-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_847.780', 'a10': [0.5800569095711982, -0.8145759520503357], 'a2': [-0.0475819158237423, -0.998867339183008], 'a3': [0.5, 0.8660254037844386], 'a4': [-0.9954719225730846, 0.09505604330418266], 'a5': [0.7860530947427875, 0.6181589862206052], 'a6': [0.8412535328311812, -0.5406408174555976], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.14231483827328514, 0.9898214418809327], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 3.933451463423862, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.780', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 847, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_847.670', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^49', 'a^11', 'a^32', 'a^7', 'a^60', 0, 'a^15', 'a^22', 'a^56', 0, 'a^43', 'a^54', 0, 'a^18', 'a^64', 'a^14', 'a^5', 'a^52', 'a^39', 0, 0, 'a^64', 'a^26', 'a^14', 'a^37', 'a^33', 0, 'a^63', 'a^1', 'a^23', 'a^47', 0, 'a^63', 0, 'a^54', 'a^34', 'a^35', 'a^65', 'a^22', 'a^60', 0, 'a^15', 0, 'a^29', 'a^47', 'a^61', 'a^9', 0, 'a^63', 'a^25', 'a^20', 'a^2', 'a^16', 0, 0, 'a^63', 'a^46', 'a^17', 'a^50', 'a^28', 'a^6', 0, 'a^30', 'a^61', 0, 'a^38', 'a^46', 'a^9', 0, 'a^30', 'a^37', 'a^20', 'a^17', 'a^25', 'a^18', 0, 'a^48', 'a^7', 'a^5', 'a^44', 'a^43', 'a^24', 0, 'a^21', 'a^64', 'a^8', 0, 'a^25', 'a^12', 0, 'a^30', 'a^34', 'a^44', 'a^59', 'a^58', 'a^15', 0, 0, 'a^46'], 'euler_factors': [[1, 'a^49'], [1, 'a^11'], [1, 'a^7'], [0], [0], [1, 'a^54'], [1, 'a^14'], [1, 'a^52'], [1, 'a^64'], [1, 'a^63'], [1, 'a^23'], [1, 'a^34'], [1, 'a^60'], [1, 'a^15'], [1, 'a^61'], [1, 'a^2'], [1, 'a^17'], [1, 'a^28'], [1, 'a^38'], [1, 'a^30'], [1, 'a^20'], [1, 'a^7'], [1, 'a^24'], [1, 'a^25'], [1, 'a^15'], [1, 'a^50']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-847-847.780-r0-0-0', 'leading_term': '1.75803994534568670879516954496+0.332097617228417350361538748425*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/847/780', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.7891319897648295, 2.150313179254241, 2.271441983081373, 1.5895304631211822, 0.21829644669549544, -1.1153432136556547, -1.6295705279929757, -1.1231147923645557, -0.1840381501042276, 0.2796323232310969, -0.136640616063109, -0.8941409565454248, -0.9657716217773152, 0.11275262420949406, 1.5866784634545203, 2.020865050016792, 0.7381781277292445, -1.1816896505100951, -1.5364270145634862, 0.9977161545860124, 5.266432683355298, 8.159151637263896, 7.119089023024513, 2.4829645026839975, -2.615547355182655, -4.864289853751828, -3.5356558232566715, -0.796853143492003, 0.6292921869236083, 0.01455149019170222, -1.150476029553164, -1.2212777815688634, -0.268074950522565, 0.3388279521969112, -0.0637944098477695, -0.43538096830719747, 0.613398005612197, 2.7597763259213943, 3.9113879526791147, 2.5212199877699755, -0.3980989260228382, -2.15687605430415, -1.369247580582255, 0.4711476165212754, 0.8392425833081719, -0.685810729404474, -1.8962552946875588, -0.8650273903270815, 1.2629737916888892, 1.3072565152030755, -2.000413447557037, -5.943787123427442, -6.494140379076855, -2.865808605789764, 1.4568296973678294, 2.5934363977965518, 0.5164747032502489, -1.327099880491786, -0.37738841948780216, 2.1252540570856953, 3.0821982635228844, 1.566431359193167, -0.2484603554575191, -0.1664181494683546, 1.2469448005282329, 1.7765050507115308, 0.735653191595006, -0.29456077413690535, -0.012988022965715598, 0.6569164345403924, 0.15994854217984986, -0.9729411469184376, -0.6599552406828468, 1.2200716280176003, 1.5000716400127612, -2.5775735667223345, -8.903642067974594, -11.632603091929942, -7.530841837048447, -0.008427536332274246, 4.446462923516759, 3.3190399531811767, 0.083606348108609, -0.8452290878618286, 0.6380350153689304, 1.3640104278113765, -0.05814156238406697, -1.4662464323623816, -0.7151028124986937, 1.0217290676127155, 