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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_197.178', 'a10': [-0.2225209339563144, -0.9749279121818236], 'a2': [-0.2225209339563144, 0.9749279121818236], 'a3': [-0.2225209339563144, -0.9749279121818236], 'a4': [-0.9009688679024191, -0.4338837391175581], 'a5': [-0.9009688679024191, 0.4338837391175581], 'a6': [1.0, 0.0], 'a7': [-0.2225209339563144, -0.9749279121818236], 'a8': [0.6234898018587335, -0.7818314824680298], 'a9': [-0.9009688679024191, 0.4338837391175581], 'algebraic': True, 'analytic_conductor': 0.9148641538305795, 'analytic_normalization': 0, 'bad_lfactors': [[197, [1]]], 'bad_primes': [197], 'central_character': '197.178', 'coeff_info': ['x^7 - 1', '0.623489801858734 + 0.781831482468030*I', '\\\\zeta_{7}'], 'conductor': 197, 'conductor_radical': 197, 'conjugate': 'dirichlet_L_197.114', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^5', 'a^4', 'a^3', 'a^0', 'a^5', 'a^6', 'a^3', 'a^5', 'a^2', 'a^2', 'a^1', 'a^0', 'a^1', 'a^1', 'a^3', 'a^5', 'a^0', 'a^0', 'a^3', 'a^4', 'a^2', 'a^4', 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0.32724887216393994, 'root_number': '-0.466534753808783434484717374261+0.884502867993415740213398267169*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.327248872164', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(7)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.559311151332035434618452603061+0.208225923677846903966417755443*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.41921174856', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.60307756984', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.82333638099', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.9148641538305795, 'bad_primes': [197], 'central_character': '197.178', 'conductor': 197, 'conductor_radical': 197, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/197/178'], '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': '1-197-197.178-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': '1-197-197.178-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9148641538305795, 'root_angle': 0.32724887216393994, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41921174856', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_197.178', 'Lhash_array': ['dirichlet_L_197.178'], 'factors': ['1-197-197.178-r0-0-0'], 'label': '1-197-197.178-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/197/178'}
Lfunction data - 1-197-197.178-r0-0-0