Lfunction data - 1-4760-4760.1549-r0-0-0

Formats: - HTML - YAML - JSON - 2025-02-14T02:14:46.572264

• 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_4760.1549', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.25881904510252074, 0.9659258262890683], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.8660254037844386, 0.5], 'algebraic': True, 'analytic_conductor': 22.105347067175426, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1]], [17, [1]]], 'bad_primes': [2, 5, 7, 17], 'central_character': '4760.1549', 'coeff_info': ['x^24 - 1', '0.965925826289068 + 0.258819045102521*I', '\\\\zeta_{24}'], 'conductor': 4760, 'conductor_radical': 1190, 'conjugate': 'dirichlet_L_4760.3749', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^29', 0, 0, 0, 0, 0, 'a^10', 0, 'a^23', 0, 'a^12', 0, 0, 0, 0, 0, 'a^34', 0, 0, 0, 'a^7', 0, 0, 0, 'a^15', 0, 'a^21', 0, 'a^5', 0, 'a^4', 0, 0, 0, 'a^13', 0, 'a^17', 0, 'a^15', 0, 'a^18', 0, 0, 0, 'a^16', 0, 0, 0, 0, 0, 'a^14', 0, 0, 0, 'a^15', 0, 'a^14', 0, 'a^19', 0, 0, 0, 0, 0, 'a^32', 0, 'a^12', 0, 'a^21', 0, 'a^5', 0, 0, 0, 0, 0, 'a^19', 0, 'a^20', 0, 'a^30', 0, 0, 0, 'a^2', 0, 'a^4', 0, 0, 0, 'a^34', 0, 0, 0, 'a^21', 0, 'a^33', 0], 'euler_factors': [[0], [1, 'a^29'], [0], [0], [1, 'a^23'], [1, 'a^12'], [0], [1, 'a^34'], [1, 'a^7'], [1, 'a^21'], [1, 'a^5'], [1, 'a^13'], [1, 'a^15'], [1, 'a^18'], [1, 'a^16'], [1, 'a^14'], [1, 'a^14'], [1, 'a^19'], [1, 'a^32'], [1, 'a^21'], [1, 'a^5'], [1, 'a^19'], [1, 'a^30'], [1, 'a^4'], [1, 'a^21'], [1, 'a^20']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-4760-4760.1549-r0-0-0', 'leading_term': '0.479434184584400747792589847258-0.361508277136955961282884313447*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/4760/1549', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.6004543044950541, -0.7926563771858802, -2.8759869211979154, -4.343681360638596, -3.550792043192779, -0.7751242978144629, 1.551737029690839, 1.262419797112723, -1.0522606629095095, -2.6245279545133706, -1.806031104808277, -0.04528146132545527, 0.16590566428228828, -1.236086837314505, -1.8519540472294442, -0.4707728416768254, 0.8596913244266758, -0.2444778619706804, -2.580313008607363, -2.5909262273789015, 0.3692644407090106, 2.4526825252194073, 0.4674732733091205, -3.3034663118852956, -3.966328586473717, -0.8271092516981391, 1.7921974679299404, 0.9491313515965695, -0.978342178203052, -0.5721845607842062, 1.237774786764502, 1.2506355612963633, -0.29700995667257457, -0.20370473613055862, 1.8169349088508584, 2.1780810962597066, -0.4289759390769921, -2.2390115280003857, -0.501119577909829, 1.3782085557822608, -1.0444972532086403, -5.5876049133333225, -6.146109505403679, -2.0069566315555165, 1.2196368131546746, 0.4455629381148121, -0.8934499606746865, 0.357168578315532, 1.8265534018545546, 0.7041855287856053, -0.7217509012075617, 0.6622410900341296, 2.748344352331962, 1.900398570415463, -0.22453521316263841, 0.25246613859457917, 1.6032227259761787, -1.1441099115762219, -6.708229792829395, -8.08844871502832, -3.5334643814656195, 0.5922226190672488, 0.1263285397968104, -1.129101226558499, 0.563916142488481, 2.2466936738221004, 0.5443747366851166, -1.719842682088244, -0.9452833980691229, 0.6158241951582406, -0.24627477461166067, -1.1819900948008157, 0.725868210473583, 2.2319458294601047, -0.3805831324913447, -3.2093707421484385, -0.6412165183708657, 4.257168923590537, 4.2704935181472115, 0.172517630045062, -1.219580805500406, 0.8166323146011896, 0.7345924547416325, -2.2463448688987224, -3.062926805867958, -0.7917017512153507, 0.07191249276146258, -1.2742250619140267, -1.0826040523081664, 