-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_6003.1145', 'a10': [-0.3967734145782425, 0.9179165852537594], 'a2': [-0.17587995536180925, -0.9844116218848333], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.938132482603856, 0.3462765442295015], 'a5': [-0.8338232639998672, -0.5520314886060467], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8025741491979327, -0.5965523740956988], 'a8': [0.5058773536894683, 0.8626054156009807], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 27.87781479921304, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]], [29, [1]]], 'bad_primes': [3, 23, 29], 'central_character': '6003.1145', 'coeff_info': ['x^924 - 1', '0.999976880197217 + 0.00679993169383467*I', '\\\\zeta_{924}'], 'conductor': 6003, 'conductor_radical': 2001, 'conjugate': 'dirichlet_L_6003.1274', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^667', 0, 'a^410', 'a^548', 0, 'a^556', 'a^153', 0, 'a^291', 'a^631', 0, 'a^302', 'a^299', 0, 'a^820', 'a^63', 0, 'a^333', 'a^34', 0, 'a^374', 0, 0, 'a^172', 'a^45', 0, 'a^42', 0, 0, 'a^65', 'a^563', 0, 'a^730', 'a^180', 0, 'a^783', 'a^76', 0, 'a^701', 'a^581', 0, 'a^397', 'a^117', 0, 0, 'a^253', 0, 'a^188', 'a^839', 0, 'a^712', 'a^534', 0, 'a^255', 'a^709', 0, 0, 'a^434', 0, 'a^241', 'a^732', 0, 'a^306', 'a^850', 0, 'a^62', 'a^473', 0, 'a^847', 'a^876', 0, 'a^663', 'a^526', 0, 'a^743', 'a^263', 0, 'a^181', 'a^444', 0, 'a^324', 'a^46', 0, 'a^611', 'a^140', 0, 'a^784', 'a^639', 0, 'a^858', 0, 0, 'a^920', 'a^881', 0, 'a^823', 'a^855', 0, 'a^582'], 'euler_factors': [[1, 'a^667'], [0], [1, 'a^548'], [1, 'a^556'], [1, 'a^631'], [1, 'a^302'], [1, 'a^63'], [1, 'a^333'], [0], [0], [1, 'a^65'], [1, 'a^783'], [1, 'a^581'], [1, 'a^397'], [1, 'a^253'], [1, 'a^534'], [1, 'a^434'], [1, 'a^241'], [1, 'a^62'], [1, 'a^876'], [1, 'a^663'], [1, 'a^181'], [1, 'a^46'], [1, 'a^639'], [1, 'a^823'], [1, 'a^607']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-6003-6003.1145-r0-0-0', 'leading_term': '-0.0940948565314791795478673624307-0.317964820317413317797021420717*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/6003/1145', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.33159533920904927, 0.3875667299019588, 0.8131127881672191, 0.24914936929870687, -0.9471250409643541, -1.2139897630910272, 0.3023682583043594, 2.285020475557331, 2.568442525119888, 0.9230775461715569, -0.5090934070702449, -0.12250850364626245, 0.8571614264514558, 0.33040179443162254, -1.0544989736194692, -0.43558755351084394, 2.5349684884276886, 3.905308353511798, 0.5516009244924213, -4.414326838779908, -4.668147537224486, 0.816378699558528, 5.780955102427355, 4.818687491785262, 0.3651442505252556, -1.451874379323413, 0.37282420272311756, 1.407597393609807, -0.4595539462286608, -1.9862238889359387, -0.5853895721824753, 1.265594114436345, 0.5235734028853128, -1.1805265726878078, -0.6767075992603364, 1.0400030945603436, 0.7489222758671696, -1.0796613584714503, -1.2389702455803717, 0.22501282243000886, 0.26871535947098235, -1.022194766077329, -0.32336338349922134, 2.130722934866691, 1.9757149765119226, -1.0105771855012198, -0.8589148377698491, 4.559209089834665, 8.128782962495928, 3.8567461699404153, -3.1653249651363446, -4.398650093505514, -0.7540674146431946, 0.6513349767361482, -0.7821225023633835, 0.5778930824410291, 4.961796188855013, 5.976715826225144, 1.7883637625430309, -1.7860040769894994, -1.2219844886026137, 0.1595797072063212, -0.18668875322849032, 0.002476349665711788, 1.5988380666583435, 1.6096923405823564, -0.379469287066885, -0.7566293002226573, 0.761851256353901, 0.1083623824071109, -2.695580125053682, -2.5853653897524964, 0.8452887424819809, 1.9259153195592544, -0.44628390382333893, -0.9145291744283471, 