Lfunction data - 1-287-287.208-r0-0-0

Formats: - HTML - YAML - JSON - 2025-02-10T06:34:40.037735

• 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_287.208', 'a10': [0.5, -0.8660254037844386], 'a2': [-0.8660254037844386, 0.5], 'a3': [-0.9659258262890683, 0.25881904510252074], 'a4': [0.5, -0.8660254037844386], 'a5': [-0.8660254037844386, 0.5], 'a6': [0.7071067811865476, -0.7071067811865476], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-7.040766286173228e-31, 1.0], 'a9': [0.8660254037844386, -0.5], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.208', 'coeff_info': ['x^24 - 1', '0.965925826289068 + 0.258819045102521*I', '\\\\zeta_{24}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.178', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^10', 'a^11', 'a^20', 'a^10', 'a^21', 0, 'a^6', 'a^22', 'a^20', 'a^11', 'a^7', 'a^3', 0, 'a^21', 'a^16', 'a^5', 'a^8', 'a^13', 'a^6', 0, 'a^21', 'a^4', 'a^17', 'a^20', 'a^13', 'a^9', 0, 'a^15', 'a^7', 'a^8', 'a^2', 'a^22', 'a^15', 0, 'a^18', 'a^16', 'a^23', 'a^14', 'a^16', 0, 0, 'a^18', 'a^7', 'a^8', 'a^14', 'a^13', 'a^3', 0, 'a^6', 'a^16', 'a^23', 'a^11', 'a^19', 'a^21', 0, 'a^0', 'a^1', 'a^20', 'a^17', 'a^22', 'a^18', 0, 'a^12', 'a^13', 'a^8', 'a^17', 'a^1', 'a^15', 0, 'a^15', 'a^4', 'a^14', 'a^2', 'a^7', 'a^9', 0, 'a^0', 'a^19', 'a^2', 'a^20', 0, 'a^12', 0, 'a^15', 'a^4', 'a^2', 'a^17', 'a^19', 'a^18', 0, 'a^0', 'a^19', 'a^23', 'a^23', 'a^13', 'a^9', 0, 'a^9', 'a^16'], 'euler_factors': [[1, 'a^10'], [1, 'a^11'], [1, 'a^10'], [0], [1, 'a^11'], [1, 'a^3'], [1, 'a^5'], [1, 'a^13'], [1, 'a^4'], [1, 'a^15'], [1, 'a^8'], [1, 'a^16'], [0], [1, 'a^18'], [1, 'a^13'], [1, 'a^11'], [1, 'a^20'], [1, 'a^22'], [1, 'a^17'], [1, 'a^15'], [1, 'a^14'], [1, 'a^19'], [1, 'a^12'], [1, 'a^19'], [1, 'a^9'], [1, 'a^5']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-287-287.208-r0-0-0', 'leading_term': '0.0122622731813774004135651672762+0.0198413308470850357564224884748*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/287/208', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.02332470264243955, -0.3846673518994566, -0.9494014567967672, -1.5282327059754297, -1.703705490004545, -1.071243637948484, 0.4930277473850518, 2.6460231478276697, 4.60971967951535, 5.476947036301644, 4.68374795796218, 2.3952335565274447, -0.4615387726430685, -2.6140537056169615, -3.126194945416451, -1.947721908390277, 0.041780920777680704, 1.5733091068320582, 1.7951836190160262, 0.807626099755981, -0.4639001211152048, -0.9883238006216942, -0.42231437811815825, 0.6315888527611073, 1.1269125545729095, 0.46188894431587985, -0.9618551670870519, -2.0033632560998753, -1.7024901509254664, -0.11425377023362022, 1.6694951322102312, 2.3867544571421053, 1.6597310692336997, 0.31426297525570435, -0.3697981528037065, 0.13682627142082848, 1.044816319119247, 0.9215016294130298, -0.8886516089834389, -3.3632734714256762, -4.36123945340747, -2.3424593725122103, 2.157411916584193, 6.641250787216728, 8.411399978198908, 6.593062709551828, 2.736055646981805, -0.5096605589703259, -1.4929108984832493, -0.6362956562871884, 0.3447782257662493, 0.21469412668218074, -0.7276636017352172, -1.2298828268287443, -0.5786025058296731, 0.5917535938860027, 1.0064839988901864, 0.18841573273363202, -0.9603082218204317, -1.1323259787842226, -0.15062664279456892, 0.6420229306227967, -0.2692320045740284, -2.7761331818785284, -4.856892707307506, -4.346493319938532, -1.1685246020868054, 2.2518775604989996, 3.0212545057661457, 0.4346465001177694, -3.3211168333348304, -5.166945926885487, -3.9219663756511625, -1.174995845646674, 0.5414330554753496, 0.3323811530211488, -0.37376567280886897, 0.35473882783836047, 2.6625313477756847, 4.634638120060222, 