-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2057.150', 'a10': [-0.17755319625430327, 0.9841112043361161], 'a2': [0.9828184036767557, 0.1845751483658454], 'a3': [0.5224985647159489, 0.8526401643540922], 'a4': [0.9318640292114523, 0.362807705350641], 'a5': [0.007139922638469387, 0.9999745104274992], 'a6': [0.3561450204591895, 0.934430695344563], 'a7': [-0.12108188703135471, 0.9926425220757603], 'a8': [0.8488878315900227, 0.528573031262842], 'a9': [-0.4539904997395468, 0.8910065241883679], 'algebraic': True, 'analytic_conductor': 9.552667839743666, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [17, [1]]], 'bad_primes': [11, 17], 'central_character': '2057.150', 'coeff_info': ['x^880 - 1', '0.999974510427499 + 0.00713992263846939*I', '\\\\zeta_{880}'], 'conductor': 2057, 'conductor_radical': 187, 'conjugate': 'dirichlet_L_2057.96', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^26', 'a^143', 'a^52', 'a^219', 'a^169', 'a^237', 'a^78', 'a^286', 'a^245', 0, 'a^195', 'a^756', 'a^263', 'a^362', 'a^104', 0, 'a^312', 'a^618', 'a^271', 'a^380', 0, 'a^225', 'a^221', 'a^438', 'a^782', 'a^429', 'a^289', 'a^827', 'a^388', 'a^311', 'a^130', 0, 0, 'a^456', 'a^338', 'a^47', 'a^644', 'a^19', 'a^297', 'a^653', 'a^406', 'a^870', 0, 'a^505', 'a^251', 'a^348', 'a^247', 'a^474', 'a^464', 0, 'a^808', 'a^226', 'a^455', 0, 'a^315', 'a^761', 'a^853', 'a^502', 'a^414', 'a^469', 'a^337', 'a^523', 'a^156', 'a^95', 0, 'a^840', 0, 'a^368', 'a^482', 'a^79', 'a^364', 'a^467', 'a^73', 'a^581', 'a^670', 0, 'a^45', 'a^241', 'a^323', 'a^572', 'a^679', 'a^754', 'a^432', 0, 'a^16', 'a^90', 0, 'a^20', 'a^531', 'a^113', 'a^277', 'a^454', 'a^374', 'a^837', 'a^273', 'a^771', 'a^500', 0, 'a^490'], 'euler_factors': [[1, 'a^26'], [1, 'a^143'], [1, 'a^219'], [1, 'a^237'], [0], [1, 'a^756'], [0], [1, 'a^618'], [1, 'a^225'], [1, 'a^827'], [1, 'a^311'], [1, 'a^47'], [1, 'a^653'], [1, 'a^870'], [1, 'a^348'], [1, 'a^226'], [1, 'a^502'], [1, 'a^469'], [1, 'a^840'], [1, 'a^79'], [1, 'a^467'], [1, 'a^241'], [1, 'a^754'], [1, 'a^20'], [1, 'a^771'], [1, 'a^656']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-2057-2057.150-r0-0-0', 'leading_term': '0.788861064425409261959033771465+3.73572333925474896309414609803*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/2057/150', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [3.8181056358381498, 5.953886191689193, 8.415774321989712, 9.219442584371503, 7.2693708985050645, 3.4280492031886, -0.10204629118180314, -1.5506554314902687, -0.9942432207538061, -0.042485708891679574, -0.06237578232620651, -0.7964693201868475, -0.9064461656127687, 0.1834205047627782, 1.385622064222384, 1.2189706893273882, -0.229060834585396, -1.2207695338016877, -0.5366106166335002, 0.7678070746086958, 0.5232257791203571, -1.6170389528313485, -3.2810146677803456, -2.142255226378133, 0.8601307838936729, 2.2170364558772913, 0.12840717933150478, -2.916942849540428, -2.935762967127286, 0.5236628341888967, 3.56507209449438, 2.6824646554807394, -0.8955467391851253, -2.9233603834201154, -1.6566109865066894, 0.1889420278686478, -0.43961093767426296, -2.55506139344988, -2.6231486994117663, 0.24759059507853015, 2.8388669658348404, 2.180823962233265, -0.4796497731139638, -1.6521821074117797, -0.44426673670668665, 0.7260512550988218, 0.12688319940813034, -0.92992519521324, -0.7077126463716085, 0.03964382557661891, -0.2034645751225156, -0.38716030114694544, 1.799287348184155, 5.300467541337355, 5.600457874062652, 0.9685916728438781, -3.72112213455987, -2.470078078613768, 3.6298116981109647, 7.233431434725784, 