Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,4,Mod(24,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.24");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.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: | \(1.47504775014\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 5) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.24 |
Dual form | 25.4.b.a.24.2 |
$q$-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 \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4.00000i | − 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(3\) | − 2.00000i | − 0.384900i | −0.981307 | − | 0.192450i | \(-0.938357\pi\) | ||||
0.981307 | − | 0.192450i | \(-0.0616434\pi\) | |||||||
\(4\) | −8.00000 | −1.00000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −8.00000 | −0.544331 | ||||||||
\(7\) | 6.00000i | 0.323970i | 0.986793 | + | 0.161985i | \(0.0517895\pi\) | ||||
−0.986793 | + | 0.161985i | \(0.948210\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 23.0000 | 0.851852 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 32.0000 | 0.877124 | 0.438562 | − | 0.898701i | \(-0.355488\pi\) | ||||
0.438562 | + | 0.898701i | \(0.355488\pi\) | |||||||
\(12\) | 16.0000i | 0.384900i | ||||||||
\(13\) | 38.0000i | 0.810716i | 0.914158 | + | 0.405358i | \(0.132853\pi\) | ||||
−0.914158 | + | 0.405358i | \(0.867147\pi\) | |||||||
\(14\) | 24.0000 | 0.458162 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −64.0000 | −1.00000 | ||||||||
\(17\) | 26.0000i | 0.370937i | 0.982650 | + | 0.185468i | \(0.0593802\pi\) | ||||
−0.982650 | + | 0.185468i | \(0.940620\pi\) | |||||||
\(18\) | − 92.0000i | − 1.20470i | ||||||||
\(19\) | −100.000 | −1.20745 | −0.603726 | − | 0.797192i | \(-0.706318\pi\) | ||||
−0.603726 | + | 0.797192i | \(0.706318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.0000 | 0.124696 | ||||||||
\(22\) | − 128.000i | − 1.24044i | ||||||||
\(23\) | 78.0000i | 0.707136i | 0.935409 | + | 0.353568i | \(0.115032\pi\) | ||||
−0.935409 | + | 0.353568i | \(0.884968\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 152.000 | 1.14653 | ||||||||
\(27\) | − 100.000i | − 0.712778i | ||||||||
\(28\) | − 48.0000i | − 0.323970i | ||||||||
\(29\) | 50.0000 | 0.320164 | 0.160082 | − | 0.987104i | \(-0.448824\pi\) | ||||
0.160082 | + | 0.987104i | \(0.448824\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −108.000 | −0.625722 | −0.312861 | − | 0.949799i | \(-0.601287\pi\) | ||||
−0.312861 | + | 0.949799i | \(0.601287\pi\) | |||||||
\(32\) | 256.000i | 1.41421i | ||||||||
\(33\) | − 64.0000i | − 0.337605i | ||||||||
\(34\) | 104.000 | 0.524584 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −184.000 | −0.851852 | ||||||||
\(37\) | 266.000i | 1.18190i | 0.806710 | + | 0.590948i | \(0.201246\pi\) | ||||
−0.806710 | + | 0.590948i | \(0.798754\pi\) | |||||||
\(38\) | 400.000i | 1.70759i | ||||||||
\(39\) | 76.0000 | 0.312045 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 22.0000 | 0.0838006 | 0.0419003 | − | 0.999122i | \(-0.486659\pi\) | ||||
0.0419003 | + | 0.999122i | \(0.486659\pi\) | |||||||
\(42\) | − 48.0000i | − 0.176347i | ||||||||
\(43\) | − 442.000i | − 1.56754i | −0.621049 | − | 0.783772i | \(-0.713293\pi\) | ||||
0.621049 | − | 0.783772i | \(-0.286707\pi\) | |||||||
\(44\) | −256.000 | −0.877124 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 312.000 | 1.00004 | ||||||||
\(47\) | − 514.000i | − 1.59520i | −0.603184 | − | 0.797602i | \(-0.706101\pi\) | ||||
0.603184 | − | 0.797602i | \(-0.293899\pi\) | |||||||
\(48\) | 128.000i | 0.384900i | ||||||||
\(49\) | 307.000 | 0.895044 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 52.0000 | 0.142774 | ||||||||
\(52\) | − 304.000i | − 0.810716i | ||||||||
\(53\) | − 2.00000i | − 0.00518342i | −0.999997 | − | 0.00259171i | \(-0.999175\pi\) | ||||
0.999997 | − | 0.00259171i | \(-0.000824967\pi\) | |||||||
\(54\) | −400.000 | −1.00802 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 200.000i | 0.464748i | ||||||||
\(58\) | − 200.000i | − 0.452781i | ||||||||
\(59\) | −500.000 | −1.10330 | −0.551648 | − | 0.834077i | \(-0.686001\pi\) | ||||
−0.551648 | + | 0.834077i | \(0.686001\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −518.000 | −1.08726 | −0.543632 | − | 0.839324i | \(-0.682951\pi\) | ||||
−0.543632 | + | 0.839324i | \(0.682951\pi\) | |||||||
\(62\) | 432.000i | 0.884904i | ||||||||
\(63\) | 138.000i | 0.275974i | ||||||||
\(64\) | 512.000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −256.000 | −0.477446 | ||||||||
\(67\) | 126.000i | 0.229751i | 0.993380 | + | 0.114876i | \(0.0366470\pi\) | ||||
−0.993380 | + | 0.114876i | \(0.963353\pi\) | |||||||
\(68\) | − 208.000i | − 0.370937i | ||||||||
\(69\) | 156.000 | 0.272177 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 412.000 | 0.688668 | 0.344334 | − | 0.938847i | \(-0.388105\pi\) | ||||
0.344334 | + | 0.938847i | \(0.388105\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 878.000i | 1.40770i | 0.710348 | + | 0.703850i | \(0.248537\pi\) | ||||
−0.710348 | + | 0.703850i | \(0.751463\pi\) | |||||||
\(74\) | 1064.00 | 1.67145 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 800.000 | 1.20745 | ||||||||
\(77\) | 192.000i | 0.284161i | ||||||||
\(78\) | − 304.000i | − 0.441298i | ||||||||
\(79\) | −600.000 | −0.854497 | −0.427249 | − | 0.904134i | \(-0.640517\pi\) | ||||
−0.427249 | + | 0.904134i | \(0.640517\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 421.000 | 0.577503 | ||||||||
\(82\) | − 88.0000i | − 0.118512i | ||||||||
\(83\) | − 282.000i | − 0.372934i | −0.982461 | − | 0.186467i | \(-0.940296\pi\) | ||||
0.982461 | − | 0.186467i | \(-0.0597037\pi\) | |||||||
\(84\) | −96.0000 | −0.124696 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1768.00 | −2.21684 | ||||||||
\(87\) | − 100.000i | − 0.123231i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 150.000 | 0.178651 | 0.0893257 | − | 0.996002i | \(-0.471529\pi\) | ||||
0.0893257 | + | 0.996002i | \(0.471529\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −228.000 | −0.262647 | ||||||||
\(92\) | − 624.000i | − 0.707136i | ||||||||
\(93\) | 216.000i | 0.240840i | ||||||||
\(94\) | −2056.00 | −2.25596 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 512.000 | 0.544331 | ||||||||
\(97\) | 386.000i | 0.404045i | 0.979381 | + | 0.202022i | \(0.0647514\pi\) | ||||
−0.979381 | + | 0.202022i | \(0.935249\pi\) | |||||||
\(98\) | − 1228.00i | − 1.26578i | ||||||||
\(99\) | 736.000 | 0.747180 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 702.000 | 0.691600 | 0.345800 | − | 0.938308i | \(-0.387608\pi\) | ||||
0.345800 | + | 0.938308i | \(0.387608\pi\) | |||||||
\(102\) | − 208.000i | − 0.201912i | ||||||||
\(103\) | 598.000i | 0.572065i | 0.958220 | + | 0.286032i | \(0.0923365\pi\) | ||||
