Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,2,Mod(1351,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1521.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(12.1452461474\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.4 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1351 |
Dual form | 1521.2.b.j.1351.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1521\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.41421i | 1.70711i | 0.521005 | + | 0.853553i | \(0.325557\pi\) | ||||
−0.521005 | + | 0.853553i | \(0.674443\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.82843 | −1.91421 | ||||||||
\(5\) | − 2.82843i | − 1.26491i | −0.774597 | − | 0.632456i | \(-0.782047\pi\) | ||||
0.774597 | − | 0.632456i | \(-0.217953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843i | 1.06904i | 0.845154 | + | 0.534522i | \(0.179509\pi\) | ||||
−0.845154 | + | 0.534522i | \(0.820491\pi\) | |||||||
\(8\) | − 4.41421i | − 1.56066i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.82843 | 2.15934 | ||||||||
\(11\) | − 2.00000i | − 0.603023i | −0.953463 | − | 0.301511i | \(-0.902509\pi\) | ||||
0.953463 | − | 0.301511i | \(-0.0974911\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −6.82843 | −1.82497 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | −3.65685 | −0.886917 | −0.443459 | − | 0.896295i | \(-0.646249\pi\) | ||||
−0.443459 | + | 0.896295i | \(0.646249\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.82843i | 0.648886i | 0.945905 | + | 0.324443i | \(0.105177\pi\) | ||||
−0.945905 | + | 0.324443i | \(0.894823\pi\) | |||||||
\(20\) | 10.8284i | 2.42131i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.82843 | 1.02942 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | −0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 10.8284i | − 2.04638i | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 6.82843i | − 1.22642i | −0.789919 | − | 0.613211i | \(-0.789878\pi\) | ||||
0.789919 | − | 0.613211i | \(-0.210122\pi\) | |||||||
\(32\) | − 1.58579i | − 0.280330i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 8.82843i | − 1.51406i | ||||||||
\(35\) | 8.00000 | 1.35225 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 3.65685i | − 0.601183i | −0.953753 | − | 0.300592i | \(-0.902816\pi\) | ||||
0.953753 | − | 0.300592i | \(-0.0971841\pi\) | |||||||
\(38\) | −6.82843 | −1.10772 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −12.4853 | −1.97410 | ||||||||
\(41\) | − 10.8284i | − 1.69112i | −0.533883 | − | 0.845558i | \(-0.679268\pi\) | ||||
0.533883 | − | 0.845558i | \(-0.320732\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.65685 | −1.47266 | −0.736328 | − | 0.676625i | \(-0.763442\pi\) | ||||
−0.736328 | + | 0.676625i | \(0.763442\pi\) | |||||||
\(44\) | 7.65685i | 1.15431i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − 9.65685i | − 1.42383i | ||||||||
\(47\) | − 0.343146i | − 0.0500530i | −0.999687 | − | 0.0250265i | \(-0.992033\pi\) | ||||
0.999687 | − | 0.0250265i | \(-0.00796701\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | − 7.24264i | − 1.02426i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.65685 | −0.762770 | ||||||||
\(56\) | 12.4853 | 1.66842 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 4.82843i | − 0.634004i | ||||||||
\(59\) | − 3.65685i | − 0.476082i | −0.971255 | − | 0.238041i | \(-0.923495\pi\) | ||||
0.971255 | − | 0.238041i | \(-0.0765052\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.31371 | −1.19250 | −0.596249 | − | 0.802799i | \(-0.703343\pi\) | ||||
−0.596249 | + | 0.802799i | \(0.703343\pi\) | |||||||
\(62\) | 16.4853 | 2.09363 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 9.82843 | 1.22855 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.17157i | 0.143130i | 0.997436 | + | 0.0715652i | \(0.0227994\pi\) | ||||
−0.997436 | + | 0.0715652i | \(0.977201\pi\) | |||||||
\(68\) | 14.0000 | 1.69775 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 19.3137i | 2.30843i | ||||||||
\(71\) | − 2.00000i | − 0.237356i | −0.992933 | − | 0.118678i | \(-0.962134\pi\) | ||||
0.992933 | − | 0.118678i | \(-0.0378657\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 11.6569i | − 1.36433i | −0.731198 | − | 0.682166i | \(-0.761038\pi\) | ||||
0.731198 | − | 0.682166i | \(-0.238962\pi\) | |||||||
\(74\) | 8.82843 | 1.02628 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 10.8284i | − 1.24211i | ||||||||
\(77\) | 5.65685 | 0.644658 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3137 | 1.27289 | 0.636446 | − | 0.771321i | \(-0.280404\pi\) | ||||
0.636446 | + | 0.771321i | \(0.280404\pi\) | |||||||
\(80\) | − 8.48528i | − 0.948683i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 26.1421 | 2.88692 | ||||||||
\(83\) | 7.65685i | 0.840449i | 0.907420 | + | 0.420224i | \(0.138049\pi\) | ||||
−0.907420 | + | 0.420224i | \(0.861951\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.3431i | 1.12187i | ||||||||
\(86\) | − 23.3137i | − 2.51398i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.82843 | −0.941113 | ||||||||
\(89\) | 9.17157i | 0.972185i | 0.873907 | + | 0.486092i | \(0.161578\pi\) | ||||
−0.873907 | + | 0.486092i | \(0.838422\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 15.3137 | 1.59656 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.828427 | 0.0854457 | ||||||||
\(95\) | 8.00000 | 0.820783 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 7.65685i | − 0.777436i | −0.921357 | − | 0.388718i | \(-0.872918\pi\) | ||||
0.921357 | − | 0.388718i | \(-0.127082\pi\) | |||||||
\(98\) | − 2.41421i | − 0.243872i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 11.4853 | 1.14853 | ||||||||
\(101\) | −3.65685 | −0.363871 | −0.181935 | − | 0.983311i | \(-0.558236\pi\) | ||||
−0.181935 | + | 0.983311i | \(0.558236\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.6569 | −1.34565 | −0.672825 | − | 0.739802i | \(-0.734919\pi\) | ||||
−0.672825 | + | 0.739802i | \(0.734919\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.82843i | 0.468978i | ||||||||
\(107\) | −11.3137 | −1.09374 | −0.546869 | − | 0.837218i | \(-0.684180\pi\) | ||||
−0.546869 | + | 0.837218i | \(0.684180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 17.3137i | − 1.65835i | −0.558987 | − | 0.829176i | \(-0.688810\pi\) | ||||
