-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_57.53', 'a10': [-0.766044443118978, 0.6427876096865394], 'a2': [0.766044443118978, 0.6427876096865394], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.17364817766693036, 0.984807753012208], 'a5': [-0.17364817766693036, 0.984807753012208], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, -0.8660254037844386], 'a8': [-0.5, 0.8660254037844386], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.2647068871489494, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [19, [1]]], 'bad_primes': [3, 19], 'central_character': '57.53', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 57, 'conductor_radical': 57, 'conjugate': 'dirichlet_L_57.14', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 0, 'a^4', 'a^5', 0, 'a^12', 'a^6', 0, 'a^7', 'a^15', 0, 'a^1', 'a^14', 0, 'a^8', 'a^11', 0, 0, 'a^9', 0, 'a^17', 'a^13', 0, 'a^10', 'a^3', 0, 'a^16', 'a^16', 0, 'a^3', 'a^10', 0, 'a^13', 'a^17', 0, 'a^9', 0, 0, 'a^11', 'a^8', 0, 'a^14', 'a^1', 0, 'a^15', 'a^7', 0, 'a^6', 'a^12', 0, 'a^5', 'a^4', 0, 'a^2', 'a^0', 0, 'a^0', 'a^2', 0, 'a^4', 'a^5', 0, 'a^12', 'a^6', 0, 'a^7', 'a^15', 0, 'a^1', 'a^14', 0, 'a^8', 'a^11', 0, 0, 'a^9', 0, 'a^17', 'a^13', 0, 'a^10', 'a^3', 0, 'a^16', 'a^16', 0, 'a^3', 'a^10', 0, 'a^13', 'a^17', 0, 'a^9', 0, 0, 'a^11', 'a^8', 0, 'a^14'], 'euler_factors': [[1, 'a^2'], [0], [1, 'a^5'], [1, 'a^12'], [1, 'a^15'], [1, 'a^1'], [1, 'a^11'], [0], [1, 'a^13'], [1, 'a^16'], [1, 'a^3'], [1, 'a^9'], [1, 'a^8'], [1, 'a^14'], [1, 'a^7'], [1, 'a^4'], [1, 'a^2'], [1, 'a^4'], [1, 'a^7'], [1, 'a^14'], [1, 'a^8'], [1, 'a^17'], [1, 'a^3'], [1, 'a^10'], [1, 'a^11'], [1, 'a^1']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-57-57.53-r0-0-0', 'leading_term': '0.976751140114436497291408356909+0.724093447922312520326441593924*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/57/53', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.2158758616893723, 1.5652510972890235, 2.2032459299377876, 2.8792278192174896, 3.3900204595302736, 3.5829993877282886, 3.366853884469683, 2.737417562860816, 1.7949574657060916, 0.7358488725976721, -0.18873851143472647, -0.7417397995972467, -0.7780850361390946, -0.30428739859201337, 0.5069378531173379, 1.3615148815955163, 1.9413991056109858, 2.024167370433024, 1.5790208935296928, 0.7949050316686193, 0.018062616646013968, -0.38745675373292404, -0.20575393654798788, 0.5097602881124405, 1.422537318496612, 2.0292674113198146, 1.8720006256251625, 0.7610375891778514, -1.094370740498317, -3.121717307065538, -4.592635398325615, -4.926071036812501, -3.956153454365846, -2.035680057336119, 0.08822553078693822, 1.585575871691002, 1.90696307300769, 1.028267460536752, -0.5466011608354794, -2.0343581927682233, -2.7552766459881393, -2.4596413109816706, -1.4295054504917704, -0.30101498023847434, 0.2986751185786276, 0.10166412267196293, -0.6599747495887278, -1.406654699431662, -1.5736451668930365, -0.9728333790315141, 0.06671540702015898, 0.8786365692981535, 0.8691443808316411, -0.08209026098592659, -1.4828074884526898, -2.4629214600826783, -2.273670839788119, -0.7683414343235977, 1.4324149921623581, 3.2206065476496786, 3.596020584175297, 2.2455796511465, -0.23723951807089602, -2.6420182066303988, -3.7923028984167644, -3.1881892538945724, -1.2645646173229463, 0.8883017401624274, 2.172611163283434, 2.1056801330692796, 1.0410421238361418, -0.13455374985273014, -0.6179953674081924, -0.21186457225098726, 0.5891568200081142, 0.9946285136562927, 0.5169025722951913, -0.6493421780092068, -1.7405139808837193, -1.9620252595106074, -1.0764120599850906, 0.3855885882496655, 1.4687612834766322, 1.4787675184810414, 0.533645999861632, -0.43287701881259755, -0.2686519246029693, 1.5719004442100213, 4.5390639644167, 7.206227162491301, 8.100931216893477, 6.626934204569952, 3.4669179300009736, 0.18265570710143283, -1.7380584643263337, -1.7633321986351291, -0.5502096460580582, 0.6051866703278619, 0.6986324446988278, -0.3241145249149812, -1.6258750323728361, -2.1747465460666926, -1.5431805177954192, -0.2139381645990589, 