-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.65', 'a10': [0.9796677814463811, 0.2006266133789972], 'a2': [0.97858746968012, 0.20583139747147455], 'a3': [0.6393879136855247, -0.7688843188886557], 'a4': [0.9152668716298797, 0.4028480528646667], 'a5': [0.9999858715745192, -0.005315698575843133], 'a6': [0.7839575344483235, -0.6208144522977099], 'a7': [-0.9963852943444703, 0.08494907423911843], 'a8': [0.8127499143005265, 0.5826127159653203], 'a9': [-0.1823661916657439, -0.9832306810394665], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.65', 'coeff_info': ['x^2364 - 1', '0.999996467887392 + 0.00265785867577771*I', '\\\\zeta_{2364}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.4438', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^78', 'a^2034', 'a^156', 'a^2362', 'a^2112', 'a^1150', 'a^234', 'a^1704', 'a^76', 'a^1203', 'a^2190', 'a^364', 'a^1228', 'a^2032', 'a^312', 'a^253', 'a^1782', 'a^748', 'a^154', 'a^820', 'a^1281', 'a^525', 'a^2268', 'a^2360', 'a^442', 'a^1374', 'a^1306', 'a^513', 'a^2110', 'a^1635', 'a^390', 'a^873', 'a^331', 'a^1148', 'a^1860', 'a^604', 'a^826', 'a^34', 'a^232', 'a^705', 'a^898', 'a^1085', 'a^1359', 'a^1702', 'a^603', 'a^361', 'a^2346', 'a^2300', 'a^74', 'a^2287', 'a^520', 'a^1289', 'a^1452', 'a^1201', 'a^1384', 'a^418', 'a^591', 'a^1394', 'a^2188', 'a^401', 'a^1713', 'a^490', 'a^468', 'a^362', 'a^951', 'a^1172', 'a^409', 'a^195', 'a^1226', 'a^134', 'a^1938', 'a^2314', 'a^682', 'a^2030', 'a^904', 'a^2353', 'a^112', 'a^1379', 'a^310', 'a^1044', 'a^783', 'a^2024', 'a^976', 'a^251', 'a^1163', 'a^183', 'a^1437', 'a^901', 'a^1780', 'a^1514', 'a^681', 'a^1305', 'a^439', 'a^746', 'a^60', 'a^2332', 'a^14', 'a^543', 'a^152'], 'euler_factors': [[1, 'a^78'], [1, 'a^2034'], [1, 'a^2362'], [1, 'a^1150'], [1, 'a^1203'], [1, 'a^364'], [1, 'a^253'], [1, 'a^748'], [1, 'a^525'], [1, 'a^513'], [1, 'a^1635'], [1, 'a^604'], [1, 'a^705'], [1, 'a^1085'], [1, 'a^361'], [1, 'a^1289'], [1, 'a^1394'], [1, 'a^401'], [1, 'a^1172'], [1, 'a^134'], [1, 'a^2314'], [1, 'a^1379'], [1, 'a^2024'], [1, 'a^901'], [1, 'a^2332'], [1, 'a^1421']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-4729-4729.65-r0-0-0', 'leading_term': '4.09909217255667361832972374837+1.93037193787376858278471221598*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/4729/65', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [4.5308820838381925, 5.814780382662068, 6.091155676194119, 4.149520895916765, 1.2103698686493725, -0.3536113316867456, 0.28173070299224956, 1.5322130673823118, 1.4634772328303165, 0.2595171760737645, -0.17106189042177194, 0.9136618030724255, 1.684182534885521, 0.1288924070542712, -2.80664288696631, -3.956613114099117, -2.009580602722151, 0.6614226110773365, 1.2098174350026119, 0.08251193533987129, -0.17234927152785479, 0.8332109937136888, 0.7715009247276459, -1.1868030885142486, -2.3019296012043413, -0.4139477832383617, 1.8841232437211308, 0.4742479372177715, -3.6324097804612947, -4.831744715336488, -1.0811005824190127, 2.431696162662295, 0.5749509495018926, -3.8547451417421055, -3.903723604907559, 1.3120135309860987, 5.267335938865202, 3.4669883672632458, -0.7382520777204606, -2.0276869572302014, -0.5359328817194182, 0.21381564822162782, -0.3785621893363172, -0.28639332035027315, 0.3851071570153779, -0.22297417223765187, -1.3599542427806124, -0.5602360697874753, 1.167126453911368, 0.18598166484135792, -3.0338633574975473, -3.6088146589024435, -0.4676204267350463, 1.0429623552850407, -1.9055187637835842, -3.9867323643043524, -0.1857335402817823, 5.234847833724749, 5.080088311812808, 0.7825533139877756, -0.4131442544797112, 2.2932424194186414, 2.6531555368549764, -1.1662228950308435, -3.516803650460343, -1.4011476389967619, 