0.558987 | − | 0.829176i | \(-0.311190\pi\) | |||||||
\(110\) | − 13.6569i | − 1.30213i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.48528i | 0.801784i | ||||||||
\(113\) | −17.3137 | −1.62874 | −0.814368 | − | 0.580348i | \(-0.802916\pi\) | ||||
−0.814368 | + | 0.580348i | \(0.802916\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.3137i | 1.05501i | ||||||||
\(116\) | 7.65685 | 0.710921 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.82843 | 0.812723 | ||||||||
\(119\) | − 10.3431i | − 0.948155i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | − 22.4853i | − 2.03572i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 26.1421i | 2.34763i | ||||||||
\(125\) | − 5.65685i | − 0.505964i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.65685 | 0.501965 | 0.250982 | − | 0.967992i | \(-0.419246\pi\) | ||||
0.250982 | + | 0.967992i | \(0.419246\pi\) | |||||||
\(128\) | 20.5563i | 1.81694i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.00000 | 0.698963 | 0.349482 | − | 0.936943i | \(-0.386358\pi\) | ||||
0.349482 | + | 0.936943i | \(0.386358\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | −0.693688 | ||||||||
\(134\) | −2.82843 | −0.244339 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16.1421i | 1.38418i | ||||||||
\(137\) | − 5.17157i | − 0.441837i | −0.975292 | − | 0.220919i | \(-0.929094\pi\) | ||||
0.975292 | − | 0.220919i | \(-0.0709055\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.3137 | 1.29889 | 0.649446 | − | 0.760408i | \(-0.275001\pi\) | ||||
0.649446 | + | 0.760408i | \(0.275001\pi\) | |||||||
\(140\) | −30.6274 | −2.58849 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.82843 | 0.405193 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.65685i | 0.469776i | ||||||||
\(146\) | 28.1421 | 2.32906 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14.0000i | 1.15079i | ||||||||
\(149\) | 14.8284i | 1.21479i | 0.794399 | + | 0.607396i | \(0.207786\pi\) | ||||
−0.794399 | + | 0.607396i | \(0.792214\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.4853i | 1.66707i | 0.552468 | + | 0.833534i | \(0.313686\pi\) | ||||
−0.552468 | + | 0.833534i | \(0.686314\pi\) | |||||||
\(152\) | 12.4853 | 1.01269 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 13.6569i | 1.10050i | ||||||||
\(155\) | −19.3137 | −1.55131 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | 27.3137i | 2.17296i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.48528 | −0.354593 | ||||||||
\(161\) | − 11.3137i | − 0.891645i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 13.1716i | − 1.03168i | −0.856686 | − | 0.515839i | \(-0.827480\pi\) | ||||
0.856686 | − | 0.515839i | \(-0.172520\pi\) | |||||||
\(164\) | 41.4558i | 3.23716i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.4853 | −1.43474 | ||||||||
\(167\) | 7.65685i | 0.592505i | 0.955110 | + | 0.296253i | \(0.0957370\pi\) | ||||
−0.955110 | + | 0.296253i | \(0.904263\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −24.9706 | −1.91515 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 36.9706 | 2.81898 | ||||||||
\(173\) | −0.343146 | −0.0260889 | −0.0130444 | − | 0.999915i | \(-0.504152\pi\) | ||||
−0.0130444 | + | 0.999915i | \(0.504152\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 8.48528i | − 0.641427i | ||||||||
\(176\) | − 6.00000i | − 0.452267i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −22.1421 | −1.65962 | ||||||||
\(179\) | −0.686292 | −0.0512958 | −0.0256479 | − | 0.999671i | \(-0.508165\pi\) | ||||
−0.0256479 | + | 0.999671i | \(0.508165\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 17.6569i | 1.30168i | ||||||||
\(185\) | −10.3431 | −0.760443 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.31371i | 0.534831i | ||||||||
\(188\) | 1.31371i | 0.0958120i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 19.3137i | 1.40116i | ||||||||
\(191\) | 19.3137 | 1.39749 | 0.698745 | − | 0.715370i | \(-0.253742\pi\) | ||||
0.698745 | + | 0.715370i | \(0.253742\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.3137i | 1.24627i | 0.782115 | + | 0.623134i | \(0.214141\pi\) | ||||
−0.782115 | + | 0.623134i | \(0.785859\pi\) | |||||||
\(194\) | 18.4853 | 1.32717 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.82843 | 0.273459 | ||||||||
\(197\) | 16.4853i | 1.17453i | 0.809396 | + | 0.587264i | \(0.199795\pi\) | ||||
−0.809396 | + | 0.587264i | \(0.800205\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.3431 | −0.733206 | −0.366603 | − | 0.930377i | \(-0.619479\pi\) | ||||
−0.366603 | + | 0.930377i | \(0.619479\pi\) | |||||||
\(200\) | 13.2426i | 0.936396i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 8.82843i | − 0.621166i | ||||||||
\(203\) | − 5.65685i | − 0.397033i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −30.6274 | −2.13911 | ||||||||
\(206\) | − 32.9706i | − 2.29717i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − 27.3137i | − 1.86713i | ||||||||
\(215\) | 27.3137i | 1.86278i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.3137 | 1.31110 | ||||||||
\(218\) | 41.7990 | 2.83098 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 21.6569 | 1.46010 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.48528i | 0.300357i | 0.988659 | + | 0.150178i | \(0.0479848\pi\) | ||||
−0.988659 | + | 0.150178i | \(0.952015\pi\) | |||||||
\(224\) | 4.48528 | 0.299685 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − 41.7990i | − 2.78043i | ||||||||
\(227\) | − 5.31371i | − 0.352683i | −0.984329 | − | 0.176342i | \(-0.943574\pi\) | ||||
0.984329 | − | 0.176342i | \(-0.0564263\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 21.3137i | − 1.40845i | −0.709977 | − | 0.704225i | \(-0.751295\pi\) | ||||
0.709977 | − | 0.704225i | \(-0.248705\pi\) | |||||||
\(230\) | −27.3137 | −1.80101 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.82843i | 0.579615i | ||||||||
\(233\) | −26.9706 | −1.76690 | −0.883450 | − | 0.468525i | \(-0.844786\pi\) | ||||
−0.883450 | + | 0.468525i | \(0.844786\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.970563 | −0.0633125 | ||||||||
\(236\) | 14.0000i | 0.911322i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 24.9706 | 1.61860 | ||||||||
\(239\) | − 2.00000i | − 0.129369i | −0.997906 | − | 0.0646846i | \(-0.979396\pi\) | ||||
