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lfunc_lfunctions • Show schema
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{'Lhash': '2102402975589493802053778259736', 'a10': [-49.703902608486345, 0.0], 'a2': [3.1069496056559287, 0.0], 'a3': [8.397550689767135, 0.0], 'a4': [1.6531358520855322, 0.0], 'a5': [-15.99765329891568, 0.0], 'a6': [26.090766804047675, 0.0], 'a7': [0.0, 0.0], 'a8': [-19.71938706151461, 0.0], 'a9': [43.51885758720849, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 118.53483720153295, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [41, [[1.0, 0], [41.0, 0]]]], 'bad_primes': [7, 41], 'central_character': '2009.1', 'coefficient_field': 'CDF', 'conductor': 2009, 'conductor_radical': 287, 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.1069496056559287, 0], [8.0, 0]], [[1.0, 0], [-8.397550689767135, 0], [27.0, 0]], [[1.0, 0], [15.99765329891568, 0], [125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-25.154627838260627, 0], [1331.0, 0]], [[1.0, 0], [-75.93593846258254, 0], [2197.0, 0]], [[1.0, 0], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 118.53483720153295, 'bad_primes': [7, 41], 'central_character': '1.1', 'conductor': 2009, 'conductor_radical': 287, 'degree': 2, 'index': 371, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2009/4/a/h/1/24'], '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': '2-2009-1.1-c3-0-371', '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': '2-2009-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.887370536614107, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.65850351446287686651805870166', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2102402975589493802053778259736', 'Lhash_array': ['2102402975589493802053778259736'], 'label': '2-2009-1.1-c3-0-371', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2009/4/a/h/1/24'}