-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '305025707352585563541234240570,1022739005118207492135608845497,1166575453326681489022219273909,1231729985780193935550527465019', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 8, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29327719.396729242, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '9216.1', 'coefficient_field': '1.1.1.1', 'conductor': 7213895789838336, 'conductor_radical': 6, 'degree': 8, 'euler_factors': [[1], [1], [1, -8, 40, -136, 354, -680, 1000, -1000, 625], [1, 0, 12, 0, 102, 0, 588, 0, 2401], [1, 0, 4, 0, 238, 0, 484, 0, 14641], [1, 8, 72, 328, 1538, 4264, 12168, 17576, 28561], [1, 0, 52, 0, 1254, 0, 15028, 0, 83521], [1, 0, 36, 0, 654, 0, 12996, 0, 130321], [1, 0, 12, 0, 1062, 0, 6348, 0, 279841], [1, -24, 328, -2904, 18498, -84216, 275848, -585336, 707281], [1, 0, 60, 0, 2310, 0, 57660, 0, 923521], [1, 8, 72, 520, 4706, 19240, 98568, 405224, 1874161], [1, -16, 260, -2224, 18214, -91184, 437060, -1102736, 2825761], [1, 0, 164, 0, 10414, 0, 303236, 0, 3418801], [1, 0, 124, 0, 7750, 0, 273916, 0, 4879681], [1, -24, 424, -4632, 40482, -245496, 1191016, -3573048, 7890481], [1, 0, 228, 0, 19950, 0, 793668, 0, 12117361], [1, 24, 360, 4056, 36674, 247416, 1339560, 5447544, 13845841], [1, 0, 164, 0, 13390, 0, 736196, 0, 20151121], [1, 0, 76, 0, 9958, 0, 383116, 0, 25411681], [1, -8, 172, -1208, 19078, -88184, 916588, -3112136, 28398241], [1, 0, 60, 0, 5190, 0, 374460, 0, 38950081], [1, 0, 132, 0, 10446, 0, 909348, 0, 47458321], [1, 8, 364, 2104, 48966, 187256, 2883244, 5639752, 62742241], [1, -32, 756, -11104, 130982, -1077088, 7113204, -29205536, 88529281], [1, -40, 904, -14120, 164706, -1426120, 9221704, -41212040, 104060401], [1, 0, 204, 0, 22374, 0, 2164236, 0, 112550881], [1, 0, 324, 0, 46830, 0, 3709476, 0, 131079601], [1, -24, 552, -7512, 96770, -818808, 6558312, -31080696, 141158161], [1, -8, 412, -2488, 68358, -281144, 5260828, -11543176, 163047361]], 'euler_factors_factorization': [[1], [1], [[[1, -4, 12, -20, 25], 2]], [[[1, 0, 12, 0, 102, 0, 588, 0, 2401], 1]], [[[1, 0, 4, 0, 238, 0, 484, 0, 14641], 1]], [[[1, 4, 28, 52, 169], 2]], [[[1, 0, 26, 0, 289], 2]], [[[1, 0, 36, 0, 654, 0, 12996, 0, 130321], 1]], [[[1, 0, 12, 0, 1062, 0, 6348, 0, 279841], 1]], [[[1, -12, 92, -348, 841], 2]], [[[1, 0, 60, 0, 2310, 0, 57660, 0, 923521], 1]], [[[1, 4, 28, 148, 1369], 2]], [[[1, -4, 41], 4]], [[[1, 0, 164, 0, 10414, 0, 303236, 0, 3418801], 1]], [[[1, 0, 124, 0, 7750, 0, 273916, 0, 4879681], 1]], [[[1, -12, 140, -636, 2809], 2]], [[[1, 0, 228, 0, 19950, 0, 793668, 0, 12117361], 1]], [[[1, 12, 108, 732, 3721], 2]], [[[1, 0, 164, 0, 13390, 0, 736196, 0, 20151121], 1]], [[[1, 0, 76, 0, 9958, 0, 383116, 0, 25411681], 1]], [[[1, -4, 78, -292, 5329], 2]], [[[1, 0, 60, 0, 5190, 0, 374460, 0, 38950081], 1]], [[[1, 0, 132, 0, 10446, 0, 909348, 0, 47458321], 1]], [[[1, 4, 174, 356, 7921], 2]], [[[1, -16, 250, -1552, 9409], 2]], [[[1, -20, 252, -2020, 10201], 2]], [[[1, 0, 204, 0, 22374, 0, 2164236, 0, 112550881], 1]], [[[1, 0, 324, 0, 46830, 0, 3709476, 0, 131079601], 1]], [[[1, -12, 204, -1308, 11881], 2]], [[[1, -4, 198, -452, 12769], 2]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 5, 'label': '8-96e8-1.1-c1e4-0-5', 'leading_term': '9.0859683632661207225177401705932079001804286204758880208656577139651907089572283352651968', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/9216/2/a/bp', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.01171875', 'prec': 34}, 'plot_values': [9.085968363266122, 9.020783522613169, 8.938722907890954, 8.822984835385343, 8.657168248586297, 8.429077039469162, 8.141356486065703, 7.800495760867165, 7.413126009679536, 6.985027679238174, 6.518516870609193, 6.015309411965866, 