/* 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([-79, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([5, 5, w + 2]) primes_array = [ [2, 2, -w + 9],\ [3, 3, w + 1],\ [3, 3, w + 2],\ [5, 5, w + 2],\ [5, 5, w + 3],\ [7, 7, w + 3],\ [7, 7, w + 4],\ [13, 13, w + 1],\ [13, 13, w + 12],\ [43, 43, -w - 6],\ [43, 43, w - 6],\ [47, 47, w + 19],\ [47, 47, w + 28],\ [59, 59, w + 16],\ [59, 59, w + 43],\ [71, 71, w + 24],\ [71, 71, w + 47],\ [73, 73, 3*w - 28],\ [73, 73, 12*w - 107],\ [79, 79, -w],\ [89, 89, w + 41],\ [89, 89, w + 48],\ [97, 97, w + 46],\ [97, 97, w + 51],\ [101, 101, w + 33],\ [101, 101, w + 68],\ [103, 103, w + 39],\ [103, 103, w + 64],\ [107, 107, w + 20],\ [107, 107, w + 87],\ [121, 11, -11],\ [127, 127, w + 29],\ [127, 127, w + 98],\ [139, 139, w + 45],\ [139, 139, w + 94],\ [181, 181, 6*w - 55],\ [181, 181, 15*w - 134],\ [191, 191, w + 35],\ [191, 191, w + 156],\ [199, 199, w + 26],\ [199, 199, w + 173],\ [211, 211, -5*w + 42],\ [211, 211, 22*w - 195],\ [227, 227, -3*w - 22],\ [227, 227, 3*w - 22],\ [241, 241, w + 101],\ [241, 241, w + 140],\ [251, 251, w + 62],\ [251, 251, w + 189],\ [257, 257, 31*w - 276],\ [257, 257, 4*w - 39],\ [269, 269, w + 50],\ [269, 269, w + 219],\ [271, 271, 20*w - 177],\ [271, 271, -7*w + 60],\ [277, 277, w + 112],\ [277, 277, w + 165],\ [281, 281, w + 109],\ [281, 281, w + 172],\ [289, 17, -17],\ [307, 307, 2*w - 3],\ [307, 307, -2*w - 3],\ [311, 311, 3*w - 20],\ [311, 311, -3*w - 20],\ [313, 313, -3*w - 32],\ [313, 313, 3*w - 32],\ [317, 317, w + 57],\ [317, 317, w + 260],\ [331, 331, 17*w - 150],\ [331, 331, -10*w + 87],\ [337, 337, w + 42],\ [337, 337, w + 295],\ [359, 359, w + 34],\ [359, 359, w + 325],\ [361, 19, -19],\ [379, 379, w + 107],\ [379, 379, w + 272],\ [389, 389, w + 63],\ [389, 389, w + 326],\ [397, 397, w + 85],\ [397, 397, w + 312],\ [419, 419, w + 181],\ [419, 419, w + 238],\ [421, 421, w + 105],\ [421, 421, w + 316],\ [433, 433, w + 168],\ [433, 433, w + 265],\ [443, 443, 39*w - 346],\ [443, 443, -6*w + 49],\ [457, 457, w + 203],\ [457, 457, w + 254],\ [463, 463, w + 81],\ [463, 463, w + 382],\ [491, 491, w + 55],\ [491, 491, w + 436],\ [503, 503, w + 60],\ [503, 503, w + 443],\ [529, 23, -23],\ [541, 541, w + 151],\ [541, 541, w + 390],\ [557, 557, w + 242],\ [557, 557, w + 315],\ [569, 569, 8*w - 75],\ [569, 569, 35*w - 312],\ [587, 587, w + 133],\ [587, 587, w + 454],\ [593, 593, w + 240],\ [593, 593, w + 353],\ [607, 607, w + 61],\ [607, 607, w + 546],\ [617, 617, w + 90],\ [617, 617, w + 527],\ [619, 619, w + 44],\ [619, 619, w + 575],\ [631, 631, w + 292],\ [631, 631, w + 339],\ [641, 641, w + 274],\ [641, 641, w + 367],\ [647, 647, 3*w - 8],\ [647, 647, -3*w - 8],\ [653, 653, w + 262],\ [653, 653, w + 391],\ [659, 659, w + 279],\ [659, 659, w + 380],\ [677, 677, w + 247],\ [677, 677, w + 430],\ [691, 691, w + 65],\ [691, 691, w + 626],\ [733, 