Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6024,2,Mod(1,6024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6024 = 2^{3} \cdot 3 \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6024.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: | \(48.1018821776\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 43 x^{12} + 119 x^{11} + 679 x^{10} - 1667 x^{9} - 4890 x^{8} + 9662 x^{7} + 16575 x^{6} - 20277 x^{5} - 25196 x^{4} + 8040 x^{3} + 10776 x^{2} + \cdots - 416 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.155434\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6024.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.155434 | −0.0695122 | −0.0347561 | − | 0.999396i | \(-0.511065\pi\) | ||||
−0.0347561 | + | 0.999396i | \(0.511065\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.91825 | −1.48096 | −0.740480 | − | 0.672079i | \(-0.765402\pi\) | ||||
−0.740480 | + | 0.672079i | \(0.765402\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.98599 | −0.900309 | −0.450154 | − | 0.892951i | \(-0.648631\pi\) | ||||
−0.450154 | + | 0.892951i | \(0.648631\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.24976 | 0.901321 | 0.450661 | − | 0.892695i | \(-0.351188\pi\) | ||||
0.450661 | + | 0.892695i | \(0.351188\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.155434 | 0.0401329 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.57836 | 1.11041 | 0.555207 | − | 0.831712i | \(-0.312639\pi\) | ||||
0.555207 | + | 0.831712i | \(0.312639\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.89924 | 1.35338 | 0.676689 | − | 0.736269i | \(-0.263414\pi\) | ||||
0.676689 | + | 0.736269i | \(0.263414\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.91825 | 0.855032 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.13728 | −0.237139 | −0.118569 | − | 0.992946i | \(-0.537831\pi\) | ||||
−0.118569 | + | 0.992946i | \(0.537831\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.97584 | −0.995168 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.58606 | −1.03731 | −0.518653 | − | 0.854985i | \(-0.673566\pi\) | ||||
−0.518653 | + | 0.854985i | \(0.673566\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.95207 | −0.709812 | −0.354906 | − | 0.934902i | \(-0.615487\pi\) | ||||
−0.354906 | + | 0.934902i | \(0.615487\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.98599 | 0.519793 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.609029 | 0.102945 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.88043 | 0.802337 | 0.401169 | − | 0.916004i | \(-0.368604\pi\) | ||||
0.401169 | + | 0.916004i | \(0.368604\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.24976 | −0.520378 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.92467 | −0.612931 | −0.306466 | − | 0.951882i | \(-0.599146\pi\) | ||||
−0.306466 | + | 0.951882i | \(0.599146\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.68821 | 0.714945 | 0.357473 | − | 0.933924i | \(-0.383639\pi\) | ||||
0.357473 | + | 0.933924i | \(0.383639\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.155434 | −0.0231707 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.0714 | −1.61493 | −0.807467 | − | 0.589913i | \(-0.799162\pi\) | ||||
−0.807467 | + | 0.589913i | \(0.799162\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.35268 | 1.19324 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.57836 | −0.641098 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.2510 | 1.54544 | 0.772721 | − | 0.634746i | \(-0.218895\pi\) | ||||
0.772721 | + | 0.634746i | \(0.218895\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.464124 | 0.0625824 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.89924 | −0.781373 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.51311 | 0.587557 | 0.293779 | − | 0.955873i | \(-0.405087\pi\) | ||||
0.293779 | + | 0.955873i | \(0.405087\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.90103 | 0.883586 | 0.441793 | − | 0.897117i | \(-0.354343\pi\) | ||||
0.441793 | + | 0.897117i | \(0.354343\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.91825 | −0.493653 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.505123 | −0.0626528 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.82967 | −0.590038 | −0.295019 | − | 0.955491i | \(-0.595326\pi\) | ||||
−0.295019 | + | 0.955491i | \(0.595326\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.13728 | 0.136912 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.5370 | 1.84390 | 0.921949 | − | 0.387312i | \(-0.126597\pi\) | ||||
0.921949 | + | 0.387312i | \(0.126597\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.21490 | 0.493317 | 0.246658 | − | 0.969102i | \(-0.420667\pi\) | ||||
0.246658 | + | 0.969102i | \(0.420667\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.97584 | 0.574561 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.6998 | 1.33332 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.279589 | 0.0314563 | 0.0157281 | − | 0.999876i | \(-0.494993\pi\) | ||||
0.0157281 | + | 0.999876i | \(0.494993\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.21288 | −0.901481 | −0.450741 | − | 0.892655i | \(-0.648840\pi\) | ||||
−0.450741 | + | 0.892655i | \(0.648840\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.711633 | −0.0771874 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.58606 | 0.598889 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.919299 | 0.0974455 | 0.0487228 | − | 0.998812i | \(-0.484485\pi\) | ||||
0.0487228 | + | 0.998812i | \(0.484485\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.7334 | −1.33482 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.95207 | 0.409810 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.916943 | −0.0940763 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.23550 | −0.633119 | −0.316559 | − | 0.948573i | \(-0.602528\pi\) | ||||
−0.316559 | + | 0.948573i | \(0.602528\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.98599 | −0.300103 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.2888 | 1.32228 | 0.661141 | − | 0.750262i | \(-0.270073\pi\) | ||||
0.661141 | + | 0.750262i | \(0.270073\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.20637 | 0.414466 | 0.207233 | − | 0.978292i | \(-0.433554\pi\) | ||||
0.207233 | + | 0.978292i | \(0.433554\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.609029 | −0.0594352 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.56486 | −0.731322 | −0.365661 | − | 0.930748i | \(-0.619157\pi\) | ||||
