-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_3381.2573', 'a10': [-0.6650780269803587, -0.7467738734234838], 'a2': [0.6340646982057246, -0.7732800000577302], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.19592391697856662, -0.980619099730255], 'a5': [0.15576280242346308, -0.9877944874219481], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.8825215767863213, -0.4702719069927368], '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': '3381.2573', 'coeff_info': ['x^462 - 1', '0.999907521857918 + 0.0135995489615099*I', '\\\\zeta_{462}'], 'conductor': 3381, 'conductor_radical': 483, 'conjugate': 'dirichlet_L_3381.590', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^397', 0, 'a^332', 'a^358', 0, 0, 'a^267', 0, 'a^293', 'a^362', 0, 'a^348', 0, 0, 'a^202', 'a^284', 0, 'a^343', 'a^228', 0, 'a^297', 0, 0, 'a^254', 'a^283', 0, 0, 'a^207', 0, 'a^14', 'a^137', 0, 'a^219', 0, 0, 'a^445', 'a^278', 0, 'a^163', 'a^435', 0, 'a^195', 'a^232', 0, 0, 'a^187', 0, 0, 'a^189', 0, 'a^218', 'a^290', 0, 'a^258', 0, 0, 'a^142', 'a^293', 0, 'a^25', 'a^411', 0, 'a^72', 'a^244', 0, 'a^287', 'a^154', 0, 0, 'a^45', 0, 'a^2', 'a^380', 0, 'a^213', 0, 0, 'a^7', 'a^98', 0, 'a^370', 'a^324', 0, 'a^180', 'a^130', 0, 'a^167', 'a^184', 0, 0, 0, 0, 'a^122', 'a^239', 0, 'a^105', 0, 0, 'a^124'], 'euler_factors': [[1, 'a^397'], [0], [1, 'a^358'], [0], [1, 'a^362'], [1, 'a^348'], [1, 'a^284'], [1, 'a^343'], [0], [1, 'a^207'], [1, 'a^14'], [1, 'a^445'], [1, 'a^435'], [1, 'a^195'], [1, 'a^187'], [1, 'a^290'], [1, 'a^293'], [1, 'a^25'], [1, 'a^287'], [1, 'a^45'], [1, 'a^2'], [1, 'a^7'], [1, 'a^324'], [1, 'a^184'], [1, 'a^105'], [1, 'a^71']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-3381-3381.2573-r0-0-0', 'leading_term': '-0.896139674973135608467522635720-1.48985626554707530634361939982*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/3381/2573', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-1.7386023148065899, -0.40088889542338, 0.4940062346737911, 0.3411991971726053, -0.8524980433777511, -1.8247703290571278, -1.3406212637995518, 0.26963652910516794, 1.2976284006578698, 0.6178759964807995, -0.8445765041962876, -1.1342112721964013, 0.26409802303244256, 1.667525717287758, 1.3712251389870893, 0.003804580341534517, -0.30141023442107984, 0.946219357957769, 1.6124606541296256, 0.043150754455376375, -1.8248833187172404, -0.3339775651949672, 4.668293126456819, 8.389234722745794, 6.413894839456298, 0.4376487968009779, -3.4365507427050574, -2.1033405768449613, 1.132358418253642, 1.5936907260020248, -0.46498505114762995, -1.0086690199325732, 1.3777604975186653, 3.4817756354408127, 2.524670067106867, 0.26833106867229173, -0.013045758004200065, 1.3839559176332044, 1.4776983739408358, -0.3369450025323528, -1.4563741680095255, -0.6018268908118095, 0.1531002565603603, -0.6677379108512328, -1.044618839381797, 0.87773236955904, 2.6835008113279986, 0.959045274027945, -2.6636545433820946, -3.223686950922833, -0.2753693938823583, 0.865121881529015, -2.481830733384726, -5.4414436724759785, -2.799586975533969, 2.5324312211977644, 3.567199279063403, -0.14983275547742614, -2.0958747443816956, 0.9479260882253716, 4.3432970636115815, 3.430595734289125, 0.43002314799167934, -0.2018793892223233, 1.009876331755909, 0.7526996562309658, -0.6600639098597685, -0.3948796699766899, 1.0974978177524004, 0.8425444714778284, -0.8122897575742966, -0.6078360308391757, 1.3113774214275058, 1.1523999468953823, -1.5466506291811382, -2.51622971949602, -0.18657385280278743, 1.4360476232152684, 0.21915402275061077, 0.04881390720686425, 3.079946723312949, 3.8767405179507075, -2.185042028814384, -9.417914893986302, -8.79187743481593, -1.5778224471123883, 2.6287280658339522, 0.368625168172821, -2.1924951570563365, -0.7894147022396074, 1.0027919998892991, -0.10210800254614913, -1.2832017931792912, 0.10158787737441077, 1.387403278429803, 0.26306219459974745, -0.5055410885955972, 1.3018341300271532, 2.577519219025111, 0.6111015326229761, -1.6274928876808836, -0.9643721107529892, 0.3282643686068653, -0.43341062015641174, -0.9779158037498038, 0.5593339045917204, 