/* 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([-5, -9, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([11, 11, w^2 - 2*w - 2]) primes_array = [ [2, 2, -w - 1],\ [5, 5, w],\ [7, 7, w^2 - 2*w - 8],\ [7, 7, -2*w^2 + 3*w + 16],\ [7, 7, -w^2 + 2*w + 6],\ [11, 11, w^2 - 2*w - 2],\ [19, 19, -w + 2],\ [23, 23, -w^2 + 3*w + 1],\ [25, 5, w^2 - w - 9],\ [27, 3, 3],\ [29, 29, -w^2 - w + 1],\ [29, 29, w^2 - 2*w - 4],\ [29, 29, -w^2 + w + 11],\ [43, 43, 2*w^2 - 3*w - 18],\ [47, 47, -2*w + 7],\ [53, 53, w^2 - w - 3],\ [61, 61, w^2 + 2*w + 2],\ [67, 67, -2*w^2 + 5*w + 8],\ [79, 79, w^2 - 3*w - 9],\ [97, 97, -w^2 - 2*w + 2],\ [109, 109, -2*w^2 + 4*w + 11],\ [109, 109, -3*w^2 + 4*w + 26],\ [109, 109, -3*w^2 + 4*w + 28],\ [113, 113, -4*w^2 + 8*w + 27],\ [121, 11, 5*w^2 - 8*w - 38],\ [127, 127, -3*w^2 + 4*w + 24],\ [131, 131, -4*w^2 + 5*w + 38],\ [139, 139, 2*w - 3],\ [149, 149, -w^2 + 3*w - 1],\ [151, 151, w^2 - 4*w - 6],\ [157, 157, 2*w^2 - 3*w - 12],\ [167, 167, -3*w^2 + 6*w + 22],\ [173, 173, -3*w^2 + 8*w + 8],\ [181, 181, w^2 - 2*w - 12],\ [181, 181, w^2 - 12],\ [181, 181, -4*w - 1],\ [191, 191, 2*w^2 - 6*w - 9],\ [193, 193, -8*w^2 + 12*w + 67],\ [197, 197, 2*w^2 - 3*w - 4],\ [199, 199, 2*w^2 - 2*w - 11],\ [211, 211, 4*w^2 - 6*w - 29],\ [223, 223, 3*w^2 - 5*w - 27],\ [227, 227, -4*w^2 + 7*w + 28],\ [229, 229, 3*w^2 - 8*w - 14],\ [229, 229, w^2 - 4*w - 8],\ [229, 229, -2*w - 7],\ [233, 233, -5*w^2 + 7*w + 43],\ [241, 241, 2*w^2 - 4*w - 7],\ [251, 251, w^2 + 2],\ [251, 251, -2*w^2 + 2*w + 1],\ [251, 251, 2*w^2 - 5*w - 2],\ [263, 263, 2*w^2 - 5*w - 14],\ [269, 269, -w^2 + 5*w - 1],\ [271, 271, -2*w^2 - w + 2],\ [277, 277, -3*w^2 + 7*w + 7],\ [281, 281, -5*w^2 + 10*w + 34],\ [293, 293, -2*w^2 + 5*w + 16],\ [311, 311, w^2 + w + 3],\ [313, 313, 2*w^2 + w - 4],\ [317, 317, -7*w^2 + 13*w + 49],\ [331, 331, w^2 - 5*w - 7],\ [337, 337, -w^2 + 2*w - 2],\ [337, 337, 7*w^2 - 12*w - 52],\ [337, 337, -2*w^2 + 3],\ [347, 347, -10*w^2 + 17*w + 76],\ [349, 349, 2*w^2 - 2*w - 9],\ [353, 353, 2*w^2 - 3*w - 8],\ [359, 359, -4*w^2 + 5*w + 36],\ [361, 19, w^2 + w - 7],\ [367, 367, -4*w^2 + 8*w + 29],\ [373, 373, 2*w^2 - 6*w - 11],\ [373, 373, 8*w^2 - 14*w - 59],\ [379, 379, -2*w^2 + w + 4],\ [383, 383, -3*w^2 + 2*w + 34],\ [383, 383, 5*w^2 - 7*w - 41],\ [383, 383, 3*w^2 - 7*w - 19],\ [397, 397, -7*w^2 + 13*w + 51],\ [431, 431, -8*w^2 + 14*w + 63],\ [433, 433, -2*w^2 + 9*w + 8],\ [443, 443, -6*w^2 + 10*w + 51],\ [443, 443, 3*w - 4],\ [443, 443, w^2 - 7*w - 3],\ [449, 449, -7*w^2 + 10*w + 62],\ [461, 461, -6*w^2 + 11*w + 46],\ [461, 461, 2*w^2 - 4*w - 1],\ [461, 461, w^2 - 5*w - 9],\ [463, 463, 7*w + 6],\ [463, 463, -5*w^2 + 8*w + 36],\ [463, 463, 3*w^2 - 2*w - 16],\ [467, 467, 3*w^2 - 7*w - 9],\ [467, 467, 4*w - 1],\ [467, 467, 6*w^2 - 11*w - 48],\ [479, 479, 2*w^2 - 4*w - 21],\ [479, 479, w^2 + 7*w + 7],\ [479, 479, w^2 - 2*w - 14],\ [487, 487, w^2 - 5*w - 11],\ [487, 487, 3*w^2 - 3*w - 23],\ [487, 487, w^2 + 3*w - 3],\ [491, 491, w^2 - 8*w - 4],\ [499, 499, -6*w^2 + 14*w + 31],\ [509, 509, -w - 8],\ [523, 523, 2*w^2 + 1],\ [529, 23, 2*w^2 - 5*w - 22],\ [541, 541, -w^2 + 5*w - 7],\ [547, 547, 2*w^2 - 6*w - 13],\ [563, 563, 2*w^2 - 9*w - 4],\ [569, 569, 4*w^2 - 7*w - 26],\ [569, 569, -3*w^2 + 5*w + 3],\ [569, 569, 4*w^2 - 6*w - 27],\ [577, 577, 3*w^2 - 7*w - 21],\ [577, 577, -8*w^2 + 12*w + 69],\ [577, 577, -2*w^2 + w + 26],\ [587, 587, w^2 - 6*w - 8],\ [593, 593, -2*w^2 + w + 16],\ [593, 593, 3*w^2 - 5*w - 17],\ [593, 593, 2*w^2 - 8*w - 9],\ [601, 601, -6*w^2 + 8*w + 53],\ [607, 607, -2*w - 9],\ [613, 613, w^2 + 2*w - 6],\ [617, 617, 5*w^2 - 11*w - 31],\ [619, 619, -4*w^2 + 6*w + 37],\ [641, 641, 3*w^2 - 6*w - 14],\ [647, 647, -2*w^2 + 3*w + 22],\ [653, 653, 2*w^2 - 7*w - 22],\ [653, 653, 2*w^2 + w + 2],\ [653, 653, -3*w^2 + 5*w + 29],\ [659, 659, 4*w^2 - 11*w - 18],\ [659, 659, 3*w^2 - 6*w - 8],\ [659, 659, 4*w^2 - 8*w - 23],\ [661, 661, w^2 + w - 11],\ [677, 677, -w^2 - 4],\ [701, 701, -2*w^2 - 5*w + 2],\ [727, 727, -2*w^2 + w + 18],\ [733, 733, -9*w^2 + 13*w + 79],\ [733, 733, -7*w^2 + 10*w + 56],\ [733, 733, 2*w^2 - 13],\ [739, 739, 6*w^2 - 10*w - 43],\ [739, 739, 4*w^2 - 4*w - 29],\ [739, 739, -8*w^2 + 15*w + 58],\ [751, 751, -11*w^2 + 19*w + 87],\ [757, 757, 3*w^2 - 10*w - 12],\ [761, 761, 4*w - 3],\ [769, 769, 3*w^2 - w - 13],\ [811, 811, 5*w^2 - 9*w - 33],\ [823, 823, 2*w^2 - 7*w - 12],\ [853, 853, -7*w - 8],\ [853, 853, -3*w^2 + 4*w + 2],\ [853, 853, 2*w^2 + 5*w + 6],\ [857, 857, 10*w^2 - 15*w - 82],\ [857, 857, 3*w^2 - 8*w - 18],\ [857, 857, -4*w^2 + 3*w + 44],\ [859, 859, -w^2 + 4*w - 6],\ [877, 877, -4*w^2 + 13*w + 14],\ [881, 881, 2*w^2 - 9*w - 2],\ [887, 887, 3*w - 14],\ [907, 907, -11*w^2 + 21*w + 77],\ [919, 919, 12*w^2 - 21*w - 92],\ [929, 929, w^2 - 18],\ [937, 937, 9*w + 4],\ [941, 941, -2*w^2 + 2*w - 1],\ [947, 947, 4*w^2 - 9*w - 18],\ [953, 953, -7*w^2 + 14*w + 48],\ [977, 977, w^2 - 2*w - 16],\ [983, 983, 4*w^2 - 7*w - 24],\ [991, 991, -3*w^2 - 2*w + 4]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^16 - 24*x^14 + 2*x^13 + 231*x^12 - 35*x^11 - 1140*x^10 + 233*x^9 + 3059*x^8 - 739*x^7 - 4357*x^6 + 1145*x^5 + 2958*x^4 - 787*x^3 - 713*x^2 + 186*x + 6 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, 344/66325*e^15 + 5322/66325*e^14 + 251/13265*e^13 - 106872/66325*e^12 - 96947/66325*e^11 + 118732/9475*e^10 + 834327/66325*e^9 - 3153522/66325*e^8 - 575203/13265*e^7 + 6041839/66325*e^6 + 4218099/66325*e^5 - 5409658/66325*e^4 - 2132652/66325*e^3 + 1697471/66325*e^2 + 31051/66325*e - 96678/66325, -1448/66325*e^15 - 682/9475*e^14 + 5598/13265*e^13 + 100824/66325*e^12 - 201626/66325*e^11 - 833333/66325*e^10 + 91663/9475*e^9 + 3389499/66325*e^8 - 139779/13265*e^7 - 6965813/66325*e^6 - 639658/66325*e^5 + 6587586/66325*e^4 + 1789859/66325*e^3 - 2223457/66325*e^2 - 944892/66325*e + 147376/66325, 7439/66325*e^15 + 7547/66325*e^14 - 33846/13265*e^13 - 148912/66325*e^12 + 1532683/66325*e^11 + 1140719/66325*e^10 - 7025923/66325*e^9 - 609381/9475*e^8 + 3420727/13265*e^7 + 8009184/66325*e^6 - 21111866/66325*e^5 - 6909463/66325*e^4 + 11295163/66325*e^3 + 2130456/66325*e^2 - 1722144/66325*e - 73908/66325, -223/9475*e^15 - 1333/66325*e^14 + 7253/13265*e^13 + 22098/66325*e^12 - 350097/66325*e^11 - 129431/66325*e^10 + 1823072/66325*e^9 + 299153/66325*e^8 - 1098568/13265*e^7 - 136616/66325*e^6 + 9287879/66325*e^5 - 341508/66325*e^4 - 1074716/9475*e^3 + 372846/66325*e^2 + 1887656/66325*e - 118128/66325, -1, -1859/66325*e^15 - 6362/66325*e^14 + 1538/2653*e^13 + 134907/66325*e^12 - 317378/66325*e^11 - 1119564/66325*e^10 + 193194/9475*e^9 + 651996/9475*e^8 - 651017/13265*e^7 - 1331147/9475*e^6 + 4680566/66325*e^5 + 8383958/66325*e^4 - 606654/9475*e^3 - 1948746/66325*e^2 + 1937714/66325*e - 40296/9475, -12879/66325*e^15 - 14102/66325*e^14 + 56724/13265*e^13 + 265602/66325*e^12 - 354064/9475*e^11 - 1896284/66325*e^10 + 10952843/66325*e^9 + 6343902/66325*e^8 - 5167992/13265*e^7 - 9880949/66325*e^6 + 