Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8042,2,Mod(1,8042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8042 = 2 \cdot 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8042.a (trivial) |
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: | yes |
Analytic conductor: | \(64.2156933055\) |
Analytic rank: | \(1\) |
Dimension: | \(67\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 8042.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −3.09236 | −1.78537 | −0.892687 | − | 0.450677i | \(-0.851183\pi\) | ||||
−0.892687 | + | 0.450677i | \(0.851183\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.36808 | 0.611822 | 0.305911 | − | 0.952060i | \(-0.401039\pi\) | ||||
0.305911 | + | 0.952060i | \(0.401039\pi\) | |||||||
\(6\) | −3.09236 | −1.26245 | ||||||||
\(7\) | −2.10219 | −0.794553 | −0.397277 | − | 0.917699i | \(-0.630045\pi\) | ||||
−0.397277 | + | 0.917699i | \(0.630045\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 6.56268 | 2.18756 | ||||||||
\(10\) | 1.36808 | 0.432623 | ||||||||
\(11\) | 5.99202 | 1.80666 | 0.903330 | − | 0.428946i | \(-0.141115\pi\) | ||||
0.903330 | + | 0.428946i | \(0.141115\pi\) | |||||||
\(12\) | −3.09236 | −0.892687 | ||||||||
\(13\) | −2.57624 | −0.714519 | −0.357260 | − | 0.934005i | \(-0.616289\pi\) | ||||
−0.357260 | + | 0.934005i | \(0.616289\pi\) | |||||||
\(14\) | −2.10219 | −0.561834 | ||||||||
\(15\) | −4.23058 | −1.09233 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.248087 | 0.0601699 | 0.0300850 | − | 0.999547i | \(-0.490422\pi\) | ||||
0.0300850 | + | 0.999547i | \(0.490422\pi\) | |||||||
\(18\) | 6.56268 | 1.54684 | ||||||||
\(19\) | 4.56321 | 1.04687 | 0.523436 | − | 0.852065i | \(-0.324650\pi\) | ||||
0.523436 | + | 0.852065i | \(0.324650\pi\) | |||||||
\(20\) | 1.36808 | 0.305911 | ||||||||
\(21\) | 6.50073 | 1.41857 | ||||||||
\(22\) | 5.99202 | 1.27750 | ||||||||
\(23\) | −3.33361 | −0.695105 | −0.347553 | − | 0.937661i | \(-0.612987\pi\) | ||||
−0.347553 | + | 0.937661i | \(0.612987\pi\) | |||||||
\(24\) | −3.09236 | −0.631225 | ||||||||
\(25\) | −3.12837 | −0.625674 | ||||||||
\(26\) | −2.57624 | −0.505241 | ||||||||
\(27\) | −11.0171 | −2.12024 | ||||||||
\(28\) | −2.10219 | −0.397277 | ||||||||
\(29\) | −7.82796 | −1.45361 | −0.726807 | − | 0.686841i | \(-0.758997\pi\) | ||||
−0.726807 | + | 0.686841i | \(0.758997\pi\) | |||||||
\(30\) | −4.23058 | −0.772395 | ||||||||
\(31\) | −7.22741 | −1.29808 | −0.649041 | − | 0.760754i | \(-0.724829\pi\) | ||||
−0.649041 | + | 0.760754i | \(0.724829\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −18.5295 | −3.22556 | ||||||||
\(34\) | 0.248087 | 0.0425466 | ||||||||
\(35\) | −2.87596 | −0.486125 | ||||||||
\(36\) | 6.56268 | 1.09378 | ||||||||
\(37\) | 0.882506 | 0.145083 | 0.0725416 | − | 0.997365i | \(-0.476889\pi\) | ||||
0.0725416 | + | 0.997365i | \(0.476889\pi\) | |||||||
\(38\) | 4.56321 | 0.740250 | ||||||||
\(39\) | 7.96665 | 1.27568 | ||||||||
\(40\) | 1.36808 | 0.216312 | ||||||||
\(41\) | 3.49989 | 0.546590 | 0.273295 | − | 0.961930i | \(-0.411886\pi\) | ||||
0.273295 | + | 0.961930i | \(0.411886\pi\) | |||||||
\(42\) | 6.50073 | 1.00308 | ||||||||
\(43\) | −1.48430 | −0.226353 | −0.113177 | − | 0.993575i | \(-0.536103\pi\) | ||||
−0.113177 | + | 0.993575i | \(0.536103\pi\) | |||||||
\(44\) | 5.99202 | 0.903330 | ||||||||
\(45\) | 8.97824 | 1.33840 | ||||||||
\(46\) | −3.33361 | −0.491513 | ||||||||
\(47\) | 0.681955 | 0.0994734 | 0.0497367 | − | 0.998762i | \(-0.484162\pi\) | ||||
0.0497367 | + | 0.998762i | \(0.484162\pi\) | |||||||
\(48\) | −3.09236 | −0.446343 | ||||||||
\(49\) | −2.58079 | −0.368685 | ||||||||
\(50\) | −3.12837 | −0.442418 | ||||||||
\(51\) | −0.767174 | −0.107426 | ||||||||
\(52\) | −2.57624 | −0.357260 | ||||||||
\(53\) | −14.3164 | −1.96651 | −0.983254 | − | 0.182239i | \(-0.941665\pi\) | ||||
−0.983254 | + | 0.182239i | \(0.941665\pi\) | |||||||
\(54\) | −11.0171 | −1.49923 | ||||||||
\(55\) | 8.19753 | 1.10535 | ||||||||
\(56\) | −2.10219 | −0.280917 | ||||||||
\(57\) | −14.1111 | −1.86906 | ||||||||
\(58\) | −7.82796 | −1.02786 | ||||||||
\(59\) | 4.85974 | 0.632685 | 0.316342 | − | 0.948645i | \(-0.397545\pi\) | ||||
0.316342 | + | 0.948645i | \(0.397545\pi\) | |||||||
\(60\) | −4.23058 | −0.546165 | ||||||||
\(61\) | 7.46200 | 0.955411 | 0.477705 | − | 0.878520i | \(-0.341469\pi\) | ||||
0.477705 | + | 0.878520i | \(0.341469\pi\) | |||||||
\(62\) | −7.22741 | −0.917882 | ||||||||
\(63\) | −13.7960 | −1.73813 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.52449 | −0.437159 | ||||||||
\(66\) | −18.5295 | −2.28082 | ||||||||
\(67\) | −4.61731 | −0.564094 | −0.282047 | − | 0.959401i | \(-0.591013\pi\) | ||||
−0.282047 | + | 0.959401i | \(0.591013\pi\) | |||||||
\(68\) | 0.248087 | 0.0300850 | ||||||||
\(69\) | 10.3087 | 1.24102 | ||||||||
\(70\) | −2.87596 | −0.343742 | ||||||||
\(71\) | 8.72880 | 1.03592 | 0.517959 | − | 0.855405i | \(-0.326692\pi\) | ||||
0.517959 | + | 0.855405i | \(0.326692\pi\) | |||||||
\(72\) | 6.56268 | 0.773419 | ||||||||
\(73\) | 9.86687 | 1.15483 | 0.577415 | − | 0.816451i | \(-0.304062\pi\) | ||||
0.577415 | + | 0.816451i | \(0.304062\pi\) | |||||||
\(74\) | 0.882506 | 0.102589 | ||||||||
\(75\) | 9.67404 | 1.11706 | ||||||||
\(76\) | 4.56321 | 0.523436 | ||||||||
\(77\) | −12.5964 | −1.43549 | ||||||||
\(78\) | 7.96665 | 0.902045 | ||||||||
\(79\) | −12.6367 | −1.42174 | −0.710870 | − | 0.703324i | \(-0.751698\pi\) | ||||
−0.710870 | + | 0.703324i | \(0.751698\pi\) | |||||||
\(80\) | 1.36808 | 0.152955 | ||||||||
\(81\) | 14.3807 | 1.59786 | ||||||||
\(82\) | 3.49989 | 0.386498 | ||||||||
\(83\) | −8.10500 | −0.889640 | −0.444820 | − | 0.895620i | \(-0.646732\pi\) | ||||
−0.444820 | + | 0.895620i | \(0.646732\pi\) | |||||||
\(84\) | 6.50073 | 0.709287 | ||||||||
\(85\) | 0.339402 | 0.0368133 | ||||||||
\(86\) | −1.48430 | −0.160056 | ||||||||
\(87\) | 24.2068 | 2.59525 | ||||||||
\(88\) | 5.99202 | 0.638751 | ||||||||
\(89\) | 8.27053 | 0.876675 | 0.438337 | − | 0.898811i | \(-0.355568\pi\) | ||||
0.438337 | + | 0.898811i | \(0.355568\pi\) | |||||||
\(90\) | 8.97824 | 0.946390 | ||||||||
\(91\) | 5.41574 | 0.567724 | ||||||||
\(92\) | −3.33361 | −0.347553 | ||||||||
\(93\) | 22.3497 | 2.31756 | ||||||||
\(94\) | 0.681955 | 0.0703383 | ||||||||
\(95\) | 6.24282 | 0.640499 | ||||||||
\(96\) | −3.09236 | −0.315612 | ||||||||
\(97\) | −9.54244 | −0.968888 | −0.484444 | − | 0.874822i | \(-0.660978\pi\) | ||||
−0.484444 | + | 0.874822i | \(0.660978\pi\) | |||||||
\(98\) | −2.58079 | −0.260700 | ||||||||
\(99\) | 39.3237 | 3.95218 | ||||||||
\(100\) | −3.12837 | −0.312837 | ||||||||
\(101\) | 1.23076 | 0.122465 | 0.0612327 | − | 0.998124i | \(-0.480497\pi\) | ||||
0.0612327 | + | 0.998124i | \(0.480497\pi\) | |||||||
\(102\) | −0.767174 | −0.0759615 | ||||||||
\(103\) | −5.37778 | −0.529888 | −0.264944 | − | 0.964264i | \(-0.585354\pi\) | ||||
−0.264944 | + | 0.964264i | \(0.585354\pi\) | |||||||
\(104\) | −2.57624 | −0.252621 | ||||||||
\(105\) | 8.89349 | 0.867915 | ||||||||
\(106\) | −14.3164 | −1.39053 | ||||||||
\(107\) | 8.26019 | 0.798543 | 0.399271 | − | 0.916833i | \(-0.369263\pi\) | ||||
