-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_145.143', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.2225209339563144, 0.9749279121818236], 'a3': [0.9009688679024191, -0.4338837391175581], 'a4': [-0.9009688679024191, -0.4338837391175581], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.2225209339563144, 0.9749279121818236], 'a7': [0.4338837391175581, 0.9009688679024191], 'a8': [0.6234898018587335, -0.7818314824680298], 'a9': [0.6234898018587335, -0.7818314824680298], 'algebraic': True, 'analytic_conductor': 0.673377169063117, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [29, [1]]], 'bad_primes': [5, 29], 'central_character': '145.143', 'coeff_info': ['x^28 - 1', '0.974927912181824 + 0.222520933956314*I', '\\\\zeta_{28}'], 'conductor': 145, 'conductor_radical': 145, 'conjugate': 'dirichlet_L_145.72', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 'a^26', 'a^16', 0, 'a^6', 'a^5', 'a^24', 'a^24', 0, 'a^11', 'a^14', 'a^25', 'a^13', 0, 'a^4', 'a^0', 'a^4', 'a^9', 0, 'a^3', 'a^19', 'a^27', 'a^22', 0, 'a^5', 'a^22', 'a^21', 0, 0, 'a^15', 'a^12', 'a^9', 'a^8', 0, 'a^12', 'a^10', 'a^17', 'a^23', 0, 'a^21', 'a^11', 'a^6', 'a^27', 0, 'a^7', 'a^18', 'a^2', 'a^10', 0, 'a^26', 'a^13', 'a^15', 'a^2', 0, 'a^1', 'a^7', 0, 'a^14', 0, 'a^19', 'a^23', 'a^1', 'a^20', 0, 'a^17', 'a^3', 'a^16', 'a^25', 0, 'a^18', 'a^20', 'a^20', 'a^18', 0, 'a^25', 'a^16', 'a^3', 'a^17', 0, 'a^20', 'a^1', 'a^23', 'a^19', 0, 'a^14', 0, 'a^7', 'a^1', 0, 'a^2', 'a^15', 'a^13', 'a^26', 0, 'a^10', 'a^2', 'a^18', 'a^7', 0], 'euler_factors': [[1, 'a^8'], [1, 'a^26'], [0], [1, 'a^5'], [1, 'a^11'], [1, 'a^25'], [1, 'a^0'], [1, 'a^9'], [1, 'a^27'], [0], [1, 'a^15'], [1, 'a^10'], [1, 'a^21'], [1, 'a^6'], [1, 'a^18'], [1, 'a^15'], [1, 'a^14'], [1, 'a^19'], [1, 'a^3'], [1, 'a^18'], [1, 'a^20'], [1, 'a^17'], [1, 'a^23'], [1, 'a^1'], [1, 'a^2'], [1, 'a^27']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-145-145.143-r0-0-0', 'leading_term': '1.11252230263565050461269682029+0.592545852117198548706509326961*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/145/143', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.2604826300758876, 1.5187278382569467, 1.8588088701581686, 1.895284799875698, 1.3995276365073788, 0.365063377154598, -0.9747173672306721, -2.194599172467173, -2.8158240861511796, -2.5048849471570502, -1.2534010056968174, 0.5568214919926698, 2.2643061724340146, 3.1944791596428086, 2.9730333855133697, 1.7289296861386012, 0.0626791786381016, -1.2327239343343919, -1.5717695953733646, -0.8844718919394015, 0.35104581711603466, 1.3890430642596217, 1.6593232585701634, 1.1074990330790322, 0.2102273250297008, -0.3618286964832964, -0.22544048817943177, 0.4167260222523072, 0.8933037704865411, 0.5583815668802955, -0.6553457818801092, -2.0302754864305426, -2.4161471547658615, -0.9769262392998104, 2.1418872103670608, 5.710914570862775, 8.029561036618025, 7.920807061608467, 5.475458920155664, 2.0312887579322054, -0.6370015931525739, -1.4000944184931976, -0.40692722936023945, 1.1533895828083018, 1.9703677335284366, 1.5356429947660413, 0.40162843141478854, -0.3857964077950736, -0.20694736472670977, 0.6044826854097781, 1.0555834232916412, 0.37076293341531136, -1.278177102554502, -2.819797424584989, -3.109699885999352, -1.8751975030921204, 0.020062996349337427, 1.2545604915412762, 1.1409528193582827, 0.21452971110864352, -0.22112809529060326, 0.7404308680828808, 2.7090313110242707, 4.1843289692878045, 3.7646672675755255, 1.4163670047172268, -1.2939203517762055, -2.300101984337657, -0.6539443943998796, 2.648282498035686, 5.348773550563249, 5.619600945018403, 3.419025580650412, 