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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_763.149', 'a10': [-0.9983081582712682, -0.05814482891047583], 'a2': [0.984807753012208, 0.17364817766693036], 'a3': [-0.05814482891047583, 0.9983081582712682], 'a4': [0.9396926207859084, 0.3420201433256687], 'a5': [-0.993238357741943, 0.11609291412523023], 'a6': [-0.23061587074244017, 0.9730448705798238], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.8660254037844386, 0.5], 'a9': [-0.993238357741943, -0.11609291412523023], 'algebraic': True, 'analytic_conductor': 81.99573761829889, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [109, [1]]], 'bad_primes': [7, 109], 'central_character': '763.149', 'coeff_info': ['x^108 - 1', '0.998308158271268 + 0.0581448289104758*I', '\\\\zeta_{108}'], 'conductor': 763, 'conductor_radical': 763, 'conjugate': 'dirichlet_L_763.466', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^3', 'a^28', 'a^6', 'a^52', 'a^31', 0, 'a^9', 'a^56', 'a^55', 'a^17', 'a^34', 'a^25', 0, 'a^80', 'a^12', 'a^3', 'a^59', 'a^21', 'a^58', 0, 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'194.43748645502708282439247248036', '195.26714163581363207169189221598', '195.70202380348823817898874972769', '196.12241953021845148073775082834', '197.24322920421061232347293995207', '197.82998818792476839001234455010', '198.06493654312420054915234848386', '198.87377558434012207425639310722', '199.295435857261112994897091507406'], 'prelabel': '1-763-763.149-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 81.99573761829889, 'root_angle': 0.49605395388759554, 'root_number': '-0.999692650999509669139668362274+0.0247911987925666740086928864981*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.496053953888', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(108)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.28374550436459632466863898788+1.13925164818298491140472211431*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.5533501354', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '3.04744509373', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.79313254864', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 81.99573761829889, 'bad_primes': [7, 109], 'central_character': '763.149', 'conductor': 763, 'conductor_radical': 763, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/763/149'], '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': '1-763-763.149-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-763-763.149-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 81.99573761829889, 'root_angle': 0.49605395388759554, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.5533501354', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_763.149', 'Lhash_array': ['dirichlet_L_763.149'], 'factors': ['1-763-763.149-r1-0-0'], 'label': '1-763-763.149-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/763/149'}
Lfunction data - 1-763-763.149-r1-0-0