-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '615255292609348091371101696227,2805426790552450104080287031316', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.82094501927158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 9]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '300.1', 'coefficient_field': '1.1.1.1', 'conductor': 90000, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1, 0, 9], [1], [1, 0, -94, 0, 2401], [1, 0, -242, 0, 14641], [1, 0, 146, 0, 28561], [1, 0, 578, 0, 83521], [1, 52, 1398, 18772, 130321], [1, 0, 1058, 0, 279841], [1, 0, -1682, 0, 707281], [1, 92, 4038, 88412, 923521], [1, 0, -2062, 0, 1874161], [1, 0, -3362, 0, 2825761], [1, 0, -3214, 0, 3418801], [1, 0, 4418, 0, 4879681], [1, 0, 5618, 0, 7890481], [1, 0, -6962, 0, 12117361], [1, -148, 12918, -550708, 13845841], [1, 0, 5906, 0, 20151121], [1, 0, -10082, 0, 25411681], [1, 0, -8542, 0, 28398241], [1, -284, 32646, -1772444, 38950081], [1, 0, 13778, 0, 47458321], [1, 0, -15842, 0, 62742241], [1, 0, -18814, 0, 88529281], [1, 0, -20402, 0, 104060401], [1, 0, 16418, 0, 112550881], [1, 0, 22898, 0, 131079601], [1, -428, 69558, -5085068, 141158161], [1, 0, 25538, 0, 163047361]], 'euler_factors_factorization': [[1], [[[1, 0, 9], 1]], [1], [[[1, 0, -94, 0, 2401], 1]], [[[1, -11], 2], [[1, 11], 2]], [[[1, 0, 146, 0, 28561], 1]], [[[1, 0, 289], 2]], [[[1, 26, 361], 2]], [[[1, 0, 529], 2]], [[[1, -29], 2], [[1, 29], 2]], [[[1, 46, 961], 2]], [[[1, 0, -2062, 0, 1874161], 1]], [[[1, -41], 2], [[1, 41], 2]], [[[1, 0, -3214, 0, 3418801], 1]], [[[1, 0, 2209], 2]], [[[1, 0, 2809], 2]], [[[1, -59], 2], [[1, 59], 2]], [[[1, -74, 3721], 2]], [[[1, 0, 5906, 0, 20151121], 1]], [[[1, -71], 2], [[1, 71], 2]], [[[1, 0, -8542, 0, 28398241], 1]], [[[1, -142, 6241], 2]], [[[1, 0, 6889], 2]], [[[1, -89], 2], [[1, 89], 2]], [[[1, 0, -18814, 0, 88529281], 1]], [[[1, -101], 2], [[1, 101], 2]], [[[1, 0, 16418, 0, 112550881], 1]], [[[1, 0, 11449], 2]], [[[1, -214, 11881], 2]], [[[1, 0, 12769], 2]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 3, 'label': '4-300e2-1.1-c2e2-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/300/3/b/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.0904656671216357, 1.071400016536475, 1.0158846689860015, 0.9231149922629185, 0.7936940197185244, 0.6287593770890328, 0.4295716058204836, 0.19785186562449517, -0.06387969016146189, -0.3523502074596975, -0.6633265363826751, -0.9916719037913047, -1.3311124137288903, -1.6744408497914844, -2.013398835599797, -2.3390019704838223, -2.6416051003153584, -2.9113281818445573, -3.1383680190509247, -3.313455389396264, -3.4284243140799235, -3.476593424805761, -3.453538840719447, -3.3572622113411583, -3.1890411124638236, -2.953241232468292, -2.658061575078869, -2.314881538703918, -1.9387009719490076, -1.5469916351899142, -1.1596750090757024, -0.7975657087066882, -0.48184036316434664, -0.23229496484735215, -0.0664220817322004, 0.0021841248266804593, -0.03515329924551289, -0.18112264642347276, -0.43173829201062763, -0.7761010188927034, -1.1965018940562977, -1.6691304986777906, -2.165297260363295, -2.6529154433233684, -3.0988918989348337, -3.470893028417651, -3.7405799807268876, -3.8849350045919153, -3.8896629754969636, -3.7493133675416668, -3.4699774183946466, -3.067662974328567, -2.5695049251053805, -2.0103236945101535, -1.431975773465519, -0.8786362173344576, -0.39456594835534514, -0.019201355611192662, 