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lfunc_lfunctions • Show schema
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{'Lhash': '2102684746983212885860352252646', 'a10': [-2.32600718610061, -2.1423563126166294], 'a2': [0.09417641045095253, 1.411074343794321], 'a3': [1.6812233022910785, 0.4165191566224544], 'a4': [-1.9822616074291475, 0.265779833155965], 'a5': [-1.621039517734604, 1.5402048181793104], 'a6': [-0.42940791983252347, 2.411557347106866], 'a7': [-0.36198928490127213, 0.36198928490127213], 'a8': [-0.5617173864267297, -2.7720883062748785], 'a9': [2.6530235843330385, 1.4005234239285955], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.09417641045095253, -1.411074343794321]]], [3, [[1.0, 0], [-1.6812233022910785, -0.4165191566224544]]], [5, [[1.0, 0], [1.621039517734604, -1.5402048181793104]]]], 'bad_primes': [2, 3, 5], 'central_character': '120.53', 'coefficient_field': 'CDF', 'conductor': 120, 'conductor_radical': 30, 'conjugate': 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'root_angle': -0.5519887348977602, 'root_number': '-0.16260224591986278 - 0.986691699378188*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.275994367449', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.65872579289959148908992274036', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.65142442294130293079231987175', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.39966148601663446658278058449', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'bad_primes': [2, 3, 5], 'central_character': '120.53', 'conductor': 120, 'conductor_radical': 30, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/120/2/w/c/53/9'], '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': '2-120-120.53-c1-0-5', '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': '2-120-120.53-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': -0.2759943674488801, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.65872579289959148908992274036', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2102684746983212885860352252646', 'Lhash_array': ['2102684746983212885860352252646'], 'label': '2-120-120.53-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/120/2/w/c/53/9'}