Lfunction data - 1-1305-1305.727-r0-0-0

Formats: - HTML - YAML - JSON - 2026-07-15T11:49:52.026385

• 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
  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_1305.727', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.9555728057861407, -0.2947551744109042], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.8262387743159949, -0.5633200580636221], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5633200580636221, 0.8262387743159949], 'a8': [0.6234898018587335, -0.7818314824680298], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 6.060394521568052, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [29, [1]]], 'bad_primes': [3, 5, 29], 'central_character': '1305.727', 'coeff_info': ['x^84 - 1', '0.997203797181180 + 0.0747300935864243*I', '\\\\zeta_{84}'], 'conductor': 1305, 'conductor_radical': 435, 'conjugate': 'dirichlet_L_1305.508', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^80', 0, 'a^76', 0, 0, 'a^29', 'a^72', 0, 0, 'a^47', 0, 'a^61', 'a^25', 0, 'a^68', 'a^0', 0, 'a^69', 0, 0, 'a^43', 'a^67', 0, 0, 'a^57', 0, 'a^21', 0, 0, 'a^31', 'a^64', 0, 'a^80', 0, 0, 'a^30', 'a^65', 0, 0, 'a^49', 0, 'a^74', 'a^39', 0, 'a^63', 'a^26', 0, 'a^58', 0, 0, 'a^53', 'a^3', 0, 0, 'a^17', 0, 0, 'a^70', 0, 'a^71', 'a^27', 0, 'a^60', 0, 0, 'a^79', 'a^76', 0, 0, 'a^54', 0, 'a^60', 'a^26', 0, 'a^61', 'a^76', 0, 'a^65', 0, 0, 'a^45', 'a^83', 0, 0, 'a^70', 0, 'a^35', 'a^45', 0, 'a^6', 'a^59', 0, 'a^22', 0, 0, 'a^62', 'a^54', 0, 0], 'euler_factors': [[1, 'a^80'], [0], [0], [1, 'a^29'], [1, 'a^47'], [1, 'a^61'], [1, 'a^0'], [1, 'a^69'], [1, 'a^67'], [0], [1, 'a^31'], [1, 'a^30'], [1, 'a^49'], [1, 'a^74'], [1, 'a^26'], [1, 'a^3'], [1, 'a^70'], [1, 'a^71'], [1, 'a^79'], [1, 'a^54'], [1, 'a^60'], [1, 'a^65'], [1, 'a^83'], [1, 'a^45'], [1, 'a^62'], [1, 'a^11']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1305-1305.727-r0-0-0', 'leading_term': '1.68472970395390808846194160782-1.70927827690738500433028804643*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/1305/727', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.3999888339932127, 1.586205548044151, 0.1964248360254769, -1.703560489724671, -3.056218773081481, -2.9298099305576937, -1.427483016044113, 0.30329330974505225, 1.020726364574545, 0.5069084039360254, -0.22581100098912849, 0.04682885322346211, 1.4487542703379708, 2.7742534992416945, 2.7093292790285135, 1.2889624816761058, -0.051126926503914434, -0.042266739503380654, 0.9110259548447963, 1.1247555883953708, -0.29854067836211096, -2.080466333082292, -1.9522139086974377, 0.5997376368727033, 3.2004906739502257, 2.8061327886694376, -0.8282414789359415, -4.401480876954119, -4.2973382030056735, -0.4716021756410903, 3.4078236560712374, 3.8944944616679678, 1.3759648394424633, -0.7314234329768847, -0.12252623670383739, 1.9106010502420117, 2.4726555586214802, 0.7941351339726757, -1.0427596984503766, -1.0609098097330882, 0.0769527530021753, 0.29512122898522186, -0.7882515618855166, -1.3170114637964567, -0.006210308351111433, 1.7407084742368135, 1.6083027773320655, -0.32103472089199575, -1.5286470507247634, -0.6143766262269164, 0.5810215632278852, -0.3379062559275556, -2.34884904777717, -1.716948573054007, 2.833530599161277, 7.395495414779058, 6.987907212480177, 1.7388571579819776, -2.983021111694254, -2.9895490657496575, -0.042284494839834985, 1.0805337481531316, -1.0102555454963429, -3.043059966187836, -2.144237505091814, 0.228985396722366, 0.7898725798102799, -0.7599393754675151, -1.678023604219473, -0.5474980954935245, 0.7588586542624598, 0.3078157011779893, -0.7694552702222939, -0.22492195262959558, 1.4580196668472292, 1.632976765049149, -0.19415685344888514, -1.221873769862375, 0.3880614139215209, 2.3662604592203, 1.6596490924721163, -0.5130960175271623, -0.05956349443752346, 3.462938155696695, 5.065343545347038, 0.9430636781448051, -5.544965305782929, -7.5836756904140525, -3.6614265232357526, 0.780116917795476, 