Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.28 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.320895 | 0.185269 | 0.0926343 | − | 0.995700i | \(-0.470471\pi\) | ||||
0.0926343 | + | 0.995700i | \(0.470471\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.20543 | 0.539084 | 0.269542 | − | 0.962989i | \(-0.413128\pi\) | ||||
0.269542 | + | 0.962989i | \(0.413128\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.62503 | 0.992166 | 0.496083 | − | 0.868275i | \(-0.334771\pi\) | ||||
0.496083 | + | 0.868275i | \(0.334771\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.89703 | −0.965676 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.62663 | 0.490446 | 0.245223 | − | 0.969467i | \(-0.421139\pi\) | ||||
0.245223 | + | 0.969467i | \(0.421139\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.31735 | −0.920067 | −0.460033 | − | 0.887902i | \(-0.652163\pi\) | ||||
−0.460033 | + | 0.887902i | \(0.652163\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.386816 | 0.0998753 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.66730 | −0.646914 | −0.323457 | − | 0.946243i | \(-0.604845\pi\) | ||||
−0.323457 | + | 0.946243i | \(0.604845\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.21646 | 0.967323 | 0.483661 | − | 0.875255i | \(-0.339307\pi\) | ||||
0.483661 | + | 0.875255i | \(0.339307\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.842357 | 0.183817 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.23332 | −0.257164 | −0.128582 | − | 0.991699i | \(-0.541043\pi\) | ||||
−0.128582 | + | 0.991699i | \(0.541043\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.54694 | −0.709388 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.89232 | −0.364178 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.10559 | −1.69086 | −0.845432 | − | 0.534082i | \(-0.820657\pi\) | ||||
−0.845432 | + | 0.534082i | \(0.820657\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.03784 | 0.904823 | 0.452412 | − | 0.891809i | \(-0.350564\pi\) | ||||
0.452412 | + | 0.891809i | \(0.350564\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.521975 | 0.0908642 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.16428 | 0.534861 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.64255 | −1.42083 | −0.710414 | − | 0.703784i | \(-0.751492\pi\) | ||||
−0.710414 | + | 0.703784i | \(0.751492\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.06452 | −0.170459 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.06053 | −0.946496 | −0.473248 | − | 0.880929i | \(-0.656919\pi\) | ||||
−0.473248 | + | 0.880929i | \(0.656919\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.22644 | −0.797025 | −0.398513 | − | 0.917163i | \(-0.630473\pi\) | ||||
−0.398513 | + | 0.917163i | \(0.630473\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.49216 | −0.520580 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.33691 | −0.340874 | −0.170437 | − | 0.985369i | \(-0.554518\pi\) | ||||
−0.170437 | + | 0.985369i | \(0.554518\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.109239 | −0.0156056 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.855921 | −0.119853 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.51550 | 0.208170 | 0.104085 | − | 0.994568i | \(-0.466809\pi\) | ||||
0.104085 | + | 0.994568i | \(0.466809\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.96078 | 0.264392 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.35304 | 0.179215 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.59427 | 1.24907 | 0.624534 | − | 0.780998i | \(-0.285289\pi\) | ||||
0.624534 | + | 0.780998i | \(0.285289\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.73345 | 0.990167 | 0.495083 | − | 0.868845i | \(-0.335138\pi\) | ||||
0.495083 | + | 0.868845i | \(0.335138\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.60477 | −0.958111 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.99883 | −0.495993 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.1614 | −1.36358 | −0.681792 | − | 0.731546i | \(-0.738799\pi\) | ||||
−0.681792 | + | 0.731546i | \(0.738799\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.395764 | −0.0476444 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.47848 | −0.887532 | −0.443766 | − | 0.896143i | \(-0.646358\pi\) | ||||
−0.443766 | + | 0.896143i | \(0.646358\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.57210 | −0.418083 | −0.209042 | − | 0.977907i | \(-0.567034\pi\) | ||||
−0.209042 | + | 0.977907i | \(0.567034\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.13819 | −0.131427 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.26993 | 0.486604 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.62845 | 0.295723 | 0.147862 | − | 0.989008i | \(-0.452761\pi\) | ||||
0.147862 | + | 0.989008i | \(0.452761\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.08384 | 0.898205 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.9519 | −1.53142 | −0.765709 | − | 0.643187i | \(-0.777612\pi\) | ||||
−0.765709 | + | 0.643187i | \(0.777612\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.21523 | −0.348741 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.92193 | −0.313264 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.3260 | 1.20055 | 0.600276 | − | 0.799793i | \(-0.295057\pi\) | ||||
0.600276 | + | 0.799793i | \(0.295057\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.70812 | −0.912859 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.61662 | 0.167635 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.08265 | 0.521468 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.2165 | −1.64654 | −0.823269 | − | 0.567651i | \(-0.807852\pi\) | ||||
−0.823269 | + | 0.567651i | \(0.807852\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.71238 | −0.473612 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.00960 | 0.299467 | 0.149733 | − | 0.988726i | \(-0.452158\pi\) | ||||
0.149733 | + | 0.988726i | \(0.452158\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.21638 | 0.316919 | 0.158460 | − | 0.987365i | \(-0.449347\pi\) | ||||
0.158460 | + | 0.987365i | \(0.449347\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.01540 | 0.0990930 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.5902 | 1.31381 | 0.656907 | − | 0.753972i | \(-0.271864\pi\) | ||||
0.656907 | + | 0.753972i | \(0.271864\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.40152 | 0.134241 | 0.0671205 | − | 0.997745i | \(-0.478619\pi\) | ||||
