Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1911,2,Mod(1,1911)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1911, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1911.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1911 = 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1911.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: | \(15.2594118263\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1911.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41421 | −1.70711 | −0.853553 | − | 0.521005i | \(-0.825557\pi\) | ||||
−0.853553 | + | 0.521005i | \(0.825557\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | −2.82843 | −1.26491 | −0.632456 | − | 0.774597i | \(-0.717953\pi\) | ||||
−0.632456 | + | 0.774597i | \(0.717953\pi\) | |||||||
\(6\) | 2.41421 | 0.985599 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4.41421 | −1.56066 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 6.82843 | 2.15934 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | −3.82843 | −1.10517 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.82843 | 0.730297 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 3.65685 | 0.886917 | 0.443459 | − | 0.896295i | \(-0.353751\pi\) | ||||
0.443459 | + | 0.896295i | \(0.353751\pi\) | |||||||
\(18\) | −2.41421 | −0.569036 | ||||||||
\(19\) | −2.82843 | −0.648886 | −0.324443 | − | 0.945905i | \(-0.605177\pi\) | ||||
−0.324443 | + | 0.945905i | \(0.605177\pi\) | |||||||
\(20\) | −10.8284 | −2.42131 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.82843 | 1.02942 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 4.41421 | 0.901048 | ||||||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | −2.41421 | −0.473466 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | −6.82843 | −1.24669 | ||||||||
\(31\) | 6.82843 | 1.22642 | 0.613211 | − | 0.789919i | \(-0.289878\pi\) | ||||
0.613211 | + | 0.789919i | \(0.289878\pi\) | |||||||
\(32\) | 1.58579 | 0.280330 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | −8.82843 | −1.51406 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.82843 | 0.638071 | ||||||||
\(37\) | 3.65685 | 0.601183 | 0.300592 | − | 0.953753i | \(-0.402816\pi\) | ||||
0.300592 | + | 0.953753i | \(0.402816\pi\) | |||||||
\(38\) | 6.82843 | 1.10772 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 12.4853 | 1.97410 | ||||||||
\(41\) | −10.8284 | −1.69112 | −0.845558 | − | 0.533883i | \(-0.820732\pi\) | ||||
−0.845558 | + | 0.533883i | \(0.820732\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.65685 | 1.47266 | 0.736328 | − | 0.676625i | \(-0.236558\pi\) | ||||
0.736328 | + | 0.676625i | \(0.236558\pi\) | |||||||
\(44\) | −7.65685 | −1.15431 | ||||||||
\(45\) | −2.82843 | −0.421637 | ||||||||
\(46\) | 9.65685 | 1.42383 | ||||||||
\(47\) | 0.343146 | 0.0500530 | 0.0250265 | − | 0.999687i | \(-0.492033\pi\) | ||||
0.0250265 | + | 0.999687i | \(0.492033\pi\) | |||||||
\(48\) | −3.00000 | −0.433013 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −7.24264 | −1.02426 | ||||||||
\(51\) | −3.65685 | −0.512062 | ||||||||
\(52\) | 3.82843 | 0.530907 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 2.41421 | 0.328533 | ||||||||
\(55\) | 5.65685 | 0.762770 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.82843 | 0.374634 | ||||||||
\(58\) | −4.82843 | −0.634004 | ||||||||
\(59\) | 3.65685 | 0.476082 | 0.238041 | − | 0.971255i | \(-0.423495\pi\) | ||||
0.238041 | + | 0.971255i | \(0.423495\pi\) | |||||||
\(60\) | 10.8284 | 1.39794 | ||||||||
\(61\) | 9.31371 | 1.19250 | 0.596249 | − | 0.802799i | \(-0.296657\pi\) | ||||
0.596249 | + | 0.802799i | \(0.296657\pi\) | |||||||
\(62\) | −16.4853 | −2.09363 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | −2.82843 | −0.350823 | ||||||||
\(66\) | −4.82843 | −0.594338 | ||||||||
\(67\) | 1.17157 | 0.143130 | 0.0715652 | − | 0.997436i | \(-0.477201\pi\) | ||||
0.0715652 | + | 0.997436i | \(0.477201\pi\) | |||||||
\(68\) | 14.0000 | 1.69775 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | −4.41421 | −0.520220 | ||||||||
\(73\) | −11.6569 | −1.36433 | −0.682166 | − | 0.731198i | \(-0.738962\pi\) | ||||
−0.682166 | + | 0.731198i | \(0.738962\pi\) | |||||||
\(74\) | −8.82843 | −1.02628 | ||||||||
\(75\) | −3.00000 | −0.346410 | ||||||||
\(76\) | −10.8284 | −1.24211 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.41421 | 0.273356 | ||||||||
\(79\) | 11.3137 | 1.27289 | 0.636446 | − | 0.771321i | \(-0.280404\pi\) | ||||
0.636446 | + | 0.771321i | \(0.280404\pi\) | |||||||
\(80\) | −8.48528 | −0.948683 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 26.1421 | 2.88692 | ||||||||
\(83\) | 7.65685 | 0.840449 | 0.420224 | − | 0.907420i | \(-0.361951\pi\) | ||||
0.420224 | + | 0.907420i | \(0.361951\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.3431 | −1.12187 | ||||||||
\(86\) | −23.3137 | −2.51398 | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | 8.82843 | 0.941113 | ||||||||
\(89\) | −9.17157 | −0.972185 | −0.486092 | − | 0.873907i | \(-0.661578\pi\) | ||||
−0.486092 | + | 0.873907i | \(0.661578\pi\) | |||||||
\(90\) | 6.82843 | 0.719779 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −15.3137 | −1.59656 | ||||||||
\(93\) | −6.82843 | −0.708075 | ||||||||
\(94\) | −0.828427 | −0.0854457 | ||||||||
\(95\) | 8.00000 | 0.820783 | ||||||||
\(96\) | −1.58579 | −0.161849 | ||||||||
\(97\) | 7.65685 | 0.777436 | 0.388718 | − | 0.921357i | \(-0.372918\pi\) | ||||
0.388718 | + | 0.921357i | \(0.372918\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 11.4853 | 1.14853 | ||||||||
\(101\) | 3.65685 | 0.363871 | 0.181935 | − | 0.983311i | \(-0.441764\pi\) | ||||
0.181935 | + | 0.983311i | \(0.441764\pi\) | |||||||
\(102\) | 8.82843 | 0.874145 | ||||||||
\(103\) | −13.6569 | −1.34565 | −0.672825 | − | 0.739802i | \(-0.734919\pi\) | ||||
−0.672825 | + | 0.739802i | \(0.734919\pi\) | |||||||
\(104\) | −4.41421 | −0.432849 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.82843 | 0.468978 | ||||||||
\(107\) | 11.3137 | 1.09374 | 0.546869 | − | 0.837218i | \(-0.315820\pi\) | ||||
0.546869 | + | 0.837218i | \(0.315820\pi\) | |||||||
\(108\) | −3.82843 | −0.368391 | ||||||||
\(109\) | −17.3137 | −1.65835 | −0.829176 | − | 0.558987i | \(-0.811190\pi\) | ||||
−0.829176 | + | 0.558987i | \(0.811190\pi\) | |||||||
\(110\) | −13.6569 | −1.30213 | ||||||||
\(111\) | −3.65685 | −0.347093 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3137 | 1.62874 | 0.814368 | − | 0.580348i | \(-0.197084\pi\) | ||||
0.814368 | + | 0.580348i | \(0.197084\pi\) | |||||||
\(114\) | −6.82843 | −0.639541 | ||||||||
\(115\) | 11.3137 | 1.05501 | ||||||||