0.577443359342278, -3.006560923888812, -4.520681171584182, 0.6366520291574551, 6.306994817796904, 4.185393479731022, -2.3035829624171695, -3.3390901058246643, 1.2936847491414607, 3.005785763184175, -0.4418297312227566, -2.4433516617640936, -0.2714865923913766, 1.2154392062066603, -0.0032014624346953175, 0.2723826904256997, 3.194695998212864, 4.0675576603555905, 1.3542432357249687, -0.48981102350831435, 0.509962770963891, 1.0279716021700045, -0.1125906191207986, -0.10145825043703244, 0.9382159432710033, -0.19267690351410682, -2.1911061803400367, -0.6133241172759674, 2.854565685804067, 2.338305727365871, -1.0161422302428094, -0.7444493076420103, 2.0010177639548727, -0.4246285603665424, -7.273039476002487, -8.951823039934695, -3.4619011450413453, 0.28983672658602927, -1.470885360479946, -1.752868882653945, 2.856306437288996, 5.651999464984536, 2.589293751353871, -0.7315601173024974, 0.024786193413349675, 1.2289653108013183, 0.03995454559363322, -0.6071553496362505, 0.485544113799617, 0.15929197194690803, -1.5846294845677846, -1.0275593547253066, 1.0732848037560965, 0.4507042504127834, -1.6457149018376311, -0.5459141940160812, 2.083423539100849, 1.2914148415953086, -0.9052907513151824, 0.30996626258457705, 1.962075730600708, -0.768085799897456, -2.90546655906887, 2.2404129350056863, 8.640230376020654, 6.171223514841601, -1.3864342479102978, -2.5543627457475466, 2.3791422929075035, 3.8017226477108377, 0.365618371282483, -1.169212681529335, 0.1829841980540713, 0.02884084407434213, -0.9960133431579686, 0.34888395546905093, 1.6352971556962703, -0.36153555234458606, -2.240639200457439, -0.5835137120202027, 1.1328475615692497, 0.0013990819400223188, -0.4645675671009912, 1.5803316097978788, 2.1469929447617306, 0.3024711902755819, 0.20805730325011287, 1.1395346183210953, -1.817696612279833, -5.658020162133221, -2.8149902090320125, 2.998030495233709, 0.952328131940851, -7.007281952261691, -8.335138549347299, -1.6060811966559811, 2.328163302952699, 0.2847611741100202, -0.4085720404527062, 1.958427792589911, 1.9428418607070426, -0.018886281012995658, 1.0916595353162897, 3.2990912498154774, 1.3889192188312631, -2.1493206608006474, -2.094550533698433, -0.24762069883155535, -0.027141826393431413, 0.667372118992558, 2.9509408679492894, 2.926800453179903, 0.19577927602037473, -0.5413494844492697, 0.4026085987577589, -1.4268861955790548, -3.346300224597945, 0.2746686784122883, 4.600431794391113, 1.367364341593825, -4.71132761842068, -3.8659372113598307, 0.4468150413274396, -0.80942408419753, -4.101666793665159, -1.2476859992289608, 3.350206654291218, 1.3280265645756477, -3.2638276361873175, -2.525953948976972, 0.6008648805932767, 0.22828247196308762, -0.9917189279452101, 0.39673885577645523, 1.1171964707023339, -0.48931731649422694, -0.640879929417693, 0.8744785331955413, 0.24727547695031438, -1.1475352543672122, 0.3307317545244782, 1.5455683994519407, -1.1245631910895393, -3.0439938174256005, -0.5752951021083, 0.8431885977348058, -1.75487401433576, -2.422632430488224, 0.046629517250035044, -1.4714031889682415, -5.628284779034108, -1.7471350715871448, 8.819520331820256, 11.80329140527456, 4.439635610052694, -0.9797526951835579, 0.2468971922954681, 0.6392006986768157, -1.7222288840886237, -1.31066521080177, 1.1580527131656448, 0.7683053176614689, -0.6701515842513809, 0.215583215677694, 0.3680177251584061, -1.8694067091537003, -1.8850414246832092, 0.9684809476618329, 1.1938600330775029, -1.2682469543457746, -1.2677525422351916, 0.29364373115012066, -0.4007829198249384, -0.6017404010765117, 1.8744930672417222, 1.613586351043893, -2.100482123143016, -0.3214274225384539, 7.392562877550731, 8.41177661034307, 0.07546752262023784, -4.174078484723401, 0.7270670088195781, 3.9165575433245388, 0.7338417144764793, -0.9469029508121862, 1.0372656493544945, 0.6590546174738873, -1.3828568296569899, 0.09782992945081066, 2.2670465768533403, 0.4856918376073421, -1.3529526461274852, 0.39636866170092316, 1.4821290241241054, -0.2297553932059525, -0.5885591135457133, 0.6415892240818488, -0.26587475380995307, -1.5203253020433494, -0.26808071492253116, -0.4687514430822808, -3.6285331872255724, -3.118791473918028, 