-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1183.593', 'a10': [-0.20002569377604443, -0.9797906520422677], 'a2': [-0.9605181116313724, 0.27821746391645263], 'a3': [-0.7994427634035012, -0.6007422642379789], 'a4': [0.8451900855437947, -0.5344658261278011], 'a5': [-0.08046656871672588, 0.99675730813421], 'a6': [0.9350162426854148, 0.3546048870425356], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.6631226582407952, 0.7485107481711011], 'a9': [0.27821746391645263, 0.9605181116313724], 'algebraic': True, 'analytic_conductor': 5.493828903459774, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [13, [1]]], 'bad_primes': [7, 13], 'central_character': '1183.593', 'coeff_info': ['x^156 - 1', '0.999188998171570 + 0.0402659401094151*I', '\\\\zeta_{156}'], 'conductor': 1183, 'conductor_radical': 91, 'conjugate': 'dirichlet_L_1183.395', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^71', 'a^94', 'a^142', 'a^41', 'a^9', 0, 'a^57', 'a^32', 'a^112', 'a^85', 'a^80', 0, 0, 'a^135', 'a^128', 'a^148', 'a^103', 'a^65', 'a^27', 0, 'a^0', 'a^26', 'a^151', 'a^82', 0, 'a^126', 0, 'a^84', 'a^50', 'a^61', 'a^43', 'a^23', 'a^63', 0, 'a^18', 'a^113', 'a^136', 0, 'a^98', 'a^81', 0, 'a^30', 'a^71', 'a^73', 'a^97', 'a^131', 'a^66', 0, 'a^153', 'a^86', 0, 'a^148', 'a^41', 'a^126', 0, 'a^3', 'a^155', 'a^67', 'a^121', 'a^86', 'a^132', 0, 'a^114', 0, 'a^94', 'a^79', 'a^134', 'a^120', 0, 'a^3', 'a^89', 'a^7', 'a^28', 'a^20', 'a^51', 0, 0, 'a^92', 'a^13', 'a^64', 'a^152', 'a^153', 0, 'a^33', 'a^101', 'a^22', 'a^142', 'a^143', 'a^144', 0, 'a^12', 'a^155', 'a^46', 'a^106', 'a^137', 'a^141', 0, 'a^117', 'a^68'], 'euler_factors': [[1, 'a^71'], [1, 'a^94'], [1, 'a^41'], [0], [1, 'a^85'], [0], [1, 'a^148'], [1, 'a^65'], [1, 'a^26'], [1, 'a^84'], [1, 'a^61'], [1, 'a^113'], [1, 'a^81'], [1, 'a^30'], [1, 'a^131'], [1, 'a^148'], [1, 'a^67'], [1, 'a^86'], [1, 'a^79'], [1, 'a^3'], [1, 'a^7'], [1, 'a^92'], [1, 'a^153'], [1, 'a^143'], [1, 'a^141'], [1, 'a^4']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1183-1183.593-r0-0-0', 'leading_term': '0.116320335271208019950474015107-0.154749698492709197476630643529*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/1183/593', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.19359207003694867, -0.28105188675776205, -0.9725655293677409, -1.467508238553363, -1.1727095920165473, -0.03359482723720107, 1.1344638975821146, 1.140086027068579, -0.478379764638244, -2.6584878379882384, -3.270186531708793, -0.7872810311400904, 4.1210221731734356, 8.651247956555052, 9.876457583812867, 7.138994116354676, 2.6387631461645884, -0.46459019075100805, -0.7416623089432042, 0.5741544263585039, 1.238910957484566, 0.40940585482973474, -0.763233668793335, -0.8610459713441377, -0.09330053989113546, -0.027189507278693504, -1.4514028878974314, -3.0492041904463263, -2.722045670323551, -0.15715899064675162, 2.5093065359013282, 2.9591199080586144, 1.2951456912165689, -0.21443007245132603, -0.003001188955729473, 0.9155385104319487, 0.5302331849424997, -1.1248157407989612, -1.6213693409620733, 0.666436955499935, 3.8128340330429564, 4.005336169226542, 0.14447872830265093, -4.264114095837112, -4.731682983502627, -0.9215977365249418, 2.9236535782542012, 2.9153290670037233, -0.14349407938791944, -2.197638831245012, -1.0731353917285937, 1.239699571194953, 1.687726648885737, 0.1532246943317669, -0.8831486252482479, -0.05281148122345405, 1.2107807181958645, 1.1073619610094623, 0.1189173601372396, -0.06955123492428857, 0.5162404407173394, 0.18092139873051072, -1.249134617647643, -1.1976327722712594, 2.201967268514605, 6.497022387431436, 7.006428435443019, 2.8214711754270487, -1.3082816074513444, -0.4906006097042124, 4.172706253589249, 6.991848387646397, 4.903559523532793, 0.9395837564069067, -0.3883854696163668, 0.9391620082470873, 1.2779912060160326, -0.8571473197594786, -2.682946413297596, -1.5581630780886786, 0.9652365470284169, 1.5022154648105182, -0.1337077493296515, -0.8746492895456679, 0.757928869559987, 2.427192498806896, 