Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6422,2,Mod(1,6422)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6422.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6422 = 2 \cdot 13^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6422.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: | \(51.2799281781\) |
Analytic rank: | \(0\) |
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: | \( x^{14} - 4 x^{13} - 22 x^{12} + 98 x^{11} + 164 x^{10} - 912 x^{9} - 374 x^{8} + 3996 x^{7} - 817 x^{6} - 8194 x^{5} + 4418 x^{4} + 6430 x^{3} - 4327 x^{2} - 922 x + 358 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 494) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(2.81805\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6422.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 2.81805 | 1.62700 | 0.813500 | − | 0.581565i | \(-0.197559\pi\) | ||||
0.813500 | + | 0.581565i | \(0.197559\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.87767 | 1.73415 | 0.867074 | − | 0.498179i | \(-0.165998\pi\) | ||||
0.867074 | + | 0.498179i | \(0.165998\pi\) | |||||||
\(6\) | −2.81805 | −1.15046 | ||||||||
\(7\) | −2.87057 | −1.08497 | −0.542486 | − | 0.840065i | \(-0.682517\pi\) | ||||
−0.542486 | + | 0.840065i | \(0.682517\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 4.94139 | 1.64713 | ||||||||
\(10\) | −3.87767 | −1.22623 | ||||||||
\(11\) | −3.63541 | −1.09612 | −0.548059 | − | 0.836440i | \(-0.684633\pi\) | ||||
−0.548059 | + | 0.836440i | \(0.684633\pi\) | |||||||
\(12\) | 2.81805 | 0.813500 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.87057 | 0.767191 | ||||||||
\(15\) | 10.9275 | 2.82146 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.24396 | 1.51438 | 0.757191 | − | 0.653193i | \(-0.226571\pi\) | ||||
0.757191 | + | 0.653193i | \(0.226571\pi\) | |||||||
\(18\) | −4.94139 | −1.16470 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 3.87767 | 0.867074 | ||||||||
\(21\) | −8.08939 | −1.76525 | ||||||||
\(22\) | 3.63541 | 0.775073 | ||||||||
\(23\) | −8.25037 | −1.72032 | −0.860161 | − | 0.510023i | \(-0.829637\pi\) | ||||
−0.860161 | + | 0.510023i | \(0.829637\pi\) | |||||||
\(24\) | −2.81805 | −0.575232 | ||||||||
\(25\) | 10.0364 | 2.00727 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.47093 | 1.05288 | ||||||||
\(28\) | −2.87057 | −0.542486 | ||||||||
\(29\) | 4.57590 | 0.849724 | 0.424862 | − | 0.905258i | \(-0.360323\pi\) | ||||
0.424862 | + | 0.905258i | \(0.360323\pi\) | |||||||
\(30\) | −10.9275 | −1.99507 | ||||||||
\(31\) | 3.50294 | 0.629146 | 0.314573 | − | 0.949233i | \(-0.398139\pi\) | ||||
0.314573 | + | 0.949233i | \(0.398139\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −10.2448 | −1.78338 | ||||||||
\(34\) | −6.24396 | −1.07083 | ||||||||
\(35\) | −11.1311 | −1.88150 | ||||||||
\(36\) | 4.94139 | 0.823565 | ||||||||
\(37\) | −0.0117786 | −0.00193638 | −0.000968192 | − | 1.00000i | \(-0.500308\pi\) | ||||
−0.000968192 | 1.00000i | \(0.500308\pi\) | ||||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.87767 | −0.613114 | ||||||||
\(41\) | 7.96875 | 1.24451 | 0.622255 | − | 0.782815i | \(-0.286217\pi\) | ||||
0.622255 | + | 0.782815i | \(0.286217\pi\) | |||||||
\(42\) | 8.08939 | 1.24822 | ||||||||
\(43\) | 11.3957 | 1.73783 | 0.868915 | − | 0.494962i | \(-0.164818\pi\) | ||||
0.868915 | + | 0.494962i | \(0.164818\pi\) | |||||||
\(44\) | −3.63541 | −0.548059 | ||||||||
\(45\) | 19.1611 | 2.85637 | ||||||||
\(46\) | 8.25037 | 1.21645 | ||||||||
\(47\) | 1.96020 | 0.285924 | 0.142962 | − | 0.989728i | \(-0.454337\pi\) | ||||
0.142962 | + | 0.989728i | \(0.454337\pi\) | |||||||
\(48\) | 2.81805 | 0.406750 | ||||||||
\(49\) | 1.24015 | 0.177164 | ||||||||
\(50\) | −10.0364 | −1.41936 | ||||||||
\(51\) | 17.5958 | 2.46390 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.92897 | 1.22649 | 0.613244 | − | 0.789893i | \(-0.289864\pi\) | ||||
0.613244 | + | 0.789893i | \(0.289864\pi\) | |||||||
\(54\) | −5.47093 | −0.744499 | ||||||||
\(55\) | −14.0969 | −1.90083 | ||||||||
\(56\) | 2.87057 | 0.383596 | ||||||||
\(57\) | −2.81805 | −0.373259 | ||||||||
\(58\) | −4.57590 | −0.600845 | ||||||||
\(59\) | 5.83570 | 0.759743 | 0.379872 | − | 0.925039i | \(-0.375968\pi\) | ||||
0.379872 | + | 0.925039i | \(0.375968\pi\) | |||||||
\(60\) | 10.9275 | 1.41073 | ||||||||
\(61\) | −0.214830 | −0.0275062 | −0.0137531 | − | 0.999905i | \(-0.504378\pi\) | ||||
−0.0137531 | + | 0.999905i | \(0.504378\pi\) | |||||||
\(62\) | −3.50294 | −0.444874 | ||||||||
\(63\) | −14.1846 | −1.78709 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 10.2448 | 1.26104 | ||||||||
\(67\) | −8.68818 | −1.06143 | −0.530715 | − | 0.847550i | \(-0.678077\pi\) | ||||
−0.530715 | + | 0.847550i | \(0.678077\pi\) | |||||||
\(68\) | 6.24396 | 0.757191 | ||||||||
\(69\) | −23.2499 | −2.79896 | ||||||||
\(70\) | 11.1311 | 1.33042 | ||||||||
\(71\) | 6.62648 | 0.786419 | 0.393209 | − | 0.919449i | \(-0.371365\pi\) | ||||
0.393209 | + | 0.919449i | \(0.371365\pi\) | |||||||
\(72\) | −4.94139 | −0.582348 | ||||||||
\(73\) | 13.4954 | 1.57951 | 0.789756 | − | 0.613421i | \(-0.210207\pi\) | ||||
0.789756 | + | 0.613421i | \(0.210207\pi\) | |||||||
\(74\) | 0.0117786 | 0.00136923 | ||||||||
\(75\) | 28.2829 | 3.26583 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 10.4357 | 1.18926 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.33212 | 0.712419 | 0.356209 | − | 0.934406i | \(-0.384069\pi\) | ||||
0.356209 | + | 0.934406i | \(0.384069\pi\) | |||||||
\(80\) | 3.87767 | 0.433537 | ||||||||
\(81\) | 0.593170 | 0.0659078 | ||||||||
\(82\) | −7.96875 | −0.880002 | ||||||||
\(83\) | −7.39527 | −0.811736 | −0.405868 | − | 0.913932i | \(-0.633031\pi\) | ||||
−0.405868 | + | 0.913932i | \(0.633031\pi\) | |||||||
\(84\) | −8.08939 | −0.882625 | ||||||||
\(85\) | 24.2120 | 2.62616 | ||||||||
\(86\) | −11.3957 | −1.22883 | ||||||||
\(87\) | 12.8951 | 1.38250 | ||||||||
\(88\) | 3.63541 | 0.387536 | ||||||||
\(89\) | −7.06857 | −0.749267 | −0.374633 | − | 0.927173i | \(-0.622231\pi\) | ||||
−0.374633 | + | 0.927173i | \(0.622231\pi\) | |||||||
\(90\) | −19.1611 | −2.01976 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.25037 | −0.860161 | ||||||||
\(93\) | 9.87145 | 1.02362 | ||||||||
\(94\) | −1.96020 | −0.202179 | ||||||||
\(95\) | −3.87767 | −0.397841 | ||||||||
\(96\) | −2.81805 | −0.287616 | ||||||||
\(97\) | −6.09538 | −0.618892 | −0.309446 | − | 0.950917i | \(-0.600144\pi\) | ||||
−0.309446 | + | 0.950917i | \(0.600144\pi\) | |||||||
\(98\) | −1.24015 | −0.125274 | ||||||||
\(99\) | −17.9640 | −1.80545 | ||||||||
\(100\) | 10.0364 | 1.00364 | ||||||||
\(101\) | −0.590697 | −0.0587765 | −0.0293883 | − | 0.999568i | \(-0.509356\pi\) | ||||
−0.0293883 | + | 0.999568i | \(0.509356\pi\) | |||||||
\(102\) | −17.5958 | −1.74224 | ||||||||
\(103\) | 0.525578 | 0.0517868 | 0.0258934 | − | 0.999665i | \(-0.491757\pi\) | ||||
0.0258934 | + | 0.999665i | \(0.491757\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −31.3680 | −3.06121 | ||||||||
\(106\) | −8.92897 | −0.867259 | ||||||||
\(107\) | −8.94396 | −0.864645 | −0.432322 | − | 0.901719i | \(-0.642306\pi\) | ||||
