Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8649,2,Mod(1,8649)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8649, 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("8649.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8649 = 3^{2} \cdot 31^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8649.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: | \(69.0626127082\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 961) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.28825\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8649.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.61803 | −1.85123 | −0.925615 | − | 0.378467i | \(-0.876451\pi\) | ||||
−0.925615 | + | 0.378467i | \(0.876451\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.85410 | 2.42705 | ||||||||
\(5\) | −2.23607 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | −0.188982 | − | 0.981981i | \(-0.560519\pi\) | ||||
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | −7.47214 | −2.64180 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.85410 | 1.85123 | ||||||||
\(11\) | −4.24264 | −1.27920 | −0.639602 | − | 0.768706i | \(-0.720901\pi\) | ||||
−0.639602 | + | 0.768706i | \(0.720901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.62210 | −0.727239 | −0.363619 | − | 0.931548i | \(-0.618459\pi\) | ||||
−0.363619 | + | 0.931548i | \(0.618459\pi\) | |||||||
\(14\) | 2.61803 | 0.699699 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 9.85410 | 2.46353 | ||||||||
\(17\) | −3.70246 | −0.897978 | −0.448989 | − | 0.893537i | \(-0.648216\pi\) | ||||
−0.448989 | + | 0.893537i | \(0.648216\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | 0.114708 | − | 0.993399i | \(-0.463407\pi\) | ||||
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | −10.8541 | −2.42705 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 11.1074 | 2.36810 | ||||||||
\(23\) | 2.62210 | 0.546745 | 0.273372 | − | 0.961908i | \(-0.411861\pi\) | ||||
0.273372 | + | 0.961908i | \(0.411861\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.86474 | 1.34629 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.85410 | −0.917339 | ||||||||
\(29\) | 0.540182 | 0.100309 | 0.0501546 | − | 0.998741i | \(-0.484029\pi\) | ||||
0.0501546 | + | 0.998741i | \(0.484029\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | ||||||||
\(32\) | −10.8541 | −1.91875 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.69316 | 1.66236 | ||||||||
\(35\) | 2.23607 | 0.377964 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.24264 | 0.697486 | 0.348743 | − | 0.937218i | \(-0.386609\pi\) | ||||
0.348743 | + | 0.937218i | \(0.386609\pi\) | |||||||
\(38\) | −2.61803 | −0.424701 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 16.7082 | 2.64180 | ||||||||
\(41\) | 1.47214 | 0.229909 | 0.114955 | − | 0.993371i | \(-0.463328\pi\) | ||||
0.114955 | + | 0.993371i | \(0.463328\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.69316 | −1.47819 | −0.739097 | − | 0.673599i | \(-0.764747\pi\) | ||||
−0.739097 | + | 0.673599i | \(0.764747\pi\) | |||||||
\(44\) | −20.5942 | −3.10469 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.86474 | −1.01215 | ||||||||
\(47\) | 9.70820 | 1.41609 | 0.708044 | − | 0.706169i | \(-0.249578\pi\) | ||||
0.708044 | + | 0.706169i | \(0.249578\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −12.7279 | −1.76505 | ||||||||
\(53\) | 13.7295 | 1.88589 | 0.942944 | − | 0.332951i | \(-0.108044\pi\) | ||||
0.942944 | + | 0.332951i | \(0.108044\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.48683 | 1.27920 | ||||||||
\(56\) | 7.47214 | 0.998506 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.41421 | −0.185695 | ||||||||
\(59\) | −11.9443 | −1.55501 | −0.777506 | − | 0.628876i | \(-0.783515\pi\) | ||||
−0.777506 | + | 0.628876i | \(0.783515\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.9358 | 1.78430 | 0.892148 | − | 0.451742i | \(-0.149197\pi\) | ||||
0.892148 | + | 0.451742i | \(0.149197\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.70820 | 1.08853 | ||||||||
\(65\) | 5.86319 | 0.727239 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.00000 | 0.733017 | 0.366508 | − | 0.930415i | \(-0.380553\pi\) | ||||
0.366508 | + | 0.930415i | \(0.380553\pi\) | |||||||
\(68\) | −17.9721 | −2.17944 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.85410 | −0.699699 | ||||||||
\(71\) | 1.47214 | 0.174710 | 0.0873552 | − | 0.996177i | \(-0.472158\pi\) | ||||
0.0873552 | + | 0.996177i | \(0.472158\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.24264 | 0.496564 | 0.248282 | − | 0.968688i | \(-0.420134\pi\) | ||||
0.248282 | + | 0.968688i | \(0.420134\pi\) | |||||||
\(74\) | −11.1074 | −1.29121 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.85410 | 0.556804 | ||||||||
\(77\) | 4.24264 | 0.483494 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.62054 | −0.182326 | −0.0911628 | − | 0.995836i | \(-0.529058\pi\) | ||||
−0.0911628 | + | 0.995836i | \(0.529058\pi\) | |||||||
\(80\) | −22.0344 | −2.46353 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.85410 | −0.425614 | ||||||||
\(83\) | 3.16228 | 0.347105 | 0.173553 | − | 0.984825i | \(-0.444475\pi\) | ||||
0.173553 | + | 0.984825i | \(0.444475\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.27895 | 0.897978 | ||||||||
\(86\) | 25.3770 | 2.73648 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 31.7016 | 3.37940 | ||||||||
\(89\) | 15.3500 | 1.62710 | 0.813549 | − | 0.581496i | \(-0.197532\pi\) | ||||
0.813549 | + | 0.581496i | \(0.197532\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.62210 | 0.274870 | ||||||||
\(92\) | 12.7279 | 1.32698 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −25.4164 | −2.62150 | ||||||||
\(95\) | −2.23607 | −0.229416 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.00000 | −0.710742 | −0.355371 | − | 0.934725i | \(-0.615646\pi\) | ||||
−0.355371 | + | 0.934725i | \(0.615646\pi\) | |||||||
\(98\) | 15.7082 | 1.58677 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.23607 | −0.222497 | −0.111249 | − | 0.993793i | \(-0.535485\pi\) | ||||
−0.111249 | + | 0.993793i | \(0.535485\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.7082 | 1.05511 | 0.527555 | − | 0.849521i | \(-0.323109\pi\) | ||||
0.527555 | + | 0.849521i | \(0.323109\pi\) | |||||||
\(104\) | 19.5927 | 1.92122 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −35.9442 | −3.49121 | ||||||||
