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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_147.32', 'a10': [0.07473009358642425, 0.9972037971811801], 'a2': [0.9888308262251285, -0.14904226617617444], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9555728057861407, -0.2947551744109042], 'a5': [-0.07473009358642425, 0.9972037971811801], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9009688679024191, -0.4338837391175581], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 15.797343944809878, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '147.32', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 147, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_147.23', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^41', 0, 'a^40', 'a^11', 0, 0, 'a^39', 0, 'a^10', 'a^13', 0, 'a^6', 0, 0, 'a^38', 'a^37', 0, 'a^14', 'a^9', 0, 'a^12', 'a^5', 0, 'a^22', 'a^5', 0, 0, 'a^9', 0, 'a^28', 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'195.03369155104913335809972323769', '195.72671277965323910830473333823', '196.23702758730475763642626858800', '197.41889762423686908750783499700', '197.794381007011531426788833708102', '198.504392172473281722936162894398', '199.511918196957059839968848181146'], 'prelabel': '1-147-147.32-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.797343944809878, 'root_angle': 0.2585034013605442, 'root_number': '0.687966921205718681469246518198+0.725742044618282028876263223792*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.12925170068', 'prec': 44}, 'spectral_label': 'r1-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.99148040995203549470750720195+0.353171087304395091528552970266*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.79844538658', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.08138734635', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.21534623999', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 15.797343944809878, 'bad_primes': [3, 7], 'central_character': '147.32', 'conductor': 147, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/147/32'], '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': '1-147-147.32-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': '1-147-147.32-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.797343944809878, 'root_angle': 0.1292517006802721, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79844538658', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_147.32', 'Lhash_array': ['dirichlet_L_147.32'], 'label': '1-147-147.32-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/147/32'}
Lfunction data - 1-147-147.32-r1-0-0