-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_967.34', 'a10': [-0.9982870823553307, -0.05850556556842369], 'a2': [-0.7838550368705215, -0.6209438631411969], 'a3': [0.9248101959793065, -0.38042883882891515], 'a4': [0.22885743765457325, 0.9734599494741338], 'a5': [0.8188410296463207, -0.5740203551859057], 'a6': [-0.9611420831003398, -0.276054154276909], 'a7': [-0.9923734190148416, 0.12326798948954168], 'a8': [0.42507292640888433, -0.9051591060328494], 'a9': [0.7105477971745666, -0.703648937987098], 'algebraic': True, 'analytic_conductor': 4.490729120579545, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.34', 'coeff_info': ['x^483 - 1', '0.999915388507649 + 0.0130082983359933*I', '\\\\zeta_{483}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.256', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^293', 'a^453', 'a^103', 'a^436', 'a^263', 'a^232', 'a^396', 'a^423', 'a^246', 'a^285', 'a^73', 'a^37', 'a^42', 'a^406', 'a^206', 'a^261', 'a^233', 'a^62', 'a^56', 'a^202', 'a^95', 'a^471', 'a^366', 'a^389', 'a^330', 'a^393', 'a^335', 'a^474', 'a^216', 'a^373', 'a^16', 'a^255', 'a^71', 'a^185', 'a^43', 'a^106', 'a^355', 'a^7', 'a^349', 'a^378', 'a^12', 'a^107', 'a^388', 'a^376', 'a^281', 'a^337', 'a^176', 'a^464', 'a^199', 'a^231', 'a^140', 'a^287', 'a^203', 'a^238', 'a^145', 'a^32', 'a^284', 'a^265', 'a^26', 'a^217', 'a^183', 'a^172', 'a^309', 'a^473', 'a^65', 'a^432', 'a^364', 'a^441', 'a^478', 'a^351', 'a^336', 'a^196', 'a^399', 'a^359', 'a^165', 'a^34', 'a^300', 'a^472', 'a^159', 'a^363', 'a^188', 'a^401', 'a^305', 'a^214', 'a^400', 'a^444', 'a^198', 'a^271', 'a^186', 'a^269', 'a^91', 'a^343', 'a^147', 'a^15', 'a^469', 'a^207', 'a^274', 'a^225', 'a^9'], 'euler_factors': [[1, 'a^293'], [1, 'a^453'], [1, 'a^436'], [1, 'a^232'], [1, 'a^285'], [1, 'a^37'], [1, 'a^261'], [1, 'a^62'], [1, 'a^471'], [1, 'a^474'], [1, 'a^373'], [1, 'a^106'], [1, 'a^378'], [1, 'a^107'], [1, 'a^337'], [1, 'a^287'], [1, 'a^265'], [1, 'a^217'], [1, 'a^432'], [1, 'a^351'], [1, 'a^196'], [1, 'a^472'], [1, 'a^401'], [1, 'a^271'], [1, 'a^207'], [1, 'a^344']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-967-967.34-r0-0-0', 'leading_term': '0.799498923811177414741869779117-1.19549070368470855481769199548*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/967/34', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.4381921122617065, 1.0184806200950705, 0.3560327752694094, -0.48102609115088113, -0.9309007066818966, -0.6067864456142744, 0.23710738765245534, 0.8331914533333113, 0.5877246011059502, -0.24238281661037395, -0.6062692154044175, 0.38477824398467253, 2.350881562558278, 3.5329966562838515, 2.11145732645868, -1.9940458423869023, -6.542809428332009, -8.471372724150106, -6.420540348188298, -2.0353145698930897, 1.3289032100299671, 1.4708756513261607, -0.8550986565941927, -2.911030044021313, -2.718201952328277, -0.800653991560851, 0.746987207957274, 0.676102968450115, -0.24149942979309708, -0.4800414387323405, 0.20921021178308885, 0.5496243848836766, -0.4061000179646689, -1.6996085687322569, -1.3611476020627828, 1.0834101626289967, 3.5918655769069243, 3.6303810961326572, 1.0752873620468044, -1.5215849621056594, -1.816813411045601, -0.3096527003230601, 0.560724573690429, -0.18826502899392358, -0.5396666637019861, 1.9670014840592907, 6.572298524308259, 9.324149373867435, 7.295504137748798, 2.131368948944417, -1.5251289145953144, -1.1063402681219143, 1.2762034711427048, 1.733587424430469, -0.6689203451814131, -3.1252368251029736, -2.899415470470114, -0.6558197809549227, 0.7971322825250945, 0.29070388666769537, -0.5508835457907614, -0.02784707088236872, 1.152340073901775, 1.1232912088511093, -0.18988009476503054, -0.9129086712129365, -0.1521152508148416, 0.4803610379596689, -0.6086154177559916, -1.9583976487651904, -0.4875793071038638, 3.7842064456329667, 6.333024030549975, 3.0389285036399882, -4.24642528727533, -8.957331875777772, -7.025627461440633, -1.2980291688275538, 2.248536345601563, 