0.399271 | + | 0.916833i | \(0.369263\pi\) | |||||||
\(108\) | −11.0171 | −1.06012 | ||||||||
\(109\) | −15.7223 | −1.50592 | −0.752960 | − | 0.658066i | \(-0.771375\pi\) | ||||
−0.752960 | + | 0.658066i | \(0.771375\pi\) | |||||||
\(110\) | 8.19753 | 0.781604 | ||||||||
\(111\) | −2.72903 | −0.259028 | ||||||||
\(112\) | −2.10219 | −0.198638 | ||||||||
\(113\) | 2.25758 | 0.212375 | 0.106187 | − | 0.994346i | \(-0.466136\pi\) | ||||
0.106187 | + | 0.994346i | \(0.466136\pi\) | |||||||
\(114\) | −14.1111 | −1.32162 | ||||||||
\(115\) | −4.56063 | −0.425281 | ||||||||
\(116\) | −7.82796 | −0.726807 | ||||||||
\(117\) | −16.9070 | −1.56305 | ||||||||
\(118\) | 4.85974 | 0.447376 | ||||||||
\(119\) | −0.521526 | −0.0478082 | ||||||||
\(120\) | −4.23058 | −0.386197 | ||||||||
\(121\) | 24.9042 | 2.26402 | ||||||||
\(122\) | 7.46200 | 0.675577 | ||||||||
\(123\) | −10.8229 | −0.975868 | ||||||||
\(124\) | −7.22741 | −0.649041 | ||||||||
\(125\) | −11.1202 | −0.994623 | ||||||||
\(126\) | −13.7960 | −1.22905 | ||||||||
\(127\) | 2.84754 | 0.252678 | 0.126339 | − | 0.991987i | \(-0.459677\pi\) | ||||
0.126339 | + | 0.991987i | \(0.459677\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 4.58998 | 0.404125 | ||||||||
\(130\) | −3.52449 | −0.309118 | ||||||||
\(131\) | 11.9236 | 1.04177 | 0.520885 | − | 0.853627i | \(-0.325602\pi\) | ||||
0.520885 | + | 0.853627i | \(0.325602\pi\) | |||||||
\(132\) | −18.5295 | −1.61278 | ||||||||
\(133\) | −9.59274 | −0.831796 | ||||||||
\(134\) | −4.61731 | −0.398875 | ||||||||
\(135\) | −15.0722 | −1.29721 | ||||||||
\(136\) | 0.248087 | 0.0212733 | ||||||||
\(137\) | −2.54852 | −0.217735 | −0.108867 | − | 0.994056i | \(-0.534722\pi\) | ||||
−0.108867 | + | 0.994056i | \(0.534722\pi\) | |||||||
\(138\) | 10.3087 | 0.877535 | ||||||||
\(139\) | 6.71861 | 0.569865 | 0.284933 | − | 0.958548i | \(-0.408029\pi\) | ||||
0.284933 | + | 0.958548i | \(0.408029\pi\) | |||||||
\(140\) | −2.87596 | −0.243063 | ||||||||
\(141\) | −2.10885 | −0.177597 | ||||||||
\(142\) | 8.72880 | 0.732505 | ||||||||
\(143\) | −15.4368 | −1.29089 | ||||||||
\(144\) | 6.56268 | 0.546890 | ||||||||
\(145\) | −10.7092 | −0.889354 | ||||||||
\(146\) | 9.86687 | 0.816588 | ||||||||
\(147\) | 7.98074 | 0.658240 | ||||||||
\(148\) | 0.882506 | 0.0725416 | ||||||||
\(149\) | 0.229505 | 0.0188017 | 0.00940087 | − | 0.999956i | \(-0.497008\pi\) | ||||
0.00940087 | + | 0.999956i | \(0.497008\pi\) | |||||||
\(150\) | 9.67404 | 0.789882 | ||||||||
\(151\) | 16.0131 | 1.30312 | 0.651562 | − | 0.758595i | \(-0.274114\pi\) | ||||
0.651562 | + | 0.758595i | \(0.274114\pi\) | |||||||
\(152\) | 4.56321 | 0.370125 | ||||||||
\(153\) | 1.62812 | 0.131625 | ||||||||
\(154\) | −12.5964 | −1.01504 | ||||||||
\(155\) | −9.88764 | −0.794195 | ||||||||
\(156\) | 7.96665 | 0.637842 | ||||||||
\(157\) | −15.6839 | −1.25171 | −0.625856 | − | 0.779938i | \(-0.715250\pi\) | ||||
−0.625856 | + | 0.779938i | \(0.715250\pi\) | |||||||
\(158\) | −12.6367 | −1.00532 | ||||||||
\(159\) | 44.2714 | 3.51095 | ||||||||
\(160\) | 1.36808 | 0.108156 | ||||||||
\(161\) | 7.00788 | 0.552298 | ||||||||
\(162\) | 14.3807 | 1.12986 | ||||||||
\(163\) | −9.45836 | −0.740836 | −0.370418 | − | 0.928865i | \(-0.620786\pi\) | ||||
−0.370418 | + | 0.928865i | \(0.620786\pi\) | |||||||
\(164\) | 3.49989 | 0.273295 | ||||||||
\(165\) | −25.3497 | −1.97347 | ||||||||
\(166\) | −8.10500 | −0.629070 | ||||||||
\(167\) | 7.09820 | 0.549275 | 0.274637 | − | 0.961548i | \(-0.411442\pi\) | ||||
0.274637 | + | 0.961548i | \(0.411442\pi\) | |||||||
\(168\) | 6.50073 | 0.501542 | ||||||||
\(169\) | −6.36301 | −0.489462 | ||||||||
\(170\) | 0.339402 | 0.0260309 | ||||||||
\(171\) | 29.9469 | 2.29010 | ||||||||
\(172\) | −1.48430 | −0.113177 | ||||||||
\(173\) | −10.4870 | −0.797310 | −0.398655 | − | 0.917101i | \(-0.630523\pi\) | ||||
−0.398655 | + | 0.917101i | \(0.630523\pi\) | |||||||
\(174\) | 24.2068 | 1.83512 | ||||||||
\(175\) | 6.57643 | 0.497131 | ||||||||
\(176\) | 5.99202 | 0.451665 | ||||||||
\(177\) | −15.0281 | −1.12958 | ||||||||
\(178\) | 8.27053 | 0.619903 | ||||||||
\(179\) | −15.3884 | −1.15018 | −0.575091 | − | 0.818089i | \(-0.695033\pi\) | ||||
−0.575091 | + | 0.818089i | \(0.695033\pi\) | |||||||
\(180\) | 8.97824 | 0.669199 | ||||||||
\(181\) | 12.5150 | 0.930229 | 0.465115 | − | 0.885250i | \(-0.346013\pi\) | ||||
0.465115 | + | 0.885250i | \(0.346013\pi\) | |||||||
\(182\) | 5.41574 | 0.401441 | ||||||||
\(183\) | −23.0752 | −1.70577 | ||||||||
\(184\) | −3.33361 | −0.245757 | ||||||||
\(185\) | 1.20734 | 0.0887650 | ||||||||
\(186\) | 22.3497 | 1.63876 | ||||||||
\(187\) | 1.48654 | 0.108707 | ||||||||
\(188\) | 0.681955 | 0.0497367 | ||||||||
\(189\) | 23.1600 | 1.68464 | ||||||||
\(190\) | 6.24282 | 0.452901 | ||||||||
\(191\) | 7.68452 | 0.556032 | 0.278016 | − | 0.960576i | \(-0.410323\pi\) | ||||
0.278016 | + | 0.960576i | \(0.410323\pi\) | |||||||
\(192\) | −3.09236 | −0.223172 | ||||||||
\(193\) | −9.27752 | −0.667811 | −0.333905 | − | 0.942607i | \(-0.608367\pi\) | ||||
−0.333905 | + | 0.942607i | \(0.608367\pi\) | |||||||
\(194\) | −9.54244 | −0.685108 | ||||||||
\(195\) | 10.8990 | 0.780492 | ||||||||
\(196\) | −2.58079 | −0.184342 | ||||||||
\(197\) | 9.06369 | 0.645761 | 0.322881 | − | 0.946440i | \(-0.395349\pi\) | ||||
0.322881 | + | 0.946440i | \(0.395349\pi\) | |||||||
\(198\) | 39.3237 | 2.79461 | ||||||||
\(199\) | −3.54355 | −0.251196 | −0.125598 | − | 0.992081i | \(-0.540085\pi\) | ||||
−0.125598 | + | 0.992081i | \(0.540085\pi\) | |||||||
\(200\) | −3.12837 | −0.221209 | ||||||||
\(201\) | 14.2784 | 1.00712 | ||||||||
\(202\) | 1.23076 | 0.0865961 | ||||||||
\(203\) | 16.4559 | 1.15497 | ||||||||
\(204\) | −0.767174 | −0.0537129 | ||||||||
\(205\) | 4.78811 | 0.334416 | ||||||||
\(206\) | −5.37778 | −0.374688 | ||||||||
\(207\) | −21.8774 | −1.52058 | ||||||||
\(208\) | −2.57624 | −0.178630 | ||||||||
\(209\) | 27.3428 | 1.89134 | ||||||||
\(210\) | 8.89349 | 0.613709 | ||||||||
\(211\) | 11.1019 | 0.764286 | 0.382143 | − | 0.924103i | \(-0.375186\pi\) | ||||
0.382143 | + | 0.924103i | \(0.375186\pi\) | |||||||
\(212\) | −14.3164 | −0.983254 | ||||||||
\(213\) | −26.9926 | −1.84950 | ||||||||
\(214\) | 8.26019 | 0.564655 | ||||||||
\(215\) | −2.03063 | −0.138488 | ||||||||
\(216\) | −11.0171 | −0.749617 | ||||||||
\(217\) | 15.1934 | 1.03139 | ||||||||
\(218\) | −15.7223 | −1.06485 | ||||||||
\(219\) | −30.5119 | −2.06180 | ||||||||
\(220\) | 8.19753 | 0.552677 | ||||||||
\(221\) | −0.639131 | −0.0429926 | ||||||||
\(222\) | −2.72903 | −0.183160 | ||||||||
\(223\) | 5.88417 | 0.394033 | 0.197017 | − | 0.980400i | \(-0.436875\pi\) | ||||
0.197017 | + | 0.980400i | \(0.436875\pi\) | |||||||
\(224\) | −2.10219 | −0.140459 | ||||||||
\(225\) | −20.5305 | −1.36870 | ||||||||
\(226\) | 2.25758 | 0.150172 | ||||||||
\(227\) | −26.4098 | −1.75288 | −0.876441 | − | 0.481509i | \(-0.840089\pi\) | ||||
−0.876441 | + | 0.481509i | \(0.840089\pi\) | |||||||
\(228\) | −14.1111 | −0.934529 | ||||||||
\(229\) | −12.5836 | −0.831547 | −0.415774 | − | 0.909468i | \(-0.636489\pi\) | ||||
−0.415774 | + | 0.909468i | \(0.636489\pi\) | |||||||
\(230\) | −4.56063 | −0.300719 | ||||||||
