Properties

Label 8041.2.a.j.1.14
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 82
CM No

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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 1.14
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.00119 q^{2}\) \(-0.510214 q^{3}\) \(+2.00475 q^{4}\) \(+2.33538 q^{5}\) \(+1.02103 q^{6}\) \(-3.93653 q^{7}\) \(-0.00949577 q^{8}\) \(-2.73968 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.00119 q^{2}\) \(-0.510214 q^{3}\) \(+2.00475 q^{4}\) \(+2.33538 q^{5}\) \(+1.02103 q^{6}\) \(-3.93653 q^{7}\) \(-0.00949577 q^{8}\) \(-2.73968 q^{9}\) \(-4.67353 q^{10}\) \(+1.00000 q^{11}\) \(-1.02285 q^{12}\) \(+5.23418 q^{13}\) \(+7.87773 q^{14}\) \(-1.19154 q^{15}\) \(-3.99049 q^{16}\) \(+1.00000 q^{17}\) \(+5.48261 q^{18}\) \(-2.97160 q^{19}\) \(+4.68184 q^{20}\) \(+2.00847 q^{21}\) \(-2.00119 q^{22}\) \(+0.0593703 q^{23}\) \(+0.00484488 q^{24}\) \(+0.453998 q^{25}\) \(-10.4746 q^{26}\) \(+2.92847 q^{27}\) \(-7.89174 q^{28}\) \(-9.76766 q^{29}\) \(+2.38450 q^{30}\) \(-0.151436 q^{31}\) \(+8.00470 q^{32}\) \(-0.510214 q^{33}\) \(-2.00119 q^{34}\) \(-9.19330 q^{35}\) \(-5.49236 q^{36}\) \(-1.80139 q^{37}\) \(+5.94671 q^{38}\) \(-2.67055 q^{39}\) \(-0.0221762 q^{40}\) \(+7.48468 q^{41}\) \(-4.01933 q^{42}\) \(+1.00000 q^{43}\) \(+2.00475 q^{44}\) \(-6.39820 q^{45}\) \(-0.118811 q^{46}\) \(-1.63126 q^{47}\) \(+2.03600 q^{48}\) \(+8.49628 q^{49}\) \(-0.908534 q^{50}\) \(-0.510214 q^{51}\) \(+10.4932 q^{52}\) \(+2.27586 q^{53}\) \(-5.86041 q^{54}\) \(+2.33538 q^{55}\) \(+0.0373804 q^{56}\) \(+1.51615 q^{57}\) \(+19.5469 q^{58}\) \(+4.09795 q^{59}\) \(-2.38874 q^{60}\) \(-7.28320 q^{61}\) \(+0.303052 q^{62}\) \(+10.7848 q^{63}\) \(-8.03792 q^{64}\) \(+12.2238 q^{65}\) \(+1.02103 q^{66}\) \(+12.8220 q^{67}\) \(+2.00475 q^{68}\) \(-0.0302916 q^{69}\) \(+18.3975 q^{70}\) \(-9.00003 q^{71}\) \(+0.0260154 q^{72}\) \(-15.6354 q^{73}\) \(+3.60492 q^{74}\) \(-0.231636 q^{75}\) \(-5.95729 q^{76}\) \(-3.93653 q^{77}\) \(+5.34427 q^{78}\) \(+13.8794 q^{79}\) \(-9.31930 q^{80}\) \(+6.72490 q^{81}\) \(-14.9782 q^{82}\) \(-5.94659 q^{83}\) \(+4.02648 q^{84}\) \(+2.33538 q^{85}\) \(-2.00119 q^{86}\) \(+4.98360 q^{87}\) \(-0.00949577 q^{88}\) \(-9.06518 q^{89}\) \(+12.8040 q^{90}\) \(-20.6045 q^{91}\) \(+0.119022 q^{92}\) \(+0.0772650 q^{93}\) \(+3.26444 q^{94}\) \(-6.93980 q^{95}\) \(-4.08411 q^{96}\) \(+11.3857 q^{97}\) \(-17.0026 q^{98}\) \(-2.73968 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 82q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 117q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 31q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 29q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut +\mathstrut 82q^{43} \) \(\mathstrut +\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut -\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 136q^{49} \) \(\mathstrut +\mathstrut 59q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut +\mathstrut 83q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 23q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 96q^{59} \) \(\mathstrut +\mathstrut 184q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 148q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 78q^{67} \) \(\mathstrut +\mathstrut 98q^{68} \) \(\mathstrut +\mathstrut 61q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut +\mathstrut 50q^{72} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 150q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 11q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 111q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00119 −1.41505 −0.707526 0.706687i \(-0.750189\pi\)
−0.707526 + 0.706687i \(0.750189\pi\)
\(3\) −0.510214 −0.294572 −0.147286 0.989094i \(-0.547054\pi\)
−0.147286 + 0.989094i \(0.547054\pi\)
\(4\) 2.00475 1.00237
\(5\) 2.33538 1.04441 0.522207 0.852819i \(-0.325109\pi\)
0.522207 + 0.852819i \(0.325109\pi\)
\(6\) 1.02103 0.416835
\(7\) −3.93653 −1.48787 −0.743935 0.668252i \(-0.767043\pi\)
−0.743935 + 0.668252i \(0.767043\pi\)
\(8\) −0.00949577 −0.00335726
\(9\) −2.73968 −0.913227
\(10\) −4.67353 −1.47790
\(11\) 1.00000 0.301511
\(12\) −1.02285 −0.295271
\(13\) 5.23418 1.45170 0.725850 0.687853i \(-0.241447\pi\)
0.725850 + 0.687853i \(0.241447\pi\)
\(14\) 7.87773 2.10541
\(15\) −1.19154 −0.307655
\(16\) −3.99049 −0.997622
\(17\) 1.00000 0.242536
\(18\) 5.48261 1.29226
\(19\) −2.97160 −0.681731 −0.340865 0.940112i \(-0.610720\pi\)
−0.340865 + 0.940112i \(0.610720\pi\)
\(20\) 4.68184 1.04689
\(21\) 2.00847 0.438285
\(22\) −2.00119 −0.426654
\(23\) 0.0593703 0.0123796 0.00618978 0.999981i \(-0.498030\pi\)
0.00618978 + 0.999981i \(0.498030\pi\)
\(24\) 0.00484488 0.000988957 0
\(25\) 0.453998 0.0907996
\(26\) −10.4746 −2.05423
\(27\) 2.92847 0.563584
\(28\) −7.89174 −1.49140
\(29\) −9.76766 −1.81381 −0.906904 0.421337i \(-0.861561\pi\)
−0.906904 + 0.421337i \(0.861561\pi\)
\(30\) 2.38450 0.435348
\(31\) −0.151436 −0.0271988 −0.0135994 0.999908i \(-0.504329\pi\)
−0.0135994 + 0.999908i \(0.504329\pi\)
\(32\) 8.00470 1.41504
\(33\) −0.510214 −0.0888169
\(34\) −2.00119 −0.343201
\(35\) −9.19330 −1.55395
\(36\) −5.49236 −0.915394
\(37\) −1.80139 −0.296147 −0.148073 0.988976i \(-0.547307\pi\)
−0.148073 + 0.988976i \(0.547307\pi\)
