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lfunc_lfunctions • Show schema
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{'Lhash': '1352337616147116363659457637342', 'a10': [-66.8404648011266, 0.0], 'a2': [-2.673618592045064, 0.0], 'a3': [-11.130912565148929, 0.0], 'a4': [-24.85176362427097, 0.0], 'a5': [25.0, 0.0], 'a6': [29.759814780610192, 0.0], 'a7': [158.86556985884866, 0.0], 'a8': [151.99993221640213, 0.0], 'a9': [-119.10278546700967, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 167.6010917045648, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-25.0, 0]]], [11, [[1.0, 0], [-121.0, 0]]], [19, [[1.0, 0], [361.0, 0]]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.1', 'coefficient_field': 'CDF', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.673618592045064, 0], [32.0, 0]], [[1.0, 0], [11.130912565148929, 0], [243.0, 0]], [[1.0, 0], [-25.0, 0]], [[1.0, 0], [-158.86556985884866, 0], [16807.0, 0]], [[1.0, 0], [-121.0, 0]], [[1.0, 0], [-28.09947353130773, 0], [371293.0, 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['1.06680627603823940584757622315438', '1.93972849025771988703805673517479', '3.52715467290135538291256934214420', '4.72033297648406893085865603822200', '5.23461019906784696950597631403171', '6.05716999636026521099627434978038', '7.21915284716735108639020262238598', '8.170087203102391649322155292151012', '8.729523573155949931578702702691805'], 'prelabel': '2-1045-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.946084029719751, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06680627603823940584757622315', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.93972849025771988703805673517', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52715467290135538291256934214', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 167.6010917045648, 'bad_primes': [5, 11, 19], 'central_character': '1.1', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 2, 'index': 204, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1045/6/a/e/1/16'], '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': '2-1045-1.1-c5-0-204', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-1045-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.946084029719751, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06680627603823940584757622315', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1352337616147116363659457637342', 'Lhash_array': ['1352337616147116363659457637342'], 'label': '2-1045-1.1-c5-0-204', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1045/6/a/e/1/16'}