-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1984.653', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.7604059656000309, -0.6494480483301837], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.9238795325112867, -0.3826834323650898], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.15643446504023087, -0.9876883405951378], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.15643446504023087, 0.9876883405951378], 'algebraic': True, 'analytic_conductor': 9.213657264973959, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [31, [1]]], 'bad_primes': [2, 31], 'central_character': '1984.653', 'coeff_info': ['x^80 - 1', '0.996917333733128 + 0.0784590957278449*I', '\\\\zeta_{80}'], 'conductor': 1984, 'conductor_radical': 62, 'conjugate': 'dirichlet_L_1984.1349', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^129', 0, 'a^75', 0, 'a^62', 0, 'a^98', 0, 'a^87', 0, 'a^69', 0, 'a^124', 0, 'a^68', 0, 'a^61', 0, 'a^31', 0, 'a^58', 0, 'a^70', 0, 'a^67', 0, 'a^41', 0, 0, 0, 'a^56', 0, 'a^57', 0, 'a^35', 0, 'a^118', 0, 'a^26', 0, 'a^31', 0, 'a^93', 0, 'a^84', 0, 'a^124', 0, 'a^37', 0, 'a^103', 0, 'a^82', 0, 'a^30', 0, 'a^139', 0, 'a^65', 0, 'a^0', 0, 'a^64', 0, 'a^65', 0, 'a^107', 0, 'a^78', 0, 'a^82', 0, 'a^119', 0, 'a^69', 0, 'a^108', 0, 'a^36', 0, 'a^61', 0, 'a^63', 0, 'a^10', 0, 'a^102', 0, 'a^51', 0, 0, 0, 'a^56', 0, 'a^72', 0, 'a^25', 0], 'euler_factors': [[0], [1, 'a^129'], [1, 'a^75'], [1, 'a^62'], [1, 'a^87'], [1, 'a^69'], [1, 'a^68'], [1, 'a^61'], [1, 'a^58'], [1, 'a^41'], [0], [1, 'a^35'], [1, 'a^26'], [1, 'a^31'], [1, 'a^84'], [1, 'a^103'], [1, 'a^139'], [1, 'a^65'], [1, 'a^65'], [1, 'a^78'], [1, 'a^82'], [1, 'a^108'], [1, 'a^61'], [1, 'a^102'], [1, 'a^72'], [1, 'a^83']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1984-1984.653-r0-0-0', 'leading_term': '0.770550638653859292511186693779-1.43328620487967869624782819068*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/1984/653', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.6272853566072125, 0.9698806133280806, 0.14405856760892, -0.46313262224730434, -0.1760011688439107, 0.8402017998772537, 1.38177240995762, 0.2843347168616688, -2.158201169789905, -4.000480490680323, -3.2678321645138695, -0.027265320564998592, 3.3172019269114448, 4.162500153423332, 2.2686688629386675, -0.036216846814327304, -0.39366898376513715, 1.0646261387785068, 2.1187067553387227, 1.3109085299788377, -0.25805978546133035, -0.48226856401289964, 0.8112694227792715, 1.4740203098483111, -0.0436894517160476, -2.228752255394588, -2.063798654406371, 1.0116248762853666, 3.9073421135476765, 3.4244061241358352, 0.249397944383422, -1.8501659168453197, -0.7700013169894971, 1.416155639190751, 1.4899401058458452, -0.48941243300576853, -1.4405495144894018, 0.24800011688966847, 2.392955388930221, 2.168143481587217, 0.14365035590238903, -0.6895126726390342, 0.5694584376149552, 1.500959389066755, 0.39085919098276645, -0.6348395757868401, 1.4179147922121547, 5.327571380367457, 6.307640864443142, 2.2764397876658795, -2.925251541045416, -4.227591036668005, -1.5904869325668696, 0.7584154475123289, 0.502112816011575, -0.3299593077090599, 0.4009546923623202, 1.336101975814376, 0.39170032296131285, -0.9851199212274568, 0.40470559086366387, 4.062099055488112, 5.634184141592241, 3.1200661737231226, 0.07209831277289787, 0.42930450376781376, 2.603972055412584, 2.016546373720782, -1.685450168355131, -3.915170246307662, -2.0671599886416194, 0.7240983460927477, 0.6831451458927469, -0.9620730540574747, -0.6264072116389254, 1.4574685854507183, 1.7953463717273996, -0.2695009171666884, -1.3805980049010071, 0.04087981443188005, 1.0107536467640033, -0.7209649721142783, -2.208217884279682, 0.14247940706932255, 3.985526511513276, 3.7166032969344873, -1.0103803483809646, -4.3979764095379394, -2.958669479828681, -0.12573407604703693, -0.17328096486170272, -1.746668733023807, -1.1390270968463914, 1.1006025747386479, 1.5259483147225437, 0.03498774359075726, -0.39726045430098567, 0.1917640930330834, -1.5936481386999517, -5.647382131619523, -6.571833315552424, -1.6158109959523732, 