-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_456.275', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.766044443118978, 0.6427876096865394], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5, 0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.1176550971915953, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1]]], 'bad_primes': [2, 3, 19], 'central_character': '456.275', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 456, 'conductor_radical': 114, 'conjugate': 'dirichlet_L_456.131', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^20', 0, 'a^21', 0, 0, 0, 'a^15', 0, 'a^13', 0, 0, 0, 'a^17', 0, 0, 0, 0, 0, 'a^16', 0, 'a^4', 0, 0, 0, 'a^10', 0, 'a^21', 0, 0, 0, 'a^5', 0, 'a^9', 0, 0, 0, 'a^5', 0, 'a^2', 0, 0, 0, 'a^10', 0, 'a^6', 0, 0, 0, 'a^16', 0, 'a^17', 0, 0, 0, 'a^17', 0, 'a^25', 0, 0, 0, 'a^15', 0, 'a^10', 0, 0, 0, 'a^20', 0, 'a^14', 0, 0, 0, 'a^0', 0, 'a^23', 0, 0, 0, 'a^3', 0, 'a^19', 0, 0, 0, 'a^13', 0, 'a^16', 0, 0, 0, 0, 0, 'a^8', 0, 0, 0], 'euler_factors': [[0], [0], [1, 'a^20'], [1, 'a^21'], [1, 'a^15'], [1, 'a^13'], [1, 'a^17'], [0], [1, 'a^16'], [1, 'a^10'], [1, 'a^21'], [1, 'a^9'], [1, 'a^5'], [1, 'a^2'], [1, 'a^10'], [1, 'a^16'], [1, 'a^17'], [1, 'a^25'], [1, 'a^10'], [1, 'a^20'], [1, 'a^14'], [1, 'a^23'], [1, 'a^3'], [1, 'a^13'], [1, 'a^8'], [1, 'a^22']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-456-456.275-r0-0-0', 'leading_term': '1.67626056463971774016445275165+0.309248352302987378614583046828*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/456/275', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.7045480409681557, 1.9094939933953734, 1.9727494615725467, 1.4000548371970076, 0.206689635186247, -1.098505055833781, -1.8201807020857204, -1.5343289327067446, -0.4448990330828706, 0.6395542479773462, 0.7837985348506172, -0.403119280295791, -2.383653038917155, -3.9521393768847393, -4.04933389674509, -2.570809289593744, -0.5175850448768287, 0.7172840647768535, 0.4349928010274634, -0.7827796650896985, -1.5350444698548347, -0.8040088862802441, 1.0968765578965243, 2.7001996850194114, 2.624850528667881, 0.837692499130554, -1.2211590574700124, -1.8523193615536622, -0.6162523574041877, 1.2431252263159358, 1.929265241472275, 0.7786986487978539, -1.0942324060682707, -1.8646314061523812, -0.7966150398512308, 0.9868807778258236, 1.5869788019827662, 0.2542171552503322, -1.771157620356466, -2.4255923211515893, -0.8976658399737564, 1.4845008442254684, 2.5212915438588803, 1.3310711715600205, -0.7848922147917607, -1.732231941545161, -0.8375195609835734, 0.4676121869411841, 0.2652075090373237, -1.641530183995656, -3.360812975322836, -2.8825284379482303, -0.3120520837027948, 2.095243518383736, 2.2297519009288105, 0.3105301646502374, -1.4334298479610021, -1.2459548019954338, 0.27013390307649454, 0.987673055790665, -0.137978778876425, -1.7051791715880662, -1.4000885815883546, 1.2530775209206846, 4.108464254107199, 4.602372384220241, 2.524929233448682, 0.2037545584929749, -0.13157749135530392, 1.228144771516342, 2.0620561425151593, 1.0803399920319225, -0.4003185330622693, -0.04046421731477785, 2.53122413290997, 4.962659222786272, 4.71162236488118, 1.9541127020395728, -0.6025838289383127, -0.8323662966932405, 0.46291946041543564, 0.7668358203022269, -0.8988376645476196, -2.705123561404717, -2.3218587886656317, 0.058191496351337524, 1.796313278494633, 0.992665201281979, -1.137710438882761, -1.7126552713377567, 0.25633267891097367, 2.595523694052364, 2.6094569346336605, 0.3696499662298267, -1.4531293297462138, -0.9851122356269968, 0.5426303675944473, 0.5179769041547339, -1.517657937673259, -3.119986933922136, -2.0363234512667074, 0.79158531855348, 2.248124649406487, 0.8976425643152414, -1.222099256877449, -1.1958033973471587, 