Properties

Label 8041.2.a.j.1.9
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 82
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: \(0\)
Dimension: \(82\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.30854 q^{2}\) \(-0.184135 q^{3}\) \(+3.32934 q^{4}\) \(-0.542742 q^{5}\) \(+0.425082 q^{6}\) \(-0.304747 q^{7}\) \(-3.06883 q^{8}\) \(-2.96609 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.30854 q^{2}\) \(-0.184135 q^{3}\) \(+3.32934 q^{4}\) \(-0.542742 q^{5}\) \(+0.425082 q^{6}\) \(-0.304747 q^{7}\) \(-3.06883 q^{8}\) \(-2.96609 q^{9}\) \(+1.25294 q^{10}\) \(+1.00000 q^{11}\) \(-0.613048 q^{12}\) \(-5.72441 q^{13}\) \(+0.703519 q^{14}\) \(+0.0999378 q^{15}\) \(+0.425823 q^{16}\) \(+1.00000 q^{17}\) \(+6.84734 q^{18}\) \(+1.89879 q^{19}\) \(-1.80697 q^{20}\) \(+0.0561145 q^{21}\) \(-2.30854 q^{22}\) \(-4.78957 q^{23}\) \(+0.565079 q^{24}\) \(-4.70543 q^{25}\) \(+13.2150 q^{26}\) \(+1.09857 q^{27}\) \(-1.01461 q^{28}\) \(-8.33283 q^{29}\) \(-0.230710 q^{30}\) \(+0.864559 q^{31}\) \(+5.15463 q^{32}\) \(-0.184135 q^{33}\) \(-2.30854 q^{34}\) \(+0.165399 q^{35}\) \(-9.87513 q^{36}\) \(+6.24616 q^{37}\) \(-4.38342 q^{38}\) \(+1.05406 q^{39}\) \(+1.66558 q^{40}\) \(-3.09302 q^{41}\) \(-0.129542 q^{42}\) \(+1.00000 q^{43}\) \(+3.32934 q^{44}\) \(+1.60982 q^{45}\) \(+11.0569 q^{46}\) \(-7.40841 q^{47}\) \(-0.0784089 q^{48}\) \(-6.90713 q^{49}\) \(+10.8627 q^{50}\) \(-0.184135 q^{51}\) \(-19.0585 q^{52}\) \(+0.618875 q^{53}\) \(-2.53608 q^{54}\) \(-0.542742 q^{55}\) \(+0.935215 q^{56}\) \(-0.349633 q^{57}\) \(+19.2366 q^{58}\) \(-6.68953 q^{59}\) \(+0.332727 q^{60}\) \(-0.290764 q^{61}\) \(-1.99587 q^{62}\) \(+0.903907 q^{63}\) \(-12.7513 q^{64}\) \(+3.10688 q^{65}\) \(+0.425082 q^{66}\) \(-11.3482 q^{67}\) \(+3.32934 q^{68}\) \(+0.881927 q^{69}\) \(-0.381829 q^{70}\) \(+16.0839 q^{71}\) \(+9.10243 q^{72}\) \(-8.64826 q^{73}\) \(-14.4195 q^{74}\) \(+0.866435 q^{75}\) \(+6.32171 q^{76}\) \(-0.304747 q^{77}\) \(-2.43334 q^{78}\) \(+6.41459 q^{79}\) \(-0.231112 q^{80}\) \(+8.69600 q^{81}\) \(+7.14034 q^{82}\) \(-5.43137 q^{83}\) \(+0.186824 q^{84}\) \(-0.542742 q^{85}\) \(-2.30854 q^{86}\) \(+1.53437 q^{87}\) \(-3.06883 q^{88}\) \(-13.4338 q^{89}\) \(-3.71634 q^{90}\) \(+1.74449 q^{91}\) \(-15.9461 q^{92}\) \(-0.159196 q^{93}\) \(+17.1026 q^{94}\) \(-1.03055 q^{95}\) \(-0.949148 q^{96}\) \(+0.218025 q^{97}\) \(+15.9454 q^{98}\) \(-2.96609 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 82q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 117q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 31q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 29q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut +\mathstrut 82q^{43} \) \(\mathstrut +\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut -\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 136q^{49} \) \(\mathstrut +\mathstrut 59q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut +\mathstrut 83q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 23q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 96q^{59} \) \(\mathstrut +\mathstrut 184q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 148q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 78q^{67} \) \(\mathstrut +\mathstrut 98q^{68} \) \(\mathstrut +\mathstrut 61q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut +\mathstrut 50q^{72} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 150q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 11q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 111q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.30854 −1.63238 −0.816191 0.577782i \(-0.803918\pi\)
−0.816191 + 0.577782i \(0.803918\pi\)
\(3\) −0.184135 −0.106310 −0.0531552 0.998586i \(-0.516928\pi\)
−0.0531552 + 0.998586i \(0.516928\pi\)
\(4\) 3.32934 1.66467
\(5\) −0.542742 −0.242722 −0.121361 0.992608i \(-0.538726\pi\)
−0.121361 + 0.992608i \(0.538726\pi\)
\(6\) 0.425082 0.173539
\(7\) −0.304747 −0.115183 −0.0575917 0.998340i \(-0.518342\pi\)
−0.0575917 + 0.998340i \(0.518342\pi\)
\(8\) −3.06883 −1.08499
\(9\) −2.96609 −0.988698
\(10\) 1.25294 0.396214
\(11\) 1.00000 0.301511
\(12\) −0.613048 −0.176972
\(13\) −5.72441 −1.58766 −0.793832 0.608137i \(-0.791917\pi\)
−0.793832 + 0.608137i \(0.791917\pi\)
\(14\) 0.703519 0.188023
\(15\) 0.0999378 0.0258038
\(16\) 0.425823 0.106456
\(17\) 1.00000 0.242536
\(18\) 6.84734 1.61393
\(19\) 1.89879 0.435612 0.217806 0.975992i \(-0.430110\pi\)
0.217806 + 0.975992i \(0.430110\pi\)
\(20\) −1.80697 −0.404051
\(21\) 0.0561145 0.0122452
\(22\) −2.30854 −0.492182
\(23\) −4.78957 −0.998694 −0.499347 0.866402i \(-0.666427\pi\)
−0.499347 + 0.866402i \(0.666427\pi\)
\(24\) 0.565079 0.115346
\(25\) −4.70543 −0.941086
\(26\) 13.2150 2.59167
\(27\) 1.09857 0.211419
\(28\) −1.01461 −0.191742
\(29\) −8.33283 −1.54737 −0.773684 0.633572i \(-0.781588\pi\)
−0.773684 + 0.633572i \(0.781588\pi\)
\(30\) −0.230710 −0.0421217
\(31\) 0.864559 0.155279 0.0776397 0.996981i \(-0.475262\pi\)
0.0776397 + 0.996981i \(0.475262\pi\)
\(32\) 5.15463 0.911218
\(33\) −0.184135 −0.0320538
\(34\) −2.30854 −0.395911
\(35\) 0.165399 0.0279575
\(36\) −9.87513 −1.64586
\(37\) 6.24616 1.02686 0.513431 0.858131i \(-0.328374\pi\)
0.513431 + 0.858131i \(0.328374\pi\)
\(38\) −4.38342 −0.711085
