Properties

Label 108.4.i.a.13.6
Level 108
Weight 4
Character 108.13
Analytic conductor 6.372
Analytic rank 0
Dimension 54
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.i (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(9\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 13.6
Character \(\chi\) \(=\) 108.13
Dual form 108.4.i.a.25.6

$q$-expansion

\(f(q)\) \(=\) \(q+(2.34095 - 4.63896i) q^{3} +(-5.19451 - 4.35871i) q^{5} +(-17.8009 - 6.47901i) q^{7} +(-16.0399 - 21.7191i) q^{9} +O(q^{10})\) \(q+(2.34095 - 4.63896i) q^{3} +(-5.19451 - 4.35871i) q^{5} +(-17.8009 - 6.47901i) q^{7} +(-16.0399 - 21.7191i) q^{9} +(-0.134044 + 0.112476i) q^{11} +(-1.24242 + 7.04614i) q^{13} +(-32.3799 + 13.8936i) q^{15} +(-26.6029 + 46.0776i) q^{17} +(-65.4831 - 113.420i) q^{19} +(-71.7270 + 67.4109i) q^{21} +(129.122 - 46.9965i) q^{23} +(-13.7215 - 77.8183i) q^{25} +(-138.303 + 23.5653i) q^{27} +(-9.32414 - 52.8798i) q^{29} +(139.135 - 50.6411i) q^{31} +(0.207983 + 0.885126i) q^{33} +(64.2270 + 111.244i) q^{35} +(58.6266 - 101.544i) q^{37} +(29.7783 + 22.2582i) q^{39} +(-27.9173 + 158.327i) q^{41} +(51.8941 - 43.5443i) q^{43} +(-11.3478 + 182.734i) q^{45} +(597.576 + 217.500i) q^{47} +(12.1427 + 10.1889i) q^{49} +(151.476 + 231.275i) q^{51} +36.5908 q^{53} +1.18654 q^{55} +(-679.444 + 38.2632i) q^{57} +(574.476 + 482.043i) q^{59} +(-64.9040 - 23.6231i) q^{61} +(144.807 + 490.544i) q^{63} +(37.1659 - 31.1859i) q^{65} +(109.760 - 622.479i) q^{67} +(84.2524 - 709.008i) q^{69} +(-66.9800 + 116.013i) q^{71} +(-435.761 - 754.761i) q^{73} +(-393.117 - 118.515i) q^{75} +(3.11484 - 1.13371i) q^{77} +(55.7069 + 315.930i) q^{79} +(-214.441 + 696.747i) q^{81} +(-197.919 - 1122.46i) q^{83} +(339.028 - 123.396i) q^{85} +(-267.135 - 80.5346i) q^{87} +(-259.505 - 449.475i) q^{89} +(67.7684 - 117.378i) q^{91} +(90.7863 - 763.992i) q^{93} +(-154.213 + 874.583i) q^{95} +(-1153.80 + 968.155i) q^{97} +(4.59294 + 1.10721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q + 12q^{5} - 48q^{9} + O(q^{10}) \) \( 54q + 12q^{5} - 48q^{9} - 87q^{11} + 234q^{15} + 204q^{17} - 12q^{21} + 96q^{23} - 216q^{25} + 27q^{27} + 318q^{29} - 54q^{31} + 63q^{33} + 6q^{35} + 66q^{39} + 867q^{41} - 513q^{43} - 306q^{45} - 1548q^{47} + 594q^{49} - 1368q^{51} - 1068q^{53} - 1269q^{57} - 1218q^{59} - 54q^{61} + 30q^{63} + 96q^{65} - 2997q^{67} + 1476q^{69} - 120q^{71} - 216q^{73} + 732q^{75} + 3480q^{77} + 2808q^{79} + 3348q^{81} + 4464q^{83} + 2160q^{85} + 4824q^{87} + 4029q^{89} + 270q^{91} + 1164q^{93} - 1650q^{95} - 3483q^{97} - 5076q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.34095 4.63896i 0.450516 0.892769i
\(4\) 0 0
\(5\) −5.19451 4.35871i −0.464611 0.389855i 0.380213 0.924899i \(-0.375851\pi\)
−0.844824 + 0.535044i \(0.820295\pi\)
\(6\) 0 0
\(7\) −17.8009 6.47901i −0.961160 0.349834i −0.186672 0.982422i \(-0.559770\pi\)
−0.774488 + 0.632588i \(0.781992\pi\)
\(8\) 0 0
\(9\) −16.0399 21.7191i −0.594072 0.804412i
\(10\) 0 0
\(11\) −0.134044 + 0.112476i −0.00367416 + 0.00308299i −0.644623 0.764501i \(-0.722986\pi\)
0.640949 + 0.767584i \(0.278541\pi\)
\(12\) 0 0
\(13\) −1.24242 + 7.04614i −0.0265067 + 0.150327i −0.995189 0.0979783i \(-0.968762\pi\)
0.968682 + 0.248305i \(0.0798735\pi\)
\(14\) 0 0
\(15\) −32.3799 + 13.8936i −0.557364 + 0.239154i
\(16\) 0 0
\(17\) −26.6029 + 46.0776i −0.379538 + 0.657380i −0.990995 0.133898i \(-0.957251\pi\)
0.611457 + 0.791278i \(0.290584\pi\)
\(18\) 0 0
\(19\) −65.4831 113.420i −0.790677 1.36949i −0.925548 0.378629i \(-0.876396\pi\)
0.134872 0.990863i \(-0.456938\pi\)
\(20\) 0 0
\(21\) −71.7270 + 67.4109i −0.745338 + 0.700488i
\(22\) 0 0
\(23\) 129.122 46.9965i 1.17060 0.426063i 0.317726 0.948182i \(-0.397081\pi\)
0.852872 + 0.522119i \(0.174858\pi\)
\(24\) 0 0
\(25\) −13.7215 77.8183i −0.109772 0.622546i
\(26\) 0 0
\(27\) −138.303 + 23.5653i −0.985792 + 0.167968i
\(28\) 0 0
\(29\) −9.32414 52.8798i −0.0597052 0.338605i 0.940293 0.340365i \(-0.110551\pi\)
−0.999998 + 0.00176047i \(0.999440\pi\)
\(30\) 0 0
\(31\) 139.135 50.6411i 0.806111 0.293401i 0.0940949 0.995563i \(-0.470004\pi\)
0.712017 + 0.702163i \(0.247782\pi\)
\(32\) 0 0
\(33\) 0.207983 + 0.885126i 0.00109713 + 0.00466911i
\(34\) 0 0
\(35\) 64.2270 + 111.244i 0.310181 + 0.537249i
\(36\) 0 0
\(37\) 58.6266 101.544i 0.260491 0.451183i −0.705882 0.708330i \(-0.749449\pi\)
0.966372 + 0.257147i \(0.0827824\pi\)
\(38\) 0 0
\(39\) 29.7783 + 22.2582i 0.122265 + 0.0913889i
