-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_31.27', 'a10': [-0.8090169943749475, 0.5877852522924731], 'a2': [-0.8090169943749475, 0.5877852522924731], 'a3': [0.8090169943749475, 0.5877852522924731], 'a4': [0.30901699437494745, -0.9510565162951535], 'a5': [1.0, 0.0], 'a6': [-1.0, -1.4081532572346456e-30], 'a7': [0.30901699437494745, -0.9510565162951535], 'a8': [0.30901699437494745, 0.9510565162951535], 'a9': [0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 3.3314126686333756, 'analytic_normalization': 0, 'bad_lfactors': [[31, [1]]], 'bad_primes': [31], 'central_character': '31.27', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 31, 'conductor_radical': 31, 'conjugate': 'dirichlet_L_31.23', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^1', 'a^8', 'a^0', 'a^5', 'a^8', 'a^2', 'a^2', 'a^4', 'a^3', 'a^9', 'a^1', 'a^2', 'a^1', 'a^6', 'a^7', 'a^6', 'a^4', 'a^8', 'a^9', 'a^7', 'a^7', 'a^3', 'a^0', 'a^5', 'a^3', 'a^6', 'a^9', 'a^5', 0, 'a^0', 'a^4', 'a^1', 'a^8', 'a^0', 'a^5', 'a^8', 'a^2', 'a^2', 'a^4', 'a^3', 'a^9', 'a^1', 'a^2', 'a^1', 'a^6', 'a^7', 'a^6', 'a^4', 'a^8', 'a^9', 'a^7', 'a^7', 'a^3', 'a^0', 'a^5', 'a^3', 'a^6', 'a^9', 'a^5', 0, 'a^0', 'a^4', 'a^1', 'a^8', 'a^0', 'a^5', 'a^8', 'a^2', 'a^2', 'a^4', 'a^3', 'a^9', 'a^1', 'a^2', 'a^1', 'a^6', 'a^7', 'a^6', 'a^4', 'a^8', 'a^9', 'a^7', 'a^7', 'a^3', 'a^0', 'a^5', 'a^3', 'a^6', 'a^9', 'a^5', 0, 'a^0', 'a^4', 'a^1', 'a^8', 'a^0', 'a^5', 'a^8'], 'euler_factors': [[1, 'a^4'], [1, 'a^1'], [1, 'a^0'], [1, 'a^8'], [1, 'a^3'], [1, 'a^1'], [1, 'a^7'], [1, 'a^4'], [1, 'a^7'], [1, 'a^9'], [0], [1, 'a^5'], [1, 'a^4'], [1, 'a^9'], [1, 'a^6'], [1, 'a^7'], [1, 'a^6'], [1, 'a^5'], [1, 'a^0'], [1, 'a^2'], [1, 'a^3'], [1, 'a^7'], [1, 'a^9'], [1, 'a^3'], [1, 'a^8'], [1, 'a^2']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-31-31.27-r1-0-0', 'leading_term': '1.26348560245457911200510592145+0.686175711329828024140160307438*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/31/27', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.4377875275676186, 1.5347272947749302, 1.5656232760862123, 1.4891890181195755, 1.2553668148978918, 0.8264448781950624, 0.196261839367868, -0.596564162466269, -1.4643742930449446, -2.2778247793589905, -2.8859836492402806, -3.14729920091545, -2.965844162364661, -2.3240134814076177, -1.3014893998108275, -0.0718499158039511, 1.1269973947192806, 2.0450866027847834, 2.484001369600712, 2.3545388179825317, 1.7097727234456856, 0.7395491054700106, -0.2771335854913074, -1.0517965218190435, -1.3756340157927345, -1.1889764398642995, -0.6047534397921176, 0.1273752147004308, 0.7095923780620269, 0.9100616346420001, 0.6622637241875936, 0.10955415839950582, -0.42902556280100007, -0.5679607379501846, -0.005716237969225533, 1.3380365556919285, 3.254471612715786, 5.282196740387905, 6.845985159652684, 7.454083258267208, 6.882442304778676, 5.272464606624804, 3.097135989547356, 1.0000587622112609, -0.4359504620795318, -0.9013755327151763, -0.46694294523944024, 0.46187792941713246, 1.32708424531457, 1.6618164679390783, 1.29059822565309, 0.3968760153486912, -0.574520212601431, -1.1377301066786585, -1.007975533027444, -0.25015313956687474, 0.7413868267344002, 1.4286658245537358, 1.3968390590444932, 0.5725116930220405, -0.7191419683060808, -1.8971942266116528, -2.4079905375606385, -2.0135123400872046, -0.9380529290362436, 0.21215100105640727, 0.7321379180581433, 0.1750215811886701, -1.3934861011774, -3.3788376749571145, -4.903933817016021, -5.211080604477908, -4.028466728756932, -1.718523516319563, 0.8725254796967064, 2.7972675969339886, 3.4367177884916096, 2.7649486492104005, 1.3187565135302455, -0.10647620345669706, -0.871525590258095, -0.7987114762774743, -0.2090270086606271, 0.3197505252083397, 0.3293766298053613, -0.2287129801895357, -0.9616526476879759, -1.2850892948864772, -0.8108827676380451, 0.3604948913538606, 1.631251365711785, 2.2105828156740555, 