Newspace parameters
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
Defining polynomial: | \(x^{4} + 3 x^{2} + 1\) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 65.2 | ||
Root | \(1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.65 |
Dual form | 384.3.h.e.65.1 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.23607 | + | 2.00000i | −0.745356 | + | 0.666667i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.00000 | −0.800000 | −0.400000 | − | 0.916515i | \(-0.630990\pi\) | ||||
−0.400000 | + | 0.916515i | \(0.630990\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.94427 | 1.27775 | 0.638877 | − | 0.769309i | \(-0.279399\pi\) | ||||
0.638877 | + | 0.769309i | \(0.279399\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | − | 8.94427i | 0.111111 | − | 0.993808i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.47214 | 0.406558 | 0.203279 | − | 0.979121i | \(-0.434840\pi\) | ||||
0.203279 | + | 0.979121i | \(0.434840\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.8885i | 1.37604i | 0.725691 | + | 0.688021i | \(0.241520\pi\) | ||||
−0.725691 | + | 0.688021i | \(0.758480\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.94427 | − | 8.00000i | 0.596285 | − | 0.533333i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 17.8885i | 1.05227i | 0.850402 | + | 0.526134i | \(0.176359\pi\) | ||||
−0.850402 | + | 0.526134i | \(0.823641\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 20.0000i | − | 1.05263i | −0.850289 | − | 0.526316i | \(-0.823573\pi\) | ||
0.850289 | − | 0.526316i | \(-0.176427\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −20.0000 | + | 17.8885i | −0.952381 | + | 0.851835i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 16.0000i | 0.695652i | 0.937559 | + | 0.347826i | \(0.113080\pi\) | ||||
−0.937559 | + | 0.347826i | \(0.886920\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.00000 | −0.360000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 15.6525 | + | 22.0000i | 0.579721 | + | 0.814815i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −52.0000 | −1.79310 | −0.896552 | − | 0.442939i | \(-0.853936\pi\) | ||||
−0.896552 | + | 0.442939i | \(0.853936\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −26.8328 | −0.865575 | −0.432787 | − | 0.901496i | \(-0.642470\pi\) | ||||
−0.432787 | + | 0.901496i | \(0.642470\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.0000 | + | 8.94427i | −0.303030 | + | 0.271039i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −35.7771 | −1.02220 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 53.6656i | 1.45042i | 0.688526 | + | 0.725211i | \(0.258258\pi\) | ||||
−0.688526 | + | 0.725211i | \(0.741742\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −35.7771 | − | 40.0000i | −0.917361 | − | 1.02564i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 35.7771i | − | 0.872612i | −0.899798 | − | 0.436306i | \(-0.856287\pi\) | ||
0.899798 | − | 0.436306i | \(-0.143713\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 36.0000i | 0.837209i | 0.908169 | + | 0.418605i | \(0.137481\pi\) | ||||
−0.908169 | + | 0.418605i | \(0.862519\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.00000 | + | 35.7771i | −0.0888889 | + | 0.795046i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 64.0000i | 1.36170i | 0.732422 | + | 0.680851i | \(0.238390\pi\) | ||||
−0.732422 | + | 0.680851i | \(0.761610\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 31.0000 | 0.632653 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −35.7771 | − | 40.0000i | −0.701512 | − | 0.784314i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −20.0000 | −0.377358 | −0.188679 | − | 0.982039i | \(-0.560421\pi\) | ||||
−0.188679 | + | 0.982039i | \(0.560421\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17.8885 | −0.325246 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 40.0000 | + | 44.7214i | 0.701754 | + | 0.784585i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 102.859 | 1.74338 | 0.871688 | − | 0.490062i | \(-0.163026\pi\) | ||||
0.871688 | + | 0.490062i | \(0.163026\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 17.8885i | 0.293255i | 0.989192 | + | 0.146627i | \(0.0468418\pi\) | ||||
−0.989192 | + | 0.146627i | \(0.953158\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.94427 | − | 80.0000i | 0.141973 | − | 1.26984i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 71.5542i | − | 1.10083i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 44.0000i | − | 0.656716i | −0.944553 | − | 0.328358i | \(-0.893505\pi\) | ||
0.944553 | − | 0.328358i | \(-0.106495\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −32.0000 | − | 35.7771i | −0.463768 | − | 0.518509i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 80.0000i | 1.12676i | 0.826198 | + | 0.563380i | \(0.190499\pi\) | ||||
−0.826198 | + | 0.563380i | \(0.809501\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −50.0000 | −0.684932 | −0.342466 | − | 0.939530i | \(-0.611262\pi\) | ||||
−0.342466 | + | 0.939530i | \(0.611262\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 20.1246 | − | 18.0000i | 0.268328 | − | 0.240000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 40.0000 | 0.519481 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 80.4984 | 1.01897 | 0.509484 | − | 0.860480i | \(-0.329836\pi\) | ||||
0.509484 | + | 0.860480i | \(0.329836\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −79.0000 | − | 17.8885i | −0.975309 | − | 0.220846i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −102.859 | −1.23927 | −0.619633 | − | 0.784891i | \(-0.712719\pi\) | ||||
−0.619633 | + | 0.784891i | \(0.712719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 71.5542i | − | 0.841814i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 116.276 | − | 104.000i | 1.33650 | − | 1.19540i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 160.997i | 1.80895i | 0.426523 | + | 0.904477i | \(0.359738\pi\) | ||||
