-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.448', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.20791169081775934, -0.9781476007338057], 'a3': [-0.4067366430758002, 0.9135454576426009], 'a4': [-0.9135454576426009, 0.4067366430758002], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9781476007338057, 0.20791169081775934], 'a7': [0.5877852522924731, -0.8090169943749475], 'a8': [0.5877852522924731, 0.8090169943749475], 'a9': [-0.6691306063588582, -0.7431448254773942], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.448', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.7', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^43', 'a^19', 'a^26', 0, 'a^2', 'a^51', 'a^9', 'a^38', 0, 0, 'a^45', 'a^53', 'a^34', 0, 'a^52', 'a^7', 'a^21', 0, 0, 'a^10', 0, 'a^35', 'a^28', 0, 'a^36', 'a^57', 'a^17', 'a^56', 0, 'a^48', 'a^35', 0, 'a^50', 0, 'a^4', 'a^21', 0, 'a^12', 0, 'a^34', 'a^53', 'a^25', 0, 0, 'a^18', 'a^29', 'a^11', 'a^42', 0, 'a^26', 'a^19', 'a^23', 'a^40', 0, 'a^0', 0, 'a^39', 'a^46', 0, 'a^2', 'a^31', 'a^29', 'a^18', 0, 0, 'a^5', 'a^33', 'a^54', 0, 'a^52', 'a^47', 'a^1', 'a^4', 0, 0, 0, 'a^55', 'a^28', 0, 'a^16', 'a^17', 'a^57', 'a^36', 0, 'a^8', 'a^15', 0, 'a^50', 0, 'a^44', 'a^1', 'a^7', 'a^12', 0, 'a^54', 'a^13', 'a^25', 0, 0], 'euler_factors': [[1, 'a^43'], [1, 'a^19'], [0], [1, 'a^51'], [0], [1, 'a^53'], [1, 'a^7'], [0], [1, 'a^35'], [1, 'a^56'], [1, 'a^48'], [1, 'a^21'], [1, 'a^34'], [1, 'a^25'], [1, 'a^29'], [1, 'a^23'], [1, 'a^46'], [1, 'a^2'], [1, 'a^5'], [1, 'a^52'], [1, 'a^1'], [1, 'a^28'], [1, 'a^57'], [1, 'a^50'], [1, 'a^13'], [1, 'a^38']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1045-1045.448-r0-0-0', 'leading_term': '0.685449970935406515158717722736-0.729137890944728380623063022472*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/1045/448', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.0007415883566935, 0.5938328735266574, -0.12800879813309732, -0.9850408756211742, -1.2786262334832916, -0.4939672573763101, 1.1048426175587158, 2.5036540337304274, 2.6777473867601493, 1.4909002727563978, -0.08523773307260919, -0.7763756227065177, -0.20082939089050691, 0.7156656267180441, 0.6695991216823438, -0.5391664369283, -1.5396563700899397, -0.685284994184385, 1.977479290698836, 4.1641936739297964, 3.1832754897555877, -1.3495335087812148, -6.65304380370026, -8.969024977623894, -6.919630609345834, -2.7424030762517555, -0.08640941428742065, -0.5622561210690427, -2.548062566048931, -3.325385617049241, -2.0402248379853174, -0.24481521995734315, 0.2972638842919655, -0.2988051174269597, -0.5475531998572356, 0.18122492402017146, 0.7745373028148076, 0.061457616583991244, -1.2208107980523155, -1.0577441462620498, 1.1160914687862136, 3.1702835485760374, 2.569965014371073, -0.3295037823868548, -2.2897282911006243, -0.9742822124219699, 1.9747523470076818, 2.6457552461776146, -0.3845053845355894, -4.061821725420752, -4.318135460817099, -0.8918938209333089, 2.440435873027547, 2.48530141896895, 0.2674190885406875, -0.7967878475026806, 0.44574438244973896, 1.5968941413892324, 0.3261296422582176, -2.177791938640189, -2.6721995309974274, -0.22320315459952683, 2.501363108968989, 2.714401308969384, 0.9430664548083958, -0.1584530241432878, 0.36919448143980965, 0.8492305749940886, -0.016484762561135503, -0.9544196321914373, -0.17032570886651863, 1.5308867392061214, 1.6388334756725522, -0.1039188256607554, -0.7967562889540682, 1.3154369686891156, 3.2194111099015985, 0.213459533938029, -7.438630360594853, -13.329685684343321, -11.782820735325288, -4.506420930490992, 1.4927648861234182, 2.034864863011371, -0.40219459897237037, -1.2629883175545715, 0.13174166595472633, 1.0499167211246456, 0.2417049081299394, -0.48849133334574574, 0.21689467093102088, 0.8441782383402325, -0.380786734462934, -2.231398652966072, -2.1106467219688887, -0.21372951060881953, 