1.5594194585341408, 1.190920940672445, -4.458950495700365, -4.720092310512238, 0.4768914227647278, 0.43906987571412337, -3.8126047934873117, -1.7649087042626213, 4.315461849073246, 4.026639563750216, -0.23397133436219172, 0.2203342475172109, 2.4713025638667983, 0.3050564699518995, -2.115933016129275, -0.3793038814367256, 0.9114579488332382, -0.7838851511755689, -1.1767509590608158, 0.15260979110580777, -0.23048750848616786, -0.48679019041324484, 1.5029906790792373, 1.3277447014418533, -2.199632040921304, -2.7224677363247998, 0.39195455852918504, 0.5078094335637424, -1.5945301958359734, -0.08214286230617238, 1.597822168808227, -1.4330493507547528, -2.103140952391214, 4.283790779439371, 6.936552306980791, -0.43691259319050313, -5.821373017576052, -1.3965876877170427, 2.748743285723204, 0.07962245830163273, -1.4772391314082736, 1.6280909086335063, 2.5918882395346765, 0.24182784363232104, -0.18768907794544137, 0.4836872844513239, -0.5445489580995926, 0.011321645044586489, 2.865264827471917, 2.4175847136297235, -1.0836528595991761, -1.320377433573714, 0.8906425519781912, 0.53748271070834, -0.38376116634387675, 0.4502974399126872, -1.2421566991060233, -5.053688800705525, -3.9320709685815496, 0.16808773094343663, -0.5520564453001882, -1.0937640093598353, 7.2165059748374025, 15.165012517307762, 9.781870330844079, -0.9808747408782288, -3.0196002397738133, -0.01813989192831887, -0.8257004342488801, -2.057491185791869, -0.18568305383132597, -0.3220167871996897, -2.7998915830987894, -1.5859052453808111, 1.5896186744852947, 0.8727465879789778, -0.8713451225606104, 0.6438297846758942, 1.6743664591062246, 0.10722457251182002, 0.026149631190017633, 1.0949706375302672, -0.3317624921041323, -1.2845550955750125, 0.7877654101378975, 0.44506837999262344, -3.0541329659979066, -1.9969914720227941, 2.0705759389431755, -0.6694378494378561, -6.479246470988203, -3.653043018538274, 3.1476561539485526, 1.8875410983781196, -2.945692649458963, -1.757723254745062, 0.20703518400610932, -3.047575050641191, -4.151244404698698, 0.7229625698717566, 3.1992816388668603, 0.5737618812101323, -0.3838241341874856, 0.7851590499815911, -0.37651702898024003, -1.5197627915477123, 0.06583651438847582, 0.49041701877874067, -0.9607079227745585, -0.3097578116276506, 0.35084948021930495, -2.436467028236097, -3.519494669620369, 0.17036539023321778, 1.8157411220942052, -0.39291391906983236, 0.34409994443410424, 2.460661977573933, -0.9761621531591592, -4.315534554319062, 0.028714443852025987, 3.2885751966747003, -2.2378520639862614, -5.579441307817453, 0.832953836515768, 5.443025216351174, 1.1557789639814808, -2.3822554114197847, -0.3807623847399074, 0.37630544957677947, -1.1549201903482615, -0.4937643117394439, 0.17363032752878726, -1.3599066678843619, -0.5996147200404286, 2.467432213728636, 2.1105044287002217, -0.20378710623423682, 0.3545194647508557, 0.565624460628204, -2.1954031788115556, -2.5866210858819008, 0.1262942836208366, 0.015202237667884939, -1.4610723111973691, 0.04610092016715821, -0.6243991085400719, -5.215598684670481, -2.9198920502286074, 7.046241266323606, 8.466893582260324, -1.801233680055724, -7.0861635372630705, -2.200705987449585, 1.0386035409412664, -0.09762182779491228, 1.1806646457749632, 2.598441700107718, -0.25583540376774594, -1.9281633516160572, 0.3677699780693683, 0.6598425766977197, -1.3300654072708769, -0.30937462847228187, 1.3129881422099206, -0.5182837210515119, -1.5808717809518915, 0.32550561638242825, 0.5090671957630346, -0.7712941039106884, 0.21320763076549015, 0.33655676421844366, -1.7875811099165742, 0.2557372204197075, 4.787653595347854, 1.7114014789786154, -5.241608969062923, -3.686495555976233, 1.8579261246320373, -0.07590482875787675, -3.4415541281524304, 0.6166254802384766, 3.770695539837524, -0.509527983813656, -2.9990125145815707, 0.2232882308214295, 0.7828477387691372, -1.8037108235505617, -0.5901185201251903, 1.790184292120912, 0.08978700389695446, -1.3994793963013814, 0.17709328415931103, 0.3326763778435715, -0.8711535936480113, 0.15795794841922692, 