1.7081362814913081, -0.1394458007720487, -0.23671699616825082, 1.3319861751827358, 1.6981212578268179, -0.14193368045311713, -1.6715528112894176, -0.9124003438115987, 0.38677649438928535, -0.169481872479037, -1.1687634936263795, 0.6559724412624683, 4.375070760464965, 4.614487843292952, -0.9313791374207693, -6.77064155008974, -5.646778820367542, 2.0260888330272806, 8.362138502799237, 7.757543900530042, 2.953536472750297, -0.016094504060225896, 0.30046411935329476, 0.8831971362885602, 0.1724924504473453, -0.13349985598958702, 0.8723658693553665, 1.2957938506691038, -0.057035312116529215, -1.1638665758277125, -0.09017829187584256, 1.4083246286640532, 0.5708955267159993, -1.46162582235018, -1.0277200500762234, 1.99983524353239, 3.4612192858313917, 1.373585373619379, -0.6363705969836946, 0.9536148397369504, 3.455178094617451, 1.7106649406256387, -3.529559253767971, -5.855072113042115, -2.322793800550926, 2.323941486802608, 2.7365223453769127, 0.306261321886982, -0.18941756117073044, 1.526612756996561, 1.5718464051990144, -0.7934281320408788, -1.4644620194149245, 1.7203882178083258, 5.023971870595391, 4.293461767795809, 1.0193302404414142, -0.5012966761075985, 0.30947465735195884, 0.6012235825924819, -0.404184664059882, -0.5839749663833025, 0.5076481031574198, 0.6099679633717197, -0.7371305766603784, -0.94099819399508, 0.40103413026402346, -0.7239320660557264, -6.172757849879554, -10.403306765686136, -7.0109840043792175, 1.2651676346006313, 5.007757970169886, 0.7838098314335042, -4.559186000107955, -4.213518349062507, -0.4745337967253972, 0.4156466658059576, -1.8854871650061595, -2.658824960289515, -0.5125159769296561, 1.0774421494938422, 0.3345532595885377, -0.3058401696460526, 0.6445278335016856, 1.0448768783554852, -0.31920726241983716, -0.9325588422388124, 0.7731401140047903, 1.8198398018316306, -0.4690749360851906, -3.212781576609347, -2.1540123813250567, 1.1866133114663855, 1.7962425745139163, -0.6105519388913258, -1.4523722216376445, 0.6234218845333087, 1.7148928757795443, 0.3111599100081039, 0.6694911397968826, 5.038183372778583, 8.11981395564957, 4.692878770814939, -1.3029561755187822, -1.863863313562251, 3.1125099256975473, 6.012042255892046, 3.246567449486422, -0.32299551676672583, -0.1525337950637841, 1.4661713268801608, 0.8344741829315715, -0.7568762480631397, -0.3987393652497401, 0.8319529134971249, 0.40492080469309655, -0.5868862620762068, 0.2583385816765171, 1.6279053344155698, 0.7974405870917604, -0.9246708079760144, -0.3991453831116911, 1.2012478264461923, 0.5545264820510053, -0.30581021989399715, 4.066812305396821, 12.081554346573942, 14.365012438642315, 6.879810263768706, -2.095297421281565, -3.1976596954292096, 1.5070264398594113, 3.5653531052378327, 1.1715000316187143, -0.49811962397535825, 0.5788513498138185, 1.0358677291869383, -0.32721375302964173, -0.47537165328630354, 1.2054611703724412, 1.124927179531591, -1.5475870832344414, -2.476167425897581, 0.4308682432396528, 3.001492333873658, 1.7024544330638294, -0.732653015130148, -0.6630383113640843, 0.35818611981935966, -0.4340414535318474, -1.390742083744673, -0.2222650308167352, 0.5582607734784474, -1.8883253691631927, -4.203976832606081, -1.792230148690655, 2.3495150384707255, 1.7742729782609818, -1.916257135364157, -0.751670147546791, 6.017065192635519, 9.440772620314199, 4.675001030414844, -1.5689465139997543, -1.936326147271907, 0.9441819435668717, 0.7633237689448672, -1.8607822241847272, -2.1585644073102923, -0.1170793852113062, 0.6037778128639013, -0.2567274926236484, -0.2167200405928357, 0.4270558778485448, -0.117666302029028, -0.42642837289604896, 1.4559998948310977, 2.7654919674366445, 0.06054831729851955, -3.4606752810090993, -2.089227625847121, 2.3508000787692467, 2.838719397969694, -0.9190283326058001, -1.9569052390939108, 1.606565361432664, 3.2626137033017075, -0.05370279570941551, -2.246401154256877, 1.139545691867981, 4.956856212602638, 3.429426831385876, -0.269060693310978, -0.4777576593322351, 