Lfunction data - 1-3381-3381.1247-r0-0-0

Formats: - HTML - YAML - JSON - 2024-04-20T04:27:17.260681

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': 'dirichlet_L_3381.1247', 'a10': [-0.9179165852537594, -0.3967734145782425], 'a2': [-0.9472030102919101, 0.3206344605527355], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.7943870854121126, -0.6074118524777475], 'a5': [0.7422341230042699, 0.6701406618375595], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.5576886669868294, 0.8300502097550806], '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': '3381.1247', 'coeff_info': ['x^154 - 1', '0.999167799344583 + 0.0407885860615856*I', '\\\\zeta_{154}'], 'conductor': 3381, 'conductor_radical': 483, 'conjugate': 'dirichlet_L_3381.911', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^69', 0, 'a^138', 'a^18', 0, 0, 'a^53', 0, 'a^87', 'a^118', 0, 'a^76', 0, 0, 'a^122', 'a^16', 0, 'a^105', 'a^2', 0, 'a^33', 0, 0, 'a^36', 'a^145', 0, 0, 'a^93', 0, 'a^42', 'a^37', 0, 'a^85', 0, 0, 'a^37', 'a^20', 0, 'a^71', 'a^95', 0, 'a^101', 'a^102', 0, 0, 'a^55', 0, 0, 'a^105', 0, 'a^60', 'a^12', 0, 'a^136', 0, 0, 'a^8', 'a^87', 0, 'a^9', 'a^111', 0, 'a^106', 'a^94', 0, 'a^91', 'a^0', 0, 0, 'a^47', 0, 'a^50', 'a^106', 0, 'a^89', 0, 0, 'a^21', 'a^140', 0, 'a^10', 'a^92', 0, 'a^34', 'a^16', 0, 'a^17', 'a^134', 0, 0, 0, 0, 'a^124', 'a^123', 0, 'a^7', 0, 0, 'a^20'], 'euler_factors': [[1, 'a^69'], [0], [1, 'a^18'], [0], [1, 'a^118'], [1, 'a^76'], [1, 'a^16'], [1, 'a^105'], [0], [1, 'a^93'], [1, 'a^42'], [1, 'a^37'], [1, 'a^95'], [1, 'a^101'], [1, 'a^55'], [1, 'a^12'], [1, 'a^87'], [1, 'a^9'], [1, 'a^91'], [1, 'a^47'], [1, 'a^50'], [1, 'a^21'], [1, 'a^92'], [1, 'a^134'], [1, 'a^7'], [1, 'a^81']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-3381-3381.1247-r0-0-0', 'leading_term': '0.185581813497792028872521437307+0.561610224663223036072798008346*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/3381/1247', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.5914783630424747, 1.2836769141743074, 1.5579219410293703, 0.7531518882342092, -0.7711312092632053, -1.584526018993745, -0.7072599134191888, 0.975068468362066, 1.353410686358947, -0.39025399030818947, -2.1906501049871454, -0.877892639030532, 4.020529165219468, 8.864252803961728, 9.22764434970145, 4.704800866211869, -0.4662062861867799, -2.0323668051395707, -0.21294604527183855, 1.3415356240039527, 0.5180750698108783, -0.953905585710069, -0.6243566302224562, 0.9009871910630496, 0.9995607775592602, -0.8319122976085633, -2.0812494255990237, -1.000523568857138, 0.7017270725369157, 0.47204944283562456, -1.1692102591949807, -1.5748789522002808, -0.3167985754470161, 0.14659321624159935, -1.2245653020674707, -1.902919729349743, 0.021383197612361255, 1.7679725926504926, -0.6172001610976331, -5.502670660576211, -6.532800514970513, -1.3172689730379734, 4.50666730198833, 4.557474811247296, 0.2017082151939909, -2.0822868165284176, -0.20176422797449237, 1.5213680939940797, 0.05056821153903093, -1.6741442847872323, -0.12095389512321665, 2.813572118866905, 2.9924402846148204, 0.671027821261162, -0.473606386173575, 0.34041494052439125, 0.3327935527078208, -1.2926714155704235, -1.8673828939185841, -0.36588914280336354, 0.5366594328927717, -0.48813914864914365, -0.6629047251362257, 1.5915254354085155, 2.6936268893029425, -0.4554324693102395, -4.2584642639135915, -3.3672276583329546, 0.45120449509580546, 0.9379267140956609, -2.0284512849778684, -1.8662330793495727, 3.4157013804504244, 6.9312736918502065, 3.493678665380891, -2.138699892093662, -2.8792518837174454, 0.08096674352928125, 