-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_312.269', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, 0.0], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, 0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 33.529056535923004, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [13, [1]]], 'bad_primes': [2, 3, 13], 'central_character': '312.269', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 312, 'conductor_radical': 78, 'conjugate': 'dirichlet_L_312.29', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^0', 0, 'a^2', 0, 0, 0, 'a^4', 0, 0, 0, 0, 0, 'a^5', 0, 'a^5', 0, 0, 0, 'a^1', 0, 'a^0', 0, 0, 0, 'a^4', 0, 'a^0', 0, 0, 0, 'a^8', 0, 'a^7', 0, 0, 0, 'a^1', 0, 'a^5', 0, 0, 0, 'a^3', 0, 'a^4', 0, 0, 0, 'a^0', 0, 'a^4', 0, 0, 0, 'a^8', 0, 'a^5', 0, 0, 0, 0, 0, 'a^7', 0, 0, 0, 'a^5', 0, 'a^0', 0, 0, 0, 'a^0', 0, 'a^0', 0, 0, 0, 'a^0', 0, 'a^5', 0, 0, 0, 'a^1', 0, 0, 0, 0, 0, 'a^5', 0, 'a^2', 0, 0, 0], 'euler_factors': [[0], [0], [1, 'a^0'], [1, 'a^2'], [1, 'a^4'], [0], [1, 'a^5'], [1, 'a^5'], [1, 'a^1'], [1, 'a^4'], [1, 'a^0'], [1, 'a^7'], [1, 'a^1'], [1, 'a^5'], [1, 'a^3'], [1, 'a^0'], [1, 'a^8'], [1, 'a^5'], [1, 'a^7'], [1, 'a^5'], [1, 'a^0'], [1, 'a^0'], [1, 'a^0'], [1, 'a^1'], [1, 'a^2'], [1, 'a^4']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-312-312.269-r1-0-0', 'leading_term': '2.21953038171185003791515468924-0.299448765059589802941194394251*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/312/269', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.2396394080828426, 1.7586387165986492, 0.7750130225033911, -0.48182174753255846, -1.6159696074978147, -2.1759284504406478, -1.892857660775407, -0.9027488000206318, 0.22624014873745507, 0.7460779828731631, 0.16462669427674662, -1.390906294444101, -3.1521952298118125, -4.1159378204082975, -3.6722635084460737, -2.0465942948017646, -0.20967654774964162, 0.7505349935760318, 0.3967401486849918, -0.7116384688200025, -1.4039377936052295, -0.7906198679605712, 0.9910368770980486, 2.788285045141081, 3.2646347776861475, 1.95107553661322, -0.32382911293061595, -2.0266583977102295, -2.1142302258525163, -0.8690932351603686, 0.34983458343548357, 0.28138443711081584, -1.115335600115974, -2.583103724348052, -2.6589910504530647, -1.0181633285323466, 1.1367474148601384, 2.0531365851057863, 0.9584972638137599, -1.2272144241032779, -2.68625678519304, -2.3293511582862334, -0.7708968327185045, 0.27834965289016583, -0.33281485187328747, -2.0508537389592814, -3.1109409865646986, -2.247208919252963, 0.014069803765221423, 1.7742071282233862, 1.5536018237746, -0.2624128176207034, -1.768021871249661, -1.3857805617618373, 0.5812736362517912, 2.2529139867956824, 2.058244866905269, 0.31644194653393154, -1.1120448841471866, -0.778620035802569, 0.7988447043830585, 1.6285320440852253, 0.33592441187387656, -2.298815966669173, -4.005765679661615, -3.2738857452263943, -0.8734471666361634, 0.9523192065725566, 0.7990319137444768, -0.5206130953171857, -1.0008220021679184, 0.23838042789903763, 1.876824074194832, 1.7936099317703678, -0.5328433585339198, -3.260705710042412, -3.9796147853051034, -2.1946394776066804, 0.1839917620460848, 0.8990288596038916, -0.28411252980061164, -1.4923909177750287, -1.0123487889199847, 0.6653183153190465, 1.3744647558202716, -0.17849489470357266, -2.7444956776383633, -3.7217234532890147, -1.966360641676629, 0.9135474367986685, 2.2756112967805437, 1.2738672524220922, -0.37879903990112385, -0.5499284376751931, 0.7729567433838058, 1.5136380408363093, 0.08639071967570632, -2.516646234294809, -3.6592792394823213, -2.025897219789272, 0.8154179474268703, 2.127620281732042, 1.060775694817473, -0.4927512159737709, -0.23465673547853894, 