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lfunc_lfunctions • Show schema
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{'Lhash': '1883989422024267887111722195507', 'a10': [1.1251813596539546, 0.0], 'a2': [1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [1.1251813596539546, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.6866633676879146, 0.0], 'a8': [1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.24763346632223, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [149, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 149], 'central_character': '8046.1', 'coefficient_field': 'CDF', 'conductor': 8046, 'conductor_radical': 894, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.1251813596539546, 0], [5.0, 0]], [[1.0, 0], [0.6866633676879146, 0], [7.0, 0]], [[1.0, 0], [3.0544800818819176, 0], [11.0, 0]], [[1.0, 0], [3.9903996561658497, 0], [13.0, 0]], [[1.0, 0], [5.800427096069154, 0], [17.0, 0]], [[1.0, 0], [-8.321676071757986, 0], [19.0, 0]], 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['1.48620560088487480092757346852833', '2.57219669026795524313442132060442', '2.87034583836617110304461496903207', '3.99457697646388290797457627628310', '4.80733420809220822730469496129208', '5.31305624640855346992313067326585', '5.96903184182939777579952468926648', '6.74489815685244030740476955917543', '7.43970864711213395084349431130004'], 'prelabel': '2-8046-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.015462149266392, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48620560088487480092757346853', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.57219669026795524313442132060', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.87034583836617110304461496903', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.24763346632223, 'bad_primes': [2, 3, 149], 'central_character': '1.1', 'conductor': 8046, 'conductor_radical': 894, 'degree': 2, 'index': 172, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8046/2/a/m/1/8'], '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': '2-8046-1.1-c1-0-172', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-8046-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.015462149266392, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48620560088487480092757346853', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1883989422024267887111722195507', 'Lhash_array': ['1883989422024267887111722195507'], 'label': '2-8046-1.1-c1-0-172', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8046/2/a/m/1/8'}