-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1410294908139662640744910533754,1707053208003968621373672642795,1967111318664148693134012806624,2382728206441169568138069533432', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 8, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 82.99952890949935, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1, 0, 1]], [3, [1]], [7, [1, -8, 30, -56, 49]]], 'bad_primes': [2, 3, 7], 'central_character': '378.1', 'coefficient_field': '1.1.1.1', 'conductor': 20415837456, 'conductor_radical': 42, 'degree': 8, 'euler_factors': [[1, 0, -1, 0, 1], [1], [1, 0, -7, 0, 24, 0, -175, 0, 625], [1, -8, 30, -56, 49], [1, 0, 22, 0, 363, 0, 2662, 0, 14641], [1, 0, -52, 0, 1014, 0, -8788, 0, 28561], [1, 0, -22, 0, 195, 0, -6358, 0, 83521], [1, -24, 278, -2064, 10683, -39216, 100358, -164616, 130321], [1, 0, 10, 0, -429, 0, 5290, 0, 279841], [1, 0, 46, 0, 2211, 0, 38686, 0, 707281], [1, -12, 122, -888, 6003, -27528, 117242, -357492, 923521], [1, 8, -26, 128, 4363, 4736, -35594, 405224, 1874161], [1, 0, 140, 0, 8262, 0, 235340, 0, 2825761], [1, 32, 556, 6176, 48214, 265568, 1028044, 2544224, 3418801], [1, 0, -82, 0, 4515, 0, -181138, 0, 4879681], [1, 0, 97, 0, 6600, 0, 272473, 0, 7890481], [1, 0, 29, 0, -2640, 0, 100949, 0, 12117361], [1, -12, 182, -1608, 17163, -98088, 677222, -2723772, 13845841], [1, 28, 454, 5488, 51883, 367696, 2038006, 8421364, 20151121], [1, 0, -212, 0, 21318, 0, -1068692, 0, 25411681], [1, 42, 881, 12306, 123444, 898338, 4694849, 16338714, 28398241], [1, 22, 205, 2662, 33364, 210298, 1279405, 10846858, 38950081], [1, 0, -268, 0, 31734, 0, -1846252, 0, 47458321], [1, 0, -70, 0, -3021, 0, -554470, 0, 62742241], [1, 0, -292, 0, 40134, 0, -2747428, 0, 88529281], [1, 0, -175, 0, 20424, 0, -1785175, 0, 104060401], [1, -36, 746, -11304, 132483, -1164312, 7914314, -39338172, 112550881], [1, 0, 205, 0, 30576, 0, 2347045, 0, 131079601], [1, 32, 550, 8192, 101179, 892928, 6534550, 41440928, 141158161], [1, 0, 196, 0, 35142, 0, 2502724, 0, 163047361]], 'euler_factors_factorization': [[[[1, 0, -1, 0, 1], 1]], [1], [[[1, 0, -7, 0, 24, 0, -175, 0, 625], 1]], [[[1, -4, 7], 2]], [[[1, 0, 11, 0, 121], 2]], [[[1, 0, -13], 4]], [[[1, 0, -22, 0, 195, 0, -6358, 0, 83521], 1]], [[[1, -12, 67, -228, 361], 2]], [[[1, 0, 10, 0, -429, 0, 5290, 0, 279841], 1]], [[[1, 0, 23, 0, 841], 2]], [[[1, -6, 43, -186, 961], 2]], [[[1, 4, -21, 148, 1369], 2]], [[[1, 0, 70, 0, 1681], 2]], [[[1, 8, 43], 4]], [[[1, 0, -82, 0, 4515, 0, -181138, 0, 4879681], 1]], [[[1, 0, 97, 0, 6600, 0, 272473, 0, 7890481], 1]], [[[1, 0, 29, 0, -2640, 0, 100949, 0, 12117361], 1]], [[[1, -6, 73, -366, 3721], 2]], [[[1, 14, 129, 938, 4489], 2]], [[[1, 0, -106, 0, 5041], 2]], [[[1, 21, 220, 1533, 5329], 2]], [[[1, 11, 42, 869, 6241], 2]], [[[1, 0, -134, 0, 6889], 2]], [[[1, 0, -70, 0, -3021, 0, -554470, 0, 62742241], 1]], [[[1, 0, -146, 0, 9409], 2]], [[[1, 0, -175, 0, 20424, 0, -1785175, 0, 104060401], 1]], [[[1, -18, 211, -1854, 10609], 2]], [[[1, 0, 205, 0, 30576, 0, 2347045, 0, 131079601], 1]], [[[1, 16, 147, 1744, 11881], 2]], [[[1, 0, 98, 0, 12769], 2]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 9, 'label': '8-378e4-1.1-c1e4-0-9', '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/378/2/k/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 24}, 'plot_values': [5.045773411963037, 5.04204564523939, 5.036739198909265, 5.0285500371696115, 5.016171107528014, 4.998376663369294, 4.974278673812663, 4.943088332982358, 4.904042646467064, 4.856280666609196, 4.798458256413152, 4.729177289502064, 4.647145065296983, 4.551174539924904, 4.440138416481805, 4.31309390000925, 4.169349303297543, 4.008497865309581, 3.8304421590293787, 3.635450708977831, 3.424198104693301, 3.1978226601718727, 