Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(353,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.353");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.m (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: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 353.8 | ||
Character | \(\chi\) | \(=\) | 684.353 |
Dual form | 684.3.m.a.653.8 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.55262 | − | 1.57611i | −0.850873 | − | 0.525372i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9.08186i | 1.81637i | 0.418567 | + | 0.908186i | \(0.362532\pi\) | ||||
−0.418567 | + | 0.908186i | \(0.637468\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.71777 | − | 6.43936i | 0.531110 | − | 0.919909i | −0.468231 | − | 0.883606i | \(-0.655109\pi\) |
0.999341 | − | 0.0363030i | \(-0.0115581\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.03172 | + | 8.04644i | 0.447969 | + | 0.894049i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.75893 | − | 2.17022i | −0.341721 | − | 0.197293i | 0.319312 | − | 0.947650i | \(-0.396548\pi\) |
−0.661033 | + | 0.750357i | \(0.729882\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.81239 | − | 10.0674i | 0.447107 | − | 0.774412i | −0.551089 | − | 0.834446i | \(-0.685788\pi\) |
0.998196 | + | 0.0600340i | \(0.0191209\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 14.3141 | − | 23.1825i | 0.954270 | − | 1.54550i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18.6676 | + | 10.7777i | 1.09809 | + | 0.633985i | 0.935720 | − | 0.352745i | \(-0.114752\pi\) |
0.162374 | + | 0.986729i | \(0.448085\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9.10009 | − | 16.6790i | −0.478952 | − | 0.877841i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −19.6392 | + | 10.5776i | −0.935201 | + | 0.503696i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.34831 | − | 1.93315i | −0.145579 | − | 0.0840498i | 0.425441 | − | 0.904986i | \(-0.360119\pi\) |
−0.571020 | + | 0.820936i | \(0.693452\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −57.4802 | −2.29921 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.39066 | − | 26.8940i | 0.0885428 | − | 0.996072i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 50.7205i | 1.74898i | 0.485042 | + | 0.874491i | \(0.338804\pi\) | ||||
−0.485042 | + | 0.874491i | \(0.661196\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 17.5657 | + | 30.4248i | 0.566637 | + | 0.981444i | 0.996895 | + | 0.0787382i | \(0.0250891\pi\) |
−0.430258 | + | 0.902706i | \(0.641578\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.17460 | + | 11.4642i | 0.187109 | + | 0.347401i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 58.4814 | + | 33.7642i | 1.67090 | + | 0.964693i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 22.6583 | 0.612388 | 0.306194 | − | 0.951969i | \(-0.400944\pi\) | ||||
0.306194 | + | 0.951969i | \(0.400944\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −30.7041 | + | 16.5371i | −0.787286 | + | 0.424029i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 39.2048i | 0.956214i | 0.878301 | + | 0.478107i | \(0.158677\pi\) | ||||
−0.878301 | + | 0.478107i | \(0.841323\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.94146 | + | 6.82682i | 0.0916619 | + | 0.158763i | 0.908211 | − | 0.418514i | \(-0.137449\pi\) |
−0.816549 | + | 0.577277i | \(0.804115\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −73.0766 | + | 36.6156i | −1.62393 | + | 0.813679i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 66.6664i | − | 1.41843i | −0.704990 | − | 0.709217i | \(-0.749049\pi\) | ||
0.704990 | − | 0.709217i | \(-0.250951\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.14360 | − | 5.44487i | −0.0641551 | − | 0.111120i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −30.6643 | − | 56.9337i | −0.601261 | − | 1.11635i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.7574 | − | 6.21080i | 0.202970 | − | 0.117185i | −0.395070 | − | 0.918651i | \(-0.629280\pi\) |
0.598040 | + | 0.801466i | \(0.295946\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.7096 | − | 34.1381i | 0.358357 | − | 0.620692i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.05893 | + | 56.9179i | −0.0536654 | + | 0.998559i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 113.530i | 1.92424i | 0.272626 | + | 0.962120i | \(0.412108\pi\) | ||||
−0.272626 | + | 0.962120i | \(0.587892\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 100.522 | 1.64791 | 0.823955 | − | 0.566656i | \(-0.191763\pi\) | ||||
0.823955 | + | 0.566656i | \(0.191763\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 66.8030 | + | 3.95306i | 1.06036 | + | 0.0627469i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 91.4303 | + | 52.7873i | 1.40662 | + | 0.812113i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −36.7385 | + | 63.6330i | −0.548336 | + | 0.949746i | 0.450053 | + | 0.893002i | \(0.351405\pi\) |
−0.998389 | + | 0.0567438i | \(0.981928\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.50009 | + | 10.2119i | 0.0797115 | + | 0.147999i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.86289 | − | 1.65289i | −0.0403224 | − | 0.0232802i | 0.479703 | − | 0.877431i | \(-0.340744\pi\) |
−0.520026 | + | 0.854151i | \(0.674078\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 17.9246 | − | 31.0463i | 0.245542 | − | 0.425292i | −0.716742 | − | 0.697339i | \(-0.754367\pi\) |
0.962284 | + | 0.272047i | \(0.0877007\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 146.725 | + | 90.5953i | 1.95633 | + | 1.20794i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −27.9496 | + | 16.1367i | −0.362982 | + | 0.209568i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 63.5801 | + | 110.124i | 0.804812 | + | 1.39397i | 0.916418 | + | 0.400222i | \(0.131067\pi\) |
−0.111607 | + | 0.993752i | \(0.535600\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −48.4904 | + | 64.8821i | −0.598647 | + | 0.801013i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −76.8076 | − | 44.3449i | −0.925393 | − | 0.534276i | −0.0400412 | − | 0.999198i | \(-0.512749\pi\) |
−0.885351 | + | 0.464922i | \(0.846082\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −97.8819 | + | 169.536i | −1.15155 | + | 1.99455i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 79.9413 | − | 129.470i | 0.918865 | − | 1.48816i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 78.4512 | − | 45.2938i | 0.881474 | − | 0.508919i | 0.0103298 | − | 0.999947i | \(-0.496712\pi\) |
0.871144 | + | 0.491027i | \(0.163379\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −43.2183 | − | 74.8562i | −0.474926 | − | 0.822596i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.11427 | − | 105.348i | 0.0334867 | − | 1.13278i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 151.476 | − | 82.6457i | 1.59449 | − | 0.869955i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 29.8352 | + | 51.6761i | 0.307579 | + | 0.532743i | 0.977832 | − | 0.209390i | \(-0.0671477\pi\) |
−0.670253 | + | 0.742133i | \(0.733814\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.30757 | − | 38.9957i | 0.0233087 | − | 0.393896i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 160.036i | 1.58452i | 0.610185 | + | 0.792259i | \(0.291095\pi\) | ||||
−0.610185 | + | 0.792259i | \(0.708905\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.7614 | − | 29.0316i | −0.162732 | − | 0.281860i | 0.773116 | − | 0.634265i | \(-0.218697\pi\) |
−0.935848 | + | 0.352405i | \(0.885364\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −96.0644 | − | 178.361i | −0.914899 | − | 1.69867i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 113.499i | 1.06073i | 0.847768 | + | 0.530367i | \(0.177946\pi\) | ||||
−0.847768 | + | 0.530367i | \(0.822054\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −27.9996 | + | 48.4968i | −0.256877 | + | 0.444925i | −0.965404 | − | 0.260760i | \(-0.916027\pi\) |
0.708526 | + | 0.705684i | \(0.249360\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −57.8381 | − | 35.7121i | −0.521064 | − | 0.321731i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 27.7838 | − | 16.0410i | 0.245874 | − | 0.141955i | −0.372000 | − | 0.928233i | \(-0.621328\pi\) |