0.7282989730185535, -1.491540718654769, -2.0931417279968674, -0.2056776515225089, 0.5465657309111454, -0.7201265502302137, -0.9599922921225239, 0.3954584299016697, 0.40138199693021165, -1.123215217541379, -0.7342017399647013, 1.7947768339355632, 2.2497279351828423, -0.417229222764186, -1.843639442210899, -0.17220915573116596, 0.669080337512197, -1.0909264065763467, -1.2452681062807052, 1.606600289839533, 1.1128576755897202, -6.335574314946652, -13.07029505982528, -10.466528436766161, -2.343346195345145, 1.2115284379977171, -0.7899896029398674, -1.1183117146247523, 2.1500320344351644, 3.6427612885521548, 1.46318602616478, -0.19153635347055456, 0.2563360330818867, -0.3475709834809755, -2.256930873295646, -1.7192656145885423, 1.2085438427653883, 1.9166803104903294, -0.3980297407148357, -1.5130963725331386, -0.3077427729098302, -0.07477161486920511, -0.9836500415625093, 0.24810988037228904, 2.5167021348228307, 1.3509107496953212, -1.5923173784033275, -0.22724800310155427, 3.754655708264596, 1.7906212003037454, -6.268173089314596, -9.932179338136564, -4.824521549363671, 0.5045672072258173, -0.5695694892620669, -3.033959473931209, -1.471970511469245, 0.38298507567220197, -1.5185703988937285, -3.349260308027432, -1.4509817315792097, 0.43687425911652866, -1.0974281761782168, -2.535206371702535, -0.7497554902373117, 1.115027095495893, 0.46969644824461776, -0.04226823607194142, 0.8652942456447115, 0.22179375082785666, -1.9651044096850505, -1.576333318887933, 0.7993693021160346, -0.17125390065889373, -3.7539686705014716, -3.435261247812931, 0.2996361210404194, -0.010094368539991497, -4.21282862260152, -3.775279995835592, 2.028128577233734, 3.8063864463655284, -0.9018189102208196, -3.2318837459138945, 0.48861240352312485, 2.677505094275909, -0.6157182683678131, -3.0265486543878755, -0.7174409200892733, 1.3448867919752887, 0.14748079711997583, -0.5124369132064035, 0.90219605282216, 1.0118600036702956, -0.35140548992343706, 0.027986357730665552, 0.8568548757885353, -1.3768725303907787, -4.060715848195502, -2.7122488757374428, -0.07524354400216754, -0.7618278921376284, -2.1143319351800045, -0.6242613974024, -0.2242917123000022, -3.6597665212648085, -4.6432196650030155, 0.3596559571648144, 3.147206927925708, -1.74164979672049, -5.398823836989478, 0.13431356891509513, 7.187866167011887, 6.000371161872991, 0.8613547025881493, 0.1455796684241642, 1.8953343151221815, 0.9931006026914228, -0.4254469802050638, 0.29487390278787334, -0.05210469771729705, -2.528995407441403, -2.5066431773188333, 0.6888534846217611, 1.7525216353602107, -0.19987652770143288, -0.7209651654373823, 0.11518163245872817, -1.2345143197868769, -2.7988718589525474, -0.9536557297646302, 1.0474199901291879, -0.2226224508862786, -0.3986583280697211, 2.702178408682903, 1.6123026392228, -6.382701842590849, -10.194340766773703, -2.934443156889119, 5.066045492273075, 3.7959349057680405, -0.7997775732227783, -0.6525557645423805, 0.5493774939936347, -1.496653729505874, -2.0769369857125275, 1.3412762257004003, 2.8772964798154894, 0.2395294721184986, -1.0890160878917963, 0.40546579932198906, 0.15308395992448767, -1.826674107571776, -1.4042739201902013, 0.2052859276273133, -0.43488515034724834, -1.064811344572641, 0.5104126808117871, 0.5289411104728232, -2.0290160627186453, -1.7433495831426251, 1.3275042528628922, -0.040952559987496875, -4.986103354441951, -4.268670443858394, 1.5441866101924089, 2.360866158663924, -1.6414233682461654, -0.8186834902786642, 3.819768897525985, 2.4950370718991515, -3.2966120202436517, -3.549653476653497, 0.9479270147929633, 1.6363466982916959, -0.8617952821935156, -0.35256281529816375, 