-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_81.76', 'a10': [0.17364817766693036, 0.984807753012208], 'a2': [0.8936326403234123, -0.44879918020046217], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.5971585917027862, -0.8021231927550437], 'a5': [-0.28680323271109026, 0.9579895123154889], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.39607976603915684, -0.918216106880274], 'a8': [0.17364817766693036, -0.984807753012208], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.37616241858008603, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]]], 'bad_primes': [3], 'central_character': '81.76', 'coeff_info': ['x^27 - 1', '0.973044870579824 + 0.230615870742440*I', '\\\\zeta_{27}'], 'conductor': 81, 'conductor_radical': 3, 'conjugate': 'dirichlet_L_81.16', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^25', 0, 'a^23', 'a^8', 0, 'a^22', 'a^21', 0, 'a^6', 'a^1', 0, 'a^11', 'a^20', 0, 'a^19', 'a^15', 0, 'a^12', 'a^4', 0, 'a^26', 'a^5', 0, 'a^16', 'a^9', 0, 'a^18', 'a^7', 0, 'a^14', 'a^17', 0, 'a^13', 'a^3', 0, 'a^24', 'a^10', 0, 'a^2', 'a^2', 0, 'a^10', 'a^24', 0, 'a^3', 'a^13', 0, 'a^17', 'a^14', 0, 'a^7', 'a^18', 0, 'a^9', 'a^16', 0, 'a^5', 'a^26', 0, 'a^4', 'a^12', 0, 'a^15', 'a^19', 0, 'a^20', 'a^11', 0, 'a^1', 'a^6', 0, 'a^21', 'a^22', 0, 'a^8', 'a^23', 0, 'a^25', 'a^0', 0, 'a^0', 'a^25', 0, 'a^23', 'a^8', 0, 'a^22', 'a^21', 0, 'a^6', 'a^1', 0, 'a^11', 'a^20', 0, 'a^19', 'a^15', 0, 'a^12'], 'euler_factors': [[1, 'a^25'], [0], [1, 'a^8'], [1, 'a^22'], [1, 'a^1'], [1, 'a^11'], [1, 'a^15'], [1, 'a^12'], [1, 'a^5'], [1, 'a^7'], [1, 'a^14'], [1, 'a^24'], [1, 'a^2'], [1, 'a^10'], [1, 'a^13'], [1, 'a^18'], [1, 'a^26'], [1, 'a^4'], [1, 'a^20'], [1, 'a^6'], [1, 'a^21'], [1, 'a^25'], [1, 'a^25'], [1, 'a^21'], [1, 'a^19'], [1, 'a^4']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-3e4-81.76-r0-0-0', 'leading_term': '1.44336925475428366268880507150-0.462797727919013127167941660007*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/81/76', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.515749498610155, 1.6436109765543672, 1.903925098815816, 1.9587002089912087, 1.665354974403814, 1.0338666734572683, 0.19643450876680904, -0.6285803124394134, -1.2007612640943608, -1.342784735320838, -1.0190864463078428, -0.3725299992101116, 0.3076110977855609, 0.6879231850298339, 0.5318606433092592, -0.1783237968392811, -1.2006900810552759, -2.10971910865841, -2.4750257521110277, -2.073875600574726, -1.0377642772482463, 0.15260101154997863, 0.8482132255245438, 0.5270370426407227, -0.9272532769704371, -3.10663975317655, -5.202884496570604, -6.343030238412919, -5.9911154259170765, -4.21941710521997, -1.7001412597413852, 0.5981629544215213, 1.8697397904474569, 1.8534818581541233, 0.9328105610013624, -0.10623965834447165, -0.5300730842150141, -0.07115470764179099, 0.9386517329960684, 1.7956230280476273, 1.8782218683818788, 1.0497135880042534, -0.24649165123863093, -1.2693841839982893, -1.4698949755070954, -0.8709053995416902, -0.07406453101346461, 0.1379009784786834, -0.6374243567920038, -2.070813832148037, -3.2255766339609124, -3.124137319032078, -1.4195054458128076, 1.2705662348170341, 3.624961929308732, 4.360728636426305, 3.0123681661032506, 0.2500961000958882, -2.490221822675918, -3.8547749255074635, -3.367421106918148, -1.6645750318765864, -0.02223838822172726, 0.503781902267864, -0.25410053445228714, -1.5416864321713128, -2.2841247968175513, -1.878915176456243, -0.6092126374898973, 0.6115522872318161, 0.9585011004029713, 0.32720122887337433, -0.6071973378678966, -0.9535208861255209, -0.35471221534339353, 0.6750333014965467, 1.1251036132850505, 0.32049956239006505, -1.4305752175692688, -2.920011715536338, -2.865057758838272, -0.9003114632421083, 2.020526691392412, 4.176702680575139, 4.247137725358829, 2.2635868870631835, -0.3649153030435254, -1.8110317833847756, -1.0977305820851573, 1.2414305585963175, 3.587697019393363, 4.4205890056057955, 3.3717922018906297, 1.3779126851636139, -0.13546704260350867, -0.36269441534233166, 0.35577823718498314, 0.9688432105039303, 