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lfunc_lfunctions • Show schema
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{'Lhash': '1372476474566361958996131771030', 'a10': [-3.059043340159675, 0.0], 'a2': [-2.430452561191019, 0.0], 'a3': [1.4342061952774268, 0.0], 'a4': [3.9070996521999843, 0.0], 'a5': [1.2586311656544416, 0.0], 'a6': [-3.485770120588049, 0.0], 'a7': [1.0, 0.0], 'a8': [-4.635115234135953, 0.0], 'a9': [-0.9430525894278474, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.763329051202452, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 11], 'central_character': '847.1', 'coefficient_field': 'CDF', 'conductor': 847, 'conductor_radical': 77, 'conjugate': '1372476474566361958996131771030', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.430452561191019, 0], [2.0, 0]], [[1.0, 0], [-1.4342061952774268, 0], [3.0, 0]], [[1.0, 0], [-1.2586311656544416, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.1783093540402523, 0], [13.0, 0]], [[1.0, 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'3.14544369580271069295246989922872', '5.00463565674862708188020105237045', '6.12698725256112835203212804348500', '7.33365505439333673522099543687996', '7.79902651178570854862055107897191', '8.652506607179913389457976232902698', '9.262121081836067426609730739851068', '9.985125871788603687791865697391415'], 'prelabel': '2-847-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6006401233547196, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08269303412096328106029741899', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33360035185413230789288829731', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.14544369580271069295246989923', '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': '1.1', 'conductor': 847, 'conductor_radical': 77, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/847/2/a/p/1/1'], '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': '2-847-1.1-c1-0-15', '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': '2-847-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6006401233547196, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08269303412096328106029741899', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1372476474566361958996131771030', 'Lhash_array': ['1372476474566361958996131771030'], 'label': '2-847-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/847/2/a/p/1/1'}