Lfunction data - 1-143-143.108-r0-0-0

Formats: - HTML - YAML - JSON - 2023-05-30T23:17:11.848515

• 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_143.108', 'a10': [-0.5, -0.8660254037844386], 'a2': [0.10452846326765347, -0.9945218953682733], 'a3': [-0.9781476007338057, 0.20791169081775934], 'a4': [-0.9781476007338057, -0.20791169081775934], 'a5': [0.8090169943749475, -0.5877852522924731], 'a6': [0.10452846326765347, 0.9945218953682733], 'a7': [0.9781476007338057, 0.20791169081775934], 'a8': [-0.30901699437494745, 0.9510565162951535], 'a9': [0.9135454576426009, -0.4067366430758002], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.108', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.49', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^23', 'a^14', 'a^16', 'a^27', 'a^7', 'a^1', 'a^9', 'a^28', 'a^20', 0, 'a^0', 0, 'a^24', 'a^11', 'a^2', 'a^22', 'a^21', 'a^19', 'a^13', 'a^15', 0, 'a^20', 'a^23', 'a^24', 0, 'a^12', 'a^17', 'a^26', 'a^4', 'a^3', 'a^25', 0, 'a^15', 'a^28', 'a^14', 'a^11', 'a^12', 0, 'a^6', 'a^29', 'a^8', 'a^10', 0, 'a^25', 'a^13', 'a^9', 'a^16', 'a^2', 'a^17', 'a^6', 0, 'a^18', 'a^5', 0, 'a^10', 'a^3', 'a^19', 'a^1', 'a^27', 'a^22', 'a^26', 'a^29', 'a^18', 0, 0, 'a^5', 'a^8', 'a^4', 'a^21', 'a^7', 'a^7', 'a^21', 'a^4', 'a^8', 'a^5', 0, 0, 'a^18', 'a^29', 'a^26', 'a^22', 'a^27', 'a^1', 'a^19', 'a^3', 'a^10', 0, 'a^5', 'a^18', 0, 'a^6', 'a^17', 'a^2', 'a^16', 'a^9', 'a^13', 'a^25', 0, 'a^10'], 'euler_factors': [[1, 'a^23'], [1, 'a^14'], [1, 'a^27'], [1, 'a^1'], [0], [0], [1, 'a^22'], [1, 'a^19'], [1, 'a^20'], [1, 'a^26'], [1, 'a^3'], [1, 'a^11'], [1, 'a^29'], [1, 'a^10'], [1, 'a^9'], [1, 'a^18'], [1, 'a^1'], [1, 'a^22'], [1, 'a^5'], [1, 'a^7'], [1, 'a^21'], [1, 'a^18'], [1, 'a^27'], [1, 'a^5'], [1, 'a^13'], [1, 'a^8']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-143-143.108-r0-0-0', 'leading_term': '0.569107943848872338258061725310-0.736916610357436424162251018679*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/143/108', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9310907272508864, 0.8068920447589082, 0.6103567973309447, 0.1761426423278222, -0.40549424617788943, -0.8901121997648636, -0.9994885666411891, -0.5554835392116106, 0.4072212201458583, 1.6073641066870725, 2.6017544009682254, 2.974088060912183, 2.5499121700767198, 1.5233894788354436, 0.40380421492973556, -0.2262512542160655, -0.03877890086946728, 0.8023806642557234, 1.654820228786361, 1.7018717238625736, 0.4188881495763759, -2.0507810869385352, -4.851703223560099, -6.782425254179683, -6.9109773210804155, -5.1048020501813625, -2.152253012230534, 0.630168844338343, 2.103105033482038, 1.9123243773883711, 0.6280304105962972, -0.6733911835428615, -1.116635188321793, -0.559951396172018, 0.3985426379563163, 0.9313695067989857, 0.6325562416572008, -0.1755894508239051, -0.7176792569331613, -0.4212272019488724, 0.5582140037268626, 1.386166959012328, 1.1902635664324788, -0.1693733499425139, -1.821721498549606, -2.3970680966527746, -1.0300832367175103, 1.8735028406636232, 4.733159132504404, 5.776163531532818, 4.251149070497962, 0.9885929536570958, -2.139086053192487, -3.4971685343346754, -2.7765431316004876, -1.084200393081956, 0.014945875270915508, -0.25408261660407544, -1.3211517402215707, -1.8333889833510026, -0.8556224720452603, 1.2901475630518917, 3.245069207887797, 3.708331984452211, 2.485908500675414, 0.6107076718003964, -0.5560351720546124, -0.4560869209720168, 0.2868324492085269, 0.5584665268846216, -0.1273696709450171, -1.1260330162639955, -1.272982355722187, -0.0739973420474424, 1.6502500433992024, 