\(39\) 1.05406 0.168785
\(40\) 1.66558 0.263352
\(41\) −3.09302 −0.483048 −0.241524 0.970395i \(-0.577647\pi\)
−0.241524 + 0.970395i \(0.577647\pi\)
\(42\) −0.129542 −0.0199888
\(43\) 1.00000 0.152499
\(44\) 3.32934 0.501917
\(45\) 1.60982 0.239978
\(46\) 11.0569 1.63025
\(47\) −7.40841 −1.08063 −0.540314 0.841464i \(-0.681694\pi\)
−0.540314 + 0.841464i \(0.681694\pi\)
\(48\) −0.0784089 −0.0113173
\(49\) −6.90713 −0.986733
\(50\) 10.8627 1.53621
\(51\) −0.184135 −0.0257841
\(52\) −19.0585 −2.64294
\(53\) 0.618875 0.0850090 0.0425045 0.999096i \(-0.486466\pi\)
0.0425045 + 0.999096i \(0.486466\pi\)
\(54\) −2.53608 −0.345117
\(55\) −0.542742 −0.0731833
\(56\) 0.935215 0.124973
\(57\) −0.349633 −0.0463101
\(58\) 19.2366 2.52590
\(59\) −6.68953 −0.870903 −0.435451 0.900212i \(-0.643411\pi\)
−0.435451 + 0.900212i \(0.643411\pi\)
\(60\) 0.332727 0.0429549
\(61\) −0.290764 −0.0372285 −0.0186142 0.999827i \(-0.505925\pi\)
−0.0186142 + 0.999827i \(0.505925\pi\)
\(62\) −1.99587 −0.253475
\(63\) 0.903907 0.113882
\(64\) −12.7513 −1.59391
\(65\) 3.10688 0.385361
\(66\) 0.425082 0.0523240
\(67\) −11.3482 −1.38640 −0.693201 0.720744i \(-0.743800\pi\)
−0.693201 + 0.720744i \(0.743800\pi\)
\(68\) 3.32934 0.403742
\(69\) 0.881927 0.106172
\(70\) −0.381829 −0.0456373
\(71\) 16.0839 1.90881 0.954403 0.298522i \(-0.0964937\pi\)
0.954403 + 0.298522i \(0.0964937\pi\)
\(72\) 9.10243 1.07273
\(73\) −8.64826 −1.01220 −0.506101 0.862474i \(-0.668914\pi\)
−0.506101 + 0.862474i \(0.668914\pi\)
\(74\) −14.4195 −1.67623
\(75\) 0.866435 0.100047
\(76\) 6.32171 0.725150
\(77\) −0.304747 −0.0347291
\(78\) −2.43334 −0.275522
\(79\) 6.41459 0.721698 0.360849 0.932624i \(-0.382487\pi\)
0.360849 + 0.932624i \(0.382487\pi\)
\(80\) −0.231112 −0.0258391
\(81\) 8.69600 0.966222
\(82\) 7.14034 0.788519
\(83\) −5.43137 −0.596170 −0.298085 0.954539i \(-0.596348\pi\)
−0.298085 + 0.954539i \(0.596348\pi\)
\(84\) 0.186824 0.0203842
\(85\) −0.542742 −0.0588686
\(86\) −2.30854 −0.248936
\(87\) 1.53437 0.164501
\(88\) −3.06883 −0.327138
\(89\) −13.4338 −1.42398 −0.711990 0.702190i \(-0.752206\pi\)
−0.711990 + 0.702190i \(0.752206\pi\)
\(90\) −3.71634 −0.391736
\(91\) 1.74449 0.182873
\(92\) −15.9461 −1.66250
\(93\) −0.159196 −0.0165078
\(94\) 17.1026 1.76400
\(95\) −1.03055 −0.105732
\(96\) −0.949148 −0.0968720
\(97\) 0.218025 0.0221370 0.0110685 0.999939i \(-0.496477\pi\)
0.0110685 + 0.999939i \(0.496477\pi\)
\(98\) 15.9454 1.61072
\(99\) −2.96609 −0.298104
\(100\) −15.6660 −1.56660
\(101\) 2.59099 0.257813 0.128907 0.991657i \(-0.458853\pi\)
0.128907 + 0.991657i \(0.458853\pi\)
\(102\) 0.425082 0.0420894
\(103\) −6.08702 −0.599772 −0.299886 0.953975i \(-0.596949\pi\)
−0.299886 + 0.953975i \(0.596949\pi\)
\(104\) 17.5672 1.72261
\(105\) −0.0304557 −0.00297217
\(106\) −1.42870 −0.138767
\(107\) −14.2140 −1.37412 −0.687061 0.726599i \(-0.741100\pi\)
−0.687061 + 0.726599i \(0.741100\pi\)
\(108\) 3.65750 0.351943
\(109\) −7.35830 −0.704797 −0.352399 0.935850i \(-0.614634\pi\)
−0.352399 + 0.935850i \(0.614634\pi\)
\(110\) 1.25294 0.119463
\(111\) −1.15014 −0.109166
\(112\) −0.129768 −0.0122619
\(113\) 12.4767 1.17371 0.586853 0.809694i \(-0.300367\pi\)
0.586853 + 0.809694i \(0.300367\pi\)
\(114\) 0.807142 0.0755957
\(115\) 2.59950 0.242405
\(116\) −27.7428 −2.57586
\(117\) 16.9791 1.56972
\(118\) 15.4430 1.42165
\(119\) −0.304747 −0.0279361
\(120\) −0.306692 −0.0279970
\(121\) 1.00000 0.0909091
\(122\) 0.671239 0.0607711
\(123\) 0.569533 0.0513531
\(124\) 2.87841 0.258489
\(125\) 5.26755 0.471144
\(126\) −2.08670 −0.185898
\(127\) −5.67904 −0.503933 −0.251967 0.967736i \(-0.581077\pi\)
−0.251967 + 0.967736i \(0.581077\pi\)
\(128\) 19.1276 1.69065
\(129\) −0.184135 −0.0162122
\(130\) −7.17234 −0.629056
\(131\) −10.2293 −0.893736 −0.446868 0.894600i \(-0.647461\pi\)
−0.446868 + 0.894600i \(0.647461\pi\)
\(132\) −0.613048 −0.0533590
\(133\) −0.578649 −0.0501753
\(134\) 26.1977 2.26314
\(135\) −0.596239 −0.0513160
\(136\) −3.06883 −0.263150
\(137\) 14.9785 1.27970 0.639848 0.768502i \(-0.278997\pi\)
0.639848 + 0.768502i \(0.278997\pi\)
\(138\) −2.03596 −0.173313
\(139\) 1.37038 0.116234 0.0581170 0.998310i \(-0.481490\pi\)
0.0581170 + 0.998310i \(0.481490\pi\)
\(140\) 0.550669 0.0465400
\(141\) 1.36415 0.114882
\(142\) −37.1302 −3.11590
\(143\) −5.72441 −0.478699
\(144\) −1.26303 −0.105252
\(145\) 4.52258 0.375580
\(146\) 19.9648 1.65230
\(147\) 1.27184 0.104900
\(148\) 20.7956 1.70939
\(149\) 9.65315 0.790817 0.395408 0.918505i \(-0.370603\pi\)
0.395408 + 0.918505i \(0.370603\pi\)
\(150\) −2.00020 −0.163315
\(151\) −19.2433 −1.56600 −0.782999 0.622023i \(-0.786311\pi\)
−0.782999 + 0.622023i \(0.786311\pi\)
\(152\) −5.82706 −0.472637
\(153\) −2.96609 −0.239795
\(154\) 0.703519 0.0566911
\(155\) −0.469233 −0.0376897
\(156\) 3.50934 0.280972
\(157\) −21.0854 −1.68280 −0.841400 0.540413i \(-0.818268\pi\)
−0.841400 + 0.540413i \(0.818268\pi\)
\(158\) −14.8083 −1.17809
\(159\) −0.113957 −0.00903734
\(160\) −2.79763 −0.221172
\(161\) 1.45961 0.115033
\(162\) −20.0750 −1.57724
\(163\) 14.9433 1.17045 0.585224 0.810872i \(-0.301007\pi\)
0.585224 + 0.810872i \(0.301007\pi\)
\(164\) −10.2977 −0.804116
\(165\) 0.0999378 0.00778015
\(166\) 12.5385 0.973177
\(167\) −4.50817 −0.348853 −0.174426 0.984670i \(-0.555807\pi\)
