Formats: - HTML - YAML - JSON - 2026-09-21T19:43:35.037843
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': 'dirichlet_L_231.164', 'a10': [-0.5, -0.8660254037844386], 'a2': [-0.5, 0.8660254037844386], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.5, -0.8660254037844386], 'a5': [-0.5, 0.8660254037844386], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, 0.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 24.82439762755838, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [11, [1]]], 'bad_primes': [3, 7, 11], 'central_character': '231.164', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 231, 'conductor_radical': 231, 'conjugate': 'dirichlet_L_231.131', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 0, 'a^4', 'a^2', 0, 0, 'a^0', 0, 'a^4', 0, 0, 'a^0', 0, 0, 'a^2', 'a^1', 0, 'a^2', 'a^0', 0, 0, 'a^5', 0, 'a^4', 'a^2', 0, 0, 'a^0', 0, 'a^1', 'a^4', 0, 'a^3', 0, 0, 'a^2', 'a^4', 0, 'a^2', 'a^3', 0, 'a^3', 0, 0, 'a^1', 'a^2', 0, 0, 'a^0', 0, 'a^4', 'a^1', 0, 0, 0, 0, 'a^2', 'a^4', 0, 'a^2', 'a^3', 0, 'a^0', 'a^2', 0, 'a^4', 'a^5', 0, 0, 'a^3', 0, 'a^4', 'a^4', 0, 'a^0', 0, 0, 'a^5', 'a^4', 0, 'a^5', 'a^3', 0, 'a^3', 'a^5', 0, 0, 'a^2', 0, 0, 'a^3', 0, 'a^4', 'a^4', 0, 'a^3', 0, 0, 'a^2'], 'euler_factors': [[1, 'a^2'], [0], [1, 'a^2'], [0], [0], [1, 'a^0'], [1, 'a^1'], [1, 'a^2'], [1, 'a^5'], [1, 'a^0'], [1, 'a^1'], [1, 'a^2'], [1, 'a^3'], [1, 'a^3'], [1, 'a^2'], [1, 'a^1'], [1, 'a^4'], [1, 'a^2'], [1, 'a^4'], [1, 'a^3'], [1, 'a^4'], [1, 'a^5'], [1, 'a^3'], [1, 'a^2'], [1, 'a^3'], [1, 'a^1']], 'gamma_factors': [[1], []], 'id': 9820, 'index': 0, 'label': '1-231-231.164-r1-0-0', 'leading_term': '-0.0504106598213868938027408955041+0.794366736435870751732051733245*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/231/164', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 14}, 'plot_values': [-0.7959646641525011, -1.45413160489792, -1.8103793722103463, -1.6200698522338097, -0.7255100540347521, 0.7978281157176836, 2.5572888309620896, 3.919152399674667, 4.258395248999596, 3.2849313466601555, 1.270982958505309, -0.983190826767254, -2.4860962239656668, -2.554836027945914, -1.2063949639960192, 0.8128831440054608, 2.4227809998548904, 2.826845629222303, 1.9786700852288983, 0.5845770119673119, -0.3831578293157339, -0.3506534164286308, 0.47645285762314127, 1.3012559938872679, 1.3737788437022254, 0.6073084407935917, -0.3171795607263228, -0.47981546895602334, 0.4991840888620671, 2.058672802475462, 3.0550248920221157, 2.6659804378665077, 1.1377960750899685, -0.28253738687876995, -0.2809507452769892, 1.401165581217841, 3.5784498327947736, 4.386044087108518, 2.700939987677139, -0.873829814200498, -4.299420913380137, -5.527550846775336, -3.9910340425187814, -0.9832486014215019, 1.3831544487810299, 1.7956500697852809, 0.6240388966176741, -0.618466145018325, -0.7041740208091738, 0.2693162660071094, 1.1232318070672105, 0.838252188538224, -0.4070303699868769, -1.3939849608394723, -1.0660194617582603, 0.39563171705442657, 1.6981211984791624, 1.684053465862616, 0.49047725811741033, -0.5661644191289981, -0.3437471056821174, 0.8427254054133583, 1.3632917477985904, -0.13821120191433628, -3.1712328360821025, -5.457619707922781, -4.786591605028503, -1.0744387836477105, 3.311304349223838, 5.398867718452513, 4.050373298908261, 0.804306979432082, -1.62163495216937, -1.7464159733822373, -0.41906222973575646, 0.33132454345452367, -0.5623667462980791, -2.215946673518001, -2.857673390232654, -1.7458175191339498, 0.07675836408256788, 0.930872831619542, 