1.7782297579748794, 3.227276873247014, 2.3642083898742494, 0.173182352073464, -0.7739617556360427, 0.5698465623934998, 2.4088290079459953, 2.2367736250519017, -0.09467430697207561, -2.086182613204043, -1.4942764851003603, 1.0254215628891807, 2.7179653148281693, 2.0057474876254062, 0.2661067377821959, -0.033243204802472524, 1.4948897287233995, 2.6428657264369333, 1.4316370791595006, -1.2318563134549028, -2.4471796321709536, -0.781097856163222, 1.9286020224876632, 2.692878621971605, 0.8651343572218015, -1.251384628064658, -1.3718140559395664, -0.023197432046622397, 0.3335304820537292, -1.3141409227396872, -3.021500575063229, -2.281804148488251, 0.6447775248125309, 2.7466491079573387, 1.7572928500577674, -1.1502573826353508, -2.821196248260895, -1.895287361334876, -0.17777430466721175, 0.018565843205137364, -0.9750789581815585, -0.6764824222292494, 2.0354452966416843, 5.01842856963619, 5.217631955029116, 2.4096604939958977, -0.4371047280893936, -0.7209273246447043, 0.7878824610815249, 1.260228323107926, -0.354247159185405, -1.9896487926419604, -1.3359611824242437, 0.923707674336768, 1.8651433132221416, 0.16016927911403628, -2.0496096175158716, -1.8070982090784242, 0.8535884564921676, 2.913983992355907, 2.2208171359193054, 0.1738731614568124, -0.2353558633309648, 1.5954878384287354, 3.1574591080641206, 2.2914569797218034, 0.16275614737565391, -0.2856871320713143, 1.6348679082883337, 3.282217998083867, 2.113049258165442, -0.8867228907304484, -2.3749473947704467, -0.9440428489105898, 1.131481891141898, 0.983578167948137, -1.079946810178979, -2.154903795215255, -0.8029515144340986, 0.9830831004822955, 0.6156183716111083, -1.3422573077073614, -1.7461541294319949, 0.862342454988438, 4.032828074730343, 4.3419533259369025, 1.6762123736325747, -0.7959390167551676, -0.8296986321378024, 0.23352158278431628, -0.15384797279129897, -1.802425250092915, -1.897868971642371, 0.893946828904148, 4.067864132125965, 4.161659479745663, 1.1756180528094964, -1.425317238021307, -1.1742874097780391, 0.45574928108172985, 0.48182840765170815, -1.317173031844676, -2.255979141011257, -0.8310647419918481, 0.8410641618740609, -0.16556979952452083, -3.351545961319973, -5.124439515637293, -3.443571401336692, -0.4853868477890215, 0.3236731196247872, -1.17844052716822, -2.0012894538033055, -0.42684439962103793, 1.561484358239247, 1.2538528386200958, -0.7062309412307449, -1.052925047494817, 1.4652528624951353, 4.091003401024438, 3.6569947122358935, 0.8584660674289389, -0.7519345962558998, 0.3575126954956887, 1.7689002202693935, 0.769958772061833, -1.6665925153612242, -2.251995232767092, -0.11033678455520808, 1.9401193013669453, 1.4278642742774799, -0.2032625568379291, 0.30986986640123027, 3.2053400947884665, 5.059009570132302, 3.4046420447905272, 0.1558856297751575, -0.9916776520388453, 0.5057855407648345, 1.7027388414153743, 0.7061749365692506, -0.5998418062759772, 0.3984465567144879, 2.7640689314204105, 2.941835495644617, -0.19675568645506133, -3.42073697473312, -3.274506562941736, -0.583445970774382, 0.9469675433991915, -0.07753797598974219, -1.181157409987797, -0.10988920531799724, 1.635602082683687, 1.106772342003313, -1.376098349504178, -2.229163882788635, 0.38022430683072533, 3.6854041756605973, 3.899781273250695, 1.265908172174155, -0.5350660097170551, 0.3774794190822497, 1.7913144572878275, 1.175141610456672, -0.30335141005217237, 0.4060162249209962, 3.292701285213099, 4.735636369856959, 2.4762793156471097, -1.0147904682581128, -1.7805065682164107, 0.3218930413814358, 1.8126856715057367, 0.8185672055507096, -0.39640453452876484, 0.8011542315626697, 3.1381491106354886, 3.158477055958217, 