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lfunc_lfunctions • Show schema
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{'Lhash': '2352917448197901127909097182741', 'a10': [0.8786796564403574, 0.5073059361772883], 'a2': [0.7071067811865476, 1.224744871391589], 'a3': [1.5, 0.8660254037844386], 'a4': [-1.0, 1.7320508075688772], 'a5': [0.6213203435596426, -0.3587194676071504], 'a6': [-6.93381710251136e-61, 2.449489742783178], 'a7': [-2.6213203435596424, -0.3587194676071504], 'a8': [-2.8284271247461903, 0.0], 'a9': [1.5, 2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, -1.224744871391589]]], [3, [[1.0, 0], [-1.5, -0.8660254037844386]]], [7, [[1.0, 0], [2.6213203435596424, 0.3587194676071504]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': '3965766517940311784630184674413', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7071067811865476, 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'0.009251554731678302 - 0.9999572034517511*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.248527548328', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.85612458809570943607386661198', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.15682033607213618155360099238', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.39130656411964321773884536855', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/ba/b/101/2'], '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': '2-168-168.101-c1-0-12', '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': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.24852754832782525, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.85612458809570943607386661198', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2352917448197901127909097182741', 'Lhash_array': ['2352917448197901127909097182741'], 'label': '2-168-168.101-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/ba/b/101/2'}