\(116\) | 7.65685 | 0.710921 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −8.82843 | −0.812723 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −12.4853 | −1.13975 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −22.4853 | −2.03572 | ||||||||
\(123\) | 10.8284 | 0.976366 | ||||||||
\(124\) | 26.1421 | 2.34763 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.65685 | −0.501965 | −0.250982 | − | 0.967992i | \(-0.580754\pi\) | ||||
−0.250982 | + | 0.967992i | \(0.580754\pi\) | |||||||
\(128\) | 20.5563 | 1.81694 | ||||||||
\(129\) | −9.65685 | −0.850239 | ||||||||
\(130\) | 6.82843 | 0.598893 | ||||||||
\(131\) | 8.00000 | 0.698963 | 0.349482 | − | 0.936943i | \(-0.386358\pi\) | ||||
0.349482 | + | 0.936943i | \(0.386358\pi\) | |||||||
\(132\) | 7.65685 | 0.666444 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.82843 | −0.244339 | ||||||||
\(135\) | 2.82843 | 0.243432 | ||||||||
\(136\) | −16.1421 | −1.38418 | ||||||||
\(137\) | −5.17157 | −0.441837 | −0.220919 | − | 0.975292i | \(-0.570906\pi\) | ||||
−0.220919 | + | 0.975292i | \(0.570906\pi\) | |||||||
\(138\) | −9.65685 | −0.822046 | ||||||||
\(139\) | −15.3137 | −1.29889 | −0.649446 | − | 0.760408i | \(-0.724999\pi\) | ||||
−0.649446 | + | 0.760408i | \(0.724999\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.343146 | −0.0288981 | ||||||||
\(142\) | −4.82843 | −0.405193 | ||||||||
\(143\) | −2.00000 | −0.167248 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | −5.65685 | −0.469776 | ||||||||
\(146\) | 28.1421 | 2.32906 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14.0000 | 1.15079 | ||||||||
\(149\) | −14.8284 | −1.21479 | −0.607396 | − | 0.794399i | \(-0.707786\pi\) | ||||
−0.607396 | + | 0.794399i | \(0.707786\pi\) | |||||||
\(150\) | 7.24264 | 0.591359 | ||||||||
\(151\) | −20.4853 | −1.66707 | −0.833534 | − | 0.552468i | \(-0.813686\pi\) | ||||
−0.833534 | + | 0.552468i | \(0.813686\pi\) | |||||||
\(152\) | 12.4853 | 1.01269 | ||||||||
\(153\) | 3.65685 | 0.295639 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.3137 | −1.55131 | ||||||||
\(156\) | −3.82843 | −0.306519 | ||||||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | −27.3137 | −2.17296 | ||||||||
\(159\) | 2.00000 | 0.158610 | ||||||||
\(160\) | −4.48528 | −0.354593 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.41421 | −0.189679 | ||||||||
\(163\) | 13.1716 | 1.03168 | 0.515839 | − | 0.856686i | \(-0.327480\pi\) | ||||
0.515839 | + | 0.856686i | \(0.327480\pi\) | |||||||
\(164\) | −41.4558 | −3.23716 | ||||||||
\(165\) | −5.65685 | −0.440386 | ||||||||
\(166\) | −18.4853 | −1.43474 | ||||||||
\(167\) | −7.65685 | −0.592505 | −0.296253 | − | 0.955110i | \(-0.595737\pi\) | ||||
−0.296253 | + | 0.955110i | \(0.595737\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 24.9706 | 1.91515 | ||||||||
\(171\) | −2.82843 | −0.216295 | ||||||||
\(172\) | 36.9706 | 2.81898 | ||||||||
\(173\) | 0.343146 | 0.0260889 | 0.0130444 | − | 0.999915i | \(-0.495848\pi\) | ||||
0.0130444 | + | 0.999915i | \(0.495848\pi\) | |||||||
\(174\) | 4.82843 | 0.366042 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.00000 | −0.452267 | ||||||||
\(177\) | −3.65685 | −0.274866 | ||||||||
\(178\) | 22.1421 | 1.65962 | ||||||||
\(179\) | −0.686292 | −0.0512958 | −0.0256479 | − | 0.999671i | \(-0.508165\pi\) | ||||
−0.0256479 | + | 0.999671i | \(0.508165\pi\) | |||||||
\(180\) | −10.8284 | −0.807103 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.31371 | −0.688489 | ||||||||
\(184\) | 17.6569 | 1.30168 | ||||||||
\(185\) | −10.3431 | −0.760443 | ||||||||
\(186\) | 16.4853 | 1.20876 | ||||||||
\(187\) | −7.31371 | −0.534831 | ||||||||
\(188\) | 1.31371 | 0.0958120 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −19.3137 | −1.40116 | ||||||||
\(191\) | −19.3137 | −1.39749 | −0.698745 | − | 0.715370i | \(-0.746258\pi\) | ||||
−0.698745 | + | 0.715370i | \(0.746258\pi\) | |||||||
\(192\) | 9.82843 | 0.709306 | ||||||||
\(193\) | −17.3137 | −1.24627 | −0.623134 | − | 0.782115i | \(-0.714141\pi\) | ||||
−0.623134 | + | 0.782115i | \(0.714141\pi\) | |||||||
\(194\) | −18.4853 | −1.32717 | ||||||||
\(195\) | 2.82843 | 0.202548 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.4853 | −1.17453 | −0.587264 | − | 0.809396i | \(-0.699795\pi\) | ||||
−0.587264 | + | 0.809396i | \(0.699795\pi\) | |||||||
\(198\) | 4.82843 | 0.343141 | ||||||||
\(199\) | −10.3431 | −0.733206 | −0.366603 | − | 0.930377i | \(-0.619479\pi\) | ||||
−0.366603 | + | 0.930377i | \(0.619479\pi\) | |||||||
\(200\) | −13.2426 | −0.936396 | ||||||||
\(201\) | −1.17157 | −0.0826364 | ||||||||
\(202\) | −8.82843 | −0.621166 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −14.0000 | −0.980196 | ||||||||
\(205\) | 30.6274 | 2.13911 | ||||||||
\(206\) | 32.9706 | 2.29717 | ||||||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 3.00000 | 0.208013 | ||||||||
\(209\) | 5.65685 | 0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | −7.65685 | −0.525875 | ||||||||
\(213\) | −2.00000 | −0.137038 | ||||||||
\(214\) | −27.3137 | −1.86713 | ||||||||
\(215\) | −27.3137 | −1.86278 | ||||||||
\(216\) | 4.41421 | 0.300349 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 41.7990 | 2.83098 | ||||||||
\(219\) | 11.6569 | 0.787697 | ||||||||
\(220\) | 21.6569 | 1.46010 | ||||||||
\(221\) | 3.65685 | 0.245987 | ||||||||
\(222\) | 8.82843 | 0.592525 | ||||||||
\(223\) | −4.48528 | −0.300357 | −0.150178 | − | 0.988659i | \(-0.547985\pi\) | ||||
−0.150178 | + | 0.988659i | \(0.547985\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | −41.7990 | −2.78043 | ||||||||
\(227\) | −5.31371 | −0.352683 | −0.176342 | − | 0.984329i | \(-0.556426\pi\) | ||||
−0.176342 | + | 0.984329i | \(0.556426\pi\) | |||||||
\(228\) | 10.8284 | 0.717130 | ||||||||
\(229\) | −21.3137 | −1.40845 | −0.704225 | − | 0.709977i | \(-0.748705\pi\) | ||||
−0.704225 | + | 0.709977i | \(0.748705\pi\) | |||||||
\(230\) | −27.3137 | −1.80101 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.82843 | −0.579615 | ||||||||
\(233\) | −26.9706 | −1.76690 | −0.883450 | − | 0.468525i | \(-0.844786\pi\) | ||||
−0.883450 | + | 0.468525i | \(0.844786\pi\) | |||||||
\(234\) | −2.41421 | −0.157822 | ||||||||
\(235\) | −0.970563 | −0.0633125 | ||||||||
\(236\) | 14.0000 | 0.911322 | ||||||||
\(237\) | −11.3137 | −0.734904 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.00000 | 0.129369 | 0.0646846 | − | 0.997906i | \(-0.479396\pi\) | ||||
0.0646846 | + | 0.997906i | \(0.479396\pi\) | |||||||
\(240\) | 8.48528 | 0.547723 | ||||||||
\(241\) | −11.6569 | −0.750884 | −0.375442 | − | 0.926846i | \(-0.622509\pi\) | ||||
−0.375442 | + | 0.926846i | \(0.622509\pi\) | |||||||
\(242\) | 16.8995 | 1.08634 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 35.6569 | 2.28270 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −26.1421 | −1.66676 | ||||||||
