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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_389.73', 'a10': [0.7128089045468292, 0.7013583004418992], 'a2': [0.9979028262377116, -0.06472981837443574], 'a3': [0.27183007223634287, 0.9623452664340302], 'a4': [0.9916201012264251, -0.12918813739540638], 'a5': [0.6659152250116811, 0.746027421143246], 'a6': [0.3335524316508206, 0.9427315499864342], 'a7': [-0.7351463937072004, -0.6779083860075031], 'a8': [0.981178176898239, -0.1931045964720879], 'a9': [-0.8522168236559693, 0.5231887665821301], 'algebraic': True, 'analytic_conductor': 1.8065084052796723, 'analytic_normalization': 0, 'bad_lfactors': [[389, [1]]], 'bad_primes': [389], 'central_character': '389.73', 'coeff_info': ['x^97 - 1', '0.997902826237712 + 0.0647298183744357*I', '\\\\zeta_{97}'], 'conductor': 389, 'conductor_radical': 389, 'conjugate': 'dirichlet_L_389.16', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^96', 'a^20', 'a^95', 'a^13', 'a^19', 'a^60', 'a^94', 'a^40', 'a^12', 'a^22', 'a^18', 'a^65', 'a^59', 'a^33', 'a^93', 'a^12', 'a^39', 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47}, 'spectral_label': 'r0-0', 'st_group': 'mu(97)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.95072298296500629827934969111+0.756719725568364347483774852603*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.00223232991', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.11073042432', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.79820442488', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8065084052796723, 'bad_primes': [389], 'central_character': '389.73', 'conductor': 389, 'conductor_radical': 389, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/389/73'], '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': '1-389-389.73-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': '1-389-389.73-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8065084052796723, 'root_angle': 0.19247803293171648, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.00223232991', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_389.73', 'Lhash_array': ['dirichlet_L_389.73'], 'label': '1-389-389.73-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/389/73'}