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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_512.21', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.33688985339222005, -0.9415440651830208], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.5956993044924334, -0.8032075314806449], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9951847266721969, 0.0980171403295606], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.773010453362737, -0.6343932841636455], 'algebraic': True, 'analytic_conductor': 2.3777180038642474, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]]], 'bad_primes': [2], 'central_character': '512.21', 'coeff_info': ['x^128 - 1', '0.998795456205172 + 0.0490676743274180*I', '\\\\zeta_{128}'], 'conductor': 512, 'conductor_radical': 2, 'conjugate': 'dirichlet_L_512.317', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^103', 0, 'a^109', 0, 'a^2', 0, 'a^78', 0, 'a^49', 0, 'a^67', 0, 'a^84', 0, 'a^108', 0, 'a^75', 0, 'a^105', 0, 'a^118', 0, 'a^90', 0, 'a^53', 0, 'a^95', 0, 'a^104', 0, 'a^24', 0, 'a^111', 0, 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'data': '-0.326171875', 'prec': 40}, 'spectral_label': 'r0-0', 'st_group': 'mu(128)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.08857400265029479687215798284-0.655638880148278596805088041343*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.801100347934', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.05595401517', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.6500343875', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.3777180038642474, 'bad_primes': [2], 'central_character': '512.21', 'conductor': 512, 'conductor_radical': 2, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/512/21'], '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': '1-2e9-512.21-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': '1-2e9-512.21-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3777180038642474, 'root_angle': -0.326171875, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.801100347934', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_512.21', 'Lhash_array': ['dirichlet_L_512.21'], 'label': '1-2e9-512.21-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/512/21'}
Lfunction data - 1-2e9-512.21-r0-0-0