0.7014616535031498, -0.25725503852763704, -0.9449202119187525, -0.5204071118256521, 0.9234409636761699, 2.35842023150233, 2.6697757759005514, 1.6434773460729877, 0.21752891395888296, -0.28206437711682647, 0.6768344764637739, 2.2441797005639517, 2.7676235749026414, 1.1497934912579144, -2.1072902793660115, -5.080808953795251, -5.779795583003983, -3.6502668393765134, -0.03817531838502244, 2.782565498688571, 3.2669729023863114, 1.6432721574826157, -0.4466411425229709, -1.356224183817884, -0.7054268031896747, 0.5042046949553465, 0.9362891464587986, 0.1530343495171936, -1.050727526608358, -1.4619182517774716, -0.6269640601632478, 0.7033006703252057, 1.272073573720921, 0.5077087970497468, -0.9120639286809766, -1.6770315804016063, -1.0955710846959037, 0.19550185899383926, 0.7862214109184698, -0.12399529508590207, -1.7790377030687412, -2.313861281683048, -0.3362758803601866, 3.6906671711945522, 7.532234282507172, 8.785190554965657, 6.725123095044519, 2.8563488027615094, -0.30761625353881933, -1.2079224916890796, -0.3051597215280595, 0.5929844810594112, 0.06356860781853467, -1.7009304610686458, -3.205220320209049, -3.1247790612800945, -1.5328866392120102, 0.23264305620377698, 0.8689285253596967, 0.29542030076492387, -0.39775867290361644, -0.14342550860245848, 0.9788253440558072, 1.826411069695808, 1.4220044266947953, 0.0956343615673351, -0.6661716555034951, 0.3696241763414365, 2.8330673642563826, 4.840261745889542, 4.595406409955835, 2.103658622346513, -0.6330239439291122, -1.245932991470485, 0.9267718752883772, 4.1869808461280105, 5.879109213458024, 4.634471378796038, 1.4753519039079888, -1.1692483605523198, -1.595683327402379, -0.16728535388968208, 1.2731227835824477, 1.2435688925201367, -0.06989656400130387, -1.2113155667373727, -1.0365701076574103, 0.15379766157008373, 1.0325190906369883, 0.7124500526805022, -0.2965107342287976, -0.6515709573840396, 0.3183458644385113, 1.7591348946624183, 2.0540629788103, 0.5010307898918942, -1.8143034266832334, -2.949039189069734, -2.028693901411242, -0.2607460821124997, 0.09177528145843421, -2.076653220082081, -5.424340479284122, -7.14107839856212, -5.409704436031955, -1.1020822821820329, 2.887376481907647, 4.081209811559635, 2.4013937929061933, -0.0608677032776698, -1.1300691450646352, -0.4301144872994352, 0.654648178384528, 0.6948851714136559, -0.25088128595489323, -0.826299717336249, 0.022344967767252637, 1.801145833641945, 2.918920389956988, 2.3473850152590905, 0.7093218841681178, -0.38581271322590405, -0.06517044378994577, 0.8842073970342526, 0.938327319565528, -0.3323315131385139, -1.5265737043376366, -0.724816132240244, 2.360152679293891, 5.638834883994869, 6.283940799137867, 3.337938591281014, -1.2272750737697085, -4.128339258048758, -3.6181526457861297, -0.8965815734409429, 1.2030448700573517, 0.9106187059989338, -1.0155703870114257, -2.353334186700855, -1.7736515504522752, -0.06420781636929394, 0.9087360212941491, 0.2599086431884585, -1.0470043357474115, -1.3646937646017847, -0.2070044289578714, 1.2548293584974222, 1.5445430331517758, 0.5395474839200174, -0.43370168809371534, -0.18775682676467892, 0.8489107369211265, 1.0100976237179167, -0.662720790399382, -3.0278390109049838, -3.695713962303492, -1.4591503567933195, 2.1854158289880767, 4.167270792913506, 2.6908923744753785, -0.9857804357502992, -3.6807575470192933, -3.2766758465731325, -0.6377509656335851, 1.4031844606733417, 0.8996647406155329, -1.4006482978814876, -3.020807282685575, -2.3496517869225086, -0.1475274053823906, 1.468250981515629, 1.295768059652348, 0.10216264708910852, -0.5388687506293602, -0.1569525627446648, 0.16376189948653153, -0.7477287293092149, -2.5299703378428675, -3.476234920444881, -2.412743070392125, -0.14831854746730136, 1.2522547631351477, 0.6993229284126863, -0.6504231977254192, -0.6276827394788191, 1.4131158509329427, 3.5395432166791334, 3.0206553864834005, -0.747756810329885, -5.248785003713618, -6.992629488427258, -4.768529431490751, -0.7494071968793972, 1.6477387419246052, 0.9528635306858152, -1.293780602065259, -2.481229933450386, -1.648340435451709, -0.14258147274405558, 