4.1308417769013905, 4.547251804361198, 1.021007554882083, -0.689235321518554, 0.39607160402390845, 0.3168926930469377, -1.8526630777568456, -2.296599199588798, 0.3256136043597085, 1.980002331700843, 0.05183205854684164, -2.1846396754979436, -1.3375657446633937, 0.42595248276804715, -0.17023160502007548, -1.30929989739057, 0.24465066336654934, 2.19807038469259, -0.10689073090637716, -4.989255459158123, -5.829312489580884, -1.4450761369578677, 1.7783522401068528, -0.13227263544420573, -3.134294643212917, -2.5980210559630863, -0.3750538007508931, -0.12898251464331167, -0.7150024288971382, 0.4562109490601586, 1.5289602234038404, -0.2979293139096583, -2.44944836067302, -0.6974085781818798, 2.8948536839753265, 2.7979214294576114, -0.27571384118289777, -0.07383173937586882, 4.456909595527765, 6.924432724357408, 3.8920736892564474, 0.08367109196767769, -0.035720309682469434, 1.0151629747268693, -0.20379098789935615, -1.4875838917120887, 0.08958773879359085, 1.9325623852267737, 0.6993204081557755, -1.0237840664986368, 0.6743185376377012, 3.4324282154271266, 2.657174015795316, 0.14516893806500297, 0.9769072160778526, 3.9428412123266154, 3.4335610167120487, -0.08023352707458103, -0.28355508542117874, 3.798140482545781, 5.662698652191249, 2.248879431102797, -1.3587189221056448, -1.0217708631833604, 0.47664491039130025, 0.1529826421911788, 0.099703723739473, 1.7629292838079373, 1.9727407364079914, -0.4567972370880016, -0.9360045675171039, 2.6039477870518253, 4.259273792639643, -0.5360099079854371, -6.377122930132434, -5.950915685925155, -1.4037250037247286, 0.3452266746162963, -0.9583223795181588, -0.79351677156315, 0.5196911994706606, -0.7450037672624021, -3.1861708765690198, -2.259192593061996, 0.8634906501510922, 1.1601036630136896, -0.9041534780989147, -0.6685868008636711, 1.3706074006656364, 0.7254264730572698, -1.4272895748904997, 0.4177733958405601, 5.124503702351555, 5.4464026621072, 0.5022135050221206, -2.401799019709429, -0.19384463416323974, 1.7458571935450728, 0.27796763305699046, -0.512977234406746, 1.6357495484172206, 2.5953551497344565, 0.21642614287020193, -1.503189957217012, -0.42045895198853067, 0.1634307871910662, -0.5558166139438216, 1.539303235007451, 6.085170027732834, 6.017923115635933, -0.4619359566136331, -5.221835747869313, -2.9377064203805965, 0.8040230078299611, 0.07877877793182254, -1.9101318164001673, -0.590476326537334, 1.4339912116315687, 0.6567649504314629, -0.44905806339502724, 0.37834711724100023, -0.15511281909845373, -3.5331980020344957, -4.633707468032163, -0.8214789100760856, 2.262047522299526, 0.5545472511126458, -1.219485040002407, 1.0361742330795871, 3.0347360356168753, 1.1412444995785829, 0.1884526913183867, 4.151819067386471, 7.591502392464471, 4.913954879117906, 0.21148612595332192, -0.49220522585959126, 0.8494841603982068, 0.16122308311011227, -0.6670106308777412, 0.7071422854988103, 1.173246206775118, -0.9573351994428538, -1.259939630830122, 1.7580080726290066, 1.8523502438939197, -3.638037213550345, -7.208010961188999, -3.5326963743097965, 1.2603671051368293, 0.6064069540496956, -1.841812220439973, -0.7393151105794755, 1.2024707048625876, 0.20270392079492414, -0.8397885374106393, 0.7052124662665322, 1.27147740916648, -1.052867664580681, -1.8189543265632218, 0.6465000168825055, 1.187232137711343, -1.6501730674457367, -1.7282394397540517, 2.6756205816929186, 4.369481922480073, 0.25576227990873, -2.852200315617254, -0.9031139510722442, 0.7690980337587104, -1.1508332600657336, -1.9035586901357489, 0.7576277670297397, 1.6950793034021459, -1.064992381690415, -2.3198274186370904, -0.164331630840732, 0.7713772973842528, -0.7009376109073671, -0.5584123217896925, 0.7824777106858494, -0.8710182390082644, -2.8114103157394252, 1.5104156364150318, 8.813757075184526, 9.12036195738816, 2.415077303980227, -1.6103445551185862, 0.04727376905700106, 1.2876969699598928, -0.04605184797508313, -0.2009786228523772, 0.6587107010646713, -0.6847691737267968, -1.96314084341726, 0.5343601012836712, 3.065032452402285, 