Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(1,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 74x^{6} + 1469x^{4} - 8828x^{2} + 2500 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(3.98569\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.39991 | 1.90916 | 0.954578 | − | 0.297962i | \(-0.0963070\pi\) | ||||
0.954578 | + | 0.297962i | \(0.0963070\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 21.1590 | 2.64487 | ||||||||
\(5\) | 15.5768 | 1.39323 | 0.696615 | − | 0.717446i | \(-0.254689\pi\) | ||||
0.696615 | + | 0.717446i | \(0.254689\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 71.0573 | 3.14032 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 84.1131 | 2.65989 | ||||||||
\(11\) | 31.9702 | 0.876306 | 0.438153 | − | 0.898900i | \(-0.355633\pi\) | ||||
0.438153 | + | 0.898900i | \(0.355633\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −72.5746 | −1.54835 | −0.774176 | − | 0.632971i | \(-0.781835\pi\) | ||||
−0.774176 | + | 0.632971i | \(0.781835\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 214.431 | 3.35048 | ||||||||
\(17\) | −29.0288 | −0.414148 | −0.207074 | − | 0.978325i | \(-0.566394\pi\) | ||||
−0.207074 | + | 0.978325i | \(0.566394\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −108.829 | −1.31406 | −0.657030 | − | 0.753864i | \(-0.728188\pi\) | ||||
−0.657030 | + | 0.753864i | \(0.728188\pi\) | |||||||
\(20\) | 329.589 | 3.68492 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 172.636 | 1.67300 | ||||||||
\(23\) | −55.2869 | −0.501222 | −0.250611 | − | 0.968088i | \(-0.580632\pi\) | ||||
−0.250611 | + | 0.968088i | \(0.580632\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 117.636 | 0.941088 | ||||||||
\(26\) | −391.896 | −2.95604 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 17.7363 | 0.113570 | 0.0567852 | − | 0.998386i | \(-0.481915\pi\) | ||||
0.0567852 | + | 0.998386i | \(0.481915\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −56.1189 | −0.325137 | −0.162568 | − | 0.986697i | \(-0.551978\pi\) | ||||
−0.162568 | + | 0.986697i | \(0.551978\pi\) | |||||||
\(32\) | 589.448 | 3.25627 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −156.753 | −0.790673 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −295.816 | −1.31437 | −0.657187 | − | 0.753728i | \(-0.728254\pi\) | ||||
−0.657187 | + | 0.753728i | \(0.728254\pi\) | |||||||
\(38\) | −587.668 | −2.50875 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1106.84 | 4.37518 | ||||||||
\(41\) | 238.605 | 0.908873 | 0.454437 | − | 0.890779i | \(-0.349841\pi\) | ||||
0.454437 | + | 0.890779i | \(0.349841\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16.8202 | 0.0596526 | 0.0298263 | − | 0.999555i | \(-0.490505\pi\) | ||||
0.0298263 | + | 0.999555i | \(0.490505\pi\) | |||||||
\(44\) | 676.457 | 2.31772 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −298.544 | −0.956911 | ||||||||
\(47\) | 511.909 | 1.58871 | 0.794357 | − | 0.607451i | \(-0.207808\pi\) | ||||
0.794357 | + | 0.607451i | \(0.207808\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 635.223 | 1.79668 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1535.60 | −4.09519 | ||||||||
\(53\) | 265.205 | 0.687335 | 0.343667 | − | 0.939091i | \(-0.388331\pi\) | ||||
0.343667 | + | 0.939091i | \(0.388331\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 497.992 | 1.22090 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 95.7742 | 0.216823 | ||||||||
\(59\) | −254.181 | −0.560875 | −0.280437 | − | 0.959872i | \(-0.590480\pi\) | ||||
−0.280437 | + | 0.959872i | \(0.590480\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 72.8352 | 0.152878 | 0.0764392 | − | 0.997074i | \(-0.475645\pi\) | ||||
0.0764392 | + | 0.997074i | \(0.475645\pi\) | |||||||
\(62\) | −303.037 | −0.620737 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1467.52 | 2.86625 | ||||||||
\(65\) | −1130.48 | −2.15721 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −506.360 | −0.923308 | −0.461654 | − | 0.887060i | \(-0.652744\pi\) | ||||
−0.461654 | + | 0.887060i | \(0.652744\pi\) | |||||||
\(68\) | −614.220 | −1.09537 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −827.722 | −1.38356 | −0.691779 | − | 0.722110i | \(-0.743173\pi\) | ||||
−0.691779 | + | 0.722110i | \(0.743173\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 372.577 | 0.597354 | 0.298677 | − | 0.954354i | \(-0.403455\pi\) | ||||
0.298677 | + | 0.954354i | \(0.403455\pi\) | |||||||
\(74\) | −1597.38 | −2.50934 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2302.72 | −3.47552 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1028.45 | 1.46468 | 0.732341 | − | 0.680938i | \(-0.238428\pi\) | ||||
0.732341 | + | 0.680938i | \(0.238428\pi\) | |||||||
\(80\) | 3340.14 | 4.66799 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1288.44 | 1.73518 | ||||||||
\(83\) | 453.148 | 0.599270 | 0.299635 | − | 0.954054i | \(-0.403135\pi\) | ||||
0.299635 | + | 0.954054i | \(0.403135\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −452.175 | −0.577003 | ||||||||
\(86\) | 90.8276 | 0.113886 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2271.71 | 2.75188 | ||||||||
\(89\) | 332.065 | 0.395493 | 0.197746 | − | 0.980253i | \(-0.436638\pi\) | ||||
0.197746 | + | 0.980253i | \(0.436638\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1169.81 | −1.32567 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2764.26 | 3.03310 | ||||||||
\(95\) | −1695.21 | −1.83079 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1164.54 | 1.21898 | 0.609489 | − | 0.792795i | \(-0.291375\pi\) | ||||
0.609489 | + | 0.792795i | \(0.291375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2489.06 | 2.48906 | ||||||||
\(101\) | −1863.54 | −1.83593 | −0.917967 | − | 0.396656i | \(-0.870171\pi\) | ||||
−0.917967 | + | 0.396656i | \(0.870171\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −986.280 | −0.943506 | −0.471753 | − | 0.881731i | \(-0.656379\pi\) | ||||
−0.471753 | + | 0.881731i | \(0.656379\pi\) | |||||||
\(104\) | −5156.95 | −4.86232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1432.08 | 1.31223 | ||||||||
\(107\) | −695.685 | −0.628546 | −0.314273 | − | 0.949333i | \(-0.601761\pi\) | ||||
−0.314273 | + | 0.949333i | \(0.601761\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1715.00 | 1.50703 | 0.753517 | − | 0.657428i | \(-0.228356\pi\) | ||||