0.23299168403884532, -0.6718788616888371, -1.3397212587963168, -0.5229626729593075, 1.2097459073445684, 2.1225167831118283, 1.3658587263252766, 0.0006879990279155491, -0.24215371935048743, 0.9598489529063866, 2.068063766559284, 1.4741039337145525, -0.5022789038212361, -1.8243069156611296, -1.1090491875344672, 0.477904519577391, 0.1380478558348952, -3.540081347677716, -8.644724954868959, -11.354146118491538, -9.472165838310008, -4.526122170584691, -0.274911623798761, 0.8212612325292058, -0.4316982666861514, -1.388940618221505, -0.6051047323515888, 0.8400838484370525, 0.9572675343106648, -0.65493751250835, -2.3127328822677446, -2.2045093476556055, -0.4427483808456124, 1.1534007157614214, 1.1988858150026465, 0.23938007936640726, -0.12614397360646945, 0.6411679682466548, 1.2990632732788967, 0.4449784669878137, -1.4625990295091533, -2.264854067053473, -0.5291057428814977, 2.4800645020551912, 3.7597285444111312, 1.7040887848159927, -1.957699560299288, -3.71566793190094, -1.8542377572175028, 1.7351550905994535, 3.492228454336118, 1.8439209509835046, -1.296094121396382, -2.6915251367776243, -1.1674107270749652, 1.417634876382221, 2.4508144672024157, 1.3782469608235515, -0.03591328293966822, -0.025987726241771834, 1.1443525791891933, 1.7433450491200306, 0.8520134642918877, -0.496303543275021, -0.6789280863275201, 0.39597023874981535, 1.0985109855320285, 0.12903450947397618, -1.6977723320283595, -2.2526436896607223, -0.6939153941645884, 1.2387829240981048, 1.002870396582557, -1.7494694133846567, -4.460192754026499, -4.3189758420295625, -1.4752355466199985, 0.8528208575246318, -0.295904271294535, -4.394598099136081, -7.831729984828222, -7.549824187260672, -4.014682334963599, -0.4347422453375874, 0.6888877227026798, -0.18272498483832544, -0.8098102463943229, -0.056101813190734304, 0.9886907304261383, 0.7413471656672349, -0.6572755274692339, -1.444713103367997, -0.4841274411905871, 1.203265454489184, 1.5924388968922039, 0.12016145055894549, -1.59094623880892, -1.7015870479471242, -0.41562434547581123, 0.33402469641995297, -0.4885563065277784, -1.3298191372504427, 0.3647703837120155, 4.859317808554533, 9.033925781425523, 9.151263842781464, 4.7221943750923705, -0.7824589913048493, -3.2957335479377354, -2.034477955855872, 0.20765088728945744, 0.4420071226179072, -1.36137602774722, -2.7312621739617287, -1.881673403411253, 0.24771218097296685, 1.3392626679423647, 0.5612503767117906, -0.5777998728518452, -0.27965054950000817, 1.2616126785610295, 2.179633281736722, 1.363483489800291, -0.12972590039134013, -0.47202355983260513, 0.5319153757446502, 1.1718631947915261, 0.15200460621746703, -1.4283298161697031, -1.156495504563382, 1.5871189771702716, 4.295898906615696, 3.7600990998437376, -0.24258755025823645, -4.279401496055173, -4.665492288396113, -1.30524814314216, 2.2965369463632475, 2.8526913410604, 0.6505797473064359, -1.20443347322708, -0.5468788568581281, 1.514098891507873, 2.206788770402802, 0.4860253802467034, -1.8657026052204753, -2.5181597542931913, -1.283629966805515, 0.008378132609045318, 0.026989046743466465, -0.487160820124412, -0.03255204591756506, 1.3212522463584475, 1.774004155398999, 0.15581146893798034, -2.2332037906249047, -2.8760757244891106, -1.06148880611255, 1.0924173767827465, 1.1208641670982291, -0.6642694929587943, -1.3328463088825184, 1.120273044604808, 4.9702988773522385, 6.234735577692079, 3.0182816265813, -2.181954389639938, -4.9353597073936735, -3.4030152491055583, 0.08509275084750154, 1.94581423947582, 1.1926888277644558, -0.10572864814763538, 0.16289366431743338, 1.5998946283585924, 2.1749218706528968, 1.0794601168727076, -0.2268996195126436, -0.02720005212688452, 1.3265550488327866, 1.8582333375238547, 0.6085926040807205, -1.0067285220076754, -0.9724794787774129, 0.6684050292883622, 1.789554017964455, 0.9735319652661976, -0.44706962182395593, 0.060136331414342374, 2.780942929221378, 4.796952237740337, 3.1288687606341608, -1.4961241253726008, -4.861935946385643, -3.585920919391449, 1.226327084685367, 5.152896856350623, 5.106488628256546, 2.2092382857825688, -0.10238973030083333, -0.13785310168354592, 0.6520126950521619, 