Lfunction data - 1-475-475.284-r1-0-0

Formats: - HTML - YAML - JSON - 2024-04-19T08:08:36.552371

• 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_475.284', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.30901699437494745, 0.9510565162951535], 'a3': [-0.8090169943749475, 0.5877852522924731], 'a4': [-0.8090169943749475, 0.5877852522924731], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.8090169943749475, -0.5877852522924731], 'a7': [-1.0, -1.4081532572346456e-30], 'a8': [-0.8090169943749475, -0.5877852522924731], 'a9': [0.30901699437494745, -0.9510565162951535], 'algebraic': True, 'analytic_conductor': 51.04583927744689, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [19, [1]]], 'bad_primes': [5, 19], 'central_character': '475.284', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 475, 'conductor_radical': 95, 'conjugate': 'dirichlet_L_475.189', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^4', 'a^4', 0, 'a^6', 'a^5', 'a^6', 'a^8', 0, 'a^2', 'a^8', 'a^8', 'a^7', 0, 'a^8', 'a^1', 'a^0', 0, 0, 'a^9', 'a^4', 'a^7', 'a^0', 0, 'a^0', 'a^2', 'a^9', 'a^9', 0, 'a^1', 'a^0', 'a^6', 'a^3', 0, 'a^2', 'a^8', 0, 'a^2', 0, 'a^3', 'a^1', 'a^5', 'a^6', 0, 'a^9', 'a^9', 'a^2', 'a^0', 0, 'a^5', 'a^2', 'a^4', 'a^4', 0, 'a^1', 0, 'a^1', 'a^3', 0, 'a^2', 'a^3', 'a^3', 'a^2', 0, 'a^8', 'a^6', 'a^5', 'a^1', 0, 'a^9', 'a^4', 'a^7', 'a^0', 0, 0, 'a^7', 'a^4', 'a^9', 0, 'a^6', 'a^5', 'a^1', 'a^3', 0, 'a^7', 'a^3', 'a^8', 'a^7', 0, 'a^3', 'a^1', 'a^5', 'a^1', 0, 'a^4', 'a^4', 'a^2', 'a^0', 0], 'euler_factors': [[1, 'a^2'], [1, 'a^4'], [0], [1, 'a^5'], [1, 'a^2'], [1, 'a^8'], [1, 'a^1'], [0], [1, 'a^7'], [1, 'a^9'], [1, 'a^1'], [1, 'a^8'], [1, 'a^3'], [1, 'a^5'], [1, 'a^9'], [1, 'a^4'], [1, 'a^3'], [1, 'a^2'], [1, 'a^6'], [1, 'a^9'], [1, 'a^7'], [1, 'a^9'], [1, 'a^1'], [1, 'a^7'], [1, 'a^4'], [1, 'a^0']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-475-475.284-r1-0-0', 'leading_term': '0.440415671808986550794629413150+1.11236301050374523624637715723*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/475/284', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.1963767931182532, 1.3081875902871594, 0.5085603220975663, -1.3487213175122186, -3.9882716444297452, -6.622741263850509, -8.185522676660923, -7.860861763590343, -5.620521127674388, -2.380100769479949, 0.4261096371228667, 1.66218700194724, 1.1788661772424605, -0.13445640312191465, -1.021298479441272, -0.7851910650320818, 0.24078746649333035, 1.0713150033703147, 0.9900764082783335, 0.2165278962210428, -0.3052909838897725, 0.14972092814276397, 1.2734453683536986, 1.8720118170553277, 0.9602646428689914, -1.1602876784505445, -2.9291909704611196, -2.80660237914068, -0.7251297109661489, 1.6879589870498102, 2.4891922141675438, 1.2348992117344813, -0.49303323504538854, -0.49001491626348564, 1.9420850418648041, 5.166619906123563, 6.591840226367868, 5.0511198696705115, 1.9151361668444808, -0.19286211967552017, 0.12143084210169924, 1.7665255931867658, 2.372817064909264, 0.7374659821034956, -1.9741215569447614, -3.4643998407665775, -2.6460282396377304, -0.6381308814351326, 0.5555180703058424, 0.1640979192969395, -0.7552707419747673, -0.7903445714651569, 0.09295416435908237, 0.6157599163587673, -0.061140011272085876, -1.0957519794811703, -0.9153606022543299, 0.622357113420613, 1.544437565204921, -0.227228622045817, -4.159254632624734, -6.90708071622317, -5.368719593563624, -0.029219407525485346, 5.07110111352006, 6.018184086174051, 2.6822217430721667, -1.4128935012797104, -2.765369843820667, -1.1444363902717432, 0.8789038026784383, 1.1695646114600726, 0.1624911634929662, -0.3270006264579194, 0.24727621788985993, 0.5001478093517056, -0.8249800959935665, -2.8723808339421435, -3.475907761666229, -1.8531570134635724, 0.24826102665302113, 0.5595644823628754, -0.9495928850415263, -2.0577742918164525, -1.1433340171850457, 