-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_196.135', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.07473009358642425, 0.9972037971811801], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.8262387743159949, 0.5633200580636221], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9888308262251285, -0.14904226617617444], 'algebraic': True, 'analytic_conductor': 21.063125259746503, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '196.135', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 196, 'conductor_radical': 14, 'conjugate': 'dirichlet_L_196.151', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^53', 0, 'a^4', 0, 0, 0, 'a^22', 0, 'a^41', 0, 'a^6', 0, 'a^57', 0, 'a^2', 0, 'a^49', 0, 0, 0, 'a^61', 0, 'a^8', 0, 'a^33', 0, 'a^30', 0, 'a^35', 0, 'a^10', 0, 0, 0, 'a^16', 0, 'a^59', 0, 'a^18', 0, 'a^45', 0, 'a^26', 0, 'a^55', 0, 0, 0, 'a^55', 0, 'a^26', 0, 'a^45', 0, 'a^18', 0, 'a^59', 0, 'a^16', 0, 0, 0, 'a^10', 0, 'a^35', 0, 'a^30', 0, 'a^33', 0, 'a^8', 0, 'a^61', 0, 0, 0, 'a^49', 0, 'a^2', 0, 'a^57', 0, 'a^6', 0, 'a^41', 0, 'a^22', 0, 0, 0, 'a^4', 0, 'a^53', 0, 'a^0', 0, 'a^21', 0], 'euler_factors': [[0], [1, 'a^53'], [1, 'a^4'], [0], [1, 'a^41'], [1, 'a^6'], [1, 'a^2'], [1, 'a^49'], [1, 'a^61'], [1, 'a^30'], [1, 'a^35'], [1, 'a^16'], [1, 'a^18'], [1, 'a^45'], [1, 'a^55'], [1, 'a^26'], [1, 'a^59'], [1, 'a^16'], [1, 'a^35'], [1, 'a^33'], [1, 'a^8'], [1, 'a^49'], [1, 'a^57'], [1, 'a^22'], [1, 'a^0'], [1, 'a^32']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-14e2-196.135-r1-0-0', 'leading_term': '1.14416593396181105378261097514+1.79951491326169763904421045093*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/196/135', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.132456238118371, 2.7035993156571934, 2.873901987328678, 2.499195504469655, 1.5409099661010002, 0.16491385133810563, -1.2448105121352133, -2.2037585991442605, -2.342753738615143, -1.6188948937814036, -0.39445257628279184, 0.6951450850618045, 1.0521207857130643, 0.45468451561822226, -0.7789091796964133, -1.9326745468451887, -2.3013300644762715, -1.6432010866756896, -0.38794516206816126, 0.5744704379502815, 0.4413662223806174, -0.9429745379697811, -2.895493546253371, -4.247960515799047, -4.066918474419358, -2.2834916131329535, 0.2094946287826245, 2.102004199973065, 2.51410005787006, 1.5638989843041025, 0.2388155177576087, -0.3573260347492986, 0.16383014958930964, 1.1986527183518536, 1.6669425531762851, 0.9423407548297058, -0.5381225743253184, -1.5143313622790657, -0.867900019359839, 1.4202679384197034, 4.107631662997461, 5.523234281954676, 4.798143771530612, 2.5306809301355293, 0.32954286553869694, -0.43233169559837326, 0.338941219810245, 1.4703363138985925, 1.5799514745731824, 0.28714985672018517, -1.4652333723389153, -2.2651014608784634, -1.5199177118820084, -0.02833952553395279, 0.7116139212639766, -0.12252253262152082, -1.8545932120374597, -2.833944764218703, -1.90820465847766, 0.4508112938649965, 2.422661386648284, 2.3483345492794725, 0.17599041209478766, -2.4532956535093877, -3.588945726984766, -2.608481031278969, -0.6504886531546848, 0.522042166164372, 0.1481531511975543, -0.9415348792061737, -1.3038719993977543, -0.4466255156451895, 0.592914690864964, 0.27957306460722964, -1.7512996132178114, -4.062087569160679, -4.555846549276152, -2.4074650325997573, 1.0479503530104968, 3.3864221990062413, 3.190023291584488, 1.2194149979763396, -0.4296917914414908, -0.35133510058369277, 0.930985287221679, 1.6818755242961516, 0.847729185874105, -0.8240054555280604, -1.5872561951508541, -0.5852603740461254, 1.1588051736955494, 