0.617874 | + | 0.786278i | \(0.287994\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.5566 | − | 30.4089i | 0.152666 | − | 0.264425i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 104.440 | + | 6.18024i | 0.892653 | + | 0.0528226i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 138.804 | − | 80.1383i | 1.16642 | − | 0.673431i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −51.0803 | − | 88.4737i | −0.422151 | − | 0.731187i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 61.7912 | − | 100.075i | 0.502368 | − | 0.813617i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 294.980i | − | 2.35984i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 113.530 | + | 196.639i | 0.893934 | + | 1.54834i | 0.835119 | + | 0.550070i | \(0.185399\pi\) |
0.0588151 | + | 0.998269i | \(0.481268\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.698790 | − | 23.6385i | 0.00541698 | − | 0.183244i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 80.7881i | 0.616703i | 0.951272 | + | 0.308352i | \(0.0997773\pi\) | ||||
−0.951272 | + | 0.308352i | \(0.900223\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −141.234 | − | 3.40980i | −1.06191 | − | 0.0256376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 244.247 | + | 21.7116i | 1.80924 | + | 0.160827i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 200.994i | − | 1.46711i | −0.679631 | − | 0.733555i | \(-0.737860\pi\) | ||
0.679631 | − | 0.733555i | \(-0.262140\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −115.620 | + | 200.259i | −0.831797 | + | 1.44072i | 0.0648140 | + | 0.997897i | \(0.479355\pi\) |
−0.896611 | + | 0.442818i | \(0.853979\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −105.074 | + | 170.174i | −0.745205 | + | 1.20691i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −43.6967 | + | 25.2283i | −0.305572 | + | 0.176422i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −460.636 | −3.17680 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.557335 | + | 18.8534i | −0.00379139 | + | 0.128254i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 215.584i | − | 1.44688i | −0.690390 | − | 0.723438i | \(-0.742561\pi\) | ||
0.690390 | − | 0.723438i | \(-0.257439\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 37.9858 | − | 65.7932i | 0.251561 | − | 0.435717i | −0.712395 | − | 0.701779i | \(-0.752389\pi\) |
0.963956 | + | 0.266062i | \(0.0857227\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.4598 | + | 193.661i | −0.0749009 | + | 1.26576i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −276.313 | + | 159.530i | −1.78267 | + | 1.02922i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −77.9228 | −0.496324 | −0.248162 | − | 0.968719i | \(-0.579826\pi\) | ||||
−0.248162 | + | 0.968719i | \(0.579826\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −37.2485 | − | 1.10113i | −0.234268 | − | 0.00692532i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.8965 | + | 14.3740i | −0.154636 | + | 0.0892794i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.6477 | 0.0837281 | 0.0418641 | − | 0.999123i | \(-0.486670\pi\) | ||||
0.0418641 | + | 0.999123i | \(0.486670\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −104.117 | + | 56.0768i | −0.631010 | + | 0.339860i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 55.3372 | + | 31.9490i | 0.331361 | + | 0.191311i | 0.656445 | − | 0.754374i | \(-0.272059\pi\) |
−0.325084 | + | 0.945685i | \(0.605393\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.9322 | + | 29.3274i | 0.100190 | + | 0.173535i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 97.5174 | − | 140.468i | 0.570277 | − | 0.821453i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −149.313 | + | 86.2059i | −0.863081 | + | 0.498300i | −0.865043 | − | 0.501698i | \(-0.832709\pi\) |
0.00196174 | + | 0.999998i | \(0.499376\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −213.698 | + | 370.136i | −1.22113 | + | 2.11506i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 178.937 | − | 289.799i | 1.01094 | − | 1.63728i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 58.2650i | − | 0.325503i | −0.986667 | − | 0.162751i | \(-0.947963\pi\) | ||
0.986667 | − | 0.162751i | \(-0.0520369\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −149.077 | − | 258.209i | −0.823631 | − | 1.42657i | −0.902961 | − | 0.429723i | \(-0.858611\pi\) |
0.0793295 | − | 0.996848i | \(-0.474722\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −256.596 | − | 158.435i | −1.40216 | − | 0.865765i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 205.780i | 1.11232i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −46.7801 | − | 81.0255i | −0.250161 | − | 0.433291i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −164.292 | − | 115.380i | −0.869270 | − | 0.610475i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −108.988 | − | 62.9245i | −0.570620 | − | 0.329448i | 0.186777 | − | 0.982402i | \(-0.440196\pi\) |
−0.757397 | + | 0.652955i | \(0.773529\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 77.3511 | 0.400783 | 0.200391 | − | 0.979716i | \(-0.435779\pi\) | ||||
0.200391 | + | 0.979716i | \(0.435779\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −150.188 | − | 278.851i | −0.770194 | − | 1.43000i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 107.228i | 0.544304i | 0.962254 | + | 0.272152i | \(0.0877354\pi\) | ||||
−0.962254 | + | 0.272152i | \(0.912265\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.3491 | − | 42.1738i | −0.122357 | − | 0.211929i | 0.798340 | − | 0.602207i | \(-0.205712\pi\) |
−0.920697 | + | 0.390279i | \(0.872379\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 194.072 | − | 104.527i | 0.965534 | − | 0.520033i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 326.608 | + | 188.567i | 1.60890 | + | 0.928901i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −356.052 | −1.73684 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.05549 | − | 34.7359i | 0.00992990 | − | 0.167806i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.99045 | + | 82.4443i | −0.00952367 | + | 0.394470i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.00077 | −0.0426577 | −0.0213288 | − | 0.999773i | \(-0.506790\pi\) | ||||
−0.0213288 | + | 0.999773i | \(0.506790\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.70273 | + | 8.73145i | 0.0220785 | + | 0.0409927i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −62.0002 | + | 35.7958i | −0.288373 | + | 0.166492i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 261.221 | 1.20379 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −94.6871 | + | 50.9981i | −0.432361 | + | 0.232868i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 217.007 | − | 125.289i | 0.981931 | − | 0.566918i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −116.684 | − | 202.102i | −0.523246 | − | 0.906288i | −0.999634 | − | 0.0270532i | \(-0.991388\pi\) |
0.476388 | − | 0.879235i | \(-0.341946\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −231.744 | − | 462.511i | −1.02997 | − | 2.05560i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 127.238 | + | 73.4611i | 0.560522 | + | 0.323617i | 0.753355 | − | 0.657614i | \(-0.228434\pi\) |
−0.192833 | + | 0.981232i | \(0.561768\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −109.935 | − | 190.413i | −0.480065 | − | 0.831496i | 0.519674 | − | 0.854365i | \(-0.326053\pi\) |
−0.999738 | + | 0.0228685i | \(0.992720\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 96.7781 | + | 2.86091i | 0.418953 | + | 0.0123849i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 87.1319 | + | 50.3056i | 0.373956 | + | 0.215904i | 0.675186 | − | 0.737648i | \(-0.264064\pi\) |
−0.301229 | + | 0.953552i | \(0.597397\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 605.455 | 2.57640 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.2722 | − | 381.314i | 0.0475622 | − | 1.60892i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 224.956 | − | 129.878i | 0.941237 | − | 0.543423i | 0.0508891 | − | 0.998704i | \(-0.483794\pi\) |
