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lfunc_lfunctions • Show schema
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{'Lhash': '3171108626245730791716890835085', 'a10': [-0.8412535328311812, -0.5406408174555976], 'a2': [0.14231483827328514, 0.9898214418809327], 'a3': [1.4054919914710264, -3.0775981720496457], 'a4': [-0.9594929736144974, 0.28173255684142967], 'a5': [-0.6548607339452851, 0.7557495743542583], 'a6': [3.2462950256489, 0.9531982234245516], 'a7': [2.976173571286555, -1.9126706155455793], 'a8': [-0.41541501300188644, -0.9096319953545183], 'a9': [-5.531620568678273, -6.383830444500519], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.14231483827328514, -0.9898214418809327]]], [5, [[1.0, 0], [0.6548607339452851, -0.7557495743542583]]], [23, [[1.0, 0], [-4.724369850137824, -0.8248209012317198]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.141', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': 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0.2485431878009339, 'root_number': '0.7103355873053785 + 0.7038631638376333*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1242715939', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.50156362145436638738342834881', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.64328212554166266657907772934', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.82560711386507855592890595746', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'bad_primes': [2, 5, 23], 'central_character': '23.3', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/g/b/141/2'], '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': '2-230-23.3-c1-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-230-23.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': 0.12427159390046695, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.50156362145436638738342834881', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3171108626245730791716890835085', 'Lhash_array': ['3171108626245730791716890835085'], 'label': '2-230-23.3-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/g/b/141/2'}