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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_77.2', 'a10': [0.5, -0.8660254037844386], 'a2': [0.10452846326765347, -0.9945218953682733], 'a3': [0.6691306063588582, 0.7431448254773942], 'a4': [-0.9781476007338057, -0.20791169081775934], 'a5': [0.9135454576426009, 0.4067366430758002], 'a6': [0.8090169943749475, -0.5877852522924731], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.30901699437494745, 0.9510565162951535], 'a9': [-0.10452846326765347, 0.9945218953682733], 'algebraic': True, 'analytic_conductor': 8.274799209186126, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '77.2', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 77, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_77.39', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^23', 'a^4', 'a^16', 'a^2', 'a^27', 0, 'a^9', 'a^8', 'a^25', 0, 'a^20', 'a^3', 0, 'a^6', 'a^2', 'a^7', 'a^1', 'a^29', 'a^18', 0, 0, 'a^20', 'a^13', 'a^4', 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'prec': 54}, 'spectral_label': 'r1-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.49840272709143647682289519707-0.141371634601358946113522408524*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.81470676097', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.10894384438', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.41551453044', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 8.274799209186126, 'bad_primes': [7, 11], 'central_character': '77.2', 'conductor': 77, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/77/2'], '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': '1-77-77.2-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': '1-77-77.2-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.274799209186126, 'root_angle': 0.006587343698751571, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.81470676097', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_77.2', 'Lhash_array': ['dirichlet_L_77.2'], 'label': '1-77-77.2-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/77/2'}
Lfunction data - 1-77-77.2-r1-0-0