0.6735745266102454, 0.9105382687620489, -1.0225111078281164, -2.8921169804530145, -2.435065151309382, -0.4524254665546133, -0.10054621471433596, -2.9265206416225262, -6.509313646283513, -6.932194084236285, -3.4152782568724125, 0.47497565675482933, 0.7089490274722532, -2.697895521922581, -5.836665432635631, -5.420562542185687, -2.2341962169773453, 0.34583747581486046, 0.4998953255133875, -0.42538644027183015, -0.38302899872695145, 0.5406184680721898, 0.6585874639034471, -0.546580258566655, -1.5386503646759777, -0.9845088147785371, 0.19381083701579851, 0.11668566622136547, -1.112828901140859, -1.2115431276340791, 0.9551165408206062, 2.968275832318403, 1.2463209528852373, -4.178224545992494, -8.69040889239637, -7.856281608149331, -2.504306282179868, 2.1367429481814137, 2.335861145555079, -0.33223552190448413, -1.6629230738778207, -0.2030994389201609, 1.5110039803390334, 0.9262312397794527, -1.0443966138109269, -1.594819500619473, -0.10397504943870134, 1.0928387931053094, 0.18614668242883126, -1.4351720374164607, -1.1493814590485554, 1.0955579991342905, 2.5704044980226235, 1.4895048837946818, -0.5684811587651909, -0.9344389125311365, 0.4653308779152113, 1.2620905514691607, 0.2927996469929633, -0.7149378079689137, 0.0003927265504399396, 1.1234369985620816, -0.06514712010089721, -3.1455267528731494, -3.895489690760274, 0.5401552694384776, 7.09488120790028, 9.416378138910629, 5.107031721985818, -1.4151240997024304, -4.122246229725055, -2.0851932848825605, 0.5147923279070427, 0.31327394110353, -1.4819442988424032, -1.8273623095542504, -0.3808972860937065, 0.5427454581185711, -0.2199413407819609, -1.1375151986802177, -0.7229862150121867, 0.08690893929601862, -0.2541716266058486, -0.8852222640456291, 0.5266596274920191, 3.851974668869799, 5.679622479758286, 3.6123502535946743, -0.14938536248094872, -1.4684173618133585, 0.07943509580017834, 0.5752916914531756, -2.5848352146818847, -6.562502850252322, -6.54269010231164, -2.251630118839925, 1.5140160992517822, 1.150737243526591, -1.3398846158059212, -1.6964275663255104, 0.5504227249812198, 1.8860328215796855, 0.3291269087842308, -1.6249569016903003, -0.8149489387702895, 1.8399082888868072, 2.6564308097637186, 0.4904705346859015, -1.78011011284201, -1.5105830152886792, 0.20801198482220964, 0.7258820584399049, -0.11358454745886411, -0.31502039950469984, 0.5259777643028364, 0.45486412480487454, -1.2530061348370323, -2.1841349260948735, -0.32292106255897446, 2.1580438385585006, 1.4602702274925146, -1.762702091871693, -2.0281377413029933, 3.7840883746545537, 11.162309792558183, 12.562839415756574, 6.482099378770924, -0.8720957916246982, -3.311794459564411, -1.3534260176666706, 0.3160350748648674, -0.27444040853236146, -0.9572646448665633, -0.09816164271668454, 0.7248820070240526, -0.18133182149705146, -1.4692793362736682, -0.9160881120234814, 0.7325586511365603, 0.7825670206303088, -0.9172845617590938, -1.3493386810153662, 1.0078130221384847, 3.446284575714648, 2.8574690855375464, 0.4658162092209419, -0.0068365192580860205, 1.8340842514538678, 2.3189232479291624, -0.4778028206167027, -3.2899644479081576, -2.2755388688426805, 1.0364180790989437, 1.7403006262467067, -1.0993300645664983, -2.796011416892861, 0.08064317644336227, 4.341701859425111, 4.404593799490201, 0.06536245722325584, -3.3943255307873654, -2.5976918982084465, -0.08953188720068783, 0.22180622781368356, -1.351887951403594, -1.7620907377965276, -0.4420179019470918, 0.22199576378467487, -0.7469816043487236, -1.337577888525393, -0.19788392216448816, 0.957066838274592, 0.37860337270011113, -0.5539185137945127, 0.12502434556648453, 0.776718762097832, -1.8698706887902028, -6.56471927216234, -7.289504724667915, -1.1302042361594462, 6.572209653400259, 8.178144724588133, 3.342950512279456, -1.0432854454050664, -0.3011784778411073, 