0.9153952810236111, -1.595292879292666, -2.263986614227785, -0.6333996155623478, -0.09775111689973828, -1.9169703581791158, -3.263881470479842, -2.0118266997609635, -0.15331400683056703, -0.4173993783956089, -1.891400637234947, -1.8079111594355695, -0.2424322267699751, 0.28420106578427035, -0.48860166362935487, 0.14369379458247314, 2.9422942755006956, 4.553777370267044, 2.4692772313481965, -0.6344330936884292, -0.8464080350923759, 0.5002797646515353, -1.330962131238505, -6.340589059532051, -8.306775810181648, -3.4265683896024566, 3.544992683204106, 5.367966807743469, 1.957280101732568, -0.4901617838653247, 1.0826097936453698, 3.060011432558246, 1.863490592348401, -0.582990758001266, -0.8057347509272638, 0.39396443394628977, -0.07098260957854052, -1.8805421319363929, -1.9348550158201294, 0.052490497883165385, 0.9289481429905126, -0.4860509764829494, -1.4949007088808297, -0.4402877408414136, 0.3799827382333586, -0.835586656346598, -1.5716590024786634, 0.7198387851244692, 3.2486749980604532, 1.5926094912623017, -2.602478734458181, -3.1587417638044433, 1.060702181591059, 3.8429130527630737, 1.1408971765974392, -2.3653402570289352, -0.4095367891273432, 5.079592069453414, 6.909674749655402, 3.3267530979577606, -0.2969519601964655, -0.33153101018060976, 0.5936570489564491, -0.418915908831438, -1.487553302401489, -0.13864625032554376, 1.695407573671345, 1.0087887501542843, -0.8987188459821784, -0.8269534097977795, 0.5855961636000163, 0.27250000554294584, -1.3510572618226253, -1.002744615842983, 1.2380416860712835, 1.7085958854376742, -0.09339595589089325, -0.20945090227385205, 2.27170941700516, 2.1661511632908277, -3.4419954839141784, -8.808235930878723, -7.102976143320545, -0.8691186217246676, 1.7232115119592257, -0.8001345218271227, -1.9843620031000364, 1.3862405176555106, 4.426178668442685, 2.8155822978751894, -0.3308779402792224, -0.33962521207584, 1.520225319427728, 1.4199639950703304, -0.03839830633132373, 0.2664965448190225, 1.7257787152578277, 1.3709839705225373, -0.11406778630038841, 0.5098842237066945, 2.7044340635042823, 2.6897762930199214, 0.2595036979803119, -0.8168488604707012, 0.1830633279285353, -0.2726586275941631, -2.59472490483672, -2.1455126807280793, 2.189101829559264, 4.075070992681945, -0.6407459332733076, -6.05790973728866, -4.518151637394137, 1.5097730440669592, 3.4817867618973763, 0.049623696065469486, -2.1351797125154652, -0.15212837318578715, 1.3093521895871991, -0.7929385455574157, -2.7350414634640403, -1.2932995791143496, 0.6653575407863603, -0.08876232908538582, -1.491309889630619, -0.7333625065337661, 0.38743347255247584, -0.5456688205825481, -1.4848394551455644, 0.0876850760039488, 1.8724594061399125, 0.8934191490169052, -0.531796669359278, 1.086306706511265, 3.4398802903068, 2.2774808971250504, -0.4096333808276517, 0.2342669654365607, 2.1171923951845297, -1.330693283604144, -8.876771205259189, -11.156458708906253, -4.83033683578369, 1.9214209646595313, 1.9347370936594526, -1.1772144548326957, -1.0805961197417635, 0.9128115160217032, 0.36029220215744834, -1.310961275960182, -0.00937864560709079, 2.8241631092802533, 2.761217198727733, 0.36725279795217464, -0.41029239630126974, 0.3885169155513627, -0.15908421652292104, -1.2805953485852613, 0.006136589094852006, 2.3182874221284058, 1.872519557150866, -0.17539858048948745, 0.3537025994581988, 2.444322986068083, 1.5558769014325913, -1.0443267724410592, 0.4645951603145918, 5.315296929794105, 5.912316161920805, 0.8789661137692378, -1.5454254520136521, 2.8858959122794685, 6.963559056180703, 3.915513168898524, -1.7868925588758227, -2.6410266276549716, 0.06513546229871826, 0.6021632388889001, -0.8258244124523556, -0.44078349000485645, 0.7628174299861218, -0.6425410659584009, -3.028869627993119, -2.378535523910332, 0.13372591355485713, 0.48918671760037036, -0.7481977013994688, -0.43128528768938673, 0.38091392606783425, -1.0696283034693164, -2.6176997186568096, -0.7793376991340965, 1.6432836555484944, -0.1361841373893043, -3.500371549691846, -2.536254199620671, 