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lfunc_lfunctions • Show schema
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{'Lhash': '2427535399588328164487505882210', 'a10': [-1.0, 0.0], 'a2': [0.8660254037844386, 0.5], 'a3': [0.0, 1.0], 'a4': [4.582907174078835e-80, 2.6459426906630975e-80], 'a5': [-0.8660254037844386, 0.5], 'a6': [-0.5, 0.8660254037844386], 'a7': [1.0, 0.0], 'a8': [1.3229713452751261e-80, -1.0], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.13624474844880965, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, -1.0]]], [7, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.263', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '3929527212551645910392336165091', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0.8660254037844386, -0.5], [0.5, -0.8660254037844386]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 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'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91498777277529916463850108324', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.43217743974993885628629774674', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.69790133843077734416287782185', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.13624474844880965, 'bad_primes': [3, 7, 13], 'central_character': '273.263', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/1/bm/b/263/2', 'ArtinRepresentation/2.273.16t60.a.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': '2-273-273.263-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-273-273.263-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3691134628387451, 'root_angle': -0.1992673325026436, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91498777277529916463850108324', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24603003
{'Lhash': '2427535399588328164487505882210', 'Lhash_array': ['2427535399588328164487505882210'], 'label': '2-273-273.263-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.273.16t60.a.a'}
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id: 19801704
{'Lhash': '2427535399588328164487505882210', 'Lhash_array': ['2427535399588328164487505882210'], 'label': '2-273-273.263-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/1/bm/b/263/2'}