-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_6003.1001', 'a10': [0.8300502097550806, -0.5576886669868294], 'a2': [0.9493614035755648, -0.3141861317770625], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.8025741491979327, -0.5965523740956988], 'a5': [0.9632356771877736, -0.268657831065114], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9976889015579163, -0.06794744813573399], 'a8': [0.5745044379364633, -0.8185014665785935], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 27.87781479921304, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]], [29, [1]]], 'bad_primes': [3, 23, 29], 'central_character': '6003.1001', 'coeff_info': ['x^924 - 1', '0.999976880197217 + 0.00679993169383467*I', '\\\\zeta_{924}'], 'conductor': 6003, 'conductor_radical': 2001, 'conjugate': 'dirichlet_L_6003.2003', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^877', 0, 'a^830', 'a^884', 0, 'a^472', 'a^783', 0, 'a^837', 'a^421', 0, 'a^386', 'a^425', 0, 'a^736', 'a^105', 0, 'a^291', 'a^790', 0, 'a^374', 0, 0, 'a^844', 'a^339', 0, 'a^378', 0, 0, 'a^695', 'a^689', 0, 'a^58', 'a^432', 0, 'a^909', 'a^244', 0, 'a^743', 'a^455', 0, 'a^691', 'a^327', 0, 0, 'a^715', 0, 'a^20', 'a^797', 0, 'a^292', 'a^450', 0, 'a^381', 'a^331', 0, 0, 'a^518', 0, 'a^871', 'a^648', 0, 'a^642', 'a^346', 0, 'a^734', 'a^11', 0, 'a^385', 'a^624', 0, 'a^621', 'a^862', 0, 'a^197', 'a^893', 0, 'a^727', 'a^696', 0, 'a^408', 'a^634', 0, 'a^65', 'a^644', 0, 'a^280', 'a^9', 0, 'a^858', 0, 0, 'a^668', 'a^251', 0, 'a^697', 'a^897', 0, 'a^750'], 'euler_factors': [[1, 'a^877'], [0], [1, 'a^884'], [1, 'a^472'], [1, 'a^421'], [1, 'a^386'], [1, 'a^105'], [1, 'a^291'], [0], [0], [1, 'a^695'], [1, 'a^909'], [1, 'a^455'], [1, 'a^691'], [1, 'a^715'], [1, 'a^450'], [1, 'a^518'], [1, 'a^871'], [1, 'a^734'], [1, 'a^624'], [1, 'a^621'], [1, 'a^727'], [1, 'a^634'], [1, 'a^9'], [1, 'a^697'], [1, 'a^733']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-6003-6003.1001-r0-0-0', 'leading_term': '1.24860437916991293899450306027-2.26374832715386250655712912067*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/6003/1001', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.585260022584613, 0.7450847897434083, -1.7634582700960113, -3.6205159884018543, -3.193008102267996, -1.0762905860274552, 0.36508604292399716, -0.15021728659412448, -1.2589983019150122, -0.9160337536539671, 0.6327530184708093, 1.1068864916937236, -0.44031993791664864, -1.9939168506627705, -1.3736463012293407, 0.49113169243497373, 0.895041108180031, -0.5053517545852987, -1.243532146695837, -0.2362069731430438, 0.20334218601572468, -1.6209114171347707, -3.084179739853671, -0.8822000226848331, 2.744058340782578, 1.8146593922199168, -4.525294532345583, -9.334109088040378, -6.779644590886871, -0.1711616671624857, 2.9552810147717454, 1.25192831706071, -0.2166750011697726, 0.8553146341629021, 0.865021644897596, -2.358754551373375, -4.987971590022766, -3.321260745823803, 0.13506240959545962, 0.9756275656315656, -0.2588140605147548, -0.30053449417284667, 0.6050698841779181, 0.015617293626145074, -1.1643402833212775, -0.21059843490406557, 1.6166806021648772, 0.8716639212389378, -1.19427210503864, -0.17018409399630952, 3.158469964635034, 3.3268444891935167, -0.07066351380001067, -1.249693601967944, 0.9959528620100043, 0.1859197578698629, -6.102073265584979, -10.182687935358677, -6.129939024032843, 0.22785360634401383, 0.8288439870738773, -1.97931144543458, -1.1184274692163265, 2.573480987283794, 3.0853490603509046, 0.5395954239727354, -0.027570868587746638, 1.594589622007762, 1.509530521679523, -0.04284129552919247, 0.16883032810915713, 1.1335620937976887, -0.23049508581458772, -2.12097629417472, -1.1321063915027114, 