Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,2,Mod(7,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([3, 11]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.7");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.x (of order \(12\), degree \(4\), 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: | \(2.59513806569\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 318.2 | ||
Character | \(\chi\) | \(=\) | 325.318 |
Dual form | 325.2.x.c.232.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{5}{12}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.98606 | − | 1.14665i | −1.40436 | − | 0.810805i | −0.409519 | − | 0.912301i | \(-0.634304\pi\) |
−0.994836 | + | 0.101497i | \(0.967637\pi\) | |||||||
\(3\) | 1.80624 | − | 0.483980i | 1.04283 | − | 0.279426i | 0.303545 | − | 0.952817i | \(-0.401830\pi\) |
0.739286 | + | 0.673391i | \(0.235163\pi\) | |||||||
\(4\) | 1.62962 | + | 2.82258i | 0.814809 | + | 1.41129i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −4.14225 | − | 1.10991i | −1.69107 | − | 0.453120i | ||||
\(7\) | −1.60759 | − | 2.78443i | −0.607612 | − | 1.05242i | −0.991633 | − | 0.129091i | \(-0.958794\pi\) |
0.384021 | − | 0.923325i | \(-0.374539\pi\) | |||||||
\(8\) | − | 2.88781i | − | 1.02100i | ||||||
\(9\) | 0.430177 | − | 0.248363i | 0.143392 | − | 0.0827877i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.45476 | + | 0.925701i | −1.04165 | + | 0.279109i | −0.738797 | − | 0.673928i | \(-0.764606\pi\) |
−0.302853 | + | 0.953037i | \(0.597939\pi\) | |||||||
\(12\) | 4.30955 | + | 4.30955i | 1.24406 | + | 1.24406i | ||||
\(13\) | −3.07882 | − | 1.87639i | −0.853912 | − | 0.520418i | ||||
\(14\) | 7.37338i | 1.97062i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.0520747 | + | 0.0901960i | −0.0130187 | + | 0.0225490i | ||||
\(17\) | 1.55440 | − | 5.80109i | 0.376997 | − | 1.40697i | −0.473409 | − | 0.880843i | \(-0.656977\pi\) |
0.850405 | − | 0.526128i | \(-0.176357\pi\) | |||||||
\(18\) | −1.13914 | −0.268499 | ||||||||
\(19\) | 2.03669 | − | 7.60104i | 0.467249 | − | 1.74380i | −0.182075 | − | 0.983285i | \(-0.558281\pi\) |
0.649324 | − | 0.760512i | \(-0.275052\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.25130 | − | 4.25130i | −0.927709 | − | 0.927709i | ||||
\(22\) | 7.92281 | + | 2.12291i | 1.68915 | + | 0.452606i | ||||
\(23\) | 0.296828 | + | 1.10778i | 0.0618930 | + | 0.230988i | 0.989943 | − | 0.141468i | \(-0.0451824\pi\) |
−0.928050 | + | 0.372456i | \(0.878516\pi\) | |||||||
\(24\) | −1.39764 | − | 5.21607i | −0.285292 | − | 1.06473i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.96315 | + | 7.25696i | 0.777238 | + | 1.42321i | ||||
\(27\) | −3.30997 | + | 3.30997i | −0.637004 | + | 0.637004i | ||||
\(28\) | 5.23952 | − | 9.07511i | 0.990176 | − | 1.71503i | ||||
\(29\) | 0.877436 | + | 0.506588i | 0.162936 | + | 0.0940710i | 0.579251 | − | 0.815150i | \(-0.303345\pi\) |
−0.416315 | + | 0.909221i | \(0.636679\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.47451 | − | 4.47451i | 0.803645 | − | 0.803645i | −0.180018 | − | 0.983663i | \(-0.557616\pi\) |
0.983663 | + | 0.180018i | \(0.0576156\pi\) | |||||||
\(32\) | −4.79499 | + | 2.76839i | −0.847642 | + | 0.489386i | ||||
\(33\) | −5.79210 | + | 3.34407i | −1.00827 | + | 0.582128i | ||||
\(34\) | −9.73895 | + | 9.73895i | −1.67022 | + | 1.67022i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.40205 | + | 0.809474i | 0.233675 | + | 0.134912i | ||||
\(37\) | −0.372686 | + | 0.645511i | −0.0612692 | + | 0.106121i | −0.895033 | − | 0.446000i | \(-0.852848\pi\) |
0.833764 | + | 0.552121i | \(0.186181\pi\) | |||||||
\(38\) | −12.7607 | + | 12.7607i | −2.07006 | + | 2.07006i | ||||
\(39\) | −6.46922 | − | 1.89912i | −1.03590 | − | 0.304103i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.65312 | + | 6.16954i | 0.258175 | + | 0.963521i | 0.966297 | + | 0.257431i | \(0.0828759\pi\) |
−0.708122 | + | 0.706090i | \(0.750457\pi\) | |||||||
\(42\) | 3.56857 | + | 13.3181i | 0.550642 | + | 2.05502i | ||||
\(43\) | 1.25260 | + | 0.335632i | 0.191019 | + | 0.0511834i | 0.353060 | − | 0.935601i | \(-0.385141\pi\) |
−0.162041 | + | 0.986784i | \(0.551808\pi\) | |||||||
\(44\) | −8.24281 | − | 8.24281i | −1.24265 | − | 1.24265i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.680717 | − | 2.54047i | 0.100366 | − | 0.374572i | ||||
\(47\) | −8.22199 | −1.19930 | −0.599650 | − | 0.800262i | \(-0.704694\pi\) | ||||
−0.599650 | + | 0.800262i | \(0.704694\pi\) | |||||||
\(48\) | −0.0504062 | + | 0.188118i | −0.00727551 | + | 0.0271526i | ||||
\(49\) | −1.66870 | + | 2.89027i | −0.238385 | + | 0.412895i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 11.2304i | − | 1.57258i | ||||||
\(52\) | 0.278965 | − | 11.7480i | 0.0386854 | − | 1.62916i | ||||
\(53\) | 3.01886 | + | 3.01886i | 0.414672 | + | 0.414672i | 0.883363 | − | 0.468690i | \(-0.155274\pi\) |
−0.468690 | + | 0.883363i | \(0.655274\pi\) | |||||||
\(54\) | 10.3692 | − | 2.77841i | 1.41107 | − | 0.378094i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −8.04090 | + | 4.64242i | −1.07451 | + | 0.620369i | ||||
\(57\) | − | 14.7150i | − | 1.94905i | ||||||
\(58\) | −1.16176 | − | 2.01223i | −0.152546 | − | 0.264218i | ||||