−0.174426 + 0.984670i \(0.555807\pi\)
\(168\) −0.172206 −0.0132860
\(169\) 19.7688 1.52068
\(170\) 1.25294 0.0960961
\(171\) −5.63199 −0.430689
\(172\) 3.32934 0.253860
\(173\) 21.4508 1.63087 0.815437 0.578846i \(-0.196497\pi\)
0.815437 + 0.578846i \(0.196497\pi\)
\(174\) −3.54214 −0.268529
\(175\) 1.43396 0.108398
\(176\) 0.425823 0.0320976
\(177\) 1.23178 0.0925860
\(178\) 31.0124 2.32448
\(179\) −17.7072 −1.32350 −0.661749 0.749726i \(-0.730185\pi\)
−0.661749 + 0.749726i \(0.730185\pi\)
\(180\) 5.35965 0.399485
\(181\) −3.26694 −0.242829 −0.121415 0.992602i \(-0.538743\pi\)
−0.121415 + 0.992602i \(0.538743\pi\)
\(182\) −4.02723 −0.298518
\(183\) 0.0535398 0.00395777
\(184\) 14.6984 1.08358
\(185\) −3.39006 −0.249242
\(186\) 0.367509 0.0269471
\(187\) 1.00000 0.0731272
\(188\) −24.6651 −1.79889
\(189\) −0.334785 −0.0243520
\(190\) 2.37907 0.172596
\(191\) 20.7606 1.50218 0.751092 0.660197i \(-0.229527\pi\)
0.751092 + 0.660197i \(0.229527\pi\)
\(192\) 2.34796 0.169449
\(193\) 18.0198 1.29709 0.648546 0.761175i \(-0.275377\pi\)
0.648546 + 0.761175i \(0.275377\pi\)
\(194\) −0.503318 −0.0361361
\(195\) −0.572085 −0.0409678
\(196\) −22.9962 −1.64258
\(197\) −13.4070 −0.955208 −0.477604 0.878575i \(-0.658495\pi\)
−0.477604 + 0.878575i \(0.658495\pi\)
\(198\) 6.84734 0.486619
\(199\) 17.5992 1.24757 0.623787 0.781594i \(-0.285593\pi\)
0.623787 + 0.781594i \(0.285593\pi\)
\(200\) 14.4402 1.02107
\(201\) 2.08960 0.147389
\(202\) −5.98140 −0.420850
\(203\) 2.53940 0.178231
\(204\) −0.613048 −0.0429219
\(205\) 1.67871 0.117246
\(206\) 14.0521 0.979057
\(207\) 14.2063 0.987407
\(208\) −2.43758 −0.169016
\(209\) 1.89879 0.131342
\(210\) 0.0703081 0.00485172
\(211\) 4.29967 0.296002 0.148001 0.988987i \(-0.452716\pi\)
0.148001 + 0.988987i \(0.452716\pi\)
\(212\) 2.06045 0.141512
\(213\) −2.96161 −0.202926
\(214\) 32.8136 2.24309
\(215\) −0.542742 −0.0370147
\(216\) −3.37131 −0.229389
\(217\) −0.263472 −0.0178856
\(218\) 16.9869 1.15050
\(219\) 1.59245 0.107608
\(220\) −1.80697 −0.121826
\(221\) −5.72441 −0.385065
\(222\) 2.65513 0.178201
\(223\) −22.2114 −1.48738 −0.743692 0.668522i \(-0.766927\pi\)
−0.743692 + 0.668522i \(0.766927\pi\)
\(224\) −1.57086 −0.104957
\(225\) 13.9568 0.930450
\(226\) −28.8028 −1.91593
\(227\) −14.6353 −0.971376 −0.485688 0.874132i \(-0.661431\pi\)
−0.485688 + 0.874132i \(0.661431\pi\)
\(228\) −1.16405 −0.0770910
\(229\) −25.1737 −1.66352 −0.831762 0.555132i \(-0.812668\pi\)
−0.831762 + 0.555132i \(0.812668\pi\)
\(230\) −6.00104 −0.395697
\(231\) 0.0561145 0.00369207
\(232\) 25.5720 1.67889
\(233\) 17.5381 1.14896 0.574480 0.818519i \(-0.305204\pi\)
0.574480 + 0.818519i \(0.305204\pi\)
\(234\) −39.1969 −2.56238
\(235\) 4.02086 0.262292
\(236\) −22.2717 −1.44977
\(237\) −1.18115 −0.0767240
\(238\) 0.703519 0.0456023
\(239\) −1.97029 −0.127447 −0.0637236 0.997968i \(-0.520298\pi\)
−0.0637236 + 0.997968i \(0.520298\pi\)
\(240\) 0.0425558 0.00274696
\(241\) 23.4376 1.50975 0.754875 0.655869i \(-0.227698\pi\)
0.754875 + 0.655869i \(0.227698\pi\)
\(242\) −2.30854 −0.148398
\(243\) −4.89694 −0.314139
\(244\) −0.968051 −0.0619731
\(245\) 3.74879 0.239501
\(246\) −1.31479 −0.0838278
\(247\) −10.8694 −0.691606
\(248\) −2.65318 −0.168477
\(249\) 1.00011 0.0633791
\(250\) −12.1603 −0.769086
\(251\) 23.0204 1.45303 0.726517 0.687149i \(-0.241138\pi\)
0.726517 + 0.687149i \(0.241138\pi\)
\(252\) 3.00941 0.189575
\(253\) −4.78957 −0.301118
\(254\) 13.1103 0.822611
\(255\) 0.0999378 0.00625835
\(256\) −18.6541 −1.16588
\(257\) −13.2455 −0.826233 −0.413116 0.910678i \(-0.635560\pi\)
−0.413116 + 0.910678i \(0.635560\pi\)
\(258\) 0.425082 0.0264645
\(259\) −1.90350 −0.118278
\(260\) 10.3438 0.641498
\(261\) 24.7160 1.52988
\(262\) 23.6147 1.45892
\(263\) 8.76348 0.540379 0.270190 0.962807i \(-0.412914\pi\)
0.270190 + 0.962807i \(0.412914\pi\)
\(264\) 0.565079 0.0347782
\(265\) −0.335890 −0.0206335
\(266\) 1.33583 0.0819052
\(267\) 2.47363 0.151384
\(268\) −37.7820 −2.30790
\(269\) 31.7833 1.93786 0.968930 0.247336i \(-0.0795551\pi\)
0.968930 + 0.247336i \(0.0795551\pi\)
\(270\) 1.37644 0.0837674
\(271\) −16.0076 −0.972395 −0.486197 0.873849i \(-0.661616\pi\)
−0.486197 + 0.873849i \(0.661616\pi\)
\(272\) 0.425823 0.0258193
\(273\) −0.321222 −0.0194413
\(274\) −34.5783 −2.08895
\(275\) −4.70543 −0.283748
\(276\) 2.93624 0.176741
\(277\) −14.9075 −0.895704 −0.447852 0.894108i \(-0.647811\pi\)
−0.447852 + 0.894108i \(0.647811\pi\)
\(278\) −3.16357 −0.189738
\(279\) −2.56436 −0.153524
\(280\) −0.507581 −0.0303337
\(281\) 20.0100 1.19370 0.596849 0.802354i \(-0.296419\pi\)
0.596849 + 0.802354i \(0.296419\pi\)
\(282\) −3.14918 −0.187531
\(283\) −24.7266 −1.46984 −0.734921 0.678152i \(-0.762781\pi\)
−0.734921 + 0.678152i \(0.762781\pi\)
\(284\) 53.5487 3.17753
\(285\) 0.189761 0.0112405
\(286\) 13.2150 0.781419
\(287\) 0.942587 0.0556391
\(288\) −15.2891 −0.900920
\(289\) 1.00000 0.0588235
\(290\) −10.4405 −0.613089
\(291\) −0.0401460 −0.00235340
\(292\) −28.7930 −1.68498
\(293\) −12.9573 −0.756972 −0.378486 0.925607i \(-0.623555\pi\)
−0.378486 + 0.925607i \(0.623555\pi\)
\(294\) −2.93610 −0.171237
\(295\) 3.63069 0.211387
\(296\) −19.1684 −1.11414
\(297\) 1.09857 0.0637453
\(298\) −22.2846 −1.29091
\(299\) 27.4174 1.58559
\(300\) 2.88466 0.166546
\(301\) −0.304747 −0.0175653
