Lfunction data - 1-33e2-1089.1055-r0-0-0

Formats: - HTML - YAML - JSON - 2024-05-17T00:06:11.202629

• 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_1089.1055', 'a10': [-0.8412535328311812, -0.5406408174555976], 'a2': [0.7237340381050702, 0.690079011482112], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.0475819158237423, 0.998867339183008], 'a5': [-0.9819286972627067, 0.18925124436041021], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5800569095711982, 0.8145759520503357], 'a8': [-0.6548607339452851, 0.7557495743542583], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 5.057294738687823, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [11, [1]]], 'bad_primes': [3, 11], 'central_character': '1089.1055', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 1089, 'conductor_radical': 33, 'conjugate': 'dirichlet_L_1089.32', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 0, 'a^16', 'a^31', 0, 'a^23', 'a^24', 0, 'a^39', 0, 0, 'a^49', 'a^31', 0, 'a^32', 'a^18', 0, 'a^15', 'a^47', 0, 0, 'a^43', 0, 'a^62', 'a^57', 0, 'a^39', 'a^26', 0, 'a^28', 'a^40', 0, 'a^26', 'a^54', 0, 'a^6', 'a^23', 0, 'a^55', 'a^52', 0, 'a^35', 0, 0, 'a^51', 'a^47', 0, 'a^46', 'a^4', 0, 'a^65', 'a^45', 0, 0, 'a^47', 0, 'a^34', 'a^25', 0, 'a^47', 'a^36', 0, 'a^48', 'a^14', 0, 'a^52', 'a^34', 0, 'a^62', 'a^15', 0, 'a^21', 'a^14', 0, 'a^31', 0, 0, 'a^53', 'a^63', 0, 'a^60', 'a^56', 0, 'a^49', 'a^43', 0, 0, 'a^51', 0, 'a^6', 'a^59', 0, 'a^55', 'a^46', 0, 'a^2', 'a^54', 0, 'a^12'], 'euler_factors': [[1, 'a^8'], [0], [1, 'a^31'], [1, 'a^23'], [0], [1, 'a^49'], [1, 'a^18'], [1, 'a^15'], [1, 'a^43'], [1, 'a^26'], [1, 'a^28'], [1, 'a^6'], [1, 'a^52'], [1, 'a^35'], [1, 'a^47'], [1, 'a^45'], [1, 'a^25'], [1, 'a^47'], [1, 'a^52'], [1, 'a^15'], [1, 'a^21'], [1, 'a^53'], [1, 'a^56'], [1, 'a^51'], [1, 'a^2'], [1, 'a^14']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-33e2-1089.1055-r0-0-0', 'leading_term': '-0.175872280015541986069431021851+0.198874138569011148632967291330*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/1089/1055', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.26548442867601707, -1.5860347592642017, -3.681737743919075, -5.836901420729663, -6.726987942795464, -5.47619963451925, -2.4472461343506655, 0.8146186814083811, 2.5894114415247738, 2.255076487098362, 0.7588096008837529, -0.22206279936366066, 0.22346420042434437, 1.4484485232723996, 1.9632956010659575, 1.0070323307653557, -0.6140770753250184, -1.3506706637449246, -0.5894086997959457, 0.6342499649004533, 0.7655629255579427, -0.47119633337085387, -1.6709752290650335, -1.344452287997231, 0.24284140674882698, 1.247148648106928, 0.47526933015830686, -0.8795837059989391, -0.31669769765798617, 2.933054463356699, 6.378691427942073, 6.435709445214214, 2.303773610897086, -2.757239128539354, -4.497310587021166, -1.9519450242091028, 1.7707991347930858, 3.0348097352414554, 1.4639375672802428, -0.28214225211371874, -0.14324201108186924, 0.9066624238744148, 0.5052808217170339, -1.7330819116686722, -3.5854903892512295, -3.084260517927452, -1.0269219210120868, 0.17714267492643734, -0.32414173636363064, -0.9767290422415537, -0.355627314542042, 0.6298652540384498, 0.15551318430694547, -1.4183121987127798, -1.451374642603957, 1.3781103663507814, 4.614281676380241, 4.623214966424186, 1.3721392603293876, -1.041666759442854, 0.619660900651759, 4.458505562257708, 5.674152489434192, 2.6936230550814946, -0.757065071552093, -0.4375249031780347, 3.0121973455045783, 5.0911469051872675, 3.3071089650972176, 0.025674791929623984, -1.1344943354843102, 0.006777359101535534, 0.7437299587660784, -0.1645906536063435, -0.9398473729756036, 0.014537775232745381, 1.393824195091502, 1.01568816056407, -0.6226848910575578, -0.94442884332539, 0.6867631398982558, 1.791249484563006, 0.5664855870981105, -1.0557685104869383, -0.12946319875254178, 2.559836173613883, 3.154638335100585, 0.46369626981955986, -1.6558798363571885, 0.5073373624318692, 