1.0867201113975316, -0.3083795707003461, -3.100162241462292, -2.61692316726051, 0.060808869786636424, 0.48393861127819704, -0.6551597640074147, 0.6677112285323165, 3.520569461290372, 3.384670108862986, 0.4727318166430434, -0.8532676880025266, 0.035510511936337856, 0.05179146925773647, -0.7251958398151073, 0.33587359164056, 1.9445842437218843, 0.9504195490821885, -0.21091932056473298, 2.85656463051583, 6.0502394669607575, 0.5488725563669481, -11.649661460130147, -17.168794443787252, -9.866491983469976, 0.4549770074921986, 3.034916669938268, 0.057124279827608745, -0.9275747913257861, 0.3969505522397824, 0.1561309446758045, -0.9124990155707792, -0.04845457747422964, 1.0595273435711339, -0.19595025497469776, -1.5582238052029198, -0.20706723324208048, 1.4633901855741032, 0.5736712990529358, -0.36896115301455756, 1.3591204755013182, 2.607999468600788, 0.20147928112927008, -2.2153201383199246, -0.5347358545544829, 1.725733532564414, -0.21238613139831905, -2.9809734221494373, -1.0982963989064416, 2.19709682555424, 0.24063565924323066, -4.645450544769359, -4.81573807892863, -0.67344510897588, 0.8133569230864204, -0.8140303303918345, 0.41984078167222527, 4.320683645636367, 3.871356189466379, -1.7827753933222117, -4.949070450397533, -2.1290245569112916, 1.119460583009877, 0.6170829006208619, -0.6737547330886358, -0.14030948157937462, 0.0447564298729629, -1.1284205401048153, -1.0918139237525417, 0.4142201637425102, 0.5544949039703704, -0.1368553577544966, 1.5876419650038625, 3.997131682393366, 2.3177100084433597, -1.2701565639060237, 0.09764549110555819, 4.827297916245018, 3.6764249077026574, -4.118258409108659, -7.997932348609634, -3.2908391208014494, 1.2018243287822248, -1.5644097251281186, -5.87840401493343, -4.528042687995684, -0.5011630417513382, 0.3611376418297818, -0.6007848624008173, 0.12021380502895593, 0.9168942364549079, -0.17561037651982497, -0.5336171096799478, 1.148890111960328, 1.1128366676251835, -1.9115149267411904, -2.9436589225579626, 0.293890108185276, 2.591381228672435, 0.5394612164529391, -1.6157450909771296, -0.4894840763838536, 0.581453641751805, -0.7579284540874048, -1.161426864157494, 0.5277139037503499, 0.15872686585932672, -2.0261997345695426, 0.8494005696831949, 9.064863469490065, 12.113093763218778, 4.88123724637151, -3.0966580464258566, -2.7051347300284743, 1.203780781256121, 0.4028477498124432, -2.7225703688214815, -1.8748266966812472, 1.1138633616649012, 1.094036869628944, -0.5894711054301547, -0.22654922407835226, 0.57251276806028, -0.8013838844623472, -2.0172579651988394, -0.8449444855912492, 0.1285532360651971, -0.7848166373623383, -0.933418972866306, 0.10321688510168003, -1.2145333538097862, -3.8371216029188036, -1.7712744021327753, 3.8227972584321708, 3.623471307987183, -3.9205171308197637, -7.978743925121704, -2.6851207793701697, 3.455849247145882, 2.5547873057286448, -0.6824687575397026, 0.07462819176785672, 1.664224820676615, -0.09538463256871545, -1.5571186770642744, 0.6426953967501164, 2.3619063708142654, 0.5014803382944567, -0.6078812220812928, 1.7975091396815759, 2.9427619661061746, -0.16963767393776633, -2.7924494497528234, -1.4485410163049464, 0.2697044560985793, -0.2995022024416742, -0.3764223276639032, 0.8828736749631996, 0.031238875725944294, -2.645930153979629, -2.537396956899803, -0.011672484562642664, 0.014484627071525029, -1.6379388036198488, -0.12779977459860803, 1.8221822378296109, -2.4902968035495916, -8.92021970966076, -6.378033438602834, 3.723386511339816, 7.7753350466612705, 1.600879877389961, -4.0058105571756215, -2.1322198845650595, 1.194274974188254, 0.4477864984228151, -1.0341441464928995, -0.20777675386012717, 0.33679200853977365, -0.497694124624168, -0.19913027680393514, 0.8572845810939597, 0.1455997489946601, -0.4720491103489327, 1.8257989887277906, 3.493095313033197, 0.36772942005733666, -3.3378613293563872, -1.896023995892113, 1.3657932115781275, 0.8129925769776356, -0.6915289864438571, 1.2078809602473688, 2.0777060092970028, -2.6846932823212697, -6.910317075343825, -3.7732364403994056, 