Formats: - HTML - YAML - JSON - 2026-09-06T13:18:19.858325
  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_92.51', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.14231483827328514, 0.9898214418809327], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.9594929736144974, 0.28173255684142967], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6548607339452851, 0.7557495743542583], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9594929736144974, 0.28173255684142967], 'algebraic': True, 'analytic_conductor': 0.42724620381935696, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [23, [1]]], 'bad_primes': [2, 23], 'central_character': '92.51', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 92, 'conductor_radical': 46, 'conjugate': 'dirichlet_L_92.83', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^27', 0, 'a^1', 0, 'a^30', 0, 'a^10', 0, 'a^20', 0, 'a^14', 0, 'a^28', 0, 'a^7', 0, 'a^26', 0, 'a^13', 0, 0, 0, 'a^2', 0, 'a^15', 0, 'a^18', 0, 'a^17', 0, 'a^3', 0, 'a^31', 0, 'a^21', 0, 'a^19', 0, 'a^12', 0, 'a^16', 0, 'a^11', 0, 'a^11', 0, 'a^16', 0, 'a^12', 0, 'a^19', 0, 'a^21', 0, 'a^9', 0, 'a^25', 0, 'a^17', 0, 'a^18', 0, 'a^15', 0, 'a^24', 0, 0, 0, 'a^13', 0, 'a^4', 0, 'a^29', 0, 'a^6', 0, 'a^14', 0, 'a^20', 0, 'a^32', 0, 'a^8', 0, 'a^23', 0, 'a^5', 0, 'a^0', 0, 'a^0', 0, 'a^27', 0, 'a^1', 0, 'a^30', 0], 'euler_factors': [[0], [1, 'a^27'], [1, 'a^1'], [1, 'a^30'], [1, 'a^20'], [1, 'a^14'], [1, 'a^7'], [1, 'a^26'], [0], [1, 'a^18'], [1, 'a^17'], [1, 'a^21'], [1, 'a^12'], [1, 'a^16'], [1, 'a^11'], [1, 'a^19'], [1, 'a^25'], [1, 'a^17'], [1, 'a^24'], [1, 'a^13'], [1, 'a^4'], [1, 'a^14'], [1, 'a^32'], [1, 'a^5'], [1, 'a^1'], [1, 'a^10']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-92-92.51-r0-0-0', 'leading_term': '0.869932092389699050942997405688+0.663119638746372291157444439063*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/92/51', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 14}, 'plot_values': [1.0938507670887465, 1.443081701103412, 2.0100502410231287, 2.510562020671459, 2.7088570215864887, 2.4646649764093964, 1.7678070588186139, 0.7607175451846999, -0.28199161514485327, -1.0297247475424105, -1.2134389330711424, -0.7437975269080963, 0.22357376275136026, 1.3182638186403621, 2.0874810867487743, 2.18889196209375, 1.5628737707282996, 0.4964795852725839, -0.4712900238255104, -0.7818904652486189, -0.13177546671652068, 1.3443058894180335, 3.087945748504273, 4.347737101426035, 4.531669162597161, 3.5095464788320623, 1.7003412550005046, -0.12108195971629476, -1.2147399900076727, -1.262091243581355, -0.531258894815309, 0.2866770982827317, 0.49391814296842146, -0.177930569292365, -1.3749875392167454, -2.307142106447426, -2.2256744589260795, -0.9160437817773446, 1.103256835847229, 2.8252173581208306, 3.3232043653333405, 2.310291613303943, 0.3370760191768797, -1.516662696551063, -2.285519594749685, -1.7012642606263733, -0.339652255303313, 0.7742710719162136, 0.853557915434161, -0.1243509923364494, -1.4131010158036892, -2.0302789779427344, -1.4704196877802738, -0.0990718919432829, 1.0684652149655485, 1.075813580326153, -0.26313516430459216, -2.164358895124112, -3.3603805798777375, -2.9635872677151314, -1.1082930967445566, 1.096950864641655, 2.3000190095447435, 1.8203198166062755, 0.10119086085026535, -1.6285086573018954, -2.241588717474719, -1.4996600110759464, -0.15829115169712948, 0.684862321114917, 0.49703011051369916, -0.23712281818312247, -0.39082698913281333, 0.8686869818294798, 3.308062646065699, 5.6517278371413475, 6.437830361338352, 5.088347656086276, 2.3766053071092172, -0.09115640858206751, -1.0127781530024398, -0.2903112400886823, 0.9927212527417999, 1.4901020719148608, 0.6769282724172896, -0.7639421193136924, -1.5564804556597516, -0.9375548791038146, 0.664334435186894, 1.9556599358243918, 1.8584440827974553, 0.4506556371006566, -1.0407160755717348, -1.231332211492966, 0.23782641780783187, 2.316272168796009, 3.318767048707355, 2.2637682006163335, -0.31014536704288154, -2.733092272883648, -3.497583635286407, -2.404394990784767, -0.6258994738335768, 