−0.365661 | + | 0.930748i | \(0.619157\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.16079 | 0.590097 | 0.295048 | − | 0.955482i | \(-0.404664\pi\) | ||||
0.295048 | + | 0.955482i | \(0.404664\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.88043 | −0.463230 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.52532 | 0.519778 | 0.259889 | − | 0.965639i | \(-0.416314\pi\) | ||||
0.259889 | + | 0.965639i | \(0.416314\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.176772 | 0.0164840 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.24976 | 0.300440 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.9392 | −1.64448 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.08389 | −0.189444 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.92467 | 0.353876 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.55058 | 0.138689 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.74541 | 0.421087 | 0.210544 | − | 0.977584i | \(-0.432477\pi\) | ||||
0.210544 | + | 0.977584i | \(0.432477\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.68821 | −0.412774 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.77369 | 0.679191 | 0.339595 | − | 0.940572i | \(-0.389710\pi\) | ||||
0.339595 | + | 0.940572i | \(0.389710\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −23.1147 | −2.00430 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.155434 | 0.0133776 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.5804 | −1.24569 | −0.622843 | − | 0.782347i | \(-0.714023\pi\) | ||||
−0.622843 | + | 0.782347i | \(0.714023\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.6727 | −1.58380 | −0.791900 | − | 0.610650i | \(-0.790908\pi\) | ||||
−0.791900 | + | 0.610650i | \(0.790908\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.0714 | 0.932383 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.70374 | −0.811467 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.868264 | 0.0721054 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.35268 | −0.688917 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.0745 | −1.15303 | −0.576515 | − | 0.817087i | \(-0.695588\pi\) | ||||
−0.576515 | + | 0.817087i | \(0.695588\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.47923 | −0.690030 | −0.345015 | − | 0.938597i | \(-0.612126\pi\) | ||||
−0.345015 | + | 0.938597i | \(0.612126\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.57836 | 0.370138 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.614286 | 0.0493406 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.4129 | 1.46951 | 0.734755 | − | 0.678332i | \(-0.237297\pi\) | ||||
0.734755 | + | 0.678332i | \(0.237297\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.2510 | −0.892261 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.45614 | 0.351193 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24.0573 | −1.88431 | −0.942157 | − | 0.335173i | \(-0.891205\pi\) | ||||
−0.942157 | + | 0.335173i | \(0.891205\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.464124 | −0.0361320 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.2283 | 1.02364 | 0.511820 | − | 0.859093i | \(-0.328971\pi\) | ||||
0.511820 | + | 0.859093i | \(0.328971\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.43906 | −0.187620 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.89924 | 0.451126 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.3763 | −1.16904 | −0.584520 | − | 0.811379i | \(-0.698717\pi\) | ||||
−0.584520 | + | 0.811379i | \(0.698717\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 19.4966 | 1.47380 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.51311 | −0.339226 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.6831 | −1.84490 | −0.922450 | − | 0.386116i | \(-0.873817\pi\) | ||||
−0.922450 | + | 0.386116i | \(0.873817\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.0257 | −1.71149 | −0.855745 | − | 0.517398i | \(-0.826901\pi\) | ||||
−0.855745 | + | 0.517398i | \(0.826901\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.90103 | −0.510139 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.758584 | −0.0557722 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.6709 | −0.999716 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.91825 | 0.285011 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.4253 | −0.971418 | −0.485709 | − | 0.874121i | \(-0.661439\pi\) | ||||
−0.485709 | + | 0.874121i | \(0.661439\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.8267 | −0.851304 | −0.425652 | − | 0.904887i | \(-0.639955\pi\) | ||||
−0.425652 | + | 0.904887i | \(0.639955\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.505123 | 0.0361726 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.8298 | −1.12782 | −0.563912 | − | 0.825835i | \(-0.690704\pi\) | ||||
−0.563912 | + | 0.825835i | \(0.690704\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.91582 | −0.348473 | −0.174237 | − | 0.984704i | \(-0.555746\pi\) | ||||
−0.174237 | + | 0.984704i | \(0.555746\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.82967 | 0.340659 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.8876 | 1.53621 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.610028 | 0.0426062 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.13728 | −0.0790462 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.6151 | −1.21846 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.8470 | 0.815584 | 0.407792 | − | 0.913075i | \(-0.366299\pi\) | ||||
0.407792 | + | 0.913075i | \(0.366299\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.5370 | −1.06457 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.728707 | −0.0496974 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.4852 | 1.05120 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.21490 | −0.284817 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.8786 | 1.00084 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.6435 | 1.11453 | 0.557264 | − | 0.830335i | \(-0.311851\pi\) | ||||
0.557264 | + | 0.830335i | \(0.311851\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.97584 | −0.331723 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.8781 | −1.05387 | −0.526934 | − | 0.849906i | \(-0.676659\pi\) | ||||
−0.526934 | + | 0.849906i | \(0.676659\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.5448 | −0.696819 | −0.348410 | − | 0.937342i | \(-0.613278\pi\) | ||||