0.5238871198808215, -0.76337088198184, -2.2779695513469784, -0.045521850376496684, 2.7542283445035265, 1.5718647958131748, -0.41283101969343583, 1.1503198590583654, 2.108179778096421, -2.0678591296120934, -4.895745822163703, 1.3654615607493088, 10.365988473550155, 10.146939834553178, 2.1805600283011937, -2.2804931900973315, -0.6315391674522913, 0.48233891782699184, -0.7799981473412573, -0.6209620948513068, 0.3641073874091095, -1.0995909113587572, -2.564286177075964, -0.20308988582815213, 2.7744776247376586, 1.8168320240801967, -0.48522231806602995, -0.30435463226897413, 0.06275866508381844, -1.532831626039202, -1.8294200335339577, 0.23548322535075578, 0.3617738155834343, -1.6044617078462944, -0.5604614838049613, 1.8880776252368718, -1.6697227907771155, -8.757245425982287, -8.341311109300955, -0.4799010713734373, 2.796862158740704, -1.4984717637526992, -3.718346879469734, -0.782425709350289, -0.205574477556413, -3.4247073344345367, -3.334097916235338, 0.6618830490457739, 1.8950682563275585, -0.014978170846447505, 0.036935411696867246, 1.2147937192994844, -0.29011763306092514, -1.901521716593606, -0.10375149518858029, 1.751856483302597, 0.646323996639546, -0.11573291379113157, 0.9746439609332894, 0.560862397760886, -0.553843881955161, 1.677764346486291, 3.7471145399423484, -0.4152932328892893, -5.841495559970601, -4.256355842317308, -0.13476908005861934, -1.6531769256809115, -3.8908864030360544, 0.7253974007126228, 5.8613956981521875, 3.37607873848828, -0.4623590866476888, 2.0535469245110063, 4.91855614921474, 1.4902012650190042, -2.3715902348362246, -0.9181306398220571, 1.160374067527198, 0.15198495448460972, -0.2802387232811973, 0.8944273666510593, 0.43715703799874517, -0.3229417542955447, 1.3406795220287133, 1.7675299733612544, -1.566815045767203, -3.267238051644624, -0.7691351739844161, 0.2520818714111278, -1.7721253503547116, -1.54247540976382, 0.4162754911857709, -0.5535581501839133, -0.5141349119173162, 5.198052035580819, 7.998570894455777, 0.2348730666413414, -7.528505748430495, -3.878296128956257, 3.1643873411171644, 2.4649987845152985, -0.8734090511236146, 0.518907367578763, 1.8242329187443402, -0.8894620088338321, -2.118397431271519, 0.03720814141334228, 0.5350913383244033, -0.3889316492506714, 1.2649549290942341, 2.781494952247904, 0.7395322899734127, -0.7392967021714444, 0.6718702371802353, 0.28801914424171654, -2.2892763406678274, -1.865187472627965, 0.3448479571233608, -0.3360461694742143, -1.1270994099766265, 0.5432709148912414, -0.7443418411701122, -4.586696146210792, -0.6800217785383349, 9.798131951410285, 11.593539116088223, 2.6658875197107053, -2.135276181846075, 1.1038275647257993, 1.6698694178872748, -2.007154956062259, -2.0160852055273555, 0.39282389712078364, -0.5729858154099802, -1.5630365841080784, 0.6962044997247202, 0.6641020352310387, -3.181776710252964, -3.9420619967135364, -0.6932587524038232, 0.5929482077491444, -0.18770296046998813, 0.11062315026160435, -0.36938369362943296, -1.6384097495035619, 0.5344066929032834, 3.3967398195961787, 0.5725297980580762, -3.4938534409603963, -1.724335318690378, 0.6553329460368905, -1.3461932092486653, -0.2976136548072595, 6.027821269397637, 6.648761686817002, 0.250575440878145, -0.44762448492343865, 5.3534185255451625, 5.34962928653264, -0.23606649598196938, -0.9754181909930311, 1.478853655372554, -0.3547466874160765, -2.750258361673069, -0.7008416556848035, 0.9987696367574548, -0.24067948760540384, -0.02244725941664622, 1.2072820843848728, -0.12241771435264447, -0.951239784226206, 0.9017408420805295, 0.6305005053105283, -1.9073590802948235, -0.9958565275590295, 1.4517295282858276, 0.3724760599262947, 0.08432243124934204, 3.5886962866274956, 