4.755390171708259, 5.304240450865518, 0.5966333162660723, -4.227531912806393, -3.9001198533003714, 0.33599047392800746, 2.975405333850872, 1.7286671326571783, -0.3262653826419611, -0.08061888376270737, 1.331280460705676, 1.2340903352714667, -0.026668813535172503, -0.020477294988072325, 1.3136439710009882, 1.3202168681581974, -0.9069432910380869, -2.620147945560893, -1.4607793953833803, 0.8826421833011354, 1.3312624044017776, 0.14143580245728793, -0.01713603018496176, 0.928112171146721, 0.02552206112000618, -3.1343108626492335, -3.9970754227010143, 0.935086599389928, 7.888910680292454, 9.53247288222046, 4.466705195953592, -0.918824702703728, -1.0698059423577568, 1.9304813550343656, 2.6393544860778597, 0.3914122276599268, -0.8093659055226442, 0.666330088405277, 1.6869443529708872, -0.1057701388290884, -2.3235181136351457, -1.7577915690599748, 0.5390545194239956, 1.2466256617918992, 0.13213808791268442, -0.18462233796487892, 0.8126693963754663, 0.6819855549613101, -1.2773228200385613, -2.22966775246033, -0.5176877648663494, 1.1477247355173281, 0.13352665313678683, -1.1208966215935385, 1.3412009348528326, 5.80710360657436, 6.2294803416705005, 1.298990860144026, -2.726578407293259, -0.6863327492108043, 4.07644995521257, 4.871317902192702, 1.4020869698373866, -0.6980716700646259, 0.9608440846255137, 2.3758914566355833, 0.286364805846574, -2.5665054443325857, -2.214197864537621, 0.24403629781743852, 0.9928304747211321, -0.2521949609598535, -0.6699210631069861, 0.20527424808855183, 0.007547694284322202, -1.50271491279213, -1.5619893691844677, 0.3902168443299696, 0.9591219625366618, -1.5256084319781458, -3.4925484542956533, -1.5925896000912978, 1.597322971231128, 1.6792760453531783, -0.17579834628015018, 0.55225188762383, 3.0552938574451165, 1.1625890232032783, -6.549307372100969, -12.650677138281761, -10.518196341179447, -3.5268211536718774, 0.20464105516985504, -0.9780407836934493, -2.0039901421474178, -0.3156448280104483, 1.0369237279640173, -0.022828820247140464, -0.946614976957593, 0.2948234371330445, 1.3681873502313482, 0.062156506760055505, -1.3556466588461307, -0.07206100913653285, 2.104059187254938, 1.7904068052647033, -0.12159446233880317, -0.3997233600903278, 0.4192692248362476, -0.8078383613670548, -3.276619019487649, -2.7918497473012636, 0.48137040469563314, 1.096762802361698, -2.5129156063176117, -4.081214108155929, 1.0047740571358268, 7.403855061599314, 6.964296281467664, 0.739412866357051, -2.995571259375653, -1.1033816464904203, 1.3273185021150922, 0.48384056493836275, -0.8695371764343925, 0.1310555649946227, 1.1080355985658583, -0.5534861635748645, -2.3925855171055743, -1.194314925571052, 1.1346482142282976, 0.9120705611526777, -0.9510944294711396, -1.0168005195363257, 0.4237764396412849, 0.5320444268524236, -0.20685046037977448, 0.8945565601285168, 2.576334368366538, 0.9986042460313019, -2.5120442741753877, -1.9857595096378908, 3.1867630969891776, 5.758902216914422, 1.576070200718556, -3.5120575937306793, -2.7595001784888655, 1.1297056465398083, 1.418838879372299, -1.1718938868268625, -0.4113870792344304, 4.122551380522103, 6.106725567157719, 2.990078631710541, -0.38241114448317437, -0.31938325625019953, 0.5802774370232322, -0.44727958892240505, -1.36294212117287, -0.09336742139280324, 1.120779230633346, 0.23848835225730605, -0.3866441703513262, 1.3257581816046413, 2.627238384546332, 0.8449807287855657, -1.174553931003461, 0.05073096651748328, 1.9901899316990308, 0.5919124006820198, -1.7661604455800166, -0.19077532162410865, 3.057357876214618, 1.3132750842378844, -4.574203044874272, -6.1560258326093695, -0.7546084376703217, 3.9689925895432676, 2.228617305637633, -1.3454441262437704, -0.47819045428471063, 2.585833383162663, 2.2292160999232493, -0.725216056521854, -1.5639967131534993, -0.21098504005364233, -0.04062799588043368, -0.8599274780850625, -0.047999321533694565, 1.2164792656613495, -0.2794167692866741, -3.098874348301381, -2.9750990056678965, -0.42248313085186356, 