31509791/66325*e^5 + 5994378/66325*e^4 - 17613718/66325*e^3 - 710611/66325*e^2 + 3491884/66325*e - 31602/66325, -121/2653*e^15 - 698/13265*e^14 + 13897/13265*e^13 + 13856/13265*e^12 - 126013/13265*e^11 - 3048/379*e^10 + 568297/13265*e^9 + 58101/1895*e^8 - 261727/2653*e^7 - 163957/2653*e^6 + 1375792/13265*e^5 + 121489/1895*e^4 - 83868/2653*e^3 - 345721/13265*e^2 - 6179/2653*e - 25422/13265, -8536/66325*e^15 - 5183/66325*e^14 + 38053/13265*e^13 + 12764/9475*e^12 - 1682097/66325*e^11 - 579881/66325*e^10 + 7496147/66325*e^9 + 254429/9475*e^8 - 3534563/13265*e^7 - 2771416/66325*e^6 + 21091054/66325*e^5 + 2460492/66325*e^4 - 10973262/66325*e^3 - 1507679/66325*e^2 + 1727156/66325*e + 222622/66325, -1144/13265*e^15 - 1816/13265*e^14 + 22991/13265*e^13 + 6610/2653*e^12 - 178342/13265*e^11 - 224979/13265*e^10 + 676014/13265*e^9 + 713078/13265*e^8 - 264594/2653*e^7 - 156792/1895*e^6 + 1316157/13265*e^5 + 840887/13265*e^4 - 553268/13265*e^3 - 263419/13265*e^2 - 6221/13265*e - 36618/13265, 3428/66325*e^15 + 1649/66325*e^14 - 17361/13265*e^13 - 44909/66325*e^12 + 877196/66325*e^11 + 475288/66325*e^10 - 4519766/66325*e^9 - 2457979/66325*e^8 + 359457/1895*e^7 + 6389518/66325*e^6 - 2644036/9475*e^5 - 7666081/66325*e^4 + 13092326/66325*e^3 + 3201447/66325*e^2 - 459309/9475*e + 146754/66325, -2211/66325*e^15 - 5638/66325*e^14 + 9857/13265*e^13 + 129683/66325*e^12 - 430152/66325*e^11 - 1176981/66325*e^10 + 1862367/66325*e^9 + 5312348/66325*e^8 - 842428/13265*e^7 - 12294741/66325*e^6 + 4935949/66325*e^5 + 13417247/66325*e^4 - 2972387/66325*e^3 - 5470739/66325*e^2 + 109408/9475*e + 466002/66325, 7646/66325*e^15 + 11708/66325*e^14 - 33024/13265*e^13 - 227368/66325*e^12 + 1421787/66325*e^11 + 1699566/66325*e^10 - 6277472/66325*e^9 - 6150313/66325*e^8 + 437204/1895*e^7 + 1597493/9475*e^6 - 2952432/9475*e^5 - 9638357/66325*e^4 + 14187132/66325*e^3 + 3150759/66325*e^2 - 3361116/66325*e - 202562/66325, 6239/66325*e^15 - 838/66325*e^14 - 28543/13265*e^13 + 36733/66325*e^12 + 1298448/66325*e^11 - 454306/66325*e^10 - 5985908/66325*e^9 + 2425673/66325*e^8 + 2952952/13265*e^7 - 6161266/66325*e^6 - 18907076/66325*e^5 + 7286472/66325*e^4 + 1564309/9475*e^3 - 3388289/66325*e^2 - 1535194/66325*e + 115002/66325, 1184/9475*e^15 + 8794/66325*e^14 - 35863/13265*e^13 - 155219/66325*e^12 + 1544156/66325*e^11 + 1000473/66325*e^10 - 6776471/66325*e^9 - 2770944/66325*e^8 + 3218259/13265*e^7 + 2595028/66325*e^6 - 19946527/66325*e^5 + 1376959/66325*e^4 + 10767796/66325*e^3 - 2938108/66325*e^2 - 1523023/66325*e + 67842/9475, 3183/66325*e^15 + 1172/9475*e^14 - 14088/13265*e^13 - 150229/66325*e^12 + 653746/66325*e^11 + 1007243/66325*e^10 - 3320711/66325*e^9 - 2957679/66325*e^8 + 1974304/13265*e^7 + 3357023/66325*e^6 - 16321482/66325*e^5 - 10481/66325*e^4 + 12293261/66325*e^3 - 319129/9475*e^2 - 2553618/66325*e + 881404/66325, -5624/66325*e^15 - 21/9475*e^14 + 23537/13265*e^13 - 26443/66325*e^12 - 956048/66325*e^11 + 467921/66325*e^10 + 3816023/66325*e^9 - 2889973/66325*e^8 - 226206/1895*e^7 + 7692431/66325*e^6 + 1250048/9475*e^5 - 8216647/66325*e^4 - 5748758/66325*e^3 + 2282839/66325*e^2 + 2449654/66325*e + 209298/66325, 5553/66325*e^15 + 1219/66325*e^14 - 28702/13265*e^13 - 24699/66325*e^12 + 1509241/66325*e^11 + 203263/66325*e^10 - 8246471/66325*e^9 - 846884/66325*e^8 + 4938364/13265*e^7 + 1826668/66325*e^6 - 38974157/66325*e^5 - 1903701/66325*e^4 + 28024726/66325*e^3 + 76791/9475*e^2 - 6080388/66325*e + 552934/66325, 1774/13265*e^15 + 22/379*e^14 - 37622/13265*e^13 - 10418/13265*e^12 + 43688/1895*e^11 + 27934/13265*e^10 - 236398/2653*e^9 + 184581/13265*e^8 + 429591/2653*e^7 - 1210376/13265*e^6 - 1415788/13265*e^5 + 338792/1895*e^4 - 19886/1895*e^3 - 1603033/13265*e^2 + 20233/1895*e + 214584/13265, -4468/66325*e^15 + 14961/66325*e^14 + 3476/1895*e^13 - 330231/66325*e^12 - 1300146/66325*e^11 + 2845747/66325*e^10 + 6969201/66325*e^9 - 1726003/9475*e^8 - 3944904/13265*e^7 + 26171442/66325*e^6 + 28129067/66325*e^5 - 26981169/66325*e^4 - 16838331/66325*e^3 + 10893378/66325*e^2 + 320929/9475*e - 956304/66325, -1741/13265*e^15 - 601/13265*e^14 + 38442/13265*e^13 + 8539/13265*e^12 - 66984/2653*e^11 - 36586/13265*e^10 + 1467519/13265*e^9 + 5049/2653*e^8 - 682193/2653*e^7 + 99934/13265*e^6 + 4028916/13265*e^5 + 10583/2653*e^4 - 281336/1895*e^3 - 83091/2653*e^2 + 61441/13265*e + 16038/2653, 647/9475*e^15 - 18898/66325*e^14 - 27704/13265*e^13 + 394748/66325*e^12 + 1594798/66325*e^11 - 3215416/66325*e^10 - 8955668/66325*e^9 + 1839689/9475*e^8 + 742611/1895*e^7 - 26214401/66325*e^6 - 5369413/9475*e^5 + 24980122/66325*e^4 + 23816393/66325*e^3 - 1182702/9475*e^2 - 4748484/66325*e + 274952/66325, 2469/66325*e^15 + 12472/66325*e^14 - 5784/13265*e^13 - 253422/66325*e^12 - 35297/66325*e^11 + 1999299/66325*e^10 + 260611/9475*e^9 - 7712547/66325*e^8 - 1903243/13265*e^7 + 15047189/66325*e^6 + 20086924/66325*e^5 - 13810508/66325*e^4 - 17226527/66325*e^3 + 4781096/66325*e^2 + 3684626/66325*e - 342378/66325, 828/13265*e^15 + 3379/13265*e^14 - 2776/2653*e^13 - 69369/13265*e^12 + 75646/13265*e^11 + 554523/13265*e^10 - 93151/13265*e^9 - 2175734/13265*e^8 - 12920/379*e^7 + 4343698/13265*e^6 + 219544/1895*e^5 - 4125791/13265*e^4 - 1689544/13265*e^3 + 1526752/13265*e^2 + 749337/13265*e - 28578/1895, 5312/66325*e^15 - 934/66325*e^14 - 5555/2653*e^13 + 13199/66325*e^12 + 1446554/66325*e^11 - 16423/66325*e^10 - 7639994/66325*e^9 - 604496/66325*e^8 + 4294656/13265*e^7 + 3870422/66325*e^6 - 30710763/66325*e^5 - 8982094/66325*e^4 + 19387954/66325*e^3 + 7534153/66325*e^2 - 4218352/66325*e - 955854/66325, 4743/66325*e^15 + 2239/66325*e^14 - 17912/13265*e^13 - 4419/66325*e^12 + 624921/66325*e^11 - 340647/66325*e^10 - 1902051/66325*e^9 + 2962746/66325*e^8 + 379474/13265*e^7 - 9176217/66325*e^6 + 2215558/66325*e^5 + 1559242/9475*e^4 - 6083169/66325*e^3 - 3369678/66325*e^2 + 3257872/66325*e - 528846/66325, 14614/66325*e^15 + 23217/66325*e^14 - 64077/13265*e^13 - 468502/66325*e^12 + 396454/9475*e^11 + 523142/9475*e^10 - 12053378/66325*e^9 - 13874872/66325*e^8 + 5511152/13265*e^7 + 25894884/66325*e^6 - 32045071/66325*e^5 - 20940683/66325*e^4 + 17313788/66325*e^3 + 661578/9475*e^2 - 3674144/66325*e - 10404/9475, -20837/66325*e^15 - 34471/66325*e^14 + 87784/13265*e^13 + 655961/66325*e^12 - 3654184/66325*e^11 - 4755102/66325*e^10 + 15350614/66325*e^9 + 16325816/66325*e^8 - 6904346/13265*e^7 - 26659772/66325*e^6 + 40479708/66325*e^5 + 17325249/66325*e^4 - 21241029/66325*e^3 - 843638/66325*e^2 + 368986/9475*e - 135288/9475, -1811/66325*e^15 + 8527/66325*e^14 + 2578/2653*e^13 - 147597/66325*e^12 - 779712/66325*e^11 + 127092/9475*e^10 + 4262182/66325*e^9 - 292191/9475*e^8 - 2175973/13265*e^7 + 763584/66325*e^6 + 11242839/66325*e^5 + 271776/9475*e^4 - 2355212/66325*e^3 - 402709/66325*e^2 - 1185144/66325*e - 214738/66325, -519/9475*e^15 - 15849/66325*e^14 + 10439/13265*e^13 + 44367/9475*e^12 - 156266/66325*e^11 - 2352718/66325*e^10 - 1002859/66325*e^9 + 8649584/66325*e^8 + 1521606/13265*e^7 - 