Lfunction data - 1-287-287.188-r0-0-0

Formats: - HTML - YAML - JSON - 2024-04-16T14:53:11.140291

• 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_287.188', 'a10': [0.8090169943749475, 0.5877852522924731], 'a2': [-0.9510565162951535, 0.30901699437494745], 'a3': [-0.7071067811865476, 0.7071067811865476], 'a4': [0.8090169943749475, -0.5877852522924731], 'a5': [-0.5877852522924731, -0.8090169943749475], 'a6': [0.4539904997395468, -0.8910065241883679], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.5877852522924731, 0.8090169943749475], 'a9': [2.9010907910729803e-30, -1.0], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.188', 'coeff_info': ['x^40 - 1', '0.987688340595138 + 0.156434465040231*I', '\\\\zeta_{40}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.258', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^18', 'a^15', 'a^36', 'a^26', 'a^33', 0, 'a^14', 'a^30', 'a^4', 'a^39', 'a^11', 'a^23', 0, 'a^1', 'a^32', 'a^9', 'a^8', 'a^17', 'a^22', 0, 'a^17', 'a^28', 'a^29', 'a^12', 'a^1', 'a^5', 0, 'a^11', 'a^19', 'a^24', 'a^10', 'a^14', 'a^27', 0, 'a^26', 'a^16', 'a^35', 'a^38', 'a^0', 0, 0, 'a^18', 'a^35', 'a^16', 'a^6', 'a^33', 'a^7', 0, 'a^30', 'a^24', 'a^19', 'a^31', 'a^23', 'a^25', 0, 'a^32', 'a^29', 'a^28', 'a^37', 'a^22', 'a^2', 0, 'a^28', 'a^9', 'a^32', 'a^21', 'a^5', 'a^3', 0, 'a^19', 'a^4', 'a^30', 'a^34', 'a^27', 'a^13', 0, 'a^16', 'a^15', 'a^18', 'a^20', 0, 'a^20', 0, 'a^35', 'a^36', 'a^26', 'a^13', 'a^7', 'a^34', 0, 'a^24', 'a^39', 'a^11', 'a^3', 'a^25', 'a^21', 0, 'a^29', 'a^8'], 'euler_factors': [[1, 'a^18'], [1, 'a^15'], [1, 'a^26'], [0], [1, 'a^39'], [1, 'a^23'], [1, 'a^9'], [1, 'a^17'], [1, 'a^28'], [1, 'a^11'], [1, 'a^24'], [1, 'a^16'], [0], [1, 'a^18'], [1, 'a^33'], [1, 'a^31'], [1, 'a^28'], [1, 'a^22'], [1, 'a^21'], [1, 'a^19'], [1, 'a^30'], [1, 'a^15'], [1, 'a^20'], [1, 'a^7'], [1, 'a^21'], [1, 'a^17']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-287-287.188-r0-0-0', 'leading_term': '0.0132051861202794455154967552178-0.0476243556906468781704532426326*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/287/188', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.049421211998700317, -0.3015230685093711, -0.7647722010006525, -1.1209324475388316, -0.9750153434558099, -0.027907961115902276, 1.6826471475116886, 3.672656264911537, 5.138610826778897, 5.320039162769332, 3.939698274473569, 1.4604961683354079, -1.051693947812995, -2.4563996930109493, -2.1887653534705014, -0.6257148191121974, 1.1132482989195656, 1.862111586087955, 1.1739095444359375, -0.3721285967177127, -1.5734552719383652, -1.470071493835552, -0.059528417508285185, 1.684777011435086, 2.53781400027625, 1.9562925201508752, 0.49068147330937606, -0.6714901472169508, -0.6809306456749793, 0.28055666450133376, 1.1881932858351067, 1.1062829112034906, 0.06044118379220733, -0.9502148595027883, -0.8685744993948853, 0.37132329499986494, 1.662056166763438, 1.6941164128238106, 0.29615861650879116, -1.1035706713484772, -0.48628948369335195, 2.9840368807589, 7.934499500003774, 11.524687765502234, 11.50594044616554, 7.951640421721309, 3.1969510527545513, 0.014109150637529957, -0.44021362315291973, 0.8015949129757843, 1.7847162289869367, 1.4614731269882046, 0.3923466425688237, -0.19368819649750518, 0.12390296643739476, 0.5133171649557253, -0.08457104335079849, -1.6037217880327843, -2.7001766495301056, -2.0785869669293997, 0.04260958034668272, 1.9390378724826012, 2.0105738170162932, 0.43580426050597104, -0.9187021514374416, -0.38682451777438454, 1.6758621909924785, 3.0858217073357954, 2.0038831059479456, -1.0482575503055243, -3.4578049944086198, -2.963045122038534, 0.10754805210196339, 3.0824892583910595, 3.5014732149707166, 1.4394924379849212, -0.7293045810844171, -0.8434542386821621, 