2.361276302795724, 1.2152197744560431, -0.9599484403460803, -2.1079737966924057, -0.5909730352426295, 3.296229502585785, 7.2897185189997105, 8.75669660369243, 6.689583774658818, 2.463933737426762, -1.2633495113317987, -2.5833899827377955, -1.6075969865627528, -0.006282848892695284, 0.6341717161941353, 0.10661754162789927, -0.5639098555408915, -0.4013485758638281, 0.45547791494154466, 0.9596304081480552, 0.3767536050272067, -0.7815165308234541, -1.1430628923849102, 0.12662163133409676, 2.3077707985922125, 3.6037038836597266, 2.781622585907784, 0.43105644542383786, -1.4508386911651958, -1.2699287014112814, 0.6365071134564834, 2.262507609561757, 1.829971090505063, -0.44267182080550405, -2.424549123833918, -2.01439330410565, 0.8495133976767716, 4.027413522652964, 5.062045097349664, 3.3628950915017706, 0.6517243239728092, -0.7117902542579653, 0.1076817660411201, 1.8207350746965427, 2.457305154949019, 1.3463964977637988, -0.32881556943555934, -0.8616350795072805, 0.2051161451084076, 1.6873161064974005, 2.0784780601292647, 1.1197291877103, -0.052074893236139445, -0.27845512136654105, 0.29758098485833673, 0.49098756551913797, -0.31193491188149947, -1.0194281777776946, 0.3387776849576209, 4.414568232792504, 9.2215020128303, 11.323435493630669, 8.721375313893311, 2.7836522741543037, -2.7163024652496133, -4.684851763801213, -3.09848197031331, -0.5565448401132645, 0.39839770619658965, -0.4931785753407705, -1.4830523210318358, -1.0170061414011957, 0.5870010707937827, 1.6797954313516643, 1.2623829314790194, 0.12084236313414902, -0.13511399138679533, 1.0037754700265946, 2.276942182140721, 2.043647976473496, 0.19614867813878045, -1.5866585308177883, -1.614422066937919, -0.062033957582105365, 1.1786747074094412, 0.5950613992197537, -1.1949243280044377, -2.0526465583738527, -0.7323417111934721, 1.5435602348870758, 2.2110600524256423, 0.13480942152008413, -2.952598021013312, -4.0419482084969465, -1.9489476825259748, 1.3171628260009256, 2.4500238432639434, 0.13274716653587315, -3.6469826358134894, -5.5742660050502595, -4.192720604790003, -1.0587935644321247, 1.1187288801902942, 1.1799925959171855, 0.21957366431848, -0.14048598508744498, 0.32043139172779306, 0.495913971287359, -0.29524749640000714, -1.2065783101509422, -0.8714145823114696, 0.6903080725832368, 1.7240007721595876, 0.6413638721018717, -1.9265843209741733, -3.4819362973423624, -2.3482684771595266, 0.20133422953916644, 0.9533214860739063, -1.8841690825269906, -6.500078731680195, -8.971591698180571, -7.044742522465801, -2.3097042610944056, 1.4655985314417785, 2.0150154350670877, 0.4012676660147124, -0.7043869861401695, -0.0992511617476928, 0.9787583145229056, 0.8152452177782099, -0.44579202011775876, -0.9285726674523077, 0.602168346888726, 3.044640739430095, 4.043136640623014, 2.623920390963429, 0.2867648334123889, -0.7288961002298355, 0.055551142470063805, 1.0285188567687114, 0.6322072206656827, -0.7028632159097934, -1.2310192268877422, -0.31775201396030933, 0.5107381088806738, -0.5552177622451051, -2.929488976790466, -3.5881160756443267, -0.22434316689878514, 5.733578596622456, 9.845306549631383, 8.759853054235261, 3.4940973252703995, -1.600776945368642, -3.076683202416275, -1.3476268235160793, 0.5255091443061515, 0.4735975470043872, -0.6840456118634902, -0.8725879984611964, 0.4460166724385609, 1.7442280294784274, 1.542690693720794, 0.29951108166783535, -0.3075124448970937, 0.34971927991681695, 1.071940853851775, 0.6152496353970669, -0.3169338382272413, 0.3247637585188168, 3.195925058090741, 6.090848456849463, 5.943130954971847, 