Formats: - HTML - YAML - JSON - 2026-07-18T18:39:12.516057
  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_231.74', 'a10': [0.5, 0.8660254037844386], 'a2': [0.6691306063588582, 0.7431448254773942], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.10452846326765347, 0.9945218953682733], 'a5': [0.9781476007338057, 0.20791169081775934], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.8090169943749475, 0.5877852522924731], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 1.0727594900246897, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [11, [1]]], 'bad_primes': [3, 7, 11], 'central_character': '231.74', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 231, 'conductor_radical': 231, 'conjugate': 'dirichlet_L_231.128', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 0, 'a^8', 'a^1', 0, 0, 'a^12', 0, 'a^5', 0, 0, 'a^9', 0, 0, 'a^16', 'a^26', 0, 'a^7', 'a^9', 0, 0, 'a^25', 0, 'a^2', 'a^13', 0, 0, 'a^18', 0, 'a^14', 'a^20', 0, 'a^0', 0, 0, 'a^28', 'a^11', 0, 'a^13', 'a^12', 0, 'a^15', 0, 0, 'a^29', 'a^7', 0, 0, 'a^6', 0, 'a^17', 'a^29', 0, 0, 0, 0, 'a^22', 'a^23', 0, 'a^1', 'a^18', 0, 'a^24', 'a^10', 0, 'a^20', 'a^4', 0, 0, 'a^21', 0, 'a^23', 'a^2', 0, 'a^15', 0, 0, 'a^19', 'a^17', 0, 'a^16', 'a^6', 0, 'a^27', 'a^19', 0, 0, 'a^25', 0, 0, 'a^3', 0, 'a^11', 'a^8', 0, 'a^24', 0, 0, 'a^10'], 'euler_factors': [[1, 'a^4'], [0], [1, 'a^1'], [0], [0], [1, 'a^9'], [1, 'a^26'], [1, 'a^7'], [1, 'a^25'], [1, 'a^18'], [1, 'a^14'], [1, 'a^28'], [1, 'a^12'], [1, 'a^15'], [1, 'a^7'], [1, 'a^29'], [1, 'a^23'], [1, 'a^1'], [1, 'a^20'], [1, 'a^21'], [1, 'a^23'], [1, 'a^19'], [1, 'a^6'], [1, 'a^25'], [1, 'a^24'], [1, 'a^14']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-231-231.74-r0-0-0', 'leading_term': '1.24067969820252346234390581764+1.38647611482291887392378828767*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/231/74', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.8605381292804402, 2.4746003169082895, 3.350645741253298, 3.8967502980916193, 3.674687188408708, 2.5722077981502807, 0.864893769790571, -0.8569960138288178, -1.9239047051371325, -1.908112019453002, -0.870605345568715, 0.6248684804111317, 1.780484665977345, 1.9967721976283683, 1.2231484158068178, -0.005102085558945289, -0.8998513864340787, -0.935387735191546, -0.20784665704027866, 0.628979562091927, 0.8424887678707356, 0.19604603131811094, -0.8112931614383531, -1.2675741246914043, -0.5499923378862407, 1.1039670673451594, 2.636431136409301, 2.881330827882016, 1.4790473959133568, -0.7081490401190467, -2.0823516479816564, -1.4364595796937811, 1.0819298104177744, 3.9368460789824784, 5.2161805333731435, 3.9959687032724664, 1.0348570734667868, -1.761246707928751, -2.726354352762172, -1.6140303671746417, 0.34210276693862535, 1.5054028376327369, 1.1465128098231128, -0.09408166495885358, -0.9346272405529659, -0.6819998094473555, 0.15485259288136088, 0.4149567044835138, -0.5297180989628669, -2.0882839217625984, -2.9513464854630738, -2.343474019992888, -0.8338884991654375, 0.13137930985681487, -0.38975746983145343, -1.8439732854459587, -2.6136219178077864, -1.5892248377874016, 0.5612943694329888, 1.7293356406650913, 0.18134400479311147, -3.7179693346011926, -7.511595253215409, -8.535585947993761, -6.102854089745479, -2.0539673844216435, 0.8289965594207859, 1.1219710353370929, -0.2799983909859523, -1.3138925133200607, -0.8080443091729298, 0.5418160138393715, 1.1260987642407712, 0.22193104179537057, -1.2353393132008383, -1.667869633898597, -0.5462229707008118, 1.0487452027959177, 1.5899116235186421, 0.7427398134405008, -0.3017341145939167, -0.18998136813896488, 1.0105264282541149, 1.8040076984410027, 