−0.958220 | + | 0.286032i | \(0.907663\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.00000 | −0.00733046 | ||||||||
\(107\) | − 1194.00i | − 1.07877i | −0.842059 | − | 0.539385i | \(-0.818657\pi\) | ||||
0.842059 | − | 0.539385i | \(-0.181343\pi\) | |||||||
\(108\) | 800.000i | 0.712778i | ||||||||
\(109\) | 550.000 | 0.483307 | 0.241653 | − | 0.970363i | \(-0.422310\pi\) | ||||
0.241653 | + | 0.970363i | \(0.422310\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 532.000 | 0.454912 | ||||||||
\(112\) | − 384.000i | − 0.323970i | ||||||||
\(113\) | − 1562.00i | − 1.30036i | −0.759781 | − | 0.650180i | \(-0.774694\pi\) | ||||
0.759781 | − | 0.650180i | \(-0.225306\pi\) | |||||||
\(114\) | 800.000 | 0.657253 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −400.000 | −0.320164 | ||||||||
\(117\) | 874.000i | 0.690610i | ||||||||
\(118\) | 2000.00i | 1.56030i | ||||||||
\(119\) | −156.000 | −0.120172 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −307.000 | −0.230654 | ||||||||
\(122\) | 2072.00i | 1.53762i | ||||||||
\(123\) | − 44.0000i | − 0.0322548i | ||||||||
\(124\) | 864.000 | 0.625722 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 552.000 | 0.390286 | ||||||||
\(127\) | 1846.00i | 1.28981i | 0.764262 | + | 0.644906i | \(0.223103\pi\) | ||||
−0.764262 | + | 0.644906i | \(0.776897\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −884.000 | −0.603348 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2208.00 | −1.47262 | −0.736312 | − | 0.676642i | \(-0.763435\pi\) | ||||
−0.736312 | + | 0.676642i | \(0.763435\pi\) | |||||||
\(132\) | 512.000i | 0.337605i | ||||||||
\(133\) | − 600.000i | − 0.391177i | ||||||||
\(134\) | 504.000 | 0.324918 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 2334.00i | − 1.45553i | −0.685829 | − | 0.727763i | \(-0.740560\pi\) | ||||
0.685829 | − | 0.727763i | \(-0.259440\pi\) | |||||||
\(138\) | − 624.000i | − 0.384916i | ||||||||
\(139\) | 700.000 | 0.427146 | 0.213573 | − | 0.976927i | \(-0.431490\pi\) | ||||
0.213573 | + | 0.976927i | \(0.431490\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1028.00 | −0.613994 | ||||||||
\(142\) | − 1648.00i | − 0.973923i | ||||||||
\(143\) | 1216.00i | 0.711098i | ||||||||
\(144\) | −1472.00 | −0.851852 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3512.00 | 1.99079 | ||||||||
\(147\) | − 614.000i | − 0.344502i | ||||||||
\(148\) | − 2128.00i | − 1.18190i | ||||||||
\(149\) | −2050.00 | −1.12713 | −0.563566 | − | 0.826071i | \(-0.690571\pi\) | ||||
−0.563566 | + | 0.826071i | \(0.690571\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1852.00 | 0.998103 | 0.499052 | − | 0.866572i | \(-0.333682\pi\) | ||||
0.499052 | + | 0.866572i | \(0.333682\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 598.000i | 0.315983i | ||||||||
\(154\) | 768.000 | 0.401865 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −608.000 | −0.312045 | ||||||||
\(157\) | − 2494.00i | − 1.26779i | −0.773420 | − | 0.633894i | \(-0.781455\pi\) | ||||
0.773420 | − | 0.633894i | \(-0.218545\pi\) | |||||||
\(158\) | 2400.00i | 1.20844i | ||||||||
\(159\) | −4.00000 | −0.00199510 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −468.000 | −0.229090 | ||||||||
\(162\) | − 1684.00i | − 0.816713i | ||||||||
\(163\) | − 2762.00i | − 1.32722i | −0.748080 | − | 0.663609i | \(-0.769024\pi\) | ||||
0.748080 | − | 0.663609i | \(-0.230976\pi\) | |||||||
\(164\) | −176.000 | −0.0838006 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1128.00 | −0.527408 | ||||||||
\(167\) | 3126.00i | 1.44849i | 0.689545 | + | 0.724243i | \(0.257811\pi\) | ||||
−0.689545 | + | 0.724243i | \(0.742189\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 753.000 | 0.342740 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2300.00 | −1.02857 | ||||||||
\(172\) | 3536.00i | 1.56754i | ||||||||
\(173\) | 78.0000i | 0.0342788i | 0.999853 | + | 0.0171394i | \(0.00545591\pi\) | ||||
−0.999853 | + | 0.0171394i | \(0.994544\pi\) | |||||||
\(174\) | −400.000 | −0.174275 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2048.00 | −0.877124 | ||||||||
\(177\) | 1000.00i | 0.424659i | ||||||||
\(178\) | − 600.000i | − 0.252651i | ||||||||
\(179\) | 1300.00 | 0.542830 | 0.271415 | − | 0.962462i | \(-0.412508\pi\) | ||||
0.271415 | + | 0.962462i | \(0.412508\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1742.00 | 0.715369 | 0.357685 | − | 0.933842i | \(-0.383566\pi\) | ||||
0.357685 | + | 0.933842i | \(0.383566\pi\) | |||||||
\(182\) | 912.000i | 0.371439i | ||||||||
\(183\) | 1036.00i | 0.418488i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 864.000 | 0.340600 | ||||||||
\(187\) | 832.000i | 0.325358i | ||||||||
\(188\) | 4112.00i | 1.59520i | ||||||||
\(189\) | 600.000 | 0.230918 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3772.00 | 1.42897 | 0.714483 | − | 0.699653i | \(-0.246662\pi\) | ||||
0.714483 | + | 0.699653i | \(0.246662\pi\) | |||||||
\(192\) | − 1024.00i | − 0.384900i | ||||||||
\(193\) | 358.000i | 0.133520i | 0.997769 | + | 0.0667601i | \(0.0212662\pi\) | ||||
−0.997769 | + | 0.0667601i | \(0.978734\pi\) | |||||||
\(194\) | 1544.00 | 0.571406 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2456.00 | −0.895044 | ||||||||
\(197\) | − 2214.00i | − 0.800716i | −0.916359 | − | 0.400358i | \(-0.868886\pi\) | ||||
0.916359 | − | 0.400358i | \(-0.131114\pi\) | |||||||
\(198\) | − 2944.00i | − 1.05667i | ||||||||
\(199\) | 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 | ||||||||
\(202\) | − 2808.00i | − 0.978070i | ||||||||
\(203\) | 300.000i | 0.103724i | ||||||||
\(204\) | −416.000 | −0.142774 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2392.00 | 0.809022 | ||||||||
\(207\) | 1794.00i | 0.602375i | ||||||||
\(208\) | − 2432.00i | − 0.810716i | ||||||||
\(209\) | −3200.00 | −1.05908 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1168.00 | −0.381083 | −0.190541 | − | 0.981679i | \(-0.561024\pi\) | ||||
−0.190541 | + | 0.981679i | \(0.561024\pi\) | |||||||
\(212\) | 16.0000i | 0.00518342i | ||||||||
\(213\) | − 824.000i | − 0.265068i | ||||||||
\(214\) | −4776.00 | −1.52561 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 648.000i | − 0.202715i | ||||||||
\(218\) | − 2200.00i | − 0.683499i | ||||||||
\(219\) | 1756.00 | 0.541824 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −988.000 | −0.300724 | ||||||||
\(222\) | − 2128.00i | − 0.643342i | ||||||||
\(223\) | 6478.00i | 1.94529i | 0.232303 | + | 0.972643i | \(0.425374\pi\) | ||||
−0.232303 | + | 0.972643i | \(0.574626\pi\) | |||||||
\(224\) | −1536.00 | −0.458162 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6248.00 | −1.83899 | ||||||||
\(227\) | 646.000i | 0.188883i | 0.995530 | + | 0.0944417i | \(0.0301066\pi\) | ||||
