Properties

Label 8042.2.a.c.1.16
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(0\)
Dimension: \(86\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.10336 q^{3}\) \(+1.00000 q^{4}\) \(-2.86600 q^{5}\) \(+2.10336 q^{6}\) \(+3.42965 q^{7}\) \(-1.00000 q^{8}\) \(+1.42413 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.10336 q^{3}\) \(+1.00000 q^{4}\) \(-2.86600 q^{5}\) \(+2.10336 q^{6}\) \(+3.42965 q^{7}\) \(-1.00000 q^{8}\) \(+1.42413 q^{9}\) \(+2.86600 q^{10}\) \(-1.51191 q^{11}\) \(-2.10336 q^{12}\) \(-1.17483 q^{13}\) \(-3.42965 q^{14}\) \(+6.02824 q^{15}\) \(+1.00000 q^{16}\) \(-7.28415 q^{17}\) \(-1.42413 q^{18}\) \(-3.37924 q^{19}\) \(-2.86600 q^{20}\) \(-7.21380 q^{21}\) \(+1.51191 q^{22}\) \(-2.46602 q^{23}\) \(+2.10336 q^{24}\) \(+3.21397 q^{25}\) \(+1.17483 q^{26}\) \(+3.31463 q^{27}\) \(+3.42965 q^{28}\) \(+4.84908 q^{29}\) \(-6.02824 q^{30}\) \(-8.53296 q^{31}\) \(-1.00000 q^{32}\) \(+3.18010 q^{33}\) \(+7.28415 q^{34}\) \(-9.82939 q^{35}\) \(+1.42413 q^{36}\) \(-3.32091 q^{37}\) \(+3.37924 q^{38}\) \(+2.47109 q^{39}\) \(+2.86600 q^{40}\) \(-9.68874 q^{41}\) \(+7.21380 q^{42}\) \(-1.96662 q^{43}\) \(-1.51191 q^{44}\) \(-4.08155 q^{45}\) \(+2.46602 q^{46}\) \(-0.645154 q^{47}\) \(-2.10336 q^{48}\) \(+4.76251 q^{49}\) \(-3.21397 q^{50}\) \(+15.3212 q^{51}\) \(-1.17483 q^{52}\) \(-9.65253 q^{53}\) \(-3.31463 q^{54}\) \(+4.33315 q^{55}\) \(-3.42965 q^{56}\) \(+7.10777 q^{57}\) \(-4.84908 q^{58}\) \(-0.822649 q^{59}\) \(+6.02824 q^{60}\) \(+10.3443 q^{61}\) \(+8.53296 q^{62}\) \(+4.88426 q^{63}\) \(+1.00000 q^{64}\) \(+3.36706 q^{65}\) \(-3.18010 q^{66}\) \(-5.13750 q^{67}\) \(-7.28415 q^{68}\) \(+5.18693 q^{69}\) \(+9.82939 q^{70}\) \(-10.7203 q^{71}\) \(-1.42413 q^{72}\) \(+6.12864 q^{73}\) \(+3.32091 q^{74}\) \(-6.76013 q^{75}\) \(-3.37924 q^{76}\) \(-5.18534 q^{77}\) \(-2.47109 q^{78}\) \(+15.3907 q^{79}\) \(-2.86600 q^{80}\) \(-11.2442 q^{81}\) \(+9.68874 q^{82}\) \(-6.42446 q^{83}\) \(-7.21380 q^{84}\) \(+20.8764 q^{85}\) \(+1.96662 q^{86}\) \(-10.1994 q^{87}\) \(+1.51191 q^{88}\) \(-12.7659 q^{89}\) \(+4.08155 q^{90}\) \(-4.02925 q^{91}\) \(-2.46602 q^{92}\) \(+17.9479 q^{93}\) \(+0.645154 q^{94}\) \(+9.68491 q^{95}\) \(+2.10336 q^{96}\) \(+3.11750 q^{97}\) \(-4.76251 q^{98}\) \(-2.15316 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 45q^{13} \) \(\mathstrut -\mathstrut 35q^{14} \) \(\mathstrut +\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 86q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 72q^{18} \) \(\mathstrut +\mathstrut 47q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 112q^{25} \) \(\mathstrut -\mathstrut 45q^{26} \) \(\mathstrut +\mathstrut 51q^{27} \) \(\mathstrut +\mathstrut 35q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 17q^{30} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 86q^{32} \) \(\mathstrut +\mathstrut 43q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 42q^{35} \) \(\mathstrut +\mathstrut 72q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 15q^{42} \) \(\mathstrut +\mathstrut 72q^{43} \) \(\mathstrut +\mathstrut 13q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 12q^{48} \) \(\mathstrut +\mathstrut 89q^{49} \) \(\mathstrut -\mathstrut 112q^{50} \) \(\mathstrut +\mathstrut 56q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut -\mathstrut 7q^{53} \) \(\mathstrut -\mathstrut 51q^{54} \) \(\mathstrut +\mathstrut 48q^{55} \) \(\mathstrut -\mathstrut 35q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 31q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 98q^{63} \) \(\mathstrut +\mathstrut 86q^{64} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut -\mathstrut 43q^{66} \) \(\mathstrut +\mathstrut 157q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 42q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 74q^{73} \) \(\mathstrut -\mathstrut 61q^{74} \) \(\mathstrut +\mathstrut 76q^{75} \) \(\mathstrut +\mathstrut 47q^{76} \) \(\mathstrut -\mathstrut 13q^{77} \) \(\mathstrut -\mathstrut 20q^{78} \) \(\mathstrut +\mathstrut 57q^{79} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 34q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut 65q^{83} \) \(\mathstrut +\mathstrut 15q^{84} \) \(\mathstrut +\mathstrut 102q^{85} \) \(\mathstrut -\mathstrut 72q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 91q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 57q^{93} \) \(\mathstrut -\mathstrut 11q^{94} \) \(\mathstrut -\mathstrut 13q^{95} \) \(\mathstrut -\mathstrut 12q^{96} \) \(\mathstrut +\mathstrut 64q^{97} \) \(\mathstrut -\mathstrut 89q^{98} \) \(\mathstrut +\mathstrut 56q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.10336 −1.21438 −0.607188 0.794558i \(-0.707703\pi\)
−0.607188 + 0.794558i \(0.707703\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.86600 −1.28172 −0.640858 0.767660i \(-0.721421\pi\)
−0.640858 + 0.767660i \(0.721421\pi\)
\(6\) 2.10336 0.858694
\(7\) 3.42965 1.29629 0.648143 0.761518i \(-0.275546\pi\)
0.648143 + 0.761518i \(0.275546\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.42413 0.474709
\(10\) 2.86600 0.906309
\(11\) −1.51191 −0.455859 −0.227930 0.973678i \(-0.573196\pi\)
−0.227930 + 0.973678i \(0.573196\pi\)
\(12\) −2.10336 −0.607188
\(13\) −1.17483 −0.325839 −0.162919 0.986639i \(-0.552091\pi\)
−0.162919 + 0.986639i \(0.552091\pi\)
\(14\) −3.42965 −0.916613
\(15\) 6.02824 1.55648