0.42964362671615847, -1.598471822307555, -0.5199216109850794, 1.541096089903785, 1.095197049833076, -1.5114263853155139, -2.5459350234226017, -0.3487989062886027, 2.2459381340693603, 2.06023800193495, 0.08246150141959183, -0.321500865362922, 1.3292916419609742, 1.9165438569723803, -0.3336985366406954, -2.7829805575329614, -2.023744500434299, 1.0400509681702714, 2.2891903542411796, 0.1898593563609732, -2.176534784797919, -1.743905058552376, 0.2095913556312176, 0.3799589988924603, -1.339805051092784, -1.7873360001886673, 0.3016945683597977, 1.9241818341917167, 0.13090053445652, -3.3183264587078893, -4.099775236021639, -1.3316031411477147, 1.3275962112338462, 1.0004739105202305, -0.6253628067751629, -0.47334188447581105, 0.9675936752998979, 0.6281992069036862, -1.8263484197074422, -2.8122604781121225, 0.005909067911979265, 3.8704841715550917, 4.41722986302639, 1.5741957015636014, -0.721279480713147, -0.360246525064498, 0.3591179346431112, -0.9830059935917503, -2.7204384309576763, -1.6385726702171757, 1.6844598315286219, 3.2064347070112156, 1.238550055211192, -1.0223469776816487, -0.21832046960547274, 2.231549274835704, 2.3946872817989875, -0.22041119594921016, -2.0721881670840308, -1.10711885949192, 0.21371655927753552, -0.9873761909077003, -3.2681597734346264, -2.98899879179394, -0.08598282846398198, 1.53338777577563, -0.2136157586214677, -2.4209573639093347, -1.5738867362719462, 1.1716102332922076, 1.8440377224737947, -0.28192715261460055, -1.7477649302130684, -0.40344461524227987, 1.3246480818267357, 0.46573851200894545, -1.5889795912279332, -1.1532234567092674, 1.8257163310337887, 3.316464880984895, 1.1901043022021247, -1.4710516895687877, -0.8892715194767362, 1.9068476628345215, 2.8845161592373296, 1.0978908452369645, -0.40387416332022014, 0.03828709250969138, -0.1440772605823452, -3.3378613439876514, -7.1023716623270445, -7.0097708835771595, -3.0427407927122916, 0.20165370397053559, -0.05812548255511043, -1.3803966922766226, -0.5674757210281967, 1.2968907334356963, 1.076668256418728, -0.8212934917042921, -0.7453803706506963, 2.2639117937309403, 4.411959703143573, 2.6194570293442023, -0.7451110775119366, -1.2663324277562964, 1.1151171441672163, 2.441280086768438, 1.0195652758899678, -0.2818469708085348, 0.9060335935104931, 2.4021822339321455, 1.0591647750624449, -1.7809988139569615, -1.928473720479353, 1.1925079257619697, 3.4107036931616634, 1.9720026352003075, -0.4877183320436399, -0.2455815386675949, 1.7974233423314048, 1.9144497795577164, -0.2449110326889081, -1.0860632169088105, 0.9800158694870926, 2.7281320958544315, 1.1209939565891252, -1.8008461125522053, -2.043196248952106, 0.05757209633800033, 0.3922461453457208, -2.3291468407777782, -4.383494760744616, -2.736171279044391, 0.3595231872218919, 1.0248062554213617, -0.33180583094226024, -0.27545321349463014, 1.5241754764800184, 1.501465959702852, -1.7705127387923463, -4.534586499998561, -3.1075306401079046, 0.5541040289176108, 1.736776962886319, -0.1473720630098396, -1.3093837914165938, 0.05495777984471361, 1.1756830612864881, -0.1756456047452632, -1.5801240848628362, 0.12437287090640972, 3.215006479343336, 3.186786509475865, -0.32137667864862757, -2.7115452717879847, -1.191272046868679, 1.3761878221536958, 1.3297922389617434, -0.22463192583904934, 0.09760712161309193, 1.93190807856838, 1.7553178816021513, -0.8449066669561556, -1.779227423665784, 1.2758874221555887, 4.833950100945432, 4.4915097242023165, 1.2831632530582828, -0.34427747737944203, 0.5525055886992699, 0.6600438418545117, -1.4139708285343877, -2.519618737247263, -0.3084994387545104, 2.3849962324788363, 1.6669893751233653, -1.2213992240750455, -1.7387352668503586, 