0.753517 | + | 0.657428i | \(0.228356\pi\) | |||||||
\(110\) | 2689.11 | 2.33088 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 877.721 | 0.730700 | 0.365350 | − | 0.930870i | \(-0.380949\pi\) | ||||
0.365350 | + | 0.930870i | \(0.380949\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −861.191 | −0.698317 | ||||||||
\(116\) | 375.281 | 0.300379 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1372.56 | −1.07080 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −308.908 | −0.232087 | ||||||||
\(122\) | 393.303 | 0.291869 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1187.42 | −0.859946 | ||||||||
\(125\) | −114.708 | −0.0820784 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 781.088 | 0.545751 | 0.272875 | − | 0.962049i | \(-0.412025\pi\) | ||||
0.272875 | + | 0.962049i | \(0.412025\pi\) | |||||||
\(128\) | 3208.88 | 2.21584 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6104.48 | −4.11845 | ||||||||
\(131\) | 1961.24 | 1.30805 | 0.654024 | − | 0.756474i | \(-0.273080\pi\) | ||||
0.654024 | + | 0.756474i | \(0.273080\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2734.29 | −1.76274 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2062.71 | −1.30056 | ||||||||
\(137\) | −1220.31 | −0.761009 | −0.380504 | − | 0.924779i | \(-0.624250\pi\) | ||||
−0.380504 | + | 0.924779i | \(0.624250\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1068.10 | −0.651765 | −0.325882 | − | 0.945410i | \(-0.605661\pi\) | ||||
−0.325882 | + | 0.945410i | \(0.605661\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4469.62 | −2.64143 | ||||||||
\(143\) | −2320.22 | −1.35683 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 276.274 | 0.158230 | ||||||||
\(146\) | 2011.88 | 1.14044 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6259.16 | −3.47635 | ||||||||
\(149\) | −2590.82 | −1.42449 | −0.712243 | − | 0.701933i | \(-0.752321\pi\) | ||||
−0.712243 | + | 0.701933i | \(0.752321\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1929.54 | 1.03989 | 0.519946 | − | 0.854199i | \(-0.325952\pi\) | ||||
0.519946 | + | 0.854199i | \(0.325952\pi\) | |||||||
\(152\) | −7733.12 | −4.12657 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −874.151 | −0.452990 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2625.73 | −1.33475 | −0.667377 | − | 0.744720i | \(-0.732583\pi\) | ||||
−0.667377 | + | 0.744720i | \(0.732583\pi\) | |||||||
\(158\) | 5553.54 | 2.79630 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9181.70 | 4.53673 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3100.17 | −1.48972 | −0.744858 | − | 0.667223i | \(-0.767483\pi\) | ||||
−0.744858 | + | 0.667223i | \(0.767483\pi\) | |||||||
\(164\) | 5048.63 | 2.40385 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2446.95 | 1.14410 | ||||||||
\(167\) | 3264.73 | 1.51277 | 0.756386 | − | 0.654126i | \(-0.226963\pi\) | ||||
0.756386 | + | 0.654126i | \(0.226963\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3070.07 | 1.39739 | ||||||||
\(170\) | −2441.70 | −1.10159 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 355.899 | 0.157773 | ||||||||
\(173\) | −2036.31 | −0.894900 | −0.447450 | − | 0.894309i | \(-0.647668\pi\) | ||||
−0.447450 | + | 0.894309i | \(0.647668\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6855.39 | 2.93605 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1793.12 | 0.755057 | ||||||||
\(179\) | −3582.35 | −1.49585 | −0.747925 | − | 0.663783i | \(-0.768950\pi\) | ||||
−0.747925 | + | 0.663783i | \(0.768950\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1637.35 | 0.672392 | 0.336196 | − | 0.941792i | \(-0.390860\pi\) | ||||
0.336196 | + | 0.941792i | \(0.390860\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3928.53 | −1.57400 | ||||||||
\(185\) | −4607.86 | −1.83122 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −928.056 | −0.362921 | ||||||||
\(188\) | 10831.5 | 4.20195 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9153.97 | −3.49526 | ||||||||
\(191\) | 2824.78 | 1.07013 | 0.535063 | − | 0.844812i | \(-0.320288\pi\) | ||||
0.535063 | + | 0.844812i | \(0.320288\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1657.53 | −0.618195 | −0.309098 | − | 0.951030i | \(-0.600027\pi\) | ||||
−0.309098 | + | 0.951030i | \(0.600027\pi\) | |||||||
\(194\) | 6288.39 | 2.32722 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1890.78 | 0.683819 | 0.341909 | − | 0.939733i | \(-0.388926\pi\) | ||||
0.341909 | + | 0.939733i | \(0.388926\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1392.75 | 0.496126 | 0.248063 | − | 0.968744i | \(-0.420206\pi\) | ||||
0.248063 | + | 0.968744i | \(0.420206\pi\) | |||||||
\(200\) | 8358.89 | 2.95532 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10063.0 | −3.50508 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3716.69 | 1.26627 | ||||||||
\(206\) | −5325.82 | −1.80130 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −15562.2 | −5.18772 | ||||||||
\(209\) | −3479.29 | −1.15152 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3314.53 | 1.08143 | 0.540714 | − | 0.841206i | \(-0.318154\pi\) | ||||
0.540714 | + | 0.841206i | \(0.318154\pi\) | |||||||
\(212\) | 5611.47 | 1.81791 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3756.64 | −1.19999 | ||||||||
\(215\) | 262.005 | 0.0831097 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 9260.82 | 2.87716 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10537.0 | 3.22911 | ||||||||
\(221\) | 2106.75 | 0.641247 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5576.50 | 1.67457 | 0.837287 | − | 0.546764i | \(-0.184140\pi\) | ||||
0.837287 | + | 0.546764i | \(0.184140\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4739.61 | 1.39502 | ||||||||
\(227\) | 1447.92 | 0.423357 | 0.211678 | − | 0.977339i | \(-0.432107\pi\) | ||||
0.211678 | + | 0.977339i | \(0.432107\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1617.55 | −0.466771 | −0.233385 | − | 0.972384i | \(-0.574980\pi\) | ||||
−0.233385 | + | 0.972384i | \(0.574980\pi\) | |||||||
\(230\) | −4650.35 | −1.33320 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1260.29 | 0.356647 | ||||||||
\(233\) | −6092.11 | −1.71291 | −0.856454 | − | 0.516224i | \(-0.827337\pi\) | ||||
−0.856454 | + | 0.516224i | \(0.827337\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7973.89 | 2.21344 | ||||||||
