Lfunction data - 1-287-287.156-r0-0-0

Formats: - HTML - YAML - JSON - 2025-04-18T16:29:54.303833

• 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_287.156', 'a10': [0.9135454576426009, -0.4067366430758002], 'a2': [-0.6691306063588582, 0.7431448254773942], 'a3': [0.8660254037844386, 0.5], 'a4': [-0.10452846326765347, -0.9945218953682733], 'a5': [-0.9135454576426009, -0.4067366430758002], 'a6': [-0.9510565162951535, 0.30901699437494745], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.8090169943749475, 0.5877852522924731], 'a9': [0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.156', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.46', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^22', 'a^5', 'a^44', 'a^34', 'a^27', 0, 'a^6', 'a^10', 'a^56', 'a^41', 'a^49', 'a^57', 0, 'a^39', 'a^28', 'a^11', 'a^32', 'a^43', 'a^18', 0, 'a^3', 'a^52', 'a^11', 'a^8', 'a^19', 'a^15', 0, 'a^9', 'a^1', 'a^56', 'a^50', 'a^46', 'a^33', 0, 'a^54', 'a^4', 'a^5', 'a^2', 'a^40', 0, 0, 'a^42', 'a^25', 'a^44', 'a^14', 'a^7', 'a^33', 0, 'a^30', 'a^16', 'a^41', 'a^29', 'a^37', 'a^15', 0, 'a^48', 'a^31', 'a^32', 'a^23', 'a^58', 'a^18', 0, 'a^12', 'a^31', 'a^8', 'a^59', 'a^55', 'a^57', 0, 'a^21', 'a^16', 'a^50', 'a^26', 'a^13', 'a^27', 0, 'a^24', 'a^25', 'a^2', 'a^20', 0, 'a^0', 0, 'a^45', 'a^4', 'a^14', 'a^47', 'a^13', 'a^6', 0, 'a^36', 'a^1', 'a^29', 'a^17', 'a^55', 'a^39', 0, 'a^51', 'a^52'], 'euler_factors': [[1, 'a^22'], [1, 'a^5'], [1, 'a^34'], [0], [1, 'a^41'], [1, 'a^57'], [1, 'a^11'], [1, 'a^43'], [1, 'a^52'], [1, 'a^9'], [1, 'a^56'], [1, 'a^4'], [0], [1, 'a^42'], [1, 'a^7'], [1, 'a^29'], [1, 'a^32'], [1, 'a^58'], [1, 'a^59'], [1, 'a^21'], [1, 'a^50'], [1, 'a^25'], [1, 'a^0'], [1, 'a^13'], [1, 'a^39'], [1, 'a^23']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-287-287.156-r0-0-0', 'leading_term': '0.982622070318842018070071013611+0.364237909003563427751186896921*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/287/156', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.0479577221591416, 1.1247234443496694, 1.0287623957529468, 0.3788746752731814, -0.8731336084014595, -2.383001753232327, -3.531044170543748, -3.702776230516681, -2.6398536180185688, -0.6715408781703148, 1.3527439710027958, 2.4633532715449347, 2.1207601930976767, 0.5881907897588169, -1.1511665028940798, -1.95055813068654, -1.222496695903809, 0.6431102017942475, 2.4858889209907926, 3.119594050219278, 2.129610477667388, 0.15659778089662665, -1.5621544560810865, -2.0771341300843877, -1.3773253908012095, -0.30285128399423844, 0.21107307704878825, -0.06452831799479603, -0.4930047388909343, -0.21552957358655034, 0.9532164472495512, 2.2088228404874966, 2.400445729126575, 1.1542785368379511, -0.5297942648955013, -0.8787116650016226, 1.1946975215496993, 4.9569925588504145, 8.110232014808517, 8.411585157634661, 5.431329193598727, 0.9871267222381852, -2.1827716358005724, -2.4710437464305763, -0.4988142273081434, 1.6192500741059224, 2.14166635924609, 1.0407758005542767, -0.301955546661261, -0.6212986010485492, 0.018165624563265603, 0.4761219087994128, -0.07922281404256915, -1.1377297810798017, -1.2894876730078733, 0.2603139519370971, 2.6713759871298937, 4.085842578104946, 3.371924558221145, 1.2609338762269489, -0.3339013565681624, -0.2024161299891707, 0.9801075041214405, 1.4395447160478587, 0.3038010983126789, -1.285693702835708, -1.2480779511218438, 1.1416001924244792, 4.1119052118586925, 4.779652710657683, 1.8886930537175048, -2.7782750966950367, -5.828199683676127, -5.256567481058694, -2.1458381671515463, 0.547164784573991, 0.8409953568890809, -0.6268485031570896, -1.663929490981876, -0.9797640318629643, 0.6047256305725349, 1.3307606706541106, 