5.477443614300052, 4.9075063365311635, 4.309250649440815, 3.686818262838569, 3.0444753949654952, 2.386542062483503, 1.7172518441414142, 1.0408737745013033, 0.36173065912488317, -0.3158069204474927, -0.9872932805674192, -1.6483173953876715, -2.294556668573563, -2.9217987680726547, -3.5259515868783446, -4.103103762269144, -4.649561755911525, -5.1618676056448844, -5.636804705807103, -6.071462156007737, -6.463267205136381, -6.809998809814639, -7.1097953746694165, -7.361198785407386, -7.563171702564828, -7.715102179368463, -7.816808889707347, -7.868558810924873, -7.8710646600992815, -7.825476738367298, -7.733381407791595, -7.596787025948369, -7.418098855694117, -7.200095874771575, -6.945918742129968, -6.659024888502886, -6.343142593309918, -6.002233528376369, -5.640468866464928, -5.262160862277894, -4.871702666184883, -4.473521361035823, -4.072044897394203, -3.6716233240384875, -3.276465299442121, -2.8905903294504, -2.517793718860622, -2.161574121084894, -1.8250802713554641, -1.5110737386451658, -1.2219025152409226, -0.9594514013230432, -0.7251120396677614, -0.5197674677638288, -0.34378566209236017, -0.1970048661910829, -0.0787359881137543, 0.012223199489030999, 0.07756640417257152, 0.11945455799099362, 0.1404791893730957, 0.14361741449142398, 0.1321810592550795, 0.10975954646524082, 0.08015602800375148, 0.04731902583289356, 0.015270778389569495, -0.011967431845856538, -0.030451271373306398, -0.03638937438732878, -0.026217873842017948, 0.0033280210033769107, 0.05514571532778723, 0.13170233893229238, 0.23498135078256177, 0.36643383826679277, 0.5269368471496799, 0.7167640750191825, 0.9355776064280007, 1.18241406043773, 1.4556814490721566, 1.7531772282505007, 2.072141759186087, 2.4092780757627645, 2.7607872307764523, 3.122435559480124, 3.4896727686794047, 3.8576692322730053, 4.221376292381561, 4.575630577818406, 4.915323124273755, 5.235426580097364, 5.531056320210126, 5.797587983771393, 6.0308497895150355, 6.227108541108902, 6.383103855250489, 6.49615004609227, 6.5643168524337785, 6.586350272437243, 6.561657990369703, 6.490370887335266, 6.373480857099885, 6.212689423425687, 6.010336779144531, 5.769411071531007, 5.493625575071377, 5.187210167491291, 4.854795176339549, 4.5013743862407996, 4.132323510879894, 3.75316972588597, 3.369458401340975, 2.9866923832433954, 2.6103127075465165, 2.245492035856293, 1.897020857287436, 1.5692546310053268, 1.2660888758454139, 0.9908186275078891, 0.7460767456395604, 0.5338178583630856, 0.3553186473539843, 0.21112728674591538, 0.10107038171738639, 0.024288451855048115, -0.020721637984936717, -0.03607044234123677, -0.024406997334557663, 0.011162008781887929, 0.06715246187163505, 0.1397959770780149, 0.22514244247247156, 0.31916043066283717, 0.4178308164138477, 0.5172508084814613, 0.613730013936165, 0.7038747280669554, 0.7846605809727453, 0.8535023904179466, 0.9083073143485741, 0.9475119139900674, 0.9701047370007377, 0.9756351582567883, 0.9642054493063839, 0.9364476663025763, 0.8934863027988486, 0.8368876382322196, 0.7685983867944205, 0.6908741161834032, 0.6061975188453692, 0.517196436514334, 0.42655931885972626, 0.3369474548524205, 0.25090468424385237, 0.17078549485544342, 0.09868670641906734, 0.036382713052332344, -0.014732345117971576, -0.05367148407698093, -0.07987642904090626, -0.09323089699315193, -0.0940584465410726, -0.08309309213716104, -0.061447038880981714, -0.03056833911795222, 0.007821677465459571, 0.05179543592951952, 0.09928487683398304, 0.148156680165737, 0.1963073377766753, 0.24172768569400366, 0.28256400127316156, 0.3171870923761577, 0.3442764007839269, 0.36284043070403454, 0.3722364743079425, 0.37219791704866145, 0.3628700333979923, 0.3447656491458313, 0.3187282310426286, 0.2859044632402656, 0.24772065542078125, 0.20578718995522988, 0.16182141008485446, 