0.8152786339272059, -2.164337462202803, -0.5590251979466014, 1.5246007531590156, -1.1502631023349303, -3.9030784936537435, -0.9855492350525528, 3.0159131048068923, 2.014069935292022, -0.3124858071638159, 1.080242998754938, 2.4439613563970983, -0.30893454441734314, -2.79507627448398, -0.9969531636048317, 1.0964133132478155, 0.2596174847230326, -0.2342173709239217, 0.5122789163462906, -1.782507699934587, -6.036074248203771, -5.3235341960028295, -0.22901112561891998, 1.0543463661717807, -1.9765036838300971, -1.4287601396141643, 3.1993334198974406, 3.899540084956727, -0.38974823116126667, -2.348607441054789, -0.36211342342087616, 0.2821887518723326, -0.9471540043428474, -0.33943628412315924, 0.7762834210499792, -0.436558915539639, -0.5352271395403989, 2.9595138796111624, 3.8984527610124, -1.692495530797265, -6.365433414851707, -3.7722917882173532, 0.18622084902622954, -0.829062514768219, -2.4575925099197797, -0.18183461262895326, 1.50797671460651, -0.5408943768087385, -1.3575308993772675, 1.2291313337858647, 1.8442240379549908, -0.8889127439055342, -1.3754105823985139, 1.113631788789563, 1.2038853528028195, -0.9631557273010658, -0.5821277172655763, 0.8327889713956014, -0.6818521776690143, -0.6885397689928178, 5.957681308775284, 12.334144292596198, 9.355345502581137, 1.5923858827227493, -1.112539121508642, 0.3309777264798004, -0.04990004541319727, -0.9992582348776459, 0.3805172599996618, 0.7711071252389335, -1.5857919142042216, -2.0362038985872477, 0.44091119855773475, 0.6155526585201379, -1.2337473239804935, 0.920914922347565, 5.190095481070552, 3.536650541491239, -2.3345874097406827, -3.3014341359041186, 0.19734735896083527, 0.14237168429301397, -3.032475738719179, -2.7129214220977165, 0.018804899540056128, -0.01421507199742878, -0.7197175359378608, 1.5425424148292775, 2.9748063894392285, 0.6016357720600118, -0.5976749095056952, 1.842817807069124, 2.370641620798395, -0.6041868397776398, -1.1980217002032398, 0.7860125147525315, -1.1678957678822024, -5.61952034313579, -4.341317991973947, 1.2403955496949326, 2.086119007764693, -1.3480040636575124, -1.1673898909966165, 2.11684740670697, 2.0919473467730527, -0.2980424907743067, -0.45691055079637544, 0.025783902049768825, -0.8821004007851142, 0.2192154489296585, 3.1112097039473348, 1.5649496152536306, -3.2470348076645417, -2.070440153503986, 4.986563392883481, 7.269001380972669, 2.6171869025702508, -0.20650327251758166, 1.2152546041414163, 1.1763381544433091, -0.2048328965271385, 1.5265321774953835, 3.5061970333835504, 0.9599498316224476, -2.0819523510598827, -0.8267728576472567, 0.7277938391734923, -0.7886804263118431, -1.1083600343933397, 0.8592012380257894, -0.48962978937463003, -4.42743576020451, -3.5011686611771995, 0.9515404251226307, 0.36250448747594866, -3.9344769114864704, -3.333309657950632, 0.8174896837009107, 0.7009977043323702, -2.119728309171832, -1.2521931927205483, 1.2160774001677803, 0.6821612809075008, -0.04395366356421553, 1.4972656714575776, 1.390736255941552, -0.6789527018460086, 0.6236781228025441, 3.82425964545508, 2.1567441316657257, -1.5377714890495062, 0.8244840918696074, 5.554358841374336, 3.228757157103903, -3.052727573008603, -3.7932430744761914, -0.41583424819875014, 0.22972965917917676, -0.645815623866382, 0.1671131052681436, -0.19573341790930154, -2.0461042279043444, 0.04189905489326004, 5.016184896287982, 5.194478317306359, 1.0672294960342628, -0.1603305951657203, 0.6118442392871477, -1.856880034236551, -3.8714892762894815, -0.43439277094535717, 2.420899921570235, -1.032421276614082, -4.08929393438239, -0.9180070894186005, 2.1076493506633427, 0.002850343721721915, -1.666569738661583, 0.30158611701445925, 1.096114939106839, -0.30177784939045155, 0.09172399461039295, 0.8018010533545794, -1.2469390886214007, -1.6465620271933545, 2.0925052400047783, 2.1751295272207964, -4.8143588561548105, -8.877338792082133, -4.292422764069272, 0.3275580395208062, -0.7523715923747567, -1.5623286734566046, 0.614837969265176, 0.49070047143895945, -1.899205024477947, -1.2865956734256851, 