-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3968.3595', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.9807852804032304, -0.19509032201612828], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.5555702330196022, -0.8314696123025452], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9238795325112867, 0.3826834323650898], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9238795325112867, -0.3826834323650898], 'algebraic': True, 'analytic_conductor': 18.427314529947918, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [31, [1]]], 'bad_primes': [2, 31], 'central_character': '3968.3595', 'coeff_info': ['x^32 - 1', '0.980785280403230 + 0.195090322016128*I', '\\\\zeta_{32}'], 'conductor': 3968, 'conductor_radical': 62, 'conjugate': 'dirichlet_L_3968.2851', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^31', 0, 'a^21', 0, 'a^2', 0, 'a^30', 0, 'a^25', 0, 'a^43', 0, 'a^20', 0, 'a^28', 0, 'a^19', 0, 'a^33', 0, 'a^38', 0, 'a^10', 0, 'a^29', 0, 'a^39', 0, 0, 0, 'a^24', 0, 'a^23', 0, 'a^29', 0, 'a^10', 0, 'a^22', 0, 'a^33', 0, 'a^19', 0, 'a^12', 0, 'a^4', 0, 'a^27', 0, 'a^25', 0, 'a^46', 0, 'a^18', 0, 'a^21', 0, 'a^31', 0, 'a^0', 0, 'a^0', 0, 'a^31', 0, 'a^5', 0, 'a^18', 0, 'a^30', 0, 'a^41', 0, 'a^27', 0, 'a^36', 0, 'a^28', 0, 'a^19', 0, 'a^17', 0, 'a^6', 0, 'a^42', 0, 'a^45', 0, 0, 0, 'a^8', 0, 'a^8', 0, 'a^23', 0], 'euler_factors': [[0], [1, 'a^31'], [1, 'a^21'], [1, 'a^2'], [1, 'a^25'], [1, 'a^43'], [1, 'a^28'], [1, 'a^19'], [1, 'a^38'], [1, 'a^39'], [0], [1, 'a^29'], [1, 'a^22'], [1, 'a^33'], [1, 'a^12'], [1, 'a^25'], [1, 'a^21'], [1, 'a^31'], [1, 'a^31'], [1, 'a^18'], [1, 'a^30'], [1, 'a^36'], [1, 'a^19'], [1, 'a^42'], [1, 'a^8'], [1, 'a^29']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-3968-3968.3595-r0-0-0', 'leading_term': '2.30598975931909112983300193014-1.46025191046580796309967322182*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/3968/3595', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.729454966124842, 2.0300463378600675, 0.6816800931326403, -0.8612461992994853, -1.2088199642125361, -0.01281078545320962, 1.2761102158105813, 0.9285338777730259, -0.8988200105166627, -2.1029217090083807, -1.136576036459155, 0.8812649041569551, 1.395311419638072, -0.2404586463609139, -1.72476304855492, -0.8857570616202777, 1.0205168637208415, 0.625599281658183, -2.8253329516040857, -5.754539305031414, -4.4814667579220835, -0.09544666085891354, 2.7744159713678176, 1.8433198505712132, -0.3333064745128374, -0.5007995679621641, 0.8212649548361513, 0.9986068305441713, -0.06322212979633819, 0.0051954267012920986, 1.3533340551110595, 0.7176078123428132, -3.4093140144977547, -7.202414614862503, -6.113413497557113, -1.5096779315066424, 0.9480254868053114, -0.7351932358380989, -2.5432646187288954, -1.1544068985804905, 1.004715227289662, 0.19140217342571297, -2.3205604419232078, -2.453442944556584, -0.13933385234013695, 0.822070452908536, -0.5722701192853298, -0.9735850931620151, 1.0766494824745, 2.2296776915980634, 0.24399538106773308, -1.5818050368939154, 0.15263036551021616, 2.627990290227326, 1.0990623365834484, -2.7798515439423612, -2.996543547444886, 1.1267053621234877, 3.6774949915271207, 1.5284190832867672, -1.2904221308040271, -0.9676727683988292, 0.22155960278192183, -0.8359702029491723, -2.1421145059688538, -0.7556915154611161, 1.291315848080828, 0.8082931537142319, -0.2779770126245236, 1.2476889295602585, 2.537360613394063, -1.488377159911765, -8.339442346009076, -9.939696828108975, -4.663619544441852, 0.4241206984387951, 0.7171465388591899, -0.3524118668961319, 0.6421692597347012, 1.325328200505081, -0.2685287530577658, -0.8611785572434806, 