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lfunc_lfunctions • Show schema
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{'Lhash': '1010070905771783761194451477193', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.659470158300444, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, 1]], [7, [1, -1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '6720.1', 'coefficient_field': '1.1.1.1', 'conductor': 6720, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 1], [1, -1], [1, 4, 11], [1, -2, 13], [1, -2, 17], [1, -4, 19], [1, -8, 23], [1, -2, 29], [1, 0, 31], [1, 6, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, -10, 53], [1, -12, 59], [1, 14, 61], [1, 12, 67], [1, -8, 71], [1, -10, 73], [1, 16, 79], [1, 12, 83], [1, -10, 89], [1, -2, 97], [1, 6, 101], [1, -8, 103], [1, -12, 107], [1, 14, 109], [1, -18, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, 1], 1]], [[[1, -1], 1]], [[[1, 4, 11], 1]], [[[1, -2, 13], 1]], [[[1, -2, 17], 1]], [[[1, -4, 19], 1]], [[[1, -8, 23], 1]], [[[1, -2, 29], 1]], [[[1, 0, 31], 1]], [[[1, 6, 37], 1]], [[[1, 6, 41], 1]], [[[1, 4, 43], 1]], [[[1, 0, 47], 1]], [[[1, -10, 53], 1]], [[[1, -12, 59], 1]], [[[1, 14, 61], 1]], [[[1, 12, 67], 1]], [[[1, -8, 71], 1]], [[[1, -10, 73], 1]], [[[1, 16, 79], 1]], [[[1, 12, 83], 1]], [[[1, -10, 89], 1]], [[[1, -2, 97], 1]], [[[1, 6, 101], 1]], [[[1, -8, 103], 1]], [[[1, -12, 107], 1]], [[[1, 14, 109], 1]], [[[1, -18, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-6720-1.1-c1-0-28', 'leading_term': '2.43755475593333286777554473059000000000000000000000000000000000000000000000000000000000000', '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/6720/2/a/bq', 'plot_delta': {'__RealLiteral__': 0, 'data': 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2.380776209559776, 2.000573809966322, 1.5083716043529203, 0.9333313883777358, 0.3094284783856002, -0.32673259558932666, -0.9382688671106527, -1.490382484207045, -1.9525817289314427, -2.30061290929898, -2.5179750726405956, -2.5969167248353733, -2.538847919974565, -2.3541399753037147, -2.0613260878783217], 'positive_zeros': ['0.796805449064536655798640765275632', '1.83674354485910906002811308802435', '3.00705106888789716184359223974169', '3.30832192254682250069710858165009', '4.41113790939785504303303719118994', '5.13429871643228048050619453892522', '5.66837498117775023160756110430783', '6.91165704585120918415943435579464', '7.29466767342624434535662347401888', '8.067792919413443572268908629008902'], 'prelabel': '2-6720-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.325262463441187, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1435825109912323295, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.796805449064536655798640765276', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.83674354485910906002811308802', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.00705106888789716184359223974', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 53.659470158300444, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 6720, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -4, 0, 2, 0, -1, 0, 2, 0, 4, 0, 1, 0, 8, 0, 1, 0, 1, 0, 2, 0, 0, 0, -4, 0, -1, 0, -6, 0, 2, 0, -6, 0, -4, 0, -1, 0, 0, 0, 1, 0, 2, 0, 10, 0, 4, 0, 4, 0, 12, 0, -14, 0, 1, 0, -2, 0, -12, 0, 8, 0, 8, 0, 10, 0, 1, 0, -4, 0, -16, 0, 1, 0, -12, 0, -2, 0, 2, 0, 10, 0, 2, 0, 0, 0, -4, 0, 2, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, -2, 13], 'euler17': [1, -2, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, -2, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 6, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, -10, 53], 'euler59': [1, -12, 59], 'euler61': [1, 14, 61], 'euler67': [1, 12, 67], 'euler7': [1, -1, 0], 'euler71': [1, -8, 71], 'euler73': [1, -10, 73], 'euler79': [1, 16, 79], 'euler83': [1, 12, 83], 'euler89': [1, -10, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 1, 0], [1, -1, 0], [1, 4, 11], [1, -2, 13], [1, -2, 17], [1, -4, 19], [1, -8, 23], [1, -2, 29], [1, 0, 31], [1, 6, 37], [1, 6, 41], [1, 4, 43], [1, 0, 47], [1, -10, 53], [1, -12, 59], [1, 14, 61], [1, 12, 67], [1, -8, 71], [1, -10, 73], [1, 16, 79], [1, 12, 83], [1, -10, 89], [1, -2, 97]], 'index': 28, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6720/bq', 'ModularForm/GL2/Q/holomorphic/6720/2/a/bq/1/1', 'ModularForm/GL2/Q/holomorphic/6720/2/a/bq'], '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': '2-6720-1.1-c1-0-28', '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': '2-6720-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.325262463441187, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1435825109912323295, 'z1': {'__RealLiteral__': 0, 'data': '0.796805449064536655798640765276', 'prec': 107}}
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lfunc_instances • Show schema
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id: 21704545
{'Lhash': '1010070905771783761194451477193', 'Lhash_array': ['1010070905771783761194451477193'], 'label': '2-6720-1.1-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6720/2/a/bq'}
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id: 24576362
{'Lhash': '1010070905771783761194451477193', 'Lhash_array': ['1010070905771783761194451477193'], 'label': '2-6720-1.1-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6720/2/a/bq/1/1'}
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id: 29887
{'Lhash': '1435825109912323295', 'Lhash_array': ['1435825109912323295'], 'label': '2-6720-1.1-c1-0-28', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6720/bq'}