0.27476820825472714, -0.8082591530027223, -0.90396108696399, 0.11155514717570035, 0.9480766007411265, 0.4492584299837923, -0.9190830495727818, -1.4113513394989186, 0.03208892379086689, 2.307002613176675, 2.945148277506022, 0.6092022787412344, -3.2580429108620597, -5.517413210190257, -4.276488565287435, -0.7844777810926128, 1.7100247497839807, 1.0775654584648862, -1.705635248277798, -3.6775851854506993, -2.911342926458726, -0.32186388461481197, 1.5018861226537765, 1.0540427184880412, -0.7018025816750812, -1.6516184603545374, -0.918735006128204, 0.3605090231512623, 0.5964200104591661, -0.31155610219033203, -0.9504871101354447, -0.2582764202342064, 1.0244396537391003, 1.1495990645160932, -0.4599772225470192, -2.276938078790116, -2.2659315650209706, -0.29304370326178975, 1.5173281072901075, 1.1229400382175478, -0.9381501753986314, -1.8627803129389084, 0.36104354209590894, 4.436798977191033, 6.716454836983584, 4.8436580507105464, 0.2553443887333311, -3.1804123999449287, -2.976610226831723, -0.2601730472598369, 1.8036217490798045, 1.4535694838170174, -0.16706712578153288, -0.836306035377814, 0.014848018807619639, 0.8879436135063422, 0.37690753797406706, -0.9311047196876894, -1.1902163160420145, 0.30138801639076235, 2.0908562588388846, 2.2806752066366487, 0.8650415996644852, -0.25642317233638595, 0.3186603226133201, 1.6706887687505103, 1.721193766026055, 0.08188962659371948, -1.0256351682579372, 0.7336837321247133, 4.63953703490165, 7.011014971672403, 4.919343325710505, -0.4630015717928246, -4.755584553254689, -4.7169791122786675, -1.336468857231616, 1.6261516892667731, 1.807962943854879, 0.3691658026350205, -0.04519634009552959, 1.2751369851142076, 2.445528941523742, 1.614809423814913, -0.6020410420142521, -1.914239295206715, -1.230161047533002, 0.09232915569358911, 0.1396063331879634, -1.061648411192881, -1.702765788837698, -0.7394925118488398, 0.6185602448357587, 0.5671287152811242, -0.6145244764682258, -0.5724957139068827, 2.0647322705082503, 5.3718627517780675, 5.838778015045713, 2.481137285481825, -1.5782307854652897, -2.2952324995917492, 0.8128688127890037, 4.130594160771047, 4.0581523718725805, 0.9864554953402043, -1.452524677895493, -0.7780098804635809, 1.6260442274719162, 2.531403400550544, 0.8570322908778547, -1.2958991505407034, -1.5385184193507015, -0.10703844609641494, 0.8140174404808083, 0.1476564136351828, -0.8114956928990594, -0.4670484346981524, 0.6880203396794299, 0.7410666592479899, -0.7990481442455718, -1.9912240884539385, -0.9200591344735178, 1.5383776307045318, 2.527911843262027, 0.8658753942229187, -1.197075628228791, -0.7162602432373653, 1.9547372747993297, 3.1566571937527885, 0.33134112884859346, -4.4682277367669005, -6.518111765369314, -3.748460187905553, 0.8907239947080556, 2.8500904521658077, 1.0170238775148215, -1.5800302021188777, -1.8281037276322285, -0.05324102066088832, 1.1157490543113955, 0.4964402121944256, -0.38664602433103434, 0.12108776328294207, 1.2687700081155007, 0.9817268077530328, -1.0429045251541156, -2.6671143363435745, -2.1166454036323743, -0.4009494363234848, 0.08354373260209308, -1.0847158271582644, -1.7375759347753612, -0.2645615295314643, 1.8159295227557561, 1.7243888716600377, -0.4549095506094957, -1.0982692013905782, 2.633404393307806, 8.670723484544851, 11.64699775500584, 8.770143432586645, 2.952194489609092, -0.5999106283979522, -0.11142710146480463, 1.583235534650572, 1.3179399607974571, -0.5036819003878302, -1.1519804584768303, 0.297816589120499, 1.7340828909547266, 1.1065574866271064, -0.6868964442899539, -1.1287631964883518, 0.37755732219392635, 