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lfunc_lfunctions • Show schema
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{'Lhash': '714949493359627878968446152938', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [1.9364916731037085, 1.118033988749895], 'a6': [0, 0], 'a7': [1.8729833462074168, 3.2441023173616146], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 58.85573710182414, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.9364916731037085, -1.118033988749895]]]], 'bad_primes': [2, 3, 5], 'central_character': '2160.881', 'coefficient_field': 'CDF', 'conductor': 2160, 'conductor_radical': 30, 'conjugate': '1331411085587132988566027627931', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.9364916731037085, -1.118033988749895]], [[1.0, 0], [-1.8729833462074168, -3.2441023173616146], [-24.5, 42.4352447854375]], [[1.0, 0], [10.11895003862225, -5.84217852871493], [60.5, -104.78907385791707]], [[1.0, 0], 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'primitive': True, 'rational': False, 'root_analytic_conductor': 7.671749285646928, 'root_angle': -0.38888888888888895, 'root_number': '0.3420201433256687330440996146822595807630833675141606285 - 0.9396926207859083840541092773247314699362081342644646331*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.19444444444444445', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56399570451897981737189089946', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.70210117489154571244647799554', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.83693312245337143217560867850', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 58.85573710182414, 'bad_primes': [2, 3, 5], 'central_character': '9.5', 'conductor': 2160, 'conductor_radical': 30, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2160/3/bs/a/881/2'], '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': '2-2160-9.5-c2-0-16', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-2160-9.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.671749285646928, 'root_angle': -0.19444444444444448, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.56399570451897981737189089946', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '714949493359627878968446152938', 'Lhash_array': ['714949493359627878968446152938'], 'label': '2-2160-9.5-c2-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2160/3/bs/a/881/2'}