\(38\) 5.94671 0.964684
\(39\) −2.67055 −0.427631
\(40\) −0.0221762 −0.00350637
\(41\) 7.48468 1.16891 0.584456 0.811426i \(-0.301308\pi\)
0.584456 + 0.811426i \(0.301308\pi\)
\(42\) −4.01933 −0.620196
\(43\) 1.00000 0.152499
\(44\) 2.00475 0.302227
\(45\) −6.39820 −0.953787
\(46\) −0.118811 −0.0175177
\(47\) −1.63126 −0.237943 −0.118972 0.992898i \(-0.537960\pi\)
−0.118972 + 0.992898i \(0.537960\pi\)
\(48\) 2.03600 0.293872
\(49\) 8.49628 1.21375
\(50\) −0.908534 −0.128486
\(51\) −0.510214 −0.0714443
\(52\) 10.4932 1.45514
\(53\) 2.27586 0.312613 0.156307 0.987709i \(-0.450041\pi\)
0.156307 + 0.987709i \(0.450041\pi\)
\(54\) −5.86041 −0.797500
\(55\) 2.33538 0.314903
\(56\) 0.0373804 0.00499517
\(57\) 1.51615 0.200819
\(58\) 19.5469 2.56663
\(59\) 4.09795 0.533507 0.266754 0.963765i \(-0.414049\pi\)
0.266754 + 0.963765i \(0.414049\pi\)
\(60\) −2.38874 −0.308385
\(61\) −7.28320 −0.932518 −0.466259 0.884648i \(-0.654399\pi\)
−0.466259 + 0.884648i \(0.654399\pi\)
\(62\) 0.303052 0.0384877
\(63\) 10.7848 1.35876
\(64\) −8.03792 −1.00474
\(65\) 12.2238 1.51618
\(66\) 1.02103 0.125681
\(67\) 12.8220 1.56645 0.783227 0.621736i \(-0.213572\pi\)
0.783227 + 0.621736i \(0.213572\pi\)
\(68\) 2.00475 0.243111
\(69\) −0.0302916 −0.00364668
\(70\) 18.3975 2.19892
\(71\) −9.00003 −1.06811 −0.534054 0.845451i \(-0.679332\pi\)
−0.534054 + 0.845451i \(0.679332\pi\)
\(72\) 0.0260154 0.00306594
\(73\) −15.6354 −1.82999 −0.914995 0.403466i \(-0.867805\pi\)
−0.914995 + 0.403466i \(0.867805\pi\)
\(74\) 3.60492 0.419063
\(75\) −0.231636 −0.0267470
\(76\) −5.95729 −0.683348
\(77\) −3.93653 −0.448609
\(78\) 5.34427 0.605120
\(79\) 13.8794 1.56156 0.780778 0.624808i \(-0.214823\pi\)
0.780778 + 0.624808i \(0.214823\pi\)
\(80\) −9.31930 −1.04193
\(81\) 6.72490 0.747211
\(82\) −14.9782 −1.65407
\(83\) −5.94659 −0.652723 −0.326361 0.945245i \(-0.605823\pi\)
−0.326361 + 0.945245i \(0.605823\pi\)
\(84\) 4.02648 0.439325
\(85\) 2.33538 0.253307
\(86\) −2.00119 −0.215793
\(87\) 4.98360 0.534298
\(88\) −0.00949577 −0.00101225
\(89\) −9.06518 −0.960907 −0.480453 0.877020i \(-0.659528\pi\)
−0.480453 + 0.877020i \(0.659528\pi\)
\(90\) 12.8040 1.34966
\(91\) −20.6045 −2.15994
\(92\) 0.119022 0.0124089
\(93\) 0.0772650 0.00801201
\(94\) 3.26444 0.336702
\(95\) −6.93980 −0.712009
\(96\) −4.08411 −0.416833
\(97\) 11.3857 1.15605 0.578023 0.816020i \(-0.303824\pi\)
0.578023 + 0.816020i \(0.303824\pi\)
\(98\) −17.0026 −1.71753
\(99\) −2.73968 −0.275348
\(100\) 0.910150 0.0910150
\(101\) −4.24687 −0.422579 −0.211290 0.977423i \(-0.567766\pi\)
−0.211290 + 0.977423i \(0.567766\pi\)
\(102\) 1.02103 0.101097
\(103\) 3.21297 0.316583 0.158292 0.987392i \(-0.449401\pi\)
0.158292 + 0.987392i \(0.449401\pi\)
\(104\) −0.0497026 −0.00487374
\(105\) 4.69055 0.457751
\(106\) −4.55442 −0.442364
\(107\) 15.6026 1.50836 0.754181 0.656666i \(-0.228034\pi\)
0.754181 + 0.656666i \(0.228034\pi\)
\(108\) 5.87083 0.564921
\(109\) −7.44771 −0.713361 −0.356680 0.934226i \(-0.616091\pi\)
−0.356680 + 0.934226i \(0.616091\pi\)
\(110\) −4.67353 −0.445603
\(111\) 0.919096 0.0872367
\(112\) 15.7087 1.48433
\(113\) −13.7104 −1.28977 −0.644883 0.764282i \(-0.723094\pi\)
−0.644883 + 0.764282i \(0.723094\pi\)
\(114\) −3.03410 −0.284169
\(115\) 0.138652 0.0129294
\(116\) −19.5817 −1.81811
\(117\) −14.3400 −1.32573
\(118\) −8.20075 −0.754940
\(119\) −3.93653 −0.360861
\(120\) 0.0113146 0.00103288
\(121\) 1.00000 0.0909091
\(122\) 14.5750 1.31956
\(123\) −3.81879 −0.344329
\(124\) −0.303591 −0.0272633
\(125\) −10.6166 −0.949581
\(126\) −21.5825 −1.92272
\(127\) 9.22368 0.818469 0.409235 0.912429i \(-0.365796\pi\)
0.409235 + 0.912429i \(0.365796\pi\)
\(128\) 0.0759660 0.00671451
\(129\) −0.510214 −0.0449219
\(130\) −24.4621 −2.14547
\(131\) 6.83688 0.597341 0.298671 0.954356i \(-0.403457\pi\)
0.298671 + 0.954356i \(0.403457\pi\)
\(132\) −1.02285 −0.0890276
\(133\) 11.6978 1.01433
\(134\) −25.6592 −2.21661
\(135\) 6.83908 0.588615
\(136\) −0.00949577 −0.000814256 0
\(137\) 16.5748 1.41608 0.708039 0.706173i \(-0.249580\pi\)
0.708039 + 0.706173i \(0.249580\pi\)
\(138\) 0.0606191 0.00516024
\(139\) −14.8185 −1.25689 −0.628446 0.777853i \(-0.716309\pi\)
−0.628446 + 0.777853i \(0.716309\pi\)
\(140\) −18.4302 −1.55764
\(141\) 0.832290 0.0700914
\(142\) 18.0107 1.51143
\(143\) 5.23418 0.437704
\(144\) 10.9327 0.911055
\(145\) −22.8112 −1.89437
\(146\) 31.2894 2.58953
\(147\) −4.33493 −0.357539
\(148\) −3.61133 −0.296850
\(149\) −2.86405 −0.234632 −0.117316 0.993095i \(-0.537429\pi\)
−0.117316 + 0.993095i \(0.537429\pi\)
\(150\) 0.463547 0.0378485
\(151\) −0.818528 −0.0666109 −0.0333054 0.999445i \(-0.510603\pi\)
−0.0333054 + 0.999445i \(0.510603\pi\)
\(152\) 0.0282176 0.00228875
\(153\) −2.73968 −0.221490
\(154\) 7.87773 0.634806
\(155\) −0.353661 −0.0284068
\(156\) −5.35378 −0.428645
\(157\) 4.17895 0.333517 0.166758 0.985998i \(-0.446670\pi\)
0.166758 + 0.985998i \(0.446670\pi\)
\(158\) −27.7753 −2.20968
\(159\) −1.16118 −0.0920872
\(160\) 18.6940 1.47789
\(161\) −0.233713 −0.0184192
\(162\) −13.4578 −1.05734
\(163\) −1.56120 −0.122283 −0.0611413 0.998129i \(-0.519474\pi\)
−0.0611413 + 0.998129i \(0.519474\pi\)
\(164\) 15.0049 1.17168
\(165\) −1.19154 −0.0927616
\(166\) 11.9002 0.923637
\(167\) 8.02859 0.621271 0.310636 0.950529i \(-0.399458\pi\)
