-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_4024.421', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.31377458721695767, 0.9494975031124767], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.6869157154728436, -0.7267370912760897], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.6591497456732824, -0.7520117105330522], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.8030910168336557, -0.5958563742052988], 'algebraic': True, 'analytic_conductor': 18.68737743662057, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [503, [1]]], 'bad_primes': [2, 503], 'central_character': '4024.421', 'coeff_info': ['x^502 - 1', '0.999921672072223 + 0.0125159785989932*I', '\\\\zeta_{502}'], 'conductor': 4024, 'conductor_radical': 1006, 'conjugate': 'dirichlet_L_4024.3613', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^653', 0, 'a^437', 0, 'a^434', 0, 'a^302', 0, 'a^533', 0, 'a^725', 0, 'a^86', 0, 'a^426', 0, 'a^659', 0, 'a^585', 0, 'a^198', 0, 'a^372', 0, 'a^453', 0, 'a^435', 0, 'a^244', 0, 'a^182', 0, 'a^369', 0, 'a^483', 0, 'a^374', 0, 'a^36', 0, 'a^479', 0, 'a^739', 0, 'a^74', 0, 'a^366', 0, 'a^577', 0, 'a^345', 0, 'a^468', 0, 'a^308', 0, 'a^729', 0, 'a^571', 0, 'a^234', 0, 'a^158', 0, 'a^667', 0, 'a^349', 0, 'a^392', 0, 'a^336', 0, 'a^523', 0, 'a^465', 0, 'a^362', 0, 'a^102', 0, 'a^615', 0, 'a^361', 0, 'a^84', 0, 'a^422', 0, 'a^657', 0, 'a^395', 0, 'a^92', 0, 'a^38', 0, 'a^333', 0], 'euler_factors': [[0], [1, 'a^653'], [1, 'a^437'], [1, 'a^434'], [1, 'a^533'], [1, 'a^725'], [1, 'a^426'], [1, 'a^659'], [1, 'a^198'], [1, 'a^435'], [1, 'a^244'], [1, 'a^483'], [1, 'a^36'], [1, 'a^479'], [1, 'a^74'], [1, 'a^345'], [1, 'a^729'], [1, 'a^571'], [1, 'a^667'], [1, 'a^392'], [1, 'a^336'], [1, 'a^362'], [1, 'a^615'], [1, 'a^422'], [1, 'a^38'], [1, 'a^489']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-4024-4024.421-r0-0-0', 'leading_term': '1.89996684190423591054372774294-0.219367707529414443722674578451*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/4024/421', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.912588871514803, 1.4647846620190643, 0.24480290177507166, -1.3349138554182445, -1.7191461706603162, -0.1513798258009728, 1.9570951666407597, 2.119802336993792, -0.47714398984627004, -3.680496262548887, -4.449834902414717, -2.234992570702832, 0.42607596955191224, 1.0255015662757594, 0.04236947962290174, -0.1513324394624528, 1.0911089364825677, 1.7502623291931412, 0.4216893643618414, -0.9861700621144198, 0.3785925566679396, 3.786746971684031, 5.092772155000282, 2.2223513606158534, -1.523662772222504, -1.5462868547905444, 1.8787545008641886, 4.0884110141300285, 2.540253089349785, -0.0867734015470378, -0.4395273340176138, 0.6201526812207852, 0.2300235762539729, -1.223902791440417, -0.7055757830841252, 1.9737123626721467, 3.206968318478355, 1.3480506673449513, -0.2566376477487077, 1.3987384951049675, 3.6014361354857822, 1.7779148148448671, -2.995433799015137, -5.0516419317922505, -2.5367875752964055, 0.17655080817295968, -0.1771036903484056, -0.8436710873599913, 1.5201355503264276, 4.598728220874813, 4.070069119328685, 0.8147900561370542, -0.6639669499871208, 0.3950377335579392, 0.6949494267348248, -0.47326831224238564, -0.2344851353091158, 1.257374238734124, -0.5271066416275609, -6.444595870220134, -10.057308254569813, -6.45336522606857, -0.018106375414411274, 1.9396336421031783, -0.3923508167726814, -1.428782309560083, 0.07381657035732525, 0.466651520031835, -0.8983050021592404, -0.6926920091794194, 1.250381578725666, 1.1017758663061796, -1.3895395696533106, -1.6132821775815889, 1.4677010089317717, 2.735021892127494, -0.07474890046119585, -1.8715116352061745, 