Properties

Label 8041.2.a.g.1.9
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 1
Dimension 69
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.42698 q^{2} +0.265461 q^{3} +3.89025 q^{4} +3.56663 q^{5} -0.644270 q^{6} -2.27175 q^{7} -4.58762 q^{8} -2.92953 q^{9} +O(q^{10})\) \(q-2.42698 q^{2} +0.265461 q^{3} +3.89025 q^{4} +3.56663 q^{5} -0.644270 q^{6} -2.27175 q^{7} -4.58762 q^{8} -2.92953 q^{9} -8.65616 q^{10} -1.00000 q^{11} +1.03271 q^{12} +0.560903 q^{13} +5.51350 q^{14} +0.946802 q^{15} +3.35357 q^{16} +1.00000 q^{17} +7.10992 q^{18} -5.53686 q^{19} +13.8751 q^{20} -0.603061 q^{21} +2.42698 q^{22} +0.0941365 q^{23} -1.21783 q^{24} +7.72087 q^{25} -1.36130 q^{26} -1.57406 q^{27} -8.83768 q^{28} +3.09247 q^{29} -2.29787 q^{30} +0.672520 q^{31} +1.03618 q^{32} -0.265461 q^{33} -2.42698 q^{34} -8.10249 q^{35} -11.3966 q^{36} +1.72926 q^{37} +13.4379 q^{38} +0.148898 q^{39} -16.3623 q^{40} -0.709853 q^{41} +1.46362 q^{42} +1.00000 q^{43} -3.89025 q^{44} -10.4486 q^{45} -0.228468 q^{46} -5.78116 q^{47} +0.890241 q^{48} -1.83916 q^{49} -18.7384 q^{50} +0.265461 q^{51} +2.18206 q^{52} +4.54147 q^{53} +3.82022 q^{54} -3.56663 q^{55} +10.4219 q^{56} -1.46982 q^{57} -7.50538 q^{58} +14.9209 q^{59} +3.68330 q^{60} -3.26994 q^{61} -1.63220 q^{62} +6.65516 q^{63} -9.22192 q^{64} +2.00054 q^{65} +0.644270 q^{66} -1.08719 q^{67} +3.89025 q^{68} +0.0249896 q^{69} +19.6646 q^{70} +12.9951 q^{71} +13.4396 q^{72} -2.05221 q^{73} -4.19690 q^{74} +2.04959 q^{75} -21.5398 q^{76} +2.27175 q^{77} -0.361373 q^{78} -5.52944 q^{79} +11.9609 q^{80} +8.37074 q^{81} +1.72280 q^{82} -5.42574 q^{83} -2.34606 q^{84} +3.56663 q^{85} -2.42698 q^{86} +0.820931 q^{87} +4.58762 q^{88} +13.3425 q^{89} +25.3585 q^{90} -1.27423 q^{91} +0.366215 q^{92} +0.178528 q^{93} +14.0308 q^{94} -19.7479 q^{95} +0.275065 q^{96} +6.01597 q^{97} +4.46361 q^{98} +2.92953 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.42698 −1.71614 −0.858069 0.513535i \(-0.828336\pi\)
−0.858069 + 0.513535i \(0.828336\pi\)
\(3\) 0.265461 0.153264 0.0766320 0.997059i \(-0.475583\pi\)
0.0766320 + 0.997059i \(0.475583\pi\)
\(4\) 3.89025 1.94513
\(5\) 3.56663 1.59505 0.797523 0.603288i \(-0.206143\pi\)
0.797523 + 0.603288i \(0.206143\pi\)
\(6\) −0.644270 −0.263022
\(7\) −2.27175 −0.858640 −0.429320 0.903152i \(-0.641247\pi\)
−0.429320 + 0.903152i \(0.641247\pi\)
\(8\) −4.58762 −1.62197
\(9\) −2.92953 −0.976510
\(10\) −8.65616 −2.73732
\(11\) −1.00000 −0.301511
\(12\) 1.03271 0.298118
\(13\) 0.560903 0.155567 0.0777833 0.996970i \(-0.475216\pi\)
0.0777833 + 0.996970i \(0.475216\pi\)
\(14\) 5.51350 1.47354
\(15\) 0.946802 0.244463
\(16\) 3.35357 0.838392
\(17\) 1.00000 0.242536
\(18\) 7.10992 1.67583
\(19\) −5.53686 −1.27024 −0.635121 0.772413i \(-0.719050\pi\)
−0.635121 + 0.772413i \(0.719050\pi\)
\(20\) 13.8751 3.10257
\(21\) −0.603061 −0.131599
\(22\) 2.42698 0.517435
\(23\) 0.0941365 0.0196288 0.00981441 0.999952i \(-0.496876\pi\)
0.00981441 + 0.999952i \(0.496876\pi\)
\(24\) −1.21783 −0.248589
\(25\) 7.72087 1.54417
\(26\) −1.36130 −0.266974
\(27\) −1.57406 −0.302928
\(28\) −8.83768 −1.67016
\(29\) 3.09247 0.574258 0.287129 0.957892i \(-0.407299\pi\)
0.287129 + 0.957892i \(0.407299\pi\)
\(30\) −2.29787 −0.419532
\(31\) 0.672520 0.120788 0.0603941 0.998175i \(-0.480764\pi\)
0.0603941 + 0.998175i \(0.480764\pi\)
\(32\) 1.03618 0.183172
\(33\) −0.265461 −0.0462108
\(34\) −2.42698 −0.416224
\(35\) −8.10249 −1.36957
\(36\) −11.3966 −1.89944
\(37\) 1.72926 0.284289 0.142145 0.989846i \(-0.454600\pi\)
0.142145 + 0.989846i \(0.454600\pi\)
\(38\) 13.4379 2.17991
\(39\) 0.148898 0.0238428
\(40\) −16.3623 −2.58711
\(41\) −0.709853 −0.110860 −0.0554302 0.998463i \(-0.517653\pi\)
−0.0554302 + 0.998463i \(0.517653\pi\)
\(42\) 1.46362 0.225841
\(43\) 1.00000 0.152499
\(44\) −3.89025 −0.586478
\(45\) −10.4486 −1.55758
\(46\) −0.228468 −0.0336857
\(47\) −5.78116 −0.843269 −0.421634 0.906766i \(-0.638543\pi\)
−0.421634 + 0.906766i \(0.638543\pi\)
\(48\) 0.890241 0.128495
\(49\) −1.83916 −0.262737
\(50\) −18.7384 −2.65001
\(51\) 0.265461 0.0371720
\(52\) 2.18206 0.302597
\(53\) 4.54147 0.623818 0.311909 0.950112i \(-0.399032\pi\)
0.311909 + 0.950112i \(0.399032\pi\)
\(54\) 3.82022 0.519866
\(55\) −3.56663 −0.480925
\(56\) 10.4219 1.39269
\(57\) −1.46982 −0.194682
\(58\) −7.50538 −0.985505
\(59\) 14.9209 1.94253 0.971266 0.237998i \(-0.0764912\pi\)
0.971266 + 0.237998i \(0.0764912\pi\)
\(60\) 3.68330 0.475512
\(61\) −3.26994 −0.418673 −0.209337 0.977844i \(-0.567130\pi\)
−0.209337 + 0.977844i \(0.567130\pi\)
\(62\) −1.63220 −0.207289
\(63\) 6.65516 0.838471
\(64\) −9.22192 −1.15274
\(65\) 2.00054 0.248136
\(66\) 0.644270 0.0793041
\(67\) −1.08719 −0.132822 −0.0664108 0.997792i \(-0.521155\pi\)
−0.0664108 + 0.997792i \(0.521155\pi\)
\(68\) 3.89025 0.471763
\(69\) 0.0249896 0.00300839
\(70\) 19.6646 2.35037
\(71\) 12.9951 1.54223 0.771116 0.636695i \(-0.219699\pi\)
0.771116 + 0.636695i \(0.219699\pi\)
\(72\) 13.4396 1.58387
\(73\) −2.05221 −0.240192 −0.120096 0.992762i \(-0.538320\pi\)
−0.120096 + 0.992762i \(0.538320\pi\)
