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lfunc_lfunctions • Show schema
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{'Lhash': '675376804405524095761672117182', 'a10': [1909.362940080233, -1719.1981132806561], 'a2': [-7.935179209958162, -0.8340209425587473], 'a3': [-69.19886990549442, -50.275921876252006], 'a4': [-62.93141473240147, -13.376485136549432], 'a5': [-215.46837455010075, 239.30187332524585], 'a6': [507.1742620754372, 456.6617567364962], 'a7': [51.78774762829891, -116.31718561083021], 'a8': [1459.527631658472, 474.22927472200394], 'a9': [1584.9951089925366, 4878.113353449627], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.055486554531434, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[61, [[1.0, 0], [1402827.6432340592, -1083889.9572370688]]]], 'bad_primes': [61], 'central_character': '61.4', 'coefficient_field': 'CDF', 'conductor': 61, 'conductor_radical': 61, 'conjugate': '133300714398878663208056656547', 'degree': 2, 'euler_factors': [[[1.0, 0], [7.935179209958162, 0.8340209425587473], [125.20289289392713, 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'-0.24366019685930745 + 0.9698606644598406*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.289174081531', 'prec': 47}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.53277835728861597205672808575', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.32443734062168688528409294813', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.71608591579393388428610815186', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.055486554531434, 'bad_primes': [61], 'central_character': '61.4', 'conductor': 61, 'conductor_radical': 61, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/61/8/k/a/4/14'], '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': '2-61-61.4-c7-0-6', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-61-61.4-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.365259047815082, 'root_angle': 0.28917408153144786, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '0.53277835728861597205672808575', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '675376804405524095761672117182', 'Lhash_array': ['675376804405524095761672117182'], 'label': '2-61-61.4-c7-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/61/8/k/a/4/14'}