1.7359647883858051, 0.3561790780203884, -1.7215451760762317, -2.3802739567523563, -0.819773164772503, 1.5107149362160632, 2.25485760135295, 0.48402036833537404, -2.3260262944243517, -3.6970829763319353, -2.5392358371872277, -0.12672549687306467, 1.2893942594235388, 0.7479380130750362, -0.6326954230206943, -1.0911608041847884, -0.2506873803011013, 0.5106719063066988, -0.2400436874201152, -2.124223894237626, -3.0839996354270074, -1.5312055498498789, 1.7431926490030645, 4.048764638614213, 3.3364868301067485, 0.23232625507543075, -2.564652292265749, -2.9205912142576778, -1.2133070837966293, 0.3773898117058008, 0.3504135939309407, -0.6051376080702489, -0.6579129527047628, 0.8443639993120229, 2.477182697341485, 2.328590301886568, 0.27926437612875693, -1.6795891618794878, -1.5726404937915544, 0.31147816256859656, 1.6257174108588541, 0.5189111061693296, -2.2351713620106524, -3.93809481248238, -2.812856790800704, 0.09041679617850043, 2.0205715672674307, 1.4424212385860342, -0.4587538889353778, -1.2779239661765671, -0.11911140206906454, 1.5437713644437625, 1.7569747973575092, 0.42367308863532377, -0.6935701909165651, -0.29264230699627125, 0.6461039295741656, -0.14823423844764166, -3.427622651049451, -7.074789104375247, -7.985105538954697, -5.274979691352078, -1.2771501701325911, 0.8373032497282172, 0.218531064183794, -1.1561712019852914, -1.023935277102623, 0.6061411014541729, 1.778693532976795, 1.2209198584814487, -0.008684435764356709, 0.12583641638015416, 1.9567639314494825, 3.4615647569752945, 2.5907683269145014, -0.1356325862422755, -1.9573641103387016, -0.9278140741061937, 1.8088693201254613, 3.2408424670658698, 1.8809982443392659, -0.5801718351643523, -1.2771793235424203, 0.521806307388102, 2.6552890399258637, 2.6727311838334114, 0.6540588998589794, -1.0702119633675493, -0.8245268816193633, 0.49362478058957465, 0.7892027862502475, -0.3798880005899364, -1.1479310604526076, 0.19176065965316677, 2.662639292136874, 3.344883490593023, 0.762413964961401, -3.0824669935413693, -4.624437291195298, -2.55103215148414, 0.8544718547366972, 2.3549549336695166, 1.2415013842329434, -0.3537105725139873, -0.4056875986769761, 0.5836205978748807, 0.6137978650738191, -0.8587838963281875, -1.981462339850158, -0.8911100438811186, 1.619352110735918, 2.720136137216551, 0.9273856366620404, -1.888067678718818, -2.508031018226845, -0.1228355888484148, 2.691516091963355, 3.0063070909786287, 0.938344583011152, -0.6720992645870633, 0.17879477629750629, 2.277966380296493, 2.853877659466762, 1.073042083569161, -1.0394986530356374, -1.3066749930311947, -0.1619745846717671, 0.096706915076732, -1.4726277471026668, -3.056544814651038, -2.4700457325495613, -0.2968339589557488, 0.429728492381448, -2.088150628821635, -5.873557534895337, -7.112064922262269, -4.418826333971425, -0.34416486182140554, 1.6359379973475874, 0.9134171225684822, -0.19085492282200964, 0.19163515432475706, 1.1753207714394707, 0.745980804669363, -1.1080032791194063, -2.1293258818044385, -0.8595503912511078, 1.0832254767138374, 0.7914210140826281, -2.1341382309788544, -4.693836372298727, -3.913070236000672, -0.4554064146903428, 2.1079642446037603, 1.5175263795028513, -0.6929260186059265, -1.4376825792711836, -0.040663526481279896, 1.1458433275963802, 0.08006117413656644, -2.176925106216364, -2.8687820807375526, -1.1930584446340111, 0.7050224577029437, 0.6905605183429562, -0.483431317666503, -0.33379644211412357, 1.655854306497276, 2.8658404686465557, 0.7621717280907975, -3.5233668446592845, -6.05247460904706, -4.587248605906002, -1.1842743314020852, 0.3660055015574913, -0.9961792996951784, -2.7744016937829623, -2.4630025830830227, -0.643523975603003, 