Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3675,2,Mod(1,3675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3675.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3675.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: | \(29.3450227428\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} + 11 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 735) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.54336\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3675.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.49721 | 1.76580 | 0.882898 | − | 0.469565i | \(-0.155589\pi\) | ||||
0.882898 | + | 0.469565i | \(0.155589\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.23607 | 2.11803 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.49721 | −1.01948 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 5.58394 | 1.97422 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.47214 | −1.34840 | −0.674200 | − | 0.738549i | \(-0.735511\pi\) | ||||
−0.674200 | + | 0.738549i | \(0.735511\pi\) | |||||||
\(12\) | −4.23607 | −1.22285 | ||||||||
\(13\) | −5.23607 | −1.45222 | −0.726112 | − | 0.687576i | \(-0.758675\pi\) | ||||
−0.726112 | + | 0.687576i | \(0.758675\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.47214 | 1.36803 | ||||||||
\(17\) | −0.763932 | −0.185281 | −0.0926404 | − | 0.995700i | \(-0.529531\pi\) | ||||
−0.0926404 | + | 0.995700i | \(0.529531\pi\) | |||||||
\(18\) | 2.49721 | 0.588599 | ||||||||
\(19\) | −8.08115 | −1.85394 | −0.926971 | − | 0.375132i | \(-0.877597\pi\) | ||||
−0.926971 | + | 0.375132i | \(0.877597\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −11.1679 | −2.38100 | ||||||||
\(23\) | 3.08672 | 0.643626 | 0.321813 | − | 0.946803i | \(-0.395708\pi\) | ||||
0.321813 | + | 0.946803i | \(0.395708\pi\) | |||||||
\(24\) | −5.58394 | −1.13982 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −13.0756 | −2.56433 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.90770 | 0.342633 | 0.171317 | − | 0.985216i | \(-0.445198\pi\) | ||||
0.171317 | + | 0.985216i | \(0.445198\pi\) | |||||||
\(32\) | 2.49721 | 0.441449 | ||||||||
\(33\) | 4.47214 | 0.778499 | ||||||||
\(34\) | −1.90770 | −0.327168 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.23607 | 0.706011 | ||||||||
\(37\) | −6.17345 | −1.01491 | −0.507454 | − | 0.861679i | \(-0.669413\pi\) | ||||
−0.507454 | + | 0.861679i | \(0.669413\pi\) | |||||||
\(38\) | −20.1803 | −3.27368 | ||||||||
\(39\) | 5.23607 | 0.838442 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.90212 | −1.07793 | −0.538965 | − | 0.842328i | \(-0.681185\pi\) | ||||
−0.538965 | + | 0.842328i | \(0.681185\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.98885 | −1.52329 | −0.761643 | − | 0.647997i | \(-0.775607\pi\) | ||||
−0.761643 | + | 0.647997i | \(0.775607\pi\) | |||||||
\(44\) | −18.9443 | −2.85596 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.70820 | 1.13651 | ||||||||
\(47\) | 4.94427 | 0.721196 | 0.360598 | − | 0.932721i | \(-0.382573\pi\) | ||||
0.360598 | + | 0.932721i | \(0.382573\pi\) | |||||||
\(48\) | −5.47214 | −0.789835 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.763932 | 0.106972 | ||||||||
\(52\) | −22.1803 | −3.07586 | ||||||||
\(53\) | 1.90770 | 0.262043 | 0.131021 | − | 0.991380i | \(-0.458174\pi\) | ||||
0.131021 | + | 0.991380i | \(0.458174\pi\) | |||||||
\(54\) | −2.49721 | −0.339828 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.08115 | 1.07037 | ||||||||
\(58\) | 4.99442 | 0.655800 | ||||||||
\(59\) | 9.98885 | 1.30044 | 0.650219 | − | 0.759747i | \(-0.274677\pi\) | ||||
0.650219 | + | 0.759747i | \(0.274677\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.81540 | −0.488512 | −0.244256 | − | 0.969711i | \(-0.578544\pi\) | ||||
−0.244256 | + | 0.969711i | \(0.578544\pi\) | |||||||
\(62\) | 4.76393 | 0.605020 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.70820 | −0.588525 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 11.1679 | 1.37467 | ||||||||
\(67\) | 6.17345 | 0.754207 | 0.377103 | − | 0.926171i | \(-0.376920\pi\) | ||||
0.377103 | + | 0.926171i | \(0.376920\pi\) | |||||||
\(68\) | −3.23607 | −0.392431 | ||||||||
\(69\) | −3.08672 | −0.371598 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.472136 | 0.0560322 | 0.0280161 | − | 0.999607i | \(-0.491081\pi\) | ||||
0.0280161 | + | 0.999607i | \(0.491081\pi\) | |||||||
\(72\) | 5.58394 | 0.658073 | ||||||||
\(73\) | −2.76393 | −0.323494 | −0.161747 | − | 0.986832i | \(-0.551713\pi\) | ||||
−0.161747 | + | 0.986832i | \(0.551713\pi\) | |||||||
\(74\) | −15.4164 | −1.79212 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −34.2323 | −3.92671 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 13.0756 | 1.48052 | ||||||||
\(79\) | 12.9443 | 1.45634 | 0.728172 | − | 0.685394i | \(-0.240370\pi\) | ||||
0.728172 | + | 0.685394i | \(0.240370\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −17.2361 | −1.90341 | ||||||||
\(83\) | −6.47214 | −0.710409 | −0.355205 | − | 0.934789i | \(-0.615589\pi\) | ||||
−0.355205 | + | 0.934789i | \(0.615589\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −24.9443 | −2.68981 | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | −24.9721 | −2.66204 | ||||||||
\(89\) | 9.26017 | 0.981576 | 0.490788 | − | 0.871279i | \(-0.336709\pi\) | ||||
0.490788 | + | 0.871279i | \(0.336709\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 13.0756 | 1.36322 | ||||||||
\(93\) | −1.90770 | −0.197819 | ||||||||
\(94\) | 12.3469 | 1.27349 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.49721 | −0.254871 | ||||||||
\(97\) | −10.1803 | −1.03366 | −0.516828 | − | 0.856089i | \(-0.672887\pi\) | ||||
−0.516828 | + | 0.856089i | \(0.672887\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.47214 | −0.449467 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.0756 | 1.30107 | 0.650534 | − | 0.759477i | \(-0.274545\pi\) | ||||
0.650534 | + | 0.759477i | \(0.274545\pi\) | |||||||
\(102\) | 1.90770 | 0.188890 | ||||||||
\(103\) | −1.52786 | −0.150545 | −0.0752725 | − | 0.997163i | \(-0.523983\pi\) | ||||
−0.0752725 | + | 0.997163i | \(0.523983\pi\) | |||||||
\(104\) | −29.2379 | −2.86701 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.76393 | 0.462714 | ||||||||
\(107\) | −6.90212 | −0.667254 | −0.333627 | − | 0.942705i | \(-0.608273\pi\) | ||||
−0.333627 | + | 0.942705i | \(0.608273\pi\) | |||||||
\(108\) | −4.23607 | −0.407616 | ||||||||
\(109\) | 12.4721 | 1.19461 | 0.597307 | − | 0.802013i | \(-0.296237\pi\) | ||||
