Formats: - HTML - YAML - JSON - 2026-04-18T08:16:09.416906
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '1799676007800083775034794987222', 'a10': [0.0, 0.0], 'a2': [0.9396926207859084, 0.3420201433256687], 'a3': [0.07831410307939192, 0.74510891860289], 'a4': [0.766044443118978, 0.6427876096865394], 'a5': [0.0, 0.0], 'a6': [-0.18125107436662288, 0.7269583532525385], 'a7': [0.0, 0.0], 'a8': [0.5, 0.8660254037844386], 'a9': [0.4290933988933672, -0.0912066175040774], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.423333416029323, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9396926207859084, -0.3420201433256687]]], [23, [[1.0, 0], [0.30901699437494745, -0.9510565162951535]]], [31, [[1.0, 0], [0.5591929034707468, 0.8290375725550417]]]], 'bad_primes': [2, 23, 31], 'central_character': '2852.827', 'coefficient_field': 'CDF', 'conductor': 2852, 'conductor_radical': 1426, 'conjugate': '2068183082531729565804125419297', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9396926207859084, -0.3420201433256687]], [[1.0, 0], [-0.07831410307939192, -0.74510891860289], [-0.9781476007338057, 0.20791169081775934]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.9135454576426009, 0.4067366430758002]], [[1.0, 0], [0, 0], [0.10452846326765347, 0.9945218953682733]], [[1.0, 0], [-0.8129777402049895, 1.8259779008659545], [-0.6691306063588582, -0.7431448254773942]], [[1.0, 0], [0, 0], [-0.10452846326765347, 0.9945218953682733]], [[1.0, 0], [0, 0], [0.6691306063588582, -0.7431448254773942]], [[1.0, 0], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [-0.5518969219524928, 0.7596209453391015], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0.5591929034707468, 0.8290375725550417]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0.12870829581777482, -1.2245776346922022], [-0.9781476007338057, -0.20791169081775934]], [[1.0, 0], [0, 0], [-0.6691306063588582, 0.7431448254773942]], [[1.0, 0], [0.9745921174884093, 1.3414109703447645], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [0.9135454576426009, -0.4067366430758002]], [[1.0, 0], [1.8916930583764064, -0.19882495225804087], [0.9781476007338057, -0.20791169081775934]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.05787142947391587, 0.2722636695815434], [-0.9135454576426009, 0.4067366430758002]], [[1.0, 0], [0.7876135182713885, 0.7091703971952089], [0.10452846326765347, 0.9945218953682733]], [[1.0, 0], [0, 0], [0.10452846326765347, -0.9945218953682733]], [[1.0, 0], [0, 0], [0.9781476007338057, 0.20791169081775934]], [[1.0, 0], [0, 0], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0.5, -1.5388417685876268], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [-0.9781476007338057, -0.20791169081775934]], [[1.0, 0], [0, 0], [-0.10452846326765347, 0.9945218953682733]], [[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [0.10452846326765347, 0.9945218953682733]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 19510429, 'index': 5, 'label': '2-2852-2852.827-c0-0-5', 'leading_term': '2.45569273448866493368835298085', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2852/1/bn/b/827/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.455692734488665, 2.4147864112758186, 2.39059868541395, 2.3803275332640257, 2.380451125358846, 2.38704877988895, 2.3961004058870836, 2.403726026687508, 2.406353722198974, 2.4008235253976236, 2.3844433899729016, 2.355013928337297, 2.310835210551132, 2.250704517235189, 2.17391008928432, 2.080223101076067, 1.969888260042372, 1.843612381249043, 1.7025497673116148, 1.5482830562940855, 1.3827982538327062, 1.2084528563971388, 1.0279362475136222, 0.8442218750054455, 0.6605110737037904, 0.48016876997238467, 0.3066516803305476, 0.14342998636739612, -0.006096177706137115, -0.13868375992267631, -0.2513353898301492, -0.34138733665103793, -0.4065944286744887, -0.44520940871529585, -0.4560541458807059, -0.43858014912897747, -0.39291593831042276, -0.3198990265004733, -0.22109055388874518, -0.09877098589461955, 0.044084258854958404, 0.20384986003740127, 0.37631635055863166, 0.5567759675975267, 0.7401273328731783, 0.9209970270311306, 1.0938754679357188, 1.2532638836461547, 1.3938286115437535, 1.5105584788721298, 1.5989206492084789, 1.655010074521515, 1.6756875910778977, 1.658701753425246, 1.6027897234013517, 1.5077529247969006, 1.374503737377957, 1.2050802287523612, 1.0026267949992038, 0.7713395807225873, 0.5163766498536854, 0.243734048208053, -0.03990989913476912, -0.32737851849850075, -0.6112042659978602, -0.8838540249429478, -1.137965583455037, -1.3665879229620823, -1.5634174347223668, -1.7230219168917256, -1.841044213640868, -1.9143776566089283, -1.9413060639406967, -1.9216019390174794, -1.856577674252178, -1.749085978105237, -1.6034673678365818, -1.4254443581519862, -1.221963869413146, -1.0009913135595354, -0.7712617210102136, -0.5419950742288898, -0.32258463966676143, -0.12226846830893659, 