Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
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: | \( x^{14} - 3 x^{13} - 27 x^{12} + 78 x^{11} + 273 x^{10} - 750 x^{9} - 1306 x^{8} + 3378 x^{7} + \cdots - 128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.53687\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | −1.53687 | −0.887313 | −0.443657 | − | 0.896197i | \(-0.646319\pi\) | ||||
−0.443657 | + | 0.896197i | \(0.646319\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.216819 | −0.0969644 | −0.0484822 | − | 0.998824i | \(-0.515438\pi\) | ||||
−0.0484822 | + | 0.998824i | \(0.515438\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.638026 | −0.212675 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.333223 | 0.0860378 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.18307 | 0.286936 | 0.143468 | − | 0.989655i | \(-0.454175\pi\) | ||||
0.143468 | + | 0.989655i | \(0.454175\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.88361 | 1.80862 | 0.904312 | − | 0.426872i | \(-0.140385\pi\) | ||||
0.904312 | + | 0.426872i | \(0.140385\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.53687 | −0.335373 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.22149 | −0.254698 | −0.127349 | − | 0.991858i | \(-0.540647\pi\) | ||||
−0.127349 | + | 0.991858i | \(0.540647\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.95299 | −0.990598 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.59118 | 1.07602 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.20441 | −0.966434 | −0.483217 | − | 0.875501i | \(-0.660532\pi\) | ||||
−0.483217 | + | 0.875501i | \(0.660532\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.80232 | −0.862522 | −0.431261 | − | 0.902227i | \(-0.641931\pi\) | ||||
−0.431261 | + | 0.902227i | \(0.641931\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.53687 | 0.267535 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.216819 | −0.0366491 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.61831 | 1.41684 | 0.708420 | − | 0.705791i | \(-0.249408\pi\) | ||||
0.708420 | + | 0.705791i | \(0.249408\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.53687 | 0.246096 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.95896 | −1.24298 | −0.621490 | − | 0.783422i | \(-0.713472\pi\) | ||||
−0.621490 | + | 0.783422i | \(0.713472\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.91246 | −0.596644 | −0.298322 | − | 0.954465i | \(-0.596427\pi\) | ||||
−0.298322 | + | 0.954465i | \(0.596427\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.138336 | 0.0206219 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.51062 | 0.512077 | 0.256038 | − | 0.966667i | \(-0.417583\pi\) | ||||
0.256038 | + | 0.966667i | \(0.417583\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.81822 | −0.254602 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.35917 | 0.873499 | 0.436750 | − | 0.899583i | \(-0.356130\pi\) | ||||
0.436750 | + | 0.899583i | \(0.356130\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.216819 | 0.0292359 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.1161 | −1.60482 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.23350 | −0.551155 | −0.275577 | − | 0.961279i | \(-0.588869\pi\) | ||||
−0.275577 | + | 0.961279i | \(0.588869\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.624073 | −0.0799043 | −0.0399522 | − | 0.999202i | \(-0.512721\pi\) | ||||
−0.0399522 | + | 0.999202i | \(0.512721\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.638026 | −0.0803837 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.216819 | 0.0268931 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.74600 | 0.579817 | 0.289908 | − | 0.957054i | \(-0.406375\pi\) | ||||
0.289908 | + | 0.957054i | \(0.406375\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.87727 | 0.225997 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.7254 | −1.62890 | −0.814452 | − | 0.580231i | \(-0.802962\pi\) | ||||
−0.814452 | + | 0.580231i | \(0.802962\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.1174 | 1.88640 | 0.943202 | − | 0.332220i | \(-0.107798\pi\) | ||||
0.943202 | + | 0.332220i | \(0.107798\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.61211 | 0.878971 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.0838 | 1.47204 | 0.736019 | − | 0.676960i | \(-0.236703\pi\) | ||||
0.736019 | + | 0.676960i | \(0.236703\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.67884 | −0.742094 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.48532 | −0.382564 | −0.191282 | − | 0.981535i | \(-0.561265\pi\) | ||||
−0.191282 | + | 0.981535i | \(0.561265\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.256512 | −0.0278226 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.99850 | 0.857530 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.11011 | 0.329671 | 0.164836 | − | 0.986321i | \(-0.447291\pi\) | ||||
0.164836 | + | 0.986321i | \(0.447291\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.38054 | 0.765327 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.70932 | −0.175372 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.26128 | −0.331133 | −0.165567 | − | 0.986199i | \(-0.552945\pi\) | ||||
−0.165567 | + | 0.986199i | \(0.552945\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.638026 | 0.0641240 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.7866 | 1.17281 | 0.586406 | − | 0.810018i | \(-0.300542\pi\) | ||||
0.586406 | + | 0.810018i | \(0.300542\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.9517 | −1.57177 | −0.785884 | − | 0.618373i | \(-0.787792\pi\) | ||||
−0.785884 | + | 0.618373i | \(0.787792\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.333223 | 0.0325192 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.08272 | −0.394691 | −0.197346 | − | 0.980334i | \(-0.563232\pi\) | ||||
−0.197346 | + | 0.980334i | \(0.563232\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.93859 | −0.856162 | −0.428081 | − | 0.903740i | \(-0.640810\pi\) | ||||
−0.428081 | + | 0.903740i | \(0.640810\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.2452 | −1.25718 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.43235 | 0.699177 | 0.349588 | − | 0.936903i | \(-0.386321\pi\) | ||||
