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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1183.110', 'a10': [0.8854560256532099, 0.46472317204376856], 'a2': [-0.7746049618276546, 0.6324453755953773], 'a3': [-0.5680647467311558, -0.8229838658936564], 'a4': [0.20002569377604443, -0.9797906520422677], 'a5': [-0.3919666098600751, -0.9199794436588242], 'a6': [0.9605181116313724, 0.27821746391645263], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.46472317204376856, 0.8854560256532099], 'a9': [-0.3546048870425356, 0.9350162426854148], 'algebraic': True, 'analytic_conductor': 5.493828903459774, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [13, [1]]], 'bad_primes': [7, 13], 'central_character': '1183.110', 'coeff_info': ['x^156 - 1', '0.999188998171570 + 0.0402659401094151*I', '\\\\zeta_{156}'], 'conductor': 1183, 'conductor_radical': 91, 'conjugate': 'dirichlet_L_1183.570', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^61', 'a^102', 'a^122', 'a^107', 'a^7', 0, 'a^27', 'a^48', 'a^12', 'a^147', 'a^68', 0, 0, 'a^53', 'a^88', 'a^92', 'a^109', 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'199.98672185008870747409038477685'], 'prelabel': '1-1183-1183.110-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.493828903459774, 'root_angle': -0.12766802208747668, 'root_number': '0.695154273002055550070387230428-0.718860582259859079394395536336*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.127668022087', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(156)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.622856461821765742494202541627-0.115404125523175975614319678202*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.733340430043', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.33747321839', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.55045264665', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 5.493828903459774, 'bad_primes': [7, 13], 'central_character': '1183.110', 'conductor': 1183, 'conductor_radical': 91, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1183/110'], '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': '1-1183-1183.110-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': '1-1183-1183.110-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.493828903459774, 'root_angle': -0.12766802208747668, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.733340430043', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1183.110', 'Lhash_array': ['dirichlet_L_1183.110'], 'factors': ['1-1183-1183.110-r0-0-0'], 'label': '1-1183-1183.110-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1183/110'}
Lfunction data - 1-1183-1183.110-r0-0-0