\(231\) | 38.9525 | 2.56288 | ||||||||
\(232\) | −7.82796 | −0.513930 | ||||||||
\(233\) | −16.5173 | −1.08208 | −0.541042 | − | 0.840996i | \(-0.681970\pi\) | ||||
−0.541042 | + | 0.840996i | \(0.681970\pi\) | |||||||
\(234\) | −16.9070 | −1.10525 | ||||||||
\(235\) | 0.932966 | 0.0608600 | ||||||||
\(236\) | 4.85974 | 0.316342 | ||||||||
\(237\) | 39.0772 | 2.53834 | ||||||||
\(238\) | −0.521526 | −0.0338055 | ||||||||
\(239\) | −20.5683 | −1.33045 | −0.665225 | − | 0.746643i | \(-0.731665\pi\) | ||||
−0.665225 | + | 0.746643i | \(0.731665\pi\) | |||||||
\(240\) | −4.23058 | −0.273083 | ||||||||
\(241\) | −7.95649 | −0.512523 | −0.256261 | − | 0.966608i | \(-0.582491\pi\) | ||||
−0.256261 | + | 0.966608i | \(0.582491\pi\) | |||||||
\(242\) | 24.9042 | 1.60091 | ||||||||
\(243\) | −11.4191 | −0.732536 | ||||||||
\(244\) | 7.46200 | 0.477705 | ||||||||
\(245\) | −3.53072 | −0.225569 | ||||||||
\(246\) | −10.8229 | −0.690043 | ||||||||
\(247\) | −11.7559 | −0.748010 | ||||||||
\(248\) | −7.22741 | −0.458941 | ||||||||
\(249\) | 25.0636 | 1.58834 | ||||||||
\(250\) | −11.1202 | −0.703305 | ||||||||
\(251\) | −25.3474 | −1.59991 | −0.799957 | − | 0.600057i | \(-0.795145\pi\) | ||||
−0.799957 | + | 0.600057i | \(0.795145\pi\) | |||||||
\(252\) | −13.7960 | −0.869067 | ||||||||
\(253\) | −19.9750 | −1.25582 | ||||||||
\(254\) | 2.84754 | 0.178671 | ||||||||
\(255\) | −1.04955 | −0.0657255 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −26.2281 | −1.63606 | −0.818031 | − | 0.575174i | \(-0.804935\pi\) | ||||
−0.818031 | + | 0.575174i | \(0.804935\pi\) | |||||||
\(258\) | 4.58998 | 0.285760 | ||||||||
\(259\) | −1.85520 | −0.115276 | ||||||||
\(260\) | −3.52449 | −0.218579 | ||||||||
\(261\) | −51.3724 | −3.17987 | ||||||||
\(262\) | 11.9236 | 0.736642 | ||||||||
\(263\) | 31.8182 | 1.96199 | 0.980997 | − | 0.194025i | \(-0.0621543\pi\) | ||||
0.980997 | + | 0.194025i | \(0.0621543\pi\) | |||||||
\(264\) | −18.5295 | −1.14041 | ||||||||
\(265\) | −19.5859 | −1.20315 | ||||||||
\(266\) | −9.59274 | −0.588169 | ||||||||
\(267\) | −25.5754 | −1.56519 | ||||||||
\(268\) | −4.61731 | −0.282047 | ||||||||
\(269\) | −32.2727 | −1.96770 | −0.983852 | − | 0.178986i | \(-0.942718\pi\) | ||||
−0.983852 | + | 0.178986i | \(0.942718\pi\) | |||||||
\(270\) | −15.0722 | −0.917265 | ||||||||
\(271\) | −7.56067 | −0.459278 | −0.229639 | − | 0.973276i | \(-0.573755\pi\) | ||||
−0.229639 | + | 0.973276i | \(0.573755\pi\) | |||||||
\(272\) | 0.248087 | 0.0150425 | ||||||||
\(273\) | −16.7474 | −1.01360 | ||||||||
\(274\) | −2.54852 | −0.153962 | ||||||||
\(275\) | −18.7452 | −1.13038 | ||||||||
\(276\) | 10.3087 | 0.620511 | ||||||||
\(277\) | −2.99103 | −0.179713 | −0.0898567 | − | 0.995955i | \(-0.528641\pi\) | ||||
−0.0898567 | + | 0.995955i | \(0.528641\pi\) | |||||||
\(278\) | 6.71861 | 0.402956 | ||||||||
\(279\) | −47.4312 | −2.83963 | ||||||||
\(280\) | −2.87596 | −0.171871 | ||||||||
\(281\) | −16.1628 | −0.964193 | −0.482097 | − | 0.876118i | \(-0.660125\pi\) | ||||
−0.482097 | + | 0.876118i | \(0.660125\pi\) | |||||||
\(282\) | −2.10885 | −0.125580 | ||||||||
\(283\) | 16.2054 | 0.963308 | 0.481654 | − | 0.876361i | \(-0.340036\pi\) | ||||
0.481654 | + | 0.876361i | \(0.340036\pi\) | |||||||
\(284\) | 8.72880 | 0.517959 | ||||||||
\(285\) | −19.3050 | −1.14353 | ||||||||
\(286\) | −15.4368 | −0.912800 | ||||||||
\(287\) | −7.35743 | −0.434295 | ||||||||
\(288\) | 6.56268 | 0.386710 | ||||||||
\(289\) | −16.9385 | −0.996380 | ||||||||
\(290\) | −10.7092 | −0.628868 | ||||||||
\(291\) | 29.5087 | 1.72983 | ||||||||
\(292\) | 9.86687 | 0.577415 | ||||||||
\(293\) | 4.28849 | 0.250536 | 0.125268 | − | 0.992123i | \(-0.460021\pi\) | ||||
0.125268 | + | 0.992123i | \(0.460021\pi\) | |||||||
\(294\) | 7.98074 | 0.465446 | ||||||||
\(295\) | 6.64850 | 0.387090 | ||||||||
\(296\) | 0.882506 | 0.0512946 | ||||||||
\(297\) | −66.0145 | −3.83055 | ||||||||
\(298\) | 0.229505 | 0.0132948 | ||||||||
\(299\) | 8.58816 | 0.496666 | ||||||||
\(300\) | 9.67404 | 0.558531 | ||||||||
\(301\) | 3.12028 | 0.179850 | ||||||||
\(302\) | 16.0131 | 0.921448 | ||||||||
\(303\) | −3.80596 | −0.218646 | ||||||||
\(304\) | 4.56321 | 0.261718 | ||||||||
\(305\) | 10.2086 | 0.584541 | ||||||||
\(306\) | 1.62812 | 0.0930732 | ||||||||
\(307\) | 4.34903 | 0.248212 | 0.124106 | − | 0.992269i | \(-0.460394\pi\) | ||||
0.124106 | + | 0.992269i | \(0.460394\pi\) | |||||||
\(308\) | −12.5964 | −0.717744 | ||||||||
\(309\) | 16.6300 | 0.946049 | ||||||||
\(310\) | −9.88764 | −0.561580 | ||||||||
\(311\) | −8.43326 | −0.478206 | −0.239103 | − | 0.970994i | \(-0.576853\pi\) | ||||
−0.239103 | + | 0.970994i | \(0.576853\pi\) | |||||||
\(312\) | 7.96665 | 0.451022 | ||||||||
\(313\) | −21.6656 | −1.22461 | −0.612307 | − | 0.790620i | \(-0.709758\pi\) | ||||
−0.612307 | + | 0.790620i | \(0.709758\pi\) | |||||||
\(314\) | −15.6839 | −0.885095 | ||||||||
\(315\) | −18.8740 | −1.06343 | ||||||||
\(316\) | −12.6367 | −0.710870 | ||||||||
\(317\) | −27.3935 | −1.53857 | −0.769286 | − | 0.638905i | \(-0.779388\pi\) | ||||
−0.769286 | + | 0.638905i | \(0.779388\pi\) | |||||||
\(318\) | 44.2714 | 2.48262 | ||||||||
\(319\) | −46.9052 | −2.62619 | ||||||||
\(320\) | 1.36808 | 0.0764777 | ||||||||
\(321\) | −25.5435 | −1.42570 | ||||||||
\(322\) | 7.00788 | 0.390534 | ||||||||
\(323\) | 1.13207 | 0.0629902 | ||||||||
\(324\) | 14.3807 | 0.798929 | ||||||||
\(325\) | 8.05942 | 0.447056 | ||||||||
\(326\) | −9.45836 | −0.523850 | ||||||||
\(327\) | 48.6189 | 2.68863 | ||||||||
\(328\) | 3.49989 | 0.193249 | ||||||||
\(329\) | −1.43360 | −0.0790369 | ||||||||
\(330\) | −25.3497 | −1.39546 | ||||||||
\(331\) | 21.1062 | 1.16010 | 0.580050 | − | 0.814581i | \(-0.303033\pi\) | ||||
0.580050 | + | 0.814581i | \(0.303033\pi\) | |||||||
\(332\) | −8.10500 | −0.444820 | ||||||||
\(333\) | 5.79161 | 0.317378 | ||||||||
\(334\) | 7.09820 | 0.388396 | ||||||||
\(335\) | −6.31683 | −0.345125 | ||||||||
\(336\) | 6.50073 | 0.354644 | ||||||||
\(337\) | 14.7214 | 0.801924 | 0.400962 | − | 0.916095i | \(-0.368676\pi\) | ||||
0.400962 | + | 0.916095i | \(0.368676\pi\) | |||||||
\(338\) | −6.36301 | −0.346102 | ||||||||
\(339\) | −6.98123 | −0.379168 | ||||||||
\(340\) | 0.339402 | 0.0184066 | ||||||||
\(341\) | −43.3068 | −2.34519 | ||||||||
\(342\) | 29.9469 | 1.61934 | ||||||||
\(343\) | 20.1407 | 1.08749 | ||||||||
\(344\) | −1.48430 | −0.0800279 | ||||||||
\(345\) | 14.1031 | 0.759285 | ||||||||
\(346\) | −10.4870 | −0.563784 | ||||||||
\(347\) | −10.2337 | −0.549373 | −0.274687 | − | 0.961534i | \(-0.588574\pi\) | ||||
−0.274687 | + | 0.961534i | \(0.588574\pi\) | |||||||
\(348\) | 24.2068 | 1.29762 | ||||||||
\(349\) | 24.1958 | 1.29517 | 0.647585 | − | 0.761993i | \(-0.275779\pi\) | ||||
0.647585 | + | 0.761993i | \(0.275779\pi\) | |||||||
\(350\) | 6.57643 | 0.351525 | ||||||||
\(351\) | 28.3826 | 1.51495 | ||||||||
\(352\) | 5.99202 | 0.319375 | ||||||||
\(353\) | 22.2544 | 1.18448 | 0.592241 | − | 0.805761i | \(-0.298243\pi\) | ||||
0.592241 | + | 0.805761i | \(0.298243\pi\) | |||||||
\(354\) | −15.0281 | −0.798733 | ||||||||
\(355\) | 11.9417 | 0.633798 | ||||||||
\(356\) | 8.27053 | 0.438337 | ||||||||