0.9709180727392055, -0.8152923544127357, -1.347280391921799, 0.900257556380841, 4.894268420093311, 7.590870232107649, 6.624858611456316, 2.59207616527685, -1.3874917740124237, -2.499908896464197, -0.7287049486508418, 1.4051317572172208, 1.49975333591436, -0.41335806543465325, -2.1815710798858015, -1.9694492631235585, -0.15954656431414238, 1.2352363536902684, 0.8519119641533266, -0.6184143179336393, -1.3792029748765318, -0.6320701372594113, 0.6078120239991088, 0.8689706940433364, 0.08499438597810045, -0.30381484028277794, 0.8106700474633836, 2.6132012896362244, 3.0547850524261744, 1.2253162810918303, -1.3094416794642603, -1.9656779586052655, -0.00663151577121499, 2.3760650162032637, 2.2005013817761396, -1.0669627860335769, -4.6971496323887045, -5.358801828567424, -2.535186513021252, 0.9345795298667485, 1.777916965802817, -0.4459535183495188, -3.1614997544799386, -3.6867896854188915, -1.9444316314586159, -0.11621316103947983, 0.06410791487589902, -0.870154334215708, -1.154121605205849, -0.18335062902537647, 0.7472658456705196, 0.20814984244183507, -1.38360995445884, -2.1288671275783098, -0.9884630171492272, 0.8068348856225934, 1.1473250505501529, -0.35297912373141166, -1.7770931533141194, -1.2445001946297118, 0.5760365085319951, 0.9940970879835798, -1.4464779450102339, -4.748760233693511, -5.168219812041064, -1.2644350178713233, 4.198869362367265, 6.8124247896217405, 4.882841998014262, 0.887893237722156, -1.4203736795894704, -0.8804434406999617, 0.4817280646380816, 0.3883855526832559, -0.9686827491378318, -1.559007204148643, -0.37756302953348825, 1.2026116590737639, 1.2298174840892728, -0.282360980402499, -1.3614562275341284, -0.6081987402216843, 1.0263010054975148, 1.5219806531402125, 0.45895539860164886, -0.4528973383319719, 0.2335338011247381, 1.513457945429409, 1.0312259694825547, -1.631973675038832, -3.699497147494876, -2.029089146520968, 2.9939324169916124, 7.251194707503015, 7.031882429818314, 2.9712978290916663, -0.7373905794517245, -0.9593476847359302, 1.2482093667746774, 2.41908350968276, 0.9587577178510736, -1.2483832075288965, -1.5455846528193518, 0.12121870035981078, 1.3420058974311728, 0.4507450851640948, -1.4361660790429907, -2.0456668101498714, -0.9148465094791627, 0.22204155450926769, -0.02587422255809712, -0.8059271193252671, -0.3835036733234163, 1.1340713549885832, 1.6027760811557152, -0.284299329210418, -2.8478841445335505, -3.1827050997433965, -0.9222396126727429, 0.8815868408043109, -0.687746507449819, -4.600250523118688, -6.710959785750866, -4.557113246488571, -0.3864514012390137, 1.3706987932827062, -0.7707753449919188, -3.773417704476936, -3.8365180080132513, -0.7997352531931148, 2.0546470240438848, 2.1779202430475113, 0.527922005855988, -0.24039479945834835, 0.6391179552968593, 1.4377350836202438, 0.7426155781749764, -0.45240415515058113, -0.2663264139968152, 1.1992655769154124, 1.808302994304501, 0.3663315155634579, -1.514764532618042, -1.4381579093867753, 0.4719771845884681, 1.587980865992979, 0.349476795309737, -1.3997036066749007, -0.7679329329675512, 1.9656619216778175, 3.015825730089251, -0.35659022295929577, -5.9355253936402965, -8.488142197405038, -5.576217164302771, -0.28060184380829833, 2.4261637808410574, 1.1497466937227108, -1.1361402525610145, -1.383162415030945, -0.038399473471108406, 0.3780920028819676, -0.8472512663513183, -1.736751920983133, -0.6639980974256886, 1.1991684148957265, 1.506908677948584, 0.06755926224627169, -0.8797174462156141, 0.15869728565968433, 1.815829767693575, 1.8366148142356078, 0.32012821629583543, -0.49849560140610694, 0.2513149881757905, 0.38986739862451136, -2.325728868218067, -6.365881790116796, -7.384418462492817, -3.480506603742778, 