1.7664389970806857, 1.3075802561126446, -0.013539378060162689, -0.12032293198188698, 0.9593978841689867, 1.100431541949005, -0.5563655084218696, -1.8222497487471414, -0.2916928986937581, 2.807878114978859, 3.3873408457912673, -0.41765205822713536, -5.3377288845929005, -6.458380154939468, -3.0727891484988925, 0.4983438942979515, 0.2373878260417567, -2.8417191400472706, -4.4398115089359855, -2.626319829754183, 0.008751789178043973, 0.1541472477453532, -1.8805987826445576, -2.9725057623439857, -1.5982002569673517, 0.34749669279407985, 0.5085550269842691, -0.7031752962075605, -1.1095818374348636, -0.19469433835461686, 0.23739544509256366, -0.9187518311704338, -2.0417864855423753, -1.0292662400719674, 1.3263456943581908, 1.9990476395861312, -0.0817777757443572, -2.2279143421589236, -1.5396851954747772, 0.8449886852078319, 0.9438506297445518, -2.5785669350751297, -6.0282249674072395, -5.0648971541951395, -0.39077050996253615, 2.815061236774278, 1.1931087501976438, -2.839773920788798, -4.414632930360469, -2.2180750781401466, 0.5534269135546385, 0.8980966112632174, -0.38027303544957525, -0.6739091798367174, 0.365989347535549, 0.6717992023186227, -0.6836009320296633, -1.8362936633125893, -0.9153680606801844, 0.9889870680260524, 1.2655133059733725, -0.38275424047812023, -1.439142252780563, -0.3013366710156321, 1.2525866507221302, 0.6949425961644323, -1.2741538113488213, -1.5237119024559285, 0.6195409264276028, 1.4928370083856994, -2.324493414304186, -8.742047874034727, -11.707418537918745, -8.24221576397923, -2.0340119522243643, 1.0836664055040583, -0.14166147519777783, -1.948309452911353, -1.2398753138429182, 0.6689949035894189, 0.8327066471112692, -0.7297109506819308, -1.3064193522871905, 0.22421485342497915, 1.6939047409490586, 0.9535329788267384, -0.9032584362847822, -1.210010364196391, 0.3236656567694146, 1.3472875247064902, 0.5750800329263183, -0.31336687781849326, 0.4388764254165155, 1.5085579933069087, 0.3000259217165821, -2.6192682970616437, -3.387776704338791, -0.10421600152818303, 3.7338880596912807, 3.1051742232336728, -1.958432334659214, -6.032430410895647, -5.014717495580973, -1.076467697226267, 0.6265802093884563, -1.227228186929651, -2.9933832032305134, -1.6234389190328267, 1.199542725828276, 1.8673636275253318, 0.05981286723111937, -1.147206434890144, 0.03844363930170101, 1.7565977372785953, 1.6086233047179708, 0.17861722469113633, -0.3065155354640578, 0.2711909085780972, -0.1670436211457615, -2.18145989244338, -3.347380328011385, -1.7603391301650957, 0.7043576221485262, 0.7597376112231078, -1.3605717059960012, -1.889361013861894, 0.9636176665000666, 3.8601854268262272, 2.624054342957421, -1.6821318189527663, -3.688121009679502, -0.8505555843430983, 2.965589445600719, 2.5409843999481003, -1.8659981100782117, -5.1263960225594225, -4.0752659977946175, -1.049493186370185, 0.13608661792172771, -0.640851875225515, -0.6791401286279564, 0.8458345075660876, 1.7916574749516827, 0.8160281888790132, -0.3113133329320069, 0.43535837680438166, 1.9374900208859722, 1.5442746084266608, -0.6760269266986628, -1.7736800862543836, -0.3420430684902812, 1.2755123112521076, 0.6229440926375284, -0.9046472273464145, -0.20990007869494975, 2.1425196273850093, 1.813095161752464, -3.0507133947982723, -8.008243942399833, -7.217431845252809, -1.0039532154134585, 4.257119893839914, 3.992624637710524, 0.5057067031547114, -1.0889215130459144, 0.25836475366602, 1.2898907148637577, 0.08191257369426092, -1.2871589197444482, -0.521595956535545, 1.0944602814511026, 0.8020871293391549, -1.1837699400037869, -1.9590785279655, -0.43049140146074655, 