0.9280569134053211, 3.8580239697499303, 2.313742169240993, -0.22957282503241203, 1.3337289449896603, 4.39876517319171, 3.40504972555535, -0.275368124616107, -1.2691801056592524, 0.24304583220221354, 0.14386705655685153, -1.0614764682064797, 0.2134152506657392, 2.5410277113221915, 1.597370052890653, -1.1737589490342661, -0.9164311391830642, 0.9266640396601565, -1.174979104347098, -5.636629565942821, -5.072146419845389, 0.776943246989044, 3.895032238657986, 1.1937036841079598, -1.4410371513119666, -0.3989511568879977, 0.5222258218119498, -1.0210153264315704, -1.714028318197717, -0.2857777429661976, -0.04336424661805328, -0.9372911922598548, 1.3325871618568492, 5.657569362063839, 5.126502425497992, -0.7668482804576136, -4.027812789799888, -1.507865706726189, 0.4969494278567161, -1.4551959911206156, -2.329268208381564, 0.4968477499594179, 1.9554507750944854, -0.3785578860481993, -1.4872692340709592, 0.8930968224235973, 1.80589785919466, -0.8641730552819009, -2.2851589136078725, -0.43277259534571544, 0.5211906074826043, -0.42816807939582696, 0.6625824985482314, 2.8347023555964803, 0.47575407011230575, -4.551621622215033, -3.7134288641676356, 3.117638956338474, 6.406987548729382, 2.9050648504373733, -0.2658187988065853, 0.6357690941530871, 1.2929476137326377, 0.08317900795159608, 0.6530407051763174, 2.546147195115639, 1.4345710675461598, -1.2804054122548354, -0.7935309156354786, 0.949070347981448, -0.7110779484967508, -2.4444096131821165, 1.12034286249863, 5.358445986048691, 2.8253145000266775, -2.728286092497381, -2.8818776654671083, 0.7048777511686625, 1.1422962941038555, -0.606877961316623, -0.10513250170713187, 0.28309223656140675, -2.6926435209323394, -4.797628618562912, -2.3611315724778184, 0.058127434420836455, -1.0913135308722497, -1.6523816564099407, 0.3472165510719455, -0.06760953761134514, -3.5174258433078864, -3.410318061873202, 0.6307040810324798, 0.8642720489917664, -3.265205681355684, -3.3208158792888067, 1.834081394571174, 3.805579549236012, 0.5474788012421379, -1.126991363709853, 0.6315133785389417, 1.1437000117897842, 0.043700485207294304, 0.11299784031582574, -0.7906684045888878, -4.198294521138751, -4.2808454365177795, 1.6459777715841715, 5.37198428133566, 1.600566752885717, -2.230914988609758, -0.15729806978507083, 1.9089952723177857, -0.6656096634337224, -2.4349859823803235, -0.33222885198945495, 0.19377676080341596, -2.447912079843362, -2.6436713198393313, 0.02867375773634892, 0.1428716904627923, -1.4774221833150079, 0.13610564142997664, 2.6289680523901966, 1.2866030479048272, -0.4203550649054124, 1.2943447000905839, 1.2471452566398376, -3.5613259176010152, -5.488071076103455, -0.5012541233686635, 3.1582073781317153, 0.5062053110810144, -1.6015482556386023, 0.7240332176665362, 1.6315554551197482, -0.896576270432135, -1.3537383088199386, 0.7944705655033134, 0.8209482288906814, -0.146292705939427, 1.4579034828930346, 2.2608324486800133, -0.46188406727920106, -1.0905652215472543, 2.3223465069143843, 1.4651933216276012, -5.97737598354764, -9.460959743380128, -4.212347273264387, 0.7803425246494691, 0.14533840788486604, -0.7352105054199208, 0.3807990283523557, -0.2961565374259013, -1.3194556266641928, 1.217026128498199, 3.355518436031541, 0.8026717713040034, -1.2387435719313562, 1.279519533650558, 2.7012567644006826, 0.18775588824123324, -0.3138304534615747, 2.1000358287208445, 1.0440724493443478, -1.901724577044599, 1.0203458713669364, 6.643659955937852, 5.478168598447045, -0.009778951509446321, -0.8819637441825883, 1.395981778369351, 0.8100769104440807, -0.49433997994298257, 0.46238353321022996, 