-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_2009.2', 'a10': [0.01495940701526362, 0.9998881018102734], 'a2': [0.9995524322835033, -0.029915466169398455], 'a3': [-0.6801727377709194, 0.7330518718298263], 'a4': [0.9982101297677352, -0.05980415394503417], 'a5': [-0.01495940701526362, 0.9998881018102734], 'a6': [-0.6579387259397126, 0.753071466003611], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9959742939952391, -0.0896393089034335], 'a9': [-0.07473009358642425, -0.9972037971811801], 'algebraic': True, 'analytic_conductor': 9.329756776881393, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '2009.2', 'coeff_info': ['x^420 - 1', '0.999888101810273 + 0.0149594070152636*I', '\\\\zeta_{420}'], 'conductor': 2009, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_2009.1005', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^418', 'a^155', 'a^416', 'a^106', 'a^153', 0, 'a^414', 'a^310', 'a^104', 'a^299', 'a^151', 'a^243', 0, 'a^261', 'a^412', 'a^389', 'a^308', 'a^217', 'a^102', 0, 'a^297', 'a^388', 'a^149', 'a^212', 'a^241', 'a^45', 0, 'a^291', 'a^259', 'a^224', 'a^410', 'a^34', 'a^387', 0, 'a^306', 'a^256', 'a^215', 'a^398', 'a^100', 0, 0, 'a^258', 'a^295', 'a^416', 'a^386', 'a^313', 'a^147', 0, 'a^210', 'a^124', 'a^239', 'a^311', 'a^43', 'a^405', 0, 'a^372', 'a^289', 'a^188', 'a^257', 'a^382', 'a^222', 0, 'a^408', 'a^349', 'a^32', 'a^161', 'a^385', 'a^123', 0, 'a^339', 'a^304', 'a^170', 'a^254', 'a^367', 'a^213', 0, 'a^396', 'a^175', 'a^98', 'a^200', 0, 'a^240', 0, 'a^75', 'a^256', 'a^26', 'a^293', 'a^247', 'a^414', 0, 'a^384', 'a^379', 'a^311', 'a^323', 'a^145', 'a^21', 0, 'a^189', 'a^208'], 'euler_factors': [[1, 'a^418'], [1, 'a^155'], [1, 'a^106'], [0], [1, 'a^299'], [1, 'a^243'], [1, 'a^389'], [1, 'a^217'], [1, 'a^388'], [1, 'a^291'], [1, 'a^224'], [1, 'a^256'], [0], [1, 'a^258'], [1, 'a^313'], [1, 'a^311'], [1, 'a^188'], [1, 'a^382'], [1, 'a^161'], [1, 'a^339'], [1, 'a^170'], [1, 'a^175'], [1, 'a^240'], [1, 'a^247'], [1, 'a^21'], [1, 'a^197']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-2009-2009.2-r0-0-0', 'leading_term': '1.42918318161751621924286254742-0.796222130484210225277919401276*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/2009/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.636011689350409, 0.44997798532871697, -1.692292375562937, -4.343948458361938, -5.859743946685417, -4.972704444908322, -2.0931907226901383, 0.8351297001570188, 1.9422294595538452, 1.074458593840499, -0.19198361051022858, -0.2757457687786638, 0.7418349293334132, 1.3658746140023774, 0.5906291933154407, -0.8125780460877023, -1.2581943029431732, -0.4180402016432536, 0.29807459280530674, -0.34416785799788063, -1.5372231177466638, -1.3488648584049676, 0.40259905376520977, 1.1940703845005163, -1.2767880589394998, -5.488180050720867, -6.7579915016539145, -2.3253398840397352, 4.909008892676603, 8.91262144598037, 6.856734626200613, 1.8714056843084028, -0.9779194622162733, -0.3600492179967903, 0.902093234672741, 0.4500988711659292, -0.6050270724787478, -0.10268840256511873, 1.4081855633252092, 1.3544870597684153, -0.767041731878906, -2.190910728515747, -0.6938038902547576, 2.055955101684855, 2.6757248663202193, 0.7369907751833307, -0.8926622061393529, -0.43034932847190804, 0.4177058112768054, -0.39097287842988504, -1.6681086430952927, -0.8953846600418184, 1.3057472521724351, 1.6318857604002852, -0.5323420770740637, -1.2671503466787624, 2.3172041975062014, 6.907279892955785, 6.679634844877109, 1.4931252207721828, -2.3177624826800365, -0.3745836407919744, 3.8366084272362744, 4.015768812322092, -0.2894517433273093, -3.6797659699883436, -2.795731115276727, -0.2306437615622737, 0.354473491160329, -0.5856257835259644, -0.5477901856093651, 0.3959036899113195, 0.3331447844457372, -0.5137933871866032, -0.18473470856226187, 0.9328567920056487, 0.19429265111554989, -2.3268049856927386, -2.7526541919046537, 0.6047001478669609, 3.5416210586142594, 1.6747386254130516, -2.570820647058117, -3.159135049194182, 0.4394191236258143, 2.5157395732448813, 0.20478899510644516, -2.026586118545128, 