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lfunc_lfunctions • Show schema
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{'Lhash': '423017956578274079404407194630', 'a10': [0.19201836470182537, 0.3325855636498518], 'a2': [-0.9785146734413378, -1.6948371303520655], 'a3': [-1.7302237301209775, -0.07953517288754071], 'a4': [-0.9149819322800161, 1.5847951947165337], 'a5': [-0.19623452760960247, 0.0], 'a6': [1.5582501440810068, 3.010273755350436], 'a7': [-2.2336833631584394, 3.8688530730117403], 'a8': [-0.3327657070865344, 0.0], 'a9': [2.987348312547498, 0.27522728701859506], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.7302237301209775, 0.07953517288754071]]], [19, [[1.0, 0], [0.1322161354420738, -4.356893261663495]]]], 'bad_primes': [3, 19], 'central_character': '171.106', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '2468316025978949852457920524298', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9785146734413378, 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'8.246944560834746443359941630969364', '9.710221650251483133707747248534363', '10.29291439625311549035189353007325', '11.48091325196090926499849942117983', '12.68085236678829182172227424674634'], 'prelabel': '2-171-171.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': -0.3066308194840297, 'root_number': '0.5708060396273368 - 0.8210849317366353*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.153315409742', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.33370232815107995592194707497', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.88921274937118640684405196172', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.38652416033291191569483623420', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'bad_primes': [3, 19], 'central_character': '171.106', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/g/c/106/3'], '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': '2-171-171.106-c1-0-1', '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': '2-171-171.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': -0.15331540974201485, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.33370232815107995592194707497', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '423017956578274079404407194630', 'Lhash_array': ['423017956578274079404407194630'], 'label': '2-171-171.106-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/g/c/106/3'}