\(247\) | −2.82843 | −0.179969 | ||||||||
\(248\) | −30.1421 | −1.91403 | ||||||||
\(249\) | −7.65685 | −0.485233 | ||||||||
\(250\) | −13.6569 | −0.863735 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000 | 0.502956 | ||||||||
\(254\) | 13.6569 | 0.856907 | ||||||||
\(255\) | 10.3431 | 0.647713 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 15.6569 | 0.976648 | 0.488324 | − | 0.872662i | \(-0.337608\pi\) | ||||
0.488324 | + | 0.872662i | \(0.337608\pi\) | |||||||
\(258\) | 23.3137 | 1.45145 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −10.8284 | −0.671551 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | −19.3137 | −1.19320 | ||||||||
\(263\) | 12.0000 | 0.739952 | 0.369976 | − | 0.929041i | \(-0.379366\pi\) | ||||
0.369976 | + | 0.929041i | \(0.379366\pi\) | |||||||
\(264\) | −8.82843 | −0.543352 | ||||||||
\(265\) | 5.65685 | 0.347498 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.17157 | 0.561291 | ||||||||
\(268\) | 4.48528 | 0.273982 | ||||||||
\(269\) | −18.0000 | −1.09748 | −0.548740 | − | 0.835993i | \(-0.684892\pi\) | ||||
−0.548740 | + | 0.835993i | \(0.684892\pi\) | |||||||
\(270\) | −6.82843 | −0.415565 | ||||||||
\(271\) | −11.7990 | −0.716738 | −0.358369 | − | 0.933580i | \(-0.616667\pi\) | ||||
−0.358369 | + | 0.933580i | \(0.616667\pi\) | |||||||
\(272\) | 10.9706 | 0.665188 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.4853 | 0.754263 | ||||||||
\(275\) | −6.00000 | −0.361814 | ||||||||
\(276\) | 15.3137 | 0.921777 | ||||||||
\(277\) | −2.00000 | −0.120168 | −0.0600842 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600842 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(278\) | 36.9706 | 2.21735 | ||||||||
\(279\) | 6.82843 | 0.408807 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.8284 | 1.60045 | 0.800225 | − | 0.599700i | \(-0.204713\pi\) | ||||
0.800225 | + | 0.599700i | \(0.204713\pi\) | |||||||
\(282\) | 0.828427 | 0.0493321 | ||||||||
\(283\) | 4.97056 | 0.295469 | 0.147735 | − | 0.989027i | \(-0.452802\pi\) | ||||
0.147735 | + | 0.989027i | \(0.452802\pi\) | |||||||
\(284\) | 7.65685 | 0.454351 | ||||||||
\(285\) | −8.00000 | −0.473879 | ||||||||
\(286\) | 4.82843 | 0.285511 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.58579 | 0.0934434 | ||||||||
\(289\) | −3.62742 | −0.213377 | ||||||||
\(290\) | 13.6569 | 0.801958 | ||||||||
\(291\) | −7.65685 | −0.448853 | ||||||||
\(292\) | −44.6274 | −2.61162 | ||||||||
\(293\) | 26.1421 | 1.52724 | 0.763620 | − | 0.645666i | \(-0.223420\pi\) | ||||
0.763620 | + | 0.645666i | \(0.223420\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.3431 | −0.602201 | ||||||||
\(296\) | −16.1421 | −0.938243 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | 35.7990 | 2.07378 | ||||||||
\(299\) | −4.00000 | −0.231326 | ||||||||
\(300\) | −11.4853 | −0.663103 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 49.4558 | 2.84586 | ||||||||
\(303\) | −3.65685 | −0.210081 | ||||||||
\(304\) | −8.48528 | −0.486664 | ||||||||
\(305\) | −26.3431 | −1.50840 | ||||||||
\(306\) | −8.82843 | −0.504688 | ||||||||
\(307\) | 17.1716 | 0.980033 | 0.490017 | − | 0.871713i | \(-0.336991\pi\) | ||||
0.490017 | + | 0.871713i | \(0.336991\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.6569 | 0.776911 | ||||||||
\(310\) | 46.6274 | 2.64826 | ||||||||
\(311\) | −34.6274 | −1.96354 | −0.981770 | − | 0.190071i | \(-0.939128\pi\) | ||||
−0.981770 | + | 0.190071i | \(0.939128\pi\) | |||||||
\(312\) | 4.41421 | 0.249906 | ||||||||
\(313\) | −6.00000 | −0.339140 | −0.169570 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169570 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(314\) | −24.1421 | −1.36242 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 43.3137 | 2.43659 | ||||||||
\(317\) | −8.48528 | −0.476581 | −0.238290 | − | 0.971194i | \(-0.576587\pi\) | ||||
−0.238290 | + | 0.971194i | \(0.576587\pi\) | |||||||
\(318\) | −4.82843 | −0.270765 | ||||||||
\(319\) | −4.00000 | −0.223957 | ||||||||
\(320\) | 27.7990 | 1.55401 | ||||||||
\(321\) | −11.3137 | −0.631470 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.3431 | −0.575508 | ||||||||
\(324\) | 3.82843 | 0.212690 | ||||||||
\(325\) | 3.00000 | 0.166410 | ||||||||
\(326\) | −31.7990 | −1.76118 | ||||||||
\(327\) | 17.3137 | 0.957450 | ||||||||
\(328\) | 47.7990 | 2.63926 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 13.6569 | 0.751785 | ||||||||
\(331\) | −2.14214 | −0.117742 | −0.0588712 | − | 0.998266i | \(-0.518750\pi\) | ||||
−0.0588712 | + | 0.998266i | \(0.518750\pi\) | |||||||
\(332\) | 29.3137 | 1.60880 | ||||||||
\(333\) | 3.65685 | 0.200394 | ||||||||
\(334\) | 18.4853 | 1.01147 | ||||||||
\(335\) | −3.31371 | −0.181047 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.3137 | −0.725244 | −0.362622 | − | 0.931936i | \(-0.618118\pi\) | ||||
−0.362622 | + | 0.931936i | \(0.618118\pi\) | |||||||
\(338\) | −2.41421 | −0.131316 | ||||||||
\(339\) | −17.3137 | −0.940352 | ||||||||
\(340\) | −39.5980 | −2.14750 | ||||||||
\(341\) | −13.6569 | −0.739560 | ||||||||
\(342\) | 6.82843 | 0.369239 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −42.6274 | −2.29832 | ||||||||
\(345\) | −11.3137 | −0.609110 | ||||||||
\(346\) | −0.828427 | −0.0445365 | ||||||||
\(347\) | −31.3137 | −1.68101 | −0.840504 | − | 0.541805i | \(-0.817741\pi\) | ||||
−0.840504 | + | 0.541805i | \(0.817741\pi\) | |||||||
\(348\) | −7.65685 | −0.410450 | ||||||||
\(349\) | 7.65685 | 0.409862 | 0.204931 | − | 0.978776i | \(-0.434303\pi\) | ||||
0.204931 | + | 0.978776i | \(0.434303\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −3.17157 | −0.169045 | ||||||||
\(353\) | −17.4558 | −0.929081 | −0.464540 | − | 0.885552i | \(-0.653780\pi\) | ||||
−0.464540 | + | 0.885552i | \(0.653780\pi\) | |||||||
\(354\) | 8.82843 | 0.469226 | ||||||||
\(355\) | −5.65685 | −0.300235 | ||||||||
\(356\) | −35.1127 | −1.86097 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.65685 | 0.0875675 | ||||||||
\(359\) | 1.02944 | 0.0543316 | 0.0271658 | − | 0.999631i | \(-0.491352\pi\) | ||||
0.0271658 | + | 0.999631i | \(0.491352\pi\) | |||||||
\(360\) | 12.4853 | 0.658032 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 33.7990 | 1.77644 | ||||||||
\(363\) | 7.00000 | 0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.9706 | 1.72576 | ||||||||
\(366\) | 22.4853 | 1.17532 | ||||||||
\(367\) | 24.0000 | 1.25279 | 0.626395 | − | 0.779506i | \(-0.284530\pi\) | ||||
0.626395 | + | 0.779506i | \(0.284530\pi\) | |||||||
\(368\) | −12.0000 | −0.625543 | ||||||||
\(369\) | −10.8284 | −0.563705 | ||||||||
\(370\) | 24.9706 | 1.29816 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −26.1421 | −1.35541 | ||||||||