0.5673661256783641, -0.5880221782011357, -0.7460245949986826, 0.09171698742084591, 0.6273252877673157, 0.004407785575103615, -0.9775289659494291, -0.7999101300709629, 0.6545185971859164, 1.405192445900009, -0.697617190626501, -5.283105551305365, -9.101739981876454, -8.826346291066189, -4.357120884351034, 0.8510244971279503, 2.95612950303809, 1.2280010270489807, -1.6614660952352245, -2.683112823969845, -1.458513813460935, -0.09778903867195163, -0.3688393928968172, -1.6036863674648603, -1.6890092712846472, 0.20037465134825427, 2.463102368562102, 2.8886541924246925, 1.238263721397945, -0.5014717004017475, -0.4774821136278769, 0.9042571112287376, 1.6196725209871923, 0.5904002231723913, -1.0098311677965248, -1.312671685032711, -0.2008487394976273, 0.49453271186886116, -0.6064635779427574, -2.447147298112004, -2.651920405648058, -0.6109159196329671, 1.3021065330462638, 0.25083437462494007, -3.4769690432405307, -6.152142760693725, -4.367089162069169, 1.1162031928838068, 5.818593508904825, 5.973891099561955, 2.1543445741407923, -1.7347742446313192, -2.6848865839624367, -1.2266312596183502, 0.08969731888705801, 8.592727385196395e-05, -0.4548838274242014, 0.021327922306252377, 0.9718182461417249, 0.9321237279701702, -0.2599344787867078, -0.9571063924387392, 0.08578646160342657, 1.6999344083953665, 1.4380795385310952, -1.2584616770542467, -3.917307255238825, -3.720604985945124, -0.9390241176841863, 1.241092417854838, 0.5641477497031715, -1.4034431116304062, -1.055080388760925, 2.7647185041111286, 7.0142949313648, 7.723013511341801, 4.450244882908596, 0.6271541047867555, -0.5172530598408281, 0.5703984650803318, 0.9705595861922717, -0.660208207318503, -2.4259746671719835, -1.871054450153585, 0.6502628646009361, 2.3171674170821124, 1.380423438843419, -0.7318343575933357, -1.3807022722635123, -0.05688482089359009, 1.2482890846807944, 0.89384250263221, -0.33507782155476284, -0.6535029265024032, 0.020673455495539318, 0.0872050560297924, -0.9318461424569029, -0.9855144403929186, 1.9046931166733898, 6.098530312803878, 6.982052134970482, 1.998352492239716, -5.726927247094906, -9.98782605872368, -7.8248776459761125, -2.3768782448155754, 0.943272528804523, 0.26140852338527965, -1.6754030809926488, -1.729901819940673, -0.15292759682864432, 0.5607628110250102, -0.5050852462921391, -1.5752657820869187, -0.9706381173749945, 0.4366149792740123, 0.5877456965560828, -0.6719563621587299, -1.333851953422586, -0.25100412518536425, 0.933638021871493, -0.04647998617945441, -2.6638461506633133, -3.855281490068341, -1.9876666394019227, 0.7492933494973819, 1.0055670688241722, -1.3454198165872298, -3.0139690319757144, -1.7241350679116807, 0.6396567373823452, 0.5507392493246159, -2.2180119597728623, -3.9549823198595466, -1.8062146374669632, 2.2250771097924558, 3.4997100004127977, 0.4970454856720936, -3.275912778793968, -3.6184761161345724, -0.5772086118179155, 2.1475004388558356, 2.0610530200615567, 0.47098292623232724, -0.08319246221782058, 0.5892319238932631, 0.6802806377382198, -0.4241444364824453, -1.1459958640693095, -0.3335199986354479, 0.6748498748385888, -0.06894741720621501, -1.9675457774646032, -2.4045639685385423, -0.6497304630836473, 0.5418018132333147, -1.3981767237344518, -4.56800914725086, -4.073933541050142, 1.7791756812420996, 8.474996843451843, 9.88541531547185, 5.157311499487957, -0.6017819660019753, -2.491862565853907, -0.9468458741256313, 0.17081863218334659, -0.8969119164121261, -2.17792964213421, -1.6364045966693979, -0.21769980427923663, 0.027837117037460984, -0.5259836466075875, 0.5007383325078278, 3.623344267085332, 6.029532196126307, 5.030343491327766, 1.704032332678303, -0.47943567120227615, -0.1617571523825997, 