0.5536186945560011, -0.9142111940227617, -2.2780284015697303, -0.05134186085218831, 1.0456873759748524, -0.7751060019507934, 0.7533774128349855, 5.4946859437195545, 4.762419825400739, -1.2279719474921014, -2.9797576179346237, -0.10469680547661067, -0.1809101677486075, -1.9486140687542814, 0.6550364407586727, 3.930497362660386, 1.894464253374649, -1.1296540034261333, -0.23096554986521445, 0.33743025190731873, -1.956009220217335, -2.2748712429506837, -0.06214029175101511, -0.027838752778922456, -0.5371429442860159, 1.8912745208448987, 1.302548023245499, -6.727884012289675, -12.411736445636036, -7.375017105958108, 0.0925281142679547, 0.6333297231395695, -1.3068183319437314, -0.35497400638675386, -0.14392467460938013, -1.956987946797455, -1.3233170835826704, 0.7429123241686896, 0.043357909936622585, -0.1428943603635749, 3.4379432808902806, 4.530459508884155, -0.32192719458787233, -3.297839754098628, -0.6565933515608935, 0.4148474282571575, -1.8915074486755699, -0.6220909479745484, 3.2490150676068708, 1.816723356710984, -2.528139099487976, -1.520975602510621, 2.2277231587943627, 1.718172791083651, -0.341727535105039, 0.3661657322796747, 0.30579585336862525, -1.8704357286481788, -1.2424718882925783, 1.3530310315556178, 0.42291654453532884, -1.0329931955246523, 2.341821919631012, 4.915566000455274, 1.0665581753293945, -1.6372996818377799, 2.7778550144888468, 6.037073844631026, 2.15536791086573, -1.4479832935416246, 0.06014669664472862, 1.1870712619030737, -0.012023071628127036, 0.47565816041655395, 1.1665503702156568, -1.1832711332532702, -2.380896895852653, -0.13185082194734601, -0.6757637700847313, -4.808104616971048, -4.231663018551959, 0.7818968037601775, 0.5350278615966044, -4.317116588266932, -4.141758287246352, 0.21331309349669283, 0.8854761816370083, -0.6028481468027025, 0.293463202166186, -0.43127640245727844, -4.792412044121496, -5.635203668443161, -1.030952715956975, 1.4369764189585603, -0.03473261941468318, -0.215826570706034, 0.3442244331633431, -0.8154431043729642, 0.9563296221761659, 6.448280413694213, 6.2619110996938065, -1.2805912063389384, -4.428719732656389, 0.3361155139578008, 2.66190760095042, -0.6472842101127478, -1.8972903035985422, -0.08466417733810531, -0.5020718516968261, -1.4538570317768817, 0.3796871744536846, 1.103009369273802, -0.6347299404686124, 0.4238340705848964, 3.134374874609012, 1.1031086307747366, -2.0904026332019057, 0.8788364711778477, 4.725434295481725, 1.8705765454868786, -1.6496662187479572, 0.7331086258457967, 2.608714651458984, -0.6678022238872674, -2.460909633278379, -0.20797230247347986, 0.023131472958339706, -1.7637667138810997, -0.47509635728269606, 1.1083965940497995, -1.1787278344494236, -2.4483167021596253, 0.23242573914199346, 0.8748851534436822, -1.4242199667461157, -0.19447114117528289, 2.7129355538573625, 0.3800316699076668, -2.662174771607263, 0.8993248028042606, 4.574245301372325, 0.8287699954179424, -3.354920794244352, -1.1250214824450644, 1.5205924000035385], 'positive_zeros': ['0.679431322765313613105024263465', '1.31385022920770509767125219462', '2.230184520516688319710117855167', '3.43973576860312934923273478217', '4.68037885449869454337313488322', '5.10865550860017547634052223087', '6.18826506996404401616838798215', '6.70095912825053855867566977637', '7.4941816156221567250624803072', '8.35086407275717771330059322597', '9.39902278487055455383715733388', '10.10121975930020839803895057956', '10.86550341383316886193659380028', '11.53121250643547525764278758484', '12.52441948181552376198258623744', '13.01502342565152197485503268817', '13.82378260901930012177999873593', '14.22588393831990763057996217943', '15.43719776417153992582605792040', '16.4222827240875741215596839665', '17.01746021947179242533001381044', '17.39579227984496891487351255751', '18.19417897052958710038757947525', '18.70596910615289926977756093034', '20.0146856749197179469800718274', '20.23384087024848638294845600028', '21.11882847695197670378112903337', '22.08355284712466382590274010797', '22.62361943679971484368720530674', '23.22424393448123713629024701228', '24.02567938740274101313564