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lfunc_lfunctions • Show schema
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{'Lhash': '1188580904329243299998866118696', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -2.1451026912004223], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 1.1451026912004225], 'a8': [0, 0], 'a9': [-1.6014655557952948, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.731184929788995, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 5, 23], 'central_character': '4600.4049', 'coefficient_field': 'CDF', 'conductor': 4600, 'conductor_radical': 230, 'conjugate': '1150090320893325824954937345959', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.1451026912004223], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.1451026912004225], [-7.0, 0]], [[1.0, 0], [-5.89167093819614, 0], [11.0, 0]], [[1.0, 0], [0, 4.89167093819614], [-13.0, 0]], [[1.0, 0], [0, -5.89167093819614], [-17.0, 0]], [[1.0, 0], [-2.3480338027910124, 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'5.19027630655108844096440801190773', '6.47229399241828668527458561107257', '6.81778489746481608507098660482804', '7.67001691405298536189260137579569', '8.876991173894774500159533445812687'], 'prelabel': '2-4600-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.06062578697852, 'root_angle': 0.35241638234956674, 'root_number': '0.4472135954999579392818347337462552470881236719223051449 + 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.17620819117478337', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.937625008117575699146003111847', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.13256248045723337378687682754', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.49234594401900469184531078792', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.731184929788995, 'bad_primes': [2, 5, 23], 'central_character': '5.4', 'conductor': 4600, 'conductor_radical': 230, 'degree': 2, 'index': 55, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4600/2/e/r/4049/2'], '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': '2-4600-5.4-c1-0-55', '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': '2-4600-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.06062578697852, 'root_angle': 0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.937625008117575699146003111847', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1188580904329243299998866118696', 'Lhash_array': ['1188580904329243299998866118696'], 'label': '2-4600-5.4-c1-0-55', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4600/2/e/r/4049/2'}