0.8217636892831538, 0.8504077517662663, -0.008362692740356238, -0.9130551530030173, -0.9954899149531679, -0.09216451932196232, 1.0824951595619916, 1.4924588962520655, 0.6578911402736743, -0.8405484271279319, -1.6779082489209622, -0.7498756985438194, 1.9119988688880154, 4.990991570127786, 6.682728668996997, 5.913699532498102, 3.109492187245751, -0.06282242184831562, -1.8162984433910494, -1.432121310661996, 0.3358853793861738, 1.9104746351246158, 2.084652094853868, 0.8608807073963837, -0.6683173745451141, -1.2548527498726618, -0.482651978593048, 0.9638062862168604, 1.925057143699557, 1.7395256662829215, 0.7510520621726071, -0.05909972852352473, 0.01358861001895612, 0.7313189726130126, 1.0903508349538322, 0.2194969123147863, -1.7556136311361337, -3.654920527492052, -4.118626915866658, -2.745051013435969, -0.5440995618886459, 0.7385920416238644, -0.036393361349218015, -2.438769325991116, -4.684900838923161, -4.927393546970722, -2.6505904831927163, 0.909386320866825, 3.656001338920375, 4.148627920286931, 2.575328065518459, 0.46044756750369903, -0.601989563097732, -0.1426845395512413, 0.99720540173703, 1.5585609829334564, 1.013590882430139, -0.021557921563479264, -0.42896558169255383, 0.3263681270172441, 1.6604665933024338, 2.3746802965769516, 1.7528391281251001, 0.2540696544816497, -0.8575116204945354, -0.6575649330453782, 0.5339842575859566, 1.3452687977711109, 0.5549424773589431, -1.7062140719420842, -3.8448665103575945, -3.9916909774564595, -1.5672974013453187, 2.0830927204607668, 4.582571360523447, 4.284870006937465, 1.505168481654829, -1.7688761257734686, -3.435125414179008, -2.824986172487765, -1.009486156527377, 0.29759933413704137, 0.2302322063256687, -0.6263205341467533, -0.9638539996633273, -0.07126940692324125, 1.4804839608341522, 2.3908589444213115, 1.8708495894137318, 0.3976264762968363, -0.7268893297291107, -0.597352097600911, 0.4533025837172677, 1.2115130808309877, 0.8316048437364749, -0.21025951024165512, -0.4284558650938089, 1.276235794915604, 4.378379370970279, 6.8522303074653514, 6.700855592641265, 3.6489478146417857, -0.4794956384440334, -3.1028310591858577, -2.86868810103197, -0.6315509051006558, 1.3832621542319, 1.4824619453953254, -0.1646408523738499, -1.861755946394994, -1.9983481494186321, -0.45839171805585666, 1.3978361535332582, 2.064783203065406, 1.2452626536797438, -0.013427217819005362, -0.4492087570939377, 0.16444530128827306, 0.8660202506419015, 0.5717421779263254, -0.7249686858657469, -1.8487244681416435, -1.5891801224290905, 0.005220402529355334, 1.5075065578681954, 1.3986632128795575, -0.39550613283695646, -2.2181423561259614, -2.052031502572271, 0.6092951212234312, 4.108743499730293, 5.884855686251692, 4.6124749541374275, 1.3489239118897862, -1.3473564697145306, -1.5633810121565292, 0.4389860471287056, 2.6161447585951403, 3.024763650528803, 1.457305135031872, -0.5921522118174973, -1.4632236955667575, -0.8386207634762451, 0.16945340546802734, 0.3149962032743573, -0.47387972927771393, -1.08790919251569, -0.4934820917939908, 1.071206611337794, 2.226180771120833, 1.8208036131281857, 0.16712141162180286, -1.1648112800096422, -0.8726072456320081, 0.7188532986060715, 1.8811850892174435, 1.192140212027641, -0.8826205336464712, -2.151033222799025, -0.6132630840486551, 3.566461168428665, 7.9051882154454365, 9.520777342580661, 7.468087196512506, 3.423836311575644, 0.15174957992306273, -0.8105212137673088, -0.16184654273972504, 0.2354191194228824, -0.671004644125606, -2.183591569768999, -2.756654292886814, -1.7043270960120678, 0.05706365055776713, 0.9511987568794873, 0.34943200539846353, -0.83293665856915, -1.1566721410245573, -0.21120201179365378, 0.9469270085751785, 0.9591765314346844, -0.27820916355649333, -1.3552211048098188, -0.7810833168797885, 1.2889159846938958, 2.8709592585514203, 1.9003010217816136, -1.6696388323652736, -5.4947230096192925, -6.716125592745553, -4.444278345710067, -0.5524015329267362, 1.9789165353600509, 