0.5238411144660222, -0.9955873312679504, -2.0377853914342987, -0.15134668275061827, 2.68662242288811, 2.5757407677746493, -0.5170924924277298, -2.5161432334401725, -1.2706929903096258, 0.18915471107284634, -1.6118742406804225, -4.888705702319937, -4.870462963419825, -1.0439314555455386, 1.5793738608140855, -0.4856346508071437, -4.072144063789932, -3.8395985434627806, 0.1441115677860086, 2.744751135162045, 1.1911008921801405, -1.4858744809091928, -1.5187581338983969, 0.2725076387960482, 0.6517320662418647, -0.6582155522936884, -1.0393148505899146, 0.3152163513380625, 1.1812042069475046, 0.31690906820821496, -0.44704614827204675, 0.3608514918363843, 1.1023132289357709, 0.19976862710076412, -0.14543661681531836, 2.933946667781603, 7.035416535320788, 6.090476331641573, -0.9732730832070713, -7.174975822221517, -5.906331294988831, 0.3908566266686715, 3.7668506803811885, 1.4426503873005216, -1.6047910111061285, -0.8816243685814262, 1.5668263028171454, 1.5825012656342043, -0.42901657239813334, -1.0277924601989046, 0.20468497721881385, 0.5045673875959267, -0.7260945656960888, -0.7798631902593508, 1.2733220646677783, 2.3522627105306357, 0.32081727362329876, -2.0847779531298043, -1.3249849135868497, 1.307480675707602, 1.822638964511539, -0.08544943943322329, -1.0000956331512225, 0.16590079282189635, 0.6715873388953393, -0.3972400813350144, 0.36700860510621397, 4.672337628635454, 7.942472195481649, 5.245640053688017, -0.5702676417201409, -2.0784887495815045, 1.9458750686065869, 4.639686648376166, 1.317339936890385, -3.7262425541871957, -3.971707368934736, -0.06378165093135973, 2.2408906115936493, 1.020722913413107, -0.2641640872093049, 0.529856999373618, 1.3077594069814296, 0.43563967595424347, -0.32747157842589264, 0.3988363729088572, 0.8635478911181457, -0.142044175822822, -0.32130810045011704, 2.038617304356548, 3.985863885313284, 2.19534590107882, -0.8348850864730428, -0.07966249037934386, 3.4935416340146435, 3.6775367792683067, -0.9041330066359289, -3.6446420740765957, 0.2117747811623127, 5.946702407744449, 6.23845003327066, 1.7243322292984913, -1.0794551711166953, -0.08119238776274872, 0.6856428377677212, -0.7828581487157193, -1.3055564224141774, 0.8589045317962771, 2.2083488156750732, 0.03234600651696359, -2.5205160139818608, -1.522244159654785, 1.2251490028699383, 1.4186129865384725, -0.6477504802559119, -1.3024653596245845, -0.1659273938154841, -0.1885892620172024, -1.6154583697535378, -1.4488536750457406, 0.6378327481471877, 1.372932112820379, 0.16724319312364766, 0.6592930846474793, 3.587264751159144, 3.991322250950123, -0.28159690838790674, -2.656195424454844, 3.3263569982884267, 12.849232404865798, 14.973797123198342, 7.59632748814759, -0.30710484880572847, -1.7850174545661277, 0.24618632386848818, 0.4893508184333112, -0.48103370438513715, 0.22074574791261542, 1.4257288091678424, 0.4988753080295755, -1.2651454406373173, -1.0878264216574267, 0.025546767639143063, -0.47300093297378654, -1.3617041384793782, 0.044579676132268306, 1.9932182749136627, 0.6435672492794811, -2.59641280545392, -2.540775200366355, 0.8433208056713671, 1.831210021932144, -1.3304260035223425, -3.1505153939686106, -0.313396216700104, 2.475150425745278, 0.7099391484346254, -1.9504619128615337, -0.18175748991573915, 3.364661943837663, 2.414247521124375, -2.0152153474505954, -3.189124720845074, 0.0998660292682387, 2.0853769649272516, 0.2539176576598976, -0.9516858040241126, 1.3289346483508597, 3.430005811879593, 2.085950412259385, 0.040399243549148076, 0.6276870920553616, 2.003857695105168, 1.2528627411275788, -0.24671839224733222, -0.18980136140121842, -0.023482559780245806, -1.4558041335208456, -2.210142906969253, -0.5121672212887359, 0.17503010181810397, -2.801310132084307, -4.2440840855914646, 1.9508212831606677, 11.207611512927265, 12.770415761540507, 5.457463596109481, -0.475094773739828, 1.2317906743221365, 4.844336318431283, 3.5964150770994285, -0.04199617533857409, -0.6185707442017466, 