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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_173.88', 'a10': [0.957600599908406, 0.2880990993652376], 'a2': [0.5818589155579529, 0.8132897407355654], 'a3': [0.8720494081438076, 0.4894178478110855], 'a4': [-0.3228804047714462, 0.9464397731576093], 'a5': [0.7914964884292541, -0.6111737140978493], 'a6': [0.10937120837787438, 0.9940009752399459], 'a7': [-0.6396730215588913, 0.768647139778532], 'a8': [-0.957600599908406, 0.2880990993652376], 'a9': [0.5209403404879303, 0.8535930890373464], 'algebraic': True, 'analytic_conductor': 0.803408622399443, 'analytic_normalization': 0, 'bad_lfactors': [[173, [1]]], 'bad_primes': [173], 'central_character': '173.88', 'coeff_info': ['x^86 - 1', '0.997332283663552 + 0.0729953146609075*I', '\\\\zeta_{86}'], 'conductor': 173, 'conductor_radical': 173, 'conjugate': 'dirichlet_L_173.116', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 'a^7', 'a^26', 'a^77', 'a^20', 'a^31', 'a^39', 'a^14', 'a^4', 'a^41', 'a^33', 'a^56', 'a^44', 'a^84', 'a^52', 'a^3', 'a^27', 'a^85', 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'-0.243340511598507004744322768078+0.969940923672662075340741780520*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.289121623085', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(86)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.37685902545694221058985025209+1.01885390341561638435705199304*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.46669465081', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.38913041099', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.13253514175', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.803408622399443, 'bad_primes': [173], 'central_character': '173.88', 'conductor': 173, 'conductor_radical': 173, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/173/88'], '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': '1-173-173.88-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': '1-173-173.88-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.803408622399443, 'root_angle': 0.2891216230848308, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.46669465081', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_173.88', 'Lhash_array': ['dirichlet_L_173.88'], 'label': '1-173-173.88-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/173/88'}