0.6003752823371817, -0.14907576227385672, -1.3155548028762187, -0.765908860864624, 0.8798595984376023, 0.7618275312733959, -1.7061249658187698, -3.0837848498160585, -0.2868513806376047, 4.520230823760672, 5.754738291570573, 1.3302935848390736, -4.341873650061283, -5.519701569363043, -1.9236684649883862, 1.5278561604373844, 1.2735358214681025, -0.8973219597440477, -1.1806974826648005, 0.87867070793579, 2.3490133153953563, 1.4666771287300762, -0.13819489787785325, -0.31977903788438056, 0.46430629315216565, 0.4347707001508258, -0.329140375984818, -0.14730836296441968, 0.9760969633837803, 0.6499945610759463, -2.2127966905525707, -4.7897293874297455, -3.564233791557743, 0.4714708331311189, 2.2879014487208593, -0.8095388906944941, -5.338663436150971, -5.892791607947233, -2.0155884501165415, 1.540507383359814, 1.3428523507813888, -0.5055660864963413, -0.01934747525895119, 2.745282888726848, 3.9549259578075295, 1.7160816723158114, -1.2221572266838057, -1.520713323488372, 0.09637141056829421, 0.31014953068977524, -1.6913075018794106, -3.1317840842078244, -1.956293581773544, 0.13074282670425583, 0.3702237724384844, -0.9220651710963221, -1.1011399670856854, 0.5268292162155794, 1.6334222430154293, 0.6299901607127092, -0.7547926537932441, -0.27881979775990706, 1.050517379915961, 0.556644770149978, -1.2224689370200268, -0.2921445950006285, 4.835410414854347, 9.329355037482193, 6.967465214594119, -1.7651013709126544, -9.320685669509324, -9.548569447511541, -4.264775087421164, 0.08387293006560116, 0.43324075394931005, -0.7571578826597687, -0.6025437521221952, 0.2233052033351579, -0.22457390457307713, -1.4004156647178225, -1.2699325141493696, -0.020853273353167286, -0.02360753124859576, -1.878619843880479, -3.0379302866194484, -1.6263194291843184, 0.36890874052657596, -0.147916603896387, -2.575817094560488, -3.270842023097309, -1.0333111430859931, 0.9071866174156553, -0.20392012789215214, -2.0930620915126212, -0.503646322559334, 4.210900797600404, 6.800418453429964, 4.092046107646014, -0.6088356424418248, -2.0563884102209773, -0.015478354050914888, 1.2491762564210414, -0.25716694286061215, -1.4444765330213456, 0.7736021576870544, 4.409540846220145, 5.001026287322718, 1.9104062005780826, -0.9707089169860663, -0.8001779252962872, 0.7860176748627955, 0.939716514085416, -0.11672788498240391, -0.24083965112713007, 0.6773570898903063, 0.716427045472277, -0.42608500317577586, -0.7377380849079275, 0.27477309569286695, -0.165409700185, -3.796646280148196, -7.1707657148495985, -5.155429402760441, 1.6430638722944706, 6.384603304007178, 4.319379147803289, -1.0825123187402401, -2.8123809859017124, 0.5648217653497603, 3.8012231142064645, 2.7054513082590597, -0.6144491946663418, -1.7577568099656, -0.3836985577872426, 0.3557315904640018, -0.7100729550941104, -1.3588741201001944, -0.23477800841854096, 0.7275318942974778, -0.3098086516842298, -1.7541548300825616, -1.1172242651382849, 0.580765298605102, -0.003759131817277103, -3.174624100828326, -5.151872563450611, -3.4139601802666513, -0.3650089449649828, 0.36885142032955825, -0.7793563460550952, -0.7268716545659355, 0.6196563445058744, -0.06725149792908892, -3.5995151674373913, -5.577449692589689, -2.2687290953851873, 3.1586964951142633, 3.978596490922685, -1.07501315995171, -5.884369522694187, -5.027797592087887, -0.4997586520961085, 1.9276854970855108, 0.6395295610359006, -0.9200469111116514, -0.3274990445495172, 0.6975485403982129, 0.093260765680085, -0.9423583224939274, -0.35403797799803344, 0.9756258546258236, 0.6896682494655865, -0.892074459571877, -1.1923414383371285, 0.1895494717832744, 0.7254613454868303, -0.3958165737515764, -0.10900153854410805, 3.591753974477139, 6.983078287327429, 