Properties

Label 336.4.q.m.289.3
Level $336$
Weight $4$
Character 336.289
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 289.3
Root \(-2.57353i\) of defining polynomial
Character \(\chi\) \(=\) 336.289
Dual form 336.4.q.m.193.3

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

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

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 −0.868886 0.495011i \(-0.835164\pi\)
0.863136 + 0.504972i \(0.168497\pi\)
\(6\) 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 0.952421 + 0.304787i \(0.0985852\pi\)
−0.212257 + 0.977214i \(0.568081\pi\)
\(12\) 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 0.769285 + 0.638906i \(0.220613\pi\)
0.168666 + 0.985673i \(0.446054\pi\)
\(18\) 0 0
\(19\) 45.7547 79.2495i 0.552466 0.956899i −0.445630 0.895217i \(-0.647020\pi\)
0.998096 0.0616814i \(-0.0196463\pi\)
\(20\) 0 0
\(21\) 49.3638 25.4994i 0.512955 0.264972i
\(22\) 0 0
\(23\) 89.7436 155.441i 0.813602 1.40920i −0.0967260 0.995311i \(-0.530837\pi\)
0.910328 0.413888i \(-0.135830\pi\)
\(24\) 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 0.752046 + 0.659110i \(0.229067\pi\)
0.194783 + 0.980846i \(0.437600\pi\)
\(32\) 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 0.307578 + 0.951523i \(0.400481\pi\)
−0.977832 + 0.209391i \(0.932852\pi\)
\(38\) 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 0.438836 + 0.898567i \(0.355391\pi\)
−0.997600 + 0.0692409i \(0.977942\pi\)
\(48\) 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 0.864834 0.502058i \(-0.167424\pi\)
−0.867212 + 0.497939i \(0.834090\pi\)
\(54\) 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 \(-0.185374\pi\)
−0.893899 + 0.448268i \(0.852041\pi\)
\(60\) 0 0
\(61\) 54.0605 93.6356i 0.113471 0.196538i −0.803696 0.595040i \(-0.797136\pi\)
0.917168 + 0.398502i \(0.130470\pi\)
\(62\) 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 0.938824 + 0.344396i \(0.111916\pi\)
−0.171156 + 0.985244i \(0.554750\pi\)
\(68\) 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 0.936985 0.349370i \(-0.113605\pi\)
−0.771056 + 0.636767i \(0.780271\pi\)
\(74\) 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 \(-0.702781\pi\)
0.993571 + 0.113215i \(0.0361148\pi\)
\(80\) 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 −0.703282 0.710911i \(-0.748283\pi\)
0.967308 + 0.253604i \(0.0816161\pi\)
\(90\) 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 0.622617 0.782526i \(-0.286069\pi\)
−0.988996 + 0.147939i \(0.952736\pi\)
\(102\) 0 0
\(103\) 52.3253 90.6300i 0.0500559 0.0866994i −0.839912 0.542723i \(-0.817393\pi\)
0.889968 + 0.456024i \(0.150727\pi\)
\(104\) 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 \(-0.758786\pi\)
0.958415 + 0.285379i \(0.0921194\pi\)
\(108\) 0 0
\(109\) −487.519 844.408i −0.428402 0.742015i 0.568329 0.822801i \(-0.307590\pi\)
−0.996731 + 0.0807868i \(0.974257\pi\)
\(110\) 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 −0.502038 0.864845i \(-0.667416\pi\)
0.999997 + 0.00235541i \(0.000749751\pi\)
\(132\) 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 0.543233 0.839582i \(-0.317200\pi\)
−0.998716 + 0.0506627i \(0.983867\pi\)
\(138\) 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 −0.915163 0.403083i \(-0.867939\pi\)
0.806662 + 0.591013i \(0.201272\pi\)
\(150\) 0 0
\(151\) −1562.10 2705.64i −0.841867 1.45816i −0.888314 0.459236i \(-0.848123\pi\)
0.0464473 0.998921i \(-0.485210\pi\)
\(152\) 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 0.806633 + 0.591053i \(0.201288\pi\)
0.108551 + 0.994091i \(0.465379\pi\)
\(158\) 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 \(-0.676039\pi\)
0.999567 + 0.0294409i \(0.00937269\pi\)
\(164\) 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 −0.834271 0.551355i \(-0.814111\pi\)
0.894623 + 0.446823i \(0.147445\pi\)
\(174\) 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 \(-0.129745\pi\)
−0.802339 + 0.596869i \(0.796411\pi\)
\(180\) 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 0.141155 0.989988i \(-0.454918\pi\)
0.786777 0.617237i \(-0.211748\pi\)
\(192\) 0 0
\(193\) −1570.13 2719.55i −0.585598 1.01429i −0.994801 0.101842i \(-0.967526\pi\)
0.409202 0.912444i \(-0.365807\pi\)
