Properties

Label 8001.2.a.o.1.13
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 13
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(1\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Root \(-2.45160\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.45160 q^{2}\) \(+4.01034 q^{4}\) \(-1.23909 q^{5}\) \(+1.00000 q^{7}\) \(+4.92856 q^{8}\) \(+O(q^{10})\) \(q\)\(+2.45160 q^{2}\) \(+4.01034 q^{4}\) \(-1.23909 q^{5}\) \(+1.00000 q^{7}\) \(+4.92856 q^{8}\) \(-3.03775 q^{10}\) \(-2.19586 q^{11}\) \(+1.52432 q^{13}\) \(+2.45160 q^{14}\) \(+4.06217 q^{16}\) \(-7.06712 q^{17}\) \(-1.45237 q^{19}\) \(-4.96917 q^{20}\) \(-5.38336 q^{22}\) \(-2.60977 q^{23}\) \(-3.46466 q^{25}\) \(+3.73703 q^{26}\) \(+4.01034 q^{28}\) \(-6.11799 q^{29}\) \(+1.83292 q^{31}\) \(+0.101697 q^{32}\) \(-17.3258 q^{34}\) \(-1.23909 q^{35}\) \(+0.914123 q^{37}\) \(-3.56064 q^{38}\) \(-6.10692 q^{40}\) \(+1.13505 q^{41}\) \(+2.48757 q^{43}\) \(-8.80614 q^{44}\) \(-6.39812 q^{46}\) \(-0.620901 q^{47}\) \(+1.00000 q^{49}\) \(-8.49396 q^{50}\) \(+6.11305 q^{52}\) \(-6.86259 q^{53}\) \(+2.72086 q^{55}\) \(+4.92856 q^{56}\) \(-14.9989 q^{58}\) \(-8.13041 q^{59}\) \(+5.09932 q^{61}\) \(+4.49360 q^{62}\) \(-7.87502 q^{64}\) \(-1.88877 q^{65}\) \(-5.28798 q^{67}\) \(-28.3416 q^{68}\) \(-3.03775 q^{70}\) \(-4.94368 q^{71}\) \(+3.24571 q^{73}\) \(+2.24106 q^{74}\) \(-5.82451 q^{76}\) \(-2.19586 q^{77}\) \(-8.62522 q^{79}\) \(-5.03339 q^{80}\) \(+2.78269 q^{82}\) \(+14.6973 q^{83}\) \(+8.75679 q^{85}\) \(+6.09853 q^{86}\) \(-10.8224 q^{88}\) \(-2.62512 q^{89}\) \(+1.52432 q^{91}\) \(-10.4661 q^{92}\) \(-1.52220 q^{94}\) \(+1.79962 q^{95}\) \(+4.23555 q^{97}\) \(+2.45160 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 21q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 29q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut -\mathstrut 22q^{26} \) \(\mathstrut +\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 21q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 12q^{35} \) \(\mathstrut +\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 29q^{40} \) \(\mathstrut -\mathstrut 21q^{41} \) \(\mathstrut -\mathstrut 9q^{43} \) \(\mathstrut +\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 28q^{46} \) \(\mathstrut -\mathstrut 23q^{47} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut +\mathstrut 15q^{52} \) \(\mathstrut -\mathstrut 31q^{53} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut -\mathstrut 25q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut +\mathstrut 29q^{61} \) \(\mathstrut +\mathstrut 3q^{62} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 30q^{65} \) \(\mathstrut -\mathstrut 18q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 19q^{74} \) \(\mathstrut -\mathstrut 3q^{77} \) \(\mathstrut -\mathstrut 28q^{79} \) \(\mathstrut -\mathstrut 26q^{80} \) \(\mathstrut +\mathstrut 18q^{82} \) \(\mathstrut -\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 2q^{86} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 44q^{89} \) \(\mathstrut +\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 6q^{92} \) \(\mathstrut -\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 17q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.45160 1.73354 0.866772 0.498705i \(-0.166191\pi\)
0.866772 + 0.498705i \(0.166191\pi\)
\(3\) 0 0
\(4\) 4.01034 2.00517
\(5\) −1.23909 −0.554137 −0.277069 0.960850i \(-0.589363\pi\)
−0.277069 + 0.960850i \(0.589363\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 4.92856 1.74251
\(9\) 0 0
\(10\) −3.03775 −0.960621
\(11\) −2.19586 −0.662076 −0.331038 0.943618i \(-0.607399\pi\)
−0.331038 + 0.943618i \(0.607399\pi\)
\(12\) 0 0
\(13\) 1.52432 0.422771 0.211385 0.977403i \(-0.432203\pi\)
0.211385 + 0.977403i \(0.432203\pi\)
\(14\) 2.45160 0.655218
\(15\) 0 0
\(16\) 4.06217 1.01554
\(17\) −7.06712 −1.71403 −0.857014 0.515292i \(-0.827683\pi\)
−0.857014 + 0.515292i \(0.827683\pi\)
\(18\) 0 0
\(19\) −1.45237 −0.333197 −0.166599 0.986025i \(-0.553278\pi\)
−0.166599 + 0.986025i \(0.553278\pi\)
\(20\) −4.96917 −1.11114
\(21\) 0 0
\(22\) −5.38336 −1.14774
\(23\) −2.60977 −0.544175 −0.272088 0.962272i \(-0.587714\pi\)
−0.272088 + 0.962272i \(0.587714\pi\)
\(24\) 0 0
\(25\) −3.46466 −0.692932
\(26\) 3.73703 0.732891
\(27\) 0 0
\(28\) 4.01034 0.757884
\(29\) −6.11799 −1.13608 −0.568041 0.823000i \(-0.692299\pi\)
−0.568041 + 0.823000i \(0.692299\pi\)
\(30\) 0 0
\(31\) 1.83292 0.329203 0.164601 0.986360i \(-0.447366\pi\)
0.164601 + 0.986360i \(0.447366\pi\)
\(32\) 0.101697 0.0179777
\(33\) 0 0
\(34\) −17.3258 −2.97134
\(35\) −1.23909 −0.209444
\(36\) 0 0