0.9348060671929607, -1.2190399663525398, -7.113516382874218, -7.298675674903157, 0.796246640696597, 6.7077296031935525, 3.4397289365394124, -1.9765819943861214, -1.6982234863991916, 0.9164643722874375, 0.42886529613673813, -0.598863048394687, 1.1669219741569972, 2.4220852747609554, 0.5076277298358427, -0.974499869246821, 0.1779922818976709, 0.5325699587841977, -1.0877847552506723, -1.0025383497456575, 0.8978628463005134, 0.24315602969847439, -2.4155603429285373, -1.9838169666954681, 0.8911574515405677, 1.1348937741341487, -0.3702940789486825, 0.2415202787932684, -0.3500372454215258, -6.2690288995848515, -10.498852483531442, -4.655381931218574, 4.425067655826464, 4.25934869190952, -2.5850320342231705, -4.229348865252286, -0.09240847119687329, 1.287078027951765, -0.7588749845482429, -0.5715164728713543, 1.0470095110717903, 0.16729852997705205, -0.5564494300473994, 2.1005932452484286, 3.8853680530820682, 1.288696666685779, -1.2017315271602125, -0.11796260266330166, 0.968794146413023, 0.08933336614790839, 0.23946762548063158, 1.1317658450671433, -0.31558289874313455, -1.3794980863665662, 1.6979556898122175, 3.8714762290917815, 0.018980337829448846, -3.307381704412124, 0.48346227733679237, 4.398865325448779, 1.1392773255275654, -2.2735326524249637, 1.3715392343284372, 4.865665782676189, 1.1802216021664944, -2.663142687334951, -0.10095221210463734, 2.620765859179158, 0.22014801104539186, -1.826076934705824, -0.042205761117569476, 0.6888588367142366, -1.0789589449624655, -0.8173018306520404, 1.07015818628844, 0.3493126494166733, -1.2683794920130285, -0.3450625974332289, 0.38731875273438615, -1.0051292404364136, -0.5873584476415823, 1.6851647998790271, 0.2225865624929108, -3.5844575853250276, -2.726057462291347, 0.6672951205634394, -0.39315777013460934, -2.2143869284551285, 1.682654512210243, 4.825213494715182, -0.1460044312848066, -5.051383271960915, -1.3203189649315898, 3.0336905878401437, -0.34301951743070463, -4.047606287300451, -0.8324880295464825, 2.817690448429711, 1.3193722462650954, -0.3605446738709317, 0.6403059703508099, 0.564375196285649, -0.4735617829305372, 0.3712481767602192, 0.2681258313745736, -2.747822139763708, -3.270418816001498, 0.6168393258048834, 2.493490511052441, 0.5134293913275696, -0.05210140302805845, 0.8514469827190732, -0.32695200167350247, -0.5607938276003533, 2.042459557029897, 0.5275226272513269, -5.80942574628, -5.183968797185941, 4.456153422971734, 8.722618217805536, 2.9707107775615715, -0.12355777799901378, 3.7429686131926116, 4.328782143883818, -0.4615531154090973, -2.0430642886416597, 0.0632507274788797, 0.0952493492659077, 0.05410779076708723, 3.0266638428434804, 3.9624861321901044, 0.6527404542320672, -0.8996396604952623, 0.6688766629872122, 0.47112841995053856, -0.7774832021344273, 0.2573360707943831, 0.4089587113106119, -2.121659202953866, -2.1793551311995385, 0.6275081882188935, 0.5893193473937097, -0.7237146616771626, 1.0426990833641576, -0.18532121478733193, -8.403008213306782, -11.930049424954102, -3.657390947156549, 3.5209100376377176, 0.3776191000958622, -3.0858156729541184, -0.1720865456082738, 1.2781783513941398, -1.0279180617820254, 0.05463117923785779, 2.926364331205435, 0.6432487156267718, -2.7400732619329564, -0.7929798197448288, 1.850275584978145, 0.5947920415236627, -0.4003494172574893, 0.5365907408637874, 0.16560192042191216, 0.04550816968981553, 2.21451165789711, 2.2895459152566775, -0.31597050182476166, 0.5479234025705892, 3.502197474395973, 1.6765109640710922, -1.3422364517736423, 0.913526646415039, 2.8214083393358793, -0.2002938259487776, -0.5210555687616291, 3.0259629225729228, -0.18518213029456584, -8.209018470153858, -6.69028966643306, 