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lfunc_lfunctions • Show schema
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{'Lhash': '2494356253703910726851242380518', 'a10': [0.5, -0.8660254037844386], 'a2': [0.8660254037844386, 0.5], 'a3': [0.5, -0.8660254037844386], 'a4': [0.5, 0.8660254037844386], 'a5': [0.0, -1.0], 'a6': [0.8660254037844386, -0.5], 'a7': [1.7320508075688772, -1.0], 'a8': [0.0, 1.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [5, [[1.0, 0], [0, 1.0]]], [13, [[1.0, 0], [-1.0, 3.4641016151377544]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.121', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '1897280542666040442963295006620', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 1.0]], [[1.0, 0], 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'2-390-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.08537428472590003, 'root_number': '0.9642464765553398 + 0.26500704226607374*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.042687142363', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.96770013224055879699421583161', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.22727748026356694840297128846', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.35518390664800572302136329605', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '13.4', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/bb/b/121/2'], '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': '2-390-13.4-c1-0-6', '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': '2-390-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.042687142362950015, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.96770013224055879699421583161', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2494356253703910726851242380518', 'Lhash_array': ['2494356253703910726851242380518'], 'label': '2-390-13.4-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/bb/b/121/2'}