-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_384.365', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.19509032201612828, 0.9807852804032304], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.3826834323650898, 0.9238795325112867], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 41.26653112113601, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '384.365', 'coeff_info': ['x^32 - 1', '0.980785280403230 + 0.195090322016128*I', '\\\\zeta_{32}'], 'conductor': 384, 'conductor_radical': 6, 'conjugate': 'dirichlet_L_384.101', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^39', 0, 'a^6', 0, 0, 0, 'a^19', 0, 'a^25', 0, 0, 0, 'a^20', 0, 'a^17', 0, 0, 0, 'a^18', 0, 'a^14', 0, 0, 0, 'a^29', 0, 'a^24', 0, 0, 0, 'a^45', 0, 'a^31', 0, 0, 0, 'a^34', 0, 'a^27', 0, 0, 0, 'a^36', 0, 'a^12', 0, 0, 0, 'a^35', 0, 'a^26', 0, 0, 0, 'a^23', 0, 'a^21', 0, 0, 0, 'a^0', 0, 'a^21', 0, 0, 0, 'a^38', 0, 'a^26', 0, 0, 0, 'a^25', 0, 'a^12', 0, 0, 0, 'a^17', 0, 'a^27', 0, 0, 0, 'a^46', 0, 'a^31', 0, 0, 0, 'a^24', 0, 'a^24', 0, 0, 0], 'euler_factors': [[0], [0], [1, 'a^39'], [1, 'a^6'], [1, 'a^19'], [1, 'a^25'], [1, 'a^20'], [1, 'a^17'], [1, 'a^18'], [1, 'a^29'], [1, 'a^24'], [1, 'a^31'], [1, 'a^34'], [1, 'a^27'], [1, 'a^36'], [1, 'a^35'], [1, 'a^23'], [1, 'a^21'], [1, 'a^21'], [1, 'a^38'], [1, 'a^26'], [1, 'a^12'], [1, 'a^17'], [1, 'a^46'], [1, 'a^24'], [1, 'a^31']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-384-384.365-r1-0-0', 'leading_term': '0.798291530782920823726678020783-0.688611010123661387604191487904*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/384/365', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.0542554203717756, -0.08057726075105073, -1.4436785774794398, -2.630389699444642, -3.1892212982363803, -2.844553864969887, -1.7313044144540612, -0.43340667420785367, 0.2834343907001023, -0.059536397837379934, -1.2768025151646165, -2.535213957093927, -2.8405748370371913, -1.7256181275861846, 0.34238459815475897, 2.1915020198904016, 2.732274377672929, 1.7666232372435529, 0.1853043238871356, -0.6712205268121729, -0.05659006037097018, 1.5515555364921794, 2.7968827027169696, 2.555244574299798, 0.921364490145537, -0.7956973560166645, -1.1434467863741715, 0.20186477437412403, 2.0811263786268874, 2.7988022853516634, 1.6006628776824905, -0.6272683018009617, -2.1181432223117027, -1.809370576455223, -0.3111104297686498, 0.6789793946669431, 0.016619051131663447, -1.7357747624760773, -2.793832176971147, -1.8783651317895576, 0.4612744274938636, 2.2645937176982573, 1.9928034643120238, 0.021233599963208588, -1.7044424780988416, -1.5589048836941999, 0.1878441129116722, 1.710820065012943, 1.5648843849252323, 0.22892587070787634, -0.3817050367615945, 1.0119196693440462, 3.5475510855501433, 4.93099747347555, 3.716297712046368, 0.8095277158367991, -1.413243778276476, -1.4915513357721537, -0.26246095989096835, 0.23129428688825282, -0.8859111834814868, -2.286760355834031, -1.932025096698706, 0.5191250512383613, 3.083551201249964, 3.4178544680175333, 1.2964307661128756, -1.1268543254545424, -1.6133716829843026, -0.18669965464273702, 1.0662716123908507, 0.4961959717405171, -1.1671079436130924, -1.6816485863181272, 0.0026923475540419194, 2.346044768001243, 2.8329462619044614, 0.8257990019457514, -1.6312809258151009, -2.0563410521576078, -0.2924483747964152, 1.3942564384538647, 1.0005715818209717, -0.8843007070171742, -1.8492609721806434, -0.6157508717595837, 1.3637383598845392, 1.6237456319977461, -0.297009438261613, -2.1864449154723586, -1.729260797691242, 0.706013920993818, 2.4300295660701017, 1.57439318819188, -0.7285136684927237, -1.7532444830639917, -0.4734842155204687, 1.2668259403129216, 