-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3465703095131300026078848571088', 'a10': [-16.595287845026153, 4.872816169237735], 'a2': [-0.22029133515009786, -0.2542297532035687], 'a3': [7.571281795480631, 4.8657673571003786], 'a4': [4.5379703296733895, -31.56227691665366], 'a5': [21.35879335924676, -46.76923369076273], 'a6': [-0.43086494118244817, -2.9967314899251187], 'a7': [-219.257339197351, -64.37976355951606], 'a8': [-18.07951458569507, 11.618998510371888], 'a9': [33.6486160531528, 73.68019162371598], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.066483567095666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-7.571281795480631, -4.8657673571003786]]], [23, [[1.0, 0], [65.80030172161412, 2536.1414235592906]]]], 'bad_primes': [3, 23], 'central_character': '69.13', 'coefficient_field': 'CDF', 'conductor': 69, 'conductor_radical': 69, 'conjugate': '569474557633779386477989515013', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.22029133515009786, 0.2542297532035687], [-4.554074824745125, 31.674286140189846]], [[1.0, 0], [-7.571281795480631, -4.8657673571003786]], [[1.0, 0], [-21.35879335924676, 46.76923369076273], [-2046.4397935790157, -2361.717419857057]], [[1.0, 0], [219.257339197351, 64.37976355951606], [14138.948126293662, 9086.550218976228]], [[1.0, 0], [314.56557471968523, -363.02802546833993], [-22919.947018750845, -159411.7330363661]], [[1.0, 0], [42.32948462577414, -12.429058118554574], [312351.54796548776, -200736.1510355412]], [[1.0, 0], [95.5235894014214, 664.3811575950473], [-1362342.8150373595, 400019.9429592019]], [[1.0, 0], [6.768326953685572, -47.07474797219532], [-2375799.592473883, -697597.7022625073]], [[1.0, 0], [65.80030172161412, 2536.1414235592906]], [[1.0, 0], [660.8921675581139, 4596.605991035195], [-19680303.346260026, 5778658.451525534]], [[1.0, 0], [-2965.8162496256946, 1906.0143690861637], [11892979.13489797, -26041991.749435805]], [[1.0, 0], [5157.01744326896, 11292.29305676899], [-45410634.575690284, 52406665.98678999]], [[1.0, 0], [-5914.4005174421845, 12950.730656386508], [-75869676.81897247, -87558274.59205139]], [[1.0, 0], [-18465.23779945051, -11866.88776784047], [61069514.260232076, 133723583.34005098]], [[1.0, 0], [-7823.342558367348, 0], [229345007.0, 0]], [[1.0, 0], [26100.275024161023, 7663.732220071246], [351808435.9003275, 226093553.19176665]], [[1.0, 0], [-9105.929387379598, 2673.7421109606817], [601432592.2406057, -386517257.4302301]], [[1.0, 0], [21604.097881873786, -13884.11065560528], [350857983.3612602, -768271818.5476754]], [[1.0, 0], [-30873.65088136172, -35630.092480549596], [-192142836.2514068, 1336382780.1303885]], [[1.0, 0], [7495.684390175659, 8650.480924761665], [-256768608.2954792, 1785864897.6907194]], [[1.0, 0], [-3953.8118739727843, 27499.36561433268], [-1989097627.283313, -584051760.4112257]], [[1.0, 0], [65575.28291886214, -19254.64034690667], [2588584566.379543, -1663582286.9123375]], [[1.0, 0], [48242.65948960627, 105636.68918855338], [-2579523046.5152874, 2976928289.3113737]], [[1.0, 0], [-66395.88316813654, -42670.043156788975], [2319702128.6096416, 5079439138.772122]], [[1.0, 0], [-24362.63588586911, 53346.73133938488], [-5623511943.336913, -6489878744.062937]], [[1.0, 0], [28410.16007083824, 62209.573040781026], [-6882652127.923569, 7943003980.051227]], [[1.0, 0], [-20362.721871438447, 23499.833765143023], [-1649819023.9841685, -11474743357.588095]], [[1.0, 0], [145677.7117681584, -93621.38059657117], [5826410454.445588, -12758059293.845741]], [[1.0, 0], [-8969.607386185253, -62384.98967374618], [-14762988737.614994, 4334804608.314496]], [[1.0, 