-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2742862403650844496348621176257', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.9804035968077678, -2.725791705882295], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, -0.7943753643143628], 'a8': [0.0, 0.0], 'a9': [-2.580891034482726, -7.943165848070695], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.985040202128042, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '1000.649', 'coefficient_field': 'CDF', 'conductor': 1000, 'conductor_radical': 10, 'conjugate': '1182283965228001454590746044586', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.9804035968077678, 2.725791705882295], [-0.9270509831248422, -2.853169548885461]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0.7943753643143628], [-7.0, 0]], [[1.0, 0], [-0.6735041872253285, 2.072832749241993], [-8.899186938124421, -6.465637775217204]], [[1.0, 0], [-2.735377384632639, 0.8887779888971987], [10.517220926874316, -7.641208279802151]], [[1.0, 0], [0.07368497676062244, 0.10141866982365931], [-5.253288904374106, 16.167960777017612]], [[1.0, 0], [5.661138914750533, -4.113058178512378], [5.871322893124001, -18.07007380960792]], [[1.0, 0], [-5.384041163946812, -1.7493810194950619], [18.607390870623792, 13.519060802726882]], [[1.0, 0], [-0.9892374744232657, -0.718723095465118], [8.961492836873475, 27.580638972559452]], [[1.0, 0], [5.531234961684227, -4.0186774320536935], [9.57952682562337, -29.48275200514976]], [[1.0, 0], [-6.554854019392968, 2.129801176832208], [29.933628791873055, -21.748054334821507]], [[1.0, 0], [-0.24494126419646312, -0.7538516963923488], [-33.16969676937284, 24.099195343991397]], [[1.0, 0], [0, 6.6945986691600075], [-43.0, 0]], [[1.0, 0], [1.790366243424542, -2.464227728471432], [-14.52379873562253, -44.69965626587222]], [[1.0, 0], [-0.5366004733336478, 0.7385671900127069], [-16.377900701872214, -50.405995363643136]], [[1.0, 0], [-0.8535190559680869, -2.6268615472183448], [-47.7320026681219, 34.67932988525592]], [[1.0, 0], [-3.2240837786276666, 9.922709567956154], [-49.350036656871794, -35.854900389840864]], [[1.0, 0], [-2.9057562772042402, -3.99943040523954], [-20.704138623121477, 63.72078659177529]], [[1.0, 0], [6.399745880297824, 4.649687550463475], [21.940206600621266, 67.52501265695591]], [[1.0, 0], [3.0173684993138545, 0.980402456219798], [59.05824058937116, 42.90832341735054]], [[1.0, 0], [-1.7876716293256634, -1.29881946481373], [24.412342555620846, 75.13346478731714]], [[1.0, 0], [-0.2803289813083611, -0.3858397416569298], [-25.648410533120636, 78.93769085249775]], [[1.0, 0], [4.61944213026678, -14.21718099525585], [-72.00251249937033, -52.31288745403011]], [[1.0, 0], [-5.065012604491945, 6.971391775781323], [-29.974648454369902, -92.2524820806299]], [[1.0, 0], [3.116616000617817, 0], [101.0, 0]], [[1.0, 0], [-6.86649389342885, 9.450918051941187], [-31.828750420619585, -97.95882117840081]], [[1.0, 0], [0, -12.292207974310687], [-107.0, 0]], [[1.0, 0], [-4.624008251742361, -14.231234072149988], [-88.18285238686927, 64.06859249987957]], [[1.0, 0], [3.6546195554738397, -1.1874578758113992], [91.41892036436906, -66.41973350904946]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 21, 'label': '2-10e3-25.4-c1-0-21', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1000/2/q/c/649/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.2523291036979978, 2.5449095046765753, 2.8453034319042096, 3.1494161605947797, 3.4467803163242032, 3.721048738687782, 3.951434282064581, 4.114794994629643, 4.188125453064342, 4.151269301721367, 3.989666117845578, 3.696901013276697, 3.2767724884593865, 2.744564489670776, 2.1272237725651992, 1.4622145492397076, 0.7949501123727384, 0.17487688957094308, -0.34950848328252965, -0.7362214831915906, -0.9552687500741578, -0.9932737869213546, -0.8564714672399452, -0.5714071551320223, -0.1829167237682203, 0.2506843894600224, 0.6648497676867602, 0.9976948930664423, 1.1993586555625089, 1.2404094008611781, 1.1178234512217238, 0.8572593023415926, 0.5107957675629003, 0.1499595310897491, -0.14534607682738762, -0.3006045336047316, -0.2610745612650185, -0.004350409508744932, 0.45135826732792883, 1.0452345877058773, 1.679287987503049, 2.231155739300402, 2.572874014202185, 2.592964346564594, 2.218258890424625, 1.4315163455475124, 0.2812000949334956, -1.1191749825326818, -2.603083006240788, -3.973375585614796, -5.031970961621528, -5.612163625577236, -5.6079740593868825, -4.995041028799984, -3.8387041112708986, -2.287004883164794, -0.5490217239913281, 1.138239747447439, 2.5488061680520584, 3.5055286264402716, 3.909578837583191, 3.7558370709496764, 3.130928333961337, 2.1940281670909214, 1.1440592282710242, 0.17979644888293334, -0.5389661830917883, -0.9210850954375768, -0.9582858836176322, -0.720910746856133, -0.3362300531920922, 0.04568417582364582, 0.2905723888493347, 0.31393213114119367, 0.10204565050993211, -0.2852412402938919, -0.7309963243156931, -1.0931833765078856, -1.2443490182865002, -1.108911653482727, -0.6880719431189497, -0.06502565023147736, 0.6121514296839388, 1.166917501200156, 1.4416947071978272, 1.3445518260608686, 0.8826844760646914, 