2.6400453012864884, 2.757458795045938, 0.2646951074189796, -0.8175873444009014, 0.6278446522396721, 1.6420644125719324, 0.5613261122946963, -0.40420401162875375, 0.6364617820384412, 1.7430675615630433, 0.39250293630583516, -1.964439526674907, -1.878625109529993, 0.5452337451233215, 1.6179096014350767, -0.1862893885566408, -1.9167176685556315, -0.9581343664257213, 0.9432770680574537, 0.9412129970434517, -0.051688209836268595, 0.689279859397788, 2.1748680939800327, 0.5235425917585509, -4.141873692162882, -6.016547934227027, -1.3905996262979103, 5.14985272004613, 6.141645814030456, 1.1942611014398523, -2.862419317754603, -1.6842204216213108, 1.2709559171482228, 0.8517196834960556, -2.273955101823367, -3.5961614963007564, -1.8710698981560339, -0.10659647216839056, -0.1445174614869568, -0.3880349023384377, 0.362757427697414, 0.5343879384195317, -0.9310559484700218, -1.973096974620781, -0.7749418762438963, 0.5910031952052264, -0.7163492248523745, -2.9913019261341396, -1.9295406769160024, 2.218866820785244, 3.9319232596505893, 0.44469070049112386, -3.592501990797545, -2.698940401523165, 1.207864630477308, 1.6558986178708253, -2.6531183386519057, -6.042944005340928, -4.403547977660123, -0.7088873150885423, 0.3673054407691594, -0.6286142104654502, -0.22880751651768239, 1.3154377397520607, 0.524681789005334, -2.8052702786066845, -4.418008685504409, -2.0329661869225313, 1.0992283058356824, 1.2521529492038226, -0.4667353031635236, -0.8355059602390178, -0.0003626329814022441, -0.4507424023412287, -1.9550746706767803, -1.7937430200874938, 0.11637547523472729, 0.6619123023709775, -0.9382139762300994, -1.361382606383724, 0.7856756628234567, 1.2590056883762477, -3.424789625839712, -8.71718752937052, -6.681650224275209, 2.6305640979010736, 10.011326513249276, 8.749409733363558, 2.6068177925849563, -0.6702671792826752, 0.3305539509792032, 1.2232884077447483, -0.0030208563504893317, -0.8300041098887478, 0.1854276437404329, 0.8754232102760351, -0.13791328092273475, -0.7996831196311366, 0.3721153181584674, 1.174302137638267, -0.4514881998419209, -2.361479712161655, -1.6309188329151414, 0.08932451982528425, -0.976611441596797, -3.9706966112999793, -4.057350153555719, -0.241389178864863, 2.5439308991511353, 1.1393169676132937, -0.7553975668730932, 1.2526090396373255, 4.8051126959389645, 4.523843250361715, 0.9618634205825097, -0.08347098370447169, 3.009801777241844, 4.968868879284233, 2.1404583571512847, -1.6194244169750984, -1.1068437078556526, 2.241789591509124, 3.202247744989253, 1.081500482331709, -0.09149510211830819, 1.2015382562950234, 1.89530941540025, 0.1852068852331717, -1.4128706974096203, -0.721391405238541, 0.4876783112364043, 0.13071312468956792, -0.4713623955909463, 0.26516451782623673, 0.4423248642335144, -1.8143108824328342, -3.571326371738683, -1.0288354200093164, 2.9328587128692347, 1.2653276318673135, -6.340686089765957, -11.152109459554127, -6.946751585700527, 1.2401102028777191, 4.3671375899777445, 1.517857172013569, -0.8861351873757648, 0.25503846233713656, 1.4489717397398336, 0.0612035276643463, -1.3405632310141962, -0.25884666246489846, 1.2622678836388044, 0.6850152452658665, -0.49375369420496773, -0.0719245048948624, 0.17748638098955588, -2.3719541365191543, -5.5838573318743, -5.0543869442636105, -1.2357138977883362, 1.024823012506952, 0.055145253314208005, -0.7241684913925037, 0.5815476250582126, 1.2106131195442473, -0.3729706338136118, -0.6599658715297586, 2.7876569377590696, 5.664506746306591, 2.824497212301053, -2.9395743607075793, -4.3820102891177255, -0.9726209241006188, 0.2925000598396881, -3.861573647166791, -7.708307363709684, -5.5382187420299855, -0.24587889772603078, 1.7582884027124186, 0.08424768057152118, -0.7342498653731608, 0.6369650153299699, 1.239361016271738, 0.009978441076456065, -0.6153813141598634, 