−0.426523 | + | 0.904477i | \(0.640262\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 160.000i | 1.75824i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 60.0000 | − | 53.6656i | 0.645161 | − | 0.577050i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 80.0000i | 0.842105i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 50.0000 | 0.515464 | 0.257732 | − | 0.966216i | \(-0.417025\pi\) | ||||
0.257732 | + | 0.966216i | \(0.417025\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.47214 | − | 40.0000i | 0.0451731 | − | 0.404040i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 92.0000 | 0.910891 | 0.455446 | − | 0.890264i | \(-0.349480\pi\) | ||||
0.455446 | + | 0.890264i | \(0.349480\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 44.7214 | 0.434188 | 0.217094 | − | 0.976151i | \(-0.430342\pi\) | ||||
0.217094 | + | 0.976151i | \(0.430342\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 80.0000 | − | 71.5542i | 0.761905 | − | 0.681468i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −40.2492 | −0.376161 | −0.188080 | − | 0.982154i | \(-0.560227\pi\) | ||||
−0.188080 | + | 0.982154i | \(0.560227\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 125.220i | − | 1.14881i | −0.818573 | − | 0.574403i | \(-0.805234\pi\) | ||
0.818573 | − | 0.574403i | \(-0.194766\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −107.331 | − | 120.000i | −0.966948 | − | 1.08108i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 35.7771i | 0.316611i | 0.987390 | + | 0.158306i | \(0.0506031\pi\) | ||||
−0.987390 | + | 0.158306i | \(0.949397\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 64.0000i | − | 0.556522i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 160.000 | + | 17.8885i | 1.36752 | + | 0.152894i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 160.000i | 1.34454i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −101.000 | −0.834711 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 71.5542 | + | 80.0000i | 0.581741 | + | 0.650407i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 136.000 | 1.08800 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −26.8328 | −0.211282 | −0.105641 | − | 0.994404i | \(-0.533689\pi\) | ||||
−0.105641 | + | 0.994404i | \(0.533689\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −72.0000 | − | 80.4984i | −0.558140 | − | 0.624019i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 67.0820 | 0.512077 | 0.256038 | − | 0.966667i | \(-0.417583\pi\) | ||||
0.256038 | + | 0.966667i | \(0.417583\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 178.885i | − | 1.34500i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −62.6099 | − | 88.0000i | −0.463777 | − | 0.651852i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 143.108i | − | 1.04459i | −0.852766 | − | 0.522293i | \(-0.825077\pi\) | ||
0.852766 | − | 0.522293i | \(-0.174923\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 260.000i | − | 1.87050i | −0.353983 | − | 0.935252i | \(-0.615173\pi\) | ||
0.353983 | − | 0.935252i | \(-0.384827\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −128.000 | − | 143.108i | −0.907801 | − | 1.01495i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 80.0000i | 0.559441i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 208.000 | 1.43448 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −69.3181 | + | 62.0000i | −0.471552 | + | 0.421769i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 28.0000 | 0.187919 | 0.0939597 | − | 0.995576i | \(-0.470048\pi\) | ||||
0.0939597 | + | 0.995576i | \(0.470048\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −241.495 | −1.59931 | −0.799653 | − | 0.600462i | \(-0.794983\pi\) | ||||
−0.799653 | + | 0.600462i | \(0.794983\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 160.000 | + | 17.8885i | 1.04575 | + | 0.116919i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 107.331 | 0.692460 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 53.6656i | − | 0.341819i | −0.985287 | − | 0.170910i | \(-0.945329\pi\) | ||
0.985287 | − | 0.170910i | \(-0.0546706\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 44.7214 | − | 40.0000i | 0.281266 | − | 0.251572i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 143.108i | 0.888872i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 124.000i | 0.760736i | 0.924835 | + | 0.380368i | \(0.124203\pi\) | ||||
−0.924835 | + | 0.380368i | \(0.875797\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 40.0000 | − | 35.7771i | 0.242424 | − | 0.216831i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 16.0000i | − | 0.0958084i | −0.998852 | − | 0.0479042i | \(-0.984746\pi\) | ||
0.998852 | − | 0.0479042i | \(-0.0152542\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −151.000 | −0.893491 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −178.885 | − | 20.0000i | −1.04611 | − | 0.116959i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 140.000 | 0.809249 | 0.404624 | − | 0.914483i | \(-0.367402\pi\) | ||||
0.404624 | + | 0.914483i | \(0.367402\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −80.4984 | −0.459991 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −230.000 | + | 205.718i | −1.29944 | + | 1.16225i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 67.0820 | 0.374760 | 0.187380 | − | 0.982288i | \(-0.440000\pi\) | ||||
0.187380 | + | 0.982288i | \(0.440000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 125.220i | 0.691822i | 0.938267 | + | 0.345911i | \(0.112430\pi\) | ||||