15765348/66325*e^6 - 17694613/66325*e^5 + 12503926/66325*e^4 + 15443339/66325*e^3 - 2309312/66325*e^2 - 3021007/66325*e - 489834/66325, 922/13265*e^15 + 919/1895*e^14 - 11728/13265*e^13 - 25678/2653*e^12 + 16391/13265*e^11 + 987262/13265*e^10 + 367348/13265*e^9 - 525692/1895*e^8 - 413516/2653*e^7 + 6896917/13265*e^6 + 4267789/13265*e^5 - 6151856/13265*e^4 - 3742471/13265*e^3 + 2210277/13265*e^2 + 1114798/13265*e - 237186/13265, 15217/66325*e^15 + 16141/66325*e^14 - 62803/13265*e^13 - 292836/66325*e^12 + 2517799/66325*e^11 + 2055257/66325*e^10 - 9900544/66325*e^9 - 7198451/66325*e^8 + 3972181/13265*e^7 + 13940702/66325*e^6 - 19152898/66325*e^5 - 15697739/66325*e^4 + 7161864/66325*e^3 + 8461668/66325*e^2 - 99301/9475*e - 385974/66325, 10428/66325*e^15 + 3027/9475*e^14 - 38378/13265*e^13 - 375839/66325*e^12 + 1282486/66325*e^11 + 2460163/66325*e^10 - 3522276/66325*e^9 - 7238039/66325*e^8 + 373789/13265*e^7 + 9362568/66325*e^6 + 8268188/66325*e^5 - 4789171/66325*e^4 - 13367549/66325*e^3 + 168061/9475*e^2 + 4948212/66325*e - 172586/66325, -3163/13265*e^15 - 2474/13265*e^14 + 14107/2653*e^13 + 45784/13265*e^12 - 628776/13265*e^11 - 331148/13265*e^10 + 2868696/13265*e^9 + 1204834/13265*e^8 - 1423306/2653*e^7 - 341024/1895*e^6 + 9348467/13265*e^5 + 2568786/13265*e^4 - 5711861/13265*e^3 - 1258542/13265*e^2 + 1150413/13265*e + 52146/13265, -12021/66325*e^15 + 13032/66325*e^14 + 61367/13265*e^13 - 253212/66325*e^12 - 3057022/66325*e^11 + 1812784/66325*e^10 + 2150666/9475*e^9 - 5757797/66325*e^8 - 7629558/13265*e^7 + 7347224/66325*e^6 + 47008889/66325*e^5 - 1029733/66325*e^4 - 24071932/66325*e^3 - 3578304/66325*e^2 + 3206141/66325*e + 412572/66325, 17291/66325*e^15 + 14933/66325*e^14 - 77016/13265*e^13 - 278508/66325*e^12 + 3430492/66325*e^11 + 1984036/66325*e^10 - 15729747/66325*e^9 - 6775408/66325*e^8 + 7968658/13265*e^7 + 11475746/66325*e^6 - 55184214/66325*e^5 - 8767137/66325*e^4 + 37339847/66325*e^3 + 1191669/66325*e^2 - 8986536/66325*e + 760908/66325, -261/1895*e^15 - 682/1895*e^14 + 34812/13265*e^13 + 97792/13265*e^12 - 241042/13265*e^11 - 784442/13265*e^10 + 675751/13265*e^9 + 3107523/13265*e^8 - 50335/2653*e^7 - 6289677/13265*e^6 - 444245/2653*e^5 + 6056607/13265*e^4 + 3587456/13265*e^3 - 2287129/13265*e^2 - 1478903/13265*e + 209532/13265, -3821/13265*e^15 - 733/13265*e^14 + 16855/2653*e^13 + 5268/13265*e^12 - 727157/13265*e^11 + 6157/1895*e^10 + 3096377/13265*e^9 - 539932/13265*e^8 - 1346330/2653*e^7 + 1913694/13265*e^6 + 6925034/13265*e^5 - 2744898/13265*e^4 - 2660207/13265*e^3 + 1423841/13265*e^2 + 242731/13265*e - 156318/13265, -12596/66325*e^15 - 4843/66325*e^14 + 8621/1895*e^13 + 13459/9475*e^12 - 2870047/66325*e^11 - 695491/66325*e^10 + 13773637/66325*e^9 + 2328253/66325*e^8 - 6996568/13265*e^7 - 2933926/66325*e^6 + 44919414/66325*e^5 - 1062108/66325*e^4 - 3561951/9475*e^3 + 3877371/66325*e^2 + 4167816/66325*e - 1701978/66325, -6206/13265*e^15 - 3541/13265*e^14 + 144672/13265*e^13 + 69024/13265*e^12 - 38439/379*e^11 - 528376/13265*e^10 + 6369219/13265*e^9 + 402607/2653*e^8 - 3248002/2653*e^7 - 3959901/13265*e^6 + 21703261/13265*e^5 + 732870/2653*e^4 - 13608267/13265*e^3 - 217906/2653*e^2 + 2977596/13265*e - 49548/2653, -2218/9475*e^15 + 8462/66325*e^14 + 73671/13265*e^13 - 212762/66325*e^12 - 3454462/66325*e^11 + 2041779/66325*e^10 + 16271617/66325*e^9 - 9398612/66325*e^8 - 8060313/13265*e^7 + 3013867/9475*e^6 + 49659329/66325*e^5 - 2873424/9475*e^4 - 24815267/66325*e^3 + 4258091/66325*e^2 + 2084196/66325*e + 828712/66325, 19547/66325*e^15 + 17356/66325*e^14 - 87683/13265*e^13 - 46743/9475*e^12 + 3913984/66325*e^11 + 2349012/66325*e^10 - 17791929/66325*e^9 - 1143288/9475*e^8 + 8768106/13265*e^7 + 13096507/66325*e^6 - 57732568/66325*e^5 - 8951949/66325*e^4 + 36865849/66325*e^3 + 1606638/66325*e^2 - 7704512/66325*e - 398784/66325, 73/13265*e^15 + 3291/13265*e^14 + 9727/13265*e^13 - 57653/13265*e^12 - 199742/13265*e^11 + 371403/13265*e^10 + 1470926/13265*e^9 - 1083262/13265*e^8 - 145095/379*e^7 + 1520943/13265*e^6 + 243869/379*e^5 - 1360883/13265*e^4 - 6565464/13265*e^3 + 953331/13265*e^2 + 242616/1895*e - 187168/13265, 621/66325*e^15 - 6467/66325*e^14 + 571/13265*e^13 + 23226/9475*e^12 - 228463/66325*e^11 - 1582859/66325*e^10 + 2235878/66325*e^9 + 7525787/66325*e^8 - 1812367/13265*e^7 - 2573507/9475*e^6 + 16873526/66325*e^5 + 20086718/66325*e^4 - 13903018/66325*e^3 - 1215438/9475*e^2 + 653862/9475*e + 504688/66325, 181/379*e^15 + 123/379*e^14 - 4162/379*e^13 - 2370/379*e^12 + 38184/379*e^11 + 17802/379*e^10 - 178224/379*e^9 - 65864/379*e^8 + 446417/379*e^7 + 124523/379*e^6 - 578650/379*e^5 - 110644/379*e^4 + 338372/379*e^3 + 32577/379*e^2 - 60966/379*e + 1286/379, -6541/66325*e^15 - 27698/66325*e^14 + 26778/13265*e^13 + 556313/66325*e^12 - 1136557/66325*e^11 - 614823/9475*e^10 + 5355457/66325*e^9 + 16120618/66325*e^8 - 3135058/13265*e^7 - 30258421/66325*e^6 + 28258974/66325*e^5 + 26817202/66325*e^4 - 26593422/66325*e^3 - 9364149/66325*e^2 + 8419561/66325*e + 149082/66325, -981/13265*e^15 - 2302/13265*e^14 + 17796/13265*e^13 + 46796/13265*e^12 - 111466/13265*e^11 - 380381/13265*e^10 + 220698/13265*e^9 + 1590139/13265*e^8 + 87246/2653*e^7 - 3661111/13265*e^6 - 487770/2653*e^5 + 4560936/13265*e^4 + 475934/1895*e^3 - 387131/1895*e^2 - 1318399/13265*e + 366456/13265, -3141/66325*e^15 + 15957/66325*e^14 + 20154/13265*e^13 - 330047/66325*e^12 - 1204677/66325*e^11 + 2636339/66325*e^10 + 1007041/9475*e^9 - 10169302/66325*e^8 - 4336678/13265*e^7 + 19220904/66325*e^6 + 34335254/66325*e^5 - 2208354/9475*e^4 - 24488397/66325*e^3 + 350598/9475*e^2 + 4750486/66325*e + 1086252/66325, 9343/66325*e^15 + 3114/66325*e^14 - 38177/13265*e^13 - 1092/9475*e^12 + 212628/9475*e^11 - 503572/66325*e^10 - 787968/9475*e^9 + 4760421/66325*e^8 + 279647/1895*e^7 - 16295217/66325*e^6 - 1004306/9475*e^5 + 22704769/66325*e^4 + 308456/66325*e^3 - 10675178/66325*e^2 + 870472/66325*e + 412704/66325, 18692/66325*e^15 + 648/9475*e^14 - 90864/13265*e^13 - 107451/66325*e^12 + 4399469/66325*e^11 + 1015832/66325*e^10 - 3090057/9475*e^9 - 4694681/66325*e^8 + 11371711/13265*e^7 + 10389377/66325*e^6 - 76953453/66325*e^5 - 8894134/66325*e^4 + 47145814/66325*e^3 + 1252458/66325*e^2 - 9358532/66325*e + 831456/66325, 5069/13265*e^15 + 26/2653*e^14 - 121932/13265*e^13 - 169/1895*e^12 + 166423/1895*e^11 + 6114/13265*e^10 - 160418/379*e^9 - 36929/13265*e^8 + 408179/379*e^7 + 79699/13265*e^6 - 2602514/1895*e^5 + 118449/13265*e^4 + 9764828/13265*e^3 - 243413/13265*e^2 - 1310754/13265*e + 124944/13265, 3026/13265*e^15 - 1719/13265*e^14 - 78292/13265*e^13 + 5153/1895*e^12 + 160638/2653*e^11 - 41672/1895*e^10 - 4164719/13265*e^9 + 230506/2653*e^8 + 2302597/2653*e^7 - 2380194/13265*e^6 - 16433426/13265*e^5 + 537305/2653*e^4 + 10742167/13265*e^3 - 324957/2653*e^2 - 2204561/13265*e + 40632/2653, -8549/66325*e^15 - 9097/66325*e^14 + 36392/13265*e^13 + 166807/66325*e^12 - 1504848/66325*e^11 - 1157204/66325*e^10 + 862914/9475*e^9 + 3771302/66325*e^8 - 