\(16\) 1.00000 0.250000
\(17\) −7.28415 −1.76667 −0.883333 0.468745i \(-0.844706\pi\)
−0.883333 + 0.468745i \(0.844706\pi\)
\(18\) −1.42413 −0.335670
\(19\) −3.37924 −0.775251 −0.387626 0.921817i \(-0.626705\pi\)
−0.387626 + 0.921817i \(0.626705\pi\)
\(20\) −2.86600 −0.640858
\(21\) −7.21380 −1.57418
\(22\) 1.51191 0.322341
\(23\) −2.46602 −0.514200 −0.257100 0.966385i \(-0.582767\pi\)
−0.257100 + 0.966385i \(0.582767\pi\)
\(24\) 2.10336 0.429347
\(25\) 3.21397 0.642793
\(26\) 1.17483 0.230403
\(27\) 3.31463 0.637900
\(28\) 3.42965 0.648143
\(29\) 4.84908 0.900451 0.450226 0.892915i \(-0.351344\pi\)
0.450226 + 0.892915i \(0.351344\pi\)
\(30\) −6.02824 −1.10060
\(31\) −8.53296 −1.53257 −0.766283 0.642503i \(-0.777896\pi\)
−0.766283 + 0.642503i \(0.777896\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.18010 0.553585
\(34\) 7.28415 1.24922
\(35\) −9.82939 −1.66147
\(36\) 1.42413 0.237355
\(37\) −3.32091 −0.545954 −0.272977 0.962021i \(-0.588008\pi\)
−0.272977 + 0.962021i \(0.588008\pi\)
\(38\) 3.37924 0.548185
\(39\) 2.47109 0.395691
\(40\) 2.86600 0.453155
\(41\) −9.68874 −1.51313 −0.756563 0.653921i \(-0.773123\pi\)
−0.756563 + 0.653921i \(0.773123\pi\)
\(42\) 7.21380 1.11311
\(43\) −1.96662 −0.299907 −0.149954 0.988693i \(-0.547912\pi\)
−0.149954 + 0.988693i \(0.547912\pi\)
\(44\) −1.51191 −0.227930
\(45\) −4.08155 −0.608442
\(46\) 2.46602 0.363595
\(47\) −0.645154 −0.0941054 −0.0470527 0.998892i \(-0.514983\pi\)
−0.0470527 + 0.998892i \(0.514983\pi\)
\(48\) −2.10336 −0.303594
\(49\) 4.76251 0.680359
\(50\) −3.21397 −0.454524
\(51\) 15.3212 2.14540
\(52\) −1.17483 −0.162919
\(53\) −9.65253 −1.32588 −0.662938 0.748674i \(-0.730691\pi\)
−0.662938 + 0.748674i \(0.730691\pi\)
\(54\) −3.31463 −0.451064
\(55\) 4.33315 0.584282
\(56\) −3.42965 −0.458307
\(57\) 7.10777 0.941447
\(58\) −4.84908 −0.636715
\(59\) −0.822649 −0.107100 −0.0535499 0.998565i \(-0.517054\pi\)
−0.0535499 + 0.998565i \(0.517054\pi\)
\(60\) 6.02824 0.778242
\(61\) 10.3443 1.32445 0.662223 0.749307i \(-0.269613\pi\)
0.662223 + 0.749307i \(0.269613\pi\)
\(62\) 8.53296 1.08369
\(63\) 4.88426 0.615359
\(64\) 1.00000 0.125000
\(65\) 3.36706 0.417632
\(66\) −3.18010 −0.391443
\(67\) −5.13750 −0.627645 −0.313823 0.949482i \(-0.601610\pi\)
−0.313823 + 0.949482i \(0.601610\pi\)
\(68\) −7.28415 −0.883333
\(69\) 5.18693 0.624433
\(70\) 9.82939 1.17484
\(71\) −10.7203 −1.27226 −0.636132 0.771581i \(-0.719466\pi\)
−0.636132 + 0.771581i \(0.719466\pi\)
\(72\) −1.42413 −0.167835
\(73\) 6.12864 0.717302 0.358651 0.933472i \(-0.383237\pi\)
0.358651 + 0.933472i \(0.383237\pi\)
\(74\) 3.32091 0.386048
\(75\) −6.76013 −0.780593
\(76\) −3.37924 −0.387626
\(77\) −5.18534 −0.590924
\(78\) −2.47109 −0.279795
\(79\) 15.3907 1.73159 0.865794 0.500400i \(-0.166814\pi\)
0.865794 + 0.500400i \(0.166814\pi\)
\(80\) −2.86600 −0.320429
\(81\) −11.2442 −1.24936
\(82\) 9.68874 1.06994
\(83\) −6.42446 −0.705176 −0.352588 0.935779i \(-0.614698\pi\)
−0.352588 + 0.935779i \(0.614698\pi\)
\(84\) −7.21380 −0.787090
\(85\) 20.8764 2.26436
\(86\) 1.96662 0.212066
\(87\) −10.1994 −1.09349
\(88\) 1.51191 0.161171
\(89\) −12.7659 −1.35318 −0.676591 0.736359i \(-0.736544\pi\)
−0.676591 + 0.736359i \(0.736544\pi\)
\(90\) 4.08155 0.430234
\(91\) −4.02925 −0.422380
\(92\) −2.46602 −0.257100
\(93\) 17.9479 1.86111
\(94\) 0.645154 0.0665425
\(95\) 9.68491 0.993651
\(96\) 2.10336 0.214673
\(97\) 3.11750 0.316534 0.158267 0.987396i \(-0.449409\pi\)
0.158267 + 0.987396i \(0.449409\pi\)
\(98\) −4.76251 −0.481086
\(99\) −2.15316 −0.216401
\(100\) 3.21397 0.321397
\(101\) −12.3350 −1.22737 −0.613687 0.789549i \(-0.710314\pi\)
−0.613687 + 0.789549i \(0.710314\pi\)
\(102\) −15.3212 −1.51703
\(103\) −7.97045 −0.785352 −0.392676 0.919677i \(-0.628451\pi\)
−0.392676 + 0.919677i \(0.628451\pi\)
\(104\) 1.17483 0.115201
\(105\) 20.6748 2.01765
\(106\) 9.65253 0.937537
\(107\) 0.791050 0.0764737 0.0382369 0.999269i \(-0.487826\pi\)
0.0382369 + 0.999269i \(0.487826\pi\)
\(108\) 3.31463 0.318950
\(109\) −1.22575 −0.117406 −0.0587029 0.998275i \(-0.518696\pi\)
−0.0587029 + 0.998275i \(0.518696\pi\)
\(110\) −4.33315 −0.413150
\(111\) 6.98507 0.662994
\(112\) 3.42965 0.324072
\(113\) 12.5726 1.18273 0.591363 0.806405i \(-0.298590\pi\)
0.591363 + 0.806405i \(0.298590\pi\)
\(114\) −7.10777 −0.665703
\(115\) 7.06761 0.659058
\(116\) 4.84908 0.450226
\(117\) −1.67311 −0.154679
\(118\) 0.822649 0.0757310
\(119\) −24.9821 −2.29011
\(120\) −6.02824 −0.550300
\(121\) −8.71412 −0.792192
\(122\) −10.3443 −0.936525
\(123\) 20.3789 1.83750
\(124\) −8.53296 −0.766283
\(125\) 5.11877 0.457837
\(126\) −4.88426 −0.435125
\(127\) 3.10468 0.275496 0.137748 0.990467i \(-0.456014\pi\)
0.137748 + 0.990467i \(0.456014\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 4.13652 0.364200
\(130\) −3.36706 −0.295311
\(131\) 0.692149 0.0604734 0.0302367 0.999543i \(-0.490374\pi\)
0.0302367 + 0.999543i \(0.490374\pi\)
\(132\) 3.18010 0.276792
\(133\) −11.5896 −1.00495
\(134\) 5.13750 0.443812
\(135\) −9.49973 −0.817606
\(136\) 7.28415 0.624611
\(137\) 5.61252 0.479510 0.239755 0.970833i \(-0.422933\pi\)
0.239755 + 0.970833i \(0.422933\pi\)
\(138\) −5.18693 −0.441540
\(139\) −3.42114 −0.290177 −0.145089 0.989419i \(-0.546347\pi\)
−0.145089 + 0.989419i \(0.546347\pi\)
\(140\) −9.82939 −0.830735
\(141\) 1.35699 0.114279
\(142\) 10.7203 0.899626
\(143\) 1.77624 0.148537