0.6051471795400245, -1.155983802960208, -6.404342038171715, -6.327209029765557, 0.10998602866691501, 3.710008547528393, 0.17311085048476288, -3.549464344944136, -1.8818289759280482, 0.9352587077098424, 0.11035266557041262, -1.478027061875823, -0.2220928380511356, 1.2376648913832475, -0.007939910288837723, -1.3085513301853295, -0.25665615206017184, 0.3065361716825457, -1.6461332520071454, -2.7512516212732243, -0.7544926077080074, 0.9292828485275836, -0.09812307596839058, -0.8300329064905598, 0.22753772618608695, -0.6494383674981051, -4.143225717239742, -4.240800590327368, 1.1794041014542578, 4.761966692838633, 1.7461055734711532, -1.138117760489415, 2.7651899185717994, 8.01702003150305, 6.448592158728852, 1.1246398330650922, 0.14363638272582227, 2.556468374035433, 1.7221109265212315, -1.9147167411212676, -2.525558007198548, -0.03673844014768928, 0.7880970866348276, -0.2610531461208034, 0.1742216410268357, 1.236979159016714, -0.09727015456995661, -1.8953629164064931, -0.5417715532236241, 1.872353965741719, 1.3804666855625505, -0.2722430214780923, 0.26886640104620935, 0.7127030755071245, -1.7916792763207257, -3.4405197005511416, -0.6151169773576975, 1.6802718640216439, -1.7770302679592618, -5.371239393115932, -1.3272200205237046, 5.826588895143249, 5.9133542295650745, -0.020747961186651384, -2.474897853327789, 0.06222665782281901, 0.6749092411067871, -1.9872694616123905, -2.3261631131277722, 0.38598425319123736, 0.9093086776891769, -1.422793047857252, -1.9504323863849506, -0.14232744322121565, 0.12919964556463764, -1.1147185905430976, -0.7097073069508673, 0.21171382395736174, -1.4595700680344117, -3.421683487455194, -1.7949099342184096, 0.817614478761628, 0.007560024041008405, -1.8131156651236937, -0.6625486355361836, 0.3577310140030948, -2.2216979212290555, -2.8856972298355563, 3.8870523079024295, 11.149273558352489, 8.807057157483877, 0.33452775292598946, -3.0977763583798175, -0.6464371072422487, -0.2377929782517984, -2.8354710476900573, -2.3248937492053963, 1.3703431434486109, 2.3483516381099956, 0.25720303787869536, -0.08876230360157371, 1.2231586693961072, 0.3014452228351428, -1.7349604815368718, -0.9938791945741092, 1.067071165163016, 0.8196750708961777, -0.1238562654584442, 0.9111238259406182, 1.1972909719511935, -1.5003841869503445, -2.8465778027801876, 0.10588213583756444, 2.259298450558789, -0.06776171887420054, -1.7146039772895831, 0.6847593501863726, 0.6573906487721993, -5.7059606630481206, -9.845983609165055, -4.3868247631869615, 3.3764458177131944, 3.3790511394529372, -1.2785677018050565, -2.1010953107594657, 0.06709531342891303, -0.12798317929123668, -1.1511508637390973, 0.741120518732783, 2.7051687138809277, 1.100018938510312, -0.9249191299240527, 0.09214522902258218, 1.249808800742844, -0.03423979517976258, -0.7145420760036237, 0.8021403355503034, 0.9968799474893002, -0.8227808255791551, -0.47434265399937575, 1.8954155309231255, 1.206854962905841, -1.6716561696535146, -0.419005028349099, 3.7919522911770573, 3.2498223446778916, -1.1240153132394315, -0.3486135103728785, 5.37613963500683, 5.796048411008419, -0.8785880751952402, -4.622863314290177, -1.482982049994681, 0.8888117774453193, -1.4428124223106793, -2.8412998022524265, -0.547189559443747, 0.8491512123816638, -0.22332993756895503, 0.0031911542165374293, 1.450276184402614, 0.24570109118724895, -2.3556672151083786, -1.896702295122315, 0.2878365281665416, 0.10181838858955869, -0.8484752628921708, 0.568464988221331, 1.649352167271588, -0.10363682174717052, -0.62565672617558, 2.095435566269721, 2.0132160354334654, -3.314833449768924, -5.770817491491148, -0.9242837075641817, 2.743972704459695, -1.041571499781173, -4.845080183489307, -1.8067720275054298, 1.7085253527708992, -1.1036852091476221, -4.78551174030416, -2.704176581388632, 1.066036410488107, 0.9571677873696083, -0.23902741384063259, 0.7857648870711202, 1.0385183175232462, -0.9802011724373947, -1.2787595917069017, 1.0187095750745772, 1.5783754703008936, -0.00798590326330785, 0.26914399945084777, 1.6692223202639658, 