\(37\) 0.914123 0.150281 0.0751404 0.997173i \(-0.476059\pi\)
0.0751404 + 0.997173i \(0.476059\pi\)
\(38\) −3.56064 −0.577611
\(39\) 0 0
\(40\) −6.10692 −0.965589
\(41\) 1.13505 0.177265 0.0886325 0.996064i \(-0.471750\pi\)
0.0886325 + 0.996064i \(0.471750\pi\)
\(42\) 0 0
\(43\) 2.48757 0.379351 0.189675 0.981847i \(-0.439256\pi\)
0.189675 + 0.981847i \(0.439256\pi\)
\(44\) −8.80614 −1.32758
\(45\) 0 0
\(46\) −6.39812 −0.943352
\(47\) −0.620901 −0.0905677 −0.0452839 0.998974i \(-0.514419\pi\)
−0.0452839 + 0.998974i \(0.514419\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −8.49396 −1.20123
\(51\) 0 0
\(52\) 6.11305 0.847728
\(53\) −6.86259 −0.942649 −0.471325 0.881960i \(-0.656224\pi\)
−0.471325 + 0.881960i \(0.656224\pi\)
\(54\) 0 0
\(55\) 2.72086 0.366881
\(56\) 4.92856 0.658606
\(57\) 0 0
\(58\) −14.9989 −1.96945
\(59\) −8.13041 −1.05849 −0.529245 0.848469i \(-0.677525\pi\)
−0.529245 + 0.848469i \(0.677525\pi\)
\(60\) 0 0
\(61\) 5.09932 0.652901 0.326451 0.945214i \(-0.394147\pi\)
0.326451 + 0.945214i \(0.394147\pi\)
\(62\) 4.49360 0.570687
\(63\) 0 0
\(64\) −7.87502 −0.984377
\(65\) −1.88877 −0.234273
\(66\) 0 0
\(67\) −5.28798 −0.646029 −0.323015 0.946394i \(-0.604696\pi\)
−0.323015 + 0.946394i \(0.604696\pi\)
\(68\) −28.3416 −3.43692
\(69\) 0 0
\(70\) −3.03775 −0.363081
\(71\) −4.94368 −0.586707 −0.293353 0.956004i \(-0.594771\pi\)
−0.293353 + 0.956004i \(0.594771\pi\)
\(72\) 0 0
\(73\) 3.24571 0.379882 0.189941 0.981796i \(-0.439170\pi\)
0.189941 + 0.981796i \(0.439170\pi\)
\(74\) 2.24106 0.260518
\(75\) 0 0
\(76\) −5.82451 −0.668117
\(77\) −2.19586 −0.250241
\(78\) 0 0
\(79\) −8.62522 −0.970413 −0.485206 0.874400i \(-0.661255\pi\)
−0.485206 + 0.874400i \(0.661255\pi\)
\(80\) −5.03339 −0.562750
\(81\) 0 0
\(82\) 2.78269 0.307296
\(83\) 14.6973 1.61324 0.806621 0.591069i \(-0.201294\pi\)
0.806621 + 0.591069i \(0.201294\pi\)
\(84\) 0 0
\(85\) 8.75679 0.949807
\(86\) 6.09853 0.657621
\(87\) 0 0
\(88\) −10.8224 −1.15367
\(89\) −2.62512 −0.278262 −0.139131 0.990274i \(-0.544431\pi\)
−0.139131 + 0.990274i \(0.544431\pi\)
\(90\) 0 0
\(91\) 1.52432 0.159792
\(92\) −10.4661 −1.09117
\(93\) 0 0
\(94\) −1.52220 −0.157003
\(95\) 1.79962 0.184637
\(96\) 0 0
\(97\) 4.23555 0.430055 0.215028 0.976608i \(-0.431016\pi\)
0.215028 + 0.976608i \(0.431016\pi\)
\(98\) 2.45160 0.247649
\(99\) 0 0
\(100\) −13.8945 −1.38945
\(101\) 8.53644 0.849407 0.424704 0.905332i \(-0.360378\pi\)
0.424704 + 0.905332i \(0.360378\pi\)
\(102\) 0 0
\(103\) −0.764721 −0.0753502 −0.0376751 0.999290i \(-0.511995\pi\)
−0.0376751 + 0.999290i \(0.511995\pi\)
\(104\) 7.51271 0.736681
\(105\) 0 0
\(106\) −16.8243 −1.63412
\(107\) −5.26387 −0.508878 −0.254439 0.967089i \(-0.581891\pi\)
−0.254439 + 0.967089i \(0.581891\pi\)
\(108\) 0 0
\(109\) −7.88983 −0.755709 −0.377854 0.925865i \(-0.623338\pi\)
−0.377854 + 0.925865i \(0.623338\pi\)
\(110\) 6.67046 0.636004
\(111\) 0 0
\(112\) 4.06217 0.383839
\(113\) 3.38966 0.318872 0.159436 0.987208i \(-0.449032\pi\)
0.159436 + 0.987208i \(0.449032\pi\)
\(114\) 0 0
\(115\) 3.23374 0.301548
\(116\) −24.5352 −2.27804
\(117\) 0 0
\(118\) −19.9325 −1.83494
\(119\) −7.06712 −0.647842
\(120\) 0 0
\(121\) −6.17822 −0.561656
\(122\) 12.5015 1.13183
\(123\) 0 0
\(124\) 7.35066 0.660108
\(125\) 10.4885 0.938117
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) −19.5098 −1.72444
\(129\) 0 0
\(130\) −4.63051 −0.406122
\(131\) 15.2901 1.33590 0.667951 0.744205i \(-0.267172\pi\)
0.667951 + 0.744205i \(0.267172\pi\)
\(132\) 0 0
\(133\) −1.45237 −0.125937
\(134\) −12.9640 −1.11992
\(135\) 0 0
\(136\) −34.8307 −2.98671
\(137\) −11.5984 −0.990920 −0.495460 0.868631i \(-0.665001\pi\)
−0.495460 + 0.868631i \(0.665001\pi\)
\(138\) 0 0
\(139\) −13.6844 −1.16069 −0.580347 0.814369i \(-0.697083\pi\)
−0.580347 + 0.814369i \(0.697083\pi\)
\(140\) −4.96917 −0.419972
\(141\) 0 0
\(142\) −12.1199 −1.01708
\(143\) −3.34719 −0.279906
\(144\) 0 0
\(145\) 7.58073 0.629545
\(146\) 7.95719 0.658541
\(147\) 0 0
\(148\) 3.66595 0.301339
\(149\) 17.3140 1.41842 0.709210 0.704997i \(-0.249052\pi\)
0.709210 + 0.704997i \(0.249052\pi\)
\(150\) 0 0
\(151\) 1.01569 0.0826559 0.0413280 0.999146i \(-0.486841\pi\)
0.0413280 + 0.999146i \(0.486841\pi\)
\(152\) −7.15810 −0.580599
\(153\) 0 0
\(154\) −5.38336 −0.433804
\(155\) −2.27115 −0.182424
\(156\) 0 0
\(157\) −7.65737 −0.611125 −0.305562 0.952172i \(-0.598844\pi\)
−0.305562 + 0.952172i \(0.598844\pi\)
\(158\) −21.1456 −1.68225
\(159\) 0 0
\(160\) −0.126012 −0.00996212
\(161\) −2.60977 −0.205679
\(162\) 0 0
\(163\) 21.5168 1.68533 0.842664 0.538439i \(-0.180986\pi\)
0.842664 + 0.538439i \(0.180986\pi\)
