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{'Lhash': 'dirichlet_L_143.75', 'a10': [-0.5, 0.8660254037844386], 'a2': [-0.9135454576426009, 0.4067366430758002], 'a3': [0.6691306063588582, 0.7431448254773942], 'a4': [0.6691306063588582, -0.7431448254773942], 'a5': [0.8090169943749475, -0.5877852522924731], 'a6': [-0.9135454576426009, -0.4067366430758002], 'a7': [-0.6691306063588582, 0.7431448254773942], 'a8': [-0.30901699437494745, 0.9510565162951535], 'a9': [-0.10452846326765347, 0.9945218953682733], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.75', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.82', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 'a^4', 'a^26', 'a^27', 'a^17', 'a^11', 'a^9', 'a^8', 'a^10', 0, 'a^0', 0, 'a^24', 'a^1', 'a^22', 'a^2', 'a^21', 'a^29', 'a^23', 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'194.03476786042359565153774588200', '195.602304415176294559162924485418', '196.43452261163449478932298636227', '196.69320712599584282660313135941', '197.5186490838742951891469427582', '198.02910956185870786603659926027', '199.01481284781965236621297078734', '199.55464940238479365391878981858'], 'prelabel': '1-143-143.75-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.4104838370756531, 'root_number': '0.277531119652670040009847932083+0.960716647937535922395457605655*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.205241918538', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.856612422094873632611725236439+0.380280882546224955816111236409*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.77769552624', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.12643168507', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.16103319581', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.75', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/75'], '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': '1-143-143.75-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': '1-143-143.75-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.20524191853782656, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.77769552624', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_143.75', 'Lhash_array': ['dirichlet_L_143.75'], 'label': '1-143-143.75-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/75'}