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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_143.97', 'a10': [0.5, 0.8660254037844386], 'a2': [0.9945218953682733, 0.10452846326765347], 'a3': [-0.9781476007338057, 0.20791169081775934], 'a4': [0.9781476007338057, 0.20791169081775934], 'a5': [0.5877852522924731, 0.8090169943749475], 'a6': [-0.9945218953682733, 0.10452846326765347], 'a7': [0.20791169081775934, -0.9781476007338057], 'a8': [0.9510565162951535, 0.30901699437494745], 'a9': [0.9135454576426009, -0.4067366430758002], 'algebraic': True, 'analytic_conductor': 15.367484245631378, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.97', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.115', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^28', 'a^2', 'a^9', 'a^29', 'a^47', 'a^3', 'a^56', 'a^10', 0, 'a^30', 0, 'a^48', 'a^37', 'a^4', 'a^14', 'a^57', 'a^53', 'a^11', 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'191.21176035061525063480505060763', '192.28444253043373150076705967164', '192.955593774216955794926675086674', '193.65334027195863919573501543968', '194.38791847312164697472192976832', '194.64122635410289099263046223976', '195.400687549581678745124811466128', '196.26198677083798330356694567609', '197.30438819411129133115962947873', '197.69292059636895408460662849187', '198.553394918224440234950674611446', '199.25302545535846004480341557255'], 'prelabel': '1-143-143.97-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.367484245631378, 'root_angle': 0.235607934229387, 'root_number': '0.738344372514038604645743006508+0.674423893094580831572780573186*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.117803967115', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.75951157397061201853331354157+0.394783090911865813255386158286*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.43515472527', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.26525846184', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.4903382767', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 15.367484245631378, 'bad_primes': [11, 13], 'central_character': '143.97', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/97'], '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': '1-143-143.97-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-143-143.97-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.367484245631378, 'root_angle': 0.1178039671146935, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43515472527', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_143.97', 'Lhash_array': ['dirichlet_L_143.97'], 'label': '1-143-143.97-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/97'}
Lfunction data - 1-143-143.97-r1-0-0