Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [120,4,Mod(49,120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("120.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 120 = 2^{3} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 120.f (of order \(2\), degree \(1\), 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: | \(7.08022920069\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{129})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 65x^{2} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Root | \(6.17891i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 120.49 |
Dual form | 120.4.f.d.49.2 |
$q$-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 \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(41\) | \(61\) | \(97\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 11.1789 | + | 0.178908i | 0.999872 | + | 0.0160020i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 33.0735i | − | 1.78580i | −0.450257 | − | 0.892899i | \(-0.648667\pi\) | ||
0.450257 | − | 0.892899i | \(-0.351333\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 48.3578 | 1.32549 | 0.662747 | − | 0.748844i | \(-0.269391\pi\) | ||||
0.662747 | + | 0.748844i | \(0.269391\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 60.3578i | 1.28771i | 0.765147 | + | 0.643856i | \(0.222666\pi\) | ||||
−0.765147 | + | 0.643856i | \(0.777334\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.536725 | + | 33.5367i | −0.00923879 | + | 0.577276i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 17.7891i | − | 0.253793i | −0.991916 | − | 0.126897i | \(-0.959498\pi\) | ||
0.991916 | − | 0.126897i | \(-0.0405017\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 130.863 | 1.58010 | 0.790051 | − | 0.613042i | \(-0.210054\pi\) | ||||
0.790051 | + | 0.613042i | \(0.210054\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 99.2204 | 1.03103 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 70.8625i | − | 0.642429i | −0.947007 | − | 0.321214i | \(-0.895909\pi\) | ||
0.947007 | − | 0.321214i | \(-0.104091\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 124.936 | + | 4.00000i | 0.999488 | + | 0.0320000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 27.0000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −104.505 | −0.669174 | −0.334587 | − | 0.942365i | \(-0.608597\pi\) | ||||
−0.334587 | + | 0.942365i | \(0.608597\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −210.441 | −1.21923 | −0.609617 | − | 0.792696i | \(-0.708677\pi\) | ||||
−0.609617 | + | 0.792696i | \(0.708677\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 145.073i | 0.765274i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.91712 | − | 369.725i | 0.0285764 | − | 1.78557i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 300.945i | 1.33717i | 0.743638 | + | 0.668583i | \(0.233099\pi\) | ||||
−0.743638 | + | 0.668583i | \(0.766901\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −181.073 | −0.743460 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 240.147 | 0.914747 | 0.457374 | − | 0.889275i | \(-0.348790\pi\) | ||||
0.457374 | + | 0.889275i | \(0.348790\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 108.000i | 0.383020i | 0.981491 | + | 0.191510i | \(0.0613384\pi\) | ||||
−0.981491 | + | 0.191510i | \(0.938662\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −100.610 | − | 1.61018i | −0.333291 | − | 0.00533402i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 278.991i | − | 0.865850i | −0.901430 | − | 0.432925i | \(-0.857481\pi\) | ||
0.901430 | − | 0.432925i | \(-0.142519\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −750.853 | −2.18908 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 53.3673 | 0.146528 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 328.358i | − | 0.851008i | −0.904957 | − | 0.425504i | \(-0.860097\pi\) | ||
0.904957 | − | 0.425504i | \(-0.139903\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 540.588 | + | 8.65162i | 1.32532 | + | 0.0212106i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 392.588i | 0.912272i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −889.533 | −1.96284 | −0.981418 | − | 0.191882i | \(-0.938541\pi\) | ||||
−0.981418 | + | 0.191882i | \(0.938541\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −241.450 | −0.506795 | −0.253398 | − | 0.967362i | \(-0.581548\pi\) | ||||
−0.253398 | + | 0.967362i | \(0.581548\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 297.661i | 0.595266i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.7985 | + | 674.735i | −0.0206060 | + | 1.28755i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 103.834i | 0.189334i | 0.995509 | + | 0.0946669i | \(0.0301786\pi\) | ||||
−0.995509 | + | 0.0946669i | \(0.969821\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 212.588 | 0.370906 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −277.597 | −0.464010 | −0.232005 | − | 0.972715i | \(-0.574529\pi\) | ||||
−0.232005 | + | 0.972715i | \(0.574529\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 274.403i | − | 0.439951i | −0.975505 | − | 0.219976i | \(-0.929402\pi\) | ||
0.975505 | − | 0.219976i | \(-0.0705978\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.0000 | + | 374.808i | −0.0184752 | + | 0.577055i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1599.36i | − | 2.36706i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −366.991 | −0.522654 | −0.261327 | − | 0.965250i | \(-0.584160\pi\) | ||||
−0.261327 | + | 0.965250i | \(0.584160\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 57.7251i | − | 0.0763391i | −0.999271 | − | 0.0381696i | \(-0.987847\pi\) | ||