2.9580236990528754, 2.706965446977587, 2.44723916279131, 2.1818854538739654, 1.914459930180948, 1.6488024258829717, 1.3889113930430683, 1.1388932219899253, 0.9029373647530826, 0.6849993138596594, 0.48862243985148035, 0.31683574305036927, 0.17205902017785474, 0.05583275573236699, -0.03130145471973505, -0.08985031606586831, -0.12140942755122444, -0.1287130457446541, -0.11555453677375636, -0.08664993385766458, -0.04747436434048457, -0.004000181325680081, 0.037628894621459893, 0.07144711652539883, 0.09204491096352443, 0.09500510100214123, 0.07730275534688272, 0.037665907481785166, -0.02308771166392877, -0.10181858712468102, -0.1929598378554026, -0.2885212667227247, -0.37821199419512336, -0.4497857324336599, -0.48952324681393755, -0.4828396466977273, -0.4150489147505785, -0.2722480062194979, -0.04222870186813292, 0.28459560647485466, 0.7142533905240421, 1.2484218838225043, 1.883790328280484, 2.6116461558277084, 3.417810990048043, 4.282723665762463, 5.181818934628522, 6.086390308231836, 6.965196175425889, 7.785447944129636, 8.514114572005157, 9.119854190431825, 9.575828870844038, 9.860358807070789, 9.957902216369684, 9.860661890101825, 9.570844516357889, 9.09928716970114, 8.464655928651803, 7.6932826911304835, 6.819297857170167, 5.880943281117415, 4.918037897120144, 3.9702641453449985, 3.075662620193135, 2.2667994608901125, 1.568652329123805, 0.9975404436531183, 0.5604896216423518, 0.254304876909829, 0.06626401868540911, -0.02431307510246768, -0.044019041464264545, -0.022795677938434122, 0.009214666853378697, 0.024884189578474804, 0.0031748229092625926, -0.06811815480645844, -0.19035205385994053, -0.3529251081908345, -0.5331662735086015, -0.6974432057954765, -0.8034116957275116, -0.8032837041380074, -0.647972647500946, -0.2917024859209729, 0.3031691410134306, 1.16152380128627, 2.2917605053457333, 3.682937380944526, 5.302964448100068, 7.098690848084459, 8.999212359724986, 10.918520436006833, 12.759460217849961, 14.420333504061185, 15.805457268411885, 16.829304139249643, 17.421397609207343, 17.53336560117276, 17.148452978886546, 16.2785920035495, 14.962650019688226, 13.26642365724338, 11.283201376445191, 9.12169957022263, 6.897436177182116, 4.726567815944424, 2.7200859377666173, 0.9719200161510906, -0.4474707653861401, -1.4942701396605311, -2.153215949077336, -2.438738206069677, -2.3917277163747737, -2.0742532273968006, -1.563425457797993, -0.9435266813370834, -0.29774163583502267, 0.2992913384458376, 0.7876776419431982, 1.12700447349367, 1.2986904347439205, 1.305959329149577, 1.1715848013361123, 0.9335162807583887, 0.6392298523003747, 0.3392812821889191, 0.08067694122306135, -0.09863065053796599, -0.1739779628789209, -0.1366358388282588, 0.005909980977913543, 0.231993278299402, 0.5089632569166098, 0.7978336010093174, 1.059779889729159, 1.2609235716403353, 1.3761550457448073, 1.3925582831578966, 1.3122638863755827, 1.1501243362065992, 0.9306178030010474, 0.6844678101126506, 0.4446055318092776, 0.23965913566532307, 0.08960146043585376, 0.0032436350048192335, -0.02280283761895905, -0.0033392420605246353, 0.038995934208229874, 0.07894960775359525, 0.09483344260936213, 0.075125938593839, 0.024146220711685196, -0.03416470880734342, -0.05505609278988211, 0.024973470123982697, 0.2827317612944024, 0.7998806940473816, 1.6524157181189345, 2.8989621999309727, 4.568984369325764, 6.6530752291523445, 9.099038924285976, 11.809155247886377, 14.64149841236191, 17.418961172418594, 19.950554300885244, 22.04269493581364, 23.513439697884447, 24.213710854360833, 24.05706620786164, 23.01931229927822, 21.1394079213259, 18.523924755445922, 15.351957076353038, 11.845652251254798, 8.247816381340577, 4.804766005093471, 