−0.995530 | + | 0.0944417i | \(0.969893\pi\) | |||||||
\(228\) | − 1600.00i | − 0.464748i | ||||||||
\(229\) | −3750.00 | −1.08213 | −0.541063 | − | 0.840982i | \(-0.681978\pi\) | ||||
−0.541063 | + | 0.840982i | \(0.681978\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 384.000 | 0.109374 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 1482.00i | − 0.416691i | −0.978055 | − | 0.208346i | \(-0.933192\pi\) | ||||
0.978055 | − | 0.208346i | \(-0.0668079\pi\) | |||||||
\(234\) | 3496.00 | 0.976670 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4000.00 | 1.10330 | ||||||||
\(237\) | 1200.00i | 0.328896i | ||||||||
\(238\) | 624.000i | 0.169949i | ||||||||
\(239\) | −1400.00 | −0.378906 | −0.189453 | − | 0.981890i | \(-0.560671\pi\) | ||||
−0.189453 | + | 0.981890i | \(0.560671\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3022.00 | 0.807735 | 0.403867 | − | 0.914817i | \(-0.367666\pi\) | ||||
0.403867 | + | 0.914817i | \(0.367666\pi\) | |||||||
\(242\) | 1228.00i | 0.326194i | ||||||||
\(243\) | − 3542.00i | − 0.935059i | ||||||||
\(244\) | 4144.00 | 1.08726 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −176.000 | −0.0456152 | ||||||||
\(247\) | − 3800.00i | − 0.978900i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −564.000 | −0.143542 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1248.00 | −0.313837 | −0.156918 | − | 0.987612i | \(-0.550156\pi\) | ||||
−0.156918 | + | 0.987612i | \(0.550156\pi\) | |||||||
\(252\) | − 1104.00i | − 0.275974i | ||||||||
\(253\) | 2496.00i | 0.620246i | ||||||||
\(254\) | 7384.00 | 1.82407 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | 2106.00i | 0.511162i | 0.966788 | + | 0.255581i | \(0.0822668\pi\) | ||||
−0.966788 | + | 0.255581i | \(0.917733\pi\) | |||||||
\(258\) | 3536.00i | 0.853263i | ||||||||
\(259\) | −1596.00 | −0.382898 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1150.00 | 0.272733 | ||||||||
\(262\) | 8832.00i | 2.08261i | ||||||||
\(263\) | 3638.00i | 0.852961i | 0.904497 | + | 0.426480i | \(0.140247\pi\) | ||||
−0.904497 | + | 0.426480i | \(0.859753\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2400.00 | −0.553208 | ||||||||
\(267\) | − 300.000i | − 0.0687629i | ||||||||
\(268\) | − 1008.00i | − 0.229751i | ||||||||
\(269\) | 6550.00 | 1.48461 | 0.742306 | − | 0.670061i | \(-0.233732\pi\) | ||||
0.742306 | + | 0.670061i | \(0.233732\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4388.00 | −0.983587 | −0.491793 | − | 0.870712i | \(-0.663658\pi\) | ||||
−0.491793 | + | 0.870712i | \(0.663658\pi\) | |||||||
\(272\) | − 1664.00i | − 0.370937i | ||||||||
\(273\) | 456.000i | 0.101093i | ||||||||
\(274\) | −9336.00 | −2.05842 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1248.00 | −0.272177 | ||||||||
\(277\) | 546.000i | 0.118433i | 0.998245 | + | 0.0592165i | \(0.0188602\pi\) | ||||
−0.998245 | + | 0.0592165i | \(0.981140\pi\) | |||||||
\(278\) | − 2800.00i | − 0.604075i | ||||||||
\(279\) | −2484.00 | −0.533022 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6858.00 | −1.45592 | −0.727961 | − | 0.685619i | \(-0.759532\pi\) | ||||
−0.727961 | + | 0.685619i | \(0.759532\pi\) | |||||||
\(282\) | 4112.00i | 0.868319i | ||||||||
\(283\) | − 9282.00i | − 1.94967i | −0.222920 | − | 0.974837i | \(-0.571559\pi\) | ||||
0.222920 | − | 0.974837i | \(-0.428441\pi\) | |||||||
\(284\) | −3296.00 | −0.688668 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4864.00 | 1.00564 | ||||||||
\(287\) | 132.000i | 0.0271488i | ||||||||
\(288\) | 5888.00i | 1.20470i | ||||||||
\(289\) | 4237.00 | 0.862406 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 772.000 | 0.155517 | ||||||||
\(292\) | − 7024.00i | − 1.40770i | ||||||||
\(293\) | − 4842.00i | − 0.965436i | −0.875776 | − | 0.482718i | \(-0.839650\pi\) | ||||
0.875776 | − | 0.482718i | \(-0.160350\pi\) | |||||||
\(294\) | −2456.00 | −0.487200 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 3200.00i | − 0.625195i | ||||||||
\(298\) | 8200.00i | 1.59400i | ||||||||
\(299\) | −2964.00 | −0.573286 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2652.00 | 0.507836 | ||||||||
\(302\) | − 7408.00i | − 1.41153i | ||||||||
\(303\) | − 1404.00i | − 0.266197i | ||||||||
\(304\) | 6400.00 | 1.20745 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2392.00 | 0.446868 | ||||||||
\(307\) | − 2594.00i | − 0.482239i | −0.970495 | − | 0.241120i | \(-0.922485\pi\) | ||||
0.970495 | − | 0.241120i | \(-0.0775146\pi\) | |||||||
\(308\) | − 1536.00i | − 0.284161i | ||||||||
\(309\) | 1196.00 | 0.220188 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7332.00 | 1.33685 | 0.668424 | − | 0.743781i | \(-0.266969\pi\) | ||||
0.668424 | + | 0.743781i | \(0.266969\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 1562.00i | − 0.282075i | −0.990004 | − | 0.141037i | \(-0.954956\pi\) | ||||
0.990004 | − | 0.141037i | \(-0.0450438\pi\) | |||||||
\(314\) | −9976.00 | −1.79292 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4800.00 | 0.854497 | ||||||||
\(317\) | 1426.00i | 0.252657i | 0.991988 | + | 0.126328i | \(0.0403193\pi\) | ||||
−0.991988 | + | 0.126328i | \(0.959681\pi\) | |||||||
\(318\) | 16.0000i | 0.00282150i | ||||||||
\(319\) | 1600.00 | 0.280824 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2388.00 | −0.415219 | ||||||||
\(322\) | 1872.00i | 0.323983i | ||||||||
\(323\) | − 2600.00i | − 0.447888i | ||||||||
\(324\) | −3368.00 | −0.577503 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11048.0 | −1.87697 | ||||||||
\(327\) | − 1100.00i | − 0.186025i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3084.00 | 0.516798 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4008.00 | −0.665558 | −0.332779 | − | 0.943005i | \(-0.607986\pi\) | ||||
−0.332779 | + | 0.943005i | \(0.607986\pi\) | |||||||
\(332\) | 2256.00i | 0.372934i | ||||||||
\(333\) | 6118.00i | 1.00680i | ||||||||
\(334\) | 12504.0 | 2.04847 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −768.000 | −0.124696 | ||||||||
\(337\) | 8866.00i | 1.43312i | 0.697525 | + | 0.716561i | \(0.254285\pi\) | ||||
−0.697525 | + | 0.716561i | \(0.745715\pi\) | |||||||
\(338\) | − 3012.00i | − 0.484708i | ||||||||
\(339\) | −3124.00 | −0.500509 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3456.00 | −0.548835 | ||||||||
\(342\) | 9200.00i | 1.45462i | ||||||||
\(343\) | 3900.00i | 0.613936i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 312.000 | 0.0484775 | ||||||||
\(347\) | − 1714.00i | − 0.265165i | −0.991172 | − | 0.132583i | \(-0.957673\pi\) | ||||
0.991172 | − | 0.132583i | \(-0.0423270\pi\) | |||||||
\(348\) | 800.000i | 0.123231i | ||||||||
\(349\) | −1150.00 | −0.176384 | −0.0881921 | − | 0.996103i | \(-0.528109\pi\) | ||||
−0.0881921 | + | 0.996103i | \(0.528109\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3800.00 | 0.577860 | ||||||||