\(59\) | 6.45324 | + | 1.72914i | 0.840141 | + | 0.225115i | 0.653133 | − | 0.757243i | \(-0.273454\pi\) |
0.187008 | + | 0.982358i | \(0.440121\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.928497 | + | 1.60820i | 0.118882 | + | 0.205909i | 0.919325 | − | 0.393500i | \(-0.128736\pi\) |
−0.800443 | + | 0.599409i | \(0.795402\pi\) | |||||||
\(62\) | −14.0173 | + | 3.75593i | −1.78020 | + | 0.477004i | ||||
\(63\) | −1.38310 | − | 0.798532i | −0.174254 | − | 0.100606i | ||||
\(64\) | 12.9058 | 1.61322 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 15.3379 | 1.88797 | ||||||||
\(67\) | 7.23362 | + | 4.17633i | 0.883727 | + | 0.510220i | 0.871885 | − | 0.489710i | \(-0.162897\pi\) |
0.0118416 | + | 0.999930i | \(0.496231\pi\) | |||||||
\(68\) | 18.9071 | − | 5.06615i | 2.29283 | − | 0.614361i | ||||
\(69\) | 1.07228 | + | 1.85725i | 0.129088 | + | 0.223587i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.01343 | − | 2.41514i | −1.06970 | − | 0.286625i | −0.319329 | − | 0.947644i | \(-0.603457\pi\) |
−0.750369 | + | 0.661019i | \(0.770124\pi\) | |||||||
\(72\) | −0.717225 | − | 1.24227i | −0.0845258 | − | 0.146403i | ||||
\(73\) | 7.93972i | 0.929274i | 0.885501 | + | 0.464637i | \(0.153815\pi\) | ||||
−0.885501 | + | 0.464637i | \(0.846185\pi\) | |||||||
\(74\) | 1.48035 | − | 0.854682i | 0.172088 | − | 0.0993548i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 24.7736 | − | 6.63806i | 2.84172 | − | 0.761438i | ||||
\(77\) | 8.13139 | + | 8.13139i | 0.926658 | + | 0.926658i | ||||
\(78\) | 10.6706 | + | 11.1897i | 1.20821 | + | 1.26698i | ||||
\(79\) | − | 10.1869i | − | 1.14611i | −0.819517 | − | 0.573056i | \(-0.805758\pi\) | ||
0.819517 | − | 0.573056i | \(-0.194242\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.12172 | + | 8.87108i | −0.569080 | + | 0.985676i | ||||
\(82\) | 3.79111 | − | 14.1486i | 0.418658 | − | 1.56245i | ||||
\(83\) | 9.01936 | 0.990003 | 0.495002 | − | 0.868892i | \(-0.335167\pi\) | ||||
0.495002 | + | 0.868892i | \(0.335167\pi\) | |||||||
\(84\) | 5.07164 | − | 18.9276i | 0.553361 | − | 2.06517i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.10288 | − | 2.10288i | −0.226759 | − | 0.226759i | ||||
\(87\) | 1.83003 | + | 0.490356i | 0.196200 | + | 0.0525717i | ||||
\(88\) | 2.67325 | + | 9.97670i | 0.284969 | + | 1.06352i | ||||
\(89\) | 0.176147 | + | 0.657390i | 0.0186716 | + | 0.0696832i | 0.974633 | − | 0.223809i | \(-0.0718492\pi\) |
−0.955961 | + | 0.293492i | \(0.905183\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.275194 | + | 11.5892i | −0.0288481 | + | 1.21488i | ||||
\(92\) | −2.64308 | + | 2.64308i | −0.275560 | + | 0.275560i | ||||
\(93\) | 5.91645 | − | 10.2476i | 0.613507 | − | 1.06263i | ||||
\(94\) | 16.3294 | + | 9.42776i | 1.68424 | + | 0.972399i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.32104 | + | 7.32104i | −0.747200 | + | 0.747200i | ||||
\(97\) | 11.7851 | − | 6.80414i | 1.19660 | − | 0.690856i | 0.236803 | − | 0.971558i | \(-0.423900\pi\) |
0.959795 | + | 0.280702i | \(0.0905671\pi\) | |||||||
\(98\) | 6.62825 | − | 3.82682i | 0.669555 | − | 0.386568i | ||||
\(99\) | −1.25625 | + | 1.25625i | −0.126258 | + | 0.126258i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.78812 | + | 4.49648i | 0.774947 | + | 0.447416i | 0.834637 | − | 0.550801i | \(-0.185678\pi\) |
−0.0596893 | + | 0.998217i | \(0.519011\pi\) | |||||||
\(102\) | −12.8774 | + | 22.3043i | −1.27505 | + | 2.20845i | ||||
\(103\) | −1.73771 | + | 1.73771i | −0.171222 | + | 0.171222i | −0.787516 | − | 0.616294i | \(-0.788633\pi\) |
0.616294 | + | 0.787516i | \(0.288633\pi\) | |||||||
\(104\) | −5.41867 | + | 8.89106i | −0.531344 | + | 0.871840i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.53405 | − | 9.45721i | −0.246129 | − | 0.918566i | ||||
\(107\) | −2.54648 | − | 9.50358i | −0.246177 | − | 0.918745i | −0.972788 | − | 0.231696i | \(-0.925572\pi\) |
0.726611 | − | 0.687049i | \(-0.241094\pi\) | |||||||
\(108\) | −14.7367 | − | 3.94867i | −1.41804 | − | 0.379961i | ||||
\(109\) | −6.16709 | − | 6.16709i | −0.590700 | − | 0.590700i | 0.347121 | − | 0.937820i | \(-0.387159\pi\) |
−0.937820 | + | 0.347121i | \(0.887159\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.360745 | + | 1.34632i | −0.0342404 | + | 0.127787i | ||||
\(112\) | 0.334859 | 0.0316412 | ||||||||
\(113\) | 3.92715 | − | 14.6563i | 0.369435 | − | 1.37875i | −0.491872 | − | 0.870668i | \(-0.663687\pi\) |
0.861307 | − | 0.508084i | \(-0.169646\pi\) | |||||||
\(114\) | −16.8730 | + | 29.2248i | −1.58030 | + | 2.73715i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.30218i | 0.306600i | ||||||||
\(117\) | −1.79047 | − | 0.0425158i | −0.165529 | − | 0.00393058i | ||||
\(118\) | −10.8338 | − | 10.8338i | −0.997332 | − | 0.997332i | ||||
\(119\) | −18.6516 | + | 4.99767i | −1.70979 | + | 0.458136i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.55218 | − | 0.896149i | 0.141107 | − | 0.0814681i | ||||
\(122\) | − | 4.25865i | − | 0.385560i | ||||||
\(123\) | 5.97187 | + | 10.3436i | 0.538465 | + | 0.932649i | ||||
\(124\) | 19.9214 | + | 5.33792i | 1.78900 | + | 0.479360i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.83128 | + | 3.17186i | 0.163143 | + | 0.282572i | ||||