3.3368788998137733, -1.985181134933663, -2.7819923161895703, 0.4939163635004049, -1.2366377681103216, -2.865004697330443, 5.539902146095762, 14.264903723445709, 9.75586448403691, 0.2180706660244423, -1.3372541471948678, 0.8521314107309526, -0.007570438919611745, -0.329596404525256, 0.9695506212264977, -0.013282739900620339, -0.7601327865206913, 1.6947622926816102, 2.221787265208128, -0.6789149786190931, -0.6813862502373595, 1.995981606426306, 1.5058278846705695, -0.12431079846551309, 0.9241335092688331, 0.935223368344088, -0.9347471168205916, -0.2481066649644078, -0.25255786350377907, -5.119646472590479, -6.084760629448217, 1.6065794974623284, 4.665055936391632, -2.963595643237334, -6.778477870694711, -0.789011109124787, 2.270719962219791, -1.0651741050951224, -0.9942621136243412, 1.822264276986302, 0.17470589657729788, -1.6994973839805774, 0.9971790255909374, 2.166152703903904, -0.32187798783975874, -0.289270056584972, 1.5664636989749394, 0.36548436708144755, -0.7931010776708386, 0.6996814301900733, 0.3505790369924996, -1.6272581868811746, -0.6455603837472346, 0.38890432899400335, -1.6047526818203646, -1.635748973686318, 0.17867374626175792, -2.525549327789277, -5.032176763995739, 0.24740939910870274, 4.099150078991283, -2.2021842114875674, -7.130975476181889, -2.239786750825195, 1.5817763655360029, -0.6129127279452583, 0.5472702518516006, 4.206430375663207, 1.1614350143326244, -3.585120070021741, -1.2814051845340637, 1.9613894208672562, 0.06896181829178356, -1.212094017423409, 0.3368000762254367, 0.23491294294266105, -0.15822021160450075, 1.407599846583813, 1.0273699649026007, -0.7615901873131108, 0.7570222383636376, 1.9082744838629988, -1.2671025989182572, -2.2966373047379895, 1.0618964904468238, 1.224485722092259, -1.319434573798361, -0.1592243676808159, 0.40473172118056344, -2.8506983123639698, -0.9068222399548544, 5.155226515589092, 0.4137926717149385, -12.019640510125939, -12.996159537615878, -3.39877528144546, 0.7052924702463751, -0.8129072616259649, 0.09591708939305615, 0.4242008002891433, -1.6122031616462897, -0.04974346815027067, 3.337566415785452, 2.25214414318967, -0.02564649304631688, 0.044960316042323555, -1.3698571483252695, -3.1455950245585855, -0.7297923953337293, 1.3874712861126508, -0.6555761683144384, -1.1127344219768047, 1.0619230831963404, 0.37612671341000764, -0.7110154420815253, 0.7760513795496806, -1.5338630938293627, -6.242438268207512, -2.7169922024602853, 3.500518845421494, -1.0736964418542359, -7.712440022293431, -2.131707145667099, 5.7293023271334365, 3.35193521980874, -0.748972447933519, 0.5924102415320732, 0.7093961850533486, -1.1035402875533775, 0.11436486846045993, 0.25553028455614457, -3.0836529303501328, -2.967092533150872, 0.3619271533162838, -0.2500215410033544, -2.2823002060122306, -0.6996528436355057, 0.5745242350942227, -0.21766697071382968, 0.26045568407354475, -0.11620031579578996, -1.9340530917515597, 1.0373223993604619, 5.7072680499015505, 2.605646162988913, -2.430396865930588, 0.033778435626994674, 2.1316654507500092, -1.4374310326741413, 0.16983585519850553, 7.111785905990127, 5.841101556215824, -0.49778112934293584, 0.8295552848602249, 4.223325406318914, 1.0315707269416632, -0.7221876830574987, 3.058455303819548, 3.532984620394903, 0.1961325933320165, -0.23473042293704072, -0.10364484489538695, -1.9756482598647414, -1.4309254921294168, 0.21008011415261174, -1.4079107272460576, -2.208976815244551, -0.16410599250985408, -0.39658708795572595, -1.058226372191025, 2.1018864589109776, 2.831020089011189, -1.3262053863173304, -1.8789850625376134, 0.3652623293984704, -2.0106590911639213, -2.643072567980739, 3.3425822329994452, 3.640636604183849, -4.250109393407314, -4.96727660490933, 1.298402341267431, 