1.0772527569510277, -0.6257374192596462, -1.3988761595771029, 0.18842930775656389, 2.086372225084728, 1.704405458422809, -0.3213022553408437, -1.1584299190075464, -0.07825437595668021, 0.4754662566449042, -1.2507793620024286, -3.3668949414341123, -2.963674937066039, -0.5251904382304994, 0.6939462869527333, -0.2819252539120568, -0.3320454807746733, 3.041266620189792, 7.124682019955039, 6.8642138332180975, 1.961125999596613, -1.8179535538823535, 0.3317627375780756, 6.04404123254908, 8.779605095006456, 5.94182954393395, 1.3396081125823847, -0.513753451308914, 0.23836696552745304, 0.6035071575821085, -0.2795340579396617, -0.6581233561978654, 0.09705182687217793, 0.2649170186122661, -1.0268274289991208, -1.917334051235323, -0.8334160386609047, 0.4507210406859557, -0.7448668489470246, -3.4052764505248474, -3.666556949728483, -0.6292813741066344, 1.7061076130937791, 0.09891693721676828, -2.741039370083463, -1.6769444231673343, 3.17520309241618, 5.967394696018528, 3.0574916348332004, -1.9020065440034766, -3.0377497568398475, -0.05757043625545048, 2.2680428604320624, 1.3781059017498902, -0.17544534561356923, 0.22649010561639416, 0.9762850326792469, -0.5705373244782641, -3.0654812448824904, -2.798031984117297, 0.45073905242861473, 2.731843575448315, 1.6526528722872105, -0.3946864670886988, -0.29276567169514234, 1.1840578246970552, 1.319212907920107, 0.14111816046720554, -0.10252313816378762, 0.651805803407249, 0.14485135257325438, -1.454776757471356, -0.5847169444220229, 3.7369620094895084, 6.269558939962426, 1.7506027999696208, -6.8371892653042154, -10.718862437434524, -6.369528237795619, 0.12758636752540875, 1.5223271186091258, -1.55524037037949, -3.240235196254344, -1.44250140286602, 0.38166733360907845, -0.2027619336436012, -1.0688206550815278, 0.07672365389427285, 1.6678501178074114, 1.2671351039176078, -0.17777485403100118, -0.27253684199438083, 0.4429552746744599, -0.2858524801114189, -1.7067391820501616, -0.6750720156092369, 2.615250362150206, 3.692123196545117, 0.41282911826109575, -3.177766098970632, -2.6359882687138216, 0.12815217196458834, 0.0334065984731579, -2.947814975881026, -3.8157481694638404, -0.8655631027887486, 1.3147591029214811, -0.7406573417713141, -3.6002673811957777, -2.424447523276349, 1.0313706916676546, 0.9668931687716313, -3.2858278772211182, -6.076059685894327, -3.967305244487183, -0.4131013229672076, 0.18362667205578967, -1.1843415373978894, -1.05055400013942, 0.43474134696992117, 0.549578823476905, -0.6608202938203812, -0.5995328128449913, 0.8735585382131756, 1.0855917566145805, -0.39172615696363944, -0.7004819541184045, 0.9858740524198198, 1.4928186977002624, -0.5576362660845334, -1.26127140353474, 2.1672244461686847, 4.917725180394568, 0.30688402627564004, -9.354087552048961, -14.002645427332073, -8.912098545746005, -0.7241559137510267, 2.1589926088768707, 0.06008382822314215, -1.1990504704940945, 0.08769907746632843, 0.782915962363417, -0.2340826585805605, -0.555152883783936, 0.39394412129734463, -0.003242562992847338, -2.2500888030527313, -2.970925053621294, -0.6788865231000903, 1.02825147702848, -0.8644278836548719, -3.6213281421250874, -3.129114676790472, -0.4748594306671526, 0.41861411873405974, -0.4280627667460343, 0.04938509469787852, 1.3774582133481639, -0.11172633270743666, -3.880176773305859, -4.369820958620565, 0.13446826337803816, 3.637579134375338, 1.3561584009848728, -2.4424156916293427, -0.9772005992968903, 4.238556623227106, 5.80194986721604, 2.0190712555842194, -1.0637983763043892, 0.27133448094606855, 2.1951293344945637, 0.6238383050545347, -2.1726785589983018, -2.1370631148593335, -0.11189747255075161, 0.5733422278730022, -0.02967122081525888, 0.2440042739728499, 0.8946246722701332, 0.09996564207227267, -0.895561759581377, 0.1635995718484376, 1.3272406117156044, -1.0114195030111768, -4.737035409146777, -3.6546399334995567, 2.3388605664834072, 5.4374885400459005, 1.2731881272379368, -4.167688963788123, -3.6687161565525725, 