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lfunc_lfunctions • Show schema
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{'Lhash': '1573755761091156952334866364267', 'a10': [-31.181569028511117, 12.504806949636928], 'a2': [-3.712584128652224, 1.4888650333994702], 'a3': [10.911290494585296, 0], 'a4': [11.566561824640788, -11.055073385408274], 'a5': [8.398885506153077, 0], 'a6': [-40.50908391331125, 16.24543888665206], 'a7': [64.74288080264388, 0], 'a8': [-26.482321648036617, 58.26393944911322], 'a9': [38.05626025722745, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.952673945750476, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [3.712584128652224, -1.4888650333994702]]], [41, [[1.0, 0], [-1638.2024273376492, -376.9002614287162]]]], 'bad_primes': [2, 41], 'central_character': '164.163', 'coefficient_field': 'CDF', 'conductor': 164, 'conductor_radical': 82, 'conjugate': '1830144493730345646224734578598', 'degree': 2, 'euler_factors': [[[1.0, 0], [3.712584128652224, -1.4888650333994702]], [[1.0, 0], [-10.911290494585296, 0], 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{'__RealLiteral__': 0, 'data': '-0.08541163367832061', 'prec': 67}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24147439429115246295179011236', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46210055906629137413594689058', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68067685862193241813369920441', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.952673945750476, 'bad_primes': [2, 41], 'central_character': '164.163', 'conductor': 164, 'conductor_radical': 82, 'degree': 2, 'index': 43, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/164/5/d/f/163/4'], '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': '2-164-164.163-c4-0-43', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-164-164.163-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.117362498705996, 'root_angle': -0.08541163367832061, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24147439429115246295179011236', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1573755761091156952334866364267', 'Lhash_array': ['1573755761091156952334866364267'], 'factors': ['2-164-164.163-c4-0-43'], 'label': '2-164-164.163-c4-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/164/5/d/f/163/4'}