-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_67.9', 'a10': [0.8412535328311812, -0.5406408174555976], 'a2': [0.41541501300188644, 0.9096319953545183], 'a3': [0.8412535328311812, 0.5406408174555976], 'a4': [-0.6548607339452851, 0.7557495743542583], 'a5': [-0.14231483827328514, -0.9898214418809327], 'a6': [-0.14231483827328514, 0.9898214418809327], 'a7': [0.41541501300188644, 0.9096319953545183], 'a8': [-0.9594929736144974, -0.28173255684142967], 'a9': [0.41541501300188644, 0.9096319953545183], 'algebraic': True, 'analytic_conductor': 0.311146691911923, 'analytic_normalization': 0, 'bad_lfactors': [[67, [1]]], 'bad_primes': [67], 'central_character': '67.9', 'coeff_info': ['x^11 - 1', '0.841253532831181 + 0.540640817455598*I', '\\\\zeta_{11}'], 'conductor': 67, 'conductor_radical': 67, 'conjugate': 'dirichlet_L_67.15', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^1', 'a^4', 'a^8', 'a^3', 'a^2', 'a^6', 'a^2', 'a^10', 'a^8', 'a^5', 'a^5', 'a^4', 'a^9', 'a^8', 'a^7', 'a^4', 'a^9', 'a^1', 'a^3', 'a^10', 'a^1', 'a^7', 'a^5', 'a^7', 'a^3', 'a^6', 'a^0', 'a^0', 'a^6', 'a^10', 'a^9', 'a^9', 'a^10', 'a^6', 'a^0', 'a^0', 'a^6', 'a^3', 'a^7', 'a^5', 'a^7', 'a^1', 'a^10', 'a^3', 'a^1', 'a^9', 'a^4', 'a^7', 'a^8', 'a^9', 'a^4', 'a^5', 'a^5', 'a^8', 'a^10', 'a^2', 'a^6', 'a^2', 'a^3', 'a^8', 'a^4', 'a^1', 'a^2', 'a^0', 0, 'a^0', 'a^2', 'a^1', 'a^4', 'a^8', 'a^3', 'a^2', 'a^6', 'a^2', 'a^10', 'a^8', 'a^5', 'a^5', 'a^4', 'a^9', 'a^8', 'a^7', 'a^4', 'a^9', 'a^1', 'a^3', 'a^10', 'a^1', 'a^7', 'a^5', 'a^7', 'a^3', 'a^6', 'a^0', 'a^0', 'a^6', 'a^10', 'a^9'], 'euler_factors': [[1, 'a^2'], [1, 'a^1'], [1, 'a^8'], [1, 'a^2'], [1, 'a^8'], [1, 'a^5'], [1, 'a^7'], [1, 'a^9'], [1, 'a^1'], [1, 'a^0'], [1, 'a^6'], [1, 'a^0'], [1, 'a^7'], [1, 'a^7'], [1, 'a^1'], [1, 'a^4'], [1, 'a^6'], [1, 'a^3'], [0], [1, 'a^4'], [1, 'a^3'], [1, 'a^5'], [1, 'a^8'], [1, 'a^10'], [1, 'a^0'], [1, 'a^9']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-67-67.9-r0-0-0', 'leading_term': '0.926506545520910456037637194676+0.896613854674280530665451115391*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/67/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.2893140747261556, 1.6741775652933044, 2.3650508886636397, 3.0832207058631105, 3.593430160336078, 3.7170913596980015, 3.352180198736133, 2.5064763292848142, 1.3159127720373647, 0.02769615898253874, -1.0586616405397862, -1.6816386931745726, -1.7116528705539817, -1.2120582766492285, -0.43574347058333324, 0.2534894400724517, 0.5151275668018203, 0.17369943404462257, -0.6923062221978579, -1.7614626760777727, -2.5893962203763086, -2.797283302870477, -2.2495892222709726, -1.1350565136020294, 0.1003197284889867, 0.9535272421322438, 1.1141184703535907, 0.6423944942587763, -0.024692345848045725, -0.265451976467228, 0.41102573182011515, 2.074822167277633, 4.266004553726358, 6.146342732175542, 6.86437735810974, 5.968632284170825, 3.6610785201530884, 0.7471694033611136, -1.7136440228280323, -2.8947093131508708, -2.5814674736454966, -1.2438253649986863, 0.2399817766147852, 1.0606425059516849, 0.8944792494823662, 0.02874323485176193, -0.8696885956015175, -1.1980800772513163, -0.800676605359175, -0.050964678678294024, 0.4219506588654875, 0.1905983642567433, -0.6307768300229083, -1.4044472621700486, -1.3644485561454847, -0.15544844275010292, 1.8365417514214033, 3.6088019585434847, 4.0913602546737025, 2.8081433052740867, 0.23490707115551232, -2.4001262702806376, -3.788453336223755, -3.2942651295312357, -1.32300436866409, 