Formats: - HTML - YAML - JSON - 2026-09-11T19:01:11.451131
  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_231.53', 'a10': [-0.5, -0.8660254037844386], 'a2': [-0.9135454576426009, 0.4067366430758002], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.6691306063588582, -0.7431448254773942], 'a5': [0.10452846326765347, 0.9945218953682733], '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': '231.53', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 231, 'conductor_radical': 231, 'conjugate': 'dirichlet_L_231.170', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 0, 'a^26', 'a^7', 0, 0, 'a^9', 0, 'a^20', 0, 0, 'a^18', 0, 0, 'a^22', 'a^17', 0, 'a^4', 'a^3', 0, 0, 'a^25', 0, 'a^14', 'a^1', 0, 0, 'a^21', 0, 'a^8', 'a^5', 0, 'a^0', 0, 0, 'a^16', 'a^17', 0, 'a^16', 'a^9', 0, 'a^0', 0, 0, 'a^8', 'a^19', 0, 0, 'a^27', 0, 'a^14', 'a^23', 0, 0, 0, 0, 'a^4', 'a^11', 0, 'a^22', 'a^21', 0, 'a^18', 'a^25', 0, 'a^20', 'a^13', 0, 0, 'a^27', 0, 'a^26', 'a^29', 0, 'a^0', 0, 0, 'a^28', 'a^29', 0, 'a^22', 'a^27', 0, 'a^24', 'a^13', 0, 0, 'a^25', 0, 0, 'a^21', 0, 'a^2', 'a^11', 0, 'a^18', 0, 0, 'a^10'], 'euler_factors': [[1, 'a^13'], [0], [1, 'a^7'], [0], [0], [1, 'a^18'], [1, 'a^17'], [1, 'a^4'], [1, 'a^25'], [1, 'a^21'], [1, 'a^8'], [1, 'a^16'], [1, 'a^9'], [1, 'a^0'], [1, 'a^19'], [1, 'a^23'], [1, 'a^11'], [1, 'a^22'], [1, 'a^20'], [1, 'a^27'], [1, 'a^26'], [1, 'a^28'], [1, 'a^27'], [1, 'a^25'], [1, 'a^18'], [1, 'a^23']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-231-231.53-r1-0-0', 'leading_term': '0.322083094077373730894920719816-0.295182862872863670621847615529*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/231/53', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 14}, 'plot_values': [0.4368872188840896, -0.2816919230105108, -1.101399697639535, -1.772889102881017, -2.001497849923988, -1.577704024135042, -0.5450846040859149, 0.7117530727533959, 1.557431314961268, 1.3826867749494514, -0.044695022910044034, -2.350968226554887, -4.624014748184268, -5.808255025297338, -5.2558540675113345, -3.1266239188472396, -0.36772037924660284, 1.7696157461081616, 2.424566713387751, 1.6113568525850217, 0.16882250988730085, -0.8167933087135106, -0.7438606308494939, 0.12230729728223184, 0.8977236171776728, 0.7889398301649623, -0.263636466873629, -1.5127751608494235, -1.985114949267268, -1.277398532298789, 0.07773089755958121, 1.014066698546321, 0.8196608806209431, -0.21458840788586397, -0.9775985142933656, -0.4848060353346781, 1.1562834323027478, 2.6176941810604495, 2.2943601109723417, -0.3476952430300503, -4.117941685844945, -6.7786908949626605, -6.634257430292292, -3.81543030499433, -0.20826081176278485, 1.9632811103424157, 1.78401250068808, 0.1981238849184762, -0.9546311826395795, -0.5596256342345246, 0.8954466384749132, 1.9080778467775439, 1.4227112536807391, -0.19319700691902997, -1.5415688608329468, -1.546081502048968, -0.45347861548238366, 0.4792821996476629, 0.29059563669292476, -0.6984675449172143, -1.2335078445016665, -0.49769590990491874, 0.8908852054283284, 1.362142174162345, 0.00563933540458706, -2.2647018501857397, -3.2827243366762295, -1.5887265437110658, 2.0250783604022087, 4.959240753598154, 5.004890540077667, 2.3338345547154318, -0.604326744411683, -1.2562011396763388, 0.7755862217239244, 3.481524244445124, 4.398754156007197, 2.8736295523547244, 0.4937154664649498, -0.6151229576057924, 0.15167787371872532, 1.4956558220997695, 1.7589412182393096, 0.6741859253760627, -0.5168258892197723, -0.6006910629293152, 0.18133473687029814, 0.43015329272742475, -0.7169639390628705, -2.4252247413793815, -2.936836893859791, -1.5320676506561521, 0.5007112192736541, 