0.890348 | + | 0.455281i | \(0.150461\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 80.0410 | 0.332120 | 0.166060 | − | 0.986116i | \(-0.446895\pi\) | ||||
0.166060 | + | 0.986116i | \(0.446895\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 226.039 | − | 89.1928i | 0.930202 | − | 0.367048i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 49.4495 | − | 28.5497i | 0.201835 | − | 0.116529i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −220.807 | − | 5.33092i | −0.893954 | − | 0.0215827i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 126.168 | + | 234.253i | 0.506698 | + | 0.940776i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −99.7198 | + | 57.5732i | −0.397290 | + | 0.229375i | −0.685314 | − | 0.728248i | \(-0.740335\pi\) |
0.288024 | + | 0.957623i | \(0.407002\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.39070 | + | 14.5331i | 0.0331648 | + | 0.0574432i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 517.064 | − | 278.489i | 2.02770 | − | 1.09211i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 283.621 | + | 163.749i | 1.10358 | + | 0.637154i | 0.937160 | − | 0.348900i | \(-0.113445\pi\) |
0.166424 | + | 0.986054i | \(0.446778\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 84.2385 | − | 145.905i | 0.325245 | − | 0.563341i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −408.119 | + | 204.491i | −1.56368 | + | 0.783491i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −59.4198 | + | 34.3060i | −0.225931 | + | 0.130441i | −0.608693 | − | 0.793405i | \(-0.708306\pi\) |
0.382763 | + | 0.923847i | \(0.374973\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 56.4056 | + | 97.6974i | 0.212851 | + | 0.368670i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −271.644 | − | 8.03023i | −1.01739 | − | 0.0300758i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 59.6954 | + | 34.4652i | 0.221916 | + | 0.128123i | 0.606837 | − | 0.794826i | \(-0.292438\pi\) |
−0.384921 | + | 0.922949i | \(0.625771\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 156.478 | − | 271.029i | 0.577411 | − | 1.00011i | −0.418364 | − | 0.908280i | \(-0.637396\pi\) |
0.995775 | − | 0.0918261i | \(-0.0292704\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.66225 | + | 259.196i | −0.0280669 | + | 0.949437i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 216.064 | + | 124.744i | 0.785687 | + | 0.453616i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 253.618 | − | 439.279i | 0.915588 | − | 1.58584i | 0.109549 | − | 0.993981i | \(-0.465059\pi\) |
0.806039 | − | 0.591863i | \(-0.201607\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −173.991 | + | 264.006i | −0.623623 | + | 0.946258i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 462.014i | − | 1.64418i | −0.569359 | − | 0.822089i | \(-0.692809\pi\) | ||
0.569359 | − | 0.822089i | \(-0.307191\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 52.1104 | 0.184136 | 0.0920678 | − | 0.995753i | \(-0.470652\pi\) | ||||
0.0920678 | + | 0.995753i | \(0.470652\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −516.920 | − | 27.7808i | −1.81375 | − | 0.0974764i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 252.454 | + | 145.754i | 0.879630 | + | 0.507855i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 87.8193 | + | 152.108i | 0.303873 | + | 0.526324i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.28954 | − | 178.933i | 0.0181771 | − | 0.614890i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 209.042 | − | 120.691i | 0.713455 | − | 0.411913i | −0.0988841 | − | 0.995099i | \(-0.531527\pi\) |
0.812339 | + | 0.583186i | \(0.198194\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1031.06 | −3.49514 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −67.3521 | + | 95.9042i | −0.226775 | + | 0.322910i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −38.9234 | + | 22.4724i | −0.130178 | + | 0.0751586i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 58.6138 | 0.194730 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 252.236 | − | 408.512i | 0.832461 | − | 1.34822i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 912.931i | 2.99322i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.6736 | + | 18.4872i | −0.0347673 | + | 0.0602187i | −0.882885 | − | 0.469588i | \(-0.844402\pi\) |
0.848118 | + | 0.529807i | \(0.177736\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.97166 | + | 100.524i | −0.00961702 | + | 0.325322i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −228.456 | + | 131.899i | −0.734587 | + | 0.424114i | −0.820098 | − | 0.572223i | \(-0.806081\pi\) |
0.0855112 | + | 0.996337i | \(0.472748\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.08946 | −0.0258449 | −0.0129225 | − | 0.999917i | \(-0.504113\pi\) | ||||
−0.0129225 | + | 0.999917i | \(0.504113\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −35.9011 | + | 606.695i | −0.113972 | + | 1.92602i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 13.8994i | − | 0.0438466i | −0.999760 | − | 0.0219233i | \(-0.993021\pi\) | ||
0.999760 | − | 0.0219233i | \(-0.00697897\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 110.075 | − | 190.655i | 0.345061 | − | 0.597664i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 178.887 | − | 289.719i | 0.557280 | − | 0.902550i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.88496 | − | 409.435i | 0.0306036 | − | 1.26760i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −334.097 | + | 578.673i | −1.02799 | + | 1.78053i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 147.909 | − | 79.6632i | 0.452321 | − | 0.243618i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −429.289 | − | 247.850i | −1.30483 | − | 0.753344i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.4470 | − | 21.5588i | 0.0376041 | − | 0.0651322i | −0.846611 | − | 0.532212i | \(-0.821361\pi\) |
0.884215 | + | 0.467080i | \(0.154694\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 91.3522 | + | 182.319i | 0.274331 | + | 0.547504i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −577.906 | − | 333.654i | −1.72509 | − | 0.995982i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 435.422 | 1.29205 | 0.646027 | − | 0.763315i | \(-0.276429\pi\) | ||||
0.646027 | + | 0.763315i | \(0.276429\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −96.2037 | − | 2.84393i | −0.283787 | − | 0.00838918i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 152.486i | − | 0.447173i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 317.593 | 0.925926 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −92.7431 | + | 49.9511i | −0.268820 | + | 0.144786i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 295.665i | 0.852060i | 0.904709 | + | 0.426030i | \(0.140088\pi\) | ||||
−0.904709 | + | 0.426030i | \(0.859912\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −331.114 | + | 573.506i | −0.948750 | + | 1.64328i | −0.200687 | + | 0.979655i | \(0.564317\pi\) |
−0.748063 | + | 0.663628i | \(0.769016\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −256.856 | − | 180.386i | −0.731783 | − | 0.513920i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 244.745 | + | 141.304i | 0.693328 | + | 0.400293i | 0.804858 | − | 0.593468i | \(-0.202242\pi\) |
−0.111529 | + | 0.993761i | \(0.535575\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.0113 | − | 26.0004i | 0.0422855 | − | 0.0732406i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −480.620 | − | 14.2079i | −1.34627 | − | 0.0397980i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 197.563 | + | 114.063i | 0.550316 | + | 0.317725i | 0.749249 | − | 0.662288i | \(-0.230414\pi\) |
−0.198934 | + | 0.980013i | \(0.563748\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −195.377 | + | 303.560i | −0.541210 | + | 0.840888i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.05613 | + | 306.348i | −0.0249480 | + | 0.843934i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 281.958 | + | 162.789i | 0.772488 | + | 0.445996i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 224.046 | 0.610479 | 0.305239 | − | 0.952276i | \(-0.401264\pi\) | ||||