0.999271 | − | 0.0381696i | \(-0.0121527\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.18262 | − | 198.863i | 0.00406121 | − | 0.253761i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 313.514i | − | 0.386348i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 203.175 | 0.241983 | 0.120992 | − | 0.992654i | \(-0.461393\pi\) | ||||
0.120992 | + | 0.992654i | \(0.461393\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1996.24 | 2.29959 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 631.322i | − | 0.703925i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1462.90 | + | 23.4124i | 1.57990 | + | 0.0252849i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1283.45i | 1.34345i | 0.740801 | + | 0.671725i | \(0.234446\pi\) | ||||
−0.740801 | + | 0.671725i | \(0.765554\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −435.220 | −0.441831 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 886.908 | 0.873768 | 0.436884 | − | 0.899518i | \(-0.356082\pi\) | ||||
0.436884 | + | 0.899518i | \(0.356082\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 783.055i | 0.749094i | 0.927208 | + | 0.374547i | \(0.122202\pi\) | ||||
−0.927208 | + | 0.374547i | \(0.877798\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1109.18 | + | 17.7513i | 1.03090 | + | 0.0164986i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1301.51i | 1.17590i | 0.808897 | + | 0.587950i | \(0.200065\pi\) | ||||
−0.808897 | + | 0.587950i | \(0.799935\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1161.91 | −1.02102 | −0.510508 | − | 0.859873i | \(-0.670543\pi\) | ||||
−0.510508 | + | 0.859873i | \(0.670543\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −902.836 | −0.772013 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 507.808i | − | 0.422748i | −0.977405 | − | 0.211374i | \(-0.932206\pi\) | ||
0.977405 | − | 0.211374i | \(-0.0677938\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.6779 | − | 792.166i | 0.0102802 | − | 0.642346i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 543.220i | − | 0.429237i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −588.346 | −0.453224 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1007.48 | 0.756933 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 720.441i | 0.528130i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1395.93 | + | 67.0677i | 0.998848 | + | 0.0479898i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 796.064i | 0.556215i | 0.960550 | + | 0.278107i | \(0.0897071\pi\) | ||||
−0.960550 | + | 0.278107i | \(0.910293\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −324.000 | −0.221137 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −91.4764 | −0.0610102 | −0.0305051 | − | 0.999535i | \(-0.509712\pi\) | ||||
−0.0305051 | + | 0.999535i | \(0.509712\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 4328.08i | − | 2.82174i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.83053 | − | 301.831i | 0.00307960 | − | 0.192425i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2273.28i | 1.41766i | 0.705380 | + | 0.708829i | \(0.250776\pi\) | ||||
−0.705380 | + | 0.708829i | \(0.749224\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 738.735 | 0.450782 | 0.225391 | − | 0.974268i | \(-0.427634\pi\) | ||||
0.225391 | + | 0.974268i | \(0.427634\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 836.972 | 0.499899 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2918.77i | 1.70685i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1168.25 | − | 18.6968i | −0.669088 | − | 0.0107082i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 2252.56i | − | 1.26386i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1507.15 | −0.828661 | −0.414330 | − | 0.910127i | \(-0.635984\pi\) | ||||
−0.414330 | + | 0.910127i | \(0.635984\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 154.365 | 0.0831925 | 0.0415962 | − | 0.999135i | \(-0.486756\pi\) | ||||
0.0415962 | + | 0.999135i | \(0.486756\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 160.102i | 0.0845978i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2352.50 | − | 37.6496i | −1.21908 | − | 0.0195102i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 315.514i | − | 0.160387i | −0.996779 | − | 0.0801935i | \(-0.974446\pi\) | ||
0.996779 | − | 0.0801935i | \(-0.0255538\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 985.073 | 0.491330 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2343.67 | −1.14725 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1457.85i | 0.700539i | 0.936649 | + | 0.350270i | \(0.113910\pi\) | ||||
−0.936649 | + | 0.350270i | \(0.886090\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −25.9549 | + | 1621.76i | −0.0122460 | + | 0.765176i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2198.61i | − | 1.01876i | −0.860541 | − | 0.509381i | \(-0.829874\pi\) | ||
0.860541 | − | 0.509381i | \(-0.170126\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1446.07 | −0.658200 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1177.76 | −0.526700 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2030.49i | 0.892343i | 0.894948 | + | 0.446171i | \(0.147213\pi\) | ||||
−0.894948 | + | 0.446171i | \(0.852787\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 132.294 | − | 4132.06i | 0.0571456 | − | 1.78488i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 2668.60i | − | 1.13324i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −427.220 | −0.178391 | −0.0891954 | − | 0.996014i | \(-0.528430\pi\) | ||||