0.3244881350501063, -1.1865634472757196, -4.299749608283476, -3.3910689421583236, 0.5370910217291966, 0.690362271612599, -2.9795941098706793, -3.2853789249536423, 0.8758839929156547, 2.3586714825812365, -1.097041194444583, -3.208011081545262, -1.0966669391704922, 0.4644154258329274, -0.6733888030967977, -0.6150013371137721, 1.3456470388743837, 0.9606308426446151, -1.6233343386625154, -1.5784734574707926, 0.5076807134813092, -0.5039585233307224, -3.114531915617187, -0.9678703461844648, 4.270855944396125, 4.657844137891388, 0.44741424048414324, -0.4089595283869813, 3.006451492578803, 3.783725116768566, 0.7777968767353459, -0.302821614981754, 1.216376943564462, 0.7953194076566251, -0.9525966253919718, 0.07520657769679959, 1.9090089570618622, 0.29941511896141637, -1.8972949359661881, -0.5220403471399898, 0.40089742667712286, -3.464914206327063, -6.594685600378208, -3.1971363735704244, 1.192981236235983, -0.3452270541596342, -3.5428237165882552, -1.9691660649184515, 0.9516989683971205, 0.02102600121090372, -1.6383016401510693, -0.46428868615995955, 0.03779456516715868, -2.106683370938746, -2.4269305720663072, 0.06346415625180399, 0.16829492996224116, -2.163541148559391, -1.2179767453843908, 1.6915549165738508, -0.3984918031236028, -5.426970459207344, -4.808892187772096, 0.20468664161076935, 0.8423107577475416, -2.6893786904242916, -3.0215642386449586, -0.31873525120285806, 0.10946772678931284, -0.29230589838945126, 2.186995951782669, 4.027605666303835, 1.6613391349572124, -0.6585301342958687, -0.050667163124646065, -0.8568867403631604, -3.667642897604353, -2.2734654708474675, 2.5674964312276902, 2.0434755986074764, -3.9156651200583363, -5.634730138472292, -1.5573280969397993, 0.36762217027401534, -0.9661725846177583, 0.3498822949927962, 3.2552575470873686, 2.2576927854888544, -0.398898936367376, 0.13886783156198648, 1.132583614276729, -0.45991772155567767, -0.6602103598391729, 1.6896873493413156, 0.8237666972744673, -2.976354063044644, -1.9165604439538184, 3.2611967711495886, 3.3120522173634717, -1.5854376358391296, -2.5544124516584605, 0.2652452353525152, -0.45067727720848816, -3.2916457970279507, -2.0005028788397317, 0.8944310968904781, 0.1839200591077684, -1.1586506602055686, 0.042117226586972936, 0.07081265028266137, -1.6497036338867224, 0.13448625996106295, 3.8872238951921507, 2.486866972583515, -1.762898359483116, -1.2395554610179427, 0.9042855432443095, -2.534132728127809, -6.721037198204333, -3.9149436396688304, 0.9786011494364544, 0.6352112110662049, -1.1934277212844255, 0.02721276584832807, 0.41620380825739633, -1.5151566740859255, -0.8824625784347326, 1.7429068792411901, 1.1393964302274944, -0.36761929794301884, 1.8471208146333409, 3.2168030854417533, -0.2662536771265705, -1.7966622363699865, 2.2633988527017608, 3.3809509122643977, -2.063041391010406, -4.986213576537455, -1.73209724695364, 0.005213121244996134, -1.921161183037457, -1.6105947895441006, 0.41396848854389806, -0.6149057356675605, -1.8505026670924887, 0.3537937339083449, 1.477250213773268, -0.6276236740098392, -0.44397671710202435, 1.9128479834533154, 0.01867571900444371, -3.3038190341712244, -0.1366065158281979, 5.024667499664086, 3.0832612531623584, -1.4739372009351566, -0.3369107595169556, 2.3122357111921605, 0.6883787073158623, -0.5687868304945836, 1.5661293171161335, 1.8739111338060048, -0.24302092973994488, 0.30867498613904476, 1.6722933751603368, -0.5529105727970238, -2.1666676238903158, 0.0675936250692908, -0.009616458678026761, -3.7087224537540244, -2.5784096793036335, 3.291914689485358, 3.6280490834515278, -1.326220584039767, -1.7097563611795659, 1.7901966377266847, 1.4368614493452407, -0.767350935648605, 