\(74\) −4.19690 −0.487880
\(75\) 2.04959 0.236666
\(76\) −21.5398 −2.47078
\(77\) 2.27175 0.258890
\(78\) −0.361373 −0.0409175
\(79\) −5.52944 −0.622110 −0.311055 0.950392i \(-0.600682\pi\)
−0.311055 + 0.950392i \(0.600682\pi\)
\(80\) 11.9609 1.33727
\(81\) 8.37074 0.930082
\(82\) 1.72280 0.190252
\(83\) −5.42574 −0.595553 −0.297776 0.954636i \(-0.596245\pi\)
−0.297776 + 0.954636i \(0.596245\pi\)
\(84\) −2.34606 −0.255976
\(85\) 3.56663 0.386856
\(86\) −2.42698 −0.261708
\(87\) 0.820931 0.0880131
\(88\) 4.58762 0.489042
\(89\) 13.3425 1.41431 0.707154 0.707060i \(-0.249979\pi\)
0.707154 + 0.707060i \(0.249979\pi\)
\(90\) 25.3585 2.67302
\(91\) −1.27423 −0.133576
\(92\) 0.366215 0.0381805
\(93\) 0.178528 0.0185125
\(94\) 14.0308 1.44716
\(95\) −19.7479 −2.02610
\(96\) 0.275065 0.0280737
\(97\) 6.01597 0.610830 0.305415 0.952219i \(-0.401205\pi\)
0.305415 + 0.952219i \(0.401205\pi\)
\(98\) 4.46361 0.450893
\(99\) 2.92953 0.294429
\(100\) 30.0361 3.00361
\(101\) −4.48745 −0.446518 −0.223259 0.974759i \(-0.571670\pi\)
−0.223259 + 0.974759i \(0.571670\pi\)
\(102\) −0.644270 −0.0637922
\(103\) 9.56546 0.942512 0.471256 0.881996i \(-0.343801\pi\)
0.471256 + 0.881996i \(0.343801\pi\)
\(104\) −2.57321 −0.252324
\(105\) −2.15090 −0.209906
\(106\) −11.0221 −1.07056
\(107\) 1.95259 0.188764 0.0943821 0.995536i \(-0.469912\pi\)
0.0943821 + 0.995536i \(0.469912\pi\)
\(108\) −6.12349 −0.589233
\(109\) 16.9918 1.62752 0.813759 0.581203i \(-0.197418\pi\)
0.813759 + 0.581203i \(0.197418\pi\)
\(110\) 8.65616 0.825333
\(111\) 0.459052 0.0435713
\(112\) −7.61846 −0.719877
\(113\) −4.77576 −0.449266 −0.224633 0.974443i \(-0.572118\pi\)
−0.224633 + 0.974443i \(0.572118\pi\)
\(114\) 3.56723 0.334102
\(115\) 0.335750 0.0313089
\(116\) 12.0305 1.11700
\(117\) −1.64318 −0.151912
\(118\) −36.2127 −3.33365
\(119\) −2.27175 −0.208251
\(120\) −4.34356 −0.396511
\(121\) 1.00000 0.0909091
\(122\) 7.93610 0.718501
\(123\) −0.188438 −0.0169909
\(124\) 2.61627 0.234948
\(125\) 9.70434 0.867982
\(126\) −16.1520 −1.43893
\(127\) −14.6468 −1.29970 −0.649849 0.760063i \(-0.725168\pi\)
−0.649849 + 0.760063i \(0.725168\pi\)
\(128\) 20.3091 1.79509
\(129\) 0.265461 0.0233725
\(130\) −4.85527 −0.425835
\(131\) −10.2817 −0.898313 −0.449156 0.893453i \(-0.648275\pi\)
−0.449156 + 0.893453i \(0.648275\pi\)
\(132\) −1.03271 −0.0898859
\(133\) 12.5783 1.09068
\(134\) 2.63860 0.227940
\(135\) −5.61409 −0.483184
\(136\) −4.58762 −0.393385
\(137\) −11.5639 −0.987973 −0.493987 0.869470i \(-0.664461\pi\)
−0.493987 + 0.869470i \(0.664461\pi\)
\(138\) −0.0606493 −0.00516281
\(139\) −8.22923 −0.697994 −0.348997 0.937124i \(-0.613478\pi\)
−0.348997 + 0.937124i \(0.613478\pi\)
\(140\) −31.5207 −2.66399
\(141\) −1.53467 −0.129243
\(142\) −31.5388 −2.64668
\(143\) −0.560903 −0.0469051
\(144\) −9.82437 −0.818698
\(145\) 11.0297 0.915968
\(146\) 4.98067 0.412203
\(147\) −0.488225 −0.0402682
\(148\) 6.72728 0.552979
\(149\) −12.3816 −1.01434 −0.507169 0.861847i \(-0.669308\pi\)
−0.507169 + 0.861847i \(0.669308\pi\)
\(150\) −4.97432 −0.406152
\(151\) 7.09973 0.577768 0.288884 0.957364i \(-0.406716\pi\)
0.288884 + 0.957364i \(0.406716\pi\)
\(152\) 25.4010 2.06029
\(153\) −2.92953 −0.236838
\(154\) −5.51350 −0.444290
\(155\) 2.39863 0.192663
\(156\) 0.579251 0.0463772
\(157\) −21.0258 −1.67804 −0.839021 0.544100i \(-0.816871\pi\)
−0.839021 + 0.544100i \(0.816871\pi\)
\(158\) 13.4199 1.06763
\(159\) 1.20558 0.0956089
\(160\) 3.69567 0.292169
\(161\) −0.213854 −0.0168541
\(162\) −20.3157 −1.59615
\(163\) −4.43888 −0.347680 −0.173840 0.984774i \(-0.555618\pi\)
−0.173840 + 0.984774i \(0.555618\pi\)
\(164\) −2.76151 −0.215638
\(165\) −0.946802 −0.0737084
\(166\) 13.1682 1.02205
\(167\) −22.7629 −1.76144 −0.880722 0.473633i \(-0.842942\pi\)
−0.880722 + 0.473633i \(0.842942\pi\)
\(168\) 2.76661 0.213449
\(169\) −12.6854 −0.975799
\(170\) −8.65616 −0.663897
\(171\) 16.2204 1.24040
\(172\) 3.89025 0.296629
\(173\) 11.0979 0.843759 0.421880 0.906652i \(-0.361370\pi\)
0.421880 + 0.906652i \(0.361370\pi\)
\(174\) −1.99239 −0.151042
\(175\) −17.5399 −1.32589
\(176\) −3.35357 −0.252785
\(177\) 3.96091 0.297720
\(178\) −32.3822 −2.42715
\(179\) −9.24728 −0.691174 −0.345587 0.938387i \(-0.612320\pi\)
−0.345587 + 0.938387i \(0.612320\pi\)
\(180\) −40.6475 −3.02969
\(181\) −21.0477 −1.56446 −0.782232 0.622987i \(-0.785919\pi\)
−0.782232 + 0.622987i \(0.785919\pi\)
\(182\) 3.09254 0.229234
\(183\) −0.868042 −0.0641675
\(184\) −0.431862 −0.0318373
\(185\) 6.16765 0.453455
\(186\) −0.433284 −0.0317699
\(187\) −1.00000 −0.0731272
\(188\) −22.4902 −1.64026
\(189\) 3.57587 0.260106
\(190\) 47.9279 3.47706
\(191\) 12.4313 0.899500 0.449750 0.893154i \(-0.351513\pi\)
0.449750 + 0.893154i \(0.351513\pi\)
\(192\) −2.44806 −0.176674
\(193\) −0.198958 −0.0143213 −0.00716064 0.999974i \(-0.502279\pi\)
−0.00716064 + 0.999974i \(0.502279\pi\)
\(194\) −14.6007 −1.04827
\(195\) 0.531065 0.0380303
\(196\) −7.15480 −0.511057
\(197\) 0.475159 0.0338537 0.0169268 0.999857i \(-0.494612\pi\)
0.0169268 + 0.999857i \(0.494612\pi\)
