Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,4,Mod(641,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.641");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.d (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: | \(75.5224448073\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 5) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 641.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.641 |
Dual form | 1280.4.d.e.641.2 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 2.00000i | − 0.384900i | −0.981307 | − | 0.192450i | \(-0.938357\pi\) | ||||
0.981307 | − | 0.192450i | \(-0.0616434\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 5.00000i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.00000 | −0.323970 | −0.161985 | − | 0.986793i | \(-0.551790\pi\) | ||||
−0.161985 | + | 0.986793i | \(0.551790\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 23.0000 | 0.851852 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 32.0000i | 0.877124i | 0.898701 | + | 0.438562i | \(0.144512\pi\) | ||||
−0.898701 | + | 0.438562i | \(0.855488\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 38.0000i | 0.810716i | 0.914158 | + | 0.405358i | \(0.132853\pi\) | ||||
−0.914158 | + | 0.405358i | \(0.867147\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.0000 | −0.172133 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 26.0000 | 0.370937 | 0.185468 | − | 0.982650i | \(-0.440620\pi\) | ||||
0.185468 | + | 0.982650i | \(0.440620\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 100.000i | − 1.20745i | −0.797192 | − | 0.603726i | \(-0.793682\pi\) | ||||
0.797192 | − | 0.603726i | \(-0.206318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.0000i | 0.124696i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 78.0000 | 0.707136 | 0.353568 | − | 0.935409i | \(-0.384968\pi\) | ||||
0.353568 | + | 0.935409i | \(0.384968\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −25.0000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 100.000i | − 0.712778i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 50.0000i | 0.320164i | 0.987104 | + | 0.160082i | \(0.0511759\pi\) | ||||
−0.987104 | + | 0.160082i | \(0.948824\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −108.000 | −0.625722 | −0.312861 | − | 0.949799i | \(-0.601287\pi\) | ||||
−0.312861 | + | 0.949799i | \(0.601287\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 64.0000 | 0.337605 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 30.0000i | 0.144884i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 266.000i | 1.18190i | 0.806710 | + | 0.590948i | \(0.201246\pi\) | ||||
−0.806710 | + | 0.590948i | \(0.798754\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 76.0000 | 0.312045 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −22.0000 | −0.0838006 | −0.0419003 | − | 0.999122i | \(-0.513341\pi\) | ||||
−0.0419003 | + | 0.999122i | \(0.513341\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 442.000i | 1.56754i | 0.621049 | + | 0.783772i | \(0.286707\pi\) | ||||
−0.621049 | + | 0.783772i | \(0.713293\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 115.000i | − 0.380960i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −514.000 | −1.59520 | −0.797602 | − | 0.603184i | \(-0.793899\pi\) | ||||
−0.797602 | + | 0.603184i | \(0.793899\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −307.000 | −0.895044 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 52.0000i | − 0.142774i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000i | 0.00518342i | 0.999997 | + | 0.00259171i | \(0.000824967\pi\) | ||||
−0.999997 | + | 0.00259171i | \(0.999175\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 160.000 | 0.392262 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −200.000 | −0.464748 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 500.000i | 1.10330i | 0.834077 | + | 0.551648i | \(0.186001\pi\) | ||||
−0.834077 | + | 0.551648i | \(0.813999\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 518.000i | 1.08726i | 0.839324 | + | 0.543632i | \(0.182951\pi\) | ||||
−0.839324 | + | 0.543632i | \(0.817049\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −138.000 | −0.275974 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 190.000 | 0.362563 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 126.000i | − 0.229751i | −0.993380 | − | 0.114876i | \(-0.963353\pi\) | ||||
0.993380 | − | 0.114876i | \(-0.0366470\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 156.000i | − 0.272177i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −412.000 | −0.688668 | −0.344334 | − | 0.938847i | \(-0.611895\pi\) | ||||
−0.344334 | + | 0.938847i | \(0.611895\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 878.000 | 1.40770 | 0.703850 | − | 0.710348i | \(-0.251463\pi\) | ||||
0.703850 | + | 0.710348i | \(0.251463\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 50.0000i | 0.0769800i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 192.000i | − 0.284161i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 600.000 | 0.854497 | 0.427249 | − | 0.904134i | \(-0.359483\pi\) | ||||
0.427249 | + | 0.904134i | \(0.359483\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 421.000 | 0.577503 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 282.000i | − 0.372934i | −0.982461 | − | 0.186467i | \(-0.940296\pi\) | ||||
0.982461 | − | 0.186467i | \(-0.0597037\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 130.000i | − 0.165888i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 100.000 | 0.123231 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 150.000 | 0.178651 | 0.0893257 | − | 0.996002i | \(-0.471529\pi\) | ||||
0.0893257 | + | 0.996002i | \(0.471529\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 228.000i | − 0.262647i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 216.000i | 0.240840i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −500.000 | −0.539989 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 386.000 | 0.404045 | 0.202022 | − | 0.979381i | \(-0.435249\pi\) | ||||
0.202022 | + | 0.979381i | \(0.435249\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 736.000i | 0.747180i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 702.000i | 0.691600i | 0.938308 | + | 0.345800i | \(0.112392\pi\) | ||||
−0.938308 | + | 0.345800i | \(0.887608\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 598.000 | 0.572065 | 0.286032 | − | 0.958220i | \(-0.407663\pi\) | ||||