−0.432322 | + | 0.901719i | \(0.642306\pi\) | |||||||
\(108\) | 5.47093 | 0.526441 | ||||||||
\(109\) | 0.271028 | 0.0259598 | 0.0129799 | − | 0.999916i | \(-0.495868\pi\) | ||||
0.0129799 | + | 0.999916i | \(0.495868\pi\) | |||||||
\(110\) | 14.0969 | 1.34409 | ||||||||
\(111\) | −0.0331926 | −0.00315050 | ||||||||
\(112\) | −2.87057 | −0.271243 | ||||||||
\(113\) | 0.112771 | 0.0106086 | 0.00530430 | − | 0.999986i | \(-0.498312\pi\) | ||||
0.00530430 | + | 0.999986i | \(0.498312\pi\) | |||||||
\(114\) | 2.81805 | 0.263934 | ||||||||
\(115\) | −31.9923 | −2.98329 | ||||||||
\(116\) | 4.57590 | 0.424862 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.83570 | −0.537219 | ||||||||
\(119\) | −17.9237 | −1.64306 | ||||||||
\(120\) | −10.9275 | −0.997537 | ||||||||
\(121\) | 2.21623 | 0.201475 | ||||||||
\(122\) | 0.214830 | 0.0194498 | ||||||||
\(123\) | 22.4563 | 2.02482 | ||||||||
\(124\) | 3.50294 | 0.314573 | ||||||||
\(125\) | 19.5294 | 1.74676 | ||||||||
\(126\) | 14.1846 | 1.26366 | ||||||||
\(127\) | 13.4369 | 1.19233 | 0.596165 | − | 0.802862i | \(-0.296691\pi\) | ||||
0.596165 | + | 0.802862i | \(0.296691\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 32.1137 | 2.82745 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.52443 | 0.657412 | 0.328706 | − | 0.944432i | \(-0.393387\pi\) | ||||
0.328706 | + | 0.944432i | \(0.393387\pi\) | |||||||
\(132\) | −10.2448 | −0.891692 | ||||||||
\(133\) | 2.87057 | 0.248910 | ||||||||
\(134\) | 8.68818 | 0.750545 | ||||||||
\(135\) | 21.2145 | 1.82585 | ||||||||
\(136\) | −6.24396 | −0.535415 | ||||||||
\(137\) | 0.458171 | 0.0391442 | 0.0195721 | − | 0.999808i | \(-0.493770\pi\) | ||||
0.0195721 | + | 0.999808i | \(0.493770\pi\) | |||||||
\(138\) | 23.2499 | 1.97917 | ||||||||
\(139\) | 11.9096 | 1.01016 | 0.505078 | − | 0.863074i | \(-0.331464\pi\) | ||||
0.505078 | + | 0.863074i | \(0.331464\pi\) | |||||||
\(140\) | −11.1311 | −0.940751 | ||||||||
\(141\) | 5.52393 | 0.465199 | ||||||||
\(142\) | −6.62648 | −0.556082 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.94139 | 0.411783 | ||||||||
\(145\) | 17.7439 | 1.47355 | ||||||||
\(146\) | −13.4954 | −1.11688 | ||||||||
\(147\) | 3.49480 | 0.288246 | ||||||||
\(148\) | −0.0117786 | −0.000968192 0 | ||||||||
\(149\) | −6.67440 | −0.546788 | −0.273394 | − | 0.961902i | \(-0.588146\pi\) | ||||
−0.273394 | + | 0.961902i | \(0.588146\pi\) | |||||||
\(150\) | −28.2829 | −2.30929 | ||||||||
\(151\) | −5.22614 | −0.425298 | −0.212649 | − | 0.977129i | \(-0.568209\pi\) | ||||
−0.212649 | + | 0.977129i | \(0.568209\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 30.8538 | 2.49439 | ||||||||
\(154\) | −10.4357 | −0.840932 | ||||||||
\(155\) | 13.5833 | 1.09103 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.58330 | −0.685022 | −0.342511 | − | 0.939514i | \(-0.611277\pi\) | ||||
−0.342511 | + | 0.939514i | \(0.611277\pi\) | |||||||
\(158\) | −6.33212 | −0.503756 | ||||||||
\(159\) | 25.1623 | 1.99550 | ||||||||
\(160\) | −3.87767 | −0.306557 | ||||||||
\(161\) | 23.6832 | 1.86650 | ||||||||
\(162\) | −0.593170 | −0.0466038 | ||||||||
\(163\) | −22.1972 | −1.73862 | −0.869308 | − | 0.494271i | \(-0.835435\pi\) | ||||
−0.869308 | + | 0.494271i | \(0.835435\pi\) | |||||||
\(164\) | 7.96875 | 0.622255 | ||||||||
\(165\) | −39.7259 | −3.09265 | ||||||||
\(166\) | 7.39527 | 0.573984 | ||||||||
\(167\) | 22.0652 | 1.70746 | 0.853730 | − | 0.520716i | \(-0.174335\pi\) | ||||
0.853730 | + | 0.520716i | \(0.174335\pi\) | |||||||
\(168\) | 8.08939 | 0.624110 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −24.2120 | −1.85698 | ||||||||
\(171\) | −4.94139 | −0.377878 | ||||||||
\(172\) | 11.3957 | 0.868915 | ||||||||
\(173\) | 21.2498 | 1.61559 | 0.807796 | − | 0.589462i | \(-0.200660\pi\) | ||||
0.807796 | + | 0.589462i | \(0.200660\pi\) | |||||||
\(174\) | −12.8951 | −0.977576 | ||||||||
\(175\) | −28.8100 | −2.17783 | ||||||||
\(176\) | −3.63541 | −0.274030 | ||||||||
\(177\) | 16.4453 | 1.23610 | ||||||||
\(178\) | 7.06857 | 0.529812 | ||||||||
\(179\) | −22.6071 | −1.68974 | −0.844868 | − | 0.534975i | \(-0.820321\pi\) | ||||
−0.844868 | + | 0.534975i | \(0.820321\pi\) | |||||||
\(180\) | 19.1611 | 1.42818 | ||||||||
\(181\) | −4.83570 | −0.359435 | −0.179717 | − | 0.983718i | \(-0.557518\pi\) | ||||
−0.179717 | + | 0.983718i | \(0.557518\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.605401 | −0.0447525 | ||||||||
\(184\) | 8.25037 | 0.608225 | ||||||||
\(185\) | −0.0456734 | −0.00335798 | ||||||||
\(186\) | −9.87145 | −0.723810 | ||||||||
\(187\) | −22.6994 | −1.65994 | ||||||||
\(188\) | 1.96020 | 0.142962 | ||||||||
\(189\) | −15.7047 | −1.14235 | ||||||||
\(190\) | 3.87767 | 0.281316 | ||||||||
\(191\) | 18.0400 | 1.30533 | 0.652666 | − | 0.757646i | \(-0.273651\pi\) | ||||
0.652666 | + | 0.757646i | \(0.273651\pi\) | |||||||
\(192\) | 2.81805 | 0.203375 | ||||||||
\(193\) | 6.52151 | 0.469428 | 0.234714 | − | 0.972064i | \(-0.424585\pi\) | ||||
0.234714 | + | 0.972064i | \(0.424585\pi\) | |||||||
\(194\) | 6.09538 | 0.437623 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.24015 | 0.0885820 | ||||||||
\(197\) | 16.0992 | 1.14702 | 0.573510 | − | 0.819199i | \(-0.305581\pi\) | ||||
0.573510 | + | 0.819199i | \(0.305581\pi\) | |||||||
\(198\) | 17.9640 | 1.27665 | ||||||||
\(199\) | −6.01255 | −0.426218 | −0.213109 | − | 0.977028i | \(-0.568359\pi\) | ||||
−0.213109 | + | 0.977028i | \(0.568359\pi\) | |||||||
\(200\) | −10.0364 | −0.709678 | ||||||||
\(201\) | −24.4837 | −1.72695 | ||||||||
\(202\) | 0.590697 | 0.0415613 | ||||||||
\(203\) | −13.1354 | −0.921926 | ||||||||
\(204\) | 17.5958 | 1.23195 | ||||||||
\(205\) | 30.9002 | 2.15817 | ||||||||
\(206\) | −0.525578 | −0.0366188 | ||||||||
\(207\) | −40.7683 | −2.83359 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.63541 | 0.251467 | ||||||||
\(210\) | 31.3680 | 2.16460 | ||||||||
\(211\) | −4.97594 | −0.342558 | −0.171279 | − | 0.985223i | \(-0.554790\pi\) | ||||
−0.171279 | + | 0.985223i | \(0.554790\pi\) | |||||||
\(212\) | 8.92897 | 0.613244 | ||||||||
\(213\) | 18.6737 | 1.27950 | ||||||||
\(214\) | 8.94396 | 0.611396 | ||||||||
\(215\) | 44.1889 | 3.01366 | ||||||||
\(216\) | −5.47093 | −0.372250 | ||||||||
\(217\) | −10.0554 | −0.682606 | ||||||||
\(218\) | −0.271028 | −0.0183563 | ||||||||
\(219\) | 38.0306 | 2.56987 | ||||||||
\(220\) | −14.0969 | −0.950416 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.0331926 | 0.00222774 | ||||||||
\(223\) | 18.1338 | 1.21433 | 0.607163 | − | 0.794577i | \(-0.292307\pi\) | ||||
0.607163 | + | 0.794577i | \(0.292307\pi\) | |||||||
\(224\) | 2.87057 | 0.191798 | ||||||||
\(225\) | 49.5936 | 3.30624 | ||||||||
\(226\) | −0.112771 | −0.00750141 | ||||||||
\(227\) | 12.3853 | 0.822040 | 0.411020 | − | 0.911626i | \(-0.365173\pi\) | ||||
0.411020 | + | 0.911626i | \(0.365173\pi\) | |||||||
\(228\) | −2.81805 | −0.186630 | ||||||||
\(229\) | 2.20870 | 0.145955 | 0.0729774 | − | 0.997334i | \(-0.476750\pi\) | ||||
0.0729774 | + | 0.997334i | \(0.476750\pi\) | |||||||
\(230\) | 31.9923 | 2.10951 | ||||||||