\(164\) 4.55194 0.355447
\(165\) 0 0
\(166\) 36.0320 2.79662
\(167\) 15.3106 1.18477 0.592387 0.805654i \(-0.298186\pi\)
0.592387 + 0.805654i \(0.298186\pi\)
\(168\) 0 0
\(169\) −10.6764 −0.821265
\(170\) 21.4681 1.64653
\(171\) 0 0
\(172\) 9.97601 0.760664
\(173\) −25.8227 −1.96326 −0.981632 0.190784i \(-0.938897\pi\)
−0.981632 + 0.190784i \(0.938897\pi\)
\(174\) 0 0
\(175\) −3.46466 −0.261904
\(176\) −8.91994 −0.672366
\(177\) 0 0
\(178\) −6.43573 −0.482379
\(179\) −5.00100 −0.373792 −0.186896 0.982380i \(-0.559843\pi\)
−0.186896 + 0.982380i \(0.559843\pi\)
\(180\) 0 0
\(181\) 7.03422 0.522850 0.261425 0.965224i \(-0.415808\pi\)
0.261425 + 0.965224i \(0.415808\pi\)
\(182\) 3.73703 0.277007
\(183\) 0 0
\(184\) −12.8624 −0.948231
\(185\) −1.13268 −0.0832762
\(186\) 0 0
\(187\) 15.5184 1.13482
\(188\) −2.49003 −0.181604
\(189\) 0 0
\(190\) 4.41194 0.320076
\(191\) 9.51278 0.688321 0.344160 0.938911i \(-0.388164\pi\)
0.344160 + 0.938911i \(0.388164\pi\)
\(192\) 0 0
\(193\) 5.64395 0.406261 0.203130 0.979152i \(-0.434888\pi\)
0.203130 + 0.979152i \(0.434888\pi\)
\(194\) 10.3839 0.745519
\(195\) 0 0
\(196\) 4.01034 0.286453
\(197\) 0.962282 0.0685597 0.0342799 0.999412i \(-0.489086\pi\)
0.0342799 + 0.999412i \(0.489086\pi\)
\(198\) 0 0
\(199\) −8.51386 −0.603532 −0.301766 0.953382i \(-0.597576\pi\)
−0.301766 + 0.953382i \(0.597576\pi\)
\(200\) −17.0758 −1.20744
\(201\) 0 0
\(202\) 20.9279 1.47248
\(203\) −6.11799 −0.429399
\(204\) 0 0
\(205\) −1.40643 −0.0982291
\(206\) −1.87479 −0.130623
\(207\) 0 0
\(208\) 6.19205 0.429341
\(209\) 3.18920 0.220602
\(210\) 0 0
\(211\) 4.62207 0.318196 0.159098 0.987263i \(-0.449141\pi\)
0.159098 + 0.987263i \(0.449141\pi\)
\(212\) −27.5213 −1.89017
\(213\) 0 0
\(214\) −12.9049 −0.882161
\(215\) −3.08232 −0.210212
\(216\) 0 0
\(217\) 1.83292 0.124427
\(218\) −19.3427 −1.31005
\(219\) 0 0
\(220\) 10.9116 0.735659
\(221\) −10.7726 −0.724641
\(222\) 0 0
\(223\) −2.37627 −0.159127 −0.0795635 0.996830i \(-0.525353\pi\)
−0.0795635 + 0.996830i \(0.525353\pi\)
\(224\) 0.101697 0.00679494
\(225\) 0 0
\(226\) 8.31009 0.552779
\(227\) −23.8414 −1.58241 −0.791205 0.611550i \(-0.790546\pi\)
−0.791205 + 0.611550i \(0.790546\pi\)
\(228\) 0 0
\(229\) 1.15914 0.0765981 0.0382991 0.999266i \(-0.487806\pi\)
0.0382991 + 0.999266i \(0.487806\pi\)
\(230\) 7.92784 0.522746
\(231\) 0 0
\(232\) −30.1529 −1.97963
\(233\) −0.949682 −0.0622157 −0.0311079 0.999516i \(-0.509904\pi\)
−0.0311079 + 0.999516i \(0.509904\pi\)
\(234\) 0 0
\(235\) 0.769351 0.0501869
\(236\) −32.6057 −2.12245
\(237\) 0 0
\(238\) −17.3258 −1.12306
\(239\) 5.71424 0.369623 0.184812 0.982774i \(-0.440833\pi\)
0.184812 + 0.982774i \(0.440833\pi\)
\(240\) 0 0
\(241\) 22.3910 1.44233 0.721166 0.692762i \(-0.243607\pi\)
0.721166 + 0.692762i \(0.243607\pi\)
\(242\) −15.1465 −0.973655
\(243\) 0 0
\(244\) 20.4500 1.30918
\(245\) −1.23909 −0.0791625
\(246\) 0 0
\(247\) −2.21388 −0.140866
\(248\) 9.03367 0.573639
\(249\) 0 0
\(250\) 25.7135 1.62627
\(251\) 1.54081 0.0972550 0.0486275 0.998817i \(-0.484515\pi\)
0.0486275 + 0.998817i \(0.484515\pi\)
\(252\) 0 0
\(253\) 5.73069 0.360285
\(254\) −2.45160 −0.153827
\(255\) 0 0
\(256\) −32.0802 −2.00501
\(257\) 3.86350 0.240999 0.120499 0.992713i \(-0.461550\pi\)
0.120499 + 0.992713i \(0.461550\pi\)
\(258\) 0 0
\(259\) 0.914123 0.0568008
\(260\) −7.57461 −0.469757
\(261\) 0 0
\(262\) 37.4852 2.31584
\(263\) 3.85898 0.237955 0.118977 0.992897i \(-0.462038\pi\)
0.118977 + 0.992897i \(0.462038\pi\)
\(264\) 0 0
\(265\) 8.50336 0.522357
\(266\) −3.56064 −0.218317
\(267\) 0 0
\(268\) −21.2066 −1.29540
\(269\) −29.8634 −1.82080 −0.910401 0.413727i \(-0.864227\pi\)
−0.910401 + 0.413727i \(0.864227\pi\)
\(270\) 0 0
\(271\) 31.4327 1.90940 0.954700 0.297571i \(-0.0961767\pi\)
0.954700 + 0.297571i \(0.0961767\pi\)
\(272\) −28.7078 −1.74067
\(273\) 0 0
\(274\) −28.4347 −1.71780
\(275\) 7.60789 0.458773
\(276\) 0 0
\(277\) 6.75055 0.405601 0.202801 0.979220i \(-0.434996\pi\)
0.202801 + 0.979220i \(0.434996\pi\)
\(278\) −33.5486 −2.01211
\(279\) 0 0
\(280\) −6.10692 −0.364958
\(281\) −7.23858 −0.431818 −0.215909 0.976414i \(-0.569271\pi\)
−0.215909 + 0.976414i \(0.569271\pi\)
\(282\) 0 0
\(283\) 12.0636 0.717108 0.358554 0.933509i \(-0.383270\pi\)
0.358554 + 0.933509i \(0.383270\pi\)
\(284\) −19.8259 −1.17645
\(285\) 0 0
\(286\) −8.20597 −0.485229
\(287\) 1.13505 0.0669998
\(288\) 0 0
\(289\) 32.9442 1.93790
\(290\) 18.5849 1.09134
\(291\) 0 0
\(292\) 13.0164 0.761728
\(293\) 1.86633 0.109032 0.0545162 0.998513i \(-0.482638\pi\)
0.0545162 + 0.998513i \(0.482638\pi\)
\(294\) 0 0
\(295\) 10.0743 0.586548
