-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_111.14', 'a10': [1.0, 0.0], 'a2': [-0.8660254037844386, 0.5], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.5, -0.8660254037844386], 'a5': [-0.8660254037844386, -0.5], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, 0.8660254037844386], 'a8': [-7.040766286173228e-31, 1.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.5154818328690067, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [37, [1]]], 'bad_primes': [3, 37], 'central_character': '111.14', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 111, 'conductor_radical': 111, 'conjugate': 'dirichlet_L_111.8', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 0, 'a^10', 'a^7', 0, 'a^4', 'a^3', 0, 'a^0', 'a^0', 0, 'a^1', 'a^9', 0, 'a^8', 'a^11', 0, 'a^1', 'a^5', 0, 'a^5', 'a^3', 0, 'a^2', 'a^6', 0, 'a^2', 'a^9', 0, 'a^3', 'a^1', 0, 'a^4', 'a^11', 0, 0, 'a^6', 0, 'a^10', 'a^4', 0, 'a^9', 'a^10', 0, 'a^8', 'a^6', 0, 'a^8', 'a^7', 0, 'a^11', 'a^2', 0, 'a^7', 'a^7', 0, 'a^2', 'a^11', 0, 'a^7', 'a^8', 0, 'a^6', 'a^8', 0, 'a^10', 'a^9', 0, 'a^4', 'a^10', 0, 'a^6', 0, 0, 'a^11', 'a^4', 0, 'a^1', 'a^3', 0, 'a^9', 'a^2', 0, 'a^6', 'a^2', 0, 'a^3', 'a^5', 0, 'a^5', 'a^1', 0, 'a^11', 'a^8', 0, 'a^9', 'a^1', 0, 'a^0'], 'euler_factors': [[1, 'a^5'], [0], [1, 'a^7'], [1, 'a^4'], [1, 'a^0'], [1, 'a^1'], [1, 'a^11'], [1, 'a^1'], [1, 'a^3'], [1, 'a^9'], [1, 'a^3'], [0], [1, 'a^4'], [1, 'a^9'], [1, 'a^6'], [1, 'a^2'], [1, 'a^11'], [1, 'a^7'], [1, 'a^10'], [1, 'a^10'], [1, 'a^6'], [1, 'a^1'], [1, 'a^2'], [1, 'a^5'], [1, 'a^9'], [1, 'a^0']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-111-111.14-r0-0-0', 'leading_term': '0.568430402023608213813536766713+0.257236673101360387221510762557*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/111/14', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.6239261398058085, 0.7618230378199865, 0.8929992761130178, 0.7801752893058526, 0.27162443620653187, -0.6386996159254037, -1.7839531518243583, -2.8422173080400914, -3.42063140765185, -3.1958734402660522, -2.065409375518269, -0.24206065910194036, 1.7679425752218987, 3.3215295579635122, 3.885260160309491, 3.2717149979702924, 1.7504041671938222, -0.03970589807963736, -1.3591158370672667, -1.7043076417771497, -1.047077086685579, 0.155807082771071, 1.204173381644636, 1.5312476278176956, 1.0124669270117654, 0.025277648582318492, -0.788286081301882, -0.9281955728901135, -0.3687365392837865, 0.40109009678898283, 0.6788300735072198, 0.022719557077165792, -1.402285954874491, -2.8552924899833743, -3.4508460907735214, -2.7467058893494385, -1.1083123221520645, 0.42456680633318034, 0.7399340829292953, -0.6235319712063272, -3.09940343806427, -5.344865206830796, -6.0108463046566545, -4.568469562061271, -1.6603541099311687, 1.2702989738542256, 2.8521765369934338, 2.598797598382427, 1.1302604105269816, -0.3320064944964352, -0.8347212050963455, -0.31285939145564995, 0.46896192789528923, 0.586338431867323, -0.2826578962971142, -1.5892424667336695, -2.3482829437221486, -1.936719901317979, -0.6203748311312001, 0.6296972872677786, 0.9124149082935716, 0.15363753561080076, -0.7885135852928602, -0.8095546567206221, 0.47055375499128593, 2.2400483367188118, 2.978656649893604, 1.6018952656022118, -1.5889003700181106, -4.9288637712934635, -6.455726660330543, -5.277806740406897, -2.223887477593169, 0.736862665936388, 1.889007442171375, 0.9348463482772181, -0.9382194272523083, -2.0955522619291536, -1.7458228979699226, -0.4593500896957134, 0.454767932614661, 