0.0671205 | + | 0.997745i | \(0.478619\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.77335 | −0.263235 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.17404 | 0.486733 | 0.243366 | − | 0.969934i | \(-0.421748\pi\) | ||||
0.243366 | + | 0.969934i | \(0.421748\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.48667 | −0.138633 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.61044 | 0.888486 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.00172 | −0.641847 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.35409 | −0.759463 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.94479 | −0.175356 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.3027 | −0.921504 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.5742 | −1.29325 | −0.646624 | − | 0.762809i | \(-0.723820\pi\) | ||||
−0.646624 | + | 0.762809i | \(0.723820\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.67714 | −0.147664 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.71162 | 0.499027 | 0.249513 | − | 0.968371i | \(-0.419729\pi\) | ||||
0.249513 | + | 0.968371i | \(0.419729\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.0683 | 0.959745 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.28106 | −0.196323 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.504909 | 0.0431373 | 0.0215686 | − | 0.999767i | \(-0.493134\pi\) | ||||
0.0215686 | + | 0.999767i | \(0.493134\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.0652126 | 0.00553126 | 0.00276563 | − | 0.999996i | \(-0.499120\pi\) | ||||
0.00276563 | + | 0.999996i | \(0.499120\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.749903 | −0.0631532 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.39608 | −0.451243 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.9761 | −0.911518 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.0350544 | −0.00289124 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.1474 | −1.24092 | −0.620461 | − | 0.784238i | \(-0.713054\pi\) | ||||
−0.620461 | + | 0.784238i | \(0.713054\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.53357 | −0.613074 | −0.306537 | − | 0.951859i | \(-0.599170\pi\) | ||||
−0.306537 | + | 0.951859i | \(0.599170\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.72723 | 0.624709 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.07276 | 0.487776 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.54733 | 0.203299 | 0.101650 | − | 0.994820i | \(-0.467588\pi\) | ||||
0.101650 | + | 0.994820i | \(0.467588\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.486316 | 0.0385674 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.23749 | −0.255150 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.3582 | −1.75123 | −0.875614 | − | 0.483011i | \(-0.839543\pi\) | ||||
−0.875614 | + | 0.483011i | \(0.839543\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.629204 | 0.0489835 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.90327 | 0.379427 | 0.189713 | − | 0.981840i | \(-0.439244\pi\) | ||||
0.189713 | + | 0.981840i | \(0.439244\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.99521 | −0.153478 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.2152 | −0.934120 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.74521 | 0.360771 | 0.180386 | − | 0.983596i | \(-0.442265\pi\) | ||||
0.180386 | + | 0.983596i | \(0.442265\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.31081 | −0.703831 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.07875 | 0.231413 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.1050 | 0.904770 | 0.452385 | − | 0.891823i | \(-0.350573\pi\) | ||||
0.452385 | + | 0.891823i | \(0.350573\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.83231 | −0.284853 | −0.142427 | − | 0.989805i | \(-0.545491\pi\) | ||||
−0.142427 | + | 0.989805i | \(0.545491\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.48162 | 0.183447 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.4180 | −0.765945 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.33869 | −0.317277 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.96740 | −0.361325 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.9858 | 1.44612 | 0.723060 | − | 0.690786i | \(-0.242735\pi\) | ||||
0.723060 | + | 0.690786i | \(0.242735\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.4999 | 1.33165 | 0.665825 | − | 0.746108i | \(-0.268080\pi\) | ||||
0.665825 | + | 0.746108i | \(0.268080\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.28320 | −0.0918920 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.7677 | −1.40839 | −0.704196 | − | 0.710006i | \(-0.748692\pi\) | ||||
−0.704196 | + | 0.710006i | \(0.748692\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.2396 | 0.938527 | 0.469264 | − | 0.883058i | \(-0.344519\pi\) | ||||
0.469264 | + | 0.883058i | \(0.344519\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.58164 | −0.252629 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −23.9024 | −1.67762 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.30554 | −0.510241 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.57295 | 0.248337 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.85861 | 0.474420 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0915 | 0.970099 | 0.485050 | − | 0.874487i | \(-0.338802\pi\) | ||||
0.485050 | + | 0.874487i | \(0.338802\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.39980 | −0.164432 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.30010 | −0.429663 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.2245 | 0.897736 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.14627 | −0.0774577 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.84834 | 0.595204 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.51822 | −0.302563 | −0.151281 | − | 0.988491i | \(-0.548340\pi\) | ||||
−0.151281 | + | 0.988491i | \(0.548340\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.2756 | 0.685039 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.24400 | −0.547174 | −0.273587 | − | 0.961847i | \(-0.588210\pi\) | ||||
−0.273587 | + | 0.961847i | \(0.588210\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.4909 | 1.61840 | 0.809201 | − | 0.587532i | \(-0.199900\pi\) | ||||