−0.938267 | + | 0.345911i | \(0.887570\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −35.7771 | − | 40.0000i | −0.195503 | − | 0.218579i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 214.663i | − | 1.16034i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 80.0000i | 0.427807i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 140.000 | + | 196.774i | 0.740741 | + | 1.04113i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 160.000i | 0.837696i | 0.908056 | + | 0.418848i | \(0.137566\pi\) | ||||
−0.908056 | + | 0.418848i | \(0.862434\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 30.0000 | 0.155440 | 0.0777202 | − | 0.996975i | \(-0.475236\pi\) | ||||
0.0777202 | + | 0.996975i | \(0.475236\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 143.108 | + | 160.000i | 0.733889 | + | 0.820513i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −180.000 | −0.913706 | −0.456853 | − | 0.889542i | \(-0.651023\pi\) | ||||
−0.456853 | + | 0.889542i | \(0.651023\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 259.384 | 1.30344 | 0.651718 | − | 0.758461i | \(-0.274048\pi\) | ||||
0.651718 | + | 0.758461i | \(0.274048\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 88.0000 | + | 98.3870i | 0.437811 | + | 0.489488i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −465.102 | −2.29114 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 143.108i | 0.698090i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 143.108 | + | 16.0000i | 0.691345 | + | 0.0772947i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 89.4427i | − | 0.427956i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 60.0000i | − | 0.284360i | −0.989841 | − | 0.142180i | \(-0.954589\pi\) | ||
0.989841 | − | 0.142180i | \(-0.0454112\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −160.000 | − | 178.885i | −0.751174 | − | 0.839838i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 144.000i | − | 0.669767i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −240.000 | −1.10599 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 111.803 | − | 100.000i | 0.510518 | − | 0.456621i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −320.000 | −1.44796 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 152.053 | 0.681850 | 0.340925 | − | 0.940090i | \(-0.389260\pi\) | ||||
0.340925 | + | 0.940090i | \(0.389260\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.00000 | + | 80.4984i | −0.0400000 | + | 0.357771i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 254.912 | 1.12296 | 0.561480 | − | 0.827491i | \(-0.310232\pi\) | ||||
0.561480 | + | 0.827491i | \(0.310232\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 196.774i | 0.859275i | 0.903001 | + | 0.429638i | \(0.141359\pi\) | ||||
−0.903001 | + | 0.429638i | \(0.858641\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −89.4427 | + | 80.0000i | −0.387198 | + | 0.346320i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 160.997i | 0.690974i | 0.938424 | + | 0.345487i | \(0.112286\pi\) | ||||
−0.938424 | + | 0.345487i | \(0.887714\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 256.000i | − | 1.08936i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −180.000 | + | 160.997i | −0.759494 | + | 0.679312i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 320.000i | − | 1.33891i | −0.742852 | − | 0.669456i | \(-0.766527\pi\) | ||
0.742852 | − | 0.669456i | \(-0.233473\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 318.000 | 1.31950 | 0.659751 | − | 0.751484i | \(-0.270662\pi\) | ||||
0.659751 | + | 0.751484i | \(0.270662\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 212.426 | − | 118.000i | 0.874183 | − | 0.485597i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −124.000 | −0.506122 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 357.771 | 1.44847 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 230.000 | − | 205.718i | 0.923695 | − | 0.826178i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 147.580 | 0.587970 | 0.293985 | − | 0.955810i | \(-0.405018\pi\) | ||||
0.293985 | + | 0.955810i | \(0.405018\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 71.5542i | 0.282823i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 143.108 | + | 160.000i | 0.561209 | + | 0.627451i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 107.331i | − | 0.417631i | −0.977955 | − | 0.208816i | \(-0.933039\pi\) | ||
0.977955 | − | 0.208816i | \(-0.0669609\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 480.000i | 1.85328i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −52.0000 | + | 465.102i | −0.199234 | + | 1.78200i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 144.000i | 0.547529i | 0.961797 | + | 0.273764i | \(0.0882688\pi\) | ||||
−0.961797 | + | 0.273764i | \(0.911731\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 80.0000 | 0.301887 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −321.994 | − | 360.000i | −1.20597 | − | 1.34831i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −132.000 | −0.490706 | −0.245353 | − | 0.969434i | \(-0.578904\pi\) | ||||
−0.245353 | + | 0.969434i | \(0.578904\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −277.272 | −1.02315 | −0.511573 | − | 0.859240i | \(-0.670937\pi\) | ||||
−0.511573 | + | 0.859240i | \(0.670937\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −320.000 | − | 357.771i | −1.17216 | − | 1.31052i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −40.2492 | −0.146361 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 268.328i | 0.968694i | 0.874876 | + | 0.484347i | \(0.160943\pi\) | ||||
−0.874876 | + | 0.484347i | \(0.839057\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −26.8328 | + | 240.000i | −0.0961750 | + | 0.860215i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 196.774i | 0.700263i | 0.936701 | + | 0.350132i | \(0.113863\pi\) | ||||