\(296\) 4.50531 0.261866
\(297\) 0 0
\(298\) 42.4471 2.45889
\(299\) −3.97813 −0.230061
\(300\) 0 0
\(301\) 2.48757 0.143381
\(302\) 2.49007 0.143288
\(303\) 0 0
\(304\) −5.89978 −0.338376
\(305\) −6.31851 −0.361797
\(306\) 0 0
\(307\) −3.17131 −0.180996 −0.0904981 0.995897i \(-0.528846\pi\)
−0.0904981 + 0.995897i \(0.528846\pi\)
\(308\) −8.80614 −0.501776
\(309\) 0 0
\(310\) −5.56796 −0.316239
\(311\) 6.97271 0.395386 0.197693 0.980264i \(-0.436655\pi\)
0.197693 + 0.980264i \(0.436655\pi\)
\(312\) 0 0
\(313\) −10.0961 −0.570668 −0.285334 0.958428i \(-0.592105\pi\)
−0.285334 + 0.958428i \(0.592105\pi\)
\(314\) −18.7728 −1.05941
\(315\) 0 0
\(316\) −34.5901 −1.94584
\(317\) −32.1544 −1.80597 −0.902986 0.429670i \(-0.858630\pi\)
−0.902986 + 0.429670i \(0.858630\pi\)
\(318\) 0 0
\(319\) 13.4342 0.752172
\(320\) 9.75784 0.545480
\(321\) 0 0
\(322\) −6.39812 −0.356553
\(323\) 10.2641 0.571109
\(324\) 0 0
\(325\) −5.28125 −0.292951
\(326\) 52.7507 2.92159
\(327\) 0 0
\(328\) 5.59416 0.308886
\(329\) −0.620901 −0.0342314
\(330\) 0 0
\(331\) −24.3663 −1.33930 −0.669648 0.742679i \(-0.733555\pi\)
−0.669648 + 0.742679i \(0.733555\pi\)
\(332\) 58.9413 3.23483
\(333\) 0 0
\(334\) 37.5356 2.05386
\(335\) 6.55227 0.357989
\(336\) 0 0
\(337\) 7.06781 0.385008 0.192504 0.981296i \(-0.438339\pi\)
0.192504 + 0.981296i \(0.438339\pi\)
\(338\) −26.1744 −1.42370
\(339\) 0 0
\(340\) 35.1177 1.90453
\(341\) −4.02484 −0.217957
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 12.2601 0.661022
\(345\) 0 0
\(346\) −63.3070 −3.40340
\(347\) −26.8575 −1.44178 −0.720892 0.693047i \(-0.756268\pi\)
−0.720892 + 0.693047i \(0.756268\pi\)
\(348\) 0 0
\(349\) −25.3862 −1.35889 −0.679445 0.733726i \(-0.737779\pi\)
−0.679445 + 0.733726i \(0.737779\pi\)
\(350\) −8.49396 −0.454021
\(351\) 0 0
\(352\) −0.223313 −0.0119026
\(353\) −25.8412 −1.37539 −0.687695 0.726000i \(-0.741377\pi\)
−0.687695 + 0.726000i \(0.741377\pi\)
\(354\) 0 0
\(355\) 6.12566 0.325116
\(356\) −10.5276 −0.557963
\(357\) 0 0
\(358\) −12.2604 −0.647985
\(359\) 24.9557 1.31711 0.658556 0.752531i \(-0.271167\pi\)
0.658556 + 0.752531i \(0.271167\pi\)
\(360\) 0 0
\(361\) −16.8906 −0.888980
\(362\) 17.2451 0.906383
\(363\) 0 0
\(364\) 6.11305 0.320411
\(365\) −4.02172 −0.210507
\(366\) 0 0
\(367\) −11.8416 −0.618126 −0.309063 0.951042i \(-0.600015\pi\)
−0.309063 + 0.951042i \(0.600015\pi\)
\(368\) −10.6013 −0.552633
\(369\) 0 0
\(370\) −2.77688 −0.144363
\(371\) −6.86259 −0.356288
\(372\) 0 0
\(373\) −0.196072 −0.0101522 −0.00507611 0.999987i \(-0.501616\pi\)
−0.00507611 + 0.999987i \(0.501616\pi\)
\(374\) 38.0449 1.96725
\(375\) 0 0
\(376\) −3.06015 −0.157815
\(377\) −9.32578 −0.480302
\(378\) 0 0
\(379\) −24.0964 −1.23775 −0.618874 0.785490i \(-0.712411\pi\)
−0.618874 + 0.785490i \(0.712411\pi\)
\(380\) 7.21709 0.370229
\(381\) 0 0
\(382\) 23.3215 1.19323
\(383\) −20.1432 −1.02927 −0.514635 0.857409i \(-0.672073\pi\)
−0.514635 + 0.857409i \(0.672073\pi\)
\(384\) 0 0
\(385\) 2.72086 0.138668
\(386\) 13.8367 0.704270
\(387\) 0 0
\(388\) 16.9860 0.862334
\(389\) 21.1063 1.07013 0.535067 0.844810i \(-0.320286\pi\)
0.535067 + 0.844810i \(0.320286\pi\)
\(390\) 0 0
\(391\) 18.4436 0.932733
\(392\) 4.92856 0.248930
\(393\) 0 0
\(394\) 2.35913 0.118851
\(395\) 10.6874 0.537742
\(396\) 0 0
\(397\) 11.3506 0.569673 0.284836 0.958576i \(-0.408061\pi\)
0.284836 + 0.958576i \(0.408061\pi\)
\(398\) −20.8726 −1.04625
\(399\) 0 0
\(400\) −14.0740 −0.703702
\(401\) −21.6751 −1.08240 −0.541200 0.840894i \(-0.682030\pi\)
−0.541200 + 0.840894i \(0.682030\pi\)
\(402\) 0 0
\(403\) 2.79396 0.139177
\(404\) 34.2340 1.70321
\(405\) 0 0
\(406\) −14.9989 −0.744381
\(407\) −2.00728 −0.0994973
\(408\) 0 0
\(409\) 24.7253 1.22259 0.611294 0.791404i \(-0.290649\pi\)
0.611294 + 0.791404i \(0.290649\pi\)
\(410\) −3.44800 −0.170284
\(411\) 0 0
\(412\) −3.06679 −0.151090
\(413\) −8.13041 −0.400071
\(414\) 0 0
\(415\) −18.2113 −0.893957
\(416\) 0.155019 0.00760045
\(417\) 0 0
\(418\) 7.81864 0.382422
\(419\) 0.0686235 0.00335248 0.00167624 0.999999i \(-0.499466\pi\)
0.00167624 + 0.999999i \(0.499466\pi\)
\(420\) 0 0
\(421\) −11.2289 −0.547261 −0.273630 0.961835i \(-0.588224\pi\)
−0.273630 + 0.961835i \(0.588224\pi\)
\(422\) 11.3315 0.551607
\(423\) 0 0
\(424\) −33.8227 −1.64257
\(425\) 24.4852 1.18771
\(426\) 0 0
\(427\) 5.09932 0.246773
\(428\) −21.1099 −1.02039
\(429\) 0 0
\(430\) −7.55661 −0.364412
\(431\) −3.76067 −0.181145 −0.0905725 0.995890i \(-0.528870\pi\)
−0.0905725 + 0.995890i \(0.528870\pi\)
\(432\) 0 0
\(433\) 1.15019 0.0552748 0.0276374 0.999618i \(-0.491202\pi\)
0.0276374 + 0.999618i \(0.491202\pi\)