0.349588 | + | 0.936903i | \(0.386321\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.264842 | 0.0246967 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.638026 | 0.0589855 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.18307 | 0.108452 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.2319 | 1.10291 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.15800 | 0.193017 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.10500 | 0.0980525 | 0.0490263 | − | 0.998797i | \(-0.484388\pi\) | ||||
0.0490263 | + | 0.998797i | \(0.484388\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.01294 | 0.529410 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.4517 | −1.17528 | −0.587642 | − | 0.809121i | \(-0.699943\pi\) | ||||
−0.587642 | + | 0.809121i | \(0.699943\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.88361 | 0.683596 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.21227 | −0.104336 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.13711 | 0.438893 | 0.219447 | − | 0.975625i | \(-0.429575\pi\) | ||||
0.219447 | + | 0.975625i | \(0.429575\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.18510 | 0.270156 | 0.135078 | − | 0.990835i | \(-0.456871\pi\) | ||||
0.135078 | + | 0.990835i | \(0.456871\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.39537 | −0.454372 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.12841 | 0.0937097 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.53687 | −0.126759 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.25902 | −0.758529 | −0.379264 | − | 0.925288i | \(-0.623823\pi\) | ||||
−0.379264 | + | 0.925288i | \(0.623823\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.48990 | −0.528141 | −0.264070 | − | 0.964503i | \(-0.585065\pi\) | ||||
−0.264070 | + | 0.964503i | \(0.585065\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.754828 | −0.0610242 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.04123 | 0.0836339 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.3997 | 0.829989 | 0.414995 | − | 0.909824i | \(-0.363783\pi\) | ||||
0.414995 | + | 0.909824i | \(0.363783\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.77323 | −0.775068 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.22149 | −0.0962670 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.6197 | −1.22343 | −0.611716 | − | 0.791077i | \(-0.709521\pi\) | ||||
−0.611716 | + | 0.791077i | \(0.709521\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.333223 | −0.0259414 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.3584 | 1.34323 | 0.671617 | − | 0.740898i | \(-0.265600\pi\) | ||||
0.671617 | + | 0.740898i | \(0.265600\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.02995 | −0.384650 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −23.0133 | −1.74967 | −0.874834 | − | 0.484422i | \(-0.839030\pi\) | ||||
−0.874834 | + | 0.484422i | \(0.839030\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.95299 | −0.374411 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.50635 | 0.489047 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.2298 | −1.13833 | −0.569163 | − | 0.822225i | \(-0.692733\pi\) | ||||
−0.569163 | + | 0.822225i | \(0.692733\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.68362 | −0.571119 | −0.285559 | − | 0.958361i | \(-0.592179\pi\) | ||||
−0.285559 | + | 0.958361i | \(0.592179\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.959120 | 0.0709002 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.86861 | −0.137383 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.18307 | −0.0865145 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.59118 | 0.406698 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.5121 | −1.62892 | −0.814459 | − | 0.580221i | \(-0.802966\pi\) | ||||
−0.814459 | + | 0.580221i | \(0.802966\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.9282 | 1.43446 | 0.717230 | − | 0.696837i | \(-0.245410\pi\) | ||||
0.717230 | + | 0.696837i | \(0.245410\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.333223 | −0.0238626 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.3502 | 1.44989 | 0.724947 | − | 0.688804i | \(-0.241864\pi\) | ||||
0.724947 | + | 0.688804i | \(0.241864\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.68637 | 0.686648 | 0.343324 | − | 0.939217i | \(-0.388447\pi\) | ||||
0.343324 | + | 0.939217i | \(0.388447\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.29400 | −0.514479 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.20441 | −0.365278 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.72565 | 0.120525 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.779343 | 0.0541681 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.88361 | −0.545321 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.97542 | −0.617893 | −0.308947 | − | 0.951079i | \(-0.599976\pi\) | ||||
−0.308947 | + | 0.951079i | \(0.599976\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21.0942 | 1.44535 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.848295 | 0.0578532 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.80232 | −0.326003 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −24.7704 | −1.67383 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.18307 | −0.0795817 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.5413 | 0.973760 | 0.486880 | − | 0.873469i | \(-0.338135\pi\) | ||||
0.486880 | + | 0.873469i | \(0.338135\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.16014 | 0.210676 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.69756 | −0.510905 | −0.255453 | − | 0.966822i | \(-0.582224\pi\) | ||||
−0.255453 | + | 0.966822i | \(0.582224\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.9995 | 1.45377 | 0.726883 | − | 0.686761i | \(-0.240968\pi\) | ||||
0.726883 | + | 0.686761i | \(0.240968\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.53687 | 0.101119 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.1946 | 1.25748 | 0.628739 | − | 0.777617i | \(-0.283571\pi\) | ||||
0.628739 | + | 0.777617i | \(0.283571\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.761169 | −0.0496532 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −20.1081 | −1.30616 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.74464 | 0.436274 | 0.218137 | − | 0.975918i | \(-0.430002\pi\) | ||||