733, -3*w - 38],\ [733, 733, 3*w - 38],\ [739, 739, w + 170],\ [739, 739, w + 569],\ [757, 757, w + 222],\ [757, 757, w + 535],\ [761, 761, 4*w - 45],\ [761, 761, -4*w - 45],\ [773, 773, 2*w - 33],\ [773, 773, -2*w - 33],\ [809, 809, w + 121],\ [809, 809, w + 688],\ [821, 821, -w - 30],\ [821, 821, w - 30],\ [823, 823, -4*w - 21],\ [823, 823, 4*w - 21],\ [827, 827, w + 71],\ [827, 827, w + 756],\ [841, 29, -29],\ [857, 857, w + 93],\ [857, 857, w + 764],\ [859, 859, w + 259],\ [859, 859, w + 600],\ [877, 877, 6*w - 61],\ [877, 877, -6*w - 61],\ [883, 883, w + 163],\ [883, 883, w + 720],\ [941, 941, -5*w - 54],\ [941, 941, 5*w - 54],\ [947, 947, 27*w - 238],\ [947, 947, -18*w + 157],\ [953, 953, w + 293],\ [953, 953, w + 660],\ [961, 31, -31],\ [983, 983, 24*w - 211],\ [983, 983, -21*w + 184],\ [991, 991, w + 216],\ [991, 991, w + 775],\ [997, 997, 9*w - 86],\ [997, 997, 54*w - 481]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^12 + 22*x^10 + 331*x^8 + 2690*x^6 + 15973*x^4 + 51714*x^2 + 114244 K. = NumberField(heckePol) hecke_eigenvalues_array = [1, -550021/18232265870*e^11 - 14605349/9116132935*e^9 - 439488229/18232265870*e^7 - 2261993862/9116132935*e^5 - 21208294507/18232265870*e^3 - 203147127/53941615*e, e, 50643/1402481990*e^10 + 475277/701240995*e^8 + 14301517/1402481990*e^6 + 49599026/701240995*e^4 + 690145411/1402481990*e^2 + 6610671/4149355, -202572/701240995*e^10 - 3802216/701240995*e^8 - 57206068/701240995*e^6 - 396792208/701240995*e^4 - 2059340649/701240995*e^2 - 19690528/4149355, 2222/7705945*e^11 + 33431/7705945*e^9 + 422153/7705945*e^7 + 1613273/7705945*e^5 + 401778/592765*e^3 - 19760978/7705945*e, -206594/1823226587*e^11 - 7106770/1823226587*e^9 - 106924585/1823226587*e^7 - 1052745397/1823226587*e^5 - 5159838055/1823226587*e^3 - 98848710/10788323*e, -6/46865*e^10 - 418/46865*e^8 - 6289/46865*e^6 - 65969/46865*e^4 - 303487/46865*e^2 - 75582/3605, -899793/701240995*e^10 - 19007399/701240995*e^8 - 254100367/701240995*e^6 - 1762488652/701240995*e^4 - 7457192101/701240995*e^2 - 87462232/4149355, -8721/15840370*e^11 - 92889/7920185*e^9 - 2462799/15840370*e^7 - 8541222/7920185*e^5 - 72407967/15840370*e^3 - 32604/3605*e, 14042187/18232265870*e^11 + 148732253/9116132935*e^9 + 3965495253/18232265870*e^7 + 13752716034/9116132935*e^5 + 120093983699/18232265870*e^3 + 52497588/4149355*e, -32098/53941615*e^11 - 482929/53941615*e^9 - 5945637/53941615*e^7 - 23304607/53941615*e^5 - 5803902/4149355*e^3 + 219385332/53941615*e, -46776/260460941*e^11 - 1609080/260460941*e^9 - 24209340/260460941*e^7 - 233443091/260460941*e^5 - 1168265220/260460941*e^3 - 22380840/1541189*e, -2222/7705945*e^11 - 33431/7705945*e^9 - 422153/7705945*e^7 - 1613273/7705945*e^5 - 401778/592765*e^3 + 42878813/7705945*e, 1650063/18232265870*e^11 + 43816047/9116132935*e^9 + 1318464687/18232265870*e^7 + 6785981586/9116132935*e^5 + 63624883521/18232265870*e^3 + 609441381/53941615*e, 120776/701240995*e^11 + 2571558/701240995*e^9 + 38690259/701240995*e^7 + 337404594/701240995*e^5 + 1867067997/701240995*e^3 + 35768034/4149355*e, 1606/7705945*e^11 + 24163/7705945*e^9 + 228824/7705945*e^7 + 1166029/7705945*e^5 + 290394/592765*e^3 + 41871526/7705945*e, 1166/829871*e^10 + 17543/829871*e^8 + 226221/829871*e^6 + 846569/829871*e^4 + 2740842/829871*e^2 - 10742888/829871, -2442/4149355*e^10 - 36741/4149355*e^8 - 364178/4149355*e^6 - 1773003/4149355*e^4 - 5740254/4149355*e^2 - 17334552/4149355, -1275255/1823226587*e^11 - 27749551/1823226587*e^9 - 360130345/1823226587*e^7 - 2497932820/1823226587*e^5 - 10272687176/1823226587*e^3 - 9535240/829871*e, -23326/100177285*e^10 + 780692/100177285*e^8 + 11745866/100177285*e^6 + 157283286/100177285*e^4 + 566817878/100177285*e^2 + 10858716/592765, 2192949/701240995*e^10 + 47516657/701240995*e^8 + 619285931/701240995*e^6 + 4295485436/701240995*e^4 + 17573845178/701240995*e^2 + 213160376/4149355, -101286/140248199*e^10 - 1901108/140248199*e^8 - 28603034/140248199*e^6 - 198396104/140248199*e^4 - 1240042623/140248199*e^2 - 9845264/829871, -50488/701240995*e^10 + 3012526/701240995*e^8 + 45324823/701240995*e^6 + 510681063/701240995*e^4 + 2187230809/701240995*e^2 + 41901498/4149355, 432461/701240995*e^10 + 9335678/701240995*e^8 + 140459519/701240995*e^6 + 1250420324/701240995*e^4 + 6778126577/701240995*e^2 + 129850794/4149355, -646578/701240995*e^10 - 14254629/701240995*e^8 - 182592782/701240995*e^6 - 1266498392/701240995*e^4 - 4707706041/701240995*e^2 - 62849072/4149355, -8074/10788323*e^11 - 121477/10788323*e^9 - 1488184/10788323*e^7 - 5862091/10788323*e^5 - 1459926/829871*e^3 + 62771238/10788323*e, -448270/1823226587*e^11 - 15420350/1823226587*e^9 - 232006175/1823226587*e^7 - 2215457877/1823226587*e^5 - 11195875025/1823226587*e^3 - 214483050/10788323*e, -3339377/18232265870*e^11 - 42001553/9116132935*e^9 - 1263864913/18232265870*e^7 - 6098418169/9116132935*e^5 - 60990073279/18232265870*e^3 - 584203419/53941615*e, -616/7705945*e^11 - 9268/7705945*e^9 - 193329/7705945*e^7 - 447244/7705945*e^5 - 111384/592765*e^3 + 69338449/7705945*e, 10, -241552/701240995*e^11 - 5143116/701240995*e^9 - 77380518/701240995*e^7 - 674809188/701240995*e^5 - 3734135994/701240995*e^3 - 71536068/4149355*e, -16346/10788323*e^11 - 245933/10788323*e^9 - 2983467/10788323*e^7 - 11867939/10788323*e^5 - 2955654/829871*e^3 + 114088804/10788323*e, 59411/2604609410*e^11 - 1183171/1302304705*e^9 - 35602691/2604609410*e^7 - 217464943/1302304705*e^5 - 1718071853/2604609410*e^3 - 16456833/7705945*e, 8272/7705945*e^11 + 124456/7705945*e^9 + 1495283/7705945*e^7 + 6005848/7705945*e^5 + 1495728/592765*e^3 - 9705463/7705945*e, 1738/592765*e^10 + 26149/592765*e^8 + 312592/592765*e^6 + 1261867/592765*e^4 + 4085406/592765*e^2 - 4869002/592765, 5368/4149355*e^10 + 80764/4149355*e^8 + 837917/4149355*e^6 + 