0.153721502302352, -2.357945239317352, -1.5013633911696007, 0.10652532372663337, -1.5899994158716888, -2.7486120445444375, 0.11526773349702454, 0.32434456685476065, -7.258111525440862, -13.72296440848583, -9.519417716757433, -0.9122175132160026, 1.2930523674566272, -0.56548485992837, 1.0216191634589302, 3.4188229370982595, 0.890386040379645, -2.7159896573080764, -1.5118424831076058, 1.3074494773670455, 0.843005656940228, -0.3623045409550533, 0.6683863240091578, 1.0706546558109202, -0.44287234087254357, -0.19759868237855718, 1.9744740539608496, 1.6801112539270333, -0.5150096925384812, 0.1294444630804348, 2.3992576948700783, 1.6180530512472624, -0.2535345691438666, 0.6839661325771369, 0.46844388865203324, -4.748333474790912, -8.098586264305103, -3.378504730755479, 1.753231371140871, -1.3219539946130903, -6.056486426225776, -2.7692768747374394, 3.7387611431545356, 3.9030755858459307, 0.20724380048126434, -0.1681348973146619, 0.9655544684629503, -0.5549611679199861, -1.3755338112730924, 1.538778476094831, 3.5874849165658804, 1.6243007906250455, -0.22281908470807937, 0.39108693483984147, 0.27657755722140087, -0.8223074957106518, 0.36057470827523586, 2.0448724220515757, 0.08620862930225429, -2.647612234997794, -1.4199295520555537, 0.48433998692840585, -1.1503343430948823, -1.945456933235163, 1.5050767597162906, 2.6531026419870942, -2.071227971969196, -3.648975188879009, 3.4210425611935897, 9.128246318093296, 4.973510275560013, -1.4143268386729466, -1.0742718058431926, 1.5916543914560404, 0.34587270363257494, -1.2527090269048091, 0.2713269975571575, 0.7285869162139642, -1.7332098551348685, -2.289516116724626, 0.08297669273240953, 0.6155809253451853, -0.9194498768735104, -0.3634766188332597, 1.3170316771765438, 0.575527606771169, -0.3768751034697426, 1.2209373443207299, 1.650258778956331, -1.2123678023591005, -2.112207634081496, 0.6327044017717538, 0.5193391903741982, -3.3645145511042083, -2.7664136030350104, 3.0909759300904627, 4.363941211599608, -0.33873796898331765, -0.47783299206820135, 5.956009825422777, 8.111928860796304, 2.5868686445285944, -1.337160432759715, 0.21649633130897517, 0.876459305371637, -1.325896379928109, -1.5409011158749126, 0.16342247741255497, -0.24325762463359707, -0.967689747695312, 1.4142190719879089, 3.4754434643105188, 1.6465749791480278, -0.39094400383221567, 0.28478827856174305, 0.33232318986787995, -1.2120154080488832, -0.6044321090910885, 0.8863828576946258, -1.611834244727643, -4.953153823542102, -2.6613421807207835, 1.2782233949474695, -0.4467822003942344, -2.9560809234008674, 1.629223530503661, 7.10362425788188, 3.7696005089767626, -2.8959705471680612, -2.4675874163438087, 1.6721906577125825, 1.0723741014912866, -1.4069892643347877, 0.34370738871990175, 2.834554383608677, 1.4348047777005506, -0.1656214893308572, 1.1091745204403964, 1.6042617963338137, 0.08589275718745626, 0.27872153714474074, 1.4974250648236143, -0.3191189567928045, -2.888913873103095, -1.5836684976731903, 0.8260344215451739, 0.185452148984443, -0.6206235011790391, 0.39940858641493326, -1.1170791108912574, -4.563676987551494, -1.9071450421660145, 5.934757551269705, 7.361147522070208, 0.7601642792845295, -2.3150653772043905, 1.0278665721930045, 0.9365856115294545, -4.453205585097814], 'positive_zeros': ['0.65907447006668571710706445659', '2.123506684482410055472180419567', '3.00102644848795122886364395136', '3.42150516779018395148769441623', '4.98031809967993219020566934493', '5.33040275691857759701812761778', '6.20186254302615065865192161349', '7.127377297432594789409681251668', '8.06494389034481814005792374587', '9.094499824129360900735853362642', '10.163509419016455898607062348998', '10.64566504425790032481890898733', '11.67603003865298614293972713069', '12.47621195445708625922111029036', '12.92115341554118618703645802219', '13.75098935640127828921731175495', '14.6394091945465117482386612927', '15.436559542060271020521448072667', '15.880422624366761481502339084077', '16.70484828218926171840309873038', '17.90543380638140836367356850