Properties

Label 128.4.g.a.49.4
Level $128$
Weight $4$
Character 128.49
Analytic conductor $7.552$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.g (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.55224448073\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 49.4
Character \(\chi\) \(=\) 128.49
Dual form 128.4.g.a.81.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.56924 + 1.89264i) q^{3} +(1.37033 - 3.30826i) q^{5} +(6.14642 + 6.14642i) q^{7} +(-1.79604 + 1.79604i) q^{9} +O(q^{10})\) \(q+(-4.56924 + 1.89264i) q^{3} +(1.37033 - 3.30826i) q^{5} +(6.14642 + 6.14642i) q^{7} +(-1.79604 + 1.79604i) q^{9} +(-17.2398 - 7.14095i) q^{11} +(-25.9810 - 62.7238i) q^{13} +17.7098i q^{15} -87.5919i q^{17} +(-48.8193 - 117.860i) q^{19} +(-39.7174 - 16.4515i) q^{21} +(55.7254 - 55.7254i) q^{23} +(79.3216 + 79.3216i) q^{25} +(55.9086 - 134.975i) q^{27} +(-114.139 + 47.2779i) q^{29} -229.997 q^{31} +92.2879 q^{33} +(28.7565 - 11.9113i) q^{35} +(-123.846 + 298.992i) q^{37} +(237.427 + 237.427i) q^{39} +(111.562 - 111.562i) q^{41} +(-76.5574 - 31.7111i) q^{43} +(3.48061 + 8.40293i) q^{45} +367.843i q^{47} -267.443i q^{49} +(165.780 + 400.228i) q^{51} +(-244.994 - 101.480i) q^{53} +(-47.2482 + 47.2482i) q^{55} +(446.134 + 446.134i) q^{57} +(183.495 - 442.997i) q^{59} +(524.604 - 217.298i) q^{61} -22.0784 q^{63} -243.109 q^{65} +(-393.028 + 162.797i) q^{67} +(-149.155 + 360.091i) q^{69} +(354.722 + 354.722i) q^{71} +(-22.2443 + 22.2443i) q^{73} +(-512.566 - 212.312i) q^{75} +(-62.0716 - 149.854i) q^{77} -396.453i q^{79} +653.969i q^{81} +(410.445 + 990.903i) q^{83} +(-289.777 - 120.029i) q^{85} +(432.048 - 432.048i) q^{87} +(170.977 + 170.977i) q^{89} +(225.836 - 545.217i) q^{91} +(1050.91 - 435.301i) q^{93} -456.811 q^{95} -1723.11 q^{97} +(43.7888 - 18.1379i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −4.56924 + 1.89264i −0.879350 + 0.364239i −0.776245 0.630432i \(-0.782878\pi\)
−0.103105 + 0.994670i \(0.532878\pi\)
\(4\) 0 0
\(5\) 1.37033 3.30826i 0.122566 0.295900i −0.850673 0.525695i \(-0.823806\pi\)
0.973239 + 0.229795i \(0.0738055\pi\)
\(6\) 0 0
\(7\) 6.14642 + 6.14642i 0.331875 + 0.331875i 0.853298 0.521423i \(-0.174599\pi\)
−0.521423 + 0.853298i \(0.674599\pi\)
\(8\) 0 0
\(9\) −1.79604 + 1.79604i −0.0665200 + 0.0665200i
\(10\) 0 0
\(11\) −17.2398 7.14095i −0.472544 0.195734i 0.133685 0.991024i \(-0.457319\pi\)
−0.606230 + 0.795290i \(0.707319\pi\)
\(12\) 0 0
\(13\) −25.9810 62.7238i −0.554296 1.33819i −0.914224 0.405209i \(-0.867199\pi\)
0.359928 0.932980i \(-0.382801\pi\)
\(14\) 0 0
\(15\) 17.7098i 0.304843i
\(16\) 0 0
\(17\) 87.5919i 1.24966i −0.780762 0.624828i \(-0.785169\pi\)
0.780762 0.624828i \(-0.214831\pi\)
\(18\) 0 0
\(19\) −48.8193 117.860i −0.589470 1.42311i −0.884011 0.467467i \(-0.845167\pi\)
0.294541 0.955639i \(-0.404833\pi\)
\(20\) 0 0
\(21\) −39.7174 16.4515i −0.412716 0.170953i
\(22\) 0 0
\(23\) 55.7254 55.7254i 0.505198 0.505198i −0.407851 0.913049i \(-0.633722\pi\)
0.913049 + 0.407851i \(0.133722\pi\)
\(24\) 0 0
\(25\) 79.3216 + 79.3216i 0.634572 + 0.634572i
\(26\) 0 0
\(27\) 55.9086 134.975i 0.398504 0.962074i
\(28\) 0 0
\(29\) −114.139 + 47.2779i −0.730865 + 0.302734i −0.716907 0.697168i \(-0.754443\pi\)
−0.0139575 + 0.999903i \(0.504443\pi\)
\(30\) 0 0
\(31\) −229.997 −1.33254 −0.666269 0.745711i \(-0.732110\pi\)
−0.666269 + 0.745711i \(0.732110\pi\)
\(32\) 0 0
\(33\) 92.2879 0.486826
\(34\) 0 0
\(35\) 28.7565 11.9113i 0.138878 0.0575253i
\(36\) 0 0
\(37\) −123.846 + 298.992i −0.550277 + 1.32849i 0.366995 + 0.930223i \(0.380387\pi\)
−0.917272 + 0.398262i \(0.869613\pi\)
\(38\) 0 0
\(39\) 237.427 + 237.427i 0.974840 + 0.974840i
\(40\) 0 0
\(41\) 111.562 111.562i 0.424952 0.424952i −0.461953 0.886904i \(-0.652851\pi\)
0.886904 + 0.461953i \(0.152851\pi\)
\(42\) 0 0
\(43\) −76.5574 31.7111i −0.271509 0.112463i 0.242775 0.970083i \(-0.421942\pi\)
−0.514284 + 0.857620i \(0.671942\pi\)
\(44\) 0 0
\(45\) 3.48061 + 8.40293i 0.0115302 + 0.0278363i
\(46\) 0 0
\(47\) 367.843i 1.14161i 0.821087 + 0.570803i \(0.193368\pi\)
−0.821087 + 0.570803i \(0.806632\pi\)
\(48\) 0 0
\(49\) 267.443i 0.779718i
\(50\) 0 0