1.7489502198382227, -0.7323918504864665, -2.5138404046954155, -3.539397972124887, -3.82575001041482, -3.459598018142163, -2.5841004247667554, -1.3803484853657315, -0.046629660025095825, 1.225377076011745, 2.272104854469838, 2.974956456934138, 3.2715336426877957, 3.1590127096106073, 2.690129016412188, 1.9627593289072691, 1.1040187321709285, 0.2511233232522213, -0.4673636238500659, -0.9486802442069547, -1.1291672244611162, -0.9899927781838307, -0.5575681443836049, 0.1016978958196081, 0.8940312573224436, 1.7128110665827487, 2.4525197366358653, 3.0232653218890264, 3.3660819906761277, 3.456115752163623, 3.3018635239707748, 2.9425085416685874, 2.4428140855431253, 1.8775146493235442, 1.3187099962443565, 0.8264859500059218, 0.44184186398763126, 0.18091965906213395, 0.036167207328527635, -0.01810926490950483, -0.01759906265451787, 0.0017397603475352349, 0.013316557045297864, 0.007251561155011716, -0.005872193407554507, 0.004308420711256408, 0.082779152786896, 0.2803130962459051, 0.6427173574111854, 1.1997899917862918, 1.9555794301130653, 2.882498013048176, 3.9230825688702824, 4.993631043120458, 5.9917626074683925, 6.810175055375135, 7.358151694392695, 7.570164106439546, 7.413457967604079, 6.896397873467959, 6.075685086049577, 5.0409007976626246, 3.9004885873130717, 2.769483449450231, 1.7563620917464673, 0.9420309030267038, 0.3696478310199388, 0.042103744852530926, -0.0753214664986696, -0.0467789198339871, 0.049389217188485726, 0.13798338692881537, 0.1634356543539313, 0.10310652904794766, -0.025942461309657397, -0.16820669525355028, -0.2390371008043961, -0.14092651364231298, 0.21535800894449425, 0.8885158455849974, 1.8896363574566035, 3.1698235200443263, 4.615124205413029, 6.05435344161487, 7.287146721168166, 8.104978946663698, 8.316340990169266, 7.780792816012545, 6.451660167321377, 4.376207000481199, 1.6924250036126425, -1.3751989382614986, -4.528017400998967, -7.445412979011026, -9.826141725253963, -11.422303958268618, -12.072866055465417, -11.731556468105751, -10.470395145689544, -8.46853536383741, -5.991261384530422, -3.3496578704741, -0.8554912128933744, 1.2209002085818794, 2.6863013490688665, 3.45036204943827, 3.533684638621332, 3.0590791916141344, 2.2275943723023537, 1.2827539304580202, 0.4701184365865466, -0.002984706341749464, -0.0003062902763765417, 0.5251266644790767, 1.5252858617276124, 2.866591797053798, 4.360028325468032, 5.792495069587267, 6.957952571227592, 7.69150754686513, 7.905963914368487, 7.592824140124624, 6.815128651641641, 5.696912474521519, 4.406906160139731, 3.1170798364043137, 1.9729391072306766, 1.0747308415616172, 0.46662226028863585, 0.13262609047970303, 0.009599300344695073, 0.009428768341211115, 0.04494363147224849, 0.05546676246906022, 0.026646826245128475, 1.999211423940655e-06, 0.07005604995845326, 0.3691558258304334, 1.0422055856022543, 2.2156094429340354, 3.9687365352004726, 6.309654562852455, 9.158514083053923, 12.346605822922882, 15.643285993937424, 18.775896038448394, 21.455780967842355, 23.418935629256875, 24.485775822273727, 24.56485537946553, 23.654382033222205, 21.848886703970827, 19.346931930619228, 16.39746531567522, 13.261321330981767, 10.186558315753942, 7.389698422118481, 5.02056705689247, 3.1535231973441014, 1.794231574338914, 0.893622955729711, 0.364099108399234, 0.101420092531178, 0.004822014817659896, -0.008263237599623593, 0.0055465136004330335, 0.016124975503812533, 0.01483519390946849, 0.006150083628961284, -0.0013982143230353346, -0.002109531206039691, 0.003506546863196677, 0.009389879289125925, 0.007676283258143634, -0.006487710079913681, -0.030953867742288706, -0.0555290568230857, -0.06524662398338056, -0.04684430626419589, 0.002736615371826987, 0.06797322594417661, 0.11148343666266777, 0.07732404120673393, -0.09806287382676711, -0.4659845202576059, -1.040478649112782, -1.7735850337156835, -2.5351800838632323, -3.1039625698724733, -3.1759846628061683, -2.3909014617629794, -0.3759899276771881, 