072', '18.754876100740674533876210890987', '19.25807261750413782568678134390', '20.27669004569326994204082683155', '20.80556747598305461502449476318', '21.66487231929765087121037453645', '22.26401201508038391244525071899', '22.8568176844279183705877453863', '23.720256657359688450952128551557', '24.324282370569426614085944749684', '25.22427479628245306953209182899', '25.63239745540292224642605884661', '26.60703134031944230576877206917', '27.735886480888587155701020487805', '28.244503253957817297036720717506', '29.24097246058870128857663975688', '29.32650049806322812923059169643', '30.6891872625756839495970706750', '30.79940632349767726619414509621', '31.93367273701421081241646256722', '32.31461626402522578731921474544', '32.78878039486222414621183641597', '33.9806796866669588508291178764', '34.54259789360558284507965766580', '34.87030556318071609160570079181', '36.07974370783811656568268475572', '37.06355576776829943010477229466', '37.35903492673430100260314388691', '38.34677643938817801893365950991', '38.94518389919922926209382612146', '39.36072853072695671089448738167', '40.30433131983412057776515639641', '40.85372802764531943591724642897', '41.66058067041435503790864338785', '42.021533334997191190366994966529', '42.74235731403050413500506011802', '43.55411470467458553418567249183', '44.30709250826746038630503051904', '45.07968780123759118284981527798', '45.65063538751385233022305634114', '46.831772052936123365602690917748', '47.26885893043517802018284412609', '47.73069012358385386936381423630', '48.45665540077314043243205003664', '49.2141225978045697803816392385', '49.85894839219973004446525853637', '50.36609238892752997639366374574', '51.08133417120773992263152946655', '51.857980288442153227173122086847', '52.223104174032730119418034319933', '52.96190225561222957082575928639', '54.115134105819416466866045415762', '54.609398388778448312292962729792', '55.21210487687054522951582584697', '56.2036008662823837320078824622', '56.620979324238440028537169161113', '57.48755764274061820515026142069', '57.74382612876968255723393838387', '58.71315983983947613680717696996', '58.96343631930772491570155182928', '60.03589504099340923179064279053', '60.56859202485711691684497631961', '60.887245954629135758394125996369', '61.730758036139362165717171316291', '62.469920683911742180144909612316', '63.355095477375107792807803690319', '64.06637317604564724575876056194', '64.704892481356393125019477250236', '65.22744023385048062978182331937', '66.104776831346111954379746834980', '66.54667177343790330957002359708', '67.34062839218036432027753459280', '67.6972210207797438828210023652', '68.42609507501107784679220536250', '69.20609135360660071723664647752', '69.550722638403540610832369575817', '70.55740781677601957120349985932', '70.905193973483948575400962735599', '71.49461472797612328691184973535', '72.69496275503401086086559790187', '73.305258094257928880291691863526', '73.902753649073446220135196008851', '74.43115951951748294514496878033', '75.00102301030728650913331263545', '75.99922909668217767018574698455', '76.407362349766978389345743406769', '76.83761462646038947944001993714', '77.4992315956265356755777135294', '78.3987166584085618215685853930', '78.6906429487314425276034346200', '79.54018119057985075599040985887', '79.963247518856330276701490549546', '80.99223332773641326516396521824', '81.40217683990029480726106700054', '82.38628041111496778519326727607', '83.116232432813224048421991547356', '83.56702213532021862382673442977', '84.15104101322469089544080845041', '84.60538817862722060682520596916', '85.603729931285033677307041191475', '86.05721127282099908746625547721', '86.67507892184080040840130722477', '87.01910187860520680895866664807', '87.889055517770772083592226559377', '88.42590880729223402572662155871', '89.29033331729358765946541990590', '89.59877291911018255071941466136', '90.61990611283988069280413340325', '91.26031592211770838470586119355', '92.048086549071440002299575513576', '92.515842785725866628194878619513', '