\(352\) | 8192.00i | 1.24044i | ||||||||
\(353\) | 4398.00i | 0.663122i | 0.943434 | + | 0.331561i | \(0.107575\pi\) | ||||
−0.943434 | + | 0.331561i | \(0.892425\pi\) | |||||||
\(354\) | 4000.00 | 0.600558 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1200.00 | −0.178651 | ||||||||
\(357\) | 312.000i | 0.0462543i | ||||||||
\(358\) | − 5200.00i | − 0.767677i | ||||||||
\(359\) | −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 | ||||||||
\(362\) | − 6968.00i | − 1.01168i | ||||||||
\(363\) | 614.000i | 0.0887786i | ||||||||
\(364\) | 1824.00 | 0.262647 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4144.00 | 0.591832 | ||||||||
\(367\) | − 5874.00i | − 0.835478i | −0.908567 | − | 0.417739i | \(-0.862823\pi\) | ||||
0.908567 | − | 0.417739i | \(-0.137177\pi\) | |||||||
\(368\) | − 4992.00i | − 0.707136i | ||||||||
\(369\) | 506.000 | 0.0713857 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0000 | 0.00167927 | ||||||||
\(372\) | − 1728.00i | − 0.240840i | ||||||||
\(373\) | 2078.00i | 0.288458i | 0.989544 | + | 0.144229i | \(0.0460702\pi\) | ||||
−0.989544 | + | 0.144229i | \(0.953930\pi\) | |||||||
\(374\) | 3328.00 | 0.460125 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1900.00i | 0.259562i | ||||||||
\(378\) | − 2400.00i | − 0.326568i | ||||||||
\(379\) | −7900.00 | −1.07070 | −0.535351 | − | 0.844630i | \(-0.679821\pi\) | ||||
−0.535351 | + | 0.844630i | \(0.679821\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3692.00 | 0.496449 | ||||||||
\(382\) | − 15088.0i | − 2.02086i | ||||||||
\(383\) | 7518.00i | 1.00301i | 0.865155 | + | 0.501504i | \(0.167220\pi\) | ||||
−0.865155 | + | 0.501504i | \(0.832780\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1432.00 | 0.188826 | ||||||||
\(387\) | − 10166.0i | − 1.33531i | ||||||||
\(388\) | − 3088.00i | − 0.404045i | ||||||||
\(389\) | 1950.00 | 0.254162 | 0.127081 | − | 0.991892i | \(-0.459439\pi\) | ||||
0.127081 | + | 0.991892i | \(0.459439\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2028.00 | −0.262303 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4416.00i | 0.566814i | ||||||||
\(394\) | −8856.00 | −1.13238 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5888.00 | −0.747180 | ||||||||
\(397\) | 13786.0i | 1.74282i | 0.490555 | + | 0.871410i | \(0.336794\pi\) | ||||
−0.490555 | + | 0.871410i | \(0.663206\pi\) | |||||||
\(398\) | − 10400.0i | − 1.30981i | ||||||||
\(399\) | −1200.00 | −0.150564 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6402.00 | 0.797258 | 0.398629 | − | 0.917112i | \(-0.369486\pi\) | ||||
0.398629 | + | 0.917112i | \(0.369486\pi\) | |||||||
\(402\) | − 1008.00i | − 0.125061i | ||||||||
\(403\) | − 4104.00i | − 0.507282i | ||||||||
\(404\) | −5616.00 | −0.691600 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1200.00 | 0.146687 | ||||||||
\(407\) | 8512.00i | 1.03667i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11150.0 | −1.34800 | −0.674000 | − | 0.738731i | \(-0.735425\pi\) | ||||
−0.674000 | + | 0.738731i | \(0.735425\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4668.00 | −0.560232 | ||||||||
\(412\) | − 4784.00i | − 0.572065i | ||||||||
\(413\) | − 3000.00i | − 0.357434i | ||||||||
\(414\) | 7176.00 | 0.851887 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −9728.00 | −1.14653 | ||||||||
\(417\) | − 1400.00i | − 0.164408i | ||||||||
\(418\) | 12800.0i | 1.49777i | ||||||||
\(419\) | 13700.0 | 1.59735 | 0.798674 | − | 0.601764i | \(-0.205535\pi\) | ||||
0.798674 | + | 0.601764i | \(0.205535\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5438.00 | −0.629529 | −0.314765 | − | 0.949170i | \(-0.601926\pi\) | ||||
−0.314765 | + | 0.949170i | \(0.601926\pi\) | |||||||
\(422\) | 4672.00i | 0.538932i | ||||||||
\(423\) | − 11822.0i | − 1.35888i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3296.00 | −0.374863 | ||||||||
\(427\) | − 3108.00i | − 0.352240i | ||||||||
\(428\) | 9552.00i | 1.07877i | ||||||||
\(429\) | 2432.00 | 0.273702 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7692.00 | 0.859653 | 0.429827 | − | 0.902911i | \(-0.358575\pi\) | ||||
0.429827 | + | 0.902911i | \(0.358575\pi\) | |||||||
\(432\) | 6400.00i | 0.712778i | ||||||||
\(433\) | 1118.00i | 0.124082i | 0.998074 | + | 0.0620412i | \(0.0197610\pi\) | ||||
−0.998074 | + | 0.0620412i | \(0.980239\pi\) | |||||||
\(434\) | −2592.00 | −0.286682 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4400.00 | −0.483307 | ||||||||
\(437\) | − 7800.00i | − 0.853832i | ||||||||
\(438\) | − 7024.00i | − 0.766255i | ||||||||
\(439\) | 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 | ||||||||
\(442\) | 3952.00i | 0.425288i | ||||||||
\(443\) | 11958.0i | 1.28249i | 0.767337 | + | 0.641243i | \(0.221581\pi\) | ||||
−0.767337 | + | 0.641243i | \(0.778419\pi\) | |||||||
\(444\) | −4256.00 | −0.454912 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 25912.0 | 2.75105 | ||||||||
\(447\) | 4100.00i | 0.433833i | ||||||||
\(448\) | 3072.00i | 0.323970i | ||||||||
\(449\) | 17050.0 | 1.79207 | 0.896035 | − | 0.443984i | \(-0.146435\pi\) | ||||
0.896035 | + | 0.443984i | \(0.146435\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 704.000 | 0.0735035 | ||||||||
\(452\) | 12496.0i | 1.30036i | ||||||||
\(453\) | − 3704.00i | − 0.384170i | ||||||||
\(454\) | 2584.00 | 0.267121 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 9494.00i | − 0.971796i | −0.874016 | − | 0.485898i | \(-0.838493\pi\) | ||||
0.874016 | − | 0.485898i | \(-0.161507\pi\) | |||||||
\(458\) | 15000.0i | 1.53036i | ||||||||
\(459\) | 2600.00 | 0.264396 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11418.0 | −1.15356 | −0.576778 | − | 0.816901i | \(-0.695690\pi\) | ||||
−0.576778 | + | 0.816901i | \(0.695690\pi\) | |||||||
\(462\) | − 1536.00i | − 0.154678i | ||||||||
\(463\) | − 7962.00i | − 0.799191i | −0.916692 | − | 0.399596i | \(-0.869151\pi\) | ||||
0.916692 | − | 0.399596i | \(-0.130849\pi\) | |||||||
\(464\) | −3200.00 | −0.320164 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5928.00 | −0.589290 | ||||||||
\(467\) | 6526.00i | 0.646654i | 0.946287 | + | 0.323327i | \(0.104801\pi\) | ||||
−0.946287 | + | 0.323327i | \(0.895199\pi\) | |||||||
\(468\) | − 6992.00i | − 0.690610i | ||||||||
\(469\) | −756.000 | −0.0744325 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4988.00 | −0.487972 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 14144.0i | − 1.37493i | ||||||||
\(474\) | 4800.00 | 0.465129 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1248.00 | 0.120172 | ||||||||
\(477\) | − 46.0000i | − 0.00441550i | ||||||||
\(478\) | 5600.00i | 0.535854i | ||||||||
\(479\) | −17400.0 | −1.65976 | −0.829881 | − | 0.557940i | \(-0.811592\pi\) | ||||