0.8115219244120321, -0.18538060809666615, 2.0464778947294877, 5.604105753839864, 3.2904633177980127, -1.237064326652856, -0.8458285368268058, -0.04300501762622135, -2.098445445629403, 0.2917519667725046, 5.934551413150368, 3.6490791119256656, -2.8571724930295024, -0.5659231199605704, 5.243074500831204, 2.216246019590328, -2.9559064257978425, 0.00936414617059503, 3.8675475158102848, 1.4081805831458893, -0.8943926307285786, 0.1225945814203989, -0.4680473061530355, -1.5662758725501544, 0.19869868077071268, 0.9307064668063889, -0.6069252393829189, 0.46970941932283167, 2.38173201923518, 0.1415408544888682, -2.0183953691730214, -0.20065603610461036, 0.25427958249088956, -1.8339941906696486, -0.980561389442578, 0.7461904487368552, -0.4713165394633129, 1.3060912978453605, 6.3310884152141, 2.87573938622084, -7.343556046941048, -7.726325274397913, 0.9172635844874996, 2.327523254926071, -2.5503276152191003, -1.2096961287342247, 3.2416042092750943, 2.124858351234832, -0.2105495438403321, 0.3223765639164746, -0.9139559031557487, -2.9138364224037216, -0.6674563336354961, 1.555598313146794, -0.4553206575614869, -1.2264244031525617, 1.0374163315831224, 0.8572870653838149, -0.8335422155060201, 0.06355865870000432, 0.43514151346727875, -0.9247475625237415, 0.4040556524866915, 1.6525556946662607, -1.801109374947535, -2.6212476278422336, 3.390951049760976, 5.165728521148043, -0.3086654998995667, -0.17456741191842134, 5.880667011462112, 4.287265809095126, -2.554844215283208, -1.8425803027354282, 2.4999533954236632, 1.0595941051553344, -1.1248965450675592, 0.05903933112424593, -1.9761607823073561, -6.418642770451825, -5.050741443369934, -0.4968345778622283, 0.2766402162917764, -0.1033246341100495, 0.9175057260760906, 0.2305359179246769, -0.4742184628318179, 1.5229252288806043, 1.3285548857145317, -2.150690822678537, -2.223332012405525, 0.011230612506284154, -1.3428875638907094, -1.6936954507653346, 2.5188209572807985, 2.5937553214487066, -2.753676494069839, -2.647114375222559, 1.1828208043401092, -1.8800314843230503, -5.518597983846805, 0.270203969517862, 5.3526110666282625, 0.4816061816820905, -3.362336414958697, 0.63662215784554, 2.889302834961624, 0.3030798615460375, -0.2666751062796486, 0.43399045860853996, -0.9744823773238871, -0.7309198140865287, 1.222439913867638, 0.061188395610962, -1.30854426421384, 0.9871859329480662, 1.7931117852591163, -0.48190043875507405, 0.0865571343021336, 2.003416248576359, 0.287442192926421, -0.4592400446649889, 2.269446210402212, 1.722605332852034, -1.0481523534284003, 0.3423347853306562, -1.36930870697931, -11.880759313630493, -16.046008680188088, -5.0240506511313106, 4.357069001384058, 1.6238478974529524, -1.2720660336136311, 1.212120708101246, 1.1874622012529639], 'positive_zeros': ['0.426614636668664739828234340844', '1.04614656068401626503580944127', '2.137223449372517965045924758785', '2.940254301093693667713916222447', '3.70362992273734736399012256221', '4.68852839183250211097196021212', '5.101800083951977795806741707891', '5.9432367536450912992794446773', '6.58938915554512460982412637530', '7.83587644733115682262930804395', '8.627432787768431990773347977321', '9.30654152588034268138605087141', '9.85009542260485723687901412150', '10.99834522946334837071503863703', '11.25407309022759495683300857106', '12.135387183841373532276522291149', '12.98523096290549845981157832517', '13.23697755851885731295468929195', '13.95247977453392526283689603390', '14.76862317224681718227345452071', '15.65417519001338524318763563397', '16.05604682307610264676350861984', '17.03076695341899488085594460635', '17.80096172717798504981817560986', '18.368243424258570297720219075578', '19.44524949927115411641555333711', '19.74820398972086112184132612445', '20.46794352438862616056516284293', '21.01904119284613367687128786869', '21.71559980279058164752426629894', '22.28999320170566188671461751519', '22.957674555965278592287789818156', '23.77095054950445578333337884093', '24.42160620210807625704392674907', '24.67843747378996721271985992354', '25.540219994526972756829102792014', '26.635708588572668621976581714683', '27