Formats: - HTML - YAML - JSON - 2026-09-13T10:52:39.473273
  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_231.167', 'a10': [1.0, 0.0], 'a2': [-0.8090169943749475, -0.5877852522924731], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [-0.8090169943749475, 0.5877852522924731], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 24.82439762755838, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [11, [1]]], 'bad_primes': [3, 7, 11], 'central_character': '231.167', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 231, 'conductor_radical': 231, 'conjugate': 'dirichlet_L_231.83', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^6', 0, 'a^2', 'a^4', 0, 0, 'a^8', 0, 'a^0', 0, 0, 'a^6', 0, 0, 'a^4', 'a^9', 0, 'a^8', 'a^6', 0, 0, 'a^5', 0, 'a^8', 'a^2', 0, 0, 'a^2', 0, 'a^1', 'a^0', 0, 'a^5', 0, 0, 'a^2', 'a^4', 0, 'a^2', 'a^3', 0, 'a^5', 0, 0, 'a^1', 'a^8', 0, 0, 'a^4', 0, 'a^8', 'a^1', 0, 0, 0, 0, 'a^8', 'a^2', 0, 'a^4', 'a^7', 0, 'a^6', 'a^0', 0, 'a^0', 'a^1', 0, 0, 'a^9', 0, 'a^2', 'a^8', 0, 'a^0', 0, 0, 'a^1', 'a^8', 0, 'a^9', 'a^9', 0, 'a^3', 'a^1', 0, 0, 'a^0', 0, 0, 'a^7', 0, 'a^4', 'a^2', 0, 'a^1', 0, 0, 'a^0'], 'euler_factors': [[1, 'a^6'], [0], [1, 'a^4'], [0], [0], [1, 'a^6'], [1, 'a^9'], [1, 'a^8'], [1, 'a^5'], [1, 'a^2'], [1, 'a^1'], [1, 'a^2'], [1, 'a^3'], [1, 'a^5'], [1, 'a^8'], [1, 'a^1'], [1, 'a^2'], [1, 'a^4'], [1, 'a^0'], [1, 'a^9'], [1, 'a^2'], [1, 'a^1'], [1, 'a^9'], [1, 'a^0'], [1, 'a^1'], [1, 'a^1']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-231-231.167-r1-0-0', 'leading_term': '0.825408213259034643346216318539+0.121446405303714667744478898908*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/231/167', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 14}, 'plot_values': [0.834294880648723, 0.8203657932273631, 0.39772787093436573, -0.34920588170291916, -1.195854126806607, -1.8057117967386083, -1.8671807488163317, -1.2839919855119455, -0.30032431342012267, 0.5514157294629727, 0.705651102581994, -0.08411924846571027, -1.500546818799055, -2.7169267506675427, -2.793287021433157, -1.237164236543969, 1.600209856755308, 4.582300975322136, 6.342501057567591, 6.053262214426781, 3.9395202202333324, 1.1767526771149095, -0.8096317485367024, -1.2160838408920158, -0.325029575421011, 0.7674169180992136, 0.9793764769203486, 0.03410843502037033, -1.3713124398416228, -2.1496447093467523, -1.7091152201523723, -0.4374880374400353, 0.6171818591538242, 0.622510654722721, -0.33153657298569705, -1.3133148726176223, -1.3862835994123006, -0.4985566094967312, 0.38438989752572905, 0.1049301266618473, -1.555377393165426, -3.4480886413907865, -3.829732824188544, -1.8077400114472044, 1.733870781253052, 4.603033873012784, 4.910320920958176, 2.5593981924213485, -0.6371037381275746, -2.3732021163258117, -1.6592153086219474, 0.47670486106117393, 1.9700580541997326, 1.5143047326867547, -0.3958781495499921, -2.046191750209357, -2.117121598979236, -0.8279738171641988, 0.410156316551916, 0.4288284534287046, -0.5984750678115314, -1.451544977991598, -1.214091808708329, -0.27694167053488133, 0.06679417248204919, -0.946964957036492, -2.583603995369123, -3.198697139025425, -1.9077241177671893, 0.3390985047611411, 1.4926846025551537, 0.39067896463158136, -1.9290346500492546, -3.0108053423297187, -1.2818424270535864, 2.289417632506572, 4.865583012880122, 4.243753903925419, 0.8777285147608993, -2.5099920746748756, -3.376406170028038, -1.546972736608253, 0.8866199441923497, 1.7283457201783436, 0.6910420245708042, -0.6695653785960818, -0.8335740519063599, 0.08000600104309868, 0.6505760104672927, -0.06312031950737684, -1.352616578917809, -1.6317498179798635, -0.28394544648015757, 