1.5751375621312491, -0.17650474922834436, -2.2950251421478822, -3.7226240191028257, -3.63967580272974, -1.9208106483085712, 0.7598003284311821, 3.248174046621638, 4.492856294221308, 4.075024951834891, 2.394522611175338, 0.4106429214588756, -0.9115098871001385, -1.1305089340716004, -0.5316449692607332, 0.10531697943250118, 0.024458885128135675, -1.0201842496188709, -2.6064373088284256, -3.9070107733402715, -4.206852700072953, -3.349864953536323, -1.833697686764798, -0.49249522352122527, 0.030295217842647864, -0.32054499878731996, -1.0054011209739737, -1.2854872317442114, -0.766644768605297, 0.27194224920147353, 1.0023612717791335, 0.5758686566378762, -1.2675774694613497, -3.9069355083501467, -6.085916107475967, -6.587008615565239, -4.9444126565763895, -1.760307171955142, 1.5850244962150213, 3.673502466627078, 3.8064582062729193, 2.331963953222094, 0.3594966296502688, -0.9436650006636969, -1.0281327454013733, -0.19772222593988018, 0.712439889648017, 0.9682448097408388, 0.4397577968614189, -0.36051513136341257, -0.7111811781249638, -0.26427237956309957, 0.6516023600827032, 1.239953184666566, 0.8251863959227017, -0.592521615706754, -2.228719363186135, -2.9696152066563357, -2.1132173958446594, 0.10162398308978779, 2.561349682942017, 3.934373791139722, 3.50922015601215, 1.6619426591560347, -0.371933015911493, -1.2895137989251786, -0.563929494175869, 1.2184182812774964, 2.7536691866240326, 2.8879151133516494, 1.3781733937853797, -0.9584886644423127, -2.798111219514377, -3.1810698858865036, -2.108513620767391, -0.4712992202804658, 0.6134881512443654, 0.575994696539264, -0.2670676542431873, -1.0270339866450793, -0.9560760234892116, -0.018827632451270504, 1.1025218136131585, 1.5662718563805713, 1.060104897200681, 0.07941250065078313, -0.4461632827617228, 0.07731575945279649, 1.3228372407284292, 2.124676945093372, 1.240103555157995, -1.7092720418850895, -5.791832236921495, -9.183397330648239, -10.2241494722038, -8.431577012358233, -4.791530456651177, -1.1294601747112014, 1.0126265831486991, 1.2399133609484119, 0.3548108953932364, -0.37972305267434636, -0.19196502791522138, 0.7216471712370891, 1.5005639009261271, 1.4177851669813142, 0.5243655405494164, -0.36665294105009466, -0.3383847614210153, 0.8558518008748242, 2.5267724297483816, 3.5249254156262335, 3.1088495722391865, 1.5333386874974746, -0.11870751704563849, -0.7603078713971626, -0.1596385655732397, 0.8412957232507112, 0.9537996592381932, -0.530450012826414, -3.0924773241451136, -5.245538324646115, -5.5578468825687155, -3.7071439764700442, -0.7805204224457131, 1.4308426013298567, 1.6539256513437777, -0.004233401413482473, -2.1750267267084538, -3.229763291601826, -2.42412536924366, -0.3578356883428947, 1.5506288284310934, 2.137149485467102, 1.2895644338727872, -0.10351193459146454, -0.9477605975464775, -0.8073818559464296, -0.1456526233290238, 0.2148594983875234, -0.08220089034249395, -0.5464263272355232, -0.2605968110483229, 1.2285941104128615, 3.3118572741618104, 4.582715111044113, 3.8524317035008964, 1.1582616605235267, -2.058426078254719, -3.832007382039401, -3.0216910834180575, -0.14175434985638355, 2.964691993461475, 4.393230294775048, 3.464971108305323, 1.0977878909167236, -0.9767859302422762, -1.520642447864721, -0.6190174212260905, 0.5607734520189663, 0.822367440791, -0.07545730880018192, -1.2879102722452047, -1.671030630944191, -0.7990536049036299, 0.6478147501390883, 1.4464875669121033, 0.8661964924912965, -0.700071701241561, -2.047121931298573, -2.1587277811870655, -1.057478853413215, 0.22262611258848122, 0.5331534674669248, -0.375590532273233, -1.6044282136856145, -1.8762685332102913, -0.7166918408244993, 0.9592482830115172, 1.4194104053462062, -0.52795809186383, -4.447418228236553, -8.364947239543515, -10.043116426910684, -8.517929499241674, -4.74590973686008, -0.8853229916839563, 1.2189035637186274, 1.1909803734438598, 0.09580775410405708, -0.6362992951046244, -0.3888489544947015, 