.21839335465691959709009032659', '27.91093438038231022759349975072', '28.42095949725710561757984888749', '29.04708963593976173142132788781', '29.73844296027623716997978433294', '30.12824912372568205525760754856', '31.00274123770378294384048600340', '31.748638262090026371016491876306', '32.0812269270874487115471866212', '32.71555482786406180182949912091', '33.19465949626778781986779938971', '34.034736223269409774045276450592', '34.88042265762030421268962880108', '35.54273504097830180421784715402', '36.21584597609344538676611941352', '36.90598763397765042435023808599', '37.49921670773484284117090950454', '37.76582431136674535732516084469', '38.91232770459693231920715498028', '39.26523689609351906831933498246', '39.96781471078235850155692005768', '40.34156741019762908210890507608', '40.91118892148101183978049720985', '41.61445956500137212961864418533', '42.39368342252892061207473443143', '42.89011101771834150075111076539', '43.41431216534488950355170725228', '44.61571871491392498454966015960', '44.811065890798409915644314298590', '45.4548933048065385843714252372', '46.45367542297487314642658579673', '46.87098692349213976546160456637', '47.50792380048953513127291299058', '47.99529808332069886443866741001', '48.46736348650910001548756874603', '49.201423757491321583253784898617', '49.74734786902349760404946050895', '50.37017157345916908852400370782', '51.08965926907931739181190851910', '51.52450946940896533409819908232', '52.127762591738537732084184661659', '52.71772146514909102482440357689', '53.68333816955150997544351273703', '54.23259942650585637130428151599', '55.034183429991370255246767026111', '55.5805132161560962728469909828', '55.94448125323127573993888151346', '56.511869015010275255625197573225', '57.14878858690334958837254829519', '57.88314877642641098660500013261', '58.43776664467040974208322321646', '58.84316071313735643010270963559', '59.76193462066098122079929569457', '59.94007342096241685271532916481', '60.4910983738063626562670781138', '61.383048410223414020550145035289', '61.915747277296339905077973316171', '62.88896887918499389336596019672', '63.4732058717961019987793440397', '63.81646354701684715745263834821', '64.6813807594079375000062758040', '64.82985718886554705152068127007', '65.73322068530710057451251398355', '66.66304384632559211741439501455', '66.83383478536982630495513663022', '67.00407155144596842207785008238', '68.15153707435053359156962396023', '68.580990384351018643691591056183', '68.89026459237355259333277742257', '69.672480065066613449304739036365', '70.37460499562070698463022065213', '71.200523634651828831720351545254', '71.49291482806398322777318745096', '72.25604625917251863153265117745', '72.89133439834434518797525843230', '73.66762664839728682883726849286', '74.101099390784691349681445021559', '74.62322833158412012323813987637', '75.22465017357199954574569653619', '75.750825186769359918390490626264', '76.29106288799679518047723674904', '76.83171537145846622575148817760', '77.40048036533717688727605411014', '78.18392946229739260064916887557', '78.56945305693303244785193926485', '79.36603604924136631272184217716', '79.54644735267169981174512069696', '80.368000589956648953456246344460', '81.45497581366531481800051791072', '81.84043791031739181695651114639', '82.279543666181957654676403975809', '82.96352753525825216629523983187', '83.56517907316575794434927663601', '84.01445761564173938627213281437', '84.44013438147583835717900567676', '85.204970060950998213785806225501', '85.775513421085488262037630569994', '86.47361344878345758617463639130', '86.78216076218005939427766782190', '87.28059516902628994410618054743', '87.94667870686663349884493729288', '88.45310463237947240431028867964', '89.377697019809276653666268302489', '89.96383551963731530091979730448', '90.688770146294357590149174659181', '91.099612566273863927295468770893', '91.64737400767888134324684757514', '92.17726977467732585026480950184', '92.86399508831989113603741780954', '93.387339066073444406739825799801', '94.02380371461394141020609135123', '94.50961457237177358514321042202', '94.955263270403722292289728207548', '95.69016966537123652828402369667', '95.85403813782235808198563258866', '96.7655761164957425516681857847', '97.26009893953614988941587544737', '98.09083715867058971244202166677', '98.47070196983318643563267931280', '99.14810813347137252350891540122', '99.974677171942195874507592027194', '100.28741784183491089486040046085', '100.96359249660993850554976202071', '101.60892194614046583646224898658', '102.065573584941854104928837620074', '102.762196773244950023978047451453', '103.05660382531368839345437370063', '103.53476667111134864230796826513', '104.189738805424241280794685388914', '104.95594931523315362843264553033', '105.37992438003937366303328144555', '105.9460273503476663054786701491', '106.44764226312198457913860341730', '107.002630629342360224125525671480', '107.79761811255134403182841337199', '108.50521796252466999841788038482', '109.06901705389294680199618546229', '109.54495813338940894707528255329', '110.35401552710382766857789590273', '110.684421944577521196211142860853', '111.11468358748226114611793889525', '111.56100628080813349767358997449', '112.39546788167792108450976490124', '112.98404291115741096437097894848', '113.55057401576017222411448772739', '113.905599353713355742825421083484', '114.24604442025060572351605370361', '115.29165694040479681758511387610', '115.55783362483288562090012620435', '116.00780955885423935823806821368', '117.14993301649789227275362266313', '117.816080650874045672326729921254', '117.99553013432142382596045615340', '118.7841015689133006334343897801', '119.010526852323642967742330058647', '119.8231613106321412806785634258', '120.42412196769988056946682723838', '120.84902252097468700008745304258', '121.586337564302230117200920154620', '121.86832191912667780044120573644', '122.45286481187667746836522355265', '123.01906846806455758709837889998', '123.481122936527855318208934694996', '124.19534829167996082054303252902', '124.6539370982714480013007941410', '125.46008109041656280665732778548', '126.04200127319225809293992140287', '126.74748761595511054775093150250', '126.92161306752797517870881430894', '127.77116101352151970591027292571', '128.50934647928382186791985457998', '128.845278512628382953443777715846', '129.31746710469385391439624578488', '129.98884475875297607119540243439', '130.41764639572534820763967506808', '130.99700810169375607688713591237', '131.31637582803261691524952193892', '132.17446961225758174053111579992', '132.752067794808405744968861226957', '133.08482809899603698622048063950', '133.6928909022400202053343898799', '134.37357568389942438189713530295', '134.9037448248698803012325607742', '135.59350242885297416074760265883', '136.312785097792623004815465161035', '136.92531659271160126292776467344', '137.26621553115637952809093652590', '137.919974916847443336081218902808', '138.17771665634409055554868655388', '138.81136259705669703687912908659', '139.64172998149215705051092871532', '139.922686150278060986749526406785', '140.39430189308623856708214651997', '141.23162148287130369705005655203', '141.564986681123187929957454226365', '142.17963822090115323443477756301', '142.437261837598758825205673330186', '143.22276962213519443471658771795', '144.0118661362880599929807149173', '144.82316044947488040820817080023', '145.27665436033095226567086722152', '145.4464805813105472254235083837', '146.22817012886278311746412577034', '146.8288799887517630313488298522', '147.284894271981263839445582154553', '147.85154116436293317448930189271', '148.3748996186621311876850251242', '149.01094129326772807122768355736', '149.47738811503408885389317064217', '149.95740646125682717671297503994', '150.36639568420141246765401244056', '150.9209291016920311007977989809', '151.63168972086149663737010023580', '152.367177096353530060632899603155', '152.807783998997344221942080967765', '153.40522369546944649841190392609', '154.03355436296090208161357686021', '154.66691869247195663155326183400', '155.091693229524492899800814513717', '155.682079963774741578391223320382', '156.26005448769154413977000071086', '156.84294424671609605756580396319', '157.2601155190392946226744716515', '157.783289