0.11758398642483998, 0.07481874754186606, 0.0351497786186308, 6.159128233406424e-06, -0.029435698156994993, -0.052302626123248236, -0.06808177530072013, -0.07664751753308159, -0.07826951159242312, -0.07360940111491221, -0.06369842526556665, -0.04989163389707609, -0.03380758222202523, -0.017256508500150997, -0.0021463062485750904, 0.009620008102345985, 0.01625080862437822, 0.016176506012270792, 0.008164124994878046, -0.00857765750874209, -0.03430380268773063, -0.068648053002207, -0.11055983947318765, -0.15826498324003196, -0.20924932787007003, -0.26026628981397876, -0.30738057806774516, -0.34604008768485106, -0.3711746552497933, -0.3773223518261282, -0.3587845634618428, -0.30980103798879155, -0.22474116235583236, -0.09830574036737318, 0.07426308277743485, 0.29697115230912835, 0.5728728416620871, 0.9039032694890158, 1.2907072495543837, 1.7324931416579004, 2.226939332861267, 2.77019460610003, 3.3568260518774236, 3.9798191902354487, 4.630678819537371, 5.299691316152565, 5.976004203463677, 6.647784888052279, 7.302525568288955, 7.927563037287729, 8.510209138438212, 9.037988891371231, 9.499059678387011, 9.8828682964888, 10.180180872715324, 10.383254736794143, 10.486211969429718, 10.485637659099623, 10.380356821503367, 10.17139605214814, 9.86215437345668, 9.458757793998124, 8.96951730248941, 8.40461981605879, 7.776026949413928, 7.097507470705414, 6.383857464745378, 5.650396352009874, 4.912664108529644, 4.18621320605799, 3.485813198652097, 2.824952396041788, 2.2155285851340762, 1.6676170503714756, 1.1889399709591335, 0.7846166925164958, 0.45708011315365926, 0.2060686949574597, 0.028568126823451993, -0.08102715350317767, -0.1306277268321347, -0.13009323128231282, -0.09080240682490603, -0.025102282792990715, 0.05430286686905198, 0.1349995211609154, 0.20556668358443425, 0.2562829025776782, 0.27981067135299925, 0.2718491677369024, 0.23172988516910922, 0.16291530351161299, 0.07339146549759926, -0.024057632430685844, -0.11173628255210126, -0.16708045115302605, -0.16286178887839378, -0.06756749105614615, 0.15404240779604178, 0.5402203256787692, 1.1313648190972243, 1.969012304993324, 3.0947166275077747, 4.548834084703332, 6.36925873400753, 8.590195238461392, 11.240847481751791, 14.344130978659226, 17.91554417031662, 21.962421395517296, 26.482887260857222, 31.464999309568313, 36.886357180935256, 42.71456993978475, 48.90676492040058, 55.40949375396462, 62.15948236180006, 69.08576720680789, 76.10967775754362, 83.14547750554867, 90.10225183089267, 96.8876551720121, 103.40788049955646, 109.56861136909497, 115.27759862129044, 120.44941605977911, 125.00469740473169, 128.87073910453992, 131.9840330448589, 134.29508624620877, 135.76629557574267, 136.37159847880363, 136.0982482042304, 134.9507701484287, 132.9472636873601, 130.1178507611401, 126.50530742176302, 122.16760479499564, 117.17301959283718, 111.59763467081265, 105.52493370837178, 99.04694242917611, 92.25903803489197, 85.25718302386758, 78.13702192676635, 70.9941423884373, 63.91966075897657, 56.9980163486457, 50.30627847053196, 43.91426398385234, 37.881740403247505, 32.25739537271522, 27.078892913674842, 22.37343338703973, 18.156849202596035, 14.433887298160412, 11.199135841962718, 8.438195522251032, 6.128294151014564, 4.239500568803298, 2.736189493466311, 1.5785390766714127, 0.7238447869484997, 0.1279629822978622, -0.25328174076777216, -0.4628111783224624, -0.5411595769299481, -0.5254834853701136, -0.4487572233238074, -0.33916929129181134, -0.21972831915421856, -0.10808364231217298, -0.016546674118758896, 0.047697308085594546, 0.08219231831682791, 0.08867291758129595, 0.07240664182707557, 0.04143948818755497, 0.0057877556147900786, -0.023387266119489953, -0.03460062104690002, -0.016818701739366157, 0.039848019688615385, 0.14353157322825774, 0.30010669760807135, 