Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(95,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.95");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.r (of order \(6\), degree \(2\), 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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 95.6 | ||
Root | \(-1.75780 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.95 |
Dual form | 224.3.r.d.191.6 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 4.23009 | + | 2.44224i | 1.41003 | + | 0.814081i | 0.995390 | − | 0.0959056i | \(-0.0305747\pi\) |
0.414639 | + | 0.909986i | \(0.363908\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.16012 | + | 2.00939i | 0.232025 | + | 0.401878i | 0.958404 | − | 0.285416i | \(-0.0921317\pi\) |
−0.726379 | + | 0.687294i | \(0.758798\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.65898 | − | 5.22436i | −0.665568 | − | 0.746337i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.42909 | + | 12.8676i | 0.825455 | + | 1.42973i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.2789 | + | 7.66660i | 1.20718 | + | 0.696964i | 0.962142 | − | 0.272550i | \(-0.0878671\pi\) |
0.245035 | + | 0.969514i | \(0.421200\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.8582 | 1.14294 | 0.571469 | − | 0.820624i | \(-0.306374\pi\) | ||||
0.571469 | + | 0.820624i | \(0.306374\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 11.3332i | 0.755547i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.19938 | − | 2.07739i | 0.0705520 | − | 0.122200i | −0.828591 | − | 0.559854i | \(-0.810857\pi\) |
0.899143 | + | 0.437654i | \(0.144191\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −25.9124 | + | 14.9605i | −1.36381 | + | 0.787397i | −0.990129 | − | 0.140159i | \(-0.955239\pi\) |
−0.373683 | + | 0.927557i | \(0.621905\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.94872 | − | 33.4778i | −0.330891 | − | 1.59418i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −23.0146 | + | 13.2875i | −1.00063 | + | 0.577716i | −0.908436 | − | 0.418025i | \(-0.862722\pi\) |
−0.0921976 | + | 0.995741i | \(0.529389\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.80823 | − | 16.9884i | 0.392329 | − | 0.679534i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 28.6142i | 1.05978i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.75828 | −0.164078 | −0.0820392 | − | 0.996629i | \(-0.526143\pi\) | ||||
−0.0820392 | + | 0.996629i | \(0.526143\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −17.0976 | − | 9.87133i | −0.551537 | − | 0.318430i | 0.198205 | − | 0.980161i | \(-0.436489\pi\) |
−0.749742 | + | 0.661731i | \(0.769822\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 37.4474 | + | 64.8608i | 1.13477 | + | 1.96548i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.09280 | − | 15.4226i | 0.145509 | − | 0.440646i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −24.3582 | − | 42.1896i | −0.658329 | − | 1.14026i | −0.981048 | − | 0.193765i | \(-0.937930\pi\) |
0.322719 | − | 0.946495i | \(-0.395403\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 62.8514 | + | 36.2873i | 1.61157 | + | 0.930443i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 34.4746 | 0.840845 | 0.420422 | − | 0.907328i | \(-0.361882\pi\) | ||||
0.420422 | + | 0.907328i | \(0.361882\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 59.4327i | − | 1.38216i | −0.722780 | − | 0.691078i | \(-0.757136\pi\) | ||
0.722780 | − | 0.691078i | \(-0.242864\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −17.2373 | + | 29.8559i | −0.383052 | + | 0.663465i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 32.8182 | − | 18.9476i | 0.698259 | − | 0.403140i | −0.108440 | − | 0.994103i | \(-0.534585\pi\) |
0.806699 | + | 0.590963i | \(0.201252\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.58789 | + | 48.6803i | −0.114039 | + | 0.993476i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.1470 | − | 5.85837i | 0.198961 | − | 0.114870i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 33.2663 | − | 57.6189i | 0.627666 | − | 1.08715i | −0.360352 | − | 0.932816i | \(-0.617344\pi\) |
0.988019 | − | 0.154334i | \(-0.0493231\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 35.5768i | 0.646851i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −146.149 | −2.56402 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −78.2440 | − | 45.1742i | −1.32617 | − | 0.765665i | −0.341465 | − | 0.939894i | \(-0.610923\pi\) |
−0.984705 | + | 0.174230i | \(0.944256\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 44.0772 | + | 76.3439i | 0.722577 | + | 1.25154i | 0.959964 | + | 0.280125i | \(0.0903759\pi\) |
−0.237387 | + | 0.971415i | \(0.576291\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 32.6128 | − | 98.7619i | 0.517664 | − | 1.56765i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.2373 | + | 29.8559i | 0.265190 | + | 0.459322i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.0906 | + | 8.71254i | 0.225232 | + | 0.130038i | 0.608371 | − | 0.793653i | \(-0.291823\pi\) |
−0.383138 | + | 0.923691i | \(0.625157\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −129.805 | −1.88123 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 23.0492i | − | 0.324636i | −0.986738 | − | 0.162318i | \(-0.948103\pi\) | ||
0.986738 | − | 0.162318i | \(-0.0518971\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 34.2297 | − | 59.2876i | 0.468900 | − | 0.812159i | −0.530468 | − | 0.847705i | \(-0.677984\pi\) |
0.999368 | + | 0.0355462i | \(0.0113171\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 82.9793 | − | 47.9081i | 1.10639 | − | 0.638775i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −21.8132 | − | 105.093i | −0.283288 | − | 1.36484i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −54.0184 | + | 31.1876i | −0.683778 | + | 0.394779i | −0.801277 | − | 0.598294i | \(-0.795846\pi\) |
0.117499 | + | 0.993073i | \(0.462512\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.02096 | + | 5.23245i | −0.0372958 | + | 0.0645982i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 36.3835i | 0.438356i | 0.975685 | + | 0.219178i | \(0.0703375\pi\) | ||||
−0.975685 | + | 0.219178i | \(0.929662\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.56573 | 0.0654792 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −20.1279 | − | 11.6209i | −0.231355 | − | 0.133573i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −44.2137 | − | 76.5804i | −0.496783 | − | 0.860454i | 0.503210 | − | 0.864164i | \(-0.332152\pi\) |
−0.999993 | + | 0.00371041i | \(0.998819\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −69.2239 | − | 77.6245i | −0.760702 | − | 0.853016i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −48.2164 | − | 83.5132i | −0.518456 | − | 0.897991i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −60.1232 | − | 34.7122i | −0.632876 | − | 0.365391i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.8582 | 0.153177 | 0.0765886 | − | 0.997063i | \(-0.475597\pi\) | ||||
0.0765886 | + | 0.997063i | \(0.475597\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 227.824i | 2.30125i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.72475 | − | 15.1117i | 0.0863836 | − | 0.149621i | −0.819596 | − | 0.572941i | \(-0.805802\pi\) |
0.905980 | + | 0.423321i | \(0.139136\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −75.8801 | + | 43.8094i | −0.736700 | + | 0.425334i | −0.820868 | − | 0.571118i | \(-0.806510\pi\) |
0.0841682 | + | 0.996452i | \(0.473177\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 59.2087 | − | 52.8011i | 0.563893 | − | 0.502868i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 76.1380 | − | 43.9583i | 0.711570 | − | 0.410825i | −0.100072 | − | 0.994980i | \(-0.531907\pi\) |
0.811642 | + | 0.584155i | \(0.198574\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −103.462 | + | 179.201i | −0.949190 | + | 1.64405i | −0.202054 | + | 0.979374i | \(0.564762\pi\) |