\(194\) 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 \(-0.236071\pi\)
−0.953679 + 0.300827i \(0.902737\pi\)
\(200\) 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 0.974098 0.226124i \(-0.0726056\pi\)
−0.682879 + 0.730532i \(0.739272\pi\)
\(228\) 0 0
\(229\) −351.738 + 609.228i −0.101500 + 0.175803i −0.912303 0.409516i \(-0.865698\pi\)
0.810803 + 0.585319i \(0.199031\pi\)
\(230\) 0 0
\(231\) 2525.62 + 1620.23i 0.719365 + 0.461486i
\(232\) 0 0
\(233\) −480.892 + 832.929i −0.135211 + 0.234193i −0.925678 0.378312i \(-0.876505\pi\)
0.790467 + 0.612505i \(0.209838\pi\)
\(234\) 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 0.893647 0.448771i \(-0.148138\pi\)
−0.835471 + 0.549535i \(0.814805\pi\)
\(242\) 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 −0.831620 0.555344i \(-0.812586\pi\)
0.896753 + 0.442532i \(0.145920\pi\)
\(258\) 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 \(-0.152784\pi\)
−0.843403 + 0.537282i \(0.819451\pi\)
\(264\) 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 0.999924 + 0.0123024i \(0.00391609\pi\)
−0.489308 + 0.872111i \(0.662751\pi\)
\(270\) 0 0
\(271\) −198.058 + 343.046i −0.0443954 + 0.0768951i −0.887369 0.461059i \(-0.847469\pi\)
0.842974 + 0.537955i \(0.180803\pi\)
\(272\) 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 0.966363 + 0.257181i \(0.0827935\pi\)
−0.260457 + 0.965486i \(0.583873\pi\)
\(278\) 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 \(-0.166646\pi\)
−0.865993 + 0.500056i \(0.833313\pi\)
\(284\) 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 0.999582 0.0289155i \(-0.00920538\pi\)
−0.524833 + 0.851206i \(0.675872\pi\)
\(312\) 0 0
\(313\) 1995.86 3456.92i 0.360423 0.624271i −0.627607 0.778530i \(-0.715966\pi\)
0.988030 + 0.154259i \(0.0492990\pi\)
\(314\) 0 0
\(315\) −19.0432 + 9.83698i −0.00340624 + 0.00175953i
\(316\) 0 0
\(317\) −902.519 + 1563.21i −0.159907 + 0.276967i −0.934835 0.355083i \(-0.884453\pi\)
0.774928 + 0.632050i \(0.217786\pi\)
\(318\) 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 −0.422801 0.906222i \(-0.638953\pi\)
0.996212 0.0869547i \(-0.0277136\pi\)
\(332\) 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 −0.992465 0.122531i \(-0.960899\pi\)
0.390117 0.920765i \(-0.372434\pi\)
\(348\) 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 0.965341 0.260992i \(-0.0840497\pi\)
−0.708696 + 0.705514i \(0.750716\pi\)
\(354\) 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 \(-0.728075\pi\)
0.981448 + 0.191727i \(0.0614088\pi\)
\(360\) 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 \(-0.284243\pi\)
−0.988131 + 0.153612i \(0.950910\pi\)
\(368\) 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 −0.522370 0.852719i \(-0.674952\pi\)
0.999661 + 0.0260264i \(0.00828540\pi\)
\(374\) 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 0.487476 + 0.873136i \(0.337918\pi\)
−0.999896 + 0.0144017i \(0.995416\pi\)
\(384\) 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 −0.997298 0.0734585i \(-0.976596\pi\)
0.435032 0.900415i \(-0.356737\pi\)
\(390\) 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 −0.988379 0.152008i \(-0.951426\pi\)
0.625832 + 0.779957i \(0.284759\pi\)
\(398\) 0 0
\(399\) 237.812 5078.77i 0.0298384 0.637234i
\(400\) 0 0
\(401\) 3608.89 6250.79i 0.449425 0.778427i −0.548923 0.835873i \(-0.684962\pi\)
0.998349 + 0.0574453i \(0.0182955\pi\)
\(402\) 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 0.982386 + 0.186861i \(0.0598313\pi\)
−0.329367 + 0.944202i \(0.606835\pi\)
\(410\) 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 0.970526 0.240997i \(-0.0774745\pi\)
−0.693973 + 0.720001i \(0.744141\pi\)
\(432\) 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 \(-0.915720\pi\)
0.709208 + 0.705000i \(0.249053\pi\)
\(440\) 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 \(-0.862399\pi\)
0.816825 + 0.576886i \(0.195732\pi\)
\(444\) 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 −0.434712 0.900569i \(-0.643150\pi\)
0.997272 0.0738128i \(-0.0235167\pi\)
\(458\) 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 −0.810160 0.586208i \(-0.800620\pi\)
0.912751 + 0.408515i \(0.133953\pi\)
\(468\) 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 \(-0.169381\pi\)