0.597307 | + | 0.802013i | \(0.296237\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.17345 | 0.585958 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.26575 | −0.401288 | −0.200644 | − | 0.979664i | \(-0.564303\pi\) | ||||
−0.200644 | + | 0.979664i | \(0.564303\pi\) | |||||||
\(114\) | 20.1803 | 1.89006 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.47214 | 0.786618 | ||||||||
\(117\) | −5.23607 | −0.484075 | ||||||||
\(118\) | 24.9443 | 2.29631 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | −9.52786 | −0.862612 | ||||||||
\(123\) | 6.90212 | 0.622344 | ||||||||
\(124\) | 8.08115 | 0.725709 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.81540 | −0.338562 | −0.169281 | − | 0.985568i | \(-0.554145\pi\) | ||||
−0.169281 | + | 0.985568i | \(0.554145\pi\) | |||||||
\(128\) | −16.7518 | −1.48066 | ||||||||
\(129\) | 9.98885 | 0.879469 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.98885 | −0.872730 | −0.436365 | − | 0.899770i | \(-0.643734\pi\) | ||||
−0.436365 | + | 0.899770i | \(0.643734\pi\) | |||||||
\(132\) | 18.9443 | 1.64889 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 15.4164 | 1.33177 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.26575 | −0.365785 | ||||||||
\(137\) | −8.08115 | −0.690419 | −0.345210 | − | 0.938526i | \(-0.612192\pi\) | ||||
−0.345210 | + | 0.938526i | \(0.612192\pi\) | |||||||
\(138\) | −7.70820 | −0.656166 | ||||||||
\(139\) | 14.2546 | 1.20906 | 0.604530 | − | 0.796583i | \(-0.293361\pi\) | ||||
0.604530 | + | 0.796583i | \(0.293361\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.94427 | −0.416383 | ||||||||
\(142\) | 1.17902 | 0.0989415 | ||||||||
\(143\) | 23.4164 | 1.95818 | ||||||||
\(144\) | 5.47214 | 0.456011 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.90212 | −0.571224 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −26.1511 | −2.14961 | ||||||||
\(149\) | −18.9443 | −1.55198 | −0.775988 | − | 0.630748i | \(-0.782748\pi\) | ||||
−0.775988 | + | 0.630748i | \(0.782748\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.94427 | −0.727875 | −0.363937 | − | 0.931423i | \(-0.618568\pi\) | ||||
−0.363937 | + | 0.931423i | \(0.618568\pi\) | |||||||
\(152\) | −45.1246 | −3.66009 | ||||||||
\(153\) | −0.763932 | −0.0617602 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 22.1803 | 1.77585 | ||||||||
\(157\) | 8.65248 | 0.690543 | 0.345271 | − | 0.938503i | \(-0.387787\pi\) | ||||
0.345271 | + | 0.938503i | \(0.387787\pi\) | |||||||
\(158\) | 32.3246 | 2.57161 | ||||||||
\(159\) | −1.90770 | −0.151290 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.49721 | 0.196200 | ||||||||
\(163\) | 3.81540 | 0.298845 | 0.149423 | − | 0.988773i | \(-0.452259\pi\) | ||||
0.149423 | + | 0.988773i | \(0.452259\pi\) | |||||||
\(164\) | −29.2379 | −2.28309 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.1623 | −1.25444 | ||||||||
\(167\) | 15.4164 | 1.19296 | 0.596479 | − | 0.802629i | \(-0.296566\pi\) | ||||
0.596479 | + | 0.802629i | \(0.296566\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.4164 | 1.10895 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.08115 | −0.617981 | ||||||||
\(172\) | −42.3134 | −3.22637 | ||||||||
\(173\) | −19.2361 | −1.46249 | −0.731246 | − | 0.682114i | \(-0.761061\pi\) | ||||
−0.731246 | + | 0.682114i | \(0.761061\pi\) | |||||||
\(174\) | −4.99442 | −0.378626 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −24.4721 | −1.84466 | ||||||||
\(177\) | −9.98885 | −0.750808 | ||||||||
\(178\) | 23.1246 | 1.73326 | ||||||||
\(179\) | −7.52786 | −0.562659 | −0.281329 | − | 0.959611i | \(-0.590775\pi\) | ||||
−0.281329 | + | 0.959611i | \(0.590775\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.98885 | 0.742465 | 0.371233 | − | 0.928540i | \(-0.378935\pi\) | ||||
0.371233 | + | 0.928540i | \(0.378935\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.81540 | 0.282043 | ||||||||
\(184\) | 17.2361 | 1.27066 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.76393 | −0.349308 | ||||||||
\(187\) | 3.41641 | 0.249832 | ||||||||
\(188\) | 20.9443 | 1.52752 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.52786 | −0.255267 | −0.127634 | − | 0.991821i | \(-0.540738\pi\) | ||||
−0.127634 | + | 0.991821i | \(0.540738\pi\) | |||||||
\(192\) | 4.70820 | 0.339785 | ||||||||
\(193\) | −13.8042 | −0.993652 | −0.496826 | − | 0.867850i | \(-0.665501\pi\) | ||||
−0.496826 | + | 0.867850i | \(0.665501\pi\) | |||||||
\(194\) | −25.4225 | −1.82523 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.90770 | −0.135918 | −0.0679590 | − | 0.997688i | \(-0.521649\pi\) | ||||
−0.0679590 | + | 0.997688i | \(0.521649\pi\) | |||||||
\(198\) | −11.1679 | −0.793666 | ||||||||
\(199\) | 11.8965 | 0.843324 | 0.421662 | − | 0.906753i | \(-0.361447\pi\) | ||||
0.421662 | + | 0.906753i | \(0.361447\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.17345 | −0.435441 | ||||||||
\(202\) | 32.6525 | 2.29742 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.23607 | 0.226570 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.81540 | −0.265832 | ||||||||
\(207\) | 3.08672 | 0.214542 | ||||||||
\(208\) | −28.6525 | −1.98669 | ||||||||
\(209\) | 36.1400 | 2.49986 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.9443 | −0.891120 | −0.445560 | − | 0.895252i | \(-0.646995\pi\) | ||||
−0.445560 | + | 0.895252i | \(0.646995\pi\) | |||||||
\(212\) | 8.08115 | 0.555016 | ||||||||
\(213\) | −0.472136 | −0.0323502 | ||||||||
\(214\) | −17.2361 | −1.17823 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.58394 | −0.379939 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 31.1456 | 2.10944 | ||||||||
\(219\) | 2.76393 | 0.186769 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.00000 | 0.269069 | ||||||||
\(222\) | 15.4164 | 1.03468 | ||||||||
\(223\) | 17.8885 | 1.19791 | 0.598953 | − | 0.800784i | \(-0.295584\pi\) | ||||
0.598953 | + | 0.800784i | \(0.295584\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.6525 | −0.708592 | ||||||||
\(227\) | 1.52786 | 0.101408 | 0.0507039 | − | 0.998714i | \(-0.483854\pi\) | ||||
0.0507039 | + | 0.998714i | \(0.483854\pi\) | |||||||
\(228\) | 34.2323 | 2.26709 | ||||||||
\(229\) | −22.3357 | −1.47599 | −0.737994 | − | 0.674808i | \(-0.764227\pi\) | ||||
−0.737994 | + | 0.674808i | \(0.764227\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.1679 | 0.733207 | ||||||||
\(233\) | −11.8965 | −0.779369 | −0.389684 | − | 0.920948i | \(-0.627416\pi\) | ||||
−0.389684 | + | 0.920948i | \(0.627416\pi\) | |||||||
\(234\) | −13.0756 | −0.854777 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 42.3134 | 2.75437 | ||||||||
\(237\) | −12.9443 | −0.840821 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.52786 | −0.486937 | −0.243469 | − | 0.969909i | \(-0.578285\pi\) | ||||