0.43053805935741724, -1.3301507654164966, -1.0625569836143396, 0.37980803176098427, 1.4340251481308697, 1.2388040166481353, 0.24885060688047872, -0.42081695157213816, -0.204604003943131, 0.35440536118183324, 0.23550431915591585, -0.8866552008253246, -2.145314452468589, -2.2508939681483464, -0.852893657203321, 0.8613637371568579, 1.0661661660605357, -0.9878710045205684, -4.017215746343581, -5.529004400684545, -3.86264368418425, 0.2995394467861023, 4.342082468022426, 5.774216957915563, 4.180057328386025, 1.3778427092232197, -0.29584459883560976, 0.01210432337949146, 1.1748207721655912, 1.4368855576106225, 0.22879791878109113, -1.3136706606705126, -1.5692962465664957, -0.12450169795532656, 1.7642778437893294, 2.3929191890358847, 1.2810015164235808, -0.38711045345841744, -0.9839280847075205, -0.07187787414554435, 1.2169362081936432, 1.4280515323587766, 0.34494581905548616, -0.7928501978950917, -0.6730719799589091, 0.5653047272604019, 1.362355179660442, 0.4360369993483195, -1.5606518771853504, -2.277240382688289, 0.1699441066059475, 5.104248214594649, 9.409536202091983, 9.986425616720908, 6.38523099678093, 1.1854564338219453, -2.2330680775740563, -2.449243869320503, -0.7909321583202128, 0.3684082277245528, -0.04767648498510991, -1.1257121882753172, -1.362548392146225, -0.4548998487658509, 0.46386486179239844, 0.2614283852182623, -0.8147523030115466, -1.4301425368644762, -0.8048638089754288, 0.2082611887163639, -0.03676249994979629, -2.023780085231693, -4.188363267221226, -4.276801413221519, -1.6949632653740094, 1.6430054863307517, 3.0367993328825382, 1.6657896730122825, -0.5475998254137525, -0.8644721072469247, 1.4583472691634185, 4.362583075466261, 5.053215161482628, 2.8228472937683073, -0.2731524199203549, -1.55662448629387, -0.4159650032382735, 1.247137525535493, 1.1898835763381097, -0.76415362984254, -2.630348443925335, -2.477592857872928, -0.48276684970969785, 1.3679296769608933, 1.4831053872284725, 0.27702366740392803, -0.5329696874625657, -0.0017518177918776094, 1.0410488808524572, 1.167957857973161, 0.2121380603434829, -0.513877095950439, 0.0046200001164421346, 0.8531805570179536, -0.11188500937810415, -3.6943175126384338, -7.773443608613493, -8.821782896242985, -5.331868312030254, 0.3504375059097538, 3.901913365587777, 2.9263169916405345, -0.9736914244512604, -3.9779636582245663, -3.7574338724790004, -1.3290383285826242, 0.5733660765247734, 0.5267502115303234, -0.47183999125788373, -0.7035868802891296, 0.06289242485492538, 0.4894309146406956, -0.36988513145260893, -1.624587020082417, -1.4984338512189896, 0.4271229724817813, 2.4502027283460794, 2.5464604250819294, 0.7127991764118335, -0.9432332119337119, -0.5957256386753522, 1.16957353470089, 2.0427450406021532, 0.7850222084374765, -1.1467207204472953, -1.1902667140016976, 1.2216340141819797, 3.677227629205303, 3.2652742573117775, -0.13121553748040296, -3.481355791964846, -3.751117936016518, -1.1494480772812998, 1.1172382988937648, 0.3207231970743625, -2.913601679767444, -5.421966472396099, -4.944801774807573, -2.317862856578388, -0.17004125795676345, 0.07900706404200537, -0.5926630922649538, -0.524511252087378, 0.4075753247289098, 0.8374995749214635, -0.035605011129038695, -1.1989544873472946, -1.101176604867114, 0.18058245103739531, 0.8294166609059507, -0.34251578834906804, -1.9422722604328662, -1.2143594020950617, 2.576493923043355, 6.546705595390674, 6.675038795114876, 2.0115285319949527, -4.004021053122596, -6.760241653075072, -4.879397333856613, -1.141438301020839, 0.8392727770348107, 0.3048305383330665, -0.5711113166851486, 0.16565450304851267, 1.8741064667562375, 2.4279021524892026, 