0.9360796342575884, 2.244473492060942, 2.067852457087949, 0.869456018485054, -0.24306426387893154, -0.28191636248479995, 0.9535629430216676, 2.750782350779536, 3.97816025720069, 3.8566959211113643, 2.476211504569829, 0.7027578393118613, -0.4480552312137013, -0.5188607233894965, 0.11009965204458814, 0.5674063649046789, 0.19857308929357728, -0.9027010861446595, -1.9557699916065996, -2.119450696641197, -1.2142561012735973, 0.03350945220036381, 0.46737048215792276, -0.6055451137021642, -2.7574737883591505, -4.555543491647221, -4.450633734137061, -1.863286412058363, 2.299819113998397, 6.104159991809992, 7.750801958466598, 6.668233735380394, 3.7931444671422065, 0.8683443843327061, -0.7227541741818405, -0.7564533860077706, -0.07455103476382591, 0.25412871333173964, -0.1780683690855559, -0.8713653183534072, -0.9667421297126736, -0.09459831934782145, 1.2092112075775252, 1.8912922656855824, 1.2693484244689235, -0.32075963310500727, -1.6948473350798423, -1.7246861416101111, -0.27045630563927836, 1.6347874628974242, 2.553458590278313, 1.794516875184259, 0.026759121281686095, -1.1808821370108862, -0.5828400606985631, 1.7020647064751318, 4.1793257230409395, 5.056541983476634, 3.60229292471682, 0.7282105140848308, -1.675731899669954, -2.1481021675422807, -0.7138869279036014, 1.2204325462382637, 2.023554040405674, 1.1078989222992401, -0.6935583545378526, -1.8991585252549315, -1.6187245946207156, -0.22709305243878214, 1.051781960033782, 1.2383748840301718, 0.3980061544293421, -0.5326472097096517, -0.693719416430643, -0.1295438874312865, 0.29195757291775376, -0.17664825573589388, -1.2247161649929377, -1.4891486502148532, 0.3574065139882886, 4.292483562702087, 8.571803873190335, 10.764362646216282, 9.488113559398968, 5.487920397889383, 1.1557702292414067, -1.1755610473844715, -0.8407097202613153, 0.8909730243208349, 2.0313721035549017, 1.5153962809769392, -0.08278711546906242, -1.2680860742200772, -1.0499532498582562, 0.21290146405006055, 1.2551987118183128, 1.160310472694675, 0.23461924158234443, -0.3113970732659092, 0.43370452034801654, 2.1355323122761556, 3.437243083261779, 3.1809185011611234, 1.5057745240471996, -0.22052301678815261, -0.62058692882072, 0.4239036381224525, 1.645868306834314, 1.5779926458389304, -0.01014130740519688, -1.7767082166403134, -1.96913013997983, -0.09727528411977479, 2.409456347112449, 3.2525345942595, 1.2003572937915359, -2.7532357502445453, -6.0556957724014415, -6.572340206202215, -4.2199968813424205, -0.905533273247591, 1.1104207225218765, 0.9714011846328773, -0.3679339515707387, -1.2878804189687423, -1.0289225869817922, -0.18792192270431113, 0.15302707302819998, -0.31902774166630515, -0.8085089144067699, -0.3165124800904729, 1.1646862975195558, 2.4498301522478405, 2.2574002540424605, 0.5710127969579144, -1.1371953334400502, -1.1937038911982298, 0.5974770272344315, 2.5083020554571904, 2.250578625073432, -0.9591485064505195, -5.492033208378536, -8.462618074285036, -8.016332731287328, -4.773882179694207, -1.1913264086713429, 0.5468796203346168, 0.2044137764087228, -0.6909158007997694, -0.5675620218841025, 0.6436884463361878, 1.5842360987550068, 0.9907519015107746, -0.9006305273185253, -2.475183688705214, -2.262342716435355, -0.3526242027363706, 1.6842901986797976, 2.286431537994604, 1.3167422828828719, 0.029787749676663065, -0.3231088925634305, 0.20948979286659933, 0.42658853782253814, -0.5880028923979723, -2.268156419966231, -2.9616903766689715, -1.6610888648735989, 0.648494103546468, 