0.34337477374155906, -0.05602542627091907, -1.0564054439606172, -1.3552643917981884, -0.37552036615858086, 1.1420315449443124, 1.7715653538790854, 0.7287251221321975, -1.2897659699096098, -2.5509849986941893, -1.7016954159139313, 1.0370137805674164, 3.9473786795913637, 5.14487026278159, 4.056031702576394, 1.7969287885791614, 0.14836936078309954, 0.03925188257899192, 0.8651409340083954, 1.2096955288318856, 0.27285001585223484, -1.324300780125387, -2.111592799676453, -1.1974488098577665, 0.7827240585000284, 2.1228020392970026, 1.5479369337629714, -0.5898293118833642, -2.5458870988929414, -2.693194991610687, -0.9760777043869537, 1.012449665957262, 1.4270090547028114, -0.2000253767208611, -2.558642320386651, -3.7437223101642547, -2.932928550882613, -1.0321768613501923, 0.2680073937962447, 0.09876530654458728, -0.8514535951093388, -1.1587236259270373, -0.2235018541947395, 0.983279322189647, 0.7787480666383498, -1.5328973652405704, -4.752563218149425, -6.6199271396810415, -5.712584076005109, -2.6931604326706786, 0.25747908888024734, 1.3193855615832684, 0.5094466498622998, -0.5709279184401308, -0.40696284474396693, 0.9739379177955947, 2.145961750730797, 1.8306908670162003, 0.2721533631846792, -0.9560191443804513, -0.5438441457576496, 1.149758540372374, 2.32897665114067, 1.4822117813081641, -1.059032485052888, -3.2845043946072914, -3.3118259073777594, -1.1407605247470258, 1.3330397828565348, 2.077210004272535, 0.777383307989222, -0.9796133633882873, -1.3306566420998664, 0.050231814664779655, 1.7223730820947183, 2.007200203371064, 0.6946021738735377, -0.8087909296431196, -1.0220208406695255, -0.012005224605548053, 0.6211894484353744, -0.5549247996704098, -3.1357292310119935, -5.008772455845099, -4.27918189666211, -1.1508699964192755, 2.1127335037853863, 3.1738149288606685, 1.6630545082219363, -0.6652044030355146, -1.7419060956382917, -1.1093036067170978, -0.0714481547948877, -0.03728122646886031, -0.8777603101698984, -1.0603105927546586, 0.5799163405596837, 3.339372906275849, 5.093164526033541, 4.342841506043336, 1.7904225727591419, -0.2382319121979666, -0.027167931864659108, 1.860263561387752, 3.17529536429689, 2.2591131378490648, -0.2959955412069517, -2.27007693436715, -2.0582495297892267, -0.22525512209569049, 1.1897918696030276, 0.8300489642900969, -0.6474056768774813, -1.4344563317937857, -0.6446960085058486, 0.6804085724051039, 0.753916122739981, -0.8485694312119365, -2.4814984263427835, -2.0104485330465973, 0.8879732945796368, 4.139332699450181, 5.1226876604234395, 3.1525627308811663, 0.08652710626284059, -1.5436925631960674, -0.9466856174965306, 0.4124348523388725, 0.6045322488404379, -0.6667234917701313, -1.9050418340530528, -1.6766277850898854, -0.34857070125594797, 0.2764491001377916, -0.9310835937239021, -2.924494992034667, -3.3575575351601414, -1.0415516533656433, 2.613854711428176, 4.797714221395245, 3.985126313976517, 1.3543499899510636, -0.523216506563261, -0.3172131225302588, 0.8724089851848658, 0.9517838130991216, -0.7479784986286153, -2.722267625775361, -2.9885611145533018, -1.3041677048122031, 0.5694390500712785, 0.8404395413759891, -0.3255133961402715, -1.0614923794199198, -0.049896333877949624, 1.7626479025183843, 2.0037519545699234, -0.5211015721587555, -4.276449900210002, -6.282645098459781, -4.993077215545759, -1.769818948746674, 0.5679129183482916, 0.5407235080563595, -0.8030430211039602, -1.4279377415886116, -0.7087083633998925, 0.029917776845964805, -0.6554954152775659, -2.3479460973953814, -3.03847533734293, -1.4383886932453227, 1.2970487750913702, 2.5268053633513032, 0.8789126373162538, -2.1820948117955963, -3.768057118562489, -2.5166902736702528, 0.076376561813498, 1.353791484779363, 0.33559466386429015, -1.3896713861443915, -1.6038526472931978, 0.03023466020223687, 1.7061014888589563, 1.6667703781544438, 0.2634810461055277, -0.5139905566012775, 0.5237956544408483, 2.2311582273020605, 2.361941244430078, 0.2278268128560289, -2.29628223094131, -2.7002396968216194, -0.6354646061143142, 1.56927656529349, 1.344881340963044, -1.3568024468507427, -4.004445424190941, -4.176310224133452, -2.02073845034028, 0.15808043938363467, 