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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2667.524', 'a10': [0.9009688679024191, -0.4338837391175581], 'a2': [0.9009688679024191, 0.4338837391175581], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.6234898018587335, 0.7818314824680298], 'a5': [0.6234898018587335, -0.7818314824680298], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.2225209339563144, 0.9749279121818236], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 12.385495930285055, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [127, [1]]], 'bad_primes': [3, 7, 127], 'central_character': '2667.524', 'coeff_info': ['x^14 - 1', '0.900968867902419 + 0.433883739117558*I', '\\\\zeta_{14}'], 'conductor': 2667, 'conductor_radical': 2667, 'conjugate': 'dirichlet_L_2667.1532', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 0, 'a^2', 'a^12', 0, 0, 'a^3', 0, 'a^13', 'a^13', 0, 'a^5', 0, 0, 'a^4', 'a^12', 0, 'a^7', 'a^0', 0, 'a^0', 'a^1', 0, 'a^10', 'a^6', 0, 0, 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'189.99261671022226656886250140699', '190.51485325981824284295380611010', '191.47210018788297215910379597473', '192.14399899300502212523781246509', '192.36119708633364165407549964439', '193.06602264841998598210619916842', '193.58739564876176464436030831742', '193.91742523703632102017271023334', '194.68812201941338850702275700637', '195.34143223972437795134284415982', '195.69765348589662402614736062097', '196.197192397044190878141755639495', '196.70853905921149242647611769825', '197.34381455222633982055365366426', '197.7722269691843086308801006587', '198.29823214719691064548120000728', '198.75247035127116047859080451669', '199.83178643092363261578316340807'], 'prelabel': '1-2667-2667.524-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.385495930285055, 'root_angle': 0.05264051342423494, 'root_number': '0.945799012564751521572139768740+0.324752564010726470236717979720*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0526405134242', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(14)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.08502362141122775060660195476+0.345823840292792948855122235655*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.973617251059', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.06574231828', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.76378438214', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 12.385495930285055, 'bad_primes': [3, 7, 127], 'central_character': '2667.524', 'conductor': 2667, 'conductor_radical': 2667, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2667/524'], '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': '1-2667-2667.524-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': '1-2667-2667.524-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.385495930285055, 'root_angle': 0.05264051342423494, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.973617251059', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2667.524', 'Lhash_array': ['dirichlet_L_2667.524'], 'factors': ['1-2667-2667.524-r0-0-0'], 'label': '1-2667-2667.524-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2667/524'}
Lfunction data - 1-2667-2667.524-r0-0-0