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lfunc_lfunctions • Show schema
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{'Lhash': '857410337533409253553743672334', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.5, -0.8660254037844386], 'a6': [0, 0], 'a7': [2.6224084846585756, 4.542144733628362], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.623843418298286, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.5, 0.8660254037844386]]]], 'bad_primes': [2, 3, 5], 'central_character': '1080.361', 'coefficient_field': 'CDF', 'conductor': 1080, 'conductor_radical': 30, 'conjugate': '2404941489694085585868222677879', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [-2.6224084846585756, -4.542144733628362], [-3.5, 6.06217782649107]], [[1.0, 0], [-1.336411850500474, -2.314733224903964], [-5.5, 9.526279441628825]], [[1.0, 0], [1.908405118816677, -3.305454627215005], [-6.5, 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'root_analytic_conductor': 2.936638114970635, 'root_angle': -0.25137716900390555, 'root_number': '-0.0086529000695683485411706662140398592048999595577445960 - 0.9999625629594270286033349668301195528407954378765506046*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25137716900390555', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67637749501245849817071905456', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.09930460299801887100033127262', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.50616422195252876109324100465', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.623843418298286, 'bad_primes': [2, 3, 5], 'central_character': '9.4', 'conductor': 1080, 'conductor_radical': 30, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1080/2/q/d/361/3'], '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': '2-1080-9.4-c1-0-2', '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': '2-1080-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.936638114970635, 'root_angle': -0.25137716900390555, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.67637749501245849817071905456', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '857410337533409253553743672334', 'Lhash_array': ['857410337533409253553743672334'], 'factors': ['2-1080-9.4-c1-0-2'], 'label': '2-1080-9.4-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1080/2/q/d/361/3'}