1.281144166023762, 0.29945829960054277, -2.8857710550360482, -0.8645146768056059, 3.275530971981051, 2.8055712944016213, 0.14634398545605748, 0.6522468447581689, 1.6439488598154397, -0.9894893283618843, -3.283630115765121, -0.7580626329597921, 2.5198239270621388, 1.649328361039082, -0.4650425327587563, 0.009665453717073304, 0.7982141572498829, -0.2597696136053691, -0.6883001954351351, 0.2980210805176847, 0.1058243562624834, -0.20274731606160784, 2.5154727469320015, 4.691991604099146, 1.1468567577025353, -2.2996330269350773, 3.8631979975879216, 14.3517758980605, 14.675674375826505, 4.504086442301533, -2.079287759109067, 0.3932478132720376, 3.168638829568935, 1.2307194660048504, -0.3752147390340317, 0.5867010782967264, -0.013334637088831704, -2.2649590909335395, -1.747902515247158, 0.7604286529595032, 0.8089846207518495, -0.656716176296176, -0.22953134898965244, 0.15490633127737127, -1.9387554874535318, -2.814896685641213, 0.06130946917617185, 1.7441905787085363, -0.8440163296525404, -2.3693690305352906, 0.4360619053628687, 2.304607238592765, 0.4068174835252462, -0.058452246613280405, 2.551006018076829, 2.230666825057058, -1.7463156422366306, -2.0352625359219525, 2.034385818674536, 2.3230774632543962, -1.5232687806238043, 0.04910357109455911, 8.018310946679339, 11.232755138035369, 5.547135989953562, 0.055796663005075214, 0.43650253257565547, 1.6419693956799581, 0.22672560565149968, -0.44376322927757794, 0.6538038420796177, 0.45927115231508275, -0.5043720043608061, 0.4564137584362878, 1.365757526166884, -0.3140609548073392, -1.534897339361714, -0.10430572944190881, 0.09617550249907228, -2.102740888707761, -1.1976181430905397, 3.1779217038842975, 3.101765013114152, -2.1821341204996894, -2.5620828934142468, 4.127736247077058, 6.160737295026867, -1.522956399605665, -7.919817680630504, -5.117607947746492, -0.11632417570479622, 0.04230746312520515, -1.0165142954744888, 0.2751317504548545, 0.8049342168179747, -0.2698172146968568, 0.5493865705370483, 1.9769733226006223, -0.4324017100394517, -3.9580783959376, -2.629040491270698, 1.1599628915104327, 1.240926084319884, -0.6531939451914247, 0.4325259788023633, 2.4335481872525877, 1.5004222920331036, 0.03027822612135488, 0.39405931870166233, -0.216051588704063, -1.7040534399831098, 0.6651380565109954, 4.761065013801682, 2.4603082505369076, -4.044166752734782, -3.3416182298593675, 4.49781047943376, 6.710867074228358, 0.40243758043618444, -3.0851895067777004, 0.6051462579967433, 2.723020036491291, -0.5686658225544747, -2.541810085743461, -0.6233768627046451, -0.09692042975975133, -2.0582800891667192, -2.1472017157653864, -0.37440290024199635, -0.011196950835058386, -0.01611144908361439, 1.398071310502587, 1.562446089724878, -0.3703152505499489, -0.47977615782604993, 0.8671436418570946, -1.5969450561959027, -5.674954916218673, -2.9166543915455163, 4.977283016451964, 7.057455851097258, 2.128169425125864, -0.45811058454239684, 0.7758219135023712, -1.3306214314845604, -5.751460222863182, -4.582476408472061, 0.44746213769027693, 0.8963146016519716, -2.0657182403786694, -1.2926878632515924, 1.3732216743509662, -0.11482911864160866, -2.7697244029477446, -0.8925027439529946, 2.112389032686302, 1.092600557895792, -0.7066952588991938, 0.5149645339722246, 1.3512224852287693, -0.47169702301390615, -1.1194284668372574, 0.3776755660481795], 'positive_zeros': ['0.1469794540090728131799209097', '1.5702607170400919720544681060', '2.429320624562148434575741438302', '3.49531380167475711225515169934', '5.24132486593238790685070010596', '5.8104994336963592565573737603', '6.65917645137002612878843374313', '7.54633634338423253239869235433', '7.80012335973653712295900619972', '9.07835148965167788710706733752', '10.240275682651136775974540538515', '10.6260128043895794524752394831', '11.35948732828192139440491671409', '12.12234278920025044959876407610', '13.13401955777103733728313037502', '14.12405960454956248424741732577', '14.98628520333332524001103257816', '15.76107518525185421297931330090', '16.59061017438944940192