−0.936701 | + | 0.350132i | \(0.886137\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 76.0000i | 0.268551i | 0.990944 | + | 0.134276i | \(0.0428707\pi\) | ||||
−0.990944 | + | 0.134276i | \(0.957129\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −160.000 | − | 178.885i | −0.561404 | − | 0.627668i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 320.000i | − | 1.11498i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −31.0000 | −0.107266 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −111.803 | + | 100.000i | −0.384204 | + | 0.343643i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 140.000 | 0.477816 | 0.238908 | − | 0.971042i | \(-0.423211\pi\) | ||||
0.238908 | + | 0.971042i | \(0.423211\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −411.437 | −1.39470 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 70.0000 | + | 98.3870i | 0.235690 | + | 0.331269i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −286.217 | −0.957246 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 321.994i | 1.06975i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −205.718 | + | 184.000i | −0.678938 | + | 0.607261i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 71.5542i | − | 0.234604i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 244.000i | 0.794788i | 0.917648 | + | 0.397394i | \(0.130085\pi\) | ||||
−0.917648 | + | 0.397394i | \(0.869915\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −100.000 | + | 89.4427i | −0.323625 | + | 0.289459i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 400.000i | − | 1.28617i | −0.765793 | − | 0.643087i | \(-0.777653\pi\) | ||
0.765793 | − | 0.643087i | \(-0.222347\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −290.000 | −0.926518 | −0.463259 | − | 0.886223i | \(-0.653320\pi\) | ||||
−0.463259 | + | 0.886223i | \(0.653320\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −35.7771 | + | 320.000i | −0.113578 | + | 1.01587i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −420.000 | −1.32492 | −0.662461 | − | 0.749097i | \(-0.730488\pi\) | ||||
−0.662461 | + | 0.749097i | \(0.730488\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −232.551 | −0.729000 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 90.0000 | − | 80.4984i | 0.280374 | − | 0.250774i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 357.771 | 1.10765 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 160.997i | − | 0.495375i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 250.440 | + | 280.000i | 0.765870 | + | 0.856269i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 572.433i | 1.73992i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 340.000i | − | 1.02719i | −0.858033 | − | 0.513595i | \(-0.828313\pi\) | ||
0.858033 | − | 0.513595i | \(-0.171687\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 480.000 | + | 53.6656i | 1.44144 | + | 0.161158i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 176.000i | 0.525373i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 110.000 | 0.326409 | 0.163205 | − | 0.986592i | \(-0.447817\pi\) | ||||
0.163205 | + | 0.986592i | \(0.447817\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −71.5542 | − | 80.0000i | −0.211074 | − | 0.235988i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −120.000 | −0.351906 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −160.997 | −0.469379 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 128.000 | + | 143.108i | 0.371014 | + | 0.414807i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 147.580 | 0.425304 | 0.212652 | − | 0.977128i | \(-0.431790\pi\) | ||||
0.212652 | + | 0.977128i | \(0.431790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.8885i | 0.0512566i | 0.999672 | + | 0.0256283i | \(0.00815863\pi\) | ||||
−0.999672 | + | 0.0256283i | \(0.991841\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −393.548 | + | 280.000i | −1.12122 | + | 0.797721i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 214.663i | 0.608109i | 0.952655 | + | 0.304055i | \(0.0983405\pi\) | ||||
−0.952655 | + | 0.304055i | \(0.901659\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 320.000i | − | 0.901408i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −320.000 | − | 357.771i | −0.896359 | − | 1.00216i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 560.000i | − | 1.55989i | −0.625849 | − | 0.779944i | \(-0.715247\pi\) | ||
0.625849 | − | 0.779944i | \(-0.284753\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −39.0000 | −0.108033 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 225.843 | − | 202.000i | 0.622157 | − | 0.556474i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 200.000 | 0.547945 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 617.155 | 1.68162 | 0.840810 | − | 0.541330i | \(-0.182079\pi\) | ||||
0.840810 | + | 0.541330i | \(0.182079\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −320.000 | − | 35.7771i | −0.867209 | − | 0.0969569i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −178.885 | −0.482171 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 375.659i | − | 1.00713i | −0.863957 | − | 0.503565i | \(-0.832021\pi\) | ||
0.863957 | − | 0.503565i | \(-0.167979\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −304.105 | + | 272.000i | −0.810947 | + | 0.725333i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 930.204i | − | 2.46739i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 260.000i | 0.686016i | 0.939333 | + | 0.343008i | \(0.111446\pi\) | ||||
−0.939333 | + | 0.343008i | \(0.888554\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 60.0000 | − | 53.6656i | 0.157480 | − | 0.140855i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 544.000i | − | 1.42037i | −0.704017 | − | 0.710183i | \(-0.748612\pi\) | ||