1.0827010601510954, 2.855479725277253, 2.104993118891079, 0.09029062729757444, -0.4958434231994844, 0.7331662228286231, 1.2598911913239037, -0.8883463389313149, -4.184522823768314, -5.183648564726836, -2.7571426061483955, 0.48107861794253115, 1.427046137845899, 0.18184810406528987, -0.5801138436530051, 0.450977408009719, 1.3966366496882856, -0.01935478995654089, -2.914598963985753, -3.945767672453796, -1.5649798116891658, 1.8024837838963133, 2.6836425694401655, 0.8203385558595356, -0.8196063456366266, -0.1813571431053045, 1.2395463148806152, 0.7771931880107047, -1.4192185576005512, -2.425994542848342, -0.6473830099632432, 1.7205681086514821, 1.4445875713908316, -1.3834956533097447, -3.3405403754164764, -2.1212998228067113, 0.5574205216903844, 1.4895433776931273, 0.3676573762794855, -0.060735040749274175, 1.8110287202375268, 3.9101094748917076, 3.290625961214228, 0.3919185372888878, -1.3221458466104379, -0.0010823247316040605, 2.0909404420640136, 1.7439434715713533, -0.7400669526403835, -2.019477261457898, -0.4295869351960974, 1.7081509842194038, 1.4131791896224746, -0.7620446019094277, -1.659069543339554, -0.19908345717411308, 0.9682550708177998, -0.6710328487013382, -3.6220295144854626, -4.173022905819646, -1.4896243762528694, 1.1607524702459, 0.8301999054497048, -1.2518487142274801, -1.7437416188931494, -0.048477530497111475, 1.0907049279384253, 0.003672376821724658, -1.1158945133961775, 0.6598099042216319, 4.388419666161459, 6.0193682934155115, 3.7352437021979226, 0.3889345129196019, -0.4175438435604383, 0.9785366540931957, 1.4187167398886722, -0.07526075465444908, -0.9109879035852555, 0.8530945996339379, 3.1152323669457145, 2.476423223675363, -0.7129368005291662, -2.494272106422934, -0.6917305056352223, 2.109472289076982, 2.26431975188189, 0.060842742217288394, -1.1517711650807723, -0.15020698979170266, 0.5067285823657032, -1.2351197145046222, -3.314637914893625, -2.312542178580709, 1.339583934077302, 3.5297125989679947, 2.031369270990084, -0.5564779394164777, -0.7416095208787123, 0.9035393879154137, 1.0158671371773338, -1.1692260604477842, -2.551316698227612, -0.9427396771017057, 1.412740804811052, 1.0441465083198105, -1.5605594646451943, -2.6550777876228016, -0.871407566307406, 0.6805056200820981, -0.9112566543842542, -3.8856799821812693, -4.274768885856965, -1.6344769772579366, 0.5167160217718644, 0.06228376032957705, -0.7880800027941531, 0.6012022970178039, 2.7430877593976346, 2.058831662651231, -1.4547283317391286, -3.68316971838286, -2.1137104253409844, 0.6274101540511245, 0.7128433372146553, -1.3993836123040246, -2.0906749818823323, -0.3358890949382679, 0.8629231219319505, -0.5498819580837024, -2.243756858496012, -1.1515166916483184, 1.401593701805869, 1.2705026991717923, -2.2938794599966092, -5.18738384586677, -4.118023820431646, -0.9890852598838822, 0.3769500034567464, -0.13902999335040106, 0.38630596996822164, 2.4098125942001074, 2.6454141893231062, -0.6758544296647471, -4.289039454031879, -4.045771182487313, -0.7707521022541359, 1.0445051764291535, -0.24006496776994726, -1.5246381524911228, -0.28143483157806054, 1.461746378424752, 0.6459741672637649, -1.5966646662057653, -1.5292452345070613, 1.1675844160827336, 2.5520745956185, 0.36787871168996683, -2.3893129004358964, -1.9352386254169505, 0.6491452526530216, 1.29205938606766, -0.7034148927637505, -1.7843893288587382, 0.02265136278889186, 1.9536937104714927, 1.0413160341262793, -0.9838395687897754, -0.392700607352897, 2.4444299035230586, 3.3600562401089604, 0.82795044947052, -1.5651719220969347, -0.5957382532348748, 1.7155488767766134, 1.428582119375114, -1.1297180330049144, -2.0795943310827925, -0.2689739034708361, 1.0531968918003352, -0.20711694713508091, -1.3480073831644375, 