0.8383210052190875, 0.3107208592018779, -1.4061592934661622, -1.1639178377316397, 0.10449579502300727, -0.1485199389482153, -0.4095176850615373, 1.7310130849975005, 3.604909998173295, 1.3053482662365083, -2.827153359850171, -3.4144594512320063, -0.8901542833129965, -0.03497811175923249, -1.1518159410324862, -0.39573550072632496, 1.8759203755300362, 1.3731133326123037, -1.309978756703614, -0.8271728231889249, 2.6821134169149583, 2.513939955552454, -2.7814552910694927, -5.633366141103358, -1.8014474169827677, 2.2514562930011572, 0.2664149908529112, -3.428854152696658, -1.8930123121480373, 2.5523981811201493, 2.9192880700965587, -0.6271087434381205, -2.250914606326063, -0.7023664247580065, 0.23340895744822382, -0.4091133182398799, -0.23180734520724045, 0.5279118742878899, -0.3784593409803644, -1.7159119162731242, -0.6591878091157068, 1.184450034456416, 0.4901041461164818, -0.8064948810088892, 1.1313179326799503, 3.510565943103683, 0.7027056253335293, -4.413696081427689, -3.118221521110451, 4.457933380522982, 8.023339897374477, 3.068042589570494, -2.408551780660596, -1.3364499415399689, 2.205960303022453, 1.9725937882292723, -0.16864671489490696, 0.10581118896972402, 1.110476580944782, -0.20787619852322137, -1.309324592837584, 0.872959959131521, 3.1605354388561366, 1.5909868996502263, -1.108262593338284, -0.5360431524189974, 1.4062700734320257, 0.6489518742454707, -1.222360867832124, -0.5394237049589993, 1.0498268821677141, 0.10808905738145189, -1.479182223928563, -0.3287818005365952, 1.3770063305352584, 0.2782060453074517, -0.9489842293586308, 0.8192385813148513, 0.8838693826096589, -5.904166723345069, -13.265580824237016, -10.583271963865016, 0.07346017088755945, 6.037851754096323, 2.8348684953090486, -1.139922662283432, 0.15742997964460584, 2.4504880168950427, 1.3360741266456093, -0.41114209437444427, 0.05672924965996648, 0.3492689112275041, -1.130448459932086, -1.6166098591998437, -0.020754234653423402, 0.6289657491917656, -0.4776499665644761, -0.3957046528764186, 0.7766003758803306, -0.5011818621235931, -3.032167215991385, -1.2066132535261576, 4.282646803112467, 5.680270863012083, 1.038002980742932, -2.2894612558616703, -0.6970666060358199, -0.1677905686444208, -4.119454903180821, -6.280408503005249, -2.244932970149566, 1.973545494105017, 0.48821652219304557, -2.5150628627914116, -1.3714044688171732, 0.9627603624479879, -0.1836388310734658, -1.8566077058732662, 0.2578822509964348, 2.988652746844753, 1.6912364058191645, -0.9231717418738137, -0.20634479637775652, 1.7752756434322354, 0.8670284376897869, -1.202011383446644, -0.8699995458961628, 0.41268993591144354, 0.1335047932041931, 0.0261089116872648, 1.2768537211220525, 0.7203188917350102, -2.2331899029972426, -2.342711285236027, 1.408660831401739, 1.2451571680666573, -6.148923532504856, -11.141454518562893, -5.5755091585142855, 3.1391372854267074, 3.51022005431592, -2.18323268629604, -3.6527815942354684, 0.09938833911414699, 1.8705142867484685, 0.10765879181490423, -0.49068788483165154, 0.8100775045612959, 0.7509504650805776, -0.2405081638667165, 0.37836603745813463, 0.9327434875537949, -0.9761972701688898, -2.4360996667279533, -0.5141928319186451, 1.1159950991665326, -1.3001793741771324, -3.872754810810932, -1.9668874600916861, 1.1322407266611727, 0.7957457667751325, -0.2420563651166508, 1.4916728048024772, 1.9768211567660652, -2.3866213779579906, -5.887737887521263, -2.7506501850858935, 1.8694129765499885, 0.801472462031857, -2.418940967630195, -1.0726832450081396, 1.5454548518479683, -1.2968606299817385, -6.156741574851957, -5.01618692950572, 0.45113250058084736, 2.371282579561316, 0.24961160868207785, -0.3389404762730039, 1.146498014762329, 1.01433697257691, -0.23794045542781195, 0.2535526835667144, 1.0974764770746364, -0.04715446824282536, -0.9886834506954185, 0.13177271197734036, 0.22930845083532267, -2.041101738832562, -2.274221107391034, 