−0.829881 | + | 0.557940i | \(0.811592\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10108.0 | −0.958181 | ||||||||
\(482\) | − 12088.0i | − 1.14231i | ||||||||
\(483\) | 936.000i | 0.0881770i | ||||||||
\(484\) | 2456.00 | 0.230654 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −14168.0 | −1.32237 | ||||||||
\(487\) | 1166.00i | 0.108494i | 0.998528 | + | 0.0542469i | \(0.0172758\pi\) | ||||
−0.998528 | + | 0.0542469i | \(0.982724\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5524.00 | −0.510846 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7072.00 | 0.650010 | 0.325005 | − | 0.945712i | \(-0.394634\pi\) | ||||
0.325005 | + | 0.945712i | \(0.394634\pi\) | |||||||
\(492\) | 352.000i | 0.0322548i | ||||||||
\(493\) | 1300.00i | 0.118761i | ||||||||
\(494\) | −15200.0 | −1.38437 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6912.00 | 0.625722 | ||||||||
\(497\) | 2472.00i | 0.223107i | ||||||||
\(498\) | 2256.00i | 0.203000i | ||||||||
\(499\) | −100.000 | −0.00897117 | −0.00448559 | − | 0.999990i | \(-0.501428\pi\) | ||||
−0.00448559 | + | 0.999990i | \(0.501428\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6252.00 | 0.557522 | ||||||||
\(502\) | 4992.00i | 0.443832i | ||||||||
\(503\) | − 2602.00i | − 0.230651i | −0.993328 | − | 0.115325i | \(-0.963209\pi\) | ||||
0.993328 | − | 0.115325i | \(-0.0367911\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9984.00 | 0.877160 | ||||||||
\(507\) | − 1506.00i | − 0.131921i | ||||||||
\(508\) | − 14768.0i | − 1.28981i | ||||||||
\(509\) | −11150.0 | −0.970953 | −0.485476 | − | 0.874250i | \(-0.661354\pi\) | ||||
−0.485476 | + | 0.874250i | \(0.661354\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5268.00 | −0.456052 | ||||||||
\(512\) | − 16384.0i | − 1.41421i | ||||||||
\(513\) | 10000.0i | 0.860645i | ||||||||
\(514\) | 8424.00 | 0.722892 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7072.00 | 0.603348 | ||||||||
\(517\) | − 16448.0i | − 1.39919i | ||||||||
\(518\) | 6384.00i | 0.541500i | ||||||||
\(519\) | 156.000 | 0.0131939 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3638.00 | −0.305919 | −0.152959 | − | 0.988232i | \(-0.548880\pi\) | ||||
−0.152959 | + | 0.988232i | \(0.548880\pi\) | |||||||
\(522\) | − 4600.00i | − 0.385702i | ||||||||
\(523\) | 2078.00i | 0.173737i | 0.996220 | + | 0.0868686i | \(0.0276860\pi\) | ||||
−0.996220 | + | 0.0868686i | \(0.972314\pi\) | |||||||
\(524\) | 17664.0 | 1.47262 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14552.0 | 1.20627 | ||||||||
\(527\) | − 2808.00i | − 0.232103i | ||||||||
\(528\) | 4096.00i | 0.337605i | ||||||||
\(529\) | 6083.00 | 0.499959 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11500.0 | −0.939845 | ||||||||
\(532\) | 4800.00i | 0.391177i | ||||||||
\(533\) | 836.000i | 0.0679384i | ||||||||
\(534\) | −1200.00 | −0.0972455 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 2600.00i | − 0.208935i | ||||||||
\(538\) | − 26200.0i | − 2.09956i | ||||||||
\(539\) | 9824.00 | 0.785064 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5622.00 | 0.446781 | 0.223391 | − | 0.974729i | \(-0.428287\pi\) | ||||
0.223391 | + | 0.974729i | \(0.428287\pi\) | |||||||
\(542\) | 17552.0i | 1.39100i | ||||||||
\(543\) | − 3484.00i | − 0.275346i | ||||||||
\(544\) | −6656.00 | −0.524584 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1824.00 | 0.142967 | ||||||||
\(547\) | 16486.0i | 1.28865i | 0.764753 | + | 0.644324i | \(0.222861\pi\) | ||||
−0.764753 | + | 0.644324i | \(0.777139\pi\) | |||||||
\(548\) | 18672.0i | 1.45553i | ||||||||
\(549\) | −11914.0 | −0.926188 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5000.00 | −0.386583 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 3600.00i | − 0.276831i | ||||||||
\(554\) | 2184.00 | 0.167490 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5600.00 | −0.427146 | ||||||||
\(557\) | 11706.0i | 0.890483i | 0.895410 | + | 0.445242i | \(0.146882\pi\) | ||||
−0.895410 | + | 0.445242i | \(0.853118\pi\) | |||||||
\(558\) | 9936.00i | 0.753807i | ||||||||
\(559\) | 16796.0 | 1.27083 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1664.00 | 0.125230 | ||||||||
\(562\) | 27432.0i | 2.05898i | ||||||||
\(563\) | 25038.0i | 1.87429i | 0.348939 | + | 0.937146i | \(0.386542\pi\) | ||||
−0.348939 | + | 0.937146i | \(0.613458\pi\) | |||||||
\(564\) | 8224.00 | 0.613994 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −37128.0 | −2.75725 | ||||||||
\(567\) | 2526.00i | 0.187094i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17550.0 | −1.29303 | −0.646515 | − | 0.762901i | \(-0.723774\pi\) | ||||
−0.646515 | + | 0.762901i | \(0.723774\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10712.0 | 0.785084 | 0.392542 | − | 0.919734i | \(-0.371596\pi\) | ||||
0.392542 | + | 0.919734i | \(0.371596\pi\) | |||||||
\(572\) | − 9728.00i | − 0.711098i | ||||||||
\(573\) | − 7544.00i | − 0.550009i | ||||||||
\(574\) | 528.000 | 0.0383942 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 11776.0 | 0.851852 | ||||||||
\(577\) | − 13654.0i | − 0.985136i | −0.870274 | − | 0.492568i | \(-0.836058\pi\) | ||||
0.870274 | − | 0.492568i | \(-0.163942\pi\) | |||||||
\(578\) | − 16948.0i | − 1.21963i | ||||||||
\(579\) | 716.000 | 0.0513920 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1692.00 | 0.120819 | ||||||||
\(582\) | − 3088.00i | − 0.219934i | ||||||||
\(583\) | − 64.0000i | − 0.00454650i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19368.0 | −1.36533 | ||||||||
\(587\) | 14166.0i | 0.996071i | 0.867157 | + | 0.498035i | \(0.165945\pi\) | ||||
−0.867157 | + | 0.498035i | \(0.834055\pi\) | |||||||
\(588\) | 4912.00i | 0.344502i | ||||||||
\(589\) | 10800.0 | 0.755528 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4428.00 | −0.308196 | ||||||||
\(592\) | − 17024.0i | − 1.18190i | ||||||||
\(593\) | − 17842.0i | − 1.23555i | −0.786354 | − | 0.617777i | \(-0.788034\pi\) | ||||
0.786354 | − | 0.617777i | \(-0.211966\pi\) | |||||||
\(594\) | −12800.0 | −0.884159 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16400.0 | 1.12713 | ||||||||
\(597\) | − 5200.00i | − 0.356485i | ||||||||
\(598\) | 11856.0i | 0.810749i | ||||||||
\(599\) | 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 | \(-0.122789\pi\) | ||||
0.926516 | + | 0.376256i | \(0.122789\pi\) | |||||||
\(602\) | − 10608.0i | − 0.718189i | ||||||||
\(603\) | 2898.00i | 0.195714i | ||||||||
\(604\) | −14816.0 | −0.998103 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5616.00 | −0.376459 | ||||||||
\(607\) | − 3794.00i | − 0.253696i | −0.991922 | − | 0.126848i | \(-0.959514\pi\) | ||||
0.991922 | − | 0.126848i | \(-0.0404861\pi\) | |||||||
\(608\) | − 25600.0i | − 1.70759i | ||||||||