0.5643588322253682, -0.2738108217637409, -0.5228485901808229, 0.47589375832649, 1.3194443754673848, 0.3615315114311407, -1.9431109769005588, -3.097834218348065, -1.2084780829785344, 2.706138342490018, 5.465037622518081, 4.884116953811583, 1.9394753896069816, -0.4142845631438426, -0.41039430062847176, 0.900370489627738, 1.2459141039850872, -0.04924131958376639, -1.3339480607406358, -0.7570625261313282, 1.3596145478509984, 2.771467447747631, 1.9095033251386355, -0.2716332524166652, -1.4397836471602323, -0.7109323125291338, 0.22050927674647236, -0.9082347625096278, -4.052831019826216, -6.532166796753456, -5.791880688877842, -2.213328800151488, 1.2157018800012929, 2.0188001285787505, 0.646082913106787, -0.4326383703986055, 0.26546824313624307, 1.6784627439712458, 1.7829572496634882, 0.2360947458598311, -1.2023950581373142, -0.9713032120738628, 0.14829812163624664, -0.18787891250477926, -2.9564589053069232, -6.187643017447467, -6.816321043075857, -4.027729352312766, -0.28648989195347635, 1.2056390624994031, -0.1959470481444546, -2.19452302615144, -2.3641448999676933, -0.8074102069951872, 0.35011505404950344, -0.19862922965277896, -1.3200562295480653, -0.9889934614193179, 0.9777265823842068, 2.468052264823541, 1.575893022293447, -0.9493668465107064, -2.3736908845171327, -1.1192204978062912, 1.327219166984275, 2.087621627824031, 0.26331622577264036, -1.9595128747117752, -1.8153581141860244, 0.8288021991310554, 3.2994811982807004, 3.1471749112946643, 0.8100627115491484, -1.1296411184455033, -1.035679339208995, 0.12068546005712949, 0.4041271816387919, -0.3785646989279638, -0.42109371823977126, 1.5132022953134687, 3.9761624775076077, 4.05994527242766, 0.7704130489614882, -3.4525521467845692, -5.076010603023419, -3.152461072082599, -0.16144596191347246, 0.891328479030992, -0.3050486569135131, -1.490836593346595, -0.8971581968343458, 0.6054118507897119, 0.8194897762723621, -0.8089678141701799, -2.383516418633145, -1.9584658290524732, -0.10785756887115491, 0.661975114488085, -0.9453504914186834, -3.20348975198009, -3.2628264061300953, -0.5990533141334716, 2.170935279380027, 2.2096296487588143, -0.2889795236445278, -2.3718013300043155, -1.7789254513378883, 0.547229482674685, 1.8067957898286962, 0.7675437922031727, -0.9293454320690575, -1.0420881423743669, 0.40503923883540943, 1.2796978362355453, 0.23789377580117033, -1.430710894587183, -1.4692355676655982, 0.22672186011804937, 1.0982824970047138, -1.062171659404983, -5.13054781011061, -7.462586248116424, -5.773619843419843, -1.6177387080548762, 1.4001734924271845, 1.5041203096499616, 0.18106850844059985, -0.2395090177751269, 0.41395795035940336, 0.3195463078453802, -1.4554889154181512, -3.2896094166282372, -2.874036943230534, -0.28596312638672905, 1.7703513481351598, 1.1037894134606063, -1.2410945251052015, -2.142042044926082, -0.15645348403138348, 2.687653076727446, 3.2990887995727878, 1.2206099546896672, -0.8842962989885181, -0.5065795677151215, 1.7206710762572865, 2.936194186638094, 1.607444307430905, -0.7297236414136206, -1.5902745300309595, -0.661922177317991, 0.08684277884457263, -0.6637930154849168, -1.579319293842077, -0.3747985750020839, 2.862231621958891, 5.127189381053177, 3.7737969786184475, -0.2408300583012622, -3.1978299478992707, -2.70072740973104, -0.18179060069129038, 1.0754219179431712, -0.1427384215661958, -1.8803437372929808, -1.8219485940411175, -0.23835672828374888, 0.6464198484735737, -0.17691939232474205, -1.1131424837237882, -0.24622835887211175, 1.7388528462522366, 2.022727740863074, -0.8104531901328751, -4.611827428125102, -5.833053255900596, -3.5735798002958385, -0.5838204230869668, 0.030779340677151327, -1.6293151209958636, -2.736445165115584, -1.4815116088577405, 0.6986705081871531, 1.1257153830266398, -0.6011312559072496, -2.128508301290668, -1.4470813095486683, 0.5337101774942435, 1.2826075209653887, 0.05091320504963872, -1.1679046112885034, -0.4626590549558398, 1.1091313553550761, 0.5553230073210226, -3.145772877600508, -7.210340672544412, -7.850100569188935, -4.497178233874434, -0.36812529883198486, 1.2544468613966246, 0.44728416804989807, -0.21478028331114116, 