745802', '24.68077071201268402000651117607', '25.21802932703717752074727252417', '25.92638375178085341909624273823', '26.81507179229227615464277513254', '27.83759643238520037454460773957', '28.08568780097140874775136018513', '28.90562503746720390560042232259', '29.69544980246988107476462735315', '30.16763124033860643027973444676', '30.41503336914335201892787166953', '31.63785648520235816126025582658', '32.60970298708580478253528954471', '33.03171813171024957613717694057', '33.494298674846269859039744670810', '34.341617808353440888696124482839', '35.00548454366187032947712711064', '35.83059645834177844971982372613', '36.21536961781276022676147389984', '36.84568440040390866057146568844', '37.49265714836212762555783115356', '38.53298512040451118237849628757', '39.05083726857623421856163342805', '40.112901315481340292731690040476', '40.24828674835997263119143085426', '40.85557009742002354542807410769', '41.52968419989917760029205826695', '42.24475462883149844208908538280', '43.0917150353328767064181243221', '43.44496945243301646484922572115', '44.700358454682298701915665095310', '45.00833973758010110229715154965', '45.59300001720959334033906903580', '46.2389252781769492907348826329', '46.967085450467302649001348090398', '47.42878423266598730214587309041', '48.47831566654793015013416549117', '48.59013489192097462647478825805', '49.67881481961642347518910440092', '50.03074024908511848997161694621', '51.09789366010311713405086178033', '51.74164060012459120392459295136', '52.25412626316386035214873858803', '52.464952245453737035784624359092', '53.381910466660645824391504488258', '53.85798215567132100879006986208', '54.66300674672888637894354421667', '55.77129796586214043585228394331', '56.04612227240334628104146650616', '56.72106904344691040435386031518', '57.08767942207618537480683333484', '58.02809463451142499703248819693', '58.60867100737215779501846173648', '59.16027108414111366749347350921', '59.77807880864761633324422139891', '60.28091652524166123564216628593', '61.28073022103247784787535220270', '61.89390987423818512675560365439', '62.54404259619413681200434855232', '62.91750542227959723004461264441', '63.77355016433560780998335554816', '64.47592827804619558869326310197', '64.75818208890506449614573308982', '65.16478724951752155893992975018', '66.23040433546970791461398757691', '67.089861316499500514835802750052', '67.50984132522975571092465914861', '68.19542720368687976858225135397', '68.87648441390640809211495389228', '69.26595201250074639912384244924', '69.66581032098611772490955741103', '70.68053672651956475011405039974', '71.30923789201824890396023360420', '71.77388598120306059092450564299', '72.69044483319761609473488775245', '72.76109122745202357133034203244', '74.08488978190758736557556651434', '74.47746101833233094922045236172', '75.03399409078014950170018023329', '75.499544393402804488978455326963', '76.12486518732460941975141497446', '76.70741315661614322108167412678', '77.316429654310509158524133144754', '78.32425150895010116609952846294', '78.81370373800916762614833854614', '79.46532990153907269366531697454', '80.03371259387526589144237286692', '80.514363238227107371228192634966', '81.12661194794639806681348633780', '81.80045690455800718863807066236', '82.33235994751928559764267377983', '82.951602935802746981524072497281', '83.765876083756254091903254919710', '84.474899564185989433114677439996', '84.85395530744981224649633516848', '85.546615349952976609584427519686', '86.14595374001121429673943463734', '86.897021609000114088909036473050', '87.36195972922264733628696769576', '87.91800323302079757864548200299', '88.339924765285590187386887586370', '88.994762888451797800718352904653', '90.126160201597260880840949976397', '90.61924546917241095164283894770', '91.23935060332854332105806443025', '91.62150327630256865751323067765', '92.08495949618166491295994126067', '92.76707570735781652056905249972', '93.50169121373446354203076325902', '94.11695059286829504858908125364', '94.59810413774220372910440255386', '95.37403934638317451263205336616', '96.169217237373