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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_287.167', 'a10': [-1.0, -1.4081532572346456e-30], 'a2': [2.9010907910729803e-30, -1.0], 'a3': [0.7071067811865476, 0.7071067811865476], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [2.9010907910729803e-30, -1.0], 'a6': [0.7071067811865476, -0.7071067811865476], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-7.040766286173228e-31, 1.0], 'a9': [-7.040766286173228e-31, 1.0], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.167', 'coeff_info': ['x^8 - 1', '0.707106781186548 + 0.707106781186547*I', '\\\\zeta_{8}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.55', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^6', 'a^1', 'a^4', 'a^6', 'a^7', 0, 'a^2', 'a^2', 'a^4', 'a^1', 'a^5', 'a^1', 0, 'a^7', 'a^0', 'a^7', 'a^0', 'a^7', 'a^2', 0, 'a^7', 'a^4', 'a^3', 'a^4', 'a^7', 'a^3', 0, 'a^5', 'a^5', 'a^0', 'a^6', 'a^2', 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'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': -0.13695617861466294, 'root_number': '0.652042506355606945154446966867-0.758182412025957165393761212363*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.136956178615', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(8)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.19876539888693962191889693702-0.425971089645024407706327858899*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.29189474459', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.47983555451', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.89337955594', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.167', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/167'], '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': '1-287-287.167-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': '1-287-287.167-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': -0.13695617861466294, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29189474459', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_287.167', 'Lhash_array': ['dirichlet_L_287.167'], 'factors': ['1-287-287.167-r0-0-0'], 'label': '1-287-287.167-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/167'}
Lfunction data - 1-287-287.167-r0-0-0