0.03556614120721695, -2.34494773702815, -1.714355078670895, 0.6976530249163666, -0.13402313666354004, -0.07116419511317179, 6.494465771163316, 12.052831429408958, 7.8895183884522595, 0.6707851526758508, -0.30854446870174324, 1.0256660155067412, -0.7265542334213049, -1.1944167568331145, 1.74596157006607, 2.286809688530553, -0.23901038652009823, -0.2950648386351484, 1.0239340601982891, -0.6738830220808821, -2.0496380053597556, -0.18082580463862555, -1.0334157756239497, -6.314016424594843, -7.266822541733573, -1.8094604655652016, 0.9249199370925637, -0.9644505250863956, -0.12525180869271382, 2.6026927675382447, 0.47869532794609965, -3.044515118209548, -1.086494441379476, 1.9837409793369374, 0.2332925662839948, -1.8463723542591248, -0.3746039856703078, 0.4167500405264266, -0.4321990206650414, 0.9370373526850795, 2.0949306442601903, -0.3216737500365606, 0.053162387309334175, 6.8325044789542995, 9.945034314927105, 3.613355578189619, -1.8678306973843135, 0.2130469297756808, 2.045243846355777, -0.7376151390770777, -2.032010347514722, -0.33966057940905076, -0.03568766924601757, 0.30073510133959314, 2.729955665937305, 1.9581096015523052, -3.1125237648285724, -4.348831531901752, -0.38388293433761844, 0.9474144467206563, -0.4408143003274668, 1.3626048024402553, 2.589913008651177, -2.3423264079171484, -6.241964901946167, -2.4142391801778285, 1.6920747835991372, 0.15350011564370517, -0.6980584400240527, 1.9589117256223676, 2.0190407452799284, -0.4572503231920915, 0.21847684849105203, 1.8931789055362265, 0.44941355223520574, -0.004009487759523946, 2.427670858350939, 2.031102693180494, -0.44573728172501276, 1.7613892756961187, 4.695979232671402, 0.19267366607764203, -5.4841271892059025, -2.7699295302027287, 2.2502025705999937, 1.0087462186551734, -1.417180759027884, 0.2184546119673984, 1.0695628172356157, -0.6097492684556917, -0.3452512985561645, 0.5404671147070849, -1.0279560275058475, -0.4928400599476021, 3.447418864195534, 3.0690426745998023, -1.6599029589907324, -1.0891002390556646, 3.8199908946446515, 3.1814429121876113, -1.080902457254883, -0.6659493086607439, 1.1021186530167348, -1.3089867826291153, -2.646494849482123, -0.1787869353378405, -0.7403024111275283, -4.5523825670938685, -3.8852136428346427, 0.045529448998928905, 0.4598928310183477, -0.6404635877515792, 0.20832292257954926, -0.44242452278852434, -1.7261205448817516, 1.8599199233461587, 5.076236551983387, -0.4732301190033392, -7.154606228982337, -4.137995502602182, 1.9751431084218374, 1.6268395105686133, -0.2771193212018899, 1.310848430377262, 1.4350193330430392, -0.7204374536845286, 0.013987225073664301, 1.5437068884657745, -0.12254490320884327, -0.6153483735271214, 1.7088183696216137, 0.7793551103270822, -1.85877055830746, 1.2563121002347994, 5.42870001301166, 2.0174026192854897, -2.7224883174603147, -0.6072980919558011, 1.9007654673056753, -0.6058410391129622, -1.3668416913677688, 1.5303904023624333, 1.1476615749759007, -1.5579790220634775, -0.6970275587083481, 0.44630968850668906, -1.6035724584786337, -1.387739273760034, 1.8906323919906818, 1.5272395633115738, -0.8098489543361858, 1.0769174051216601, 2.872491754352962, 0.21317272399378537, -0.12888993814599053, 2.963221880762063, -0.5708626080028038, -9.509724216887335, -10.590123105460414, -3.6186714298296607, 0.20875546560072036, -0.15953818656931387, 0.20907144757143156, -0.49658256441826787, -2.4285523725200244, -1.0107674693458135, 1.0500952776672168, -0.8785704298786866, -1.0375183971564046, 3.6683708952415732, 3.9963773288852593, -1.936307865536117, -2.846599214385482, 2.3593787678644613, 3.1861984817109583, 0.09580688084869846, 0.6466548923358473, 