0.23140953345471837, -1.2117413325425335, -0.9599951785110936, 0.9430217741397657, 0.6700348143470387, -1.068405379146908, 0.7020816159617624, 4.886173963171286, 3.4201612695692454, -5.531727055366799, -12.27210732464616, -9.077782004130498, -1.3321119043863225, 1.586445509726921, -0.2151617312162712, -0.7090044798847454, 0.53658222669317, -0.49875806974521003, -3.097349288255536, -2.88611258485367, -0.4076379136760405, -0.26328941761852653, -2.5658682932693315, -2.98337677564087, -0.8263861488348505, 0.34030984873664727, -0.0781661308201449, 0.7841000020442637, 2.553739406525712, 1.8569538454314984, -0.5453276352695915, -0.5170866694701288, 1.178321564313044, -0.37209424207343805, -4.328714561896924, -4.091980789279903, 0.7271630119555066, 2.035591288121415, -3.3011256286223762, -7.3782203254094005, -4.0486034245729385, 1.2096562376099373, 1.1429577693514987, -1.581836033052055, -0.7099945390984704, 2.204764217863132, 1.7310268808273448, -1.0702576304426268, -1.2570761600702336, 0.5743327464231933, 0.10792298357405834, -2.133582210247223, -2.162609446866529, -0.2855613998596683, 0.09655548800381497, -0.6685624989000232, -0.15214588926663053, 0.00827957707571402, -2.814257573755123, -5.4535793824277246, -3.2614277386780057, 1.1244263255684372, 1.7947634024695935, 0.014724039228035977, 1.2930638022260401, 4.062269314603991, 1.9673618178527992, -3.4061626223703954, -3.681307100824854, 1.6144749974040962, 3.27536043276179, -2.151581059222577, -6.567583573444743, -3.9659948977686867, 0.6901366795523037, 1.324976564903137, -0.027939927512069116, 0.39777883754528065, 0.9059562666811274, -0.4984516757142766, -1.0670412191567833, 0.8890338833009088, 1.7998170612947684, -0.4431969756560613, -2.119369206642913, -0.7415781917108077, 0.3094372233912471, -1.220667125294118, -2.0082711454740765, -0.3084945735934874, 0.12053062352972208, -1.8816264934748326, -1.227568404041151, 3.393491472259161, 4.842525840031445, -0.301321457802189, -4.046934493252881, 0.24084443123362892, 6.043922303936487, 4.295431421613657, -1.8637013154752002, -3.4806026397036205, -0.5803279127070176, 0.4223627944042865, -0.9095647283322463, -0.19721585981005213, 1.9265246454201104, 1.4341278132641972, -0.5326072358933636, -0.023217481610743173, 1.5889195533093665, 0.44856436578892234, -1.8273554178251972, -1.2725301609405124, 0.6368662252204775, 0.23608368578545308, -1.0144696705434628, -0.1998286404441084, 0.5502287695505923, -0.826398426245621, -0.11299689250771658, 5.4231005754623425, 8.935452253310967, 3.8374443393829516, -3.8654473771382163, -4.253788664037019, 0.6117103907697987, 1.5180065867531871, -1.6500358006361626, -1.4962275743324647, 2.192472730792425, 2.6571662906698448, -0.5178592961596241, -1.0051715543125386, 1.9535076946635024, 2.5947134499934106, -0.18571051879957923, -1.498880976237582, -0.13830847226786613, 0.3180984897308777, -0.48392439433174606, 0.18278818788226858, 1.185715087075002, -0.3867275054401684, -2.18537637264948, -0.4123444897413379, 2.1639569326744565, 0.9546812640579267, -1.4161476900394128, -0.30203004852974313, 1.2965240088492087, -1.2778734862860863, -3.675703232480087, 0.3626749429724988, 5.99430364443752, 4.220131942666526, -2.181146384219117, -3.1641513448207306, 1.3409085188679726, 2.5633837836394777, -0.9372784923178301, -2.08172599410848, 0.8108102733770135, 2.020255302539319, 0.03327275404957403, -0.7219358135414374, 0.5429226171805487, 0.3564312388201951, -0.8723707078194269, 0.10229188541870474, 1.826581656231104, 0.8595077968208208, -0.637400768230602, 1.0270372132648324, 3.0863574682757893, 1.355333547720364, -1.3330209606903185, -0.7351698476690953, 0.3715651458422659, -1.395389245702259, -2.041838086106398, 1.251302344072552, 1.4211824623563714, -6.9685136471522435, -15.222751197207572, -12.390815705275681, -2.7821765861899577, 1.542843007098643, -0.5288407286492554, -1.2964347651050265, 0.6385008280149828, 0.7908448026784458, -0.251284801624594, 