Newspace parameters
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(4.82290067918\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
Defining polynomial: | \(x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + 5962230 x^{6} + 6517782 x^{4} + 3428244 x^{2} + 570861\) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.8 | ||
Root | \(-1.39995i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.3.c.a.58.13 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.39995i | − | 0.699974i | −0.936755 | − | 0.349987i | \(-0.886186\pi\) | ||
0.936755 | − | 0.349987i | \(-0.113814\pi\) | |||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 2.04015 | 0.510037 | ||||||||
\(5\) | 0.273484 | 0.0546968 | 0.0273484 | − | 0.999626i | \(-0.491294\pi\) | ||||
0.0273484 | + | 0.999626i | \(0.491294\pi\) | |||||||
\(6\) | 2.42478i | 0.404130i | ||||||||
\(7\) | −10.8938 | −1.55626 | −0.778132 | − | 0.628101i | \(-0.783832\pi\) | ||||
−0.778132 | + | 0.628101i | \(0.783832\pi\) | |||||||
\(8\) | − | 8.45589i | − | 1.05699i | ||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 0.382863i | − | 0.0382863i | ||||||
\(11\) | − | 15.0527i | − | 1.36842i | −0.729284 | − | 0.684212i | \(-0.760146\pi\) | ||
0.729284 | − | 0.684212i | \(-0.239854\pi\) | |||||||
\(12\) | −3.53364 | −0.294470 | ||||||||
\(13\) | − | 11.1132i | − | 0.854858i | −0.904049 | − | 0.427429i | \(-0.859419\pi\) | ||
0.904049 | − | 0.427429i | \(-0.140581\pi\) | |||||||
\(14\) | 15.2508i | 1.08934i | ||||||||
\(15\) | −0.473689 | −0.0315792 | ||||||||
\(16\) | −3.67721 | −0.229825 | ||||||||
\(17\) | −3.40920 | −0.200541 | −0.100271 | − | 0.994960i | \(-0.531971\pi\) | ||||
−0.100271 | + | 0.994960i | \(0.531971\pi\) | |||||||
\(18\) | − | 4.19984i | − | 0.233325i | ||||||
\(19\) | −15.7121 | −0.826954 | −0.413477 | − | 0.910515i | \(-0.635686\pi\) | ||||
−0.413477 | + | 0.910515i | \(0.635686\pi\) | |||||||
\(20\) | 0.557948 | 0.0278974 | ||||||||
\(21\) | 18.8687 | 0.898509 | ||||||||
\(22\) | −21.0729 | −0.957860 | ||||||||
\(23\) | 15.2765i | 0.664194i | 0.943245 | + | 0.332097i | \(0.107756\pi\) | ||||
−0.943245 | + | 0.332097i | \(0.892244\pi\) | |||||||
\(24\) | 14.6460i | 0.610251i | ||||||||
\(25\) | −24.9252 | −0.997008 | ||||||||
\(26\) | −15.5578 | −0.598378 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | −22.2251 | −0.793752 | ||||||||
\(29\) | 22.5689 | 0.778237 | 0.389118 | − | 0.921188i | \(-0.372780\pi\) | ||||
0.389118 | + | 0.921188i | \(0.372780\pi\) | |||||||
\(30\) | 0.663139i | 0.0221046i | ||||||||
\(31\) | − | 59.5188i | − | 1.91996i | −0.280067 | − | 0.959981i | \(-0.590357\pi\) | ||
0.280067 | − | 0.959981i | \(-0.409643\pi\) | |||||||
\(32\) | − | 28.6757i | − | 0.896114i | ||||||
\(33\) | 26.0720i | 0.790060i | ||||||||
\(34\) | 4.77271i | 0.140374i | ||||||||
\(35\) | −2.97929 | −0.0851227 | ||||||||
\(36\) | 6.12044 | 0.170012 | ||||||||
\(37\) | 42.4500i | 1.14730i | 0.819101 | + | 0.573649i | \(0.194473\pi\) | ||||
−0.819101 | + | 0.573649i | \(0.805527\pi\) | |||||||
\(38\) | 21.9961i | 0.578846i | ||||||||
\(39\) | 19.2485i | 0.493553i | ||||||||
\(40\) | − | 2.31255i | − | 0.0578138i | ||||||
\(41\) | 78.4822 | 1.91420 | 0.957101 | − | 0.289756i | \(-0.0935741\pi\) | ||||
0.957101 | + | 0.289756i | \(0.0935741\pi\) | |||||||
\(42\) | − | 26.4152i | − | 0.628933i | ||||||
\(43\) | 78.3986i | 1.82322i | 0.411052 | + | 0.911612i | \(0.365162\pi\) | ||||
−0.411052 | + | 0.911612i | \(0.634838\pi\) | |||||||
\(44\) | − | 30.7096i | − | 0.697946i | ||||||
\(45\) | 0.820453 | 0.0182323 | ||||||||
\(46\) | 21.3862 | 0.464918 | ||||||||
\(47\) | − | 35.3465i | − | 0.752054i | −0.926609 | − | 0.376027i | \(-0.877290\pi\) | ||
0.926609 | − | 0.376027i | \(-0.122710\pi\) | |||||||
\(48\) | 6.36911 | 0.132690 | ||||||||
\(49\) | 69.6759 | 1.42196 | ||||||||
\(50\) | 34.8940i | 0.697879i | ||||||||
\(51\) | 5.90491 | 0.115783 | ||||||||
\(52\) | − | 22.6725i | − | 0.436009i | ||||||
\(53\) | 37.2779 | 0.703357 | 0.351678 | − | 0.936121i | \(-0.385611\pi\) | ||||
0.351678 | + | 0.936121i | \(0.385611\pi\) | |||||||
\(54\) | 7.27434i | 0.134710i | ||||||||
\(55\) | − | 4.11666i | − | 0.0748484i | ||||||
\(56\) | 92.1171i | 1.64495i | ||||||||
\(57\) | 27.2142 | 0.477442 | ||||||||
\(58\) | − | 31.5952i | − | 0.544745i | ||||||
\(59\) | 52.6472 | − | 26.6321i | 0.892326 | − | 0.451392i | ||||
\(60\) | −0.966395 | −0.0161066 | ||||||||
\(61\) | − | 44.2464i | − | 0.725350i | −0.931916 | − | 0.362675i | \(-0.881864\pi\) | ||
0.931916 | − | 0.362675i | \(-0.118136\pi\) | |||||||
\(62\) | −83.3232 | −1.34392 | ||||||||
\(63\) | −32.6815 | −0.518755 | ||||||||
\(64\) | −54.8532 | −0.857082 | ||||||||
\(65\) | − | 3.03927i | − | 0.0467580i | ||||||
\(66\) | 36.4994 | 0.553021 | ||||||||
\(67\) | 17.3224i | 0.258544i | 0.991609 | + | 0.129272i | \(0.0412640\pi\) | ||||
−0.991609 | + | 0.129272i | \(0.958736\pi\) | |||||||
\(68\) | −6.95528 | −0.102284 | ||||||||
\(69\) | − | 26.4596i | − | 0.383473i | ||||||
\(70\) | 4.17086i | 0.0595836i | ||||||||
\(71\) | −59.0750 | −0.832043 | −0.416021 | − | 0.909355i | \(-0.636576\pi\) | ||||
−0.416021 | + | 0.909355i | \(0.636576\pi\) | |||||||
\(72\) | − | 25.3677i | − | 0.352329i | ||||||
\(73\) | − | 85.3122i | − | 1.16866i | −0.811516 | − | 0.584330i | \(-0.801357\pi\) | ||
0.811516 | − | 0.584330i | \(-0.198643\pi\) | |||||||
\(74\) | 59.4278 | 0.803079 | ||||||||
\(75\) | 43.1717 | 0.575623 | ||||||||
\(76\) | −32.0550 | −0.421777 | ||||||||
\(77\) | 163.981i | 2.12963i | ||||||||
\(78\) | 26.9470 | 0.345474 | ||||||||
\(79\) | 62.2163 | 0.787548 | 0.393774 | − | 0.919207i | \(-0.371169\pi\) | ||||
0.393774 | + | 0.919207i | \(0.371169\pi\) | |||||||
\(80\) | −1.00566 | −0.0125707 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 109.871i | − | 1.33989i | ||||||
\(83\) | − | 98.9653i | − | 1.19235i | −0.802853 | − | 0.596177i | \(-0.796686\pi\) | ||
0.802853 | − | 0.596177i | \(-0.203314\pi\) | |||||||
\(84\) | 38.4949 | 0.458273 | ||||||||