0.5128795539740368, 0.7823626762895732, 1.1061612306016548, 1.4790369846979883, 1.8932541628132524, 2.3388166708173586, 2.8037989602767373, 3.274870689437318, 3.738124333746971, 4.179455950355226, 4.58501771045641, 4.941853403923151, 5.238795627337428, 5.466585159195164, 5.618077872835022, 5.68862436436357, 5.6766425221316075, 5.583247257590748, 5.412031245601288, 5.169024324199994, 4.862787708333771, 4.503641330396735, 4.103125256267193, 3.6736565233352705, 3.228292776669828, 2.7798970943181285, 2.340591137059624, 1.9214096987795735, 1.532056206612439, 1.1803808143776862, 0.8721339061339336, 0.6108939004407138, 0.39808630551431623, 0.23295648605856617, 0.11273360541172153, 0.032902327844222166, -0.01247051265765932, -0.03038163145184132, -0.028467954028665147, -0.014564571114599061, 0.0037292500579173813, 0.019465759371185037, 0.02672560637889579, 0.020935292547277235, -0.0008865778014891986, -0.0399663234449176, -0.09570303122254309, -0.1656903455623752, -0.24583383871356448, -0.33055139326696614, -0.4130509775855036, -0.4856788361800305, -0.5403223055371846, -0.5688259089535702, -0.5634295838367389, -0.517207038609325, -0.4244572797854505, -0.28105021733966545, -0.084735255565704, 0.16463702311928047, 0.4650648530895969, 0.8123344118636527, 1.2000324015803514, 1.6197174843706301, 2.061361041153687, 2.513555480375131, 2.963809980914533, 3.399044515261135, 3.806386843351887, 4.1734074030737025, 4.488455600923811, 4.741204087410361, 4.923461684065586, 5.029128437917477, 5.054289768673698, 4.997514210301195, 4.8603454777995125, 4.646822172192621, 4.363200865770907, 4.017878085221791, 3.6214325204050146, 3.1858252357863215, 2.723868844903726, 2.248891239054533, 1.774473027912776, 1.3136572830717619, 0.8784553623838858, 0.47953097692638386, 0.1259394274521241, -0.1753126615993099, -0.41945078365094207, -0.6039798784025332, -0.7286879883628504, -0.7955972029900155, -0.8087582381800047, -0.7739778989438932, -0.6985291884372575, -0.5907565883724395, -0.4596473781831944, -0.31441369998802154, -0.16410141594978767, -0.017173468111494887, 0.11884848968719759, 0.23767449055109313, 0.33446818368487446, 0.4059981339839596, 0.4507033287656079, 0.4686777924764683, 0.4615765730053728, 0.43243292921982074, 0.38542407185900357, 0.3255895202754628, 0.25850686398224626, 0.18994885043480994, 0.12554902723257225, 0.07047772798557893, 0.029143597196823846, 0.00496183461424519, 0.00017232095882831452, 0.015716485270928032, 0.051203136537584466, 0.10494876538210193, 0.1740673343644878, 0.2546337849424495, 0.341959234129683, 0.43083562038326295, 0.5157994435228971, 0.5914507706664813, 0.6528555477710941, 0.6957554705145872, 0.7167714596309986, 0.7136327655924902, 0.6854327470750232, 0.6325831476796661, 0.5567713191950044, 0.46092931182530944, 0.3491847540285331, 0.22653632111871286, 0.09857695015858904, -0.028757954213898453, -0.149465814983614, -0.2578756965664493, -0.34895020628641765, -0.41853651856034096, -0.46361195856564835, -0.48247354607907944, -0.4748179176297283, -0.4417608673711345, -0.3858229561731699, -0.3107678078197366, -0.2213741443141048, -0.12317550912753006, -0.02217423647379183, 0.07554829086538874, 0.16420694834644592, 0.23866103514803036, 0.29473765425504417, 0.3295387218835519, 0.34166237666777105, 0.3313407526098166, 0.3004962642206997, 0.25270052077260124, 0.1930296253954256, 0.12782439527322212, 0.06436324250496003, 0.010469236114929078, -0.02594115228364779, -0.0373495706436228, -0.017133415962323692, 0.03997198546855781, 0.13743176118598563, 0.27653419233004767, 0.45615810601689055, 0.6726033585414579, 0.9195078062692416, 1.1879368717560168, 1.4667687922308974, 1.7429595320790423, 2.001919925665799, 2.2281304851396, 2.406121753648161, 2.520933127629467, 2.558683020372062, 2.5073807313267245, 