0.809201 | + | 0.587532i | \(0.199900\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.37020 | 0.0901525 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.5272 | 0.951706 | 0.475853 | − | 0.879525i | \(-0.342139\pi\) | ||||
0.475853 | + | 0.879525i | \(0.342139\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.81698 | −0.183760 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.843454 | 0.0547882 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.7484 | −1.14805 | −0.574026 | − | 0.818837i | \(-0.694619\pi\) | ||||
−0.574026 | + | 0.818837i | \(0.694619\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.6534 | 1.39482 | 0.697409 | − | 0.716674i | \(-0.254336\pi\) | ||||
0.697409 | + | 0.716674i | \(0.254336\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.27103 | 0.530587 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.131680 | −0.00841275 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.9875 | −0.890002 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.47708 | −0.283724 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.705326 | 0.0445198 | 0.0222599 | − | 0.999752i | \(-0.492914\pi\) | ||||
0.0222599 | + | 0.999752i | \(0.492914\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00614 | −0.126125 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.03175 | −0.0646108 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.809803 | −0.0505141 | −0.0252571 | − | 0.999681i | \(-0.508040\pi\) | ||||
−0.0252571 | + | 0.999681i | \(0.508040\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.6869 | −1.40970 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 26.3791 | 1.63283 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.1848 | −0.874672 | −0.437336 | − | 0.899298i | \(-0.644078\pi\) | ||||
−0.437336 | + | 0.899298i | \(0.644078\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.82683 | 0.112221 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.63445 | 0.222425 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.154171 | 0.00939995 | 0.00469997 | − | 0.999989i | \(-0.498504\pi\) | ||||
0.00469997 | + | 0.999989i | \(0.498504\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.4281 | 0.997934 | 0.498967 | − | 0.866621i | \(-0.333713\pi\) | ||||
0.498967 | + | 0.866621i | \(0.333713\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.79439 | −0.169124 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.76955 | −0.347917 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.8540 | −1.79375 | −0.896877 | − | 0.442281i | \(-0.854170\pi\) | ||||
−0.896877 | + | 0.442281i | \(0.854170\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.5948 | −0.873766 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.8895 | 0.888233 | 0.444117 | − | 0.895969i | \(-0.353518\pi\) | ||||
0.444117 | + | 0.895969i | \(0.353518\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.5236 | 1.51722 | 0.758610 | − | 0.651545i | \(-0.225879\pi\) | ||||
0.758610 | + | 0.651545i | \(0.225879\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.63099 | 0.0966117 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.9091 | −0.939082 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.88554 | −0.581502 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.20380 | −0.305052 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.46654 | 0.377780 | 0.188890 | − | 0.981998i | \(-0.439511\pi\) | ||||
0.188890 | + | 0.981998i | \(0.439511\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.5652 | 0.673352 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.07810 | −0.178610 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.09134 | 0.236608 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.7195 | −0.790782 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.965765 | 0.0554818 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.32212 | 0.533783 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.9859 | −1.08358 | −0.541791 | − | 0.840513i | \(-0.682254\pi\) | ||||
−0.541791 | + | 0.840513i | \(0.682254\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.03212 | 0.0587152 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.11973 | 0.347018 | 0.173509 | − | 0.984832i | \(-0.444489\pi\) | ||||
0.173509 | + | 0.984832i | \(0.444489\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.73279 | 0.324037 | 0.162018 | − | 0.986788i | \(-0.448200\pi\) | ||||
0.162018 | + | 0.986788i | \(0.448200\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.16701 | −0.516502 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.8637 | −0.947158 | −0.473579 | − | 0.880751i | \(-0.657038\pi\) | ||||
−0.473579 | + | 0.880751i | \(0.657038\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.8114 | −0.829278 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.36102 | 0.243408 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.2466 | −0.625775 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.7664 | 0.652684 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.449739 | 0.0248706 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.13446 | −0.338204 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.6510 | 0.750325 | 0.375162 | − | 0.926959i | \(-0.377587\pi\) | ||||
0.375162 | + | 0.926959i | \(0.377587\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 25.0377 | 1.37206 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.4543 | −0.735087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.3359 | −0.998821 | −0.499410 | − | 0.866366i | \(-0.666450\pi\) | ||||
−0.499410 | + | 0.866366i | \(0.666450\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.66032 | 0.0901763 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.19469 | 0.443767 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.6619 | −1.00765 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.477066 | −0.0256844 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.0533 | 1.61335 | 0.806673 | − | 0.590998i | \(-0.201266\pi\) | ||||
0.806673 | + | 0.590998i | \(0.201266\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.3946 | 0.770527 | 0.385263 | − | 0.922807i | \(-0.374111\pi\) | ||||
0.385263 | + | 0.922807i | \(0.374111\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.27750 | 0.335068 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.3940 | −1.56448 | −0.782241 | − | 0.622975i | \(-0.785924\pi\) | ||||