\(144\) 1.42413 0.118677
\(145\) −13.8975 −1.15412
\(146\) −6.12864 −0.507209
\(147\) −10.0173 −0.826212
\(148\) −3.32091 −0.272977
\(149\) 17.9357 1.46935 0.734677 0.678417i \(-0.237334\pi\)
0.734677 + 0.678417i \(0.237334\pi\)
\(150\) 6.76013 0.551963
\(151\) −13.4578 −1.09518 −0.547591 0.836746i \(-0.684455\pi\)
−0.547591 + 0.836746i \(0.684455\pi\)
\(152\) 3.37924 0.274093
\(153\) −10.3736 −0.838653
\(154\) 5.18534 0.417847
\(155\) 24.4555 1.96431
\(156\) 2.47109 0.197845
\(157\) 6.87183 0.548432 0.274216 0.961668i \(-0.411582\pi\)
0.274216 + 0.961668i \(0.411582\pi\)
\(158\) −15.3907 −1.22442
\(159\) 20.3028 1.61011
\(160\) 2.86600 0.226577
\(161\) −8.45758 −0.666551
\(162\) 11.2442 0.883431
\(163\) −24.4552 −1.91548 −0.957740 0.287635i \(-0.907131\pi\)
−0.957740 + 0.287635i \(0.907131\pi\)
\(164\) −9.68874 −0.756563
\(165\) −9.11418 −0.709538
\(166\) 6.42446 0.498635
\(167\) −13.8409 −1.07104 −0.535522 0.844521i \(-0.679885\pi\)
−0.535522 + 0.844521i \(0.679885\pi\)
\(168\) 7.21380 0.556557
\(169\) −11.6198 −0.893829
\(170\) −20.8764 −1.60115
\(171\) −4.81247 −0.368019
\(172\) −1.96662 −0.149954
\(173\) −7.18295 −0.546110 −0.273055 0.961998i \(-0.588034\pi\)
−0.273055 + 0.961998i \(0.588034\pi\)
\(174\) 10.1994 0.773212
\(175\) 11.0228 0.833245
\(176\) −1.51191 −0.113965
\(177\) 1.73033 0.130059
\(178\) 12.7659 0.956845
\(179\) −2.51685 −0.188118 −0.0940591 0.995567i \(-0.529984\pi\)
−0.0940591 + 0.995567i \(0.529984\pi\)
\(180\) −4.08155 −0.304221
\(181\) 8.28994 0.616186 0.308093 0.951356i \(-0.400309\pi\)
0.308093 + 0.951356i \(0.400309\pi\)
\(182\) 4.02925 0.298668
\(183\) −21.7577 −1.60838
\(184\) 2.46602 0.181797
\(185\) 9.51773 0.699758
\(186\) −17.9479 −1.31600
\(187\) 11.0130 0.805351
\(188\) −0.645154 −0.0470527
\(189\) 11.3680 0.826902
\(190\) −9.68491 −0.702617
\(191\) −12.2518 −0.886512 −0.443256 0.896395i \(-0.646177\pi\)
−0.443256 + 0.896395i \(0.646177\pi\)
\(192\) −2.10336 −0.151797
\(193\) 4.61562 0.332239 0.166120 0.986106i \(-0.446876\pi\)
0.166120 + 0.986106i \(0.446876\pi\)
\(194\) −3.11750 −0.223824
\(195\) −7.08214 −0.507163
\(196\) 4.76251 0.340180
\(197\) −12.3012 −0.876426 −0.438213 0.898871i \(-0.644388\pi\)
−0.438213 + 0.898871i \(0.644388\pi\)
\(198\) 2.15316 0.153018
\(199\) −18.0187 −1.27731 −0.638655 0.769493i \(-0.720509\pi\)
−0.638655 + 0.769493i \(0.720509\pi\)
\(200\) −3.21397 −0.227262
\(201\) 10.8060 0.762197
\(202\) 12.3350 0.867885
\(203\) 16.6307 1.16724
\(204\) 15.3212 1.07270
\(205\) 27.7679 1.93940
\(206\) 7.97045 0.555328
\(207\) −3.51193 −0.244096
\(208\) −1.17483 −0.0814596
\(209\) 5.10912 0.353405
\(210\) −20.6748 −1.42669
\(211\) −27.1505 −1.86911 −0.934557 0.355813i \(-0.884204\pi\)
−0.934557 + 0.355813i \(0.884204\pi\)
\(212\) −9.65253 −0.662938
\(213\) 22.5486 1.54501
\(214\) −0.791050 −0.0540751
\(215\) 5.63634 0.384396
\(216\) −3.31463 −0.225532
\(217\) −29.2651 −1.98664
\(218\) 1.22575 0.0830184
\(219\) −12.8907 −0.871075
\(220\) 4.33315 0.292141
\(221\) 8.55762 0.575648
\(222\) −6.98507 −0.468807
\(223\) −2.51162 −0.168190 −0.0840952 0.996458i \(-0.526800\pi\)
−0.0840952 + 0.996458i \(0.526800\pi\)
\(224\) −3.42965 −0.229153
\(225\) 4.57710 0.305140
\(226\) −12.5726 −0.836314
\(227\) 22.5312 1.49545 0.747723 0.664011i \(-0.231147\pi\)
0.747723 + 0.664011i \(0.231147\pi\)
\(228\) 7.10777 0.470723
\(229\) −18.3882 −1.21512 −0.607562 0.794273i \(-0.707852\pi\)
−0.607562 + 0.794273i \(0.707852\pi\)
\(230\) −7.06761 −0.466025
\(231\) 10.9066 0.717604
\(232\) −4.84908 −0.318358
\(233\) −8.43449 −0.552561 −0.276281 0.961077i \(-0.589102\pi\)
−0.276281 + 0.961077i \(0.589102\pi\)
\(234\) 1.67311 0.109374
\(235\) 1.84901 0.120616
\(236\) −0.822649 −0.0535499
\(237\) −32.3722 −2.10280
\(238\) 24.9821 1.61935
\(239\) 19.8057 1.28112 0.640561 0.767907i \(-0.278702\pi\)
0.640561 + 0.767907i \(0.278702\pi\)
\(240\) 6.02824 0.389121
\(241\) −28.3492 −1.82613 −0.913066 0.407811i \(-0.866292\pi\)
−0.913066 + 0.407811i \(0.866292\pi\)
\(242\) 8.71412 0.560165
\(243\) 13.7068 0.879293
\(244\) 10.3443 0.662223
\(245\) −13.6494 −0.872026
\(246\) −20.3789 −1.29931
\(247\) 3.97003 0.252607
\(248\) 8.53296 0.541844
\(249\) 13.5130 0.856349
\(250\) −5.11877 −0.323740
\(251\) −21.0654 −1.32964 −0.664818 0.747006i \(-0.731491\pi\)
−0.664818 + 0.747006i \(0.731491\pi\)
\(252\) 4.88426 0.307680
\(253\) 3.72841 0.234403
\(254\) −3.10468 −0.194805
\(255\) −43.9106 −2.74979
\(256\) 1.00000 0.0625000
\(257\) −6.93510 −0.432600 −0.216300 0.976327i \(-0.569399\pi\)
−0.216300 + 0.976327i \(0.569399\pi\)
\(258\) −4.13652 −0.257528
\(259\) −11.3896 −0.707713
\(260\) 3.36706 0.208816
\(261\) 6.90571 0.427453
\(262\) −0.692149 −0.0427611
\(263\) −30.6371 −1.88916 −0.944581 0.328278i \(-0.893532\pi\)
−0.944581 + 0.328278i \(0.893532\pi\)
\(264\) −3.18010 −0.195722
\(265\) 27.6642 1.69940
\(266\) 11.5896 0.710605
\(267\) 26.8513 1.64327
\(268\) −5.13750 −0.313823
\(269\) −5.70907 −0.348088 −0.174044 0.984738i \(-0.555684\pi\)
−0.174044 + 0.984738i \(0.555684\pi\)
\(270\) 9.49973 0.578135
\(271\) 31.4036 1.90763 0.953817 0.300388i \(-0.0971161\pi\)
0.953817 + 0.300388i \(0.0971161\pi\)
\(272\) −7.28415 −0.441667
\(273\) 8.47497 0.512928
\(274\) −5.61252 −0.339065
\(275\) −4.85924 −0.293023
\(276\) 5.18693 0.312216
\(277\) 4.12553 0.247879 0.123940 0.992290i \(-0.460447\pi\)
0.123940 + 0.992290i \(0.460447\pi\)
\(278\) 3.42114 0.205186