2.3580525223265547, 2.1048969731458493, 1.7455670354310242, 1.2816575283042086, 0.7193646750964805, 0.06894050382699254, -0.6556604092522215, -1.4369647281540772, -2.254142289085702, -3.084207255359985, -3.902922463344246, -4.685543354363181, -5.407618865220667, -6.046299230591551, -6.581265358438004, -6.9954908201835115, -7.27604781127524, -7.4147801076095385, -7.408614231738134, -7.259722314904303, -6.975676646557655, -6.569055428250775, -6.056834988510129, -5.459717568720295, -4.801443327829719, -4.107551072236231, -3.404161360220354, -2.716840429301892, -2.069531328848861, -1.4832628110669381, -0.9750977601514474, -0.5573104901713603, -0.2367640667996377, -0.014432982147365651, 0.11474438176359524, 0.1617203512359948, 0.1429227281128996, 0.07957266422863962, -0.0032485401384772894, -0.07774346476867433, -0.11470734758855171, -0.08493170103717551, 0.03933748025800422, 0.2829530550234238, 0.6665611801082387, 1.2054112736448823, 1.908317189251015, 2.7769160241387185, 3.805479035463983, 4.980693569400555, 6.281722525229358, 7.680807725865935, 9.144769727113674, 10.635745873831503, 12.112247255796506, 13.530897425225257, 14.849199084204123, 16.026366872846026, 17.024515051984768, 17.810560200351933, 18.359041227580953, 18.651897855204496, 18.678732986523798, 18.437780533521348, 17.937540769743322, 17.194903529046105, 16.234004946613325, 15.085799970503485, 13.7880746832684, 12.382386770133815, 10.912021046818843, 9.420696498817128, 7.951612336306519, 6.544553298027327, 5.2341571141075, 4.048929597901267, 3.0106007295265576, 2.132773041778063, 1.4206066680096217, 0.8711192988908161, 0.4738043602351686, 0.21129428097365516, 0.06065517667614411, -0.005000914502021864, -0.01475299681328661, 0.0020046936666112776, 0.017534961049426322, 0.007656381221978894, -0.0465131653702288, -0.15704441652368548, -0.3280213629630638, -0.5547611149348655, -0.8234662261883815, -1.111365574121183, -1.3873424748718202, -1.613035856476538, -1.7443790764914147, -1.733504228946873, -1.5309717773390303, -1.0882203027680197, -0.3600259496986038, 0.692970081451654, 2.101761893543576, 3.8867894556270475, 6.056552490167925, 8.606008802252324, 11.515372748156706, 14.749866673088667, 18.261212068299432, 21.987719464899342, 25.855073475077127, 29.77864072883487, 33.668232001107974, 37.42917584943862, 40.96434373845297, 44.17808210841393, 46.98284814219675, 49.299437272531925, 51.05849875150243, 52.20414950498305, 52.70005877696217, 52.527092257044316, 51.68273044482468, 50.18264221925057, 48.06420560572642, 45.38119441909644, 42.200789300544244, 38.6027121920491, 34.6797556611982, 30.530936696734006, 26.257356089899996, 21.96004386553569, 17.73878775590564, 13.686231389235255, 9.884640662943374, 6.4043520898320345, 3.3029330769633103, 0.6222863705377805, -1.6121282486326327, -3.390893045330843, -4.719765064388394, -5.619142866102586, -6.1223288914255996, -6.273248584916708, -6.124020858306735, -5.732383878392071, -5.158853619152055, -4.46394238446642, -3.705592721276665, -2.9367873490520555, -2.203511988058624, -1.5431578358740896, -0.9834035114366211, -0.5416375510486312, -0.22488046068351758, -0.03019535280373976, 0.054416607110868966, 0.04867095004832646, -0.021617301261982223, -0.12639994302696245, -0.23345182513572155, -0.31040204678628597, -0.32669980202873605, -0.25546824353245845, -0.07507974195641505, 0.22964834340687382, 0.666525555931457, 1.2354651781228783, 1.9286562552919682, 2.730863965940619, 3.6199910244805076, 4.568165522549286, 5.543704099130286, 6.512294928991191, 7.438339675913932, 8.286798392658607, 9.02581997066097, 9.627477576480985, 10.068648286984597, 10.33233586526476, 10.409539526772956, 10.298547820875816, 10.004543414348507, 9.539647741679525, 8.923295173932823, 8.180169811230245, 7.338728313544068, 