\(434\) 4.49360 0.215700
\(435\) 0 0
\(436\) −31.6409 −1.51533
\(437\) 3.79036 0.181318
\(438\) 0 0
\(439\) 10.1838 0.486046 0.243023 0.970021i \(-0.421861\pi\)
0.243023 + 0.970021i \(0.421861\pi\)
\(440\) 13.4099 0.639293
\(441\) 0 0
\(442\) −26.4100 −1.25620
\(443\) −3.18877 −0.151503 −0.0757514 0.997127i \(-0.524136\pi\)
−0.0757514 + 0.997127i \(0.524136\pi\)
\(444\) 0 0
\(445\) 3.25275 0.154195
\(446\) −5.82567 −0.275854
\(447\) 0 0
\(448\) −7.87502 −0.372060
\(449\) −19.2378 −0.907889 −0.453945 0.891030i \(-0.649984\pi\)
−0.453945 + 0.891030i \(0.649984\pi\)
\(450\) 0 0
\(451\) −2.49240 −0.117363
\(452\) 13.5937 0.639394
\(453\) 0 0
\(454\) −58.4496 −2.74318
\(455\) −1.88877 −0.0885468
\(456\) 0 0
\(457\) 9.07754 0.424629 0.212315 0.977201i \(-0.431900\pi\)
0.212315 + 0.977201i \(0.431900\pi\)
\(458\) 2.84175 0.132786
\(459\) 0 0
\(460\) 12.9684 0.604655
\(461\) 22.2184 1.03481 0.517407 0.855739i \(-0.326897\pi\)
0.517407 + 0.855739i \(0.326897\pi\)
\(462\) 0 0
\(463\) −10.3963 −0.483156 −0.241578 0.970381i \(-0.577665\pi\)
−0.241578 + 0.970381i \(0.577665\pi\)
\(464\) −24.8523 −1.15374
\(465\) 0 0
\(466\) −2.32824 −0.107854
\(467\) −10.0389 −0.464547 −0.232273 0.972651i \(-0.574616\pi\)
−0.232273 + 0.972651i \(0.574616\pi\)
\(468\) 0 0
\(469\) −5.28798 −0.244176
\(470\) 1.88614 0.0870012
\(471\) 0 0
\(472\) −40.0712 −1.84443
\(473\) −5.46235 −0.251159
\(474\) 0 0
\(475\) 5.03198 0.230883
\(476\) −28.3416 −1.29903
\(477\) 0 0
\(478\) 14.0090 0.640758
\(479\) 8.89671 0.406501 0.203251 0.979127i \(-0.434849\pi\)
0.203251 + 0.979127i \(0.434849\pi\)
\(480\) 0 0
\(481\) 1.39342 0.0635343
\(482\) 54.8938 2.50034
\(483\) 0 0
\(484\) −24.7768 −1.12622
\(485\) −5.24822 −0.238310
\(486\) 0 0
\(487\) 28.1080 1.27369 0.636847 0.770990i \(-0.280238\pi\)
0.636847 + 0.770990i \(0.280238\pi\)
\(488\) 25.1323 1.13769
\(489\) 0 0
\(490\) −3.03775 −0.137232
\(491\) 3.08069 0.139030 0.0695149 0.997581i \(-0.477855\pi\)
0.0695149 + 0.997581i \(0.477855\pi\)
\(492\) 0 0
\(493\) 43.2366 1.94728
\(494\) −5.42755 −0.244197
\(495\) 0 0
\(496\) 7.44565 0.334319
\(497\) −4.94368 −0.221754
\(498\) 0 0
\(499\) −3.72255 −0.166644 −0.0833221 0.996523i \(-0.526553\pi\)
−0.0833221 + 0.996523i \(0.526553\pi\)
\(500\) 42.0623 1.88108
\(501\) 0 0
\(502\) 3.77745 0.168596
\(503\) −4.44735 −0.198298 −0.0991488 0.995073i \(-0.531612\pi\)
−0.0991488 + 0.995073i \(0.531612\pi\)
\(504\) 0 0
\(505\) −10.5774 −0.470688
\(506\) 14.0494 0.624570
\(507\) 0 0
\(508\) −4.01034 −0.177930
\(509\) −6.22906 −0.276098 −0.138049 0.990425i \(-0.544083\pi\)
−0.138049 + 0.990425i \(0.544083\pi\)
\(510\) 0 0
\(511\) 3.24571 0.143582
\(512\) −39.6282 −1.75133
\(513\) 0 0
\(514\) 9.47177 0.417782
\(515\) 0.947557 0.0417544
\(516\) 0 0
\(517\) 1.36341 0.0599627
\(518\) 2.24106 0.0984667
\(519\) 0 0
\(520\) −9.30891 −0.408223
\(521\) −11.1532 −0.488631 −0.244316 0.969696i \(-0.578563\pi\)
−0.244316 + 0.969696i \(0.578563\pi\)
\(522\) 0 0
\(523\) 10.4772 0.458134 0.229067 0.973411i \(-0.426432\pi\)
0.229067 + 0.973411i \(0.426432\pi\)
\(524\) 61.3186 2.67871
\(525\) 0 0
\(526\) 9.46067 0.412505
\(527\) −12.9535 −0.564263
\(528\) 0 0
\(529\) −16.1891 −0.703873
\(530\) 20.8468 0.905528
\(531\) 0 0
\(532\) −5.82451 −0.252525
\(533\) 1.73018 0.0749424
\(534\) 0 0
\(535\) 6.52240 0.281988
\(536\) −26.0621 −1.12571
\(537\) 0 0
\(538\) −73.2131 −3.15644
\(539\) −2.19586 −0.0945822
\(540\) 0 0
\(541\) 6.36150 0.273502 0.136751 0.990605i \(-0.456334\pi\)
0.136751 + 0.990605i \(0.456334\pi\)
\(542\) 77.0604 3.31003
\(543\) 0 0
\(544\) −0.718708 −0.0308143
\(545\) 9.77620 0.418766
\(546\) 0 0
\(547\) 4.58101 0.195870 0.0979349 0.995193i \(-0.468776\pi\)
0.0979349 + 0.995193i \(0.468776\pi\)
\(548\) −46.5137 −1.98697
\(549\) 0 0
\(550\) 18.6515 0.795303
\(551\) 8.88560 0.378539
\(552\) 0 0
\(553\) −8.62522 −0.366781
\(554\) 16.5497 0.703127
\(555\) 0 0
\(556\) −54.8791 −2.32739
\(557\) −3.52897 −0.149527 −0.0747637 0.997201i \(-0.523820\pi\)
−0.0747637 + 0.997201i \(0.523820\pi\)
\(558\) 0 0
\(559\) 3.79185 0.160378
\(560\) −5.03339 −0.212699
\(561\) 0 0
\(562\) −17.7461 −0.748575
\(563\) 9.67953 0.407944 0.203972 0.978977i \(-0.434615\pi\)
0.203972 + 0.978977i \(0.434615\pi\)
\(564\) 0 0
\(565\) −4.20009 −0.176699
\(566\) 29.5752 1.24314
\(567\) 0 0
\(568\) −24.3652 −1.02234
\(569\) 26.8002 1.12352 0.561762 0.827299i \(-0.310124\pi\)
0.561762 + 0.827299i \(0.310124\pi\)
\(570\) 0 0
\(571\) −1.99922 −0.0836649 −0.0418325 0.999125i \(-0.513320\pi\)
−0.0418325 + 0.999125i \(0.513320\pi\)
\(572\) −13.4234 −0.561260
\(573\) 0 0
\(574\) 2.78269 0.116147
\(575\) 9.04198 0.377077
