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lfunc_lfunctions • Show schema
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{'Lhash': '5638341194635474438727938269749', 'a10': [-0.5625806192161705, -6.8517815963759015], 'a2': [-0.16366365488050694, -1.993292303720444], 'a3': [0.0, -1.56027897424672], 'a4': [-3.9464284161423087, 0.6524590073441467], 'a5': [3.4374193807838296, 0.0], 'a6': [-3.1100920710228155, 0.2553609595584266], 'a7': [0.0, 2.6457513110645907], 'a8': [1.9464284161423087, 7.7596015632784745], 'a9': [6.565529522523604, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7629447402088314, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.16366365488050694, 1.993292303720444]]], [7, [[1.0, 0], [0, -2.6457513110645907]]]], 'bad_primes': [2, 7], 'central_character': '28.15', 'coefficient_field': 'CDF', 'conductor': 28, 'conductor_radical': 14, 'conjugate': '2775438315489109714242114691884', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.16366365488050694, 1.993292303720444]], [[1.0, 0], [0, 1.56027897424672], [-9.0, 0]], 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.75328382635326175735943251381', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7629447402088314, 'bad_primes': [2, 7], 'central_character': '4.3', 'conductor': 28, 'conductor_radical': 14, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/28/3/c/a/15/3'], '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': '2-28-4.3-c2-0-5', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-28-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8734670802089975, 'root_angle': 0.22392296098820427, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '4.44786693874506147779299708564', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5638341194635474438727938269749', 'Lhash_array': ['5638341194635474438727938269749'], 'label': '2-28-4.3-c2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/28/3/c/a/15/3'}