4.2331675270176605, -1.0928747204748845, -2.3559319737386817, 0.42869652692670845, 1.982537600566227, -0.09166655698235024, -2.517532130180577, -2.0958044335890054, -0.2612331411072348, 0.13800269057828313, -0.463651314306504, 0.042218462875160796, 1.0997339295952995, 0.4958242195711747, -1.0226823939428955, -0.16629803900575493, 3.2582413937787433, 4.996675762230708, 2.4678927429322735, -1.1149992410001508, -1.5446617634034447, 0.22311792227060445, 0.50388528498889, -0.45731286340326405, 0.8331571764230346, 4.139880101639205, 4.672571574912469, 0.918830931126794, -1.7817512162006204, 0.9734519402171874, 5.30287927348168, 4.47075389952538, -0.769446801830953, -3.167842884031163, 0.17015048107946837, 3.986700241319142, 3.359342596990782, 0.43182889349559717, -0.41949988036951363, 0.40199285229004394, -0.13698777562300526, -1.6875177856242662, -1.5882364974548935, -0.19068413380581137, -0.1620227396254443, -1.259573076630315, -0.7134920742215387, 1.2885583362370268, 1.5717429925418218, -0.0030548486656682963, 0.05278589478554318, 1.8557845317715354, 0.5470336499080564, -4.920094625747038, -7.182826209680668, -0.3086741674390345, 9.958690273895275, 12.743955194473314, 6.595309578519172, 0.18137792683650925, -0.8082213512809205, 0.342602666854662, -0.36591718606035806, -1.1957800101865539, 0.07305922398222976, 0.9562153298178253, -0.8448258129747022, -2.3302057211810183, -0.2433176566355871, 2.6748135682602547, 2.0207755761060464, -0.7824532132702156, -1.1971066964641914, 0.5975364418053766, 0.7960756345315162, -0.7151456058106906, -0.6649875228941519, 0.75836519579415, 0.12792175721300572, -2.1537932403471665, -1.986757010822715, 0.4686310700623665, 0.31629903766339806, -2.905735640556636, -3.4649963573003513, -0.004100775549247104, 0.3061472875907191, -6.527070446193585, -12.919406583881434, -10.267113967580606, -2.059655982299656, 1.8918213782012403, 0.08581786378925238, -0.8649902280493915, 1.478649373863177, 2.733891670939277, 0.8759409487150598, -0.6734043784235366, -0.07895809845185145, 0.30706692192569923, -0.37422223716467473, 0.014909791746133017, 1.3240971852583951, 0.9475141249748111, -0.15377114651553275, 1.696598820843982, 4.989523109070967, 3.79990532660974, -1.7689793054551344, -4.300019810551437, -1.0308385711202201, 1.6276022459841928, -0.4750045709594276, -2.2892999322082117, 0.34221896462675055, 2.4182724625364687, -1.0081602004694779, -5.016576168260531, -2.855857925128323, 2.4015907717661307, 3.3826158370779855, 0.6187140630437654, -0.11257103926742218, 1.3503950552480806, 0.8708294031527428, -0.8106830971772578, 0.3028568517249157, 2.7377816330632343, 1.576102360215065, -2.231026158185219, -3.2339739459902446, -0.9742949900399632, 0.1886601577733893, -0.4810657557990249, 0.010398541950982096, 1.354675902820484, 0.8768696495133728, -0.12198600405509097, 0.8922571002881183, 1.0509380833131865, -2.6312575739300588, -4.274273393858638, 3.399656806424847, 14.570811301986868, 15.896201950880489, 6.416093852254314, -1.0353205104688952, 0.41926144487991224, 3.63350649666525, 1.9785728710706634, -0.8624473358268108, -0.3644758451186005, 0.8290099880689569, -0.15212986694122768, -0.831731420463685, 0.3484786418486765, 0.5129093643284675, -1.0278438353788073, -0.7207879576815874, 1.6945015998186472, 1.8940663269108224, -0.5000915659782504, -0.8668392033896772, 1.1596926687719722, 0.8408200651423217, -1.7536114780658658, -1.2605088361075274, 2.016003525497178, 1.7359686841005437, -2.0940800929923022, -2.159607061609638, 2.4840445106950026, 4.08181053358313, 0.33990857838052335, -1.6996135488641042, 0.7497305539614807, 