\(198\) −7.10992 −0.505280
\(199\) −4.61260 −0.326979 −0.163489 0.986545i \(-0.552275\pi\)
−0.163489 + 0.986545i \(0.552275\pi\)
\(200\) −35.4204 −2.50460
\(201\) −0.288607 −0.0203568
\(202\) 10.8910 0.766287
\(203\) −7.02532 −0.493081
\(204\) 1.03271 0.0723042
\(205\) −2.53179 −0.176828
\(206\) −23.2152 −1.61748
\(207\) −0.275776 −0.0191677
\(208\) 1.88103 0.130426
\(209\) 5.53686 0.382992
\(210\) 5.22019 0.360227
\(211\) −4.98729 −0.343339 −0.171669 0.985155i \(-0.554916\pi\)
−0.171669 + 0.985155i \(0.554916\pi\)
\(212\) 17.6675 1.21341
\(213\) 3.44969 0.236369
\(214\) −4.73891 −0.323945
\(215\) 3.56663 0.243242
\(216\) 7.22118 0.491339
\(217\) −1.52780 −0.103714
\(218\) −41.2388 −2.79304
\(219\) −0.544781 −0.0368129
\(220\) −13.8751 −0.935459
\(221\) 0.560903 0.0377304
\(222\) −1.11411 −0.0747744
\(223\) −4.70781 −0.315259 −0.157629 0.987498i \(-0.550385\pi\)
−0.157629 + 0.987498i \(0.550385\pi\)
\(224\) −2.35394 −0.157279
\(225\) −22.6185 −1.50790
\(226\) 11.5907 0.771001
\(227\) −1.63824 −0.108734 −0.0543669 0.998521i \(-0.517314\pi\)
−0.0543669 + 0.998521i \(0.517314\pi\)
\(228\) −5.71797 −0.378682
\(229\) −11.0325 −0.729045 −0.364523 0.931195i \(-0.618768\pi\)
−0.364523 + 0.931195i \(0.618768\pi\)
\(230\) −0.814861 −0.0537303
\(231\) 0.603061 0.0396785
\(232\) −14.1871 −0.931427
\(233\) −15.0223 −0.984144 −0.492072 0.870554i \(-0.663760\pi\)
−0.492072 + 0.870554i \(0.663760\pi\)
\(234\) 3.98798 0.260702
\(235\) −20.6193 −1.34505
\(236\) 58.0460 3.77847
\(237\) −1.46785 −0.0953471
\(238\) 5.51350 0.357387
\(239\) −24.6565 −1.59489 −0.797447 0.603389i \(-0.793817\pi\)
−0.797447 + 0.603389i \(0.793817\pi\)
\(240\) 3.17516 0.204956
\(241\) −9.99166 −0.643620 −0.321810 0.946804i \(-0.604291\pi\)
−0.321810 + 0.946804i \(0.604291\pi\)
\(242\) −2.42698 −0.156012
\(243\) 6.94428 0.445476
\(244\) −12.7209 −0.814372
\(245\) −6.55961 −0.419078
\(246\) 0.457337 0.0291587
\(247\) −3.10564 −0.197607
\(248\) −3.08526 −0.195914
\(249\) −1.44032 −0.0912768
\(250\) −23.5523 −1.48958
\(251\) −0.301048 −0.0190020 −0.00950099 0.999955i \(-0.503024\pi\)
−0.00950099 + 0.999955i \(0.503024\pi\)
\(252\) 25.8902 1.63093
\(253\) −0.0941365 −0.00591831
\(254\) 35.5477 2.23046
\(255\) 0.946802 0.0592911
\(256\) −30.8460 −1.92788
\(257\) −15.0251 −0.937242 −0.468621 0.883399i \(-0.655249\pi\)
−0.468621 + 0.883399i \(0.655249\pi\)
\(258\) −0.644270 −0.0401105
\(259\) −3.92845 −0.244102
\(260\) 7.78259 0.482656
\(261\) −9.05949 −0.560769
\(262\) 24.9534 1.54163
\(263\) −14.6691 −0.904536 −0.452268 0.891882i \(-0.649385\pi\)
−0.452268 + 0.891882i \(0.649385\pi\)
\(264\) 1.21783 0.0749525
\(265\) 16.1977 0.995019
\(266\) −30.5274 −1.87176
\(267\) 3.54193 0.216762
\(268\) −4.22945 −0.258355
\(269\) −1.54034 −0.0939161 −0.0469581 0.998897i \(-0.514953\pi\)
−0.0469581 + 0.998897i \(0.514953\pi\)
\(270\) 13.6253 0.829210
\(271\) −20.7782 −1.26218 −0.631091 0.775708i \(-0.717393\pi\)
−0.631091 + 0.775708i \(0.717393\pi\)
\(272\) 3.35357 0.203340
\(273\) −0.338259 −0.0204724
\(274\) 28.0655 1.69550
\(275\) −7.72087 −0.465586
\(276\) 0.0972158 0.00585170
\(277\) 12.1567 0.730424 0.365212 0.930924i \(-0.380996\pi\)
0.365212 + 0.930924i \(0.380996\pi\)
\(278\) 19.9722 1.19785
\(279\) −1.97017 −0.117951
\(280\) 37.1711 2.22140
\(281\) 2.10752 0.125724 0.0628620 0.998022i \(-0.479977\pi\)
0.0628620 + 0.998022i \(0.479977\pi\)
\(282\) 3.72463 0.221798
\(283\) −21.6008 −1.28404 −0.642018 0.766689i \(-0.721903\pi\)
−0.642018 + 0.766689i \(0.721903\pi\)
\(284\) 50.5541 2.99984
\(285\) −5.24231 −0.310528
\(286\) 1.36130 0.0804956
\(287\) 1.61261 0.0951892
\(288\) −3.03552 −0.178870
\(289\) 1.00000 0.0588235
\(290\) −26.7689 −1.57193
\(291\) 1.59701 0.0936182
\(292\) −7.98360 −0.467205
\(293\) 4.77366 0.278880 0.139440 0.990230i \(-0.455470\pi\)
0.139440 + 0.990230i \(0.455470\pi\)
\(294\) 1.18492 0.0691057
\(295\) 53.2172 3.09843
\(296\) −7.93320 −0.461108
\(297\) 1.57406 0.0913362
\(298\) 30.0499 1.74074
\(299\) 0.0528015 0.00305359
\(300\) 7.97343 0.460346
\(301\) −2.27175 −0.130941
\(302\) −17.2309 −0.991529
\(303\) −1.19124 −0.0684352
\(304\) −18.5682 −1.06496
\(305\) −11.6627 −0.667803
\(306\) 7.10992 0.406447
\(307\) −21.3459 −1.21828 −0.609138 0.793064i \(-0.708484\pi\)
−0.609138 + 0.793064i \(0.708484\pi\)
\(308\) 8.83768 0.503573
\(309\) 2.53926 0.144453
\(310\) −5.82144 −0.330636
\(311\) −25.7859 −1.46219 −0.731093 0.682278i \(-0.760990\pi\)
−0.731093 + 0.682278i \(0.760990\pi\)
\(312\) −0.683087 −0.0386722
\(313\) 11.1647 0.631068 0.315534 0.948914i \(-0.397816\pi\)
0.315534 + 0.948914i \(0.397816\pi\)
\(314\) 51.0293 2.87975
\(315\) 23.7365 1.33740
\(316\) −21.5109 −1.21008
\(317\) 6.58877 0.370062 0.185031 0.982733i \(-0.440761\pi\)
0.185031 + 0.982733i \(0.440761\pi\)
\(318\) −2.92593 −0.164078
\(319\) −3.09247 −0.173145
\(320\) −32.8912 −1.83867
\(321\) 0.518337 0.0289308
\(322\) 0.519021 0.0289239
\(323\) −5.53686 −0.308079
\(324\) 32.5643 1.80913
\(325\) 4.33066 0.240222
\(326\) 10.7731 0.596666
\(327\) 4.51066 0.249440
\(328\) 3.25653 0.179812
\(329\) 13.1333 0.724064
