Lfunction data - 1-143-143.140-r1-0-0

Formats: - HTML - YAML - JSON - 2024-10-14T05:34:18.528788

• 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_143.140', 'a10': [0.5, -0.8660254037844386], 'a2': [0.6691306063588582, 0.7431448254773942], 'a3': [-0.10452846326765347, -0.9945218953682733], 'a4': [-0.10452846326765347, 0.9945218953682733], 'a5': [-0.30901699437494745, -0.9510565162951535], 'a6': [0.6691306063588582, -0.7431448254773942], 'a7': [-0.10452846326765347, 0.9945218953682733], 'a8': [-0.8090169943749475, 0.5877852522924731], 'a9': [-0.9781476007338057, 0.20791169081775934], 'algebraic': True, 'analytic_conductor': 15.367484245631378, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.140', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.95', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^22', 'a^8', 'a^21', 'a^26', 'a^8', 'a^12', 'a^14', 'a^25', 0, 'a^0', 0, 'a^12', 'a^13', 'a^16', 'a^11', 'a^18', 'a^2', 'a^29', 'a^0', 0, 'a^10', 'a^4', 'a^12', 0, 'a^6', 'a^16', 'a^13', 'a^17', 'a^9', 'a^20', 0, 'a^15', 'a^29', 'a^22', 'a^13', 'a^6', 0, 'a^3', 'a^22', 'a^4', 'a^5', 0, 'a^5', 'a^14', 'a^27', 'a^8', 'a^16', 'a^16', 'a^3', 0, 'a^24', 'a^10', 0, 'a^20', 'a^24', 'a^17', 'a^23', 'a^21', 'a^11', 'a^13', 'a^22', 'a^24', 0, 0, 'a^25', 'a^19', 'a^2', 'a^3', 'a^11', 'a^26', 'a^18', 'a^17', 'a^4', 'a^10', 0, 0, 'a^9', 'a^7', 'a^28', 'a^26', 'a^6', 'a^8', 'a^2', 'a^9', 'a^5', 0, 'a^25', 'a^9', 0, 'a^18', 'a^1', 'a^1', 'a^23', 'a^12', 'a^29', 'a^20', 0, 'a^20'], 'euler_factors': [[1, 'a^4'], [1, 'a^22'], [1, 'a^21'], [1, 'a^8'], [0], [0], [1, 'a^11'], [1, 'a^2'], [1, 'a^10'], [1, 'a^13'], [1, 'a^9'], [1, 'a^13'], [1, 'a^22'], [1, 'a^5'], [1, 'a^27'], [1, 'a^24'], [1, 'a^23'], [1, 'a^11'], [1, 'a^25'], [1, 'a^11'], [1, 'a^18'], [1, 'a^9'], [1, 'a^6'], [1, 'a^25'], [1, 'a^29'], [1, 'a^19']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-143-143.140-r1-0-0', 'leading_term': '0.268800929766938235282623083124+0.914758139988505942477145609313*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/143/140', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9534340011342167, 1.8544438630494962, 2.4736261304941722, 2.6519653001946963, 2.2521152849863038, 1.2609511464168692, -0.13163637668698236, -1.5386334818581346, -2.4872129477674427, -2.6041170332087744, -1.7972571469742333, -0.3388321791334467, 1.2138163013952836, 2.248922158440244, 2.3860904760825505, 1.6719279487173395, 0.5666901114252286, -0.2948548537256413, -0.4548344176195637, 0.1002802875512647, 0.9262429939870046, 1.3937578985290702, 1.1000139328820475, 0.1617909192839906, -0.822379912869442, -1.1586450002719149, -0.5734088933759945, 0.48481762497451947, 1.0062604289070083, 0.011345618030412096, -2.761534549396173, -6.522935969499569, -9.728188750274883, -10.888882867123737, -9.430455140053533, -6.051625781647136, -2.329438553596103, 0.20224916388719308, 0.9146271010394241, 0.3274641496923046, -0.407657811356192, -0.39876879955389555, 0.3675805585942704, 1.1205730044608448, 1.0160567258733828, -0.10487377620986599, -1.5209228027861723, -2.172677752618282, -1.5229345825708345, -0.03709096665724877, 1.1378586012924872, 1.0776609141948295, -0.14851169061478872, -1.4935587629379348, -1.7725588328382695, -0.6751171958559392, 0.8962489705441163, 1.5032382333796026, 0.37315442547382605, -1.8510933803251708, -3.487834104741432, -3.1031053657975503, -0.7112934492967588, 2.107106233599766, 3.3388418093595225, 2.073277507128745, -0.7764513098335214, -3.162758423101332, -3.4697018708023606, -1.707485935208855, 0.6068165521709129, 1.7393897741114226, 