2.448593271525211, 4.244299500742088, -0.791746940713819, -1.5919139343144622, 0.6086301439056898, -0.24632033099755885, -0.6868549074970594, 1.5158459369562503, 1.3463809888030251, -0.8365890012951819, -0.38019582770677607, 0.13909545491365352, -2.070211433967128, -2.2267196257230655, 0.5449169035924841, 0.5843377324589192, -0.9978241544456613, 0.3733034724644574, 0.8625992245044392, -2.0923042859574275, -1.9295202818688035, 1.762660209048382, 1.2483229768482502, -0.953867585051887, 1.939353782425813, 1.8428625892977388, -8.2563565045395, -14.443274975681456, -6.019376631656997, 3.5864178570609817, 2.7051461684614693, -0.312197100361854, 0.9099860781036481, 0.9477296468561777, -0.3737042359875792, 1.3089894702272784, 2.295361552826593, -0.13339663595049228, -0.20876096050486065, 2.583762431348715, 1.9785824725526802, -0.3850896684880163, 0.6247315411390969, 1.5896547045906932, -0.27228024336649853, -0.5873935915856292, 0.5929226163095876, -0.26514209584918624, 0.3750658564543149, 3.3237667646443763, 0.27311560048562394, -6.89028582925207, -4.957130907328448, 3.5044562847266993, 3.642274805012026, -1.8183447914525421, -0.5043259049627334, 3.104052710602277, 0.9553125710172392, 0.48799578758878226, 5.725440300587289, 6.601086066457622, 1.2546579395080275, -0.7202006084311342, 0.7428051473502673, -0.44004712506399657, -1.3240765608749636, 0.7832671738692397, 0.8650924380354292, -1.069095962126236, -0.19670500888730427, 0.974361440605475, -0.49516228812590773, -0.3717744469128397, 1.2412745321145144, -0.25663790128822817, -0.8634317026978329, 3.350884400451119, 4.730202621636442, 0.6324372354109489, 0.10022773001800706, 2.3276899560809823, -1.6634845995441405, -5.5736939017703335, 0.2964240867148504, 5.951940031069901, 1.9459843772606469, -1.0692612213828425, 3.0163434689129454, 3.649068630084294, -0.8763045097423255, -0.6127285996765772, 2.801655132458251, 1.5337733506169708, -0.8335888463566958, 0.1304747408596389, 0.4426427590015167, -0.44590660128706366, 0.08193872598755883, -1.350453361931444, -4.859400197489047, -3.539761427866364, 0.9853231285769217, 0.9206461051481607, -1.0301264558063206, 0.23393394811808085, 0.4897212757017123, -0.888648284684608, 1.3111093064284178, 2.7519828351123072, -0.6971810084556184, 1.4431975537875807, 11.545899875031278, 12.468499803918922, 0.8876740111437929, -4.332539325672462, 1.2153741904160777, 3.292639022522125, 0.20173161851044147, -0.06110181226731641, -0.41298559329242146, -3.7567353430513064, -3.6736636888926615, -0.3974111900884963, -0.2880323068575165, -0.5450573166816458, 2.3020957538651325, 2.747550718575954, 0.00036441555443527356, -0.1331605564321433, 0.5489702783598048, -1.438458933923277, -1.641393213795577, 0.43820834018127197, -0.12307030863081622, 0.12345736969845365, 4.333650375568188, 4.503504135695034, -0.06449021843646514, 0.942447935681505, 3.5481742938691347, -3.669733592396465, -10.941531469115523, -4.784935495123954, 3.724953799715105, 2.4047844694909988, -0.07434994156028829, 1.9103873812934755, 1.179731122850674, -1.084092259144292, 0.9734532134193481, 1.8647293060638894, -1.5841513635295925, -1.8003549332754905, 1.4392676206264583, 1.0302512517527307, -0.9442639836449582, -0.1961772751614433, 0.09776593546176959, -0.25978999896450017, 1.1713468102972615, 0.23280870784004484, -3.0416532320449376, -0.691921583368913, 4.480110041387776, 3.019378927945072, -0.38399667659216163, 0.6341506867800585, -1.1812437144519845, -5.999741386533354, -2.663524018229958, 4.025611703948854, 1.0624927647190976, -3.93875435437988, -0.4932579735141591, 1.2427835143076957, -4.625399372487385, -5.957786196025896, -0.24267011542457242, 