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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_147.5', 'a10': [0.9888308262251285, -0.14904226617617444], 'a2': [-0.9555728057861407, 0.2947551744109042], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.8262387743159949, -0.5633200580636221], 'a5': [-0.9888308262251285, -0.14904226617617444], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.6234898018587335, 0.7818314824680298], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.6826651300157116, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '147.5', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 147, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_147.59', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^19', 0, 'a^38', 'a^22', 0, 0, 'a^15', 0, 'a^41', 'a^5', 0, 'a^33', 0, 0, 'a^34', 'a^32', 0, 'a^7', 'a^18', 0, 'a^24', 'a^31', 0, 'a^2', 'a^10', 0, 0, 'a^39', 0, 'a^35', 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'195.926490025782092093226921534753', '196.60483463891181650314575452105', '197.49935076563271792228001467229', '198.410174719887098838786762746604', '198.611327293762812914137581681204', '199.64485183675844217861288807074'], 'prelabel': '1-147-147.5-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6826651300157116, 'root_angle': -0.0782312925170068, 'root_number': '0.969950061278416807934283432993-0.243304086743308689627615364703*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0391156462585', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.655286889023328179356500871076+0.000936243775465598070667380590864*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.933619498113', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.83591344808', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.49470973844', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.6826651300157116, 'bad_primes': [3, 7], 'central_character': '147.5', 'conductor': 147, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/147/5'], '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': '1-147-147.5-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': '1-147-147.5-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6826651300157116, 'root_angle': -0.0391156462585034, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.933619498113', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_147.5', 'Lhash_array': ['dirichlet_L_147.5'], 'label': '1-147-147.5-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/147/5'}
Lfunction data - 1-147-147.5-r0-0-0