\(302\) 44.4239 2.55631
\(303\) −0.477092 −0.0274082
\(304\) 0.808547 0.0463734
\(305\) 0.157810 0.00903616
\(306\) 6.84734 0.391436
\(307\) 4.53338 0.258733 0.129367 0.991597i \(-0.458706\pi\)
0.129367 + 0.991597i \(0.458706\pi\)
\(308\) −1.01461 −0.0578125
\(309\) 1.12083 0.0637620
\(310\) 1.08324 0.0615239
\(311\) −11.8619 −0.672627 −0.336313 0.941750i \(-0.609180\pi\)
−0.336313 + 0.941750i \(0.609180\pi\)
\(312\) −3.23474 −0.183131
\(313\) 6.73806 0.380858 0.190429 0.981701i \(-0.439012\pi\)
0.190429 + 0.981701i \(0.439012\pi\)
\(314\) 48.6765 2.74697
\(315\) −0.490588 −0.0276415
\(316\) 21.3563 1.20139
\(317\) 2.35683 0.132373 0.0661865 0.997807i \(-0.478917\pi\)
0.0661865 + 0.997807i \(0.478917\pi\)
\(318\) 0.263073 0.0147524
\(319\) −8.33283 −0.466549
\(320\) 6.92066 0.386877
\(321\) 2.61730 0.146084
\(322\) −3.36955 −0.187778
\(323\) 1.89879 0.105651
\(324\) 28.9519 1.60844
\(325\) 26.9358 1.49413
\(326\) −34.4971 −1.91062
\(327\) 1.35492 0.0749273
\(328\) 9.49194 0.524105
\(329\) 2.25769 0.124470
\(330\) −0.230710 −0.0127002
\(331\) 16.3735 0.899969 0.449984 0.893036i \(-0.351430\pi\)
0.449984 + 0.893036i \(0.351430\pi\)
\(332\) −18.0829 −0.992426
\(333\) −18.5267 −1.01526
\(334\) 10.4073 0.569461
\(335\) 6.15914 0.336510
\(336\) 0.0238948 0.00130357
\(337\) −12.7380 −0.693885 −0.346942 0.937886i \(-0.612780\pi\)
−0.346942 + 0.937886i \(0.612780\pi\)
\(338\) −45.6371 −2.48233
\(339\) −2.29739 −0.124777
\(340\) −1.80697 −0.0979969
\(341\) 0.864559 0.0468185
\(342\) 13.0016 0.703048
\(343\) 4.23815 0.228839
\(344\) −3.06883 −0.165460
\(345\) −0.478659 −0.0257701
\(346\) −49.5200 −2.66221
\(347\) −33.1422 −1.77917 −0.889583 0.456774i \(-0.849005\pi\)
−0.889583 + 0.456774i \(0.849005\pi\)
\(348\) 5.10843 0.273840
\(349\) −30.3445 −1.62430 −0.812151 0.583447i \(-0.801704\pi\)
−0.812151 + 0.583447i \(0.801704\pi\)
\(350\) −3.31036 −0.176946
\(351\) −6.28864 −0.335663
\(352\) 5.15463 0.274743
\(353\) −4.96394 −0.264204 −0.132102 0.991236i \(-0.542173\pi\)
−0.132102 + 0.991236i \(0.542173\pi\)
\(354\) −2.84360 −0.151136
\(355\) −8.72940 −0.463308
\(356\) −44.7257 −2.37046
\(357\) 0.0561145 0.00296990
\(358\) 40.8777 2.16045
\(359\) −23.0991 −1.21912 −0.609562 0.792738i \(-0.708655\pi\)
−0.609562 + 0.792738i \(0.708655\pi\)
\(360\) −4.94027 −0.260375
\(361\) −15.3946 −0.810242
\(362\) 7.54184 0.396390
\(363\) −0.184135 −0.00966458
\(364\) 5.80801 0.304423
\(365\) 4.69378 0.245683
\(366\) −0.123599 −0.00646060
\(367\) 33.7485 1.76166 0.880828 0.473436i \(-0.156986\pi\)
0.880828 + 0.473436i \(0.156986\pi\)
\(368\) −2.03951 −0.106317
\(369\) 9.17418 0.477589
\(370\) 7.82607 0.406858
\(371\) −0.188600 −0.00979163
\(372\) −0.530016 −0.0274801
\(373\) 12.0955 0.626282 0.313141 0.949707i \(-0.398619\pi\)
0.313141 + 0.949707i \(0.398619\pi\)
\(374\) −2.30854 −0.119372
\(375\) −0.969940 −0.0500875
\(376\) 22.7351 1.17248
\(377\) 47.7005 2.45670
\(378\) 0.772862 0.0397517
\(379\) 18.0263 0.925950 0.462975 0.886371i \(-0.346782\pi\)
0.462975 + 0.886371i \(0.346782\pi\)
\(380\) −3.43106 −0.176010
\(381\) 1.04571 0.0535733
\(382\) −47.9266 −2.45214
\(383\) −21.2909 −1.08792 −0.543958 0.839112i \(-0.683075\pi\)
−0.543958 + 0.839112i \(0.683075\pi\)
\(384\) −3.52206 −0.179734
\(385\) 0.165399 0.00842950
\(386\) −41.5993 −2.11735
\(387\) −2.96609 −0.150775
\(388\) 0.725878 0.0368509
\(389\) 25.4585 1.29080 0.645398 0.763847i \(-0.276692\pi\)
0.645398 + 0.763847i \(0.276692\pi\)
\(390\) 1.32068 0.0668752
\(391\) −4.78957 −0.242219
\(392\) 21.1968 1.07060
\(393\) 1.88357 0.0950135
\(394\) 30.9505 1.55926
\(395\) −3.48147 −0.175172
\(396\) −9.87513 −0.496244
\(397\) −13.0162 −0.653262 −0.326631 0.945152i \(-0.605913\pi\)
−0.326631 + 0.945152i \(0.605913\pi\)
\(398\) −40.6284 −2.03652
\(399\) 0.106550 0.00533415
\(400\) −2.00368 −0.100184
\(401\) −33.5385 −1.67483 −0.837416 0.546566i \(-0.815935\pi\)
−0.837416 + 0.546566i \(0.815935\pi\)
\(402\) −4.82392 −0.240595
\(403\) −4.94909 −0.246532
\(404\) 8.62629 0.429174
\(405\) −4.71968 −0.234523
\(406\) −5.86230 −0.290941
\(407\) 6.24616 0.309611
\(408\) 0.565079 0.0279756
\(409\) −16.2233 −0.802189 −0.401095 0.916037i \(-0.631370\pi\)
−0.401095 + 0.916037i \(0.631370\pi\)
\(410\) −3.87536 −0.191391
\(411\) −2.75806 −0.136045
\(412\) −20.2658 −0.998422
\(413\) 2.03861 0.100314
\(414\) −32.7958 −1.61183
\(415\) 2.94783 0.144703
\(416\) −29.5072 −1.44671
\(417\) −0.252335 −0.0123569
\(418\) −4.38342 −0.214400
\(419\) 31.4749 1.53765 0.768824 0.639460i \(-0.220842\pi\)
0.768824 + 0.639460i \(0.220842\pi\)
\(420\) −0.101397 −0.00494769
\(421\) 32.9680 1.60676 0.803382 0.595464i \(-0.203032\pi\)
0.803382 + 0.595464i \(0.203032\pi\)
\(422\) −9.92595 −0.483188
\(423\) 21.9740 1.06841
\(424\) −1.89922 −0.0922343
\(425\) −4.70543 −0.228247
\(426\) 6.83697 0.331252
\(427\) 0.0886093 0.00428810
\(428\) −47.3234 −2.28746
\(429\) 1.05406 0.0508907
\(430\) 1.25294 0.0604221
\(431\) −16.6396 −0.801502 −0.400751 0.916187i \(-0.631251\pi\)
−0.400751 + 0.916187i \(0.631251\pi\)
\(432\) 0.467795 0.0225068
\(433\) −25.0432 −1.20350 −0.601750 0.798685i \(-0.705530\pi\)
−0.601750 + 0.798685i \(0.705530\pi\)
\(434\) 0.608234 0.0291961
\(435\) −0.832765 −0.0399280
\(436\) −24.4983 −1.17325
\(437\) −9.09438 −0.435043
\(438\) −3.67622 −0.175657