6.430219652813, 5.487941636620163, 4.544887840699525, 3.6321789956159285, 2.7780279229237204, 2.006944294277666, 1.3383308148137547, 0.7858298227200397, 0.35712841253265765, 0.053993597206273086, -0.1276537092813388, -0.19718899525325467, -0.16848169976269797, -0.05896850462737912, 0.11141604088047329, 0.32141532669983164, 0.5496212613352791, 0.7755861115932909, 0.9808498141776971, 1.149804857554101, 1.2703706515709097, 1.3344567098040252, 1.3381635696512693, 1.2817624511970684, 1.1694555870816892, 1.0089119862453464, 0.8106351808376804, 0.5872224221622835, 0.35251856610060406, 0.12069074207165947, -0.09459188040749261, -0.28093953647418335, -0.4279663608455361, -0.5278778498938993, -0.5757925677879011, -0.569963286220339, -0.5118330889286198, -0.4057971821629033, -0.2588667516870851, -0.08027235064606651, 0.11911239693398605, 0.32766258365690965, 0.5335495528607727, 0.7252889612638114, 0.8924286923549501, 1.0264616012708743, 1.1209620101088003, 1.1717381880164666, 1.177100210600211, 1.138242694392076, 1.058715568240279, 0.9440212464143445, 0.8013527652814875, 0.6393965656121986, 0.46744968927528224, 0.29479408883432606, 0.13025834783618057, -0.018141544031529275, -0.14384741218733793, -0.24210100618688363, -0.3100940015240784, -0.34702010239667597, -0.3541150795809784, -0.33447837843157047, -0.29277510187156214, -0.23487666776728233, -0.1674336508438532, -0.09739366154968473, -0.03152063259289369, 0.02405684962282291, 0.06425791064695964, 0.08538148510828868, 0.08534095977380812, 0.0637908726213818, 0.022136582711420678, -0.03656706116912156, -0.10782575093832315, -0.18602004075333625, -0.2647723800177118, -0.33736159770886054, -0.39717405174820913, -0.43816138292934215, -0.45521345702465943, -0.4444982283745442, -0.40374188837426306, -0.3323860291966853, -0.23162435493890965, -0.10437953786931636, 0.044835011091422954, 0.21025247121180518, 0.385139592942108, 0.5621135065912748, 0.7335690047826164, 0.8922890346448059, 1.0317060964449007, 1.1461664408592764, 1.2312761706192221, 1.2843584473145488, 1.3043398845984104, 1.2916744357774035, 1.248346192938149, 1.1779262096109226, 1.08507035459524, 0.9751460698704911, 0.8539716885281136, 0.7276061873394193, 0.6017997741190025, 0.48165066827987885, 0.37140442119568917, 0.2743261592185286, 0.19248297648257653, 0.12672159843656639, 0.07676322020025327, 0.04136056680267172, 0.018476101724549023, 0.00555002058031267, -0.0002017939466089697, -0.0014936845577809047, -0.000695992091457969, 0.000403123484755393, 0.0007733783546327296, 0.00024232052263142045, -0.0004891667626708736, 8.023042946704016e-05, 0.004095579159161594, 0.01411678324523822, 0.0328337552371541, 0.06274544594348981, 0.10583088426168924, 0.16325528381078128, 0.2351070731896492, 0.3201961044077439, 0.4159597056108985, 0.5185432621186076, 0.62289564315743, 0.7229734904820486, 0.8121113709431143, 0.8836132412629663, 0.9311347062523048, 0.949134058017407, 0.9334378746745563, 0.8819178867572799, 0.7946403462737565, 0.6740167480411495, 0.5249590335740845, 0.35495653220232265, 0.17350063495871113, -0.008478894576936164, -0.17922341489426385, -0.32692413669328196, -0.4408794412359544, -0.5125113789687332, -0.5363386042754786, -0.5109836888807484, -0.44001486456534433, -0.33248548548470536, -0.2032511888857403, -0.07302636536724787, 0.03210094281764957, 0.08148661423902019, 0.041070738708400355, -0.1250188231688822, -0.4525145801715565, -0.9749294141833859, -1.7212899964823238, -2.7135500676072244, -3.9643687700581927, -5.47513230758682, -7.234159253611467, -9.215084791258425, -11.37626176829019, -13.660726217579528, -15.996737466412535, -18.299019871335812, -20.47092606050778, -22.407217918405735, -23.997518278853182, -25.130498095073538, -25.698035676074298, -25.599722443552746, -24.747625834269137, -23.070985492844482, -20.51992348964195, -17.069040609792562, -12.720382568315603, -7.504807922897544, -1.482837810991718, 