-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_529.50', 'a10': [0.05584905608451058, 0.9984392234555237], 'a2': [0.5458534386348967, -0.8378806738017408], 'a3': [-0.7598008035516799, 0.6501559343128551], 'a4': [-0.4040880470609183, -0.9147200939208087], 'a5': [-0.8060875299907577, 0.5917963281344345], 'a6': [0.13001321102201333, 0.9915122616285416], 'a7': [-0.999922905547776, 0.012417043162265879], 'a8': [-0.9869991386338209, -0.16072554350847726], 'a9': [0.15459452215555688, -0.987978002649601], 'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '529.50', 'coeff_info': ['x^253 - 1', '0.999691634078213 + 0.0248321717542501*I', '\\\\zeta_{253}'], 'conductor': 529, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_529.328', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^213', 'a^98', 'a^173', 'a^101', 'a^58', 'a^126', 'a^133', 'a^196', 'a^61', 'a^62', 'a^18', 'a^215', 'a^86', 'a^199', 'a^93', 'a^146', 'a^156', 'a^52', 'a^21', 'a^224', 'a^22', 0, 'a^231', 'a^202', 'a^175', 'a^41', 'a^46', 'a^223', 'a^159', 'a^67', 'a^53', 'a^160', 'a^106', 'a^227', 'a^116', 'a^229', 'a^12', 'a^60', 'a^234', 'a^211', 'a^184', 'a^197', 'a^235', 'a^44', 0, 'a^209', 'a^191', 'a^252', 'a^162', 'a^244', 'a^135', 'a^192', 'a^1', 'a^163', 'a^6', 'a^150', 'a^183', 'a^17', 'a^119', 'a^78', 'a^27', 'a^69', 'a^13', 'a^63', 'a^120', 'a^246', 'a^66', 0, 'a^187', 'a^180', 'a^76', 'a^30', 'a^189', 'a^47', 'a^225', 'a^188', 'a^20', 'a^105', 'a^194', 'a^139', 'a^171', 'a^9', 'a^144', 'a^247', 'a^157', 'a^68', 'a^195', 'a^43', 'a^4', 'a^88', 0, 'a^165', 'a^169', 'a^153', 'a^151', 'a^134', 'a^212', 'a^5', 'a^122'], 'euler_factors': [[1, 'a^213'], [1, 'a^98'], [1, 'a^101'], [1, 'a^126'], [1, 'a^62'], [1, 'a^215'], [1, 'a^146'], [1, 'a^52'], [0], [1, 'a^223'], [1, 'a^67'], [1, 'a^229'], [1, 'a^211'], [1, 'a^197'], [1, 'a^209'], [1, 'a^192'], [1, 'a^17'], [1, 'a^78'], [1, 'a^246'], [1, 'a^180'], [1, 'a^30'], [1, 'a^105'], [1, 'a^9'], [1, 'a^43'], [1, 'a^134'], [1, 'a^130']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-23e2-529.50-r0-0-0', 'leading_term': '0.723653914729703692909160288706-0.381183889640967802993390188660*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/529/50', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.8179096197168986, 0.5993170616801641, -0.0384264527293956, -1.2255622931778027, -2.55088226476445, -3.3171537903378105, -3.004890649630307, -1.670323081944583, 0.004755572453173956, 1.114763316625747, 1.1548892937330482, 0.40673958572978663, -0.26834624009310026, -0.13793582008202193, 0.7395526587568811, 1.5020976774626456, 1.2307913289360823, -0.12780961936084503, -1.5256679425133446, -1.6316658952998349, -0.12167985326653698, 1.721779576633896, 1.8319646973967032, -0.8862246378671739, -5.33175430139637, -8.728897390768013, -8.675764814151925, -5.0814258290322565, -0.29669854729103284, 2.750721792534404, 2.8270123143576713, 1.094946628819867, -0.27856445159031606, -0.18955999355762157, 0.6440980105716687, 0.8234503386546811, -0.04578860488929948, -0.9708832932978282, -0.856148925702441, 0.06602645191212601, 0.3823788334752545, -0.8241659582757029, -2.651681889561659, -3.0712735561674713, -1.0936379932774716, 1.9297416845285036, 3.4736734271384697, 2.407231225419217, 0.19464717644533935, -0.7151597377528508, 0.3378311934596917, 1.385642369284298, 0.02766722770091883, -3.6522362587480908, -6.762832006092198, -6.4612533309922435, -2.9959062875383378, 0.431642323798365, 0.9389029890314323, -1.1538804317562332, -2.9412977901306676, -2.2593500982831998, 0.058384486404457044, 1.4343540599959488, 0.6637739620418194, -0.8095305444857553, -0.8298369407124458, 0.8131309816985257, 2.2403898166519816, 1.8876570495124734, 0.35759730460301936, -0.5546468573338484, -0.24491325919338938, 0.13503415463725044, -0.3099294115631416, -0.46621248597349635, 1.5333555670469599, 