0.2829358030582301, 0.5938619543294597, -0.21456171801363863, 0.20240471535191787, 2.035164800374519, 1.808419145634068, -1.4603957459594363, -3.293612850290471, -0.7705968982319267, 1.788303834356869, -0.5772271472738458, -4.486315740330798, -2.549386734183986, 4.712742039193261, 8.631332486550583, 4.896540902903461, -0.7060427851007705, -1.692643360969181, 0.32105450429197024, 0.5071631502472864, -0.7278739408167343, 0.02927310502645447, 1.9534195236541527, 1.3955106799610553, -1.0311304656421, -1.0813862877504121, 1.6094537783109069, 2.629742754866903, 0.27045760990744505, -1.7530958674563424, -0.8717111767569197, 0.33452444621687993, -0.5669048061880811, -1.399136019399458, 0.155576611058528, 1.8380315057566732, 0.9451457511553979, -0.39843487100375946, 0.8149794932131494, 2.3088078325178385, 0.46336149076844135, -1.6439040714564068, 2.3989477343386887, 10.952133342366313, 14.175333318381902, 7.683044958080435, -0.6991640125433491, -1.9799368129234536, 2.14025282590814, 3.971027691273061, 1.7225010016644389, -0.13416917430317585, 0.26290668244336324, 0.19451809970621164, -1.2715129506743015, -1.5617015978754472, -0.05595177039313977, 0.4617838217140929, -0.8260220975023982, -1.1949829219408503, 0.12751912358645356, 0.14014605172616812, -1.9169618694981594, -2.0874830795966295, 1.314791624942816, 3.3941711468604217, 0.10636021878046166, -4.430685665853724, -3.9995350992083054, -0.2611470359682379, 0.3121487706271566, -2.5530012731077694, -2.8726619286395296, 0.7513843965530431, 2.3839984333970685, -1.0776348248110312, -4.491639325349686, -3.0317411269756285, 0.2540994107553399, 0.4884123931822108, -0.6974070223613755, 1.0161323915556586, 4.274552180205183, 4.268703653447633, 1.1913451796753236, -0.22476242627861537, 1.2192699057919718, 1.9721461390268546, 0.6406676938606645, -0.05797875502766153, 0.8884316287294467, 0.9201073247851947, -0.6484214848446717, -1.0103045773714734, 0.36629580154304087, 0.2818644861527092, -1.1535032798668239, 1.5328942379789945, 9.656864627437665, 14.871628697791497, 9.763394012396173, -0.5009648207451848, -4.794978597119224, -1.5011406278832682, 1.0348137385581944, -1.5387901404069375, -4.164772483851963, -2.3434757666373067, 0.8405321205696452, 1.1740517268077564, 0.04095173806662162, 0.2798372955101611, 0.7115287748392048, -0.4614509771757738, -1.2537641392982606, 0.1754741229763265, 1.032684562308783, -1.4764298406490308, -4.3663615884444855, -3.337272768445194, -0.21138491622800942, 0.20108913825331914, -1.551818243620715, -1.096658547217376, 1.2919370161434847, 1.1887003209373095, -1.2073894159678553, -0.7003274861936886, 3.2071252129064254, 4.260785332782755, 0.03517248512281114, -3.129646704304684, -0.34886236726599007, 3.6030160493418344, 2.4188656424833423, -1.2077079949552931, -0.6382961500699158, 3.2283940888853513, 3.798145621217281, 0.0015436503926791229, -2.5494704853005747, -1.2245999272653805, 0.4514280301015956, 0.04082698915499821, -0.3893094670540631, 0.3581957098786024, 0.17735640191614468, -1.3642160217384711, -1.4578576266656755, 0.3302299926643976, 0.6155692308743037, -1.2469378189385902, -1.311634763149179, 1.1681964123328565, 0.8324234917252961, -4.241259573168709, -6.760552974324395, -0.7083063282643396, 7.823465575500771, 8.494398322189774, 1.7774780805120978, -2.7301830899060104, -1.0981013896918235, 1.1927602734477798, 0.24264390630667637, -0.8606202983808733, 0.34247167122433797, 1.0143202441266932, -0.6101896879937403, -1.2339507961857705, 1.1373157019767046, 2.9464941759811487, 1.4538589050564954, -0.2095528596517652, 1.0359345182880066, 2.4220225262904873, 0.6100828320519305, -1.8966432815336567, -1.2770310994659142, 0.7473834090651608, 0.5959442254311909, -0.28969820719165457, 1.226182350383234, 3.0217746794920766, 1.3361811462619197], 