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lfunc_lfunctions • Show schema
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{'Lhash': '1942267904240389952299807241184', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -0.12354390965672797], 'a4': [0, 0], 'a5': [0, -0.45426949272314654], 'a6': [0, 0], 'a7': [0, -3.5607554659734992], 'a8': [0, 0], 'a9': [2.98473690238673, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.035981290937706, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-2.556630482435826, 3.234755102983834]]], [59, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 17, 59], 'central_character': '4012.237', 'coefficient_field': 'CDF', 'conductor': 4012, 'conductor_radical': 2006, 'conjugate': '689934951162734460583714821670', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0.12354390965672797], [-3.0, 0]], [[1.0, 0], [0, 0.45426949272314654], [-5.0, 0]], [[1.0, 0], [0, 3.5607554659734992], [-7.0, 0]], [[1.0, 0], [0, 2.559137986138853], [-11.0, 0]], [[1.0, 0], [-1.0590698953243123, 0], [13.0, 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'3.34000181359291149742845063304', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.035981290937706, 'bad_primes': [2, 17, 59], 'central_character': '17.16', 'conductor': 4012, 'conductor_radical': 2006, 'degree': 2, 'index': 75, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4012/2/b/b/237/23'], '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': '2-4012-17.16-c1-0-75', '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': '2-4012-17.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.660033682844803, 'root_angle': 0.3564487125149043, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.53217921712079149143355568648', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1942267904240389952299807241184', 'Lhash_array': ['1942267904240389952299807241184'], 'label': '2-4012-17.16-c1-0-75', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4012/2/b/b/237/23'}