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lfunc_lfunctions • Show schema
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{'Lhash': '4193937973728170616794522704838', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5, 0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.02844670572008114, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5, -0.8660254037844386]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 19], 'central_character': '57.11', 'coefficient_field': 'CDF', 'conductor': 57, 'conductor_radical': 57, 'conjugate': '4935461633433389337063670908883', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 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'7.02046440325267567096761130699270', '8.113025414063899120618495471630216', '9.530714621167639954748207724265877', '11.16295984834053954222603330509653', '12.40570419368847873598634726769194', '13.04786003793567616204031954427229', '13.91118790105346893717398966072401', '15.78158863451418310600567398366108'], 'prelabel': '2-57-57.11-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.16866151226667317, 'root_angle': -0.06775328806227679, 'root_number': '0.97743215002793716646276568393226 - 0.21124959666651231416736753193571*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.03387664403113839', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.30843370639598070011740501216', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.50846861495591810506841875830', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.02046440325267567096761130699', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.02844670572008114, 'bad_primes': [3, 19], 'central_character': '57.11', 'conductor': 57, 'conductor_radical': 57, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/57/1/h/a/11/1', 'ArtinRepresentation/2.57.6t5.a.a'], 'is_instance_Artin': True, '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': '2-57-57.11-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-57-57.11-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.16866151226667317, 'root_angle': -0.033876644031138395, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.30843370639598070011740501216', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24596353
{'Lhash': '4193937973728170616794522704838', 'Lhash_array': ['4193937973728170616794522704838'], 'label': '2-57-57.11-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.57.6t5.a.a'}
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id: 19804621
{'Lhash': '4193937973728170616794522704838', 'Lhash_array': ['4193937973728170616794522704838'], 'label': '2-57-57.11-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/57/1/h/a/11/1'}