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lfunc_lfunctions • Show schema
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{'Lhash': '3767964925130167959628061320110', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.5, -0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [-1.6374586088176875, -2.8361615057632856], 'a6': [0.0, 0.0], 'a7': [-1.5, -2.179449471770337], 'a8': [0.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [7, [[1.0, 0], [1.5, 2.179449471770337]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.25', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': '1385431792112561565660273007112', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [1.6374586088176875, 2.8361615057632856], [-2.5, 4.330127018922194]], [[1.0, 0], [1.5, 2.179449471770337]], [[1.0, 0], [1.6374586088176875, 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0.4949641542418304, 'root_number': '0.01581991608975559 + 0.9998748572971085*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.247482077121', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.97240022167920627026528298975', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.66089444704539507203586502099', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.63810465534148831552591221915', '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': '7.4', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/q/c/25/1'], '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': '2-168-7.4-c1-0-3', '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': '2-168-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.2474820771209152, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.97240022167920627026528298975', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3767964925130167959628061320110', 'Lhash_array': ['3767964925130167959628061320110'], 'label': '2-168-7.4-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/q/c/25/1'}