0.997906 | − | 0.0646846i | \(-0.0206041\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 11.6569i | − 0.750884i | −0.926846 | − | 0.375442i | \(-0.877491\pi\) | ||||
0.926846 | − | 0.375442i | \(-0.122509\pi\) | |||||||
\(242\) | 16.8995i | 1.08634i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 35.6569 | 2.28270 | ||||||||
\(245\) | 2.82843i | 0.180702i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −30.1421 | −1.91403 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.6569 | 0.863735 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000i | 0.502956i | ||||||||
\(254\) | 13.6569i | 0.856907i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | −15.6569 | −0.976648 | −0.488324 | − | 0.872662i | \(-0.662392\pi\) | ||||
−0.488324 | + | 0.872662i | \(0.662392\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.3431 | 0.642692 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 19.3137i | 1.19320i | ||||||||
\(263\) | −12.0000 | −0.739952 | −0.369976 | − | 0.929041i | \(-0.620634\pi\) | ||||
−0.369976 | + | 0.929041i | \(0.620634\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 5.65685i | − 0.347498i | ||||||||
\(266\) | − 19.3137i | − 1.18420i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 4.48528i | − 0.273982i | ||||||||
\(269\) | −18.0000 | −1.09748 | −0.548740 | − | 0.835993i | \(-0.684892\pi\) | ||||
−0.548740 | + | 0.835993i | \(0.684892\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 11.7990i | − 0.716738i | −0.933580 | − | 0.358369i | \(-0.883333\pi\) | ||||
0.933580 | − | 0.358369i | \(-0.116667\pi\) | |||||||
\(272\) | −10.9706 | −0.665188 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.4853 | 0.754263 | ||||||||
\(275\) | 6.00000i | 0.361814i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000 | 0.120168 | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600842 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(278\) | 36.9706i | 2.21735i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − 35.3137i | − 2.11040i | ||||||||
\(281\) | 26.8284i | 1.60045i | 0.599700 | + | 0.800225i | \(0.295287\pi\) | ||||
−0.599700 | + | 0.800225i | \(0.704713\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.97056 | 0.295469 | 0.147735 | − | 0.989027i | \(-0.452802\pi\) | ||||
0.147735 | + | 0.989027i | \(0.452802\pi\) | |||||||
\(284\) | 7.65685i | 0.454351i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 30.6274 | 1.80788 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.62742 | −0.213377 | ||||||||
\(290\) | −13.6569 | −0.801958 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 44.6274i | 2.61162i | ||||||||
\(293\) | − 26.1421i | − 1.52724i | −0.645666 | − | 0.763620i | \(-0.723420\pi\) | ||||
0.645666 | − | 0.763620i | \(-0.276580\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.3431 | −0.602201 | ||||||||
\(296\) | −16.1421 | −0.938243 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −35.7990 | −2.07378 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 27.3137i | − 1.57434i | ||||||||
\(302\) | −49.4558 | −2.84586 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.48528i | 0.486664i | ||||||||
\(305\) | 26.3431i | 1.50840i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.1716i | 0.980033i | 0.871713 | + | 0.490017i | \(0.163009\pi\) | ||||
−0.871713 | + | 0.490017i | \(0.836991\pi\) | |||||||
\(308\) | −21.6569 | −1.23401 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − 46.6274i | − 2.64826i | ||||||||
\(311\) | 34.6274 | 1.96354 | 0.981770 | − | 0.190071i | \(-0.0608718\pi\) | ||||
0.981770 | + | 0.190071i | \(0.0608718\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.00000 | 0.339140 | 0.169570 | − | 0.985518i | \(-0.445762\pi\) | ||||
0.169570 | + | 0.985518i | \(0.445762\pi\) | |||||||
\(314\) | − 24.1421i | − 1.36242i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −43.3137 | −2.43659 | ||||||||
\(317\) | 8.48528i | 0.476581i | 0.971194 | + | 0.238290i | \(0.0765870\pi\) | ||||
−0.971194 | + | 0.238290i | \(0.923413\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000i | 0.223957i | ||||||||
\(320\) | − 27.7990i | − 1.55401i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 27.3137 | 1.52213 | ||||||||
\(323\) | − 10.3431i | − 0.575508i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 31.7990 | 1.76118 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −47.7990 | −2.63926 | ||||||||
\(329\) | 0.970563 | 0.0535089 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 2.14214i | − 0.117742i | −0.998266 | − | 0.0588712i | \(-0.981250\pi\) | ||||
0.998266 | − | 0.0588712i | \(-0.0187501\pi\) | |||||||
\(332\) | − 29.3137i | − 1.60880i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −18.4853 | −1.01147 | ||||||||
\(335\) | 3.31371 | 0.181047 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.3137 | 0.725244 | 0.362622 | − | 0.931936i | \(-0.381882\pi\) | ||||
0.362622 | + | 0.931936i | \(0.381882\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − 39.5980i | − 2.14750i | ||||||||
\(341\) | −13.6569 | −0.739560 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706i | 0.916324i | ||||||||
\(344\) | 42.6274i | 2.29832i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 0.828427i | − 0.0445365i | ||||||||
\(347\) | 31.3137 | 1.68101 | 0.840504 | − | 0.541805i | \(-0.182259\pi\) | ||||
0.840504 | + | 0.541805i | \(0.182259\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.65685i | 0.409862i | 0.978776 | + | 0.204931i | \(0.0656970\pi\) | ||||
−0.978776 | + | 0.204931i | \(0.934303\pi\) | |||||||
\(350\) | 20.4853 | 1.09498 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.17157 | −0.169045 | ||||||||
\(353\) | − 17.4558i | − 0.929081i | −0.885552 | − | 0.464540i | \(-0.846220\pi\) | ||||
0.885552 | − | 0.464540i | \(-0.153780\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.65685 | −0.300235 | ||||||||
\(356\) | − 35.1127i | − 1.86097i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 1.65685i | − 0.0875675i | ||||||||
\(359\) | 1.02944i | 0.0543316i | 0.999631 | + | 0.0271658i | \(0.00864821\pi\) | ||||
−0.999631 | + | 0.0271658i | \(0.991352\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0000 | 0.578947 | ||||||||
\(362\) | − 33.7990i | − 1.77644i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −32.9706 | −1.72576 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.0000 | −1.25279 | −0.626395 | − | 0.779506i | \(-0.715470\pi\) | ||||