\(40\) 0 0
\(41\) −27.9173 + 158.327i −0.106340 + 0.603085i 0.884336 + 0.466850i \(0.154611\pi\)
−0.990677 + 0.136235i \(0.956500\pi\)
\(42\) 0 0
\(43\) 51.8941 43.5443i 0.184041 0.154429i −0.546113 0.837712i \(-0.683893\pi\)
0.730154 + 0.683283i \(0.239448\pi\)
\(44\) 0 0
\(45\) −11.3478 + 182.734i −0.0375919 + 0.605340i
\(46\) 0 0
\(47\) 597.576 + 217.500i 1.85458 + 0.675013i 0.982674 + 0.185345i \(0.0593402\pi\)
0.871909 + 0.489668i \(0.162882\pi\)
\(48\) 0 0
\(49\) 12.1427 + 10.1889i 0.0354013 + 0.0297052i
\(50\) 0 0
\(51\) 151.476 + 231.275i 0.415900 + 0.635000i
\(52\) 0 0
\(53\) 36.5908 0.0948328 0.0474164 0.998875i \(-0.484901\pi\)
0.0474164 + 0.998875i \(0.484901\pi\)
\(54\) 0 0
\(55\) 1.18654 0.00290897
\(56\) 0 0
\(57\) −679.444 + 38.2632i −1.57885 + 0.0889138i
\(58\) 0 0
\(59\) 574.476 + 482.043i 1.26763 + 1.06367i 0.994825 + 0.101603i \(0.0323973\pi\)
0.272809 + 0.962068i \(0.412047\pi\)
\(60\) 0 0
\(61\) −64.9040 23.6231i −0.136231 0.0495841i 0.273005 0.962013i \(-0.411982\pi\)
−0.409236 + 0.912429i \(0.634205\pi\)
\(62\) 0 0
\(63\) 144.807 + 490.544i 0.289587 + 0.980996i
\(64\) 0 0
\(65\) 37.1659 31.1859i 0.0709209 0.0595097i
\(66\) 0 0
\(67\) 109.760 622.479i 0.200139 1.13504i −0.704769 0.709437i \(-0.748949\pi\)
0.904908 0.425607i \(-0.139939\pi\)
\(68\) 0 0
\(69\) 84.2524 709.008i 0.146997 1.23702i
\(70\) 0 0
\(71\) −66.9800 + 116.013i −0.111959 + 0.193918i −0.916560 0.399897i \(-0.869046\pi\)
0.804601 + 0.593816i \(0.202379\pi\)
\(72\) 0 0
\(73\) −435.761 754.761i −0.698658 1.21011i −0.968932 0.247327i \(-0.920448\pi\)
0.270274 0.962783i \(-0.412886\pi\)
\(74\) 0 0
\(75\) −393.117 118.515i −0.605244 0.182466i
\(76\) 0 0
\(77\) 3.11484 1.13371i 0.00460999 0.00167790i
\(78\) 0 0
\(79\) 55.7069 + 315.930i 0.0793357 + 0.449935i 0.998436 + 0.0559108i \(0.0178062\pi\)
−0.919100 + 0.394024i \(0.871083\pi\)
\(80\) 0 0
\(81\) −214.441 + 696.747i −0.294158 + 0.955757i
\(82\) 0 0
\(83\) −197.919 1122.46i −0.261741 1.48440i −0.778159 0.628068i \(-0.783846\pi\)
0.516418 0.856337i \(-0.327265\pi\)
\(84\) 0 0
\(85\) 339.028 123.396i 0.432620 0.157461i
\(86\) 0 0
\(87\) −267.135 80.5346i −0.329194 0.0992438i
\(88\) 0 0
\(89\) −259.505 449.475i −0.309073 0.535329i 0.669087 0.743184i \(-0.266685\pi\)
−0.978160 + 0.207855i \(0.933352\pi\)
\(90\) 0 0
\(91\) 67.7684 117.378i 0.0780665 0.135215i
\(92\) 0 0
\(93\) 90.7863 763.992i 0.101227 0.851853i
\(94\) 0 0
\(95\) −154.213 + 874.583i −0.166546 + 0.944530i
\(96\) 0 0
\(97\) −1153.80 + 968.155i −1.20774 + 1.01341i −0.208366 + 0.978051i \(0.566814\pi\)
−0.999375 + 0.0353635i \(0.988741\pi\)
\(98\) 0 0
\(99\) 4.59294 + 1.10721i 0.00466271 + 0.00112403i
\(100\) 0 0
\(101\) −956.621 348.182i −0.942449 0.343023i −0.175317 0.984512i \(-0.556095\pi\)
−0.767132 + 0.641489i \(0.778317\pi\)
\(102\) 0 0
\(103\) 749.339 + 628.770i 0.716840 + 0.601500i 0.926509 0.376272i \(-0.122794\pi\)
−0.209669 + 0.977772i \(0.567239\pi\)
\(104\) 0 0
\(105\) 666.410 37.5292i 0.619381 0.0348807i
\(106\) 0 0
\(107\) −1665.48 −1.50475 −0.752374 0.658736i \(-0.771091\pi\)
−0.752374 + 0.658736i \(0.771091\pi\)
\(108\) 0 0
\(109\) 531.528 0.467075 0.233538 0.972348i \(-0.424970\pi\)
0.233538 + 0.972348i \(0.424970\pi\)
\(110\) 0 0
\(111\) −333.818 509.676i −0.285447 0.435823i
\(112\) 0 0
\(113\) −277.167 232.571i −0.230740 0.193614i 0.520086 0.854114i \(-0.325900\pi\)
−0.750826 + 0.660500i \(0.770344\pi\)
\(114\) 0 0
\(115\) −875.568 318.681i −0.709975 0.258410i
\(116\) 0 0
\(117\) 172.964 86.0352i 0.136672 0.0679826i
\(118\) 0 0
\(119\) 772.094 647.864i 0.594771 0.499072i
\(120\) 0 0
\(121\) −231.120 + 1310.75i −0.173644 + 0.984785i
\(122\) 0 0
\(123\) 669.119 + 500.142i 0.490507 + 0.366636i
\(124\) 0 0
\(125\) −691.720 + 1198.09i −0.494955 + 0.857287i
\(126\) 0 0
\(127\) −947.516 1641.15i −0.662035 1.14668i −0.980080 0.198603i \(-0.936360\pi\)
0.318045 0.948076i \(-0.396974\pi\)
\(128\) 0 0
\(129\) −80.5190 342.669i −0.0549559 0.233879i
\(130\) 0 0
\(131\) 2543.01 925.581i 1.69606 0.617316i 0.700695 0.713461i \(-0.252873\pi\)
0.995367 + 0.0961447i \(0.0306512\pi\)
\(132\) 0 0
\(133\) 430.811 + 2443.25i 0.280873 + 1.59291i
\(134\) 0 0
\(135\) 821.129 + 480.412i 0.523493 + 0.306276i
\(136\) 0 0
\(137\) −255.797 1450.70i −0.159520 0.904681i −0.954537 0.298094i \(-0.903649\pi\)
0.795017 0.606587i \(-0.207462\pi\)
\(138\) 0 0
\(139\) 2088.85 760.279i 1.27463 0.463928i 0.385979 0.922507i \(-0.373864\pi\)