0.310636 + 0.950529i \(0.399458\pi\)
\(168\) −0.0190720 −0.00147144
\(169\) 14.3966 1.10743
\(170\) −4.67353 −0.358443
\(171\) 8.14122 0.622575
\(172\) 2.00475 0.152860
\(173\) −23.0098 −1.74941 −0.874703 0.484659i \(-0.838944\pi\)
−0.874703 + 0.484659i \(0.838944\pi\)
\(174\) −9.97311 −0.756059
\(175\) −1.78718 −0.135098
\(176\) −3.99049 −0.300794
\(177\) −2.09083 −0.157156
\(178\) 18.1411 1.35973
\(179\) −14.1309 −1.05619 −0.528096 0.849185i \(-0.677094\pi\)
−0.528096 + 0.849185i \(0.677094\pi\)
\(180\) −12.8268 −0.956050
\(181\) 14.2374 1.05826 0.529130 0.848541i \(-0.322518\pi\)
0.529130 + 0.848541i \(0.322518\pi\)
\(182\) 41.2335 3.05643
\(183\) 3.71599 0.274694
\(184\) −0.000563767 0 −4.15614e−5 0
\(185\) −4.20693 −0.309300
\(186\) −0.154622 −0.0113374
\(187\) 1.00000 0.0731272
\(188\) −3.27025 −0.238508
\(189\) −11.5280 −0.838539
\(190\) 13.8878 1.00753
\(191\) 6.93198 0.501580 0.250790 0.968041i \(-0.419310\pi\)
0.250790 + 0.968041i \(0.419310\pi\)
\(192\) 4.10106 0.295968
\(193\) −0.666990 −0.0480110 −0.0240055 0.999712i \(-0.507642\pi\)
−0.0240055 + 0.999712i \(0.507642\pi\)
\(194\) −22.7850 −1.63587
\(195\) −6.23676 −0.446623
\(196\) 17.0329 1.21663
\(197\) 7.56580 0.539041 0.269520 0.962995i \(-0.413135\pi\)
0.269520 + 0.962995i \(0.413135\pi\)
\(198\) 5.48261 0.389632
\(199\) 18.7514 1.32925 0.664627 0.747176i \(-0.268591\pi\)
0.664627 + 0.747176i \(0.268591\pi\)
\(200\) −0.00431106 −0.000304838 0
\(201\) −6.54195 −0.461434
\(202\) 8.49877 0.597972
\(203\) 38.4507 2.69871
\(204\) −1.02285 −0.0716138
\(205\) 17.4796 1.22083
\(206\) −6.42975 −0.447982
\(207\) −0.162656 −0.0113054
\(208\) −20.8869 −1.44825
\(209\) −2.97160 −0.205550
\(210\) −9.38666 −0.647741
\(211\) 9.51422 0.654986 0.327493 0.944854i \(-0.393796\pi\)
0.327493 + 0.944854i \(0.393796\pi\)
\(212\) 4.56252 0.313355
\(213\) 4.59194 0.314635
\(214\) −31.2237 −2.13441
\(215\) 2.33538 0.159272
\(216\) −0.0278081 −0.00189210
\(217\) 0.596134 0.0404682
\(218\) 14.9042 1.00944
\(219\) 7.97742 0.539064
\(220\) 4.68184 0.315650
\(221\) 5.23418 0.352089
\(222\) −1.83928 −0.123444
\(223\) 9.20959 0.616720 0.308360 0.951270i \(-0.400220\pi\)
0.308360 + 0.951270i \(0.400220\pi\)
\(224\) −31.5108 −2.10540
\(225\) −1.24381 −0.0829206
\(226\) 27.4370 1.82508
\(227\) 0.569489 0.0377983 0.0188992 0.999821i \(-0.493984\pi\)
0.0188992 + 0.999821i \(0.493984\pi\)
\(228\) 3.03949 0.201295
\(229\) 6.29506 0.415989 0.207995 0.978130i \(-0.433306\pi\)
0.207995 + 0.978130i \(0.433306\pi\)
\(230\) −0.277469 −0.0182957
\(231\) 2.00847 0.132148
\(232\) 0.0927514 0.00608943
\(233\) −15.0067 −0.983119 −0.491559 0.870844i \(-0.663573\pi\)
−0.491559 + 0.870844i \(0.663573\pi\)
\(234\) 28.6970 1.87598
\(235\) −3.80960 −0.248511
\(236\) 8.21534 0.534773
\(237\) −7.08148 −0.459991
\(238\) 7.87773 0.510638
\(239\) 23.2725 1.50537 0.752687 0.658379i \(-0.228757\pi\)
0.752687 + 0.658379i \(0.228757\pi\)
\(240\) 4.75484 0.306924
\(241\) 5.92917 0.381931 0.190966 0.981597i \(-0.438838\pi\)
0.190966 + 0.981597i \(0.438838\pi\)
\(242\) −2.00119 −0.128641
\(243\) −12.2165 −0.783691
\(244\) −14.6010 −0.934731
\(245\) 19.8421 1.26766
\(246\) 7.64211 0.487243
\(247\) −15.5539 −0.989669
\(248\) 0.00143800 9.13134e−5 0
\(249\) 3.03403 0.192274
\(250\) 21.2459 1.34371
\(251\) 5.75160 0.363038 0.181519 0.983387i \(-0.441899\pi\)
0.181519 + 0.983387i \(0.441899\pi\)
\(252\) 21.6209 1.36199
\(253\) 0.0593703 0.00373258
\(254\) −18.4583 −1.15818
\(255\) −1.19154 −0.0746174
\(256\) 15.9238 0.995238
\(257\) 3.40258 0.212247 0.106123 0.994353i \(-0.466156\pi\)
0.106123 + 0.994353i \(0.466156\pi\)
\(258\) 1.02103 0.0635668
\(259\) 7.09124 0.440628
\(260\) 24.5056 1.51977
\(261\) 26.7603 1.65642
\(262\) −13.6819 −0.845269
\(263\) 12.9937 0.801227 0.400613 0.916247i \(-0.368797\pi\)
0.400613 + 0.916247i \(0.368797\pi\)
\(264\) 0.00484488 0.000298182 0
\(265\) 5.31499 0.326497
\(266\) −23.4094 −1.43532
\(267\) 4.62518 0.283057
\(268\) 25.7048 1.57017
\(269\) −28.8142 −1.75683 −0.878416 0.477897i \(-0.841399\pi\)
−0.878416 + 0.477897i \(0.841399\pi\)
\(270\) −13.6863 −0.832920
\(271\) 21.0282 1.27737 0.638685 0.769468i \(-0.279479\pi\)
0.638685 + 0.769468i \(0.279479\pi\)
\(272\) −3.99049 −0.241959
\(273\) 10.5127 0.636259
\(274\) −33.1692 −2.00383
\(275\) 0.453998 0.0273771
\(276\) −0.0607269 −0.00365533
\(277\) −15.5587 −0.934830 −0.467415 0.884038i \(-0.654815\pi\)
−0.467415 + 0.884038i \(0.654815\pi\)
\(278\) 29.6546 1.77857
\(279\) 0.414887 0.0248387
\(280\) 0.0872974 0.00521702
\(281\) −4.25632 −0.253911 −0.126955 0.991908i \(-0.540520\pi\)
−0.126955 + 0.991908i \(0.540520\pi\)
\(282\) −1.66557 −0.0991830
\(283\) −27.4760 −1.63328 −0.816639 0.577148i \(-0.804165\pi\)
−0.816639 + 0.577148i \(0.804165\pi\)
\(284\) −18.0428 −1.07064
\(285\) 3.54079 0.209738
\(286\) −10.4746 −0.619374
\(287\) −29.4637 −1.73919
\(288\) −21.9303 −1.29226
\(289\) 1.00000 0.0588235
\(290\) 45.6494 2.68063
\(291\) −5.80916 −0.340539
\(292\) −31.3451 −1.83433
\(293\) −22.3199 −1.30394 −0.651972 0.758243i \(-0.726058\pi\)
−0.651972 + 0.758243i \(0.726058\pi\)
\(294\) 8.67499 0.505936
\(295\) 9.57026 0.557202
\(296\) 0.0171056 0.000994243 0
\(297\) 2.92847 0.169927
\(298\) 5.73150 0.332017
\(299\) 0.310755 0.0179714
\(300\) −0.464371 −0.0268105
\(301\) −3.93653 −0.226898