0.2485811122973154, 4.055033041421966, 3.579197710096423, -0.7276851407223224, -3.0642951063099853, -1.2824251482966842, 0.7099464400718377, 0.2142075486764015, -0.13866738668783923, 2.060631185635546, 4.0890507675699626, 2.5567096350902863, -0.6404906401784749, -1.3177221165760584, 0.2791710117413405, 0.5451987091119356, -0.9507291188407448, -1.1065885539361007, 0.7154880186020324, 1.4985794385363975, 0.20032902698677035, -0.5108872410191565, 0.26005831756904707, -0.21876168779758995, -1.8357720494117338, 1.0646642147731025, 10.8338189172478, 19.443184422746004, 17.187971950421126, 6.27796105289898, -1.5692227111653516, -0.6625500695821789, 2.984378299752624, 2.6679346994509863, 0.03431792720571053, -0.43385006778542407, 0.5651415528055799, -0.010475553025844212, -1.2319363535121906, -0.48315604499033693, 0.9765652337747358, 0.33080153376366805, -1.1500360895379638, -0.35070669941552235, 1.5481092121930806, 0.9929037118978588, -1.101230664535296, -0.6836857039327867, 1.7988944601821004, 1.8759834353228857, -0.4438137517032662, 0.07161905562071742, 4.388055403245204, 6.4345877607686175, 3.0856606020506647, -0.28325767714797007, 1.0619751517569989, 3.2030756479546847, 0.9158051223922314, -2.7453350672252275, -1.839863161400669, 1.8094984123373297, 1.943523967156581, -0.8235619095042024, -0.11474361323171285, 4.649038791752727, 6.829143240982197, 3.5552017317828604, -0.20212034178800692, -0.4829913824608677, 0.3226222109590487, -0.3765140297810444, -0.8308794712622483, 0.28479426489312093, 0.8004520112386071, -0.051420853384896145, 0.41693051885261645, 2.4718736842795237, 2.2928693558300797, -0.5662482532169406, -0.9979360705168488, 2.2912423099570645, 2.8450543762672096, -2.457516561821008, -6.0988850415536735, -1.381838395018863, 5.614483670374398, 4.906704889898277, -1.7723882370039161, -4.584502211828402, -1.3628202169062429, 1.0386205587064006, -0.4533371622479546, -1.6460947924012972, -0.46669574567730765, -0.03523112784228402, -1.2872213561868042, -1.2166351763746779, 0.31916846449345526, 0.11278944965511263, -1.135634722727247, 0.7920827566172497, 4.991497490218633, 5.541162355714035, 1.5801641195291372, -1.1008782089885818, -0.04614160560528959, 0.8305528403986465, -0.1848492932412977, 0.033351503333447656, 1.5753038983393262, 0.4128610274011098, -2.4227721450187745, -0.6282984137524594, 5.290254931474714, 6.440205084910024, 0.409254687284043, -3.296874981082667, 1.408416489954492, 7.102774083746478, 5.478139599197327, 0.2613387885685739, -0.945054839678702, 0.8106133124802032, 0.49396364998349074, -0.8631270333120108, 0.24307518246345647, 1.9363524080838277, 0.8918475177667323, -0.921398901707739, -0.45370726899964436, 0.5604637048761414, -0.031483008127265726, -0.27124855548173366, 0.7417313041139948, -0.12456355117103192, -2.7438868764420836, -1.4960103589266676, 4.13446284330348, 5.953716177942432, 0.6691826724814585, -2.8671112306181574, 1.9190250683962284, 7.711118213836347, 5.612053131098223, -0.37805456399971754, -1.6934054584013147, 0.49472618708247246, 0.27963602264914483, -1.1906893598082189, 0.08067593154793774, 1.517022061751268, -0.7422971767101079, -3.123446907101595, -0.940939313488307, 2.445795137946895, 1.8460590043644984, -0.4752030952547994, -0.24506068796411498, 0.4682961768311804, -1.4790826145598968, -3.2211524980592823, -1.6818121342310217, 0.24818494264128402, 0.03664880080464449, 0.5731741480870274, 2.9736913560529223, 2.8715620683691294, -0.5667158251875837, -1.6259985125931293, 0.7460865527200663, -0.006501717728339332, -4.292965310091925, -2.7120224173446945, 6.881954015783817, 12.32468968102124, 5.820150541239151, -3.3593004581850283, -4.290610809255738, -0.28898438042675256, 0.410481835475651, -1.3876557265094442, -1.0836523755813825, 0.11616764981089542, -0.37564583336706897, -0.715036216937831, 0.21477699621891652, -0.15371943641868177, -1.6071819493283441, -0.4491578038910451, 2.276418164061503, 1.6225917495727773, -1.1226098824412762, -0.046797352324394415, 3.5841238767290955, 3.1230189781438216, -0.5807726007045861, -0.9772745792665326, 