0.7836218120062106, -0.2787718199485767, -1.3742946241014435, 0.14991439216934746, 0.9834129529233246, -1.5374787748432106, -3.771892954850273, -2.1434949804057375, 0.48324338831046554, 0.3655869302230631, -0.50197717441428, 0.8807140725985565, 2.299946486576721, 0.8829311519980839, -1.0369619523376288, -0.6041801687425291, 0.20979086045061432, -0.05552303611817182, 1.986909859585704, 6.365384184990412, 4.477396068667332, -8.284019466551404, -21.03916601890131, -20.05592843114654, -8.198688748563466, 0.17294699498928767, -0.034587325778938416, -1.6570306915520763, -0.46610346033039124, 0.03380392913309671, -1.3313986829637647, -0.8564496172762864, 1.5959349598251855, 1.9395518579372666, 0.09417917667285887, -0.2732761472226676, 0.4852408742609696, -0.6816810129696125, -2.233871647178243, -0.9396972068522949, 0.7185930598783722, -0.8864176483613098, -2.4134306702049857, 0.4084424176981569, 3.468422849978103, 1.3477351041406995, -1.863086358953182, 0.056084637803560336, 3.3938481093555044, 1.716736179822339, -1.403122381288051, 0.5239519433683839, 3.823491932817172, 1.7732344089079621, -1.9969368273338768, -0.5372005985469201, 2.884180491371837, 1.5914108374237939, -1.1755909381041576, 1.0409995657199658, 4.8746401180874575, 3.5490932409036557, -0.46967404469892654, -0.9578595400691567, 0.7872210755367873, 0.44606337545946645, -0.7022961238094557, -0.2210721562288223, 0.06460583481813231, -0.5154534312522113, 0.7765499876777219, 2.902925240811636, 1.673090179762116, -0.7036236304470393, 1.4175162255522105, 4.917682746647481, 2.7063103382880325, -1.254534189740558, 1.9845158730526653, 8.179109319820894, 6.032805317922721, -1.5980880947307632, -2.016299953937142, 4.737143051157589, 7.008281819436422, 2.415227838585573, -0.7617156882149253, 0.0030512128150179665, 0.18027701128555781, -0.5446542271543575, 0.322781755005658, 0.6763997152250182, -1.1553915372128867, -1.4320578440711507, 0.6373869291604933, -0.3664310706085828, -4.758193957647567, -5.397981352601642, -1.0632217560497417, 1.3145306546677755, 0.023193230607413687, 0.014429880853775117, 1.2891393582923405, 0.2096238639788732, -0.7933957509447978, 1.093872173145064, 0.38899809289075754, -5.818407024136124, -8.593713662216036, -2.53834240965993, 2.9030902823389133, 0.9495271639977596, 0.2255190073901096, 6.820946473980466, 11.346633621060251, 6.582078643516752, 0.2708456697841801, -0.4029197303145049, 0.2340569931767258, -1.3675438891457388, -1.5129935407593555, 0.33756457082629693, 0.03493365317321026, -1.5441012757717294, -0.6434215696201638, 0.7664959437938179, -0.1694018498716971, -0.7476146972176256, 0.32927714753814435, -0.06370466231709151, -0.583854730732445, 2.6321596482577596, 4.173129402727987, -3.089974078120462, -11.177678226871095, -7.919503295228078, 0.7892560422773561, 1.2883211319934929, -3.588468824875482, -2.587431350586132, 2.107053663934287, 2.044358003063835, -0.4053564079457467, 0.020580422436868792, 0.05868046267111371, -2.069956361143978, -0.732644730264305, 4.083143993777432, 4.623554648980644, 0.5388631160703181, -0.9378882794036081, 0.5226700245430437, 0.2559450349967657, 0.030186896495137974, 2.604082116265877, 3.5823674242492345, 0.6795355288701025, -0.7267243040129062, 0.9508522042034597, 0.8958504103056625, -0.4438330392108343, 1.0065574724510202, 2.204774375348382, -0.04951947622019281, -0.017843947652846113, 3.8944425711296544, 2.0182377390934865, -6.4277217021584345, -6.769775997437009, 4.549178483051319, 11.19644669882044, 5.5508001039177834, -0.04352268753060331, 1.748364808526008, 3.1962143173317408, 0.5730248003175452, -0.6252191912192008, 0.34017119050303246, -0.24341415972587424, -0.8965364843662892, 