0.286032 | + | 0.958220i | \(0.407663\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 60.0000 | 0.0557657 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1194.00i | − 1.07877i | −0.842059 | − | 0.539385i | \(-0.818657\pi\) | ||||
0.842059 | − | 0.539385i | \(-0.181343\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 550.000i | 0.483307i | 0.970363 | + | 0.241653i | \(0.0776897\pi\) | ||||
−0.970363 | + | 0.241653i | \(0.922310\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 532.000 | 0.454912 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1562.00 | 1.30036 | 0.650180 | − | 0.759781i | \(-0.274694\pi\) | ||||
0.650180 | + | 0.759781i | \(0.274694\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 390.000i | − 0.316241i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 874.000i | 0.690610i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −156.000 | −0.120172 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 307.000 | 0.230654 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 44.0000i | 0.0322548i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1846.00 | 1.28981 | 0.644906 | − | 0.764262i | \(-0.276897\pi\) | ||||
0.644906 | + | 0.764262i | \(0.276897\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 884.000 | 0.603348 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2208.00i | 1.47262i | 0.676642 | + | 0.736312i | \(0.263435\pi\) | ||||
−0.676642 | + | 0.736312i | \(0.736565\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 600.000i | 0.391177i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −500.000 | −0.318764 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2334.00 | 1.45553 | 0.727763 | − | 0.685829i | \(-0.240560\pi\) | ||||
0.727763 | + | 0.685829i | \(0.240560\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 700.000i | − 0.427146i | −0.976927 | − | 0.213573i | \(-0.931490\pi\) | ||||
0.976927 | − | 0.213573i | \(-0.0685100\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1028.00i | 0.613994i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1216.00 | −0.711098 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 250.000 | 0.143182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 614.000i | 0.344502i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2050.00i | 1.12713i | 0.826071 | + | 0.563566i | \(0.190571\pi\) | ||||
−0.826071 | + | 0.563566i | \(0.809429\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1852.00 | −0.998103 | −0.499052 | − | 0.866572i | \(-0.666318\pi\) | ||||
−0.499052 | + | 0.866572i | \(0.666318\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 598.000 | 0.315983 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 540.000i | 0.279831i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2494.00i | 1.26779i | 0.773420 | + | 0.633894i | \(0.218545\pi\) | ||||
−0.773420 | + | 0.633894i | \(0.781455\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.00000 | 0.00199510 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −468.000 | −0.229090 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2762.00i | − 1.32722i | −0.748080 | − | 0.663609i | \(-0.769024\pi\) | ||||
0.748080 | − | 0.663609i | \(-0.230976\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 320.000i | − 0.150982i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3126.00 | −1.44849 | −0.724243 | − | 0.689545i | \(-0.757811\pi\) | ||||
−0.724243 | + | 0.689545i | \(0.757811\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 753.000 | 0.342740 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 2300.00i | − 1.02857i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 78.0000i | 0.0342788i | 0.999853 | + | 0.0171394i | \(0.00545591\pi\) | ||||
−0.999853 | + | 0.0171394i | \(0.994544\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 150.000 | 0.0647939 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1000.00 | 0.424659 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1300.00i | 0.542830i | 0.962462 | + | 0.271415i | \(0.0874916\pi\) | ||||
−0.962462 | + | 0.271415i | \(0.912508\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1742.00i | 0.715369i | 0.933842 | + | 0.357685i | \(0.116434\pi\) | ||||
−0.933842 | + | 0.357685i | \(0.883566\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1036.00 | 0.418488 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1330.00 | 0.528560 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 832.000i | 0.325358i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 600.000i | 0.230918i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3772.00 | 1.42897 | 0.714483 | − | 0.699653i | \(-0.246662\pi\) | ||||
0.714483 | + | 0.699653i | \(0.246662\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −358.000 | −0.133520 | −0.0667601 | − | 0.997769i | \(-0.521266\pi\) | ||||
−0.0667601 | + | 0.997769i | \(0.521266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 380.000i | − 0.139551i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 2214.00i | − 0.800716i | −0.916359 | − | 0.400358i | \(-0.868886\pi\) | ||||
0.916359 | − | 0.400358i | \(-0.131114\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2600.00 | 0.926176 | 0.463088 | − | 0.886312i | \(-0.346741\pi\) | ||||
0.463088 | + | 0.886312i | \(0.346741\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −252.000 | −0.0884314 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 300.000i | − 0.103724i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 110.000i | 0.0374767i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1794.00 | 0.602375 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3200.00 | 1.05908 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1168.00i | 0.381083i | 0.981679 | + | 0.190541i | \(0.0610243\pi\) | ||||
−0.981679 | + | 0.190541i | \(0.938976\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 824.000i | 0.265068i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2210.00 | 0.701027 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 648.000 | 0.202715 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 1756.00i | − 0.541824i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 988.000i | 0.300724i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6478.00 | −1.94529 | −0.972643 | − | 0.232303i | \(-0.925374\pi\) | ||||
−0.972643 | + | 0.232303i | \(0.925374\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −575.000 | −0.170370 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 646.000i | − 0.188883i | −0.995530 | − | 0.0944417i | \(-0.969893\pi\) | ||||
0.995530 | − | 0.0944417i | \(-0.0301066\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3750.00i | 1.08213i | 0.840982 | + | 0.541063i | \(0.181978\pi\) | ||||