0.306257749732592, 0.4614142748867041, -0.3383090139248728, -1.5087050517410638, -2.007749761338739, -1.331817107485727, -0.03856657892519985, 0.7166454644086344, 0.2549808356317895, -0.9003771137794788, -1.3537751651455339, -0.026128491400618604, 2.778183959783348, 5.38216934704534, 5.921160788192648, 3.803389507694165, 0.2608663138332351, -2.5005586715365373, -2.9158069701461278, -1.171557039621085, 1.057161700582188, 2.004576231772056, 1.1953522012856919, -0.29972991451809994, -0.8907402991937248, 0.12611426494362388, 1.974158245516984, 3.0857755344602213, 2.4526026647855197, 0.47141995755186833, -1.4175703667509558, -1.9527760003874888, -1.060333268690614, 0.2036795152636384, 0.6753000580278965, 0.12175792056935983, -0.6379015060912425, -0.6141506462828139, 0.3131732969725678, 1.2023910226794166, 0.9443473956167381, -0.5400850389858367, -1.9360434011968002, -1.46621837247228, 1.5694491246872277, 5.951985952042092, 9.211458584793824, 9.381630243356632, 6.476716864795113, 2.4969294450875372, -0.059874028288469244, -0.00023283211346920783, 1.8592247659739274, 3.564469358630529, 3.6648364808951017, 2.2439853976996074, 0.5705961660338713, -0.18310272839090733, 0.0516671412422802, 0.3758244518895946, -0.0220955007861795, -0.9542206781478507, -1.364119451623392, -0.39424379667786363, 1.627350882063843, 3.265963771734422, 3.143019217363551, 1.173553344160957, -1.2647236668255566, -2.4546216073525304, -1.8085441338748751, -0.376952465169926, 0.09945425321688167, -1.2028277480380865, -3.3451215586561025, -4.339280511157134, -2.8546546632908134, 0.5458063710488603, 3.738668182389729, 4.701909237718515, 3.1146494067316235, 0.5498237438755532, -0.8784138707303959, -0.23692105653894638, 1.5887945580889489, 2.815060902127497, 2.356352497480545, 0.6808525397778002, -0.7613065078077207, -0.9216403332040601, -0.0444598110807031, 0.7139297481444253, 0.498227464840566, -0.4075769047387469, -0.9288263963614986, -0.37532943571490707, 0.7481001837911784, 1.1674488037673316, 0.17670251113761148, -1.390453697378744, -1.6030937308249849, 0.9270873678353244, 5.595825388940175, 9.904743556257621, 11.189274893619416, 8.625812884349665, 3.8617061253460925, -0.2614947082514924, -1.8252859439997113, -1.051990225013495, 0.2897463723765519, 0.6266533215309146, -0.12287745661841809, -0.7757451351471413, -0.27205608427941796, 1.1704639696113708, 2.2319301304940145, 1.785748725080292, 0.035204789725465355, -1.6203173493083791, -1.8730838290333744, -0.7190840935797598, 0.5712661326238965, 0.7040479309677484, -0.3658754821456784, -1.3825213707020867, -1.038480920214878, 0.6614987113831787, 2.270245279046102, 2.206079088141732, 0.3114119399125863, -1.840946322262091, -2.286713653840968, -0.5039023797368254, 1.9466495077619115, 2.648133425375229, 0.4151249794731683, -3.584907354224368, -6.689761413054554, -6.861055552887395, -4.2468138585622945, -0.8918006586540287, 1.0527549437232477, 0.9939670905397082, 0.03768499224357683, -0.3357927197407113, 0.3035059273806329, 1.1344030870552095, 1.1567314167521507, 0.34314659385861956, -0.33594744592710285, -0.026533955449924155, 0.9422780526644908, 1.221989349812679, -0.20728267854571594, -2.805062209132899, -4.666308275572071, -4.138003086604573, -1.4302495814757896, 1.334630974793192, 1.8259709515220925, -0.48160225599782314, -3.7926244256612813, -5.483254087509913, -4.309505679913812, -1.3885745161206926, 0.878804235236362, 0.9233082682437079, -0.7550651464989375, -2.2700008459386454, -2.2043337603810045, -0.8571282690071721, 0.23514351455353918, -0.061714756439977245, -1.3249544647573561, -2.019841338737946, -1.0678273623104384, 1.0296716589757249, 2.6209954704652123, 2.458166365017576, 0.8458903454882722, -0.7270870323568592, -1.0728601285554624, -0.3962576570058952, 0.10859824385091843, -0.27102441327919824, -0.7859790958428283, 0.140616621542598, 3.1632601728815244, 6.8748455037555285, 8.573767919564489, 