−0.747136 | + | 0.664671i | \(0.768572\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 237.954i | − | 2.14373i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −195.807 | −1.73281 | −0.866405 | − | 0.499342i | \(-0.833575\pi\) | ||||
−0.866405 | + | 0.499342i | \(0.833575\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −53.3995 | − | 30.8302i | −0.464343 | − | 0.268089i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 110.383 | + | 191.189i | 0.943442 | + | 1.63409i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.4410 | + | 3.41252i | −0.138159 | + | 0.0286766i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 57.0536 | + | 98.8197i | 0.471517 | + | 0.816692i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 145.831 | + | 84.1954i | 1.18562 | + | 0.684515i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 103.521 | 0.828169 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 187.616i | 1.47729i | 0.674092 | + | 0.738647i | \(0.264535\pi\) | ||||
−0.674092 | + | 0.738647i | \(0.735465\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 145.149 | − | 251.406i | 1.12519 | − | 1.94888i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 202.242 | − | 116.764i | 1.54383 | − | 0.891331i | 0.545239 | − | 0.838281i | \(-0.316439\pi\) |
0.998592 | − | 0.0530503i | \(-0.0168944\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 198.885 | + | 65.6750i | 1.49537 | + | 0.493797i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −57.4971 | + | 33.1960i | −0.425905 | + | 0.245896i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −64.2120 | + | 111.218i | −0.468700 | + | 0.811813i | −0.999360 | − | 0.0357721i | \(-0.988611\pi\) |
0.530660 | + | 0.847585i | \(0.321944\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 55.4166i | 0.398681i | 0.979930 | + | 0.199340i | \(0.0638800\pi\) | ||||
−0.979930 | + | 0.199340i | \(0.936120\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 185.098 | 1.31275 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 197.301 | + | 113.912i | 1.37973 | + | 0.796586i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.52019 | − | 9.56124i | −0.0380703 | − | 0.0659396i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −142.526 | + | 192.275i | −0.969567 | + | 1.30799i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.4625 | + | 21.5857i | 0.0836409 | + | 0.144870i | 0.904811 | − | 0.425813i | \(-0.140012\pi\) |
−0.821170 | + | 0.570683i | \(0.806678\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.9802 | − | 6.91675i | −0.0793388 | − | 0.0458063i | 0.459806 | − | 0.888020i | \(-0.347919\pi\) |
−0.539145 | + | 0.842213i | \(0.681252\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 35.6413 | 0.232950 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 45.8078i | − | 0.295534i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −43.1200 | + | 74.6860i | −0.274649 | + | 0.475707i | −0.970047 | − | 0.242919i | \(-0.921895\pi\) |
0.695397 | + | 0.718626i | \(0.255228\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 281.439 | − | 162.489i | 1.77006 | − | 1.02194i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 176.643 | + | 58.3304i | 1.09716 | + | 0.362301i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −134.226 | + | 77.4953i | −0.823471 | + | 0.475431i | −0.851612 | − | 0.524173i | \(-0.824375\pi\) |
0.0281408 | + | 0.999604i | \(0.491041\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −86.8872 | + | 150.493i | −0.526589 | + | 0.912079i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 239.152i | 1.43205i | 0.698076 | + | 0.716023i | \(0.254040\pi\) | ||||
−0.698076 | + | 0.716023i | \(0.745960\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 51.7655 | 0.306305 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −385.012 | − | 222.287i | −2.25153 | − | 1.29992i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −54.2968 | − | 94.0448i | −0.313854 | − | 0.543611i | 0.665339 | − | 0.746541i | \(-0.268287\pi\) |
−0.979193 | + | 0.202930i | \(0.934954\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −134.450 | + | 27.9066i | −0.768283 | + | 0.159466i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −220.653 | − | 382.182i | −1.24663 | − | 2.15922i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −144.105 | − | 83.1988i | −0.805054 | − | 0.464798i | 0.0401815 | − | 0.999192i | \(-0.487206\pi\) |
−0.845235 | + | 0.534394i | \(0.820540\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.9376 | −0.0991025 | −0.0495513 | − | 0.998772i | \(-0.515779\pi\) | ||||
−0.0495513 | + | 0.998772i | \(0.515779\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 430.589i | 2.35294i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 56.5170 | − | 97.8903i | 0.305497 | − | 0.529137i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31.8531 | − | 18.3904i | 0.170338 | − | 0.0983444i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 149.491 | − | 133.313i | 0.790957 | − | 0.705359i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −44.6004 | + | 25.7500i | −0.233510 | + | 0.134817i | −0.612190 | − | 0.790711i | \(-0.709711\pi\) |
0.378680 | + | 0.925528i | \(0.376378\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 35.8784 | − | 62.1432i | 0.185898 | − | 0.321985i | −0.757981 | − | 0.652277i | \(-0.773814\pi\) |
0.943879 | + | 0.330292i | \(0.107147\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 168.391i | 0.863543i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −57.3256 | −0.290993 | −0.145496 | − | 0.989359i | \(-0.546478\pi\) | ||||
−0.145496 | + | 0.989359i | \(0.546478\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 90.9399 | + | 52.5042i | 0.456984 | + | 0.263840i | 0.710775 | − | 0.703419i | \(-0.248344\pi\) |
−0.253791 | + | 0.967259i | \(0.581678\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 42.5562 | + | 73.7096i | 0.211723 | + | 0.366714i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 22.1687 | + | 24.8590i | 0.109205 | + | 0.122458i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 39.9948 | + | 69.2731i | 0.195097 | + | 0.337917i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −341.955 | − | 197.428i | −1.65195 | − | 0.953756i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −458.786 | −2.19515 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.68267i | 0.00797473i | 0.999992 | + | 0.00398737i | \(0.00126922\pi\) | ||||
−0.999992 | + | 0.00398737i | \(0.998731\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 56.2917 | − | 97.5000i | 0.264280 | − | 0.457747i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 119.424 | − | 68.9493i | 0.555459 | − | 0.320694i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28.0861 | + | 135.315i | 0.129429 | + | 0.623570i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 289.589 | − | 167.194i | 1.32233 | − | 0.763445i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.8207 | − | 30.8663i | 0.0806365 | − | 0.139667i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 247.049i | − | 1.10784i | −0.832569 | − | 0.553922i | \(-0.813131\pi\) | ||
0.832569 | − | 0.553922i | \(-0.186869\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 291.465 | 1.29540 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 153.492 | + | 88.6186i | 0.676176 | + | 0.390390i | 0.798413 | − | 0.602111i | \(-0.205673\pi\) |
−0.122237 | + | 0.992501i | \(0.539007\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 56.8684 | + | 98.4990i | 0.248334 | + | 0.430127i | 0.963064 | − | 0.269274i | \(-0.0867837\pi\) |
−0.714730 | + | 0.699401i | \(0.753450\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 164.390 | − | 497.824i | 0.711643 | − | 2.15508i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 29.2127 | + | 50.5979i | 0.125377 | + | 0.217158i | 0.921880 | − | 0.387475i | \(-0.126653\pi\) |
−0.796504 | + | 0.604634i | \(0.793319\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 76.1463 | + | 43.9631i | 0.324027 | + | 0.187077i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −304.670 | −1.28553 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 128.390i | − | 0.537197i | −0.963252 | − | 0.268598i | \(-0.913440\pi\) | ||