0.14569967619031823, -4.408524730753616, -0.9220206061116358, 3.555425533648643, 1.2954780193160575, -0.5664741659073678, 0.8765642141982264, 0.5291364469711938, -0.17372305104474461, 0.3094807929398562, -1.9440932379620697, -3.806167485222242, -0.16228330310484868, 2.6440748298951724, 0.27858248284930487, -0.5871667608042316, 1.0861635438496722, 0.35023464338255234, -0.030918511456216356, 1.1815766779480021, -1.296852000992623, -3.100015932170589, 1.7050270026838894, 2.19862908918288, -6.754935796489418, -8.418364144657101, 1.656833810026853, 5.248810570794977, -0.5117517042379576, -1.2214763472661827, 1.8770003915804945, -0.06917917393747366, -1.8034108629424317, 0.1967525244942242, -0.3148221118432029, -1.2440296888074054, 2.5682354412465496, 4.621505163160819, 1.3859621392211563, -0.20301021327938196, 0.45832399404027635, -0.6218788775357758, -0.2304502074869788, 1.9252491384849422, 0.6702070690974863, -0.7841898142555228, 1.5164049276020455, 1.5698798953079445, -0.9618658148049877, 0.5335783497362185, 1.2941144802534086, -2.5259299143764724, 0.9170001316769973, 12.239540736518556, 13.161161122028954, 3.2392297894904956, -0.35034894209420675, 1.3082734183477698, -1.7909546561143659, -3.413680636321624, 0.13645543926775783, -0.591165721227396, -4.197560370294481, -1.4929557434169856, 2.4379210740209345, 1.0074287121424121, -0.0736893283951868, 0.9695194580728337, -0.23783495597633478, -0.9463921331574257, 0.6539987814351366, 0.04422578745698583, -1.0045498325175026, 0.4469270064115776, -1.2432162135560278, -5.166796085000026, -2.6471544339229203, 2.001948320141264, 0.545113259890321, -0.7529927360356216, 1.2789375227204889, -0.5262365316512096, -1.4303131412891286, 5.389084877803, 6.551576137173767, -4.525626339704661, -9.316433817013722, -1.5430789477003055, 2.098293004929861, -1.286772620790894, -0.7604550305075168, 1.3694547620294069, -0.09974094164227763, -0.18464747954676922, 0.9119612051797629, -1.04865747923554, -1.4107589098540538, 1.3465728470887222, 0.772785530619041, -1.2982385532240932, 0.03480269411015783, 0.15087571891023688, -1.9321579620886788, -0.6788132215753309, 0.4350661116579604, -2.3195432723764418, -2.2326095697858235, 0.3784255934359246, -1.4217282301362704, -2.048576381947801, 1.4750900044348314, -3.063595896252438, -13.10499971930345, -10.066970469201422, 1.0665468594983842, 1.462397920650397, -3.086584309363706, -0.1596298001178092, 2.662957618168928, 0.2828706249855446, 0.10907530162679271, 1.3276005351480566, 0.06108417301539651, 1.417123120526306, 4.431444507330133, 2.23283869727138, -0.6760570815768817, 0.8178231651775933, 0.928451148712841, -1.1224759746562385, -0.30946295210068264, 0.2690560482629809, -1.2650563985313186, -0.2800792674184631, 0.784866366006442, -0.0827864619236024, 4.575018104484715, 10.68047585777385, 5.022698654103529, -3.9746430716447945, -1.3060959149296112, 3.3959904369211733, 0.2982054380613854, -0.5610812718032605, 1.5705822384548769, -3.472615449432453, -8.077000945479362, -2.620998828354866, 2.120504313585136, -0.09549189464199874, -0.48174871774873473, 0.9181876655151521, -1.0992597856703092, -1.5023975417977284, 1.0767753829297944, 0.6496094657147553, -0.6646602878993484, 0.23994149169877144, -0.7619211040170185, -1.9052958330423941, 0.538152191042059, 0.45374128964925, -3.0060977693434072, -2.0064347913320604, 0.07128018782896857, -2.425301045560022, -2.0297699626743353, 1.3686749075948432, -1.870305396269723, -4.5621510568909995, 2.5223095668692403, 5.877522676711641, -1.0486401577021633, -2.524091834572852, 2.967505729888809, 1.8551818756685723, -1.3721038092228763, 2.1628482324988334, 3.8498259105478683, 0.02189586616411771, -0.7355314129783893, 