-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_3381.1223', 'a10': [0.8338232639998672, 0.5520314886060467], 'a2': [0.9668002242694236, -0.25553341533465307], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.8694053472948153, -0.4940995265077487], 'a5': [0.6650780269803587, 0.7467738734234838], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.7142823452219036, -0.6998576507435618], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 15.701297990361368, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [23, [1]]], 'bad_primes': [3, 7, 23], 'central_character': '3381.1223', 'coeff_info': ['x^462 - 1', '0.999907521857918 + 0.0135995489615099*I', '\\\\zeta_{462}'], 'conductor': 3381, 'conductor_radical': 483, 'conjugate': 'dirichlet_L_3381.857', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^443', 0, 'a^424', 'a^62', 0, 0, 'a^405', 0, 'a^43', 'a^415', 0, 'a^219', 0, 0, 'a^386', 'a^346', 0, 'a^413', 'a^24', 0, 'a^396', 0, 0, 'a^124', 'a^200', 0, 0, 'a^423', 0, 'a^427', 'a^367', 0, 'a^327', 0, 0, 'a^290', 'a^394', 0, 'a^5', 'a^216', 0, 'a^288', 'a^377', 0, 0, 'a^44', 0, 0, 'a^105', 0, 'a^181', 'a^67', 0, 'a^15', 0, 0, 'a^404', 'a^274', 0, 'a^185', 'a^408', 0, 'a^348', 'a^281', 0, 'a^322', 'a^308', 0, 0, 'a^333', 0, 'a^61', 'a^271', 0, 'a^375', 0, 0, 'a^98', 'a^448', 0, 'a^197', 'a^180', 0, 'a^408', 'a^269', 0, 'a^358', 'a^68', 0, 0, 0, 0, 'a^25', 'a^13', 0, 'a^315', 0, 0, 'a^86'], 'euler_factors': [[1, 'a^443'], [0], [1, 'a^62'], [0], [1, 'a^415'], [1, 'a^219'], [1, 'a^346'], [1, 'a^413'], [0], [1, 'a^423'], [1, 'a^427'], [1, 'a^290'], [1, 'a^216'], [1, 'a^288'], [1, 'a^44'], [1, 'a^67'], [1, 'a^274'], [1, 'a^185'], [1, 'a^322'], [1, 'a^333'], [1, 'a^61'], [1, 'a^98'], [1, 'a^180'], [1, 'a^68'], [1, 'a^315'], [1, 'a^202']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-3381-3381.1223-r0-0-0', 'leading_term': '3.66092247419058260567043222880-1.83096279575765625320366823804*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/3381/1223', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [4.093260084759139, 3.3339672009012142, 1.6569281664855058, -0.8489697521331128, -2.4676939232775874, -1.9695815239412269, -0.0919788370700324, 1.1809223742215968, 0.7976725771073101, -0.21461493794190362, -0.12155695556357868, 1.2007159000415508, 1.986369359249469, 0.9006427557170402, -1.0014239419502917, -1.4791084316057725, -0.10514567296137096, 1.0492991570325612, 0.25318687223978964, -1.3669680993649347, -1.422776154231792, 0.055364339028544395, 0.4033345973135262, -1.4857662488242356, -2.5285965473804635, 0.9065101545144263, 7.299863339763471, 10.532628457951313, 7.1189636465816335, 0.8149096517969621, -1.9628704732330324, -0.020502404219979384, 2.016894858462753, 0.7419806134163156, -1.658591307608757, -1.5203165892498895, 0.5863998654243024, 1.2425706532931322, -0.09544050460183376, -0.3929257504522986, 1.7285233800901254, 3.5495651475035666, 2.580416970596843, 0.4265788012805117, -0.12403537813557883, 0.3552796669112514, -0.4653427622822668, -1.9590475813166441, -1.4308577404452605, 0.5332758030183625, 0.06172997146158289, -3.435318303515926, -5.134360532541168, -2.054562074951173, 1.4426911664448263, -0.19673631945639936, -4.769492776928275, -5.173729346054083, -0.30570338280552234, 3.172565524710992, 1.1089376404368199, -2.2134232335479416, -1.5737837315320726, 1.0304984018440515, 0.5916658812622461, -2.2885834320492444, -2.8830925657287434, -0.5042540282556432, 0.8942832607161779, -0.18604307683215365, -0.9529962813648994, -0.157836330815251, -0.10584152473637679, -1.3687954298561387, -0.9646353622777692, 1.8417364462214485, 3.1383166910643348, 0.8671923501988154, -1.2972554155879366, -0.43407437473505983, 0.28259638063645237, -2.221088804948307, -4.156852330662696, -0.9451055472981611, 3.7471600903810858, 3.0727309295635328, -1.155058328967058, -0.7049412006589014, 5.334105990224096, 8.482967763271954, 4.322357624329593, -1.008838318276477, -1.3206173565354722, 0.7933203137812309, 0.5160730581569026, -0.9293818141618708, -0.45954003978192737, 0.289589129476008, -1.1693413395861398, -2.493175309142175, -0.8596855514447787, 