0.963252 | − | 0.268598i | \(-0.0865604\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −149.311 | + | 258.614i | −0.619548 | + | 1.07309i | 0.370021 | + | 0.929023i | \(0.379351\pi\) |
−0.989568 | + | 0.144064i | \(0.953983\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 197.468 | − | 114.008i | 0.812624 | − | 0.469169i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −104.301 | + | 45.2469i | −0.425716 | + | 0.184681i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −385.012 | + | 222.287i | −1.55875 | + | 0.899945i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −88.8574 | + | 153.906i | −0.356857 | + | 0.618095i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 90.1849i | − | 0.359302i | −0.983730 | − | 0.179651i | \(-0.942503\pi\) | ||
0.983730 | − | 0.179651i | \(-0.0574969\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −407.479 | −1.61059 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 23.5435 | + | 13.5929i | 0.0923276 | + | 0.0533054i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 134.768 | + | 233.425i | 0.524388 | + | 0.908267i | 0.999597 | + | 0.0283939i | \(0.00903926\pi\) |
−0.475209 | + | 0.879873i | \(0.657627\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −106.930 | + | 323.816i | −0.412855 | + | 1.25026i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −35.3497 | − | 61.2274i | −0.135439 | − | 0.234588i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 319.625 | + | 184.535i | 1.21530 | + | 0.701655i | 0.963910 | − | 0.266230i | \(-0.0857781\pi\) |
0.251393 | + | 0.967885i | \(0.419111\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 154.372 | 0.582536 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 431.922i | − | 1.61769i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 224.911 | − | 389.557i | 0.836099 | − | 1.44817i | −0.0570334 | − | 0.998372i | \(-0.518164\pi\) |
0.893132 | − | 0.449794i | \(-0.148503\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 100.007 | − | 57.7393i | 0.369031 | − | 0.213060i | −0.304004 | − | 0.952671i | \(-0.598324\pi\) |
0.673035 | + | 0.739611i | \(0.264990\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −103.245 | − | 497.420i | −0.378188 | − | 1.82205i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 260.486 | − | 150.392i | 0.947221 | − | 0.546878i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −45.7829 | + | 79.2983i | −0.165281 | + | 0.286275i | −0.936755 | − | 0.349986i | \(-0.886186\pi\) |
0.771474 | + | 0.636261i | \(0.219520\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 293.340i | − | 1.05140i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −106.341 | −0.378437 | −0.189218 | − | 0.981935i | \(-0.560595\pi\) | ||||
−0.189218 | + | 0.981935i | \(0.560595\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 50.0462 | + | 28.8942i | 0.176842 | + | 0.102100i | 0.585808 | − | 0.810450i | \(-0.300777\pi\) |
−0.408966 | + | 0.912550i | \(0.634111\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −169.551 | − | 293.671i | −0.594916 | − | 1.03042i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −160.617 | − | 180.108i | −0.559639 | − | 0.627554i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 141.623 | + | 245.298i | 0.490045 | + | 0.848783i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 62.8514 | + | 36.2873i | 0.215984 | + | 0.124699i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 306.168 | 1.04494 | 0.522471 | − | 0.852657i | \(-0.325010\pi\) | ||||
0.522471 | + | 0.852657i | \(0.325010\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 209.631i | − | 0.710612i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −219.374 | + | 379.966i | −0.738632 | + | 1.27935i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −341.955 | + | 197.428i | −1.14366 | + | 0.660293i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −310.498 | + | 276.896i | −1.03155 | + | 0.919919i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 73.8129 | − | 42.6159i | 0.243607 | − | 0.140646i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −102.270 | + | 177.137i | −0.335311 | + | 0.580776i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.03215i | − | 0.0261634i | −0.999914 | − | 0.0130817i | \(-0.995836\pi\) | ||
0.999914 | − | 0.0130817i | \(-0.00416415\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −427.973 | −1.38502 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.54480 | + | 3.20129i | 0.0178289 | + | 0.0102935i | 0.508888 | − | 0.860833i | \(-0.330057\pi\) |
−0.491059 | + | 0.871126i | \(0.663390\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.9567 | − | 46.6903i | −0.0861236 | − | 0.149170i | 0.819746 | − | 0.572727i | \(-0.194115\pi\) |
−0.905869 | + | 0.423557i | \(0.860781\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 236.286 | − | 49.0440i | 0.750115 | − | 0.155695i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −38.7321 | − | 67.0860i | −0.122183 | − | 0.211628i | 0.798445 | − | 0.602068i | \(-0.205656\pi\) |
−0.920628 | + | 0.390440i | \(0.872323\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −63.1849 | − | 36.4798i | −0.198072 | − | 0.114357i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 429.427 | 1.33778 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 71.7738i | 0.222210i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 145.732 | − | 252.416i | 0.448408 | − | 0.776665i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −875.304 | + | 505.357i | −2.67677 | + | 1.54543i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −251.888 | − | 83.1777i | −0.765617 | − | 0.252820i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −292.056 | + | 168.619i | −0.882345 | + | 0.509422i | −0.871431 | − | 0.490518i | \(-0.836807\pi\) |
−0.0109142 | + | 0.999940i | \(0.503474\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 361.918 | − | 626.861i | 1.08684 | − | 1.88246i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 40.4305i | 0.120688i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −58.4923 | −0.173568 | −0.0867838 | − | 0.996227i | \(-0.527659\pi\) | ||||
−0.0867838 | + | 0.996227i | \(0.527659\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −828.283 | − | 478.209i | −2.44331 | − | 1.41065i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −151.359 | − | 262.162i | −0.443869 | − | 0.768803i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 280.357 | − | 197.607i | 0.817369 | − | 0.576115i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −150.590 | − | 260.829i | −0.436491 | − | 0.756025i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 544.761 | + | 314.518i | 1.56992 | + | 0.906391i | 0.996178 | + | 0.0873520i | \(0.0278405\pi\) |
0.573738 | + | 0.819039i | \(0.305493\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 377.340 | 1.08120 | 0.540602 | − | 0.841279i | \(-0.318197\pi\) | ||||
0.540602 | + | 0.841279i | \(0.318197\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 425.155i | 1.21127i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −197.007 | + | 341.226i | −0.558093 | + | 0.966646i | 0.439562 | + | 0.898212i | \(0.355134\pi\) |
−0.997656 | + | 0.0684338i | \(0.978200\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 46.3148 | − | 26.7399i | 0.130464 | − | 0.0753236i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −77.8809 | − | 25.7176i | −0.218154 | − | 0.0720380i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −62.5991 | + | 36.1416i | −0.174371 | + | 0.100673i | −0.584645 | − | 0.811289i | \(-0.698766\pi\) |
0.410274 | + | 0.911962i | \(0.365433\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 267.136 | − | 462.693i | 0.739989 | − | 1.28170i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 557.355i | 1.53541i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 158.843 | 0.435185 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 455.370 | + | 262.908i | 1.24079 | + | 0.716371i | 0.969255 | − | 0.246058i | \(-0.0791353\pi\) |