1.0788992227895766, 0.5594666860937638, -0.6153632183481397, -0.14055596348392732, 1.3034084958406225, 1.2072801384960674, -0.1802790088193021, 0.5132895092816782, 4.497485525848048, 7.808587293614385, 6.0757293771480105, 0.9482910192552658, -1.3584438136300068, 1.8841836693016003, 6.292949870602055, 6.296986258213219, 2.3368712223691586, -0.4968936037500939, 0.16287087204467507, 1.3079602101096637, -0.19406431150658746, -2.8103631640621187, -2.9569603879278548, -0.5155039896637823, 1.1790275136184738, 0.40716910257726335, -0.8161774123435094, -0.44210902884134357, 0.3865658694530061, -0.34706379780111163, -1.8118408053733757, -1.5724763219069198, 0.13164663424609466, 0.3238629635184457, -1.920219040273756, -3.4329724484262365, -1.5404185482438542, 1.420956799763311, 1.0661992506162679, -2.4046910482262427, -3.958264591922556, -0.8965051489932324, 2.8690398785858564, 2.0624743596941477, -2.450792191125948, -4.721872340797143, -1.8703463128391546, 2.271349603857055, 2.82111866805498, 0.2542192761896874, -1.3074012197684155, -0.41561588350546685, 0.39194097857719706, -0.6388073430826211, -1.7428866498203277, -0.9680980664416493, 0.38177435296410267, -0.025137702803263464, -1.4461320076944033, -1.0736555735943438, 1.2690244346576849, 2.4654226942566706, 0.8846668210400748, -0.9642724566934875, -0.3960850992262034, 1.0699079160159453, 0.23209691200772534, -2.0090263451410624, -1.1517449611720212, 3.8800133604248757, 7.7148235971133525, 5.073236619235264, -1.8114098480701455, -5.658825269504187, -3.3702132281401056, 0.7199081407536906, 1.508056201221355, -0.3628582392565277, -0.9302110024911212, 0.6013439344976397, 1.341738262755149, 0.009887862682421129, -0.9659502765753033, 0.3236550290970337, 1.955147650084353, 1.2458181066701406, -0.8688453794972626, -1.3075397691354143, 0.28317947334629656, 1.2076526247629802, 0.3442053950370564, -0.09646165264007495, 1.2807249264620189, 2.058490636003669, -0.20689636506731862, -3.1319652660048836, -2.114183224799971, 2.487989140757542, 4.664144330505761, 0.7375299482023632, -5.129438680671475, -6.23071938067493, -2.1320247678431765, 1.4300716598178376, 0.8917569677264369, -0.9267275416052526, -0.18765298693905846, 1.9630137469894349, 1.737780414369066, -1.0061253000744923, -2.564385408749944, -1.1473062345970422, 0.7270433478068842, 0.5887822922778326, -0.30934933067338893, 0.27920279750678195, 1.5134827317801418, 1.0160451779474693, -0.745347711139411, -0.9980310555261298, 0.46465874076979274, 0.44444134136808977, -2.366144865667076, -4.4238055281493045, -2.2893292195240154, 1.6886061794542158, 2.2943864213995955, -0.7479430168754698, -2.035966651961524, 1.4716862449782846, 5.540600476748363, 4.525339984345509, -0.49497460528577936, -3.306755580546709, -1.32532485405725, 1.4183600401015946, 0.8081388059424109, -1.6854257933062136, -2.2060436315645426, -0.5837126332279076, 0.21846287529905128, -0.5975035009921316, -0.713867361020309, 0.8017029755694562, 1.629632839296642, 0.2542761995128807, -1.0960695942311156, 0.04080524676858773, 2.070731287098457, 1.6775124337908713, -0.729643448132567, -1.530233932207754, 0.14306420765221037, 0.8660561129571671, -1.1187740799073251, -2.0477014440430206, 1.9461971354348053, 7.830103684533253, 8.517210743053637, 2.4928545051882685, -3.7245552306602274, -4.174746036397635, -0.8094026616631868, 0.49152989866927965, -1.537316986358486, -3.0001142759079586, -1.7065634426323069, -0.0727873404337271, -0.3121638799816556, -0.6887434539370693, 1.055544271079976, 3.3461882730663435, 