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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1183.349', 'a10': [0.7994427634035012, 0.6007422642379789], 'a2': [-0.5344658261278011, -0.8451900855437947], 'a3': [-0.6927243535095994, 0.7212024473438146], 'a4': [-0.4286925614030542, 0.9034504346103823], 'a5': [-0.9350162426854148, 0.3546048870425356], 'a6': [0.9797906520422677, 0.20002569377604443], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.992708874098054, -0.12053668025532305], 'a9': [-0.040265940109415144, -0.9991889981715696], 'algebraic': True, 'analytic_conductor': 5.493828903459774, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [13, [1]]], 'bad_primes': [7, 13], 'central_character': '1183.349', 'coeff_info': ['x^156 - 1', '0.999188998171570 + 0.0402659401094151*I', '\\\\zeta_{156}'], 'conductor': 1183, 'conductor_radical': 91, 'conjugate': 'dirichlet_L_1183.461', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^103', 'a^58', 'a^50', 'a^69', 'a^5', 0, 'a^153', 'a^116', 'a^16', 'a^1', 'a^108', 0, 0, 'a^127', 'a^100', 'a^140', 'a^63', 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False, 'root_analytic_conductor': 5.493828903459774, 'root_angle': -0.3057199211045365, 'root_number': '-0.342990418169998922132681946141-0.939338902124025348431721831895*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.305719921105', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(156)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.503075710022309362633735754256-0.0853736819842245231093718581784*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.267474215233', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.49651155052', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.98307436727', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 5.493828903459774, 'bad_primes': [7, 13], 'central_character': '1183.349', 'conductor': 1183, 'conductor_radical': 91, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1183/349'], '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': '1-1183-1183.349-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': '1-1183-1183.349-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.493828903459774, 'root_angle': -0.3057199211045365, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.267474215233', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1183.349', 'Lhash_array': ['dirichlet_L_1183.349'], 'factors': ['1-1183-1183.349-r0-0-0'], 'label': '1-1183-1183.349-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1183/349'}
Lfunction data - 1-1183-1183.349-r0-0-0