1.7819714951271843, -0.036199966815661, -0.029604623159059523, -0.5588916114961264, -1.5788672342862273, 0.773752626378104, 2.1635242707617213, -0.762503595761972, -1.7691235218596124, 0.01563466407082748, -0.8850763541214044, -1.5811742687752026, 0.9604275709162863, 0.9706685267190662, -0.7759245858381287, 2.1128820388240426, 4.125297002099866, 0.18733157052890204, -0.8848569559771648, 1.523592920196116, -3.2709624755251125, -8.66653245147412, -1.3600757620429458, 7.3496159355028805, 3.26881789981874, -2.3995127192039645, 0.5285495597938742, 2.7352305384668276, 0.3982788795967482, 0.19946468095583017, 0.5319493025156037, -1.4668019544279658, -0.8722863045896626, 1.0612271344450703, -1.1298048402927596, -2.846275588840719, -0.5966718239238578, -0.5359384478020763, -2.5656446379505073, -0.9587832136260721, 0.8981337695092777, -0.2467318213444116, 0.17639813290084824, 1.0878720824371, -0.28403532332520043, 2.7405347681424965, 8.374569306593033, 3.082483078472605, -7.7472850968008125, -5.992746726501045, 2.3552792789444554, 1.408866919726746, -2.133466828867151, 0.550780258705913, 1.0300907439684672, -2.1387432564781865, -0.07854658564613679, 3.0260698757203484, 0.251818672711993, -1.157122235663006, 1.9375383040812841, 1.974135524287254, -0.2876395459361401, 0.26371841176601424, 0.13971383322486797, -1.5321528848726937, -0.361437246511803, 0.6440845122143571, -1.0523337844754463, 0.030094034509297152, 2.5491580200748443, 0.651309408093487, -0.5134158561422885, 1.942902137033459, -0.1187119063794002, -4.10495667159409, -0.3799225118767023, 2.687760927637178, -3.5571514363829215, -6.423402665122618, -0.507463847535095, 0.3513148112355063, -3.956578976666164, -1.3410685216186953, 2.5759368098494457, -1.0783886707858321, -3.488596422415199, -0.19369562907046226, 0.31528316098653975, -1.6005306319844723, -0.37721607404875057, 0.15582177282518117, -1.3939922581972293, -0.41424691827128174, 0.6126856529189075, -0.7876692665765971, -0.10436517008850565, 0.4259640795733609, -3.9360781569677785, -5.812352539644335, -1.1440371845799229, 1.1351517805710305, -0.24269169283799885, 0.6358433751882756, -0.04095523006933319, -2.3662545215018165, 2.2270896136205978, 5.541648053141038, -5.870313409905297, -17.226835758523446, -10.874318500249803, -0.3877728015695351, -0.07702988212088924, -1.0439556828681897, 1.0684975684968643, -0.3415521711221305, -2.003859906890952, 0.09931970973179803, 0.11737099506457754, -1.3246238426380375, 1.028912997106449, 2.254867140735842, -0.3455133198954826, -0.3663815390730757, 1.0401162474009673, -0.9745163781227566, -1.7240705043703457, 0.3839733635187167, 0.004716616615596126, -0.303570951603405, 1.940826098457888, 0.6365790171542938, -0.917187316160128, 5.1533745023692275, 8.689158537407462, 1.8035327291230772, -1.4609985588245726, 2.814525168100805, -0.31085610524558843, -7.610091275515415, -3.8829052567188533, 3.4848231316362446, 2.3784018995691136, -0.03331594412101573, 0.831480930532838, -0.4627701360797994, -0.8680013120525212, 2.174428789444085, 0.9471581198270043, -3.6091822473826336, -2.8989964252692064, -0.02593096373599879, -0.171612944003667, 0.2724987284323181, 0.8460747870733297, -1.0425944621859278, -0.8310626409967508, 0.7460014703671248, -1.5698600784993815, -1.7231859991881586, 3.352940239012863, 2.7805823689407476, -2.5476169221820326, -0.31121298347507576, 3.747574799725245, 0.2033021961918056, -0.8375918144180146, 3.645897716010033, 0.7401153616840762, -5.466101031752082, -1.9346944975803761, 2.5837637100474904, -1.257592368553369, -3.145685778242447, 0.40514868513574304, 0.5330288289630649, -1.1314844560418948, 0.15566215675984757, 0.17702866821174315, -0.8870098906533903, 0.08307538405588047, -1.297747676285253, -4.322820790158974, -2.279403045134784, 