\(236\) | −5378.22 | −1.48344 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1595.90 | −0.431927 | −0.215963 | − | 0.976401i | \(-0.569289\pi\) | ||||
−0.215963 | + | 0.976401i | \(0.569289\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2188.83 | −0.585041 | −0.292521 | − | 0.956259i | \(-0.594494\pi\) | ||||
−0.292521 | + | 0.956259i | \(0.594494\pi\) | |||||||
\(242\) | −1668.07 | −0.443090 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1541.12 | 0.404344 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7898.24 | 2.03463 | ||||||||
\(248\) | −3987.65 | −1.02103 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −619.413 | −0.156700 | ||||||||
\(251\) | 6203.07 | 1.55990 | 0.779949 | − | 0.625843i | \(-0.215245\pi\) | ||||
0.779949 | + | 0.625843i | \(0.215245\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1767.53 | −0.439224 | ||||||||
\(254\) | 4217.80 | 1.04192 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5587.48 | 1.36413 | ||||||||
\(257\) | 268.323 | 0.0651266 | 0.0325633 | − | 0.999470i | \(-0.489633\pi\) | ||||
0.0325633 | + | 0.999470i | \(0.489633\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −23919.8 | −5.70554 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10590.5 | 2.49727 | ||||||||
\(263\) | 3724.96 | 0.873349 | 0.436675 | − | 0.899619i | \(-0.356156\pi\) | ||||
0.436675 | + | 0.899619i | \(0.356156\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4131.04 | 0.957615 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10714.1 | −2.44203 | ||||||||
\(269\) | 8557.25 | 1.93957 | 0.969786 | − | 0.243958i | \(-0.0784458\pi\) | ||||
0.969786 | + | 0.243958i | \(0.0784458\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5279.66 | 1.18346 | 0.591728 | − | 0.806137i | \(-0.298446\pi\) | ||||
0.591728 | + | 0.806137i | \(0.298446\pi\) | |||||||
\(272\) | −6224.67 | −1.38760 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6589.56 | −1.45288 | ||||||||
\(275\) | 3760.84 | 0.824681 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −441.548 | −0.0957764 | −0.0478882 | − | 0.998853i | \(-0.515249\pi\) | ||||
−0.0478882 | + | 0.998853i | \(0.515249\pi\) | |||||||
\(278\) | −5767.66 | −1.24432 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3766.49 | −0.799609 | −0.399804 | − | 0.916601i | \(-0.630922\pi\) | ||||
−0.399804 | + | 0.916601i | \(0.630922\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1811.02 | −0.380403 | −0.190201 | − | 0.981745i | \(-0.560914\pi\) | ||||
−0.190201 | + | 0.981745i | \(0.560914\pi\) | |||||||
\(284\) | −17513.8 | −3.65933 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12529.0 | −2.59040 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4070.33 | −0.828481 | ||||||||
\(290\) | 1491.85 | 0.302085 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7883.35 | 1.57993 | ||||||||
\(293\) | −5815.74 | −1.15959 | −0.579794 | − | 0.814763i | \(-0.696867\pi\) | ||||
−0.579794 | + | 0.814763i | \(0.696867\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3959.33 | −0.781427 | ||||||||
\(296\) | −21019.9 | −4.12755 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13990.2 | −2.71957 | ||||||||
\(299\) | 4012.42 | 0.776068 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10419.3 | 1.98532 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −23336.4 | −4.40274 | ||||||||
\(305\) | 1134.54 | 0.212995 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1974.93 | 0.367150 | 0.183575 | − | 0.983006i | \(-0.441233\pi\) | ||||
0.183575 | + | 0.983006i | \(0.441233\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4720.33 | −0.864829 | ||||||||
\(311\) | 1159.07 | 0.211334 | 0.105667 | − | 0.994402i | \(-0.466302\pi\) | ||||
0.105667 | + | 0.994402i | \(0.466302\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4493.67 | −0.811494 | −0.405747 | − | 0.913986i | \(-0.632989\pi\) | ||||
−0.405747 | + | 0.913986i | \(0.632989\pi\) | |||||||
\(314\) | −14178.7 | −2.54825 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 21761.0 | 3.87390 | ||||||||
\(317\) | 4677.50 | 0.828752 | 0.414376 | − | 0.910106i | \(-0.364000\pi\) | ||||
0.414376 | + | 0.910106i | \(0.364000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 567.031 | 0.0995225 | ||||||||
\(320\) | 22859.2 | 3.99334 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3159.19 | 0.544216 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8537.38 | −1.45713 | ||||||||
\(326\) | −16740.6 | −2.84410 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 16954.6 | 2.85415 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2982.71 | −0.495301 | −0.247650 | − | 0.968849i | \(-0.579658\pi\) | ||||
−0.247650 | + | 0.968849i | \(0.579658\pi\) | |||||||
\(332\) | 9588.15 | 1.58499 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17629.3 | 2.88811 | ||||||||
\(335\) | −7887.45 | −1.28638 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7328.53 | 1.18460 | 0.592301 | − | 0.805717i | \(-0.298220\pi\) | ||||
0.592301 | + | 0.805717i | \(0.298220\pi\) | |||||||
\(338\) | 16578.1 | 2.66784 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9567.57 | −1.52610 | ||||||||
\(341\) | −1794.13 | −0.284920 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1195.20 | 0.187328 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10995.9 | −1.70850 | ||||||||
\(347\) | 8309.33 | 1.28550 | 0.642749 | − | 0.766076i | \(-0.277794\pi\) | ||||
0.642749 | + | 0.766076i | \(0.277794\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −334.303 | −0.0512745 | −0.0256373 | − | 0.999671i | \(-0.508161\pi\) | ||||
−0.0256373 | + | 0.999671i | \(0.508161\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 18844.8 | 2.85349 | ||||||||
\(353\) | 5458.19 | 0.822975 | 0.411487 | − | 0.911415i | \(-0.365009\pi\) | ||||
0.411487 | + | 0.911415i | \(0.365009\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12893.2 | −1.92761 | ||||||||
\(356\) | 7026.17 | 1.04603 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −19344.3 | −2.85581 | ||||||||
\(359\) | 7196.90 | 1.05804 | 0.529022 | − | 0.848608i | \(-0.322559\pi\) | ||||
0.529022 | + | 0.848608i | \(0.322559\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4984.82 | 0.726755 | ||||||||