3.0639600316556197, 0.6497644218246792, -0.566861540753929, 0.3155496480223227, 0.7003530350045791, -0.6944458601045067, -1.5236755118633942, -0.1077429931532836, 1.1329680237017474, -0.39217538088158466, -2.3099107003708164, -0.25914405404036606, 4.624895765544403, 5.8394179437189555, 0.48897026451317793, -5.9013577352588085, -6.458789533533793, -1.9681115888326155, 1.112623042200324, 0.07719950232365465, -1.302525374834195, 0.19985439212864697, 2.224131216680012, 1.22610010962569, -1.5566502546155256, -2.20916341853035, -0.3738346024553082, 0.6235137418116311, -0.555159109544785, -1.4141134490760636, -0.2439735948800278, 1.0327714189673118, 0.5299587486772387, -0.12584523680492177, 1.1719728083647216, 2.7396741566133755, 1.5429336602379693], 'positive_zeros': ['1.411384482692903596729552619856', '3.29636121454598608162825425472', '4.563507476474801986456470594373', '6.09227477959860989454018215602', '6.7166808322927764782960754758', '8.002919225277005233801725263837', '8.628959237859456398669364121638', '10.22927047001386459046282827335', '10.7018436860016602406917062547', '12.117389606329563488808608491279', '13.54492948449322864301721944742', '14.5102178013077563132438892356', '15.23913412750183803104140281827', '16.157309136498564600785869396596', '17.112217459750719319261440081722', '18.241083679253083005820156173033', '18.85177216846684172249995424379', '19.670139322038965228332559247055', '21.00991231006536251219090822034', '22.26835570067120376505542436388', '23.23346238808895929710590996955', '23.61792860054613623186147306227', '24.984987574968944513719296177813', '25.6978077769602727483003421773', '26.53353235390391998324999606471', '27.294927669132734692990307242', '28.12048087288250683682593119565', '29.1140345440496073706041239877', '30.38478093091188887851043101243', '31.07027807542599152408088807646', '32.22655545214263023142709924557', '33.00301460926783839932000617631', '33.961225361773128945940259983539', '34.59679706879246270549910460172', '35.37375617335785341860473432864', '36.17985556543884577184200303592', '37.22684216252735473693251710735', '37.990011895814827084101208940282', '38.71820540193624632332140407954', '40.017218189438242054866836103330', '40.9658580914694393677454586639', '41.84030453518589995208462039808', '42.49612490257316381088106819312', '43.216109080132675131195000114447', '44.0148540719113061501834875780', '45.194580489612351686382251704638', '45.538687694562650744727634999380', '46.57620222073359936943106505763', '47.109756376889431749216642685032', '48.41201944083545457603570781773', '49.49014102966277461168657898298', '50.424249316021845287956386181145', '50.646213743880428382221216584877', '51.791336895000742742217086416862', '52.78258760446057133905623090647', '53.173537151299744916594059114', '54.2132300815514751128751856802', '54.84176111296721807521276745072', '55.410833388374188710036495432', '56.737124686893411125308712798946', '57.435495774056481940162054580299', '58.53246733631178174472995140689', '59.16745600556603019325322694347', '60.109621906035486085460180942982', '60.959434897707933751331228649', '61.60176340614409868264746548838', '62.31204862609054026760729962177', '62.98578585323901557396724344423', '63.869223333864192940276041661690', '64.797746170627909800020344049213', '65.40792747957111613230368344564', '66.27243129628197227050508233606', '67.43355685219618345881462912218', '68.23291900457437464457800596683', '69.07128304754531039674660315766', '69.82627835609146077022793444443', '70.278651570867332046027669509842