\(576\) 0 0
\(577\) −6.27902 −0.261399 −0.130699 0.991422i \(-0.541722\pi\)
−0.130699 + 0.991422i \(0.541722\pi\)
\(578\) 80.7661 3.35943
\(579\) 0 0
\(580\) 30.4013 1.26235
\(581\) 14.6973 0.609748
\(582\) 0 0
\(583\) 15.0693 0.624105
\(584\) 15.9967 0.661947
\(585\) 0 0
\(586\) 4.57551 0.189012
\(587\) 24.0066 0.990859 0.495429 0.868648i \(-0.335011\pi\)
0.495429 + 0.868648i \(0.335011\pi\)
\(588\) 0 0
\(589\) −2.66209 −0.109689
\(590\) 24.6981 1.01681
\(591\) 0 0
\(592\) 3.71332 0.152617
\(593\) −12.2147 −0.501599 −0.250799 0.968039i \(-0.580693\pi\)
−0.250799 + 0.968039i \(0.580693\pi\)
\(594\) 0 0
\(595\) 8.75679 0.358993
\(596\) 69.4352 2.84418
\(597\) 0 0
\(598\) −9.75279 −0.398821
\(599\) 0.687692 0.0280983 0.0140492 0.999901i \(-0.495528\pi\)
0.0140492 + 0.999901i \(0.495528\pi\)
\(600\) 0 0
\(601\) 1.55551 0.0634504 0.0317252 0.999497i \(-0.489900\pi\)
0.0317252 + 0.999497i \(0.489900\pi\)
\(602\) 6.09853 0.248557
\(603\) 0 0
\(604\) 4.07328 0.165739
\(605\) 7.65536 0.311234
\(606\) 0 0
\(607\) 24.4768 0.993485 0.496742 0.867898i \(-0.334529\pi\)
0.496742 + 0.867898i \(0.334529\pi\)
\(608\) −0.147702 −0.00599012
\(609\) 0 0
\(610\) −15.4905 −0.627190
\(611\) −0.946453 −0.0382894
\(612\) 0 0
\(613\) −5.97120 −0.241174 −0.120587 0.992703i \(-0.538478\pi\)
−0.120587 + 0.992703i \(0.538478\pi\)
\(614\) −7.77478 −0.313765
\(615\) 0 0
\(616\) −10.8224 −0.436047
\(617\) 46.9374 1.88963 0.944814 0.327607i \(-0.106242\pi\)
0.944814 + 0.327607i \(0.106242\pi\)
\(618\) 0 0
\(619\) 11.9186 0.479047 0.239524 0.970891i \(-0.423009\pi\)
0.239524 + 0.970891i \(0.423009\pi\)
\(620\) −9.10811 −0.365791
\(621\) 0 0
\(622\) 17.0943 0.685419
\(623\) −2.62512 −0.105173
\(624\) 0 0
\(625\) 4.32717 0.173087
\(626\) −24.7517 −0.989278
\(627\) 0 0
\(628\) −30.7087 −1.22541
\(629\) −6.46022 −0.257586
\(630\) 0 0
\(631\) −30.4351 −1.21160 −0.605802 0.795615i \(-0.707148\pi\)
−0.605802 + 0.795615i \(0.707148\pi\)
\(632\) −42.5099 −1.69095
\(633\) 0 0
\(634\) −78.8298 −3.13073
\(635\) 1.23909 0.0491717
\(636\) 0 0
\(637\) 1.52432 0.0603958
\(638\) 32.9354 1.30392
\(639\) 0 0
\(640\) 24.1744 0.955575
\(641\) 40.1834 1.58715 0.793574 0.608474i \(-0.208218\pi\)
0.793574 + 0.608474i \(0.208218\pi\)
\(642\) 0 0
\(643\) −22.8069 −0.899415 −0.449708 0.893176i \(-0.648472\pi\)
−0.449708 + 0.893176i \(0.648472\pi\)
\(644\) −10.4661 −0.412422
\(645\) 0 0
\(646\) 25.1635 0.990043
\(647\) 8.81515 0.346559 0.173280 0.984873i \(-0.444564\pi\)
0.173280 + 0.984873i \(0.444564\pi\)
\(648\) 0 0
\(649\) 17.8532 0.700800
\(650\) −12.9475 −0.507844
\(651\) 0 0
\(652\) 86.2899 3.37937
\(653\) −12.8758 −0.503871 −0.251935 0.967744i \(-0.581067\pi\)
−0.251935 + 0.967744i \(0.581067\pi\)
\(654\) 0 0
\(655\) −18.9458 −0.740273
\(656\) 4.61076 0.180020
\(657\) 0 0
\(658\) −1.52220 −0.0593416
\(659\) 19.2643 0.750430 0.375215 0.926938i \(-0.377569\pi\)
0.375215 + 0.926938i \(0.377569\pi\)
\(660\) 0 0
\(661\) 30.2257 1.17565 0.587823 0.808990i \(-0.299985\pi\)
0.587823 + 0.808990i \(0.299985\pi\)
\(662\) −59.7365 −2.32173
\(663\) 0 0
\(664\) 72.4366 2.81109
\(665\) 1.79962 0.0697862
\(666\) 0 0
\(667\) 15.9666 0.618228
\(668\) 61.4009 2.37567
\(669\) 0 0
\(670\) 16.0636 0.620589
\(671\) −11.1974 −0.432270
\(672\) 0 0
\(673\) −42.8167 −1.65046 −0.825232 0.564794i \(-0.808956\pi\)
−0.825232 + 0.564794i \(0.808956\pi\)
\(674\) 17.3274 0.667428
\(675\) 0 0
\(676\) −42.8162 −1.64678
\(677\) 8.01207 0.307929 0.153964 0.988076i \(-0.450796\pi\)
0.153964 + 0.988076i \(0.450796\pi\)
\(678\) 0 0
\(679\) 4.23555 0.162546
\(680\) 43.1584 1.65505
\(681\) 0 0
\(682\) −9.86729 −0.377838
\(683\) −12.8698 −0.492451 −0.246225 0.969213i \(-0.579190\pi\)
−0.246225 + 0.969213i \(0.579190\pi\)
\(684\) 0 0
\(685\) 14.3715 0.549106
\(686\) 2.45160 0.0936025
\(687\) 0 0
\(688\) 10.1049 0.385247
\(689\) −10.4608 −0.398524
\(690\) 0 0
\(691\) −9.04215 −0.343980 −0.171990 0.985099i \(-0.555020\pi\)
−0.171990 + 0.985099i \(0.555020\pi\)
\(692\) −103.558 −3.93668
\(693\) 0 0
\(694\) −65.8438 −2.49940
\(695\) 16.9562 0.643184
\(696\) 0 0
\(697\) −8.02153 −0.303837
\(698\) −62.2367 −2.35569
\(699\) 0 0
\(700\) −13.8945 −0.525162
\(701\) −43.2487 −1.63348 −0.816741 0.577004i \(-0.804222\pi\)
−0.816741 + 0.577004i \(0.804222\pi\)
\(702\) 0 0
\(703\) −1.32765 −0.0500731
\(704\) 17.2924 0.651732
\(705\) 0 0
\(706\) −63.3523 −2.38430
\(707\) 8.53644 0.321046
\(708\) 0 0
\(709\) 21.8179 0.819388 0.409694 0.912223i \(-0.365635\pi\)
0.409694 + 0.912223i \(0.365635\pi\)
\(710\) 15.0177 0.563603
\(711\) 0 0
\(712\) −12.9380 −0.484874
\(713\) −4.78352 −0.179144
\(714\) 0 0
\(715\) 4.14746 0.155106