1.101623742518185, -0.43263551765870245, -1.441732302770256, -1.227777258911594, -0.30710038981383225, 0.2593905734831756, -0.00963527452449466, -0.553597727864737, -0.43308581344470576, 0.5349179593778697, 1.3430448070802894, 0.6193324379011643, -1.9537341350479542, -4.979300694678632, -6.229097768480111, -4.463876784678451, -0.6290069031760301, 2.720384464624679, 3.401373538056628, 1.3483675345139996, -1.387008032777359, -2.39665475042381, -0.9111324761736137, 1.6919785834369536, 3.2433577478110154, 2.7127113662255953, 0.9641185727464656, -0.2642641092789602, -0.08724614426366856, 0.7743472479505944, 0.8889422743793932, -0.2996502537865717, -1.8169167697800868, -2.1057159619058514, -0.6292258410941995, 1.497809960013051, 2.5190712117187624, 1.705000453488456, 0.009988763336494134, -0.9504528104748946, -0.5615852584079635, 0.2138519897289571, -0.0187173840433373, -1.384926264348045, -2.3273745581055056, -1.0905744640505561, 2.260463399046575, 5.37513089596706, 5.417145898333313, 1.6192397093624442, -3.798500981846278, -7.319600538346277, -6.978349317574022, -3.811010830927501, -0.6730847219489302, 0.3526253724339449, -0.49167397220220754, -1.413601115017537, -1.1371559564389377, -0.07963046749749464, 0.43111100551946563, -0.15252199642794065, -0.9388651048713008, -0.676504676800527, 0.6950017068714716, 1.8398287095699173, 1.488411125793638, -0.027634865011180954, -0.9668344549819005, -0.06114918694234114, 1.884637778878553, 2.540239059237789, 0.4072244735445829, -3.376852811943386, -5.783484182630902, -4.650158117970394, -0.7793775047015539, 2.749327084610847, 3.4239260916873766, 1.4956001474779115, -0.6063240143189866, -0.923668620876126, 0.10636692389777415, 0.3915246996174403, -1.3192786649169324, -3.9171142232832787, -5.015472834521925, -3.4425664782379437, -0.4647972549765308, 1.5269208102066105, 1.4004343515433042, 0.1867759473588296, -0.3370814905111835, 0.3271742418448131, 1.0503864740399433, 0.6794698398589253, -0.40005330297311004, -0.6639622187836685, 0.6153405829808737, 2.242439599303675, 2.316964782021561, 0.5941946469761009, -0.7683567518486114, 0.7333777774309697, 5.04539727309463, 8.987388314584592, 8.963181349513343, 4.414402647189386, -1.483858739796319, -4.672419117009026, -3.7868626213888597, -0.9649725144665598, 0.6830670560366889, 0.11913389387085364, -1.1466846266328585, -1.252946769280611, -0.13099943611605827, 0.7509139758747299, 0.43973376818178567, -0.2940706951252684, -0.05586037836627695, 1.1940773032890486, 1.8341575986886485, 0.49055091097804415, -2.062195692515423, -3.409106785561826, -2.0568166903078127, 0.8174370690628969, 2.5358148262927096, 1.807980996900805, 0.07155490753109656, -0.3069709630313858, 1.0523077431056385, 1.931221269669844, 0.07017733048155934, -3.934995708254703, -6.795402862951719, -5.806427613488924, -1.74208647457285, 1.8365364660729018, 2.1626910905368786, -0.11678847205919006, -2.0127081481246183, -1.5811282557020419, 0.18599275589037995, 0.8846851688597882, -0.3719923063008371, -2.0539234376417803, -2.200362929812216, -0.7468013802436573, 0.5753190716419926, 0.4627413297749747, -0.4661511034468385, -0.7153662199389285, -0.025581725044849804, 0.29030074852517157, -0.6563470992600025, -1.598175286800233, -0.20631570163085428, 3.8719050778682558, 7.66579218457092, 7.337404909301416, 2.1950412144333824, -4.133912903335611, -6.947792002680345, -4.885513545763877, -0.9003058668589126, 1.084485796663, 0.06702092941076232, -1.7018519453476364, -1.8486306009502829, -0.5713703825084087, 0.09284034859801252, -0.857843676135909, -2.0966204883372654, -1.7842220515984977, -0.06869932366451292, 