1.128320708180173, -0.35102275492049123, -0.1253910946944161, 1.4460696000407214, 2.162083189019845, 0.7547248182371947, -1.4590041433466292, -2.1522834711288836, -0.834662019380225, 0.6028003382463912, 0.3261002183615024, -1.1197206482110842, -1.5818726302366426, -0.19208170431781818, 1.393112928899514, 1.1679222678072794, -0.3053474151714657, -0.15108279599716573, 3.266307244134187, 7.678101315003525, 8.699530110750635, 4.479487451441097, -1.9897774085680884, -5.68688730293856, -4.499665087785074, -0.9044800916147289, 1.1958150497543234, 0.6098344642964739, -0.6215299939682726, -0.34467670322268573, 1.0869548387053136, 1.7075387417318577, 0.7391246211178674, -0.4970206688969465, -0.5603403659470565, 0.1290094997978151, 0.07453276102830501, -0.8625682833247699, -0.8864305281792144, 1.3513682975667414, 4.447174345060196, 5.361608389670028, 3.0294163197031487, 0.030041566312326826, -0.11580843570773097, 2.9088135545251004, 5.637692508736752, 4.733179484747333, 0.86706413082407, -2.047266893556598, -1.364067497654767, 1.4135948420741458, 2.7015424334194615, 1.1601777757766265, -0.9944655274002051, -1.0553990470638812, 0.7778002397337661, 1.8929983928729828, 0.8023550150098633, -0.9214505721659829, -0.7390209409517539, 1.5280251820543524, 3.4304381195980103, 2.945038875982587, 0.8637036635354293, -0.4551505815421161, -0.1366280867395046, 0.4312837281372603, -0.053203049782753115, -0.7577825409341212, 0.04735984313369538, 2.1248097600988025, 2.97196036897207, 1.030942524265477, -1.6269809431756668, -1.1171298174386644, 3.52339240046678, 8.408095165012707, 8.527157116296427, 3.1941997966451807, -3.068218114382428, -5.288506128645075, -2.9877252084606987, 0.14369517142158764, 0.8886699752341527, -0.30601241135550206, -0.9452577332610463, -0.10865060498132405, 0.7337050706374677, 0.28504161266214845, -0.5818797821980111, -0.21045012523518153, 1.1838320837683651, 1.5378947404654952, -0.17349611900760198, -2.1731185640033077, -1.9269852575520787, 0.4968682250621913, 2.303410286551417, 1.5094518787975066, -0.40746573903780114, -0.38977706336177115, 2.0558345359984953, 3.906006290376096, 2.358987906553091, -1.4049144010434396, -3.3915451856221406, -1.619690306897142, 1.4544004036004683, 2.0429978701719325, -0.22940127081393774, -1.9408625463692522, -0.29142149074675694, 3.310054950434605, 4.9714469974798625, 3.039750064449768, -0.14106615340823914, -1.3764162449506427, -0.37838144807870083, 0.5429967594845333, -0.06424642725241408, -1.0490691524144662, -0.7218249225925002, 0.524077867012017, 0.8312812695147948, -0.2707882660308222, -1.0610106205681968, -0.1950967033445313, 1.067468317147705, 0.5441489929939386, -1.23803168177163, -0.7276828914670742, 4.34724021916662, 11.19822382529309, 14.018874925506834, 10.131877536102397, 3.069073219114789, -1.2249649671728315, -0.6292936833361584, 1.7200562938313049, 1.951009064752027, -0.06260028179281305, -1.524695966927024, -0.96043304575631, 0.04831815541003851, -0.4267654835797406, -1.7248575433353746, -1.6241707093187978, 0.2827544885228948, 1.805728386461913, 1.1726280749987272, -0.40525405718338714, -0.33942589538920015, 1.6762413043403328, 3.0653813196974418, 1.7975216259614273, -0.8144028390280751, -1.8475433486186585, -0.6830260232954384, 0.3588396188091484, -0.39115069422293847, -1.2216536370869748, 0.6809306212934803, 4.763910164078231, 6.764868150056378, 3.658078924609449, -2.190142349329928, -5.2579240624264925, -3.09274863864631, 1.0783691073584443, 2.4699529740127675, 0.29898900048611654, -1.9908748511994876, -1.5313508745173952, 0.6293504450022436, 1.5681285718504854, 0.5224706229796044, -0.5995268536102001, -0.36576509780240785, 