1.7273539462382939, -0.712490447527013, -0.7754238125145206, 2.676512429649383, 2.3485066129027743, -0.676005750809375, 0.008367955711055182, 1.1741629287709943, -0.9973344266405131, -1.3508782114819429, 0.6032517711134104, -0.9964934306553228, -2.147466568672047, 3.505906584538072, 7.5377550201725745, 2.323765572378438, -2.6097079881655985, -0.31727359737606015, 1.2844744131749204, -0.7350151159105368, 0.3004956789873194, 2.8461707061091235, 1.0257216311875748, -1.1105790362320354, 0.31114619536077504, 0.671999630380066, -0.3716232844656843, 0.8100985149871923, -0.49400435768052614, -6.727368999895766, -7.852600190173064, -1.3141512793359773, 0.4973595335598515, -4.538512243039839, -4.669926118959152, 0.5186327369398447, 1.6269858159626933, -0.038971154931472116, 0.5295781816786048, -0.2604479916996861, -2.683955708242004, -1.0185295445776519, 1.5228309063865137, -1.1079398063574395, -3.259997371983157, -0.2800535329322005, 1.2472301270394162, -0.18687049723310958, 1.4733623208346402, 2.9316147322511945, -1.1279337433294983, -2.7162437692041754, 2.915433114951157, 5.159524294703566, 0.3520748254762004, -1.0564265698141753, 2.2356952615899255, 1.7010065616025807, -1.108828354871068, -0.42874308475283673, 0.4606248103959998, -0.41706764779187017, 0.24421721658774012, -0.6756110820875375, -5.740142296524856, -6.405324669871175, -0.19930500984136504, 1.6226895114977116, -2.4242985212535517, -1.3843808110573979, 3.3401775975328274, 2.1472723128265025, -0.8417286407799903, 1.3707009588889312, 2.8771825979445564, 0.15818841941278466, -0.5345064819753728, 0.616767030473537, -1.1787474269427278, -2.1204371410667036, -0.03682076190911522, -1.2786083601869933, -4.506429687814347, -1.9774514367096325, 1.943203174120877, 0.26539587603248943, -0.399940489284389, 3.7465268112026373, 3.813154781437301, -0.6285980665136399, 0.04268458468925587, 3.148010610395321, 0.3229204442266208, -3.1060036925814227, -1.1076528046412468, 0.28039990317134245, -1.0403993882472027, 0.4376167604715539, 2.4961417455452404, 0.7865516015420654, -0.16291504323780512, 0.8864404146615857, -0.5352792527662702, 0.821746288310749, 10.148143864018977, 15.124224231761415, 6.760632271748113, -2.0278721150366255, -1.3357850769633122, 0.6160538629637802, -0.5921552828923341, 0.06093707995130555, 1.0168604103543852, -0.36432765512115595, 1.0496833480135335, 4.391354152528379, 2.321150480961116, -1.5515549231773986, -0.29202672343494035, 0.9470706933613576, -1.0372418080137267, 0.3567692418434072, 3.046796152343774, -1.0782138307927274, -5.730669105357414, -2.451078882797643, 1.0730970569426617, -0.6162940266205101, 0.5591967469652241, 5.094292633386715, 4.2204004459354705, 0.3666624837005133, 0.4953822471772147, 0.9913249543027294, -0.3897254974288855, 0.9288059905556659, 2.3850580230020406, -0.1750337447878701, -0.5416246280081549, 2.8940440470799413, 1.5420446707437194, -2.0730983598684176, 2.060723273529782, 7.474015652208026, 3.7471176169731826, -1.281409561737282, 0.3848247138226333, 1.4498849100699813, -1.1980999268836103, -1.2371591476263957, 0.1309887008625704, -0.939193725347713, -0.4661622343355824, 1.2301380278334784, -1.1342515548115366, -2.574224512354138, 1.8366608536938496, 3.003929648778876, -2.5636044370309268, -3.7581007912733435, 0.73298253326491, 1.0297242434647376, -0.879716760417485, 1.2115684660108952, 1.262110680696159, -2.88767000279834, -2.2246880423587223, 2.3521478738724504, 1.8473331448066912, -0.7013411231207428, 0.5538859755602696, 1.0052147600180463, -0.7248498468903296, 0.03435104360423979, 0.3448514093799061, -1.816916152203428, 0.8978899683181539, 6.3465084293582255, 2.9468410029535406, -4.231951588656152, -1.8860288569013728, 