0.7417201192970502, 4.125543736699019, 4.280417442052038, 0.9299458342539033, -1.436622939337081, -0.226876798319856, 1.7842336087429813, 1.3208015535865403, -0.29308569911023746, 0.07487269093510637, 1.6080230554802533, 0.6099494855453321, -3.0961203013053735, -5.00865274389672, -2.4594757541197128, 1.2369939780912842, 1.6069210011711335, -0.6515271697221763, -1.522522763526664, -0.27367216435365893, -0.057098355205408916, -1.9194423714599778, -2.519498670915414, 0.3578115318519733, 3.526987360829956, 2.779918692931063, -0.7011009547415492, -2.124250183061139, -0.33529529128460706, 0.89283386948457, -0.70359629901381, -2.3040001490814572, -0.9329683964011863, 1.4737260837585562, 1.3305455017060885, -0.45195848681648526, 0.190895973274263, 3.5999213773531338, 5.290542366274133, 2.740899750944157, -0.721260580638332, -1.1594321112171107, 0.09561656458832724, -0.7067325061458735, -3.1531950541215354, -3.319334669478759, -0.49314291129541243, 1.3321736744863921, -0.17463256897965823, -1.9599760030351312, -0.7535219055720762, 1.374461413013893, 0.363076294972668, -2.9632668371566924, -3.8448345554560444, -0.979896139481127, 1.5742318252038634, 0.9156985182399231, -0.5362484189036466, 0.20577242298874143, 1.3910383175668486, -0.22305769056602864, -3.109502212656416, -2.643983274448856, 1.4890029385185402, 4.268883694504518, 2.707604073478621, -0.047725138811101964, -0.19944896415849725, 0.872259002752717, -0.21095929544671488, -2.536436567093784, -2.406222645008464, -0.044023094410883465, 0.19963716462633402, -3.002904351810407, -5.293457362130076, -3.2587095046436922, 0.22158203491609324, 0.5692955253368661, -1.511034376015978, -1.8795904152653362, -0.036406925870043114, 0.591152310453649, -0.7365716432089603, -0.3138614652235446, 3.5081379390847616, 6.596571616051767, 4.9443892757191685, 0.9178773048786165, -0.3950330771909867, 1.1841925244128748, 1.6152153401496752, -0.04916045840514811, -0.26089856055862953, 2.3862569277972265, 4.158169457361107, 2.233108831550851, -0.4209641556971, 0.16078984068451818, 2.3670711279669407, 1.7687972528462264, -1.3325500002288615, -2.259158966652865, 0.3423058436677353, 2.357040813174615, 1.1046848193864014, -0.4374402440558454, 0.9191645949042504, 2.9751682831368793, 2.0297397687845784, -0.5160654785527191, -0.3889676919874123, 2.1143161321720507, 2.2906924450912487, -1.1322883388205471, -3.595068665461758, -1.8998725052402303, 0.9173977102469743, 0.937415591082586, -0.3816831364110348, 0.5089566502532079, 2.5655973227613433, 1.9428141612073677, -0.8229481520562245, -1.0232712845680165, 2.401657186234561, 4.629034409424169, 2.4602107056785827, -0.7127177557653687, -0.588847273211922, 1.3872009837232828, 1.295453323105209, -0.2925839180158245, 0.1601250615735269, 2.153042690562057, 1.4468215991825213, -2.352809222289261, -4.133572336520617, -1.0973442057514775, 2.6910702059209646, 2.646231831245187, 0.38482824932293425, 0.010398061866274379, 0.9756786397990809, -0.14435466897163246, -2.6271222669301895, -2.2296260371498957, 1.2475876326191115, 2.8098693729511752, 0.16240029985548105, -2.5133387850215607, -1.4039766215502478, 0.9572371336948713, 0.4831786949110057, -1.4358525874357237, -0.7320309618305394, 1.9000960800546622, 2.0882853901892906, -0.5226676971839206, -1.565580453773016, 0.3842680595257269, 1.2006852128641736, -1.5653965691756235, -4.085261967484863, -2.449345365546675, 0.8062544351005028, 0.9801748296602001, -1.1234389207077586, -1.192015710339962, 0.7985235093498508, 0.7617124426655717, -1.846322635711001, -2.658869571973667, 0.033187297611988964, 2.0860501983247155, 0.5636873396007993, -1.108374550977315, 0.9765902332173467, 4.301008058057091, 3.9251538681983, 0.5630192671422057, -0.9660643224106082, 