−0.243469 | + | 0.969909i | \(0.578285\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.17345 | 0.397667 | 0.198833 | − | 0.980033i | \(-0.436285\pi\) | ||||
0.198833 | + | 0.980033i | \(0.436285\pi\) | |||||||
\(242\) | 22.4749 | 1.44474 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −16.1623 | −1.03468 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 17.2361 | 1.09893 | ||||||||
\(247\) | 42.3134 | 2.69234 | ||||||||
\(248\) | 10.6525 | 0.676433 | ||||||||
\(249\) | 6.47214 | 0.410155 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.35805 | −0.148839 | −0.0744193 | − | 0.997227i | \(-0.523710\pi\) | ||||
−0.0744193 | + | 0.997227i | \(0.523710\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.8042 | −0.867866 | ||||||||
\(254\) | −9.52786 | −0.597831 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.4164 | −2.02603 | ||||||||
\(257\) | −21.7082 | −1.35412 | −0.677060 | − | 0.735928i | \(-0.736746\pi\) | ||||
−0.677060 | + | 0.735928i | \(0.736746\pi\) | |||||||
\(258\) | 24.9443 | 1.55296 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | −24.9443 | −1.54106 | ||||||||
\(263\) | −15.4336 | −0.951678 | −0.475839 | − | 0.879532i | \(-0.657855\pi\) | ||||
−0.475839 | + | 0.879532i | \(0.657855\pi\) | |||||||
\(264\) | 24.9721 | 1.53693 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.26017 | −0.566713 | ||||||||
\(268\) | 26.1511 | 1.59744 | ||||||||
\(269\) | 6.90212 | 0.420830 | 0.210415 | − | 0.977612i | \(-0.432518\pi\) | ||||
0.210415 | + | 0.977612i | \(0.432518\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.0700 | 1.09767 | 0.548837 | − | 0.835929i | \(-0.315071\pi\) | ||||
0.548837 | + | 0.835929i | \(0.315071\pi\) | |||||||
\(272\) | −4.18034 | −0.253470 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.1803 | −1.21914 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −13.0756 | −0.787057 | ||||||||
\(277\) | 9.98885 | 0.600172 | 0.300086 | − | 0.953912i | \(-0.402985\pi\) | ||||
0.300086 | + | 0.953912i | \(0.402985\pi\) | |||||||
\(278\) | 35.5967 | 2.13495 | ||||||||
\(279\) | 1.90770 | 0.114211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.0000 | −1.31241 | −0.656205 | − | 0.754583i | \(-0.727839\pi\) | ||||
−0.656205 | + | 0.754583i | \(0.727839\pi\) | |||||||
\(282\) | −12.3469 | −0.735247 | ||||||||
\(283\) | −12.3607 | −0.734766 | −0.367383 | − | 0.930070i | \(-0.619746\pi\) | ||||
−0.367383 | + | 0.930070i | \(0.619746\pi\) | |||||||
\(284\) | 2.00000 | 0.118678 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 58.4757 | 3.45774 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.49721 | 0.147150 | ||||||||
\(289\) | −16.4164 | −0.965671 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.1803 | 0.596782 | ||||||||
\(292\) | −11.7082 | −0.685171 | ||||||||
\(293\) | −20.1803 | −1.17895 | −0.589474 | − | 0.807787i | \(-0.700665\pi\) | ||||
−0.589474 | + | 0.807787i | \(0.700665\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −34.4721 | −2.00365 | ||||||||
\(297\) | 4.47214 | 0.259500 | ||||||||
\(298\) | −47.3079 | −2.74047 | ||||||||
\(299\) | −16.1623 | −0.934690 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −22.3357 | −1.28528 | ||||||||
\(303\) | −13.0756 | −0.751172 | ||||||||
\(304\) | −44.2211 | −2.53626 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.90770 | −0.109056 | ||||||||
\(307\) | −2.47214 | −0.141092 | −0.0705461 | − | 0.997509i | \(-0.522474\pi\) | ||||
−0.0705461 | + | 0.997509i | \(0.522474\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.52786 | 0.0869171 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.81540 | 0.216352 | 0.108176 | − | 0.994132i | \(-0.465499\pi\) | ||||
0.108176 | + | 0.994132i | \(0.465499\pi\) | |||||||
\(312\) | 29.2379 | 1.65527 | ||||||||
\(313\) | −24.6525 | −1.39344 | −0.696720 | − | 0.717343i | \(-0.745358\pi\) | ||||
−0.696720 | + | 0.717343i | \(0.745358\pi\) | |||||||
\(314\) | 21.6071 | 1.21936 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 54.8328 | 3.08459 | ||||||||
\(317\) | −10.4392 | −0.586324 | −0.293162 | − | 0.956063i | \(-0.594707\pi\) | ||||
−0.293162 | + | 0.956063i | \(0.594707\pi\) | |||||||
\(318\) | −4.76393 | −0.267148 | ||||||||
\(319\) | −8.94427 | −0.500783 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.90212 | 0.385239 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.17345 | 0.343500 | ||||||||
\(324\) | 4.23607 | 0.235337 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.52786 | 0.527700 | ||||||||
\(327\) | −12.4721 | −0.689711 | ||||||||
\(328\) | −38.5410 | −2.12807 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | −27.4164 | −1.50467 | ||||||||
\(333\) | −6.17345 | −0.338303 | ||||||||
\(334\) | 38.4980 | 2.10652 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.81540 | −0.207838 | −0.103919 | − | 0.994586i | \(-0.533138\pi\) | ||||
−0.103919 | + | 0.994586i | \(0.533138\pi\) | |||||||
\(338\) | 36.0008 | 1.95819 | ||||||||
\(339\) | 4.26575 | 0.231684 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.53149 | −0.462006 | ||||||||
\(342\) | −20.1803 | −1.09123 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −55.7771 | −3.00730 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −48.0365 | −2.58246 | ||||||||
\(347\) | 25.4225 | 1.36475 | 0.682375 | − | 0.731003i | \(-0.260947\pi\) | ||||
0.682375 | + | 0.731003i | \(0.260947\pi\) | |||||||
\(348\) | −8.47214 | −0.454154 | ||||||||
\(349\) | −8.53149 | −0.456680 | −0.228340 | − | 0.973581i | \(-0.573330\pi\) | ||||
−0.228340 | + | 0.973581i | \(0.573330\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.23607 | 0.279481 | ||||||||
\(352\) | −11.1679 | −0.595250 | ||||||||
\(353\) | 3.23607 | 0.172239 | 0.0861193 | − | 0.996285i | \(-0.472553\pi\) | ||||
0.0861193 | + | 0.996285i | \(0.472553\pi\) | |||||||
\(354\) | −24.9443 | −1.32577 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 39.2267 | 2.07901 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.7987 | −0.993541 | ||||||||
\(359\) | 20.4721 | 1.08048 | 0.540239 | − | 0.841512i | \(-0.318334\pi\) | ||||
0.540239 | + | 0.841512i | \(0.318334\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 46.3050 | 2.43710 | ||||||||
\(362\) | 24.9443 | 1.31104 | ||||||||
\(363\) | −9.00000 | −0.472377 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.52786 | 0.498029 | ||||||||
\(367\) | 16.0000 | 0.835193 | 0.417597 | − | 0.908633i | \(-0.362873\pi\) | ||||
0.417597 | + | 0.908633i | \(0.362873\pi\) | |||||||
\(368\) | 16.8910 | 0.880503 | ||||||||
\(369\) | −6.90212 | −0.359310 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −8.08115 | −0.418988 | ||||||||