5.25506747438668, 12.58995281134246, 20.379107300906277, 28.458397684232896, 36.6455793725181, 44.74629105137032, 52.56449587070348, 59.90547019165366, 66.58027173115562, 72.41352726547763, 77.25584576018393, 80.98346079915856, 83.50016534999153, 84.74287929064036, 84.69113997267279, 83.36068673918878, 80.80047594719417, 77.09342690803238, 72.36000442505434, 66.74653061828411, 60.418049213496865, 53.554849291459, 46.350884158222115, 39.00101562914838, 31.69334165024327, 24.604850076101496, 17.89838669629761, 11.713957935442913, 6.164609959277335, 1.334903149380909, -2.719679151516827, -5.9745709179403255, -8.43489778228866, -10.132774657030678, -11.124138843956759, -11.48495443260745, -11.306285369685321, -10.689132996166846, -9.739461920957014, -8.562938168045594, -7.260081067763039, -5.922113935253636, -4.627605849177763, -3.439852155689176, -2.4052668348293125, -1.5527618305234878, -0.8940909595448461, -0.4252150745606825, -0.12835384206463155, 0.025350763198951385, 0.07265072363622856, 0.05472299487523389, 0.013733841601674233, -0.010498094114055116, 0.01649638604656124, 0.12141031995510573, 0.3212607660454852, 0.6221769540145756, 1.0192995300380827, 1.4971168029928328, 2.030320444184684, 2.5855278161589332, 3.1243586951049127, 3.6055515660406456, 3.9873033590051064, 4.230328418601105, 4.302006957353468, 4.177577793700366, 3.8414189154512672, 3.288726394325736, 2.5275481940768425, 1.5776103339130858, 0.4693071855187866, -0.756870693418363, -2.0510317543534904, -3.3588756549831333, -4.625021795764671, -5.795163071951166, -6.815914667721811, -7.636374403001533, -8.210851791323575, -8.505397740902175, -8.516313878807992, -8.265700747557622], 'positive_zeros': ['0.24062285561784008402405755151088', '0.806798817382386188210046916022247', '0.920265768119898167165551029765496', '0.971663631570427787010944184089386', '1.61079682983465789731624670870682', '1.64935330006008947707760524551863', '1.98851783320433540659273266238056', '2.08369959087877303281486562871706', '2.34375222322220878823217840625030', '2.47452323554506054653881933389539', '2.52602173933100596976584331261922', '2.70238174324831103660305658054386', '3.22513146189023912108186503465849', '3.28508627262278690585487828848633', '3.39552769413043676028813203711456', '3.44978020427279514449331512107170', '4.22207167097453826938374598141532', '4.32678298577289670732472416705965', '4.39654270232539166449484612737884', '4.43421999045745900996774178151728', '4.89431044042490087014278762260095', '4.94292750858969238332474964932673', '4.99184284003444374814508651687800', '5.16051772802319597396429900491880', '5.51245643345618831060533296473658', '5.66157424462578842873286400542447', '5.85364678838840296312805774287348', '5.85896937066670654130327477082377', '6.10278856972606752230623476287357', '6.26041334754195146385969250882021', '6.41292475810817374276055460017247', '6.44976771600785105531422039963668', '6.69257194932593075607619989673224', '7.02052367515963930868049892727137', '7.07766966871399613050478130331563', '7.12222565493543744131544676085271', '7.60387094126565903666454149938456', '7.62776422252898989175756203128338', '7.65494427304782719233062189449945', '7.80914048425868442864125748488140'], 'prelabel': '8-96e8-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.578469006927287, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 2131842781072921468, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.24062285561784008402405755151', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.806798817382386188210046916022', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '0.920265768119898167165551029765', 