\(107\) | −1.47214 | −0.142317 | −0.0711584 | − | 0.997465i | \(-0.522670\pi\) | ||||
−0.0711584 | + | 0.997465i | \(0.522670\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.29180 | −0.123732 | −0.0618658 | − | 0.998084i | \(-0.519705\pi\) | ||||
−0.0618658 | + | 0.998084i | \(0.519705\pi\) | |||||||
\(110\) | −24.8369 | −2.36810 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.85410 | −0.931125 | ||||||||
\(113\) | 9.76393 | 0.918513 | 0.459257 | − | 0.888304i | \(-0.348116\pi\) | ||||
0.459257 | + | 0.888304i | \(0.348116\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.86319 | −0.546745 | ||||||||
\(116\) | 2.62210 | 0.243456 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 31.2705 | 2.87868 | ||||||||
\(119\) | 3.70246 | 0.339404 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | −36.4844 | −3.30314 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803 | 1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.48683 | −0.841820 | −0.420910 | − | 0.907102i | \(-0.638289\pi\) | ||||
−0.420910 | + | 0.907102i | \(0.638289\pi\) | |||||||
\(128\) | −1.09017 | −0.0963583 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −15.3500 | −1.34629 | ||||||||
\(131\) | −7.41641 | −0.647975 | −0.323987 | − | 0.946061i | \(-0.605024\pi\) | ||||
−0.323987 | + | 0.946061i | \(0.605024\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | −0.0867110 | ||||||||
\(134\) | −15.7082 | −1.35698 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 27.6653 | 2.37228 | ||||||||
\(137\) | 2.62210 | 0.224021 | 0.112010 | − | 0.993707i | \(-0.464271\pi\) | ||||
0.112010 | + | 0.993707i | \(0.464271\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.9721 | −1.52437 | −0.762187 | − | 0.647356i | \(-0.775875\pi\) | ||||
−0.762187 | + | 0.647356i | \(0.775875\pi\) | |||||||
\(140\) | 10.8541 | 0.917339 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.85410 | −0.323429 | ||||||||
\(143\) | 11.1246 | 0.930287 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.20788 | −0.100309 | ||||||||
\(146\) | −11.1074 | −0.919253 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 20.5942 | 1.69283 | ||||||||
\(149\) | 13.4164 | 1.09911 | 0.549557 | − | 0.835456i | \(-0.314796\pi\) | ||||
0.549557 | + | 0.835456i | \(0.314796\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.5216 | 1.01899 | 0.509496 | − | 0.860473i | \(-0.329832\pi\) | ||||
0.509496 | + | 0.860473i | \(0.329832\pi\) | |||||||
\(152\) | −7.47214 | −0.606070 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −11.1074 | −0.895058 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.70820 | 0.694990 | 0.347495 | − | 0.937682i | \(-0.387032\pi\) | ||||
0.347495 | + | 0.937682i | \(0.387032\pi\) | |||||||
\(158\) | 4.24264 | 0.337526 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 24.2705 | 1.91875 | ||||||||
\(161\) | −2.62210 | −0.206650 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.4164 | 1.12918 | 0.564590 | − | 0.825371i | \(-0.309034\pi\) | ||||
0.564590 | + | 0.825371i | \(0.309034\pi\) | |||||||
\(164\) | 7.14590 | 0.558001 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.27895 | −0.642571 | ||||||||
\(167\) | 1.08036 | 0.0836010 | 0.0418005 | − | 0.999126i | \(-0.486691\pi\) | ||||
0.0418005 | + | 0.999126i | \(0.486691\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.12461 | −0.471124 | ||||||||
\(170\) | −21.6746 | −1.66236 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −47.0516 | −3.58765 | ||||||||
\(173\) | −18.0000 | −1.36851 | −0.684257 | − | 0.729241i | \(-0.739873\pi\) | ||||
−0.684257 | + | 0.729241i | \(0.739873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −41.8074 | −3.15135 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −40.1869 | −3.01213 | ||||||||
\(179\) | −13.2681 | −0.991705 | −0.495852 | − | 0.868407i | \(-0.665144\pi\) | ||||
−0.495852 | + | 0.868407i | \(0.665144\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.69161 | 0.646042 | 0.323021 | − | 0.946392i | \(-0.395301\pi\) | ||||
0.323021 | + | 0.946392i | \(0.395301\pi\) | |||||||
\(182\) | −6.86474 | −0.508848 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −19.5927 | −1.44439 | ||||||||
\(185\) | −9.48683 | −0.697486 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.7082 | 1.14870 | ||||||||
\(188\) | 47.1246 | 3.43692 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.85410 | 0.424701 | ||||||||
\(191\) | −9.76393 | −0.706493 | −0.353247 | − | 0.935530i | \(-0.614922\pi\) | ||||
−0.353247 | + | 0.935530i | \(0.614922\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.7082 | −1.49061 | −0.745305 | − | 0.666724i | \(-0.767696\pi\) | ||||
−0.745305 | + | 0.666724i | \(0.767696\pi\) | |||||||
\(194\) | 18.3262 | 1.31575 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −29.1246 | −2.08033 | ||||||||
\(197\) | 1.08036 | 0.0769727 | 0.0384863 | − | 0.999259i | \(-0.487746\pi\) | ||||
0.0384863 | + | 0.999259i | \(0.487746\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.2163 | 1.64576 | 0.822880 | − | 0.568215i | \(-0.192366\pi\) | ||||
0.822880 | + | 0.568215i | \(0.192366\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.85410 | 0.411893 | ||||||||
\(203\) | −0.540182 | −0.0379133 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.29180 | −0.229909 | ||||||||
\(206\) | −28.0344 | −1.95325 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −25.8384 | −1.79157 | ||||||||
\(209\) | −4.24264 | −0.293470 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.00000 | −0.344214 | −0.172107 | − | 0.985078i | \(-0.555058\pi\) | ||||
−0.172107 | + | 0.985078i | \(0.555058\pi\) | |||||||
\(212\) | 66.6443 | 4.57715 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.85410 | 0.263461 | ||||||||
\(215\) | 21.6746 | 1.47819 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.38197 | 0.229056 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 46.0501 | 3.10469 | ||||||||
\(221\) | 9.70820 | 0.653044 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.1452 | 1.08117 | 0.540583 | − | 0.841291i | \(-0.318204\pi\) | ||||
0.540583 | + | 0.841291i | \(0.318204\pi\) | |||||||
\(224\) | 10.8541 | 0.725220 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −25.5623 | −1.70038 | ||||||||
\(227\) | −2.29180 | −0.152112 | −0.0760559 | − | 0.997104i | \(-0.524233\pi\) | ||||
−0.0760559 | + | 0.997104i | \(0.524233\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.24264 | 0.280362 | 0.140181 | − | 0.990126i | \(-0.455232\pi\) | ||||
