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lfunc_lfunctions • Show schema
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{'Lhash': '2478274776125905751943935276081', 'a10': [-1.0803646044680124, 1.002431859259193], 'a2': [-0.9829543388146594, 0.47336586101987593], 'a3': [0.10907001170481151, 1.4554381589907772], 'a4': [-0.5048556099019914, 0.6330689110636114], 'a5': [1.2908502480903412, -0.39817456891859354], 'a6': [-0.7961655785316626, -1.3789992332543084], 'a7': [-0.10816262176240109, 0.1873431563723338], 'a8': [0.6821161482031607, -2.9885461129862563], 'a9': [0.8600885114822104, -0.12963748445501655], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3433567286915058, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [-5.900916615161149, -2.859927114615876]]]], 'bad_primes': [43], 'central_character': '43.14', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'conjugate': '4822064707833313698842944010663', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9829543388146594, -0.47336586101987593], [1.246979603717467, 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'root_number': '0.4117465042819889 - 0.9112984232465028*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.182459458937', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.95501408328108238800113214660', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.22612001412813298720435669375', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.04183416608363028040395053365', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.3433567286915058, 'bad_primes': [43], 'central_character': '43.14', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/2/g/a/14/2'], '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': '2-43-43.14-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': '2-43-43.14-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5859664910995387, 'root_angle': -0.18245945893747123, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.95501408328108238800113214660', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2478274776125905751943935276081', 'Lhash_array': ['2478274776125905751943935276081'], 'label': '2-43-43.14-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/2/g/a/14/2'}