1.8576996277554576, 3.347916882554756, -0.0363800633746924, -4.027332761248739, -4.291772529012441, -1.3252935117159648, 0.905630141670499, 0.3140820219078329, -1.0693615980152158, -0.47019409011203617, 1.6635784233189437, 2.4712744576223624, 0.7929980750112668, -1.2804744805748445, -1.3976963124528154, -0.05742540972421056, 0.48626278438679066, -0.3244219623204675, -0.6828298357645418, 0.5733579843035146, 1.9061406595923307, 1.271038020683938, -0.5283469969316152, -0.5112331966277174, 2.224780272660969, 4.638089796529406, 3.4390213597622457, -0.2634320540239489, -1.875637032165595, 0.894950093012697, 4.8765310171894285, 5.282256256986665, 1.73662417348719, -1.3485352912504185, -0.47416042693360966, 2.6729642878933744, 3.764131378058402, 1.4718054029037084, -1.2689089677358383, -1.5456533012592548, -0.09088292123688795, 0.4360744232187471, -0.5300977094026402, -1.0203510777117089, 0.08645333081982491, 1.2078003493110923, 0.5451638879224082, -0.9436830974091133, -0.769242759827673, 1.3005207314374418, 2.5936229123734553, 1.3012159339110572, -0.7293066160665549, -0.5048377149148765, 1.6572248398063185, 2.323108148679422, -0.007181482748820105, -2.0623470546061835, 0.2633206296987335, 6.040968123245685, 9.598748250419296, 7.1457978809660965, 1.3248330080609743, -2.1492013409868242, -1.25445662500327, 0.8288314928452493, 0.7196672811028625, -0.9067763013466152, -1.2101740572034303, 0.2885934243903882, 1.2583360764918983, 0.39357289616264945, -0.530978854522386, 0.5363436206755634, 2.6246404404997046, 3.0223860873578845, 1.260402898032017, -0.2063470574183526, 0.32830484133534293, 1.359470408790425, 0.7238278735062394, -0.7216905763053899, -0.19845729387434619, 2.3393196029886814, 3.0985005125279, -0.5966768999432608, -5.827052464586674, -6.874040353661573, -2.3152591303119205, 2.9175631711611527, 3.4955895944056286, -0.04727447194020118, -2.7619596914515587, -1.981769112361408, -0.10397111294719552, -0.3156478625982694, -1.9358034334599628, -1.8831717638302163, 0.4399171351796507, 2.218938930247202, 1.381828801084467, -0.523619389746369, -0.8553568289291874, 0.26215335832709147, 0.558895326227539, -0.5286067792380127, -0.9515051058593902, 0.4721714555186598, 1.80032909373366, 0.8490407300078131, -0.9985829714976799, -0.29883593318274365, 3.1968723149873615, 5.330009761722389, 2.9121393995919425, -1.5147465023165831, -2.6030735507716245, 0.7319754975351929, 3.8008905032172744, 2.430672394055021, -1.5302731398037241, -2.96379913527114, -0.45294594506071384, 2.1790028112130657, 1.4502135095661175, -1.2475522236477683, -2.2081127573197152, -0.7306426905759513, 0.5185613897452607, -0.06171180275862137, -0.8475190337651796, -0.07143286632489468, 1.1211070005351673, 0.5702402935558715, -1.1754282053408314, -1.4594560198275865, 0.24327530276227582, 1.1515753102974533, -0.6997628375585607, -3.1883783703023, -3.004383438346319, -0.6777092132015774, 0.04545028917657417, -1.9489133717477853, -2.768709221125721, 1.172658752945412, 7.32905070954515, 9.371268754414222, 5.134980908262984, -0.5640537670453598, -2.0990078999731847, 0.2585570253052538, 1.8564108594251918, 0.455130676110171, -1.4342236052870918, -1.1041190324548675, 0.3941418990109002, 0.5341952064644236, -0.4108663481138161, 0.018176465652746544, 2.1776683732686135, 3.3918916619166732, 1.9882490594076043, -0.051256225600629646, -0.07114936864706455, 1.276813137234986, 1.3342034331925423, -0.05794445646285076, -0.18779515664137242, 1.8650026651051597, 2.9993979419553334, 0.5751070344729228, -2.7183672693454928, -1.5946244608964346, 4.382275696650957, 9.196759900214596, 7.614259583115873, 1.7065408746603516, -2.1592941417880493, -1.4838142817489357, 