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lfunc_lfunctions • Show schema
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{'Lhash': '2310265225333794094938892379877', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-13.84388101258358, 0.0], 'a6': [0.0, 0.0], 'a7': [30.7079951006374, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.116618841859967, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '324.1', 'coefficient_field': 'CDF', 'conductor': 324, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [13.84388101258358, 0], [125.0, 0]], [[1.0, 0], [-30.7079951006374, 0], [343.0, 0]], [[1.0, 0], [43.9045802389943, 0], [1331.0, 0]], [[1.0, 0], [12.237051289297378, 0], [2197.0, 0]], [[1.0, 0], [-76.0285655409065, 0], [4913.0, 0]], [[1.0, 0], [44.178938911977426, 0], [6859.0, 0]], [[1.0, 0], [78.62706279875644, 0], [12167.0, 0]], 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'8.091546932654772261947723606892380', '8.267568062817477187672210142479102', '9.965394745523732154336430393901578', '10.92335061200544187155397449271741'], 'prelabel': '2-18e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.372255578286792, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.82247791695744162524810630956', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.47679365842392856476033943570', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.67729159446221980300532215655', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.116618841859967, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 324, 'conductor_radical': 6, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/324/4/a/c/1/1'], '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': '2-18e2-1.1-c3-0-7', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-18e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.372255578286792, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.82247791695744162524810630956', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2310265225333794094938892379877', 'Lhash_array': ['2310265225333794094938892379877'], 'label': '2-18e2-1.1-c3-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/324/4/a/c/1/1'}