0.7281839890858577, -0.36786648755238366, -0.4663748577986621, 0.25643574125579494, -0.8282552455893132, 1.169709933510255, 5.09305244194366, 2.6219044959560858, -2.08632414199778, -1.3668436139633475, 0.035470773413914095, 0.13625618395977657, 2.833152373952821, 3.124732420062704, -0.43355913936402773, 0.44866627423646543, 0.2812395245431911, -9.694914470386854, -14.084165672831253, -2.7829070404189853, 4.3423800191363995, -1.7187778341041269, -4.086389206348652], 'positive_zeros': ['0.411700716219794095801072256617', '1.74769007083631689119117108674', '2.14712170788331385079083232022', '2.99941759864792023550130547378', '3.6819147524619936984496173177', '4.59806761493170132865196673962', '5.21406251628509056005118061107', '6.00031398303546306333024731853', '6.31233669240526353614789759318', '7.256378101477685928114591930761', '7.92037526244905169140474632295', '9.07171345038018695854997903412', '9.88356302184220961205764616922', '10.11737268328294549798183367380', '10.73577560775314619512402803239', '11.85915531498132984354440180664', '12.43121685515975628577388805237', '12.90682540515070628631737048373', '13.440971640654619345947492928584', '14.094211129816747876342193709124', '14.8039904981802499548275720981', '15.32995835198067196978964251135', '16.24330176786031990381070020046', '16.74660992571709042194783231578', '17.20111827804167955024964318739', '18.420978480306599866243075732070', '18.841147903991640409360633963186', '19.47035573671088828107034717556', '20.4062867143550337267247312195', '20.63249705047591678385619575500', '21.54984478575083954734934217954', '21.82798565799006006887921651325', '22.4691648035639744634186866147', '23.29243228174702986801198038037', '23.6395564275934753006481541062', '24.37894394545073421390893888975', '25.19622368763733582874016222042', '25.47151896574460437580536388504', '26.128024807027242528503677055492', '26.83059769273903617963032858917', '27.90988379926972401545543473127', '28.525797523666850271050105392418', '28.88785014842898618782387759273', '29.52121319759721593407818321388', '29.83345314897988541208263576949', '30.64186058973362044028686284707', '31.47099672552666846458634630267', '31.97367179661621330198309146984', '32.20988068224509878806812757435', '33.08754939563147012986846822186', '33.49765464483204534931975662718', '34.11890554801633377908179250964', '34.60456355163780416929368301663', '35.64547812238754990397868415181', '36.16045477544982410234877007274', '36.97570146468129689194244778959', '37.15439100427419093878162826744', '38.071258877385644684954489300033', '38.74698288704050256730802314659', '39.054255459817522414951143800270', '39.65086730218536168112004647299', '40.32412961139068465611293342040', '41.08069248214344485554284284276', '41.300688135836607277095414206531', '41.98282515825812638634496543673', '42.32683334045001910543701826953', '43.10515683814269966599460050943', '44.091761966622388219141009323552', '44.1843216720531403943834543705', '44.96704934744836021014246857603', '45.85841255542131771134131091871', '46.084362656765902424017845076079', '46.96419176056588356603660543741', '47.59679711254170603701985324313', '48.15798190254618090127808001228', '48.518764634445116943343594166249', '49.16538956886164649884313345414', '49.47649146161534681198428153928', '50.186148810194724404328037004561', '51.03641242020745524325782452403', '51.3038760826067338114479664445', '52.091175526675274164536432984835', '52.407319013946100844390555467643', '52.85687986685331037836558898792', '53.756862069479342990724710976565', '54.52259742401985635231357399643', '55.19265363629828011862243467636', '55.56609177871978644577648716628', '56.165638784950036768145441180380