\(231\) | 29.4083 | 1.93492 | ||||||||
\(232\) | −4.57590 | −0.300423 | ||||||||
\(233\) | 3.73725 | 0.244835 | 0.122418 | − | 0.992479i | \(-0.460935\pi\) | ||||
0.122418 | + | 0.992479i | \(0.460935\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.60101 | 0.495835 | ||||||||
\(236\) | 5.83570 | 0.379872 | ||||||||
\(237\) | 17.8442 | 1.15911 | ||||||||
\(238\) | 17.9237 | 1.16182 | ||||||||
\(239\) | 2.20869 | 0.142868 | 0.0714342 | − | 0.997445i | \(-0.477242\pi\) | ||||
0.0714342 | + | 0.997445i | \(0.477242\pi\) | |||||||
\(240\) | 10.9275 | 0.705365 | ||||||||
\(241\) | −22.9135 | −1.47599 | −0.737995 | − | 0.674806i | \(-0.764227\pi\) | ||||
−0.737995 | + | 0.674806i | \(0.764227\pi\) | |||||||
\(242\) | −2.21623 | −0.142464 | ||||||||
\(243\) | −14.7412 | −0.945649 | ||||||||
\(244\) | −0.214830 | −0.0137531 | ||||||||
\(245\) | 4.80889 | 0.307229 | ||||||||
\(246\) | −22.4563 | −1.43176 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.50294 | −0.222437 | ||||||||
\(249\) | −20.8402 | −1.32070 | ||||||||
\(250\) | −19.5294 | −1.23515 | ||||||||
\(251\) | −1.22889 | −0.0775666 | −0.0387833 | − | 0.999248i | \(-0.512348\pi\) | ||||
−0.0387833 | + | 0.999248i | \(0.512348\pi\) | |||||||
\(252\) | −14.1846 | −0.893545 | ||||||||
\(253\) | 29.9935 | 1.88568 | ||||||||
\(254\) | −13.4369 | −0.843104 | ||||||||
\(255\) | 68.2307 | 4.27277 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.3311 | −0.769190 | −0.384595 | − | 0.923085i | \(-0.625659\pi\) | ||||
−0.384595 | + | 0.923085i | \(0.625659\pi\) | |||||||
\(258\) | −32.1137 | −1.99931 | ||||||||
\(259\) | 0.0338111 | 0.00210092 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.6113 | 1.39961 | ||||||||
\(262\) | −7.52443 | −0.464861 | ||||||||
\(263\) | −7.51111 | −0.463155 | −0.231577 | − | 0.972816i | \(-0.574389\pi\) | ||||
−0.231577 | + | 0.972816i | \(0.574389\pi\) | |||||||
\(264\) | 10.2448 | 0.630522 | ||||||||
\(265\) | 34.6237 | 2.12691 | ||||||||
\(266\) | −2.87057 | −0.176006 | ||||||||
\(267\) | −19.9196 | −1.21906 | ||||||||
\(268\) | −8.68818 | −0.530715 | ||||||||
\(269\) | −16.8519 | −1.02748 | −0.513739 | − | 0.857946i | \(-0.671740\pi\) | ||||
−0.513739 | + | 0.857946i | \(0.671740\pi\) | |||||||
\(270\) | −21.2145 | −1.29107 | ||||||||
\(271\) | −9.80221 | −0.595442 | −0.297721 | − | 0.954653i | \(-0.596227\pi\) | ||||
−0.297721 | + | 0.954653i | \(0.596227\pi\) | |||||||
\(272\) | 6.24396 | 0.378596 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.458171 | −0.0276791 | ||||||||
\(275\) | −36.4863 | −2.20021 | ||||||||
\(276\) | −23.2499 | −1.39948 | ||||||||
\(277\) | −21.3755 | −1.28433 | −0.642165 | − | 0.766566i | \(-0.721964\pi\) | ||||
−0.642165 | + | 0.766566i | \(0.721964\pi\) | |||||||
\(278\) | −11.9096 | −0.714289 | ||||||||
\(279\) | 17.3094 | 1.03629 | ||||||||
\(280\) | 11.1311 | 0.665212 | ||||||||
\(281\) | −3.05650 | −0.182336 | −0.0911678 | − | 0.995836i | \(-0.529060\pi\) | ||||
−0.0911678 | + | 0.995836i | \(0.529060\pi\) | |||||||
\(282\) | −5.52393 | −0.328945 | ||||||||
\(283\) | −2.99153 | −0.177828 | −0.0889141 | − | 0.996039i | \(-0.528340\pi\) | ||||
−0.0889141 | + | 0.996039i | \(0.528340\pi\) | |||||||
\(284\) | 6.62648 | 0.393209 | ||||||||
\(285\) | −10.9275 | −0.647288 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −22.8748 | −1.35026 | ||||||||
\(288\) | −4.94139 | −0.291174 | ||||||||
\(289\) | 21.9870 | 1.29335 | ||||||||
\(290\) | −17.7439 | −1.04196 | ||||||||
\(291\) | −17.1771 | −1.00694 | ||||||||
\(292\) | 13.4954 | 0.789756 | ||||||||
\(293\) | −10.1240 | −0.591449 | −0.295724 | − | 0.955273i | \(-0.595561\pi\) | ||||
−0.295724 | + | 0.955273i | \(0.595561\pi\) | |||||||
\(294\) | −3.49480 | −0.203821 | ||||||||
\(295\) | 22.6289 | 1.31751 | ||||||||
\(296\) | 0.0117786 | 0.000684615 0 | ||||||||
\(297\) | −19.8891 | −1.15408 | ||||||||
\(298\) | 6.67440 | 0.386638 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 28.2829 | 1.63292 | ||||||||
\(301\) | −32.7121 | −1.88550 | ||||||||
\(302\) | 5.22614 | 0.300731 | ||||||||
\(303\) | −1.66461 | −0.0956295 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −0.833041 | −0.0476998 | ||||||||
\(306\) | −30.8538 | −1.76380 | ||||||||
\(307\) | −19.5892 | −1.11802 | −0.559008 | − | 0.829162i | \(-0.688818\pi\) | ||||
−0.559008 | + | 0.829162i | \(0.688818\pi\) | |||||||
\(308\) | 10.4357 | 0.594629 | ||||||||
\(309\) | 1.48110 | 0.0842571 | ||||||||
\(310\) | −13.5833 | −0.771477 | ||||||||
\(311\) | −19.4946 | −1.10544 | −0.552719 | − | 0.833368i | \(-0.686410\pi\) | ||||
−0.552719 | + | 0.833368i | \(0.686410\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.3035 | −1.14762 | −0.573811 | − | 0.818987i | \(-0.694536\pi\) | ||||
−0.573811 | + | 0.818987i | \(0.694536\pi\) | |||||||
\(314\) | 8.58330 | 0.484383 | ||||||||
\(315\) | −55.0032 | −3.09908 | ||||||||
\(316\) | 6.33212 | 0.356209 | ||||||||
\(317\) | 11.2881 | 0.634001 | 0.317000 | − | 0.948425i | \(-0.397324\pi\) | ||||
0.317000 | + | 0.948425i | \(0.397324\pi\) | |||||||
\(318\) | −25.1623 | −1.41103 | ||||||||
\(319\) | −16.6353 | −0.931397 | ||||||||
\(320\) | 3.87767 | 0.216769 | ||||||||
\(321\) | −25.2045 | −1.40678 | ||||||||
\(322\) | −23.6832 | −1.31982 | ||||||||
\(323\) | −6.24396 | −0.347423 | ||||||||
\(324\) | 0.593170 | 0.0329539 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 22.1972 | 1.22939 | ||||||||
\(327\) | 0.763769 | 0.0422365 | ||||||||
\(328\) | −7.96875 | −0.440001 | ||||||||
\(329\) | −5.62688 | −0.310220 | ||||||||
\(330\) | 39.7259 | 2.18684 | ||||||||
\(331\) | 0.417820 | 0.0229654 | 0.0114827 | − | 0.999934i | \(-0.496345\pi\) | ||||
0.0114827 | + | 0.999934i | \(0.496345\pi\) | |||||||
\(332\) | −7.39527 | −0.405868 | ||||||||
\(333\) | −0.0582025 | −0.00318948 | ||||||||
\(334\) | −22.0652 | −1.20736 | ||||||||
\(335\) | −33.6900 | −1.84068 | ||||||||
\(336\) | −8.08939 | −0.441312 | ||||||||
\(337\) | 17.1029 | 0.931652 | 0.465826 | − | 0.884876i | \(-0.345757\pi\) | ||||
0.465826 | + | 0.884876i | \(0.345757\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.317794 | 0.0172602 | ||||||||
\(340\) | 24.2120 | 1.31308 | ||||||||
\(341\) | −12.7346 | −0.689619 | ||||||||
\(342\) | 4.94139 | 0.267200 | ||||||||
\(343\) | 16.5340 | 0.892754 | ||||||||
\(344\) | −11.3957 | −0.614416 | ||||||||
\(345\) | −90.1557 | −4.85382 | ||||||||
\(346\) | −21.2498 | −1.14240 | ||||||||
\(347\) | −20.8002 | −1.11661 | −0.558305 | − | 0.829636i | \(-0.688548\pi\) | ||||
−0.558305 | + | 0.829636i | \(0.688548\pi\) | |||||||
\(348\) | 12.8951 | 0.691250 | ||||||||
\(349\) | −3.29845 | −0.176562 | −0.0882810 | − | 0.996096i | \(-0.528137\pi\) | ||||
−0.0882810 | + | 0.996096i | \(0.528137\pi\) | |||||||
\(350\) | 28.8100 | 1.53996 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.63541 | 0.193768 | ||||||||
\(353\) | −9.00845 | −0.479472 | −0.239736 | − | 0.970838i | \(-0.577061\pi\) | ||||
−0.239736 | + | 0.970838i | \(0.577061\pi\) | |||||||
\(354\) | −16.4453 | −0.874056 | ||||||||
\(355\) | 25.6953 | 1.36377 | ||||||||
\(356\) | −7.06857 | −0.374633 | ||||||||
\(357\) | −50.5098 | −2.67326 | ||||||||