2380767/13265*e^7 - 5883419/66325*e^6 + 10045761/66325*e^5 + 595854/9475*e^4 - 2046433/66325*e^3 - 132223/9475*e^2 - 911896/66325*e - 692502/66325, -1369/13265*e^15 - 8102/13265*e^14 + 4555/2653*e^13 + 169312/13265*e^12 - 124408/13265*e^11 - 197142/1895*e^10 + 155678/13265*e^9 + 5510312/13265*e^8 + 151555/2653*e^7 - 11030119/13265*e^6 - 2478624/13265*e^5 + 9913623/13265*e^4 + 1948822/13265*e^3 - 2737981/13265*e^2 - 42941/13265*e + 7188/13265, 3244/66325*e^15 + 13742/66325*e^14 - 1597/2653*e^13 - 265737/66325*e^12 + 4189/9475*e^11 + 1992499/66325*e^10 + 1420072/66325*e^9 - 7401552/66325*e^8 - 1362013/13265*e^7 + 14674589/66325*e^6 + 10634119/66325*e^5 - 15513403/66325*e^4 - 4046652/66325*e^3 + 6814086/66325*e^2 - 1502474/66325*e - 368448/66325, 25432/66325*e^15 + 10226/66325*e^14 - 24169/2653*e^13 - 183486/66325*e^12 + 820317/9475*e^11 + 1279822/66325*e^10 - 27758309/66325*e^9 - 4434431/66325*e^8 + 14327356/13265*e^7 + 1156506/9475*e^6 - 94394968/66325*e^5 - 7516884/66325*e^4 + 54605594/66325*e^3 + 3304958/66325*e^2 - 8884672/66325*e - 288144/66325, 1248/9475*e^15 + 13213/66325*e^14 - 36347/13265*e^13 - 286733/66325*e^12 + 1437202/66325*e^11 + 2508581/66325*e^10 - 5281467/66325*e^9 - 1612289/9475*e^8 + 238999/1895*e^7 + 27250966/66325*e^6 - 260632/9475*e^5 - 32531697/66325*e^4 - 7464438/66325*e^3 + 2073352/9475*e^2 + 4858394/66325*e - 1393002/66325, -38968/66325*e^15 - 38029/66325*e^14 + 170824/13265*e^13 + 720099/66325*e^12 - 1052548/9475*e^11 - 5203603/66325*e^10 + 31685386/66325*e^9 + 2544702/9475*e^8 - 14170514/13265*e^7 - 28782683/66325*e^6 + 77646327/66325*e^5 + 17962421/66325*e^4 - 34403406/66325*e^3 - 1292252/66325*e^2 + 3987653/66325*e - 689964/66325, -9558/66325*e^15 - 20179/66325*e^14 + 6494/1895*e^13 + 447754/66325*e^12 - 2165196/66325*e^11 - 3905368/66325*e^10 + 10441736/66325*e^9 + 16814779/66325*e^8 - 5274564/13265*e^7 - 36560248/66325*e^6 + 32273307/66325*e^5 + 36128231/66325*e^4 - 15305711/66325*e^3 - 11555497/66325*e^2 + 1465843/66325*e - 80172/9475, -5459/13265*e^15 - 5366/13265*e^14 + 125196/13265*e^13 + 21409/2653*e^12 - 163106/1895*e^11 - 831724/13265*e^10 + 5252764/13265*e^9 + 3150208/13265*e^8 - 2550832/2653*e^7 - 5885104/13265*e^6 + 15562097/13265*e^5 + 4696242/13265*e^4 - 8184718/13265*e^3 - 976989/13265*e^2 + 1365354/13265*e - 92068/13265, -4712/9475*e^15 - 46547/66325*e^14 + 140428/13265*e^13 + 128011/9475*e^12 - 5844838/66325*e^11 - 6577314/66325*e^10 + 23994948/66325*e^9 + 22812562/66325*e^8 - 10041037/13265*e^7 - 37094129/66325*e^6 + 49441081/66325*e^5 + 22556818/66325*e^4 - 18420478/66325*e^3 - 23141/66325*e^2 + 2978964/66325*e - 1245112/66325, 151/9475*e^15 + 5126/66325*e^14 - 1986/2653*e^13 - 21748/9475*e^12 + 717244/66325*e^11 + 1649572/66325*e^10 - 4705434/66325*e^9 - 8398381/66325*e^8 + 3108451/13265*e^7 + 20936742/66325*e^6 - 25938068/66325*e^5 - 23826434/66325*e^4 + 20684044/66325*e^3 + 9936083/66325*e^2 - 5974347/66325*e - 185244/66325, 3129/9475*e^15 + 692/9475*e^14 - 15011/1895*e^13 - 14332/9475*e^12 + 712913/9475*e^11 + 120759/9475*e^10 - 3395503/9475*e^9 - 508662/9475*e^8 + 1691602/1895*e^7 + 1034224/9475*e^6 - 10496126/9475*e^5 - 771093/9475*e^4 + 5790393/9475*e^3 + 44916/9475*e^2 - 1188859/9475*e + 15912/9475, 6564/13265*e^15 + 7947/13265*e^14 - 28708/2653*e^13 - 158237/13265*e^12 + 1242778/13265*e^11 + 175872/1895*e^10 - 5434213/13265*e^9 - 4709462/13265*e^8 + 2549728/2653*e^7 + 9079174/13265*e^6 - 15956056/13265*e^5 - 7840893/13265*e^4 + 10275178/13265*e^3 + 1859616/13265*e^2 - 2892034/13265*e + 67392/13265, -1961/9475*e^15 - 36476/66325*e^14 + 55312/13265*e^13 + 104193/9475*e^12 - 2177324/66325*e^11 - 5613142/66325*e^10 + 8627084/66325*e^9 + 20905326/66325*e^8 - 3778651/13265*e^7 - 39029812/66325*e^6 + 24150958/66325*e^5 + 34233989/66325*e^4 - 17157884/66325*e^3 - 10711843/66325*e^2 + 4708567/66325*e - 852276/66325, 33462/66325*e^15 + 19766/66325*e^14 - 31095/2653*e^13 - 381726/66325*e^12 + 7181429/66325*e^11 + 2831852/66325*e^10 - 33571094/66325*e^9 - 9980421/66325*e^8 + 16700261/13265*e^7 + 16332972/66325*e^6 - 106213238/66325*e^5 - 9032594/66325*e^4 + 8674197/9475*e^3 - 212371/9475*e^2 - 11522977/66325*e + 1268346/66325, -11804/66325*e^15 + 23848/66325*e^14 + 63904/13265*e^13 - 74739/9475*e^12 - 487864/9475*e^11 + 4495716/66325*e^10 + 2632049/9475*e^9 - 19213298/66325*e^8 - 1515486/1895*e^7 + 42810151/66325*e^6 + 11255813/9475*e^5 - 47060297/66325*e^4 - 52385843/66325*e^3 + 20221814/66325*e^2 + 10049684/66325*e - 1961052/66325, -3412/13265*e^15 - 7677/13265*e^14 + 70584/13265*e^13 + 148958/13265*e^12 - 116489/2653*e^11 - 1109312/13265*e^10 + 2487143/13265*e^9 + 798060/2653*e^8 - 1205444/2653*e^7 - 7236512/13265*e^6 + 8517522/13265*e^5 + 1277400/2653*e^4 - 933112/1895*e^3 - 452678/2653*e^2 + 2089567/13265*e + 14352/2653, 5071/66325*e^15 + 42393/66325*e^14 - 12067/13265*e^13 - 854713/66325*e^12 + 27047/66325*e^11 + 6633266/66325*e^10 + 2316413/66325*e^9 - 24894778/66325*e^8 - 2333462/13265*e^7 + 46770376/66325*e^6 + 22367486/66325*e^5 - 41555817/66325*e^4 - 17351668/66325*e^3 + 14555404/66325*e^2 + 2779134/66325*e - 1486822/66325, -1608/66325*e^15 + 19501/66325*e^14 + 17574/13265*e^13 - 365481/66325*e^12 - 1280666/66325*e^11 + 369801/9475*e^10 + 8074291/66325*e^9 - 8681891/66325*e^8 - 697272/1895*e^7 + 14342752/66325*e^6 + 4878266/9475*e^5 - 11114049/66325*e^4 - 2735773/9475*e^3 + 2612263/66325*e^2 + 2617368/66325*e - 343634/66325, 12164/66325*e^15 + 18652/66325*e^14 - 9453/2653*e^13 - 310797/66325*e^12 + 1721263/66325*e^11 + 1761594/66325*e^10 - 5637918/66325*e^9 - 3317712/66325*e^8 + 198611/1895*e^7 - 2459266/66325*e^6 + 441902/9475*e^5 + 13218482/66325*e^4 - 12573587/66325*e^3 - 10711984/66325*e^2 + 778883/9475*e + 1630362/66325, 6908/66325*e^15 + 20849/66325*e^14 - 25804/13265*e^13 - 431869/66325*e^12 + 867266/66325*e^11 + 3515693/66325*e^10 - 2323991/66325*e^9 - 14324934/66325*e^8 + 155704/13265*e^7 + 4428189/9475*e^6 + 6569638/66325*e^5 - 35014626/66325*e^4 - 9029964/66325*e^3 + 18205437/66325*e^2 + 3273132/66325*e - 2007666/66325, -571/9475*e^15 - 4161/66325*e^14 + 20402/13265*e^13 + 57611/66325*e^12 - 1098114/66325*e^11 - 174162/66325*e^10 + 6319899/66325*e^9 - 110577/9475*e^8 - 579293/1895*e^7 + 5236743/66325*e^6 + 4911909/9475*e^5 - 9061796/66325*e^4 - 26113299/66325*e^3 + 721611/9475*e^2 + 5754912/66325*e - 1334286/66325, 47652/66325*e^15 + 48851/66325*e^14 - 218742/13265*e^13 - 998301/66325*e^12 + 10010524/66325*e^11 + 1146781/9475*e^10 - 46519209/66325*e^9 - 4585218/9475*e^8 + 23115481/13265*e^7 + 66145612/66325*e^6 - 148084158/66325*e^5 - 9310527/9475*e^4 + 86068484/66325*e^3 + 24120493/66325*e^2 - 15891592/66325*e - 1164774/66325, -1453/13265*e^15 - 2606/13265*e^14 + 31093/13265*e^13 + 51988/13265*e^12 - 266803/13265*e^11 - 404958/13265*e^10 + 1188884/13265*e^9 + 1566312/13265*e^8 - 593804/2653*e^7 - 3161978/13265*e^6 + 809363/2653*e^5 + 3089118/13265*e^4 - 2470591/13265*e^3 - 128463/1895*e^2 + 340618/13265*e - 93402/13265, 