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lfunc_lfunctions • Show schema
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{'Lhash': '1594146111538942929463820526693', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.14636548903290855, 0.0], 'a4': [0.0, 0.0], 'a5': [2.3429230827771703, 0.0], 'a6': [0.0, 0.0], 'a7': [3.832211654587249, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.9785771436201576, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.060796103745787, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 19], 'central_character': '2888.1', 'coefficient_field': 'CDF', 'conductor': 2888, 'conductor_radical': 38, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.14636548903290855, 0], [3.0, 0]], [[1.0, 0], [-2.3429230827771703, 0], [5.0, 0]], [[1.0, 0], [-3.832211654587249, 0], [7.0, 0]], [[1.0, 0], [-3.3429230827771703, 0], [11.0, 0]], [[1.0, 0], [-6.175134737364419, 0], [13.0, 0]], [[1.0, 0], [-5.196557593744262, 0], [17.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'5.17394061017284096222034441430571', '5.65081038553404361773733689541596', '6.28863265323901321591171644067173', '7.24251204551751573295572654712158', '8.338553062832413241488433992245895', '8.617781758286401411401147026806665'], 'prelabel': '2-2888-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.80216577220589, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25755954460316657228148922143', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.76512126888006407099374772359', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.13011180503176896545404690110', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.060796103745787, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 2888, 'conductor_radical': 38, 'degree': 2, 'index': 47, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2888/2/a/r/1/2'], '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': '2-2888-1.1-c1-0-47', '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': '2-2888-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.80216577220589, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25755954460316657228148922143', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1594146111538942929463820526693', 'Lhash_array': ['1594146111538942929463820526693'], 'factors': ['2-2888-1.1-c1-0-47'], 'label': '2-2888-1.1-c1-0-47', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2888/2/a/r/1/2'}