'prec': 107}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 29327719.396729242, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 7213895789838336, 'conductor_radical': 6, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0], 'euler11': [1, 0, 4, 0, 238, 0, 484, 0, 14641], 'euler13': [1, 8, 72, 328, 1538, 4264, 12168, 17576, 28561], 'euler17': [1, 0, 52, 0, 1254, 0, 15028, 0, 83521], 'euler19': [1, 0, 36, 0, 654, 0, 12996, 0, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, 12, 0, 1062, 0, 6348, 0, 279841], 'euler29': [1, -24, 328, -2904, 18498, -84216, 275848, -585336, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, 60, 0, 2310, 0, 57660, 0, 923521], 'euler37': [1, 8, 72, 520, 4706, 19240, 98568, 405224, 1874161], 'euler41': [1, -16, 260, -2224, 18214, -91184, 437060, -1102736, 2825761], 'euler43': [1, 0, 164, 0, 10414, 0, 303236, 0, 3418801], 'euler47': [1, 0, 124, 0, 7750, 0, 273916, 0, 4879681], 'euler5': [1, -8, 40, -136, 354, -680, 1000, -1000, 625], 'euler53': [1, -24, 424, -4632, 40482, -245496, 1191016, -3573048, 7890481], 'euler59': [1, 0, 228, 0, 19950, 0, 793668, 0, 12117361], 'euler61': [1, 24, 360, 4056, 36674, 247416, 1339560, 5447544, 13845841], 'euler67': [1, 0, 164, 0, 13390, 0, 736196, 0, 20151121], 'euler7': [1, 0, 12, 0, 102, 0, 588, 0, 2401], 'euler71': [1, 0, 76, 0, 9958, 0, 383116, 0, 25411681], 'euler73': [1, -8, 172, -1208, 19078, -88184, 916588, -3112136, 28398241], 'euler79': [1, 0, 60, 0, 5190, 0, 374460, 0, 38950081], 'euler83': [1, 0, 132, 0, 10446, 0, 909348, 0, 47458321], 'euler89': [1, 8, 364, 2104, 48966, 187256, 2883244, 5639752, 62742241], 'euler97': [1, -32, 756, -11104, 130982, -1077088, 7113204, -29205536, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -8, 40, -136, 354, -680, 1000, -1000, 625], [1, 0, 12, 0, 102, 0, 588, 0, 2401], [1, 0, 4, 0, 238, 0, 484, 0, 14641], [1, 8, 72, 328, 1538, 4264, 12168, 17576, 28561], [1, 0, 52, 0, 1254, 0, 15028, 0, 83521], [1, 0, 36, 0, 654, 0, 12996, 0, 130321], [1, 0, 12, 0, 1062, 0, 6348, 0, 279841], [1, -24, 328, -2904, 18498, -84216, 275848, -585336, 707281], [1, 0, 60, 0, 2310, 0, 57660, 0, 923521], [1, 8, 72, 520, 4706, 19240, 98568, 405224, 1874161], [1, -16, 260, -2224, 18214, -91184, 437060, -1102736, 2825761], [1, 0, 164, 0, 10414, 0, 303236, 0, 3418801], [1, 0, 124, 0, 7750, 0, 273916, 0, 4879681], [1, -24, 424, -4632, 40482, -245496, 1191016, -3573048, 7890481], [1, 0, 228, 0, 19950, 0, 793668, 0, 12117361], [1, 24, 360, 4056, 36674, 247416, 1339560, 5447544, 13845841], [1, 0, 164, 0, 13390, 0, 736196, 0, 20151121], [1, 0, 76, 0, 9958, 0, 383116, 0, 25411681], [1, -8, 172, -1208, 19078, -88184, 916588, -3112136, 28398241], [1, 0, 60, 0, 5190, 0, 374460, 0, 38950081], [1, 0, 132, 0, 10446, 0, 909348, 0, 47458321], [1, 8, 364, 2104, 48966, 187256, 2883244, 5639752, 62742241], [1, -32, 756, -11104, 130982, -1077088, 7113204, -29205536, 88529281]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9216/2/a/bp'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '8-96e8-1.1-c1e4-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-96e8-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.578469006927287, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 2131842781072921468, 'z1': {'__RealLiteral__': 0, 'data': '0.24062285561784008402405755151', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '305025707352585563541234240570,1022739005118207492135608845497,1166575453326681489022219273909,1231729985780193935550527465019', 'Lhash_array': ['305025707352585563541234240570', '1022739005118207492135608845497', '1166575453326681489022219273909', '1231729985780193935550527465019'], 'label': '8-96e8-1.1-c1e4-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9216/2/a/bp'}