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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_571.400', 'a10': [0.37119724891822076, 0.9285540384897071], 'a2': [-0.6772815716257411, 0.7357239106731316], 'a3': [-0.34029317444164303, 0.9403193901161613], 'a4': [-0.08257934547233232, -0.9965844930066698], 'a5': [0.43175435233849296, -0.9019912301329589], 'a6': [-0.46134116297868777, -0.8872228194436118], 'a7': [-0.9950829025450114, -0.09904553025046271], 'a8': [0.7891405093963936, 0.6142127126896678], 'a9': [-0.768401110856859, -0.6399685405033165], 'algebraic': True, 'analytic_conductor': 2.6517128519657915, 'analytic_normalization': 0, 'bad_lfactors': [[571, [1]]], 'bad_primes': [571], 'central_character': '571.400', 'coeff_info': ['x^95 - 1', '0.997813627218775 + 0.0660905843256994*I', '\\\\zeta_{95}'], 'conductor': 571, 'conductor_radical': 571, 'conjugate': 'dirichlet_L_571.384', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^35', 'a^29', 'a^70', 'a^78', 'a^64', 'a^49', 'a^10', 'a^58', 'a^18', 'a^77', 'a^4', 'a^43', 'a^84', 'a^12', 'a^45', 'a^7', 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[1, 'a^63']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-571-571.400-r0-0-0', 'leading_term': '0.0293335413551150703024085079025+0.148414774295968330115870544873*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/571/400', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.1512858284101835, -0.6499369608217667, -1.1785741988108787, -1.2567629348822642, -0.3443123113663691, 1.6401285341169047, 4.048509293237732, 5.688629891161216, 5.471248340861072, 3.1739248263225743, -0.22701102016502575, -3.0140326175860648, -3.7877593527731666, -2.417868799128119, -0.1386174396881633, 1.36921526223424, 1.2493977374856509, 0.07168804565840316, -0.7683089508884143, -0.36483663233343533, 0.8290380975574455, 1.4046206648656807, 0.3555560691145302, -1.8630010258068923, -3.625894959290628, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.6517128519657915, 'bad_primes': [571], 'central_character': '571.400', 'conductor': 571, 'conductor_radical': 571, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/571/400'], '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': '1-571-571.400-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': '1-571-571.400-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6517128519657915, 'root_angle': -0.43788794221138305, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31673677332', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_571.400', 'Lhash_array': ['dirichlet_L_571.400'], 'label': '1-571-571.400-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/571/400'}