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lfunc_lfunctions • Show schema
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{'Lhash': '2585182702623734625132231034496', 'a10': [-0.1924027630515958, 0.16144508751408362], 'a2': [-0.9730448705798238, -0.23061587074244017], 'a3': [1.566081656436701, -0.7398569087144343], 'a4': [0.8936326403234123, 0.44879918020046217], 'a5': [0.14998472223859066, -0.201464445020285], 'a6': [-1.6944904679328752, 0.35875068513471237], 'a7': [1.839635443658437, 1.2099472653682442], 'a8': [-0.766044443118978, -0.6427876096865394], 'a9': [1.9052235092550425, -2.3173526662512764], '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], [-1.566081656436701, 0.7398569087144343]]]], 'bad_primes': [2, 3], 'central_character': '162.97', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '2244055306080502472828479358519', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'root_angle': 0.16645628884517874, 'root_number': '0.8663556753222574 + 0.49942751609909847*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0832281444226', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.03934956695346106728769090903', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.76489310020126840729830417693', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.26695245496582049391488325955', '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': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/g/a/97/4'], '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': '2-162-81.16-c1-0-4', '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': 0.08322814442258937, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.03934956695346106728769090903', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2585182702623734625132231034496', 'Lhash_array': ['2585182702623734625132231034496'], 'label': '2-162-81.16-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/g/a/97/4'}