1.6488911544452305, -0.9558788131295824, -0.5488326910198356, 4.571597813323524, 6.396874068017782, 1.1086782585570873, -3.9813010623975833, -2.98999361991355, -0.005343567796287816, 0.14967283076123525, -0.5811086932081742, 0.05978918335466568, 0.1797885444440973, -0.5088263081542937, 0.700474859595896, 2.899590625575171, 2.309839849320215, 0.1713500954557659, 0.6429186574469246, 1.9613989820266493, 0.09007953565115005, -1.3122143254178584, 3.273720624632533, 8.489862336587379, 5.2048018503755875, -2.3647586910441323, -1.9947130209851711, 5.940149641118785, 9.21250268952174, 4.2562189693738075, -0.04070136641281711, 0.8596682260115642, 1.8414114180205166, 0.3582374072007003, 0.003992262491366726, 1.1581135539746579, 0.297373306627732, -1.6475031744721824, -1.0762382599293232, 0.14700021083150386, -1.4810977476251943, -2.844022236421175, 0.15056939192381485, 3.612052131848662, 2.323607483551172, -0.5389287134122185, 0.06287891037546056, 1.6684298346537696, 0.5564976708595137, -0.5717224322358373, 0.5506455065106549, 0.4847131697403208, -0.8563458384127375, 2.860444876161081, 10.954231559671017, 12.307430338520785, 3.524690240248437, -3.4450750628407345, -0.4883879537564963, 4.293877983950585, 2.401590676001377, -1.387461957110348, -0.613944640805522, 1.2548651753893885, -0.029856935055547706, -1.0586650515280256, 0.7603609103520768, 1.522066316061386, -0.6031293928617658, -1.664362552669403, -0.3116682484938207, 0.23498381258648227, -0.3444271898148448, 0.07924866071761501, -0.21453479008573495, -2.6511533649078607, -2.3463476064253737, 3.1242516921987136, 5.8817201626667845, 0.33528601167448235, -5.237374930224104, -2.382657630457706, 2.514089302312893, 0.5168457481444108, -3.6040318470595643, -1.6636176441903636, 2.456546496138133, 1.6792594047515232, -0.7269352519590033, 0.6047601238591784, 2.184655145044972, 0.25922170412456125, -0.7761139855558594, 1.9631568726403383, 3.342326599713493, 0.8960638459896697, -0.05203409964921506, 2.4091873640020935, 2.9391517865437162, 0.11521062680032564, -1.0685748914919584, 0.32066252564465286, 0.40322724684815664, -0.29070850178189767, 1.307448654454853, 2.670731351367679, 0.7148175176427396, -0.6372807799893603, 1.4437305978624801, 1.612719114424983, -2.453083231536792, -3.4537056636524275, 0.754906842860528, 0.3101566951282855, -7.902869101086443, -11.082600915115766, -1.8418516299594085, 8.085901049947696, 7.261785501425184, 1.3427980448131578, -0.3623454828461271, 0.5050991019586063, -0.2967867788564473, -0.836983771357778, 0.1970938411343135, 0.18048429137454552, -0.5095556143521386, 0.6726894074726035, 1.3790690761425712, -1.0283019405016358, -2.1335703253209255, 1.5555826600563687, 4.530430151269452, 2.3504071570186587, -0.029296062269751736, 0.8782846901874878, 0.26816636403817834, -2.975288776034406, -2.16791874626191, 2.5584048935682815, 2.0396570620492245, -4.169416991706477, -5.670470274453622, -0.5985201199974975, 1.6075111664872423, -1.1328243196672063, -1.217665846603263, 1.940975562778938, 1.7081601608484924, -0.732184844503794, 1.029739404872414, 4.459654183961258, 2.9455946649516185, -0.6881966594830425, -0.21406656983337108, 1.8923081632666212, 0.9415196227783591, -0.4245117007349658, 0.7709018479279438, 1.4865185508019259, 0.23111077876163488, -0.008226528980185988, 0.45020957102670545, -1.0317691219182665, -1.71750712605564, 0.8705110678194521, 1.3357255614735104, -2.225790490285367, 0.42303340797589134, 13.700605723845047, 22.972083907741027, 16.00918845418435, 2.9975511836113813, -1.3464821623708598, 0.2691620258505097, -0.8218800998403912, -2.445833769465354, -0.6137796172693676, 