\(127\) | 11.6985 | − | 3.13461i | 1.03807 | − | 0.278151i | 0.300759 | − | 0.953700i | \(-0.402760\pi\) |
0.737315 | + | 0.675549i | \(0.236093\pi\) | |||||||
\(128\) | −16.0417 | − | 9.26167i | −1.41790 | − | 0.818624i | ||||
\(129\) | 2.42492 | 0.213503 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.0696124 | 0.00608206 | 0.00304103 | − | 0.999995i | \(-0.499032\pi\) | ||||
0.00304103 | + | 0.999995i | \(0.499032\pi\) | |||||||
\(132\) | −18.8778 | − | 10.8991i | −1.64310 | − | 0.948646i | ||||
\(133\) | −24.4387 | + | 6.54833i | −2.11910 | + | 0.567812i | ||||
\(134\) | −9.57759 | − | 16.5889i | −0.827378 | − | 1.43306i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −16.7524 | − | 4.48880i | −1.43651 | − | 0.384912i | ||||
\(137\) | 5.27754 | + | 9.14097i | 0.450891 | + | 0.780966i | 0.998442 | − | 0.0558064i | \(-0.0177730\pi\) |
−0.547551 | + | 0.836773i | \(0.684440\pi\) | |||||||
\(138\) | − | 4.91814i | − | 0.418660i | ||||||
\(139\) | −8.01918 | + | 4.62988i | −0.680178 | + | 0.392701i | −0.799922 | − | 0.600104i | \(-0.795126\pi\) |
0.119744 | + | 0.992805i | \(0.461793\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.8509 | + | 3.97928i | −1.25067 | + | 0.335116i | ||||
\(142\) | 15.1319 | + | 15.1319i | 1.26984 | + | 1.26984i | ||||
\(143\) | 12.3736 | + | 3.63242i | 1.03473 | + | 0.303758i | ||||
\(144\) | 0.0517337i | 0.00431114i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 9.10409 | − | 15.7687i | 0.753460 | − | 1.30503i | ||||
\(147\) | −1.61523 | + | 6.02812i | −0.133222 | + | 0.497191i | ||||
\(148\) | −2.42934 | −0.199691 | ||||||||
\(149\) | 3.85291 | − | 14.3792i | 0.315642 | − | 1.17799i | −0.607748 | − | 0.794130i | \(-0.707927\pi\) |
0.923390 | − | 0.383863i | \(-0.125407\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.3382 | + | 10.3382i | 0.841308 | + | 0.841308i | 0.989029 | − | 0.147721i | \(-0.0471937\pi\) |
−0.147721 | + | 0.989029i | \(0.547194\pi\) | |||||||
\(152\) | −21.9503 | − | 5.88158i | −1.78041 | − | 0.477059i | ||||
\(153\) | −0.772110 | − | 2.88155i | −0.0624214 | − | 0.232960i | ||||
\(154\) | −6.82555 | − | 25.4733i | −0.550018 | − | 2.05270i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.18193 | − | 21.3547i | −0.414887 | − | 1.70975i | ||||
\(157\) | −15.9216 | + | 15.9216i | −1.27068 | + | 1.27068i | −0.324946 | + | 0.945733i | \(0.605346\pi\) |
−0.945733 | + | 0.324946i | \(0.894654\pi\) | |||||||
\(158\) | −11.6808 | + | 20.2317i | −0.929272 | + | 1.60955i | ||||
\(159\) | 6.91384 | + | 3.99171i | 0.548303 | + | 0.316563i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.60735 | − | 2.60735i | 0.205488 | − | 0.205488i | ||||
\(162\) | 20.3441 | − | 11.7457i | 1.59838 | − | 0.922826i | ||||
\(163\) | 7.53208 | − | 4.34865i | 0.589958 | − | 0.340612i | −0.175123 | − | 0.984547i | \(-0.556032\pi\) |
0.765081 | + | 0.643934i | \(0.222699\pi\) | |||||||
\(164\) | −14.7201 | + | 14.7201i | −1.14944 | + | 1.14944i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.9130 | − | 10.3421i | −1.39032 | − | 0.802699i | ||||
\(167\) | −1.67124 | + | 2.89467i | −0.129324 | + | 0.223996i | −0.923415 | − | 0.383803i | \(-0.874614\pi\) |
0.794091 | + | 0.607799i | \(0.207947\pi\) | |||||||
\(168\) | −12.2769 | + | 12.2769i | −0.947186 | + | 0.947186i | ||||
\(169\) | 5.95830 | + | 11.5542i | 0.458331 | + | 0.888782i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.01168 | − | 3.77563i | −0.0773649 | − | 0.288730i | ||||
\(172\) | 1.09390 | + | 4.08251i | 0.0834094 | + | 0.311288i | ||||
\(173\) | −4.66127 | − | 1.24898i | −0.354390 | − | 0.0949585i | 0.0772319 | − | 0.997013i | \(-0.475392\pi\) |
−0.431622 | + | 0.902055i | \(0.642058\pi\) | |||||||
\(174\) | −3.07229 | − | 3.07229i | −0.232910 | − | 0.232910i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.0964112 | − | 0.359811i | 0.00726727 | − | 0.0271218i | ||||
\(177\) | 12.4930 | 0.939028 | ||||||||
\(178\) | 0.403959 | − | 1.50760i | 0.0302780 | − | 0.112999i | ||||
\(179\) | 1.57907 | − | 2.73504i | 0.118025 | − | 0.204426i | −0.800960 | − | 0.598718i | \(-0.795677\pi\) |
0.918985 | + | 0.394292i | \(0.129010\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.80661i | 0.134284i | 0.997743 | + | 0.0671422i | \(0.0213881\pi\) | ||||
−0.997743 | + | 0.0671422i | \(0.978612\pi\) | |||||||
\(182\) | 13.8354 | − | 22.7013i | 1.02555 | − | 1.68274i | ||||
\(183\) | 2.45542 | + | 2.45542i | 0.181510 | + | 0.181510i | ||||
\(184\) | 3.19905 | − | 0.857184i | 0.235837 | − | 0.0631924i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −23.5008 | + | 13.5682i | −1.72316 | + | 0.994869i | ||||
\(187\) | 21.4803i | 1.57079i | ||||||||
\(188\) | −13.3987 | − | 23.2072i | −0.977201 | − | 1.69256i | ||||
\(189\) | 14.5375 | + | 3.89530i | 1.05744 | + | 0.283341i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.0167 | − | 19.0815i | −0.797142 | − | 1.38069i | −0.921470 | − | 0.388449i | \(-0.873011\pi\) |
0.124328 | − | 0.992241i | \(-0.460322\pi\) | |||||||
\(192\) | 23.3109 | − | 6.24614i | 1.68232 | − | 0.450776i | ||||
\(193\) | −14.4151 | − | 8.32256i | −1.03762 | − | 0.599071i | −0.118463 | − | 0.992958i | \(-0.537797\pi\) |
−0.919159 | + | 0.393887i | \(0.871130\pi\) | |||||||
