-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_23.11', 'a10': [0.14231483827328514, 0.9898214418809327], 'a2': [0.41541501300188644, -0.9096319953545183], 'a3': [-0.9594929736144974, -0.28173255684142967], 'a4': [-0.6548607339452851, -0.7557495743542583], 'a5': [-0.8412535328311812, 0.5406408174555976], 'a6': [-0.6548607339452851, 0.7557495743542583], 'a7': [0.14231483827328514, -0.9898214418809327], 'a8': [-0.9594929736144974, 0.28173255684142967], 'a9': [0.8412535328311812, 0.5406408174555976], 'algebraic': True, 'analytic_conductor': 2.4716932702763756, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '23.11', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 23, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_23.21', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^18', 'a^12', 'a^14', 'a^9', 'a^8', 'a^17', 'a^10', 'a^2', 'a^5', 'a^15', 'a^4', 'a^16', 'a^13', 'a^21', 'a^6', 'a^19', 'a^20', 'a^3', 'a^1', 'a^7', 'a^11', 0, 'a^0', 'a^18', 'a^12', 'a^14', 'a^9', 'a^8', 'a^17', 'a^10', 'a^2', 'a^5', 'a^15', 'a^4', 'a^16', 'a^13', 'a^21', 'a^6', 'a^19', 'a^20', 'a^3', 'a^1', 'a^7', 'a^11', 0, 'a^0', 'a^18', 'a^12', 'a^14', 'a^9', 'a^8', 'a^17', 'a^10', 'a^2', 'a^5', 'a^15', 'a^4', 'a^16', 'a^13', 'a^21', 'a^6', 'a^19', 'a^20', 'a^3', 'a^1', 'a^7', 'a^11', 0, 'a^0', 'a^18', 'a^12', 'a^14', 'a^9', 'a^8', 'a^17', 'a^10', 'a^2', 'a^5', 'a^15', 'a^4', 'a^16', 'a^13', 'a^21', 'a^6', 'a^19', 'a^20', 'a^3', 'a^1', 'a^7', 'a^11', 0, 'a^0', 'a^18', 'a^12', 'a^14', 'a^9', 'a^8', 'a^17', 'a^10'], 'euler_factors': [[1, 'a^18'], [1, 'a^12'], [1, 'a^9'], [1, 'a^17'], [1, 'a^15'], [1, 'a^16'], [1, 'a^19'], [1, 'a^3'], [0], [1, 'a^8'], [1, 'a^10'], [1, 'a^13'], [1, 'a^20'], [1, 'a^1'], [1, 'a^0'], [1, 'a^17'], [1, 'a^16'], [1, 'a^21'], [1, 'a^7'], [1, 'a^18'], [1, 'a^14'], [1, 'a^5'], [1, 'a^13'], [1, 'a^1'], [1, 'a^9'], [1, 'a^2']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-23-23.11-r1-0-0', 'leading_term': '0.0238979240364856307130210370539-0.728961131419547436758659766974*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/23/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.729352755457687, 0.345711488021288, -0.036627173233051064, -0.4303510901214183, -0.8247646013804264, -1.1855721600234568, -1.4620531261648841, -1.5986382751156996, -1.5489749105097412, -1.2904983962622536, -0.836728018195321, -0.2439044078015943, 0.39119341116608164, 0.944100611408927, 1.2857032641021942, 1.3120382686843595, 0.9746338683778513, 0.3034068423471308, -0.5857502330597869, -1.5040879271626189, -2.2245482835124823, -2.5324891188194854, -2.2816011318531806, -1.4404036745944078, -0.11477904189527753, 1.4634582078588936, 2.9835088611206277, 4.129201291534296, 4.6610709055239505, 4.483665343413657, 3.6764819772445985, 2.475818629958243, 1.209055199949018, 0.19844206021909971, -0.33680673755238927, -0.3480348579879985, 0.03036330110275379, 0.5312201216922309, 0.8539084581213332, 0.7801561913492219, 0.26494029105410266, -0.5334532530506262, -1.3006043458815353, -1.679035862442579, -1.4095767657496616, -0.44885414249322175, 0.9850988510529449, 2.463889363062816, 3.485989428444329, 3.655084182920691, 2.8343746672674586, 1.2154666803712, -0.7310491188141636, -2.412271696333174, -3.3228574751453355, -3.2295225937592593, -2.2571336765690133, -0.8388866490070236, 0.4538873756148418, 1.1371209133649829, 1.0042875307121588, 0.20271023621724474, -0.8375627090001954, -1.5941044113370268, -1.681409082200147, -1.0197726983931443, 0.13159067996905705, 1.2939071033883396, 1.9888309687368426, 1.959471313675806, 1.2889830669291746, 0.35741304976063754, -0.348273771236411, -0.48499263436265927, -0.04515412536746727, 0.6093608637014226, 0.8989982732433197, 0.3037530891014293, -1.3597543800702923, -3.7959116041576153, -6.301776225131231, -8.035162480793836, -8.367124899855417, -7.160579273572617, -4.8437127371868005, -2.237640082307446, -0.2115593108164017, 