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lfunc_lfunctions • Show schema
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{'Lhash': '2010475601084534654693683508270', 'a10': [0.31988604544302757, -2.2248563156147285], 'a2': [-0.41541501300188644, -0.9096319953545183], 'a3': [0.0, 0.0], 'a4': [-0.6548607339452851, 0.7557495743542583], 'a5': [1.8909150240228902, 1.2152172970808288], 'a6': [0.0, 0.0], 'a7': [-0.5210483017105777, -3.6239705398701854], 'a8': [0.9594929736144974, 0.28173255684142967], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3058066436810094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.41541501300188644, 0.9096319953545183]]], [3, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [-3.102713868159457, 3.6569340508588586]]]], 'bad_primes': [2, 3, 23], 'central_character': '414.73', 'coefficient_field': 'CDF', 'conductor': 414, 'conductor_radical': 138, 'conjugate': '1417065582703444985741799469502', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.41541501300188644, 0.9096319953545183]], [[1.0, 0], [0, 0]], 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'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.58598560259630383153744486651', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.19369621831014243988893709531', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.25177324707132998129068769129', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.3058066436810094, 'bad_primes': [2, 3, 23], 'central_character': '23.4', 'conductor': 414, 'conductor_radical': 138, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/414/2/i/h/73/2'], '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': '2-414-23.4-c1-0-5', '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': '2-414-23.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8181877360935557, 'root_angle': 0.18415022966827, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.58598560259630383153744486651', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2010475601084534654693683508270', 'Lhash_array': ['2010475601084534654693683508270'], 'label': '2-414-23.4-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/414/2/i/h/73/2'}