4.320390233103579, 1.8436480426051134, -0.6874833119462836, -1.349645827007056, -0.28007660279564767, 0.7332909601081851, 0.3728476530018928, -0.8233557457924011, -1.3320509348960632, -0.6365674944441624, 0.10724046879689424, -0.41307234143135263, -1.7956405550910008, -2.113736879241934, -0.22268260833239087, 2.4300047962031086, 2.8723096057212403, -0.219563253229275, -4.635337668106052, -6.375010516125935, -3.5258480750154226, 1.7037725142665194, 5.013656554043787, 4.083705383900746, 0.5282687172379511, -2.1149380674367997, -1.9984142465667036, -0.3335858784065086, 0.5867666684944727, 0.09284972270504369, -0.532591000880653, -0.11481675939814581, 0.7881953400457462, 0.7573954967842297, -0.3522008922038013, -0.9205968927714232, 0.44433349658716886, 2.8551679329082678, 3.780114628327339, 1.8984298663779247, -1.1771073165757877, -2.544893794162406, -1.2630317935944004, 0.6405281559391228, 0.7020720727982295, -0.8738734561787439, -1.355469830849419, 1.126747585412974, 4.950012451393214, 6.442880454659648, 3.9441349191836617, -0.2039258239855435, -2.1353449249560406, -0.6274743885129126, 1.8003079967299367, 1.9967510232865384, -0.25325869083764047, -2.312614354771459, -2.0529160559126804, -0.29105164971779907, 0.5111360396134321, -0.5985150691943683, -2.059978830730276, -2.0148233678311986, -0.692742287807043, 0.10607425043434901, -0.431932597281604, -1.0841649301197973, -0.47957265755714984, 0.7488530298236789, 0.752555867719182, -0.5747220865272391, -0.5589909609784103, 3.3129525653086422, 9.637207246292784, 13.417123889171314, 10.878533882311277, 3.61897956596035, -2.75976074477128, -4.19237845558022, -1.7358107842639132, 0.5325527346259038, 0.38266612557186996, -0.7198858452690632, -0.412839608504466, 1.2143795700207092, 2.0033032191178632, 0.9280445302894393, -0.4203498777894307, -0.0593422759887707, 1.5663188667016885, 2.0865793416640606, 0.41302840960643744, -1.686774475012935, -1.8425357165221472, -0.1827086126110137, 0.9133918509637228, 0.12460206869100675, -0.9403742893398958, 0.03366431880334412, 2.673946415984441, 4.074082417606014, 2.5651701946801926, 0.13077388388615513, -0.01932504144319632, 2.193477570975139, 3.233333007606874, 0.3795906561966485, -4.39927147898513, -6.275102099377267, -3.1614789256132534, 1.7326275566484153, 3.558576997252917, 1.216344688847324, -1.9508504144415808, -2.540871165126929, -0.8115517204022263, 0.5521046007089838, 0.27401540660271934, -0.3375148609261908, 0.09175188111185992, 0.8786781123649807, 0.628526448479638, -0.21888568170749836, 0.24925252834813783, 2.4003742192481203, 3.878471175750329, 2.503957454868255, -0.4478082904839679, -1.434137993529518, 0.7056100038373049, 2.7638178500701125, 0.9720495488729823, -3.940040498838288, -7.09702859762836, -5.184590888704157, -0.4479468901712078, 2.067002967352255, 0.4970517494230109, -2.13340885086697, -2.246335223502469, -0.11591101921641386, 1.1987586488866613, 0.34366087815335145, -0.7837105003175313, -0.2511195919627104, 0.8541875241321457, 0.003810868282979185, -2.8599807247079805, -4.775971824432319, -3.5262468367232374, -0.5360458954784062, 1.0778998447950225, 0.5176552471678814, -0.17364006712323934, 0.49557030739190316, 1.3084278653010437, 0.5523238256312785, -0.9238800983492663, -0.7926887105481133, 0.737197909399215, 0.12994451928297313, -4.887671192176834, -11.13695181498094, -12.505295419160873, -6.940003666701932, 0.7256678561302329, 3.9829848148660396, 1.6440038662322403, -1.7960520170714591, -2.2419102120024497, -0.4358323489721999, 0.3476188923254198, -0.755430971761921, -1.5213113141574657, -0.42638904573561687, 1.0834835917845411, 0.978268255089172, -0.2618474629322609, -0.5778553265213414, 0.3193229012355258, 