−0.0891954 | + | 0.996014i | \(0.528430\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3779.97 | −1.55228 | −0.776140 | − | 0.630561i | \(-0.782825\pi\) | ||||
−0.776140 | + | 0.630561i | \(0.782825\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 724.350i | − | 0.292598i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −53.8416 | + | 3364.24i | −0.0213974 | + | 1.33699i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 860.241i | − | 0.336401i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −892.983 | −0.343677 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1565.60 | 0.593103 | 0.296551 | − | 0.955017i | \(-0.404163\pi\) | ||||
0.296551 | + | 0.955017i | \(0.404163\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2642.63i | 0.985599i | 0.870143 | + | 0.492800i | \(0.164026\pi\) | ||||
−0.870143 | + | 0.492800i | \(0.835974\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2024.20 | − | 32.3956i | −0.743365 | − | 0.0118969i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 98.4522i | 0.0356062i | 0.999842 | + | 0.0178031i | \(0.00566721\pi\) | ||||
−0.999842 | + | 0.0178031i | \(0.994333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1131.62 | −0.403106 | −0.201553 | − | 0.979478i | \(-0.564599\pi\) | ||||
−0.201553 | + | 0.979478i | \(0.564599\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −311.503 | −0.109312 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3456.33i | 1.19501i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2684.58 | + | 42.9643i | 0.914630 | + | 0.0146378i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 637.763i | 0.214143i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6328.23 | 2.09441 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1902.85 | −0.620841 | −0.310420 | − | 0.950599i | \(-0.600470\pi\) | ||||
−0.310420 | + | 0.950599i | \(0.600470\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 832.791i | − | 0.267896i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.3221 | + | 1207.32i | −0.00612910 | + | 0.382971i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6960.00i | 2.17731i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 823.209 | 0.254006 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1073.71 | 0.326813 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4855.59i | − | 1.45809i | −0.684465 | − | 0.729046i | \(-0.739964\pi\) | ||
0.684465 | − | 0.729046i | \(-0.260036\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1124.42 | − | 36.0000i | −0.333163 | − | 0.0106667i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 6536.19i | − | 1.91111i | −0.294812 | − | 0.955555i | \(-0.595257\pi\) | ||
0.294812 | − | 0.955555i | \(-0.404743\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5510.35 | 1.59011 | 0.795053 | − | 0.606539i | \(-0.207443\pi\) | ||||
0.795053 | + | 0.606539i | \(0.207443\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4798.08 | 1.36663 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 5915.65i | − | 1.66329i | −0.555306 | − | 0.831646i | \(-0.687399\pi\) | ||
0.555306 | − | 0.831646i | \(-0.312601\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 49.9137 | − | 3118.81i | 0.0138554 | − | 0.865739i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1100.97i | − | 0.301754i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2263.25 | −0.612543 | −0.306272 | − | 0.951944i | \(-0.599082\pi\) | ||||
−0.306272 | + | 0.951944i | \(0.599082\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 772.493 | 0.206476 | 0.103238 | − | 0.994657i | \(-0.467080\pi\) | ||||
0.103238 | + | 0.994657i | \(0.467080\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8393.72 | − | 134.334i | −2.18880 | − | 0.0350297i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7898.58i | 2.03471i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 173.175 | 0.0440744 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 596.192 | 0.149926 | 0.0749628 | − | 0.997186i | \(-0.476116\pi\) | ||||
0.0749628 | + | 0.997186i | \(0.476116\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3426.76i | − | 0.851535i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 596.588 | + | 9.54785i | 0.146509 | + | 0.00234474i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4139.19i | 1.00465i | 0.864678 | + | 0.502326i | \(0.167522\pi\) | ||||
−0.864678 | + | 0.502326i | \(0.832478\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9953.30 | 2.38791 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 940.542 | 0.223058 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1611.34i | 0.377792i | 0.981997 | + | 0.188896i | \(0.0604909\pi\) | ||||
−0.981997 | + | 0.188896i | \(0.939509\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 58.7460 | − | 3670.68i | 0.0136179 | − | 0.850899i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 609.526i | 0.139709i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7031.33 | 1.59371 | 0.796855 | − | 0.604171i | \(-0.206496\pi\) | ||||
0.796855 | + | 0.604171i | \(0.206496\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5441.27 | −1.21968 | −0.609840 | − | 0.792524i | \(-0.708766\pi\) | ||||
−0.609840 | + | 0.792524i | \(0.708766\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5988.72i | 1.32767i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6041.63 | + | 193.431i | 1.32481 | + | 0.0424158i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1080.43i | 0.234355i | 0.993111 | + | 0.117178i | \(0.0373847\pi\) | ||||