1.1962479415935647, 0.3307127093937119, -1.2725699753548545, -0.2468015057174752, 1.3455175561824766, 0.2246379705127381, -1.3869823076089025, -0.23049793241861383, 1.0317874509322804, -0.9159951938759544, -2.178402445480001, 1.8295244614978456, 5.902982509621629, 1.7654565780101459, -7.269791500149589, -9.906493145829788, -4.175408132531098, 0.644007632207326, -0.2555634784149435, -1.5193104855403514, 0.5168748723367236, 1.9174370737344597, 0.3778345591564058, -0.1459267633363106, 2.0761306806818407, 2.7915419380466817, 0.22558165080341586, -1.3795330574223024, -0.00136722180652651, 0.7717782599048174, -0.5816979024430472, -0.8246886100405061, 0.7149689908051563, 0.6887764401257765, -0.6461801189338631, 0.6053360770622274, 3.2206913722686705, 2.0602325336385485, -1.129078032275394, 0.6059492878275023, 5.829857087306912, 5.344938638503514, -1.6260113655822492, -5.194002021043303, -1.6929601901452649, 0.8588077643171265, -1.892351948001966, -3.5771421739072924, -0.3883414477204702, 1.7790822397361614, -0.8055582857471845, -2.831276544705979, -0.6012378180601818, 1.5427827977523023, 0.4705682881387718, -0.4494842148361694, 0.6277673569690934, 0.6436903794507489, -0.8394704786887732, -0.4342210442230944, 1.245466779882468, 0.3179060972574208, -1.7952346507818768, -0.6999696054833366, 1.5201951385961971, 0.041111980118271566, -2.2927378902270736, -0.0351375255102154, 3.2805795632349066, 1.317283514305876, -2.178506928970388, -0.43707158150622, 1.9854348148301435, -2.995237057491389, -10.383193885745792, -9.21548094395819, -1.3896472784709224, 2.2963725832947026, 0.28272311706363107, -0.5916942444227045, 0.6230253784531483, -0.23914936497639902, -1.933976003641706, -0.6739326497802409, 1.3336675570338274, 0.6699403493189249, -0.10446300949199884, 1.3426351531872425, 1.4926062574109946, -1.1779680183191379, -1.9016357222227236, 0.9078975609122694, 2.183604236124081, 0.4390556386937981, -0.03029788526918411, 0.55074091191075, -1.9787333682722221, -4.405783965507079, -0.3974041285036539, 4.842420099484987, 0.9445450638414281, -8.211201987957445, -9.409024442620373, -2.368325853861153, 1.323550348512113, -0.9754499300203303, -1.6280445660630463, 0.5977463203978342, 0.09214454759157312, -2.416154485037679, -1.8813240009937582, -0.003172290447756088, -0.9565561703150545, -2.026623505769295, 0.18482871803404116, 1.9566791098576801, 0.21624112417067579, -1.122255398489415, 0.29514536022893906, 0.8890699028837976, -0.1613315895839935, 0.42877032555962624, 1.1003329701898257, -1.8651266437274603, -4.119176836759969, -0.0025544748300028704, 4.741164186823356, 2.4926568318200153, -0.9515975762680035, 2.771421566221831, 7.543976289851339, 4.027560015989212, -2.3781242585415154, -2.107467829301532, 1.3100651152935676, 0.6599437478979999, -0.5283454940292455, 2.53850764897701, 4.790049895842566, 1.8590356465706916, -1.1473608784499207, -0.4665969118987772, -0.05857116582008115, -1.5875509038897162, -1.4271117615518367, 0.1059445588587568, -0.519414023975458, -1.515847189654743, -0.0505491353099439, 0.2741898292749931, -2.7208389567018787, -3.44675535070299, 0.2065232131982356, 1.528809598737049, -1.2753049799747962, -1.2965597182946074, 1.601004060524788, -0.3296534833187226, -5.060663044566329, -2.4973003202069997, 4.891935917884493, 4.917243806932305, -1.649137737252543, -3.2307895518214558, 0.653138406679455, 0.996942238122224, -2.0614397747507485, -1.8008163261603392, 0.49342432112855095, -0.00598294955881711, -1.1236781368902258, -0.1378577747502271, -0.15512541772142627, -1.7193022650360406, -0.5513875688972529, 2.24046419029072, 1.3995232203307597, -1.1712608960055995, -0.3488379998557309, 1.3056132790926847, -0.08235200225247594, -0.8898660521713961, 0.8234848511534437, -0.06583996961235761, -2.838850728030974, 0.5453900343847297, 7.5755717916649274, 6.322372706689704, -1.6620055859906349, -2.6089677372153446, 3.99009913954811, 5.43256204096472, 0.15534908794226615, -1.8634877092808515, 0.5509658519080456, 0.806949739697857, -0.3619501552989617, 0.8478727266868611, 1.149460486008801, -1.6912448259955744, -2.4617274426678986, 0.3441110092289157, 