0.160907592204398, 0.423006536554715, -2.276874853483724, -2.4080756798463367, 0.4556274786476945, 0.5682864896695652, -0.5773570062903517, 1.2175652049849959, 1.140878451432465, -3.5995178034295363, -4.302443265895912, 2.0672864951920635, 5.069017895031548, 1.2353840273447778, -0.2679470049089355, 2.235047768956681, 1.3599298735077165, -1.6131440643238277, -0.4869095912814812, 1.3730605136069987, -0.5492310063570968, -1.7628779556282415, -0.21001960132457315, -0.6442862220805041, -1.7876489767774686, 1.107963425480284, 3.2269782661862756, -0.1821172974996783, -1.5640349634553454, 3.408026803542663, 5.428219020530296, 0.7935960378604854, -1.2797671952592649, 1.1714314091022509, 0.16975230222623972, -3.315166505459378, -2.1647865228871543, 0.75592215118266, 0.048525538871976415, -0.7162968845228077, 0.4365241054880994, -0.8295151149013098, -2.507486635207273, 0.7598828382363219, 3.895432145104708, 1.1425061464812427, -1.0220543607921497, 1.249911060555202, -0.1204740460986343, -6.1071638893518365, -6.154748842136585, -0.01736726071994096, 1.912130001703839, -0.34485474325672316, 0.19555686481488566, 1.2269516149348278, -0.8537093894748944, -1.3181161153518364, 0.7812176688013657, -0.133896853465801, -2.1605301516067117, -0.06148261722660988, 1.6011903201943356, -0.8502933184860874, -0.5449522182409697, 3.4577434955335105, 1.6679644130448872, -4.757697364458633, -4.574578694594816, 0.607965268970551, 0.8605435229685715, -1.5668364642646802, -0.37251230128575774, 0.45525632262173144, -1.6446997840217732, -1.1341159738076096, 1.4962198949608931, 0.5294782019342902, -1.150113232825092, 0.456963846332502, 0.22159071654391552, -2.825916118705681, -1.3870345847030012, 2.1248105511730317, -1.4832461738963731, -7.272646975207226, -5.070214643200166, -0.24591892671721596, -1.0073057276229753, -1.9446772353813815, 0.9811900299903212, 1.4361483480888517, -1.1519749188577213, -0.6020285026142915, 1.0212365830478067, -0.49167968738633827, -0.6920156587891507, 1.721833051368744, 0.6883810800468866, -1.7926402752581045, 0.6853479775961036, 2.532588789558464, -2.1283819632105616, -4.437828749823343, 0.8942368246618088, 3.776172014503447, 0.26659051529184336, -0.7741416342766774, 1.5595533906301204, 0.5432275001566651, -1.1831356075175232, 0.8759779557478378, 1.7498796423399199, -0.29199986477145773, 0.452108636156378, 2.4912032287524357, 0.9194743278602044, 0.3068119964897961, 2.907440759029991, 0.5831806381315612, -6.128340282736854, -5.802683152087464, 0.2395053684993179, 0.9976101347809448, -1.145892674370909, 1.285571720632909, 3.0287855249195266, -0.4143945352310292, -2.1060031799926, -0.04637650052484801, -0.04884407845390887, -0.5371428872814893, 2.1236568075946076, 2.8691435350951773, 0.2759979415201953, 0.5736985757569811, 1.321903757280268, -3.881020437488173, -7.935452831425076, -3.6577850555300917, 0.08923758865190351, -2.425714861016111, -2.490276643232276, 1.582417433593304, 0.8958884456006516, -2.9669449640220313, -2.134760693169128, 0.18292784503780296, -0.4928224986870759, -0.029791511887573827, 1.3325713220580062, -1.075763657593037, -2.75599880606726, 0.5004906761947223, 1.512790879400903, -1.789914478037487, -1.2662499864230337, 1.1458795415740275, -3.0078560342982352, -7.377037334452666, -2.918517283409765, 2.41891503853663, 0.9406088751938403, -0.5677804054385617, 1.0049196415176562, 0.0377198844880386, -1.709033159875875, -0.0094669603271093, 0.1808762937075784, -2.721155684139499, -2.1652733085867464, 0.3615167501181318, -0.9582781223219319, -1.2540528076863862, 2.3058485620495937, 