0.305239 | + | 0.952276i | \(0.401264\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −315.459 | + | 158.063i | −0.854902 | + | 0.428355i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 92.3613i | − | 0.248952i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −44.0874 | − | 76.3616i | −0.118197 | − | 0.204723i | 0.800856 | − | 0.598856i | \(-0.204378\pi\) |
−0.919053 | + | 0.394134i | \(0.871045\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −464.923 | + | 752.972i | −1.23979 | + | 2.00793i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 510.621 | + | 294.807i | 1.35443 | + | 0.781982i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −420.700 | −1.11003 | −0.555013 | − | 0.831841i | \(-0.687287\pi\) | ||||
−0.555013 | + | 0.831841i | \(0.687287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.1279 | − | 680.880i | 0.0528291 | − | 1.78709i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 264.276i | − | 0.690016i | −0.938600 | − | 0.345008i | \(-0.887876\pi\) | ||
0.938600 | − | 0.345008i | \(-0.112124\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −146.552 | − | 253.835i | −0.380653 | − | 0.659311i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −39.0407 | + | 59.2386i | −0.100880 | + | 0.153071i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 201.953i | − | 0.519160i | −0.965722 | − | 0.259580i | \(-0.916416\pi\) | ||
0.965722 | − | 0.259580i | \(-0.0835841\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −41.6699 | − | 72.1744i | −0.106573 | − | 0.184589i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 127.331 | − | 206.221i | 0.323998 | − | 0.524736i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1000.13 | + | 577.426i | −2.53198 | + | 1.46184i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −190.682 | + | 330.271i | −0.480308 | + | 0.831918i | −0.999745 | − | 0.0225909i | \(-0.992808\pi\) |
0.519437 | + | 0.854509i | \(0.326142\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 355.142 | + | 231.305i | 0.890081 | + | 0.579712i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 632.695i | − | 1.57779i | −0.614526 | − | 0.788896i | \(-0.710653\pi\) | ||
0.614526 | − | 0.788896i | \(-0.289347\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 408.396 | 1.01339 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −589.250 | − | 440.383i | −1.45494 | − | 1.08737i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −85.1711 | − | 49.1736i | −0.209266 | − | 0.120820i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 105.950 | − | 183.511i | 0.259047 | − | 0.448683i | −0.706940 | − | 0.707274i | \(-0.749925\pi\) |
0.965987 | + | 0.258591i | \(0.0832582\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −316.790 | + | 513.061i | −0.770777 | + | 1.24832i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 731.062 | + | 422.079i | 1.77013 | + | 1.02198i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 402.734 | − | 697.556i | 0.970443 | − | 1.68086i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 610.765 | − | 328.956i | 1.46466 | − | 0.788863i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.7373 | − | 8.50858i | 0.0351726 | − | 0.0203069i | −0.482311 | − | 0.876000i | \(-0.660202\pi\) |
0.517483 | + | 0.855693i | \(0.326869\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 106.884 | + | 185.129i | 0.253881 | + | 0.439735i | 0.964591 | − | 0.263750i | \(-0.0849594\pi\) |
−0.710710 | + | 0.703485i | \(0.751626\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 536.427 | − | 268.781i | 1.26815 | − | 0.635415i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1073.02 | − | 619.506i | −2.52474 | − | 1.45766i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 373.719 | − | 647.301i | 0.875221 | − | 1.51593i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 151.304 | + | 4.47278i | 0.352690 | + | 0.0104261i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.09834 | − | 2.36618i | 0.00950891 | − | 0.00548997i | −0.495238 | − | 0.868757i | \(-0.664919\pi\) |
0.504747 | + | 0.863267i | \(0.331586\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 329.460 | + | 570.641i | 0.760877 | + | 1.31788i | 0.942399 | + | 0.334491i | \(0.108564\pi\) |
−0.181522 | + | 0.983387i | \(0.558102\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1175.83 | + | 726.016i | 2.70305 | + | 1.66900i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.77301 | + | 73.4382i | −0.00405724 | + | 0.168051i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 146.973 | + | 254.565i | 0.334791 | + | 0.579874i | 0.983445 | − | 0.181209i | \(-0.0580011\pi\) |
−0.648654 | + | 0.761083i | \(0.724668\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 31.1377 | − | 47.2470i | 0.0706070 | − | 0.107136i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 387.744i | 0.875269i | 0.899153 | + | 0.437634i | \(0.144184\pi\) | ||||
−0.899153 | + | 0.437634i | \(0.855816\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 411.352 | + | 712.482i | 0.924386 | + | 1.60108i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −339.786 | + | 550.305i | −0.760147 | + | 1.23111i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 732.714i | − | 1.63188i | −0.578137 | − | 0.815940i | \(-0.696220\pi\) | ||
0.578137 | − | 0.815940i | \(-0.303780\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 85.0830 | − | 147.368i | 0.188654 | − | 0.326758i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −200.661 | + | 108.075i | −0.442960 | + | 0.238577i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 679.834 | − | 392.502i | 1.49414 | − | 0.862642i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 208.608 | − | 361.319i | 0.456472 | − | 0.790632i | −0.542300 | − | 0.840185i | \(-0.682446\pi\) |
0.998772 | + | 0.0495528i | \(0.0157796\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 334.484 | − | 476.279i | 0.728723 | − | 1.03765i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −389.307 | + | 224.767i | −0.844484 | + | 0.487563i | −0.858786 | − | 0.512334i | \(-0.828781\pi\) |
0.0143016 | + | 0.999898i | \(0.495448\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −268.570 | − | 465.176i | −0.580064 | − | 1.00470i | −0.995471 | − | 0.0950649i | \(-0.969694\pi\) |
0.415407 | − | 0.909636i | \(-0.363639\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 956.760 | + | 28.2833i | 2.05755 | + | 0.0608243i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 582.780i | − | 1.24792i | −0.781455 | − | 0.623961i | \(-0.785522\pi\) | ||
0.781455 | − | 0.623961i | \(-0.214478\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 273.171 | + | 473.145i | 0.582453 | + | 1.00884i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 198.907 | + | 122.815i | 0.422308 | + | 0.260754i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 34.2153i | − | 0.0723369i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 523.075 | + | 958.710i | 1.10121 | + | 2.01834i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 93.3458 | + | 61.5187i | 0.195694 | + | 0.128970i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 46.4224i | 0.0969153i | 0.998825 | + | 0.0484577i | \(0.0154306\pi\) | ||||
−0.998825 | + | 0.0484577i | \(0.984569\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 131.699 | − | 228.110i | 0.273803 | − | 0.474241i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 86.2062 | + | 2.54839i | 0.178481 | + | 0.00527617i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −469.315 | + | 270.959i | −0.967659 | + | 0.558678i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −98.2155 | −0.201674 | −0.100837 | − | 0.994903i | \(-0.532152\pi\) | ||||
−0.100837 | + | 0.994903i | \(0.532152\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −34.8373 | − | 21.5103i | −0.0712420 | − | 0.0439884i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 669.171i | − | 1.36287i | −0.731877 | − | 0.681437i | \(-0.761356\pi\) | ||