1.6359461349390727, -0.5017018769971779, -2.032476588498275, -1.5724830613165781, 0.09804598409920136, 1.0675546061454453, 0.3270557925088705, -1.2734472322017871, -2.024361747879277, -1.17231095288085, 0.3578397612592833, 1.027915807461553, 0.3384075906309947, -0.7175292472060925, -0.8645788803705243, -0.07208244698695805, 0.32388284654093874, -0.8740250529138445, -3.17660362190411, -4.57661689470853, -3.457568049689222, -0.3748000948759934, 2.2002570097635337, 2.111896422148253, -0.37640166556404364, -2.7190248968716384, -2.4436462289438707, 0.49500106110786124, 3.6366794946640866, 4.298026178804454, 2.01959601996525, -1.1389138778270282, -2.6342171793946427, -1.7403549050351101, 0.08402801445688458, 0.9293900500154857, 0.35884655172441743, -0.4226682231409989, -0.1508457116710291, 0.9972730418843474, 1.6264468112802422, 0.7698839896909717, -0.9134496759774933, -1.7683094294562078, -0.9531119825472594, 0.5654585261041668, 1.0019591263165313, -0.2682791512722808, -1.902609614011568, -1.9612015338368818, -0.11585758928373335, 1.6781104585231688, 0.9529910525351152, -2.7002015173464904, -6.882192819048873, -8.374219233192074, -6.046564381725858, -1.8827006265618103, 0.8736944955468551, 0.6324770756705502, -1.3656266605086018, -2.5992968551316795, -1.8229435490553945, -0.046048136849495616, 0.8664212356683345, 0.29360140799078843, -0.6100406628355473, -0.3969119711441525, 0.9334209480344187, 1.8999444825998357, 1.2274839761173122, -0.6593679706166042, -2.034808454743912, -1.741686556703384, -0.4368698128945679, 0.2277551055729715, -0.38327132446188067, -0.9790765676665886, 0.2849506346231106, 3.5051535317999107, 6.353655643860289, 6.028674808100648, 2.045983788334428, -2.9789621271289475, -5.513993409964747, -4.22755678115816, -1.0178556763947342, 0.9978792500188899, 0.46086400173427944, -1.2336286592252266, -1.7415464356777348, -0.3283144449697167, 1.4947848229404146, 1.7623168897679489, 0.2067086981427732, -1.546523633361913, -1.8233642859167511, -0.6585585631419703, 0.4516996113151181, 0.4041936651420982, -0.24231643297617958, -0.050832962209470436, 1.3929481405827602, 2.739641699779066, 2.2889794950766587, 0.041932400638870077, -2.0076067680292606, -1.8930290466700284, 0.07020457997502882, 1.3391538089387591, -0.31291382382184924, -4.321016292240094, -7.590548524241218, -7.397022192321901, -4.0397544149759606, -0.5420458184261054, 0.2992024079646281, -1.490173963300476, -3.3885669214531764, -3.125215984445167, -0.9055399734897616, 1.1000118072304002, 1.22461558318861, -0.036913151946279095, -0.8638810808060309, -0.2936162040057783, 0.791873643368833, 0.9134640130490178, -0.10020840712750048, -0.8503661092292172, -0.08258481344501217, 1.6541507263011075, 2.4455160654558874, 1.1742077726538258, -1.0553038150151728, -1.9912893187082845, -0.7550530505982578, 1.0220984095406425, 0.8953307933564212, -1.5577835909478452, -3.893359685333198, -3.090685562118952, 1.2648029900173616, 6.250207267837857, 8.207861752663522, 6.099360096597497, 2.2537501818863297, -0.1112817210317581, 0.08710746967277158, 1.2816023965903436, 1.4644055861917589, 0.4701244741808007, -0.14142295430538115, 0.7805765291826308, 2.450899208106252, 3.0077073092459847, 1.6915153655013437, -0.2503210521493304, -1.001237498787722, -0.25593530317129204, 0.5208828357551505, -0.026671014603464584, -1.3798246110800572, -1.688955428195033, -0.11880218969585414, 1.7670865894217564, 1.4367415813045499, -1.7109414622193801, -5.214042562126437, -5.709823776955988, -2.332564355730875, 2.2281721971370336, 4.238955584844576, 2.4746686387218397, -0.8219939167659589, -2.44459942802536, -1.4324247596616948, 0.3548937369459461, 0.6439697772558697, -0.7116685102394869, -1.820805982483318, -1.136798955203533, 0.7350865275028033, 1.834872439065378, 1.1795663518661945, -0.16550610430264995, -0.4807879809519112, 0.49874432609842834, 1.3270722022336678, 0.7389442539109998, -0.6549368381672974, -1.0415225004998057, 0.2369692570889197, 1.5012794485871557, 