0.8730765806438514, 2.1973161851215677, 1.3637728556879654, -1.0533113733772914, -2.794968394030144, -2.3186126831757345, -0.32141311600180905, 1.1824424161523164, 1.0728206307286567, 0.11779700324813229, -0.2486993080635728, 0.2281031247093763, 0.4226011334030314, -0.5037028934836987, -1.7003257372963854, -1.4414935229314678, 0.5610356467202213, 2.1295626540992663, 0.5161327143770242, -4.465765883688508, -9.527058522522562, -10.602736905989397, -6.681082472763377, -0.8367568994161024, 2.6842446747494, 2.362805467200185, 0.33725487212394323, -0.3451393054702206, 1.0238027448138258, 2.5220689791672832, 2.2179166129325214, 0.44684248388529835, -0.8257106603629514, -0.5336178045416031, 0.26961918724467304, -0.05851228826962705, -1.4869736355985144, -2.240948903084953, -1.0859900421565116, 0.8934073795799428, 1.3743363891871365, -0.4283727424512391, -2.6776669737048504, -2.9835782054102884, -1.2287836960789693, 0.30434423095629626, -0.24444831616702628, -1.963680624018981, -2.2844034609033455, -0.33941942580736273, 1.5842074367347214, 0.5599939923611921, -3.2571841418432133, -6.212051041789887, -4.876174990810943, 0.13997222988193034, 4.649718696175675, 5.1800576876740765, 2.3158192538906768, -0.46163715114680287, -0.7695956703172355, 0.5386815932186466, 1.1847822185109136, 0.5113022667176497, -0.06942384602806613, 0.5925489637140463, 1.6492341901932228, 1.4570963880921604, -0.027778954100732754, -1.061217864370102, -0.5225881850824692, 0.3534374949855318, -0.47989118140848347, -2.8559587265180952, -4.022606013766817, -1.9392059426909514, 1.6483676913728895, 2.5353656812848415, -1.2254434743571905, -6.675413239359893, -8.772729679776239, -5.689670600793087, -0.5642724514922005, 2.171325318480921, 1.434789953402801, -0.18608121846260844, -0.24275769773860928, 0.7040018342196077, 0.5379778664963206, -1.0222270498804964, -1.8204910647571853, -0.22927510725985353, 2.3916278131565853, 3.16212305293472, 1.253309952734581, -1.0921735555383698, -1.4090285971227037, 0.02268991330133443, 0.9038544093629164, 0.16395158027474008, -0.7577528378779085, -0.2594659899726029, 0.8919574708980045, 0.6218391671282899, -1.0940035876844807, -1.4358080405959242, 1.764044737382863, 6.516238593163666, 8.152552634613345, 4.6545143797841115, -0.5870867411810667, -2.3130398131460024, 0.7262589886954901, 4.547279641257725, 4.732652837712839, 1.3475423393017198, -1.7631214398222603, -1.8763368058232357, -0.17465798304551453, 0.5864884038331555, -0.1818777399461673, -0.7210447451618028, 0.05714023607166723, 0.9821151553222959, 0.6110784060407022, -0.4248020652647163, -0.40821987743971755, 0.5043573893065157, -0.06293532707360937, -3.3776179483759035, -7.072012196853979, -7.403859319540604, -3.8850067899020346, -0.18458405795857405, 0.26307281649798575, -1.5457266529917202, -1.7042230722317, 1.27292511624277, 4.3332915255008055, 3.8466361295344935, 0.4347410797450886, -1.7372366647590267, -0.279658353574033, 2.5071100870822765, 2.8545259475106186, 0.45079471798435544, -1.4365208198632184, -0.5187800795815689, 1.585333661791294, 1.830446040173774, -0.06715352721091652, -1.51018157553707, -0.8336760577563279, 0.49274583738052385, 0.24295139419759643, -1.2623594213000473, -1.738444836689901, -0.4081217915978225, 0.8630403700935239, 0.4517278495131981, -0.5451163131700182, -0.21368910410476233, 0.5804882988512807, -1.2978560110151596, -6.4396615749477055, -10.377174288056782, -7.877329002450937, 0.5213504947553703, 8.133322466413201, 9.045403170204533, 4.196120078057312, -0.5331803115556861, -1.3308110684330234, 0.23065730632185188, 0.7936187579672075, -0.07903369976009873, -0.3080199937946523, 0.8102169362977729, 1.4423632182020285, 0.2960589614690654, -1.0869334139810838, -0.5296616616577333, 