Properties

Label 168.4.q.f.25.3
Level $168$
Weight $4$
Character 168.25
Analytic conductor $9.912$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 168.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.91232088096\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 173 x^{6} + 9457 x^{4} + 168048 x^{2} + 746496\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 25.3
Root \(2.57353i\) of defining polynomial
Character \(\chi\) \(=\) 168.25
Dual form 168.4.q.f.121.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 + 2.59808i) q^{3} +(-0.0642956 - 0.111363i) q^{5} +(-0.866259 - 18.5000i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.50000 + 2.59808i) q^{3} +(-0.0642956 - 0.111363i) q^{5} +(-0.866259 - 18.5000i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(-27.0033 + 46.7711i) q^{11} -50.2350 q^{13} +0.385773 q^{15} +(65.7436 - 113.871i) q^{17} +(-45.7547 - 79.2495i) q^{19} +(49.3638 + 25.4994i) q^{21} +(-89.7436 - 155.441i) q^{23} +(62.4917 - 108.239i) q^{25} +27.0000 q^{27} -69.8961 q^{29} +(-163.423 + 283.058i) q^{31} +(-81.0099 - 140.313i) q^{33} +(-2.00452 + 1.28594i) q^{35} +(-150.849 - 261.278i) q^{37} +(75.3525 - 130.514i) q^{39} +296.048 q^{41} -144.302 q^{43} +(-0.578660 + 1.00227i) q^{45} +(180.043 + 311.843i) q^{47} +(-341.499 + 32.0516i) q^{49} +(197.231 + 341.614i) q^{51} +(-0.917567 + 1.58927i) q^{53} +6.94477 q^{55} +274.528 q^{57} +(26.6193 - 46.1060i) q^{59} +(54.0605 + 93.6356i) q^{61} +(-140.295 + 90.0018i) q^{63} +(3.22989 + 5.59433i) q^{65} +(-421.004 + 729.199i) q^{67} +538.462 q^{69} -241.111 q^{71} +(103.492 - 179.253i) q^{73} +(187.475 + 324.717i) q^{75} +(888.656 + 459.045i) q^{77} +(-279.981 - 484.942i) q^{79} +(-40.5000 + 70.1481i) q^{81} +986.652 q^{83} -16.9081 q^{85} +(104.844 - 181.595i) q^{87} +(221.683 + 383.966i) q^{89} +(43.5165 + 929.348i) q^{91} +(-490.270 - 849.173i) q^{93} +(-5.88365 + 10.1908i) q^{95} -740.815 q^{97} +486.059 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 12q^{3} - 4q^{5} + 18q^{7} - 36q^{9} + O(q^{10}) \) \( 8q - 12q^{3} - 4q^{5} + 18q^{7} - 36q^{9} - 14q^{11} + 44q^{13} + 24q^{15} - 96q^{17} + 26q^{19} - 36q^{21} - 96q^{23} - 110q^{25} + 216q^{27} - 152q^{29} - 238q^{31} - 42q^{33} + 152q^{35} - 562q^{37} - 66q^{39} + 856q^{41} - 516q^{43} - 36q^{45} + 80q^{47} + 156q^{49} - 288q^{51} + 2952q^{55} - 156q^{57} - 262q^{59} + 276q^{61} - 54q^{63} - 2196q^{65} - 150q^{67} + 576q^{69} - 1696q^{71} + 218q^{73} - 330q^{75} - 764q^{77} - 1762q^{79} - 324q^{81} + 6900q^{83} + 2904q^{85} + 228q^{87} + 344q^{89} - 2806q^{91} - 714q^{93} - 2004q^{95} - 1244q^{97} + 252q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(85\) \(113\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(1\)

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
\(3\) −1.50000 + 2.59808i −0.288675 + 0.500000i
\(4\) 0 0
\(5\) −0.0642956 0.111363i −0.00575077 0.00996063i 0.863136 0.504972i \(-0.168497\pi\)
−0.868886 + 0.495011i \(0.835164\pi\)
\(6\) 0 0
\(7\) −0.866259 18.5000i −0.0467736 0.998906i
\(8\) 0 0
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) 0 0
\(11\) −27.0033 + 46.7711i −0.740163 + 1.28200i 0.212257 + 0.977214i \(0.431919\pi\)
−0.952421 + 0.304787i \(0.901415\pi\)
\(12\) 0 0
\(13\) −50.2350 −1.07175 −0.535873 0.844299i \(-0.680017\pi\)
−0.535873 + 0.844299i \(0.680017\pi\)
\(14\) 0 0
\(15\) 0.385773 0.00664042
\(16\) 0 0
\(17\) 65.7436 113.871i 0.937951 1.62458i 0.168666 0.985673i \(-0.446054\pi\)
0.769285 0.638906i \(-0.220613\pi\)
\(18\) 0 0
\(19\) −45.7547 79.2495i −0.552466 0.956899i −0.998096 0.0616814i \(-0.980354\pi\)
0.445630 0.895217i \(-0.352980\pi\)
\(20\) 0 0
\(21\) 49.3638 + 25.4994i 0.512955 + 0.264972i
\(22\) 0 0
\(23\) −89.7436 155.441i −0.813602 1.40920i −0.910328 0.413888i \(-0.864170\pi\)
0.0967260 0.995311i \(-0.469163\pi\)
\(24\) 0 0
\(25\) 62.4917 108.239i 0.499934 0.865911i
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) −69.8961 −0.447565 −0.223782 0.974639i \(-0.571841\pi\)
−0.223782 + 0.974639i \(0.571841\pi\)
\(30\) 0 0
\(31\) −163.423 + 283.058i −0.946829 + 1.63996i −0.194783 + 0.980846i \(0.562400\pi\)
−0.752046 + 0.659110i \(0.770933\pi\)
\(32\) 0 0
\(33\) −81.0099 140.313i −0.427334 0.740163i
\(34\) 0 0
\(35\) −2.00452 + 1.28594i −0.00968074 + 0.00621037i