0.39692587179911576, -3.2649834799554593, -6.770142750450875, -7.004755226045038, -3.6897098927979037, 0.18674941386663643, 1.3543927973183227, -0.4446736578313255, -2.3554270707060128, -1.5697156582185952, 1.688744210379479, 4.512633684990991, 4.4600426602100045, 1.9955765950581401, -0.31051279951863187, -0.6772124071988963, 0.23095908184074754, 0.5563940298718847, -0.33841319504994405, -1.227314406978807, -0.7764472990327229, 0.6030565848246006, 1.165800828435072, 0.03381446274044527, -1.5504538295987558, -1.5786608533924582, 0.2857495058242892, 2.157833169213094, 2.0966929506859175, 0.5174899283738367, -0.11517232993485946, 1.7991003334516278, 4.759545878390892, 5.373750365559873, 1.9626367433093888, -3.3403338234116906, -6.437782743120802, -5.234758136155772, -1.550509341163609, 0.9707194480028916, 0.5800983549304787, -1.2057058374918501, -1.782839606631655, -0.4645898480195845, 1.0607531420248077, 1.0339648636237646, -0.2548337477210575, -1.0180915100401537, -0.33918372910677974, 0.6520593228607183, 0.24350471207437688, -1.604658238702379, -3.0556419721394694, -2.5599532166972514, -0.7470794687741122, 0.33879906945069677, -0.19956286854433153, -0.9241083835928138, 0.11772266052111668, 2.6162849982574157, 3.736213974713366, 1.0790898943183485, -4.2881946298664895, -8.312962185037303, -7.75979736374874, -3.3846797750104423, 0.9190497041142691, 2.0527561398782233, 0.48776533027121627, -0.9134917853530176, -0.38429598979714763, 0.9796999996505691, 0.9486243595948856, -0.9428230458419258, -2.8163369469793964, -2.7316011450726907, -0.9567772266207429, 0.4805621104409825, 0.28108111950138237, -0.7098334900425084, -0.8263214448177887, 0.13863630376150768, 0.6592353589767667, -0.39847375646118166, -1.984451931885205, -1.8732852475065263, 0.5256431611773319, 3.009453500279517, 2.798886161177233, -0.19724683612054963, -2.9300609356488594, -2.3900004613399966, 1.002318415437843, 3.668702685557205, 2.6507954923268855, -1.239714829151071, -4.3595043622088, -4.1424975931924735, -1.6092800697941263, 0.15117572212994937, -0.4563678886479438, -2.0420792693591223, -2.2649703607622778, -0.7087628971464053, 0.8241934727289988, 0.7040286191846188, -0.565902544014147, -1.1982892212331533, -0.545758370019248, 0.07795207812257918, -0.7560677889555943, -2.4843258248134297, -3.0115362964206702, -1.3373011541367064, 0.9311526390668398, 1.2805889785386704, -0.6540798028784813, -2.4363445254546012, -1.6308939894433874, 1.1037966114404212, 2.420650069401066, 0.012710642366588858, -4.508619308433626, -7.005800107233147, -5.099009732879648, -0.6333857456367926, 2.355746253399645, 1.8204201638139517, -0.5909705289114313, -1.8828557618196404, -1.0902472974666952, 0.18559540624447507, 0.2864091217246092, -0.3356015094236353, 0.058031470505189975, 1.9383238205548783, 3.6273810939317777, 3.271706771640485, 1.165344898660144, -0.5602263098047967, -0.5272498765058082, 0.2976203359723114, 0.06686209544062154, -1.290002239653906, -1.7305833180633692, 0.23733984601711583, 3.1443049616358945, 3.6853898649056167, 0.48202138319787363, -3.8664309624298836], 'positive_zeros': ['3.05264398190378724706401307006', '4.18971569348015419628187312811', '6.2588285258460393877005356274', '6.986347355265703604031475910026', '8.57656934094403387390761687380', '10.6108711247087023108230919278', '11.7725497887800773966645219789', '13.54992984075997721751113328659', '14.115053591798576692528383729876', '15.60520423219151143759517762256', '16.54257296197703713137949413541', '17.92550290524197437959346215209', '19.34722399455726448170423429061', '20.80121938811289109863826944851', '22.14434593921332734753186482834', '22.89763745434151662563110171146', '23.90117265168570621862572843080', '25.23082423092246179398228967895', '26.39901131709837712824127124542', '26.94518064586343169915945639911', '29.08330768633168966646313716740', '30.12711441603230070099260780331', '30.85952212499981240506074857458', '32.23811050457515754264183524501', '33.12251750024732692882093875921', '34.08603367014076036872327250216', '35.