2.3063745349396814, -1.7728863143814384, -2.7995894156799452, -0.5179317283969471, 1.9561262757154747, 1.7408654112205415, -0.6145556361925187, -2.0046150904316753, -0.5909772164975416, 1.9842480676245398, 2.579095462809988, 0.3045334236764527, -2.427021765636027, -2.7378005902931277, -0.5633848386302223, 1.475329997606271, 1.2767017154929652, -0.409906108962518, -1.2081601691667294, -0.14934219692644735, 1.3038807688351464, 1.346445023966685, 0.18332813527720965, -0.391266267595694, 0.48178001889456606, 1.5307999137628139, 1.13852943884361, -0.2713117104198156, -0.6044939657111725, 0.9652571275303663, 2.2991935656904587, 0.48688655303442785, -4.288012481416367, -7.991573989328657, -6.593681479387613, -0.5188381735505806, 5.405479282124263, 6.674671367015261, 3.390095227150621, -0.4511107116694222, -1.4920670955773474, -0.11000785249928663, 1.0271108137889498, 0.5399220368393742, -0.45095989601411535, -0.4904186013676456, -0.002631196170778507, -0.5231510797627684, -2.164871578546337, -2.994212155691141, -1.4222162734968147, 1.4571630966225049, 2.8279412084774336, 1.4479426761581629, -0.8478444447353093, -1.4325864229840275, -0.1143651792016611, 0.845938119442845, -0.009294416952069187, -1.070069916598166, 0.4483024919411365, 4.637801525577377, 8.050380353831898, 7.333361327083505, 3.1560426045828684, -0.40319400466624206, -0.4400693305141562, 1.648240868920535, 2.1773689858376355, -0.2251434855942087, -3.0422972852280314, -3.074719606231766, -0.33161049443963897, 2.121269239459015, 1.909643789807552, -0.07987049794190078, -1.2609011399389205, -0.6602251049534845, 0.3158917815737798, 0.2655408688129597, -0.23857838147664656, 0.21518609978604195, 1.4595992004296003, 1.7371796213854027, 0.35686470131780923, -0.7592710446273917, 0.6927945870350017, 3.8840633986854063, 4.887004475849211, 1.002081280832924, -5.558539367442348, -9.403124521988369, -7.557573035884334, -2.5488920588597974, 0.5913842517263053, -0.20021942871128354, -2.4287053760819495, -2.7447633707764902, -1.0006228463982294, 0.2136491167970123, -0.6031554968455609, -1.919459650005803, -1.4724473008308137, 0.5506724096467797, 1.7942709832820147, 0.9823465977655107, -0.37291649269955085, -0.13061353954898025, 1.445287783793549, 1.987729577902921, 0.31900008491445375, -1.7569917971086326, -1.7073876641919608, 0.37828589916214017, 1.877952985360262, 1.1179065861811524, -0.459658375798444, -0.4671549003904274, 0.8395901085573743, 0.6584474665777246, -2.293960905094915, -5.095378551126987, -3.40141026744408, 3.1804868620582782, 9.777564793033703, 11.044452803339384, 6.662228446465542, 1.2198585843205947, -1.0640319821039894, -0.3536144123014138, 0.3541288156226533, -0.4499382921410236, -1.3831312455775515, -0.8552279082683589, 0.4301315850769941, 0.6275613675610292, -0.4074551673184814, -0.8665619776313949, 0.283446849316773, 1.6299451217975767, 1.3156674144027818, -0.03346309555646638, 0.14960043457100874, 2.6842026743638994, 4.861543030248068, 3.531691655411304, -0.5653602016378442, -3.063264500226224, -1.0467751138223957, 3.242772636383136, 4.893554505804486, 2.0962363965796764, -1.8974996721783812, -2.910218360989369, -0.7093052700800675, 1.3725718526013189, 1.0764940849446074, -0.17966397322212885, 0.12140193121670372, 1.7584826289743083, 2.0466006338940863, -0.2599883895770234, -2.9306936320021455, -2.966900943241593, -0.4228046912977548, 1.7625873479532215, 1.55927415564023, 0.10294573989321305, -0.3787381773294223, 0.2813057902176568, 0.4478055303972378, -0.3182610126377575, -0.26877530891630375, 1.7279303990118504, 3.6671403382509293, 