\(36\) 0 0
\(37\) −150.849 261.278i −0.670254 1.16091i −0.977832 0.209391i \(-0.932852\pi\)
0.307578 0.951523i \(-0.400481\pi\)
\(38\) 0 0
\(39\) 75.3525 130.514i 0.309386 0.535873i
\(40\) 0 0
\(41\) 296.048 1.12768 0.563840 0.825884i \(-0.309324\pi\)
0.563840 + 0.825884i \(0.309324\pi\)
\(42\) 0 0
\(43\) −144.302 −0.511764 −0.255882 0.966708i \(-0.582366\pi\)
−0.255882 + 0.966708i \(0.582366\pi\)
\(44\) 0 0
\(45\) −0.578660 + 1.00227i −0.00191692 + 0.00332021i
\(46\) 0 0
\(47\) 180.043 + 311.843i 0.558764 + 0.967808i 0.997600 + 0.0692409i \(0.0220577\pi\)
−0.438836 + 0.898567i \(0.644609\pi\)
\(48\) 0 0
\(49\) −341.499 + 32.0516i −0.995624 + 0.0934448i
\(50\) 0 0
\(51\) 197.231 + 341.614i 0.541526 + 0.937951i
\(52\) 0 0
\(53\) −0.917567 + 1.58927i −0.00237807 + 0.00411893i −0.867212 0.497939i \(-0.834090\pi\)
0.864834 + 0.502058i \(0.167424\pi\)
\(54\) 0 0
\(55\) 6.94477 0.0170260
\(56\) 0 0
\(57\) 274.528 0.637932
\(58\) 0 0
\(59\) 26.6193 46.1060i 0.0587379 0.101737i −0.835161 0.550005i \(-0.814626\pi\)
0.893899 + 0.448268i \(0.147959\pi\)
\(60\) 0 0
\(61\) 54.0605 + 93.6356i 0.113471 + 0.196538i 0.917168 0.398502i \(-0.130470\pi\)
−0.803696 + 0.595040i \(0.797136\pi\)
\(62\) 0 0
\(63\) −140.295 + 90.0018i −0.280564 + 0.179987i
\(64\) 0 0
\(65\) 3.22989 + 5.59433i 0.00616336 + 0.0106753i
\(66\) 0 0
\(67\) −421.004 + 729.199i −0.767668 + 1.32964i 0.171156 + 0.985244i \(0.445250\pi\)
−0.938824 + 0.344396i \(0.888084\pi\)
\(68\) 0 0
\(69\) 538.462 0.939466
\(70\) 0 0
\(71\) −241.111 −0.403023 −0.201511 0.979486i \(-0.564585\pi\)
−0.201511 + 0.979486i \(0.564585\pi\)
\(72\) 0 0
\(73\) 103.492 179.253i 0.165929 0.287397i −0.771056 0.636767i \(-0.780271\pi\)
0.936985 + 0.349370i \(0.113605\pi\)
\(74\) 0 0
\(75\) 187.475 + 324.717i 0.288637 + 0.499934i
\(76\) 0 0
\(77\) 888.656 + 459.045i 1.31522 + 0.679390i
\(78\) 0 0
\(79\) −279.981 484.942i −0.398738 0.690635i 0.594832 0.803850i \(-0.297219\pi\)
−0.993571 + 0.113215i \(0.963885\pi\)
\(80\) 0 0
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 986.652 1.30481 0.652404 0.757871i \(-0.273760\pi\)
0.652404 + 0.757871i \(0.273760\pi\)
\(84\) 0 0
\(85\) −16.9081 −0.0215758
\(86\) 0 0
\(87\) 104.844 181.595i 0.129201 0.223782i
\(88\) 0 0
\(89\) 221.683 + 383.966i 0.264026 + 0.457307i 0.967308 0.253604i \(-0.0816161\pi\)
−0.703282 + 0.710911i \(0.748283\pi\)
\(90\) 0 0
\(91\) 43.5165 + 929.348i 0.0501294 + 1.07057i
\(92\) 0 0
\(93\) −490.270 849.173i −0.546652 0.946829i
\(94\) 0 0
\(95\) −5.88365 + 10.1908i −0.00635421 + 0.0110058i
\(96\) 0 0
\(97\) −740.815 −0.775447 −0.387723 0.921776i \(-0.626738\pi\)
−0.387723 + 0.921776i \(0.626738\pi\)
\(98\) 0 0
\(99\) 486.059 0.493442
\(100\) 0 0
\(101\) −371.888 + 644.130i −0.366379 + 0.634587i −0.988996 0.147939i \(-0.952736\pi\)
0.622617 + 0.782526i \(0.286069\pi\)
\(102\) 0 0
\(103\) −52.3253 90.6300i −0.0500559 0.0866994i 0.839912 0.542723i \(-0.182607\pi\)
−0.889968 + 0.456024i \(0.849273\pi\)
\(104\) 0 0
\(105\) −0.334180 7.13680i −0.000310596 0.00663315i
\(106\) 0 0
\(107\) −256.850 444.878i −0.232062 0.401943i 0.726353 0.687322i \(-0.241214\pi\)
−0.958415 + 0.285379i \(0.907881\pi\)
\(108\) 0 0
\(109\) −487.519 + 844.408i −0.428402 + 0.742015i −0.996731 0.0807868i \(-0.974257\pi\)
0.568329 + 0.822801i \(0.307590\pi\)
\(110\) 0 0
\(111\) 905.093 0.773942
\(112\) 0 0
\(113\) 1926.07 1.60345 0.801723 0.597696i \(-0.203917\pi\)
0.801723 + 0.597696i \(0.203917\pi\)
\(114\) 0 0
\(115\) −11.5402 + 19.9883i −0.00935767 + 0.0162080i
\(116\) 0 0
\(117\) 226.058 + 391.543i 0.178624 + 0.309386i
\(118\) 0 0
\(119\) −2163.57 1117.61i −1.66667 0.860937i
\(120\) 0 0
\(121\) −792.855 1373.27i −0.595684 1.03175i
\(122\) 0 0
\(123\) −444.071 + 769.154i −0.325533 + 0.563840i
\(124\) 0 0
\(125\) −32.1457 −0.0230016
\(126\) 0 0
\(127\) −1125.95 −0.786709 −0.393355 0.919387i \(-0.628686\pi\)
−0.393355 + 0.919387i \(0.628686\pi\)
\(128\) 0 0
\(129\) 216.453 374.908i 0.147734 0.255882i
\(130\) 0 0
\(131\) −746.621 1293.19i −0.497959 0.862490i 0.502038 0.864845i \(-0.332584\pi\)
−0.999997 + 0.00235541i \(0.999250\pi\)
\(132\) 0 0
\(133\) −1426.48 + 915.112i −0.930010 + 0.596619i
\(134\) 0 0
\(135\) −1.73598 3.00681i −0.00110674 0.00191692i
\(136\) 0 0