1.3442020974519482, 1.7608017167969794, -0.17704687284093726, -2.002375881110667, -1.3237098325239893, 0.7155844580132279, 1.12368676603911, -0.4227647682629262, -0.9239905277234167, 1.4769542613806168, 4.30134118054664, 3.7903885175646357, 0.2554208912842635, -1.933615754305564, -0.11550556447242111, 2.9942206173217203, 2.969837840162453, -0.24583637498824765, -2.2528941749066504, -0.25106712695605865, 3.1168655581016256, 3.371344063491409, 0.17796069943657017, -2.434713247208509, -1.567399803032533, 1.0798904101801292, 2.105489908640767, 0.9866918054901914, -0.03629603659136568, 0.22427812575339118, 0.5038863408743522, -0.17361752913881653, -0.5180060522745215, 0.7886582940970316, 2.289282606214491, 1.427887063373146, -1.2471742084103472, -2.0170842881998747, 0.8241681370430811, 3.6935950552115484, 1.814858203654941, -4.159919148263216, -8.193051796334071, -6.15731916511046, -0.9242966112366655, 1.4956829482843643, -0.5118854751316297, -2.9183479780942805, -2.1055636055811418, 0.5425401727437421, 1.4035051691859597, -0.046633810380570274, -1.0857569617697995, -0.26551014203555573, 0.6546159457936727, 0.05964706844642014, -0.5300922140613157, 1.225585934963862, 4.390824981649605, 5.448071875851849, 3.1416508391840217, 0.3320236172641047, 0.0006772396279912548, 1.2782585587520243, 1.2938418381948589, -0.21090374949290144, -0.6989968437924681, 0.7263437751042717, 1.50933780532461, -0.19441366481413974, -1.6802817333453608, 1.115288160851302, 7.106765098460154, 9.891527757736316, 5.368712750702516, -2.6893506358775605, -6.854312549897967, -4.677775223063751, -0.5668848493090055, 0.7637375336650433, -0.21174808773773776, -0.21708027406654856, 1.324888071912487, 1.9419122799409823, 0.5145256453099101, -0.9429345169485346, -0.6488131271558495, 0.19044974434680817, -0.3372365144531687, -1.4737413922610194, -1.0481726430173652, 0.6122506832932972, 0.7988201205978385, -1.0608211953654576, -1.7217095724482656, 1.1741046102043442, 4.631205529475093, 3.4835315286769073, -2.3589994426481304, -6.947039584947437, -5.656781003098215, -0.9879288980706503, 1.1530692587900508, -0.7215450834644663, -2.623310339598264, -1.5296861058546067, 0.5465192457167782, 0.42936093546181875, -0.9701258204138263, -0.20649070065863798, 2.9775483213086624, 4.795988188851552, 2.8527634548159804, -0.3776339527434146, -1.1849360091208232, 0.26966784215956374, 0.9042201225220294, -0.2827850773371603, -1.077347791878854, -0.09454625240325029, 0.92657501801581, 0.2989344177547097, -0.4613688276483668, 0.9015145209063095, 3.138404624284682, 2.8721143786891887, 0.184364981180289, -0.5614989153614666, 2.9033865995163133, 6.316900843354551, 3.917615123888031, -3.2774763671078535, -7.840702472888213, -5.140736781000147, 0.996881151279916, 3.662621803025035, 1.4514796050949148, -1.2166536012331448, -1.0842753293684424, 0.2865699270141041, 0.34722847346107905, -0.3260298563080888, 0.1379423761059443, 1.1934596842319756, 0.9141414698951422, -0.19731734946839452, 0.41043287960936076, 2.8704021114704723, 3.8407284079144772, 1.3765144616865588, -1.6132691525057563, -1.2183809939308694, 1.7314131048918329, 2.8817182355685382, 0.8563432608327098, -0.9808104019083813, -0.30018155220309145, 0.03816284818174593, -3.591679962230135, -9.095816471809837, -10.477559631520581, -5.977347714552145, -0.6465739471124605, 0.5709749917952145, -0.8464294262383583, -0.25180852917914215, 2.7873277029376453, 4.138365378670631, 1.7501140629909435, -1.2201927793078782, -1.29278223820849, 0.3836364287886431, 0.460350976250796, -1.2114181136536333, -1.7821077058513741, -0.30129625378879765, 0.911926716438865, 0.3074278562154701, -0.5491975370552435, -0.15705603793116613, 