0.2312022534225709, -0.5268840836957537, -2.4309630664820157, -2.215227107398279, -0.09823748221640524, 0.6572972282287526, -1.0769231944639601, -2.6220057440407984, -1.7193828806005216, 0.13514225400049723, 0.3065053567454473, -0.8518854318887785, -0.9354160710874168, 0.2901916885481687, 0.47968102252619604, -1.107893206372284, -1.8474592187912682, 0.1556774748167287, 2.394111391251406, 1.1686279836808477, -2.46181913221482, -3.2691498635827028, 0.9314951722088654, 5.689935774336324, 5.640860305582021, 1.738727069841048, -0.3015442687511061, 1.9077375560260257, 4.405731944140895, 2.9461153256356893, -0.9710767603396686, -2.6287828002748763, -0.8731649180367991, 0.8880963691609685, 0.21696015253246373, -1.1019823708048195, -0.5511453272377427, 1.0305377421866864, 1.1734459783804916, 0.010575860073599907, -0.12246834034967338, 1.0629109212636834, 1.0094027832512764, -1.374206899171355, -3.3219458331797074, -2.117336358466741, 0.5604669404684146, 1.013102135242547, -0.6690966304908676, -0.5935442610348847, 2.5723286304814144, 4.650302436013053, 1.715684246841057, -3.499870610089096, -4.484804500433868, 0.3222833446097504, 5.293301549365242, 5.110623123021105, 1.380017916161072, -0.5553100726225569, 0.8089685311882999, 2.1244371922620076, 1.062761365842931, -0.519724146122856, -0.3681501294315678, 0.3224341633664934, -0.7509951023514729, -2.720340705863035, -2.6560657940537675, -0.3409381440577095, 1.1822991986536455, 0.3370928708243892, -0.6277678074436746, 0.4769228483242798, 2.045431308711033, 1.4162931105457872, -0.3005467398552401, 0.3457083106901573, 3.06948267391446, 3.058448843434058, -2.0349658698177326, -7.410588092731409, -6.614851163445715, -0.19099224150680386, 4.834023727125207, 4.060797458117794, 0.6413418204033947, -0.276067134890276, 1.3055018775436336, 1.644829216939994, -0.16176674230545465, -1.0159710167682074, 0.7613848446563132, 2.5864977169010284, 1.7775723238064594, -0.2530154385046314, -0.4635663338161685, 0.9705725175101299, 1.312038506026407, 0.011175717058201244, -0.5206297365790047, 0.6928998699816786, 1.2937543868525978, -0.2565047291758545, -1.4300147987323486, 0.573394274526805, 3.549778297703647, 2.615103299904315, -2.345060748960458, -5.507700101513905, -2.9457699033283284, 1.701634490881641, 2.3284108761510707, -1.0633578966070494, -2.8358050972494158, -0.21849764931700588, 2.9432588816800855, 2.3277483889885633, -0.5975714102787293, -1.3849109459562028, 0.5702270293323582, 1.7589297965572417, 0.4583209289614497, -0.9336114489729657, -0.29386503693375743, 0.8581947464612885, 0.3877450894251932, -0.6382252939590027, -0.020828253718296455, 1.2640076479343847, 0.27311553648582276, -2.747856669155395, -4.02263621651357, -1.9607397878206696, 0.1811630953453225, -0.509809756143178, -1.6222337493562917, 0.8778095192374968, 5.5598005032695985, 6.587149533336226, 2.2646462965290257, -1.7623252265686606, -0.11793010999002741, 4.750461013747592, 6.146620513154858, 2.4277891405025143, -1.4664084382247669, -1.6056625748888227, 0.09587030194281822, 0.18794968046639646, -0.8098154208748056, -0.25526663185500964, 1.5254040028967641, 1.781048014180109, 0.2710681912013886, -0.12280758723395686, 1.6992919127990185, 2.9783871781939504, 1.5460765902191556, -0.5710143712069233, -0.5287223608738671, 0.5881940012228317, -0.20928798691182277, -2.289572347847847, -2.059139376878803, 0.5596637178350788, 0.6885384513164908, -4.221300856161717, -9.188869980394319, -7.607837854489821, -0.5214688911653568, 4.3950536137734515, 2.9476653802976025, -0.8779321860818642, -1.676268795398612, 0.026402221031383646, 0.2930915422150792, -1.227953592883383, -1.2286456850333844, 