Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(599,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.599");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 599.3 | ||
Character | \(\chi\) | \(=\) | 690.599 |
Dual form | 690.3.b.a.599.4 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | −2.90508 | − | 0.748659i | −0.968361 | − | 0.249553i | ||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | −4.90392 | − | 0.975491i | −0.980784 | − | 0.195098i | ||||
\(6\) | 4.10841 | + | 1.05876i | 0.684735 | + | 0.176461i | ||||
\(7\) | − | 3.09484i | − | 0.442120i | −0.975260 | − | 0.221060i | \(-0.929048\pi\) | ||
0.975260 | − | 0.221060i | \(-0.0709517\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 7.87902 | + | 4.34983i | 0.875447 | + | 0.483315i | ||||
\(10\) | 6.93519 | + | 1.37955i | 0.693519 | + | 0.137955i | ||||
\(11\) | − | 10.9962i | − | 0.999652i | −0.866126 | − | 0.499826i | \(-0.833397\pi\) | ||
0.866126 | − | 0.499826i | \(-0.166603\pi\) | |||||||
\(12\) | −5.81017 | − | 1.49732i | −0.484181 | − | 0.124776i | ||||
\(13\) | 23.5927i | 1.81482i | 0.420244 | + | 0.907411i | \(0.361945\pi\) | ||||
−0.420244 | + | 0.907411i | \(0.638055\pi\) | |||||||
\(14\) | 4.37677i | 0.312626i | ||||||||
\(15\) | 13.5160 | + | 6.50524i | 0.901066 | + | 0.433683i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −14.9626 | −0.880150 | −0.440075 | − | 0.897961i | \(-0.645048\pi\) | ||||
−0.440075 | + | 0.897961i | \(0.645048\pi\) | |||||||
\(18\) | −11.1426 | − | 6.15159i | −0.619034 | − | 0.341755i | ||||
\(19\) | −24.8534 | −1.30807 | −0.654037 | − | 0.756462i | \(-0.726926\pi\) | ||||
−0.654037 | + | 0.756462i | \(0.726926\pi\) | |||||||
\(20\) | −9.80784 | − | 1.95098i | −0.490392 | − | 0.0975491i | ||||
\(21\) | −2.31698 | + | 8.99077i | −0.110332 | + | 0.428132i | ||||
\(22\) | 15.5509i | 0.706861i | ||||||||
\(23\) | 4.79583 | 0.208514 | ||||||||
\(24\) | 8.21682 | + | 2.11753i | 0.342367 | + | 0.0882303i | ||||
\(25\) | 23.0968 | + | 9.56746i | 0.923873 | + | 0.382698i | ||||
\(26\) | − | 33.3651i | − | 1.28327i | ||||||
\(27\) | −19.6327 | − | 18.5353i | −0.727136 | − | 0.686494i | ||||
\(28\) | − | 6.18968i | − | 0.221060i | ||||||
\(29\) | 42.9868i | 1.48230i | 0.671338 | + | 0.741152i | \(0.265720\pi\) | ||||
−0.671338 | + | 0.741152i | \(0.734280\pi\) | |||||||
\(30\) | −19.1145 | − | 9.19980i | −0.637150 | − | 0.306660i | ||||
\(31\) | −31.1614 | −1.00521 | −0.502603 | − | 0.864517i | \(-0.667624\pi\) | ||||
−0.502603 | + | 0.864517i | \(0.667624\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | −8.23238 | + | 31.9448i | −0.249466 | + | 0.968024i | ||||
\(34\) | 21.1603 | 0.622360 | ||||||||
\(35\) | −3.01899 | + | 15.1768i | −0.0862568 | + | 0.433624i | ||||
\(36\) | 15.7580 | + | 8.69967i | 0.437723 | + | 0.241657i | ||||
\(37\) | − | 48.5503i | − | 1.31217i | −0.754687 | − | 0.656085i | \(-0.772211\pi\) | ||
0.754687 | − | 0.656085i | \(-0.227789\pi\) | |||||||
\(38\) | 35.1480 | 0.924948 | ||||||||
\(39\) | 17.6629 | − | 68.5387i | 0.452894 | − | 1.75740i | ||||
\(40\) | 13.8704 | + | 2.75910i | 0.346759 | + | 0.0689776i | ||||
\(41\) | 31.4396i | 0.766819i | 0.923578 | + | 0.383410i | \(0.125250\pi\) | ||||
−0.923578 | + | 0.383410i | \(0.874750\pi\) | |||||||
\(42\) | 3.27670 | − | 12.7149i | 0.0780168 | − | 0.302735i | ||||
\(43\) | − | 37.4985i | − | 0.872057i | −0.899933 | − | 0.436029i | \(-0.856385\pi\) | ||
0.899933 | − | 0.436029i | \(-0.143615\pi\) | |||||||
\(44\) | − | 21.9923i | − | 0.499826i | ||||||
\(45\) | −34.3949 | − | 29.0171i | −0.764330 | − | 0.644825i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | 50.4805 | 1.07405 | 0.537027 | − | 0.843565i | \(-0.319547\pi\) | ||||
0.537027 | + | 0.843565i | \(0.319547\pi\) | |||||||
\(48\) | −11.6203 | − | 2.99464i | −0.242090 | − | 0.0623882i | ||||
\(49\) | 39.4220 | 0.804530 | ||||||||
\(50\) | −32.6639 | − | 13.5304i | −0.653277 | − | 0.270609i | ||||
\(51\) | 43.4675 | + | 11.2019i | 0.852304 | + | 0.219644i | ||||
\(52\) | 47.1854i | 0.907411i | ||||||||
\(53\) | 37.0253 | 0.698590 | 0.349295 | − | 0.937013i | \(-0.386421\pi\) | ||||
0.349295 | + | 0.937013i | \(0.386421\pi\) | |||||||
\(54\) | 27.7648 | + | 26.2129i | 0.514163 | + | 0.485424i | ||||
\(55\) | −10.7267 | + | 53.9243i | −0.195030 | + | 0.980443i | ||||
\(56\) | 8.75353i | 0.156313i | ||||||||
\(57\) | 72.2013 | + | 18.6067i | 1.26669 | + | 0.326434i | ||||
\(58\) | − | 60.7925i | − | 1.04815i | ||||||
\(59\) | 35.4084i | 0.600143i | 0.953917 | + | 0.300071i | \(0.0970105\pi\) | ||||
−0.953917 | + | 0.300071i | \(0.902989\pi\) | |||||||
\(60\) | 27.0320 | + | 13.0105i | 0.450533 | + | 0.216841i | ||||
\(61\) | −17.9790 | −0.294737 | −0.147369 | − | 0.989082i | \(-0.547080\pi\) | ||||
−0.147369 | + | 0.989082i | \(0.547080\pi\) | |||||||
\(62\) | 44.0688 | 0.710788 | ||||||||
\(63\) | 13.4620 | − | 24.3843i | 0.213683 | − | 0.387053i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 23.0145 | − | 115.697i | 0.354069 | − | 1.77995i | ||||
\(66\) | 11.6423 | − | 45.1768i | 0.176399 | − | 0.684497i | ||||
\(67\) | 68.1965i | 1.01786i | 0.860808 | + | 0.508929i | \(0.169959\pi\) | ||||
−0.860808 | + | 0.508929i | \(0.830041\pi\) | |||||||
\(68\) | −29.9251 | −0.440075 | ||||||||
\(69\) | −13.9323 | − | 3.59044i | −0.201917 | − | 0.0520354i | ||||
\(70\) | 4.26949 | − | 21.4633i | 0.0609928 | − | 0.306619i | ||||
\(71\) | − | 99.8069i | − | 1.40573i | −0.711323 | − | 0.702866i | \(-0.751904\pi\) | ||
0.711323 | − | 0.702866i | \(-0.248096\pi\) | |||||||
\(72\) | −22.2852 | − | 12.3032i | −0.309517 | − | 0.170878i | ||||
\(73\) | − | 39.3878i | − | 0.539558i | −0.962922 | − | 0.269779i | \(-0.913049\pi\) | ||
0.962922 | − | 0.269779i | \(-0.0869507\pi\) | |||||||
\(74\) | 68.6605i | 0.927845i | ||||||||
\(75\) | −59.9355 | − | 45.0859i | −0.799140 | − | 0.601145i | ||||
\(76\) | −49.7068 | −0.654037 | ||||||||
\(77\) | −34.0314 | −0.441966 | ||||||||
\(78\) | −24.9791 | + | 96.9284i | −0.320245 | + | 1.24267i | ||||
\(79\) | 30.7676 | 0.389463 | 0.194732 | − | 0.980857i | \(-0.437616\pi\) | ||||
0.194732 | + | 0.980857i | \(0.437616\pi\) | |||||||
\(80\) | −19.6157 | − | 3.90196i | −0.245196 | − | 0.0487745i | ||||
\(81\) | 43.1579 | + | 68.5448i | 0.532814 | + | 0.846233i | ||||
\(82\) | − | 44.4623i | − | 0.542223i | ||||||
\(83\) | 110.238 | 1.32817 | 0.664086 | − | 0.747657i | \(-0.268821\pi\) | ||||
0.664086 | + | 0.747657i | \(0.268821\pi\) | |||||||
\(84\) | −4.63396 | + | 17.9815i | −0.0551662 | + | 0.214066i | ||||
\(85\) | 73.3752 | + | 14.5958i | 0.863237 | + | 0.171716i | ||||
\(86\) | 53.0308i | 0.616638i | ||||||||
\(87\) | 32.1824 | − | 124.880i | 0.369913 | − | 1.43540i | ||||
\(88\) | 31.1019i | 0.353430i | ||||||||
\(89\) | − | 146.036i | − | 1.64086i | −0.571748 | − | 0.820429i | \(-0.693734\pi\) | ||
0.571748 | − | 0.820429i | \(-0.306266\pi\) | |||||||
\(90\) | 48.6417 | + | 41.0364i | 0.540463 | + | 0.455960i | ||||
\(91\) | 73.0156 | 0.802369 | ||||||||
\(92\) | 9.59166 | 0.104257 | ||||||||
\(93\) | 90.5264 | + | 23.3292i | 0.973402 | + | 0.250852i | ||||
\(94\) | −71.3903 | −0.759471 | ||||||||
\(95\) | 121.879 | + | 24.2443i | 1.28294 | + | 0.255203i | ||||
\(96\) | 16.4336 | + | 4.23505i | 0.171184 | + | 0.0441151i | ||||
\(97\) | − | 118.760i | − | 1.22433i | −0.790732 | − | 0.612163i | \(-0.790300\pi\) | ||
0.790732 | − | 0.612163i | \(-0.209700\pi\) | |||||||
\(98\) | −55.7511 | −0.568889 | ||||||||
\(99\) | 47.8315 | − | 86.6391i | 0.483147 | − | 0.875142i | ||||
\(100\) | 46.1937 | + | 19.1349i | 0.461937 | + | 0.191349i | ||||
\(101\) | 152.807i | 1.51294i | 0.654030 | + | 0.756469i | \(0.273077\pi\) | ||||
−0.654030 | + | 0.756469i | \(0.726923\pi\) | |||||||
\(102\) | −61.4723 | − | 15.8418i | −0.602670 | − | 0.155312i | ||||
\(103\) | − | 153.920i | − | 1.49437i | −0.664616 | − | 0.747185i | \(-0.731405\pi\) | ||
0.664616 | − | 0.747185i | \(-0.268595\pi\) | |||||||
\(104\) | − | 66.7302i | − | 0.641637i | ||||||
\(105\) | 20.1327 | − | 41.8298i | 0.191740 | − | 0.398379i | ||||
\(106\) | −52.3616 | −0.493977 | ||||||||
\(107\) | −5.89126 | −0.0550585 | −0.0275292 | − | 0.999621i | \(-0.508764\pi\) | ||||
−0.0275292 | + | 0.999621i | \(0.508764\pi\) | |||||||
\(108\) | −39.2653 | − | 37.0706i | −0.363568 | − | 0.343247i | ||||
\(109\) | 93.4247 | 0.857107 | 0.428554 | − | 0.903516i | \(-0.359023\pi\) | ||||
0.428554 | + | 0.903516i | \(0.359023\pi\) | |||||||
\(110\) | 15.1698 | − | 76.2605i | 0.137907 | − | 0.693278i | ||||
\(111\) | −36.3476 | + | 141.043i | −0.327456 | + | 1.27066i | ||||
\(112\) | − | 12.3794i | − | 0.110530i | ||||||
\(113\) | 158.025 | 1.39845 | 0.699226 | − | 0.714901i | \(-0.253528\pi\) | ||||
0.699226 | + | 0.714901i | \(0.253528\pi\) | |||||||
\(114\) | −102.108 | − | 26.3139i | −0.895684 | − | 0.230824i | ||||
\(115\) | −23.5184 | − | 4.67829i | −0.204508 | − | 0.0406808i | ||||