\(302\) 1.63803 0.0942579
\(303\) 2.16681 0.124480
\(304\) 11.8581 0.680109
\(305\) −17.0090 −0.973935
\(306\) 5.48261 0.313420
\(307\) −20.3931 −1.16390 −0.581949 0.813225i \(-0.697710\pi\)
−0.581949 + 0.813225i \(0.697710\pi\)
\(308\) −7.89174 −0.449674
\(309\) −1.63930 −0.0932566
\(310\) 0.707742 0.0401971
\(311\) 11.5468 0.654757 0.327379 0.944893i \(-0.393835\pi\)
0.327379 + 0.944893i \(0.393835\pi\)
\(312\) 0.0253590 0.00143567
\(313\) 4.96935 0.280884 0.140442 0.990089i \(-0.455148\pi\)
0.140442 + 0.990089i \(0.455148\pi\)
\(314\) −8.36286 −0.471943
\(315\) 25.1867 1.41911
\(316\) 27.8247 1.56526
\(317\) −16.5534 −0.929730 −0.464865 0.885381i \(-0.653897\pi\)
−0.464865 + 0.885381i \(0.653897\pi\)
\(318\) 2.32373 0.130308
\(319\) −9.76766 −0.546884
\(320\) −18.7716 −1.04936
\(321\) −7.96068 −0.444322
\(322\) 0.467703 0.0260641
\(323\) −2.97160 −0.165344
\(324\) 13.4817 0.748984
\(325\) 2.37631 0.131814
\(326\) 3.12425 0.173036
\(327\) 3.79993 0.210136
\(328\) −0.0710728 −0.00392434
\(329\) 6.42149 0.354028
\(330\) 2.38450 0.131262
\(331\) 8.22636 0.452162 0.226081 0.974109i \(-0.427409\pi\)
0.226081 + 0.974109i \(0.427409\pi\)
\(332\) −11.9214 −0.654271
\(333\) 4.93524 0.270449
\(334\) −16.0667 −0.879131
\(335\) 29.9442 1.63602
\(336\) −8.01479 −0.437243
\(337\) −5.61124 −0.305664 −0.152832 0.988252i \(-0.548839\pi\)
−0.152832 + 0.988252i \(0.548839\pi\)
\(338\) −28.8104 −1.56708
\(339\) 6.99524 0.379929
\(340\) 4.68184 0.253908
\(341\) −0.151436 −0.00820074
\(342\) −16.2921 −0.880976
\(343\) −5.89017 −0.318039
\(344\) −0.00949577 −0.000511978 0
\(345\) −0.0707423 −0.00380864
\(346\) 46.0470 2.47550
\(347\) 29.3420 1.57516 0.787580 0.616213i \(-0.211334\pi\)
0.787580 + 0.616213i \(0.211334\pi\)
\(348\) 9.99084 0.535565
\(349\) −18.4204 −0.986024 −0.493012 0.870023i \(-0.664104\pi\)
−0.493012 + 0.870023i \(0.664104\pi\)
\(350\) 3.57647 0.191171
\(351\) 15.3281 0.818155
\(352\) 8.00470 0.426652
\(353\) 24.7243 1.31594 0.657970 0.753044i \(-0.271415\pi\)
0.657970 + 0.753044i \(0.271415\pi\)
\(354\) 4.18414 0.222385
\(355\) −21.0185 −1.11555
\(356\) −18.1734 −0.963187
\(357\) 2.00847 0.106300
\(358\) 28.2785 1.49457
\(359\) 8.36752 0.441621 0.220810 0.975317i \(-0.429130\pi\)
0.220810 + 0.975317i \(0.429130\pi\)
\(360\) 0.0607558 0.00320211
\(361\) −10.1696 −0.535243
\(362\) −28.4918 −1.49749
\(363\) −0.510214 −0.0267793
\(364\) −41.3068 −2.16507
\(365\) −36.5147 −1.91127
\(366\) −7.43639 −0.388707
\(367\) 1.01560 0.0530137 0.0265068 0.999649i \(-0.491562\pi\)
0.0265068 + 0.999649i \(0.491562\pi\)
\(368\) −0.236916 −0.0123501
\(369\) −20.5057 −1.06748
\(370\) 8.41885 0.437675
\(371\) −8.95899 −0.465128
\(372\) 0.154897 0.00803101
\(373\) 19.5396 1.01172 0.505861 0.862615i \(-0.331175\pi\)
0.505861 + 0.862615i \(0.331175\pi\)
\(374\) −2.00119 −0.103479
\(375\) 5.41676 0.279720
\(376\) 0.0154900 0.000798837 0
\(377\) −51.1257 −2.63311
\(378\) 23.0697 1.18658
\(379\) −9.99246 −0.513278 −0.256639 0.966507i \(-0.582615\pi\)
−0.256639 + 0.966507i \(0.582615\pi\)
\(380\) −13.9125 −0.713698
\(381\) −4.70605 −0.241098
\(382\) −13.8722 −0.709762
\(383\) −6.99998 −0.357682 −0.178841 0.983878i \(-0.557235\pi\)
−0.178841 + 0.983878i \(0.557235\pi\)
\(384\) −0.0387589 −0.00197791
\(385\) −9.19330 −0.468534
\(386\) 1.33477 0.0679381
\(387\) −2.73968 −0.139266
\(388\) 22.8255 1.15879
\(389\) 22.8231 1.15718 0.578588 0.815620i \(-0.303604\pi\)
0.578588 + 0.815620i \(0.303604\pi\)
\(390\) 12.4809 0.631995
\(391\) 0.0593703 0.00300248
\(392\) −0.0806788 −0.00407489
\(393\) −3.48827 −0.175960
\(394\) −15.1406 −0.762771
\(395\) 32.4137 1.63091
\(396\) −5.49236 −0.276002
\(397\) 7.72213 0.387563 0.193781 0.981045i \(-0.437925\pi\)
0.193781 + 0.981045i \(0.437925\pi\)
\(398\) −37.5251 −1.88096
\(399\) −5.96837 −0.298792
\(400\) −1.81167 −0.0905836
\(401\) 38.6727 1.93122 0.965612 0.259987i \(-0.0837184\pi\)
0.965612 + 0.259987i \(0.0837184\pi\)
\(402\) 13.0917 0.652953
\(403\) −0.792645 −0.0394845
\(404\) −8.51389 −0.423582
\(405\) 15.7052 0.780397
\(406\) −76.9470 −3.81882
\(407\) −1.80139 −0.0892917
\(408\) 0.00484488 0.000239857 0
\(409\) −0.587094 −0.0290299 −0.0145150 0.999895i \(-0.504620\pi\)
−0.0145150 + 0.999895i \(0.504620\pi\)
\(410\) −34.9799 −1.72753
\(411\) −8.45669 −0.417138
\(412\) 6.44118 0.317334
\(413\) −16.1317 −0.793789
\(414\) 0.325504 0.0159977
\(415\) −13.8875 −0.681713
\(416\) 41.8980 2.05422
\(417\) 7.56063 0.370246
\(418\) 5.94671 0.290863
\(419\) 3.61037 0.176378 0.0881890 0.996104i \(-0.471892\pi\)
0.0881890 + 0.996104i \(0.471892\pi\)
\(420\) 9.40336 0.458837
\(421\) 36.9882 1.80269 0.901346 0.433099i \(-0.142580\pi\)
0.901346 + 0.433099i \(0.142580\pi\)
\(422\) −19.0397 −0.926839
\(423\) 4.46912 0.217296
\(424\) −0.0216110 −0.00104952
\(425\) 0.453998 0.0220221
\(426\) −9.18933 −0.445225
\(427\) 28.6706 1.38747
\(428\) 31.2793 1.51194
\(429\) −2.67055 −0.128936
\(430\) −4.67353 −0.225378
\(431\) 3.29861 0.158888 0.0794442 0.996839i \(-0.474685\pi\)
0.0794442 + 0.996839i \(0.474685\pi\)
\(432\) −11.6860 −0.562243
\(433\) 13.4354 0.645666 0.322833 0.946456i \(-0.395365\pi\)
0.322833 + 0.946456i \(0.395365\pi\)
\(434\) −1.19298 −0.0572646
\(435\) 11.6386 0.558028
\(436\) −14.9308 −0.715053
\(437\) −0.176424 −0.00843953
\(438\) −15.9643 −0.762804