3897412/4149355*e^4 + 12618216/4149355*e^2 + 51786438/4149355, 2657227/9116132935*e^11 + 60537356/9116132935*e^9 + 910812038/9116132935*e^7 + 8032780183/9116132935*e^5 + 43952872154/9116132935*e^3 + 842019588/53941615*e, -682/829871*e^11 - 10261/829871*e^9 - 116660/829871*e^7 - 495163/829871*e^5 - 1603134/829871*e^3 - 3674876/829871*e, 2804274/9116132935*e^11 + 137626742/9116132935*e^9 + 2070656891/9116132935*e^7 + 21002732096/9116132935*e^5 + 99923270453/9116132935*e^3 + 1914262866/53941615*e, 1606/7705945*e^11 + 24163/7705945*e^9 + 228824/7705945*e^7 + 1166029/7705945*e^5 + 290394/592765*e^3 + 41871526/7705945*e, 25946811/18232265870*e^11 + 264692479/9116132935*e^9 + 7327345509/18232265870*e^7 + 25411933602/9116132935*e^5 + 246276815627/18232265870*e^3 + 97003764/4149355*e, -13933863/18232265870*e^11 - 139241437/9116132935*e^9 - 3934904697/18232265870*e^7 - 13646625066/9116132935*e^5 - 136019574581/18232265870*e^3 - 52092612/4149355*e, -2029239/18232265870*e^11 - 23281211/9116132935*e^9 - 573054441/18232265870*e^7 - 1987407498/9116132935*e^5 - 9836742653/18232265870*e^3 - 7586436/4149355*e, 3150117/2604609410*e^11 + 33195183/1302304705*e^9 + 889588923/2604609410*e^7 + 3085179294/1302304705*e^5 + 27656973009/2604609410*e^3 + 11776908/592765*e, -112949/140248199*e^10 - 1510762/140248199*e^8 - 22730101/140248199*e^6 - 159825375/140248199*e^4 - 1096881883/140248199*e^2 - 21013326/829871, 499698/100177285*e^10 + 10589784/100177285*e^8 + 141114062/100177285*e^6 + 978794072/100177285*e^4 + 4164245511/100177285*e^2 + 48571952/592765, 25806/53941615*e^11 + 388263/53941615*e^9 + 4521344/53941615*e^7 + 18736329/53941615*e^5 + 4666194/4149355*e^3 - 172202599/53941615*e, 54833/177012290*e^11 + 893167/88506145*e^9 + 26876207/177012290*e^7 + 131351331/88506145*e^5 + 1296959681/177012290*e^3 + 12423141/523705*e, 23364/4149355*e^10 + 351522/4149355*e^8 + 4157166/4149355*e^6 + 16963326/4149355*e^4 + 54920268/4149355*e^2 - 69205856/4149355, 14586/4149355*e^10 + 219453/4149355*e^8 + 2735949/4149355*e^6 + 10590099/4149355*e^4 + 34286382/4149355*e^2 - 64678284/4149355, 269179/701240995*e^10 + 14800522/701240995*e^8 + 222680581/701240995*e^6 + 2351403326/701240995*e^4 + 10745851723/701240995*e^2 + 205861806/4149355, 3244671/701240995*e^10 + 69375718/701240995*e^8 + 916290849/701240995*e^6 + 6355568244/701240995*e^4 + 26400232517/701240995*e^2 + 315390504/4149355, -863991/1823226587*e^11 - 17487985/1823226587*e^9 - 243989929/1823226587*e^7 - 1692360724/1823226587*e^5 - 8190004896/1823226587*e^3 - 6460168/829871*e, -9090954/9116132935*e^11 - 202412787/9116132935*e^9 - 2567273526/9116132935*e^7 - 17807099256/9116132935*e^5 - 61632604688/9116132935*e^3 - 67974192/4149355*e, -962837/701240995*e^10 - 33912846/701240995*e^8 - 510234183/701240995*e^6 - 5025520443/701240995*e^4 - 24622267689/701240995*e^2 - 471696858/4149355, -1647657/701240995*e^10 - 