\(85\) | −0.932363 | −0.0109690 | ||||||||
\(86\) | 109.754 | 1.27621 | ||||||||
\(87\) | −39.0904 | −0.449315 | ||||||||
\(88\) | −127.284 | −1.44640 | ||||||||
\(89\) | 35.9346i | 0.403759i | 0.979410 | + | 0.201880i | \(0.0647050\pi\) | ||||
−0.979410 | + | 0.201880i | \(0.935295\pi\) | |||||||
\(90\) | − | 1.14859i | − | 0.0127621i | ||||||
\(91\) | 121.065i | 1.33038i | ||||||||
\(92\) | 31.1663i | 0.338764i | ||||||||
\(93\) | 103.090i | 1.10849i | ||||||||
\(94\) | −49.4833 | −0.526418 | ||||||||
\(95\) | −4.29702 | −0.0452318 | ||||||||
\(96\) | 49.6677i | 0.517372i | ||||||||
\(97\) | − | 11.0179i | − | 0.113587i | −0.998386 | − | 0.0567935i | \(-0.981912\pi\) | ||
0.998386 | − | 0.0567935i | \(-0.0180877\pi\) | |||||||
\(98\) | − | 97.5426i | − | 0.995332i | ||||||
\(99\) | − | 45.1580i | − | 0.456141i | ||||||
\(100\) | −50.8511 | −0.508511 | ||||||||
\(101\) | 110.774i | 1.09677i | 0.836227 | + | 0.548384i | \(0.184757\pi\) | ||||
−0.836227 | + | 0.548384i | \(0.815243\pi\) | |||||||
\(102\) | − | 8.26657i | − | 0.0810448i | ||||||
\(103\) | 43.0668i | 0.418125i | 0.977902 | + | 0.209062i | \(0.0670412\pi\) | ||||
−0.977902 | + | 0.209062i | \(0.932959\pi\) | |||||||
\(104\) | −93.9716 | −0.903573 | ||||||||
\(105\) | 5.16029 | 0.0491456 | ||||||||
\(106\) | − | 52.1871i | − | 0.492331i | ||||||
\(107\) | −146.405 | −1.36827 | −0.684137 | − | 0.729353i | \(-0.739821\pi\) | ||||
−0.684137 | + | 0.729353i | \(0.739821\pi\) | |||||||
\(108\) | −10.6009 | −0.0981567 | ||||||||
\(109\) | 141.124i | 1.29472i | 0.762185 | + | 0.647359i | \(0.224127\pi\) | ||||
−0.762185 | + | 0.647359i | \(0.775873\pi\) | |||||||
\(110\) | −5.76311 | −0.0523919 | ||||||||
\(111\) | − | 73.5256i | − | 0.662393i | ||||||
\(112\) | 40.0589 | 0.357669 | ||||||||
\(113\) | − | 21.1887i | − | 0.187511i | −0.995595 | − | 0.0937555i | \(-0.970113\pi\) | ||
0.995595 | − | 0.0937555i | \(-0.0298872\pi\) | |||||||
\(114\) | − | 38.0984i | − | 0.334197i | ||||||
\(115\) | 4.17787i | 0.0363293i | ||||||||
\(116\) | 46.0438 | 0.396929 | ||||||||
\(117\) | − | 33.3395i | − | 0.284953i | ||||||
\(118\) | −37.2836 | − | 73.7033i | −0.315963 | − | 0.624604i | ||||
\(119\) | 37.1393 | 0.312095 | ||||||||
\(120\) | 4.00546i | 0.0333788i | ||||||||
\(121\) | −105.582 | −0.872582 | ||||||||
\(122\) | −61.9426 | −0.507726 | ||||||||
\(123\) | −135.935 | −1.10516 | ||||||||
\(124\) | − | 121.427i | − | 0.979251i | ||||||
\(125\) | −13.6538 | −0.109230 | ||||||||
\(126\) | 45.7524i | 0.363115i | ||||||||
\(127\) | 215.084 | 1.69358 | 0.846789 | − | 0.531929i | \(-0.178533\pi\) | ||||
0.846789 | + | 0.531929i | \(0.178533\pi\) | |||||||
\(128\) | − | 37.9110i | − | 0.296180i | ||||||
\(129\) | − | 135.790i | − | 1.05264i | ||||||
\(130\) | −4.25482 | −0.0327294 | ||||||||
\(131\) | − | 79.8202i | − | 0.609314i | −0.952462 | − | 0.304657i | \(-0.901458\pi\) | ||
0.952462 | − | 0.304657i | \(-0.0985419\pi\) | |||||||
\(132\) | 53.1907i | 0.402960i | ||||||||
\(133\) | 171.165 | 1.28696 | ||||||||
\(134\) | 24.2505 | 0.180974 | ||||||||
\(135\) | −1.42107 | −0.0105264 | ||||||||
\(136\) | 28.8278i | 0.211969i | ||||||||
\(137\) | −138.442 | −1.01053 | −0.505265 | − | 0.862965i | \(-0.668605\pi\) | ||||
−0.505265 | + | 0.862965i | \(0.668605\pi\) | |||||||
\(138\) | −37.0421 | −0.268421 | ||||||||
\(139\) | 59.8615 | 0.430658 | 0.215329 | − | 0.976542i | \(-0.430918\pi\) | ||||
0.215329 | + | 0.976542i | \(0.430918\pi\) | |||||||
\(140\) | −6.07820 | −0.0434157 | ||||||||
\(141\) | 61.2220i | 0.434198i | ||||||||
\(142\) | 82.7019i | 0.582408i | ||||||||
\(143\) | −167.282 | −1.16981 | ||||||||
\(144\) | −11.0316 | −0.0766085 | ||||||||
\(145\) | 6.17223 | 0.0425671 | ||||||||
\(146\) | −119.433 | −0.818031 | ||||||||
\(147\) | −120.682 | −0.820967 | ||||||||
\(148\) | 86.6044i | 0.585165i | ||||||||
\(149\) | − | 218.369i | − | 1.46556i | −0.680464 | − | 0.732782i | \(-0.738222\pi\) | ||
0.680464 | − | 0.732782i | \(-0.261778\pi\) | |||||||
\(150\) | − | 60.4381i | − | 0.402921i | ||||||
\(151\) | 26.4104i | 0.174904i | 0.996169 | + | 0.0874518i | \(0.0278724\pi\) | ||||
−0.996169 | + | 0.0874518i | \(0.972128\pi\) | |||||||
\(152\) | 132.860i | 0.874078i | ||||||||
\(153\) | −10.2276 | −0.0668471 | ||||||||
\(154\) | 229.565 | 1.49068 | ||||||||
\(155\) | − | 16.2774i | − | 0.105016i | ||||||
\(156\) | 39.2699i | 0.251730i | ||||||||
\(157\) | − | 18.4659i | − | 0.117617i | −0.998269 | − | 0.0588087i | \(-0.981270\pi\) | ||
0.998269 | − | 0.0588087i | \(-0.0187302\pi\) | |||||||
\(158\) | − | 87.0995i | − | 0.551263i | ||||||
\(159\) | −64.5672 | −0.406083 | ||||||||
\(160\) | − | 7.84234i | − | 0.0490146i | ||||||
\(161\) | − | 166.419i | − | 1.03366i | ||||||
\(162\) | − | 12.5995i | − | 0.0777748i | ||||||
\(163\) | −247.452 | −1.51811 | −0.759055 | − | 0.651026i | \(-0.774339\pi\) | ||||
−0.759055 | + | 0.651026i | \(0.774339\pi\) | |||||||
\(164\) | 160.115 | 0.976313 | ||||||||
\(165\) | 7.13027i | 0.0432138i | ||||||||
\(166\) | −138.546 | −0.834616 | ||||||||
\(167\) | 63.0046 | 0.377273 | 0.188637 | − | 0.982047i | \(-0.439593\pi\) | ||||
0.188637 | + | 0.982047i | \(0.439593\pi\) | |||||||
\(168\) | − | 159.552i | − | 0.949712i | ||||||
\(169\) | 45.4978 | 0.269218 | ||||||||
\(170\) | 1.30526i | 0.00767800i | ||||||||
\(171\) | −47.1364 | −0.275651 | ||||||||
\(172\) | 159.945i | 0.929912i | ||||||||
\(173\) | − | 163.258i | − | 0.943690i | −0.881681 | − | 0.471845i | \(-0.843588\pi\) | ||
0.881681 | − | 0.471845i | \(-0.156412\pi\) | |||||||
\(174\) | 54.7245i | 0.314509i | ||||||||
\(175\) | 271.531 | 1.55161 | ||||||||
\(176\) | 55.3517i | 0.314498i | ||||||||
\(177\) | −91.1876 | + | 46.1282i | −0.515184 | + | 0.260611i | ||||
\(178\) | 50.3065 | 0.282621 | ||||||||
\(179\) | − | 80.5355i | − | 0.449919i | −0.974368 | − | 0.224960i | \(-0.927775\pi\) | ||
0.974368 | − | 0.224960i | \(-0.0722250\pi\) | |||||||
\(180\) | 1.67384 | 0.00929914 | ||||||||