1.5274890060207664, -0.7722298144092639, -5.487366527425404, -9.646285887739475, -10.392322787951283, -7.322215030145636, -2.757890910577991, 0.26655926769434735, 0.4594479592812214, -0.9980598667147749, -1.9274612547024124, -1.2737512435450409, 0.14498135994661515, 0.79082923848606, 0.10814953991659813, -0.9971363127603742, -1.284626764061151, -0.5928429232088702, 0.03302273169903719, -0.3614791101587157, -1.364924842133221, -1.4357061425072635, 0.4567986216654176, 3.4695775840819283, 5.349303103911188, 4.4580832506715, 1.424146605128868, -1.2931079846890219, -1.62959908753692, 0.17614464567339472, 1.8739633108929146, 1.4454582455656895, -0.8840786907403938, -2.8511755400438505, -2.3873250759452516, 0.31686448543758483, 2.9486889960553277, 3.2662776567969964, 1.1841015170369573, -1.2649667491464114, -1.9710225776215982, -0.7135396624458771, 0.8553579314089526, 1.0535618777971116, -0.13602633423897667, -1.2249194171888511, -0.9378243977053905, 0.4123244284153269, 1.3439187219944582, 0.8908042792256587, -0.34391917664524446, -0.9391340475175037, -0.36224311176703833, 0.3362664388201877, -0.2527368790157881, -2.0050188073819637, -2.8705946493162027, -0.7120175921746653, 4.2940239771685125, 9.194903231263233, 10.497372876919002, 7.1779880682820565, 1.6444254932006603, -2.3055932311665797, -2.6368137281325486, -0.4448434033393688, 1.5452910962669664, 1.662778838853602, 0.5047341198326215, -0.2636282278493204, 0.0418504567474427, 0.4924373040944859, -0.12221456285863228, -1.6501566595609711, -2.562403794920714, -1.632260167609981, 0.5715731890304762, 2.111071747049453, 1.6560697677835057, -0.10961868995943547, -1.222321393557732, -0.5673365673993556, 0.911493116781408, 1.2963360165786717, -0.051757471017363235, -1.5591568953808386, -0.9837520983252542, 2.0856144508092753, 5.457164745960698, 6.277085929317284, 3.818237149578992, 0.2584449535579882, -1.4217172420828335, -0.33746264954032584, 1.5301383339091852, 1.4438966534803743, -1.284747591823545, -4.634645077080588, -5.929724622479727, -4.410017885963065, -1.7253999273049354, -0.05072277909578856, 0.023819160599230872, -0.3544541449993824, 0.001843740482839299, 0.8796450692154117, 1.1198391282708726, 0.2942994203978188, -0.5317316572314348, -0.008701996999279567, 1.6619894172209182, 2.5406721068677443, 0.9434187832970247, -2.4134245961380825, -4.614371336525637, -3.23226717802663, 1.1089528772760742, 5.024417965760847, 5.419443331682875, 2.3387585782381195, -1.2158647018927415, -2.2652445374387664, -0.5858347844599948, 1.4762825765897778, 1.6811918000626005, 0.12123718505319826, -1.2506225611956423, -1.0212409992222176, 0.13168980767256128, 0.39579964710246696, -0.9417775536940322, -2.605337257962712, -2.8001242428623137, -1.322932387755257, 0.1414725545197142, -0.08934707368160869, -1.7660012420663234, -2.957968867015702, -2.224166205825405, -0.23137746529506908, 1.0439324788594802, 0.6161468908123416, -0.40236352625730065, -0.2625070347402471, 1.0222812685345835, 1.2289287456102689, -1.7400466921686504, -7.11673364193299, -11.249230025913933, -10.70341453937434, -5.516911299109267, 0.7037644249855943, 3.99546580947714, 3.369438324852705, 1.0699197709238635, -0.16056410274872726, 0.2580856344547722, 0.8053734003700654, 0.13506707148209873, -1.2552181435222347, -1.7825956438674193, -0.832037134096682, 0.4715243057649703, 0.6850519633459828, -0.13001398794467972, -0.482322976972597, 0.5910934431677131, 2.0730448578792964, 1.9554715758280106, -0.27879048814604757, -2.594525293980357, -2.2837460429461625, 