1.648498420325345, 3.209732573463588, 0.5888595995428281, -2.422228341905165, -1.6418089269443152, 0.22919050674959862, -0.5267896289134523, -0.9980749238451136, 2.5526490353943494, 6.1684716106324995, 4.093951873263771, -0.7229869460192848, -1.164734875979578, 2.0295528430829806, 2.2675363862886315, -1.0323440874338705, -2.3350395211055885, -0.49919420826014216, 0.2383875571989857, -0.8675045029209636, -0.5964919678074777, 0.38397409617923584, -1.3480710021996858, -3.52282277203512, -0.7713969503768087, 4.64604080591021, 5.117165726579758, 0.7744909212899382, -0.5671162263885798, 2.816063488215758, 4.167874718543202, 1.03276491621864, -0.9700854838221467, 0.6918888527169308, 1.5339711704486145, -0.280735517792985, -0.9116668831023891, 0.279465674260988, -0.7833293595954423, -3.678064732852613, -3.2853570624429294, -0.1932770336242685, -0.3672570135874085, -3.3873860181427244, -2.5988883263851132, 1.9998643501180537, 3.1599038319358863, -0.23199065546785608, -1.6278616288956465, 0.18652397477566318, -0.6791331866787934, -4.690953442198229, -5.326059981158634, -1.4781379117086222, 0.7591860247149683, -0.35006162344777403, -0.5344001119147725, 0.6530523195573199, -0.09422388494047275, -1.16125310938164, 0.941134192338395, 2.374271662174903, -2.013159700539106, -7.036914377871206, -4.458678416243021, 2.1672471366317625, 3.240959908192008, -0.7207716206851467, -2.009389010214221, -0.02768685484603147, 0.39633796504882546, -0.10606850433501812, 1.4677835889667625, 2.214953785061022, -0.7524782430191052, -2.90862437692245, -0.7229020426173889, 0.8908459225420887, -1.5299753712780075, -2.7103570530706276, 0.42445404758079874, 2.0510499829982862, -0.48904767693494444, -0.6325295394246361, 4.076891724187051, 6.0961290748014125, 2.006514462800694, -1.2589258259927028, 0.12253742480525256, 1.10502559146303, -0.446006493349848, -0.2499296869157687, 1.6441972483355272, 0.4298909498026409, -2.6171694122090727, -2.20918410207288, 0.0611300839147211, -0.04362010910052965, 0.8185313554896567, 6.142402998398703, 9.1708084721791, 3.7924120125711394, -2.823802203835306, -2.004656457491135, 1.9475030908596536, 1.626987399389288, -0.3070015659085404, 0.6912050007621057, 1.5398086215081552, -0.19442315088224277, -0.6676498756507873, 0.8900867373179724, 0.11354433335034514, -1.8221253034369225, 0.34041000571627755, 3.4283937288437856, 0.263417934921233, -5.470076047871134, -4.9126069954746105, -0.3020119014693962, 0.4703457232527313, -1.0153448045981237, 0.4410211447558695, 1.3516424177723578, -2.3321212096908246, -5.006384965876004, -2.0516543580756066, 0.9241166345598204, -0.458600016800928, -1.705678746711488, -0.30995997253744484, -0.0024805222190317465, -0.44430249851098425, 2.2070594863416746, 4.440562670835863, 0.9879291556826824, -2.4191054315972145, 1.6359653369347344, 7.063959785562275, 4.905149890453465, -0.2911290566088519, -0.3958943789892671, 1.4710236378282353, -0.022316990798725955, -1.4839095826141926, -0.07892105615735744, 0.12724839093714435, -1.5703528283003934, -0.6438526936048516, 1.4327340874752323, -0.35994122644957066, -2.5534769037648366, 0.32320587230359166, 3.14355005592031, 0.09854330086396915, -2.485125626453805, 1.4186346034165507, 4.997624740730344, 2.2366205106902353, -0.8321083497830253, 0.4067145894388301, 0.9185830118859333, -1.1309128701183386, -0.6312100036051793, 1.7555592137803766, 0.4605835319033961, -2.240714236448348, -0.8678947664946551, 1.3071497943116945, -0.0867275067660752, -0.7430447757285686, 1.8374609745055404, 1.9702778130455776, -0.5092922256844893, 2.385812371521182, 9.302398418130014, 9.318783562216574, 