-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_621.11', 'a10': [-0.9283679330160726, -0.3716624556603275], 'a2': [-0.9679487013963562, -0.2511479871810792], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.8738493770697849, 0.4861967361004687], 'a5': [0.9919548128307953, 0.12659245357374926], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.4722710747726827, 0.8814533634475821], 'a8': [-0.7237340381050702, -0.690079011482112], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.8839118757806594, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]]], 'bad_primes': [3, 23], 'central_character': '621.11', 'coeff_info': ['x^198 - 1', '0.999496542383185 + 0.0317279334980676*I', '\\\\zeta_{198}'], 'conductor': 621, 'conductor_radical': 69, 'conjugate': 'dirichlet_L_621.113', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^107', 0, 'a^16', 'a^4', 0, 'a^65', 'a^123', 0, 'a^111', 'a^14', 0, 'a^100', 'a^172', 0, 'a^32', 'a^138', 0, 'a^159', 'a^20', 0, 'a^121', 0, 0, 'a^8', 'a^9', 0, 'a^81', 'a^17', 0, 'a^178', 'a^139', 0, 'a^47', 'a^69', 0, 'a^183', 'a^68', 0, 'a^127', 'a^37', 0, 'a^185', 'a^30', 0, 0, 'a^11', 0, 'a^130', 'a^115', 0, 'a^116', 'a^54', 0, 'a^18', 'a^188', 0, 'a^124', 'a^67', 0, 'a^101', 'a^87', 0, 'a^48', 'a^104', 0, 'a^19', 'a^154', 0, 'a^176', 'a^129', 0, 'a^60', 'a^92', 0, 'a^175', 'a^79', 0, 'a^89', 'a^36', 0, 'a^144', 'a^62', 0, 'a^142', 'a^94', 0, 'a^137', 'a^42', 0, 'a^165', 0, 0, 'a^118', 'a^163', 0, 'a^59', 'a^39', 0, 'a^24'], 'euler_factors': [[1, 'a^107'], [0], [1, 'a^4'], [1, 'a^65'], [1, 'a^14'], [1, 'a^100'], [1, 'a^138'], [1, 'a^159'], [0], [1, 'a^17'], [1, 'a^178'], [1, 'a^183'], [1, 'a^37'], [1, 'a^185'], [1, 'a^11'], [1, 'a^54'], [1, 'a^67'], [1, 'a^101'], [1, 'a^19'], [1, 'a^129'], [1, 'a^60'], [1, 'a^89'], [1, 'a^62'], [1, 'a^42'], [1, 'a^59'], [1, 'a^29']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-621-621.11-r0-0-0', 'leading_term': '1.04588171181196205142286355821+0.179837009335401479450775762560*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/621/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.0612303732128208, 1.18743624893355, 1.0902573413561287, 0.457109961769169, -0.5445262064945857, -1.350975808265616, -1.4254423605924298, -0.7484889187192545, 0.002432102366597254, -0.16183817567333986, -1.7501819567710495, -4.16799555090756, -5.866029375302407, -5.347966725253541, -2.38251491228855, 1.5711074797428572, 4.234354831897698, 4.1476441365961625, 1.7949347630487886, -0.781768457715569, -1.6512806963917601, -0.5633449026490224, 0.9593524510459293, 1.105559154928787, -0.5196979653732167, -2.5641746357279485, -3.27342570888026, -2.1809687753093487, -0.4635676741283722, 0.3664866376800671, 0.035553927715910254, -0.33752322615325486, 0.33071436920734365, 1.6832778306872123, 2.1962274184243484, 0.9416206256834502, -1.1298544936636137, -2.001128667661777, -0.8109300410866473, 0.9656094272059007, 0.9268699036137437, -1.541724769061378, -4.2268462116742835, -4.139205452818301, -0.711569428238277, 3.302433090493901, 4.416181012818096, 1.906739814395211, -1.4867455387910131, -2.444512405877899, -0.43700220596681716, 2.0118481876619767, 2.2894316226384834, 0.4597140512659804, -1.192492900314105, -1.0361830925817976, 0.13991895291121034, 0.45301454619663506, -0.5239302858029101, -1.2753093177398427, -0.47901347427609015, 1.0881334592951344, 1.4640675486123362, 0.14115500636586303, -1.0536961092338715, -0.1972842043793016, 2.115901518465763, 3.278785502081391, 1.9232141793060245, -0.17981505377963103, -0.2772268225964563, 1.585553674791196, 2.041526838159001, -1.704781170911869, -8.021378034432376, -11.90530244658393, -10.125915609516095, -4.610551959943928, -0.17234794528868883, 0.6402463899199778, -0.4508954343723143, -0.5030874191830673, 0.8160514328266, 1.392184768709037, 0.08881910166521888, -1.4666122464374836, -1.1137546852586668, 