\(373\) | 10.0000 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(374\) | 17.6569 | 0.913014 | ||||||||
\(375\) | −5.65685 | −0.292119 | ||||||||
\(376\) | −1.51472 | −0.0781156 | ||||||||
\(377\) | 2.00000 | 0.103005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.4853 | −0.846792 | −0.423396 | − | 0.905945i | \(-0.639162\pi\) | ||||
−0.423396 | + | 0.905945i | \(0.639162\pi\) | |||||||
\(380\) | 30.6274 | 1.57115 | ||||||||
\(381\) | 5.65685 | 0.289809 | ||||||||
\(382\) | 46.6274 | 2.38567 | ||||||||
\(383\) | 2.97056 | 0.151789 | 0.0758943 | − | 0.997116i | \(-0.475819\pi\) | ||||
0.0758943 | + | 0.997116i | \(0.475819\pi\) | |||||||
\(384\) | −20.5563 | −1.04901 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 41.7990 | 2.12751 | ||||||||
\(387\) | 9.65685 | 0.490885 | ||||||||
\(388\) | 29.3137 | 1.48818 | ||||||||
\(389\) | 6.97056 | 0.353422 | 0.176711 | − | 0.984263i | \(-0.443454\pi\) | ||||
0.176711 | + | 0.984263i | \(0.443454\pi\) | |||||||
\(390\) | −6.82843 | −0.345771 | ||||||||
\(391\) | −14.6274 | −0.739740 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.00000 | −0.403547 | ||||||||
\(394\) | 39.7990 | 2.00504 | ||||||||
\(395\) | −32.0000 | −1.61009 | ||||||||
\(396\) | −7.65685 | −0.384771 | ||||||||
\(397\) | 2.97056 | 0.149088 | 0.0745441 | − | 0.997218i | \(-0.476250\pi\) | ||||
0.0745441 | + | 0.997218i | \(0.476250\pi\) | |||||||
\(398\) | 24.9706 | 1.25166 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.00000 | 0.450000 | ||||||||
\(401\) | −2.14214 | −0.106973 | −0.0534866 | − | 0.998569i | \(-0.517033\pi\) | ||||
−0.0534866 | + | 0.998569i | \(0.517033\pi\) | |||||||
\(402\) | 2.82843 | 0.141069 | ||||||||
\(403\) | 6.82843 | 0.340148 | ||||||||
\(404\) | 14.0000 | 0.696526 | ||||||||
\(405\) | −2.82843 | −0.140546 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.31371 | −0.362527 | ||||||||
\(408\) | 16.1421 | 0.799155 | ||||||||
\(409\) | 1.02944 | 0.0509024 | 0.0254512 | − | 0.999676i | \(-0.491898\pi\) | ||||
0.0254512 | + | 0.999676i | \(0.491898\pi\) | |||||||
\(410\) | −73.9411 | −3.65169 | ||||||||
\(411\) | 5.17157 | 0.255095 | ||||||||
\(412\) | −52.2843 | −2.57586 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 9.65685 | 0.474608 | ||||||||
\(415\) | −21.6569 | −1.06309 | ||||||||
\(416\) | 1.58579 | 0.0777496 | ||||||||
\(417\) | 15.3137 | 0.749916 | ||||||||
\(418\) | −13.6569 | −0.667979 | ||||||||
\(419\) | 30.6274 | 1.49625 | 0.748124 | − | 0.663559i | \(-0.230955\pi\) | ||||
0.748124 | + | 0.663559i | \(0.230955\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.6863 | 0.715766 | 0.357883 | − | 0.933766i | \(-0.383499\pi\) | ||||
0.357883 | + | 0.933766i | \(0.383499\pi\) | |||||||
\(422\) | 28.9706 | 1.41026 | ||||||||
\(423\) | 0.343146 | 0.0166843 | ||||||||
\(424\) | 8.82843 | 0.428746 | ||||||||
\(425\) | 10.9706 | 0.532150 | ||||||||
\(426\) | 4.82843 | 0.233938 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 43.3137 | 2.09365 | ||||||||
\(429\) | 2.00000 | 0.0965609 | ||||||||
\(430\) | 65.9411 | 3.17996 | ||||||||
\(431\) | 19.6569 | 0.946837 | 0.473419 | − | 0.880838i | \(-0.343020\pi\) | ||||
0.473419 | + | 0.880838i | \(0.343020\pi\) | |||||||
\(432\) | −3.00000 | −0.144338 | ||||||||
\(433\) | −1.31371 | −0.0631328 | −0.0315664 | − | 0.999502i | \(-0.510050\pi\) | ||||
−0.0315664 | + | 0.999502i | \(0.510050\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.65685 | 0.271225 | ||||||||
\(436\) | −66.2843 | −3.17444 | ||||||||
\(437\) | 11.3137 | 0.541208 | ||||||||
\(438\) | −28.1421 | −1.34468 | ||||||||
\(439\) | 16.9706 | 0.809961 | 0.404980 | − | 0.914325i | \(-0.367278\pi\) | ||||
0.404980 | + | 0.914325i | \(0.367278\pi\) | |||||||
\(440\) | −24.9706 | −1.19042 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.82843 | −0.419925 | ||||||||
\(443\) | 41.9411 | 1.99268 | 0.996342 | − | 0.0854611i | \(-0.0272364\pi\) | ||||
0.996342 | + | 0.0854611i | \(0.0272364\pi\) | |||||||
\(444\) | −14.0000 | −0.664411 | ||||||||
\(445\) | 25.9411 | 1.22973 | ||||||||
\(446\) | 10.8284 | 0.512741 | ||||||||
\(447\) | 14.8284 | 0.701361 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.79899 | 0.368057 | 0.184029 | − | 0.982921i | \(-0.441086\pi\) | ||||
0.184029 | + | 0.982921i | \(0.441086\pi\) | |||||||
\(450\) | −7.24264 | −0.341421 | ||||||||
\(451\) | 21.6569 | 1.01978 | ||||||||
\(452\) | 66.2843 | 3.11775 | ||||||||
\(453\) | 20.4853 | 0.962482 | ||||||||
\(454\) | 12.8284 | 0.602068 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.4853 | −0.584677 | ||||||||
\(457\) | 3.65685 | 0.171060 | 0.0855302 | − | 0.996336i | \(-0.472742\pi\) | ||||
0.0855302 | + | 0.996336i | \(0.472742\pi\) | |||||||
\(458\) | 51.4558 | 2.40437 | ||||||||
\(459\) | −3.65685 | −0.170687 | ||||||||
\(460\) | 43.3137 | 2.01951 | ||||||||
\(461\) | −10.8284 | −0.504330 | −0.252165 | − | 0.967684i | \(-0.581143\pi\) | ||||
−0.252165 | + | 0.967684i | \(0.581143\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.51472 | −0.349239 | −0.174619 | − | 0.984636i | \(-0.555869\pi\) | ||||
−0.174619 | + | 0.984636i | \(0.555869\pi\) | |||||||
\(464\) | 6.00000 | 0.278543 | ||||||||
\(465\) | 19.3137 | 0.895652 | ||||||||
\(466\) | 65.1127 | 3.01629 | ||||||||
\(467\) | 8.00000 | 0.370196 | 0.185098 | − | 0.982720i | \(-0.440740\pi\) | ||||
0.185098 | + | 0.982720i | \(0.440740\pi\) | |||||||
\(468\) | 3.82843 | 0.176969 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.34315 | 0.108081 | ||||||||
\(471\) | −10.0000 | −0.460776 | ||||||||
\(472\) | −16.1421 | −0.743002 | ||||||||
\(473\) | −19.3137 | −0.888045 | ||||||||
\(474\) | 27.3137 | 1.25456 | ||||||||
\(475\) | −8.48528 | −0.389331 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | −4.82843 | −0.220847 | ||||||||
\(479\) | −2.68629 | −0.122740 | −0.0613699 | − | 0.998115i | \(-0.519547\pi\) | ||||
−0.0613699 | + | 0.998115i | \(0.519547\pi\) | |||||||
\(480\) | 4.48528 | 0.204724 | ||||||||
\(481\) | 3.65685 | 0.166738 | ||||||||
\(482\) | 28.1421 | 1.28184 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −26.7990 | −1.21814 | ||||||||
\(485\) | −21.6569 | −0.983387 | ||||||||
\(486\) | 2.41421 | 0.109511 | ||||||||
\(487\) | 31.7990 | 1.44095 | 0.720475 | − | 0.693481i | \(-0.243924\pi\) | ||||
0.720475 | + | 0.693481i | \(0.243924\pi\) | |||||||
\(488\) | −41.1127 | −1.86108 | ||||||||
\(489\) | −13.1716 | −0.595639 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.6274 | −0.660126 | −0.330063 | − | 0.943959i | \(-0.607070\pi\) | ||||
−0.330063 | + | 0.943959i | \(0.607070\pi\) | |||||||
\(492\) | 41.4558 | 1.86897 | ||||||||
\(493\) | 7.31371 | 0.329393 | ||||||||
\(494\) | 6.82843 | 0.307225 | ||||||||