0.218137 | + | 0.975918i | \(0.430002\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.1910 | −1.04296 | −0.521478 | − | 0.853264i | \(-0.674619\pi\) | ||||
−0.521478 | + | 0.853264i | \(0.674619\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.50901 | −0.417553 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.216819 | −0.0138521 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.88361 | −0.501622 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.35650 | 0.339454 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.71405 | −0.550026 | −0.275013 | − | 0.961440i | \(-0.588682\pi\) | ||||
−0.275013 | + | 0.961440i | \(0.588682\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.22149 | 0.0767945 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.394225 | 0.0246873 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.6186 | −1.34853 | −0.674265 | − | 0.738489i | \(-0.735540\pi\) | ||||
−0.674265 | + | 0.738489i | \(0.735540\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.61831 | 0.535515 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.32055 | 0.205537 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.8633 | −1.03984 | −0.519918 | − | 0.854216i | \(-0.674038\pi\) | ||||
−0.519918 | + | 0.854216i | \(0.674038\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.37879 | −0.0846984 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.77984 | −0.292522 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.95831 | 0.485227 | 0.242613 | − | 0.970123i | \(-0.421995\pi\) | ||||
0.242613 | + | 0.970123i | \(0.421995\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.64947 | 0.160944 | 0.0804719 | − | 0.996757i | \(-0.474357\pi\) | ||||
0.0804719 | + | 0.996757i | \(0.474357\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.53687 | 0.0930157 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.95299 | 0.298677 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.8295 | −0.951103 | −0.475551 | − | 0.879688i | \(-0.657751\pi\) | ||||
−0.475551 | + | 0.879688i | \(0.657751\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.06400 | 0.183437 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.7268 | 0.818871 | 0.409436 | − | 0.912339i | \(-0.365726\pi\) | ||||
0.409436 | + | 0.912339i | \(0.365726\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −33.1130 | −1.96836 | −0.984181 | − | 0.177169i | \(-0.943306\pi\) | ||||
−0.984181 | + | 0.177169i | \(0.943306\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.62700 | 0.155610 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.95896 | −0.469802 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6004 | −0.917668 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.01217 | 0.293819 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −30.8767 | −1.80384 | −0.901919 | − | 0.431905i | \(-0.857842\pi\) | ||||
−0.901919 | + | 0.431905i | \(0.857842\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.917903 | 0.0534424 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.59118 | −0.324433 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.22149 | 0.0706406 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.91246 | −0.225510 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −18.1145 | −1.04065 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.135311 | 0.00774788 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.9074 | −1.76398 | −0.881990 | − | 0.471268i | \(-0.843796\pi\) | ||||
−0.881990 | + | 0.471268i | \(0.843796\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24.5157 | 1.39465 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.5426 | 1.22157 | 0.610785 | − | 0.791796i | \(-0.290854\pi\) | ||||
0.610785 | + | 0.791796i | \(0.290854\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.1297 | −1.47694 | −0.738470 | − | 0.674286i | \(-0.764451\pi\) | ||||
−0.738470 | + | 0.674286i | \(0.764451\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.138336 | 0.00779436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.7543 | −0.997179 | −0.498590 | − | 0.866838i | \(-0.666148\pi\) | ||||
−0.498590 | + | 0.866838i | \(0.666148\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.20441 | 0.291391 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.27461 | 0.350215 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.32684 | 0.518959 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.95299 | 0.274742 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.7375 | 0.759684 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.51062 | 0.193547 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.34621 | 0.348819 | 0.174410 | − | 0.984673i | \(-0.444198\pi\) | ||||
0.174410 | + | 0.984673i | \(0.444198\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.49870 | −0.301327 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.02902 | −0.0562216 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.4535 | −1.33206 | −0.666032 | − | 0.745923i | \(-0.732009\pi\) | ||||
−0.666032 | + | 0.745923i | \(0.732009\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.4226 | −0.620389 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.80232 | 0.260060 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.407029 | −0.0219137 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.7975 | −0.848057 | −0.424028 | − | 0.905649i | \(-0.639384\pi\) | ||||
−0.424028 | + | 0.905649i | \(0.639384\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.3768 | −0.608988 | −0.304494 | − | 0.952514i | \(-0.598487\pi\) | ||||
−0.304494 | + | 0.952514i | \(0.598487\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.59118 | −0.298435 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.1377 | 1.33795 | 0.668973 | − | 0.743287i | \(-0.266734\pi\) | ||||
0.668973 | + | 0.743287i | \(0.266734\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.97593 | 0.157946 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.81822 | −0.0962306 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.7034 | 1.03991 | 0.519954 | − | 0.854195i | \(-0.325949\pi\) | ||||
0.519954 | + | 0.854195i | \(0.325949\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 43.1513 | 2.27112 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.53687 | −0.0806648 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.49457 | −0.182914 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.32182 | 0.173398 | 0.0866988 | − | 0.996235i | \(-0.472368\pi\) | ||||