−0.993111 | + | 0.117178i | \(0.962615\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1893.97 | 0.406411 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1602.99 | −0.340308 | −0.170154 | − | 0.985417i | \(-0.554427\pi\) | ||||
−0.170154 | + | 0.985417i | \(0.554427\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 334.810i | − | 0.0703265i | −0.999382 | − | 0.0351632i | \(-0.988805\pi\) | ||
0.999382 | − | 0.0351632i | \(-0.0111951\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −70.2372 | + | 4388.70i | −0.0145982 | + | 0.912155i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 7942.49i | − | 1.63355i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4596.55 | 0.935589 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3850.35 | −0.775641 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 539.250i | − | 0.107520i | −0.998554 | − | 0.0537599i | \(-0.982879\pi\) | ||
0.998554 | − | 0.0537599i | \(-0.0171206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9944.01 | − | 159.145i | −1.96258 | − | 0.0314094i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1305.66i | − | 0.255091i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4277.11 | 0.827263 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3571.93 | 0.683996 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2660.72i | 0.504470i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2699.15 | − | 43.1974i | −0.506731 | − | 0.00810977i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8477.58i | 1.57603i | 0.615656 | + | 0.788015i | \(0.288891\pi\) | ||||
−0.615656 | + | 0.788015i | \(0.711109\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2349.16 | −0.432490 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3646.92 | 0.664945 | 0.332473 | − | 0.943113i | \(-0.392117\pi\) | ||||
0.332473 | + | 0.943113i | \(0.392117\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 7537.05i | − | 1.36108i | −0.732709 | − | 0.680542i | \(-0.761745\pi\) | ||
0.732709 | − | 0.680542i | \(-0.238255\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −53.2540 | + | 3327.53i | −0.00952548 | + | 0.595190i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 10721.2i | − | 1.89956i | −0.312916 | − | 0.949781i | \(-0.601306\pi\) | ||
0.312916 | − | 0.949781i | \(-0.398694\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5053.62 | −0.886986 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3904.52 | −0.678907 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2327.92i | − | 0.401019i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −241.431 | + | 7540.86i | −0.0412068 | + | 1.28705i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 3485.73i | − | 0.589484i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9227.18 | −1.54623 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4405.14 | −0.731505 | −0.365753 | − | 0.930712i | \(-0.619188\pi\) | ||||
−0.365753 | + | 0.930712i | \(0.619188\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2708.51i | − | 0.445722i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.5768 | + | 1160.75i | −0.00302973 | + | 0.189310i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 186.117i | − | 0.0300844i | −0.999887 | − | 0.0150422i | \(-0.995212\pi\) | ||
0.999887 | − | 0.0150422i | \(-0.00478827\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1523.42 | 0.244074 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10176.5 | −1.61609 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13489.1i | 2.12345i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2376.50 | + | 38.0337i | 0.370859 | + | 0.00593526i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5547.38i | 0.858211i | 0.903254 | + | 0.429105i | \(0.141171\pi\) | ||||
−0.903254 | + | 0.429105i | \(0.858829\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9078.82 | −1.39249 | −0.696244 | − | 0.717805i | \(-0.745147\pi\) | ||||
−0.696244 | + | 0.717805i | \(0.745147\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1629.66 | 0.247820 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 10678.1i | − | 1.61002i | −0.593262 | − | 0.805009i | \(-0.702160\pi\) | ||
0.593262 | − | 0.805009i | \(-0.297840\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3103.23 | − | 49.6644i | −0.463951 | − | 0.00742511i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 1765.04i | − | 0.261669i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 265.733 | 0.0390665 | 0.0195332 | − | 0.999809i | \(-0.493782\pi\) | ||||
0.0195332 | + | 0.999809i | \(0.493782\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10266.0 | 1.49672 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3022.44i | 0.437016i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 49.0930 | − | 3067.53i | 0.00704012 | − | 0.439895i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 5854.21i | − | 0.832663i | −0.909213 | − | 0.416332i | \(-0.863316\pi\) | ||
0.909213 | − | 0.416332i | \(-0.136684\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2161.32 | −0.304916 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10859.9 | −1.51973 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10134.5i | 1.40682i | 0.710787 | + | 0.703408i | \(0.248339\pi\) | ||||
−0.710787 | + | 0.703408i | \(0.751661\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −201.203 | + | 4187.80i | −0.0277069 | + | 0.576685i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 6307.68i | − | 0.861703i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4235.70 | 0.574072 | 0.287036 | − | 0.957920i | \(-0.407330\pi\) | ||||