0.6920086593435143, 1.8384968784530613, 1.4487028108803774, 0.13083562125000353, 0.23662225142993812, 2.5192424781894975, 4.6535574396803625, 3.8887207487468567, 0.6197590428649544, -1.7957748882666724, -0.9913743500279334, 1.548327782086351, 2.338096665014849, 0.17066207696618285, -2.507446506806059, -2.748186358216129, -0.6990440369475083, 0.8588793835121845, 0.2268219516356358, -1.160496513888772, -0.9156606916527985, 0.9445293235048281, 2.0029592054383603, 0.7825255268258738, -1.1211966577628902, -1.1000762911297872, 0.858138718293408, 1.887412560670454, -0.09572823851310117, -3.436840922848649, -4.455511669934934, -1.8649526467030548, 1.611406757417005, 2.469747593102279, 0.46231918790877746, -1.507481976101981, -1.2235109390018055, 0.3177550933140233, 0.7403429840507152, -0.30256399948780527, -0.8444672746471887, 0.2811358550127908, 1.3947823837436613, 0.07601365179001453, -3.2155042485230125, -4.99966709079346, -2.7539756113286336, 1.8487055313789695, 4.639521204775282, 3.6239451423455034, 0.9006617542933022, -0.3655020216897735, 0.1396733926389348, 0.03543141464665602, -2.0487852083227494, -4.338815355733246, -4.198685277178803, -1.6868323198435653, 0.4455676345953043, 0.3209384936361452, -0.7508590678639355, -0.3445175177088193, 1.4517085275151616, 1.887788237484593, -0.7032198231726636, -4.21545660811975, -4.939668642695248, -2.0702545120421036, 1.1867568499140155, 1.4097744373050163, -1.0804532230937456, -2.982923815555988, -2.27608886661961, -0.4121106777382989, 0.1221863150479067, -0.7322115840817452, -0.8488297520457213, 0.68006848967508, 1.919984868489221, 0.7134857597531983, -1.9816946721687345, -2.8267755160546097, -0.32454476594371, 2.9397407999082423, 3.207796186596662, 0.10698100811241608, -2.911667337575453, -2.8004074882885934, -0.4142360889144055, 1.0168388490503595, 0.15044932738264816, -1.128033538026315, -0.7752584831083871, 0.3940393288352221, -0.05906166276557803, -2.5024285260067556, -4.333177522776943, -3.314448588899653, -0.6802811783843783, 0.33604523631149147, -1.2458422530324276, -2.8067976969654147, -1.625464717259908, 1.3409596311389533, 2.4761790776034367, 0.12281853874730228, -3.195151456018225, -3.846316392766087, -1.4651266290183593, 0.9508724742059731, 1.0661534669839625, -0.10650018692305352, -0.19928688335601305, 0.9609197102817978, 1.31721070010296, 0.008376875035685214, -0.814150874316614, 1.28066164769755, 5.232482412709385, 7.04158597138623, 4.433272909173374, -0.22069466488319428, -2.5916637555532454, -1.3736687180147193, 0.6845443811722648, 0.7198252107581093, -0.7008347246874478, -0.939920539475783, 0.685934922759278, 1.8988429094722283, 0.7635035576655622, -1.4457230108065744, -1.9193047673796488, -0.24274318710334056, 0.9529469824047977], 'positive_zeros': ['2.41078521595007270158527949605', '3.685813524694320283470891712127', '5.45702594261120162886315880564', '6.28510851245094473151220477986', '8.41362636400138028612654544132', '9.56279500228719041893709275400', '10.256217758003344275196216268893', '11.70932480926545010870221357393', '13.17535348484071716382517269260', '14.45258856836559178088295450246', '15.282235642973892830609609757470', '16.58379877447502009505215425230', '17.453482373233588609153003344752', '18.90062007297593438612889621206', '20.01618901279982941645308112182', '21.29065221636662376876239679579', '22.08440708297201115061082529859', '22.64430577181990227915578041375', '24.67225826150396045479443123128', '25.38238890610317215086020965424', '26.39715509289183907115402164487', '27.37869859747077600542408831886', '28.52009167964194084292726206820', '29.3378507837610345072127231880', '30.590603920422019803284150590632', '32.02275259656849049891317224369', '32.480405399444228766786558409607', '33.51424260886036287374736428186', '34.49268241237864073137903770729', '35.5207879421867409679952296137', '37.25068321351642572333081811592', '37.476996451597958198821296985772', '38.49282189358135285491604586727', '39.5680093988446301466496821651', '40.54791000762128300624409863709', '41.70147721629195843691469595340', '42.4726210844754329539440606832', '43.96215884866