13954220537988714223208274579', '36.04324431841953927258299008482', '37.80528352608197097858442844865', '38.69630648115862061826322654617', '39.852948886465773056396911723400', '40.73307151226490255772406863557', '42.14879938285515608118642379935', '42.491685727217875067717566301836', '43.47967273187962351182320587291', '45.09133267784849175054619714407', '45.61862824764812804082076205783', '47.108235122981925710648180592675', '48.52708611570727393227294762248', '49.10453232254507845951108936167', '50.30502053436515823629695596782', '50.84626221500675648845594522995', '52.24087635391596460511208102870', '52.99667941759297644158756022625', '53.840877519187257237339005030191', '55.13555482351047608484521376041', '56.38591685700789067002645284304', '57.70781102786544762051802182782', '58.21832889197840806072564352829', '59.07803754519048678239958973172', '60.39784423328774331776805042407', '61.12684827135242630793285885838', '62.120390397294375565427543557316', '62.62313124300046812934653747953', '64.33616438159758722458824857705', '65.392835179081946079388065705840', '66.22435292394107955989483477946', '67.25861349787702604012784459921', '68.433332647889386991268764499847', '69.00263044906094088514948981619', '69.842344612088417003608025618624', '70.93661960315425800275402730655', '71.81784711396084504062728782997', '72.75658014212856969426528508911', '74.19354715637085900837417380712', '74.94438934482154721428897633039', '76.14967398309786002215151338287', '77.122106039338908720486836807775', '77.65056579470424986386295273811', '78.54675581219599868567776182305', '79.71693128635917570589271745239', '80.49611008247828821341600838096', '81.43678356835624317419932147804', '82.24443214603867711779905043824', '84.08516601952906080786758267837', '84.75244065770082836382287411025', '85.135424909600191731188754165210', '86.55118411546127306595744874399', '87.27758718721727213200957406341', '88.17484234458789485520168535397', '89.0033137381521695424240402188', '89.82010157027179297830800700762', '90.80926749452480975861003459301', '92.236344286129500401148703919689', '93.05623920901196040479444246066', '94.04392108439254545278004389888', '94.75421747783085117087435045205', '95.85883302455442398603959225960', '96.653942772285149608413783262304', '97.52642197554322950127371376145', '97.9533518537285214566390796588', '99.4108306681522894609609100652', '100.27240169532780679492288864158', '101.20632552504287126261857943605', '102.37949613438989242652489956537', '103.42111830911384136392725299823', '104.180718442354997426109720758192', '104.73679295905277118455118862584', '105.76910263075157203518024353289', '106.75135862969832452539447681954', '107.45241372674174801818184165383', '108.45338631038820336448633016787', '109.16583729610218405845040643902', '110.79975924592484239468295258185', '111.36000084611695653959256694081', '112.5090290595712404324152260441', '113.21219215159219699084251764619', '113.85979992103620650849512357970', '114.896829365412632503469617241514', '116.06856228816340163795308053459', '116.424367941697711778872743345031', '117.14902606679505589600096501639', '118.55936016519234878824478519097', '119.802897333630471987531262619233', '120.39920768532705023994502881213', '121.300779914121657387694532154180', '122.21955828304493989345829199101', '123.27987918379551993771357984443', '123.93458437664643961316679884594', '124.39177350629263885360989206518', '125.63009951183834561863399484998', '126.55221427328727908362377520601', '127.155592685797046021339952770581', '128.83301060463802137252395626313', '129.14634151344645353772188811150', '130.42978815486738868531978411170', '131.24147421293098152044281410200', '131.95478707897228806541317144731', '132.78614727604707928275832634631', '133.454224569219814223478535872399', '134.53611145308993998172825119002', '135.4308143163823066344801901597', '136.0764294208822553140548140852', '137.111778656300608324479445336660', '138.71952341609184277334006916347', '139.03651994