4.670910965475707, -2.333149431016386, -6.660026650373289, -3.853072404717652, 1.85747336137733, 3.4568923342347686, 0.22592136280967146, -2.5849449546955627, -1.8564889824848254, -0.09026716066494792, -0.17714102196278095, -0.7578168162958983, 0.6558876451638959, 2.7250831675808533, 2.089109770800558, -0.9654016357437589, -2.4254034994205775, -0.5053809009744229, 1.7315461380911603, 1.1564593291792304, -0.8985267916643018, -1.2822039804765284, -0.06215869744083845, 0.27599426386107223, -0.4001844418082121, 0.373555692729749, 2.8311804079457064, 3.6650414244174003, 1.2962476717055211, -0.7873863906249885, 0.9268799732435442, 3.7844131156065304, 2.049421468418393, -4.233416540269988, -8.006936874070723, -4.4437144597815905, 2.326600932984023, 4.786094196543926, 1.8201089782620312, -1.0403990005236008, -0.15853234782474485, 1.9119511033752146, 1.5743320546008297, -0.3796543384494649, -1.0208593022252284, -0.21262164637720946, 0.03800501727495093, -0.3170309309473065, 0.4516806452895963, 1.8882790172210537, 1.3016765023733599, -1.4298625891846724, -2.49452899880578, 0.328781607542771, 3.6420796427740503, 3.0240142487161257, -0.27678884842414886, -1.1841018178912235, 1.3071433171513833, 2.557369807116359, -0.2551986848533333, -3.3600813040146873, -2.0844248091249034, 1.7485929966210498, 2.398463309639649, -1.1181511385202758, -3.6738190988924786, -1.8976156893556533, 1.0723540883771845, 0.9289866346875331, -1.2938146390589698, -1.6075659775354838, 0.21492606082653132, 0.6240107697987658, -1.4870542680894512, -2.8487381611815383, -1.172565664038954, 1.2315163166999141, 1.3325946344004123, -0.010601658344877224, -0.19345343011691685, 0.4774427673776853, -0.18696051662229485, -1.6961027819280163, -1.3923873064925179, 0.42835059418180743, 0.3014961430168171, -1.890262399755833, -0.4649418128712185, 8.307358751163076, 18.759842134931183, 21.042821141465566, 13.23702252767653, 3.6023127601540024, -0.08351076222914805, 1.0450798695585934, 1.3995749657749599, -0.3091565809247009, -1.042051841090233, 0.07726780522148012, 0.36232109717045724, -1.2686926779048706, -2.2427566973775903, -0.9226312824769822, 0.45130327897142786, -0.2580716553886853, -1.1684110620323473, 0.41476264790860934, 3.0188031365536014, 3.04844049702401, 0.7549313209688047, -0.05711322302601366, 1.5507178348598278, 1.9157695741334653, -0.9384715984933689, -3.380541408615248, -1.677838435013277, 1.70453548788176, 1.6554142008526995, -1.4336359034708335, -2.1591912265100786, 1.2001616273898357, 3.7464319764480623, 1.7708283032980074, -1.0941332184128096, 0.6002425839406219, 5.483058765901508, 7.169526953256255, 3.5917284856659393, -0.5051889751619892, -0.9669060792462392, 0.5122008590593586, 0.5238185685066242, -0.5709423608356674, -0.4880530395880176, 0.37711698452317555, 0.030407966932706365, -0.9513732964854354, -0.3492528890709029, 1.1736499628008852, 0.6873266194366539, -1.460833458207968, -1.1440656144493577, 2.749175959319821, 5.277078774651675, 2.5561566589967932, -1.461196680741789, -0.12220337136513579, 5.740957949318981, 8.356594682445417, 4.080749280612335, -1.5511420592677754, -2.098556601808957, 1.1114559355178981, 2.419051578267953, 0.6123914183460505, -0.6998639829890232, 0.02470745075042613, 0.3506696727411216, -0.8214648903613053, -0.9915111306840767, 1.0588492850489102, 2.2878728304800395, 0.20522812969119625, -2.538700599534491, -2.0074595960548334, 0.7795303478133526, 1.5837904709399644, -0.2709052463819518, -1.3434668176591298, -0.21143207543876116, 0.5230796192509872, -0.49342355953154504, -0.7736515455863797, 0.7169319260949452, -0.030545278749645535, -5.988238847260826, -12.335876179648828, -11.419838864840004, -3.664316257625536, 2.223913441475835, 