0.18935612219369188, -1.3302813106076228, -1.8094288540497707, -0.1766770087033597, 2.055130136067085, 2.6080604471905633, 1.2292767175592492, -0.14812191800796548, 0.010529069717652217, 0.9684993730591593, 1.0111008740981808, 0.09827628044276362, 0.16217652021200013, 2.4081107667681625, 5.1269016473885145, 5.230362589301037, 2.039587989752793, -1.3550455919553361, -1.2491732222068088, 2.4281520185664442, 5.826825814760932, 5.384718055163086, 1.7200965985644587, -1.2833565426820805, -1.0115976203178203, 1.108359087929075, 1.691541855901726, -0.44037435396437374, -3.0609495895263117, -3.4692999536587354, -1.680965194601152, -0.02068235130012084, 0.00965789920804448, -0.5877748950147739, -0.07032162059137642, 1.4375154557836547, 2.0689535944503845, 0.8546979712288615, -0.786263222166945, -0.8545177922878655, 0.46895661529320704, 0.9189238437665581, -0.77781401154954, -2.835368485649438, -2.3413084167677147, 0.9478408210773306, 3.8047373921486436, 3.1224669852393623, -0.25900371942700795, -2.273564356092248, -0.2977229287420352, 3.717617055015197, 5.427007439439262, 3.024119661265978, -0.8723056070849926, -2.422132800359142, -0.834203744131024, 1.2918414650219388, 1.498934953376864, 0.23338989843352673, -0.37233643023316526, 0.36679024875716515, 0.9196272061265747, -0.0396657470259791, -1.5311316390749643, -1.4687319358312851, 0.4317875289543677, 2.0445456180259582, 1.5007215229503728, -0.35469171019709206, -1.0657241350397129, 0.13812517439402675, 1.2942163221474996, 0.5200748571114925, -0.9354816071754369, 0.27417438958104884, 5.270525778916991, 10.678265483657993, 11.675859207707255, 7.178708491622311, 1.1093604789251728, -1.804487810649185, -0.8179258399617114, 0.8688365463696154, 0.45037245496376976, -1.3502085358783407, -1.8916995911790622, -0.40013388282655804, 1.0797867815910178, 0.5452584837059256, -1.3004636832494563, -2.085977063569725, -0.9618791421019639, 0.3937967976797945, 0.20926634758974422, -0.9321357482865364, -1.0044905773723043, 0.4782815784984779, 1.619547279194819, 0.7602785606199316, -0.9857218683825778, -0.9971154344078739, 1.1338995903854194, 2.4140016002127282, -0.12569558475688652, -5.362544706640775, -8.662799248071883, -6.881870169622403, -1.9495426187594411, 1.311225801637045, 0.5539057832299775, -1.9076778042671592, -2.439531208633776, -0.5503237803568176, 0.9674789417791922, -0.03332300189551639, -2.3146364009461724, -3.0523345524773857, -1.5200485446039669, 0.2064886932608303, 0.1888808784092123, -0.9185548630835965, -1.094889600751445, 0.08549968983666664, 0.9776684812238411, 0.4866830565734486, -0.050151646138702946, 1.3797939637109753, 4.3105967451606215, 5.758469093590522, 3.8191084782667266, 0.329990597224377, -1.1659427450395115, 0.13263087360468886, 1.1574588523174039, -1.0906686420803753, -5.352987222276202, -7.121172739565655, -3.892107439807506, 1.7017473712598945, 4.751891770768125], 'positive_zeros': ['1.94565726491062724902198633715', '3.6006334021083603504720132135', '4.62496920131118462907909300353', '6.51853136401614816729002635013', '7.328213203984210235769732069375', '9.59550691148332290549137474799', '10.89908417254955990918633208079', '11.58843840558957668041031612506', '13.06605282754740238731530469885', '14.41493591756224817087198250785', '14.78607536204184762790281939251', '16.42034540424357170921668621309', '17.83844439745558660579678863183', '19.38084755744708837282732320952', '19.929767870362231791586906672177', '21.38901204428253711188396114946', '22.29234775720741746147515756479', '23.2328159393720863430591556672', '24.128254881958670832080754044850', '25.41175410741605187189511429426', '26.82745339839898230028578610978', '27.66187715083165133546490908790', '29.332819340363506368172995014094', '29.86835302121381307870969230018', '30.85957254570640124719075496246', '31.692398246085521438679543039143', '33.19028391503779892669867500699', '33.5819371255385677429090751295', '34.80836861858455287772723392524', '36.25332846255813246155334397381', '37.42418993744876412594729527078', '38.30054182458809831117414324915', '39.10145410109012353794052485269', '40.1433878215603