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lfunc_lfunctions • Show schema
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'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44826297439707773287003253848', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.61201028299603333833511605368', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.856932412507434451914351824898', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.311344069505296, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 10995116277760000000000000000, 'conductor_radical': 10, 'degree': 16, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], 'euler11': [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], 'euler13': [1, 2, 2, 2, 3, 2, 0, 0, 1, 0, 0, 2, 3, 2, 2, 2, 1], 'euler17': [1, 2, 2, 2, 3, 2, 0, 0, 1, 0, 0, 2, 3, 2, 2, 2, 1], 'euler19': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler29': [1, -4, 10, -20, 35, -52, 68, -80, 85, -80, 68, -52, 35, -20, 10, -4, 1], 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4, 0, 3, 0, 2, 0, 1], 'euler83': [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], 'euler89': [1, -10, 47, -140, 303, -520, 749, -930, 1000, -930, 749, -520, 303, -140, 47, -10, 1], 'euler97': [1, -2, 2, -2, 3, -2, 0, 0, 1, 0, 0, -2, 3, -2, 2, -2, 1], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 2, 2, 2, 3, 2, 0, 0, 1, 0, 0, 2, 3, 2, 2, 2, 1], [1, 2, 2, 2, 3, 2, 0, 0, 1, 0, 0, 2, 3, 2, 2, 2, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], [1, -4, 10, -20, 35, -52, 68, -80, 85, -80, 68, -52, 35, -20, 10, -4, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 2, 7, 12, 23, 32, 45, 50, 56, 50, 45, 32, 23, 12, 7, 2, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], [1, -2, 7, -12, 23, -32, 45, -50, 56, -50, 45, -32, 23, -12, 7, -2, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, -2, 2, -2, 3, -2, 0, 0, 1, 0, 0, -2, 3, -2, 2, -2, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], [1, -10, 47, -140, 303, -520, 749, -930, 1000, -930, 749, -520, 303, -140, 47, -10, 1], [1, -2, 2, -2, 3, -2, 0, 0, 1, 0, 0, -2, 3, -2, 2, -2, 1]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3200/1/bz/a'], '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': '16-3200e8-1.1-c0e8-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0, 0, 0, 0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '16-3200e8-1.1-c0e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2637278347910228, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e8-0', 'trace_hash': 1257286338018927533, 'z1': {'__RealLiteral__': 0, 'data': '0.44826297439707773287003253848', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '568240828554547016679113512780,775815202585770199558525509991,1086290887070073959059596988533,1269891650010324804884835539360,1435562127865635032462478355317,1677900557520454031659038995507,2038923412095382597924741813123,2243239105795984659243871407463', 'Lhash_array': ['568240828554547016679113512780', '775815202585770199558525509991', '1086290887070073959059596988533', '1269891650010324804884835539360', '1435562127865635032462478355317', '1677900557520454031659038995507', '2038923412095382597924741813123', '2243239105795984659243871407463'], 'label': '16-3200e8-1.1-c0e8-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3200/1/bz/a'}