\(181\) | −130.162 | −0.719125 | −0.359563 | − | 0.933121i | \(-0.617074\pi\) | ||||
−0.359563 | + | 0.933121i | \(0.617074\pi\) | |||||||
\(182\) | 169.485 | 0.931234 | ||||||||
\(183\) | 76.6369i | 0.418781i | ||||||||
\(184\) | 129.176 | 0.702044 | ||||||||
\(185\) | 11.6094i | 0.0627536i | ||||||||
\(186\) | 144.320 | 0.775914 | ||||||||
\(187\) | 51.3176i | 0.274426i | ||||||||
\(188\) | − | 72.1121i | − | 0.383575i | ||||||
\(189\) | 56.6061 | 0.299503 | ||||||||
\(190\) | 6.01560i | 0.0316610i | ||||||||
\(191\) | 206.275i | 1.07997i | 0.841674 | + | 0.539987i | \(0.181571\pi\) | ||||
−0.841674 | + | 0.539987i | \(0.818429\pi\) | |||||||
\(192\) | 95.0086 | 0.494836 | ||||||||
\(193\) | 174.658 | 0.904964 | 0.452482 | − | 0.891773i | \(-0.350539\pi\) | ||||
0.452482 | + | 0.891773i | \(0.350539\pi\) | |||||||
\(194\) | −15.4245 | −0.0795079 | ||||||||
\(195\) | 5.26417i | 0.0269958i | ||||||||
\(196\) | 142.149 | 0.725250 | ||||||||
\(197\) | 262.732 | 1.33367 | 0.666833 | − | 0.745207i | \(-0.267649\pi\) | ||||
0.666833 | + | 0.745207i | \(0.267649\pi\) | |||||||
\(198\) | −63.2188 | −0.319287 | ||||||||
\(199\) | −36.7705 | −0.184776 | −0.0923882 | − | 0.995723i | \(-0.529450\pi\) | ||||
−0.0923882 | + | 0.995723i | \(0.529450\pi\) | |||||||
\(200\) | 210.765i | 1.05382i | ||||||||
\(201\) | − | 30.0033i | − | 0.149270i | ||||||
\(202\) | 155.077 | 0.767709 | ||||||||
\(203\) | −245.862 | −1.21114 | ||||||||
\(204\) | 12.0469 | 0.0590534 | ||||||||
\(205\) | 21.4637 | 0.104701 | ||||||||
\(206\) | 60.2913 | 0.292676 | ||||||||
\(207\) | 45.8294i | 0.221398i | ||||||||
\(208\) | 40.8654i | 0.196468i | ||||||||
\(209\) | 236.509i | 1.13162i | ||||||||
\(210\) | − | 7.22413i | − | 0.0344006i | ||||||
\(211\) | − | 332.832i | − | 1.57740i | −0.614775 | − | 0.788702i | \(-0.710753\pi\) | ||
0.614775 | − | 0.788702i | \(-0.289247\pi\) | |||||||
\(212\) | 76.0525 | 0.358738 | ||||||||
\(213\) | 102.321 | 0.480380 | ||||||||
\(214\) | 204.960i | 0.957756i | ||||||||
\(215\) | 21.4408i | 0.0997246i | ||||||||
\(216\) | 43.9381i | 0.203417i | ||||||||
\(217\) | 648.389i | 2.98797i | ||||||||
\(218\) | 197.567 | 0.906269 | ||||||||
\(219\) | 147.765i | 0.674726i | ||||||||
\(220\) | − | 8.39860i | − | 0.0381755i | ||||||
\(221\) | 37.8870i | 0.171434i | ||||||||
\(222\) | −102.932 | −0.463658 | ||||||||
\(223\) | −68.0441 | −0.305131 | −0.152565 | − | 0.988293i | \(-0.548753\pi\) | ||||
−0.152565 | + | 0.988293i | \(0.548753\pi\) | |||||||
\(224\) | 312.388i | 1.39459i | ||||||||
\(225\) | −74.7756 | −0.332336 | ||||||||
\(226\) | −29.6631 | −0.131253 | ||||||||
\(227\) | − | 297.497i | − | 1.31056i | −0.755386 | − | 0.655280i | \(-0.772551\pi\) | ||
0.755386 | − | 0.655280i | \(-0.227449\pi\) | |||||||
\(228\) | 55.5210 | 0.243513 | ||||||||
\(229\) | 27.5954i | 0.120504i | 0.998183 | + | 0.0602519i | \(0.0191904\pi\) | ||||
−0.998183 | + | 0.0602519i | \(0.980810\pi\) | |||||||
\(230\) | 5.84880 | 0.0254296 | ||||||||
\(231\) | − | 284.024i | − | 1.22954i | ||||||
\(232\) | − | 190.840i | − | 0.822585i | ||||||
\(233\) | − | 359.245i | − | 1.54182i | −0.636943 | − | 0.770911i | \(-0.719801\pi\) | ||
0.636943 | − | 0.770911i | \(-0.280199\pi\) | |||||||
\(234\) | −46.6735 | −0.199459 | ||||||||
\(235\) | − | 9.66672i | − | 0.0411350i | ||||||
\(236\) | 107.408 | − | 54.3335i | 0.455119 | − | 0.230227i | ||||
\(237\) | −107.762 | −0.454691 | ||||||||
\(238\) | − | 51.9931i | − | 0.218458i | ||||||
\(239\) | −265.127 | −1.10932 | −0.554659 | − | 0.832078i | \(-0.687151\pi\) | ||||
−0.554659 | + | 0.832078i | \(0.687151\pi\) | |||||||
\(240\) | 1.74185 | 0.00725771 | ||||||||
\(241\) | −58.8858 | −0.244340 | −0.122170 | − | 0.992509i | \(-0.538985\pi\) | ||||
−0.122170 | + | 0.992509i | \(0.538985\pi\) | |||||||
\(242\) | 147.810i | 0.610784i | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | − | 90.2691i | − | 0.369955i | ||||||
\(245\) | 19.0553 | 0.0777765 | ||||||||
\(246\) | 190.302i | 0.773586i | ||||||||
\(247\) | 174.611i | 0.706928i | ||||||||
\(248\) | −503.284 | −2.02937 | ||||||||
\(249\) | 171.413i | 0.688406i | ||||||||
\(250\) | 19.1145i | 0.0764581i | ||||||||
\(251\) | 1.34813 | 0.00537104 | 0.00268552 | − | 0.999996i | \(-0.499145\pi\) | ||||
0.00268552 | + | 0.999996i | \(0.499145\pi\) | |||||||
\(252\) | −66.6752 | −0.264584 | ||||||||
\(253\) | 229.951 | 0.908899 | ||||||||
\(254\) | − | 301.107i | − | 1.18546i | ||||||
\(255\) | 1.61490 | 0.00633294 | ||||||||
\(256\) | −272.486 | −1.06440 | ||||||||
\(257\) | 301.120 | 1.17167 | 0.585837 | − | 0.810429i | \(-0.300766\pi\) | ||||
0.585837 | + | 0.810429i | \(0.300766\pi\) | |||||||
\(258\) | −190.099 | −0.736819 | ||||||||
\(259\) | − | 462.444i | − | 1.78550i | ||||||
\(260\) | − | 6.20056i | − | 0.0238483i | ||||||
\(261\) | 67.7066 | 0.259412 | ||||||||
\(262\) | −111.744 | −0.426504 | ||||||||
\(263\) | 82.6739 | 0.314350 | 0.157175 | − | 0.987571i | \(-0.449761\pi\) | ||||
0.157175 | + | 0.987571i | \(0.449761\pi\) | |||||||
\(264\) | 220.462 | 0.835082 | ||||||||
\(265\) | 10.1949 | 0.0384714 | ||||||||
\(266\) | − | 239.623i | − | 0.900837i | ||||||
\(267\) | − | 62.2405i | − | 0.233111i | ||||||
\(268\) | 35.3403i | 0.131867i | ||||||||
\(269\) | 208.155i | 0.773810i | 0.922120 | + | 0.386905i | \(0.126456\pi\) | ||||
−0.922120 | + | 0.386905i | \(0.873544\pi\) | |||||||
\(270\) | 1.98942i | 0.00736821i | ||||||||
\(271\) | 38.7081 | 0.142834 | 0.0714171 | − | 0.997447i | \(-0.477248\pi\) | ||||
0.0714171 | + | 0.997447i | \(0.477248\pi\) | |||||||
\(272\) | 12.5363 | 0.0460895 | ||||||||
\(273\) | − | 209.691i | − | 0.768098i | ||||||
\(274\) | 193.812i | 0.707344i | ||||||||
\(275\) | 375.191i | 1.36433i | ||||||||
\(276\) | − | 53.9815i | − | 0.195585i | ||||||
\(277\) | 209.375 | 0.755866 | 0.377933 | − | 0.925833i | \(-0.376635\pi\) | ||||
0.377933 | + | 0.925833i | \(0.376635\pi\) | |||||||
\(278\) | − | 83.8030i | − | 0.301450i | ||||||
\(279\) | − | 178.556i | − | 0.639987i | ||||||