'positive_zeros': ['0.72990175158668665863825443297', '3.06692479430383769676801986912', '4.03050793736489827140009976956', '4.93269772912863837651450649003', '6.0252409718432923097581457098', '6.508721712199221444529310737287', '7.6523426512192929514412397880', '8.8360970203818387104079648236', '9.89347506029496118415109467327', '10.40354672602153197441934005859', '12.13489912509574035340936380742', '12.47019814961970073881499878164', '13.52373715000778341141338669497', '14.80684290756239494763834329647', '15.36525454072608981372416326805', '16.21991194494868429148546452744', '16.8578408239318803708062104693', '17.69930989318825729044080538665', '18.41490030486968824447129518999', '19.68901189013388406407579589239', '20.81559676115219189561640978964', '21.718654487560398719786011514657', '22.55303634811412126399664107507', '23.02147737185795399262507150536', '23.602196118123483838886171478731', '24.95183791430627781445063548343', '25.45317675194331935989400330220', '26.436461597945754257743412651011', '27.04971259454478152630829740604', '28.23040429513340676441427346337', '28.41021788266773701031058504411', '29.94738877379732768636021812936', '30.39968876571741372277649804662', '31.810047510332044060532623619957', '32.34871431626695283762614803412', '32.94758971671371181810099369534', '33.63085000860499470141179739533', '34.62169078877470532865568924324', '35.03650941486371842272751218870', '35.825668676917772435078675638184', '36.64778066715470999603821988896', '37.95300577077250837452952398371', '38.71168883339501239899073273109', '39.40393069340870747555971509131', '40.14619721183170620827069365342', '40.95528792363558888841915157103', '41.59525385695978764749149432344', '42.3609325873645236952343901013', '43.338689578575804955837930019546', '43.97106316349234521176639662382', '44.75228377135066283109354194429', '45.312412547909792787845040895792', '45.92963413457487215692769884783', '46.84858785762284245127944457402', '48.04902704862662861295824156475', '48.97465145926044982786015765983', '49.43337835465589159490323432935', '50.39211382038986354638761047979', '50.88003575103917164041192525131', '51.81773860135604149001116832177', '52.08137919336154714190814109174', '52.74625205111526565896715147888', '54.04763653443003075789904335074', '54.67390159759050167232598327498', '55.092301485711078247547565049', '56.40340234091934026174205614582', '57.01684230794625830891658644530', '57.744734975531307620967480555430', '58.479378543460809010561804366941', '59.16217594868505192477396385717', '60.05368757360326527768155306672', '60.89516697487229584653187117548', '61.52242221707945053940932954079', '62.00673901004596885422821016951', '62.604066258350801675495817961773', '63.472167676382141260270055743036', '64.20734090969729117123198630187', '64.8319007304248169523370237174', '66.20346603613060080813376543881', '67.07821775610932237550188389023', '67.42229333400041914634940885444', '68.14902606108647267169375408602', '68.71263811188723355713400925642', '69.5404626505417126168900613834', '70.15554819717721943609228555996', '70.83218658418217974111250561438', '71.96836171784300808926150706169', '72.18946061226993975672555977961', '73.083957651458356167065771079936', '73.95896993725272272979672917936', '74.584583881545413033051412772890', '75.30699469326704580976104595551', '76.25417755280570284599294604938', '77.20365963084659964418611837954', '77.55484659752902864885119848266', '78.55053159281863690309679702290', '78.86188159308245932824079640905', '79.72620999195842328946049178261', '80.408637412534213994566451681322', '80.906466721736634625459513236720', '81.400093587291716399857428159434', '82.54168587378867933619008750346', '83.63989527868929944931997393881', '84.09454597141401702227485244188', '85.03593119172555746077605933955', '85.518577405881350234683044394149', '86.370733246