1.124663595443391, -0.7720131693656316, -1.9697072093149943, -0.8169669481118248, 1.317374656792305, 1.5869564302085628, -0.8291028500333826, -3.580158049438511, -3.8414909602491556, -1.5940397166741418, 0.523208388469356, 0.5453007007742545, -0.5129531525555956, -0.26010047255996227, 1.673849016895876, 2.8948376772258664, 1.2436683263946302, -2.230276456203802, -4.204584947142884, -2.920609602234742, -0.1841555371188881, 0.9580539896902952, -0.0919415756011191, -1.0826156733363315, -0.1907956956341415, 1.3928722417982233, 1.0195403692877205, -1.7319285723161275, -4.144690161819254, -3.600944507890429, -0.8891275117941883, 0.7225909025528606, -0.46372784527825384, -2.5719657926045647, -2.725787400753992, -0.7804856198726423, 0.678948744859133, -0.008580315306551723, -1.227332636903134, -0.26369967849247544, 2.842043195044722, 4.983268973206631, 3.80272268203554, 0.6940766535819486, -0.9834046838265025, -0.158142317775111, 0.8225955522825756, -0.3886483074323276, -2.822105490383582, -3.4640496133643524, -1.3864375273604885, 0.9049775597805972, 0.7970286336246503, -0.917062514462982, -1.1576703160487307, 1.134559306082702, 3.3552112903689, 2.5807825574843064, -0.5383351993578488, -2.5831575567265164, -1.789278865430005, -0.12223209257525144, -0.2820002579270833, -1.8705619755032168, -2.0677703522668653, 0.14057950496590918, 2.162293893119796, 1.1252197615779496, -2.119878129076983, -3.878548399335689, -2.326990736070502, 0.26539835527924394, 0.7518796932299392, -0.7249788695523103, -1.3147425082644588, 0.2032337378779982, 1.5703758813923434, 0.37142851243180475, -2.191268244097898, -2.5838042501930225, 0.2698919061160443, 3.3105519960777285, 3.229253420600831, 0.6767471469237291, -0.9021836774467029, -0.03826563346376329, 1.097180053061029, 0.3100966307724712, -1.098463691831749, -0.12628547050451758, 3.3125472405475707, 5.670088029823101, 4.265544774998908, 0.8532448719105205, -0.7495783068259186, 0.29796064796438637, 1.1406935153085025, -0.3450972382008564, -2.428870275865072, -2.170279965857797, 0.09585373762671943, 1.0590571169583423, -0.7937472198765835, -2.8281197657810004, -1.8687035275001547, 1.2886305423731463, 2.9282721127964213, 1.581285666999339, -0.05323806103742308, 0.8662335919356502, 3.203506540871479, 3.5684587926432716, 1.3062488600012452, -0.5696862111781898, 0.13911506149298986, 1.5382509848940313, 0.475695346951843, -2.595884328160114, -3.9271113388540777, -1.6909775341335895, 1.3681177643536078, 1.714557628259168, -0.19153953561359158, -0.9335558968548892, 0.6960527490911205, 2.0698367476552137, 0.9481187952482453, -0.8866671348151576, -0.17164781429120768, 2.787839389872479, 4.1586451143320105, 1.9216526161655223, -1.170059228505793, -1.3735688818691334, 0.9501292332190161, 2.2169259694623324, 0.9486143882535664, -0.41401948702601055, 0.26876189924280397, 1.2016550784337083, -0.670532366425239, -4.594289857213829, -6.34640658867127, -3.8894849713586916, -0.2352241067743246, 0.6837568802519659, -0.8446640719133705, -1.4912665060957166, -0.2616749193957054, 0.16841311714101154, -1.9437344811671504, -4.120047582447339, -3.0004458025572704, 0.5451840469073426, 2.34121112692718, 0.7529995753177517, -1.1157105906562867, -0.10890543874600785, 2.4068929634835534, 2.824104897820402, 0.8244848853416834, -0.26325440280629836, 1.2795881277795087, 2.8490822852743802, 1.593951739266292, -0.961321609890966, -0.9720859140587335, 1.927084633828795, 3.8663977214214795, 2.30317835955952, -0.3887340032973872, -0.6360787704224823, 1.0209645555751152, 1.0565803744028837, -1.3553275385852495, -2.9410337884453543, -1.3810581642447162, 1.037885722415084, 0.912678027621346, -0.9762171306731411, -0.8171846593773924, 2.2448219655579975, 4.460628817559424, 