0.9669322674421269, -0.11577671432719425, -2.2421385206234383, -3.0476962908265084, -1.7109726706754411, 0.12518808541571508, 0.49343826555426185, -0.4002129509569582, -0.5134198325626822, 1.2385393689142152, 3.3100094402359614, 3.2757558572928165, 0.9868961033058987, -0.8801481674313467, 0.12560367805690648, 3.101496296309638, 4.518761845102157, 2.2695241567097932, -1.6119444597114354, -2.898958089190495, 0.23154671934096466, 5.1258986668564015, 7.432218988184621, 5.550793741432616, 1.8455436130138194, -0.36551269470637804, -0.25244726671268763, 0.46749132964936907, 0.2883240722706394, -0.2944144718478138, -0.01860434208669157, 0.9560095065108043, 1.0944627731520449, -0.2546899676663562, -1.5853713468112072, -0.9708822957154297, 1.2499042101485502, 2.4894965495276664, 1.016600974878236, -1.6062681718223817, -2.0764194694744287, 0.624042379677191, 3.5911012662912905, 3.044386792496331, -1.281464792302649, -5.579093625306876, -6.03469714244397, -2.8589816298837114, 0.30574886701078546, 0.6844037846908694, -0.8046179410968964, -1.3109182702961995, 0.1530788397206791, 1.6852644511606296, 1.2732726142002342, -0.42251835923771225, -0.9075203465964192, 0.8490359945264273, 2.984290030019365, 3.037881081717031, 1.0055940660692244, -0.748836535758202, -0.5179784892874283, 0.7511040722885812, 0.9845857721785588, -0.1585888093361076, -0.9906587274437123, -0.4002269521797849, 0.3706974312105202, -0.4767642657710349, -2.132596485243913, -1.1915650783603517, 4.36499154557627, 11.812020690174663, 15.49658649216694, 12.412295970563411, 5.3685496767685965, 0.07665430763965664, -0.5693372065634608, 1.3492106415533907, 2.124391677800097, 0.8146062251876218, -0.44661791599606604, 0.11057072380491026, 1.5160350805493412, 1.623086575512926, 0.12211410876678638, -1.1574133686912682, -0.8759708989782949, 0.05126727940885148, 0.01570657781645159, -0.682001448614507, -0.04235621542080793, 2.6369656708472706, 5.106614445458778, 4.530343435049527, 1.1667260407118085, -1.4943480485052536, -0.7239436465145566, 2.156399263205066, 3.4190598706295927, 1.5801927197363979, -0.7844946741877026, -0.39410317881631923, 2.461978958085466, 4.204300475062429, 2.484615226957595, -0.7978803556328206, -1.8275014623716952, 0.4103623906072632, 2.968466248562245, 2.683605180442868, -0.004031164303271663, -1.8703890120575173, -1.0303405021222845, 1.0032910502079926, 1.6701863866933455, 0.6732149622843198, -0.10281340495294533, 0.4486886148324163, 1.1596120548845996, 0.5680882819694701, -0.6626878647942104, -0.5673292006608737, 1.092216783078066, 2.057006113181181, 0.6091392568075578, -1.5593452598668605, -0.9983821608127679, 2.8434654382581117, 5.984167660952679, 4.063000595813251, -2.3158266954668085, -7.659190251622838, -7.354518905719308, -2.466808650315585, 1.9157119727857368, 2.453845503821659, 0.4910320150555375, -0.7229912281767943, -0.24180461617967403, 0.2771141443778654, -0.2542398438774877, -0.6495562102398953, 0.4536633181864698, 2.025862298393268, 1.6366975098474597, -1.1284807223643254, -3.644127285117867, -3.333957379553382, -0.894739853747782, 0.6919143944419514, 0.0554422071627577, -1.0375452696812846, -0.546135659581409, 0.6891505876111439, 0.08871863978961032, -2.6435722717534413, -4.343770895283137, -2.2007457239248045, 2.223527953084404, 4.351452350140446, 2.0631997634858568, -1.5900651443180887, -2.05863181018782, 1.1592573253021443, 4.049461977263288, 3.1556149120214205, -0.3193486206504958, -2.3756208196904973, -1.2614545267958368, 0.8377196687941957, 1.1566211495166292, -0.14322202116107371, -0.8265715633714684, -0.029548390970948694, 0.7507802396477073, 