\(116\) | 85.9736i | 0.741152i | ||||||||
\(117\) | −102.624 | + | 185.887i | −0.877130 | + | 1.58878i | ||||
\(118\) | − | 50.0751i | − | 0.424365i | ||||||
\(119\) | 46.3067i | 0.389132i | ||||||||
\(120\) | −38.2290 | − | 18.3996i | −0.318575 | − | 0.153330i | ||||
\(121\) | 0.0841400 | 0.000695372 | ||||||||
\(122\) | 25.4261 | 0.208411 | ||||||||
\(123\) | 23.5375 | − | 91.3346i | 0.191362 | − | 0.742558i | ||||
\(124\) | −62.3227 | −0.502603 | ||||||||
\(125\) | −103.932 | − | 69.4488i | −0.831456 | − | 0.555590i | ||||
\(126\) | −19.0382 | + | 34.4846i | −0.151097 | + | 0.273687i | ||||
\(127\) | 202.869i | 1.59739i | 0.601735 | + | 0.798696i | \(0.294477\pi\) | ||||
−0.601735 | + | 0.798696i | \(0.705523\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | −28.0736 | + | 108.936i | −0.217624 | + | 0.844467i | ||||
\(130\) | −32.5474 | + | 163.620i | −0.250364 | + | 1.25861i | ||||
\(131\) | − | 232.701i | − | 1.77635i | −0.459510 | − | 0.888173i | \(-0.651975\pi\) | ||
0.459510 | − | 0.888173i | \(-0.348025\pi\) | |||||||
\(132\) | −16.4648 | + | 63.8896i | −0.124733 | + | 0.484012i | ||||
\(133\) | 76.9174i | 0.578326i | ||||||||
\(134\) | − | 96.4444i | − | 0.719735i | ||||||
\(135\) | 78.1960 | + | 110.047i | 0.579229 | + | 0.815165i | ||||
\(136\) | 42.3205 | 0.311180 | ||||||||
\(137\) | −28.9097 | −0.211020 | −0.105510 | − | 0.994418i | \(-0.533647\pi\) | ||||
−0.105510 | + | 0.994418i | \(0.533647\pi\) | |||||||
\(138\) | 19.7032 | + | 5.07765i | 0.142777 | + | 0.0367946i | ||||
\(139\) | 19.0941 | 0.137367 | 0.0686837 | − | 0.997638i | \(-0.478120\pi\) | ||||
0.0686837 | + | 0.997638i | \(0.478120\pi\) | |||||||
\(140\) | −6.03798 | + | 30.3537i | −0.0431284 | + | 0.216812i | ||||
\(141\) | −146.650 | − | 37.7927i | −1.04007 | − | 0.268033i | ||||
\(142\) | 141.148i | 0.994002i | ||||||||
\(143\) | 259.429 | 1.81419 | ||||||||
\(144\) | 31.5161 | + | 17.3993i | 0.218862 | + | 0.120829i | ||||
\(145\) | 41.9332 | − | 210.804i | 0.289195 | − | 1.45382i | ||||
\(146\) | 55.7027i | 0.381525i | ||||||||
\(147\) | −114.524 | − | 29.5136i | −0.779075 | − | 0.200773i | ||||
\(148\) | − | 97.1006i | − | 0.656085i | ||||||
\(149\) | − | 2.09186i | − | 0.0140394i | −0.999975 | − | 0.00701968i | \(-0.997766\pi\) | ||
0.999975 | − | 0.00701968i | \(-0.00223445\pi\) | |||||||
\(150\) | 84.7616 | + | 63.7611i | 0.565077 | + | 0.425074i | ||||
\(151\) | 295.609 | 1.95767 | 0.978837 | − | 0.204640i | \(-0.0656023\pi\) | ||||
0.978837 | + | 0.204640i | \(0.0656023\pi\) | |||||||
\(152\) | 70.2961 | 0.462474 | ||||||||
\(153\) | −117.890 | − | 65.0846i | −0.770525 | − | 0.425390i | ||||
\(154\) | 48.1277 | 0.312517 | ||||||||
\(155\) | 152.813 | + | 30.3976i | 0.985889 | + | 0.196114i | ||||
\(156\) | 35.3258 | − | 137.077i | 0.226447 | − | 0.878702i | ||||
\(157\) | 93.0158i | 0.592457i | 0.955117 | + | 0.296229i | \(0.0957290\pi\) | ||||
−0.955117 | + | 0.296229i | \(0.904271\pi\) | |||||||
\(158\) | −43.5119 | −0.275392 | ||||||||
\(159\) | −107.561 | − | 27.7193i | −0.676487 | − | 0.174335i | ||||
\(160\) | 27.7408 | + | 5.51821i | 0.173380 | + | 0.0344888i | ||||
\(161\) | − | 14.8423i | − | 0.0921884i | ||||||
\(162\) | −61.0345 | − | 96.9370i | −0.376756 | − | 0.598377i | ||||
\(163\) | 15.1239i | 0.0927848i | 0.998923 | + | 0.0463924i | \(0.0147725\pi\) | ||||
−0.998923 | + | 0.0463924i | \(0.985228\pi\) | |||||||
\(164\) | 62.8792i | 0.383410i | ||||||||
\(165\) | 71.5328 | − | 148.624i | 0.433532 | − | 0.900752i | ||||
\(166\) | −155.900 | −0.939159 | ||||||||
\(167\) | 51.7925 | 0.310135 | 0.155067 | − | 0.987904i | \(-0.450441\pi\) | ||||
0.155067 | + | 0.987904i | \(0.450441\pi\) | |||||||
\(168\) | 6.55341 | − | 25.4297i | 0.0390084 | − | 0.151367i | ||||
\(169\) | −387.615 | −2.29358 | ||||||||
\(170\) | −103.768 | − | 20.6416i | −0.610401 | − | 0.121421i | ||||
\(171\) | −195.821 | − | 108.108i | −1.14515 | − | 0.632212i | ||||
\(172\) | − | 74.9969i | − | 0.436029i | ||||||
\(173\) | −21.8513 | −0.126308 | −0.0631540 | − | 0.998004i | \(-0.520116\pi\) | ||||
−0.0631540 | + | 0.998004i | \(0.520116\pi\) | |||||||
\(174\) | −45.5128 | + | 176.607i | −0.261568 | + | 1.01498i | ||||
\(175\) | 29.6097 | − | 71.4810i | 0.169199 | − | 0.408463i | ||||
\(176\) | − | 43.9847i | − | 0.249913i | ||||||
\(177\) | 26.5088 | − | 102.864i | 0.149767 | − | 0.581155i | ||||
\(178\) | 206.527i | 1.16026i | ||||||||
\(179\) | − | 131.395i | − | 0.734050i | −0.930211 | − | 0.367025i | \(-0.880376\pi\) | ||
0.930211 | − | 0.367025i | \(-0.119624\pi\) | |||||||
\(180\) | −68.7897 | − | 58.0343i | −0.382165 | − | 0.322413i | ||||
\(181\) | −294.584 | −1.62753 | −0.813767 | − | 0.581191i | \(-0.802587\pi\) | ||||
−0.813767 | + | 0.581191i | \(0.802587\pi\) | |||||||
\(182\) | −103.260 | −0.567361 | ||||||||
\(183\) | 52.2304 | + | 13.4601i | 0.285412 | + | 0.0735526i | ||||
\(184\) | −13.5647 | −0.0737210 | ||||||||
\(185\) | −47.3604 | + | 238.087i | −0.256002 | + | 1.28696i | ||||
\(186\) | −128.024 | − | 32.9925i | −0.688299 | − | 0.177379i | ||||
\(187\) | 164.531i | 0.879844i | ||||||||
\(188\) | 100.961 | 0.537027 | ||||||||
\(189\) | −57.3639 | + | 60.7600i | −0.303513 | + | 0.321481i | ||||
\(190\) | −172.363 | − | 34.2866i | −0.907174 | − | 0.180456i | ||||
\(191\) | 181.966i | 0.952700i | 0.879256 | + | 0.476350i | \(0.158040\pi\) | ||||
−0.879256 | + | 0.476350i | \(0.841960\pi\) | |||||||
\(192\) | −23.2407 | − | 5.98927i | −0.121045 | − | 0.0311941i | ||||
\(193\) | − | 8.26140i | − | 0.0428052i | −0.999771 | − | 0.0214026i | \(-0.993187\pi\) | ||
0.999771 | − | 0.0214026i | \(-0.00681318\pi\) | |||||||
\(194\) | 167.951i | 0.865729i | ||||||||
\(195\) | −153.476 | + | 318.878i | −0.787058 | + | 1.63527i | ||||
\(196\) | 78.8439 | 0.402265 | ||||||||
\(197\) | −61.8888 | −0.314156 | −0.157078 | − | 0.987586i | \(-0.550207\pi\) | ||||
−0.157078 | + | 0.987586i | \(0.550207\pi\) | |||||||
\(198\) | −67.6440 | + | 122.526i | −0.341636 | + | 0.618819i | ||||
\(199\) | −314.790 | −1.58186 | −0.790930 | − | 0.611906i | \(-0.790403\pi\) | ||||
−0.790930 | + | 0.611906i | \(0.790403\pi\) | |||||||
\(200\) | −65.3277 | − | 27.0609i | −0.326639 | − | 0.135304i | ||||
\(201\) | 51.0559 | − | 198.117i | 0.254010 | − | 0.985655i | ||||
\(202\) | − | 216.101i | − | 1.06981i | ||||||
\(203\) | 133.037 | 0.655356 | ||||||||
\(204\) | 86.9350 | + | 22.4037i | 0.426152 | + | 0.109822i | ||||
\(205\) | 30.6690 | − | 154.177i | 0.149605 | − | 0.752084i | ||||
\(206\) | 217.676i | 1.05668i | ||||||||
\(207\) | 37.7865 | + | 20.8611i | 0.182543 | + | 0.100778i | ||||
\(208\) | 94.3708i | 0.453706i | ||||||||
\(209\) | 273.293i | 1.30762i | ||||||||
\(210\) | −28.4719 | + | 59.1563i | −0.135581 | + | 0.281697i | ||||
\(211\) | 97.7183 | 0.463120 | 0.231560 | − | 0.972821i | \(-0.425617\pi\) | ||||
0.231560 | + | 0.972821i | \(0.425617\pi\) | |||||||
\(212\) | 74.0505 | 0.349295 | ||||||||
\(213\) | −74.7213 | + | 289.947i | −0.350804 | + | 1.36126i | ||||
\(214\) | 8.33150 | 0.0389322 | ||||||||
\(215\) | −36.5794 | + | 183.889i | −0.170137 | + | 0.855300i | ||||
\(216\) | 55.5296 | + | 52.4258i | 0.257081 | + | 0.242712i | ||||
\(217\) | 96.4395i | 0.444422i | ||||||||
\(218\) | −132.122 | −0.606066 | ||||||||
\(219\) | −29.4880 | + | 114.425i | −0.134648 | + | 0.522487i | ||||
\(220\) | −21.4533 | + | 107.849i | −0.0975152 | + | 0.490221i | ||||
\(221\) | − | 353.007i | − | 1.59732i | ||||||
\(222\) | 51.4033 | − | 199.465i | 0.231546 | − | 0.898489i | ||||
\(223\) | 289.459i | 1.29802i | 0.760779 | + | 0.649011i | \(0.224817\pi\) | ||||
−0.760779 | + | 0.649011i | \(0.775183\pi\) | |||||||
\(224\) | 17.5071i | 0.0781565i | ||||||||
\(225\) | 140.364 | + | 175.850i | 0.623838 | + | 0.781554i | ||||
\(226\) | −223.481 | −0.988854 | ||||||||
\(227\) | −272.278 | −1.19946 | −0.599731 | − | 0.800201i | \(-0.704726\pi\) | ||||
−0.599731 | + | 0.800201i | \(0.704726\pi\) | |||||||
\(228\) | 144.403 | + | 37.2135i | 0.633344 | + | 0.163217i | ||||
\(229\) | 97.0820 | 0.423939 | 0.211970 | − | 0.977276i | \(-0.432012\pi\) | ||||
0.211970 | + | 0.977276i | \(0.432012\pi\) | |||||||
\(230\) | 33.2600 | + | 6.61610i | 0.144609 | + | 0.0287657i | ||||
\(231\) | 98.8641 | + | 25.4779i | 0.427983 | + | 0.110294i | ||||
\(232\) | − | 121.585i | − | 0.524073i | ||||||
\(233\) | 160.963 | 0.690828 | 0.345414 | − | 0.938450i | \(-0.387739\pi\) | ||||
0.345414 | + | 0.938450i | \(0.387739\pi\) | |||||||
\(234\) | 145.133 | − | 262.884i | 0.620225 | − | 1.12344i | ||||
\(235\) | −247.552 | − | 49.2433i | −1.05341 | − | 0.209546i | ||||
\(236\) | 70.8169i | 0.300071i | ||||||||
\(237\) | −89.3824 | − | 23.0344i | −0.377141 | − | 0.0971917i | ||||
\(238\) | − | 65.4876i | − | 0.275158i | ||||||
\(239\) | 47.0387i | 0.196815i | 0.995146 | + | 0.0984073i | \(0.0313748\pi\) | ||||
−0.995146 | + | 0.0984073i | \(0.968625\pi\) | |||||||