\(358\) | 22.6071 | 1.19482 | ||||||||
\(359\) | −17.6429 | −0.931154 | −0.465577 | − | 0.885007i | \(-0.654153\pi\) | ||||
−0.465577 | + | 0.885007i | \(0.654153\pi\) | |||||||
\(360\) | −19.1611 | −1.00988 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 4.83570 | 0.254159 | ||||||||
\(363\) | 6.24543 | 0.327800 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 52.3306 | 2.73911 | ||||||||
\(366\) | 0.605401 | 0.0316448 | ||||||||
\(367\) | −17.9215 | −0.935493 | −0.467746 | − | 0.883863i | \(-0.654934\pi\) | ||||
−0.467746 | + | 0.883863i | \(0.654934\pi\) | |||||||
\(368\) | −8.25037 | −0.430080 | ||||||||
\(369\) | 39.3767 | 2.04987 | ||||||||
\(370\) | 0.0456734 | 0.00237445 | ||||||||
\(371\) | −25.6312 | −1.33071 | ||||||||
\(372\) | 9.87145 | 0.511811 | ||||||||
\(373\) | 7.67742 | 0.397522 | 0.198761 | − | 0.980048i | \(-0.436308\pi\) | ||||
0.198761 | + | 0.980048i | \(0.436308\pi\) | |||||||
\(374\) | 22.6994 | 1.17376 | ||||||||
\(375\) | 55.0347 | 2.84198 | ||||||||
\(376\) | −1.96020 | −0.101090 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 15.7047 | 0.807761 | ||||||||
\(379\) | 14.0050 | 0.719390 | 0.359695 | − | 0.933070i | \(-0.382881\pi\) | ||||
0.359695 | + | 0.933070i | \(0.382881\pi\) | |||||||
\(380\) | −3.87767 | −0.198921 | ||||||||
\(381\) | 37.8657 | 1.93992 | ||||||||
\(382\) | −18.0400 | −0.923009 | ||||||||
\(383\) | −7.25286 | −0.370604 | −0.185302 | − | 0.982682i | \(-0.559326\pi\) | ||||
−0.185302 | + | 0.982682i | \(0.559326\pi\) | |||||||
\(384\) | −2.81805 | −0.143808 | ||||||||
\(385\) | 40.4662 | 2.06235 | ||||||||
\(386\) | −6.52151 | −0.331936 | ||||||||
\(387\) | 56.3107 | 2.86243 | ||||||||
\(388\) | −6.09538 | −0.309446 | ||||||||
\(389\) | 9.44818 | 0.479042 | 0.239521 | − | 0.970891i | \(-0.423010\pi\) | ||||
0.239521 | + | 0.970891i | \(0.423010\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −51.5150 | −2.60522 | ||||||||
\(392\) | −1.24015 | −0.0626370 | ||||||||
\(393\) | 21.2042 | 1.06961 | ||||||||
\(394\) | −16.0992 | −0.811066 | ||||||||
\(395\) | 24.5539 | 1.23544 | ||||||||
\(396\) | −17.9640 | −0.902725 | ||||||||
\(397\) | 1.04634 | 0.0525144 | 0.0262572 | − | 0.999655i | \(-0.491641\pi\) | ||||
0.0262572 | + | 0.999655i | \(0.491641\pi\) | |||||||
\(398\) | 6.01255 | 0.301382 | ||||||||
\(399\) | 8.08939 | 0.404976 | ||||||||
\(400\) | 10.0364 | 0.501818 | ||||||||
\(401\) | −23.9797 | −1.19749 | −0.598744 | − | 0.800940i | \(-0.704333\pi\) | ||||
−0.598744 | + | 0.800940i | \(0.704333\pi\) | |||||||
\(402\) | 24.4837 | 1.22114 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.590697 | −0.0293883 | ||||||||
\(405\) | 2.30012 | 0.114294 | ||||||||
\(406\) | 13.1354 | 0.651900 | ||||||||
\(407\) | 0.0428199 | 0.00212251 | ||||||||
\(408\) | −17.5958 | −0.871121 | ||||||||
\(409\) | −38.8529 | −1.92115 | −0.960575 | − | 0.278021i | \(-0.910322\pi\) | ||||
−0.960575 | + | 0.278021i | \(0.910322\pi\) | |||||||
\(410\) | −30.9002 | −1.52605 | ||||||||
\(411\) | 1.29115 | 0.0636876 | ||||||||
\(412\) | 0.525578 | 0.0258934 | ||||||||
\(413\) | −16.7518 | −0.824300 | ||||||||
\(414\) | 40.7683 | 2.00365 | ||||||||
\(415\) | −28.6765 | −1.40767 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 33.5617 | 1.64352 | ||||||||
\(418\) | −3.63541 | −0.177814 | ||||||||
\(419\) | 29.2905 | 1.43094 | 0.715468 | − | 0.698645i | \(-0.246213\pi\) | ||||
0.715468 | + | 0.698645i | \(0.246213\pi\) | |||||||
\(420\) | −31.3680 | −1.53060 | ||||||||
\(421\) | 20.6974 | 1.00873 | 0.504365 | − | 0.863490i | \(-0.331727\pi\) | ||||
0.504365 | + | 0.863490i | \(0.331727\pi\) | |||||||
\(422\) | 4.97594 | 0.242225 | ||||||||
\(423\) | 9.68611 | 0.470955 | ||||||||
\(424\) | −8.92897 | −0.433629 | ||||||||
\(425\) | 62.6666 | 3.03978 | ||||||||
\(426\) | −18.6737 | −0.904746 | ||||||||
\(427\) | 0.616684 | 0.0298434 | ||||||||
\(428\) | −8.94396 | −0.432322 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −44.1889 | −2.13098 | ||||||||
\(431\) | −23.9545 | −1.15385 | −0.576923 | − | 0.816799i | \(-0.695747\pi\) | ||||
−0.576923 | + | 0.816799i | \(0.695747\pi\) | |||||||
\(432\) | 5.47093 | 0.263220 | ||||||||
\(433\) | −32.1161 | −1.54340 | −0.771701 | − | 0.635986i | \(-0.780594\pi\) | ||||
−0.771701 | + | 0.635986i | \(0.780594\pi\) | |||||||
\(434\) | 10.0554 | 0.482675 | ||||||||
\(435\) | 50.0030 | 2.39746 | ||||||||
\(436\) | 0.271028 | 0.0129799 | ||||||||
\(437\) | 8.25037 | 0.394669 | ||||||||
\(438\) | −38.0306 | −1.81717 | ||||||||
\(439\) | −22.7654 | −1.08653 | −0.543266 | − | 0.839561i | \(-0.682813\pi\) | ||||
−0.543266 | + | 0.839561i | \(0.682813\pi\) | |||||||
\(440\) | 14.0969 | 0.672046 | ||||||||
\(441\) | 6.12806 | 0.291812 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 41.0644 | 1.95103 | 0.975515 | − | 0.219934i | \(-0.0705842\pi\) | ||||
0.975515 | + | 0.219934i | \(0.0705842\pi\) | |||||||
\(444\) | −0.0331926 | −0.00157525 | ||||||||
\(445\) | −27.4096 | −1.29934 | ||||||||
\(446\) | −18.1338 | −0.858659 | ||||||||
\(447\) | −18.8088 | −0.889625 | ||||||||
\(448\) | −2.87057 | −0.135621 | ||||||||
\(449\) | 19.7108 | 0.930209 | 0.465104 | − | 0.885256i | \(-0.346017\pi\) | ||||
0.465104 | + | 0.885256i | \(0.346017\pi\) | |||||||
\(450\) | −49.5936 | −2.33786 | ||||||||
\(451\) | −28.9697 | −1.36413 | ||||||||
\(452\) | 0.112771 | 0.00530430 | ||||||||
\(453\) | −14.7275 | −0.691959 | ||||||||
\(454\) | −12.3853 | −0.581270 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.81805 | 0.131967 | ||||||||
\(457\) | 13.3513 | 0.624548 | 0.312274 | − | 0.949992i | \(-0.398909\pi\) | ||||
0.312274 | + | 0.949992i | \(0.398909\pi\) | |||||||
\(458\) | −2.20870 | −0.103206 | ||||||||
\(459\) | 34.1603 | 1.59446 | ||||||||
\(460\) | −31.9923 | −1.49165 | ||||||||
\(461\) | 11.0636 | 0.515285 | 0.257642 | − | 0.966240i | \(-0.417054\pi\) | ||||
0.257642 | + | 0.966240i | \(0.417054\pi\) | |||||||
\(462\) | −29.4083 | −1.36820 | ||||||||
\(463\) | 12.7149 | 0.590913 | 0.295456 | − | 0.955356i | \(-0.404528\pi\) | ||||
0.295456 | + | 0.955356i | \(0.404528\pi\) | |||||||
\(464\) | 4.57590 | 0.212431 | ||||||||
\(465\) | 38.2783 | 1.77511 | ||||||||
\(466\) | −3.73725 | −0.173125 | ||||||||
\(467\) | −15.3190 | −0.708877 | −0.354438 | − | 0.935079i | \(-0.615328\pi\) | ||||
−0.354438 | + | 0.935079i | \(0.615328\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.9400 | 1.15162 | ||||||||
\(470\) | −7.60101 | −0.350609 | ||||||||
\(471\) | −24.1881 | −1.11453 | ||||||||
\(472\) | −5.83570 | −0.268610 | ||||||||
\(473\) | −41.4281 | −1.90487 | ||||||||
\(474\) | −17.8442 | −0.819611 | ||||||||
\(475\) | −10.0364 | −0.460500 | ||||||||
\(476\) | −17.9237 | −0.821531 | ||||||||
\(477\) | 44.1216 | 2.02019 | ||||||||
\(478\) | −2.20869 | −0.101023 | ||||||||
\(479\) | 15.5689 | 0.711363 | 0.355682 | − | 0.934607i | \(-0.384249\pi\) | ||||
0.355682 | + | 0.934607i | \(0.384249\pi\) | |||||||
\(480\) | −10.9275 | −0.498769 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 22.9135 | 1.04368 | ||||||||
\(483\) | 66.7405 | 3.03680 | ||||||||
\(484\) | 2.21623 | 0.100738 | ||||||||