0.271535 | + | 0.962428i | \(0.412469\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 256.115 | + | 443.605i | 0.694079 | + | 1.20218i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −456.009 | + | 94.6501i | −1.22914 | + | 0.255121i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 55.5660 | + | 96.2432i | 0.148971 | + | 0.258025i | 0.930847 | − | 0.365409i | \(-0.119071\pi\) |
−0.781877 | + | 0.623433i | \(0.785737\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 437.904 | + | 252.824i | 1.16774 | + | 0.674197i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −70.6993 | −0.187531 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 276.174i | − | 0.728692i | −0.931264 | − | 0.364346i | \(-0.881293\pi\) | ||
0.931264 | − | 0.364346i | \(-0.118707\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −458.205 | + | 793.634i | −1.20264 | + | 2.08303i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −97.7065 | + | 56.4109i | −0.255108 | + | 0.147287i | −0.622101 | − | 0.782937i | \(-0.713721\pi\) |
0.366993 | + | 0.930224i | \(0.380387\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 185.866 | − | 165.752i | 0.482769 | − | 0.430523i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 764.754 | − | 441.531i | 1.97611 | − | 1.14091i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 333.410 | − | 577.483i | 0.857096 | − | 1.48453i | −0.0175914 | − | 0.999845i | \(-0.505600\pi\) |
0.874687 | − | 0.484688i | \(-0.161067\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 63.7471i | 0.163036i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1140.67 | 2.90246 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −125.336 | − | 72.3628i | −0.317307 | − | 0.183197i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 138.416 | + | 239.743i | 0.348654 | + | 0.603886i | 0.986011 | − | 0.166683i | \(-0.0533055\pi\) |
−0.637357 | + | 0.770569i | \(0.719972\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 680.905 | + | 763.536i | 1.70653 | + | 1.91362i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 311.419 | + | 539.394i | 0.776606 | + | 1.34512i | 0.933887 | + | 0.357567i | \(0.116394\pi\) |
−0.157281 | + | 0.987554i | \(0.550273\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −254.040 | − | 146.670i | −0.630372 | − | 0.363946i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −14.0187 | −0.0346141 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 746.978i | − | 1.83533i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −36.1189 | + | 62.5598i | −0.0883103 | + | 0.152958i | −0.906797 | − | 0.421568i | \(-0.861480\pi\) |
0.818487 | + | 0.574525i | \(0.194813\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −543.244 | + | 313.642i | −1.32176 | + | 0.763120i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 128.531 | + | 619.241i | 0.311212 | + | 1.49937i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −73.1088 | + | 42.2094i | −0.176166 | + | 0.101709i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −135.341 | + | 234.417i | −0.324558 | + | 0.562152i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 331.864i | 0.792039i | 0.918242 | + | 0.396020i | \(0.129609\pi\) | ||||
−0.918242 | + | 0.396020i | \(0.870391\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −685.770 | −1.62891 | −0.814454 | − | 0.580228i | \(-0.802963\pi\) | ||||
−0.814454 | + | 0.580228i | \(0.802963\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 487.619 | + | 281.527i | 1.15276 | + | 0.665548i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −23.5277 | − | 40.7511i | −0.0553592 | − | 0.0958850i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 193.494 | − | 585.960i | 0.453147 | − | 1.37227i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 556.400 | + | 963.713i | 1.29697 | + | 2.24642i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −520.232 | − | 300.356i | −1.20703 | − | 0.696882i | −0.244924 | − | 0.969542i | \(-0.578763\pi\) |
−0.962110 | + | 0.272661i | \(0.912096\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 281.591 | 0.650326 | 0.325163 | − | 0.945658i | \(-0.394581\pi\) | ||||
0.325163 | + | 0.945658i | \(0.394581\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 53.9265i | − | 0.123969i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 397.575 | − | 688.621i | 0.909784 | − | 1.57579i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −74.2090 | + | 42.8446i | −0.169041 | + | 0.0975958i | −0.582134 | − | 0.813093i | \(-0.697782\pi\) |
0.413093 | + | 0.910689i | \(0.364449\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −667.910 | + | 289.748i | −1.51454 | + | 0.657025i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −317.017 | + | 183.030i | −0.715613 | + | 0.413159i | −0.813136 | − | 0.582074i | \(-0.802241\pi\) |
0.0975227 | + | 0.995233i | \(0.468908\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 102.587 | − | 177.685i | 0.230532 | − | 0.399293i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 121.746i | 0.272362i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −189.922 | −0.422989 | −0.211494 | − | 0.977379i | \(-0.567833\pi\) | ||||
−0.211494 | + | 0.977379i | \(0.567833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 457.787 | + | 264.303i | 1.01505 | + | 0.586038i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −33.7847 | − | 58.5169i | −0.0745800 | − | 0.129176i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 75.6698 | − | 229.152i | 0.166307 | − | 0.503631i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −309.139 | − | 535.445i | −0.676453 | − | 1.17165i | −0.976042 | − | 0.217583i | \(-0.930183\pi\) |
0.299589 | − | 0.954068i | \(-0.403150\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 59.4430 | + | 34.3194i | 0.129505 | + | 0.0747700i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −191.089 | −0.414509 | −0.207254 | − | 0.978287i | \(-0.566453\pi\) | ||||
−0.207254 | + | 0.978287i | \(0.566453\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 61.7661i | 0.133404i | 0.997773 | + | 0.0667021i | \(0.0212477\pi\) | ||||
−0.997773 | + | 0.0667021i | \(0.978752\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 111.874 | − | 193.771i | 0.240589 | − | 0.416712i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 66.2316 | − | 38.2388i | 0.141824 | − | 0.0818819i | −0.427409 | − | 0.904058i | \(-0.640574\pi\) |
0.569233 | + | 0.822176i | \(0.307240\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.7891 | − | 119.430i | −0.0528552 | − | 0.254648i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −364.802 | + | 210.619i | −0.774527 | + | 0.447174i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 455.647 | − | 789.204i | 0.963313 | − | 1.66851i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 586.946i | 1.23568i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 988.554 | 2.07244 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −61.4566 | − | 35.4820i | −0.128302 | − | 0.0740751i | 0.434475 | − | 0.900684i | \(-0.356934\pi\) |
−0.562777 | + | 0.826609i | \(0.690267\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −361.918 | − | 626.861i | −0.752429 | − | 1.30324i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 604.757 | + | 678.147i | 1.25209 | + | 1.40403i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.2373 | + | 29.8559i | 0.0355409 | + | 0.0615586i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −707.416 | − | 408.427i | −1.45260 | − | 0.838659i | −0.453972 | − | 0.891016i | \(-0.649993\pi\) |
−0.998628 | + | 0.0523570i | \(0.983327\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −757.049 | −1.54816 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 200.042i | − | 0.407417i | −0.979032 | − | 0.203708i | \(-0.934701\pi\) | ||