2.3600590690009535, -0.8729686520377151, 1.1630319976282613, 1.197661949155247, -0.8560720565759412, -0.5213426830199923, 0.3134496686461643, -0.42318140687723893, 0.772795382806092, 2.924319536124051, -0.06516850626253995, -5.233864612701272, -3.862511318476745, 1.1068869876142067, 0.6414178743460269, -2.2601553726604418, -0.0058351303177399515, 3.1274726130410992, 0.6886320788519278, -2.26173811521798, -0.6827513300623124, 0.5568736512123134, -0.7379565733489956, 0.7697497304908569, 4.388260435110769, 3.563067293987781, -0.022211944891871723, -0.37821665354504735, 0.3187984535679957, -0.9029675674714245, 0.6000809978089489, 5.025193402796427, 3.984032957127038, -2.2305903054281977, -3.1013564455920877, 1.6961477387550337, 2.298619864647641, -1.2075220440921528, -1.0239366675573358, 1.0206745041707672, -0.9328122092270635, -3.1716793530785234, -1.313216085549955, 0.28030538995846044, -0.602463675299346, 0.21385713866422484, 1.8156152538551025, 0.414914915574251, 0.6680871860460152, 6.157707985289111, 7.853473392833437, 0.17771937020328651, -6.255338234015324, -3.6358714767609603, 0.22881414734101274, -0.47634697597671916, -0.6582523706649144, 0.7880455991012338, -0.9176947865795748, -3.2417182397828577, -1.2580536502055975, 0.6966663235454809, -1.1402608526343125, -1.2513916048375973, 1.9871522173887832, 1.9637426558489457, -0.970090696708538, -0.14455351448601855, 1.9798243079800966, -0.14865897834941752, -1.2726057934001473, 2.7663694187627867, 3.362276668520628, -3.5496413266450446, -7.507361878818939, -3.40531104011039, 0.3059928536144565, -0.2233733024784815, -0.09972941653426579, 0.5822633325508718, -0.8576383289338998, -0.6201927471140608, 2.4122112937587015, 2.026322703174819, -1.1528705531064243, 0.12233771817995429, 2.652975682324653, -1.4969444025298644, -6.477251008126768, -3.2160607609255245, 2.110350682988349, 1.3174625844353904, -0.24283826403629874, 2.098355052935493, 2.6289196201246163, -0.07980604112939554, -0.2743255115603717, 0.955670670076898, -0.7455497139951575, -1.530774068829649, 1.0639223234257111, 0.6820441958653626, -3.3182889718170916, -3.1683092928553496, -0.059566820723465565, -1.5739889049856137, -3.983786729577321, -0.4961032690927376, 2.6201623349780183, -0.657337046440071, -3.0351438594317974, -0.43226776436666214, -0.3119257277638161, -3.866768544452858, -3.4424886123430998, 0.19242200101391516, 0.5833542251198627, -0.2968536802426671, 0.7839798182019717, 0.1450519879313496, -1.9066952589764916, -0.6296436570473278, -0.4988177712014686, -7.0538752447782365, -11.020845506657102, -3.9608553162547073, 3.9454002996822757, 2.7344648257395407, -0.5692161100073267, 0.4590442671532055, 0.8776340317023936, -0.6513699436964252, 0.009660555165674788, 0.11527330078717475, -3.194493949610706, -3.6840058108511577, 0.5691170601498573, 1.871655576972351, -0.41933700430005316, 0.2415121985749016, 1.3666589036138106, -1.7859918564235007, -2.6216752144861832, 2.5855285157937677, 4.361923107503716, -0.3593493126518277, -1.7372583208116712, 1.6633379755828044, 1.415572393313143, -1.2037693196952177, 0.28490206781910093, 2.067742670644617, -0.09265082827845197, -0.9994104616788, 0.8898656328246879, 0.5005809776690096, -0.5070296524098707, 1.3451063225652111, 0.47817796210106717, -4.524765732585615, -3.932264676131482, 2.7876776723870718, 3.9374813911599187, -0.4953908803364267, 0.0016230386137145603, 3.4261607652088806, 1.3036173827537807, -2.3040857705550577, -1.1146693940641914, 0.5278854309925399, -0.0998084571606841, 0.5027276303835733, 0.3993706170173731, -2.7657479178549687, -2.3326550843548577, 3.239892449281989, 