3.1944039728838094, 8.53676167268849, 15.698110063992775, 24.511528818362716, 34.59263890124965, 45.34617020868377, 55.99720128743324, 65.67025989473915, 73.54023025386444, 78.89153704859852, 81.18341048740866, 80.14294312701992, 75.88096924207767, 68.80689047089966, 59.559260921912085, 48.957457098145035, 37.94895674382431, 27.425997576203333, 18.118378427941643, 10.538102256312836, 4.94869013611009, 1.3370545239545726, -0.5444950718465636, -1.1037919035549277, -0.8238155228942373, -0.17587986266703468, 0.45728996170885405, 0.8328357159253061, 0.8671137428334493, 0.6222237034278644, 0.2663257026206452, 0.01617616138971612, 0.07470534680634033, 0.5792450326460673, 1.5653520875380031, 2.9537550901810574, 4.572698382538517, 6.191226153521145, 7.558997946928158, 8.456553657581697, 8.755407340296264, 8.425934842605907, 7.532327734209741, 6.22247955912061, 4.708825881495943, 3.208951815161648, 1.9039792442033125, 0.913663339322403, 0.28312200002964966, -0.020608466175392696, -0.08876919257213887, -0.04043953021656692, 0.009980842783957068, -0.018555403434710366, -0.15556208259250737, -0.3753995413032455, -0.6087155988680455, -0.7643990633094658, -0.7567869503862598, -0.532430928497998, -0.08805715670029755, 0.525898355868469, 1.2123806291202184, 1.8470249649557298, 2.311300757966335, 2.5170470192675545, 2.423648420318653, 2.0496215209733752, 1.4751418007171013, 0.816167625609896, 0.1969245530638782, -0.27547759651638837, -0.5343624724301933, -0.570513821157307, -0.4299715583302814, -0.19828191285908686, 0.024484645561775372, 0.15463289362361207, 0.15214609318621072, 0.03725203242632345, -0.10800914338120744, -0.15525691775636796, 0.04075246665693933, 0.6043117895490235, 1.6031178781245286, 3.021862515948568, 4.748988499318053, 6.5852025485744425, 8.285230946901795, 9.59507322312871, 10.292475161972716, 10.235350076627498, 9.413991926199856, 7.937676813040712, 6.011525491743373, 3.908873405301186, 1.9317376598889515, 0.33721771036762677, -0.7079768344731764, -1.1503558839752073, -1.055730260716681, -0.5913759438371802, 0.01708647944149294, 0.5375191558363331, 0.7818780351825485, 0.6475729119089707, 0.13701478989296292, -0.6475054915764453, -1.5326285139970814, -2.3172717698542593, -2.8211827299157695, -2.9295082937330656, -2.6211296738903367, -1.969545248642212, -1.125258539476012, -0.2792922324168803, 0.3908721835726223, 0.7633103914521905, 0.7994008140075207, 0.5572945214093709, 0.18245008638077087, -0.13773606111328282, -0.222245380305843, 0.05630214592711506, 0.7269988619625984, 1.7036239461845357, 2.7983850321282957, 3.7571068627948145, 4.312075352142604, 4.249611468991119, 3.4661760830336195, 2.0020562105882003, 0.04518224603041634, -2.095368882183512, -4.0437458984320225, -5.432797338392069, -5.986722780425489, -5.5719644483238, -4.229212549976589, -2.177210298800579, 0.2301767869262016, 2.5772618491915384, 4.457966674564292, 5.552903384077837, 5.710681825989074, 4.9576856402852885, 3.478832695450663, 1.5831218946600618, -0.3519323380302305, -1.977473509712835, -3.040691315294224, -3.4249304543747776, -3.1683166004420036, -2.4451864667832464, -1.5143991616264678, -0.6554125758726701, -0.10433274230677514, 0.0014609297280713674, -0.34902491564566407, -1.043761237232967, -1.880238750858385, -2.616194581829343, -3.027476196781814, -2.962477917269134, -2.377535527924114, -1.340677536203759, -0.0164709544846151, 1.3698360771295879, 2.592426630167391, 3.4694581954697075, 3.8916630782604305, 3.8414721345905773, 3.400213250868582, 2.708144812935492, 1.924365539050091, 1.1939959241959053, 0.6217842487107049, 0.2499046528690593, 0.061937595152082914, 0.002458417951931496, 0.0032500174963039576, 