074996569182780135439753', '158.3438250342897228353530140014', '158.534425781421312835985422494597', '159.57526746476574455691798131214', '160.15212036968218631611384782985', '160.30117608626044977092009311955', '160.92136583141670772230524120468', '161.71577149859626801875809396971', '162.21318971861475452108250725011', '162.91431054369513068856617951100', '163.436981959722757710583062501', '164.18760134716990892168754713397', '164.65005383931586990679188085471', '164.90550063042883056196617081932', '165.59748669310206806472099816907', '166.11744966399060808063526304115', '166.50289653834366142299527029138', '167.19999837798158416649885541789', '167.84142863233434351407314527926', '168.16818443149806261101071182917', '168.87467587162857899605885464883', '169.274985559691630749279027509140', '169.5834778458805426990426716364', '170.40019950155660757939370541244', '171.21247705550899869552727286226', '171.70478959517055476261033389678', '172.26031764037098351768702180012', '173.05893073082612311484662886006', '173.30853593100129879340617128973', '173.62255478291289861860803541067', '174.43340372384260949754271393381', '174.94747023974577019591224448698', '175.48522835576972462598420034429', '176.06598902088005417501033581840', '176.54962110402776709736858410645', '176.971324287359035169762397021158', '177.450160014410003677268960138634', '177.9931292508393481090250911697', '178.59274695999384285147470345692', '179.35564494183226858271067141551', '179.69787496435229692237237129258', '180.49193046885772141245580815666', '181.0493707904690601284173180004', '181.66026626551971135757703690233', '182.16592799315505761997597496986', '182.29795516581376849884101486552', '183.49723970875542263158377729744', '183.849550974400658647123775799784', '184.1045731699876538532023663311', '184.733495599473072686814103818459', '185.10271789589711526056979576642', '185.748518906819020604058891985588', '186.55794460722824256429823977907', '186.65790379593726812651218918789', '187.32839143221447068963923835810', '187.96515881205554854939439686291', '188.61998082338099542969324488994', '188.9541884429481217425656821477', '189.67743836920892959474490741952', '190.3341228996452819918613401054', '190.89892932013641742902780032784', '191.60475467613430536276585762021', '191.94738658305220144816209317951', '192.31667520213337215141357829685', '192.91563903115574304446056665844', '193.44524831864380383898160462091', '193.95616720726943246397820505332', '194.61369157572849551854833680736', '194.9887059940648937766173879753', '195.66148149670895622643411761730', '196.00424255187589185985847611924', '196.72329344758209025613980012383', '197.14049227093448739112410322206', '197.42327156606155970400442751381', '198.55940473323289021076993649290', '199.16455256835604135917038356433', '199.55696425609483239044934229129'], 'prelabel': '1-3381-3381.2573-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': 0.655259354053732, 'root_number': '-0.468649737650848014322109325159+0.883384074680878163892925384087*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, '0.736628167578601273171832747965-1.07754544632776707050780475885*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.426614636669', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.04614656068', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.13722344937', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 15.701297990361368, 'bad_primes': [3, 7, 23], 'central_character': '3381.2573', 'conductor': 3381, 'conductor_radical': 483, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3381/2573'], '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': '1-3381-3381.2573-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': '1-3381-3381.2573-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': 0.327629677026866, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.426614636669', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_3381.2573', 'Lhash_array': ['dirichlet_L_3381.2573'], 'label': '1-3381-3381.2573-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3381/2573'}