−0.782241 | + | 0.622975i | \(0.785924\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.01477 | −0.478454 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.24681 | −0.118914 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.1770 | −1.06490 | −0.532450 | − | 0.846462i | \(-0.678728\pi\) | ||||
−0.532450 | + | 0.846462i | \(0.678728\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.22144 | −0.0642862 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.68078 | −0.140705 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.30592 | −0.225382 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.0988134 | 0.00515801 | 0.00257901 | − | 0.999997i | \(-0.499179\pi\) | ||||
0.00257901 | + | 0.999997i | \(0.499179\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17.5575 | 0.914008 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.97823 | 0.206539 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.1809 | −1.20026 | −0.600130 | − | 0.799902i | \(-0.704885\pi\) | ||||
−0.600130 | + | 0.799902i | \(0.704885\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.30609 | −0.170726 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 30.2064 | 1.55571 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.1812 | −1.29347 | −0.646735 | − | 0.762715i | \(-0.723866\pi\) | ||||
−0.646735 | + | 0.762715i | \(0.723866\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.67677 | −0.239598 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.72699 | −0.241538 | −0.120769 | − | 0.992681i | \(-0.538536\pi\) | ||||
−0.120769 | + | 0.992681i | \(0.538536\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.14710 | 0.262321 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15.1411 | 0.769668 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.41392 | 0.122390 | 0.0611952 | − | 0.998126i | \(-0.480509\pi\) | ||||
0.0611952 | + | 0.998126i | \(0.480509\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.28962 | 0.166363 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.83283 | 0.0924540 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.16840 | 0.159420 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.1842 | 0.862451 | 0.431226 | − | 0.902244i | \(-0.358081\pi\) | ||||
0.431226 | + | 0.902244i | \(0.358081\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.55177 | 0.177811 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.65099 | −0.0824465 | −0.0412233 | − | 0.999150i | \(-0.513125\pi\) | ||||
−0.0412233 | + | 0.999150i | \(0.513125\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.7123 | −0.832498 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.74450 | 0.484208 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.0582 | −0.696839 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.54443 | 0.274155 | 0.137077 | − | 0.990560i | \(-0.456229\pi\) | ||||
0.137077 | + | 0.990560i | \(0.456229\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.162022 | 0.00799198 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 25.1852 | 1.23928 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.8180 | −0.825563 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.0209264 | 0.00102477 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.5645 | −0.809228 | −0.404614 | − | 0.914487i | \(-0.632594\pi\) | ||||
−0.404614 | + | 0.914487i | \(0.632594\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.0445 | −1.70797 | −0.853983 | − | 0.520302i | \(-0.825820\pi\) | ||||
−0.853983 | + | 0.520302i | \(0.825820\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.77010 | 0.329174 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.46074 | 0.458913 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.3005 | 0.982410 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.73157 | −0.0836012 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.1111 | −0.631542 | −0.315771 | − | 0.948836i | \(-0.602263\pi\) | ||||
−0.315771 | + | 0.948836i | \(0.602263\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.73845 | −0.323829 | −0.161915 | − | 0.986805i | \(-0.551767\pi\) | ||||
−0.161915 | + | 0.986805i | \(0.551767\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.52218 | −0.168876 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.20023 | −0.248761 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.3510 | 1.35312 | 0.676560 | − | 0.736387i | \(-0.263470\pi\) | ||||
0.676560 | + | 0.736387i | \(0.263470\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.316470 | 0.0150700 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.8531 | 1.46588 | 0.732939 | − | 0.680295i | \(-0.238148\pi\) | ||||
0.732939 | + | 0.680295i | \(0.238148\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.6527 | 0.647198 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.86071 | −0.229904 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.1984 | −1.61392 | −0.806962 | − | 0.590603i | \(-0.798890\pi\) | ||||
−0.806962 | + | 0.590603i | \(0.798890\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.85822 | −0.464205 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.41748 | −0.113583 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.4970 | −0.492108 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.8695 | 0.648787 | 0.324394 | − | 0.945922i | \(-0.394840\pi\) | ||||
0.324394 | + | 0.945922i | \(0.394840\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.04739 | 0.235592 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.4101 | −1.36976 | −0.684882 | − | 0.728654i | \(-0.740146\pi\) | ||||
−0.684882 | + | 0.728654i | \(0.740146\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.1122 | 0.469953 | 0.234976 | − | 0.972001i | \(-0.424499\pi\) | ||||
0.234976 | + | 0.972001i | \(0.424499\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.94872 | 0.0903695 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.1149 | −0.653161 | −0.326581 | − | 0.945169i | \(-0.605897\pi\) | ||||
−0.326581 | + | 0.945169i | \(0.605897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −29.2990 | −1.35290 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.817425 | 0.0376650 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.50147 | −0.390898 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.9555 | −0.686208 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.39045 | −0.201025 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.59718 | 0.347124 | 0.173562 | − | 0.984823i | \(-0.444472\pi\) | ||||