−0.348410 | + | 0.937342i | \(0.613278\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.6998 | −0.769793 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.2058 | −1.58578 | −0.792888 | − | 0.609367i | \(-0.791424\pi\) | ||||
−0.792888 | + | 0.609367i | \(0.791424\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.72088 | 0.112258 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.279589 | −0.0181613 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.3928 | −1.77189 | −0.885947 | − | 0.463786i | \(-0.846491\pi\) | ||||
−0.885947 | + | 0.463786i | \(0.846491\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.05270 | −0.454305 | −0.227152 | − | 0.973859i | \(-0.572942\pi\) | ||||
−0.227152 | + | 0.973859i | \(0.572942\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.29829 | −0.0829447 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.1711 | 1.21983 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.21288 | 0.520470 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.39589 | 0.213498 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.711633 | 0.0445642 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.02421 | −0.126267 | −0.0631333 | − | 0.998005i | \(-0.520109\pi\) | ||||
−0.0631333 | + | 0.998005i | \(0.520109\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.1227 | −1.18823 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.58606 | −0.345768 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.6471 | −0.903181 | −0.451590 | − | 0.892225i | \(-0.649143\pi\) | ||||
−0.451590 | + | 0.892225i | \(0.649143\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.74879 | −0.107427 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.919299 | −0.0562602 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.66846 | 0.345612 | 0.172806 | − | 0.984956i | \(-0.444717\pi\) | ||||
0.172806 | + | 0.984956i | \(0.444717\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.8654 | 1.44972 | 0.724861 | − | 0.688895i | \(-0.241904\pi\) | ||||
0.724861 | + | 0.688895i | \(0.241904\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.7334 | 0.770659 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.8578 | 0.895958 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.6053 | −1.89898 | −0.949491 | − | 0.313796i | \(-0.898399\pi\) | ||||
−0.949491 | + | 0.313796i | \(0.898399\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.95207 | −0.236604 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.130628 | 0.00779262 | 0.00389631 | − | 0.999992i | \(-0.498760\pi\) | ||||
0.00389631 | + | 0.999992i | \(0.498760\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.836580 | −0.0497295 | −0.0248647 | − | 0.999691i | \(-0.507916\pi\) | ||||
−0.0248647 | + | 0.999691i | \(0.507916\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.916943 | 0.0543150 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.3779 | 0.907726 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.96136 | 0.233021 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.23550 | 0.365531 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.78602 | −0.513285 | −0.256642 | − | 0.966506i | \(-0.582616\pi\) | ||||
−0.256642 | + | 0.966506i | \(0.582616\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.701491 | −0.0408424 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.98599 | 0.173264 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.69588 | −0.213738 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.3696 | −1.05881 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.2888 | −0.763420 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.07265 | −0.0614200 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.3921 | 1.27799 | 0.638994 | − | 0.769212i | \(-0.279351\pi\) | ||||
0.638994 | + | 0.769212i | \(0.279351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.20637 | −0.239292 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.44519 | 0.252064 | 0.126032 | − | 0.992026i | \(-0.459776\pi\) | ||||
0.126032 | + | 0.992026i | \(0.459776\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.7404 | −1.11579 | −0.557895 | − | 0.829911i | \(-0.688391\pi\) | ||||
−0.557895 | + | 0.829911i | \(0.688391\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.609029 | 0.0343149 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.6169 | 1.15796 | 0.578980 | − | 0.815342i | \(-0.303451\pi\) | ||||
0.578980 | + | 0.815342i | \(0.303451\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.6799 | 0.933895 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.56486 | 0.422229 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.0088 | 1.50281 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.1703 | −0.896966 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.16079 | −0.340692 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 43.3806 | 2.39165 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.0072 | 0.824868 | 0.412434 | − | 0.910987i | \(-0.364679\pi\) | ||||
0.412434 | + | 0.910987i | \(0.364679\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.88043 | 0.267446 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.750695 | 0.0410149 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.7044 | 1.34573 | 0.672867 | − | 0.739763i | \(-0.265062\pi\) | ||||
0.672867 | + | 0.739763i | \(0.265062\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.52532 | −0.300094 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.8008 | 0.639050 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.30014 | −0.286181 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.176772 | −0.00951706 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −36.5680 | −1.96307 | −0.981536 | − | 0.191280i | \(-0.938736\pi\) | ||||
−0.981536 | + | 0.191280i | \(0.938736\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.8305 | 1.11503 | 0.557515 | − | 0.830167i | \(-0.311755\pi\) | ||||
0.557515 | + | 0.830167i | \(0.311755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.24976 | −0.173459 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.5901 | 1.73460 | 0.867298 | − | 0.497789i | \(-0.165855\pi\) | ||||
0.867298 | + | 0.497789i | \(0.165855\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.41497 | −0.128173 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.9392 | 0.949441 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.7854 | −0.780342 | −0.390171 | − | 0.920742i | \(-0.627584\pi\) | ||||