\(51\) 165.780 + 400.228i 0.455173 + 1.09889i
\(52\) 0 0
\(53\) −244.994 101.480i −0.634952 0.263006i 0.0419036 0.999122i \(-0.486658\pi\)
−0.676855 + 0.736116i \(0.736658\pi\)
\(54\) 0 0
\(55\) −47.2482 + 47.2482i −0.115835 + 0.115835i
\(56\) 0 0
\(57\) 446.134 + 446.134i 1.03670 + 1.03670i
\(58\) 0 0
\(59\) 183.495 442.997i 0.404899 0.977513i −0.581560 0.813504i \(-0.697557\pi\)
0.986459 0.164009i \(-0.0524427\pi\)
\(60\) 0 0
\(61\) 524.604 217.298i 1.10113 0.456101i 0.243252 0.969963i \(-0.421786\pi\)
0.857873 + 0.513862i \(0.171786\pi\)
\(62\) 0 0
\(63\) −22.0784 −0.0441527
\(64\) 0 0
\(65\) −243.109 −0.463907
\(66\) 0 0
\(67\) −393.028 + 162.797i −0.716656 + 0.296849i −0.711056 0.703136i \(-0.751783\pi\)
−0.00560040 + 0.999984i \(0.501783\pi\)
\(68\) 0 0
\(69\) −149.155 + 360.091i −0.260233 + 0.628259i
\(70\) 0 0
\(71\) 354.722 + 354.722i 0.592926 + 0.592926i 0.938421 0.345495i \(-0.112289\pi\)
−0.345495 + 0.938421i \(0.612289\pi\)
\(72\) 0 0
\(73\) −22.2443 + 22.2443i −0.0356644 + 0.0356644i −0.724714 0.689050i \(-0.758028\pi\)
0.689050 + 0.724714i \(0.258028\pi\)
\(74\) 0 0
\(75\) −512.566 212.312i −0.789147 0.326876i
\(76\) 0 0
\(77\) −62.0716 149.854i −0.0918664 0.221785i
\(78\) 0 0
\(79\) 396.453i 0.564614i −0.959324 0.282307i \(-0.908900\pi\)
0.959324 0.282307i \(-0.0910996\pi\)
\(80\) 0 0
\(81\) 653.969i 0.897077i
\(82\) 0 0
\(83\) 410.445 + 990.903i 0.542798 + 1.31043i 0.922741 + 0.385420i \(0.125943\pi\)
−0.379943 + 0.925010i \(0.624057\pi\)
\(84\) 0 0
\(85\) −289.777 120.029i −0.369773 0.153165i
\(86\) 0 0
\(87\) 432.048 432.048i 0.532419 0.532419i
\(88\) 0 0
\(89\) 170.977 + 170.977i 0.203635 + 0.203635i 0.801555 0.597920i \(-0.204006\pi\)
−0.597920 + 0.801555i \(0.704006\pi\)
\(90\) 0 0
\(91\) 225.836 545.217i 0.260155 0.628069i
\(92\) 0 0
\(93\) 1050.91 435.301i 1.17177 0.485362i
\(94\) 0 0
\(95\) −456.811 −0.493345
\(96\) 0 0
\(97\) −1723.11 −1.80367 −0.901833 0.432085i \(-0.857778\pi\)
−0.901833 + 0.432085i \(0.857778\pi\)
\(98\) 0 0
\(99\) 43.7888 18.1379i 0.0444539 0.0184134i
\(100\) 0 0
\(101\) −134.279 + 324.178i −0.132290 + 0.319376i −0.976119 0.217236i \(-0.930296\pi\)
0.843829 + 0.536612i \(0.180296\pi\)
\(102\) 0 0
\(103\) −694.181 694.181i −0.664075 0.664075i 0.292263 0.956338i \(-0.405592\pi\)
−0.956338 + 0.292263i \(0.905592\pi\)
\(104\) 0 0
\(105\) −108.852 + 108.852i −0.101170 + 0.101170i
\(106\) 0 0
\(107\) 264.682 + 109.635i 0.239138 + 0.0990544i 0.499034 0.866582i \(-0.333688\pi\)
−0.259896 + 0.965637i \(0.583688\pi\)
\(108\) 0 0
\(109\) 69.2899 + 167.281i 0.0608878 + 0.146996i 0.951395 0.307973i \(-0.0996505\pi\)
−0.890507 + 0.454969i \(0.849650\pi\)
\(110\) 0 0
\(111\) 1600.56i 1.36864i
\(112\) 0 0
\(113\) 2198.94i 1.83061i −0.402758 0.915306i \(-0.631949\pi\)
0.402758 0.915306i \(-0.368051\pi\)
\(114\) 0 0
\(115\) −107.992 260.716i −0.0875680 0.211408i
\(116\) 0 0
\(117\) 159.318 + 65.9915i 0.125888 + 0.0521446i
\(118\) 0 0
\(119\) 538.376 538.376i 0.414730 0.414730i
\(120\) 0 0
\(121\) −694.943 694.943i −0.522121 0.522121i
\(122\) 0 0
\(123\) −298.606 + 720.898i −0.218897 + 0.528465i
\(124\) 0 0
\(125\) 784.645 325.011i 0.561446 0.232559i
\(126\) 0 0
\(127\) −1982.34 −1.38507 −0.692535 0.721384i \(-0.743506\pi\)
−0.692535 + 0.721384i \(0.743506\pi\)
\(128\) 0 0
\(129\) 409.827 0.279715
\(130\) 0 0
\(131\) −201.609 + 83.5090i −0.134463 + 0.0556963i −0.448900 0.893582i \(-0.648184\pi\)
0.314437 + 0.949278i \(0.398184\pi\)
\(132\) 0 0
\(133\) 424.354 1024.48i 0.276663 0.667924i
\(134\) 0 0
\(135\) −369.920 369.920i −0.235834 0.235834i
\(136\) 0 0
\(137\) −332.511 + 332.511i −0.207360 + 0.207360i −0.803144 0.595784i \(-0.796841\pi\)
0.595784 + 0.803144i \(0.296841\pi\)
\(138\) 0 0
\(139\) 917.619 + 380.090i 0.559938 + 0.231934i 0.644658 0.764471i \(-0.277000\pi\)
−0.0847201 + 0.996405i \(0.527000\pi\)
\(140\) 0 0
\(141\) −696.195 1680.76i −0.415817 1.00387i
\(142\) 0 0
\(143\) 1266.87i 0.740848i
\(144\) 0 0
\(145\) 442.388i 0.253368i
\(146\) 0 0
\(147\) 506.174 + 1222.01i 0.284003 + 0.685645i
\(148\) 0 0
\(149\) 2064.41 + 855.107i 1.13505 + 0.470155i 0.869496 0.493940i \(-0.164444\pi\)
0.265558 + 0.964095i \(0.414444\pi\)