2.8425939742535844, -0.4886814022166649, -1.4845976920966535, 0.06205786224929036, 0.8800241674075904, -0.1952501315221616, -0.3826974194822525, 2.2007994210686337, 4.770337735043844, 3.4920787924809504, -0.721821726659961, -3.1569949968172595, -1.789180624011283, 0.3122578723556787, 0.03534156105848149, -1.226329280319084, -0.3861368398956252, 1.9608041430227139, 2.330359134533194, 0.11882525608478982, -0.950529648651981, 1.6193156614504907, 4.989330525228851, 4.849136348156541, 1.565352281084336, -0.6405603082021541, -0.028367407476993668, 0.612514816948809, -0.9510175600250443, -2.553126919131544, -1.237454855308771, 1.5268545155530826, 1.6219728682365626, -1.4060834127887274, -3.3829501648634346, -1.636194072071596, 1.1217583120007215, 1.0754175367951118, -0.9945814576689302, -1.3904433810129306, 0.375025336631497, 0.8671738686410988, -1.4856471738964296, -3.5043452389720064, -2.0855578325710793, 0.836401914514624, 1.178842002084695, -0.9684867233289535, -1.5582722592642035, 0.9558931377168174, 3.098015155935181, 1.761555946962117, -1.0101249330310365, -1.3396805275152261, 0.47395260752569207, 0.8254151793256564, -1.0279715856938756, -1.6261487966242993, 0.9127338489175962, 3.358645134698875, 2.07680135442027, -1.2433689856899313, -1.9488517957800202, 0.6756981207997603, 2.6483210316443535, 1.5964650945136942, -0.0016775983716960353, 0.47236093072326446, 1.1617810628347787, -1.043356751187616, -4.7102127454783895, -5.277090252037925, -1.9241529818901861, 0.9275807800132078, 0.08209198730614392, -1.9833661003072107, -1.44866409177778, 0.8653258277426675, 1.301823185568289, -0.38294259703977224, -0.7546818406033506, 1.1956705174956408, 1.868399729421229, -1.1993431166127937, -4.800040946376631, -4.361821730881679, -0.6502640892175771, 1.5575799442368106, 0.5878478436938679, -0.44880906940603404, 0.4316120448808236, 0.6736110119107462, -2.0932991248399473, -5.242746024004161, -4.644924518915758, -1.154529302977894, 0.48306857650656, -1.1817425280108915, -2.412042530671228, -0.5955158071496764, 1.527468226190303, 0.48033998430188346, -2.1760851699693857, -2.3795362595493117, -0.16253932338201935, 0.5876277768135421, -1.2387682621682066, -2.016667742547548, 0.5173260372194943, 3.1547220778396747, 2.081098598403311, -1.0071461271039537, -1.4931127120371546, 0.9808028027350082, 2.273103587864129, 0.5975612312680996, -0.8489503573279841, 0.4036076012763091, 1.7933950910570504, 0.11504659820265284, -2.758636788206024, -2.6065691921902676, 0.19162461041169343, 0.9882950065476314, -1.77507508591844, -4.029106352096815, -2.461179066934563, 0.5170978291989567, 1.0262811388079927, -0.17300397104322696, 0.21149934630382167, 1.6540906941153084, 0.3714217977556829, -3.8300260462304547, -6.054828284587283, -3.3467945789861315, 0.7784186254158929, 1.627858644352824, 0.007367441047989962, -0.14189897733024875, 1.3743492409976212, 1.1813147080168627, -1.1461735104170536, -1.748758190046288, 1.0267439379416246, 3.2545281926291456, 1.3210782857807848, -2.2541461429738647, -2.659669924775927, -0.16207691676065583, 0.8484524653073091, -0.7828535825418467, -1.4929309868961742, 0.4817297499883135, 1.9196186281824086, 0.24983128205852326, -1.6663904932717237, -0.034896196852862035, 3.3920471700478205, 3.8232467762019064, 1.0333106760342954, -0.4228508760227758, 1.317777776502377, 2.6625568497171948, 0.8974417948892554, -1.200497763023541, -0.18468875965966342, 2.134342431917042, 1.8045850194145094, -0.41476008348043786, -0.24249511634151166, 2.732285500889036, 3.997443689705971, 1.435850849026832, -1.1214634719998138, -0.09629057448947306, 2.1607332376639836, 1.549504626038246, -0.94380138142873, -1.1923092989161024, 0.9521685878147447, 1.6543239184189433, 0.10627615840034467, 