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lfunc_lfunctions • Show schema
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{'Lhash': '1287169957876862449674780537314', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.8660254037844386, -0.5], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.8660254037844386, 1.5], 'a8': [0.0, 0.0], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.48658838731717735, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8660254037844386, 0.5]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [3, 5, 13], 'central_character': '975.524', 'coefficient_field': 'CDF', 'conductor': 975, 'conductor_radical': 195, 'conjugate': '1729404950753927579961168659571', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.8660254037844386, -1.5], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, -1.0]], 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'4.85934612011265895961897678509795', '5.67753303725468628286875505595738', '7.08196140541923604655411812722409', '7.63440485442352029590414145920035', '8.400953683789989162753654423496853', '9.665138723163920567651939078481088', '10.18863945354725809606002214696188'], 'prelabel': '2-975-195.134-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6975588773122864, 'root_angle': 0.015001146231100002, 'root_number': '0.99888970532557898781488233304392 + 0.047110047702989823111308027008167*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.007500573115550001', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01539805814403334687306830811', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.30059615882169244256446176012', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05243665191458890328968573765', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.48658838731717735, 'bad_primes': [3, 5, 13], 'central_character': '195.134', 'conductor': 975, 'conductor_radical': 195, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/975/1/z/a/524/1'], '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': '2-975-195.134-c0-0-0', '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': '2-975-195.134-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6975588773122864, 'root_angle': 0.007500573115550001, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01539805814403334687306830811', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1287169957876862449674780537314', 'Lhash_array': ['1287169957876862449674780537314'], 'label': '2-975-195.134-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/975/1/z/a/524/1'}