1.5660613652456445, 0.62003103692081, -0.5103756460348006, 0.8793875864602376, 1.4010327571258072, -0.08527295967360807, 0.04440191818438985, 0.9103877743304852, -1.5050818785708113, -4.254231159947374, -2.365492792458316, 0.4976733783421475, -0.39161513240967544, -0.9800571831695063, 1.5960162616728877, 1.589695721299652, -2.054710371297572, -1.1006000612281113, 4.392373322823321, 3.342330320947266, -4.482957413091362, -5.789268198456984, 1.8493722164788844, 5.846817984246154, 1.897831868310822, -1.1466872539720685, -0.13543299552405347, -0.2837747122471719, -1.3415671834848926, 0.5266473922260606, 2.381151339417282, 0.7012016461326152, -0.6997763820355344, 0.45274877659638785, -0.131381108270746, -2.839003766546064, -2.546537709648608, -0.04559258340469468, -0.43460120051848916, -1.9705701325225176, -0.7165294274521982, 0.31994903327223273, -0.6390587710290832, 1.4886297846983594, 5.642469617435193, 2.670389878716785, -5.465320787653448, -5.335984430146969, 3.4108236962221223, 6.6480050715861525, 1.6908553409517089, -0.22781055653251392, 2.829687812245008, 2.4625247208004124, -1.033980332482006, -1.0583529762880763, 0.22344670628227367, -1.9673834867018942, -3.612606430283641, -1.1947195060185702, 0.3609738463143109, -1.1706911918329315, -0.9740229893722424, 1.2720552148710504, 0.9476098183464544, -0.7972668139996328, -0.353397713812647, -0.014048284342545498, -0.9358093085684247, 1.3032762372762001, 5.290486569684849, 3.52149190201291, -1.6888083001734442, -1.1496429720870698, 2.507406768263987, 0.7099805301989782, -1.8136870111246244, 3.187850897969101, 8.330853818504803, 4.079396609293873, -2.2350945509725855, -1.3615732464342172, 0.9417138801882612, -1.2484883034616807, -1.8431205093619485, 2.1057430218685576, 3.4604251383612716, 0.386829580938084, -0.8624268317630048, 0.31121842676964495, -0.08776679215031999, -0.5061492197741427, 0.901927190559778, 0.48780627267417387, -1.6965584702007366, -0.47522477086537435, 2.466822210065179, 1.2537886301350092, -1.2819406923363075, -0.112830907514513, 0.5317638633644459, -2.226572620554665, -1.8675803541677396, 2.3047120622795414, 1.3910757206289266, -3.2124680395573013, -0.25592283442125063, 7.377307680306609, 6.224058935088092, -1.3473803561980624, -2.0446329177716733, 2.8561698071963546, 3.002938298009752, -0.09967186445390974, 0.16709497338477736, 1.238101665102896, 0.06823544801494201, 0.3927585801260258, 2.235301710758064, 1.1210412449223146, -0.6681186618798157, 1.2932177166978258, 3.093591830038405, 1.1032361858707012, -0.07144961423505802, 1.3726398744871071, 0.7547018621040315, -1.1351565931151513, 0.06342053476178511, 0.9101664538371657, -1.578170746191925, -0.697521950152257, 4.586058105372441, 3.1650501003008813, -5.5641757872510125, -6.884853001343626, 1.4356616769769748, 4.667970175346866, -0.5199800497739817, -2.640569330783996, 0.19309234852376433, 0.35322534583693926, -0.9114301590677154, 1.0864971008234545, 2.0289723910991944, -0.8734152818575427, -1.6171748034952038, 1.0433520875129667, 1.0505165523934599, -1.143249595472597, -0.56686565860354, 0.714665096043115, -0.2894874969575985, -0.23878978021644126, 1.1741855372380856, -0.2671469831420479, -1.9419433055150008, 0.5693645027690719, 1.7198167498201382, -2.332525935363788, -3.23287118663384, 1.7692899885734032, 2.003144864110469, -3.8203661459493543, -3.245633629391783, 4.025788161533077, 5.2413937742654655, 0.4827310502544999, -0.1452140654796844, 1.0763167110576182, -2.8067708461187606, -5.905670164105022, -2.1845198826055334, 1.485614176320222, 0.24701572973096808, -0.6127099442850359, 