0.6962863578695291, -0.4675820130544869, 0.11167210061973046, 2.3804643873743965, 0.6627270385890635, 0.10155677227123598, 2.6070555185696414, -0.2583644551464168, -3.7762996449621458, 1.1981531539650998, 3.456079225222055, -3.041954636599626, -2.1772896306232097, 6.950603493603156, 6.575999816376777, -0.1909023368837172, 0.2743582540031096, 1.7149062165610989, -1.9003397494299619, -2.312879189776253, 0.4941765581063559, 0.221899920562646], 'positive_zeros': ['0.1446038603393090365431991407', '1.005134124897414366123638954356', '1.82966829363989061981653409127', '2.97371027297807729934869823759', '3.47140288266190590794738077445', '4.13268379211941659755994408026', '4.7441924784506529434990708504', '5.65749556202201893059447659007', '6.52371814459337509063793460859', '7.53011037459675509725634739162', '8.07460763401745865603942304399', '8.69185048160610965287463419874', '9.452399474394280039959528717838', '10.08328354274124468791916594964', '10.73889195316668801356793835312', '11.37750450371428863579083938878', '12.13432713546770429786295341984', '12.567196149543382016821806538696', '13.168911007935768258974230259216', '13.95607181017133225700750472277', '14.44286160328096574938617080529', '15.47052174978403725446341459036', '16.32668545419934441257819981689', '16.709646093217366278327279474578', '17.132998604260249823040115786837', '18.24367730831952963281943776830', '18.99234307435137781514646307790', '19.28682331205857399469543725915', '19.68685138359365548789225750878', '20.56385922383133632357820188476', '21.09296233594148586949421771186', '21.576300638519052570457865937230', '22.424086553016725894625760865206', '23.069120631151519476215727621940', '23.5813288635820672276964564973', '23.97653105954740826807206782307', '24.97320277665469569689515372971', '25.79706966189166789343201394168', '26.42774409035487758127050842249', '26.95324475923588145811010868440', '27.34158358760783285706882094193', '28.18972473935239893871169294942', '28.71353634657657721331897998636', '29.17905668569991214518665528957', '29.84466729887972733198876145201', '30.3421738594672589960343408779', '31.14409510127670912409294315434', '31.77085535640145385710541674633', '32.12637948696641908296439851373', '32.46315126673917364188112838752', '33.57999965116959158436822082426', '34.25509006262195047803341169323', '35.00741630266726723239199581260', '35.50892173228293587836244800199', '36.03050377529764667371404812599', '36.592540351295279327409971828794', '36.97620587948497128457254006422', '37.929030120579493402744456120942', '38.45665055939724644056973098331', '39.09833773100927800509366333614', '39.294087981596070813375268416859', '39.95620609816870321910359380587', '40.491679690818171785830649037095', '41.251090374415288268952712261298', '41.849200021723915324107597223890', '42.56717814457235119988534247367', '43.04699676538968272254351632632', '43.81559741341207538580338210599', '44.3822935664007388218531249618', '45.01941678628516800873662592740', '45.63091188363385865314782926804', '46.07033312089565969259412470695', '46.684025155313133149162813464174', '47.23988082326741561772342514429', '47.88130921008244517586615938737', '48.23596280549697457447729445549', '48.82664121693092456469999715263', '49.39278416341447706512816895618', '50.22711875574786796541815213686', '50.58302389309931118290667107904', '51.15313214182579052661711177081', '51.86875673398630220019757745207', '52.565080399433635822825538302561', '53.10601752676303674333931851722', '53.80040975193127819024432012726', '54.54909887385160229869220289659', '54.84369815567720491098510873039', '55.44672295082008485930479705937', '55.84824236085645039771