\(485\) | −23.6359 | −1.07325 | ||||||||
\(486\) | 14.7412 | 0.668675 | ||||||||
\(487\) | −30.8664 | −1.39869 | −0.699346 | − | 0.714784i | \(-0.746525\pi\) | ||||
−0.699346 | + | 0.714784i | \(0.746525\pi\) | |||||||
\(488\) | 0.214830 | 0.00972489 | ||||||||
\(489\) | −62.5526 | −2.82873 | ||||||||
\(490\) | −4.80889 | −0.217244 | ||||||||
\(491\) | −29.6957 | −1.34015 | −0.670074 | − | 0.742294i | \(-0.733738\pi\) | ||||
−0.670074 | + | 0.742294i | \(0.733738\pi\) | |||||||
\(492\) | 22.4563 | 1.01241 | ||||||||
\(493\) | 28.5717 | 1.28681 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −69.6585 | −3.13092 | ||||||||
\(496\) | 3.50294 | 0.157287 | ||||||||
\(497\) | −19.0218 | −0.853242 | ||||||||
\(498\) | 20.8402 | 0.933873 | ||||||||
\(499\) | 16.4665 | 0.737141 | 0.368571 | − | 0.929600i | \(-0.379847\pi\) | ||||
0.368571 | + | 0.929600i | \(0.379847\pi\) | |||||||
\(500\) | 19.5294 | 0.873380 | ||||||||
\(501\) | 62.1809 | 2.77804 | ||||||||
\(502\) | 1.22889 | 0.0548479 | ||||||||
\(503\) | −26.3001 | −1.17267 | −0.586333 | − | 0.810070i | \(-0.699429\pi\) | ||||
−0.586333 | + | 0.810070i | \(0.699429\pi\) | |||||||
\(504\) | 14.1846 | 0.631832 | ||||||||
\(505\) | −2.29053 | −0.101927 | ||||||||
\(506\) | −29.9935 | −1.33337 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.4369 | 0.596165 | ||||||||
\(509\) | 32.6972 | 1.44928 | 0.724639 | − | 0.689128i | \(-0.242006\pi\) | ||||
0.724639 | + | 0.689128i | \(0.242006\pi\) | |||||||
\(510\) | −68.2307 | −3.02131 | ||||||||
\(511\) | −38.7393 | −1.71373 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.47093 | −0.241547 | ||||||||
\(514\) | 12.3311 | 0.543900 | ||||||||
\(515\) | 2.03802 | 0.0898060 | ||||||||
\(516\) | 32.1137 | 1.41372 | ||||||||
\(517\) | −7.12613 | −0.313407 | ||||||||
\(518\) | −0.0338111 | −0.00148558 | ||||||||
\(519\) | 59.8829 | 2.62857 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −42.1295 | −1.84573 | −0.922863 | − | 0.385129i | \(-0.874157\pi\) | ||||
−0.922863 | + | 0.385129i | \(0.874157\pi\) | |||||||
\(522\) | −22.6113 | −0.989670 | ||||||||
\(523\) | −14.2840 | −0.624597 | −0.312298 | − | 0.949984i | \(-0.601099\pi\) | ||||
−0.312298 | + | 0.949984i | \(0.601099\pi\) | |||||||
\(524\) | 7.52443 | 0.328706 | ||||||||
\(525\) | −81.1881 | −3.54334 | ||||||||
\(526\) | 7.51111 | 0.327500 | ||||||||
\(527\) | 21.8722 | 0.952768 | ||||||||
\(528\) | −10.2448 | −0.445846 | ||||||||
\(529\) | 45.0686 | 1.95951 | ||||||||
\(530\) | −34.6237 | −1.50396 | ||||||||
\(531\) | 28.8365 | 1.25140 | ||||||||
\(532\) | 2.87057 | 0.124455 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 19.9196 | 0.862004 | ||||||||
\(535\) | −34.6818 | −1.49942 | ||||||||
\(536\) | 8.68818 | 0.375272 | ||||||||
\(537\) | −63.7080 | −2.74920 | ||||||||
\(538\) | 16.8519 | 0.726537 | ||||||||
\(539\) | −4.50845 | −0.194193 | ||||||||
\(540\) | 21.2145 | 0.912926 | ||||||||
\(541\) | 17.2406 | 0.741232 | 0.370616 | − | 0.928786i | \(-0.379147\pi\) | ||||
0.370616 | + | 0.928786i | \(0.379147\pi\) | |||||||
\(542\) | 9.80221 | 0.421041 | ||||||||
\(543\) | −13.6272 | −0.584800 | ||||||||
\(544\) | −6.24396 | −0.267708 | ||||||||
\(545\) | 1.05096 | 0.0450181 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.5996 | −0.709748 | −0.354874 | − | 0.934914i | \(-0.615476\pi\) | ||||
−0.354874 | + | 0.934914i | \(0.615476\pi\) | |||||||
\(548\) | 0.458171 | 0.0195721 | ||||||||
\(549\) | −1.06156 | −0.0453062 | ||||||||
\(550\) | 36.4863 | 1.55578 | ||||||||
\(551\) | −4.57590 | −0.194940 | ||||||||
\(552\) | 23.2499 | 0.989583 | ||||||||
\(553\) | −18.1768 | −0.772954 | ||||||||
\(554\) | 21.3755 | 0.908159 | ||||||||
\(555\) | −0.128710 | −0.00546343 | ||||||||
\(556\) | 11.9096 | 0.505078 | ||||||||
\(557\) | 21.0519 | 0.891997 | 0.445998 | − | 0.895034i | \(-0.352849\pi\) | ||||
0.445998 | + | 0.895034i | \(0.352849\pi\) | |||||||
\(558\) | −17.3094 | −0.732765 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −11.1311 | −0.470376 | ||||||||
\(561\) | −63.9679 | −2.70073 | ||||||||
\(562\) | 3.05650 | 0.128931 | ||||||||
\(563\) | −15.0002 | −0.632185 | −0.316092 | − | 0.948728i | \(-0.602371\pi\) | ||||
−0.316092 | + | 0.948728i | \(0.602371\pi\) | |||||||
\(564\) | 5.52393 | 0.232599 | ||||||||
\(565\) | 0.437289 | 0.0183969 | ||||||||
\(566\) | 2.99153 | 0.125744 | ||||||||
\(567\) | −1.70273 | −0.0715081 | ||||||||
\(568\) | −6.62648 | −0.278041 | ||||||||
\(569\) | 0.572295 | 0.0239919 | 0.0119959 | − | 0.999928i | \(-0.496181\pi\) | ||||
0.0119959 | + | 0.999928i | \(0.496181\pi\) | |||||||
\(570\) | 10.9275 | 0.457701 | ||||||||
\(571\) | −38.8818 | −1.62715 | −0.813577 | − | 0.581457i | \(-0.802483\pi\) | ||||
−0.813577 | + | 0.581457i | \(0.802483\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 50.8377 | 2.12378 | ||||||||
\(574\) | 22.8748 | 0.954777 | ||||||||
\(575\) | −82.8037 | −3.45315 | ||||||||
\(576\) | 4.94139 | 0.205891 | ||||||||
\(577\) | −3.71329 | −0.154586 | −0.0772931 | − | 0.997008i | \(-0.524628\pi\) | ||||
−0.0772931 | + | 0.997008i | \(0.524628\pi\) | |||||||
\(578\) | −21.9870 | −0.914540 | ||||||||
\(579\) | 18.3779 | 0.763760 | ||||||||
\(580\) | 17.7439 | 0.736774 | ||||||||
\(581\) | 21.2286 | 0.880711 | ||||||||
\(582\) | 17.1771 | 0.712012 | ||||||||
\(583\) | −32.4605 | −1.34438 | ||||||||
\(584\) | −13.4954 | −0.558442 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.1240 | 0.418217 | ||||||||
\(587\) | −5.88784 | −0.243017 | −0.121509 | − | 0.992590i | \(-0.538773\pi\) | ||||
−0.121509 | + | 0.992590i | \(0.538773\pi\) | |||||||
\(588\) | 3.49480 | 0.144123 | ||||||||
\(589\) | −3.50294 | −0.144336 | ||||||||
\(590\) | −22.6289 | −0.931619 | ||||||||
\(591\) | 45.3683 | 1.86620 | ||||||||
\(592\) | −0.0117786 | −0.000484096 0 | ||||||||
\(593\) | −12.5482 | −0.515293 | −0.257647 | − | 0.966239i | \(-0.582947\pi\) | ||||
−0.257647 | + | 0.966239i | \(0.582947\pi\) | |||||||
\(594\) | 19.8891 | 0.816059 | ||||||||
\(595\) | −69.5023 | −2.84932 | ||||||||
\(596\) | −6.67440 | −0.273394 | ||||||||
\(597\) | −16.9436 | −0.693457 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.9454 | 0.488075 | 0.244038 | − | 0.969766i | \(-0.421528\pi\) | ||||
0.244038 | + | 0.969766i | \(0.421528\pi\) | |||||||
\(600\) | −28.2829 | −1.15465 | ||||||||
\(601\) | 35.0150 | 1.42829 | 0.714147 | − | 0.699996i | \(-0.246815\pi\) | ||||
0.714147 | + | 0.699996i | \(0.246815\pi\) | |||||||
\(602\) | 32.7121 | 1.33325 | ||||||||
\(603\) | −42.9317 | −1.74831 | ||||||||
\(604\) | −5.22614 | −0.212649 | ||||||||
\(605\) | 8.59380 | 0.349388 | ||||||||
\(606\) | 1.66461 | 0.0676202 | ||||||||
\(607\) | 7.18015 | 0.291433 | 0.145717 | − | 0.989326i | \(-0.453451\pi\) | ||||
0.145717 | + | 0.989326i | \(0.453451\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −37.0163 | −1.49997 | ||||||||
\(610\) | 0.833041 | 0.0337288 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 30.8538 | 1.24719 | ||||||||
\(613\) | −25.1763 | −1.01686 | −0.508430 | − | 0.861103i | \(-0.669774\pi\) | ||||
−0.508430 | + | 0.861103i | \(0.669774\pi\) | |||||||
\(614\) | 19.5892 | 0.790556 | ||||||||