0], [-38688.29714463461, -44648.67502956992], [-2622058645.710906, 18236818457.468807]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-69-23.13-c5-0-19', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/69/6/e/b/13/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1232470438257316, 1.4202842754535672, 1.6997966501758626, 1.9563463575542668, 2.1847388746559213, 2.380075404126592, 2.5378327709907396, 2.653973400476245, 2.725085194652883, 2.7485480876238633, 2.722720922560568, 2.6471392089537233, 2.522711450987229, 2.3518992703466095, 2.138864676169151, 1.8895667674216736, 1.6117900936590035, 1.3150880371530087, 1.010627064731239, 0.7109216241679476, 0.4294548375382423, 0.1801868771245172, -0.02303922080700389, -0.16717589657749568, -0.24070620886525687, -0.23439980107823152, -0.14204612897829677, 0.03888438894165184, 0.30670381932921414, 0.6551471499996557, 1.073238073184932, 1.5454201710389557, 2.0519808947835663, 2.569778969044201, 3.073265653162474, 3.535767715579073, 3.9309764772686138, 4.2345646343969685, 4.425832782436426, 4.489272719911046, 4.41592670205422, 4.204422542845782, 3.8615750299229346, 3.4024650307979525, 2.8499385892287687, 2.2335079405147593, 1.5876824334876334, 0.9498066351759917, 0.3575314574755463, -0.15391245818862048, -0.5544362048879364, -0.8215863895068095, -0.9425865936016344, -0.9157196348301803, -0.7508820604677311, -0.46919998520190814, -0.10166920688414804, 0.3131327133817353, 0.7321259605874888, 1.111378505450307, 1.4100338529165866, 1.5941731897912725, 1.640246639362238, 1.5377199928648806, 1.2906308451157262, 0.9178302964656232, 0.4517983304906744, -0.06394597651037946, -0.5786758609134584, -1.0392285538796164, -1.3952976284823273, -1.6047419399838487, -1.638368501700105, -1.483662169680974, -1.1470077577204854, -0.6540772492316933, -0.04822688695876172, 0.6130490145718311, 1.2633485444447445, 1.8338185422072675, 2.2602150639436083, 2.4898402558372297, 2.4875958513458323, 2.2404446757878804, 1.75970638351204, 1.0808228285840664, 0.2604931171951822, -0.6286284421151805, -1.5051890623743056, -2.2876157136863826, -2.9029019655245034, -3.29470812260586, -3.4298106722399444, -3.3020857597753297, -2.9334668566633217, -2.37165433637676, -1.6847376853025482, -0.953274656831887, -0.26070780529172116, 0.31675769625740113, 0.7195765854248739, 0.9123846610439361, 0.8886085378090257, 0.67148476835102, 0.3112437171556333, -0.12129908480232265, -0.5440225706504751, -0.8745228218391501, -1.041474911828719, -0.9948284137284044, -0.7134267468227058, -0.20893087091013576, 0.4746165710402596, 1.265683547912879, 2.0740881369028137, 2.802712587663155, 3.3605790953612438, 3.675524996922176, 3.7047009177150687, 3.4413499904172484, 2.9167885173472583, 2.1971435607218215, 1.3751284202941831, 0.5578529518834481, -0.14773143752156853, -0.6497549881400142, -0.8845992596806405, -0.8263701321878854, -0.491200018788043, 0.06439165959630883, 0.75100722014992, 1.4588116612122002, 2.07321128151406, 2.4915428810529257, 2.6383281515769257, 2.4767895571739054, 2.014818576808876, 1.3043731719256892, 0.4342497751134542, -0.4828159317375044, -1.3268699786444529, -1.9887950814963664, -2.386939635287151, -2.4797105763959455, -2.2720837877781226, -1.8148894919642005, -1.1968426738610098, -0.5304402228707484, 0.06614567145161435, 0.4883512809419475, 0.6625927576986281, 0.5588646882594399, 0.19640598202997114, -0.3586523311168764, -1.00345801308671, -1.6149367934563343, -2.070045038851531, -2.2665103264820363, -2.140625268333686, -1.6790584472754735, -0.9225647189086399, 0.03922160276822011, 1.0812497727344177, 2.0627016446314053, 2.8496567974890947, 