35163136/701240995*e^8 - 465296183/701240995*e^6 - 3227383148/701240995*e^4 - 12843947969/701240995*e^2 - 160156568/4149355, 822069/701240995*e^10 + 13311437/701240995*e^8 + 232151211/701240995*e^6 + 1610245116/701240995*e^4 + 9696582918/701240995*e^2 + 79907256/4149355, 561529/701240995*e^10 + 24857272/701240995*e^8 + 373988956/701240995*e^6 + 3735289681/701240995*e^4 + 18047509348/701240995*e^2 + 345742056/4149355, 20438/4149355*e^10 + 307499/4149355*e^8 + 3683427/4149355*e^6 + 14838917/4149355*e^4 + 48042306/4149355*e^2 - 103657742/4149355, 72050607/18232265870*e^11 + 750333548/9116132935*e^9 + 20346997233/18232265870*e^7 + 70565328474/9116132935*e^5 + 606269979919/18232265870*e^3 + 269365668/4149355*e, 3071781/3646453174*e^11 + 32217891/1823226587*e^9 + 867466939/3646453174*e^7 + 3008458142/1823226587*e^5 + 23961099703/3646453174*e^3 + 11484044/829871*e, -1425042/9116132935*e^11 - 43696036/9116132935*e^9 - 402429998/9116132935*e^7 - 2791331288/9116132935*e^5 + 7097943131/9116132935*e^3 - 10655216/4149355*e, 21284136/9116132935*e^11 + 433393728/9116132935*e^9 + 6010612184/9116132935*e^7 + 41690753504/9116132935*e^5 + 191436378667/9116132935*e^3 + 159144128/4149355*e, 3894/4149355*e^10 + 58587/4149355*e^8 + 692861/4149355*e^6 + 2827221/4149355*e^4 + 9153378/4149355*e^2 + 43790424/4149355, 1650/829871*e^10 + 24825/829871*e^8 + 335782/829871*e^6 + 1197975/829871*e^4 + 3878550/829871*e^2 - 21841168/829871, -50643/140248199*e^10 - 950554/140248199*e^8 - 14301517/140248199*e^6 - 99198052/140248199*e^4 - 690145411/140248199*e^2 - 4922632/829871, 939976/701240995*e^10 + 46582778/701240995*e^8 + 700859069/701240995*e^6 + 7212795644/701240995*e^4 + 33821214227/701240995*e^2 + 647924094/4149355, -854199/2604609410*e^11 - 8621831/1302304705*e^9 - 241224681/2604609410*e^7 - 836590218/1302304705*e^5 - 9095440673/2604609410*e^3 - 3193476/592765*e, -32855373/18232265870*e^11 - 354950937/9116132935*e^9 - 9278314387/18232265870*e^7 - 32178079886/9116132935*e^5 - 251754414671/18232265870*e^3 - 122831852/4149355*e, -1090584/701240995*e^10 - 24707042/701240995*e^8 - 307979496/701240995*e^6 - 2136204576/701240995*e^4 - 8057312428/701240995*e^2 - 106007616/4149355, 982172/701240995*e^10 + 30620216/701240995*e^8 + 460695068/701240995*e^6 + 4554649818/701240995*e^4 + 22231668644/701240995*e^2 + 425899368/4149355, 10252/53941615*e^11 + 154246/53941615*e^9 + 1566273/53941615*e^7 + 7443418/53941615*e^5 + 1853748/4149355*e^3 + 235832322/53941615*e, -712528/9116132935*e^11 - 3930454/9116132935*e^9 - 59135467/9116132935*e^7 + 327631848/9116132935*e^5 - 2853688261/9116132935*e^3 - 54669042/53941615*e, 17996/4149355*e^10 + 270758/4149355*e^8 + 3319249/4149355*e^6 + 13065914/4149355*e^4 + 42302052/4149355*e^2 - 71200034/4149355, -7678/10788323*e^11 - 115519/10788323*e^9 - 1473986/10788323*e^7 - 5574577/10788323*e^5 - 1388322/829871*e^3 + 161196843/10788323*e, -6297827/18232265870*e^11 - 41435713/9116132935*e^9 - 1246838273/18232265870*e^7 - 3825947949/9116132935*e^5 - 60168422159/18232265870*e^3 - 576333099/53941615*e, -58501/140248199*e^10 - 2803966/140248199*e^8 - 42186943/140248199*e^6 - 398753094/140248199*e^4 - 2035806769/140248199*e^2 - 39000618/829871, -1522809/701240995*e^10 - 37056882/701240995*e^8 - 430039271/701240995*e^6 - 2982834476/701240995*e^4 - 8545216503/701240995*e^2 - 148021016/4149355, -2907/609245*e^10 - 61926/609245*e^8 - 820933/609245*e^6 - 5694148/609245*e^4 - 25354479/609245*e^2 - 282568/3605, 35237/140248199*e^10 + 5169890/140248199*e^8 + 77783345/140248199*e^6 + 860094397/140248199*e^4 + 3753575135/140248199*e^2 + 71908470/829871, 757287/2604609410*e^11 + 19640313/1302304705*e^9 + 590994873/2604609410*e^7 + 2986825739/1302304705*e^5 + 28519519959/2604609410*e^3 + 273178899/7705945*e, -8074/10788323*e^11 - 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33431/592765*e^8 - 422153/592765*e^6 - 1613273/592765*e^4 - 5223114/592765*e^2 + 19760978/592765, -11198/4149355*e^10 - 168479/4149355*e^8 - 1969022/4149355*e^6 - 8130257/4149355*e^4 - 26322426/4149355*e^2 - 81059098/4149355, -34078/4149355*e^10 - 512719/4149355*e^8 - 6016627/4149355*e^6 - 24742177/4149355*e^4 - 80104986/4149355*e^2 + 63355062/4149355, 2344878/701240995*e^10 + 50368319/701240995*e^8 + 662190482/701240995*e^6 + 4593079592/701240995*e^4 + 21046763401/701240995*e^2 + 227928272/4149355, 4115/140248199*e^10 + 5682402/140248199*e^8 + 85494321/140248199*e^6 + 1021880658/140248199*e^4 + 4125682143/140248199*e^2 + 79037046/829871, -31152/4149355*e^10 - 468696/4149355*e^8 - 5542888/4149355*e^6 - 22617768/4149355*e^4 - 73227024/4149355*e^2 + 139300498/4149355, -18458/4149355*e^10 - 277709/4149355*e^8 - 3612437/4149355*e^6 - 13401347/4149355*e^4 - 43388046/4149355*e^2 + 251389302/4149355, 18488214/9116132935*e^11 + 355492472/9116132935*e^9 + 5221047466/9116132935*e^7 + 36214181896/9116132935*e^5 + 188553336553/9116132935*e^3 + 138238672/4149355*e, 14042187/9116132935*e^11 + 297464506/9116132935*e^9 + 3965495253/9116132935*e^7 + 27505432068/9116132935*e^5 + 120093983699/9116132935*e^3 + 104995176/4149355*e, 9186377/18232265870*e^11 + 142569053/9116132935*e^9 + 4290032413/18232265870*e^7 + 21339763709/9116132935*e^5 + 207023225779/18232265870*e^3 + 1983005919/53941615*e, -7282/10788323*e^11 - 109561/10788323*e^9 - 1459788/10788323*e^7 - 5287063/10788323*e^5 - 1316718/829871*e^3 + 248834125/10788323*e, 484/829871*e^10 + 7282/829871*e^8 + 109561/829871*e^6 + 351406/829871*e^4 + 1137708/829871*e^2 - 7778796/829871, -114791/53941615*e^10 - 2670118/53941615*e^8 - 40173139/53941615*e^6 - 341546529/53941615*e^4 - 1938627037/53941615*e^2 - 482805882/4149355, -548658/100177285*e^10 - 11811399/100177285*e^8 - 154940302/100177285*e^6 - 1074695512/100177285*e^4 - 4545753591/100177285*e^2 - 53330992/592765, 127693/520921882*e^11 + 4401331/260460941*e^9 + 132440051/520921882*e^7 + 684351125/260460941*e^5 + 6391132733/520921882*e^3 + 61218513/1541189*e, -31482/7705945*e^11 - 473661/7705945*e^9 - 5752308/7705945*e^7 - 22857363/7705945*e^5 - 5692518/592765*e^3 + 180870663/7705945*e, -484/4149355*e^10 - 7282/4149355*e^8 - 109561/4149355*e^6 - 351406/4149355*e^4 - 1137708/4149355*e^2 - 149896694/4149355, 5698/592765*e^10 + 85729/592765*e^8 + 1047337/592765*e^6 + 4137007/592765*e^4 + 13393926/592765*e^2 - 20014742/592765, -813471/2604609410*e^11 - 41186959/1302304705*e^9 - 1239353039/2604609410*e^7 - 6793589077/1302304705*e^5 - 59807208737/2604609410*e^3 - 572873157/7705945*e, -159148/53941615*e^11 - 2394454/53941615*e^9 - 28481367/53941615*e^7 - 115548682/53941615*e^5 - 28776852/4149355*e^3 + 763402127/53941615*e, 3014/829871*e^10 + 45347/829871*e^8 + 569102/829871*e^6 + 2188301/829871*e^4 + 7084818/829871*e^2 + 10404714/829871, -47168/4149355*e^10 - 709664/4149355*e^8 - 8791147/4149355*e^6 - 34246112/4149355*e^4 - 110874816/4149355*e^2 + 250348862/4149355, -2660517/2604609410*e^11 - 27087108/1302304705*e^9 - 751326523/2604609410*e^7 - 2605672094/1302304705*e^5 - 20836573659/2604609410*e^3 - 9946508/592765*e, 9210753/2604609410*e^11 + 100666112/1302304705*e^9 + 2601104607/2604609410*e^7 + 9020879046/1302304705*e^5 + 72218188681/2604609410*e^3 + 34434972/592765*e, -3980754/701240995*e^10 - 87428882/701240995*e^8 - 1124159726/701240995*e^6 - 7797386456/701240995*e^4 - 30327768063/701240995*e^2 - 386939696/4149355, -1866119/701240995*e^10 - 38072782/701240995*e^8 - 572822311/701240995*e^6 - 4663620616/701240995*e^4 - 27642570313/701240995*e^2 - 529557786/4149355, -2046/829871*e^10 - 30783/829871*e^8 - 349980/829871*e^6 - 1485489/829871*e^4 - 4809402/829871*e^2 - 25962306/829871, -2907/1131455*e^11 - 61926/1131455*e^9 - 820933/1131455*e^7 - 5694148/1131455*e^5 - 24135989/1131455*e^3 - 21736/515*e, 17866269/9116132935*e^11 + 401019677/9116132935*e^9 + 5045411011/9116132935*e^7 + 34995933916/9116132935*e^5 + 128183731513/9116132935*e^3 + 133588312/4149355*e, 127402/53941615*e^11 + 1916821/53941615*e^9 + 23747053/53941615*e^7 + 92499643/53941615*e^5 + 23036598/4149355*e^3 - 1150576148/53941615*e, -538513/701240995*e^11 - 33564124/701240995*e^9 - 504987502/701240995*e^7 - 5312685767/701240995*e^5 - 24369079666/701240995*e^3 - 466846452/4149355*e, 19448/4149355*e^10 + 292604/4149355*e^8 + 3647932/4149355*e^6 + 14120132/4149355*e^4 + 45715176/4149355*e^2 - 177523522/4149355, -946/4149355*e^10 - 14233/4149355*e^8 - 402749/4149355*e^6 - 686839/4149355*e^4 - 2223702/4149355*e^2 + 80084834/4149355] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([5, 5, w + 2])] = -50643/1402481990*e^10 - 475277/701240995*e^8 - 14301517/1402481990*e^6 - 49599026/701240995*e^4 - 690145411/1402481990*e^2 - 6610671/4149355 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]