\(279\) −12.1520 −0.727523
\(280\) 9.82939 0.587418
\(281\) −23.9809 −1.43058 −0.715290 0.698828i \(-0.753705\pi\)
−0.715290 + 0.698828i \(0.753705\pi\)
\(282\) −1.35699 −0.0808077
\(283\) −14.1399 −0.840531 −0.420265 0.907401i \(-0.638063\pi\)
−0.420265 + 0.907401i \(0.638063\pi\)
\(284\) −10.7203 −0.636132
\(285\) −20.3709 −1.20667
\(286\) −1.77624 −0.105031
\(287\) −33.2290 −1.96145
\(288\) −1.42413 −0.0839176
\(289\) 36.0589 2.12111
\(290\) 13.8975 0.816087
\(291\) −6.55723 −0.384392
\(292\) 6.12864 0.358651
\(293\) 8.61165 0.503098 0.251549 0.967845i \(-0.419060\pi\)
0.251549 + 0.967845i \(0.419060\pi\)
\(294\) 10.0173 0.584220
\(295\) 2.35771 0.137271
\(296\) 3.32091 0.193024
\(297\) −5.01143 −0.290793
\(298\) −17.9357 −1.03899
\(299\) 2.89715 0.167546
\(300\) −6.76013 −0.390297
\(301\) −6.74483 −0.388766
\(302\) 13.4578 0.774411
\(303\) 25.9449 1.49049
\(304\) −3.37924 −0.193813
\(305\) −29.6466 −1.69756
\(306\) 10.3736 0.593017
\(307\) −10.2691 −0.586091 −0.293045 0.956099i \(-0.594669\pi\)
−0.293045 + 0.956099i \(0.594669\pi\)
\(308\) −5.18534 −0.295462
\(309\) 16.7647 0.953713
\(310\) −24.4555 −1.38898
\(311\) −3.65819 −0.207437 −0.103719 0.994607i \(-0.533074\pi\)
−0.103719 + 0.994607i \(0.533074\pi\)
\(312\) −2.47109 −0.139898
\(313\) −13.5030 −0.763235 −0.381617 0.924320i \(-0.624633\pi\)
−0.381617 + 0.924320i \(0.624633\pi\)
\(314\) −6.87183 −0.387800
\(315\) −13.9983 −0.788715
\(316\) 15.3907 0.865794
\(317\) 0.0257917 0.00144860 0.000724302 1.00000i \(-0.499769\pi\)
0.000724302 1.00000i \(0.499769\pi\)
\(318\) −20.3028 −1.13852
\(319\) −7.33139 −0.410479
\(320\) −2.86600 −0.160214
\(321\) −1.66386 −0.0928679
\(322\) 8.45758 0.471323
\(323\) 24.6149 1.36961
\(324\) −11.2442 −0.624680
\(325\) −3.77586 −0.209447
\(326\) 24.4552 1.35445
\(327\) 2.57820 0.142575
\(328\) 9.68874 0.534971
\(329\) −2.21265 −0.121988
\(330\) 9.11418 0.501719
\(331\) 14.0491 0.772210 0.386105 0.922455i \(-0.373820\pi\)
0.386105 + 0.922455i \(0.373820\pi\)
\(332\) −6.42446 −0.352588
\(333\) −4.72940 −0.259170
\(334\) 13.8409 0.757343
\(335\) 14.7241 0.804462
\(336\) −7.21380 −0.393545
\(337\) 24.2966 1.32352 0.661761 0.749715i \(-0.269809\pi\)
0.661761 + 0.749715i \(0.269809\pi\)
\(338\) 11.6198 0.632033
\(339\) −26.4446 −1.43628
\(340\) 20.8764 1.13218
\(341\) 12.9011 0.698634
\(342\) 4.81247 0.260229
\(343\) −7.67380 −0.414346
\(344\) 1.96662 0.106033
\(345\) −14.8657 −0.800345
\(346\) 7.18295 0.386158
\(347\) 0.948564 0.0509216 0.0254608 0.999676i \(-0.491895\pi\)
0.0254608 + 0.999676i \(0.491895\pi\)
\(348\) −10.1994 −0.546743
\(349\) −10.6983 −0.572665 −0.286333 0.958130i \(-0.592436\pi\)
−0.286333 + 0.958130i \(0.592436\pi\)
\(350\) −11.0228 −0.589193
\(351\) −3.89412 −0.207853
\(352\) 1.51191 0.0805853
\(353\) −10.1166 −0.538453 −0.269227 0.963077i \(-0.586768\pi\)
−0.269227 + 0.963077i \(0.586768\pi\)
\(354\) −1.73033 −0.0919659
\(355\) 30.7243 1.63068
\(356\) −12.7659 −0.676591
\(357\) 52.5464 2.78105
\(358\) 2.51685 0.133020
\(359\) 0.328326 0.0173284 0.00866420 0.999962i \(-0.497242\pi\)
0.00866420 + 0.999962i \(0.497242\pi\)
\(360\) 4.08155 0.215117
\(361\) −7.58073 −0.398986
\(362\) −8.28994 −0.435710
\(363\) 18.3289 0.962019
\(364\) −4.02925 −0.211190
\(365\) −17.5647 −0.919377
\(366\) 21.7577 1.13729
\(367\) 15.4184 0.804835 0.402417 0.915456i \(-0.368170\pi\)
0.402417 + 0.915456i \(0.368170\pi\)
\(368\) −2.46602 −0.128550
\(369\) −13.7980 −0.718295
\(370\) −9.51773 −0.494803
\(371\) −33.1048 −1.71872
\(372\) 17.9479 0.930555
\(373\) 26.7105 1.38302 0.691509 0.722368i \(-0.256946\pi\)
0.691509 + 0.722368i \(0.256946\pi\)
\(374\) −11.0130 −0.569469
\(375\) −10.7666 −0.555986
\(376\) 0.645154 0.0332713
\(377\) −5.69683 −0.293402
\(378\) −11.3680 −0.584708
\(379\) 30.8165 1.58294 0.791469 0.611209i \(-0.209317\pi\)
0.791469 + 0.611209i \(0.209317\pi\)
\(380\) 9.68491 0.496826
\(381\) −6.53027 −0.334556
\(382\) 12.2518 0.626858
\(383\) 36.1044 1.84485 0.922425 0.386177i \(-0.126205\pi\)
0.922425 + 0.386177i \(0.126205\pi\)
\(384\) 2.10336 0.107337
\(385\) 14.8612 0.757397
\(386\) −4.61562 −0.234929
\(387\) −2.80072 −0.142369
\(388\) 3.11750 0.158267
\(389\) 30.8209 1.56268 0.781342 0.624103i \(-0.214536\pi\)
0.781342 + 0.624103i \(0.214536\pi\)
\(390\) 7.08214 0.358618
\(391\) 17.9629 0.908421
\(392\) −4.76251 −0.240543
\(393\) −1.45584 −0.0734374
\(394\) 12.3012 0.619727
\(395\) −44.1098 −2.21940
\(396\) −2.15316 −0.108200
\(397\) 14.9668 0.751161 0.375581 0.926790i \(-0.377443\pi\)
0.375581 + 0.926790i \(0.377443\pi\)
\(398\) 18.0187 0.903195
\(399\) 24.3772 1.22038
\(400\) 3.21397 0.160698
\(401\) −4.58532 −0.228980 −0.114490 0.993424i \(-0.536523\pi\)
−0.114490 + 0.993424i \(0.536523\pi\)
\(402\) −10.8060 −0.538955
\(403\) 10.0248 0.499369
\(404\) −12.3350 −0.613687
\(405\) 32.2260 1.60132
\(406\) −16.6307 −0.825365
\(407\) 5.02093 0.248878
\(408\) −15.3212 −0.758513
\(409\) 17.5640 0.868482 0.434241 0.900797i \(-0.357017\pi\)
0.434241 + 0.900797i \(0.357017\pi\)
\(410\) −27.7679 −1.37136
\(411\) −11.8052 −0.582305
\(412\) −7.97045 −0.392676
\(413\) −2.82140 −0.138832
\(414\) 3.51193 0.172602
\(415\) 18.4125 0.903835
\(416\) 1.17483 0.0576007
\(417\) 7.19589 0.352384
\(418\) −5.10912 −0.249895
\(419\) 35.6335 1.74081 0.870405 0.492336i \(-0.163857\pi\)
0.870405 + 0.492336i \(0.163857\pi\)
\(420\) 20.6748 1.00882
\(421\) 37.4786 1.82660 0.913298 0.407291i \(-0.133527\pi\)