0.7233806851412036, 1.0255909098539344, -2.4367296185286893, -0.7193740677014601, 9.689308752512654, 17.45586485519484, 12.79606795003622, 2.814912588121916, -0.6185968647623972, 1.5278417955241916, 1.5585544894954098, -0.3436640094781393, 0.3618057798174619, 2.006678891310613, 0.8482662220335865, -0.6993860167337037, 0.5692200129939127, 1.6442335699754755, -0.2633467127867552, -1.515110859539476, 0.5339060038948681, 1.8033835802801592, -0.29629693419980013, -1.422159121003964, 0.9559326382760487, 2.3933233812426757, 0.4453643663076534, -0.6955327404286633, 0.7878031194467108, 0.781157300559698, -1.4494374511974888, -1.3416462920681789, 0.5164672085953845, -1.7129172241902944, -6.079357294320602, -3.5555144882236185, 4.978446310728022, 7.349494704934397, -0.05165613718896406, -6.05654684589951, -3.390285720626242, 1.1786610739085996, 0.9662574276959823, -0.42034166978308485, 0.9216448205142165, 1.6708903902812566, -0.4369664341514249, -1.7456814773523481, -0.4998021177160552, 0.1785174641347237, -0.4837325124985129, 0.021686471961719852, 0.8196485664389408, -0.651636495486444, -1.8514763682714204, 0.2924997918303753, 1.4946359445476927, -2.677911001323205, -6.699223434178299, -3.8829550380074482, 0.6951760216768678, -1.074821220331907, -5.210408208474383, -3.172462898625179, 1.9981082836594402, 1.7340974825136704, -1.9718344701519745, -1.2676545649573692, 2.405565912902716, 2.09289818690556, -1.0796359910962325, -1.3207625447130105, 0.2993896565507676, -0.18712245706180483, -0.2411491064502214, 3.435156676715099, 6.359442943679141, 3.7763570189895836, -0.2922907649775437, -0.5706051734275128, 0.5628555953900641, -0.4265225772431471, -1.2279905062138932, 0.020292209097519453, 0.318229720730578, -1.0584508373910309, -0.6076914968543361, 0.8690620763538961, -1.1782634785458301, -4.284633496432308, -1.8173409362343038, 2.686875937174503, -0.6952505047353693, -9.372133710222647, -10.090084833451595, -1.2717024918788706, 4.115790239071027, 0.4263318796658142, -3.387251958445728, -1.3855352504955387, 1.0652215595468142, 0.019934234376763116, -0.8546777229855197, 0.29246027870073077, 0.5389767847248175, -0.13594434318312626, 0.8403284755831008, 1.7596768468958155, -0.015220884697602643, -1.2877137973752457, 1.0156465151903376, 2.7356384505758085, 0.36019929162069947, -1.5322676885623545, 0.5136794265569677, 1.4949397049871838, -1.556126990675223, -2.619421754081655, 1.2532968748813786, 3.050251395850356, -0.6970985361038481, -2.6674447877521867, 0.934119991961594, 2.783324080544694, -1.078489901615152, -3.650796405323276, -1.1648080296791046, -0.08258266672733112, -3.1868846308983576, -3.5668082281270497, 1.3260995791897527, 4.122210259137642, 1.3298627752121943, -1.0871512263059047, 0.1433194234375303, 0.9358460955339308, -0.2940928180265665, -0.3539417281608903, 0.4734929850564302, -0.8639842081514703, -2.5964989154100753, -1.4298690530883955, 0.26190451044396, -0.3302901643043059, -0.4708963862336438, 0.5286165995209133, -2.61676881536374, -9.06233096988057, -8.36159257651696, 1.4940148221901322, 6.930563518468704, 0.09701064514257417, -7.870525386553853, -5.872793353407547, 0.2742726019403403, 1.2297812148262817, -0.5157458888798895, 0.3578837060982454, 1.2766537352607257, -0.38450216181064467, -0.9610855663160383, 1.0010886569795925], 