−0.840982 | + | 0.541063i | \(0.818022\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −384.000 | −0.109374 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1482.00 | −0.416691 | −0.208346 | − | 0.978055i | \(-0.566808\pi\) | ||||
−0.208346 | + | 0.978055i | \(0.566808\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2570.00i | 0.713397i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1200.00i | − 0.328896i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1400.00 | 0.378906 | 0.189453 | − | 0.981890i | \(-0.439329\pi\) | ||||
0.189453 | + | 0.981890i | \(0.439329\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3022.00 | 0.807735 | 0.403867 | − | 0.914817i | \(-0.367666\pi\) | ||||
0.403867 | + | 0.914817i | \(0.367666\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 3542.00i | − 0.935059i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1535.00i | 0.400276i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3800.00 | 0.978900 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −564.000 | −0.143542 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 1248.00i | − 0.313837i | −0.987612 | − | 0.156918i | \(-0.949844\pi\) | ||||
0.987612 | − | 0.156918i | \(-0.0501560\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2496.00i | 0.620246i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −260.000 | −0.0638503 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2106.00 | 0.511162 | 0.255581 | − | 0.966788i | \(-0.417733\pi\) | ||||
0.255581 | + | 0.966788i | \(0.417733\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1596.00i | − 0.382898i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1150.00i | 0.272733i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3638.00 | 0.852961 | 0.426480 | − | 0.904497i | \(-0.359753\pi\) | ||||
0.426480 | + | 0.904497i | \(0.359753\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.0000 | 0.00231809 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 300.000i | − 0.0687629i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6550.00i | 1.48461i | 0.670061 | + | 0.742306i | \(0.266268\pi\) | ||||
−0.670061 | + | 0.742306i | \(0.733732\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4388.00 | −0.983587 | −0.491793 | − | 0.870712i | \(-0.663658\pi\) | ||||
−0.491793 | + | 0.870712i | \(0.663658\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −456.000 | −0.101093 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 800.000i | − 0.175425i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 546.000i | 0.118433i | 0.998245 | + | 0.0592165i | \(0.0188602\pi\) | ||||
−0.998245 | + | 0.0592165i | \(0.981140\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2484.00 | −0.533022 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6858.00 | 1.45592 | 0.727961 | − | 0.685619i | \(-0.240468\pi\) | ||||
0.727961 | + | 0.685619i | \(0.240468\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9282.00i | 1.94967i | 0.222920 | + | 0.974837i | \(0.428441\pi\) | ||||
−0.222920 | + | 0.974837i | \(0.571559\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1000.00i | 0.207842i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 132.000 | 0.0271488 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4237.00 | −0.862406 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 772.000i | − 0.155517i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4842.00i | 0.965436i | 0.875776 | + | 0.482718i | \(0.160350\pi\) | ||||
−0.875776 | + | 0.482718i | \(0.839650\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2500.00 | 0.493409 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3200.00 | 0.625195 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2964.00i | 0.573286i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 2652.00i | − 0.507836i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1404.00 | 0.266197 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2590.00 | 0.486239 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2594.00i | 0.482239i | 0.970495 | + | 0.241120i | \(0.0775146\pi\) | ||||
−0.970495 | + | 0.241120i | \(0.922485\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 1196.00i | − 0.220188i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7332.00 | −1.33685 | −0.668424 | − | 0.743781i | \(-0.733031\pi\) | ||||
−0.668424 | + | 0.743781i | \(0.733031\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1562.00 | −0.282075 | −0.141037 | − | 0.990004i | \(-0.545044\pi\) | ||||
−0.141037 | + | 0.990004i | \(0.545044\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 690.000i | 0.123419i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1426.00i | − 0.252657i | −0.991988 | − | 0.126328i | \(-0.959681\pi\) | ||||
0.991988 | − | 0.126328i | \(-0.0403193\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1600.00 | −0.280824 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2388.00 | −0.415219 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2600.00i | − 0.447888i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 950.000i | − 0.162143i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1100.00 | 0.186025 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3084.00 | 0.516798 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 4008.00i | − 0.665558i | −0.943005 | − | 0.332779i | \(-0.892014\pi\) | ||||
0.943005 | − | 0.332779i | \(-0.107986\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6118.00i | 1.00680i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −630.000 | −0.102748 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8866.00 | 1.43312 | 0.716561 | − | 0.697525i | \(-0.245715\pi\) | ||||
0.716561 | + | 0.697525i | \(0.245715\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 3124.00i | − 0.500509i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 3456.00i | − 0.548835i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3900.00 | 0.613936 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −780.000 | −0.121721 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1714.00i | − 0.265165i | −0.991172 | − | 0.132583i | \(-0.957673\pi\) | ||||
0.991172 | − | 0.132583i | \(-0.0423270\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 1150.00i | − 0.176384i | −0.996103 | − | 0.0881921i | \(-0.971891\pi\) | ||||
0.996103 | − | 0.0881921i | \(-0.0281089\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3800.00 | 0.577860 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4398.00 | −0.663122 | −0.331561 | − | 0.943434i | \(-0.607575\pi\) | ||||