0.888654 + 0.458579i \(0.151641\pi\)
\(140\) 0 0
\(141\) 2407.87 2262.98i 1.43815 1.35161i
\(142\) 0 0
\(143\) −0.625984 1.08424i −0.000366066 0.000634045i
\(144\) 0 0
\(145\) −182.053 + 315.326i −0.104267 + 0.180596i
\(146\) 0 0
\(147\) 75.6912 32.4776i 0.0424687 0.0182225i
\(148\) 0 0
\(149\) −387.086 + 2195.27i −0.212828 + 1.20701i 0.671809 + 0.740724i \(0.265518\pi\)
−0.884637 + 0.466281i \(0.845594\pi\)
\(150\) 0 0
\(151\) −1652.75 + 1386.82i −0.890720 + 0.747403i −0.968354 0.249579i \(-0.919708\pi\)
0.0776345 + 0.996982i \(0.475263\pi\)
\(152\) 0 0
\(153\) 1427.47 161.289i 0.754277 0.0852253i
\(154\) 0 0
\(155\) −943.470 343.395i −0.488912 0.177949i
\(156\) 0 0
\(157\) 2419.53 + 2030.22i 1.22993 + 1.03204i 0.998243 + 0.0592452i \(0.0188694\pi\)
0.231688 + 0.972790i \(0.425575\pi\)
\(158\) 0 0
\(159\) 85.6572 169.744i 0.0427237 0.0846637i
\(160\) 0 0
\(161\) −2602.98 −1.27418
\(162\) 0 0
\(163\) −1919.61 −0.922428 −0.461214 0.887289i \(-0.652586\pi\)
−0.461214 + 0.887289i \(0.652586\pi\)
\(164\) 0 0
\(165\) 2.77764 5.50433i 0.00131054 0.00259704i
\(166\) 0 0
\(167\) −531.834 446.262i −0.246435 0.206783i 0.511201 0.859461i \(-0.329201\pi\)
−0.757635 + 0.652678i \(0.773645\pi\)
\(168\) 0 0
\(169\) 2016.40 + 733.910i 0.917797 + 0.334051i
\(170\) 0 0
\(171\) −1413.04 + 3241.49i −0.631918 + 1.44961i
\(172\) 0 0
\(173\) 2035.08 1707.63i 0.894358 0.750456i −0.0747211 0.997204i \(-0.523807\pi\)
0.969080 + 0.246749i \(0.0793622\pi\)
\(174\) 0 0
\(175\) −259.931 + 1474.14i −0.112280 + 0.636769i
\(176\) 0 0
\(177\) 3581.00 1536.54i 1.52070 0.652504i
\(178\) 0 0
\(179\) −554.255 + 959.998i −0.231436 + 0.400858i −0.958231 0.285996i \(-0.907676\pi\)
0.726795 + 0.686854i \(0.241009\pi\)
\(180\) 0 0
\(181\) 1019.98 + 1766.65i 0.418864 + 0.725493i 0.995825 0.0912779i \(-0.0290952\pi\)
−0.576962 + 0.816771i \(0.695762\pi\)
\(182\) 0 0
\(183\) −261.523 + 245.787i −0.105641 + 0.0992845i
\(184\) 0 0
\(185\) −747.138 + 271.936i −0.296922 + 0.108071i
\(186\) 0 0
\(187\) −1.61667 9.16862i −0.000632208 0.00358543i
\(188\) 0 0
\(189\) 2614.60 + 476.582i 1.00627 + 0.183419i
\(190\) 0 0
\(191\) 187.456 + 1063.12i 0.0710149 + 0.402745i 0.999507 + 0.0313936i \(0.00999454\pi\)
−0.928492 + 0.371352i \(0.878894\pi\)
\(192\) 0 0
\(193\) −231.941 + 84.4197i −0.0865051 + 0.0314853i −0.384910 0.922954i \(-0.625768\pi\)
0.298405 + 0.954439i \(0.403545\pi\)
\(194\) 0 0
\(195\) −57.6667 245.415i −0.0211774 0.0901260i
\(196\) 0 0
\(197\) −2154.60 3731.87i −0.779232 1.34967i −0.932385 0.361466i \(-0.882276\pi\)
0.153154 0.988202i \(-0.451057\pi\)
\(198\) 0 0
\(199\) 1279.40 2215.99i 0.455751 0.789383i −0.542980 0.839745i \(-0.682704\pi\)
0.998731 + 0.0503621i \(0.0160376\pi\)
\(200\) 0 0
\(201\) −2630.72 1966.36i −0.923166 0.690033i
\(202\) 0 0
\(203\) −176.631 + 1001.72i −0.0610692 + 0.346340i
\(204\) 0 0
\(205\) 835.117 700.746i 0.284522 0.238743i
\(206\) 0 0
\(207\) −3091.83 2050.59i −1.03815 0.688532i
\(208\) 0 0
\(209\) 21.5347 + 7.83798i 0.00712720 + 0.00259409i
\(210\) 0 0
\(211\) −1331.28 1117.08i −0.434357 0.364468i 0.399236 0.916848i \(-0.369275\pi\)
−0.833593 + 0.552380i \(0.813720\pi\)
\(212\) 0 0
\(213\) 381.382 + 582.298i 0.122685 + 0.187316i
\(214\) 0 0
\(215\) −459.361 −0.145712
\(216\) 0 0
\(217\) −2804.85 −0.877444
\(218\) 0 0
\(219\) −4521.40 + 254.625i −1.39511 + 0.0785660i
\(220\) 0 0
\(221\) −291.617 244.696i −0.0887615 0.0744797i
\(222\) 0 0
\(223\) −3665.27 1334.05i −1.10065 0.400603i −0.273093 0.961988i \(-0.588047\pi\)
−0.827555 + 0.561385i \(0.810269\pi\)
\(224\) 0 0
\(225\) −1470.05 + 1546.22i −0.435572 + 0.458139i
\(226\) 0 0
\(227\) 2227.65 1869.22i 0.651342 0.546541i −0.256136 0.966641i \(-0.582449\pi\)
0.907478 + 0.420100i \(0.138005\pi\)
\(228\) 0 0
\(229\) 862.951 4894.04i 0.249019 1.41226i −0.561950 0.827171i \(-0.689949\pi\)
0.810970 0.585088i \(-0.198940\pi\)
\(230\) 0 0
\(231\) 2.03245 17.1036i 0.000578897 0.00487158i
\(232\) 0 0
\(233\) −254.515 + 440.832i −0.0715614 + 0.123948i −0.899586 0.436744i \(-0.856132\pi\)
0.828024 + 0.560692i \(0.189465\pi\)
\(234\) 0 0
\(235\) −2156.09 3734.46i −0.598502 1.03664i
\(236\) 0 0
\(237\) 1595.99 + 481.152i 0.437430 + 0.131874i
\(238\) 0 0
\(239\) 4164.81 1515.87i 1.12719 0.410265i 0.289921 0.957051i \(-0.406371\pi\)
0.837272 + 0.546786i \(0.184149\pi\)
\(240\) 0 0
\(241\) 90.6192 + 513.927i 0.0242211 + 0.137365i 0.994520 0.104543i \(-0.0333380\pi\)
−0.970299 + 0.241908i \(0.922227\pi\)