\(373\) | 32.3246 | 1.67370 | 0.836852 | − | 0.547429i | \(-0.184393\pi\) | ||||
0.836852 | + | 0.547429i | \(0.184393\pi\) | |||||||
\(374\) | 8.53149 | 0.441153 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 27.6085 | 1.42380 | ||||||||
\(377\) | −10.4721 | −0.539342 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.05573 | 0.156962 | 0.0784811 | − | 0.996916i | \(-0.474993\pi\) | ||||
0.0784811 | + | 0.996916i | \(0.474993\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.81540 | 0.195469 | ||||||||
\(382\) | −8.80982 | −0.450750 | ||||||||
\(383\) | −10.4721 | −0.535101 | −0.267551 | − | 0.963544i | \(-0.586214\pi\) | ||||
−0.267551 | + | 0.963544i | \(0.586214\pi\) | |||||||
\(384\) | 16.7518 | 0.854862 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −34.4721 | −1.75459 | ||||||||
\(387\) | −9.98885 | −0.507762 | ||||||||
\(388\) | −43.1246 | −2.18932 | ||||||||
\(389\) | −11.8885 | −0.602773 | −0.301387 | − | 0.953502i | \(-0.597449\pi\) | ||||
−0.301387 | + | 0.953502i | \(0.597449\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.35805 | −0.119252 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.98885 | 0.503871 | ||||||||
\(394\) | −4.76393 | −0.240003 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −18.9443 | −0.951985 | ||||||||
\(397\) | 9.23607 | 0.463545 | 0.231772 | − | 0.972770i | \(-0.425548\pi\) | ||||
0.231772 | + | 0.972770i | \(0.425548\pi\) | |||||||
\(398\) | 29.7082 | 1.48914 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.8328 | 1.83934 | 0.919672 | − | 0.392689i | \(-0.128455\pi\) | ||||
0.919672 | + | 0.392689i | \(0.128455\pi\) | |||||||
\(402\) | −15.4164 | −0.768901 | ||||||||
\(403\) | −9.98885 | −0.497580 | ||||||||
\(404\) | 55.3890 | 2.75571 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 27.6085 | 1.36850 | ||||||||
\(408\) | 4.26575 | 0.211186 | ||||||||
\(409\) | 33.7819 | 1.67041 | 0.835205 | − | 0.549939i | \(-0.185349\pi\) | ||||
0.835205 | + | 0.549939i | \(0.185349\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.08115 | 0.398614 | ||||||||
\(412\) | −6.47214 | −0.318859 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 7.70820 | 0.378838 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −13.0756 | −0.641083 | ||||||||
\(417\) | −14.2546 | −0.698051 | ||||||||
\(418\) | 90.2492 | 4.41423 | ||||||||
\(419\) | 1.45735 | 0.0711964 | 0.0355982 | − | 0.999366i | \(-0.488666\pi\) | ||||
0.0355982 | + | 0.999366i | \(0.488666\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.4721 | 0.802803 | 0.401401 | − | 0.915902i | \(-0.368523\pi\) | ||||
0.401401 | + | 0.915902i | \(0.368523\pi\) | |||||||
\(422\) | −32.3246 | −1.57354 | ||||||||
\(423\) | 4.94427 | 0.240399 | ||||||||
\(424\) | 10.6525 | 0.517330 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.17902 | −0.0571239 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −29.2379 | −1.41327 | ||||||||
\(429\) | −23.4164 | −1.13055 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.47214 | −0.215415 | −0.107708 | − | 0.994183i | \(-0.534351\pi\) | ||||
−0.107708 | + | 0.994183i | \(0.534351\pi\) | |||||||
\(432\) | −5.47214 | −0.263278 | ||||||||
\(433\) | −35.7082 | −1.71603 | −0.858013 | − | 0.513627i | \(-0.828301\pi\) | ||||
−0.858013 | + | 0.513627i | \(0.828301\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 52.8328 | 2.53023 | ||||||||
\(437\) | −24.9443 | −1.19325 | ||||||||
\(438\) | 6.90212 | 0.329796 | ||||||||
\(439\) | 24.2434 | 1.15708 | 0.578538 | − | 0.815655i | \(-0.303623\pi\) | ||||
0.578538 | + | 0.815655i | \(0.303623\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.98885 | 0.475121 | ||||||||
\(443\) | −31.5959 | −1.50117 | −0.750584 | − | 0.660775i | \(-0.770228\pi\) | ||||
−0.750584 | + | 0.660775i | \(0.770228\pi\) | |||||||
\(444\) | 26.1511 | 1.24108 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 44.6715 | 2.11526 | ||||||||
\(447\) | 18.9443 | 0.896033 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.0557 | −0.804910 | −0.402455 | − | 0.915440i | \(-0.631843\pi\) | ||||
−0.402455 | + | 0.915440i | \(0.631843\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.8672 | 1.45348 | ||||||||
\(452\) | −18.0700 | −0.849941 | ||||||||
\(453\) | 8.94427 | 0.420239 | ||||||||
\(454\) | 3.81540 | 0.179066 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 45.1246 | 2.11315 | ||||||||
\(457\) | 23.7931 | 1.11299 | 0.556497 | − | 0.830850i | \(-0.312145\pi\) | ||||
0.556497 | + | 0.830850i | \(0.312145\pi\) | |||||||
\(458\) | −55.7771 | −2.60629 | ||||||||
\(459\) | 0.763932 | 0.0356573 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.8687 | 1.71715 | 0.858573 | − | 0.512692i | \(-0.171352\pi\) | ||||
0.858573 | + | 0.512692i | \(0.171352\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.5092 | 1.32493 | 0.662467 | − | 0.749091i | \(-0.269509\pi\) | ||||
0.662467 | + | 0.749091i | \(0.269509\pi\) | |||||||
\(464\) | 10.9443 | 0.508075 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −29.7082 | −1.37621 | ||||||||
\(467\) | 27.4164 | 1.26868 | 0.634340 | − | 0.773054i | \(-0.281272\pi\) | ||||
0.634340 | + | 0.773054i | \(0.281272\pi\) | |||||||
\(468\) | −22.1803 | −1.02529 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.65248 | −0.398685 | ||||||||
\(472\) | 55.7771 | 2.56735 | ||||||||
\(473\) | 44.6715 | 2.05400 | ||||||||
\(474\) | −32.3246 | −1.48472 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.90770 | 0.0873476 | ||||||||
\(478\) | −18.7987 | −0.859831 | ||||||||
\(479\) | 28.5092 | 1.30262 | 0.651309 | − | 0.758813i | \(-0.274220\pi\) | ||||
0.651309 | + | 0.758813i | \(0.274220\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.3246 | 1.47387 | ||||||||
\(482\) | 15.4164 | 0.702198 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 38.1246 | 1.73294 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.49721 | −0.113276 | ||||||||
\(487\) | 9.98885 | 0.452638 | 0.226319 | − | 0.974053i | \(-0.427331\pi\) | ||||
0.226319 | + | 0.974053i | \(0.427331\pi\) | |||||||
\(488\) | −21.3050 | −0.964430 | ||||||||
\(489\) | −3.81540 | −0.172538 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.3607 | 0.828606 | 0.414303 | − | 0.910139i | \(-0.364025\pi\) | ||||
0.414303 | + | 0.910139i | \(0.364025\pi\) | |||||||
\(492\) | 29.2379 | 1.31814 | ||||||||
\(493\) | −1.52786 | −0.0688115 | ||||||||
\(494\) | 105.666 | 4.75412 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.4392 | 0.468734 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 16.1623 | 0.724250 | ||||||||