\(330\) 2.29787 0.126494
\(331\) −5.40053 −0.296840 −0.148420 0.988924i \(-0.547419\pi\)
−0.148420 + 0.988924i \(0.547419\pi\)
\(332\) −21.1075 −1.15843
\(333\) −5.06593 −0.277611
\(334\) 55.2452 3.02288
\(335\) −3.87762 −0.211857
\(336\) −2.02240 −0.110331
\(337\) 22.5485 1.22829 0.614147 0.789191i \(-0.289500\pi\)
0.614147 + 0.789191i \(0.289500\pi\)
\(338\) 30.7872 1.67460
\(339\) −1.26778 −0.0688563
\(340\) 13.8751 0.752483
\(341\) −0.672520 −0.0364190
\(342\) −39.3666 −2.12870
\(343\) 20.0803 1.08424
\(344\) −4.58762 −0.247348
\(345\) 0.0891286 0.00479852
\(346\) −26.9345 −1.44801
\(347\) −27.2409 −1.46237 −0.731185 0.682179i \(-0.761033\pi\)
−0.731185 + 0.682179i \(0.761033\pi\)
\(348\) 3.19363 0.171197
\(349\) −16.4422 −0.880130 −0.440065 0.897966i \(-0.645045\pi\)
−0.440065 + 0.897966i \(0.645045\pi\)
\(350\) 42.5690 2.27541
\(351\) −0.882895 −0.0471255
\(352\) −1.03618 −0.0552286
\(353\) 5.60309 0.298222 0.149111 0.988820i \(-0.452359\pi\)
0.149111 + 0.988820i \(0.452359\pi\)
\(354\) −9.61306 −0.510929
\(355\) 46.3487 2.45993
\(356\) 51.9059 2.75101
\(357\) −0.603061 −0.0319174
\(358\) 22.4430 1.18615
\(359\) −5.37033 −0.283435 −0.141718 0.989907i \(-0.545262\pi\)
−0.141718 + 0.989907i \(0.545262\pi\)
\(360\) 47.9340 2.52634
\(361\) 11.6568 0.613515
\(362\) 51.0825 2.68483
\(363\) 0.265461 0.0139331
\(364\) −4.95708 −0.259822
\(365\) −7.31946 −0.383118
\(366\) 2.10673 0.110120
\(367\) −28.0390 −1.46362 −0.731811 0.681508i \(-0.761325\pi\)
−0.731811 + 0.681508i \(0.761325\pi\)
\(368\) 0.315693 0.0164566
\(369\) 2.07954 0.108256
\(370\) −14.9688 −0.778191
\(371\) −10.3171 −0.535635
\(372\) 0.694519 0.0360091
\(373\) 2.74950 0.142364 0.0711819 0.997463i \(-0.477323\pi\)
0.0711819 + 0.997463i \(0.477323\pi\)
\(374\) 2.42698 0.125496
\(375\) 2.57612 0.133030
\(376\) 26.5217 1.36775
\(377\) 1.73458 0.0893353
\(378\) −8.67857 −0.446378
\(379\) −18.1234 −0.930936 −0.465468 0.885065i \(-0.654114\pi\)
−0.465468 + 0.885065i \(0.654114\pi\)
\(380\) −76.8245 −3.94101
\(381\) −3.88817 −0.199197
\(382\) −30.1707 −1.54367
\(383\) 4.58617 0.234342 0.117171 0.993112i \(-0.462617\pi\)
0.117171 + 0.993112i \(0.462617\pi\)
\(384\) 5.39128 0.275122
\(385\) 8.10249 0.412941
\(386\) 0.482867 0.0245773
\(387\) −2.92953 −0.148916
\(388\) 23.4037 1.18814
\(389\) 17.0800 0.865990 0.432995 0.901396i \(-0.357457\pi\)
0.432995 + 0.901396i \(0.357457\pi\)
\(390\) −1.28889 −0.0652653
\(391\) 0.0941365 0.00476069
\(392\) 8.43736 0.426151
\(393\) −2.72938 −0.137679
\(394\) −1.15320 −0.0580976
\(395\) −19.7215 −0.992295
\(396\) 11.3966 0.572702
\(397\) 36.6708 1.84045 0.920226 0.391387i \(-0.128005\pi\)
0.920226 + 0.391387i \(0.128005\pi\)
\(398\) 11.1947 0.561140
\(399\) 3.33906 0.167162
\(400\) 25.8924 1.29462
\(401\) 1.32855 0.0663445 0.0331722 0.999450i \(-0.489439\pi\)
0.0331722 + 0.999450i \(0.489439\pi\)
\(402\) 0.700445 0.0349350
\(403\) 0.377219 0.0187906
\(404\) −17.4573 −0.868535
\(405\) 29.8554 1.48352
\(406\) 17.0503 0.846194
\(407\) −1.72926 −0.0857165
\(408\) −1.21783 −0.0602917
\(409\) −22.7390 −1.12437 −0.562186 0.827011i \(-0.690040\pi\)
−0.562186 + 0.827011i \(0.690040\pi\)
\(410\) 6.14460 0.303460
\(411\) −3.06977 −0.151421
\(412\) 37.2121 1.83331
\(413\) −33.8964 −1.66794
\(414\) 0.669303 0.0328945
\(415\) −19.3516 −0.949934
\(416\) 0.581197 0.0284955
\(417\) −2.18454 −0.106977
\(418\) −13.4379 −0.657268
\(419\) −24.0820 −1.17648 −0.588242 0.808685i \(-0.700180\pi\)
−0.588242 + 0.808685i \(0.700180\pi\)
\(420\) −8.36753 −0.408294
\(421\) −35.2258 −1.71680 −0.858401 0.512980i \(-0.828541\pi\)
−0.858401 + 0.512980i \(0.828541\pi\)
\(422\) 12.1041 0.589217
\(423\) 16.9361 0.823461
\(424\) −20.8345 −1.01181
\(425\) 7.72087 0.374517
\(426\) −8.37234 −0.405641
\(427\) 7.42848 0.359490
\(428\) 7.59608 0.367170
\(429\) −0.148898 −0.00718886
\(430\) −8.65616 −0.417437
\(431\) 12.4389 0.599158 0.299579 0.954071i \(-0.403154\pi\)
0.299579 + 0.954071i \(0.403154\pi\)
\(432\) −5.27871 −0.253972
\(433\) 21.5156 1.03398 0.516988 0.855993i \(-0.327053\pi\)
0.516988 + 0.855993i \(0.327053\pi\)
\(434\) 3.70794 0.177987
\(435\) 2.92796 0.140385
\(436\) 66.1023 3.16573
\(437\) −0.521220 −0.0249333
\(438\) 1.32217 0.0631759
\(439\) 14.2630 0.680736 0.340368 0.940292i \(-0.389448\pi\)
0.340368 + 0.940292i \(0.389448\pi\)
\(440\) 16.3623 0.780044
\(441\) 5.38788 0.256566
\(442\) −1.36130 −0.0647506
\(443\) 30.6206 1.45483 0.727415 0.686198i \(-0.240722\pi\)
0.727415 + 0.686198i \(0.240722\pi\)
\(444\) 1.78583 0.0847518
\(445\) 47.5880 2.25589
\(446\) 11.4258 0.541027
\(447\) −3.28682 −0.155461
\(448\) 20.9499 0.989789
\(449\) −25.3899 −1.19822 −0.599112 0.800665i \(-0.704479\pi\)
−0.599112 + 0.800665i \(0.704479\pi\)
\(450\) 54.8948 2.58777
\(451\) 0.709853 0.0334257
\(452\) −18.5789 −0.873879
\(453\) 1.88470 0.0885510
\(454\) 3.97599 0.186602
\(455\) −4.54472 −0.213060
\(456\) 6.74297 0.315769
\(457\) 33.6698 1.57501 0.787503 0.616311i \(-0.211374\pi\)
0.787503 + 0.616311i \(0.211374\pi\)
\(458\) 26.7756 1.25114
\(459\) −1.57406 −0.0734708
\(460\) 1.30615 0.0608997