653788409099683784', '44.41203961179609011527365722037', '45.363642390751412488222972792458', '46.07405266421708338966247507254', '47.77743868289294160342046400117', '48.56302024836544426147604625973', '49.17349128720529046691581067591', '50.36373670524050850517527987489', '51.05099782788859948274669990461', '52.06862906411172071693383829848', '53.25619035801215783404980415196', '54.1887751749347695320229515912', '54.99152022922634264830472556982', '56.06496477489768710232582768458', '56.87827799007174026962335463813', '57.407658050757962163816909300', '58.84887094163626354937353410573', '59.90317859479351790614529446110', '60.97439094718412280987526196153', '61.22872209084421394434645674872', '62.10913381376049864130164037279', '63.6907267085615557618063349227', '64.068729349838096630487150508249', '65.27817378204558108290647585699', '66.28611430127749520145194896811', '67.05534213744441927078901014646', '67.953084456238532430385801046512', '68.61180326385988605602459240675', '69.60761653440101863263056792139', '70.94766277416764754697242415299', '71.76802991718087293950913267203', '72.36303209073746788107646403454', '73.53186711198689074016569328515', '73.876825699950660595204011909467', '75.0905560598301616951518333351', '76.43715504171039897635955951590', '76.95996221133625114244187746793', '77.701599515616971547817323641979', '78.94747532744005318935381246264', '79.611594199867960934391421336877', '80.32128010849164098810891608618', '81.20337430954084920846529974215', '82.7035352518544549030871061251', '83.258951769018245247201115468689', '84.33710584892993661922247817278', '84.46875117266107025459625392017', '85.78695795973797072529381614290', '86.65417309582985749174450948006', '87.80231345052000559738037308189', '88.49442218170994211170013666505', '89.37038299163011738891678383515', '90.372935476432865851799954833640', '90.83321864048510850240093920442', '91.90030720078103612721014951173', '92.887601518205119590894111995117', '93.61362638552082882598121034525', '94.96744054245515215541820670454', '95.5304930339830005736315070198', '96.130069814263834019243886534541', '96.92981864464387114883660844980', '97.91588649711420929759220296802', '99.29273854946247321596060867028', '99.79219821482498727867248385397', '100.61585646923306371582786246179', '101.3735412849314019939496822620', '102.45958499204357580169641889777', '103.314369085917114199230300727020', '103.59017464986515657657114728023', '105.1807299141260515057152922335', '106.073052479030797652401872324671', '106.499286374500521962285975183984', '107.53973906176469286495144167603', '108.38551144201261435213680995723', '108.709854074758502574246537737950', '110.34348501618179151364384250398', '110.90946365753625246644641567253', '112.04279238898013075544534942813', '112.44488429048092036496617565633', '113.298047751700742285775299339331', '114.2608876923904778003541900070', '115.13895183593955653891633689835', '115.96938107557770756879060893197', '116.79133018017500680987717810731', '117.915210277015058368231485022606', '118.7131765903729619040308995069', '119.23930704191986468231405709542', '119.78870439180488502902806630634', '120.991520872088489817649507484923', '122.209572242627182683222501335426', '122.75415837481016126201081260488', '123.61652338773111581444940084325', '124.24654855918812054648390235928', '125.3323167329313546954777993020', '125.8015022482684645997547472670', '126.93171686505440196994153559257', '127.78111343696285179412664107694', '128.67728267365768857312191499170', '129.50286846764844281420111451224', '130.2341285153266451910852406275', '130.97877301057645674332142049202', '131.836916673270345295159090698881', '132.39640019498238078337991496807', '133.88421302330402939045363298160', '134.742061578172080220080028940879', '135.1354529812772355907871783500', '135.70556443049714510806550274859', '136.90659171298383399220254883269', '137.65035627098757386563436178829', '138.45377983673904000352820887035', '139.52592540385059567068870423599', '140.08173592855229541586748350561', '141.14404629061960165057252918715', '142.08992996501979176096998