0.3285991832882972, -2.1125338646062075, -2.7881513857736513, -0.15172194931821492, 0.8678457256407084, -0.2934465130534791, 0.1148101038938224, 0.8472374419531458, -0.7124192511137698, -1.023504812027519, 2.0021494330895226, 2.8276211211297997, -0.5543957139489117, -1.4105081504893482, 2.1820569717750935, 3.1598894934567783, -0.039927259794837675, -0.9998629392447325, 0.6964082038318878, 0.10049615791894553, -0.31309902534371514, 3.726086461987929, 5.656479468684387, -0.6307770848732646, -6.189160302661865, -1.9871762501908405, 3.764901648549147, 0.94392418964267, -4.248538840765775, -2.8214093341547617, 0.7496300013701601, 0.03300551378056533, -1.235970186868417, 0.5468099953040324, 1.5507934247102668, 0.1850579053098566, -0.09799456443200708, 0.4160883017593729, -0.9072997734132584, -1.7082516764886357, 0.006213888332871633, 0.37481530207859837, -1.506434714612797, -0.5971367959131706, 2.32288180604597, 0.9729192024101024, -1.8092563535415689, 1.7839335886477403, 6.660247088005205, 2.375402769082592, -5.310796539439226, -3.3970318782362097, 4.143761501659108, 4.302316121358195, -1.1969469921504297, -2.014406819940481, 0.9498630276962295, 0.9921629477504478, -0.4396161754776726, -0.05594442931789601, -0.23622885938801402, -0.6915785260973959, 2.8908459547332455, 7.4606928475433705, 5.695634846612658, 0.3487114540804644, -0.5220336783776385, 1.6487619885590792, 1.0481076648837193, -0.4980194408295092, 0.32102988748979455, 0.7327230178300703, -0.19015161472660327, 1.0013894412004325, 2.3546415704919097, -0.5177937145018713, -2.6910151282755286, 1.6361696580737197, 5.285259338150036, 1.2041494019907704, -1.8627795092727142, 3.99849801983552, 8.896098870916713, 3.71793293592812, -2.336614906861225, -0.14500537120707357, 3.004379623351727, 0.010240056401398592, -3.0598299738264605, -1.3542381618705992, 0.3921373669372028, -0.1601401989133186, 0.24679462421083206, 1.0132481581864463, -0.35188895476652765, -1.1996786015070537, 0.12471007147005768, 0.1042987084279679, -1.0466906431835106, 0.7291194314549105, 2.367607654898328, -1.3045085777199859, -4.354256571324482, 0.3891400422134665, 5.7686322152594665, 3.198537331051784, -0.8885193105862965, 0.7920091764109868, 1.8433275196476258, -2.428279731346969, -4.179175062678398, -0.10560955735699032, 1.5526774586960177, -0.9485655524360812, 0.14319169689893813, 4.05721264874517, 2.7025836209356084, -1.8114285811675297, -1.692503222920692, 0.6741461731377397, -0.540239224406685, -2.18461613089359, -0.7172585334315515, -0.039713405341621086, -1.259651166100983, 0.25397731176475274, 3.4201992160770773, 2.802863662466636, 0.18217786234536185, 0.08438583848123851, 0.3396695823900933, -0.8730367467375186, -0.11630683224914601, 1.4996835821827554, -0.1643187983565318, 0.9424542373488299, 11.525520259543262, 19.635612905805765, 10.41049084476621, -6.046687009306571, -9.546893119257463, -2.0554749144728923, 1.1221302726010138, -1.1475472488292253, -1.041575863044222, 0.3017144323639878, -0.7805311011062915, -1.0798183862491975, 0.556740684126485, 0.20194765556009656, -1.091099008651919, 0.49582015780183814, 2.032175868921633, 0.4728420824812001, 0.056578278346051517, 2.030518913704735, 0.6848086830178488, -3.302670458486455, -2.669814421489897, 1.159690794298439, 1.1818884963877927, -0.5279109149015841, 0.3784759315794759, -0.9475589824591237, -6.306084128804362, -6.4309033369537385, 0.6735998538690261, 3.5612197980793407, -0.6937690024999859, -1.866420688058486, 1.469036304226209, 0.7390397339543202, -2.540558317550106, -0.6644534479212492, 