\(194\) | −31.2079 | −2.24060 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.8773 | −0.776953 | ||||||||
\(197\) | −2.43530 | − | 1.40602i | −0.173508 | − | 0.100175i | 0.410731 | − | 0.911757i | \(-0.365274\pi\) |
−0.584239 | + | 0.811582i | \(0.698607\pi\) | |||||||
\(198\) | 3.93547 | − | 1.05451i | 0.279682 | − | 0.0749404i | ||||
\(199\) | −9.27945 | − | 16.0725i | −0.657803 | − | 1.13935i | −0.981183 | − | 0.193079i | \(-0.938153\pi\) |
0.323380 | − | 0.946269i | \(-0.395181\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.0869 | + | 4.04252i | 1.06415 | + | 0.285137i | ||||
\(202\) | −10.3118 | − | 17.8605i | −0.725534 | − | 1.25666i | ||||
\(203\) | − | 3.25754i | − | 0.228635i | ||||||
\(204\) | 31.6988 | − | 18.3013i | 2.21936 | − | 1.28135i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.44375 | − | 1.45865i | 0.379284 | − | 0.101629i | ||||
\(207\) | 0.402820 | + | 0.402820i | 0.0279979 | + | 0.0279979i | ||||
\(208\) | 0.329572 | − | 0.179985i | 0.0228517 | − | 0.0124797i | ||||
\(209\) | 28.1451i | 1.94684i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1084 | − | 17.5083i | 0.695892 | − | 1.20532i | −0.273987 | − | 0.961733i | \(-0.588343\pi\) |
0.969879 | − | 0.243587i | \(-0.0783241\pi\) | |||||||
\(212\) | −3.60139 | + | 13.4406i | −0.247345 | + | 0.923102i | ||||
\(213\) | −17.4493 | −1.19560 | ||||||||
\(214\) | −5.83984 | + | 21.7946i | −0.399203 | + | 1.48985i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 9.55857 | + | 9.55857i | 0.650378 | + | 0.650378i | ||||
\(217\) | −19.6521 | − | 5.26577i | −1.33407 | − | 0.357464i | ||||
\(218\) | 5.17670 | + | 19.3197i | 0.350610 | + | 1.30849i | ||||
\(219\) | 3.84266 | + | 14.3410i | 0.259663 | + | 0.969075i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.6708 | + | 14.9439i | −1.05413 | + | 1.00523i | ||||
\(222\) | 2.26022 | − | 2.26022i | 0.151696 | − | 0.151696i | ||||
\(223\) | 10.1883 | − | 17.6466i | 0.682257 | − | 1.18170i | −0.292033 | − | 0.956408i | \(-0.594332\pi\) |
0.974290 | − | 0.225296i | \(-0.0723349\pi\) | |||||||
\(224\) | 15.4168 | + | 8.90087i | 1.03008 | + | 0.594714i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −24.6053 | + | 24.6053i | −1.63672 | + | 1.63672i | ||||
\(227\) | 5.88999 | − | 3.40059i | 0.390932 | − | 0.225705i | −0.291632 | − | 0.956531i | \(-0.594198\pi\) |
0.682564 | + | 0.730826i | \(0.260865\pi\) | |||||||
\(228\) | 41.5342 | − | 23.9798i | 2.75067 | − | 1.58810i | ||||
\(229\) | 6.74680 | − | 6.74680i | 0.445841 | − | 0.445841i | −0.448128 | − | 0.893969i | \(-0.647909\pi\) |
0.893969 | + | 0.448128i | \(0.147909\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.6226 | + | 10.7518i | 1.22528 | + | 0.707416i | ||||
\(232\) | 1.46293 | − | 2.53387i | 0.0960460 | − | 0.166357i | ||||
\(233\) | 15.0352 | − | 15.0352i | 0.984989 | − | 0.984989i | −0.0148998 | − | 0.999889i | \(-0.504743\pi\) |
0.999889 | + | 0.0148998i | \(0.00474292\pi\) | |||||||
\(234\) | 3.50722 | + | 2.13748i | 0.229274 | + | 0.139731i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.63568 | + | 21.0326i | 0.366852 | + | 1.36911i | ||||
\(237\) | −4.93023 | − | 18.3999i | −0.320253 | − | 1.19520i | ||||
\(238\) | 42.7737 | + | 11.4612i | 2.77260 | + | 0.742917i | ||||
\(239\) | 8.18783 | + | 8.18783i | 0.529627 | + | 0.529627i | 0.920461 | − | 0.390834i | \(-0.127813\pi\) |
−0.390834 | + | 0.920461i | \(0.627813\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.74605 | + | 17.7125i | −0.305720 | + | 1.14096i | 0.626604 | + | 0.779338i | \(0.284444\pi\) |
−0.932324 | + | 0.361624i | \(0.882222\pi\) | |||||||
\(242\) | −4.11028 | −0.264219 | ||||||||
\(243\) | −1.32302 | + | 4.93756i | −0.0848715 | + | 0.316745i | ||||
\(244\) | −3.02619 | + | 5.24152i | −0.193732 | + | 0.335554i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 27.3906i | − | 1.74636i | ||||||
\(247\) | −20.5331 | + | 19.5806i | −1.30649 | + | 1.24588i | ||||
\(248\) | −12.9215 | − | 12.9215i | −0.820518 | − | 0.820518i | ||||
\(249\) | 16.2911 | − | 4.36518i | 1.03241 | − | 0.276632i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.6574 | − | 13.0812i | 1.43012 | − | 0.825681i | 0.432992 | − | 0.901398i | \(-0.357458\pi\) |
0.997129 | + | 0.0757168i | \(0.0241245\pi\) | |||||||
\(252\) | − | 5.20521i | − | 0.327897i | ||||||
\(253\) | −2.05094 | − | 3.55234i | −0.128942 | − | 0.223333i | ||||
\(254\) | −26.8282 | − | 7.18860i | −1.68335 | − | 0.451053i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.33402 | + | 14.4350i | 0.520877 | + | 0.902185i | ||||
\(257\) | −7.98901 | + | 2.14065i | −0.498341 | + | 0.133530i | −0.499230 | − | 0.866470i | \(-0.666384\pi\) |
0.000888947 | 1.00000i | \(0.499717\pi\) | ||||||||
\(258\) | −4.81604 | − | 2.78054i | −0.299833 | − | 0.173109i | ||||
\(259\) | 2.39651 | 0.148912 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.503271 | 0.0311517 | ||||||||
\(262\) | −0.138254 | − | 0.0798211i | −0.00854137 | − | 0.00493136i | ||||
\(263\) | 12.7688 | − | 3.42140i | 0.787360 | − | 0.210972i | 0.157333 | − | 0.987546i | \(-0.449710\pi\) |
0.630027 | + | 0.776573i | \(0.283044\pi\) | |||||||
