-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_63.25', 'a10': [-0.5, -0.8660254037844386], 'a2': [1.0, 0.0], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, 0.0], 'a5': [-0.5, -0.8660254037844386], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, 0.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.29257077000673354, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '63.25', 'coeff_info': ['x^3 - 1', '-0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{3}'], 'conductor': 63, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_63.58', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^0', 0, 'a^0', 'a^2', 0, 0, 'a^0', 0, 'a^2', 'a^1', 0, 'a^1', 0, 0, 'a^0', 'a^2', 0, 'a^1', 'a^2', 0, 'a^1', 'a^2', 0, 'a^1', 'a^1', 0, 0, 'a^2', 0, 'a^0', 'a^0', 0, 'a^2', 0, 0, 'a^1', 'a^1', 0, 'a^2', 'a^1', 0, 'a^2', 'a^1', 0, 'a^2', 'a^0', 0, 0, 'a^1', 0, 'a^1', 'a^2', 0, 'a^0', 0, 0, 'a^2', 'a^0', 0, 'a^0', 'a^0', 0, 'a^0', 'a^0', 0, 'a^0', 'a^2', 0, 0, 'a^0', 0, 'a^2', 'a^1', 0, 'a^1', 0, 0, 'a^0', 'a^2', 0, 'a^1', 'a^2', 0, 'a^1', 'a^2', 0, 'a^1', 'a^1', 0, 0, 'a^2', 0, 'a^0', 'a^0', 0, 'a^2', 0, 0, 'a^1'], 'euler_factors': [[1, 'a^0'], [0], [1, 'a^2'], [0], [1, 'a^1'], [1, 'a^1'], [1, 'a^2'], [1, 'a^1'], [1, 'a^2'], [1, 'a^2'], [1, 'a^0'], [1, 'a^1'], [1, 'a^1'], [1, 'a^2'], [1, 'a^0'], [1, 'a^2'], [1, 'a^0'], [1, 'a^0'], [1, 'a^0'], [1, 'a^0'], [1, 'a^2'], [1, 'a^0'], [1, 'a^2'], [1, 'a^1'], [1, 'a^2'], [1, 'a^1']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-63-63.25-r0-0-0', 'leading_term': '1.43641559877705495612158809143-0.171677988560501183935258934522*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/63/25', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.4466385533941175, 1.6181222504929396, 1.9658289265613096, 2.171943801263987, 2.069321450423977, 1.6063964756329494, 0.833293256625773, -0.10563548077635493, -0.9995779109218762, -1.6257249758889583, -1.820209517715754, -1.5428971679773666, -0.9088593760350288, -0.16608027705032474, 0.38319594457794903, 0.4962799345056438, 0.09755449975068509, -0.6680812339818476, -1.4694651301922232, -1.9118282000864268, -1.708155825694345, -0.8293674261716204, 0.4397361868734983, 1.580734243012037, 2.042984380273845, 1.4910379193686096, -0.011027515587322305, -1.9739015519706118, -3.6491323692436333, -4.332377518695052, -3.6762234068896005, -1.8658960415931483, 0.43707927426999876, 2.3731968986301437, 3.2647390586772924, 2.917327329514783, 1.6919892074507814, 0.30570099455221117, -0.5427783168249143, -0.5290682625165173, 0.14852825277536152, 0.9110381691849863, 1.1544597090658417, 0.6183089230089327, -0.4486398628627802, -1.4306849371287813, -1.7213285598500074, -1.112630882866814, 0.044881399351463395, 1.0289828275935462, 1.1885135505751327, 0.3828072423918525, -0.8625833855803905, -1.6114204091423565, -1.0645816400457195, 0.913036453843991, 3.6152368963899533, 5.807635767898174, 6.381600994154662, 4.980443343668108, 2.223592133387273, -0.6204859403920298, -2.333482231023674, -2.408300072484989, -1.277712934414612, 0.02105025973487258, 0.5272474046699793, -0.051284862364309465, -1.2079851258252456, -2.0383805389890157, -1.890141683536692, -0.8165490851911619, 0.4756447831782614, 1.1425806841009782, 0.8157850345434674, -0.13128225846416103, -0.865442494677056, -0.7337395109804526, 0.20219944834320092, 1.1484093018588875, 1.1314577727006019, -0.24436725564129003, -2.383275829019863, -3.9695341032895675, -3.7961234678456983, -1.610003522809135, 1.6197615548516804, 4.238172284669089, 4.923169287184339, 3.516020275523752, 1.0989493683727, -0.7390012901292848, -0.9489293206960656, 0.3330989709589286, 1.972661637046926, 2.695473877364513, 1.9874469153786634, 0.3942946507063168, -0.966162553496471, -1.28088301971833, -0.6309918007656373, 0.14628081510758673, 0.1915833411311398, -0.6451837468077114, -1.6722584497641115, -1.9409873326759022, -1.082982266213063, 0.2929276646212188, 1.0095988761838475, 