0.140181 | + | 0.990126i | \(0.455232\pi\) | |||||||
\(230\) | 15.3500 | 1.01215 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.03631 | −0.264997 | ||||||||
\(233\) | 13.4721 | 0.882589 | 0.441294 | − | 0.897362i | \(-0.354519\pi\) | ||||
0.441294 | + | 0.897362i | \(0.354519\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.7082 | −1.41609 | ||||||||
\(236\) | −57.9787 | −3.77409 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.69316 | −0.628314 | ||||||||
\(239\) | −12.1089 | −0.783262 | −0.391631 | − | 0.920122i | \(-0.628089\pi\) | ||||
−0.391631 | + | 0.920122i | \(0.628089\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.2163 | −1.49549 | −0.747747 | − | 0.663984i | \(-0.768864\pi\) | ||||
−0.747747 | + | 0.663984i | \(0.768864\pi\) | |||||||
\(242\) | −18.3262 | −1.17806 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 67.6458 | 4.33058 | ||||||||
\(245\) | 13.4164 | 0.857143 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.62210 | −0.166840 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −29.2705 | −1.85123 | ||||||||
\(251\) | −11.0286 | −0.696117 | −0.348058 | − | 0.937473i | \(-0.613159\pi\) | ||||
−0.348058 | + | 0.937473i | \(0.613159\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.1246 | −0.699398 | ||||||||
\(254\) | 24.8369 | 1.55840 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.5623 | −0.910144 | ||||||||
\(257\) | −6.05573 | −0.377746 | −0.188873 | − | 0.982002i | \(-0.560483\pi\) | ||||
−0.188873 | + | 0.982002i | \(0.560483\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.24264 | −0.263625 | ||||||||
\(260\) | 28.4605 | 1.76505 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 19.4164 | 1.19955 | ||||||||
\(263\) | −18.5123 | −1.14152 | −0.570759 | − | 0.821118i | \(-0.693351\pi\) | ||||
−0.570759 | + | 0.821118i | \(0.693351\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −30.7000 | −1.88589 | ||||||||
\(266\) | 2.61803 | 0.160522 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 29.1246 | 1.77907 | ||||||||
\(269\) | −2.16073 | −0.131742 | −0.0658709 | − | 0.997828i | \(-0.520983\pi\) | ||||
−0.0658709 | + | 0.997828i | \(0.520983\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.5911 | −1.12933 | −0.564665 | − | 0.825320i | \(-0.690994\pi\) | ||||
−0.564665 | + | 0.825320i | \(0.690994\pi\) | |||||||
\(272\) | −36.4844 | −2.21219 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.86474 | −0.414714 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.1058 | 0.607200 | 0.303600 | − | 0.952800i | \(-0.401811\pi\) | ||||
0.303600 | + | 0.952800i | \(0.401811\pi\) | |||||||
\(278\) | 47.0516 | 2.82197 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −16.7082 | −0.998506 | ||||||||
\(281\) | −13.3607 | −0.797031 | −0.398516 | − | 0.917162i | \(-0.630475\pi\) | ||||
−0.398516 | + | 0.917162i | \(0.630475\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.0000 | 1.42665 | 0.713326 | − | 0.700832i | \(-0.247188\pi\) | ||||
0.713326 | + | 0.700832i | \(0.247188\pi\) | |||||||
\(284\) | 7.14590 | 0.424031 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −29.1246 | −1.72217 | ||||||||
\(287\) | −1.47214 | −0.0868974 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.29180 | −0.193635 | ||||||||
\(290\) | 3.16228 | 0.185695 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 20.5942 | 1.20519 | ||||||||
\(293\) | 2.29180 | 0.133888 | 0.0669441 | − | 0.997757i | \(-0.478675\pi\) | ||||
0.0669441 | + | 0.997757i | \(0.478675\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 26.7082 | 1.55501 | ||||||||
\(296\) | −31.7016 | −1.84262 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −35.1246 | −2.03471 | ||||||||
\(299\) | −6.87539 | −0.397614 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.69316 | 0.558705 | ||||||||
\(302\) | −32.7820 | −1.88639 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.85410 | 0.565172 | ||||||||
\(305\) | −31.1614 | −1.78430 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.1246 | 1.37686 | 0.688432 | − | 0.725301i | \(-0.258299\pi\) | ||||
0.688432 | + | 0.725301i | \(0.258299\pi\) | |||||||
\(308\) | 20.5942 | 1.17346 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.4721 | −1.44439 | −0.722196 | − | 0.691688i | \(-0.756867\pi\) | ||||
−0.722196 | + | 0.691688i | \(0.756867\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.5200 | −0.651151 | −0.325576 | − | 0.945516i | \(-0.605558\pi\) | ||||
−0.325576 | + | 0.945516i | \(0.605558\pi\) | |||||||
\(314\) | −22.7984 | −1.28659 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.86629 | −0.442513 | ||||||||
\(317\) | −26.2361 | −1.47356 | −0.736782 | − | 0.676130i | \(-0.763656\pi\) | ||||
−0.736782 | + | 0.676130i | \(0.763656\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.29180 | −0.128316 | ||||||||
\(320\) | −19.4721 | −1.08853 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.86474 | 0.382557 | ||||||||
\(323\) | −3.70246 | −0.206010 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −37.7426 | −2.09037 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −11.0000 | −0.607373 | ||||||||
\(329\) | −9.70820 | −0.535231 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.2889 | 1.71979 | 0.859897 | − | 0.510467i | \(-0.170527\pi\) | ||||
0.859897 | + | 0.510467i | \(0.170527\pi\) | |||||||
\(332\) | 15.3500 | 0.842442 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.82843 | −0.154765 | ||||||||
\(335\) | −13.4164 | −0.733017 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.3500 | −0.836169 | −0.418084 | − | 0.908408i | \(-0.637298\pi\) | ||||
−0.418084 | + | 0.908408i | \(0.637298\pi\) | |||||||
\(338\) | 16.0344 | 0.872159 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 40.1869 | 2.17944 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | 72.4286 | 3.90509 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 47.1246 | 2.53343 | ||||||||
\(347\) | 21.5958 | 1.15932 | 0.579661 | − | 0.814858i | \(-0.303185\pi\) | ||||
0.579661 | + | 0.814858i | \(0.303185\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.00000 | 0.321173 | 0.160586 | − | 0.987022i | \(-0.448662\pi\) | ||||
0.160586 | + | 0.987022i | \(0.448662\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 46.0501 | 2.45448 | ||||||||
\(353\) | −9.56564 | −0.509128 | −0.254564 | − | 0.967056i | \(-0.581932\pi\) | ||||