', '71.10659720147979694721802026854', '72.297469444965254008644000484899', '72.53935225404517018415257708903', '73.47328982743285376603586919659', '74.31246143896882071812500975655', '74.825123750857547351333931510075', '76.47053269599515595897689913294', '76.8941719963037226626076907816', '77.72587366623971258122387267355', '78.38910207973089396335395750622', '79.2502731251706329032922743548', '79.937582360130490642655013985591', '80.9331569302761358947040477730', '81.29469027201384229235938725824', '82.10091101524480467449553136687', '82.84314174705674392975594416514', '83.72489936117601781657890832115', '84.93523735871926298102406028527', '85.34297708834195138323503227693', '86.56091620793998083860623655228', '86.90750790530190033397550061790', '88.0522898401830621904223703214', '88.57896638207368142876369984198', '89.43765066759907102282819144282', '89.79193745990888012043605077277', '90.76111116944569833120524304333', '91.55325049665978734943236097383', '92.38260885426845751783133585661', '92.924044324517721949433484327374', '94.08786268994458817603755862683', '94.78144236612114140816685373638', '95.85596934116057023450109864066', '96.46959420908965163537309986355', '97.08765358452233261678751434940', '97.68438638152773593764113038616', '98.5800736911363256879236543982', '99.31190387464537625631074836', '100.04976429047499896232536710990', '100.73650356625278702440185791519', '101.48302992488023510279591546655', '102.046256936659945664188639854907', '103.57995298722971352692817361019', '104.04317739204082517854770008962', '104.87829785610585277615970354986', '105.489728429626726384563202139606', '106.21529166805577844892467314733', '107.02862693559497156211380153897', '107.755148428443935294031398350553', '108.588557341084914317367780553456', '108.95262489679669291161823005418', '109.72276842664894116565108432529', '110.63220151309001406839221009071', '111.454981842411959910118126096871', '112.61296866674521833459632819282', '112.966520666391149379045943937800', '113.92103118246201715193489329949', '114.69651304701456590860386223240', '115.30639506035831616078463439815', '116.29841824928703654438736315438', '116.734503247602517910073759404751', '117.14744434846770897213584683865', '118.33063799645348637542892058568', '118.87420523086302828204970415190', '119.60537430371238997810563330854', '120.505914202830304338492816549643', '121.3099827598800761588517445915', '122.067943286489185438417395159762', '123.31352767153705471900142461148', '123.53110022172968897995948241023', '124.22175472279805606639238116789', '125.18123768775360994273237745842', '125.52755161777333674626060892344', '126.47166788312723821625699590764', '127.23801951280482403221071487326', '127.923215623850221431647285795638', '128.46775546359931619191476815149', '129.20637257795628247882979357505', '130.358359976374859637219510085792', '131.30265163606552612244560706493', '131.83122941818714314424737417635', '132.51383663828082986752471177939', '133.215856997068083407309416782968', '133.88477566441275737874936118403', '134.75404812836785765676946307810', '135.438796656999214531825935104451', '135.96832270042963251892653697522', '136.82421101160345956571841435415', '137.11192938427127628479022203423', '138.50569588403383568717910897791', '138.93136383193988397541811421941', '140.21526577253398896540044430285', '140.59380095162625224047944166956', '141.227027273160364385189886386269', '142.25070745290109645788447863719', '142.895421151780124486913868968379', '143.568469778206941188195808922279', '143.983441