\(280\) | 25.1926i | 0.0899735i | ||||||||
\(281\) | 307.082 | 1.09282 | 0.546409 | − | 0.837519i | \(-0.315995\pi\) | ||||
0.546409 | + | 0.837519i | \(0.315995\pi\) | |||||||
\(282\) | 85.7075 | 0.303927 | ||||||||
\(283\) | 229.159i | 0.809749i | 0.914372 | + | 0.404875i | \(0.132685\pi\) | ||||
−0.914372 | + | 0.404875i | \(0.867315\pi\) | |||||||
\(284\) | −120.522 | −0.424373 | ||||||||
\(285\) | 7.44265 | 0.0261146 | ||||||||
\(286\) | 234.187i | 0.818834i | ||||||||
\(287\) | −854.974 | −2.97900 | ||||||||
\(288\) | − | 86.0270i | − | 0.298705i | ||||||
\(289\) | −277.377 | −0.959783 | ||||||||
\(290\) | − | 8.64079i | − | 0.0297958i | ||||||
\(291\) | 19.0836i | 0.0655795i | ||||||||
\(292\) | − | 174.049i | − | 0.596060i | ||||||
\(293\) | 56.5578 | 0.193030 | 0.0965150 | − | 0.995332i | \(-0.469230\pi\) | ||||
0.0965150 | + | 0.995332i | \(0.469230\pi\) | |||||||
\(294\) | 168.949i | 0.574655i | ||||||||
\(295\) | 14.3982 | − | 7.28347i | 0.0488074 | − | 0.0246897i | ||||
\(296\) | 358.953 | 1.21268 | ||||||||
\(297\) | 78.2159i | 0.263353i | ||||||||
\(298\) | −305.705 | −1.02586 | ||||||||
\(299\) | 169.770 | 0.567792 | ||||||||
\(300\) | 88.0767 | 0.293589 | ||||||||
\(301\) | − | 854.063i | − | 2.83742i | ||||||
\(302\) | 36.9732 | 0.122428 | ||||||||
\(303\) | − | 191.865i | − | 0.633219i | ||||||
\(304\) | 57.7767 | 0.190055 | ||||||||
\(305\) | − | 12.1007i | − | 0.0396744i | ||||||
\(306\) | 14.3181i | 0.0467912i | ||||||||
\(307\) | −38.1615 | −0.124305 | −0.0621523 | − | 0.998067i | \(-0.519796\pi\) | ||||
−0.0621523 | + | 0.998067i | \(0.519796\pi\) | |||||||
\(308\) | 334.546i | 1.08619i | ||||||||
\(309\) | − | 74.5940i | − | 0.241404i | ||||||
\(310\) | −22.7876 | −0.0735083 | ||||||||
\(311\) | −237.381 | −0.763282 | −0.381641 | − | 0.924311i | \(-0.624641\pi\) | ||||
−0.381641 | + | 0.924311i | \(0.624641\pi\) | |||||||
\(312\) | 162.764 | 0.521678 | ||||||||
\(313\) | − | 468.363i | − | 1.49637i | −0.663491 | − | 0.748184i | \(-0.730926\pi\) | ||
0.663491 | − | 0.748184i | \(-0.269074\pi\) | |||||||
\(314\) | −25.8513 | −0.0823291 | ||||||||
\(315\) | −8.93788 | −0.0283742 | ||||||||
\(316\) | 126.930 | 0.401679 | ||||||||
\(317\) | −97.7779 | −0.308447 | −0.154224 | − | 0.988036i | \(-0.549288\pi\) | ||||
−0.154224 | + | 0.988036i | \(0.549288\pi\) | |||||||
\(318\) | 90.3907i | 0.284248i | ||||||||
\(319\) | − | 339.721i | − | 1.06496i | ||||||
\(320\) | −15.0015 | −0.0468797 | ||||||||
\(321\) | 253.582 | 0.789974 | ||||||||
\(322\) | −232.978 | −0.723536 | ||||||||
\(323\) | 53.5658 | 0.165838 | ||||||||
\(324\) | 18.3613 | 0.0566708 | ||||||||
\(325\) | 276.998i | 0.852300i | ||||||||
\(326\) | 346.420i | 1.06264i | ||||||||
\(327\) | − | 244.434i | − | 0.747506i | ||||||
\(328\) | − | 663.637i | − | 2.02328i | ||||||
\(329\) | 385.060i | 1.17039i | ||||||||
\(330\) | 9.98200 | 0.0302485 | ||||||||
\(331\) | −248.132 | −0.749644 | −0.374822 | − | 0.927097i | \(-0.622296\pi\) | ||||
−0.374822 | + | 0.927097i | \(0.622296\pi\) | |||||||
\(332\) | − | 201.904i | − | 0.608144i | ||||||
\(333\) | 127.350i | 0.382433i | ||||||||
\(334\) | − | 88.2032i | − | 0.264081i | ||||||
\(335\) | 4.73741i | 0.0141415i | ||||||||
\(336\) | −69.3841 | −0.206500 | ||||||||
\(337\) | 84.1105i | 0.249586i | 0.992183 | + | 0.124793i | \(0.0398267\pi\) | ||||
−0.992183 | + | 0.124793i | \(0.960173\pi\) | |||||||
\(338\) | − | 63.6945i | − | 0.188445i | ||||||
\(339\) | 36.7000i | 0.108260i | ||||||||
\(340\) | −1.90216 | −0.00559459 | ||||||||
\(341\) | −895.916 | −2.62732 | ||||||||
\(342\) | 65.9884i | 0.192949i | ||||||||
\(343\) | −225.240 | −0.656676 | ||||||||
\(344\) | 662.930 | 1.92712 | ||||||||
\(345\) | − | 7.23629i | − | 0.0209747i | ||||||
\(346\) | −228.553 | −0.660558 | ||||||||
\(347\) | − | 521.687i | − | 1.50342i | −0.659493 | − | 0.751711i | \(-0.729229\pi\) | ||
0.659493 | − | 0.751711i | \(-0.270771\pi\) | |||||||
\(348\) | −79.7502 | −0.229167 | ||||||||
\(349\) | 299.873i | 0.859234i | 0.903011 | + | 0.429617i | \(0.141351\pi\) | ||||
−0.903011 | + | 0.429617i | \(0.858649\pi\) | |||||||
\(350\) | − | 380.130i | − | 1.08608i | ||||||
\(351\) | 57.7456i | 0.164518i | ||||||||
\(352\) | −431.645 | −1.22626 | ||||||||
\(353\) | 633.470i | 1.79453i | 0.441491 | + | 0.897266i | \(0.354450\pi\) | ||||
−0.441491 | + | 0.897266i | \(0.645550\pi\) | |||||||
\(354\) | 64.5771 | + | 127.658i | 0.182421 | + | 0.360616i | ||||
\(355\) | −16.1561 | −0.0455101 | ||||||||
\(356\) | 73.3119i | 0.205932i | ||||||||
\(357\) | −64.3272 | −0.180188 | ||||||||
\(358\) | −112.745 | −0.314932 | ||||||||
\(359\) | 456.186 | 1.27071 | 0.635356 | − | 0.772219i | \(-0.280853\pi\) | ||||
0.635356 | + | 0.772219i | \(0.280853\pi\) | |||||||
\(360\) | − | 6.93765i | − | 0.0192713i | ||||||
\(361\) | −114.129 | −0.316148 | ||||||||
\(362\) | 182.220i | 0.503369i | ||||||||
\(363\) | 182.874 | 0.503786 | ||||||||
\(364\) | 246.990i | 0.678545i | ||||||||
\(365\) | − | 23.3315i | − | 0.0639220i | ||||||
\(366\) | 107.288 | 0.293136 | ||||||||
\(367\) | 505.395i | 1.37710i | 0.725190 | + | 0.688549i | \(0.241752\pi\) | ||||
−0.725190 | + | 0.688549i | \(0.758248\pi\) | |||||||
\(368\) | − | 56.1747i | − | 0.152649i | ||||||
\(369\) | 235.447 | 0.638067 | ||||||||
\(370\) | 16.2526 | 0.0439259 | ||||||||
\(371\) | −406.100 | −1.09461 | ||||||||
\(372\) | 210.318i | 0.565371i | ||||||||
\(373\) | −262.292 | −0.703195 | −0.351598 | − | 0.936151i | \(-0.614361\pi\) | ||||
−0.351598 | + | 0.936151i | \(0.614361\pi\) | |||||||
\(374\) | 71.8419 | 0.192091 | ||||||||
\(375\) | 23.6490 | 0.0630640 | ||||||||
\(376\) | −298.886 | −0.794910 | ||||||||
\(377\) | − | 250.811i | − | 0.665282i | ||||||
\(378\) | − | 79.2455i | − | 0.209644i | ||||||
\(379\) | 532.499 | 1.40501 | 0.702505 | − | 0.711679i | \(-0.252065\pi\) | ||||
0.702505 | + | 0.711679i | \(0.252065\pi\) | |||||||
\(380\) | −8.76655 | −0.0230699 | ||||||||
\(381\) | −372.537 | −0.977787 | ||||||||
\(382\) | 288.774 | 0.755953 | ||||||||