6.464078869014659, 1.3674016302352539, -3.6766664393999893, -5.699604851869982, -4.050187041981279, -0.686314903551215, 1.65282184472382, 1.7010385315802832, 0.3837790036899149, -0.4483741134156501, 0.10224582517853519, 1.2900578135614522, 1.7316698511992945, 0.9353737965794137, -0.24039239838227264, -0.6072743676826722, -0.0031769590738593414, 0.49245077262353526, -0.2489602928525956, -2.0461633801971955, -3.367896665346679, -2.7840997504838607, -0.5119269760369958, 1.5558725030848946, 1.5218695065733079, -0.6741337247612812, -3.049512296247974, -3.314994045460172, -0.9832133172445954, 2.140014274545819, 3.580679923042482, 2.433397077153401, 0.11444046437073417, -1.05874638128318, -0.08816067812438566, 1.7988951630428445, 2.389758949585647, 0.6455049076600232, -2.2940918312581395, -4.178292784212181, -3.704073668518506, -1.5873110637100964, 0.2938413644662998, 0.7261000411477304, 0.12881104275579408, -0.19775131277719626, 0.3728100783140495, 1.1188363534165138, 0.8650515629446806, -0.5653112647270631, -1.9731952524761227, -1.9882331894325962, -0.6378684132234046, 0.4467214650859098, -0.3987635337578589, -2.9808968787791197, -5.000528061189923, -3.931874602332994, 0.5824118420699229, 6.078443129616693, 9.100324430593288, 7.9577478236515145, 3.9757896829155848, 0.18648239182571652, -1.2524828455221333, -0.5579228647610518, 0.4506023148068492, 0.38945472521642854, -0.46884204701361354, -0.8673951447284279, -0.21350497346409858, 0.6433890560262167, 0.3337073290789135, -1.4335499771150673, -3.359885195094537, -3.760109325311302, -2.2785937536330314, -0.3217437489083391, 0.3044527848317429, -0.8013958114989304, -2.2485285184911525, -2.3202701957768075, -0.8080314687605448, 0.7103250365798262, 0.5161306558830785, -1.3176175673184423, -2.7393681246308192, -1.6198352773979872, 2.04606275265943, 5.838362313452798, 6.9331890923349695, 4.603335228444243, 0.8455082917036025, -1.447951395312011, -1.0256668894463947, 0.843231042930968, 1.8488845685323627, 0.9134027450664378, -0.9570110666504724, -1.9184468873969025, -1.2114733591719606, 0.21496162767575475, 0.8837342009351249, 0.3887173083402825, -0.3164930399914865, -0.16715296779809466, 0.7015428298923284, 1.1178118095332956, 0.392495266459003, -0.5167565610814402, 0.32942225028357885, 3.801087863017945, 8.325718438400658, 10.801463662640874, 9.194989184331714, 4.440689846635467, -0.23274454216061644, -2.020490349055161, -0.812156946892713, 1.0521101217192876, 1.1911629685349765, -0.6224837557455367, -2.531992372506265, -2.6733348144331437, -1.062536000289221, 0.571725924348126, 0.6945359990535422, -0.45759150514582053, -1.252726683657483, -0.5139508749315617, 1.1697250303445976, 2.0650068936547394, 1.160921528443946, -0.730481551522012, -1.8209929439359636, -1.232923229031604, 0.10151879814172517, 0.5010489316651957, -0.5873933712721742, -1.9518162313210663, -1.9700646877007562, -0.5319436659210852, 0.6123137863250857, -0.3698448152382712, -3.233659137638757, -5.441657405470244, -4.362230962767718, 0.12774522977807226, 5.207246548257165, 7.399155539576961, 5.504641496143603, 1.4720548189122198, -1.5140293436973935, -1.8049405978569133, -0.3284427672230711, 0.8344209177761672, 0.6422711149966038, -0.18556216440821496, -0.41200137557267297, 0.11436557169299039, 0.333114979956724, -0.612537585436022, -2.1304095409505686, -2.6354755450530156, -1.3046207918363135, 0.8192943512121157], 