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lfunc_lfunctions • Show schema
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{'Lhash': '997952976235728428791288117187', 'a10': [-2.186140661634507, 1.2621688994810694], 'a2': [0.5, 0.8660254037844386], 'a3': [-0.5, 1.6583123951777], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.0, 2.5243377989621387], 'a6': [-1.6861406616345072, 0.39614349569663065], 'a7': [0.5, 2.598076211353316], 'a8': [-1.0, 0.0], 'a9': [-2.5, -1.6583123951777], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0.5, -1.6583123951777]]], [7, [[1.0, 0], [-0.5, -2.598076211353316]]], [13, [[1.0, 0], [-3.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.335', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '3448550837855057595590733132601', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0.5, -1.6583123951777]], 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'10.60244576020437907831848559119662'], 'prelabel': '2-546-273.62-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.9473216054509304, 'root_number': '-0.9863370848947569 + 0.16473965813158992*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.473660802725', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78724608820131961066438979290', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.76812145425410242318035840060', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.48519190233748406800961158027', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.62', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/q/g/335/2'], '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': '2-546-273.62-c1-0-9', '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': '2-546-273.62-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.4736608027254652, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78724608820131961066438979290', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '997952976235728428791288117187', 'Lhash_array': ['997952976235728428791288117187'], 'label': '2-546-273.62-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/q/g/335/2'}