0.6787105428798408, 0.4027957177668625, -0.5778548030140538, -1.567911681897601, -1.9904084636931743, -1.6580028776417928, -0.830214272176379, -0.03367438378850105, 0.25473562940422867, -0.1102063213053677, -0.8497136572652259, -1.4124865443740227, -1.292096512243599, -0.3380341608985473, 1.1157280009783077, 2.388426340050383, 2.797414984564854, 2.0334486127395355, 0.3622170822133111, -1.4692098040454031, -2.588989853807786, -2.4440881865018946, -1.0988637536521766, 0.7764472295994728, 2.233578324071055, 2.527995925768786, 1.5048408274625729, -0.31638554746344016, -2.0076618364249135, -2.711736798054817, -2.0820281598021624, -0.44990724929776643, 1.3671191472528144, 2.5078432017362964, 2.516053028602437, 1.5506643459027476, 0.2487885444053681, -0.6696673567281324, -0.8213182073451706, -0.35753038425487116, 0.17096432848260196, 0.19593677570364992, -0.4771116468652231, -1.5153606037612877, -2.2497451294505906, -2.1073402994401027, -1.0254777133716293, 0.4170825616649001, 1.2603304215671245, 0.6916211235536025, -1.4511871270520347, -4.50116256901278, -7.235494511016732, -8.472442225068411, -7.672573650063391, -5.211937630717533, -2.1735180203297295, 0.22617816570061716, 1.2527376551690415, 0.969253662013998, 0.08838518536446231, -0.5291806595501266, -0.4159169884767288, 0.24894376587398667, 0.8157492737954677, 0.6435279388682711, -0.43325310123172095, -1.954746584773819, -3.1036076289428323, -3.222228109543026, -2.2458270741918334, -0.7647147808276804, 0.3375638676427968, 0.448781871298073, -0.36629977735148683, -1.3913645837809503, -1.7178930611055752, -0.8588696403975764, 0.8764999694843951, 2.505494570570231, 2.943341873013291, 1.6852312416051531, -0.8258113202552212, -3.390795531773879, -4.7118994960358105, -4.129269939495801, -1.9943881954037896, 0.5460865639384332, 2.2226299274335393, 2.360326473871854, 1.209559549340208, -0.2933323638451468, -1.1592467558276351, -0.9569167972382698, -0.016157736114349255, 0.8814613728624802, 1.0883008347022516, 0.5394721125652702, -0.24387047619294533, -0.5904849342317139, -0.23642816018837406, 0.40766020076055803, 0.497214069083241, -0.6349866884001765, -2.9099612611822554, -5.3905428819765335, -6.753792231843595, -6.0829324768130055, -3.478598064476072, -0.07778076454409726, 2.5640060013021375, 3.3604916503869657, 2.3016089352105658, 0.4000663909862807, -0.9816254265916625, -0.9865799865431386, 0.24656307619361303, 1.7589568160729128, 2.469659271703411, 1.9135269600963343, 0.5239095082860791, -0.7134462545979063, -0.9756837620555364, -0.1798422950720133, 0.979520126236068, 1.548769179552529, 1.0134158026551519, -0.32565875952120454, -1.568493124935817, -1.8695334470431186, -1.0547363740078999, 0.2520440505263401, 1.098206151799186, 0.9365116983628552, 0.08487059278890098, -0.45064794507822015, 0.2971891464751656, 2.475255247318941, 5.142144654211031, 6.751768551997651, 6.110445725971489, 3.184207766860511, -0.7936082154657522, -4.010685628134624, -5.126690028085614, -4.011299504593327, -1.7070087081328826, 0.3230224287826971, 1.1308197480810915, 0.7758549535185726, 0.08404758740376919, -0.09132921340276363, 0.46514777043792244, 1.2250926621979055, 1.4174583517088688, 0.7230252089088094, -0.39508688774581674, -1.0010892706645373, -0.41599544982255826, 1.1924152612468248, 2.838049572468083, 3.390136880442897, 2.423880110644079, 0.6145005704114489, -0.6559845684387416, -0.24416000346094435, 1.9120901490420266, 4.666567142576459, 6.376342226251275, 5.9792714569500856, 3.6929937055314075, 0.846803406255134, -1.0342232163408487, -1.2469034590134325, -0.3177147546342912, 0.46796490353717124, 0.05278504974283807, -1.613193823711529, -3.5564572292780774, -4.5146119058931395, -3.861429669031736, -2.0383339609893736, -0.19290606108958602, 0.6764392148856265, 0.40993995030758484, -0.3030191702507312, -0.5693030625949811, -0.05891476590356976, 