\(383\) | 286.541 | 0.748150 | 0.374075 | − | 0.927398i | \(-0.377960\pi\) | ||||
0.374075 | + | 0.927398i | \(0.377960\pi\) | |||||||
\(384\) | 65.6638i | 0.170999i | ||||||||
\(385\) | 44.8463i | 0.116484i | ||||||||
\(386\) | − | 244.512i | − | 0.633451i | ||||||
\(387\) | 235.196i | 0.607741i | ||||||||
\(388\) | − | 22.4782i | − | 0.0579336i | ||||||
\(389\) | 620.394 | 1.59484 | 0.797421 | − | 0.603423i | \(-0.206197\pi\) | ||||
0.797421 | + | 0.603423i | \(0.206197\pi\) | |||||||
\(390\) | 7.36956 | 0.0188963 | ||||||||
\(391\) | − | 52.0806i | − | 0.133198i | ||||||
\(392\) | − | 589.171i | − | 1.50299i | ||||||
\(393\) | 138.253i | 0.351788i | ||||||||
\(394\) | − | 367.811i | − | 0.933531i | ||||||
\(395\) | 17.0152 | 0.0430764 | ||||||||
\(396\) | − | 92.1289i | − | 0.232649i | ||||||
\(397\) | − | 434.013i | − | 1.09323i | −0.837383 | − | 0.546616i | \(-0.815916\pi\) | ||
0.837383 | − | 0.546616i | \(-0.184084\pi\) | |||||||
\(398\) | 51.4767i | 0.129339i | ||||||||
\(399\) | −296.467 | −0.743026 | ||||||||
\(400\) | 91.6551 | 0.229138 | ||||||||
\(401\) | 107.207i | 0.267350i | 0.991025 | + | 0.133675i | \(0.0426778\pi\) | ||||
−0.991025 | + | 0.133675i | \(0.957322\pi\) | |||||||
\(402\) | −42.0031 | −0.104485 | ||||||||
\(403\) | −661.442 | −1.64129 | ||||||||
\(404\) | 225.994i | 0.559392i | ||||||||
\(405\) | 2.46136 | 0.00607743 | ||||||||
\(406\) | 344.193i | 0.847767i | ||||||||
\(407\) | 638.986 | 1.56999 | ||||||||
\(408\) | − | 49.9313i | − | 0.122381i | ||||||
\(409\) | 550.503i | 1.34597i | 0.739654 | + | 0.672987i | \(0.234989\pi\) | ||||
−0.739654 | + | 0.672987i | \(0.765011\pi\) | |||||||
\(410\) | − | 30.0480i | − | 0.0732878i | ||||||
\(411\) | 239.789 | 0.583429 | ||||||||
\(412\) | 87.8627i | 0.213259i | ||||||||
\(413\) | −573.531 | + | 290.126i | −1.38869 | + | 0.702485i | ||||
\(414\) | 64.1587 | 0.154973 | ||||||||
\(415\) | − | 27.0655i | − | 0.0652180i | ||||||
\(416\) | −318.677 | −0.766050 | ||||||||
\(417\) | −103.683 | −0.248641 | ||||||||
\(418\) | 331.100 | 0.792106 | ||||||||
\(419\) | 274.431i | 0.654967i | 0.944857 | + | 0.327483i | \(0.106201\pi\) | ||||
−0.944857 | + | 0.327483i | \(0.893799\pi\) | |||||||
\(420\) | 10.5278 | 0.0250661 | ||||||||
\(421\) | 46.0928i | 0.109484i | 0.998501 | + | 0.0547420i | \(0.0174336\pi\) | ||||
−0.998501 | + | 0.0547420i | \(0.982566\pi\) | |||||||
\(422\) | −465.948 | −1.10414 | ||||||||
\(423\) | − | 106.040i | − | 0.250685i | ||||||
\(424\) | − | 315.218i | − | 0.743438i | ||||||
\(425\) | 84.9751 | 0.199941 | ||||||||
\(426\) | − | 143.244i | − | 0.336253i | ||||||
\(427\) | 482.013i | 1.12884i | ||||||||
\(428\) | −298.689 | −0.697871 | ||||||||
\(429\) | 289.742 | 0.675389 | ||||||||
\(430\) | 30.0160 | 0.0698046 | ||||||||
\(431\) | 256.182i | 0.594389i | 0.954817 | + | 0.297195i | \(0.0960510\pi\) | ||||
−0.954817 | + | 0.297195i | \(0.903949\pi\) | |||||||
\(432\) | 19.1073 | 0.0442299 | ||||||||
\(433\) | 76.7056 | 0.177149 | 0.0885746 | − | 0.996070i | \(-0.471769\pi\) | ||||
0.0885746 | + | 0.996070i | \(0.471769\pi\) | |||||||
\(434\) | 907.710 | 2.09150 | ||||||||
\(435\) | −10.6906 | −0.0245761 | ||||||||
\(436\) | 287.914i | 0.660354i | ||||||||
\(437\) | − | 240.026i | − | 0.549258i | ||||||
\(438\) | 206.863 | 0.472291 | ||||||||
\(439\) | 622.390 | 1.41775 | 0.708873 | − | 0.705336i | \(-0.249204\pi\) | ||||
0.708873 | + | 0.705336i | \(0.249204\pi\) | |||||||
\(440\) | −34.8100 | −0.0791137 | ||||||||
\(441\) | 209.028 | 0.473986 | ||||||||
\(442\) | 53.0398 | 0.120000 | ||||||||
\(443\) | 682.698i | 1.54108i | 0.637392 | + | 0.770540i | \(0.280013\pi\) | ||||
−0.637392 | + | 0.770540i | \(0.719987\pi\) | |||||||
\(444\) | − | 150.003i | − | 0.337845i | ||||||
\(445\) | 9.82754i | 0.0220844i | ||||||||
\(446\) | 95.2582i | 0.213583i | ||||||||
\(447\) | 378.226i | 0.846144i | ||||||||
\(448\) | 597.563 | 1.33385 | ||||||||
\(449\) | −144.491 | −0.321806 | −0.160903 | − | 0.986970i | \(-0.551441\pi\) | ||||
−0.160903 | + | 0.986970i | \(0.551441\pi\) | |||||||
\(450\) | 104.682i | 0.232626i | ||||||||
\(451\) | − | 1181.37i | − | 2.61944i | ||||||
\(452\) | − | 43.2282i | − | 0.0956375i | ||||||
\(453\) | − | 45.7442i | − | 0.100981i | ||||||
\(454\) | −416.480 | −0.917358 | ||||||||
\(455\) | 33.1094i | 0.0727678i | ||||||||
\(456\) | − | 230.120i | − | 0.504649i | ||||||
\(457\) | − | 293.853i | − | 0.643004i | −0.946909 | − | 0.321502i | \(-0.895812\pi\) | ||
0.946909 | − | 0.321502i | \(-0.104188\pi\) | |||||||
\(458\) | 38.6321 | 0.0843495 | ||||||||
\(459\) | 17.7147 | 0.0385942 | ||||||||
\(460\) | 8.52348i | 0.0185293i | ||||||||
\(461\) | 457.634 | 0.992698 | 0.496349 | − | 0.868123i | \(-0.334674\pi\) | ||||
0.496349 | + | 0.868123i | \(0.334674\pi\) | |||||||
\(462\) | −397.619 | −0.860646 | ||||||||
\(463\) | 671.285i | 1.44986i | 0.688822 | + | 0.724930i | \(0.258128\pi\) | ||||
−0.688822 | + | 0.724930i | \(0.741872\pi\) | |||||||
\(464\) | −82.9904 | −0.178859 | ||||||||
\(465\) | 28.1934i | 0.0606309i | ||||||||
\(466\) | −502.923 | −1.07923 | ||||||||
\(467\) | − | 358.075i | − | 0.766756i | −0.923592 | − | 0.383378i | \(-0.874761\pi\) | ||
0.923592 | − | 0.383378i | \(-0.125239\pi\) | |||||||
\(468\) | − | 68.0174i | − | 0.145336i | ||||||
\(469\) | − | 188.708i | − | 0.402362i | ||||||
\(470\) | −13.5329 | −0.0287934 | ||||||||
\(471\) | 31.9839i | 0.0679065i | ||||||||
\(472\) | −225.198 | − | 445.179i | −0.477115 | − | 0.943176i | ||||
\(473\) | 1180.11 | 2.49494 | ||||||||
\(474\) | 150.861i | 0.318272i | ||||||||
\(475\) | 391.628 | 0.824480 | ||||||||
\(476\) | 75.7697 | 0.159180 | ||||||||
\(477\) | 111.834 | 0.234452 | ||||||||
\(478\) | 371.164i | 0.776493i | ||||||||
\(479\) | −23.3301 | −0.0487059 | −0.0243530 | − | 0.999703i | \(-0.507753\pi\) | ||||
−0.0243530 | + | 0.999703i | \(0.507753\pi\) | |||||||
\(480\) | 13.5833i | 0.0282986i | ||||||||
\(481\) | 471.754 | 0.980777 | ||||||||
\(482\) | 82.4371i | 0.171031i | ||||||||
