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lfunc_lfunctions • Show schema
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{'Lhash': '1757592808435665845080126634903', 'a10': [0.0, 0.0], 'a2': [-0.9659258262890683, -0.25881904510252074], 'a3': [0.0, 0.0], 'a4': [0.8660254037844386, 0.5], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8803506822846163, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9659258262890683, 0.25881904510252074]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1764.1403', 'coefficient_field': 'CDF', 'conductor': 1764, 'conductor_radical': 42, 'conjugate': '1069858318811556331056225798988', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9659258262890683, 0.25881904510252074]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.7071067811865476, 1.224744871391589], [-0.5, 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{'__RealLiteral__': 0, 'data': '3.68610370810542115210532468104', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8803506822846163, 'bad_primes': [2, 3, 7], 'central_character': '84.59', 'conductor': 1764, 'conductor_radical': 42, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1764/1/q/a/1403/1'], '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': '2-42e2-84.59-c0-0-4', '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': '2-42e2-84.59-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9382700476326719, 'root_angle': 0.16212983851932128, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38649625387249975259853539489', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1757592808435665845080126634903', 'Lhash_array': ['1757592808435665845080126634903'], 'label': '2-42e2-84.59-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1764/1/q/a/1403/1'}