0.2594740624536968, -1.6613265699865638, -3.446355522305516, -3.7026347848509125, -2.041570015898218, 0.5098488692325504, 2.1507912004777494, 1.5803074333443754, -1.0266691272201873, -4.084466973342929, -5.682990265709404, -4.907223901696312, -2.42185043249074, 0.09152420471754498, 1.189074140910503, 0.6471766706081695, -0.5478733662889537, -1.126286023178892, -0.5877345556119132, 0.4711376809703301, 0.9793852815994393, 0.39432959082596997, -0.7912388179069089, -1.475961207879293, -0.9392651087311589, 0.47587672613619714, 1.6080987533017668, 1.4742832202357152, 0.16698377874881293, -1.157791380101868, -1.2594787214577656, 0.03353972064885965, 1.5022290099574258, 1.4105892305692116, -1.0608094759362054, -4.981320197566402, -8.176113715863515, -8.751279316576564, -6.474901942688932, -2.9304265621794423, -0.3200631707128617, 0.13425391700478292, -1.0576386551591168, -2.2878651186944863, -2.274212380297584, -1.0672233257783665, 0.15768352027934185, 0.26019223026567123, -0.8143657218255728, -2.013522925456392, -2.1654670332444748, -1.056064687310664, 0.3895667634182173, 0.9811654868766828, 0.38145190470813584, -0.5806319484535087, -0.7221235252466718, 0.2863202423764595, 1.4619263225772678, 1.3119308312346312, -0.742516824450109, -3.597699368652647, -5.1417694030667445, -3.919138256391455, -0.41243060639352996, 3.189436792500026, 4.623907766527745, 3.277765831451856, 0.584712011258651, -1.2158343051672047, -0.8984148868195923, 0.8722968029302552, 2.286961525649113, 2.0337354820612576, 0.37928056378321506, -1.207607834251595, -1.4600221403799134, -0.4249625674251792, 0.7046035272448951, 0.8071179387734523, -0.09759286327175513, -0.9453890062799746, -0.7709533683198209, 0.24379666665550936, 0.8797403969823019, 0.09433018576954441, -1.8213373740677203, -3.3218740212622677, -2.966649292868849, -0.8480823727316475, 1.291450038598366, 1.4937345665908843, -0.6371909216298525, -3.4277059556718603, -4.446010247625195, -2.5573927338235953, 1.0623342960202045, 3.863167218685184, 4.008596482583731, 1.8097830842361258, -0.6979099393577052, -1.581912149047966, -0.5799879616231536, 0.9341072458023771, 1.415180590010582, 0.5865272655076599, -0.4764109749578533, -0.587709162227383, 0.2849694639965695, 1.0037838443302323, 0.48436269591652903, -1.101289748273059, -2.393820570754727, -2.1655388115734313, -0.5843177091287829, 0.8859181233761086, 0.9305907861190859, -0.21933366598095527, -0.8828332100279679, 0.4441753883818964, 3.429178248996417, 5.869027106467813, 5.482635607662061, 1.9857744091657912, -2.463451359443976, -4.93883809766143, -4.104995058531712, -1.1898414146193301, 1.2397955445571938, 1.5231295052004021, 0.13142125852445014, -1.126324188260739, -1.0039206881360594, 0.05223124511097847, 0.556564481268185, -0.357538700598965, -1.999583385945562, -2.8314063591356633, -2.0523696453089446, -0.4090324143949243, 0.6034273713056357, 0.308839459877425, -0.46277152283968787, -0.3183431886308885, 1.0866697497226623, 2.49429557466635, 2.2517084627596256, 0.1539658220954609, -1.985392582137562, -1.8003117092745355, 1.3785822700382067, 5.64445193021342, 7.971078751995022, 6.772096757377198, 3.231727864406069, 0.18275984939908735, -0.4093511733380545, 0.9781690172739393, 2.1755731081780003, 1.5474720643794, -0.4974252504023419, -2.0941268846972005, -1.8799067385933605, -0.30488693304553766, 0.9595598278025596, 0.7909587518619047, -0.31487581535768183, -0.9408290373712478, -0.38740871552735257, 0.5489823744931439, 0.5095021568521764, -0.8007069720828154, -2.1093880769389948, -1.8542821150956494, 0.037984756401678824, 1.8083749346319242, 1.4974354712046645, -0.9892001380081594, -3.523865160009051, -3.6445371273384506, -0.9522836757718618, 2.347235925360417, 3.3926952969909445, 1.3056862415471, -1.9999147496761163, -3.608914430703509, -2.261512823291295, 0.6504562618863577, 2.593144533066291, 2.306576931682682, 0.7535065034589821, -0.17136901537405594, 0.32879291900963864, 1.3078167616455123, 1.3553164574374696, 0.28187833166447246, -0.6649780111904597, -0.2609425724498874, 