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lfunc_lfunctions • Show schema
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{'Lhash': '3761776982419490302105897302855', 'a10': [3.3254596267623633, 0.3122163709784554], 'a2': [-0.8567688765734294, 1.2235927633170238], 'a3': [-0.9607421366554023, -1.4411712413363], 'a4': [-0.0790860559255567, -0.21728715284919248], 'a5': [-1.105722955456809, -1.943547464245692], 'a6': [2.5865406626987144, 0.05919353956435096], 'a7': [-4.366422002062327, 2.0360960182981445], 'a8': [-2.5520371499213304, -0.6838162933756444], 'a9': [-1.1539490937096244, 2.769187875375511], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0779804272872857, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.9607421366554023, 1.4411712413363]]], [5, [[1.0, 0], [1.105722955456809, 1.943547464245692]]]], 'bad_primes': [3, 5], 'central_character': '135.68', 'coefficient_field': 'CDF', 'conductor': 135, 'conductor_radical': 15, 'conjugate': '146020248686610332867468559669', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.96751879559100533179879741090', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.07546276413086268434945474012', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.11699950256766796445645161840', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0779804272872857, 'bad_primes': [3, 5], 'central_character': '135.68', 'conductor': 135, 'conductor_radical': 15, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/135/2/q/a/68/5'], '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': '2-135-135.68-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': '2-135-135.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0382583624933082, 'root_angle': 0.382446448083086, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.96751879559100533179879741090', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3761776982419490302105897302855', 'Lhash_array': ['3761776982419490302105897302855'], 'factors': ['2-135-135.68-c1-0-12'], 'label': '2-135-135.68-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/135/2/q/a/68/5'}