3.972439977711912, -1.3320672886358285, -2.5305888258117277, 0.043344022042899014, -1.5599446504984544, -3.722794028319267, -0.8503750442622445, 0.3882925776689268, -3.2420836400590467, -3.2824893748705777, 1.2411015299694124, 1.867426248339876, -0.43166520801735864, 0.5674603669857701, 1.6142148146530313, -0.44735451706169915, -0.7544513659890476, 0.6845219363817021, -0.4591641342067227, 0.2902897961335975, 5.849852805636882, 6.256326067925139, -1.5453612552740188, -4.520444664373153, 1.113434413323335, 3.503412273679702, 0.13277188062096176, -0.6223765189019991, 0.6981263454134353, -0.47502794911016105, -0.6014118169845015, 1.152961218856761, -0.65791996290431, -3.515599693928609, -1.6039343185406054, 0.2612336896060795, -1.786788948063927, -1.3264234928442464, 1.2984118609842792, -2.634254969813708, -8.957461860241912, -6.660134704945217, -0.597641363663144, -0.42115680743246225, -1.6422768223287336, 0.33742561438473756, -0.15216925418813837, -2.9120660419184468, -1.2841723321217497, 1.4821204919170032, -0.26521601681719575, -1.5060965838524052, 0.47342338041862686, -0.24509417690497065, -2.648127691359485, -1.0084877320884351, 0.4546879232960471, -1.5493650752062285, 0.5541178516874683, 6.154096810189477, 3.2239822268057026, -6.077775137551206, -7.522542008302684, -1.9078485561992706, 0.2769294177019367, 0.10331841622693451, 1.6372507827409373, 1.1542200141378796, -0.9833171996823474, -0.08388862149746477, 0.661033160625729, -1.0655962329965911, 1.1884770524970472, 6.07731737835915, 3.6355316905270763, -2.501716063995891, -1.1410084129594638, 3.1704928964895385, 1.5863833441582664, -0.4250079835505236, 1.3794153407194782, 0.33827393516052995, -2.9746216888157857, -1.163770404394507, 1.8295521120042313, -0.44383877694835505, -2.410370925421902, -0.4113370723746246, -0.006778220388005234, -0.8178663084463281, 1.291178026034234, 1.6236345092787352, -1.475075525081266, 0.3487454928830501, 5.803546915502086, 4.230405522824389, -0.8488587165061916, 0.6727061027711914, 3.18275135338885, -0.6164240196256989, -3.070849370704888, 0.09380051149801304, 1.2244669990287427, -0.5064318315099741, 0.5692480588483962, 1.7590904549925617, 0.163222843985463, 0.01935733412260454, -0.19990485866696478, -4.749555346209097, -6.3043753239073785, -0.0448764914775885, 3.3278149216692796, -0.27538634648474486, 0.18296567323537932, 5.402473659660804, 4.519616625887252, -0.47417570839018924, -0.7846271512645526, 0.5138329118484335, -0.2511202351830385, 1.171609007507982, 2.7178222705661685, -0.7985181862700816, -3.1245814180046967, 0.6444853064281156, 2.697314557932188, 0.2278232677476877, -0.16626060199144652, 0.3992963670730148, -1.2455156870664328, 1.687178693026769, 8.965925996753597, 8.059071572074323, -0.030616165901197888, -1.382601942336757, 2.8443870930569948, 2.176539743892837, -0.5637759706074743, 0.1625066136171467, 0.0845492348641816, -1.3422673390554727, 0.16975848937844512, 1.0249935277664985, -1.2195675488553621, -0.49103040839470813, 1.7017893642859887, -1.9188254721346492, -4.912631920445274, 0.6366194323475205, 4.925970149022146, 0.6330772724836383, -2.2953822533601453, 0.1295350203439936, -0.3449374158026485, -2.7278511787679127, -0.816330075811538, 0.6443177869504013, -1.6396245400269378, -1.493420709306674, 0.5882111855318002, -0.7062096453957182, -0.959606964561122, 2.5544067711228924, 2.4219558328389192, -0.7519103178121058, 1.1237596028217516, 3.479554458859727, -0.45044636602075516, -2.487952393198539, 1.6779178824579395, 2.3212711387947937, -1.248738423893022, 0.010185342833078738, 2.5400087055656706, -0.877430684763958, -3.743842240877184, -1.2990401484272767, 