0.23524559635010764, -0.3086161292130342, -1.4638686801034675, -1.453066464999734, -0.24280543786332726, 0.008993572440928051, -1.8094082485313412, -3.4271148371765157, -1.691669622704211, 2.8917582690719605, 5.8890064524715715, 4.03885150893408, -0.535329911872374, -2.6665335394532703, -0.37698029331257554, 2.8443853750643644, 2.5729445696147746, -1.091172243528886, -4.005980000604021, -3.379684358686532, -0.8544307313784151, 0.36967934450745954, -0.07221613249449077, 0.16527073722744054, 2.124491703062024, 3.655279172308697, 2.3907350033452506, -0.710743588403747, -2.370093348418819, -1.2072235209810656, 0.6614436625122764, 0.7308996196556632, -0.5821717500403106, -1.0002679239080055, 0.015636249434107116, 0.5509623915747847, -0.5719097511786082, -1.6250123115036428, -0.41976013991857913, 1.9885625251684067, 2.11515887357301, -1.0091785450670803, -3.5327669887430178, -1.0631939662283476, 5.420268733385958, 9.863723314509905, 7.861401075273997, 1.6497508802994676, -2.7344058171910093, -2.359110409129297, 0.1690061555242116, 0.9991709197589325, -0.224907665951042, -1.067156070929262, -0.40095045436036714, 0.277507241108015, -0.30790112566541933, -1.02406945768535, -0.2101220894772221, 1.411501642578739, 1.5216061675245591, -0.23071108365826298, -1.3063928343846114, 0.20419243744084292, 2.538020327092231, 2.413496412673294, -0.254668896720525, -1.8078012956202996, 0.29461627063539747, 3.7038540432552214, 3.945457405719014, 0.29342347680716047, -3.1620618421405986, -2.8064445493437638, -0.056195269475783585, 0.9056230243786938, -1.0385933471214293, -2.5728851388955585, -0.7670404559367996, 2.7277768378241793, 3.8739306805118305, 1.6524005497065488, -0.7831409117318826, -0.5339792218219612, 1.3694835479945071, 1.9209127443007992, 0.5074779690879585, -0.5803504509443362, 0.18339080102304645, 1.383054230947573, 1.052171771358893, -0.2644959840938228, -0.5330075650357289, 0.34123350452764584, 0.23174245933052084, -1.58204271678607, -2.5272816515161765, -0.2503014208482144, 2.9905536569035682, 1.943472806986628, -4.970808523111298, -12.530085577671205, -13.940724672836891, -8.411420040306144, -1.701070627667945, 0.8043849590828531, -0.41922855033561857, -1.3297967632726586, -0.2655452411522475, 0.6285002527305619, -0.5105174079600231, -2.2728335398855646, -2.258708920496946, -0.708260189034076, 0.12179482411181458, -0.33835773450294465, -0.09010598291173157, 2.0133261235857867, 3.850530189887116, 2.670843130380341, -0.7935146082827716, -2.9036579119576724, -1.88879808258659, -0.059573868773702535, -0.2340554958471629, -1.5933565550421056, -1.1295122483472873, 1.3823080442854274, 2.419191644728928, -0.3318068389472166, -4.0591584431512215, -4.01185687658059, 0.10653550320464235, 3.3704946525729866, 1.8814428998891541, -2.2594041364828277, -3.886255242762606, -1.4888329670276634, 1.3076117306717525, 1.0137606912456751, -1.2970224679146944, -2.1529406950354946, -0.6853339584749006, 0.7063091090975853, 0.30185790287820047, -0.6476003270531727, -0.38386541728636187, 0.4753479154213296, 0.24822726988939423, -0.6494876297661066, -0.15188723954119096, 1.7304025297876073, 1.9685344857825497, -1.28879200187093, -5.200042828569876, -5.25951839300394, -1.5181351540425412, 0.7441345616889142, -2.3802952814070633, -8.058583759828991, -9.967294325635958, -6.069952276331368, -0.7579760784328318, 1.0713629683487367, -0.27608264989105846, -1.0354885546559194, 0.2510052151754453, 1.340234572452443, 0.496894484068173, -0.6360302422060716, 0.1894848576831815, 1.9761374450185973, 1.708065176601004, -1.061185804365421, -3.2232604767367263, -2.360069667661816, -0.0018187201773334472, 0.8366183633822364, 