0.2726660703729618, 0.35764476112746807, -0.5871036028178711, 0.7282969858423124, 1.5371485505143652, -1.758358892063241, -3.6670530775508223, -0.09561009637069065, 1.8626118074136089, -1.6686800343829449, -3.06453072340144, 0.23063121323553412, 0.9403385822420678, -0.6797796187691068, 2.138070154609889, 4.573540246835731, -1.9290852830385592, -9.657072982433014, -7.089593806562176, -0.19489068901734313, 0.6538649211440254, -0.9188838106378274, 0.37775428564773217, 0.24347939094372786, -2.1212786448980836, -0.7580675688712506, 2.1777999876463223, -0.4164170270433341, -4.6626023209295555, -2.9729873269960074, 0.8859743570764097, 0.7567365716739365, -0.4599563181818309, 0.13647264244409701, -0.005237352324575577, -0.4825369276910495, 0.6505734571962681, 0.09688537896206185, -2.7225132524963094, -2.01291506820398, 0.7298110639433345, -1.849532635499744, -4.036149481325426, 4.932131839170923, 15.739217694970595, 11.724327994676772, -0.41847408372922534, -3.187978741331757, 1.146288200239016, 0.9111444694321825, -1.3078620537534782, 0.7097566233182577, 2.1887463188567735, -0.09455749677038254, -0.899889979143967, 0.4943882888119867, -0.09074010909260828, -0.8072165309092594, 0.7755132656774114, 0.6438637668718298, -1.5237849795710305, -0.28405407357699375, 2.555664067191518, 1.1042218722463353, -1.2221785244798697, 0.0850822784687326, -0.25318159957947617, -4.1164306254965535, -3.5469121562696797, 1.7008704267269183, 2.4716686256389684, -0.4505539051379566, 0.393778265818129, 1.8463542973337796, -0.3614801561230533, 0.8401091685184663, 6.625690942721514, 4.999875793786649, -4.4627318873011195, -6.701966887885695, 0.11079187513143644, 2.5315377639375987, -1.1467020646668233, -1.4837262150449928, 1.0765106863999938, 0.7111766214581046, -0.2870339981903164, 0.5216301287851168, 0.01425800093412641, -0.9685758528297104, 0.6573964057422987, 1.4069475162762297, -0.9298018444377123, -1.4540683891438948, 0.22709954860572001, -0.604888199069959, -1.314125788680367, 1.469806791683152, 1.4587259700759874, -1.7430033970039098, 3.7256063740388083, 16.141085496941418, 16.675988508778197, 3.626057972223871, -3.7395408040956295, -0.24063577585567553, 1.6024921649719983, -0.42549229152620033, 0.6076222074525739, 2.0704053479788094, -0.23051104096132194, -1.4135625380570995, 0.17883765396031157, -0.09302114984378668, -0.565629528673026, 1.8953963634115722, 1.836236258593524, -2.5631930685296433, -3.1602725682571027, 1.1147278590735794, 2.06273598390505, -0.22028103253956702, 0.19424834041318703, 1.2214076928442499, 0.08625585271106219, 0.508932232992836, 1.6796846568080324, -0.5038339908764932, -1.335791287966179, 1.7500609904064979, -1.2372339883956907, -11.389725492368546, -12.968183067823114, -3.4485231212165264, 0.5570501530214571, -3.8794563697620914, -3.6059575914398225, 0.9127220562157917, -0.47273528289575173, -3.6612485895903006, -0.8249035213357976, 2.2810616229700096, 0.623258881586471, -0.3304430333666258, 0.9636979723283154, 0.26868010079583093, -0.9059870231373707, -0.015536140364126174, 0.2616361265516259, 0.020444138991771475, 0.8011843030998567, -1.91077968507475, -7.739703390975405, -6.599315537784602, 0.9901196256694202, 2.2045057970535753, -2.5444808866129183, -2.082636451996548, 0.8271564164700919, -1.3359710430692255, -1.2531927156592728, 5.689228913187158, 8.039936596204853, 2.1718042936538997, -0.6090325197700185, 1.0351743132876936, -1.2028861040832313, -4.1386489208845365, -1.599056367245412, 0.642736560858665, -0.5076578308942966, 1.5137418440860215, 5.457307689122914, 3.7914709057349363, -0.13900248856061154, -0.06906697380436887, 0.4052245038407962, -0.6960632516385818, 0.9881449030678808, 