0.6114284842245931, -6.452430514429868, -6.663431275478735, -1.0110057078923544, -0.8099385121389012, -3.5456156881580934, -1.564040628117414, 0.5968090485070845, -0.3391082891384032, 1.1335869738281512, 3.5900059547436682, 1.3382503787135696, -1.2000602268151694, -0.0724308258860232, -0.40053576866339347, -1.4163689412972944, 2.245646316842683, 4.162847222909186, -1.472687505066266, -4.581080921922371, 0.007685320125766076, 1.5359988070769992, -2.3700756265406806, -2.0366738760246554, 1.312277890923563, 0.46289198766697914, -0.33526613252822807, 2.465453253470974, 2.5801889049295808, -0.2183091970487417, -0.2890605180148136, -0.5712994717325198, -3.4451500639898, -2.5832328216986777, 0.7400967849421908, -1.47097789837554, -4.216821515843995, -0.04186291043455476, 2.5152384950792324, -2.263847094167358, -4.005933577727383, 0.39133556733053776, 1.272586250151836, -1.0969485972514632, 0.0636452503628114, 0.936303357168646, -1.5971782940187396, -1.4673569341598665, 0.9725094182040233, 0.0813267427248492, -0.6539176125400347, 1.160644229154114, -0.988654694386891, -5.0209282910223845, -2.0890877183438543, 2.1578286576005783, -0.993342282492456, -3.4302650754982826, 0.9197868250579713, 2.508999680781763, -1.1578867427101314, -1.1221615132343035, 1.33181640107902, -0.2286854324741798, -1.449649628806, 0.42078249735122314, -0.21297935185898698, -1.9444901019514114, -0.13216799966501272, 0.12843167146958398, -2.7285911355076213, -0.9657320105013852, 2.7225069676477367, -0.6191156319786333, -4.471337126334621, -0.6829041592607745, 2.03572270801368, -1.234460595154973, -1.0436827688268708, 3.1512631719120225, 2.4287021813507663, -0.5855670620790983, 0.1327449931380852, 0.4327197730833044, -0.6434667796616013, 1.4926451798081206, 2.5959142178047823, -1.1795786487231645, -2.3631180760917636, 0.40843788719678176, -0.555625356379056, -1.713817202942063, 3.342186984317323, 5.35124764121686, -1.2167536987608956, -4.443821260816311, -0.34472643036897704, 0.8699715172502873, -1.1554248526060444, -0.07265962851570658, 0.3282503236531218, -2.1063871194794594, -1.3259941890067128, 0.8166257228819971, -1.1973207086958115, -2.2679638184351725, 0.18139628623722487, -0.3792931353383586, -1.5223803549822486, 3.009206058333345, 4.9047878408861685, -1.4032210506007887, -3.904893136553416, 1.5960972444762056, 3.4100136525272386, 0.2213870312865062, -0.012955804345553696, -0.21413015450343237, -3.542381248527755, -3.3014993864619218, 0.19119278394845277, 0.11052163762692299, -0.5120564105255643, 1.520747797801288, 0.7166859356606838, -1.215031002901204, 1.7004473829775868, 2.2832012251765343, -4.304580867358668, -6.371891562655096, -0.4278478961042028, 1.5356937802619433, -0.9056347562414833, 1.0481424540508393, 3.055352893801048, -0.13544783889606368, -1.306472886850827, 1.117981940055107, 0.4732327891758349, -0.9608033995139725, 0.29937211046273327, -0.8518354037161963, -3.142631988831155, -0.5029473764550765, 1.0978009320042434, -2.8815790687022815, -2.9720567290134436, 1.7534062553038003, 0.1716531317750459, -4.452754369857406, -1.6654756441827097, 2.236476282450746, 0.010895936924911866, -1.1025134497271425, 0.9495670008779602, -0.248258317663402, -1.6815034791163148, 0.7540373494638981, 1.342280234310956, -0.2008643582210892, 1.3163302924591609, 1.1818700708662737, -3.1402865349243543, -2.558005542853741, 2.182394823023132, 0.8782574033246191, -1.519509911303901, 3.379954741833789, 6.334087277725803, 1.4134132034137916, -1.279587445650165, 0.3473952695737083, -1.1097183224124985, -2.550037112456682, 0.0723325855637851, 0.7835441360846662, -0.5073930754496841, 1.3822244913579078, 1.9450442265602605, -1.139062995522715, -0.5835329590939258, 