\(357\) | 1.61275 | 0.0853556 | ||||||||
\(358\) | −15.3884 | −0.813302 | ||||||||
\(359\) | 2.15262 | 0.113611 | 0.0568055 | − | 0.998385i | \(-0.481909\pi\) | ||||
0.0568055 | + | 0.998385i | \(0.481909\pi\) | |||||||
\(360\) | 8.97824 | 0.473195 | ||||||||
\(361\) | 1.82289 | 0.0959414 | ||||||||
\(362\) | 12.5150 | 0.657771 | ||||||||
\(363\) | −77.0129 | −4.04213 | ||||||||
\(364\) | 5.41574 | 0.283862 | ||||||||
\(365\) | 13.4986 | 0.706550 | ||||||||
\(366\) | −23.0752 | −1.20616 | ||||||||
\(367\) | 2.92078 | 0.152464 | 0.0762318 | − | 0.997090i | \(-0.475711\pi\) | ||||
0.0762318 | + | 0.997090i | \(0.475711\pi\) | |||||||
\(368\) | −3.33361 | −0.173776 | ||||||||
\(369\) | 22.9686 | 1.19570 | ||||||||
\(370\) | 1.20734 | 0.0627664 | ||||||||
\(371\) | 30.0958 | 1.56250 | ||||||||
\(372\) | 22.3497 | 1.15878 | ||||||||
\(373\) | 27.6528 | 1.43181 | 0.715905 | − | 0.698198i | \(-0.246014\pi\) | ||||
0.715905 | + | 0.698198i | \(0.246014\pi\) | |||||||
\(374\) | 1.48654 | 0.0768672 | ||||||||
\(375\) | 34.3877 | 1.77577 | ||||||||
\(376\) | 0.681955 | 0.0351692 | ||||||||
\(377\) | 20.1667 | 1.03864 | ||||||||
\(378\) | 23.1600 | 1.19122 | ||||||||
\(379\) | −18.4122 | −0.945773 | −0.472887 | − | 0.881123i | \(-0.656788\pi\) | ||||
−0.472887 | + | 0.881123i | \(0.656788\pi\) | |||||||
\(380\) | 6.24282 | 0.320250 | ||||||||
\(381\) | −8.80562 | −0.451125 | ||||||||
\(382\) | 7.68452 | 0.393174 | ||||||||
\(383\) | 14.0045 | 0.715599 | 0.357799 | − | 0.933798i | \(-0.383527\pi\) | ||||
0.357799 | + | 0.933798i | \(0.383527\pi\) | |||||||
\(384\) | −3.09236 | −0.157806 | ||||||||
\(385\) | −17.2328 | −0.878263 | ||||||||
\(386\) | −9.27752 | −0.472213 | ||||||||
\(387\) | −9.74096 | −0.495161 | ||||||||
\(388\) | −9.54244 | −0.484444 | ||||||||
\(389\) | −10.4227 | −0.528451 | −0.264225 | − | 0.964461i | \(-0.585116\pi\) | ||||
−0.264225 | + | 0.964461i | \(0.585116\pi\) | |||||||
\(390\) | 10.8990 | 0.551891 | ||||||||
\(391\) | −0.827025 | −0.0418244 | ||||||||
\(392\) | −2.58079 | −0.130350 | ||||||||
\(393\) | −36.8720 | −1.85995 | ||||||||
\(394\) | 9.06369 | 0.456622 | ||||||||
\(395\) | −17.2880 | −0.869851 | ||||||||
\(396\) | 39.3237 | 1.97609 | ||||||||
\(397\) | 6.26976 | 0.314670 | 0.157335 | − | 0.987545i | \(-0.449710\pi\) | ||||
0.157335 | + | 0.987545i | \(0.449710\pi\) | |||||||
\(398\) | −3.54355 | −0.177622 | ||||||||
\(399\) | 29.6642 | 1.48507 | ||||||||
\(400\) | −3.12837 | −0.156418 | ||||||||
\(401\) | −24.2227 | −1.20962 | −0.604811 | − | 0.796369i | \(-0.706751\pi\) | ||||
−0.604811 | + | 0.796369i | \(0.706751\pi\) | |||||||
\(402\) | 14.2784 | 0.712141 | ||||||||
\(403\) | 18.6195 | 0.927504 | ||||||||
\(404\) | 1.23076 | 0.0612327 | ||||||||
\(405\) | 19.6739 | 0.977605 | ||||||||
\(406\) | 16.4559 | 0.816690 | ||||||||
\(407\) | 5.28799 | 0.262116 | ||||||||
\(408\) | −0.767174 | −0.0379808 | ||||||||
\(409\) | 3.27243 | 0.161811 | 0.0809056 | − | 0.996722i | \(-0.474219\pi\) | ||||
0.0809056 | + | 0.996722i | \(0.474219\pi\) | |||||||
\(410\) | 4.78811 | 0.236468 | ||||||||
\(411\) | 7.88093 | 0.388738 | ||||||||
\(412\) | −5.37778 | −0.264944 | ||||||||
\(413\) | −10.2161 | −0.502702 | ||||||||
\(414\) | −21.8774 | −1.07522 | ||||||||
\(415\) | −11.0883 | −0.544301 | ||||||||
\(416\) | −2.57624 | −0.126310 | ||||||||
\(417\) | −20.7764 | −1.01742 | ||||||||
\(418\) | 27.3428 | 1.33738 | ||||||||
\(419\) | 28.7923 | 1.40659 | 0.703297 | − | 0.710896i | \(-0.251710\pi\) | ||||
0.703297 | + | 0.710896i | \(0.251710\pi\) | |||||||
\(420\) | 8.89349 | 0.433958 | ||||||||
\(421\) | −5.08828 | −0.247988 | −0.123994 | − | 0.992283i | \(-0.539570\pi\) | ||||
−0.123994 | + | 0.992283i | \(0.539570\pi\) | |||||||
\(422\) | 11.1019 | 0.540432 | ||||||||
\(423\) | 4.47545 | 0.217604 | ||||||||
\(424\) | −14.3164 | −0.695266 | ||||||||
\(425\) | −0.776108 | −0.0376468 | ||||||||
\(426\) | −26.9926 | −1.30780 | ||||||||
\(427\) | −15.6865 | −0.759125 | ||||||||
\(428\) | 8.26019 | 0.399271 | ||||||||
\(429\) | 47.7363 | 2.30473 | ||||||||
\(430\) | −2.03063 | −0.0979257 | ||||||||
\(431\) | 18.1842 | 0.875904 | 0.437952 | − | 0.898998i | \(-0.355704\pi\) | ||||
0.437952 | + | 0.898998i | \(0.355704\pi\) | |||||||
\(432\) | −11.0171 | −0.530060 | ||||||||
\(433\) | 20.9723 | 1.00787 | 0.503933 | − | 0.863743i | \(-0.331886\pi\) | ||||
0.503933 | + | 0.863743i | \(0.331886\pi\) | |||||||
\(434\) | 15.1934 | 0.729306 | ||||||||
\(435\) | 33.1168 | 1.58783 | ||||||||
\(436\) | −15.7223 | −0.752960 | ||||||||
\(437\) | −15.2119 | −0.727686 | ||||||||
\(438\) | −30.5119 | −1.45791 | ||||||||
\(439\) | 15.1799 | 0.724499 | 0.362250 | − | 0.932081i | \(-0.382009\pi\) | ||||
0.362250 | + | 0.932081i | \(0.382009\pi\) | |||||||
\(440\) | 8.19753 | 0.390802 | ||||||||
\(441\) | −16.9369 | −0.806520 | ||||||||
\(442\) | −0.639131 | −0.0304004 | ||||||||
\(443\) | −20.6263 | −0.979987 | −0.489993 | − | 0.871726i | \(-0.663001\pi\) | ||||
−0.489993 | + | 0.871726i | \(0.663001\pi\) | |||||||
\(444\) | −2.72903 | −0.129514 | ||||||||
\(445\) | 11.3147 | 0.536369 | ||||||||
\(446\) | 5.88417 | 0.278624 | ||||||||
\(447\) | −0.709710 | −0.0335681 | ||||||||
\(448\) | −2.10219 | −0.0993192 | ||||||||
\(449\) | −27.8874 | −1.31609 | −0.658045 | − | 0.752979i | \(-0.728616\pi\) | ||||
−0.658045 | + | 0.752979i | \(0.728616\pi\) | |||||||
\(450\) | −20.5305 | −0.967816 | ||||||||
\(451\) | 20.9714 | 0.987503 | ||||||||
\(452\) | 2.25758 | 0.106187 | ||||||||
\(453\) | −49.5181 | −2.32656 | ||||||||
\(454\) | −26.4098 | −1.23948 | ||||||||
\(455\) | 7.40914 | 0.347346 | ||||||||
\(456\) | −14.1111 | −0.660812 | ||||||||
\(457\) | 12.6366 | 0.591116 | 0.295558 | − | 0.955325i | \(-0.404494\pi\) | ||||
0.295558 | + | 0.955325i | \(0.404494\pi\) | |||||||
\(458\) | −12.5836 | −0.587993 | ||||||||
\(459\) | −2.73320 | −0.127575 | ||||||||
\(460\) | −4.56063 | −0.212640 | ||||||||
\(461\) | 3.60201 | 0.167763 | 0.0838813 | − | 0.996476i | \(-0.473268\pi\) | ||||
0.0838813 | + | 0.996476i | \(0.473268\pi\) | |||||||
\(462\) | 38.9525 | 1.81223 | ||||||||
\(463\) | 10.6340 | 0.494204 | 0.247102 | − | 0.968989i | \(-0.420522\pi\) | ||||
0.247102 | + | 0.968989i | \(0.420522\pi\) | |||||||
\(464\) | −7.82796 | −0.363404 | ||||||||
\(465\) | 30.5761 | 1.41793 | ||||||||
\(466\) | −16.5173 | −0.765148 | ||||||||
\(467\) | −21.5758 | −0.998410 | −0.499205 | − | 0.866484i | \(-0.666375\pi\) | ||||
−0.499205 | + | 0.866484i | \(0.666375\pi\) | |||||||
\(468\) | −16.9070 | −0.781527 | ||||||||
\(469\) | 9.70647 | 0.448203 | ||||||||
\(470\) | 0.932966 | 0.0430345 | ||||||||
\(471\) | 48.5003 | 2.23478 | ||||||||
\(472\) | 4.85974 | 0.223688 | ||||||||
\(473\) | −8.89393 | −0.408943 | ||||||||
\(474\) | 39.0772 | 1.79487 | ||||||||
\(475\) | −14.2754 | −0.655001 | ||||||||
\(476\) | −0.521526 | −0.0239041 | ||||||||
\(477\) | −93.9539 | −4.30185 | ||||||||
\(478\) | −20.5683 | −0.940771 | ||||||||
\(479\) | 8.95356 | 0.409099 | 0.204549 | − | 0.978856i | \(-0.434427\pi\) | ||||
0.204549 | + | 0.978856i | \(0.434427\pi\) | |||||||
\(480\) | −4.23058 | −0.193099 | ||||||||
\(481\) | −2.27354 | −0.103665 | ||||||||
\(482\) | −7.95649 | −0.362408 | ||||||||