0.0866988 | + | 0.996235i | \(0.472368\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.07802 | 0.264351 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.35917 | 0.330152 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.60634 | 0.186729 | 0.0933645 | − | 0.995632i | \(-0.470238\pi\) | ||||
0.0933645 | + | 0.995632i | \(0.470238\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.31656 | −0.171267 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.20441 | 0.268041 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.21587 | 0.319288 | 0.159644 | − | 0.987175i | \(-0.448965\pi\) | ||||
0.159644 | + | 0.987175i | \(0.448965\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.69824 | −0.0870033 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.4018 | −0.582607 | −0.291303 | − | 0.956631i | \(-0.594089\pi\) | ||||
−0.291303 | + | 0.956631i | \(0.594089\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.216819 | 0.0110501 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.49625 | 0.126891 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.4648 | −0.682692 | −0.341346 | − | 0.939938i | \(-0.610883\pi\) | ||||
−0.341346 | + | 0.939938i | \(0.610883\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.44511 | −0.0730822 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.6736 | 1.04284 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.83681 | −0.142735 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.9250 | 0.799254 | 0.399627 | − | 0.916678i | \(-0.369140\pi\) | ||||
0.399627 | + | 0.916678i | \(0.369140\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.1161 | −0.606563 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.83195 | 0.391109 | 0.195555 | − | 0.980693i | \(-0.437349\pi\) | ||||
0.195555 | + | 0.980693i | \(0.437349\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.80232 | 0.239220 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.44810 | 0.0719567 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.61831 | −0.427194 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.3616 | −1.55073 | −0.775367 | − | 0.631511i | \(-0.782435\pi\) | ||||
−0.775367 | + | 0.631511i | \(0.782435\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.89508 | −0.389436 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.23350 | −0.208317 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.755685 | 0.0370951 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.89508 | −0.239713 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.0041 | 1.56350 | 0.781751 | − | 0.623591i | \(-0.214327\pi\) | ||||
0.781751 | + | 0.623591i | \(0.214327\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.0636 | −0.539208 | −0.269604 | − | 0.962971i | \(-0.586893\pi\) | ||||
−0.269604 | + | 0.962971i | \(0.586893\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.23987 | −0.108906 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.85972 | −0.284238 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.624073 | −0.0302010 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.53687 | −0.0742009 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.5456 | −0.845142 | −0.422571 | − | 0.906330i | \(-0.638872\pi\) | ||||
−0.422571 | + | 0.906330i | \(0.638872\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.7819 | 1.76763 | 0.883814 | − | 0.467839i | \(-0.154967\pi\) | ||||
0.883814 | + | 0.467839i | \(0.154967\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.73423 | −0.0831499 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.62975 | −0.460654 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.35920 | −0.208053 | −0.104027 | − | 0.994575i | \(-0.533173\pi\) | ||||
−0.104027 | + | 0.994575i | \(0.533173\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.638026 | −0.0303822 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.75163 | −0.463314 | −0.231657 | − | 0.972798i | \(-0.574415\pi\) | ||||
−0.231657 | + | 0.972798i | \(0.574415\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.674331 | −0.0319664 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.2299 | 0.673052 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.07433 | −0.333858 | −0.166929 | − | 0.985969i | \(-0.553385\pi\) | ||||
−0.166929 | + | 0.985969i | \(0.553385\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.95896 | 0.374773 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.97415 | 0.468626 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.216819 | 0.0101646 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.9154 | 0.884823 | 0.442412 | − | 0.896812i | \(-0.354123\pi\) | ||||
0.442412 | + | 0.896812i | \(0.354123\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.61474 | 0.308750 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.96871 | −0.417714 | −0.208857 | − | 0.977946i | \(-0.566974\pi\) | ||||
−0.208857 | + | 0.977946i | \(0.566974\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.7098 | −0.497728 | −0.248864 | − | 0.968538i | \(-0.580057\pi\) | ||||
−0.248864 | + | 0.968538i | \(0.580057\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.60024 | −0.0742094 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.1611 | −1.30314 | −0.651571 | − | 0.758588i | \(-0.725890\pi\) | ||||
−0.651571 | + | 0.758588i | \(0.725890\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.74600 | 0.219150 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.9831 | −0.736460 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.91246 | 0.179895 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −39.0474 | −1.79162 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.05732 | −0.185772 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.12403 | 0.0970494 | 0.0485247 | − | 0.998822i | \(-0.484548\pi\) | ||||
0.0485247 | + | 0.998822i | \(0.484548\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.61831 | −0.392961 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.87727 | 0.0854189 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.707108 | 0.0321081 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.5415 | 0.930822 | 0.465411 | − | 0.885095i | \(-0.345907\pi\) | ||||