1.2151681897786433, 2.173124348279667, 1.4272500135432318, -0.4318119764841754, -1.5809713179841638, -0.9363530986977426, 0.5627100855269435, 0.8564351585169793, -0.9559952186776339, -3.3548416706115427, -3.6503709208414348, -0.6707945517148678, 3.7908308276183194, 6.350381975016014, 5.027920211289885, 1.0071117716840603, -2.5214386659815244, -3.2634329594698457, -1.649542904445699, 0.048539975417311663, 0.20100326403621332, -0.7013363686127736, -0.9480712820718623, 0.28918698101871776, 2.0033191677248547, 2.5177158731982847, 1.390034227173793, -0.09283466378890948, -0.3633710548772404, 0.6775007015610182, 1.5859068588313614, 1.0665586007875794, -0.4898170641231347, -1.4219433664536096, -0.7844817898038505, 0.32987436422073213, -0.2210736302449808, -3.194603620182959, -6.687098704116871, -7.601456339115885, -4.60065772675223, 0.4015711434014493, 3.8280760787525345, 3.639318056994219, 1.0284050124992106, -0.9988695124745178, -0.6351699393540244, 1.1723152308443199, 2.047865118053511, 0.8201048786859773, -1.3436054455095594, -2.3596160150758316, -1.5091958627342106, -0.0794269644189767, 0.2142741527258619, -0.8482078905621755, -1.8783786964128253, -1.6099470426649738, -0.4086881489566778, 0.2118279233359148, -0.49630752772767905, -1.4505020117281753, -0.8909291900797799, 1.4457764696485333, 3.6518323300430957, 3.4655989130060982, 0.7747756085688471, -1.9618986436967247, -2.056801463323246, 0.6120949122363378, 3.3130324518391463, 3.1147297101277536, -0.1708779829905661, -3.7741314194830884, -4.697469507131942, -2.579201939506374, 0.18646721476968003, 1.0343480823400542, -0.2840655285498181, -1.8236081738901266, -1.7890956122863022, -0.4068002849375897, 0.6325923645218613, 0.3027364769415614, -0.6055755830667029, -0.5900864669096643, 0.5991574434031998, 1.5310829159383275, 0.766311696625914, -1.320200945972377, -2.7803526422126246, -2.248881044376142, -0.5653542313980068, 0.1135805830673943, -1.1469066665421717, -2.745412414886313, -2.1350503143850026, 1.2288726668512835, 4.826920357386868, 5.289735788569747, 1.7610589186997372, -3.08403755723483, -5.501899702720041, -4.144068569447864, -1.0341838958733018, 0.7686911021194162, 0.21259740789545992, -1.1432539785664764, -1.2982453389442263, -0.11789391553226877, 0.7630795669812517, 0.10182479675193656, -1.3855244390133974, -1.8785000732421682, -0.6510094169901327, 1.0300661201610424, 1.3813581744590695, 0.19754165939372514, -0.9445268878593787, -0.641776005339091, 0.5634777971237238, 0.8115160145797696, -0.6573530977126238, -2.1681003394816285, -1.183868563144115, 2.7196578713871147, 6.825171924430972, 7.630948782311788, 4.329970246776956, -0.2541710793892715, -2.36022845629823, -0.8604712900347652, 1.9557380360425203, 3.042658266817808, 1.7272719631016944, 0.017452560178179134, 0.031009915758330443, 1.594146265061978, 2.639315335381458, 1.7308943803647552, -0.30217595970733835, -1.441673310580893, -0.8575021155661391, 0.2604979977535273, 0.314368698912309, -0.699219470061453, -1.273477480718297, -0.45200866095599035, 0.7258420795194394, 0.3245713809789051, -2.0127732294395564, -4.231227113929078, -3.9440714434210316, -1.2463886749504238, 1.032825785715037, 0.21614295698543967, -3.225493198649874, -5.9342659900322365, -5.076265821919161, -1.2941319774385693, 1.981882898304134, 2.106488694333243, -0.1836814519388087, -1.847524288438817, -0.9251922888158411, 1.5402910060926402, 2.9736211259475973, 2.206244156044133, 0.5039510137241404, -0.25509375051944555, 0.1445461850257141, 0.25780838298814396, -0.9158950552031169, -2.4632678303123994, -2.610506352726456, -1.0083172817205583, 0.6430335084096869, 0.5413082365281537, -0.987862701193871, -1.770356390367224, -0.4151050552830846, 1.8035740313768807, 2.2359154174311966, 0.04241204470125264, -2.4296026259601087, -1.9385832232846507, 2.0157475743495534, 6.274688402436496, 7.029523233980841, 3.6319982539855302, -0.8511707421521827, -2.8464245454115416, -1.7025218427229472, 0.2401731952118596, 