\(240\) | 54.0639 | + | 26.0210i | 0.225266 | + | 0.108421i | ||||
\(241\) | 193.872 | 0.804450 | 0.402225 | − | 0.915541i | \(-0.368237\pi\) | ||||
0.402225 | + | 0.915541i | \(0.368237\pi\) | |||||||
\(242\) | −0.118992 | −0.000491702 | ||||||||
\(243\) | −74.0606 | − | 231.439i | −0.304776 | − | 0.952424i | ||||
\(244\) | −35.9580 | −0.147369 | ||||||||
\(245\) | −193.322 | − | 38.4558i | −0.789070 | − | 0.156962i | ||||
\(246\) | −33.2871 | + | 129.167i | −0.135313 | + | 0.525068i | ||||
\(247\) | − | 586.359i | − | 2.37392i | ||||||
\(248\) | 88.1377 | 0.355394 | ||||||||
\(249\) | −320.251 | − | 82.5308i | −1.28615 | − | 0.331449i | ||||
\(250\) | 146.982 | + | 98.2154i | 0.587928 | + | 0.392862i | ||||
\(251\) | − | 141.050i | − | 0.561953i | −0.959715 | − | 0.280977i | \(-0.909342\pi\) | ||
0.959715 | − | 0.280977i | \(-0.0906583\pi\) | |||||||
\(252\) | 26.9241 | − | 48.7686i | 0.106842 | − | 0.193526i | ||||
\(253\) | − | 52.7358i | − | 0.208442i | ||||||
\(254\) | − | 286.900i | − | 1.12953i | ||||||
\(255\) | −202.234 | − | 97.3351i | −0.793073 | − | 0.381706i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 135.744 | 0.528186 | 0.264093 | − | 0.964497i | \(-0.414927\pi\) | ||||
0.264093 | + | 0.964497i | \(0.414927\pi\) | |||||||
\(258\) | 39.7020 | − | 154.059i | 0.153884 | − | 0.597128i | ||||
\(259\) | −150.255 | −0.580137 | ||||||||
\(260\) | 46.0289 | − | 231.393i | 0.177034 | − | 0.889974i | ||||
\(261\) | −186.985 | + | 338.694i | −0.716419 | + | 1.29768i | ||||
\(262\) | 329.089i | 1.25607i | ||||||||
\(263\) | 305.350 | 1.16103 | 0.580513 | − | 0.814251i | \(-0.302852\pi\) | ||||
0.580513 | + | 0.814251i | \(0.302852\pi\) | |||||||
\(264\) | 23.2847 | − | 90.3536i | 0.0881996 | − | 0.342248i | ||||
\(265\) | −181.569 | − | 36.1178i | −0.685165 | − | 0.136294i | ||||
\(266\) | − | 108.778i | − | 0.408938i | ||||||
\(267\) | −109.331 | + | 424.248i | −0.409481 | + | 1.58894i | ||||
\(268\) | 136.393i | 0.508929i | ||||||||
\(269\) | 305.759i | 1.13665i | 0.822804 | + | 0.568325i | \(0.192408\pi\) | ||||
−0.822804 | + | 0.568325i | \(0.807592\pi\) | |||||||
\(270\) | −110.586 | − | 155.630i | −0.409577 | − | 0.576408i | ||||
\(271\) | 353.781 | 1.30547 | 0.652733 | − | 0.757588i | \(-0.273622\pi\) | ||||
0.652733 | + | 0.757588i | \(0.273622\pi\) | |||||||
\(272\) | −59.8502 | −0.220038 | ||||||||
\(273\) | −212.116 | − | 54.6638i | −0.776983 | − | 0.200234i | ||||
\(274\) | 40.8845 | 0.149213 | ||||||||
\(275\) | 105.205 | − | 253.977i | 0.382565 | − | 0.923552i | ||||
\(276\) | −27.8646 | − | 7.18088i | −0.100959 | − | 0.0260177i | ||||
\(277\) | 24.6890i | 0.0891299i | 0.999006 | + | 0.0445650i | \(0.0141902\pi\) | ||||
−0.999006 | + | 0.0445650i | \(0.985810\pi\) | |||||||
\(278\) | −27.0031 | −0.0971334 | ||||||||
\(279\) | −245.521 | − | 135.547i | −0.880004 | − | 0.485831i | ||||
\(280\) | 8.53899 | − | 42.9266i | 0.0304964 | − | 0.153309i | ||||
\(281\) | − | 135.704i | − | 0.482931i | −0.970409 | − | 0.241466i | \(-0.922372\pi\) | ||
0.970409 | − | 0.241466i | \(-0.0776281\pi\) | |||||||
\(282\) | 207.395 | + | 53.4469i | 0.735442 | + | 0.189528i | ||||
\(283\) | 34.6037i | 0.122275i | 0.998129 | + | 0.0611373i | \(0.0194728\pi\) | ||||
−0.998129 | + | 0.0611373i | \(0.980527\pi\) | |||||||
\(284\) | − | 199.614i | − | 0.702866i | ||||||
\(285\) | −335.918 | − | 161.678i | −1.17866 | − | 0.567290i | ||||
\(286\) | −366.889 | −1.28283 | ||||||||
\(287\) | 97.3005 | 0.339026 | ||||||||
\(288\) | −44.5705 | − | 24.6064i | −0.154759 | − | 0.0854388i | ||||
\(289\) | −65.1219 | −0.225335 | ||||||||
\(290\) | −59.3025 | + | 298.121i | −0.204491 | + | 1.02801i | ||||
\(291\) | −88.9104 | + | 345.006i | −0.305534 | + | 1.18559i | ||||
\(292\) | − | 78.7755i | − | 0.269779i | ||||||
\(293\) | 472.467 | 1.61252 | 0.806258 | − | 0.591563i | \(-0.201489\pi\) | ||||
0.806258 | + | 0.591563i | \(0.201489\pi\) | |||||||
\(294\) | 161.962 | + | 41.7385i | 0.550890 | + | 0.141968i | ||||
\(295\) | 34.5406 | − | 173.640i | 0.117087 | − | 0.588610i | ||||
\(296\) | 137.321i | 0.463922i | ||||||||
\(297\) | −203.818 | + | 215.884i | −0.686255 | + | 0.726883i | ||||
\(298\) | 2.95834i | 0.00992732i | ||||||||
\(299\) | 113.147i | 0.378417i | ||||||||
\(300\) | −119.871 | − | 90.1718i | −0.399570 | − | 0.300573i | ||||
\(301\) | −116.052 | −0.385554 | ||||||||
\(302\) | −418.054 | −1.38429 | ||||||||
\(303\) | 114.400 | − | 443.916i | 0.377558 | − | 1.46507i | ||||
\(304\) | −99.4137 | −0.327019 | ||||||||
\(305\) | 88.1675 | + | 17.5383i | 0.289074 | + | 0.0575027i | ||||
\(306\) | 166.722 | + | 92.0436i | 0.544843 | + | 0.300796i | ||||
\(307\) | 170.489i | 0.555340i | 0.960676 | + | 0.277670i | \(0.0895622\pi\) | ||||
−0.960676 | + | 0.277670i | \(0.910438\pi\) | |||||||
\(308\) | −68.0628 | −0.220983 | ||||||||
\(309\) | −115.234 | + | 447.151i | −0.372924 | + | 1.44709i | ||||
\(310\) | −216.110 | − | 42.9887i | −0.697129 | − | 0.138673i | ||||
\(311\) | 18.3636i | 0.0590468i | 0.999564 | + | 0.0295234i | \(0.00939896\pi\) | ||||
−0.999564 | + | 0.0295234i | \(0.990601\pi\) | |||||||
\(312\) | −49.9582 | + | 193.857i | −0.160122 | + | 0.621336i | ||||
\(313\) | − | 301.845i | − | 0.964361i | −0.876072 | − | 0.482181i | \(-0.839845\pi\) | ||
0.876072 | − | 0.482181i | \(-0.160155\pi\) | |||||||
\(314\) | − | 131.544i | − | 0.418930i | ||||||
\(315\) | −89.8034 | + | 106.447i | −0.285090 | + | 0.337926i | ||||
\(316\) | 61.5352 | 0.194732 | ||||||||
\(317\) | −178.155 | −0.562003 | −0.281002 | − | 0.959707i | \(-0.590667\pi\) | ||||
−0.281002 | + | 0.959707i | \(0.590667\pi\) | |||||||
\(318\) | 152.115 | + | 39.2010i | 0.478349 | + | 0.123274i | ||||
\(319\) | 472.690 | 1.48179 | ||||||||
\(320\) | −39.2313 | − | 7.80393i | −0.122598 | − | 0.0243873i | ||||
\(321\) | 17.1146 | + | 4.41054i | 0.0533165 | + | 0.0137400i | ||||
\(322\) | 20.9902i | 0.0651870i | ||||||||
\(323\) | 371.871 | 1.15130 | ||||||||
\(324\) | 86.3158 | + | 137.090i | 0.266407 | + | 0.423116i | ||||
\(325\) | −225.722 | + | 544.916i | −0.694529 | + | 1.67667i | ||||
\(326\) | − | 21.3885i | − | 0.0656088i | ||||||
\(327\) | −271.407 | − | 69.9432i | −0.829989 | − | 0.213894i | ||||
\(328\) | − | 88.9246i | − | 0.271112i | ||||||
\(329\) | − | 156.229i | − | 0.474861i | ||||||
\(330\) | −101.163 | + | 210.186i | −0.306554 | + | 0.636928i | ||||
\(331\) | 276.457 | 0.835219 | 0.417609 | − | 0.908627i | \(-0.362868\pi\) | ||||
0.417609 | + | 0.908627i | \(0.362868\pi\) | |||||||
\(332\) | 220.476 | 0.664086 | ||||||||
\(333\) | 211.186 | − | 382.529i | 0.634192 | − | 1.14874i | ||||
\(334\) | −73.2456 | −0.219298 | ||||||||
\(335\) | 66.5251 | − | 334.430i | 0.198582 | − | 0.998299i | ||||
\(336\) | −9.26792 | + | 35.9631i | −0.0275831 | + | 0.107033i | ||||
\(337\) | 317.196i | 0.941236i | 0.882337 | + | 0.470618i | \(0.155969\pi\) | ||||
−0.882337 | + | 0.470618i | \(0.844031\pi\) | |||||||
\(338\) | 548.170 | 1.62181 | ||||||||
\(339\) | −459.076 | − | 118.307i | −1.35421 | − | 0.348988i | ||||
\(340\) | 146.750 | + | 29.1917i | 0.431619 | + | 0.0858579i | ||||
\(341\) | 342.656i | 1.00486i | ||||||||
\(342\) | 276.932 | + | 152.888i | 0.809743 | + | 0.447041i | ||||
\(343\) | − | 273.652i | − | 0.797819i | ||||||
\(344\) | 106.062i | 0.308319i | ||||||||
\(345\) | 64.8204 | + | 31.1981i | 0.187885 | + | 0.0904291i | ||||
\(346\) | 30.9024 | 0.0893132 | ||||||||
\(347\) | 143.949 | 0.414839 | 0.207419 | − | 0.978252i | \(-0.433494\pi\) | ||||
0.207419 | + | 0.978252i | \(0.433494\pi\) | |||||||
\(348\) | 64.3649 | − | 249.760i | 0.184957 | − | 0.717702i | ||||
\(349\) | 392.805 | 1.12552 | 0.562758 | − | 0.826622i | \(-0.309740\pi\) | ||||
0.562758 | + | 0.826622i | \(0.309740\pi\) | |||||||
\(350\) | −41.8745 | + | 101.089i | −0.119641 | + | 0.288827i | ||||
\(351\) | 437.298 | − | 463.188i | 1.24586 | − | 1.31962i | ||||
\(352\) | 62.2038i | 0.176715i | ||||||||
\(353\) | −409.836 | −1.16101 | −0.580505 | − | 0.814257i | \(-0.697145\pi\) | ||||
−0.580505 | + | 0.814257i | \(0.697145\pi\) | |||||||
\(354\) | −37.4891 | + | 145.472i | −0.105902 | + | 0.410939i | ||||
\(355\) | −97.3607 | + | 489.445i | −0.274256 | + | 1.37872i | ||||
\(356\) | − | 292.073i | − | 0.820429i | ||||||
\(357\) | 34.6679 | − | 134.525i | 0.0971091 | − | 0.376820i | ||||
\(358\) | 185.820i | 0.519052i | ||||||||
\(359\) | − | 333.035i | − | 0.927674i | −0.885921 | − | 0.463837i | \(-0.846472\pi\) | ||
0.885921 | − | 0.463837i | \(-0.153528\pi\) | |||||||
\(360\) | 97.2833 | + | 82.0729i | 0.270231 | + | 0.227980i | ||||
\(361\) | 256.692 | 0.711059 | ||||||||
\(362\) | 416.604 | 1.15084 | ||||||||
\(363\) | −0.244434 | − | 0.0629922i | −0.000673371 | − | 0.000173532i | ||||
\(364\) | 146.031 | 0.401185 | ||||||||
\(365\) | −38.4224 | + | 193.154i | −0.105267 | + | 0.529190i | ||||
\(366\) | −73.8650 | − | 19.0355i | −0.201817 | − | 0.0520095i | ||||