5.2818180507716095, 7.365140515587655, 4.646262477950056, -1.7983093528384242, -6.932973356547325, -6.557143821388777, -1.5612154578597919, 3.1470703508160245, 3.8492130006196073, 1.481045818469995, -0.28727550686197223, 0.39373367758908995, 1.8980250733141626, 1.8938031336873395, 0.5303081872261338, -0.07005216503408536, 1.0078049007828698, 2.124467371200402, 1.4072140624958065, -0.5177629571811404, -1.23403471443012, 0.18534217744029122, 1.8134622712374093, 1.401837461954016, -0.5494984818269713, -1.416879299542853, -0.034017916983070384, 1.6569089412634999, 1.281039366058121, -0.5407823524500467, -0.865750508659944, 1.4249377139891477, 3.629408309989608, 2.4640575297735046, -1.4471670702278479, -3.932492148324913, -2.457783770627312, 0.4267079501800851, 0.060711390572968774, -4.456983081391406, -8.908331505981192, -8.852251903653057, -4.634074629244596, -0.46606029221126377, 0.7406917861433076, 0.061547020707747396, -0.024699924910835187, 0.7996293230519051, 1.0103082639524665, 0.23560811523755765, 0.005062856522589216, 1.1275770004442038, 1.9605354803228632, 0.6350456679135642, -1.835196526680672, -2.4763600386933535, -0.531113719978924, 1.0842188206916428, -0.2984125739129313, -2.9102965223070445, -2.3086011555177386, 2.6061488054969706, 7.336877801601053, 6.8488995247106725, 1.7312336033550344, -2.5270166254544915, -2.199405842349636, 0.7106068971096409, 1.9291134864626984, 0.5714614265656439, -0.5835645464764215, 0.22127115101019185, 1.253817834182668, 0.39000120856782894, -1.2444720013237571, -0.7423877449572743, 2.1360341275935677, 4.220669563105942, 3.169523791189006, 0.606872007611877, -0.3266849160519381, 0.6699444374115907, 1.1203370886181332, -0.15807987062353568, -1.3241152421896019, -0.6767737444578834, 0.4506885961523617, -0.08672448406427344, -1.2324725897063735, 0.28830170066268523, 4.495445427862378, 6.309647679130211, 1.338972177343388, -7.715241045913757, -13.087552924273743, -10.60690128666728, -4.077644355747989, -0.010783448297485577, -0.022194324973448108, -0.5911969295830755, 0.7993566731902102, 2.3818623477521816, 1.6378401479062847, -0.5295890412330586, -1.2693981880826444, -0.0956307868830305, 0.7929418071863631, 0.2988771794883379, -0.021735736568814498, 0.9474109815972381, 1.520614191256331, -0.08488368387435208, -2.1194022594221003, -1.1410838736544169, 2.6193888342614002, 4.595902130071566, 1.8636106586988146, -2.4878436098720735, -3.2602905131572624, -0.12906746937320032, 2.2609067956993267, 1.1688503401777792, -0.5041105384534823, 0.987101862471198, 4.227233903791867, 4.519130399530342, 0.875464318226817, -2.3289735641353917, -1.5095776956647502, 1.2815747549150263, 1.7660264349389734, -0.30139850930833195, -1.2884033078339399, 0.5097281572365575, 2.4663774456543934, 1.8941928428752994, -0.030359544248453066, -0.5837248559517472, 0.16245005599877033, 0.011330819390826492, -1.202463838072783, -1.2145169088389962, 0.5418586906452489, 1.4351623390534265, -0.14965508717167897, -1.660647801871895, -0.2334829651003509, 1.8713171334911252, -0.4832011526252058, -7.339003550992286, -11.742745312663654, -8.057708199314355, 0.3918280471913811, 5.174274062802867, 3.0426127795942564, -1.1839708057831477, -2.0820673827549667, -0.16607996861083274, 0.8310150293640272, 0.10507414116355135, -0.14015218452668116, 0.6849867766085046, 0.6867144934350372, -0.5150419933044866, -0.4301058348088729, 2.1008503478920475, 4.1306971075087375, 2.534935692345921, -1.0929125173172156, -2.5031207711131875, -0.895328593402765, 0.4161052218368324, -0.37149868032092986, -0.911499816625694, 0.6262194680401426, 1.5447036415362525, -1.4089096822991856, -5.967457085788771, -6.463318257453016, -1.9494095351628047, 1.9852160271467412, 1.0442558310768633, -1.8080618229532996, -1.2162550326288346, 2.3450216219471702, 3.4901469044450035, 0.3046667497352802, -2.7669721283904813, -1.638587118423545, 