0.9617257548532773, -2.8093520930215004, -2.367397152810363, 1.5000884201520024, 3.157542355386653, 1.209192271734255, -0.539071260313257, -0.10746867304375987, 0.1469244184822543, -1.271085976636189, -2.129534589061351, -0.7375127168550718, 0.860194509056943, 0.5494353112876454, -0.2613933599509798, 0.1884171747452536, 0.14120477454454536, -2.3859493262566405], 'positive_zeros': ['1.0467235850562963197039817448', '2.9096845297987150441949789607', '4.16174303024866779236104213893', '5.21495736959170880333819533894', '6.58641004872623845344873380389', '7.935226406767015717024039482515', '8.39669499774701759256210930362', '9.13775059527889761112411396061', '10.51562830871314434539477655107', '11.11472643127606437838808520734', '12.88888124452752990032455158882', '13.814239350665876160985005835393', '14.914103106777635137282999076802', '15.61760626257075228374106161396', '16.2248234194494489253646976898', '17.15042010632294633165633614546', '18.65284898733115781525173027652', '19.12427934766062347137713846949', '20.05458491924488094735036634214', '20.81655110187501126996821988416', '22.00325392084744075526254515655', '23.35077083484328502765906185071', '23.94466207150222561609510762268', '24.87864478506094788895257643309', '25.76449988146632786175870213602', '26.53227199459553593206122460675', '27.18879402450126663345623644397', '27.9978426231895971163233450752', '28.685813367071647836515748593335', '30.25241886090736451685300617744', '31.06328294201996070697107301784', '32.25510194351721333530129397804', '32.332581776803928977882370772909', '33.41217262723348275505291811290', '34.5716158394976305589348030001', '35.121794455119901851858994232205', '36.04443472302140844513545270731', '36.926266219130444732329013681211', '37.384200763009613289615640182316', '38.51382841583610918490323774702', '39.0893200154944866102578386579', '40.25439263822679923007463811453', '41.40308559884834709194881180235', '42.46032410925214336884750155351', '42.81254758657651889095913416293', '43.430418590364783836627646137609', '44.313631856361816929438164011678', '44.98430604870210031217297706489', '45.813087287348386974920317697574', '46.9758149498913371604916068962', '47.58591805458396519781049685706', '48.237254464542765414516829344324', '49.771340163293303069966776516848', '50.17651256609813561080091478089', '50.84023401170040735983643001972', '51.79944298500161437632254631897', '52.69714875917754367653291519570', '53.44776093351734649116590974841', '54.28262369200949579402466742587', '54.99021812747829707914669686686', '55.350955861848367182475173778215', '56.08434693690104655292103010019', '57.26909357325476688128111947111', '58.61325838174533497280207789889', '59.10226995765928194953484399244', '60.03213090809694978581069282513', '60.5145409387501828161880898052', '61.4541579753114763050408919887', '62.038575093530462049140269827025', '62.861711232182500473244512146997', '63.43081919248617583845307204418', '64.58576750850406614934430210429', '65.15506808144716888084514871078', '66.14896505014855266429676159731', '66.64163486924108721758743834757', '67.63643999576793052754292796727', '68.47378653512945559376548444040', '69.42632058445715725440632204307', '70.45670996309995471216240389108', '70.68717161696813456775643261177', '71.45959337727590693326517008134', '72.26680511423120165946637775704', '72.79955333404213168088770196332', '73.85498971825879609044992222026', '74.2138219636528684122756395763', '75.23555100796012571817302696089', '76.52112773559763680500386169689', '77.37984566945665482887865752480', '77.6100550850551841768617107008', '78.82955030255668801434386633577', '79.07937459762566932668169968274', '79.60886944709552259231