0.13770950893567366, -1.0881200927037347, -2.0517106535377914, -1.806889740345853, -0.48340284881212947, 0.8427923480971572, 1.1403880345254216, 0.3726898181762476, -0.47801308046563545, -0.3688619351826077, 0.7225037876075638, 1.6261071558906368, 0.9739167708933598, -1.4545932359046845, -4.257593841980225, -5.351092374700545, -3.6408719066650956, -0.03144815233316439, 3.1478742025081288, 3.9083521550979663, 2.1303392786035382, -0.4155802113069673, -1.5708443797566203, -0.5442937012985819, 1.5493684452962349, 2.7709627402936676, 2.0616341861684364, 0.07448162472890263, -1.535347340765081, -1.6363387474135667, -0.5422829195463136, 0.4681232091593386, 0.4940612401297366, -0.11605795223646993, -0.20578744623890766, 0.8966553879629342, 2.5501154282637324, 3.317426336743841, 2.37811873596267, 0.44754308623815275, -0.7840763113970267, -0.2602564531392789, 1.3065055766428675, 1.9539821511298645, 0.2945030605308941, -3.0102411555753967, -5.575966730365367, -5.2677062744152074, -2.103892867770372, 1.646081631213951, 3.3179900541120486, 2.040112640459563, -0.6741179140734537, -2.395284983493978, -1.9094402306428084, -0.07609221915962798, 1.2543666566018485, 1.0956391597682655, 0.13838470259906244, -0.17261181297521083, 0.7517995569436746, 2.0305994133283436, 2.297509851330302, 1.2177769037110315, -0.08530976371205029, -0.1799790814888696, 1.129426761347551, 2.510060030465662, 2.445121037140474, 0.8679821403615883, -0.6601493504277977, -0.5460973498046342, 1.0153234890638838, 1.925206704665702, 0.09185114738297485, -4.371876819447837, -8.849138288500043, -10.277738140796291, -7.753057651416934, -3.271511155999734, 0.06704865157372578, 0.6916133617242927, -0.41032703473902815, -1.0816531992293985, -0.27327438256855013, 1.0689458898659698, 1.2561116646330328, -0.20199249212540626, -2.033286734765564, -2.551224044651298, -1.415438905872417, 0.08531794683469571, 0.4901376017732662, -0.25962735658601016, -0.8616415086842784, -0.25391446637802384, 1.0334417927092439, 1.3685751602338645, -0.07621486924459084, -2.091183217892652, -2.3911502791817574, 0.01952320143686531, 3.513635132074909, 5.1038480657114285, 3.244680426615989, -0.5734527479250403, -3.111015589493343, -2.373779036828716, 0.5953422324597223, 2.857243839916247, 2.4569635397407277, 0.16124329437628032, -1.5779509419049587, -1.2113927309815096, 0.48008603395424165, 1.4708577637515503, 0.7546426411797522, -0.6891813377750569, -1.160119231512775, -0.19615334264075907, 0.9920819075091816, 1.0357195805133221, 0.06496014643388495, -0.4460037480623608, 0.5009932999900139, 2.068056895074724, 2.3735837405444338, 0.688348181154491, -1.4418981161222977, -1.6016229710621328, 0.8908127815044891, 4.004775609905764, 4.896382607250417, 2.8543987417268664, 0.1904340590995261, 0.0019847069095294103, 3.015133911886851, 6.753709513868868, 7.915781483150052, 5.530782535761418, 1.7124366472418218, -0.6134641949467137, -0.5103366121144214, 0.5028740266884162, 0.5282656218488959, -0.5822856266486006, -1.3645585808787906, -0.759769650047375, 0.4845972247848919, 0.6916760694728946, -0.6679299481580909, -2.2132397669849713, -2.1792465059130306, -0.4837036570820532, 1.1248607182978594, 1.095597225731047, -0.06600295758206227, -0.3836990911371483, 1.0868062521461876, 2.733016805278635, 1.8380588270375477, -2.32515716694617, -7.1566328183749945, -8.874440203708902, -6.127489329814791, -1.3414608556438414, 1.6486713507076443, 1.2351870218865548, -0.7833973997366744, -1.5074411421127452, -0.05692596712608121, 1.8276565811912646, 2.078192479949184, 