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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_763.174', 'a10': [-0.8021231927550437, -0.5971585917027862], 'a2': [-0.984807753012208, 0.17364817766693036], 'a3': [-0.5971585917027862, 0.8021231927550437], 'a4': [0.9396926207859084, -0.3420201433256687], 'a5': [0.6862416378687336, 0.7273736415730487], 'a6': [0.44879918020046217, -0.8936326403234123], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.8660254037844386, 0.5], 'a9': [-0.28680323271109026, -0.9579895123154889], 'algebraic': True, 'analytic_conductor': 3.543357103414884, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [109, [1]]], 'bad_primes': [7, 109], 'central_character': '763.174', 'coeff_info': ['x^108 - 1', '0.998308158271268 + 0.0581448289104758*I', '\\\\zeta_{108}'], 'conductor': 763, 'conductor_radical': 763, 'conjugate': 'dirichlet_L_763.706', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^51', 'a^38', 'a^102', 'a^14', 'a^89', 0, 'a^45', 'a^76', 'a^65', 'a^97', 'a^32', 'a^23', 0, 'a^52', 'a^96', 'a^69', 'a^19', 'a^87', 'a^8', 0, 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'192.08603374100026129959708216731', '192.80171492966111996930727830406', '193.027457193491107431250451269752', '193.51664483971379878583857125761', '194.546906507838672939125271630183', '194.96751288445045410469450737845', '195.58330214140296043795383028227', '196.76636489164624929671285056183', '197.335419493957156871171287752388', '197.551983986697375841870087305417', '198.42987275381565140598469944884', '198.66553582750758852620524779216', '199.46447920148672081578853482796'], 'prelabel': '1-763-763.174-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.543357103414884, 'root_angle': 0.0978029569298259, 'root_number': '0.817053693474445114719799260189+0.576561585591485174311262716346*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0978029569298', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(108)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.682801868462221653720831206156+0.210381240500970192305351712985*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.78012224512', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.21962017513', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.21564280067', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.543357103414884, 'bad_primes': [7, 109], 'central_character': '763.174', 'conductor': 763, 'conductor_radical': 763, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/763/174'], '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': '1-763-763.174-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': '1-763-763.174-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.543357103414884, 'root_angle': 0.0978029569298259, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78012224512', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_763.174', 'Lhash_array': ['dirichlet_L_763.174'], 'factors': ['1-763-763.174-r0-0-0'], 'label': '1-763-763.174-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/763/174'}
Lfunction data - 1-763-763.174-r0-0-0