0.27765777492600524, -0.3754500565463151, -0.7336934047755119, 0.611192164349537, 2.114592212204263, 1.059311636150265, -2.5360130077175347, -5.244464963778795, -4.116432524039935, -0.3350929630703867, 2.125740344437831, 1.256587643195055, -0.8187463108373252, -0.8916430928710168, 1.1801195794736432, 2.590955496965311, 1.557666274912964, -0.32712053501503113, -0.44716531217475053, 1.1515080585029098, 1.860173940686439, 0.22541361138991228, -1.9182122758246392, -1.944532824706071, -0.1626514127878541, 0.47462645605845283, -1.5064134416866888, -3.7302163494835328, -2.8133778441235835, 1.1171699305926945, 4.221844302641212, 3.5067748741286358, 0.3345543107803798, -1.5356636271399513, -0.6360525067783058, 0.9101251786278018, 0.7990296065257079, -0.313220136166533, -0.195424431388753, 1.3233312481960582, 1.8988960691444594, 0.21016997249946873, -1.5907910696506598, -0.36777484464734156, 3.6034842000953278, 6.382490375624839, 5.004481407782069, 1.1333747831101189, -1.0490047242510907, 0.03666227270938445, 1.8678271249754779, 1.6107882974803946, -0.14797025900848917, -0.6767884063403317, 0.7347764972206349, 1.720054110386901, 0.32580893865741267, -2.0137326883683726, -2.3583749982470747, -0.4124991734547748, 0.9803001813764889, -0.14771011412295693, -1.96243607988669, -1.27154274584495, 1.8517509852339884, 3.7134564411999103, 1.6811004850077347, -2.277184393803826, -3.9874689127117104, -2.246089012272306, 0.041119165739142455, 0.00353883040479616, -1.5877586541495181, -1.9761567707156522, -0.578798668035631, 0.4024613817460991, -0.4062314786845908, -1.2475318961655573, 0.14153126826743462, 2.684852999011932, 2.758879387177069, -0.935123452256275, -5.038169978071359, -5.305448227336774, -1.7772290456606585, 1.4304808533536633, 1.3519707405341166, -0.5644691108705475, -1.1929417842788042, -0.23684420233801737, -0.18815156232543456, -2.174899168903205, -3.9720964495592264, -3.1293561469416016, -0.6118999959137439, 0.47926148198263474, -0.6035411582092356, -1.0798528505259637, 1.309787371430944, 4.711389994965353, 5.32471394122604, 2.5572159653152604, -0.013168318099854144, 0.6307257652460628, 2.9527810785407365, 3.0785039247616823, 0.10884884139651752, -2.7682485398475833, -2.685563532619336, -0.7223172510232245, 0.12093683220718249, -0.7087685795100741, -1.0184103600923426, 0.20646800378364744, 0.83129490744168, -1.2022491534398674, -4.1531885128073425, -4.147398489865298, -0.4589927942694598, 2.9595705605518265, 2.2457299701885423, -1.5095043962473977, -3.823924565909359, -2.6014264823084625, -0.3064924796090638, 0.00907602682154311, -1.152047077858133, -1.1492613809287315, 0.40065316159110875, 1.003475862850803, -0.6786496793668192, -2.36001561101884, -1.2170965479878197, 1.8268359837889092, 3.063081328582896, 1.1486997688940277, -0.8931291263898129, 0.1120821618301166, 2.9202910353151674, 3.496969960504159, 0.6550293724037461, -2.223279408124868, -1.785797699557002, 0.8709930006238655, 2.0530813656488975, 0.6810402187208348, -0.6165445616419932, 0.2502008056615913, 1.7645975718136828, 1.3733693011416561, -0.4329967344080313, -0.9053287844717386, 0.4023950275259351, 0.3812346724814095, -3.1545688474650118, -7.550364260064084, -8.026132661520633, -3.7821576666098453, 0.8463090008744741, 1.8489724439214918, 0.1787702633037345, -0.47335874611605644, 0.9222228669370585, 1.9028870285374895, 0.8590297288648924, -0.38249143187814943, 0.3865415175575674, 1.9655693789668824, 1.3120395679692345, -1.6653415389101782, -3.429789776295274, -1.710156597319929, 1.0295227252746428, 