1.03684135084978, 4.636252426163379, 5.196781093918747, 2.1407105172144543, -1.7685501149273493, -3.2322772184656037, -1.666714704068739, 0.5082300965849972, 0.6998018387003511, -1.0984514162115635, -2.585478095017545, -1.96961179615846, -0.04027242092898912, 0.8135059748062937, -0.5838334138465716, -2.809365134135003, -3.4306707510360708, -1.6970010000949427, 0.7263819334809071, 1.707888974712183, 0.9373766162975442, -0.049065483662643516, 0.05881429634597973, 0.8016564659556897, 0.8025240550712529, -0.13994769452376896, -0.47833942349562386, 1.2006154481242388, 4.034057266587435, 5.29565673719394, 3.314670828567345, -0.2726757684200046, -1.7391507326297506, 0.9824428656194919, 5.9301666969036395, 8.799832102299295, 7.082368570477608, 2.3961042626221936, -1.320095118572073, -1.7019715918987373, 0.15119501158410675, 1.4688807517300306, 0.9343690725055336, -0.34019505665340877, -0.6832032546051445, 0.006134398385143578, 0.44100858148103467, -0.033262240588069564, -0.342786165607751, 0.9631987574165639, 3.562146389796579, 5.2226220529564795, 4.132236945039963, 1.0529115983746162, -1.342584938876254, -1.3578422522399758, -0.0837273009308507, 0.0333354486498302, -1.749551112814561, -3.408138952582191, -2.4665802332560363, 0.9106181191228011, 3.7186223673813354, 3.2441275465248856, 0.08911913346059644, -2.3711817234157166, -1.5881180323723354, 1.4665905787707492, 3.464611557964692, 2.3675590575317287, -0.5226833686819967, -2.248869341634848, -1.506006674850213, 0.20280963725580656, 0.6415489388180926, -0.5192795594035722, -1.5880151629118224, -1.1477871440616993, 0.20729870176338722, 0.783881824694563, 0.04732112598741663, -0.7254697487883719, -0.2329402524854126, 0.9921339892082655, 1.2259783127156505, 0.09037231936449344, -0.2874063161442009, 2.589836254327958, 8.258869582093975, 12.755147199752024, 12.040529108498857, 6.053367791674746, -0.9773247713735168, -4.432427243138656, -3.3761704465760998, -0.676138663242158, 0.5523829540621452, 0.032695182838551204, -0.2520741886299723, 0.9169510055418755, 2.3847246317137367, 2.232224541095877, 0.37331727876436716, -1.1959304407574405, -0.7990614325397025, 0.8881611767556463, 1.7154149866347237, 0.7483162670541161, -0.5902575143670465, -0.36426180865038077, 1.3478332311359953, 2.4433017892694355, 1.3946306350344186, -0.7559306293891732, -1.5754494507723582, -0.24789060485865222, 1.3220953670921425, 0.8376648858889829, -1.3537852098358965, -2.3343927095023638, -0.016644710087643285, 4.026441491127329, 5.817637445075147, 3.18700240246745, -1.730425046495982, -4.587718649288332, -3.2482294014272917, 0.2907856038623355, 2.3810221555746685, 1.5887939516984222, -0.33398886348819895, -1.0132392073875827, -0.16780636890281922, 0.6320472203904408, 0.3832227706123092, -0.0854525003837454, 0.4707260621286709, 1.723285467753055, 2.0513708373827546, 0.8482009075097554, -0.26293170275675676, 0.7702210867530653, 3.6052108849371614, 5.317339243107598, 3.5298303696158637, -0.6393220169172832, -3.476901930456169, -2.70136659486153, -0.07220719101905015, 0.5355087629753185, -2.489392001536082, -6.632708409706172, -8.008139868975576, -5.528020053339582, -1.7874951695967998, 0.08409553558571375, -0.2796344704730651, -0.7782066010079703, 0.03998830421511802, 1.1097904516437143, 0.4714118320099686, -1.8606991888478015, -3.5477634401787412, -2.6164293445161793, 0.15089977357476686, 2.1005897788724415, 1.760841561851348, 0.30834057971887985, -0.22685121868776698, 0.42868781518283544, 