−0.254564 | + | 0.967056i | \(0.581932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.29180 | −0.174710 | ||||||||
\(356\) | 74.5106 | 3.94905 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 34.7363 | 1.83587 | ||||||||
\(359\) | −14.2361 | −0.751351 | −0.375675 | − | 0.926751i | \(-0.622589\pi\) | ||||
−0.375675 | + | 0.926751i | \(0.622589\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | −22.7549 | −1.19597 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.7279 | 0.667124 | ||||||||
\(365\) | −9.48683 | −0.496564 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.65841 | 0.347566 | 0.173783 | − | 0.984784i | \(-0.444401\pi\) | ||||
0.173783 | + | 0.984784i | \(0.444401\pi\) | |||||||
\(368\) | 25.8384 | 1.34692 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 24.8369 | 1.29121 | ||||||||
\(371\) | −13.7295 | −0.712799 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.29180 | −0.481111 | −0.240555 | − | 0.970635i | \(-0.577330\pi\) | ||||
−0.240555 | + | 0.970635i | \(0.577330\pi\) | |||||||
\(374\) | −41.1246 | −2.12650 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −72.5410 | −3.74102 | ||||||||
\(377\) | −1.41641 | −0.0729487 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.41641 | 0.380955 | 0.190478 | − | 0.981692i | \(-0.438996\pi\) | ||||
0.190478 | + | 0.981692i | \(0.438996\pi\) | |||||||
\(380\) | −10.8541 | −0.556804 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 25.5623 | 1.30788 | ||||||||
\(383\) | 6.40337 | 0.327197 | 0.163598 | − | 0.986527i | \(-0.447690\pi\) | ||||
0.163598 | + | 0.986527i | \(0.447690\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.48683 | −0.483494 | ||||||||
\(386\) | 54.2148 | 2.75946 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −33.9787 | −1.72501 | ||||||||
\(389\) | 16.8129 | 0.852450 | 0.426225 | − | 0.904617i | \(-0.359843\pi\) | ||||
0.426225 | + | 0.904617i | \(0.359843\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.70820 | −0.490965 | ||||||||
\(392\) | 44.8328 | 2.26440 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.82843 | −0.142494 | ||||||||
\(395\) | 3.62365 | 0.182326 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.7082 | 0.738184 | 0.369092 | − | 0.929393i | \(-0.379669\pi\) | ||||
0.369092 | + | 0.929393i | \(0.379669\pi\) | |||||||
\(398\) | −60.7811 | −3.04668 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.540182 | 0.0269754 | 0.0134877 | − | 0.999909i | \(-0.495707\pi\) | ||||
0.0134877 | + | 0.999909i | \(0.495707\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −10.8541 | −0.540012 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.41421 | 0.0701862 | ||||||||
\(407\) | −18.0000 | −0.892227 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.0810 | 1.48741 | 0.743706 | − | 0.668507i | \(-0.233066\pi\) | ||||
0.743706 | + | 0.668507i | \(0.233066\pi\) | |||||||
\(410\) | 8.61803 | 0.425614 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 51.9787 | 2.56081 | ||||||||
\(413\) | 11.9443 | 0.587739 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.07107 | −0.347105 | ||||||||
\(416\) | 28.4605 | 1.39539 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 11.1074 | 0.543280 | ||||||||
\(419\) | −30.5967 | −1.49475 | −0.747374 | − | 0.664403i | \(-0.768686\pi\) | ||||
−0.747374 | + | 0.664403i | \(0.768686\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.4164 | 1.28746 | 0.643728 | − | 0.765254i | \(-0.277387\pi\) | ||||
0.643728 | + | 0.765254i | \(0.277387\pi\) | |||||||
\(422\) | 13.0902 | 0.637220 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −102.588 | −4.98214 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.9358 | −0.674401 | ||||||||
\(428\) | −7.14590 | −0.345410 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −56.7448 | −2.73648 | ||||||||
\(431\) | 35.8885 | 1.72869 | 0.864345 | − | 0.502899i | \(-0.167733\pi\) | ||||
0.864345 | + | 0.502899i | \(0.167733\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.8384 | −1.24171 | −0.620857 | − | 0.783924i | \(-0.713215\pi\) | ||||
−0.620857 | + | 0.783924i | \(0.713215\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.27051 | −0.300303 | ||||||||
\(437\) | 2.62210 | 0.125432 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.0000 | −1.19318 | −0.596592 | − | 0.802544i | \(-0.703479\pi\) | ||||
−0.596592 | + | 0.802544i | \(0.703479\pi\) | |||||||
\(440\) | −70.8869 | −3.37940 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −25.4164 | −1.20894 | ||||||||
\(443\) | −6.05573 | −0.287716 | −0.143858 | − | 0.989598i | \(-0.545951\pi\) | ||||
−0.143858 | + | 0.989598i | \(0.545951\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −34.3237 | −1.62710 | ||||||||
\(446\) | −42.2688 | −2.00148 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.70820 | −0.411424 | ||||||||
\(449\) | −33.7047 | −1.59062 | −0.795311 | − | 0.606201i | \(-0.792693\pi\) | ||||
−0.795311 | + | 0.606201i | \(0.792693\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.24574 | −0.294101 | ||||||||
\(452\) | 47.3951 | 2.22928 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.00000 | 0.281594 | ||||||||
\(455\) | −5.86319 | −0.274870 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.3137 | 0.529233 | 0.264616 | − | 0.964354i | \(-0.414755\pi\) | ||||
0.264616 | + | 0.964354i | \(0.414755\pi\) | |||||||
\(458\) | −11.1074 | −0.519014 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −28.4605 | −1.32698 | ||||||||
\(461\) | −5.16538 | −0.240576 | −0.120288 | − | 0.992739i | \(-0.538382\pi\) | ||||
−0.120288 | + | 0.992739i | \(0.538382\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.82998 | −0.177994 | −0.0889971 | − | 0.996032i | \(-0.528366\pi\) | ||||
−0.0889971 | + | 0.996032i | \(0.528366\pi\) | |||||||
\(464\) | 5.32300 | 0.247114 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −35.2705 | −1.63387 | ||||||||
\(467\) | 15.6525 | 0.724310 | 0.362155 | − | 0.932118i | \(-0.382041\pi\) | ||||
0.362155 | + | 0.932118i | \(0.382041\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.00000 | −0.277054 | ||||||||
\(470\) | 56.8328 | 2.62150 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 89.2492 | 4.10803 | ||||||||
\(473\) | 41.1246 | 1.89091 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 17.9721 | 0.823751 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 31.7016 | 1.45000 | ||||||||
\(479\) | −16.5279 | −0.755177 | −0.377589 | − | 0.925973i | \(-0.623247\pi\) | ||||
