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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_6001.1528', 'a10': [-1.0, -1.4081532572346456e-30], 'a2': [2.9010907910729803e-30, -1.0], 'a3': [2.9010907910729803e-30, -1.0], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [2.9010907910729803e-30, -1.0], 'a6': [-1.0, -1.4081532572346456e-30], 'a7': [-7.040766286173228e-31, 1.0], 'a8': [-7.040766286173228e-31, 1.0], 'a9': [-1.0, -1.4081532572346456e-30], 'algebraic': True, 'analytic_conductor': 27.868526838260447, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]], [353, [1]]], 'bad_primes': [17, 353], 'central_character': '6001.1528', 'coeff_info': ['x^8 - 1', '0.707106781186548 + 0.707106781186547*I', '\\\\zeta_{8}'], 'conductor': 6001, 'conductor_radical': 6001, 'conjugate': 'dirichlet_L_6001.2541', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^6', 'a^6', 'a^4', 'a^6', 'a^4', 'a^2', 'a^2', 'a^4', 'a^4', 'a^1', 'a^2', 'a^7', 'a^0', 'a^4', 'a^0', 0, 'a^2', 'a^4', 'a^2', 'a^0', 'a^7', 'a^7', 'a^0', 'a^4', 'a^5', 'a^2', 'a^6', 'a^3', 'a^2', 'a^2', 'a^6', 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0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(8)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.619693653784452284813850045610-0.684137303300358496294492331516*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.504176272176', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.61112248599', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '1.6872704135', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.868526838260447, 'bad_primes': [17, 353], 'central_character': '6001.1528', 'conductor': 6001, 'conductor_radical': 6001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6001/1528'], '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': '1-6001-6001.1528-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': '1-6001-6001.1528-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.868526838260447, 'root_angle': -0.4210125371118962, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.504176272176', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_6001.1528', 'Lhash_array': ['dirichlet_L_6001.1528'], 'label': '1-6001-6001.1528-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6001/1528'}