0.173562 | + | 0.984823i | \(0.444472\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.6704 | 1.30726 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.03889 | −0.0472712 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.5479 | −0.887623 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.6079 | −1.16040 | −0.580202 | − | 0.814473i | \(-0.697026\pi\) | ||||
−0.580202 | + | 0.814473i | \(0.697026\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.17462 | −0.324448 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.943905 | −0.0425978 | −0.0212989 | − | 0.999773i | \(-0.506780\pi\) | ||||
−0.0212989 | + | 0.999773i | \(0.506780\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.2873 | 1.09384 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.68044 | −0.255317 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19.6312 | −0.880580 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.2486 | −1.44364 | −0.721822 | − | 0.692078i | \(-0.756695\pi\) | ||||
−0.721822 | + | 0.692078i | \(0.756695\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.57343 | 0.0702959 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.0618 | 1.11745 | 0.558726 | − | 0.829352i | \(-0.311290\pi\) | ||||
0.558726 | + | 0.829352i | \(0.311290\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.62786 | 0.161438 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.640252 | −0.0284346 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.8515 | 0.613958 | 0.306979 | − | 0.951716i | \(-0.400682\pi\) | ||||
0.306979 | + | 0.951716i | \(0.400682\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.37687 | −0.414808 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.97891 | −0.352278 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.87712 | 0.170846 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.80129 | −0.167180 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.52271 | 0.0668396 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.29758 | −0.232091 | −0.116046 | − | 0.993244i | \(-0.537022\pi\) | ||||
−0.116046 | + | 0.993244i | \(0.537022\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.42411 | −0.105999 | −0.0529994 | − | 0.998595i | \(-0.516878\pi\) | ||||
−0.0529994 | + | 0.998595i | \(0.516878\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.98779 | −0.130398 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.4374 | −0.585343 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.4789 | −0.933867 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.7949 | −1.20619 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.1049 | 0.870839 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.3820 | 0.708256 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.88443 | 0.167626 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.177692 | −0.00765373 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.2679 | −0.441453 | −0.220727 | − | 0.975336i | \(-0.570843\pi\) | ||||
−0.220727 | + | 0.975336i | \(0.570843\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.22977 | −0.0527744 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.68943 | 0.0723671 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −40.1700 | −1.71755 | −0.858773 | − | 0.512356i | \(-0.828773\pi\) | ||||
−0.858773 | + | 0.512356i | \(0.828773\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −22.4040 | −0.956180 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −38.3934 | −1.63561 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.89974 | 0.293407 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.34307 | −0.141906 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.69529 | 0.0718317 | 0.0359159 | − | 0.999355i | \(-0.488565\pi\) | ||||
0.0359159 | + | 0.999355i | \(0.488565\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.3379 | 0.733316 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.39226 | −0.0587814 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.796711 | −0.0335774 | −0.0167887 | − | 0.999859i | \(-0.505344\pi\) | ||||
−0.0167887 | + | 0.999859i | \(0.505344\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.23694 | 0.262390 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.2203 | 0.891169 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.3408 | −1.43964 | −0.719820 | − | 0.694161i | \(-0.755776\pi\) | ||||
−0.719820 | + | 0.694161i | \(0.755776\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.1193 | −0.549027 | −0.274513 | − | 0.961583i | \(-0.588517\pi\) | ||||
−0.274513 | + | 0.961583i | \(0.588517\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.41333 | 0.267921 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.37450 | 0.182429 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.1973 | −1.38202 | −0.691011 | − | 0.722844i | \(-0.742834\pi\) | ||||
−0.691011 | + | 0.722844i | \(0.742834\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.93651 | 0.246713 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −36.6240 | −1.51942 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.46515 | 0.102096 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.5847 | 0.478969 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 45.0798 | 1.86064 | 0.930321 | − | 0.366745i | \(-0.119528\pi\) | ||||
0.930321 | + | 0.366745i | \(0.119528\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.2419 | 0.875257 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.34336 | −0.260931 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −35.5467 | −1.45973 | −0.729865 | − | 0.683592i | \(-0.760417\pi\) | ||||
−0.729865 | + | 0.683592i | \(0.760417\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.44007 | −0.346009 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.24850 | 0.173880 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.70384 | 0.110476 | 0.0552379 | − | 0.998473i | \(-0.482408\pi\) | ||||
0.0552379 | + | 0.998473i | \(0.482408\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.1644 | −0.455406 | −0.227703 | − | 0.973731i | \(-0.573122\pi\) | ||||
−0.227703 | + | 0.973731i | \(0.573122\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.3349 | 1.31678 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.0703 | −0.409414 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.2066 | −0.536038 | −0.268019 | − | 0.963414i | \(-0.586369\pi\) | ||||