\(461\) 2.67596 0.124632 0.0623159 0.998056i \(-0.480151\pi\)
0.0623159 + 0.998056i \(0.480151\pi\)
\(462\) −1.46362 −0.0680937
\(463\) 20.9166 0.972076 0.486038 0.873938i \(-0.338442\pi\)
0.486038 + 0.873938i \(0.338442\pi\)
\(464\) 10.3708 0.481453
\(465\) 0.636743 0.0295283
\(466\) 36.4589 1.68893
\(467\) 35.6656 1.65041 0.825204 0.564835i \(-0.191060\pi\)
0.825204 + 0.564835i \(0.191060\pi\)
\(468\) −6.39240 −0.295489
\(469\) 2.46983 0.114046
\(470\) 50.0427 2.30830
\(471\) −5.58153 −0.257183
\(472\) −68.4512 −3.15072
\(473\) −1.00000 −0.0459800
\(474\) 3.56245 0.163629
\(475\) −42.7493 −1.96147
\(476\) −8.83768 −0.405074
\(477\) −13.3044 −0.609165
\(478\) 59.8409 2.73706
\(479\) −22.3899 −1.02302 −0.511511 0.859277i \(-0.670914\pi\)
−0.511511 + 0.859277i \(0.670914\pi\)
\(480\) 0.981057 0.0447789
\(481\) 0.969950 0.0442259
\(482\) 24.2496 1.10454
\(483\) −0.0567700 −0.00258312
\(484\) 3.89025 0.176830
\(485\) 21.4568 0.974302
\(486\) −16.8537 −0.764498
\(487\) 8.46910 0.383771 0.191886 0.981417i \(-0.438540\pi\)
0.191886 + 0.981417i \(0.438540\pi\)
\(488\) 15.0012 0.679074
\(489\) −1.17835 −0.0532868
\(490\) 15.9201 0.719195
\(491\) −5.97261 −0.269540 −0.134770 0.990877i \(-0.543030\pi\)
−0.134770 + 0.990877i \(0.543030\pi\)
\(492\) −0.733073 −0.0330495
\(493\) 3.09247 0.139278
\(494\) 7.53735 0.339121
\(495\) 10.4486 0.469628
\(496\) 2.25534 0.101268
\(497\) −29.5215 −1.32422
\(498\) 3.49564 0.156644
\(499\) −27.7930 −1.24419 −0.622093 0.782943i \(-0.713718\pi\)
−0.622093 + 0.782943i \(0.713718\pi\)
\(500\) 37.7523 1.68834
\(501\) −6.04266 −0.269966
\(502\) 0.730639 0.0326100
\(503\) −30.0007 −1.33767 −0.668833 0.743412i \(-0.733206\pi\)
−0.668833 + 0.743412i \(0.733206\pi\)
\(504\) −30.5313 −1.35997
\(505\) −16.0051 −0.712217
\(506\) 0.228468 0.0101566
\(507\) −3.36748 −0.149555
\(508\) −56.9800 −2.52808
\(509\) 7.48214 0.331640 0.165820 0.986156i \(-0.446973\pi\)
0.165820 + 0.986156i \(0.446973\pi\)
\(510\) −2.29787 −0.101752
\(511\) 4.66209 0.206239
\(512\) 34.2446 1.51341
\(513\) 8.71534 0.384792
\(514\) 36.4658 1.60844
\(515\) 34.1165 1.50335
\(516\) 1.03271 0.0454626
\(517\) 5.78116 0.254255
\(518\) 9.53430 0.418913
\(519\) 2.94607 0.129318
\(520\) −9.17769 −0.402468
\(521\) 7.12546 0.312172 0.156086 0.987743i \(-0.450112\pi\)
0.156086 + 0.987743i \(0.450112\pi\)
\(522\) 21.9872 0.962356
\(523\) 30.3756 1.32823 0.664117 0.747628i \(-0.268808\pi\)
0.664117 + 0.747628i \(0.268808\pi\)
\(524\) −39.9983 −1.74733
\(525\) −4.65615 −0.203211
\(526\) 35.6017 1.55231
\(527\) 0.672520 0.0292954
\(528\) −0.890241 −0.0387428
\(529\) −22.9911 −0.999615
\(530\) −39.3117 −1.70759
\(531\) −43.7111 −1.89690
\(532\) 48.9330 2.12151
\(533\) −0.398159 −0.0172462
\(534\) −8.59620 −0.371994
\(535\) 6.96418 0.301088
\(536\) 4.98762 0.215432
\(537\) −2.45479 −0.105932
\(538\) 3.73838 0.161173
\(539\) 1.83916 0.0792182
\(540\) −21.8402 −0.939854
\(541\) 40.2347 1.72983 0.864913 0.501922i \(-0.167373\pi\)
0.864913 + 0.501922i \(0.167373\pi\)
\(542\) 50.4283 2.16608
\(543\) −5.58735 −0.239776
\(544\) 1.03618 0.0444258
\(545\) 60.6034 2.59597
\(546\) 0.820949 0.0351334
\(547\) 2.24499 0.0959890 0.0479945 0.998848i \(-0.484717\pi\)
0.0479945 + 0.998848i \(0.484717\pi\)
\(548\) −44.9866 −1.92173
\(549\) 9.57939 0.408839
\(550\) 18.7384 0.799009
\(551\) −17.1226 −0.729446
\(552\) −0.114643 −0.00487951
\(553\) 12.5615 0.534169
\(554\) −29.5041 −1.25351
\(555\) 1.63727 0.0694983
\(556\) −32.0138 −1.35769
\(557\) −3.78858 −0.160527 −0.0802636 0.996774i \(-0.525576\pi\)
−0.0802636 + 0.996774i \(0.525576\pi\)
\(558\) 4.78157 0.202420
\(559\) 0.560903 0.0237237
\(560\) −27.1722 −1.14824
\(561\) −0.265461 −0.0112078
\(562\) −5.11491 −0.215760
\(563\) −16.4438 −0.693022 −0.346511 0.938046i \(-0.612634\pi\)
−0.346511 + 0.938046i \(0.612634\pi\)
\(564\) −5.97027 −0.251394
\(565\) −17.0334 −0.716600
\(566\) 52.4249 2.20358
\(567\) −19.0162 −0.798606
\(568\) −59.6164 −2.50145
\(569\) −29.4783 −1.23579 −0.617896 0.786259i \(-0.712015\pi\)
−0.617896 + 0.786259i \(0.712015\pi\)
\(570\) 12.7230 0.532908
\(571\) 4.56327 0.190967 0.0954834 0.995431i \(-0.469560\pi\)
0.0954834 + 0.995431i \(0.469560\pi\)
\(572\) −2.18206 −0.0912364
\(573\) 3.30004 0.137861
\(574\) −3.91377 −0.163358
\(575\) 0.726815 0.0303103
\(576\) 27.0159 1.12566
\(577\) 17.0384 0.709318 0.354659 0.934996i \(-0.384597\pi\)
0.354659 + 0.934996i \(0.384597\pi\)
\(578\) −2.42698 −0.100949
\(579\) −0.0528155 −0.00219494
\(580\) 42.9084 1.78167
\(581\) 12.3259 0.511365
\(582\) −3.87591 −0.160662
\(583\) −4.54147 −0.188088
\(584\) 9.41473 0.389584
\(585\) −5.86063 −0.242307
\(586\) −11.5856 −0.478597
\(587\) −10.4283 −0.430424 −0.215212 0.976567i \(-0.569044\pi\)
−0.215212 + 0.976567i \(0.569044\pi\)
\(588\) −1.89932 −0.0783267
\(589\) −3.72365 −0.153430
\(590\) −129.157 −5.31733
\(591\) 0.126136 0.00518855
\(592\) 5.79920 0.238346
\(593\) 9.00871 0.369943 0.184972 0.982744i \(-0.440781\pi\)
0.184972 + 0.982744i \(0.440781\pi\)
\(594\) −3.82022 −0.156745
\(595\) −8.10249 −0.332170
\(596\) −48.1674 −1.97301
