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lfunc_lfunctions • Show schema
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{'Lhash': '3677636383968287440046953923436', 'a10': [1.0747379611199743, 6.705522218702987], 'a2': [-0.31651348687789327, -1.9747959926595957], 'a3': [1.2690842493461205, 0.41235046879150744], 'a4': [-3.7996384252487956, 1.2500991310183582], 'a5': [-3.3955518664346647, 0.0], 'a6': [0.4126257724384202, -2.636696974649064], 'a7': [-4.7442379755547766, -6.529883375966357], 'a8': [3.6713275612130203, 7.1078375008350925], 'a9': [-5.840611026548697, -4.243452300324676], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3787552780676817, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.31651348687789327, 1.9747959926595957]]], [31, [[1.0, 0], [-8.73750609988985, 29.743167066645537]]]], 'bad_primes': [2, 31], 'central_character': '124.35', 'coefficient_field': 'CDF', 'conductor': 124, 'conductor_radical': 62, 'conjugate': '572086524831135761958319990695', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.31651348687789327, 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'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.90114356693095177812426553642', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.81998341341185196775765353569', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.91249299631116962277662059047', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.3787552780676817, 'bad_primes': [2, 31], 'central_character': '124.35', 'conductor': 124, 'conductor_radical': 62, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/124/3/l/a/35/15'], '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': '2-124-124.35-c2-0-27', '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': '2-124-124.35-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8381390801752955, 'root_angle': -0.49910673431160885, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.90114356693095177812426553642', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3677636383968287440046953923436', 'Lhash_array': ['3677636383968287440046953923436'], 'label': '2-124-124.35-c2-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/124/3/l/a/35/15'}