3.3158349961782867, 1.46753824423617, -0.5697633409978187, 0.22137480514882132, -0.15690998984802923, -0.49002891391281245, 2.4605478112926993, 2.5584337016379695, -1.6236950354579605, 0.3102076770330504, 5.67280703316783, -1.3305104621565902, -14.504005637053206, -11.77921869579638, 2.952305102491051, 7.589446352549179, 1.5811082873633726, -1.0321670735399802, 0.22387476501016684, 0.0156007597290754, 0.25614631954942313, 0.8100907495841778, -0.5188728806131361, 0.2145806965732454, 3.66867770918906, 3.329804159230117, 0.10697609457527182, 0.231497257949399, 0.9171242052154194, -1.028806882675082, -0.14598540534018625, 3.2128831038307024, 1.8374344499633595, -0.9743316540372527, 0.9497253898254578, 1.3044652857942034, -2.6357023589567055, -1.1065099902035394, 5.138246814237974, 4.33139159116301, -0.2366242013584883, 1.8504483296875736, 4.629520714409737, 1.1791440449406203, -0.4934452885477086, 1.7258952965253451, -1.073350466550645, -5.5227856496772, -1.8856752749053518, 3.3709997100353544, 1.3242532855241802, -1.5532713685720925, -0.0911931230956382, 0.295295098687661, -0.8905758041227225, 0.3164400277527655, 1.1460667764561407, -0.13089238852667254, 0.19760308243332314, 0.9471271110016026, -0.2399727262873981, 0.47476349911431076, 1.8814624093787664, -1.3064105440115859, -1.6607461014546905, 7.809484967630521, 13.31226456136383, 5.2507166232880085, -0.7086868760288573, 4.428311056799079, 6.265081821333291, 0.13477681675999106, -1.4469380807105083, 1.3771826543721752, -0.7338894337185783, -3.215859223003859, -0.042337435849042454, 2.0733495135301485, 0.27864076320665787, 0.11621653284746901, 0.8061476146213636, -0.3065547995300187, 0.08206257703273238, 0.47873889305546913, -3.3777679338610054, -5.385623262451802, -1.1295309355949055, 0.6605516670350049, -3.002595783200559, -3.2726865684929116, 0.12803850401996222, 0.4819290466333186, 0.10356745617724557, 1.2106049393828238, -0.4603609097287297, -1.3653416151924163, 3.2207367924405084, 3.7784374601139215, -3.0056841885644765, -1.8405625691012937, 8.886244912055258, 10.04065270191864, 0.16906260349613697, -3.262000953318988, 0.3724833413142469, 0.14178112914920557, -0.965216549047058, 1.7246072785818467, 1.9312365692662823, -1.0749427538311798, -1.0134369227765987, 0.3851299372694785, -0.21223772515116227, 0.24941436454713325, 1.072833078466627, -0.4877746778635887, -0.21073411554354238, 2.5675060948542616, 1.6771496931857035, -0.609668906592153, 0.7385197893128512, -0.06994612716365566, -3.1634923051561654, 2.6992206113389603, 12.46153160979386, 9.145377704502632, -0.6773709280415147, 0.6203992303984066, 6.465983715407428, 3.8515325862006344, -0.25423326491237264, 0.7722911994285445, 0.6174523998541122, -0.7986182813258442, 0.948555225972709, 1.1428715253438184, -1.2385487862301667, 0.874151859916956, 3.9951764129146166, 0.26317319100625425, -3.7219807840752694, -1.2078081671859169, 0.9966765852780268, -0.3171875562518532, -0.11947368413749446, 0.5017950817895258, -0.6457407988424441, -0.07395341661620972, -0.015600153253310683, -4.345654740901264, -5.856137645803475, -1.1321756576676723, 0.7986926056539096, -0.5506089545093462, 1.2489584226974846, -1.0553373764430303, -10.72168985515349, -10.304277867141744, 4.1097784944488485, 10.025822205869687, 1.325411352554673, -3.409387866367744, -0.07604585703838541, 0.3811801860678474, -0.7532837252657789, 1.4726250288573732, 2.1458158707654524, 0.18285129346648768, 0.03578139175233841, 0.13296137774987768, -0.4490570404319846, 1.3200196997131999, 2.1237588195903956, -0.4955934136814285, -0.04784651095656683, 2.990776471949107, 0.8017955428351192, -1.753651047522116, 2.5195476422562235, 4.811206757080734, 