Properties

Label 336.4.q.m.193.3
Level $336$
Weight $4$
Character 336.193
Analytic conductor $19.825$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8246417619\)
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: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 193.3
Root \(2.57353i\) of defining polynomial
Character \(\chi\) \(=\) 336.193
Dual form 336.4.q.m.289.3

$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 \(-0.568081\pi\)
0.952421 0.304787i \(-0.0985852\pi\)
\(12\) 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 \(0.0196463\pi\)
−0.445630 + 0.895217i \(0.647020\pi\)
\(20\) 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 \(0.135830\pi\)
−0.0967260 + 0.995311i \(0.530837\pi\)
\(24\) 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 \(-0.437600\pi\)
0.752046 0.659110i \(-0.229067\pi\)
\(32\) 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 \(-0.417634\pi\)
0.255882 + 0.966708i \(0.417634\pi\)
\(44\) 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 \(-0.977942\pi\)
0.438836 0.898567i \(-0.355391\pi\)
\(48\) 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 −0.893899 0.448268i \(-0.852041\pi\)
0.835161 + 0.550005i \(0.185374\pi\)
\(60\) 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 \(-0.554750\pi\)
0.938824 0.344396i \(-0.111916\pi\)
\(68\) 0 0
\(69\) 538.462 0.939466
\(70\) 0 0
\(71\) 241.111 0.403023 0.201511 0.979486i \(-0.435415\pi\)
0.201511 + 0.979486i \(0.435415\pi\)
\(72\) 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 0.993571 0.113215i \(-0.0361148\pi\)
−0.594832 + 0.803850i \(0.702781\pi\)
\(80\) 0 0
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −986.652 −1.30481 −0.652404 0.757871i \(-0.726240\pi\)
−0.652404 + 0.757871i \(0.726240\pi\)
\(84\) 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 0.889968 0.456024i \(-0.150727\pi\)
−0.839912 + 0.542723i \(0.817393\pi\)
\(104\) 0 0
\(105\) −0.334180 7.13680i −0.000310596 0.00663315i
\(106\) 0 0
\(107\) 256.850 + 444.878i 0.232062 + 0.401943i 0.958415 0.285379i \(-0.0921194\pi\)
−0.726353 + 0.687322i \(0.758786\pi\)
\(108\) 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 \(-0.371314\pi\)
0.393355 + 0.919387i \(0.371314\pi\)
\(128\) 0 0
\(129\) 216.453 374.908i 0.147734 0.255882i
\(130\) 0 0
\(131\) 746.621 + 1293.19i 0.497959 + 0.862490i 0.999997 0.00235541i \(-0.000749751\pi\)
−0.502038 + 0.864845i \(0.667416\pi\)
\(132\) 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 \(-0.737637\pi\)
−0.679116 + 0.734031i \(0.737637\pi\)
\(140\) 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 \(0.485210\pi\)
−0.888314 + 0.459236i \(0.848123\pi\)
\(152\) 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 0.999567 0.0294409i \(-0.00937269\pi\)
−0.525280 + 0.850930i \(0.676039\pi\)
\(164\) 0 0
\(165\) −10.4172 + 18.0430i −0.00491499 + 0.00851302i
\(166\) 0 0
\(167\) −1067.09 −0.494453 −0.247227 0.968958i \(-0.579519\pi\)
−0.247227 + 0.968958i \(0.579519\pi\)
\(168\) 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 −0.802339 0.596869i \(-0.796411\pi\)
0.918073 + 0.396412i \(0.129745\pi\)
\(180\) 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 \(0.211748\pi\)
0.141155 + 0.989988i \(0.454918\pi\)
\(192\) 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 −0.953679 0.300827i \(-0.902737\pi\)
0.737363 + 0.675497i \(0.236071\pi\)
\(200\) 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 \(-0.814306\pi\)
−0.834608 + 0.550844i \(0.814306\pi\)
\(212\) 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 \(-0.505706\pi\)
−0.0179250 + 0.999839i \(0.505706\pi\)
\(224\) 0 0
\(225\) −1124.85 −0.333289
\(226\) 0 0
\(227\) 996.000 1725.12i 0.291220 0.504407i −0.682879 0.730532i \(-0.739272\pi\)
0.974098 + 0.226124i \(0.0726056\pi\)
\(228\) 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 \(-0.293501\pi\)
0.604179 + 0.796848i \(0.293501\pi\)
\(240\) 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 \(-0.534608\pi\)
−0.108510 + 0.994095i \(0.534608\pi\)
\(252\) 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 −0.843403 0.537282i \(-0.819451\pi\)
0.887001 + 0.461767i \(0.152784\pi\)
\(264\) 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 0.842974 0.537955i \(-0.180803\pi\)
−0.887369 + 0.461059i \(0.847469\pi\)
\(272\) 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 −0.865993 0.500056i \(-0.833313\pi\)
0.866058 + 0.499944i \(0.166646\pi\)
\(284\) 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 \(-0.558334\pi\)
−0.182236 + 0.983255i \(0.558334\pi\)
\(308\) 0 0
\(309\) 313.952 0.0577996
\(310\) 0 0
\(311\) 2603.78 4509.89i 0.474749 0.822290i −0.524833 0.851206i \(-0.675872\pi\)
0.999582 + 0.0289155i \(0.00920538\pi\)
\(312\) 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 \(0.0277136\pi\)
−0.422801 + 0.906222i \(0.638953\pi\)
\(332\) 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 \(0.372434\pi\)
