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lfunc_lfunctions • Show schema
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{'Lhash': '2163703304618951330421434881923', 'a10': [3721.0335903823116, 1354.345467603858], 'a2': [7.517540966287267, -2.7361611466053497], 'a3': [8.600725128936881, -48.77713605926891], 'a4': [49.02684435961459, -41.13840701993852], 'a5': [379.17679695455143, 318.1671104755465], 'a6': [-68.80580103149505, -390.2170884741513], 'a7': [612.2056868781435, 1060.3713543555477], 'a8': [256.0, -443.40500673763256], 'a9': [-250.12876774212378, -91.03942619181731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.870630968396632, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-7.517540966287267, 2.7361611466053497]]], [19, [[1.0, 0], [24181.89767814278, -17581.455107124457]]]], 'bad_primes': [2, 19], 'central_character': '38.5', 'coefficient_field': 'CDF', 'conductor': 38, 'conductor_radical': 38, 'conjugate': '2358784567822190733897175645071', 'degree': 2, 'euler_factors': [[[1.0, 0], [-7.517540966287267, 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0.5261838721207142*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0881888199546', 'prec': 50}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70686094751140060039636488040', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.30412555391383228006378756091', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.89656417626145525260091137045', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.870630968396632, 'bad_primes': [2, 19], 'central_character': '19.5', 'conductor': 38, 'conductor_radical': 38, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/38/8/e/b/5/5'], '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': '2-38-19.5-c7-0-6', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-38-19.5-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.445378203970739, 'root_angle': 0.0881888199546224, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70686094751140060039636488040', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2163703304618951330421434881923', 'Lhash_array': ['2163703304618951330421434881923'], 'label': '2-38-19.5-c7-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/38/8/e/b/5/5'}