0.8017084055832744, 1.8397282205345227, 0.7620722624580892, -0.8596650988725637, -0.9334841918194173, 0.22643317958075246, 0.5119766893649766, -0.6937987297755367, -1.3919598436628475, 0.0752402124345359, 2.0592454461015617, 1.2497369870869774, -2.6903076286016, -5.783402187065038, -4.181481797067653, 0.8746004646408133, 4.120143983993173, 2.40703727951477, -1.6900256918953402, -3.298988840188584, -1.2076384308878052, 1.2120152494458403, 0.8539275728841932, -1.2255492083908726, -1.8158126587737673, -0.19745803272504112, 1.1132523151903781, 0.20850070687310232, -1.5163974864080436, -1.5713637136785048, -0.028401254850501975, 0.7566736823122278, -0.2295850883048349, -1.2217387989405828, -0.5697888276525767, 0.5515537127191371, -0.01578785935744772, -1.6422758235043733, -1.2133283584711658, 2.2681437252219316, 5.37065127809897, 4.243733373859601, -0.057550011932908124, -2.5118789191121467, -0.59986760300504, 2.362211159412829, 1.7560421869733345, -1.995801580876298, -3.9597794431927076, -1.3566220525416914, 2.7731930011683006, 3.726957664672212, 1.1444100181655474, -1.2280703318265953, -1.0017868246619965, 0.16453054295912606, -0.1127591947485068, -1.2413632451089054, -1.0924652945944544, 0.1834389820192952, 0.2619931851108075, -1.4659510762125267, -2.5385331654416428, -1.0675401056100378, 1.146905118214642, 1.099148442092283, -0.8903376431993427, -1.6461064526521225, -0.15197597606013188, 0.6747836193752148, -1.3092455993375842, -3.221054736456882, -0.4761506911277341, 6.257524946421171, 10.616884056378785, 8.143064438977243, 1.8746407679337498, -1.730407087676408, -0.8731335559154042, 0.43446776148527033, -1.0888413556953935, -3.5838055212428754, -3.565044659153827, -1.2765252452056595, 0.14406782159372306, -0.3060614455801686, -0.40310925465287495, 1.1080024959383936, 2.1438022401651353, 0.6562576983809164, -1.7731169190452145, -2.092695520341684, -0.3827400110080682, 0.47421659357987883, -0.4544934641493647, -0.751769594810736, 0.9523375866029858, 2.060978909388462, 0.011704752463263702, -2.668485916811545, -0.9478537646832601, 5.1294593387037, 9.123200878362042, 6.156974267084358, -0.5656019936577741, -3.954544485124214, -2.053372449627043, 0.6232679631341238, 0.4075462000730431, -0.8201088977764104, 0.17378819110357951, 2.3477682073857618, 2.1687969497594883, -0.5334674185537938, -2.1549683039306777, -0.8138286310022318, 1.078772981937905, 0.9166841986813654, -0.2979649946053331, -0.3790423774274966, 0.026011774918523134, -1.1184198089324298, -2.9010688464663743, -2.1653233385865613, 1.1921583691218605, 3.1779490482746797, 1.5456928296975865, -0.4275108716222138, 1.1337321343254954, 4.21632667384961, 3.3882125466321167, -1.8026622877055594, -5.344087482589959, -3.0829957270565393, 1.3106405987115468, 1.6913788876574043, -1.8879439684039498, -3.914692116472632, -1.820222731034426, 0.8515089220627382, 0.5275965617681305, -1.2209309315621208, -1.0461050065223907, 0.6174101795407793, 0.8324125438164589, -0.5861593674558476, -0.9435595241855119, 0.4697612000933881, 1.189629807439357, 0.15004319806230362, -0.10777665220739845, 2.1747180969844484, 4.365520930726596, 3.279068966562727, 0.5184661374579225, 0.11992470721319685, 1.8360564147707554, 1.295154172603473, -2.5187105272841577, -4.629175109304211, -1.5200418746360707, 2.5665894841438295, 1.0548956613514129, -5.259135354531983, -8.894524950912903, -5.959472732695147, -0.8709105199815, 0.7167538813656565, -0.6771121940297993, -1.1011537770125481, -9.623018344452361e-05, 0.07646910624586185, -0.9825958999132454, -0.37930686700852667, 2.3020982134285437, 3.662096259243581, 1.801049051778114, -0.5697576869762098, -0.5577482266464076, 0.47946021483572154, -0.06995560737712742, -1.1916891583669709, -0.3023225790826011, 1.373374508969776, 0.23725515327956667, -2.9606071712918167, -2.9623691144706092, 1.6947156777682126, 