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lfunc_lfunctions • Show schema
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{'Lhash': '1538356968143383776910992232165', 'a10': [1.0, 0.0], 'a2': [0.25881904510252074, -0.9659258262890683], 'a3': [0.0, 0.0], 'a4': [-0.8660254037844386, -0.5], 'a5': [0.25881904510252074, 0.9659258262890683], 'a6': [0.0, 0.0], 'a7': [0.5, -0.8660254037844386], 'a8': [-0.7071067811865476, 0.7071067811865476], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.2576438318351661, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.25881904510252074, 0.9659258262890683]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.25881904510252074, -0.9659258262890683]]], [7, [[1.0, 0], [-0.5, 0.8660254037844386]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '2520.613', 'coefficient_field': 'CDF', 'conductor': 2520, 'conductor_radical': 210, 'conjugate': '1449975705819802370296515653904', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.25881904510252074, 0.9659258262890683]], [[1.0, 0], [0, 0]], [[1.0, 0], 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[[1.0, 0], [-1.5, 0.8660254037844386], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.7071067811865476, 0.7071067811865476], [0, -1.0]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0.36602540378443865, -0.36602540378443865], [0, -1.0]], [[1.0, 0], [1.224744871391589, 0.7071067811865476], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.36602540378443865, 1.3660254037844386], [-0.8660254037844386, -0.5]], [[1.0, 0], [-0.25881904510252074, 0.9659258262890683], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0, 1.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-2520-280.53-c0-0-1', 'leading_term': '1.4186478503833354912974027942558', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2520/1/ik/b/613/2', 'plot_delta': 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.1815239054476981', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21354967044264094691340569144', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.68321378210836323913352064999', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86916830248358277741343485253', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.2576438318351661, 'bad_primes': [2, 3, 5, 7], 'central_character': '280.53', 'conductor': 2520, 'conductor_radical': 210, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2520/1/ik/b/613/2'], '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': '2-2520-280.53-c0-0-1', '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': '2-2520-280.53-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1214472042121137, 'root_angle': 0.1815239054476981, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21354967044264094691340569144', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1538356968143383776910992232165', 'Lhash_array': ['1538356968143383776910992232165'], 'label': '2-2520-280.53-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2520/1/ik/b/613/2'}