0.24314116829899743, 3.8367911966889197, 6.652774536877438, 4.637395129896403, 0.2681281281275755, -1.3283979605235625, -0.038210690314165116, 0.20101905586543817, -1.368347508182826, -1.4528076879198886, 0.6374934172524582, 0.9004532312970571, -2.664721180270455, -5.912921536605358, -4.562963882483238, -0.8490155522062259, 0.1278890500458978, -1.7050245564428383, -2.1405543649931857, -0.23075067728510137, 0.4214189393200139, -1.5309176585923994, -2.4876096378079646, -0.2522037175980835, 1.6343800063376626, -0.47469258405245585, -3.9656101424852226, -3.80783320689794, -0.4703163934666755, 1.1513281889439246, -0.24054214081110817, -0.8797351368679336, 0.9888228939616795, 2.0674865740762187, 0.21925996033831796, -1.1749824190619644, 1.264562595963828, 4.787664450885863, 4.536644204591191, 1.2522630575962705, -0.2465511801358866, 0.8747226726547779, 0.5644425909295301, -2.5659221432059063, -4.431455403581348, -2.2841764218263583, 0.6284403303529136, 0.5595456943718401, -0.6738359904394963, 0.46650928435259553, 2.380630360871559, 0.7424880544678388, -3.6729439223270632, -5.376284120143916, -2.5980139233392623, 0.21542463382128021, -0.1585925138266893, -1.044310448857513, 0.5258293951009234, 2.231914742679327, 0.7688444612310679, -1.7840851321105782, -1.162415973979116, 1.543958881030687, 1.3008099772361776, -2.4294938377602064, -4.49033917160446, -2.251693902030686, 0.5136865102477812, 0.271953411677907, -0.8209970053036216, 0.28426785659297327, 1.574241305770237, -0.2846362684381942, -3.1942224859879373, -2.3512002776624756, 1.5881059202119931, 2.9953827933764448, 0.0846405780283707, -2.5393494929273817, -1.5870599076502148, 0.20078751258455066, -0.17271133950085352, -0.5205077056063546, 1.9416215989843453, 4.512568565187593, 2.888929511125826, -1.2599961722279287, -2.413977337154047, 0.08003926194545713, 1.3589025538494715, -0.5841517378385551, -1.897404682531997, -0.03819490548009425, 1.738402842526619, 0.3563139376203626, -1.4534278525568947, 0.0024714791869675946, 2.6265616550482322, 2.009626797918262, -0.763605846699179, -0.7666957809750714, 2.3046202106746474, 3.547087804594734, 1.2165715453754877, -0.445260295234917, 1.308558635267776, 3.11168739444419, 1.6381640948691447, -0.5629409984838569, 0.1481119301295975, 1.8172184820577155, 0.45031520613829246, -2.398637196162861, -1.7402013110969887, 2.263180839011755, 4.15320548208218, 1.964621855394404, -0.023746036867182, 1.0305428569196995, 2.0231802392406664, 0.09147195607787131, -2.011282340960938, -1.0714917416312522, 0.3737272945684272, -1.6245161022271188, -4.912287246831199, -4.163633787616705, 0.22811553059814496, 2.530519010599922, 0.7624965885971317, -0.9019526701990619, 0.14428408765239809, 1.0860986453011277, 0.014124989350161998, 0.19713895033565645, 3.982461440519756, 7.285899735341356, 5.363918088167324, 0.6092478184305044, -1.110591841719839, 0.47753467959019014, 0.792407585075821, -1.0772536806491704, -1.2774238227367647, 1.1033733949298123, 1.940649814676343, -0.41743092593094044, -1.7330675637780133, 0.8299660331361919, 3.46370721540049, 2.084313533247993, -0.6387810337346131, 0.07799539635319179, 2.9464383435065566, 3.1142624589126893, 0.6338518421548143, -0.12493667482400025, 1.3501691213542937, 0.9422961799500565, -2.0937110756250075, -3.087931764039278, -0.010528405664769055, 2.6274576957805063, 1.2545498919570583, -0.8932998231319561, 0.21524126453313822, 2.254005068931914, 0.8794019451366817, -2.3416083170142357, -2.585865951560667, -0.13046425015317353, 0.5528693448065183, -0.935675995832244, -0.4603016173231398, 2.4664477479039055, 2.997471403074245], 