0.26402777446864334, -1.044998993538042, 1.4366328567501132, -0.29110124532098813, -0.5588077866468047, 5.048003721858139, 5.013598461376358, -1.7864903507073167, -1.6541139389729596, 3.352878861705886, 1.8492079559383887, -0.6607226496032454, 2.3678271186188304, 2.892071236941688, -0.7076528651358683, -0.71448873002645, 0.4416830383798852, -1.2827036525967017, 0.0861898339280994, 4.219258556964214, 3.2721845132367053, -0.0014900393961144454, 0.3653973862718166, 0.7732682709756564, -0.3189452828813745, 0.2681763281649067, 0.2730907944722117, -0.6884652121275656, 0.9167177566873762, -0.23227653680822463, -5.6498021913118075, -0.3717138236999193, 15.881698186724512, 18.704852300713014, 4.77804879136456, -1.4954133575096218], 'positive_zeros': ['1.436263131102258836598074059856', '1.80427998358588048099922950842', '2.893176285004522157187378799516', '3.20624009855371350253108068011', '4.077222432195656130978053144358', '5.21908246582811147395234897397', '5.96296284397788460250735335918', '6.31863248837493530362664683240', '7.01898784182800530272916357726', '7.85681379524486692827304868933', '8.47750205126100395145487538849', '9.44579420633990468783045410988', '10.04016945101464165079988346771', '10.868891145104751344554323418087', '11.81141033319177215813158105938', '12.62742966296633491999853787805', '12.95054599402444172319571345765', '13.55175305497879402153369754945', '14.00570730166844832026381499176', '14.776391160264528999990988810142', '15.33302835853788370806435438583', '16.29508056778975247324509089644', '16.71338020450195897395246727977', '17.50957027386601665244508822727', '18.51306323727855266131595627597', '18.81579374456747317718638868039', '19.603877629671744490296248166308', '20.46275312009954924180725161672', '20.89194723656457696152324315329', '21.53970580862100820064456319892', '22.03570774345963025131611450153', '23.04413583285126139565605730020', '23.52625795152140416961235289680', '23.92139335225254887725577940827', '24.80247216862779935459736468747', '25.48034330760461321921457778579', '25.83028159311943952294765683925', '25.98223258948394962733667508835', '27.00999205654502392731955914466', '28.42309704102069180989101293923', '28.74546446275315247103804552938', '29.48464680789413494976205786685', '29.69924160449474510264337261098', '30.42475176897795531142912194250', '31.26937184184427615795339724903', '31.65624121252006427563418643410', '32.07331475480994661685878136995', '32.93984469777305440288123363717', '33.326417911465388814745743290003', '34.03226519314568949969173669640', '34.78931648138238434773773770695', '35.30816748228392484159889463312', '36.074947952579618756690631218242', '36.52095492176721122068913348073', '37.30936170944363377938453750684', '37.85449942278309291582382816750', '38.57923518546408328135660670643', '38.98279854462357381322834438336', '39.95333825738838504458122428311', '40.47119466007766288204707592266', '41.032924684869897950389048397418', '41.65114350582029258309261049464', '41.91171217643207988996235310000', '42.38533059818131626075867058881', '43.30380471599789372723066969836', '43.62837334945632080413995586932', '44.54886813475419775562774011581', '44.894909017903101405632086962825', '45.8618774345132184514456664947', '46.35524988939719342065939365219', '47.365397401987521171552963724', '47.81167473560432524750009396892', '48.18796664342620832646522504130', '48.672891968539501587333346303', '49.19942835876330404575298762531', '49.896810921786490068800359657046', '50.2781582738072360603939702089', '51.33101671691616735201330245361', '51.88029105062602361322279304508', '52.18408215746935632698778018059', '52.84593648471307300431675525170', '53.28559360736