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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_6025.739', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.9781476007338057, -0.20791169081775934], 'a3': [-0.9135454576426009, 0.4067366430758002], 'a4': [0.9135454576426009, -0.4067366430758002], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.8090169943749475, 0.5877852522924731], 'a7': [-0.5, -0.8660254037844386], 'a8': [0.8090169943749475, -0.5877852522924731], 'a9': [0.6691306063588582, -0.7431448254773942], 'algebraic': True, 'analytic_conductor': 27.979982369691584, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [241, [1]]], 'bad_primes': [5, 241], 'central_character': '6025.739', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 6025, 'conductor_radical': 1205, 'conjugate': 'dirichlet_L_6025.3359', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^29', 'a^13', 'a^28', 0, 'a^12', 'a^20', 'a^27', 'a^26', 0, 'a^29', 'a^11', 'a^16', 'a^19', 0, 'a^26', 'a^12', 'a^25', 'a^17', 0, 'a^3', 'a^28', 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27.979982369691584, 'root_angle': -0.9496219985149987, 'root_number': '-0.987501874107927224141741372939-0.157607260725296065901792963962*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.16372477899321235962777083364-0.369131861175479967314933438127*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.219293645734', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.15824526952', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.11940405562', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 27.979982369691584, 'bad_primes': [5, 241], 'central_character': '6025.739', 'conductor': 6025, 'conductor_radical': 1205, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6025/739'], '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': '1-6025-6025.739-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': '1-6025-6025.739-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.979982369691584, 'root_angle': -0.47481099925749937, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.219293645734', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_6025.739', 'Lhash_array': ['dirichlet_L_6025.739'], 'label': '1-6025-6025.739-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6025/739'}
Lfunction data - 1-6025-6025.739-r0-0-0