4.9659416894201796, 1.4466074998055012, -5.2966002823672325, -7.33899647945813, -3.4155579405362024, 0.13334290947071825, -0.7628826222191535, -2.7928346651127662, -1.8738694717728264, 0.2325768729769321, -0.3280888137689326, -2.672097724151123, -2.8336784743040044, -0.47930784417025435, 0.9020972350698728, 0.12581832955975605, -0.10424184476091915, 1.4961392403426044, 2.354808615574029, 0.7741420028322091, -0.8416029663490855, -0.2236315632452794, 0.7029158543609526, -0.4177326991393272, -1.388445757052161, 1.0580449236282206, 4.482759937538494, 3.0947630734129, -2.9819043127389993, -6.566272481223083, -3.510025448209571, 1.339069238820728, 1.8178735280682845, -0.363876068442877, 0.67015159205061, 4.903103494050143, 6.4331686585038526, 3.0511258433393222, -0.4442515338943461, -0.011447976831331374, 1.9758873330456563, 1.7032015005108383, 0.10843065947007029, 0.19197789082768396, 1.3805149049311367, 1.104263368936501, -0.04450260836776536, 0.48435954502966616, 1.8762102079075547, 0.812633407728799, -2.3535867992291766, -3.3314306755280674, -0.8439187175555465, 1.1288415557333202, 0.1307674315768448, -0.7117341212664106, 1.099575312701702, 1.7695923465914598, -2.8820922848202537, -8.950495711565097, -8.547601574543963, -1.5252363391919617, 3.674241261946876, 1.9576203466474031, -2.0159086948665146, -2.095036335972065, 0.47916086136921976, 0.9462404376841642, -0.602071363181493, -0.4760733146492176, 1.422700151836107, 1.6632404092359232, -0.22972075552891041, -1.01223194505554, 0.20401926309066812, 0.4322832925218265, -1.3903538398640038, -2.1354349753210538, -0.16102417473241454, 1.4278675517480353, 0.18178489614659912, -1.3227672404631163, -0.3428741697008978, 0.743515071616802, -0.9974712782482352, -2.4344605256964664, 1.2597789559878483, 7.218590517490112, 7.177060969435636, -0.19833149318391613, -6.376483872673554, -4.898371017699902, 0.13180020007796206, 1.543145304237608, -0.4531633557750239, -0.9697910066931281, 0.41266344790008724, 0.03761553494141682, -2.134267940852693, -2.1154750135379783, 0.7941395039373391, 2.5028279564331255, 1.0860805362034027, -0.32194396805289255, 0.5398158554547628, 1.4011478778451918, 0.30031083354775323, -0.7265551690170989, -0.0721440554264443, -0.17255702636221018, -2.5659338642506473, -3.4598708257283786, 0.5080036292205343, 5.359614785515326, 4.880556861544415, 0.5213933589760322, -0.8555934640069837, 1.5984395784484984, 1.3676877727673427, -3.9978365988138345, -7.917255833387703, -4.947601619541541, 0.7245625596238894, 2.2423901522351946, 0.35513491050689083, 0.4194629733001473, 2.756653416004794, 3.0539225901368585, 0.6421808687870334, -0.6078600660644384, 0.539722280048107, 1.0216254690470816, -0.30599600663013493, -0.7596166461121088, 0.4651361600077055, 0.39697627943716585, -1.8123265183885722, -2.5974487740900183, -0.38478804631386976, 1.06281627105353, -0.6694985664919485, -1.8434279713460795, 0.7939081918133468, 3.4090399149991497, 1.2910304800186845, -2.2189857955047345, -0.5228657833871216, 4.789129278252956, 5.697849618133407, 0.7238746966130388, -2.4594470155932147, 0.7251516101669623, 4.93344155795975, 4.063917076163744, 0.32979498028897436, -0.908538062562157, 0.16438794610241078, 0.18313422042052127, -0.5060466773425497, 0.3995702686966754, 1.3897536639598247, -0.5479553078448175, -3.6757557555029092, -3.694626768243679, -1.0193727223201199, 0.15339802448237302, -0.7527485509052669, -0.5287658757053068, 0.8770068411702698, 0.08986170910528404, -2.4132532383444336, -2.086216156218152, 0.7724166776324849, -0.42899532308230703, -7.481568089818558, -12.218231413970008, -7.981731857064154, -0.022240283770339365, 2.413310273854535, -0.5349591670528387, -1.7602886032011358, 0.4354084037075033, 1.2150771074981699, -0.8333426779886208, -1.436423432754216, 0.9083266815340606, 2.128375983130886, 0.18291820848678236, -1.4694720057525918, -0.55969504255029, 