'positive_zeros': ['0.29310534390922544889944033691', '2.32735817233445744090279513192', '2.790364494652196776777625063821', '4.326157590546893784434849688113', '5.66726268269438584227556133738', '6.26343845966069753112048036881', '7.65081710282482990517486565915', '8.4036674188776895595943910956', '9.59985954284195390772264957271', '10.69128907957211452987976680644', '11.2535673995225763994053884176', '12.44172843946852237031572056910', '13.44049087833037574650574632610', '14.34551962572179839461300863265', '15.370594813977334190197536727510', '15.76668722268293441333213554735', '17.27716522521937875718465728585', '18.20285184336749206991691618546', '18.54606994267184703532829197734', '19.63226085325118348645318101039', '20.774985039416156006968829355127', '21.59616704615042883151521816389', '22.28436916149462149315669211279', '23.12465660340969804116824576719', '24.1564379567855353108907934303', '25.041975068912802393527174612500', '25.797525390158288538596866603075', '26.653158737735049938672995174642', '27.4612607314336933609669685386', '28.35413317415138169687799946290', '29.27437176419858858370819592480', '30.073516753355651379267305091215', '30.82184279917105943673466655664', '31.67617672821625813756012733425', '32.415178015115833206424454093636', '33.644621894849274981708163334889', '34.21645870443411884206386601575', '34.74250713248297550298630836352', '35.74130314320255950939819771189', '36.90047985823446848373033288843', '37.48082435290968767746010088082', '38.15965086410846035432518587821', '38.88657663608303666088859509068', '40.11545582349002810761851945831', '40.554146739616890506313519768736', '41.68397350160502427144945515760', '42.185655266806292508556197468026', '42.845431395223753618716373506983', '44.144850784960878512207094495999', '44.721475328953595611464006390', '45.2556386377509158650710643233', '46.412758305731366874846551627587', '47.02344562639587842703738067626', '47.68517634564503104814253985260', '48.69827612458350661043148696287', '49.731739226761194938685525551702', '49.91093014737689643834853266876', '50.92150398369311469004670629709', '51.678460206176898394867946584122', '52.771596488991327829875048904137', '53.29988037550466494803348730810', '54.03081040454752377313059269989', '54.73347897263978033485470915555', '55.60194009109860143793495386313', '56.64994784319258271231613871557', '57.1952588682495063210070905991', '57.87064821913761278269525169802', '58.452398744040600796841566149', '59.78864135025578722378792880567', '60.252287683805961723918090263432', '60.89019834610822912072628151000', '61.86151637693581912901351045709', '62.4013279891050593878320597698', '63.31322686730437901912100167615', '64.35029214595414290738902126116', '64.51284398040412919912010829149', '65.797236409664327465685437799491', '66.2232052704687097066614367541', '66.92929114189811297091940308386', '67.96762214848061193048286076482', '68.71913144455313725472099147289', '69.27035162742353313644875340914', '70.13819503596809726734828406589', '70.64733067678779242934787607035', '71.73763722683412598967978312516', '72.38295187351654046734450644252', '73.29659951607779510353447932474', '73.68728549553017589899674829693', '74.309018526840431323589183682976', '75.65402155913713457229474228561', '76.098482329253786458478990514264', '76.93885291046679753866161326312', '77.234383256163850482105738610167', '78.388704163816759102810827759679', '79.1587368499661456894270681111', '79.70162575206059197889911477172', '80.76980871662260286648782562484', '81.03853992191057679781119424350', '82.05664049555982289715700349835', '82.62457350958881815181423520763', '83.691595209523469566788249972571', '84.189539741772780869934670382165', '84.84468015691470053185782751930', '85.7828599985863508663383560041', '86.39927925717005272009099116097', '86