1.0155084356606572, -0.5387602588813549, -3.1058597872711857, 0.4747148967029012, 6.839431890452494, 6.232671449869704, -0.2659320694338407, -2.9598365809807183, -0.6140035719748737, -0.13857086467794447, -1.933897110251036, -0.5920235601962828, 2.544687914490836, 1.8356629494157533, -0.7369598685170883, 0.7031464198948155, 4.102637301749028, 3.5292698297145, 0.42326360050718875, -0.19561714731299215, 0.6818419041647681, -0.10465576135427963, -0.8301350929591386, 0.2893768230635091, 0.654380656825959, -0.28804860448723135, 0.7937664532057005, 2.6162199368229215, 0.4652735228646241, -1.713336552296899, 4.971865975137126, 16.176786838768663, 16.819693974236078, 5.012160178905857, -4.274499608368376, -3.035906340779841, 0.4124265906850705, -0.3742280322558322, -0.648638999128748, 2.2772457493957745, 3.1871916392415356, 0.452153345735794, -0.939607798657305, 0.12218287431488593, -0.024312530045018665, -0.769626704596358, 0.965858091268605, 2.689784838483128, 0.9274220735720341, -1.0953674032439884, -0.13351889082146648, -0.01428053502422201, -3.1015744377881855, -4.086296588651615, -0.5881700854128399, 1.0942909479406173, -1.853644949614734, -3.302196681787419, -0.8490482756076247, -0.08742346913997759, -1.725670352991599, 0.2290273198350371, 4.347584399573563, 2.571239439031482, -2.998945550747785, -1.9479988462920703, 4.881970456802149, 6.157427684193646, 0.5977465311269473, -1.7653564348676087, 1.515574152505188, 2.930099199014253, 0.5185433284768389, -0.42626260614963324, 0.8052612372609423, 0.636385661940573, -0.22032293921005872, 0.3284301943781831, -0.02188166058813066, -2.192254115581804, -2.1593269396854677, 0.5970521709660125, 1.2184953719708844, -0.329617063060761, 0.5337053354308527, 1.6801456353700641, -2.141511263085156, -5.803633220515371, -0.9971840174722113, 6.078364672332434, 3.17608934378144, -5.867612861556976, -7.343945174813938, -1.2456757914350611, 1.282563151628064, -1.2752568342044317, -1.609329434482385, 0.5698762265099699, 0.4316969019958608, -0.6810111166242173, 0.33433991339470764, 0.7093677450489673, -0.854988491112757, 0.4732555787966818, 5.0859916771953575, 5.914678256487397, 1.550985915889893, -0.9395967642963095, 0.6029152890787327, 1.1175089367892357, -0.15282610786988593, 0.34941645608026245, 1.1799345810676325, -0.5226197311557914, -1.5017326899877437, 0.09605861503979124, -1.0645240548546122, -5.453674696727793, -4.137451005820283, 3.9371319979014445, 6.690895859779394, 0.2937320751775902, -3.095347795834676, 2.2791472242385566, 5.939221434641717, 1.7805101128756036, -1.9667040806926943, -0.22935622187462557, 0.9468492024008569, -1.2234947656534767, -1.699776436899672, 0.3681423017413883, 0.5896044012833654, -0.6441745434630074, -0.08322484692814443, 0.7202239899947867, -0.09553547518584334, -0.08724219166929804, 0.5127391145904558, -1.9864147433212778, -4.623719599121196, -0.8356014147178119, 5.357731986186797, 4.561820675224176, -0.420351735140288, -0.22868912858003343, 2.568394789997967, -0.1819688588628963, -4.487217003417589, -2.215956732204856, 2.152101557942953, 0.9620403754480789, -1.5062073902162516, 0.45341540704563, 1.5946846976080327, -2.2166690151072816, -4.361008061863283, -1.0337350898911664, 1.2767020766003965, -0.3845525864816778, -0.4530089950256968, 2.1087148527837476, 2.055992106416473, -0.11270146788106772, 0.30981004533880463, 1.542263181981561, -0.17385658350246375, -1.6910760368718585, -0.004328641984059681, 1.126836787479281, -0.10764733805283927, -0.16355765529927618, 0.2421302364144188, -2.4945275859038203, -4.085984968705349, 0.2627878787724224, 2.5684228744039963, -4.533681445242321, -9.931800131810373, -1.1543613263418377, 11.810506034704481, 12.130119178901326, 3.178655001237899, -1.1355861051841494, 0.23172072428025398, 0.4491566556900197, -0.30248118250524486, 0.17439638037471938, -0.759002347608988, -3.036781817784787, -2.4443766692433133, -0.12611577192868484, -0.3742738525380801, -0.9933139684650467, 1.1440802375285357, 1.7251117260925122, -1.795031464997292, -3.256517620694214, -0.0055549763781378506, 1.6757725094454003, 