0.704017 | − | 0.710183i | \(-0.251388\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −160.000 | −0.415584 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 321.994 | + | 36.0000i | 0.832025 | + | 0.0930233i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 332.000 | 0.853470 | 0.426735 | − | 0.904377i | \(-0.359664\pi\) | ||||
0.426735 | + | 0.904377i | \(0.359664\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −286.217 | −0.732012 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −150.000 | + | 134.164i | −0.381679 | + | 0.341384i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −321.994 | −0.815174 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 268.328i | − | 0.675890i | −0.941166 | − | 0.337945i | \(-0.890268\pi\) | ||
0.941166 | − | 0.337945i | \(-0.109732\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 357.771 | + | 400.000i | 0.896669 | + | 1.00251i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 160.997i | − | 0.401489i | −0.979644 | − | 0.200744i | \(-0.935664\pi\) | ||
0.979644 | − | 0.200744i | \(-0.0643360\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 480.000i | − | 1.19107i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 316.000 | + | 71.5542i | 0.780247 | + | 0.176677i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 240.000i | 0.589681i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 178.000 | 0.435208 | 0.217604 | − | 0.976037i | \(-0.430176\pi\) | ||||
0.217604 | + | 0.976037i | \(0.430176\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 286.217 | + | 320.000i | 0.696391 | + | 0.778589i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 920.000 | 2.22760 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 411.437 | 0.991413 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 520.000 | + | 581.378i | 1.24700 | + | 1.39419i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −245.967 | −0.587035 | −0.293517 | − | 0.955954i | \(-0.594826\pi\) | ||||
−0.293517 | + | 0.955954i | \(0.594826\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 53.6656i | 0.127472i | 0.997967 | + | 0.0637359i | \(0.0203015\pi\) | ||||
−0.997967 | + | 0.0637359i | \(0.979698\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 572.433 | + | 64.0000i | 1.35327 | + | 0.151300i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 160.997i | − | 0.378816i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 160.000i | 0.374707i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −160.000 | − | 178.885i | −0.372960 | − | 0.416982i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 320.000i | − | 0.742459i | −0.928541 | − | 0.371230i | \(-0.878936\pi\) | ||
0.928541 | − | 0.371230i | \(-0.121064\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 530.000 | 1.22402 | 0.612009 | − | 0.790851i | \(-0.290362\pi\) | ||||
0.612009 | + | 0.790851i | \(0.290362\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −465.102 | + | 416.000i | −1.06920 | + | 0.956322i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 320.000 | 0.732265 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 474.046 | 1.07983 | 0.539916 | − | 0.841719i | \(-0.318456\pi\) | ||||
0.539916 | + | 0.841719i | \(0.318456\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 31.0000 | − | 277.272i | 0.0702948 | − | 0.628736i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 505.351 | 1.14075 | 0.570374 | − | 0.821385i | \(-0.306798\pi\) | ||||
0.570374 | + | 0.821385i | \(0.306798\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 643.988i | − | 1.44716i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −62.6099 | + | 56.0000i | −0.140067 | + | 0.125280i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 268.328i | − | 0.597613i | −0.954314 | − | 0.298806i | \(-0.903412\pi\) | ||
0.954314 | − | 0.298806i | \(-0.0965885\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 160.000i | − | 0.354767i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 540.000 | − | 482.991i | 1.19205 | − | 1.06620i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 640.000i | − | 1.40659i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 210.000 | 0.459519 | 0.229759 | − | 0.973247i | \(-0.426206\pi\) | ||||
0.229759 | + | 0.973247i | \(0.426206\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −393.548 | + | 280.000i | −0.857403 | + | 0.610022i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −372.000 | −0.806941 | −0.403471 | − | 0.914993i | \(-0.632196\pi\) | ||||
−0.403471 | + | 0.914993i | \(0.632196\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −169.941 | −0.367044 | −0.183522 | − | 0.983016i | \(-0.558750\pi\) | ||||
−0.183522 | + | 0.983016i | \(0.558750\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −240.000 | + | 214.663i | −0.516129 | + | 0.461640i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −460.630 | −0.986360 | −0.493180 | − | 0.869927i | \(-0.664166\pi\) | ||||
−0.493180 | + | 0.869927i | \(0.664166\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 393.548i | − | 0.839121i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 107.331 | + | 120.000i | 0.227880 | + | 0.254777i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 160.997i | 0.340374i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 180.000i | 0.378947i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.0000 | + | 178.885i | −0.0419287 | + | 0.375022i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 320.000i | 0.668058i | 0.942563 | + | 0.334029i | \(0.108408\pi\) | ||||
−0.942563 | + | 0.334029i | \(0.891592\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −960.000 | −1.99584 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −286.217 | − | 320.000i | −0.592581 | − | 0.662526i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −200.000 | −0.412371 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −62.6099 | −0.128562 | −0.0642812 | − | 0.997932i | \(-0.520475\pi\) | ||||
