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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_517.175', 'a10': [-0.9629172873477992, -0.2697967711570243], 'a2': [0.33487961217098616, -0.9422609221188205], 'a3': [0.20345601305263378, -0.9790840876823229], 'a4': [-0.7757112907044198, -0.6310879443260528], 'a5': [-0.06824241336467098, -0.9976687691905392], 'a6': [-0.8544194045464886, -0.5195839500354336], 'a7': [0.5766803221148672, 0.816969893010442], 'a8': [-0.8544194045464886, 0.5195839500354336], 'a9': [-0.917211301505453, -0.39840108984624145], 'algebraic': True, 'analytic_conductor': 55.55936611882114, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [47, [1]]], 'bad_primes': [11, 47], 'central_character': '517.175', 'coeff_info': ['x^46 - 1', '0.990685946036331 + 0.136166649096247*I', '\\\\zeta_{46}'], 'conductor': 517, 'conductor_radical': 517, 'conjugate': 'dirichlet_L_517.65', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^37', 'a^36', 'a^28', 'a^34', 'a^27', 'a^7', 'a^19', 'a^26', 'a^25', 0, 'a^18', 'a^29', 'a^44', 'a^24', 'a^10', 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'199.49000448869132755790282644279'], 'prelabel': '1-517-517.175-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 55.55936611882114, 'root_angle': 0.12337266846339774, 'root_number': '0.925823886082265936306873612339+0.377955198349660837574792636952*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0616863342317', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(46)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.553043722272075958962172434638-0.780031359488153141897288513013*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0112113906854', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.16502532022', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.08785779432', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 55.55936611882114, 'bad_primes': [11, 47], 'central_character': '517.175', 'conductor': 517, 'conductor_radical': 517, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/517/175'], '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': '1-517-517.175-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': '1-517-517.175-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 55.55936611882114, 'root_angle': 0.06168633423169887, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0112113906854', 'prec': 50}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_517.175', 'Lhash_array': ['dirichlet_L_517.175'], 'label': '1-517-517.175-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/517/175'}