'positive_zeros': ['0.578802713912966152525297751962', '1.66911252522255796829647471499', '3.1050741771708538855802301898', '3.812119494738917292517845568094', '4.568021672227952789028297571040', '5.4072761692757330175343813738', '6.48482419689510995542179806951', '8.15493931577401493468986097906', '8.296155732783204313645514332', '9.75212096846125262369812238573', '10.18165258571819294990264199615', '10.8772143604618924001791231846', '11.577065691276260625812508015171', '12.362812042609942482577849497286', '13.404264694481036376988298045982', '14.16494358608150996265595885593', '14.97063975946627682386831106624', '16.00558284566278270346369670900', '16.91555151767608749389317687238', '17.41956144408291849710258910174', '18.16608830854057022526889162687', '19.08421470648870907777652536447', '20.21137056977762292175597177692', '20.48392600600460303378259116094', '21.2459983224035045521840184287', '21.906532999701762034025911730140', '22.79476662058156142392791519927', '23.28341230915379609670140512222', '24.073438456094079152920442881888', '25.51892685779877381479517654503', '26.19666539342997017113090642288', '26.85032673103569070791105001152', '27.56547714833952368799887573969', '28.062217366005619980057396886979', '28.68755858220610450031484100569', '29.72609814643388427452076212625', '30.1448620850945954375939655983', '30.95284362905884420802999977040', '31.82715111924280282175602707572', '32.71641580123342385133565935938', '32.91454700814989259781181880075', '34.14444763575682939970792546098', '34.6464457151382003653279128986', '35.61438475243833525549353967452', '36.37259573605215484668627097693', '37.13557827054907641415100247292', '37.669171413195076174494663965422', '38.376039948637467129446528310833', '39.14449518923827067224505787901', '39.5930389116139571307434315989', '40.36371199149012163918082870112', '40.65736475738011237766509259168', '41.83793738490940449040422679178', '42.79264720794811702353992514882', '43.55692013629427208578549092065', '44.16788692784678525836380154999', '44.93132223441749408281648810021', '45.57589010503225346602299292518', '46.080729079326149617386673393839', '46.7022871407336937309503214679', '47.53332253410942447325935534880', '48.27834530383090448745792139850', '49.0492552549611478121772882977', '49.65076785967635000298802964643', '50.201299576816064964867194531276', '50.57852542322962889068841702095', '51.83916775735398961345484735630', '52.37362452394351882029980756367', '53.19798568476295418804011841649', '54.06749985409063354413193660190', '54.87810318686856068013759333497', '55.17630920565377963435409489989', '56.05367587017428481178445125330', '56.44048711271264445445803886722', '57.150459662212806701248329857778', '57.56688399128452811073300074186', '58.64032482419103454246220506709', '59.0705978790651172622716596447', '59.94549546774484690597445474815', '60.61433301589062407692309069187', '61.69643530683787535103742676261', '62.202655729631137972396746372464', '62.675388195980392573433639371575', '63.33533276063075107151817049495', '64.06559377112623320137484539267', '64.84951539470076554947661168495', '65.52839124354993127389526481423', '66.31121175650183666597908398890', '66.49747241458848595200078165508', '67.40725274012569203940474785865', '68.19443785059685617335030857019', '68.28616916620647010356853454070', '69.357277628388973771447113666827', '69.87710258121435949471727729296', '71.23160524429313506813622322477', '71.83177464656788819205568365594', '72.32338937717361316968337333493', '72.764768007917094789601789285118', '73.515597138323552293310504595837', '74.36071138040074592069890442179', '74.53741489482129325957778411903', '75.3066925632127732009220553791', '75.99830714567898984094393324485', '76.79843711379111517873208765773', '77.3892593744765860339181814494', '78.14943167021562506173084948052', '78.81423189343977541143653407067', '79.38971064983498371960562437810', '80.17024823281495927153457135245', '80.92911545774637895758080987614', '81.594996338965608782494872547155', '82.047375408239075536987616162918', '83.14067256022856590919866904853', '83.28074059830925253107601719745', '84.30172855321890405694949489761', '84.79058363153801129927272907922', '84.988418766555902073403518452976', '86.02403750819564632117016515622', '86.28504655666299201755882785517', '87.119885122744442952733551383981', '88.38464000465807600376176168479', '88.64734849275968314048554262581', '89.68253199550315442130118123868', '90.126