0.863872453482698, 2.5254528599312636, 0.9945989922785152, -0.6601421874090722, 0.7570706327804289, 3.2587718795438447, 2.910711974653859, 0.21787328474452938, -0.8540440784365952, 0.46492458275565746, 0.5142028385447469, -2.4543901217500044, -4.8453778016507325, -3.123706294742572, 0.5089979928112852, 1.3903025661700004, -0.564322064538221, -1.2673496502408108, 0.6538921825677926, 1.855627476110475, 0.20849926890791434, -1.4615832155886597, -0.18400518973970187, 1.84797771579588, 0.5923050665639378, -3.04805024782033, -4.1622096856967525, -1.3051940091877674, 1.377447972666152, 0.663256005390051, -1.1698281251542892, -0.7793385167473333, 0.5960221330483966, -0.265187415689067, -2.3767346889354557, -1.6146593780004395, 2.2901888344858214, 4.485741837973479, 2.094952230369459, -1.4501895194269956, -1.7258089672537587, 0.29534561500744955, 0.7700213729015045, -0.3555886297802996, 0.21120724649679534, 2.650660908038048, 2.9349238587132676, -0.5797330456827718, -3.807779862407393, -2.835323031688203, 0.18936682472222316, 0.6705837868320501, -1.2359437799509327, -1.4597279425954637, 0.8661629821461192, 1.986543119987095, 0.006219710357752137, -1.814946895601588, -0.5933426448155896, 1.1671194294981746, -0.2925977882460675, -3.4608098852177216, -3.6445233180025465, -0.4674159472268081, 1.5192870009051622, 0.1164096720644431, -1.3251906666749658, 0.14165957178369307, 2.08798410333006, 0.9876239447429797, -1.64134625958429, -1.7152001170311602, 0.48091482165898636, 0.7215333953458782, -1.916247870440341, -3.190738169170505, -0.5833354833290363, 2.388767636734333, 1.6565154111201836, -1.0900878698697187, -1.5148451421583873, 0.27366470334204585, 0.46057579161867057, -1.5596113574400634, -2.1439292579583253, -0.061852105402255726, 0.7407428068812318, -2.4918797493301934, -6.226508229879235, -5.601807235985605, -1.7038622826973113, 0.4814925752333869, -0.231441521435148, -0.4964615016091547, 0.8495971145671001, 0.6170427920867084, -2.597366665879461, -4.8625887435742134, -2.7231837477353724, 0.9898638361260332, 1.2985908069249077, -1.2816326216726446, -1.9813484774490138, 0.37183899223833883, 1.8961413769044897, 0.556721179782204, -0.5903454023745256, 0.8172061197780056, 1.9321004923696345, -0.43281999723963066, -3.766994619165344, -3.313140225410323, 0.30878052449793814, 1.9751086196724035, 0.10632393256275005, -1.3313342301911826, 0.15548562422156237, 1.6012370165288907, 0.15096354220475297, -1.7191091850253588, -0.4799409397386236, 2.052005852708871, 1.4373646055707328, -1.8926828695048608, -3.124060704462173, -0.906835246052567, 0.589625858746578, -1.1647835500753116, -2.8276453497665575, -0.9741186658952333, 2.0242592903123424, 1.9922550362438716, -0.12609928689515404, -0.2324734354908754, 1.6561784550187904, 1.5499829542064314, -1.1393365814836731, -1.9088850150297643, 1.4602171647306785, 4.778227349604117, 3.7608741393135032, 0.47800583757548637, -0.5358761897644085, 0.4096281321865838, -0.3130780075210621, -2.5582046854823837, -2.4883333834855366, 0.25148623544023757, 1.0854621090212113, -2.060486143300337, -4.897543111624652, -3.376984199416095, -0.013953564231887582, 0.45497734888716657, -1.3940919983966187, -1.430296718073008, 0.6113668646327697, 1.0741987729663365, -0.5420129837222746, -0.2331384742365205, 3.32737352415477, 5.575580507842558, 2.993797349783645, -1.0901659102480807, -1.6361945179646382, 0.49787317191595154, 0.880110990920386, -0.7896453455986948, -0.8766171092026338, 0.9978089862834008, 0.8874518387526559, -2.2835563360110265, -4.00783342555613, -1.2936453703030872, 2.2297438526704827, 2.0358234518908103, -0.24484937612358987, -0.16774591588041882], 