\(242\) 0 0
\(243\) 2730.19 + 2625.83i 0.720747 + 0.693198i
\(244\) 0 0
\(245\) −18.6647 105.853i −0.00486711 0.0276027i
\(246\) 0 0
\(247\) 880.532 320.487i 0.226830 0.0825592i
\(248\) 0 0
\(249\) −5670.35 1709.47i −1.44315 0.435073i
\(250\) 0 0
\(251\) 3252.48 + 5633.46i 0.817907 + 1.41666i 0.907221 + 0.420653i \(0.138199\pi\)
−0.0893143 + 0.996003i \(0.528468\pi\)
\(252\) 0 0
\(253\) −12.0220 + 20.8227i −0.00298742 + 0.00517437i
\(254\) 0 0
\(255\) 221.217 1861.60i 0.0543260 0.457168i
\(256\) 0 0
\(257\) −993.934 + 5636.88i −0.241245 + 1.36817i 0.587810 + 0.808999i \(0.299990\pi\)
−0.829054 + 0.559168i \(0.811121\pi\)
\(258\) 0 0
\(259\) −1701.51 + 1427.74i −0.408212 + 0.342531i
\(260\) 0 0
\(261\) −998.946 + 1050.70i −0.236909 + 0.249183i
\(262\) 0 0
\(263\) −2466.09 897.584i −0.578197 0.210446i 0.0363333 0.999340i \(-0.488432\pi\)
−0.614530 + 0.788893i \(0.710654\pi\)
\(264\) 0 0
\(265\) −190.071 159.489i −0.0440603 0.0369710i
\(266\) 0 0
\(267\) −2692.59 + 151.634i −0.617167 + 0.0347561i
\(268\) 0 0
\(269\) 2872.70 0.651122 0.325561 0.945521i \(-0.394447\pi\)
0.325561 + 0.945521i \(0.394447\pi\)
\(270\) 0 0
\(271\) 3701.45 0.829695 0.414847 0.909891i \(-0.363835\pi\)
0.414847 + 0.909891i \(0.363835\pi\)
\(272\) 0 0
\(273\) −385.871 589.151i −0.0855457 0.130612i
\(274\) 0 0
\(275\) 10.5920 + 8.88773i 0.00232262 + 0.00194891i
\(276\) 0 0
\(277\) 1213.14 + 441.548i 0.263143 + 0.0957763i 0.470223 0.882548i \(-0.344174\pi\)
−0.207079 + 0.978324i \(0.566396\pi\)
\(278\) 0 0
\(279\) −3331.60 2209.62i −0.714903 0.474145i
\(280\) 0 0
\(281\) −3031.24 + 2543.52i −0.643519 + 0.539977i −0.905097 0.425206i \(-0.860202\pi\)
0.261578 + 0.965182i \(0.415757\pi\)
\(282\) 0 0
\(283\) −174.948 + 992.178i −0.0367476 + 0.208406i −0.997653 0.0684704i \(-0.978188\pi\)
0.960906 + 0.276876i \(0.0892992\pi\)
\(284\) 0 0
\(285\) 3696.15 + 2762.74i 0.768215 + 0.574212i
\(286\) 0 0
\(287\) 1522.75 2637.49i 0.313189 0.542460i
\(288\) 0 0
\(289\) 1041.07 + 1803.19i 0.211901 + 0.367024i
\(290\) 0 0
\(291\) 1790.24 + 7618.84i 0.360639 + 1.53479i
\(292\) 0 0
\(293\) 7284.28 2651.26i 1.45240 0.528629i 0.509137 0.860686i \(-0.329965\pi\)
0.943259 + 0.332057i \(0.107743\pi\)
\(294\) 0 0
\(295\) −883.036 5007.95i −0.174279 0.988387i
\(296\) 0 0
\(297\) 15.8881 18.7146i 0.00310412 0.00365633i
\(298\) 0 0
\(299\) 170.720 + 968.201i 0.0330200 + 0.187266i
\(300\) 0 0
\(301\) −1205.89 + 438.907i −0.230918 + 0.0840471i
\(302\) 0 0
\(303\) −3854.60 + 3622.65i −0.730828 + 0.686851i
\(304\) 0 0
\(305\) 234.178 + 405.608i 0.0439639 + 0.0761477i
\(306\) 0 0
\(307\) 4498.36 7791.39i 0.836271 1.44846i −0.0567205 0.998390i \(-0.518064\pi\)
0.892991 0.450074i \(-0.148602\pi\)
\(308\) 0 0
\(309\) 4671.00 2004.24i 0.859948 0.368987i
\(310\) 0 0
\(311\) −933.478 + 5294.02i −0.170202 + 0.965261i 0.773336 + 0.633996i \(0.218587\pi\)
−0.943538 + 0.331265i \(0.892525\pi\)
\(312\) 0 0
\(313\) 2795.71 2345.88i 0.504865 0.423632i −0.354453 0.935074i \(-0.615333\pi\)
0.859318 + 0.511442i \(0.170888\pi\)
\(314\) 0 0
\(315\) 1385.93 3179.31i 0.247900 0.568678i
\(316\) 0 0
\(317\) 9666.93 + 3518.47i 1.71277 + 0.623398i 0.997175 0.0751153i \(-0.0239325\pi\)
0.715597 + 0.698513i \(0.246155\pi\)
\(318\) 0 0
\(319\) 7.19757 + 6.03948i 0.00126328 + 0.00106002i
\(320\) 0 0
\(321\) −3898.80 + 7726.10i −0.677912 + 1.34339i
\(322\) 0 0
\(323\) 6968.17 1.20037
\(324\) 0 0
\(325\) 565.367 0.0964951
\(326\) 0 0
\(327\) 1244.28 2465.74i 0.210425 0.416990i
\(328\) 0 0
\(329\) −9228.23 7743.40i −1.54641 1.29759i
\(330\) 0 0
\(331\) 807.479 + 293.898i 0.134088 + 0.0488039i 0.408192 0.912896i \(-0.366159\pi\)
−0.274105 + 0.961700i \(0.588381\pi\)
\(332\) 0 0
\(333\) −3145.82 + 355.444i −0.517687 + 0.0584931i
\(334\) 0 0
\(335\) −3283.35 + 2755.06i −0.535489 + 0.449329i
\(336\) 0 0
\(337\) 475.226 2695.14i 0.0768166 0.435648i −0.922008 0.387171i \(-0.873452\pi\)
0.998824 0.0484770i \(-0.0154368\pi\)
\(338\) 0 0
\(339\) −1727.72 + 741.331i −0.276805 + 0.118772i
\(340\) 0 0
\(341\) −12.9543 + 22.4376i −0.00205723 + 0.00356323i
\(342\) 0 0
\(343\) 3098.65 + 5367.02i 0.487788 + 0.844874i
\(344\) 0 0
\(345\) −3528.01 + 3315.71i −0.550555 + 0.517426i
\(346\) 0 0
\(347\) 9139.24 3326.41i 1.41389 0.514614i 0.481622 0.876379i \(-0.340048\pi\)
0.932269 + 0.361765i \(0.117826\pi\)
\(348\) 0 0
\(349\) −244.747 1388.03i −0.0375387 0.212892i 0.960269 0.279077i \(-0.0900285\pi\)
−0.997807 + 0.0661847i \(0.978917\pi\)