0.979032 | − | 0.203708i | \(-0.0652995\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.70700 | + | 9.88482i | −0.0115761 | + | 0.0200503i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −457.787 | + | 264.303i | −0.924822 | + | 0.533946i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −120.417 | + | 107.386i | −0.242288 | + | 0.216068i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −72.7683 | + | 42.0128i | −0.145828 | + | 0.0841940i | −0.571139 | − | 0.820853i | \(-0.693498\pi\) |
0.425311 | + | 0.905047i | \(0.360165\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −584.067 | + | 1011.63i | −1.16580 | + | 2.01923i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 655.443i | − | 1.30307i | −0.758620 | − | 0.651533i | \(-0.774126\pi\) | ||
0.758620 | − | 0.651533i | \(-0.225874\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 40.4871 | 0.0801725 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 218.973 | + | 126.424i | 0.431899 | + | 0.249357i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −171.207 | − | 296.540i | −0.336360 | − | 0.582593i | 0.647385 | − | 0.762163i | \(-0.275863\pi\) |
−0.983745 | + | 0.179570i | \(0.942529\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −469.215 | + | 97.3911i | −0.918229 | + | 0.190589i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −428.084 | − | 741.463i | −0.834472 | − | 1.44535i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −176.061 | − | 101.649i | −0.341865 | − | 0.197376i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 581.054 | 1.12390 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 530.423i | − | 1.02201i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −153.678 | + | 266.179i | −0.294968 | + | 0.510900i | −0.974977 | − | 0.222304i | \(-0.928642\pi\) |
0.680009 | + | 0.733203i | \(0.261976\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.5522 | + | 17.0620i | −0.0565052 | + | 0.0326233i | −0.527986 | − | 0.849253i | \(-0.677053\pi\) |
0.471481 | + | 0.881876i | \(0.343719\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −636.888 | − | 210.311i | −1.21312 | − | 0.400592i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −41.0133 | + | 23.6790i | −0.0778241 | + | 0.0449318i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 88.6134 | − | 153.483i | 0.167511 | − | 0.290138i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1342.41i | − | 2.52809i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 512.230 | 0.961033 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 176.659 | + | 101.994i | 0.330203 | + | 0.190643i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −406.383 | − | 703.877i | −0.756766 | − | 1.31076i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −447.414 | + | 603.583i | −0.830082 | + | 1.11982i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −383.984 | − | 665.079i | −0.709767 | − | 1.22935i | −0.964944 | − | 0.262458i | \(-0.915467\pi\) |
0.255177 | − | 0.966894i | \(-0.417866\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −75.8774 | − | 43.8078i | −0.139737 | − | 0.0806774i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −480.113 | −0.880942 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 321.892i | − | 0.588468i | −0.955733 | − | 0.294234i | \(-0.904935\pi\) | ||
0.955733 | − | 0.294234i | \(-0.0950645\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −654.907 | + | 1134.33i | −1.19291 | + | 2.06618i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 123.298 | − | 71.1864i | 0.223772 | − | 0.129195i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 414.606 | + | 136.910i | 0.749739 | + | 0.247576i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 478.143 | − | 276.056i | 0.861520 | − | 0.497399i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −427.107 | + | 739.771i | −0.766799 | + | 1.32814i | 0.172491 | + | 0.985011i | \(0.444819\pi\) |
−0.939290 | + | 0.343124i | \(0.888515\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 883.062i | − | 1.57972i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 179.655 | 0.320241 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 237.695 | + | 137.233i | 0.422194 | + | 0.243754i | 0.696016 | − | 0.718027i | \(-0.254954\pi\) |
−0.273821 | + | 0.961781i | \(0.588288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −227.161 | − | 393.454i | −0.402054 | − | 0.696379i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 41.4108 | − | 8.59529i | 0.0730349 | − | 0.0151593i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 490.671 | + | 849.867i | 0.862339 | + | 1.49362i | 0.869665 | + | 0.493642i | \(0.164335\pi\) |
−0.00732570 | + | 0.999973i | \(0.502332\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 100.747 | + | 58.1661i | 0.176439 | + | 0.101867i | 0.585619 | − | 0.810587i | \(-0.300852\pi\) |
−0.409179 | + | 0.912454i | \(0.634185\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −251.551 | −0.439008 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 521.306i | 0.906619i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 146.753 | − | 254.184i | 0.254339 | − | 0.440527i | −0.710377 | − | 0.703821i | \(-0.751476\pi\) |
0.964716 | + | 0.263294i | \(0.0848089\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 303.537 | − | 175.247i | 0.524244 | − | 0.302672i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 190.081 | − | 169.510i | 0.327161 | − | 0.291756i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 883.483 | − | 510.079i | 1.51541 | − | 0.874921i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −256.115 | + | 443.605i | −0.437804 | + | 0.758298i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 307.133i | − | 0.523224i | −0.965173 | − | 0.261612i | \(-0.915746\pi\) | ||
0.965173 | − | 0.261612i | \(-0.0842541\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 590.722 | 1.00292 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −242.492 | − | 140.003i | −0.410308 | − | 0.236891i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −233.319 | − | 404.121i | −0.393456 | − | 0.681486i | 0.599447 | − | 0.800415i | \(-0.295387\pi\) |
−0.992903 | + | 0.118929i | \(0.962054\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25.9306 | − | 29.0774i | −0.0435809 | − | 0.0488696i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 256.456 | + | 444.194i | 0.429574 | + | 0.744044i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 529.994 | + | 305.992i | 0.884798 | + | 0.510838i | 0.872237 | − | 0.489083i | \(-0.162668\pi\) |
0.0125605 | + | 0.999921i | \(0.496002\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 133.327 | 0.221842 | 0.110921 | − | 0.993829i | \(-0.464620\pi\) | ||||
0.110921 | + | 0.993829i | \(0.464620\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 258.905i | 0.429361i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −132.378 | + | 229.286i | −0.218807 | + | 0.378985i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 783.900 | − | 452.585i | 1.29143 | − | 0.745610i | 0.312525 | − | 0.949909i | \(-0.398825\pi\) |
0.978908 | + | 0.204300i | \(0.0654917\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 33.0639 | + | 159.297i | 0.0542922 | + | 0.261571i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 487.619 | − | 281.527i | 0.798066 | − | 0.460764i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −137.160 | + | 237.569i | −0.223753 | + | 0.387551i | −0.955945 | − | 0.293547i | \(-0.905164\pi\) |
0.732192 | + | 0.681099i | \(0.238497\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 390.708i | 0.635298i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −255.450 | −0.414019 | −0.207010 | − | 0.978339i | \(-0.566373\pi\) | ||||
−0.207010 | + | 0.978339i | \(0.566373\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 375.221 | + | 216.634i | 0.606173 | + | 0.349974i | 0.771466 | − | 0.636270i | \(-0.219524\pi\) |