0.612638644580655, 0.29939249080507147, 0.18035070480046653, 2.3634992074063534, 2.4165281783830923, -0.42599077467174407, -0.6846639297562762, 0.7809889954955824, -0.5061265540997288, -0.6326702754128347, 3.620375604310972, 5.0642431078951, 1.0239519996004878, -0.5369773798088364, 0.6494726962087276, -2.899617800786795, -6.4757873211785775, -1.4081231640204646, 3.3913949440744675, -2.8729984155045294, -10.004205373636532, -6.181779562445023, 0.3962122687247016, 0.3796417074366579, -0.7342835559598574, 0.9209494111854751, 0.44725049216734314, -1.5962707055574261, -0.6654967918713753, 0.3032157000527815, -1.371872828420468, -1.082437654733254, 1.4604363684405421, 0.7992205612800841, -1.2808938706484707, 0.0009834506181114772, 0.9493613161894837, -1.2903013512199046, -1.3633213347193613, 1.3056752863148642, 1.0479649109932976, -0.12149124808785697, 1.0434616225002145, -3.093669075031633, -14.037520308325673, -16.42515742019977, -5.057265379141464, 3.401386528818284, 1.0091117706156407, -0.4761930143160366, 3.021277377980442, 2.738525781996537, -0.6518277136967979, 0.16890314716878949, 2.043865550191591, 0.35932473469400616, -0.14068403985805103, 1.857193276999198, 0.6715230151386394, -2.1372168319555986, -0.8820309636350085, 1.2420938699997353, 0.1149005583361198, -0.5187859198497071, 0.4285144708059285, -0.6980165525548927, -1.4606944266213235, 0.9562580399555961, 0.9636993390920784, -2.3018729368606246, -0.6769049826306631, 3.8056047525440695, 0.911092229231913, -4.399133523192513, -0.6473206831304357, 5.286851953355571, 2.394108318157905, -1.808892299500776, 0.5882113148486864, 1.2434682371947434, -3.593833666339416, -4.3252486265015415, 0.07262877835631648, 0.7179091299487432, -1.2666055761147097, 0.2723439683245508, 1.74675117822988, -0.2795091658650003, -1.004785548712212, 0.4318659346265669, -0.05593623775369967, -0.5391196316270497, 1.070605048345767, 0.29212395425984383, -2.433294014733212, -1.136125349220948, 1.0547610410143795, -1.800356459401628, -4.006717908947796, -0.9747359976015391, 0.18806711280847155, -1.6113662356631897, 1.5323982252203014, 5.112008397286511, -0.96430562029433, -7.9509572419596495, -3.505719459486743, 2.9561361789466742, -0.04516769607151507, -4.094920664569472, -1.5075870895556576, 0.36362871062376506, -1.4812169192429039, -0.8503403058828928, 1.215959957097056, 0.1365712203131524, -0.7088926035902536, 0.5768911211115095, -0.18210628060437012, -1.3155587165987148, 1.3115624501161847, 2.7792641183733866, -0.5064003139190267, -2.220207432164968, -0.30133568902219754, 0.04285659331641262, 0.147167817682016, 2.7908856719130966, 2.2676184512780986, -1.3343358159812293, 1.5336286532289412, 7.2569521347226456, 2.791115020012797, -5.705360957801741, -3.165287662323947, 3.886836817027442, 2.0104553294148815, -2.340314210322707, -0.010680096428926155, 2.311054516188758, 0.16533944770156395, -0.37876376095575925, 0.7279971247380354, -0.6088470400293005, -0.16012178345485847, 4.113005949671672, 4.937239760941284, 1.2490435676216, -0.15408737093847297, 0.33194059001760373, -0.842811428971902, -0.6202868635777503, 1.2615373013631055, 0.24807731455466148, -0.6706420732830674, 2.5176594578796316, 3.4405948593190137, 0.10027727094180088, 1.316181311314936, 5.091050241899481, 0.1507499417228352, -7.416649718380401, -3.926378154682138, 3.5252437411838122, 2.5183101339148464, -0.23681354888470052, 2.2810314111700176, 2.2284089320467486, -1.9796494461307617, -1.3423167676868937, 2.261326917266984, 0.7709224097066629, -1.8509989285384156, -0.2873926894804909, 0.6679287879144371, -0.7019056303264642, -0.1061201816226565, 