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lfunc_lfunctions • Show schema
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{'Lhash': '2294649267239265779749996026199', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.4992075094487403, -1.4992075094487403], 'a4': [0.0, 0.0], 'a5': [1.7251435512152204, -2.3744563941100654], 'a6': [0.0, 0.0], 'a7': [1.113294738634362, -2.18496394976741], 'a8': [0.0, 0.0], 'a9': [0.0, 1.495246312774989], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.238186372595996, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [41, [[1.0, 0], [1.2931305424898334, 6.271189153588014]]]], 'bad_primes': [2, 41], 'central_character': '656.513', 'coefficient_field': 'CDF', 'conductor': 656, 'conductor_radical': 82, 'conjugate': '1298251528020255912619939620627', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.4992075094487403, 1.4992075094487403], [0, 3.0]], [[1.0, 0], [-1.7251435512152204, 2.3744563941100654], [-1.545084971874737, -4.755282581475768]], [[1.0, 0], [-1.113294738634362, 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.40557133594641513415711001263', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.238186372595996, 'bad_primes': [2, 41], 'central_character': '41.21', 'conductor': 656, 'conductor_radical': 82, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/656/2/bs/d/513/1'], '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': '2-656-41.21-c1-0-14', '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': '2-656-41.21-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2887084507634423, 'root_angle': 0.31570552680197844, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.81015909811909863188836268646', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2294649267239265779749996026199', 'Lhash_array': ['2294649267239265779749996026199'], 'label': '2-656-41.21-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/656/2/bs/d/513/1'}