0.6821483578366808, -0.5183797289190307, -0.1666561483707214, 1.0056999228055779, 1.175103612846079, -0.26870023790527464, -1.930141484013721, -2.078671725384963, -0.7331213752732733, 0.40500437688877233, 0.11607116656754335, -0.7459931344311659, -0.3102980127026852, 1.7474837456532168, 3.2952348362170696, 1.9060797047957678, -2.1433524693257517, -5.559685749603025, -5.125374099629549, -1.0441621182303096, 3.120854202265957, 3.9711336765363194, 1.5397282998544652, -1.1241334574036554, -1.4267178886269083, 0.1389402813710174, 0.9685284992075158, -0.4397445869633031, -2.7949160028062296, -3.640204351621477, -2.2030352189923477, -0.11337246224042279, 0.6714509654484708, 0.08533166597128061, -0.32841269073628276, 0.34038060879898785, 1.1093677489600071, 0.4614081512948515, -1.4207696544680735, -2.5035257494013634, -1.2583478896447013, 1.2883159544704457, 2.4965290465737193, 1.1831532032042007, -0.7984148861708998, -0.570971814066525, 2.283082619008571, 4.849764220257545, 3.8926584143528684, -0.4790684405660117, -4.645971234741056, -5.134945321822368, -2.121374192746081, 1.0136911215062656, 1.4173963309746955, -0.4481654466945716, -1.8849286616996543, -1.2996491162459871, 0.19252959544007964, 0.5306335664785906, -0.6193785424472592, -1.611548955800783, -1.1138164246195639, 0.11057159185483074, 0.23394843422420897, -1.1500310243801195, -2.3454546843571284, -1.657174421045043, 0.3513521779170482, 1.4095888811480635, 0.3706747479425447, -1.2158064033579432, -0.9549732390587007, 1.2144454725918625, 2.5188072982580327, 0.5015675316987718, -3.7103266823662473, -6.0535970153595935, -3.7206157386988474, 1.6982363473485935, 5.712354496496881, 5.461380699881637, 2.2964871566854725, -0.22251886157928438, -0.3129960360958314, 0.6469921983680963, 0.5218979106259714, -0.7080902791248166, -1.1406338264980707, 0.3065846605816123, 2.278276465842288, 2.5729223126717344, 0.8656308446459412, -0.9308119091182443, -1.0896588035328245, -0.12402457401896727, 0.16780211018626254, -0.6504963143247106, -0.9109209074904628, 0.8358357310202226, 3.4022104835365172, 3.864653710884336, 1.104566224022846, -2.304529135422916, -2.553932172006695, 1.1046295317676904, 5.231764277652978, 5.7764113925901395, 2.3966610280735066, -1.3758508153639148, -2.2095214961642977, -0.49571964238216243, 0.6233332434871024, -0.7530435186532686, -3.1600949329328887, -3.8397317067231156, -2.166232771416569, -0.17908959653249823, 0.168331917811085, -0.6442149253095949, -0.6748669519143456, 0.6896499243636284, 1.8989527358807399, 1.4149352295441613, -0.10264205855723309, -0.629854140662404, 0.40658246008189214, 1.1662061905110588, -0.1819261447941546, -2.6724706224525625, -3.2366620835240982, -0.42601602457350213, 3.3817064511421515, 4.346408493916979, 1.5834430951433873, -1.6608405747935944, -1.6845579973832034, 1.3804510002496735, 3.747631063755759, 2.4061024983113213, -1.4568333774003488, -3.983619680780306, -3.0916770610142126, -0.49991776490683953, 0.765389866862539, -0.03655490453194135, -1.05600020357062, -0.7492245157434646, 0.09126123506372316, -0.2554565186166722, -1.7553982215893753, -2.468105155897342, -1.20113427804832, 0.6614580618442913, 0.7849729666635327, -1.0539310667146344, -2.569501867169498, -1.9194777484797751, -0.16215951384543148, 0.19261669692980823, -1.158542329252009, -1.3352471789035016, 2.2836208144845447, 8.225838079307001, 11.705659746834499, 9.59756356066293, 3.91864633801634, -0.3261215053459137, -0.44905177800162477, 1.591739357680715, 2.2134837208228384, 0.5504246256557942, -1.095223737757416, -0.7163941006505044, 