305666028', '81.1379945861825957132077522769', '81.610434422613013640286052869087', '82.15268871643553116804888920125', '82.95252754457841984410764739628', '83.55379546824575687329237384816', '84.394009485079888243003852862355', '85.3788707749568395562104923762', '86.392961290187186133260803385963', '87.052689518821978752575164419018', '87.69656658199199478888984865965', '88.71317600753732029707736434836', '89.191929104083481802525246048522', '89.85881426537745876608016097777', '90.358428774509793173623920300282', '91.03131693552700395132618771974', '92.15015909556297056366865014998', '92.75799192617238744083501852614', '93.89516748688329079418370078737', '94.58462352523073728816464748474', '95.00286396633006612611364910937', '96.10026673750793712524317398088', '96.85442091543373590646877593011', '97.25620750986613645270595559781', '98.41096923231516786266076393961', '98.8512851280551867004353959215', '99.600726880320554397537138934902', '100.42838542545566530591937653582', '100.99754157240886254354661207459', '101.6570382636042645922076773654', '102.21345970347987264442512306191', '103.380631818998892596633394267624', '104.67653237661882253681212139560', '105.106650909936423285786469988405', '105.82497816822760698569130413370', '106.182595137312790678716742539358', '107.19404387544776285380689795397', '107.49344466401188606885212387378', '108.66810746457677393297087557446', '109.03797814745032838796430022382', '110.12247885326272707604265219879', '110.596373390510009335796616698553', '111.28939651407275657585638439978', '112.45193463258035656620757226557', '113.12700994628012758560901994215', '113.71212754685317385945197418111', '114.3050840567207191552123786737', '115.48655545696724696487575025492', '116.08766822280894061922428017928', '116.83646600149368184335405783794', '117.280462856227012702212580289266', '118.01497337579329035988423362286', '118.66710126280089161645782843153', '119.03648223477851042867843514418', '120.24180374691842171486969702985', '121.18130551935587943474893971000', '121.834910959464036585515014190778', '122.748541493907367967090897198556', '123.52109174005919931308170357463', '123.89362391546520533702388817028', '124.73609520329285638603702566325', '125.25539929994599937695373815189', '126.125169341047681210232534598855', '126.56198216999083315263095267790', '127.86980235283734581853354688505', '128.239844797543663173497531996558', '128.91270904926596308822950686679', '129.366340153835231316151662767260', '130.43512395574366910537117527972', '131.19610657940362548399756322904', '132.2252978824993819798156350274', '132.908038350521806278941589634200', '133.513753347528859066881962327356', '134.08533357028000323796712895496', '134.76322875309411978389834217505', '135.45102345270325435139272971222', '136.20996877793170478243353560326', '136.77598389676569425911225891124', '137.20297626550943566655501969872', '138.33809599469258870258329611891', '139.26384646895047226453545574614', '140.017750302499022779224322852', '140.96971510595162139017379531557', '141.17814947604255879225897887389', '141.77901648488577444226131334192', '142.717135922501349585882505279716', '143.493237030473177640323844557453', '144.23096378570703536659941492367', '145.01766026769622857480679717805', '145.43874773938146854765717455195', '145.869836549426002967053889542631', '147.01772606847025792045754280391', '147.40145694178954413531988135850', '148.23891323382603260213615035108', '149.26016225505235313916814065047', '150.15651261157699213124185530608', '150.64653777227107578298540744313', '151.496943067117110277146016401624', '152.289578602330974243234724710652', '152.53384181504631263801224792287', '153.01421203210