980627236688060085715863067', '90.678148969324533880815278940788', '91.52182689987021452519537998482', '91.81851949697579051703037537469', '92.28323342368121773613313184654', '93.21743989675763769833656024023', '94.2450070378343229253953885871', '94.357073900927974476787350024050', '95.05357014758623180350394191385', '95.77804833249105517289044319123', '96.32934174697408595583451976746', '97.03933131633536511598470814665', '97.916553669223460985143864910927', '98.456538207493737252427091786655', '99.18907801086798702997445972344', '99.94609036121748000568245918538', '100.76995635266325092613439621551', '101.07935782146934364692060255517', '101.639101940433271856936354485558', '102.112953757555252531447231430303', '102.905218841091035609363212876360', '103.51984427764896723927837043067', '103.94243185489079588279287464000', '104.72714325179413254116598954761', '105.45153817415166219950661325705', '106.39147861605700468353585470444', '106.980136518806861368824147377851', '107.77544659611845508948435609756', '108.10054730270467076588287296888', '108.71799245549536288319462595134', '109.28670987914034542195886299318', '110.15769344537840365555181438520', '110.69974327293133876285658281321', '111.34214330470038375552796963643', '111.9606679119402881429795874066', '112.5164704049636476401190689717', '113.17021655669682088449425391346', '113.792353736031730011256374586360', '114.266690740366538378757554352575', '114.754198127935642680597196160156', '115.935284785760476652444084373', '116.74245113905823818320260922526', '117.17099148289037973521486457848', '118.011449432383345556709506824788', '118.420079398204279843493904558392', '118.848326166587267698275951023097', '119.69135149037017114729216407891', '120.187907438245159795547126311357', '120.71857045165247444108949247804', '121.18866693000708601093541876375', '121.94843396144673289828207353562', '122.874980216010346741466322975571', '123.547671459559713119005793270344', '123.7210329189245413183586600843', '124.81655014056615498974728399476', '125.353915736317243264364840604311', '126.08569395442250727990919745580', '126.538896801787696646237672753906', '127.16429755810215419446466113326', '127.98615309183347327678603020051', '128.46551006364150521161028495191', '129.17581265937131500038324688266', '129.8687698018221472859938765183', '130.37388706124033793653315969271', '130.61452209332610879198968597500', '131.3343338735532755195056034080', '132.07424328831983662698546362701', '132.57232904945927404992677278395', '133.61801646531090370584261915825', '134.255276815464713254484509677468', '134.99203769905002998519475779836', '135.64304972352940558288208043597', '136.06512602363417496507127119233', '136.76644493203674058337519956067', '137.084304315596513523990874501524', '137.68894969016530243746848308260', '138.49597319601651552231001861240', '138.943961519626352574540726542523', '139.857820747253160152279118830012', '140.470063359154319722145786341438', '140.71231672947115052346999416356', '141.42221466162423922676706737283', '142.34419144925674805895155952154', '142.87862566090777332494832789350', '143.53320609124783860467390237675', '143.98022613678106298597540486557', '144.971260463496424538343503018982', '145.66417532271648555521413484231', '146.0188429563793149868855203602', '146.791042029504549913079734023460', '147.12083063439138648279477076510', '147.8038004136481793054959903458', '148.40756246350482505656631218418', '148.79302363977520485270444590626', '149.61363936272287245703916040492', '150.10168851627981358778062390210', '150.65554451407361410723591869806', '152.02949070236706773710869827726', '152.30535243260727012146288798431', '153.047753780189767520293201683940', '153.37734728220771923254489176156', '154.18545879888312228779834640532', '154.59857062164472492718676977871', '155.28006285184582560721790258627', '155.87527923684523723691554390712