−0.390171 | + | 0.920742i | \(0.627584\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.8010 | 0.831634 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.08389 | 0.109376 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.655139 | −0.0342915 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.9599 | −0.885299 | −0.442649 | − | 0.896695i | \(-0.645961\pi\) | ||||
−0.442649 | + | 0.896695i | \(0.645961\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.92467 | −0.204310 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −44.0842 | −2.28874 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.655098 | 0.0339197 | 0.0169598 | − | 0.999856i | \(-0.494601\pi\) | ||||
0.0169598 | + | 0.999856i | \(0.494601\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.55058 | −0.0800719 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.1534 | −0.934946 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.04647 | −0.259220 | −0.129610 | − | 0.991565i | \(-0.541372\pi\) | ||||
−0.129610 | + | 0.991565i | \(0.541372\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.74541 | −0.243115 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.65268 | 0.135545 | 0.0677727 | − | 0.997701i | \(-0.478411\pi\) | ||||
0.0677727 | + | 0.997701i | \(0.478411\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.81855 | −0.0926820 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.68821 | 0.238315 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.0810 | 1.06885 | 0.534425 | − | 0.845216i | \(-0.320528\pi\) | ||||
0.534425 | + | 0.845216i | \(0.320528\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.20686 | −0.263322 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.77369 | −0.392131 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.0434577 | −0.00218659 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.0049 | −1.20477 | −0.602385 | − | 0.798206i | \(-0.705783\pi\) | ||||
−0.602385 | + | 0.798206i | \(0.705783\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 23.1147 | 1.15718 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.2594 | −0.612208 | −0.306104 | − | 0.951998i | \(-0.599025\pi\) | ||||
−0.306104 | + | 0.951998i | \(0.599025\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.8433 | −0.639769 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.155434 | −0.00772358 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.5729 | −0.722351 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.99591 | −0.148138 | −0.0740692 | − | 0.997253i | \(-0.523599\pi\) | ||||
−0.0740692 | + | 0.997253i | \(0.523599\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.5804 | 0.719197 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.6835 | −0.870148 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.27656 | 0.0626639 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.6727 | 0.914408 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.6776 | −0.619343 | −0.309672 | − | 0.950844i | \(-0.600219\pi\) | ||||
−0.309672 | + | 0.950844i | \(0.600219\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.8534 | −1.60118 | −0.800588 | − | 0.599215i | \(-0.795479\pi\) | ||||
−0.800588 | + | 0.599215i | \(0.795479\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.0714 | −0.538311 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −22.7812 | −1.10505 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.0400 | −1.30856 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.70374 | 0.468501 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.23222 | −0.252027 | −0.126014 | − | 0.992029i | \(-0.540218\pi\) | ||||
−0.126014 | + | 0.992029i | \(0.540218\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.18616 | 0.153117 | 0.0765586 | − | 0.997065i | \(-0.475607\pi\) | ||||
0.0765586 | + | 0.997065i | \(0.475607\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.868264 | −0.0416301 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.70907 | −0.320938 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.4806 | 0.929756 | 0.464878 | − | 0.885375i | \(-0.346098\pi\) | ||||
0.464878 | + | 0.885375i | \(0.346098\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.35268 | 0.397747 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.11370 | 0.385494 | 0.192747 | − | 0.981249i | \(-0.438260\pi\) | ||||
0.192747 | + | 0.981249i | \(0.438260\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.142890 | −0.00677365 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.0745 | 0.665702 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.7683 | 0.696957 | 0.348479 | − | 0.937317i | \(-0.386698\pi\) | ||||
0.348479 | + | 0.937317i | \(0.386698\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.7190 | 0.551827 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.47923 | 0.398389 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.97920 | 0.0927863 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.9120 | −0.557220 | −0.278610 | − | 0.960404i | \(-0.589874\pi\) | ||||
−0.278610 | + | 0.960404i | \(0.589874\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.57836 | −0.213699 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.2214 | 1.22125 | 0.610626 | − | 0.791919i | \(-0.290918\pi\) | ||||
0.610626 | + | 0.791919i | \(0.290918\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.0737 | 1.44412 | 0.722059 | − | 0.691832i | \(-0.243196\pi\) | ||||
0.722059 | + | 0.691832i | \(0.243196\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.614286 | −0.0284868 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.8183 | 0.500610 | 0.250305 | − | 0.968167i | \(-0.419469\pi\) | ||||
0.250305 | + | 0.968167i | \(0.419469\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.9239 | 0.873823 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.4129 | −0.848423 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.9989 | −0.643672 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −29.3537 | −1.34684 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.2510 | 0.515147 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.1839 | −1.28776 | −0.643878 | − | 0.765128i | \(-0.722676\pi\) | ||||