0.9727840205689772, -1.3362843463588947, -1.5128424830504845, 0.051996469743142884, -0.06743882725909216, 0.42977372344770914, 3.058672801588691, 2.939926374655522, -0.36189961739392984, -0.4529727397020595, 1.5020363620685155, -1.730101249541397, -5.96602053510752, -1.461998526105028, 6.039303903499462, 3.924447895081387, -3.596704650136257, -4.226867519667895, -0.2986487112467381, -0.40176333687009286, -1.3628713560754506, 1.773274304010421, 3.2148539876207534, -0.66833420794268, -2.856337194574933, -0.1821629850121494, 1.3576010777402643, 0.10065643461513285, 0.1379709250114192, 0.4633414831129368, -1.6549135454185733, -2.710645881682817, -0.644860225681116, 0.2412235581122997, -0.36581133354946194, 1.919860051387253, 4.3167202318535125, 1.4138666634845147, -1.8094402248503325, 0.6170629364667671, 2.599141584138758, -0.5749881575860225, -1.0527149410302266, 4.091983813044504, 4.584299588104305, -1.566342038682822, -2.383562502806095, 3.927485510278075, 5.238201088811692, -0.24501076060292382, -2.11561613636539, 0.7210180904329015, 0.7911950395736873, -1.205506583318949, -0.5776551869046985, 0.12866084396061783, -1.2685361329951337, -0.8776174483972646, 1.1879348748460599, 0.34339287254608636, -1.4207826567663908, 0.152021743823656, 1.3475525558724581, -1.0175951277151105, -1.7874394691860027, 0.7565841754685868, 0.8686836693229555, -1.052334164457442, 0.3650638715156793, 1.597949342064826, -1.659184678597616, -0.9127503959661222, 8.840584233792022, 14.343461000054056, 6.637669345038071, -1.8290203838377335, -0.7159798615391317, 1.5762420383550864, -1.5332670357867326, -3.2519648276672504, -0.7921041017223687, 0.09932413133345364, -0.36132657899986564, 1.7415332408957176, 2.7657844954723587, -0.3421676256169288, -2.0252150447751243, 0.08277338448333818, 0.7052968617859724, -0.5553111616181634, 0.5570683644237887, 1.8056070685715564, -0.1071664332342375, -1.1409433083950902, 0.2693359412285413, -0.7687197705867189, -2.811975910134037, -0.6239069282358852, -0.2448128372985367, -8.468908518184168, -14.840075146050907, -8.693007840734435, 0.007066735190385749, -0.1384885967114321, -2.1109751338507943, 0.8747756661662919, 1.4450791333822641, -3.070104948101555, -3.9264196653839605, -0.23739079166889673, 0.19686757118826526, -1.5887310663684622, 0.06835944217134395, 1.8252493647383723, -0.09213134431205568, -1.0562409022408952, 0.7735758323704688, 0.889059142111815, -0.23509743924117196, 0.7890348290133834, 1.1589902316673284, -0.4857501470997953, 0.8823300378154064, 4.081905956132134, 2.033551168572952, -2.0285600604716296, -0.22986607624355104, 2.649544751530446, 0.11289279455350833, -0.8038729446664571, 3.8261339451634258, 3.630167316840982, -3.5544892190426394, -4.505320221308696, 2.839077420472582, 5.322753751680333, 1.0662696506651632, 0.12415807246460124, 2.089094149967739, 0.14044734098065956, -2.413249914395206, -0.8550044498473377, 0.47046081901751535, -0.6277423393977363, -0.1845060696875315, 0.9324383553703396, -0.09990815667621412, 0.6193668468225013, 4.36390994354339, 4.534112786732704, 0.5983240498588311, -0.5872189260330027, 0.27489571110928335, -1.430768746003445, -2.0239252948559163, 0.41169801984189014, -1.0707828925764986, -5.2714589934436145, -1.944370775774506, 4.8459599450117326, 1.7552655186744548, -5.958388548413013, -3.6726633048223323, 3.7265606727104004, 3.221970970658501, -1.1457334850366176, -0.632060332467924, 0.7098180794191995, -0.8734257370985357, -0.7194823504910917, 0.9268348626330863, -0.39010281014888093, -1.2956609952313065, 1.645571868644026, 2.934175305614663, 0.42433328533092673, -0.1447400472459467, 1.3189213190392126, 0.290316327633886, -0.7859214862630198, 0.6047855902075095, 0.019263868679328475, -2.1338335841597473, -0.3295142279519323, 1.1761388969193196, -3.387430145535038, -4.969016144338853, 3.0514414294505245, 8.010199076236043, 1.9472478414556031, -2.5166551797241374, 1.4126943814478659, 2.944533038428198, -1.078520659496038, -1.466099427756989, 1.3515567831736943, 0.40700889402350654, -0.7011241810379178, 2.321316973983254, 3.3166440805372464, 0.013906003247098894, -0.9556885066979389, 