−0.331561 | + | 0.943434i | \(0.607575\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2060.00i | 0.307982i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 312.000i | 0.0462543i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1800.00 | −0.264625 | −0.132312 | − | 0.991208i | \(-0.542240\pi\) | ||||
−0.132312 | + | 0.991208i | \(0.542240\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3141.00 | −0.457938 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 614.000i | − 0.0887786i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 4390.00i | − 0.629543i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5874.00 | −0.835478 | −0.417739 | − | 0.908567i | \(-0.637177\pi\) | ||||
−0.417739 | + | 0.908567i | \(0.637177\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −506.000 | −0.0713857 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 12.0000i | − 0.00167927i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 2078.00i | − 0.288458i | −0.989544 | − | 0.144229i | \(-0.953930\pi\) | ||||
0.989544 | − | 0.144229i | \(-0.0460702\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 250.000 | 0.0344265 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1900.00 | −0.259562 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7900.00i | 1.07070i | 0.844630 | + | 0.535351i | \(0.179821\pi\) | ||||
−0.844630 | + | 0.535351i | \(0.820179\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 3692.00i | − 0.496449i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7518.00 | −1.00301 | −0.501504 | − | 0.865155i | \(-0.667220\pi\) | ||||
−0.501504 | + | 0.865155i | \(0.667220\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −960.000 | −0.127081 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10166.0i | 1.33531i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 1950.00i | − 0.254162i | −0.991892 | − | 0.127081i | \(-0.959439\pi\) | ||||
0.991892 | − | 0.127081i | \(-0.0405608\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2028.00 | 0.262303 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4416.00 | 0.566814 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 3000.00i | − 0.382143i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 13786.0i | − 1.74282i | −0.490555 | − | 0.871410i | \(-0.663206\pi\) | ||||
0.490555 | − | 0.871410i | \(-0.336794\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1200.00 | 0.150564 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6402.00 | 0.797258 | 0.398629 | − | 0.917112i | \(-0.369486\pi\) | ||||
0.398629 | + | 0.917112i | \(0.369486\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 4104.00i | − 0.507282i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 2105.00i | − 0.258267i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8512.00 | −1.03667 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11150.0 | −1.34800 | −0.674000 | − | 0.738731i | \(-0.735425\pi\) | ||||
−0.674000 | + | 0.738731i | \(0.735425\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 4668.00i | − 0.560232i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 3000.00i | − 0.357434i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1410.00 | −0.166781 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1400.00 | −0.164408 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13700.0i | 1.59735i | 0.601764 | + | 0.798674i | \(0.294465\pi\) | ||||
−0.601764 | + | 0.798674i | \(0.705535\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 5438.00i | − 0.629529i | −0.949170 | − | 0.314765i | \(-0.898074\pi\) | ||||
0.949170 | − | 0.314765i | \(-0.101926\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11822.0 | −1.35888 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −650.000 | −0.0741874 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3108.00i | − 0.352240i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2432.00i | 0.273702i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7692.00 | 0.859653 | 0.429827 | − | 0.902911i | \(-0.358575\pi\) | ||||
0.429827 | + | 0.902911i | \(0.358575\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1118.00 | −0.124082 | −0.0620412 | − | 0.998074i | \(-0.519761\pi\) | ||||
−0.0620412 | + | 0.998074i | \(0.519761\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 500.000i | − 0.0551107i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 7800.00i | − 0.853832i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2600.00 | 0.282668 | 0.141334 | − | 0.989962i | \(-0.454861\pi\) | ||||
0.141334 | + | 0.989962i | \(0.454861\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7061.00 | −0.762445 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 11958.0i | − 1.28249i | −0.767337 | − | 0.641243i | \(-0.778419\pi\) | ||||
0.767337 | − | 0.641243i | \(-0.221581\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 750.000i | − 0.0798953i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4100.00 | 0.433833 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17050.0 | −1.79207 | −0.896035 | − | 0.443984i | \(-0.853565\pi\) | ||||
−0.896035 | + | 0.443984i | \(0.853565\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 704.000i | − 0.0735035i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3704.00i | 0.384170i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1140.00 | −0.117459 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9494.00 | 0.971796 | 0.485898 | − | 0.874016i | \(-0.338493\pi\) | ||||
0.485898 | + | 0.874016i | \(0.338493\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 2600.00i | − 0.264396i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11418.0i | 1.15356i | 0.816901 | + | 0.576778i | \(0.195690\pi\) | ||||
−0.816901 | + | 0.576778i | \(0.804310\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7962.00 | 0.799191 | 0.399596 | − | 0.916692i | \(-0.369151\pi\) | ||||
0.399596 | + | 0.916692i | \(0.369151\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1080.00 | 0.107707 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 6526.00i | − 0.646654i | −0.946287 | − | 0.323327i | \(-0.895199\pi\) | ||||
0.946287 | − | 0.323327i | \(-0.104801\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 756.000i | 0.0744325i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4988.00 | 0.487972 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14144.0 | −1.37493 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2500.00i | 0.241490i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 46.0000i | 0.00441550i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17400.0 | 1.65976 | 0.829881 | − | 0.557940i | \(-0.188408\pi\) | ||||