0.6457912278379745, -0.34706114577456815, -0.8319186209245549, 0.18779229823172403, 1.5280260122302498, 1.404626169347667, -0.23364913445647129, -1.5667810556744948, -1.123699777156965, 0.4154482223879361, 1.092735960593677, 0.1460049873978282, -1.0236654928553017, -0.6672345336986261, 0.9438214446552083, 1.6680801386692372, 0.22208906041912901, -1.7734594629050946, -1.1828270122154985, 3.0503214021054226, 8.171729844911942, 10.000636767455305, 7.083194795945653, 2.141275764441514, -0.7686613334339822, -0.27272526721994206, 1.4310984796512474, 1.5006354734036758, -0.33635561731646046, -1.8527715836406193, -1.2618134517098116, 0.6346325186314988, 1.549465918492196, 0.5255728720014655, -1.0191770851290503, -1.1725152200295175, 0.12142356372476379, 1.1599760940806263, 0.7922856798822729, -0.08069772993401673, 0.2264815544287323, 1.7730630140079167, 2.638043586688438, 1.3075151045389066, -1.0854954700359243, -1.6718615496376201, 0.8220052727424947, 4.204939918127126, 4.8912242471082035, 1.8295445414739728, -2.1605653901972937, -3.3177325962957283, -0.9537931698450611, 1.9212955755169359, 2.014888244167147, -0.6909424128912978, -3.1735810510487026, -2.903644079446303, -0.5137112324879906, 1.2958500816077247, 1.0094415409851967, -0.23259021648748757, -0.4499990615630756, 0.6009585197244715, 1.3248926717334735, 0.5959537243017485, -0.6405279261967278, -0.59393779948307, 0.9117409566533616, 2.0101663409249575, 1.1117829134799908, -0.9092207193900276, -1.5675203799366064, 0.18432445515916102, 2.4722053588482065, 2.6438673067382656, 0.6442489837334304, -0.5441663671044552, 1.7431048077993494, 6.449477385881065, 9.439141128424309, 7.728291362902201, 2.654513840495093, -1.548470838592827, -2.1212489654701887, -0.22354438712443847, 1.007549793332187, 0.1810351084800907, -1.2000056503811547, -1.1249268745327419, 0.2772199897401576, 1.0937572822575623, 0.2846400904322561, -0.9120743448141841, -0.626879011890936, 1.1272614972717105, 2.3729933698511574, 1.6679274539830549, -0.02996848482344544, -0.5840634145430728, 0.538646840646233, 1.5676174328682544, 0.877753653113065, -0.48383044614009413, 0.3399686397377315, 4.4178557878457125, 9.011246587444711, 9.951101248031962, 6.06812899194251, 0.657880581897434, -1.842183509696112, -0.33092305074517797, 2.257531994156696, 2.5788959091784665, 0.49097269330064447, -1.361609647940568, -1.0723248506374456, 0.33464322328255025, 0.5178308319794616, -1.0713957269703256, -2.5501502455147955, -2.0893606998195478, -0.22989851473426642, 0.8946065946999002, 0.29843930657368023, -0.7591501404886214, -0.68920397966222, 0.1287378776501209, -0.1732202846052127, -2.219189843473452, -4.07401692579347, -3.396549492421635, -0.5949097489434071, 1.1311454796683345, -0.6342792413754601, -4.43076987771097, -6.20346780456838, -3.765566448619056, 0.6725007357317142, 2.9184173821416137], 'positive_zeros': ['2.1529959313093544231969574101', '4.14022906279380746878277374178', '5.04673640052099617779085922190', '6.77027576449304127125513693512', '8.1231298607054143440724777139', '9.94039552823299905250001110737', '11.64719657936340570885271950233', '12.44344646685592426687320555254', '13.62693597437755972136620955645', '14.988363826995783892640581326566', '16.03532399263962021408568402645', '17.06571045062561068492299915515', '18.987152355584578371776042771983', '20.306110030425296125436977741168', '20.92130282078276344863347994774', '22.37708662019528224026103520488', '23.39647963853528082536616738209', '24.317844932477225142751654136640', '25.27189730300615054107016496546', '26.72131737528539753035523890827', '28.28428480725796869335824495436', '28.99937466633912832789599636201', '30.38838507045460863059745361144', '31.48669907677979793529516492932', '31.97528462018729448844350280799', '33.36773855323595962642800333870', '34.1135713195810806718723889506', '35.56085818928806614024653075643', '36.45735609700208347725956875601', '38.11068553881670528638945838357', '38.91732957127361485648586897450', '39.85937874293758576272177611947', '40.73312347704802446070702285073', '41.77687789627264248732119711409', '42.84600005521458667951087098789', '43.743727460078964228174235095426', '44.584038513526400312384002958638', '46.63902281164630861373932381963', '46.93181267128780016592887931268', '48.38210356605519175710083722328', '48.85324323499729443283284517829', '50.21886736842925805934885289971', '51.05288874457208237377996704766', '51.80657594075530167526684554214', '52.72384328424890436226399523029', '54.094772823686784904434597546303', '55.38700102558869491062800161314', '56.1088203107185739189513401323', '57.25054036023301654766434871946', '58.22630148176623539213449616693', '59.03459912445227161967219900661', '59.93043961690993556636706666194', '60.643780902097949751266197836453', '61.9825439865537785195452350945', '62.74048320323302528173386260928', '63.97364920438371599261506723371', '65.21202378660530269335536292306', '66.04970750123315474181818945745', '67.02960566143064499674176787292', '67.72651911896249714870760729979', '68.546197738783765918487193380029', '69.79103492401026559847457188512', '70.57119142943842955261650757785', '71.18713675758450114293662323121', '72.6348989002990428405531188579', '73.87785596659307432572664415849', '74.712648030395340568563796401827', '75.60940075210556121481443705342', '76.16983521335726164134391330515', '77.588898290513347605142413791017', '78.24047821977311824414517016811', '78.84341353855277187054518932099', '80.01890154631286427356128080040', '80.82836653204120109307969900329', '82.53130293358339500276951473834', '82.93444715925523391260994331521', '83.99175295904610281662563757458', '85.05705254416683390689799487143', '85.85204634997224722335111630445', '86.68046015286231785541784358857', '87.33521005655496374208728156556', '88.43215427928652010465318243641', '89.26887652417690513743055123080', '90.395985092434296288652624795022', '91.371208684425243393063085499575', '92.430273772231401087577480076386', '93.6368764970922685638505230486', '93.94340282932439778871053629103', '95.07035938284170870852566221881', '95.69009896707196913190361821476', '96.80356685184738021177447408499', '97.68895683803871691621837407907', '98.30883797249470253118558809153', '99.42312149645032592389652158589', '100.69941162101212985954930125028', '101.86082328825822681353481752350', '102.27011708818019757881183191378', '103.07223867941953258066656157468', '104.34889212162705034321577174355', '104.8260079108057443884108129335', '105.842472294119087561200400793234', '106.75888569492145058877058207175', '107.14641171109179987714633088309', '108.72414196037960661827181715416', '109.811089091063888423058839042236', '110.43007373544800243991904565039', '111.36726130068804214696997421809', '112.524435661999264414165631384642', '112.90457712135515253162410520290', '114.19189608777504757564580751380', '114.529715236989251035668530063710', '115.45118242963802315843378123933', '116.637493698150439294250364651211', '117.44113607648191898216436851981', '118.424270925822843688270667351778', '119.660768591703030953535384098948', '120.26335901027912882096525712690', '121.33911580800757435349857185605', '121.97420879477260424265012550602', '122.675807226554009556055496432322', '123.56220396563348037648592393292', '124.83731553874050186406319554892', '125.06269865154817049950576469004', '126.15355566459029060514143388717', '127.29734639945553724343198536448', '128.56698776327578081832924608731', '129.1097658302939833380351859356', '130.02756536689322188906596518039', '130.64793430126476702547378904862', '131.67351548588982170443050935599', '132.54155903982050438062529481386', '133.291118720672341740778130120582', '133.95198266565091034899178303901', '134.80252597664286000929692118686', '136.229797027432849776959443304350', '136.96833749864861301123983626920', '138.13026434342295403852281296239', '138.42795426919584765679246751544', '139.6394497859253330869470653285', '140.53647709061422968420