1.5265980225264801, 2.0685387668314394, 0.9803711320654127, -0.27299554473287213, -0.04655175059452345, 1.510546855656101, 2.449514952981989, 1.1981656146958826, -1.3777031063636473, -2.440644869016331, 0.014526689976206052, 4.8342513434832375, 8.411950727658187, 7.930259253953009, 3.9575166071818586, -0.20679723359187926, -1.7297193563624407, -0.7074554645358678, 0.49514652268345305, 0.06384892756435366, -1.4313617046285474, -2.0403262613608155, -0.9013931166108173, 0.7323815254479222, 1.0161160101125615, -0.295035478796244, -1.587560730475575, -1.3354511075049469, 0.09909073247840292, 0.9713254788541446, 0.34227684067752945, -0.7434688251345032, -0.609433353491864, 0.7566471478591161, 1.3639172275368898, -0.46806725054093856, -3.7226517774864725, -5.222085687853159, -2.886132615614031, 1.7630479706216373, 4.799046385152089, 3.754956000865839, 0.07360387228911314, -2.507689673591744, -1.8714312223386274, 0.5135913289783222, 1.5723143919433757, 0.1413083554794166, -1.9486135614254676, -2.2372411492288347, -0.5036479009631953, 1.1815748520274028, 1.0597639688126357, -0.316171913998865, -1.0169789740343291, -0.257223105841936, 0.7251561858001727, 0.47140796286676734, -0.6268447593240503, -0.7619144471478353, 0.8080796289012299, 2.4509705872078458, 1.9405552532542663, -0.6798928457610064, -2.7927782270604418, -2.1727047213523965, 0.17775679400621872, 0.9027418678599224, -1.8309639371244852, -5.914598270586601, -7.353884181414343, -4.6529241112956505, -0.5407227501992207, 0.9812774272425193, -1.0789679785776343, -3.911996669594679, -4.294246666909139, -2.064114186037618, 0.21434155443450004, 0.5834185351151825, -0.21504092299514488, -0.22312947312688114, 0.925766323881431, 1.6016896502740727, 0.5676902999304143, -1.147177247668146, -1.4769875572293738, -0.0724854310909277, 1.1161747611377892, 0.339057334173951, -1.5825732575692684, -2.230241601280358, -0.8016616130768524, 0.6555901232692631, -0.1260509514861557, -2.3157520617564336, -2.4264636394930963, 1.529094711192124, 7.075160570007077, 9.393479928169905, 6.423425916040113, 1.1022532001918333, -1.8660008878681937, -0.931441503936995, 1.2988823413023822, 1.7202499616432234, 0.31536576195643057, -0.5200391051620854, 0.47231842692609777, 1.7868021351648564, 1.3841064480473464, -0.4344455543250201, -1.4055118821160115, -0.3502647277750727, 1.2686656844705844, 1.3647644919134732, 0.040002681651399336, -0.6590207358190828, 0.30691135746316384, 1.4472512132565405, 0.9155363802756401, -0.5210837566190117, -0.044549815376705555, 3.3752014670233197, 6.835414081461762, 6.3595593767010765, 1.707724219405071, -2.842194205938871, -3.0816063421638615, 0.48579552543542903, 3.4878988438128125, 2.8981042326470168, 0.24833320746702203, -0.8266270210390267, 0.7306250431100054, 2.42170102945151, 1.784219365643529, -0.4016155769711124, -1.3735863635999008, -0.12692675863545896, 1.4466847773456974, 1.3176573748425757, -0.014696850778693262, -0.5616848234362031, 0.10046934064272293, 0.23691048407437496, -1.2976902787498, -2.9880503532342297, -2.5033430456293164, -0.12523092748638498, 1.1696736205391756, -0.43751530762613466, -2.8475086251460198, -2.4251607736639826, 1.1842920102320573, 4.134214957309333, 2.9521480670059064, -1.005150405165141, -3.001503462316988, -0.6414016450647901, 3.2724924062477525, 4.266443543607442, 1.555055940487645, -1.4251234537508417, -1.5697339473426608, 0.34859706622116704, 1.4031675948728881, 0.6204199160171284, -0.17384601075486433, 0.5314103878086702, 1.6315109204962264, 1.1843143412948902, -0.5042990755655595, -1.1365981675207029, 0.23794379489937253, 1.6614003498565202, 