1.1076791416513094, -0.27651880646777544, -1.9296580433666226, -1.5574106002300776, 1.133286615325243, 3.7705316963586935, 3.4883871910703186, -0.13295653965123008, -4.391103399596853, -5.875820656323985, -3.631787337912094, 0.07761077608747992, 2.102588437106042, 1.3823219719685973, -0.42882132334845713, -1.0892115352050773, -0.1747899986578186, 0.8055183197494067, 0.46615826648096115, -0.7436704784717122, -1.1462144663995166, 0.04513755838875672, 1.6692943111643932, 1.9217623622744262, 0.4924507550092672, -1.0301627735457517, -1.0337886212934175, 0.1685227981462919, 0.7123902696462144, -0.44378493754524373, -1.9709367959673891, -1.5073805156769804, 1.410325110598522, 4.2214289926550475, 3.6511521787462042, -0.7757391402700828, -5.852881055384344, -7.6156657848788445, -5.120636588778692, -1.13539117989558, 0.8894638884679351, 0.21658078277602205, -0.9899957007509427, -0.5650528674913036, 1.161306873233402, 2.035519196553724, 0.8660073155396444, -1.1154357470049068, -1.791790182197419, -0.7070888488417049, 0.5077345044532146, 0.267465085692665, -0.999778923479534, -1.5114620320411407, -0.5331190764951577, 0.6056250089153992, 0.2904142272799531, -1.0163038435986433, -1.000682250302852, 1.6339057801125816, 5.079901446858169, 5.968538872843425, 3.1332019507591355, -0.7351531299525565, -1.7299617866537613, 1.0867190145177466, 4.668198709431049, 5.344326295221216, 2.776301331421045, 0.07184165742536851, 0.09541045831589853, 2.3365790234158044, 3.8411216246497104, 2.825272909891254, 0.5776022143050806, -0.4126423752738005, 0.47364095857413796, 1.5239178675721745, 1.1573427179044609, -0.044598931209770855, -0.34075438720632434, 0.6063837101457955, 1.138404966703648, -0.12859436966490997, -2.1774956427243457, -2.6054870746114895, -0.703686443892047, 1.3869826929882807, 1.2096146439389808, -0.7874751275535289, -1.545091784773208, 0.8130469484492906, 4.260275273869309, 4.831528177876246, 1.252617807915772, -3.251667124627943, -4.313961123823393, -1.1648260651252131, 2.707873044620731, 3.6061312808488877, 1.5149568179390267, -0.5452540152033063, -0.45165139766875717, 0.8052398818414263, 1.0337774000995834, -0.03900804967949367, -0.5979082707942387, 0.49776832380501634, 1.950249671678586, 1.7141264403388732, -0.16593693086885716, -1.489971151098485, -0.7956242271597023, 0.6767641901736502, 0.6862187364732916, -0.86687084354138, -1.7060202674057137, -0.4029761966390437, 1.2270692757243196, 0.13237855969788784, -3.7300912562939827, -6.444820459241532, -4.2731296404297945, 1.801886263270567, 6.726726854412869, 6.7135647616014715, 3.0581411225777497, 0.10038037984153841, 0.09453496771619596, 1.2343742919117164, 0.7679316333785955, -1.241952730381802, -2.312009337240975, -1.148044807537211, 0.5782938335039535, 0.5716628396962207, -0.9819085036655545, -1.7918330245165819, -0.6813876203547171, 0.8611084721212543, 0.8895614864825991, -0.23085485210580214, -0.47195978150478646, 0.6839758453399548, 1.1852098570166996, -0.6870949697356943, -3.323456907686007, -3.2094965843552146, 0.5178847151931182, 4.305708666948625, 4.028363430604572, -0.0002403835721043242, -3.191913078049736, -2.0607315161556015, 1.765069605429963, 3.799062897121544, 2.228085114046186, -0.24548843686714075, -0.2578666249632078, 1.9315802642938522, 3.1603969849319564, 1.7191145857280734, -0.5985298273890567, -1.194498208879296, -0.09701723816421609, 0.5261990990322413, -0.28173946486332474, -1.0019495652415218, -0.16821467844982332, 1.182867317880259, 0.9050230694627506, -0.9231905130325765, -1.69463551907326, 0.18268095693361447, 2.7658893859873195, 2.935774611012811, 0.7372617587049249, -0.36121722857466904, 