0.7840053581862549, 1.0583979238893113, -0.40630333211508707, -1.6633239366105428, -1.0408097460910897, 0.5799426246277763, 1.0280934339753127, -0.1392437280261363, -1.0381187411545272, -0.12199748632456586, 1.5709369145089451, 1.7877175536873295, 0.28070893133503544, -0.6378362463326132, 0.6952388921919894, 2.4768021787361265, 1.129945376875661, -4.1002546121810495, -9.395846747627596, -10.111498911747754, -5.879262880015007, -1.0008256150964816, 0.37533263574099895, -1.4540715204992605, -2.902540594301131, -1.8437954224515536, 0.06893341518925764, 0.06902581543494732, -1.9108570100977709, -3.2454729755047333, -2.1545695387915553, 0.057431354632413306, 0.8913535436224813, -0.07729492908701112, -0.9451533082061113, -0.34305054732417006, 0.7220476070138, 0.5939959028781061, -0.3097948314654645, 0.1456357409756947, 2.6184038867751496, 4.729605563562622, 3.7255343362272946, 0.1778908202664885, -2.3130456143851967, -1.4767261330431927, 0.6503827142446363, 0.18031183619193977, -3.570159762667612, -6.822717440605057, -5.6962934012297355, -0.9148471944867311, 2.9405618182385465, 2.6799776651003753, -0.18616603679632282, -1.8553884930777516, -0.94153036560263, 0.43418106878497104, 0.022610680723296223, -1.551965569766878, -2.0088661949150515, -0.7623376853851616, 0.37203473190939956, -0.05699581421180871, -0.9768988105593164, -0.3724142352405743, 1.636452983600403, 2.6910608350216823, 1.4066710317544224, -0.5494714661395155, -0.6151711096717659, 1.0514636384410323, 1.5908503052910425, -0.5725500394686988, -3.0697362285163416, -2.218078248564793, 2.051922839252367, 5.422394838221524, 4.034870562508377, -0.8280701974535059, -4.087661853467454, -2.677504573966728, 1.2414226607662555, 3.30951034113299, 2.0987072885441833, 0.01719432927730086, -0.4808070353526067, 0.05951565017831082, -0.39492608568154003, -1.9417557959742033, -2.4271574180402826, -0.6006279085101063, 1.8559177471157036, 2.3912347049027023, 0.8999370007464859, -0.3313819633766492, 0.08070952707556715, 0.7954321809155831, 0.013875174330150697, -1.4814307062065353, -1.159790920756975, 1.3421706459518858, 2.779474170094109, 0.016144493436552217, -5.509075547917518, -8.650315751057379, -6.286661330970502, -0.9914755202648979, 2.002201786494954, 0.8217140941072776, -1.4324991189272873, -1.1305649236511826, 1.3576857531290902, 2.6868695763105372, 1.2568701138644702, -0.8155052802761382, -0.8048398486062249, 0.9797890809046197, 1.9175287027518362, 0.826892750454158, -0.6069492543193782, -0.5133357052701714, 0.4427380239778078, 0.23189631125476787, -1.3035077480628243, -2.020858411632201, -0.6379528158277507, 1.1213525781105105, 0.8050483512246754, -1.0310381642516044, -1.114275157972741, 2.07282255312678, 5.589699525515519, 5.229327588793652, 0.9030955105189094, -2.8340512468700894, -2.146427515774442, 1.5104224160175839, 3.4121358299093676, 1.5169534958978839, -1.2789742021191326, -1.2106161459422213, 1.5327730613908783, 3.406631014097339, 2.2911270525440623, -0.07350117261895144, -0.8626283912125485, 0.10801711502316566, 0.7734567557910449, 0.24427030272387226, 0.029994455722636433, 1.3757126107004507, 2.8847937976327334, 2.2118145085548364, -0.4561769304804724, -2.2941439831606893, -1.5836137622130488, -0.09711856118587064, -0.5548958500927028, -2.5785318335175105, -3.023554934978976, -0.6115182364281122, 1.5539285524155086, -0.3905336307967052, -5.652595370423617, -8.896852880888959, -6.30166942165951, -0.11624371447965394, 4.003222039699282, 3.4299800010803807, 0.7696404953876511, -0.3246879436172223, 