0.21058249765157253, 0.5547463963720642, -0.5349179743244199, 0.7285929706365121, 5.107603920885071, 7.447367510700855, 4.336660182778929, -0.26896126767830997, -1.1580272274643435, 0.4356037263257452, 0.12581330781008068, -1.7967392859051738, -1.6955314031658688, 0.01401717843784016, -0.7475626335541999, -3.9902440262983454, -4.703272242762335, -1.1421532192478374, 1.851107924122904, 0.5905728569114413, -1.6818850981369384, -0.6768418739168092, 1.8083605071495938, 1.6348202709866995, -0.2378280997873399, 0.058276071542578994, 1.753290796952835, 0.5305907942876189, -3.3615069317508137, -4.630304371550809, -1.5833380615383592, 0.9459669015379247, -0.3967376413886727, -2.289954794631547, -1.035919833278314, 1.0524826650210273, 0.2981660905089191, -1.3849201945728362, 0.08209513009806782, 3.287860404030317, 3.4027875754200125, 0.5738384216686052, -0.29229962349204, 1.8527137106334495, 2.4127284395265334, -0.5702181865881942, -2.708143653399842, -0.7458902610531237, 1.9167813745609878, 1.2384792680438501, -0.7511902254439957, -0.2740289940548855, 1.064229264350819, -0.555771553158648, -3.4922210721179665, -2.78466686308414, 1.1129316878917457, 2.52241237255386, -0.20317282405792425, -2.2338356000415054, -0.6443842035324786, 1.1296910960250532, 0.0504324513399272, -1.2372842617021753, -0.007927102131460672, 0.8116842659820563, -2.1476826438136447, -5.714785896492543, -4.578464098907302, -0.11045100615054729, 1.7109465667870922, -0.17686281051143699, -1.2109749193013384, 0.21080407098795548, 0.4337029417552023, -1.9193789009262503, -2.958989096078227, -0.8118856718444744, 0.34265504553773496, -2.495525417766883, -5.282809124989761, -3.3217837999086086, 0.862343343649759, 1.8070933497991972, -0.07118551308429616, -0.33159281575698685, 1.1092434497757857, 0.46570076302904295, -1.9368949431071267, -1.4785123758324565, 2.2652633439488703, 3.8882483127566525, 1.021009159910665, -1.7172204516107594, -0.6984889633181304, 0.9014385215304228, -0.5185422496876073, -2.273853801573037, -0.47472137505443596, 2.552209264527513, 2.141531211834797, -0.5624568127366245, -1.0053921399240173, 0.3118211988339745, -1.0748467482956041, -4.828885780905729, -5.572282933871441, -2.1195832704063275, 0.2334118602321394, -1.379869079083967, -2.980885403421618, -1.291348297488369, 0.6734882494588033, -0.23191871702111624, -1.2368313457303146, 0.9026421845736828, 3.1652938980596925, 1.1993108431945196, -2.5795553523151553, -2.6309541629035795, 0.35085899933911124, 0.8812517620046604, -1.7343947257580947, -2.674542577195698, -0.47660487280132185, 0.8064205026222886, -0.4173945536425921, -0.46412561746973213, 1.9377348369165737, 2.1481240934876817, -2.2908544528081616, -6.26077748379201, -4.713720033813976, -0.5221021317853101, 0.8403341667209545, -0.04389275520975033, 0.5247939343065602, 1.4956854825789592, -0.6220377641989816, -3.922365304071712, -3.2457504582827887, 0.7080959780015214, 1.9785417091341135, -0.723543784533936, -2.1851246506620696, -0.05897765824411996, 1.4123429768561158, -0.43669186738338855, -1.939398805247426, -0.254595663223988, 1.226413963929957, -0.5935558869122816, -2.343012932727167, -0.2266905997332044, 2.6247027618219434, 1.316426984814434, -2.1429325656494638, -2.3600239510207857, 0.07052774582671471, 0.1881750251484285, -2.059438556284964, -1.995251251079923, 0.8068025311496029, 1.625096714420566, -0.5767558199989189, -1.1804140366736007, 1.3627540765316404, 2.3852450472388367, -0.406302786980693, -2.336837587466017], 