1.4655026787150414, -0.5568889664538182, -0.5640839680091118, 0.7748089359676157, 0.9503403897481059, -0.05672819254363616, 0.11605740525551833, 2.0993711842298195, 3.2514868940042367, 1.3256619954056192, -2.026940897241081, -3.2620850616402937, -1.665076615920238, 0.06541080493847284, 0.04831913690512349, -0.22752030184337785, 1.1911365735377082, 3.0893836555614724, 2.663206610064604, 0.0631838689082068, -1.3560813025381786, 0.007199549041925338, 1.302275572639131, -0.5823766482918256, -3.8473143225488013, -3.8103125328401486, 0.07778181515798731, 2.4953173325961537, -0.8640775915946936, -7.021510815106282, -9.076053127872871, -4.892399212169135, 0.620966860887219, 2.2535762278149725, 0.5376964413683581, -0.6092310927063191, 0.09157476236230275, 0.5495002021477147, -0.3305846767690775, -0.893426362542569, -0.003858617717643666, 0.792344093930719, 0.11062103826017802, -0.4360956538299532, 1.2249104952523413, 3.5569027160339237, 3.0671006308081044, -0.051027435259363894, -1.3337035645997424, 1.5397630157357463, 4.76677686956393, 3.5828764712615557, -0.5931088547249297, -1.9203726068699019, 1.3939365997566329, 4.480023237360711, 3.02357767573854, -0.5114602851071354, -0.8656618910545271, 2.1576539014188265, 3.8312199421260478, 1.8637482685463413, -0.6197513708750334, -0.5357911502497393, 0.5059395223271596, -0.412596505249991, -2.2212828613464315, -1.596271463520253, 1.2333210201436369, 2.3712250253963436, 0.20577299923602882, -2.1695738120825423, -1.8314947625045725, -0.1403941938663064, 0.2528896755388204, -0.15530824292429934, 0.5646376015710408, 1.5160761691771725, 0.5120935917947749, -0.7787758967859525, 1.9821669171319927, 8.197428413586204, 10.522730841541135, 4.03732397600538, -5.916525118475127, -9.537813143158855, -4.765695855717013, 1.1058331819754603, 1.9297016956683304, -0.3178177368107652, -0.8925871621777407, 0.12119415335857034, -0.47195164594058986, -2.578089698821959, -2.9786707511939134, -1.011500284682318, 0.4593509537079178, 0.08755873689788435, -0.12520126180563945, 0.7498747084085537, 0.3333796232987198, -2.5562550554435326, -4.668390975002579, -2.9816532805330613, 0.026629917620862472, -0.063522024257153, -2.4571556809794304, -2.4496357001520406, 0.4788228906132335, 1.3322565952135537, -2.160486682135201, -5.19480078409329, -3.096837958144524, 1.3253500778996683, 2.3193492593753535, 0.206478560036487, 0.11306547257204927, 2.7935578286482934, 3.0716798028632013, -1.383358340412999, -5.563856339446392, -4.489533015534257, -0.5344152812821159, 0.7596297338519354, -1.0374145478963988, -1.9646522852496593, -0.7408874910359173, 0.07913758106168814, -0.5169560197076117, -0.560161475564378, 0.3550510066140931, -0.11489315179684804, -2.2202254366634495, -2.6444850044569783, -0.20230043760946775, 1.3497311717127571, -0.4835843418243431, -2.0716196596296808, 0.24766424893046035, 2.5905775151064505, -1.484215098957611, -9.791908851554972, -12.59443793196251, -6.004434464983502, 2.3681247921206783, 4.127382132668518, 0.6672124303365575, -1.346549249149992, -0.31125441555596667, 0.364451170406488, -0.27765536080539266, 0.1302936332081698, 1.5736965970037717, 1.224930707145346, -0.8166604110234951, -0.9577039510539741, 1.4196637499449973, 2.2185113521993323, -0.4944421440119572, -2.86262943367733, -1.554160144885347, 0.8400648385447331, 0.6595582775693087, -0.5867831118913086, 0.30999969040633896, 1.855558312163228, 0.7262811786179015, -1.260332840215721, 0.24739985292298336, 3.500937292426449, 2.0479773778218795, -4.296160547299429, -7.390459679070322, -2.6951522845278784, 3.5309374964703584, 3.66944593222931, -0.2890846799755905, -1.3228068165816358, 1.2753079309782085, 2.3358250791753994, 0.3931328359479629, -0.6441219485155902, 0.8250521350930644, 1.625007321241143, 0.12267471390439451, -1.0231841237862958, -0.22898650711784904, 0.29287084081907766, -0.6729755022984667, -0.9346219214244479, 0.3037171315445908, 0.5035789973052767, -0.25996008218470956, 