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lfunc_lfunctions • Show schema
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{'Lhash': '1089152275310379360635146582831', 'a10': [-0.5, 0.8660254037844386], 'a2': [-1.0, 0.0], 'a3': [-1.0201039867609476, -1.3997813601396543], 'a4': [1.0, 0.0], 'a5': [0.5, -0.8660254037844386], 'a6': [1.0201039867609476, 1.3997813601396543], 'a7': [-2.523360296491915, -0.7953947536212663], 'a8': [-1.0, 0.0], 'a9': [-0.9187757123888407, 2.8558450921442464], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.030575327340666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [1.0201039867609476, 1.3997813601396543]]], [5, [[1.0, 0], [-0.5, 0.8660254037844386]]], [7, [[1.0, 0], [2.523360296491915, 0.7953947536212663]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '630.151', 'coefficient_field': 'CDF', 'conductor': 630, 'conductor_radical': 210, 'conjugate': '1325001694753708215677419151240', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0201039867609476, 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'8.432425692866661983710112189111543', '8.900348728438647732795867531881663', '9.945267235189693428217614050223798', '10.53770899882903709329317453315292'], 'prelabel': '2-630-63.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2428944084242275, 'root_angle': 0.1053363001431849, 'root_number': '0.9457426062646118 + 0.32491679349614944*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0526681500716', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.859189649824870529058602089556', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.18495903759112065820338445337', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62195477544153621109262493417', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.030575327340666, 'bad_primes': [2, 3, 5, 7], 'central_character': '63.25', 'conductor': 630, 'conductor_radical': 210, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/630/2/i/i/151/2'], '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': '2-630-63.25-c1-0-3', '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': '2-630-63.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2428944084242275, 'root_angle': 0.05266815007159245, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.859189649824870529058602089556', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1089152275310379360635146582831', 'Lhash_array': ['1089152275310379360635146582831'], 'label': '2-630-63.25-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/630/2/i/i/151/2'}