−0.643878 | + | 0.765128i | \(0.722676\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.8602 | 0.723164 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.45614 | −0.202761 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.969208 | 0.0440095 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.28447 | 0.239462 | 0.119731 | − | 0.992806i | \(-0.461797\pi\) | ||||
0.119731 | + | 0.992806i | \(0.461797\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.0573 | 1.08791 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.6779 | −1.06857 | −0.534285 | − | 0.845305i | \(-0.679419\pi\) | ||||
−0.534285 | + | 0.845305i | \(0.679419\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.5750 | −1.15184 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.464124 | 0.0208608 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −60.8777 | −2.73074 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −41.1262 | −1.84106 | −0.920530 | − | 0.390671i | \(-0.872243\pi\) | ||||
−0.920530 | + | 0.390671i | \(0.872243\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.2283 | −0.590999 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.31325 | −0.370670 | −0.185335 | − | 0.982675i | \(-0.559337\pi\) | ||||
−0.185335 | + | 0.982675i | \(0.559337\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.06553 | −0.0919147 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.43906 | 0.108322 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.2694 | −0.942751 | −0.471375 | − | 0.881933i | \(-0.656242\pi\) | ||||
−0.471375 | + | 0.881933i | \(0.656242\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.5150 | −0.730582 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.89924 | −0.260458 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.653813 | −0.0288104 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.0591 | 1.45394 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.3763 | 0.674946 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.8865 | −0.871242 | −0.435621 | − | 0.900130i | \(-0.643471\pi\) | ||||
−0.435621 | + | 0.900130i | \(0.643471\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.4890 | 1.50810 | 0.754050 | − | 0.656817i | \(-0.228097\pi\) | ||||
0.754050 | + | 0.656817i | \(0.228097\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −19.4966 | −0.850901 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.0940 | −0.788186 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.7066 | −0.943765 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.51311 | 0.195852 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.7543 | −0.552448 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.17584 | 0.0508358 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24.6831 | 1.06515 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24.9410 | −1.07428 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.8257 | 0.981352 | 0.490676 | − | 0.871342i | \(-0.336750\pi\) | ||||
0.490676 | + | 0.871342i | \(0.336750\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.0257 | 0.988129 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.957596 | −0.0410189 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.2778 | 0.952532 | 0.476266 | − | 0.879301i | \(-0.341990\pi\) | ||||
0.476266 | + | 0.879301i | \(0.341990\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.90103 | 0.294529 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −32.9535 | −1.40387 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.09550 | −0.0465854 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.758584 | 0.0322001 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.8688 | 0.799496 | 0.399748 | − | 0.916625i | \(-0.369098\pi\) | ||||
0.399748 | + | 0.916625i | \(0.369098\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.2356 | 0.644396 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.6709 | 0.577186 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.7575 | −0.874822 | −0.437411 | − | 0.899262i | \(-0.644105\pi\) | ||||
−0.437411 | + | 0.899262i | \(0.644105\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.858822 | −0.0361309 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.91825 | −0.164551 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.492918 | −0.0206642 | −0.0103321 | − | 0.999947i | \(-0.503289\pi\) | ||||
−0.0103321 | + | 0.999947i | \(0.503289\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.7383 | −1.37006 | −0.685028 | − | 0.728517i | \(-0.740210\pi\) | ||||
−0.685028 | + | 0.728517i | \(0.740210\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.4253 | 0.560849 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.65891 | 0.235993 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.7733 | 0.656650 | 0.328325 | − | 0.944565i | \(-0.393516\pi\) | ||||
0.328325 | + | 0.944565i | \(0.393516\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.8267 | 0.491501 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 32.1801 | 1.33506 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −33.5953 | −1.39137 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.505123 | −0.0208843 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.18009 | −0.131257 | −0.0656283 | − | 0.997844i | \(-0.520905\pi\) | ||||
−0.0656283 | + | 0.997844i | \(0.520905\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.3142 | −0.960645 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.8298 | 0.651149 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −31.7048 | −1.30196 | −0.650979 | − | 0.759096i | \(-0.725642\pi\) | ||||
−0.650979 | + | 0.759096i | \(0.725642\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.78835 | 0.114311 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.91582 | 0.201191 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.4566 | −1.08099 | −0.540495 | − | 0.841348i | \(-0.681763\pi\) | ||||
−0.540495 | + | 0.841348i | \(0.681763\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.4907 | 0.835832 | 0.417916 | − | 0.908486i | \(-0.362761\pi\) | ||||
0.417916 | + | 0.908486i | \(0.362761\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.82967 | −0.196679 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.323907 | 0.0131687 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.2895 | 1.43236 | 0.716179 | − | 0.697917i | \(-0.245890\pi\) | ||||
0.716179 | + | 0.697917i | \(0.245890\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −21.8876 | −0.886930 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35.9795 | −1.45557 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.5780 | 1.23503 | 0.617517 | − | 0.786557i | \(-0.288139\pi\) | ||||