'positive_zeros': ['0.82019068857016229462907972727', '2.42984789122909523537898114360', '3.167233953130792849210948759120', '5.044314447245213161460938943506', '5.74547681564961332263521919268', '6.71721190351518430745142900013', '8.0806778015351116574378574459', '9.25944391383033771235229094672', '9.77204535778447846707350508512', '11.07839838779587240203505983649', '12.01621387998681008198903969085', '13.30430293411993906066473714242', '13.66469727493765526596090202036', '14.9981387249281524523714454050', '15.89727876653529630415584795524', '16.79232131278504827137844914073', '17.864638565570353653984858407813', '18.600157481853458774007155814571', '19.419142242646436462155988879782', '20.74274168079906144938298067389', '21.44158279587228840020603062745', '22.145386308683433534697729923922', '23.0679130200795859765771583158', '24.34467202146730336742365993675', '24.94364409332480860854938268745', '25.816353520484710409816905233', '26.539481659925758698392004599518', '27.70783894799754528469052002718', '28.663009210538206914523402630420', '29.212369090751482897216854529445', '30.011123334499439594611614872586', '31.155034553411381390818054403756', '32.06430536779752626445766708382', '32.54752420420170043427476071298', '33.778422151090646440695725998020', '34.28325637693701153510043110450', '35.301490946440176442143945409782', '36.13066974655575719278862795025', '37.261107778891726528191767228163', '37.512100649725382857227577492101', '38.605951658992531080406038510220', '39.46116083267685633045100595089', '40.42198608717469711338200433631', '41.25582283679749825139479135209', '41.6587276374825534198296299573', '42.74875089326103306952385186918', '43.629132613569412043298921859650', '44.74188788603718465813606852646', '45.007802566845653810444221853108', '45.72875402503099798823379076697', '47.12100644378616410219794250181', '47.65948082269419748997551198425', '48.38512665516849543350593958739', '49.249306933240608469726641818229', '50.019642958367868759035926024973', '50.848285738744337666344690349387', '51.91063899552333059960480567207', '52.24988980172629028721132391202', '53.46906822764742427939936756940', '53.821494604905122647562994085990', '54.90706486126429727058858129047', '55.74886311449513729031784803813', '56.41017980647906539106398944940', '57.30604498821722084654467900688', '57.91706221387876108840028568163', '58.67121165729656070509862509079', '59.86871037164445112512268595978', '60.53822521540396451960375296091', '60.89964251992498630692699476472', '61.796215594382095526230526140835', '62.9243172928359852477116663751', '63.65199344571411296969365457492', '64.16342179839441653820397134446', '65.123542005128090367727825560349', '65.6040346332090811165255564608', '66.952649579780088703405862577948', '67.28326249531002815924839400457', '68.18133649226016386531867545382', '68.94871686495604727010160140420', '69.53752327244742837086657281999', '70.73326818595446934309557965904', '71.18841845151049361099815936947', '71.974079508227511387644032835949', '72.82518654421114502808486854663', '73.69622623268529404736624349533', '74.00925365964538936605703741036', '75.33121783866452915117284405235', '75.85594918558944551306607081688', '76.6939156685376520786030651367', '77.12574633707121006641152648899', '78.1093969903370943947489436671', '79.13539538815858294285401494455', '79.6727600260460798368447354802', '80.32989880398170909477312871893', '81.08362279509834887345745669094', '81.842539884010617592390971661082', '82.97578869237356309641179603056', '83.366374148281027504975026046083', '84.28790646711396806769424307777', '84.621319414686756848275027498340', '85.833521922580622337459628185432', '86.52180315274953