0.15199052792949735, -0.4286733899902023, 0.5510048022473083, -0.11997661591765994, -2.125522091732178, 0.5546311611630862, 2.401363027556183, -4.208530279208499, -8.588456390734605, -1.615942535368018, 4.675291157719512, 2.0408909470232794, -0.2509671316488806, 1.1119230142291558, 0.19487515886616275, -0.7276385871632388, 0.9826691145163081, -0.46313380678797755, -3.8775137814936307, -2.2395909632100546, 0.1954383707574086, -1.7753490925606994, -1.8227021085629835, 1.0793969021284757, -0.3304319663429741, -2.354158017558502, 1.2942141868745196, 2.694250360569387], 'positive_zeros': ['0.7518707929885622718816668041', '1.565017685961882852535420999595', '2.35866635353832940343540791446', '3.29502154368032030798622259680', '4.02646201072330692298754495819', '4.821718742439106922723401393497', '5.38741891783984672785619796569', '6.56930358237747099679734688038', '7.43834809815121793055520673672', '7.936361533632073033352993430499', '8.72835914785700137022992790096', '9.06096164653504968283952563626', '9.7610741901526268135040976271', '11.062316261098998588167214279083', '11.473045052643214955379663042473', '12.32653245219361402654528306285', '12.83718860149856007196748501509', '13.76975732868038251511335821842', '14.26770989497560967686019942206', '14.86026533869422722840062196232', '15.652564212537219186082917216177', '16.2343064830740335247334506174', '16.96184992960540953600845103731', '17.73603587170089229235942418295', '18.577315009765379658000049262633', '19.26905975009210718390042197810', '19.52280801094468474078734963606', '20.40741813140578875495261774384', '21.10777750349646108360726876474', '21.37160100932733879255545662330', '22.112348177400713621304681751998', '23.394536303769516637713046757891', '23.90825268069314283924068502323', '24.23763122264168690148769846811', '24.956739412664292902113915315645', '25.45145803361075282179426863366', '26.29742023548357949129769249887', '27.11914208701315681800999389449', '27.38842191015595776297120742758', '27.93993280916057536962284490230', '29.00440066498381972103225439629', '29.495517181989932861621513778340', '30.21922754939170050715943336297', '31.0299931600058676568484081932', '31.333054173774368786564047851302', '32.01441358469710204098466136329', '32.32654979759810019468141107337', '33.16863800233198671648893674897', '34.129116756523384127805118947029', '34.44981519859910831269093830069', '35.40931493091683494218087210174', '35.84068953525303991700378521283', '36.518971871104501908902625747460', '37.10013399721973815609073732786', '37.3898617903301374238434528768', '38.46649686428002037354719946901', '38.6986374495381116691875195565', '39.55286340829653622722732179333', '40.29209806223786879341309296975', '40.90107224372948133580151975257', '41.17204971913711579584467721706', '42.32231374404503556463214984161', '42.73758936941207368227387685837', '43.25404039346596921664314838586', '43.73267219809962421368584515373', '44.27581223394552264029154407883', '44.896355759199167585672634349802', '45.82440506600474604539802591499', '46.505270104229023829815383491844', '47.19243024638464987423481657594', '47.65028457063294071534995623594', '47.862217265979911624121396307064', '48.687499362132959299342455137475', '49.45146992514642374423898525869', '49.84345786383395300052545894939', '50.58947878838577244761623329264', '51.196840918649745344043792089647', '51.61953292419667193048559258083', '52.63681256241609125606688042867', '53.10811598782261387692783153216', '53.664985455451228990377147729062', '54.10311704125107090485528202509', '54.7291497939523770615073750842', '55.61087282163671108978786299031', '55.9198961508149