0.5035987427444224, 1.293625390931501, -1.5709721554938796, -2.2334262016763833, 0.7625744603099235, 2.472189773904673, 0.5449759592637327, -1.1172863488024227, 0.22160810110750975, 1.55092141179331, 0.17162083943309533, -1.2815970093720024, 0.019611472584624833, 1.6445669283633972, 0.3581118103276049, -1.7751747393223978, -0.9938537984328936, 1.385999181051125, 1.4052765821682716, -0.46021924953692084, -0.5634290147965535, 0.9562899183057643, 0.7180905456883554, -1.0208497736268427, -0.6821626341065874, 1.2183880293235396, 0.29309894371627365, -2.4631784393282747, 0.45018726451678953, 10.921928797120616, 19.188166003477434, 16.03649953239724, 5.666472040727536, -0.6792512328786156, 0.016947420253416834, 1.4922875557473874, 0.02710754453136265, -1.3058041407547027, -0.2595328610400981, 0.7123569075460093, 0.03447401962314259, -0.13340286782513722, 1.0329338808530835, 0.8669556333842635, -1.3302848745725184, -2.127991092732721, -0.09850907682212108, 1.2590936064281475, 0.013173704714635234, -0.30170908268897395, 2.5418463235597284, 4.310040466766576, 1.4060750373571265, -1.883281261868882, -0.0595461228738625, 3.672318074375661, 2.174170148124244, -3.453009845557066, -5.261043788739304, -1.3017921660373926, 1.8908196000218296, 0.6539675526734557, -0.7749513616568872, 0.7860696109457508, 1.7986219539681318, -0.4448814405532348, -1.9008491033910924, 1.0890160577460488, 4.660287191717768, 3.541437475784989, -0.3389555151430533, -1.6355718871148632, -0.24445483945296204, 0.198032958233646, -0.5226466128770536, -0.02370919958923554, 0.9670665852115663, 0.11778318689174981, -1.1891741234426507, -0.41504782864066714, 0.20451812785790946, -2.693543907689267, -5.7919686881048165, -3.208226798792341, 2.285116427109942, 1.5400572751982191, -6.280150872885207, -11.00043676418512, -6.68234338952514, -0.2896567373568326, 0.041265506992138885, -2.985920163729827, -2.440510842881481, 1.0105771818879572, 1.951562103569124, 0.16052228060828422, -0.41270190992235134, 0.483901744154836, 0.09753979200635994, -1.0144330932408272, -0.37343988532189326, 0.6484234667680194, -0.7444463872094034, -2.4220187106267446, -0.46753271598219787, 2.933858805117165, 2.2713717399381093, -1.685614030576633, -2.9706892000361345, -0.6605996785460582, 0.2801567052007122, -1.370464631705861, -1.4519759476217675, 0.3773292314122492, -0.8763736455159254, -5.2524323073055434, -5.474579149772662, 0.8913394352790117, 5.912046597814171, 3.5788280539300454, -0.6216212839747938, 0.6508911152108828, 4.655736217210802, 4.403065828295913, 0.6319125326377626, -0.8092812010763296, 0.5602755422874262, 0.6705711295032204, -0.6253701666780155, -0.1279148794026547, 1.5826567286356525, 1.2046777518902716, -0.6023493446853319, -0.5956284038450032, 0.6030588092352983, 0.20233018609323014, -0.6583777400234001, 0.37970581656341407, 0.5577396621825409, -3.4383871599001683, -6.949063401542025, -3.0805654830398805, 4.290054234724025, 4.129042221227104, -4.565972479396235, -10.381114293560085, -6.682682029895468, -0.28755395860680083, 1.0507877837879362, -0.5224193527572629, -0.2110556633392768, 0.5363481074067034, -0.9059552496006054, -1.88867684737558, 0.07995446720005758, 1.7206996028907764, 0.16365406976380048, -1.1166981905201105, 1.2572186553023899, 3.8835308019741754, 2.659108717295328, 0.10045054315092831, 0.1810169718431062, 1.1348358464789323, -0.035997481571237125, -1.0833593856465984, 0.6765738980573126, 2.2554418653258663, 0.7179715696306141, -0.33934368667245085, 2.404676801740925, 4.308691137485591, 0.5111172689683214, -4.0730968206248335, -2.417642339001148, 1.6791519139428037, -0.4627390490572085, -6.900081494614314, -7.633913885919899, -1.2294922113849047, 3.263318726625921, 1.3295936666770474, -1.5241650745492068, -0.89964279740035, 0.38831513586658273, -0.15387770770231446, -0.29621610214206995, 1.0213718224349182, 1.3098534868708913, 