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lfunc_lfunctions • Show schema
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{'Lhash': '2183416380979527620159603064140', 'a10': [-1.0, 0.0], 'a2': [0.5, 0.8660254037844386], 'a3': [0.0, 0.0], 'a4': [-4.582907174201562e-80, 2.6459426906140066e-80], 'a5': [-0.5, 0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, -1.3229713455367871e-80], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.202121330116366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [3, 5], 'central_character': '405.134', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'conjugate': '2997625299538619615963123487575', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 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'3.20070404887720902396814416449904', '4.30746236260083919008629593265681', '5.01996500504280180830195282942431', '6.57761387172952325273896913429625', '7.73355615850760394401301738470809', '8.567094889802317980942082513127748', '9.569657504300470819616103727246689', '10.78043409833624124403047556994655', '11.37914445742390888364191252847893'], 'prelabel': '2-405-45.14-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.44957905880541854, 'root_angle': -0.38888888888888895, 'root_number': '0.34202014332566873304409961468239 - 0.93969262078590838405410927732446*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.19444444444444445', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72241182277389574123742867895', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.20070404887720902396814416450', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.30746236260083919008629593266', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.202121330116366, 'bad_primes': [3, 5], 'central_character': '45.14', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/1/h/b/134/1', 'ArtinRepresentation/2.405.6t5.a.b'], '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': '2-405-45.14-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': '2-405-45.14-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.44957905880541854, 'root_angle': -0.19444444444444448, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72241182277389574123742867895', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24596721
{'Lhash': '2183416380979527620159603064140', 'Lhash_array': ['2183416380979527620159603064140'], 'label': '2-405-45.14-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.405.6t5.a.b'}
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id: 19811388
{'Lhash': '2183416380979527620159603064140', 'Lhash_array': ['2183416380979527620159603064140'], 'label': '2-405-45.14-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/1/h/b/134/1'}