4.066702152882727, 2.719748002415847, -0.24393290171651094, 0.46921138866062445, -0.4999170007543716, -2.4586914486956486, -0.8092796903058366, 0.14566020501770593, -1.3097301010875317, 0.3847150300170159, 2.0657264586994706, -1.9711142788998905, -4.272271591035399, -0.3241996530753216, 0.9268381388472544, -1.0054328518345272, 2.6503990977649243, 6.610786588428767, 1.9007746560286367, -3.233888849931092, -1.2842893293390287, 0.46434773995852446, -0.6216640560636466, 0.37342757178045655, 5.026532252584717e-05, -4.23826289004328, -4.3989028390073095, 0.1142420448718803, 0.8948985617883543], 'positive_zeros': ['0.671599299660053680171824133282', '1.58339007722047446525194120391', '2.45605303404710986064773208255', '3.68585446962595103399167238551', '4.389249766943732838824088385997', '4.7437079488046891220995954612', '5.69358000381386029515935105993', '6.20689010285822125335059227133', '7.35276830449718998026717382075', '7.96954598843966849194928044552', '9.04764086200006029308170990241', '9.5009204808885968961376488136', '10.04918196835054396586557101061', '10.71899401122478218642890309768', '11.763065239503265469802425230745', '11.99309644573593840932494312121', '12.932771709989505684077718677245', '14.02400223255296683281121864706', '14.33200271571761772586178672308', '14.84858215642895287220944045343', '16.03529390491825619546683066172', '16.46969085234705862519855131132', '17.062404068102220261520019308385', '17.54759292202912697317883242887', '18.08484984448219575819543350384', '19.37613504784602210553446633095', '19.953399259346339341643756035473', '20.61046421164036793705846200529', '21.0554244126742011218849055806', '21.67711364288626720664664880118', '22.33169988852583606219342031116', '22.99048550581563513013684297470', '23.74325687537093522668141462404', '24.302071110705016696290761655966', '25.25560660920113658267972894257', '25.46923539750152407123561076739', '26.53496997021034250267009042468', '27.132521478714170827435346866312', '27.53317363481307511138779873648', '28.09863880451117038610687069303', '28.915206886290306264332377989977', '29.50310982739157531853507623146', '29.90447505850139472277585830572', '30.89745069676286131982532228294', '31.66279327363231111126346281722', '32.25706808768289403996307195372', '32.64198177785430403097999123049', '33.51384866963287360529887745378', '33.73482945815525261724941080769', '34.26100808590389606435844122649', '35.27372799711248318209491974803', '36.092667436266725080215182746189', '36.37932090735352115888656028229', '37.140683840800405305393572612987', '37.77096075471360372004724035299', '38.33872813766224242352610419232', '38.9766849257305129234736402862', '39.754806920338502922679037929943', '40.16934497442752289237159945152', '40.530632840854931511127172019844', '41.27894783505250979612618646688', '42.05294025212544389514664339222', '43.06388005550082553130985761423', '43.31579945438768731978572157235', '44.09711557186311442646626794790', '44.22407940231241415670598779541', '45.147075887754209307476461490876', '45.73518902367641529580758651825', '46.17130122161953630835936802835', '46.80932386005615950180275356851', '47.64511293204704117798146276091', '48.36758737942589129264613971002', '48.93371071108673777951626652082', '49.39893322778933503195119735317', '49.739338282250588299242085819521', '50.91058380400822443481123129259', '51.034694938971815997390797476243', '51.81924805733255774752422951234', '52.179628891314294112481393771092', '53.07178676091854884483467849694', '53.51254379987141946730644694320', '54.26957291100568446912740440102', '55.04999401866617439068630180706