0.1376371993941432, -1.3469874176917909, -2.323484820647466, -0.9031447267552171, 0.14916553006110345, -1.1337994970307503, -1.8923399334537212, -0.1702050861459716, 0.6218026218301911, -1.8687756288753914, -3.275814201280788, 0.2502046632087558, 3.7721836337828205, 0.4457379599749899, -6.603082339956929, -8.174174184376248, -3.18712182320985, 0.35818513682119446, -1.2831035470985956, -2.850831497079322, -0.7160853444298578, 0.9055574405728503, -1.5532573188585819, -4.167657039359098, -2.4891225563313886, 0.8953926602675982, 1.4214792320438134, 0.054912592012411755, 0.05945731184982947, 0.6688228271847899, -0.20513040348998324, -0.7786507114592294, 1.1563228134329557, 2.9886216112750064, 1.566291597340773, -0.447034960913113, 1.0450012476547237, 3.789308511798793, 2.9455137956582913, 0.0978608557442332, 0.4264924331636716, 2.6224315258699984, 0.7833298052477535, -3.92404511469259, -3.4381438122181334, 3.5666384563581923, 7.997215220852233, 4.07657701666296, -2.0939553346787334, -2.8778900577831736, -0.15047924978391314, 0.3423628691105677, -0.98539901156241, -0.48233700097761856, 0.824158957927987, -0.2343558792546931, -2.097649017959721, -1.2597004626512185, 0.8898791158514439, 0.707650203963536, -0.7737821168581509, -0.20425168931247384, 1.2093273199861945, 0.10582149441508125, -1.8945760336189337, -0.7599964704103173, 2.02636636063789, 1.8380021132868494, -0.29183774105135984, 0.2008987672583033, 1.365834248534719, -3.3504441301781256, -12.299001223869967, -15.072205426079469, -7.797561417884133, 0.6492362326105898, 2.1605867002897297, 0.146105720094032, 1.0493160424797443, 3.3803027601378712, 2.523104999602251, -0.05673758626127587, -0.3238983514081787, 0.44553630807243594, -1.0793188450793931, -3.0125651017109485, -1.594785546110836, 1.381214498447731, 1.5673927027919956, -0.2836387873563619, -0.4614450534468043, 0.6256513083051238, 0.35912429042632477, 0.08391242718190976, 2.0982473519424873, 3.2646807395026762, -0.30796034396506367, -4.623065997257637, -2.8143280036115845, 2.8498955678207123, 3.7905001445366033, -0.6264316941123949, -2.211948800697575, 1.7192147869009022, 4.095283698301808, 1.0405617150115647, -1.4981910094267203, 1.2076702304546665, 4.469705650685884, 2.966692537927541, -0.3535235060323972, -0.6550373768663922, 0.36963377726401053, -0.8463563441515229, -2.5212304018288982, -1.5811118523510732, 0.08587836697556032, -0.31324861448112795, -0.8635743718693902, 0.6597836338810074, 1.5682064223745604, -0.5456035359870783, -2.3159443348010034, -0.6068301751465324, 1.1276115227263386, -0.6579998210797962, -2.111664954063736, 1.092774254999113, 4.543266211856228, 2.0162520606583203, -2.8060359317767682, -1.899855745422954, 3.0345501942904214, 3.2876940146154174, -1.721355398871063, -3.6407118265948375, 0.31467054881935586, 3.376227327677292, 1.4875132729658644, -0.919333433901276, -0.2422537241062705, 0.6399063631549272, -0.5531635511361548, -1.1834249627231963, 0.06145155064446299, 0.2601879611471548, -1.190608312894762, -0.5311193163884008, 2.8081240852591796, 4.033715926353899, 1.4025350111693637, -0.6839056677187176, 0.0724135319472897, 0.4312722958014082, -0.5875220007713675, 0.7471804354530663, 3.7913883800457038, 1.5689996879254273, -6.834851672925849, -11.513308280214622, -6.199728657383937, 1.4304080849382743, 1.8489956305094042, -2.1629999418228136, -2.485713562709612, 0.4400456944357537, 0.7984534347852007, -1.0509351727577694, -0.5209017209295265, 1.5937659925247314, 1.1327060800327953, -0.7616301744531739, 0.08799404209377092, 2.5342782806007054, 2.338809221180817, 0.2729036454837465], 