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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_441.283', 'a10': [0.7330518718298263, -0.6801727377709194], 'a2': [0.8262387743159949, 0.5633200580636221], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.36534102436639504, 0.9308737486442042], 'a5': [0.2225209339563144, -0.9749279121818236], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.2225209339563144, 0.9749279121818236], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 47.39203183442964, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '441.283', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 441, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_441.187', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 0, 'a^8', 'a^33', 0, 0, 'a^12', 0, 'a^37', 'a^18', 0, 'a^25', 0, 0, 'a^16', 'a^13', 0, 'a^35', 'a^41', 0, 'a^22', 'a^36', 0, 'a^24', 'a^29', 0, 0, 'a^20', 0, 'a^35', 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'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.23360559137732431501801183042+0.226210471163142155428491109710*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0940170604698', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.95681843511', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.06152936734', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 47.39203183442964, 'bad_primes': [3, 7], 'central_character': '441.283', 'conductor': 441, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/441/283'], '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': '1-21e2-441.283-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': '1-21e2-441.283-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 47.39203183442964, 'root_angle': -0.3463718820861678, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0940170604698', 'prec': 50}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_441.283', 'Lhash_array': ['dirichlet_L_441.283'], 'label': '1-21e2-441.283-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/441/283'}
Lfunction data - 1-21e2-441.283-r1-0-0