'positive_zeros': ['1.9575110911927671996819340224', '4.70537739853280268441677070753', '6.78587563857315644526855742999', '8.382017691832167994469099926492', '9.743978946147242402454810485946', '10.62685027631303779612388912885', '13.632252253007252212759739530260', '14.54112386648540209978080324748', '16.05896232245202353545686819417', '17.26676079122562009841168679365', '18.582300535998321819840690501829', '20.24662057477490309204052670546', '20.98315621033433075010335712111', '23.01611571659203062093857124786', '24.65977506247253393639896099802', '25.72776733429796362458188710719', '26.46002958084717865813369353190', '27.727513912860947960025559247302', '29.03603797667819291572472798408', '30.540233406937276302805905379717', '32.26341591888114120131762511493', '33.36540498809011424117486673539', '33.7627320533376208152470772283', '36.18254404947046433419816951247', '36.34586104068203256795808869184', '37.73338352296173638818149741014', '38.56132289961565944017148921453', '40.46966838378656904876538941043', '41.9404996869923430414742918339', '42.87283480796517156558711491835', '43.91609806885618438597320193828', '44.78372023686711298060377737711', '45.8245675349134118737180971730', '47.175115764272609483668582524318', '48.68424934110947247501114110621', '49.484573507983189594331598226287', '50.811453675251404594999964818405', '52.2923861015471185939994246301', '53.038401202659246722461106275387', '54.067474379535331339354671488517', '55.34056783314345380968973666407', '55.91316730761786164904969896223', '57.030773105427936049809082663636', '59.19250099212402910788771498989', '60.11762824650931046085957604429', '60.7046225113087707177101828575', '62.03577808303389728187335178213', '62.61968878606590860683548713401', '64.34702747978823495619650175731', '65.04797260870371807805363501134', '65.85671383356329894060526952258', '67.589278550151147129194587885260', '68.43690036085184607559466143444', '69.737909876055606076721026021485', '70.91245867152456427031825843895', '71.95302461876854828462192792775', '72.448987934868640419950342921', '73.20233000324863726469353882548', '74.79584654318667357412058786148', '75.95068296704942007596382337851', '77.332223697555891381345636473437', '78.27506612569561917946150078659', '79.04358396542801783837315384545', '80.17119458910536397252264884026', '81.120411330140827016897442539943', '82.433309617441255902020105289382', '83.028229547441700722462122752428', '84.19042231681227649747701955097', '84.944364863943396140475792067766', '86.97106064301294218606540715612', '87.839882450210964255836730358187', '88.60780637269494569970869150841', '89.27621906075073209823754078642', '90.63500191481699709089395598070', '91.323842661501161188005027008101', '92.19110702754963791374483802812', '93.77337574689220865920796731886', '94.84238317518826567600699126364', '95.86917244796891552048174635761', '96.53837052883749296241197724448', '97.88004722112304265278998276931', '99.003857170315894352508520771496', '99.7317791108600801125881230596', '100.53664204501496356282123894226', '101.46458489394298543558732720689', '102.367146684269025974093537757735', '104.36101942744633705124270214725', '104.68755857337993356188528127973', '106.42534318551971925492042731730', '106.83963937886167649535083895916', '107.49120307316797863557225998313', '108.50647321027550270518524280538', '109.83072331013873619005360894409', '111.05773453971420559247587392442', '111.30319596736154449219905433284', '112.76659040600007514787748268314', '114.14370698586085911769005965956', '114.73389321900677389756512836415', '116.061221206775408438962311958792', '116.88855308503618663930355661851', '117.67916701448694682574360593126', '118.54327471924495320578250482700', '119.4098269215046510695764354860', '120.23145167139498844069144211477', '122.1612336226367597309463224490', '123.0450876773841104962560858540', '123.70934744330766653443615789577', '124.44363471617333227669284970070', '125.630555861281999958857661095543', '126.71691279220416493232880034906', '127.41179027762653921578337966648', '128.33105889300043789512218923872', '129.41560401357015584711861044629', '130.37369703500158421819412623309', '131.28602342134020439970694205654', '132.91885874615911109162538594250', '133.76399478101007412192203089829', '134.266453401659351924596965504779', '135.43347463022431880762513567988', '135.94758472321721609270520189571', '136.84542284854174369