−0.0642812 | + | 0.997932i | \(0.520475\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −248.000 | − | 277.272i | −0.507157 | − | 0.567019i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 889.955 | 1.81254 | 0.906268 | − | 0.422704i | \(-0.138919\pi\) | ||||
0.906268 | + | 0.422704i | \(0.138919\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 930.204i | − | 1.88682i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −17.8885 | + | 160.000i | −0.0361385 | + | 0.323232i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 715.542i | 1.43972i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 100.000i | 0.200401i | 0.994967 | + | 0.100200i | \(0.0319484\pi\) | ||||
−0.994967 | + | 0.100200i | \(0.968052\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 32.0000 | + | 35.7771i | 0.0638723 | + | 0.0714114i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 16.0000i | − | 0.0318091i | −0.999874 | − | 0.0159046i | \(-0.994937\pi\) | ||
0.999874 | − | 0.0159046i | \(-0.00506280\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −368.000 | −0.728713 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 337.646 | − | 302.000i | 0.665969 | − | 0.595661i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 332.000 | 0.652259 | 0.326130 | − | 0.945325i | \(-0.394255\pi\) | ||||
0.326130 | + | 0.945325i | \(0.394255\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −447.214 | −0.875173 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 440.000 | − | 313.050i | 0.857700 | − | 0.610233i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −178.885 | −0.347350 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 286.217i | 0.553611i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −313.050 | + | 280.000i | −0.603178 | + | 0.539499i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 214.663i | − | 0.412020i | −0.978550 | − | 0.206010i | \(-0.933952\pi\) | ||
0.978550 | − | 0.206010i | \(-0.0660480\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 76.0000i | − | 0.145315i | −0.997357 | − | 0.0726577i | \(-0.976852\pi\) | ||
0.997357 | − | 0.0726577i | \(-0.0231481\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 180.000 | − | 160.997i | 0.342857 | − | 0.306661i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 480.000i | − | 0.910816i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 273.000 | 0.516068 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 102.859 | − | 920.000i | 0.193708 | − | 1.73258i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 640.000 | 1.20075 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 160.997 | 0.300929 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −150.000 | + | 134.164i | −0.279330 | + | 0.249840i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 138.636 | 0.257210 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1019.65i | 1.88474i | 0.334566 | + | 0.942372i | \(0.391410\pi\) | ||||
−0.334566 | + | 0.942372i | \(0.608590\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −250.440 | − | 280.000i | −0.461215 | − | 0.515654i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 500.879i | 0.919044i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 244.000i | − | 0.446069i | −0.974810 | − | 0.223035i | \(-0.928404\pi\) | ||
0.974810 | − | 0.223035i | \(-0.0715963\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 160.000 | + | 17.8885i | 0.291439 | + | 0.0325839i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1040.00i | 1.88748i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 720.000 | 1.30199 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 429.325 | + | 480.000i | 0.773559 | + | 0.864865i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 60.0000 | 0.107720 | 0.0538600 | − | 0.998548i | \(-0.482848\pi\) | ||||
0.0538600 | + | 0.998548i | \(0.482848\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −643.988 | −1.15204 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −160.000 | − | 178.885i | −0.285205 | − | 0.318869i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 111.803 | 0.198585 | 0.0992925 | − | 0.995058i | \(-0.468342\pi\) | ||||
0.0992925 | + | 0.995058i | \(0.468342\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 143.108i | − | 0.253289i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −706.597 | − | 160.000i | −1.24620 | − | 0.282187i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 858.650i | 1.50905i | 0.656271 | + | 0.754526i | \(0.272133\pi\) | ||||
−0.656271 | + | 0.754526i | \(0.727867\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 940.000i | 1.64623i | 0.567871 | + | 0.823117i | \(0.307767\pi\) | ||||
−0.567871 | + | 0.823117i | \(0.692233\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −320.000 | − | 357.771i | −0.558464 | − | 0.624382i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 144.000i | − | 0.250435i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −370.000 | −0.641248 | −0.320624 | − | 0.947207i | \(-0.603893\pi\) | ||||
−0.320624 | + | 0.947207i | \(0.603893\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −67.0820 | + | 60.0000i | −0.115858 | + | 0.103627i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −920.000 | −1.58348 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −89.4427 | −0.153418 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −640.000 | − | 71.5542i | −1.09402 | − | 0.122315i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −469.574 | −0.799956 | −0.399978 | − | 0.916525i | \(-0.630982\pi\) | ||||
−0.399978 | + | 0.916525i | \(0.630982\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 536.656i | 0.911131i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 402.492 | − | 360.000i | 0.681036 | − | 0.609137i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 572.433i | − | 0.965318i | −0.875808 | − | 0.482659i | \(-0.839671\pi\) | ||
