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lfunc_lfunctions • Show schema
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{'Lhash': '2111671578090517265672048726067', 'a10': [-0.19170496466188894, 0.2212393230114264], 'a2': [0.227213642826444, -0.14602134172481865], 'a3': [-0.9898214418809327, -0.14231483827328514], 'a4': [-0.8005262187564263, 1.7529079087416346], 'a5': [-1.0399649554762533, 0.305361262655297], 'a6': [-0.2456819391895057, 0.11219918217911905], 'a7': [-2.1746470855592435, 1.5069538988531432], 'a8': [0.1509469385098482, 1.0498590177674907], 'a9': [0.9594929736144974, 0.28173255684142967], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.9898214418809327, 0.14231483827328514]]], [7, [[1.0, 0], [2.1746470855592435, -1.5069538988531432]]], [23, [[1.0, 0], [0.2772899774666365, -4.787808503730758]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.34', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': 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[[1.0, 0], [0.6957524532267994, 0.20429135279425012], [69.82404322498803, 44.8731878488146]], [[1.0, 0], [1.6637545428986988, -11.571667020592594], [-85.39487465169027, -25.074197558887242]], [[1.0, 0], [7.694640611888954, -2.259350337290082], [81.60159268462458, -52.442159293192965]], [[1.0, 0], [2.7071753077000094, -9.21979239887], [-84.9666068159493, -54.60472256301536]], [[1.0, 0], [-8.38523156751358, -5.388861112961014], [42.7877463391943, 93.6920955215154]], [[1.0, 0], [5.563215460949198, -0.7998696281017348], [102.66574817675122, -30.145383582032977]], [[1.0, 0], [2.8202961212855286, -1.2879860821478504], [71.37982000003608, -82.37670360461415]], [[1.0, 0], [-4.776476090487171, -7.432341872589033], [-46.94189646921317, 102.78841547506057]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 23, 'label': '2-483-161.34-c1-0-23', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 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0.7137501432274664, 'root_number': '-0.6221734524285382 + 0.7828794256417483*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.356875071614', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.66581515262196797002659697471', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.98985926146761577686166637158', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.41920570075188841573099538546', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.34', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/r/a/34/19'], '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': '2-483-161.34-c1-0-23', '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': '2-483-161.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': 0.3568750716137332, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.66581515262196797002659697471', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2111671578090517265672048726067', 'Lhash_array': ['2111671578090517265672048726067'], 'label': '2-483-161.34-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/r/a/34/19'}