0.17270789040615261, -0.5769978081952624, -1.109813509982794, -1.1813921578020634, -0.623233463541229, 0.6064459705700384, 2.3982813339521782, 4.501845328809699, 6.570259253879686, 8.230760896542112, 9.165733037929991, 9.185278410334293, 8.273580693157307, 6.596956060700493, 4.470445017295879, 2.2898775595007477, 0.44502820968568607, -0.7655229088955121, -1.1973050265187963, -0.8854551058045764, -0.026914481842723534, 1.0756132591339653, 2.093141119547622, 2.752587650770716, 2.9004828090392243, 2.532188217805375, 1.7801320461266867, 0.865809151558879, 0.030192528393433764, -0.5370413647630458, -0.7491196420698825, -0.640154021662182, -0.3451366112458993, -0.048993985905046396, 0.07889893572182284, -0.056143396812345675, -0.44038297791060443, -0.9546343199069385, -1.4138006417442488, -1.6310646961653446, -1.486403683378768, -0.9767553378319074, -0.22989993490819305, 0.5252029626885742, 1.0253088971149587, 1.0583096492164892, 0.5412038174078551, -0.4349567633151493, -1.6103121847078017, -2.6145155235339774, -3.064906545914069, -2.678217646056513, -1.363577915664447, 0.7319517787903908, 3.241783117171999, 5.660752316823555, 7.468907803251394, 8.26511641792455, 7.873364883701048, 6.391291106452315, 4.166269636691603, 1.704851894667212, -0.4594687295329368, -1.90308809732984, -2.415335401326257, -2.0393761122657725, -1.0410626555932456, 0.18286165179403124, 1.2280956644375267, 1.7998739224838098, 1.7890618685930262, 1.2861952164992854, 0.5324155583976113, -0.17381675897342086, -0.5818752360620145, -0.5708996232606042, -0.18224222173326454, 0.4064608510264355, 0.9543830342355647, 1.250504872462868, 1.1927079855643017, 0.8243911689642404, 0.3153251530166235, -0.10640221648330281, -0.24650824681274458, -0.026416567522644537, 0.47667633436891405, 1.0489575104793616, 1.4146457546811468, 1.3416460954824105, 0.7407584668441134, -0.2791939430927609, -1.424628550011111, -2.300336376109653, -2.539137075506172, -1.936488724362631, -0.5435930173935526, 1.3165906509913328, 3.122259655564705, 4.297279292223531, 4.385026461189084, 3.1972439771857184, 0.8890212654068355, -2.0671758131308913, -5.004020879067574, -7.2429939567078305, -8.283600174487306, -7.940046830014494, -6.3836266358244105, -4.079051072716318, -1.636788567060523, 0.3701327238365941, 1.5661866872853927, 1.8609121040853223, 1.4401179454575388, 0.6697216183250141, -0.049929242618968785, -0.42639731588570823, -0.3651014723108672, 0.021308417415710015, 0.48211763025748716, 0.7457052583446843, 0.6376183425878372, 0.15380069976930258, -0.5383533997602776, -1.1699649993388552, -1.4827614224338481, -1.3379498488766048, -0.777704754414667, -0.013582597702684955, 0.6549711037073017, 0.960679458147422, 0.7792315651488491, 0.18498908922944754, -0.5739322603516023, -1.1754190137497629, -1.3616364627055098, -1.0617489297365492, -0.4475691365699584, 0.10644686242449579, 0.15192348145731122, -0.6580621765248024, -2.410329148713003, -4.851647614489774, -7.42471272129254, -9.417134934410596, -10.179221467963085, -9.33897089317886, -6.93993169511658, -3.4513320963258263, 0.3575402079616881, 3.6401491651003983, 5.720191167179, 6.2822580278824764, 5.443721887078699, 3.687098898564509, 1.6803252269846742, 0.05020845719921776, -0.8117172810770475, -0.8463249820688432, -0.2997932110557206, 0.40897956583101047, 0.8703024242573382, 0.8437105545709275, 0.3370661764537458, -0.4200914126938642, -1.091395052566263, -1.3852088090184242, -1.1790031370919658, -0.5662019125133997], 'positive_zeros': ['2.16373691864068546523066903073984', '3.05325462393104379251824679034676', '4.18298905347806903505279946108334', '4.62649369372463264886361141963562', '5.77652475044411611596766203035668', '7.03943212827518439710998206202794', '8.151910946723141702748591509563820', '8.858287592140459419388498602940384', '9.287440349047988971501157610534127', '10.13693437938864532862904731014605'], 'prelabel': '2-10e3-25.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8257813436513524, 'root_angle': 0.7164623749059456, 'root_number': '-0.628821488033027 + 0.7775497001400808*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.358231187453', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.16373691864068546523066903074', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.05325462393104379251824679035', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.18298905347806903505279946108', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.985040202128042, 'bad_primes': [2, 5], 'central_character': '25.4', 'conductor': 1000, 'conductor_radical': 10, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1000/2/q/c/649/8'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-10e3-25.4-c1-0-21', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-10e3-25.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8257813436513524, 'root_angle': 0.3582311874529728, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.16373691864068546523066903074', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2742862403650844496348621176257', 'Lhash_array': ['2742862403650844496348621176257'], 'label': '2-10e3-25.4-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1000/2/q/c/649/8'}