\(609\) | 600.000 | 0.0399232 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19532.0 | 1.29326 | ||||||||
\(612\) | − 4784.00i | − 0.315983i | ||||||||
\(613\) | 13238.0i | 0.872231i | 0.899891 | + | 0.436116i | \(0.143646\pi\) | ||||
−0.899891 | + | 0.436116i | \(0.856354\pi\) | |||||||
\(614\) | −10376.0 | −0.681989 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 11574.0i | − 0.755189i | −0.925971 | − | 0.377595i | \(-0.876751\pi\) | ||||
0.925971 | − | 0.377595i | \(-0.123249\pi\) | |||||||
\(618\) | − 4784.00i | − 0.311393i | ||||||||
\(619\) | −8300.00 | −0.538942 | −0.269471 | − | 0.963008i | \(-0.586849\pi\) | ||||
−0.269471 | + | 0.963008i | \(0.586849\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7800.00 | 0.504031 | ||||||||
\(622\) | − 29328.0i | − 1.89059i | ||||||||
\(623\) | 900.000i | 0.0578776i | ||||||||
\(624\) | −4864.00 | −0.312045 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6248.00 | −0.398914 | ||||||||
\(627\) | 6400.00i | 0.407642i | ||||||||
\(628\) | 19952.0i | 1.26779i | ||||||||
\(629\) | −6916.00 | −0.438409 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7508.00 | −0.473675 | −0.236837 | − | 0.971549i | \(-0.576111\pi\) | ||||
−0.236837 | + | 0.971549i | \(0.576111\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2336.00i | 0.146679i | ||||||||
\(634\) | 5704.00 | 0.357310 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 32.0000 | 0.00199510 | ||||||||
\(637\) | 11666.0i | 0.725626i | ||||||||
\(638\) | − 6400.00i | − 0.397145i | ||||||||
\(639\) | 9476.00 | 0.586643 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27378.0 | −1.68700 | −0.843499 | − | 0.537130i | \(-0.819508\pi\) | ||||
−0.843499 | + | 0.537130i | \(0.819508\pi\) | |||||||
\(642\) | 9552.00i | 0.587208i | ||||||||
\(643\) | − 1842.00i | − 0.112973i | −0.998403 | − | 0.0564863i | \(-0.982010\pi\) | ||||
0.998403 | − | 0.0564863i | \(-0.0179897\pi\) | |||||||
\(644\) | 3744.00 | 0.229090 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10400.0 | −0.633409 | ||||||||
\(647\) | − 10114.0i | − 0.614563i | −0.951619 | − | 0.307282i | \(-0.900581\pi\) | ||||
0.951619 | − | 0.307282i | \(-0.0994193\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16000.0 | −0.967727 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1296.00 | −0.0780250 | ||||||||
\(652\) | 22096.0i | 1.32722i | ||||||||
\(653\) | − 10402.0i | − 0.623372i | −0.950185 | − | 0.311686i | \(-0.899106\pi\) | ||||
0.950185 | − | 0.311686i | \(-0.100894\pi\) | |||||||
\(654\) | −4400.00 | −0.263079 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1408.00 | −0.0838006 | ||||||||
\(657\) | 20194.0i | 1.19915i | ||||||||
\(658\) | − 12336.0i | − 0.730862i | ||||||||
\(659\) | −7100.00 | −0.419692 | −0.209846 | − | 0.977734i | \(-0.567296\pi\) | ||||
−0.209846 | + | 0.977734i | \(0.567296\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7118.00 | −0.418847 | −0.209424 | − | 0.977825i | \(-0.567159\pi\) | ||||
−0.209424 | + | 0.977825i | \(0.567159\pi\) | |||||||
\(662\) | 16032.0i | 0.941241i | ||||||||
\(663\) | 1976.00i | 0.115749i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 24472.0 | 1.42383 | ||||||||
\(667\) | 3900.00i | 0.226400i | ||||||||
\(668\) | − 25008.0i | − 1.44849i | ||||||||
\(669\) | 12956.0 | 0.748741 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16576.0 | −0.953665 | ||||||||
\(672\) | 3072.00i | 0.176347i | ||||||||
\(673\) | 31278.0i | 1.79150i | 0.444560 | + | 0.895749i | \(0.353360\pi\) | ||||
−0.444560 | + | 0.895749i | \(0.646640\pi\) | |||||||
\(674\) | 35464.0 | 2.02674 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6024.00 | −0.342740 | ||||||||
\(677\) | − 30054.0i | − 1.70616i | −0.521782 | − | 0.853079i | \(-0.674732\pi\) | ||||
0.521782 | − | 0.853079i | \(-0.325268\pi\) | |||||||
\(678\) | 12496.0i | 0.707826i | ||||||||
\(679\) | −2316.00 | −0.130898 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1292.00 | 0.0727012 | ||||||||
\(682\) | 13824.0i | 0.776171i | ||||||||
\(683\) | 4518.00i | 0.253113i | 0.991959 | + | 0.126557i | \(0.0403926\pi\) | ||||
−0.991959 | + | 0.126557i | \(0.959607\pi\) | |||||||
\(684\) | 18400.0 | 1.02857 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 15600.0 | 0.868237 | ||||||||
\(687\) | 7500.00i | 0.416511i | ||||||||
\(688\) | 28288.0i | 1.56754i | ||||||||
\(689\) | 76.0000 | 0.00420228 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29272.0 | 1.61152 | 0.805759 | − | 0.592243i | \(-0.201758\pi\) | ||||
0.805759 | + | 0.592243i | \(0.201758\pi\) | |||||||
\(692\) | − 624.000i | − 0.0342788i | ||||||||
\(693\) | 4416.00i | 0.242063i | ||||||||
\(694\) | −6856.00 | −0.375000 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 572.000i | 0.0310847i | ||||||||
\(698\) | 4600.00i | 0.249445i | ||||||||
\(699\) | −2964.00 | −0.160385 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5798.00 | −0.312393 | −0.156196 | − | 0.987726i | \(-0.549923\pi\) | ||||
−0.156196 | + | 0.987726i | \(0.549923\pi\) | |||||||
\(702\) | − 15200.0i | − 0.817218i | ||||||||
\(703\) | − 26600.0i | − 1.42708i | ||||||||
\(704\) | 16384.0 | 0.877124 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17592.0 | 0.937796 | ||||||||
\(707\) | 4212.00i | 0.224057i | ||||||||
\(708\) | − 8000.00i | − 0.424659i | ||||||||
\(709\) | −8950.00 | −0.474082 | −0.237041 | − | 0.971500i | \(-0.576178\pi\) | ||||
−0.237041 | + | 0.971500i | \(0.576178\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13800.0 | −0.727905 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 8424.00i | − 0.442470i | ||||||||
\(714\) | 1248.00 | 0.0654135 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10400.0 | −0.542830 | ||||||||
\(717\) | 2800.00i | 0.145841i | ||||||||
\(718\) | 7200.00i | 0.374236i | ||||||||
\(719\) | −7800.00 | −0.404577 | −0.202289 | − | 0.979326i | \(-0.564838\pi\) | ||||
−0.202289 | + | 0.979326i | \(0.564838\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3588.00 | −0.185332 | ||||||||
\(722\) | − 12564.0i | − 0.647623i | ||||||||
\(723\) | − 6044.00i | − 0.310897i | ||||||||
\(724\) | −13936.0 | −0.715369 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2456.00 | 0.125552 | ||||||||
\(727\) | − 8554.00i | − 0.436383i | −0.975906 | − | 0.218191i | \(-0.929984\pi\) | ||||
0.975906 | − | 0.218191i | \(-0.0700157\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4283.00 | 0.217599 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11492.0 | 0.581460 | ||||||||
\(732\) | − 8288.00i | − 0.418488i | ||||||||
\(733\) | − 2882.00i | − 0.145224i | −0.997360 | − | 0.0726119i | \(-0.976867\pi\) | ||||
0.997360 | − | 0.0726119i | \(-0.0231335\pi\) | |||||||
\(734\) | −23496.0 | −1.18154 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19968.0 | −1.00004 | ||||||||
\(737\) | 4032.00i | 0.201521i | ||||||||