0.7017561922531061, -0.8339856076306221, -0.5992492570534047, 1.0574208817390696, -0.956956465364017, -2.9144596961524987, -0.08325999596591226, 1.3526647787331567, -0.9197219596993877, 0.6424200899226038, 4.029372733236106, 0.799315305528117, -2.921053826318821, 0.526028913059184, 1.6654978247266956, -4.026009534053728, -3.288100647261528, 5.832106284434907, 7.93482730442049, 1.7650221324199515, 0.11171531997689017, 2.4971394639375446, 1.243199069615473, -0.28860990966703104, 1.0849813550440623, 0.6342174552906704, -0.9789738105731257, 0.3424405972211978, 1.062682505732409, -0.4742899992987323, 1.0449174407100854, 3.95209076213031, 2.153016530849855], 'positive_zeros': ['1.09451963833752152685124090999', '2.00304639622537091039900591163', '2.7593825942188121567569460056', '3.50891535101772016119701791259', '4.96367882526372028500997083502', '5.65379804330044658524714440540', '6.34407214364550925241367632113', '7.00219931926246187838672676253', '7.68862622038866266461591529879', '8.59860507758284850361102758178', '9.1582003941706615197365851074', '10.08544242753257682794538723561', '10.36873300144119525439166109206', '11.24747771915975891929271554941', '11.8300095386629561443018507343', '12.87201492819409919096873623405', '13.76481807410037960442796999860', '14.398225687667710803735222259296', '15.00647648159866616903137218121', '15.637437869248616008485576489159', '16.669074260660404230396457330225', '17.08175556956801577676091240381', '17.57940243729246316508235114889', '18.50695347212247695561113374158', '18.945586369632405411753735193911', '19.49292505295383684822218898872', '20.281053556676970175301167414720', '21.206585578394076749080996573048', '21.672504460621495681434257307849', '22.31929057506017126500455556176', '23.302091323180527999483346409134', '24.0529307808451560447440492185', '24.49371613545497408851603778351', '25.34739742617384136930581028482', '25.78138969391130698064189013178', '26.4710304628796166838850432309', '26.962680110354067697769908541706', '27.59891226794894624682844143124', '28.39367295325596193700724150827', '29.08905455125599023542831274699', '29.52014999403218789754057933586', '30.1480811970460948171031608904', '30.69212617087356083972147137764', '32.00094714820858032786545159001', '32.403489901230638073221003696637', '32.937910921519182621782858425576', '33.975039439401098914639979513430', '34.25029090664662870445948067108', '34.616009647479430138237038839424', '35.496641808401184699707710974310', '36.2010174921565387589622133124', '36.971969232573432057769138189527', '37.15600012869065689856771492896', '37.780598933815616943639871246596', '38.56372871738787313325301219455', '39.08007157165358203632501170849', '39.76659219441542236938913356886', '40.88239089028661519533712384640', '41.191506649608360147970896906937', '42.05740378733675562494649282865', '42.314814921801776466440680484', '43.30336909888697483054793743169', '43.59516938409266589103187068510', '44.46590313654314433088173549202', '45.148402271683277740232015950549', '45.33652611712943176679528629893', '45.970752013081113991468937408648', '46.75380211452718421371982920973', '47.17052177486583547450837849812', '48.09395869562920697970340379072', '48.43657195562354915093920960574', '49.26912573477938554689796143318', '49.94780063805054784684650548153', '50.59191525706943485070593370700', '51.20533929390910750713097968240', '51.94523766040859089057566618528', '52.52725433270722889942620003593', '52.94584755196904356018350287508', '53.654674114522546417357623790545', '54.055928557827498210924706945826', '54.54849034009