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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_113.100', 'a10': [0.5320320765153366, 0.8467241992282841], 'a2': [-0.6234898018587335, 0.7818314824680298], 'a3': [-0.3302790619551671, -0.9438833303083676], 'a4': [-0.2225209339563144, -0.9749279121818236], 'a5': [0.3302790619551671, -0.9438833303083676], 'a6': [0.9438833303083676, 0.3302790619551671], 'a7': [-0.9009688679024191, -0.4338837391175581], 'a8': [0.9009688679024191, 0.4338837391175581], 'a9': [-0.7818314824680298, 0.6234898018587335], 'algebraic': True, 'analytic_conductor': 0.5247697938216015, 'analytic_normalization': 0, 'bad_lfactors': [[113, [1]]], 'bad_primes': [113], 'central_character': '113.100', 'coeff_info': ['x^56 - 1', '0.993712209893243 + 0.111964476103308*I', '\\\\zeta_{56}'], 'conductor': 113, 'conductor_radical': 113, 'conjugate': 'dirichlet_L_113.26', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^20', 'a^39', 'a^40', 'a^45', 'a^3', 'a^32', 'a^4', 'a^22', 'a^9', 'a^30', 'a^23', 'a^18', 'a^52', 'a^28', 'a^24', 'a^27', 'a^42', 'a^53', 'a^29', 'a^15', 'a^50', 'a^31', 'a^43', 'a^34', 'a^38', 'a^5', 'a^16', 'a^55', 'a^48', 'a^46', 'a^44', 'a^13', 'a^47', 'a^21', 'a^6', 'a^37', 'a^17', 'a^1', 'a^49', 'a^26', 'a^35', 'a^41', 'a^14', 'a^11', 'a^51', 'a^33', 'a^7', 'a^8', 'a^54', 'a^10', 'a^2', 'a^12', 'a^25', 'a^19', 'a^36', 'a^36', 'a^19', 'a^25', 'a^12', 'a^2', 'a^10', 'a^54', 'a^8', 'a^7', 'a^33', 'a^51', 'a^11', 'a^14', 'a^41', 'a^35', 'a^26', 'a^49', 'a^1', 'a^17', 'a^37', 'a^6', 'a^21', 'a^47', 'a^13', 'a^44', 'a^46', 'a^48', 'a^55', 'a^16', 'a^5', 'a^38', 'a^34', 'a^43', 'a^31', 'a^50', 'a^15', 'a^29', 'a^53', 'a^42', 'a^27', 'a^24', 'a^28', 'a^52', 'a^18'], 'euler_factors': [[1, 'a^20'], [1, 'a^39'], [1, 'a^45'], [1, 'a^32'], [1, 'a^30'], [1, 'a^18'], [1, 'a^27'], [1, 'a^53'], [1, 'a^31'], [1, 'a^55'], [1, 'a^46'], [1, 'a^37'], [1, 'a^26'], [1, 'a^41'], [1, 'a^33'], [1, 'a^12'], [1, 'a^25'], [1, 'a^2'], [1, 'a^51'], [1, 'a^35'], [1, 'a^49'], [1, 'a^47'], [1, 'a^48'], [1, 'a^43'], [1, 'a^24'], [1, 'a^23']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-113-113.100-r0-0-0', 'leading_term': '0.119874544539188442979817964654-0.318598087450306210521791754312*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/113/100', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.3404036541452972, 0.08090243903480394, -0.2932395173462541, -0.7829823335858517, -1.2006090482899348, -1.2763513200020318, -0.7631716852651173, 0.4501311334477647, 2.247300291631855, 4.2612250717657485, 5.951716513194743, 6.778208985092351, 6.412136700845789, 4.899397373484199, 2.6868028068210066, 0.4759750274408876, -1.0519745533140856, -1.5245609833647027, -1.0382656253961424, -0.09867052468063112, 0.6454567877644698, 0.7459799656388735, 0.19270473186360204, -0.5965654725083319, -1.0417287521638583, 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lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.5247697938216015, 'bad_primes': [113], 'central_character': '113.100', 'conductor': 113, 'conductor_radical': 113, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/113/100'], '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': '1-113-113.100-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': '1-113-113.100-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5247697938216015, 'root_angle': -0.3854492966990317, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.392941544949', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_113.100', 'Lhash_array': ['dirichlet_L_113.100'], 'factors': ['1-113-113.100-r0-0-0'], 'label': '1-113-113.100-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/113/100'}
Lfunction data - 1-113-113.100-r0-0-0