−0.377589 | + | 0.925973i | \(0.623247\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.1246 | −0.507239 | ||||||||
\(482\) | 60.7811 | 2.76850 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 33.9787 | 1.54449 | ||||||||
\(485\) | 15.6525 | 0.710742 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.0779 | 1.27233 | 0.636166 | − | 0.771552i | \(-0.280519\pi\) | ||||
0.636166 | + | 0.771552i | \(0.280519\pi\) | |||||||
\(488\) | −104.130 | −4.71375 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −35.1246 | −1.58677 | ||||||||
\(491\) | 15.8902 | 0.717115 | 0.358557 | − | 0.933508i | \(-0.383269\pi\) | ||||
0.358557 | + | 0.933508i | \(0.383269\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.00000 | −0.0900755 | ||||||||
\(494\) | 6.86474 | 0.308859 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.47214 | −0.0660343 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.3848 | 0.823016 | 0.411508 | − | 0.911406i | \(-0.365002\pi\) | ||||
0.411508 | + | 0.911406i | \(0.365002\pi\) | |||||||
\(500\) | 54.2705 | 2.42705 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.8732 | 1.28867 | ||||||||
\(503\) | 32.8885 | 1.46643 | 0.733214 | − | 0.679998i | \(-0.238019\pi\) | ||||
0.733214 | + | 0.679998i | \(0.238019\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.00000 | 0.222497 | ||||||||
\(506\) | 29.1246 | 1.29475 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −46.0501 | −2.04314 | ||||||||
\(509\) | 7.94510 | 0.352160 | 0.176080 | − | 0.984376i | \(-0.443658\pi\) | ||||
0.176080 | + | 0.984376i | \(0.443658\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.24264 | −0.187683 | ||||||||
\(512\) | 40.3050 | 1.78124 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.8541 | 0.699294 | ||||||||
\(515\) | −23.9443 | −1.05511 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −41.1884 | −1.81146 | ||||||||
\(518\) | 11.1074 | 0.488030 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −43.8105 | −1.92122 | ||||||||
\(521\) | 13.4164 | 0.587784 | 0.293892 | − | 0.955839i | \(-0.405049\pi\) | ||||
0.293892 | + | 0.955839i | \(0.405049\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.618993 | 0.0270667 | 0.0135333 | − | 0.999908i | \(-0.495692\pi\) | ||||
0.0135333 | + | 0.999908i | \(0.495692\pi\) | |||||||
\(524\) | −36.0000 | −1.57267 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 48.4658 | 2.11321 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.1246 | −0.701070 | ||||||||
\(530\) | 80.3737 | 3.49121 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.85410 | −0.210452 | ||||||||
\(533\) | −3.86008 | −0.167199 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.29180 | 0.142317 | ||||||||
\(536\) | −44.8328 | −1.93648 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.65685 | 0.243884 | ||||||||
\(539\) | 25.4558 | 1.09646 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.8328 | 1.11064 | 0.555320 | − | 0.831637i | \(-0.312596\pi\) | ||||
0.555320 | + | 0.831637i | \(0.312596\pi\) | |||||||
\(542\) | 48.6722 | 2.09065 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 40.1869 | 1.72300 | ||||||||
\(545\) | 2.88854 | 0.123732 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.41641 | 0.103318 | 0.0516591 | − | 0.998665i | \(-0.483549\pi\) | ||||
0.0516591 | + | 0.998665i | \(0.483549\pi\) | |||||||
\(548\) | 12.7279 | 0.543710 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.540182 | 0.0230125 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.62054 | 0.0689126 | ||||||||
\(554\) | −26.4574 | −1.12407 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −87.2385 | −3.69974 | ||||||||
\(557\) | 10.6460 | 0.451086 | 0.225543 | − | 0.974233i | \(-0.427584\pi\) | ||||
0.225543 | + | 0.974233i | \(0.427584\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.4164 | 1.07500 | ||||||||
\(560\) | 22.0344 | 0.931125 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 34.9787 | 1.47549 | ||||||||
\(563\) | −9.76393 | −0.411501 | −0.205750 | − | 0.978605i | \(-0.565963\pi\) | ||||
−0.205750 | + | 0.978605i | \(0.565963\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.8328 | −0.918513 | ||||||||
\(566\) | −62.8328 | −2.64106 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.0000 | −0.461550 | ||||||||
\(569\) | 11.7264 | 0.491595 | 0.245798 | − | 0.969321i | \(-0.420950\pi\) | ||||
0.245798 | + | 0.969321i | \(0.420950\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.62210 | −0.109731 | −0.0548657 | − | 0.998494i | \(-0.517473\pi\) | ||||
−0.0548657 | + | 0.998494i | \(0.517473\pi\) | |||||||
\(572\) | 54.0000 | 2.25785 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.85410 | 0.160867 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.0000 | −1.24892 | −0.624458 | − | 0.781058i | \(-0.714680\pi\) | ||||
−0.624458 | + | 0.781058i | \(0.714680\pi\) | |||||||
\(578\) | 8.61803 | 0.358463 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.86319 | −0.243456 | ||||||||
\(581\) | −3.16228 | −0.131193 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −58.2492 | −2.41244 | ||||||||
\(584\) | −31.7016 | −1.31182 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | 15.7326 | 0.649353 | 0.324676 | − | 0.945825i | \(-0.394745\pi\) | ||||
0.324676 | + | 0.945825i | \(0.394745\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −69.9230 | −2.87868 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 41.8074 | 1.71827 | ||||||||
\(593\) | −5.18034 | −0.212731 | −0.106366 | − | 0.994327i | \(-0.533921\pi\) | ||||
−0.106366 | + | 0.994327i | \(0.533921\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.27895 | −0.339404 | ||||||||
\(596\) | 65.1246 | 2.66761 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 18.0000 | 0.736075 | ||||||||
\(599\) | −6.05573 | −0.247430 | −0.123715 | − | 0.992318i | \(-0.539481\pi\) | ||||
−0.123715 | + | 0.992318i | \(0.539481\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.1784 | 0.741514 | 0.370757 | − | 0.928730i | \(-0.379098\pi\) | ||||
0.370757 | + | 0.928730i | \(0.379098\pi\) | |||||||
\(602\) | −25.3770 | −1.03429 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 60.7811 | 2.47315 | ||||||||
\(605\) | −15.6525 | −0.636364 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.1246 | 0.613889 | 0.306945 | − | 0.951727i | \(-0.400693\pi\) | ||||
0.306945 | + | 0.951727i | \(0.400693\pi\) | |||||||
\(608\) | −10.8541 | −0.440192 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 81.5816 | 3.30314 | ||||||||