0.7340198241844028, 0.0462165103979567, -1.0653275808715779, 0.05140902725407943, 0.0011348022857280613, -0.6406178213059268, 2.0687052330509634, 3.961463349491212, 1.0641890509651273, -0.11315820327785434, 2.644474078459598, 1.2661096064087833, -3.259634469660895, -1.8339338009098798, 0.9418462565691686, -4.1407389663184, -8.8676214784793, -4.1569079585426145, 0.1459960196344019, -3.1325565218997653, -3.816106219572466, 1.6845779636957503, 2.8139536535879617, -1.4018032679660704, -1.822963722396955, 0.5156288022790257, -0.292629610053066, -1.2312999230204238, 0.17462808044018427, 0.10582328949418002, -0.5647189655281882, 1.175143700650222, 0.9383989296920928, -3.058053358170857, -3.971161605004193, -0.9360020596041203, -0.05011591939465694, 0.30519251833808103, 3.4830599121649706, 3.516337700000382, -1.0927204077204213, -1.8509253724179766, 0.3392453046754442, -2.6103492697479607, -4.237111360081831, 4.0624206055675405, 10.087970433783358, 2.3821112419727397, -6.2445993983864865, -3.687238044830364, 1.0399343608899199, 0.30827324938915895, -0.3419903784019944, 0.11079120364135629, -2.249784801168595, -3.3892946099134313, -0.3684814051097052, 0.835985472105753, -0.8307726483038712, 0.050338513787228555, 1.4383827976200465, -0.7241173107966155, -1.8172022364380276, 0.36943414919107487, 0.5145966529540509, -0.8601874109172134, 0.4282708277789082, 0.6358293643345814, -1.7239579414903285, 0.10002321379942267, 3.4477490796395145, -1.2599943037322834, -6.681874346619088, -0.044872680922178595, 9.01512213295687, 6.178681584769146, -0.304189198156247, 0.41205363206668577, 1.5719221701809958, -0.9881022039483444, -0.025171015561509177, 3.258594092882175, 1.4201229199520915, -1.4956877349346107, 0.14173397134728305, 1.0942442238407788, -0.919224406221662, -0.4733494538131384, 1.3194757651675026, -0.03524090407344121, -1.1777043915432557, 0.05031553046304253, -0.45622485900999815, -1.4521351434965286, 0.32786877272269327, -0.2793751085242195, -4.522182912276353, -3.5468076264456765, 1.8862116885760036, 1.5350009436918455, -1.3603672109248208, 1.6809504112864062, 2.895009287497483, -4.1579145759409375, -7.41937898976001, -1.4953465287588465, 1.1373087166261553, -1.8884738601494178, 0.30839898240487595, 5.489264829063896, 3.8320112152473866, -0.28743450586961644, 0.18429107875578085, 0.8554169916359919, -0.45074215483885965, 0.5098436220682391, 1.7375685366896885, 0.032104651705467536, -0.3222485911511345, 1.3565225024672438, 0.27239833390343904, -0.786900113228166, 2.1712118438940187, 3.1736111379917196, -0.09298542411482304, -0.35788346121595593, 1.8110820622440884, 0.11432293669239543, -0.9667703118162523, 1.9170470016604617, -0.05815422926621199, -5.593735944656289, -0.27102381702839895, 11.890526397140917, 12.201389315476188, 2.9593479950691024], 'positive_zeros': ['0.83154280060458684103309549426', '1.89024515844596461003358430524', '2.73110541199766845152783335303', '3.16395436045269994293858248586', '4.20377276310102855739370206614', '5.01932045805960904173221885697', '5.671832607600181387765644440753', '6.55033348488964793773796461762', '6.96981609365290676990262508656', '7.76016561531695664541543301482', '9.11320990095570459118773047900', '9.68968290989701791106120565728', '10.398792438021979852907515223969', '11.16183195727076442602334999245', '11.85404726440491424539346325842', '12.27244561360110114900444160606', '13.54399101740480675458941942768', '13.82724411450187025303933230712', '14.27101334091676486184847173974', '15.21545800711246096771488836995', '15.63272656090993799363298960793', '16.71075587101816015255703698059', '17.17265443005385887665727394598', '18.14257185717141753590212301691', '18.83712179223869698270414651363', '19.547701775700312895251761924304', '20.069748240434330327486780828701', '21.00265254411151241948170266847', '21.52386866062062308691467052161', '22.25270876376669992277642889506', '22.4582199675403553566125881339', '23.24713794673762682369160884745', '24.15310438898237978819561607417', '24.77334155160864085177385192333', '25.06625670573100794419354934431', '25.99228739298133050209877461201', '26.77