193873825067179', '56.14028985880084295454733167719', '57.33789816636847965977923408871', '57.95369142468849686231785142370', '58.663269837812298854892117339622', '58.93765908414233188708724366525', '59.65644743837547306956417890715', '60.13441835114737679056591144759', '60.64003285964049828820179587239', '61.2233034305129049884899636811', '61.8882642535220355568676439369', '62.84165956519184253523393485973', '63.20803097323615991814991149286', '63.69264587723753037142781199256', '64.21300039269311286830390302366', '65.16276783210035368435063279380', '65.56482415290856854237685665868', '66.32813656774677590301261058418', '66.56153277708783109026685171952', '66.96954228405327738952465699892', '67.87187419663025657512681863637', '68.35800731581019267087018599405', '69.34872185021277723492662310943', '69.73977795880374998709101255672', '70.30973883416036600366962395574', '70.953054918852734269342239369238', '71.27670930332508463864200466883', '71.95120132186111126700201199663', '72.46579200289875894796030755600', '73.10234307319263801619006442301', '73.75668311762049733027940909756', '74.29430349549725011749694552491', '75.17517261529604271374077470175', '75.56319498181336959381300747648', '76.08319735611383994506138869926', '76.63693916276480860955361210385', '77.23123361409960055914797932300', '77.90254804216085153739302780797', '78.42512669281768890832655519397', '78.860005104656118283651143865159', '79.596383564728054197327058506059', '79.84847883810007989910454199977', '81.07634612126510361285868619501', '81.41265825211793198983330870836', '82.04132644412445642119086489261', '82.62212203302995941394805331909', '82.96141271922251273116250809453', '83.33141320176978898980584690496', '84.0588994629418367894092408054', '84.91261307424686363907344238026', '85.36919740884639188904748258563', '85.93791953750341801534176966130', '86.61335419008582189247811711991', '87.27706381350003179006612125220', '87.64331089533853520329780804551', '88.05076345193124689440608080865', '89.059684177120073302866761335789', '89.470659094848040390757051611742', '89.79281349353423163273392535236', '90.26126520481257260717066182515', '91.13436389725920913784873478030', '91.76449132016401170686242716323', '92.384087386709034859725498890037', '92.93423855232993626154937219788', '93.34716664635740682081577609698', '94.24316573017108918529075927662', '94.507068531985891618524205836987', '94.96682947463130331709081456320', '95.70342257889561863106029159979', '95.851514912990571005124354720994', '96.88082458551592685574335946536', '97.771594410363644651735048973319', '98.03001717548724332306128323982', '98.559366737749330288565465029541', '98.96512142554724316266484035514', '99.81823068745835782070760003815', '100.16188444335598356385553418871', '100.752918327422723243129149721869', '101.44277115608702161983756451043', '101.89075302842365899978791612444', '102.48561215452528107850243427753', '102.93778710468844485064137348363', '103.60948739134822742834365281205', '104.62818251256587694197292369375', '104.934754265324323153855077030003', '105.33969158146677117917710231731', '105.78447846798693299480296638524', '106.32102315038378584706214225068', '107.05504069652085541400969742755', '107.48929034538268254681053548260', '108.05252144469822734720810113310', '108.90761147298179730290849843545', '109.541834209851987597494629214442', '109.75040718501313086249878016058', '110.613986755162074417610954633215', '110.98938270153179949007313792147', '111.466593240036887574094190222587', '112.06812664213840013284258180694', '112.55835846645568911189518606465', '113.45161916480354449162345116298', '113.565579652563530356702890132920', '114.40501853886913723004212714342', '114.95586979574338229752504600493', '115.68085368132861694727495666182', '115.8978211035433259914458972671', '116.853002101951240851170890607229', '117.32378081377808391979534893874', '117.62092699956106216030689531077', '118.14477526822435034409050023166', '118.84839343718242002749949960109', '119.00262481656237512852084368431', '120.124674660014837544339688314681', '120.842657791941697711492300430529', '121.17410816229556799561980578111', '121.72706958702249464616621411423', '122.18543346269639731054653207711', '122.51707244902392465191892261384', '123.39596890718099649408903852717', '123.99382863031262739925410099789', '124.34014618521165040357573613600', '124.85620148739555502246520446099', '125.48753403379714236312431865738', '126.22698248183257283349855608647', '126.72557482680840380673469276339', '127.32882368213137272313301114562', '127.78271739736307021381737918100', '128.42680664712716157111457035261', '128.91669818536535325197491368811', '129.46385432446114792580624712797', '129.80696101755914344341521971833', '130.34728822127771809864026749989', '131.1203140731191650941805156000', '131.83226293476924106284866200410', '132.18736276939981222429846215411', '132.90067343903407912068156483545', '133.584493163092132592202708958572', '134.009724281677817237921214566', '134.231194880385540271663439091966', '134.73939071360210217211470600168', '135.450978169448697279222981429828', '136.17090856708926210370486574552', '136.86424518682619300321187102639', '137.00614799141527859519713200368', '137.89200950425699545289616450597', '138.173959993620042408715488373947', '138.9722005374102461089477323472', '139.60348918628448240264311132737', '139.91637072390698629936917081248', '140.56362026605196909153969247360', '141.07241659141070085768311447871', '141.48045523068362670864096654090', '141.85018843780195133372566530529', '142.75400243614277091406693204803', '143.38263878728058326111498010339', '144.07601506051620515089353617393', '144.49158150479967347890872423623', '144.91305754255717575487741999718', '145.410240627883604554011622472259', '145.87878013287546899624808325426', '146.74142673644352475501113349045', '146.947330443303089985965418000329', '147.62525421117783437540436640924', '147.992961455820669225187146543499', '149.12898123593064961766783065818', '149.30623416617118332618895461576', '149.948780415079041560189283279072', '150.29484813984646662433016400771', '151.04517206148905838601880186117', '151.53369929418295644108691514085', '152.11055252147935978310148759471', '152.47099017904840343075761524036', '153.24201329593248014741458885354', '153.53024554401298950511046595897', '154.02984704552478835524427333266', '154.79444614875818200691742595108', '155.80221896775175795466473872853', '156.13619187548373303414274203918', '156.18353367989921771789083815596', '157.019856455564680743292659879035', '157.5135074014507636399330610275', '157.93624813503691837158760896103', '158.35647408656579573530746572398', '159.22558687574050404089329299682', '159.75558398779136335064187483201', '160.474169028726105921687247547694', '160.73201883677037969829998036661', '161.27890662157662388764223252922', '161.96248904880152602104328152047', '162.46218017583379935776470413751', '163.19660126607797356996138621037', '163.435707759512727238389652867119', '163.90961272233456401401257813443', '164.53459888339978202428897417591', '164.97920311136242794561965663820', '165.86000570540391757679821999471', '166.19724587252815834824333317543', '166.83743677084922103207101595788', '167.49167312349433121