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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_731.394', 'a10': [-0.9914448613738104, -0.1305261922200516], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [0.7933533402912352, -0.6087614290087207], 'a4': [2.9010907910729803e-30, -1.0], 'a5': [0.6087614290087207, 0.7933533402912352], 'a6': [-0.1305261922200516, 0.9914448613738104], 'a7': [0.6087614290087207, -0.7933533402912352], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [0.25881904510252074, -0.9659258262890683], 'algebraic': True, 'analytic_conductor': 3.3947497281733687, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]], [43, [1]]], 'bad_primes': [17, 43], 'central_character': '731.394', 'coeff_info': ['x^48 - 1', '0.991444861373810 + 0.130526192220052*I', '\\\\zeta_{48}'], 'conductor': 731, 'conductor_radical': 731, 'conjugate': 'dirichlet_L_731.295', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^18', 'a^43', 'a^36', 'a^7', 'a^13', 'a^41', 'a^6', 'a^38', 'a^25', 'a^21', 'a^31', 'a^44', 'a^11', 'a^2', 'a^24', 0, 'a^8', 'a^34', 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'194.684533556555758649074268923706', '195.33375789533311428319373916503', '196.101948694992041315196283550074', '196.71705715044582461333966887315', '197.14563047994179754863532873354', '197.616632820268886574767736836264', '198.46373352636088163958976473398', '198.56859446910310262483877486376', '199.35141103497969256736449671788'], 'prelabel': '1-731-731.394-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3947497281733687, 'root_angle': -0.07993768524824016, 'root_number': '0.968631827981857792614393568089-0.248500265232302428235753712796*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0399688426241', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(48)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.16043374671972085954068278113+0.0266886119778585191194373731000*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.962382066399', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.00737122536', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.95101912278', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.3947497281733687, 'bad_primes': [17, 43], 'central_character': '731.394', 'conductor': 731, 'conductor_radical': 731, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/731/394'], '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': '1-731-731.394-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': '1-731-731.394-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3947497281733687, 'root_angle': -0.03996884262412008, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.962382066399', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_731.394', 'Lhash_array': ['dirichlet_L_731.394'], 'label': '1-731-731.394-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/731/394'}