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lfunc_lfunctions • Show schema
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{'Lhash': '124340780715362345758899038102', 'a10': [-1.2031176428701482, 8.457254306354641e-61], 'a2': [-2.1869315694698748, -1.5888987910573742], 'a3': [-0.8674696076074059, 2.66979693033319], 'a4': [1.640036332570489, 5.047512821121472], 'a5': [0.36007103805518675, -0.2616069222501299], 'a6': [6.139133785407375, -4.460341780212994], 'a7': [0.30901699437494745, 0.9510565162951535], 'a8': [2.762672731615827, -8.502632384697018], 'a9': [-3.948261145969135, -2.8685796342177583], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.763329051202452, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-0.30901699437494745, -0.9510565162951535]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 11], 'central_character': '847.323', 'coefficient_field': 'CDF', 'conductor': 847, 'conductor_radical': 77, 'conjugate': '2312185455646416460371239694941', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.1869315694698748, 1.5888987910573742], 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.098087580831008067910494081516', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.28538910638404859907114673898', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.33753180529087762257487355049', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.763329051202452, 'bad_primes': [7, 11], 'central_character': '11.4', 'conductor': 847, 'conductor_radical': 77, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/847/2/f/y/323/1'], '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': '2-847-11.4-c1-0-0', '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': '2-847-11.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6006401233547196, 'root_angle': 0.4645864361830086, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.098087580831008067910494081516', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '124340780715362345758899038102', 'Lhash_array': ['124340780715362345758899038102'], 'label': '2-847-11.4-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/847/2/f/y/323/1'}