\(495\) | 5.65685 | 0.254257 | ||||||||
\(496\) | 20.4853 | 0.919816 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 18.4853 | 0.828345 | ||||||||
\(499\) | −2.14214 | −0.0958952 | −0.0479476 | − | 0.998850i | \(-0.515268\pi\) | ||||
−0.0479476 | + | 0.998850i | \(0.515268\pi\) | |||||||
\(500\) | 21.6569 | 0.968524 | ||||||||
\(501\) | 7.65685 | 0.342083 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.3137 | −0.682805 | −0.341402 | − | 0.939917i | \(-0.610902\pi\) | ||||
−0.341402 | + | 0.939917i | \(0.610902\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.3431 | −0.460264 | ||||||||
\(506\) | −19.3137 | −0.858599 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −21.6569 | −0.960868 | ||||||||
\(509\) | 27.7990 | 1.23217 | 0.616084 | − | 0.787680i | \(-0.288718\pi\) | ||||
0.616084 | + | 0.787680i | \(0.288718\pi\) | |||||||
\(510\) | −24.9706 | −1.10572 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 31.2426 | 1.38074 | ||||||||
\(513\) | 2.82843 | 0.124878 | ||||||||
\(514\) | −37.7990 | −1.66724 | ||||||||
\(515\) | 38.6274 | 1.70213 | ||||||||
\(516\) | −36.9706 | −1.62754 | ||||||||
\(517\) | −0.686292 | −0.0301831 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.343146 | −0.0150624 | ||||||||
\(520\) | 12.4853 | 0.547516 | ||||||||
\(521\) | −2.68629 | −0.117689 | −0.0588443 | − | 0.998267i | \(-0.518742\pi\) | ||||
−0.0588443 | + | 0.998267i | \(0.518742\pi\) | |||||||
\(522\) | −4.82843 | −0.211335 | ||||||||
\(523\) | −7.31371 | −0.319806 | −0.159903 | − | 0.987133i | \(-0.551118\pi\) | ||||
−0.159903 | + | 0.987133i | \(0.551118\pi\) | |||||||
\(524\) | 30.6274 | 1.33796 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.9706 | −1.26318 | ||||||||
\(527\) | 24.9706 | 1.08773 | ||||||||
\(528\) | 6.00000 | 0.261116 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | −13.6569 | −0.593216 | ||||||||
\(531\) | 3.65685 | 0.158694 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.8284 | −0.469031 | ||||||||
\(534\) | −22.1421 | −0.958184 | ||||||||
\(535\) | −32.0000 | −1.38348 | ||||||||
\(536\) | −5.17157 | −0.223378 | ||||||||
\(537\) | 0.686292 | 0.0296157 | ||||||||
\(538\) | 43.4558 | 1.87351 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 10.8284 | 0.465981 | ||||||||
\(541\) | 10.0000 | 0.429934 | 0.214967 | − | 0.976621i | \(-0.431036\pi\) | ||||
0.214967 | + | 0.976621i | \(0.431036\pi\) | |||||||
\(542\) | 28.4853 | 1.22355 | ||||||||
\(543\) | 14.0000 | 0.600798 | ||||||||
\(544\) | 5.79899 | 0.248630 | ||||||||
\(545\) | 48.9706 | 2.09767 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.686292 | 0.0293437 | 0.0146719 | − | 0.999892i | \(-0.495330\pi\) | ||||
0.0146719 | + | 0.999892i | \(0.495330\pi\) | |||||||
\(548\) | −19.7990 | −0.845771 | ||||||||
\(549\) | 9.31371 | 0.397499 | ||||||||
\(550\) | 14.4853 | 0.617654 | ||||||||
\(551\) | −5.65685 | −0.240990 | ||||||||
\(552\) | −17.6569 | −0.751526 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.82843 | 0.205140 | ||||||||
\(555\) | 10.3431 | 0.439042 | ||||||||
\(556\) | −58.6274 | −2.48636 | ||||||||
\(557\) | 31.7990 | 1.34737 | 0.673683 | − | 0.739020i | \(-0.264711\pi\) | ||||
0.673683 | + | 0.739020i | \(0.264711\pi\) | |||||||
\(558\) | −16.4853 | −0.697878 | ||||||||
\(559\) | 9.65685 | 0.408441 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.31371 | 0.308785 | ||||||||
\(562\) | −64.7696 | −2.73214 | ||||||||
\(563\) | −4.00000 | −0.168580 | −0.0842900 | − | 0.996441i | \(-0.526862\pi\) | ||||
−0.0842900 | + | 0.996441i | \(0.526862\pi\) | |||||||
\(564\) | −1.31371 | −0.0553171 | ||||||||
\(565\) | −48.9706 | −2.06021 | ||||||||
\(566\) | −12.0000 | −0.504398 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.82843 | −0.370433 | ||||||||
\(569\) | −9.02944 | −0.378534 | −0.189267 | − | 0.981926i | \(-0.560611\pi\) | ||||
−0.189267 | + | 0.981926i | \(0.560611\pi\) | |||||||
\(570\) | 19.3137 | 0.808962 | ||||||||
\(571\) | 20.9706 | 0.877591 | 0.438795 | − | 0.898587i | \(-0.355405\pi\) | ||||
0.438795 | + | 0.898587i | \(0.355405\pi\) | |||||||
\(572\) | −7.65685 | −0.320149 | ||||||||
\(573\) | 19.3137 | 0.806842 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.0000 | −0.500435 | ||||||||
\(576\) | −9.82843 | −0.409518 | ||||||||
\(577\) | −35.9411 | −1.49625 | −0.748124 | − | 0.663559i | \(-0.769045\pi\) | ||||
−0.748124 | + | 0.663559i | \(0.769045\pi\) | |||||||
\(578\) | 8.75736 | 0.364258 | ||||||||
\(579\) | 17.3137 | 0.719533 | ||||||||
\(580\) | −21.6569 | −0.899252 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 18.4853 | 0.766240 | ||||||||
\(583\) | 4.00000 | 0.165663 | ||||||||
\(584\) | 51.4558 | 2.12926 | ||||||||
\(585\) | −2.82843 | −0.116941 | ||||||||
\(586\) | −63.1127 | −2.60716 | ||||||||
\(587\) | −22.9706 | −0.948097 | −0.474048 | − | 0.880499i | \(-0.657208\pi\) | ||||
−0.474048 | + | 0.880499i | \(0.657208\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.3137 | −0.795807 | ||||||||
\(590\) | 24.9706 | 1.02802 | ||||||||
\(591\) | 16.4853 | 0.678114 | ||||||||
\(592\) | 10.9706 | 0.450887 | ||||||||
\(593\) | 3.51472 | 0.144332 | 0.0721661 | − | 0.997393i | \(-0.477009\pi\) | ||||
0.0721661 | + | 0.997393i | \(0.477009\pi\) | |||||||
\(594\) | −4.82843 | −0.198113 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −56.7696 | −2.32537 | ||||||||
\(597\) | 10.3431 | 0.423317 | ||||||||
\(598\) | 9.65685 | 0.394898 | ||||||||
\(599\) | −0.686292 | −0.0280411 | −0.0140206 | − | 0.999902i | \(-0.504463\pi\) | ||||
−0.0140206 | + | 0.999902i | \(0.504463\pi\) | |||||||
\(600\) | 13.2426 | 0.540629 | ||||||||
\(601\) | −44.6274 | −1.82039 | −0.910195 | − | 0.414180i | \(-0.864069\pi\) | ||||
−0.910195 | + | 0.414180i | \(0.864069\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.17157 | 0.0477101 | ||||||||
\(604\) | −78.4264 | −3.19113 | ||||||||
\(605\) | 19.7990 | 0.804943 | ||||||||
\(606\) | 8.82843 | 0.358630 | ||||||||
\(607\) | 25.9411 | 1.05292 | 0.526459 | − | 0.850201i | \(-0.323519\pi\) | ||||
0.526459 | + | 0.850201i | \(0.323519\pi\) | |||||||
\(608\) | −4.48528 | −0.181902 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 63.5980 | 2.57501 | ||||||||
\(611\) | 0.343146 | 0.0138822 | ||||||||
\(612\) | 14.0000 | 0.565916 | ||||||||
\(613\) | −36.3431 | −1.46789 | −0.733943 | − | 0.679211i | \(-0.762322\pi\) | ||||
−0.733943 | + | 0.679211i | \(0.762322\pi\) | |||||||
\(614\) | −41.4558 | −1.67302 | ||||||||
\(615\) | −30.6274 | −1.23502 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.1716 | −1.17440 | −0.587202 | − | 0.809441i | \(-0.699770\pi\) | ||||
−0.587202 | + | 0.809441i | \(0.699770\pi\) | |||||||
\(618\) | −32.9706 | −1.32627 | ||||||||