\(264\) | 9.65703 | + | 16.7265i | 0.594349 | + | 1.02944i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 56.0453 | + | 15.0173i | 3.43636 | + | 0.920770i | ||||
\(267\) | 0.636327 | + | 1.10215i | 0.0389426 | + | 0.0674505i | ||||
\(268\) | 27.2233i | 1.66293i | ||||||||
\(269\) | −4.88179 | + | 2.81850i | −0.297648 | + | 0.171847i | −0.641386 | − | 0.767218i | \(-0.721640\pi\) |
0.343738 | + | 0.939066i | \(0.388307\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.32435 | + | 1.96255i | −0.444922 | + | 0.119217i | −0.474323 | − | 0.880351i | \(-0.657307\pi\) |
0.0294001 | + | 0.999568i | \(0.490640\pi\) | |||||||
\(272\) | 0.442291 | + | 0.442291i | 0.0268178 | + | 0.0268178i | ||||
\(273\) | 5.11189 | + | 21.0661i | 0.309386 | + | 1.27498i | ||||
\(274\) | − | 24.2060i | − | 1.46234i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.49483 | + | 6.05322i | −0.210364 | + | 0.364361i | ||||
\(277\) | −3.01947 | + | 11.2688i | −0.181422 | + | 0.677078i | 0.813946 | + | 0.580941i | \(0.197315\pi\) |
−0.995368 | + | 0.0961367i | \(0.969351\pi\) | |||||||
\(278\) | 21.2354 | 1.27362 | ||||||||
\(279\) | 0.813530 | − | 3.03613i | 0.0487048 | − | 0.181769i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.46111 | − | 9.46111i | −0.564402 | − | 0.564402i | 0.366153 | − | 0.930555i | \(-0.380675\pi\) |
−0.930555 | + | 0.366153i | \(0.880675\pi\) | |||||||
\(282\) | 34.0575 | + | 9.12569i | 2.02810 | + | 0.543427i | ||||
\(283\) | 1.03853 | + | 3.87586i | 0.0617344 | + | 0.230396i | 0.989899 | − | 0.141774i | \(-0.0452806\pi\) |
−0.928165 | + | 0.372170i | \(0.878614\pi\) | |||||||
\(284\) | −7.87152 | − | 29.3769i | −0.467089 | − | 1.74320i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.4095 | − | 21.4024i | −1.20684 | − | 1.26555i | ||||
\(287\) | 14.5211 | − | 14.5211i | 0.857154 | − | 0.857154i | ||||
\(288\) | −1.37513 | + | 2.38180i | −0.0810303 | + | 0.140349i | ||||
\(289\) | −16.5141 | − | 9.53440i | −0.971415 | − | 0.560847i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.9937 | − | 17.9937i | 1.05481 | − | 1.05481i | ||||
\(292\) | −22.4105 | + | 12.9387i | −1.31148 | + | 0.757181i | ||||
\(293\) | −21.3692 | + | 12.3375i | −1.24840 | + | 0.720766i | −0.970791 | − | 0.239927i | \(-0.922877\pi\) |
−0.277613 | + | 0.960693i | \(0.589543\pi\) | |||||||
\(294\) | 10.1201 | − | 10.1201i | 0.590215 | − | 0.590215i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.86411 | + | 1.07625i | 0.108349 | + | 0.0625556i | ||||
\(297\) | 8.37112 | − | 14.4992i | 0.485742 | − | 0.841329i | ||||
\(298\) | −24.1401 | + | 24.1401i | −1.39840 | + | 1.39840i | ||||
\(299\) | 1.16474 | − | 3.96762i | 0.0673589 | − | 0.229453i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.07912 | − | 4.02732i | −0.0621993 | − | 0.232131i | ||||
\(302\) | −8.67793 | − | 32.3865i | −0.499359 | − | 1.86363i | ||||
\(303\) | 16.2434 | + | 4.35240i | 0.933159 | + | 0.250039i | ||||
\(304\) | 0.579523 | + | 0.579523i | 0.0332379 | + | 0.0332379i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.77068 | + | 6.60827i | −0.101223 | + | 0.377770i | ||||
\(307\) | 7.41296 | 0.423080 | 0.211540 | − | 0.977369i | \(-0.432152\pi\) | ||||
0.211540 | + | 0.977369i | \(0.432152\pi\) | |||||||
\(308\) | −9.70045 | + | 36.2026i | −0.552734 | + | 2.06283i | ||||
\(309\) | −2.29770 | + | 3.97974i | −0.130712 | + | 0.226399i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.67111i | 0.0947601i | 0.998877 | + | 0.0473800i | \(0.0150872\pi\) | ||||
−0.998877 | + | 0.0473800i | \(0.984913\pi\) | |||||||
\(312\) | −5.48430 | + | 18.6819i | −0.310487 | + | 1.05765i | ||||
\(313\) | 15.8540 | + | 15.8540i | 0.896123 | + | 0.896123i | 0.995091 | − | 0.0989679i | \(-0.0315541\pi\) |
−0.0989679 | + | 0.995091i | \(0.531554\pi\) | |||||||
\(314\) | 49.8776 | − | 13.3647i | 2.81476 | − | 0.754212i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 28.7532 | − | 16.6007i | 1.61750 | − | 0.933862i | ||||
\(317\) | 1.50512i | 0.0845357i | 0.999106 | + | 0.0422679i | \(0.0134583\pi\) | ||||
−0.999106 | + | 0.0422679i | \(0.986542\pi\) | |||||||
\(318\) | −9.15420 | − | 15.8555i | −0.513342 | − | 0.889134i | ||||
\(319\) | −3.50028 | − | 0.937897i | −0.195978 | − | 0.0525122i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.19907 | − | 15.9333i | −0.513442 | − | 0.889308i | ||||
\(322\) | −8.16807 | + | 2.18863i | −0.455189 | + | 0.121968i | ||||
\(323\) | −40.9285 | − | 23.6301i | −2.27732 | − | 1.31481i | ||||
\(324\) | −33.3858 | −1.85477 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −19.9455 | −1.10468 | ||||||||
\(327\) | −14.1240 | − | 8.15447i | −0.781057 | − | 0.450943i | ||||
\(328\) | 17.8165 | − | 4.77391i | 0.983750 | − | 0.263595i | ||||
\(329\) | 13.2176 | + | 22.8936i | 0.728710 | + | 1.26216i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.29629 | + | 0.615289i | 0.126215 | + | 0.0338193i | 0.321374 | − | 0.946952i | \(-0.395855\pi\) |
−0.195158 | + | 0.980772i | \(0.562522\pi\) | |||||||
\(332\) | 14.6981 | + | 25.4579i | 0.806663 | + | 1.39718i | ||||
\(333\) | 0.370246i | 0.0202894i | ||||||||
\(334\) | 6.63834 | − | 3.83265i | 0.363234 | − | 0.209713i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.604835 | − | 0.162065i | 0.0329965 | − | 0.00884137i | ||||