0.09546154007724508, -1.1784057484694679, -1.6796861252038204, 1.6497712338646455, 6.499675682656129, 6.212971483483999, -1.4430404391294471, -9.874932270917997, -11.027323502995653, -5.186675587603662, 0.10853068551438354, 0.1316089496844493, -2.140680562486298, -2.0049620495604374, 0.14904212322072707, 0.8387930169403817, -0.3480730802533633, -0.5854868926733292, 0.9209183351580824, 1.489094263372686, -0.3507444929202763, -2.1214773657189854, -1.3301776868699327, 0.4640241759804557, 0.28589751778709505, -1.2431864416987375, -0.9291495826230628, 1.486095002614267, 2.5286655934370694, 0.5373473556722159, -1.4467940773179544, -0.4359407027186078, 1.665176626816818, 1.199157056731934, -1.0214361800958982, -0.7749970933071775, 2.433222204771116, 3.7467262899199647, 0.2826399417114965, -3.682498395906217, -2.349604733546318, 2.9908323993104013, 5.338785226503511, 1.6148250049564166, -3.4263475103939856, -4.193013897453185, -1.3977641499872913, 0.4619943466187829, 0.011667030984567017, -0.34885596769011024, 0.5168508409935417, 0.8736944511271986, -0.06931717661752859, -0.4078320674941937, 0.8651817662973987, 1.56707550391572, -0.01666434891976558, -1.610879549430567, -0.27358233218755545, 2.324430216376435, 1.9093328467354194, -1.354583477334932, -2.2286721943313266, 1.6668328001235015, 5.293261999216597, 2.873384339960136, -3.5308577669068515, -6.495181878000543, -3.370597218993793, 0.7166933759146696, 0.7860689162501412, -1.5205568776519307, -1.8997274557985537, -0.3116626987839546, 0.012442137026817292, -1.3681049508111642, -1.6006271206927747, -0.053273538992690765, 0.045641027600609126, -2.9854400554980582, -5.836907776434952, -4.804909242021573, -1.2794111124474263, 0.5705509440527846, -0.04223882309457097, -0.3437494955823147, 0.696734678176364, 0.9726419711668257, -0.20994570851339567, -0.2691428400467545, 1.9059305780522333, 2.955492265439946, 0.2883611598678435, -2.247417039101061, 1.2762360503431485, 9.48199846884517, 13.772730166651781, 9.239720964879814, 1.1261796928225358, -2.4432011901776143, -0.7354412025846938, 0.6676695696958126, -0.9339609312985693, -2.4172581643026447, -1.1611250458681714, 0.6698703059703763, 0.23882018406932912, -1.3027122624405485, -1.2984611421192518, -0.19188028695838621, -0.1828093389867916, -0.8906815190595194, -0.21784647208994282, 1.083721694851016, -0.09631044424935321, -3.5579679866794147, -4.802168622773089, -1.7009812003113924, 1.5422938790602345, 0.3750060313661906, -2.957617492508497, -2.643276775389727, 1.7052659202576033, 4.379836205813719, 2.3127118919636245, -0.6179998275087831, -0.3023163465625574, 1.006419399039356, -1.1353095125408859, -5.473592198298737, -6.492225430502668, -2.920923750660104, 0.3601357294364102, -0.1373770989337435, -1.712920919978395, -0.5829676400476994, 2.0259427445515508, 2.44635018815349, 0.7117069716871769, -0.049043904748639955, 0.8150995061546722, 0.8376241781461621, -0.6144087374294137, -1.0000773309306754, 0.6528949587542305, 1.6191746320978986, 0.20526040005637095, -0.9949185362743109, 0.24479404989410325, 0.9878396838763304, -2.3652306940149077, -6.525781482963976, -4.077586255961409, 5.529784925788056, 13.250399414758977, 11.470005302873409, 3.5470918517162815, -1.519054399109827, -0.815813645574432, 1.0240853466643767, 0.4515668731824528, -0.7017369534823116, -0.24679380263932654, 0.31135562822968327, -0.7198478966983064, -1.5961591893197753, -0.3818309428894162, 0.9839653688225906, -0.2914103849695575, -2.6082706642783284, -2.019080443441703, 1.2557435601349736, 2.8476701186472955, 1.1125923060782759, -0.5456064434568858, 0.28156254597900476, 1.0793007599622833, -0.5571164245811835, -1.8348651615452702, 0.8392080099156756, 4.875651469459905, 4.388941071030553, -0.5766945336412534, -3.4060151643380587, -0.6672700975578778, 