\(483\) | 288.247i | 0.596785i | ||||||||
\(484\) | −215.404 | −0.445049 | ||||||||
\(485\) | − | 3.01323i | − | 0.00621285i | ||||||
\(486\) | 21.8230i | 0.0449033i | ||||||||
\(487\) | 718.517 | 1.47539 | 0.737697 | − | 0.675132i | \(-0.235913\pi\) | ||||
0.737697 | + | 0.675132i | \(0.235913\pi\) | |||||||
\(488\) | −374.142 | −0.766685 | ||||||||
\(489\) | 428.600 | 0.876482 | ||||||||
\(490\) | − | 26.6763i | − | 0.0544415i | ||||||
\(491\) | 406.760 | 0.828431 | 0.414215 | − | 0.910179i | \(-0.364056\pi\) | ||||
0.414215 | + | 0.910179i | \(0.364056\pi\) | |||||||
\(492\) | −277.328 | −0.563675 | ||||||||
\(493\) | −76.9419 | −0.156069 | ||||||||
\(494\) | 244.446 | 0.494831 | ||||||||
\(495\) | − | 12.3500i | − | 0.0249495i | ||||||
\(496\) | 218.863i | 0.441256i | ||||||||
\(497\) | 643.554 | 1.29488 | ||||||||
\(498\) | 239.969 | 0.481866 | ||||||||
\(499\) | −828.694 | −1.66071 | −0.830355 | − | 0.557235i | \(-0.811862\pi\) | ||||
−0.830355 | + | 0.557235i | \(0.811862\pi\) | |||||||
\(500\) | −27.8557 | −0.0557114 | ||||||||
\(501\) | −109.127 | −0.217819 | ||||||||
\(502\) | − | 1.88731i | − | 0.00375959i | ||||||
\(503\) | − | 491.016i | − | 0.976175i | −0.872795 | − | 0.488088i | \(-0.837695\pi\) | ||
0.872795 | − | 0.488088i | \(-0.162305\pi\) | |||||||
\(504\) | 276.351i | 0.548316i | ||||||||
\(505\) | 30.2948i | 0.0599897i | ||||||||
\(506\) | − | 321.920i | − | 0.636205i | ||||||
\(507\) | −78.8045 | −0.155433 | ||||||||
\(508\) | 438.804 | 0.863787 | ||||||||
\(509\) | − | 299.875i | − | 0.589146i | −0.955629 | − | 0.294573i | \(-0.904823\pi\) | ||
0.955629 | − | 0.294573i | \(-0.0951774\pi\) | |||||||
\(510\) | − | 2.26078i | − | 0.00443289i | ||||||
\(511\) | 929.378i | 1.81874i | ||||||||
\(512\) | 229.822i | 0.448872i | ||||||||
\(513\) | 81.6426 | 0.159147 | ||||||||
\(514\) | − | 421.553i | − | 0.820141i | ||||||
\(515\) | 11.7781i | 0.0228701i | ||||||||
\(516\) | − | 277.033i | − | 0.536885i | ||||||
\(517\) | −532.059 | −1.02913 | ||||||||
\(518\) | −647.398 | −1.24980 | ||||||||
\(519\) | 282.772i | 0.544840i | ||||||||
\(520\) | −25.6997 | −0.0494226 | ||||||||
\(521\) | −793.658 | −1.52334 | −0.761668 | − | 0.647967i | \(-0.775619\pi\) | ||||
−0.761668 | + | 0.647967i | \(0.775619\pi\) | |||||||
\(522\) | − | 94.7857i | − | 0.181582i | ||||||
\(523\) | −991.881 | −1.89652 | −0.948261 | − | 0.317493i | \(-0.897159\pi\) | ||||
−0.948261 | + | 0.317493i | \(0.897159\pi\) | |||||||
\(524\) | − | 162.845i | − | 0.310773i | ||||||
\(525\) | −470.306 | −0.895821 | ||||||||
\(526\) | − | 115.739i | − | 0.220036i | ||||||
\(527\) | 202.912i | 0.385032i | ||||||||
\(528\) | − | 95.8720i | − | 0.181576i | ||||||
\(529\) | 295.630 | 0.558846 | ||||||||
\(530\) | − | 14.2723i | − | 0.0269290i | ||||||
\(531\) | 157.942 | − | 79.8964i | 0.297442 | − | 0.150464i | ||||
\(532\) | 349.203 | 0.656396 | ||||||||
\(533\) | − | 872.185i | − | 1.63637i | ||||||
\(534\) | −87.1335 | −0.163171 | ||||||||
\(535\) | −40.0396 | −0.0748403 | ||||||||
\(536\) | 146.477 | 0.273277 | ||||||||
\(537\) | 139.492i | 0.259761i | ||||||||
\(538\) | 291.406 | 0.541646 | ||||||||
\(539\) | − | 1048.81i | − | 1.94584i | ||||||
\(540\) | −2.89918 | −0.00536886 | ||||||||
\(541\) | − | 200.875i | − | 0.371303i | −0.982616 | − | 0.185652i | \(-0.940560\pi\) | ||
0.982616 | − | 0.185652i | \(-0.0594396\pi\) | |||||||
\(542\) | − | 54.1893i | − | 0.0999802i | ||||||
\(543\) | 225.447 | 0.415187 | ||||||||
\(544\) | 97.7612i | 0.179708i | ||||||||
\(545\) | 38.5953i | 0.0708170i | ||||||||
\(546\) | −293.556 | −0.537648 | ||||||||
\(547\) | −412.389 | −0.753911 | −0.376955 | − | 0.926231i | \(-0.623029\pi\) | ||||
−0.376955 | + | 0.926231i | \(0.623029\pi\) | |||||||
\(548\) | −282.443 | −0.515407 | ||||||||
\(549\) | − | 132.739i | − | 0.241783i | ||||||
\(550\) | 525.247 | 0.954994 | ||||||||
\(551\) | −354.605 | −0.643566 | ||||||||
\(552\) | −223.740 | −0.405325 | ||||||||
\(553\) | −677.775 | −1.22563 | ||||||||
\(554\) | − | 293.114i | − | 0.529086i | ||||||
\(555\) | − | 20.1081i | − | 0.0362308i | ||||||
\(556\) | 122.126 | 0.219652 | ||||||||
\(557\) | −214.797 | −0.385632 | −0.192816 | − | 0.981235i | \(-0.561762\pi\) | ||||
−0.192816 | + | 0.981235i | \(0.561762\pi\) | |||||||
\(558\) | −249.970 | −0.447974 | ||||||||
\(559\) | 871.256 | 1.55860 | ||||||||
\(560\) | 10.9555 | 0.0195634 | ||||||||
\(561\) | − | 88.8846i | − | 0.158440i | ||||||
\(562\) | − | 429.898i | − | 0.764943i | ||||||
\(563\) | − | 104.763i | − | 0.186079i | −0.995662 | − | 0.0930396i | \(-0.970342\pi\) | ||
0.995662 | − | 0.0930396i | \(-0.0296583\pi\) | |||||||
\(564\) | 124.902i | 0.221457i | ||||||||
\(565\) | − | 5.79479i | − | 0.0102563i | ||||||
\(566\) | 320.810 | 0.566803 | ||||||||
\(567\) | −98.0446 | −0.172918 | ||||||||
\(568\) | 499.532i | 0.879458i | ||||||||
\(569\) | 765.436i | 1.34523i | 0.739992 | + | 0.672615i | \(0.234829\pi\) | ||||
−0.739992 | + | 0.672615i | \(0.765171\pi\) | |||||||
\(570\) | − | 10.4193i | − | 0.0182795i | ||||||
\(571\) | 249.624i | 0.437170i | 0.975818 | + | 0.218585i | \(0.0701441\pi\) | ||||
−0.975818 | + | 0.218585i | \(0.929856\pi\) | |||||||
\(572\) | −341.281 | −0.596645 | ||||||||
\(573\) | − | 357.279i | − | 0.623523i | ||||||
\(574\) | 1196.92i | 2.08522i | ||||||||
\(575\) | − | 380.769i | − | 0.662207i | ||||||
\(576\) | −164.560 | −0.285694 | ||||||||
\(577\) | −268.842 | −0.465930 | −0.232965 | − | 0.972485i | \(-0.574843\pi\) | ||||
−0.232965 | + | 0.972485i | \(0.574843\pi\) | |||||||
\(578\) | 388.314i | 0.671823i | ||||||||
\(579\) | −302.517 | −0.522481 | ||||||||
\(580\) | 12.5923 | 0.0217108 | ||||||||
\(581\) | 1078.11i | 1.85562i | ||||||||
\(582\) | 26.7161 | 0.0459039 | ||||||||
\(583\) | − | 561.132i | − | 0.962490i | ||||||
\(584\) | −721.390 | −1.23526 | ||||||||
\(585\) | − | 9.11782i | − | 0.0155860i | ||||||
\(586\) | − | 79.1779i | − | 0.135116i | ||||||
\(587\) | 793.085i | 1.35108i | 0.737322 | + | 0.675541i | \(0.236090\pi\) | ||||