0.04653395787444969, 0.44950176009741394, 1.5689548822491375, -2.356731339951883, -6.770503259241572, -3.9163810869517044, 0.5124180537683485, -2.3535281489308444, -6.860821493398049, -4.438583412514075, -0.1511707057738504, -0.4031352605721, 0.1530579807229422, 4.757593769074386, 5.5681492229178104, 0.040097868084780774, -2.7127180265924533, 0.5131285536968411, 2.1732795315121374, -0.039537481333728836, -0.6851338516088183, 0.68464145702281, 0.39602132960238495, -0.24724413187227282, 0.7303919426602161, 0.7290266011963547, -0.3999927820221502, 0.517962658679263, 1.1978814604347983, -1.6017292815845257, -1.9267857509943016, 4.580475938149201, 8.385604280160658, 2.4635298696763765, -2.5175061781512125, 2.314911992796529, 6.918181491234504, 2.3260186689096876, -2.5347526616933505, 0.206262065097007, 3.0993253492643436, 0.5491109236004245, -1.2063718101436316, 0.6694269743597031, 0.7624527873470305, -1.2859228839871943, -0.8886349689546823, 0.5177991753453544, -0.09569861415286975, 0.4025589996736481, 2.9028851516683867, 1.9871186166940484, -2.0190489629434336, -2.1408178331197645, 0.89681711642928, 0.32592474546849326, -2.244088522823736, -1.164882353199555, 0.7206304018338148, -0.6241095850200937, -1.2750342388290354, 0.44979765882377565, -0.28859207153712213, -1.6248054189257606, 2.993594033462764, 7.300869076329846, 0.17956497885178294, -10.934739424464192, -10.222283297240729, -1.1543571252345621, 1.6202588170701469, -1.4716703806686224, -0.9072352512295799, 1.80653381875224, 0.7439903251708918, -1.0997693606438603, -0.1972525124375786, 0.11715939731105249, -1.0077904237661581, -0.1025154496844753, 1.3647825776186377, 0.14333179512231298, -0.7432247891798816, 0.8421623895389, 0.7208043301422585, -1.4616907845396299, -0.8909215284207324, 0.34731224068297906, -2.312064439049694, -2.1936663598830557, 7.085072923730663, 14.694520472929945, 9.476321854725844, 0.7262218361187478, 0.6455933264565659, 3.306042110700667, 0.3799973890771757, -2.3587082778294337, 0.07382735805144928, 1.609125674070063, -0.25605738389939253, -0.42737704029491347, 0.22624767584048044, -2.652027725762789, -4.638378646544048, -1.0221758587912333, 1.890033201407742, -0.8876857811460117, -3.1938656884457983, -1.0815102837450703, 0.42787420710846635, -0.3964219106373459, 0.022593208625690107, 0.6051677771255195, -0.7792150101919469, -0.2756894506635231, 2.8711439514374457, 2.6238760311143574, -0.5166760972865774, 0.07242398697006387, 1.3752282179867756, -3.015860834422591, -5.2760346986673685, 3.379477557913667, 11.815946574789457, 6.9381386323456065, -2.2009124610726873, -2.2704003635650754, 1.0952291284859483, -1.1479326615986412, -3.6930782823210513, -1.094506941306423, 1.1990158540522007, 0.028792952765319214, -0.5078536619903112, 0.12696622961175488, -0.39858690194754126, -0.16817341902323577, 1.1403270710662703, -0.3504562402050861, -2.709489203449667, -0.5298934797859436, 2.1924877598758052, -0.8079906670092422, -3.913592489354864, -0.7966947500517562, 2.148948085584303, -0.13244605100654722, -1.085936977178959, 1.4167564406785822, 0.3291104833006324, -2.6387352018039145, 1.1277994492493773, 7.04336065917945, 4.656291311395142], 'positive_zeros': ['0.39350041147099782130198352698', '2.084127280319604517349648042242', '3.06246316196173599814054445045', '3.5414722218951308516091182771', '4.502275977335351721047201560', '5.442922824750224967067893506720', '5.8392488912093396782179993422', '6.80872280234318924713868857078', '7.386841141749764633641153591629', '8.53885789863729414830147447041', '9.84039465372309950342596641969', '10.38348353132542290666160360385', '11.05035897399342937212267679548', '11.58497667784374447484413326940', '12.40086925258881839526113852364', '13.201164670656943149333739798', '14.16697443820943706935549603507', '14.80509100035854926234756627075', '15.224505702736666045332150939257', '16.06398510559665290171525334505', '16.80587660261666371801263784891', '17.34032280368190065064816897597', '18.523551226684477728909561881', '19.08955047676342036978020200700', '19.98151684640586479679166839435', '20.