\(337\) | 3.02028 | + | 3.02028i | 0.164525 | + | 0.164525i | 0.784568 | − | 0.620043i | \(-0.212885\pi\) |
−0.620043 | + | 0.784568i | \(0.712885\pi\) | |||||||
\(338\) | 1.41506 | − | 29.7793i | 0.0769689 | − | 1.61978i | ||||
\(339\) | − | 28.3735i | − | 1.54104i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.3163 | + | 19.6004i | −0.612812 | + | 1.06142i | ||||
\(342\) | −2.32008 | + | 8.65867i | −0.125456 | + | 0.468207i | ||||
\(343\) | −11.7760 | −0.635842 | ||||||||
\(344\) | 0.969242 | − | 3.61726i | 0.0522580 | − | 0.195030i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.82541 | + | 7.82541i | 0.420697 | + | 0.420697i | ||||
\(347\) | −3.55664 | − | 0.952998i | −0.190930 | − | 0.0511596i | 0.162087 | − | 0.986777i | \(-0.448178\pi\) |
−0.353017 | + | 0.935617i | \(0.614844\pi\) | |||||||
\(348\) | 1.59819 | + | 5.96452i | 0.0856718 | + | 0.319732i | ||||
\(349\) | 2.60923 | + | 9.73777i | 0.139669 | + | 0.521251i | 0.999935 | + | 0.0114057i | \(0.00363061\pi\) |
−0.860266 | + | 0.509845i | \(0.829703\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.4016 | − | 3.98001i | 0.875454 | − | 0.212437i | ||||
\(352\) | 14.0028 | − | 14.0028i | 0.746354 | − | 0.746354i | ||||
\(353\) | −13.5575 | + | 23.4823i | −0.721593 | + | 1.24984i | 0.238768 | + | 0.971077i | \(0.423257\pi\) |
−0.960361 | + | 0.278759i | \(0.910077\pi\) | |||||||
\(354\) | −24.8117 | − | 14.3251i | −1.31873 | − | 0.761368i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.56849 | + | 1.56849i | −0.0831296 | + | 0.0831296i | ||||
\(357\) | −31.2703 | + | 18.0539i | −1.65500 | + | 0.955516i | ||||
\(358\) | −6.27226 | + | 3.62129i | −0.331499 | + | 0.191391i | ||||
\(359\) | −0.894231 | + | 0.894231i | −0.0471957 | + | 0.0471957i | −0.730311 | − | 0.683115i | \(-0.760625\pi\) |
0.683115 | + | 0.730311i | \(0.260625\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −37.1731 | − | 21.4619i | −1.95648 | − | 1.12957i | ||||
\(362\) | 2.07155 | − | 3.58804i | 0.108879 | − | 0.188583i | ||||
\(363\) | 2.36988 | − | 2.36988i | 0.124386 | − | 0.124386i | ||||
\(364\) | −33.1600 | + | 18.1093i | −1.73806 | + | 0.949184i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.06110 | − | 7.69212i | −0.107735 | − | 0.402074i | ||||
\(367\) | −3.36959 | − | 12.5755i | −0.175891 | − | 0.656436i | −0.996398 | − | 0.0847988i | \(-0.972975\pi\) |
0.820507 | − | 0.571637i | \(-0.193691\pi\) | |||||||
\(368\) | −0.115374 | − | 0.0309145i | −0.00601431 | − | 0.00161153i | ||||
\(369\) | 2.24342 | + | 2.24342i | 0.116788 | + | 0.116788i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.55271 | − | 13.2589i | 0.184448 | − | 0.688368i | ||||
\(372\) | 38.5662 | 1.99957 | ||||||||
\(373\) | −2.71659 | + | 10.1385i | −0.140660 | + | 0.524950i | 0.859250 | + | 0.511555i | \(0.170930\pi\) |
−0.999910 | + | 0.0133946i | \(0.995736\pi\) | |||||||
\(374\) | 24.6304 | − | 42.6611i | 1.27361 | − | 2.20595i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 23.7436i | 1.22448i | ||||||||
\(377\) | −1.75091 | − | 3.20611i | −0.0901766 | − | 0.165123i | ||||
\(378\) | −24.4057 | − | 24.4057i | −1.25529 | − | 1.25529i | ||||
\(379\) | 9.74593 | − | 2.61141i | 0.500615 | − | 0.134139i | 0.000329419 | − | 1.00000i | \(-0.499895\pi\) |
0.500285 | + | 0.865861i | \(0.333228\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.6132 | − | 11.3237i | 1.00481 | − | 0.580130i | ||||
\(382\) | 50.5293i | 2.58531i | ||||||||
\(383\) | 5.37726 | + | 9.31368i | 0.274765 | + | 0.475907i | 0.970076 | − | 0.242802i | \(-0.0780666\pi\) |
−0.695311 | + | 0.718709i | \(0.744733\pi\) | |||||||
\(384\) | −33.4575 | − | 8.96492i | −1.70737 | − | 0.457489i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 19.0862 | + | 33.0582i | 0.971460 | + | 1.68262i | ||||
\(387\) | 0.622197 | − | 0.166717i | 0.0316281 | − | 0.00847471i | ||||
\(388\) | 38.4105 | + | 22.1763i | 1.95000 | + | 1.12583i | ||||
\(389\) | −34.9585 | −1.77247 | −0.886234 | − | 0.463238i | \(-0.846687\pi\) | ||||
−0.886234 | + | 0.463238i | \(0.846687\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.88771 | 0.348326 | ||||||||
\(392\) | 8.34654 | + | 4.81888i | 0.421564 | + | 0.243390i | ||||
\(393\) | 0.125736 | − | 0.0336910i | 0.00634256 | − | 0.00169948i | ||||
\(394\) | 3.22443 | + | 5.58487i | 0.162444 | + | 0.281362i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.59308 | − | 1.49866i | −0.281063 | − | 0.0753105i | ||||
\(397\) | 3.05319 | + | 5.28828i | 0.153235 | + | 0.265411i | 0.932415 | − | 0.361389i | \(-0.117697\pi\) |
−0.779180 | + | 0.626801i | \(0.784364\pi\) | |||||||
\(398\) | 42.5612i | 2.13340i | ||||||||
\(399\) | −40.9728 | + | 23.6557i | −2.05121 | + | 1.18426i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.267716 | − | 0.0717343i | 0.0133691 | − | 0.00358224i | −0.252128 | − | 0.967694i | \(-0.581130\pi\) |
0.265497 | + | 0.964112i | \(0.414464\pi\) | |||||||
\(402\) | −25.3281 | − | 25.3281i | −1.26325 | − | 1.26325i | ||||
\(403\) | −22.1722 | + | 5.38029i | −1.10447 | + | 0.268011i | ||||
\(404\) | 29.3102i | 1.45823i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.73527 | + | 6.46967i | −0.185378 | + | 0.321084i | ||||
\(407\) | 0.689992 | − | 2.57508i | 0.0342016 | − | 0.127642i | ||||