−0.737322 | + | 0.675541i | \(0.763910\pi\) | |||||||
\(588\) | −246.209 | −0.418724 | ||||||||
\(589\) | 935.166i | 1.58772i | ||||||||
\(590\) | −10.1965 | − | 20.1567i | −0.0172822 | − | 0.0341639i | ||||
\(591\) | −455.066 | −0.769993 | ||||||||
\(592\) | − | 156.098i | − | 0.263678i | ||||||
\(593\) | −108.147 | −0.182373 | −0.0911866 | − | 0.995834i | \(-0.529066\pi\) | ||||
−0.0911866 | + | 0.995834i | \(0.529066\pi\) | |||||||
\(594\) | 109.498 | 0.184340 | ||||||||
\(595\) | 10.1570 | 0.0170706 | ||||||||
\(596\) | − | 445.505i | − | 0.747492i | ||||||
\(597\) | 63.6884 | 0.106681 | ||||||||
\(598\) | − | 237.669i | − | 0.397439i | ||||||
\(599\) | 21.0152 | 0.0350837 | 0.0175419 | − | 0.999846i | \(-0.494416\pi\) | ||||
0.0175419 | + | 0.999846i | \(0.494416\pi\) | |||||||
\(600\) | − | 365.055i | − | 0.608425i | ||||||
\(601\) | − | 792.854i | − | 1.31922i | −0.751606 | − | 0.659612i | \(-0.770721\pi\) | ||
0.751606 | − | 0.659612i | \(-0.229279\pi\) | |||||||
\(602\) | −1195.64 | −1.98612 | ||||||||
\(603\) | 51.9673i | 0.0861813i | ||||||||
\(604\) | 53.8812i | 0.0892073i | ||||||||
\(605\) | −28.8751 | −0.0477275 | ||||||||
\(606\) | −268.602 | −0.443237 | ||||||||
\(607\) | 848.008 | 1.39705 | 0.698524 | − | 0.715587i | \(-0.253841\pi\) | ||||
0.698524 | + | 0.715587i | \(0.253841\pi\) | |||||||
\(608\) | 450.555i | 0.741045i | ||||||||
\(609\) | 425.845 | 0.699253 | ||||||||
\(610\) | −16.9403 | −0.0277710 | ||||||||
\(611\) | −392.811 | −0.642899 | ||||||||
\(612\) | −20.8658 | −0.0340945 | ||||||||
\(613\) | 355.689i | 0.580243i | 0.956990 | + | 0.290121i | \(0.0936957\pi\) | ||||
−0.956990 | + | 0.290121i | \(0.906304\pi\) | |||||||
\(614\) | 53.4241i | 0.0870100i | ||||||||
\(615\) | −37.1761 | −0.0604490 | ||||||||
\(616\) | 1386.61 | 2.25099 | ||||||||
\(617\) | 120.858 | 0.195880 | 0.0979402 | − | 0.995192i | \(-0.468775\pi\) | ||||
0.0979402 | + | 0.995192i | \(0.468775\pi\) | |||||||
\(618\) | −104.428 | −0.168977 | ||||||||
\(619\) | −112.377 | −0.181546 | −0.0907732 | − | 0.995872i | \(-0.528934\pi\) | ||||
−0.0907732 | + | 0.995872i | \(0.528934\pi\) | |||||||
\(620\) | − | 33.2084i | − | 0.0535619i | ||||||
\(621\) | − | 79.3789i | − | 0.127824i | ||||||
\(622\) | 332.320i | 0.534277i | ||||||||
\(623\) | − | 391.466i | − | 0.628356i | ||||||
\(624\) | − | 70.7809i | − | 0.113431i | ||||||
\(625\) | 619.396 | 0.991034 | ||||||||
\(626\) | −655.684 | −1.04742 | ||||||||
\(627\) | − | 409.646i | − | 0.653343i | ||||||
\(628\) | − | 37.6732i | − | 0.0599892i | ||||||
\(629\) | − | 144.721i | − | 0.230081i | ||||||
\(630\) | 12.5126i | 0.0198612i | ||||||||
\(631\) | 467.803 | 0.741368 | 0.370684 | − | 0.928759i | \(-0.379123\pi\) | ||||
0.370684 | + | 0.928759i | \(0.379123\pi\) | |||||||
\(632\) | − | 526.094i | − | 0.832427i | ||||||
\(633\) | 576.483i | 0.910715i | ||||||||
\(634\) | 136.884i | 0.215905i | ||||||||
\(635\) | 58.8222 | 0.0926333 | ||||||||
\(636\) | −131.727 | −0.207117 | ||||||||
\(637\) | − | 774.319i | − | 1.21557i | ||||||
\(638\) | −475.592 | −0.745442 | ||||||||
\(639\) | −177.225 | −0.277348 | ||||||||
\(640\) | − | 10.3681i | − | 0.0162001i | ||||||
\(641\) | −1006.77 | −1.57062 | −0.785311 | − | 0.619102i | \(-0.787497\pi\) | ||||
−0.785311 | + | 0.619102i | \(0.787497\pi\) | |||||||
\(642\) | − | 355.001i | − | 0.552961i | ||||||
\(643\) | 65.4231 | 0.101747 | 0.0508734 | − | 0.998705i | \(-0.483800\pi\) | ||||
0.0508734 | + | 0.998705i | \(0.483800\pi\) | |||||||
\(644\) | − | 339.520i | − | 0.527205i | ||||||
\(645\) | − | 37.1365i | − | 0.0575760i | ||||||
\(646\) | − | 74.9893i | − | 0.116083i | ||||||
\(647\) | 1000.16 | 1.54584 | 0.772920 | − | 0.634503i | \(-0.218795\pi\) | ||||
0.772920 | + | 0.634503i | \(0.218795\pi\) | |||||||
\(648\) | − | 76.1030i | − | 0.117443i | ||||||
\(649\) | −400.884 | − | 792.480i | −0.617696 | − | 1.22108i | ||||
\(650\) | 387.782 | 0.596588 | ||||||||
\(651\) | − | 1123.04i | − | 1.72510i | ||||||
\(652\) | −504.839 | −0.774293 | ||||||||
\(653\) | −635.037 | −0.972492 | −0.486246 | − | 0.873822i | \(-0.661634\pi\) | ||||
−0.486246 | + | 0.873822i | \(0.661634\pi\) | |||||||
\(654\) | −342.195 | −0.523234 | ||||||||
\(655\) | − | 21.8296i | − | 0.0333276i | ||||||
\(656\) | −288.595 | −0.439932 | ||||||||
\(657\) | − | 255.937i | − | 0.389553i | ||||||
\(658\) | 539.063 | 0.819245 | ||||||||
\(659\) | 445.774i | 0.676440i | 0.941067 | + | 0.338220i | \(0.109825\pi\) | ||||
−0.941067 | + | 0.338220i | \(0.890175\pi\) | |||||||
\(660\) | 14.5468i | 0.0220406i | ||||||||
\(661\) | 4.13501 | 0.00625568 | 0.00312784 | − | 0.999995i | \(-0.499004\pi\) | ||||
0.00312784 | + | 0.999995i | \(0.499004\pi\) | |||||||
\(662\) | 347.372i | 0.524731i | ||||||||
\(663\) | − | 65.6222i | − | 0.0989777i | ||||||
\(664\) | −836.840 | −1.26030 | ||||||||
\(665\) | 46.8110 | 0.0703925 | ||||||||
\(666\) | 178.283 | 0.267693 | ||||||||
\(667\) | 344.773i | 0.516900i | ||||||||
\(668\) | 128.539 | 0.192423 | ||||||||
\(669\) | 117.856 | 0.176167 | ||||||||
\(670\) | 6.63213 | 0.00989870 | ||||||||
\(671\) | −666.025 | −0.992586 | ||||||||
\(672\) | − | 541.072i | − | 0.805167i | ||||||
\(673\) | − | 144.454i | − | 0.214641i | −0.994224 | − | 0.107321i | \(-0.965773\pi\) | ||
0.994224 | − | 0.107321i | \(-0.0342271\pi\) | |||||||
\(674\) | 117.750 | 0.174704 | ||||||||
\(675\) | 129.515 | 0.191874 | ||||||||
\(676\) | 92.8222 | 0.137311 | ||||||||
\(677\) | 567.757 | 0.838637 | 0.419318 | − | 0.907839i | \(-0.362269\pi\) | ||||
0.419318 | + | 0.907839i | \(0.362269\pi\) | |||||||
\(678\) | 51.3780 | 0.0757788 | ||||||||
\(679\) | 120.028i | 0.176771i | ||||||||
\(680\) | 7.88396i | 0.0115941i | ||||||||
\(681\) | 515.280i | 0.756652i | ||||||||
\(682\) | 1254.24i | 1.83905i | ||||||||
\(683\) | 505.717i | 0.740435i | 0.928945 | + | 0.370218i | \(0.120717\pi\) | ||||
−0.928945 | + | 0.370218i | \(0.879283\pi\) | |||||||
\(684\) | −96.1651 | −0.140592 | ||||||||
