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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_197.44', 'a10': [0.09602302590768176, 0.9953791129491982], 'a2': [0.5455349012105487, 0.8380881048918407], 'a3': [-0.6956825506034864, -0.7183493500977276], 'a4': [-0.40478334312239383, 0.9144126230158125], 'a5': [0.8865993063730001, 0.46253829024083526], 'a6': [0.2225209339563144, -0.9749279121818236], 'a7': [0.8380881048918407, 0.5455349012105487], 'a8': [-0.9871817834144502, 0.15959989503337924], 'a9': [-0.03205157757165517, 0.9994862162006879], 'algebraic': True, 'analytic_conductor': 21.17059018454113, 'analytic_normalization': 0, 'bad_lfactors': [[197, [1]]], 'bad_primes': [197], 'central_character': '197.44', 'coeff_info': ['x^196 - 1', '0.999486216200688 + 0.0320515775716552*I', '\\\\zeta_{196}'], 'conductor': 197, 'conductor_radical': 197, 'conjugate': 'dirichlet_L_197.103', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^31', 'a^123', 'a^62', 'a^15', 'a^154', 'a^18', 'a^93', 'a^50', 'a^46', 'a^115', 'a^185', 'a^187', 'a^49', 'a^138', 'a^124', 'a^29', 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False, 'root_analytic_conductor': 21.17059018454113, 'root_angle': 0.7242223743095498, 'root_number': '-0.647588453205884331466209947317+0.761990285551207115607450372315*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.362111187155', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(196)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.09208571330166915348447375335+0.714802993678036582022682205072*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.60183096489', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.06816446289', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.98100652535', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.17059018454113, 'bad_primes': [197], 'central_character': '197.44', 'conductor': 197, 'conductor_radical': 197, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/197/44'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-197-197.44-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-197-197.44-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.17059018454113, 'root_angle': 0.3621111871547749, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60183096489', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_197.44', 'Lhash_array': ['dirichlet_L_197.44'], 'label': '1-197-197.44-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/197/44'}