0.829881 | + | 0.557940i | \(0.188408\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10108.0 | −0.958181 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 936.000i | 0.0881770i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 1930.00i | − 0.180694i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1166.00 | −0.108494 | −0.0542469 | − | 0.998528i | \(-0.517276\pi\) | ||||
−0.0542469 | + | 0.998528i | \(0.517276\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5524.00 | −0.510846 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7072.00i | 0.650010i | 0.945712 | + | 0.325005i | \(0.105366\pi\) | ||||
−0.945712 | + | 0.325005i | \(0.894634\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1300.00i | 0.118761i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3680.00 | 0.334149 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2472.00 | 0.223107 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 100.000i | − 0.00897117i | −0.999990 | − | 0.00448559i | \(-0.998572\pi\) | ||||
0.999990 | − | 0.00448559i | \(-0.00142781\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6252.00i | 0.557522i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2602.00 | −0.230651 | −0.115325 | − | 0.993328i | \(-0.536791\pi\) | ||||
−0.115325 | + | 0.993328i | \(0.536791\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3510.00 | 0.309293 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 1506.00i | − 0.131921i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 11150.0i | − 0.970953i | −0.874250 | − | 0.485476i | \(-0.838646\pi\) | ||||
0.874250 | − | 0.485476i | \(-0.161354\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5268.00 | −0.456052 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10000.0 | −0.860645 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 2990.00i | − 0.255835i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 16448.0i | − 1.39919i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 156.000 | 0.0131939 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3638.00 | 0.305919 | 0.152959 | − | 0.988232i | \(-0.451120\pi\) | ||||
0.152959 | + | 0.988232i | \(0.451120\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2078.00i | − 0.173737i | −0.996220 | − | 0.0868686i | \(-0.972314\pi\) | ||||
0.996220 | − | 0.0868686i | \(-0.0276860\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 300.000i | − 0.0249392i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2808.00 | −0.232103 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6083.00 | −0.499959 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11500.0i | 0.939845i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 836.000i | − 0.0679384i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5970.00 | −0.482440 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2600.00 | 0.208935 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 9824.00i | − 0.785064i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 5622.00i | − 0.446781i | −0.974729 | − | 0.223391i | \(-0.928287\pi\) | ||||
0.974729 | − | 0.223391i | \(-0.0717126\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3484.00 | 0.275346 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2750.00 | 0.216141 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 16486.0i | − 1.28865i | −0.764753 | − | 0.644324i | \(-0.777139\pi\) | ||||
0.764753 | − | 0.644324i | \(-0.222861\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11914.0i | 0.926188i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5000.00 | 0.386583 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3600.00 | −0.276831 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 2660.00i | − 0.203443i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 11706.0i | − 0.890483i | −0.895410 | − | 0.445242i | \(-0.853118\pi\) | ||||
0.895410 | − | 0.445242i | \(-0.146882\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16796.0 | −1.27083 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1664.00 | 0.125230 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25038.0i | 1.87429i | 0.348939 | + | 0.937146i | \(0.386542\pi\) | ||||
−0.348939 | + | 0.937146i | \(0.613458\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 7810.00i | − 0.581538i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2526.00 | −0.187094 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17550.0 | −1.29303 | −0.646515 | − | 0.762901i | \(-0.723774\pi\) | ||||
−0.646515 | + | 0.762901i | \(0.723774\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10712.0i | 0.785084i | 0.919734 | + | 0.392542i | \(0.128404\pi\) | ||||
−0.919734 | + | 0.392542i | \(0.871596\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 7544.00i | − 0.550009i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1950.00 | −0.141427 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13654.0 | −0.985136 | −0.492568 | − | 0.870274i | \(-0.663942\pi\) | ||||
−0.492568 | + | 0.870274i | \(0.663942\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 716.000i | 0.0513920i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1692.00i | 0.120819i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −64.0000 | −0.00454650 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4370.00 | 0.308850 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14166.0i | 0.996071i | 0.867157 | + | 0.498035i | \(0.165945\pi\) | ||||
−0.867157 | + | 0.498035i | \(0.834055\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10800.0i | 0.755528i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4428.00 | −0.308196 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17842.0 | 1.23555 | 0.617777 | − | 0.786354i | \(-0.288034\pi\) | ||||
0.617777 | + | 0.786354i | \(0.288034\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 780.000i | 0.0537427i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 5200.00i | − 0.356485i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17600.0 | 1.20053 | 0.600264 | − | 0.799802i | \(-0.295062\pi\) | ||||
0.600264 | + | 0.799802i | \(0.295062\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27302.0 | −1.85303 | −0.926516 | − | 0.376256i | \(-0.877211\pi\) | ||||
−0.926516 | + | 0.376256i | \(0.877211\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 2898.00i | − 0.195714i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 1535.00i | − 0.103151i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3794.00 | −0.253696 | −0.126848 | − | 0.991922i | \(-0.540486\pi\) | ||||