0.5275417619208358, -0.7518583069958577, -1.378163233073673, 0.7978051411572108, 4.2335537642374454, 5.039272531913133, 2.175612603832159, -0.6927318227991455, 0.22588490547129542, 3.7647194160270923, 5.256007381386475, 2.741572556559358, -0.5062676531181617, -0.5795665226282751, 1.777116463960803, 2.495926237875108, 0.10718938441442573, -2.1690555557381677, -1.060526768455075, 2.023210221949296, 2.838727423291699, 0.07462624073669862, -3.0101011799072945, -3.100300624909459, -0.9610873033962888, 0.3142870676106523, -0.16564623426802985, -0.4386100190444562, 0.6838966240704077, 1.6376234602116997, 0.7550871337962664, -0.8456507522981231, -0.8830438756458954, 0.4067996697085834, 0.5165841721888085, -1.1419542001638936, -1.6587837257511304, 1.1401384773355108, 4.467828346143647, 3.2733776694596717, -2.790080920024917, -7.683141947527807, -5.775874824113144, 1.2439313879723335, 6.350096589639767, 5.458943823141077, 1.387463403267464, -0.8377445322589147, -0.18569289194081967, 0.6611408363021997, 0.21083626053846685, -0.07376256281421435, 0.9428558345682587, 1.701575413174377, 0.4685363994154648, -1.4375259390198485, -1.2345291748374492, 1.0013702171138286, 2.021147240793233, 0.004643509605992832, -2.64598953978579, -2.6454857515954524, -0.46698447852082603, 0.6171465279295159, -0.4146157632529093, -0.9821786497733933, 0.563603082785477, 1.5896693232908563, -1.2778000008622483, -6.496392404051036, -8.54607028094899, -4.990065833103537, 0.060776976266399364, 1.2318879810722105, -1.219349310775816, -2.363761621796717, 0.22213996715775616, 3.2830576710759107, 2.831485325455177, -0.26880445832997196, -1.9073582734080423, -0.5963660727402866, 1.045383355186896, 0.6966589370084205, -0.48115950429496473, -0.3232474730196589, 0.7474200402747329, 0.7634514867369104, -0.26180764662245304, -0.47094495142117676, 0.2247668838553062, -0.5271360631893189, -3.3141666385008057, -4.48663357473788, -0.5384266574238128, 6.076858127209097, 8.694049095958675, 4.6087073452700125, -1.2282609912503493, -2.422390422190764, 0.977861671743649, 3.4631086345350615, 1.9675712297442272, -0.5738384162324918, -0.3292021555802681, 1.8521160703776474, 2.376428161597363, 0.6458130279200843, -0.3586752514065139, 0.9143265563942661, 2.139912827328409, 0.9619448995433506, -1.1629028692539929, -1.2570827597874765, 0.44589069647527985, 0.8916502804985414, -0.88036404134635, -2.11974074070046, -0.676707980788554, 1.5613571051410386, 1.5971848459765359, -0.010736197034218097, -0.2255551790622815, 1.3421014817467616, 1.6774066854292955, -0.42917923244556655, -1.596252797113278, 1.1813417003678799, 4.797561361203583, 2.9829307779011778, -5.011966610490623, -12.197058022740855, -11.940183539873575, -5.75964414201577, -0.585852498712187, 0.08096475312133289, -0.9849246126736886, -0.3678011997234798, 1.2055698249374538, 1.2906459529702672, 0.13353965673253143, -0.17511434422938935, 0.3730844636610825, -0.23934682606638247, -2.139899040577609, -2.7487202140119864, -0.9245415242373894, 0.7196777824787008, -0.3232707156760155, -2.2665961662581826, -1.614337295406644, 1.0143312925653154, 1.2223248438803265, -2.3606089253026052, -5.082298690608065, -2.422540244789717, 3.2383877173021487, 5.408880679115706, 2.18130085986114, -1.5824512708696783, -1.4061668246309023, 1.0197095207938915, 1.4346698233945305, -0.31383165230308757, -0.761123341927957, 1.021987825469654, 1.7880095181792557, -0.4826986954102585, -2.952534085882908, -2.001524908342512, 1.3068313808341046, 2.8095410132456697, 1.243685693390209, -0.5439043629117256, -0.41559046740044053, 0.2684859971077607, -0.12925293482632427, -0.44367560430630165, 0.7759219010575824, 1.7829829479973422, -0.013861494963797958, -3.103145500479301, -3.145994625978007, 