0.731877 | − | 0.681437i | \(-0.238644\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −546.652 | + | 946.829i | −1.10883 | + | 1.92055i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 354.154 | + | 20.9570i | 0.715462 | + | 0.0423373i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −21.2871 | + | 12.2901i | −0.0428313 | + | 0.0247287i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 133.576 | 0.267686 | 0.133843 | − | 0.991003i | \(-0.457268\pi\) | ||||
0.133843 | + | 0.991003i | \(0.457268\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −90.8996 | − | 168.771i | −0.181436 | − | 0.336869i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −768.121 | + | 443.475i | −1.52708 | + | 0.881659i | −0.527596 | + | 0.849495i | \(0.676907\pi\) |
−0.999483 | + | 0.0321643i | \(0.989760\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1453.43 | −2.87807 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.00194 | − | 101.549i | 0.00592098 | − | 0.200293i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.94903 | − | 2.85732i | −0.00972305 | − | 0.00561360i | 0.495131 | − | 0.868819i | \(-0.335120\pi\) |
−0.504854 | + | 0.863205i | \(0.668454\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −133.279 | − | 230.846i | −0.260820 | − | 0.451753i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −470.319 | + | 204.864i | −0.916801 | + | 0.399344i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 263.661 | − | 152.225i | 0.511963 | − | 0.295582i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −144.681 | + | 250.594i | −0.279847 | + | 0.484708i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 517.010 | + | 15.2836i | 0.996165 | + | 0.0294482i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 399.843i | 0.767453i | 0.923447 | + | 0.383726i | \(0.125359\pi\) | ||||
−0.923447 | + | 0.383726i | \(0.874641\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −199.151 | − | 344.940i | −0.380786 | − | 0.659541i | 0.610389 | − | 0.792102i | \(-0.291013\pi\) |
−0.991175 | + | 0.132561i | \(0.957680\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1128.87 | − | 608.003i | 2.15022 | − | 1.15810i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 757.276i | 1.43696i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −257.026 | − | 445.182i | −0.485871 | − | 0.841554i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −913.514 | + | 457.722i | −1.72036 | + | 0.862001i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 394.689 | + | 227.874i | 0.740504 | + | 0.427530i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1030.78 | −1.92669 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −91.8324 | + | 148.728i | −0.171010 | + | 0.276962i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27.2892i | 0.0506293i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 142.004 | + | 245.957i | 0.262484 | + | 0.454635i | 0.966901 | − | 0.255151i | \(-0.0821251\pi\) |
−0.704418 | + | 0.709786i | \(0.748792\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.4302 | + | 894.073i | −0.0486744 | + | 1.64654i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −440.441 | − | 254.289i | −0.808149 | − | 0.466585i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 688.387 | 1.25848 | 0.629239 | − | 0.777212i | \(-0.283367\pi\) | ||||
0.629239 | + | 0.777212i | \(0.283367\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 405.279 | + | 808.848i | 0.738213 | + | 1.47331i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 845.966 | − | 461.561i | 1.53533 | − | 0.837679i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 945.504 | 1.70977 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 324.333 | − | 525.278i | 0.584383 | − | 0.946446i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −640.827 | + | 369.982i | −1.15050 | + | 0.664240i | −0.949008 | − | 0.315251i | \(-0.897911\pi\) |
−0.201489 | + | 0.979491i | \(0.564578\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 91.6373 | 0.163931 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.29374 | + | 280.558i | −0.0147838 | + | 0.500103i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 537.579 | − | 310.371i | 0.954847 | − | 0.551281i | 0.0602639 | − | 0.998182i | \(-0.480806\pi\) |
0.894583 | + | 0.446901i | \(0.147472\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 145.682 | + | 252.328i | 0.257844 | + | 0.446599i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 237.523 | + | 553.464i | 0.418912 | + | 0.976126i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 536.511 | + | 309.755i | 0.942902 | + | 0.544385i | 0.890869 | − | 0.454261i | \(-0.150097\pi\) |
0.0520329 | + | 0.998645i | \(0.483430\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −87.0815 | − | 150.830i | −0.152507 | − | 0.264150i | 0.779641 | − | 0.626226i | \(-0.215401\pi\) |
−0.932148 | + | 0.362076i | \(0.882068\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 179.030 | + | 332.401i | 0.312443 | + | 0.580106i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 192.461 | + | 111.118i | 0.334715 | + | 0.193248i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −715.882 | −1.24070 | −0.620348 | − | 0.784327i | \(-0.713009\pi\) | ||||
−0.620348 | + | 0.784327i | \(0.713009\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −197.448 | − | 121.914i | −0.341015 | − | 0.210560i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −571.106 | + | 329.728i | −0.982970 | + | 0.567518i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −53.9152 | −0.0924789 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −56.1281 | + | 948.513i | −0.0959455 | + | 1.62139i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −699.883 | + | 404.077i | −1.19230 | + | 0.688377i | −0.958829 | − | 0.283986i | \(-0.908343\pi\) |
−0.233476 | + | 0.972363i | \(0.575010\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 347.604 | − | 569.847i | 0.590160 | − | 0.967482i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 169.003 | − | 273.712i | 0.285962 | − | 0.463134i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −639.673 | + | 369.316i | −1.07871 | + | 0.622792i | −0.930547 | − | 0.366172i | \(-0.880668\pi\) |
−0.148160 | + | 0.988963i | \(0.547335\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 727.804 | + | 1260.59i | 1.22320 | + | 2.11865i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.31689 | + | 146.031i | −0.00723098 | + | 0.244607i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 728.812 | + | 420.780i | 1.21671 | + | 0.702470i | 0.964214 | − | 0.265126i | \(-0.0854137\pi\) |
0.252501 | + | 0.967597i | \(0.418747\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −65.8638 | + | 114.079i | −0.109590 | + | 0.189816i | −0.915604 | − | 0.402080i | \(-0.868287\pi\) |
0.806014 | + | 0.591896i | \(0.201621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −660.138 | − | 39.0636i | −1.09476 | − | 0.0647821i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 803.505 | − | 463.904i | 1.32811 | − | 0.766784i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −399.055 | − | 691.184i | −0.657422 | − | 1.13869i | −0.981281 | − | 0.192583i | \(-0.938313\pi\) |
0.323858 | − | 0.946106i | \(-0.395020\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −536.501 | − | 996.111i | −0.880955 | − | 1.63565i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −671.155 | − | 387.491i | −1.09845 | − | 0.634192i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 520.371 | − | 901.308i | 0.848892 | − | 1.47032i | −0.0333062 | − | 0.999445i | \(-0.510604\pi\) |
0.882198 | − | 0.470879i | \(-0.156063\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 908.866 | + | 561.179i | 1.47783 | + | 0.912487i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −463.269 | − | 267.468i | −0.750841 | − | 0.433498i | 0.0751567 | − | 0.997172i | \(-0.476054\pi\) |
−0.825998 | + | 0.563673i | \(0.809388\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 57.3192 | − | 99.2797i | 0.0925996 | − | 0.160387i | −0.816005 | − | 0.578045i | \(-0.803816\pi\) |
