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lfunc_lfunctions • Show schema
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{'Lhash': '1355326222759002754889479403858,2503816557888245172068646328369', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -1, 'a5': 2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.33283571094870656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 1]], [17, [1]]], 'bad_primes': [2, 17], 'central_character': '1156.1', 'coefficient_field': '1.1.1.1', 'conductor': 1336336, 'conductor_radical': 34, 'degree': 4, 'euler_factors': [[1, 0, 1], [1, 0, 0, 0, 1], [1, -2, 2, -2, 1], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [1, 0, 2, 0, 1], [1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1], [1, 2, 2, 2, 1], [1, 0, 0, 0, 1], [1, -2, 2, -2, 1], [1, 2, 2, 2, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, -2, 2, -2, 1], [1, 0, -2, 0, 1], [1, 0, 0, 0, 1], [1, 2, 2, 2, 1], [1, 0, 0, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, -2, 2, -2, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 0, 0, 1], [1, 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'8.439657804706711083837858769857582', '8.595052282691261720801964921958056', '9.062988826822614822111352980273222', '9.607415386083401094956271544170026', '9.652845597817256245731247013465545', '10.00970584902981600579973287175434'], 'prelabel': '4-34e4-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7595519433216867, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e2-0', 'trace_hash': 676303676745476242, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06916387095544160553343369755', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.97516299636307899317861391759', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.13342109937984989800887388856', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.33283571094870656, 'bad_primes': [2, 17], 'central_character': '1.1', 'conductor': 1336336, 'conductor_radical': 34, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2], 'euler11': [1, 0, 0, 0, 1], 'euler13': [1, 0, 2, 0, 1], 'euler17': [1, 0, 0, 0, 0], 'euler19': [1, 0, 2, 0, 1], 'euler2': [1, 0, 1, 0, 0], 'euler23': [1, 0, 0, 0, 1], 'euler29': [1, 2, 2, 2, 1], 'euler3': [1, 0, 0, 0, 1], 'euler31': [1, 0, 0, 0, 1], 'euler37': [1, -2, 2, -2, 1], 'euler41': [1, 2, 2, 2, 1], 'euler43': [1, 0, 2, 0, 1], 'euler47': [1, 0, -2, 0, 1], 'euler5': [1, -2, 2, -2, 1], 'euler53': [1, 0, -2, 0, 1], 'euler59': [1, 0, 2, 0, 1], 'euler61': [1, -2, 2, -2, 1], 'euler67': [1, 0, -2, 0, 1], 'euler7': [1, 0, 0, 0, 1], 'euler71': [1, 0, 0, 0, 1], 'euler73': [1, 2, 2, 2, 1], 'euler79': [1, 0, 0, 0, 1], 'euler83': [1, 0, 2, 0, 1], 'euler89': [1, 0, 2, 0, 1], 'euler97': [1, -2, 2, -2, 1], 'euler_factors': [[1, 0, 1, 0, 0], [1, 0, 0, 0, 1], [1, -2, 2, -2, 1], [1, 0, 0, 0, 1], [1, 0, 0, 0, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 0], [1, 0, 2, 0, 1], [1, 0, 0, 0, 1], [1, 2, 2, 2, 1], [1, 0, 0, 0, 1], [1, -2, 2, -2, 1], [1, 2, 2, 2, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, -2, 2, -2, 1], [1, 0, -2, 0, 1], [1, 0, 0, 0, 1], [1, 2, 2, 2, 1], [1, 0, 0, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, -2, 2, -2, 1]], 'index': 1, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1156/1/f/b', 'ArtinRepresentation/2.1156.8t17.a'], 'is_instance_Artin': True, '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': '4-34e4-1.1-c0e2-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-34e4-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7595519433216867, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 676303676745476242, 'z1': {'__RealLiteral__': 0, 'data': '1.06916387095544160553343369755', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24604208
{'Lhash': '1355326222759002754889479403858,2503816557888245172068646328369', 'Lhash_array': ['1355326222759002754889479403858', '2503816557888245172068646328369'], 'label': '4-34e4-1.1-c0e2-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.1156.8t17.a'}
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id: 19832824
{'Lhash': '1355326222759002754889479403858,2503816557888245172068646328369', 'Lhash_array': ['1355326222759002754889479403858', '2503816557888245172068646328369'], 'label': '4-34e4-1.1-c0e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1156/1/f/b'}