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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4011.1094', 'a10': [-0.1917106319237384, 0.9814514932524179], 'a2': [-0.9939306773179495, 0.1100082209940793], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9757963826274356, -0.2186810912063758], 'a5': [0.2985148110016945, -0.9544050018795074], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9458172417006346, 0.3246994692046835], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 18.627005690428703, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [191, [1]]], 'bad_primes': [3, 7, 191], 'central_character': '4011.1094', 'coeff_info': ['x^114 - 1', '0.998481516433316 + 0.0550877603558654*I', '\\\\zeta_{114}'], 'conductor': 4011, 'conductor_radical': 4011, 'conjugate': 'dirichlet_L_4011.11', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^55', 0, 'a^110', 'a^91', 0, 0, 'a^51', 0, 'a^32', 'a^92', 0, 'a^102', 0, 0, 'a^106', 'a^113', 0, 'a^25', 'a^87', 0, 'a^33', 'a^25', 0, 'a^68', 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'196.52531607144087624686362593981', '196.846473290848453610184061228234', '197.30150613800461537546879048931', '198.04928798861323835502370211513', '198.30199652841886243562371543085', '199.12318623268611104150566493563', '199.699266603827359661572077748500', '199.92173815401846147865857953663'], 'prelabel': '1-4011-4011.1094-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.627005690428703, 'root_angle': -0.29736934014336563, 'root_number': '0.594451192987432077877293202895-0.804131692669688764828651537248*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(114)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.866096847625033491629170313078-0.191821097459216900820154588661*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.823970768473', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.14865771821', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.16193299021', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 18.627005690428703, 'bad_primes': [3, 7, 191], 'central_character': '4011.1094', 'conductor': 4011, 'conductor_radical': 4011, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4011/1094'], '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': '1-4011-4011.1094-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': '1-4011-4011.1094-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.627005690428703, 'root_angle': -0.14868467007168282, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.823970768473', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4011.1094', 'Lhash_array': ['dirichlet_L_4011.1094'], 'label': '1-4011-4011.1094-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4011/1094'}
Lfunction data - 1-4011-4011.1094-r0-0-0