2.89801493084165, 11.253832656876934, 17.125814396027586, 13.316029392288115, 4.03726187762612, -0.8263065693209799, 0.2814984993647043, 0.4470550054010776, -3.034789155758001, -4.89496948015508, -2.1278904591436074, 0.6425207993909064, -0.47491883058626766, -2.2098308607262362, -0.7145521811268152, 1.515882633475843, 0.7404431490662874, -0.983706865595077, 0.1567187409939499, 2.5151046913752024, 2.0943868009361446, -0.03815600851477459, 0.10808841612347378, 1.9781324334768797, 1.715086421687626, -0.46263580562552953, -0.7905227587214183, 0.7970412058723323, 0.7054800575827992, -1.1341682980732988, -1.111758107261259, 0.5846152826128305, -0.08160277405616571, -2.1864953672429537, 0.6477847243271456, 8.705914949253293, 12.549840996540583, 6.383235920261922, -2.2811002236292657, -3.3362759689680566, 1.4789951816336293, 3.052045018444625, -0.5368443003311655, -3.047938848093977, -1.514028545497174, 0.40367959582780283, 0.263714216619073, -0.030777978367644968, 0.2848778160064007, -0.6276978921388809, -2.1072549820018787, -1.0420514272444814, 1.8145468807674083, 2.094917425094649, -0.3575425070335382, -0.7337166509587079, 2.016017623810515, 3.0060136708101344, 0.4380818122743646, -0.8985420153978874, 1.2085949949668584, 1.6187377202035393, -2.577343969961625, -5.247197477847087, -0.8867129705424649, 5.331055579639251, 5.244026110424653, 0.37708665424890203, -1.7667820335899544, -0.19044364313005813, 0.15482585737608326, -1.1411315796587296, 0.16582759835982075, 3.4114204379969104, 2.93988012494467, -1.697688322899387, -4.2405537442052275, -1.9710042301300472, 0.5722223387317543, 0.1132306269744846, -0.746834565587962, 0.14096001181828752, 0.7061910101562565, -0.061392773698694586, 0.20369544742923335, 1.6488914958049525, 1.0224931599704359, -1.4472894053825833, -1.367741230946854, 0.8462755661650064, -1.203461264855007, -7.927613448192884, -9.714847834165539, -1.288077811674563, 8.289778705813319, 8.150118631864082, 1.1393287176373765, -2.4143696486401707, -0.6893781251630902, 0.13729936671657644, -1.5784203953878857, -1.650504734388846, 0.46385008245134085, 0.7855632746344197, -1.022435047973547, -1.230546218932508, 0.4290259321519403, 0.6614167356251621, -0.39003783465807373, 0.2702732776865279, 1.5273404846541128, -0.2627132551216611, -3.276478410033615, -2.185299670873337, 2.08767416273467, 3.279515536557105, 0.6296249047001976, -0.2902569772829572, 1.785834215409118, 1.975163345763789, -0.6061725248693358, -0.9311243596303099, 1.4382631761328355, 0.4222271111511452, -4.527431037972212, -5.1346004462649, 1.8488287155795837, 7.66337150570187, 4.91551207866326, -1.1967356383525085, -2.3703817744662166, 0.22756821708197708, 0.8846506552697478, -0.14607249566717756, 0.5119077174825736, 1.5542559655101083, 0.10642212414544465, -1.8149026682606424, -1.0793148224730253, 0.507660636998576, 0.17746041378364535, -0.39358714222830204, 0.5281309314881334, 0.3078272252787548, -2.154760469484283, -2.2778524996998932, 1.8998979381946592, 4.2074155103578414, 0.8683017421981869, -0.8203208769153049, 6.081327399516089, 14.762769642981564, 13.91559408259508, 5.223699371794338, -0.23813067786684233, 0.6657211832250037, 1.5270412286766666, -0.2592463184646465, -0.6770921690655848, 1.1059222941589129, 1.2280148995190556, -0.49070618666131505, -0.48761964201020425, 0.42906399717107724, -1.7270097997872842, -5.301314626953598, -4.725562455158383, -0.6283132359659477, 0.9752978985329971, -0.8897673736812919, -1.611578940974519, -0.18478672847737004, 0.1441311577312993, -0.48818552801765935, 0.5183763033980283, 1.0035229037941238, -2.574261842073815, -6.205172313678011, -3.3569488615528806, 2.6530652268177946, 2.881921160215096, -1.815357734619103, -2.241471317196503, 2.466023434516088, 3.209347170058561, -2.475062384452282, -5.7873568387819105, -1.9564311868429176, 2.4151683444614505, 1.6540397383047305, -0.6238472542398827, -0.19272764884294802, 0.7517953915979954, -0.11973048886300572, -0.6696922676810069, 