−0.126848 | + | 0.991922i | \(0.540486\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −600.000 | −0.0399232 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 19532.0i | − 1.29326i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 13238.0i | − 0.872231i | −0.899891 | − | 0.436116i | \(-0.856354\pi\) | ||||
0.899891 | − | 0.436116i | \(-0.143646\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 220.000 | 0.0144248 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11574.0 | 0.755189 | 0.377595 | − | 0.925971i | \(-0.376751\pi\) | ||||
0.377595 | + | 0.925971i | \(0.376751\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8300.00i | 0.538942i | 0.963008 | + | 0.269471i | \(0.0868489\pi\) | ||||
−0.963008 | + | 0.269471i | \(0.913151\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 7800.00i | − 0.504031i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −900.000 | −0.0578776 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 6400.00i | − 0.407642i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6916.00i | 0.438409i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7508.00 | 0.473675 | 0.236837 | − | 0.971549i | \(-0.423889\pi\) | ||||
0.236837 | + | 0.971549i | \(0.423889\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2336.00 | 0.146679 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 9230.00i | − 0.576821i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 11666.0i | − 0.725626i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9476.00 | −0.586643 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27378.0 | −1.68700 | −0.843499 | − | 0.537130i | \(-0.819508\pi\) | ||||
−0.843499 | + | 0.537130i | \(0.819508\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1842.00i | − 0.112973i | −0.998403 | − | 0.0564863i | \(-0.982010\pi\) | ||||
0.998403 | − | 0.0564863i | \(-0.0179897\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 4420.00i | − 0.269825i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10114.0 | 0.614563 | 0.307282 | − | 0.951619i | \(-0.400581\pi\) | ||||
0.307282 | + | 0.951619i | \(0.400581\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16000.0 | −0.967727 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 1296.00i | − 0.0780250i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 10402.0i | − 0.623372i | −0.950185 | − | 0.311686i | \(-0.899106\pi\) | ||||
0.950185 | − | 0.311686i | \(-0.100894\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11040.0 | 0.658578 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20194.0 | 1.19915 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 7100.00i | − 0.419692i | −0.977734 | − | 0.209846i | \(-0.932704\pi\) | ||||
0.977734 | − | 0.209846i | \(-0.0672962\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 7118.00i | − 0.418847i | −0.977825 | − | 0.209424i | \(-0.932841\pi\) | ||||
0.977825 | − | 0.209424i | \(-0.0671588\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1976.00 | 0.115749 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3000.00 | 0.174940 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3900.00i | 0.226400i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12956.0i | 0.748741i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16576.0 | −0.953665 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31278.0 | −1.79150 | −0.895749 | − | 0.444560i | \(-0.853360\pi\) | ||||
−0.895749 | + | 0.444560i | \(0.853360\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2500.00i | 0.142556i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 30054.0i | − 1.70616i | −0.521782 | − | 0.853079i | \(-0.674732\pi\) | ||||
0.521782 | − | 0.853079i | \(-0.325268\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2316.00 | −0.130898 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1292.00 | −0.0727012 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 4518.00i | − 0.253113i | −0.991959 | − | 0.126557i | \(-0.959607\pi\) | ||||
0.991959 | − | 0.126557i | \(-0.0403926\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 11670.0i | − 0.650931i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7500.00 | 0.416511 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −76.0000 | −0.00420228 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 29272.0i | − 1.61152i | −0.592243 | − | 0.805759i | \(-0.701758\pi\) | ||||
0.592243 | − | 0.805759i | \(-0.298242\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 4416.00i | − 0.242063i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3500.00 | −0.191025 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −572.000 | −0.0310847 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2964.00i | 0.160385i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5798.00i | 0.312393i | 0.987726 | + | 0.156196i | \(0.0499233\pi\) | ||||
−0.987726 | + | 0.156196i | \(0.950077\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26600.0 | 1.42708 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5140.00 | 0.274587 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 4212.00i | − 0.224057i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8950.00i | 0.474082i | 0.971500 | + | 0.237041i | \(0.0761776\pi\) | ||||
−0.971500 | + | 0.237041i | \(0.923822\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13800.0 | 0.727905 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8424.00 | −0.442470 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6080.00i | 0.318013i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2800.00i | − 0.145841i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7800.00 | 0.404577 | 0.202289 | − | 0.979326i | \(-0.435162\pi\) | ||||
0.202289 | + | 0.979326i | \(0.435162\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3588.00 | −0.185332 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 6044.00i | − 0.310897i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 1250.00i | − 0.0640329i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8554.00 | 0.436383 | 0.218191 | − | 0.975906i | \(-0.429984\pi\) | ||||
0.218191 | + | 0.975906i | \(0.429984\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4283.00 | 0.217599 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11492.0i | 0.581460i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 2882.00i | − 0.145224i | −0.997360 | − | 0.0726119i | \(-0.976867\pi\) | ||||
0.997360 | − | 0.0726119i | \(-0.0231335\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3070.00 | 0.154066 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4032.00 | 0.201521 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 18700.0i | − 0.930840i | −0.885090 | − | 0.465420i | \(-0.845903\pi\) | ||||