\(362\) | 8841.52 | 1.28370 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5803.55 | 0.832251 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6324.43 | 0.899544 | 0.449772 | − | 0.893143i | \(-0.351505\pi\) | ||||
0.449772 | + | 0.893143i | \(0.351505\pi\) | |||||||
\(368\) | −11855.2 | −1.67934 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −24882.0 | −3.49609 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10931.8 | −1.51749 | −0.758746 | − | 0.651386i | \(-0.774188\pi\) | ||||
−0.758746 | + | 0.651386i | \(0.774188\pi\) | |||||||
\(374\) | −5011.42 | −0.692872 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 36374.9 | 4.98907 | ||||||||
\(377\) | −1287.20 | −0.175847 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6024.02 | 0.816446 | 0.408223 | − | 0.912882i | \(-0.366149\pi\) | ||||
0.408223 | + | 0.912882i | \(0.366149\pi\) | |||||||
\(380\) | −35868.9 | −4.84220 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15253.6 | 2.04304 | ||||||||
\(383\) | −6848.10 | −0.913633 | −0.456816 | − | 0.889561i | \(-0.651010\pi\) | ||||
−0.456816 | + | 0.889561i | \(0.651010\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8950.51 | −1.18023 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 24640.4 | 3.22404 | ||||||||
\(389\) | 5161.88 | 0.672796 | 0.336398 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336398 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1604.91 | 0.207580 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10210.0 | 1.30552 | ||||||||
\(395\) | 16020.0 | 2.04064 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 344.768 | 0.0435854 | 0.0217927 | − | 0.999763i | \(-0.493063\pi\) | ||||
0.0217927 | + | 0.999763i | \(0.493063\pi\) | |||||||
\(398\) | 7520.70 | 0.947182 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 25224.8 | 3.15310 | ||||||||
\(401\) | 5098.84 | 0.634972 | 0.317486 | − | 0.948263i | \(-0.397161\pi\) | ||||
0.317486 | + | 0.948263i | \(0.397161\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4072.80 | 0.503426 | ||||||||
\(404\) | −39430.7 | −4.85582 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9457.28 | −1.15179 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −323.124 | −0.0390647 | −0.0195323 | − | 0.999809i | \(-0.506218\pi\) | ||||
−0.0195323 | + | 0.999809i | \(0.506218\pi\) | |||||||
\(410\) | 20069.8 | 2.41750 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −20868.7 | −2.49545 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7058.58 | 0.834921 | ||||||||
\(416\) | −42779.0 | −5.04185 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −18787.8 | −2.19843 | ||||||||
\(419\) | 4415.98 | 0.514880 | 0.257440 | − | 0.966294i | \(-0.417121\pi\) | ||||
0.257440 | + | 0.966294i | \(0.417121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1379.37 | 0.159683 | 0.0798415 | − | 0.996808i | \(-0.474559\pi\) | ||||
0.0798415 | + | 0.996808i | \(0.474559\pi\) | |||||||
\(422\) | 17898.1 | 2.06461 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 18844.8 | 2.15845 | ||||||||
\(425\) | −3414.83 | −0.389750 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −14720.0 | −1.66243 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1414.80 | 0.158669 | ||||||||
\(431\) | 1655.79 | 0.185050 | 0.0925248 | − | 0.995710i | \(-0.470506\pi\) | ||||
0.0925248 | + | 0.995710i | \(0.470506\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8612.65 | 0.955883 | 0.477942 | − | 0.878392i | \(-0.341383\pi\) | ||||
0.477942 | + | 0.878392i | \(0.341383\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 36287.6 | 3.98592 | ||||||||
\(437\) | 6016.83 | 0.658636 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5975.39 | −0.649635 | −0.324817 | − | 0.945777i | \(-0.605303\pi\) | ||||
−0.324817 | + | 0.945777i | \(0.605303\pi\) | |||||||
\(440\) | 35386.0 | 3.83400 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11376.3 | 1.22424 | ||||||||
\(443\) | 806.532 | 0.0865000 | 0.0432500 | − | 0.999064i | \(-0.486229\pi\) | ||||
0.0432500 | + | 0.999064i | \(0.486229\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5172.51 | 0.551012 | ||||||||
\(446\) | 30112.6 | 3.19702 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6253.04 | 0.657237 | 0.328618 | − | 0.944463i | \(-0.393417\pi\) | ||||
0.328618 | + | 0.944463i | \(0.393417\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7628.23 | 0.796451 | ||||||||
\(452\) | 18571.7 | 1.93261 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7818.65 | 0.808254 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 160.288 | 0.0164069 | 0.00820344 | − | 0.999966i | \(-0.497389\pi\) | ||||
0.00820344 | + | 0.999966i | \(0.497389\pi\) | |||||||
\(458\) | −8734.60 | −0.891138 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −18221.9 | −1.84696 | ||||||||
\(461\) | −2408.80 | −0.243360 | −0.121680 | − | 0.992569i | \(-0.538828\pi\) | ||||
−0.121680 | + | 0.992569i | \(0.538828\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1092.89 | −0.109699 | −0.0548496 | − | 0.998495i | \(-0.517468\pi\) | ||||
−0.0548496 | + | 0.998495i | \(0.517468\pi\) | |||||||
\(464\) | 3803.20 | 0.380516 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −32896.8 | −3.27021 | ||||||||
\(467\) | −15054.8 | −1.49177 | −0.745884 | − | 0.666076i | \(-0.767973\pi\) | ||||
−0.745884 | + | 0.666076i | \(0.767973\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 43058.3 | 4.22581 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −18061.5 | −1.76133 | ||||||||
\(473\) | 537.745 | 0.0522739 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12802.2 | −1.23665 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8617.73 | −0.824615 | ||||||||
\(479\) | −10455.6 | −0.997346 | −0.498673 | − | 0.866790i | \(-0.666179\pi\) | ||||
−0.498673 | + | 0.866790i | \(0.666179\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21468.7 | 2.03511 | ||||||||
\(482\) | −11819.5 | −1.11693 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6536.18 | −0.613841 | ||||||||
\(485\) | 18139.7 | 1.69831 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12717.7 | −1.18335 | −0.591675 | − | 0.806176i | \(-0.701533\pi\) | ||||
−0.591675 | + | 0.806176i | \(0.701533\pi\) | |||||||
\(488\) | 5175.47 | 0.480087 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20983.1 | 1.92863 | 0.964313 | − | 0.264763i | \(-0.0852937\pi\) | ||||