\(615\) | 87.0783 | 3.51134 | ||||||||
\(616\) | −10.4357 | −0.420466 | ||||||||
\(617\) | 6.50472 | 0.261870 | 0.130935 | − | 0.991391i | \(-0.458202\pi\) | ||||
0.130935 | + | 0.991391i | \(0.458202\pi\) | |||||||
\(618\) | −1.48110 | −0.0595788 | ||||||||
\(619\) | 19.3211 | 0.776580 | 0.388290 | − | 0.921537i | \(-0.373066\pi\) | ||||
0.388290 | + | 0.921537i | \(0.373066\pi\) | |||||||
\(620\) | 13.5833 | 0.545517 | ||||||||
\(621\) | −45.1372 | −1.81129 | ||||||||
\(622\) | 19.4946 | 0.781662 | ||||||||
\(623\) | 20.2908 | 0.812933 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.5468 | 1.02187 | ||||||||
\(626\) | 20.3035 | 0.811492 | ||||||||
\(627\) | 10.2448 | 0.409137 | ||||||||
\(628\) | −8.58330 | −0.342511 | ||||||||
\(629\) | −0.0735449 | −0.00293243 | ||||||||
\(630\) | 55.0032 | 2.19138 | ||||||||
\(631\) | −20.6678 | −0.822772 | −0.411386 | − | 0.911461i | \(-0.634955\pi\) | ||||
−0.411386 | + | 0.911461i | \(0.634955\pi\) | |||||||
\(632\) | −6.33212 | −0.251878 | ||||||||
\(633\) | −14.0224 | −0.557341 | ||||||||
\(634\) | −11.2881 | −0.448306 | ||||||||
\(635\) | 52.1038 | 2.06768 | ||||||||
\(636\) | 25.1623 | 0.997749 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.6353 | 0.658597 | ||||||||
\(639\) | 32.7440 | 1.29533 | ||||||||
\(640\) | −3.87767 | −0.153279 | ||||||||
\(641\) | −23.0621 | −0.910897 | −0.455448 | − | 0.890262i | \(-0.650521\pi\) | ||||
−0.455448 | + | 0.890262i | \(0.650521\pi\) | |||||||
\(642\) | 25.2045 | 0.994742 | ||||||||
\(643\) | −28.3674 | −1.11870 | −0.559351 | − | 0.828931i | \(-0.688949\pi\) | ||||
−0.559351 | + | 0.828931i | \(0.688949\pi\) | |||||||
\(644\) | 23.6832 | 0.933250 | ||||||||
\(645\) | 124.526 | 4.90322 | ||||||||
\(646\) | 6.24396 | 0.245665 | ||||||||
\(647\) | 0.127715 | 0.00502100 | 0.00251050 | − | 0.999997i | \(-0.499201\pi\) | ||||
0.00251050 | + | 0.999997i | \(0.499201\pi\) | |||||||
\(648\) | −0.593170 | −0.0233019 | ||||||||
\(649\) | −21.2152 | −0.832768 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −28.3366 | −1.11060 | ||||||||
\(652\) | −22.1972 | −0.869308 | ||||||||
\(653\) | −34.3776 | −1.34530 | −0.672649 | − | 0.739961i | \(-0.734844\pi\) | ||||
−0.672649 | + | 0.739961i | \(0.734844\pi\) | |||||||
\(654\) | −0.763769 | −0.0298657 | ||||||||
\(655\) | 29.1773 | 1.14005 | ||||||||
\(656\) | 7.96875 | 0.311128 | ||||||||
\(657\) | 66.6858 | 2.60166 | ||||||||
\(658\) | 5.62688 | 0.219359 | ||||||||
\(659\) | −0.0515489 | −0.00200806 | −0.00100403 | − | 0.999999i | \(-0.500320\pi\) | ||||
−0.00100403 | + | 0.999999i | \(0.500320\pi\) | |||||||
\(660\) | −39.7259 | −1.54633 | ||||||||
\(661\) | −4.51042 | −0.175435 | −0.0877174 | − | 0.996145i | \(-0.527957\pi\) | ||||
−0.0877174 | + | 0.996145i | \(0.527957\pi\) | |||||||
\(662\) | −0.417820 | −0.0162390 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.39527 | 0.286992 | ||||||||
\(665\) | 11.1311 | 0.431646 | ||||||||
\(666\) | 0.0582025 | 0.00225530 | ||||||||
\(667\) | −37.7529 | −1.46180 | ||||||||
\(668\) | 22.0652 | 0.853730 | ||||||||
\(669\) | 51.1018 | 1.97571 | ||||||||
\(670\) | 33.6900 | 1.30156 | ||||||||
\(671\) | 0.780995 | 0.0301500 | ||||||||
\(672\) | 8.08939 | 0.312055 | ||||||||
\(673\) | 8.33824 | 0.321416 | 0.160708 | − | 0.987002i | \(-0.448622\pi\) | ||||
0.160708 | + | 0.987002i | \(0.448622\pi\) | |||||||
\(674\) | −17.1029 | −0.658778 | ||||||||
\(675\) | 54.9082 | 2.11342 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.4629 | −1.20922 | −0.604609 | − | 0.796522i | \(-0.706671\pi\) | ||||
−0.604609 | + | 0.796522i | \(0.706671\pi\) | |||||||
\(678\) | −0.317794 | −0.0122048 | ||||||||
\(679\) | 17.4972 | 0.671480 | ||||||||
\(680\) | −24.2120 | −0.928489 | ||||||||
\(681\) | 34.9023 | 1.33746 | ||||||||
\(682\) | 12.7346 | 0.487634 | ||||||||
\(683\) | 11.9211 | 0.456150 | 0.228075 | − | 0.973644i | \(-0.426757\pi\) | ||||
0.228075 | + | 0.973644i | \(0.426757\pi\) | |||||||
\(684\) | −4.94139 | −0.188939 | ||||||||
\(685\) | 1.77664 | 0.0678818 | ||||||||
\(686\) | −16.5340 | −0.631272 | ||||||||
\(687\) | 6.22422 | 0.237469 | ||||||||
\(688\) | 11.3957 | 0.434457 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 90.1557 | 3.43217 | ||||||||
\(691\) | 21.6103 | 0.822096 | 0.411048 | − | 0.911614i | \(-0.365163\pi\) | ||||
0.411048 | + | 0.911614i | \(0.365163\pi\) | |||||||
\(692\) | 21.2498 | 0.807796 | ||||||||
\(693\) | 51.5668 | 1.95886 | ||||||||
\(694\) | 20.8002 | 0.789563 | ||||||||
\(695\) | 46.1814 | 1.75176 | ||||||||
\(696\) | −12.8951 | −0.488788 | ||||||||
\(697\) | 49.7566 | 1.88466 | ||||||||
\(698\) | 3.29845 | 0.124848 | ||||||||
\(699\) | 10.5317 | 0.398347 | ||||||||
\(700\) | −28.8100 | −1.08892 | ||||||||
\(701\) | −52.0824 | −1.96713 | −0.983563 | − | 0.180563i | \(-0.942208\pi\) | ||||
−0.983563 | + | 0.180563i | \(0.942208\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0117786 | 0.000444237 0 | ||||||||
\(704\) | −3.63541 | −0.137015 | ||||||||
\(705\) | 21.4200 | 0.806724 | ||||||||
\(706\) | 9.00845 | 0.339038 | ||||||||
\(707\) | 1.69563 | 0.0637709 | ||||||||
\(708\) | 16.4453 | 0.618051 | ||||||||
\(709\) | −13.1704 | −0.494625 | −0.247312 | − | 0.968936i | \(-0.579547\pi\) | ||||
−0.247312 | + | 0.968936i | \(0.579547\pi\) | |||||||
\(710\) | −25.6953 | −0.964329 | ||||||||
\(711\) | 31.2895 | 1.17345 | ||||||||
\(712\) | 7.06857 | 0.264906 | ||||||||
\(713\) | −28.9005 | −1.08233 | ||||||||
\(714\) | 50.5098 | 1.89028 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −22.6071 | −0.844868 | ||||||||
\(717\) | 6.22420 | 0.232447 | ||||||||
\(718\) | 17.6429 | 0.658425 | ||||||||
\(719\) | −2.90129 | −0.108200 | −0.0540999 | − | 0.998536i | \(-0.517229\pi\) | ||||
−0.0540999 | + | 0.998536i | \(0.517229\pi\) | |||||||
\(720\) | 19.1611 | 0.714092 | ||||||||
\(721\) | −1.50871 | −0.0561872 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −64.5714 | −2.40144 | ||||||||
\(724\) | −4.83570 | −0.179717 | ||||||||
\(725\) | 45.9254 | 1.70563 | ||||||||
\(726\) | −6.24543 | −0.231790 | ||||||||
\(727\) | −32.5084 | −1.20567 | −0.602835 | − | 0.797866i | \(-0.705962\pi\) | ||||
−0.602835 | + | 0.797866i | \(0.705962\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.3209 | −1.60448 | ||||||||
\(730\) | −52.3306 | −1.93684 | ||||||||
\(731\) | 71.1544 | 2.63174 | ||||||||
\(732\) | −0.605401 | −0.0223763 | ||||||||
\(733\) | 35.7248 | 1.31952 | 0.659762 | − | 0.751475i | \(-0.270657\pi\) | ||||
0.659762 | + | 0.751475i | \(0.270657\pi\) | |||||||
\(734\) | 17.9215 | 0.661493 | ||||||||
\(735\) | 13.5517 | 0.499862 | ||||||||
\(736\) | 8.25037 | 0.304113 | ||||||||
\(737\) | 31.5851 | 1.16345 | ||||||||
\(738\) | −39.3767 | −1.44948 | ||||||||
\(739\) | 3.02329 | 0.111213 | 0.0556067 | − | 0.998453i | \(-0.482291\pi\) | ||||
0.0556067 | + | 0.998453i | \(0.482291\pi\) | |||||||
\(740\) | −0.0456734 | −0.00167899 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 25.6312 | 0.940951 | ||||||||
\(743\) | 5.27755 | 0.193615 | 0.0968073 | − | 0.995303i | \(-0.469137\pi\) | ||||
0.0968073 | + | 0.995303i | \(0.469137\pi\) | |||||||