\(597\) −1.22447 −0.0501141
\(598\) −0.128148 −0.00524038
\(599\) −0.515451 −0.0210608 −0.0105304 0.999945i \(-0.503352\pi\)
−0.0105304 + 0.999945i \(0.503352\pi\)
\(600\) −9.40273 −0.383865
\(601\) 5.18341 0.211436 0.105718 0.994396i \(-0.466286\pi\)
0.105718 + 0.994396i \(0.466286\pi\)
\(602\) 5.51350 0.224713
\(603\) 3.18496 0.129702
\(604\) 27.6197 1.12383
\(605\) 3.56663 0.145004
\(606\) 2.89113 0.117444
\(607\) 3.25608 0.132160 0.0660801 0.997814i \(-0.478951\pi\)
0.0660801 + 0.997814i \(0.478951\pi\)
\(608\) −5.73718 −0.232673
\(609\) −1.86495 −0.0755715
\(610\) 28.3051 1.14604
\(611\) −3.24267 −0.131184
\(612\) −11.3966 −0.460681
\(613\) 9.21578 0.372222 0.186111 0.982529i \(-0.440412\pi\)
0.186111 + 0.982529i \(0.440412\pi\)
\(614\) 51.8062 2.09073
\(615\) −0.672090 −0.0271013
\(616\) −10.4219 −0.419911
\(617\) −15.5452 −0.625826 −0.312913 0.949782i \(-0.601305\pi\)
−0.312913 + 0.949782i \(0.601305\pi\)
\(618\) −6.16274 −0.247902
\(619\) 16.6783 0.670356 0.335178 0.942155i \(-0.391204\pi\)
0.335178 + 0.942155i \(0.391204\pi\)
\(620\) 9.33128 0.374753
\(621\) −0.148176 −0.00594611
\(622\) 62.5821 2.50931
\(623\) −30.3109 −1.21438
\(624\) 0.499339 0.0199896
\(625\) −3.99253 −0.159701
\(626\) −27.0966 −1.08300
\(627\) 1.46982 0.0586990
\(628\) −81.7957 −3.26400
\(629\) 1.72926 0.0689503
\(630\) −57.6081 −2.29516
\(631\) −22.5981 −0.899616 −0.449808 0.893125i \(-0.648508\pi\)
−0.449808 + 0.893125i \(0.648508\pi\)
\(632\) 25.3669 1.00904
\(633\) −1.32393 −0.0526215
\(634\) −15.9908 −0.635078
\(635\) −52.2399 −2.07308
\(636\) 4.69002 0.185971
\(637\) −1.03159 −0.0408731
\(638\) 7.50538 0.297141
\(639\) −38.0695 −1.50601
\(640\) 72.4351 2.86325
\(641\) −5.97068 −0.235828 −0.117914 0.993024i \(-0.537621\pi\)
−0.117914 + 0.993024i \(0.537621\pi\)
\(642\) −1.25800 −0.0496492
\(643\) 17.8129 0.702472 0.351236 0.936287i \(-0.385761\pi\)
0.351236 + 0.936287i \(0.385761\pi\)
\(644\) −0.831948 −0.0327833
\(645\) 0.946802 0.0372803
\(646\) 13.4379 0.528706
\(647\) −31.2569 −1.22884 −0.614419 0.788980i \(-0.710609\pi\)
−0.614419 + 0.788980i \(0.710609\pi\)
\(648\) −38.4017 −1.50856
\(649\) −14.9209 −0.585695
\(650\) −10.5104 −0.412254
\(651\) −0.405570 −0.0158956
\(652\) −17.2684 −0.676281
\(653\) −0.160921 −0.00629733 −0.00314867 0.999995i \(-0.501002\pi\)
−0.00314867 + 0.999995i \(0.501002\pi\)
\(654\) −10.9473 −0.428073
\(655\) −36.6709 −1.43285
\(656\) −2.38054 −0.0929444
\(657\) 6.01200 0.234550
\(658\) −31.8744 −1.24259
\(659\) −14.2421 −0.554793 −0.277397 0.960756i \(-0.589472\pi\)
−0.277397 + 0.960756i \(0.589472\pi\)
\(660\) −3.68330 −0.143372
\(661\) 10.6546 0.414418 0.207209 0.978297i \(-0.433562\pi\)
0.207209 + 0.978297i \(0.433562\pi\)
\(662\) 13.1070 0.509418
\(663\) 0.148898 0.00578272
\(664\) 24.8912 0.965967
\(665\) 44.8623 1.73969
\(666\) 12.2949 0.476419
\(667\) 0.291114 0.0112720
\(668\) −88.5534 −3.42623
\(669\) −1.24974 −0.0483178
\(670\) 9.41091 0.363575
\(671\) 3.26994 0.126235
\(672\) −0.624879 −0.0241052
\(673\) 19.6795 0.758590 0.379295 0.925276i \(-0.376167\pi\)
0.379295 + 0.925276i \(0.376167\pi\)
\(674\) −54.7249 −2.10792
\(675\) −12.1531 −0.467773
\(676\) −49.3494 −1.89805
\(677\) 41.9652 1.61285 0.806426 0.591335i \(-0.201399\pi\)
0.806426 + 0.591335i \(0.201399\pi\)
\(678\) 3.07688 0.118167
\(679\) −13.6668 −0.524483
\(680\) −16.3623 −0.627467
\(681\) −0.434889 −0.0166650
\(682\) 1.63220 0.0625000
\(683\) 1.41580 0.0541742 0.0270871 0.999633i \(-0.491377\pi\)
0.0270871 + 0.999633i \(0.491377\pi\)
\(684\) 63.1014 2.41274
\(685\) −41.2443 −1.57586
\(686\) −48.7347 −1.86070
\(687\) −2.92869 −0.111736
\(688\) 3.35357 0.127854
\(689\) 2.54732 0.0970453
\(690\) −0.216314 −0.00823492
\(691\) −46.1662 −1.75624 −0.878122 0.478437i \(-0.841203\pi\)
−0.878122 + 0.478437i \(0.841203\pi\)
\(692\) 43.1737 1.64122
\(693\) −6.65516 −0.252808
\(694\) 66.1134 2.50963
\(695\) −29.3506 −1.11333
\(696\) −3.76612 −0.142754
\(697\) −0.709853 −0.0268876
\(698\) 39.9049 1.51042
\(699\) −3.98784 −0.150834
\(700\) −68.2345 −2.57902
\(701\) 31.3644 1.18462 0.592308 0.805712i \(-0.298217\pi\)
0.592308 + 0.805712i \(0.298217\pi\)
\(702\) 2.14277 0.0808738
\(703\) −9.57469 −0.361116
\(704\) 9.22192 0.347564
\(705\) −5.47361 −0.206148
\(706\) −13.5986 −0.511791
\(707\) 10.1944 0.383398
\(708\) 15.4089 0.579103
\(709\) −16.1781 −0.607583 −0.303791 0.952739i \(-0.598253\pi\)
−0.303791 + 0.952739i \(0.598253\pi\)
\(710\) −112.487 −4.22158
\(711\) 16.1987 0.607497
\(712\) −61.2105 −2.29396
\(713\) 0.0633086 0.00237093
\(714\) 1.46362 0.0547746
\(715\) −2.00054 −0.0748158
\(716\) −35.9743 −1.34442
\(717\) −6.54533 −0.244440
\(718\) 13.0337 0.486414
\(719\) 14.7977 0.551861 0.275931 0.961178i \(-0.411014\pi\)
0.275931 + 0.961178i \(0.411014\pi\)
\(720\) −35.0399 −1.30586
\(721\) −21.7303 −0.809279
\(722\) −28.2908 −1.05288
\(723\) −2.65240 −0.0986437
\(724\) −81.8809 −3.04308
\(725\) 23.8766 0.886754
\(726\) −0.644270 −0.0239111
\(727\) 4.00979 0.148715 0.0743574 0.997232i \(-0.476309\pi\)
0.0743574 + 0.997232i \(0.476309\pi\)
\(728\) 5.84568 0.216655