0.964313 | + | 0.264763i | \(0.0852937\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −514.863 | −0.0470350 | ||||||||
\(494\) | 42649.8 | 3.88442 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12033.6 | −1.08937 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12718.1 | 1.14096 | 0.570480 | − | 0.821311i | \(-0.306757\pi\) | ||||
0.570480 | + | 0.821311i | \(0.306757\pi\) | |||||||
\(500\) | −2427.11 | −0.217087 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 33496.0 | 2.97809 | ||||||||
\(503\) | −15675.9 | −1.38957 | −0.694785 | − | 0.719218i | \(-0.744500\pi\) | ||||
−0.694785 | + | 0.719218i | \(0.744500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29028.0 | −2.55788 | ||||||||
\(506\) | −9544.50 | −0.838547 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16527.0 | 1.44344 | ||||||||
\(509\) | −10218.3 | −0.889819 | −0.444910 | − | 0.895575i | \(-0.646764\pi\) | ||||
−0.444910 | + | 0.895575i | \(0.646764\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 4500.87 | 0.388501 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1448.92 | 0.124337 | ||||||||
\(515\) | −15363.1 | −1.31452 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16365.8 | 1.39220 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −80328.7 | −6.77432 | ||||||||
\(521\) | −4808.13 | −0.404315 | −0.202157 | − | 0.979353i | \(-0.564795\pi\) | ||||
−0.202157 | + | 0.979353i | \(0.564795\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9936.18 | −0.830744 | −0.415372 | − | 0.909652i | \(-0.636349\pi\) | ||||
−0.415372 | + | 0.909652i | \(0.636349\pi\) | |||||||
\(524\) | 41497.8 | 3.45962 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20114.4 | 1.66736 | ||||||||
\(527\) | 1629.06 | 0.134655 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9110.36 | −0.748777 | ||||||||
\(530\) | 22307.2 | 1.82823 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17316.6 | −1.40725 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10836.5 | −0.875709 | ||||||||
\(536\) | −35980.5 | −2.89948 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 46208.4 | 3.70294 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2048.66 | −0.162808 | −0.0814038 | − | 0.996681i | \(-0.525940\pi\) | ||||
−0.0814038 | + | 0.996681i | \(0.525940\pi\) | |||||||
\(542\) | 28509.7 | 2.25940 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −17111.0 | −1.34858 | ||||||||
\(545\) | 26714.1 | 2.09964 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6154.72 | 0.481091 | 0.240546 | − | 0.970638i | \(-0.422674\pi\) | ||||
0.240546 | + | 0.970638i | \(0.422674\pi\) | |||||||
\(548\) | −25820.5 | −2.01277 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 20308.2 | 1.57444 | ||||||||
\(551\) | −1930.22 | −0.149238 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2384.32 | −0.182852 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −22600.0 | −1.72384 | ||||||||
\(557\) | −4446.75 | −0.338267 | −0.169134 | − | 0.985593i | \(-0.554097\pi\) | ||||
−0.169134 | + | 0.985593i | \(0.554097\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1220.72 | −0.0923631 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20338.7 | −1.52658 | ||||||||
\(563\) | 9686.59 | 0.725117 | 0.362559 | − | 0.931961i | \(-0.381903\pi\) | ||||
0.362559 | + | 0.931961i | \(0.381903\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13672.1 | 1.01803 | ||||||||
\(566\) | −9779.35 | −0.726248 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −58815.7 | −4.34481 | ||||||||
\(569\) | 7306.92 | 0.538351 | 0.269176 | − | 0.963091i | \(-0.413249\pi\) | ||||
0.269176 | + | 0.963091i | \(0.413249\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9109.34 | 0.667625 | 0.333813 | − | 0.942639i | \(-0.391665\pi\) | ||||
0.333813 | + | 0.942639i | \(0.391665\pi\) | |||||||
\(572\) | −49093.6 | −3.58864 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6503.72 | −0.471694 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18707.7 | −1.34976 | −0.674880 | − | 0.737927i | \(-0.735805\pi\) | ||||
−0.674880 | + | 0.737927i | \(0.735805\pi\) | |||||||
\(578\) | −21979.4 | −1.58170 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5845.67 | 0.418497 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8478.66 | 0.602316 | ||||||||
\(584\) | 26474.3 | 1.87588 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −31404.4 | −2.21383 | ||||||||
\(587\) | −24610.4 | −1.73046 | −0.865230 | − | 0.501375i | \(-0.832828\pi\) | ||||
−0.865230 | + | 0.501375i | \(0.832828\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6107.38 | 0.427250 | ||||||||
\(590\) | −21380.0 | −1.49187 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −63432.0 | −4.40378 | ||||||||
\(593\) | 18840.0 | 1.30466 | 0.652332 | − | 0.757933i | \(-0.273791\pi\) | ||||
0.652332 | + | 0.757933i | \(0.273791\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −54819.2 | −3.76759 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 21666.7 | 1.48163 | ||||||||
\(599\) | 20647.6 | 1.40841 | 0.704206 | − | 0.709996i | \(-0.251303\pi\) | ||||
0.704206 | + | 0.709996i | \(0.251303\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15772.8 | −1.07053 | −0.535264 | − | 0.844685i | \(-0.679788\pi\) | ||||
−0.535264 | + | 0.844685i | \(0.679788\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 40827.1 | 2.75038 | ||||||||
\(605\) | −4811.79 | −0.323350 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5182.64 | 0.346552 | 0.173276 | − | 0.984873i | \(-0.444565\pi\) | ||||
0.173276 | + | 0.984873i | \(0.444565\pi\) | |||||||
\(608\) | −64149.2 | −4.27894 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6126.39 | 0.406640 | ||||||||
\(611\) | −37151.6 | −2.45989 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28839.1 | −1.90016 | −0.950081 | − | 0.312004i | \(-0.899000\pi\) | ||||
−0.950081 | + | 0.312004i | \(0.899000\pi\) | |||||||
\(614\) | 10664.4 | 0.700946 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5114.80 | 0.333734 | 0.166867 | − | 0.985979i | \(-0.446635\pi\) | ||||
0.166867 | + | 0.985979i | \(0.446635\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29213.9 | 1.89694 | 0.948471 | − | 0.316864i | \(-0.102630\pi\) | ||||
0.948471 | + | 0.316864i | \(0.102630\pi\) | |||||||