0.21569600583393062, 0.2898146958707677, 0.19633836494392257, -0.05652046318959509, -0.4456875550420562, -0.9343362634545653, -1.4750847279295856, -2.013145691586839, -2.492333345835401, -2.858703578518243, -3.0680090800699475, -3.087802818745141, -2.9042040604272406, -2.520731668724007, -1.9622373230070667, -1.2698242524711405, -0.500708894779306, 0.2798617056918015, 1.0024861178063238, 1.6023580033019622, 2.0249028562791445, 2.2322366291865174, 2.2076088187543554, 1.9572058111382955, 1.5106908703761173, 0.9177253432500962, 0.24342999324701323, -0.4387454114508026, -1.0555353053612035, -1.5412107882613295, -1.846934236498506, -1.944480931872346, -1.8325547323871814, -1.534370136419382, -1.0981336222984657, -0.5886689487163687, -0.08189267069417729, 0.34645033935024133, 0.6294510382223449, 0.7184646967438136, 0.5901026257316978, 0.2496556570471111, -0.2680989914382785, -0.9028965406129953, -1.5761952111915292, -2.2002402022477074, -2.6911759860643256, -2.977888748491374, -3.0156315656711135, -2.7889308617587827, -2.319575639311253, -1.6604624043306473, -0.8942624172122078, -0.11961711616779601, 0.5584836753653887, 1.0445312987787945, 1.264730265836136, 1.1777097830053194, 0.7816772713445924, 0.11518531020277138, -0.7464771535452835, -1.7000306895751383, -2.62897405597687, -3.4158820383526503, -3.9628355642943673, -4.198637466207739, -4.0961833805490135, -3.6679654264045953, -2.973161541372398, -2.1007773005408157, -1.1649247022408542, -0.28181375758211297, 0.4414689120709001, 0.9260805796097424, 1.1298429230955045, 1.0541312100671103, 0.7416602714345047, 0.26943112801182056, -0.26553718520304864, -0.7609463755611127, -1.1292221955566373, -1.3090805578501465, -1.2806584824969598, -1.0648230995162014, -0.7250165134501824, -0.35265586335455923, -0.055144798362246436, 0.06551401250150365, -0.06993404385151909, -0.501557503266225, -1.2204950864881934, -2.1664036871855687, -3.2349243045629614, -4.2890229320751185, -5.1835229275242884, -5.780687767679034, -5.9812424171002965, -5.730502178060139, -5.040817198674833, -3.9793001102739436, -2.6713723126745363, -1.2723064893556981, 0.04696693854569605, 1.131558710758972, 1.8622685010492894, 2.1744257277290417, 2.0672368386087645, 1.6007430249142722, 0.885941978748875, 0.06416479494868843, -0.7179595573996373, -1.3312743774885605, -1.6896204054082908, -1.7579041483131093, -1.5626395554166415, -1.1781611278276005, -0.7167372730037092, -0.30047350443786786, -0.0399407917516478, -0.00913879803600849, -0.2303868305607303, -0.6676629317888032, -1.2321170758484392, -1.796136980224796, -2.219929750186105, -2.3735409625429043, -2.1698345933571934, -1.575183533319984, -0.6286556533658108, 0.5706197925691191, 1.8696155640243934, 3.092805271157588, 4.067846465784074, 4.656930710862248, 4.7821293918571035, 4.436528464456337, 3.689086749888856, 2.668718572537203, 1.5428524991568353, 0.48670386569001767, -0.35115276438402204, -0.8709664220152518, -1.0459394039622638, -0.9179589414007869, -0.5952115885867009, -0.2223055930594173, 0.04519741018182238, 0.07676301960461403, -0.2060572412133232, -0.8116143282852946, -1.6737331347481887, -2.662143863951898, -3.609457516738628, -4.338303775449834, -4.70570687957966, -4.621008837757192, -4.080524168505525, -3.155509173718608, -1.996928590091091, -0.7942752035726595, 