0.287036 | + | 0.957920i | \(0.407330\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2388.19 | −0.321131 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 8100.84i | − | 1.08077i | −0.841419 | − | 0.540383i | \(-0.818279\pi\) | ||
0.841419 | − | 0.540383i | \(-0.181721\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 286.139 | − | 17879.1i | 0.0378779 | − | 2.36676i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 972.000i | − | 0.127673i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13820.2 | 1.80131 | 0.900656 | − | 0.434532i | \(-0.143086\pi\) | ||||
0.900656 | + | 0.434532i | \(0.143086\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1260.58 | −0.163044 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 274.429i | − | 0.0352242i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4102.55 | − | 65.6577i | −0.522587 | − | 0.00836353i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11523.9i | 1.45685i | 0.685125 | + | 0.728425i | \(0.259748\pi\) | ||||
−0.685125 | + | 0.728425i | \(0.740252\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12984.2 | 1.62913 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 700.915 | 0.0872869 | 0.0436434 | − | 0.999047i | \(-0.486103\pi\) | ||||
0.0436434 | + | 0.999047i | \(0.486103\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 12701.7i | − | 1.57002i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 905.492 | + | 14.4916i | 0.111097 | + | 0.00177801i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14553.1i | 1.77240i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6650.69 | −0.804047 | −0.402024 | − | 0.915629i | \(-0.631693\pi\) | ||||
−0.402024 | + | 0.915629i | \(0.631693\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6819.83 | −0.818485 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29419.9i | 3.50523i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.3275 | − | 645.303i | 0.00122158 | − | 0.0763294i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2216.20i | 0.260259i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13844.4 | −1.61418 | −0.807091 | − | 0.590426i | \(-0.798960\pi\) | ||||
−0.807091 | + | 0.590426i | \(0.798960\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12576.3 | 1.45590 | 0.727949 | − | 0.685631i | \(-0.240474\pi\) | ||||
0.727949 | + | 0.685631i | \(0.240474\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2510.92i | 0.288617i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 71.1563 | − | 2222.50i | 0.00812139 | − | 0.253663i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7985.59i | 0.905035i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8756.32 | −0.985452 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13440.6 | 1.50212 | 0.751059 | − | 0.660236i | \(-0.229544\pi\) | ||||
0.751059 | + | 0.660236i | \(0.229544\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3012.87i | − | 0.334387i | −0.985924 | − | 0.167193i | \(-0.946530\pi\) | ||
0.985924 | − | 0.167193i | \(-0.0534704\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 56.0903 | − | 3504.75i | 0.00618235 | − | 0.386298i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 9273.25i | − | 1.01510i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10675.0 | −1.16057 | −0.580283 | − | 0.814415i | \(-0.697058\pi\) | ||||
−0.580283 | + | 0.814415i | \(0.697058\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6757.68 | 0.729692 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 125.868i | − | 0.0134992i | −0.999977 | − | 0.00674962i | \(-0.997852\pi\) | ||
0.999977 | − | 0.00674962i | \(-0.00214849\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2271.28 | + | 36.3497i | 0.241952 | + | 0.00387223i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 4521.45i | − | 0.478428i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9707.21 | 1.02029 | 0.510146 | − | 0.860088i | \(-0.329591\pi\) | ||||
0.510146 | + | 0.860088i | \(0.329591\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11613.0 | 1.21249 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 463.096i | 0.0480312i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 22315.8 | + | 357.144i | 2.29930 | + | 0.0367982i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1279.97i | − | 0.131016i | −0.997852 | − | 0.0655082i | \(-0.979133\pi\) | ||
0.997852 | − | 0.0655082i | \(-0.0208668\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −480.305 | −0.0488425 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3080.48 | 0.311220 | 0.155610 | − | 0.987819i | \(-0.450266\pi\) | ||||
0.155610 | + | 0.987819i | \(0.450266\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 18017.3i | − | 1.80850i | −0.427008 | − | 0.904248i | \(-0.640432\pi\) | ||
0.427008 | − | 0.904248i | \(-0.359568\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 112.949 | − | 7057.49i | 0.0112642 | − | 0.703835i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 7236.77i | − | 0.717083i | −0.933514 | − | 0.358541i | \(-0.883274\pi\) | ||
0.933514 | − | 0.358541i | \(-0.116726\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3434.16 | 0.338112 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 946.542 | 0.0925995 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5222.64i | 0.507690i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16349.4 | + | 523.450i | 1.57929 | + | 0.0505632i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2955.22i | 0.283669i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4932.78 | −0.470532 | −0.235266 | − | 0.971931i | \(-0.575596\pi\) | ||||