528733332088454961', '96.41350833725525590699079358447', '97.16229266312278463380232728590', '97.92008587478908875178596434419', '98.49943950303280822168259537175', '98.835634716775318297587662125309', '99.2074532131308449445208175308', '100.32928647700927783172640207054', '100.7450812830581283773470991748', '101.35307843943588964719975027866', '102.15999970628809631408260780769', '102.87167127143559639204959082586', '103.20176438176903257325087520072', '103.81487162579062973251047699691', '104.29508954396839617919224140453', '104.75389877793742455231060902685', '105.54914614455964778045340632360', '106.53227671852059545410974433583', '106.76609252355760225886430950805', '107.5181335469112031112739059830', '108.06077283592213862714019598852', '108.618280448749393059213471160479', '109.27838034234504339819681834487', '109.86323080884460252821643164396', '110.47661401238716623120706584338', '111.03156243535023024311713366733', '111.46712921172471679669638280406', '111.92851066529347539958354370165', '113.22110540592470896905592100338', '113.67454767152569868730370122430', '114.05184579629804560698394172727', '114.62218639766272133054005787038', '115.121635181406973329998239966042', '115.87967742724920211306776968375', '116.342886408935088179415189955305', '116.80594030018871894620476695295', '117.6816548255773697334627995343', '118.41623195826695600557009923835', '118.7658041108131980914053979586', '119.684219890683217467540255701172', '119.996671978322979037162047394506', '120.45310194636558502807555959982', '121.31973538879982140325904677649', '121.667714056602820239329446923922', '122.43742024177484188964418217762', '122.983568175129985649332666631419', '123.34423894264283599138108787135', '124.29758863858127565915402788659', '124.87397314076382623679355168200', '125.42243445090162726076056058916', '126.199968113190514946877141628621', '126.73692402843715769481561872840', '126.89185777955846410620717062665', '127.47489416719166452862632139193', '128.22250855957079685477213744551', '128.84984371288124465415497847852', '129.91479903626294009936408666661', '130.09354658845435191035150228654', '130.84701244873845299295375308695', '131.048695778854809239218759320610', '131.94854705846187688016239801462', '132.60568289034397779599140674653', '133.00105126867019682664473160199', '133.60597020926323691370159019697', '134.01894240918078107285020401850', '134.91951116295363209397370110997', '135.34034783081683408018563214603', '136.17581140628077829843754623485', '136.63528322750377134697275906338', '137.32134917089569532776912351704', '137.97555797522068557058334057854', '138.14319238070230926140782229610', '138.94184413142949235113356681053', '139.31269192119063490595573833264', '140.15173502531771026741599737459', '140.57408409831238375788408591792', '141.40057468378671711342742119646', '142.244049758617511044092024734424', '142.564015145061021527054523104447', '143.074301674519540627553710884833', '143.400698577005076531690717627857', '144.05970252589188671739546025418', '145.12630675652602529034080584585', '145.36178024365409272221384893358', '145.756253170906157691160363292412', '146.59068337646074502673407891562', '147.1232679245722191822267372912', '147.874290442334889736997600147835', '148.43777796125761457372417946512', '149.02298255640492548598238972086', '149.61053648817585206858568597156', '149.97910776613390718490024808097', '150.46978864405468067617919749152', '151.09130797019142222509265320256', '151.68162470661819124412798029074', '152.76304975924684920555202804485', '153.019485254195183941287842523288', '153.66380497423767849940169416233', '154.12671932784238310260760113440', '154.86119307782282646106380210934', '155.19197128782120171829969045393', '155.94333102358449778714197395075', '156.43058676330604611553306597843', '156.81399010353062660134123919124', '157.74540032259269278464307225213', '158.45223190050292793104935050077', '158.722293895052016380720354114938', '159.32729770075909874842510535311', '160.15566736058513286904563905536', '160.66518606156