0.2472324631375831, 0.9540921761263891, 1.2112838225477296, 0.9875041151675374, 0.33870189983183857, -0.6013971643809544, -1.6507126584825274, -2.6094969639579526, -3.306936499389148, -3.623367227555753, -3.5245714423536074, -3.052401615544905, -2.3265759008381197, -1.5053829061215582, -0.7602836418752235, -0.23224464571949577, -0.006100659005714182, -0.09194806674718287, -0.42629840595820045, -0.8882027976439053, -1.3319283546099956, -1.6194365729098046, -1.662228961728172, -1.438130123163924, -1.0104951953851942, -0.5096574551784389, -0.11482394059074924, -0.009649151990427023, -0.343171238154813, -1.1910896160534648, -2.531981312897499, -4.242059433478895, -6.114395924910302, -7.887117801527197, -9.30172926796293, -10.135099916201463, -10.262852803635651, -9.659092068164199, -8.426689981603177, -6.752340648913496, -4.891462639662909, -3.10183769317683, -1.606176735098936, -0.5463030202331632, 0.03763907047289276, 0.2049168912913615, 0.09605242738038189, -0.10836282438739502, -0.231800066801668, -0.1434829742807559, 0.20832569810552898, 0.7901232593822487, 1.489176710286086, 2.1467092089213797, 2.597740275703836, 2.712983533978741, 2.4367857698912805, 1.7997150272007183, 0.9192039510107431, -0.02870653813729828, -0.8495711741334362, -1.373738635087847, -1.5046317810671261, -1.2357353129338797, -0.6656022456195554, 0.031156736707685734, 0.6353048344396091, 0.9376020029116853, 0.7881957486617109, 0.1329212576398471, -0.9665066350669519, -2.343310539861641, -3.7598223648489655, -4.952119463072873, -5.6986936582128, -5.853143063252819, -5.398207597621998, -4.42761601762977, -3.1491209189659153, -1.8185835023192645, -0.7002473546853082, 0.0026186642528459973, 0.18431911970581952, -0.13863272543575264, -0.8370453902982089, -1.6992084221119703, -2.4880975558946137, -2.989178389633632, -3.073541400898849, -2.711662899452944, -1.9947646439669509, -1.0943383637029978, -0.23142605145771283, 0.38873583333672174, 0.622520951768257, 0.4260477622184388, -0.13485695919219942, -0.9006645583808576, -1.6620831390307775, -2.206623082849139, -2.3844771905612676, -2.132758277037698, -1.5105054749491855, -0.667432858830961, 0.17623443164530778, 0.7982411360449898, 1.0216963464682416, 0.7669756774635481, 0.07126672967084936, -0.9156094131100757, -1.9700152618273716, -2.8421707471616084, -3.3291719098788675, -3.311900950548494, -2.804354678535395, -1.9340784558148834, -0.9301567166701411, -0.053545153378139795, 0.45684856188908396, 0.45028084438232957, -0.10045267674558789, -1.0873272251039823, -2.296155349447592, -3.448606930012557, -4.28344192312619, -4.599245390137392, -4.327498406513405, -3.520429069022474, -2.363142441527583, -1.1022740208673223, -0.0010903550658085735, 0.7377492037603598, 1.0178684721995175, 0.870230675860771, 0.4455188291113083, -0.03316093638376491, -0.3302334615759626, -0.26326377337772583, 0.24052642342541933, 1.1256353225002937, 2.2115448044026005, 3.239577636964602, 3.936423952417441, 4.080820391684779, 3.568680840684027, 2.4346992312359252, 0.8558246946847979, -0.8921206535899161, -2.500096516634958, -3.688375967506138, -4.285718921489816, -4.2434816355241605, -3.6633201606389467, -2.740085093340015, -1.7262688254788523, -0.8492022117998239, -0.26331878784564666, -0.01182376471306271, -0.027410437204170898, -0.16461071611345532, -0.25595247022450346, -0.17172839992064418, 