1.2776432632378993, -3.1068451896720863, -6.002588616245007, -1.1022023904503992, 0.784410367664818, -3.271370225478106, -2.3007315045010293, 1.8905351638454035, 0.17784020806640818, -2.256393039727685, -0.19334245197050315, 0.43510474632837326, -0.34613813269721616, 1.5825037040014225, 1.1588068332352905, -2.4984339512186198, -1.6726260987795063, 0.9828861280505606], 'positive_zeros': ['0.156650588727731560560388166026', '1.644708044237540223468223834713', '2.3693671016130372280575564614', '3.44880074583953836323492337942', '3.80087792812307916888651586607', '4.76685079988833927629852722809', '5.27744304663824431952574879654', '6.21597702210377349023229117892', '6.91321907705601700786350188933', '7.88396187140543288158855319429', '8.57098277259237611072726355106', '9.159011398170656727244508747492', '9.933186893576065583847815507015', '10.35213059681203390411363953625', '11.20665764287824267502607902905', '11.93130090389543097177564847130', '12.42012651250208350433708017125', '13.586329981356605776276112436263', '14.134288166285138509496312988869', '14.63286576431102683828721872143', '15.42357244523053107452552065837', '15.84807753213833136160306995949', '16.825430628796114475285300112242', '17.14029712712123256856132876750', '17.73573558097533000816842936342', '18.98679138045541572770146274495', '19.39561233536661662728058946410', '19.93042814066917354302116073614', '20.683786342263979008654939233723', '21.40016446854759230477128979590', '21.82848150519523746245540574556', '22.41420521783209893545568053534', '23.09471723653467965530839955385', '23.78857894533623717546049057114', '24.70237010529932943389820677860', '25.19622677200486400465162857806', '25.71334134870826853449110264438', '26.70507720012180953372923155785', '26.90166869738912299501875543984', '27.7073750044193071813898010406', '27.97927737977006893878426263493', '29.01207931862493506565463422875', '29.443206823965451001617375663693', '30.24953649043282477068096626705', '30.85471903722986692810187912764', '31.70481039284226963997545447645', '32.04129644832806135772252264748', '32.60233687252785415490691030703', '33.24115766112851735172968457761', '33.96690136242458832984531907635', '34.31517974671133460993909807520', '35.057575909421226866116038399769', '35.97839667755918985094335710712', '36.30005916553798111468915864284', '37.28745053339142804038202084222', '37.577340851100155316189755543733', '38.24682788132140543486621855113', '38.7399838867317525300564446533', '39.40630278881245871369609764520', '40.07169977663882029595001882839', '40.3724996434884236587639006881', '41.44054820950810490940154134041', '41.846500337974491796676322371410', '42.676092192450561458940058708050', '43.12779759005289052624008409446', '43.84596190230006669573009589878', '44.07201493649646720781869822241', '44.990876990915354925936635079150', '45.33785273366889578858214557215', '46.049941108865015996347848592658', '46.53672102966826329720744344195', '47.48436882546195415718217627949', '47.89580129642873716414839519123', '48.80489144949142468572840952765', '49.09897056608135658514519987645', '49.44245722583761353539713506621', '50.48404457069538251597326525979', '50.959530303411952863071048478798', '51.09407064636708809587801990716', '52.01606725811946788359743041828', '52.61557760946920439480399283430', '53.58651141089703491401356755137', '53.8528394903905226417582168202', '54.338651135233951866968013532975', '55.2419087573536047660501496607', '55.59976796580726329970268631963', '56.17639451057116576689724364943', '56.65787549467615903449867498103', '57.25546397911879048527675162177', '57.92775187003812393152530803118', '58.64673