2.8852253029487396, 1.9646020184814954, -1.1897655036824435, -0.9761979920475345, 2.372103205987213, 3.3900754736113874, 0.25407250428444456, -2.6129477704426374, -1.7472807478320058, 0.5395286316648267, 0.8069252716056171, -0.16931301067171933, 0.09067955275598419, 1.0229028369109852, 0.5995799506146233, -0.4441365710604724], 'positive_zeros': ['0.04937912902229875504119660387', '1.5688189313646799219924639633', '3.60982103635311005439137838073', '4.79179792467507048245804318368', '5.86552334241619985067914602626', '6.88533849839207900942757271863', '8.23176169734429938206837273673', '8.984897569421301896275778283320', '10.01524343269579630246971130244', '10.85957329445200218711994914053', '11.92828788757834679310569288755', '12.563584954167717299325338108578', '14.68994720314889977509171839726', '15.13410580522749388555540317890', '16.39645099948782666972436710675', '16.803383280478362604051740941940', '17.47724497970238008529350019159', '18.744353557910018807062570117765', '19.76374606862540059252751143929', '20.382209019925964587077866128539', '21.46292075692729258504093652038', '22.49054744840485379050400231964', '23.62113944421060318952731089329', '24.23531063663506638795345621186', '25.18397792823065283743335055050', '26.29955435146758629735558728435', '27.23405481535944343898304717641', '27.69207195362397866117366698684', '28.30871861934074196489812616688', '29.29932819103760029198233691391', '30.04206887696007588579025603412', '31.61444559626696019509767390143', '32.56789424689834291724472973485', '32.93140136651126690017034720169', '34.1417389636048782104405152747', '34.87115967840489521049479981268', '35.2949575575324250449429379711', '36.413877127717859655287501097232', '37.13238609553892051708825419757', '38.33834697811401749458246455640', '38.69523180769961646245222984465', '39.72993005299162065556133311842', '40.369326273003779181420852019698', '41.55465457231792247787689745073', '42.73990021734999137133210759572', '43.31763087299018146458914557596', '44.275887590945217535011045602342', '44.47071921114809730629080747330', '45.61957933068753827836164308469', '46.39964880444594901088999585898', '46.78222967132369196904246115078', '47.97520351443208401888290361382', '48.67604412114699833701335398903', '50.04092545803298846800595682060', '50.887705188045202636749896964837', '51.33319969176537898605272653127', '51.998760380556367587300209471986', '52.83980293558686554402299604175', '53.898561745628266216426802735028', '54.68292337970754115896956886938', '55.35487770017560138787534531328', '56.00324903072111296261747304436', '56.68621566392901050830840696880', '57.36788985575280130909337355417', '58.708601275565747673881361277323', '59.32161725512467065400317277116', '60.42314505379613998221932908857', '61.28576819690271340904031208833', '61.81917992891587783869207101338', '62.48478319856857868502455714720', '63.29748006371101263090006592221', '63.88795835807219793757427892537', '64.36500994241526382295311326040', '65.963931890182005612034295721753', '66.30638834664436392986098932234', '67.07878420409472720877394001825', '68.16463910762140168238421149575', '68.78030080289786814104296572220', '69.73939239965591739582134084150', '70.38674235975287605823444048273', '71.24036625957125365638554501766', '72.0490346567027022091254695527', '72.557610272394328856711565737100', '73.513008384316511832729001891483', '74.18452133594567549770770403815', '74.75005883176504478799173925449', '75.1771576296912329286154383063', '76.54510873834534749745575510561', '77.761815911282154251839611412575', '78.39127471143280162298555606552', '79.03618231076797553446055536939', '79.48754521614960777941190821074', '80.366084800960673564217070814