\(350\) 0 0
\(351\) 5.78654 1003.78i 0.000879951 0.152643i
\(352\) 0 0
\(353\) 145.344 + 824.287i 0.0219147 + 0.124284i 0.993803 0.111160i \(-0.0354566\pi\)
−0.971888 + 0.235444i \(0.924345\pi\)
\(354\) 0 0
\(355\) 853.594 310.683i 0.127617 0.0464488i
\(356\) 0 0
\(357\) −1197.98 5098.33i −0.177602 0.755833i
\(358\) 0 0
\(359\) 2517.07 + 4359.69i 0.370044 + 0.640935i 0.989572 0.144040i \(-0.0460093\pi\)
−0.619528 + 0.784975i \(0.712676\pi\)
\(360\) 0 0
\(361\) −5146.58 + 8914.13i −0.750339 + 1.29963i
\(362\) 0 0
\(363\) 5539.47 + 4140.55i 0.800956 + 0.598685i
\(364\) 0 0
\(365\) −1026.22 + 5819.97i −0.147163 + 0.834606i
\(366\) 0 0
\(367\) 4798.61 4026.51i 0.682521 0.572703i −0.234221 0.972183i \(-0.575254\pi\)
0.916742 + 0.399480i \(0.130809\pi\)
\(368\) 0 0
\(369\) 3886.51 1933.21i 0.548303 0.272734i
\(370\) 0 0
\(371\) −651.351 237.073i −0.0911495 0.0331757i
\(372\) 0 0
\(373\) −9425.34 7908.80i −1.30838 1.09786i −0.988632 0.150359i \(-0.951957\pi\)
−0.319749 0.947502i \(-0.603598\pi\)
\(374\) 0 0
\(375\) 3938.63 + 6013.54i 0.542374 + 0.828101i
\(376\) 0 0
\(377\) 384.183 0.0524840
\(378\) 0 0
\(379\) −4996.58 −0.677195 −0.338598 0.940931i \(-0.609953\pi\)
−0.338598 + 0.940931i \(0.609953\pi\)
\(380\) 0 0
\(381\) −9831.30 + 553.655i −1.32198 + 0.0744477i
\(382\) 0 0
\(383\) −10520.9 8828.08i −1.40364 1.17779i −0.959458 0.281851i \(-0.909052\pi\)
−0.444177 0.895939i \(-0.646504\pi\)
\(384\) 0 0
\(385\) −21.1216 7.68763i −0.00279599 0.00101766i
\(386\) 0 0
\(387\) −1778.12 428.647i −0.233558 0.0563032i
\(388\) 0 0
\(389\) −6156.52 + 5165.93i −0.802437 + 0.673324i −0.948790 0.315908i \(-0.897691\pi\)
0.146353 + 0.989232i \(0.453246\pi\)
\(390\) 0 0
\(391\) −1269.53 + 7199.87i −0.164202 + 0.931235i
\(392\) 0 0
\(393\) 1659.33 13963.7i 0.212982 1.79230i
\(394\) 0 0
\(395\) 1087.68 1883.91i 0.138549 0.239974i
\(396\) 0 0
\(397\) 3689.69 + 6390.72i 0.466448 + 0.807912i 0.999266 0.0383180i \(-0.0122000\pi\)
−0.532817 + 0.846230i \(0.678867\pi\)
\(398\) 0 0
\(399\) 12342.6 + 3721.00i 1.54863 + 0.466875i
\(400\) 0 0
\(401\) −7940.72 + 2890.19i −0.988880 + 0.359923i −0.785286 0.619133i \(-0.787484\pi\)
−0.203593 + 0.979056i \(0.565262\pi\)
\(402\) 0 0
\(403\) 183.959 + 1043.29i 0.0227386 + 0.128957i
\(404\) 0 0
\(405\) 4150.83 2684.57i 0.509275 0.329376i
\(406\) 0 0
\(407\) 3.56277 + 20.2055i 0.000433907 + 0.00246081i
\(408\) 0 0
\(409\) −12312.8 + 4481.48i −1.48857 + 0.541796i −0.953073 0.302739i \(-0.902099\pi\)
−0.535500 + 0.844535i \(0.679877\pi\)
\(410\) 0 0
\(411\) −7328.53 2209.37i −0.879537 0.265159i
\(412\) 0 0
\(413\) −7103.06 12302.9i −0.846292 1.46582i
\(414\) 0 0
\(415\) −3864.37 + 6693.28i −0.457095 + 0.791711i
\(416\) 0 0
\(417\) 1362.98 11469.9i 0.160061 1.34696i
\(418\) 0 0
\(419\) 978.770 5550.88i 0.114119 0.647204i −0.873063 0.487607i \(-0.837870\pi\)
0.987182 0.159596i \(-0.0510192\pi\)
\(420\) 0 0
\(421\) 8502.48 7134.42i 0.984288 0.825916i −0.000442623 1.00000i \(-0.500141\pi\)
0.984731 + 0.174084i \(0.0556964\pi\)
\(422\) 0 0
\(423\) −4861.17 16467.5i −0.558766 1.89285i
\(424\) 0 0
\(425\) 3950.71 + 1437.94i 0.450912 + 0.164119i
\(426\) 0 0
\(427\) 1002.30 + 841.027i 0.113594 + 0.0953165i
\(428\) 0 0
\(429\) −6.49513 + 0.365776i −0.000730973 + 4.11651e-5i
\(430\) 0 0
\(431\) −3944.54 −0.440839 −0.220420 0.975405i \(-0.570743\pi\)
−0.220420 + 0.975405i \(0.570743\pi\)
\(432\) 0 0
\(433\) 1909.68 0.211948 0.105974 0.994369i \(-0.466204\pi\)
0.105974 + 0.994369i \(0.466204\pi\)
\(434\) 0 0
\(435\) 1036.61 + 1582.70i 0.114256 + 0.174448i
\(436\) 0 0
\(437\) −13785.7 11567.5i −1.50906 1.26625i
\(438\) 0 0
\(439\) 7600.00 + 2766.17i 0.826260 + 0.300734i 0.720323 0.693639i \(-0.243994\pi\)
0.105937 + 0.994373i \(0.466216\pi\)
\(440\) 0 0
\(441\) 26.5266 427.157i 0.00286434 0.0461243i
\(442\) 0 0
\(443\) −4879.88 + 4094.71i −0.523364 + 0.439155i −0.865803 0.500386i \(-0.833192\pi\)
0.342439 + 0.939540i \(0.388747\pi\)
\(444\) 0 0
\(445\) −611.133 + 3465.91i −0.0651022 + 0.369213i
\(446\) 0 0
\(447\) 9277.64 + 6934.70i 0.981694 + 0.733780i
\(448\) 0 0
\(449\) 6820.97 11814.3i 0.716929 1.24176i −0.245281 0.969452i \(-0.578880\pi\)
0.962211 0.272306i \(-0.0877864\pi\)
\(450\) 0 0
\(451\) −14.0659 24.3628i −0.00146859 0.00254368i
\(452\) 0 0
\(453\) 2564.41 + 10913.5i 0.265975 + 1.13192i
\(454\) 0 0
\(455\) −863.641 + 314.340i −0.0889849 + 0.0323878i
\(456\) 0 0
\(457\) −2344.18 13294.5i −0.239947 1.36081i −0.831940 0.554865i \(-0.812770\pi\)