', '55.52850472519181028420229505703', '56.27237474276876994281016994151', '56.4717882678161649688181811338', '56.734507525020539628097775915701', '57.73720024071712764226608292794', '58.52926121704141219126949889902', '59.07612247578865974160015994551', '59.62834359735146233495682600472', '60.35926193417454572246934395269', '60.6569770220727534909432601717', '61.558280295871982147960611876518', '61.90029131836255396074668967287', '62.48637497102273489662298798110', '63.29001280452545179827096988982', '63.56663704184070088655688365087', '64.16366194575781280904602481192', '65.02583539145811590765121226603', '65.66620132619519843044100642671', '66.17359306497494379585744255136', '66.772199738518512025543248985671', '67.3805383668761888622842950125', '68.0073885057628966740264023847', '68.19817833650341855134048428529', '69.0155357271491768577086757719', '69.488991108618214877069906086261', '70.07554021688641958881239457124', '71.16454713347990552191710800245', '71.58641945621900281203309426483', '72.076132933695513834664552097862', '72.44428831534103680918693105917', '73.01565116025866375000446130373', '73.82098752239791499982605247155', '74.25493682866568567248500369894', '75.023338347483556549607589892', '75.35935651697355578582154326155', '76.0278880120410098131900029468', '76.50602788254030381932074369071', '77.49925578540352408156104134183', '77.926870633281788778567247563052', '78.57363360322002620575486089925', '78.94725199537112215742677948116', '79.38027973610560929558220328049', '80.19400026142039426569681258060', '80.603064004877872804416182842695', '80.944013842939826436719694150130', '82.24068135889488381776589271060', '82.55209937139356668707744575023', '83.02915985167850173806277841782', '83.57941770281073134145687047098', '84.34035989552716701461872496355', '84.74118680542835614821657714497', '85.23154573276731339760755461991', '85.972736896313164648202235184001', '86.13533013981196764351286788505', '87.306749850317803863456226143479', '87.67048146745795836940648879792', '88.13768877017644695709179668081', '88.78351487853814465179381799066', '89.457348624832151453512892493661', '90.02254946634239005569009971930', '90.687596221851754949836764213944', '91.071715556758107149059328188002', '91.42196741018626982929164089449', '92.151200545468151631024235449636', '92.49605676815786045337218144536', '93.59144991685654685533828789181', '94.04477605073374136266076094963', '94.61892392058239606063484667621', '95.40982178845825380237628828017', '95.60146637217714320455442836854', '95.869367083998192606156956073242', '96.69159626438275158171925416184', '97.533276958982160345820742261408', '97.993433616659409491953259826334', '98.28009497303764346516161874736', '98.94668962471057059156364119094', '99.82390646269550914758124193953', '100.33086319297200945254227762182', '100.72471705234508711546666037304', '101.487548230973528958492025202836', '101.84407207607127594574961801331', '102.578177637186086785010361167953', '102.81328438384290496400104888693', '103.66015176850371927563271107334', '103.91048868590704205967977499184', '104.695671714189994240585735642817', '105.454555038979031233098141440060', '106.02798323233683176857500960828', '106.534085010399801909987881084155', '107.07283846753163467607248433342', '107.57161718796250246591228642809', '107.95504693438051656036757875858', '108.48288638168354523152564026168', '109.25730848502509617168094102546', '109.75734848059544250445081574551', '110.52725406178058017288143247872', '111.014617178840903204997091211967', '111.43756677542748204797707751891', '112.21599522759145794097023182721', '112.41308864579727575