\(611\) | −25.4558 | −1.02983 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.588890 | 0.0237850 | 0.0118925 | − | 0.999929i | \(-0.496214\pi\) | ||||
0.0118925 | + | 0.999929i | \(0.496214\pi\) | |||||||
\(614\) | −63.1591 | −2.54889 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −31.7016 | −1.27729 | ||||||||
\(617\) | 6.87539 | 0.276793 | 0.138396 | − | 0.990377i | \(-0.455805\pi\) | ||||
0.138396 | + | 0.990377i | \(0.455805\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.8384 | 1.03853 | 0.519267 | − | 0.854612i | \(-0.326205\pi\) | ||||
0.519267 | + | 0.854612i | \(0.326205\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 66.6869 | 2.67390 | ||||||||
\(623\) | −15.3500 | −0.614985 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 30.1599 | 1.20543 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 42.2705 | 1.68678 | ||||||||
\(629\) | −15.7082 | −0.626327 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.6290 | −0.940654 | −0.470327 | − | 0.882492i | \(-0.655864\pi\) | ||||
−0.470327 | + | 0.882492i | \(0.655864\pi\) | |||||||
\(632\) | 12.1089 | 0.481667 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 68.6869 | 2.72791 | ||||||||
\(635\) | 21.2132 | 0.841820 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.7326 | 0.623347 | ||||||||
\(638\) | 6.00000 | 0.237542 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.43769 | 0.0963583 | ||||||||
\(641\) | 8.48528 | 0.335148 | 0.167574 | − | 0.985859i | \(-0.446407\pi\) | ||||
0.167574 | + | 0.985859i | \(0.446407\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.65530 | −0.183587 | −0.0917936 | − | 0.995778i | \(-0.529260\pi\) | ||||
−0.0917936 | + | 0.995778i | \(0.529260\pi\) | |||||||
\(644\) | −12.7279 | −0.501550 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.69316 | 0.381372 | ||||||||
\(647\) | −31.7804 | −1.24942 | −0.624708 | − | 0.780858i | \(-0.714782\pi\) | ||||
−0.624708 | + | 0.780858i | \(0.714782\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 50.6753 | 1.98918 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 69.9787 | 2.74058 | ||||||||
\(653\) | −24.6525 | −0.964726 | −0.482363 | − | 0.875971i | \(-0.660221\pi\) | ||||
−0.482363 | + | 0.875971i | \(0.660221\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.5836 | 0.647975 | ||||||||
\(656\) | 14.5066 | 0.566387 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 25.4164 | 0.990835 | ||||||||
\(659\) | −24.8197 | −0.966837 | −0.483418 | − | 0.875389i | \(-0.660605\pi\) | ||||
−0.483418 | + | 0.875389i | \(0.660605\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.83282 | 0.304661 | 0.152331 | − | 0.988330i | \(-0.451322\pi\) | ||||
0.152331 | + | 0.988330i | \(0.451322\pi\) | |||||||
\(662\) | −81.9155 | −3.18374 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −23.6290 | −0.916982 | ||||||||
\(665\) | 2.23607 | 0.0867110 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.41641 | 0.0548435 | ||||||||
\(668\) | 5.24419 | 0.202904 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 35.1246 | 1.35698 | ||||||||
\(671\) | −59.1246 | −2.28248 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.9805 | 1.54114 | 0.770568 | − | 0.637357i | \(-0.219973\pi\) | ||||
0.770568 | + | 0.637357i | \(0.219973\pi\) | |||||||
\(674\) | 40.1869 | 1.54794 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −29.7295 | −1.14344 | ||||||||
\(677\) | 21.2132 | 0.815290 | 0.407645 | − | 0.913141i | \(-0.366350\pi\) | ||||
0.407645 | + | 0.913141i | \(0.366350\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.00000 | 0.268635 | ||||||||
\(680\) | −61.8614 | −2.37228 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.1803 | 1.57572 | 0.787861 | − | 0.615853i | \(-0.211189\pi\) | ||||
0.787861 | + | 0.615853i | \(0.211189\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.86319 | −0.224021 | ||||||||
\(686\) | −34.0344 | −1.29944 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −95.5174 | −3.64157 | ||||||||
\(689\) | −36.0000 | −1.37149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −48.4164 | −1.84185 | −0.920923 | − | 0.389743i | \(-0.872564\pi\) | ||||
−0.920923 | + | 0.389743i | \(0.872564\pi\) | |||||||
\(692\) | −87.3738 | −3.32145 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −56.5384 | −2.14617 | ||||||||
\(695\) | 40.1869 | 1.52437 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.45052 | −0.206453 | ||||||||
\(698\) | −15.7082 | −0.594564 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.65248 | 0.137952 | 0.0689761 | − | 0.997618i | \(-0.478027\pi\) | ||||
0.0689761 | + | 0.997618i | \(0.478027\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.24264 | 0.160014 | ||||||||
\(704\) | −36.9458 | −1.39245 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 25.0432 | 0.942513 | ||||||||
\(707\) | 2.23607 | 0.0840960 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.1884 | −1.54686 | −0.773432 | − | 0.633880i | \(-0.781462\pi\) | ||||
−0.773432 | + | 0.633880i | \(0.781462\pi\) | |||||||
\(710\) | 8.61803 | 0.323429 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −114.697 | −4.29847 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.8754 | −0.930287 | ||||||||
\(716\) | −64.4047 | −2.40692 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 37.2705 | 1.39092 | ||||||||
\(719\) | 37.5648 | 1.40093 | 0.700465 | − | 0.713687i | \(-0.252976\pi\) | ||||
0.700465 | + | 0.713687i | \(0.252976\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.7082 | −0.398794 | ||||||||
\(722\) | 47.1246 | 1.75380 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 42.1900 | 1.56798 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.4164 | −1.12808 | −0.564041 | − | 0.825747i | \(-0.690754\pi\) | ||||
−0.564041 | + | 0.825747i | \(0.690754\pi\) | |||||||
\(728\) | −19.5927 | −0.726152 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 24.8369 | 0.919253 | ||||||||
\(731\) | 35.8885 | 1.32739 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.4164 | −0.532482 | −0.266241 | − | 0.963906i | \(-0.585782\pi\) | ||||
−0.266241 | + | 0.963906i | \(0.585782\pi\) | |||||||
\(734\) | −17.4319 | −0.643424 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −28.4605 | −1.04907 | ||||||||
\(737\) | −25.4558 | −0.937678 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.1490 | −1.29298 | −0.646489 | − | 0.762924i | \(-0.723763\pi\) | ||||
−0.646489 | + | 0.762924i | \(0.723763\pi\) | |||||||
