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lfunc_lfunctions • Show schema
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{'Lhash': '627243130295608978009889314797', 'a10': [1.603627345569151, -1.345603114212875], 'a2': [-0.9730448705798238, -0.23061587074244017], 'a3': [-0.5982384014813555, 1.625457109551966], 'a4': [0.8936326403234123, 0.44879918020046217], 'a5': [-1.2500839290696595, 1.6791541247658928], 'a6': [0.9569690146191229, -1.443679432927859], 'a7': [-0.7257418451144687, -0.4773279205326034], 'a8': [-0.766044443118978, -0.6427876096865394], 'a9': [-2.284221629986065, -1.9448217257897455], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9730448705798238, 0.23061587074244017]]], [3, [[1.0, 0], [0.5982384014813555, -1.625457109551966]]]], 'bad_primes': [2, 3], 'central_character': '162.97', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '3665406339760983222343592608176', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[70.59697858554956, 35.455135235836515]], [[1.0, 0], [-1.5641506501368845, -0.37071051403695776], [74.17150914684322, 37.25033195663836]], [[1.0, 0], [-8.4871540061751, -7.121567796326301], [15.4546878123568, 87.64789001808651]], [[1.0, 0], [-2.0731546167486044, -2.784729924959214], [-27.819913572975754, 92.92498269460242]], [[1.0, 0], [-7.644915576026991, 3.839420907881052], [60.3130177619814, -81.01444246825942]], [[1.0, 0], [6.278632188917167, 0.7338668526545634], [100.22362166972185, 23.753434686471337]], [[1.0, 0], [-3.6096615410240753, 6.252117187181067], [-53.5, -92.66471820493493]], [[1.0, 0], [10.128407393454754, 17.542916205219896], [-54.5, 94.39676901250381]], [[1.0, 0], [6.772280580667473, 15.699911085249958], [-77.5453050791669, 82.19322149775451]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-162-81.16-c1-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 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-0.8225872933117659, 'root_number': '-0.8486553051359689 - 0.5289462856137432*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.411293646656', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49480758355865515257774302174', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.63752577919122728863237155190', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.02654544100634515596151922130', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.293576512744743, 'bad_primes': [2, 3], 'central_character': '81.16', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/g/a/97/2'], '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': '2-162-81.16-c1-0-0', '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': '2-162-81.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': -0.41129364665588297, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.49480758355865515257774302174', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '627243130295608978009889314797', 'Lhash_array': ['627243130295608978009889314797'], 'label': '2-162-81.16-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/g/a/97/2'}