795321961874', '113.432430824182646790134459043641', '113.84391801335402755838402695388', '114.308792860922133638004588399099', '114.608903552456529261639557241087', '115.19779264416211029313583662606', '115.92037546123757372032537502951', '116.74736776741660778785393888946', '117.390090858019553742035909238604', '117.60682376829864417196303063921', '118.31740446424309964062857555215', '118.74803492290535204249312692949', '119.357802665336109250577168341', '119.778891748799794225996730090133', '120.384552030355901062593425198291', '120.86371321766912468001683559425', '121.66363795318823634906906268872', '122.23304526331098263043884644554', '122.75404544369352983855744032263', '123.27668521488743531089635645600', '123.86635664950290576901702836825', '124.477207701843338234932604063692', '124.786354779439064715320956309795', '125.443373279306897727542897731439', '126.102587309182360916269592129954', '126.455777602325383891219622280547', '127.210930384813871690444323160739', '127.514686687775317627898584905197', '128.102539258136875365782363337862', '129.32049815780190713561304389504', '129.59446202093094598161289346662', '129.89552065887680293816590363412', '130.22039461571063835590443096957', '131.043643524581951360860069977119', '131.46169589977718465150992168062', '131.959296457885498508968721426255', '132.712131635935648154445666899372', '133.29945109577349131227354452146', '134.079797211656132835120730121153', '134.2680939130423512386293215845', '134.92024011223137923571096830131', '135.38909903110913575564872377104', '136.15805144525321860715637362560', '136.561315445898000170369199032758', '137.06753414500399988791880511650', '137.68900473710104411910911508938', '138.01603182973100764907985881397', '138.59289380984652613423519630371', '139.47733647759607146872236341991', '140.02763719271528325014823306111', '140.50969097524913184594263486377', '140.905908818078998313208585576061', '141.662524448718740869185342626450', '142.13647509398134919103053855378', '142.65503323912668138667046711780', '142.96318386184976657635665111738', '143.40101105297196381520333659474', '144.45004421809017450722917250782', '144.729735716965241464255064404584', '145.58902456169026429936894294919', '146.2328684382679531379993848181', '146.38699315669557599314920459667', '146.840623850764573896620775783251', '147.58733199766882361634890755242', '148.0383649241448017575746204377', '148.7748590561532834396564205682', '149.3113539030920235923359594306', '149.50331944925692925203057112336', '150.24294956831812279720739911940', '150.79797612463001658338374974122', '151.586027222740455890816978083356', '151.982758664566202320423159317130', '152.66205058779234498089132960503', '153.20263862980095020726406027992', '153.59661359911253606024816607333', '153.994554975209857887078499254642', '154.30309204287864483029835692247', '155.32311477048863638912938594038', '155.75714271094492062475730003565', '156.33354936560717126635092098453', '157.04791959214902995439575739012', '157.37248292471906212272078738490', '158.14372348944641102064522902547', '158.5473973371189540556059638499', '158.914007390972405849909902802016', '159.695870456390578676939590245243', '159.85063595171746666954829882001', '160.746480407883229398836608063564', '161.278579373357129924962315578319', '161.60460421480113873910436645728', '162.44473918795854845659315238413', '162.80890250494168034106652924103', '163.4576794050987777493507128961', '164.19818775230111915379368920434', '164.45231988209784633263039686800', '164.952512141586275561612322054769', '165.74785174257078125500320718296', '165.98764883969910063090078356776', '166