941099758530600084820870540', '27.23487923906802664973801998534', '28.35657242209008591074727469580', '28.92926175209465231348859198357', '29.471092835702987383976007729886', '30.118488332877750375145076803347', '30.42587302617659172469038031251', '31.35179933184437002740620621825', '31.925058530741884198838071949050', '32.536590768235346595372684648151', '33.15710763193373694938897755064', '33.78440209038397750687502767492', '34.27036035112645246428480746336', '34.8951708838252378143905870229', '35.68736031324060870434966107197', '36.79674133421773503988942772377', '37.15285794739490756804772051297', '37.752486939339187970608356735093', '38.50763174313959923891614943318', '38.78301358259155419963679946738', '39.711834321552679831964957744701', '40.312735527937851094062415765547', '40.82122445371932283213462549765', '41.4210667843206917462543811738', '42.01618953210508317820455705359', '42.42515229551515449151401095106', '43.303123424468816790154111024621', '43.70783606317037980507116207091', '44.61859572654040229607632613288', '45.4413176789820487612655005958', '45.7711106804275547349617892610', '46.5932394410159479320785697878', '47.11697045103765692781847320924', '47.87166867695123822568921621767', '48.525886818383168793761418648', '48.910210574029411335295979803670', '49.50885822331296201804340783343', '50.0730547657156392093534511662', '50.665610961912644619960689277930', '51.32900251134562014531254699242', '51.87914591143131035535790908279', '52.50262921905087007621598531960', '53.21936950981899181821192891783', '53.78529385225787067850349910276', '54.24574609105450834670498450914', '55.378059953405500412507468909620', '55.97547994869859353259762488515', '56.396980394370485108087303436054', '56.837615791931267970431171984461', '57.582894183564258971221976568713', '58.28558970318957424807215644839', '58.48346216461745243528136910910', '59.24885084568084990812255241887', '59.91053832332577713701048661531', '60.72070057842837855825714218085', '60.94899861042357814836385517176', '61.37078677737719764208460717685', '62.20608561995828532876171944524', '62.84527022939325206835497192055', '63.87300613775289212686753615914', '64.271376575862962999413472675692', '64.90816756874441981603908230373', '65.32414625462646676265379214317', '66.251476405229606530817223310117', '66.362215252400873460441282997198', '67.16837653919659679252209880985', '67.84017296694111747028796440021', '68.38591347007776639164647437932', '69.001052224388641731153895675339', '69.273532836585926837424858623748', '69.84601415495141858410613257684', '70.62512721547871780312241165663', '71.41973366031578950607793356436', '71.71614863543741937820608781129', '72.67411607156931527490854144505', '73.294941916244988149519885713171', '73.842365649985687256689254989435', '74.15613316330749098380526131648', '75.14863758571712099818104015260', '75.75039829666735470875667930587', '75.91653065817198895520240427584', '76.838848932190415312366502316141', '77.069783032668002122376335663491', '77.82110448093993243302839296812', '78.16740407801720396041524118935', '79.04568204083864831546042598500', '79.55660913102037274030533755916', '80.12963041057302903579517095093', '80.60378225168563179293361450346', '81.35184962166579192538036119707', '82.106237311309218708806697903554', '82.75691368376811172457892468386', '83.22775954176155918657963025274', '83.97216820774850243546052319713', '84.37388064386416674159579044146', '85.04000060679341053844242185109', '85.272596731550260976749812525', '85.99363484551521369142760830180', '86.70879665849862080553751227181', '87.23418012680496424991971376878', '87.80019915009383520602932207984', '88.29481035636436554172386130621', '88.743126952227767361724208786442', '89.35023150378977470820440213972', '90.24095076358448475573088205362', '90.75863909976061026415112775350', '91.57211521607595996169890166762', '92.11664516733955196620553488850', '92.66645430213745306347988097672', '92.96968320808156585304557530477', '93.582786287867412480133021908498', '94.33706414129250334952089363851', '94.826902890480044409343258206520', '95.6081494199040345260122916311