93.15684564766163877152256249260', '93.748774569808671790758289315798', '94.42991358979797507433117820406', '94.7650678318905352132955009576', '95.71883316232222891313217774247', '96.23082207510967685610117819672', '96.80625227476757945044386410867', '97.09774247350739630738535140526', '98.065841587878481017658723945', '98.874537639524416190622223734029', '99.21689224880476498120540773994', '100.43565507578580584142868920918', '100.5975443254775308481307177250', '101.39589617084289520855912480778', '102.1925190564875373377892483996', '102.72472129749309039464706024654', '103.08279674742548833946964046769', '103.736981032859117383586058364745', '104.43508323310448302544381181794', '105.23289981451669237455254700456', '105.5582895386788409520603229452', '106.06230524260721423842735812472', '106.92442145268555942823656344884', '107.38809571560084403511925957225', '108.178697077152048378921905286910', '109.061335795583693405031456984188', '109.680342705274684349696378339712', '110.09415188701573661390046396201', '110.89141721214278722777038031673', '111.38479183408785594023722366887', '112.21744887463139706657557519862', '112.5360715890479049360058414441', '113.29675341784879867329724530582', '113.53345270732515874564399619426', '114.557900086851827043332599531348', '115.00103876411269108895623960927', '115.72966676720589459485607653101', '116.01458934725278600380083678577', '116.73174181112021946237412160228', '117.82694292897920763241181268798', '118.53745887713584177427066832533', '118.704619495796433226408606821889', '119.57054322524773559968441342697', '120.36043429827794918156593284417', '120.64798364041343546045921530986', '121.2908968586443238874844561774', '122.00826683010978239796631660374', '122.71275498744363524555230422813', '122.90675573291969338212452103341', '123.60147270952650189864204441604', '124.36630100357895793032444371991', '124.99352108219520109826227302523', '125.55174268830849658027210747531', '125.98595278495382062016299803899', '127.029640987442734420960831383625', '127.71862598577357067818176268413', '128.42391626034990704350843510315', '128.72198332100652980330087812282', '129.29199687287666268564423307809', '130.12807036241282896990463329940', '130.60998112314888774016430580494', '131.24378999384012710755860538471', '131.7307184085791534541680518499', '132.35899241475696949015322645753', '132.8762618519293903805030700633', '133.55780720960585125016535113747', '134.09442481952344297890521577806', '134.90843358990191288728865907892', '135.335084231606326436836706254361', '136.21196396741432534226994670914', '136.99576788852509809756909428038', '137.35246989742574490835864501897', '138.19175189576682194633434297461', '138.69012162372464294447952177854', '139.06181527180917086673402391674', '139.715008314626970116089491923385', '140.568793532968241411586209297889', '140.960756280400658742790940003382', '141.47633494732741173890389984381', '142.17239559955462582698386565440', '142.59191513916085189479041376579', '143.26224496608847785937754756423', '144.10990587398446005286327279900', '144.63032664560953615551743696032', '145.42693960730886494065972028860', '145.86432125728103047426797980041', '146.76057582491188930768277242506', '147.37887543271778845681122415206', '147.63500566486888593115213385546', '148.29781414924261009086139600635', '148.93197464236558368330434185267', '149.68540117875777660922034020744', '149.9399275618506351661440417067', '150.64114800824472996776520459826', '151.49498001402804422169162627292', '151.63557203780046280961005727664', '152.48900858940270734678843786867', '152.835923375234879810603559172931', '154.11255149384626098876470471731', '154.569820149736424754720019657944', '154.89108910144162857889423632303', '155.68656782871686648657491120804', '156.39216000098115410998411561265', '157.033608525972060666139330263958', '157.35448429117411239875290661343', '158.03422715332814584761815035838', '158.469259948088721981769974724745', '159.28429694930398202489882341423', '159.66980537426499042356277539427', '160.54697285118716980011250599205', '160.801378635346225569917234129320', '161.293527761975391652926156298199', '162.3468271698688082392659989561', '162.74063209613975257865211554915', '163.55684778646951788021232712505', '164.40135843368995384058317489352', '164.7225439245172339902110588547', '165.234148457267245802534106111302', '165.80330554779150111615820300440', '166.78933173518793908397014677451', '167.057962968898905290769523082949', '167.56877992604349139219970501844', '168.07415612854953980774962662716', '168.75778585390922608964945344432', '169.55019457524962601479550723025', '169.84648579851000362983565901336', '170.509525674802878622898943254661', '171.132639163595812372191370904075', '171.75233051475455929834660168099', '172.71722231784294008062268795795', '173.22665868934942944313655641100', '173.79215403115690643107604462086', '174.33325419945463987480650728301', '174.799074526519361470802195272016', '175.61339299931694895114298318050', '176.06260926108407186482775287102', '176.6202743273425374106152891661', '177.29971064306787647145364108439', '177.61694301331530986134377755884', '178.32011077810251819818656258220', '178.99222931425021317587214731605', '179.42378859784202106918631818749', '180.153353118013817466971573420234', '180.91343670067389215048761102770', '181.28144820561110640852695678470', '182.332596546222035336064107531730', '182.783856860009864919682888900407', '183.26229833927085924903405101400', '184.020082009710138659187369070978', '184.31848674311171471973910017667', '184.856827503005642461344478801239', '185.8298280619070957225517731318', '186.17324986086166512049163420533', '186.63428571619720870309965293773', '187.27869549580325439186296479520', '187.67784745628764377728281961790', '188.61366531673359548143280029554', '189.02639936590641074276783525942', '189.61399364744841833507067069547', '190.46917519931610559669394641602', '191.10583139236722681608512903298', '191.66933270815642051057896048341', '192.15511807908562121499056918878', '193.03095293435605794518597705346', '193.21987499575764623323077616014', '194.08651794936940236733037532327', '194.30549077212609430279272962945', '194.9682850549406661325659088290', '195.79601994526957592035582502994', '196.28649959310428508275419553318', '196.75073165971618287634439544940', '197.06543889701437672097982423080', '197.89190608300924835978267705596', '198.7865018555261669464246909067', '199.289629668224546749737690537257', '199.75248351589588257828497063794'], 'prelabel': '1-1305-1305.727-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.060394521568052, 'root_angle': -0.24769773163560826, 'root_number': '0.0144650742713918030122079659581-0.999895375340001819582181400567*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.252302268364', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(84)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.59516013169707873416773299353-0.577143800867347617682019021467*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.659074470067', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.12350668448', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.00102644849', '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': 6.060394521568052, 'bad_primes': [3, 5, 29], 'central_character': '1305.727', 'conductor': 1305, 'conductor_radical': 435, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1305/727'], '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': '1-1305-1305.727-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': '1-1305-1305.727-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.060394521568052, 'root_angle': -0.24769773163560826, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.659074470067', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_1305.727', 'Lhash_array': ['dirichlet_L_1305.727'], 'factors': ['1-1305-1305.727-r0-0-0'], 'label': '1-1305-1305.727-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1305/727'}