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lfunc_lfunctions • Show schema
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{'Lhash': '145786446957447339319438142598', 'a10': [4.414166575601539, -1.507862625800201], 'a2': [-1.412792675989181, -0.06337866100928091], 'a3': [-0.028644075861277044, 0.19004102612665233], 'a4': [1.9919662906573412, 0.17908181617582627], 'a5': [-3.0703679471984704, 1.2050306205809436], 'a6': [0.05251268636002769, -0.266673146675267], 'a7': [0.3840377415601886, 2.61773089011406], 'a8': [-2.802885420537694, -0.3792536345735345], 'a9': [2.831423308829098, 0.8733784240944591], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1301357592341925, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.412792675989181, 0.06337866100928091]]], [7, [[1.0, 0], [-0.3840377415601886, -2.61773089011406]]]], 'bad_primes': [2, 7], 'central_character': '392.205', 'coefficient_field': 'CDF', 'conductor': 392, 'conductor_radical': 14, 'conjugate': '2869341866995837565816869809559', 'degree': 2, 'euler_factors': [[[1.0, 0], 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0.11385279429718125*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.481840387743', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.11500522851580693043200069656', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.81582601391938178340592869829', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.87590583085935309916811160123', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1301357592341925, 'bad_primes': [2, 7], 'central_character': '392.205', 'conductor': 392, 'conductor_radical': 14, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/392/2/z/a/205/2'], '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': '2-392-392.205-c1-0-1', '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': '2-392-392.205-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.769218968707433, 'root_angle': 0.48184038774263116, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.11500522851580693043200069656', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '145786446957447339319438142598', 'Lhash_array': ['145786446957447339319438142598'], 'label': '2-392-392.205-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/392/2/z/a/205/2'}