1.6732162222460474, 2.6509616344319156, 0.9028999499562946, -0.3000762122057672, 0.3016211537188844, 0.6346881142756341, -0.3770180176495803, -0.9187425554957462, 0.0994093707056508, 0.8196631875235619, -0.09959080567555235, -0.6273117000216333, 0.9890197221644791, 1.854378366638554, -2.08222555662624, -8.763336080967969, -10.970742396941532, -5.9210666252357465, 0.23724733440911, 0.4199200409300594, -4.045544754138703, -6.120381600849912, -3.2725590142004197, -0.023324019742889307, -0.1773341595594521, -1.5713617020627666, -0.8037511320594367, 0.8607639519470485, 0.07317507010206162, -2.53094868879843, -3.2012822811302497, -1.1984989426811934, 0.25384814120352656, -0.43798563632159415, -0.8170163722235798, 0.8347121977706441, 1.9867485760877863, -0.010712122587744047, -3.040061033252608, -3.117126424520503, -0.5583039709979173, 0.7954731243513736, -0.10658751491376692, -0.4078194521423671, 0.9033817284012255, 0.8559679757039865, -1.6018898560546355, -1.915637631601488, 3.5927469153613867, 10.31473528023757, 9.901385537628247, 1.7147613006969342, -5.638898833727601, -5.475662813012182, -0.8958552191328635, 1.179432144728129, -0.35741497213906653, -1.4099150703978867, -0.2773791000702398, 0.6169662971324902, 0.07128491600743941, 0.15350310541551582, 1.8175724577265755, 2.6985756108827568, 1.28376286528566, -0.2399450003377014, 0.10120602216342595, 0.4090027876091565, -1.4389332339291172, -3.020597055175239, -0.6853603852482226, 3.7196564838078823, 4.575875485245671, 1.1358754053918252, -0.8979897911358964, 1.6753014135011053, 4.086187819601911, 0.8625145831035627, -5.296865929939152, -7.137275778546787, -3.326247428508532, 0.4240455990671006, 0.44885330747689867, -0.5020745845176051, 0.4688929666517549, 1.2470965429915075, -0.7270459065269815, -2.886808601259854, -1.245770509225737, 2.7055858749221713, 3.8138535738235877, 1.0513459640767606, -1.385657571205447, -0.9166953949506422, 0.2432695153714037, -0.06303272637348244, -0.4398686205806113, 0.42219787517220836, 0.6706144331703112, -0.8983637594785159, -1.4236307113907256, 1.4096391473226633, 4.0485343726474685, 1.6785935342630927, -3.2352430845660014, -3.1951702477085697, 2.9922549158510754, 7.414064211114197, 4.236829432910236, -1.8448868568473615, -2.8031089815639265, 1.2414892602526517, 3.5308940815325345, 1.386591276366706, -1.0232391579462699, -0.49044284911188507, 0.8079568629333754, 0.34631871577625567, -0.5034323201187962, -0.029182857636386415, 0.24349044558511768, -1.0558275768964829, -1.6188559044734312, 0.6879801381683361, 3.167792546832736, 2.0693246652191477, -0.8653908540837513, -0.7675669732794583, 2.328613744781287, 3.4642406607302827, 1.1623536628726494, -0.07211150854621814, 2.3347690831576062, 4.334532269331137, 2.199462062825487, -0.7558925172799856, 0.3220357834383926, 3.1461817996248183, 1.6098199468770797, -3.844503347698007, -6.1864037235335925, -2.603143712550095, 1.3473169598565273, 0.651769868166202, -2.0117751398260917, -1.7810880467471402, 0.5539864364051307, 1.1190968138392527, 0.010853042528484742, 0.31670336047002823, 1.9384458449519224, 1.8792440408254198, 0.027111577476959088, -0.5950709654441658, 0.5223589159422874, 0.5814110460019308, -0.9368185580301759, -1.0995289588036787, 0.6037403603897005, 0.8094990873298707, -0.5193592027617593, 2.729633458986812, 13.385912865070758, 23.313380266330114, 21.994332911190767, 10.59484994160633, 0.48431888238589865, -1.6224704380576997, 0.11189841400958939, 0.08017318369550955, -0.6950700980419345, 0.6660174168534626, 2.357850537450789, 1.3558389160735844, -0.6931976784740508, -0.47793450927817316, 0.8680924138076291, 0.07819587049478198, -1.8010006266223173, -0.9730696420962697, 2.080481264319409, 2.968113889700253, 0.8114281627743642, -0.4929827223494448, 0.6543325231330038, 1.0444557170949473, -0.8419241939971166, -1.5783480806382695, 