\(499\) | 8.00000 | 0.358129 | 0.179065 | − | 0.983837i | \(-0.442693\pi\) | ||||
0.179065 | + | 0.983837i | \(0.442693\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.4164 | −0.688754 | ||||||||
\(502\) | −5.88854 | −0.262819 | ||||||||
\(503\) | −29.5279 | −1.31658 | −0.658291 | − | 0.752763i | \(-0.728720\pi\) | ||||
−0.658291 | + | 0.752763i | \(0.728720\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −34.4721 | −1.53247 | ||||||||
\(507\) | −14.4164 | −0.640255 | ||||||||
\(508\) | −16.1623 | −0.717086 | ||||||||
\(509\) | 13.0756 | 0.579565 | 0.289782 | − | 0.957093i | \(-0.406417\pi\) | ||||
0.289782 | + | 0.957093i | \(0.406417\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −47.4470 | −2.09688 | ||||||||
\(513\) | 8.08115 | 0.356791 | ||||||||
\(514\) | −54.2100 | −2.39110 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 42.3134 | 1.86275 | ||||||||
\(517\) | −22.1115 | −0.972461 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.2361 | 0.844370 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.2267 | −1.71855 | −0.859277 | − | 0.511511i | \(-0.829086\pi\) | ||||
−0.859277 | + | 0.511511i | \(0.829086\pi\) | |||||||
\(522\) | 4.99442 | 0.218600 | ||||||||
\(523\) | −15.0557 | −0.658341 | −0.329171 | − | 0.944270i | \(-0.606769\pi\) | ||||
−0.329171 | + | 0.944270i | \(0.606769\pi\) | |||||||
\(524\) | −42.3134 | −1.84847 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −38.5410 | −1.68047 | ||||||||
\(527\) | −1.45735 | −0.0634833 | ||||||||
\(528\) | 24.4721 | 1.06501 | ||||||||
\(529\) | −13.4721 | −0.585745 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.98885 | 0.433479 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 36.1400 | 1.56540 | ||||||||
\(534\) | −23.1246 | −1.00070 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 34.4721 | 1.48897 | ||||||||
\(537\) | 7.52786 | 0.324851 | ||||||||
\(538\) | 17.2361 | 0.743100 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.4721 | −1.05214 | −0.526070 | − | 0.850441i | \(-0.676335\pi\) | ||||
−0.526070 | + | 0.850441i | \(0.676335\pi\) | |||||||
\(542\) | 45.1246 | 1.93827 | ||||||||
\(543\) | −9.98885 | −0.428663 | ||||||||
\(544\) | −1.90770 | −0.0817920 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.4980 | −1.64606 | −0.823029 | − | 0.568000i | \(-0.807717\pi\) | ||||
−0.823029 | + | 0.568000i | \(0.807717\pi\) | |||||||
\(548\) | −34.2323 | −1.46233 | ||||||||
\(549\) | −3.81540 | −0.162837 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.1623 | −0.688537 | ||||||||
\(552\) | −17.2361 | −0.733616 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 24.9443 | 1.05978 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 60.3834 | 2.56083 | ||||||||
\(557\) | −30.4169 | −1.28881 | −0.644403 | − | 0.764686i | \(-0.722894\pi\) | ||||
−0.644403 | + | 0.764686i | \(0.722894\pi\) | |||||||
\(558\) | 4.76393 | 0.201673 | ||||||||
\(559\) | 52.3023 | 2.21215 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.41641 | −0.144241 | ||||||||
\(562\) | −54.9387 | −2.31745 | ||||||||
\(563\) | −13.8885 | −0.585332 | −0.292666 | − | 0.956215i | \(-0.594542\pi\) | ||||
−0.292666 | + | 0.956215i | \(0.594542\pi\) | |||||||
\(564\) | −20.9443 | −0.881913 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −30.8672 | −1.29745 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.63638 | 0.110620 | ||||||||
\(569\) | 36.8328 | 1.54411 | 0.772056 | − | 0.635555i | \(-0.219228\pi\) | ||||
0.772056 | + | 0.635555i | \(0.219228\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.8328 | −1.79250 | −0.896249 | − | 0.443552i | \(-0.853718\pi\) | ||||
−0.896249 | + | 0.443552i | \(0.853718\pi\) | |||||||
\(572\) | 99.1935 | 4.14749 | ||||||||
\(573\) | 3.52786 | 0.147379 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.70820 | −0.196175 | ||||||||
\(577\) | −16.6525 | −0.693252 | −0.346626 | − | 0.938003i | \(-0.612673\pi\) | ||||
−0.346626 | + | 0.938003i | \(0.612673\pi\) | |||||||
\(578\) | −40.9953 | −1.70518 | ||||||||
\(579\) | 13.8042 | 0.573685 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 25.4225 | 1.05380 | ||||||||
\(583\) | −8.53149 | −0.353338 | ||||||||
\(584\) | −15.4336 | −0.638648 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −50.3946 | −2.08178 | ||||||||
\(587\) | −8.94427 | −0.369170 | −0.184585 | − | 0.982817i | \(-0.559094\pi\) | ||||
−0.184585 | + | 0.982817i | \(0.559094\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.4164 | −0.635222 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.90770 | 0.0784723 | ||||||||
\(592\) | −33.7819 | −1.38843 | ||||||||
\(593\) | 17.7082 | 0.727189 | 0.363594 | − | 0.931557i | \(-0.381549\pi\) | ||||
0.363594 | + | 0.931557i | \(0.381549\pi\) | |||||||
\(594\) | 11.1679 | 0.458223 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −80.2492 | −3.28714 | ||||||||
\(597\) | −11.8965 | −0.486893 | ||||||||
\(598\) | −40.3607 | −1.65047 | ||||||||
\(599\) | 9.41641 | 0.384744 | 0.192372 | − | 0.981322i | \(-0.438382\pi\) | ||||
0.192372 | + | 0.981322i | \(0.438382\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.3469 | 0.503640 | 0.251820 | − | 0.967774i | \(-0.418971\pi\) | ||||
0.251820 | + | 0.967774i | \(0.418971\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.17345 | 0.251402 | ||||||||
\(604\) | −37.8885 | −1.54166 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −32.6525 | −1.32642 | ||||||||
\(607\) | −38.8328 | −1.57618 | −0.788088 | − | 0.615563i | \(-0.788929\pi\) | ||||
−0.788088 | + | 0.615563i | \(0.788929\pi\) | |||||||
\(608\) | −20.1803 | −0.818421 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.8885 | −1.04734 | ||||||||
\(612\) | −3.23607 | −0.130810 | ||||||||
\(613\) | 44.6715 | 1.80426 | 0.902132 | − | 0.431460i | \(-0.142001\pi\) | ||||
0.902132 | + | 0.431460i | \(0.142001\pi\) | |||||||
\(614\) | −6.17345 | −0.249140 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.4280 | 0.822402 | 0.411201 | − | 0.911545i | \(-0.365109\pi\) | ||||
0.411201 | + | 0.911545i | \(0.365109\pi\) | |||||||
\(618\) | 3.81540 | 0.153478 | ||||||||
\(619\) | −22.7861 | −0.915850 | −0.457925 | − | 0.888991i | \(-0.651407\pi\) | ||||
−0.457925 | + | 0.888991i | \(0.651407\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.08672 | −0.123866 | ||||||||
\(622\) | 9.52786 | 0.382033 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 28.6525 | 1.14702 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −61.5625 | −2.46053 | ||||||||
\(627\) | −36.1400 | −1.44329 | ||||||||
\(628\) | 36.6525 | 1.46259 | ||||||||
\(629\) | 4.71609 | 0.188043 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.0557 | 1.07707 | 0.538536 | − | 0.842603i | \(-0.318978\pi\) | ||||
