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lfunc_lfunctions • Show schema
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{'Lhash': '740136604387567973563346170028', 'a10': [-4.2299136763247205, -7.326425399024871], 'a2': [1.010156124700462, 1.7496417315580828], 'a3': [-1.7037748087722693, 0.3116911949237851], 'a4': [-1.040830792539711, 1.8027718147609608], 'a5': [-4.187386061317008, 0.0], 'a6': [-2.2664264801895255, -2.6661387370378877], 'a7': [-0.9761070303343495, 1.6906669701642687], 'a8': [-0.16498190064145157, 0.0], 'a9': [2.805697198013966, -1.0621032120545442], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.7037748087722693, -0.3116911949237851]]], [19, [[1.0, 0], [-4.113172511508616, 1.4428485334815644]]]], 'bad_primes': [3, 19], 'central_character': '171.106', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '4922386429288538992808991418452', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.010156124700462, 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'5.17298410870564508811532078619427', '7.11129455285726244736030915638984', '7.74219952109247183554849489238851', '9.707295044680612506521147155936461', '10.94966183691660231861118909539775', '11.32744530001886813099496802386663', '12.03653587449847624822748283531417'], 'prelabel': '2-171-171.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.4659441961384624, 'root_number': '-0.9771937282921949 + 0.2123497524990315*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.465944196138', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58386483172438276956120003415', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.19912908138102271888578294809', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.22121642600204879555252794815', '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': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/g/c/106/13'], '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-c1-0-2', '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': 0.4659441961384624, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58386483172438276956120003415', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '740136604387567973563346170028', 'Lhash_array': ['740136604387567973563346170028'], 'factors': ['2-171-171.106-c1-0-2'], 'label': '2-171-171.106-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/g/c/106/13'}