0.913298 + 0.407291i \(0.133527\pi\)
\(422\) 27.1505 1.32166
\(423\) −0.918782 −0.0446727
\(424\) 9.65253 0.468768
\(425\) −23.4110 −1.13560
\(426\) −22.5486 −1.09248
\(427\) 35.4772 1.71686
\(428\) 0.791050 0.0382369
\(429\) −3.73607 −0.180379
\(430\) −5.63634 −0.271809
\(431\) 31.3578 1.51045 0.755226 0.655464i \(-0.227527\pi\)
0.755226 + 0.655464i \(0.227527\pi\)
\(432\) 3.31463 0.159475
\(433\) 21.2769 1.02250 0.511250 0.859432i \(-0.329182\pi\)
0.511250 + 0.859432i \(0.329182\pi\)
\(434\) 29.2651 1.40477
\(435\) 29.2314 1.40154
\(436\) −1.22575 −0.0587029
\(437\) 8.33327 0.398634
\(438\) 12.8907 0.615943
\(439\) −2.41774 −0.115393 −0.0576963 0.998334i \(-0.518376\pi\)
−0.0576963 + 0.998334i \(0.518376\pi\)
\(440\) −4.33315 −0.206575
\(441\) 6.78243 0.322973
\(442\) −8.55762 −0.407045
\(443\) 29.6406 1.40827 0.704133 0.710068i \(-0.251336\pi\)
0.704133 + 0.710068i \(0.251336\pi\)
\(444\) 6.98507 0.331497
\(445\) 36.5871 1.73439
\(446\) 2.51162 0.118929
\(447\) −37.7254 −1.78435
\(448\) 3.42965 0.162036
\(449\) −17.6851 −0.834611 −0.417305 0.908766i \(-0.637025\pi\)
−0.417305 + 0.908766i \(0.637025\pi\)
\(450\) −4.57710 −0.215767
\(451\) 14.6485 0.689773
\(452\) 12.5726 0.591363
\(453\) 28.3067 1.32996
\(454\) −22.5312 −1.05744
\(455\) 11.5478 0.541371
\(456\) −7.10777 −0.332852
\(457\) 0.459735 0.0215055 0.0107527 0.999942i \(-0.496577\pi\)
0.0107527 + 0.999942i \(0.496577\pi\)
\(458\) 18.3882 0.859222
\(459\) −24.1443 −1.12696
\(460\) 7.06761 0.329529
\(461\) 7.88790 0.367376 0.183688 0.982985i \(-0.441196\pi\)
0.183688 + 0.982985i \(0.441196\pi\)
\(462\) −10.9066 −0.507423
\(463\) −37.5488 −1.74504 −0.872521 0.488576i \(-0.837517\pi\)
−0.872521 + 0.488576i \(0.837517\pi\)
\(464\) 4.84908 0.225113
\(465\) −51.4387 −2.38541
\(466\) 8.43449 0.390720
\(467\) −41.4338 −1.91733 −0.958664 0.284542i \(-0.908158\pi\)
−0.958664 + 0.284542i \(0.908158\pi\)
\(468\) −1.67311 −0.0773393
\(469\) −17.6198 −0.813608
\(470\) −1.84901 −0.0852886
\(471\) −14.4539 −0.666003
\(472\) 0.822649 0.0378655
\(473\) 2.97336 0.136715
\(474\) 32.3722 1.48690
\(475\) −10.8608 −0.498326
\(476\) −24.9821 −1.14505
\(477\) −13.7464 −0.629406
\(478\) −19.8057 −0.905890
\(479\) −27.2202 −1.24372 −0.621860 0.783128i \(-0.713623\pi\)
−0.621860 + 0.783128i \(0.713623\pi\)
\(480\) −6.02824 −0.275150
\(481\) 3.90150 0.177893
\(482\) 28.3492 1.29127
\(483\) 17.7894 0.809444
\(484\) −8.71412 −0.396096
\(485\) −8.93477 −0.405707
\(486\) −13.7068 −0.621754
\(487\) 7.85504 0.355946 0.177973 0.984035i \(-0.443046\pi\)
0.177973 + 0.984035i \(0.443046\pi\)
\(488\) −10.3443 −0.468262
\(489\) 51.4381 2.32611
\(490\) 13.6494 0.616616
\(491\) 28.6606 1.29343 0.646717 0.762730i \(-0.276141\pi\)
0.646717 + 0.762730i \(0.276141\pi\)
\(492\) 20.3789 0.918752
\(493\) −35.3214 −1.59080
\(494\) −3.97003 −0.178620
\(495\) 6.17096 0.277364
\(496\) −8.53296 −0.383141
\(497\) −36.7668 −1.64922
\(498\) −13.5130 −0.605530
\(499\) 35.3208 1.58118 0.790589 0.612347i \(-0.209775\pi\)
0.790589 + 0.612347i \(0.209775\pi\)
\(500\) 5.11877 0.228918
\(501\) 29.1125 1.30065
\(502\) 21.0654 0.940194
\(503\) −23.4898 −1.04736 −0.523679 0.851915i \(-0.675441\pi\)
−0.523679 + 0.851915i \(0.675441\pi\)
\(504\) −4.88426 −0.217562
\(505\) 35.3520 1.57314
\(506\) −3.72841 −0.165748
\(507\) 24.4406 1.08544
\(508\) 3.10468 0.137748
\(509\) 13.6674 0.605797 0.302898 0.953023i \(-0.402046\pi\)
0.302898 + 0.953023i \(0.402046\pi\)
\(510\) 43.9106 1.94439
\(511\) 21.0191 0.929830
\(512\) −1.00000 −0.0441942
\(513\) −11.2009 −0.494533
\(514\) 6.93510 0.305894
\(515\) 22.8433 1.00660
\(516\) 4.13652 0.182100
\(517\) 0.975417 0.0428988
\(518\) 11.3896 0.500429
\(519\) 15.1083 0.663183
\(520\) −3.36706 −0.147655
\(521\) −20.5598 −0.900740 −0.450370 0.892842i \(-0.648708\pi\)
−0.450370 + 0.892842i \(0.648708\pi\)
\(522\) −6.90571 −0.302255
\(523\) 23.1195 1.01094 0.505472 0.862843i \(-0.331318\pi\)
0.505472 + 0.862843i \(0.331318\pi\)
\(524\) 0.692149 0.0302367
\(525\) −23.1849 −1.01187
\(526\) 30.6371 1.33584
\(527\) 62.1554 2.70753
\(528\) 3.18010 0.138396
\(529\) −16.9188 −0.735598
\(530\) −27.6642 −1.20165
\(531\) −1.17156 −0.0508413
\(532\) −11.5896 −0.502474
\(533\) 11.3826 0.493035
\(534\) −26.8513 −1.16197
\(535\) −2.26715 −0.0980175
\(536\) 5.13750 0.221906
\(537\) 5.29384 0.228446
\(538\) 5.70907 0.246136
\(539\) −7.20051 −0.310148
\(540\) −9.49973 −0.408803
\(541\) −28.1794 −1.21153 −0.605764 0.795644i \(-0.707133\pi\)
−0.605764 + 0.795644i \(0.707133\pi\)
\(542\) −31.4036 −1.34890
\(543\) −17.4367 −0.748282
\(544\) 7.28415 0.312305
\(545\) 3.51301 0.150481
\(546\) −8.47497 −0.362695
\(547\) 39.8372 1.70332 0.851658 0.524097i \(-0.175597\pi\)
0.851658 + 0.524097i \(0.175597\pi\)
\(548\) 5.61252 0.239755
\(549\) 14.7315 0.628727
\(550\) 4.85924 0.207199
\(551\) −16.3862 −0.698076
\(552\) −5.18693 −0.220770
\(553\) 52.7847 2.24464
\(554\) −4.12553 −0.175277
\(555\) −20.0192 −0.849769
\(556\) −3.42114 −0.145089
\(557\) 27.5288 1.16643 0.583216 0.812317i \(-0.301794\pi\)
0.583216 + 0.812317i \(0.301794\pi\)
\(558\) 12.1520 0.514437
\(559\) 2.31044 0.0977213
\(560\) −9.82939 −0.415368
\(561\) −23.1643 −0.977999
\(562\) 23.9809 1.01157
\(563\) −23.5606 −0.992962 −0.496481 0.868047i \(-0.665375\pi\)
−0.496481 + 0.868047i \(0.665375\pi\)
\(564\) 1.35699 0.0571397
\(565\) −36.0330 −1.51592
\(566\) 14.1399 0.594345
\(567\) −38.5638 −1.61953