\(439\) 0.441484 0.0210709 0.0105354 0.999945i \(-0.496646\pi\)
0.0105354 + 0.999945i \(0.496646\pi\)
\(440\) −0.0221762 −0.00105721
\(441\) −23.2771 −1.10843
\(442\) −10.4746 −0.498224
\(443\) −1.34419 −0.0638643 −0.0319321 0.999490i \(-0.510166\pi\)
−0.0319321 + 0.999490i \(0.510166\pi\)
\(444\) 1.84255 0.0874437
\(445\) −21.1706 −1.00358
\(446\) −18.4301 −0.872691
\(447\) 1.46128 0.0691162
\(448\) 31.6415 1.49492
\(449\) 23.9721 1.13131 0.565657 0.824641i \(-0.308623\pi\)
0.565657 + 0.824641i \(0.308623\pi\)
\(450\) 2.48909 0.117337
\(451\) 7.48468 0.352440
\(452\) −27.4858 −1.29283
\(453\) 0.417625 0.0196217
\(454\) −1.13965 −0.0534866
\(455\) −48.1194 −2.25587
\(456\) −0.0143970 −0.000674202 0
\(457\) −15.3473 −0.717917 −0.358959 0.933353i \(-0.616868\pi\)
−0.358959 + 0.933353i \(0.616868\pi\)
\(458\) −12.5976 −0.588647
\(459\) 2.92847 0.136689
\(460\) 0.277962 0.0129601
\(461\) −40.5155 −1.88700 −0.943498 0.331379i \(-0.892486\pi\)
−0.943498 + 0.331379i \(0.892486\pi\)
\(462\) −4.01933 −0.186996
\(463\) 24.2300 1.12606 0.563031 0.826436i \(-0.309635\pi\)
0.563031 + 0.826436i \(0.309635\pi\)
\(464\) 38.9777 1.80949
\(465\) 0.180443 0.00836785
\(466\) 30.0311 1.39116
\(467\) −21.9439 −1.01544 −0.507721 0.861521i \(-0.669512\pi\)
−0.507721 + 0.861521i \(0.669512\pi\)
\(468\) −28.7480 −1.32888
\(469\) −50.4741 −2.33068
\(470\) 7.62372 0.351656
\(471\) −2.13216 −0.0982448
\(472\) −0.0389132 −0.00179112
\(473\) 1.00000 0.0459800
\(474\) 14.1714 0.650912
\(475\) −1.34910 −0.0619008
\(476\) −7.89174 −0.361717
\(477\) −6.23513 −0.285487
\(478\) −46.5726 −2.13018
\(479\) 3.16129 0.144443 0.0722216 0.997389i \(-0.476991\pi\)
0.0722216 + 0.997389i \(0.476991\pi\)
\(480\) −9.53795 −0.435346
\(481\) −9.42881 −0.429917
\(482\) −11.8654 −0.540453
\(483\) 0.119244 0.00542578
\(484\) 2.00475 0.0911248
\(485\) 26.5900 1.20739
\(486\) 24.4476 1.10896
\(487\) −14.6023 −0.661694 −0.330847 0.943684i \(-0.607334\pi\)
−0.330847 + 0.943684i \(0.607334\pi\)
\(488\) 0.0691596 0.00313071
\(489\) 0.796546 0.0360210
\(490\) −39.7076 −1.79381
\(491\) −23.5476 −1.06269 −0.531344 0.847156i \(-0.678313\pi\)
−0.531344 + 0.847156i \(0.678313\pi\)
\(492\) −7.65571 −0.345146
\(493\) −9.76766 −0.439913
\(494\) 31.1262 1.40043
\(495\) −6.39820 −0.287578
\(496\) 0.604305 0.0271341
\(497\) 35.4289 1.58920
\(498\) −6.07167 −0.272078
\(499\) −39.9410 −1.78800 −0.894002 0.448063i \(-0.852114\pi\)
−0.894002 + 0.448063i \(0.852114\pi\)
\(500\) −21.2837 −0.951834
\(501\) −4.09630 −0.183009
\(502\) −11.5100 −0.513717
\(503\) 19.9446 0.889287 0.444644 0.895708i \(-0.353330\pi\)
0.444644 + 0.895708i \(0.353330\pi\)
\(504\) −0.102410 −0.00456172
\(505\) −9.91805 −0.441347
\(506\) −0.118811 −0.00528179
\(507\) −7.34537 −0.326220
\(508\) 18.4911 0.820411
\(509\) −24.6342 −1.09189 −0.545946 0.837820i \(-0.683830\pi\)
−0.545946 + 0.837820i \(0.683830\pi\)
\(510\) 2.38450 0.105587
\(511\) 61.5494 2.72278
\(512\) −32.0184 −1.41503
\(513\) −8.70222 −0.384212
\(514\) −6.80919 −0.300340
\(515\) 7.50350 0.330644
\(516\) −1.02285 −0.0450284
\(517\) −1.63126 −0.0717425
\(518\) −14.1909 −0.623511
\(519\) 11.7400 0.515327
\(520\) −0.116074 −0.00509020
\(521\) 14.4156 0.631560 0.315780 0.948832i \(-0.397734\pi\)
0.315780 + 0.948832i \(0.397734\pi\)
\(522\) −53.5523 −2.34392
\(523\) −37.9966 −1.66148 −0.830739 0.556663i \(-0.812082\pi\)
−0.830739 + 0.556663i \(0.812082\pi\)
\(524\) 13.7062 0.598758
\(525\) 0.911843 0.0397961
\(526\) −26.0028 −1.13378
\(527\) −0.151436 −0.00659667
\(528\) 2.03600 0.0886057
\(529\) −22.9965 −0.999847
\(530\) −10.6363 −0.462011
\(531\) −11.2271 −0.487213
\(532\) 23.4511 1.01673
\(533\) 39.1762 1.69691
\(534\) −9.25585 −0.400540
\(535\) 36.4380 1.57535
\(536\) −0.121755 −0.00525899
\(537\) 7.20977 0.311125
\(538\) 57.6625 2.48601
\(539\) 8.49628 0.365961
\(540\) 13.7106 0.590011
\(541\) −2.41675 −0.103904 −0.0519521 0.998650i \(-0.516544\pi\)
−0.0519521 + 0.998650i \(0.516544\pi\)
\(542\) −42.0813 −1.80755
\(543\) −7.26414 −0.311734
\(544\) 8.00470 0.343199
\(545\) −17.3932 −0.745044
\(546\) −21.0379 −0.900339
\(547\) 4.93835 0.211148 0.105574 0.994411i \(-0.466332\pi\)
0.105574 + 0.994411i \(0.466332\pi\)
\(548\) 33.2282 1.41944
\(549\) 19.9537 0.851601
\(550\) −0.908534 −0.0387400
\(551\) 29.0255 1.23653
\(552\) 0.000287642 0 1.22428e−5 0
\(553\) −54.6368 −2.32339
\(554\) 31.1358 1.32283
\(555\) 2.14644 0.0911112
\(556\) −29.7074 −1.25987
\(557\) 38.2611 1.62117 0.810587 0.585619i \(-0.199148\pi\)
0.810587 + 0.585619i \(0.199148\pi\)
\(558\) −0.830267 −0.0351480
\(559\) 5.23418 0.221382
\(560\) 36.6857 1.55026
\(561\) −0.510214 −0.0215413
\(562\) 8.51768 0.359297
\(563\) −3.87484 −0.163305 −0.0816526 0.996661i \(-0.526020\pi\)
−0.0816526 + 0.996661i \(0.526020\pi\)
\(564\) 1.66853 0.0702577
\(565\) −32.0190 −1.34705
\(566\) 54.9846 2.31117
\(567\) −26.4728 −1.11175
\(568\) 0.0854622 0.00358592
\(569\) −20.1346 −0.844087 −0.422043 0.906576i \(-0.638687\pi\)
−0.422043 + 0.906576i \(0.638687\pi\)
\(570\) −7.08577 −0.296790
\(571\) 40.9352 1.71308 0.856542 0.516077i \(-0.172608\pi\)
0.856542 + 0.516077i \(0.172608\pi\)
\(572\) 10.4932 0.438743
\(573\) −3.53679 −0.147752
\(574\) 58.9623 2.46104
\(575\) 0.0269540 0.00112406
\(576\) 22.0213 0.917555
\(577\) 30.3027 1.26152 0.630759 0.775979i \(-0.282744\pi\)