3.33701124332193, 3.4659194573986145, 3.2337012884271408, 2.6943716930753974, 1.9495197120390926, 1.1309233339781761, 0.3777534495994631, -0.18776863329035479, -0.4820307081109222, -0.47514245262755617, -0.19669249859226695, 0.26907967350431855, 0.7980850620610044, 1.2487625522100951, 1.4882250247078954, 1.4175939102018191, 0.9919634909693379, 0.2312720624953535, -0.7801186547760565, -1.905375404384392, -2.9768623073786347, -3.823931453852354, -4.302060583791349, -4.318215187471293, -3.847879884510811, -2.9406065925608527, -1.7129290513043374, -0.32974254113272045, 1.0226628243038112, 2.167184829816131, 2.9646788432865803, 3.335776051905468, 3.2718564109336232, 2.833265672240179, 2.1352283706663195, 1.3242112093625773, 0.5492961288957818, -0.06592319890118808, -0.44550132928654335, -0.573079522851355, -0.49131344646582215, -0.28896475859755294, -0.0782979144213572, 0.03259180875305117, -0.033207276484521486, -0.30077020115858877, -0.7335788071320727, -1.237085499973213, -1.6753628062222066, -1.8979153814815255, -1.7715489645544307, -1.2109675881436321, -0.20178047244482197, 1.1891204208540957, 2.818518886021535, 4.4869246040374655, 5.970471477012384, 7.0589714303642905, 7.593036376959805, 7.493149384850843, 6.774940878832636, 5.54746940623714, 3.9945405242900334, 2.342392138119517, 0.8197729082683685, -0.3820102081494256, -1.14143126133987, -1.4252807573475894, -1.2899129294178102, -0.8651513608064181, -0.32426829884109076, 0.15374703449760868, 0.42186651813562354, 0.3949181332845215, 0.06559941794925131, -0.4965824275003135, -1.1630448620120684, -1.7766097875919067, -2.188074910876591, -2.2908901724900668, -2.0463148196602465, -1.4934350145535327, -0.7416646617935582, 0.05284304407396187, 0.7218893710987008, 1.123510397513995, 1.1753815922950326, 0.8757694838915329, 0.30701454114145055, -0.37975297092887006, -0.9958711551375576, -1.356003202430288], 'positive_zeros': ['2.73395768085253973047506837896119', '3.35262149785667960441763963528590', '6.08474490942004361181395424470875', '7.03148489361140014679139514204370', '8.359745213164002073364729195373692', '9.509330034488059934602249844816183', '10.78712915223891276706114947725850', '12.30255199779173290728691995678766', '13.09069619140327677145211563154458', '13.91627684340420424005939728023630'], 'prelabel': '2-69-23.13-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.326632466488546, 'root_angle': 0.8061765501074305, 'root_number': '-0.820269481817745 + 0.5719772523435247*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.403088275054', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.73395768085253973047506837896', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.35262149785667960441763963529', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.08474490942004361181395424471', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 11.066483567095666, 'bad_primes': [3, 23], 'central_character': '23.13', 'conductor': 69, 'conductor_radical': 69, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/69/6/e/b/13/5'], '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': '2-69-23.13-c5-0-19', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-69-23.13-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.326632466488546, 'root_angle': 0.40308827505371525, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.73395768085253973047506837896', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3465703095131300026078848571088', 'Lhash_array': ['3465703095131300026078848571088'], 'label': '2-69-23.13-c5-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/69/6/e/b/13/5'}