−0.165293 | + | 0.986244i | \(0.552857\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −380.210 | − | 658.543i | −0.612254 | − | 1.06046i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −194.093 | + | 587.775i | −0.311546 | + | 0.943458i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −125.108 | − | 216.694i | −0.200173 | − | 0.346711i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1940.71 | − | 1120.47i | −3.09522 | − | 1.78703i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −116.859 | −0.185786 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 339.246i | − | 0.537632i | −0.963192 | − | 0.268816i | \(-0.913368\pi\) | ||
0.963192 | − | 0.268816i | \(-0.0866324\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.10948 | + | 7.11784i | −0.00649208 | + | 0.0112446i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −376.995 | + | 217.658i | −0.593693 | + | 0.342769i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −83.0258 | + | 723.301i | −0.130339 | + | 1.13548i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 296.587 | − | 171.234i | 0.464142 | − | 0.267973i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −445.832 | + | 772.203i | −0.695526 | + | 1.20469i | 0.274478 | + | 0.961593i | \(0.411495\pi\) |
−0.970003 | + | 0.243092i | \(0.921838\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 535.530i | − | 0.832861i | −0.909167 | − | 0.416431i | \(-0.863281\pi\) | ||
0.909167 | − | 0.416431i | \(-0.136719\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 673.563 | 1.04428 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −329.954 | − | 190.499i | −0.509975 | − | 0.294434i | 0.222848 | − | 0.974853i | \(-0.428465\pi\) |
−0.732823 | + | 0.680419i | \(0.761798\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −692.666 | − | 1199.73i | −1.06728 | − | 1.84859i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −211.664 | + | 640.986i | −0.325137 | + | 0.984617i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −205.764 | − | 356.393i | −0.315105 | − | 0.545778i | 0.664355 | − | 0.747417i | \(-0.268706\pi\) |
−0.979460 | + | 0.201639i | \(0.935373\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 469.251 | + | 270.922i | 0.716413 | + | 0.413622i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1017.18 | 1.54822 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 949.241i | − | 1.44043i | −0.693753 | − | 0.720213i | \(-0.744044\pi\) | ||
0.693753 | − | 0.720213i | \(-0.255956\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −356.235 | + | 617.018i | −0.538934 | + | 0.933461i | 0.460028 | + | 0.887905i | \(0.347839\pi\) |
−0.998962 | + | 0.0455565i | \(0.985494\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 150.766 | − | 87.0448i | 0.227400 | − | 0.131289i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 98.7638 | + | 475.828i | 0.148517 | + | 0.715531i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 109.510 | − | 63.2254i | 0.164182 | − | 0.0947907i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 603.354 | − | 1045.04i | 0.901874 | − | 1.56209i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1351.69i | 2.01444i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1229.52 | −1.82692 | −0.913462 | − | 0.406925i | \(-0.866601\pi\) | ||||
−0.913462 | + | 0.406925i | \(0.866601\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 486.108 | + | 280.655i | 0.720160 | + | 0.415784i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 658.050 | + | 1139.78i | 0.972008 | + | 1.68357i | 0.689473 | + | 0.724311i | \(0.257842\pi\) |
0.282535 | + | 0.959257i | \(0.408825\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −69.2239 | − | 77.6245i | −0.101950 | − | 0.114322i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 432.856 | + | 749.729i | 0.635618 | + | 1.10092i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −186.553 | − | 107.706i | −0.273138 | − | 0.157696i | 0.357175 | − | 0.934037i | \(-0.383740\pi\) |
−0.630313 | + | 0.776341i | \(0.717073\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −297.975 | −0.435000 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 555.546i | 0.808655i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 494.277 | − | 856.113i | 0.717383 | − | 1.24254i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −377.039 | + | 217.684i | −0.545643 | + | 0.315027i | −0.747363 | − | 0.664416i | \(-0.768680\pi\) |
0.201720 | + | 0.979443i | \(0.435347\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1190.23 | − | 1061.42i | 1.71751 | − | 1.53164i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −111.354 | + | 64.2901i | −0.160221 | + | 0.0925038i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 41.3483 | − | 71.6174i | 0.0593233 | − | 0.102751i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 285.378i | 0.408266i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 134.132 | 0.191344 | 0.0956722 | − | 0.995413i | \(-0.469500\pi\) | ||||
0.0956722 | + | 0.995413i | \(0.469500\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1262.36 | + | 728.823i | 1.79567 | + | 1.03673i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 214.737 | + | 371.935i | 0.304591 | + | 0.527568i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −119.597 | + | 24.8238i | −0.169162 | + | 0.0351115i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −576.723 | − | 998.913i | −0.813431 | − | 1.40890i | −0.910449 | − | 0.413621i | \(-0.864264\pi\) |
0.0970181 | − | 0.995283i | \(-0.469070\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −802.616 | − | 463.390i | −1.12885 | − | 0.651745i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 524.660 | 0.735848 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 528.607i | 0.739310i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 313.560 | − | 543.101i | 0.437322 | − | 0.757463i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −109.915 | + | 63.4596i | −0.152872 | + | 0.0882609i | −0.574485 | − | 0.818515i | \(-0.694798\pi\) |
0.421613 | + | 0.906776i | \(0.361464\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 582.400 | + | 192.318i | 0.807767 | + | 0.266738i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1263.20 | + | 729.307i | −1.74716 | + | 1.00872i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −46.6703 | + | 80.8353i | −0.0643728 | + | 0.111497i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 141.915i | 0.195206i | 0.995225 | + | 0.0976029i | \(0.0311175\pi\) | ||||
−0.995225 | + | 0.0976029i | \(0.968882\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1168.12 | 1.60236 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −123.465 | − | 71.2827i | −0.168899 | − | 0.0975139i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −604.395 | − | 1046.84i | −0.824550 | − | 1.42816i | −0.902263 | − | 0.431187i | \(-0.858095\pi\) |
0.0777128 | − | 0.996976i | \(-0.475238\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −551.704 | − | 63.3287i | −0.750618 | − | 0.0861615i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 133.591 | + | 231.387i | 0.181263 | + | 0.313957i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 854.802 | + | 493.520i | 1.15670 | + | 0.667821i | 0.950511 | − | 0.310691i | \(-0.100560\pi\) |
0.206189 | + | 0.978512i | \(0.433894\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2171.51 | −2.93051 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 370.978i | 0.499297i | 0.968336 | + | 0.249649i | \(0.0803151\pi\) | ||||
−0.968336 | + | 0.249649i | \(0.919685\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.9160 | + | 50.0841i | −0.0388135 | + | 0.0672269i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −468.167 | + | 270.297i | −0.626730 | + | 0.361843i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −584.379 | − | 192.972i | −0.780212 | − | 0.257639i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −781.000 | + | 450.911i | −1.03995 | + | 0.600414i | −0.919818 | − | 0.392345i | \(-0.871664\pi\) |
−0.120129 | + | 0.992758i | \(0.538331\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 220.253 | − | 381.490i | 0.292501 | − | 0.506627i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 32.0971i | − | 0.0425127i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 696.663 | 0.920295 | 0.460147 | − | 0.887842i | \(-0.347797\pi\) | ||||