575971598233554', '41.05106985707244265494873582457', '42.13774086512291291917953410178', '42.78675227857325781507009406931', '43.78119787400892867325257144856', '45.58308420240717225399660235393', '46.32925485374493731302751395101', '46.88964006977191781618413938967', '48.38689777338976577427977720685', '49.17061479322924740446780078297', '49.73773584213439773678023347714', '50.9603852719078135027108297515', '51.498359409840575562666582462188', '53.03804804567892841610526256309', '53.65092455788907842923851899822', '55.14953731261226816346733552056', '55.966985727405581164415339579350', '56.860496373204446493335081894563', '57.77521277222295593473073009391', '58.65612980315418354212336572938', '59.303243427671393960603529759745', '60.379924793068809646764849808491', '61.62828231621525469614358799556', '61.90255071070674807249819120551', '63.51215515675981587672726750125', '64.67817064318968060353272512261', '65.42224155320550366656387091318', '66.175685380887842058793176297691', '66.87042301536924599866840627035', '68.282032558488925189545988792413', '68.7723581005777843034919885613', '69.62129773401579211948104530930', '70.40449298414846590702205929699', '71.78879952741624085593848887240', '72.91591759114688456988341045838', '73.59679546023650038508658078526', '74.69991313513920399157670381761', '75.373988575826864236444389956423', '76.29010195800534848647289007691', '77.32827972570963064944012360712', '77.87448066209664952330934032179', '78.65708277910704213954135807084', '79.81294029079457031452513754997', '80.857110535997342076879640530825', '81.9480267401287234885577598457', '82.63416093578858874915274912910', '83.770643849078591476962911273155', '84.716339002231112186133677896527', '85.39685817417539378809532283477', '85.73752994573463510204115504129', '87.20917947801948863128213382537', '87.964931521814609939198126730700', '88.56191733631722215596463804044', '89.63743116898529179784318529852', '91.00465750022653433002456367994', '91.698803727678707267339597982524', '92.85461668393450432829964625032', '93.23619947714698153667458843535', '94.16086241415120563138093567567', '95.31270835487512424799785233127', '95.715856214193074670039045437384', '96.79993674597578019053519408581', '97.70413325316994088216635795942', '98.14502913062837817454144402660', '100.03256565576209471385621520015', '100.538608090177734424937691756325', '101.372023609228523359532667943021', '102.08316413959973444717637332979', '103.19467406925751965559448742246', '104.159180168776065178281880631961', '104.46194175916170183883692967382', '105.390281084947446624459554791861', '106.30642040604239084966418242908', '107.33195677935140778530440655554', '108.28522880550334714602433869611', '109.2421164515172477324697210440', '110.13581389616779094043629378349', '111.23740353881570402007731129880', '111.57214316086463286011734937214', '112.68262716165016226907061297219', '113.338372992920042507802351411060', '114.0854962017800779081252218947', '115.09722296515222536314235309132', '115.76258017624293238552389609124', '117.03199697534878939378204197231', '117.46794859494762393756489626040', '119.12228840782858233863108116315', '119.63731746624233368521847187536', '120.326865101758695027964183932950', '121.11301598087590498887479476006', '121.96163644345049928198397514403', '122.83143626125772079271516939113', '123.856755873698573876805789181298', '124.24538772858842819706437736491', '124.96417593421581625104723404784', '126.51113216586647283265548499454', '127.46144718569652359113980312271', '127.91129482417079443185785128487', '129.02424481896260364001878915085', '129.81798576673424129035868503679', '130.379980211080269177922758810504', '131.52917249856349845269475937621', '132.0473097118481646519781245704', '132.84022082207091589786940567764', '133.59361613848261335794290925454', '134.671600178886337838979586690452', '135.72295362414780684255508751898', '136.64366880959326985190879654328', '137.27399459892253563551833227555', '138.1848043751887269845510441810', '139.371352093520285060326882497194', '139.7032513631155326055767772530', '140