0.591993 0.805943i \(-0.298341\pi\)
\(458\) 0 0
\(459\) 2593.43 6999.57i 0.263727 0.711790i
\(460\) 0 0
\(461\) 2081.24 + 11803.3i 0.210267 + 1.19248i 0.888933 + 0.458037i \(0.151447\pi\)
−0.678666 + 0.734447i \(0.737442\pi\)
\(462\) 0 0
\(463\) −6171.60 + 2246.28i −0.619479 + 0.225472i −0.632646 0.774442i \(-0.718031\pi\)
0.0131668 + 0.999913i \(0.495809\pi\)
\(464\) 0 0
\(465\) −3801.61 + 3572.85i −0.379130 + 0.356316i
\(466\) 0 0
\(467\) 2152.08 + 3727.52i 0.213247 + 0.369355i 0.952729 0.303822i \(-0.0982627\pi\)
−0.739482 + 0.673177i \(0.764929\pi\)
\(468\) 0 0
\(469\) −5986.88 + 10369.6i −0.589442 + 1.02094i
\(470\) 0 0
\(471\) 15082.1 6471.45i 1.47547 0.633097i
\(472\) 0 0
\(473\) −2.05839 + 11.6737i −0.000200095 + 0.00113479i
\(474\) 0 0
\(475\) −7927.63 + 6652.07i −0.765778 + 0.642564i
\(476\) 0 0
\(477\) −586.915 794.721i −0.0563375 0.0762847i
\(478\) 0 0
\(479\) −14016.5 5101.57i −1.33701 0.486632i −0.428141 0.903712i \(-0.640831\pi\)
−0.908870 + 0.417080i \(0.863053\pi\)
\(480\) 0 0
\(481\) 642.656 + 539.252i 0.0609201 + 0.0511181i
\(482\) 0 0
\(483\) −6093.44 + 12075.1i −0.574040 + 1.13755i
\(484\) 0 0
\(485\) 10213.3 0.956214
\(486\) 0 0
\(487\) 21294.9 1.98144 0.990722 0.135901i \(-0.0433931\pi\)
0.990722 + 0.135901i \(0.0433931\pi\)
\(488\) 0 0
\(489\) −4493.71 + 8905.01i −0.415568 + 0.823514i
\(490\) 0 0
\(491\) −8618.26 7231.58i −0.792132 0.664677i 0.154140 0.988049i \(-0.450739\pi\)
−0.946272 + 0.323372i \(0.895184\pi\)
\(492\) 0 0
\(493\) 2684.63 + 977.124i 0.245252 + 0.0892646i
\(494\) 0 0
\(495\) −19.0321 25.7707i −0.00172814 0.00234001i
\(496\) 0 0
\(497\) 1943.96 1631.17i 0.175449 0.147220i
\(498\) 0 0
\(499\) 137.225 778.243i 0.0123107 0.0698175i −0.978033 0.208448i \(-0.933159\pi\)
0.990344 + 0.138630i \(0.0442700\pi\)
\(500\) 0 0
\(501\) −3315.19 + 1422.48i −0.295632 + 0.126850i
\(502\) 0 0
\(503\) −5970.64 + 10341.5i −0.529260 + 0.916705i 0.470158 + 0.882583i \(0.344197\pi\)
−0.999418 + 0.0341229i \(0.989136\pi\)
\(504\) 0 0
\(505\) 3451.55 + 5978.26i 0.304143 + 0.526791i
\(506\) 0 0
\(507\) 8124.87 7635.96i 0.711712 0.668885i
\(508\) 0 0
\(509\) 10169.7 3701.49i 0.885592 0.322329i 0.141128 0.989991i \(-0.454927\pi\)
0.744464 + 0.667662i \(0.232705\pi\)
\(510\) 0 0
\(511\) 2866.86 + 16258.8i 0.248185 + 1.40752i
\(512\) 0 0
\(513\) 11729.3 + 14143.2i 1.00947 + 1.21723i
\(514\) 0 0
\(515\) −1151.82 6532.30i −0.0985539 0.558927i
\(516\) 0 0
\(517\) −104.565 + 38.0585i −0.00889509 + 0.00323755i
\(518\) 0 0
\(519\) −3157.63 13438.1i −0.267061 1.13655i
\(520\) 0 0
\(521\) 6195.35 + 10730.7i 0.520966 + 0.902339i 0.999703 + 0.0243806i \(0.00776137\pi\)
−0.478737 + 0.877958i \(0.658905\pi\)
\(522\) 0 0
\(523\) −4693.00 + 8128.52i −0.392372 + 0.679609i −0.992762 0.120099i \(-0.961679\pi\)
0.600390 + 0.799708i \(0.295012\pi\)
\(524\) 0 0
\(525\) 6230.00 + 4656.69i 0.517904 + 0.387114i
\(526\) 0 0
\(527\) −1367.98 + 7758.23i −0.113075 + 0.641278i
\(528\) 0 0
\(529\) 5143.32 4315.76i 0.422727 0.354710i
\(530\) 0 0
\(531\) 1254.99 20209.1i 0.102565 1.65160i
\(532\) 0 0
\(533\) −1080.91 393.418i −0.0878411 0.0319715i
\(534\) 0 0
\(535\) 8651.35 + 7259.34i 0.699122 + 0.586633i
\(536\) 0 0
\(537\) 3155.91 + 4818.47i 0.253608 + 0.387211i
\(538\) 0 0
\(539\) −2.77366 −0.000221651
\(540\) 0 0
\(541\) 1596.07 0.126840 0.0634202 0.997987i \(-0.479799\pi\)
0.0634202 + 0.997987i \(0.479799\pi\)
\(542\) 0 0
\(543\) 10583.1 595.995i 0.836402 0.0471024i
\(544\) 0 0
\(545\) −2761.03 2316.78i −0.217008 0.182091i
\(546\) 0 0
\(547\) −9720.40 3537.94i −0.759807 0.276547i −0.0670804 0.997748i \(-0.521368\pi\)
−0.692726 + 0.721201i \(0.743591\pi\)
\(548\) 0 0
\(549\) 527.982 + 1788.57i 0.0410450 + 0.139043i
\(550\) 0 0
\(551\) −5387.06 + 4520.28i −0.416509 + 0.349493i
\(552\) 0 0
\(553\) 1055.28 5984.77i 0.0811481 0.460214i
\(554\) 0 0
\(555\) −487.510 + 4102.53i −0.0372858 + 0.313771i
\(556\) 0 0
\(557\) 4716.05 8168.44i 0.358753 0.621379i −0.629000 0.777406i \(-0.716535\pi\)
0.987753 + 0.156027i \(0.0498687\pi\)
\(558\) 0 0
\(559\) 242.345 + 419.753i 0.0183365 + 0.0317597i
\(560\) 0 0
\(561\) −46.3174 13.9636i −0.00348578 0.00105088i
\(562\) 0 0
\(563\) 20619.8 7504.98i 1.54355 0.561807i 0.576658 0.816986i \(-0.304356\pi\)
0.966894 + 0.255179i \(0.0821343\pi\)
\(564\) 0 0
\(565\) 426.038 + 2416.18i 0.0317231 + 0.179911i
\(566\) 0 0
\(567\) 8331.49 11013.4i 0.617089 0.815729i
\(568\) 0 0