\(619\) | 15.7990 | 0.635015 | 0.317508 | − | 0.948256i | \(-0.397154\pi\) | ||||
0.317508 | + | 0.948256i | \(0.397154\pi\) | |||||||
\(620\) | −73.9411 | −2.96955 | ||||||||
\(621\) | 4.00000 | 0.160514 | ||||||||
\(622\) | 83.5980 | 3.35197 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.00000 | −0.120096 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 14.4853 | 0.578948 | ||||||||
\(627\) | −5.65685 | −0.225913 | ||||||||
\(628\) | 38.2843 | 1.52771 | ||||||||
\(629\) | 13.3726 | 0.533200 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.1127 | −0.760865 | −0.380432 | − | 0.924809i | \(-0.624225\pi\) | ||||
−0.380432 | + | 0.924809i | \(0.624225\pi\) | |||||||
\(632\) | −49.9411 | −1.98655 | ||||||||
\(633\) | 12.0000 | 0.476957 | ||||||||
\(634\) | 20.4853 | 0.813574 | ||||||||
\(635\) | 16.0000 | 0.634941 | ||||||||
\(636\) | 7.65685 | 0.303614 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.65685 | 0.382319 | ||||||||
\(639\) | 2.00000 | 0.0791188 | ||||||||
\(640\) | −58.1421 | −2.29827 | ||||||||
\(641\) | −26.2843 | −1.03817 | −0.519083 | − | 0.854724i | \(-0.673727\pi\) | ||||
−0.519083 | + | 0.854724i | \(0.673727\pi\) | |||||||
\(642\) | 27.3137 | 1.07799 | ||||||||
\(643\) | −17.1716 | −0.677181 | −0.338590 | − | 0.940934i | \(-0.609950\pi\) | ||||
−0.338590 | + | 0.940934i | \(0.609950\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 27.3137 | 1.07548 | ||||||||
\(646\) | 24.9706 | 0.982454 | ||||||||
\(647\) | 11.3137 | 0.444788 | 0.222394 | − | 0.974957i | \(-0.428613\pi\) | ||||
0.222394 | + | 0.974957i | \(0.428613\pi\) | |||||||
\(648\) | −4.41421 | −0.173407 | ||||||||
\(649\) | −7.31371 | −0.287088 | ||||||||
\(650\) | −7.24264 | −0.284080 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 50.4264 | 1.97485 | ||||||||
\(653\) | −2.68629 | −0.105123 | −0.0525614 | − | 0.998618i | \(-0.516739\pi\) | ||||
−0.0525614 | + | 0.998618i | \(0.516739\pi\) | |||||||
\(654\) | −41.7990 | −1.63447 | ||||||||
\(655\) | −22.6274 | −0.884126 | ||||||||
\(656\) | −32.4853 | −1.26834 | ||||||||
\(657\) | −11.6569 | −0.454777 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.6863 | −0.961641 | −0.480821 | − | 0.876819i | \(-0.659661\pi\) | ||||
−0.480821 | + | 0.876819i | \(0.659661\pi\) | |||||||
\(660\) | −21.6569 | −0.842992 | ||||||||
\(661\) | 1.02944 | 0.0400405 | 0.0200202 | − | 0.999800i | \(-0.493627\pi\) | ||||
0.0200202 | + | 0.999800i | \(0.493627\pi\) | |||||||
\(662\) | 5.17157 | 0.200999 | ||||||||
\(663\) | −3.65685 | −0.142020 | ||||||||
\(664\) | −33.7990 | −1.31166 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.82843 | −0.342095 | ||||||||
\(667\) | −8.00000 | −0.309761 | ||||||||
\(668\) | −29.3137 | −1.13418 | ||||||||
\(669\) | 4.48528 | 0.173411 | ||||||||
\(670\) | 8.00000 | 0.309067 | ||||||||
\(671\) | −18.6274 | −0.719103 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.6274 | −1.10351 | −0.551753 | − | 0.834008i | \(-0.686041\pi\) | ||||
−0.551753 | + | 0.834008i | \(0.686041\pi\) | |||||||
\(674\) | 32.1421 | 1.23807 | ||||||||
\(675\) | −3.00000 | −0.115470 | ||||||||
\(676\) | 3.82843 | 0.147247 | ||||||||
\(677\) | −49.3137 | −1.89528 | −0.947640 | − | 0.319341i | \(-0.896538\pi\) | ||||
−0.947640 | + | 0.319341i | \(0.896538\pi\) | |||||||
\(678\) | 41.7990 | 1.60528 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 45.6569 | 1.75086 | ||||||||
\(681\) | 5.31371 | 0.203622 | ||||||||
\(682\) | 32.9706 | 1.26251 | ||||||||
\(683\) | −19.9411 | −0.763026 | −0.381513 | − | 0.924363i | \(-0.624597\pi\) | ||||
−0.381513 | + | 0.924363i | \(0.624597\pi\) | |||||||
\(684\) | −10.8284 | −0.414035 | ||||||||
\(685\) | 14.6274 | 0.558885 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.3137 | 0.813169 | ||||||||
\(688\) | 28.9706 | 1.10449 | ||||||||
\(689\) | −2.00000 | −0.0761939 | ||||||||
\(690\) | 27.3137 | 1.03982 | ||||||||
\(691\) | 34.1421 | 1.29883 | 0.649414 | − | 0.760435i | \(-0.275014\pi\) | ||||
0.649414 | + | 0.760435i | \(0.275014\pi\) | |||||||
\(692\) | 1.31371 | 0.0499397 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 75.5980 | 2.86966 | ||||||||
\(695\) | 43.3137 | 1.64298 | ||||||||
\(696\) | 8.82843 | 0.334641 | ||||||||
\(697\) | −39.5980 | −1.49988 | ||||||||
\(698\) | −18.4853 | −0.699678 | ||||||||
\(699\) | 26.9706 | 1.02012 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.9706 | 1.47190 | 0.735949 | − | 0.677037i | \(-0.236736\pi\) | ||||
0.735949 | + | 0.677037i | \(0.236736\pi\) | |||||||
\(702\) | 2.41421 | 0.0911186 | ||||||||
\(703\) | −10.3431 | −0.390099 | ||||||||
\(704\) | 19.6569 | 0.740846 | ||||||||
\(705\) | 0.970563 | 0.0365535 | ||||||||
\(706\) | 42.1421 | 1.58604 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −14.0000 | −0.526152 | ||||||||
\(709\) | 40.6274 | 1.52579 | 0.762897 | − | 0.646520i | \(-0.223776\pi\) | ||||
0.762897 | + | 0.646520i | \(0.223776\pi\) | |||||||
\(710\) | 13.6569 | 0.512533 | ||||||||
\(711\) | 11.3137 | 0.424297 | ||||||||
\(712\) | 40.4853 | 1.51725 | ||||||||
\(713\) | −27.3137 | −1.02291 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.65685 | 0.211554 | ||||||||
\(716\) | −2.62742 | −0.0981912 | ||||||||
\(717\) | −2.00000 | −0.0746914 | ||||||||
\(718\) | −2.48528 | −0.0927499 | ||||||||
\(719\) | −37.9411 | −1.41497 | −0.707483 | − | 0.706731i | \(-0.750169\pi\) | ||||
−0.707483 | + | 0.706731i | \(0.750169\pi\) | |||||||
\(720\) | −8.48528 | −0.316228 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 26.5563 | 0.988325 | ||||||||
\(723\) | 11.6569 | 0.433523 | ||||||||
\(724\) | −53.5980 | −1.99195 | ||||||||
\(725\) | 6.00000 | 0.222834 | ||||||||
\(726\) | −16.8995 | −0.627199 | ||||||||
\(727\) | 21.6569 | 0.803208 | 0.401604 | − | 0.915813i | \(-0.368453\pi\) | ||||
0.401604 | + | 0.915813i | \(0.368453\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −79.5980 | −2.94605 | ||||||||
\(731\) | 35.3137 | 1.30612 | ||||||||
\(732\) | −35.6569 | −1.31792 | ||||||||
\(733\) | −8.62742 | −0.318661 | −0.159330 | − | 0.987225i | \(-0.550934\pi\) | ||||
−0.159330 | + | 0.987225i | \(0.550934\pi\) | |||||||
\(734\) | −57.9411 | −2.13865 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.34315 | −0.233811 | ||||||||
\(737\) | −2.34315 | −0.0863109 | ||||||||
\(738\) | 26.1421 | 0.962305 | ||||||||
\(739\) | 10.1421 | 0.373084 | 0.186542 | − | 0.982447i | \(-0.440272\pi\) | ||||
0.186542 | + | 0.982447i | \(0.440272\pi\) | |||||||
\(740\) | −39.5980 | −1.45565 | ||||||||
\(741\) | 2.82843 | 0.103905 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.00000 | 0.0733729 | 0.0366864 | − | 0.999327i | \(-0.488320\pi\) | ||||
0.0366864 | + | 0.999327i | \(0.488320\pi\) | |||||||
\(744\) | 30.1421 | 1.10506 | ||||||||