0.22020561395520605, -0.686978865585097, -0.39295092183649066, 0.6260584109527493, 0.37795475927880506, -1.3133117699722074, -1.6983351622952396, 1.4068756379199248, 5.84331367929598, 6.643399204189782, 1.8069544397359683, -4.788827207712, -7.403047715373866, -4.7413082658219645, -0.8979667380144581, -0.022222301424068187, -1.6185963814106281, -2.151225633837388, -0.22217419889543935, 1.7396293263211666, 1.1642101115070125, -1.021085170518507, -1.7858004359088193, -0.23488647708408197, 1.3040343190121106, 0.7018502745970245, -1.0219084642197966, -1.3510431907248797, -0.017911375238499935, 0.601627182184665, -0.9899091143795888, -3.070289803480131, -2.9712445661200717, -0.7728354742490874, 0.8664002617839661, 0.5020014683326015, -0.19143432710776576, 0.7635234011787617, 2.2532490101903266, 1.4281232966317468, -1.6209910214083456, -2.6262604947413277, 1.9701538032087205, 9.832909483819876, 14.328139992555895, 11.61474810357764, 4.752213773164629, -0.07843896829715526, -0.35300617244898275, 1.1895443238745949, 1.161940325827341, -0.30337209299109186, -0.8652775092644334, 0.09355028868540347, 0.7884449703986268, 0.08337832937129656, -0.7273655616734954, -0.12547729950522873, 0.9756427086222029, 0.4315409299902706, -1.6743691007371388, -2.644625333320838, -0.9045331619072735, 1.3810643710424617, 0.955915838093019, -1.9253807771767686, -3.498547100465728, -1.562255770251729, 1.1906931841705148, 0.4668762018709333, -3.800944748514328, -6.939853469591426, -5.262519004918126, -0.5934964031305596, 2.2455913958901146, 1.4370370615666268, -0.29293512902826646, -0.13939609764440417, 0.8969151113603555, 0.0028912969706116525, -2.7973102771088274, -4.190950751354191, -2.0249029142581563, 1.6393875098497745, 3.1271741611994814, 1.7257614163167065, 0.024502905013027616, 0.014086274104413552, 0.7357035254687639, 0.4888378771823282, -0.275940208407333, 0.033255634375983965, 0.9856990632336671, 0.19806522635150448, -2.8382963526660823, -4.926483672819652, -2.956813987542142, 1.2937325696811588, 2.4325526739116197, -1.906028787858853, -7.514585077284083, -8.247996862772663, -3.299377965909274, 2.0592200710726667, 3.0100397053422574, 0.4844281087000337, -1.1182288650478145, 0.06415029526219158, 1.7296473395386147, 1.4603927294043584, 0.045477800966361934, -0.36400688178934315, 0.20150937635130303, -0.153835177844871, -1.7711456171737068, -2.5219886550122883, -1.0741913423235532, 0.6495456495101317, -0.06760389426984859, -2.639164861082818, -3.594419069240912, -1.3332308176366137, 1.4823185931220535, 1.5292202154394037, -0.5557220730648315, -1.1907530211324129, 0.8541118100530422, 2.548417707934729, 1.0429686382801897, -1.8306457222818602, -1.7291742706059994, 2.0294743313465613, 4.94992100046393, 2.9937630430457944, -2.069716059305062, -4.8135945515349885, -2.885651792852879, 0.58937282292482, 1.6234022654332771, 0.25924702601051325, -0.5994087974831508, 0.14975658919702292, 0.6416128025839062, -0.48955729911727613, -1.7584193911660464, -1.1750670828765895, 0.555281296857331, 1.0623549797592153, -0.03776857245613419, -0.6624960599314003, 0.18892660683019252, 0.5619869209340059, -1.1700752129980536, -2.589927384421477, 0.5208067994694754, 7.959673453654785, 13.579316578453415, 11.721203131008872, 3.979237883405136, -2.4915366630458142, -3.113966761511545, -0.21256958942704518, 1.3016923657998092, 0.30718179719341443, -0.4434561912690403, 0.6064923768872975, 1.54225771558937, 0.4027197214778545, -1.475542353876128, -1.4511699788394292, 0.24669724671296975, 0.691594536716342, -1.340396640453947, -3.3671758183969773, -2.70044169050856, -0.29940725001501345, 