−0.626395 | + | 0.779506i | \(0.715470\pi\) | |||||||
\(368\) | −12.0000 | −0.625543 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 24.9706i | − 1.29816i | ||||||||
\(371\) | 5.65685i | 0.293689i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0000 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(374\) | −17.6569 | −0.913014 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.51472 | −0.0781156 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 16.4853i | − 0.846792i | −0.905945 | − | 0.423396i | \(-0.860838\pi\) | ||||
0.905945 | − | 0.423396i | \(-0.139162\pi\) | |||||||
\(380\) | −30.6274 | −1.57115 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 46.6274i | 2.38567i | ||||||||
\(383\) | 2.97056i | 0.151789i | 0.997116 | + | 0.0758943i | \(0.0241812\pi\) | ||||
−0.997116 | + | 0.0758943i | \(0.975819\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − 16.0000i | − 0.815436i | ||||||||
\(386\) | −41.7990 | −2.12751 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 29.3137i | 1.48818i | ||||||||
\(389\) | 6.97056 | 0.353422 | 0.176711 | − | 0.984263i | \(-0.443454\pi\) | ||||
0.176711 | + | 0.984263i | \(0.443454\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.6274 | 0.739740 | ||||||||
\(392\) | 4.41421i | 0.222951i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −39.7990 | −2.00504 | ||||||||
\(395\) | − 32.0000i | − 1.61009i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.97056i | 0.149088i | 0.997218 | + | 0.0745441i | \(0.0237502\pi\) | ||||
−0.997218 | + | 0.0745441i | \(0.976250\pi\) | |||||||
\(398\) | − 24.9706i | − 1.25166i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.00000 | −0.450000 | ||||||||
\(401\) | − 2.14214i | − 0.106973i | −0.998569 | − | 0.0534866i | \(-0.982967\pi\) | ||||
0.998569 | − | 0.0534866i | \(-0.0170334\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 14.0000 | 0.696526 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.6569 | 0.677778 | ||||||||
\(407\) | −7.31371 | −0.362527 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 1.02944i | − 0.0509024i | −0.999676 | − | 0.0254512i | \(-0.991898\pi\) | ||||
0.999676 | − | 0.0254512i | \(-0.00810224\pi\) | |||||||
\(410\) | − 73.9411i | − 3.65169i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 52.2843 | 2.57586 | ||||||||
\(413\) | 10.3431 | 0.508953 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21.6569 | 1.06309 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 13.6569i | 0.667979i | ||||||||
\(419\) | 30.6274 | 1.49625 | 0.748124 | − | 0.663559i | \(-0.230955\pi\) | ||||
0.748124 | + | 0.663559i | \(0.230955\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.6863i | 0.715766i | 0.933766 | + | 0.357883i | \(0.116501\pi\) | ||||
−0.933766 | + | 0.357883i | \(0.883499\pi\) | |||||||
\(422\) | − 28.9706i | − 1.41026i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − 8.82843i | − 0.428746i | ||||||||
\(425\) | 10.9706 | 0.532150 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 26.3431i | − 1.27483i | ||||||||
\(428\) | 43.3137 | 2.09365 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −65.9411 | −3.17996 | ||||||||
\(431\) | − 19.6569i | − 0.946837i | −0.880838 | − | 0.473419i | \(-0.843020\pi\) | ||||
0.880838 | − | 0.473419i | \(-0.156980\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.31371 | −0.0631328 | −0.0315664 | − | 0.999502i | \(-0.510050\pi\) | ||||
−0.0315664 | + | 0.999502i | \(0.510050\pi\) | |||||||
\(434\) | 46.6274i | 2.23819i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 66.2843i | 3.17444i | ||||||||
\(437\) | − 11.3137i | − 0.541208i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.9706 | 0.809961 | 0.404980 | − | 0.914325i | \(-0.367278\pi\) | ||||
0.404980 | + | 0.914325i | \(0.367278\pi\) | |||||||
\(440\) | 24.9706i | 1.19042i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −41.9411 | −1.99268 | −0.996342 | − | 0.0854611i | \(-0.972764\pi\) | ||||
−0.996342 | + | 0.0854611i | \(0.972764\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.9411 | 1.22973 | ||||||||
\(446\) | −10.8284 | −0.512741 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 27.7990i | 1.31338i | ||||||||
\(449\) | 7.79899i | 0.368057i | 0.982921 | + | 0.184029i | \(0.0589139\pi\) | ||||
−0.982921 | + | 0.184029i | \(0.941086\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.6569 | −1.01978 | ||||||||
\(452\) | 66.2843 | 3.11775 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.8284 | 0.602068 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.65685i | 0.171060i | 0.996336 | + | 0.0855302i | \(0.0272584\pi\) | ||||
−0.996336 | + | 0.0855302i | \(0.972742\pi\) | |||||||
\(458\) | 51.4558 | 2.40437 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 43.3137i | − 2.01951i | ||||||||
\(461\) | − 10.8284i | − 0.504330i | −0.967684 | − | 0.252165i | \(-0.918857\pi\) | ||||
0.967684 | − | 0.252165i | \(-0.0811426\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.51472i | 0.349239i | 0.984636 | + | 0.174619i | \(0.0558695\pi\) | ||||
−0.984636 | + | 0.174619i | \(0.944131\pi\) | |||||||
\(464\) | −6.00000 | −0.278543 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − 65.1127i | − 3.01629i | ||||||||
\(467\) | −8.00000 | −0.370196 | −0.185098 | − | 0.982720i | \(-0.559260\pi\) | ||||
−0.185098 | + | 0.982720i | \(0.559260\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.31371 | −0.153013 | ||||||||
\(470\) | − 2.34315i | − 0.108081i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −16.1421 | −0.743002 | ||||||||
\(473\) | 19.3137i | 0.888045i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 8.48528i | − 0.389331i | ||||||||
\(476\) | 39.5980i | 1.81497i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.82843 | 0.220847 | ||||||||
\(479\) | 2.68629i | 0.122740i | 0.998115 | + | 0.0613699i | \(0.0195469\pi\) | ||||
−0.998115 | + | 0.0613699i | \(0.980453\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 28.1421 | 1.28184 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −26.7990 | −1.21814 | ||||||||
\(485\) | −21.6569 | −0.983387 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.7990i | 1.44095i | 0.693481 | + | 0.720475i | \(0.256076\pi\) | ||||