\(439\) −12.4601 −0.594688 −0.297344 0.954770i \(-0.596101\pi\)
−0.297344 + 0.954770i \(0.596101\pi\)
\(440\) 1.66558 0.0794035
\(441\) 20.4872 0.975581
\(442\) 13.2150 0.628573
\(443\) −5.16365 −0.245332 −0.122666 0.992448i \(-0.539144\pi\)
−0.122666 + 0.992448i \(0.539144\pi\)
\(444\) −3.82920 −0.181726
\(445\) 7.29108 0.345631
\(446\) 51.2758 2.42798
\(447\) −1.77748 −0.0840720
\(448\) 3.88591 0.183592
\(449\) 14.4908 0.683865 0.341933 0.939724i \(-0.388919\pi\)
0.341933 + 0.939724i \(0.388919\pi\)
\(450\) −32.2197 −1.51885
\(451\) −3.09302 −0.145645
\(452\) 41.5390 1.95383
\(453\) 3.54337 0.166482
\(454\) 33.7860 1.58566
\(455\) −0.946810 −0.0443871
\(456\) 1.07297 0.0502462
\(457\) −26.4648 −1.23797 −0.618985 0.785402i \(-0.712456\pi\)
−0.618985 + 0.785402i \(0.712456\pi\)
\(458\) 58.1144 2.71551
\(459\) 1.09857 0.0512767
\(460\) 8.65462 0.403524
\(461\) −4.18075 −0.194717 −0.0973585 0.995249i \(-0.531039\pi\)
−0.0973585 + 0.995249i \(0.531039\pi\)
\(462\) −0.129542 −0.00602686
\(463\) 15.0713 0.700424 0.350212 0.936670i \(-0.386110\pi\)
0.350212 + 0.936670i \(0.386110\pi\)
\(464\) −3.54831 −0.164726
\(465\) 0.0864022 0.00400680
\(466\) −40.4874 −1.87554
\(467\) 3.97247 0.183824 0.0919121 0.995767i \(-0.470702\pi\)
0.0919121 + 0.995767i \(0.470702\pi\)
\(468\) 56.5293 2.61307
\(469\) 3.45832 0.159691
\(470\) −9.28229 −0.428160
\(471\) 3.88257 0.178899
\(472\) 20.5290 0.944925
\(473\) 1.00000 0.0459800
\(474\) 2.72673 0.125243
\(475\) −8.93462 −0.409948
\(476\) −1.01461 −0.0465043
\(477\) −1.83564 −0.0840483
\(478\) 4.54848 0.208043
\(479\) −4.96724 −0.226959 −0.113479 0.993540i \(-0.536200\pi\)
−0.113479 + 0.993540i \(0.536200\pi\)
\(480\) 0.515143 0.0235129
\(481\) −35.7556 −1.63031
\(482\) −54.1066 −2.46449
\(483\) −0.268764 −0.0122292
\(484\) 3.32934 0.151334
\(485\) −0.118331 −0.00537314
\(486\) 11.3048 0.512794
\(487\) −32.3995 −1.46816 −0.734081 0.679062i \(-0.762387\pi\)
−0.734081 + 0.679062i \(0.762387\pi\)
\(488\) 0.892304 0.0403927
\(489\) −2.75158 −0.124431
\(490\) −8.65422 −0.390958
\(491\) 25.5740 1.15414 0.577069 0.816695i \(-0.304196\pi\)
0.577069 + 0.816695i \(0.304196\pi\)
\(492\) 1.89617 0.0854859
\(493\) −8.33283 −0.375292
\(494\) 25.0925 1.12896
\(495\) 1.60982 0.0723562
\(496\) 0.368149 0.0165304
\(497\) −4.90151 −0.219863
\(498\) −2.30878 −0.103459
\(499\) −8.40594 −0.376302 −0.188151 0.982140i \(-0.560249\pi\)
−0.188151 + 0.982140i \(0.560249\pi\)
\(500\) 17.5374 0.784299
\(501\) 0.830112 0.0370867
\(502\) −53.1434 −2.37191
\(503\) 8.07205 0.359915 0.179957 0.983674i \(-0.442404\pi\)
0.179957 + 0.983674i \(0.442404\pi\)
\(504\) −2.77394 −0.123561
\(505\) −1.40624 −0.0625769
\(506\) 11.0569 0.491539
\(507\) −3.64013 −0.161664
\(508\) −18.9074 −0.838882
\(509\) 44.1180 1.95550 0.977748 0.209782i \(-0.0672756\pi\)
0.977748 + 0.209782i \(0.0672756\pi\)
\(510\) −0.230710 −0.0102160
\(511\) 2.63553 0.116589
\(512\) 4.80851 0.212508
\(513\) 2.08595 0.0920968
\(514\) 30.5778 1.34873
\(515\) 3.30368 0.145578
\(516\) −0.613048 −0.0269879
\(517\) −7.40841 −0.325822
\(518\) 4.39429 0.193074
\(519\) −3.94984 −0.173379
\(520\) −9.53447 −0.418114
\(521\) −2.04995 −0.0898101 −0.0449050 0.998991i \(-0.514299\pi\)
−0.0449050 + 0.998991i \(0.514299\pi\)
\(522\) −57.0577 −2.49735
\(523\) 10.7757 0.471189 0.235595 0.971851i \(-0.424296\pi\)
0.235595 + 0.971851i \(0.424296\pi\)
\(524\) −34.0567 −1.48778
\(525\) −0.264043 −0.0115238
\(526\) −20.2308 −0.882105
\(527\) 0.864559 0.0376608
\(528\) −0.0784089 −0.00341231
\(529\) −0.0600275 −0.00260989
\(530\) 0.775413 0.0336818
\(531\) 19.8418 0.861060
\(532\) −1.92652 −0.0835252
\(533\) 17.7057 0.766919
\(534\) −5.71047 −0.247116
\(535\) 7.71456 0.333529
\(536\) 34.8257 1.50424
\(537\) 3.26051 0.140702
\(538\) −73.3728 −3.16333
\(539\) −6.90713 −0.297511
\(540\) −1.98508 −0.0854243
\(541\) 16.0124 0.688426 0.344213 0.938892i \(-0.388146\pi\)
0.344213 + 0.938892i \(0.388146\pi\)
\(542\) 36.9542 1.58732
\(543\) 0.601557 0.0258153
\(544\) 5.15463 0.221003
\(545\) 3.99366 0.171070
\(546\) 0.741554 0.0317356
\(547\) −3.92698 −0.167906 −0.0839528 0.996470i \(-0.526755\pi\)
−0.0839528 + 0.996470i \(0.526755\pi\)
\(548\) 49.8684 2.13027
\(549\) 0.862433 0.0368077
\(550\) 10.8627 0.463185
\(551\) −15.8223 −0.674052
\(552\) −2.70648 −0.115196
\(553\) −1.95482 −0.0831276
\(554\) 34.4145 1.46213
\(555\) 0.624228 0.0264970
\(556\) 4.56245 0.193491
\(557\) 20.3925 0.864060 0.432030 0.901859i \(-0.357797\pi\)
0.432030 + 0.901859i \(0.357797\pi\)
\(558\) 5.91993 0.250611
\(559\) −5.72441 −0.242117
\(560\) 0.0704306 0.00297623
\(561\) −0.184135 −0.00777419
\(562\) −46.1939 −1.94857
\(563\) 14.1735 0.597342 0.298671 0.954356i \(-0.403457\pi\)
0.298671 + 0.954356i \(0.403457\pi\)
\(564\) 4.54171 0.191241
\(565\) −6.77161 −0.284884
\(566\) 57.0822 2.39934
\(567\) −2.65008 −0.111293
\(568\) −49.3587 −2.07104
\(569\) −22.0930 −0.926188 −0.463094 0.886309i \(-0.653261\pi\)
−0.463094 + 0.886309i \(0.653261\pi\)
\(570\) −0.438070 −0.0183487
\(571\) 10.0568 0.420862 0.210431 0.977609i \(-0.432513\pi\)
0.210431 + 0.977609i \(0.432513\pi\)
\(572\) −19.0585 −0.796876
\(573\) −3.82275 −0.159698
\(574\) −2.17600 −0.0908243
\(575\) 22.5370 0.939857
\(576\) 37.8215 1.57590
\(577\) −1.79973 −0.0749237 −0.0374619 0.999298i \(-0.511927\pi\)