0.12385314144947984, 0.5543892977773178, 0.936598756139209, 1.0280295793613468, 0.5952241849052544, -0.5180417386490572, -2.326401908650178, -4.683206942778324, -7.2930552145759595, -9.760461116164723, -11.686486189200416, -12.73112835277592, -12.724718882750725, -11.665767804616493, -9.765195711552709, -7.3562455590318905, -4.854218033703037, -2.6374731515793424, -0.9843538256662847, -0.013359371198023901, 0.32484482870446424, 0.21435727423460377, -0.08992399276259283, -0.3365605906725274, -0.355170196682008, -0.08725888580564121, 0.3935014005944909, 0.9277909618383244, 1.316747461139877, 1.3985036199929126, 1.0986854568099782, 0.46111281923974345, -0.36430125009456155, -1.160169166813196, -1.7159753267096547, -1.882382147416418, -1.6384153610071086, -1.0882771479883977, -0.4558285299884185, -0.010768716991867813, -0.0009578595198879403, -0.5716675887838798, -1.7164876299470082, -3.2641729459169593, -4.9176742256728945, -6.312984470321237, -7.130569478357672, -7.151072437244459, -6.349898839477542, -4.870678370694495, -3.0287866189005745, -1.2034947263317226, 0.23334942062474018, 1.021790001456231, 1.0696982000816615, 0.4690337163424096, -0.5351254775187508, -1.615242998462526, -2.4587171265168575, -2.8390884722770995, -2.69009017066187, -2.0945440459487585, -1.2711827041954409, -0.48648708328145285, 0.01641812152229796, 0.09748123607660977, -0.2416274748575436, -0.86002235218868, -1.525239305719112, -1.9814821685949784, -2.042191758919224, -1.636040053134947, -0.8521166782569278, 0.09964951773116501, 0.9333364218286956, 1.3808163432854197, 1.2711466036316312, 0.5853015427458882, -0.5257678486179096, -1.779035423430586, -2.8354298506364457, -3.3836830348128215, -3.2426089964093046, -2.3918579486552485, -1.0029003618783896, 0.6279371026329128, 2.1427054914886305, 3.2263817578308758, 3.6878984020862897, 3.499837874050823, 2.804578543151236, 1.853936299642504, 0.9329478856588271, 0.2695693978225909, -0.03778039175371447, -0.04094450743882932, 0.07321266946711526, 0.05257410213384918, -0.3316104191863919, -1.2037213085881742, -2.5237500432744113, -4.084585714882519, -5.561343040821586, -6.58362933549946, -6.864068513986486, -6.248464387882118, -4.811506232021797, -2.799588427072029, -0.6184813687940253, 1.3069156671001667, 2.611468725241569, 3.0988314131175425, 2.7754555082925454, 1.8430548900625274, 0.6290826507856853, -0.5035011553620692, -1.271199123071098, -1.527368031360092, -1.313405612740525, -0.8110541201673, -0.29167046761328014, -0.010063813076465793, -0.12726733272658047, -0.6548155529151556, -1.4549608612038079, -2.2823534991282646, -2.8752330238470005, -3.0283928679285124, -2.688687893004071, -1.9478444796171999, -1.039097522292108, -0.26272824271452755], 'positive_zeros': ['0.48535084706982882982774333538859', '2.18127135462061597737397001789294', '2.21309151752648367900254771233898', '3.56643886117874732401939577164219', '3.80122920765454181374172985339051', '4.66485083460652070047981802162159', '5.27202927199347490164345987490963', '5.88583030440727972690620875082176', '6.21991501236242035894940905654133', '6.94767676644916616494534931884574', '7.32157117934016320868338868758091', '8.084862373590894508443976560871133', '8.469124244425378967815587703750363', '9.017331377980182466971970882402411', '9.106530733035266101682380655753055', '9.997613870902732190259176458327542', '10.44235121939280235955224392966849', '11.02248816653733503534775540611596', '11.05554593106336849182783927498247', '11.65894457312569996036557439796375'], 