2.4272862565025206, -1.7298593531379198, -4.397304714604767, -1.8939356607412012, 3.942424636885507, 7.357267348063915, 5.176167136245715, 0.3598748846861234, -1.6957389332964206, 0.5726511079079383, 3.6872581235921835, 3.9156943480302013, 1.5921105441354326, -0.17156095394378462, 0.12439481256141913, 0.9495643261085212, 0.5986347926559179, -0.30987647600690554, -0.23146766705171135, 0.49865264696128764, -0.014756176041644163, -2.078323682050756, -3.2538373480648577, -1.409320498686953, 2.035794515598237, 3.4836701471862948, 1.7266376917767403, -0.42426234649203465, 0.11602953520134998, 2.5246391503223586, 3.2139929385513426, 0.8777986130147749, -1.4679684746024788, -0.43453266742916846, 3.020149906416532, 4.586905086195028, 2.1864422627229128, -1.2538152111241883, -1.5672369662833527, 1.306490226331058, 3.4020597887291633, 1.946580904273891, -1.2718105461745548, -2.579460365700074, -1.1680262053552717, 0.42510809786365916, 0.21591663212155723, -0.7033628437044074, -0.3027992516042889, 1.122004876436796, 1.4343600733535085, -0.00404432630510904, -1.2710110013547897, -0.7437831705870588, 0.4654917672260278, 0.3417680646075642, -0.5796278719836838, 0.3335052877532451, 3.4127770132856208, 4.647422529074341, -0.06177916105724024, -9.0768869714326, -15.461321172772825, -14.054435376160185, -6.917849251526854, -0.6352914314716744, 0.9656549434293457, -0.19556563281747397, -0.4966311171871156, 0.5274872925864893, 0.7349494659017348, -0.5258680300100396, -1.2040967060143684, 0.2152830862285927, 2.1678691222738484, 2.132167404887178, 0.33992358078793433, -0.45526709621383604, 1.067626842471905, 2.853665983754374, 2.424809989617848, 0.4700644808399752, -0.19248870627642903, 1.1826278218166955, 2.0906179110133865, 0.49702326280586817, -1.932226198851505, -2.035799390428989, 0.11847742756221072, 0.9247529228416252, -1.7214881620588067, -4.946083950989765, -4.242807847195988, 0.4563716283991598, 4.2320797366822545, 3.2192308442971953, -0.5997609264341706, -2.110083378074505, 0.42588651008134104, 3.5903333141445994, 3.6388109255831274, 1.1062268493885525, -0.6544457866697742, -0.2203092993106177, 0.6203905760917171, 0.15989508371975525, -0.7553086253463499, -0.5435377118112072, 0.349521158091502, 0.33500879673929607, -0.2345646970381108, 0.9413138828042229, 4.358364919641545, 6.806135287681203, 5.003245967924183, 0.342595634762668, -2.1708622195311547, -0.12371183962269316, 3.093497408984068, 2.674576613940636, -1.246262554010562, -3.77535420498187, -1.7407276811540924, 2.2341298570711396, 3.3562360681365844, 0.8215529499280726, -1.7211075178696937, -1.4384502687806588, 0.3083022640332017, 0.7483933392609097, -0.04059447387094369, 0.28735152172681455, 2.185419725260825, 3.0470289525754484, 0.9611193919237294, -2.185678313784933, -3.000145193920212, -1.0897333499084068, 0.6577123249768847, 0.2705915516353048, -0.844734484719874, -0.5785167569790017, 0.4523155773065876, 0.11501851064077595, -1.328243730951997, -1.080564722000571, 1.640776333283424, 3.130270203417634, -0.5236705335994822, -7.481729799640748, -11.062308466845437, -7.360459139635996, -0.06932696405770244, 3.8283072072198454, 2.026909413302873, -1.444082487686864, -2.157247763441497, -0.4089256425860655, 0.6617219631130719, 0.07651719927175508, -0.2231726735011918, 0.896870041352652, 1.8379201707791364, 1.0004850479575025, -0.4405160314660446, -0.27532243497059466, 1.1824678320970587, 1.4546151524836315, -0.14048287647428614, -1.113319347168806, 0.44267462080887754, 2.464063071990393, 1.4684594964925584, -2.0963644281938296, -3.6245304622020584, -0.32605607799852976, 4.629614465007133, 5.84380645260482, 