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lfunc_lfunctions • Show schema
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{'Lhash': '1733484094860127083013530764251', 'a10': [-1.4443059768129947, 0.0], 'a2': [0.6434499099025948, 0.0], 'a3': [2.0185230168620603, 0.0], 'a4': [-1.5859722134463425, 0.0], 'a5': [-2.244628454500263, 0.0], 'a6': [1.2988184533362064, 0.0], 'a7': [4.307714393126643, 0.0], 'a8': [-2.3073934976552577, 0.0], 'a9': [1.074435169601913, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 73.86960690988651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-1.0, 0]]], [29, [[1.0, 0], [0, 0]]]], 'bad_primes': [11, 29], 'central_character': '9251.1', 'coefficient_field': 'CDF', 'conductor': 9251, 'conductor_radical': 319, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6434499099025948, 0], [2.0, 0]], [[1.0, 0], [-2.0185230168620603, 0], [3.0, 0]], [[1.0, 0], [2.244628454500263, 0], [5.0, 0]], [[1.0, 0], [-4.307714393126643, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.439898468327944, 0], [13.0, 0]], [[1.0, 0], 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'4.42160358173566464017063236845379', '4.86604626095079192086717660718710', '5.90839341206540513194529696432082', '6.80298424287145182291982213699183', '7.84112103219677247760634356816800'], 'prelabel': '2-9251-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.594742981025465, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36747783225758614857861683440', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44267414391303925164260899307', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.07407446589329387431461529461', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 73.86960690988651, 'bad_primes': [11, 29], 'central_character': '1.1', 'conductor': 9251, 'conductor_radical': 319, 'degree': 2, 'index': 545, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9251/2/a/ba/1/24'], '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': '2-9251-1.1-c1-0-545', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-9251-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.594742981025465, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36747783225758614857861683440', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1733484094860127083013530764251', 'Lhash_array': ['1733484094860127083013530764251'], 'label': '2-9251-1.1-c1-0-545', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9251/2/a/ba/1/24'}