0.908604 | + | 0.417658i | \(0.137149\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −59.9946 | + | 85.4278i | −0.0966097 | + | 0.137565i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 673.567i | − | 1.08117i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1241.96 | 1.98714 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 135.022 | − | 207.312i | 0.215347 | − | 0.330641i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 422.977 | + | 244.206i | 0.672459 | + | 0.388244i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −319.956 | − | 554.181i | −0.507063 | − | 0.878258i | −0.999967 | − | 0.00817442i | \(-0.997398\pi\) |
0.492904 | − | 0.870084i | \(-0.335935\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.9755 | + | 14.1862i | 0.0362963 | + | 0.0224111i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1785.85 | + | 1031.06i | −2.81236 | + | 1.62372i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −73.0873 | −0.114737 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.75750 | − | 29.7001i | 0.00275039 | − | 0.0464790i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 252.396 | − | 145.721i | 0.393754 | − | 0.227334i | −0.290031 | − | 0.957017i | \(-0.593666\pi\) |
0.683785 | + | 0.729683i | \(0.260332\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 913.504 | 1.42069 | 0.710346 | − | 0.703853i | \(-0.248539\pi\) | ||||
0.710346 | + | 0.703853i | \(0.248539\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 214.681 | + | 6.34631i | 0.332839 | + | 0.00983924i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 179.023i | − | 0.276697i | −0.990384 | − | 0.138349i | \(-0.955821\pi\) | ||
0.990384 | − | 0.138349i | \(-0.0441795\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 246.385 | − | 426.752i | 0.379638 | − | 0.657553i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −666.799 | − | 411.715i | −1.02427 | − | 0.632435i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 62.3253 | − | 35.9836i | 0.0954446 | − | 0.0551050i | −0.451518 | − | 0.892262i | \(-0.649117\pi\) |
0.546963 | + | 0.837157i | \(0.315784\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −733.706 | −1.12016 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 322.079 | + | 19.0590i | 0.490227 | + | 0.0290091i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.4949i | 0.0508269i | 0.999677 | + | 0.0254134i | \(0.00809022\pi\) | ||||
−0.999677 | + | 0.0254134i | \(0.991910\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −58.6617 | + | 101.605i | −0.0887469 | + | 0.153714i | −0.906982 | − | 0.421170i | \(-0.861620\pi\) |
0.818235 | + | 0.574884i | \(0.194953\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −751.405 | − | 22.2127i | −1.13334 | − | 0.0335033i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 30.9674 | − | 1282.67i | 0.0465675 | − | 1.92882i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 98.0501 | − | 169.828i | 0.147002 | − | 0.254614i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.6871 | + | 699.797i | −0.0309224 | + | 1.04603i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −377.857 | − | 218.156i | −0.563125 | − | 0.325120i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 194.081 | − | 336.158i | 0.288382 | − | 0.499492i | −0.685042 | − | 0.728504i | \(-0.740216\pi\) |
0.973424 | + | 0.229012i | \(0.0735494\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −137.415 | + | 1545.87i | −0.203578 | + | 2.29018i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −724.175 | − | 418.103i | −1.06968 | − | 0.617582i | −0.141588 | − | 0.989926i | \(-0.545221\pi\) |
−0.928095 | + | 0.372344i | \(0.878554\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 443.681 | 0.653433 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −209.008 | − | 388.061i | −0.306913 | − | 0.569839i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 911.489i | 1.33454i | 0.744817 | + | 0.667268i | \(0.232537\pi\) | ||||
−0.744817 | + | 0.667268i | \(0.767463\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1825.40 | 2.66482 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.4906 | + | 659.321i | −0.0283705 | + | 0.959710i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 144.399i | − | 0.209577i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 617.578 | − | 1069.68i | 0.893745 | − | 1.54801i | 0.0583958 | − | 0.998294i | \(-0.481401\pi\) |
0.835350 | − | 0.549719i | \(-0.185265\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −242.529 | − | 159.836i | −0.349969 | − | 0.230644i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1818.73 | − | 1050.04i | −2.61687 | − | 1.51085i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −422.539 | + | 731.859i | −0.606225 | + | 1.05001i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −143.127 | − | 265.741i | −0.204760 | − | 0.380173i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 126.432 | + | 72.9953i | 0.180359 | + | 0.104130i | 0.587461 | − | 0.809252i | \(-0.300127\pi\) |
−0.407102 | + | 0.913383i | \(0.633461\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −206.193 | − | 377.918i | −0.293304 | − | 0.537579i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1545.50 | − | 954.266i | −2.19219 | − | 1.35357i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1030.53 | + | 594.978i | 1.45761 | + | 0.841553i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 743.280 | 1.04835 | 0.524175 | − | 0.851611i | \(-0.324374\pi\) | ||||
0.524175 | + | 0.851611i | \(0.324374\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −629.769 | + | 955.583i | −0.885750 | + | 1.34400i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 135.829i | − | 0.190503i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −229.120 | − | 396.848i | −0.320448 | − | 0.555032i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −778.929 | − | 23.0264i | −1.08637 | − | 0.0321149i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 299.714 | + | 173.040i | 0.416848 | + | 0.240667i | 0.693728 | − | 0.720237i | \(-0.255967\pi\) |
−0.276880 | + | 0.960905i | \(0.589300\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −249.260 | −0.345714 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −204.314 | − | 126.154i | −0.282592 | − | 0.174487i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 2915.42i | − | 4.02127i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −471.068 | − | 815.913i | −0.647961 | − | 1.12230i | −0.983609 | − | 0.180314i | \(-0.942289\pi\) |
0.335648 | − | 0.941987i | \(-0.391045\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −717.570 | − | 128.588i | −0.984320 | − | 0.176390i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 169.920i | 0.232449i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.7338 | − | 61.8927i | −0.0487500 | − | 0.0844376i | 0.840621 | − | 0.541624i | \(-0.182190\pi\) |
−0.889371 | + | 0.457187i | \(0.848857\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −171.223 | − | 5.06163i | −0.232957 | − | 0.00688658i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 276.195 | − | 159.461i | 0.374756 | − | 0.216365i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.461491 | − | 0.799326i | 0.000624481 | − | 0.00108163i | −0.865713 | − | 0.500541i | \(-0.833135\pi\) |
0.866337 | + | 0.499459i | \(0.166468\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 555.233 | + | 361.624i | 0.749302 | + | 0.488022i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 373.582i | − | 0.502802i | −0.967883 | − | 0.251401i | \(-0.919109\pi\) | ||
0.967883 | − | 0.251401i | \(-0.0808912\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1957.91 | 2.62806 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 47.1514 | − | 796.814i | 0.0631210 | − | 1.06669i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 730.858 | + | 421.961i | 0.975779 | + | 0.563366i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −182.718 | + | 316.476i | −0.243299 | + | 0.421406i | −0.961652 | − | 0.274272i | \(-0.911563\pi\) |