0.9335777625258344, -1.1672229884831542, -1.8229424138176074, -0.17219280924137192, 1.3166362047106417, 0.36571703021192936, -1.4385320422893797, -0.29222997718689, 4.497873223093263, 8.616574376581429, 7.382346294712653, 1.432697103215659, -3.784909783638987, -4.21087368068717, -1.3722246371941713, 0.33076820660089856, -0.7520977079321227, -2.2462604995431112, -1.7734601760362387, -0.25270226289352915, -0.12240389662929409, -1.5226046525892403, -2.0930927030965276, -0.5342200986803344, 1.3883304924097148, 1.336289389218027, -0.27461863071583426, -0.974908208713704, 0.09659496615815458, 1.010324425920379, 0.1322990315704029, -1.1671716046666005, -0.50458176892647, 1.4690227163235965, 1.1554182475956782, -3.0994024158177735, -7.846926337463909, -8.055396484818443, -3.331903339063292, 1.272379209318644, 1.2359094266514472, -2.2121882498385896, -4.179108843941557, -2.4541740456152956, 0.24952836392601185, 0.5992315966086558, -0.8391832383692093, -0.9150519722070048, 1.3276644887484783, 3.3307876141315864, 2.7573526674059115, 0.6794468329352114, -0.23050584638176763, 0.4553366741745225, 0.7310014678040871, -0.38430331133384843, -1.2114953119103495, -0.16511872682576928, 1.3978355006274064, 0.906498319058005, -1.38298020689237, -2.2386357956112577, -0.01967293752728846, 2.4444293061519446, 1.2955175061900883, -2.8851344314951457, -5.31566276606742, -3.16168411521873, 0.572796797947144, 0.8774468106289331, -2.6856464175432175, -5.45677722786372, -3.8259676242025127, 0.2627847988450363, 2.2372989412559416, 0.8475374951380593, -0.9162824706574038, -0.5120353800565166, 0.8924968327401228, 0.8358463006100122, -0.5431723583986747, -1.0137545396090832, -0.007826312948625904, 0.4150324946489402, -1.0715118110712278, -2.6679974356829046, -1.9629336545499632, 0.29449111292857494, 1.0368111180503894, -0.6246841341792988, -1.9780336297759147, -0.7969316803500495, 1.0181274423641962, 0.040486887552348715, -3.1685563863119937, -3.861637693613098, 0.6459641854995989, 6.626666198428249, 7.914941824582131, 3.3870927147282357, -1.852538357801282, -2.976752732700319, -0.8578885497136627, 0.33579952072714647, -0.8103333055226415, -1.7797944720341141, -0.6229622848296045, 1.0843891177503475, 0.9943435216112929, -0.2170304272241395, 0.04249915124010869, 2.0981247761710633, 3.313260958175204, 2.0044962045124515, -0.051657220461804335, -0.3730491993193893, 0.5107887298046873, 0.20855753344535893, -1.3085076002303082, -1.2682266828247653, 1.3693974265680642, 3.3342954676271863, 1.1658543228878318, -3.283251569214563, -4.288549237629037, 0.41562667383279006, 6.240146154503094, 7.250420068561584, 3.386692457775746, -0.1463950263899773, -0.019592849510635377, 1.5320557946448938, 0.9527709185642834, -1.26272715688359, -1.7526962943822928, 0.3570051387921336, 2.1468892839840166, 1.311714814988685, -0.6086975021028268, -0.8676374835945708, 0.3614070511483907, 0.6961306017471927, -0.38140270224159306, -0.7470123447414776, 0.6460260372524338, 1.7151362172400773, 0.5146158882895777, -1.2039082354238573, -0.21285759011545788, 2.986049857846042, 4.077338921093936, 0.9365375876729543, -2.794965889258126, -2.3122442526588696, 1.6333514783875573, 3.549496895872216, 0.7274528255671062, -3.034713817857427, -2.7398265623964058, 1.0176655254431708, 3.2074197102733373, 1.4025211344234634, -1.4013160136792862, -1.6073917406137253, 0.08891414063494771, 0.567849908253281, -0.722793713647532, -1.406009063508498, -0.4005724202187101, 0.36454822871242554, -0.6202522725513022, -1.6872384334353456, -0.6139003904156415, 1.5011092402915436, 1.5743404078110077, -0.6475716023720652, -1.9012985494500294, -0.3120292195743929, 1.6145041059895568, 0.917659671055181, -0.7578675386333367, 