\(137\) −730.386 + 1265.07i −0.455483 + 0.788919i −0.998716 0.0506627i \(-0.983867\pi\)
0.543233 + 0.839582i \(0.317200\pi\)
\(138\) 0 0
\(139\) 2225.85 1.35823 0.679116 0.734031i \(-0.262363\pi\)
0.679116 + 0.734031i \(0.262363\pi\)
\(140\) 0 0
\(141\) −1080.26 −0.645206
\(142\) 0 0
\(143\) 1356.51 2349.55i 0.793267 1.37398i
\(144\) 0 0
\(145\) 4.49401 + 7.78385i 0.00257384 + 0.00445803i
\(146\) 0 0
\(147\) 428.976 935.318i 0.240690 0.524787i
\(148\) 0 0
\(149\) −197.340 341.804i −0.108502 0.187930i 0.806662 0.591013i \(-0.201272\pi\)
−0.915163 + 0.403083i \(0.867939\pi\)
\(150\) 0 0
\(151\) 1562.10 2705.64i 0.841867 1.45816i −0.0464473 0.998921i \(-0.514790\pi\)
0.888314 0.459236i \(-0.151877\pi\)
\(152\) 0 0
\(153\) −1183.39 −0.625301
\(154\) 0 0
\(155\) 42.0296 0.0217800
\(156\) 0 0
\(157\) 1800.35 3118.30i 0.915183 1.58514i 0.108551 0.994091i \(-0.465379\pi\)
0.806633 0.591053i \(-0.201288\pi\)
\(158\) 0 0
\(159\) −2.75270 4.76782i −0.00137298 0.00237807i
\(160\) 0 0
\(161\) −2797.91 + 1794.91i −1.36960 + 0.878624i
\(162\) 0 0
\(163\) −987.012 1709.55i −0.474287 0.821489i 0.525280 0.850930i \(-0.323961\pi\)
−0.999567 + 0.0294409i \(0.990627\pi\)
\(164\) 0 0
\(165\) −10.4172 + 18.0430i −0.00491499 + 0.00851302i
\(166\) 0 0
\(167\) 1067.09 0.494453 0.247227 0.968958i \(-0.420481\pi\)
0.247227 + 0.968958i \(0.420481\pi\)
\(168\) 0 0
\(169\) 326.559 0.148638
\(170\) 0 0
\(171\) −411.792 + 713.245i −0.184155 + 0.318966i
\(172\) 0 0
\(173\) 137.327 + 237.858i 0.0603515 + 0.104532i 0.894623 0.446823i \(-0.147445\pi\)
−0.834271 + 0.551355i \(0.814111\pi\)
\(174\) 0 0
\(175\) −2056.55 1062.33i −0.888347 0.458885i
\(176\) 0 0
\(177\) 79.8578 + 138.318i 0.0339123 + 0.0587379i
\(178\) 0 0
\(179\) −277.166 + 480.066i −0.115734 + 0.200457i −0.918073 0.396412i \(-0.870255\pi\)
0.802339 + 0.596869i \(0.203589\pi\)
\(180\) 0 0
\(181\) −685.436 −0.281481 −0.140741 0.990047i \(-0.544948\pi\)
−0.140741 + 0.990047i \(0.544948\pi\)
\(182\) 0 0
\(183\) −324.363 −0.131025
\(184\) 0 0
\(185\) −19.3978 + 33.5980i −0.00770895 + 0.0133523i
\(186\) 0 0
\(187\) 3550.59 + 6149.80i 1.38847 + 2.40491i
\(188\) 0 0
\(189\) −23.3890 499.500i −0.00900158 0.192239i
\(190\) 0 0
\(191\) −2449.44 4242.55i −0.927932 1.60722i −0.786777 0.617237i \(-0.788252\pi\)
−0.141155 0.989988i \(-0.545082\pi\)
\(192\) 0 0
\(193\) −1570.13 + 2719.55i −0.585598 + 1.01429i 0.409202 + 0.912444i \(0.365807\pi\)
−0.994801 + 0.101842i \(0.967526\pi\)
\(194\) 0 0
\(195\) −19.3793 −0.00711684
\(196\) 0 0
\(197\) −227.412 −0.0822460 −0.0411230 0.999154i \(-0.513094\pi\)
−0.0411230 + 0.999154i \(0.513094\pi\)
\(198\) 0 0
\(199\) 607.250 1051.79i 0.216316 0.374670i −0.737363 0.675497i \(-0.763929\pi\)
0.953679 + 0.300827i \(0.0972626\pi\)
\(200\) 0 0
\(201\) −1263.01 2187.60i −0.443213 0.767668i
\(202\) 0 0
\(203\) 60.5481 + 1293.08i 0.0209342 + 0.447075i
\(204\) 0 0
\(205\) −19.0345 32.9688i −0.00648502 0.0112324i
\(206\) 0 0
\(207\) −807.693 + 1398.96i −0.271201 + 0.469733i
\(208\) 0 0
\(209\) 4942.11 1.63566
\(210\) 0 0
\(211\) 5116.07 1.66922 0.834608 0.550844i \(-0.185694\pi\)
0.834608 + 0.550844i \(0.185694\pi\)
\(212\) 0 0
\(213\) 361.666 626.425i 0.116343 0.201511i
\(214\) 0 0
\(215\) 9.27799 + 16.0699i 0.00294304 + 0.00509749i
\(216\) 0 0
\(217\) 5378.13 + 2778.13i 1.68245 + 0.869087i
\(218\) 0 0
\(219\) 310.475 + 537.759i 0.0957989 + 0.165929i
\(220\) 0 0
\(221\) −3302.63 + 5720.33i −1.00524 + 1.74114i
\(222\) 0 0
\(223\) 119.384 0.0358499 0.0179250 0.999839i \(-0.494294\pi\)
0.0179250 + 0.999839i \(0.494294\pi\)
\(224\) 0 0
\(225\) −1124.85 −0.333289
\(226\) 0 0
\(227\) −996.000 + 1725.12i −0.291220 + 0.504407i −0.974098 0.226124i \(-0.927394\pi\)
0.682879 + 0.730532i \(0.260728\pi\)
\(228\) 0 0
\(229\) −351.738 609.228i −0.101500 0.175803i 0.810803 0.585319i \(-0.199031\pi\)
−0.912303 + 0.409516i \(0.865698\pi\)
\(230\) 0 0
\(231\) −2525.62 + 1620.23i −0.719365 + 0.461486i
\(232\) 0 0
\(233\) −480.892 832.929i −0.135211 0.234193i 0.790467 0.612505i \(-0.209838\pi\)
−0.925678 + 0.378312i \(0.876505\pi\)
\(234\) 0 0
\(235\) 23.1519 40.1003i 0.00642665 0.0111313i
\(236\) 0 0
\(237\) 1679.89 0.460423
\(238\) 0 0
\(239\) −4464.71 −1.20836 −0.604179 0.796848i \(-0.706499\pi\)
−0.604179 + 0.796848i \(0.706499\pi\)
\(240\) 0 0