0.630759 + 0.775979i \(0.282744\pi\)
\(578\) −2.00119 −0.0832384
\(579\) 0.340308 0.0141427
\(580\) −45.7306 −1.89886
\(581\) 23.4089 0.971166
\(582\) 11.6252 0.481881
\(583\) 2.27586 0.0942564
\(584\) 0.148471 0.00614375
\(585\) −33.4893 −1.38461
\(586\) 44.6663 1.84515
\(587\) 10.5504 0.435461 0.217731 0.976009i \(-0.430135\pi\)
0.217731 + 0.976009i \(0.430135\pi\)
\(588\) −8.69042 −0.358387
\(589\) 0.450008 0.0185422
\(590\) −19.1519 −0.788470
\(591\) −3.86018 −0.158786
\(592\) 7.18843 0.295443
\(593\) 5.41032 0.222175 0.111088 0.993811i \(-0.464567\pi\)
0.111088 + 0.993811i \(0.464567\pi\)
\(594\) −5.86041 −0.240455
\(595\) −9.19330 −0.376888
\(596\) −5.74169 −0.235189
\(597\) −9.56724 −0.391561
\(598\) −0.621878 −0.0254305
\(599\) 40.3259 1.64767 0.823835 0.566829i \(-0.191830\pi\)
0.823835 + 0.566829i \(0.191830\pi\)
\(600\) 0.00219956 8.97968e−5 0
\(601\) 12.5929 0.513675 0.256837 0.966455i \(-0.417320\pi\)
0.256837 + 0.966455i \(0.417320\pi\)
\(602\) 7.87773 0.321072
\(603\) −35.1281 −1.43053
\(604\) −1.64094 −0.0667689
\(605\) 2.33538 0.0949467
\(606\) −4.33620 −0.176146
\(607\) −33.9938 −1.37976 −0.689882 0.723922i \(-0.742338\pi\)
−0.689882 + 0.723922i \(0.742338\pi\)
\(608\) −23.7867 −0.964679
\(609\) −19.6181 −0.794965
\(610\) 34.0383 1.37817
\(611\) −8.53828 −0.345422
\(612\) −5.49236 −0.222016
\(613\) −3.43514 −0.138744 −0.0693720 0.997591i \(-0.522100\pi\)
−0.0693720 + 0.997591i \(0.522100\pi\)
\(614\) 40.8105 1.64698
\(615\) −8.91833 −0.359622
\(616\) 0.0373804 0.00150610
\(617\) −6.32568 −0.254662 −0.127331 0.991860i \(-0.540641\pi\)
−0.127331 + 0.991860i \(0.540641\pi\)
\(618\) 3.28055 0.131963
\(619\) 13.9742 0.561673 0.280836 0.959756i \(-0.409388\pi\)
0.280836 + 0.959756i \(0.409388\pi\)
\(620\) −0.709001 −0.0284742
\(621\) 0.173864 0.00697692
\(622\) −23.1072 −0.926515
\(623\) 35.6854 1.42970
\(624\) 10.6568 0.426614
\(625\) −27.0639 −1.08255
\(626\) −9.94460 −0.397466
\(627\) 1.51615 0.0605492
\(628\) 8.37773 0.334308
\(629\) −1.80139 −0.0718262
\(630\) −50.4033 −2.00811
\(631\) −6.84549 −0.272514 −0.136257 0.990673i \(-0.543507\pi\)
−0.136257 + 0.990673i \(0.543507\pi\)
\(632\) −0.131796 −0.00524256
\(633\) −4.85429 −0.192941
\(634\) 33.1264 1.31562
\(635\) 21.5408 0.854820
\(636\) −2.32786 −0.0923057
\(637\) 44.4711 1.76201
\(638\) 19.5469 0.773869
\(639\) 24.6572 0.975425
\(640\) 0.177409 0.00701272
\(641\) 22.7772 0.899646 0.449823 0.893118i \(-0.351487\pi\)
0.449823 + 0.893118i \(0.351487\pi\)
\(642\) 15.9308 0.628739
\(643\) 25.5687 1.00833 0.504166 0.863607i \(-0.331800\pi\)
0.504166 + 0.863607i \(0.331800\pi\)
\(644\) −0.468535 −0.0184629
\(645\) −1.19154 −0.0469170
\(646\) 5.94671 0.233970
\(647\) 24.0035 0.943673 0.471837 0.881686i \(-0.343591\pi\)
0.471837 + 0.881686i \(0.343591\pi\)
\(648\) −0.0638581 −0.00250858
\(649\) 4.09795 0.160858
\(650\) −4.75543 −0.186523
\(651\) −0.304156 −0.0119208
\(652\) −3.12980 −0.122573
\(653\) −39.5512 −1.54776 −0.773878 0.633334i \(-0.781686\pi\)
−0.773878 + 0.633334i \(0.781686\pi\)
\(654\) −7.60436 −0.297354
\(655\) 15.9667 0.623871
\(656\) −29.8675 −1.16613
\(657\) 42.8361 1.67120
\(658\) −12.8506 −0.500968
\(659\) 12.4586 0.485316 0.242658 0.970112i \(-0.421981\pi\)
0.242658 + 0.970112i \(0.421981\pi\)
\(660\) −2.38874 −0.0929816
\(661\) −6.31587 −0.245659 −0.122829 0.992428i \(-0.539197\pi\)
−0.122829 + 0.992428i \(0.539197\pi\)
\(662\) −16.4625 −0.639833
\(663\) −2.67055 −0.103716
\(664\) 0.0564674 0.00219136
\(665\) 27.3188 1.05938
\(666\) −9.87633 −0.382700
\(667\) −0.579909 −0.0224542
\(668\) 16.0953 0.622745
\(669\) −4.69887 −0.181669
\(670\) −59.9239 −2.31506
\(671\) −7.28320 −0.281165
\(672\) 16.0772 0.620193
\(673\) 21.1714 0.816096 0.408048 0.912960i \(-0.366210\pi\)
0.408048 + 0.912960i \(0.366210\pi\)
\(674\) 11.2291 0.432530
\(675\) 1.32952 0.0511732
\(676\) 28.8616 1.11006
\(677\) 31.2475 1.20094 0.600469 0.799648i \(-0.294980\pi\)
0.600469 + 0.799648i \(0.294980\pi\)
\(678\) −13.9988 −0.537619
\(679\) −44.8203 −1.72005
\(680\) −0.0221762 −0.000850420 0
\(681\) −0.290561 −0.0111343
\(682\) 0.303052 0.0116045
\(683\) 39.9494 1.52862 0.764311 0.644848i \(-0.223079\pi\)
0.764311 + 0.644848i \(0.223079\pi\)
\(684\) 16.3211 0.624052
\(685\) 38.7084 1.47897
\(686\) 11.7873 0.450042
\(687\) −3.21183 −0.122539
\(688\) −3.99049 −0.152136
\(689\) 11.9123 0.453821
\(690\) 0.141568 0.00538942
\(691\) 5.13326 0.195278 0.0976392 0.995222i \(-0.468871\pi\)
0.0976392 + 0.995222i \(0.468871\pi\)
\(692\) −46.1289 −1.75356
\(693\) 10.7848 0.409682
\(694\) −58.7187 −2.22893
\(695\) −34.6069 −1.31271
\(696\) −0.0473231 −0.00179378
\(697\) 7.48468 0.283503
\(698\) 36.8627 1.39527
\(699\) 7.65661 0.289600
\(700\) −3.58283 −0.135418
\(701\) 48.2753 1.82333 0.911666 0.410933i \(-0.134797\pi\)
0.911666 + 0.410933i \(0.134797\pi\)
\(702\) −30.6744 −1.15773
\(703\) 5.35301 0.201892
\(704\) −8.03792 −0.302940
\(705\) 1.94371 0.0732044
\(706\) −49.4779 −1.86212
\(707\) 16.7179 0.628743
\(708\) −4.19158 −0.157529
\(709\) −1.05698 −0.0396958 −0.0198479 0.999803i \(-0.506318\pi\)
−0.0198479 + 0.999803i \(0.506318\pi\)
\(710\) 42.0619 1.57856
\(711\) −38.0252 −1.42606
\(712\) 0.0860809 0.00322602
\(713\) −0.00899082 −0.000336709 0
\(714\) −4.01933 −0.150420
\(715\) 12.2238 0.457144
\(716\) −28.3288 −1.05870