97893670235316636818154976977', '21.37666256186859356911127378827', '22.04944534876226919550393180049', '22.61651064213346437955736160235', '23.17404599880127212504201489449', '23.778020814356631331495550822253', '24.64237232200096161856384406854', '25.43076077672176199632583568177', '26.215552878660210820223467268558', '26.893908252081436666716829053009', '27.48088761080317414511681439837', '28.386288356617276428825509304518', '29.22103302672054826044582048851', '29.74931710189084332807970981808', '30.038372480124381601121592224688', '31.17679259232966568406803052778', '31.81988978150836539821679522260', '32.31361603123992064476533965048', '33.01291147001475071732711844001', '33.7929543809302776733030820401', '34.27601190003776416863465967293', '34.64225742322819118615877619879', '35.25796385421136056056359939220', '36.774659618440912629963190980', '37.23891058933773306855132369717', '38.130485599961800715112051532328', '38.56291480471965668741400922466', '39.060206405271085586658926607929', '39.77380557666268452436142284921', '40.371819852031952923592900098456', '40.99008450966008809057721692706', '41.70047032682930757666540825335', '42.27654074875456905195349096681', '43.05800630483320416992140548493', '43.42995973643000677134230472848', '44.6320667645291829845826704507', '44.869565919714181220496189728651', '45.69179311292156220459447921865', '46.40000797963484402834208788914', '47.08511203217677357354482271011', '47.51000880874864292105612460074', '48.72231201546497839896802089017', '49.20420081123043608066459454379', '49.57646066746894576898737232496', '50.24609964977254450163722562979', '50.91554327052706055250095636536', '51.153228860366146478178153123242', '52.12450326711959812206481857564', '52.61330556256344193423028322084', '53.315880005716509522808568588490', '54.11643421676269434464746080208', '54.91722586970900608455732698919', '55.74171518054191126190652356024', '56.18655647810429358398706137128', '57.00997898441137415118403104822', '57.171642897438609046962981567787', '58.04989429451538354078292806610', '58.46192969448577704999165084094', '58.99269065911615731183933344431', '60.12826826711336880335207171003', '60.63320011039708494314263403276', '61.196219550169048377574563251798', '61.55515218410905395484910442201', '62.229686189101885478484065729540', '62.84983547132562236610073169879', '63.76890758058368627830328459709', '64.3121677739694922875091416988', '65.33422747760506060883099483869', '65.78984379488191841255144012913', '66.34125903512482479641960331138', '66.839003494851162842167001963216', '67.62663026297177641197491367224', '68.22836917227033913707111490528', '68.739514952925900071120466577575', '69.15554884522068216648469424544', '69.67098865676689842806620503954', '70.40563133843446484074015892361', '71.28331059617911287600669155007', '71.789868875369130084083465827748', '72.787467313258371453420803118115', '73.357950854720390351575786402245', '73.79849095625511761307498224487', '74.36411132759218885269497429405', '74.931287715178468159551334425187', '75.697711652510944907137096440', '76.47676446653341003611250261573', '76.9332973734771664623549357258', '77.308952072841154837725733045', '78.366125450198659251808589242014', '78.77354170612880545196484168041', '78.917086192186392228640644927266', '79.94887102931276040854875826744', '80.52723128251300643293426979636', '80.93693552743147360032972456971', '81.66657116771489754423288025779', '82.67676096689174245397126335933', '83.46836876064965251624081110369', '83.82347576303688734051278681698', '84.628786775945901669694521686739', '84.86786485225906171374218354806', '85.549996007138034290932739933099', '85.902325077267792892026914424688', '86.61099822259596789949995051974', '87.35414099456830242101291404152', '87.81672616528836316076119505792', '88.693267792998855593514134131320', '89.19810234188444813079619697532', '89.63563937290078773653066815895', '90.28977945889891710873021795700', '91.23631215703085969624281118551', '91.97733401456454808829041643563', '92.15530328820349419419319653500', '92.86638599682018803