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lfunc_lfunctions • Show schema
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{'Lhash': '568244784396562060109003125944', 'a10': [4.453698458524305, 5.584761222899001], 'a2': [-1.1670114364150386, 5.113011180421297], 'a3': [-1.2406512827920528, 1.5557275014915894], 'a4': [-17.573216695170334, -8.462815131198752], 'a5': [0.8492128779774614, -1.064879267216134], 'a6': [-6.506597873194072, -8.15901566610587], 'a7': [-18.237539304356652, 3.22368734868105], 'a8': [37.61946618706437, -47.173318522621905], 'a9': [5.126992763416792, 22.462822988108407], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8910935902812915, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [18.237539304356652, -3.22368734868105]]]], 'bad_primes': [7], 'central_character': '49.15', 'coefficient_field': 'CDF', 'conductor': 49, 'conductor_radical': 7, 'conjugate': '5748411869809184533498360124648', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.1670114364150386, -5.113011180421297], [-7.207750943219353, -3.471069912940465]], 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'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44826609500619063134153523109', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.63951369049817178523612602638', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.25578675151271142181000478655', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8910935902812915, 'bad_primes': [7], 'central_character': '49.15', 'conductor': 49, 'conductor_radical': 7, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/49/4/e/a/15/1'], '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': '2-7e2-49.15-c3-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-7e2-49.15-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.700321613778197, 'root_angle': 0.33206554145966405, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44826609500619063134153523109', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '568244784396562060109003125944', 'Lhash_array': ['568244784396562060109003125944'], 'label': '2-7e2-49.15-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/49/4/e/a/15/1'}