0.617517 | + | 0.786557i | \(0.288139\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.610028 | −0.0245987 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.3421 | −1.46308 | −0.731539 | − | 0.681800i | \(-0.761198\pi\) | ||||
−0.731539 | + | 0.681800i | \(0.761198\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.1128 | −1.00937 | −0.504684 | − | 0.863304i | \(-0.668391\pi\) | ||||
−0.504684 | + | 0.863304i | \(0.668391\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.13728 | 0.0456374 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.60204 | −0.144313 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.6382 | 0.985528 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.6151 | 0.703477 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.3443 | 0.890927 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.7218 | 0.586065 | 0.293032 | − | 0.956102i | \(-0.405336\pi\) | ||||
0.293032 | + | 0.956102i | \(0.405336\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.8470 | −0.470878 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.737598 | −0.0292707 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.1442 | 1.07549 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.5370 | 0.614632 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.2029 | 1.58792 | 0.793959 | − | 0.607971i | \(-0.208016\pi\) | ||||
0.793959 | + | 0.607971i | \(0.208016\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.8577 | 1.33522 | 0.667608 | − | 0.744513i | \(-0.267318\pi\) | ||||
0.667608 | + | 0.744513i | \(0.267318\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.728707 | 0.0286928 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.9308 | −1.17670 | −0.588350 | − | 0.808606i | \(-0.700222\pi\) | ||||
−0.588350 | + | 0.808606i | \(0.700222\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.4761 | −0.528983 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.4852 | −0.606912 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.4369 | 0.564961 | 0.282480 | − | 0.959273i | \(-0.408843\pi\) | ||||
0.282480 | + | 0.959273i | \(0.408843\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.20830 | −0.0472120 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.21490 | 0.164439 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.8984 | 1.16468 | 0.582339 | − | 0.812946i | \(-0.302138\pi\) | ||||
0.582339 | + | 0.812946i | \(0.302138\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.5483 | −1.57715 | −0.788573 | − | 0.614942i | \(-0.789180\pi\) | ||||
−0.788573 | + | 0.614942i | \(0.789180\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.8786 | −0.577836 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.59281 | 0.139323 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.35290 | 0.245985 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.6435 | −0.643473 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.6064 | −0.795500 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.77832 | 0.261285 | 0.130643 | − | 0.991430i | \(-0.458296\pi\) | ||||
0.130643 | + | 0.991430i | \(0.458296\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.97584 | 0.191520 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.3266 | −0.512184 | −0.256092 | − | 0.966652i | \(-0.582435\pi\) | ||||
−0.256092 | + | 0.966652i | \(0.582435\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.4322 | 0.937623 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.8781 | 0.608451 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.1796 | 0.542568 | 0.271284 | − | 0.962499i | \(-0.412552\pi\) | ||||
0.271284 | + | 0.962499i | \(0.412552\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.26629 | 0.0865904 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.5448 | 0.402309 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 36.5630 | 1.39294 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.6675 | 1.28077 | 0.640385 | − | 0.768054i | \(-0.278775\pi\) | ||||
0.640385 | + | 0.768054i | \(0.278775\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.6998 | 0.444440 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.90238 | 0.110093 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.9686 | −0.680608 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.2058 | 0.915548 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.6588 | −1.00689 | −0.503445 | − | 0.864027i | \(-0.667934\pi\) | ||||
−0.503445 | + | 0.864027i | \(0.667934\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.7908 | 1.08587 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.72088 | −0.0648120 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −52.0687 | −1.95825 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.2754 | 0.986794 | 0.493397 | − | 0.869804i | \(-0.335755\pi\) | ||||
0.493397 | + | 0.869804i | \(0.335755\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.279589 | 0.0104854 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.49460 | 0.168324 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.50829 | 0.0564069 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 27.3928 | 1.02300 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.97360 | −0.260071 | −0.130036 | − | 0.991509i | \(-0.541509\pi\) | ||||
−0.130036 | + | 0.991509i | \(0.541509\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.4816 | −0.613807 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.05270 | 0.262293 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 27.7953 | 1.03229 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.2590 | 1.19642 | 0.598210 | − | 0.801339i | \(-0.295879\pi\) | ||||
0.598210 | + | 0.801339i | \(0.295879\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.4643 | 0.793886 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 47.4501 | 1.75261 | 0.876305 | − | 0.481756i | \(-0.160001\pi\) | ||||
0.876305 | + | 0.481756i | \(0.160001\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.29829 | 0.0478882 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.4213 | 0.531217 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.4672 | −1.67254 | −0.836268 | − | 0.548320i | \(-0.815267\pi\) | ||||
−0.836268 | + | 0.548320i | \(0.815267\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.1711 | −0.704269 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.95302 | −0.108336 | −0.0541679 | − | 0.998532i | \(-0.517251\pi\) | ||||