0.885090 | − | 0.465420i | \(-0.154097\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 7600.00i | − 0.376779i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12242.0 | −0.604462 | −0.302231 | − | 0.953235i | \(-0.597731\pi\) | ||||
−0.302231 | + | 0.953235i | \(0.597731\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10250.0 | 0.504068 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 6486.00i | − 0.317685i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7164.00i | 0.349488i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31148.0 | −1.51346 | −0.756729 | − | 0.653729i | \(-0.773204\pi\) | ||||
−0.756729 | + | 0.653729i | \(0.773204\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2496.00 | −0.120796 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9260.00i | 0.446365i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 7694.00i | − 0.369410i | −0.982794 | − | 0.184705i | \(-0.940867\pi\) | ||||
0.982794 | − | 0.184705i | \(-0.0591329\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4992.00 | 0.238733 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4518.00 | 0.215213 | 0.107607 | − | 0.994194i | \(-0.465681\pi\) | ||||
0.107607 | + | 0.994194i | \(0.465681\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 3300.00i | − 0.156577i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 2990.00i | − 0.141312i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19000.0 | −0.894459 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39550.0 | −1.85463 | −0.927314 | − | 0.374283i | \(-0.877889\pi\) | ||||
−0.927314 | + | 0.374283i | \(0.877889\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 4212.00i | − 0.196746i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22122.0i | 1.02933i | 0.857391 | + | 0.514666i | \(0.172084\pi\) | ||||
−0.857391 | + | 0.514666i | \(0.827916\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2700.00 | 0.125144 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3192.00 | −0.147378 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2200.00i | 0.101185i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 13184.0i | − 0.604047i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5000.00 | 0.228206 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12470.0 | 0.566972 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16634.0i | 0.753416i | 0.926332 | + | 0.376708i | \(0.122944\pi\) | ||||
−0.926332 | + | 0.376708i | \(0.877056\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 7276.00i | − 0.328305i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9372.00 | −0.421277 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19684.0 | −0.881462 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 20.0000i | 0 0.000892235i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 27586.0i | − 1.22603i | −0.790071 | − | 0.613015i | \(-0.789956\pi\) | ||||
0.790071 | − | 0.613015i | \(-0.210044\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13364.0 | −0.591720 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3450.00 | 0.152184 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28096.0i | 1.23473i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2340.00i | 0.102452i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13100.0 | 0.571427 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3850.00 | −0.167316 | −0.0836581 | − | 0.996495i | \(-0.526660\pi\) | ||||
−0.0836581 | + | 0.996495i | \(0.526660\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10032.0i | 0.434366i | 0.976131 | + | 0.217183i | \(0.0696869\pi\) | ||||
−0.976131 | + | 0.217183i | \(0.930313\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8776.00i | 0.378583i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13810.0 | −0.593550 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 44200.0 | 1.89273 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 5244.00i | − 0.223736i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20562.0i | 0.874079i | 0.899442 | + | 0.437039i | \(0.143973\pi\) | ||||
−0.899442 | + | 0.437039i | \(0.856027\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10322.0 | −0.437184 | −0.218592 | − | 0.975816i | \(-0.570146\pi\) | ||||
−0.218592 | + | 0.975816i | \(0.570146\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1600.00 | −0.0675210 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8846.00i | 0.371954i | 0.982554 | + | 0.185977i | \(0.0595449\pi\) | ||||
−0.982554 | + | 0.185977i | \(0.940455\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25350.0i | 1.06205i | 0.847355 | + | 0.531026i | \(0.178194\pi\) | ||||
−0.847355 | + | 0.531026i | \(0.821806\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1092.00 | 0.0455849 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7982.00 | −0.332005 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15630.0i | 0.647783i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10800.0i | 0.446001i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46000.0 | −1.89284 | −0.946422 | − | 0.322932i | \(-0.895331\pi\) | ||||
−0.946422 | + | 0.322932i | \(0.895331\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21889.0 | 0.897495 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 13716.0i | − 0.560385i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 3765.00i | − 0.153278i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1842.00 | −0.0747248 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18564.0 | 0.750430 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20748.0i | 0.835761i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 16998.0i | − 0.682298i | −0.940009 | − | 0.341149i | \(-0.889184\pi\) | ||||
0.940009 | − | 0.341149i | \(-0.110816\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11500.0 | −0.459990 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26494.0 | 1.05603 | 0.528015 | − | 0.849235i | \(-0.322936\pi\) | ||||
0.528015 | + | 0.849235i | \(0.322936\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 21500.0i | − 0.853982i | −0.904256 | − | 0.426991i | \(-0.859574\pi\) | ||||
0.904256 | − | 0.426991i | \(-0.140426\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 264.000i | − 0.0104496i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25762.0 | 1.01616 | 0.508082 | − | 0.861309i | \(-0.330355\pi\) | ||||