−0.693481 | + | 0.720475i | \(0.743924\pi\) | |||||||
\(488\) | 41.1127i | 1.86108i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.82843 | −0.308477 | ||||||||
\(491\) | −14.6274 | −0.660126 | −0.330063 | − | 0.943959i | \(-0.607070\pi\) | ||||
−0.330063 | + | 0.943959i | \(0.607070\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.31371 | 0.329393 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 20.4853i | − 0.919816i | ||||||||
\(497\) | 5.65685 | 0.253745 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 2.14214i | − 0.0958952i | −0.998850 | − | 0.0479476i | \(-0.984732\pi\) | ||||
0.998850 | − | 0.0479476i | \(-0.0152680\pi\) | |||||||
\(500\) | 21.6569i | 0.968524i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.3137 | −0.682805 | −0.341402 | − | 0.939917i | \(-0.610902\pi\) | ||||
−0.341402 | + | 0.939917i | \(0.610902\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.3431i | 0.460264i | ||||||||
\(506\) | −19.3137 | −0.858599 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −21.6569 | −0.960868 | ||||||||
\(509\) | 27.7990i | 1.23217i | 0.787680 | + | 0.616084i | \(0.211282\pi\) | ||||
−0.787680 | + | 0.616084i | \(0.788718\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.9706 | 1.45853 | ||||||||
\(512\) | − 31.2426i | − 1.38074i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 37.7990i | − 1.66724i | ||||||||
\(515\) | 38.6274i | 1.70213i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.686292 | −0.0301831 | ||||||||
\(518\) | 24.9706i | 1.09714i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.68629 | −0.117689 | −0.0588443 | − | 0.998267i | \(-0.518742\pi\) | ||||
−0.0588443 | + | 0.998267i | \(0.518742\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.31371 | 0.319806 | 0.159903 | − | 0.987133i | \(-0.448882\pi\) | ||||
0.159903 | + | 0.987133i | \(0.448882\pi\) | |||||||
\(524\) | −30.6274 | −1.33796 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − 28.9706i | − 1.26318i | ||||||||
\(527\) | 24.9706i | 1.08773i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 13.6569 | 0.593216 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 30.6274 | 1.32787 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.0000i | 1.38348i | ||||||||
\(536\) | 5.17157 | 0.223378 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 43.4558i | − 1.87351i | ||||||||
\(539\) | 2.00000i | 0.0861461i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 10.0000i | − 0.429934i | −0.976621 | − | 0.214967i | \(-0.931036\pi\) | ||||
0.976621 | − | 0.214967i | \(-0.0689643\pi\) | |||||||
\(542\) | 28.4853 | 1.22355 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.79899i | 0.248630i | ||||||||
\(545\) | −48.9706 | −2.09767 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.686292 | 0.0293437 | 0.0146719 | − | 0.999892i | \(-0.495330\pi\) | ||||
0.0146719 | + | 0.999892i | \(0.495330\pi\) | |||||||
\(548\) | 19.7990i | 0.845771i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −14.4853 | −0.617654 | ||||||||
\(551\) | − 5.65685i | − 0.240990i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.0000i | 1.36078i | ||||||||
\(554\) | 4.82843i | 0.205140i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −58.6274 | −2.48636 | ||||||||
\(557\) | 31.7990i | 1.34737i | 0.739020 | + | 0.673683i | \(0.235289\pi\) | ||||
−0.739020 | + | 0.673683i | \(0.764711\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 24.0000 | 1.01419 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −64.7696 | −2.73214 | ||||||||
\(563\) | 4.00000 | 0.168580 | 0.0842900 | − | 0.996441i | \(-0.473138\pi\) | ||||
0.0842900 | + | 0.996441i | \(0.473138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 48.9706i | 2.06021i | ||||||||
\(566\) | 12.0000i | 0.504398i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.82843 | −0.370433 | ||||||||
\(569\) | −9.02944 | −0.378534 | −0.189267 | − | 0.981926i | \(-0.560611\pi\) | ||||
−0.189267 | + | 0.981926i | \(0.560611\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.9706 | −0.877591 | −0.438795 | − | 0.898587i | \(-0.644595\pi\) | ||||
−0.438795 | + | 0.898587i | \(0.644595\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 73.9411i | 3.08624i | ||||||||
\(575\) | 12.0000 | 0.500435 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.9411i | 1.49625i | 0.663559 | + | 0.748124i | \(0.269045\pi\) | ||||
−0.663559 | + | 0.748124i | \(0.730955\pi\) | |||||||
\(578\) | − 8.75736i | − 0.364258i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 21.6569i | − 0.899252i | ||||||||
\(581\) | −21.6569 | −0.898478 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 4.00000i | − 0.165663i | ||||||||
\(584\) | −51.4558 | −2.12926 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 63.1127 | 2.60716 | ||||||||
\(587\) | − 22.9706i | − 0.948097i | −0.880499 | − | 0.474048i | \(-0.842792\pi\) | ||||
0.880499 | − | 0.474048i | \(-0.157208\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.3137 | 0.795807 | ||||||||
\(590\) | − 24.9706i | − 1.02802i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 10.9706i | − 0.450887i | ||||||||
\(593\) | − 3.51472i | − 0.144332i | −0.997393 | − | 0.0721661i | \(-0.977009\pi\) | ||||
0.997393 | − | 0.0721661i | \(-0.0229912\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −29.2548 | −1.19933 | ||||||||
\(596\) | − 56.7696i | − 2.32537i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.686292 | 0.0280411 | 0.0140206 | − | 0.999902i | \(-0.495537\pi\) | ||||
0.0140206 | + | 0.999902i | \(0.495537\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.6274 | 1.82039 | 0.910195 | − | 0.414180i | \(-0.135931\pi\) | ||||
0.910195 | + | 0.414180i | \(0.135931\pi\) | |||||||
\(602\) | 65.9411 | 2.68756 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − 78.4264i | − 3.19113i | ||||||||
\(605\) | − 19.7990i | − 0.804943i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.9411 | −1.05292 | −0.526459 | − | 0.850201i | \(-0.676481\pi\) | ||||
−0.526459 | + | 0.850201i | \(0.676481\pi\) | |||||||
\(608\) | 4.48528 | 0.181902 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −63.5980 | −2.57501 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 36.3431i | − 1.46789i | −0.679211 | − | 0.733943i | \(-0.737678\pi\) | ||||