\(408\) | −32.4314 | −1.60559 | ||||||||
\(409\) | −3.90517 | + | 14.5743i | −0.193098 | + | 0.720653i | 0.799653 | + | 0.600463i | \(0.205017\pi\) |
−0.992751 | + | 0.120190i | \(0.961650\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.9565 | + | 13.9565i | 0.688425 | + | 0.688425i | ||||
\(412\) | −7.73665 | − | 2.07303i | −0.381157 | − | 0.102131i | ||||
\(413\) | −5.55950 | − | 20.7483i | −0.273565 | − | 1.02096i | ||||
\(414\) | −0.338130 | − | 1.26192i | −0.0166182 | − | 0.0620199i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 19.9575 | + | 0.473904i | 0.978497 | + | 0.0232350i | ||||
\(417\) | −12.2438 | + | 12.2438i | −0.599580 | + | 0.599580i | ||||
\(418\) | 32.2726 | − | 55.8979i | 1.57851 | − | 2.73405i | ||||
\(419\) | 7.65847 | + | 4.42162i | 0.374141 | + | 0.216010i | 0.675266 | − | 0.737574i | \(-0.264029\pi\) |
−0.301125 | + | 0.953585i | \(0.597362\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.58165 | − | 6.58165i | 0.320770 | − | 0.320770i | −0.528292 | − | 0.849062i | \(-0.677168\pi\) |
0.849062 | + | 0.528292i | \(0.177168\pi\) | |||||||
\(422\) | −40.1518 | + | 23.1816i | −1.95456 | + | 1.12847i | ||||
\(423\) | −3.53692 | + | 2.04204i | −0.171971 | + | 0.0992873i | ||||
\(424\) | 8.71790 | − | 8.71790i | 0.423379 | − | 0.423379i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 34.6553 | + | 20.0082i | 1.67905 | + | 0.969402i | ||||
\(427\) | 2.98529 | − | 5.17067i | 0.144468 | − | 0.250226i | ||||
\(428\) | 22.6748 | − | 22.6748i | 1.09603 | − | 1.09603i | ||||
\(429\) | 24.1076 | + | 0.572451i | 1.16393 | + | 0.0276382i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.88510 | + | 7.03529i | 0.0908021 | + | 0.338878i | 0.996350 | − | 0.0853669i | \(-0.0272062\pi\) |
−0.905547 | + | 0.424245i | \(0.860540\pi\) | |||||||
\(432\) | −0.126180 | − | 0.470912i | −0.00607086 | − | 0.0226568i | ||||
\(433\) | 10.5986 | + | 2.83990i | 0.509338 | + | 0.136477i | 0.504330 | − | 0.863511i | \(-0.331739\pi\) |
0.00500749 | + | 0.999987i | \(0.498406\pi\) | |||||||
\(434\) | 32.9923 | + | 32.9923i | 1.58368 | + | 1.58368i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.35711 | − | 27.4571i | 0.352342 | − | 1.31496i | ||||
\(437\) | 9.02481 | 0.431715 | ||||||||
\(438\) | 8.81238 | − | 32.8883i | 0.421072 | − | 1.57146i | ||||
\(439\) | 5.86048 | − | 10.1506i | 0.279705 | − | 0.484464i | −0.691606 | − | 0.722275i | \(-0.743097\pi\) |
0.971311 | + | 0.237811i | \(0.0764299\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.65777i | 0.0789414i | ||||||||
\(442\) | 48.2586 | − | 11.7104i | 2.29543 | − | 0.557007i | ||||
\(443\) | 19.3277 | + | 19.3277i | 0.918288 | + | 0.918288i | 0.996905 | − | 0.0786170i | \(-0.0250504\pi\) |
−0.0786170 | + | 0.996905i | \(0.525050\pi\) | |||||||
\(444\) | −4.38797 | + | 1.17575i | −0.208244 | + | 0.0557988i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −40.4690 | + | 23.3648i | −1.91626 | + | 1.10635i | ||||
\(447\) | − | 27.8370i | − | 1.31665i | ||||||
\(448\) | −20.7472 | − | 35.9353i | −0.980215 | − | 1.69778i | ||||
\(449\) | 19.9671 | + | 5.35017i | 0.942306 | + | 0.252490i | 0.697094 | − | 0.716979i | \(-0.254476\pi\) |
0.245212 | + | 0.969470i | \(0.421142\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.4223 | − | 19.7840i | −0.537855 | − | 0.931592i | ||||
\(452\) | 47.7685 | − | 12.7995i | 2.24684 | − | 0.602039i | ||||
\(453\) | 23.6766 | + | 13.6697i | 1.11243 | + | 0.642259i | ||||
\(454\) | −15.5972 | −0.732011 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −42.4941 | −1.98997 | ||||||||
\(457\) | −2.21747 | − | 1.28025i | −0.103729 | − | 0.0598878i | 0.447238 | − | 0.894415i | \(-0.352408\pi\) |
−0.550967 | + | 0.834527i | \(0.685741\pi\) | |||||||
\(458\) | −21.1358 | + | 5.66331i | −0.987610 | + | 0.264629i | ||||
\(459\) | 14.0564 | + | 24.3464i | 0.656098 | + | 1.13639i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.77044 | − | 2.61798i | −0.455055 | − | 0.121932i | 0.0240087 | − | 0.999712i | \(-0.492357\pi\) |
−0.479064 | + | 0.877780i | \(0.659024\pi\) | |||||||
\(462\) | −24.6571 | − | 42.7073i | −1.14715 | − | 1.98693i | ||||
\(463\) | − | 12.2556i | − | 0.569565i | −0.958592 | − | 0.284782i | \(-0.908079\pi\) | ||
0.958592 | − | 0.284782i | \(-0.0919213\pi\) | |||||||
\(464\) | −0.0913844 | + | 0.0527608i | −0.00424242 | + | 0.00244936i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −47.1009 | + | 12.6207i | −2.18191 | + | 0.584641i | ||||
\(467\) | 16.2946 | + | 16.2946i | 0.754023 | + | 0.754023i | 0.975227 | − | 0.221205i | \(-0.0709988\pi\) |
−0.221205 | + | 0.975227i | \(0.570999\pi\) | |||||||
\(468\) | −2.79777 | − | 5.12302i | −0.129327 | − | 0.236812i | ||||
\(469\) | − | 26.8553i | − | 1.24006i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.0524 | + | 36.4638i | −0.970043 | + | 1.68016i | ||||
\(472\) | 4.99343 | − | 18.6357i | 0.229841 | − | 0.857780i | ||||
\(473\) | −4.63811 | −0.213261 | ||||||||
\(474\) | −11.3065 | + | 42.1965i | −0.519325 | + | 1.93815i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −44.5012 | − | 44.5012i | −2.03971 | − | 2.03971i | ||||
\(477\) | 2.04842 | + | 0.548872i | 0.0937907 | + | 0.0251311i | ||||
\(478\) | −6.87292 | − | 25.6501i | −0.314360 | − | 1.17321i | ||||
