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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_539.267', 'a10': [-0.9009688679024191, 0.4338837391175581], 'a2': [-0.5508969814521025, -0.8345732537213026], 'a3': [0.9839295885986297, -0.17855689479863665], 'a4': [-0.3930250316539236, 0.9195277725514507], 'a5': [0.1342332658176555, -0.9909497617679347], 'a6': [-0.6910626489868646, -0.7227948638273916], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9839295885986297, -0.17855689479863665], 'a9': [0.9362348706397372, -0.3513748240813427], 'algebraic': True, 'analytic_conductor': 2.503105476724276, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '539.267', 'coeff_info': ['x^35 - 1', '0.983929588598630 + 0.178556894798637*I', '\\\\zeta_{35}'], 'conductor': 539, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_539.323', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^23', 'a^34', 'a^11', 'a^27', 'a^22', 0, 'a^34', 'a^33', 'a^15', 0, 'a^10', 'a^23', 0, 'a^26', 'a^22', 'a^17', 'a^21', 'a^14', 'a^3', 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'primitive': True, 'rational': False, 'root_analytic_conductor': 2.503105476724276, 'root_angle': -0.4139878187348248, 'root_number': '-0.857487279948126642588455284909-0.514505164917868524500769795193*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.413987818735', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(35)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.785565454668957997433817439790-0.672614065750182694739424040252*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.677799339102', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.97728592752', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.67855062917', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.503105476724276, 'bad_primes': [7, 11], 'central_character': '539.267', 'conductor': 539, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/539/267'], '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': '1-539-539.267-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': '1-539-539.267-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.503105476724276, 'root_angle': -0.4139878187348248, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.677799339102', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_539.267', 'Lhash_array': ['dirichlet_L_539.267'], 'factors': ['1-539-539.267-r0-0-0'], 'label': '1-539-539.267-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/539/267'}
Lfunction data - 1-539-539.267-r0-0-0