0.18214726639088824, 0.17416527098537657, -0.6016172210228381, 0.42248983193307044, 1.5851210354423848, -1.159235228753019, -5.2968714027600505, -4.380753152618519, 0.24807659922366962, 1.128983688192171, -1.749143817970909, -1.0063074671863304, 3.7133085854394396, 4.320469659256993, -0.7640853118684581, -3.4036494508670603, -0.5061079603242108, 0.9859118139706662, -2.334643662071389, -4.3948768878828375, -1.7350523096104888, 0.4225906278908297, -1.0265047326079126, -1.484786250598114, 1.3437963754287978, 2.5513580221947145, -0.21126253467482628, -2.1117659506464457, -0.4860318621048143, 0.7778948580744136, -0.24841980519286969, -0.10588458147868315, 1.9693317606707574, 1.9042521274073172, -0.8329204982084004, -1.8735460473267334, -0.4572038034874867, -0.0939261770424771, -0.5874849868764604, 0.5824734944442833, 0.06798714880559228, -6.267927327317793, -11.450942765229666, -4.6027635364500386, 9.981467828073697, 15.873649284050973, 8.105930563270146, -1.0428182864058835, -2.1555429904064747, 0.22149669095930846, 0.12150321407662437, -0.34031449150928117, 1.1055623639624412, 1.4879599183772187, -0.23731922090302188, -0.6551304091517034, 0.5031741337305597, -0.44232866836422324, -2.9682984937821395, -2.7605921525209425, -0.3941422648308327, -0.07773566994341968, -0.805216438281865, 1.2614058292578456, 3.669169259662798, 1.618813922542245, -1.7212049096240793, -0.14316491497711117, 3.6305638228420793, 2.7664559199917935, -0.6823196034872046, -0.18604295525464734, 1.9273011664666373, -1.034231248353294, -6.172723214423959, -5.441384241034778, -0.5743293740375461, 0.30467810913230164, -2.3363136686656447, -1.7242689677487357, 1.1373388033615623, -0.413371591353723, -5.096975402909951, -5.520808220232176, -1.4674901539754925, 0.736317042663829, -0.19277454170867228, -0.4355190631551631, 0.2635430312728791, -0.3722624147388809, -0.9951615734886108, 0.09632289414156071, 0.30262656517625985, -1.5363413261263474, -1.4334750504624472, 1.2243970710505465, 0.3588006231638416, -4.853682949794883, -5.5840673452489655, 1.3659111225560685, 5.957405125374717, 1.4915336086354787, -3.831099019458998, -1.9256803664634954, 1.2735765506743326, -1.9649353273129193, -6.876235350300874, -5.7221583474178885, -1.272863988300442, 0.0650654152586769, -0.6190567636525764, 0.16194923828017893, 0.7912882625587375, -0.18355183651204793, 0.03151581977260053, 1.4692056200135402, -0.39501877184606116, -5.102961973117437, -6.034294601430104, -2.080358260545333, 0.2718892561556711, -1.148120089814066, -1.514202844129309, 0.3862970916207062, 0.6089414851555486, -0.46852926936034445, 0.8946234519331717, 2.3044379080883735, -0.7664109787336446, -3.8721229749646153, -0.15350108402339338, 5.34360181462867, 2.903761890112521, -3.8952050639447213, -3.525518416264299, 3.3895169669248584, 5.8158231752836445, 1.6134091267982227, -1.0448798832513, 0.40720729093212504, 0.7359072344748249, -1.0231175149139151, -0.828215162089397, 0.9249076023453457, 0.7217534408973618, -0.2608495133588096, 0.6825044735785931, 1.3483521230780318, -0.4214907481986306, -1.5172721085189749, -0.18251742650374553, 0.1313372205297969, -0.8484589466947475, 1.744173656625408, 6.518244385985069, 5.122755361505993, -1.897644051874549, -2.984279910464605, 4.8931011586174025, 9.96335146507143, 5.326396114284915, -0.7196552725903103, -0.6956056343337108, 1.084864864222584, 0.12580802526057722, -0.39346265833087546, 0.6669478580605561, -1.2950207077815392, -5.846344044216298, -6.170514752635752, -1.6714442834337429, 0.736422219312874, -0.6291054911999079, -0.7339344329542132], 