606908868862784005', '53.777775922578884099353367942107', '54.79226612136639081296694134882', '55.41114449317382049841394249383', '55.60163836727543390335208741966', '56.90043834826699601772680981480', '57.287160189839080630780969078960', '57.57133306580187508453660561478', '58.37028232475329688476307595503', '58.75635950579274395986183209841', '59.47803813861073323752033909595', '59.96418662434669472065369944245', '60.52663492344193903418414774934', '60.92226777108622427374956313718', '61.343094090123147613986209806161', '62.088968009350370788343271809032', '63.08729136069716258785592081180', '63.51916736807296445549813036664', '64.22095689836393006213827739584', '64.92328205092565788822528839318', '65.30724565989241387183987340396', '65.63610221513234578301666746770', '66.30139328655413330983124127913', '67.23570129032806385238796435680', '67.696696086033873892799018523915', '68.200313217899368026920240246364', '68.43020397400801168755450064081', '69.44790726675953996443071978251', '69.842210898583535628532117119735', '70.4786542509620316255741781814', '70.79450827940653115872597719829', '71.55618631094391497886441365592', '71.876872033046814294546856091925', '72.58097249131751502126169320115', '73.32536609114890725530965711071', '74.36654746730624410328289321521', '74.49321099883501460999989511431', '75.382421705904883538536376330', '75.816426667438941565393375642434', '76.18935770403711842568005354480', '76.81009299695959006074142822085', '77.281982143253873407248619096644', '77.69949783753028814260262261361', '78.302792295211636510251202811719', '79.06930278799455916683286265977', '79.56531156857865447255357956502', '80.290496317729640421728611816', '80.766820618410545630643347793855', '81.08254080249724138480780628348', '81.81121656455552112124793030143', '82.82645247507759092973638673365', '83.221367853735974672867526388007', '83.68255670336115572070948323541', '84.096339845938499125011517605871', '84.75148482456371688451657493269', '85.286438494903510152556411429761', '86.153995608394088653843399130867', '86.704763778814567943076473724', '87.13212960750523186151879070080', '87.49808503178649405909049539133', '87.97156427959701340898577525477', '88.44978185299009272419427205489', '89.2528932865400756260431880621', '89.549375865932440026256659417905', '90.18584565076812322869573979287', '91.236241302611586316750979656809', '91.78350271308753498948100083762', '92.282018128746136993281966571094', '92.74101192899117478344064840088', '93.425855537304331036010181692822', '93.93861281103684945834442775361', '94.35590302996691918930650985416', '94.86722356642042575974038724558', '95.40159087388006058224418257494', '95.96418986126531179207406258532', '96.66993912558692305031711038417', '97.17292738819137804859244164454', '97.47091051599151685839114890936', '98.33173071601699896851558586426', '98.99739958121951172044902691181', '99.32514178900842114830650412098', '99.95170921647607661356230219518', '100.250073283439837690486050277410', '101.1047709967870229102211624846', '101.86982880613888792990301329837', '102.405041787067319128825553154998', '102.97787980596978563039909783557', '103.58480660896579372110365525838', '103.89067016420036464302803336769', '104.37798726192718408732853944264', '104.90756771491195203216269217026', '105.51381989662938641041567399529', '106.18942926825824312716226037001', '106.45458622224683433446138956812', '107.04307053820987567638305342522', '107.62283921960421835289863971196', '108.00012914426766960172768097549', '109.15739559868298981605964866017', '109.70393596692149640166574369482', '110.23191969496205681266018751475', '110.54447536929693973407397524400', '111.22526764145517