', '56.8694781327180564571505188633', '57.32423090567942860862154580734', '57.638058569564276687831678603538', '58.52655900613671105032019746925', '58.93662972128100694421307376528', '59.412384567505156141010140735822', '60.23958631461700203110583018033', '60.56295375617936614169678060396', '61.150088037002466183886657491623', '61.494759129571826046938509483468', '62.2098124515105532952845911712', '63.226681399093738852150834425415', '63.66389972427732459101153040436', '64.20624912068214013173335613644', '64.92245354782432263632212741121', '65.225705518779072478135459365883', '65.85269010892759362571883200293', '66.315122093333276026877888922696', '67.268698124436483369911941818013', '67.71843076039453364042307111475', '68.06093130021956758299820347390', '68.34487185216824891458871458391', '69.01766174248309848960012449204', '69.72177883682711631254562670541', '70.469304824825771569025488977189', '70.77236014607092107315574340302', '71.26842045987133223145308637177', '72.20210572404121983634306591736', '72.52999170058424264179115617932', '73.421194831933077313919636779852', '73.856585997838351068472434521124', '74.343542509293261315959595491212', '75.07513439086054857646537012337', '75.56976451685795295716085662313', '75.94211916430566443286115208622', '76.54379343705683529637349622974', '77.050269811043652471866936647239', '77.57596209231974422901195694765', '78.227693120841736417212521973935', '78.81269630281502150578948025678', '79.04987974147936903604870457406', '79.88349626149647616461395124178', '80.5576071938445578332246126518', '80.830641839192120304394670434962', '81.40001174110792805185969903108', '82.51099139524227812289121676129', '82.97314131425756782992061107442', '83.435966728908182956499410406585', '83.826054785401773937074083791861', '84.3727919383085393695513390042', '84.81297142606632902200867526830', '85.549488953173870289882841641080', '86.01615280878092309455260220201', '86.81172320294901158285525918303', '86.982294272948064105182914126539', '87.64465876952391477197490910478', '88.17296127397752438919023469810', '88.40525241538822988249847377262', '89.31670711173698905850061563511', '89.89801959018191184528102964376', '90.66242992602541681392611181606', '91.15681890929066729353834960396', '91.657150942124259930219506512553', '92.2039099335478732829800217934', '92.72240243631006951732514663055', '93.39437017474932321526411996673', '93.7927124828935456791715094526', '94.42716506327934517728188367822', '94.87153302231816846987377601977', '95.36272861320794576680020240300', '96.03892618988800437608233860063', '96.340403155015240447551701374112', '97.11421277421390728974172840496', '97.26892369877889965830128921828', '98.11439070831267879158552652258', '98.6696400347765903958798480993', '99.48985915197802483758299062410', '99.922502327599086726133155342081', '100.26783787480061193959148543780', '100.99645879213434932452781850812', '101.64859257371509088080861601577', '102.195000645119880155162860481719', '102.74186973673425818049657125420', '103.19418750583076948607189947572', '103.484042658536385703699001126', '104.20804626200451706741781913500', '104.59540339508536082796727651238', '105.208618279162632485431240493233', '105.84110580433184391217631877650', '106.38144166055463770924640413288', '106.896203558434818470830109968202', '107.23744134559116739448692069726', '107.85595223534164638502090834331', '108.44848166159902355677328300879', '109.54152810312986762488348106032', '109.84003068422394477741657177804', '110.29575877710598931359435646082', '110.69417076618348639660505276218', '111.254076978335584948214379446279', '112.178647247644879361031197936297', '112.430426463653959342199116320303', '112.560