029', '81.029494784952067437175471033805', '81.85247313504284981895638624217', '82.695838569569147740957876807313', '83.36064542083937235449953366193', '83.90971500151504194029511083602', '85.02207615450570681583712649665', '85.63588842611921260993006753162', '86.54049261567641918538210961441', '87.209554399284590128547156093255', '88.140139373876657915053949549115', '88.93160707323007180735292031397', '89.97191109803565958528864661423', '90.177934813327971270862492078143', '90.87565675288978689083811908195', '91.41785615646408686418169254687', '92.355975494037559453483189002099', '93.05605587786889049572587096142', '93.856181619785329225398971184043', '95.06762959202775146685958888149', '95.57241439430913559227584577586', '96.49294992826621098640731405817', '97.17922203792612420640626799542', '97.8761507649025531408083474037', '98.45480647380457360952903117043', '98.90426499400083488055690684574', '100.38364828250832861139475446658', '100.624776710438207408420946765607', '101.519097465409765038701635308145', '102.05477285305938516716912808270', '102.787043617580522152682770227882', '103.363257679295301754476621517400', '104.579627490916786386318976796758', '105.68875218036975852566284768057', '106.18732100920143660345161045563', '106.619162247288183688198887163770', '107.58555456275603315875549052346', '108.33198717841884304063188021933', '108.649316018391769207389642838943', '109.56846528180074941367119139481', '110.1532533048349897563101103670', '110.84330569969838681355260624445', '111.76141613685798922939857046285', '112.89411356846158090532909858477', '113.35319931640452148754149504710', '114.271701390230241286877989648', '114.77823217645484568787977595320', '115.33834609392102299058175885493', '116.51726390456702284622372519310', '117.13516106466537156371226473985', '117.75294843317842056424780267416', '118.45780589180362566547205936726', '119.14195221328067044668588969588', '119.54624261575395773140804916014', '120.64847192075560990119890580447', '121.01921460713106190812828891468', '122.05247670325964862664974016368', '123.069604829517325762622070874432', '123.89098682848088770077953934862', '124.607663589628497033933023623195', '125.14023801320574845102995241610', '125.58365132311788704974220372948', '126.48853133618349984169383752179', '126.793663708789385898590220883460', '127.934630869074002168873393422461', '128.57388913566368063832831514611', '129.4811932224977343073169906088', '130.07558031544304378379782595491', '130.32070610404618390153058716713', '131.93969660851426327918936281845', '132.32044039783602786840941757203', '132.84481612969170901406478991498', '133.9103718518476467097008955698', '134.60818549272237325736617320391', '135.09961610830008605023271367888', '135.98998844125435241229075520021', '136.64595331811004795417888320333', '137.257990589258946017340028082600', '137.54379082211979438790634477883', '138.3248420061959325101411422122', '139.32783087085870933599240368313', '140.61320072527376677525502443611', '140.95657763141384685127246581183', '141.85134490356702936220090790385', '142.41685734971881928297667873057', '142.954410194174486873212844487511', '143.70469938945803777161824409346', '144.58737766589839469988466811430', '145.0604502474942872322577952435', '145.75740682580060719606615450864', '146.624582837594622863524734050199', '147.24540846590697291944533363962', '147.97442683750286755429242249763', '148.52769621532884440732905786790', '149.39295411329255109370016646010', '150.14372580495615312354083605071', '151.02629740549982541866211443531', '152.055095050132700011556309606266', '152.5041835566214370101699775514', '152.96743441024572991729745809979', '153.72975171518154748991795012451', '154.19378978952377339547642