425818188757696', '87.34667020372282744597185565324', '87.68465777671393461954350706758', '88.794752538793235088239007699553', '89.44469646419007963829223810072', '90.13952423178356186854335733197', '90.97238209531551820188558664154', '91.89099622355075618506718722950', '92.26868381849685559843759452562', '93.090733637679752462802896400801', '93.957120218282401933844966005334', '94.70746857613705982444921143595', '95.5842940540973129030447487676', '96.020934130161547534830446886672', '96.83860845166835789526595693697', '97.51216308066386809300573292742', '98.56312050354264462010752208038', '99.23939329633682293608300716483', '99.78946676924966547512850927530', '100.40592255436904932770054290456', '101.24955644662926955488251288173', '102.35921877495170631959445436450', '102.91118924431143698578179633904', '103.268461862040624355073788431265', '104.221065632542199760298203603625', '105.138063582310834245735626272291', '105.65390396294086093077542905334', '106.53911157393738745420759628223', '107.40250813721526887987104107344', '107.64445489224526074287008180551', '108.759069101024522149918157191198', '109.35052590841475756633392137270', '110.17555060569230402887770370710', '110.90254119764165415451008990490', '111.61905738073807256979534648026', '112.25357861175225641481280514050', '112.945862336816411311695578557382', '113.86608007227068825364952861831', '114.47975160928229540216513842514', '115.49034120439880727624291127978', '115.92233696388816202033003222818', '116.21934143900391317870182138286', '117.77598220917011797191308082922', '118.11272399847054937624757263716', '118.83770067473752360180814988932', '119.54968134223543249799172605836', '120.09863809833625313086129500727', '121.168434286633873210717985881418', '121.74472517363736541120697197408', '122.68293880456186825143073827624', '122.95980459078507439714407691440', '123.861089388588979891527206982572', '124.58324250110302602461274844599', '125.541985474038332492952047056870', '125.978717649031748499911074408695', '126.84073451577975023849721673265', '127.38343176286884976151157171548', '128.23547636641556909781742955820', '129.05313835561611652150219744567', '129.44128429964247946429831947256', '130.57981305934823493725222623578', '131.17188652347158277396918700173', '131.619393694977073749283632326695', '132.35531877101388336407897367087', '133.38452745560665064065391631618', '134.0419967622184057714950338628', '134.67848676228278699162137001698', '135.28609603509045434960794364504', '135.92499743139267961038625463253', '136.84911708126062264794332924556', '137.62679523011785102456170582191', '138.37935518810191843057288807235', '138.7299246512384318855559357016', '139.59199994022165192100153214460', '140.214155293228084798406999904531', '141.420287140057114570723627040315', '141.73135625303112771578518428805', '142.31055729333454837042166371365', '143.154229418600834734264055334714', '143.926485463445375422623890673108', '144.59778828381145792751596849691', '145.450720736572186313006823224127', '145.839972616961945349162391982614', '146.90350172587623711292775999845', '147.40562890128507424417094948831', '147.889513471267764608143671829359', '149.010714413773558429383252759598', '149.60594428717952644629051692178', '150.2247869403279050590626110820', '150.964603836097958500092448467394', '151.58581498833681994564190709960', '152.24243978441786708891393780276', '153.24213470170085499768236847186', '153.847780339690396608407382298906', '154.52589530228949201206506801237', '154.958605766880303151354784876', '155.766883951730298450825688996800', '156.727761772479907156571922045', '157.45078208104290357417181558530', '158.01904