0.100939713358432, 0.9465726510387326, -4.640449339778145, -12.30543443744979, -13.909152181908105, -7.865486307747757, -0.9174150194069186, 0.8982764656978367, -0.811848629086681, -0.9368213293408605, 1.2971531034432102, 2.3079144010871007, 0.5420439638478133, -1.3121185158755277, -0.9783078304246251, 0.1583717500486852, 0.15009155337679053, -0.04573137178375892, 1.1949586898296296, 2.447024875330068, 1.1095450718880109, -1.7722641387646365, -2.190259594947753, 0.7799104759933629, 3.060522580674274, 1.4318213590598572, -1.6396645000309107, -1.8799783221846886, 0.1865047775853378, 0.3900288225466766, -1.997037629157355, -2.7657535242976143, 0.3753327226851257, 3.4819338475317303, 1.982816591803203, -2.0796460319107295, -2.595100018208173, 1.7274993876352436, 5.445527810380112, 4.208257127353419, 0.4992027337696159, -0.7898081213111048, 0.5546101108583821, 0.9361220215472446, -0.7538112762131989, -1.821446690578927, -0.771008369272193, 0.26064686338282866, -0.5596537662340587, -1.5897086933848326, -0.7495703037215365, 0.7213599127420594, 0.49911488500071677, -0.5161677908729283, 0.2539338042221246, 1.9036048137361454, 0.7141294443249557, -3.0712747557011113, -3.472736602080328, 3.2071554725117943, 11.614823685849597, 12.900453492291964, 5.929164442008821, -1.4862502399898048, -2.881827863279345, -0.27622301832582513, 0.8334469231157818, -0.42413447954007893, -0.9271439481018435, 0.1255513205255135, 0.27437155300415417, -1.1105150982220142, -1.280837635728287, 1.014671029437781, 2.798700699682558, 1.3949725859149613, -1.103973224295189, -1.007092206853774, 1.1966916909129874, 1.8800100849337813, 0.2782089930496128, -0.5715881323723603, 0.678611559883602, 1.3184056162682958, -0.48114280819614985, -1.9975072624264487, -0.4273570297262611, 1.647954266753382, -0.3581280228682418, -5.303120942681872, -6.90962966584089, -2.8673487269860676, 1.3891750407925378, 0.5644651010898233, -2.693305012084176, -1.9800051828430068, 3.136923350898268, 6.567416452950458, 4.633846223660932, 0.702481686613541, -0.6007320623597765, 0.3385477444626522, 0.45147276266940206, -0.4830736482924499, -0.39418876403818826, 0.649129127691727, 0.5751020957041243, -0.5635626436085523, -0.5308657951600394, 0.5691571996673183, -0.29580598785993767, -3.548291519293426, -4.701126526578785, -0.6449009986378729, 4.698338545770243, 5.18620137349465, 1.3102103487272616, -0.6416989482057126, 1.7617137024228486, 3.509533323150029, 0.22313597450869208, -4.7937164083915995, -5.465237918236539, -1.8874483945347853, 0.50118935114817, -0.5565463098082108, -1.6336188613255092, -0.1712416430789735, 1.4254205445629278, 0.5246810097237439, -0.8990714866319196, 0.29592278881651085, 2.797564201340286, 2.8114657841428308, 0.3437231958686821, -0.8360884450285381, 0.5757390821912195, 1.5209854877156865, -0.01853756834986258, -1.7247595047007092, -1.1873030453576316, 0.053446663164063615, -0.21574952623411345, -0.510768429202125, 1.2200365284503933, 2.051151882087011, -2.845244188548558, -11.43592387052134, -14.811745392794338, -8.432126374797027, 1.0813943655331286, 4.205846724046624, 0.3911553053501845, -3.0140340896555315, -1.7942928520222443, 0.8177924533898762, 1.0266119662388784, 0.046055674173315415, 0.40546788738175504, 1.0573069964024453, -0.16085941980137136, -1.9805933750880242, -1.653498769599409, 0.16000510187400824, 0.5517196241075704, -0.3614193052043783, 0.35077809432239343, 2.779369142810712, 3.288512055195315, 0.729086484593457, -0.8599473012927604, 1.3830722382648564, 3.8468094476040102, 1.73381095098434, -2.926406299160613, -3.795508531112164, 0.13133981636917405, 3.048010454263652, 1.4224013853314659, -0.9311190092700915, 