0.465411 | + | 0.885095i | \(0.345907\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.0055 | 1.08557 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.18566 | −0.279155 | −0.139577 | − | 0.990211i | \(-0.544574\pi\) | ||||
−0.139577 | + | 0.990211i | \(0.544574\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.15717 | −0.277305 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.138336 | −0.00621775 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.7254 | −0.615668 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.87923 | −0.263190 | −0.131595 | − | 0.991304i | \(-0.542010\pi\) | ||||
−0.131595 | + | 0.991304i | \(0.542010\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −26.6777 | −1.19187 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.7941 | −1.81892 | −0.909460 | − | 0.415791i | \(-0.863505\pi\) | ||||
−0.909460 | + | 0.415791i | \(0.863505\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.55556 | −0.113721 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.53687 | −0.0682549 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.7132 | −1.13972 | −0.569858 | − | 0.821743i | \(-0.693002\pi\) | ||||
−0.569858 | + | 0.821743i | \(0.693002\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.1174 | 0.712994 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 44.0787 | 1.94612 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.45863 | 0.152406 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.51062 | −0.154397 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 35.3685 | 1.55250 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.0574 | −1.53589 | −0.767947 | − | 0.640513i | \(-0.778722\pi\) | ||||
−0.767947 | + | 0.640513i | \(0.778722\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.2540 | −1.19174 | −0.595868 | − | 0.803082i | \(-0.703192\pi\) | ||||
−0.595868 | + | 0.803082i | \(0.703192\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.61211 | 0.332220 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.68147 | −0.247489 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.5080 | −0.935129 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.70108 | 0.117217 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.95896 | 0.344741 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.885210 | 0.0382710 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23.4062 | 1.01005 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.6761 | −1.74880 | −0.874401 | − | 0.485204i | \(-0.838745\pi\) | ||||
−0.874401 | + | 0.485204i | \(0.838745\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.8087 | 0.506761 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.93806 | 0.0830172 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.1108 | 1.50123 | 0.750615 | − | 0.660740i | \(-0.229758\pi\) | ||||
0.750615 | + | 0.660740i | \(0.229758\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.398175 | 0.0169937 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −41.0295 | −1.74792 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.0838 | 0.556378 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.87182 | 0.121902 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.7242 | −1.64080 | −0.820399 | − | 0.571791i | \(-0.806249\pi\) | ||||
−0.820399 | + | 0.571791i | \(0.806249\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.91246 | 0.165479 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.81822 | 0.0767654 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.6682 | −1.16608 | −0.583038 | − | 0.812445i | \(-0.698136\pi\) | ||||
−0.583038 | + | 0.812445i | \(0.698136\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.61147 | −0.0677952 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.67884 | −0.280485 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.3371 | 1.02026 | 0.510132 | − | 0.860096i | \(-0.329597\pi\) | ||||
0.510132 | + | 0.860096i | \(0.329597\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.19074 | −0.175377 | −0.0876886 | − | 0.996148i | \(-0.527948\pi\) | ||||
−0.0876886 | + | 0.996148i | \(0.527948\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 34.5982 | 1.44536 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.05003 | 0.252304 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.6102 | 1.64900 | 0.824498 | − | 0.565866i | \(-0.191458\pi\) | ||||
0.824498 | + | 0.565866i | \(0.191458\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −30.6270 | −1.27282 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.48532 | −0.144596 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.35917 | −0.263370 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.138336 | −0.00571950 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −45.5309 | −1.87926 | −0.939631 | − | 0.342188i | \(-0.888832\pi\) | ||||
−0.939631 | + | 0.342188i | \(0.888832\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −37.8596 | −1.55998 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −31.2757 | −1.28651 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.1339 | −0.580408 | −0.290204 | − | 0.956965i | \(-0.593723\pi\) | ||||
−0.290204 | + | 0.956965i | \(0.593723\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.256512 | −0.0105159 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.8867 | −0.609272 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.9941 | 0.776077 | 0.388039 | − | 0.921643i | \(-0.373153\pi\) | ||||
0.388039 | + | 0.921643i | \(0.373153\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.8536 | −1.01380 | −0.506899 | − | 0.862005i | \(-0.669208\pi\) | ||||
−0.506899 | + | 0.862005i | \(0.669208\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.02807 | −0.123313 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.216819 | −0.00881495 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.1691 | −1.30570 | −0.652852 | − | 0.757486i | \(-0.726427\pi\) | ||||
−0.652852 | + | 0.757486i | \(0.726427\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.99850 | 0.324116 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.51062 | −0.142025 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.8049 | 1.56732 | 0.783658 | − | 0.621192i | \(-0.213351\pi\) | ||||
0.783658 | + | 0.621192i | \(0.213351\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.65211 | −0.106943 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.1541 | 0.408788 | 0.204394 | − | 0.978889i | \(-0.434478\pi\) | ||||