327128139479588755628', '86.74372129164171860667824291559', '87.54839621275701330479196349075', '88.37007682609247151527415098040', '89.03883720874982458352583903885', '89.82808029817466466315517261542', '90.59340854617567978193970266140', '90.76478104735621668443533361877', '91.6032787690305161124808407879', '92.56105319200228356524591540466', '93.504000710757524243916851130512', '94.22130460185355167370106368870', '94.78129225564447848755981408485', '95.98867498666406458389120453387', '96.15660311026524675201212225862', '96.74966939956045610582586743743', '97.33117586131278501000370591905', '98.25637149106922004323031373130', '98.65008483493927529462796785345', '99.52755843018629011150192061115', '100.34032652181866160877231326795', '101.14668323327774466854557271923', '101.707121407308757326563059256031', '102.90838879775456149895364690385', '103.251837228880198444884820741937', '103.79555789496905983106232811620', '104.43361663264861559090751413619', '105.492366810633283137370541536072', '106.16018598238538651115428964511', '106.87522068179087833080049363724', '107.045580080772565158193919986308', '108.10487597065042863524827294053', '108.588860369139643183641600181238', '109.27547517865300203719980461075', '109.80873530138097539043253937621', '110.85768843620385245934807628153', '112.063114407280722910441726478491', '112.440683695727478149332436195676', '113.12440168779822285069465667291', '113.707568720933933919007235422981', '114.34304369468816325176841240366', '114.92586692468130071016603918139', '115.565297533711069660941776744107', '116.53145806588224550521678986384', '116.72122937053215318636531486973', '117.83016328906967639708613892024', '118.57530407004233272949784250956', '118.941848625566930664741453705644', '120.11811219090703058636061379630', '120.328766846876948926339498975562', '121.402688436882119109091594611645', '121.98244625819328259840002954403', '123.01273561015676671760029777403', '123.17766650754761292057757971238', '124.08808926014205525708640361690', '124.84049551583524521152193134954', '125.35627992157117206658215212095', '125.857296759193122711763385039662', '126.34183120172497012493533032105', '127.25814225930158848161276876775', '127.8761731453639886924943488786', '129.00887210462628432693812556339', '129.829406491186655118579887028769', '130.27226079904857689249907957669', '130.94666579726422853229742030118', '131.60406582978556314497385244798', '132.336244765629835248300004737803', '132.83649458431386106765090123781', '133.1693453073439733731129489402', '134.489318909710531524417888003444', '135.010924854436198777963190671314', '135.51507485320881964857796679059', '136.187223395174212615781352765604', '136.65087837499011866449609933042', '137.64710869268889496105200020364', '138.53604459959319377892814830019', '138.792091443953195884390838888462', '140.01786703838634288884023912788', '140.63856970196741916769220896083', '141.127917207440516523915772688150', '141.87724053162269873693447397151', '142.41749502820184754830128068623', '143.037854643362499025850954872762', '143.39121090481716706187556134764', '144.25010771254442506056971321157', '145.06550003875253733811905035867', '145.582909412500947413689428647348', '146.369539743053832506116937020490', '147.44772171862318542565523303687', '148.069674678622451312802991801359', '148.5553708862043453784671427001', '149.057795813054609795572491623737', '149.86136707362976110262587485026', '150.451654396523674289800286751403', '151.27842009216347510037315596222', '152.04577851932636464327836785324', '152.37345781048833054289016131626', '153.10377416294945187532405942108', '153.91896880691310665719383165942', '154.24215221698263916349985959154', '155.04582091511063582771611218396', '155.50781687363683959192930175863', '156.83895623061264121520766670276', '157.