815510273818', '138.26906972229831612147331137970', '139.0148831558936105376968091128', '140.47311176617365047588854482630', '141.12722286956131738463429623895', '142.397090789982925594614517533824', '142.79220661818103658654805659442', '143.916279523156835281200304294944', '145.147573804147705195265356606132', '146.124036822603670744565323230423', '146.41928509210814340166759013063', '147.16489556849938243520192631872', '148.82603202133921849973821166274', '150.06925583728090417253232442629', '151.03419723771076581220082087205', '151.53252737400905062998725670019', '152.738586337413734084049075829214', '153.43875858079156119494255495307', '154.00370928310381645116060495303', '155.375926124919278127915844383686', '156.17099211576742253456064080359', '157.28199891859939843139390509511', '158.45493488137514102917216126449', '159.07771353486726129905821221750', '160.07153989554933106213469093686', '161.49652724017129436092022111951', '162.25172188241195742758735531068', '162.66005725434674748621634961321', '163.64361565008558330184689673254', '164.82633097179581052569240124679', '165.23988299744601396621293332490', '166.5295847165256605276259270874', '168.14659426471381628477499805267', '168.89850183322364828352893832135', '169.526254636971482216267748316554', '170.37851035696941100888331037085', '171.01584365875824997979249278765', '172.57545814720201237789939057750', '172.94445509982901008482991007032', '174.20307792115649344761578020950', '174.79434996434338393546204461442', '175.78090566184201207761386635641', '177.270109906630917394174566395997', '177.98816703816606066432398677257', '178.902217779234187124817267409128', '179.94872914571395458929564671857', '180.7724568407225687994963302719', '181.32067311513359270027983002989', '182.29654279808479578568556918829', '182.76009544011411970523853369477', '184.667380392288795130874341245662', '185.434717939018715854861389077271', '186.1619884480965351103760493254', '187.366604050567386711826521972', '188.015556025441329833181321901878', '188.85039307592077719815122868560', '189.87974702276029916282628176875', '190.90997054684135308828009831224', '191.432630735616332469418430908139', '192.60515132455990466709154110635', '193.06692395638796074308268199182', '194.36762157122496413506862323017', '195.750148072398229689511865423964', '196.62732575309715025039634303593', '197.42341478600787981687868475822', '198.06682766834929677198895464175', '198.596068316481206024293773232079', '199.87424583880759230852753504196'], 'prelabel': '1-31-31.27-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3314126686333756, 'root_angle': 0.15836426880119428, 'root_number': '0.544476009580829984496950250466+0.838776415375954603938423790085*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.158364268801', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(10)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.05346071726558211144336669163+0.404620636219078106031724744418*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.95751109119', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.70537739853', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.78587563857', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.3314126686333756, 'bad_primes': [31], 'central_character': '31.27', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/27'], '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': '1-31-31.27-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-31-31.27-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3314126686333756, 'root_angle': 0.15836426880119428, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.95751109119', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_31.27', 'Lhash_array': ['dirichlet_L_31.27'], 'factors': ['1-31-31.27-r1-0-0'], 'label': '1-31-31.27-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/31/27'}
Lfunction data - 1-31-31.27-r1-0-0