−0.0541679 | + | 0.998532i | \(0.517251\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.18766 | 0.0801496 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.21288 | −0.300494 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.6410 | 1.08306 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.8627 | 1.71005 | 0.855023 | − | 0.518590i | \(-0.173543\pi\) | ||||
0.855023 | + | 0.518590i | \(0.173543\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.00000 | −0.0364420 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.31796 | 0.0479655 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.3044 | 1.02874 | 0.514370 | − | 0.857568i | \(-0.328026\pi\) | ||||
0.514370 | + | 0.857568i | \(0.328026\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.39589 | −0.123263 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.0132 | −0.834227 | −0.417113 | − | 0.908855i | \(-0.636958\pi\) | ||||
−0.417113 | + | 0.908855i | \(0.636958\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.1395 | −0.873909 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.711633 | −0.0257291 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.6665 | 0.529578 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.42938 | 0.0876057 | 0.0438029 | − | 0.999040i | \(-0.486053\pi\) | ||||
0.0438029 | + | 0.999040i | \(0.486053\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.02421 | 0.0729001 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −48.6153 | −1.74857 | −0.874286 | − | 0.485411i | \(-0.838670\pi\) | ||||
−0.874286 | + | 0.485411i | \(0.838670\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.6649 | 0.706383 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.1227 | 0.686024 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.1526 | −0.829528 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −46.3931 | −1.66008 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.58606 | 0.199630 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.86199 | −0.102149 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.7728 | −1.31081 | −0.655405 | − | 0.755277i | \(-0.727502\pi\) | ||||
−0.655405 | + | 0.755277i | \(0.727502\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.6471 | 0.521452 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.6496 | −0.769770 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.4267 | 0.796395 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.74879 | 0.0620230 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.36397 | −0.0483143 | −0.0241572 | − | 0.999708i | \(-0.507690\pi\) | ||||
−0.0241572 | + | 0.999708i | \(0.507690\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −50.6890 | −1.79325 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.919299 | 0.0324818 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.5856 | −0.444137 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.692635 | −0.0244122 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.66846 | −0.199539 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.83746 | −0.240392 | −0.120196 | − | 0.992750i | \(-0.538352\pi\) | ||||
−0.120196 | + | 0.992750i | \(0.538352\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.61278 | −0.161976 | −0.0809882 | − | 0.996715i | \(-0.525808\pi\) | ||||
−0.0809882 | + | 0.996715i | \(0.525808\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.8654 | −0.836997 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.73932 | 0.130983 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.6569 | 0.967592 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.7334 | −0.444940 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −47.8754 | −1.67086 | −0.835431 | − | 0.549595i | \(-0.814782\pi\) | ||||
−0.835431 | + | 0.549595i | \(0.814782\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.56063 | 0.158974 | 0.0794868 | − | 0.996836i | \(-0.474672\pi\) | ||||
0.0794868 | + | 0.996836i | \(0.474672\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14.8578 | −0.517282 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.3776 | −1.23020 | −0.615099 | − | 0.788450i | \(-0.710884\pi\) | ||||
−0.615099 | + | 0.788450i | \(0.710884\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.69107 | 0.267122 | 0.133561 | − | 0.991041i | \(-0.457359\pi\) | ||||
0.133561 | + | 0.991041i | \(0.457359\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 31.6053 | 1.09638 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 38.2416 | 1.32499 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.05613 | −0.0711555 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.95207 | 0.136603 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −47.8718 | −1.65272 | −0.826359 | − | 0.563144i | \(-0.809592\pi\) | ||||
−0.826359 | + | 0.563144i | \(0.809592\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.20407 | 0.0760025 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.130628 | −0.00449907 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.379112 | 0.0130419 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.16519 | 0.280559 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.836580 | 0.0287113 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.55040 | −0.190265 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46.4819 | −1.59151 | −0.795755 | − | 0.605618i | \(-0.792926\pi\) | ||||
−0.795755 | + | 0.605618i | \(0.792926\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.916943 | −0.0313588 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.4642 | 0.733204 | 0.366602 | − | 0.930378i | \(-0.380521\pi\) | ||||
0.366602 | + | 0.930378i | \(0.380521\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.6830 | 1.11513 | 0.557565 | − | 0.830133i | \(-0.311736\pi\) | ||||
0.557565 | + | 0.830133i | \(0.311736\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.3779 | −0.524076 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.7235 | 1.55645 | 0.778223 | − | 0.627989i | \(-0.216122\pi\) | ||||
0.778223 | + | 0.627989i | \(0.216122\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.39000 | 0.0812626 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.96136 | −0.134535 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.834850 | −0.0283203 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.6953 | −0.531814 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.23550 | −0.211040 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.07558 | −0.205392 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.7830 | −0.634258 | −0.317129 | − | 0.948382i | \(-0.602719\pi\) | ||||