34327/66325*e^15 + 24081/66325*e^14 - 153611/13265*e^13 - 449986/66325*e^12 + 967822/9475*e^11 + 3238167/66325*e^10 - 29817454/66325*e^9 - 11297096/66325*e^8 + 13628936/13265*e^7 + 2838966/9475*e^6 - 75823878/66325*e^5 - 17082544/66325*e^4 + 33313384/66325*e^3 + 7243503/66325*e^2 - 3110892/66325*e - 1130504/66325, 15472/66325*e^15 - 14079/66325*e^14 - 15222/2653*e^13 + 316444/66325*e^12 + 3723974/66325*e^11 - 393959/9475*e^10 - 18571139/66325*e^9 + 11735824/66325*e^8 + 10040241/13265*e^7 - 25201168/66325*e^6 - 72152853/66325*e^5 + 25604961/66325*e^4 + 49807299/66325*e^3 - 10758807/66325*e^2 - 12667412/66325*e + 1610676/66325, -7761/66325*e^15 - 19073/66325*e^14 + 6185/2653*e^13 + 334753/66325*e^12 - 179091/9475*e^11 - 300383/9475*e^10 + 5522882/66325*e^9 + 5516263/66325*e^8 - 2957328/13265*e^7 - 5133766/66325*e^6 + 23296289/66325*e^5 + 1075957/66325*e^4 - 16326487/66325*e^3 - 175637/9475*e^2 + 2300856/66325*e - 75334/9475, -1276/66325*e^15 + 11152/66325*e^14 + 1332/1895*e^13 - 234967/66325*e^12 - 620572/66325*e^11 + 1932029/66325*e^10 + 588326/9475*e^9 - 7829022/66325*e^8 - 2997948/13265*e^7 + 16241594/66325*e^6 + 29609194/66325*e^5 - 16274358/66325*e^4 - 27805692/66325*e^3 + 7051396/66325*e^2 + 8692496/66325*e - 1468128/66325, 12119/66325*e^15 + 50292/66325*e^14 - 8154/2653*e^13 - 960287/66325*e^12 + 1222598/66325*e^11 + 993007/9475*e^10 - 3183053/66325*e^9 - 23737352/66325*e^8 + 900762/13265*e^7 + 39008464/66325*e^6 - 8759806/66325*e^5 - 28836903/66325*e^4 + 14797173/66325*e^3 + 8575236/66325*e^2 - 7671974/66325*e - 1086948/66325, -4981/13265*e^15 - 7891/13265*e^14 + 100747/13265*e^13 + 21742/1895*e^12 - 22219/379*e^11 - 1128286/13265*e^10 + 404537/1895*e^9 + 806420/2653*e^8 - 135894/379*e^7 - 7142921/13265*e^6 + 367648/1895*e^5 + 1150349/2653*e^4 + 1173398/13265*e^3 - 302691/2653*e^2 - 1036964/13265*e - 18618/2653, 21216/66325*e^15 + 46978/66325*e^14 - 90437/13265*e^13 - 922398/66325*e^12 + 3865287/66325*e^11 + 987698/9475*e^10 - 17092877/66325*e^9 - 24642213/66325*e^8 + 8398743/13265*e^7 + 42343171/66325*e^6 - 56145294/66325*e^5 - 31244782/66325*e^4 + 35194672/66325*e^3 + 6566159/66325*e^2 - 7015686/66325*e + 44238/66325, -13606/66325*e^15 - 21328/66325*e^14 + 63746/13265*e^13 + 463478/66325*e^12 - 2997822/66325*e^11 - 3945051/66325*e^10 + 14473427/66325*e^9 + 16486178/66325*e^8 - 7613178/13265*e^7 - 4927673/9475*e^6 + 53530124/66325*e^5 + 32390392/66325*e^4 - 36889652/66325*e^3 - 9946779/66325*e^2 + 8758676/66325*e + 167922/66325, 419/2653*e^15 - 1047/2653*e^14 - 11938/2653*e^13 + 21542/2653*e^12 + 131804/2653*e^11 - 171011/2653*e^10 - 722489/2653*e^9 + 658762/2653*e^8 + 2072071/2653*e^7 - 181272/379*e^6 - 2973980/2653*e^5 + 1103379/2653*e^4 + 1803033/2653*e^3 - 235279/2653*e^2 - 259530/2653*e - 48366/2653, 369/9475*e^15 + 12539/66325*e^14 - 11626/13265*e^13 - 306599/66325*e^12 + 507256/66325*e^11 + 2971693/66325*e^10 - 2081551/66325*e^9 - 14266044/66325*e^8 + 731329/13265*e^7 + 4930414/9475*e^6 - 671172/66325*e^5 - 5419538/9475*e^4 - 4327839/66325*e^3 + 14717567/66325*e^2 + 3632282/66325*e - 1330356/66325, 29817/66325*e^15 + 24356/66325*e^14 - 27448/2653*e^13 - 461016/66325*e^12 + 6328739/66325*e^11 + 474501/9475*e^10 - 29874129/66325*e^9 - 11190161/66325*e^8 + 15248956/13265*e^7 + 16833777/66325*e^6 - 101249308/66325*e^5 - 6574854/66325*e^4 + 59719764/66325*e^3 - 5278202/66325*e^2 - 9911682/66325*e + 1952686/66325, 6011/66325*e^15 - 972/66325*e^14 - 32019/13265*e^13 - 8513/66325*e^12 + 1644067/66325*e^11 + 329706/66325*e^10 - 8246177/66325*e^9 - 337944/9475*e^8 + 4191238/13265*e^7 + 6195491/66325*e^6 - 25287009/66325*e^5 - 4257737/66325*e^4 + 12497637/66325*e^3 - 2454131/66325*e^2 - 2302206/66325*e + 953958/66325, 107/13265*e^15 + 484/2653*e^14 + 32/1895*e^13 - 51584/13265*e^12 - 23127/13265*e^11 + 432087/13265*e^10 + 33660/2653*e^9 - 255396/1895*e^8 - 72298/2653*e^7 + 3734217/13265*e^6 - 205794/13265*e^5 - 3493233/13265*e^4 + 1294159/13265*e^3 + 922321/13265*e^2 - 117356/1895*e + 14622/13265, -2663/13265*e^15 - 1728/13265*e^14 + 61161/13265*e^13 + 31567/13265*e^12 - 113544/2653*e^11 - 220368/13265*e^10 + 2731387/13265*e^9 + 146670/2653*e^8 - 1440545/2653*e^7 - 1210523/13265*e^6 + 9906578/13265*e^5 + 215077/2653*e^4 - 5772771/13265*e^3 - 149330/2653*e^2 + 756368/13265*e + 66204/2653, -479/1895*e^15 - 3849/13265*e^14 + 14874/2653*e^13 + 72509/13265*e^12 - 659436/13265*e^11 - 524238/13265*e^10 + 2992891/13265*e^9 + 1854534/13265*e^8 - 1477615/2653*e^7 - 3511983/13265*e^6 + 9643267/13265*e^5 + 3852126/13265*e^4 - 5766486/13265*e^3 - 2195052/13265*e^2 + 1061418/13265*e + 17448/1895, -30049/66325*e^15 - 10097/66325*e^14 + 133457/13265*e^13 + 147482/66325*e^12 - 5825523/66325*e^11 - 705704/66325*e^10 + 25227498/66325*e^9 + 962877/66325*e^8 - 1597151/1895*e^7 + 202683/9475*e^6 + 8263373/9475*e^5 - 3941897/66325*e^4 - 20109333/66325*e^3 + 1987639/66325*e^2 - 763346/66325*e - 420402/66325, 20976/66325*e^15 - 27467/66325*e^14 - 106962/13265*e^13 + 584872/66325*e^12 + 760601/9475*e^11 - 4837654/66325*e^10 - 26250722/66325*e^9 + 2804601/9475*e^8 + 13385683/13265*e^7 - 40791544/66325*e^6 - 84001234/66325*e^5 + 41147348/66325*e^4 + 45673242/66325*e^3 - 15660776/66325*e^2 - 8664846/66325*e + 484518/66325, 13289/66325*e^15 + 17867/66325*e^14 - 53492/13265*e^13 - 321277/66325*e^12 + 292104/9475*e^11 + 309192/9475*e^10 - 7227978/66325*e^9 - 6699547/66325*e^8 + 2180457/13265*e^7 + 9275184/66325*e^6 - 2742121/66325*e^5 - 4493358/66325*e^4 - 5196012/66325*e^3 + 84578/9475*e^2 + 1324656/66325*e - 87504/9475, 451/66325*e^15 + 20628/66325*e^14 + 12727/13265*e^13 - 368043/66325*e^12 - 1297248/66325*e^11 + 2434321/66325*e^10 + 9434998/66325*e^9 - 7329373/66325*e^8 - 6318857/13265*e^7 + 10230856/66325*e^6 + 49137561/66325*e^5 - 7098472/66325*e^4 - 30792758/66325*e^3 + 2854014/66325*e^2 + 4498504/66325*e - 204852/66325, -2389/9475*e^15 + 8706/66325*e^14 + 77404/13265*e^13 - 257961/66325*e^12 - 3588496/66325*e^11 + 2765792/66325*e^10 + 17067121/66325*e^9 - 1972678/9475*e^8 - 1260542/1895*e^7 + 33082962/66325*e^6 + 8509071/9475*e^5 - 33979469/66325*e^4 - 34527716/66325*e^3 + 1466879/9475*e^2 + 3372858/66325*e - 362704/66325, -27731/66325*e^15 - 17578/66325*e^14 + 122811/13265*e^13 + 315653/66325*e^12 - 5335497/66325*e^11 - 2132426/66325*e^10 + 22917177/66325*e^9 + 6587303/66325*e^8 - 1428604/1895*e^7 - 1214898/9475*e^6 + 7116757/9475*e^5 + 1664392/66325*e^4 - 14529552/66325*e^3 + 1736071/66325*e^2 - 2471974/66325*e + 256122/66325, 47818/66325*e^15 + 36149/66325*e^14 - 44725/2653*e^13 - 726489/66325*e^12 + 10422056/66325*e^11 + 5737853/66325*e^10 - 49244791/66325*e^9 - 22516294/66325*e^8 + 24797904/13265*e^7 + 6501569/9475*e^6 - 160230232/66325*e^5 - 43839891/66325*e^4 + 93987281/66325*e^3 + 15639942/66325*e^2 - 17989478/66325*e - 121956/66325, -14404/66325*e^15 + 1759/9475*e^14 + 69772/13265*e^13 - 303178/66325*e^12 - 3379008/66325*e^11 + 2920616/66325*e^10 + 2391369/9475*e^9 - 14059008/66325*e^8 - 