891306660', '17.19887159623986820917016656067', '18.17702250093456561189450318122', '18.482299451625783120046513463587', '19.10868774016055069589974642607', '19.832376531010067482305748623036', '21.11979372075503479477713052554', '21.60312697902829359611738454659', '22.93018251260280123081384742994', '23.24905272753510020818270476241', '23.96024659229294760750373278618', '24.87127420651195361471656095408', '25.60153814009743001361154456722', '26.13988638427329254604590341247', '27.15671789169978289782216834137', '27.55811529566758209101996247414', '28.417845172108914099414131822205', '29.24741457261058689165545903117', '29.64716331450731606606608335116', '30.24817413935002564098331874698', '31.20877768176536381743124189538', '32.11384932044326917599388879255', '33.43272574776208493750186517612', '33.65055625204537859304240687207', '34.44071360531710558746200899886', '34.75278869776895203221421726958', '35.61480691339840337003879396152', '36.26505363082447578552827495962', '36.95719346019843824516933278242', '37.61889134859982444270161018378', '38.59811342884303193023867200199', '38.95063766388761842106025809164', '39.796330500787308033493532470779', '40.761991674255005939397950862105', '41.61408461772876951664104610037', '41.9205596297672850203049409759', '42.714478395423695872637363093103', '43.30217906027704152849085384840', '44.50735907416495314707812735302', '44.91086939185233243652602317775', '45.50951293855700097868568125184', '46.11344357973959032706496066266', '46.71520537482903877428717511206', '47.3993647149439092628501540089', '47.73598957276934651322882567537', '49.012271561210355386882116218598', '49.72551019195332944675635360949', '50.67886992416397971763633034211', '51.01251553899933204019947678637', '51.94074046979364359355024936929', '52.59028802013973724074411933085', '52.9539038051206235536494661246', '53.68849682328678087398814602112', '54.261919746783958505047897558052', '54.95621113616968008790716286210', '55.81928242339457197004225283049', '56.488343387632302768261422172570', '57.1078228307475188914471842433', '57.904508009830599076350123936878', '57.99820053032427685316724030206', '59.29346448405716951638486952604', '59.82303495189210474989321347435', '60.891904162468800983813485278245', '61.27676085544154087628840250928', '62.01746246460865697264535162412', '62.58794194447880555859386434598', '63.22461156656255387702503688493', '63.69935074730873050229542410275', '64.500145332243980708453949835735', '65.068745049361109801530935148421', '65.72845039536934284132221531847', '65.99445847955343839410152770218', '67.40748408553436875407231468618', '68.02983720966731966597893050140', '68.896904195579762726962744088322', '69.25237352406653184191179826146', '69.929259918819045522319468966830', '70.41292958148105844874241538702', '71.08330574370818554430902048333', '71.83891989717333228276522826780', '72.69448404051355709349331418144', '73.28845610354225817175748407441', '73.65122321925684520855648802229', '74.415840377368417438904274797959', '74.802517547036043951570031955157', '75.74461729349334183658924260905', '76.392359892552857555246890710623', '76.91864729977928848961308149531', '78.02379279507051314566274334028', '78.63631827986739591716240746130', '79.15644508011888239291232752148', '80.02010310930646478318001343359', '80.532383811273837100544740186872', '81.02366929496099335596287271206', '81.52371529730645216843640344695', '81.98188100412318615082974264488', '82.81696257565219201871603539063', '83.58024051006031256861571341381', '84.300947988815629418482149228091', '84.87790141398856590714588589193', '85.62096220144753193214883119434', '86.17700256573253072759915468622', '87.155603826126356482534624668324', '87.582414746868683491711377258327', '88.09129437324461217313627603090', '89.053424867643581872195749478513', '89.491997231344082968748368883791', '89.91688108739435800175370683982', '90.99557049510154515518773629536', '91.55038209768615427582892037079', '91.89378403389646909893202451116