\(738\) | − 2024.00i | − 0.100955i | ||||||||
\(739\) | −18700.0 | −0.930840 | −0.465420 | − | 0.885090i | \(-0.654097\pi\) | ||||
−0.465420 | + | 0.885090i | \(0.654097\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7600.00 | −0.376779 | ||||||||
\(742\) | − 48.0000i | − 0.00237485i | ||||||||
\(743\) | − 12242.0i | − 0.604462i | −0.953235 | − | 0.302231i | \(-0.902269\pi\) | ||||
0.953235 | − | 0.302231i | \(-0.0977314\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8312.00 | 0.407941 | ||||||||
\(747\) | − 6486.00i | − 0.317685i | ||||||||
\(748\) | − 6656.00i | − 0.325358i | ||||||||
\(749\) | 7164.00 | 0.349488 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31148.0 | −1.51346 | −0.756729 | − | 0.653729i | \(-0.773204\pi\) | ||||
−0.756729 | + | 0.653729i | \(0.773204\pi\) | |||||||
\(752\) | 32896.0i | 1.59520i | ||||||||
\(753\) | 2496.00i | 0.120796i | ||||||||
\(754\) | 7600.00 | 0.367076 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4800.00 | −0.230918 | ||||||||
\(757\) | − 7694.00i | − 0.369410i | −0.982794 | − | 0.184705i | \(-0.940867\pi\) | ||||
0.982794 | − | 0.184705i | \(-0.0591329\pi\) | |||||||
\(758\) | 31600.0i | 1.51420i | ||||||||
\(759\) | 4992.00 | 0.238733 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4518.00 | −0.215213 | −0.107607 | − | 0.994194i | \(-0.534319\pi\) | ||||
−0.107607 | + | 0.994194i | \(0.534319\pi\) | |||||||
\(762\) | − 14768.0i | − 0.702084i | ||||||||
\(763\) | 3300.00i | 0.156577i | ||||||||
\(764\) | −30176.0 | −1.42897 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30072.0 | 1.41847 | ||||||||
\(767\) | − 19000.0i | − 0.894459i | ||||||||
\(768\) | − 8192.00i | − 0.384900i | ||||||||
\(769\) | 39550.0 | 1.85463 | 0.927314 | − | 0.374283i | \(-0.122111\pi\) | ||||
0.927314 | + | 0.374283i | \(0.122111\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4212.00 | 0.196746 | ||||||||
\(772\) | − 2864.00i | − 0.133520i | ||||||||
\(773\) | − 22122.0i | − 1.02933i | −0.857391 | − | 0.514666i | \(-0.827916\pi\) | ||||
0.857391 | − | 0.514666i | \(-0.172084\pi\) | |||||||
\(774\) | −40664.0 | −1.88842 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3192.00i | 0.147378i | ||||||||
\(778\) | − 7800.00i | − 0.359439i | ||||||||
\(779\) | −2200.00 | −0.101185 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13184.0 | 0.604047 | ||||||||
\(782\) | 8112.00i | 0.370952i | ||||||||
\(783\) | − 5000.00i | − 0.228206i | ||||||||
\(784\) | −19648.0 | −0.895044 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 17664.0 | 0.801595 | ||||||||
\(787\) | − 16634.0i | − 0.753416i | −0.926332 | − | 0.376708i | \(-0.877056\pi\) | ||||
0.926332 | − | 0.376708i | \(-0.122944\pi\) | |||||||
\(788\) | 17712.0i | 0.800716i | ||||||||
\(789\) | 7276.00 | 0.328305 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9372.00 | 0.421277 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 19684.0i | − 0.881462i | ||||||||
\(794\) | 55144.0 | 2.46472 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20800.0 | −0.926176 | ||||||||
\(797\) | 27586.0i | 1.22603i | 0.790071 | + | 0.613015i | \(0.210044\pi\) | ||||
−0.790071 | + | 0.613015i | \(0.789956\pi\) | |||||||
\(798\) | 4800.00i | 0.212930i | ||||||||
\(799\) | 13364.0 | 0.591720 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3450.00 | 0.152184 | ||||||||
\(802\) | − 25608.0i | − 1.12749i | ||||||||
\(803\) | 28096.0i | 1.23473i | ||||||||
\(804\) | −2016.00 | −0.0884314 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16416.0 | −0.717406 | ||||||||
\(807\) | − 13100.0i | − 0.571427i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3850.00 | −0.167316 | −0.0836581 | − | 0.996495i | \(-0.526660\pi\) | ||||
−0.0836581 | + | 0.996495i | \(0.526660\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10032.0 | 0.434366 | 0.217183 | − | 0.976131i | \(-0.430313\pi\) | ||||
0.217183 | + | 0.976131i | \(0.430313\pi\) | |||||||
\(812\) | − 2400.00i | − 0.103724i | ||||||||
\(813\) | 8776.00i | 0.378583i | ||||||||
\(814\) | 34048.0 | 1.46607 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3328.00 | −0.142774 | ||||||||
\(817\) | 44200.0i | 1.89273i | ||||||||
\(818\) | 44600.0i | 1.90636i | ||||||||
\(819\) | −5244.00 | −0.223736 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20562.0 | 0.874079 | 0.437039 | − | 0.899442i | \(-0.356027\pi\) | ||||
0.437039 | + | 0.899442i | \(0.356027\pi\) | |||||||
\(822\) | 18672.0i | 0.792288i | ||||||||
\(823\) | − 10322.0i | − 0.437184i | −0.975816 | − | 0.218592i | \(-0.929854\pi\) | ||||
0.975816 | − | 0.218592i | \(-0.0701464\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12000.0 | −0.505488 | ||||||||
\(827\) | 8846.00i | 0.371954i | 0.982554 | + | 0.185977i | \(0.0595449\pi\) | ||||
−0.982554 | + | 0.185977i | \(0.940455\pi\) | |||||||
\(828\) | − 14352.0i | − 0.602375i | ||||||||
\(829\) | 25350.0 | 1.06205 | 0.531026 | − | 0.847355i | \(-0.321806\pi\) | ||||
0.531026 | + | 0.847355i | \(0.321806\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1092.00 | 0.0455849 | ||||||||
\(832\) | 19456.0i | 0.810716i | ||||||||
\(833\) | 7982.00i | 0.332005i | ||||||||
\(834\) | −5600.00 | −0.232509 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 25600.0 | 1.05908 | ||||||||
\(837\) | 10800.0i | 0.446001i | ||||||||
\(838\) | − 54800.0i | − 2.25899i | ||||||||
\(839\) | −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 | ||||||||
\(842\) | 21752.0i | 0.890289i | ||||||||
\(843\) | 13716.0i | 0.560385i | ||||||||
\(844\) | 9344.00 | 0.381083 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −47288.0 | −1.92174 | ||||||||
\(847\) | − 1842.00i | − 0.0747248i | ||||||||
\(848\) | 128.000i | 0.00518342i | ||||||||
\(849\) | −18564.0 | −0.750430 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20748.0 | −0.835761 | ||||||||
\(852\) | 6592.00i | 0.265068i | ||||||||
\(853\) | 16998.0i | 0.682298i | 0.940009 | + | 0.341149i | \(0.110816\pi\) | ||||
−0.940009 | + | 0.341149i | \(0.889184\pi\) | |||||||
\(854\) | −12432.0 | −0.498143 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 26494.0i | − 1.05603i | −0.849235 | − | 0.528015i | \(-0.822936\pi\) | ||||
0.849235 | − | 0.528015i | \(-0.177064\pi\) | |||||||
\(858\) | − 9728.00i | − 0.387073i | ||||||||
\(859\) | 21500.0 | 0.853982 | 0.426991 | − | 0.904256i | \(-0.359574\pi\) | ||||
0.426991 | + | 0.904256i | \(0.359574\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 264.000 | 0.0104496 | ||||||||
\(862\) | − 30768.0i | − 1.21573i | ||||||||
\(863\) | − 25762.0i | − 1.01616i | −0.861309 | − | 0.508082i | \(-0.830355\pi\) | ||||
0.861309 | − | 0.508082i | \(-0.169645\pi\) | |||||||
\(864\) | 25600.0 | 1.00802 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4472.00 | 0.175479 | ||||||||