1.8999806702504183, 5.102254434550653, 4.825586467744786, 0.38550071082603926, -3.8399623921702464, -3.504174938063926, 0.5206579901352206, 3.385804264127594, 2.1999746931570687, -0.9201428154351428, -2.1490648499641773, -0.7843791022120159, 0.639746823712404, 0.3891531311136829, -0.26035575509660436, 0.5484125633115919, 2.1501370695944946, 2.2498532885912157, 0.41933161735948365, -1.0786498939002844, -0.48476509158166053, 0.877426338366946, 0.5096821246578815, -1.5361804505807455, -2.6134885519027056, -1.371193149945804, 0.0876918576278293, -0.7280794227296012, -2.5258187536254333, -1.2508167989496173, 4.342287275490106, 9.978370097507991, 10.260708282110551, 5.040806181503045, -0.3569930288756004, -1.4053662871612829, 0.8119494453094391, 2.001579372905031, 0.49726705389097237, -1.254452849016454, -0.8453839362472058, 0.6386661092629242, 0.5616562095075337, -1.1845265820342838, -2.032665956160573, -0.5770992807700515, 1.357495597594458, 1.4034865059569719, 0.028072914795532283, -0.38123625855276766, 0.7741148074205487, 1.4882770805617713, 0.5108986106223413, -0.32869729884109833, 1.2436490400290179, 3.971006448503517, 4.001946995047708, 0.21677871997289264, -3.399450912922919, -2.315497892931781, 2.6315979847361906, 5.963749201143509, 4.300005173701113, 0.35261016029612124, -0.9464156457439392, 1.1980525088887193, 3.024732520769543, 1.7775840432139747, -0.6885435880537387, -0.9309350575801886, 1.1663476967116289, 2.5302441485388876, 1.4350190891722308, -0.323752953292488, -0.44945305585826034, 0.5100711468101035, 0.44762266931913774, -0.6970440978479319, -0.7961007030810624, 0.866744996521445, 1.984574000970483, 0.48833756521049887, -2.0504797427849666, -2.334010186180354, -0.2221497059294285, 0.6602717631539358, -1.9648012349952593, -5.31765999136196, -4.979843355067716, -1.1274490515479532, 1.214308067122518, -1.287875876129859, -5.687372409786526, -6.456102752141199, -2.538228965599141, 1.6337520012944518, 2.125410521599857, 0.10376878179982243, -0.7409909984870728, 0.47344145822763184, 1.3447015560738564, 0.45232517621706336, -0.5016798001721986, 0.30929035308717523, 1.730213768700808, 1.3907313612899619, -0.437376263196756, -1.041152811439316, 0.590110387040305, 2.0542696893491468, 1.088403293760598, -0.9376457536141862, -1.0935749448678, 0.44600615114265374, 0.4711730020383944, -2.0305122463474894, -3.2931025571311823, 0.4928986753038856, 7.21141100577988, 10.37593853100707, 6.906035484305762, 0.9207580313927283, -1.5372119272692806, 0.28637282281986015, 2.093801851767653, 1.0296644333351257, -0.9590264777433894, -0.9185841724158089, 0.5469152201690571, 0.6538616369713302, -0.9272524686328133, -1.5361403965382865, 0.2397725161228331, 2.2625290512733502, 2.0264362751712786, 0.33105562657169985, -0.20804471479971975, 0.6696324356440717, 0.6699262347337833, -0.9949921805547878, -1.9532601388944646, -0.4895743490259312, 1.0275822035338522, -0.8881949412606203, -5.175109531520028, -6.549661554608337, -2.3980173222223358, 3.154640427560694, 4.167750856076272, 0.43980022789107265, -2.5950249697122105, -1.3043972809084838, 1.7724984966863297, 2.26045349361692, 0.21326632710072285, -0.5942820783981735, 1.3700759072869015, 3.2602409888584476, 2.320615304698141, -0.13476294345641252, -1.0273411211588777, -0.10485341055489786, 0.2583707869328078, -0.7515754170539999, -1.1631474799491144, 0.1822334875728118, 1.3063274133259541, 0.14961120009964257, -1.7676770901862828, -1.3198285694048715, 1.191983979575977, 1.9350822486282768, -0.7704817484849477, -3.3916477473869193, -1.936795896127094, 2.0056410947222276, 3.077915155844868, -0.2552297714617125, -3.2067779749273178, -1.1638775044775946, 