\(367\) | − | 345.521i | − | 0.941473i | −0.882274 | − | 0.470737i | \(-0.843988\pi\) | ||
0.882274 | − | 0.470737i | \(-0.156012\pi\) | |||||||
\(368\) | 19.1833 | 0.0521286 | ||||||||
\(369\) | −136.757 | + | 247.713i | −0.370615 | + | 0.671309i | ||||
\(370\) | 66.9777 | − | 336.706i | 0.181021 | − | 0.910015i | ||||
\(371\) | − | 114.587i | − | 0.308860i | ||||||
\(372\) | 181.053 | + | 46.6585i | 0.486701 | + | 0.125426i | ||||
\(373\) | 601.127i | 1.61160i | 0.592188 | + | 0.805800i | \(0.298264\pi\) | ||||
−0.592188 | + | 0.805800i | \(0.701736\pi\) | |||||||
\(374\) | − | 232.682i | − | 0.622144i | ||||||
\(375\) | 249.938 | + | 279.564i | 0.666501 | + | 0.745504i | ||||
\(376\) | −142.781 | −0.379735 | ||||||||
\(377\) | −1014.17 | −2.69012 | ||||||||
\(378\) | 81.1248 | − | 85.9276i | 0.214616 | − | 0.227322i | ||||
\(379\) | 366.586 | 0.967246 | 0.483623 | − | 0.875277i | \(-0.339321\pi\) | ||||
0.483623 | + | 0.875277i | \(0.339321\pi\) | |||||||
\(380\) | 243.758 | + | 48.4886i | 0.641469 | + | 0.127601i | ||||
\(381\) | 151.880 | − | 589.351i | 0.398634 | − | 1.54685i | ||||
\(382\) | − | 257.338i | − | 0.673661i | ||||||
\(383\) | 699.790 | 1.82713 | 0.913563 | − | 0.406696i | \(-0.133319\pi\) | ||||
0.913563 | + | 0.406696i | \(0.133319\pi\) | |||||||
\(384\) | 32.8673 | + | 8.47011i | 0.0855918 | + | 0.0220576i | ||||
\(385\) | 166.887 | + | 33.1973i | 0.433473 | + | 0.0862268i | ||||
\(386\) | 11.6834i | 0.0302678i | ||||||||
\(387\) | 163.112 | − | 295.451i | 0.421478 | − | 0.763440i | ||||
\(388\) | − | 237.519i | − | 0.612163i | ||||||
\(389\) | − | 192.793i | − | 0.495613i | −0.968810 | − | 0.247807i | \(-0.920290\pi\) | ||
0.968810 | − | 0.247807i | \(-0.0797097\pi\) | |||||||
\(390\) | 217.048 | − | 450.962i | 0.556534 | − | 1.15631i | ||||
\(391\) | −71.7579 | −0.183524 | ||||||||
\(392\) | −111.502 | −0.284444 | ||||||||
\(393\) | −174.214 | + | 676.016i | −0.443292 | + | 1.72014i | ||||
\(394\) | 87.5240 | 0.222142 | ||||||||
\(395\) | −150.882 | − | 30.0135i | −0.381979 | − | 0.0759835i | ||||
\(396\) | 95.6630 | − | 173.278i | 0.241573 | − | 0.437571i | ||||
\(397\) | − | 160.829i | − | 0.405111i | −0.979271 | − | 0.202555i | \(-0.935075\pi\) | ||
0.979271 | − | 0.202555i | \(-0.0649246\pi\) | |||||||
\(398\) | 445.181 | 1.11854 | ||||||||
\(399\) | 57.5849 | − | 223.451i | 0.144323 | − | 0.560028i | ||||
\(400\) | 92.3873 | + | 38.2698i | 0.230968 | + | 0.0956746i | ||||
\(401\) | 771.410i | 1.92371i | 0.273551 | + | 0.961857i | \(0.411802\pi\) | ||||
−0.273551 | + | 0.961857i | \(0.588198\pi\) | |||||||
\(402\) | −72.2040 | + | 280.179i | −0.179612 | + | 0.696963i | ||||
\(403\) | − | 735.181i | − | 1.82427i | ||||||
\(404\) | 305.613i | 0.756469i | ||||||||
\(405\) | −144.778 | − | 378.238i | −0.357477 | − | 0.933922i | ||||
\(406\) | −188.143 | −0.463407 | ||||||||
\(407\) | −533.868 | −1.31171 | ||||||||
\(408\) | −122.945 | − | 31.6836i | −0.301335 | − | 0.0776559i | ||||
\(409\) | 740.399 | 1.81027 | 0.905134 | − | 0.425127i | \(-0.139771\pi\) | ||||
0.905134 | + | 0.425127i | \(0.139771\pi\) | |||||||
\(410\) | −43.3726 | + | 218.039i | −0.105787 | + | 0.531804i | ||||
\(411\) | 83.9850 | + | 21.6435i | 0.204343 | + | 0.0526606i | ||||
\(412\) | − | 307.840i | − | 0.747185i | ||||||
\(413\) | 109.583 | 0.265335 | ||||||||
\(414\) | −53.4381 | − | 29.5020i | −0.129078 | − | 0.0712609i | ||||
\(415\) | −540.599 | − | 107.536i | −1.30265 | − | 0.259124i | ||||
\(416\) | − | 133.460i | − | 0.320818i | ||||||
\(417\) | −55.4698 | − | 14.2949i | −0.133021 | − | 0.0342804i | ||||
\(418\) | − | 386.494i | − | 0.924627i | ||||||
\(419\) | 374.440i | 0.893652i | 0.894621 | + | 0.446826i | \(0.147446\pi\) | ||||
−0.894621 | + | 0.446826i | \(0.852554\pi\) | |||||||
\(420\) | 40.2654 | − | 83.6596i | 0.0958700 | − | 0.199190i | ||||
\(421\) | 112.190 | 0.266484 | 0.133242 | − | 0.991084i | \(-0.457461\pi\) | ||||
0.133242 | + | 0.991084i | \(0.457461\pi\) | |||||||
\(422\) | −138.194 | −0.327475 | ||||||||
\(423\) | 397.737 | + | 219.582i | 0.940277 | + | 0.519106i | ||||
\(424\) | −104.723 | −0.246989 | ||||||||
\(425\) | −345.588 | − | 143.154i | −0.813148 | − | 0.336832i | ||||
\(426\) | 105.672 | − | 410.048i | 0.248056 | − | 0.962553i | ||||
\(427\) | 55.6421i | 0.130309i | ||||||||
\(428\) | −11.7825 | −0.0275292 | ||||||||
\(429\) | −753.664 | − | 194.224i | −1.75679 | − | 0.452737i | ||||
\(430\) | 51.7311 | − | 260.059i | 0.120305 | − | 0.604788i | ||||
\(431\) | − | 110.755i | − | 0.256973i | −0.991711 | − | 0.128486i | \(-0.958988\pi\) | ||
0.991711 | − | 0.128486i | \(-0.0410119\pi\) | |||||||
\(432\) | −78.5307 | − | 74.1413i | −0.181784 | − | 0.171623i | ||||
\(433\) | 505.829i | 1.16820i | 0.811683 | + | 0.584099i | \(0.198552\pi\) | ||||
−0.811683 | + | 0.584099i | \(0.801448\pi\) | |||||||
\(434\) | − | 136.386i | − | 0.314253i | ||||||
\(435\) | −279.640 | + | 581.009i | −0.642850 | + | 1.33565i | ||||
\(436\) | 186.849 | 0.428554 | ||||||||
\(437\) | −119.193 | −0.272752 | ||||||||
\(438\) | 41.7023 | − | 161.821i | 0.0952108 | − | 0.369454i | ||||
\(439\) | 98.1758 | 0.223635 | 0.111818 | − | 0.993729i | \(-0.464333\pi\) | ||||
0.111818 | + | 0.993729i | \(0.464333\pi\) | |||||||
\(440\) | 30.3396 | − | 152.521i | 0.0689536 | − | 0.346639i | ||||
\(441\) | 310.606 | + | 171.479i | 0.704323 | + | 0.388841i | ||||
\(442\) | 499.227i | 1.12947i | ||||||||
\(443\) | 385.457 | 0.870107 | 0.435053 | − | 0.900405i | \(-0.356729\pi\) | ||||
0.435053 | + | 0.900405i | \(0.356729\pi\) | |||||||
\(444\) | −72.6953 | + | 282.085i | −0.163728 | + | 0.635328i | ||||
\(445\) | −142.457 | + | 716.151i | −0.320129 | + | 1.60933i | ||||
\(446\) | − | 409.356i | − | 0.917839i | ||||||
\(447\) | −1.56609 | + | 6.07704i | −0.00350356 | + | 0.0135952i | ||||
\(448\) | − | 24.7587i | − | 0.0552650i | ||||||
\(449\) | − | 636.951i | − | 1.41860i | −0.704907 | − | 0.709300i | \(-0.749011\pi\) | ||
0.704907 | − | 0.709300i | \(-0.250989\pi\) | |||||||
\(450\) | −198.504 | − | 248.689i | −0.441120 | − | 0.552642i | ||||
\(451\) | 345.715 | 0.766552 | ||||||||
\(452\) | 316.050 | 0.699226 | ||||||||
\(453\) | −858.768 | − | 221.310i | −1.89574 | − | 0.488543i | ||||
\(454\) | 385.059 | 0.848148 | ||||||||
\(455\) | −358.063 | − | 71.2261i | −0.786951 | − | 0.156541i | ||||
\(456\) | −204.216 | − | 52.6278i | −0.447842 | − | 0.115412i | ||||
\(457\) | 335.828i | 0.734853i | 0.930053 | + | 0.367427i | \(0.119761\pi\) | ||||
−0.930053 | + | 0.367427i | \(0.880239\pi\) | |||||||
\(458\) | −137.295 | −0.299770 | ||||||||
\(459\) | 293.755 | + | 277.336i | 0.639989 | + | 0.604218i | ||||
\(460\) | −47.0367 | − | 9.35658i | −0.102254 | − | 0.0203404i | ||||
\(461\) | − | 480.066i | − | 1.04136i | −0.853752 | − | 0.520679i | \(-0.825679\pi\) | ||
0.853752 | − | 0.520679i | \(-0.174321\pi\) | |||||||
\(462\) | −139.815 | − | 36.0312i | −0.302630 | − | 0.0779896i | ||||
\(463\) | − | 397.487i | − | 0.858504i | −0.903185 | − | 0.429252i | \(-0.858777\pi\) | ||
0.903185 | − | 0.429252i | \(-0.141223\pi\) | |||||||
\(464\) | 171.947i | 0.370576i | ||||||||
\(465\) | −421.177 | − | 202.712i | −0.905756 | − | 0.435941i | ||||
\(466\) | −227.636 | −0.488489 | ||||||||
\(467\) | −360.185 | −0.771274 | −0.385637 | − | 0.922651i | \(-0.626018\pi\) | ||||
−0.385637 | + | 0.922651i | \(0.626018\pi\) | |||||||
\(468\) | −205.249 | + | 371.775i | −0.438565 | + | 0.794390i | ||||
\(469\) | 211.057 | 0.450016 | ||||||||
\(470\) | 350.092 | + | 69.6405i | 0.744877 | + | 0.148171i | ||||
\(471\) | 69.6371 | − | 270.219i | 0.147849 | − | 0.573712i | ||||
\(472\) | − | 100.150i | − | 0.212183i | ||||||
\(473\) | −412.340 | −0.871754 | ||||||||
\(474\) | 126.406 | + | 32.5756i | 0.266679 | + | 0.0687249i | ||||
\(475\) | −574.035 | − | 237.784i | −1.20850 | − | 0.500598i | ||||
\(476\) | 92.6135i | 0.194566i | ||||||||
\(477\) | 291.723 | + | 161.054i | 0.611578 | + | 0.337639i | ||||
\(478\) | − | 66.5227i | − | 0.139169i | ||||||
\(479\) | 462.822i | 0.966226i | 0.875558 | + | 0.483113i | \(0.160494\pi\) | ||||
−0.875558 | + | 0.483113i | \(0.839506\pi\) | |||||||
\(480\) | −76.4579 | − | 36.7992i | −0.159287 | − | 0.0766650i | ||||
\(481\) | 1145.43 | 2.38136 | ||||||||
\(482\) | −274.177 | −0.568832 | ||||||||
\(483\) | −11.1118 | + | 43.1182i | −0.0230059 | + | 0.0892717i | ||||
\(484\) | 0.168280 | 0.000347686 | ||||||||
\(485\) | −115.849 | + | 582.387i | −0.238864 | + | 1.20080i | ||||
\(486\) | 104.738 | + | 327.304i | 0.215509 | + | 0.673465i | ||||
\(487\) | 327.948i | 0.673404i | 0.941611 | + | 0.336702i | \(0.109311\pi\) | ||||
−0.941611 | + | 0.336702i | \(0.890689\pi\) | |||||||
\(488\) | 50.8522 | 0.104205 | ||||||||
\(489\) | 11.3227 | − | 43.9363i | 0.0231547 | − | 0.0898492i | ||||
\(490\) | 273.399 | + | 54.3847i | 0.557957 | + | 0.110989i | ||||
\(491\) | − | 33.6438i | − | 0.0685209i | −0.999413 | − | 0.0342604i | \(-0.989092\pi\) | ||