0.7279176075688065, -0.3279324902237187, -1.0114676676897372, 0.25588316237236225, 1.6596326278628357, 1.0001916467089118, -0.42389993878048665, 0.569200745206747, 3.8492445539440694, 5.145023747228301, 1.6947949689441022, -3.274412746422, -4.072437469823254, 0.12457902040839394, 4.0766552444838675, 3.236059221253701, -0.5826034429299174, -2.0611652332517485, 0.5079638780379545, 3.516584022241456, 3.383006187879696, 1.0220120312970182, -0.30992145527819587, 0.23965115149957392, 0.7473282027478685, 0.15471324162305933, -0.2731383035379436, 0.3336699289664158, 0.5500841905728431, -0.8719649354291721, -2.1174443261687372, -0.3247745119862401, 3.7651854818812707, 5.733379639237404, 3.08043001429406, -1.130018098818183, -2.196404285781449, -0.1742115601400143, 0.3203920160178262], 'positive_zeros': ['1.84711440417369159310719873576', '3.5029368480719583222694772598', '5.181199599897408348606242316822', '5.896938407008474942721877033377', '7.23399210950028704354019975196', '8.29486411873791397533568415503', '9.06433514156026507604850797279', '11.526123403454739292822514107645', '12.30716370964788708540060851088', '12.99690164680568231115670479176', '14.03961552014453934879197488428', '15.32006213607362196654491749699', '16.21906306074693168357058635540', '17.31672269234023615960499196585', '18.18312461256030071199145850923', '19.449275222879658164656294058241', '20.5446177140381714312651308755', '21.78534544619400926973569036232', '22.72524820050539308549258559049', '23.86935943566630305852604179090', '24.36968969594391601591171684564', '25.16119266897235810491678561038', '26.03255657594247387754851739422', '27.5490141308252314196230120950', '28.58244757806177551600147400996', '29.48579072110245487532127851238', '30.833239120083943165878719595476', '31.28449559904631837086331674407', '32.12791270998018454190198619867', '33.2154387043432859507056397438', '34.37700193470982320292345821604', '35.20404213623508079488085400872', '35.61868695137241320299175903794', '36.67927176958688366342988462418', '37.9064474762035641167584101764', '39.49235333558868940216353714472', '39.86487568808459535395838494288', '40.96329478677013772365044951869', '41.50921122482563006803018704906', '42.35825287941430091262535556563', '43.4319637900700851545415305902', '44.07330913380398935368082053955', '45.03656916595871204998474555265', '46.30777751878660399884724488465', '47.38829505139588269689664566672', '48.093674569235165023624494457121', '48.54980083328185902667666370197', '50.05292751186937681149877306659', '50.99430022444409140218384483278', '51.44996573057218118554294600681', '52.38169644777600509604747579232', '53.00949642083855072499969318050', '54.15825023379684431834748219208', '54.605363853642112210236707042052', '56.16487223796821102248818617010', '57.3189331288113641943282636694', '57.840659837348847552459640661602', '58.78250247781629662445289255730', '59.54198134911463937953670297440', '60.01847543770384347876690615810', '61.00123451663559979198821283941', '62.09840251621952417727455397855', '63.14190228724313227478620347578', '63.5358877604658382266608093031', '64.38153598821641560642562385572', '65.75296496856659515069559035130', '66.548590713097663422883330060667', '67.46488634105548316730689304548', '68.06013513188642367294373299806', '69.20743328720981210944990522011', '69.84382606593698644688566820688', '70.63542382689219709802130674061', '71.077585177272092285335131766556', '71.89599135773442899930642572531', '73.22726185647649514709599548186', '74.46537866771859948212045239993', '75.01090005389351907715299128338', '76.11491626572452766936836123