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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_2001.1007', 'a10': [-0.80661210923753, -0.5910811325286766], 'a2': [0.3206344605527355, 0.9472030102919101], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.7943870854121126, 0.6074118524777475], 'a5': [-0.8185014665785935, 0.5745044379364633], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5910811325286766, -0.80661210923753], 'a8': [-0.8300502097550806, -0.5576886669868294], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 9.292604933071013, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]], [29, [1]]], 'bad_primes': [3, 23, 29], 'central_character': '2001.1007', 'coeff_info': ['x^308 - 1', '0.999791928189206 + 0.0203985373914054*I', '\\\\zeta_{308}'], 'conductor': 2001, 'conductor_radical': 2001, 'conjugate': 'dirichlet_L_2001.308', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^61', 0, 'a^122', 'a^124', 0, 'a^200', 'a^183', 0, 'a^185', 'a^181', 0, 'a^174', 'a^261', 0, 'a^244', 'a^21', 0, 'a^199', 'a^246', 0, 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'192.22480913964332236988542698008', '193.413264433927038340278880700789', '193.93799809287981798123821838430', '194.14430939431907429660060673637', '194.81892975860460982324226810729', '195.08337972361337824703960988099', '196.083177668951675149659813069799', '196.44455861435860021636994203789', '196.832193718439236107464537276566', '197.66972381078782452027761354693', '198.08588071583932830768382962773', '198.65185032103431091926032603672', '199.03180078803606065484985016765', '199.625543526653281842567765980706'], 'prelabel': '1-2001-2001.1007-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.292604933071013, 'root_angle': 0.7316696856956394, 'root_number': '-0.665237436158511438111667726602+0.746631872835100992008899545662*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.365834842848', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(308)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.647825684809743920440254369796+0.344738299404226471715776640940*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.675592691453', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.7692677038', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.23855936345', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.292604933071013, 'bad_primes': [3, 23, 29], 'central_character': '2001.1007', 'conductor': 2001, 'conductor_radical': 2001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2001/1007'], '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': '1-2001-2001.1007-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': '1-2001-2001.1007-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.292604933071013, 'root_angle': 0.3658348428478197, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.675592691453', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_2001.1007', 'Lhash_array': ['dirichlet_L_2001.1007'], 'label': '1-2001-2001.1007-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2001/1007'}