138467', '142.287137603711463976617648069839', '143.16849751493518184066293421592', '144.35697507123431540479611517232', '145.33704775667594660919329425326', '145.914557436426219192985160641233', '146.9234469073634348259921307814', '147.456667158406155795816900288789', '148.16574604393566288826190029438', '148.99556471086278200233393907910', '150.4273677601400198669275925082', '150.635595597582224851026139200902', '151.7632757569231767570125391985', '152.411094407700208561921401853', '153.349962384909894819875967338961', '154.07194804954554655329069830653', '154.772751225088338482329703349279', '155.37790621653132131992809578681', '156.91309985388787638515259179779', '157.63331335585331161780870207084', '157.94400856723417261707573728250', '159.11067231593237643523082901702', '159.30565656817694169365846660454', '160.68255504112400871252759020602', '161.37340403281959369980235807676', '162.20503473381105678101796413057', '163.22623525683696398957042332888', '163.7968819770209220967172674076', '164.54083095857242117936743661503', '165.42797624216201881044124430373', '166.12594013189004649228933505937', '166.86571628671136935163444388711', '167.96686313353685843729997431195', '168.807073414091112851041901311573', '169.61787570508621581297440612463', '170.235259785694797108813091477892', '170.881641710067203392033438791979', '171.5711401004621069853118210716', '172.68815635502953308815467809768', '173.90013673911411838963850828810', '174.31285636506458889585996988790', '174.696987293523153119419042442869', '176.15365835828237909815862172693', '176.64942191010217497509035651476', '177.25546310314892721707806411807', '178.06319072041604996179050511375', '179.23915187700530480851823372309', '179.88074150540027909893118925655', '181.046933941263230004229399608930', '181.316009931030839505941713476402', '182.07235039490099293084553002016', '182.89764424775799543314560482455', '183.77804356887436976339318005486', '184.69635249659479181550876691348', '185.68133266480343127078177646078', '186.28010807137269542201339469407', '187.06438741810745489437136755685', '187.4888066355369619598910596804', '188.86056331778731916690910625871', '189.1722775047680892357279324952', '190.171337596389520628320749214685', '190.94834472081883683348892075105', '192.03711322472498805877534192723', '192.779104468558039435702654184995', '193.19259257373777872553047813198', '194.06413582490510827184570238271', '194.55466267055363959046423178863', '195.92102141640874890140221192654', '196.74988347776826596338708244791', '197.349041338881751287781608356287', '198.013948095025707721645701093954', '198.85407242008723774941324162756', '199.72665765095266678062596199811'], 'prelabel': '1-92-92.51-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.42724620381935696, 'root_angle': 0.20731689312196697, 'root_number': '0.264982593036948483589794070487+0.964253195684315552385731981970*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.207316893122', 'prec': 40}, 'spectral_label': 'r0-0', 'st_group': 'mu(22)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.03305494599513838736164304502+0.451332556659350328526241256116*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.41078521595', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '3.68581352469', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '5.45702594261', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.42724620381935696, 'bad_primes': [2, 23], 'central_character': '92.51', 'conductor': 92, 'conductor_radical': 46, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/92/51'], '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': '1-92-92.51-r0-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-92-92.51-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.42724620381935696, 'root_angle': 0.20731689312196697, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.41078521595', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_92.51', 'Lhash_array': ['dirichlet_L_92.51'], 'factors': ['1-92-92.51-r0-0-0'], 'label': '1-92-92.51-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/92/51'}