0.1571310600964958, -0.046139703347973474, -0.0534071221842316, -2.7690692810440245, -5.88647383003439, -4.075103706713661, 1.0054565532094848, 2.220349346843718, -0.7945964353744706, -1.1361392027322486, 2.305743330095593, 2.5394289420765226, -2.116514394063203, -3.9769942955331588, 0.37165206902967757, 3.6675228009854934, 0.755898820950474, -2.812260666305129, -1.4249839768010997, 1.1159413340659974, -0.11669599418881499, -2.2277626707981453, -1.2486822421621124, 0.07808335790557727, -1.3817282957389172, -2.315498049523349, 0.3538163024252, 2.729404260262764, 0.8748218146941555, -1.9159551017208822, -1.4230511809733026, 0.1837374716782459, -0.3740879930613759, -1.1875638801104422, -0.11658462932756744, 0.42059594362892, -0.8867158202904816, -0.8976893965446434, 0.4946567157018006, -1.9341913967477415, -7.642354311062894, -6.782382618052795, 4.323688920404435, 13.93521640003739, 10.856370155857809, 0.9505695425789993, -2.972587019703617, -0.012575326195660295, 1.6487217271772174, 0.00256539468127227, -0.517616576028234, 0.3599498979739668, -0.7514832144279082, -2.727115220145082, -1.9773467278037704, 0.12622391665676833, 0.17758531646710507, -0.3955315853396632, 0.993643505455659, 1.8940362124935946, -0.22764628584369337, -1.8785702554923718, 0.09395779325746331, 1.7758055867252964, -0.3884293269709387, -1.9254440143674154, 1.4321221428205135, 4.724510647548145, 2.311797743903715, -1.4466369998544482, -0.10932145289794867, 3.010686847081641, 1.65216863596278, -1.2465715014799716, 0.3889817124275137, 3.527839767247358, 1.7679023770680242, -1.946468685097948, -0.5197565504533005, 3.8153344881111426, 3.3559938937294826, -1.3018935935804477, -3.0495617142198603, -0.9132204940538151, 0.04683882828097785, -1.0603724992121175, -0.9240541861794465, 0.2714401087633091, 0.09865849982232518, -0.09555394761470792, 1.597963948025206, 2.3646024153534064, -0.0019181822403721226, -1.6934739924182858, -0.06455948210182309, 0.5119757848571534, -2.2787772830922437, -2.0223194972083696, 4.757520997535889, 9.1672484145396, 3.2891161095389227, -5.439846913318316, -5.531898735778753, 0.3629182367560205, 1.643662925670238, -2.2665619433909634, -3.5863319095039614, -0.9327127288057601, 0.47788584388144456, -0.2247491309580787, 0.14665502636982236, 0.9026903713934519, -0.28132204220938056, -1.0370730435354183, 1.0054789276054807, 2.0200963205563065, -1.2515246037814116, -4.270387591476232, -2.356402764731255, 0.8134100088300261, 0.3424954054901217, -1.2163662516006393, -0.15130511071817515, 0.9760556721760063, -0.2232510087405288, -0.29335369778910897, 1.9869055565714966, 1.136831804167761, -3.938493114361122, -4.8284310054817565, 2.0988164313407607, 7.30697012950429, 3.305844705812934, -2.7613830364425533, -1.8884372211942058, 2.1216502551876606, 1.627933751971362, -1.043089771609778, 0.03304595640418892, 2.7036852473164954, 2.0452242022813745, 0.0009421661449534245, 0.4549640057086801, 1.5191349528012195, 0.4546315745749607, -0.5722790261717133, 0.1852414954159131, 0.2488119858960974, -0.9901251976264509, -0.48892229692553457, 1.0803640537295796, -0.2341858457372529, -1.8983387818528308, 2.835099038177287, 10.950040696232076, 11.274077048012524, 2.7261832597018554, -3.184213717655712, -1.3391459861691362, 0.2851515242789568, -3.103145472278978, -5.17143733575962, -1.9154672959146573, 1.1072325473802815, 0.38042358050552055, 0.2814999666106602, 2.6075424771116475, 2.5918324919042277, -0.6195865693229826], 