2.197880479109982, -1.1135232443450422, -4.641392573649284, -1.55167553848233, 2.142105482325439, 0.7266965007338468, -1.1149329185056207, -0.19645500304713592, 0.21001733902085176, -0.16379489361689298, 0.6395179103682526, 0.504648511972158, -0.813121139655191, 0.3770771720181877, 1.5314800368521877, -2.743452682424289, -6.811444958254598, -3.0228082503601263, 1.5004105993670946, -1.4254077816886055, -3.3031946336602025, 3.191782708079521, 7.136049001350021, 0.762302731109928, -4.509733791913385, -0.6315114682077799, 3.135791936536857, 0.8483528193553558, -0.680318295949179, 0.9342894268281805, 0.4708936739272124, -1.298540775493937, -0.5170115648797082, 0.08318716897783351, -1.1356862245268684, 0.12340458116553843, 2.80628233649727, 0.9120872006049725, -2.70826920639149, -1.167548586791704, 2.090454396688446, 1.1512875824475681, -0.28210237011097206, 1.0375200401865752, 0.6821274168298669, -1.482165506006744, -0.23990563343495797, 1.8914652653045039, 0.04410569586420886, -0.6226159287668708, 2.6469813987760333, 0.0754302815790286, -9.937388888207616], 'positive_zeros': ['1.86317585780093479879342120762', '2.83749581037435970647625541488', '3.08678614186657953284368751636', '4.02209381722931578700130289991', '4.95487763100615359236881989874', '5.74172841985534394951729717055', '6.345765592384263825147403004', '7.41001130171426368514900497891', '8.137142753684304248414110698640', '9.02250964134254815121273178686', '9.92341092116934336963949632922', '10.88339121680434912449648799963', '11.16599908774868731091506143299', '12.1651035201562949531794710687', '13.06645298536002089222822790058', '13.834754038022738907786196956048', '14.406738940721449814542169364394', '15.282632568252872671544711864226', '15.512943491850665320474865174942', '16.03698169105295923073636241475', '17.23905727978520750901571452363', '17.95015614835935519441600369916', '18.98695137520120281461866629685', '19.64511946013661648755262431703', '20.30309667553735560132732152938', '21.31923090908139946892205320698', '21.63504757249965492697410018792', '22.17605463676784893733358724630', '22.9047993630261011447144609832', '23.45686133133135827330697391214', '24.57114106469884111091284847666', '25.268845233064755935260139820138', '25.76960001905486369032215019346', '26.14067343094220076165862394320', '27.25516473679552537969986438610', '27.74579631651467472894140543587', '28.70416182742416346027690071597', '29.3639330541197132619591311789', '30.37880298376407751953535014987', '30.782370159875487919918914594402', '31.21981923685693773436438046450', '32.25782065159592206375591497006', '32.43557725370706541888360511340', '33.23805353014107038385120315480', '34.06177538618989240168128752411', '34.36361593889897436214892180468', '35.03953357114855459092126148243', '35.94665706917700515347783586976', '37.20304775337070995914303576326', '37.68811705680392613230167180252', '38.03913645681779569037882224679', '38.737135549809660738847058529430', '39.26573462936654905162021143329', '40.022027769530154424483419161893', '40.841188770256887379146785211865', '41.45789591969309821661649700541', '42.03982235971997523910813306950', '42.63776750671170539820175146587', '43.14390012477060307262733324521', '43.99610790001529166429416226772', '44.413453644986205289044715031190', '45.312882030162901136318195454534', '45.64939630471372295590266296901', '46.97523952691851795014211884995', '47.51075677784944271653735102557', '47.95665686595451753492122912361', '48.87469413561393247139054075981', '49.40081731611291067084967612036', '49.83693923797949383728725626252', '50.30875933838301894695755492023', '51.1564000842029431269548287700', '51.34267354880689619603716319244', '52.40392407694220346482253239861', '53.20260345939520739749525166700', '53.7041976725858161756441422418', '54.346318312621393716152162543851', '54.93808770259955722981423587383', '55.785374989517317198226305503650', '56.65845007293824388954750028495', '56.90568835447177814968538133807', '57.63825544552350430944425616319', '58.0873776060815609730736088677', '58.87946171383888336689877626136', '59.85886279040973027750024000276', '60.1156188398610305669047537361', '60.62267953481800703207137138350', '61.47201506163803808601742826035', '61.66371267159103613585515606800', '62.30613853833428716996175138126', '63.026165610524308808112347338096', '64.29582139629071377173634355292', '64.65500237650946637650630303676', '65.49745849000591074028750930218', '66.003777358199930855131945183941', '66.53065913396387012416811705399', '67.10785920138871431412597352255', '67.6128636790075452444855136702', '68.22461679594192875972455361826', '68.99560316520485875555404473667', '69.513312919565589766329573266281', '70.10173077833468135004767200457', '70.74505408675966124187856214018', '71.39408825522339712782005106852', '72.03169504318324690007992394443', '72.83818802456789762881425655451', '73.35994758750668111123604478846', '73.9542091322944773553724537603', '74.41868729789924029675422512056', '75.36351386365198818155254107266', '76.250937561542336876515599738813', '76.60795030237521375399656624476', '77.165140317508198776641573172927', '77.57283624704846832558161958826', '78.01798695715336536394792401824', '79.12306724891034103261841725174', '79.21502871364840570700602267086', '80.00960756707852015435832303667', '80.451044686372994606088751688611', '81.449898158135816027888886106098', '81.965252098818562675568222153456', '83.11637210336388849640323308016', '83.28920701315714719160346327994', '84.14885322576186444920007823549', '84.37364954546131505206577209634', '85.04257137797211814617428029280', '85.84000696876904834221802094713', '86.02037514111357927580811434718', '86.864446248543148778050904316137', '87.72753971516190747932544689202', '88.11536829512218897837824983191', '88.843991559098345546958063001629', '89.252884086573342753830716488604', '89.776379739317798400181994730225', '90.14980842784230356729202127506', '91.36416302154652863183100981555', '91.89987375023040475934931359324', '92.66735181779427179012854783050', '93.19974399711664702427109255336', '93.74557444325301974501262634569', '94.26990333837094894987395230844', '94.92381182326698460675205330473', '95.70001115558087268730060171952', '96.057085244007799408049528266883', '96.52743754981276942580331521660', '96.82867504683139790153528678050', '97.6536891952840140986554032472', '98.4509969784335419422410748080', '99.18532593550487398388962527516', '99.719766235162024963977619471661', '100.41994284970324654715560559415', '101.11560967406362066123087330742', '101.48672229253083391292473717416', '102.21949175622147284403541565806', '102.62092499140649429614811794314', '103.56543408685735196874381215941', '103.76196039586982287573393171538', '104.70037396061877183632951185388', '105.242449632407325743722109192110', '105.74594592197706221609361829495', '106.047873749204657523242019256749', '106.96385948127007289453864758779', '107.31982830014971958564896719442', '107.95296650761999961577031282415', '108.69388931938290745475738137528', '109.07952300630164431964938036352', '110.0460798714026494983366242439', '111.06252205681172405900528407648', '111.36723683145633781042257273252', '111.803844805650087672