\(150\) 0 0
\(151\) 609.506 609.506i 0.328482 0.328482i −0.523527 0.852009i \(-0.675384\pi\)
0.852009 + 0.523527i \(0.175384\pi\)
\(152\) 0 0
\(153\) 157.319 + 157.319i 0.0831272 + 0.0831272i
\(154\) 0 0
\(155\) −315.171 + 760.890i −0.163323 + 0.394298i
\(156\) 0 0
\(157\) −2898.83 + 1200.73i −1.47358 + 0.610376i −0.967672 0.252213i \(-0.918842\pi\)
−0.505906 + 0.862589i \(0.668842\pi\)
\(158\) 0 0
\(159\) 1311.50 0.654142
\(160\) 0 0
\(161\) 685.023 0.335325
\(162\) 0 0
\(163\) −112.364 + 46.5428i −0.0539942 + 0.0223651i −0.409517 0.912302i \(-0.634303\pi\)
0.355523 + 0.934668i \(0.384303\pi\)
\(164\) 0 0
\(165\) 126.464 305.312i 0.0596681 0.144052i
\(166\) 0 0
\(167\) 1557.93 + 1557.93i 0.721895 + 0.721895i 0.968991 0.247096i \(-0.0794763\pi\)
−0.247096 + 0.968991i \(0.579476\pi\)
\(168\) 0 0
\(169\) −1705.75 + 1705.75i −0.776398 + 0.776398i
\(170\) 0 0
\(171\) 299.363 + 124.000i 0.133877 + 0.0554535i
\(172\) 0 0
\(173\) 1117.57 + 2698.06i 0.491141 + 1.18572i 0.954140 + 0.299361i \(0.0967734\pi\)
−0.462999 + 0.886359i \(0.653227\pi\)
\(174\) 0 0
\(175\) 975.087i 0.421198i
\(176\) 0 0
\(177\) 2371.45i 1.00706i
\(178\) 0 0
\(179\) −1394.97 3367.75i −0.582485 1.40624i −0.890553 0.454879i \(-0.849683\pi\)
0.308069 0.951364i \(-0.400317\pi\)
\(180\) 0 0
\(181\) −16.5037 6.83606i −0.00677741 0.00280730i 0.379292 0.925277i \(-0.376168\pi\)
−0.386070 + 0.922470i \(0.626168\pi\)
\(182\) 0 0
\(183\) −1985.77 + 1985.77i −0.802145 + 0.802145i
\(184\) 0 0
\(185\) 819.433 + 819.433i 0.325653 + 0.325653i
\(186\) 0 0
\(187\) −625.489 + 1510.06i −0.244600 + 0.590518i
\(188\) 0 0
\(189\) 1173.25 485.977i 0.451542 0.187035i
\(190\) 0 0
\(191\) 3640.57 1.37917 0.689587 0.724203i \(-0.257792\pi\)
0.689587 + 0.724203i \(0.257792\pi\)
\(192\) 0 0
\(193\) 3234.02 1.20616 0.603082 0.797679i \(-0.293939\pi\)
0.603082 + 0.797679i \(0.293939\pi\)
\(194\) 0 0
\(195\) 1110.82 460.118i 0.407937 0.168973i
\(196\) 0 0
\(197\) −556.709 + 1344.01i −0.201339 + 0.486076i −0.992009 0.126167i \(-0.959733\pi\)
0.790670 + 0.612243i \(0.209733\pi\)
\(198\) 0 0
\(199\) −1366.73 1366.73i −0.486860 0.486860i 0.420454 0.907314i \(-0.361871\pi\)
−0.907314 + 0.420454i \(0.861871\pi\)
\(200\) 0 0
\(201\) 1487.72 1487.72i 0.522068 0.522068i
\(202\) 0 0
\(203\) −992.136 410.956i −0.343026 0.142086i
\(204\) 0 0
\(205\) −216.199 521.951i −0.0736586 0.177828i
\(206\) 0 0
\(207\) 200.170i 0.0672116i
\(208\) 0 0
\(209\) 2380.50i 0.787860i
\(210\) 0 0
\(211\) −1144.59 2763.28i −0.373444 0.901574i −0.993161 0.116749i \(-0.962753\pi\)
0.619717 0.784825i \(-0.287247\pi\)
\(212\) 0 0
\(213\) −2292.17 949.447i −0.737356 0.305423i
\(214\) 0 0
\(215\) −209.817 + 209.817i −0.0665554 + 0.0665554i
\(216\) 0 0
\(217\) −1413.66 1413.66i −0.442236 0.442236i
\(218\) 0 0
\(219\) 59.5391 143.740i 0.0183711 0.0443519i
\(220\) 0 0
\(221\) −5494.09 + 2275.73i −1.67228 + 0.692679i
\(222\) 0 0
\(223\) 1712.42 0.514226 0.257113 0.966381i \(-0.417229\pi\)
0.257113 + 0.966381i \(0.417229\pi\)
\(224\) 0 0
\(225\) −284.930 −0.0844236
\(226\) 0 0
\(227\) 2071.09 857.873i 0.605564 0.250833i −0.0587668 0.998272i \(-0.518717\pi\)
0.664330 + 0.747439i \(0.268717\pi\)
\(228\) 0 0
\(229\) 1656.50 3999.14i 0.478010 1.15402i −0.482530 0.875879i \(-0.660282\pi\)
0.960541 0.278140i \(-0.0897179\pi\)
\(230\) 0 0
\(231\) 567.240 + 567.240i 0.161565 + 0.161565i
\(232\) 0 0
\(233\) 4732.54 4732.54i 1.33064 1.33064i 0.425844 0.904797i \(-0.359977\pi\)
0.904797 0.425844i \(-0.140023\pi\)
\(234\) 0 0
\(235\) 1216.92 + 504.065i 0.337801 + 0.139922i
\(236\) 0 0
\(237\) 750.343 + 1811.49i 0.205654 + 0.496493i
\(238\) 0 0
\(239\) 3120.14i 0.844457i 0.906489 + 0.422229i \(0.138752\pi\)
−0.906489 + 0.422229i \(0.861248\pi\)
\(240\) 0 0
\(241\) 1994.40i 0.533073i −0.963825 0.266537i \(-0.914121\pi\)
0.963825 0.266537i \(-0.0858793\pi\)
\(242\) 0 0
\(243\) 271.803 + 656.192i 0.0717539 + 0.173229i
\(244\) 0 0
\(245\) −884.771 366.484i −0.230718 0.0955666i
\(246\) 0 0
\(247\) −6124.27 + 6124.27i −1.57764 + 1.57764i
\(248\) 0 0
\(249\) −3750.84 3750.84i −0.954619 0.954619i
\(250\) 0 0
\(251\) 759.835 1834.40i 0.191077 0.461301i −0.799086 0.601216i \(-0.794683\pi\)