.97891125370403994460280174910', '88.07176261371732106800460897637', '88.73896594918788325349797771716', '89.32804258593448132846325719847', '89.76047276327607369156080998405', '90.884489222004754305317420670706', '91.80538925912674059500695539417', '92.19556889661629877288892756202', '92.866356926093237208555310039014', '93.76567864211317403266737255608', '94.22568106905463409855937630123', '95.481913032608940604981252645664', '95.94445732900605467617205835196', '96.41833178479189892481539071527', '97.31922391997707370665444045570', '97.99642729826994779669277830459', '98.91494849176884066503605131031', '99.53882923625662843908000301871', '100.25040912832887892251803220537', '100.772758242935329007273883656080', '101.77255230415323601832914380549', '102.36861518375334269221582563510', '103.02911076216557170451778470853', '103.93503865999232779220092538700', '104.60638655112716715991411262530', '105.157444718384514622525510627058', '105.850130267454853701356982422634', '106.750959781786804972145838861227', '107.43233985180592310524974061660', '108.43671312067507389817450057132', '108.60162183600414911149289985531', '109.27575991874002209137377748350', '110.48086312474068479916107236172', '110.94880958040798253124514643932', '111.75298114369647277260584752573', '112.43189374987963075147267075455', '112.95570185960159891194296574796', '113.65801669883128804895159676287', '114.74521095940780323371980035346', '115.43028565334473189888242094254', '115.82954926277563370717510993971', '116.36239642589618865551108567485', '117.6331271495585733885735736743', '117.951503643469512205038422670554', '118.817454698301869886625665123892', '119.43058681690675616870269639787', '120.337265716944930706058037147805', '120.75456425061322042460430616647', '121.51521519925482519580630203728', '122.38922054656541472293593376292', '123.01439535798139756653750527861', '123.83503433434657770848376152676', '124.31238064673019449682478742429', '125.01174757466350349191289000455', '125.91489884565304605974834400942', '126.3937322107630768857862766531', '127.4328010953331287540163819608', '128.06874086143506234621493328866', '128.3881211240991302634051699648', '129.096148512297967195418568784878', '130.23963164710834182785098278773', '130.93914694011101107675289064651', '131.28570020782177676976106519138', '132.04192872957748709823107708069', '132.71888401057325489246968915175', '133.544520699224645503448927495031', '134.39628872461675461198819697212', '134.87572053997193885078752542386', '135.564635634897855357886051314244', '136.279530814177688946177441148126', '136.87825787399824674695708041059', '137.94516477734940095726163026567', '138.24838249630742309336967825701', '139.166178973969567163240443640578', '139.71090938673344752604835388748', '140.557156958941744580670215814189', '140.97117207901122833024719186906', '142.01137371140325039567092556004', '142.51205674454322825585453756411', '143.31177720483375750914591214308', '143.93232790503769071871498716066', '144.71138587982403177454120340179', '144.95895283936714759516103810030', '146.27424945782852807087073103512', '146.883842238227078695764836336496', '147.23932069668235300522157691927', '148.03391687369606446687367341779', '148.54549839580987592621751517075', '149.80467270586354000543348324089', '150.03419415990864859342728391894', '150.976548661178844737036609836', '151.34547101266918869532039344512', '152.21416790111228777769584095329', '152.77149868641969166652533538491', '153.79800807032828534846228157113', '154.33322304429607616504921735378', '154.86291377170396379025520370454', '155.65276017247872852285066039473', '156.1391945677508697516965223349', '157.35698559558546259714883618601', '157.60596791