0.204394 | + | 0.978889i | \(0.434478\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.67915 | 0.0674908 | 0.0337454 | − | 0.999430i | \(-0.489256\pi\) | ||||
0.0337454 | + | 0.999430i | \(0.489256\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.82957 | −0.274061 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.11011 | 0.124604 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.2971 | 0.971882 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.1161 | 0.483870 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.1960 | 0.406543 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.3599 | −0.850323 | −0.425161 | − | 0.905118i | \(-0.639783\pi\) | ||||
−0.425161 | + | 0.905118i | \(0.639783\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.7941 | 0.548265 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.239584 | −0.00950761 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.75716 | 0.346428 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.7163 | 0.620755 | 0.310378 | − | 0.950613i | \(-0.399544\pi\) | ||||
0.310378 | + | 0.950613i | \(0.399544\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.1370 | 0.399766 | 0.199883 | − | 0.979820i | \(-0.435944\pi\) | ||||
0.199883 | + | 0.979820i | \(0.435944\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.30372 | −0.0513339 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −36.0162 | −1.41594 | −0.707972 | − | 0.706241i | \(-0.750390\pi\) | ||||
−0.707972 | + | 0.706241i | \(0.750390\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.23350 | 0.166179 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.38054 | 0.289266 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.4509 | −0.917705 | −0.458853 | − | 0.888512i | \(-0.651739\pi\) | ||||
−0.458853 | + | 0.888512i | \(0.651739\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.91659 | 0.113961 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.2833 | −0.401192 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −43.1008 | −1.67897 | −0.839484 | − | 0.543384i | \(-0.817143\pi\) | ||||
−0.839484 | + | 0.543384i | \(0.817143\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.7391 | −1.58457 | −0.792285 | − | 0.610152i | \(-0.791108\pi\) | ||||
−0.792285 | + | 0.610152i | \(0.791108\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.81822 | 0.0706139 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.70932 | −0.0662844 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.35713 | 0.246149 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22.3482 | −0.864030 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.624073 | 0.0240921 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.4837 | −0.404118 | −0.202059 | − | 0.979373i | \(-0.564763\pi\) | ||||
−0.202059 | + | 0.979373i | \(0.564763\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −27.6930 | −1.06591 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −50.8887 | −1.95581 | −0.977905 | − | 0.209049i | \(-0.932963\pi\) | ||||
−0.977905 | + | 0.209049i | \(0.932963\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.26128 | −0.125157 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.8302 | 0.453333 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.7447 | 1.21468 | 0.607338 | − | 0.794443i | \(-0.292237\pi\) | ||||
0.607338 | + | 0.794443i | \(0.292237\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.11382 | −0.0425570 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −33.8104 | −1.28995 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.35917 | −0.242265 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.9350 | −0.910532 | −0.455266 | − | 0.890356i | \(-0.650456\pi\) | ||||
−0.455266 | + | 0.890356i | \(0.650456\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.638026 | 0.0242366 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.690589 | −0.0261956 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.41598 | −0.356656 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −29.4996 | −1.11578 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.4956 | 1.52950 | 0.764748 | − | 0.644329i | \(-0.222863\pi\) | ||||
0.764748 | + | 0.644329i | \(0.222863\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 67.9433 | 2.56253 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.16982 | 0.0440579 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.7866 | 0.443281 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.3601 | 1.55331 | 0.776655 | − | 0.629926i | \(-0.216915\pi\) | ||||
0.776655 | + | 0.629926i | \(0.216915\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.34778 | −0.313066 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.86599 | 0.219683 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.216819 | −0.00810857 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.3656 | −0.387112 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.2601 | −1.31498 | −0.657490 | − | 0.753464i | \(-0.728382\pi\) | ||||
−0.657490 | + | 0.753464i | \(0.728382\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.9517 | −0.594073 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24.8836 | 0.925429 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.7774 | 0.957348 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −52.5398 | −1.94859 | −0.974297 | − | 0.225268i | \(-0.927674\pi\) | ||||
−0.974297 | + | 0.225268i | \(0.927674\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 30.0400 | 1.11259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.62870 | −0.171199 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −51.6413 | −1.90742 | −0.953708 | − | 0.300734i | \(-0.902768\pi\) | ||||
−0.953708 | + | 0.300734i | \(0.902768\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.333223 | 0.0122911 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.74600 | −0.174821 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.1117 | −1.14446 | −0.572231 | − | 0.820093i | \(-0.693922\pi\) | ||||
−0.572231 | + | 0.820093i | \(0.693922\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.1161 | 0.445096 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.4366 | 0.382883 | 0.191442 | − | 0.981504i | \(-0.438684\pi\) | ||||