0.8242151033657816, 2.6762840473328486, 1.1042823551990948, -0.06167542000445876, 3.4078797348123904, 7.808859252971619, 6.504645514368503, 1.0561229815862725, -0.4895219592337041, 3.757234195721066, 6.588102241634629, 3.2791415209563413, -1.3702051671017053, -1.3838897700780535, 1.310529558981081, 1.3875960086662156, -0.9870611962476388, -1.747603408791457, -0.37702893468513765, 0.22694819541981942, -0.43087308941449975, -0.40476623805890666, 0.030001964254832387, -0.8126697242304151, -1.311809819555283, 1.5307974251720229, 5.574351976377553, 5.261408481240877, 0.7265655617182698, -1.442964371658961, 1.3527866166141305, 3.368791938193991, 0.3470278060950893, -2.89028022982261, -0.45806838927876664, 4.317155632515197, 4.014400595628022, -0.8532711178969683, -2.993908695305235, -0.1488021327634873, 2.34582163310678, 1.183125765397876, -0.48088519394235657, -0.11523183588783396, -0.19886572957212792, -2.2987745155377506, -2.9942429338804812, 0.06884218030684151, 3.1977547684547143, 2.445139137326525, 0.11018520065479964, 0.4095226750973458, 2.2920854181257466, 2.062479327765064, 0.2359706679172212, -0.09071198999383852, 0.546044679885464, -0.4356065597355342, -1.627929063006163, 0.023289010028605568, 1.9377955749037281, -1.256073376443985, -7.269344753661776, -7.057817599298446, 1.3041620937594645, 7.885013107394107, 4.64917132217077, -3.1681592531255935, -5.5728435506953575, -1.9102384703983526, 0.9283523880976978, 0.3038503409935858, -0.3759163411631322, 0.2935801816793239, -0.08927928093515836, -1.6244555934079703, -1.3086250524573013, 0.9109720791358296, 1.540406280462699, -0.03227852407888787, -0.4854301356204979, 0.9359801591092675, 1.0491152299380866, -0.5306511804937172, 0.13814957279159748, 3.5288237682173436, 4.103581429501737, -0.5018259939201539, -4.258013763079876, -2.0095136686304698, 1.8973853576100015, 0.8472784435750822, -3.083352067755306, -3.2075895264787926, 0.21945481453839655, 1.2032123945556505, -1.0323453947543628, -1.3656225432903093, 0.9562219624767839, 0.4299463525414405, -4.460161436340877, -7.475073051172272, -4.471192268649763, 0.17834491900481375, 1.1469840066641115, -0.142189592036649, -0.05876866041271677, 0.5412569886961026, -0.5383518596857252, -1.5696389289533657, -0.27383024111344684, 1.3002922963602521, 0.5747283453932418, -0.45560576015111287, 0.6982524092048579, 1.6395993774002573, -0.03953788427991686, -0.33596494038946456, 5.042518711594921, 11.070470041481805, 9.031336653463994, 0.639984903110653, -3.1943162865408437, 1.3952173214953831, 5.978953680672544, 3.65165313591411, -1.182057961412336, -1.6884493471233988, 0.7544275166570674, 1.1200211755054827, -0.2802061554245092, -0.2206871544369317, 0.6021676765017705, -0.20508309749479273, -1.2363977124164156, -0.2627665133359783, 0.5051247964369139, -1.6269059151240888, -3.6410511980410103, -1.232286299263587, 3.1151811385703114, 3.5428029713974496, 0.3709580404550956, -1.116010255513326, 0.021023259939288552, 0.13303918131475642, -0.8013242240233497, 0.6978653730097581, 3.039892608310068, 0.3202908023727409, -6.535072416586082, -8.645180253599943, -2.673995374034716, 3.3130955549413326, 2.3274179363286995, -1.401911802674297, -0.9911560571242435, 1.7373596682232473, 1.1911900548952463, -1.3922879190746111, -0.8380449848903975, 2.19668102253383, 2.706685420805451, 0.32465716602161065, -0.882294507081306, -0.0807870710791164, 0.011309422419303251, -0.7051181617314509, -0.02079005761924536, 1.1823679139546226, 0.49643898327753355, -0.334227607721504, 1.6330570852806106, 3.3539123343240695, -0.21253093763364972, -5.7268488879160415, -4.544812516533268, 3.0535577148034294, 6.726086987866904, 1.797962622012593, -3.7622745769853396, -2.5107886383781515, 1.643902238172649, 1.8988524400333135, -0.33370369373024183, -0.24044769663307972, 1.0077065258158793], 