0.460147 | + | 0.887842i | \(0.347797\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1723.67 | − | 995.162i | −2.27098 | − | 1.31115i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 242.666 | + | 420.310i | 0.318878 | + | 0.552312i | 0.980254 | − | 0.197742i | \(-0.0633607\pi\) |
−0.661376 | + | 0.750054i | \(0.730027\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1418.24 | − | 294.372i | 1.85876 | − | 0.385808i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 41.3483 | + | 71.6174i | 0.0540501 | + | 0.0936176i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1162.56 | − | 671.207i | −1.51573 | − | 0.875106i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −810.918 | −1.05451 | −0.527255 | − | 0.849707i | \(-0.676779\pi\) | ||||
−0.527255 | + | 0.849707i | \(0.676779\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1316.54i | 1.70758i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 410.825 | − | 711.569i | 0.531468 | − | 0.920529i | −0.467858 | − | 0.883804i | \(-0.654974\pi\) |
0.999325 | − | 0.0367254i | \(-0.0116927\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −335.395 | + | 193.641i | −0.432768 | + | 0.249859i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1243.16 | + | 1108.62i | −1.59995 | + | 1.42680i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −893.322 | + | 515.759i | −1.14675 | + | 0.662079i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 176.709 | − | 306.069i | 0.226260 | − | 0.391893i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 136.154i | − | 0.173888i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −200.098 | −0.254902 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 442.326 | + | 255.377i | 0.562041 | + | 0.324494i | 0.753964 | − | 0.656916i | \(-0.228139\pi\) |
−0.191924 | + | 0.981410i | \(0.561473\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 901.360 | + | 1561.20i | 1.14241 | + | 1.97871i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 912.262 | + | 1022.97i | 1.15330 | + | 1.29326i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 654.907 | + | 1134.33i | 0.825860 | + | 1.43043i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 653.007 | + | 377.014i | 0.821393 | + | 0.474231i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1252.13 | 1.57106 | 0.785528 | − | 0.618826i | \(-0.212392\pi\) | ||||
0.785528 | + | 0.618826i | \(0.212392\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 90.9018i | − | 0.113769i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 656.935 | − | 1137.85i | 0.820144 | − | 1.42053i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 909.069 | − | 524.851i | 1.13209 | − | 0.653613i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 87.7187 | + | 422.615i | 0.108967 | + | 0.524988i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1902.78 | − | 1098.57i | 2.35785 | − | 1.36130i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.4418 | + | 61.3870i | −0.0438094 | + | 0.0758802i | −0.887099 | − | 0.461580i | \(-0.847283\pi\) |
0.843289 | + | 0.537460i | \(0.180616\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 501.734i | − | 0.618661i | −0.950955 | − | 0.309330i | \(-0.899895\pi\) | ||
0.950955 | − | 0.309330i | \(-0.100105\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 564.053 | 0.693793 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −311.437 | − | 179.808i | −0.382131 | − | 0.220624i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 889.146 | + | 1540.05i | 1.08831 | + | 1.88500i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 484.567 | − | 1467.42i | 0.591657 | − | 1.79172i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −225.044 | − | 389.788i | −0.274110 | − | 0.474772i | 0.695800 | − | 0.718235i | \(-0.255050\pi\) |
−0.969910 | + | 0.243463i | \(0.921716\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 890.836 | + | 514.324i | 1.08243 | + | 0.624938i | 0.931550 | − | 0.363614i | \(-0.118457\pi\) |
0.150876 | + | 0.988553i | \(0.451791\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1469.17 | 1.78081 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 731.829i | 0.884921i | 0.896788 | + | 0.442460i | \(0.145894\pi\) | ||||
−0.896788 | + | 0.442460i | \(0.854106\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −594.397 | + | 1029.53i | −0.717005 | + | 1.24189i | 0.245176 | + | 0.969479i | \(0.421154\pi\) |
−0.962181 | + | 0.272411i | \(0.912179\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −387.331 | + | 223.626i | −0.466102 | + | 0.269104i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 94.4263 | + | 69.9947i | 0.113357 | + | 0.0840272i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −480.550 | + | 277.446i | −0.575509 | + | 0.332270i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 282.460 | − | 489.235i | 0.337467 | − | 0.584511i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 774.801i | 0.923482i | 0.887015 | + | 0.461741i | \(0.152775\pi\) | ||||
−0.887015 | + | 0.461741i | \(0.847225\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −818.359 | −0.973078 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −449.830 | − | 259.710i | −0.533607 | − | 0.308078i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 60.0544 | + | 104.017i | 0.0710703 | + | 0.123097i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 250.459 | − | 758.467i | 0.295701 | − | 0.895475i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 141.133 | + | 244.450i | 0.166235 | + | 0.287927i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1121.19 | + | 647.317i | 1.31749 | + | 0.760654i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 359.661 | 0.421642 | 0.210821 | − | 0.977525i | \(-0.432386\pi\) | ||||
0.210821 | + | 0.977525i | \(0.432386\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1031.52i | − | 1.20645i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −476.449 | + | 825.234i | −0.555950 | + | 0.962933i | 0.441879 | + | 0.897075i | \(0.354312\pi\) |
−0.997829 | + | 0.0658586i | \(0.979021\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 973.259 | − | 561.911i | 1.13301 | − | 0.654146i | 0.188323 | − | 0.982107i | \(-0.439695\pi\) |
0.944691 | + | 0.327961i | \(0.106362\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −239.555 | − | 1154.14i | −0.278228 | − | 1.34046i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 94.4467 | − | 54.5288i | 0.109440 | − | 0.0631852i | −0.444281 | − | 0.895888i | \(-0.646541\pi\) |
0.553721 | + | 0.832702i | \(0.313207\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 125.982 | − | 218.207i | 0.145644 | − | 0.252262i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1383.51i | 1.59574i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −956.410 | −1.10059 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 224.218 | + | 129.452i | 0.257426 | + | 0.148625i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 110.383 | + | 191.189i | 0.126441 | + | 0.219002i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −482.303 | − | 540.832i | −0.551203 | − | 0.618094i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −337.620 | − | 584.775i | −0.384971 | − | 0.666790i | 0.606794 | − | 0.794859i | \(-0.292455\pi\) |
−0.991765 | + | 0.128069i | \(0.959122\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1295.12 | + | 747.736i | 1.47340 | + | 0.850667i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 297.930 | 0.338173 | 0.169086 | − | 0.985601i | \(-0.445918\pi\) | ||||
0.169086 | + | 0.985601i | \(0.445918\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 171.710i | − | 0.194462i | −0.995262 | − | 0.0972309i | \(-0.969001\pi\) | ||
0.995262 | − | 0.0972309i | \(-0.0309985\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 511.969 | − | 886.756i | 0.578496 | − | 1.00198i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 422.073 | − | 243.684i | 0.475843 | − | 0.274728i | −0.242839 | − | 0.970067i | \(-0.578079\pi\) |
