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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': 4, 'A8': 0, 'A9': 1, 'Lhash': '439415758660244908', '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': [1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 498.26650861278983, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [13, [1, -1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '62400.1', 'coefficient_field': '1.1.1.1', 'conductor': 62400, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1, -4, 7], [1, 0, 11], [1, -1], [1, 2, 17], [1, -8, 19], [1, -4, 23], [1, 6, 29], [1, -8, 31], [1, -6, 37], [1, 6, 41], [1, -4, 43], [1, -4, 47], [1, -6, 53], [1, -8, 59], [1, -10, 61], [1, 4, 67], [1, 8, 71], [1, -14, 73], [1, 0, 79], [1, 12, 83], [1, 6, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 121, 'label': '2-62400-1.1-c1-0-121', 'leading_term': '5.22606157016', '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/62400/hv', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [5.226061570162638, 4.544122661424801, 2.737828014145545, 0.6246928536915805, -0.5840961881647113, -0.1809446609580521, 1.169754085277004, 1.816441481336009, 0.8062333886845309, -0.8528181585482522, -1.138367596237754, 0.4944119202471623, 2.089467434486375, 1.400601122989599, -1.076551254838047, -2.407139533191258, -1.008503165793055, 1.040652558154944, 0.7771231624967017, -1.339706000291175, -2.029815089840068, -0.328050849374887, 0.4651413803039664, -2.26812752112012, -5.684454403878578, -4.820856249454044, 0.09721284399159334, 3.513244876592303, 2.328958147672374, -0.1223784311168758, 0.1050409138588979, 1.608863153955095, 1.04077212740781, -0.6573426829625076, -0.3038417119242813, 1.184490402617638, 0.2304583453406361, -2.377326280727229, -2.211804891542491, 0.6135453085954892, 0.8089278855050044, -2.83510626472858, -4.675765570183738, -1.736025859396878, 1.223232392583602, 0.3870929896606351, -0.6842911875071515, 1.166890782134531, 1.844290014098642, -2.076326367346763, -5.465965510107355, -2.820399694828163, 1.89186130392803, 2.179078239202388, -0.1070008488929778, 0.2003399936601038, 1.631512988119007, 0.4222977330854453, -1.139482314898021, 0.1451415856072685, 1.233583942955023, -0.5073943131741954, -0.973975497840763, 1.974587166640166, 2.525468591324546, -1.923513202418886, -4.128429383137119, -0.0956585025087538, 2.965474611649188, 0.1740265723551586, -2.443243918396852, -0.7109725401827289, 0.2518984683654039, -1.908957918097496, -1.993846882008792, 0.3982213822837027, -0.8527011517562645, -4.827946666707018, -4.208752170497414, 0.1015731803987272, 0.9220191160369939, -1.12096192569076, -0.7766885237632274, 0.2833859564175428, -0.9043126528828863, -0.5827174936192228, 2.320120689423197, 1.533285987753536, -3.003419889428688, -3.226542793700864, 0.1597476947221372, -1.693834969937021, -6.76824596316797, -5.240824573492034, 0.6910238169460599, 1.613668870242774, -0.835739471425814, -0.242176317091077, 0.7552094934534151, -0.852566257107869, -0.5822920620446252, 1.655411213460968, -0.3021967688147279, -4.123531929530152, -2.249472963349681, 2.081800290626179, 1.741173887862629, -0.07203211035888814, 0.5520149529647342, -0.6376088748422819, -3.390668007812619, -1.206984157846942, 2.925492413127914, 1.485911897820684, -0.7728184043716367, 2.177909915656236, 2.656176192190963, -3.866984523771304, -6.992267855813757, -2.303721352723919, 0.5825935902899229], 'positive_zeros': ['0.8445083024729771', '1.288162784951851', '2.114711629786990', '2.689854507216347', '3.396141281486262', '4.107077168121648', '4.598220564066052', '5.293730584191700', '5.574974792027579', '6.495326001269788', '7.229790462262849', '7.482128116016887', '8.138342467385082', '8.546350547609295', '9.022675562090735', '9.692892925422773', '10.07065066550584', '10.86372552238619', '11.30057897891857', '11.62621116794627', '12.14348757329769', '12.88480863857393', '13.48284298378062', '13.71875440862263', '14.29704839500457', '14.73253555324408', '15.19227997856770', '15.59992246273804', '16.15607608027663', '16.75460479673427', '17.26047359234946', '17.83116860931528', '18.04415561140453', '18.69638274980106', '18.93376193331876', '19.74273752014871'], 'prelabel': '2-62400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 22.321884073993168, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 439415758660244908, 'z1': {'__RealLiteral__': 0, 'data': '0.8445083024729771', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.288162784951851', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.114711629786990', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 498.26650861278983, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 62400, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 4, 0, 1, 0, 0, 0, 1, 0, 0, 0, -2, 0, 8, 0, 4, 0, 4, 0, 0, 0, 1, 0, -6, 0, 8, 0, 0, 0, 0, 0, 6, 0, 1, 0, -6, 0, 4, 0, 0, 0, 4, 0, 9, 0, -2, 0, 6, 0, 0, 0, 8, 0, 8, 0, 10, 0, 4, 0, 0, 0, -4, 0, 4, 0, -8, 0, 14, 0, 0, 0, 0, 0, 0, 0, 1, 0, -12, 0, 0, 0, -6, 0, -6, 0, 4, 0, 8, 0, 0, 0, 6, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -1, 0], 'euler17': [1, 2, 17], 'euler19': [1, -8, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -6, 37], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, -4, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, -8, 59], 'euler61': [1, -10, 61], 'euler67': [1, 4, 67], 'euler7': [1, -4, 7], 'euler71': [1, 8, 71], 'euler73': [1, -14, 73], 'euler79': [1, 0, 79], 'euler83': [1, 12, 83], 'euler89': [1, 6, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, -4, 7], [1, 0, 11], [1, -1, 0], [1, 2, 17], [1, -8, 19], [1, -4, 23], [1, 6, 29], [1, -8, 31], [1, -6, 37], [1, 6, 41], [1, -4, 43], [1, -4, 47], [1, -6, 53], [1, -8, 59], [1, -10, 61], [1, 4, 67], [1, 8, 71], [1, -14, 73], [1, 0, 79], [1, 12, 83], [1, 6, 89], [1, -6, 97]], 'index': 121, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/62400/hv'], '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': '2-62400-1.1-c1-0-121', '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': '2-62400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 22.321884073993168, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 439415758660244908, 'z1': {'__RealLiteral__': 0, 'data': '0.8445083024729771', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '439415758660244908', 'Lhash_array': ['439415758660244908'], 'factors': ['2-62400-1.1-c1-0-121'], 'label': '2-62400-1.1-c1-0-121', 'type': 'ECQ', 'url': 'EllipticCurve/Q/62400/hv'}