0.7312064479519478, 0.9372601863612036, 0.14619636381525036, -1.1059443958465283, -1.6104362404446766, -0.3929207857950096, 2.415472310855174, 5.44109092078837, 6.853007898591134, 5.571886771322616, 2.0548993611442716, -1.9245765540466404, -4.380156329686631, -4.345596597799084, -2.3928227747126103, -0.10697643302274394, 1.0636530548888277, 0.7401497183613941, -0.3122987006892261, -0.9438342896410332, -0.5736008581411902, 0.40794993358764, 1.0640446584301937, 0.7733518077720025, -0.20032959557528185, -0.9078767877720912, -0.5256521189047908, 0.8911927742868114, 2.3529012953633823, 2.663790450279501, 1.3804511077831432, -0.7698259304042121, -2.3795937966333147, -2.4158472038379473, -1.0265619104479788, 0.551243669709223, 0.9475797625782921, -0.23857319102034863, -2.053149481745412, -2.851238452506303, -1.5409476003694818, 1.5272690874419668, 4.7142261706776925, 6.198726022258511, 5.228413314043502, 2.5975197826377094, 0.020123393365206996, -1.1040947341599519, -0.5999146898651131, 0.5445535201602959, 1.089364820660051, 0.540661380679382, -0.5491830058196127, -1.1642525603929652, -0.752869185206574, 0.2977291969182504, 1.032667629767745, 0.8106640359332682, -0.08483153598497434, -0.6676824416972724, -0.15877732511511508, 1.1777823689421503, 2.0306850769469764, 0.9787684164746258, -2.3093788514467675, -6.573964306531596, -9.636523584068842, -9.825272984645128, -7.122959059939189, -3.1791873249950324, -0.16884233171825186, 0.6587480853049764, -0.3208593839519982, -1.623737595790568, -1.9177946566933934, -1.013749825367945, 0.1573866591155844, 0.48140702660775825, -0.3156494119643079, -1.4182250271342842, -1.63394750099292, -0.44495846865316946, 1.5029916894933886, 2.894112335786444, 2.807294171090792, 1.455585830945604, -0.024808830899101193, -0.5579908784764804, -0.04530876766628652, 0.5785997853683569, 0.21893628767494708, -1.3142255118211252, -2.986354231149784, -3.3044455125265966, -1.590689798894273, 1.2889604079169101, 3.4066140842589445, 3.1665518451808743, 0.5492740731363137, -2.786752358879218, -4.665427949658919, -3.9475759920743805, -1.3005193341704295, 1.3794765871339476, 2.4040297006912215, 1.458894851486286, -0.3619886150475519, -1.5794328526913446, -1.505768563981017, -0.620586227386325, 0.07540088608101311, 0.07235947972879178, -0.2014804481903098, 0.11659218588772037, 1.358597520275179, 2.822115487638318, 3.2551331083733244, 1.9662198733645075, -0.41022703617294626, -2.234885296787991, -2.1073510165429914, -0.04708117351883678, 2.3964138019209344, 3.273573617728132, 1.7492118051743166, -1.2092671045075265, -3.545232141147284, -3.679379314753202, -1.6885212631266062, 0.8303293579847788, 2.070593923676127, 1.4194436480753996, -0.17241051733415047, -1.1027174737239005, -0.5012119862329578, 1.0827722285990418, 2.2300596470625567, 1.9195133425558888, 0.40466658861036564, -1.0397958842270094, -1.2469345184363378, -0.15654958954660417, 1.183476871284653, 1.5878613790484344, 0.7920041388270274, -0.35449490417336266, -0.7264016048335783, -0.019029421717118945, 0.9281728772234381, 0.9324115430686806, -0.28706780869118564, -1.5670258541759747, -1.064887322766123, 2.1940041822392833, 7.256086807507319, 11.626832620303276, 12.91651248281957, 10.509120579683316, 5.9601404206231, 1.8261477688730237, -0.1337648425768718, 0.01305655194022419, 0.8275695149636855, 0.9213588305241831, 0.09203017718335346, -0.7345697735165867, -0.5715517860127366, 0.6006116520361853, 1.7911733245335697, 1.9461613019790434, 0.9713825377848581, -0.14884627463163433, -0.27647411799526844, 0.7549438216630029, 1.8798499241000797, 1.7103214139583982, -0.15518492186826474, -2.612798180046736, -3.8644272751410442, -2.9268754025153565, -0.5426374320963147, 1.3437834615525799, 1.1606666985701322, -0.9781962589421633, -3.3513507015802433, -4.059290210534555, -2.610186350026901, -0.32103681923696703, 