\(483\) | −21.6709 | −0.986059 | ||||||||
\(484\) | 24.9042 | 1.13201 | ||||||||
\(485\) | −13.0548 | −0.592787 | ||||||||
\(486\) | −11.4191 | −0.517981 | ||||||||
\(487\) | −24.7815 | −1.12296 | −0.561479 | − | 0.827491i | \(-0.689767\pi\) | ||||
−0.561479 | + | 0.827491i | \(0.689767\pi\) | |||||||
\(488\) | 7.46200 | 0.337789 | ||||||||
\(489\) | 29.2486 | 1.32267 | ||||||||
\(490\) | −3.53072 | −0.159502 | ||||||||
\(491\) | 40.2848 | 1.81803 | 0.909015 | − | 0.416764i | \(-0.136836\pi\) | ||||
0.909015 | + | 0.416764i | \(0.136836\pi\) | |||||||
\(492\) | −10.8229 | −0.487934 | ||||||||
\(493\) | −1.94201 | −0.0874639 | ||||||||
\(494\) | −11.7559 | −0.528923 | ||||||||
\(495\) | 53.7978 | 2.41803 | ||||||||
\(496\) | −7.22741 | −0.324520 | ||||||||
\(497\) | −18.3496 | −0.823093 | ||||||||
\(498\) | 25.0636 | 1.12313 | ||||||||
\(499\) | −30.8820 | −1.38247 | −0.691234 | − | 0.722631i | \(-0.742933\pi\) | ||||
−0.691234 | + | 0.722631i | \(0.742933\pi\) | |||||||
\(500\) | −11.1202 | −0.497312 | ||||||||
\(501\) | −21.9502 | −0.980661 | ||||||||
\(502\) | −25.3474 | −1.13131 | ||||||||
\(503\) | 42.2660 | 1.88455 | 0.942273 | − | 0.334846i | \(-0.108684\pi\) | ||||
0.942273 | + | 0.334846i | \(0.108684\pi\) | |||||||
\(504\) | −13.7960 | −0.614523 | ||||||||
\(505\) | 1.68377 | 0.0749270 | ||||||||
\(506\) | −19.9750 | −0.887998 | ||||||||
\(507\) | 19.6767 | 0.873873 | ||||||||
\(508\) | 2.84754 | 0.126339 | ||||||||
\(509\) | −18.9976 | −0.842055 | −0.421028 | − | 0.907048i | \(-0.638331\pi\) | ||||
−0.421028 | + | 0.907048i | \(0.638331\pi\) | |||||||
\(510\) | −1.04955 | −0.0464749 | ||||||||
\(511\) | −20.7420 | −0.917574 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −50.2733 | −2.21962 | ||||||||
\(514\) | −26.2281 | −1.15687 | ||||||||
\(515\) | −7.35721 | −0.324197 | ||||||||
\(516\) | 4.58998 | 0.202062 | ||||||||
\(517\) | 4.08629 | 0.179715 | ||||||||
\(518\) | −1.85520 | −0.0815126 | ||||||||
\(519\) | 32.4295 | 1.42350 | ||||||||
\(520\) | −3.52449 | −0.154559 | ||||||||
\(521\) | −5.64189 | −0.247176 | −0.123588 | − | 0.992334i | \(-0.539440\pi\) | ||||
−0.123588 | + | 0.992334i | \(0.539440\pi\) | |||||||
\(522\) | −51.3724 | −2.24851 | ||||||||
\(523\) | −1.70483 | −0.0745471 | −0.0372736 | − | 0.999305i | \(-0.511867\pi\) | ||||
−0.0372736 | + | 0.999305i | \(0.511867\pi\) | |||||||
\(524\) | 11.9236 | 0.520885 | ||||||||
\(525\) | −20.3367 | −0.887565 | ||||||||
\(526\) | 31.8182 | 1.38734 | ||||||||
\(527\) | −1.79303 | −0.0781055 | ||||||||
\(528\) | −18.5295 | −0.806391 | ||||||||
\(529\) | −11.8871 | −0.516829 | ||||||||
\(530\) | −19.5859 | −0.850758 | ||||||||
\(531\) | 31.8929 | 1.38404 | ||||||||
\(532\) | −9.59274 | −0.415898 | ||||||||
\(533\) | −9.01653 | −0.390549 | ||||||||
\(534\) | −25.5754 | −1.10676 | ||||||||
\(535\) | 11.3006 | 0.488566 | ||||||||
\(536\) | −4.61731 | −0.199437 | ||||||||
\(537\) | 47.5864 | 2.05351 | ||||||||
\(538\) | −32.2727 | −1.39138 | ||||||||
\(539\) | −15.4642 | −0.666088 | ||||||||
\(540\) | −15.0722 | −0.648604 | ||||||||
\(541\) | −7.76184 | −0.333707 | −0.166854 | − | 0.985982i | \(-0.553361\pi\) | ||||
−0.166854 | + | 0.985982i | \(0.553361\pi\) | |||||||
\(542\) | −7.56067 | −0.324759 | ||||||||
\(543\) | −38.7007 | −1.66081 | ||||||||
\(544\) | 0.248087 | 0.0106366 | ||||||||
\(545\) | −21.5093 | −0.921356 | ||||||||
\(546\) | −16.7474 | −0.716723 | ||||||||
\(547\) | 32.8392 | 1.40410 | 0.702050 | − | 0.712127i | \(-0.252268\pi\) | ||||
0.702050 | + | 0.712127i | \(0.252268\pi\) | |||||||
\(548\) | −2.54852 | −0.108867 | ||||||||
\(549\) | 48.9707 | 2.09002 | ||||||||
\(550\) | −18.7452 | −0.799300 | ||||||||
\(551\) | −35.7206 | −1.52175 | ||||||||
\(552\) | 10.3087 | 0.438768 | ||||||||
\(553\) | 26.5647 | 1.12965 | ||||||||
\(554\) | −2.99103 | −0.127077 | ||||||||
\(555\) | −3.73351 | −0.158479 | ||||||||
\(556\) | 6.71861 | 0.284933 | ||||||||
\(557\) | −43.0435 | −1.82381 | −0.911906 | − | 0.410400i | \(-0.865389\pi\) | ||||
−0.911906 | + | 0.410400i | \(0.865389\pi\) | |||||||
\(558\) | −47.4312 | −2.00792 | ||||||||
\(559\) | 3.82390 | 0.161734 | ||||||||
\(560\) | −2.87596 | −0.121531 | ||||||||
\(561\) | −4.59692 | −0.194082 | ||||||||
\(562\) | −16.1628 | −0.681788 | ||||||||
\(563\) | −34.8590 | −1.46913 | −0.734565 | − | 0.678538i | \(-0.762614\pi\) | ||||
−0.734565 | + | 0.678538i | \(0.762614\pi\) | |||||||
\(564\) | −2.10885 | −0.0887986 | ||||||||
\(565\) | 3.08853 | 0.129936 | ||||||||
\(566\) | 16.2054 | 0.681162 | ||||||||
\(567\) | −30.2310 | −1.26958 | ||||||||
\(568\) | 8.72880 | 0.366252 | ||||||||
\(569\) | −10.8582 | −0.455199 | −0.227599 | − | 0.973755i | \(-0.573088\pi\) | ||||
−0.227599 | + | 0.973755i | \(0.573088\pi\) | |||||||
\(570\) | −19.3050 | −0.808598 | ||||||||
\(571\) | −27.9029 | −1.16770 | −0.583850 | − | 0.811862i | \(-0.698454\pi\) | ||||
−0.583850 | + | 0.811862i | \(0.698454\pi\) | |||||||
\(572\) | −15.4368 | −0.645447 | ||||||||
\(573\) | −23.7633 | −0.992725 | ||||||||
\(574\) | −7.35743 | −0.307093 | ||||||||
\(575\) | 10.4288 | 0.434909 | ||||||||
\(576\) | 6.56268 | 0.273445 | ||||||||
\(577\) | −37.9808 | −1.58116 | −0.790581 | − | 0.612357i | \(-0.790221\pi\) | ||||
−0.790581 | + | 0.612357i | \(0.790221\pi\) | |||||||
\(578\) | −16.9385 | −0.704547 | ||||||||
\(579\) | 28.6894 | 1.19229 | ||||||||
\(580\) | −10.7092 | −0.444677 | ||||||||
\(581\) | 17.0383 | 0.706866 | ||||||||
\(582\) | 29.5087 | 1.22317 | ||||||||
\(583\) | −85.7841 | −3.55281 | ||||||||
\(584\) | 9.86687 | 0.408294 | ||||||||
\(585\) | −23.1301 | −0.956311 | ||||||||
\(586\) | 4.28849 | 0.177156 | ||||||||
\(587\) | 42.7518 | 1.76456 | 0.882278 | − | 0.470728i | \(-0.156009\pi\) | ||||
0.882278 | + | 0.470728i | \(0.156009\pi\) | |||||||
\(588\) | 7.98074 | 0.329120 | ||||||||
\(589\) | −32.9802 | −1.35893 | ||||||||
\(590\) | 6.64850 | 0.273714 | ||||||||
\(591\) | −28.0282 | −1.15292 | ||||||||
\(592\) | 0.882506 | 0.0362708 | ||||||||
\(593\) | −10.7785 | −0.442621 | −0.221311 | − | 0.975203i | \(-0.571033\pi\) | ||||
−0.221311 | + | 0.975203i | \(0.571033\pi\) | |||||||
\(594\) | −66.0145 | −2.70861 | ||||||||
\(595\) | −0.713487 | −0.0292501 | ||||||||
\(596\) | 0.229505 | 0.00940087 | ||||||||
\(597\) | 10.9579 | 0.448478 | ||||||||
\(598\) | 8.58816 | 0.351196 | ||||||||
\(599\) | −47.2491 | −1.93055 | −0.965273 | − | 0.261242i | \(-0.915868\pi\) | ||||
−0.965273 | + | 0.261242i | \(0.915868\pi\) | |||||||
\(600\) | 9.67404 | 0.394941 | ||||||||
\(601\) | 31.3870 | 1.28030 | 0.640151 | − | 0.768249i | \(-0.278872\pi\) | ||||
0.640151 | + | 0.768249i | \(0.278872\pi\) | |||||||
\(602\) | 3.12028 | 0.127173 | ||||||||
\(603\) | −30.3019 | −1.23399 | ||||||||
\(604\) | 16.0131 | 0.651562 | ||||||||
\(605\) | 34.0709 | 1.38518 | ||||||||
\(606\) | −3.80596 | −0.154606 | ||||||||
\(607\) | −41.1417 | −1.66989 | −0.834946 | − | 0.550332i | \(-0.814501\pi\) | ||||
−0.834946 | + | 0.550332i | \(0.814501\pi\) | |||||||
\(608\) | 4.56321 | 0.185063 | ||||||||
\(609\) | −50.8874 | −2.06206 | ||||||||
\(610\) | 10.2086 | 0.413333 | ||||||||
\(611\) | −1.75688 | −0.0710757 | ||||||||
\(612\) | 1.62812 | 0.0658127 | ||||||||
