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lfunc_lfunctions • Show schema
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{'Lhash': '3713897836434516655242622423440', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.5, -0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [-0.5, -2.179449471770337], 'a6': [0.0, 0.0], 'a7': [-1.1374586088176875, -2.3887628415618263], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1179056282979258, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.5, 2.179449471770337]]], [7, [[1.0, 0], [1.1374586088176875, 2.3887628415618263]]]], 'bad_primes': [2, 5, 7], 'central_character': '140.9', 'coefficient_field': 'CDF', 'conductor': 140, 'conductor_radical': 70, 'conjugate': '2157388793333706673986657317396', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5, 0.8660254037844386], [1.5, -2.598076211353316]], [[1.0, 0], [0.5, 2.179449471770337]], [[1.0, 0], [1.1374586088176875, 2.3887628415618263]], [[1.0, 0], [-2.6374586088176875, 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[3.04983443527075, -1.7608227321873575], [33.5, -58.023702053557386]], [[1.0, 0], [4.54983443527075, 0], [71.0, 0]], [[1.0, 0], [-5.6374586088176875, 3.254788245346265], [36.5, -63.21985447626402]], [[1.0, 0], [-3.6374586088176875, 6.3002631209010405], [-39.5, -68.41600689897065]], [[1.0, 0], [0, 7.404373819095449], [-83.0, 0]], [[1.0, 0], [3.5, -6.06217782649107], [-44.5, -77.07626093681505]], [[1.0, 0], [0, -6.928203230275509], [-97.0, 0]], [[1.0, 0], [-6.774917217635375, -11.734500838017642], [-50.5, 87.4685657822283]], [[1.0, 0], [9.774917217635375, 5.643551086908091], [51.5, 89.20061658979718]], [[1.0, 0], [-3.04983443527075, -1.7608227321873575], [53.5, 92.66471820493493]], [[1.0, 0], [5.774917217635375, 10.002450030448765], [-54.5, 94.39676901250381]], [[1.0, 0], [0, -4.301355094303713], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-140-35.9-c1-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/140/2/q/b/9/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.319526687641637, 1.37620366101361, 1.4483382581385649, 1.5354583777716615, 1.6353876628541408, 1.7445149120619805, 1.8580924064248294, 1.9705055091481463, 2.075508371360245, 2.166450915621467, 2.2365284398940295, 2.2790772026586206, 2.2879263259428706, 2.257803025105753, 2.184776170472197, 2.0667128440110676, 1.9037139938831693, 1.6984888149430932, 1.4566236311271692, 1.186700501496285, 0.9002241898356603, 0.6113240546110936, 0.3362100715767471, 0.09237942779874145, -0.10240874383917922, -0.23134910402051417, -0.27993019702037325, -0.23730935509377313, -0.09761338087678059, 0.1389568927057555, 0.46534370581081214, 0.8672889556271128, 1.323527628041497, 1.806581990388922, 2.2841750582868703, 2.721227037738753, 3.082338235165216, 3.334601646305556, 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1.0573105637881075, 'root_angle': 0.26658603252714985, 'root_number': '0.6693188380525552 + 0.74297529772394*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.133293016264', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.92974880914809004783737323761', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.55780134359169229725739791947', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.67768649321110556795598673553', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1179056282979258, 'bad_primes': [2, 5, 7], 'central_character': '35.9', 'conductor': 140, 'conductor_radical': 70, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/140/2/q/b/9/1'], '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': '2-140-35.9-c1-0-3', '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': '2-140-35.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0573105637881075, 'root_angle': 0.13329301626357493, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.92974880914809004783737323761', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3713897836434516655242622423440', 'Lhash_array': ['3713897836434516655242622423440'], 'label': '2-140-35.9-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/140/2/q/b/9/1'}