648046526761660', '111.83449823632094724418472994328', '112.165615194224506462975606641093', '112.597685026564147459753009172872', '113.26525279453424849231720809232', '113.98045019271717113187949271166', '114.64637673945946374425251378573', '114.963133629389293253361208885227', '115.65440711347664336731926897790', '115.81851520882053670736469225281', '116.50969650271344659705123732922', '117.015691826394834542307167354047', '117.449049328390197039838007426274', '118.58816232556647954274240671306', '118.809872927289273487821535289734', '119.60378558697392392319367351342', '119.963944031266338044822860334148', '120.680489961517249052556980557487', '121.34032926206846692916938907519', '121.65088128410479184736891768348', '122.23535666205271736355657698690', '122.81689525133293702981523505282', '123.278231142021964833886446240812', '123.42429376732111558390368087613', '123.92598852779862732249708891218', '124.95409955585166695702328339018', '125.456017941027479969257887295287', '126.11352823388717115144190939824', '126.43323756028504344393450710559', '126.94777175461252816569811680901', '127.95266514382209774882592353127', '128.243450504023020725328820462244', '128.65351871091734808621726570794', '129.521860082322029743232496797366', '129.86970998947100914994104412369', '130.17904413899828364163754873718', '131.231094391927059266901315640056', '131.578461132478505705312186440560', '131.982272880653785552382758690165', '132.391023856346837020050230540833', '133.28996429544502935771132980516', '133.681293064417661162986722784816', '134.02412538060470919634523569958', '134.449557242256044237388720476013', '135.1831794007585209953492001504', '135.60901454631333559068672524326', '136.2190198675916936337804338966', '137.11996215464826854101464017904', '137.91134955504541641399506548450', '138.36879185226669116942362638835', '138.75903423113107059495797827721', '138.966493270302562351599098474921', '139.57993422248772779450400217286', '139.97590029960742388678312744526', '140.95496099314465377220187924090', '141.202063517203336743116600172673', '141.72279778477172357843055748219', '142.20092631277493711746514652371', '142.96784726965180724939152352961', '143.336190904489536710562976864137', '143.86042607577572494340987500443', '144.43028590019391971706062410074', '145.28042116175121721620201169029', '145.47612397982397294136347355991', '146.34788910694363032917512253682', '146.63761081535533864032178643148', '147.124972561737807533130869616754', '147.89840587707862706524387272651', '148.53591654338568272161101220301', '149.07756547431004567685600213068', '149.44149309429536901620261579100', '149.94851123431983052911874433216', '150.587863959021212295514824814797', '150.88826714332793862418294614158', '151.49899801803806318804070062793', '151.79957788762904728539858033158', '152.404032062897630838341885748941', '152.89102306386264984358646356573', '153.94993654712730405128594382475', '154.1516884192558879838145392421', '155.00744445632628402830189105427', '155.45427703733066268873010639307', '155.88082783790129655630010793964', '156.56566146879772201718281914367', '157.247877379046668735794729657919', '157.46503938193850110108739791635', '158.04334976326337854400687479319', '158.41948842507084610989489278163', '158.8146304702062926374181946906', '159.769295389535949603682253353582', '160.07615712183102216879685201815', '160.92179109106905179105026976891', '161.41741798596104719864426781587', '161.51379643859911390402255317994', '162.13607159715980212877399871599', '162.6203257326199766179733109745', '163.3027691380407943953244305299', '163.8109247843078647415392009243', '164.69338879697333667600042214218', '165.27394