\(241\) 217.656 376.991i 0.0581761 0.100764i −0.835471 0.549535i \(-0.814805\pi\)
0.893647 + 0.448771i \(0.148138\pi\)
\(242\) 0 0
\(243\) −121.500 210.444i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) 25.5262 + 35.9697i 0.00665638 + 0.00937966i
\(246\) 0 0
\(247\) 2298.49 + 3981.10i 0.592103 + 1.02555i
\(248\) 0 0
\(249\) −1479.98 + 2563.40i −0.376666 + 0.652404i
\(250\) 0 0
\(251\) 863.003 0.217021 0.108510 0.994095i \(-0.465392\pi\)
0.108510 + 0.994095i \(0.465392\pi\)
\(252\) 0 0
\(253\) 9693.49 2.40879
\(254\) 0 0
\(255\) 25.3621 43.9285i 0.00622839 0.0107879i
\(256\) 0 0
\(257\) 268.346 + 464.790i 0.0651322 + 0.112812i 0.896753 0.442532i \(-0.145920\pi\)
−0.831620 + 0.555344i \(0.812586\pi\)
\(258\) 0 0
\(259\) −4702.96 + 3017.03i −1.12829 + 0.723820i
\(260\) 0 0
\(261\) 314.533 + 544.786i 0.0745942 + 0.129201i
\(262\) 0 0
\(263\) −185.954 + 322.082i −0.0435986 + 0.0755149i −0.887001 0.461767i \(-0.847216\pi\)
0.843403 + 0.537282i \(0.180549\pi\)
\(264\) 0 0
\(265\) 0.235982 5.47029e−5
\(266\) 0 0
\(267\) −1330.10 −0.304871
\(268\) 0 0
\(269\) 2252.80 3901.97i 0.510616 0.884414i −0.489308 0.872111i \(-0.662751\pi\)
0.999924 0.0123024i \(-0.00391609\pi\)
\(270\) 0 0
\(271\) 198.058 + 343.046i 0.0443954 + 0.0768951i 0.887369 0.461059i \(-0.152531\pi\)
−0.842974 + 0.537955i \(0.819197\pi\)
\(272\) 0 0
\(273\) −2479.79 1280.96i −0.549757 0.283983i
\(274\) 0 0
\(275\) 3374.96 + 5845.61i 0.740066 + 1.28183i
\(276\) 0 0
\(277\) 3254.37 5636.73i 0.705907 1.22267i −0.260457 0.965486i \(-0.583873\pi\)
0.966363 0.257181i \(-0.0827935\pi\)
\(278\) 0 0
\(279\) 2941.62 0.631220
\(280\) 0 0
\(281\) 2785.80 0.591413 0.295707 0.955279i \(-0.404445\pi\)
0.295707 + 0.955279i \(0.404445\pi\)
\(282\) 0 0
\(283\) −0.305923 + 0.529874i −6.42588e−5 + 0.000111299i −0.866058 0.499944i \(-0.833354\pi\)
0.865993 + 0.500056i \(0.166687\pi\)
\(284\) 0 0
\(285\) −17.6509 30.5723i −0.00366860 0.00635421i
\(286\) 0 0
\(287\) −256.454 5476.88i −0.0527456 1.12645i
\(288\) 0 0
\(289\) −6187.95 10717.8i −1.25950 2.18153i
\(290\) 0 0
\(291\) 1111.22 1924.69i 0.223852 0.387723i
\(292\) 0 0
\(293\) −4145.98 −0.826657 −0.413329 0.910582i \(-0.635634\pi\)
−0.413329 + 0.910582i \(0.635634\pi\)
\(294\) 0 0
\(295\) −6.84601 −0.00135115
\(296\) 0 0
\(297\) −729.089 + 1262.82i −0.142445 + 0.246721i
\(298\) 0 0
\(299\) 4508.27 + 7808.56i 0.871974 + 1.51030i
\(300\) 0 0
\(301\) 125.003 + 2669.59i 0.0239371 + 0.511204i
\(302\) 0 0
\(303\) −1115.67 1932.39i −0.211529 0.366379i
\(304\) 0 0
\(305\) 6.95171 12.0407i 0.00130509 0.00226049i
\(306\) 0 0
\(307\) 1960.53 0.364473 0.182236 0.983255i \(-0.441666\pi\)
0.182236 + 0.983255i \(0.441666\pi\)
\(308\) 0 0
\(309\) 313.952 0.0577996
\(310\) 0 0
\(311\) −2603.78 + 4509.89i −0.474749 + 0.822290i −0.999582 0.0289155i \(-0.990795\pi\)
0.524833 + 0.851206i \(0.324128\pi\)
\(312\) 0 0
\(313\) 1995.86 + 3456.92i 0.360423 + 0.624271i 0.988030 0.154259i \(-0.0492990\pi\)
−0.627607 + 0.778530i \(0.715966\pi\)
\(314\) 0 0
\(315\) 19.0432 + 9.83698i 0.00340624 + 0.00175953i
\(316\) 0 0
\(317\) −902.519 1563.21i −0.159907 0.276967i 0.774928 0.632050i \(-0.217786\pi\)
−0.934835 + 0.355083i \(0.884453\pi\)
\(318\) 0 0
\(319\) 1887.43 3269.12i 0.331271 0.573779i
\(320\) 0 0
\(321\) 1541.10 0.267962
\(322\) 0 0
\(323\) −12032.3 −2.07274
\(324\) 0 0
\(325\) −3139.27 + 5437.38i −0.535802 + 0.928036i
\(326\) 0 0
\(327\) −1462.56 2533.22i −0.247338 0.428402i
\(328\) 0 0
\(329\) 5613.13 3600.92i 0.940614 0.603421i
\(330\) 0 0
\(331\) −3453.09 5980.93i −0.573411 0.993177i −0.996212 0.0869547i \(-0.972286\pi\)
0.422801 0.906222i \(-0.361047\pi\)
\(332\) 0 0
\(333\) −1357.64 + 2351.50i −0.223418 + 0.386971i
\(334\) 0 0
\(335\) 108.275 0.0176587
\(336\) 0 0
\(337\) −6081.36 −0.983006 −0.491503 0.870876i \(-0.663552\pi\)
−0.491503 + 0.870876i \(0.663552\pi\)
\(338\) 0 0
\(339\) −2889.10 + 5004.07i −0.462875 + 0.801723i
\(340\) 0 0
\(341\) −8825.94 15287.0i −1.40162 2.42767i
\(342\) 0 0
\(343\) 888.780 + 6289.97i 0.139911 + 0.990164i
\(344\) 0 0
\(345\) −34.6207 59.9648i −0.00540265 0.00935767i
\(346\) 0 0
\(347\) 3893.51 6743.75i 0.602347 1.04330i −0.390117 0.920765i \(-0.627566\pi\)
0.992465 0.122531i \(-0.0391011\pi\)
\(348\) 0 0
\(349\) −1928.25 −0.295751 −0.147875 0.989006i \(-0.547243\pi\)
−0.147875 + 0.989006i \(0.547243\pi\)