0.679211 | − | 0.733943i | \(-0.262322\pi\) | |||||||
\(614\) | −41.4558 | −1.67302 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − 24.9706i | − 1.00609i | ||||||||
\(617\) | 29.1716i | 1.17440i | 0.809441 | + | 0.587202i | \(0.199770\pi\) | ||||
−0.809441 | + | 0.587202i | \(0.800230\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.7990i | 0.635015i | 0.948256 | + | 0.317508i | \(0.102846\pi\) | ||||
−0.948256 | + | 0.317508i | \(0.897154\pi\) | |||||||
\(620\) | 73.9411 | 2.96955 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 83.5980i | 3.35197i | ||||||||
\(623\) | −25.9411 | −1.03931 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 14.4853i | 0.578948i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 38.2843 | 1.52771 | ||||||||
\(629\) | 13.3726i | 0.533200i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.1127i | 0.760865i | 0.924809 | + | 0.380432i | \(0.124225\pi\) | ||||
−0.924809 | + | 0.380432i | \(0.875775\pi\) | |||||||
\(632\) | − 49.9411i | − 1.98655i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −20.4853 | −0.813574 | ||||||||
\(635\) | − 16.0000i | − 0.634941i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −9.65685 | −0.382319 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 58.1421 | 2.29827 | ||||||||
\(641\) | −26.2843 | −1.03817 | −0.519083 | − | 0.854724i | \(-0.673727\pi\) | ||||
−0.519083 | + | 0.854724i | \(0.673727\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.1716i | 0.677181i | 0.940934 | + | 0.338590i | \(0.109950\pi\) | ||||
−0.940934 | + | 0.338590i | \(0.890050\pi\) | |||||||
\(644\) | 43.3137i | 1.70680i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.9706 | 0.982454 | ||||||||
\(647\) | −11.3137 | −0.444788 | −0.222394 | − | 0.974957i | \(-0.571387\pi\) | ||||
−0.222394 | + | 0.974957i | \(0.571387\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.31371 | −0.287088 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 50.4264i | 1.97485i | ||||||||
\(653\) | 2.68629 | 0.105123 | 0.0525614 | − | 0.998618i | \(-0.483261\pi\) | ||||
0.0525614 | + | 0.998618i | \(0.483261\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 22.6274i | − 0.884126i | ||||||||
\(656\) | − 32.4853i | − 1.26834i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.34315i | 0.0913453i | ||||||||
\(659\) | 24.6863 | 0.961641 | 0.480821 | − | 0.876819i | \(-0.340339\pi\) | ||||
0.480821 | + | 0.876819i | \(0.340339\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.02944i | 0.0400405i | 0.999800 | + | 0.0200202i | \(0.00637306\pi\) | ||||
−0.999800 | + | 0.0200202i | \(0.993627\pi\) | |||||||
\(662\) | 5.17157 | 0.200999 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 33.7990 | 1.31166 | ||||||||
\(665\) | 22.6274i | 0.877454i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.00000 | 0.309761 | ||||||||
\(668\) | − 29.3137i | − 1.13418i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.00000i | 0.309067i | ||||||||
\(671\) | 18.6274i | 0.719103i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.6274 | 1.10351 | 0.551753 | − | 0.834008i | \(-0.313959\pi\) | ||||
0.551753 | + | 0.834008i | \(0.313959\pi\) | |||||||
\(674\) | 32.1421i | 1.23807i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −49.3137 | −1.89528 | −0.947640 | − | 0.319341i | \(-0.896538\pi\) | ||||
−0.947640 | + | 0.319341i | \(0.896538\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.6569 | 0.831114 | ||||||||
\(680\) | 45.6569 | 1.75086 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 32.9706i | − 1.26251i | ||||||||
\(683\) | − 19.9411i | − 0.763026i | −0.924363 | − | 0.381513i | \(-0.875403\pi\) | ||||
0.924363 | − | 0.381513i | \(-0.124597\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.6274 | −0.558885 | ||||||||
\(686\) | −40.9706 | −1.56426 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −28.9706 | −1.10449 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 34.1421i | − 1.29883i | −0.760435 | − | 0.649414i | \(-0.775014\pi\) | ||||
0.760435 | − | 0.649414i | \(-0.224986\pi\) | |||||||
\(692\) | 1.31371 | 0.0499397 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 75.5980i | 2.86966i | ||||||||
\(695\) | − 43.3137i | − 1.64298i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39.5980i | 1.49988i | ||||||||
\(698\) | −18.4853 | −0.699678 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 32.4853i | 1.22783i | ||||||||
\(701\) | 38.9706 | 1.47190 | 0.735949 | − | 0.677037i | \(-0.236736\pi\) | ||||
0.735949 | + | 0.677037i | \(0.236736\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.3431 | 0.390099 | ||||||||
\(704\) | − 19.6569i | − 0.740846i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 42.1421 | 1.58604 | ||||||||
\(707\) | − 10.3431i | − 0.388994i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 40.6274i | − 1.52579i | −0.646520 | − | 0.762897i | \(-0.723776\pi\) | ||||
0.646520 | − | 0.762897i | \(-0.276224\pi\) | |||||||
\(710\) | − 13.6569i | − 0.512533i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 40.4853 | 1.51725 | ||||||||
\(713\) | 27.3137i | 1.02291i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.62742 | 0.0981912 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.48528 | −0.0927499 | ||||||||
\(719\) | 37.9411 | 1.41497 | 0.707483 | − | 0.706731i | \(-0.249831\pi\) | ||||
0.707483 | + | 0.706731i | \(0.249831\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − 38.6274i | − 1.43856i | ||||||||
\(722\) | 26.5563i | 0.988325i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 53.5980 | 1.99195 | ||||||||
\(725\) | 6.00000 | 0.222834 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.6569 | 0.803208 | 0.401604 | − | 0.915813i | \(-0.368453\pi\) | ||||
0.401604 | + | 0.915813i | \(0.368453\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − 79.5980i | − 2.94605i | ||||||||
\(731\) | 35.3137 | 1.30612 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.62742i | 0.318661i | 0.987225 | + | 0.159330i | \(0.0509335\pi\) | ||||
−0.987225 | + | 0.159330i | \(0.949066\pi\) | |||||||
\(734\) | − 57.9411i | − 2.13865i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.34315i | 0.233811i | ||||||||
\(737\) | 2.34315 | 0.0863109 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 10.1421i | − 0.373084i | −0.982447 | − | 0.186542i | \(-0.940272\pi\) | ||||