0.7342189223198712, -0.23023608388818323, -1.2385259415599443, -0.571354096106811, 1.1644320620036919, 0.9705379457998432, -3.1344931545362553, -9.07938852230472, -12.054845122073344, -9.268353725829357, -2.9932267091474474, 1.6091164831912803, 1.6045240040888782, -1.2103515384109396, -2.888208193221273, -1.7304726813239, 0.456478894247465, 1.1524864427108668, 0.16615429509590401, -0.6549997168707149, -0.18238612785369887, 0.5718595283481532, 0.09434893249883122, -1.3437281174857632, -1.9437275399296108, -0.8671395528666496, 0.45415179965015595, 0.13286192018564327, -1.4806932920140765, -1.8906231723839897, 0.4346321879137007, 3.741426438077982, 4.628647878464346, 1.9918842060333308, -1.4556652234304068, -2.121983473453536, 0.4055245545332424, 2.9950504960570767, 2.7364682063853545, 0.30666455655795527, -1.0842197307291754, 0.21076408136499455, 2.1928406461925394, 1.6841599386459545, -1.7067920603027658, -4.960897935992194, -5.078437974496432, -2.388258217959762, 0.12620582946535794, 0.40185021010427474, -0.6711456749383826, -0.9636613907853571, -0.012561639900417084, 0.6646331066789144, -0.018257605137145645, -1.0386268605909266, -0.6538335269059696, 1.0640343813142685, 2.1209422184585085, 1.2581172112474512, -0.17726066977470958, 0.06022338381262026, 1.7510698289932747, 1.708158895918462], 'positive_zeros': ['2.819507937899483640549572727486', '4.55681601998545573653826544306', '5.38956917427975994286106851963', '7.47242974824482681993855829939', '8.73639744088836855505346643354', '9.24430368759659639710539780830', '11.64634918382107773496452502658', '13.06808317331795903045278886334', '14.07144593464437148946256049149', '15.33513354538160978083968875875', '16.02508946916506972185501977962', '17.21502614895044618781756132805', '18.77581145200831569746419705534', '20.17568684801332705161259907859', '21.472547188816554394687581287605', '21.97707963395967888873462539266', '23.90665346618277833543390387509', '24.6387739418190318962279026485', '25.381122967115446329319715539102', '26.86492581303449476094113428149', '27.376275708410634624589269185643', '28.89667269216094828414607193495', '30.75529995601635374577301219710', '31.59984257367058543665679335648', '32.102381244409732317793170307847', '33.1484002327477713708587955159', '34.31685929845429536044824789060', '35.355775075676536887359632568055', '36.56724255319416466823206360201', '37.285259777592697204980332641603', '38.82896867693464858826998054444', '39.79693827587949858589373641091', '40.81885771373467283267497601289', '41.921002328481164005662322603934', '42.92978582953423641404049284534', '43.81285088924968341425578509085', '44.3093321867772915430343697790', '45.274111967568357915803844950871', '47.30059327295903157431721705798', '47.97238477411522717557832271960', '49.0468817551378470059370786851', '49.952229332228602969679883169156', '51.02008070844921101874757721909', '51.44750288790527839057407605104', '53.07327241372375057428522905985', '53.65231767796665648960054781677', '54.68590991470435271388281204370', '55.63681101314748562087451979430', '56.66534895871045214547236977365', '58.23000803928107056485224936787', '58.98137315512498764934332405042', '60.091088452208924742687000804614', '60.46200772636108405576205013698', '61.33005374186488477558513142327', '62.58924064641568867942930474317', '63.35269560663472950533681161745', '64.30235139829192849480229759542', '66.09790025565551963437193462376', '66.62712526883795403814808409657', '67.35171308495247179687613934634', '68.3008946438447