\(350\) 0 0
\(351\) −1356.35 −0.206258
\(352\) 0 0
\(353\) 1702.14 2948.18i 0.256645 0.444521i −0.708696 0.705514i \(-0.750716\pi\)
0.965341 + 0.260992i \(0.0840497\pi\)
\(354\) 0 0
\(355\) 15.5024 + 26.8509i 0.00231769 + 0.00401436i
\(356\) 0 0
\(357\) 6149.00 3944.69i 0.911595 0.584805i
\(358\) 0 0
\(359\) −2208.53 3825.28i −0.324684 0.562369i 0.656764 0.754096i \(-0.271925\pi\)
−0.981448 + 0.191727i \(0.938591\pi\)
\(360\) 0 0
\(361\) −757.484 + 1312.00i −0.110436 + 0.191282i
\(362\) 0 0
\(363\) 4757.13 0.687837
\(364\) 0 0
\(365\) −26.6162 −0.00381687
\(366\) 0 0
\(367\) 2538.33 4396.51i 0.361034 0.625329i −0.627097 0.778941i \(-0.715757\pi\)
0.988131 + 0.153612i \(0.0490905\pi\)
\(368\) 0 0
\(369\) −1332.21 2307.46i −0.187947 0.325533i
\(370\) 0 0
\(371\) 30.1964 + 15.5983i 0.00422566 + 0.00218281i
\(372\) 0 0
\(373\) 3438.32 + 5955.35i 0.477291 + 0.826692i 0.999661 0.0260264i \(-0.00828540\pi\)
−0.522370 + 0.852719i \(0.674952\pi\)
\(374\) 0 0
\(375\) 48.2185 83.5169i 0.00663998 0.0115008i
\(376\) 0 0
\(377\) 3511.23 0.479676
\(378\) 0 0
\(379\) −9285.61 −1.25850 −0.629248 0.777205i \(-0.716637\pi\)
−0.629248 + 0.777205i \(0.716637\pi\)
\(380\) 0 0
\(381\) 1688.93 2925.31i 0.227103 0.393355i
\(382\) 0 0
\(383\) 3840.83 + 6652.51i 0.512420 + 0.887538i 0.999896 + 0.0144017i \(0.00458437\pi\)
−0.487476 + 0.873136i \(0.662082\pi\)
\(384\) 0 0
\(385\) −6.01597 128.478i −0.000796369 0.0170074i
\(386\) 0 0
\(387\) 649.360 + 1124.72i 0.0852941 + 0.147734i
\(388\) 0 0
\(389\) −4313.86 + 7471.83i −0.562266 + 0.973873i 0.435032 + 0.900415i \(0.356737\pi\)
−0.997298 + 0.0734585i \(0.976596\pi\)
\(390\) 0 0
\(391\) −23600.3 −3.05247
\(392\) 0 0
\(393\) 4479.73 0.574993
\(394\) 0 0
\(395\) −36.0031 + 62.3592i −0.00458611 + 0.00794337i
\(396\) 0 0
\(397\) −2867.81 4967.19i −0.362547 0.627949i 0.625832 0.779957i \(-0.284759\pi\)
−0.988379 + 0.152008i \(0.951426\pi\)
\(398\) 0 0
\(399\) −237.812 5078.77i −0.0298384 0.637234i
\(400\) 0 0
\(401\) 3608.89 + 6250.79i 0.449425 + 0.778427i 0.998349 0.0574453i \(-0.0182955\pi\)
−0.548923 + 0.835873i \(0.684962\pi\)
\(402\) 0 0
\(403\) 8209.58 14219.4i 1.01476 1.75762i
\(404\) 0 0
\(405\) 10.4159 0.00127795
\(406\) 0 0
\(407\) 16293.7 1.98439
\(408\) 0 0
\(409\) 5401.46 9355.60i 0.653019 1.13106i −0.329367 0.944202i \(-0.606835\pi\)
0.982386 0.186861i \(-0.0598313\pi\)
\(410\) 0 0
\(411\) −2191.16 3795.20i −0.262973 0.455483i
\(412\) 0 0
\(413\) −876.019 452.517i −0.104373 0.0539150i
\(414\) 0 0
\(415\) −63.4373 109.877i −0.00750365 0.0129967i
\(416\) 0 0
\(417\) −3338.78 + 5782.93i −0.392088 + 0.679116i
\(418\) 0 0
\(419\) 13257.1 1.54571 0.772856 0.634582i \(-0.218828\pi\)
0.772856 + 0.634582i \(0.218828\pi\)
\(420\) 0 0
\(421\) −6252.11 −0.723774 −0.361887 0.932222i \(-0.617867\pi\)
−0.361887 + 0.932222i \(0.617867\pi\)
\(422\) 0 0
\(423\) 1620.38 2806.59i 0.186255 0.322603i
\(424\) 0 0
\(425\) −8216.87 14232.0i −0.937827 1.62436i
\(426\) 0 0
\(427\) 1685.43 1081.23i 0.191015 0.122540i
\(428\) 0 0
\(429\) 4069.53 + 7048.64i 0.457993 + 0.793267i
\(430\) 0 0
\(431\) −2474.54 + 4286.03i −0.276553 + 0.479004i −0.970526 0.240997i \(-0.922526\pi\)
0.693973 + 0.720001i \(0.255859\pi\)
\(432\) 0 0
\(433\) −16602.8 −1.84267 −0.921337 0.388764i \(-0.872902\pi\)
−0.921337 + 0.388764i \(0.872902\pi\)
\(434\) 0 0
\(435\) −26.9641 −0.00297202
\(436\) 0 0
\(437\) −8212.38 + 14224.3i −0.898974 + 1.55707i
\(438\) 0 0
\(439\) 2354.19 + 4077.57i 0.255944 + 0.443307i 0.965151 0.261692i \(-0.0842805\pi\)
−0.709208 + 0.705000i \(0.750947\pi\)
\(440\) 0 0
\(441\) 1786.56 + 2517.49i 0.192913 + 0.271838i
\(442\) 0 0
\(443\) 850.218 + 1472.62i 0.0911852 + 0.157937i 0.908010 0.418948i \(-0.137601\pi\)
−0.816825 + 0.576886i \(0.804268\pi\)
\(444\) 0 0
\(445\) 28.5065 49.3746i 0.00303671 0.00525973i
\(446\) 0 0
\(447\) 1184.04 0.125287
\(448\) 0 0
\(449\) 10050.2 1.05635 0.528173 0.849137i \(-0.322877\pi\)
0.528173 + 0.849137i \(0.322877\pi\)
\(450\) 0 0
\(451\) −7994.26 + 13846.5i −0.834667 + 1.44569i
\(452\) 0 0
\(453\) 4686.30 + 8116.91i 0.486052 + 0.841867i
\(454\) 0 0
\(455\) 100.697 64.5991i 0.0103753 0.00665594i
\(456\) 0 0
\(457\) 5495.95 + 9519.27i 0.562560 + 0.974382i 0.997272 + 0.0738128i \(0.0235167\pi\)
−0.434712 + 0.900569i \(0.643150\pi\)