\(568\) 10.7203 0.449813
\(569\) −41.1421 −1.72476 −0.862382 0.506257i \(-0.831029\pi\)
−0.862382 + 0.506257i \(0.831029\pi\)
\(570\) 20.3709 0.853242
\(571\) −8.88139 −0.371675 −0.185837 0.982581i \(-0.559500\pi\)
−0.185837 + 0.982581i \(0.559500\pi\)
\(572\) 1.77624 0.0742683
\(573\) 25.7700 1.07656
\(574\) 33.2290 1.38695
\(575\) −7.92570 −0.330525
\(576\) 1.42413 0.0593387
\(577\) 23.0948 0.961450 0.480725 0.876871i \(-0.340373\pi\)
0.480725 + 0.876871i \(0.340373\pi\)
\(578\) −36.0589 −1.49985
\(579\) −9.70831 −0.403463
\(580\) −13.8975 −0.577061
\(581\) −22.0337 −0.914110
\(582\) 6.55723 0.271806
\(583\) 14.5938 0.604413
\(584\) −6.12864 −0.253605
\(585\) 4.79512 0.198254
\(586\) −8.61165 −0.355744
\(587\) −3.56091 −0.146974 −0.0734872 0.997296i \(-0.523413\pi\)
−0.0734872 + 0.997296i \(0.523413\pi\)
\(588\) −10.0173 −0.413106
\(589\) 28.8349 1.18812
\(590\) −2.35771 −0.0970655
\(591\) 25.8739 1.06431
\(592\) −3.32091 −0.136489
\(593\) −9.58874 −0.393762 −0.196881 0.980427i \(-0.563081\pi\)
−0.196881 + 0.980427i \(0.563081\pi\)
\(594\) 5.01143 0.205622
\(595\) 71.5988 2.93526
\(596\) 17.9357 0.734677
\(597\) 37.8998 1.55114
\(598\) −2.89715 −0.118473
\(599\) 26.7794 1.09418 0.547088 0.837075i \(-0.315736\pi\)
0.547088 + 0.837075i \(0.315736\pi\)
\(600\) 6.76013 0.275981
\(601\) 21.0157 0.857249 0.428624 0.903483i \(-0.358998\pi\)
0.428624 + 0.903483i \(0.358998\pi\)
\(602\) 6.74483 0.274899
\(603\) −7.31645 −0.297949
\(604\) −13.4578 −0.547591
\(605\) 24.9747 1.01536
\(606\) −25.9449 −1.05394
\(607\) −32.5724 −1.32207 −0.661037 0.750353i \(-0.729883\pi\)
−0.661037 + 0.750353i \(0.729883\pi\)
\(608\) 3.37924 0.137046
\(609\) −34.9803 −1.41747
\(610\) 29.6466 1.20036
\(611\) 0.757945 0.0306632
\(612\) −10.3736 −0.419327
\(613\) 7.23880 0.292372 0.146186 0.989257i \(-0.453300\pi\)
0.146186 + 0.989257i \(0.453300\pi\)
\(614\) 10.2691 0.414429
\(615\) −58.4060 −2.35516
\(616\) 5.18534 0.208923
\(617\) 14.0526 0.565737 0.282868 0.959159i \(-0.408714\pi\)
0.282868 + 0.959159i \(0.408714\pi\)
\(618\) −16.7647 −0.674377
\(619\) −2.24759 −0.0903381 −0.0451691 0.998979i \(-0.514383\pi\)
−0.0451691 + 0.998979i \(0.514383\pi\)
\(620\) 24.4555 0.982156
\(621\) −8.17393 −0.328009
\(622\) 3.65819 0.146680
\(623\) −43.7826 −1.75411
\(624\) 2.47109 0.0989226
\(625\) −30.7403 −1.22961
\(626\) 13.5030 0.539689
\(627\) −10.7463 −0.429167
\(628\) 6.87183 0.274216
\(629\) 24.1900 0.964519
\(630\) 13.9983 0.557706
\(631\) 9.18148 0.365509 0.182754 0.983159i \(-0.441499\pi\)
0.182754 + 0.983159i \(0.441499\pi\)
\(632\) −15.3907 −0.612209
\(633\) 57.1072 2.26981
\(634\) −0.0257917 −0.00102432
\(635\) −8.89803 −0.353108
\(636\) 20.3028 0.805057
\(637\) −5.59513 −0.221687
\(638\) 7.33139 0.290252
\(639\) −15.2671 −0.603955
\(640\) 2.86600 0.113289
\(641\) −4.87165 −0.192419 −0.0962093 0.995361i \(-0.530672\pi\)
−0.0962093 + 0.995361i \(0.530672\pi\)
\(642\) 1.66386 0.0656675
\(643\) 11.1134 0.438269 0.219134 0.975695i \(-0.429677\pi\)
0.219134 + 0.975695i \(0.429677\pi\)
\(644\) −8.45758 −0.333275
\(645\) −11.8553 −0.466801
\(646\) −24.6149 −0.968461
\(647\) −4.83049 −0.189906 −0.0949530 0.995482i \(-0.530270\pi\)
−0.0949530 + 0.995482i \(0.530270\pi\)
\(648\) 11.2442 0.441716
\(649\) 1.24377 0.0488224
\(650\) 3.77586 0.148101
\(651\) 61.5551 2.41253
\(652\) −24.4552 −0.957740
\(653\) −1.00841 −0.0394620 −0.0197310 0.999805i \(-0.506281\pi\)
−0.0197310 + 0.999805i \(0.506281\pi\)
\(654\) −2.57820 −0.100816
\(655\) −1.98370 −0.0775096
\(656\) −9.68874 −0.378282
\(657\) 8.72796 0.340510
\(658\) 2.21265 0.0862582
\(659\) −40.6090 −1.58190 −0.790951 0.611879i \(-0.790414\pi\)
−0.790951 + 0.611879i \(0.790414\pi\)
\(660\) −9.11418 −0.354769
\(661\) −33.6944 −1.31056 −0.655280 0.755386i \(-0.727449\pi\)
−0.655280 + 0.755386i \(0.727449\pi\)
\(662\) −14.0491 −0.546035
\(663\) −17.9998 −0.699053
\(664\) 6.42446 0.249317
\(665\) 33.2159 1.28806
\(666\) 4.72940 0.183261
\(667\) −11.9579 −0.463012
\(668\) −13.8409 −0.535522
\(669\) 5.28284 0.204246
\(670\) −14.7241 −0.568841
\(671\) −15.6396 −0.603761
\(672\) 7.21380 0.278278
\(673\) 18.7103 0.721231 0.360615 0.932715i \(-0.382567\pi\)
0.360615 + 0.932715i \(0.382567\pi\)
\(674\) −24.2966 −0.935871
\(675\) 10.6531 0.410038
\(676\) −11.6198 −0.446915
\(677\) −35.0072 −1.34544 −0.672719 0.739898i \(-0.734874\pi\)
−0.672719 + 0.739898i \(0.734874\pi\)
\(678\) 26.4446 1.01560
\(679\) 10.6919 0.410319
\(680\) −20.8764 −0.800573
\(681\) −47.3912 −1.81603
\(682\) −12.9011 −0.494009
\(683\) 31.3377 1.19911 0.599553 0.800335i \(-0.295345\pi\)
0.599553 + 0.800335i \(0.295345\pi\)
\(684\) −4.81247 −0.184010
\(685\) −16.0855 −0.614595
\(686\) 7.67380 0.292987
\(687\) 38.6769 1.47562
\(688\) −1.96662 −0.0749768
\(689\) 11.3401 0.432022
\(690\) 14.8657 0.565929
\(691\) −12.4762 −0.474618 −0.237309 0.971434i \(-0.576265\pi\)
−0.237309 + 0.971434i \(0.576265\pi\)
\(692\) −7.18295 −0.273055
\(693\) −7.38459 −0.280517
\(694\) −0.948564 −0.0360070
\(695\) 9.80500 0.371925
\(696\) 10.1994 0.386606
\(697\) 70.5742 2.67319
\(698\) 10.6983 0.404935
\(699\) 17.7408 0.671017
\(700\) 11.0228 0.416622
\(701\) 22.1317 0.835905 0.417952 0.908469i \(-0.362748\pi\)
0.417952 + 0.908469i \(0.362748\pi\)
\(702\) 3.89412 0.146974
\(703\) 11.2222 0.423252
\(704\) −1.51191 −0.0569824
\(705\) −3.88914 −0.146474
\(706\) 10.1166 0.380744
\(707\) −42.3046 −1.59103