'positive_zeros': ['0.755384804624970907228515146879', '1.7913787486472884025222541858', '2.72356659853432249000725341706', '3.35875386123453350727205191275', '4.55323797445135269367100156897', '6.09628248676888004032698722176', '6.775345842416341484087076491643', '7.941870981964567433222625818582', '8.66349879809768486616817858635', '9.294251416788900687453023838848', '9.905861056168051913109770996885', '10.819667957691678235835600740938', '11.98543638279928092885475542909', '12.87744514359896497760243303168', '13.38295226130284170663083407827', '13.86543485333773886190017906638', '15.456448963606083026369238931744', '16.08115305943017720007826304637', '16.805759675276602056887767848878', '17.91008683922383734275179859730', '18.52073698612514190127702319492', '19.069875702865228115821371055281', '19.95765980264503735129808891781', '20.66885082325121395224716883356', '21.12933309741841298683455176627', '21.918102200096709994107065622382', '22.94900307922671775366262765798', '24.14173199161861548862333029445', '24.89402392750949845096102141340', '25.44522743618285366536626503173', '26.22924337027822870830891189923', '26.53197297149619830627272505675', '27.62014062322852355567351917071', '28.72850269085577097406861472147', '29.08726088435681791059195855410', '29.467998197581456839579432021400', '30.63259487228570296650237344590', '31.24890655820817242803891404127', '31.81716364641585258608285165085', '32.80682646319828995676064213390', '33.38920848471615093485734126766', '34.642852515961378085905568004479', '35.40354720926159095602503155627', '35.90932331935634320816432614797', '36.47033748729902188124600889010', '37.18847096409537275155936818831', '37.844365893659868626509177924862', '38.26013013001203997903507680822', '39.369762919834425786423273116184', '39.87326957336794710523308021500', '40.88983238045440234178952887325', '41.45916445568132157676470983769', '42.44475806544255424858501216310', '42.92088918267442635452978103360', '43.957210783227006813071003979238', '44.5059971772835955475829342506', '44.92683753671466852815702409658', '45.80583021557100452454570953833', '46.583890251796661421847568585782', '47.53689753114904015876354680766', '47.968343411406615956389459726611', '48.26753866752436468160688667051', '49.14758269830892134556790443344', '49.53844547607764498616619969875', '50.746432457299563731686894728345', '51.796801668485310687617222976969', '52.45239284272750732214094868262', '53.07595656003425578219839612291', '53.33522390744194417762722955317', '54.538224175090759621960906333781', '55.03903945784234447548371400899', '55.37333931124007527846317816180', '55.98756291250817267361527550721', '57.18322334991417466356767847462', '57.48952714311169832104563670608', '58.387444868751197838093529487117', '58.90254923793262582691659490159', '59.89525130168386816088381404402', '60.66264894887228672543170950259', '60.91715150846064882768022944199', '61.7961016364977971329755350640', '62.86826641998579255265268770796', '63.284105792158714554436582202107', '64.27187043014466874455097110819', '64.46065416941962819972355688215', '65.18525656824603641329367474549', '65.602139881782459678099265051205', '66.585244440584242514214441728165', '67.13079980419509894725263442998', '67.79088307311347370698060033254', '68.37059334086798187538496554606', '69.581324069549850449266644288', '70.37323374192070325684580549821', '71.01091078560775196675385205318', '71.43580188266530624747511242628', '71.84217174728499179751375685193', '72.685476668754282491824321207575', '73.2667323654508404364228984958', '74.01788506269901795262233876695', '74.8661685957209660504318068940', '75.44892569305158823766797202130', '75.883797203921383308688843206895', '76.6546270015587512779956614391', '77.163954197921414228020931622789', '77.92485313761863593149370708924', '78.86706302364834702421734597918', '79.66205590423873240095106850528', '80.17565955859147318124005639825', '80.99640052922374483961869710933', '81.4214651220111273639372094898', '82.20776436783932811117406266201', '82.8779572879062693963235872498', '83.25242794287358818071029135439', '83.98950249919141355995331116803', '84.527532543502496984177536384443', '84.772682986999258255381614415833', '86.45365153340306068607224155547', '86.829691609775440503900764997851', '87.24431251838876477508908010309', '88.32038553948940544