158394200507014320', '55.64675645355741514577992077139', '55.78446725856734101950051809390', '56.68329774754837307479983697451', '56.82874868871848649161495942117', '57.79332556478842337480579037270', '58.35408362454481026908087942343', '59.05760313608679037663427785338', '60.102117910534471346144586577594', '60.2825548787038742023497329381', '61.1025870410243444223036641801', '61.47456078022814297281818350497', '61.86622828961628427523984389682', '62.74591033485758768740746969227', '63.40585558118442748877186326128', '63.975983932434218984009464063875', '64.15451270748840232150097893656', '65.10416012066469425699029761089', '65.588256648552345916342854721788', '65.98943676584976397574288967625', '66.64084148729156300499248044030', '67.59063320212817328802087957233', '68.36211075905262374082218239314', '68.85137946776411620357594263965', '69.18877310855727639257805344084', '69.892426595031534757555347276484', '70.650700956971682528240606306137', '71.16900585510083651062745443656', '71.58782314785558205218024286776', '72.433309209000728946836804639268', '72.709166308620706514708352196435', '73.34935518061475969163313227368', '73.824232754943277296810391605525', '74.54144930901625703357477811336', '74.99714899691669194932890537167', '75.84908984135319381593471308144', '76.42934127259849280013616722990', '76.929841750720423680963718868501', '77.630457894364212462649947226125', '78.365655186712604528516433226298', '78.942160841918556126333785774624', '79.4227182535023025463741621694', '80.10486331935492655010779439853', '80.46998900753013491648524370147', '81.22899859113986494058269505738', '81.55149741702658475503664294534', '82.04742209069936548657888769069', '83.03491492487352061667938692577', '83.37262902292897558610134118542', '83.88893874622918395486858937964', '84.51339605586789883189254587156', '85.06581481775551372449706200369', '85.763239058389554284417540606675', '86.49380041086221041735594269176', '87.320169870366919645612439163817', '87.85189415900825373976462054564', '88.0502060969270166104251477257', '88.692089375773470287363423835718', '89.46810211681855918676041815116', '89.89502299651955398647235672599', '90.2945062848805168910517751581', '91.25954290100924208500080992480', '91.480561916008681491257919676433', '92.31030445816550310382935077305', '92.61427986469497951499693258450', '92.99662908727669482683156403848', '93.850405070928019001607947923094', '94.570629731070955462583527954208', '95.442463733483089580548773022572', '95.659685645819876438360140295505', '96.45705092182766252032600911663', '97.058719129031405904180891987362', '97.26476140405247423901924559681', '98.2705503855726259653820073303', '98.54415869767242861721448178466', '99.192865835056442613407003265160', '99.83269738872683698981103776870', '100.4269264887407804748154960964', '100.61912792537117430043024901049', '101.14061722350440086880003137691', '102.06945775899005618390999526457', '102.58566730608043552287366340613', '103.178000276425768146706267646903', '103.60394067282041005313643004478', '104.545419061939922536136656175931', '105.12620039643724159141361414097', '105.49409528964310864151299570764', '106.09990157301572524692488406447', '106.91621479290693763434443451433', '107.406425147574491528051484123120', '107.787932214972164960118348361480', '108.25540385579851434114712426885', '108.81651828283373288368129527617', '109.41926913752254611261886527399', '110.12151415388357724349943083374', '110.64153854379350133994550056481', '111.01654388786145379346114091562', '111.70036388265140155176589701918', '112.27351868577100457430063684719