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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_143.82', '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': '143.82', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.75', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^17', 'a^26', 'a^4', 'a^3', 'a^13', 'a^19', 'a^21', 'a^22', 'a^20', 0, 'a^0', 0, 'a^6', 'a^29', 'a^8', 'a^28', 'a^9', 'a^1', 'a^7', 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'192.591955900198177443635542040963', '193.13297056030613771708987011647', '194.14585791646189241094653987415', '194.5205048656123043152323911006', '195.82069290196760515269185970211', '196.75509127026645775139575724379', '197.198036389736172444435920060058', '197.940720172706088913000432174587', '198.25700791418727738995227427534', '199.44224398550056032112009219142'], 'prelabel': '1-143-143.82-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': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.856612422094873632611725236439-0.380280882546224955816111236409*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.19913635269', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.59806631602', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.51469234855', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.82', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/82'], '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': '1-143-143.82-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': '1-143-143.82-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': '1.19913635269', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_143.82', 'Lhash_array': ['dirichlet_L_143.82'], 'label': '1-143-143.82-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/82'}
Lfunction data - 1-143-143.82-r0-0-0