−0.268019 | + | 0.963414i | \(0.586369\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.67015 | −0.310810 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.75236 | 0.313627 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.14238 | 0.167309 | 0.0836546 | − | 0.996495i | \(-0.473341\pi\) | ||||
0.0836546 | + | 0.996495i | \(0.473341\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.34431 | −0.0945316 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.2622 | −0.533915 | −0.266958 | − | 0.963708i | \(-0.586018\pi\) | ||||
−0.266958 | + | 0.963708i | \(0.586018\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.7925 | −0.916107 | −0.458053 | − | 0.888925i | \(-0.651453\pi\) | ||||
−0.458053 | + | 0.888925i | \(0.651453\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.33383 | 0.0936535 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 29.7310 | 1.19115 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.31551 | 0.212620 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.20089 | 0.0878951 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.0522 | 0.919153 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.5766 | 0.819143 | 0.409572 | − | 0.912278i | \(-0.365678\pi\) | ||||
0.409572 | + | 0.912278i | \(0.365678\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.52189 | 0.179729 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.5681 | −0.697169 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.362385 | 0.0143582 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 21.6654 | 0.857068 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 44.1596 | 1.74420 | 0.872099 | − | 0.489329i | \(-0.162758\pi\) | ||||
0.872099 | + | 0.489329i | \(0.162758\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.0553 | 0.948650 | 0.474325 | − | 0.880350i | \(-0.342692\pi\) | ||||
0.474325 | + | 0.880350i | \(0.342692\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.02167 | −0.0796031 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.9928 | 0.589426 | 0.294713 | − | 0.955586i | \(-0.404776\pi\) | ||||
0.294713 | + | 0.955586i | \(0.404776\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.6063 | 0.612600 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.24366 | 0.166322 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.9919 | 0.547545 | 0.273773 | − | 0.961794i | \(-0.411728\pi\) | ||||
0.273773 | + | 0.961794i | \(0.411728\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.88496 | 0.269018 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.3485 | 0.403733 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.9086 | 1.47671 | 0.738354 | − | 0.674413i | \(-0.235603\pi\) | ||||
0.738354 | + | 0.674413i | \(0.235603\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.0458 | 0.935273 | 0.467637 | − | 0.883921i | \(-0.345106\pi\) | ||||
0.467637 | + | 0.883921i | \(0.345106\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.83939 | 0.110273 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.3421 | 0.517383 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.2301 | 0.434830 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.44987 | −0.0560553 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.5794 | 0.485623 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.8276 | 1.68943 | 0.844714 | − | 0.535217i | \(-0.179770\pi\) | ||||
0.844714 | + | 0.535217i | \(0.179770\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.71196 | 0.258344 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.73446 | 0.181960 | 0.0909801 | − | 0.995853i | \(-0.471000\pi\) | ||||
0.0909801 | + | 0.995853i | \(0.471000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −42.5688 | −1.63364 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.64546 | −0.101374 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27.1872 | −1.04029 | −0.520144 | − | 0.854079i | \(-0.674122\pi\) | ||||
−0.520144 | + | 0.854079i | \(0.674122\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.608631 | 0.0232546 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.85899 | 0.299839 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.02744 | −0.191530 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.2101 | 0.616663 | 0.308331 | − | 0.951279i | \(-0.400229\pi\) | ||||
0.308331 | + | 0.951279i | \(0.400229\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.3701 | −0.469902 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.0786092 | 0.00298182 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.1652 | 0.612302 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.66169 | 0.176321 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.7625 | 1.31296 | 0.656481 | − | 0.754343i | \(-0.272044\pi\) | ||||
0.656481 | + | 0.754343i | \(0.272044\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.4410 | −1.37440 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.903955 | −0.0340449 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.90028 | 0.297121 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.560357 | 0.0210447 | 0.0105223 | − | 0.999945i | \(-0.496651\pi\) | ||||
0.0105223 | + | 0.999945i | \(0.496651\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.61468 | −0.285573 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.21325 | −0.232688 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.50459 | −0.243258 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.69538 | −0.212698 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.7798 | −0.402020 | −0.201010 | − | 0.979589i | \(-0.564422\pi\) | ||||
−0.201010 | + | 0.979589i | \(0.564422\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.44308 | 0.314437 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.94845 | 0.258416 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.2970 | 1.19948 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.5181 | −0.946413 | −0.473207 | − | 0.880951i | \(-0.656904\pi\) | ||||
−0.473207 | + | 0.880951i | \(0.656904\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.5974 | −0.799904 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.9405 | 0.515607 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 49.6083 | 1.83233 | 0.916163 | − | 0.400806i | \(-0.131270\pi\) | ||||
0.916163 | + | 0.400806i | \(0.131270\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.0422555 | −0.00155862 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.1554 | −0.668765 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.0908565 | 0.00334221 | 0.00167111 | − | 0.999999i | \(-0.499468\pi\) | ||||