0.8038267521292574, -0.2385983900967685, -2.62261854929491, -4.406820082627349, -4.150025826856455, -2.0479786601181824, 0.3363793352380761, 1.4432889483847322, 0.9598371046612314, -0.1099250722206479, -0.5095105988821449, 0.10887345146223765, 0.9879687908051206, 1.1511557115852595, 0.4625781885003042, -0.20031090412660396, 0.13671889831204762, 1.4130843460059586, 2.3347451184919823, 1.4345778919531644, -1.4785483595323055, -4.819502825953391, -6.269065683070301, -4.604507808395678, -0.7999176100333394, 2.588973580330699, 3.3243438855594105, 1.1482662487684032, -2.129572125703421, -4.142214031017407, -3.7840378765981852, -1.8551703841814375, -0.11403837532183761, 0.31407472873278286, -0.24866874513358694, -0.6234156952204049, -0.09579725560015352, 0.8318848700210232, 0.9622621785705493, -0.33004824012871015, -2.3302161658604756, -3.492733196603464, -2.797955546677875, -0.7030825475506286, 1.2203047294773444, 1.66168437148722, 0.7037034994534888, -0.34647617313579016, -0.2872140270026683, 0.7272643550511512, 1.229152332724917, -0.18602869101357586, -3.370323647836021, -6.430799105584683, -7.133615395544614, -4.765542491063757, -0.840364052290788, 2.012810229056633, 2.083052510481073, -0.16075424496013696, -2.603891712537344, -3.295648283349923, -1.9597459145722986, 0.02770322702289069, 1.0323285676141691, 0.5923434220760537, -0.3728707248601024, -0.6365052126182453, 0.09849608826828642, 0.9926590816777077, 1.0315194911517438, 0.1407150298870779, -0.7006815079934515, -0.49907251793032087, 0.591106895302391, 1.2062619429905455, 0.0182120101357041, -2.81112731142845, -5.3889901465177, -5.466403568319092, -2.3434878028903956, 2.360599116203949, 5.828698689950153, 6.179277887191198, 3.8316864478331203, 0.9758985800694491, -0.33863291592362976, 0.18896955462009807, 1.1539919530808047, 0.975169901351054, -0.5626363548265025, -2.156917312409083, -2.2935272077709534, -0.7284691388355831, 1.2548299656507487, 2.0263376471461587, 1.0873409842898814, -0.5466591385454227, -1.3836710748973213, -0.8853534479824867, 0.08972571609025404, 0.2326740953861867, -0.8342139361456664, -2.122815561853675, -2.2476706616475544, -0.8599830825014612, 0.8970653360193067, 1.4488838067047074, 0.41562592458900965, -0.7861223946864145, -0.08111936810794271, 3.3006344663918714, 7.813760254253649, 10.567863526139027, 9.561731064671452, 5.301824477926762, 0.41783870285491803, -2.3862122362128155, -2.2922936341527254, -0.6392170753767749, 0.5542232837303807, 0.36654561011316855, -0.5176151410093806, -0.8401273720975492, -0.17329708380482714, 0.713879100111741, 0.8091708246973559, 0.06582986559298587, -0.4381108670160879, 0.3925911133370188, 2.4039020814917773, 4.106439546746575, 3.9806499754552984, 1.9770582169187332, -0.275412171928638, -0.8699333033056067, 0.6052919132312156, 2.5970260528094355, 2.9427075386650423, 0.8688879573478986, -2.204878675994876, -3.8431654068416368, -2.7264406038573172, 0.1833658577288646, 2.4953175807265273, 2.4739367681281292, 0.4637963663844376, -1.5948946465580365, -2.034371570590429, -0.9422925340730255, 0.08036668705934889, -0.4310335935222006, -2.365969658640093, -4.161804810780823, -4.3058583406071085, -2.730227581966771, -0.7788269632405966, 0.14272400159183887, -0.1494074664247195, -0.6573448214090558, -0.4470563404004991, 0.2545548038161288, 0.3123083670413527, -0.9206834712473846, -2.524320409874065, -2.517789533662329, 0.3148895965870607, 4.950276521521833, 8.528935057445299, 8.504729278621172, 4.747390917349517, -0.2687653700259234, -3.4098166351682075, -3.296322033926869, -1.1317322398685747, 0.653766369079803, 0.5996161601025414, -0.7368546560789733], 