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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_547.209', 'a10': [0.8130560994785325, -0.5821853477207707], 'a2': [-0.9521176659107141, -0.3057318273597529], 'a3': [-0.2225209339563144, -0.9749279121818236], 'a4': [0.8130560994785325, 0.5821853477207707], 'a5': [-0.5961324854692254, 0.8028860814388825], 'a6': [-0.0862003798806194, 0.9962778199420265], 'a7': [-0.8326664226872064, -0.5537748897605331], 'a8': [-0.5961324854692254, -0.8028860814388825], 'a9': [-0.9009688679024191, 0.4338837391175581], 'algebraic': True, 'analytic_conductor': 2.540257320534655, 'analytic_normalization': 0, 'bad_lfactors': [[547, [1]]], 'bad_primes': [547], 'central_character': '547.209', 'coeff_info': ['x^91 - 1', '0.997617272301248 + 0.0689911444043249*I', '\\\\zeta_{91}'], 'conductor': 547, 'conductor_radical': 547, 'conjugate': 'dirichlet_L_547.212', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^50', 'a^65', 'a^9', 'a^32', 'a^24', 'a^54', 'a^59', 'a^39', 'a^82', 'a^42', 'a^74', 'a^13', 'a^13', 'a^6', 'a^18', 'a^88', 'a^89', 'a^34', 'a^41', 'a^28', 'a^1', 'a^90', 'a^33', 'a^64', 'a^63', 'a^13', 'a^63', 'a^66', 'a^56', 'a^44', 'a^68', 'a^16', 'a^47', 'a^86', 'a^48', 'a^53', 'a^84', 'a^78', 'a^0', 'a^0', 'a^78', 'a^61', 'a^51', 'a^71', 'a^49', 'a^14', 'a^83', 'a^17', 'a^23', 'a^62', 'a^22', 'a^6', 'a^63', 'a^74', 'a^22', 'a^8', 'a^25', 'a^70', 'a^15', 'a^11', 'a^3', 'a^2', 'a^27', 'a^45', 'a^66', 'a^74', 'a^6', 'a^64', 'a^45', 'a^60', 'a^7', 'a^85', 'a^12', 'a^38', 'a^43', 'a^5', 'a^37', 'a^61', 'a^50', 'a^78', 'a^50', 'a^84', 'a^37', 'a^29', 'a^20', 'a^40', 'a^10', 'a^80', 'a^30', 'a^67', 'a^8', 'a^18', 'a^64', 'a^66', 'a^42', 'a^62', 'a^67', 'a^81', 'a^73'], 'euler_factors': [[1, 'a^50'], [1, 'a^65'], [1, 'a^32'], [1, 'a^54'], [1, 'a^42'], [1, 'a^13'], [1, 'a^88'], [1, 'a^34'], [1, 'a^90'], [1, 'a^66'], [1, 'a^44'], [1, 'a^53'], [1, 'a^0'], [1, 'a^61'], [1, 'a^14'], [1, 'a^6'], [1, 'a^70'], [1, 'a^11'], [1, 'a^74'], [1, 'a^60'], [1, 'a^85'], [1, 'a^61'], [1, 'a^84'], [1, 'a^80'], [1, 'a^62'], [1, 'a^46']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-547-547.209-r0-0-0', 'leading_term': '0.326296523912842400823056029177-0.315925348875663810805302832891*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/547/209', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.45417865161169113, 0.22120177810726788, -0.2589331839482345, -0.9100934665257772, -1.3217878112668366, -1.085924939207127, -0.18239817470086456, 0.8675587346157351, 1.27133168991862, 0.5700412023315073, -0.8314373403689906, -1.6968980469458295, -0.7096464266174132, 2.478003206364971, 6.69088173308353, 9.74669305953928, 9.843730683308834, 6.859023828711946, 2.5183372753727724, -0.7972782040361324, -1.734232615544495, -0.7968644338680341, 0.3469766598575573, 0.44923800493180827, -0.278261441173729, -0.6009909641345603, 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'primitive': True, 'rational': False, 'root_analytic_conductor': 2.540257320534655, 'root_angle': -0.4897201862583088, 'root_number': '0.0322893738605040975062650040078-0.999478562219168658200135300318*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.244860093129', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(91)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.469830729562748423455775057145-0.164820381194190530940852384607*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.479882747826', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.92619407703', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.94573703386', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.540257320534655, 'bad_primes': [547], 'central_character': '547.209', 'conductor': 547, 'conductor_radical': 547, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/547/209'], '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': '1-547-547.209-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': '1-547-547.209-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.540257320534655, 'root_angle': -0.2448600931291544, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.479882747826', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_547.209', 'Lhash_array': ['dirichlet_L_547.209'], 'label': '1-547-547.209-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/547/209'}
Lfunction data - 1-547-547.209-r0-0-0