\(716\) −20.0557 −0.749517
\(717\) 0 0
\(718\) 61.1815 2.28327
\(719\) −2.71418 −0.101222 −0.0506109 0.998718i \(-0.516117\pi\)
−0.0506109 + 0.998718i \(0.516117\pi\)
\(720\) 0 0
\(721\) −0.764721 −0.0284797
\(722\) −41.4090 −1.54108
\(723\) 0 0
\(724\) 28.2097 1.04840
\(725\) 21.1968 0.787228
\(726\) 0 0
\(727\) −3.24994 −0.120533 −0.0602667 0.998182i \(-0.519195\pi\)
−0.0602667 + 0.998182i \(0.519195\pi\)
\(728\) 7.51271 0.278439
\(729\) 0 0
\(730\) −9.85966 −0.364922
\(731\) −17.5800 −0.650218
\(732\) 0 0
\(733\) 22.8484 0.843925 0.421962 0.906613i \(-0.361341\pi\)
0.421962 + 0.906613i \(0.361341\pi\)
\(734\) −29.0308 −1.07155
\(735\) 0 0
\(736\) −0.265407 −0.00978303
\(737\) 11.6116 0.427720
\(738\) 0 0
\(739\) 37.8282 1.39153 0.695766 0.718269i \(-0.255065\pi\)
0.695766 + 0.718269i \(0.255065\pi\)
\(740\) −4.54243 −0.166983
\(741\) 0 0
\(742\) −16.8243 −0.617641
\(743\) 22.5284 0.826487 0.413244 0.910620i \(-0.364396\pi\)
0.413244 + 0.910620i \(0.364396\pi\)
\(744\) 0 0
\(745\) −21.4536 −0.785999
\(746\) −0.480690 −0.0175993
\(747\) 0 0
\(748\) 62.2341 2.27550
\(749\) −5.26387 −0.192338
\(750\) 0 0
\(751\) −38.7581 −1.41430 −0.707151 0.707063i \(-0.750020\pi\)
−0.707151 + 0.707063i \(0.750020\pi\)
\(752\) −2.52221 −0.0919754
\(753\) 0 0
\(754\) −22.8631 −0.832625
\(755\) −1.25853 −0.0458027
\(756\) 0 0
\(757\) 0.582273 0.0211631 0.0105815 0.999944i \(-0.496632\pi\)
0.0105815 + 0.999944i \(0.496632\pi\)
\(758\) −59.0747 −2.14569
\(759\) 0 0
\(760\) 8.86952 0.321731
\(761\) −33.7263 −1.22258 −0.611288 0.791408i \(-0.709348\pi\)
−0.611288 + 0.791408i \(0.709348\pi\)
\(762\) 0 0
\(763\) −7.88983 −0.285631
\(764\) 38.1495 1.38020
\(765\) 0 0
\(766\) −49.3831 −1.78428
\(767\) −12.3934 −0.447498
\(768\) 0 0
\(769\) 31.0918 1.12120 0.560599 0.828087i \(-0.310571\pi\)
0.560599 + 0.828087i \(0.310571\pi\)
\(770\) 6.67046 0.240387
\(771\) 0 0
\(772\) 22.6342 0.814623
\(773\) 46.5433 1.67405 0.837023 0.547168i \(-0.184294\pi\)
0.837023 + 0.547168i \(0.184294\pi\)
\(774\) 0 0
\(775\) −6.35046 −0.228115
\(776\) 20.8752 0.749375
\(777\) 0 0
\(778\) 51.7443 1.85512
\(779\) −1.64851 −0.0590641
\(780\) 0 0
\(781\) 10.8556 0.388444
\(782\) 45.2163 1.61693
\(783\) 0 0
\(784\) 4.06217 0.145077
\(785\) 9.48816 0.338647
\(786\) 0 0
\(787\) −37.7996 −1.34741 −0.673706 0.739000i \(-0.735299\pi\)
−0.673706 + 0.739000i \(0.735299\pi\)
\(788\) 3.85908 0.137474
\(789\) 0 0
\(790\) 26.2012 0.932198
\(791\) 3.38966 0.120522
\(792\) 0 0
\(793\) 7.77300 0.276027
\(794\) 27.8273 0.987552
\(795\) 0 0
\(796\) −34.1435 −1.21018
\(797\) −20.3689 −0.721504 −0.360752 0.932662i \(-0.617480\pi\)
−0.360752 + 0.932662i \(0.617480\pi\)
\(798\) 0 0
\(799\) 4.38798 0.155236
\(800\) −0.352347 −0.0124573
\(801\) 0 0
\(802\) −53.1386 −1.87639
\(803\) −7.12711 −0.251510
\(804\) 0 0
\(805\) 3.23374 0.113974
\(806\) 6.84968 0.241270
\(807\) 0 0
\(808\) 42.0723 1.48010
\(809\) −8.20215 −0.288372 −0.144186 0.989551i \(-0.546056\pi\)
−0.144186 + 0.989551i \(0.546056\pi\)
\(810\) 0 0
\(811\) 26.9018 0.944648 0.472324 0.881425i \(-0.343415\pi\)
0.472324 + 0.881425i \(0.343415\pi\)
\(812\) −24.5352 −0.861018
\(813\) 0 0
\(814\) −4.92105 −0.172483
\(815\) −26.6613 −0.933903
\(816\) 0 0
\(817\) −3.61288 −0.126399
\(818\) 60.6166 2.11941
\(819\) 0 0
\(820\) −5.64025 −0.196966
\(821\) 20.6788 0.721694 0.360847 0.932625i \(-0.382488\pi\)
0.360847 + 0.932625i \(0.382488\pi\)
\(822\) 0 0
\(823\) −16.4881 −0.574740 −0.287370 0.957820i \(-0.592781\pi\)
−0.287370 + 0.957820i \(0.592781\pi\)
\(824\) −3.76897 −0.131298
\(825\) 0 0
\(826\) −19.9325 −0.693541
\(827\) −45.9300 −1.59714 −0.798571 0.601900i \(-0.794411\pi\)
−0.798571 + 0.601900i \(0.794411\pi\)
\(828\) 0 0
\(829\) 45.1979 1.56979 0.784894 0.619630i \(-0.212717\pi\)
0.784894 + 0.619630i \(0.212717\pi\)
\(830\) −44.6468 −1.54971
\(831\) 0 0
\(832\) −12.0041 −0.416166
\(833\) −7.06712 −0.244861
\(834\) 0 0
\(835\) −18.9712 −0.656527
\(836\) 12.7898 0.442344
\(837\) 0 0
\(838\) 0.168237 0.00581167
\(839\) 34.0233 1.17462 0.587308 0.809363i \(-0.300188\pi\)
0.587308 + 0.809363i \(0.300188\pi\)
\(840\) 0 0
\(841\) 8.42981 0.290683
\(842\) −27.5287 −0.948700
\(843\) 0 0
\(844\) 18.5361 0.638038
\(845\) 13.2291 0.455094
\(846\) 0 0
\(847\) −6.17822 −0.212286
\(848\) −27.8770 −0.957300
\(849\) 0 0
\(850\) 60.0279 2.05894
\(851\) −2.38565 −0.0817791
\(852\) 0 0
\(853\) 31.0563 1.06335 0.531674 0.846949i \(-0.321563\pi\)
0.531674 + 0.846949i \(0.321563\pi\)
\(854\) 12.5015 0.427792
\(855\) 0 0
\(856\) −25.9433 −0.886724
\(857\) −9.85200 −0.336538 −0.168269 0.985741i \(-0.553818\pi\)
−0.168269 + 0.985741i \(0.553818\pi\)
