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lfunc_lfunctions • Show schema
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{'Lhash': '474836075437209292900863632010', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-97085.15376163679, 0.0], 'a4': [0.0, 0.0], 'a5': [-33929229.025267154, 0.0], 'a6': [0.0, 0.0], 'a7': [-528731396.8356976, 0.0], 'a8': [0.0, 0.0], 'a9': [-1034826122.0793425, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.35818754296497, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '10.5', 'prec': 14}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '8.1', 'coefficient_field': 'CDF', 'conductor': 8, 'conductor_radical': 2, 'conjugate': '474836075437209292900863632010', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [97085.15376163679, 0], [10460353203.0, 0]], [[1.0, 0], [33929229.025267154, 0], [476837158203125.0, 0]], [[1.0, 0], [528731396.8356976, 0], [558545864083284030, 0]], [[1.0, 0], [121954562951.19382, 0], [7400249944258161000000, 0]], [[1.0, 0], [-433604793494.14075, 0], [247064529073450400000000, 0]], [[1.0, 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'10.73771173456312031815644336040091', '11.70900180027629820025749725474296', '13.13738792238965131739212931221178', '15.58216471637896654917208473543433', '16.13289687806881419688853998822829'], 'prelabel': '2-2e3-1.1-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.728444516219364, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c21-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37457961630098957177918272610', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.23777854840208600449310145602', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.96797949516263459019492487193', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.35818754296497, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 8, 'conductor_radical': 2, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8/22/a/b/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': '2-2e3-1.1-c21-0-0', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'prelabel': '2-2e3-1.1-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.728444516219364, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c21-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37457961630098957177918272610', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '474836075437209292900863632010', 'Lhash_array': ['474836075437209292900863632010'], 'label': '2-2e3-1.1-c21-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8/22/a/b/1/1'}