0.009554926948179667, -0.000921372061727565, -0.012601940638572529, 0.01879083061742608, 0.14614126732650118, 0.40610804714570453, 0.7976770083881001, 1.2746524744920649, 1.7509014708327157, 2.1176495661520405, 2.273431305323173, 2.162933946853688, 1.7921611276236507, 1.2313350715283646, 0.6057665688611584, 0.06884844569491443, -0.24720884905145674, -0.2695601825525362, -0.008855831879121995, 0.4345539880506389, 0.8951576641639559, 1.1915397520221183, 1.187101234604312, 0.8514657633100763, 0.302596277305531, -0.18570654152704721, -0.2160491720127226, 0.6619038080270813, 2.852749196918744, 6.606088306938174, 11.9233594580373, 18.525996839063303, 25.853300883660417, 33.10438362459798, 39.35626498833646, 43.787176886688904, 45.770348380623346, 44.957720902123256, 41.37924296150727, 35.53486199193603, 28.220303760965578, 20.374266760695768, 12.952837896755268, 6.798800727655738, 2.4445981222567816, 0.043223900062997825, -0.6167138285127574, -0.04340027666934882, 1.0766073955382671, 2.0362062244710395, 2.257503302371452, 1.406020878893288, -0.5546464692203148, -3.371691225934404, -6.572674195848448, -9.587328498311972, -11.870758835788957, -13.012102820463035, -12.819553399056838, -11.360021606908624, -8.9131681875377, -5.903881928744447, -2.8169550012002498, -0.09057324726494345, 1.963190742163049, 3.1916432944896274, 3.6073981528309647, 3.371462045842784, 2.7219614135144536, 1.9071685502228706, 1.135528669538708, 0.5430471841196182, 0.1770709468296158, 0.011177240896972087, -0.024063173398330525, -0.006730866617188162, 0.004992013298726523, -0.011864937600833, -0.045610320788037326, -0.06391115682385314, -0.03397611106269878, 0.05882983920110079, 0.20042553473211563, 0.35164607943968773, 0.46144817104418684, 0.4847027883725767, 0.4013025394219078, 0.23001949941386174, 0.021963756690673998, -0.15517422097934605, -0.23891425027330768, -0.19797172796365115, -0.05031335241537118, 0.13660045974475218, 0.26108030244594377, 0.21681945612378853, -0.06717472537288692, -0.5928263843450912, -1.2750762763509036, -1.946651302114754, -2.3878603126109073, -2.3772336614469656, -1.7528400355982743, -0.4657659683226421, 1.3911716964432639, 3.5789923297240076, 5.745349454394111, 7.508906211101351, 8.53025809477251, 8.576774679884792, 7.586280053721879, 5.714840315224285, 3.280703336150309, 0.6959038468515092, -1.6069125853643387, -3.2611656373635944, -4.057459460598281, -3.975434635153408, -3.173343070283787, -1.9456398072297545, -0.6406523056695452, 0.42938560746133625, 1.0609513675319882, 1.2010711874257116, 0.9475352658756342, 0.5073688771908194, 0.12537625352100193, 0.0033818985227956496, 0.2378355698248639, 0.7845563209125864, 1.463588915387408, 2.0204414418342003, 2.198232734366447, 1.8074464521856708, 0.7936660482838276, -0.7123884575964731, -2.4385612161799077, -4.037501249625247, -5.163240843540443, -5.56242110834959, -5.157100494201243, -4.0659884512478035, -2.5790729631199905, -1.0951683771555636, -0.013952965583452567, 0.37121822487420486, -0.048393402601525186, -1.1625969603043105, -2.663658006431742, -4.123000229099367, -5.10459111522398, -5.282593892051377, -4.529444002804017, -2.96376570941355, -0.9361027111619841, 1.0747553708518887, 2.572955423682809, 3.156185946559924, 2.6302585299911683, 1.1067581777798503, -1.0524219777841755, -3.3243758456304104, -5.130946580069952, -5.971001737405594, -5.571343435083894, -3.951467573206634, -1.4191952229087226, 1.4909374431559195, 4.144411882126821, 5.958840747057039, 6.541286075926287, 5.783983221329011, 3.88729275569411, 1.3136449245173314, -1.3194928176931788, -3.388377300163752, -4.398928992267737, -4.091952249609133, -2.5011853050943693, 0.06902935959576778, 3.1305684255349173, 6.113296222993706, 8.486820907170465, 9.901521288088087, 