0.8261667332594995, 5.711430728665214, 8.382069094777794, 4.772703421519853, -1.8361510397416663, -4.608300913386939, -1.6905665986085001, 2.098874888688295, 2.2267496914696885, -0.058009134844679025, -0.7919526215641488, 0.6263745704630872, 1.3700427770981347, 0.23672247941821184, -0.5723595873548263, 0.5705926808229514, 1.7896098845561386, 0.6588345237072669, -1.7634275664315404, -2.3977717133604415, -0.8393290096690319, 0.20445801074416844, -0.605354241477963, -1.1575081812049377, 0.3055693794458986, 1.75396635628453, 0.404069246452353, -2.153442543328592, -1.3591488281108057, 3.3912878386696885, 6.59587317184186, 3.4962711380368283, -3.187773974464865, -6.381968996827873, -3.5936027610590537, 0.6184688385551053, 1.516090368550664, 0.14726278523062136, 0.3789335387415248, 2.4655207306343154, 3.0034940441080256, 0.6435345011382408, -1.7061601020861243, -1.3832187220801078, 0.17029019929482178, 0.08727817871292523, -1.341461004117418, -1.4939937988388383, 0.06033932961274872, 0.9377215296508506, 0.1372545371301507, -0.1570308742042173, 1.5204838617591316, 2.7552177242154707, 0.6751461978809238, -2.9431217722049587, -3.4435893496141947, -0.19457702399638993, 1.8111376699138502, -1.1267034585500804, -5.795244492955627, -6.32333744094149, -2.4413541091838606, 0.25977135734493717, -1.6027089776552592, -4.636176357153601, -3.9783413266442005, -0.25524533308584557, 1.8738326141598174, 0.672306798189138, -0.8282601991331516, -0.08931078206371032, 1.313260944318124, 0.9312652387209909, -0.40226312155857663, -0.2964115869725753, 0.9083530931418111, 0.7371957299460137, -0.9109280382684979, -1.139504279332299, 1.2010058609507683, 3.129310430231941, 1.8778334622741024, -0.7040053640685553, -1.024677700903247, 0.3340268971886935, -0.6481247567945267, -4.558557275637629, -6.3786469719248515, -2.3817993550506285, 3.714610550980895, 5.018937628446215, 0.633846499883817, -3.338231197886653, -2.257693410843064, 1.3601828582135018, 2.4469408057942745, 0.573937478853844, -0.6914562743682383, 0.05003899663745259, 0.46395578167978846, -0.797823019748975, -1.54264282255997, 0.1404324739153294, 2.3360330316379248, 2.155388725393931, 0.3484301066220906, 0.019306214223345938, 1.5378237636100314, 2.0953470501688782, 0.6439718365944055, -0.16499094275107334, 1.4191895544585846, 2.7881728736110993, 1.1105164122361495, -1.100289213000756, 1.3179034703602812, 8.076991395982867, 12.277479796461595, 9.086236241794502, 2.240645091981535, -1.0494597190321473, 0.5533570124102071, 2.099737279246166, 0.41888962428813176, -1.848947454659266, -1.4559717408806279, 0.13065409199561356, -0.45883840985464985, -2.7734284439160923, -3.3238469333300844, -1.2595892375683053, 0.4459065458844137, -0.06674556659938446, -0.8390908933302719, 0.14233193832545693, 1.400348640818348, 0.6998694699014613, -0.8069472024780099, -0.4900914519959111, 0.7723069353278736, -0.5786875591374445, -4.602686818463904, -6.48706675413517, -3.371769881331934, 0.7284386759971144, 0.21283274565969806, -3.8923156164827555, -5.281929060587754, -1.6058131760805545, 2.1753239849892485, 1.2359811124445004, -2.2322273146748084, -2.806911771345161, 0.040335546765112626, 1.8257084914698285, 0.2993487617534902, -1.5727566459995714, -0.8523015391865549, 0.9496046437728582, 1.0022642626735445, -0.11095128368302715, 0.047757369551586146, 1.164291546365273, 0.7778991620983119, -0.9777467754441086, -1.026963751929469, 1.481087404966784, 3.2085000657973124, 1.744822676399845, -0.36469990517758755, 0.29435580564917074, 2.1505171905139413, 0.9860478161092492, -2.6807763255073773, -3.3172381499695844, 1.2831098805462995, 5.713898702872701, 