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lfunc_lfunctions • Show schema
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{'Lhash': '1596365293603666173644788328490', 'a10': [25.285010017129004, 0.0], 'a2': [0.0, 2.6309582356015198], 'a3': [2.1213203435596424, 2.1213203435596424], 'a4': [1.0780587625205371, 0.0], 'a5': [0.0, -9.610570656340371], 'a6': [-5.581105228237288, 5.581105228237288], 'a7': [6.965840212318948, 6.965840212318948], 'a8': [0.0, 23.88399346452795], 'a9': [0.0, 9.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.257234930706099, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-2.1213203435596424, -2.1213203435596424]]], [41, [[1.0, 0], [151.72054620837974, 214.24723068975922]]]], 'bad_primes': [3, 41], 'central_character': '123.91', 'coefficient_field': 'CDF', 'conductor': 123, 'conductor_radical': 123, 'conjugate': '2515834605537122613440220578381', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.6309582356015198], [-8.0, 0]], [[1.0, 0], [-2.1213203435596424, -2.1213203435596424]], [[1.0, 0], [0, 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'-0.16736012063889769 - 0.9858958312213992*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.276762128372', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25931017057559438469528527700', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80783323818071945800199479507', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.84481228809896890655302734671', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.257234930706099, 'bad_primes': [3, 41], 'central_character': '41.9', 'conductor': 123, 'conductor_radical': 123, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/123/4/e/a/91/16'], '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': '2-123-41.9-c3-0-10', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-123-41.9-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.693925561463438, 'root_angle': -0.2767621283719663, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25931017057559438469528527700', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1596365293603666173644788328490', 'Lhash_array': ['1596365293603666173644788328490'], 'label': '2-123-41.9-c3-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/123/4/e/a/91/16'}