003695475', '141.053038804282933000372733713948', '141.97871192872779693381503856161', '142.55854549541611497935333660349', '143.885885732844024554302481688753', '144.40055741979772022055192767567', '145.72595671792406524418184896111', '146.53983872145768432450117939957', '147.31019154202376305804863055654', '148.57076601504487194950041106509', '148.98249462555906024007581067175', '149.480724407787977501440863485172', '150.78944613585173062361210345385', '151.3745880483533396152381699025', '152.2441935954839661092153236037', '153.12952317192296392772018610351', '153.92590141224755919600078172243', '155.24503095110378262254149286744', '156.20086189409621055215597703010', '156.77884485431294046850893867878', '157.46055546668309203530422616857', '158.39839173976386090838780744820', '159.28972498957069483281284319418', '160.032001222776801332324454311295', '160.76352688864792428070185482545', '161.59327917867279626144151227450', '162.3007929154607910546161399744', '163.93410666777423157410736196581', '164.42395626069182333152866381106', '165.26344555277714012713374580407', '166.1458616841815091376923136757', '166.971165460863536385221134258876', '167.78724946583737654876103891786', '168.70670649100596280765138717861', '168.98738019567761728835798768664', '170.16489100640338233477394127640', '170.86170105208795256519162946969', '172.007735021086646528498287353759', '172.90238576792793077051975348795', '173.68240310260169212876541495325', '174.75270041052786390702180081116', '175.5583626706991639076520545511', '176.095150714531023695158285840701', '177.01203420456820910005651655394', '177.643727163204714042492654367149', '178.60701736836151229572445075545', '179.35191487732049176149459397492', '180.412442022128099738959277058634', '180.763492312529730950640140706181', '182.357498417803366839311531550489', '183.16002488245748083507686745259', '183.78668905858438195971545582966', '184.62972655598993567058196166457', '185.37654779269369254441537572327', '186.06507001801933195720693133308', '187.18101347096897287576200779315', '187.69505486464116431011943993573', '188.61649153751812585951276653977', '189.01680249141203187081135854890', '190.67319601976427812791349959749', '191.28706837746354649237272305960', '192.25077839688380820251368521243', '193.04327743902842566672915880508', '193.567849211751977542533627730904', '194.72786891282052933535695027153', '195.390058841979674717611538204764', '196.18986956237507422633255398502', '196.515187630013672880315608543183', '197.88069711588716563727244840647', '198.37372841228587133124768022133', '199.636719689652986912379800126699'], 'prelabel': '1-63-63.25-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.29257077000673354, 'root_angle': -0.07572850860950169, 'root_number': '0.971833093103080094489895888925-0.235670191474653953274859782322*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0378642543048', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(3)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.54408046590557472038427035751-0.121279221056204783241524829012*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.15299593131', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.14022906279', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.04673640052', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.29257077000673354, 'bad_primes': [3, 7], 'central_character': '63.25', 'conductor': 63, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/63/25'], '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': '1-63-63.25-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': '1-63-63.25-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.29257077000673354, 'root_angle': -0.03786425430475084, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.15299593131', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_63.25', 'Lhash_array': ['dirichlet_L_63.25'], 'label': '1-63-63.25-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/63/25'}