', '92.44456232478457502511072214860', '93.28523943655215684629408891375', '93.494063621323878743949462909758', '94.3909303237317875988992836061', '95.60617729572910337285665397814', '96.256338309546427848081791918460', '96.77518289483371462674761851548', '97.22515486254634441746253053354', '97.821737170687558552826685478778', '98.40718277250101791982500419772', '99.09090144280307932482446972450', '99.80011578371895324644714216780', '100.11478574163235462775221876965', '100.95563658535039455446050005820', '101.615768984785165135297145648781', '102.16869647260480818721034130063', '102.897410321642697772825232903948', '103.45313030044359040130940860524', '104.43644364561173519376592504041', '104.84706505214231421559125646102', '105.27246185320690268804995626336', '106.15891090927569541492096233191', '107.04209364828928915412916339346', '107.61201723736776207612296729938', '108.17789261254062983173508859486', '108.455102140663955162860745734484', '109.284335984884171244751577044', '109.8731364522224516472093926019', '110.075651936698927134093292968', '111.11663637583596530294107503792', '111.5554731837218223936407245590', '112.34591280066047931723379783773', '113.301210709365993627225902030115', '113.647716821658415896371673180581', '114.75010081077637053858908461373', '115.10497443354260866865908851882', '115.59749891154506483205791141802', '116.211061715842415930351918850297', '116.681216929067541473778293143', '117.31909112039892815220498235512', '118.10178623219658496287078558898', '118.8039588921924110390306380401', '119.45703537627933380298547410228', '119.86023816081098548455192667968', '120.5271269169288105225108117119', '120.95971254175693687474275900079', '121.51977793254818129132125161059', '122.661506097266614354662118855597', '123.319573971791892377644540968043', '123.787240203337558882630925545998', '124.554861772903580273295839891376', '125.18168314931045467544615392836', '125.680074514900181297144673780555', '126.11699898377522487895914633568', '127.06700662463157438419290983419', '127.27429399873378953555419400319', '128.07146984748630583841685501636', '128.247761483586187874401362087235', '129.160738579218751758339756329964', '129.85295632035586852935187176209', '130.734343105597786245215656738526', '131.4683450442825847504751575136', '131.864846681737242240589005708667', '132.48884899740199614565669235001', '133.05869568562733433982082053169', '133.81589083392661144709871560203', '134.17704941050205199107215393189', '134.98674861729290546294539650183', '135.843840716104503507259830740227', '136.15498714395683932002171812737', '136.65848038318404457926151653627', '137.191491557009623764949425725382', '138.12692817923293884995498919422', '138.44018087684149846680619730356', '139.07560440805279184214261961384', '139.56591083499296871172035493595', '140.51130650386807801897258462049', '141.31325929754149927245886053915', '142.039219145491002101366270866327', '142.566650248079700426334144854431', '143.17782029323437090833143231673', '143.57721573167309901726472935027', '144.11295372725041470449029047045', '144.72034609835748597947041173347', '145.1041586924660223984361135324', '145.96158710419320994538465855411', '146.71941611327332249928372161051', '147.30347418324211322670461749391', '147.66944457614342059722712768814', '148.29662489499898429371103193316', '149.26744067998220127478877340744', '149.71236194126286765459181828100', '150.37039732842923039575788503897', '151.28981146088688202146769013741', '151.419625520784980542258305688887', '152.101778308771178615650364578989', '152.86935425932142987315571407603', '153.64982580674502186771945698594', '154.060261317172562201364954755330', '154.62743813670625304247457772509', '155.214470353480354458265544262770', '155.6603238092794250713151657886', '155.9845271152468466481046607000', '156.941230322902236615162897512181', '157.36860569796788691479139092689', '158.59293423021638474330221520614', '159.03476676993520280547112389622', '159.84895642483254478324960