0.982447 | − | 0.186542i | \(-0.0597281\pi\) | |||||||
\(740\) | 39.5980 | 1.45565 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −13.6569 | −0.501359 | ||||||||
\(743\) | − 2.00000i | − 0.0733729i | −0.999327 | − | 0.0366864i | \(-0.988320\pi\) | ||||
0.999327 | − | 0.0366864i | \(-0.0116803\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 41.9411 | 1.53660 | ||||||||
\(746\) | 24.1421i | 0.883906i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 28.0000i | − 1.02378i | ||||||||
\(749\) | − 32.0000i | − 1.16925i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.9706 | −1.20311 | −0.601556 | − | 0.798830i | \(-0.705453\pi\) | ||||
−0.601556 | + | 0.798830i | \(0.705453\pi\) | |||||||
\(752\) | − 1.02944i | − 0.0375397i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − 35.3137i | − 1.28096i | ||||||||
\(761\) | 15.5147i | 0.562408i | 0.959648 | + | 0.281204i | \(0.0907338\pi\) | ||||
−0.959648 | + | 0.281204i | \(0.909266\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 48.9706 | 1.77285 | ||||||||
\(764\) | −73.9411 | −2.67510 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.17157 | −0.259119 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.0000i | 1.51456i | 0.653091 | + | 0.757279i | \(0.273472\pi\) | ||||
−0.653091 | + | 0.757279i | \(0.726528\pi\) | |||||||
\(770\) | 38.6274 | 1.39204 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 66.2843i | − 2.38562i | ||||||||
\(773\) | − 5.85786i | − 0.210693i | −0.994436 | − | 0.105346i | \(-0.966405\pi\) | ||||
0.994436 | − | 0.105346i | \(-0.0335951\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.4853i | 0.735853i | ||||||||
\(776\) | −33.7990 | −1.21331 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.8284i | 0.603328i | ||||||||
\(779\) | 30.6274 | 1.09734 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00000 | −0.143131 | ||||||||
\(782\) | 35.3137i | 1.26282i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | 28.2843i | 1.00951i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 32.7696i | − 1.16811i | −0.811715 | − | 0.584054i | \(-0.801466\pi\) | ||||
0.811715 | − | 0.584054i | \(-0.198534\pi\) | |||||||
\(788\) | − 63.1127i | − 2.24830i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 77.2548 | 2.74860 | ||||||||
\(791\) | − 48.9706i | − 1.74119i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −7.17157 | −0.254510 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 39.5980 | 1.40351 | ||||||||
\(797\) | 35.6569 | 1.26303 | 0.631515 | − | 0.775363i | \(-0.282433\pi\) | ||||
0.631515 | + | 0.775363i | \(0.282433\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.25483i | 0.0443928i | ||||||||
\(800\) | 4.75736i | 0.168198i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.17157 | 0.182615 | ||||||||
\(803\) | −23.3137 | −0.822723 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −32.0000 | −1.12785 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.1421i | 0.567878i | ||||||||
\(809\) | −41.3137 | −1.45251 | −0.726256 | − | 0.687424i | \(-0.758741\pi\) | ||||
−0.726256 | + | 0.687424i | \(0.758741\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1.85786i | − 0.0652384i | −0.999468 | − | 0.0326192i | \(-0.989615\pi\) | ||||
0.999468 | − | 0.0326192i | \(-0.0103849\pi\) | |||||||
\(812\) | 21.6569i | 0.760007i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − 17.6569i | − 0.618872i | ||||||||
\(815\) | −37.2548 | −1.30498 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 27.3137i | − 0.955586i | ||||||||
\(818\) | 2.48528 | 0.0868958 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 117.255 | 4.09472 | ||||||||
\(821\) | − 15.7990i | − 0.551389i | −0.961245 | − | 0.275694i | \(-0.911092\pi\) | ||||
0.961245 | − | 0.275694i | \(-0.0889077\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.9706 | −1.70701 | −0.853503 | − | 0.521088i | \(-0.825527\pi\) | ||||
−0.853503 | + | 0.521088i | \(0.825527\pi\) | |||||||
\(824\) | 60.2843i | 2.10010i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.9706i | 0.868837i | ||||||||
\(827\) | − 26.0000i | − 0.904109i | −0.891990 | − | 0.452054i | \(-0.850691\pi\) | ||||
0.891990 | − | 0.452054i | \(-0.149309\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.31371 | −0.184553 | −0.0922764 | − | 0.995733i | \(-0.529414\pi\) | ||||
−0.0922764 | + | 0.995733i | \(0.529414\pi\) | |||||||
\(830\) | 52.2843i | 1.81481i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.65685 | 0.126702 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.6569 | 0.749466 | ||||||||
\(836\) | −21.6569 | −0.749018 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 73.9411i | 2.55425i | ||||||||
\(839\) | − 47.2548i | − 1.63142i | −0.578462 | − | 0.815709i | \(-0.696347\pi\) | ||||
0.578462 | − | 0.815709i | \(-0.303653\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | −35.4558 | −1.22189 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 45.9411 | 1.58136 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.7990i | 0.680301i | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 26.4853i | 0.908438i | ||||||||
\(851\) | 14.6274i | 0.501421i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.65685i | 0.262166i | 0.991371 | + | 0.131083i | \(0.0418454\pi\) | ||||
−0.991371 | + | 0.131083i | \(0.958155\pi\) | |||||||
\(854\) | 63.5980 | 2.17628 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 49.9411i | 1.70695i | ||||||||
\(857\) | 29.5980 | 1.01105 | 0.505524 | − | 0.862813i | \(-0.331299\pi\) | ||||
0.505524 | + | 0.862813i | \(0.331299\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.3137 | −0.795453 | −0.397727 | − | 0.917504i | \(-0.630201\pi\) | ||||
−0.397727 | + | 0.917504i | \(0.630201\pi\) | |||||||
\(860\) | − 104.569i | − 3.56576i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 47.4558 | 1.61635 | ||||||||
\(863\) | 39.6569i | 1.34994i | 0.737847 | + | 0.674968i | \(0.235842\pi\) | ||||
−0.737847 | + | 0.674968i | \(0.764158\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.970563i | 0.0330001i | ||||||||
\(866\) | − 3.17157i | − 0.107774i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −73.9411 | −2.50973 | ||||||||
\(869\) | − 22.6274i | − 0.767583i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −76.4264 | −2.58812 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 27.3137 | 0.923900 | ||||||||
