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lfunc_lfunctions • Show schema
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{'Lhash': '738959708561778544750330439444', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.0, 0], 'a6': [0, 0], 'a7': [0, 0.4886571399061897], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.11613287362019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [4.645302166399186, -1.1921274188806454]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '8280.1241', 'coefficient_field': 'CDF', 'conductor': 8280, 'conductor_radical': 690, 'conjugate': '540834120378101536441413510563', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, -0.4886571399061897], [-7.0, 0]], [[1.0, 0], [0.47761801884846977, 0], [11.0, 0]], [[1.0, 0], [4.916806781049882, 0], [13.0, 0]], [[1.0, 0], [-0.06864603724416155, 0], [17.0, 0]], [[1.0, 0], [0, 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['0.58293642461789969053709212030231', '1.91424636576097719461833841837708', '2.70056500139585107487385955564946', '3.56197154046437058079367778520808', '4.37334997246589312610541138603578', '4.98998697754038830301065634686929', '5.68458788546723432827724469926058', '6.67050745671930979282086819159086', '7.14691034470990092680803166352933', '7.84213589658825809429297445297350'], 'prelabel': '2-8280-69.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.11595078478782937, 'root_number': '0.93438403760789664323158764249718688604992227812949552428 + 0.3562674139793938430011422302150790972514134746926370145*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.057975392393914686', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58293642461789969053709212030', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.91424636576097719461833841838', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.70056500139585107487385955565', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 66.11613287362019, 'bad_primes': [2, 3, 5, 23], 'central_character': '69.68', 'conductor': 8280, 'conductor_radical': 690, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8280/2/p/a/1241/26'], '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': '2-8280-69.68-c1-0-39', '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': '2-8280-69.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.057975392393914686, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58293642461789969053709212030', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '738959708561778544750330439444', 'Lhash_array': ['738959708561778544750330439444'], 'label': '2-8280-69.68-c1-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8280/2/p/a/1241/26'}