0.990163 + 0.139915i \(0.0446830\pi\)
\(252\) 0 0
\(253\) −1358.63 + 562.761i −0.337613 + 0.139844i
\(254\) 0 0
\(255\) 1551.23 0.380948
\(256\) 0 0
\(257\) 5357.21 1.30029 0.650143 0.759812i \(-0.274709\pi\)
0.650143 + 0.759812i \(0.274709\pi\)
\(258\) 0 0
\(259\) −2598.94 + 1076.52i −0.623515 + 0.258268i
\(260\) 0 0
\(261\) 120.085 289.911i 0.0284793 0.0687551i
\(262\) 0 0
\(263\) −3387.07 3387.07i −0.794127 0.794127i 0.188035 0.982162i \(-0.439788\pi\)
−0.982162 + 0.188035i \(0.939788\pi\)
\(264\) 0 0
\(265\) −671.442 + 671.442i −0.155647 + 0.155647i
\(266\) 0 0
\(267\) −1104.83 457.636i −0.253238 0.104895i
\(268\) 0 0
\(269\) −225.824 545.188i −0.0511849 0.123571i 0.896219 0.443612i \(-0.146303\pi\)
−0.947404 + 0.320041i \(0.896303\pi\)
\(270\) 0 0
\(271\) 4177.50i 0.936403i −0.883622 0.468201i \(-0.844902\pi\)
0.883622 0.468201i \(-0.155098\pi\)
\(272\) 0 0
\(273\) 2918.65i 0.647051i
\(274\) 0 0
\(275\) −801.055 1933.92i −0.175656 0.424071i
\(276\) 0 0
\(277\) −2459.54 1018.78i −0.533500 0.220983i 0.0996351 0.995024i \(-0.468232\pi\)
−0.633136 + 0.774041i \(0.718232\pi\)
\(278\) 0 0
\(279\) 413.084 413.084i 0.0886405 0.0886405i
\(280\) 0 0
\(281\) −1012.51 1012.51i −0.214952 0.214952i 0.591415 0.806367i \(-0.298569\pi\)
−0.806367 + 0.591415i \(0.798569\pi\)
\(282\) 0 0
\(283\) −567.782 + 1370.75i −0.119262 + 0.287924i −0.972225 0.234047i \(-0.924803\pi\)
0.852963 + 0.521971i \(0.174803\pi\)
\(284\) 0 0
\(285\) 2087.28 864.578i 0.433823 0.179695i
\(286\) 0 0
\(287\) 1371.41 0.282062
\(288\) 0 0
\(289\) −2759.34 −0.561640
\(290\) 0 0
\(291\) 7873.31 3261.23i 1.58605 0.656965i
\(292\) 0 0
\(293\) −421.800 + 1018.32i −0.0841018 + 0.203040i −0.960336 0.278846i \(-0.910048\pi\)
0.876234 + 0.481886i \(0.160048\pi\)
\(294\) 0 0
\(295\) −1214.10 1214.10i −0.239619 0.239619i
\(296\) 0 0
\(297\) −1927.70 + 1927.70i −0.376622 + 0.376622i
\(298\) 0 0
\(299\) −4943.12 2047.51i −0.956079 0.396021i
\(300\) 0 0
\(301\) −275.644 665.464i −0.0527836 0.127431i
\(302\) 0 0
\(303\) 1735.39i 0.329028i
\(304\) 0 0
\(305\) 2033.29i 0.381725i
\(306\) 0 0
\(307\) −2140.75 5168.22i −0.397977 0.960800i −0.988145 0.153521i \(-0.950939\pi\)
0.590169 0.807280i \(-0.299061\pi\)
\(308\) 0 0
\(309\) 4485.71 + 1858.04i 0.825836 + 0.342072i
\(310\) 0 0
\(311\) 5781.99 5781.99i 1.05423 1.05423i 0.0557904 0.998443i \(-0.482232\pi\)
0.998443 0.0557904i \(-0.0177679\pi\)
\(312\) 0 0
\(313\) 804.942 + 804.942i 0.145361 + 0.145361i 0.776042 0.630681i \(-0.217224\pi\)
−0.630681 + 0.776042i \(0.717224\pi\)
\(314\) 0 0
\(315\) −30.2546 + 73.0412i −0.00541161 + 0.0130648i
\(316\) 0 0
\(317\) −1951.08 + 808.164i −0.345690 + 0.143189i −0.548771 0.835972i \(-0.684904\pi\)
0.203082 + 0.979162i \(0.434904\pi\)
\(318\) 0 0
\(319\) 2305.34 0.404621
\(320\) 0 0
\(321\) −1416.90 −0.246366
\(322\) 0 0
\(323\) −10323.6 + 4276.18i −1.77839 + 0.736634i
\(324\) 0 0
\(325\) 2914.49 7036.21i 0.497437 1.20092i
\(326\) 0 0
\(327\) −633.204 633.204i −0.107083 0.107083i
\(328\) 0 0
\(329\) −2260.92 + 2260.92i −0.378871 + 0.378871i
\(330\) 0 0
\(331\) 7533.21 + 3120.36i 1.25095 + 0.518158i 0.907119 0.420875i \(-0.138277\pi\)
0.343826 + 0.939033i \(0.388277\pi\)
\(332\) 0 0
\(333\) −314.568 759.435i −0.0517665 0.124975i
\(334\) 0 0
\(335\) 1523.32i 0.248442i
\(336\) 0 0
\(337\) 3018.53i 0.487922i 0.969785 + 0.243961i \(0.0784469\pi\)
−0.969785 + 0.243961i \(0.921553\pi\)
\(338\) 0 0
\(339\) 4161.81 + 10047.5i 0.666780 + 1.60975i
\(340\) 0 0
\(341\) 3965.10 + 1642.40i 0.629683 + 0.260823i
\(342\) 0 0
\(343\) 3752.04 3752.04i 0.590644 0.590644i
\(344\) 0 0
\(345\) 986.884 + 986.884i 0.154006 + 0.154006i
\(346\) 0 0
\(347\) −1631.78 + 3939.46i −0.252445 + 0.609456i −0.998400 0.0565400i \(-0.981993\pi\)
0.745955 + 0.665996i \(0.231993\pi\)
\(348\) 0 0
\(349\) 2555.50 1058.52i 0.391956 0.162354i −0.177996 0.984031i \(-0.556962\pi\)
0.569953 + 0.821678i \(0.306962\pi\)
\(350\) 0 0
\(351\) −9918.72 −1.50833
\(352\) 0 0
\(353\) −4332.58 −0.653257 −0.326629 0.945153i \(-0.605913\pi\)
−0.326629 + 0.945153i \(0.605913\pi\)
\(354\) 0 0
\(355\) 1659.60 687.427i 0.248119 0.102774i
\(356\) 0 0