095492622031541866959979', '59.33680173672203668771775076706', '59.63601780901937179378273992965', '60.498178640869743342635226074162', '60.965169890943429183507146831573', '61.55344461200220854503272099631', '61.88880201291148402457016135237', '62.48933105349466412073390648802', '63.29008504600194079764969960506', '63.877866794133951909611320343552', '64.21041527507186780465470655558', '65.225173816008397483206075439770', '65.704049567940696762681203529730', '66.245205984948800736385323247446', '66.63997120239006949803535822776', '67.284470819050135499294433828', '67.97935568715733607509519026020', '68.23160391545209144350121894234', '69.04261447275546721075412500143', '69.538057450712633221424737677371', '70.20980927584205739745644659015', '71.14455970364089373931272984050', '71.251893864204219863565327495772', '72.09396899878198571136065506429', '72.40731683825639657253511895138', '73.08608310856978922387882883854', '73.662273678534370233777285633202', '74.117630993805935444405969746382', '74.68889503906939262557451435396', '75.31946372934527798936217816356', '76.1199396761463710597578740390', '76.592245434415976234638172667961', '77.2727384620401950119606520147', '77.61277045887764703949579678468', '78.390134148993033499292066829589', '78.69932378408691360253833659287', '79.320785968239423504788873564315', '79.99121839654119731415342458623', '80.31145361357003849948665445518', '81.07417840106613080004470002873', '81.785717071001356867167496622965', '82.3334600226234655554276844059', '82.98038995822458984005188121903', '83.408421775571737405990571033863', '83.813007403583577640443086665960', '84.62999295391299544162566574925', '85.1043756289441843403548914313', '85.46048453226705917516246055030', '86.02894021303957423214593889876', '86.78375537130194225412290699447', '87.61149088906336216859508709850', '87.85688632642115174035960856520', '88.55963096075469344686244596440', '89.11620259526421585020468575947', '89.62476282591364210982371143990', '90.387724673054242608290622209667', '90.46531979128088267840547353186', '91.16371067004104076586820889976', '91.861726816184121855626638521767', '92.31276958384151395525519067763', '93.17807888821504537657385060941', '93.60705869767137780320270886431', '94.07701347586474823948134200519', '94.88599328876147617277927109734', '95.32107913726433671671139843963', '95.80807924032618866790791282060', '96.139604351630249433758722297237', '96.825768242714718190125329625', '97.59285433573631171135995283991', '97.97626157010840511146708100279', '98.4299005167027607935355674888', '99.37600144061716807076522282813', '99.940998947768527408442320109133', '100.28023153135092161010667013003', '100.831445168888340528451053988006', '101.435358400600498959861703902948', '101.859158725030850161999526937611', '102.505833885644003992328255881022', '103.03134003950895256901296257605', '103.48333081416888689965446577932', '104.14268661629174283893579084706', '104.95429421741636896591883691718', '105.40524763417091847002889889753', '105.99189538495572975950409495559', '106.33534077129468595892178114025', '106.99451541452185431038122620984', '107.56405218075073791837680152795', '108.05521140720245310964221085248', '108.46253924057001199523618241154', '109.1595157031096254657529652488', '109.615793195609693429466029090823', '110.66937103922335867372077623333', '110.78086477125639133553025552260', '111.46742556646473201983308543745', '112.04019648655598318242927942658', '112.580677308136441146340182354274', '113.05122158680199086443947507984', '113.53003266941823039660870598209', '114.12776156804830075354095716636', '114.63411515779200832070793