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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_967.109', 'a10': [0.3713879660651067, 0.9284777749962695], 'a2': [0.16510106503159225, 0.9862766540506949], 'a3': [0.8225573016153944, -0.568682236015159], 'a4': [-0.9454832766508678, 0.32567065199913], 'a5': [0.9770525020210205, -0.21299861101533926], 'a6': [0.6966830995013129, 0.7173790203715493], 'a7': [-0.2415011311261381, -0.9704005377496427], 'a8': [-0.477301656920828, -0.878739511061516], 'a9': [0.3532010288815979, -0.9355474510664762], 'algebraic': True, 'analytic_conductor': 103.91858227640239, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.109', 'coeff_info': ['x^322 - 1', '0.999809627498073 + 0.0195117595865944*I', '\\\\zeta_{322}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.346', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^72', 'a^291', 'a^144', 'a^311', 'a^41', 'a^229', 'a^216', 'a^260', 'a^61', 'a^214', 'a^113', 'a^269', 'a^301', 'a^280', 'a^288', 'a^318', 'a^10', 'a^107', 'a^133', 'a^198', 'a^286', 'a^213', 'a^185', 'a^300', 'a^19', 'a^229', 'a^51', 'a^39', 'a^30', 'a^262', 'a^38', 'a^183', 'a^68', 'a^218', 'a^82', 'a^131', 'a^179', 'a^238', 'a^205', 'a^133', 'a^270', 'a^73', 'a^36', 'a^249', 'a^285', 'a^257', 'a^257', 'a^136', 'a^50', 'a^287', 'a^91', 'a^98', 'a^301', 'a^203', 'a^123', 'a^76', 'a^111', 'a^86', 'a^102', 'a^294', 'a^12', 'a^167', 'a^110', 'a^258', 'a^255', 'a^221', 'a^140', 'a^182', 'a^290', 'a^250', 'a^154', 'a^224', 'a^203', 'a^269', 'a^251', 'a^121', 'a^310', 'a^155', 'a^277', 'a^198', 'a^205', 'a^248', 'a^20', 'a^307', 'a^145', 'a^8', 'a^108', 'a^221', 'a^321', 'a^176', 'a^35', 'a^231', 'a^7', 'a^96', 'a^7', 'a^230', 'a^208', 'a^152', 'a^122'], 'euler_factors': [[1, 'a^72'], [1, 'a^291'], [1, 'a^311'], [1, 'a^229'], [1, 'a^214'], [1, 'a^269'], [1, 'a^318'], [1, 'a^107'], [1, 'a^213'], [1, 'a^39'], [1, 'a^262'], [1, 'a^131'], [1, 'a^133'], [1, 'a^73'], [1, 'a^257'], [1, 'a^98'], [1, 'a^86'], [1, 'a^294'], [1, 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103.91858227640239, 'root_angle': -0.4825825495571631, 'root_number': '0.0546912328182095722281441093241-0.998503314492658254717179920721*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.241291274779', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(322)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.54083175079172124057545347401-0.131387502699408923061414870113*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.49536045232', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.35624115869', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.93292976045', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 103.91858227640239, 'bad_primes': [967], 'central_character': '967.109', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/109'], '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': '1-967-967.109-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': '1-967-967.109-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 103.91858227640239, 'root_angle': -0.24129127477858156, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.49536045232', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_967.109', 'Lhash_array': ['dirichlet_L_967.109'], 'label': '1-967-967.109-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/109'}