\(357\) −1441.02 + 3478.92i −0.213632 + 0.515753i
\(358\) 0 0
\(359\) 9290.59 + 9290.59i 1.36585 + 1.36585i 0.866271 + 0.499574i \(0.166510\pi\)
0.499574 + 0.866271i \(0.333490\pi\)
\(360\) 0 0
\(361\) −6657.67 + 6657.67i −0.970648 + 0.970648i
\(362\) 0 0
\(363\) 4490.63 + 1860.08i 0.649303 + 0.268950i
\(364\) 0 0
\(365\) 43.1080 + 104.072i 0.00618186 + 0.0149243i
\(366\) 0 0
\(367\) 2140.92i 0.304511i −0.988341 0.152255i \(-0.951346\pi\)
0.988341 0.152255i \(-0.0486536\pi\)
\(368\) 0 0
\(369\) 400.739i 0.0565356i
\(370\) 0 0
\(371\) −882.096 2129.57i −0.123440 0.298010i
\(372\) 0 0
\(373\) 4123.46 + 1707.99i 0.572399 + 0.237095i 0.650058 0.759885i \(-0.274745\pi\)
−0.0776592 + 0.996980i \(0.524745\pi\)
\(374\) 0 0
\(375\) −2970.10 + 2970.10i −0.409001 + 0.409001i
\(376\) 0 0
\(377\) 5930.90 + 5930.90i 0.810231 + 0.810231i
\(378\) 0 0
\(379\) −2989.05 + 7216.20i −0.405111 + 0.978025i 0.581294 + 0.813694i \(0.302547\pi\)
−0.986405 + 0.164331i \(0.947453\pi\)
\(380\) 0 0
\(381\) 9057.77 3751.85i 1.21796 0.504496i
\(382\) 0 0
\(383\) −6358.57 −0.848323 −0.424161 0.905587i \(-0.639431\pi\)
−0.424161 + 0.905587i \(0.639431\pi\)
\(384\) 0 0
\(385\) −580.814 −0.0768858
\(386\) 0 0
\(387\) 194.455 80.5458i 0.0255418 0.0105798i
\(388\) 0 0
\(389\) −3947.57 + 9530.27i −0.514523 + 1.24217i 0.426703 + 0.904392i \(0.359675\pi\)
−0.941226 + 0.337777i \(0.890325\pi\)
\(390\) 0 0
\(391\) −4881.09 4881.09i −0.631324 0.631324i
\(392\) 0 0
\(393\) 763.145 763.145i 0.0979531 0.0979531i
\(394\) 0 0
\(395\) −1311.57 543.270i −0.167069 0.0692022i
\(396\) 0 0
\(397\) 1253.91 + 3027.20i 0.158519 + 0.382698i 0.983106 0.183037i \(-0.0585927\pi\)
−0.824587 + 0.565735i \(0.808593\pi\)
\(398\) 0 0
\(399\) 5484.25i 0.688110i
\(400\) 0 0
\(401\) 13053.8i 1.62562i −0.582528 0.812810i \(-0.697937\pi\)
0.582528 0.812810i \(-0.302063\pi\)
\(402\) 0 0
\(403\) 5975.56 + 14426.3i 0.738620 + 1.78319i
\(404\) 0 0
\(405\) 2163.50 + 896.150i 0.265445 + 0.109951i
\(406\) 0 0
\(407\) 4270.17 4270.17i 0.520060 0.520060i
\(408\) 0 0
\(409\) 652.548 + 652.548i 0.0788910 + 0.0788910i 0.745451 0.666560i \(-0.232234\pi\)
−0.666560 + 0.745451i \(0.732234\pi\)
\(410\) 0 0
\(411\) 889.998 2148.65i 0.106814 0.257871i
\(412\) 0 0
\(413\) 3850.68 1595.00i 0.458789 0.190036i
\(414\) 0 0
\(415\) 3840.61 0.454284
\(416\) 0 0
\(417\) −4912.19 −0.576861
\(418\) 0 0
\(419\) 382.177 158.303i 0.0445598 0.0184573i −0.360292 0.932839i \(-0.617323\pi\)
0.404852 + 0.914382i \(0.367323\pi\)
\(420\) 0 0
\(421\) −171.786 + 414.729i −0.0198868 + 0.0480111i −0.933511 0.358549i \(-0.883272\pi\)
0.913624 + 0.406560i \(0.133272\pi\)
\(422\) 0 0
\(423\) −660.662 660.662i −0.0759396 0.0759396i
\(424\) 0 0
\(425\) 6947.92 6947.92i 0.792997 0.792997i
\(426\) 0 0
\(427\) 4560.04 + 1888.83i 0.516805 + 0.214068i
\(428\) 0 0
\(429\) −2397.73 5788.64i −0.269846 0.651465i
\(430\) 0 0
\(431\) 3644.76i 0.407336i −0.979040 0.203668i \(-0.934714\pi\)
0.979040 0.203668i \(-0.0652863\pi\)
\(432\) 0 0
\(433\) 361.093i 0.0400763i 0.999799 + 0.0200382i \(0.00637877\pi\)
−0.999799 + 0.0200382i \(0.993621\pi\)
\(434\) 0 0
\(435\) −837.280 2021.37i −0.0922863 0.222799i
\(436\) 0 0
\(437\) −9288.29 3847.34i −1.01675 0.421151i
\(438\) 0 0
\(439\) −2187.45 + 2187.45i −0.237817 + 0.237817i −0.815945 0.578129i \(-0.803783\pi\)
0.578129 + 0.815945i \(0.303783\pi\)
\(440\) 0 0
\(441\) 480.339 + 480.339i 0.0518668 + 0.0518668i
\(442\) 0 0
\(443\) 6147.99 14842.6i 0.659367 1.59185i −0.139415 0.990234i \(-0.544522\pi\)
0.798783 0.601620i \(-0.205478\pi\)
\(444\) 0 0
\(445\) 799.930 331.342i 0.0852142 0.0352969i
\(446\) 0 0
\(447\) −11051.2 −1.16936
\(448\) 0 0
\(449\) −13620.0 −1.43156 −0.715779 0.698326i \(-0.753928\pi\)
−0.715779 + 0.698326i \(0.753928\pi\)
\(450\) 0 0
\(451\) −2719.96 + 1126.64i −0.283986 + 0.117631i
\(452\) 0 0
\(453\) −1631.40 + 3938.55i −0.169205 + 0.408497i
\(454\) 0 0
\(455\) −1494.25 1494.25i −0.153959 0.153959i
\(456\) 0 0
\(457\) −3302.76 + 3302.76i −0.338067 + 0.338067i −0.855639 0.517573i \(-0.826836\pi\)
0.517573 + 0.855639i \(0.326836\pi\)
\(458\) 0 0
\(459\) −11822.7 4897.14i −1.20226 0.497993i
\(460\) 0 0