0.999413 | − | 0.0342604i | \(-0.0109076\pi\) | |||||||
\(492\) | 47.0750 | − | 182.669i | 0.0956810 | − | 0.371279i | ||||
\(493\) | − | 643.192i | − | 1.30465i | ||||||
\(494\) | 829.237i | 1.67862i | ||||||||
\(495\) | −319.078 | + | 378.212i | −0.644601 | + | 0.764064i | ||||
\(496\) | −124.645 | −0.251301 | ||||||||
\(497\) | −308.886 | −0.621502 | ||||||||
\(498\) | 452.904 | + | 116.716i | 0.909445 | + | 0.234370i | ||||
\(499\) | 494.945 | 0.991875 | 0.495937 | − | 0.868358i | \(-0.334825\pi\) | ||||
0.495937 | + | 0.868358i | \(0.334825\pi\) | |||||||
\(500\) | −207.864 | − | 138.898i | −0.415728 | − | 0.277795i | ||||
\(501\) | −150.461 | − | 38.7749i | −0.300322 | − | 0.0773950i | ||||
\(502\) | 199.475i | 0.397361i | ||||||||
\(503\) | 510.268 | 1.01445 | 0.507224 | − | 0.861814i | \(-0.330672\pi\) | ||||
0.507224 | + | 0.861814i | \(0.330672\pi\) | |||||||
\(504\) | −38.0764 | + | 68.9692i | −0.0755484 | + | 0.136844i | ||||
\(505\) | 149.062 | − | 749.352i | 0.295171 | − | 1.48387i | ||||
\(506\) | 74.5797i | 0.147391i | ||||||||
\(507\) | 1126.05 | + | 290.191i | 2.22101 | + | 0.572370i | ||||
\(508\) | 405.738i | 0.798696i | ||||||||
\(509\) | 5.91018i | 0.0116114i | 0.999983 | + | 0.00580568i | \(0.00184801\pi\) | ||||
−0.999983 | + | 0.00580568i | \(0.998152\pi\) | |||||||
\(510\) | 286.002 | + | 137.653i | 0.560787 | + | 0.269907i | ||||
\(511\) | −121.899 | −0.238550 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 487.939 | + | 460.666i | 0.951148 | + | 0.897985i | ||||
\(514\) | −191.971 | −0.373484 | ||||||||
\(515\) | −150.148 | + | 754.811i | −0.291549 | + | 1.46565i | ||||
\(516\) | −56.1471 | + | 217.872i | −0.108812 | + | 0.422233i | ||||
\(517\) | − | 555.093i | − | 1.07368i | ||||||
\(518\) | 212.493 | 0.410219 | ||||||||
\(519\) | 63.4798 | + | 16.3592i | 0.122312 | + | 0.0315205i | ||||
\(520\) | −65.0947 | + | 327.239i | −0.125182 | + | 0.629307i | ||||
\(521\) | 112.546i | 0.216019i | 0.994150 | + | 0.108010i | \(0.0344477\pi\) | ||||
−0.994150 | + | 0.108010i | \(0.965552\pi\) | |||||||
\(522\) | 264.437 | − | 478.985i | 0.506585 | − | 0.917596i | ||||
\(523\) | 65.5530i | 0.125340i | 0.998034 | + | 0.0626702i | \(0.0199616\pi\) | ||||
−0.998034 | + | 0.0626702i | \(0.980038\pi\) | |||||||
\(524\) | − | 465.402i | − | 0.888173i | ||||||
\(525\) | −139.534 | + | 185.491i | −0.265778 | + | 0.353316i | ||||
\(526\) | −431.830 | −0.820969 | ||||||||
\(527\) | 466.254 | 0.884732 | ||||||||
\(528\) | −32.9295 | + | 127.779i | −0.0623665 | + | 0.242006i | ||||
\(529\) | 23.0000 | 0.0434783 | ||||||||
\(530\) | 256.777 | + | 51.0783i | 0.484485 | + | 0.0963741i | ||||
\(531\) | −154.021 | + | 278.984i | −0.290058 | + | 0.525393i | ||||
\(532\) | 153.835i | 0.289163i | ||||||||
\(533\) | −741.744 | −1.39164 | ||||||||
\(534\) | 154.618 | − | 599.977i | 0.289547 | − | 1.12355i | ||||
\(535\) | 28.8903 | + | 5.74687i | 0.0540005 | + | 0.0107418i | ||||
\(536\) | − | 192.889i | − | 0.359867i | ||||||
\(537\) | −98.3700 | + | 381.713i | −0.183184 | + | 0.710825i | ||||
\(538\) | − | 432.408i | − | 0.803732i | ||||||
\(539\) | − | 433.491i | − | 0.804250i | ||||||
\(540\) | 156.392 | + | 220.094i | 0.289615 | + | 0.407582i | ||||
\(541\) | 848.977 | 1.56927 | 0.784637 | − | 0.619955i | \(-0.212849\pi\) | ||||
0.784637 | + | 0.619955i | \(0.212849\pi\) | |||||||
\(542\) | −500.322 | −0.923104 | ||||||||
\(543\) | 855.791 | + | 220.543i | 1.57604 | + | 0.406156i | ||||
\(544\) | 84.6410 | 0.155590 | ||||||||
\(545\) | −458.147 | − | 91.1349i | −0.840637 | − | 0.167220i | ||||
\(546\) | 299.978 | + | 77.3063i | 0.549410 | + | 0.141587i | ||||
\(547\) | 341.832i | 0.624921i | 0.949931 | + | 0.312461i | \(0.101153\pi\) | ||||
−0.949931 | + | 0.312461i | \(0.898847\pi\) | |||||||
\(548\) | −57.8194 | −0.105510 | ||||||||
\(549\) | −141.657 | − | 78.2056i | −0.258027 | − | 0.142451i | ||||
\(550\) | −148.783 | + | 359.177i | −0.270514 | + | 0.653050i | ||||
\(551\) | − | 1068.37i | − | 1.93896i | ||||||
\(552\) | 39.4065 | + | 10.1553i | 0.0713885 | + | 0.0183973i | ||||
\(553\) | − | 95.2208i | − | 0.172189i | ||||||
\(554\) | − | 34.9155i | − | 0.0630244i | ||||||
\(555\) | 315.832 | − | 656.205i | 0.569066 | − | 1.18235i | ||||
\(556\) | 38.1881 | 0.0686837 | ||||||||
\(557\) | −361.120 | −0.648331 | −0.324165 | − | 0.946000i | \(-0.605083\pi\) | ||||
−0.324165 | + | 0.946000i | \(0.605083\pi\) | |||||||
\(558\) | 347.219 | + | 191.692i | 0.622257 | + | 0.343534i | ||||
\(559\) | 884.690 | 1.58263 | ||||||||
\(560\) | −12.0760 | + | 60.7074i | −0.0215642 | + | 0.108406i | ||||
\(561\) | 123.178 | − | 477.976i | 0.219568 | − | 0.852007i | ||||
\(562\) | 191.914i | 0.341484i | ||||||||
\(563\) | −607.902 | −1.07976 | −0.539878 | − | 0.841744i | \(-0.681529\pi\) | ||||
−0.539878 | + | 0.841744i | \(0.681529\pi\) | |||||||
\(564\) | −293.300 | − | 75.5854i | −0.520036 | − | 0.134017i | ||||
\(565\) | −774.942 | − | 154.152i | −1.37158 | − | 0.272835i | ||||
\(566\) | − | 48.9370i | − | 0.0864612i | ||||||
\(567\) | 212.135 | − | 133.567i | 0.374136 | − | 0.235568i | ||||
\(568\) | 282.297i | 0.497001i | ||||||||
\(569\) | − | 427.157i | − | 0.750714i | −0.926880 | − | 0.375357i | \(-0.877520\pi\) | ||
0.926880 | − | 0.375357i | \(-0.122480\pi\) | |||||||
\(570\) | 475.060 | + | 228.647i | 0.833439 | + | 0.401134i | ||||
\(571\) | −812.243 | −1.42249 | −0.711246 | − | 0.702944i | \(-0.751869\pi\) | ||||
−0.711246 | + | 0.702944i | \(0.751869\pi\) | |||||||
\(572\) | 518.859 | 0.907096 | ||||||||
\(573\) | 136.230 | − | 528.626i | 0.237749 | − | 0.922558i | ||||
\(574\) | −137.604 | −0.239728 | ||||||||
\(575\) | 110.769 | + | 45.8839i | 0.192641 | + | 0.0797981i | ||||
\(576\) | 63.0322 | + | 34.7987i | 0.109431 | + | 0.0604143i | ||||
\(577\) | − | 780.939i | − | 1.35345i | −0.736237 | − | 0.676724i | \(-0.763399\pi\) | ||
0.736237 | − | 0.676724i | \(-0.236601\pi\) | |||||||
\(578\) | 92.0962 | 0.159336 | ||||||||
\(579\) | −6.18497 | + | 24.0001i | −0.0106822 | + | 0.0414509i | ||||
\(580\) | 83.8664 | − | 421.607i | 0.144597 | − | 0.726909i | ||||
\(581\) | − | 341.170i | − | 0.587211i | ||||||
\(582\) | 125.738 | − | 487.913i | 0.216045 | − | 0.838338i | ||||
\(583\) | − | 407.136i | − | 0.698347i | ||||||
\(584\) | 111.405i | 0.190763i | ||||||||
\(585\) | 684.592 | − | 811.467i | 1.17024 | − | 1.38712i | ||||
\(586\) | −668.170 | −1.14022 | ||||||||
\(587\) | −562.376 | −0.958051 | −0.479026 | − | 0.877801i | \(-0.659010\pi\) | ||||
−0.479026 | + | 0.877801i | \(0.659010\pi\) | |||||||
\(588\) | −229.048 | − | 59.0272i | −0.389538 | − | 0.100386i | ||||
\(589\) | 774.467 | 1.31488 | ||||||||
\(590\) | −48.8478 | + | 245.564i | −0.0827928 | + | 0.416210i | ||||
\(591\) | 179.792 | + | 46.3336i | 0.304217 | + | 0.0783986i | ||||
\(592\) | − | 194.201i | − | 0.328043i | ||||||
\(593\) | −305.095 | −0.514495 | −0.257247 | − | 0.966346i | \(-0.582816\pi\) | ||||
−0.257247 | + | 0.966346i | \(0.582816\pi\) | |||||||
\(594\) | 288.242 | − | 305.306i | 0.485255 | − | 0.513984i | ||||
\(595\) | 45.1718 | − | 227.084i | 0.0759190 | − | 0.381654i | ||||
\(596\) | − | 4.18373i | − | 0.00701968i | ||||||
\(597\) | 914.492 | + | 235.671i | 1.53181 | + | 0.394758i | ||||
\(598\) | − | 160.013i | − | 0.267581i | ||||||
\(599\) | − | 615.611i | − | 1.02773i | −0.857871 | − | 0.513866i | \(-0.828213\pi\) | ||
0.857871 | − | 0.513866i | \(-0.171787\pi\) | |||||||
\(600\) | 169.523 | + | 127.522i | 0.282539 | + | 0.212537i | ||||
\(601\) | 678.158 | 1.12838 | 0.564192 | − | 0.825644i | \(-0.309188\pi\) | ||||
0.564192 | + | 0.825644i | \(0.309188\pi\) | |||||||
\(602\) | 164.122 | 0.272628 | ||||||||
\(603\) | −296.643 | + | 537.322i | −0.491946 | + | 0.891081i | ||||
\(604\) | 591.218 | 0.978837 | ||||||||
\(605\) | −0.412616 | − | 0.0820778i | −0.000682010 | − | 0.000135666i | ||||
\(606\) | −161.786 | + | 627.793i | −0.266974 | + | 1.03596i | ||||
\(607\) | − | 537.292i | − | 0.885161i | −0.896729 | − | 0.442580i | \(-0.854063\pi\) | ||
0.896729 | − | 0.442580i | \(-0.145937\pi\) | |||||||
\(608\) | 140.592 | 0.231237 | ||||||||
\(609\) | −386.484 | − | 99.5995i | −0.634621 | − | 0.163546i | ||||
\(610\) | −124.688 | − | 24.8029i | −0.204406 | − | 0.0406606i | ||||
\(611\) | 1190.97i | 1.94922i | ||||||||
\(612\) | −235.781 | − | 130.169i | −0.385262 | − | 0.212695i | ||||
\(613\) | − | 109.949i | − | 0.179362i | −0.995971 | − | 0.0896810i | \(-0.971415\pi\) | ||
0.995971 | − | 0.0896810i | \(-0.0285848\pi\) | |||||||
\(614\) | − | 241.109i | − | 0.392685i | ||||||
\(615\) | −204.522 | + | 424.937i | −0.332556 | + | 0.690954i | ||||
\(616\) | 96.2553 | 0.156259 | ||||||||
\(617\) | −789.606 | −1.27975 | −0.639875 | − | 0.768479i | \(-0.721014\pi\) | ||||
−0.639875 | + | 0.768479i | \(0.721014\pi\) | |||||||
\(618\) | 162.965 | − | 632.366i | 0.263697 | − | 1.02325i | ||||