099229282489441278165791', '158.401270598254565461376141015318', '159.333274410627627866645754393853', '160.28785921007487006255735407443', '160.74701858864464707962826332287', '161.458207351898565087963591386565', '162.188222146070596636426014780011', '162.89241056743636854250909303384', '163.40670854964950199160333294896', '164.419325532625541375573100514010', '165.016298736734542494644370465699', '165.60700033430556514387425892664', '166.36037549149203342653284482295', '167.116327979593111949139186238826', '167.60606090264528321805777311627', '168.48629242827591918207561596440', '169.24284247308105656772665693030', '169.949954881016171779594080335262', '170.39955645710173733273056168849', '171.25846875462036631067612148702', '171.67351430926004884682588026461', '172.99401326702131621827126883050', '173.37439958185166577706059742444', '173.880890799153155306758656048740', '174.45474527031676236425875077005', '175.52566065496215113716518202707', '176.10249676063864676409587655833', '176.832839424314815011999465294331', '177.593405471537568813276162450879', '177.99452641478810190386141080011', '178.71301454351047354171216175859', '179.66037817387130743745188496651', '180.32596551020441016300584684182', '180.91580884440092627016152452340', '181.58167479917655617762959858555', '182.24133500877701014455942691841', '182.953679754048871988377006918425', '183.86707527213251594178088270027', '184.22183657245450754371967905618', '185.09013786937233523410256692795', '185.91474206556839596527649914729', '186.29565801552789090754800246377', '187.0632979682939269970995521413', '187.70530305076643617407560706593', '188.81380843889677411474943433337', '189.237663662843610182369037842274', '189.63404266119530717442633984176', '190.59625014427213429990985340941', '191.07989915799607931420790585655', '192.189317531636581202011410231343', '192.5862888346104591341205885658', '193.3446275347108531750137286891', '193.95994162911825058853244418245', '194.40443972986838465825873168189', '195.524865492372817594241552786261', '196.17501999792538487014826289001', '196.73303739430029932993783745151', '197.339395954942943019282802822751', '197.91910384712463571976346047731', '198.84702191014839987880483156205', '199.6448472438814956385342496168'], 'prelabel': '1-312-312.269-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 33.529056535923004, 'root_angle': -0.042687142362950015, 'root_number': '0.964246476555339770706838344438-0.265007042266073732952667541287*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.042687142363', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.28212803120927421785490972014-0.0328904003571983549343868924352*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.82019068857', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.42984789123', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.16723395313', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 33.529056535923004, 'bad_primes': [2, 3, 13], 'central_character': '312.269', 'conductor': 312, 'conductor_radical': 78, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/312/269'], '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': '1-312-312.269-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': '1-312-312.269-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 33.529056535923004, 'root_angle': -0.042687142362950015, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.82019068857', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_312.269', 'Lhash_array': ['dirichlet_L_312.269'], 'factors': ['1-312-312.269-r1-0-0'], 'label': '1-312-312.269-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/312/269'}