0.8441304184166009, -2.1330444515530393, -3.801127392452481, -1.814078110108242, 1.2215111546091642, 1.5604159099142096, -0.4544623119975365, -1.2156787602582153, 0.7408913083098155, 2.748342760420269, 2.137623054367384, 0.12120253683545945, -0.2929273048689654, 1.0605720940018855, 1.5076317258388787, 0.11822181944624596, -0.4069034644083738, 2.131065785098583, 5.329127065745681, 4.708294570290871, -0.14332035587637335, -4.520413469231664, -4.438332962418811, -1.4077481565452326, 0.24411412741363603, -0.6783208489006742, -1.4343729663736045, -0.1501817297321007, 1.3817524940637518, 0.9109004430666213, -0.4504131059737231, 0.013510258834527628, 1.9756399880053697, 2.0225982312844075, -1.1968508572440668, -4.293087449058371, -3.402033851620599, 0.4217487796424722, 2.539514366778122, 1.0380564925905484, -0.9744416251250961, -0.21232565964355743, 2.0376660615763376, 2.1090820281493063, -0.44181663400336263, -2.2260748832968997, -1.10636039148859, 0.8144694547328521, 0.6608890680858925, -0.8318207614969801, -0.7858833898386304, 0.9375841354073112, 1.2763807817760202, -1.0911881990434347, -3.068893709558572, -1.3490270535735598, 2.3961833498302725, 3.2699171117141903, -0.20194825009940187, -3.944512628391684, -3.79330105423685, -0.7671479511077721, 1.0528440779548516, 0.3683665393874902, -0.3834474480613677, 0.35491201248382015, 0.7663261993922562, -0.8774492562217837, -2.6613212631977206, -1.523483824130003, 1.7333568049764478, 2.93749193149182, 0.4615020950557097, -2.108073581500393, -0.8604726047835543, 2.8616692672659645, 4.31485966490468, 1.9440483341753987, -0.8312407965815053, -0.9071237113181152, 0.25027241300948033, -0.4863647712043371, -2.7158103220455905, -3.124686117418298, -0.7811160001825103, 1.2604112029066037, 0.5544394161299693, -1.1531135036459268, -0.9795714341720947, 0.2514849099077783, -0.7897088780565671, -4.274025843869543, -5.998261122361093, -3.121742572920983, 1.3877242808828227, 2.426723818174284, -0.4766747599526074, -2.9292222337628693, -2.015757578095197, 0.14268894085824335, 0.31215147540318083, -1.0059323091957808, -1.0956311944554002, 0.12617394651058458, 0.013091186835458887, -2.0383883275870067, -2.9553468540972108, -0.6990063262543427, 1.8554954355117288, 0.46413946214978985, -4.198343314499163, -6.9185165909941615, -4.8455190447310255, -1.0630681477235457, 0.14632601046087484, -0.8669527467648114, -0.6037512505312127, 1.6692133440025838, 2.868919189527059, 1.222403276697394, -0.7672461296953994, -0.21890957218204796, 1.61399438272889, 1.429095781942232, -0.7409960470939198, -1.4914705771561279, 0.4155199879310335, 1.7375565068878382, -0.31036522841558467, -3.3075607434818792, -2.7077115314925124, 1.4598085705193469, 4.289788908078125, 2.7404627476251346, -0.4263602453582178, -1.0332055730509762, 0.6740446835891756, 1.2591841392755403, -0.2256220423458669, -1.1796014815994187, -0.17937794018940026, 0.6284274884484975, -0.4993088264975523, -1.2457253497985956, 1.5196658820068165, 6.169183314693664, 7.488242179055579, 3.7141782009469217, -0.7832879292345813, -1.3770332070600813, 0.83781396656268, 1.4642608803240695, -0.4783498986454027, -1.6727041205834239, -0.1707563072125178, 1.6253268877779394, 1.1261305379887976, -0.1706361120701838, 0.7237102658600955, 3.0962037635362174, 3.33331952598747, 0.6828511268282541, -1.2572227444751713, -0.0077313458819656304, 1.8487293021691251, 0.6793252430803502, -2.264647024747501, -2.3710099925931227, 1.3465774203698593, 4.402645462055461, 3.08543667919724, -0.49798670253712307, -1.8895552722841487, -0.6230514847242288, 0.06490855671911522, -1.0792915496983984, -1.610691151040926, -0.003624795268674669, 