0.538536 | + | 0.842603i | \(0.318978\pi\) | |||||||
\(632\) | 72.2800 | 2.87514 | ||||||||
\(633\) | 12.9443 | 0.514489 | ||||||||
\(634\) | −26.0689 | −1.03533 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.08115 | −0.320438 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −22.3357 | −0.884281 | ||||||||
\(639\) | 0.472136 | 0.0186774 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.0000 | 0.710957 | 0.355479 | − | 0.934684i | \(-0.384318\pi\) | ||||
0.355479 | + | 0.934684i | \(0.384318\pi\) | |||||||
\(642\) | 17.2361 | 0.680253 | ||||||||
\(643\) | −28.3607 | −1.11844 | −0.559218 | − | 0.829021i | \(-0.688899\pi\) | ||||
−0.559218 | + | 0.829021i | \(0.688899\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.4164 | 0.606550 | ||||||||
\(647\) | 47.4164 | 1.86413 | 0.932066 | − | 0.362289i | \(-0.118005\pi\) | ||||
0.932066 | + | 0.362289i | \(0.118005\pi\) | |||||||
\(648\) | 5.58394 | 0.219358 | ||||||||
\(649\) | −44.6715 | −1.75351 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.1623 | 0.632964 | ||||||||
\(653\) | 42.7638 | 1.67348 | 0.836738 | − | 0.547603i | \(-0.184460\pi\) | ||||
0.836738 | + | 0.547603i | \(0.184460\pi\) | |||||||
\(654\) | −31.1456 | −1.21789 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −37.7694 | −1.47465 | ||||||||
\(657\) | −2.76393 | −0.107831 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.47214 | −0.330028 | −0.165014 | − | 0.986291i | \(-0.552767\pi\) | ||||
−0.165014 | + | 0.986291i | \(0.552767\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.81540 | 0.148402 | 0.0742009 | − | 0.997243i | \(-0.476359\pi\) | ||||
0.0742009 | + | 0.997243i | \(0.476359\pi\) | |||||||
\(662\) | 19.9777 | 0.776455 | ||||||||
\(663\) | −4.00000 | −0.155347 | ||||||||
\(664\) | −36.1400 | −1.40250 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −15.4164 | −0.597374 | ||||||||
\(667\) | 6.17345 | 0.239037 | ||||||||
\(668\) | 65.3050 | 2.52672 | ||||||||
\(669\) | −17.8885 | −0.691611 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.0630 | 0.658709 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.8672 | −1.18984 | −0.594922 | − | 0.803783i | \(-0.702817\pi\) | ||||
−0.594922 | + | 0.803783i | \(0.702817\pi\) | |||||||
\(674\) | −9.52786 | −0.367000 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 61.0689 | 2.34880 | ||||||||
\(677\) | −31.5967 | −1.21436 | −0.607181 | − | 0.794564i | \(-0.707700\pi\) | ||||
−0.607181 | + | 0.794564i | \(0.707700\pi\) | |||||||
\(678\) | 10.6525 | 0.409106 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.52786 | −0.0585479 | ||||||||
\(682\) | −21.3050 | −0.815809 | ||||||||
\(683\) | −26.8798 | −1.02853 | −0.514264 | − | 0.857632i | \(-0.671935\pi\) | ||||
−0.514264 | + | 0.857632i | \(0.671935\pi\) | |||||||
\(684\) | −34.2323 | −1.30890 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.3357 | 0.852162 | ||||||||
\(688\) | −54.6603 | −2.08391 | ||||||||
\(689\) | −9.98885 | −0.380545 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.2323 | −1.30226 | −0.651129 | − | 0.758967i | \(-0.725704\pi\) | ||||
−0.651129 | + | 0.758967i | \(0.725704\pi\) | |||||||
\(692\) | −81.4853 | −3.09761 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 63.4853 | 2.40987 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −11.1679 | −0.423317 | ||||||||
\(697\) | 5.27275 | 0.199720 | ||||||||
\(698\) | −21.3050 | −0.806404 | ||||||||
\(699\) | 11.8965 | 0.449969 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.83282 | 0.333611 | 0.166805 | − | 0.985990i | \(-0.446655\pi\) | ||||
0.166805 | + | 0.985990i | \(0.446655\pi\) | |||||||
\(702\) | 13.0756 | 0.493506 | ||||||||
\(703\) | 49.8885 | 1.88158 | ||||||||
\(704\) | 21.0557 | 0.793568 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.08115 | 0.304138 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −42.3134 | −1.59024 | ||||||||
\(709\) | −34.0000 | −1.27690 | −0.638448 | − | 0.769665i | \(-0.720423\pi\) | ||||
−0.638448 | + | 0.769665i | \(0.720423\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.9443 | 0.485448 | ||||||||
\(712\) | 51.7082 | 1.93785 | ||||||||
\(713\) | 5.88854 | 0.220528 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −31.8885 | −1.19173 | ||||||||
\(717\) | 7.52786 | 0.281133 | ||||||||
\(718\) | 51.1233 | 1.90790 | ||||||||
\(719\) | −23.7931 | −0.887333 | −0.443666 | − | 0.896192i | \(-0.646322\pi\) | ||||
−0.443666 | + | 0.896192i | \(0.646322\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 115.633 | 4.30343 | ||||||||
\(723\) | −6.17345 | −0.229593 | ||||||||
\(724\) | 42.3134 | 1.57257 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −22.4749 | −0.834122 | ||||||||
\(727\) | 1.52786 | 0.0566653 | 0.0283327 | − | 0.999599i | \(-0.490980\pi\) | ||||
0.0283327 | + | 0.999599i | \(0.490980\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.63080 | 0.282235 | ||||||||
\(732\) | 16.1623 | 0.597376 | ||||||||
\(733\) | −34.1803 | −1.26248 | −0.631240 | − | 0.775588i | \(-0.717454\pi\) | ||||
−0.631240 | + | 0.775588i | \(0.717454\pi\) | |||||||
\(734\) | 39.9554 | 1.47478 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.70820 | 0.284128 | ||||||||
\(737\) | −27.6085 | −1.01697 | ||||||||
\(738\) | −17.2361 | −0.634468 | ||||||||
\(739\) | 24.9443 | 0.917590 | 0.458795 | − | 0.888542i | \(-0.348281\pi\) | ||||
0.458795 | + | 0.888542i | \(0.348281\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −42.3134 | −1.55442 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.08672 | 0.113241 | 0.0566205 | − | 0.998396i | \(-0.481968\pi\) | ||||
0.0566205 | + | 0.998396i | \(0.481968\pi\) | |||||||
\(744\) | −10.6525 | −0.390539 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 80.7214 | 2.95542 | ||||||||
\(747\) | −6.47214 | −0.236803 | ||||||||
\(748\) | 14.4721 | 0.529154 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.8328 | −0.395295 | −0.197648 | − | 0.980273i | \(-0.563330\pi\) | ||||
−0.197648 | + | 0.980273i | \(0.563330\pi\) | |||||||
\(752\) | 27.0557 | 0.986621 | ||||||||
\(753\) | 2.35805 | 0.0859320 | ||||||||
\(754\) | −26.1511 | −0.952368 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.5092 | −1.03618 | −0.518092 | − | 0.855325i | \(-0.673358\pi\) | ||||
−0.518092 | + | 0.855325i | \(0.673358\pi\) | |||||||
\(758\) | 7.63080 | 0.277163 | ||||||||
\(759\) | 13.8042 | 0.501062 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.54408 | −0.164723 | −0.0823613 | − | 0.996603i | \(-0.526246\pi\) | ||||
−0.0823613 | + | 0.996603i | \(0.526246\pi\) | |||||||