'positive_zeros': ['1.29560073068822158570243417516', '2.57498645468339591357650639655', '3.064343109694166327721984161158', '4.03868633334529899482656797174', '5.11440731703649546030962009364', '5.84870501515419460132431578864', '7.328923401163905154216066647435', '8.55640346742754744030414280464', '9.06616167269531125657310990937', '10.08920325652005082634581654725', '10.5950079721010511528129044875', '11.1272454109505191088471776630', '12.456535278679692284813052385660', '13.34795246820209604191940374907', '13.94570423296098320011279102145', '14.809091987152247461507379016745', '15.46757425866872457638255438387', '16.7538249159858653348604290602', '17.56293674761406591120058944250', '18.175130820544181436431447548372', '19.31276914022629609587411951398', '19.73149494716034318007640901592', '20.80915453332091278756022473575', '21.25511345579231279904151093640', '21.91750739087141861411861697651', '22.62075525358118406175998624320', '23.282140562969948236100507845568', '24.68787943796953622078213225473', '25.63543937773551711196592535656', '26.13529043568960676220415371193', '26.865653897990615737709545167966', '27.62067045678317676488268025935', '28.331852573524849503824069984113', '29.03661894032069808612007670883', '29.948889710424196145414009479247', '30.643561208913442566858857074362', '31.068767887762706379171745784218', '32.26402215453198829462795967529', '32.74372923795156997071578644185', '33.17787420433373457326371877700', '34.49476354130100319159239974334', '34.978369423872292002125295678123', '36.39853696679189388177548736191', '36.804360864417480521081737556893', '37.414274485400552730400210225', '38.08930445921146885064014282048', '38.52827945831351822366944935765', '39.5324454624363718117553833953', '39.88982635988701625995035372466', '40.9943762595033349279510319876', '41.572248590163302706017626540375', '42.30788476827736997021030694482', '43.3057282604550835558932629733', '44.06763308693983352213317200415', '44.9397836096503953816436901815', '45.24637627503604512544696739459', '45.86499805382804402736493831141', '46.83562232657829253133769899114', '47.73231638887811453210029221584', '48.19034292877853814368367052253', '49.10967989444863126736705603999', '49.42421138926035482095814229385', '50.02933841948082670870278298927', '50.6797816511618358282265107753', '51.628579001868787586543233295467', '52.80405008001960349115131597606', '53.29832928956526037586187089726', '54.266868165187586809992198966456', '54.63803827991053137515600717129', '55.29980785337526821158209591083', '56.20115550881977092408218164170', '56.66617108166498164381264556056', '57.12572221119870517820767697681', '57.88369691655020260801681041644', '58.77887315417062922056533797027', '59.668204812079668476701174538642', '60.00475990609677361585209132021', '61.0171827688508707444739394517', '61.49304609332590191592758276515', '62.39509617199658741414719863252', '62.901505413868137764232938449448', '64.12500141081267312677757114134', '64.42440721157492668656961889661', '65.21423585346547888390439463328', '65.76946435594671019973670873934', '66.384007798536239684677124839906', '67.10826965806574208122617618635', '67.64929594679844831322358878035', '68.36450587574079276316910485035', '68.90123833435656051574243765158', '69.698636538968814460847291814022', '70.97538024795048406360870621123', '71.56990369544337948250710302913', '72.170255780246823424241499251536', '72.75060520824707344779530514577', '73.310342061829089805142993081519', '73.74938989519460732354410478764', '74.76603068142894391904670757533', '75.22124620604459900162518619464', '76.32560584395092360450607837820', '76.72217915758404174640483523329', '77.17673068330246049227587842286', '77.80186990181938909951710042923', '78.74214525852418439941029220637', '79.46840330116656121013833549742', '80.06312744838316561717848289348', '81.09118462940934561602818326899', '81.53007599029543412319120466516', '82.249935187864971635569649877127', '83.14576178704422738220476119963', '83.728956121837821163087261217399', '83.951585301279123940923802732510', '84.709745842507220062540521218480', '85.284338048091868338579483092427', '85.8517455732722325109783310899', '86.760828300710140911825363814805', '87.561378590001034510292567330751', '88.39420478947569736575739236033', '88.903786876684628040135553635