\(620\) | −18496.1 | −1.19810 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6258.87 | 0.403469 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16491.3 | −1.05544 | ||||||||
\(626\) | −24265.4 | −1.54927 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −55557.8 | −3.53025 | ||||||||
\(629\) | 8587.18 | 0.544345 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19557.5 | 1.23387 | 0.616934 | − | 0.787015i | \(-0.288374\pi\) | ||||
0.616934 | + | 0.787015i | \(0.288374\pi\) | |||||||
\(632\) | 73079.0 | 4.59957 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 25258.1 | 1.58222 | ||||||||
\(635\) | 12166.8 | 0.760356 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3061.92 | 0.190004 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 49983.9 | 3.08717 | ||||||||
\(641\) | −14632.3 | −0.901624 | −0.450812 | − | 0.892619i | \(-0.648865\pi\) | ||||
−0.450812 | + | 0.892619i | \(0.648865\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23808.1 | −1.46019 | −0.730094 | − | 0.683347i | \(-0.760524\pi\) | ||||
−0.730094 | + | 0.683347i | \(0.760524\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17059.3 | 1.03899 | ||||||||
\(647\) | −17322.2 | −1.05256 | −0.526279 | − | 0.850312i | \(-0.676413\pi\) | ||||
−0.526279 | + | 0.850312i | \(0.676413\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8126.23 | −0.491498 | ||||||||
\(650\) | −46101.1 | −2.78190 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −65596.4 | −3.94011 | ||||||||
\(653\) | 3241.68 | 0.194268 | 0.0971338 | − | 0.995271i | \(-0.469033\pi\) | ||||
0.0971338 | + | 0.995271i | \(0.469033\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30549.8 | 1.82241 | ||||||||
\(656\) | 51164.2 | 3.04516 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16358.2 | 0.966958 | 0.483479 | − | 0.875356i | \(-0.339373\pi\) | ||||
0.483479 | + | 0.875356i | \(0.339373\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12572.6 | 0.739814 | 0.369907 | − | 0.929069i | \(-0.379389\pi\) | ||||
0.369907 | + | 0.929069i | \(0.379389\pi\) | |||||||
\(662\) | −16106.4 | −0.945606 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 32199.5 | 1.88190 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −980.582 | −0.0569240 | ||||||||
\(668\) | 69078.5 | 4.00109 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −42591.5 | −2.45590 | ||||||||
\(671\) | 2328.55 | 0.133968 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13130.7 | 0.752082 | 0.376041 | − | 0.926603i | \(-0.377285\pi\) | ||||
0.376041 | + | 0.926603i | \(0.377285\pi\) | |||||||
\(674\) | 39573.4 | 2.26159 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 64959.6 | 3.69592 | ||||||||
\(677\) | 18624.2 | 1.05729 | 0.528644 | − | 0.848843i | \(-0.322701\pi\) | ||||
0.528644 | + | 0.848843i | \(0.322701\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −32130.4 | −1.81198 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9688.13 | −0.543956 | ||||||||
\(683\) | −25377.0 | −1.42170 | −0.710852 | − | 0.703341i | \(-0.751691\pi\) | ||||
−0.710852 | + | 0.703341i | \(0.751691\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19008.5 | −1.06026 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3606.78 | 0.199865 | ||||||||
\(689\) | −19247.2 | −1.06424 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2135.42 | 0.117562 | 0.0587810 | − | 0.998271i | \(-0.481279\pi\) | ||||
0.0587810 | + | 0.998271i | \(0.481279\pi\) | |||||||
\(692\) | −43086.2 | −2.36690 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 44869.6 | 2.45422 | ||||||||
\(695\) | −16637.6 | −0.908058 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6926.41 | −0.376408 | ||||||||
\(698\) | −1805.20 | −0.0978910 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9679.27 | −0.521513 | −0.260757 | − | 0.965405i | \(-0.583972\pi\) | ||||
−0.260757 | + | 0.965405i | \(0.583972\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32193.4 | 1.72717 | ||||||||
\(704\) | 46916.8 | 2.51171 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 29473.7 | 1.57119 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25743.2 | −1.36362 | −0.681809 | − | 0.731530i | \(-0.738807\pi\) | ||||
−0.681809 | + | 0.731530i | \(0.738807\pi\) | |||||||
\(710\) | −69622.3 | −3.68011 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 23595.7 | 1.24197 | ||||||||
\(713\) | 3102.63 | 0.162966 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36141.6 | −1.89038 | ||||||||
\(716\) | −75798.9 | −3.95634 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 38862.6 | 2.01997 | ||||||||
\(719\) | 10508.5 | 0.545065 | 0.272532 | − | 0.962147i | \(-0.412139\pi\) | ||||
0.272532 | + | 0.962147i | \(0.412139\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 26917.5 | 1.38749 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 34644.6 | 1.77839 | ||||||||
\(725\) | 2086.42 | 0.106880 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24259.4 | −1.23759 | −0.618797 | − | 0.785551i | \(-0.712380\pi\) | ||||
−0.618797 | + | 0.785551i | \(0.712380\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 31338.6 | 1.58890 | ||||||||
\(731\) | −488.271 | −0.0247050 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19632.2 | 0.989263 | 0.494632 | − | 0.869103i | \(-0.335303\pi\) | ||||
0.494632 | + | 0.869103i | \(0.335303\pi\) | |||||||
\(734\) | 34151.3 | 1.71737 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −32588.7 | −1.63212 | ||||||||
\(737\) | −16188.4 | −0.809101 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26353.6 | −1.31182 | −0.655909 | − | 0.754840i | \(-0.727714\pi\) | ||||
−0.655909 | + | 0.754840i | \(0.727714\pi\) | |||||||
\(740\) | −97497.6 | −4.84335 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31464.6 | −1.55360 | −0.776799 | − | 0.629749i | \(-0.783158\pi\) | ||||
−0.776799 | + | 0.629749i | \(0.783158\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −40356.7 | −1.98464 | ||||||||
\(746\) | −59030.4 | −2.89713 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −19636.7 | −0.959880 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5411.52 | 0.262942 | 0.131471 | − | 0.991320i | \(-0.458030\pi\) | ||||
0.131471 | + | 0.991320i | \(0.458030\pi\) | |||||||
\(752\) | 109769. | 5.32296 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6950.77 | −0.335719 | ||||||||