'positive_zeros': ['1.08539744960320413947647488822', '2.49830893316767135356322484097', '2.73982829503667008491034459817', '4.56119751365378274919795432294', '5.828184710946999739683575460391', '6.66691609473599748287138086460', '7.421924240949240011368878823973', '8.86597325798327194767884407928', '9.393566450490367196791014637231', '9.90327107371001151658567334609', '11.07684189941498063938604806224', '12.004391278507242227116702473127', '12.645679597721817259179703942519', '13.80045738434474037464971713138', '14.85069351642139564386234390876', '15.67371813696142506755247981655', '16.63015091209407524979489961250', '17.4590666811643414649654778851', '17.98615350456764315207570303407', '18.84387223354972092158887814723', '19.71382892379852714842302126135', '20.34311659183575228591402130007', '21.52636996952158134679715348236', '21.93499497688220683908242698590', '22.70941255614013077858095667304', '24.39632171304265314688963864217', '24.87419056489611735492640240097', '25.44769977695575791982175860189', '26.26478125983058436890029975829', '27.06370192449969572791964093968', '27.94314379806038810293845893246', '28.688250246952158864915941372496', '29.22172666882432014063909419088', '29.989645445808764353689215758594', '30.741777697595368521313120113517', '31.8226082276559147739754605795', '32.67991072160959437339871199789', '33.56642508430503130026051462857', '34.193514856863297569996193903985', '35.03136171802759616105926284653', '35.66060374371566403977677129109', '36.568181213182521676944312758655', '37.13637568177610609346918122600', '37.94523579709920660607990874345', '38.434245413442135542637061295278', '39.19458378656450564959889842537', '40.30827181877947988375248572583', '40.99217329222927224024232703325', '41.71901658433615736484058245446', '42.59586941346371236685593532147', '43.55633283309772542307059859333', '44.31182320138708899901766203819', '44.65247243018452309131192545274', '45.57542649170227388008758234288', '46.00318503390421367949770273824', '47.00917493867563812007820721477', '47.67969612987299250050436266402', '48.464323988055229895686355286207', '48.90241715925284547795837390952', '49.71372428834509373526917012710', '51.05122728067531903942231138129', '51.71125790052809512688233531114', '52.035922667328889899698085895860', '53.36025936110309979131629981224', '53.62075860377057854501144223732', '54.17379188067611635657051318810', '55.07840700446159919338675344700', '56.011937347114645974493942346507', '56.44198304799927974504532154311', '57.04220435814249331715403736293', '57.813629413072839063515559000581', '58.496345110646384605250318376037', '59.65908442653166522540677139874', '60.52349096072077564493639208292', '61.02237829346088060641197689576', '61.5366501660463778483755591875', '62.44280905723206233107681599349', '63.23789220562243777799978747040', '63.97234852056773756129406801257', '64.59324179922590871207414961122', '64.71821175179685584079521639789', '65.834035741571596504995474670874', '66.76120970369233165663773447030', '67.053425159731131989287974060535', '68.02658885819687623460558185494', '68.95442105684360431433124115015', '69.53842929114839945825754228812', '70.49548679170352427537003505669', '71.02655588523140637531136587805', '71.75473936947284439397708539053', '72.378234139597023465973922841082', '73.03451891471739469295779965748', '73.79057453642028025339639475224', '74.0902075351268207370110670665', '75.41707142921664903615183093771', '75.59045706825979437754737281374', '76.37279464722820555263444511268', '77.28388740558245433504211265948', '77.873886170392489981687614649203', '79.14553895922378312621185680508', '79.556356550471602728314200677240', '80.31253087259610081646738648148', '80.65131270431098744064345211327', '81.30400692025485409885591822026', '82.39965872397164056680081063441', '82.95719788939926581445033527317', '83.42091350416408977003202089161', '84.11067151441963872143770089544', '84.71254763070275652994525399473', '85.52708731039000221607278220030', '86.31648468213061515442693079737', '87.47325448212511342868319496179', '87.69686249920887521502371033875', '88.69820190567