219485290749472002160485621', '113.50173159562564989840640475734', '113.98400569093015829979677366883', '114.526752895140871481642730741951', '115.057362577496596995630708489734', '115.468394076168653554660244121348', '115.828546752270836474567436275359', '116.6695602103161038001479244610', '117.14933103467155809014806247350', '117.87804606641233508044540959127', '118.64516908845695520968962294873', '118.97807901420759061409532469905', '119.477744827250437313140993807126', '119.982041273746284882584379633675', '120.344122909008403412555932792324', '121.20339985106716663241970243905', '121.531950091983256520906417536323', '122.28527858040661292031654014777', '122.71753410224149451076547559914', '123.034968094417584011194294140982', '123.41730402543319170336770932161', '124.00174853105314230976998323745', '124.81290295710206742299893062888', '125.31019533423313715949437216078', '125.82044264394534497108611850690', '126.24146364187350161943553216555', '127.149366893115497069413950452410', '127.442028408010651362203172310674', '128.20297375685410046380081129340', '128.51897996688683998051453682500', '129.40204461019614514187207831052', '129.76828606005248659389731324610', '129.97183949448365489454483739565', '130.84536569371612279564555955632', '131.04132895333735076631914394338', '131.911689667768505586403822873640', '132.10017780324253953114926380115', '132.63532248065555212116788952939', '133.34031321008721765367522165040', '133.96769490472419095299672424910', '134.18236967613776935756807237927', '134.84088021840184357156974887224', '135.46260934229441372811027902150', '136.17206629947388414472998363322', '136.57077792534923565283499363632', '137.2325257097131679847222687352', '137.93943858774188507784472046690', '138.26601854528827694088206854816', '138.88310131942579493538452989535', '139.15197197923441254839549593140', '139.46921946419706906230404269505', '140.32282796111415604102705506006', '140.96921872252598530249110239800', '141.35597783858819096452091280324', '141.952807366381620803587186688613', '142.19558318897402683536012250754', '142.70498741884831013498474381843', '143.34544589998582568768509482264', '143.84376721833260569358320165638', '144.63795795840268283612058841267', '145.28286459823052637692521265424', '145.728576257393801211401932894853', '146.24384695872106092941890813371', '146.84072081018347973873590765931', '147.138747894680316221950435215748', '147.63720523455774982232862722592', '148.60400248465519076887164844665', '148.83734209491836180354906617146', '149.23671323952467368937836877075', '149.71950964418712277429204830452', '150.39230109997945994385087052702', '150.76466582558591320490458854241', '151.41864951683177919468314888847', '151.81734316537211409567597650008', '152.30280760015254296382339922480', '152.78135067710923472953294497560', '153.91435788320536763588871954340', '154.12418309099465113659669835406', '154.55767200359989120146799392722', '155.29826418791496025211885014290', '155.57407323581200761598758910944', '156.33823801944900354431435487586', '157.03437506090017308966329527028', '157.21451806874816803113703506064', '157.774655591763064276370686311014', '158.307486323672660707097069579018', '158.757383245202017337523215619316', '159.27861886343251875928028243342', '159.576530733910234837068854118456', '160.45692218581339821097511923168', '160.99367990606524070254508860004', '161.36757818517082356220452957711', '161.82787541384868436384555744410', '162.27845445747210001322336981068', '163.01118237871989521658022727602', '163.81198631937116270823971435667', '164.25816626033106791752819341375', '164.76587044880600683459392348052', '165.29540897982996101056047241647', '165.661066565667