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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_539.4', 'a10': [0.8262387743159949, 0.5633200580636221], 'a2': [-0.7724169592245995, 0.6351157698421788], 'a3': [0.5256837698105047, -0.8506800656873396], 'a4': [0.19325591779555326, -0.9811483833941727], 'a5': [-0.28042738930600275, -0.9598752415428891], 'a6': [0.1342332658176555, 0.9909497617679347], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.4738686624729987, 0.880595531856738], 'a9': [-0.4473131483156326, -0.8943774076663368], 'algebraic': True, 'analytic_conductor': 2.503105476724276, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '539.4', 'coeff_info': ['x^105 - 1', '0.998210129767735 + 0.0598041539450342*I', '\\\\zeta_{105}'], 'conductor': 539, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_539.135', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^41', 'a^88', 'a^82', 'a^74', 'a^24', 0, 'a^18', 'a^71', 'a^10', 0, 'a^65', 'a^6', 0, 'a^57', 'a^59', 'a^79', 'a^7', 'a^98', 'a^51', 0, 0, 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'199.32142593182433254191334647699'], 'prelabel': '1-539-539.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.503105476724276, 'root_angle': -0.273087011197148, 'root_number': '-0.144551769665275423718740065484-0.989497238948465767681245628853*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.273087011197', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(105)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.817713992778153810379788446506-0.301943126233285751962737350498*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.727771221024', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.55184489476', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.93317831126', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.503105476724276, 'bad_primes': [7, 11], 'central_character': '539.4', 'conductor': 539, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/539/4'], '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': '1-539-539.4-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': '1-539-539.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.503105476724276, 'root_angle': -0.273087011197148, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.727771221024', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_539.4', 'Lhash_array': ['dirichlet_L_539.4'], 'factors': ['1-539-539.4-r0-0-0'], 'label': '1-539-539.4-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/539/4'}
Lfunction data - 1-539-539.4-r0-0-0