598555998337032819305', '140.159605462552331608510734557925', '140.42029316299739829123538674910', '141.82817351271019200842565105137', '142.575359122136753942333985062191', '143.118058965824722616734814704328', '144.07958470108702445264691713209', '144.85533375032817330706406241739', '146.09010296704316827010466474831', '147.10476257544563532345403540645', '148.050076000761554602777812800147', '148.610469969125779322527974312546', '149.56793140662776629077901683024', '150.57922558919773733712002055822', '151.11891336353801806397121126723', '152.03799258596980305038173085486', '152.768760131739490226581904372409', '153.48143180994939096079265130523', '154.980429621984817577188445712268', '155.56779826989894734118854391810', '156.41543067177727150901575079639', '157.75325202717950803454218125122', '158.36233334509232092167205179340', '158.97139238685872248198190619417', '159.86548789072841506053313745842', '160.631146666931896994261857528994', '161.52336203976312118374313609800', '162.62686486428637732791810365923', '162.856942467156194848532082015547', '164.17843470516686459973093423258', '165.4634520379327552861438817984', '166.04164970826917116221907217006', '166.95526007785896645074478396514', '167.75469485097194378803515828759', '168.52722654768893441766995926436', '169.11489273950978976303823072812', '170.46927211029100330330769788354', '170.873563058436674886780374935747', '171.54444785893663617230923115896', '172.56972894706333069856791308025', '173.97852849447840498278557696598', '174.76709222584230602151506107072', '175.3967343038678784612847388090', '176.11770616264144009354521275486', '177.35826136348316410716819657786', '177.90158432549802014577899088657', '178.70991544250633250098637869132', '179.29589371921682560721464788901', '180.25675188085760335045538214869', '181.23248391230031746226219061318', '182.10458676080426842149263754827', '183.03343416969401975797203266931', '184.31753675593564572814416128483', '184.57536538977590753456487742451', '185.743876420521000055645069976474', '186.42969852154286461509210474190', '187.40265534038887376970518185784', '187.595472816915281263986445447427', '188.91977369460032870796147813323', '189.60137843666604665135533083703', '190.503405060370375877087459615169', '191.25097567771097184440754879514', '192.54688702374893323628160303753', '193.36060213407956655967770506861', '194.31381429277985478357228129077', '194.825048154756035698796449486321', '195.297655048957566219562606706784', '196.74010086924920977200441583589', '197.37293911997689157327240361600', '197.83238230669970829145385345637', '198.72435307250356828212901596660', '199.72058843769142894629252614242'], 'prelabel': '1-57-57.53-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.2647068871489494, 'root_angle': 0.4061177078147533, 'root_number': '0.290682364382134679928664312016+0.956819608409658314313129212519*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.203058853907', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.20261668579756388050936714308+0.596694838417219520111456406105*I']], 'z1': {'__RealLiteral__': 0, 'data': '3.0526439819', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '4.18971569348', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.25882852585', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.2647068871489494, 'bad_primes': [3, 19], 'central_character': '57.53', 'conductor': 57, 'conductor_radical': 57, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/57/53'], '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': '1-57-57.53-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': '1-57-57.53-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.2647068871489494, 'root_angle': 0.20305885390737666, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.0526439819', 'prec': 40}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_57.53', 'Lhash_array': ['dirichlet_L_57.53'], 'label': '1-57-57.53-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/57/53'}