0.30375924553001815, 0.16667134531488864, -1.608719000401452, -2.9227031203911484, -1.9099986679544472, 0.22166773288732142, 0.8704761843551917, -0.2988992891902216, -1.0648963562867495, -0.07207293677006484, 1.133488038773926, 0.4882963498540512, -1.324730114753505, -1.6993393859635026, 0.0024911813148862354, 1.273099184783872, 0.11511803146980534, -1.5375175448625213, 0.030184601945711466, 4.9162308267097465, 8.37281506472729, 6.11880027797878, -0.2690014109187985, -4.925193804449692, -4.412904066813373, -1.1666100314697974, 0.33402647010981473, -0.7773174250310841, -1.5534878582197273, -0.011487100027995866, 2.0855120111340018, 2.029185931611315, 0.15074429310837228, -0.7368062263482316, 0.595468348940642, 2.1736292888404276, 1.8187956190387988, 0.2177822318859518, -0.3580220636720111, 0.4546404423357127, 0.7813035856540304], 'positive_zeros': ['1.35716483168152416834975152809', '3.47476126712780434319198192278', '5.30509178758140489510305563571', '6.52363081314068441063054671311', '7.82034153624179659212658148004', '8.89297404906821733405471079743', '9.6937674437313361711511555048', '11.45812116959389169236555464627', '12.08404583900962286551502108469', '13.91664364351943800799541240392', '15.22694329059216373843796223895', '16.05286125730881233581925146780', '16.79974872506722154764564604789', '18.26176831346771909827634631623', '19.10788390422501729321144596004', '19.911080735722701558235340462187', '21.108238622779739204990581400540', '22.72091248115746086000581473008', '23.59451760834280649247302558936', '24.806197213455072316650058302101', '25.35594440628681708252368319151', '26.66203493015929699299821969428', '27.61571331104620474941945861825', '28.25151077375228398012760778458', '29.20959983482436955171515615211', '30.62757327282327305734270000934', '31.8178242227305545155594643477', '32.584932336170877756766675636056', '33.761225884039950417681956584563', '34.827905207989945663243145533622', '35.56402783953985936404424930893', '36.03042850031740109495990740437', '37.57982455102241805570013517810', '38.18254524547349085724814620153', '39.09454530230418862941843191422', '40.47809782842907173473069407765', '41.484389116543308505622271812808', '42.51277329955802444642365398838', '43.49299040749564019660402714385', '43.84806044184662709509802611720', '45.28394863982950076002662473276', '45.689097626142851696029694288942', '47.02606278423163358546340760983', '47.62637679000561259665653455698', '48.445821502562461957132418328541', '50.30237132502201667267114368744', '50.83648750563272740986340431697', '51.62301144753409127173099172822', '52.46735840749982814009676764697', '53.72696588595891395556023691077', '54.28871704810358013090172042661', '55.06352690096106454253929526691', '55.92604071832874680610081413804', '56.87321533729906029757788733578', '58.07793521555715068503071423919', '59.00395006783714561439361104079', '60.02088144650209014103339768150', '60.85163162371896139367079613541', '61.72049089245104793202379124616', '62.544651132198024464749610969687', '63.45778801464016843538410248570', '63.94894340367073220258054667858', '65.09101218068861041771301948439', '65.84976609377944598209159240197', '67.22311025257522979960151235148', '67.4996096683044619565031018556', '69.25191607974332543003508007955', '69.83677666715629853022732259476', '70.47964600241755240128690345625', '71.43235916747927075698364052944', '72.06440302839200820037777856290', '73.20140654533308190143218343466', '74.043761405845111205199974514123', '74.4945354132573232527097187818', '75.