8983127/13265*e^7 + 35611826/66325*e^6 + 63255231/66325*e^5 - 45166762/66325*e^4 - 40948493/66325*e^3 + 23142494/66325*e^2 + 8386034/66325*e - 2444292/66325, 14242/66325*e^15 - 12109/66325*e^14 - 67993/13265*e^13 + 276914/66325*e^12 + 449057/9475*e^11 - 2510168/66325*e^10 - 14089244/66325*e^9 + 1649482/9475*e^8 + 6181276/13265*e^7 - 28509848/66325*e^6 - 27971848/66325*e^5 + 35850686/66325*e^4 + 2944689/66325*e^3 - 17520732/66325*e^2 + 3335618/66325*e + 620976/66325, -5801/66325*e^15 - 35508/66325*e^14 + 3601/1895*e^13 + 735778/66325*e^12 - 1201857/66325*e^11 - 5894046/66325*e^10 + 6701622/66325*e^9 + 23042268/66325*e^8 - 4640688/13265*e^7 - 45910206/66325*e^6 + 46249009/66325*e^5 + 44408627/66325*e^4 - 43721817/66325*e^3 - 2333482/9475*e^2 + 12793846/66325*e - 537618/66325, -6633/9475*e^15 - 23648/66325*e^14 + 29571/1895*e^13 + 373543/66325*e^12 - 1299931/9475*e^11 - 1938701/66325*e^10 + 40000357/66325*e^9 + 2596808/66325*e^8 - 18373188/13265*e^7 + 7650514/66325*e^6 + 104706654/66325*e^5 - 23882363/66325*e^4 - 50775352/66325*e^3 + 16949631/66325*e^2 + 8294526/66325*e - 1148108/66325, -8114/66325*e^15 - 2907/66325*e^14 + 46754/13265*e^13 + 139282/66325*e^12 - 2613243/66325*e^11 - 277342/9475*e^10 + 14565463/66325*e^9 + 11976357/66325*e^8 - 8580412/13265*e^7 - 35798209/66325*e^6 + 64844356/66325*e^5 + 49036773/66325*e^4 - 44684888/66325*e^3 - 23878826/66325*e^2 + 10116744/66325*e + 886768/66325, 43192/66325*e^15 + 21761/66325*e^14 - 205924/13265*e^13 - 462226/66325*e^12 + 9765269/66325*e^11 + 3940757/66325*e^10 - 46814324/66325*e^9 - 16956481/66325*e^8 + 23801096/13265*e^7 + 37508952/66325*e^6 - 153874978/66325*e^5 - 37744459/66325*e^4 + 12644002/9475*e^3 + 1662669/9475*e^2 - 15631032/66325*e + 702956/66325, -1381/66325*e^15 + 18022/66325*e^14 + 6666/13265*e^13 - 362672/66325*e^12 - 256122/66325*e^11 + 2743399/66325*e^10 + 75061/9475*e^9 - 1369271/9475*e^8 + 383847/13265*e^7 + 2137852/9475*e^6 - 9099726/66325*e^5 - 7240708/66325*e^4 + 1396989/9475*e^3 - 2039129/66325*e^2 - 2010924/66325*e + 43696/9475, -18668/66325*e^15 - 2427/9475*e^14 + 84747/13265*e^13 + 356569/66325*e^12 - 3793046/66325*e^11 - 3005328/66325*e^10 + 2417268/9475*e^9 + 13033854/66325*e^8 - 7777584/13265*e^7 - 30736833/66325*e^6 + 41954642/66325*e^5 + 37580331/66325*e^4 - 14316756/66325*e^3 - 20430947/66325*e^2 - 2274822/66325*e + 2978946/66325, -2088/13265*e^15 - 529/13265*e^14 + 9917/2653*e^13 + 1744/13265*e^12 - 475751/13265*e^11 + 72652/13265*e^10 + 2348981/13265*e^9 - 691396/13265*e^8 - 179000/379*e^7 + 337746/1895*e^6 + 1224866/1895*e^5 - 3474729/13265*e^4 - 4969791/13265*e^3 + 2171663/13265*e^2 + 590593/13265*e - 456054/13265, -1728/13265*e^15 - 1384/2653*e^14 + 30829/13265*e^13 + 142941/13265*e^12 - 28066/1895*e^11 - 1151498/13265*e^10 + 102414/2653*e^9 + 4560568/13265*e^8 - 80840/2653*e^7 - 9162413/13265*e^6 + 621/13265*e^5 + 8489017/13265*e^4 - 634756/13265*e^3 - 2452554/13265*e^2 + 572408/13265*e - 220518/13265, 1504/9475*e^15 + 40364/66325*e^14 - 5469/1895*e^13 - 822264/66325*e^12 + 182098/9475*e^11 + 6494413/66325*e^10 - 3669426/66325*e^9 - 25003514/66325*e^8 + 703179/13265*e^7 + 48388168/66325*e^6 + 3031438/66325*e^5 - 43503746/66325*e^4 - 7577999/66325*e^3 + 14451102/66325*e^2 + 3181337/66325*e - 2781636/66325, -139/13265*e^15 - 4008/13265*e^14 - 4166/13265*e^13 + 73539/13265*e^12 + 96496/13265*e^11 - 494329/13265*e^10 - 624903/13265*e^9 + 208718/1895*e^8 + 305416/2653*e^7 - 1759769/13265*e^6 - 185064/2653*e^5 + 603649/13265*e^4 - 703023/13265*e^3 - 55233/13265*e^2 + 264294/13265*e + 69854/13265, 4909/66325*e^15 - 27518/66325*e^14 - 28101/13265*e^13 + 576278/66325*e^12 + 1474198/66325*e^11 - 668123/9475*e^10 - 7098713/66325*e^9 + 18665723/66325*e^8 + 436411/1895*e^7 - 38717346/66325*e^6 - 1362878/9475*e^5 + 40935172/66325*e^4 - 1103521/9475*e^3 - 19426439/66325*e^2 + 7584036/66325*e + 2246002/66325, 14191/66325*e^15 + 4168/66325*e^14 - 59874/13265*e^13 - 47328/66325*e^12 + 2408327/66325*e^11 + 40436/66325*e^10 - 9040012/66325*e^9 + 1421502/66325*e^8 + 2972608/13265*e^7 - 6950304/66325*e^6 - 5032754/66325*e^5 + 1723379/9475*e^4 - 8519753/66325*e^3 - 7330661/66325*e^2 + 4049214/66325*e + 918248/66325, -7136/13265*e^15 - 1644/1895*e^14 + 30287/2653*e^13 + 217968/13265*e^12 - 182536/1895*e^11 - 1568151/13265*e^10 + 5511847/13265*e^9 + 5349493/13265*e^8 - 2609636/2653*e^7 - 8896476/13265*e^6 + 16703389/13265*e^5 + 978211/1895*e^4 - 1418066/1895*e^3 - 2111279/13265*e^2 + 226858/1895*e + 15492/13265, -412/2653*e^15 - 987/1895*e^14 + 48581/13265*e^13 + 154173/13265*e^12 - 457469/13265*e^11 - 268397/2653*e^10 + 2185741/13265*e^9 + 5713746/13265*e^8 - 1115594/2653*e^7 - 2421838/2653*e^6 + 7369661/13265*e^5 + 11251014/13265*e^4 - 896158/2653*e^3 - 401354/1895*e^2 + 167211/2653*e - 402816/13265, -26751/66325*e^15 - 7793/66325*e^14 + 26416/2653*e^13 + 181698/66325*e^12 - 6547042/66325*e^11 - 1749371/66325*e^10 + 33326437/66325*e^9 + 8707383/66325*e^8 - 18461703/13265*e^7 - 22828506/66325*e^6 + 135448799/66325*e^5 + 28367637/66325*e^4 - 93424692/66325*e^3 - 1725217/9475*e^2 + 20492771/66325*e - 188658/66325, -1191/9475*e^15 + 4237/9475*e^14 + 8865/2653*e^13 - 652649/66325*e^12 - 2262329/66325*e^11 + 5670198/66325*e^10 + 11309594/66325*e^9 - 24646179/66325*e^8 - 5819321/13265*e^7 + 55930053/66325*e^6 + 37309263/66325*e^5 - 62446406/66325*e^4 - 22034204/66325*e^3 + 27450972/66325*e^2 + 4907152/66325*e - 2207046/66325, 28848/66325*e^15 + 32314/66325*e^14 - 25324/2653*e^13 - 580354/66325*e^12 + 797413/9475*e^11 + 3848958/66325*e^10 - 25474801/66325*e^9 - 1618862/9475*e^8 + 12926934/13265*e^7 + 13402488/66325*e^6 - 90026752/66325*e^5 - 2072251/66325*e^4 + 61165816/66325*e^3 - 4555113/66325*e^2 - 14611683/66325*e + 1051734/66325, -3092/66325*e^15 + 244/66325*e^14 + 2111/2653*e^13 - 60359/66325*e^12 - 47302/9475*e^11 + 1034793/66325*e^10 + 1098704/66325*e^9 - 6615914/66325*e^8 - 621356/13265*e^7 + 18284873/66325*e^6 + 7501308/66325*e^5 - 19438696/66325*e^4 - 7754914/66325*e^3 + 4232552/66325*e^2 + 2266482/66325*e + 1109114/66325, 11516/66325*e^15 + 4308/66325*e^14 - 48866/13265*e^13 - 63383/66325*e^12 + 2014367/66325*e^11 + 380861/66325*e^10 - 8060897/66325*e^9 - 1501758/66325*e^8 + 3154148/13265*e^7 + 4762546/66325*e^6 - 12665889/66325*e^5 - 1315966/9475*e^4 + 768897/66325*e^3 + 7594694/66325*e^2 + 3163539/66325*e - 251856/9475, -40154/66325*e^15 - 37097/66325*e^14 + 5025/379*e^13 + 94881/9475*e^12 - 7629693/66325*e^11 - 4355509/66325*e^10 + 33476823/66325*e^9 + 12284557/66325*e^8 - 15744107/13265*e^7 - 11357499/66325*e^6 + 96648996/66325*e^5 - 8208327/66325*e^4 - 7816974/9475*e^3 + 14893224/66325*e^2 + 10133934/66325*e - 2158332/66325, -4041/13265*e^15 - 771/1895*e^14 + 98011/13265*e^13 + 114566/13265*e^12 - 954831/13265*e^11 - 943366/13265*e^10 + 4748123/13265*e^9 + 533497/1895*e^8 - 2533368/2653*e^7 - 7009416/13265*e^6 + 3503391/2653*e^5 + 4855721/13265*e^4 - 11269907/13265*e^3 + 141623/13265*e^2 + 2462256/13265*e - 406124/13265, 