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lfunc_lfunctions • Show schema
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{'Lhash': '3026579700627333159175816250370', 'a10': [-0.1855071824788075, -0.3213078652222456], 'a2': [0.09734672452359931, 0.1686094728252852], 'a3': [1.5526677117092953, 0.7676086092634843], 'a4': [0.981047230449053, -1.6992236477624927], 'a5': [-1.9056335319616824, 0.0], 'a6': [0.021721033064385647, 0.33651866817206183], 'a7': [1.6944577420514724, -2.9348869005115894], 'a8': [0.7713938360430532, 0.0], 'a9': [1.821554045969159, 2.3836822056669775], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.5526677117092953, -0.7676086092634843]]], [19, [[1.0, 0], [1.1446431226653253, -4.205923456475994]]]], 'bad_primes': [3, 19], 'central_character': '171.106', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '2447977790818907013340771459686', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.09734672452359931, 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'7.75229203216001470271079014632298', '8.442252834254829188668519418032755', '9.426969491971795461826356873279356', '11.37400414603056887289450513293706', '11.68121303362098467914217899267176', '12.80433009405665120657182920649260'], 'prelabel': '2-171-171.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.01567371083502599, 'root_number': '0.9951546810142331 + 0.09832172117828222*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.015673710835', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.38755040236041694754207931308', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34859675423606723252733043629', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.95352981339171122747367045196', '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': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/g/c/106/10'], '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-c1-0-12', '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': 0.01567371083502599, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.38755040236041694754207931308', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3026579700627333159175816250370', 'Lhash_array': ['3026579700627333159175816250370'], 'factors': ['2-171-171.106-c1-0-12'], 'label': '2-171-171.106-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/g/c/106/10'}