473926797655938251397386369820', '76.97848484151163103434393029391', '77.6894764982405203936504834549', '78.44599077843660387394512538111', '79.51471042062420314573404105389', '80.046806438934025718573251744721', '80.89266282437689094019158457042', '82.03686473422393911069919246989', '82.539382152239949282825103371450', '83.18577580255797369162640168424', '84.22280390365356186732465718391', '85.38017374176445923474575674378', '86.4083350985411578537195908165', '87.16165432072786276270078039020', '87.74917966080818549593440996744', '89.08472772578422693105679672815', '89.72220090866243988299199642543', '90.1996617865577641010114098465', '91.02366301413342273191737562980', '92.02974232484175059812142520264', '92.98002958668663480323385497174', '93.5200211485797730566338340277', '94.65767797489527377342495674345', '95.81377503576972075544978613986', '96.49745090848082723524889191299', '97.45277896074634335121191458094', '97.98495006722576426128989540931', '99.02792697348387682323524417313', '99.450569256542920156113553487896', '100.57010338836851974000499555828', '101.31434896473688021795175623046', '102.02825004148993521945874284864', '102.85369224499956295746581778486', '103.968480816275815598731138633116', '105.26650160178999264010112875878', '105.72466499833698486398227350658', '106.392881984093637548752222787269', '107.140782293323526187376864153438', '108.253784863521085169063788375126', '109.10928022700073775172146527994', '109.465654162400835853277872049292', '110.20212230522404859872151852843', '111.34045524630776821247571314358', '112.11211166768700583249296428823', '113.30459959257715651952542676643', '114.14697592820225536257759769039', '114.57547854941534448661680928887', '115.985251474339584652444987884638', '116.328805999197439763716600482093', '117.05367955270498624972945832516', '118.101587683974154499969554085411', '118.65401864333562011439072892322', '119.35024439617811385159162237745', '120.345526023631169221754970442131', '121.38276341016543091501822229280', '122.06377605589070175239776333344', '123.01164213271529813239664344864', '124.13611551300667177664026920382', '124.67875514953879091424536311105', '125.57413142172517757526313472527', '125.8534283230340673813356652899', '127.06037958804568658957989292325', '127.65662534658293789142605249058', '128.78915563946965770216591074016', '129.125432473982460295106783965814', '129.84581965413125797580179455741', '131.52205368806627290368356932273', '131.95161872362850727772854564383', '132.89396439621644317550363106355', '133.58443830897032888688570299161', '134.30385751716939678145460191560', '135.19493700260596865608173395048', '135.90742428348170878949994627789', '136.584700348479664229859384292287', '137.55431992918050080765104495838', '138.01410099480193065407004575696', '138.83514028484944370194943235503', '140.4259833985810851979487033537', '140.723555715922759356218554872128', '141.858859618136665976863570286365', '142.20352879980691619237875538659', '143.42791369843721403819173015962', '144.0440237712613897097281848438', '144.77609951064753182125941398767', '145.50440339370075012018517549017', '145.90744544565367351969100572530', '147.20273808196499775503206708549', '148.01216880232934943554699737282', '148.459459476585812664945105241980', '149.74430273957161554969465535450', '150.6047607461575901663685865660', '151.43277885577547793514072770802', '151.88020206925758932312874545204', '152.979560389525749781234257491689', '153.4201542517496896400054136966', '154.129155343958292813166934461866