\(745\) | 41.9411 | 1.53660 | ||||||||
\(746\) | −24.1421 | −0.883906 | ||||||||
\(747\) | 7.65685 | 0.280150 | ||||||||
\(748\) | −28.0000 | −1.02378 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 13.6569 | 0.498678 | ||||||||
\(751\) | 32.9706 | 1.20311 | 0.601556 | − | 0.798830i | \(-0.294547\pi\) | ||||
0.601556 | + | 0.798830i | \(0.294547\pi\) | |||||||
\(752\) | 1.02944 | 0.0375397 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.82843 | −0.175841 | ||||||||
\(755\) | 57.9411 | 2.10869 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.9411 | −0.579390 | −0.289695 | − | 0.957119i | \(-0.593554\pi\) | ||||
−0.289695 | + | 0.957119i | \(0.593554\pi\) | |||||||
\(758\) | 39.7990 | 1.44556 | ||||||||
\(759\) | −8.00000 | −0.290382 | ||||||||
\(760\) | −35.3137 | −1.28096 | ||||||||
\(761\) | −15.5147 | −0.562408 | −0.281204 | − | 0.959648i | \(-0.590734\pi\) | ||||
−0.281204 | + | 0.959648i | \(0.590734\pi\) | |||||||
\(762\) | −13.6569 | −0.494736 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −73.9411 | −2.67510 | ||||||||
\(765\) | −10.3431 | −0.373957 | ||||||||
\(766\) | −7.17157 | −0.259119 | ||||||||
\(767\) | 3.65685 | 0.132041 | ||||||||
\(768\) | 29.9706 | 1.08147 | ||||||||
\(769\) | −42.0000 | −1.51456 | −0.757279 | − | 0.653091i | \(-0.773472\pi\) | ||||
−0.757279 | + | 0.653091i | \(0.773472\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.6569 | −0.563868 | ||||||||
\(772\) | −66.2843 | −2.38562 | ||||||||
\(773\) | −5.85786 | −0.210693 | −0.105346 | − | 0.994436i | \(-0.533595\pi\) | ||||
−0.105346 | + | 0.994436i | \(0.533595\pi\) | |||||||
\(774\) | −23.3137 | −0.837994 | ||||||||
\(775\) | 20.4853 | 0.735853 | ||||||||
\(776\) | −33.7990 | −1.21331 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16.8284 | −0.603328 | ||||||||
\(779\) | 30.6274 | 1.09734 | ||||||||
\(780\) | 10.8284 | 0.387720 | ||||||||
\(781\) | −4.00000 | −0.143131 | ||||||||
\(782\) | 35.3137 | 1.26282 | ||||||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −28.2843 | −1.00951 | ||||||||
\(786\) | 19.3137 | 0.688897 | ||||||||
\(787\) | −32.7696 | −1.16811 | −0.584054 | − | 0.811715i | \(-0.698534\pi\) | ||||
−0.584054 | + | 0.811715i | \(0.698534\pi\) | |||||||
\(788\) | −63.1127 | −2.24830 | ||||||||
\(789\) | −12.0000 | −0.427211 | ||||||||
\(790\) | 77.2548 | 2.74860 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 8.82843 | 0.313704 | ||||||||
\(793\) | 9.31371 | 0.330739 | ||||||||
\(794\) | −7.17157 | −0.254510 | ||||||||
\(795\) | −5.65685 | −0.200628 | ||||||||
\(796\) | −39.5980 | −1.40351 | ||||||||
\(797\) | −35.6569 | −1.26303 | −0.631515 | − | 0.775363i | \(-0.717567\pi\) | ||||
−0.631515 | + | 0.775363i | \(0.717567\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.25483 | 0.0443928 | ||||||||
\(800\) | 4.75736 | 0.168198 | ||||||||
\(801\) | −9.17157 | −0.324062 | ||||||||
\(802\) | 5.17157 | 0.182615 | ||||||||
\(803\) | 23.3137 | 0.822723 | ||||||||
\(804\) | −4.48528 | −0.158184 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16.4853 | −0.580669 | ||||||||
\(807\) | 18.0000 | 0.633630 | ||||||||
\(808\) | −16.1421 | −0.567878 | ||||||||
\(809\) | 41.3137 | 1.45251 | 0.726256 | − | 0.687424i | \(-0.241259\pi\) | ||||
0.726256 | + | 0.687424i | \(0.241259\pi\) | |||||||
\(810\) | 6.82843 | 0.239926 | ||||||||
\(811\) | 1.85786 | 0.0652384 | 0.0326192 | − | 0.999468i | \(-0.489615\pi\) | ||||
0.0326192 | + | 0.999468i | \(0.489615\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.7990 | 0.413809 | ||||||||
\(814\) | 17.6569 | 0.618872 | ||||||||
\(815\) | −37.2548 | −1.30498 | ||||||||
\(816\) | −10.9706 | −0.384047 | ||||||||
\(817\) | −27.3137 | −0.955586 | ||||||||
\(818\) | −2.48528 | −0.0868958 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 117.255 | 4.09472 | ||||||||
\(821\) | 15.7990 | 0.551389 | 0.275694 | − | 0.961245i | \(-0.411092\pi\) | ||||
0.275694 | + | 0.961245i | \(0.411092\pi\) | |||||||
\(822\) | −12.4853 | −0.435474 | ||||||||
\(823\) | 48.9706 | 1.70701 | 0.853503 | − | 0.521088i | \(-0.174473\pi\) | ||||
0.853503 | + | 0.521088i | \(0.174473\pi\) | |||||||
\(824\) | 60.2843 | 2.10010 | ||||||||
\(825\) | 6.00000 | 0.208893 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.0000 | −0.904109 | −0.452054 | − | 0.891990i | \(-0.649309\pi\) | ||||
−0.452054 | + | 0.891990i | \(0.649309\pi\) | |||||||
\(828\) | −15.3137 | −0.532188 | ||||||||
\(829\) | −5.31371 | −0.184553 | −0.0922764 | − | 0.995733i | \(-0.529414\pi\) | ||||
−0.0922764 | + | 0.995733i | \(0.529414\pi\) | |||||||
\(830\) | 52.2843 | 1.81481 | ||||||||
\(831\) | 2.00000 | 0.0693792 | ||||||||
\(832\) | −9.82843 | −0.340739 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −36.9706 | −1.28019 | ||||||||
\(835\) | 21.6569 | 0.749466 | ||||||||
\(836\) | 21.6569 | 0.749018 | ||||||||
\(837\) | −6.82843 | −0.236025 | ||||||||
\(838\) | −73.9411 | −2.55425 | ||||||||
\(839\) | 47.2548 | 1.63142 | 0.815709 | − | 0.578462i | \(-0.196347\pi\) | ||||
0.815709 | + | 0.578462i | \(0.196347\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | −35.4558 | −1.22189 | ||||||||
\(843\) | −26.8284 | −0.924020 | ||||||||
\(844\) | −45.9411 | −1.58136 | ||||||||
\(845\) | −2.82843 | −0.0973009 | ||||||||
\(846\) | −0.828427 | −0.0284819 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | −4.97056 | −0.170589 | ||||||||
\(850\) | −26.4853 | −0.908438 | ||||||||
\(851\) | −14.6274 | −0.501421 | ||||||||
\(852\) | −7.65685 | −0.262320 | ||||||||
\(853\) | 7.65685 | 0.262166 | 0.131083 | − | 0.991371i | \(-0.458155\pi\) | ||||
0.131083 | + | 0.991371i | \(0.458155\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.00000 | 0.273594 | ||||||||
\(856\) | −49.9411 | −1.70695 | ||||||||
\(857\) | −29.5980 | −1.01105 | −0.505524 | − | 0.862813i | \(-0.668701\pi\) | ||||
−0.505524 | + | 0.862813i | \(0.668701\pi\) | |||||||
\(858\) | −4.82843 | −0.164840 | ||||||||
\(859\) | 23.3137 | 0.795453 | 0.397727 | − | 0.917504i | \(-0.369799\pi\) | ||||
0.397727 | + | 0.917504i | \(0.369799\pi\) | |||||||
\(860\) | −104.569 | −3.56576 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −47.4558 | −1.61635 | ||||||||
\(863\) | −39.6569 | −1.34994 | −0.674968 | − | 0.737847i | \(-0.735842\pi\) | ||||
−0.674968 | + | 0.737847i | \(0.735842\pi\) | |||||||
\(864\) | −1.58579 | −0.0539496 | ||||||||
\(865\) | −0.970563 | −0.0330001 | ||||||||
\(866\) | 3.17157 | 0.107774 | ||||||||
\(867\) | 3.62742 | 0.123194 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.6274 | −0.767583 | ||||||||
\(870\) | −13.6569 | −0.463011 | ||||||||
\(871\) | 1.17157 | 0.0396972 | ||||||||
\(872\) | 76.4264 | 2.58812 | ||||||||
\(873\) | 7.65685 | 0.259145 | ||||||||