\(569\) 1838.39 + 10426.1i 0.135447 + 0.768160i 0.974547 + 0.224182i \(0.0719711\pi\)
−0.839100 + 0.543977i \(0.816918\pi\)
\(570\) 0 0
\(571\) −2257.85 + 821.791i −0.165478 + 0.0602292i −0.423431 0.905928i \(-0.639174\pi\)
0.257953 + 0.966158i \(0.416952\pi\)
\(572\) 0 0
\(573\) 5370.58 + 1619.10i 0.391552 + 0.118043i
\(574\) 0 0
\(575\) −5428.93 9403.18i −0.393743 0.681982i
\(576\) 0 0
\(577\) 7640.34 13233.5i 0.551251 0.954794i −0.446934 0.894567i \(-0.647484\pi\)
0.998185 0.0602273i \(-0.0191825\pi\)
\(578\) 0 0
\(579\) −151.342 + 1273.59i −0.0108628 + 0.0914137i
\(580\) 0 0
\(581\) −3749.26 + 21263.1i −0.267720 + 1.51832i
\(582\) 0 0
\(583\) −4.90478 + 4.11560i −0.000348431 + 0.000292368i
\(584\) 0 0
\(585\) −1273.47 306.991i −0.0900024 0.0216966i
\(586\) 0 0
\(587\) −12260.7 4462.53i −0.862101 0.313779i −0.127137 0.991885i \(-0.540579\pi\)
−0.734964 + 0.678106i \(0.762801\pi\)
\(588\) 0 0
\(589\) −14854.7 12464.6i −1.03918 0.871978i
\(590\) 0 0
\(591\) −22355.8 + 1258.98i −1.55600 + 0.0876268i
\(592\) 0 0
\(593\) 16271.5 1.12680 0.563400 0.826185i \(-0.309493\pi\)
0.563400 + 0.826185i \(0.309493\pi\)
\(594\) 0 0
\(595\) −6834.50 −0.470903
\(596\) 0 0
\(597\) −7284.87 11122.6i −0.499414 0.762509i
\(598\) 0 0
\(599\) −12021.9 10087.6i −0.820038 0.688094i 0.132943 0.991124i \(-0.457557\pi\)
−0.952981 + 0.303030i \(0.902002\pi\)
\(600\) 0 0
\(601\) 9308.20 + 3387.91i 0.631763 + 0.229943i 0.637998 0.770038i \(-0.279763\pi\)
−0.00623571 + 0.999981i \(0.501985\pi\)
\(602\) 0 0
\(603\) −15280.3 + 7600.64i −1.03194 + 0.513303i
\(604\) 0 0
\(605\) 6913.73 5801.31i 0.464600 0.389846i
\(606\) 0 0
\(607\) −2791.61 + 15832.0i −0.186669 + 1.05865i 0.737123 + 0.675758i \(0.236184\pi\)
−0.923792 + 0.382894i \(0.874927\pi\)
\(608\) 0 0
\(609\) 4233.47 + 3164.36i 0.281689 + 0.210552i
\(610\) 0 0
\(611\) −2274.98 + 3940.38i −0.150631 + 0.260901i
\(612\) 0 0
\(613\) −2802.75 4854.51i −0.184669 0.319856i 0.758796 0.651328i \(-0.225788\pi\)
−0.943465 + 0.331472i \(0.892455\pi\)
\(614\) 0 0
\(615\) −1295.77 5514.48i −0.0849602 0.361570i
\(616\) 0 0
\(617\) 3393.93 1235.29i 0.221450 0.0806012i −0.228913 0.973447i \(-0.573517\pi\)
0.450362 + 0.892846i \(0.351295\pi\)
\(618\) 0 0
\(619\) −3759.85 21323.2i −0.244138 1.38457i −0.822487 0.568784i \(-0.807414\pi\)
0.578349 0.815789i \(-0.303697\pi\)
\(620\) 0 0
\(621\) −16750.4 + 9542.55i −1.08240 + 0.616633i
\(622\) 0 0
\(623\) 1707.27 + 9682.42i 0.109792 + 0.622661i
\(624\) 0 0
\(625\) −466.380 + 169.748i −0.0298483 + 0.0108639i
\(626\) 0 0
\(627\) 86.7717 81.5503i 0.00552684 0.00519426i
\(628\) 0 0
\(629\) 3119.28 + 5402.74i 0.197732 + 0.342482i
\(630\) 0 0
\(631\) 4449.63 7706.98i 0.280724 0.486228i −0.690839 0.723008i \(-0.742759\pi\)
0.971563 + 0.236780i \(0.0760921\pi\)
\(632\) 0 0
\(633\) −8298.55 + 3560.75i −0.521070 + 0.223581i
\(634\) 0 0
\(635\) −2231.40 + 12654.9i −0.139449 + 0.790857i
\(636\) 0 0
\(637\) −86.8787 + 72.8999i −0.00540386 + 0.00453438i
\(638\) 0 0
\(639\) 3594.05 406.090i 0.222502 0.0251403i
\(640\) 0 0
\(641\) 20334.9 + 7401.30i 1.25301 + 0.456059i 0.881418 0.472337i \(-0.156589\pi\)
0.371593 + 0.928396i \(0.378812\pi\)
\(642\) 0 0
\(643\) −6779.27 5688.49i −0.415783 0.348883i 0.410773 0.911738i \(-0.365259\pi\)
−0.826556 + 0.562854i \(0.809703\pi\)
\(644\) 0 0
\(645\) −1075.34 + 2130.96i −0.0656457 + 0.130087i
\(646\) 0 0
\(647\) −6445.91 −0.391677 −0.195838 0.980636i \(-0.562743\pi\)
−0.195838 + 0.980636i \(0.562743\pi\)
\(648\) 0 0
\(649\) −131.223 −0.00793678
\(650\) 0 0
\(651\) −6566.00 + 13011.6i −0.395302 + 0.783354i
\(652\) 0 0
\(653\) 2338.71 + 1962.41i 0.140154 + 0.117603i 0.710170 0.704031i \(-0.248618\pi\)
−0.570015 + 0.821634i \(0.693063\pi\)
\(654\) 0 0
\(655\) −17244.0 6276.32i −1.02867 0.374406i
\(656\) 0 0
\(657\) −9403.17 + 21570.7i −0.558375 + 1.28090i
\(658\) 0 0
\(659\) 11991.4 10062.0i 0.708828 0.594777i −0.215442 0.976517i \(-0.569119\pi\)
0.924270 + 0.381739i \(0.124675\pi\)
\(660\) 0 0
\(661\) 5685.36 32243.3i 0.334546 1.89730i −0.0971257 0.995272i \(-0.530965\pi\)
0.431671 0.902031i \(-0.357924\pi\)
\(662\) 0 0
\(663\) −1817.79 + 779.981i −0.106482 + 0.0456892i
\(664\) 0 0
\(665\) 8411.56 14569.3i 0.490506 0.849581i
\(666\) 0 0
\(667\) −3689.12 6389.74i −0.214158 0.370932i
\(668\) 0 0
\(669\) −14768.8 + 13880.1i −0.853505 + 0.802146i
\(670\) 0 0
\(671\) 11.3570 4.13362i 0.000653402 0.000237819i
\(672\) 0 0