', '95.90279592589415247921451811816', '96.163240793167274843177777150366', '97.14776718686482714466164304166', '97.55843124317625770826959079716', '98.02050623830835209835541385172', '98.80234946939232363367433517279', '99.52779089016590955049992392869', '100.35542296584577382505093016787', '100.55402308799359269506966768462', '101.10661997746361437171350751464', '101.82993710531609704754623444753', '102.518015582218100760069472429330', '103.15622300348869103456284240782', '103.38721393137550884337444078180', '103.85014482730166975596437551495', '104.79449457176542767447776983352', '105.09309304861571429035031327845', '105.41775185449175208791869255607', '106.346072551908697040269298963905', '106.82569490524542516605457820581', '107.452400317328819300948753568512', '107.89156952617590756063273731045', '108.67065753922533017020120407314', '109.19263399937539120765985612277', '109.98567439312399593171237797735', '110.54418112683321637508078077358', '111.046706881634433975832927662623', '111.69319637272277361252096282474', '111.92142603473128805673424858105', '112.62026791484565239861242976556', '113.16986210115372566157451804089', '113.73124327905493146675215353833', '114.26451721273008942895442345205', '114.90884812719613177816793563928', '115.4338250113442310895867656854', '115.89504155614341669954663517974', '116.42759304083083205992476116274', '116.916838682540627820231973223885', '118.02199371760657252634701489565', '118.49436628892348616026634246631', '118.94356235312555140059493948679', '119.81716262509344432986187785207', '120.041417733754658891712157685945', '120.40551085524092768589790448864', '121.220955697511449381151450251349', '121.86372218316703324764484953826', '122.341707186328406299486191802905', '122.72671133114336418967593415390', '123.423992141042834635636796672209', '123.99292831759063247883509481913', '124.26970635337349654113129977914', '125.06520064794751671364429433787', '125.292103121330274393047521575503', '126.56202277577399295664731266016', '126.86155074814625879538417978204', '127.42634661257255151722866358053', '127.927121857126261939086000394112', '128.77603206690979915730537981919', '129.09330783926387291781948392603', '129.68017793347195397876293885584', '130.30107847979503803091975161724', '130.81464062103842643829549737768', '131.45124112967793323537023973613', '131.70691303556027077043172917249', '132.39525226597545306686635472331', '132.72061691413712552875049598150', '133.56645264433682331312774192059', '134.07964347471575335472570518757', '134.69741428793949581229811491370', '135.0718206305716394822119440724', '135.788781675135399210371006159592', '136.44858110836655049386201201365', '137.301244113220360996936496350382', '137.477434716784626760027198238768', '138.13712624005295134335074424286', '138.86859976809466477790412095319', '139.21688451648236787002599665698', '139.7237311433623306708227632423', '140.286699045244234486571936901654', '140.54314820764504508085970201455', '141.62359096075804327995184900255', '142.03083146677446851079691816629', '142.28881422133181352873227511207', '143.06284386188547704916326484027', '143.34896075472559972929885870790', '144.13936268284337592843419964617', '144.75068054587678197104005176992', '145.452244963782276444095879992132', '146.14377102140481996185149935053', '146.64834825848525146914109047257', '147.0415518356126316459359838041', '147.6117821577761851073271637201', '148.07159354153890222935483591863', '148.6032191125195945745227865878', '149.436499973530955950961499413966', '149.71928651349745292769003819194', '150.35803710827802192817118814825', '150.81714375894518931862869718580', '151.25253454587516089898741392054', '151.90619353629810427008109756204', '152.3049796737379825013767250485', '153.02661713511332306459344291751', '153.83031793574722438686470634976', '154.28882421716969122142103821079', '154.91717382420247105495797340475', '155.45870688514051893265166214801', '155.98999634880106598709932611172', '156.35451574216690830499560739032', '157.18886409243460770017382157372', '157.66563375791974869437284512993', '158.13298104027743872474517908