0.191442 | + | 0.981504i | \(0.438684\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.00753 | 0.0735503 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.22373 | 0.0813620 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.08272 | −0.149179 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.0188 | −1.20487 | −0.602437 | − | 0.798166i | \(-0.705804\pi\) | ||||
−0.602437 | + | 0.798166i | \(0.705804\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.3924 | 0.488045 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.40713 | 0.0512109 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.0313 | 1.20054 | 0.600272 | − | 0.799796i | \(-0.295059\pi\) | ||||
0.600272 | + | 0.799796i | \(0.295059\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.87727 | −0.0681407 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 47.9565 | 1.73842 | 0.869211 | − | 0.494441i | \(-0.164627\pi\) | ||||
0.869211 | + | 0.494441i | \(0.164627\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.93859 | −0.323599 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.163661 | 0.00591718 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.23350 | 0.152863 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.6963 | −1.14300 | −0.571498 | − | 0.820603i | \(-0.693638\pi\) | ||||
−0.571498 | + | 0.820603i | \(0.693638\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33.2250 | 1.19657 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.39679 | −0.158141 | −0.0790707 | − | 0.996869i | \(-0.525195\pi\) | ||||
−0.0790707 | + | 0.996869i | \(0.525195\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.7858 | 0.854412 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.2452 | −0.475170 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −62.7453 | −2.24808 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.7254 | 0.491133 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −29.0988 | −1.03991 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.25486 | −0.0804794 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.2163 | 1.14839 | 0.574193 | − | 0.818720i | \(-0.305316\pi\) | ||||
0.574193 | + | 0.818720i | \(0.305316\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 25.9168 | 0.922661 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.43235 | 0.264264 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.624073 | 0.0221615 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.11902 | 0.0751540 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.19579 | 0.325731 | 0.162866 | − | 0.986648i | \(-0.447926\pi\) | ||||
0.162866 | + | 0.986648i | \(0.447926\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.15330 | 0.146933 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.98433 | −0.0701129 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.1174 | −0.568772 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.264842 | 0.00933447 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.2309 | −0.430548 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.6701 | 1.11346 | 0.556731 | − | 0.830693i | \(-0.312055\pi\) | ||||
0.556731 | + | 0.830693i | \(0.312055\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.2343 | 0.780752 | 0.390376 | − | 0.920655i | \(-0.372345\pi\) | ||||
0.390376 | + | 0.920655i | \(0.372345\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.07189 | −0.142808 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.38666 | 0.118629 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.8443 | −1.07910 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.638026 | 0.0222944 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.0362 | 0.769068 | 0.384534 | − | 0.923111i | \(-0.374362\pi\) | ||||
0.384534 | + | 0.923111i | \(0.374362\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.29612 | 0.254327 | 0.127163 | − | 0.991882i | \(-0.459413\pi\) | ||||
0.127163 | + | 0.991882i | \(0.459413\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.61211 | −0.265020 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.7818 | 0.479242 | 0.239621 | − | 0.970867i | \(-0.422977\pi\) | ||||
0.239621 | + | 0.970867i | \(0.422977\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.1029 | −0.350888 | −0.175444 | − | 0.984489i | \(-0.556136\pi\) | ||||
−0.175444 | + | 0.984489i | \(0.556136\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.3279 | 0.843926 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.18307 | 0.0409909 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.76363 | −0.130246 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −26.8506 | −0.928093 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.01500 | −0.311232 | −0.155616 | − | 0.987818i | \(-0.549736\pi\) | ||||
−0.155616 | + | 0.987818i | \(0.549736\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.91415 | −0.0660051 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.0963 | −0.726595 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.216819 | −0.00745880 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 50.8904 | 1.74655 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.5272 | −0.360867 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −49.8042 | −1.70526 | −0.852631 | − | 0.522514i | \(-0.824994\pi\) | ||||
−0.852631 | + | 0.522514i | \(0.824994\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.09059 | 0.0372973 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.8500 | −0.370630 | −0.185315 | − | 0.982679i | \(-0.559331\pi\) | ||||
−0.185315 | + | 0.982679i | \(0.559331\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.2324 | 0.417364 | 0.208682 | − | 0.977984i | \(-0.433083\pi\) | ||||
0.208682 | + | 0.977984i | \(0.433083\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.2319 | 0.416862 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.41335 | −0.286394 | −0.143197 | − | 0.989694i | \(-0.545738\pi\) | ||||
−0.143197 | + | 0.989694i | \(0.545738\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.98972 | 0.169656 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.9757 | 0.814259 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.0838 | −0.443836 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.74600 | −0.160812 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.08078 | 0.0704239 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.15800 | 0.0729536 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.242393 | 0.00818503 | 0.00409252 | − | 0.999992i | \(-0.498697\pi\) | ||||