\(740\) | −46.0501 | −1.69283 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 35.9442 | 1.31955 | ||||||||
\(743\) | 36.4844 | 1.33848 | 0.669242 | − | 0.743045i | \(-0.266619\pi\) | ||||
0.669242 | + | 0.743045i | \(0.266619\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.0000 | −1.09911 | ||||||||
\(746\) | 24.3262 | 0.890647 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 76.2492 | 2.78795 | ||||||||
\(749\) | 1.47214 | 0.0537907 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.5410 | −1.36989 | −0.684946 | − | 0.728594i | \(-0.740174\pi\) | ||||
−0.684946 | + | 0.728594i | \(0.740174\pi\) | |||||||
\(752\) | 95.6656 | 3.48857 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.70820 | 0.135045 | ||||||||
\(755\) | −27.9991 | −1.01899 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.28050 | 0.337306 | 0.168653 | − | 0.985676i | \(-0.446058\pi\) | ||||
0.168653 | + | 0.985676i | \(0.446058\pi\) | |||||||
\(758\) | −19.4164 | −0.705236 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 16.7082 | 0.606070 | ||||||||
\(761\) | −40.1869 | −1.45677 | −0.728386 | − | 0.685167i | \(-0.759729\pi\) | ||||
−0.728386 | + | 0.685167i | \(0.759729\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.29180 | 0.0467662 | ||||||||
\(764\) | −47.3951 | −1.71470 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.7642 | −0.605716 | ||||||||
\(767\) | 31.3190 | 1.13086 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 54.1246 | 1.95178 | 0.975892 | − | 0.218255i | \(-0.0700365\pi\) | ||||
0.975892 | + | 0.218255i | \(0.0700365\pi\) | |||||||
\(770\) | 24.8369 | 0.895058 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −100.520 | −3.61778 | ||||||||
\(773\) | 11.1862 | 0.402339 | 0.201170 | − | 0.979556i | \(-0.435526\pi\) | ||||
0.201170 | + | 0.979556i | \(0.435526\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 52.3050 | 1.87764 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −44.0168 | −1.57808 | ||||||||
\(779\) | 1.47214 | 0.0527447 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.24574 | −0.223490 | ||||||||
\(782\) | 25.4164 | 0.908889 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −59.1246 | −2.11159 | ||||||||
\(785\) | −19.4721 | −0.694990 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.5648 | −1.33904 | −0.669520 | − | 0.742794i | \(-0.733500\pi\) | ||||
−0.669520 | + | 0.742794i | \(0.733500\pi\) | |||||||
\(788\) | 5.24419 | 0.186817 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.48683 | −0.337526 | ||||||||
\(791\) | −9.76393 | −0.347165 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.5410 | −1.29761 | ||||||||
\(794\) | −38.5066 | −1.36655 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 112.694 | 3.99434 | ||||||||
\(797\) | 13.7295 | 0.486323 | 0.243161 | − | 0.969986i | \(-0.421816\pi\) | ||||
0.243161 | + | 0.969986i | \(0.421816\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.9442 | −1.27162 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.41421 | −0.0499376 | ||||||||
\(803\) | −18.0000 | −0.635206 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.86319 | 0.206650 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.7082 | 0.587793 | ||||||||
\(809\) | −47.5130 | −1.67047 | −0.835234 | − | 0.549895i | \(-0.814668\pi\) | ||||
−0.835234 | + | 0.549895i | \(0.814668\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.5836 | −0.582329 | −0.291164 | − | 0.956673i | \(-0.594043\pi\) | ||||
−0.291164 | + | 0.956673i | \(0.594043\pi\) | |||||||
\(812\) | −2.62210 | −0.0920175 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 47.1246 | 1.65172 | ||||||||
\(815\) | −32.2361 | −1.12918 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.69316 | −0.339121 | ||||||||
\(818\) | −78.7532 | −2.75354 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.9787 | −0.558001 | ||||||||
\(821\) | −23.8353 | −0.831858 | −0.415929 | − | 0.909397i | \(-0.636543\pi\) | ||||
−0.415929 | + | 0.909397i | \(0.636543\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.5231 | −0.471387 | −0.235694 | − | 0.971827i | \(-0.575736\pi\) | ||||
−0.235694 | + | 0.971827i | \(0.575736\pi\) | |||||||
\(824\) | −80.0132 | −2.78739 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −31.2705 | −1.08804 | ||||||||
\(827\) | 18.3547 | 0.638255 | 0.319127 | − | 0.947712i | \(-0.396610\pi\) | ||||
0.319127 | + | 0.947712i | \(0.396610\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 51.0879 | 1.77436 | 0.887178 | − | 0.461427i | \(-0.152662\pi\) | ||||
0.887178 | + | 0.461427i | \(0.152662\pi\) | |||||||
\(830\) | 18.5123 | 0.642571 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −22.8337 | −0.791618 | ||||||||
\(833\) | 22.2148 | 0.769696 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.41577 | −0.0836010 | ||||||||
\(836\) | −20.5942 | −0.712266 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 80.1033 | 2.76712 | ||||||||
\(839\) | 19.4164 | 0.670329 | 0.335164 | − | 0.942160i | \(-0.391208\pi\) | ||||
0.335164 | + | 0.942160i | \(0.391208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7082 | −0.989938 | ||||||||
\(842\) | −69.1591 | −2.38338 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −24.2705 | −0.835425 | ||||||||
\(845\) | 13.6950 | 0.471124 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.00000 | −0.240523 | ||||||||
\(848\) | 135.292 | 4.64593 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.1246 | 0.381347 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.2918 | −1.10565 | −0.552825 | − | 0.833297i | \(-0.686450\pi\) | ||||
−0.552825 | + | 0.833297i | \(0.686450\pi\) | |||||||
\(854\) | 36.4844 | 1.24847 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.0000 | 0.375972 | ||||||||
\(857\) | 6.00000 | 0.204956 | 0.102478 | − | 0.994735i | \(-0.467323\pi\) | ||||
0.102478 | + | 0.994735i | \(0.467323\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.6011 | −1.41941 | −0.709705 | − | 0.704499i | \(-0.751172\pi\) | ||||
−0.709705 | + | 0.704499i | \(0.751172\pi\) | |||||||
\(860\) | 105.211 | 3.58765 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −93.9574 | −3.20020 | ||||||||
\(863\) | 31.0826 | 1.05806 | 0.529032 | − | 0.848602i | \(-0.322555\pi\) | ||||
0.529032 | + | 0.848602i | \(0.322555\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40.2492 | 1.36851 | ||||||||