614638735', '56.28839714375266175074680341875', '57.14191301361557261915724951655', '57.908139732050480140055375936020', '58.14205248489738125628236360526', '58.69127440728158787665325949079', '59.141589324572496764639213522348', '59.71724977884798195883129084383', '60.49075983031524593085606726470', '61.44365826149740618620706703221', '61.584581156439358157153345039678', '62.4689351081823226775390092601', '63.11306999324437012595628148355', '63.46694456280820706231595430354', '63.739569200422626857283648364970', '64.75048796596866107279290046030', '65.18867069787575087392389499126', '65.71504700516302167002255568190', '66.19851218703112849292492282667', '66.62635981328417626800904123283', '67.42137954454676681023391381708', '67.90854579861019575478809243657', '68.2944083665393321783255155749', '68.739089812457380735547426697', '69.80131673523477044774663839617', '70.333116371046482655655715464399', '70.95183703099124796630243779908', '71.4233773814818685445898782214', '71.869912383813205397005254317140', '72.54458234165895753566680078128', '73.19154520819551325301032709880', '73.84888089478247944650695627190', '74.20661017949976345276362454738', '74.74167872275795941398019405038', '74.98851818102327985675608238435', '75.88913921698497608645126524267', '76.19030308496432413012240392969', '77.005222715465725272853522722792', '77.423163311148634178668211451025', '78.106353213659071668261756301372', '78.48606363601759820581945196960', '79.05505197328920241915716295917', '79.90981591993399748614319370110', '80.57114327742595954888506427663', '81.13494852124515235659764279928', '81.5189445311232876999604099958', '81.98601686941342297815088813591', '82.67350654816470051889960179664', '83.208639642613242746579905271275', '83.47028159516813898836997393642', '84.30695100521912276657240142880', '84.77884116344776017776719609542', '85.25855218196852862446972772848', '85.73312705151617238050655670251', '86.40690326766295666403928478660', '86.99953531447869145388447579639', '87.344441744745253757985528888600', '87.89202123143712594065494216036', '88.91064108529159808492615374205', '89.611664405304422371563976816455', '89.84205109278603411180924615545', '90.48439947007969870226898925859', '90.75936356234621303178108221443', '91.54522487025257157600666359579', '91.901511685108379528401459941016', '92.73021834025204308068101888114', '93.026796378120889365488793011022', '93.70741546989417068852418600896', '94.19000328690247242171001786777', '94.62152406194900227657872863524', '94.95232830328682921000907793176', '95.63681433701424275826638379706', '96.4232086518445321616168710146', '97.064557961589879936280179759179', '97.533178661135820245589215832780', '98.23913665299581108682164227734', '98.37803642784889171654395351827', '99.46821391621223442130410740162', '99.83020920188512729933075435408', '100.248109356863742460910730702', '100.83164686424631228130134757732', '101.375382902513226375499704367494', '101.90495033070189908233602762381', '102.41021866251593073282091535866', '102.873281981933472947058697965319', '103.40513415488371604597676310231', '103.83815045159017570809354109495', '104.74906930113322146235609105007', '104.98713962576303976728446243858', '105.541132301466117025944444091100', '106.2393548083725408591087292127', '106.98583466699650830975505734309', '107.302386111632213090686291040', '108.05656523450152146392082994964', '108.48870746362156544859447974385', '109.21671882870745269590467255318', '109.66043463317575795196282992134', '110.12586009758468030448583225788', '110.577906156458840574366145780051', '110.74791655801968002749588205306', '111.79110149786829768962141564781', '112.29939712058251033685999094839', '112.