0.00409252 | + | 0.999992i | \(0.498697\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 47.4536 | 1.60057 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.3393 | −0.584176 | −0.292088 | − | 0.956392i | \(-0.594350\pi\) | ||||
−0.292088 | + | 0.956392i | \(0.594350\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.8842 | 1.54413 | 0.772063 | − | 0.635547i | \(-0.219225\pi\) | ||||
0.772063 | + | 0.635547i | \(0.219225\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.41070 | −0.0474201 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −53.7338 | −1.80420 | −0.902102 | − | 0.431523i | \(-0.857976\pi\) | ||||
−0.902102 | + | 0.431523i | \(0.857976\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.10500 | 0.0370604 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.67884 | 0.223750 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.6764 | 0.926154 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.30210 | 0.110377 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.87727 | −0.0626804 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.9932 | 0.833570 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.52333 | 0.250638 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.01294 | 0.200098 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.66595 | 0.0553782 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.15037 | −0.104606 | −0.0523032 | − | 0.998631i | \(-0.516656\pi\) | ||||
−0.0523032 | + | 0.998631i | \(0.516656\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.52016 | −0.249428 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.0568 | 1.32714 | 0.663571 | − | 0.748114i | \(-0.269040\pi\) | ||||
0.663571 | + | 0.748114i | \(0.269040\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.48532 | 0.115347 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.207955 | −0.00687479 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.4517 | −0.444215 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.5917 | 0.349387 | 0.174694 | − | 0.984623i | \(-0.444107\pi\) | ||||
0.174694 | + | 0.984623i | \(0.444107\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 47.5007 | 1.56520 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.7254 | 0.451777 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −42.6864 | −1.40352 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.1776 | 0.334277 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.65036 | 0.119764 | 0.0598822 | − | 0.998205i | \(-0.480927\pi\) | ||||
0.0598822 | + | 0.998205i | \(0.480927\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.88361 | 0.258375 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −33.1082 | −1.08392 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.256512 | 0.00838882 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.2893 | 1.12018 | 0.560091 | − | 0.828431i | \(-0.310766\pi\) | ||||
0.560091 | + | 0.828431i | \(0.310766\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 40.1581 | 1.31051 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.1415 | 1.04778 | 0.523891 | − | 0.851785i | \(-0.324480\pi\) | ||||
0.523891 | + | 0.851785i | \(0.324480\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.72179 | 0.316585 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.21227 | −0.0394353 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.8830 | −0.776093 | −0.388047 | − | 0.921640i | \(-0.626850\pi\) | ||||
−0.388047 | + | 0.921640i | \(0.626850\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.1174 | −0.523194 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.2860 | 0.884810 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.13519 | −0.0691655 | −0.0345828 | − | 0.999402i | \(-0.511010\pi\) | ||||
−0.0345828 | + | 0.999402i | \(0.511010\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.88105 | 0.157947 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.99850 | −0.258555 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.13711 | 0.165886 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.93775 | −0.256057 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.60488 | 0.0839411 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.32080 | −0.139092 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.5940 | −1.53052 | −0.765261 | − | 0.643720i | \(-0.777390\pi\) | ||||
−0.765261 | + | 0.643720i | \(0.777390\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.3342 | −0.460479 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.66802 | −0.213987 | −0.106993 | − | 0.994260i | \(-0.534122\pi\) | ||||
−0.106993 | + | 0.994260i | \(0.534122\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.18510 | 0.102110 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.61211 | −0.243783 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.35855 | −0.267414 | −0.133707 | − | 0.991021i | \(-0.542688\pi\) | ||||
−0.133707 | + | 0.991021i | \(0.542688\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.11011 | −0.0993996 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.70306 | 0.182085 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.9127 | 0.507536 | 0.253768 | − | 0.967265i | \(-0.418330\pi\) | ||||
0.253768 | + | 0.967265i | \(0.418330\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.41232 | −0.140588 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.39537 | −0.171737 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.77903 | 0.151964 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.5861 | 1.22573 | 0.612863 | − | 0.790189i | \(-0.290018\pi\) | ||||
0.612863 | + | 0.790189i | \(0.290018\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.75331 | −0.309512 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.10019 | −0.0665805 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52.4700 | 1.66174 | 0.830871 | − | 0.556465i | \(-0.187843\pi\) | ||||
0.830871 | + | 0.556465i | \(0.187843\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 48.1865 | 1.52455 |
(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 | 8008.2.a.y.1.5 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.y.1.5 | ✓ | 14 | 1.1 | even | 1 | trivial |