', '112.822950490584054820388165137122', '113.68532325747393522602040932391', '114.19256251241167472804421753582', '114.98423185188812890141747219108', '115.28114616516906673693925551629', '115.956991208538634157177308803783', '116.16836058087811312577590053345', '117.01577732102191269714107770866', '117.35781296575700556999163692356', '118.30024187611368722217152353051', '118.46462952684672272806087934300', '119.16372722322307729753679896863', '119.6784688328306820437217616971', '120.13488764767624022463654198327', '120.67088132845253941855319889560', '121.36916093479288433611586325014', '122.13580035510204067836866077000', '122.78378806895856940615292051346', '123.41380471523087268300161548628', '123.810136662830770684111432455', '124.25004817610133047966808698643', '124.915946929541752925368717741940', '125.504035565802770448227083618371', '126.07381843333355591170984600014', '126.65710077604364488440330035920', '127.11918019753730166390591244602', '127.548321519376521649348670391654', '128.09394433542785137818990633570', '128.69837932764629597751672140766', '129.21890489785039553183247883562', '129.89438494784768096057644326167', '130.426053045856096659920630340740', '131.07958513268727295864375683154', '131.919971207478945834478468380271', '132.210015901017552622826725470663', '132.63348169574737883467355885090', '133.57429588027636080927307311208', '134.09978014426973965850356783177', '134.53251243078701493740186062818', '135.106368900026453311895597122230', '135.25822375152899017843171314183', '136.19801885051859344486497428387', '136.680096651688851008779951194611', '137.109465129247357851175488488710', '137.564154837714360833329343808866', '138.528239312171747037157085725564', '138.85909760434004985999904202270', '139.179795639468535239812298393665', '140.05734896077698423740025040460', '140.52857228922421229696921756057', '141.53064614600609317974386567487', '141.93040260971501901778300393137', '142.34366774812653798358124726830', '142.87190466247769293012995104534', '143.55190480400230540251272840491', '143.834074090383028438976887154616', '144.501120888599845257223522286433', '145.09486158704214471505039955615', '145.624864624460698818091422389641', '146.09182983460806922238429048668', '146.716659641151185352657949859439', '147.382801530926851030467211066392', '147.55355041626300273286775568630', '147.98360387553101611810150583400', '149.19722004415718236027407574833', '149.7699652813350874580657135090', '150.05703393821995757316902048439', '150.85696466154842387112250849949', '151.23030765078482468498736436278', '151.93081663523486227289962795867', '152.21413666897975618475754884695', '152.87537476375386393571966187286', '153.53191623879707624732065819533', '154.08327535286296984125455905373', '154.52599835552788121635210975565', '154.880530245484087923403569427626', '155.51612240916489673582493946335', '156.03073653290734157328713588139', '156.60399332977237004736029887117', '157.229921208414049753441978636868', '157.83903911007538462943864286900', '158.566710348804060915157001164187', '159.012296969735994552013150527723', '159.471317800986043205877564754293', '160.30633677732540116608324229947', '160.72084384067906910856805056473', '161.219002325248099494713928904523', '161.83890580203448670858110204148', '162.39230944218233184804580588282', '162.79937038629300264732561407556', '163.24499982482683080294821046764', '163.78162207972942257432873149711', '164.48497717176233235619286612432', '164.85919548960531831844826081459', '165.72834914625035764863420893273', '165.97172373963006492965525495072', '166.47039312