\(619\) | −387.141 | −0.625429 | −0.312714 | − | 0.949847i | \(-0.601238\pi\) | ||||
−0.312714 | + | 0.949847i | \(0.601238\pi\) | |||||||
\(620\) | 305.626 | + | 60.7953i | 0.492945 | + | 0.0980569i | ||||
\(621\) | −94.1550 | − | 88.8923i | −0.151618 | − | 0.143144i | ||||
\(622\) | − | 25.9700i | − | 0.0417524i | ||||||
\(623\) | −451.959 | −0.725457 | ||||||||
\(624\) | 70.6515 | − | 274.155i | 0.113224 | − | 0.439351i | ||||
\(625\) | 441.928 | + | 441.956i | 0.707084 | + | 0.707129i | ||||
\(626\) | 426.873i | 0.681906i | ||||||||
\(627\) | 204.603 | − | 793.938i | 0.326320 | − | 1.26625i | ||||
\(628\) | 186.032i | 0.296229i | ||||||||
\(629\) | 726.437i | 1.15491i | ||||||||
\(630\) | 127.001 | − | 150.538i | 0.201589 | − | 0.238949i | ||||
\(631\) | −707.223 | −1.12080 | −0.560399 | − | 0.828223i | \(-0.689352\pi\) | ||||
−0.560399 | + | 0.828223i | \(0.689352\pi\) | |||||||
\(632\) | −87.0239 | −0.137696 | ||||||||
\(633\) | −283.880 | − | 73.1576i | −0.448467 | − | 0.115573i | ||||
\(634\) | 251.949 | 0.397396 | ||||||||
\(635\) | 197.897 | − | 994.852i | 0.311648 | − | 1.56670i | ||||
\(636\) | −215.123 | − | 55.4386i | −0.338244 | − | 0.0871676i | ||||
\(637\) | 930.070i | 1.46008i | ||||||||
\(638\) | −668.485 | −1.04778 | ||||||||
\(639\) | 434.143 | − | 786.381i | 0.679411 | − | 1.23064i | ||||
\(640\) | 55.4815 | + | 11.0364i | 0.0866899 | + | 0.0172444i | ||||
\(641\) | 628.409i | 0.980357i | 0.871622 | + | 0.490179i | \(0.163068\pi\) | ||||
−0.871622 | + | 0.490179i | \(0.836932\pi\) | |||||||
\(642\) | −24.2037 | − | 6.23745i | −0.0377005 | − | 0.00971565i | ||||
\(643\) | 949.121i | 1.47608i | 0.674755 | + | 0.738042i | \(0.264249\pi\) | ||||
−0.674755 | + | 0.738042i | \(0.735751\pi\) | |||||||
\(644\) | − | 29.6847i | − | 0.0460942i | ||||||
\(645\) | 243.937 | − | 506.829i | 0.378196 | − | 0.785781i | ||||
\(646\) | −525.905 | −0.814094 | ||||||||
\(647\) | 1047.41 | 1.61887 | 0.809433 | − | 0.587212i | \(-0.199774\pi\) | ||||
0.809433 | + | 0.587212i | \(0.199774\pi\) | |||||||
\(648\) | −122.069 | − | 193.874i | −0.188378 | − | 0.299188i | ||||
\(649\) | 389.357 | 0.599934 | ||||||||
\(650\) | 319.219 | − | 770.628i | 0.491106 | − | 1.18558i | ||||
\(651\) | 72.2003 | − | 280.165i | 0.110907 | − | 0.430361i | ||||
\(652\) | 30.2478i | 0.0463924i | ||||||||
\(653\) | −115.915 | −0.177512 | −0.0887558 | − | 0.996053i | \(-0.528289\pi\) | ||||
−0.0887558 | + | 0.996053i | \(0.528289\pi\) | |||||||
\(654\) | 383.827 | + | 98.9147i | 0.586891 | + | 0.151246i | ||||
\(655\) | −226.998 | + | 1141.15i | −0.346562 | + | 1.74221i | ||||
\(656\) | 125.758i | 0.191705i | ||||||||
\(657\) | 171.330 | − | 310.337i | 0.260776 | − | 0.472355i | ||||
\(658\) | 220.941i | 0.335777i | ||||||||
\(659\) | 735.582i | 1.11621i | 0.829771 | + | 0.558104i | \(0.188471\pi\) | ||||
−0.829771 | + | 0.558104i | \(0.811529\pi\) | |||||||
\(660\) | 143.066 | − | 297.248i | 0.216766 | − | 0.450376i | ||||
\(661\) | 366.829 | 0.554960 | 0.277480 | − | 0.960731i | \(-0.410501\pi\) | ||||
0.277480 | + | 0.960731i | \(0.410501\pi\) | |||||||
\(662\) | −390.970 | −0.590589 | ||||||||
\(663\) | −264.282 | + | 1025.51i | −0.398615 | + | 1.54678i | ||||
\(664\) | −311.801 | −0.469579 | ||||||||
\(665\) | 75.0322 | − | 377.196i | 0.112830 | − | 0.567213i | ||||
\(666\) | −298.662 | + | 540.978i | −0.448441 | + | 0.812279i | ||||
\(667\) | 206.157i | 0.309082i | ||||||||
\(668\) | 103.585 | 0.155067 | ||||||||
\(669\) | 216.706 | − | 840.902i | 0.323925 | − | 1.25695i | ||||
\(670\) | −94.0807 | + | 472.956i | −0.140419 | + | 0.705904i | ||||
\(671\) | 197.700i | 0.294635i | ||||||||
\(672\) | 13.1068 | − | 50.8595i | 0.0195042 | − | 0.0756837i | ||||
\(673\) | − | 888.959i | − | 1.32089i | −0.750874 | − | 0.660445i | \(-0.770368\pi\) | ||
0.750874 | − | 0.660445i | \(-0.229632\pi\) | |||||||
\(674\) | − | 448.583i | − | 0.665554i | ||||||
\(675\) | −276.117 | − | 615.942i | −0.409062 | − | 0.912507i | ||||
\(676\) | −775.230 | −1.14679 | ||||||||
\(677\) | −185.045 | −0.273331 | −0.136666 | − | 0.990617i | \(-0.543639\pi\) | ||||
−0.136666 | + | 0.990617i | \(0.543639\pi\) | |||||||
\(678\) | 649.231 | + | 167.311i | 0.957568 | + | 0.246772i | ||||
\(679\) | −367.542 | −0.541299 | ||||||||
\(680\) | −207.536 | − | 41.2833i | −0.305200 | − | 0.0607107i | ||||
\(681\) | 790.990 | + | 203.843i | 1.16151 | + | 0.299329i | ||||
\(682\) | − | 484.589i | − | 0.710541i | ||||||
\(683\) | −107.048 | −0.156733 | −0.0783663 | − | 0.996925i | \(-0.524970\pi\) | ||||
−0.0783663 | + | 0.996925i | \(0.524970\pi\) | |||||||
\(684\) | −391.641 | − | 216.216i | −0.572575 | − | 0.316106i | ||||
\(685\) | 141.771 | + | 28.2011i | 0.206965 | + | 0.0411695i | ||||
\(686\) | 387.002i | 0.564143i | ||||||||
\(687\) | −282.031 | − | 72.6813i | −0.410526 | − | 0.105795i | ||||
\(688\) | − | 149.994i | − | 0.218014i | ||||||
\(689\) | 873.525i | 1.26782i | ||||||||
\(690\) | −91.6699 | − | 44.1207i | −0.132855 | − | 0.0639431i | ||||
\(691\) | −781.127 | −1.13043 | −0.565215 | − | 0.824944i | \(-0.691207\pi\) | ||||
−0.565215 | + | 0.824944i | \(0.691207\pi\) | |||||||
\(692\) | −43.7026 | −0.0631540 | ||||||||
\(693\) | −268.134 | − | 148.031i | −0.386918 | − | 0.213609i | ||||
\(694\) | −203.575 | −0.293335 | ||||||||
\(695\) | −93.6357 | − | 18.6261i | −0.134728 | − | 0.0268001i | ||||
\(696\) | −91.0257 | + | 353.215i | −0.130784 | + | 0.507492i | ||||
\(697\) | − | 470.417i | − | 0.674916i | ||||||
\(698\) | −555.510 | −0.795860 | ||||||||
\(699\) | −467.611 | − | 120.506i | −0.668971 | − | 0.172398i | ||||
\(700\) | 59.2195 | − | 142.962i | 0.0845993 | − | 0.204231i | ||||
\(701\) | 72.2854i | 0.103117i | 0.998670 | + | 0.0515587i | \(0.0164189\pi\) | ||||
−0.998670 | + | 0.0515587i | \(0.983581\pi\) | |||||||
\(702\) | −618.433 | + | 655.046i | −0.880959 | + | 0.933114i | ||||
\(703\) | 1206.64i | 1.71642i | ||||||||
\(704\) | − | 87.9694i | − | 0.124957i | ||||||
\(705\) | 682.294 | + | 328.388i | 0.967793 | + | 0.465799i | ||||
\(706\) | 579.596 | 0.820958 | ||||||||
\(707\) | 472.912 | 0.668900 | ||||||||
\(708\) | 53.0177 | − | 205.729i | 0.0748837 | − | 0.290578i | ||||
\(709\) | −1081.84 | −1.52587 | −0.762934 | − | 0.646476i | \(-0.776242\pi\) | ||||
−0.762934 | + | 0.646476i | \(0.776242\pi\) | |||||||
\(710\) | 137.689 | − | 692.180i | 0.193928 | − | 0.974901i | ||||
\(711\) | 242.418 | + | 133.834i | 0.340954 | + | 0.188233i | ||||
\(712\) | 413.053i | 0.580131i | ||||||||
\(713\) | −149.445 | −0.209600 | ||||||||
\(714\) | −49.0279 | + | 190.247i | −0.0686665 | + | 0.266452i | ||||
\(715\) | −1272.22 | − | 253.071i | −1.77933 | − | 0.353945i | ||||
\(716\) | − | 262.790i | − | 0.367025i | ||||||
\(717\) | 35.2159 | − | 136.651i | 0.0491156 | − | 0.190588i | ||||
\(718\) | 470.983i | 0.655964i | ||||||||
\(719\) | 905.857i | 1.25988i | 0.776642 | + | 0.629942i | \(0.216921\pi\) | ||||
−0.776642 | + | 0.629942i | \(0.783079\pi\) | |||||||
\(720\) | −137.579 | − | 116.069i | −0.191083 | − | 0.161206i | ||||
\(721\) | −476.358 | −0.660691 | ||||||||
\(722\) | −363.018 | −0.502795 | ||||||||
\(723\) | −563.216 | − | 145.144i | −0.778998 | − | 0.200753i | ||||
\(724\) | −589.168 | −0.813767 | ||||||||
\(725\) | −411.274 | + | 992.859i | −0.567275 | + | 1.36946i | ||||
\(726\) | 0.345682 | + | 0.0890844i | 0.000476145 | + | 0.000122706i | ||||
\(727\) | 385.245i | 0.529910i | 0.964261 | + | 0.264955i | \(0.0853571\pi\) | ||||
−0.964261 | + | 0.264955i | \(0.914643\pi\) | |||||||
\(728\) | −206.519 | −0.283680 | ||||||||
\(729\) | 41.8835 | + | 727.796i | 0.0574533 | + | 0.998348i | ||||
\(730\) | 54.3375 | − | 273.162i | 0.0744349 | − | 0.374194i | ||||
\(731\) | 561.073i | 0.767542i | ||||||||
\(732\) | 104.461 | + | 26.9202i | 0.142706 | + | 0.0367763i | ||||
\(733\) | 873.178i | 1.19124i | 0.803267 | + | 0.595619i | \(0.203093\pi\) | ||||
−0.803267 | + | 0.595619i | \(0.796907\pi\) | |||||||
\(734\) | 488.640i | 0.665722i | ||||||||
\(735\) | 532.827 | + | 256.450i | 0.724934 | + | 0.348911i | ||||
\(736\) | −27.1293 | −0.0368605 | ||||||||
\(737\) | 749.901 | 1.01750 | ||||||||
\(738\) | 193.404 | − | 350.319i | 0.262064 | − | 0.474687i | ||||
\(739\) | 302.677 | 0.409576 | 0.204788 | − | 0.978806i | \(-0.434349\pi\) | ||||
0.204788 | + | 0.978806i | \(0.434349\pi\) | |||||||
\(740\) | −94.7208 | + | 476.174i | −0.128001 | + | 0.643478i | ||||
\(741\) | −438.983 | + | 1703.42i | −0.592419 | + | 2.29881i | ||||
\(742\) | 162.051i | 0.218397i | ||||||||
\(743\) | 154.859 | 0.208424 | 0.104212 | − | 0.994555i | \(-0.466768\pi\) | ||||
0.104212 | + | 0.994555i | \(0.466768\pi\) | |||||||
\(744\) | −256.047 | − | 65.9850i | −0.344150 | − | 0.0886896i | ||||
\(745\) | −2.04059 | + | 10.2583i | −0.00273905 | + | 0.0137696i | ||||
\(746\) | − | 850.122i | − | 1.13957i | ||||||
\(747\) | 868.569 | + | 479.518i | 1.16274 | + | 0.641925i | ||||
