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lfunc_lfunctions • Show schema
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{'Lhash': '1860914075893809751855071613924', 'a10': [0.0, 0.0], 'a2': [0.5679723786437643, 0.9837570171067481], 'a3': [-0.2736252888971991, -1.0211834804000595], 'a4': [0.35481475419548886, -0.6145571815416492], 'a5': [0.0, 0.0], 'a6': [0.8491848084050204, -0.8491848084050204], 'a7': [0.422838838375477, 1.5780560282306848], 'a8': [3.0779894342483147, 0.0], 'a9': [1.630131309435413, -0.9411567503169729], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.3861621869684395, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [1.7180362386421013, 5.835096527283204]]]], 'bad_primes': [5, 37], 'central_character': '925.843', 'coefficient_field': 'CDF', 'conductor': 925, 'conductor_radical': 185, 'conjugate': '1452128615424399191033875252495', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5679723786437643, -0.9837570171067481], [-1.0, 1.7320508075688772]], [[1.0, 0], [0.2736252888971991, 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'7.38636887664130452220665390830164', '8.417185832226024280781974787350358', '9.661746725231429542278612475948440', '10.25013191332102709959285708492606'], 'prelabel': '2-925-185.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.717749470971973, 'root_angle': 0.02787758032029302, 'root_number': '0.9846986684638585 + 0.17426569463180092*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0278775803203', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.46800236244811342437560658637', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.76650006691750133423625491489', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83570205923874040604848447743', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.3861621869684395, 'bad_primes': [5, 37], 'central_character': '185.103', 'conductor': 925, 'conductor_radical': 185, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/925/2/t/b/843/12'], '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': '2-925-185.103-c1-0-33', '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': '2-925-185.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.717749470971973, 'root_angle': 0.02787758032029302, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46800236244811342437560658637', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1860914075893809751855071613924', 'Lhash_array': ['1860914075893809751855071613924'], 'factors': ['2-925-185.103-c1-0-33'], 'label': '2-925-185.103-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/925/2/t/b/843/12'}