2.501300998626378, -0.938753185897592, -0.9164499061214498, 0.8841559373652359, 0.7896742519885755, -1.1551817504541313, -1.388839058926076, 1.555840329297736, 4.415632158097735, 3.483857440666638, -0.30837066761820137, -2.6957767183387586, -1.718340131247993, 0.2753073539983982, 0.5534299908454516, -0.33549173483984, -0.2607477827830262, 0.7208677290429182, 0.5937188205957874, -1.0049829897788964, -1.8619919070556206, -0.6853389088974722, 0.5550478355228218, -0.41501861831250125, -2.2084236522612692, -1.4089597043935351, 1.8134396188005946, 2.540278875530737, -2.7153969533751643, -10.421625639015804, -13.248797608416313, -8.652380626816607, -1.771917830561686, 1.0322564382706956, -0.6275936301317173, -2.2231991001559748, -1.0474210121472503, 0.9375094700557759, 1.0692446998836407], 'positive_zeros': ['1.035562026678719863519386435121', '2.38333172475576454071575711523', '4.53000643699899567687106129005', '5.019899181795441757389828690809', '6.312727094601765455757777216497', '8.35662730609498310723167662296', '9.51094387257429679473194104681', '10.49276170418230432647116897114', '11.49676837386717751036940987878', '12.33613319672356453075281904918', '13.40642313089611368706022076440', '14.49820412820255943434887865759', '16.02617124633185625656735848774', '17.489763032013477698102176171185', '17.69439413284787347570724226891', '18.88592875828923565436316113564', '20.43759968721808599394171469720', '21.13031903855930929638723194867', '21.8353630488626008946246301340', '22.82601134289350634901358156039', '23.92559567634103938622822346719', '24.74567492244536179654008603933', '26.43807904280269310750293601849', '27.50152174020974378942173959088', '28.16558955337642723601442658934', '28.907480871689629357440094090133', '29.78989498374040952188440822523', '30.6046518481683985727376668633', '31.93046482356219367174591389797', '32.72070537394791183010214622016', '33.69626103560609498907416804633', '34.60978741267210824428095173022', '36.03454630631518928544112082799', '36.54115559720115639153118238804', '37.74212002740259183414948873383', '38.39549940126376426147631326646', '39.66814127402484996881483683238', '40.16858257547023396159066661852', '40.844278120780368403553791649135', '41.52222929052392881194888227461', '43.2664820809287533197956774342', '44.477425770883114588809174345854', '44.87392159642647958889993285072', '45.829561510408980194888916992014', '46.919004196561494736385870536064', '47.250232474226531819722402474436', '48.46574590269682864336046957062', '49.38602563612571692751125669474', '50.11070087954627795400476657162', '51.03592687883591751633511308087', '51.888584818718238227792581888037', '52.99136901605601365251028781606', '53.76142891442720153496648653806', '55.11887656717470419001516358868', '56.03228533815493588154746735261', '56.37955955088235208322317319244', '57.10023086238282925383814044198', '57.99884003492391243933913983755', '58.83524521724394493801387383959', '59.972283135943702483922637334455', '60.464015032975618771011324363702', '62.03825875982582452144376775561', '62.88772827134199503211280736861', '63.46325473637285464698868505024', '64.269577550549910667575190114207', '64.91393433803997663071755036116', '66.29864570077663985669149180475', '66.86089691073108892429460158903', '67.65114649016602568091525614311', '68.519078668361031004245666553352', '68.96693432565940714733450092686', '70.01319918724912181560341281925', '71.44534234547523631755442000785', '72.383256600254136831170350010691', '72.94284246171960293591180265628', '73.66438502667090360550408077790', '74.77557946