\(717\) −11.8740 −0.443441
\(718\) −16.7450 −0.624917
\(719\) 20.2170 0.753966 0.376983 0.926220i \(-0.376961\pi\)
0.376983 + 0.926220i \(0.376961\pi\)
\(720\) 25.5319 0.951518
\(721\) −12.6480 −0.471034
\(722\) 20.3513 0.757397
\(723\) −3.02515 −0.112506
\(724\) 28.5424 1.06077
\(725\) −4.43449 −0.164693
\(726\) 1.02103 0.0378941
\(727\) 49.4689 1.83470 0.917350 0.398081i \(-0.130324\pi\)
0.917350 + 0.398081i \(0.130324\pi\)
\(728\) 0.195656 0.00725149
\(729\) −13.9416 −0.516357
\(730\) 73.0727 2.70454
\(731\) 1.00000 0.0369863
\(732\) 7.44962 0.275346
\(733\) 21.0044 0.775815 0.387908 0.921698i \(-0.373198\pi\)
0.387908 + 0.921698i \(0.373198\pi\)
\(734\) −2.03240 −0.0750171
\(735\) −10.1237 −0.373418
\(736\) 0.475241 0.0175176
\(737\) 12.8220 0.472303
\(738\) 41.0356 1.51054
\(739\) 41.0547 1.51022 0.755110 0.655598i \(-0.227583\pi\)
0.755110 + 0.655598i \(0.227583\pi\)
\(740\) −8.43383 −0.310034
\(741\) 7.93580 0.291529
\(742\) 17.9286 0.658180
\(743\) 37.7544 1.38507 0.692537 0.721382i \(-0.256493\pi\)
0.692537 + 0.721382i \(0.256493\pi\)
\(744\) −0.000733691 0 −2.68984e−5 0
\(745\) −6.68865 −0.245053
\(746\) −39.1024 −1.43164
\(747\) 16.2918 0.596084
\(748\) 2.00475 0.0733007
\(749\) −61.4202 −2.24425
\(750\) −10.8399 −0.395819
\(751\) 51.1162 1.86526 0.932629 0.360837i \(-0.117509\pi\)
0.932629 + 0.360837i \(0.117509\pi\)
\(752\) 6.50950 0.237377
\(753\) −2.93455 −0.106941
\(754\) 102.312 3.72598
\(755\) −1.91157 −0.0695693
\(756\) −23.1107 −0.840528
\(757\) 18.0813 0.657176 0.328588 0.944473i \(-0.393427\pi\)
0.328588 + 0.944473i \(0.393427\pi\)
\(758\) 19.9968 0.726316
\(759\) −0.0302916 −0.00109951
\(760\) 0.0658988 0.00239040
\(761\) 12.5547 0.455109 0.227554 0.973765i \(-0.426927\pi\)
0.227554 + 0.973765i \(0.426927\pi\)
\(762\) 9.41769 0.341167
\(763\) 29.3181 1.06139
\(764\) 13.8968 0.502770
\(765\) −6.39820 −0.231327
\(766\) 14.0083 0.506139
\(767\) 21.4494 0.774492
\(768\) −8.12455 −0.293170
\(769\) −21.6407 −0.780385 −0.390193 0.920733i \(-0.627592\pi\)
−0.390193 + 0.920733i \(0.627592\pi\)
\(770\) 18.3975 0.663000
\(771\) −1.73604 −0.0625220
\(772\) −1.33715 −0.0481249
\(773\) −4.75588 −0.171057 −0.0855285 0.996336i \(-0.527258\pi\)
−0.0855285 + 0.996336i \(0.527258\pi\)
\(774\) 5.48261 0.197068
\(775\) −0.0687518 −0.00246964
\(776\) −0.108116 −0.00388115
\(777\) −3.61805 −0.129797
\(778\) −45.6732 −1.63746
\(779\) −22.2415 −0.796883
\(780\) −12.5031 −0.447683
\(781\) −9.00003 −0.322046
\(782\) −0.118811 −0.00424867
\(783\) −28.6043 −1.02223
\(784\) −33.9043 −1.21087
\(785\) 9.75944 0.348329
\(786\) 6.98068 0.248993
\(787\) −39.0420 −1.39170 −0.695849 0.718189i \(-0.744972\pi\)
−0.695849 + 0.718189i \(0.744972\pi\)
\(788\) 15.1675 0.540320
\(789\) −6.62958 −0.236019
\(790\) −64.8659 −2.30782
\(791\) 53.9714 1.91900
\(792\) 0.0260154 0.000924417 0
\(793\) −38.1216 −1.35374
\(794\) −15.4534 −0.548421
\(795\) −2.71178 −0.0961771
\(796\) 37.5918 1.33241
\(797\) 39.6294 1.40375 0.701873 0.712302i \(-0.252347\pi\)
0.701873 + 0.712302i \(0.252347\pi\)
\(798\) 11.9438 0.422807
\(799\) −1.63126 −0.0577097
\(800\) 3.63412 0.128485
\(801\) 24.8357 0.877526
\(802\) −77.3913 −2.73278
\(803\) −15.6354 −0.551763
\(804\) −13.1149 −0.462529
\(805\) −0.545809 −0.0192372
\(806\) 1.58623 0.0558726
\(807\) 14.7014 0.517514
\(808\) 0.0403273 0.00141871
\(809\) 49.7006 1.74738 0.873689 0.486484i \(-0.161721\pi\)
0.873689 + 0.486484i \(0.161721\pi\)
\(810\) −31.4290 −1.10430
\(811\) −30.6224 −1.07530 −0.537648 0.843169i \(-0.680687\pi\)
−0.537648 + 0.843169i \(0.680687\pi\)
\(812\) 77.0838 2.70511
\(813\) −10.7289 −0.376278
\(814\) 3.60492 0.126352
\(815\) −3.64599 −0.127713
\(816\) 2.03600 0.0712744
\(817\) −2.97160 −0.103963
\(818\) 1.17488 0.0410789
\(819\) 56.4498 1.97252
\(820\) 35.0421 1.22372
\(821\) 32.6707 1.14021 0.570107 0.821570i \(-0.306902\pi\)
0.570107 + 0.821570i \(0.306902\pi\)
\(822\) 16.9234 0.590272
\(823\) 50.9251 1.77514 0.887568 0.460676i \(-0.152393\pi\)
0.887568 + 0.460676i \(0.152393\pi\)
\(824\) −0.0305096 −0.00106285
\(825\) −0.231636 −0.00806453
\(826\) 32.2825 1.12325
\(827\) 43.7759 1.52224 0.761119 0.648612i \(-0.224650\pi\)
0.761119 + 0.648612i \(0.224650\pi\)
\(828\) −0.326083 −0.0113322
\(829\) 42.0428 1.46021 0.730104 0.683337i \(-0.239472\pi\)
0.730104 + 0.683337i \(0.239472\pi\)
\(830\) 27.7916 0.964659
\(831\) 7.93826 0.275375
\(832\) −42.0719 −1.45858
\(833\) 8.49628 0.294379
\(834\) −15.1302 −0.523917
\(835\) 18.7498 0.648864
\(836\) −5.95729 −0.206037
\(837\) −0.443476 −0.0153288
\(838\) −7.22502 −0.249584
\(839\) −1.03105 −0.0355957 −0.0177979 0.999842i \(-0.505666\pi\)
−0.0177979 + 0.999842i \(0.505666\pi\)
\(840\) −0.0445404 −0.00153679
\(841\) 66.4071 2.28990
\(842\) −74.0202 −2.55090
\(843\) 2.17163 0.0747951
\(844\) 19.0736 0.656540
\(845\) 33.6216 1.15662
\(846\) −8.94354 −0.307485
\(847\) −3.93653 −0.135261
\(848\) −9.08178 −0.311870
\(849\) 14.0186 0.481119
\(850\) −0.908534 −0.0311625
\(851\) −0.106949 −0.00366617
\(852\) 9.20568 0.315381
\(853\) −14.1009 −0.482806 −0.241403 0.970425i \(-0.577608\pi\)
−0.241403 + 0.970425i \(0.577608\pi\)
\(854\) −57.3751 −1.96334
\(855\) 19.0128 0.650226
\(856\) −0.148159 −0.00506397
\(857\) −46.9479 −1.60371 −0.801855 0.597518i \(-0.796154\pi\)
−0.801855 + 0.597518i \(0.796154\pi\)
\(858\) 5.34427 0.182451