0.019539324934076917, 0.02110301090075965, 1.673222888701897, 2.685341193370494, 1.335281075233013, -0.48471094744798127, 0.006080118687012293, 1.8184440521593597, 1.0586021855600456, -3.1375781073030646, -6.1939621405134595, -3.5865475817975767, 2.7171746124356178, 5.973828101799362, 2.8192782542791153, -2.7610918551704273, -4.699532895728314, -2.090466886046836, 0.8697151825503969, 1.0697976663490396, -0.17295384083864618, -0.3503776404527325, 0.2780060738905839, -0.15840810742074177, -1.5170818400150585, -1.7128941450920034, -0.2638998198394686, 0.6678399407099577, -0.31747417082507623, -1.4382738584675667, -0.524993883853307, 1.0760026145524675, -0.022297418601830224, -3.8938136190646633], 'positive_zeros': ['1.65121453810244789692544445184', '3.345188107284606615249340464', '5.01223199657953618586023087100', '6.1643576084094688060927646219', '7.58387664355102856216240327212', '8.24909162494879766878038736345', '9.22710843597391512474207286544', '10.425353945150149374258943465476', '12.40527530512254337101750498901', '13.20553787555602752187614392679', '14.497132702371288220857532290356', '15.090168788541775400843904019360', '16.019332327828005306082912179265', '17.49645937852847396421058339514', '18.51895308827118087962714135816', '18.88072739354247486468053953823', '20.46534319428450212910577801297', '21.31877221298341551833917186568', '22.865748716656311601872046909371', '23.67254139385490520929458048774', '24.76974676447039060552578153316', '25.41884903980726893919770521197', '26.02674100579030361786221678972', '27.32935596012251038653605105997', '28.009009483435015086041099019490', '29.35470419752758912293172391984', '30.842454297608497584203470346660', '31.24635318314720996802196119512', '32.22987483236079297375589500156', '33.14455972915750802505315513011', '34.29358130435241400865167006332', '35.01620211817131557268658120872', '36.015858282706153315829764489020', '36.74571823715515218965794493533', '37.572254299679771337603836678434', '38.4242241249079925759002433016', '40.08251765348166027174621171049', '41.10194590626113943460114479410', '41.54761724297497904869454343716', '42.626553280807938918734516493680', '43.2123227592856104129651526056', '44.292303991773092614816240520255', '44.677794240079772358566529965', '46.08802647544326389184053844556', '47.097420854124302425582412289522', '47.65070102987522746888025197827', '49.030062152061768106701117043442', '49.75646792573053161673733340084', '50.52100459612689149136873710329', '51.62905697006560567522565358338', '52.57040638085529990648139133161', '53.12552400285347353383425577054', '54.12410343293558303682949809398', '54.686066516711977310820805889720', '55.29734213904841202681080066787', '56.854630652046523622715974922877', '57.73948817131251512103537742912', '58.933353258895007558271954146080', '59.538273262480096841097948093120', '60.29010308034924079471062381389', '60.84528416167716470491883189100', '61.81823008911259159121139167155', '62.91926608470571029428362969783', '63.55259245660555960038928071243', '64.491124930273402345763799570432', '65.17983624233665160880755003208', '66.23979616639079808240447446342', '67.311906331420147138125496998737', '67.85126278273090100771790759884', '69.42581882791345706695632914905', '69.729861448729480805056169714626', '70.4983297898531380730371624522', '71.241487958630403394917148887735', '72.145849002730536697442770673099', '72.7516353978309176650230748037', '73.56054364328240358173948168243', '74.78699058199528293703594099400', '76.06379661756881361707666101120', '76.643156114770350757056992878283', '77.15253616825210969767601982387', '78.3368051493