−0.235266 | + | 0.971931i | \(0.575596\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18164.4 | −1.72188 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 7031.01i | − | 0.662364i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −229.620 | + | 14347.6i | −0.0214979 | + | 1.34328i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 5937.91i | − | 0.552510i | −0.961084 | − | 0.276255i | \(-0.910907\pi\) | ||
0.961084 | − | 0.276255i | \(-0.0890934\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4373.56 | −0.404456 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15703.5 | 1.44336 | 0.721678 | − | 0.692229i | \(-0.243371\pi\) | ||||
0.721678 | + | 0.692229i | \(0.243371\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1859.04i | 0.169832i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4865.29 | − | 77.8646i | −0.441775 | − | 0.00707020i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9181.09i | 0.828628i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5656.77 | 0.507478 | 0.253739 | − | 0.967273i | \(-0.418340\pi\) | ||||
0.253739 | + | 0.967273i | \(0.418340\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6595.82 | 0.588183 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 290.441i | − | 0.0257457i | −0.999917 | − | 0.0128729i | \(-0.995902\pi\) | ||
0.999917 | − | 0.0128729i | \(-0.00409768\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9914.66 | + | 158.675i | 0.873657 | + | 0.0139821i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 4338.20i | − | 0.380012i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17330.6 | −1.50916 | −0.754582 | − | 0.656206i | \(-0.772160\pi\) | ||||
−0.754582 | + | 0.656206i | \(0.772160\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9075.45 | −0.785664 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 3533.29i | − | 0.304091i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −140.095 | + | 8753.70i | −0.0119870 | + | 0.748998i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 13491.4i | − | 1.14768i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6091.47 | −0.515194 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6174.36 | 0.519201 | 0.259601 | − | 0.965716i | \(-0.416409\pi\) | ||||
0.259601 | + | 0.965716i | \(0.416409\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13389.4i | 1.11946i | 0.828675 | + | 0.559730i | \(0.189095\pi\) | ||||
−0.828675 | + | 0.559730i | \(0.810905\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12396.2 | + | 396.881i | 1.03050 | + | 0.0329930i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3743.55i | 0.309434i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7145.50 | 0.587285 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8005.80 | 0.654279 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14494.7i | 1.17793i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −232.850 | + | 14549.4i | −0.0188168 | + | 1.17575i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 1281.66i | − | 0.102994i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −36309.6 | −2.90161 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14355.5 | −1.14084 | −0.570418 | − | 0.821354i | \(-0.693219\pi\) | ||||
−0.570418 | + | 0.821354i | \(0.693219\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 11339.9i | − | 0.896209i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12988.9 | − | 207.875i | −1.02089 | − | 0.0163384i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 21133.9i | − | 1.65195i | −0.563704 | − | 0.825977i | \(-0.690624\pi\) | ||
0.563704 | − | 0.825977i | \(-0.309376\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2173.05 | 0.168932 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13675.8 | −1.05736 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12137.6i | 0.933355i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10092.7 | − | 161.525i | −0.771914 | − | 0.0123538i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3098.60i | 0.235713i | 0.993031 | + | 0.117856i | \(0.0376023\pi\) | ||||
−0.993031 | + | 0.117856i | \(0.962398\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6518.64 | −0.493219 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2580.72 | 0.194221 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 7908.77i | − | 0.592033i | −0.955183 | − | 0.296017i | \(-0.904342\pi\) | ||
0.955183 | − | 0.296017i | \(-0.0956584\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 90.8511 | − | 5676.74i | 0.00676484 | − | 0.422694i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2678.95i | − | 0.198422i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10740.7 | 0.791345 | 0.395673 | − | 0.918392i | \(-0.370512\pi\) | ||||
0.395673 | + | 0.918392i | \(0.370512\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14701.2 | 1.07745 | 0.538725 | − | 0.842482i | \(-0.318906\pi\) | ||||
0.538725 | + | 0.842482i | \(0.318906\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4696.79i | 0.342428i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 283.450 | − | 8853.28i | 0.0205577 | − | 0.642100i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15788.1i | 1.13911i | 0.821954 | + | 0.569554i | \(0.192884\pi\) | ||||
−0.821954 | + | 0.569554i | \(0.807116\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7927.89 | −0.569036 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1909.17 | −0.136326 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 15878.7i | − | 1.12801i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 97.1867 | − | 6072.61i | 0.00686867 | − | 0.429182i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14778.5i | 1.03913i | 0.854430 | + | 0.519567i | \(0.173907\pi\) | ||||