−0.317129 | + | 0.948382i | \(0.602719\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.78602 | 0.296345 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.8918 | 0.771244 | 0.385622 | − | 0.922657i | \(-0.373987\pi\) | ||||
0.385622 | + | 0.922657i | \(0.373987\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.8753 | −0.433287 | −0.216644 | − | 0.976251i | \(-0.569511\pi\) | ||||
−0.216644 | + | 0.976251i | \(0.569511\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.701491 | 0.0235804 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.866963 | 0.0291098 | 0.0145549 | − | 0.999894i | \(-0.495367\pi\) | ||||
0.0145549 | + | 0.999894i | \(0.495367\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.5937 | −0.623613 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.98599 | −0.100034 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −65.3130 | −2.18562 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.83659 | 0.128243 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.69588 | 0.123402 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.0765 | 0.736292 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 51.5110 | 1.71608 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 18.3696 | 0.611301 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.57898 | 0.118969 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −48.9486 | −1.62531 | −0.812656 | − | 0.582743i | \(-0.801979\pi\) | ||||
−0.812656 | + | 0.582743i | \(0.801979\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.2888 | 0.440761 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.3830 | 0.509661 | 0.254830 | − | 0.966986i | \(-0.417980\pi\) | ||||
0.254830 | + | 0.966986i | \(0.417980\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.5236 | 0.811611 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.07265 | 0.0354609 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30.4593 | −1.00585 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51.5782 | −1.70141 | −0.850704 | − | 0.525645i | \(-0.823824\pi\) | ||||
−0.850704 | + | 0.525645i | \(0.823824\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.3921 | −0.737846 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 50.4914 | 1.66194 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.2842 | −0.798460 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.20637 | 0.138155 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.1433 | 0.332791 | 0.166396 | − | 0.986059i | \(-0.446787\pi\) | ||||
0.166396 | + | 0.986059i | \(0.446787\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 49.2745 | 1.61491 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.44519 | −0.145529 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.12492 | 0.0694925 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.6550 | 1.32814 | 0.664070 | − | 0.747671i | \(-0.268828\pi\) | ||||
0.664070 | + | 0.747671i | \(0.268828\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.7404 | 0.644202 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.2211 | −0.789586 | −0.394793 | − | 0.918770i | \(-0.629184\pi\) | ||||
−0.394793 | + | 0.918770i | \(0.629184\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.46344 | 0.145350 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.609029 | −0.0198117 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.66373 | 0.249038 | 0.124519 | − | 0.992217i | \(-0.460261\pi\) | ||||
0.124519 | + | 0.992217i | \(0.460261\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.6974 | 0.444637 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.6169 | −0.668549 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.7925 | 0.965075 | 0.482537 | − | 0.875875i | \(-0.339715\pi\) | ||||
0.482537 | + | 0.875875i | \(0.339715\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.08674 | 0.0675254 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.6799 | −0.539185 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 57.1296 | 1.84481 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.3812 | −0.496166 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.56486 | −0.243774 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.83827 | 0.0591760 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.77563 | 0.282205 | 0.141103 | − | 0.989995i | \(-0.454935\pi\) | ||||
0.141103 | + | 0.989995i | \(0.454935\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −27.0088 | −0.867649 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.4608 | −0.335702 | −0.167851 | − | 0.985812i | \(-0.553683\pi\) | ||||
−0.167851 | + | 0.985812i | \(0.553683\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 73.1644 | 2.34554 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.1703 | 0.517864 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.96714 | −0.286884 | −0.143442 | − | 0.989659i | \(-0.545817\pi\) | ||||
−0.143442 | + | 0.989659i | \(0.545817\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.74502 | −0.0877311 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.16079 | 0.196699 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.0221 | 0.734292 | 0.367146 | − | 0.930163i | \(-0.380335\pi\) | ||||
0.367146 | + | 0.930163i | \(0.380335\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.46048 | 0.0783975 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −43.3806 | −1.38082 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.33179 | −0.169541 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.68998 | −0.117216 | −0.0586080 | − | 0.998281i | \(-0.518666\pi\) | ||||
−0.0586080 | + | 0.998281i | \(0.518666\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.0072 | −0.476238 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.764085 | 0.0242231 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.9206 | 1.01094 | 0.505468 | − | 0.862845i | \(-0.331320\pi\) | ||||
0.505468 | + | 0.862845i | \(0.331320\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.88043 | −0.154410 |
(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 | 6024.2.a.o.1.7 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6024.2.a.o.1.7 | ✓ | 14 | 1.1 | even | 1 | trivial |