−0.992465 + 0.122531i \(0.960899\pi\)
\(348\) 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 0.981448 0.191727i \(-0.0614088\pi\)
−0.656764 + 0.754096i \(0.728075\pi\)
\(360\) 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 −0.988131 0.153612i \(-0.950910\pi\)
0.627097 + 0.778941i \(0.284243\pi\)
\(368\) 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 \(-0.283363\pi\)
0.629248 + 0.777205i \(0.283363\pi\)
\(380\) 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 \(-0.995416\pi\)
0.487476 0.873136i \(-0.337918\pi\)
\(384\) 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 \(-0.781172\pi\)
−0.772856 + 0.634582i \(0.781172\pi\)
\(420\) 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 −0.693973 0.720001i \(-0.744141\pi\)
0.970526 + 0.240997i \(0.0774745\pi\)
\(432\) 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 0.709208 0.705000i \(-0.249053\pi\)
−0.965151 + 0.261692i \(0.915720\pi\)
\(440\) 0 0
\(441\) 1786.56 + 2517.49i 0.192913 + 0.271838i
\(442\) 0 0
\(443\) −850.218 1472.62i −0.0911852 0.157937i 0.816825 0.576886i \(-0.195732\pi\)
−0.908010 + 0.418948i \(0.862399\pi\)
\(444\) 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 \(-0.564796\pi\)
−0.202159 + 0.979353i \(0.564796\pi\)
\(464\) 0 0
\(465\) −63.0444 + 109.196i −0.00628734 + 0.0108900i
\(466\) 0 0
\(467\) 1035.35 + 1793.27i 0.102591 + 0.177693i 0.912751 0.408515i \(-0.133953\pi\)
−0.810160 + 0.586208i \(0.800620\pi\)
\(468\) 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 −0.870257 0.492597i \(-0.836048\pi\)
0.861730 + 0.507366i \(0.169381\pi\)
\(480\) 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 \(0.447488\pi\)
−0.936379 + 0.350991i \(0.885845\pi\)
\(488\) 0 0
\(489\) 5922.07 0.547659
\(490\) 0 0
\(491\) 4547.22 0.417949 0.208975 0.977921i \(-0.432987\pi\)
0.208975 + 0.977921i \(0.432987\pi\)
\(492\) 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 0.888118 0.459615i \(-0.152013\pi\)
−0.842097 + 0.539325i \(0.818679\pi\)
\(500\) 0 0
\(501\) −1600.63 + 2772.37i −0.142736 + 0.247227i
\(502\) 0 0
\(503\) −6745.26 −0.597925 −0.298962 0.954265i \(-0.596641\pi\)
−0.298962 + 0.954265i \(0.596641\pi\)
\(504\) 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 0.881706 0.471799i \(-0.156395\pi\)
−0.849443 + 0.527680i \(0.823062\pi\)
\(524\) 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 \(-0.562463\pi\)
−0.194976 + 0.980808i \(0.562463\pi\)
\(548\) 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 −0.997501 0.0706574i \(-0.977490\pi\)
0.559941 + 0.828532i \(0.310824\pi\)
\(564\) 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 \(0.361417\pi\)
−0.996110 + 0.0881136i \(0.971916\pi\)
\(572\) 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 \(-0.281583\pi\)
0.633583 + 0.773675i \(0.281583\pi\)
\(588\) 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 −0.660837 0.750529i \(-0.729799\pi\)
0.980396 + 0.197037i \(0.0631321\pi\)
\(600\) 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 0.748716 0.662891i \(-0.230671\pi\)
−0.948438 + 0.316962i \(0.897337\pi\)
\(608\) 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 −0.910278 0.413998i \(-0.864132\pi\)
0.813672 + 0.581324i \(0.197465\pi\)
\(620\) 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 \(-0.473548\pi\)
0.0830044 + 0.996549i \(0.473548\pi\)
\(632\) 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 \(-0.345916\pi\)
0.465383 + 0.885109i \(0.345916\pi\)
\(644\) 0 0
\(645\) −55.6679 −0.00339833
\(646\) 0 0
\(647\) −3784.59 + 6555.10i −0.229965 + 0.398312i −0.957798 0.287443i \(-0.907195\pi\)
0.727832 + 0.685755i \(0.240528\pi\)
\(648\) 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 \(-0.332265\pi\)
0.502904 + 0.864342i \(0.332265\pi\)
\(660\) 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 −0.754982 0.655746i \(-0.772354\pi\)
0.945383 + 0.325961i \(0.105688\pi\)
\(684\) 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 \(0.110151\pi\)
−0.176617 + 0.984280i \(0.556515\pi\)
\(692\) 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 0.818687 0.574240i \(-0.194702\pi\)
−0.906650 + 0.421884i \(0.861369\pi\)
\(720\) 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 \(-0.701157\pi\)
−0.590722 + 0.806875i \(0.701157\pi\)
\(728\) 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 −0.959415 0.281999i \(-0.909002\pi\)
0.723926 + 0.689878i \(0.242336\pi\)
\(740\) 0 0
\(741\) −13790.9 −0.683701
\(742\) 0 0
\(743\) 14316.9 0.706913 0.353457 0.935451i \(-0.385006\pi\)
0.353457 + 0.935451i \(0.385006\pi\)
\(744\) 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 0.760647 0.649166i \(-0.224882\pi\)
−0.942518 + 0.334156i \(0.891549\pi\)
\(752\) 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 −0.976004 0.217750i \(-0.930128\pi\)
0.676580 + 0.736369i \(0.263461\pi\)
\(788\) 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
\(794\) 0 0