'positive_zeros': ['0.61202989812684354451527272451', '2.499029581058064269094882785069', '3.594434609022678610832902222993', '4.12638982525795853311505672693', '5.28776701485548070011618796786', '6.26883998986477614966827878656', '7.11283825192758335945285536217', '8.77178773513015725338865220063', '9.90441776810297106732437290632', '10.3882150479349218673131622569', '11.237338763256362241174560460046', '12.1646434144268257979141450241', '12.64577290365345118766501332725', '13.86187366367873848744616751990', '15.03346648845753902203790750486', '15.55443527537925961023299086689', '16.25305217676395678293160364976', '17.75854447608741718774391588102', '18.28995503570615187067338130586', '19.3669746526214145283087104276', '20.128814514280700903187515546804', '20.80355750658674175904066278884', '21.95622753966622245679413050657', '22.63564126252906113642700799460', '22.96577759111522416314230261539', '23.55903067585836053250856802625', '24.91818348680966132222249793904', '26.02412080956300495178054676824', '27.09305426521023157601839215538', '27.41201443914550375458049779411', '28.60075086269182799190200537519', '28.796945444308702220080340002928', '29.91323812296195673524656371167', '30.59586815259912000340208492160', '31.47589812848349636237701513455', '32.192699807755125967038047070428', '33.02922424035549202687761600543', '33.58764730184936629737609709585', '34.578070568956724785684520236250', '35.564729509543491541178049786939', '35.94415929872006116762268669618', '37.55786248887906088683992155541', '38.15481053087384378789342394961', '38.45077127015335809844943437059', '39.48684226684154741126769532712', '39.68442643162093426168923876628', '40.70472140575972818169109340138', '41.63267978783347388817202840250', '42.1515863833205097282397463779', '42.98143719678787855483742233482', '44.16216713367785325941696956401', '44.92194561449730544472021001876', '45.730763191175009051377244607221', '46.19968785294442315700053222137', '46.942345991686620209113830087539', '47.59659298721550361667440755090', '48.85759250796680500763365264255', '49.201120668282525336847140616715', '49.970509682839034519936795858841', '50.78135314368654013297603530398', '51.22952191116649353945642550225', '51.84697933338239620465404473727', '52.86195656171974390101178047065', '54.37698191708373939862228401930', '54.68066068974277807565332384934', '55.17950423418454178838545848914', '56.168662248445752984318678470448', '56.89592690207161183393762486863', '57.64622325622997210114211852496', '57.828810788717279653146661994001', '58.73901474944057246072503324677', '59.48093723027753159008063996010', '60.43661778593638769683583038725', '61.26114833193362378495533900421', '62.047787483069051776171536949956', '62.38094234910869562289735864183', '63.50170764346745645344084923', '64.22477939386360617455844829603', '64.958123377777750538641124124439', '65.5608282820802203924227911322', '66.55644794798431702284260875071', '67.1173269361660919605950466353', '67.503675710479791302217870249451', '68.35107757766715380444566070166', '69.04154181936960217612725403084', '69.714919666972451886526800487877', '70.28268331416963615510302614388', '71.5471862971222405603156516178', '72.39795858485423725696778050932', '73.15201073307910697702210677254', '73.790377773882607670516369692739', '74.132299733028674947669599460901', '74.87080235621776720197577792845', '75.386854255123143527818289735165', '76.4635188748487952323988238937', '77.34019299443641568381763062760', '77.71803743241204016764014050685', '78.338943280113244686809730356231', '78.958563583012006311960067874386', '80.12011278287788691582979160439', '80.72862976164010149027806800482', '81.36444299157924265253842886020', '82.210500553271938979499562496983', '82.96318306879750794013133841347', '83.91962611885722594064330906282', '84.27127422697859580885815815236', '84.903761551504171844865223849767', '85.60154198650630658125655031683', '86.22543352483638544109600784297', '86.72236065652009459168846148294', '87.38325430403145979197126600822', '88.73150657307088993355109874343', '89.10039817211002403255248956501', '90.31690941358138995574266416826', '90.58605646977904104517710512073', '91.37930509304270409476958914395', '91.88501681262229009104103274903', '93.01378016882716538481148249840', '93.31100517031252447965894585890', '93.93524567092046831736171027357', '94.6864717383174756185063301934', '95.699418240429428493240150509641', '96.221669075855988281736862385519', '96.678813659853395236334287529620', '97.31336204915506047807180546989', '97.95838738515016302219092149501', '99.119828448348739103521758529674', '100.07406111880455733509644570889', '100.57059310283689049283757896828', '101.30938131467135271847002007964', '101.91088367507010337866904934453', '102.132162113423201079874978513059', '103.354688288775954732969146928594', '103.71412958018132330862158588227', '104.16979347139582239077657595364', '105.04845809146431353816466769443', '106.040386707390096188613481546567', '106.41127352025118072297555682640', '107.23173076789170672116923233744', '108.379899008240231582786989759087', '108.85732290629685224115329257932', '109.2769586760438595242203270014', '109.91852255515389259777150985984', '110.723959481165564780604726034666', '111.66361495291996896944257169858', '112.40025704316893316989472204995', '112.786597061260963474363380515194', '113.31436871343056882245663181350', '113.90881322120477830372627034155', '114.565397801486264729684985478524', '115.41405315222194038863973526058', '116.11711162945631631468081515039', '117.07918029020492382468397163050', '117.726195355081453707751086028546', '118.580255569587156424107713067861', '119.157308029864875782347304911783', '119.78265143919992514956597785297', '120.32368442326691997497323104683', '120.7134549135316389129375249082', '121.49376730578073868531456855344', '122.394135121138715550308952752583', '122.90213384783840438087202897736', '123.92970226859431525077568616557', '124.08666211096557660722688398888', '125.19992767601676914532051327425', '125.58993504699429241152604106382', '126.35012443221817806960700356986', '127.35943787948980894416269408232', '127.883813479665301990504130763037', '128.67013686235504165564265183953', '129.37924212648697338501196208822', '129.60027500915236159932786215228', '130.62997430024770275383812529568', '131.11802537867474153559716274421', '131.69276971583736581239190022518', '132.392937087397185783383775041', '132.97542546631531137602522204130', '133.26781796820238158876053279529', '135.02598853894231009092363298152', '135.599663088799068382550182579855', '135.96059708930224298850783207355', '136.46095150942777706054656306511', '137.3725693424274886566397173509', '137.90961790886276466765781277904', '138.44971357464775613164086497143', '139.166692559387267083208055348035', '140.11878430771992222199294683601', '140.488444457912613462179712806367', '141.12970901306890325787786239951', '141.78998073488590448162835590978', '142.67468231924952333801038004469', '142.829293276716542421060116824129', '144.14396868686551452291433252402', '144.43331368051687683529438179776', '145.50931026485572500452283861093', '146.09263219650283640000454962644', '146.74821088651840797831102694529', '147.59622617486226238682335646852', '147.94065683345142711333530263950', '148.66732960433052150185535904929', '148.79419570444127488214571434891', '149.56500094621355181979160424907', '150.67855245614853318448882144224', '151.13513161072796406334162732443', '151.89904000315964790650682439665', '152.52825919038057476031573633129', '153.38326315577246150818983426397', '154.07490206051830907212811513139', '154.86788332871258453264178144282', '155.36336998178328502856320876283', '155.56549741836741910368015710709', '156