', '155.20684657570518007785808175944', '155.75427129128842009958829341786', '156.50152043310555755044586472612', '157.36479451883719785781882244965', '158.38641794017545306056253899562', '159.27508239428506228099324578983', '160.31616016619890057198162738049', '160.890310019456643950471402656447', '161.11553706355188093517224353782', '162.25760875390850682730120048333', '163.30730135746565293027769085212', '163.72307544587355497629583843931', '164.37783429381980628635585694691', '165.1610364140194268712151794647', '165.93854142763105236828628982641', '167.255046563846994913436575455860', '167.9120193429891614629105116114', '168.58992709085186384199151051954', '169.54386072569145794776743243396', '170.15341383327038983495295344404', '171.09258563420822929061733059858', '171.72102346120291701531023489079', '172.24589870939093924430799461821', '173.22073346997874630832633474343', '173.889508066791560179779677424170', '174.51603966581463933802590510042', '175.68301770038819365064929291624', '176.438293320699906831572505511', '177.33783806055769303293918679318', '177.9665988415878275816841193660', '179.05064605364925476112788056276', '179.65924472539753691040908577289', '180.44125817627151598836947601101', '180.60639724796405240274891718154', '181.82481692300013671411136119495', '182.861665536618922904710678622936', '182.96385675466187745602614313736', '184.12560415011463936624832647688', '184.65746820855083007550176604970', '185.94354018904208625178792076835', '187.00865688990727400400969364625', '187.37690120824650360437275052933', '187.854643394043770569773847828714', '189.02463868003153141996632442401', '189.62222409248117522725033833408', '190.32708123945648770617181730965', '191.02358854858293042410750246552', '191.87461733866625292023674778896', '192.51739386261178034017628349647', '193.12244109411855897837765046263', '194.36220111631652304102181536799', '195.47295264005215711799690066624', '195.77205787089128730188141053881', '196.564020834641540849535889974640', '197.526093137899233193688819727666', '198.02458393688566643532286425807', '199.115244766522825368238044645086', '199.54130451663590021340721472712'], 'prelabel': '1-111-111.14-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5154818328690067, 'root_angle': 0.27053983839632106, 'root_number': '0.660038762259352027347602909095+0.751231543743433722054612189819*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.135269919198', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.650036019617538158436434502127+0.167760954875569027625436143531*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.35716483168', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.47476126713', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.30509178758', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.5154818328690067, 'bad_primes': [3, 37], 'central_character': '111.14', 'conductor': 111, 'conductor_radical': 111, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/111/14'], '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': '1-111-111.14-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': '1-111-111.14-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5154818328690067, 'root_angle': 0.13526991919816053, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35716483168', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_111.14', 'Lhash_array': ['dirichlet_L_111.14'], 'label': '1-111-111.14-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/111/14'}
Lfunction data - 1-111-111.14-r0-0-0