0.718683 | + | 0.695338i | \(0.244745\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 980.176 | − | 874.101i | 1.10256 | − | 0.983240i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −80.2302 | + | 46.3210i | −0.0900452 | + | 0.0519876i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −566.933 | + | 981.956i | −0.634863 | + | 1.09961i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 386.084i | − | 0.431378i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1928.66 | −2.15013 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 81.3553 | + | 46.9705i | 0.0904954 | + | 0.0522475i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −79.7982 | − | 138.215i | −0.0885663 | − | 0.153401i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1989.68 | + | 412.981i | −2.20341 | + | 0.457344i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.8098 | − | 36.0436i | −0.0229942 | − | 0.0398272i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −724.366 | − | 418.213i | −0.798639 | − | 0.461094i | 0.0443561 | − | 0.999016i | \(-0.485876\pi\) |
−0.842995 | + | 0.537921i | \(0.819210\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 259.268 | 0.285223 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1663.72i | − | 1.82626i | −0.407672 | − | 0.913128i | \(-0.633659\pi\) | ||
0.407672 | − | 0.913128i | \(-0.366341\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −278.938 | + | 483.135i | −0.305518 | + | 0.529173i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −865.222 | + | 499.536i | −0.945597 | + | 0.545941i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1552.26 | − | 512.582i | −1.69276 | − | 0.558977i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1317.95 | + | 760.919i | −1.43411 | + | 0.827985i | −0.997431 | − | 0.0716307i | \(-0.977180\pi\) |
−0.436682 | + | 0.899616i | \(0.643846\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.6165 | − | 33.9767i | 0.0212991 | − | 0.0368911i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 342.469i | − | 0.371039i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −955.642 | −1.03313 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1127.44 | − | 650.928i | −1.21622 | − | 0.702188i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −163.801 | − | 283.712i | −0.176320 | − | 0.305395i | 0.764297 | − | 0.644864i | \(-0.223086\pi\) |
−0.940617 | + | 0.339469i | \(0.889753\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −583.489 | − | 1345.02i | −0.626733 | − | 1.44471i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.6366 | + | 27.0835i | 0.0167595 | + | 0.0290284i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 73.9071 | + | 42.6703i | 0.0790450 | + | 0.0456367i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −480.629 | −0.512945 | −0.256472 | − | 0.966552i | \(-0.582560\pi\) | ||||
−0.256472 | + | 0.966552i | \(0.582560\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 263.339i | − | 0.280446i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −384.142 | + | 665.353i | −0.408227 | + | 0.707071i | −0.994691 | − | 0.102905i | \(-0.967186\pi\) |
0.586464 | + | 0.809975i | \(0.300520\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −793.419 | + | 458.081i | −0.841377 | + | 0.485769i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 441.306 | + | 145.726i | 0.466990 | + | 0.154208i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 295.937 | − | 170.859i | 0.312499 | − | 0.180421i | −0.335545 | − | 0.942024i | \(-0.608921\pi\) |
0.648044 | + | 0.761603i | \(0.275587\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 508.591 | − | 880.906i | 0.535923 | − | 0.928246i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 378.373i | − | 0.397869i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.4379 | −0.0235445 | −0.0117722 | − | 0.999931i | \(-0.503747\pi\) | ||||
−0.0117722 | + | 0.999931i | \(0.503747\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −103.484 | − | 59.7464i | −0.108360 | − | 0.0625617i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −178.185 | − | 308.626i | −0.186191 | − | 0.322493i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 880.207 | − | 182.697i | 0.917838 | − | 0.190508i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −285.614 | − | 494.697i | −0.297205 | − | 0.514773i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1131.27 | + | 653.140i | 1.17474 | + | 0.678235i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 166.493 | 0.172532 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1543.81i | 1.59649i | 0.602332 | + | 0.798246i | \(0.294238\pi\) | ||||
−0.602332 | + | 0.798246i | \(0.705762\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −175.289 | + | 303.609i | −0.180897 | + | 0.313322i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −205.420 | + | 118.599i | −0.211555 | + | 0.122142i | −0.602034 | − | 0.798470i | \(-0.705643\pi\) |
0.390479 | + | 0.920612i | \(0.372310\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 289.517 | − | 258.185i | 0.297550 | − | 0.265349i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1232.92 | − | 711.828i | 1.26454 | − | 0.730080i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 445.109 | − | 770.952i | 0.455588 | − | 0.789101i | −0.543134 | − | 0.839646i | \(-0.682762\pi\) |
0.998722 | + | 0.0505447i | \(0.0160957\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1355.88i | − | 1.38496i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3074.51 | −3.13405 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1169.43 | − | 675.170i | −1.18965 | − | 0.686847i | −0.231426 | − | 0.972853i | \(-0.574339\pi\) |
−0.958228 | + | 0.286006i | \(0.907672\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −66.5047 | − | 115.190i | −0.0675175 | − | 0.116944i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −862.369 | − | 967.021i | −0.873727 | − | 0.979757i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 789.710 | + | 1367.82i | 0.798494 | + | 1.38303i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 943.699 | + | 544.845i | 0.952269 | + | 0.549793i | 0.893785 | − | 0.448496i | \(-0.148040\pi\) |
0.0584839 | + | 0.998288i | \(0.481373\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1647.23 | −1.65884 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 243.645i | 0.244870i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 302.176 | − | 523.384i | 0.303085 | − | 0.524959i | −0.673748 | − | 0.738961i | \(-0.735317\pi\) |
0.976833 | + | 0.214002i | \(0.0686499\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1207.22 | − | 696.990i | 1.20843 | − | 0.697687i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 224.3.r.d.95.6 | yes | 12 | |
4.3 | odd | 2 | inner | 224.3.r.d.95.1 | ✓ | 12 | |
7.2 | even | 3 | inner | 224.3.r.d.191.1 | yes | 12 | |
7.3 | odd | 6 | 1568.3.d.l.1471.6 | 6 | |||
7.4 | even | 3 | 1568.3.d.i.1471.1 | 6 | |||
8.3 | odd | 2 | 448.3.r.f.319.6 | 12 | |||
8.5 | even | 2 | 448.3.r.f.319.1 | 12 | |||
28.3 | even | 6 | 1568.3.d.l.1471.1 | 6 | |||
28.11 | odd | 6 | 1568.3.d.i.1471.6 | 6 | |||
28.23 | odd | 6 | inner | 224.3.r.d.191.6 | yes | 12 | |
56.37 | even | 6 | 448.3.r.f.191.6 | 12 | |||
56.51 | odd | 6 | 448.3.r.f.191.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.r.d.95.1 | ✓ | 12 | 4.3 | odd | 2 | inner | |
224.3.r.d.95.6 | yes | 12 | 1.1 | even | 1 | trivial | |
224.3.r.d.191.1 | yes | 12 | 7.2 | even | 3 | inner | |
224.3.r.d.191.6 | yes | 12 | 28.23 | odd | 6 | inner | |
448.3.r.f.191.1 | 12 | 56.51 | odd | 6 | |||
448.3.r.f.191.6 | 12 | 56.37 | even | 6 | |||
448.3.r.f.319.1 | 12 | 8.5 | even | 2 | |||
448.3.r.f.319.6 | 12 | 8.3 | odd | 2 | |||
1568.3.d.i.1471.1 | 6 | 7.4 | even | 3 | |||
1568.3.d.i.1471.6 | 6 | 28.11 | odd | 6 | |||
1568.3.d.l.1471.1 | 6 | 28.3 | even | 6 | |||
1568.3.d.l.1471.6 | 6 | 7.3 | odd | 6 |