240706087549759129', '89.00796386345376229221097674822', '90.064916838554785100623217495998', '90.66457158903523873627779132407', '90.97087973923728002273455395645', '91.98844741616283084953233345919', '92.550517780538394604755766860231', '93.04943070113698725353209037834', '93.65881266079887804799974684389', '94.54426002880641362717347747220', '95.51963718580296892258050987286', '96.18280973268455077545493891903', '96.490240582373169363856547114747', '97.74770049009754833247487598951', '98.12676133747200775625160393068', '99.09866427091623684251698202657', '99.311021195359173950219292488843', '100.291307508833484773262692829466', '100.49481388902299838195268164693', '101.335452898931690060186230540607', '102.278870914177633034636892299495', '102.83650998967473365406938031952', '103.28692043283215058946670990977', '103.9116696018474395419480351820', '105.06439754840052575436241177627', '105.763216315402496602868170047424', '106.498231852182492824547431426250', '107.06444747741441961625124831883', '107.58579735840294638434538861241', '108.40099763392405187773673908829', '109.01572709139552635626515127549', '109.470558713666059242178257761836', '110.332642934462774493972773043130', '110.96443183924052021200966642411', '111.622957202414372603441067812512', '112.06030836329445696358982244755', '112.743853638854886728100006326', '113.742755829381142259479087345242', '114.67732847166332371979822875641', '115.245084442414900081449426340516', '115.83919807367710409263241513339', '116.256451209687053360179347759418', '117.11004235984134180634201958825', '117.99742450275544586644859123995', '118.313791110513481958191689149215', '119.12216912422049390212269934614', '119.71436138343352608842786820304', '119.95656957411330066125559877865', '120.90907413378320079252488527831', '121.92070782567266522872357506457', '122.31687781849361475882117139211', '122.9142581100710672884580180781', '124.01379092229653191805129421236', '124.781919722527460764070984705143', '124.896116777655462599568089662266', '126.0274699062457770909385177111', '126.447653287068134978296349155383', '127.123408174391217262630742009712', '127.70263788345948983472422017442', '128.19586091103885162070773784573', '129.10910590942201992486441385719', '129.60043691033642332614571601434', '130.24506888851714565095198734932', '131.03343333109973473969313159025', '131.59584007172955588977500820405', '132.54170983594200365647899576905', '133.07985546723632385077592628351', '134.09833114392409017341216476242', '134.63807485587908497720467803337', '135.066244145093516239141355612806', '135.5409928660388985039441004067', '136.19549217978479265395274548398', '137.3610599973374367462694940383', '137.58264397933952492861397494237', '138.23534923937283305433401136874', '138.76203689766821512637674435235', '139.59243510179372681681654679375', '139.96992471486677489658174515294', '141.25111862194739636368282137336', '141.824683251594581000617362054059', '142.44493412389306819778263881821', '143.01270756456286786281117396499', '143.64582489487004718923638655425', '144.39737069420852991663511162427', '145.13758264455241833175234486126', '145.36994784026024918009775617292', '146.43428848639923345795375029634', '146.6419243232085075951888087473', '147.52610799225907578605677464732', '147.92539811896616648144731336858', '148.73432649770545035596512039212', '149.39542197259688606603950600861', '150.54684682298205907496391288348', '150.778780160620042008025076959502', '151.642390923577012036289289333', '152.04186382066634818402758739575', '153.026866371250707599252416378504', '153.7685529833690185518469561746', '154.03804979060793648550806567851', '154.638971522943612616504785587373', '155.16753991123138759488483597670', '156.13744730271704526850556250677', '156.43656342930544117013367044039', '157.517837636227757733674097139224', '157.74271699976718427