−0.0374619 + 0.999298i \(0.511927\pi\)
\(578\) −2.30854 −0.0960224
\(579\) −3.31807 −0.137894
\(580\) 15.0572 0.625216
\(581\) 1.65519 0.0686689
\(582\) 0.0926784 0.00384164
\(583\) 0.618875 0.0256312
\(584\) 26.5400 1.09823
\(585\) −9.21529 −0.381005
\(586\) 29.9124 1.23567
\(587\) 26.7244 1.10303 0.551517 0.834164i \(-0.314049\pi\)
0.551517 + 0.834164i \(0.314049\pi\)
\(588\) 4.23440 0.174624
\(589\) 1.64162 0.0676416
\(590\) −8.38158 −0.345064
\(591\) 2.46869 0.101549
\(592\) 2.65976 0.109315
\(593\) 40.7115 1.67182 0.835911 0.548866i \(-0.184940\pi\)
0.835911 + 0.548866i \(0.184940\pi\)
\(594\) −2.53608 −0.104057
\(595\) 0.165399 0.00678069
\(596\) 32.1386 1.31645
\(597\) −3.24063 −0.132630
\(598\) −63.2942 −2.58829
\(599\) 0.153486 0.00627128 0.00313564 0.999995i \(-0.499002\pi\)
0.00313564 + 0.999995i \(0.499002\pi\)
\(600\) −2.65894 −0.108551
\(601\) 31.9944 1.30508 0.652539 0.757755i \(-0.273704\pi\)
0.652539 + 0.757755i \(0.273704\pi\)
\(602\) 0.703519 0.0286733
\(603\) 33.6598 1.37073
\(604\) −64.0675 −2.60687
\(605\) −0.542742 −0.0220656
\(606\) 1.10139 0.0447407
\(607\) 6.47739 0.262909 0.131455 0.991322i \(-0.458035\pi\)
0.131455 + 0.991322i \(0.458035\pi\)
\(608\) 9.78755 0.396938
\(609\) −0.467593 −0.0189478
\(610\) −0.364309 −0.0147505
\(611\) 42.4088 1.71567
\(612\) −9.87513 −0.399179
\(613\) −30.0752 −1.21473 −0.607363 0.794425i \(-0.707773\pi\)
−0.607363 + 0.794425i \(0.707773\pi\)
\(614\) −10.4655 −0.422352
\(615\) −0.309109 −0.0124645
\(616\) 0.935215 0.0376809
\(617\) 31.0786 1.25118 0.625588 0.780153i \(-0.284859\pi\)
0.625588 + 0.780153i \(0.284859\pi\)
\(618\) −2.58749 −0.104084
\(619\) −38.7555 −1.55771 −0.778857 0.627202i \(-0.784200\pi\)
−0.778857 + 0.627202i \(0.784200\pi\)
\(620\) −1.56223 −0.0627409
\(621\) −5.26166 −0.211143
\(622\) 27.3836 1.09798
\(623\) 4.09390 0.164019
\(624\) 0.448844 0.0179681
\(625\) 20.6682 0.826729
\(626\) −15.5551 −0.621705
\(627\) −0.349633 −0.0139630
\(628\) −70.2005 −2.80131
\(629\) 6.24616 0.249051
\(630\) 1.13254 0.0451215
\(631\) −3.14018 −0.125009 −0.0625043 0.998045i \(-0.519909\pi\)
−0.0625043 + 0.998045i \(0.519909\pi\)
\(632\) −19.6853 −0.783038
\(633\) −0.791721 −0.0314681
\(634\) −5.44083 −0.216083
\(635\) 3.08225 0.122315
\(636\) −0.379400 −0.0150442
\(637\) 39.5392 1.56660
\(638\) 19.2366 0.761586
\(639\) −47.7063 −1.88723
\(640\) −10.3813 −0.410358
\(641\) 0.960447 0.0379354 0.0189677 0.999820i \(-0.493962\pi\)
0.0189677 + 0.999820i \(0.493962\pi\)
\(642\) −6.04214 −0.238464
\(643\) 4.15672 0.163925 0.0819625 0.996635i \(-0.473881\pi\)
0.0819625 + 0.996635i \(0.473881\pi\)
\(644\) 4.85952 0.191492
\(645\) 0.0999378 0.00393505
\(646\) −4.38342 −0.172463
\(647\) −16.9879 −0.667862 −0.333931 0.942598i \(-0.608375\pi\)
−0.333931 + 0.942598i \(0.608375\pi\)
\(648\) −26.6865 −1.04835
\(649\) −6.68953 −0.262587
\(650\) −62.1823 −2.43899
\(651\) 0.0485143 0.00190143
\(652\) 49.7512 1.94841
\(653\) −47.4106 −1.85532 −0.927661 0.373424i \(-0.878184\pi\)
−0.927661 + 0.373424i \(0.878184\pi\)
\(654\) −3.12788 −0.122310
\(655\) 5.55186 0.216929
\(656\) −1.31708 −0.0514232
\(657\) 25.6516 1.00076
\(658\) −5.21195 −0.203183
\(659\) 30.5211 1.18893 0.594467 0.804120i \(-0.297363\pi\)
0.594467 + 0.804120i \(0.297363\pi\)
\(660\) 0.332727 0.0129514
\(661\) 10.1689 0.395525 0.197763 0.980250i \(-0.436632\pi\)
0.197763 + 0.980250i \(0.436632\pi\)
\(662\) −37.7988 −1.46909
\(663\) 1.05406 0.0409364
\(664\) 16.6679 0.646841
\(665\) 0.314057 0.0121786
\(666\) 42.7696 1.65729
\(667\) 39.9107 1.54535
\(668\) −15.0092 −0.580725
\(669\) 4.08989 0.158124
\(670\) −14.2186 −0.549313
\(671\) −0.290764 −0.0112248
\(672\) 0.289250 0.0111580
\(673\) 14.6631 0.565221 0.282611 0.959235i \(-0.408800\pi\)
0.282611 + 0.959235i \(0.408800\pi\)
\(674\) 29.4062 1.13268
\(675\) −5.16923 −0.198964
\(676\) 65.8172 2.53143
\(677\) −50.0425 −1.92329 −0.961645 0.274296i \(-0.911555\pi\)
−0.961645 + 0.274296i \(0.911555\pi\)
\(678\) 5.30361 0.203684
\(679\) −0.0664423 −0.00254982
\(680\) 1.66558 0.0638722
\(681\) 2.69486 0.103267
\(682\) −1.99587 −0.0764257
\(683\) 35.6463 1.36397 0.681983 0.731368i \(-0.261118\pi\)
0.681983 + 0.731368i \(0.261118\pi\)
\(684\) −18.7508 −0.716954
\(685\) −8.12944 −0.310610
\(686\) −9.78392 −0.373552
\(687\) 4.63536 0.176850
\(688\) 0.425823 0.0162343
\(689\) −3.54269 −0.134966
\(690\) 1.10500 0.0420667
\(691\) 10.0335 0.381693 0.190847 0.981620i \(-0.438877\pi\)
0.190847 + 0.981620i \(0.438877\pi\)
\(692\) 71.4170 2.71487
\(693\) 0.903907 0.0343366
\(694\) 76.5099 2.90428
\(695\) −0.743762 −0.0282125
\(696\) −4.70871 −0.178483
\(697\) −3.09302 −0.117156
\(698\) 70.0513 2.65148
\(699\) −3.22938 −0.122146
\(700\) 4.77415 0.180446
\(701\) 21.3942 0.808049 0.404024 0.914748i \(-0.367611\pi\)
0.404024 + 0.914748i \(0.367611\pi\)
\(702\) 14.5176 0.547930
\(703\) 11.8601 0.447314
\(704\) −12.7513 −0.480583
\(705\) −0.740380 −0.0278843
\(706\) 11.4594 0.431281
\(707\) −0.789596 −0.0296958
\(708\) 4.10100 0.154125
\(709\) 38.5450 1.44759 0.723794 0.690016i \(-0.242396\pi\)
0.723794 + 0.690016i \(0.242396\pi\)
\(710\) 20.1521 0.756296
\(711\) −19.0263 −0.713541
\(712\) 41.2260 1.54501
\(713\) −4.14087 −0.155077
\(714\) −0.129542 −0.00484800
\(715\) 3.10688 0.116191
\(716\) −58.9532 −2.20319
\(717\) 0.362799 0.0135490