10.223646640639657, 9.52459814818913, 8.050629095820494, 6.170983878003104, 4.25422443335303, 2.587837164652697, 1.3398349214192693, 0.5510316648191184, 0.15146593371726166, 0.010349339856602321, -0.008069489702749209, -0.0004248082418191885, -0.0020852582276412613, 0.0095431910986794, 0.09043573901048761, 0.2954359604589939, 0.6471867498926074, 1.11687542529584, 1.62451979505062, 2.066264725268662, 2.342375882702805, 2.383304872813872, 2.1733449724782465, 1.7652788399530306, 1.2543456254474044, 0.7482875324203205, 0.34023578687775613, 0.08510446046004128, -0.01654935495832378, -0.010375282223963063, 0.0340620221203537, 0.05097204625075929, 0.0033140242170892407, -0.10450209612761624, -0.23066228731111538, -0.31523898614884427, -0.30684007497006055, -0.1869273108529656, 0.017630959574866233, 0.24304791515497315, 0.411863985875785, 0.4627766301061783, 0.3807029671953001, 0.21390919586649335, 0.053204551674603015, -0.008447298000787083, 0.07054907231360887, 0.2228490226579323, 0.24011543403335284, -0.21318001607061746, -1.5387172167330248, -4.090128374839026, -8.032868739159625, -13.217309068043507, -19.09501514055813, -24.71356036055096, -28.809654097820413, -29.99237109771062, -27.001431548618857, -18.99654492362019, -5.767176855311581, 12.117438075563896, 33.283484439534085, 55.76794341063427, 77.26568880015408, 95.40760565511057, 108.14449432434445, 114.26645477367292, 113.41791086824662, 106.04902211737584, 93.3776377373918, 77.31637670799856, 59.94071137133798, 43.13483448111531, 28.387184727290347, 16.666387335761133, 8.299113824138173, 3.0549608373515147, 0.3257055275397725, -0.672038056052576, -0.7069567604435871, -0.39013678080805314, -0.10300354245208047, 0.002221603139308869, -0.05620132149380159, -0.17325751447256924, -0.23863144099917669, -0.1940213340731051, -0.04969659377991654, 0.13058933269505285, 0.26466590778780064, 0.29465970646482387, 0.2103170065974457, 0.049630100799457184, -0.11838482187284463, -0.2247217774545714, -0.23324819869543675, -0.15472480200203373, -0.04004709407750702, 0.04549868290070019, 0.06037163695105516, 0.019313191356785574, 0.006649372972757416, 0.16266031526396435, 0.6430181905569352, 1.5606897969615883, 2.928933873417605, 4.636327214414211, 6.446429669502643, 8.028269128915026, 9.03215746948978, 9.214990997881207, 8.485683825786001, 6.928731408413309, 4.81310294484903, 2.5629307551430602, 0.6154475713746874, -0.6885763348323326, -1.1804839017459432, -0.9124541767592987, -0.15453420000957832, 0.6840134933056669, 1.167675235953682, 0.955161797549309, -0.09822204258143973, -1.8908035064472755, -4.0925384021039255, -6.231396913896501, -7.807166087455313, -8.41534892190821, -7.858423168541523, -6.204530973340895, -3.7521912948195926, -0.9620058642104209, 1.647745145715112, 3.6459928898003593, 4.774756905590705, 4.977861071341143, 4.397197836068811, 3.3349786953441716, 2.1323529480694154, 1.0751256235638826, 0.3380285858262801, -0.03712554284665341, -0.12758815790339753, -0.07206993023324286, -0.0031862624200047047, 0.006396296648743484, -0.03185875674349166, -0.03592152824502393, 0.10196518808291578, 0.4578442914942938, 1.0290104891322365, 1.7121928535929805, 2.320210708503235, 2.6464809579549033, 2.5299668265461994, 1.9116977375746371, 0.8750323823975339, -0.35190186520675804, -1.4702742747825794, -2.19641972827653, -2.3459752936115223, -1.9063810612997765, -1.0520980000398545, -0.09421565557656558, 0.6135071531135607, 0.7952843448405544, 0.36927753918980266, -0.49061820907124465, -1.3650057348862672, -1.6765415960215357, -0.8388800419724228, 1.5692661318861854, 5.649609845518541, 11.118093228921245, 17.317882096637973, 23.306732810806462, 28.04442074068753, 30.693385174663142, 30.75346531350213, 28.144504964725982, 23.25973995646419, 