1.459335547002204, 0.5599604587967705, -0.6375203493400929, 1.305529737121939, 5.220618889824873, 6.0139614586447845, 1.8497558349372971, -2.7560684227063326, -2.8787185275493057, 0.3801626861267235, 2.1680623278357958, 0.9328602833326711, -0.3672848023915773, 0.14271255654391715, 0.3120064731446194, -1.8485794844808972, -4.180286415933418, -3.4610095489160173, -0.6567882360071002, 0.38696283299804657], 'positive_zeros': ['1.59749306007858039469304630001', '3.22455300370286750981432905180', '4.18823754629617860368555972496', '5.72554068851118908041107703211', '6.37905954018625129223059991792', '8.098048379849776937730137653621', '9.449294531447597182768844207', '9.942467583036685311380195576140', '11.13975177542918727076945106392', '12.01438941079408619238312231001', '13.82156044676035430077928372236', '14.28122535106552765387601866993', '15.36244395522496985708722544252', '16.56907867745944470337490381509', '17.161539889300036878638516966737', '18.38204142017155929090968744803', '19.39480929050719727421511912566', '20.751891993028544320947821525327', '21.29513706901895724210689330651', '22.30162725977791414022362772385', '22.87279392843152535417330229865', '24.27956235925706370560607200866', '25.51284956183013439948549884718', '26.03673559265656132444535561001', '27.03291705706978524724452362494', '27.9151832915022027809694085677', '28.80210049457091898049682137023', '29.79264229157837710850852763523', '30.67929001507974870637228588758', '31.89288572100205199052040117707', '32.66485434465710259199254105143', '33.509519845559432249408653099282', '34.010933391791179066167900637439', '35.15265221174871336828557451695', '36.27112341172525529801935387980', '37.397248414026092025714515791758', '37.93065687732931172864715333722', '38.60408785361566549164029927599', '39.72356720098222051539515320721', '40.578359191534410391119521065373', '41.315610466975419400721661233285', '42.49021323803618608132426830267', '43.359722400310807220082954766406', '44.0830887876566600089584332089', '45.087735692889950817847496029363', '45.70919249452631181467970123856', '46.22750806546459908906564419884', '47.94826513613767832697438673152', '48.4827356715899114702914180517', '49.27039356004851716628150765173', '50.30922897918955550777318765613', '50.58720224405911417330314901515', '51.85990483195814483186783893282', '52.61133108497164660259282181650', '53.66756176043987253170074305913', '54.30728810500236839291199303268', '55.40450983398252044179564472894', '56.12929248910277549627951747201', '56.79046568838374488055944886344', '57.47350257671504373689124203123', '58.49830849386041443939690211020', '59.60205524067728308537729800525', '60.53468275706440302328837822279', '61.06965868647080085504151652809', '61.71679755377989423606184133790', '62.614619234939796017047155088', '63.53478168325868235587923726421', '64.386952089156057423678717845958', '65.44855958804272611730236208966', '65.907361757590808269375991881692', '67.01476934619506550101719289279', '67.86386792834465611075871490102', '68.15990460228508685610688108750', '69.42499558804797032425011677991', '69.78123623814789341385872470616', '71.28235140944682157103727882955', '72.10108956318858285046938261040', '72.43704603613325121821308405935', '73.26237595809892461943375780267', '74.18553169808681904624049087550', '74.79301412661870126305801561537', '75.97733491897795551916142420652', '76.773029606026403641916777510146', '77.50706602394881730749051491305', '78.13678039016820971865687160905', '79.23302361576921650460547447102', '79.8657192583433990411426634561', '80.381358573294604013826973