\(708\) 1.73033 0.0650297
\(709\) 35.7153 1.34132 0.670658 0.741767i \(-0.266012\pi\)
0.670658 + 0.741767i \(0.266012\pi\)
\(710\) −30.7243 −1.15306
\(711\) 21.9183 0.822002
\(712\) 12.7659 0.478422
\(713\) 21.0424 0.788046
\(714\) −52.5464 −1.96650
\(715\) −5.09070 −0.190381
\(716\) −2.51685 −0.0940591
\(717\) −41.6585 −1.55576
\(718\) −0.328326 −0.0122530
\(719\) 28.8487 1.07587 0.537937 0.842985i \(-0.319204\pi\)
0.537937 + 0.842985i \(0.319204\pi\)
\(720\) −4.08155 −0.152111
\(721\) −27.3359 −1.01804
\(722\) 7.58073 0.282125
\(723\) 59.6286 2.21761
\(724\) 8.28994 0.308093
\(725\) 15.5848 0.578804
\(726\) −18.3289 −0.680251
\(727\) −30.3028 −1.12387 −0.561935 0.827182i \(-0.689943\pi\)
−0.561935 + 0.827182i \(0.689943\pi\)
\(728\) 4.02925 0.149334
\(729\) 4.90233 0.181568
\(730\) 17.5647 0.650098
\(731\) 14.3252 0.529836
\(732\) −21.7577 −0.804188
\(733\) 22.3506 0.825538 0.412769 0.910836i \(-0.364562\pi\)
0.412769 + 0.910836i \(0.364562\pi\)
\(734\) −15.4184 −0.569104
\(735\) 28.7096 1.05897
\(736\) 2.46602 0.0908986
\(737\) 7.76745 0.286118
\(738\) 13.7980 0.507912
\(739\) −40.2470 −1.48051 −0.740255 0.672327i \(-0.765295\pi\)
−0.740255 + 0.672327i \(0.765295\pi\)
\(740\) 9.51773 0.349879
\(741\) −8.35040 −0.306760
\(742\) 33.1048 1.21532
\(743\) −12.5623 −0.460867 −0.230433 0.973088i \(-0.574014\pi\)
−0.230433 + 0.973088i \(0.574014\pi\)
\(744\) −17.9479 −0.658002
\(745\) −51.4039 −1.88329
\(746\) −26.7105 −0.977941
\(747\) −9.14925 −0.334754
\(748\) 11.0130 0.402676
\(749\) 2.71303 0.0991319
\(750\) 10.7666 0.393142
\(751\) 7.38580 0.269512 0.134756 0.990879i \(-0.456975\pi\)
0.134756 + 0.990879i \(0.456975\pi\)
\(752\) −0.645154 −0.0235263
\(753\) 44.3081 1.61468
\(754\) 5.69683 0.207466
\(755\) 38.5702 1.40371
\(756\) 11.3680 0.413451
\(757\) −24.3461 −0.884874 −0.442437 0.896799i \(-0.645886\pi\)
−0.442437 + 0.896799i \(0.645886\pi\)
\(758\) −30.8165 −1.11931
\(759\) −7.84219 −0.284653
\(760\) −9.68491 −0.351309
\(761\) −10.2975 −0.373285 −0.186643 0.982428i \(-0.559761\pi\)
−0.186643 + 0.982428i \(0.559761\pi\)
\(762\) 6.53027 0.236567
\(763\) −4.20390 −0.152191
\(764\) −12.2518 −0.443256
\(765\) 29.7307 1.07491
\(766\) −36.1044 −1.30451
\(767\) 0.966471 0.0348972
\(768\) −2.10336 −0.0758985
\(769\) −30.8671 −1.11310 −0.556548 0.830815i \(-0.687875\pi\)
−0.556548 + 0.830815i \(0.687875\pi\)
\(770\) −14.8612 −0.535560
\(771\) 14.5870 0.525339
\(772\) 4.61562 0.166120
\(773\) −9.07233 −0.326309 −0.163154 0.986601i \(-0.552167\pi\)
−0.163154 + 0.986601i \(0.552167\pi\)
\(774\) 2.80072 0.100670
\(775\) −27.4247 −0.985123
\(776\) −3.11750 −0.111912
\(777\) 23.9564 0.859430
\(778\) −30.8209 −1.10498
\(779\) 32.7406 1.17305
\(780\) −7.08214 −0.253581
\(781\) 16.2081 0.579973
\(782\) −17.9629 −0.642350
\(783\) 16.0729 0.574398
\(784\) 4.76251 0.170090
\(785\) −19.6947 −0.702933
\(786\) 1.45584 0.0519281
\(787\) 8.12236 0.289531 0.144765 0.989466i \(-0.453757\pi\)
0.144765 + 0.989466i \(0.453757\pi\)
\(788\) −12.3012 −0.438213
\(789\) 64.4408 2.29415
\(790\) 44.1098 1.56936
\(791\) 43.1195 1.53315
\(792\) 2.15316 0.0765092
\(793\) −12.1527 −0.431556
\(794\) −14.9668 −0.531151
\(795\) −58.1877 −2.06371
\(796\) −18.0187 −0.638655
\(797\) −17.1401 −0.607132 −0.303566 0.952810i \(-0.598177\pi\)
−0.303566 + 0.952810i \(0.598177\pi\)
\(798\) −24.3772 −0.862942
\(799\) 4.69940 0.166253
\(800\) −3.21397 −0.113631
\(801\) −18.1803 −0.642369
\(802\) 4.58532 0.161913
\(803\) −9.26597 −0.326989
\(804\) 10.8060 0.381099
\(805\) 24.2395 0.854328
\(806\) −10.0248 −0.353107
\(807\) 12.0082 0.422710
\(808\) 12.3350 0.433943
\(809\) 26.6469 0.936854 0.468427 0.883502i \(-0.344821\pi\)
0.468427 + 0.883502i \(0.344821\pi\)
\(810\) −32.2260 −1.13231
\(811\) −8.06325 −0.283139 −0.141570 0.989928i \(-0.545215\pi\)
−0.141570 + 0.989928i \(0.545215\pi\)
\(812\) 16.6307 0.583621
\(813\) −66.0532 −2.31659
\(814\) −5.02093 −0.175984
\(815\) 70.0887 2.45510
\(816\) 15.3212 0.536349
\(817\) 6.64569 0.232503
\(818\) −17.5640 −0.614110
\(819\) −5.73817 −0.200508
\(820\) 27.7679 0.969698
\(821\) 29.0669 1.01444 0.507221 0.861816i \(-0.330673\pi\)
0.507221 + 0.861816i \(0.330673\pi\)
\(822\) 11.8052 0.411752
\(823\) 33.1970 1.15718 0.578588 0.815620i \(-0.303604\pi\)
0.578588 + 0.815620i \(0.303604\pi\)
\(824\) 7.97045 0.277664
\(825\) 10.2207 0.355841
\(826\) 2.82140 0.0981691
\(827\) 50.0174 1.73928 0.869638 0.493689i \(-0.164352\pi\)
0.869638 + 0.493689i \(0.164352\pi\)
\(828\) −3.51193 −0.122048
\(829\) −45.3776 −1.57603 −0.788015 0.615655i \(-0.788891\pi\)
−0.788015 + 0.615655i \(0.788891\pi\)
\(830\) −18.4125 −0.639108
\(831\) −8.67749 −0.301019
\(832\) −1.17483 −0.0407298
\(833\) −34.6909 −1.20197
\(834\) −7.19589 −0.249173
\(835\) 39.6682 1.37277
\(836\) 5.10912 0.176703
\(837\) −28.2836 −0.977624
\(838\) −35.6335 −1.23094
\(839\) 1.03059 0.0355799 0.0177900 0.999842i \(-0.494337\pi\)
0.0177900 + 0.999842i \(0.494337\pi\)
\(840\) −20.6748 −0.713347
\(841\) −5.48644 −0.189188
\(842\) −37.4786 −1.29160
\(843\) 50.4405 1.73726
\(844\) −27.1505 −0.934557
\(845\) 33.3023 1.14563
\(846\) 0.918782 0.0315884
\(847\) −29.8864 −1.02691
\(848\) −9.65253 −0.331469
\(849\) 29.7414 1.02072
\(850\) 23.4110 0.802992
\(851\) 8.18942 0.280730
\(852\) 22.5486 0.772503
\(853\) 13.8081 0.472781 0.236390 0.971658i \(-0.424036\pi\)
0.236390 + 0.971658i \(0.424036\pi\)
\(854\) −35.4772 −1.21400
\(855\) 13.7926 0.471696