0.3746907127657874, 3.158513439234622, 2.7687874159788253, 0.16859859804587457, 0.36802493802333636, 3.9074559735711683, 5.633895171179683, 2.783038785786831, -0.8462787312560573, -1.0101486417339594, 0.9281839211847601, 1.2660303167955818, -0.0021569472550196115, -0.3801156467791871, 0.08351692619924461, -0.6376572660193791, -1.9927961537756385], 'positive_zeros': ['1.79253259356975034642461396051', '3.69788617617603309768560669971', '4.99336802346453631584549990305', '6.126129627813957488637144629519', '7.00038771937304903861324259629', '7.92179478337181935824339192449', '9.08103110167198077850267673433', '10.40339368592682220192992295821', '10.88967325162288653066325274122', '11.75171963278578494194502562771', '12.98739026359079482693702275543', '14.62301369632340745145484736678', '15.48504813482587939735044526246', '16.01972637568541995239003847618', '17.025279982018294611501839795124', '17.8598234600102848787311053319', '18.79000787957408772824203457934', '19.32762423506000270110406246451', '20.7203043175833062309941929399', '21.598474120250760005492506154884', '22.98179317762476418465840035336', '23.55646679745986085767492416468', '23.98763591231882176777071393866', '25.52234848400087567960453407400', '26.314751824583090671799469103837', '26.9772964953985765245866973459', '28.04261583866706700037130736794', '28.298386719046808420549082519202', '29.400177737096706519315554557476', '30.296729838321049935990665300079', '31.460419490098385901008903055483', '32.546354103072476483805502071097', '33.50761960150709428017214688045', '34.096528707228427262718252073765', '34.72618258452783066030798720731', '35.53570484160071536930024194495', '36.184034440133394849697995768', '37.374966101751111962010640746896', '38.31296754936163077249241934572', '38.901876387101118110237158678563', '39.58385223747789163103980298353', '40.92002907757739700286320562383', '41.63599337976189404622699661257', '42.47057276059208149914090440951', '43.49650005372381748233766871523', '43.94123059603090741781531808776', '45.21162835849006845729869547797', '45.44932062898078101454031307930', '46.3650226850938078391355673559', '47.06013403341018165619510802880', '47.576193631801068888551289375461', '49.21694792829096202274450183724', '50.20577952711833756397902278615', '50.72446381222550944194125372039', '51.33987258857483065608294586423', '52.37298988202465856245927439272', '52.82627116442730613587631277619', '53.804131350640757891876010097554', '54.71975976992176348183057076341', '55.340349139699168295857029132297', '55.93261834047425852040324565611', '57.213510137206923660426321106312', '57.50423779842733811133133660867', '58.46309140845301203272886088760', '59.56825462224741300570264220233', '60.41959151472729041054645720063', '61.392246161997426367523831399069', '61.98242277741175176469942444961', '62.46640933200221020599291537799', '63.33762679086158916236297949312', '63.69087663256827744399456625734', '64.94789583355680476038374312331', '65.54721725990974407720998322487', '66.32033498303060193325919689504', '67.53307379315932596144114608415', '68.17810014795345713849127290350', '69.07892694338997694538515029350', '69.7606632225617555689749361952', '70.37260120485062078101876931648', '70.938047103482292219422636776967', '72.25332033826209358625112324742', '72.98415291107763969187396308603', '73.27689311978956399218887929945', '74.1701451784011639615712089713', '74.848302664458355099283256076393', '75.32628233353929249753318205279', '76.8402737166096027412996562620', '77.632109424822372110725171989', '78.52531549026518221242168303804', '78.88791657187660115311063665576', '79.76320434498698604450419385414', '80.55550143185234149618941330003