1.1853152762869317, 2.799184205912614, 1.5689305616052633, -0.15735829258246986, 0.2963345497209125, 1.6087104088244275, 1.0215416271086049, -0.8489612106588162, -1.2009932846970148, 0.0028262483673013603, 0.1058858893050623, -1.1401411493079374, -0.5980219544953731, 2.6120594700973387, 4.271282283711947, 0.9635564132949728, -3.873921071467875, -4.033057822182206], 'positive_zeros': ['2.02450197437646375074369272883', '3.307948901432682373895222878743', '4.686158922256562551811754382791', '5.69526376866671191141668839495', '6.62388215982485614679165754917', '7.6163575200365609633813295076', '8.96021582283089553193192301809', '9.88359906886309342932759579131', '11.35238803732416967734348884811', '12.4426755545876669234395763335', '13.41415131765983395970060212219', '14.3137935400715314082872017737', '14.869796975816974025777506539541', '16.477617131901837995678623284997', '16.748960544654047642156377654981', '18.04366841409730850087844986723', '18.76845433632275825870182128237', '20.504808459827914063110956226099', '21.19462844896241537773790244593', '22.06142199522793226404520485397', '22.8590976157139211013077995168', '23.85108063166763496907856317528', '24.88542155690948262384648798769', '25.375728913380576041034976246864', '26.41850668265302839205660210376', '27.100273967998003517780321589789', '28.62280928679061544418471320291', '29.46707425449604382603775380249', '30.25554874438385545735340870158', '31.27567518420673894731961334378', '32.05944657469133832301816399563', '32.960800833474628365978316360157', '33.781172138711773536304118400583', '34.19999032562799973126751787839', '35.45403308695494492022696519406', '36.25076224565645117775518241030', '37.10374089862618872639844654992', '38.33864041249977707667232823862', '39.01573954884534722561216518590', '40.34846165901330242263610084034', '40.6535456199097126570517683428', '41.60815353245405780105847207233', '42.233872273214841638575574599928', '43.28595151987724893611811395310', '44.00381662480125915732251769626', '44.8988577292569808042645672661', '45.47941762811259910050937196020', '46.633246180305232007223286654910', '47.89494704758477403366725416993', '48.62007371594635117091964066591', '49.16410052792961091806955625561', '50.065961495250298907221737750235', '50.885772812655554593944153504368', '51.6767752833646686443391533824', '52.61242665151167300649804188717', '53.06807732703612289603462164262', '53.89018333474312763963951437895', '54.82756410331086654578177151480', '56.16408220593165812050692330029', '56.71186619692745303047017214040', '57.6235059327287645191513371626', '58.41776227988318281139925079072', '59.13711750737410887598618684596', '60.21835770895000270514498587883', '60.61510408943681502065820004742', '61.336996958406248543735417508680', '62.15440238002974068595866279346', '63.23946495008027380811503112472', '63.67734976100604665298571588360', '65.03502997470492304073358875157', '65.54893309827450782469714638789', '66.63339688983162732571216983249', '67.62552504356026586744703745437', '67.946228892720667487434441152638', '68.92393779654824155038459815225', '69.442723080282511190650585391051', '70.36571331000439732371856934981', '71.17899603800381195078195838889', '71.92758776428678945045628685407', '72.5979867369986869594874732988', '73.41598416769209164883990206142', '74.70665913215737104067838271298', '75.45373608376159081665254360290', '76.25964551378063471733749792981', '76.6908652787442341891586468479', '77.60470883728035434949310135966', '78.450537028886680214098349302612', '79.03399406291819316021191585233', '80.06938314525501985936057885527', '80.54748360653121426923694667764', '81.01542989676047930506928714456', '82.37921767292548284603711701635', '83.122546441289708345936175566364', '84.203928894684329725278627392690', '84.74795326480533520239548776198', '85.38780817513162444085225696094', '86.35318131597806999552653227967', '87.201813001525461876895891037821', '87.71101998400904487920862065909', '88.32891176855172240575512738824', '89.27399997394709698828341334330', '89.76831335674514554836534850376', '90.91413410606549999725916180706', '91.49381244560432164370011421203', '92.63916811384113534974167336035', '93.176210472093616479895841417937', '94.20912025185712643612705699859', '95.02144932919334351486421125277', '95.48151757545681725093309230688', '96.23234593274112025765635573564', '96.98148322641966712184813741525', '97.633365561754004405752565413734', '98.61666563273467837087402317898', '99.1458052254050954481234642051', '99.999261119365591150726989634621', '100.607282155681003480233024563085', '101.956719292467594982669471912792', '102.66738736348993701581936949151', '103.265340305046997437008458336571', '104.01019314876101272889247372577', '104.779655914601558565583550744', '105.21913882315184679598329591415', '106.4803744816174309166754615238', '106.78333920442265860025614600483', '107.64076661171593641117650236339', '108.15540534907961498723623150864', '109.02727980441784853019037523758', '110.120766811205596922623374128198', '110.933798174956541355975663783485', '111.90824369653432289676017844003', '112.09923395192061167023584916929', '113.07343566585816097186765339669', '113.96425370976013445370184805345', '114.61671201837431400911066581651', '115.18008310707116620575495556376', '115.85816019980087271562436722132', '116.68980706163945912653908528525', '117.22220654423415145770679145375', '118.32145369207870947220011796455', '119.00823587224418201570925785593', '119.87678695731652927538805969416', '120.66648107366230665359710029081', '121.416919534453381533765674206997', '122.3209546127322991813748210353', '122.79523476120583587278195343666', '123.45325215908915921107650973355', '124.16599481733098587577416448039', '124.96064590663091133704985270735', '125.54311079028455671549968476723', '126.6908154181995903857079645696', '126.889166221178636819659871325717', '127.74842261583571989122628869780', '129.02306539778127324935738983530', '129.65871856811930257007330540044', '130.37396634853854664964066590717', '131.15641772636518693044927976662', '131.73205037930472604270958679883', '132.18384378646609063682944792274', '133.42528358106285015579336675468', '133.7695695382169600243573903014', '134.673305425183284086267883783263', '135.043015630836205391095740096731', '135.98445607613447049209816039698', '136.66308818362833621848537038141', '137.91164341834452876236927305954', '138.67928057810407376705891991576', '138.96268612275126679273934971264', '140.015887964095060532747456909481', '140.46739615031882330028368134199', '141.531856991443878494016852882240', '141.966338091605180237502050784239', '142.73924973302430867200682737184', '143.24288285935914102870124353474', '144.04542850686087410757451325857', '144.79135765027386075212416485325', '145.57226032014576796281704869568', '146.7462526993158648005959102399', '146.9689778871174865133937563409', '148.04414012782432308563902328940', '148.866581214888330496355136044717', '149.41770907692486154058620443568', '150.10466004427409006144459463679', '150.940820177876440896925713189933', '151.29217068030139504074072922589', '152.03211028598218122280477751742', '153.049028052880806333588177989210', '153.630409256432882554269847757', '154.14123001131452608461601397020', '155.09878347243596326721769235130', '155.9210789412201815723423936087', '157.02