0.875808 | − | 0.482659i | \(-0.160329\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 640.000i | − | 1.07563i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −580.000 | + | 518.768i | −0.971524 | + | 0.868958i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 560.000i | − | 0.934891i | −0.884022 | − | 0.467446i | \(-0.845174\pi\) | ||
0.884022 | − | 0.467446i | \(-0.154826\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 302.000 | 0.502496 | 0.251248 | − | 0.967923i | \(-0.419159\pi\) | ||||
0.251248 | + | 0.967923i | \(0.419159\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −393.548 | − | 44.0000i | −0.652650 | − | 0.0729685i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 404.000 | 0.667769 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 44.7214 | 0.0736760 | 0.0368380 | − | 0.999321i | \(-0.488271\pi\) | ||||
0.0368380 | + | 0.999321i | \(0.488271\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1040.00 | − | 930.204i | 1.70772 | − | 1.52743i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1144.87 | −1.87376 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 447.214i | − | 0.729549i | −0.931096 | − | 0.364775i | \(-0.881146\pi\) | ||
0.931096 | − | 0.364775i | \(-0.118854\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −286.217 | − | 320.000i | −0.465393 | − | 0.520325i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 447.214i | − | 0.724819i | −0.932019 | − | 0.362410i | \(-0.881954\pi\) | ||
0.932019 | − | 0.362410i | \(-0.118046\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 780.000i | 1.26010i | 0.776556 | + | 0.630048i | \(0.216965\pi\) | ||||
−0.776556 | + | 0.630048i | \(0.783035\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −352.000 | + | 250.440i | −0.566828 | + | 0.403284i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1440.00i | 2.31140i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −319.000 | −0.510400 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 178.885 | + | 200.000i | 0.285304 | + | 0.318979i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −960.000 | −1.52623 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 80.4984 | 0.127573 | 0.0637864 | − | 0.997964i | \(-0.479682\pi\) | ||||
0.0637864 | + | 0.997964i | \(0.479682\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 120.000 | + | 134.164i | 0.189573 | + | 0.211950i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 107.331 | 0.169026 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 554.545i | 0.870557i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 715.542 | + | 80.0000i | 1.11978 | + | 0.125196i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 661.876i | − | 1.03257i | −0.856417 | − | 0.516284i | \(-0.827315\pi\) | ||
0.856417 | − | 0.516284i | \(-0.172685\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 844.000i | 1.31260i | 0.754501 | + | 0.656299i | \(0.227879\pi\) | ||||
−0.754501 | + | 0.656299i | \(0.772121\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 288.000 | + | 321.994i | 0.446512 | + | 0.499215i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 16.0000i | − | 0.0247295i | −0.999924 | − | 0.0123648i | \(-0.996064\pi\) | ||
0.999924 | − | 0.0123648i | \(-0.00393593\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 460.000 | 0.708783 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 536.656 | − | 480.000i | 0.824357 | − | 0.737327i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −660.000 | −1.01072 | −0.505360 | − | 0.862909i | \(-0.668640\pi\) | ||||
−0.505360 | + | 0.862909i | \(0.668640\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −268.328 | −0.409661 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −50.0000 | + | 447.214i | −0.0761035 | + | 0.680690i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 210.190 | 0.318954 | 0.159477 | − | 0.987202i | \(-0.449019\pi\) | ||||
0.159477 | + | 0.987202i | \(0.449019\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 769.207i | 1.16370i | 0.813295 | + | 0.581851i | \(0.197671\pi\) | ||||
−0.813295 | + | 0.581851i | \(0.802329\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 715.542 | − | 640.000i | 1.07925 | − | 0.965309i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 715.542i | 1.07600i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 832.000i | − | 1.24738i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −340.000 | + | 304.105i | −0.508221 | + | 0.454567i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 80.0000i | 0.119225i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −910.000 | −1.35215 | −0.676077 | − | 0.736831i | \(-0.736321\pi\) | ||||
−0.676077 | + | 0.736831i | \(0.736321\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −140.872 | − | 198.000i | −0.208700 | − | 0.293333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −260.000 | −0.384047 | −0.192024 | − | 0.981390i | \(-0.561505\pi\) | ||||
−0.192024 | + | 0.981390i | \(0.561505\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 447.214 | 0.658636 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −570.000 | + | 509.823i | −0.837004 | + | 0.748639i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 934.676 | 1.36849 | 0.684243 | − | 0.729254i | \(-0.260133\pi\) | ||||
0.684243 | + | 0.729254i | \(0.260133\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 572.433i | 0.835669i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −393.548 | − | 440.000i | −0.572850 | − | 0.640466i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 357.771i | − | 0.519261i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 100.000i | − | 0.144718i | −0.997379 | − | 0.0723589i | \(-0.976947\pi\) | ||