932648566473693244', '161.00163057838181289500706254287', '161.88715445567409661541657264933', '162.18023080004327669692057006891', '162.59887045997338004915649571747', '163.195528844727893395645116569608', '164.36855770163310423766707642342', '164.76843747122456785014848762226', '165.40002823553623008891378960117', '165.58744064903166328718982902783', '166.42121938513234250797509603692', '166.883685591765458161716009323070', '167.20822109695436868808764188642', '168.10717991291565049066417711519', '168.8203841603548876402030892655', '169.13010310082081639672492621172', '169.734675008951446568083218917486', '170.42925757394738375879952969763', '171.05048187462838716322490398708', '171.786649681353471901241344384012', '172.09957832268195217730087353743', '172.55000522699502761481044404307', '173.257330888763876551867022097268', '173.80167710432889516007805513834', '174.20656718829962313900101122431', '175.06636385971023337051148704391', '175.47203761970025843517225787077', '176.38431021334831795340266403724', '176.86739870402347256862926658194', '177.495623266162401443856319915230', '177.69224598427500155591187898222', '178.31179621143000145522174537918', '179.08390797540671028632602634822', '179.297623643449157876233630996', '180.25512300284150963021519123539', '180.6631179840463500063050324553', '181.54331659869383238106054150856', '182.026187076394222532651903934991', '182.43203646133638737337859922586', '182.76449557037547503927523626776', '183.82274156060562747641201159414', '184.3679278139175026123703962379', '184.75432304766069438757437102267', '185.11507072267730295906822661071', '185.54996318258148961895658183884', '186.511328437182701312413620978712', '187.16842803766963711492420682407', '187.75832399652391128265205053919', '188.46122019316847553180230635627', '188.63416958482446335347217191408', '189.32378306777749999040499820284', '189.88028792860349378133452841419', '190.265800356080745103160717173836', '191.01714295799689273362227188687', '191.50918155582693968801236052943', '192.306420851168129549172966054255', '192.75280505891247988661171052300', '193.386296196885067932841324711125', '194.09416486146569626160929924923', '194.37918384152531146664509251780', '195.056860031422646959558963535786', '195.505178477455185197927681678032', '196.2250036234856685437895386433', '196.68132561051709132021122008055', '197.204821345887712021822345467600', '197.83878996578959150203001481534', '198.38733306315306203464404545852', '199.10592889762182576806237659189', '199.7776845390535853160821960562'], 'prelabel': '1-1984-1984.653-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.213657264973959, 'root_angle': -0.3429834991889178, 'root_number': '-0.551559392368710034672520467709-0.834135622479857510831278863113*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.342983499189', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(80)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.964765690180064627452360516180-0.534053936118408551670546653591*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.679431322765', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.31385022921', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.23018452052', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 9.213657264973959, 'bad_primes': [2, 31], 'central_character': '1984.653', 'conductor': 1984, 'conductor_radical': 62, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1984/653'], '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': '1-1984-1984.653-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': '1-1984-1984.653-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.213657264973959, 'root_angle': -0.3429834991889178, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.679431322765', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1984.653', 'Lhash_array': ['dirichlet_L_1984.653'], 'factors': ['1-1984-1984.653-r0-0-0'], 'label': '1-1984-1984.653-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1984/653'}
Lfunction data - 1-1984-1984.653-r0-0-0