0.718353 | + | 0.695679i | \(0.244896\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 345.289 | + | 10.2073i | 0.458551 | + | 0.0135555i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 597.525 | + | 344.981i | 0.791424 | + | 0.456929i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −678.845 | + | 1175.79i | −0.896757 | + | 1.55323i | −0.0651422 | + | 0.997876i | \(0.520750\pi\) |
−0.831615 | + | 0.555353i | \(0.812583\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.48760 | − | 50.3222i | 0.00195995 | − | 0.0663007i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −795.277 | + | 459.153i | −1.04504 | + | 0.603355i | −0.921257 | − | 0.388954i | \(-0.872836\pi\) |
−0.123784 | + | 0.992309i | \(0.539503\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 208.192 | + | 360.600i | 0.272860 | + | 0.472608i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1758.80 | − | 104.077i | −2.29908 | − | 0.136048i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1142.95 | + | 659.882i | 1.49016 | + | 0.860342i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.3693 | − | 54.3333i | 0.0407924 | − | 0.0706545i | −0.844908 | − | 0.534911i | \(-0.820345\pi\) |
0.885701 | + | 0.464257i | \(0.153678\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −465.890 | − | 865.007i | −0.604267 | − | 1.12193i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −761.999 | + | 439.940i | −0.985769 | + | 0.569134i | −0.904007 | − | 0.427518i | \(-0.859388\pi\) |
−0.0817619 | + | 0.996652i | \(0.526055\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1009.68 | − | 1748.82i | −1.30282 | − | 2.25654i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −444.992 | + | 239.671i | −0.572705 | + | 0.308457i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 653.896 | − | 356.767i | 0.839404 | − | 0.457981i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.17428 | + | 12.4262i | 0.00918601 | + | 0.0159106i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1364.07 | + | 121.255i | 1.74211 | + | 0.154860i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 707.684i | − | 0.901508i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −390.537 | − | 676.431i | −0.496236 | − | 0.859505i | 0.503755 | − | 0.863847i | \(-0.331951\pi\) |
−0.999991 | + | 0.00434131i | \(0.998618\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 205.746 | + | 6.08219i | 0.260769 | + | 0.00770873i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 238.546i | − | 0.301576i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 584.276 | − | 1012.00i | 0.736792 | − | 1.27616i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.0003 | − | 338.286i | 0.0125790 | − | 0.425517i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 105.463 | − | 60.8893i | 0.132326 | − | 0.0763982i | −0.432376 | − | 0.901693i | \(-0.642325\pi\) |
0.564701 | + | 0.825295i | \(0.308991\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 718.513 | − | 1244.50i | 0.899266 | − | 1.55757i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 680.747 | + | 448.640i | 0.849872 | + | 0.560100i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −134.754 | + | 77.8005i | −0.167814 | + | 0.0968873i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −130.542 | − | 226.106i | −0.162165 | − | 0.280877i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −98.0586 | − | 182.063i | −0.121510 | − | 0.225605i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 100.026i | 0.123641i | 0.998087 | + | 0.0618206i | \(0.0196907\pi\) | ||||
−0.998087 | + | 0.0618206i | \(0.980309\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −418.778 | − | 725.345i | −0.516373 | − | 0.894384i | −0.999819 | − | 0.0190097i | \(-0.993949\pi\) |
0.483447 | − | 0.875374i | \(-0.339385\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −826.602 | + | 445.205i | −1.01673 | + | 0.547607i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 123.946i | 0.152081i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 77.9967 | − | 127.864i | 0.0954671 | − | 0.156505i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 428.082 | − | 649.553i | 0.522689 | − | 0.793105i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 444.733i | − | 0.541697i | −0.962622 | − | 0.270848i | \(-0.912696\pi\) | ||
0.962622 | − | 0.270848i | \(-0.0873042\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −664.390 | + | 1150.76i | −0.807279 | + | 1.39825i | 0.107463 | + | 0.994209i | \(0.465727\pi\) |
−0.914742 | + | 0.404038i | \(0.867606\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −354.917 | − | 658.966i | −0.430202 | − | 0.798747i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.0177 | − | 11.5572i | 0.0242052 | − | 0.0139749i | −0.487849 | − | 0.872928i | \(-0.662218\pi\) |
0.512054 | + | 0.858953i | \(0.328885\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 536.977 | 0.647741 | 0.323870 | − | 0.946101i | \(-0.395016\pi\) | ||||
0.323870 | + | 0.946101i | \(0.395016\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1339.74 | + | 721.581i | −1.61221 | + | 0.868328i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 135.524i | − | 0.162693i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −290.156 | + | 502.565i | −0.347492 | + | 0.601874i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 860.236 | − | 399.677i | 1.02776 | − | 0.477512i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −886.610 | + | 511.884i | −1.05675 | + | 0.610112i | −0.924530 | − | 0.381109i | \(-0.875542\pi\) |
−0.132215 | + | 0.991221i | \(0.542209\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1731.57 | −2.05894 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −728.187 | + | 1179.35i | −0.863804 | + | 1.39899i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −266.347 | + | 153.776i | −0.315204 | + | 0.181983i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −759.619 | −0.896835 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −133.018 | − | 82.1319i | −0.156676 | − | 0.0967396i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −75.8671 | − | 43.8019i | −0.0891505 | − | 0.0514711i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 577.893 | + | 1000.94i | 0.677483 | + | 1.17344i | 0.975736 | + | 0.218949i | \(0.0702627\pi\) |
−0.298253 | + | 0.954487i | \(0.596404\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1275.71 | + | 885.639i | 1.49206 | + | 1.03583i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −486.622 | + | 280.952i | −0.567821 | + | 0.327832i | −0.756279 | − | 0.654250i | \(-0.772984\pi\) |
0.188458 | + | 0.982081i | \(0.439651\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 379.879 | − | 657.969i | 0.442233 | − | 0.765971i | −0.555621 | − | 0.831435i | \(-0.687520\pi\) |
0.997855 | + | 0.0654645i | \(0.0208529\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −414.693 | − | 769.951i | −0.481641 | − | 0.894253i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1588.53i | 1.84071i | 0.391089 | + | 0.920353i | \(0.372098\pi\) | ||||
−0.391089 | + | 0.920353i | \(0.627902\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −782.910 | − | 1356.04i | −0.905098 | − | 1.56768i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.5697 | − | 526.686i | 0.0179581 | − | 0.607481i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 551.931i | − | 0.635133i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 427.077 | + | 739.720i | 0.490330 | + | 0.849276i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −295.521 | + | 448.411i | −0.338512 | + | 0.513644i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1899.48 | − | 1096.67i | −2.17084 | − | 1.25333i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −159.031 | −0.181335 | −0.0906676 | − | 0.995881i | \(-0.528900\pi\) | ||||
−0.0906676 | + | 0.995881i | \(0.528900\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −723.827 | − | 21.3975i | −0.823467 | − | 0.0243430i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1052.85i | 1.19506i | 0.801848 | + | 0.597529i | \(0.203851\pi\) | ||||
