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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_367.135', 'a10': [-0.9357168190404936, 0.3527520865490948], 'a2': [-0.9880878960910772, -0.15389057670406178], 'a3': [0.4239143907098607, -0.9057022630804715], 'a4': [0.9526353808033825, 0.3041148323275179], 'a5': [0.8702852410301553, -0.4925480679538644], 'a6': [-0.5582437220268648, 0.8296770135526189], 'a7': [0.6792733388972931, 0.7338853664321991], 'a8': [-0.8944870822287956, -0.4470937929851139], 'a9': [-0.6405931786981751, -0.7678804460366], 'algebraic': True, 'analytic_conductor': 1.7043408348011304, 'analytic_normalization': 0, 'bad_lfactors': [[367, [1]]], 'bad_primes': [367], 'central_character': '367.135', 'coeff_info': ['x^61 - 1', '0.994699875614589 + 0.102820997137360*I', '\\\\zeta_{61}'], 'conductor': 367, 'conductor_radical': 367, 'conjugate': 'dirichlet_L_367.87', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^32', 'a^50', 'a^3', 'a^56', 'a^21', 'a^8', 'a^35', 'a^39', 'a^27', 'a^7', 'a^53', 'a^39', 'a^40', 'a^45', 'a^6', 'a^30', 'a^10', 'a^41', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-367-367.135-r0-0-0', 'leading_term': '0.871636148543057117233142077926-0.783779155753192179243532661734*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/367/135', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.172202772748879, 1.0019108341540217, 0.6993135224027192, 0.12892400319560948, -0.4633480212299633, -0.7103108338814292, -0.44111370924799465, 0.09684582030292156, 0.27348566098600025, -0.5739332566442722, -2.633248218027471, -5.285190563532229, -7.25380422513798, -7.271076168081399, -4.906481700178238, -1.0017143552259473, 2.6769561979625047, 4.448740204541353, 3.760750128104564, 1.5256122618851484, -0.5342489108823467, -1.098332207114293, -0.12713451800751316, 1.2575952857013495, 1.7804537383858783, 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'unitary', 'types': ['DIR'], 'values': [[1, '0.884485411826608395639602288294-0.411338300782285785501985701343*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.00008809498', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.12821687966', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.65859579932', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7043408348011304, 'bad_primes': [367], 'central_character': '367.135', 'conductor': 367, 'conductor_radical': 367, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/367/135'], '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': '1-367-367.135-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': '1-367-367.135-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7043408348011304, 'root_angle': -0.23312233995990403, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00008809498', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_367.135', 'Lhash_array': ['dirichlet_L_367.135'], 'label': '1-367-367.135-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/367/135'}