\(673\) −959.177 5439.76i −0.0549384 0.311571i 0.944939 0.327247i \(-0.106121\pi\)
−0.999877 + 0.0156762i \(0.995010\pi\)
\(674\) 0 0
\(675\) 3731.53 + 10439.1i 0.212780 + 0.595263i
\(676\) 0 0
\(677\) −621.476 3524.57i −0.0352810 0.200089i 0.962072 0.272794i \(-0.0879478\pi\)
−0.997353 + 0.0727055i \(0.976837\pi\)
\(678\) 0 0
\(679\) 26811.4 9758.57i 1.51536 0.551546i
\(680\) 0 0
\(681\) −3456.44 14709.8i −0.194495 0.827723i
\(682\) 0 0
\(683\) 813.215 + 1408.53i 0.0455590 + 0.0789105i 0.887906 0.460026i \(-0.152160\pi\)
−0.842347 + 0.538936i \(0.818826\pi\)
\(684\) 0 0
\(685\) −4994.42 + 8650.59i −0.278580 + 0.482514i
\(686\) 0 0
\(687\) −20683.1 15459.9i −1.14863 0.858561i
\(688\) 0 0
\(689\) −45.4614 + 257.824i −0.00251370 + 0.0142559i
\(690\) 0 0
\(691\) −771.115 + 647.042i −0.0424524 + 0.0356218i −0.663767 0.747939i \(-0.731043\pi\)
0.621315 + 0.783561i \(0.286599\pi\)
\(692\) 0 0
\(693\) −74.5851 49.4671i −0.00408839 0.00271154i
\(694\) 0 0
\(695\) −14164.4 5155.41i −0.773073 0.281376i
\(696\) 0 0
\(697\) −6552.63 5498.31i −0.356096 0.298800i
\(698\) 0 0
\(699\) 1449.20 + 2212.65i 0.0784174 + 0.119728i
\(700\) 0 0
\(701\) −30593.6 −1.64837 −0.824183 0.566324i \(-0.808365\pi\)
−0.824183 + 0.566324i \(0.808365\pi\)
\(702\) 0 0
\(703\) −15356.2 −0.823855
\(704\) 0 0
\(705\) −22371.3 + 1259.85i −1.19511 + 0.0673032i
\(706\) 0 0
\(707\) 14772.9 + 12395.9i 0.785843 + 0.659401i
\(708\) 0 0
\(709\) 15119.8 + 5503.15i 0.800896 + 0.291502i 0.709858 0.704345i \(-0.248759\pi\)
0.0910385 + 0.995847i \(0.470981\pi\)
\(710\) 0 0
\(711\) 5968.18 6277.40i 0.314802 0.331112i
\(712\) 0 0
\(713\) 15585.5 13077.8i 0.818626 0.686909i
\(714\) 0 0
\(715\) −1.47419 + 8.36055i −7.71072e−5 + 0.000437296i
\(716\) 0 0
\(717\) 2717.55 22869.0i 0.141547 1.19115i
\(718\) 0 0
\(719\) −13641.9 + 23628.5i −0.707591 + 1.22558i 0.258157 + 0.966103i \(0.416885\pi\)
−0.965748 + 0.259481i \(0.916449\pi\)
\(720\) 0 0
\(721\) −9265.12 16047.7i −0.478573 0.828913i
\(722\) 0 0
\(723\) 2596.22 + 782.697i 0.133547 + 0.0402611i
\(724\) 0 0
\(725\) −3987.08 + 1451.18i −0.204243 + 0.0743385i
\(726\) 0 0
\(727\) 3276.60 + 18582.5i 0.167156 + 0.947989i 0.946814 + 0.321783i \(0.104282\pi\)
−0.779657 + 0.626206i \(0.784607\pi\)
\(728\) 0 0
\(729\) 18572.4 6518.29i 0.943573 0.331164i
\(730\) 0 0
\(731\) 625.883 + 3549.56i 0.0316677 + 0.179597i
\(732\) 0 0
\(733\) −7560.06 + 2751.64i −0.380951 + 0.138655i −0.525396 0.850858i \(-0.676083\pi\)
0.144445 + 0.989513i \(0.453860\pi\)
\(734\) 0 0
\(735\) −534.739 161.211i −0.0268356 0.00809026i
\(736\) 0 0
\(737\) 55.3015 + 95.7850i 0.00276398 + 0.00478736i
\(738\) 0 0
\(739\) 13107.9 22703.6i 0.652480 1.13013i −0.330040 0.943967i \(-0.607062\pi\)
0.982519 0.186161i \(-0.0596045\pi\)
\(740\) 0 0
\(741\) 574.550 4835.00i 0.0284840 0.239700i
\(742\) 0 0
\(743\) 4176.05 23683.6i 0.206197 1.16940i −0.689348 0.724431i \(-0.742103\pi\)
0.895545 0.444971i \(-0.146786\pi\)
\(744\) 0 0
\(745\) 11579.3 9716.17i 0.569439 0.477816i
\(746\) 0 0
\(747\) −21204.2 + 22302.8i −1.03858 + 1.09239i
\(748\) 0 0
\(749\) 29647.1 + 10790.7i 1.44630 + 0.526412i
\(750\) 0 0
\(751\) 29364.6 + 24639.8i 1.42680 + 1.19723i 0.947573 + 0.319538i \(0.103528\pi\)
0.479228 + 0.877690i \(0.340917\pi\)
\(752\) 0 0
\(753\) 33747.3 1900.50i 1.63323 0.0919760i
\(754\) 0 0
\(755\) 14630.0 0.705217
\(756\) 0 0
\(757\) −13077.8 −0.627900 −0.313950 0.949440i \(-0.601652\pi\)
−0.313950 + 0.949440i \(0.601652\pi\)
\(758\) 0 0
\(759\) 68.4530 + 104.515i 0.00327363 + 0.00499821i
\(760\) 0 0
\(761\) 23600.6 + 19803.3i 1.12421 + 0.943322i 0.998809 0.0487844i \(-0.0155347\pi\)
0.125398 + 0.992106i \(0.459979\pi\)
\(762\) 0 0
\(763\) −9461.70 3443.78i −0.448934 0.163399i
\(764\) 0 0
\(765\) −8118.04 5384.12i −0.383671 0.254462i
\(766\) 0 0
\(767\) −4110.29 + 3448.94i −0.193499 + 0.162365i
\(768\) 0 0
\(769\) −2655.63 + 15060.8i −0.124531 + 0.706251i 0.857054 + 0.515226i \(0.172292\pi\)
−0.981585 + 0.191024i \(0.938819\pi\)
\(770\) 0 0
\(771\) 23822.5 + 17806.5i 1.11277 + 0.831756i
\(772\) 0 0
\(773\) −2757.85 + 4776.74i −0.128322 + 0.222260i −0.923027 0.384736i \(-0.874292\pi\)
0.794705 + 0.606996i \(0.207626\pi\)
\(774\) 0 0
\(775\) −5849.95 10132.4i −0.271144 0.469635i
\(776\) 0 0
\(777\) 2640.08 + 11235.5i 0.121895 + 0.518754i
\(778\) 0 0
\(779\) 19785.5 7201.35i 0.910001 0.331213i
\(780\) 0 0
\(781\) −4.07042 23.0845i −0.000186493 0.00105765i
\(782\) 0 0
\(783\) 2535.68 + 7093.71i 0.115732 + 0.323766i