140549879060054243', '78.781150204617515741976684610904', '79.78934445461924387293248652619', '80.77654645088505173922224387025', '81.32753644710345498032100459825', '82.218805913219740046692533706713', '83.05408184976817177675354402589', '83.46165778584101916553212234311', '84.90013176196776234308610056623', '86.0296801054884624087031696064', '86.69537469155471503269381673772', '87.27105451814204362989674272795', '88.28949166478757056522147790591', '88.996428705764983504767692853654', '89.40705009863714916234286665747', '90.160865350962996229449872045874', '91.56724961320450158697226454916', '91.89422707162479590226500320196', '93.19362849846334214027539638164', '93.90712053398125226249952084481', '94.8368999489030324667627247125', '95.50500760723102965130634166451', '96.37936208789729485616627216549', '96.9972276248204339456788595526', '98.279288423579987146371490316992', '98.80448780506674834346999860038', '99.356435186876404985589977045370', '99.99135296907270622963035836913', '101.0444362896752162079245986395', '101.66100874326868321182729985955', '102.959361045246348268754157006442', '104.042825045336011635440292089315', '104.61728697260726404288941993817', '105.34134623001338054305610670865', '106.025632352457738122684800845754', '106.61571634690908837984247357537', '107.47666927514794735864785278689', '108.38004045807359721206599017203', '109.29602156055771369751974274443', '109.7554793625735188496045107604', '110.82208524323562456730441089142', '111.71636299122197073301844051525', '112.473600212091960388081239397836', '113.15252632173891028006636760781', '114.35825724655176981268165783320', '115.088622071866738444639463588744', '115.60730294591115361590706365422', '116.42942034660926986083015574624', '117.1242627736185588937084262576', '117.85311253031285730911388003110', '118.53345540301124301844664734013', '119.13062816731051632109239671130', '120.80360036097594703061613679840', '121.33059834384097232071662660094', '122.17877600019112955382243739305', '123.09482108459538250180781515140', '123.296064533956915458417906000558', '124.33481353439821040562747521665', '125.21839607120021026885755312201', '125.69432384780254485673493809703', '126.77216525542658571965246621181', '127.64938383155992726940082247402', '128.02628735958149972957232414167', '128.68349274000276649845515904267', '129.8813613886643919559513106731', '130.84818554025265453415787379445', '131.59428884119705086083089427446', '132.40783945618089433109891696311', '133.23889047458314161720982790394', '133.90110152478505082365915387391', '134.27782767957964625125899639819', '135.389556179204241323503996826485', '135.628168158436444457720162616555', '136.68756782375411438728882854401', '137.77361876382092734018336972609', '138.469441346316497275253369664233', '139.29229406222650569950184673525', '140.45941958948960844114546144668', '140.898095956162876710569671905912', '141.20097244285400550432860433185', '142.427540516960259303133409438515', '143.30682455267069103040151862404', '143.92904681093381584402060148584', '144.68333094716017717037114906381', '145.19281923724824463523502204036', '145.99155707335629175400323521626', '146.790816755206603382492433866905', '147.55914617279214908345726720492', '148.837727589864996113716205413859', '149.66340098152315220575700019164', '150.26528928403367927202994305499', '151.06782985254805049684006679759', '151.45942255799460635922886848861', '152.227685807895668710833550823', '153.088589686171505609798620310931', '153.72406232748821025761399637175', '154.6598770993074648762340853688', '155.28585495381452759057145925960', '156.27076630674564404871881592842