1.2341092921978631, 3.1040042261615133, 1.2234540739316475, -1.8091855682992184, -1.4092732299105761, 0.4037312235352912, -0.19598648076783878, -1.1784916953493794, 0.2780797012591035, 1.539028237173016, 0.4488746564105395, 0.11743798575958342, 1.5381870429216191, 0.24098064211725473, -3.8696998236526134, -3.716564469871049, 1.958493537730286, 4.481049329063617, 0.48433079063588863, -1.5125019528194332, 3.090204259380271, 6.0237668980813215, 1.2584700663985657, -4.101005767889076, -2.914592069116354, 0.39046944818288326, 0.1251205891486439, -0.48474871789523805, 2.077833958831075, 3.7555294902410896, 1.4593060566782772, -0.5767710694213521, 0.6096651103952135, 1.412383474258645, -0.19788715868378295, -0.9026820583740036, 0.19101044860793479, -0.21879085900517126, -1.777431606559878, -0.9226837996341855, 0.6208670128794102, -1.4673714592931617, -4.228653876020206, -1.9274845513346475, 2.0690607726517305, 0.6412587542120978, -3.2526909382636053, -1.8862629508856, 2.1023041241317686, 0.7713935687861643, -3.071887462651482, -0.6719593528365874, 5.525250084603327, 5.562571777822877, -0.24959978401193664, -2.72370424837854, -0.2071356953101756, 0.9082558695721965, -0.6734929565133917, -0.7765253025376683, 0.4893117434913221, 0.2407410031129821, 0.25094653755073826, 2.8187836241273767, 4.357478198445463, 1.8992496110062862, -0.5117635365287638, 0.4199640014192684, 1.068617824358905, -0.8619958000304055, -1.3671001912972816, 0.7587199697504684, 0.6617631228861227, -1.868092704374242, -0.8689585626336672, 2.4932246468866484, -0.5369031605187558, -9.207529166516956, -11.411788896913157, -3.7650900027142824, 2.5379256071681415, 0.9183317658574879, -1.6885239087887816, -0.1514164618212398, 0.562181314978722, -2.372676342142219, -3.7805486604607026, -1.438213990041277, 0.16172722001673695, -0.24664205313016857, 0.884564938599997, 2.7916597670927956, 1.364281670436309, -1.63681326558565, -1.3667929390460873, 0.6978052159157169, 0.44122664675250245, -0.35350914804767425, 1.1360998542328598, 1.8421669148145328, -0.18076530885564443, -0.35056190792299385, 2.3029750574962646, 0.536600125114361, -6.861308385984985, -9.157502522682057, -1.4260471179526677, 5.680850585070145, 3.66442272486722, -0.711642486408142, 0.21952539055638406, 2.220924283143583, 0.41868580069548866, -0.8339215494347602, 1.5175869113679474, 2.1511587097522984, -1.5057061945771961, -3.647094569457356, -1.3578169422420268, 0.5648235799006547, -0.258474772453954, -0.5660806839200773, 0.07062904138450003, -1.0776441621823107, -2.344143668186227, -0.6891248982226289, 0.7044148734105589, -1.6007090006325704, -3.204326550853206, -0.15571445737368605, 2.477987979289248, 0.668802242040007, 0.004003561199871207, 3.773556626834721, 4.553679550718935, -1.4749572613120099, -5.221867316657564, -0.7864381664266599, 3.3140428429222344, 0.0024427780834668927, -3.824958656711636, -1.2856097188137623, 2.342350783009581, 1.3256399648985573, -0.4053860025477351, 0.7912492550175583, 1.2155631768678488, -0.9265067212907654, -1.5398384519241146, 0.17675096704923782, 0.3044076743191836, -0.8446517470987381, 0.21585884253048987, 1.626233684330525, -0.03389406902801371, -1.4077069803438347, 1.2278063513797595, 3.490176409057458, 1.2828362044400234, -0.8798482362781405, 0.3854462501177249, 0.30862094003315477, -2.2542627610449277, 0.30285116621957503], 'positive_zeros': ['2.10119669923722142477570042073', '3.3186451499946911991247582647', '3.67627293836824878182545733424', '4.87720216490247533868024410309', '5.76387483721851693663706069490', '6.464804870684530030650345284917', '7.45475563483261640507626799727', '8.222129175681129806686578612580', '8.79369070139897638128456586819', '10.13212955218727194582924813426', '11.09101377327418926597732608088', '12.11190399443829482450707657933', '12.5424855739986760807610455913', '13.212686359646901648289915151768', '14.58947024124036322824101345602', '14.88205320772991720668795426041', '15.71948963830489