'positive_zeros': ['0.595428854419990019860432101880', '3.556840269818296224727192548207', '5.42494992536204878958907862173', '7.523772029316227977289894112619', '10.39764921993340918893402839025', '11.23050428241421999713945822326', '12.61097450498563826340730970543', '14.16792048252041723320680372312', '16.13280970468500293150500055710', '18.00311216792705612564796344821', '19.12407163549371921750645334304', '20.59192156171817513312413194609', '22.321976908452752798497500746831', '23.147002474980256875151377821040', '24.1372744651950129518469277798', '26.921519015905945165008564526051', '27.64332499310706950267022878752', '29.39296573621252220254676150618', '29.94165050014673494663967477452', '31.32782148765533013536235653519', '32.87170351617143714049148322345', '34.246312678623398647916604288300', '35.57374246302482518030052360961', '36.94920847979221336197334833455', '38.504239193860861151722615080878', '39.56670974401581387768366801433', '40.1265961031799544830735672715', '41.780997305041612748169130383560', '42.62557796809906454899627578646', '44.96198013429614627266696525110', '45.96968024745211070209153640980', '46.77039097929716728246032576234', '47.71072194612646942329418359277', '49.56438430915644376919285810080', '50.19966264039383599775046894970', '51.41499902293340712403710638964', '52.718365965704846768740673099647', '54.30346377494046883123802972547', '55.5588079322920810528660392220', '56.56727199580181843676253887102', '57.70768490426226538221274352833', '58.54904819900505181111180035605', '59.24512206875920613164722510610', '61.25745473481028523200220482504', '62.57031304312491421975637195647', '63.38754484228424270836945982708', '64.80158214934597785651722939950', '65.673248545016446011793033942039', '66.80548645445175052412693591500', '68.06290282736112000015060963372', '69.09297803178416187828496027330', '69.619374316202449907686545013167', '71.499917593534410819187104257650', '73.062864659088398023188780497603', '74.11669110764885292825902703763', '74.461052646392878796171033458073', '75.82497360843332619851343127683', '76.65789993644652598380867117082', '78.24164689998711788707069731384', '78.79984705124071181287522452900', '80.736926460855075937948182784904', '81.65793030224934245063284364882', '82.20169144517814327036762127504', '84.1057899855415798387871166277', '84.86373768714372811597184622895', '85.648006712375997156897312361755', '86.59997604438094611162550231114', '87.553567426507424221559953338888', '89.2178027757277971610643583880', '90.642930267543422680047664501212', '91.47102182144858722665516431281', '92.37518310211996876968450510460', '93.377294128506779747337595055848', '94.19724955793084986768135601615', '95.51515910859691169660144323430', '96.75066366515276385878510927438', '97.45617145209931544358688258531', '98.608014825449258984929617166632', '100.315659319222038296722772562052', '101.09961858870334210142992275806', '102.03111733656968108363240975149', '103.03968927763818902852664519030', '104.034160607985053548277511178', '104.73126594032523951934986997322', '105.73946998539772692588998032369', '107.84041780164892133452495369509', '108.3642550681640837094887157044', '109.63631066393069872570108856581', '110.221685619059523011776084805216', '111.32514966441148701082051652254', '112.805675455221222048744101784864', '113.45565207208995627546188323209', '114.122248478585356352488218326851', '115.48838849236594876357283731703', '116.61295487114117866000525563373', '117.95038940424531560929549852546', '118.99930883587522797548095481011', '120.25666066027317652658797649633', '120.69904653998276485364337751463', '121.19989942938805034617687758211', '122.760006842556564723952612659022', '123.75565826084834741156360693525', '124.8772220222001774730905976483', '126.13867295039249940329573666814', '127.152664341184419595969544202302', '127.92042800030572996342064269517', '129.13676749613870103118820958169', '130.03363163444615114662681138627', '131.14290688003708903208393158373', '131.88071562866801533626483595851', '132.75362887817085890455871425943', '133.571218