269648036638768269242', '158.19767793816584215467261059719', '159.28326309990093065701329392110', '159.80234494724588597297833432836', '160.24425557515889666886885938789', '160.994785564885147075549197176734', '162.142792309010741842230925971900', '162.46363025499824350365522350134', '163.05444959282105853384002282329', '163.83184156429782996902436460070', '164.50490854143526135731495398619', '165.12480498690494284339806019793', '166.16415231971599623579385107526', '166.62078374659285560830291705563', '167.14043931691017855620791108889', '167.78450932158101850411154178953', '168.62604595779064119258189514822', '169.38205778728276494906569405526', '170.25287656048061740701565760436', '170.57342383958418673717500121989', '171.04220573053709458322656967842', '172.08623042918451762463517688521', '172.80350919848641216869340882249', '173.36495142306782901806499121210', '174.066983001506656304852766438102', '174.732644968139799128965317871726', '175.31223236563286009289700064998', '176.1542531974680299842303770646', '176.65466439852318254244624630019', '177.6538896133716067539307957391', '177.95154540492300607409947964761', '178.94994354048021040611066650302', '179.3511297930599120706643526456', '180.04605828010723782322697897196', '180.77012450262297803804771839739', '181.85965272668512006823493762972', '181.9583613753780749613011003807', '182.8225893198226817455559454682', '183.60980278000513329835664406986', '183.88135059496072571697951244026', '184.983628994862698503583277187858', '185.72189191925962670059838721590', '186.22335522142297844680899546829', '186.87859366039028645097462457895', '187.15502647755663867774294163828', '188.48983488114695432422066248088', '188.98100890147973630221926482927', '189.51972051923925956210987115197', '190.180566314543052947410063147511', '190.891464025755801539791724816346', '191.48930947503905741761535650548', '192.401794561811848050067596941073', '192.80300158793394273855196812437', '193.85882886435594422926787675563', '194.10079365705018581309559497914', '194.79670406552002289589628011496', '195.62584547153267157225796164531', '196.39560484602331183848757908013', '196.84705106378647828260997629574', '197.58189189784515984641535739870', '198.45648758358967705089567324321', '198.87699557473628514249662359619', '199.43247872177151949369120105911'], 'prelabel': '1-384-384.365-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 41.26653112113601, 'root_angle': -0.453125, 'root_number': '0.146730474455361751658850129647-0.989176509964780973451673738016*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2265625', 'prec': 34}, 'spectral_label': 'r1-0', 'st_group': 'mu(32)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.949276933565508990459178203814+0.0340153162198481992272744480629*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.293105343909', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.32735817233', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.79036449465', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 41.26653112113601, 'bad_primes': [2, 3], 'central_character': '384.365', 'conductor': 384, 'conductor_radical': 6, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/384/365'], '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': '1-384-384.365-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-384-384.365-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 41.26653112113601, 'root_angle': -0.2265625, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.293105343909', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_384.365', 'Lhash_array': ['dirichlet_L_384.365'], 'label': '1-384-384.365-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/384/365'}