250091022094959872355535940', '157.369664135099569900752980128671', '158.30687291979643072852972391118', '158.87294536845200976667573617882', '159.23175053128690284428997938701', '160.35674657070906894282429766202', '161.00998264445708001208857423799', '161.478183601760331745537990700921', '162.42647883442145834656019786308', '162.75885988527793609262581631857', '163.64899129398658198692488475651', '164.69604135456283513560985714390', '165.71411764876080805250997053119', '166.01169548865140105657628350955', '166.84950318544393679916318536101', '167.39978919021784868169004550227', '168.38883408787160069472406149882', '168.86285399009173530096702596693', '169.69005899951102972457477661513', '170.16441054308950988148199618517', '170.8983446992990032119367310214', '171.506045549326829744238497346880', '172.364252247104306512587484148126', '173.3093346677069313409390209483', '173.97426295000701025390616899125', '174.70503716786458679947242561379', '175.55581769040268373682932070230', '176.17225860038251106415836661681', '176.950530279567141517665261061109', '177.56459189103729916690069710563', '178.2219677382668111150202127808', '178.75449423614774240884329317360', '179.40789409145901373259081290635', '180.57298974106722671742177184273', '180.8320950977033386786244917256', '181.49567594240449116732708227641', '182.63804856657503820537038472473', '183.13340600139821353000998334123', '184.22887038517313786520701221002', '184.976912741708251106331643829670', '185.370568035723181081661351436915', '185.985070682311326123373891693012', '186.93961500279484836608731918999', '187.22364343448678327746738403722', '188.330351909375568501599480724693', '188.879458959964474891964875455959', '189.34008978715843863254839289019', '190.24409915794119442990012313992', '190.69209603527674727325345426269', '191.89748021888854269717575130449', '192.72861429656755403235465657945', '193.43211673556696441931640904394', '193.82236310517491793887043908588', '194.55216590319922349879877727512', '195.57554580464112009675236063921', '195.86467513584260048791474141138', '196.72803713171782160692566857787', '197.49917302521203394675366730008', '197.84516086534745225890300953209', '198.5102572595027258773113007000', '199.43157048757238836418344622858'], 'prelabel': '1-231-231.74-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0727594900246897, 'root_angle': 0.2676467971722586, 'root_number': '-0.110651047983530594261702300698+0.993859318807318126566946323845*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.267646797172', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.34794929483514942501051424404+0.849844381458222784749603520293*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.02450197438', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.30794890143', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.68615892226', 'prec': 44}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 1.0727594900246897, 'bad_primes': [3, 7, 11], 'central_character': '231.74', 'conductor': 231, 'conductor_radical': 231, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/231/74'], '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': '1-231-231.74-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': '1-231-231.74-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0727594900246897, 'root_angle': 0.2676467971722586, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.02450197438', 'prec': 44}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_231.74', 'Lhash_array': ['dirichlet_L_231.74'], 'factors': ['1-231-231.74-r0-0-0'], 'label': '1-231-231.74-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/231/74'}