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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_927.256', 'a10': [-0.2736629900720829, 0.961825643172819], 'a2': [0.44573835577653825, 0.8951632913550623], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.6026346363792564, 0.7980172272802395], 'a5': [0.7390089172206591, 0.6736956436465572], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.6506183002042422, 0.7594049166547071], 'a8': [-0.9829730996839018, -0.18374951781657034], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 4.304969901527651, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [103, [1]]], 'bad_primes': [3, 103], 'central_character': '927.256', 'coeff_info': ['x^51 - 1', '0.992420509671936 + 0.122888290664714*I', '\\\\zeta_{51}'], 'conductor': 927, 'conductor_radical': 309, 'conjugate': 'dirichlet_L_927.583', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 0, 'a^18', 'a^6', 0, 'a^7', 'a^27', 0, 'a^15', 'a^43', 0, 'a^7', 'a^16', 0, 'a^36', 'a^29', 0, 'a^4', 'a^24', 0, 'a^1', 'a^25', 0, 'a^12', 'a^16', 0, 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'191.51344709810410441745133948717', '192.5610966820734989997388031992', '192.83074983700067827696887981581', '193.47023648307894544376220946208', '194.17112996919936103190510489207', '194.78314142058546911787817254764', '195.369654481022200693352215266286', '195.696379759584272819629686890473', '196.60758053100260980965807966309', '197.229320705259612812483018394907', '197.60603461006683670870918064425', '198.03631991137372502261062210021', '198.82534607689582032590644385565', '199.4804334055363400287902320297', '199.890968787236694301403019356697'], 'prelabel': '1-927-927.256-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.304969901527651, 'root_angle': 0.806243178855127, 'root_number': '-0.820389190345068335414007370368+0.571805540691031810424144577557*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.403121589428', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(51)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.08603287745218903808905678697+1.06024656503268237198298391644*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.57663824448', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.75180497481', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.69633229939', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.304969901527651, 'bad_primes': [3, 103], 'central_character': '927.256', 'conductor': 927, 'conductor_radical': 309, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/927/256'], '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': '1-927-927.256-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': '1-927-927.256-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.304969901527651, 'root_angle': 0.4031215894275635, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.57663824448', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_927.256', 'Lhash_array': ['dirichlet_L_927.256'], 'label': '1-927-927.256-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/927/256'}
Lfunction data - 1-927-927.256-r0-0-0