\(755\) | 30056.0 | 1.44881 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3607.94 | 0.173227 | 0.0866135 | − | 0.996242i | \(-0.472395\pi\) | ||||
0.0866135 | + | 0.996242i | \(0.472395\pi\) | |||||||
\(758\) | 32529.1 | 1.55872 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −120457. | −5.74926 | ||||||||
\(761\) | −4663.70 | −0.222154 | −0.111077 | − | 0.993812i | \(-0.535430\pi\) | ||||
−0.111077 | + | 0.993812i | \(0.535430\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 59769.5 | 2.83035 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −36979.1 | −1.74427 | ||||||||
\(767\) | 18447.1 | 0.868431 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9725.21 | −0.456047 | −0.228023 | − | 0.973656i | \(-0.573226\pi\) | ||||
−0.228023 | + | 0.973656i | \(0.573226\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −35071.7 | −1.63505 | ||||||||
\(773\) | 3092.80 | 0.143907 | 0.0719536 | − | 0.997408i | \(-0.477077\pi\) | ||||
0.0719536 | + | 0.997408i | \(0.477077\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6601.60 | −0.305982 | ||||||||
\(776\) | 82748.8 | 3.82798 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27873.7 | 1.28447 | ||||||||
\(779\) | −25967.2 | −1.19431 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26462.4 | −1.21242 | ||||||||
\(782\) | 8666.37 | 0.396303 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −40900.4 | −1.85962 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22812.9 | 1.03328 | 0.516640 | − | 0.856203i | \(-0.327183\pi\) | ||||
0.516640 | + | 0.856203i | \(0.327183\pi\) | |||||||
\(788\) | 40006.9 | 1.80861 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 86506.3 | 3.89589 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5285.98 | −0.236710 | ||||||||
\(794\) | 1861.71 | 0.0832113 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 29469.1 | 1.31219 | ||||||||
\(797\) | 34305.4 | 1.52467 | 0.762334 | − | 0.647184i | \(-0.224053\pi\) | ||||
0.762334 | + | 0.647184i | \(0.224053\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14860.1 | −0.657963 | ||||||||
\(800\) | 69340.3 | 3.06444 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 27533.3 | 1.21226 | ||||||||
\(803\) | 11911.4 | 0.523465 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21992.8 | 0.961119 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −132418. | −5.76542 | ||||||||
\(809\) | 3264.80 | 0.141884 | 0.0709421 | − | 0.997480i | \(-0.477399\pi\) | ||||
0.0709421 | + | 0.997480i | \(0.477399\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27264.0 | 1.18048 | 0.590239 | − | 0.807228i | \(-0.299033\pi\) | ||||
0.590239 | + | 0.807228i | \(0.299033\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −51068.4 | −2.19895 | ||||||||
\(815\) | −48290.6 | −2.07552 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1830.53 | −0.0783871 | ||||||||
\(818\) | −1744.84 | −0.0745805 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 78641.4 | 3.34912 | ||||||||
\(821\) | −36334.2 | −1.54454 | −0.772272 | − | 0.635292i | \(-0.780880\pi\) | ||||
−0.772272 | + | 0.635292i | \(0.780880\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7791.80 | 0.330019 | 0.165009 | − | 0.986292i | \(-0.447235\pi\) | ||||
0.165009 | + | 0.986292i | \(0.447235\pi\) | |||||||
\(824\) | −70082.4 | −2.96291 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36082.7 | 1.51719 | 0.758596 | − | 0.651561i | \(-0.225886\pi\) | ||||
0.758596 | + | 0.651561i | \(0.225886\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42995.0 | −1.80130 | −0.900650 | − | 0.434545i | \(-0.856909\pi\) | ||||
−0.900650 | + | 0.434545i | \(0.856909\pi\) | |||||||
\(830\) | 38115.7 | 1.59399 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −106505. | −4.43796 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 50854.0 | 2.10764 | ||||||||
\(836\) | −73618.3 | −3.04562 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 23845.9 | 0.982986 | ||||||||
\(839\) | −28252.8 | −1.16257 | −0.581283 | − | 0.813701i | \(-0.697449\pi\) | ||||
−0.581283 | + | 0.813701i | \(0.697449\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24074.4 | −0.987102 | ||||||||
\(842\) | 7448.49 | 0.304860 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 70132.0 | 2.86024 | ||||||||
\(845\) | 47821.8 | 1.94689 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 56868.2 | 2.30290 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −18439.8 | −0.744093 | ||||||||
\(851\) | 16354.7 | 0.658793 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28994.8 | 1.16385 | 0.581924 | − | 0.813243i | \(-0.302300\pi\) | ||||
0.581924 | + | 0.813243i | \(0.302300\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −49433.5 | −1.97384 | ||||||||
\(857\) | 8632.87 | 0.344099 | 0.172050 | − | 0.985088i | \(-0.444961\pi\) | ||||
0.172050 | + | 0.985088i | \(0.444961\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33947.1 | 1.34838 | 0.674191 | − | 0.738557i | \(-0.264493\pi\) | ||||
0.674191 | + | 0.738557i | \(0.264493\pi\) | |||||||
\(860\) | 5543.76 | 0.219815 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8941.09 | 0.353288 | ||||||||
\(863\) | −70.6612 | −0.00278718 | −0.00139359 | − | 0.999999i | \(-0.500444\pi\) | ||||
−0.00139359 | + | 0.999999i | \(0.500444\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31719.1 | −1.24680 | ||||||||
\(866\) | 46507.5 | 1.82493 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32879.8 | 1.28351 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36748.8 | 1.42961 | ||||||||
\(872\) | 121863. | 4.73257 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 32490.3 | 1.25744 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11175.3 | −0.430289 | −0.215144 | − | 0.976582i | \(-0.569022\pi\) | ||||
−0.215144 | + | 0.976582i | \(0.569022\pi\) | |||||||
\(878\) | −32266.5 | −1.24025 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 106785. | 4.09059 | ||||||||
\(881\) | −14341.3 | −0.548433 | −0.274216 | − | 0.961668i | \(-0.588418\pi\) | ||||
−0.274216 | + | 0.961668i | \(0.588418\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23559.2 | −0.897884 | −0.448942 | − | 0.893561i | \(-0.648199\pi\) | ||||
−0.448942 | + | 0.893561i | \(0.648199\pi\) | |||||||
\(884\) | 44576.8 | 1.69602 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4355.20 | 0.165142 | ||||||||
\(887\) | −31744.4 | −1.20166 | −0.600831 | − | 0.799376i | \(-0.705163\pi\) | ||||