0.05020469959097083, 0.18690319499704486, 0.2810216365434206, 0.327159563659318, 0.32155808213207354, 0.26228421710432215, 0.1493542126017447, -0.015211032310219363, -0.22740289891257784, -0.48131628462231035, -0.7693142992631864, -1.0822627239736178, -1.4098276969839463, -1.740827386538693, -2.0636259556335976, -2.3665560260999077, -2.6383542119732373, -2.8685932013925757, -3.048093391777041, -3.1692972721011468, -3.2265906210662214, -3.216556145888807, -3.138147389837857, -2.9927735255276158, -2.7842889358734197, -2.5188851510749037, -2.2048866220935524, -1.8524558161837101, -1.4732170543892673, -1.0798122061779039, -0.6854046465574044, -0.3031506097195761, 0.05434089908271113, 0.37553726101032897, 0.6504777903779896, 0.8712136370346372, 1.032171623559262, 1.1304241465182372, 1.1658506873465497, 1.1411806491271481, 1.0619120109720412, 0.9361054891692462, 0.7740593045779881, 0.5878750512880241, 0.39093030542356494, 0.19727826912661897, 0.020998688527287337, -0.12447268688499909, -0.22700689350386263, -0.2764068548307396, -0.26496542860679256, -0.18792892840277833, -0.04384183577619592, 0.16524719067983387, 0.43373245811265326, 0.7525596843845344, 1.10949699188361, 1.4895624730629262, 1.8755951182493917, 2.2489489796933086, 2.590284168178064, 2.880422946904729, 3.101235078247288, 3.236513924209756, 3.272803775888711, 3.200139598544763, 3.012662859692571, 2.7090813112310186, 2.2929463960068213, 1.7727291396695843, 1.1616836943920326, 0.4774967849954452, -0.25826921465698754, -1.0209223932247986, -1.7835504196494174, -2.518058364061436, -3.1962940753323084, -3.7912147571082278, -4.278045095048986, -4.635376133173407, -4.846155196827317, -4.898520533634344, -4.786439907009567, -4.510119940411766, -4.076162286801993, -3.497453310741944, -2.7927854707331385, -1.9862204727330364, -1.1062159958047182, -0.18454882301387082, 0.7449229820878202, 1.6476081148345336, 2.4895835737428285, 3.2389894801388963, 3.8673560993411273, 4.350803920131324, 4.671062326055977, 4.816259656184243, 4.781447018913528, 4.568829689006092, 4.187692784617816, 3.654021609366457, 2.989830924706404, 2.222230838097862, 1.382269309771169, 0.5036018929239382, -0.37895230258188717, -1.2309037277064463, -2.0195671738283476, -2.715451225169182, -3.293498999445965, -3.734123438365413, -4.023989812935112, -4.15650984499015, -4.132025370631938, -3.9576741422481234, -3.6469454766713683, -3.2189482699150016, -2.6974276813486244, -2.1095788522518926, -1.484715753664158, -0.8528601549860506, -0.24331940410501407, 0.3166779937488649, 0.8032231524485144, 1.196784529472943, 1.4830326171867578, 1.6533935663727828, 1.70530757465911, 1.6421829553566876, 1.4730523273853815, 1.2119525320236821, 0.877063897701353, 0.48965660524980836, 0.07290151249654177, -0.3493906322559796, -0.7540344766118291, -1.1196731209046036, -1.427856146334654, -1.6639370881534077, -1.8177450556341184, -1.8839978340328607, -1.8624381591022057, -1.7576901506390532, -1.5788482908817447, -1.3388259889484322, -1.0535038730795225, -0.7407287692128159, -0.4192222515895775, -0.10746224108926586, 0.1773978829426062, 0.4205108628797607, 0.6101622277732186, 0.7383957931921266, 0.8014037447846691, 0.7996610112893994, 0.7377987476308483, 0.6242271493025967, 0.47053261045408945, 0.2906875537556075, 0.10012231339436503, -0.08528341733579924, -0.2502273502036442, -0.3809663578851086, -0.4661928017695312, -0.49775146605459414, -0.47115287848343124, -0.38585127446131495, -0.2452699371725528, -0.05657226283597163, 0.16980727999025802, 0.4208430660329391, 0.6817664955350063], 'positive_zeros': ['1.41969404461771078948983339504645', '2.01626644296740777682886762505191', '3.14136339390956421852752849675196', '4.24981782634810690637775284196866', '4.61696887653936566219435843598787', '5.88260279571330873919093322735284', '6.60818678077909573922478591697964', '6.91828888344072161793326815223705', '7.904349648343948220245256002287469', '8.795213011201175267939327542991632'], 'prelabel': '2-2852-2852.827-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1930353792026969, 'root_angle': -0.20046717158457564, 'root_number': '0.30622400654477685599997366399669 - 0.95195948328469550535554279668288*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.20046717158457564', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41969404461771078948983339505', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.01626644296740777682886762505', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.14136339390956421852752849675', 'prec': 103}}