5996/9475*e^15 + 55021/66325*e^14 - 5137/379*e^13 - 1045731/66325*e^12 + 1088107/9475*e^11 + 7648362/66325*e^10 - 32551889/66325*e^9 - 27109826/66325*e^8 + 14852506/13265*e^7 + 48383207/66325*e^6 - 88015828/66325*e^5 - 40542939/66325*e^4 + 47884724/66325*e^3 + 10527668/66325*e^2 - 8465787/66325*e + 1944276/66325, 6562/66325*e^15 + 4721/66325*e^14 - 27914/13265*e^13 - 53611/66325*e^12 + 168087/9475*e^11 - 3389/9475*e^10 - 5037489/66325*e^9 + 2418009/66325*e^8 + 2315816/13265*e^7 - 10730928/66325*e^6 - 13227883/66325*e^5 + 16354651/66325*e^4 + 4767354/66325*e^3 - 909566/9475*e^2 + 287298/66325*e - 157962/9475, -8984/66325*e^15 + 13138/66325*e^14 + 9754/2653*e^13 - 269943/66325*e^12 - 2575703/66325*e^11 + 2128386/66325*e^10 + 13480708/66325*e^9 - 8119528/66325*e^8 - 7367307/13265*e^7 + 15788121/66325*e^6 + 51389991/66325*e^5 - 2226581/9475*e^4 - 34611053/66325*e^3 + 6848754/66325*e^2 + 9567714/66325*e - 357822/66325, 10166/66325*e^15 + 30643/66325*e^14 - 5242/1895*e^13 - 83004/9475*e^12 + 1187327/66325*e^11 + 4104461/66325*e^10 - 3084062/66325*e^9 - 13067073/66325*e^8 + 274548/13265*e^7 + 17309746/66325*e^6 + 6198196/66325*e^5 - 4526297/66325*e^4 - 997329/9475*e^3 - 4439361/66325*e^2 + 235264/66325*e + 821598/66325, -15798/66325*e^15 + 1786/66325*e^14 + 13591/2653*e^13 - 141171/66325*e^12 - 2857166/66325*e^11 + 2177867/66325*e^10 + 11852501/66325*e^9 - 13823466/66325*e^8 - 4999039/13265*e^7 + 41069162/66325*e^6 + 23898702/66325*e^5 - 54566574/66325*e^4 - 5064566/66325*e^3 + 26174738/66325*e^2 - 443556/9475*e - 2507784/66325, 3967/9475*e^15 - 2613/66325*e^14 - 19483/1895*e^13 + 48148/66325*e^12 + 950749/9475*e^11 - 246976/66325*e^10 - 32785783/66325*e^9 + 41843/66325*e^8 + 17083912/13265*e^7 + 2242664/66325*e^6 - 112406711/66325*e^5 - 3701223/66325*e^4 + 64208048/66325*e^3 + 1352476/66325*e^2 - 10715724/66325*e - 160968/66325, 18926/66325*e^15 + 33298/66325*e^14 - 78779/13265*e^13 - 669808/66325*e^12 + 3223372/66325*e^11 + 5286796/66325*e^10 - 13300557/66325*e^9 - 20702153/66325*e^8 + 6004048/13265*e^7 + 41609356/66325*e^6 - 38923244/66325*e^5 - 38892667/66325*e^4 + 4215281/9475*e^3 + 10512654/66325*e^2 - 9060046/66325*e + 1976928/66325, 6926/66325*e^15 + 8193/66325*e^14 - 4695/2653*e^13 - 96273/66325*e^12 + 636567/66325*e^11 + 62246/66325*e^10 - 79741/9475*e^9 + 3130317/66325*e^8 - 1228162/13265*e^7 - 13787369/66325*e^6 + 22173026/66325*e^5 + 18358288/66325*e^4 - 28888558/66325*e^3 - 3653731/66325*e^2 + 12593254/66325*e - 1944042/66325, 9414/66325*e^15 - 5538/66325*e^14 - 45898/13265*e^13 + 134458/66325*e^12 + 2187798/66325*e^11 - 1316881/66325*e^10 - 10274183/66325*e^9 + 6547323/66325*e^8 + 4850422/13265*e^7 - 16822541/66325*e^6 - 24984801/66325*e^5 + 19046572/66325*e^4 + 5348913/66325*e^3 - 3069264/66325*e^2 + 379083/9475*e - 3051798/66325, -10027/66325*e^15 - 773/9475*e^14 + 8506/2653*e^13 + 74671/66325*e^12 - 258337/9475*e^11 - 337467/66325*e^10 + 8037524/66325*e^9 + 666591/66325*e^8 - 4098221/13265*e^7 - 1854812/66325*e^6 + 30090098/66325*e^5 + 921457/9475*e^4 - 3123487/9475*e^3 - 7645913/66325*e^2 + 713706/9475*e + 2513484/66325, 38954/66325*e^15 + 59032/66325*e^14 - 173983/13265*e^13 - 1192937/66325*e^12 + 7795303/66325*e^11 + 9440359/66325*e^10 - 35864863/66325*e^9 - 36981997/66325*e^8 + 2569996/1895*e^7 + 74521999/66325*e^6 - 17163998/9475*e^5 - 71750708/66325*e^4 + 76649543/66325*e^3 + 24086421/66325*e^2 - 17157459/66325*e + 106296/9475, 2369/9475*e^15 - 4808/9475*e^14 - 17175/2653*e^13 + 718091/66325*e^12 + 4349836/66325*e^11 - 5916132/66325*e^10 - 21898021/66325*e^9 + 23728861/66325*e^8 + 11475754/13265*e^7 - 48056452/66325*e^6 - 75191867/66325*e^5 + 45758404/66325*e^4 + 44305461/66325*e^3 - 15331873/66325*e^2 - 9167118/66325*e + 627114/66325, 31286/66325*e^15 + 40263/66325*e^14 - 137152/13265*e^13 - 781133/66325*e^12 + 5969702/66325*e^11 + 5862931/66325*e^10 - 26297892/66325*e^9 - 21466248/66325*e^8 + 12386453/13265*e^7 + 39991866/66325*e^6 - 76031549/66325*e^5 - 36719222/66325*e^4 + 44650287/66325*e^3 + 15430264/66325*e^2 - 1524708/9475*e - 186836/9475, -35586/66325*e^15 - 13933/66325*e^14 + 161113/13265*e^13 + 225823/66325*e^12 - 7190097/66325*e^11 - 1272006/66325*e^10 + 4576571/9475*e^9 + 2536328/66325*e^8 - 14854283/13265*e^7 + 1231359/66325*e^6 + 84725104/66325*e^5 - 1437044/9475*e^4 - 40561587/66325*e^3 + 1374103/9475*e^2 + 6414281/66325*e - 1612878/66325, 20341/66325*e^15 - 15157/66325*e^14 - 106144/13265*e^13 + 301922/66325*e^12 + 784461/9475*e^11 - 2239539/66325*e^10 - 28777537/66325*e^9 + 1074736/9475*e^8 + 16176903/13265*e^7 - 10825529/66325*e^6 - 119135579/66325*e^5 + 4457928/66325*e^4 + 83393522/66325*e^3 + 185839/66325*e^2 - 20470861/66325*e + 1413498/66325, 58936/66325*e^15 + 54153/66325*e^14 - 256989/13265*e^13 - 979163/66325*e^12 + 1578031/9475*e^11 + 6627731/66325*e^10 - 47519427/66325*e^9 - 20577708/66325*e^8 + 21449083/13265*e^7 + 28369116/66325*e^6 - 121708084/66325*e^5 - 12651537/66325*e^4 + 61212437/66325*e^3 - 813331/66325*e^2 - 12175206/66325*e - 501042/66325, -20283/66325*e^15 - 10674/66325*e^14 + 90319/13265*e^13 + 171569/66325*e^12 - 3955116/66325*e^11 - 922918/66325*e^10 + 17196741/66325*e^9 + 1433084/66325*e^8 - 1097792/1895*e^7 + 2846652/66325*e^6 + 5860416/9475*e^5 - 10049724/66325*e^4 - 16925261/66325*e^3 + 7141863/66325*e^2 + 241174/9475*e + 236766/66325, -48042/66325*e^15 - 24146/66325*e^14 + 220077/13265*e^13 + 441671/66325*e^12 - 1423022/9475*e^11 - 3109332/66325*e^10 + 45114714/66325*e^9 + 10614221/66325*e^8 - 21286996/13265*e^7 - 18100802/66325*e^6 + 123288993/66325*e^5 + 14082469/66325*e^4 - 59345514/66325*e^3 - 4714578/66325*e^2 + 8597382/66325*e + 278954/66325, 6031/13265*e^15 + 4758/13265*e^14 - 28968/2653*e^13 - 95903/13265*e^12 + 201346/1895*e^11 + 765136/13265*e^10 - 7121552/13265*e^9 - 3072413/13265*e^8 + 3976656/2653*e^7 + 6471776/13265*e^6 - 30109199/13265*e^5 - 6480517/13265*e^4 + 22338437/13265*e^3 + 1764179/13265*e^2 - 5825916/13265*e + 470048/13265, -49123/66325*e^15 - 7817/9475*e^14 + 200119/13265*e^13 + 951189/66325*e^12 - 7845396/66325*e^11 - 6009858/66325*e^10 + 29667271/66325*e^9 + 2309847/9475*e^8 - 11097544/13265*e^7 - 14274738/66325*e^6 + 47141572/66325*e^5 - 8362894/66325*e^4 - 13968041/66325*e^3 + 15225103/66325*e^2 + 63558/66325*e - 3118804/66325, -5461/66325*e^15 + 5052/66325*e^14 + 7001/2653*e^13 - 79022/66325*e^12 - 2134187/66325*e^11 + 388319/66325*e^10 + 12722007/66325*e^9 - 468487/66325*e^8 - 7774658/13265*e^7 - 724791/66325*e^6 + 57160889/66325*e^5 + 87407/66325*e^4 - 32597062/66325*e^3 + 2451441/66325*e^2 + 543933/9475*e - 104184/9475, 3594/13265*e^15 - 5368/13265*e^14 - 17317/2653*e^13 + 124573/13265*e^12 + 818768/13265*e^11 - 1130231/13265*e^10 - 3855193/13265*e^9 + 5069968/13265*e^8 + 1890891/2653*e^7 - 11679281/13265*e^6 - 11543251/13265*e^5 + 12847182/13265*e^4 + 6165693/13265*e^3 - 5127504/13265*e^2 - 969709/13265*e + 314082/13265, 3282/66325*e^15 - 40559/66325*e^14 - 32167/13265*e^13 + 111737/9475*e^12 + 2290884/66325*e^11 - 5673953/66325*e^10 - 14518219/66325*e^9 + 2738112/9475*e^8 + 9087191/13265*e^7 - 30292408/66325*e^6 - 69413928/66325*e^5 + 19322676/66325*e^4 + 46806744/66325*e^3 - 1336612/66325*e^2 - 9403122/66325*e - 125484/66325, 6911/13265*e^15 + 225/379*e^14 - 164158/13265*e^13 - 170392/13265*e^12 + 1567424/13265*e^11 + 1462966/13265*e^10 - 1537152/2653*e^9 - 6278191/13265*e^8 + 4101766/2653*e^7 + 13824491/13265*e^6 - 29066602/13265*e^5 - 14180514/13265*e^4 + 19621972/13265*e^3 + 730954/1895*e^2 - 4452066/13265*e - 29294/13265, 4374/13265*e^15 + 13063/13265*e^14 - 75679/13265*e^13 - 34757/1895*e^12 + 450559/13265*e^11 + 1705364/13265*e^10 - 904457/13265*e^9 - 5575351/13265*e^8 - 154192/2653*e^7 + 8614419/13265*e^6 + 929844/2653*e^5 - 841692/1895*e^4 - 4415347/13265*e^3 + 1818473/13265*e^2 + 999906/13265*e - 280754/13265, -10978/66325*e^15 - 32849/66325*e^14 + 41456/13265*e^13 + 96787/9475*e^12 - 1444246/66325*e^11 - 5537463/66325*e^10 + 4354341/66325*e^9 + 22950554/66325*e^8 - 819139/13265*e^7 - 51065668/66325*e^6 - 5518523/66325*e^5 + 8262733/9475*e^4 + 13304174/66325*e^3 - 25975497/66325*e^2 - 6879912/66325*e + 2513746/66325, 13422/66325*e^15 + 78901/66325*e^14 - 33904/13265*e^13 - 228513/9475*e^12 + 148829/66325*e^11 + 12634837/66325*e^10 + 6558191/66325*e^9 - 49174446/66325*e^8 - 7312884/13265*e^7 + 98302282/66325*e^6 + 77428702/66325*e^5 - 13524242/9475*e^4 - 68831101/66325*e^3 + 34135328/66325*e^2 + 19739838/66325*e - 2794154/66325, -3284/66325*e^15 + 7499/9475*e^14 + 29171/13265*e^13 - 1115278/66325*e^12 - 2055748/66325*e^11 + 9228636/66325*e^10 + 1925234/9475*e^9 - 37400098/66325*e^8 - 9120612/13265*e^7 + 76469996/66325*e^6 + 78785971/66325*e^5 - 72968047/66325*e^4 - 60449803/66325*e^3 + 25976914/66325*e^2 + 12322839/66325*e - 911202/66325, 37943/66325*e^15 + 56094/66325*e^14 - 162986/13265*e^13 - 1085929/66325*e^12 + 991418/9475*e^11 + 1156579/9475*e^10 - 30026446/66325*e^9 - 29175924/66325*e^8 + 14141784/13265*e^7 + 51990108/66325*e^6 - 90627212/66325*e^5 - 40176061/66325*e^4 + 58947431/66325*e^3 + 878426/9475*e^2 - 15413128/66325*e + 370032/9475, 358/13265*e^15 + 1753/13265*e^14 - 5311/13265*e^13 - 25162/13265*e^12 + 5861/2653*e^11 + 83063/13265*e^10 - 98527/13265*e^9 + 63173/2653*e^8 + 71475/2653*e^7 - 2381137/13265*e^6 - 1011123/13265*e^5 + 865416/2653*e^4 + 1171326/13265*e^3 - 442832/2653*e^2 - 196793/13265*e + 3498/2653, -12514/66325*e^15 - 10912/66325*e^14 + 9114/1895*e^13 + 269167/66325*e^12 - 3225123/66325*e^11 - 2625944/66325*e^10 + 16437108/66325*e^9 + 12919152/66325*e^8 - 8840227/13265*e^7 - 33647959/66325*e^6 + 59449451/66325*e^5 + 43839953/66325*e^4 - 33395513/66325*e^3 - 23230061/66325*e^2 + 4555044/66325*e + 365864/9475, -29497/66325*e^15 - 33111/66325*e^14 + 123142/13265*e^13 + 603411/66325*e^12 - 5030989/66325*e^11 - 4205612/66325*e^10 + 20411474/66325*e^9 + 14139261/66325*e^8 - 1234218/1895*e^7 - 24118632/66325*e^6 + 6588009/9475*e^5 + 20486929/66325*e^4 - 22633574/66325*e^3 - 6881373/66325*e^2 + 5913912/66325*e - 161948/9475, 8329/66325*e^15 - 3644/9475*e^14 - 46076/13265*e^13 + 553818/66325*e^12 + 2533938/66325*e^11 - 4678566/66325*e^10 - 14230903/66325*e^9 + 19387163/66325*e^8 + 8638047/13265*e^7 - 40575851/66325*e^6 - 67866751/66325*e^5 + 38990832/66325*e^4 + 45839168/66325*e^3 - 1892512/9475*e^2 - 6862809/66325*e + 1846512/66325, 38736/66325*e^15 + 73133/66325*e^14 - 164753/13265*e^13 - 1473273/66325*e^12 + 6944397/66325*e^11 + 11571506/66325*e^10 - 29820797/66325*e^9 - 44818528/66325*e^8 + 2015744/1895*e^7 + 89236891/66325*e^6 - 13473097/9475*e^5 - 85662692/66325*e^4 + 69039462/66325*e^3 + 30391029/66325*e^2 - 2886508/9475*e - 555822/66325, 51349/66325*e^15 + 16332/66325*e^14 - 47052/2653*e^13 - 279452/66325*e^12 + 10650708/66325*e^11 + 257547/9475*e^10 - 48378363/66325*e^9 - 5387967/66325*e^8 + 23097302/13265*e^7 + 6850294/66325*e^6 - 138718851/66325*e^5 - 183688/66325*e^4 + 73778633/66325*e^3 - 5733144/66325*e^2 - 13493904/66325*e + 2736142/66325, -2556/9475*e^15 - 29266/66325*e^14 + 74948/13265*e^13 + 606511/66325*e^12 - 3000824/66325*e^11 - 4917382/66325*e^10 + 11311719/66325*e^9 + 19630376/66325*e^8 - 3858861/13265*e^7 - 39407752/66325*e^6 + 9137748/66325*e^5 + 34306389/66325*e^4 + 7527536/66325*e^3 - 5529768/66325*e^2 - 5344968/66325*e - 219068/9475, -8913/66325*e^15 + 13961/66325*e^14 + 6947/1895*e^13 - 46688/9475*e^12 - 2624826/66325*e^11 + 3011102/66325*e^10 + 14198851/66325*e^9 - 13817876/66325*e^8 - 8008589/13265*e^7 + 32609522/66325*e^6 + 55180457/66325*e^5 - 35569689/66325*e^4 - 4312353/9475*e^3 + 11252118/66325*e^2 + 3552898/66325*e + 43476/66325, -8418/66325*e^15 - 13824/66325*e^14 + 1124/379*e^13 + 274139/66325*e^12 - 1897856/66325*e^11 - 2130953/66325*e^10 + 9715516/66325*e^9 + 8324994/66325*e^8 - 5563069/13265*e^7 - 17522283/66325*e^6 + 41874507/66325*e^5 + 19436416/66325*e^4 - 26236156/66325*e^3 - 1317481/9475*e^2 + 2856353/66325*e + 155856/66325, 79228/66325*e^15 + 37654/66325*e^14 - 74042/2653*e^13 - 107392/9475*e^12 + 2455893/9475*e^11 + 5989738/66325*e^10 - 11540848/9475*e^9 - 24091299/66325*e^8 + 5782947/1895*e^7 + 50012418/66325*e^6 - 37404021/9475*e^5 - 46625386/66325*e^4 + 156032176/66325*e^3 + 10995582/66325*e^2 - 31024288/66325*e + 2830074/66325, 28103/66325*e^15 + 45324/66325*e^14 - 15848/1895*e^13 - 827984/66325*e^12 + 4144846/66325*e^11 + 5604213/66325*e^10 - 14389041/66325*e^9 - 16950879/66325*e^8 + 4418264/13265*e^7 + 21086368/66325*e^6 - 8048577/66325*e^5 - 5359756/66325*e^4 - 9655124/66325*e^3 - 3770178/66325*e^2 + 4463462/66325*e + 203772/9475, -46468/66325*e^15 - 54904/66325*e^14 + 218654/13265*e^13 + 1162649/66325*e^12 - 10269636/66325*e^11 - 9622528/66325*e^10 + 6996448/9475*e^9 + 5568327/9475*e^8 - 24919984/13265*e^7 - 11219094/9475*e^6 + 162787227/66325*e^5 + 69533171/66325*e^4 - 13816633/9475*e^3 - 18201177/66325*e^2 + 19884978/66325*e - 187752/9475, -16971/66325*e^15 + 7986/9475*e^14 + 92101/13265*e^13 - 171061/9475*e^12 - 4905127/66325*e^11 + 9932584/66325*e^10 + 26244182/66325*e^9 - 40271277/66325*e^8 - 14902793/13265*e^7 + 82981949/66325*e^6 + 108306634/66325*e^5 - 82061228/66325*e^4 - 69563282/66325*e^3 + 32572186/66325*e^2 + 12284516/66325*e - 419964/9475, -5583/13265*e^15 + 4588/13265*e^14 + 143557/13265*e^13 - 19326/2653*e^12 - 1454599/13265*e^11 + 786557/13265*e^10 + 1054864/1895*e^9 - 3116364/13265*e^8 - 3937323/2653*e^7 + 6249452/13265*e^6 + 26347084/13265*e^5 - 6076416/13265*e^4 - 15316006/13265*e^3 + 2561107/13265*e^2 + 2559888/13265*e - 290586/13265, 23166/66325*e^15 + 31468/66325*e^14 - 100144/13265*e^13 - 572428/66325*e^12 + 4342327/66325*e^11 + 3869361/66325*e^10 - 19418437/66325*e^9 - 11692648/66325*e^8 + 9593543/13265*e^7 + 2041828/9475*e^6 - 64777779/66325*e^5 - 2766097/66325*e^4 + 42747847/66325*e^3 - 2764711/66325*e^2 - 8672036/66325*e + 395298/66325] 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, w^2 - 2*w - 2])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]