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lfunc_lfunctions • Show schema
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{'Lhash': '3432615107388120740098553051304', 'a10': [-8.108559598844902, 0.0], 'a2': [1.9354323319700297, 0.0], 'a3': [0.0, 0.0], 'a4': [1.7458983116349476, 0.0], 'a5': [-4.189534020335082, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [-0.49179662326989515, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.533632860074733, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 7, 11], 'central_character': '693.1', 'coefficient_field': 'CDF', 'conductor': 693, 'conductor_radical': 231, 'conjugate': '3432615107388120740098553051304', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.9354323319700297, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.189534020335082, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.1731272668748725, 0], [13.0, 0]], [[1.0, 0], [6.85445791047985, 0], [17.0, 0]], 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'6.95467925429763141050855852171114', '8.266687228494963366525791727657909', '8.936466461282421859104530205200209', '10.31892881686011013076334032188259'], 'prelabel': '2-693-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.352367501066688, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.70785586088951357545083744290', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.63280981579582015582749737956', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.45121417313434353743955773395', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.533632860074733, 'bad_primes': [3, 7, 11], 'central_character': '1.1', 'conductor': 693, 'conductor_radical': 231, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/693/2/a/l/1/3'], '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': '2-693-1.1-c1-0-23', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-693-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.352367501066688, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.70785586088951357545083744290', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3432615107388120740098553051304', 'Lhash_array': ['3432615107388120740098553051304'], 'factors': ['2-693-1.1-c1-0-23'], 'label': '2-693-1.1-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/693/2/a/l/1/3'}