087618', '115.198416643167593027916135023211', '115.893665943940430235701458984162', '116.58555951860809735303360244864', '116.97841058491382295717995680967', '117.56269222031667315424315472630', '118.026178687740373614467898824873', '118.69657324105197628211108655888', '119.00201131372148051156996903992', '119.86725280858773851874159773295', '119.914324531060609540767993047526', '120.65333707711043098784194694964', '121.546743383943361666068005902989', '121.9868599148089015989065008318', '122.3903740221740000360495875202', '123.09336401820263974478983870586', '123.75857825615153207802576751527', '124.05078388924575819619113526599', '124.465775423334582855362713408135', '125.3675667735102867746057388346', '125.51648312613900763671327130198', '126.05555829755567303191389963420', '127.14135877644342414297580224136', '127.234591615645980614569121416632', '127.99642249158318285543655193646', '128.50446799099715401828304341304', '129.32007879020396653795241359641', '129.55084633810488216867706027500', '130.00499291030600252282629260938', '130.52820499548374949538375739457', '131.2094047953796405414375399768', '131.71142999794495325528363261751', '132.30372916873046061177388157708', '132.64991161810138418996711019899', '133.568569789210581631963970479602', '134.16625479490507590457813930726', '134.501503499408551223519687352131', '135.00465754846911330639365667048', '135.62637002642968692300463609429', '135.96165011743638202182965673305', '136.79680024829260637682590404708', '137.0538802479868104250426719733', '137.6179869180901650221165704013', '138.154808708742639491857250790343', '139.18675329743907180284821736820', '139.25327330361576132658368950799', '140.15783306210216022377307441889', '140.52007533133049863012935412598', '140.80311035407348548440512201983', '141.677239665226580865799489765947', '142.205407444416518785137003151637', '142.42089611803186750579027206201', '142.975006803910069148093825181745', '143.68359222794114408481289711977', '144.37452851557989849357731235532', '144.819326904062276981827418090721', '145.47864463289100850385248324728', '146.00367195186996727767724396354', '146.3044345901515374638923721053', '147.15447650358304185318508542771', '147.63786884991501915275016590498', '147.65521180182410132694489142235', '148.64774663624295136158872597429', '148.94944193694833104701737718011', '149.68981282646169592875023289976', '150.18941672694645012875732389402', '150.90882448891762768484992348906', '151.39808733813163577183388331188', '151.86662595988714048861920034410', '152.32057254236807979069974444871', '152.976828207952880196766779128996', '153.45000503386735204055318678380', '153.86551401866004116210956958957', '154.30434173459870213818795778009', '155.11190099757836229088468207169', '155.56408931476809647834711858287', '156.19434950288439846486777104808', '156.775994233475252640777571383939', '157.30364914935573539624104105958', '157.78649761818375539909655868040', '158.363845595236980614429372413148', '158.72079275411517010830924436306', '159.39297073534994731758192694979', '159.70425092724264806639521231342', '160.37559689071668386420221450871', '160.904578523536952985826816299111', '161.602452418906949453162051423342', '162.08425619026461096291158445715', '162.57768117445883490603640526095', '163.34449985027491562082486468423', '163.72424392561183228281738331374', '164.15691274921836967980513853123', '164.52693342969090862014600176323', '165.22716656610323661997955037251', '165.87929349765112739604208143660', '166.18616333109722795904762772946', '166.7017885938642403682519825219', '167.44973643358515506419941203645', '168.1518145385