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lfunc_lfunctions • Show schema
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{'Lhash': '1072167145867040748778205274027', 'a10': [-0.8090169943749475, 0.5877852522924731], 'a2': [0.8090169943749475, -0.5877852522924731], 'a3': [0.8090169943749475, 0.5877852522924731], 'a4': [0.30901699437494745, -0.9510565162951535], 'a5': [-1.0, 0.0], 'a6': [1.0, -5.034525116044599e-61], 'a7': [-0.7850380556002166, 2.4160986997768577], 'a8': [-0.30901699437494745, -0.9510565162951535], 'a9': [0.30901699437494745, 0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.426087387979079, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8090169943749475, 0.5877852522924731]]], [3, [[1.0, 0], [-0.8090169943749475, -0.5877852522924731]]], [5, [[1.0, 0], [1.0, 0]]], [31, [[1.0, 0], [0.7537606823514509, -5.5165065787816365]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.481', 'coefficient_field': 'CDF', 'conductor': 930, 'conductor_radical': 930, 'conjugate': 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'data': '-0.130745832008', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.845790745236902371364267463352', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.81292820577386048206759645697', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.61800804309076824478383671222', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.426087387979079, 'bad_primes': [2, 3, 5, 31], 'central_character': '31.16', 'conductor': 930, 'conductor_radical': 930, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/930/2/n/b/481/1'], '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': '2-930-31.16-c1-0-9', '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': '2-930-31.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7250848405103056, 'root_angle': -0.1307458320076726, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.845790745236902371364267463352', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1072167145867040748778205274027', 'Lhash_array': ['1072167145867040748778205274027'], 'label': '2-930-31.16-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/2/n/b/481/1'}