002601904874', '88.68493188704066426022524354788', '89.45549688630400310807178045672', '90.10782808651960249133770212127', '90.6051575555237139506285087910', '91.55449334925777906363161533577', '91.85316583028201296284644742161', '92.74050834548808657109782144963', '93.28374354031382136558755872774', '93.87253369764338373741439860887', '94.56686123494883073193870162091', '94.988547852059829492278089681076', '95.591723048521893412312708776206', '96.77461090216881452831972631468', '97.40689964332893127229927225289', '98.08571903995391770599050383935', '98.96114525832013576467105571511', '99.525688102937534702351663841269', '99.72259528368692048023431130704', '100.17239314624410176112689399892', '101.049725718150091111362315350627', '101.82807299351318277087933757643', '102.2897862831708866733892843002', '103.17405470961465749365704251397', '103.60219892694865798908018714010', '104.21053542141674248738329714608', '105.03929797075281115889242422312', '105.96450887990463274424274740555', '106.60006456547878562534829702389', '106.915073960747415224042418518978', '107.48280052462278801483824682416', '108.331198395927724307508684525203', '109.26654752606557316767652823256', '109.71354297009674818238655194270', '110.277038712245910026508319331334', '110.91136269825505308455426199075', '111.19275139551535317353895497908', '112.002641671211756704639036057287', '112.67569111151867781702890433446', '113.04247800089455422592668150519', '114.09771183173336339181471358499', '115.05724454780118486043734311311', '115.73907801286283787416399848130', '115.976018815628833826713767206451', '116.80404300070454021864010903240', '117.331638769214404166740055814979', '118.04172116236348819829867494825', '118.61607628272242485107555925386', '119.00721076794619766446453643130', '119.66221086420947659488997215355', '120.47244015474399824573294103445', '121.33401149774261030454884233114', '121.6244174498768943724319470426', '122.42596526307149446185086415354', '122.93875922364455333710184893081', '123.46942374237272790306547778810', '124.30653677316881235444426413674', '125.23864941854433278216662835677', '125.90768421860166761819638609045', '126.49749667661581889554392870145', '126.74956382419572545936861583537', '127.51371293820369773017089255331', '128.307130079951455215395689612672', '128.80432368095637811736060939082', '129.22775369767198402155081803279', '129.73712583472027239331445082023', '130.500890078454955958642449037332', '131.316106321079282580520708137376', '131.633572078899122593989150225377', '133.08909953973168194160050588261', '133.33361533070595912943538582369', '134.0207125234072119763009898316', '134.505239078568607209119473800541', '135.21649342561299567613781105493', '135.743989519422703620603332919', '136.067498962503154431068485412673', '137.244843795926907035180900324130', '137.68683093753778331731816444054', '138.48477560602573619137891342641', '138.81040075935666465580954780116', '139.26920386902516113941743997314', '139.81631615904539889503088661165', '140.78708227854372222442280562627', '141.44102336033771495624887536412', '142.03276136807132363990474242764', '142.69344497443474875063887991270', '143.547688020330495316863611285217', '144.25856013424338676886379458346', '144.72992071860494751830639603297', '145.282626040995257280127889024461', '145.87457799809582620685723998258', '146.31023504392806488111675111606', '146.80048273373437840759728276037', '147.41441955084237551259737044370', '148.417692015385664523082346209068', '148.87857117778107434824931432281', '149.448689492658987369213656442240', '150.26933634067068441893001394656', '150.98342048713537597793133263539', '151.37747614297606038968634957795', '152.371632381554437079957041855010', '152.6505348615528371930413000155', '153.30788094648721837740137773272', '154.04303136891783499754363959816', '154.75732907350005710138254914068', '155.24941733939744080936417065899', '155.64498852190343996634667043171', '156.470712198