094', '76.32314836348293389492677120609', '77.51222650476288330283358081169', '78.10641934547932849928373365285', '79.346533430662609873530856971481', '79.872175892134161119472899316321', '80.438615546799478946791370784366', '81.68782843425473765493146149753', '82.17117706509369817087833789993', '83.30176026733701594399297356723', '84.04712618882716029223051002853', '85.536043007723790948264910098056', '86.03135534855753185760394667626', '86.69790256224119480963051160382', '87.19449885328226260886722510227', '88.0786443050466459013956373879', '88.89618053725063086323929755498', '89.80335773576296322199025218721', '90.569282139539829319268647347931', '91.48359873124742595509612819434', '92.76836981416495249388045921333', '93.27990675134277036760360208835', '94.03794626329153578571637252994', '94.91944697755245969167404905302', '95.50854401104915359685240603280', '96.7074164611668682313260812596', '97.31464698743320030411018096160', '98.08812581053346038266262878450', '98.870604463608687560068265273286', '99.27353299327015326586049944222', '100.09278841126021690753247809557', '101.883157580284285828755663315223', '102.29387868654582086245952303548', '103.28429456478680268368516701992', '103.72358552987970714277999384356', '104.70932531409886268798827098401', '105.60068998903498221299824916070', '105.945136642350250807414274795161', '106.56974725994701847240701521883', '107.91703792301011787798845080636', '108.522473051561309806835422632536', '109.55831678389508686031901866414', '110.05394808555306299336042697161', '111.16655115688235287302123239944', '111.83288672031509829641789263231', '112.81205722619702057019435645541', '113.59076365362348332059676035982', '114.59116308423438178486639415192', '114.82427881382932543020792203727', '115.759182436949125412871128431926', '116.37524309750745355181311874898', '117.26510272835463294610074667610', '117.9132784490751051770524445736', '118.9590959868981241808107774385', '120.14933990699703519760258462382', '121.01928741499911552546913822450', '121.65576320928187001657318158159', '122.08469120030652898764432181843', '122.72451795572215514565253455366', '123.63941407316985819859852119465', '124.813511354909846633211787623125', '125.32546299145060002072062512914', '126.06112504682965890101910488304', '126.57625318159691934608329641988', '127.656211947440316052278699795627', '128.60039304177292343365062983826', '129.28126578376466728724443584159', '130.283728276811476948448086723288', '131.1105647244843545905729862888', '131.84281925860576446249345431447', '132.50813322468996104046451905418', '133.18947358302317677999693295553', '133.86465861331854648709982807613', '134.45701049998737796992111717080', '135.206997331413438846848505886795', '136.33149834715342892459381416750', '137.65487476034833323868832245093', '137.8040523704627695149805277732', '138.777388847463637628990891762651', '139.542144988699149760668088456177', '140.348117704126846159883376864528', '141.0617187386380800245699926736', '141.87889590496264655765751067504', '142.35202117654282281107123846648', '143.54626008065562106518470973936', '144.22909010936766547370316477562', '144.5101566523137444365655123141', '145.46671667852134452788978248488', '146.15567879543916403695313739593', '147.802822343846131923116346474384', '148.19736119951160873308727899582', '148.997807164829874117418567293090', '149.66319946215173231737736329725', '150.33579137937145478057068260143', '150.968902959449222344517220333379', '151.63617506169693555521208023465', '152.60586072093673332250958175435', '153.2419095306144399363840953004', '154.2166099505714930