3.8732381459979415, 5.979473305976441, 3.1794491549744515, -0.5219276241662469, -1.1690119609743708, 0.1840679972997686, 0.20078155438679096, -1.3817655469266157, -1.9373678164613501, -0.5908341325191222, 0.4542767862699657, -0.21611928907027309, -0.7760369473242902, 0.7328280327325263, 2.818344561121228, 2.541763600128355, 0.16596461391556527, -1.042864262701756, 0.1772120179196024, 1.1750615156456041, -0.13954562870212833, -1.4757681369185152, 0.4241391119385279, 3.9044477033268925, 3.573116132050253, -2.070799601998213, -7.479594552431047, -6.6890217943307455, -0.9885356789560518, 2.973236750654733, 1.8372018847207503, -1.0736988984514881, -1.4983777667078588, -0.023706921161085373, 0.07283685577497861, -1.5185956083187118, -1.9796223142100766, -0.3172786563011286, 0.9048035550917038, -0.2398413308048141, -1.8600891355984948, -1.2397024734020157, 0.8649772764774006, 1.5252177154848858, 0.3110100818473876, -0.3344149754106837, 0.4457138553935686, 0.2223047196141224, -2.4369815425249595, -4.6642619596566455, -3.1475063132563728, 0.14395580039999184, -0.24648193621038184, -5.443856704287423, -9.738294005733149, -7.804297567114635, -1.810135782815578, 1.6531148334135257, 0.32848660697545157, -1.6736922567450356, -0.7197250608593755, 1.2638916511286769, 0.5668245155997326, -2.225850426522552, -3.2371962230153546, -1.297500592497931, 0.5811655295840817, 0.11750575368893589, -1.03320269422499, -0.5396808464426206, 0.6852138055286063, 0.33718287029608973, -1.0804298931599572, -1.0226805781328523, 0.5399373220551293, 0.6615851373047741, -1.612096700047931, -2.9415818517512866, -0.5523724339563125, 2.94260528877499, 2.8565059997075175, -0.4704807662525241, -1.752199303168165, 1.4305604702451606, 4.64121741688583, 2.795022097714997, -2.334501959106553, -4.428087608478326, -1.3998559783945081, 2.1227879569276222, 1.7528546945415733, -0.8970481637194896, -1.6094524237495194, 0.00012739686448961704, 0.7852706055894322, -0.409020880392309, -1.2612841822168819, -0.35561367058049376, 0.3843677514262914, -0.7360344280370091, -1.9044571121286331, -0.6564559338597639, 1.7482712555682958, 1.9547930871108763, -0.15395558419940816, -1.1808905572662252, 0.25714662274715716, 1.218977505840273, -0.4834349843632564, -1.957760619466747, 0.6049554453974608, 5.095329403070063, 5.1591122574868225, -0.8907392265667428, -6.882478426470777, -6.599307731398023, -1.7298428714137855, 1.1631627829159767, -0.29015288864429506, -2.258885381396881, -1.4675061357571515, 0.32982412176239606, 0.2735115260427455, -0.6726398058687302, 0.20214482236680997, 2.336179779875075, 2.589621670833614, 0.4471912272655083, -1.030010317867538, -0.10523328145232529, 1.0239974845594455, 0.14689633957534362, -1.2365375594012673, -0.7358611243505395, 0.44577521220595534, -0.6025136181664604, -2.9824967348021425, -2.5115344650539315, 1.399313972703556, 3.4121362871868817, -0.5495371744026669, -6.682614377605589, -7.713963038663749, -2.621183917553532, 2.314824498049332, 2.413778155547463, 0.24866369345259556, 0.4299547382059397, 2.4116430990039097, 2.204150095050057, -0.6800764459669904, -2.4039567044206973, -0.9345467027778445, 1.0501949840340867, 0.7920549553902098, -0.3520739803721402, 0.22251106791673936, 1.7732455129115, 1.6817328298777579, 0.13083868237701057, -0.3060213725605533, 0.5185145421353451, -0.2616132211677418, -3.289848466468911, -4.82434927432192, -2.222623180970113, 1.316784714890972, 1.0794819329058396, -1.796130030224767, -1.694645289005921, 2.76565067168, 6.049404134293496, 3.6665155626522337, -1.0841893437228527, -1.8797968018824665, 1.5594776472865681, 3.6393273597419973, 