\(461\) −2319.14 5598.89i −0.234301 0.565654i 0.762373 0.647138i \(-0.224034\pi\)
−0.996675 + 0.0814840i \(0.974034\pi\)
\(462\) 0 0
\(463\) 11103.9i 1.11456i −0.830326 0.557279i \(-0.811846\pi\)
0.830326 0.557279i \(-0.188154\pi\)
\(464\) 0 0
\(465\) 4073.19i 0.406214i
\(466\) 0 0
\(467\) 3094.31 + 7470.32i 0.306611 + 0.740225i 0.999810 + 0.0194791i \(0.00620077\pi\)
−0.693199 + 0.720746i \(0.743799\pi\)
\(468\) 0 0
\(469\) −3416.33 1415.09i −0.336357 0.139324i
\(470\) 0 0
\(471\) 10972.9 10972.9i 1.07347 1.07347i
\(472\) 0 0
\(473\) 1093.39 + 1093.39i 0.106287 + 0.106287i
\(474\) 0 0
\(475\) 5476.44 13221.3i 0.529002 1.27712i
\(476\) 0 0
\(477\) 622.280 257.757i 0.0597322 0.0247419i
\(478\) 0 0
\(479\) 2969.80 0.283285 0.141643 0.989918i \(-0.454762\pi\)
0.141643 + 0.989918i \(0.454762\pi\)
\(480\) 0 0
\(481\) 21971.6 2.08278
\(482\) 0 0
\(483\) −3130.03 + 1296.50i −0.294868 + 0.122139i
\(484\) 0 0
\(485\) −2361.23 + 5700.50i −0.221067 + 0.533704i
\(486\) 0 0
\(487\) 14166.3 + 14166.3i 1.31814 + 1.31814i 0.915246 + 0.402895i \(0.131996\pi\)
0.402895 + 0.915246i \(0.368004\pi\)
\(488\) 0 0
\(489\) 425.331 425.331i 0.0393336 0.0393336i
\(490\) 0 0
\(491\) −16702.1 6918.24i −1.53514 0.635877i −0.554589 0.832124i \(-0.687125\pi\)
−0.980555 + 0.196247i \(0.937125\pi\)
\(492\) 0 0
\(493\) 4141.16 + 9997.65i 0.378314 + 0.913330i
\(494\) 0 0
\(495\) 169.719i 0.0154108i
\(496\) 0 0
\(497\) 4360.54i 0.393555i
\(498\) 0 0
\(499\) −4361.00 10528.4i −0.391232 0.944519i −0.989672 0.143351i \(-0.954212\pi\)
0.598439 0.801168i \(-0.295788\pi\)
\(500\) 0 0
\(501\) −10067.2 4169.96i −0.897741 0.371856i
\(502\) 0 0
\(503\) −9988.91 + 9988.91i −0.885454 + 0.885454i −0.994082 0.108628i \(-0.965354\pi\)
0.108628 + 0.994082i \(0.465354\pi\)
\(504\) 0 0
\(505\) 888.460 + 888.460i 0.0782890 + 0.0782890i
\(506\) 0 0
\(507\) 4565.59 11022.3i 0.399931 0.965520i
\(508\) 0 0
\(509\) −1708.35 + 707.622i −0.148765 + 0.0616204i −0.455824 0.890070i \(-0.650655\pi\)
0.307059 + 0.951691i \(0.400655\pi\)
\(510\) 0 0
\(511\) −273.446 −0.0236723
\(512\) 0 0
\(513\) −18637.6 −1.60404
\(514\) 0 0
\(515\) −3247.78 + 1345.28i −0.277892 + 0.115107i
\(516\) 0 0
\(517\) 2626.75 6341.53i 0.223451 0.539459i
\(518\) 0 0
\(519\) −10212.9 10212.9i −0.863770 0.863770i
\(520\) 0 0
\(521\) 11373.3 11373.3i 0.956377 0.956377i −0.0427108 0.999087i \(-0.513599\pi\)
0.999087 + 0.0427108i \(0.0135994\pi\)
\(522\) 0 0
\(523\) 3452.22 + 1429.96i 0.288633 + 0.119556i 0.522302 0.852760i \(-0.325073\pi\)
−0.233669 + 0.972316i \(0.575073\pi\)
\(524\) 0 0
\(525\) −1845.49 4455.40i −0.153417 0.370380i
\(526\) 0 0
\(527\) 20145.9i 1.66521i
\(528\) 0 0
\(529\) 5956.35i 0.489550i
\(530\) 0 0
\(531\) 466.075 + 1125.21i 0.0380903 + 0.0919581i
\(532\) 0 0
\(533\) −9896.07 4099.08i −0.804214 0.333116i
\(534\) 0 0
\(535\) 725.402 725.402i 0.0586203 0.0586203i
\(536\) 0 0
\(537\) 12747.9 + 12747.9i 1.02442 + 1.02442i
\(538\) 0 0
\(539\) −1909.80 + 4610.66i −0.152617 + 0.368451i
\(540\) 0 0
\(541\) 13493.1 5589.03i 1.07230 0.444161i 0.224498 0.974475i \(-0.427926\pi\)
0.847802 + 0.530314i \(0.177926\pi\)
\(542\) 0 0
\(543\) 88.3476 0.00698224
\(544\) 0 0
\(545\) 648.357 0.0509588
\(546\) 0 0
\(547\) 10714.7 4438.16i 0.837525 0.346914i 0.0776476 0.996981i \(-0.475259\pi\)
0.759877 + 0.650067i \(0.225259\pi\)
\(548\) 0 0
\(549\) −551.934 + 1332.49i −0.0429070 + 0.103587i
\(550\) 0 0
\(551\) 11144.4 + 11144.4i 0.861645 + 0.861645i
\(552\) 0 0
\(553\) 2436.77 2436.77i 0.187381 0.187381i
\(554\) 0 0
\(555\) −5295.07 2193.29i −0.404979 0.167748i
\(556\) 0 0
\(557\) −8959.38 21629.9i −0.681546 1.64540i −0.761154 0.648571i \(-0.775367\pi\)
0.0796083 0.996826i \(-0.474633\pi\)
\(558\) 0 0
\(559\) 5625.86i 0.425668i
\(560\) 0 0
\(561\) 8083.67i 0.608365i
\(562\) 0 0
\(563\) −144.332 348.448i −0.0108044 0.0260841i 0.918385 0.395687i \(-0.129494\pi\)
−0.929190 + 0.369603i \(0.879494\pi\)
\(564\) 0 0
\(565\) −7274.68 3013.27i −0.541678 0.224370i
\(566\) 0 0
\(567\) −4019.56 + 4019.56i −0.297718 + 0.297718i
\(568\) 0 0
\(569\) −8107.90 8107.90i −0.597365 0.597365i 0.342246 0.939611i \(-0.388813\pi\)
−0.939611 + 0.342246i \(0.888813\pi\)
\(570\) 0 0