'positive_zeros': ['1.29712195549511007872339393833', '2.61274464088325685869044305421', '3.36040289478596908938621705004', '5.09520496524504234063584200135', '5.74716132184140916841520737111', '6.70661490926281867611897011344', '7.92885596751241299644313564846', '8.84960102926208165689257689092', '9.81407919434310303892514004583', '10.75975883794023478154698246185', '11.60096959910529201858187520729', '12.614914345726893731907566996430', '13.62905389184613032765841753140', '14.55361206756234493566579676608', '15.05907349429523074293432157859', '16.2832223796082702811957118103', '17.23090594428643356080987221557', '18.07009175937241175895716824336', '18.72502727935152435402835318355', '19.56214223286333700366388939405', '20.984377665211563827220330652040', '21.2943663310246831497463107055', '22.39359890167699761731264791929', '22.81994387392017149950580232905', '24.27698049400358124321738444187', '24.89193657936282748657344621737', '25.48939142158027642662582717807', '26.555430080983547076000934257030', '27.331385500129456896212669317582', '28.09499407612408611211802523978', '29.10884526898471388320224706873', '29.87787877003972549610504911415', '30.41405302841715664284357096898', '31.47487797013190977629254282609', '32.305975606148803338000468483686', '32.99410423731866243009049154649', '34.08000508483267881775678877871', '34.529176136520835662001095492162', '35.22073568368072952992568209387', '36.50553314678064919217860931762', '37.22740443405782541386630246528', '37.71465758216007821481267304507', '38.43518791424042729025831875337', '39.509553162654613450771684370129', '40.4297922494711478115357092708', '40.97350747717175104579694346438', '41.6833544797560237095779741752', '42.573880809457540694383225404934', '43.29897978439796687799035979174', '44.30294886022792839510691829410', '45.10395612173536707887175968240', '45.33456242735641308117622614338', '46.60603059274090799119606491213', '47.18764421969404872306089681324', '48.03640406390006753767685402519', '48.80327045323194874557313648725', '49.580749429969498462526384332452', '50.34509633629633559045100772062', '50.85866042934988705697118079600', '52.02023922161377635457161503124', '52.62652753195211782668675057671', '53.44525037158876229350733526177', '54.063167665355085897988449622678', '54.61965832261404568882737739733', '55.99390545707340816625174632112', '56.36581577983094229367819219730', '57.17403815161969905292239774106', '57.70461205190865137984035475100', '58.68316458493268951417696983035', '59.44437425848601955506624862494', '60.320983371942877472827581733417', '60.97144797950003988248036690842', '61.38932805919743304086071760010', '62.39113759463849928163721563320', '63.3534698117260232999965155591', '63.89586703780298793596515560968', '64.540388000228032054801420679622', '65.42053144954910311374020509883', '66.07153155319318495849409202801', '66.99724742366627361419689270411', '67.39024608131416460816312852711', '68.63310355340526070391295755042', '69.07771415479480581018640326807', '69.60201893378998294774028349102', '70.505428385988107180783610938881', '71.473531221623862223949490907267', '71.99148088303907429379817944427', '72.863954779716206922377017150390', '73.356814642537353658185586565231', '74.195382862147685531408249028188', '74.82087759416370404745814783040', '76.08430160846796425267022523768', '76.48751579116968746173092714978', '76.78206712493815163088691107060', '77.763136839616443490106229915810', '78.83063177759720406076154795848', '79.33715504819470713077718335343', '80.04053110831627215177853243324', '80.71228029474306463795376919303', '81.439161190274173752421703628116', '82.222176297565936763292637035339', '83.04223641521056061996138235418', '83.65531622776865845380129379038', '84.37226534804364707851846021775', '85.14219006644848315404772554205', '85.67493131320661109396570323677', '86.64311346633717613151952642081', '87.26149901902692027473683205336', '87.991747146041681654226706877