'prelabel': '4-300e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.8590921515069967, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c2e2-0', 'trace_hash': 1795709756418565736, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48535084706982882982774333539', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18127135462061597737397001789', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.21309151752648367900254771234', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 66.82094501927158, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 90000, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 94, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 148, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 284, 0, 81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -242, 0, 14641], 'euler13': [1, 0, 146, 0, 28561], 'euler17': [1, 0, 578, 0, 83521], 'euler19': [1, 52, 1398, 18772, 130321], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 1058, 0, 279841], 'euler29': [1, 0, -1682, 0, 707281], 'euler3': [1, 0, 9, 0, 0], 'euler31': [1, 92, 4038, 88412, 923521], 'euler37': [1, 0, -2062, 0, 1874161], 'euler41': [1, 0, -3362, 0, 2825761], 'euler43': [1, 0, -3214, 0, 3418801], 'euler47': [1, 0, 4418, 0, 4879681], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, 5618, 0, 7890481], 'euler59': [1, 0, -6962, 0, 12117361], 'euler61': [1, -148, 12918, -550708, 13845841], 'euler67': [1, 0, 5906, 0, 20151121], 'euler7': [1, 0, -94, 0, 2401], 'euler71': [1, 0, -10082, 0, 25411681], 'euler73': [1, 0, -8542, 0, 28398241], 'euler79': [1, -284, 32646, -1772444, 38950081], 'euler83': [1, 0, 13778, 0, 47458321], 'euler89': [1, 0, -15842, 0, 62742241], 'euler97': [1, 0, -18814, 0, 88529281], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 9, 0, 0], [1, 0, 0, 0, 0], [1, 0, -94, 0, 2401], [1, 0, -242, 0, 14641], [1, 0, 146, 0, 28561], [1, 0, 578, 0, 83521], [1, 52, 1398, 18772, 130321], [1, 0, 1058, 0, 279841], [1, 0, -1682, 0, 707281], [1, 92, 4038, 88412, 923521], [1, 0, -2062, 0, 1874161], [1, 0, -3362, 0, 2825761], [1, 0, -3214, 0, 3418801], [1, 0, 4418, 0, 4879681], [1, 0, 5618, 0, 7890481], [1, 0, -6962, 0, 12117361], [1, -148, 12918, -550708, 13845841], [1, 0, 5906, 0, 20151121], [1, 0, -10082, 0, 25411681], [1, 0, -8542, 0, 28398241], [1, -284, 32646, -1772444, 38950081], [1, 0, 13778, 0, 47458321], [1, 0, -15842, 0, 62742241], [1, 0, -18814, 0, 88529281]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/300/3/b/a'], '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': '4-300e2-1.1-c2e2-0-3', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-300e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.8590921515069967, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 1795709756418565736, 'z1': {'__RealLiteral__': 0, 'data': '0.48535084706982882982774333539', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '615255292609348091371101696227,2805426790552450104080287031316', 'Lhash_array': ['615255292609348091371101696227', '2805426790552450104080287031316'], 'factors': ['2-300-15.14-c2-0-1', '2-300-15.14-c2-0-11'], 'label': '4-300e2-1.1-c2e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/300/3/b/a'}