480311688837694', '16.28418159356396734270798410441', '17.06434077944782095362882312444', '18.254035833049768572820372749294', '18.69014651647889044344475371536', '19.90738461820879814390895872206', '20.36238886057863313979069890155', '21.565564007718910384197662309257', '22.186001123208075802617693190063', '22.77217593271658147887372851172', '23.434654786247373633974591451026', '24.2536987569211136177908718134', '24.88872270363231823095478579047', '25.71200385126113763389769616961', '26.26684833047257628895118470923', '27.232218643266450409716501895765', '27.77220553461954485582731325461', '28.781382937935976477750688639535', '29.6635450035940477260628529673', '30.55237910497017175941037653870', '30.95583575949960574483368161286', '31.86651642361961961631361061160', '32.19384241803768838471569838968', '33.01626152541216610390155306104', '33.93263832913781005984671847645', '34.73429210973639267494808170333', '35.00690619021154690414389243375', '35.628238326642717781710611034870', '36.52073751449208415165398427512', '37.737137750966498132309627617300', '38.24171623480483019278717938689', '39.11571749617476959970998625839', '39.58097165716317134743606958371', '40.30024037846823230652387354252', '41.17130478899934888610202235175', '41.913868387910602585086124825947', '42.26132840512773383832889435817', '42.93878543024209364575698188330', '43.81907766276117355270097656642', '44.39638357332573211727891578429', '44.890254418206272114778443249106', '46.00952389579326297370923323568', '46.60714933417764575736129286522', '47.63703308249275823770552176269', '47.99788836680244957327445683082', '48.776686049489891438782802829603', '49.652870558755860577436554409197', '50.25417187680299071827427888748', '50.86242222202478286243768999076', '51.25198915521672827661577111645', '52.12812172397473373603130359735', '52.65294024574077552178336813681', '53.57720275885599702060803245568', '54.33323568681028043550746265085', '54.60409411604934779291918720613', '55.372542705657288263271297705904', '56.822739777184804977777745743646', '57.024437836806163817154890613494', '57.857833134724788905184248416961', '58.43311707950140209228630605577', '59.010745493723696529185050653848', '59.69702712182471951216031821851', '60.32179611946614354358224858872', '61.225340487114984748156057886702', '61.69112586145284385010756030001', '62.06552583821814602459673293875', '63.07643619447658275823659674014', '63.55663374894098468277498581906', '64.33142323228054501315105057108', '65.35031396573500743753285459673', '66.0449059872892015964430474438', '66.64200458259215483463687801867', '67.16332569109411757162924800223', '67.74148728068886881962059108480', '68.57965229393594076109082766320', '69.20992309415070435005040033860', '69.90120081177426892472203897815', '70.49499370641948911044658617281', '70.76503327609753558205305327345', '71.64740208662979586243318553136', '72.32220366967593777960215353312', '73.20431583058714303722394876341', '73.96045023107016064828936971677', '74.540336744954862048411063757817', '75.035248813982369656079866001544', '76.192373454850675276232663983706', '76.639755221038212770610190741880', '77.09691401190516912263815368187', '77.828243440422467606491857496577', '78.492884059487984618036537770540', '78.860667294397422598201099912403', '79.78494755725410677554629303412', '80.30607618589558258969828817002', '81.00048584210707226336601084525', '81.57908455148151821327073347887', '82.26274891239144427059959859446', '83.16044022416545942226388428085', '83.91756161590396703838311355753', '84.42168029818269712775152319307', '85.23108655068972216010865848782', '86.003307492698494041957091434302', '86.23310505033833713364276080338', '86.88403758577562519614907368113', '87.46888176254725054220625204380', '88.50654993312400038492697657229', '88.81254735044389665054074514190', '89.52670609584687055128946337430', '90.10520515464737531576923519134', '90.56562608712485118493282868651', '91.387855993