\(458\) 0 0
\(459\) 1775.08 3074.52i 0.180509 0.312650i
\(460\) 0 0
\(461\) −548.440 −0.0554086 −0.0277043 0.999616i \(-0.508820\pi\)
−0.0277043 + 0.999616i \(0.508820\pi\)
\(462\) 0 0
\(463\) 4028.04 0.404317 0.202159 0.979353i \(-0.435204\pi\)
0.202159 + 0.979353i \(0.435204\pi\)
\(464\) 0 0
\(465\) −63.0444 + 109.196i −0.00628734 + 0.0108900i
\(466\) 0 0
\(467\) −1035.35 1793.27i −0.102591 0.177693i 0.810160 0.586208i \(-0.199380\pi\)
−0.912751 + 0.408515i \(0.866047\pi\)
\(468\) 0 0
\(469\) 13854.9 + 7156.88i 1.36409 + 0.704636i
\(470\) 0 0
\(471\) 5401.06 + 9354.91i 0.528381 + 0.915183i
\(472\) 0 0
\(473\) 3896.63 6749.16i 0.378789 0.656082i
\(474\) 0 0
\(475\) −11437.2 −1.10479
\(476\) 0 0
\(477\) 16.5162 0.00158538
\(478\) 0 0
\(479\) 89.3926 154.832i 0.00852704 0.0147693i −0.861730 0.507366i \(-0.830619\pi\)
0.870257 + 0.492597i \(0.163952\pi\)
\(480\) 0 0
\(481\) 7577.89 + 13125.3i 0.718341 + 1.24420i
\(482\) 0 0
\(483\) −466.447 9961.54i −0.0439422 0.938438i
\(484\) 0 0
\(485\) 47.6311 + 82.4995i 0.00445942 + 0.00772393i
\(486\) 0 0
\(487\) 8298.48 14373.4i 0.772156 1.33741i −0.164223 0.986423i \(-0.552512\pi\)
0.936379 0.350991i \(-0.114155\pi\)
\(488\) 0 0
\(489\) 5922.07 0.547659
\(490\) 0 0
\(491\) −4547.22 −0.417949 −0.208975 0.977921i \(-0.567013\pi\)
−0.208975 + 0.977921i \(0.567013\pi\)
\(492\) 0 0
\(493\) −4595.22 + 7959.16i −0.419794 + 0.727105i
\(494\) 0 0
\(495\) −31.2515 54.1291i −0.00283767 0.00491499i
\(496\) 0 0
\(497\) 208.864 + 4460.55i 0.0188508 + 0.402581i
\(498\) 0 0
\(499\) −512.984 888.515i −0.0460207 0.0797102i 0.842097 0.539325i \(-0.181321\pi\)
−0.888118 + 0.459615i \(0.847987\pi\)
\(500\) 0 0
\(501\) −1600.63 + 2772.37i −0.142736 + 0.247227i
\(502\) 0 0
\(503\) 6745.26 0.597925 0.298962 0.954265i \(-0.403359\pi\)
0.298962 + 0.954265i \(0.403359\pi\)
\(504\) 0 0
\(505\) 95.6431 0.00842785
\(506\) 0 0
\(507\) −489.838 + 848.424i −0.0429082 + 0.0743192i
\(508\) 0 0
\(509\) 3000.51 + 5197.03i 0.261287 + 0.452563i 0.966584 0.256349i \(-0.0825197\pi\)
−0.705297 + 0.708912i \(0.749186\pi\)
\(510\) 0 0
\(511\) −3405.83 1759.32i −0.294843 0.152304i
\(512\) 0 0
\(513\) −1235.38 2139.74i −0.106322 0.184155i
\(514\) 0 0
\(515\) −6.72856 + 11.6542i −0.000575720 + 0.000997177i
\(516\) 0 0
\(517\) −19447.0 −1.65431
\(518\) 0 0
\(519\) −823.964 −0.0696879
\(520\) 0 0
\(521\) −2347.61 + 4066.17i −0.197410 + 0.341924i −0.947688 0.319199i \(-0.896586\pi\)
0.750278 + 0.661122i \(0.229920\pi\)
\(522\) 0 0
\(523\) −385.884 668.370i −0.0322629 0.0558810i 0.849443 0.527680i \(-0.176938\pi\)
−0.881706 + 0.471799i \(0.843605\pi\)
\(524\) 0 0
\(525\) 5844.85 3749.58i 0.485886 0.311705i
\(526\) 0 0
\(527\) 21488.1 + 37218.5i 1.77616 + 3.07640i
\(528\) 0 0
\(529\) −10024.3 + 17362.7i −0.823895 + 1.42703i
\(530\) 0 0
\(531\) −479.147 −0.0391586
\(532\) 0 0
\(533\) −14872.0 −1.20859
\(534\) 0 0
\(535\) −33.0286 + 57.2073i −0.00266907 + 0.00462297i
\(536\) 0 0
\(537\) −831.498 1440.20i −0.0668190 0.115734i
\(538\) 0 0
\(539\) 7722.52 16837.8i 0.617129 1.34556i
\(540\) 0 0
\(541\) −1692.83 2932.07i −0.134529 0.233012i 0.790888 0.611961i \(-0.209619\pi\)
−0.925418 + 0.378949i \(0.876286\pi\)
\(542\) 0 0
\(543\) 1028.15 1780.82i 0.0812566 0.140741i
\(544\) 0 0
\(545\) 125.381 0.00985457
\(546\) 0 0
\(547\) 4988.75 0.389952 0.194976 0.980808i \(-0.437537\pi\)
0.194976 + 0.980808i \(0.437537\pi\)
\(548\) 0 0
\(549\) 486.545 842.720i 0.0378237 0.0655126i
\(550\) 0 0
\(551\) 3198.08 + 5539.23i 0.247264 + 0.428274i
\(552\) 0 0
\(553\) −8728.88 + 5599.73i −0.671229 + 0.430606i
\(554\) 0 0
\(555\) −58.1934 100.794i −0.00445076 0.00770895i
\(556\) 0 0
\(557\) 10103.6 17500.0i 0.768591 1.33124i −0.169736 0.985490i \(-0.554291\pi\)
0.938327 0.345749i \(-0.112375\pi\)
\(558\) 0 0
\(559\) 7249.02 0.548481
\(560\) 0 0
\(561\) −21303.5 −1.60327
\(562\) 0 0
\(563\) 5845.20 10124.2i 0.437559 0.757875i −0.559941 0.828532i \(-0.689176\pi\)
0.997501 + 0.0706574i \(0.0225097\pi\)
\(564\) 0 0
\(565\) −123.838 214.493i −0.00922104 0.0159713i
\(566\) 0 0
\(567\) 1332.82 + 688.483i 0.0987183 + 0.0509940i
\(568\) 0 0
\(569\) 8964.45 + 15526.9i 0.660473 + 1.14397i 0.980491 + 0.196562i \(0.0629777\pi\)
−0.320018 + 0.947411i \(0.603689\pi\)
\(570\) 0 0