\(874\) | −27.3137 | −0.923900 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 44.6274 | 1.50782 | ||||||||
\(877\) | −14.2843 | −0.482346 | −0.241173 | − | 0.970482i | \(-0.577532\pi\) | ||||
−0.241173 | + | 0.970482i | \(0.577532\pi\) | |||||||
\(878\) | −40.9706 | −1.38269 | ||||||||
\(879\) | −26.1421 | −0.881752 | ||||||||
\(880\) | 16.9706 | 0.572078 | ||||||||
\(881\) | −53.5980 | −1.80576 | −0.902881 | − | 0.429891i | \(-0.858552\pi\) | ||||
−0.902881 | + | 0.429891i | \(0.858552\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.5980 | −1.73641 | −0.868205 | − | 0.496205i | \(-0.834726\pi\) | ||||
−0.868205 | + | 0.496205i | \(0.834726\pi\) | |||||||
\(884\) | 14.0000 | 0.470871 | ||||||||
\(885\) | 10.3431 | 0.347681 | ||||||||
\(886\) | −101.255 | −3.40172 | ||||||||
\(887\) | 8.00000 | 0.268614 | 0.134307 | − | 0.990940i | \(-0.457119\pi\) | ||||
0.134307 | + | 0.990940i | \(0.457119\pi\) | |||||||
\(888\) | 16.1421 | 0.541695 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −62.6274 | −2.09928 | ||||||||
\(891\) | −2.00000 | −0.0670025 | ||||||||
\(892\) | −17.1716 | −0.574947 | ||||||||
\(893\) | −0.970563 | −0.0324786 | ||||||||
\(894\) | −35.7990 | −1.19730 | ||||||||
\(895\) | 1.94113 | 0.0648847 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.00000 | 0.133556 | ||||||||
\(898\) | −18.8284 | −0.628313 | ||||||||
\(899\) | 13.6569 | 0.455482 | ||||||||
\(900\) | 11.4853 | 0.382843 | ||||||||
\(901\) | −7.31371 | −0.243655 | ||||||||
\(902\) | −52.2843 | −1.74088 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −76.4264 | −2.54190 | ||||||||
\(905\) | 39.5980 | 1.31628 | ||||||||
\(906\) | −49.4558 | −1.64306 | ||||||||
\(907\) | 20.9706 | 0.696316 | 0.348158 | − | 0.937436i | \(-0.386807\pi\) | ||||
0.348158 | + | 0.937436i | \(0.386807\pi\) | |||||||
\(908\) | −20.3431 | −0.675111 | ||||||||
\(909\) | 3.65685 | 0.121290 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.0000 | −1.32526 | −0.662630 | − | 0.748947i | \(-0.730560\pi\) | ||||
−0.662630 | + | 0.748947i | \(0.730560\pi\) | |||||||
\(912\) | 8.48528 | 0.280976 | ||||||||
\(913\) | −15.3137 | −0.506810 | ||||||||
\(914\) | −8.82843 | −0.292018 | ||||||||
\(915\) | 26.3431 | 0.870878 | ||||||||
\(916\) | −81.5980 | −2.69607 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 8.82843 | 0.291382 | ||||||||
\(919\) | −19.3137 | −0.637100 | −0.318550 | − | 0.947906i | \(-0.603196\pi\) | ||||
−0.318550 | + | 0.947906i | \(0.603196\pi\) | |||||||
\(920\) | −49.9411 | −1.64651 | ||||||||
\(921\) | −17.1716 | −0.565823 | ||||||||
\(922\) | 26.1421 | 0.860945 | ||||||||
\(923\) | 2.00000 | 0.0658308 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.9706 | 0.360710 | ||||||||
\(926\) | 18.1421 | 0.596188 | ||||||||
\(927\) | −13.6569 | −0.448550 | ||||||||
\(928\) | 3.17157 | 0.104112 | ||||||||
\(929\) | 27.7990 | 0.912055 | 0.456028 | − | 0.889966i | \(-0.349272\pi\) | ||||
0.456028 | + | 0.889966i | \(0.349272\pi\) | |||||||
\(930\) | −46.6274 | −1.52897 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −103.255 | −3.38222 | ||||||||
\(933\) | 34.6274 | 1.13365 | ||||||||
\(934\) | −19.3137 | −0.631964 | ||||||||
\(935\) | 20.6863 | 0.676514 | ||||||||
\(936\) | −4.41421 | −0.144283 | ||||||||
\(937\) | −1.31371 | −0.0429170 | −0.0214585 | − | 0.999770i | \(-0.506831\pi\) | ||||
−0.0214585 | + | 0.999770i | \(0.506831\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.00000 | 0.195803 | ||||||||
\(940\) | −3.71573 | −0.121194 | ||||||||
\(941\) | −5.85786 | −0.190961 | −0.0954805 | − | 0.995431i | \(-0.530439\pi\) | ||||
−0.0954805 | + | 0.995431i | \(0.530439\pi\) | |||||||
\(942\) | 24.1421 | 0.786593 | ||||||||
\(943\) | 43.3137 | 1.41049 | ||||||||
\(944\) | 10.9706 | 0.357061 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 46.6274 | 1.51599 | ||||||||
\(947\) | −54.9706 | −1.78630 | −0.893152 | − | 0.449756i | \(-0.851511\pi\) | ||||
−0.893152 | + | 0.449756i | \(0.851511\pi\) | |||||||
\(948\) | −43.3137 | −1.40676 | ||||||||
\(949\) | −11.6569 | −0.378398 | ||||||||
\(950\) | 20.4853 | 0.664630 | ||||||||
\(951\) | 8.48528 | 0.275154 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.6569 | 1.67333 | 0.836665 | − | 0.547715i | \(-0.184502\pi\) | ||||
0.836665 | + | 0.547715i | \(0.184502\pi\) | |||||||
\(954\) | 4.82843 | 0.156326 | ||||||||
\(955\) | 54.6274 | 1.76770 | ||||||||
\(956\) | 7.65685 | 0.247640 | ||||||||
\(957\) | 4.00000 | 0.129302 | ||||||||
\(958\) | 6.48528 | 0.209530 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −27.7990 | −0.897209 | ||||||||
\(961\) | 15.6274 | 0.504110 | ||||||||
\(962\) | −8.82843 | −0.284640 | ||||||||
\(963\) | 11.3137 | 0.364579 | ||||||||
\(964\) | −44.6274 | −1.43735 | ||||||||
\(965\) | 48.9706 | 1.57642 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.1421 | −0.326149 | −0.163075 | − | 0.986614i | \(-0.552141\pi\) | ||||
−0.163075 | + | 0.986614i | \(0.552141\pi\) | |||||||
\(968\) | 30.8995 | 0.993147 | ||||||||
\(969\) | 10.3431 | 0.332270 | ||||||||
\(970\) | 52.2843 | 1.67875 | ||||||||
\(971\) | −7.31371 | −0.234708 | −0.117354 | − | 0.993090i | \(-0.537441\pi\) | ||||
−0.117354 | + | 0.993090i | \(0.537441\pi\) | |||||||
\(972\) | −3.82843 | −0.122797 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −76.7696 | −2.45986 | ||||||||
\(975\) | −3.00000 | −0.0960769 | ||||||||
\(976\) | 27.9411 | 0.894374 | ||||||||
\(977\) | 13.8579 | 0.443352 | 0.221676 | − | 0.975120i | \(-0.428847\pi\) | ||||
0.221676 | + | 0.975120i | \(0.428847\pi\) | |||||||
\(978\) | 31.7990 | 1.01682 | ||||||||
\(979\) | 18.3431 | 0.586249 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.3137 | −0.552784 | ||||||||
\(982\) | 35.3137 | 1.12691 | ||||||||
\(983\) | −2.68629 | −0.0856794 | −0.0428397 | − | 0.999082i | \(-0.513640\pi\) | ||||
−0.0428397 | + | 0.999082i | \(0.513640\pi\) | |||||||
\(984\) | −47.7990 | −1.52378 | ||||||||
\(985\) | 46.6274 | 1.48567 | ||||||||
\(986\) | −17.6569 | −0.562309 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.8284 | −0.344498 | ||||||||
\(989\) | −38.6274 | −1.22828 | ||||||||
\(990\) | −13.6569 | −0.434043 | ||||||||
\(991\) | 27.3137 | 0.867649 | 0.433824 | − | 0.900998i | \(-0.357164\pi\) | ||||
0.433824 | + | 0.900998i | \(0.357164\pi\) | |||||||
\(992\) | 10.8284 | 0.343803 | ||||||||
\(993\) | 2.14214 | 0.0679786 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 29.2548 | 0.927441 | ||||||||
\(996\) | −29.3137 | −0.928840 | ||||||||
\(997\) | −51.2548 | −1.62326 | −0.811628 | − | 0.584174i | \(-0.801419\pi\) | ||||
−0.811628 | + | 0.584174i | \(0.801419\pi\) | |||||||
\(998\) | 5.17157 | 0.163703 | ||||||||
\(999\) | −3.65685 | −0.115698 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))