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lfunc_lfunctions • Show schema
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{'Lhash': '1479461790416655606701973235688', 'a10': [-357.7650346369329, 110.35589810006898], 'a2': [0.6456270088195305, -1.3406582980187518], 'a3': [42.1659818532899, -61.846136429173534], 'a4': [158.2328588383065, 198.41772909821776], 'a5': [-171.1374342082447, -184.44228873042496], 'a6': [-55.69103926629315, -96.45970953553311], 'a7': [2100.7707940013865, 1212.8805834224045], 'a8': [739.5517267675115, -168.79785560865164], 'a9': [350.0278953039446, 891.8565321173792], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.517280232628476, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [-3418781.1706829662, -11644.07937993334]]]], 'bad_primes': [43], 'central_character': '43.18', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'conjugate': '2003687878069082025219002310341', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6456270088195305, 1.3406582980187518], [-159.61338927583577, 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-0.04993940572011789, 'root_number': '0.9877181019618999 - 0.15624644334122278*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0249697028601', 'prec': 54}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16708956722798179031389611005', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.16040280582910824219119286122', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.73659381394076777521920337624', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.517280232628476, 'bad_primes': [43], 'central_character': '43.18', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/9/h/a/18/15'], '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': '2-43-43.18-c8-0-15', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-43-43.18-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.185365005901931, 'root_angle': -0.024969702860058944, 'self_dual': False, 'spectral_label': 'c8-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16708956722798179031389611005', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1479461790416655606701973235688', 'Lhash_array': ['1479461790416655606701973235688'], 'label': '2-43-43.18-c8-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/9/h/a/18/15'}