\(571\) 7836.84 13573.8i 0.574364 0.994827i −0.421747 0.906714i \(-0.638583\pi\)
0.996110 0.0881136i \(-0.0280838\pi\)
\(572\) 0 0
\(573\) 14696.6 1.07148
\(574\) 0 0
\(575\) −22432.9 −1.62699
\(576\) 0 0
\(577\) 6826.50 11823.8i 0.492532 0.853090i −0.507431 0.861692i \(-0.669405\pi\)
0.999963 + 0.00860205i \(0.00273815\pi\)
\(578\) 0 0
\(579\) −4710.39 8158.64i −0.338095 0.585598i
\(580\) 0 0
\(581\) −854.696 18253.0i −0.0610306 1.30338i
\(582\) 0 0
\(583\) −49.5547 85.8312i −0.00352032 0.00609737i
\(584\) 0 0
\(585\) 29.0690 50.3490i 0.00205445 0.00355842i
\(586\) 0 0
\(587\) −18021.5 −1.26717 −0.633583 0.773675i \(-0.718417\pi\)
−0.633583 + 0.773675i \(0.718417\pi\)
\(588\) 0 0
\(589\) 29909.6 2.09236
\(590\) 0 0
\(591\) 341.118 590.834i 0.0237424 0.0411230i
\(592\) 0 0
\(593\) −10568.7 18305.5i −0.731877 1.26765i −0.956080 0.293105i \(-0.905311\pi\)
0.224204 0.974542i \(-0.428022\pi\)
\(594\) 0 0
\(595\) 14.6468 + 312.800i 0.00100918 + 0.0215522i
\(596\) 0 0
\(597\) 1821.75 + 3155.36i 0.124890 + 0.216316i
\(598\) 0 0
\(599\) −4684.80 + 8114.30i −0.319559 + 0.553492i −0.980396 0.197037i \(-0.936868\pi\)
0.660837 + 0.750529i \(0.270201\pi\)
\(600\) 0 0
\(601\) −22750.0 −1.54408 −0.772040 0.635573i \(-0.780764\pi\)
−0.772040 + 0.635573i \(0.780764\pi\)
\(602\) 0 0
\(603\) 7578.06 0.511779
\(604\) 0 0
\(605\) −101.954 + 176.590i −0.00685128 + 0.0118668i
\(606\) 0 0
\(607\) 2986.82 + 5173.33i 0.199722 + 0.345929i 0.948438 0.316962i \(-0.102663\pi\)
−0.748716 + 0.662891i \(0.769329\pi\)
\(608\) 0 0
\(609\) −3450.34 1782.31i −0.229581 0.118592i
\(610\) 0 0
\(611\) −9044.45 15665.4i −0.598853 1.03724i
\(612\) 0 0
\(613\) 11673.7 20219.4i 0.769162 1.33223i −0.168856 0.985641i \(-0.554007\pi\)
0.938018 0.346586i \(-0.112659\pi\)
\(614\) 0 0
\(615\) 114.207 0.00748826
\(616\) 0 0
\(617\) 28199.1 1.83996 0.919979 0.391968i \(-0.128206\pi\)
0.919979 + 0.391968i \(0.128206\pi\)
\(618\) 0 0
\(619\) 1487.78 2576.91i 0.0966057 0.167326i −0.813672 0.581324i \(-0.802535\pi\)
0.910278 + 0.413998i \(0.135868\pi\)
\(620\) 0 0
\(621\) −2423.08 4196.89i −0.156578 0.271201i
\(622\) 0 0
\(623\) 6911.33 4433.75i 0.444457 0.285127i
\(624\) 0 0
\(625\) −7809.40 13526.3i −0.499802 0.865682i
\(626\) 0 0
\(627\) −7413.16 + 12840.0i −0.472174 + 0.817830i
\(628\) 0 0
\(629\) −39669.4 −2.51466
\(630\) 0 0
\(631\) −2631.33 −0.166009 −0.0830044 0.996549i \(-0.526452\pi\)
−0.0830044 + 0.996549i \(0.526452\pi\)
\(632\) 0 0
\(633\) −7674.10 + 13291.9i −0.481861 + 0.834608i
\(634\) 0 0
\(635\) 72.3937 + 125.390i 0.00452418 + 0.00783611i
\(636\) 0 0
\(637\) 17155.2 1610.11i 1.06706 0.100149i
\(638\) 0 0
\(639\) 1085.00 + 1879.27i 0.0671704 + 0.116343i
\(640\) 0 0
\(641\) −7247.12 + 12552.4i −0.446559 + 0.773462i −0.998159 0.0606460i \(-0.980684\pi\)
0.551601 + 0.834108i \(0.314017\pi\)
\(642\) 0 0
\(643\) −15176.0 −0.930767 −0.465383 0.885109i \(-0.654084\pi\)
−0.465383 + 0.885109i \(0.654084\pi\)
\(644\) 0 0
\(645\) −55.6679 −0.00339833
\(646\) 0 0
\(647\) 3784.59 6555.10i 0.229965 0.398312i −0.727832 0.685755i \(-0.759472\pi\)
0.957798 + 0.287443i \(0.0928053\pi\)
\(648\) 0 0
\(649\) 1437.62 + 2490.02i 0.0869513 + 0.150604i
\(650\) 0 0
\(651\) −15285.0 + 9805.60i −0.920224 + 0.590341i
\(652\) 0 0
\(653\) 6966.75 + 12066.8i 0.417504 + 0.723138i 0.995688 0.0927688i \(-0.0295717\pi\)
−0.578184 + 0.815906i \(0.696238\pi\)
\(654\) 0 0
\(655\) −96.0089 + 166.292i −0.00572729 + 0.00991996i
\(656\) 0 0
\(657\) −1862.85 −0.110619
\(658\) 0 0
\(659\) −17015.5 −1.00581 −0.502904 0.864342i \(-0.667735\pi\)
−0.502904 + 0.864342i \(0.667735\pi\)
\(660\) 0 0
\(661\) 8267.70 14320.1i 0.486500 0.842642i −0.513380 0.858161i \(-0.671607\pi\)
0.999880 + 0.0155194i \(0.00494019\pi\)
\(662\) 0 0
\(663\) −9907.90 17161.0i −0.580378 1.00524i
\(664\) 0 0
\(665\) 193.626 + 100.020i 0.0112910 + 0.00583247i
\(666\) 0 0
\(667\) 6272.73 + 10864.7i 0.364140 + 0.630708i
\(668\) 0 0
\(669\) −179.076 + 310.168i −0.0103490 + 0.0179250i
\(670\) 0 0
\(671\) −5839.25 −0.335949
\(672\) 0 0
\(673\) 4571.05 0.261814 0.130907 0.991395i \(-0.458211\pi\)
0.130907 + 0.991395i \(0.458211\pi\)
\(674\) 0 0
\(675\) 1687.28 2922.45i 0.0962123 0.166645i
\(676\) 0 0
\(677\) −13142.3 22763.1i −0.746083 1.29225i −0.949687 0.313201i \(-0.898599\pi\)
0.203604 0.979053i \(-0.434735\pi\)