667', '88.78817100005954454372259980297', '89.34150757817463579400976224937', '89.92955198984557166292199529792', '91.02097393162057227195456357669', '91.591988329165713263677889856222', '92.42430095332790750681260265451', '92.796684437668454838112221182364', '93.49831917929637262897462256411', '94.56417781655486680165457103614', '95.22531539109987983318408249044', '96.01455340383591803917944709356', '96.23255765860150895742880668276', '97.15872916888889035109892141443', '98.06022904282612714539351250830', '98.79774003181022891107064058514', '99.277797137916631180307291517861', '100.10759072597300793990039629530', '100.84377811020780315203077395215', '101.22492583604327454921702680781', '102.416370004094115340689627170650', '103.08772987925991538382488472495', '103.303720955551610618595338440881', '104.42643201015054200434163002347', '104.97761168282293402458927394870', '105.71789181118477242442556518408', '106.28778253435659677044057863303', '107.27682708135787815802852542068', '107.973007077824306158695535456869', '108.396809689439219258183634453294', '109.03869854243451641226862468637', '109.8979271052945307935443034664', '110.92902962762054348524740542991', '111.30152294077119972932382513604', '111.84541643738093398285235325842', '112.8193503410299105536031073421', '113.15579055813705442167578955415', '114.347563887695039074247853026603', '114.782935979722069168583555149285', '115.631338517671072485643442959884', '116.091806679097372954498314742440', '116.5999980103763964248675583037', '117.92053016692131280521611362417', '118.23129196648059714894200652184', '119.05310708293433713851319728854', '119.42186951895280893802662589729', '120.55062791092850520321867059860', '120.91344321604716463596816365878', '121.74279022352060015448195903874', '122.46654017804356732860108331285', '123.294954350446979895843733157031', '123.61616418146849189882200659984', '124.61031404616696737764947597503', '125.055946408393627173474389093443', '125.84849801443510265874048404575', '126.75067159002194950455186631148', '127.38127080960974418087773656856', '127.72753040241319676797957074023', '128.65146633165302111177511623472', '129.17811284293034316723896200246', '130.21935915086661024959642319326', '130.71641188196611297328451278561', '131.490323826821867776984006889431', '131.84606048179776842993034660415', '132.63105585740413751327119700748', '133.51366199406522649063505997710', '134.46160310723081918497957894450', '134.68372734603636613693343668709', '135.29352849217720654793824564164', '136.1443076316116064354547800610', '136.88885388999392598307246185357', '137.66206769538600867922270182694', '138.1973741295825638492954951019', '138.83814735997894875145777273404', '139.62782424543813310445836213405', '140.2609849844529252156291125115', '140.79620107732466868841679866152', '141.7812128172991495691003495005', '142.33372140399247997571485390036', '142.99850269355155806114599952260', '143.54275945798586763349398388304', '144.37185259044323409667774101521', '145.06990368852946316136966467051', '145.533726570827928226678349574985', '146.6232305382291822851097238671', '147.141274707928359883027895726654', '147.65319383824643688436768202935', '148.043090932792612250821744202179', '149.34999013410884394892543826403', '149.90675282144659296290952851659', '150.33485360216933776150840735796', '151.24593819388853071287347394546', '151.44228746785683988541865759823', '152.58570750533282048587013106641', '153.190603405120515875264447294031', '153.828117135935538873809073568332', '154.63577764649857988624436429672', '154.988869920823244531132877995755', '155.672887405789464278454101539739', '156.70650212229993340001282642105', '157.13740995879577668596897641766', '157.940088887