\(729\) −23.2688 −0.861807
\(730\) 17.7642 0.657483
\(731\) 1.00000 0.0369863
\(732\) −3.37690 −0.124814
\(733\) −31.8557 −1.17662 −0.588308 0.808637i \(-0.700206\pi\)
−0.588308 + 0.808637i \(0.700206\pi\)
\(734\) 68.0501 2.51178
\(735\) −1.74132 −0.0642296
\(736\) 0.0975423 0.00359546
\(737\) 1.08719 0.0400472
\(738\) −5.04700 −0.185783
\(739\) 16.2278 0.596951 0.298475 0.954417i \(-0.403522\pi\)
0.298475 + 0.954417i \(0.403522\pi\)
\(740\) 23.9937 0.882027
\(741\) −0.824427 −0.0302861
\(742\) 25.0394 0.919224
\(743\) −20.1018 −0.737465 −0.368733 0.929536i \(-0.620208\pi\)
−0.368733 + 0.929536i \(0.620208\pi\)
\(744\) −0.819017 −0.0300266
\(745\) −44.1605 −1.61792
\(746\) −6.67300 −0.244316
\(747\) 15.8949 0.581563
\(748\) −3.89025 −0.142242
\(749\) −4.43580 −0.162081
\(750\) −6.25221 −0.228299
\(751\) −30.3326 −1.10685 −0.553426 0.832898i \(-0.686680\pi\)
−0.553426 + 0.832898i \(0.686680\pi\)
\(752\) −19.3875 −0.706989
\(753\) −0.0799166 −0.00291232
\(754\) −4.20980 −0.153312
\(755\) 25.3221 0.921566
\(756\) 13.9110 0.505939
\(757\) 11.0651 0.402167 0.201083 0.979574i \(-0.435554\pi\)
0.201083 + 0.979574i \(0.435554\pi\)
\(758\) 43.9852 1.59761
\(759\) −0.0249896 −0.000907064 0
\(760\) 90.5959 3.28626
\(761\) −11.8063 −0.427979 −0.213989 0.976836i \(-0.568646\pi\)
−0.213989 + 0.976836i \(0.568646\pi\)
\(762\) 9.43652 0.341849
\(763\) −38.6010 −1.39745
\(764\) 48.3611 1.74964
\(765\) −10.4486 −0.377768
\(766\) −11.1306 −0.402163
\(767\) 8.36916 0.302193
\(768\) −8.18842 −0.295474
\(769\) −14.8518 −0.535570 −0.267785 0.963479i \(-0.586292\pi\)
−0.267785 + 0.963479i \(0.586292\pi\)
\(770\) −19.6646 −0.708664
\(771\) −3.98859 −0.143645
\(772\) −0.773995 −0.0278567
\(773\) −47.2794 −1.70052 −0.850260 0.526363i \(-0.823555\pi\)
−0.850260 + 0.526363i \(0.823555\pi\)
\(774\) 7.10992 0.255561
\(775\) 5.19244 0.186518
\(776\) −27.5990 −0.990746
\(777\) −1.04285 −0.0374121
\(778\) −41.4529 −1.48616
\(779\) 3.93036 0.140820
\(780\) 2.06598 0.0739738
\(781\) −12.9951 −0.465000
\(782\) −0.228468 −0.00816999
\(783\) −4.86774 −0.173959
\(784\) −6.16775 −0.220277
\(785\) −74.9913 −2.67655
\(786\) 6.62416 0.236276
\(787\) 7.36580 0.262563 0.131281 0.991345i \(-0.458091\pi\)
0.131281 + 0.991345i \(0.458091\pi\)
\(788\) 1.84849 0.0658497
\(789\) −3.89408 −0.138633
\(790\) 47.8637 1.70291
\(791\) 10.8493 0.385757
\(792\) −13.4396 −0.477554
\(793\) −1.83412 −0.0651316
\(794\) −88.9993 −3.15847
\(795\) 4.29987 0.152501
\(796\) −17.9442 −0.636015
\(797\) 20.3167 0.719654 0.359827 0.933019i \(-0.382836\pi\)
0.359827 + 0.933019i \(0.382836\pi\)
\(798\) −8.10385 −0.286873
\(799\) −5.78116 −0.204523
\(800\) 8.00021 0.282850
\(801\) −39.0874 −1.38109
\(802\) −3.22436 −0.113856
\(803\) 2.05221 0.0724207
\(804\) −1.12276 −0.0395965
\(805\) −0.762740 −0.0268830
\(806\) −0.915504 −0.0322472
\(807\) −0.408900 −0.0143940
\(808\) 20.5867 0.724238
\(809\) −28.3218 −0.995742 −0.497871 0.867251i \(-0.665885\pi\)
−0.497871 + 0.867251i \(0.665885\pi\)
\(810\) −72.4585 −2.54593
\(811\) 2.29089 0.0804441 0.0402221 0.999191i \(-0.487193\pi\)
0.0402221 + 0.999191i \(0.487193\pi\)
\(812\) −27.3303 −0.959105
\(813\) −5.51579 −0.193447
\(814\) 4.19690 0.147101
\(815\) −15.8319 −0.554566
\(816\) 0.890241 0.0311647
\(817\) −5.53686 −0.193710
\(818\) 55.1873 1.92958
\(819\) 3.73290 0.130438
\(820\) −9.84929 −0.343952
\(821\) −53.0608 −1.85184 −0.925918 0.377725i \(-0.876706\pi\)
−0.925918 + 0.377725i \(0.876706\pi\)
\(822\) 7.45029 0.259859
\(823\) 25.0667 0.873772 0.436886 0.899517i \(-0.356081\pi\)
0.436886 + 0.899517i \(0.356081\pi\)
\(824\) −43.8826 −1.52872
\(825\) −2.04959 −0.0713576
\(826\) 82.2662 2.86241
\(827\) −23.7100 −0.824477 −0.412238 0.911076i \(-0.635253\pi\)
−0.412238 + 0.911076i \(0.635253\pi\)
\(828\) −1.07284 −0.0372837
\(829\) 23.9376 0.831386 0.415693 0.909505i \(-0.363539\pi\)
0.415693 + 0.909505i \(0.363539\pi\)
\(830\) 46.9661 1.63022
\(831\) 3.22713 0.111948
\(832\) −5.17261 −0.179328
\(833\) −1.83916 −0.0637231
\(834\) 5.30184 0.183588
\(835\) −81.1868 −2.80959
\(836\) 21.5398 0.744969
\(837\) −1.05859 −0.0365901
\(838\) 58.4467 2.01901
\(839\) 44.6869 1.54276 0.771382 0.636373i \(-0.219566\pi\)
0.771382 + 0.636373i \(0.219566\pi\)
\(840\) 9.86749 0.340461
\(841\) −19.4366 −0.670228
\(842\) 85.4925 2.94627
\(843\) 0.559464 0.0192690
\(844\) −19.4018 −0.667838
\(845\) −45.2441 −1.55644
\(846\) −41.1036 −1.41317
\(847\) −2.27175 −0.0780582
\(848\) 15.2301 0.523004
\(849\) −5.73418 −0.196797
\(850\) −18.7384 −0.642723
\(851\) 0.162787 0.00558026
\(852\) 13.4202 0.459767
\(853\) 33.8753 1.15987 0.579935 0.814663i \(-0.303078\pi\)
0.579935 + 0.814663i \(0.303078\pi\)
\(854\) −18.0288 −0.616933
\(855\) 57.8522 1.97850
\(856\) −8.95775 −0.306169
\(857\) −44.2756 −1.51242 −0.756212 0.654327i \(-0.772952\pi\)
−0.756212 + 0.654327i \(0.772952\pi\)
\(858\) 0.361373 0.0123371
\(859\) 1.80274 0.0615086 0.0307543 0.999527i \(-0.490209\pi\)
0.0307543 + 0.999527i \(0.490209\pi\)
\(860\) 13.8751 0.473137
\(861\) 0.428085 0.0145891
\(862\) −30.1889 −1.02824
\(863\) 23.5042 0.800092 0.400046 0.916495i \(-0.368994\pi\)