\(744\) | −9.87145 | −0.361905 | ||||||||
\(745\) | −25.8812 | −0.948213 | ||||||||
\(746\) | −7.67742 | −0.281090 | ||||||||
\(747\) | −36.5429 | −1.33704 | ||||||||
\(748\) | −22.6994 | −0.829971 | ||||||||
\(749\) | 25.6742 | 0.938115 | ||||||||
\(750\) | −55.0347 | −2.00958 | ||||||||
\(751\) | −18.1364 | −0.661808 | −0.330904 | − | 0.943664i | \(-0.607354\pi\) | ||||
−0.330904 | + | 0.943664i | \(0.607354\pi\) | |||||||
\(752\) | 1.96020 | 0.0714811 | ||||||||
\(753\) | −3.46306 | −0.126201 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20.2653 | −0.737529 | ||||||||
\(756\) | −15.7047 | −0.571173 | ||||||||
\(757\) | 46.3593 | 1.68496 | 0.842478 | − | 0.538731i | \(-0.181096\pi\) | ||||
0.842478 | + | 0.538731i | \(0.181096\pi\) | |||||||
\(758\) | −14.0050 | −0.508685 | ||||||||
\(759\) | 84.5231 | 3.06799 | ||||||||
\(760\) | 3.87767 | 0.140658 | ||||||||
\(761\) | 45.5300 | 1.65046 | 0.825231 | − | 0.564796i | \(-0.191045\pi\) | ||||
0.825231 | + | 0.564796i | \(0.191045\pi\) | |||||||
\(762\) | −37.8657 | −1.37173 | ||||||||
\(763\) | −0.778003 | −0.0281656 | ||||||||
\(764\) | 18.0400 | 0.652666 | ||||||||
\(765\) | 119.641 | 4.32564 | ||||||||
\(766\) | 7.25286 | 0.262057 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.81805 | 0.101688 | ||||||||
\(769\) | 51.1629 | 1.84498 | 0.922491 | − | 0.386018i | \(-0.126150\pi\) | ||||
0.922491 | + | 0.386018i | \(0.126150\pi\) | |||||||
\(770\) | −40.4662 | −1.45830 | ||||||||
\(771\) | −34.7495 | −1.25147 | ||||||||
\(772\) | 6.52151 | 0.234714 | ||||||||
\(773\) | −23.5929 | −0.848578 | −0.424289 | − | 0.905527i | \(-0.639476\pi\) | ||||
−0.424289 | + | 0.905527i | \(0.639476\pi\) | |||||||
\(774\) | −56.3107 | −2.02404 | ||||||||
\(775\) | 35.1568 | 1.26287 | ||||||||
\(776\) | 6.09538 | 0.218811 | ||||||||
\(777\) | 0.0952814 | 0.00341820 | ||||||||
\(778\) | −9.44818 | −0.338734 | ||||||||
\(779\) | −7.96875 | −0.285510 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.0900 | −0.862008 | ||||||||
\(782\) | 51.5150 | 1.84217 | ||||||||
\(783\) | 25.0344 | 0.894658 | ||||||||
\(784\) | 1.24015 | 0.0442910 | ||||||||
\(785\) | −33.2832 | −1.18793 | ||||||||
\(786\) | −21.2042 | −0.756329 | ||||||||
\(787\) | 35.9121 | 1.28013 | 0.640064 | − | 0.768321i | \(-0.278908\pi\) | ||||
0.640064 | + | 0.768321i | \(0.278908\pi\) | |||||||
\(788\) | 16.0992 | 0.573510 | ||||||||
\(789\) | −21.1667 | −0.753553 | ||||||||
\(790\) | −24.5539 | −0.873588 | ||||||||
\(791\) | −0.323716 | −0.0115100 | ||||||||
\(792\) | 17.9640 | 0.638323 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −1.04634 | −0.0371333 | ||||||||
\(795\) | 97.5711 | 3.46049 | ||||||||
\(796\) | −6.01255 | −0.213109 | ||||||||
\(797\) | 0.957289 | 0.0339089 | 0.0169545 | − | 0.999856i | \(-0.494603\pi\) | ||||
0.0169545 | + | 0.999856i | \(0.494603\pi\) | |||||||
\(798\) | −8.08939 | −0.286361 | ||||||||
\(799\) | 12.2394 | 0.432999 | ||||||||
\(800\) | −10.0364 | −0.354839 | ||||||||
\(801\) | −34.9286 | −1.23414 | ||||||||
\(802\) | 23.9797 | 0.846753 | ||||||||
\(803\) | −49.0612 | −1.73133 | ||||||||
\(804\) | −24.4837 | −0.863474 | ||||||||
\(805\) | 91.8359 | 3.23679 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −47.4895 | −1.67171 | ||||||||
\(808\) | 0.590697 | 0.0207806 | ||||||||
\(809\) | −26.5699 | −0.934147 | −0.467074 | − | 0.884218i | \(-0.654692\pi\) | ||||
−0.467074 | + | 0.884218i | \(0.654692\pi\) | |||||||
\(810\) | −2.30012 | −0.0808180 | ||||||||
\(811\) | −23.2305 | −0.815732 | −0.407866 | − | 0.913042i | \(-0.633727\pi\) | ||||
−0.407866 | + | 0.913042i | \(0.633727\pi\) | |||||||
\(812\) | −13.1354 | −0.460963 | ||||||||
\(813\) | −27.6231 | −0.968784 | ||||||||
\(814\) | −0.0428199 | −0.00150084 | ||||||||
\(815\) | −86.0734 | −3.01502 | ||||||||
\(816\) | 17.5958 | 0.615975 | ||||||||
\(817\) | −11.3957 | −0.398685 | ||||||||
\(818\) | 38.8529 | 1.35846 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 30.9002 | 1.07908 | ||||||||
\(821\) | −39.8660 | −1.39133 | −0.695666 | − | 0.718365i | \(-0.744891\pi\) | ||||
−0.695666 | + | 0.718365i | \(0.744891\pi\) | |||||||
\(822\) | −1.29115 | −0.0450339 | ||||||||
\(823\) | 24.1750 | 0.842686 | 0.421343 | − | 0.906901i | \(-0.361559\pi\) | ||||
0.421343 | + | 0.906901i | \(0.361559\pi\) | |||||||
\(824\) | −0.525578 | −0.0183094 | ||||||||
\(825\) | −102.820 | −3.57974 | ||||||||
\(826\) | 16.7518 | 0.582868 | ||||||||
\(827\) | −23.4688 | −0.816090 | −0.408045 | − | 0.912962i | \(-0.633789\pi\) | ||||
−0.408045 | + | 0.912962i | \(0.633789\pi\) | |||||||
\(828\) | −40.7683 | −1.41680 | ||||||||
\(829\) | 25.2579 | 0.877243 | 0.438621 | − | 0.898672i | \(-0.355467\pi\) | ||||
0.438621 | + | 0.898672i | \(0.355467\pi\) | |||||||
\(830\) | 28.6765 | 0.995374 | ||||||||
\(831\) | −60.2372 | −2.08961 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.74344 | 0.268294 | ||||||||
\(834\) | −33.5617 | −1.16215 | ||||||||
\(835\) | 85.5619 | 2.96099 | ||||||||
\(836\) | 3.63541 | 0.125733 | ||||||||
\(837\) | 19.1643 | 0.662416 | ||||||||
\(838\) | −29.2905 | −1.01182 | ||||||||
\(839\) | 30.6795 | 1.05917 | 0.529587 | − | 0.848255i | \(-0.322347\pi\) | ||||
0.529587 | + | 0.848255i | \(0.322347\pi\) | |||||||
\(840\) | 31.3680 | 1.08230 | ||||||||
\(841\) | −8.06113 | −0.277970 | ||||||||
\(842\) | −20.6974 | −0.713280 | ||||||||
\(843\) | −8.61337 | −0.296660 | ||||||||
\(844\) | −4.97594 | −0.171279 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.68611 | −0.333015 | ||||||||
\(847\) | −6.36182 | −0.218595 | ||||||||
\(848\) | 8.92897 | 0.306622 | ||||||||
\(849\) | −8.43029 | −0.289327 | ||||||||
\(850\) | −62.6666 | −2.14945 | ||||||||
\(851\) | 0.0971775 | 0.00333120 | ||||||||
\(852\) | 18.6737 | 0.639752 | ||||||||
\(853\) | 13.7824 | 0.471900 | 0.235950 | − | 0.971765i | \(-0.424180\pi\) | ||||
0.235950 | + | 0.971765i | \(0.424180\pi\) | |||||||
\(854\) | −0.616684 | −0.0211025 | ||||||||
\(855\) | −19.1611 | −0.655296 | ||||||||
\(856\) | 8.94396 | 0.305698 | ||||||||
\(857\) | −23.9708 | −0.818827 | −0.409414 | − | 0.912349i | \(-0.634267\pi\) | ||||
−0.409414 | + | 0.912349i | \(0.634267\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.3175 | −0.624985 | −0.312492 | − | 0.949920i | \(-0.601164\pi\) | ||||
−0.312492 | + | 0.949920i | \(0.601164\pi\) | |||||||
\(860\) | 44.1889 | 1.50683 | ||||||||
\(861\) | −64.4624 | −2.19687 | ||||||||
\(862\) | 23.9545 | 0.815892 | ||||||||
\(863\) | −2.56280 | −0.0872389 | −0.0436194 | − | 0.999048i | \(-0.513889\pi\) | ||||
−0.0436194 | + | 0.999048i | \(0.513889\pi\) | |||||||
\(864\) | −5.47093 | −0.186125 | ||||||||
\(865\) | 82.3998 | 2.80168 | ||||||||
\(866\) | 32.1161 | 1.09135 | ||||||||
\(867\) | 61.9605 | 2.10429 | ||||||||
\(868\) | −10.0554 | −0.341303 | ||||||||
\(869\) | −23.0199 | −0.780895 | ||||||||
\(870\) | −50.0030 | −1.69526 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.271028 | −0.00917816 | ||||||||
\(873\) | −30.1196 | −1.01940 | ||||||||
\(874\) | −8.25037 | −0.279073 | ||||||||
\(875\) | −56.0604 | −1.89519 | ||||||||
\(876\) | 38.0306 | 1.28493 | ||||||||