\(867\) | − 8474.00i | − 0.331940i | ||||||||
\(868\) | 5184.00i | 0.202715i | ||||||||
\(869\) | −19200.0 | −0.749500 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4788.00 | −0.186263 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8878.00i | 0.344186i | ||||||||
\(874\) | −31200.0 | −1.20750 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −14048.0 | −0.541824 | ||||||||
\(877\) | 30546.0i | 1.17613i | 0.808814 | + | 0.588064i | \(0.200110\pi\) | ||||
−0.808814 | + | 0.588064i | \(0.799890\pi\) | |||||||
\(878\) | − 10400.0i | − 0.399753i | ||||||||
\(879\) | −9684.00 | −0.371596 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32942.0 | 1.25976 | 0.629878 | − | 0.776694i | \(-0.283105\pi\) | ||||
0.629878 | + | 0.776694i | \(0.283105\pi\) | |||||||
\(882\) | − 28244.0i | − 1.07826i | ||||||||
\(883\) | 27118.0i | 1.03351i | 0.856132 | + | 0.516757i | \(0.172861\pi\) | ||||
−0.856132 | + | 0.516757i | \(0.827139\pi\) | |||||||
\(884\) | 7904.00 | 0.300724 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 47832.0 | 1.81371 | ||||||||
\(887\) | − 38634.0i | − 1.46246i | −0.682131 | − | 0.731230i | \(-0.738946\pi\) | ||||
0.682131 | − | 0.731230i | \(-0.261054\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11076.0 | −0.417860 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13472.0 | 0.506542 | ||||||||
\(892\) | − 51824.0i | − 1.94529i | ||||||||
\(893\) | 51400.0i | 1.92613i | ||||||||
\(894\) | 16400.0 | 0.613532 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5928.00i | 0.220658i | ||||||||
\(898\) | − 68200.0i | − 2.53437i | ||||||||
\(899\) | −5400.00 | −0.200334 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 52.0000 | 0.00192272 | ||||||||
\(902\) | − 2816.00i | − 0.103950i | ||||||||
\(903\) | − 5304.00i | − 0.195466i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −14816.0 | −0.543299 | ||||||||
\(907\) | − 1794.00i | − 0.0656767i | −0.999461 | − | 0.0328384i | \(-0.989545\pi\) | ||||
0.999461 | − | 0.0328384i | \(-0.0104547\pi\) | |||||||
\(908\) | − 5168.00i | − 0.188883i | ||||||||
\(909\) | 16146.0 | 0.589141 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41732.0 | 1.51772 | 0.758860 | − | 0.651254i | \(-0.225757\pi\) | ||||
0.758860 | + | 0.651254i | \(0.225757\pi\) | |||||||
\(912\) | − 12800.0i | − 0.464748i | ||||||||
\(913\) | − 9024.00i | − 0.327109i | ||||||||
\(914\) | −37976.0 | −1.37433 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 30000.0 | 1.08213 | ||||||||
\(917\) | − 13248.0i | − 0.477086i | ||||||||
\(918\) | − 10400.0i | − 0.373912i | ||||||||
\(919\) | −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 | ||||||||
\(922\) | 45672.0i | 1.63137i | ||||||||
\(923\) | 15656.0i | 0.558314i | ||||||||
\(924\) | −3072.00 | −0.109374 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −31848.0 | −1.13023 | ||||||||
\(927\) | 13754.0i | 0.487315i | ||||||||
\(928\) | 12800.0i | 0.452781i | ||||||||
\(929\) | 48650.0 | 1.71814 | 0.859071 | − | 0.511856i | \(-0.171042\pi\) | ||||
0.859071 | + | 0.511856i | \(0.171042\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30700.0 | −1.08072 | ||||||||
\(932\) | 11856.0i | 0.416691i | ||||||||
\(933\) | − 14664.0i | − 0.514553i | ||||||||
\(934\) | 26104.0 | 0.914506 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 11334.0i | − 0.395161i | −0.980287 | − | 0.197580i | \(-0.936692\pi\) | ||||
0.980287 | − | 0.197580i | \(-0.0633083\pi\) | |||||||
\(938\) | 3024.00i | 0.105263i | ||||||||
\(939\) | −3124.00 | −0.108571 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31178.0 | −1.08010 | −0.540050 | − | 0.841633i | \(-0.681595\pi\) | ||||
−0.540050 | + | 0.841633i | \(0.681595\pi\) | |||||||
\(942\) | 19952.0i | 0.690097i | ||||||||
\(943\) | 1716.00i | 0.0592584i | ||||||||
\(944\) | 32000.0 | 1.10330 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −56576.0 | −1.94444 | ||||||||
\(947\) | 4686.00i | 0.160797i | 0.996763 | + | 0.0803984i | \(0.0256193\pi\) | ||||
−0.996763 | + | 0.0803984i | \(0.974381\pi\) | |||||||
\(948\) | − 9600.00i | − 0.328896i | ||||||||
\(949\) | −33364.0 | −1.14124 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2852.00 | 0.0972476 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 598.000i | 0.0203265i | 0.999948 | + | 0.0101632i | \(0.00323511\pi\) | ||||
−0.999948 | + | 0.0101632i | \(0.996765\pi\) | |||||||
\(954\) | −184.000 | −0.00624447 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11200.0 | 0.378906 | ||||||||
\(957\) | − 3200.00i | − 0.108089i | ||||||||
\(958\) | 69600.0i | 2.34726i | ||||||||
\(959\) | 14004.0 | 0.471546 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18127.0 | −0.608472 | ||||||||
\(962\) | 40432.0i | 1.35507i | ||||||||
\(963\) | − 27462.0i | − 0.918952i | ||||||||
\(964\) | −24176.0 | −0.807735 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3744.00 | 0.124701 | ||||||||
\(967\) | 41726.0i | 1.38761i | 0.720163 | + | 0.693804i | \(0.244067\pi\) | ||||
−0.720163 | + | 0.693804i | \(0.755933\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5200.00 | −0.172392 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24312.0 | 0.803511 | 0.401756 | − | 0.915747i | \(-0.368400\pi\) | ||||
0.401756 | + | 0.915747i | \(0.368400\pi\) | |||||||
\(972\) | 28336.0i | 0.935059i | ||||||||
\(973\) | 4200.00i | 0.138382i | ||||||||
\(974\) | 4664.00 | 0.153433 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 33152.0 | 1.08726 | ||||||||
\(977\) | 40946.0i | 1.34082i | 0.741992 | + | 0.670409i | \(0.233881\pi\) | ||||
−0.741992 | + | 0.670409i | \(0.766119\pi\) | |||||||
\(978\) | 22096.0i | 0.722446i | ||||||||
\(979\) | 4800.00 | 0.156699 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12650.0 | 0.411706 | ||||||||
\(982\) | − 28288.0i | − 0.919253i | ||||||||
\(983\) | − 42282.0i | − 1.37191i | −0.727645 | − | 0.685954i | \(-0.759385\pi\) | ||||
0.727645 | − | 0.685954i | \(-0.240615\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5200.00 | 0.167953 | ||||||||
\(987\) | − 6168.00i | − 0.198916i | ||||||||
\(988\) | 30400.0i | 0.978900i | ||||||||
\(989\) | 34476.0 | 1.10847 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1172.00 | 0.0375679 | 0.0187840 | − | 0.999824i | \(-0.494021\pi\) | ||||
0.0187840 | + | 0.999824i | \(0.494021\pi\) | |||||||
\(992\) | − 27648.0i | − 0.884904i | ||||||||
\(993\) | 8016.00i | 0.256173i | ||||||||
\(994\) | 9888.00 | 0.315521 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4512.00 | 0.143542 | ||||||||
\(997\) | − 31614.0i | − 1.00424i | −0.864798 | − | 0.502119i | \(-0.832554\pi\) | ||||
0.864798 | − | 0.502119i | \(-0.167446\pi\) | |||||||
\(998\) | 400.000i | 0.0126872i | ||||||||
\(999\) | 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 \(a_p\))