\(762\) | 9.52786 | 0.345158 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −14.9443 | −0.540665 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.1511 | −0.944879 | ||||||||
\(767\) | −52.3023 | −1.88853 | ||||||||
\(768\) | 32.4164 | 1.16973 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.7082 | 0.781802 | ||||||||
\(772\) | −58.4757 | −2.10459 | ||||||||
\(773\) | −14.6525 | −0.527013 | −0.263506 | − | 0.964658i | \(-0.584879\pi\) | ||||
−0.263506 | + | 0.964658i | \(0.584879\pi\) | |||||||
\(774\) | −24.9443 | −0.896603 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −56.8464 | −2.04067 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −29.6882 | −1.06437 | ||||||||
\(779\) | 55.7771 | 1.99842 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.11146 | −0.0755538 | ||||||||
\(782\) | −5.88854 | −0.210574 | ||||||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 24.9443 | 0.889733 | ||||||||
\(787\) | 40.9443 | 1.45951 | 0.729753 | − | 0.683711i | \(-0.239635\pi\) | ||||
0.729753 | + | 0.683711i | \(0.239635\pi\) | |||||||
\(788\) | −8.08115 | −0.287879 | ||||||||
\(789\) | 15.4336 | 0.549451 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −24.9721 | −0.887346 | ||||||||
\(793\) | 19.9777 | 0.709429 | ||||||||
\(794\) | 23.0644 | 0.818526 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 50.3946 | 1.78619 | ||||||||
\(797\) | −27.2361 | −0.964751 | −0.482376 | − | 0.875965i | \(-0.660226\pi\) | ||||
−0.482376 | + | 0.875965i | \(0.660226\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.77709 | −0.133624 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.26017 | 0.327192 | ||||||||
\(802\) | 91.9794 | 3.24790 | ||||||||
\(803\) | 12.3607 | 0.436199 | ||||||||
\(804\) | −26.1511 | −0.922280 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −24.9443 | −0.878625 | ||||||||
\(807\) | −6.90212 | −0.242966 | ||||||||
\(808\) | 73.0132 | 2.56859 | ||||||||
\(809\) | −30.9443 | −1.08794 | −0.543971 | − | 0.839104i | \(-0.683080\pi\) | ||||
−0.543971 | + | 0.839104i | \(0.683080\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.4169 | −1.06808 | −0.534041 | − | 0.845459i | \(-0.679327\pi\) | ||||
−0.534041 | + | 0.845459i | \(0.679327\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.0700 | −0.633742 | ||||||||
\(814\) | 68.9443 | 2.41650 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.18034 | 0.146341 | ||||||||
\(817\) | 80.7214 | 2.82408 | ||||||||
\(818\) | 84.3607 | 2.94960 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.88854 | 0.275312 | 0.137656 | − | 0.990480i | \(-0.456043\pi\) | ||||
0.137656 | + | 0.990480i | \(0.456043\pi\) | |||||||
\(822\) | 20.1803 | 0.703870 | ||||||||
\(823\) | 11.4462 | 0.398990 | 0.199495 | − | 0.979899i | \(-0.436070\pi\) | ||||
0.199495 | + | 0.979899i | \(0.436070\pi\) | |||||||
\(824\) | −8.53149 | −0.297209 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46.8575 | −1.62940 | −0.814698 | − | 0.579886i | \(-0.803097\pi\) | ||||
−0.814698 | + | 0.579886i | \(0.803097\pi\) | |||||||
\(828\) | 13.0756 | 0.454408 | ||||||||
\(829\) | −17.6196 | −0.611956 | −0.305978 | − | 0.952039i | \(-0.598983\pi\) | ||||
−0.305978 | + | 0.952039i | \(0.598983\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.98885 | −0.346509 | ||||||||
\(832\) | 24.6525 | 0.854671 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −35.5967 | −1.23261 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 153.091 | 5.29478 | ||||||||
\(837\) | −1.90770 | −0.0659398 | ||||||||
\(838\) | 3.63932 | 0.125718 | ||||||||
\(839\) | −52.3023 | −1.80568 | −0.902838 | − | 0.429981i | \(-0.858520\pi\) | ||||
−0.902838 | + | 0.429981i | \(0.858520\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 41.1344 | 1.41759 | ||||||||
\(843\) | 22.0000 | 0.757720 | ||||||||
\(844\) | −54.8328 | −1.88742 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12.3469 | 0.424495 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10.4392 | 0.358483 | ||||||||
\(849\) | 12.3607 | 0.424217 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.0557 | −0.653222 | ||||||||
\(852\) | −2.00000 | −0.0685189 | ||||||||
\(853\) | −4.87539 | −0.166930 | −0.0834651 | − | 0.996511i | \(-0.526599\pi\) | ||||
−0.0834651 | + | 0.996511i | \(0.526599\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −38.5410 | −1.31730 | ||||||||
\(857\) | −45.1246 | −1.54143 | −0.770714 | − | 0.637182i | \(-0.780100\pi\) | ||||
−0.770714 | + | 0.637182i | \(0.780100\pi\) | |||||||
\(858\) | −58.4757 | −1.99633 | ||||||||
\(859\) | 0.450347 | 0.0153656 | 0.00768282 | − | 0.999970i | \(-0.497554\pi\) | ||||
0.00768282 | + | 0.999970i | \(0.497554\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.1679 | −0.380379 | ||||||||
\(863\) | 10.7175 | 0.364829 | 0.182414 | − | 0.983222i | \(-0.441609\pi\) | ||||
0.182414 | + | 0.983222i | \(0.441609\pi\) | |||||||
\(864\) | −2.49721 | −0.0849569 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −89.1710 | −3.03015 | ||||||||
\(867\) | 16.4164 | 0.557530 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −57.8885 | −1.96373 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.3246 | −1.09528 | ||||||||
\(872\) | 69.6436 | 2.35843 | ||||||||
\(873\) | −10.1803 | −0.344552 | ||||||||
\(874\) | −62.2911 | −2.10703 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11.7082 | 0.395584 | ||||||||
\(877\) | 15.2616 | 0.515348 | 0.257674 | − | 0.966232i | \(-0.417044\pi\) | ||||
0.257674 | + | 0.966232i | \(0.417044\pi\) | |||||||
\(878\) | 60.5410 | 2.04316 | ||||||||
\(879\) | 20.1803 | 0.680666 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.5848 | −1.40103 | −0.700513 | − | 0.713640i | \(-0.747045\pi\) | ||||
−0.700513 | + | 0.713640i | \(0.747045\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(884\) | 16.9443 | 0.569898 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −78.9017 | −2.65075 | ||||||||
\(887\) | −35.7771 | −1.20128 | −0.600639 | − | 0.799521i | \(-0.705087\pi\) | ||||
−0.600639 | + | 0.799521i | \(0.705087\pi\) | |||||||
\(888\) | 34.4721 | 1.15681 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.47214 | −0.149822 | ||||||||
\(892\) | 75.7771 | 2.53720 | ||||||||
\(893\) | −39.9554 | −1.33706 | ||||||||
\(894\) | 47.3079 | 1.58221 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.1623 | 0.539643 | ||||||||
\(898\) | −42.5918 | −1.42131 | ||||||||
\(899\) | 3.81540 | 0.127251 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.45735 | −0.0485515 | ||||||||
\(902\) | 77.0820 | 2.56655 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −23.8197 | −0.792230 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 22.3357 | 0.742055 | ||||||||