313161098609236', '69.422963752835295784964808187926', '70.63503412239611899666487704562', '71.147315228730585295334627327208', '71.7409771143714034833063753596', '73.0331225317912678381449919545', '73.68242755291021361576771942822', '75.57933813184031978660561685518', '76.0519100912717512883098550536', '77.1526123692451633819143765432', '77.84194113649113151007482351941', '79.02242906694775768328986239904', '79.19895497075050031561675079012', '80.25851138279077192239632541844', '81.70316058058872258807447956755', '82.47497635070982124402901179460', '83.3316504816429563080607550637', '84.34343522122204269952172264245', '85.4500235738548209370162891307', '86.37601077206670794090422853118', '87.157977253435217129506645980829', '88.03605394842887620773853471326', '88.974039039566199980408618617050', '89.81406241513680781031598449622', '90.248434839587953056424396347952', '91.30379742250735012804520609980', '92.91593393154557215346933211392', '93.80568199599088482634640067635', '94.8389768387012881970808775875', '95.29126684850820109380381665483', '95.90545896373133020477336568867', '97.10932790833238722871323095425', '98.10586329119726531177207784490', '98.86801560098155950463531400791', '99.678657430202731142723916033853', '100.43550074379321282166250770640', '101.90261094095049173234767484422', '102.55192988866015539201059639506', '103.31668951060462379594183347340', '105.02169579622409367610423906957', '105.32987523515226465598107952751', '105.93676119744435880777439547689', '106.960323587983411139951859848767', '107.50206580789776979658445914615', '108.53255527622159947116802873346', '109.61542891167195093798640306867', '110.81514822331790177758366440994', '111.63964884489824582134145877186', '112.52077761291232849904718763328', '113.39817206961870041324956338795', '113.879861396201694951247978449853', '115.26418718720912310055402410162', '115.60014016114972936448489543111', '116.91300057681639260994179062586', '117.672035397565719985375898033551', '118.20048176000795896526540574073', '118.92431049263019735255496913913', '120.58458856217072461620660078641', '121.78407636906822563642963598042', '122.079950086863840248047756657834', '122.84475117255123602026966525301', '123.93296076308544492340352959867', '124.6422025383986507390999631301', '125.18487746448964625627333478834', '126.21846530126577325882317485566', '127.106541861911295431129243893199', '128.28532207971096282375842612549', '129.28428507882221082223086670536', '129.83255808836861714426666727506', '130.944619318082637434119376268814', '131.474038768051296754181261640156', '132.70897244467819299310504957900', '133.723498865699009585553974695146', '134.03233834124651552841637076686', '134.95686384240149845472449744652', '135.450271664293733256911753302115', '136.84865458300465968058352805673', '137.42610621770614208864836065317', '138.922196030388338328865095384949', '139.66430402027949715414639467668', '140.53189875434054779567159743972', '141.24759881674117425347688650436', '141.85982322848190640826910464722', '142.32634974127314670338158569510', '143.85925056035693510503836639992', '144.71376761316580276146848520386', '145.010394959531118646473155571450', '146.173883096861300764780367026', '147.19562245111587091840387511983', '147.98344371278080181794906548463', '149.00550638242453486052329999809', '149.95612184749915457706873002177', '150.51220872737284218470647545922', '151.512049554813652185720320567039', '152.2015132312382045719613046928', '152.87359970060604