\(718\) 53.3252 1.99008
\(719\) 32.3961 1.20817 0.604085 0.796920i \(-0.293539\pi\)
0.604085 + 0.796920i \(0.293539\pi\)
\(720\) 0.685500 0.0255471
\(721\) 1.85500 0.0690838
\(722\) 35.5390 1.32262
\(723\) −4.31569 −0.160502
\(724\) −10.8767 −0.404231
\(725\) 39.2096 1.45621
\(726\) 0.425082 0.0157763
\(727\) −44.2866 −1.64250 −0.821250 0.570569i \(-0.806723\pi\)
−0.821250 + 0.570569i \(0.806723\pi\)
\(728\) −5.35355 −0.198416
\(729\) −25.1863 −0.932826
\(730\) −10.8358 −0.401049
\(731\) 1.00000 0.0369863
\(732\) 0.178252 0.00658839
\(733\) −52.9772 −1.95676 −0.978380 0.206817i \(-0.933689\pi\)
−0.978380 + 0.206817i \(0.933689\pi\)
\(734\) −77.9096 −2.87570
\(735\) −0.690284 −0.0254615
\(736\) −24.6885 −0.910029
\(737\) −11.3482 −0.418016
\(738\) −21.1789 −0.779607
\(739\) 0.595312 0.0218989 0.0109494 0.999940i \(-0.496515\pi\)
0.0109494 + 0.999940i \(0.496515\pi\)
\(740\) −11.2866 −0.414905
\(741\) 2.00144 0.0735249
\(742\) 0.435390 0.0159837
\(743\) 12.1942 0.447361 0.223680 0.974663i \(-0.428193\pi\)
0.223680 + 0.974663i \(0.428193\pi\)
\(744\) 0.488544 0.0179109
\(745\) −5.23917 −0.191948
\(746\) −27.9229 −1.02233
\(747\) 16.1100 0.589432
\(748\) 3.32934 0.121733
\(749\) 4.33168 0.158276
\(750\) 2.23914 0.0817619
\(751\) −32.0834 −1.17074 −0.585370 0.810766i \(-0.699051\pi\)
−0.585370 + 0.810766i \(0.699051\pi\)
\(752\) −3.15467 −0.115039
\(753\) −4.23886 −0.154473
\(754\) −110.118 −4.01027
\(755\) 10.4442 0.380102
\(756\) −1.11461 −0.0405380
\(757\) 5.83715 0.212155 0.106077 0.994358i \(-0.466171\pi\)
0.106077 + 0.994358i \(0.466171\pi\)
\(758\) −41.6144 −1.51150
\(759\) 0.881927 0.0320119
\(760\) 3.16259 0.114719
\(761\) −32.2084 −1.16755 −0.583777 0.811914i \(-0.698426\pi\)
−0.583777 + 0.811914i \(0.698426\pi\)
\(762\) −2.41406 −0.0874521
\(763\) 2.24242 0.0811810
\(764\) 69.1191 2.50064
\(765\) 1.60982 0.0582033
\(766\) 49.1509 1.77589
\(767\) 38.2936 1.38270
\(768\) 3.43487 0.123945
\(769\) −5.83271 −0.210333 −0.105166 0.994455i \(-0.533538\pi\)
−0.105166 + 0.994455i \(0.533538\pi\)
\(770\) −0.381829 −0.0137602
\(771\) 2.43896 0.0878371
\(772\) 59.9940 2.15923
\(773\) 44.3557 1.59536 0.797681 0.603079i \(-0.206060\pi\)
0.797681 + 0.603079i \(0.206060\pi\)
\(774\) 6.84734 0.246122
\(775\) −4.06812 −0.146131
\(776\) −0.669080 −0.0240186
\(777\) 0.350500 0.0125741
\(778\) −58.7718 −2.10707
\(779\) −5.87299 −0.210422
\(780\) −1.90466 −0.0681979
\(781\) 16.0839 0.575526
\(782\) 11.0569 0.395394
\(783\) −9.15417 −0.327143
\(784\) −2.94121 −0.105043
\(785\) 11.4439 0.408452
\(786\) −4.34829 −0.155098
\(787\) 11.7245 0.417934 0.208967 0.977923i \(-0.432990\pi\)
0.208967 + 0.977923i \(0.432990\pi\)
\(788\) −44.6364 −1.59011
\(789\) −1.61366 −0.0574479
\(790\) 8.03709 0.285947
\(791\) −3.80222 −0.135191
\(792\) 9.10243 0.323441
\(793\) 1.66445 0.0591063
\(794\) 30.0483 1.06637
\(795\) 0.0618490 0.00219356
\(796\) 58.5937 2.07680
\(797\) −5.06072 −0.179260 −0.0896300 0.995975i \(-0.528568\pi\)
−0.0896300 + 0.995975i \(0.528568\pi\)
\(798\) −0.245974 −0.00870737
\(799\) −7.40841 −0.262091
\(800\) −24.2548 −0.857535
\(801\) 39.8459 1.40789
\(802\) 77.4248 2.73397
\(803\) −8.64826 −0.305191
\(804\) 6.95699 0.245354
\(805\) −0.792189 −0.0279210
\(806\) 11.4252 0.402434
\(807\) −5.85241 −0.206015
\(808\) −7.95131 −0.279726
\(809\) 15.5561 0.546924 0.273462 0.961883i \(-0.411831\pi\)
0.273462 + 0.961883i \(0.411831\pi\)
\(810\) 10.8956 0.382831
\(811\) −19.9142 −0.699281 −0.349641 0.936884i \(-0.613696\pi\)
−0.349641 + 0.936884i \(0.613696\pi\)
\(812\) 8.45453 0.296696
\(813\) 2.94757 0.103376
\(814\) −14.4195 −0.505403
\(815\) −8.11034 −0.284093
\(816\) −0.0784089 −0.00274486
\(817\) 1.89879 0.0664302
\(818\) 37.4520 1.30948
\(819\) −5.17433 −0.180806
\(820\) 5.58900 0.195176
\(821\) 44.9752 1.56965 0.784823 0.619721i \(-0.212754\pi\)
0.784823 + 0.619721i \(0.212754\pi\)
\(822\) 6.36708 0.222077
\(823\) 49.0247 1.70889 0.854447 0.519539i \(-0.173896\pi\)
0.854447 + 0.519539i \(0.173896\pi\)
\(824\) 18.6800 0.650749
\(825\) 0.866435 0.0301654
\(826\) −4.70621 −0.163750
\(827\) −27.8507 −0.968463 −0.484232 0.874940i \(-0.660901\pi\)
−0.484232 + 0.874940i \(0.660901\pi\)
\(828\) 47.2976 1.64371
\(829\) 17.7690 0.617142 0.308571 0.951201i \(-0.400149\pi\)
0.308571 + 0.951201i \(0.400149\pi\)
\(830\) −6.80518 −0.236211
\(831\) 2.74499 0.0952226
\(832\) 72.9936 2.53060
\(833\) −6.90713 −0.239318
\(834\) 0.582523 0.0201711
\(835\) 2.44677 0.0846741
\(836\) 6.32171 0.218641
\(837\) 0.949776 0.0328291
\(838\) −72.6609 −2.51003
\(839\) 1.05401 0.0363884 0.0181942 0.999834i \(-0.494208\pi\)
0.0181942 + 0.999834i \(0.494208\pi\)
\(840\) 0.0934634 0.00322479
\(841\) 40.4361 1.39435
\(842\) −76.1079 −2.62285
\(843\) −3.68455 −0.126903
\(844\) 14.3151 0.492745
\(845\) −10.7294 −0.369102
\(846\) −50.7279 −1.74406
\(847\) −0.304747 −0.0104712
\(848\) 0.263531 0.00904969
\(849\) 4.55303 0.156260
\(850\) 10.8627 0.372586
\(851\) −29.9164 −1.02552
\(852\) −9.86019 −0.337805
\(853\) 17.9631 0.615044 0.307522 0.951541i \(-0.400500\pi\)
0.307522 + 0.951541i \(0.400500\pi\)
\(854\) −0.204558 −0.00699982
\(855\) 3.05672 0.104537
\(856\) 43.6204 1.49092
\(857\) 43.2990 1.47906 0.739532 0.673121i \(-0.235047\pi\)
0.739532 + 0.673121i \(0.235047\pi\)
\(858\) −2.43334 −0.0830730