786679', '81.31024576861034706790474474075', '82.65825669216900851579089556148', '82.95747717235503088673488496876', '84.204646569397658519555953365851', '84.55797403537159183010772454297', '85.206772511676322602220310156012', '86.04351172348683313502772632884', '87.215770047903422324563204481526', '87.98780180527286125761340923115', '88.590708536174417404130307592383', '89.61965528985386755790332386484', '90.10425386525920736617250969981', '90.96646657961419432164149959713', '91.90553185042192462142479887174', '92.302649397036982562879126624335', '93.356995326811314753045836165739', '94.40983953271729468015647910808', '95.110796694872680095958825422070', '95.83872377846312837403087789838', '96.30086298136794579388021940359', '97.21543054781375896403241083946', '97.848202424736906636372294946466', '99.17177997386075016220798456993', '99.68198175282015401537901053273', '100.59642960775037467419612171155', '101.11588595899538546179274654798', '101.91672672016500027525096155192', '102.87234865886075268519465586043', '103.41469346179245296377165520485', '104.20224503435045810265440243724', '105.1313839518403192195898314888', '106.240700611199206259588202276053', '106.56338158783043189536360916949', '107.62370310310045067431040388571', '108.02322710385001513106360743284', '108.73191532413602986789242425520', '109.62470471630873848412068708343', '110.767901373588420526897223227159', '111.467699865954889331524522573566', '112.28778803558132261018926501311', '112.42687879160943832055006719773', '113.84761935550557188982023801588', '114.24062544499367849203941721519', '114.87131914936810828919047866574', '116.24642031803940868314189807302', '116.44362678991560870013289578668', '117.50940244902115079889238771732', '118.60705412157417032447152387120', '118.83208796321318824248182192541', '119.64381662711100691026592634458', '120.17614279869073718153764496510', '121.2825498835939660039968855739', '122.0687030608231478671070659114', '123.199619679993991969812561596830', '123.44087244672549889440829270122', '124.29940296686355206453477190673', '124.904382472064586713074233942857', '125.75309694035107746956604733373', '126.70141182811568150481783708993', '127.173329863230717059548657052387', '128.181655130394363904075430209300', '128.961147061362482588081729470532', '129.80604243818213809432681672282', '130.26442303218301480177386884804', '131.17139080593519772677200972671', '131.78719242723017732785243031909', '132.24322207068691751695516367201', '133.676304335895460568749916129252', '134.40942125664019589584747428722', '134.827067976705326154067772168019', '135.798444925053043419933821198089', '136.17063041450305251832747540087', '137.02490493713016121743433914450', '137.98809683423847257007230057195', '138.54133642904539572458501766868', '139.54511566344910280021588279183', '140.24546740917474362155532854441', '140.84706575409729322521208562590', '141.8999671904362489815404680689', '142.27448988050054372532365806645', '143.14911710976650877393835830630', '143.524222833247131666937800144789', '144.67949818478331518716335625613', '145.82613839602912582446548516704', '146.08828462019862050942978098372', '146.89926850893237141311009819783', '147.68810591274436123982173002107', '148.1224248629523427095156006405', '148.96716586544903441433483160661', '149.96553742485871321422362583720', '150.755259042374959818011734056048', '151.2802833420540710025415919341', '152.13956745712831407539219469013', '152.97094181525214224503368649381', '153.57315829582917352672566365419', '154.21408847687987284118734679578', '154.88192478242358036357615553421', '155.