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lfunc_lfunctions • Show schema
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{'Lhash': '637287483811809788589414952147', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 67.07433769787555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [7, [1, -1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '8400.1', 'coefficient_field': '1.1.1.1', 'conductor': 8400, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, -1], [1, 4, 11], [1, 2, 13], [1, 2, 17], [1, -2, 19], [1, 6, 23], [1, -6, 29], [1, 6, 31], [1, -4, 37], [1, 0, 41], [1, 4, 43], [1, -4, 47], [1, -2, 53], [1, 4, 59], [1, 2, 61], [1, 12, 67], [1, -8, 71], [1, 14, 73], [1, 16, 79], [1, -16, 83], [1, -16, 89], [1, -14, 97], [1, -8, 101], [1, 0, 103], [1, -18, 107], [1, -18, 109], [1, -6, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [1], [[[1, -1], 1]], [[[1, 4, 11], 1]], [[[1, 2, 13], 1]], [[[1, 2, 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-2.041966752897065, -1.7598073825245215, -1.4244029043976725, -1.0572610257401018, -0.6818525268952399, -0.32220997479407804, -0.0014783018479420972, 0.2594962742298648, 0.44345373522506565, 0.5378052184664465, 0.5354476308122228, 0.4352554352836162, 0.2422158099478504], 'positive_zeros': ['0.50273118136580517687805037564654', '1.79768067173493383952295287520301', '2.55181171513341671521163672538321', '3.50101908861801476802011770115636', '4.57114548767155620108541318155960', '4.89697965516847316969092004031681', '5.78489214933156331783686829675391', '6.23306806472184064493666247969869', '7.35048406859826782523602071262446', '7.56279277731945914272912400130913'], 'prelabel': '2-8400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.189892410641031, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1409486051160630396, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.50273118136580517687805037565', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.79768067173493383952295287520', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.55181171513341671521163672538', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 67.07433769787555, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 8400, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 1, 0, 1, 0, -4, 0, -2, 0, 0, 0, -2, 0, 2, 0, -1, 0, -6, 0, 0, 0, -1, 0, 6, 0, -6, 0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, -4, 0, 0, 0, 4, 0, 1, 0, 2, 0, 2, 0, 0, 0, -2, 0, -4, 0, -2, 0, 1, 0, 0, 0, -12, 0, 6, 0, 8, 0, -14, 0, 0, 0, -4, 0, -16, 0, 1, 0, 16, 0, 0, 0, -6, 0, 16, 0, -2, 0, 6, 0, 0, 0, 14, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, 2, 13], 'euler17': [1, 2, 17], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 6, 31], 'euler37': [1, -4, 37], 'euler41': [1, 0, 41], 'euler43': [1, 4, 43], 'euler47': [1, -4, 47], 'euler5': [1, 0, 0], 'euler53': [1, -2, 53], 'euler59': [1, 4, 59], 'euler61': [1, 2, 61], 'euler67': [1, 12, 67], 'euler7': [1, -1, 0], 'euler71': [1, -8, 71], 'euler73': [1, 14, 73], 'euler79': [1, 16, 79], 'euler83': [1, -16, 83], 'euler89': [1, -16, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, -1, 0], [1, 4, 11], [1, 2, 13], [1, 2, 17], [1, -2, 19], [1, 6, 23], [1, -6, 29], [1, 6, 31], [1, -4, 37], [1, 0, 41], [1, 4, 43], [1, -4, 47], [1, -2, 53], [1, 4, 59], [1, 2, 61], [1, 12, 67], [1, -8, 71], [1, 14, 73], [1, 16, 79], [1, -16, 83], [1, -16, 89], [1, -14, 97]], 'index': 6, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/8400/o', 'ModularForm/GL2/Q/holomorphic/8400/2/a/o/1/1', 'ModularForm/GL2/Q/holomorphic/8400/2/a/o'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '2-8400-1.1-c1-0-6', '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': '2-8400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.189892410641031, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1409486051160630396, 'z1': {'__RealLiteral__': 0, 'data': '0.50273118136580517687805037565', 'prec': 103}}
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lfunc_instances • Show schema
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id: 22248103
{'Lhash': '637287483811809788589414952147', 'Lhash_array': ['637287483811809788589414952147'], 'label': '2-8400-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8400/2/a/o'}
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id: 24583854
{'Lhash': '637287483811809788589414952147', 'Lhash_array': ['637287483811809788589414952147'], 'label': '2-8400-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8400/2/a/o/1/1'}
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id: 28013
{'Lhash': '1409486051160630396', 'Lhash_array': ['1409486051160630396'], 'label': '2-8400-1.1-c1-0-6', 'type': 'ECQ', 'url': 'EllipticCurve/Q/8400/o'}