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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1183.1060', 'a10': [-0.9199794436588242, -0.3919666098600751], 'a2': [0.46472317204376856, 0.8854560256532099], 'a3': [-0.27821746391645263, 0.9605181116313724], 'a4': [-0.5680647467311558, 0.8229838658936564], 'a5': [-0.7746049618276546, 0.6324453755953773], 'a6': [-0.9797906520422677, 0.20002569377604443], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.992708874098054, -0.12053668025532305], 'a9': [-0.8451900855437947, -0.5344658261278011], 'algebraic': True, 'analytic_conductor': 5.493828903459774, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [13, [1]]], 'bad_primes': [7, 13], 'central_character': '1183.1060', 'coeff_info': ['x^156 - 1', '0.999188998171570 + 0.0402659401094151*I', '\\\\zeta_{156}'], 'conductor': 1183, 'conductor_radical': 91, 'conjugate': 'dirichlet_L_1183.327', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^27', 'a^46', 'a^54', 'a^61', 'a^73', 0, 'a^81', 'a^92', 'a^88', 'a^25', 'a^100', 0, 0, 'a^107', 'a^108', 'a^120', 'a^119', 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'1-1183-1183.1060-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.493828903459774, 'root_angle': -0.014880918349701447, 'root_number': '0.998907427869207633580111170311-0.0467327566886841019354497565873*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00744045917485', 'prec': 57}, 'spectral_label': 'r0-0', 'st_group': 'mu(156)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.477550831140472763762688387310+0.591138311919130508855484168636*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0738683731099', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '2.45068721104', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.53907907782', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.493828903459774, 'bad_primes': [7, 13], 'central_character': '1183.1060', 'conductor': 1183, 'conductor_radical': 91, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1183/1060'], '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': '1-1183-1183.1060-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1183-1183.1060-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.493828903459774, 'root_angle': -0.007440459174850723, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0738683731099', 'prec': 50}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1183.1060', 'Lhash_array': ['dirichlet_L_1183.1060'], 'label': '1-1183-1183.1060-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1183/1060'}