775627322216', '93.63113638588148072360966761670', '93.9944800395601964115166458577', '95.06674804799450115087347942798', '95.37508810539869492431122096109', '95.91361958739667079073051933787', '96.49694412889980317667167390169', '97.07138596778875256072285545956', '97.37142101596727043705924708409', '98.16297019197907332365425042220', '98.57783377035810873000740794040', '99.81607987990922334064625107922', '100.55656771242309156413781694902', '100.87071612806913585854233727384', '101.338442694347622722018460078074', '102.23900057042902749705339829693', '102.77582348452136043558739610833', '103.117950708994347041754044626995', '103.62663797042328081597583390689', '104.47867413735638626610873912285', '105.02831394841303255590905125811', '105.31005829386623978052527358846', '106.30000678312325187630371368439', '106.71132501265843360052861433482', '107.63931665441576617209061020996', '107.788191924219822052057970097775', '108.420663672113678273514125227376', '109.19696000283450242442876990441', '109.78203645831071550651041521423', '110.659976450320814290178669829878', '111.12814191787495899628767025518', '111.94802757661118366749562121860', '112.30737496815672829629972788208', '112.99560735260537120748660847789', '113.308490676008769849561205774033', '113.74583222654088941093787634253', '114.61822711722319969434241639235', '115.22825360937280135944658094366', '115.5392872052475901318216112414', '116.12096679848400095224505002286', '116.9117871217572301944167324064', '117.60783664565933791631583316076', '118.51167458360666484440771344861', '118.92465246179807916744205501686', '119.594149682624788921352239845742', '120.08898922628452604682087676540', '120.55550404104672294529742394228', '121.08189030587760857028024627324', '121.52042312629298048714974078632', '122.62135806936732492824583885267', '123.031333342414257626335339434546', '123.69908909364095157961073340643', '123.97773738189713187273813605628', '124.61571993466936253437388727706', '125.29062792870041101688335087237', '125.508730531941504475509516145', '126.41743027580417627717510675746', '127.20018734870942339044783298263', '127.70885486274460498741236247563', '128.53940848123612080695054726168', '129.08891834350870999923821575740', '129.534315399274845512561296325125', '130.25304047167856482421609884155', '130.75760292181987603173058180803', '131.26981808253375665493127935278', '131.84362086410003385350272385880', '132.21595895366174810820670783414', '132.61760319285179351394734455395', '133.47522532277440699989051030624', '134.3394186878095047697549941481', '134.70957616943291857213910497727', '135.30170660822122875776309863838', '136.069425622766695146653743048680', '136.64962909563739583398670475771', '137.14120666957174656955140824550', '137.66115383082166805831918029378', '138.52050551399478333368439610720', '139.0037352097423852165658093536', '139.43764950992979619831639953340', '140.28812396799716630016305577813', '140.56463459701522163815496380501', '141.22904688485988975492021526038', '141.87559045094025811812203678818', '142.47349494683967746338418277409', '142.86398978881919601044747995524', '143.17951807136531193786799318131', '144.04776279586176961758559571371', '144.52799112517231387923189530245', '145.33741544476838224483694188632', '146.40411892471610456310842007744', '146.83193497774678067639150253083', '147.32533694446030857703582022386', '147.712145390196393828929704514820', '147.98534264125437459312542821327', '149.09598910524907579257633462696', '149.274466934803256687328598206877', '149.862504923076083485619698764323', '150.486059343330621445950986602884', '151.25047453932522044521261952587', '151.88612087731904215726137347582', '152.10097888988893476520265473817', '152.67529829251654216023765789819', '153.67832003411032354258696645832', '153.90623107627753876790154956083', '155.02614426545617977048599911985', '155.21684507230202063847455866747', '155.60935980791067234603236540796', '156.56464808650165821353042714448', '157.14673422030987142597969498944', '157.807108328493560274848532318177', '158.27645412003