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lfunc_lfunctions • Show schema
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{'Lhash': '1026469432437340469854730602835', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-3.9837259027956806, -3.9837259027956806], 'a4': [0, 0], 'a5': [2.858291963039793, -2.858291963039793], 'a6': [0, 0], 'a7': [6.9986076409504125, 0.139610486821395], 'a8': [0, 0], 'a9': [0, 22.74014413721052], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.207115843341303, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-6.9986076409504125, -0.139610486821395]]]], 'bad_primes': [2, 7], 'central_character': '448.433', 'coefficient_field': 'CDF', 'conductor': 448, 'conductor_radical': 14, 'conjugate': '1767802650779031295099885689602', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.9837259027956806, 3.9837259027956806], [0, 9.0]], [[1.0, 0], [-2.858291963039793, 2.858291963039793], [0, -25.0]], [[1.0, 0], [-6.9986076409504125, -0.139610486821395]], [[1.0, 0], [-7.343821212861117, 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.05567252178134274', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.809741605654218621305656955250', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.05139313578685750147213282878', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.37321854958785810329634888144', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.207115843341303, 'bad_primes': [2, 7], 'central_character': '112.69', 'conductor': 448, 'conductor_radical': 14, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/448/3/l/b/433/1'], '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': '2-448-112.69-c2-0-7', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-448-112.69-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.49386832083599, 'root_angle': 0.05567252178134274, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.809741605654218621305656955250', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1026469432437340469854730602835', 'Lhash_array': ['1026469432437340469854730602835'], 'factors': ['2-448-112.69-c2-0-7'], 'label': '2-448-112.69-c2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/448/3/l/b/433/1'}