705058861615667197017', '92.57461642106311750692816714127', '93.09208286803524131958729689035', '93.60124656331785118415829418739', '93.994016203363917190100549928157', '95.08411571603163261731340977758', '95.25211101504561349652280953801', '96.392406728218318669536818758705', '96.80485505082669260082214224380', '96.99771227275713516794287181459', '98.04204251907058738202088699443', '98.524587311174702779925829145124', '99.02938064936822185136366772763', '99.95267143715374268653499171206', '100.46203428486272961086338555812', '101.46821606140555735337389409017', '101.993792801751569942785189735655', '102.57128340178597500417126601417', '103.30911106631807373911692351053', '103.95179741044932621535394423980', '104.39135889078058900667941717509', '105.380951348811414541113178949881', '105.66512103488277012048387675860', '106.29983812983515530318902583763', '106.56451173450370057178806726782', '107.718694730243006308005555522207', '108.44312747313552509383431207902', '108.55702346588694331253964383466', '109.486380062208019815984293156705', '110.22187786106510775691120505254', '110.8371363512030230265532093582', '111.81318769966217128580442259268', '112.487735624002324217098726400317', '112.68228597752418470984449962291', '113.34798499914336761024954075770', '113.94345436143805135887395216448', '114.638973027805349233715208254835', '115.44269453792774522114137872328', '115.7301462167146879915857337432', '116.62031507691534648581227952104', '116.90180577477046902412704575498', '117.59642431150289015268176100138', '118.422704032363437270578914615018', '119.05174240812358266098220226579', '119.897966217599704649608022755622', '120.69876453556314615953842848431', '121.04455577257092891379148769388', '121.59049011419228910235862877093', '122.39387053858142302583209157715', '122.81646147842732949679921670990', '123.49148950411459646504943558338', '124.24788699317268941320232603726', '124.7344513369149670330370240324', '125.35489517931450579764487057683', '125.77919619599590690660557036205', '126.2599265766602574486012041934', '127.32659162757726185638287283435', '128.08133954914473281582269682264', '128.59139775602948273909818905330', '129.19369172808131841594668777214', '129.94690865867408343829421649562', '130.43214641368007012586540845536', '131.23011965514373694660663532541', '131.90585342365173773854691675275', '132.30638424300688044611298613633', '132.77199502394591697483104033261', '133.38905462450074400180304808088', '134.10227636287607466861617790834', '134.789056099668492577346657484901', '135.35011534657901913307387889218', '135.830829741468752687890728625223', '136.54520768878573583619399862786', '137.385539713870308632828861971616', '138.03491271698988488348250239196', '138.6725400431641031643316452887', '139.296679886064517283289728806704', '140.00497265764717688317052410880', '140.49511859418364947288061333155', '141.01590906698148199418691853832', '141.54691631670300001168044962674', '142.31756971215140438489646731208', '142.687177836443079891775937239625', '143.567485883770935123381709469601', '144.194194910686449890978313413554', '144.48841005160574672088982808157', '145.20892064249103399290926079974', '145.70456410227368945334826809259', '146.99999439544038939966177685788', '147.439080987798349721446110770641', '148.02230579664329333268370140536', '148.62658174683372118196248743805', '148.877243456044413893332204864935', '149.79491704314652921247472847396', '150.52646972517053418162417733010', '150.89697695140907411376421542075', '151.52130631849448022720054816919', '152.31851843350610027497368274024', '152.45536836304424723035810427002', '153.145561783638550475582825322954', '153.96272803059182640172800154219', '154.72006915326432718725482807396', '155.138945681545683080381012249415', '155.99421904958632813143969278759', '156.81808572914519548835402783634', '157.21332841003418564481044178254', '157.59220757303760850006400512136', '158.60146394929351368168015