190069367532802578', '166.12091338342526468325115211585', '166.72015253243087269838319508812', '167.27526100468584083473932774302', '167.80672591062399308738411756713', '168.1485939383176202311232671364', '168.83661467095747410004048983872', '169.134930094171250240542490353364', '169.92162195575741803987550123736', '170.15697121411779099833860585365', '170.79305557556577818668202047056', '171.13756090493923827464852572002', '172.14735210002773541538353879517', '172.58076847333472638758096105607', '173.13477372504382005920011483', '173.791552570706078523746724321269', '174.04178171345706776645927059784', '174.710549507021780471457750393098', '174.80577007546231023081305674482', '175.80884816276950452303604670279', '176.13274961779196272225205064885', '176.68884321416058530350112424922', '177.24486160496996198689058334963', '177.56201186485382321564093040857', '178.1659475654002165186549229975', '178.64173293719625462519641623191', '178.77491954751528423426837039423', '179.830988544286794031796565952754', '180.37123254324944023437641761628', '180.961397221527308522547609025817', '181.3116711771163707651381042577', '181.718095099430412636658772824018', '182.615033705305558465843373178593', '183.11423889019767899458389953401', '183.51312710449963861733215649658', '183.9328512818500543339589202877', '184.549390938763562037770876507608', '185.10114561453101599639644730856', '185.54182302128711562684040349092', '185.812679044271946059157064883489', '186.50210721375729048024391245147', '186.918503853902190666573706866574', '187.73510912281736501340368015150', '187.84052935433687845829810440331', '188.59191802041634107513036790521', '188.954778609977300289878216107482', '189.59833721396860765744548686157', '190.26820538041558729419759497316', '190.76524316619551053181572276229', '191.37336829322079561354160736043', '191.73395390273415085375780831296', '192.50197865013840333448214780044', '192.93412142161887252536416831357', '193.36197263306096614519465355346', '193.87235050213760251589047858535', '194.15796360750834728345392122954', '194.59150615631822370376975322599', '195.45773693493569077398272584363', '196.19839545747711301384465217417', '196.3150010269136018884847130096', '196.52205698993307191147000640264', '197.45041929773871590464356573383', '197.76336579077203628815463082353', '198.14018774641143279962788338336', '199.131312010814286975719640216661', '199.61697875676808789696839097943'], 'prelabel': '1-6003-6003.1001-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': -0.6791156466501851, 'root_number': '-0.533478952331319469617978261808-0.845813340767026308927634248195*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(924)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.61680792673959629698590969705-0.622190211914768864327568288697*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.41170071622', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.74769007084', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.14712170788', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 27.87781479921304, 'bad_primes': [3, 23, 29], 'central_character': '6003.1001', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6003/1001'], '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': '1-6003-6003.1001-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': '1-6003-6003.1001-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': -0.33955782332509254, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.41170071622', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_6003.1001', 'Lhash_array': ['dirichlet_L_6003.1001'], 'label': '1-6003-6003.1001-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6003/1001'}