799', '158.73668056219319313907056645414', '159.0628028105126627372660606579', '159.492778313526770114968739765182', '160.42768477330235683966029229080', '160.64402242564075148613125156484', '161.32982942899452330522407833944', '162.01072978138476633100871429601', '162.299446099115191960396167027489', '163.38134773710512729886979760187', '163.49001401471439947154233116136', '164.28252092852201827273196321524', '164.894076119124086164974953709260', '165.529824460963739589578923031592', '165.889048588687922305399857037726', '166.52303429788035014037137117714', '166.90226101333093363173856807225', '167.32325191461568478873360516636', '167.89848234620549990412573908535', '168.94533856307834736659714988441', '169.02084223618284103024644975296', '169.31728565780176341520274177579', '170.236421537992275614842947598026', '170.84383736978664549839418912034', '171.04133439450456781965075375095', '171.75321340857234052889672201251', '172.56437985548534695391377471975', '173.33001507086388941905742477010', '173.80539795165773216375968442856', '174.184541296098859113797287823851', '174.40872787704753812501736705316', '175.349706934401953087118681158983', '175.779256292571411539542506397790', '176.24299259015468839839605613570', '176.796648356734165854821683213245', '177.44753516036995913922390472305', '177.90455253245144632841958805178', '178.36796058480258535503373987204', '178.83635643375105190982095215956', '179.36790233986864743223941054294', '179.949303729709540478233386337299', '180.626244238251378160052680913487', '181.53538060389811268602754360994', '181.82910241719745108074838329422', '182.38102770224175446826352603888', '182.814685715697851518853489739161', '183.54917200992364654640003248803', '184.04559800815295313109129033836', '184.54893850596331401174283319247', '185.06481380498201312494594371087', '185.620144898920571208719834802989', '186.2345426071855762117819120966', '186.46381496751398418717460164941', '187.136878759227399728056088262118', '187.47298337427520493269109354959', '188.31654151796733146631684017669', '188.873341575450917627445143493301', '189.2579585767718449562107368572', '189.84111556293743874031928465543', '190.70569395878673518451502945710', '191.06198191004608686621958220597', '191.54513781815405263193575867926', '192.46139822677287314166481589230', '192.77995752117820258259946268158', '193.3153733172600387869901245883', '193.6685199144871477075725172622', '194.38014072866165877079937358501', '194.74801224643173093173003087327', '195.34971732646528993354139957648', '195.742490598330501449068585809555', '196.552694219728318865053518272828', '196.92109151908647509170585710584', '197.51225091428798003189491413874', '197.930773607247148771833564611704', '198.43441274048067449849508786395', '199.06958664810438155631938591114'], 'prelabel': '1-3381-3381.1223-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': -0.29523700671289904, 'root_number': '0.599824630903308565867907834356-0.800131496793939268926489790906*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(462)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.19668654428104398339213553861-0.487023223452255960453660687706*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.831542800605', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.89024515845', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.731105412', 'prec': 37}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 15.701297990361368, 'bad_primes': [3, 7, 23], 'central_character': '3381.1223', 'conductor': 3381, 'conductor_radical': 483, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3381/1223'], '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': '1-3381-3381.1223-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': '1-3381-3381.1223-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': -0.14761850335644952, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.831542800605', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_3381.1223', 'Lhash_array': ['dirichlet_L_3381.1223'], 'label': '1-3381-3381.1223-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3381/1223'}