4.095689380566232, -1.4868172031785816, -3.8559462049838413, -0.6846846622653725, 3.0439679764014373, 2.8500331729495607, 0.5085427431778148, -0.08900492401877742, 0.8739835866346164, 0.6116351752066109, -0.7921243286270978, -0.5775216967456651, 1.549308550571439], 'positive_zeros': ['0.803416004382760950763664799769', '2.5946615251947926900462856872', '3.41525892264444150653483510787', '4.83522698340335651094540639404', '6.72076454440428700906584096983', '7.5835185417127226757894981531', '8.4453397141945716316979554238', '9.79350581143331923280011551061', '10.533945965960857710683978891611', '11.710273560929815962018798311756', '12.2167041405830207659785548685', '13.602728486321286962519560344291', '14.93243693897893770956117801928', '15.87021304527594055670029624497', '16.81628202067758918268392231005', '17.99500969400985870277867398885', '18.58814124957106020757860898637', '19.810814291571356071730752577455', '20.04767254933799703174847989246', '21.51258158369392458903522909819', '22.24363136563980911020891859974', '23.24436736486954494057075961950', '24.44560854257441360040318327609', '25.49880885443033397184123057569', '26.39099673801793031613532260102', '27.16293501577178036983037068728', '27.79650154016801086391845680017', '28.79619745921137448196117665555', '29.906494680818129716579479666999', '30.32523201506916933245940614331', '31.39679533455071193114603200851', '32.186396069804701036051716857985', '33.72981448414710366208061662300', '34.52364961940075124918288570924', '35.01557688271601523104824134524', '36.09646868221015634367340945096', '36.81872668822446203937245786124', '37.79149182022791850944073177061', '38.52565393421215793198947703667', '39.21558444725169816790818115086', '39.94822854545436547040031219308', '41.1337121803687330099708530005', '42.193659540330220264678398785538', '43.05579253780165554059235747058', '43.76957210338090645369600971997', '44.762559630297337441891775982113', '45.55513357597821288214890093748', '46.31716382100378297617123489130', '47.01076998764841003555341832933', '47.68147345020613322946995030400', '48.677559986522290710620113367512', '49.66201475047205199227665074828', '50.14809682467020242241903408192', '51.617474230943777353947505380721', '52.06926014831458088666795338330', '53.395123723294915976252977143964', '53.976276643285518356698177257718', '54.45391833400609940526231706543', '55.410486136356412870977107297', '56.26322480423998233100767263646', '56.93311549214391141299143561677', '57.94779159023719878739915535023', '58.41663015671770159930211870012', '59.282763331219931683933551226385', '60.70288577982347633679869753828', '61.37234291478381154580330612438', '62.255553700781199679801542247', '62.71168047728443598476806336687', '63.67770074592712035325295552437', '64.43609591534960758149669363234', '65.32165279655808923498690038492', '65.86947536925569113317324789557', '66.74767047202811327391188089433', '67.19398112104234390516791290215', '68.53628837976119323554445395917', '69.33816135627677836761168667443', '70.346624057642653710237473662573', '70.82881128021096569572080401270', '71.815846044100390474354888700420', '72.52114465015365763778607052570', '73.43378188898842159210122193528', '74.022684625061858337502922161257', '74.45226014819746976080186496745', '75.64158501013387284505380283680', '76.19635839396604745725642317146', '77.09776761580839334038424900331', '78.04625037731833572315229522903', '78.799349241659874819282710390239', '79.82732152040771484711649998143', '80.5706581647237847558068622236', '81.43634618398260759346677862995', '81.7185332373847730796447729979', '82.71925743037143106985644317778', '83.397823997164279595927529825432', '