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  • lfunc_lfunctions • Show schema
    {'Lhash': '504025518970080409486341165847', 'a10': [-9.170221208556528, -2.173382351475608], 'a2': [-2.579874484337798, -0.7181571463457405], 'a3': [0.0, 0.0], 'a4': [4.42766886902923, 2.6721118529007177], 'a5': [3.5165366519042847, -0.13645763683985598], 'a6': [0.0, 0.0], 'a7': [-3.4307254575702517, -0.5365556705259701], 'a8': [-5.828370132254143, -6.1777114264002355], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.685', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '2013877472665891675202928030904', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.579874484337798, 0.7181571463457405], [1.712333799060533, 1.0333987423037259]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.5165366519042847, 0.13645763683985598], [4.98496470583896, 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'-0.234233231397', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.39760602714922788967132659332', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.05786687189515553081331843359', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.92483133277921069392842952590', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '243.103', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/i/a/685/1'], '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': '2-3e6-243.103-c1-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-3e6-243.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.2342332313967304, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.39760602714922788967132659332', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '504025518970080409486341165847', 'Lhash_array': ['504025518970080409486341165847'], 'factors': ['2-3e6-243.103-c1-0-3'], 'label': '2-3e6-243.103-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/i/a/685/1'}