129035410814802212352', '75.19416978941514339050928490862', '76.11959759711226849235577251072', '76.50058360709366084640379631970', '77.97329810428262782738441045645', '78.80354206746697218425521632835', '79.61122282340734104661547097867', '80.38245357219582232409992858310', '81.280697036775886297336685717648', '82.25579410664998789031739927865', '83.05022756607788684863186501545', '83.77831990721263760445798254177', '84.738996515837489149310120483168', '85.1870547951957810819642375873', '86.18627304462435810752019188760', '86.71626775193699205264780117540', '87.538920944914915688513629147982', '88.77329096162533488748822302655', '89.95227945846038131840623831237', '90.64535549803585701606313571297', '91.402646718837848039570614529933', '92.19182234279926514550552522597', '92.27996743221838612606126061572', '93.59104212280614605749724817714', '94.56048042978751129208248569162', '95.335410408638106171719872141', '95.93550325889360129151727004446', '96.51510147251008927526897736059', '98.06996958581788799131847567259', '98.51208689832742741120290550337', '99.35320585597385234031892903258', '100.34520099176461604202567881622', '101.23747751589240468214913142334', '102.06069899430333063326321740828', '102.639932099188522559396422155100', '103.05430084928135562421500012218', '104.12861975968124776223736749740', '104.60046282706205949316756819330', '105.67522271519788257803375472471', '107.08515489016668258007664609248', '107.47015782974947700979600515942', '108.63834117917027243238431667131', '108.91478170441970270568206610478', '109.91949494476203639137283372345', '110.828220926589556866097008544067', '111.28168625933861833919040041849', '112.22924154594969041309650809738', '113.07417568891713131897759889240', '113.95484108660567788021621076253', '114.49301574599165348598747364680', '115.095012605636712857092954602890', '116.11662652706751533164733713227', '117.60584476970141775425103216838', '118.22209220401003918996682827332', '118.62815404703863295595579474344', '119.57316908446457270022430740323', '120.20270703723846495300437777594', '120.88231478489343873739378110236', '121.8648023233663606154405917582', '122.15391905140748692520534112664', '123.39550431402913706830514805402', '124.14039512270100639193982442834', '125.151533921921554762029768798331', '126.01963537268141478985691497739', '126.81401247809205783093718011540', '127.15665562894819573064673536645', '128.09840426103186876147689518092', '129.10846801741045567568239358515', '130.02720541003799922680225791305', '130.50909144173037523965818280387', '131.13105300696532605240532816930', '131.62686001715119776015299226566', '132.691395835900725579471239020289', '133.54483218655984173435477781822', '134.715364867468441182687757809634', '135.25995873004246358389111375752', '136.50374014075446485800838679888', '136.83266545428317694670126495494', '137.68852160258534258677613577117', '138.218953170312067417277784719215', '138.74691947954383372830085406665', '139.814535730461081822224065003121', '140.84804555415026011252924103953', '141.23111988581217572536225632823', '142.27835309831810031981877610767', '142.85744629961932992814681537603', '143.93145325063788004057400143205', '144.56356053070641387061929328758', '145.49722150445538252379900853382', '146.44651293014081277150541030345', '146.940862338728029651495648291642', '147.571024367934448983975402359452', '148.43679028849402056109300662555', '149.23602816292691430886650966626', '149.79208428462137623513577123419', '150.26352623827948146803834973651', '151.24749952969397155051837192307', '152.86769019