\(877\) | 5.80341 | 0.195967 | 0.0979837 | − | 0.995188i | \(-0.468761\pi\) | ||||
0.0979837 | + | 0.995188i | \(0.468761\pi\) | |||||||
\(878\) | 22.7654 | 0.768294 | ||||||||
\(879\) | −28.5298 | −0.962287 | ||||||||
\(880\) | −14.0969 | −0.475208 | ||||||||
\(881\) | 14.3781 | 0.484411 | 0.242205 | − | 0.970225i | \(-0.422129\pi\) | ||||
0.242205 | + | 0.970225i | \(0.422129\pi\) | |||||||
\(882\) | −6.12806 | −0.206342 | ||||||||
\(883\) | 38.7080 | 1.30263 | 0.651313 | − | 0.758809i | \(-0.274218\pi\) | ||||
0.651313 | + | 0.758809i | \(0.274218\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 63.7694 | 2.14359 | ||||||||
\(886\) | −41.0644 | −1.37959 | ||||||||
\(887\) | 22.0494 | 0.740347 | 0.370174 | − | 0.928963i | \(-0.379298\pi\) | ||||
0.370174 | + | 0.928963i | \(0.379298\pi\) | |||||||
\(888\) | 0.0331926 | 0.00111387 | ||||||||
\(889\) | −38.5714 | −1.29364 | ||||||||
\(890\) | 27.4096 | 0.918772 | ||||||||
\(891\) | −2.15642 | −0.0722427 | ||||||||
\(892\) | 18.1338 | 0.607163 | ||||||||
\(893\) | −1.96020 | −0.0655955 | ||||||||
\(894\) | 18.8088 | 0.629060 | ||||||||
\(895\) | −87.6631 | −2.93025 | ||||||||
\(896\) | 2.87057 | 0.0958989 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19.7108 | −0.657757 | ||||||||
\(899\) | 16.0291 | 0.534600 | ||||||||
\(900\) | 49.5936 | 1.65312 | ||||||||
\(901\) | 55.7521 | 1.85737 | ||||||||
\(902\) | 28.9697 | 0.964586 | ||||||||
\(903\) | −92.1844 | −3.06770 | ||||||||
\(904\) | −0.112771 | −0.00375071 | ||||||||
\(905\) | −18.7513 | −0.623313 | ||||||||
\(906\) | 14.7275 | 0.489289 | ||||||||
\(907\) | 29.5199 | 0.980192 | 0.490096 | − | 0.871668i | \(-0.336962\pi\) | ||||
0.490096 | + | 0.871668i | \(0.336962\pi\) | |||||||
\(908\) | 12.3853 | 0.411020 | ||||||||
\(909\) | −2.91886 | −0.0968126 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.8931 | −0.493429 | −0.246715 | − | 0.969088i | \(-0.579351\pi\) | ||||
−0.246715 | + | 0.969088i | \(0.579351\pi\) | |||||||
\(912\) | −2.81805 | −0.0933149 | ||||||||
\(913\) | 26.8849 | 0.889759 | ||||||||
\(914\) | −13.3513 | −0.441622 | ||||||||
\(915\) | −2.34755 | −0.0776075 | ||||||||
\(916\) | 2.20870 | 0.0729774 | ||||||||
\(917\) | −21.5994 | −0.713274 | ||||||||
\(918\) | −34.1603 | −1.12746 | ||||||||
\(919\) | 17.9143 | 0.590940 | 0.295470 | − | 0.955352i | \(-0.404524\pi\) | ||||
0.295470 | + | 0.955352i | \(0.404524\pi\) | |||||||
\(920\) | 31.9923 | 1.05475 | ||||||||
\(921\) | −55.2033 | −1.81901 | ||||||||
\(922\) | −11.0636 | −0.364361 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 29.4083 | 0.967461 | ||||||||
\(925\) | −0.118214 | −0.00388685 | ||||||||
\(926\) | −12.7149 | −0.417838 | ||||||||
\(927\) | 2.59709 | 0.0852996 | ||||||||
\(928\) | −4.57590 | −0.150211 | ||||||||
\(929\) | −50.0404 | −1.64177 | −0.820886 | − | 0.571092i | \(-0.806520\pi\) | ||||
−0.820886 | + | 0.571092i | \(0.806520\pi\) | |||||||
\(930\) | −38.2783 | −1.25519 | ||||||||
\(931\) | −1.24015 | −0.0406442 | ||||||||
\(932\) | 3.73725 | 0.122418 | ||||||||
\(933\) | −54.9367 | −1.79855 | ||||||||
\(934\) | 15.3190 | 0.501251 | ||||||||
\(935\) | −88.0208 | −2.87859 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.3212 | 1.51325 | 0.756624 | − | 0.653850i | \(-0.226847\pi\) | ||||
0.756624 | + | 0.653850i | \(0.226847\pi\) | |||||||
\(938\) | −24.9400 | −0.814320 | ||||||||
\(939\) | −57.2163 | −1.86718 | ||||||||
\(940\) | 7.60101 | 0.247918 | ||||||||
\(941\) | −0.505450 | −0.0164772 | −0.00823859 | − | 0.999966i | \(-0.502622\pi\) | ||||
−0.00823859 | + | 0.999966i | \(0.502622\pi\) | |||||||
\(942\) | 24.1881 | 0.788092 | ||||||||
\(943\) | −65.7452 | −2.14096 | ||||||||
\(944\) | 5.83570 | 0.189936 | ||||||||
\(945\) | −60.8976 | −1.98100 | ||||||||
\(946\) | 41.4281 | 1.34694 | ||||||||
\(947\) | 33.7211 | 1.09579 | 0.547894 | − | 0.836548i | \(-0.315430\pi\) | ||||
0.547894 | + | 0.836548i | \(0.315430\pi\) | |||||||
\(948\) | 17.8442 | 0.579553 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 10.0364 | 0.325623 | ||||||||
\(951\) | 31.8103 | 1.03152 | ||||||||
\(952\) | 17.9237 | 0.580910 | ||||||||
\(953\) | −8.77691 | −0.284312 | −0.142156 | − | 0.989844i | \(-0.545403\pi\) | ||||
−0.142156 | + | 0.989844i | \(0.545403\pi\) | |||||||
\(954\) | −44.1216 | −1.42849 | ||||||||
\(955\) | 69.9534 | 2.26364 | ||||||||
\(956\) | 2.20869 | 0.0714342 | ||||||||
\(957\) | −46.8790 | −1.51538 | ||||||||
\(958\) | −15.5689 | −0.503010 | ||||||||
\(959\) | −1.31521 | −0.0424703 | ||||||||
\(960\) | 10.9275 | 0.352683 | ||||||||
\(961\) | −18.7294 | −0.604175 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −44.1956 | −1.42418 | ||||||||
\(964\) | −22.9135 | −0.737995 | ||||||||
\(965\) | 25.2883 | 0.814058 | ||||||||
\(966\) | −66.7405 | −2.14734 | ||||||||
\(967\) | 17.1197 | 0.550533 | 0.275267 | − | 0.961368i | \(-0.411234\pi\) | ||||
0.275267 | + | 0.961368i | \(0.411234\pi\) | |||||||
\(968\) | −2.21623 | −0.0712322 | ||||||||
\(969\) | −17.5958 | −0.565258 | ||||||||
\(970\) | 23.6359 | 0.758903 | ||||||||
\(971\) | 27.5662 | 0.884641 | 0.442320 | − | 0.896857i | \(-0.354155\pi\) | ||||
0.442320 | + | 0.896857i | \(0.354155\pi\) | |||||||
\(972\) | −14.7412 | −0.472825 | ||||||||
\(973\) | −34.1872 | −1.09599 | ||||||||
\(974\) | 30.8664 | 0.989024 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.214830 | −0.00687654 | ||||||||
\(977\) | −39.0758 | −1.25015 | −0.625074 | − | 0.780566i | \(-0.714931\pi\) | ||||
−0.625074 | + | 0.780566i | \(0.714931\pi\) | |||||||
\(978\) | 62.5526 | 2.00021 | ||||||||
\(979\) | 25.6972 | 0.821285 | ||||||||
\(980\) | 4.80889 | 0.153614 | ||||||||
\(981\) | 1.33925 | 0.0427591 | ||||||||
\(982\) | 29.6957 | 0.947628 | ||||||||
\(983\) | −5.61172 | −0.178986 | −0.0894931 | − | 0.995987i | \(-0.528525\pi\) | ||||
−0.0894931 | + | 0.995987i | \(0.528525\pi\) | |||||||
\(984\) | −22.4563 | −0.715882 | ||||||||
\(985\) | 62.4274 | 1.98910 | ||||||||
\(986\) | −28.5717 | −0.909910 | ||||||||
\(987\) | −15.8568 | −0.504728 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −94.0189 | −2.98963 | ||||||||
\(990\) | 69.6585 | 2.21389 | ||||||||
\(991\) | 17.7487 | 0.563805 | 0.281902 | − | 0.959443i | \(-0.409035\pi\) | ||||
0.281902 | + | 0.959443i | \(0.409035\pi\) | |||||||
\(992\) | −3.50294 | −0.111218 | ||||||||
\(993\) | 1.17744 | 0.0373648 | ||||||||
\(994\) | 19.0218 | 0.603333 | ||||||||
\(995\) | −23.3147 | −0.739126 | ||||||||
\(996\) | −20.8402 | −0.660348 | ||||||||
\(997\) | −40.6808 | −1.28837 | −0.644186 | − | 0.764869i | \(-0.722804\pi\) | ||||
−0.644186 | + | 0.764869i | \(0.722804\pi\) | |||||||
\(998\) | −16.4665 | −0.521238 | ||||||||
\(999\) | −0.0644397 | −0.00203878 |
(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 | 6422.2.a.bm.1.13 | 14 | ||
13.2 | odd | 12 | 494.2.m.b.381.1 | yes | 28 | ||
13.7 | odd | 12 | 494.2.m.b.153.1 | ✓ | 28 | ||
13.12 | even | 2 | 6422.2.a.bn.1.13 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
494.2.m.b.153.1 | ✓ | 28 | 13.7 | odd | 12 | ||
494.2.m.b.381.1 | yes | 28 | 13.2 | odd | 12 | ||
6422.2.a.bm.1.13 | 14 | 1.1 | even | 1 | trivial | ||
6422.2.a.bn.1.13 | 14 | 13.12 | even | 2 |