\(748\) | 329.062i | 0.439922i | ||||||||
\(749\) | 18.2325i | 0.0243425i | ||||||||
\(750\) | −353.465 | − | 395.363i | −0.471287 | − | 0.527151i | ||||
\(751\) | −1121.82 | −1.49377 | −0.746885 | − | 0.664954i | \(-0.768451\pi\) | ||||
−0.746885 | + | 0.664954i | \(0.768451\pi\) | |||||||
\(752\) | 201.922 | 0.268513 | ||||||||
\(753\) | −105.599 | + | 409.763i | −0.140237 | + | 0.544174i | ||||
\(754\) | 1434.26 | 1.90220 | ||||||||
\(755\) | −1449.64 | − | 288.364i | −1.92006 | − | 0.381939i | ||||
\(756\) | −114.728 | + | 121.520i | −0.151756 | + | 0.160741i | ||||
\(757\) | − | 512.648i | − | 0.677210i | −0.940929 | − | 0.338605i | \(-0.890045\pi\) | ||
0.940929 | − | 0.338605i | \(-0.109955\pi\) | |||||||
\(758\) | −518.431 | −0.683946 | ||||||||
\(759\) | −39.4811 | + | 153.202i | −0.0520173 | + | 0.201847i | ||||
\(760\) | −344.726 | − | 68.5732i | −0.453587 | − | 0.0902279i | ||||
\(761\) | 412.254i | 0.541727i | 0.962618 | + | 0.270863i | \(0.0873092\pi\) | ||||
−0.962618 | + | 0.270863i | \(0.912691\pi\) | |||||||
\(762\) | −214.790 | + | 833.468i | −0.281877 | + | 1.09379i | ||||
\(763\) | − | 289.135i | − | 0.378944i | ||||||
\(764\) | 363.931i | 0.476350i | ||||||||
\(765\) | 514.635 | + | 434.171i | 0.672725 | + | 0.567543i | ||||
\(766\) | −989.652 | −1.29197 | ||||||||
\(767\) | −835.380 | −1.08915 | ||||||||
\(768\) | −46.4813 | − | 11.9785i | −0.0605226 | − | 0.0155971i | ||||
\(769\) | −550.481 | −0.715840 | −0.357920 | − | 0.933752i | \(-0.616514\pi\) | ||||
−0.357920 | + | 0.933752i | \(0.616514\pi\) | |||||||
\(770\) | −236.014 | − | 46.9481i | −0.306512 | − | 0.0609716i | ||||
\(771\) | −394.347 | − | 101.626i | −0.511475 | − | 0.131810i | ||||
\(772\) | − | 16.5228i | − | 0.0214026i | ||||||
\(773\) | −299.447 | −0.387383 | −0.193692 | − | 0.981062i | \(-0.562046\pi\) | ||||
−0.193692 | + | 0.981062i | \(0.562046\pi\) | |||||||
\(774\) | −230.675 | + | 417.831i | −0.298030 | + | 0.539833i | ||||
\(775\) | −719.729 | − | 298.135i | −0.928683 | − | 0.384690i | ||||
\(776\) | 335.903i | 0.432864i | ||||||||
\(777\) | 436.505 | + | 112.490i | 0.561782 | + | 0.144775i | ||||
\(778\) | 272.651i | 0.350451i | ||||||||
\(779\) | − | 781.381i | − | 1.00306i | ||||||
\(780\) | −306.952 | + | 637.757i | −0.393529 | + | 0.817637i | ||||
\(781\) | −1097.49 | −1.40524 | ||||||||
\(782\) | 101.481 | 0.129771 | ||||||||
\(783\) | 796.774 | − | 843.945i | 1.01759 | − | 1.07784i | ||||
\(784\) | 157.688 | 0.201132 | ||||||||
\(785\) | 90.7360 | − | 456.142i | 0.115587 | − | 0.581072i | ||||
\(786\) | 246.376 | − | 956.032i | 0.313455 | − | 1.21633i | ||||
\(787\) | − | 349.278i | − | 0.443809i | −0.975068 | − | 0.221905i | \(-0.928773\pi\) | ||
0.975068 | − | 0.221905i | \(-0.0712273\pi\) | |||||||
\(788\) | −123.778 | −0.157078 | ||||||||
\(789\) | −887.067 | − | 228.603i | −1.12429 | − | 0.289737i | ||||
\(790\) | 213.379 | + | 42.4455i | 0.270100 | + | 0.0537285i | ||||
\(791\) | − | 489.062i | − | 0.618283i | ||||||
\(792\) | −135.288 | + | 245.052i | −0.170818 | + | 0.309410i | ||||
\(793\) | − | 424.173i | − | 0.534896i | ||||||
\(794\) | 227.447i | 0.286457i | ||||||||
\(795\) | 500.433 | + | 240.858i | 0.629475 | + | 0.302966i | ||||
\(796\) | −629.581 | −0.790930 | ||||||||
\(797\) | 425.546 | 0.533934 | 0.266967 | − | 0.963706i | \(-0.413978\pi\) | ||||
0.266967 | + | 0.963706i | \(0.413978\pi\) | |||||||
\(798\) | −81.4373 | + | 316.008i | −0.102052 | + | 0.396000i | ||||
\(799\) | −755.318 | −0.945329 | ||||||||
\(800\) | −130.655 | − | 54.1217i | −0.163319 | − | 0.0676521i | ||||
\(801\) | 635.234 | − | 1150.62i | 0.793051 | − | 1.43648i | ||||
\(802\) | − | 1090.94i | − | 1.36027i | ||||||
\(803\) | −433.115 | −0.539371 | ||||||||
\(804\) | 102.112 | − | 396.233i | 0.127005 | − | 0.492827i | ||||
\(805\) | −14.4786 | + | 72.7856i | −0.0179858 | + | 0.0904169i | ||||
\(806\) | 1039.70i | 1.28995i | ||||||||
\(807\) | 228.909 | − | 888.254i | 0.283654 | − | 1.10069i | ||||
\(808\) | − | 432.203i | − | 0.534904i | ||||||
\(809\) | − | 1476.26i | − | 1.82479i | −0.409308 | − | 0.912396i | \(-0.634230\pi\) | ||
0.409308 | − | 0.912396i | \(-0.365770\pi\) | |||||||
\(810\) | 204.747 | + | 534.910i | 0.252774 | + | 0.660383i | ||||
\(811\) | 428.077 | 0.527839 | 0.263919 | − | 0.964545i | \(-0.414985\pi\) | ||||
0.263919 | + | 0.964545i | \(0.414985\pi\) | |||||||
\(812\) | 266.075 | 0.327678 | ||||||||
\(813\) | −1027.76 | − | 264.861i | −1.26416 | − | 0.325783i | ||||
\(814\) | 755.003 | 0.927522 | ||||||||
\(815\) | 14.7532 | − | 74.1665i | 0.0181021 | − | 0.0910018i | ||||
\(816\) | 173.870 | + | 44.8074i | 0.213076 | + | 0.0549110i | ||||
\(817\) | 931.965i | 1.14072i | ||||||||
\(818\) | −1047.08 | −1.28005 | ||||||||
\(819\) | 575.291 | + | 317.606i | 0.702432 | + | 0.387797i | ||||
\(820\) | 61.3381 | − | 308.354i | 0.0748025 | − | 0.376042i | ||||
\(821\) | − | 864.110i | − | 1.05251i | −0.850327 | − | 0.526255i | \(-0.823596\pi\) | ||
0.850327 | − | 0.526255i | \(-0.176404\pi\) | |||||||
\(822\) | −118.773 | − | 30.6085i | −0.144492 | − | 0.0372366i | ||||
\(823\) | − | 837.181i | − | 1.01723i | −0.860994 | − | 0.508616i | \(-0.830157\pi\) | ||
0.860994 | − | 0.508616i | \(-0.169843\pi\) | |||||||
\(824\) | 435.352i | 0.528339i | ||||||||
\(825\) | −495.773 | + | 659.061i | −0.600936 | + | 0.798862i | ||||
\(826\) | −154.974 | −0.187620 | ||||||||
\(827\) | −105.857 | −0.128001 | −0.0640006 | − | 0.997950i | \(-0.520386\pi\) | ||||
−0.0640006 | + | 0.997950i | \(0.520386\pi\) | |||||||
\(828\) | 75.5729 | + | 41.7221i | 0.0912716 | + | 0.0503890i | ||||
\(829\) | −90.6519 | −0.109351 | −0.0546755 | − | 0.998504i | \(-0.517412\pi\) | ||||
−0.0546755 | + | 0.998504i | \(0.517412\pi\) | |||||||
\(830\) | 764.523 | + | 152.079i | 0.921112 | + | 0.183228i | ||||
\(831\) | 18.4836 | − | 71.7236i | 0.0222426 | − | 0.0863099i | ||||
\(832\) | 188.742i | 0.226853i | ||||||||
\(833\) | −589.853 | −0.708107 | ||||||||
\(834\) | 78.4462 | + | 20.2161i | 0.0940602 | + | 0.0242399i | ||||
\(835\) | −253.986 | − | 50.5231i | −0.304175 | − | 0.0605067i | ||||
\(836\) | 546.585i | 0.653810i | ||||||||
\(837\) | 611.781 | + | 577.586i | 0.730921 | + | 0.690067i | ||||
\(838\) | − | 529.539i | − | 0.631908i | ||||||
\(839\) | 1331.77i | 1.58733i | 0.608353 | + | 0.793667i | \(0.291831\pi\) | ||||
−0.608353 | + | 0.793667i | \(0.708169\pi\) | |||||||
\(840\) | −56.9439 | + | 118.313i | −0.0677903 | + | 0.140848i | ||||
\(841\) | −1006.86 | −1.19722 | ||||||||
\(842\) | −158.660 | −0.188432 | ||||||||
\(843\) | −101.596 | + | 394.230i | −0.120517 | + | 0.467652i | ||||
\(844\) | 195.437 | 0.231560 | ||||||||
\(845\) | 1900.83 | + | 378.115i | 2.24951 | + | 0.447473i | ||||
\(846\) | −562.485 | − | 310.536i | −0.664876 | − | 0.367063i | ||||
\(847\) | − | 0.260400i | − | 0.000307438i | ||||||
\(848\) | 148.101 | 0.174647 | ||||||||
\(849\) | 25.9064 | − | 100.527i | 0.0305140 | − | 0.118406i | ||||
\(850\) | 488.735 | + | 202.450i | 0.574982 | + | 0.238176i | ||||
\(851\) | − | 232.839i | − | 0.273607i | ||||||
\(852\) | −149.443 | + | 579.895i | −0.175402 | + | 0.680628i | ||||
\(853\) | 1657.35i | 1.94296i | 0.237113 | + | 0.971482i | \(0.423799\pi\) | ||||
−0.237113 | + | 0.971482i | \(0.576201\pi\) | |||||||
\(854\) | − | 78.6898i | − | 0.0921426i | ||||||
\(855\) | 854.830 | + | 721.175i | 0.999801 | + | 0.843480i | ||||
\(856\) | 16.6630 | 0.0194661 | ||||||||
\(857\) | 756.541 | 0.882778 | 0.441389 | − | 0.897316i | \(-0.354486\pi\) | ||||
0.441389 | + | 0.897316i | \(0.354486\pi\) | |||||||
\(858\) | 1065.84 | + | 274.674i | 1.24224 | + | 0.320133i | ||||
\(859\) | 892.089 | 1.03852 | 0.519260 | − | 0.854616i | \(-0.326208\pi\) | ||||
0.519260 | + | 0.854616i | \(0.326208\pi\) | |||||||
\(860\) | −73.1588 | + | 367.779i | −0.0850684 | + | 0.427650i | ||||
\(861\) | −282.666 | − | 72.8449i | −0.328300 | − | 0.0846050i | ||||
\(862\) | 156.632i | 0.181707i | ||||||||
\(863\) | −2.66932 | −0.00309307 | −0.00154654 | − | 0.999999i | \(-0.500492\pi\) | ||||
−0.00154654 | + | 0.999999i | \(0.500492\pi\) | |||||||
\(864\) | 111.059 | + | 104.852i | 0.128541 | + | 0.121356i | ||||
\(865\) | 107.157 | + | 21.3157i | 0.123881 | + | 0.0246425i | ||||
\(866\) | − | 715.351i | − | 0.826040i | ||||||
\(867\) | 189.184 | + | 48.7541i | 0.218206 | + | 0.0562331i | ||||
\(868\) | 192.879i | 0.222211i | ||||||||
\(869\) | − | 338.326i | − | 0.389328i | ||||||
\(870\) | 395.470 | − | 821.670i | 0.454563 | − | 0.944449i | ||||
\(871\) | −1608.94 | −1.84723 | ||||||||
\(872\) | −264.245 | −0.303033 | ||||||||
\(873\) | 516.584 | − | 935.709i | 0.591735 | − | 1.07183i | ||||
\(874\) | 168.564 | 0.192865 | ||||||||
\(875\) | −214.933 | + | 321.653i | −0.245638 | + | 0.367603i | ||||
\(876\) | −58.9760 | + | 228.849i | −0.0673242 | + | 0.261244i | ||||
\(877\) | − | 996.312i | − | 1.13605i | −0.823013 | − | 0.568023i | \(-0.807709\pi\) | ||