', '157.194686959640129986146299024114', '157.67871848822946774624340491497', '158.5062997228726174614141365141', '159.557289227465155634479004812472', '160.0929935502274959617377895005', '161.03671484781021610030148413174', '161.5203651662691930025838958890', '162.4305685272314269449303810295', '163.00791538950875675418363830054', '163.492403198201047415923609548954', '164.39666468593927676097319123450', '165.11176484659403473330699913312', '166.69566787921114904894578451173', '167.112165974082524555840457246435', '167.86972182316506517884370390142', '168.34754398408461981576557488464', '169.56895120775656053961217169277', '169.82111906446056747544346020395', '170.33364913584438718730667900148', '171.49257635748272226059454737668', '172.51883224050310079762040320681', '172.74370674385986688917750930675', '173.58880847495619804740108183548', '174.34933388068046522588349223835', '175.3054180933236093223575517813', '176.080024112359304530005392747884', '177.01470164804740379268134357405', '177.64167241681913032356949224720', '178.55491998868896280794302323363', '179.14711206454949383667110870499', '179.81303541988998823023858863089', '180.39333369668462513274496488311', '180.96731218039193564768634198936', '181.77918615907217864805925019154', '182.94824063099387060788327308718', '183.2656306428322932465225757643', '184.75341325442820454469153814915', '185.26200135070664681808078258269', '185.8914937839699597965136976318', '186.66747687796724878821078849869', '187.15293386985665356172919910080', '188.019541859094819325827162318363', '189.06278996765044936862774719890', '189.69497504025634763308112130991', '189.993283917278859448816961271926', '191.13823717445850939388627707601', '191.561392266474230883897975595590', '192.28413837984117212731953158943', '193.304751930187086068113952292456', '194.21328556168312785972177219748', '195.19410358919518120933404787460', '195.88666676010927205850420064953', '196.4103945731392024450686380550', '196.82957910837279081043133231970', '197.86486598644320960216712341027', '198.371711967485511887586045074865', '199.149136578189125179270437086674', '199.68512355167115622182232008888'], 'prelabel': '1-145-145.143-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.673377169063117, 'root_angle': 0.15578014320872263, 'root_number': '0.558022470762272794063202950766+0.829825838428985293008562666868*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.155780143209', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(28)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.11093924693958735500867582731+0.425408917658309871796222322989*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.6512145381', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '3.34518810728', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.01223199658', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.673377169063117, 'bad_primes': [5, 29], 'central_character': '145.143', 'conductor': 145, 'conductor_radical': 145, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/145/143'], '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': '1-145-145.143-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': '1-145-145.143-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.673377169063117, 'root_angle': 0.15578014320872263, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.6512145381', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_145.143', 'Lhash_array': ['dirichlet_L_145.143'], 'factors': ['1-145-145.143-r0-0-0'], 'label': '1-145-145.143-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/145/143'}
Lfunction data - 1-145-145.143-r0-0-0