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lfunc_lfunctions • Show schema
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{'Lhash': '526052940915080221104679710401', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.2704554820877085, 0], 'a6': [0, 0], 'a7': [0, -2.453918204671321], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 43.69413998604465, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-0.0756670692800762, -4.358242133547259]]]], 'bad_primes': [2, 3, 19], 'central_character': '5472.2431', 'coefficient_field': 'CDF', 'conductor': 5472, 'conductor_radical': 114, 'conjugate': '1035467171524424332229260321432', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.2704554820877085, 0], [5.0, 0]], [[1.0, 0], [0, 2.453918204671321], [-7.0, 0]], [[1.0, 0], [0, -4.60851145256295], [-11.0, 0]], [[1.0, 0], [0, 5.387514372225695], [-13.0, 0]], [[1.0, 0], [2.305906035956413, 0], [17.0, 0]], [[1.0, 0], 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'1.86513649048338172715774803361163', '2.68219335576624715379121594833621', '3.64231352499243090177457996256303', '4.30094708828081771954426162569841', '5.23430692211653754303665072601840', '5.93417608309665740077932765441929', '6.63212930704565863909836111930560', '7.31244860651255748707059464099710', '8.275425317962750323575184301376955'], 'prelabel': '2-5472-76.75-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.610154308792242, 'root_angle': -0.25552588769640316, 'root_number': '0.6947254130245891024920234994948942152695778930616208909 - 0.7192750520474167552727842405226688589931533526471433531*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1277629438482016', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41498259916444562158202899009', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86513649048338172715774803361', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.68219335576624715379121594834', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 43.69413998604465, 'bad_primes': [2, 3, 19], 'central_character': '76.75', 'conductor': 5472, 'conductor_radical': 114, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5472/2/k/d/2431/17'], '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': '2-5472-76.75-c1-0-24', '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': '2-5472-76.75-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.610154308792242, 'root_angle': -0.12776294384820158, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.41498259916444562158202899009', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '526052940915080221104679710401', 'Lhash_array': ['526052940915080221104679710401'], 'label': '2-5472-76.75-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5472/2/k/d/2431/17'}