0.823013 | − | 0.568023i | \(-0.192291\pi\) | |||||||
\(878\) | −138.842 | −0.158134 | ||||||||
\(879\) | −1372.56 | − | 353.717i | −1.56150 | − | 0.402408i | ||||
\(880\) | −42.9067 | + | 215.697i | −0.0487576 | + | 0.245111i | ||||
\(881\) | − | 415.232i | − | 0.471319i | −0.971836 | − | 0.235659i | \(-0.924275\pi\) | ||
0.971836 | − | 0.235659i | \(-0.0757250\pi\) | |||||||
\(882\) | −439.264 | − | 242.508i | −0.498032 | − | 0.274952i | ||||
\(883\) | 767.309i | 0.868979i | 0.900677 | + | 0.434490i | \(0.143071\pi\) | ||||
−0.900677 | + | 0.434490i | \(0.856929\pi\) | |||||||
\(884\) | − | 706.014i | − | 0.798658i | ||||||
\(885\) | −230.340 | + | 478.580i | −0.260272 | + | 0.540768i | ||||
\(886\) | −545.119 | −0.615258 | ||||||||
\(887\) | 813.174 | 0.916769 | 0.458384 | − | 0.888754i | \(-0.348428\pi\) | ||||
0.458384 | + | 0.888754i | \(0.348428\pi\) | |||||||
\(888\) | 102.807 | − | 398.929i | 0.115773 | − | 0.449245i | ||||
\(889\) | 627.847 | 0.706239 | ||||||||
\(890\) | 201.465 | − | 1012.79i | 0.226365 | − | 1.13797i | ||||
\(891\) | 753.731 | − | 474.572i | 0.845938 | − | 0.532628i | ||||
\(892\) | 578.917i | 0.649011i | ||||||||
\(893\) | −1254.61 | −1.40494 | ||||||||
\(894\) | 2.21479 | − | 8.59423i | 0.00247739 | − | 0.00961323i | ||||
\(895\) | −128.175 | + | 644.350i | −0.143212 | + | 0.719944i | ||||
\(896\) | 35.0141i | 0.0390783i | ||||||||
\(897\) | 84.7082 | − | 328.700i | 0.0944350 | − | 0.366444i | ||||
\(898\) | 900.785i | 1.00310i | ||||||||
\(899\) | − | 1339.53i | − | 1.49002i | ||||||
\(900\) | 280.727 | + | 351.699i | 0.311919 | + | 0.390777i | ||||
\(901\) | −553.992 | −0.614864 | ||||||||
\(902\) | −488.915 | −0.542034 | ||||||||
\(903\) | 337.140 | + | 86.8832i | 0.373356 | + | 0.0962161i | ||||
\(904\) | −446.962 | −0.494427 | ||||||||
\(905\) | 1444.62 | + | 287.364i | 1.59626 | + | 0.317529i | ||||
\(906\) | 1214.48 | + | 312.980i | 1.34049 | + | 0.345452i | ||||
\(907\) | 720.635i | 0.794526i | 0.917705 | + | 0.397263i | \(0.130040\pi\) | ||||
−0.917705 | + | 0.397263i | \(0.869960\pi\) | |||||||
\(908\) | −544.556 | −0.599731 | ||||||||
\(909\) | −664.684 | + | 1203.97i | −0.731225 | + | 1.32450i | ||||
\(910\) | 506.377 | + | 100.729i | 0.556458 | + | 0.110691i | ||||
\(911\) | 1183.93i | 1.29960i | 0.760106 | + | 0.649799i | \(0.225147\pi\) | ||||
−0.760106 | + | 0.649799i | \(0.774853\pi\) | |||||||
\(912\) | 288.805 | + | 74.4269i | 0.316672 | + | 0.0816085i | ||||
\(913\) | − | 1212.20i | − | 1.32771i | ||||||
\(914\) | − | 474.932i | − | 0.519620i | ||||||
\(915\) | −243.004 | − | 116.958i | −0.265578 | − | 0.127823i | ||||
\(916\) | 194.164 | 0.211970 | ||||||||
\(917\) | −720.173 | −0.785358 | ||||||||
\(918\) | −415.432 | − | 392.212i | −0.452541 | − | 0.427246i | ||||
\(919\) | 494.646 | 0.538243 | 0.269122 | − | 0.963106i | \(-0.413267\pi\) | ||||
0.269122 | + | 0.963106i | \(0.413267\pi\) | |||||||
\(920\) | 66.5200 | + | 13.2322i | 0.0723043 | + | 0.0143828i | ||||
\(921\) | 127.638 | − | 495.286i | 0.138587 | − | 0.537770i | ||||
\(922\) | 678.916i | 0.736352i | ||||||||
\(923\) | 2354.71 | 2.55115 | ||||||||
\(924\) | 197.728 | + | 50.9558i | 0.213991 | + | 0.0551470i | ||||
\(925\) | 464.503 | − | 1121.36i | 0.502165 | − | 1.21228i | ||||
\(926\) | 562.132i | 0.607054i | ||||||||
\(927\) | 669.526 | − | 1212.74i | 0.722251 | − | 1.30824i | ||||
\(928\) | − | 243.170i | − | 0.262037i | ||||||
\(929\) | 683.479i | 0.735714i | 0.929882 | + | 0.367857i | \(0.119908\pi\) | ||||
−0.929882 | + | 0.367857i | \(0.880092\pi\) | |||||||
\(930\) | 595.634 | + | 286.679i | 0.640466 | + | 0.308257i | ||||
\(931\) | −979.771 | −1.05239 | ||||||||
\(932\) | 321.926 | 0.345414 | ||||||||
\(933\) | 13.7480 | − | 53.3477i | 0.0147353 | − | 0.0571787i | ||||
\(934\) | 509.379 | 0.545373 | ||||||||
\(935\) | 160.498 | − | 806.846i | 0.171656 | − | 0.862937i | ||||
\(936\) | 290.265 | − | 525.769i | 0.310112 | − | 0.561719i | ||||
\(937\) | 563.716i | 0.601618i | 0.953684 | + | 0.300809i | \(0.0972567\pi\) | ||||
−0.953684 | + | 0.300809i | \(0.902743\pi\) | |||||||
\(938\) | −298.480 | −0.318209 | ||||||||
\(939\) | −225.979 | + | 876.885i | −0.240659 | + | 0.933850i | ||||
\(940\) | −495.105 | − | 98.4866i | −0.526707 | − | 0.104773i | ||||
\(941\) | − | 1113.42i | − | 1.18323i | −0.806221 | − | 0.591615i | \(-0.798491\pi\) | ||
0.806221 | − | 0.591615i | \(-0.201509\pi\) | |||||||
\(942\) | −98.4817 | + | 382.147i | −0.104545 | + | 0.405676i | ||||
\(943\) | 150.779i | 0.159893i | ||||||||
\(944\) | 141.634i | 0.150036i | ||||||||
\(945\) | 340.579 | − | 242.004i | 0.360401 | − | 0.256089i | ||||
\(946\) | 583.136 | 0.616423 | ||||||||
\(947\) | 590.902 | 0.623973 | 0.311986 | − | 0.950087i | \(-0.399006\pi\) | ||||
0.311986 | + | 0.950087i | \(0.399006\pi\) | |||||||
\(948\) | −178.765 | − | 46.0689i | −0.188570 | − | 0.0485958i | ||||
\(949\) | 929.263 | 0.979202 | ||||||||
\(950\) | 811.809 | + | 336.277i | 0.854535 | + | 0.353976i | ||||
\(951\) | 517.555 | + | 133.377i | 0.544222 | + | 0.140250i | ||||
\(952\) | − | 130.975i | − | 0.137579i | ||||||
\(953\) | −516.221 | −0.541680 | −0.270840 | − | 0.962624i | \(-0.587301\pi\) | ||||
−0.270840 | + | 0.962624i | \(0.587301\pi\) | |||||||
\(954\) | −412.558 | − | 227.764i | −0.432451 | − | 0.238747i | ||||
\(955\) | 177.506 | − | 892.345i | 0.185870 | − | 0.934393i | ||||
\(956\) | 94.0773i | 0.0984073i | ||||||||
\(957\) | −1373.20 | − | 353.884i | −1.43491 | − | 0.369784i | ||||
\(958\) | − | 654.529i | − | 0.683225i | ||||||
\(959\) | 89.4708i | 0.0932960i | ||||||||
\(960\) | 108.128 | + | 52.0420i | 0.112633 | + | 0.0542104i | ||||
\(961\) | 10.0313 | 0.0104383 | ||||||||
\(962\) | −1619.89 | −1.68387 | ||||||||
\(963\) | −46.4174 | − | 25.6260i | −0.0482008 | − | 0.0266106i | ||||
\(964\) | 387.745 | 0.402225 | ||||||||
\(965\) | −8.05892 | + | 40.5132i | −0.00835121 | + | 0.0419826i | ||||
\(966\) | 15.7145 | − | 60.9784i | 0.0162676 | − | 0.0631246i | ||||
\(967\) | − | 1368.48i | − | 1.41518i | −0.706625 | − | 0.707589i | \(-0.749783\pi\) | ||
0.706625 | − | 0.707589i | \(-0.250217\pi\) | |||||||
\(968\) | −0.237984 | −0.000245851 | ||||||||
\(969\) | −1080.32 | − | 278.404i | −1.11488 | − | 0.287311i | ||||
\(970\) | 163.835 | − | 823.620i | 0.168902 | − | 0.849093i | ||||
\(971\) | 557.525i | 0.574176i | 0.957904 | + | 0.287088i | \(0.0926873\pi\) | ||||
−0.957904 | + | 0.287088i | \(0.907313\pi\) | |||||||
\(972\) | −148.121 | − | 462.878i | −0.152388 | − | 0.476212i | ||||
\(973\) | − | 59.0931i | − | 0.0607329i | ||||||
\(974\) | − | 463.788i | − | 0.476168i | ||||||
\(975\) | 1063.70 | − | 1414.04i | 1.09097 | − | 1.45030i | ||||
\(976\) | −71.9159 | −0.0736843 | ||||||||
\(977\) | 746.493 | 0.764066 | 0.382033 | − | 0.924149i | \(-0.375224\pi\) | ||||
0.382033 | + | 0.924149i | \(0.375224\pi\) | |||||||
\(978\) | −16.0127 | + | 62.1353i | −0.0163729 | + | 0.0635330i | ||||
\(979\) | −1605.84 | −1.64029 | ||||||||
\(980\) | −386.644 | − | 76.9115i | −0.394535 | − | 0.0784812i | ||||
\(981\) | 736.095 | + | 406.382i | 0.750352 | + | 0.414253i | ||||
\(982\) | 47.5795i | 0.0484516i | ||||||||
\(983\) | 1842.72 | 1.87459 | 0.937293 | − | 0.348544i | \(-0.113324\pi\) | ||||
0.937293 | + | 0.348544i | \(0.113324\pi\) | |||||||
\(984\) | −66.5742 | + | 258.333i | −0.0676567 | + | 0.262534i | ||||
\(985\) | 303.498 | + | 60.3720i | 0.308119 | + | 0.0612913i | ||||
\(986\) | 909.611i | 0.922527i | ||||||||
\(987\) | −116.962 | + | 453.859i | −0.118503 | + | 0.459837i | ||||
\(988\) | − | 1172.72i | − | 1.18696i | ||||||
\(989\) | − | 179.836i | − | 0.181837i | ||||||
\(990\) | 451.244 | − | 534.872i | 0.455802 | − | 0.540275i | ||||
\(991\) | 1346.35 | 1.35858 | 0.679290 | − | 0.733870i | \(-0.262288\pi\) | ||||
0.679290 | + | 0.733870i | \(0.262288\pi\) | |||||||
\(992\) | 176.275 | 0.177697 | ||||||||
\(993\) | −803.132 | − | 206.972i | −0.808793 | − | 0.208431i | ||||
\(994\) | 436.831 | 0.439468 | ||||||||
\(995\) | 1543.71 | + | 307.075i | 1.55146 | + | 0.308618i | ||||
\(996\) | −640.502 | − | 165.062i | −0.643075 | − | 0.165725i | ||||
\(997\) | 775.202i | 0.777535i | 0.921336 | + | 0.388767i | \(0.127099\pi\) | ||||
−0.921336 | + | 0.388767i | \(0.872901\pi\) | |||||||
\(998\) | −699.959 | −0.701361 | ||||||||
\(999\) | −899.896 | + | 953.172i | −0.900797 | + | 0.954127i |
(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 | 690.3.b.a.599.3 | ✓ | 88 | |
3.2 | odd | 2 | inner | 690.3.b.a.599.85 | yes | 88 | |
5.4 | even | 2 | inner | 690.3.b.a.599.86 | yes | 88 | |
15.14 | odd | 2 | inner | 690.3.b.a.599.4 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.b.a.599.3 | ✓ | 88 | 1.1 | even | 1 | trivial | |
690.3.b.a.599.4 | yes | 88 | 15.14 | odd | 2 | inner | |
690.3.b.a.599.85 | yes | 88 | 3.2 | odd | 2 | inner | |
690.3.b.a.599.86 | yes | 88 | 5.4 | even | 2 | inner |