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lfunc_lfunctions • Show schema
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{'Lhash': '560511135221356449613726853840', 'a10': [0.0, 0.0], 'a2': [-0.36327126400268045, 0.5], 'a3': [-0.9510565162951535, -0.30901699437494745], 'a4': [0.5, 1.5388417685876268], 'a5': [0.0, 0.0], 'a6': [0.5, -0.36327126400268045], 'a7': [-0.7265425280053609, 0.2360679774997897], 'a8': [-2.1266270208801, -0.6909830056250525], 'a9': [0.8090169943749475, 0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.587658166755635, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.9510565162951535, 0.30901699437494745]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-3.23606797749979, 0.7265425280053609]]]], 'bad_primes': [3, 5, 11], 'central_character': '825.499', 'coefficient_field': 'CDF', 'conductor': 825, 'conductor_radical': 165, 'conjugate': '2142419223089412500868147323106', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.36327126400268045, -0.5], [-0.6180339887498949, -1.902113032590307]], [[1.0, 0], 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{'__RealLiteral__': 0, 'data': '3.23586211603942235530476408559', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.587658166755635, 'bad_primes': [3, 5, 11], 'central_character': '55.4', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/2/bx/c/499/1'], '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': '2-825-55.4-c1-0-5', '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': '2-825-55.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.566643365712431, 'root_angle': -0.41514158414221847, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44216532151717620211852097535', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '560511135221356449613726853840', 'Lhash_array': ['560511135221356449613726853840'], 'label': '2-825-55.4-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/2/bx/c/499/1'}