896873679786', '158.48994218081367473727217567465', '159.23179094773920806411093976402', '160.18725999543077334392589358859', '160.959763554647470631027807893197', '161.33143522458104725815761327389', '161.967392735106280650324566002319', '162.465125301032597854543739986720', '163.2907491847646610220934421914', '163.88287470607977563547985925070', '164.41239163298643624212236944571', '165.01408228162216701145147632753', '165.704649684706139016602443719032', '166.50488539207762831896611044095', '166.84089841423112502295327021489', '167.34046673592232507915239887226', '168.71530723891424488562425638418', '169.44610039551196439763034284968', '169.46965860982334763745561424816', '170.61528418724998532422285241823', '171.03225413163515789437201974310', '171.40604083319253011850505932091', '172.34149938453672103869671939995', '173.06994103973551260175298998690', '173.56135001810904698147860633174', '174.21616182983611756857899662717', '174.33607954026332919512861389879', '175.29421811122077668324593762999', '176.08882943966816144391213699652', '176.832593981844630760976524401343', '177.386472906992324586064722196624', '178.20574260297628897585158219934', '178.65783933188211668305951470072', '179.641909804874738187089737156533', '180.15717707213041327768417232792', '180.48373578764208918271783346758', '181.53169292045197641022822741137', '181.77878216713137581652294063276', '182.39550526519627346823420351188', '183.065014819056482792552596026805', '183.82132959462212668401443899411', '184.2992648306704995193331042963', '184.92549728113561348684551477271', '185.7404012534477058319211618987', '186.369844611772162077752286770', '187.08631579611023411323864969314', '187.79256452605736542216632746421', '188.58948785790445885493152608802', '189.11179767667933006177142923260', '189.57705788783567091307829978229', '190.297905311027949233793993199472', '190.690183842546230960128188408912', '191.30905006675469707690277586574', '192.34192298981243326648095842977', '192.79438119304925565928650602905', '193.25360288575587715441955287725', '193.66237363212233767812216315147', '194.44455826868027420763759275024', '195.54739547670470985956966231993', '196.07998015309341004886741231421', '196.82219287312625356558496733617', '197.31832133513148750831546323535', '197.88503640049855819679350797828', '198.60201182945460973149968438360', '199.05088744397664763750175264858'], 'prelabel': '1-621-621.11-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8839118757806594, 'root_angle': 0.05420263153898067, 'root_number': '0.942566035368235573543809668357+0.334019863137218361836305716579*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.054202631539', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(198)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.846717663684374504154483997597+0.0368805676280931061624248632651*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.0853974496', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.49830893317', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.73982829504', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.8839118757806594, 'bad_primes': [3, 23], 'central_character': '621.11', 'conductor': 621, 'conductor_radical': 69, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/621/11'], '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': '1-621-621.11-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': '1-621-621.11-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8839118757806594, 'root_angle': 0.05420263153898067, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.0853974496', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_621.11', 'Lhash_array': ['dirichlet_L_621.11'], 'factors': ['1-621-621.11-r0-0-0'], 'label': '1-621-621.11-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/621/11'}
Lfunction data - 1-621-621.11-r0-0-0