0.997379 | − | 0.0723589i | \(-0.0230527\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 40.0000 | − | 357.771i | 0.0577201 | − | 0.516264i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1040.00i | 1.49640i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 640.000 | 0.918221 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −321.994 | − | 360.000i | −0.460649 | − | 0.515021i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1028.00 | −1.46648 | −0.733238 | − | 0.679972i | \(-0.761992\pi\) | ||||
−0.733238 | + | 0.679972i | \(0.761992\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1073.31 | 1.52676 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 512.000 | + | 572.433i | 0.726241 | + | 0.811962i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 822.873 | 1.16389 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 912.316i | 1.28676i | 0.765545 | + | 0.643382i | \(0.222469\pi\) | ||||
−0.765545 | + | 0.643382i | \(0.777531\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 80.4984 | − | 720.000i | 0.113219 | − | 1.01266i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 429.325i | − | 0.602139i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 320.000i | − | 0.447552i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 640.000 | + | 715.542i | 0.892608 | + | 0.997966i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 480.000i | − | 0.667594i | −0.942645 | − | 0.333797i | \(-0.891670\pi\) | ||
0.942645 | − | 0.333797i | \(-0.108330\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 400.000 | 0.554785 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −711.070 | + | 636.000i | −0.983499 | + | 0.879668i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 468.000 | 0.645517 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −241.495 | −0.332181 | −0.166090 | − | 0.986111i | \(-0.553114\pi\) | ||||
−0.166090 | + | 0.986111i | \(0.553114\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −239.000 | + | 688.709i | −0.327846 | + | 0.944731i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −643.988 | −0.880968 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1126.98i | − | 1.53749i | −0.639557 | − | 0.768744i | \(-0.720882\pi\) | ||
0.639557 | − | 0.768744i | \(-0.279118\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 277.272 | − | 248.000i | 0.377241 | − | 0.337415i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 196.774i | − | 0.266993i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1020.00i | − | 1.38024i | −0.723693 | − | 0.690122i | \(-0.757557\pi\) | ||
0.723693 | − | 0.690122i | \(-0.242443\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −800.000 | + | 715.542i | −1.07962 | + | 0.965643i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 176.000i | 0.236878i | 0.992961 | + | 0.118439i | \(0.0377889\pi\) | ||||
−0.992961 | + | 0.118439i | \(0.962211\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −112.000 | −0.150336 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −102.859 | + | 920.000i | −0.137696 | + | 1.23159i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −360.000 | −0.480641 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1296.92 | 1.72692 | 0.863462 | − | 0.504414i | \(-0.168292\pi\) | ||||
0.863462 | + | 0.504414i | \(0.168292\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −330.000 | + | 295.161i | −0.438247 | + | 0.391980i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 965.981 | 1.27945 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 983.870i | 1.29970i | 0.760064 | + | 0.649848i | \(0.225167\pi\) | ||||
−0.760064 | + | 0.649848i | \(0.774833\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −143.108 | − | 160.000i | −0.188549 | − | 0.210804i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 107.331i | 0.141040i | 0.997510 | + | 0.0705199i | \(0.0224658\pi\) | ||||
−0.997510 | + | 0.0705199i | \(0.977534\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1120.00i | − | 1.46789i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −640.000 | − | 71.5542i | −0.836601 | − | 0.0935349i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1840.00i | 2.39896i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1378.00 | −1.79194 | −0.895969 | − | 0.444117i | \(-0.853517\pi\) | ||||
−0.895969 | + | 0.444117i | \(0.853517\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 214.663 | + | 240.000i | 0.278421 | + | 0.311284i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1180.00 | 1.52652 | 0.763260 | − | 0.646091i | \(-0.223598\pi\) | ||||
0.763260 | + | 0.646091i | \(0.223598\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 241.495 | 0.311607 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −960.000 | − | 1073.31i | −1.23552 | − | 1.38135i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −715.542 | −0.918539 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 357.771i | 0.458093i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −813.929 | − | 1144.00i | −1.03950 | − | 1.46105i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 214.663i | 0.273455i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1244.00i | 1.58069i | 0.612665 | + | 0.790343i | \(0.290098\pi\) | ||||
−0.612665 | + | 0.790343i | \(0.709902\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −288.000 | − | 321.994i | −0.365019 | − | 0.408104i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 320.000i | 0.404551i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −320.000 | −0.403531 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −178.885 | + | 160.000i | −0.225013 | + | 0.201258i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −580.000 | −0.727729 | −0.363864 | − | 0.931452i | \(-0.618543\pi\) | ||||
−0.363864 | + | 0.931452i | \(0.618543\pi\) | |||||||
\(798\) | 0 |