475265522056', '112.440984766063223585279446879', '112.87213358552484823966375891157', '113.31298335060674481346658426444', '113.95522404741591972748059847201', '114.58383233813934615571487861745', '115.60904928994624240836965296053', '115.71274109853670186070296910206', '116.279331778033562882178678426384', '117.016446549738860327308216209336', '117.61153270403984926425928196203', '118.47518261530982177733526492484', '118.94653553030024770774259795539', '119.49655321322062762483293796365', '120.18901019671323907716290559938', '120.532821698383692431829648439552', '121.48171303668776546459197838452', '121.90203435656311959840958919220', '122.652478189730569304847869188596', '122.9802872110367202973849806608', '123.8198486906982482437608112780', '124.06631913338071469594514480054', '124.51674113542095858341560285545', '125.222089369687265193179288140263', '125.75077194966921946305011837975', '126.23472063890755304894193340868', '127.6220197944589081631072641824', '128.06139341933326643916649089334', '128.32110002581468868653077912409', '129.14796302884313493403194404775', '129.439678667095242853521439456381', '130.33100859551894041984137900733', '130.84985781948938656808740141876', '131.22152807154312858928184429329', '131.76260309496761418561568894491', '132.314000014675233076422075861929', '133.07689930224592381909890422056', '133.57800554993953868779985457831', '134.3709720928811274867479976645', '134.862909061002910391457425904228', '135.331326148215794107629674225475', '135.66789911766046646886429081213', '136.53898219930101214095051728905', '137.270033314686651134241891382112', '137.85924702224568194873886415479', '138.65427236140847061595637778294', '139.067233876123759053488034907073', '139.6142249826738482892129653146', '140.360398552545554401043896598991', '140.66598824677103814736206784170', '141.085433929870293163772505914566', '141.873957707886624701749797566874', '142.25788686204839734361658653039', '142.87137876926527297201735883643', '143.518353824338750958792910840485', '143.96749836213815122958603537135', '144.771155223913187482701970594727', '145.44543847169196771012398652789', '146.174550732811853059373762355867', '146.76515963392792281468381031825', '147.368459074715588143354084416642', '147.84081764552328311647416384288', '148.03821182748713815552185542009', '148.54468820890501176960924451462', '149.71728737345957641482054483732', '150.075569341116930711486801416161', '150.79101471540335340182136690366', '151.17566414162419200160705830785', '151.782428162691214724281244994082', '152.01674059473435882792135082245', '152.77320793247020012507362472037', '153.3518328908563041314865001249', '154.12794956281687365325696484198', '154.52062402734753014541765074457', '155.46273337247732365443977692982', '155.94697660846465585580328705585', '156.56318834747917827288808895741', '157.36750227831369685925552191602', '157.73975961876859502498953758358', '158.05447107326604377339047816386', '158.69146010700486586818486282367', '159.3462076644195419599598514502', '159.71152176677528846689035884321', '160.232605094586939209814230412648', '160.8583168544141941473556693255', '161.545700820273651851756404723547', '162.389216985832428474697434321188', '162.732947304920057779262918956252', '163.285228715572149883199466583415', '164.070111665724000858009085884207', '164.568836021155900414301766731312', '164.98816303757052333259686817631', '165.796593031837697010194551203661', '166.44000536166152919470002654875', '166.80586728919379796488002985726', '167.65486417896329112450777807027', '167.79689207219891422057865247