958083358065', '154.73204956014149197194059613787', '155.98043474377310099600265164275', '156.80097468289505429700813076271', '157.225898749433458311136655392299', '157.812906442862750672424917227102', '158.91651798319950426558577232335', '160.00840076349323547867635093394', '160.306213160648104697474239211034', '161.115400336575641457788133106989', '161.55145939644158298560209709070', '162.214604319326714798184663066252', '163.33705929602798784369247986715', '163.95865610964121654448738039394', '165.17133472000833142529490906192', '165.99516591930016833196795759819', '166.55242033609901367980573227767', '167.512435716787168541098154894593', '168.01133795948974740001508317127', '168.3929382784757900094090334121', '169.53767659783701589509996249951', '169.98978629053418536581493184937', '171.066288215911770692671809481589', '171.79287780493872710030063603776', '172.39541680686469407804402479661', '173.23062574931441678557800417405', '173.91449785532712140521122522227', '174.874078014347110350352213370589', '175.87468319796607727338571236332', '176.61618198663329341811777876743', '177.14295035040622912032486635990', '177.71414258071277399698875129052', '178.64485437053096176940734560000', '179.36569923999686399338590615283', '179.94698920780083439986085373626', '180.45361008436624357810508869399', '181.221315618838260250059898129438', '182.66304635183481823095893372853', '183.461385568149311288004433789297', '184.13432511728052803575978741622', '184.553469177950824359781407734224', '185.37355492951125211318480481627', '186.20383410871927021257972368101', '186.70355693482819233729045575544', '187.85851687199695909980861093515', '188.364071137263467171211156525084', '189.01858605720985194360043229845', '189.87787189178313447949548415587', '190.23290481374889322020215006670', '191.3484924070824150122549100749', '192.17999272873940053551760847208', '193.07490305884178181998586506690', '193.70559882482650697146966834468', '194.863570228785239329332816766548', '195.228937297352740360747693312640', '195.99950832712284709071946127900', '196.430149709547565935457023393089', '197.03278104418437697144295300342', '197.84060020103119624160800423279', '198.96638580004226261141851691603', '199.71447098255831588904332140383'], 'prelabel': '1-143-143.140-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.367484245631378, 'root_angle': 0.8180513112799965, 'root_number': '-0.841031799652382252738841317852+0.540985685553208662032449889229*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.40902565564', 'prec': 44}, 'spectral_label': 'r1-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.983067561567062272113616935515+0.323350585321947099080099487042*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.84711440417', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.50293684807', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.1811995999', 'prec': 40}}
• 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': 15.367484245631378, 'bad_primes': [11, 13], 'central_character': '143.140', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/140'], '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': '1-143-143.140-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': '1-143-143.140-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.367484245631378, 'root_angle': 0.40902565563999826, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84711440417', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_143.140', 'Lhash_array': ['dirichlet_L_143.140'], 'label': '1-143-143.140-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/140'}