\(859\) −0.793772 −0.0270832 −0.0135416 0.999908i \(-0.504311\pi\)
−0.0135416 + 0.999908i \(0.504311\pi\)
\(860\) −1.80697 −0.0616173
\(861\) −0.173563 −0.00591502
\(862\) 38.4131 1.30836
\(863\) 36.2640 1.23444 0.617221 0.786790i \(-0.288258\pi\)
0.617221 + 0.786790i \(0.288258\pi\)
\(864\) 5.66271 0.192649
\(865\) −11.6423 −0.395848
\(866\) 57.8132 1.96457
\(867\) −0.184135 −0.00625355
\(868\) −0.877186 −0.0297736
\(869\) 6.41459 0.217600
\(870\) 1.92247 0.0651778
\(871\) 64.9617 2.20114
\(872\) 22.5814 0.764701
\(873\) −0.646681 −0.0218868
\(874\) 20.9947 0.710156
\(875\) −1.60527 −0.0542679
\(876\) 5.30180 0.179131
\(877\) −25.4954 −0.860917 −0.430459 0.902610i \(-0.641648\pi\)
−0.430459 + 0.902610i \(0.641648\pi\)
\(878\) 28.7646 0.970757
\(879\) 2.38589 0.0804740
\(880\) −0.231112 −0.00779078
\(881\) 33.5368 1.12988 0.564941 0.825131i \(-0.308899\pi\)
0.564941 + 0.825131i \(0.308899\pi\)
\(882\) −47.2954 −1.59252
\(883\) −2.87100 −0.0966168 −0.0483084 0.998832i \(-0.515383\pi\)
−0.0483084 + 0.998832i \(0.515383\pi\)
\(884\) −19.0585 −0.641007
\(885\) −0.668537 −0.0224726
\(886\) 11.9205 0.400476
\(887\) 16.4315 0.551716 0.275858 0.961198i \(-0.411038\pi\)
0.275858 + 0.961198i \(0.411038\pi\)
\(888\) 3.52957 0.118445
\(889\) 1.73067 0.0580447
\(890\) −16.8317 −0.564201
\(891\) 8.69600 0.291327
\(892\) −73.9492 −2.47600
\(893\) −14.0670 −0.470734
\(894\) 4.10338 0.137238
\(895\) 9.61044 0.321241
\(896\) −5.82906 −0.194735
\(897\) −5.04851 −0.168565
\(898\) −33.4526 −1.11633
\(899\) −7.20423 −0.240274
\(900\) 46.4668 1.54889
\(901\) 0.618875 0.0206177
\(902\) 7.14034 0.237747
\(903\) 0.0561145 0.00186737
\(904\) −38.2887 −1.27346
\(905\) 1.77310 0.0589400
\(906\) −8.17999 −0.271762
\(907\) 11.3865 0.378084 0.189042 0.981969i \(-0.439462\pi\)
0.189042 + 0.981969i \(0.439462\pi\)
\(908\) −48.7257 −1.61702
\(909\) −7.68513 −0.254900
\(910\) 2.18575 0.0724568
\(911\) 43.9993 1.45776 0.728881 0.684641i \(-0.240041\pi\)
0.728881 + 0.684641i \(0.240041\pi\)
\(912\) −0.148882 −0.00492997
\(913\) −5.43137 −0.179752
\(914\) 61.0949 2.02084
\(915\) −0.0290583 −0.000960638 0
\(916\) −83.8118 −2.76922
\(917\) 3.11734 0.102944
\(918\) −2.53608 −0.0837032
\(919\) −39.4141 −1.30015 −0.650076 0.759869i \(-0.725263\pi\)
−0.650076 + 0.759869i \(0.725263\pi\)
\(920\) −7.97742 −0.263008
\(921\) −0.834753 −0.0275061
\(922\) 9.65142 0.317852
\(923\) −92.0707 −3.03054
\(924\) 0.186824 0.00614607
\(925\) −29.3909 −0.966366
\(926\) −34.7927 −1.14336
\(927\) 18.0547 0.592993
\(928\) −42.9527 −1.40999
\(929\) −18.0027 −0.590651 −0.295325 0.955397i \(-0.595428\pi\)
−0.295325 + 0.955397i \(0.595428\pi\)
\(930\) −0.199463 −0.00654063
\(931\) −13.1152 −0.429833
\(932\) 58.3903 1.91264
\(933\) 2.18419 0.0715072
\(934\) −9.17060 −0.300071
\(935\) −0.542742 −0.0177496
\(936\) −52.1060 −1.70314
\(937\) −30.0806 −0.982689 −0.491345 0.870965i \(-0.663494\pi\)
−0.491345 + 0.870965i \(0.663494\pi\)
\(938\) −7.98367 −0.260676
\(939\) −1.24071 −0.0404892
\(940\) 13.3868 0.436629
\(941\) 37.5416 1.22382 0.611910 0.790927i \(-0.290401\pi\)
0.611910 + 0.790927i \(0.290401\pi\)
\(942\) −8.96304 −0.292032
\(943\) 14.8142 0.482417
\(944\) −2.84855 −0.0927125
\(945\) 0.181702 0.00591076
\(946\) −2.30854 −0.0750570
\(947\) 48.4971 1.57595 0.787973 0.615710i \(-0.211131\pi\)
0.787973 + 0.615710i \(0.211131\pi\)
\(948\) −3.93245 −0.127720
\(949\) 49.5062 1.60704
\(950\) 20.6259 0.669192
\(951\) −0.433975 −0.0140726
\(952\) 0.935215 0.0303105
\(953\) 32.8759 1.06496 0.532478 0.846444i \(-0.321261\pi\)
0.532478 + 0.846444i \(0.321261\pi\)
\(954\) 4.23765 0.137199
\(955\) −11.2677 −0.364613
\(956\) −6.55975 −0.212158
\(957\) 1.53437 0.0495990
\(958\) 11.4670 0.370483
\(959\) −4.56463 −0.147400
\(960\) −1.27434 −0.0411290
\(961\) −30.2525 −0.975888
\(962\) 82.5430 2.66129
\(963\) 42.1602 1.35859
\(964\) 78.0318 2.51323
\(965\) −9.78009 −0.314832
\(966\) 0.620452 0.0199627
\(967\) −19.9999 −0.643155 −0.321577 0.946883i \(-0.604213\pi\)
−0.321577 + 0.946883i \(0.604213\pi\)
\(968\) −3.06883 −0.0986359
\(969\) −0.349633 −0.0112318
\(970\) 0.273172 0.00877101
\(971\) −41.0066 −1.31597 −0.657983 0.753033i \(-0.728590\pi\)
−0.657983 + 0.753033i \(0.728590\pi\)
\(972\) −16.3036 −0.522937
\(973\) −0.417618 −0.0133882
\(974\) 74.7954 2.39660
\(975\) −4.95982 −0.158842
\(976\) −0.123814 −0.00396318
\(977\) 11.2811 0.360914 0.180457 0.983583i \(-0.442242\pi\)
0.180457 + 0.983583i \(0.442242\pi\)
\(978\) 6.35212 0.203118
\(979\) −13.4338 −0.429346
\(980\) 12.4810 0.398691
\(981\) 21.8254 0.696832
\(982\) −59.0385 −1.88399
\(983\) −30.9156 −0.986054 −0.493027 0.870014i \(-0.664110\pi\)
−0.493027 + 0.870014i \(0.664110\pi\)
\(984\) −1.74780 −0.0557178
\(985\) 7.27653 0.231850
\(986\) 19.2366 0.612620
\(987\) −0.415719 −0.0132325
\(988\) −36.1880 −1.15130
\(989\) −4.78957 −0.152299
\(990\) −3.71634 −0.118113
\(991\) −3.28294 −0.104286 −0.0521430 0.998640i \(-0.516605\pi\)
−0.0521430 + 0.998640i \(0.516605\pi\)
\(992\) 4.45648 0.141493
\(993\) −3.01493 −0.0956760
\(994\) 11.3153 0.358900
\(995\) −9.55183 −0.302813
\(996\) 3.32969 0.105505
\(997\) 6.74732 0.213690 0.106845 0.994276i \(-0.465925\pi\)
0.106845 + 0.994276i \(0.465925\pi\)
\(998\) 19.4054 0.614268
\(999\) 6.86183 0.217099
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 \(a_p\))