84.202265044520997600194678717940', '85.025299641932292304198689378', '85.68041427694964619735556944849', '86.27611131916813609640017444422', '87.56927992359124633598307767413', '88.6249451883354745935907237243', '88.91911601196238349101133329321', '90.09006117980968897068605672742', '90.26152477790852736391522317480', '91.32435037871132289091388551305', '92.13488362341064817770907740249', '92.79151178754749350035091340720', '93.463877120124182033362346728936', '94.143032797334883889517922255153', '94.80015020338750543706150400993', '96.13679370226896748538441713036', '96.68806437936598652433942024184', '97.773430052269266680255585279727', '98.26363310975436086934068974142', '98.90332678477425348983187817553', '100.14651674320712093063324648218', '100.46263776688902985220584554106', '101.163680320684569144304481216841', '101.903688454705532516662375480770', '102.632176324639139958370158257679', '103.43947643647112067876057312573', '104.16987822197365061900612960719', '105.25259034811662060185806427660', '105.72461993560740510400520602130', '106.8531468857162914322736211333', '107.62109561125999154001708967819', '108.23181741032623445330530162013', '108.943345264422723510636819651120', '109.68964404266118483284575604492', '110.12812710413252466709458104738', '111.20597003086607560961434974682', '111.78225538027149182767104632562', '112.61379485879762613737470731495', '113.12969897615758468490084794075', '114.03011213771639536062849826963', '115.182653623919694484351444717', '116.07960469058709126116274542813', '116.39401392876312608566169355607', '117.28628552873455785280300008845', '118.05764001874528117090776947999', '118.42800222560215158374485520315', '119.67639200651818406477748278060', '120.132854051056800903792712685301', '120.67345329423404094528026353960', '121.42306171080214433734447511433', '122.26973488585719448830652548709', '123.10468717053317381209242707650', '124.35130947767649369188417928272', '124.69140263956415435040359294294', '125.448226965753453131453768518030', '126.206910534612335900598755463118', '127.07518188203321947391696250525', '127.72354612384757061132966057722', '128.339784990445754337578593561098', '128.945493710455919191634473026927', '129.76406422406071642416690478221', '130.33684961985397770591993621932', '131.31591828820952998341390273079', '132.06517713784274653313895302021', '132.86447808136607435747326420371', '133.67055896635478132970282470085', '134.513836837998705474016726128824', '135.29474408636720362971390335114', '135.785931813218172471439635450870', '136.663687054204730184001165586220', '137.04704268886144270623749031846', '137.898677541485224917440095430582', '138.66787257815677981094519255569', '139.4147685622191423638128933757', '140.14288452560196975574410836490', '140.546684620709015651334007361860', '141.78248258269804830763926609744', '142.61947222696976026730593504953', '143.42870256722328139205195549495', '143.945181695313082736820475257250', '144.73948181316877226139761573956', '145.20274659925929598858730537021', '146.02187495105581221770566969782', '147.05586536655503043589210898274', '147.32873958557545824852274678840', '148.07825843578926123220852003502', '148.79575567602080750705207893776', '149.48145226431763638398311642752', '150.47563630354840862553415493955', '151.503544536903045885763477533879', '152.23927937440069922333931547192', '152.398518677509304284474300944037', '153.50468006503551530535656336391', '154.32985466827638782742728555621', '154.71028909651545604233838643974', '155.61372658367154148049834776826', '156.29338483973029737223192148012', '156.61361130736762465500505142379', '157.556490384666828744908810