35018598719274765587944406521', '158.38225954087577890219630524584', '158.638897791749194059967855093169', '159.11462128737586576642208358832', '160.011715346123562098018573833623', '160.448298644724295647776023409046', '161.219365928375225425343809640290', '161.591440633663507043999285626366', '162.39655705549309352779004320498', '163.13138081475477165987935880239', '164.09135962011788021022821712146', '164.41955433920996227702655182584', '165.253348346451242738772558278129', '165.86484744159804855888436965670', '166.841117203684653970345478244228', '167.290077455305162654378239458700', '167.7010128267576214082378047462', '168.91542474676042811254284381537', '169.14907303663515230641572012955', '170.173264726243304016095723756942', '170.35004854273629160774441506431', '171.12790059104323462298688718379', '171.79180005551680971391664066991', '172.24437587502348620251764914446', '172.71760685802252283373001111853', '174.04496572931867104416326728004', '174.80440810507423866511281147132', '175.17912764669777474432458193277', '176.14769371971868865321767858122', '176.89781229364174434039117447424', '177.05903417496996202090087503601', '177.71966633393106443194525376447', '178.40894409318419319719345226196', '178.92344707300176824979967003442', '180.03080798658552986867174746337', '180.353862314306647045660404978987', '181.077531569301078564392672266817', '181.71511270558859623161230184196', '182.25367061794455005876575092166', '183.12714697939479614894678689870', '183.77257700688687106882842065656', '184.56549450307981348083730439366', '185.05668400509360790863232938814', '185.9376149022289655373989209609', '186.74751290434194492941357823694', '187.20133453804312591714977893377', '187.680217377415451447048422650880', '188.16803561261856574454854489749', '189.00424051737011789596610642439', '189.4923610043555555500808024588', '190.17056411254366818008261415584', '190.69284238481340539001241749494', '191.58618440155173114091960071647', '192.58274416418792158246738086869', '193.23596720536036374247315206457', '193.79148098562042328807364636674', '194.3106570546895938313437413250', '194.90316513010327317037832042056', '195.503396150731567196623981884774', '196.47434169927224051072086882724', '196.69556528615082338800442069764', '197.56238452245233531707601940147', '198.30264810011849050551350807347', '198.90005109874376903648534977734', '199.18618087083422713405126500377'], 'prelabel': '1-475-475.284-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 51.04583927744689, 'root_angle': 0.7600000000000001, 'root_number': '-0.728968627421411523146730319055+0.684547105928688673732283357621*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.38', 'prec': 14}, 'spectral_label': 'r1-0', 'st_group': 'mu(10)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.628013857601153317756451955923+0.538626447056327725115625432870*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.729901751587', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '3.0669247943', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.03050793736', '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': 51.04583927744689, 'bad_primes': [5, 19], 'central_character': '475.284', 'conductor': 475, 'conductor_radical': 95, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/475/284'], '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': '1-475-475.284-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-475-475.284-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 51.04583927744689, 'root_angle': 0.38000000000000006, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.729901751587', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_475.284', 'Lhash_array': ['dirichlet_L_475.284'], 'label': '1-475-475.284-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/475/284'}