736166129543169344028982644790', '156.548612255320461119920681774404', '157.5862782144241772765528508096', '158.22314555307504185773253038499', '158.64436233046580500345594336136', '159.24795919781218410328967991996', '160.14883705072659071127519191122', '160.98000021155124488860395985862', '161.63939932830539726728116823227', '162.692395513421937393527831939179', '163.34539939015934523774606365447', '163.65704457965810032234186736840', '164.776323810700596896581550122488', '165.403619228708667289057295905057', '166.1614326171166899591955427811', '166.445267854775293868620943938625', '167.70410142854379474789529141704', '168.39556170127032630959981586359', '169.34668693281174627862665169505', '169.76878717876124019329491887587', '170.58845527089168484332155283927', '170.94048388210087139910295009016', '171.94232462682729678579504612722', '172.53715086615534058993987417122', '173.91287579597970315825063217997', '174.1312879953093933378985838308', '174.78610630357638232176261881626', '175.78474691202509369583579924953', '176.28715242434069681305738629402', '177.08443772320527193356117062546', '177.758174712897833631184967943842', '178.407921846135115069375774888937', '179.27501059223537660866305899410', '180.26046549889891877191443277060', '180.82371492438336029341391411645', '181.522769934836421298419612673530', '182.22736990108528007785752146897', '182.71406260884195334515554099586', '183.31645174952207685031942324304', '184.61580717219088069317253429257', '185.19918294023083354054291567456', '185.87219638788683599105149191563', '186.585783871744510124468170109632', '187.43107934250126158031880031243', '187.67806599573344382041206153109', '188.82359067120511433876639509718', '189.37604035977667667098069154455', '190.07175495249950912740337725828', '190.841058765578056071342669260735', '191.826823661855127421613184026870', '192.66579210033096967470000253432', '192.85006142433780699294667527924', '193.75053348232239626221721655704', '194.476464406890238719852332723683', '194.86359386197097645065850376024', '196.04415689842129148823095604419', '196.83954462981952778756085162182', '197.67383118152958818478681621451', '198.07620555106632745715292569989', '198.511797352755533166260331822830', '199.78511963966649443191298344971'], 'prelabel': '1-14e2-196.135-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.063125259746503, 'root_angle': 0.6394557823129251, 'root_number': '-0.424231677899037307334093970437+0.905553688892584358975749052123*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.319727891156', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.11878538332618252037420591380+0.656427385181832493136140378872*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.59749306008', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.2245530037', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.1882375463', 'prec': 40}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 21.063125259746503, 'bad_primes': [2, 7], 'central_character': '196.135', 'conductor': 196, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/196/135'], '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': '1-14e2-196.135-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': '1-14e2-196.135-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.063125259746503, 'root_angle': 0.31972789115646255, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.59749306008', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_196.135', 'Lhash_array': ['dirichlet_L_196.135'], 'label': '1-14e2-196.135-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/196/135'}