77330833509477927927973512540', '113.21427485800446524625657814267', '113.624259815838335378716042149730', '114.31207887710475277090202224359', '114.62067727414603088435202734145', '115.64966518176182649915938774555', '116.19035094347337016473662628681', '116.90465316562976910624068677389', '117.20692755707557425806722690761', '117.4340926242379661726419842533', '118.51128045099932444143482351113', '118.67215495933226447660553518733', '119.14198368683659960532032436100', '120.000054801375401261190041713263', '120.34271341230825465730737270967', '120.74156989829918832403630803162', '121.477685157951165557449373701628', '121.849229846953157437520983737427', '122.17315471973477591433204725766', '123.11855337607090715964803665372', '123.35911311238545269052344807627', '123.94863364217489109456377931097', '124.82971469931132669816211607297', '125.55179755135930022985532453105', '125.65668682010462780988472071389', '126.371248588460259156380724715464', '126.77627020051522898652812278817', '127.36681098342598284130539349231', '127.97690448689796550703021954714', '128.56583339572382358838085741310', '129.11649625852831286404684096786', '129.416928002754816146613440959213', '129.76893414951997846703768027253', '130.33424540531504004355540399844', '130.97462678054960116815622282336', '131.80295354810897152089708189151', '132.06465350179962554761432908577', '132.41286398248643469272090015142', '133.22764676725430272324336215561', '133.797331534784132729421914591069', '134.40507085608238463066042319029', '134.77590757386197559195343162826', '135.63954187135822564054446385311', '136.24080249187577920394731341716', '136.583578700102517279003845214752', '136.71497705807173727089377095303', '137.425368576632416800522860751123', '138.054692746011799416974938343542', '138.7448400200773857572606182664', '138.89543449151712492637995118615', '139.5776953852786755333441900969', '140.12624777032703099866649341820', '140.45755985212112034940481279222', '141.26395388749230538317268010098', '141.65704860022113760893234184309', '142.04388329521962758697450661430', '142.84844248219803611858800382170', '143.568660348133689072351222488260', '144.02754647081354974414129738629', '144.76557356182829036141813688679', '144.94072853533437927105905633946', '145.40988218092145189249103947963', '146.04153849629432530645409634385', '146.45545133762368824219157314598', '147.3185635168934665837734619365', '147.375199002630442100490821499512', '148.23014077649808246288503112119', '148.69033566069569101380279211628', '149.028069288963455216825433895346', '149.6048990228520446325792666454', '149.8077080858901123888816387153', '150.70500153143078040442040014242', '151.452588256353918696422088357049', '151.96131347610189508981489784811', '152.45250893780717201876922590281', '152.907981988220321815842445114361', '153.44288114802664386277179820024', '154.08319764267349507306806358611', '154.50689528548104053694612735919', '155.24814501537525802737714077860', '155.55825196626373734095366170901', '155.96277910583510177126747226209', '156.614915310100715841940472626717', '157.00781103956050488863519163502', '157.49695025684295165580951480113', '158.19542094516439083065265378802', '158.51464011587759738467210104481', '159.0551161392870140544632624872', '159.70668795974495065316390659754', '160.168858133385627363717021169605', '160.96741557109788656276008697919', '161.27637633292414497566285599063', '161.94703439553913538680967043978', '162.43674207513163897882963220918', '163.14476302816982177902187799086', '163.4829330886699749802076855527', '164.128167811880753718795578268690', '164.41035318818256945146313026766', '165.06474285126117389319989174604', '165.46281671472