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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '1526609986169047283', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [7, [1, -1]], [11, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '369600.1', 'coefficient_field': '1.1.1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1, -1], [1, 1], [1, -4, 13], [1, -2, 17], [1, 4, 19], [1, -2, 23], [1, 0, 29], [1, 2, 31], [1, 8, 37], [1, 6, 41], [1, -4, 43], [1, 0, 47], [1, 6, 53], [1, 4, 59], [1, 6, 61], [1, -4, 67], [1, 0, 71], [1, -4, 73], [1, 14, 79], [1, 6, 83], [1, 0, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 100, 'label': '2-369600-1.1-c1-0-100', 'leading_term': '2.66782897339', 'load_key': 'Cremona', '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': 'EllipticCurve/Q/369600/tq', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.667828973390554, 1.468323647285145, -1.262217932299178, -3.329689612092209, -2.939474214217793, -0.8427019671053347, 0.1881577809596221, -1.046380859887905, -2.239089339336999, -0.8834990204623174, 1.553069629986456, 1.563571346348081, -0.6655877304779108, -1.316497555853419, 0.5287044333624712, 1.156802977356147, -0.8565205748956497, -1.453843180337506, 1.440048162407769, 3.215748921502862, 0.7269711982961797, -1.22104998865754, 1.49516190747762, 4.029444840964099, 1.416202260214168, -1.661446345644331, 0.2259455797074917, 2.617368981320608, 0.1521689214486681, -2.700989671541821, -0.8907802294297456, 1.270055891109184, -0.2778945319111394, -1.313082026848844, 0.5063177932175612, 0.847319740512246, -0.2558154469769698, 2.011510889654219, 4.853434359786454, 2.178412840971135, -1.692067003374039, -0.31618027001505, 1.467773613890255, -0.9013473979229314, -1.390889266873412, 1.621045124527947, 0.2193578704176802, -4.488095150500959, -2.947173156759035, 2.172382416698971, 1.713120351247613, -0.5414421786965482, 1.735520639443168, 2.974651414918189, 0.1404095731855002, -0.2522327842143097, 1.495533211400782, -0.248585748476832, -1.619525046979563, 1.015317231874662, 1.35435097268219, -1.230613043147818, -0.1146245460777038, 1.505190899743449, -1.017991275344128, -0.3734041991414092, 4.718107646204905, 3.892563495168495, -0.8534361249495848, 0.4060029691608815, 2.002474324850649, -2.562716121609332, -4.043092369133729, 0.3270006401390443, 1.107226439821387, -0.5671486514454549, 0.6575034539495256, -0.8476550547410863, -4.999994382214395, -3.23498141226552, 0.515551956076936, -0.7162255690474583, -0.8546132007910665, 1.854753102133957, 1.083111571548504, -0.119079853964181, 0.3975516336719451, -3.893221021074194, -7.582914120215, -1.815138371004363, 2.624282566675723, -1.321438602833915, -1.875428684323192, 1.602407273876056, -0.4390198589287319, -2.192768749805324, 0.5855955458234688, -0.6641053134314575, -2.906272980281874, 1.134529591435011, 3.057347162154858, -0.2027318991518903, -0.3844908605226201, 0.1354920794198152, -1.513866646737901, 0.737367429492305, 2.54374390182454, -1.399533259584139, -1.808529641827073, 1.558812308957611, -0.2811094085391012, -1.463300411558763, 1.133302183103586, -1.15050021267441, -2.351367090847586, 4.04048614082616, 4.962058299429591, -0.4463680234594281, 0.8345713192680224, 2.796498358260209, -1.234171445686395], 'positive_zeros': ['0.3904536200825695', '1.383551937926868', '1.577485709046841', '2.333542205365094', '2.926976937715192', '3.436607152241481', '3.908071760074793', '4.395759581012960', '5.054789047387576', '5.401049712873249', '6.084830442114141', '6.483963323528631', '7.009400368160424', '7.570199356770296', '7.970618988643170', '8.437992903380385', '8.899710729668851', '9.078371439137398', '9.862803680012704', '10.27547471670505', '10.67468694581335', '11.11532501960526', '11.51160533065045', '12.12959690056864', '12.64206401887737', '12.85900842715113', '13.51358828258605', '13.78219888098367', '14.22879348356885', '14.66700986267061', '15.12090198383453', '15.50997578603610', '15.91488298408275', '16.27083949669782', '16.93671392066197', '17.22130453731895', '17.63176154237090', '18.22977153611771', '18.62694721179234', '18.89607230903623', '19.19313456098203', '19.93765559587229'], 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1526609986169047283, 'z1': {'__RealLiteral__': 0, 'data': '0.3904536200825695', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.383551937926868', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.577485709046841', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 1, 0, 1, 0, -1, 0, 4, 0, 0, 0, 2, 0, -4, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, -2, 0, -1, 0, 0, 0, -8, 0, 4, 0, -6, 0, 4, 0, 0, 0, 0, 0, 1, 0, 2, 0, -6, 0, 0, 0, -4, 0, -4, 0, -6, 0, 1, 0, 0, 0, 4, 0, 2, 0, 0, 0, 4, 0, 0, 0, -1, 0, -14, 0, 1, 0, -6, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 10, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, -4, 13], 'euler17': [1, -2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -2, 23], 'euler29': [1, 0, 29], 'euler3': [1, -1, 0], 'euler31': [1, 2, 31], 'euler37': [1, 8, 37], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, 4, 59], 'euler61': [1, 6, 61], 'euler67': [1, -4, 67], 'euler7': [1, -1, 0], 'euler71': [1, 0, 71], 'euler73': [1, -4, 73], 'euler79': [1, 14, 79], 'euler83': [1, 6, 83], 'euler89': [1, 0, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, -1, 0], [1, 1, 0], [1, -4, 13], [1, -2, 17], [1, 4, 19], [1, -2, 23], [1, 0, 29], [1, 2, 31], [1, 8, 37], [1, 6, 41], [1, -4, 43], [1, 0, 47], [1, 6, 53], [1, 4, 59], [1, 6, 61], [1, -4, 67], [1, 0, 71], [1, -4, 73], [1, 14, 79], [1, 6, 83], [1, 0, 89], [1, -10, 97]], 'index': 100, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/369600/tq'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-369600-1.1-c1-0-100', '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': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1526609986169047283, 'z1': {'__RealLiteral__': 0, 'data': '0.3904536200825695', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1526609986169047283', 'Lhash_array': ['1526609986169047283'], 'label': '2-369600-1.1-c1-0-100', 'type': 'ECQ', 'url': 'EllipticCurve/Q/369600/tq'}