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lfunc_lfunctions • Show schema
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{'Lhash': '4355022972092361673375233648344', 'a10': [0.0013661011118159755, 3.162277365091138], 'a2': [1.1193987567960455, -0.8642606223145122], 'a3': [0.17011582554504887, -1.7236764794761013], 'a4': [0.5061071534330641, -1.9349045323332832], 'a5': [-1.3657512957992692, 1.7705150092621684], 'a6': [-1.2992782631944422, -2.076505717495243], 'a7': [2.0696279303559, 2.0696279303559], 'a8': [-1.1057260768749761, -2.603338211396797], 'a9': [-2.942121211798253, -0.5864492945573209], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.1193987567960455, 0.8642606223145122]]], [3, [[1.0, 0], [-0.17011582554504887, 1.7236764794761013]]], [5, [[1.0, 0], [1.3657512957992692, -1.7705150092621684]]]], 'bad_primes': [2, 3, 5], 'central_character': '120.77', 'coefficient_field': 'CDF', 'conductor': 120, 'conductor_radical': 30, 'conjugate': 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'root_analytic_conductor': 0.9788793716568784, 'root_angle': 0.43640293310809103, 'root_number': '0.19846946966375412 + 0.9801070704833162*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.218201466554', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.43550736402308166291778606064', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.63125321007895621233262274311', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.27721991753884187374161880759', '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': '120.77', 'conductor': 120, 'conductor_radical': 30, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/120/2/w/c/77/13'], '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': '2-120-120.77-c1-0-18', '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': '2-120-120.77-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': 0.21820146655404551, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.43550736402308166291778606064', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4355022972092361673375233648344', 'Lhash_array': ['4355022972092361673375233648344'], 'label': '2-120-120.77-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/120/2/w/c/77/13'}