1.4612691019999662, -1.4556576267756243, -1.1997529610691622, 0.8884673386643598, 1.2901739697187016, 0.08403016285939884, 0.01156563879616974, 1.3107652720126677, 1.486615124364402, 0.0828241376704327, -0.22867508477775378, 1.6156370044346353, 2.765443307385721], 'positive_zeros': ['0.19960962580671951909943482260', '2.008992430897901770855667795948', '3.11791584111105591624108779264', '5.044259095681924673293839235188', '6.289297271546192513051170910747', '7.148932021836784461416204881742', '8.0612467804752794826328142822', '9.35684220105135727641542835233', '10.25319363731647162956061893605', '11.04560632082371158929278570508', '12.15620345582993108875650333366', '13.77071177106562279184263281940', '14.72544886971802117511900282147', '15.44358003212809786222521799702', '16.528022287396710381076276859243', '17.62067473193999337790671030323', '18.22789554413205056697000199184', '19.17444409529250791972699002814', '20.000830027155229009255347713832', '21.08374346438566490459358991990', '22.42088323554692001446560374839', '23.03480404750903245548902744150', '24.460284572457607724045013141459', '24.96447627069582794938972767945', '26.09194936690289687906948251337', '26.80578219707601197686541914749', '27.34891825466307931226832757232', '28.66302662908022873350546217496', '29.32981216179734858029206822016', '30.19957606789254094934188537586', '31.24088178423726627367008918448', '32.492685283383941953115337848631', '33.35688952116603478949686320221', '34.10551492185344663865784823015', '34.81226925016700390578540036518', '35.6168246435174977518048713408', '36.64732580718029154816892002601', '37.45778984360510813648760373925', '38.04086248559496832765006358711', '38.93185947944625905355182484635', '39.955324107957553184740312085775', '41.370618009152735793615278358315', '41.92172473051461159975840303380', '42.61150840514559818123269668880', '43.56862772817751284583938950220', '44.52721650358912794431738282108', '45.073943044180979954583492581527', '46.0580916101059507725160191435', '46.63625414024829462890960198666', '47.34052015954263917069518926687', '48.679879210585118136188022362404', '49.28411685698264708882297170277', '50.63987121089460779654237172611', '50.916828332296024173956162318178', '52.295781514684990775164116332964', '52.69527318273249829231455601170', '53.73633432250183183329354165633', '54.202917406509824961021560440449', '54.97995602917782465329572476804', '56.02550326563630607311889063138', '56.75804488011453716399490255622', '57.424232101889999715665914169829', '58.51690191016710047918392348956', '59.459125232239142785125647330467', '60.51186986692628730805622295278', '61.05171100876466418371336902176', '61.864665596386189671481503452243', '62.3995611778523164397641853636', '63.41214053423625142024994038393', '64.218453413591360269116458249881', '64.84193251328257207623449765041', '65.686833194736484872549882368044', '66.264079690537639949177588386038', '67.413903084540086622319335380202', '68.773016777600731398396789151846', '69.03430623368516267715716172666', '69.81702066470191409264292272985', '70.81266426949025866249722749525', '71.37972918457870106888158604129', '72.30856646563659959576635003310', '73.058871813676730394842010401469', '73.5891514030192886337918140063', '74.29406562032532018802204183440', '75.27716653044726485980739433006', '76.249983294995388027902994905581', '77.04702111397844026364631400518', '78.081657435987831852531482425582', '78.4855483560664890244147104987', '79.59424155692006642711283317799', '80.3376489448968659764342802660', '80.859057783727355317537908977973', '81.59747564601475815080436469159', '82.35174006792367355638640665375', '83.10446061558725673