\(866\) | 67.6458 | 2.29870 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.87539 | 0.233232 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.7326 | −0.533078 | ||||||||
\(872\) | 9.65248 | 0.326874 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.86474 | −0.232203 | ||||||||
\(875\) | −11.1803 | −0.377964 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.7082 | −0.969407 | −0.484704 | − | 0.874678i | \(-0.661073\pi\) | ||||
−0.484704 | + | 0.874678i | \(0.661073\pi\) | |||||||
\(878\) | 65.4508 | 2.20886 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 93.4842 | 3.15135 | ||||||||
\(881\) | −7.24730 | −0.244168 | −0.122084 | − | 0.992520i | \(-0.538958\pi\) | ||||
−0.122084 | + | 0.992520i | \(0.538958\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.9411 | −1.14221 | −0.571105 | − | 0.820877i | \(-0.693485\pi\) | ||||
−0.571105 | + | 0.820877i | \(0.693485\pi\) | |||||||
\(884\) | 47.1246 | 1.58497 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.8541 | 0.532629 | ||||||||
\(887\) | −25.3607 | −0.851528 | −0.425764 | − | 0.904834i | \(-0.639995\pi\) | ||||
−0.425764 | + | 0.904834i | \(0.639995\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.48683 | 0.318178 | ||||||||
\(890\) | 89.8606 | 3.01213 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 78.3706 | 2.62404 | ||||||||
\(893\) | 9.70820 | 0.324873 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29.6684 | 0.991705 | ||||||||
\(896\) | 1.09017 | 0.0364200 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 88.2400 | 2.94461 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −50.8328 | −1.69349 | ||||||||
\(902\) | 16.3516 | 0.544448 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −72.9574 | −2.42653 | ||||||||
\(905\) | −19.4350 | −0.646042 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.5410 | 0.383213 | 0.191607 | − | 0.981472i | \(-0.438630\pi\) | ||||
0.191607 | + | 0.981472i | \(0.438630\pi\) | |||||||
\(908\) | −11.1246 | −0.369183 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 15.3500 | 0.508848 | ||||||||
\(911\) | 26.9188 | 0.891859 | 0.445929 | − | 0.895068i | \(-0.352873\pi\) | ||||
0.445929 | + | 0.895068i | \(0.352873\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.4164 | −0.444018 | ||||||||
\(914\) | −29.6197 | −0.979732 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.5942 | 0.680452 | ||||||||
\(917\) | 7.41641 | 0.244911 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.5410 | −1.40330 | −0.701649 | − | 0.712522i | \(-0.747553\pi\) | ||||
−0.701649 | + | 0.712522i | \(0.747553\pi\) | |||||||
\(920\) | 43.8105 | 1.44439 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.5231 | 0.445361 | ||||||||
\(923\) | −3.86008 | −0.127056 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 10.0270 | 0.329508 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.86319 | −0.192468 | ||||||||
\(929\) | −10.6460 | −0.349284 | −0.174642 | − | 0.984632i | \(-0.555877\pi\) | ||||
−0.174642 | + | 0.984632i | \(0.555877\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.00000 | −0.196642 | ||||||||
\(932\) | 65.3951 | 2.14209 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −40.9787 | −1.34086 | ||||||||
\(935\) | −35.1246 | −1.14870 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.2492 | 0.792188 | 0.396094 | − | 0.918210i | \(-0.370366\pi\) | ||||
0.396094 | + | 0.918210i | \(0.370366\pi\) | |||||||
\(938\) | 15.7082 | 0.512891 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −105.374 | −3.43692 | ||||||||
\(941\) | −25.5347 | −0.832406 | −0.416203 | − | 0.909272i | \(-0.636639\pi\) | ||||
−0.416203 | + | 0.909272i | \(0.636639\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.86008 | 0.125702 | ||||||||
\(944\) | −117.700 | −3.83081 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −107.666 | −3.50051 | ||||||||
\(947\) | −40.1869 | −1.30590 | −0.652949 | − | 0.757402i | \(-0.726468\pi\) | ||||
−0.652949 | + | 0.757402i | \(0.726468\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.1246 | −0.361120 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −27.6653 | −0.896637 | ||||||||
\(953\) | −18.6699 | −0.604778 | −0.302389 | − | 0.953185i | \(-0.597784\pi\) | ||||
−0.302389 | + | 0.953185i | \(0.597784\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.8328 | 0.706493 | ||||||||
\(956\) | −58.7780 | −1.90102 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 43.2705 | 1.39801 | ||||||||
\(959\) | −2.62210 | −0.0846719 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0 | 0 | ||||||||
\(962\) | 29.1246 | 0.939015 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −112.694 | −3.62964 | ||||||||
\(965\) | 46.3050 | 1.49061 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.0168 | 1.41549 | 0.707743 | − | 0.706470i | \(-0.249713\pi\) | ||||
0.707743 | + | 0.706470i | \(0.249713\pi\) | |||||||
\(968\) | −52.3050 | −1.68114 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −40.9787 | −1.31575 | ||||||||
\(971\) | −53.8885 | −1.72937 | −0.864683 | − | 0.502318i | \(-0.832481\pi\) | ||||
−0.864683 | + | 0.502318i | \(0.832481\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.9721 | 0.576160 | ||||||||
\(974\) | −73.5090 | −2.35538 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 137.325 | 4.39566 | ||||||||
\(977\) | 42.4853 | 1.35922 | 0.679612 | − | 0.733571i | \(-0.262148\pi\) | ||||
0.679612 | + | 0.733571i | \(0.262148\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −65.1246 | −2.08139 | ||||||||
\(980\) | 65.1246 | 2.08033 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −41.6011 | −1.32754 | ||||||||
\(983\) | −53.9163 | −1.71966 | −0.859832 | − | 0.510577i | \(-0.829432\pi\) | ||||
−0.859832 | + | 0.510577i | \(0.829432\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.41577 | −0.0769727 | ||||||||
\(986\) | 5.23607 | 0.166750 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.7279 | −0.404929 | ||||||||
\(989\) | −25.4164 | −0.808195 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.9358 | −0.442685 | −0.221343 | − | 0.975196i | \(-0.571044\pi\) | ||||
−0.221343 | + | 0.975196i | \(0.571044\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.85410 | 0.122245 | ||||||||
\(995\) | −51.9132 | −1.64576 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −58.6656 | −1.85796 | −0.928980 | − | 0.370131i | \(-0.879313\pi\) | ||||
−0.928980 | + | 0.370131i | \(0.879313\pi\) | |||||||
\(998\) | −48.1320 | −1.52359 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))