\(858\) 0 0
\(859\) −34.6137 −1.18101 −0.590503 0.807036i \(-0.701070\pi\)
−0.590503 + 0.807036i \(0.701070\pi\)
\(860\) −12.3612 −0.421512
\(861\) 0 0
\(862\) −9.21965 −0.314023
\(863\) 26.6628 0.907613 0.453806 0.891100i \(-0.350066\pi\)
0.453806 + 0.891100i \(0.350066\pi\)
\(864\) 0 0
\(865\) 31.9966 1.08792
\(866\) 2.81982 0.0958212
\(867\) 0 0
\(868\) 7.35066 0.249497
\(869\) 18.9397 0.642486
\(870\) 0 0
\(871\) −8.06058 −0.273122
\(872\) −38.8855 −1.31683
\(873\) 0 0
\(874\) 9.29246 0.314322
\(875\) 10.4885 0.354575
\(876\) 0 0
\(877\) 20.7876 0.701948 0.350974 0.936385i \(-0.385851\pi\)
0.350974 + 0.936385i \(0.385851\pi\)
\(878\) 24.9666 0.842581
\(879\) 0 0
\(880\) 11.0526 0.372583
\(881\) −27.9289 −0.940949 −0.470474 0.882414i \(-0.655917\pi\)
−0.470474 + 0.882414i \(0.655917\pi\)
\(882\) 0 0
\(883\) 38.9829 1.31188 0.655939 0.754814i \(-0.272273\pi\)
0.655939 + 0.754814i \(0.272273\pi\)
\(884\) −43.2017 −1.45303
\(885\) 0 0
\(886\) −7.81758 −0.262637
\(887\) −3.83646 −0.128816 −0.0644079 0.997924i \(-0.520516\pi\)
−0.0644079 + 0.997924i \(0.520516\pi\)
\(888\) 0 0
\(889\) −1.00000 −0.0335389
\(890\) 7.97444 0.267304
\(891\) 0 0
\(892\) −9.52967 −0.319077
\(893\) 0.901780 0.0301769
\(894\) 0 0
\(895\) 6.19668 0.207132
\(896\) −19.5098 −0.651776
\(897\) 0 0
\(898\) −47.1635 −1.57387
\(899\) −11.2138 −0.374002
\(900\) 0 0
\(901\) 48.4988 1.61573
\(902\) −6.11038 −0.203453
\(903\) 0 0
\(904\) 16.7061 0.555638
\(905\) −8.71602 −0.289730
\(906\) 0 0
\(907\) 1.86310 0.0618631 0.0309315 0.999522i \(-0.490153\pi\)
0.0309315 + 0.999522i \(0.490153\pi\)
\(908\) −95.6123 −3.17301
\(909\) 0 0
\(910\) −4.63051 −0.153500
\(911\) −31.7046 −1.05042 −0.525210 0.850973i \(-0.676013\pi\)
−0.525210 + 0.850973i \(0.676013\pi\)
\(912\) 0 0
\(913\) −32.2732 −1.06809
\(914\) 22.2545 0.736114
\(915\) 0 0
\(916\) 4.64855 0.153592
\(917\) 15.2901 0.504924
\(918\) 0 0
\(919\) −6.20652 −0.204734 −0.102367 0.994747i \(-0.532642\pi\)
−0.102367 + 0.994747i \(0.532642\pi\)
\(920\) 15.9377 0.525450
\(921\) 0 0
\(922\) 54.4707 1.79390
\(923\) −7.53575 −0.248042
\(924\) 0 0
\(925\) −3.16712 −0.104134
\(926\) −25.4875 −0.837572
\(927\) 0 0
\(928\) −0.622183 −0.0204242
\(929\) −11.9844 −0.393196 −0.196598 0.980484i \(-0.562989\pi\)
−0.196598 + 0.980484i \(0.562989\pi\)
\(930\) 0 0
\(931\) −1.45237 −0.0475996
\(932\) −3.80855 −0.124753
\(933\) 0 0
\(934\) −24.6115 −0.805312
\(935\) −19.2287 −0.628844
\(936\) 0 0
\(937\) 18.5854 0.607159 0.303580 0.952806i \(-0.401818\pi\)
0.303580 + 0.952806i \(0.401818\pi\)
\(938\) −12.9640 −0.423290
\(939\) 0 0
\(940\) 3.08536 0.100633
\(941\) −29.4475 −0.959962 −0.479981 0.877279i \(-0.659357\pi\)
−0.479981 + 0.877279i \(0.659357\pi\)
\(942\) 0 0
\(943\) −2.96222 −0.0964632
\(944\) −33.0271 −1.07494
\(945\) 0 0
\(946\) −13.3915 −0.435395
\(947\) −1.05890 −0.0344096 −0.0172048 0.999852i \(-0.505477\pi\)
−0.0172048 + 0.999852i \(0.505477\pi\)
\(948\) 0 0
\(949\) 4.94751 0.160603
\(950\) 12.3364 0.400245
\(951\) 0 0
\(952\) −34.8307 −1.12887
\(953\) 57.6761 1.86831 0.934156 0.356864i \(-0.116154\pi\)
0.934156 + 0.356864i \(0.116154\pi\)
\(954\) 0 0
\(955\) −11.7872 −0.381424
\(956\) 22.9161 0.741158
\(957\) 0 0
\(958\) 21.8112 0.704687
\(959\) −11.5984 −0.374533
\(960\) 0 0
\(961\) −27.6404 −0.891625
\(962\) 3.41610 0.110139
\(963\) 0 0
\(964\) 89.7957 2.89212
\(965\) −6.99336 −0.225124
\(966\) 0 0
\(967\) 17.5642 0.564827 0.282414 0.959293i \(-0.408865\pi\)
0.282414 + 0.959293i \(0.408865\pi\)
\(968\) −30.4497 −0.978690
\(969\) 0 0
\(970\) −12.8665 −0.413120
\(971\) 43.8415 1.40694 0.703470 0.710725i \(-0.251633\pi\)
0.703470 + 0.710725i \(0.251633\pi\)
\(972\) 0 0
\(973\) −13.6844 −0.438701
\(974\) 68.9095 2.20800
\(975\) 0 0
\(976\) 20.7143 0.663049
\(977\) 13.1600 0.421027 0.210513 0.977591i \(-0.432486\pi\)
0.210513 + 0.977591i \(0.432486\pi\)
\(978\) 0 0
\(979\) 5.76438 0.184230
\(980\) −4.96917 −0.158734
\(981\) 0 0
\(982\) 7.55263 0.241014
\(983\) 49.4485 1.57716 0.788581 0.614931i \(-0.210816\pi\)
0.788581 + 0.614931i \(0.210816\pi\)
\(984\) 0 0
\(985\) −1.19235 −0.0379915
\(986\) 105.999 3.37569
\(987\) 0 0
\(988\) −8.87843 −0.282460
\(989\) −6.49199 −0.206433
\(990\) 0 0
\(991\) −1.17880 −0.0374459 −0.0187229 0.999825i \(-0.505960\pi\)
−0.0187229 + 0.999825i \(0.505960\pi\)
\(992\) 0.186403 0.00591832
\(993\) 0 0
\(994\) −12.1199 −0.384421
\(995\) 10.5494 0.334439
\(996\) 0 0
\(997\) −6.51368 −0.206290 −0.103145 0.994666i \(-0.532891\pi\)
−0.103145 + 0.994666i \(0.532891\pi\)
\(998\) −9.12621 −0.288885
\(999\) 0 0
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 \(a_p\))