386570078584', '84.17777325973473629307515243753', '84.47219309178341866060595629920', '85.64780470922361249884214590488', '86.52521245068234505193001613366', '87.40261999756233625976291081795', '88.26172236526466830071991570896', '88.8911303229687279751426390264', '89.24259851462513093037616884776', '90.37545195839050348040547209087', '91.03692048060480740951139478205', '91.65235066434744689347806972081', '92.77185340916581497109686098654', '92.96677864844578001700116623378', '93.83917311312658885015459723421', '95.2830467936638560271560932840', '95.83604368417262772688013220095', '96.63278822301558637616248333146', '97.35430438491495493182375088701', '97.928098270212588045035670078722', '98.83099777732077464819938643671', '99.694568315685272062475629672418', '100.13262834455120561530047167264', '101.05908932397356188123744570392', '101.37951520422780542193333651235', '102.514568893997573845969092802066', '103.282675613708457133960925650810', '104.41088169137604415039254292125', '104.86005285534683832596065795970', '105.83634973284438594907149679954', '106.40774142158843192331477427788', '107.425266847369211074332499350080', '107.95807516696221033707520392907', '108.567061416474317302461333976613', '109.23477327824180089226304924180', '110.05698206291292763069001501112', '110.970174835318606434518041862713', '111.37326742518039271313574580468', '112.59497766919339636244563187824', '113.02323444937049397260406145653', '114.22897017562838865067550894857', '115.017001724535811744717546320062', '115.528971510320097255846030968021', '116.35633907194225658874522625792', '116.808458142672542687376254331975', '117.73711404566227645712910364623', '118.349223195804656730280836804985', '119.21869813742064022632812530291', '119.908936709407589547898507474637', '120.39128765103946601361376743170', '121.22449258772751828059569457584', '122.56395827761218693146434638022', '123.09116595060714642506836195958', '123.89410473920016755182300796136', '124.56694458907943147763687412951', '125.145029941468427537952741363515', '125.90678242772429690213915722713', '126.957191455659254957175412304118', '127.28473717450189208758680573600', '127.95937922687798281067360263453', '128.8205131930495029075493984510', '129.29281775537751107965369005447', '130.43522374187745694963975523828', '131.28151095003497633574567456473', '131.99991171847050927204893292587', '132.846165718729758880202974674020', '133.258623293971465133908679775', '134.355098829345523692442880119557', '135.032616311962144370953337455261', '135.42071268561901751014461277388', '136.21743954169921569562747794136', '136.89696990485729042167335797577', '137.669099426144607092666169426943', '138.36891140946887984469506765526', '139.21462678637202370366712605638', '139.981209477044502822770913394395', '140.700670032272908418778971441260', '141.81639125013964531348093804526', '142.45297047021721160017086496441', '142.862551967828953350707910871897', '143.87209990495814027579835190901', '144.31319423620328940521725029337', '144.89320718420699482511951623089', '145.96010179659298309524765279018', '146.53039298967111033257122138339', '147.1658168875899954050621259459', '147.77286908388990772750990270539', '148.65375164113141450555596179636', '149.741374084398309657733829307814', '150.495277145069300776281586107385', '151.25612112147413083345023005633', '151.582305779870832737291720096326', '152.55086053354024867148850798409', '153.08573524829930838311225594819', '153.93157899193151493861681001073', '154.76537026418771903574153356787', '155.16240699846809710889953485130', '155.664821415579461697458337745733', '156.85608371715578392566083239968