847401975335419628450', '153.388469016123082405426009132056', '153.91459617790655738358760470161', '154.57519839755152766054645778098', '155.28094913224977490382882483657', '156.31490815888652408550205809228', '156.702846797985584342215154745655', '157.913908645892300561004425592430', '158.197808744641224154056273584992', '159.12106927067097971045188314143', '159.983169242449636238608220269254', '160.46478967349833218658818283471', '161.53538106161387656858965051146', '162.44827287463921068567481160792', '163.08822761537212777652362904895', '164.210476366641474273498735902647', '164.750539310310113232492681737114', '165.360422034819083943179161088126', '166.116620249663945386403217110597', '166.71243666482816081899046691625', '167.027425022908444451745365155545', '168.462238631686810737151213198915', '169.073273893971404499017821122760', '169.90916759552621721664868703087', '170.75638505911076525495312193351', '171.642174734609663432940934365595', '172.43789451378896571858964006365', '173.10513378315236318858853139222', '173.3551425402926561734533190817', '174.46490780700796256235778151962', '175.468195540378491343690995916678', '176.00451705730189205211882611385', '176.721994229259688780379548742512', '177.21501607673813101526871684418', '177.95609790784786539583975138268', '178.72287955246269519627038488341', '180.00330018298605964850461374757', '180.79352202364859569943091793297', '181.63538128854753344903325356441', '182.21662952448724211950405807134', '182.59606195545698219367147256575', '183.633790889997125938128360765724', '184.12891465347523252615192566486', '184.97628487055758900302252347509', '185.56631301801070751768745043712', '186.38661903191492973118552039227', '187.207303914596753738605317998337', '188.32370556198677573482228101767', '188.90241056620303540473500914709', '189.50924831284305892205086515366', '190.17573763832301468668051049732', '191.224975972735265265513450738477', '192.131475199918863992599168365383', '192.68973059382949257132842222862', '193.21233370397501662490836692797', '193.882583993946599783423571678470', '194.8165461545258690781237015959', '195.24052664128346311304105531463', '196.08086092262121087492536086059', '196.7523728758541998130429435768', '198.24730179148445142822463369176', '198.66925743998422902448157019858', '199.52201046647414149971098225642'], 'prelabel': '1-143-143.108-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': -0.5813523573540802, 'root_number': '-0.252802710065598410758867875246-0.967517849852646898427204211878*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.290676178677', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.766198964657961947480664680868-0.519828882942809660601278768498*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.03556202668', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.38333172476', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.530006437', 'prec': 37}}
• 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': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.108', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/108'], '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': '1-143-143.108-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': '1-143-143.108-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': -0.2906761786770401, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03556202668', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_143.108', 'Lhash_array': ['dirichlet_L_143.108'], 'label': '1-143-143.108-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/108'}