291', '168.4128834246850443880726862570', '169.416008763928919400067779035017', '169.65606138129029470929534256521', '170.0976566795989015694072017976', '170.64200910452124137429722320536', '171.22748927721447214143854864081', '171.50267116274104502996634442131', '172.68480586674696162196892852374', '173.54449979642033256961894528323', '173.91744370406426717905600951568', '174.56338406137401332614173461011', '174.83864839550978402121896550866', '175.51285616502532867823240557248', '175.974331272838283156295736289583', '176.50086208266566554108604011698', '177.27701038683819741952667698063', '177.48712067925128057708931592227', '178.17772369106219523895078652360', '178.95393528083081154647606115839', '179.54674361846824621119586038268', '179.90884812694594033354180017315', '180.226032472242569420131503971672', '181.22095351428545360743503651804', '181.82860751252857619904204392537', '182.360625409090399848294737878693', '182.873792670396863986330321216525', '183.4870944891725610888097507140', '183.9953458084928880582377646519', '184.7844967647325116767430897474', '185.394930194137065810631447653060', '185.991016837619870600540412071453', '186.36775702246125293493501175760', '186.666992071840984794446125966359', '187.2938125418597632113212516972', '187.76134902741431035512853206693', '188.28326846512624663579103494695', '189.219927996821310556660197402062', '189.59354386961229874193960423531', '190.188135021168390522052042605077', '190.96565700850013197292958290013', '191.59566180367832817997681385367', '192.276014516366387906801033465864', '192.647311333862285069761257780950', '193.19426801992946641892683104144', '193.871524026310341615045144279236', '194.0924418446007487505257009209', '194.67452336961540936660872349009', '195.37804104733717526909222685921', '196.028930261534583439226500269841', '196.73486347910498880633713669183', '196.98295578750641570313061996253', '197.58945609692030156975545263301', '198.15025778996137618577252940268', '198.75511018699193768379622137184', '199.13444387056129520249220596223', '199.690450882331406383130480327368'], 'prelabel': '1-2057-2057.150-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.552667839743666, 'root_angle': 0.43375667876355056, 'root_number': '-0.914624126831162636409656368563+0.404305214681103666233192579562*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.433756678764', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(880)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.64452264966085749932138768258+1.58070694843896429171306974315*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.8631758578', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.83749581037', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.08678614187', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 9.552667839743666, 'bad_primes': [11, 17], 'central_character': '2057.150', 'conductor': 2057, 'conductor_radical': 187, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2057/150'], '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': '1-2057-2057.150-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': '1-2057-2057.150-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.552667839743666, 'root_angle': 0.43375667876355056, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.8631758578', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2057.150', 'Lhash_array': ['dirichlet_L_2057.150'], 'factors': ['1-2057-2057.150-r0-0-0'], 'label': '1-2057-2057.150-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2057/150'}
Lfunction data - 1-2057-2057.150-r0-0-0