0.508082 | + | 0.861309i | \(0.330355\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 390.000 | 0.0153299 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8474.00i | 0.331940i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19200.0i | 0.749500i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4788.00 | 0.186263 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8878.00 | 0.344186 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 750.000i | − 0.0289767i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 30546.0i | − 1.17613i | −0.808814 | − | 0.588064i | \(-0.799890\pi\) | ||||
0.808814 | − | 0.588064i | \(-0.200110\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9684.00 | 0.371596 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32942.0 | 1.25976 | 0.629878 | − | 0.776694i | \(-0.283105\pi\) | ||||
0.629878 | + | 0.776694i | \(0.283105\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27118.0i | 1.03351i | 0.856132 | + | 0.516757i | \(0.172861\pi\) | ||||
−0.856132 | + | 0.516757i | \(0.827139\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 5000.00i | − 0.189913i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38634.0 | 1.46246 | 0.731230 | − | 0.682131i | \(-0.238946\pi\) | ||||
0.731230 | + | 0.682131i | \(0.238946\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11076.0 | −0.417860 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13472.0i | 0.506542i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 51400.0i | 1.92613i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6500.00 | 0.242761 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5928.00 | 0.220658 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 5400.00i | − 0.200334i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 52.0000i | 0.00192272i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5304.00 | −0.195466 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8710.00 | 0.319923 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1794.00i | − 0.0656767i | −0.999461 | − | 0.0328384i | \(-0.989545\pi\) | ||||
0.999461 | − | 0.0328384i | \(-0.0104547\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16146.0i | 0.589141i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41732.0 | 1.51772 | 0.758860 | − | 0.651254i | \(-0.225757\pi\) | ||||
0.758860 | + | 0.651254i | \(0.225757\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9024.00 | 0.327109 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 5180.00i | − 0.187154i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 13248.0i | − 0.477086i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29200.0 | −1.04812 | −0.524058 | − | 0.851682i | \(-0.675583\pi\) | ||||
−0.524058 | + | 0.851682i | \(0.675583\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5188.00 | 0.185614 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 15656.0i | − 0.558314i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 6650.00i | − 0.236379i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13754.0 | 0.487315 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48650.0 | −1.71814 | −0.859071 | − | 0.511856i | \(-0.828958\pi\) | ||||
−0.859071 | + | 0.511856i | \(0.828958\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30700.0i | 1.08072i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14664.0i | 0.514553i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4160.00 | 0.145504 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11334.0 | 0.395161 | 0.197580 | − | 0.980287i | \(-0.436692\pi\) | ||||
0.197580 | + | 0.980287i | \(0.436692\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3124.00i | 0.108571i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31178.0i | 1.08010i | 0.841633 | + | 0.540050i | \(0.181595\pi\) | ||||
−0.841633 | + | 0.540050i | \(0.818405\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1716.00 | −0.0592584 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3000.00 | 0.103270 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 4686.00i | − 0.160797i | −0.996763 | − | 0.0803984i | \(-0.974381\pi\) | ||||
0.996763 | − | 0.0803984i | \(-0.0256193\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33364.0i | 1.14124i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2852.00 | −0.0972476 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 598.000 | 0.0203265 | 0.0101632 | − | 0.999948i | \(-0.496765\pi\) | ||||
0.0101632 | + | 0.999948i | \(0.496765\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 18860.0i | − 0.639053i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3200.00i | 0.108089i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14004.0 | −0.471546 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18127.0 | −0.608472 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 27462.0i | − 0.918952i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1790.00i | 0.0597121i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41726.0 | −1.38761 | −0.693804 | − | 0.720163i | \(-0.744067\pi\) | ||||
−0.693804 | + | 0.720163i | \(0.744067\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5200.00 | −0.172392 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24312.0i | 0.803511i | 0.915747 | + | 0.401756i | \(0.131600\pi\) | ||||
−0.915747 | + | 0.401756i | \(0.868400\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4200.00i | 0.138382i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1900.00 | −0.0624089 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40946.0 | 1.34082 | 0.670409 | − | 0.741992i | \(-0.266119\pi\) | ||||
0.670409 | + | 0.741992i | \(0.266119\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4800.00i | 0.156699i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12650.0i | 0.411706i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42282.0 | −1.37191 | −0.685954 | − | 0.727645i | \(-0.740615\pi\) | ||||
−0.685954 | + | 0.727645i | \(0.740615\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11070.0 | −0.358091 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 6168.00i | − 0.198916i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34476.0i | 1.10847i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1172.00 | 0.0375679 | 0.0187840 | − | 0.999824i | \(-0.494021\pi\) | ||||
0.0187840 | + | 0.999824i | \(0.494021\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8016.00 | −0.256173 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 13000.0i | − 0.414199i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 31614.0i | − 1.00424i | −0.864798 | − | 0.502119i | \(-0.832554\pi\) | ||||
0.864798 | − | 0.502119i | \(-0.167446\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 26600.0 | 0.842429 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))