130914', '160.15528562394203679609923698946', '160.62300461600305701524227345555', '161.4552794624753720486154357507', '162.02760128696183581363590146311', '162.56427263224070978940145213430', '162.85388750847326392104554070274', '163.7444421351859509536543451107', '164.2965643630247213415619147366', '164.96191378035070118221477380543', '165.68817561190868550845616956057', '165.947866512283625749036736321270', '166.73897372689477080717433708777', '167.348777813370955396244436460146', '167.994901306586572690505708054861', '168.43495306248223222813440824869', '169.69504318326338591902180084473', '169.92705846042345026004866827626', '170.667662342579189758520942200604', '171.07596603331788538019482823290', '171.6788175514352936494919121581', '172.097294296568793934453878904006', '172.76968723765822912253370545922', '173.457769693867763261541530296160', '173.76811852121181382778219186088', '174.46538882736193616848358575871', '175.18631513757763822274682478929', '175.76050827621536056720205784964', '176.51263361776523512216235249661', '177.51370954328186043748389250184', '177.820760783955586640420686089652', '178.38631130963977516128632573676', '178.96875274687491691955675791755', '179.27512275628119515591670331099', '179.96672046175564016068721142344', '180.825403404712955960021694337607', '181.42638591811256885099859475605', '181.81701425038607724410072808991', '182.845247540425740642444302362884', '182.890367285413730805631765363537', '183.395745585077889775178774781561', '184.01447659955001339684959814462', '184.80041532294996397758375853580', '185.453101591321973817912591173438', '186.2683328021392071225882657984', '186.83508788158693847752527812966', '187.45609789869930018411390488410', '188.24278983703499620573759823078', '188.41146768062317822540474930697', '189.49773634516315443705574013078', '189.67801391034165764764421651519', '190.00610966143670576068255086589', '190.87547122402597863974134248710', '191.34129114807335348429508634502', '191.74826201951289586563209508451', '192.61654501143669656547316226971', '193.60573188091703653828951666633', '193.88161685340277127826418036287', '194.26742236551452049621889917893', '195.277748589428344888309930739665', '195.71820237829915515744722756593', '196.37671464378835578491439109138', '196.86425349527666668355321617800', '197.5738115440163806165064673909', '198.2653146447547282049160438219', '198.66687782974059330870595489880', '199.30585347606308325097673547584', '199.91671006649930876408654606523'], 'prelabel': '1-1183-1183.593-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.493828903459774, 'root_angle': -0.2948277854010862, 'root_number': '-0.277951851141753138979224971643-0.960595007506739389597123720940*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.294827785401', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(156)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.436809790423625935609136397240+0.0327775780409937093490368292399*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.146979454009', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.57026071704', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.42932062456', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 5.493828903459774, 'bad_primes': [7, 13], 'central_character': '1183.593', 'conductor': 1183, 'conductor_radical': 91, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1183/593'], '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': '1-1183-1183.593-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': '1-1183-1183.593-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.493828903459774, 'root_angle': -0.2948277854010862, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.146979454009', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1183.593', 'Lhash_array': ['dirichlet_L_1183.593'], 'factors': ['1-1183-1183.593-r0-0-0'], 'label': '1-1183-1183.593-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1183/593'}
Lfunction data - 1-1183-1183.593-r0-0-0