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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_137.8', 'a10': [2.9010907910729803e-30, -1.0], 'a2': [0.2736629900720829, 0.961825643172819], 'a3': [0.18374951781657034, 0.9829730996839018], 'a4': [-0.8502171357296141, 0.5264321628773558], 'a5': [-0.961825643172819, -0.2736629900720829], 'a6': [-0.8951632913550623, 0.44573835577653825], 'a7': [-0.092268359463302, 0.9957341762950345], 'a8': [-0.7390089172206591, -0.6736956436465572], 'a9': [-0.9324722294043558, 0.3612416661871529], 'algebraic': True, 'analytic_conductor': 0.6362253252527381, 'analytic_normalization': 0, 'bad_lfactors': [[137, [1]]], 'bad_primes': [137], 'central_character': '137.8', 'coeff_info': ['x^68 - 1', '0.995734176295034 + 0.0922683594633020*I', '\\\\zeta_{68}'], 'conductor': 137, 'conductor_radical': 137, 'conjugate': 'dirichlet_L_137.120', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 'a^15', 'a^28', 'a^37', 'a^29', 'a^18', 'a^42', 'a^30', 'a^51', 'a^62', 'a^43', 'a^35', 'a^32', 'a^52', 'a^56', 'a^26', 'a^44', 'a^10', 'a^65', 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[[0], []], 'index': 0, 'label': '1-137-137.8-r0-0-0', 'leading_term': '-0.169231339515259012590285178984+0.730738092220084921546690721943*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/137/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.7500782663799677, -1.388812371773922, -2.4889471161467673, -3.868246351129665, -5.178431606532099, -6.02325597960263, -6.07726058488997, -5.215559383027774, -3.599713445550152, -1.6625931711045538, 0.028971785093346174, 0.9954621379326805, 1.0569059041383777, 0.4268236109712359, -0.37953828870397377, -0.800346224985975, -0.5279267286389762, 0.3075460816253308, 1.1905566170366528, 1.5052448692591172, 0.9083679808204081, -0.427809507550341, -1.868409378935229, -2.6646468315075524, -2.4086346768621936, -1.311716991933932, 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'193.40323365571698324932616602125', '194.32596731641982322589036094823', '195.16095014002586169228580367183', '195.57622515363060596309254412409', '196.65983146601262674831992571388', '197.06348405269155718144537350470', '198.14839959281256445544462551841', '198.63578489677842924185470956373', '199.2150668879069485444479319538', '199.92069289801078368119193422420'], 'prelabel': '1-137-137.8-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6362253252527381, 'root_angle': -0.8551196039401884, 'root_number': '-0.898192818123991602155632551278-0.439601707765657051123996671662*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.42755980197', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(68)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.452930023093269892318030572229+0.727743185836401734036984102877*I']], 'z1': {'__RealLiteral__': 0, 'data': '3.11852187626', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.22174505658', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.21082405872', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.6362253252527381, 'bad_primes': [137], 'central_character': '137.8', 'conductor': 137, 'conductor_radical': 137, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/137/8'], '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': '1-137-137.8-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': '1-137-137.8-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6362253252527381, 'root_angle': -0.4275598019700942, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.11852187626', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_137.8', 'Lhash_array': ['dirichlet_L_137.8'], 'label': '1-137-137.8-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/137/8'}
Lfunction data - 1-137-137.8-r0-0-0