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lfunc_lfunctions • Show schema
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{'Lhash': '2081688433402796063852575660927', 'a10': [-0.2680263516722761, -0.46423525886370576], 'a2': [-1.3027706875949328, 0.13692671684620492], 'a3': [2.029797961244133, 1.8276382934117277], 'a4': [-0.2778326627973179, 0.059055155523824565], 'a5': [0.16644362320086858, 0.3738384984910078], 'a6': [-2.894613796748081, -2.1030600254885465], 'a7': [-2.506343275905147, 0.8474924090073358], 'a8': [2.845532734909463, -0.9245696318475739], 'a9': [0.46623264212294674, 4.435907277612844], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6148480955638592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [2.506343275905147, -0.8474924090073358]]], [11, [[1.0, 0], [-3.263717620426872, 0.5900400783973545]]]], 'bad_primes': [7, 11], 'central_character': '77.19', 'coefficient_field': 'CDF', 'conductor': 77, 'conductor_radical': 77, 'conjugate': '3911144751584351375251328299742', 'degree': 2, 'euler_factors': [[[1.0, 0], 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0.924890177034574*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.187921667921', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64216262196223965143224546463', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.78085505659539078681908827795', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.47383666569848775898362221573', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6148480955638592, 'bad_primes': [7, 11], 'central_character': '77.19', 'conductor': 77, 'conductor_radical': 77, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/77/2/n/a/19/2'], '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': '2-77-77.19-c1-0-0', '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': '2-77-77.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7841225003555625, 'root_angle': -0.18792166792112155, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.64216262196223965143224546463', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2081688433402796063852575660927', 'Lhash_array': ['2081688433402796063852575660927'], 'label': '2-77-77.19-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/77/2/n/a/19/2'}