950440201608929058', '165.95448421560687762227089853973', '166.301207568436709849549917573935', '167.266510882748295691070350729775', '167.736396023693186684001630595382', '167.98741578279235456610349381908', '168.43301099086213719059098919147', '168.96185950336592812068648851832', '169.56666030887215536724211662887', '170.649348822437644379293380306391', '170.92821964271029293563896178686', '171.39646105572968127008807750059', '171.83897270163414570210568144865', '172.48567630971556645691777892696', '172.83120844636564660610917050470', '173.33890690771127084114055450960', '174.01905667153662260135881967155', '174.43140128544088081743128547014', '174.88754534831627299106219262091', '175.557104303518975925751534628462', '175.93847549222968634780849856015', '176.3006419614691693468565787289', '176.9342417415515890232068543612', '177.26962222213730356806906502939', '178.20292134010186717461611861209', '178.55437660446153655256883720259', '179.05048557977090939498772965387', '179.8242282826451746145408373793', '180.59332647709259890115283071690', '180.67056171192193407832371404930', '181.18386184014952590631226579609', '181.661525580047785373376807159990', '182.24901443378308450514050036682', '183.1314764562493348672628488686', '183.35910969593349773309288700748', '183.68062700836368998897481538040', '184.22159483674168488381266880694', '184.80412165341623754764191348988', '185.15318875289659607151551737910', '185.74072003598960070264900776701', '186.395766192128218416504063029309', '186.891562080339452534874206237185', '187.51359381792537694148876754431', '187.87606085211166521553454419115', '188.46799689627719190407696964473', '189.150141080444002106947534737994', '189.61395472387705949255363660817', '190.27315786705084144716820013053', '190.69743252456859549734859454674', '191.219621852535442266047861564873', '191.600350798332547970793395785588', '192.15747962392104496389330962466', '192.3335548719911665302968725717', '193.313094237466325531972180163269', '193.66488772951749988780264286763', '194.048888954960303726262841916265', '194.77808667415854059756362750781', '194.983893609079699889211577599344', '195.61044505414431840415165945842', '196.19499048533480273204697816799', '196.73945767524345728407745606879', '197.264906068505943279263123908161', '198.11080795198729597662430206070', '198.41089688478205147774529099166', '198.916247552982941210653365438645', '199.61337955706864795754303219255'], 'prelabel': '1-6003-6003.1145-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': 0.8168334700249487, 'root_number': '-0.838955858996441037701634760937+0.544199473222405594368216461181*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(924)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.500409189360974419916408336028-0.334524679388940635289548084947*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.144603860339', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.0051341249', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '1.82966829364', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 27.87781479921304, 'bad_primes': [3, 23, 29], 'central_character': '6003.1145', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6003/1145'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-6003-6003.1145-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-6003-6003.1145-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': 0.40841673501247433, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.144603860339', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_6003.1145', 'Lhash_array': ['dirichlet_L_6003.1145'], 'label': '1-6003-6003.1145-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6003/1145'}