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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_571.150', 'a10': [0.7167825131684512, 0.6972968010939954], 'a2': [0.9757963826274356, 0.2186810912063758], 'a3': [-0.9264940672148018, 0.3763093719478355], 'a4': [0.9043571606975775, 0.42677643549640365], 'a5': [0.8519194088383271, 0.5236729139878779], 'a6': [-0.9863613034027223, 0.1645945902807339], 'a7': [-0.4016954246529695, 0.9157733266550574], 'a8': [0.7891405093963936, 0.6142127126896678], 'a9': [0.7167825131684512, -0.6972968010939954], 'algebraic': True, 'analytic_conductor': 2.6517128519657915, 'analytic_normalization': 0, 'bad_lfactors': [[571, [1]]], 'bad_primes': [571], 'central_character': '571.150', 'coeff_info': ['x^57 - 1', '0.993930677317949 + 0.110008220994079*I', '\\\\zeta_{57}'], 'conductor': 571, 'conductor_radical': 571, 'conjugate': 'dirichlet_L_571.453', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^25', 'a^4', 'a^5', 'a^27', 'a^18', 'a^6', 'a^50', 'a^7', 'a^31', 'a^29', 'a^22', 'a^20', 'a^30', 'a^8', 'a^8', 'a^52', 'a^25', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-571-571.150-r0-0-0', 'leading_term': '0.760799371945146882850033143212+1.66312748735744151870179457267*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/571/150', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.8288818232887565, 2.842642950906866, 4.130250079699548, 4.850266414942918, 4.35130022883571, 2.6487808206111807, 0.48856170157801715, -1.0374748141232681, -1.1661742820776506, -0.004380154657012264, 1.4891002541629188, 2.150269075806326, 1.458280847278131, -0.07162812054492819, -1.3086430245972445, -1.4387906252582212, -0.627652623628108, 0.19323669171722702, 0.2566241658849525, -0.2609449614736342, -0.4209576552908605, 0.40802715637789777, 1.6160758846616512, 1.6184009486524769, -0.6795367340839886, 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'197.80909779964277091357494987660', '198.54542451807285261438160285089', '198.85900680375754885532593205652', '199.8656829082335783200602662518'], 'prelabel': '1-571-571.150-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6517128519657915, 'root_angle': 0.7268691754358092, 'root_number': '-0.653902072022362662290776905214+0.756579196254338487996213204917*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.363434587718', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(57)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.22284417855913508591078544085+0.808895873410755434783830677256*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.95427552608', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.81339196814', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.04837940453', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.6517128519657915, 'bad_primes': [571], 'central_character': '571.150', 'conductor': 571, 'conductor_radical': 571, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/571/150'], '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': '1-571-571.150-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': '1-571-571.150-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6517128519657915, 'root_angle': 0.3634345877179046, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.95427552608', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_571.150', 'Lhash_array': ['dirichlet_L_571.150'], 'label': '1-571-571.150-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/571/150'}