16.950995179392617, 10.254822199187563, 4.167120518371022, -0.5279364085047725, -3.3968127598267226, -4.434786821269346, -4.000516143844086, -2.678025727919611, -1.1113919614132681, 0.16740490903078634, 0.8561445367390537, 0.9211338363427881, 0.55555887668255, 0.08104543376680867, -0.17452854722299144, 0.008441758779593739, 0.675633712887652, 1.699236522137962, 2.820888802305128, 3.7345502992977266, 4.204503635039577, 4.120600517333211, 3.512787385975474, 2.540385442088642, 1.4522629688173945, 0.4889659163660444, -0.18346675988887687, -0.5040736368378425, -0.5176900798292758, -0.3445074493095599, -0.12540471119551772, 0.030471052279179834, 0.07900624678801739, 0.04574921893808926, 0.002503820563329634, 0.026412023013684043, 0.15948787539300754, 0.38566451060060397, 0.6304099430115295, 0.7867020408101563, 0.7666114821567759, 0.537442540630328, 0.14038146047220632, -0.30940826620527145, -0.6508523876390322, -0.7401556853557842, -0.5018289874563165, 0.040101229049447296, 0.7556434522189139, 1.4439249903069806, 1.895306751349167, 1.9581319740022156, 1.5934542923474888, 0.8930295553065938, 0.055184328984464716, -0.6747333697225494, -1.0830939321550528, -1.0570759751148011, -0.623668114172925, 0.05472965580813917, 0.7397911119002322, 1.1982471552757321, 1.2772893819904496, 0.9633510819484731, 0.4001763092735197, -0.1729924637036773, -0.506821068056059, -0.43257597128394465, 0.05629886134469027, 0.787215113040651, 1.4684609774229087, 1.7985296311975967, 1.5985784545774027, 0.9309077423102461, 0.16218801027865012, -0.05135941601842549, 1.0961386689439874, 4.2549870469738655, 9.567094067705952, 16.53111613982172, 24.67328627712975, 33.84882288440657], 'positive_zeros': ['1.11252651786363796098363472927727', '1.34662753892644284168327786453501', '1.55177721551189855310407424135806', '1.87964112982881891749086947555821', '2.89445959942251126558372564709438', '2.99044542318371344618484973508650', '3.06461322576285006805933191516173', '3.36073090217975545949937997347385', '4.11426028708447273297881343024519', '4.39005045929522300115716298578659', '4.69961645524062533832628721808956', '4.81150156294735924261369575909945', '5.28318262389619172018236305331264', '5.34664870189657118702090682954349', '5.51232260619763605303286153358296', '5.58817662056641939387521781205287', '6.33363202206858744427286422152992', '6.56359698330852523943630593996680', '6.85379023139379107977577663993424', '7.02690567356967042934842182194332', '7.51552018699587945037862016350640', '7.59090455383125247816478932373986', '7.67208984679378121513037700084992', '7.71448063706931187772708901242720', '8.413153416934157637785576654959482', '8.485060321652130728670686379942130', '8.619447785236854367680274018152074', '8.734347129133119504462833601153146', '9.142547576293166681048685252984304', '9.511942941367668005154788584297376', '9.780871999835371775726955519409634', '9.812513301735194813502052105993254', '10.38734646896906585185035419191032', '10.39108237792104813306345093476728', '10.52984251731754702015359603858263', '10.53121544419252486201399834854200', '11.41018617605364707510784787189464', '11.45766812145408592327141099710250', '11.58581344562692100209151232560935', '11.63958788032524503948841595735067'], 'prelabel': '8-378e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 137017330177652196, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11252651786363796098363472928', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.34662753892644284168327786454', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.55177721551189855310407424136', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 82.99952890949935, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 20415837456, 'conductor_radical': 42, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 1, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 7, 0, 0, 8, 0, 0, 12, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, -1, 0, 0, -28, 0, 0, 0, 0, 0, -42, 0, 0, 24, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7], 'euler11': [1, 0, 22, 0, 363, 0, 2662, 0, 14641], 'euler13': [1, 0, -52, 0, 1014, 0, -8788, 0, 28561], 'euler17': [1, 0, -22, 0, 195, 0, -6358, 0, 83521], 'euler19': [1, -24, 278, -2064, 10683, -39216, 100358, -164616, 130321], 'euler2': [1, 0, -1, 0, 1, 0, 0, 0, 0], 'euler23': [1, 0, 10, 0, -429, 0, 5290, 0, 279841], 'euler29': [1, 0, 46, 0, 2211, 0, 38686, 0, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, -12, 122, -888, 6003, -27528, 117242, -357492, 923521], 'euler37': [1, 8, -26, 128, 4363, 4736, -35594, 405224, 1874161], 'euler41': [1, 0, 140, 0, 8262, 0, 235340, 0, 2825761], 'euler43': [1, 32, 556, 6176, 48214, 265568, 1028044, 2544224, 3418801], 'euler47': [1, 0, -82, 0, 4515, 0, -181138, 0, 4879681], 'euler5': [1, 0, -7, 0, 24, 0, -175, 0, 625], 'euler53': [1, 0, 97, 0, 6600, 0, 272473, 0, 7890481], 'euler59': [1, 0, 29, 0, -2640, 0, 100949, 0, 12117361], 'euler61': [1, -12, 182, -1608, 17163, -98088, 677222, -2723772, 13845841], 'euler67': [1, 28, 454, 5488, 51883, 367696, 2038006, 8421364, 20151121], 'euler7': [1, -8, 30, -56, 49, 0, 0, 0, 0], 'euler71': [1, 0, -212, 0, 21318, 0, -1068692, 0, 25411681], 'euler73': [1, 42, 881, 12306, 123444, 898338, 4694849, 16338714, 28398241], 'euler79': [1, 22, 205, 2662, 33364, 210298, 1279405, 10846858, 38950081], 'euler83': [1, 0, -268, 0, 31734, 0, -1846252, 0, 47458321], 'euler89': [1, 0, -70, 0, -3021, 0, -554470, 0, 62742241], 'euler97': [1, 0, -292, 0, 40134, 0, -2747428, 0, 88529281], 'euler_factors': [[1, 0, -1, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -7, 0, 24, 0, -175, 0, 625], [1, -8, 30, -56, 49, 0, 0, 0, 0], [1, 0, 22, 0, 363, 0, 2662, 0, 14641], [1, 0, -52, 0, 1014, 0, -8788, 0, 28561], [1, 0, -22, 0, 195, 0, -6358, 0, 83521], [1, -24, 278, -2064, 10683, -39216, 100358, -164616, 130321], [1, 0, 10, 0, -429, 0, 5290, 0, 279841], [1, 0, 46, 0, 2211, 0, 38686, 0, 707281], [1, -12, 122, -888, 6003, -27528, 117242, -357492, 923521], [1, 8, -26, 128, 4363, 4736, -35594, 405224, 1874161], [1, 0, 140, 0, 8262, 0, 235340, 0, 2825761], [1, 32, 556, 6176, 48214, 265568, 1028044, 2544224, 3418801], [1, 0, -82, 0, 4515, 0, -181138, 0, 4879681], [1, 0, 97, 0, 6600, 0, 272473, 0, 7890481], [1, 0, 29, 0, -2640, 0, 100949, 0, 12117361], [1, -12, 182, -1608, 17163, -98088, 677222, -2723772, 13845841], [1, 28, 454, 5488, 51883, 367696, 2038006, 8421364, 20151121], [1, 0, -212, 0, 21318, 0, -1068692, 0, 25411681], [1, 42, 881, 12306, 123444, 898338, 4694849, 16338714, 28398241], [1, 22, 205, 2662, 33364, 210298, 1279405, 10846858, 38950081], [1, 0, -268, 0, 31734, 0, -1846252, 0, 47458321], [1, 0, -70, 0, -3021, 0, -554470, 0, 62742241], [1, 0, -292, 0, 40134, 0, -2747428, 0, 88529281]], 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/k/c'], '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': '8-378e4-1.1-c1e4-0-9', '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': '8-378e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 137017330177652196, 'z1': {'__RealLiteral__': 0, 'data': '1.11252651786363796098363472928', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1410294908139662640744910533754,1707053208003968621373672642795,1967111318664148693134012806624,2382728206441169568138069533432', 'Lhash_array': ['1410294908139662640744910533754', '1707053208003968621373672642795', '1967111318664148693134012806624', '2382728206441169568138069533432'], 'label': '8-378e4-1.1-c1e4-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/k/c'}