\(875\) | 16.0000 | 0.540899 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 14.2843i | − 0.482346i | −0.970482 | − | 0.241173i | \(-0.922468\pi\) | ||||
0.970482 | − | 0.241173i | \(-0.0775321\pi\) | |||||||
\(878\) | 40.9706i | 1.38269i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −16.9706 | −0.572078 | ||||||||
\(881\) | 53.5980 | 1.80576 | 0.902881 | − | 0.429891i | \(-0.141448\pi\) | ||||
0.902881 | + | 0.429891i | \(0.141448\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.5980 | 1.73641 | 0.868205 | − | 0.496205i | \(-0.165274\pi\) | ||||
0.868205 | + | 0.496205i | \(0.165274\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − 101.255i | − 3.40172i | ||||||||
\(887\) | 8.00000 | 0.268614 | 0.134307 | − | 0.990940i | \(-0.457119\pi\) | ||||
0.134307 | + | 0.990940i | \(0.457119\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.0000i | 0.536623i | ||||||||
\(890\) | 62.6274i | 2.09928i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 17.1716i | − 0.574947i | ||||||||
\(893\) | 0.970563 | 0.0324786 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.94113i | 0.0648847i | ||||||||
\(896\) | −58.1421 | −1.94239 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.8284 | −0.628313 | ||||||||
\(899\) | 13.6569i | 0.455482i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.31371 | −0.243655 | ||||||||
\(902\) | − 52.2843i | − 1.74088i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 76.4264i | 2.54190i | ||||||||
\(905\) | 39.5980i | 1.31628i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.9706 | −0.696316 | −0.348158 | − | 0.937436i | \(-0.613193\pi\) | ||||
−0.348158 | + | 0.937436i | \(0.613193\pi\) | |||||||
\(908\) | 20.3431i | 0.675111i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.0000 | 1.32526 | 0.662630 | − | 0.748947i | \(-0.269440\pi\) | ||||
0.662630 | + | 0.748947i | \(0.269440\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.3137 | 0.506810 | ||||||||
\(914\) | −8.82843 | −0.292018 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 81.5980i | 2.69607i | ||||||||
\(917\) | 22.6274i | 0.747223i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.3137 | −0.637100 | −0.318550 | − | 0.947906i | \(-0.603196\pi\) | ||||
−0.318550 | + | 0.947906i | \(0.603196\pi\) | |||||||
\(920\) | 49.9411 | 1.64651 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 26.1421 | 0.860945 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.9706i | 0.360710i | ||||||||
\(926\) | −18.1421 | −0.596188 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.17157i | 0.104112i | ||||||||
\(929\) | 27.7990i | 0.912055i | 0.889966 | + | 0.456028i | \(0.150728\pi\) | ||||
−0.889966 | + | 0.456028i | \(0.849272\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 2.82843i | − 0.0926980i | ||||||||
\(932\) | 103.255 | 3.38222 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 19.3137i | − 0.631964i | ||||||||
\(935\) | 20.6863 | 0.676514 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.31371 | 0.0429170 | 0.0214585 | − | 0.999770i | \(-0.493169\pi\) | ||||
0.0214585 | + | 0.999770i | \(0.493169\pi\) | |||||||
\(938\) | − 8.00000i | − 0.261209i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.71573 | 0.121194 | ||||||||
\(941\) | − 5.85786i | − 0.190961i | −0.995431 | − | 0.0954805i | \(-0.969561\pi\) | ||||
0.995431 | − | 0.0954805i | \(-0.0304387\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.3137i | 1.41049i | ||||||||
\(944\) | − 10.9706i | − 0.357061i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −46.6274 | −1.51599 | ||||||||
\(947\) | − 54.9706i | − 1.78630i | −0.449756 | − | 0.893152i | \(-0.648489\pi\) | ||||
0.449756 | − | 0.893152i | \(-0.351511\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 20.4853 | 0.664630 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −45.6569 | −1.47975 | ||||||||
\(953\) | 51.6569 | 1.67333 | 0.836665 | − | 0.547715i | \(-0.184502\pi\) | ||||
0.836665 | + | 0.547715i | \(0.184502\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 54.6274i | − 1.76770i | ||||||||
\(956\) | 7.65685i | 0.247640i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.48528 | −0.209530 | ||||||||
\(959\) | 14.6274 | 0.472344 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.6274 | −0.504110 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 44.6274i | 1.43735i | ||||||||
\(965\) | 48.9706 | 1.57642 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 10.1421i | − 0.326149i | −0.986614 | − | 0.163075i | \(-0.947859\pi\) | ||||
0.986614 | − | 0.163075i | \(-0.0521411\pi\) | |||||||
\(968\) | − 30.8995i | − 0.993147i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − 52.2843i | − 1.67875i | ||||||||
\(971\) | −7.31371 | −0.234708 | −0.117354 | − | 0.993090i | \(-0.537441\pi\) | ||||
−0.117354 | + | 0.993090i | \(0.537441\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 43.3137i | 1.38857i | ||||||||
\(974\) | −76.7696 | −2.45986 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27.9411 | −0.894374 | ||||||||
\(977\) | − 13.8579i | − 0.443352i | −0.975120 | − | 0.221676i | \(-0.928847\pi\) | ||||
0.975120 | − | 0.221676i | \(-0.0711528\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.3431 | 0.586249 | ||||||||
\(980\) | − 10.8284i | − 0.345901i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 35.3137i | − 1.12691i | ||||||||
\(983\) | 2.68629i | 0.0856794i | 0.999082 | + | 0.0428397i | \(0.0136405\pi\) | ||||
−0.999082 | + | 0.0428397i | \(0.986360\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 46.6274 | 1.48567 | ||||||||
\(986\) | 17.6569i | 0.562309i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.6274 | 1.22828 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.3137 | 0.867649 | 0.433824 | − | 0.900998i | \(-0.357164\pi\) | ||||
0.433824 | + | 0.900998i | \(0.357164\pi\) | |||||||
\(992\) | −10.8284 | −0.343803 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 13.6569i | 0.433169i | ||||||||
\(995\) | 29.2548i | 0.927441i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.2548 | 1.62326 | 0.811628 | − | 0.584174i | \(-0.198581\pi\) | ||||
0.811628 | + | 0.584174i | \(0.198581\pi\) | |||||||
\(998\) | 5.17157 | 0.163703 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))