0.00167111 | + | 0.999999i | \(0.499468\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.48850 | −0.164889 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.7804 | −1.16591 | −0.582955 | − | 0.812504i | \(-0.698104\pi\) | ||||
−0.582955 | + | 0.812504i | \(0.698104\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.2591 | −0.668961 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 40.4190 | 1.47885 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 35.6746 | 1.30352 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.226335 | 0.00824812 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.08118 | −0.330498 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.3038 | −0.410842 | −0.205421 | − | 0.978674i | \(-0.565856\pi\) | ||||
−0.205421 | + | 0.978674i | \(0.565856\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.643760 | −0.0233670 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.9436 | −1.52045 | −0.760227 | − | 0.649657i | \(-0.774912\pi\) | ||||
−0.760227 | + | 0.649657i | \(0.774912\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.67902 | 0.133189 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.31462 | 0.336771 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −31.8275 | −1.14923 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.6203 | 0.707526 | 0.353763 | − | 0.935335i | \(-0.384902\pi\) | ||||
0.353763 | + | 0.935335i | \(0.384902\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.259861 | −0.00935868 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 47.1732 | 1.69670 | 0.848352 | − | 0.529433i | \(-0.177595\pi\) | ||||
0.848352 | + | 0.529433i | \(0.177595\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.8689 | −0.641871 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.28011 | −0.261173 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.5540 | −0.915567 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.1647 | −0.435287 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.2307 | 0.615776 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.07063 | 0.109595 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.8127 | −0.920123 | −0.460062 | − | 0.887887i | \(-0.652173\pi\) | ||||
−0.460062 | + | 0.887887i | \(0.652173\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.55182 | −0.162049 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.5820 | 0.482920 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.6545 | −0.911019 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.586220 | 0.0207911 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.9003 | 0.527796 | 0.263898 | − | 0.964551i | \(-0.414992\pi\) | ||||
0.263898 | + | 0.964551i | \(0.414992\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.23324 | 0.220516 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.8117 | −1.15934 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.81048 | −0.205047 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.90256 | −0.137547 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.0494725 | 0.00174152 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.2734 | −1.24015 | −0.620073 | − | 0.784544i | \(-0.712897\pi\) | ||||
−0.620073 | + | 0.784544i | \(0.712897\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.72789 | 0.166019 | 0.0830093 | − | 0.996549i | \(-0.473547\pi\) | ||||
0.0830093 | + | 0.996549i | \(0.473547\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.27168 | 0.184886 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −26.9512 | −0.944059 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.0371 | −0.770981 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 25.2277 | 0.881526 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.0676 | 1.08427 | 0.542133 | − | 0.840293i | \(-0.317617\pi\) | ||||
0.542133 | + | 0.840293i | \(0.317617\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.6842 | −1.06958 | −0.534792 | − | 0.844984i | \(-0.679610\pi\) | ||||
−0.534792 | + | 0.844984i | \(0.679610\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.85142 | −0.0644580 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.1091 | 1.32518 | 0.662592 | − | 0.748981i | \(-0.269456\pi\) | ||||
0.662592 | + | 0.748981i | \(0.269456\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.36830 | −0.0822546 | −0.0411273 | − | 0.999154i | \(-0.513095\pi\) | ||||
−0.0411273 | + | 0.999154i | \(0.513095\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.57999 | −0.332326 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.291374 | 0.0100955 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.91055 | 0.204543 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.53323 | −0.329517 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.9016 | −0.963271 | −0.481636 | − | 0.876372i | \(-0.659957\pi\) | ||||
−0.481636 | + | 0.876372i | \(0.659957\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 53.9117 | 1.85902 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.77796 | 0.164562 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.40508 | −0.0827373 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.9297 | −0.753513 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.19039 | 0.281093 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.6590 | 0.365386 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.7080 | −0.709028 | −0.354514 | − | 0.935051i | \(-0.615354\pi\) | ||||
−0.354514 | + | 0.935051i | \(0.615354\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.7246 | −0.503569 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.7308 | 1.22054 | 0.610271 | − | 0.792193i | \(-0.291061\pi\) | ||||
0.610271 | + | 0.792193i | \(0.291061\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.5548 | 1.07663 | 0.538317 | − | 0.842742i | \(-0.319060\pi\) | ||||
0.538317 | + | 0.842742i | \(0.319060\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.10513 | −0.173982 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.9392 | 0.746819 | 0.373410 | − | 0.927667i | \(-0.378189\pi\) | ||||
0.373410 | + | 0.927667i | \(0.378189\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.72001 | 0.194486 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.17221 | −0.107734 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.27550 | 0.145036 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37.0263 | 1.25459 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 46.9797 | 1.59002 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.0449 | −0.914285 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.2204 | −0.952934 | −0.476467 | − | 0.879192i | \(-0.658083\pi\) | ||||