453702603588802568663', '167.155676467850558600041487985702', '167.943235242300778145967560485976', '168.43514864827999980924652314547', '169.20999553446460733741625450831', '169.46011764888936499655657827386', '170.10278626301665986365233852712', '170.64706369622480571972557485817', '171.11042516820149413526357656009', '171.53315036273223191578900711131', '172.068634363297071340388158808571', '172.772125469769011008396961364521', '173.49969284369767127190369854297', '173.7679870693322616145939050925', '174.03222836788440248815185960049', '174.8618969097395890191496181146', '175.23241894034001681275183310893', '176.02500176725021123985513829054', '176.68172546135821827653763925695', '177.29718792621831418227096161386', '177.81330251793651682517742651174', '178.460222142326885514294335919092', '178.83307839930109706791050056964', '179.27035453637625976106842053436', '179.7031289345986193458592145191', '180.788224665950085014458098912258', '181.01300997223030224720301414643', '181.37697602374067932620747028537', '181.96882458763685469616690049898', '182.53515655590040461152939470255', '182.90881972846644433039139700020', '183.76380173222480478374007958103', '183.94477166840285759939268665830', '184.69264827340310003921339226860', '185.45283462957290888320340720764', '186.15943686592290262203064757051', '186.32201889316062266819300753622', '187.03567523951418042495939751721', '187.600731546669205596674937895293', '188.19049525954443916216540690358', '188.788996004338130216568113741260', '189.215310764427415170544110228504', '189.708211668589053421314298177768', '190.16461695005371584018789981504', '190.71480606117197682748198040420', '191.15809106214423893659846048858', '191.88223458801153880791897554418', '192.37118963325657331566048134715', '192.76109885967145181403019066556', '193.48109002579423675751651013370', '194.02825211672889217463731748504', '194.4822891549754529882125545712', '195.12059143039327897686696090443', '196.08233920869152959267320888846', '196.23065356663000353711041211217', '197.0437587900504588475105732832', '197.28763352547647654430364626889', '197.90661453936640571469660198753', '198.386045696222955543989051376147', '198.95166408449735095515181533564', '199.26443526953988927662784496846'], 'prelabel': '1-3381-3381.1247-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': 0.7968230255760305, 'root_number': '-0.803110253520921424137919389126+0.595830446259303970845048782207*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(154)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.664614356313091155625399288883+0.180178957059828569612505605909*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.09451963834', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.00304639623', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.75938259422', 'prec': 44}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 15.701297990361368, 'bad_primes': [3, 7, 23], 'central_character': '3381.1247', 'conductor': 3381, 'conductor_radical': 483, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3381/1247'], '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': '1-3381-3381.1247-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': '1-3381-3381.1247-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': 0.39841151278801523, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09451963834', 'prec': 44}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': 'dirichlet_L_3381.1247', 'Lhash_array': ['dirichlet_L_3381.1247'], 'label': '1-3381-3381.1247-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3381/1247'}