−0.801848 | + | 0.597529i | \(0.796149\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 598.786 | + | 1037.13i | 0.678127 | + | 1.17455i | 0.975544 | + | 0.219802i | \(0.0705413\pi\) |
−0.297418 | + | 0.954747i | \(0.596125\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2631.92 | + | 1625.08i | 2.97392 | + | 1.83624i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1372.55 | − | 792.445i | −1.54741 | − | 0.893399i | −0.998338 | − | 0.0576255i | \(-0.981647\pi\) |
−0.549074 | − | 0.835774i | \(-0.685020\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1688.31 | 1.89911 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 323.080 | − | 138.652i | 0.362604 | − | 0.155614i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1111.93 | + | 606.670i | −1.24516 | + | 0.679362i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 529.155 | 0.591234 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 134.776 | + | 3.98418i | 0.150252 | + | 0.00444167i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1543.16 | + | 890.943i | −1.71653 | + | 0.991038i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 267.754 | 0.297174 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −149.619 | − | 92.3821i | −0.165691 | − | 0.102306i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2345.02 | − | 1353.90i | 2.59118 | − | 1.49602i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −603.276 | − | 1044.91i | −0.665134 | − | 1.15205i | −0.979249 | − | 0.202661i | \(-0.935041\pi\) |
0.314115 | − | 0.949385i | \(-0.398292\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1287.72 | + | 645.223i | −1.41664 | + | 0.709816i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1358.72 | − | 784.455i | −1.49145 | − | 0.861092i | −0.491503 | − | 0.870876i | \(-0.663552\pi\) |
−0.999952 | + | 0.00978430i | \(0.996886\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 192.476 | + | 333.378i | 0.210817 | + | 0.365146i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1438.88 | − | 2330.36i | 1.57255 | − | 2.54685i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 520.224 | + | 300.351i | 0.567311 | + | 0.327537i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −191.924 | −0.208840 | −0.104420 | − | 0.994533i | \(-0.533299\pi\) | ||||
−0.104420 | + | 0.994533i | \(0.533299\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 56.3834 | − | 30.3679i | 0.0612198 | − | 0.0329727i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.2805 | + | 19.2145i | −0.0360569 | + | 0.0208175i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1302.41 | −1.40801 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 166.024 | − | 251.917i | 0.179098 | − | 0.271755i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1180.04 | − | 681.296i | 1.27023 | − | 0.733365i | 0.295195 | − | 0.955437i | \(-0.404615\pi\) |
0.975030 | + | 0.222072i | \(0.0712819\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −62.2079 | + | 101.981i | −0.0668183 | + | 0.109539i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 791.051 | + | 23.3847i | 0.847857 | + | 0.0250640i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 735.862 | − | 424.850i | 0.787018 | − | 0.454385i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −862.482 | − | 1493.86i | −0.920472 | − | 1.59430i | −0.798686 | − | 0.601748i | \(-0.794471\pi\) |
−0.121787 | − | 0.992556i | \(-0.538862\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.6493 | + | 12.7499i | 0.0219908 | + | 0.0135782i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 886.266 | + | 511.686i | 0.941834 | + | 0.543768i | 0.890535 | − | 0.454915i | \(-0.150330\pi\) |
0.0512992 | + | 0.998683i | \(0.483664\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 75.7886 | − | 131.270i | 0.0803697 | − | 0.139204i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1047.86 | − | 1492.08i | 1.10885 | − | 1.57892i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −622.249 | + | 359.256i | −0.657074 | + | 0.379362i | −0.791161 | − | 0.611608i | \(-0.790523\pi\) |
0.134087 | + | 0.990970i | \(0.457190\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −208.369 | − | 360.907i | −0.219567 | − | 0.380302i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.9070 | + | 35.4798i | −0.0230358 | + | 0.0373079i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −203.586 | − | 117.541i | −0.213627 | − | 0.123337i | 0.389369 | − | 0.921082i | \(-0.372693\pi\) |
−0.602996 | + | 0.797744i | \(0.706026\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 571.471 | − | 989.818i | 0.598399 | − | 1.03646i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −581.472 | + | 313.179i | −0.607599 | + | 0.327250i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1294.27 | − | 747.249i | −1.34961 | − | 0.779196i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −136.611 | + | 236.617i | −0.142155 | + | 0.246219i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −913.259 | + | 457.595i | −0.948348 | + | 0.475176i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 702.491i | 0.727970i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 943.049 | 0.975232 | 0.487616 | − | 0.873058i | \(-0.337867\pi\) | ||||
0.487616 | + | 0.873058i | \(0.337867\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −670.549 | + | 1029.55i | −0.692001 | + | 1.06249i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −620.444 | − | 358.213i | −0.638974 | − | 0.368912i | 0.145245 | − | 0.989396i | \(-0.453603\pi\) |
−0.784219 | + | 0.620484i | \(0.786936\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 859.696 | + | 1489.04i | 0.883551 | + | 1.53036i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1764.88 | − | 950.557i | 1.81013 | − | 0.974930i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.2042 | − | 22.6345i | 0.0401271 | − | 0.0231674i | −0.479802 | − | 0.877377i | \(-0.659292\pi\) |
0.519929 | + | 0.854209i | \(0.325958\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −393.190 | −0.401624 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −503.113 | − | 29.7717i | −0.512858 | − | 0.0303483i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1053.36 | − | 608.160i | 1.07158 | − | 0.618677i | 0.142968 | − | 0.989727i | \(-0.454335\pi\) |
0.928613 | + | 0.371050i | \(0.121002\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −973.829 | −0.988659 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 705.171 | + | 1309.28i | 0.714459 | + | 1.32652i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 30.4777i | − | 0.0308167i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −317.064 | + | 549.171i | −0.319944 | + | 0.554159i | −0.980476 | − | 0.196639i | \(-0.936997\pi\) |
0.660532 | + | 0.750798i | \(0.270331\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −65.7514 | + | 35.4135i | −0.0662149 | + | 0.0356631i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 383.017 | − | 221.135i | 0.384941 | − | 0.222246i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −292.131 | −0.293010 | −0.146505 | − | 0.989210i | \(-0.546802\pi\) | ||||
−0.146505 | + | 0.989210i | \(0.546802\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 54.1683 | − | 609.372i | 0.0542225 | − | 0.609982i |
(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 | 684.3.m.a.353.8 | ✓ | 80 | |
3.2 | odd | 2 | 2052.3.m.a.1493.2 | 80 | |||
9.4 | even | 3 | 2052.3.be.a.125.39 | 80 | |||
9.5 | odd | 6 | 684.3.be.a.581.34 | yes | 80 | ||
19.7 | even | 3 | 684.3.be.a.425.34 | yes | 80 | ||
57.26 | odd | 6 | 2052.3.be.a.197.39 | 80 | |||
171.121 | even | 3 | 2052.3.m.a.881.39 | 80 | |||
171.140 | odd | 6 | inner | 684.3.m.a.653.8 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.m.a.353.8 | ✓ | 80 | 1.1 | even | 1 | trivial | |
684.3.m.a.653.8 | yes | 80 | 171.140 | odd | 6 | inner | |
684.3.be.a.425.34 | yes | 80 | 19.7 | even | 3 | ||
684.3.be.a.581.34 | yes | 80 | 9.5 | odd | 6 | ||
2052.3.m.a.881.39 | 80 | 171.121 | even | 3 | |||
2052.3.m.a.1493.2 | 80 | 3.2 | odd | 2 | |||
2052.3.be.a.125.39 | 80 | 9.4 | even | 3 | |||
2052.3.be.a.197.39 | 80 | 57.26 | odd | 6 |