416', '89.617917999680499971533802376325', '90.37819323541663786661093269921', '90.904749226392070092622861482422', '91.58721909225980139503787058543', '92.184751044966992193492479727601', '92.85656446166001146380668317142', '93.56029934189756682233339110565', '94.29098845172403325759504544391', '94.80480831854007667442058013579', '95.437399524438069757558732392846', '96.042724679208878803280649627047', '96.593822341834381116678830661745', '97.1679521513702899777769814253', '98.68230257015261129575480718777', '99.06021927771250946833356468386', '99.691424445812399750546059611207', '100.36448284329291500044717410703', '100.949759364128613091265761164520', '101.297705116762726493364237329433', '102.012193314626155457608870140317', '102.82518479380199006676124641788', '103.4400787352236761431356006201', '103.80274934728326788757885223759', '104.78979552469163482030253680629', '105.31703423412554444769905826378', '106.06221895362946258362382341237', '106.96348828355435289615715957573', '107.589875304856907633179007123959', '108.01209216581995490364429078081', '108.702479721778952983455024424022', '109.29524531916628183610291550023', '110.28110601113864550044517661355', '110.99845584883579484182652371513', '111.338779890095533642598108786005', '111.88107225196388322185848508865', '112.52196157733164359881648973798', '113.217098150297119836151758530937', '113.485712081600276125386966128763', '114.54378095859419088232616964928', '115.076337311655409004374606996978', '116.27489216802386273130114621262', '116.56729889945275480240281652562', '117.40403126791209199985861309762', '118.15563046655943001291393219430', '118.58202739196172994241812299559', '119.08666402428215873626744306262', '119.767162038370864508073683248392', '120.20462019912043274792282683160', '120.97643976818152319627216327787', '121.74307738001190425644732643022', '122.59868309888222570348459681480', '122.88716108497207566053863034312', '123.67043058326517387454714823569', '123.97186923984434061967593068077', '124.962884901847368935944553049197', '125.8658890576126325180070405223', '126.1936789548621447925231565401', '127.25242735901143593936705188748', '127.69806606964707354497903830769', '128.27773869060799770637030906959', '128.77325901670979176859748997871', '129.57107157846072148021451849488', '130.14058632085937981342888794889', '130.67623702121289502615708416389', '131.17182252266183033744072354473', '131.6332875808441573055228084190', '132.62164077580726800065366297281', '133.290179482114972391312328217210', '134.39657729274936453821286147833', '134.88344824400444264330711546281', '135.36514486624980936023938833761', '135.78842465214118273057415744598', '136.55317745005283241168095246036', '137.2092283851216724309749014927', '137.69292305131378106139826882876', '138.7729312251877181270172854891', '139.01321604046562848845308089922', '139.68143395348317735731861494047', '140.227268314367269422883347684361', '141.04527082428427654828925989367', '141.322527990094585884762604294179', '142.21511889044648296698724159499', '142.9709658411711198406979274838', '143.411561779436172820053496024753', '144.43116794036602191296979479901', '145.114201454543100920488350217934', '145.79474374525530866006375424041', '146.196940355204951949012147628891', '146.649689896357873723473812128882', '147.55714961258142642958147499571', '147.84375639733917497735243824731', '148.10894544563688772705583702054', '149.3065425854841045255908671433', '149.920522177713359266437821545569', '150.428038013899483309664415574856', '151.12091852775282081462210068027', '151.85382647715750884666968476401', '152.54979825346335167029012124515', '153.26429664030744445225567916510', '153.73626693197001653375992436097', '154.61440668311252252647523822140', '154.74687527250169642605383547188', '155.594201225784046555636661420294', '156.33038002692364701386323928374', '157.125755807727944