\(613\) | 0.386544 | 0.0156124 | 0.00780619 | − | 0.999970i | \(-0.497515\pi\) | ||||
0.00780619 | + | 0.999970i | \(0.497515\pi\) | |||||||
\(614\) | 4.34903 | 0.175512 | ||||||||
\(615\) | −14.8065 | −0.597057 | ||||||||
\(616\) | −12.5964 | −0.507522 | ||||||||
\(617\) | −20.9657 | −0.844047 | −0.422023 | − | 0.906585i | \(-0.638680\pi\) | ||||
−0.422023 | + | 0.906585i | \(0.638680\pi\) | |||||||
\(618\) | 16.6300 | 0.668957 | ||||||||
\(619\) | 19.0616 | 0.766150 | 0.383075 | − | 0.923717i | \(-0.374865\pi\) | ||||
0.383075 | + | 0.923717i | \(0.374865\pi\) | |||||||
\(620\) | −9.88764 | −0.397097 | ||||||||
\(621\) | 36.7266 | 1.47379 | ||||||||
\(622\) | −8.43326 | −0.338143 | ||||||||
\(623\) | −17.3862 | −0.696565 | ||||||||
\(624\) | 7.96665 | 0.318921 | ||||||||
\(625\) | 0.428541 | 0.0171416 | ||||||||
\(626\) | −21.6656 | −0.865933 | ||||||||
\(627\) | −84.5538 | −3.37675 | ||||||||
\(628\) | −15.6839 | −0.625856 | ||||||||
\(629\) | 0.218938 | 0.00872964 | ||||||||
\(630\) | −18.8740 | −0.751957 | ||||||||
\(631\) | 17.3131 | 0.689223 | 0.344611 | − | 0.938745i | \(-0.388011\pi\) | ||||
0.344611 | + | 0.938745i | \(0.388011\pi\) | |||||||
\(632\) | −12.6367 | −0.502661 | ||||||||
\(633\) | −34.3310 | −1.36454 | ||||||||
\(634\) | −27.3935 | −1.08793 | ||||||||
\(635\) | 3.89565 | 0.154594 | ||||||||
\(636\) | 44.2714 | 1.75548 | ||||||||
\(637\) | 6.64873 | 0.263432 | ||||||||
\(638\) | −46.9052 | −1.85700 | ||||||||
\(639\) | 57.2843 | 2.26613 | ||||||||
\(640\) | 1.36808 | 0.0540779 | ||||||||
\(641\) | −19.1137 | −0.754945 | −0.377472 | − | 0.926021i | \(-0.623207\pi\) | ||||
−0.377472 | + | 0.926021i | \(0.623207\pi\) | |||||||
\(642\) | −25.5435 | −1.00812 | ||||||||
\(643\) | 33.9579 | 1.33917 | 0.669584 | − | 0.742737i | \(-0.266473\pi\) | ||||
0.669584 | + | 0.742737i | \(0.266473\pi\) | |||||||
\(644\) | 7.00788 | 0.276149 | ||||||||
\(645\) | 6.27944 | 0.247253 | ||||||||
\(646\) | 1.13207 | 0.0445408 | ||||||||
\(647\) | −21.4306 | −0.842525 | −0.421262 | − | 0.906939i | \(-0.638413\pi\) | ||||
−0.421262 | + | 0.906939i | \(0.638413\pi\) | |||||||
\(648\) | 14.3807 | 0.564928 | ||||||||
\(649\) | 29.1197 | 1.14305 | ||||||||
\(650\) | 8.05942 | 0.316116 | ||||||||
\(651\) | −46.9834 | −1.84143 | ||||||||
\(652\) | −9.45836 | −0.370418 | ||||||||
\(653\) | 2.87892 | 0.112661 | 0.0563303 | − | 0.998412i | \(-0.482060\pi\) | ||||
0.0563303 | + | 0.998412i | \(0.482060\pi\) | |||||||
\(654\) | 48.6189 | 1.90115 | ||||||||
\(655\) | 16.3124 | 0.637377 | ||||||||
\(656\) | 3.49989 | 0.136648 | ||||||||
\(657\) | 64.7531 | 2.52626 | ||||||||
\(658\) | −1.43360 | −0.0558876 | ||||||||
\(659\) | 23.5376 | 0.916895 | 0.458447 | − | 0.888722i | \(-0.348406\pi\) | ||||
0.458447 | + | 0.888722i | \(0.348406\pi\) | |||||||
\(660\) | −25.3497 | −0.986736 | ||||||||
\(661\) | −35.8626 | −1.39489 | −0.697447 | − | 0.716636i | \(-0.745681\pi\) | ||||
−0.697447 | + | 0.716636i | \(0.745681\pi\) | |||||||
\(662\) | 21.1062 | 0.820314 | ||||||||
\(663\) | 1.97642 | 0.0767578 | ||||||||
\(664\) | −8.10500 | −0.314535 | ||||||||
\(665\) | −13.1236 | −0.508911 | ||||||||
\(666\) | 5.79161 | 0.224420 | ||||||||
\(667\) | 26.0953 | 1.01042 | ||||||||
\(668\) | 7.09820 | 0.274637 | ||||||||
\(669\) | −18.1960 | −0.703497 | ||||||||
\(670\) | −6.31683 | −0.244040 | ||||||||
\(671\) | 44.7124 | 1.72610 | ||||||||
\(672\) | 6.50073 | 0.250771 | ||||||||
\(673\) | 24.9358 | 0.961204 | 0.480602 | − | 0.876939i | \(-0.340418\pi\) | ||||
0.480602 | + | 0.876939i | \(0.340418\pi\) | |||||||
\(674\) | 14.7214 | 0.567046 | ||||||||
\(675\) | 34.4655 | 1.32658 | ||||||||
\(676\) | −6.36301 | −0.244731 | ||||||||
\(677\) | −0.296017 | −0.0113768 | −0.00568842 | − | 0.999984i | \(-0.501811\pi\) | ||||
−0.00568842 | + | 0.999984i | \(0.501811\pi\) | |||||||
\(678\) | −6.98123 | −0.268113 | ||||||||
\(679\) | 20.0600 | 0.769834 | ||||||||
\(680\) | 0.339402 | 0.0130155 | ||||||||
\(681\) | 81.6687 | 3.12955 | ||||||||
\(682\) | −43.3068 | −1.65830 | ||||||||
\(683\) | −44.6867 | −1.70989 | −0.854945 | − | 0.518719i | \(-0.826409\pi\) | ||||
−0.854945 | + | 0.518719i | \(0.826409\pi\) | |||||||
\(684\) | 29.9469 | 1.14505 | ||||||||
\(685\) | −3.48657 | −0.133215 | ||||||||
\(686\) | 20.1407 | 0.768974 | ||||||||
\(687\) | 38.9130 | 1.48462 | ||||||||
\(688\) | −1.48430 | −0.0565883 | ||||||||
\(689\) | 36.8824 | 1.40511 | ||||||||
\(690\) | 14.1031 | 0.536895 | ||||||||
\(691\) | −31.9717 | −1.21626 | −0.608130 | − | 0.793838i | \(-0.708080\pi\) | ||||
−0.608130 | + | 0.793838i | \(0.708080\pi\) | |||||||
\(692\) | −10.4870 | −0.398655 | ||||||||
\(693\) | −82.6659 | −3.14022 | ||||||||
\(694\) | −10.2337 | −0.388466 | ||||||||
\(695\) | 9.19157 | 0.348656 | ||||||||
\(696\) | 24.2068 | 0.917558 | ||||||||
\(697\) | 0.868276 | 0.0328883 | ||||||||
\(698\) | 24.1958 | 0.915823 | ||||||||
\(699\) | 51.0774 | 1.93192 | ||||||||
\(700\) | 6.57643 | 0.248566 | ||||||||
\(701\) | −14.8299 | −0.560117 | −0.280058 | − | 0.959983i | \(-0.590354\pi\) | ||||
−0.280058 | + | 0.959983i | \(0.590354\pi\) | |||||||
\(702\) | 28.3826 | 1.07123 | ||||||||
\(703\) | 4.02706 | 0.151883 | ||||||||
\(704\) | 5.99202 | 0.225833 | ||||||||
\(705\) | −2.88507 | −0.108658 | ||||||||
\(706\) | 22.2544 | 0.837556 | ||||||||
\(707\) | −2.58730 | −0.0973053 | ||||||||
\(708\) | −15.0281 | −0.564789 | ||||||||
\(709\) | −12.5701 | −0.472080 | −0.236040 | − | 0.971743i | \(-0.575850\pi\) | ||||
−0.236040 | + | 0.971743i | \(0.575850\pi\) | |||||||
\(710\) | 11.9417 | 0.448163 | ||||||||
\(711\) | −82.9306 | −3.11014 | ||||||||
\(712\) | 8.27053 | 0.309951 | ||||||||
\(713\) | 24.0933 | 0.902303 | ||||||||
\(714\) | 1.61275 | 0.0603555 | ||||||||
\(715\) | −21.1188 | −0.789797 | ||||||||
\(716\) | −15.3884 | −0.575091 | ||||||||
\(717\) | 63.6045 | 2.37535 | ||||||||
\(718\) | 2.15262 | 0.0803351 | ||||||||
\(719\) | −8.29338 | −0.309291 | −0.154646 | − | 0.987970i | \(-0.549424\pi\) | ||||
−0.154646 | + | 0.987970i | \(0.549424\pi\) | |||||||
\(720\) | 8.97824 | 0.334599 | ||||||||
\(721\) | 11.3051 | 0.421025 | ||||||||
\(722\) | 1.82289 | 0.0678408 | ||||||||
\(723\) | 24.6043 | 0.915045 | ||||||||
\(724\) | 12.5150 | 0.465115 | ||||||||
\(725\) | 24.4887 | 0.909489 | ||||||||
\(726\) | −77.0129 | −2.85822 | ||||||||
\(727\) | −10.0388 | −0.372320 | −0.186160 | − | 0.982519i | \(-0.559604\pi\) | ||||
−0.186160 | + | 0.982519i | \(0.559604\pi\) | |||||||
\(728\) | 5.41574 | 0.200721 | ||||||||
\(729\) | −7.83020 | −0.290007 | ||||||||
\(730\) | 13.4986 | 0.499606 | ||||||||
\(731\) | −0.368235 | −0.0136197 | ||||||||
\(732\) | −23.0752 | −0.852883 | ||||||||
\(733\) | 46.1604 | 1.70497 | 0.852487 | − | 0.522749i | \(-0.175093\pi\) | ||||
0.852487 | + | 0.522749i | \(0.175093\pi\) | |||||||
\(734\) | 2.92078 | 0.107808 | ||||||||
\(735\) | 10.9183 | 0.402726 | ||||||||
\(736\) | −3.33361 | −0.122878 | ||||||||
\(737\) | −27.6670 | −1.01913 | ||||||||
\(738\) | 22.9686 | 0.845487 | ||||||||
\(739\) | −27.2521 | −1.00249 | −0.501243 | − | 0.865307i | \(-0.667124\pi\) | ||||
−0.501243 | + | 0.865307i | \(0.667124\pi\) | |||||||
\(740\) | 1.20734 | 0.0443825 | ||||||||