636303', '158.95798680569412070040112496796', '159.65445305508434165495536223873', '160.25295687106381516251306720596', '160.57818298080328945984821540871', '161.38702134705222881778838287045', '161.72745275844201089029622757178', '162.62716103075812014834435489505', '163.171283855414037437294175815352', '163.87987977192997640690339655990', '164.42970802253579283205107104942', '165.03399665463543927747238097626', '165.92355454159796666757300455808', '166.58609882497579555032270675655', '167.06402591492046259236017890929', '167.67424045394626870588653339472', '168.23627234327933454051606016844', '168.35453231140827694837087439563', '169.57335354233087207013091759308', '169.922429589249685136107628409387', '170.50488946807571833954520721841', '171.14203340950234434194768830017', '171.645907453381574316418535824139', '172.259856287804665257968021534', '172.788973322945964385861696432647', '173.89126289483961267907139372744', '174.45106992236956971274581532730', '175.02078503090822490523743024506', '175.397109989636080089094531141213', '176.471977440070604301979049523350', '176.71569719933345801636559859547', '177.03224273228863117832958188330', '177.939609054988753661882293361299', '178.62473800768176750725014877286', '179.167865362174523434159044643472', '179.49537231518009525004939232527', '180.28599233654154323321070427190', '180.673224570448629436509633732495', '181.27810424873370997346814998420', '182.23318963206238154331062947290', '183.046053206954317184725884684683', '183.41317140945250128112479235495', '184.11270124904076716191851227826', '184.51908330488353459507040663106', '185.202097103160849936164894937', '186.09644797218906316140058934640', '186.49631442129307649883683312738', '187.10771305095498941006223983042', '187.2627950375527994874124685693', '188.21488334482016952915938813813', '188.5820354087365975350431719033', '189.386689093327343637640477323419', '190.092036129753975075629603583981', '190.31188476108127552098417252646', '191.18512610309957984208617245467', '191.91390512510367671915522955746', '192.50013930780431548677029922315', '193.21100943703960493941115303588', '193.92987298657388164725501142033', '194.23003538236933777844944055173', '194.877650908879449196515939010744', '195.590311806722220076671874966322', '196.01061966618681312086920761941', '196.52923415876821470556873360110', '197.18338777851986203692230243448', '197.705356526963081064285482361867', '198.56590928145705627602765561818', '198.99465583987207098595723600292', '199.41601765718971236646525667747', '199.98551765289987340305051560364'], 'prelabel': '1-33e2-1089.1055-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.057294738687823, 'root_angle': -0.5390266299357209, 'root_number': '-0.122298832766499374247459715680-0.992493322649554060471637020956*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.269513314968', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.735728386307797233578340819110+0.550366244745299810676735937896*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.10119669924', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.31864514999', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.67627293837', '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': 5.057294738687823, 'bad_primes': [3, 11], 'central_character': '1089.1055', 'conductor': 1089, 'conductor_radical': 33, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1089/1055'], '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': '1-33e2-1089.1055-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': '1-33e2-1089.1055-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.057294738687823, 'root_angle': -0.26951331496786046, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.10119669924', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_1089.1055', 'Lhash_array': ['dirichlet_L_1089.1055'], 'label': '1-33e2-1089.1055-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1089/1055'}