293394055763503255878199', '144.97296815231630423902823642985', '145.37759230820717114175040640504', '146.39467333244403292662010253537', '146.98402851302794920458017731121', '147.874400044182143378058754414512', '148.58918582165193828450415250777', '149.50163294853183298356501113099', '150.3425581786254259392306643178', '151.03650410837625007362923330323', '151.42303887651907821135062410287', '152.38445563245489858075307673327', '152.806656102979026991644097171296', '153.59228354239646782251638980131', '154.49445220712143333565792108346', '155.072379515429763077426715541037', '155.6571773163028168907632201999', '156.33943405032595577737863129179', '157.41788344209079256384155555034', '158.369283664654252381794143421300', '159.003381698808345609510909010038', '159.58120924773982562758499024179', '160.31430532871632608817727688447', '160.88658827434361963442478320323', '161.74087957873561822244136991078', '162.45074951283685626942547658197', '163.23333536385128379858962057984', '163.47975111179169672778517118806', '164.35589105227198534776817639758', '165.15295661450625759928278651941', '165.97435342212635819304247237387', '167.02379513883005349405234047187', '167.62992515713831868540761240469', '168.15228611433731371320492089356', '168.95646671002071389465164797359', '169.85014143763157686928494094702', '170.4851872419400481633709089197', '170.86612315200722766397640263939', '171.73836226815926351053872020037', '172.40365299843288280220108580770', '172.882110865006407392839114035162', '173.919133535373904900458155976622', '174.61786846529366161640103309335', '175.2151673020262191236671380697', '176.21937651652935015343341921499', '176.99945387232690044081430922226', '177.60108986527507245488300539399', '178.56985700089068087282332317970', '178.87079399344053485375795957182', '179.54315270364646700961332042378', '180.353295161179850674625715420605', '180.93165809102504790712627663234', '181.78014565256580313376741829328', '182.47677896978360745137014304928', '182.98079924944388976020305553517', '183.64001743982275823494201797113', '184.792824062445862272944674006388', '185.7192570457973157400335136846', '186.04891150226268368237850896210', '187.22549923645129323843499892451', '187.357942536906911001529716993358', '187.982651490319062654013888993304', '189.161517135574984398610919236866', '189.604801004760379857253239537118', '190.18360281969134860196756135808', '190.95451651714968765057188897676', '191.512887341464481400626929700656', '192.205846910551346470326984162627', '193.14585273066453047794274336668', '194.20928273784318941268751682864', '194.69898035480277872684065699454', '195.2874811561650560283320084759', '196.07223613128031246560489394297', '196.937514014543093397204621524765', '197.38909678822020523517456826140', '198.16901155901245057441813152540', '198.91887338193945414047440233009', '199.138334352964670912862858057592'], 'prelabel': '1-231-231.164-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.82439762755838, 'root_angle': -0.4798270469460539, 'root_number': '-0.991977916408522651694048037507-0.126411286512740018473095957624*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.479827046946', 'prec': 40}, 'spectral_label': 'r1-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.569872851050440301258451222616+0.433533915363209869453903711776*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.41138448269', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '3.29636121455', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.56350747647', 'prec': 40}}