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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_473.471', 'a10': [-0.9009688679024191, 0.4338837391175581], 'a2': [-0.9639628606958532, 0.2660368455666751], 'a3': [0.9362348706397372, -0.3513748240813427], 'a4': [0.8584487936018661, -0.5128992774059061], 'a5': [0.9839295885986297, -0.17855689479863665], 'a6': [-0.8090169943749475, 0.5877852522924731], 'a7': [0.30901699437494745, 0.9510565162951535], 'a8': [-0.6910626489868646, 0.7227948638273916], 'a9': [0.753071466003611, -0.6579387259397126], 'algebraic': True, 'analytic_conductor': 2.1966027652886506, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [43, [1]]], 'bad_primes': [11, 43], 'central_character': '473.471', 'coeff_info': ['x^35 - 1', '0.983929588598630 + 0.178556894798637*I', '\\\\zeta_{35}'], 'conductor': 473, 'conductor_radical': 473, 'conjugate': 'dirichlet_L_473.236', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^16', 'a^33', 'a^32', 'a^34', 'a^14', 'a^7', 'a^13', 'a^31', 'a^15', 0, 'a^30', 'a^6', 'a^23', 'a^32', 'a^29', 'a^29', 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'185.134177496239656247075948172845', '185.9583538882664437208442182348', '186.20312135106758796353171224276', '187.1736195061698471398568510807', '187.76538377969913771863325643705', '188.57107344299110647476104278102', '189.42386999586358468901954440963', '189.78981985042964872920504817765', '190.09826330019106498624937985145', '190.98730489514951079318542042518', '191.66220300543625639794749777513', '192.387706168058008692724114508681', '192.63547689323900674391847070021', '193.304004644022853717155397233842', '194.07606092479948735701189748019', '195.47764105379822486325772355184', '195.87527479036185969565978760398', '196.393884572961749955572679723059', '197.03246953774438851287752825522', '197.602592578909982080887753163835', '198.14743121112049277730247156403', '198.685374435213932554478928686819', '199.58740530363144906909120572501'], 'prelabel': '1-473-473.471-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1966027652886506, 'root_angle': 0.07365767561270116, 'root_number': '0.973345719077572640985675458148+0.229342780905270796282762805407*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0368288378064', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(35)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.19222232510061084716486856623+0.0765806133494795546623226509874*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.46979275934', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.07696086168', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.11146657998', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.1966027652886506, 'bad_primes': [11, 43], 'central_character': '473.471', 'conductor': 473, 'conductor_radical': 473, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/473/471'], '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': '1-473-473.471-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': '1-473-473.471-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1966027652886506, 'root_angle': 0.03682883780635058, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46979275934', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_473.471', 'Lhash_array': ['dirichlet_L_473.471'], 'label': '1-473-473.471-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/473/471'}
Lfunction data - 1-473-473.471-r0-0-0