−0.854430 | + | 0.519567i | \(0.826093\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27538.8 | −1.92651 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −295.356 | −0.0205573 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11143.9i | − | 0.771713i | −0.922559 | − | 0.385857i | \(-0.873906\pi\) | ||
0.922559 | − | 0.385857i | \(-0.126094\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6577.07 | − | 105.260i | −0.453166 | − | 0.00725251i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 3394.85i | − | 0.232733i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7707.87 | 0.525768 | 0.262884 | − | 0.964827i | \(-0.415326\pi\) | ||||
0.262884 | + | 0.964827i | \(0.415326\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13681.4 | −0.928580 | −0.464290 | − | 0.885683i | \(-0.653691\pi\) | ||||
−0.464290 | + | 0.885683i | \(0.653691\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 934.508i | − | 0.0631113i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11262.5 | + | 180.246i | 0.756837 | + | 0.0121125i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11552.4i | 0.772481i | 0.922398 | + | 0.386241i | \(0.126227\pi\) | ||||
−0.922398 | + | 0.386241i | \(0.873773\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10369.0 | −0.689939 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16839.3 | 1.11496 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9904.66i | 0.652603i | 0.945266 | + | 0.326301i | \(0.105802\pi\) | ||||
−0.945266 | + | 0.326301i | \(0.894198\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −128.893 | + | 8053.74i | −0.00845116 | + | 0.528062i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20323.5i | 1.32608i | 0.748582 | + | 0.663042i | \(0.230735\pi\) | ||||
−0.748582 | + | 0.663042i | \(0.769265\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9223.99 | 0.598940 | 0.299470 | − | 0.954106i | \(-0.403190\pi\) | ||||
0.299470 | + | 0.954106i | \(0.403190\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1913.29 | −0.123635 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 6719.70i | − | 0.432134i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15593.0 | + | 999.488i | 0.997952 | + | 0.0639672i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18984.7i | 1.20921i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5353.54 | 0.339364 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16916.0 | −1.06722 | −0.533610 | − | 0.845730i | \(-0.679165\pi\) | ||||
−0.533610 | + | 0.845730i | \(0.679165\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 5708.54i | − | 0.358443i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −142.422 | + | 8899.13i | −0.00890057 | + | 0.556143i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 45319.9i | − | 2.81890i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2498.37 | 0.154670 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5811.35 | −0.358088 | −0.179044 | − | 0.983841i | \(-0.557300\pi\) | ||||
−0.179044 | + | 0.983841i | \(0.557300\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 27931.7i | − | 1.71309i | −0.516069 | − | 0.856547i | \(-0.672605\pi\) | ||
0.516069 | − | 0.856547i | \(-0.327395\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3621.97 | − | 57.9663i | −0.221108 | − | 0.00353864i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25437.8i | 1.54569i | 0.634595 | + | 0.772845i | \(0.281167\pi\) | ||||
−0.634595 | + | 0.772845i | \(0.718833\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −43015.9 | −2.60173 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20880.0 | −1.25707 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 22647.7i | − | 1.35723i | −0.734493 | − | 0.678617i | \(-0.762580\pi\) | ||
0.734493 | − | 0.678617i | \(-0.237420\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1022.61 | − | 16.3659i | −0.0610024 | − | 0.000976288i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2469.63i | 0.146650i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25158.5 | −1.48716 | −0.743579 | − | 0.668649i | \(-0.766873\pi\) | ||||
−0.743579 | + | 0.668649i | \(0.766873\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23441.0 | 1.37935 | 0.689675 | − | 0.724119i | \(-0.257753\pi\) | ||||
0.689675 | + | 0.724119i | \(0.257753\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3221.13i | 0.188685i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 774.329 | − | 48383.2i | 0.0451537 | − | 2.82138i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7405.47i | 0.429896i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14566.8 | 0.841829 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11676.0 | −0.671754 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3145.33i | 0.180154i | 0.995935 | + | 0.0900770i | \(0.0287113\pi\) | ||||
−0.995935 | + | 0.0900770i | \(0.971289\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 108.000 | − | 3373.27i | 0.00615840 | − | 0.192352i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 10606.2i | − | 0.602109i | −0.953607 | − | 0.301054i | \(-0.902661\pi\) | ||
0.953607 | − | 0.301054i | \(-0.0973386\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 42448.1 | 2.39913 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19608.6 | 1.10338 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7825.06i | 0.438386i | 0.975682 | + | 0.219193i | \(0.0703424\pi\) | ||||