\(678\) 0 0
\(679\) 641.737 + 13705.1i 0.0362704 + 0.774598i
\(680\) 0 0
\(681\) −2988.00 5175.37i −0.168136 0.291220i
\(682\) 0 0
\(683\) −3398.61 + 5886.57i −0.190402 + 0.329785i −0.945383 0.325961i \(-0.894312\pi\)
0.754982 + 0.655746i \(0.227646\pi\)
\(684\) 0 0
\(685\) 187.842 0.0104775
\(686\) 0 0
\(687\) 2110.43 0.117202
\(688\) 0 0
\(689\) 46.0940 79.8372i 0.00254868 0.00441445i
\(690\) 0 0
\(691\) −13879.3 24039.7i −0.764103 1.32346i −0.940720 0.339185i \(-0.889849\pi\)
0.176617 0.984280i \(-0.443485\pi\)
\(692\) 0 0
\(693\) −421.053 8992.09i −0.0230801 0.492902i
\(694\) 0 0
\(695\) −143.112 247.878i −0.00781088 0.0135288i
\(696\) 0 0
\(697\) 19463.2 33711.3i 1.05771 1.83200i
\(698\) 0 0
\(699\) 2885.35 0.156129
\(700\) 0 0
\(701\) −21638.3 −1.16586 −0.582929 0.812523i \(-0.698093\pi\)
−0.582929 + 0.812523i \(0.698093\pi\)
\(702\) 0 0
\(703\) −13804.1 + 23909.4i −0.740584 + 1.28273i
\(704\) 0 0
\(705\) 69.4557 + 120.301i 0.00371043 + 0.00642665i
\(706\) 0 0
\(707\) 12238.5 + 6321.95i 0.651029 + 0.336296i
\(708\) 0 0
\(709\) 8144.36 + 14106.4i 0.431408 + 0.747220i 0.996995 0.0774687i \(-0.0246838\pi\)
−0.565587 + 0.824688i \(0.691350\pi\)
\(710\) 0 0
\(711\) −2519.83 + 4364.47i −0.132913 + 0.230212i
\(712\) 0 0
\(713\) 58664.8 3.08137
\(714\) 0 0
\(715\) −348.871 −0.0182476
\(716\) 0 0
\(717\) 6697.06 11599.6i 0.348823 0.604179i
\(718\) 0 0
\(719\) 1695.87 + 2937.33i 0.0879628 + 0.152356i 0.906650 0.421884i \(-0.138631\pi\)
−0.818687 + 0.574240i \(0.805298\pi\)
\(720\) 0 0
\(721\) −1631.33 + 1046.53i −0.0842632 + 0.0540564i
\(722\) 0 0
\(723\) 652.967 + 1130.97i 0.0335880 + 0.0581761i
\(724\) 0 0
\(725\) −4367.93 + 7565.48i −0.223753 + 0.387551i
\(726\) 0 0
\(727\) 23158.7 1.18144 0.590722 0.806875i \(-0.298843\pi\)
0.590722 + 0.806875i \(0.298843\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −9486.94 + 16431.9i −0.480010 + 0.831402i
\(732\) 0 0
\(733\) 13814.6 + 23927.6i 0.696116 + 1.20571i 0.969803 + 0.243890i \(0.0784236\pi\)
−0.273686 + 0.961819i \(0.588243\pi\)
\(734\) 0 0
\(735\) −131.741 + 12.3646i −0.00661136 + 0.000620512i
\(736\) 0 0
\(737\) −22737.0 39381.6i −1.13640 1.96830i
\(738\) 0 0
\(739\) 4730.82 8194.03i 0.235489 0.407879i −0.723926 0.689878i \(-0.757664\pi\)
0.959415 + 0.281999i \(0.0909976\pi\)
\(740\) 0 0
\(741\) −13790.9 −0.683701
\(742\) 0 0
\(743\) −14316.9 −0.706913 −0.353457 0.935451i \(-0.614994\pi\)
−0.353457 + 0.935451i \(0.614994\pi\)
\(744\) 0 0
\(745\) −25.3762 + 43.9529i −0.00124794 + 0.00216149i
\(746\) 0 0
\(747\) −4439.93 7690.19i −0.217468 0.376666i
\(748\) 0 0
\(749\) −8007.73 + 5137.10i −0.390649 + 0.250608i
\(750\) 0 0
\(751\) 3743.03 + 6483.13i 0.181871 + 0.315010i 0.942518 0.334156i \(-0.108451\pi\)
−0.760647 + 0.649166i \(0.775118\pi\)
\(752\) 0 0
\(753\) −1294.50 + 2242.15i −0.0626486 + 0.108510i
\(754\) 0 0
\(755\) −401.744 −0.0193655
\(756\) 0 0
\(757\) −17416.8 −0.836227 −0.418114 0.908395i \(-0.637309\pi\)
−0.418114 + 0.908395i \(0.637309\pi\)
\(758\) 0 0
\(759\) −14540.2 + 25184.4i −0.695359 + 1.20440i
\(760\) 0 0
\(761\) 16615.5 + 28778.9i 0.791474 + 1.37087i 0.925054 + 0.379835i \(0.124019\pi\)
−0.133580 + 0.991038i \(0.542647\pi\)
\(762\) 0 0
\(763\) 16043.9 + 8287.62i 0.761240 + 0.393227i
\(764\) 0 0
\(765\) 76.0864 + 131.786i 0.00359596 + 0.00622839i
\(766\) 0 0
\(767\) −1337.22 + 2316.13i −0.0629521 + 0.109036i
\(768\) 0 0
\(769\) 13714.2 0.643103 0.321552 0.946892i \(-0.395796\pi\)
0.321552 + 0.946892i \(0.395796\pi\)
\(770\) 0 0
\(771\) −1610.08 −0.0752082
\(772\) 0 0
\(773\) −7604.65 + 13171.6i −0.353842 + 0.612873i −0.986919 0.161216i \(-0.948458\pi\)
0.633077 + 0.774089i \(0.281792\pi\)
\(774\) 0 0
\(775\) 20425.2 + 35377.5i 0.946704 + 1.63974i
\(776\) 0 0
\(777\) −784.045 16744.2i −0.0362001 0.773095i
\(778\) 0 0
\(779\) −13545.6 23461.6i −0.623004 1.07907i
\(780\) 0 0
\(781\) 6510.79 11277.0i 0.298303 0.516675i
\(782\) 0 0
\(783\) −1887.20 −0.0861339
\(784\) 0 0
\(785\) −463.019 −0.0210520
\(786\) 0 0
\(787\) 6610.74 11450.1i 0.299425 0.518619i −0.676580 0.736369i \(-0.736539\pi\)
0.976004 + 0.217750i \(0.0698719\pi\)
\(788\) 0 0
\(789\) −557.862 966.246i −0.0251716 0.0435986i
\(790\) 0 0
\(791\) −1668.47 35632.3i −0.0749989 1.60169i
\(792\) 0 0
\(793\) −2715.73 4703.79i −0.121612 0.210639i