613249535135474738152395', '165.64430969467382890573446528594', '166.07617520731061232141702474912', '166.75437780265053368329846382009', '167.36492346960160932637121298789', '167.73024412720647426899909836296', '168.06531168217276278700744388945', '168.66735084256313672822875858511', '169.088370881975769446110685269348', '169.86692402012867196702224873722', '170.19392464535813347117325385185', '170.61872307977607204412068802241', '171.16476204314221682038812089257', '172.15448440291221400131505922748', '172.469790939635338686346990712592', '173.39021006270863817415561830664', '173.61401235922300382264171404812', '174.15881072864043718718140063113', '174.56098533039207592961049814172', '175.134994601803749382954223850876', '175.55982035040177236733207801309', '176.263810362763138187164880777712', '176.97932806831499862244957019411', '177.4306763803940489621692386618', '177.84209255035653476509513556362', '178.2723186178100444027729506859', '178.76575674978832786765988320327', '179.060436880239484340636521172283', '180.08351183695532214490008273979', '180.46246008519993742993036284467', '180.77208862438876059402762511941', '181.20106150909074657869218460559', '182.10312369406800077727223028093', '182.857068961579861583249320734088', '183.44508529565358526094310005172', '183.812997134761490329230366385262', '184.20534408431684842160228001884', '185.0462491649989714921936200075', '185.29569477691941777949252892399', '185.67543652316757927565223078184', '186.06734882663248012827491395450', '186.81508601383058101746694932621', '187.19225343756549203269189189517', '187.869480035103938662551017200143', '188.295686825108919703461063702440', '189.08066800177280717706470746381', '189.493290445415563685518424242850', '189.97008326379703325717703480041', '190.35476108935833694671376450070', '191.160347967925405109402009717119', '191.65611021716848584120748637203', '192.33693796487591856552757837395', '192.61027439694300920264211220535', '193.36693468409681248820123617503', '193.86309360350020359879526744111', '194.16936369273076794319527778376', '194.680814098926793552165924147662', '195.62470985963071954290049031313', '195.85238082637465841501782275369', '196.4472359401535977354997519325', '196.796567284133841000092814808917', '197.253016281119809535004635645764', '197.67473785864775282173518632087', '198.10918066531765933338675855489', '198.75833801894487269662224066717', '199.82286214086562161774050750703'], 'prelabel': '1-4729-4729.65-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.1400944338826559, 'root_number': '0.636966696940080951905840052619+0.770891319830002410243348530956*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(2364)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.44044735420227940094881490133+0.246791599623637590279985561280*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.4362631311', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '1.80427998359', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.893176285', 'prec': 37}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.65', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/65'], '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': '1-4729-4729.65-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': '1-4729-4729.65-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.1400944338826559, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.4362631311', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.65', 'Lhash_array': ['dirichlet_L_4729.65'], 'factors': ['1-4729-4729.65-r0-0-0'], 'label': '1-4729-4729.65-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/65'}
Lfunction data - 1-4729-4729.65-r0-0-0