067096294982559', '153.77289834358154813942589860239', '154.12796144159563633001049662145', '155.88738082431851024411257516294', '156.98285744554455080474334451531', '157.51333436338941166376963592707', '157.920686870132867439513777878692', '159.11862056216349111608777771742', '159.8413564851453915364166491979', '160.777074879202044652401123583585', '161.33079300313650321239512043686', '162.38572337643348638752187437398', '163.16513339745541414283031688734', '163.879536991243528509730940577210', '164.68888114878627084365652792846', '165.82658021657932323543826933036', '166.84834554540139184891551150233', '167.7512955601883484875620406114', '168.484869115105742244676359339653', '169.27048992954254959961461086333', '169.5095898381045156957010617634', '170.81574594322719638552411143470', '171.113420282754627088337465007565', '172.45294199013480760504181083172', '173.44787049574688786836652590699', '173.83951516452827778383578804407', '175.586586230410423761091168693556', '175.82406578179044079341681962196', '176.55285281488774773794974124847', '177.2630249872871165414563599209', '178.42082670063232640547477227090', '179.46522421906965091373311816012', '179.83127652048361293818523579953', '180.57030427808237894785261410873', '181.352514363194757439471784779332', '181.981614016719090661603654018590', '183.60670053928092891047357587943', '184.24917012345401023387522111507', '185.23795959985087434816790023751', '185.97986181719280965983289766882', '186.62328872127638931347925359311', '187.2113518290037675054216413066', '188.30207689862753137786792350776', '188.78083417424634025867048683117', '189.64613255141788720020921705881', '190.79076559884222611507979634159', '191.52301007992579245564065036773', '192.54046513029857364096553046125', '193.09466411762796651229214804486', '193.92479148889411688927216979574', '195.2877769904795941915802122388', '195.75190769887991710189748839104', '196.56598297963396355829895545833', '197.18263300895812570596624931159', '197.94402618109542875257112595075', '199.00814999547770639401594693031', '199.360185329849602517638999933915'], 'prelabel': '1-67-67.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.311146691911923, 'root_angle': 0.4895626350693837, 'root_number': '0.0327840734510486795326576734401+0.999462457788163369453430646292*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.244781317535', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(11)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.15473631937025417021386134531+0.746288155361762605752718618618*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.8195079379', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '4.55681601999', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.38956917428', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.311146691911923, 'bad_primes': [67], 'central_character': '67.9', 'conductor': 67, 'conductor_radical': 67, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/67/9'], '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': '1-67-67.9-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': '1-67-67.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.311146691911923, 'root_angle': 0.24478131753469184, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.8195079379', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_67.9', 'Lhash_array': ['dirichlet_L_67.9'], 'label': '1-67-67.9-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/67/9'}
Lfunction data - 1-67-67.9-r0-0-0