.48046060390750144145452634647', '166.8244232910332463900519440693', '168.01664932561547327128946594122', '168.57662797630647086989893934113', '168.92655510050902705496079743165', '169.36432922793844810426233082488', '169.91422284772891003387617921908', '170.20318223051688093108368148553', '171.09064039645375822889707471994', '171.59584417741507574348314276892', '172.0306351979015958300347202178', '172.46878419974022228509218500916', '173.0733950034468374650108175763', '173.904774308735232364275364018903', '174.286324501806078023598540976941', '174.64253693350704108998780045016', '175.699987686925732517558473367699', '175.81252903259902373463258666914', '176.45340753867634453891133843510', '176.750816782765396913768606407176', '177.481703494115337751321182154181', '177.86810815098977451582295194078', '178.5393597901961405113531672679', '178.96803493735758769325947540743', '179.87494238697007869837981361612', '180.27411603671847107851083450321', '180.80164889908088572416934494323', '181.48194110395884452294225084603', '181.65445696998264499009980753224', '182.25220748753157726910508001449', '182.71250114975031952101180725305', '183.32768728486938350987411769450', '183.93011521490561273837058977684', '184.63078462140903015909092975668', '185.12174078355374437547797842223', '185.49151119379123647324071451252', '186.03915869390016126315746671389', '186.70353156744380587529217915447', '187.370172561223360128612874323664', '187.72910887456671490522498428777', '188.291640162559844444416390838', '188.74359586393944503505940578454', '189.11741650677377722378448984163', '189.638057551709862919059870240984', '190.42162415947796780759437089632', '191.02049787979279042775830003510', '191.81448864019712561659870826190', '192.05676808642493516805019155561', '192.43298459048046008334603163470', '193.24654186526480339208884744789', '193.47555318869357193810851747229', '194.02477147118490486482887855629', '194.56899849010321128775406117053', '195.33740162269438120072051033458', '195.74580382104476177675787351055', '196.09312350683480704269245804846', '196.95765236720749577797704538191', '197.63609842349068238396616944051', '197.948766177004664422283176490285', '198.367477555242780338050165202349', '198.7500051914545757079823655857', '199.67789752718897740958398346021'], 'prelabel': '1-4024-4024.421-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.68737743662057, 'root_angle': -0.0731792640171974, 'root_number': '0.973689315905089991121267719889-0.227879608768046350717064632878*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(502)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.17945927829524069812547391578+0.0593271126420493943544121406601*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.67159929966', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.58339007722', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.45605303405', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 18.68737743662057, 'bad_primes': [2, 503], 'central_character': '4024.421', 'conductor': 4024, 'conductor_radical': 1006, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4024/421'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-4024-4024.421-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-4024-4024.421-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.68737743662057, 'root_angle': -0.0365896320085987, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.67159929966', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_4024.421', 'Lhash_array': ['dirichlet_L_4024.421'], 'label': '1-4024-4024.421-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4024/421'}