\(741\) | 36.3535 | 1.33548 | ||||||||
\(742\) | 30.0958 | 1.10485 | ||||||||
\(743\) | −15.0504 | −0.552145 | −0.276072 | − | 0.961137i | \(-0.589033\pi\) | ||||
−0.276072 | + | 0.961137i | \(0.589033\pi\) | |||||||
\(744\) | 22.3497 | 0.819381 | ||||||||
\(745\) | 0.313980 | 0.0115033 | ||||||||
\(746\) | 27.6528 | 1.01244 | ||||||||
\(747\) | −53.1905 | −1.94614 | ||||||||
\(748\) | 1.48654 | 0.0543533 | ||||||||
\(749\) | −17.3645 | −0.634485 | ||||||||
\(750\) | 34.3877 | 1.25566 | ||||||||
\(751\) | −40.6259 | −1.48246 | −0.741231 | − | 0.671250i | \(-0.765758\pi\) | ||||
−0.741231 | + | 0.671250i | \(0.765758\pi\) | |||||||
\(752\) | 0.681955 | 0.0248684 | ||||||||
\(753\) | 78.3833 | 2.85645 | ||||||||
\(754\) | 20.1667 | 0.734427 | ||||||||
\(755\) | 21.9071 | 0.797280 | ||||||||
\(756\) | 23.1600 | 0.842321 | ||||||||
\(757\) | 7.67309 | 0.278883 | 0.139442 | − | 0.990230i | \(-0.455469\pi\) | ||||
0.139442 | + | 0.990230i | \(0.455469\pi\) | |||||||
\(758\) | −18.4122 | −0.668763 | ||||||||
\(759\) | 61.7699 | 2.24211 | ||||||||
\(760\) | 6.24282 | 0.226451 | ||||||||
\(761\) | −39.6990 | −1.43909 | −0.719544 | − | 0.694447i | \(-0.755649\pi\) | ||||
−0.719544 | + | 0.694447i | \(0.755649\pi\) | |||||||
\(762\) | −8.80562 | −0.318994 | ||||||||
\(763\) | 33.0512 | 1.19653 | ||||||||
\(764\) | 7.68452 | 0.278016 | ||||||||
\(765\) | 2.22739 | 0.0805313 | ||||||||
\(766\) | 14.0045 | 0.506005 | ||||||||
\(767\) | −12.5198 | −0.452065 | ||||||||
\(768\) | −3.09236 | −0.111586 | ||||||||
\(769\) | 6.99626 | 0.252292 | 0.126146 | − | 0.992012i | \(-0.459739\pi\) | ||||
0.126146 | + | 0.992012i | \(0.459739\pi\) | |||||||
\(770\) | −17.2328 | −0.621026 | ||||||||
\(771\) | 81.1066 | 2.92098 | ||||||||
\(772\) | −9.27752 | −0.333905 | ||||||||
\(773\) | 4.14296 | 0.149012 | 0.0745060 | − | 0.997221i | \(-0.476262\pi\) | ||||
0.0745060 | + | 0.997221i | \(0.476262\pi\) | |||||||
\(774\) | −9.74096 | −0.350132 | ||||||||
\(775\) | 22.6100 | 0.812175 | ||||||||
\(776\) | −9.54244 | −0.342554 | ||||||||
\(777\) | 5.73693 | 0.205811 | ||||||||
\(778\) | −10.4227 | −0.373671 | ||||||||
\(779\) | 15.9707 | 0.572210 | ||||||||
\(780\) | 10.8990 | 0.390246 | ||||||||
\(781\) | 52.3031 | 1.87155 | ||||||||
\(782\) | −0.827025 | −0.0295743 | ||||||||
\(783\) | 86.2412 | 3.08201 | ||||||||
\(784\) | −2.58079 | −0.0921712 | ||||||||
\(785\) | −21.4568 | −0.765825 | ||||||||
\(786\) | −36.8720 | −1.31518 | ||||||||
\(787\) | 19.6426 | 0.700184 | 0.350092 | − | 0.936715i | \(-0.386150\pi\) | ||||
0.350092 | + | 0.936715i | \(0.386150\pi\) | |||||||
\(788\) | 9.06369 | 0.322881 | ||||||||
\(789\) | −98.3932 | −3.50289 | ||||||||
\(790\) | −17.2880 | −0.615078 | ||||||||
\(791\) | −4.74585 | −0.168743 | ||||||||
\(792\) | 39.3237 | 1.39731 | ||||||||
\(793\) | −19.2239 | −0.682659 | ||||||||
\(794\) | 6.26976 | 0.222505 | ||||||||
\(795\) | 60.5667 | 2.14808 | ||||||||
\(796\) | −3.54355 | −0.125598 | ||||||||
\(797\) | −2.52181 | −0.0893270 | −0.0446635 | − | 0.999002i | \(-0.514222\pi\) | ||||
−0.0446635 | + | 0.999002i | \(0.514222\pi\) | |||||||
\(798\) | 29.6642 | 1.05010 | ||||||||
\(799\) | 0.169184 | 0.00598531 | ||||||||
\(800\) | −3.12837 | −0.110605 | ||||||||
\(801\) | 54.2769 | 1.91778 | ||||||||
\(802\) | −24.2227 | −0.855332 | ||||||||
\(803\) | 59.1224 | 2.08639 | ||||||||
\(804\) | 14.2784 | 0.503560 | ||||||||
\(805\) | 9.58731 | 0.337908 | ||||||||
\(806\) | 18.6195 | 0.655844 | ||||||||
\(807\) | 99.7988 | 3.51309 | ||||||||
\(808\) | 1.23076 | 0.0432980 | ||||||||
\(809\) | −15.9519 | −0.560840 | −0.280420 | − | 0.959877i | \(-0.590474\pi\) | ||||
−0.280420 | + | 0.959877i | \(0.590474\pi\) | |||||||
\(810\) | 19.6739 | 0.691271 | ||||||||
\(811\) | 18.2700 | 0.641547 | 0.320773 | − | 0.947156i | \(-0.396057\pi\) | ||||
0.320773 | + | 0.947156i | \(0.396057\pi\) | |||||||
\(812\) | 16.4559 | 0.577487 | ||||||||
\(813\) | 23.3803 | 0.819983 | ||||||||
\(814\) | 5.28799 | 0.185344 | ||||||||
\(815\) | −12.9398 | −0.453260 | ||||||||
\(816\) | −0.767174 | −0.0268565 | ||||||||
\(817\) | −6.77316 | −0.236963 | ||||||||
\(818\) | 3.27243 | 0.114418 | ||||||||
\(819\) | 35.5418 | 1.24193 | ||||||||
\(820\) | 4.78811 | 0.167208 | ||||||||
\(821\) | −18.3530 | −0.640524 | −0.320262 | − | 0.947329i | \(-0.603771\pi\) | ||||
−0.320262 | + | 0.947329i | \(0.603771\pi\) | |||||||
\(822\) | 7.88093 | 0.274879 | ||||||||
\(823\) | 33.8367 | 1.17947 | 0.589737 | − | 0.807595i | \(-0.299231\pi\) | ||||
0.589737 | + | 0.807595i | \(0.299231\pi\) | |||||||
\(824\) | −5.37778 | −0.187344 | ||||||||
\(825\) | 57.9670 | 2.01815 | ||||||||
\(826\) | −10.2161 | −0.355464 | ||||||||
\(827\) | −27.1835 | −0.945264 | −0.472632 | − | 0.881260i | \(-0.656696\pi\) | ||||
−0.472632 | + | 0.881260i | \(0.656696\pi\) | |||||||
\(828\) | −21.8774 | −0.760292 | ||||||||
\(829\) | 33.5296 | 1.16453 | 0.582265 | − | 0.812999i | \(-0.302167\pi\) | ||||
0.582265 | + | 0.812999i | \(0.302167\pi\) | |||||||
\(830\) | −11.0883 | −0.384879 | ||||||||
\(831\) | 9.24932 | 0.320856 | ||||||||
\(832\) | −2.57624 | −0.0893149 | ||||||||
\(833\) | −0.640261 | −0.0221837 | ||||||||
\(834\) | −20.7764 | −0.719427 | ||||||||
\(835\) | 9.71087 | 0.336059 | ||||||||
\(836\) | 27.3428 | 0.945671 | ||||||||
\(837\) | 79.6250 | 2.75224 | ||||||||
\(838\) | 28.7923 | 0.994613 | ||||||||
\(839\) | −42.7615 | −1.47629 | −0.738145 | − | 0.674642i | \(-0.764298\pi\) | ||||
−0.738145 | + | 0.674642i | \(0.764298\pi\) | |||||||
\(840\) | 8.89349 | 0.306854 | ||||||||
\(841\) | 32.2769 | 1.11300 | ||||||||
\(842\) | −5.08828 | −0.175354 | ||||||||
\(843\) | 49.9812 | 1.72145 | ||||||||
\(844\) | 11.1019 | 0.382143 | ||||||||
\(845\) | −8.70507 | −0.299464 | ||||||||
\(846\) | 4.47545 | 0.153869 | ||||||||
\(847\) | −52.3535 | −1.79889 | ||||||||
\(848\) | −14.3164 | −0.491627 | ||||||||
\(849\) | −50.1128 | −1.71987 | ||||||||
\(850\) | −0.776108 | −0.0266203 | ||||||||
\(851\) | −2.94193 | −0.100848 | ||||||||
\(852\) | −26.9926 | −0.924751 | ||||||||
\(853\) | −27.6935 | −0.948207 | −0.474103 | − | 0.880469i | \(-0.657228\pi\) | ||||
−0.474103 | + | 0.880469i | \(0.657228\pi\) | |||||||
\(854\) | −15.6865 | −0.536782 | ||||||||
\(855\) | 40.9696 | 1.40113 | ||||||||
\(856\) | 8.26019 | 0.282327 | ||||||||
\(857\) | 5.76561 | 0.196950 | 0.0984748 | − | 0.995140i | \(-0.468604\pi\) | ||||
0.0984748 | + | 0.995140i | \(0.468604\pi\) | |||||||
\(858\) | 47.7363 | 1.62969 | ||||||||
\(859\) | 16.0286 | 0.546889 | 0.273445 | − | 0.961888i | \(-0.411837\pi\) | ||||
0.273445 | + | 0.961888i | \(0.411837\pi\) | |||||||
\(860\) | −2.03063 | −0.0692439 | ||||||||
\(861\) | 22.7518 | 0.775379 | ||||||||
\(862\) | 18.1842 | 0.619357 | ||||||||
\(863\) | 4.15194 | 0.141334 | 0.0706668 | − | 0.997500i | \(-0.477487\pi\) | ||||
0.0706668 | + | 0.997500i | \(0.477487\pi\) | |||||||
\(864\) | −11.0171 | −0.374809 | ||||||||
\(865\) | −14.3470 | −0.487812 | ||||||||
\(866\) | 20.9723 | 0.712669 | ||||||||
\(867\) | 52.3798 | 1.77891 | ||||||||
\(868\) | 15.1934 | 0.515697 | ||||||||
\(869\) | −75.7193 | −2.56860 | ||||||||
\(870\) | 33.1168 | 1.12276 | ||||||||
\(871\) | 11.8953 | 0.403056 | ||||||||