\(571\) −3680.55 + 8885.63i −0.269748 + 0.651229i −0.999471 0.0325132i \(-0.989649\pi\)
0.729723 + 0.683743i \(0.239649\pi\)
\(572\) 0 0
\(573\) −16634.6 + 6890.28i −1.21278 + 0.502349i
\(574\) 0 0
\(575\) 8840.46 0.641170
\(576\) 0 0
\(577\) 20668.9 1.49126 0.745629 0.666361i \(-0.232149\pi\)
0.745629 + 0.666361i \(0.232149\pi\)
\(578\) 0 0
\(579\) −14777.0 + 6120.83i −1.06064 + 0.439331i
\(580\) 0 0
\(581\) −3567.73 + 8613.27i −0.254758 + 0.615040i
\(582\) 0 0
\(583\) 3498.97 + 3498.97i 0.248564 + 0.248564i
\(584\) 0 0
\(585\) 436.634 436.634i 0.0308591 0.0308591i
\(586\) 0 0
\(587\) 834.858 + 345.810i 0.0587024 + 0.0243153i 0.411841 0.911256i \(-0.364886\pi\)
−0.353139 + 0.935571i \(0.614886\pi\)
\(588\) 0 0
\(589\) 11228.3 + 27107.5i 0.785491 + 1.89634i
\(590\) 0 0
\(591\) 7194.77i 0.500767i
\(592\) 0 0
\(593\) 8473.46i 0.586785i −0.955992 0.293392i \(-0.905216\pi\)
0.955992 0.293392i \(-0.0947842\pi\)
\(594\) 0 0
\(595\) −1043.34 2518.84i −0.0718868 0.173550i
\(596\) 0 0
\(597\) 8831.67 + 3658.20i 0.605454 + 0.250787i
\(598\) 0 0
\(599\) 4342.08 4342.08i 0.296181 0.296181i −0.543335 0.839516i \(-0.682839\pi\)
0.839516 + 0.543335i \(0.182839\pi\)
\(600\) 0 0
\(601\) −6136.50 6136.50i −0.416494 0.416494i 0.467499 0.883993i \(-0.345155\pi\)
−0.883993 + 0.467499i \(0.845155\pi\)
\(602\) 0 0
\(603\) 413.503 998.284i 0.0279256 0.0674184i
\(604\) 0 0
\(605\) −3251.35 + 1346.75i −0.218489 + 0.0905013i
\(606\) 0 0
\(607\) −3622.97 −0.242260 −0.121130 0.992637i \(-0.538652\pi\)
−0.121130 + 0.992637i \(0.538652\pi\)
\(608\) 0 0
\(609\) 5311.10 0.353393
\(610\) 0 0
\(611\) 23072.5 9556.95i 1.52768 0.632787i
\(612\) 0 0
\(613\) 1515.46 3658.63i 0.0998510 0.241062i −0.866058 0.499944i \(-0.833354\pi\)
0.965909 + 0.258882i \(0.0833541\pi\)
\(614\) 0 0
\(615\) 1975.73 + 1975.73i 0.129543 + 0.129543i
\(616\) 0 0
\(617\) −5257.77 + 5257.77i −0.343063 + 0.343063i −0.857518 0.514454i \(-0.827994\pi\)
0.514454 + 0.857518i \(0.327994\pi\)
\(618\) 0 0
\(619\) 23417.3 + 9699.75i 1.52055 + 0.629831i 0.977701 0.210000i \(-0.0673466\pi\)
0.542846 + 0.839832i \(0.317347\pi\)
\(620\) 0 0
\(621\) −4406.02 10637.1i −0.284714 0.687361i
\(622\) 0 0
\(623\) 2101.79i 0.135163i
\(624\) 0 0
\(625\) 10981.0i 0.702786i
\(626\) 0 0
\(627\) −4505.43 10877.1i −0.286969 0.692804i
\(628\) 0 0
\(629\) 26189.3 + 10847.9i 1.66015 + 0.687656i
\(630\) 0 0
\(631\) −19776.5 + 19776.5i −1.24768 + 1.24768i −0.290944 + 0.956740i \(0.593969\pi\)
−0.956740 + 0.290944i \(0.906031\pi\)
\(632\) 0 0
\(633\) 10459.8 + 10459.8i 0.656776 + 0.656776i
\(634\) 0 0
\(635\) −2716.45 + 6558.08i −0.169762 + 0.409842i
\(636\) 0 0
\(637\) −16775.0 + 6948.45i −1.04341 + 0.432194i
\(638\) 0 0
\(639\) −1274.19 −0.0788829
\(640\) 0 0
\(641\) 304.324 0.0187521 0.00937603 0.999956i \(-0.497015\pi\)
0.00937603 + 0.999956i \(0.497015\pi\)
\(642\) 0 0
\(643\) −16207.7 + 6713.43i −0.994040 + 0.411745i −0.819608 0.572924i \(-0.805809\pi\)
−0.174432 + 0.984669i \(0.555809\pi\)
\(644\) 0 0
\(645\) 561.596 1355.81i 0.0342835 0.0827676i
\(646\) 0 0
\(647\) −13156.7 13156.7i −0.799450 0.799450i 0.183559 0.983009i \(-0.441238\pi\)
−0.983009 + 0.183559i \(0.941238\pi\)
\(648\) 0 0
\(649\) −6326.83 + 6326.83i −0.382666 + 0.382666i
\(650\) 0 0
\(651\) 9134.88 + 3783.79i 0.549960 + 0.227801i
\(652\) 0 0
\(653\) 7533.14 + 18186.6i 0.451447 + 1.08989i 0.971772 + 0.235921i \(0.0758106\pi\)
−0.520326 + 0.853968i \(0.674189\pi\)
\(654\) 0 0
\(655\) 781.408i 0.0466139i
\(656\) 0 0
\(657\) 79.9035i 0.00474480i
\(658\) 0 0
\(659\) 4387.91 + 10593.4i 0.259376 + 0.626189i 0.998898 0.0469438i \(-0.0149482\pi\)
−0.739521 + 0.673133i \(0.764948\pi\)
\(660\) 0 0
\(661\) 17601.5 + 7290.76i 1.03573 + 0.429013i 0.834777 0.550588i \(-0.185596\pi\)
0.200953 + 0.979601i \(0.435596\pi\)
\(662\) 0 0
\(663\) 20796.7 20796.7i 1.21821 1.21821i
\(664\) 0 0
\(665\) −2807.75 2807.75i −0.163729 0.163729i
\(666\) 0 0
\(667\) −3725.86 + 8995.03i −0.216291 + 0.522172i
\(668\) 0 0
\(669\) −7824.47 + 3241.00i −0.452185 + 0.187301i
\(670\) 0 0
\(671\) −10595.8 −0.609605
\(672\) 0 0
\(673\) 1023.41 0.0586174 0.0293087 0.999570i \(-0.490669\pi\)
0.0293087 + 0.999570i \(0.490669\pi\)
\(674\) 0 0