−0.870257 + 0.492597i \(0.836048\pi\)
\(480\) 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 −0.936379 0.350991i \(-0.885845\pi\)
0.164223 0.986423i \(-0.447488\pi\)
\(488\) 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 −0.842097 0.539325i \(-0.818679\pi\)
0.888118 + 0.459615i \(0.152013\pi\)
\(500\) 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 −0.705297 0.708912i \(-0.749186\pi\)
0.966584 + 0.256349i \(0.0825197\pi\)
\(510\) 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 0.750278 0.661122i \(-0.229920\pi\)
−0.947688 + 0.319199i \(0.896586\pi\)
\(522\) 0 0
\(523\) 385.884 668.370i 0.0322629 0.0558810i −0.849443 0.527680i \(-0.823062\pi\)
0.881706 + 0.471799i \(0.156395\pi\)
\(524\) 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 −0.925418 0.378949i \(-0.876286\pi\)
0.790888 + 0.611961i \(0.209619\pi\)
\(542\) 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 0.938327 + 0.345749i \(0.112375\pi\)
−0.169736 + 0.985490i \(0.554291\pi\)
\(558\) 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 \(-0.310824\pi\)
−0.997501 + 0.0706574i \(0.977490\pi\)
\(564\) 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 −0.320018 0.947411i \(-0.603689\pi\)
0.980491 0.196562i \(-0.0629777\pi\)
\(570\) 0 0
\(571\) −7836.84 13573.8i −0.574364 0.994827i −0.996110 0.0881136i \(-0.971916\pi\)
0.421747 0.906714i \(-0.361417\pi\)
\(572\) 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 0.999963 0.00860205i \(-0.00273815\pi\)
−0.507431 + 0.861692i \(0.669405\pi\)
\(578\) 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 0.224204 + 0.974542i \(0.428022\pi\)
−0.956080 + 0.293105i \(0.905311\pi\)
\(594\) 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 \(-0.0631321\pi\)
−0.660837 + 0.750529i \(0.729799\pi\)
\(600\) 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 \(-0.897337\pi\)
0.748716 + 0.662891i \(0.230671\pi\)
\(608\) 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 0.938018 + 0.346586i \(0.112659\pi\)
−0.168856 + 0.985641i \(0.554007\pi\)
\(614\) 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 \(-0.197465\pi\)
−0.910278 + 0.413998i \(0.864132\pi\)
\(620\) 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 0.551601 0.834108i \(-0.314017\pi\)
−0.998159 + 0.0606460i \(0.980684\pi\)
\(642\) 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 0.727832 0.685755i \(-0.240528\pi\)
−0.957798 + 0.287443i \(0.907195\pi\)
\(648\) 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 −0.578184 0.815906i \(-0.696238\pi\)
0.995688 + 0.0927688i \(0.0295717\pi\)
\(654\) 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 0.999880 0.0155194i \(-0.00494019\pi\)
−0.513380 + 0.858161i \(0.671607\pi\)
\(662\) 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 0.203604 + 0.979053i \(0.434735\pi\)
−0.949687 + 0.313201i \(0.898599\pi\)
\(678\) 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 \(-0.105688\pi\)
−0.754982 + 0.655746i \(0.772354\pi\)
\(684\) 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 −0.176617 0.984280i \(-0.556515\pi\)
0.940720 0.339185i \(-0.110151\pi\)
\(692\) 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 −0.565587 0.824688i \(-0.691350\pi\)
0.996995 + 0.0774687i \(0.0246838\pi\)
\(710\) 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 \(-0.861369\pi\)
0.818687 + 0.574240i \(0.194702\pi\)
\(720\) 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 −0.273686 0.961819i \(-0.588243\pi\)
0.969803 0.243890i \(-0.0784236\pi\)
\(734\) 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 \(-0.242336\pi\)
−0.959415 + 0.281999i \(0.909002\pi\)
\(740\) 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 −0.942518 0.334156i \(-0.891549\pi\)
0.760647 + 0.649166i \(0.224882\pi\)
\(752\) 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 −0.133580 0.991038i \(-0.542647\pi\)
0.925054 0.379835i \(-0.124019\pi\)
\(762\) 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 0.633077 0.774089i \(-0.281792\pi\)
−0.986919 + 0.161216i \(0.948458\pi\)
\(774\) 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 \(-0.263461\pi\)
−0.976004 + 0.217750i \(0.930128\pi\)
\(788\) 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