.32153891703929994111243896400', '141.26991706060103318382432547108', '142.32162207032465169088528595404', '143.01671744165709863567249001431', '143.64778219899521572290990717867', '144.865674945784655145108009708678', '145.92911909264526270581672958420', '146.83412270449843314048584117452', '147.13813936839973113742930386261', '148.35978903411343966822819478410', '148.75802375898929883014569282257', '149.79055236204497311073025770747', '150.51127638272362160444004065325', '151.44110493521301452096775672711', '151.86476589649338083748572644019', '153.03012568580244781678327449458', '153.989272813946181511291176639', '155.287256236069996913049133387051', '155.675302736033927795655160855240', '156.2940594279162587349630454561', '157.21071789731894625549031380035', '158.382492453193483191750797367705', '158.7461322981932386069112188183', '159.72998559491903283451204088130', '159.94772500375269871512568466029', '161.41434039488314895737011064204', '162.00407539961048158424695520549', '163.27021855933402257306402682723', '163.90142278340580730947928526642', '164.63959789448910605254721737633', '165.945022337886783705989667948770', '166.25485150628931500900403232214', '166.89222109230025440010919415961', '167.95763067384986116170692779991', '168.64625179290570524632775143055', '169.26706370576794425493807588045', '170.23407525590957632716640302300', '171.22675973163216249388232494135', '171.899709672632945025711800897262', '173.04724495996133255143640297340', '173.856819474589155757762266905184', '174.75004410676213645630635274953', '175.19538188829222831267528344980', '175.92960266319563635952751087754', '176.81426376134796168127187314536', '177.74990098952954701661337851491', '178.41112763611294200762461170284', '179.15799817411679601122179924957', '179.65999140975093656329417083562', '181.32553827936432799636418703836', '182.00132402157325344561240057849', '182.583078146853440584616117705', '183.502294960703250894564770607107', '184.16048868198004411299792172369', '185.19338030303978890243038185943', '185.6862024860327547716232346531', '186.476942364636425523592144525474', '187.31514968625288749753702755175', '187.97834433462373060674241269379', '188.74116645817032705279701618422', '190.14273107456635355773724149324', '190.69556124474261825495939076717', '191.64156522775373148322208438275', '192.18253633844242619021206431306', '193.38194865825372444379234210482', '193.809553388881461994545837865725', '194.66819498973576594567248448433', '195.50908203339539377819487072553', '195.66563710847942495428997880289', '197.22371780452201743381695923812', '197.7902165349847965456094426814', '198.33855520563476367290889650483', '199.58910163469488244194167315038'], 'prelabel': '1-3e4-81.76-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.37616241858008603, 'root_angle': -0.19753086419753088, 'root_number': '0.813552070262967563714650849683-0.581492071288026667901088648583*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0987654320988', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(27)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.50835169064405134242268231975-0.356820217589290060437910647428*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.94565726491', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.60063340211', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.62496920131', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.37616241858008603, 'bad_primes': [3], 'central_character': '81.76', 'conductor': 81, 'conductor_radical': 3, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/81/76'], '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': '1-3e4-81.76-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': '1-3e4-81.76-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.37616241858008603, 'root_angle': -0.09876543209876544, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.94565726491', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_81.76', 'Lhash_array': ['dirichlet_L_81.76'], 'label': '1-3e4-81.76-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/81/76'}