316655546626358990', '153.90795378072461629099894181227', '154.661623643854452450311101575772', '155.595950026242310779490180797729', '156.10983048659580083349647418564', '156.85494316222296442708972990742', '157.66491995858563628096843325956', '158.352978182744983080007842439695', '159.24004900228971105993774127683', '159.8190996875299175796626695021', '160.58782165709059854871313204826', '161.05655777845328400702824644248', '162.00851230372814757311405552727', '162.80936800748044652313507838589', '163.208903715362274686998494372866', '163.70884777170943237749872638079', '164.606135223675738389254376440890', '165.04895448468528699364123160431', '165.65126778310631550094426368442', '167.46287502344362773983940104543', '167.59004640893944259208996966030', '168.38492860203794632225579500249', '169.043070764356635667669782515242', '169.46970225853634968273879387054', '170.475591427281344519721129390105', '170.878113852292164385035073814472', '171.51280827712394829329652320080', '172.64547639915247950815748739729', '172.833817647177591362232588848338', '173.66736787618915721486767068547', '174.51673509594088060242836532049', '175.17278153264709311208075036777', '175.845179199631090850418695969147', '176.72101085605890882304458103743', '177.139517386791567423007597545779', '178.38232989396140280650500940654', '178.94585918496588222553395151291', '179.51823805860459538621736167199', '180.15897763493067122356885948681', '180.63395603677473038644410372759', '181.31715269069717763404788777649', '181.976611475694476476312242378441', '182.611821530706194056295187244525', '183.6096786043044911251993423843', '184.07067618490677686587912603803', '185.20607420561730580037177280805', '185.8337224606989617386842688590', '186.656126258447768986839709149762', '187.180057756801518816030595036467', '187.6175755575659642724687161097', '188.29911141288783957190604650343', '189.08225162933842433574879156499', '189.909118248550505044412192592151', '190.585437730095082102605448436042', '191.29614037006664520772485161259', '191.75344020948712006361797451758', '192.3601538967658660894845241711', '192.80969768763631636723628697934', '194.215093346837399235973858404317', '194.76021362857236697588124062175', '195.506651825417079710963535497130', '196.417359102056859090601156130917', '196.91412504280839769983850938112', '197.24066507253147619204184548187', '198.24011232373743898742708849749', '198.91801494961430295693852296185', '199.2976331046414149767639265175', '199.7182713717966267660467216978'], 'prelabel': '1-287-287.156-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.22598570205551474, 'root_number': '0.758391193797792217628013223406+0.651799660302120414489171162810*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.112992851028', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.883282829943333963920908838178+0.289331014294396888736412959479*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.04672358506', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.9096845298', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.16174303025', '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': '287.156', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/156'], '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': '1-287-287.156-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': '1-287-287.156-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.11299285102775737, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04672358506', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_287.156', 'Lhash_array': ['dirichlet_L_287.156'], 'label': '1-287-287.156-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/156'}