460502', '154.99768182500379700414061734989', '155.6560029167923667834726347315', '156.43735586373770515178756413871', '157.08143995608401536827170128738', '157.955523848736468652393886643716', '158.98662428280770918841950013628', '159.48417830022090359987700482797', '160.39404517607783110006184963487', '160.62940283952311372067319876423', '161.57409663122612844014676531753', '161.88350788223062409919355208130', '163.27630152732741276728121906198', '163.73628623738253154659402430421', '164.18909662731611405159134081299', '164.946911901149992380273107187408', '165.36789031665932559216455530436', '166.27404888461470372059596528281', '166.812313854526648762444353620687', '168.18101882030171398263640357904', '168.84819387467260712230791163019', '169.24145350478301835597605870299', '170.16801734198814619496743315729', '170.67216669943562911174864998064', '171.677344041417251742215408926530', '171.75612535848965399947924397416', '172.54478788211046332781242998979', '173.11423992904741547925102662686', '174.19302068087976329458862732435', '174.7224068572745361967753665218', '175.51331206174590941504685687382', '176.46956980658747937132955405165', '176.92862798883700582491245336073', '177.40013093753118728461363267954', '178.68965119083274704212524165266', '179.03890724222201513982417910966', '179.75581193423277770643656858957', '180.808679123985613564129546569531', '180.97281221167481198771995818006', '181.75187135880547125010915005907', '182.39575322658614880602451110692', '183.15796723741041994713009449651', '183.708764553164691153005990166052', '184.201900731803613407916440750805', '185.14827614774387869030321865496', '186.42110208296482275051136851719', '186.985112427831490587817011502114', '187.59558665576663037766264826484', '188.20538969567771371403057624708', '188.58242284898083056754867387377', '189.43763957246109109069888078773', '189.96189206758258961747330637968', '190.8228652276034249604652243562', '191.72052522589917123515191045781', '192.12782074536823044449931177742', '192.73565642867106368226416671696', '193.37425983585738846149464718057', '194.34054342024945667135513977730', '195.04719751339003324196352928862', '195.80590692469069466961935709268', '196.351277846236830306266290063004', '197.207592648675930654559408173194', '198.03559965295495812449216680128', '198.680375176143782362577788911480', '199.0323363884756223953186198061', '199.842622656889007407252610863452'], 'prelabel': '1-287-287.188-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': -0.8278052925612518, 'root_number': '-0.857211817515358306838878464962-0.514963979237398748675633659529*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.413902646281', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(40)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.394490553276508817033055992299+0.0500263337128839499167591753955*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0493791290223', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.56881893136', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.60982103635', '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': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.188', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/188'], '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': '1-287-287.188-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': '1-287-287.188-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': -0.4139026462806259, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0493791290223', 'prec': 50}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_287.188', 'Lhash_array': ['dirichlet_L_287.188'], 'label': '1-287-287.188-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/188'}