−0.975682 | + | 0.219193i | \(0.929658\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −406.708 | + | 25412.8i | −0.0226854 | + | 1.41748i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16531.1i | 0.918049i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19819.0 | 1.09585 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22750.9 | 1.25251 | 0.626256 | − | 0.779618i | \(-0.284587\pi\) | ||||
0.626256 | + | 0.779618i | \(0.284587\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14394.2i | 0.789022i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8258.25 | + | 132.166i | 0.450724 | + | 0.00721343i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 4271.99i | − | 0.232157i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17747.0 | 0.960302 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −133.598 | −0.00719817 | −0.00359908 | − | 0.999994i | \(-0.501146\pi\) | ||||
−0.00359908 | + | 0.999994i | \(0.501146\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 39382.5i | 2.11286i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9356.43 | + | 149.741i | 0.499835 | + | 0.00799941i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 29333.1i | − | 1.56037i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6886.26 | −0.364766 | −0.182383 | − | 0.983228i | \(-0.558381\pi\) | ||||
−0.182383 | + | 0.983228i | \(0.558381\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3302.92 | 0.174218 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14912.4i | 0.783271i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −522.193 | + | 32628.7i | −0.0273131 | + | 1.70663i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 6789.76i | − | 0.353652i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1570.18 | 0.0814436 | 0.0407218 | − | 0.999171i | \(-0.487034\pi\) | ||||
0.0407218 | + | 0.999171i | \(0.487034\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25898.3 | 1.33773 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2317.48i | 0.119209i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13056.4 | − | 418.019i | −0.668831 | − | 0.0214136i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3399.18i | − | 0.173409i | −0.996234 | − | 0.0867047i | \(-0.972366\pi\) | ||
0.996234 | − | 0.0867047i | \(-0.0276337\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1921.22 | 0.0972078 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14152.1i | 0.713125i | 0.934272 | + | 0.356562i | \(0.116051\pi\) | ||||
−0.934272 | + | 0.356562i | \(0.883949\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 403.002 | − | 25181.2i | 0.0202244 | − | 1.26370i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5021.20i | 0.250961i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14919.5 | 0.742655 | 0.371328 | − | 0.928502i | \(-0.378903\pi\) | ||||
0.371328 | + | 0.928502i | \(0.378903\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23695.7 | −1.17474 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 7287.29i | − | 0.359818i | −0.983683 | − | 0.179909i | \(-0.942420\pi\) | ||
0.983683 | − | 0.179909i | \(-0.0575803\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16848.3 | − | 269.642i | −0.828555 | − | 0.0132603i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 519.526i | 0.0254464i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 43045.3 | 2.09992 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18783.4 | 0.912670 | 0.456335 | − | 0.889808i | \(-0.349162\pi\) | ||||
0.456335 | + | 0.889808i | \(0.349162\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1788.58i | 0.0865595i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1725.63 | + | 27.6172i | 0.0831818 | + | 0.00133125i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 30614.3i | − | 1.46988i | −0.678134 | − | 0.734939i | \(-0.737211\pi\) | ||
0.678134 | − | 0.734939i | \(-0.262789\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10280.3 | 0.491634 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15277.2 | −0.727723 | −0.363861 | − | 0.931453i | \(-0.618542\pi\) | ||||
−0.363861 | + | 0.931453i | \(0.618542\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38428.4i | 1.82333i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −28.6435 | + | 1789.76i | −0.00135374 | + | 0.0845869i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 53690.3i | − | 2.52757i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17700.1 | 0.830016 | 0.415008 | − | 0.909818i | \(-0.363779\pi\) | ||||
0.415008 | + | 0.909818i | \(0.363779\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12417.6 | −0.580036 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 29362.5i | − | 1.36623i | −0.730310 | − | 0.683116i | \(-0.760625\pi\) | ||
0.730310 | − | 0.683116i | \(-0.239375\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26291.6 | − | 841.763i | −1.21861 | − | 0.0390155i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 29859.9i | 1.37866i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 31426.2 | 1.44539 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13424.0 | −0.615042 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2821.63i | 0.128783i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 56.4481 | − | 3527.10i | 0.00256652 | − | 0.160367i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 2816.92i | − | 0.127589i | −0.997963 | − | 0.0637943i | \(-0.979680\pi\) | ||
0.997963 | − | 0.0637943i | \(-0.0203202\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4834.01 | −0.218118 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16795.0 | −0.754943 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) |