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lfunc_lfunctions • Show schema
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{'Lhash': '1406338092382977609532183543508', 'a10': [0.0, 0.0], 'a2': [-0.9009688679024191, 0.4338837391175581], 'a3': [0.09903113209758087, -0.4338837391175581], 'a4': [0.6234898018587335, -0.7818314824680298], 'a5': [0.0, 0.0], 'a6': [0.09903113209758087, 0.4338837391175581], 'a7': [-0.2225209339563144, 0.9749279121818236], 'a8': [-0.2225209339563144, 0.9749279121818236], 'a9': [0.7225209339563144, 0.3479477433504717], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9009688679024191, -0.4338837391175581]]], [7, [[1.0, 0], [0.2225209339563144, -0.9749279121818236]]], [17, [[1.0, 0], [-0.6234898018587335, -0.7818314824680298]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.1835', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '1617678133837954107305118719330', 'degree': 2, 'euler_factors': [[[1.0, 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'3.99028868104225092765684075007177', '4.38062174021191912654306776561190', '6.16430894839717575852009848329768', '6.70952275722340195837608770161472', '7.26179947740138308019505865352292', '8.152707662710964097548883423395137', '9.064367908270269060946305347558863'], 'prelabel': '2-3332-3332.1835-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.06122448979591837, 'root_number': '0.92691675734602176302483849969967 - 0.37526700487937413388755922567427*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.061224489795918366', 'prec': 70}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10940514060402664446714313459', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.82250609616824249987916364299', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41001227877780259508319474166', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '3332.1835', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/be/b/1835/1'], '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': '2-3332-3332.1835-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3332-3332.1835-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.06122448979591837, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10940514060402664446714313459', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1406338092382977609532183543508', 'Lhash_array': ['1406338092382977609532183543508'], 'factors': ['2-3332-3332.1835-c0-0-2'], 'label': '2-3332-3332.1835-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/be/b/1835/1'}