', '81.149799519964510902741459233288', '81.71774784437872230717337133393', '82.42165472580608551957602000763', '83.6407348688252939515369045758', '84.03700805209793105516105780822', '85.24619359807382103390269696207', '85.7131049286602739815437368390', '86.57331715745222402645235506738', '87.2960397825415791998647311143', '88.13133248172465404601535989968', '89.2362443264347762731125111590', '89.62214735388874314284794495976', '90.15773306728562013816591499688', '91.07211156978107214877849895619', '91.77554488815293829839328564855', '92.30461535474505863717915675314', '93.02965986452323510829039290954', '93.93396048821970747097272415482', '94.94759823715167359104503388825', '96.07398170671853669231537129241', '96.60889951109048553204018246125', '97.28745992444341728980122587309', '97.544481405904550087616702983179', '98.50645549702908835472038304567', '99.24454779436662787566555355183', '100.000483010656797366367282159788', '101.01191487098357814623381428992', '101.46865974945065797050157182147', '102.09988848078189209578930221164', '102.72057559129401896923619480627', '104.0573855994801698052095259898', '104.55216188544166129997135772296', '105.29355392950518976532282393665', '106.22274947946118307006780987849', '106.9652626989228588990907815255', '107.66676256283945855393512124958', '108.21979608054522897674911332909', '108.98126935900875716752756263909', '109.57438033828791918166150922535', '109.89885994836149372296507900849', '110.96382494482632913607765582833', '112.10797111893818889034517554890', '112.736278456165736393817192524750', '113.65706000839131107007738241801', '114.115250490663604993768944284876', '115.12025414090722606943784432705', '115.452712001242388577973644947160', '116.379424096098156353254479634314', '117.10688483291617171094477622718', '117.68272573541842853897447208892', '118.521559208334638124409732605393', '119.3725301364362011630705688245', '119.74649217608183094776437347674', '120.571187025405767544451007258604', '121.157242416866646054174095986542', '122.01003340321070962557046750891', '123.51977317825130578060013698865', '123.774393675194492801557143691778', '124.44490784739376914423819192393', '125.357480409945034283888121624828', '125.7272193408826110431194551323', '126.19653002129173714790155978977', '127.31825247347447769472205990753', '127.76297119127592933151500521618', '128.625926791920787468570705851219', '129.19518639203145575491793695730', '130.13296803534230158182150540485', '131.091370092357108311463887056893', '131.73931962749007757948431093216', '132.44499910021299933965784527404', '132.968713037269447268059453644658', '133.701447624415643784766887968363', '134.565113943113781261761461313230', '135.49670971879597960390683964106', '136.088799383339866350846860095388', '136.50725249933453455386702488031', '137.03078645566396249115735630501', '137.81111282059458604911595235956', '138.74027954043689553011443599170', '139.15062842828666396786797442674', '140.69447317365581306420996808335', '141.115235794025048347408777227914', '141.70887871067476669995618367488', '142.570597213994743492586354615762', '143.376780035721595303480871835977', '143.84738447077300422192004961580', '144.08968374762140134192829689922', '145.11754781231544619328682366101', '145.86868911050081746391925749969', '146.69581255330684372548081275213', '147.468846654520607137898083894951', '147.879264184022806913524335256378', '148.72170058050105106619488807163', '149.52262951269230529789566057627', '150.20770338205427597399345641361', '151.30592203593290710885216191023', '151.76536602730067359810091177031', '152.38096766496434307984462161115', '153.30030688498346023917723263980', '153.6110401477805612826070