e^2 + 887/11*e - 712/11, 95/11*e^5 + 1011/11*e^4 + 2742/11*e^3 - 1178/11*e^2 - 7270/11*e + 904/11, 2/11*e^5 + 39/11*e^4 + 180/11*e^3 + 116/11*e^2 - 402/11*e - 496/11, 95/11*e^5 + 989/11*e^4 + 2588/11*e^3 - 1376/11*e^2 - 7116/11*e + 1168/11, -58/11*e^5 - 581/11*e^4 - 1436/11*e^3 + 926/11*e^2 + 3980/11*e - 1016/11] 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 AL_eigenvalues[ZF.ideal([5, 5, -w + 5])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]