113104', '158.45429758991391183968614208583', '158.985063150523715421229918437385', '160.23488773156761327019987637172', '160.438912665183544891963802463150', '161.58464966523870442326570314780', '162.292778454110896927646988504638', '162.829721473734338731992324405953', '163.64029436681530690295410581503', '164.14189897780470595860529369555', '164.83398484703849396599801001361', '165.49041200312003299718086461417', '166.46340825467671366953356582855', '167.09588577104177968519065207308', '167.41623202266961813492220240166', '168.55168841250649052355197596809', '169.41193754188000919689291408924', '170.18906197943720965980029226112', '171.027107428219412672118925583835', '171.54810897460648070063849781854', '172.02375668717490534989532794493', '172.79504979803253387365632356062', '173.83987414273213243074804810015', '174.05573626195685503165472445780', '175.14170973118713761045325831014', '175.3796385100202474556860257020', '176.371684971837198188686050609754', '176.78497776002132190748796108686', '178.26877919680494207484022053839', '178.68153762413635213628436833564', '179.42232751946545095451503163987', '180.27266581120228675567879100224', '180.53656057753355582608425331487', '181.74698573202167353095460101835', '182.16951274553592427130301941572', '182.784610356258317686764656877265', '183.56582451937037661067785801673', '184.16660841971991972648265413086', '184.62436032839439878567143582803', '185.860584327080897379689288726661', '186.27009224885263816033990579314', '187.29267253249486321558000197064', '187.922527288971004243109071659579', '188.745987699015532697434380461521', '189.4131973842636530681526723311', '190.13490840626049486345253752822', '190.89714951358697858131101798861', '191.23483132054291962448806558428', '192.01455296272286524102285650154', '192.64997903846535000225595787998', '193.66791042469857768323617996917', '194.01269965528598521575327583308', '194.77607348857408119837706883106', '195.55564244715841636930096747117', '196.477741103080279917089015401383', '197.23418114973920601273150201663', '198.2338071078438647066622733499', '198.47565987550697164809815035037', '199.19558837223533343422823017022', '199.78621019232330381479440949231'], 'prelabel': '1-231-231.167-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.82439762755838, 'root_angle': 0.04650086717177851, 'root_number': '0.957620076587575619739038691519+0.288034353708730036260580978186*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0465008671718', 'prec': 40}, 'spectral_label': 'r1-0', 'st_group': 'mu(10)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.634935711742149488886099250882-0.0627691849220353921874346613717*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.803416004383', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.59466152519', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.41525892264', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 24.82439762755838, 'bad_primes': [3, 7, 11], 'central_character': '231.167', 'conductor': 231, 'conductor_radical': 231, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/231/167'], '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': '1-231-231.167-r1-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-231-231.167-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.82439762755838, 'root_angle': 0.04650086717177851, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.803416004383', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_231.167', 'Lhash_array': ['dirichlet_L_231.167'], 'factors': ['1-231-231.167-r1-0-0'], 'label': '1-231-231.167-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/231/167'}