862244601940200423', '158.86427473172818236020951764082', '159.17788167417483833969411484769', '159.86116899691793141808478136233', '160.21437556049346612760997693681', '160.7882223947581199794950398796', '161.36912608911618281714078887250', '162.28770469673549940438235641168', '162.711289259481278735861512133', '163.54374658258620564665236536724', '164.04891277500984453649893885110', '164.737954158303236989853123255877', '165.215683680677970193598945576535', '165.7379177541891223061011335973', '166.40600250863150340828678139954', '166.84229517181966017210690441587', '167.11611155781729935609706631080', '167.9632795021159549172270684360', '168.644254697617925565827522375575', '169.09805306770589531896784833549', '169.82931849414615018233834092624', '170.21656607332691773447123170679', '170.84874497741698639883063995122', '171.209545021818023029508870726654', '171.7232348737521040291111673160', '172.50460772824870237264798682839', '173.48968890477970494522549784795', '173.91593629646254858437029282462', '174.46383195381839600606729323040', '175.09089057094082058820270294721', '175.67379234121882346525511705399', '175.97337177322885519605386838847', '176.57847683436362234565840799560', '177.21088038409843071381344153105', '177.66781534234986656309361513371', '178.22609193216897516116944108131', '178.88800260239469147423245889881', '179.141766164659465984906963192395', '179.789333887074812603462618520156', '180.9934317485585557391794464156', '181.18426263954458126916194505112', '181.90127200677700413516178125509', '182.49307983382902625268943320369', '183.08315197059281009725011952614', '183.541114159677525183889888474532', '183.80247834074792464858070876905', '184.75497012908883036850814518331', '185.24360436735199674236576996834', '186.07948983516165781672596846460', '186.42839689645195704797809684455', '186.86905230474676979450429015974', '187.347245220812046221737077971315', '187.84413565023716814582004252794', '188.68376653008907695416381407200', '189.053364017346794379304323821205', '189.51598621065149697671889291053', '190.22060152576176626306813830456', '191.152420344093702358061349285230', '191.732806373037502387361882572451', '192.09564454653374849278621675024', '192.90996991846694057539708132677', '193.44328045627226007341941859464', '193.96265340975673542501722251254', '194.20975135538666262511200984884', '194.725255718347989795875338121820', '195.275004392820405874883495279209', '195.97877022707844040703035044483', '196.50949286471820476609688497120', '197.24048663198782473558696311362', '197.79911793557746518433430066363', '198.26536784322816123051752951212', '198.77779410468551601373553051443', '199.32223453321805235670171509393'], 'prelabel': '1-2009-2009.2-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.329756776881393, 'root_angle': -0.32358799291542456, 'root_number': '0.526275681606027244306262025847-0.850314004912368497459587801619*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.161793996458', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(420)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.36940159903328311942591516744+0.112911996632316340160125681736*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.393500411471', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.08412728032', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.06246316196', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.329756776881393, 'bad_primes': [7, 41], 'central_character': '2009.2', 'conductor': 2009, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2009/2'], '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': '1-2009-2009.2-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': '1-2009-2009.2-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.329756776881393, 'root_angle': -0.16179399645771228, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.393500411471', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_2009.2', 'Lhash_array': ['dirichlet_L_2009.2'], 'label': '1-2009-2009.2-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2009/2'}