0.400046 + 0.916495i \(0.368994\pi\)
\(864\) −1.63101 −0.0554880
\(865\) 39.5822 1.34584
\(866\) −52.2181 −1.77444
\(867\) 0.265461 0.00901553
\(868\) −5.94351 −0.201736
\(869\) 5.52944 0.187573
\(870\) −7.10611 −0.240920
\(871\) −0.609810 −0.0206626
\(872\) −77.9518 −2.63978
\(873\) −17.6240 −0.596481
\(874\) 1.26499 0.0427890
\(875\) −22.0458 −0.745284
\(876\) −2.11933 −0.0716057
\(877\) −6.32715 −0.213653 −0.106826 0.994278i \(-0.534069\pi\)
−0.106826 + 0.994278i \(0.534069\pi\)
\(878\) −34.6161 −1.16824
\(879\) 1.26722 0.0427423
\(880\) −11.9609 −0.403203
\(881\) −2.60245 −0.0876786 −0.0438393 0.999039i \(-0.513959\pi\)
−0.0438393 + 0.999039i \(0.513959\pi\)
\(882\) −13.0763 −0.440302
\(883\) 30.2445 1.01781 0.508904 0.860824i \(-0.330051\pi\)
0.508904 + 0.860824i \(0.330051\pi\)
\(884\) 2.18206 0.0733905
\(885\) 14.1271 0.474878
\(886\) −74.3158 −2.49669
\(887\) −15.3076 −0.513979 −0.256989 0.966414i \(-0.582731\pi\)
−0.256989 + 0.966414i \(0.582731\pi\)
\(888\) −2.10596 −0.0706713
\(889\) 33.2740 1.11597
\(890\) −115.495 −3.87141
\(891\) −8.37074 −0.280430
\(892\) −18.3146 −0.613218
\(893\) 32.0095 1.07116
\(894\) 7.97707 0.266793
\(895\) −32.9816 −1.10245
\(896\) −46.1372 −1.54133
\(897\) 0.0140167 0.000468005 0
\(898\) 61.6209 2.05632
\(899\) 2.07975 0.0693635
\(900\) −87.9918 −2.93306
\(901\) 4.54147 0.151298
\(902\) −1.72280 −0.0573630
\(903\) −0.603061 −0.0200686
\(904\) 21.9093 0.728694
\(905\) −75.0694 −2.49539
\(906\) −4.57414 −0.151966
\(907\) −9.14766 −0.303743 −0.151872 0.988400i \(-0.548530\pi\)
−0.151872 + 0.988400i \(0.548530\pi\)
\(908\) −6.37317 −0.211501
\(909\) 13.1461 0.436030
\(910\) 11.0300 0.365639
\(911\) −44.7738 −1.48342 −0.741712 0.670719i \(-0.765986\pi\)
−0.741712 + 0.670719i \(0.765986\pi\)
\(912\) −4.92914 −0.163220
\(913\) 5.42574 0.179566
\(914\) −81.7160 −2.70293
\(915\) −3.09599 −0.102350
\(916\) −42.9191 −1.41809
\(917\) 23.3573 0.771327
\(918\) 3.82022 0.126086
\(919\) 6.41709 0.211680 0.105840 0.994383i \(-0.466247\pi\)
0.105840 + 0.994383i \(0.466247\pi\)
\(920\) −1.54029 −0.0507820
\(921\) −5.66651 −0.186718
\(922\) −6.49451 −0.213885
\(923\) 7.28898 0.239920
\(924\) 2.34606 0.0771797
\(925\) 13.3514 0.438992
\(926\) −50.7642 −1.66822
\(927\) −28.0223 −0.920373
\(928\) 3.20436 0.105188
\(929\) 3.19854 0.104941 0.0524704 0.998622i \(-0.483290\pi\)
0.0524704 + 0.998622i \(0.483290\pi\)
\(930\) −1.54537 −0.0506745
\(931\) 10.1832 0.333740
\(932\) −58.4406 −1.91429
\(933\) −6.84516 −0.224101
\(934\) −86.5599 −2.83233
\(935\) −3.56663 −0.116641
\(936\) 7.53830 0.246397
\(937\) 49.4621 1.61586 0.807928 0.589281i \(-0.200589\pi\)
0.807928 + 0.589281i \(0.200589\pi\)
\(938\) −5.99423 −0.195719
\(939\) 2.96380 0.0967200
\(940\) −80.2142 −2.61630
\(941\) 44.7320 1.45822 0.729111 0.684396i \(-0.239934\pi\)
0.729111 + 0.684396i \(0.239934\pi\)
\(942\) 13.5463 0.441362
\(943\) −0.0668231 −0.00217606
\(944\) 50.0381 1.62860
\(945\) 12.7538 0.414881
\(946\) 2.42698 0.0789081
\(947\) −41.5474 −1.35011 −0.675054 0.737768i \(-0.735880\pi\)
−0.675054 + 0.737768i \(0.735880\pi\)
\(948\) −5.71031 −0.185462
\(949\) −1.15109 −0.0373659
\(950\) 103.752 3.36616
\(951\) 1.74906 0.0567172
\(952\) 10.4219 0.337776
\(953\) 16.5458 0.535970 0.267985 0.963423i \(-0.413642\pi\)
0.267985 + 0.963423i \(0.413642\pi\)
\(954\) 32.2895 1.04541
\(955\) 44.3380 1.43474
\(956\) −95.9199 −3.10227
\(957\) −0.820931 −0.0265369
\(958\) 54.3400 1.75564
\(959\) 26.2703 0.848313
\(960\) −8.73134 −0.281803
\(961\) −30.5477 −0.985410
\(962\) −2.35405 −0.0758978
\(963\) −5.72018 −0.184330
\(964\) −38.8701 −1.25192
\(965\) −0.709609 −0.0228431
\(966\) 0.137780 0.00443300
\(967\) 53.0556 1.70615 0.853076 0.521786i \(-0.174734\pi\)
0.853076 + 0.521786i \(0.174734\pi\)
\(968\) −4.58762 −0.147452
\(969\) −1.46982 −0.0472174
\(970\) −52.0752 −1.67204
\(971\) 2.80146 0.0899031 0.0449516 0.998989i \(-0.485687\pi\)
0.0449516 + 0.998989i \(0.485687\pi\)
\(972\) 27.0150 0.866507
\(973\) 18.6947 0.599326
\(974\) −20.5544 −0.658605
\(975\) 1.14962 0.0368174
\(976\) −10.9660 −0.351012
\(977\) −3.18958 −0.102044 −0.0510218 0.998698i \(-0.516248\pi\)
−0.0510218 + 0.998698i \(0.516248\pi\)
\(978\) 2.85984 0.0914475
\(979\) −13.3425 −0.426430
\(980\) −25.5185 −0.815160
\(981\) −49.7779 −1.58929
\(982\) 14.4954 0.462568
\(983\) 9.06196 0.289032 0.144516 0.989502i \(-0.453838\pi\)
0.144516 + 0.989502i \(0.453838\pi\)
\(984\) 0.864483 0.0275587
\(985\) 1.69472 0.0539982
\(986\) −7.50538 −0.239020
\(987\) 3.48639 0.110973
\(988\) −12.0817 −0.384371
\(989\) 0.0941365 0.00299337
\(990\) −25.3585 −0.805946
\(991\) 21.3956 0.679652 0.339826 0.940488i \(-0.389632\pi\)
0.339826 + 0.940488i \(0.389632\pi\)
\(992\) 0.696851 0.0221251
\(993\) −1.43363 −0.0454949
\(994\) 71.6483 2.27255
\(995\) −16.4515 −0.521546
\(996\) −5.60322 −0.177545
\(997\) −2.71816 −0.0860850 −0.0430425 0.999073i \(-0.513705\pi\)
−0.0430425 + 0.999073i \(0.513705\pi\)
\(998\) 67.4532 2.13519
\(999\) −2.72197 −0.0861192
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))