', '156.52767022995419935417292958046', '157.08679968069846793972000099036', '157.87323236636987017676185387269', '158.2958807249610342175295073334', '158.865170403472717928680447569938', '159.567612280099268942784516195436', '159.85599500556681551727875814968', '160.758904000820864267993803837221', '161.56071150766748634605833361299', '162.390787396360103680169386298691', '162.97001359887555808956165213560', '163.282380079899607626150515511505', '164.009126449924344007124934353159', '164.808733738561589274034838843616', '165.09825463540721344794773162656', '165.619413547791395271354159140726', '166.154113324931103533993824264328', '166.843884900622517331763418846', '167.34159285343520445238233603586', '168.36164764958259482325994092306', '168.669684357333055749535341329406', '169.55009053012317635303243727723', '170.13668828641063167223650868741', '170.72796909107289372170826952080', '171.44608551425161177929646981478', '172.10637189774890337774474253038', '172.45155054987594835969603991904', '172.84795768847543814132804657482', '174.028786481681209752051837733501', '174.49574626277481922262436675947', '174.915280324073514086098575954131', '175.62048732031653480362424959188', '176.01865992070506277869786161619', '176.66301482180283060836744107866', '177.07861612778217022177691910280', '177.9164306247018988769459779903', '178.40922141531982308803586184810', '179.41870195807322980397632660883', '180.02344309280214612232970028013', '180.75422682795685966518267542715', '181.2534656078169065348438747735', '181.80469487548090210540919778939', '182.39202749314654468439137748764', '182.61550551868333250001230350862', '183.435564101683847256458075148523', '183.95981992290574735640965268940', '184.721994053945142199492774679570', '185.25493968764941479845905387086', '185.80229085333869057774864562332', '186.47624902500748533730439609192', '187.13974725772523858872226812327', '187.74713770510714864113912734860', '188.36798938049015044016625529751', '189.21667221960457022674357914233', '189.357159963128270958286343218716', '190.23747424525177756248241052472', '191.05488352370679352246786948215', '191.53865680593718034693366752745', '192.11614477505811907307975993337', '192.6029525446435548258770422405', '192.99178152081937256981728560661', '193.97492517842604754012602704550', '194.27958769495438850765017747588', '194.804368819470732844322307535853', '195.12695218392252522795162312426', '196.20627600204735892890684370826', '196.87795899135867718192172725512', '197.79314215764582466158111540203', '198.31566414128137585878442982724', '198.68626016267789812206557615856', '199.31586891859337444062287340399', '199.85560594593815816603264430696'], 'prelabel': '1-1045-1045.448-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.51965502238071, 'root_number': '-0.0617088423010851410122409134578-0.998094193341419958548058580167*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25982751119', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.772494795808006716158004838889-0.299736526813453449716405600604*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.578802713913', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.66911252522', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.10507417717', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.448', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/448'], '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': '1-1045-1045.448-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': '1-1045-1045.448-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.259827511190355, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.578802713913', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.448', 'Lhash_array': ['dirichlet_L_1045.448'], 'label': '1-1045-1045.448-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/448'}
Lfunction data - 1-1045-1045.448-r0-0-0