156855759997269267', '168.558549291573046206036246137479', '169.07400110778655285318273401422', '169.42549456285197577325248581799', '170.14385309073584584173781387146', '170.49784779049704261632399356748', '171.222052433608265280087096856251', '171.51092108431758841378630828834', '172.01701427910009365676845569673', '172.75199404212788066928895850755', '173.35533020112035469781923574967', '174.09429058254166933074053838380', '174.37856554472820490182805271387', '174.65580228906528218486917919580', '175.60060204873273309496688092039', '175.95848216148547902715057076544', '176.344343303489617798517596270114', '176.95246092582747080979549677934', '177.36451701738129184785625883275', '177.94120120279974285485780562297', '178.77387930217876445561648990846', '179.237463666466159700977184374963', '179.59557717730979274021302064364', '180.301169734909155795505253311862', '180.78974901738907022349145552102', '181.314384592022201240047494781895', '181.80226295093791940112518074111', '182.08411798368189141441859720964', '182.85312571378503843308179605199', '183.23645061392728980416799481973', '183.934142935724461857155575957423', '184.38490429170112666029658867765', '185.093916024237610749215892608272', '185.62603706821671479670493883851', '186.0958562901542203783649709580', '186.53345762251586190450654373133', '187.10594811801917032441741723771', '187.732445015953864193066409141164', '187.92525187417309405197440980276', '188.53209984605321718387677937663', '189.215740181393983980644551513888', '189.75309317891754634808422076765', '190.14161684404170243131212896590', '191.0243001724615716122919752194', '191.47993447934302861090140439299', '191.73971277712103605638806851698', '192.49202016494013333692902920557', '192.95703202770097713401961145475', '193.2679278802729210401951647645', '193.94490984619408294907732633028', '194.43447348935637811859309573703', '194.82729796467578462748881436514', '195.69257605875512562439671095451', '196.01120193677649905555586369264', '196.707760962590456227779730026638', '197.20167183882329399776272152920', '197.83842856586706297362098915248', '198.23077505300675028912089301989', '198.52843111105931397818480794119', '199.160521120616321401806645475166', '199.83785901662126637811047363820'], 'prelabel': '1-4760-4760.1549-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 22.105347067175426, 'root_angle': -0.4113047647022936, 'root_number': '0.275052491779770938410814785859-0.961429210480802398401324815647*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(24)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.896490010657104468341154409092+0.248093760466676036762420956757*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.156650588728', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.64470804424', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.36936710161', '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': 22.105347067175426, 'bad_primes': [2, 5, 7, 17], 'central_character': '4760.1549', 'conductor': 4760, 'conductor_radical': 1190, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4760/1549'], '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': '1-4760-4760.1549-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': '1-4760-4760.1549-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 22.105347067175426, 'root_angle': -0.2056523823511468, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.156650588728', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_4760.1549', 'Lhash_array': ['dirichlet_L_4760.1549'], 'label': '1-4760-4760.1549-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4760/1549'}