\(872\) | −15.7223 | −0.532423 | ||||||||
\(873\) | −62.6240 | −2.11950 | ||||||||
\(874\) | −15.2119 | −0.514552 | ||||||||
\(875\) | 23.3768 | 0.790281 | ||||||||
\(876\) | −30.5119 | −1.03090 | ||||||||
\(877\) | −11.5177 | −0.388925 | −0.194463 | − | 0.980910i | \(-0.562296\pi\) | ||||
−0.194463 | + | 0.980910i | \(0.562296\pi\) | |||||||
\(878\) | 15.1799 | 0.512298 | ||||||||
\(879\) | −13.2616 | −0.447301 | ||||||||
\(880\) | 8.19753 | 0.276339 | ||||||||
\(881\) | 33.6704 | 1.13438 | 0.567192 | − | 0.823586i | \(-0.308030\pi\) | ||||
0.567192 | + | 0.823586i | \(0.308030\pi\) | |||||||
\(882\) | −16.9369 | −0.570296 | ||||||||
\(883\) | 3.86850 | 0.130185 | 0.0650927 | − | 0.997879i | \(-0.479266\pi\) | ||||
0.0650927 | + | 0.997879i | \(0.479266\pi\) | |||||||
\(884\) | −0.639131 | −0.0214963 | ||||||||
\(885\) | −20.5595 | −0.691101 | ||||||||
\(886\) | −20.6263 | −0.692955 | ||||||||
\(887\) | −21.5826 | −0.724673 | −0.362336 | − | 0.932047i | \(-0.618021\pi\) | ||||
−0.362336 | + | 0.932047i | \(0.618021\pi\) | |||||||
\(888\) | −2.72903 | −0.0915801 | ||||||||
\(889\) | −5.98607 | −0.200766 | ||||||||
\(890\) | 11.3147 | 0.379270 | ||||||||
\(891\) | 86.1695 | 2.88679 | ||||||||
\(892\) | 5.88417 | 0.197017 | ||||||||
\(893\) | 3.11191 | 0.104136 | ||||||||
\(894\) | −0.709710 | −0.0237363 | ||||||||
\(895\) | −21.0525 | −0.703707 | ||||||||
\(896\) | −2.10219 | −0.0702293 | ||||||||
\(897\) | −26.5577 | −0.886735 | ||||||||
\(898\) | −27.8874 | −0.930616 | ||||||||
\(899\) | 56.5758 | 1.88691 | ||||||||
\(900\) | −20.5305 | −0.684350 | ||||||||
\(901\) | −3.55171 | −0.118325 | ||||||||
\(902\) | 20.9714 | 0.698270 | ||||||||
\(903\) | −9.64901 | −0.321099 | ||||||||
\(904\) | 2.25758 | 0.0750858 | ||||||||
\(905\) | 17.1214 | 0.569135 | ||||||||
\(906\) | −49.5181 | −1.64513 | ||||||||
\(907\) | −23.2352 | −0.771512 | −0.385756 | − | 0.922601i | \(-0.626059\pi\) | ||||
−0.385756 | + | 0.922601i | \(0.626059\pi\) | |||||||
\(908\) | −26.4098 | −0.876441 | ||||||||
\(909\) | 8.07709 | 0.267900 | ||||||||
\(910\) | 7.40914 | 0.245611 | ||||||||
\(911\) | −29.8677 | −0.989561 | −0.494780 | − | 0.869018i | \(-0.664751\pi\) | ||||
−0.494780 | + | 0.869018i | \(0.664751\pi\) | |||||||
\(912\) | −14.1111 | −0.467265 | ||||||||
\(913\) | −48.5653 | −1.60728 | ||||||||
\(914\) | 12.6366 | 0.417982 | ||||||||
\(915\) | −31.5686 | −1.04362 | ||||||||
\(916\) | −12.5836 | −0.415774 | ||||||||
\(917\) | −25.0657 | −0.827741 | ||||||||
\(918\) | −2.73320 | −0.0902089 | ||||||||
\(919\) | −52.7357 | −1.73959 | −0.869795 | − | 0.493413i | \(-0.835749\pi\) | ||||
−0.869795 | + | 0.493413i | \(0.835749\pi\) | |||||||
\(920\) | −4.56063 | −0.150359 | ||||||||
\(921\) | −13.4487 | −0.443151 | ||||||||
\(922\) | 3.60201 | 0.118626 | ||||||||
\(923\) | −22.4875 | −0.740184 | ||||||||
\(924\) | 38.9525 | 1.28144 | ||||||||
\(925\) | −2.76081 | −0.0907747 | ||||||||
\(926\) | 10.6340 | 0.349455 | ||||||||
\(927\) | −35.2926 | −1.15916 | ||||||||
\(928\) | −7.82796 | −0.256965 | ||||||||
\(929\) | 23.9287 | 0.785075 | 0.392538 | − | 0.919736i | \(-0.371597\pi\) | ||||
0.392538 | + | 0.919736i | \(0.371597\pi\) | |||||||
\(930\) | 30.5761 | 1.00263 | ||||||||
\(931\) | −11.7767 | −0.385966 | ||||||||
\(932\) | −16.5173 | −0.541042 | ||||||||
\(933\) | 26.0787 | 0.853777 | ||||||||
\(934\) | −21.5758 | −0.705983 | ||||||||
\(935\) | 2.03370 | 0.0665091 | ||||||||
\(936\) | −16.9070 | −0.552623 | ||||||||
\(937\) | 31.7703 | 1.03789 | 0.518945 | − | 0.854808i | \(-0.326325\pi\) | ||||
0.518945 | + | 0.854808i | \(0.326325\pi\) | |||||||
\(938\) | 9.70647 | 0.316927 | ||||||||
\(939\) | 66.9979 | 2.18639 | ||||||||
\(940\) | 0.932966 | 0.0304300 | ||||||||
\(941\) | −15.5503 | −0.506925 | −0.253463 | − | 0.967345i | \(-0.581570\pi\) | ||||
−0.253463 | + | 0.967345i | \(0.581570\pi\) | |||||||
\(942\) | 48.5003 | 1.58022 | ||||||||
\(943\) | −11.6672 | −0.379938 | ||||||||
\(944\) | 4.85974 | 0.158171 | ||||||||
\(945\) | 31.6846 | 1.03070 | ||||||||
\(946\) | −8.89393 | −0.289167 | ||||||||
\(947\) | −12.8134 | −0.416381 | −0.208190 | − | 0.978088i | \(-0.566757\pi\) | ||||
−0.208190 | + | 0.978088i | \(0.566757\pi\) | |||||||
\(948\) | 39.0772 | 1.26917 | ||||||||
\(949\) | −25.4194 | −0.825148 | ||||||||
\(950\) | −14.2754 | −0.463155 | ||||||||
\(951\) | 84.7105 | 2.74693 | ||||||||
\(952\) | −0.521526 | −0.0169028 | ||||||||
\(953\) | −6.07738 | −0.196866 | −0.0984328 | − | 0.995144i | \(-0.531383\pi\) | ||||
−0.0984328 | + | 0.995144i | \(0.531383\pi\) | |||||||
\(954\) | −93.9539 | −3.04187 | ||||||||
\(955\) | 10.5130 | 0.340193 | ||||||||
\(956\) | −20.5683 | −0.665225 | ||||||||
\(957\) | 145.048 | 4.68873 | ||||||||
\(958\) | 8.95356 | 0.289276 | ||||||||
\(959\) | 5.35747 | 0.173002 | ||||||||
\(960\) | −4.23058 | −0.136541 | ||||||||
\(961\) | 21.2355 | 0.685015 | ||||||||
\(962\) | −2.27354 | −0.0733020 | ||||||||
\(963\) | 54.2090 | 1.74686 | ||||||||
\(964\) | −7.95649 | −0.256261 | ||||||||
\(965\) | −12.6924 | −0.408581 | ||||||||
\(966\) | −21.6709 | −0.697249 | ||||||||
\(967\) | −31.2998 | −1.00653 | −0.503266 | − | 0.864131i | \(-0.667868\pi\) | ||||
−0.503266 | + | 0.864131i | \(0.667868\pi\) | |||||||
\(968\) | 24.9042 | 0.800453 | ||||||||
\(969\) | −3.50078 | −0.112461 | ||||||||
\(970\) | −13.0548 | −0.419164 | ||||||||
\(971\) | −14.9618 | −0.480146 | −0.240073 | − | 0.970755i | \(-0.577171\pi\) | ||||
−0.240073 | + | 0.970755i | \(0.577171\pi\) | |||||||
\(972\) | −11.4191 | −0.366268 | ||||||||
\(973\) | −14.1238 | −0.452789 | ||||||||
\(974\) | −24.7815 | −0.794051 | ||||||||
\(975\) | −24.9226 | −0.798162 | ||||||||
\(976\) | 7.46200 | 0.238853 | ||||||||
\(977\) | −29.4155 | −0.941086 | −0.470543 | − | 0.882377i | \(-0.655942\pi\) | ||||
−0.470543 | + | 0.882377i | \(0.655942\pi\) | |||||||
\(978\) | 29.2486 | 0.935268 | ||||||||
\(979\) | 49.5572 | 1.58385 | ||||||||
\(980\) | −3.53072 | −0.112785 | ||||||||
\(981\) | −103.180 | −3.29429 | ||||||||
\(982\) | 40.2848 | 1.28554 | ||||||||
\(983\) | 46.8690 | 1.49489 | 0.747445 | − | 0.664324i | \(-0.231280\pi\) | ||||
0.747445 | + | 0.664324i | \(0.231280\pi\) | |||||||
\(984\) | −10.8229 | −0.345021 | ||||||||
\(985\) | 12.3998 | 0.395091 | ||||||||
\(986\) | −1.94201 | −0.0618463 | ||||||||
\(987\) | 4.43321 | 0.141110 | ||||||||
\(988\) | −11.7559 | −0.374005 | ||||||||
\(989\) | 4.94806 | 0.157339 | ||||||||
\(990\) | 53.7978 | 1.70981 | ||||||||
\(991\) | 15.4237 | 0.489950 | 0.244975 | − | 0.969529i | \(-0.421220\pi\) | ||||
0.244975 | + | 0.969529i | \(0.421220\pi\) | |||||||
\(992\) | −7.22741 | −0.229471 | ||||||||
\(993\) | −65.2678 | −2.07121 | ||||||||
\(994\) | −18.3496 | −0.582014 | ||||||||
\(995\) | −4.84784 | −0.153687 | ||||||||
\(996\) | 25.0636 | 0.794170 | ||||||||
\(997\) | 26.1900 | 0.829445 | 0.414722 | − | 0.909948i | \(-0.363879\pi\) | ||||
0.414722 | + | 0.909948i | \(0.363879\pi\) | |||||||
\(998\) | −30.8820 | −0.977553 | ||||||||
\(999\) | −9.72264 | −0.307611 |
(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 | 8042.2.a.a.1.1 | ✓ | 67 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8042.2.a.a.1.1 | ✓ | 67 | 1.1 | even | 1 | trivial |