346342796097887', '157.404494877093179804285755423457', '158.15138144823071695605568937865', '158.561452196436788003123106715023', '159.23413761809705912091464393469', '159.532169168888204399690506228345', '160.521398257522114085755119465395', '161.59972374229264918147770385340', '162.188608868025452620550610935584', '162.812957764529486001384563687774', '163.2857149632027211204851728585', '163.62608192544479994044154256729', '164.66033018015736271096135050127', '165.05825300685198917388681159396', '165.44987971724454619923444455374', '166.2250056477798526854312219608', '166.86487341480814978570892810777', '167.460811357285454612027455746017', '168.02770948384995950206732521705', '168.90976459861977477984345399529', '169.38447080178127303827562641193', '170.1462169372913224127376477191', '170.59113011082414826992004740370', '171.37740143987664151854897339377', '171.91192770150544494579197975448', '172.7245568688793167172187750250', '173.611755532843908653746244175250', '173.77321167143600861967401278569', '174.59719338847927571713068563881', '175.04210910907233873404607673988', '175.3446103454624350653843462815', '176.24979808695650892275200056034', '176.88451701732423883350484171762', '177.265331875544912849032353970902', '177.9295519691054312296527815216', '178.853518387182229735436715822027', '179.66538802711811956382907448412', '180.14593408832693822798797693214', '181.06135754599090382831958467656', '181.46723592451426919999402019273', '181.83161744215989484186229712903', '182.44891248878087974809873546708', '183.00281489050450647852642978402', '183.658993587677058131259136366289', '184.578590293328015845758103776425', '185.05273825719398613761520735601', '185.649932484373509333934208124846', '186.20395773931877282839107140716', '186.611906841240947537793359040082', '187.26813910211621283749274667786', '188.04636583988423620805747433239', '188.89423793042101685882373366100', '189.50718543228949853509428067402', '190.165108640089737255785103783770', '190.62145415279241902557317962867', '191.56278822294309614011634708119', '191.76190402633366551795114460624', '192.588685039140257132440779252466', '193.06724235768704710329856941632', '193.506051595319604929207424794', '194.14485750273464003507990253097', '194.65984987005417530342042887293', '195.18540186687957186962930860923', '196.34949608147090535124395120173', '197.01602096851447589396123197557', '197.23947164794002613685604364566', '198.27516013082318720141309466603', '198.860485439863783853329411672721', '198.98609552836273143356326075645', '199.939292309882735648389884582802'], 'prelabel': '1-847-847.780-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': 0.11885830280210713, 'root_number': '0.931090872218855818251127842235+0.364787318407219724769655988089*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0594291514011', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.29632018598610088363091277137+0.0233829758642203631664257477956*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.29560073069', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.57498645468', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.06434310969', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.933451463423862, 'bad_primes': [7, 11], 'central_character': '847.780', 'conductor': 847, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/847/780'], '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': '1-847-847.780-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': '1-847-847.780-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': 0.059429151401053565, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29560073069', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_847.780', 'Lhash_array': ['dirichlet_L_847.780'], 'label': '1-847-847.780-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/847/780'}
Lfunction data - 1-847-847.780-r0-0-0