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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_552.125', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.6548607339452851, 0.7557495743542583], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8412535328311812, -0.5406408174555976], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.5634772229161418, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [23, [1]]], 'bad_primes': [2, 3, 23], 'central_character': '552.125', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 552, 'conductor_radical': 138, 'conjugate': 'dirichlet_L_552.53', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^25', 0, 'a^13', 0, 0, 0, 'a^27', 0, 'a^31', 0, 0, 0, 'a^10', 0, 'a^12', 0, 0, 0, 0, 0, 'a^6', 0, 0, 0, 'a^32', 0, 'a^18', 0, 0, 0, 'a^16', 0, 'a^30', 0, 0, 0, 'a^3', 0, 'a^26', 0, 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'st_group': 'mu(22)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.806981751434094455568123185065+0.243582871378982974310739622576*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.83514330821', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.65862197424', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.92012107301', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.5634772229161418, 'bad_primes': [2, 3, 23], 'central_character': '552.125', 'conductor': 552, 'conductor_radical': 138, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/552/125'], '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': '1-552-552.125-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': '1-552-552.125-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5634772229161418, 'root_angle': 0.39034249926613496, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.83514330821', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_552.125', 'Lhash_array': ['dirichlet_L_552.125'], 'label': '1-552-552.125-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/552/125'}
Lfunction data - 1-552-552.125-r0-0-0