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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_403.178', 'a10': [-0.10452846326765347, 0.9945218953682733], 'a2': [-0.10452846326765347, 0.9945218953682733], 'a3': [-0.9135454576426009, -0.4067366430758002], 'a4': [-0.9781476007338057, -0.20791169081775934], 'a5': [1.0, 0.0], 'a6': [0.5, -0.8660254037844386], 'a7': [-0.9781476007338057, -0.20791169081775934], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [0.6691306063588582, 0.7431448254773942], 'algebraic': True, 'analytic_conductor': 43.30836469223389, 'analytic_normalization': 0, 'bad_lfactors': [[13, [1]], [31, [1]]], 'bad_primes': [13, 31], 'central_character': '403.178', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 403, 'conductor_radical': 403, 'conjugate': 'dirichlet_L_403.120', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 'a^17', 'a^16', 'a^0', 'a^25', 'a^16', 'a^24', 'a^4', 'a^8', 'a^11', 'a^3', 0, 'a^24', 'a^17', 'a^2', 'a^19', 'a^12', 'a^28', 'a^16', 'a^3', 'a^19', 'a^29', 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50}, 'spectral_label': 'r1-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.595990730297998137606405352827+0.232469155951345806101629895553*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.11916401882', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.76043446077', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.65778092005', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 43.30836469223389, 'bad_primes': [13, 31], 'central_character': '403.178', 'conductor': 403, 'conductor_radical': 403, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/403/178'], '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': '1-403-403.178-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': '1-403-403.178-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 43.30836469223389, 'root_angle': -0.46771807783081093, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11916401882', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_403.178', 'Lhash_array': ['dirichlet_L_403.178'], 'label': '1-403-403.178-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/403/178'}
Lfunction data - 1-403-403.178-r1-0-0