.55721112877997402571895390445', '157.527461611229752711442366728054', '157.72328120641416986674676432018', '158.81011605685328381227870369295', '159.1023089459698284007723929257', '159.60361192404875711179380755676', '160.30988778984653752156357031224', '160.86506223800689895641319197399', '161.83296644045862428214960551426', '162.678599675237660646088375763380', '163.596013806856166149301717646028', '164.13829690889517117434339903930', '164.56364405321397235341511996204', '164.978632639139796381605579417157', '165.81151682743991724002614692813', '166.55618984007819858026736305524', '166.998891447836519006217946572007', '167.70116655658400720815219238502', '168.10783977683125541794203795777', '169.03459519428847287450605676643', '169.82424184135719021211925061687', '170.379556891786845520399874746468', '171.2284853419224774816810531641', '171.74278235094671403060622724921', '172.37265923618285167406163082688', '172.85014627556147864608661703709', '174.04567271202857486931772634699', '174.644668157163360555349130383751', '175.02097326073122340885248145989', '175.51714709941909500206996450166', '176.29085464205333381765919616069', '176.9951415091660790196038614040', '177.369699773493977803935538361342', '178.11916351874572392329096791721', '178.474349993072660977558510367635', '179.7135952087389338533839313151', '180.24435505947929517612402776456', '181.156881454110367086841828286', '181.77330306572514015527558594908', '182.42726811778054311192340592524', '182.88012221889298181516594329353', '183.392968737327512306350770711217', '184.11581646356710698893357902205', '184.49542587626308287864224692452', '185.395358901924370529891150940674', '186.28917504302729164912631334524', '186.869466864852325980171909719215', '187.22756842613816416908791969159', '187.728725458242332599825088164902', '188.45407328100538581749493890088', '189.48551861222530058127245036742', '190.17540525426424145331268222689', '190.730182128875008490741294858734', '191.38322468864203096493662202413', '191.96470874802812918578623578543', '192.85668234231575464862904879056', '193.469213992475992168275759346553', '193.755169350118283938050176370517', '194.37949381792614806535553128873', '195.11101526329729031757688340217', '195.414930814497221008659574970382', '196.23879869541973272962789638914', '197.06877327760858849517225555252', '197.891686674861446577893741868680', '198.611233410719997990710326895568', '199.31656654551364219408033319617', '199.73715856481166590420750626269'], 'prelabel': '1-23e2-529.50-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4566656719613023, 'root_angle': -0.30864409692387007, 'root_number': '0.565601378808232226908726559352-0.824678774002475822652606367009*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.154322048462', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(253)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.767282575082852505334368440913-0.210280741841807709022009330927*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.612029898127', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.49902958106', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.59443460902', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'bad_primes': [23], 'central_character': '529.50', 'conductor': 529, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/529/50'], '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': '1-23e2-529.50-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': '1-23e2-529.50-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4566656719613023, 'root_angle': -0.15432204846193504, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.612029898127', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_529.50', 'Lhash_array': ['dirichlet_L_529.50'], 'label': '1-23e2-529.50-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/529/50'}