516115258752994866831202', '135.891545759036739265063156100320', '136.24465038318091077507337005609', '137.21543364533400333468608899815', '137.98532558956229760067210323237', '139.32040458045396158941128597214', '139.801540560741558272826205543053', '140.91752891491055969351879224894', '142.25789492249337977344637176233', '143.00339165207235360839080813558', '144.42798942739749927007420034405', '144.9606763009737289809890634670', '146.51091650801020616289251737714', '147.46338915797167592412733788951', '148.08781994224738207815593453882', '149.24340008038093952532214893808', '149.63709447036034363227690380723', '150.79850271927062624022964014554', '152.24992739617639907474301045256', '153.23406510747580744108201050997', '154.72057794443756979328184116551', '155.19881195529098756635356214381', '155.96971757629814292730602136666', '156.81747441940229008816564713812', '158.22303945281183379327617016280', '159.24600963828097678979900847351', '159.79185724575352240073561863507', '160.60095808539532917591490002818', '162.25921473701492055668059228947', '163.10668775159440905380196769691', '164.36994512957958475637368369714', '165.18357588228785640101104150571', '165.90681113007966538114975578138', '166.91607621925676140836489610039', '167.65581823238746121717969256485', '168.440076270821450173852845591339', '169.8448402490787737330067216633', '171.42021274549756833340974378982', '171.81625009339478517592326626752', '172.71580754826349929220244134524', '173.85775018991169530271814023657', '174.89121893750646363979200006998', '175.90192695791322065839974191914', '176.34971175692697982220076894218', '177.64251218946897739213616740076', '178.52555566984843500308672280788', '179.07423565288167265365863390630', '180.96964393866704533790601892336', '182.00387147145271356316683897497', '182.632244048370027523650243523502', '183.49234857794712556905590244068', '184.39934859636299755816063145391', '184.91141552604407815583975849435', '186.514575958841116041739133176600', '187.09240673521752069694033368100', '188.21302864821465352807198558401', '189.35618579264820354843568427905', '190.37308069865794905099693384447', '191.51435951117783918650675770466', '191.74688251977759710044119109647', '193.64906729740338777275803363788', '193.98043565757383195428183562843', '194.88294616063227816664955518590', '195.42665140144314396041721836545', '196.53807599135158203588084573150', '198.10665738901631333316243409673', '199.22826490612767652488691520921', '199.84193771370765776672572266287'], 'prelabel': '1-23-23.11-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4716932702763756, 'root_angle': -0.9791368244641263, 'root_number': '-0.997852787176232177062127875326-0.0654966802565221078541315594974*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.489568412232', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(22)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.509500708034686879561511621482-0.544267510424667883447163267049*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.59542885442', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.55684026982', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.42494992536', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.4716932702763756, 'bad_primes': [23], 'central_character': '23.11', 'conductor': 23, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/23/11'], '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': '1-23-23.11-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-23-23.11-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4716932702763756, 'root_angle': -0.48956841223206315, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.59542885442', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_23.11', 'Lhash_array': ['dirichlet_L_23.11'], 'label': '1-23-23.11-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/23/11'}