\(856\) −0.791050 −0.0270375
\(857\) 51.1022 1.74562 0.872809 0.488062i \(-0.162296\pi\)
0.872809 + 0.488062i \(0.162296\pi\)
\(858\) 3.73607 0.127547
\(859\) −8.73015 −0.297869 −0.148934 0.988847i \(-0.547584\pi\)
−0.148934 + 0.988847i \(0.547584\pi\)
\(860\) 5.63634 0.192198
\(861\) 69.8926 2.38193
\(862\) −31.3578 −1.06805
\(863\) 23.4756 0.799118 0.399559 0.916707i \(-0.369163\pi\)
0.399559 + 0.916707i \(0.369163\pi\)
\(864\) −3.31463 −0.112766
\(865\) 20.5864 0.699957
\(866\) −21.2769 −0.723017
\(867\) −75.8449 −2.57583
\(868\) −29.2651 −0.993322
\(869\) −23.2694 −0.789361
\(870\) −29.2314 −0.991037
\(871\) 6.03567 0.204511
\(872\) 1.22575 0.0415092
\(873\) 4.43972 0.150262
\(874\) −8.33327 −0.281877
\(875\) 17.5556 0.593488
\(876\) −12.8907 −0.435538
\(877\) 18.8682 0.637133 0.318567 0.947900i \(-0.396799\pi\)
0.318567 + 0.947900i \(0.396799\pi\)
\(878\) 2.41774 0.0815949
\(879\) −18.1134 −0.610950
\(880\) 4.33315 0.146070
\(881\) −28.8640 −0.972452 −0.486226 0.873833i \(-0.661627\pi\)
−0.486226 + 0.873833i \(0.661627\pi\)
\(882\) −6.78243 −0.228376
\(883\) −43.3633 −1.45929 −0.729645 0.683826i \(-0.760315\pi\)
−0.729645 + 0.683826i \(0.760315\pi\)
\(884\) 8.55762 0.287824
\(885\) −4.95912 −0.166699
\(886\) −29.6406 −0.995794
\(887\) 12.0826 0.405695 0.202848 0.979210i \(-0.434980\pi\)
0.202848 + 0.979210i \(0.434980\pi\)
\(888\) −6.98507 −0.234404
\(889\) 10.6480 0.357122
\(890\) −36.5871 −1.22640
\(891\) 17.0003 0.569532
\(892\) −2.51162 −0.0840952
\(893\) 2.18013 0.0729553
\(894\) 37.7254 1.26172
\(895\) 7.21330 0.241114
\(896\) −3.42965 −0.114577
\(897\) −6.09374 −0.203464
\(898\) 17.6851 0.590159
\(899\) −41.3770 −1.38000
\(900\) 4.57710 0.152570
\(901\) 70.3105 2.34238
\(902\) −14.6485 −0.487743
\(903\) 14.1868 0.472108
\(904\) −12.5726 −0.418157
\(905\) −23.7590 −0.789775
\(906\) −28.3067 −0.940426
\(907\) −18.5127 −0.614703 −0.307351 0.951596i \(-0.599443\pi\)
−0.307351 + 0.951596i \(0.599443\pi\)
\(908\) 22.5312 0.747723
\(909\) −17.5666 −0.582646
\(910\) −11.5478 −0.382807
\(911\) 20.7011 0.685857 0.342929 0.939361i \(-0.388581\pi\)
0.342929 + 0.939361i \(0.388581\pi\)
\(912\) 7.10777 0.235362
\(913\) 9.71323 0.321461
\(914\) −0.459735 −0.0152067
\(915\) 62.3576 2.06148
\(916\) −18.3882 −0.607562
\(917\) 2.37383 0.0783908
\(918\) 24.1443 0.796879
\(919\) −18.9549 −0.625265 −0.312633 0.949874i \(-0.601211\pi\)
−0.312633 + 0.949874i \(0.601211\pi\)
\(920\) −7.06761 −0.233012
\(921\) 21.5997 0.711734
\(922\) −7.88790 −0.259774
\(923\) 12.5945 0.414552
\(924\) 10.9066 0.358802
\(925\) −10.6733 −0.350936
\(926\) 37.5488 1.23393
\(927\) −11.3509 −0.372814
\(928\) −4.84908 −0.159179
\(929\) −16.5427 −0.542749 −0.271375 0.962474i \(-0.587478\pi\)
−0.271375 + 0.962474i \(0.587478\pi\)
\(930\) 51.4387 1.68674
\(931\) −16.0937 −0.527449
\(932\) −8.43449 −0.276281
\(933\) 7.69450 0.251907
\(934\) 41.4338 1.35576
\(935\) −31.5633 −1.03223
\(936\) 1.67311 0.0546872
\(937\) −18.9277 −0.618340 −0.309170 0.951007i \(-0.600051\pi\)
−0.309170 + 0.951007i \(0.600051\pi\)
\(938\) 17.6198 0.575308
\(939\) 28.4017 0.926854
\(940\) 1.84901 0.0603081
\(941\) 33.7968 1.10175 0.550873 0.834589i \(-0.314295\pi\)
0.550873 + 0.834589i \(0.314295\pi\)
\(942\) 14.4539 0.470935
\(943\) 23.8926 0.778050
\(944\) −0.822649 −0.0267749
\(945\) −32.5808 −1.05985
\(946\) −2.97336 −0.0966724
\(947\) 45.4634 1.47736 0.738681 0.674055i \(-0.235449\pi\)
0.738681 + 0.674055i \(0.235449\pi\)
\(948\) −32.3722 −1.05140
\(949\) −7.20009 −0.233725
\(950\) 10.8608 0.352370
\(951\) −0.0542492 −0.00175915
\(952\) 24.9821 0.809675
\(953\) −44.7905 −1.45091 −0.725453 0.688271i \(-0.758370\pi\)
−0.725453 + 0.688271i \(0.758370\pi\)
\(954\) 13.7464 0.445057
\(955\) 35.1138 1.13626
\(956\) 19.8057 0.640561
\(957\) 15.4206 0.498476
\(958\) 27.2202 0.879443
\(959\) 19.2490 0.621582
\(960\) 6.02824 0.194561
\(961\) 41.8115 1.34876
\(962\) −3.90150 −0.125789
\(963\) 1.12656 0.0363028
\(964\) −28.3492 −0.913066
\(965\) −13.2284 −0.425836
\(966\) −17.7894 −0.572363
\(967\) 60.4996 1.94554 0.972768 0.231782i \(-0.0744556\pi\)
0.972768 + 0.231782i \(0.0744556\pi\)
\(968\) 8.71412 0.280082
\(969\) −51.7741 −1.66322
\(970\) 8.93477 0.286878
\(971\) −11.0649 −0.355091 −0.177545 0.984113i \(-0.556816\pi\)
−0.177545 + 0.984113i \(0.556816\pi\)
\(972\) 13.7068 0.439647
\(973\) −11.7333 −0.376153
\(974\) −7.85504 −0.251692
\(975\) 7.94199 0.254347
\(976\) 10.3443 0.331111
\(977\) −36.3948 −1.16437 −0.582186 0.813056i \(-0.697802\pi\)
−0.582186 + 0.813056i \(0.697802\pi\)
\(978\) −51.4381 −1.64481
\(979\) 19.3009 0.616861
\(980\) −13.6494 −0.436013
\(981\) −1.74563 −0.0557336
\(982\) −28.6606 −0.914596
\(983\) 32.5565 1.03839 0.519196 0.854655i \(-0.326231\pi\)
0.519196 + 0.854655i \(0.326231\pi\)
\(984\) −20.3789 −0.649656
\(985\) 35.2553 1.12333
\(986\) 35.3214 1.12486
\(987\) 4.65401 0.148139
\(988\) 3.97003 0.126303
\(989\) 4.84973 0.154212
\(990\) −6.17096 −0.196126
\(991\) 17.7721 0.564550 0.282275 0.959334i \(-0.408911\pi\)
0.282275 + 0.959334i \(0.408911\pi\)
\(992\) 8.53296 0.270922
\(993\) −29.5504 −0.937754
\(994\) 36.7668 1.16617
\(995\) 51.6416 1.63715
\(996\) 13.5130 0.428174
\(997\) −24.1251 −0.764049 −0.382024 0.924152i \(-0.624773\pi\)
−0.382024 + 0.924152i \(0.624773\pi\)
\(998\) −35.3208 −1.11806
\(999\) −11.0076 −0.348264
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 \(a_p\))