858390051116', '168.01216280586886115574802183753', '168.35411804926625722498325017036', '169.09852165154701335982728729172', '169.368600587218848368071546937', '169.65975095476413894161073758821', '170.62698000094386787749580684540', '171.226342772903298875028757370891', '171.54941866542427983379918862997', '172.45979150395291865153657118196', '172.94217651189130668199690952397', '173.3319606486092070408513990698', '173.586966123736697953628318742159', '174.32262998042665797925205970161', '174.957169819940907415440585850473', '175.65829687800003290876508523509', '175.9793789252393560175749246430', '176.339199550558658539686994374673', '176.783597315523599133143885653937', '177.811027068895475214684535591575', '178.22713525789822230487358729326', '178.960731826059462616465966829', '179.338021268357633438968134604061', '179.703758804791538071099813613844', '180.29024923746781975033714411570', '180.77763783258376934549504940326', '181.29999438861882818045238757124', '181.76207818809165536464120485337', '182.473715659548478192633052178481', '183.16024604012735890245220118357', '183.73229838940796828427593402657', '184.02151156935413348133617659888', '184.77487668463028665588826522060', '185.11341252151758296884777886009', '185.81222397001579281773095202931', '186.14863846315222263013457624722', '186.66077911881658072155728824087', '187.39818454847016283161677669250', '187.71847103146334809090629610494', '188.41014842887475486563622834502', '188.95040401471514886269807838653', '189.56330828876853903701935914608', '189.99915135461459077065459509364', '190.56988313191359456915521312889', '191.429890011302485928189056555426', '191.640689655028179604177115245144', '192.04866521641811271586186831339', '192.483851768597373462997297135915', '193.085195298916456576073020926826', '193.58918431332401410553457619273', '194.42884755516013226343987493785', '195.19155910303591599798980604704', '195.39497581652846317155586995399', '195.967311181713015772434197374311', '196.39245915332296379994911027838', '196.83459945296479899580950335946', '197.73132119000133785227235334018', '197.893113636141636525613604099461', '198.61564777429488464371677340825', '199.03226821288455918887942221378', '199.60201986411160872068916026330'], 'prelabel': '1-3968-3968.3595-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.427314529947918, 'root_angle': -0.359375, 'root_number': '0.427555093430282094320966856889-0.903989293123443331586200297231*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(32)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.50878529048903129183417163363-0.403052858336748500505149334891*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.751870792989', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.56501768596', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.35866635354', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 18.427314529947918, 'bad_primes': [2, 31], 'central_character': '3968.3595', 'conductor': 3968, 'conductor_radical': 62, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3968/3595'], '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': '1-3968-3968.3595-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': '1-3968-3968.3595-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.427314529947918, 'root_angle': -0.1796875, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.751870792989', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3968.3595', 'Lhash_array': ['dirichlet_L_3968.3595'], 'label': '1-3968-3968.3595-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3968/3595'}
Lfunction data - 1-3968-3968.3595-r0-0-0