\(907\) | 39.9554 | 1.32670 | 0.663349 | − | 0.748311i | \(-0.269135\pi\) | ||||
0.663349 | + | 0.748311i | \(0.269135\pi\) | |||||||
\(908\) | 6.47214 | 0.214785 | ||||||||
\(909\) | 13.0756 | 0.433689 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.4164 | 0.842083 | 0.421042 | − | 0.907041i | \(-0.361665\pi\) | ||||
0.421042 | + | 0.907041i | \(0.361665\pi\) | |||||||
\(912\) | 44.2211 | 1.46431 | ||||||||
\(913\) | 28.9443 | 0.957916 | ||||||||
\(914\) | 59.4164 | 1.96532 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −94.6157 | −3.12619 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.90770 | 0.0629635 | ||||||||
\(919\) | 4.00000 | 0.131948 | 0.0659739 | − | 0.997821i | \(-0.478985\pi\) | ||||
0.0659739 | + | 0.997821i | \(0.478985\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.47214 | 0.0814596 | ||||||||
\(922\) | 92.0689 | 3.03213 | ||||||||
\(923\) | −2.47214 | −0.0813713 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 71.1935 | 2.33956 | ||||||||
\(927\) | −1.52786 | −0.0501816 | ||||||||
\(928\) | 4.99442 | 0.163950 | ||||||||
\(929\) | 3.08672 | 0.101272 | 0.0506361 | − | 0.998717i | \(-0.483875\pi\) | ||||
0.0506361 | + | 0.998717i | \(0.483875\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −50.3946 | −1.65073 | ||||||||
\(933\) | −3.81540 | −0.124911 | ||||||||
\(934\) | 68.4646 | 2.24023 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −29.2379 | −0.955670 | ||||||||
\(937\) | 26.5410 | 0.867057 | 0.433529 | − | 0.901140i | \(-0.357268\pi\) | ||||
0.433529 | + | 0.901140i | \(0.357268\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.6525 | 0.804503 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.4113 | 1.15438 | 0.577188 | − | 0.816611i | \(-0.304150\pi\) | ||||
0.577188 | + | 0.816611i | \(0.304150\pi\) | |||||||
\(942\) | −21.6071 | −0.703996 | ||||||||
\(943\) | −21.3050 | −0.693785 | ||||||||
\(944\) | 54.6603 | 1.77904 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 111.554 | 3.62694 | ||||||||
\(947\) | 14.5329 | 0.472257 | 0.236128 | − | 0.971722i | \(-0.424121\pi\) | ||||
0.236128 | + | 0.971722i | \(0.424121\pi\) | |||||||
\(948\) | −54.8328 | −1.78089 | ||||||||
\(949\) | 14.4721 | 0.469785 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.4392 | 0.338514 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −51.8519 | −1.67965 | −0.839825 | − | 0.542858i | \(-0.817342\pi\) | ||||
−0.839825 | + | 0.542858i | \(0.817342\pi\) | |||||||
\(954\) | 4.76393 | 0.154238 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −31.8885 | −1.03135 | ||||||||
\(957\) | 8.94427 | 0.289127 | ||||||||
\(958\) | 71.1935 | 2.30016 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.3607 | −0.882603 | ||||||||
\(962\) | 80.7214 | 2.60256 | ||||||||
\(963\) | −6.90212 | −0.222418 | ||||||||
\(964\) | 26.1511 | 0.842272 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.1511 | 0.840964 | 0.420482 | − | 0.907301i | \(-0.361861\pi\) | ||||
0.420482 | + | 0.907301i | \(0.361861\pi\) | |||||||
\(968\) | 50.2554 | 1.61527 | ||||||||
\(969\) | −6.17345 | −0.198320 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 58.4757 | 1.87658 | 0.938288 | − | 0.345855i | \(-0.112411\pi\) | ||||
0.938288 | + | 0.345855i | \(0.112411\pi\) | |||||||
\(972\) | −4.23607 | −0.135872 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 24.9443 | 0.799266 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −20.8784 | −0.668301 | ||||||||
\(977\) | −24.2434 | −0.775616 | −0.387808 | − | 0.921740i | \(-0.626768\pi\) | ||||
−0.387808 | + | 0.921740i | \(0.626768\pi\) | |||||||
\(978\) | −9.52786 | −0.304667 | ||||||||
\(979\) | −41.4127 | −1.32356 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.4721 | 0.398205 | ||||||||
\(982\) | 45.8505 | 1.46315 | ||||||||
\(983\) | 38.8328 | 1.23857 | 0.619287 | − | 0.785165i | \(-0.287422\pi\) | ||||
0.619287 | + | 0.785165i | \(0.287422\pi\) | |||||||
\(984\) | 38.5410 | 1.22864 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.81540 | −0.121507 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 179.243 | 5.70247 | ||||||||
\(989\) | −30.8328 | −0.980427 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.0000 | 1.14358 | 0.571789 | − | 0.820401i | \(-0.306250\pi\) | ||||
0.571789 | + | 0.820401i | \(0.306250\pi\) | |||||||
\(992\) | 4.76393 | 0.151255 | ||||||||
\(993\) | −8.00000 | −0.253872 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 27.4164 | 0.868722 | ||||||||
\(997\) | −27.7082 | −0.877528 | −0.438764 | − | 0.898602i | \(-0.644584\pi\) | ||||
−0.438764 | + | 0.898602i | \(0.644584\pi\) | |||||||
\(998\) | 19.9777 | 0.632383 | ||||||||
\(999\) | 6.17345 | 0.195319 |
(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 | 3675.2.a.bt.1.4 | 4 | ||
5.2 | odd | 4 | 735.2.d.c.589.8 | yes | 8 | ||
5.3 | odd | 4 | 735.2.d.c.589.1 | ✓ | 8 | ||
5.4 | even | 2 | 3675.2.a.bv.1.1 | 4 | |||
7.6 | odd | 2 | 3675.2.a.bv.1.4 | 4 | |||
15.2 | even | 4 | 2205.2.d.m.1324.2 | 8 | |||
15.8 | even | 4 | 2205.2.d.m.1324.8 | 8 | |||
35.2 | odd | 12 | 735.2.q.h.214.7 | 16 | |||
35.3 | even | 12 | 735.2.q.h.79.8 | 16 | |||
35.12 | even | 12 | 735.2.q.h.214.8 | 16 | |||
35.13 | even | 4 | 735.2.d.c.589.2 | yes | 8 | ||
35.17 | even | 12 | 735.2.q.h.79.1 | 16 | |||
35.18 | odd | 12 | 735.2.q.h.79.7 | 16 | |||
35.23 | odd | 12 | 735.2.q.h.214.2 | 16 | |||
35.27 | even | 4 | 735.2.d.c.589.7 | yes | 8 | ||
35.32 | odd | 12 | 735.2.q.h.79.2 | 16 | |||
35.33 | even | 12 | 735.2.q.h.214.1 | 16 | |||
35.34 | odd | 2 | inner | 3675.2.a.bt.1.1 | 4 | ||
105.62 | odd | 4 | 2205.2.d.m.1324.1 | 8 | |||
105.83 | odd | 4 | 2205.2.d.m.1324.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
735.2.d.c.589.1 | ✓ | 8 | 5.3 | odd | 4 | ||
735.2.d.c.589.2 | yes | 8 | 35.13 | even | 4 | ||
735.2.d.c.589.7 | yes | 8 | 35.27 | even | 4 | ||
735.2.d.c.589.8 | yes | 8 | 5.2 | odd | 4 | ||
735.2.q.h.79.1 | 16 | 35.17 | even | 12 | |||
735.2.q.h.79.2 | 16 | 35.32 | odd | 12 | |||
735.2.q.h.79.7 | 16 | 35.18 | odd | 12 | |||
735.2.q.h.79.8 | 16 | 35.3 | even | 12 | |||
735.2.q.h.214.1 | 16 | 35.33 | even | 12 | |||
735.2.q.h.214.2 | 16 | 35.23 | odd | 12 | |||
735.2.q.h.214.7 | 16 | 35.2 | odd | 12 | |||
735.2.q.h.214.8 | 16 | 35.12 | even | 12 | |||
2205.2.d.m.1324.1 | 8 | 105.62 | odd | 4 | |||
2205.2.d.m.1324.2 | 8 | 15.2 | even | 4 | |||
2205.2.d.m.1324.7 | 8 | 105.83 | odd | 4 | |||
2205.2.d.m.1324.8 | 8 | 15.8 | even | 4 | |||
3675.2.a.bt.1.1 | 4 | 35.34 | odd | 2 | inner | ||
3675.2.a.bt.1.4 | 4 | 1.1 | even | 1 | trivial | ||
3675.2.a.bv.1.1 | 4 | 5.4 | even | 2 | |||
3675.2.a.bv.1.4 | 4 | 7.6 | odd | 2 |