470449', '154.51356278457804833551161829579', '155.1303344054577467043236619898', '155.5775046267217837813474892831', '156.31486062244032241670459914941', '157.0695829477922049084316303305', '158.35565359932278177068252391173', '159.09798110564169595501747511253', '159.59858183966858868289534600258', '160.27677271775506190275560501936', '160.70285511513859909694447892406', '161.44676999645554210877771980322', '162.34436581571806367948577979685', '162.9614805911000941769791124761', '163.80087217082393804383840522840', '164.2407932274835189773346263862', '164.936672606606037128398239253', '165.67384482805582053818250975159', '166.223173928143521718216178127251', '167.36476899180578505625136319822', '167.8651991836689294610878336419', '168.573746010806244496938141245667', '169.772125399076200235442386988669', '170.21241174161131452478488853081', '170.776135115200691100821740254276', '171.36859987545934275575867142970', '172.03168978174696554162070105610', '172.64215846652127777317119821362', '173.084529511678576646355174643578', '174.09640111348022543489057303829', '175.121939397016643591557811416383', '175.44295725140187906233487261377', '176.26309288933930657021078687656', '177.37658964690967277528939588096', '177.71447959257930719924512030744', '178.461718521006891506406736382121', '179.15045358278639114799225263682', '179.64870195538896766245995064060', '180.67110244380922107739077223691', '181.15290724209273579232017263013', '181.872416708954570496618243010016', '182.78751160739983788745009440458', '183.035001420989070108230975619335', '183.568180862239835823720843484272', '184.244131168812421395280258690299', '185.58216320674457542820417322204', '186.27493373381651901039551367012', '187.06917097777263205642727870923', '187.85021606396981737247147427694', '187.94091361519063708891973818009', '188.72497823401273161147906476872', '189.65551593410875631170954437972', '190.17944436632199811556258000424', '190.56313062467885432111927301978', '191.64547697305283986718764823655', '192.04789994406415884259746128424', '192.925775006087078650042835199276', '193.74103708239852970579355504725', '194.52518095776139065337237504761', '194.958232119874175460526506580', '195.96756706523639317009130243073', '196.19423550244931650574310279312', '197.40478769053722636905280625387', '197.9740495195709904043710129101', '198.7494132349915079344231348184', '199.28702137247480423536925711192', '199.49823432636437518452322609502'], 'prelabel': '1-287-287.208-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': -0.6475915966705514, 'root_number': '-0.447236015814679255489468844139-0.894415980491299119364106757880*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.323795798335', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(24)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.333366772125669191162670571713+0.144691585823410221968786766922*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.79253259357', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.69788617618', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.99336802346', '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': '287.208', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/208'], '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': '1-287-287.208-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': '1-287-287.208-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': -0.3237957983352757, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79253259357', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_287.208', 'Lhash_array': ['dirichlet_L_287.208'], 'label': '1-287-287.208-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/208'}