−0.476467 | + | 0.879192i | \(0.658083\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.07508 | 0.0699907 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.1430 | −1.04924 | −0.524618 | − | 0.851338i | \(-0.675792\pi\) | ||||
−0.524618 | + | 0.851338i | \(0.675792\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.77388 | −0.261612 | −0.130806 | − | 0.991408i | \(-0.541756\pi\) | ||||
−0.130806 | + | 0.991408i | \(0.541756\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.71121 | 0.124751 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.4694 | 1.05664 | 0.528319 | − | 0.849046i | \(-0.322823\pi\) | ||||
0.528319 | + | 0.849046i | \(0.322823\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −38.2576 | −1.28312 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.1494 | 0.440521 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.85351 | −0.329735 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.5917 | 0.487747 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.31289 | 0.0438360 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −45.8725 | −1.52993 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.04229 | −0.134668 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.40253 | −0.146507 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.61958 | −0.153560 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.8828 | 0.726608 | 0.363304 | − | 0.931671i | \(-0.381649\pi\) | ||||
0.363304 | + | 0.931671i | \(0.381649\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.71890 | −0.289188 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.3720 | 1.03940 | 0.519700 | − | 0.854349i | \(-0.326044\pi\) | ||||
0.519700 | + | 0.854349i | \(0.326044\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.6945 | −0.751078 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.99142 | 0.0988932 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.9932 | 0.495118 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.7351 | 0.749962 | 0.374981 | − | 0.927033i | \(-0.377649\pi\) | ||||
0.374981 | + | 0.927033i | \(0.377649\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.09247 | −0.200754 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.8087 | 0.816589 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.6546 | 1.00792 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.31794 | −0.306041 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.3903 | 0.734603 | 0.367302 | − | 0.930102i | \(-0.380282\pi\) | ||||
0.367302 | + | 0.930102i | \(0.380282\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.460604 | −0.0150957 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.96379 | 0.0642916 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.22998 | −0.171039 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.34736 | 0.305365 | 0.152682 | − | 0.988275i | \(-0.451209\pi\) | ||||
0.152682 | + | 0.988275i | \(0.451209\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.83962 | 0.0600338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44.7622 | 1.45921 | 0.729603 | − | 0.683871i | \(-0.239705\pi\) | ||||
0.729603 | + | 0.683871i | \(0.239705\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.47455 | 0.243405 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.98785 | −0.194785 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.9382 | −0.875374 | −0.437687 | − | 0.899127i | \(-0.644202\pi\) | ||||
−0.437687 | + | 0.899127i | \(0.644202\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.8499 | 0.384664 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.41146 | −0.175479 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.50412 | −0.275475 | −0.137738 | − | 0.990469i | \(-0.543983\pi\) | ||||
−0.137738 | + | 0.990469i | \(0.543983\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.0914 | 0.779580 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.75289 | −0.153639 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.32540 | 0.0427993 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.62013 | −0.181295 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −39.3712 | −1.26872 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.3003 | 0.717871 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.3831 | −1.13784 | −0.568921 | − | 0.822392i | \(-0.692639\pi\) | ||||
−0.568921 | + | 0.822392i | \(0.692639\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.60896 | −0.115936 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.2839 | −0.458392 | −0.229196 | − | 0.973380i | \(-0.573610\pi\) | ||||
−0.229196 | + | 0.973380i | \(0.573610\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.171185 | 0.00548793 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.77579 | 0.120922 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.7758 | 1.20856 | 0.604278 | − | 0.796774i | \(-0.293462\pi\) | ||||
0.604278 | + | 0.796774i | \(0.293462\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.4231 | 0.588806 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.06023 | −0.129633 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.7633 | −0.821723 | −0.410861 | − | 0.911698i | \(-0.634772\pi\) | ||||
−0.410861 | + | 0.911698i | \(0.634772\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.8286 | −0.759242 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.96852 | −0.0626585 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.44585 | 0.204966 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.0197 | 1.39833 | 0.699167 | − | 0.714959i | \(-0.253555\pi\) | ||||
0.699167 | + | 0.714959i | \(0.253555\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.38052 | 0.139012 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.9593 | 0.505945 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47.0752 | 1.49089 | 0.745443 | − | 0.666569i | \(-0.232238\pi\) | ||||
0.745443 | + | 0.666569i | \(0.232238\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.3545 | 0.517434 |
(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 | 6008.2.a.b.1.28 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.b.1.28 | ✓ | 44 | 1.1 | even | 1 | trivial |