−0.600831 | + | 0.799376i | \(0.705163\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 27931.1 | 1.05197 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 117993. | 4.42904 | ||||||||
\(893\) | −55710.7 | −2.08767 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −55801.4 | −2.08406 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 33765.8 | 1.25477 | ||||||||
\(899\) | −995.339 | −0.0369259 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7698.59 | −0.284658 | ||||||||
\(902\) | 41191.8 | 1.52055 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 62368.5 | 2.29463 | ||||||||
\(905\) | 25504.6 | 0.936796 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6062.67 | 0.221949 | 0.110974 | − | 0.993823i | \(-0.464603\pi\) | ||||
0.110974 | + | 0.993823i | \(0.464603\pi\) | |||||||
\(908\) | 30636.6 | 1.11973 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25862.9 | −0.940589 | −0.470295 | − | 0.882509i | \(-0.655852\pi\) | ||||
−0.470295 | + | 0.882509i | \(0.655852\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14487.2 | 0.525144 | ||||||||
\(914\) | 865.539 | 0.0313233 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −34225.7 | −1.23455 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1455.14 | 0.0522314 | 0.0261157 | − | 0.999659i | \(-0.491686\pi\) | ||||
0.0261157 | + | 0.999659i | \(0.491686\pi\) | |||||||
\(920\) | −61193.9 | −2.19294 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13007.3 | −0.464612 | ||||||||
\(923\) | 60071.6 | 2.14223 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34798.6 | −1.23694 | ||||||||
\(926\) | −5901.48 | −0.209433 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10454.6 | 0.369816 | ||||||||
\(929\) | 3077.74 | 0.108695 | 0.0543474 | − | 0.998522i | \(-0.482692\pi\) | ||||
0.0543474 | + | 0.998522i | \(0.482692\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −128903. | −4.53042 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −81294.8 | −2.84802 | ||||||||
\(935\) | −14456.1 | −0.505632 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5354.80 | 0.186695 | 0.0933477 | − | 0.995634i | \(-0.470243\pi\) | ||||
0.0933477 | + | 0.995634i | \(0.470243\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 168719. | 5.85428 | ||||||||
\(941\) | −47797.8 | −1.65586 | −0.827930 | − | 0.560832i | \(-0.810482\pi\) | ||||
−0.827930 | + | 0.560832i | \(0.810482\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13191.7 | −0.455547 | ||||||||
\(944\) | −54504.4 | −1.87920 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2903.78 | 0.0997990 | ||||||||
\(947\) | 2491.69 | 0.0855006 | 0.0427503 | − | 0.999086i | \(-0.486388\pi\) | ||||
0.0427503 | + | 0.999086i | \(0.486388\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27039.6 | −0.924914 | ||||||||
\(950\) | −69130.9 | −2.36095 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13130.4 | 0.446313 | 0.223156 | − | 0.974783i | \(-0.428364\pi\) | ||||
0.223156 | + | 0.974783i | \(0.428364\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 44001.0 | 1.49093 | ||||||||
\(956\) | −33767.7 | −1.14239 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −56459.3 | −1.90409 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26641.7 | −0.894286 | ||||||||
\(962\) | 115929. | 3.88534 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −46313.4 | −1.54736 | ||||||||
\(965\) | −25819.0 | −0.861287 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43314.8 | 1.44044 | 0.720222 | − | 0.693743i | \(-0.244040\pi\) | ||||
0.720222 | + | 0.693743i | \(0.244040\pi\) | |||||||
\(968\) | −21950.2 | −0.728827 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 97952.8 | 3.24235 | ||||||||
\(971\) | −19755.8 | −0.652929 | −0.326464 | − | 0.945210i | \(-0.605857\pi\) | ||||
−0.326464 | + | 0.945210i | \(0.605857\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −68674.1 | −2.25920 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15618.1 | 0.512217 | ||||||||
\(977\) | 11140.1 | 0.364794 | 0.182397 | − | 0.983225i | \(-0.441614\pi\) | ||||
0.182397 | + | 0.983225i | \(0.441614\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10616.2 | 0.346573 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 113307. | 3.68205 | ||||||||
\(983\) | −3575.76 | −0.116021 | −0.0580107 | − | 0.998316i | \(-0.518476\pi\) | ||||
−0.0580107 | + | 0.998316i | \(0.518476\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29452.2 | 0.952716 | ||||||||
\(986\) | −2780.21 | −0.0897971 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 167119. | 5.38133 | ||||||||
\(989\) | −929.937 | −0.0298992 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22391.8 | 0.717760 | 0.358880 | − | 0.933384i | \(-0.383159\pi\) | ||||
0.358880 | + | 0.933384i | \(0.383159\pi\) | |||||||
\(992\) | −33079.2 | −1.05873 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21694.5 | 0.691218 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17466.5 | 0.554834 | 0.277417 | − | 0.960750i | \(-0.410522\pi\) | ||||
0.277417 | + | 0.960750i | \(0.410522\pi\) | |||||||
\(998\) | 68676.4 | 2.17827 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.4.a.x.1.8 | yes | 8 | |
3.2 | odd | 2 | inner | 441.4.a.x.1.1 | ✓ | 8 | |
7.2 | even | 3 | 441.4.e.z.361.1 | 16 | |||
7.3 | odd | 6 | 441.4.e.z.226.2 | 16 | |||
7.4 | even | 3 | 441.4.e.z.226.1 | 16 | |||
7.5 | odd | 6 | 441.4.e.z.361.2 | 16 | |||
7.6 | odd | 2 | inner | 441.4.a.x.1.7 | yes | 8 | |
21.2 | odd | 6 | 441.4.e.z.361.8 | 16 | |||
21.5 | even | 6 | 441.4.e.z.361.7 | 16 | |||
21.11 | odd | 6 | 441.4.e.z.226.8 | 16 | |||
21.17 | even | 6 | 441.4.e.z.226.7 | 16 | |||
21.20 | even | 2 | inner | 441.4.a.x.1.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.4.a.x.1.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
441.4.a.x.1.2 | yes | 8 | 21.20 | even | 2 | inner | |
441.4.a.x.1.7 | yes | 8 | 7.6 | odd | 2 | inner | |
441.4.a.x.1.8 | yes | 8 | 1.1 | even | 1 | trivial | |
441.4.e.z.226.1 | 16 | 7.4 | even | 3 | |||
441.4.e.z.226.2 | 16 | 7.3 | odd | 6 | |||
441.4.e.z.226.7 | 16 | 21.17 | even | 6 | |||
441.4.e.z.226.8 | 16 | 21.11 | odd | 6 | |||
441.4.e.z.361.1 | 16 | 7.2 | even | 3 | |||
441.4.e.z.361.2 | 16 | 7.5 | odd | 6 | |||
441.4.e.z.361.7 | 16 | 21.5 | even | 6 | |||
441.4.e.z.361.8 | 16 | 21.2 | odd | 6 |