\(859\) −27.4488 −0.936541 −0.468271 0.883585i \(-0.655123\pi\)
−0.468271 + 0.883585i \(0.655123\pi\)
\(860\) 4.68184 0.159649
\(861\) 15.0328 0.512316
\(862\) −6.60113 −0.224835
\(863\) 20.6359 0.702456 0.351228 0.936290i \(-0.385764\pi\)
0.351228 + 0.936290i \(0.385764\pi\)
\(864\) 23.4415 0.797496
\(865\) −53.7367 −1.82710
\(866\) −26.8868 −0.913651
\(867\) −0.510214 −0.0173278
\(868\) 1.19510 0.0405642
\(869\) 13.8794 0.470827
\(870\) −23.2910 −0.789638
\(871\) 67.1125 2.27402
\(872\) 0.0707217 0.00239494
\(873\) −31.1933 −1.05573
\(874\) 0.353058 0.0119424
\(875\) 41.7927 1.41285
\(876\) 15.9927 0.540343
\(877\) −16.5448 −0.558679 −0.279340 0.960192i \(-0.590116\pi\)
−0.279340 + 0.960192i \(0.590116\pi\)
\(878\) −0.883491 −0.0298164
\(879\) 11.3879 0.384106
\(880\) −9.31930 −0.314154
\(881\) −8.49121 −0.286076 −0.143038 0.989717i \(-0.545687\pi\)
−0.143038 + 0.989717i \(0.545687\pi\)
\(882\) 46.5818 1.56849
\(883\) 34.8691 1.17344 0.586719 0.809790i \(-0.300419\pi\)
0.586719 + 0.809790i \(0.300419\pi\)
\(884\) 10.4932 0.352924
\(885\) −4.88288 −0.164136
\(886\) 2.68997 0.0903713
\(887\) −31.7678 −1.06666 −0.533330 0.845907i \(-0.679060\pi\)
−0.533330 + 0.845907i \(0.679060\pi\)
\(888\) −0.00872752 −0.000292876 0
\(889\) −36.3093 −1.21778
\(890\) 42.3664 1.42012
\(891\) 6.72490 0.225293
\(892\) 18.4629 0.618183
\(893\) 4.84743 0.162213
\(894\) −2.92429 −0.0978030
\(895\) −33.0010 −1.10310
\(896\) −0.299042 −0.00999031
\(897\) −0.158552 −0.00529388
\(898\) −47.9726 −1.60087
\(899\) 1.47918 0.0493334
\(900\) −2.49352 −0.0831173
\(901\) 2.27586 0.0758198
\(902\) −14.9782 −0.498721
\(903\) 2.00847 0.0668379
\(904\) 0.130191 0.00433008
\(905\) 33.2498 1.10526
\(906\) −0.835745 −0.0277658
\(907\) 9.02766 0.299759 0.149879 0.988704i \(-0.452111\pi\)
0.149879 + 0.988704i \(0.452111\pi\)
\(908\) 1.14168 0.0378880
\(909\) 11.6351 0.385911
\(910\) 96.2958 3.19218
\(911\) −20.2933 −0.672346 −0.336173 0.941800i \(-0.609133\pi\)
−0.336173 + 0.941800i \(0.609133\pi\)
\(912\) −6.05018 −0.200341
\(913\) −5.94659 −0.196803
\(914\) 30.7128 1.01589
\(915\) 8.67826 0.286894
\(916\) 12.6200 0.416976
\(917\) −26.9136 −0.888765
\(918\) −5.86041 −0.193422
\(919\) −13.2130 −0.435858 −0.217929 0.975965i \(-0.569930\pi\)
−0.217929 + 0.975965i \(0.569930\pi\)
\(920\) −0.00131661 −4.34073e−5 0
\(921\) 10.4049 0.342852
\(922\) 81.0791 2.67020
\(923\) −47.1078 −1.55057
\(924\) 4.02648 0.132461
\(925\) −0.817828 −0.0268900
\(926\) −48.4887 −1.59344
\(927\) −8.80251 −0.289112
\(928\) −78.1872 −2.56662
\(929\) 51.9918 1.70580 0.852898 0.522078i \(-0.174843\pi\)
0.852898 + 0.522078i \(0.174843\pi\)
\(930\) −0.361100 −0.0118409
\(931\) −25.2475 −0.827454
\(932\) −30.0845 −0.985451
\(933\) −5.89132 −0.192873
\(934\) 43.9138 1.43690
\(935\) 2.33538 0.0763751
\(936\) 0.136169 0.00445083
\(937\) 42.4970 1.38832 0.694158 0.719823i \(-0.255777\pi\)
0.694158 + 0.719823i \(0.255777\pi\)
\(938\) 101.008 3.29803
\(939\) −2.53543 −0.0827408
\(940\) −7.63728 −0.249100
\(941\) 57.6190 1.87833 0.939163 0.343471i \(-0.111603\pi\)
0.939163 + 0.343471i \(0.111603\pi\)
\(942\) 4.26685 0.139021
\(943\) 0.444368 0.0144706
\(944\) −16.3528 −0.532238
\(945\) −26.9223 −0.875781
\(946\) −2.00119 −0.0650642
\(947\) 60.6058 1.96942 0.984712 0.174189i \(-0.0557305\pi\)
0.984712 + 0.174189i \(0.0557305\pi\)
\(948\) −14.1966 −0.461083
\(949\) −81.8387 −2.65660
\(950\) 2.69980 0.0875929
\(951\) 8.44577 0.273873
\(952\) 0.0373804 0.00121151
\(953\) −47.1823 −1.52839 −0.764193 0.644988i \(-0.776862\pi\)
−0.764193 + 0.644988i \(0.776862\pi\)
\(954\) 12.4776 0.403979
\(955\) 16.1888 0.523857
\(956\) 46.6555 1.50895
\(957\) 4.98360 0.161097
\(958\) −6.32634 −0.204395
\(959\) −65.2471 −2.10694
\(960\) 9.57753 0.309113
\(961\) −30.9771 −0.999260
\(962\) 18.8688 0.608354
\(963\) −42.7462 −1.37748
\(964\) 11.8865 0.382838
\(965\) −1.55768 −0.0501434
\(966\) −0.238629 −0.00767776
\(967\) −24.6420 −0.792432 −0.396216 0.918157i \(-0.629677\pi\)
−0.396216 + 0.918157i \(0.629677\pi\)
\(968\) −0.00949577 −0.000305206 0
\(969\) 1.51615 0.0487058
\(970\) −53.2116 −1.70852
\(971\) 11.2730 0.361768 0.180884 0.983504i \(-0.442104\pi\)
0.180884 + 0.983504i \(0.442104\pi\)
\(972\) −24.4910 −0.785551
\(973\) 58.3336 1.87009
\(974\) 29.2220 0.936332
\(975\) −1.21243 −0.0388287
\(976\) 29.0635 0.930301
\(977\) 13.8289 0.442425 0.221212 0.975226i \(-0.428999\pi\)
0.221212 + 0.975226i \(0.428999\pi\)
\(978\) −1.59404 −0.0509717
\(979\) −9.06518 −0.289724
\(980\) 39.7783 1.27067
\(981\) 20.4043 0.651460
\(982\) 47.1231 1.50376
\(983\) −32.5424 −1.03794 −0.518970 0.854792i \(-0.673684\pi\)
−0.518970 + 0.854792i \(0.673684\pi\)
\(984\) 0.0362624 0.00115600
\(985\) 17.6690 0.562981
\(986\) 19.5469 0.622500
\(987\) −3.27633 −0.104287
\(988\) −31.1815 −0.992017
\(989\) 0.0593703 0.00188787
\(990\) 12.8040 0.406937
\(991\) 20.3540 0.646565 0.323283 0.946302i \(-0.395214\pi\)
0.323283 + 0.946302i \(0.395214\pi\)
\(992\) −1.21220 −0.0384875
\(993\) −4.19721 −0.133194
\(994\) −70.8998 −2.24881
\(995\) 43.7917 1.38829
\(996\) 6.08246 0.192730
\(997\) −25.2795 −0.800610 −0.400305 0.916382i \(-0.631096\pi\)
−0.400305 + 0.916382i \(0.631096\pi\)
\(998\) 79.9294 2.53012
\(999\) −5.27532 −0.166904
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 \(a_p\))