\(675\) 15141.2 6271.69i 0.863385 0.357626i
\(676\) 0 0
\(677\) −3769.24 + 9099.74i −0.213979 + 0.516590i −0.994028 0.109128i \(-0.965194\pi\)
0.780049 + 0.625718i \(0.215194\pi\)
\(678\) 0 0
\(679\) −10591.0 10591.0i −0.598592 0.598592i
\(680\) 0 0
\(681\) −7839.65 + 7839.65i −0.441139 + 0.441139i
\(682\) 0 0
\(683\) 2058.49 + 852.656i 0.115324 + 0.0477686i 0.439599 0.898194i \(-0.355120\pi\)
−0.324276 + 0.945963i \(0.605120\pi\)
\(684\) 0 0
\(685\) 644.384 + 1555.68i 0.0359426 + 0.0867731i
\(686\) 0 0
\(687\) 21408.2i 1.18890i
\(688\) 0 0
\(689\) 18003.5i 0.995468i
\(690\) 0 0
\(691\) −11541.0 27862.4i −0.635370 1.53392i −0.832784 0.553598i \(-0.813255\pi\)
0.197415 0.980320i \(-0.436745\pi\)
\(692\) 0 0
\(693\) 380.627 + 157.661i 0.0208641 + 0.00864220i
\(694\) 0 0
\(695\) 2514.87 2514.87i 0.137258 0.137258i
\(696\) 0 0
\(697\) −9771.90 9771.90i −0.531043 0.531043i
\(698\) 0 0
\(699\) −12667.1 + 30581.1i −0.685428 + 1.65477i
\(700\) 0 0
\(701\) 3783.29 1567.09i 0.203841 0.0844339i −0.278427 0.960457i \(-0.589813\pi\)
0.482268 + 0.876024i \(0.339813\pi\)
\(702\) 0 0
\(703\) 41285.4 2.21495
\(704\) 0 0
\(705\) −6514.41 −0.348010
\(706\) 0 0
\(707\) −2817.87 + 1167.20i −0.149897 + 0.0620892i
\(708\) 0 0
\(709\) 7928.02 19139.9i 0.419948 1.01384i −0.562414 0.826856i \(-0.690127\pi\)
0.982362 0.186988i \(-0.0598727\pi\)
\(710\) 0 0
\(711\) 712.046 + 712.046i 0.0375581 + 0.0375581i
\(712\) 0 0
\(713\) −12816.7 + 12816.7i −0.673196 + 0.673196i
\(714\) 0 0
\(715\) 4191.15 + 1736.03i 0.219217 + 0.0908025i
\(716\) 0 0
\(717\) −5905.31 14256.7i −0.307584 0.742573i
\(718\) 0 0
\(719\) 35836.7i 1.85881i −0.369064 0.929404i \(-0.620322\pi\)
0.369064 0.929404i \(-0.379678\pi\)
\(720\) 0 0
\(721\) 8533.45i 0.440780i
\(722\) 0 0
\(723\) 3774.68 + 9112.89i 0.194166 + 0.468758i
\(724\) 0 0
\(725\) −12803.8 5303.53i −0.655894 0.271680i
\(726\) 0 0
\(727\) −17934.8 + 17934.8i −0.914946 + 0.914946i −0.996656 0.0817100i \(-0.973962\pi\)
0.0817100 + 0.996656i \(0.473962\pi\)
\(728\) 0 0
\(729\) −14969.4 14969.4i −0.760523 0.760523i
\(730\) 0 0
\(731\) −2777.64 + 6705.81i −0.140540 + 0.339293i
\(732\) 0 0
\(733\) 12620.5 5227.58i 0.635946 0.263418i −0.0413310 0.999146i \(-0.513160\pi\)
0.677277 + 0.735728i \(0.263160\pi\)
\(734\) 0 0
\(735\) 4736.35 0.237691
\(736\) 0 0
\(737\) 7938.23 0.396755
\(738\) 0 0
\(739\) 12203.1 5054.70i 0.607441 0.251610i −0.0576928 0.998334i \(-0.518374\pi\)
0.665134 + 0.746724i \(0.268374\pi\)
\(740\) 0 0
\(741\) 16392.2 39574.3i 0.812662 1.96194i
\(742\) 0 0
\(743\) −3084.12 3084.12i −0.152282 0.152282i 0.626854 0.779136i \(-0.284342\pi\)
−0.779136 + 0.626854i \(0.784342\pi\)
\(744\) 0 0
\(745\) 5657.83 5657.83i 0.278237 0.278237i
\(746\) 0 0
\(747\) −2516.88 1042.53i −0.123277 0.0510629i
\(748\) 0 0
\(749\) 952.985 + 2300.71i 0.0464904 + 0.112238i
\(750\) 0 0
\(751\) 30535.2i 1.48368i −0.670575 0.741842i \(-0.733952\pi\)
0.670575 0.741842i \(-0.266048\pi\)
\(752\) 0 0
\(753\) 9819.92i 0.475243i
\(754\) 0 0
\(755\) −1181.18 2851.62i −0.0569372 0.137459i
\(756\) 0 0
\(757\) −8109.52 3359.07i −0.389360 0.161278i 0.179411 0.983774i \(-0.442581\pi\)
−0.568771 + 0.822496i \(0.692581\pi\)
\(758\) 0 0
\(759\) 5142.78 5142.78i 0.245943 0.245943i
\(760\) 0 0
\(761\) −13700.0 13700.0i −0.652595 0.652595i 0.301022 0.953617i \(-0.402672\pi\)
−0.953617 + 0.301022i \(0.902672\pi\)
\(762\) 0 0
\(763\) −602.292 + 1454.06i −0.0285772 + 0.0689915i
\(764\) 0 0
\(765\) 736.028 304.873i 0.0347858 0.0144088i
\(766\) 0 0
\(767\) −32553.8 −1.53253
\(768\) 0 0
\(769\) −5576.68 −0.261509 −0.130754 0.991415i \(-0.541740\pi\)
−0.130754 + 0.991415i \(0.541740\pi\)
\(770\) 0 0
\(771\) −24478.4 + 10139.3i −1.14341 + 0.473614i
\(772\) 0 0
\(773\) 12414.0 29969.9i 0.577618 1.39449i −0.317327 0.948316i \(-0.602785\pi\)
0.894945 0.446177i \(-0.147215\pi\)
\(774\) 0 0
\(775\) −18243.7 18243.7i −0.845592 0.845592i
\(776\) 0 0
\(777\) 9837.72 9837.72i 0.454216 0.454216i
\(778\) 0 0
\(779\) −18595.1 7702.33i −0.855247 0.354255i
\(780\) 0 0
\(781\) −3582.27 8648.37i −0.164128 0.396240i
\(782\) 0 0
\(783\) 18049.2i 0.823787i
\(784\) 0 0
\(785\) 11235.5i 0.510842i
\(786\) 0 0