', '157.1622933996488366071940019169', '158.54920945439921465648026622577', '159.1016037737897407476548278640', '159.78529100202142459363095712339', '160.38225162095462366422726561586', '161.42591607294391037403400054210', '161.90206144282307838053066463744', '162.621719026956134759183617753359', '163.19993928623004656890879024988', '163.95510973653736425615247321942', '164.48947923627342475591888405081', '165.356962288502446004254921794055', '166.20654331179925654016408613616', '166.7677192210398913678301164920', '167.67056209372130939175594133574', '168.53942581851477462317372425613', '169.26488446337027777691128798241', '169.99997703755849578939222691211', '170.54180027244766587308155886521', '171.33981835418453895748072665364', '171.7244573925070076290552242675', '172.58121477398692363130308744091', '173.41576896430373465260434896561', '174.02012964224690266442375918540', '174.624474720162295098918661298178', '175.26848541533417040306331481009', '176.21245965417887202028918772507', '177.31536182955329911798790472782', '177.77690029557987409180297798403', '178.673976142549078416121848729634', '179.14034838074032279484095327855', '179.65390001674752576930763055831', '180.68568442856270183480854210645', '181.27054079777692656102417575897', '181.902444500297649970632936122775', '182.66005071095761279436051108039', '183.03123855986975146290434974380', '183.96043941763703822281327715218', '184.65974793051198662874668477560', '185.76257001297593637643018812856', '186.63240824209161117674990665984', '186.7668882673101300238338652693', '187.74469674996905466011018399216', '188.559297097763211668213703075328', '189.250477016747320077161538254518', '189.63800794786883658248451651690', '190.65650812677531850180148081104', '191.05956158559153787865851848071', '191.52275861094433317185787055094', '192.67346455647095936439032455810', '193.244528495444790598179215422197', '193.89071719530675352729927786800', '194.91706940388629956864618385064', '195.50064530173242583463225230599', '196.3824735805914683568342651687', '197.04928355734934906528960268592', '197.83970755140665331349450089759', '198.12106287213034326604810121445', '199.08212534913216617320031881480', '199.434310370128560499938501636911'], 'prelabel': '1-231-231.53-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.82439762755838, 'root_angle': -0.23613693992991316, 'root_number': '0.0869940718978521926874687970396-0.996208829239447828834795186639*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.23613693993', 'prec': 37}, 'spectral_label': 'r1-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.593836572478050423799863826020+0.108338442166722508938476551865*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.199609625807', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.0089924309', 'prec': 37}, 'z3': {'__RealLiteral__': 0, 'data': '3.11791584111', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 24.82439762755838, 'bad_primes': [3, 7, 11], 'central_character': '231.53', 'conductor': 231, 'conductor_radical': 231, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/231/53'], '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': '1-231-231.53-r1-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-231-231.53-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.82439762755838, 'root_angle': -0.23613693992991316, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.199609625807', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_231.53', 'Lhash_array': ['dirichlet_L_231.53'], 'factors': ['1-231-231.53-r1-0-0'], 'label': '1-231-231.53-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/231/53'}