\(685\) | −37.8618 | −0.0552727 | ||||||||
\(686\) | 315.324i | 0.459656i | ||||||||
\(687\) | − | 47.7966i | − | 0.0695729i | ||||||
\(688\) | − | 288.288i | − | 0.419023i | ||||||
\(689\) | − | 414.275i | − | 0.601270i | ||||||
\(690\) | −10.1304 | −0.0146818 | ||||||||
\(691\) | 843.080i | 1.22009i | 0.792368 | + | 0.610044i | \(0.208848\pi\) | ||||
−0.792368 | + | 0.610044i | \(0.791152\pi\) | |||||||
\(692\) | − | 333.071i | − | 0.481317i | ||||||
\(693\) | 491.944i | 0.709876i | ||||||||
\(694\) | −730.334 | −1.05236 | ||||||||
\(695\) | 16.3712 | 0.0235557 | ||||||||
\(696\) | 330.544i | 0.474920i | ||||||||
\(697\) | −267.562 | −0.383877 | ||||||||
\(698\) | 419.806 | 0.601441 | ||||||||
\(699\) | 622.230i | 0.890171i | ||||||||
\(700\) | 553.964 | 0.791377 | ||||||||
\(701\) | 873.826i | 1.24654i | 0.782006 | + | 0.623271i | \(0.214197\pi\) | ||||
−0.782006 | + | 0.623271i | \(0.785803\pi\) | |||||||
\(702\) | 80.8409 | 0.115158 | ||||||||
\(703\) | − | 666.980i | − | 0.948763i | ||||||
\(704\) | 825.687i | 1.17285i | ||||||||
\(705\) | 16.7432i | 0.0237493i | ||||||||
\(706\) | 886.824 | 1.25612 | ||||||||
\(707\) | − | 1206.75i | − | 1.70686i | ||||||
\(708\) | −186.036 | + | 94.1084i | −0.262763 | + | 0.132921i | ||||
\(709\) | 159.514 | 0.224985 | 0.112492 | − | 0.993653i | \(-0.464117\pi\) | ||||
0.112492 | + | 0.993653i | \(0.464117\pi\) | |||||||
\(710\) | 22.6177i | 0.0318559i | ||||||||
\(711\) | 186.649 | 0.262516 | ||||||||
\(712\) | 303.859 | 0.426768 | ||||||||
\(713\) | 909.237 | 1.27523 | ||||||||
\(714\) | 90.0547i | 0.126127i | ||||||||
\(715\) | −45.7491 | −0.0639848 | ||||||||
\(716\) | − | 164.304i | − | 0.229475i | ||||||
\(717\) | 459.213 | 0.640465 | ||||||||
\(718\) | − | 638.636i | − | 0.889465i | ||||||
\(719\) | − | 35.0202i | − | 0.0487068i | −0.999703 | − | 0.0243534i | \(-0.992247\pi\) | ||
0.999703 | − | 0.0243534i | \(-0.00775270\pi\) | |||||||
\(720\) | −3.01697 | −0.00419024 | ||||||||
\(721\) | − | 469.164i | − | 0.650712i | ||||||
\(722\) | 159.775i | 0.221295i | ||||||||
\(723\) | 101.993 | 0.141070 | ||||||||
\(724\) | −265.549 | −0.366781 | ||||||||
\(725\) | −562.534 | −0.775908 | ||||||||
\(726\) | − | 256.014i | − | 0.352637i | ||||||
\(727\) | 1123.28 | 1.54509 | 0.772544 | − | 0.634961i | \(-0.218984\pi\) | ||||
0.772544 | + | 0.634961i | \(0.218984\pi\) | |||||||
\(728\) | 1023.71 | 1.40620 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −32.6629 | −0.0447437 | ||||||||
\(731\) | − | 267.277i | − | 0.365632i | ||||||
\(732\) | 156.351i | 0.213594i | ||||||||
\(733\) | −1337.07 | −1.82411 | −0.912053 | − | 0.410073i | \(-0.865503\pi\) | ||||
−0.912053 | + | 0.410073i | \(0.865503\pi\) | |||||||
\(734\) | 707.526 | 0.963932 | ||||||||
\(735\) | −33.0047 | −0.0449043 | ||||||||
\(736\) | 438.063 | 0.595194 | ||||||||
\(737\) | 260.749 | 0.353797 | ||||||||
\(738\) | − | 329.613i | − | 0.446630i | ||||||
\(739\) | 393.835i | 0.532930i | 0.963845 | + | 0.266465i | \(0.0858556\pi\) | ||||
−0.963845 | + | 0.266465i | \(0.914144\pi\) | |||||||
\(740\) | 23.6849i | 0.0320067i | ||||||||
\(741\) | − | 302.435i | − | 0.408145i | ||||||
\(742\) | 568.518i | 0.766197i | ||||||||
\(743\) | −42.0432 | −0.0565857 | −0.0282929 | − | 0.999600i | \(-0.509007\pi\) | ||||
−0.0282929 | + | 0.999600i | \(0.509007\pi\) | |||||||
\(744\) | 871.714 | 1.17166 | ||||||||
\(745\) | − | 59.7205i | − | 0.0801617i | ||||||
\(746\) | 367.195i | 0.492218i | ||||||||
\(747\) | − | 296.896i | − | 0.397451i | ||||||
\(748\) | 104.695i | 0.139967i | ||||||||
\(749\) | 1594.92 | 2.12940 | ||||||||
\(750\) | − | 33.1073i | − | 0.0441431i | ||||||
\(751\) | − | 1078.71i | − | 1.43636i | −0.695858 | − | 0.718180i | \(-0.744975\pi\) | ||
0.695858 | − | 0.718180i | \(-0.255025\pi\) | |||||||
\(752\) | 129.976i | 0.172841i | ||||||||
\(753\) | −2.33503 | −0.00310097 | ||||||||
\(754\) | −351.123 | −0.465680 | ||||||||
\(755\) | 7.22284i | 0.00956667i | ||||||||
\(756\) | 115.485 | 0.152758 | ||||||||
\(757\) | −247.277 | −0.326654 | −0.163327 | − | 0.986572i | \(-0.552223\pi\) | ||||
−0.163327 | + | 0.986572i | \(0.552223\pi\) | |||||||
\(758\) | − | 745.470i | − | 0.983470i | ||||||
\(759\) | −398.288 | −0.524753 | ||||||||
\(760\) | 36.3351i | 0.0478093i | ||||||||
\(761\) | 681.030 | 0.894914 | 0.447457 | − | 0.894305i | \(-0.352330\pi\) | ||||
0.447457 | + | 0.894305i | \(0.352330\pi\) | |||||||
\(762\) | 521.532i | 0.684425i | ||||||||
\(763\) | − | 1537.39i | − | 2.01492i | ||||||
\(764\) | 420.831i | 0.550826i | ||||||||
\(765\) | −2.79709 | −0.00365633 | ||||||||
\(766\) | − | 401.143i | − | 0.523685i | ||||||
\(767\) | −295.967 | − | 585.077i | −0.385876 | − | 0.762812i | ||||
\(768\) | 471.960 | 0.614531 | ||||||||
\(769\) | 1018.02i | 1.32382i | 0.749582 | + | 0.661912i | \(0.230255\pi\) | ||||
−0.749582 | + | 0.661912i | \(0.769745\pi\) | |||||||
\(770\) | 62.7824 | 0.0815356 | ||||||||
\(771\) | −521.556 | −0.676466 | ||||||||
\(772\) | 356.328 | 0.461565 | ||||||||
\(773\) | − | 1082.79i | − | 1.40076i | −0.713770 | − | 0.700380i | \(-0.753014\pi\) | ||
0.713770 | − | 0.700380i | \(-0.246986\pi\) | |||||||
\(774\) | 329.262 | 0.425403 | ||||||||
\(775\) | 1483.52i | 1.91422i | ||||||||
\(776\) | −93.1664 | −0.120060 | ||||||||
\(777\) | 800.977i | 1.03086i | ||||||||
\(778\) | − | 868.518i | − | 1.11635i | ||||||
\(779\) | −1233.12 | −1.58296 | ||||||||
\(780\) | 10.7397i | 0.0137688i | ||||||||
\(781\) | 889.236i | 1.13859i | ||||||||
\(782\) | −72.9101 | −0.0932354 | ||||||||
\(783\) | −117.271 | −0.149772 | ||||||||
\(784\) | −256.213 | −0.326802 | ||||||||
\(785\) | − | 5.05014i | − | 0.00643330i | ||||||
\(786\) | 193.546 | 0.246242 | ||||||||
\(787\) | 302.623 | 0.384527 | 0.192263 | − | 0.981343i | \(-0.438417\pi\) | ||||
0.192263 | + | 0.981343i | \(0.438417\pi\) | |||||||
\(788\) | 536.013 | 0.680219 | ||||||||
\(789\) | −143.195 | −0.181490 | ||||||||
\(790\) | − | 23.8203i | − | 0.0301523i | ||||||
\(791\) | 230.827i | 0.291817i |