824323800913570209513', '157.34993806982089680008941531057', '157.43505106893333838981861641422', '158.00707932592898369931243779445', '158.443548061692524470161962604087', '159.47566598750048315242121338432', '160.57252962495721022005149487424', '161.208072707740955661301932366719', '161.59794444000000177568650275114', '161.97793422696594726493078785081', '162.77020535284519948475200603942', '163.29112803877363615202307123239', '163.68654047324362988707687236367', '164.77496682423699672296385999818', '164.972844118264151428997728574733', '165.49024708334412836510152840345', '166.37457842185339819150238943713', '166.88609238341775289236720245442', '167.73281890611696358206239088784', '168.14682701479677463077042229575', '168.687595943410999497240183139329', '169.73993593628716989698177873411', '170.04251261793828842628226503899', '170.792204218988184845053435316596', '171.21832614141674275721028830187', '172.323509016110611328412730555098', '172.762882193306625517352083770528', '173.29003128519710866986388721771', '173.64260072330875430444326473106', '174.35213603806052391553420598446', '174.75356979714278286057125540041', '175.47971796476444374167994179736', '175.964236767075467485054339876315', '176.822369860424206528123811790183', '177.56619632465298431612691228089', '178.26310245587053914167454675228', '178.63052263002159519354387253494', '179.86902501974343515634601924073', '180.03504597093926670858759536588', '180.5857886113260553460512038392', '181.19469314447250130184191713913', '181.55543988879326393792586003467', '182.15645710614154705418804469746', '183.33205452418330418638723940788', '183.55078504303106777558450298510', '184.30941226273603219610298465863', '184.83133993250706438153719969343', '185.18304537611383157553925009140', '185.88481634982570638143239551595', '186.56981004595337659838354623309', '187.31246750700549774239126361315', '187.97735262326547282161807941836', '188.87061844859006037702499468681', '189.30817257437644344796044031208', '189.822005764332347343738531182553', '190.45021945728140676131545016774', '191.11627230097492468586097332071', '191.40821661904919382347147914191', '192.128543746262556235682396730768', '192.853578909238144876781123059438', '193.16294784148676029220883312177', '193.61442308489936579316146503562', '194.60004426539075014273590840879', '195.14191713965476081087317217094', '196.19187996421396812861519057875', '196.65518998621207737465255726875', '197.21359456517365400020550896176', '197.61105821206337851428147025832', '198.00700365647797901436143687438', '199.20124154194541747689818853590', '199.574484998111252959791240278400'], 'prelabel': '1-967-967.34-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': -0.6247432563205763, 'root_number': '-0.381938121461580676293073953665-0.924187898305533346373153239003*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.31237162816', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(483)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.908026295353889349529340797378-0.555491620208987463414473791995*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.755384804625', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.79137874865', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.72356659853', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.490729120579545, 'bad_primes': [967], 'central_character': '967.34', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/34'], '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': '1-967-967.34-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': '1-967-967.34-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': -0.31237162816028813, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.755384804625', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_967.34', 'Lhash_array': ['dirichlet_L_967.34'], 'label': '1-967-967.34-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/34'}
Lfunction data - 1-967-967.34-r0-0-0