608304569051602452986', '158.4821107924054576917753667275', '159.05425441668652585599117598219', '160.078840184104844241475129349581', '160.37536109385192951923188375629', '161.20047794731250099163690101145', '161.94539680216621234428155540140', '162.670376354106799688672442279614', '163.17454345936338483359426323469', '163.69067041780970342588915076689', '164.59847617188099552956473448359', '165.29378537151126365212257626876', '166.01779125334127163196996165957', '166.570561213321150463731448493165', '167.18881353650850912177596455237', '167.6323152606907476002974647698', '168.7587269240587390080032410388', '169.35108322041342723176247736620', '169.95935024736002326332717847214', '170.389579449707292839559842724297', '171.361270302155985692274391359644', '171.63493958065673131510486227853', '172.737463251666110257469367294496', '173.42445493234207383154063959890', '173.82604857967518811229755941633', '174.43679398605111603859754801291', '175.13551954586122703055879496432', '176.02269452503967086269956343090', '176.66026115300551908891878302729', '177.11958863735003215747834271701', '177.85597434688536720174130598641', '178.67712456550766054892271850669', '179.277204234155198429727136193431', '179.55605911939834496892177492586', '180.85120398179834799286967893346', '181.05234400359105641927914536349', '182.03571601127082344878406266531', '182.45915640458725667032544709512', '183.03218662277791090578427161175', '183.841328571237972350476632989544', '184.64728138481760928013895458224', '185.12298268094545274453768545212', '186.000548601012572208785155509953', '186.475809300191970338347204096352', '186.95046685572377280985070701266', '187.67779658965905285687949750011', '188.80427900096462283526488066690', '189.35235274073372406612880371318', '189.543567730976663094458852689', '190.25584477937114384929610652449', '191.19173032732009078899986584447', '191.80409964411461658267635440791', '192.50676303920272468735440314414', '193.07216610596502540766503833370', '193.78232600706572173788883619442', '194.306452212038317063544165721258', '195.01991057424081736542169182364', '195.7373056746871412616920051465', '196.551442991752186577196912816015', '196.9067695581912655396017444232', '197.72435485426416022908278018951', '198.363255239980797821408172029499', '198.91604499080173180549369091786', '199.65103079941231964784266579692'], 'prelabel': '1-456-456.275-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1176550971915953, 'root_angle': 0.11614219753025436, 'root_number': '0.934169630524078596539477659198+0.356829232836249673885493015050*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0580710987651', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.31359643513906924878524758760+0.147140643071736039353744814880*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.2971219555', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.61274464088', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.36040289479', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.1176550971915953, 'bad_primes': [2, 3, 19], 'central_character': '456.275', 'conductor': 456, 'conductor_radical': 114, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/456/275'], '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': '1-456-456.275-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': '1-456-456.275-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1176550971915953, 'root_angle': 0.05807109876512718, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.2971219555', 'prec': 40}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_456.275', 'Lhash_array': ['dirichlet_L_456.275'], 'label': '1-456-456.275-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/456/275'}