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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_920.37', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9898214418809327, -0.14231483827328514], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.7557495743542583, 0.6548607339452851], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9594929736144974, 0.28173255684142967], 'algebraic': True, 'analytic_conductor': 4.272462038193569, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [23, [1]]], 'bad_primes': [2, 5, 23], 'central_character': '920.37', 'coeff_info': ['x^44 - 1', '0.989821441880933 + 0.142314838273285*I', '\\\\zeta_{44}'], 'conductor': 920, 'conductor_radical': 230, 'conjugate': 'dirichlet_L_920.373', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^23', 0, 0, 0, 'a^17', 0, 'a^2', 0, 'a^48', 0, 'a^27', 0, 0, 0, 'a^41', 0, 'a^58', 0, 'a^40', 0, 0, 0, 0, 0, 'a^25', 0, 'a^52', 0, 'a^32', 0, 'a^27', 0, 0, 0, 'a^35', 0, 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'194.53856928034421949692669052116', '195.50885644326431918775461073007', '195.83588295965245940310567327133', '196.31628716315561646676474020207', '196.98561471161721090475760852751', '197.955962859315223094023034633983', '198.405676540767788207878367011001', '199.05454815679735933356411217683', '199.70012944686043596116440930341'], 'prelabel': '1-920-920.37-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.272462038193569, 'root_angle': 0.4888471322035767, 'root_number': '0.0350305989848178965204819990355+0.999386240216846729504041400074*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.244423566102', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(44)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.705535640161198032367001095908+0.113333063532451001058527634412*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.09704264079', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.31078807063', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.50717583951', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.272462038193569, 'bad_primes': [2, 5, 23], 'central_character': '920.37', 'conductor': 920, 'conductor_radical': 230, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/920/37'], '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': '1-920-920.37-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': '1-920-920.37-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.272462038193569, 'root_angle': 0.24442356610178834, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09704264079', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_920.37', 'Lhash_array': ['dirichlet_L_920.37'], 'label': '1-920-920.37-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/920/37'}