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lfunc_lfunctions • Show schema
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{'Lhash': '919204799482975536136466919742', 'a10': [0.0, 0.0], 'a2': [0.36602540378443865, -0.36602540378443865], 'a3': [0.7071067811865476, -0.7071067811865476], 'a4': [0.0, 1.7320508075688772], 'a5': [0.0, 0.0], 'a6': [0.0, -0.5176380902050415], 'a7': [-1.0, 1.0], 'a8': [1.3660254037844386, 1.3660254037844386], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.587658166755635, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.7320508075688772, -2.8284271247461903]]]], 'bad_primes': [3, 5, 11], 'central_character': '825.307', 'coefficient_field': 'CDF', 'conductor': 825, 'conductor_radical': 165, 'conjugate': '2487594846674581023176647515087', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.36602540378443865, 0.36602540378443865], [0, -2.0]], [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.587658166755635, 'bad_primes': [3, 5, 11], 'central_character': '55.32', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/2/j/a/307/4'], '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': '2-825-55.32-c1-0-10', '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': '2-825-55.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.566643365712431, 'root_angle': -0.1994454763423476, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.72512473020363872580633186111', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '919204799482975536136466919742', 'Lhash_array': ['919204799482975536136466919742'], 'label': '2-825-55.32-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/2/j/a/307/4'}