\(479\) | −3.58854 | − | 13.3926i | −0.163965 | − | 0.611924i | −0.998170 | − | 0.0604705i | \(-0.980740\pi\) |
0.834205 | − | 0.551454i | \(-0.185927\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.35867 | − | 1.28811i | 0.107546 | − | 0.0587328i | ||||
\(482\) | 29.7360 | − | 29.7360i | 1.35444 | − | 1.35444i | ||||
\(483\) | 3.44759 | − | 5.97140i | 0.156871 | − | 0.271708i | ||||
\(484\) | 5.05891 | + | 2.92076i | 0.229950 | + | 0.132762i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.28925 | − | 8.28925i | 0.376008 | − | 0.376008i | ||||
\(487\) | −7.14590 | + | 4.12568i | −0.323811 | + | 0.186953i | −0.653090 | − | 0.757280i | \(-0.726528\pi\) |
0.329279 | + | 0.944233i | \(0.393194\pi\) | |||||||
\(488\) | 4.64419 | − | 2.68132i | 0.210232 | − | 0.121378i | ||||
\(489\) | 11.5001 | − | 11.5001i | 0.520051 | − | 0.520051i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.4891 | − | 18.7576i | −1.46621 | − | 0.846519i | −0.466928 | − | 0.884295i | \(-0.654639\pi\) |
−0.999286 | + | 0.0377764i | \(0.987973\pi\) | |||||||
\(492\) | −19.4637 | + | 33.7122i | −0.877492 | + | 1.51986i | ||||
\(493\) | 4.30265 | − | 4.30265i | 0.193781 | − | 0.193781i | ||||
\(494\) | 63.2321 | − | 15.3439i | 2.84495 | − | 0.690354i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.170574 | + | 0.636592i | 0.00765901 | + | 0.0285838i | ||||
\(497\) | 7.76512 | + | 28.9798i | 0.348313 | + | 1.29992i | ||||
\(498\) | −37.3604 | − | 10.0107i | −1.67416 | − | 0.448590i | ||||
\(499\) | 26.3014 | + | 26.3014i | 1.17741 | + | 1.17741i | 0.980401 | + | 0.197011i | \(0.0631235\pi\) |
0.197011 | + | 0.980401i | \(0.436876\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.61769 | + | 6.03729i | −0.0722730 | + | 0.269726i | ||||
\(502\) | −59.9985 | −2.67786 | ||||||||
\(503\) | 8.81098 | − | 32.8830i | 0.392862 | − | 1.46618i | −0.432528 | − | 0.901620i | \(-0.642378\pi\) |
0.825391 | − | 0.564562i | \(-0.190955\pi\) | |||||||
\(504\) | −2.30601 | + | 3.99413i | −0.102718 | + | 0.177912i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.40686i | 0.418186i | ||||||||
\(507\) | 16.3541 | + | 17.9858i | 0.726310 | + | 0.798780i | ||||
\(508\) | 27.9118 | + | 27.9118i | 1.23839 | + | 1.23839i | ||||
\(509\) | −33.8235 | + | 9.06297i | −1.49920 | + | 0.401709i | −0.912831 | − | 0.408337i | \(-0.866109\pi\) |
−0.586367 | + | 0.810046i | \(0.699442\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.1076 | − | 12.7638i | 0.977982 | − | 0.564638i | ||||
\(512\) | − | 1.17818i | − | 0.0520687i | ||||||
\(513\) | 18.4178 | + | 31.9006i | 0.813166 | + | 1.40845i | ||||
\(514\) | 18.3212 | + | 4.90916i | 0.808115 | + | 0.216534i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.95170 | + | 6.84454i | 0.173964 | + | 0.301314i | ||||
\(517\) | 28.4050 | − | 7.61110i | 1.24925 | − | 0.334736i | ||||
\(518\) | −4.75960 | − | 2.74796i | −0.209125 | − | 0.120738i | ||||
\(519\) | −9.02384 | −0.396103 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.65467 | 0.335357 | 0.167679 | − | 0.985842i | \(-0.446373\pi\) | ||||
0.167679 | + | 0.985842i | \(0.446373\pi\) | |||||||
\(522\) | −0.999525 | − | 0.577076i | −0.0437480 | − | 0.0252579i | ||||
\(523\) | 20.3577 | − | 5.45483i | 0.890180 | − | 0.238523i | 0.215386 | − | 0.976529i | \(-0.430899\pi\) |
0.674794 | + | 0.738006i | \(0.264232\pi\) | |||||||
\(524\) | 0.113442 | + | 0.196487i | 0.00495572 | + | 0.00858356i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −29.2828 | − | 7.84630i | −1.27679 | − | 0.342115i | ||||
\(527\) | −19.0019 | − | 32.9122i | −0.827734 | − | 1.43368i | ||||
\(528\) | − | 0.696565i | − | 0.0303141i | ||||||
\(529\) | 18.7795 | − | 10.8424i | 0.816501 | − | 0.471407i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.20549 | − | 0.858910i | 0.139107 | − | 0.0372735i | ||||
\(532\) | −58.3090 | − | 58.3090i | −2.52801 | − | 2.52801i | ||||
\(533\) | 6.48681 | − | 22.0968i | 0.280975 | − | 0.957120i | ||||
\(534\) | − | 2.91858i | − | 0.126299i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.0605 | − | 20.8893i | 0.520932 | − | 0.902281i | ||||
\(537\) | 1.52848 | − | 5.70436i | 0.0659587 | − | 0.246161i | ||||
\(538\) | 12.9274 | 0.557338 | ||||||||
\(539\) | 3.08942 | − | 11.5299i | 0.133071 | − | 0.496628i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.4272 | + | 15.4272i | 0.663267 | + | 0.663267i | 0.956149 | − | 0.292882i | \(-0.0946142\pi\) |
−0.292882 | + | 0.956149i | \(0.594614\pi\) | |||||||
\(542\) | 16.7969 | + | 4.50073i | 0.721491 | + | 0.193323i | ||||
\(543\) | 0.874364 | + | 3.26317i | 0.0375225 | + | 0.140036i | ||||
\(544\) | 8.60635 | + | 32.1193i | 0.368994 | + | 1.37710i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 14.0029 | − | 47.7000i | 0.599271 | − | 2.04137i | ||||
\(547\) | −5.79215 | + | 5.79215i | −0.247654 | + | 0.247654i | −0.820007 | − | 0.572353i | \(-0.806031\pi\) |
0.572353 | + | 0.820007i | \(0.306031\pi\) | |||||||
\(548\) | −17.2008 | + | 29.7926i | −0.734780 | + | 1.27268i | ||||
\(549\) | 0.798837 | + | 0.461209i | 0.0340935 | + | 0.0196839i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.63766 | − | 5.63766i | 0.240172 | − | 0.240172i | ||||
\(552\) | 5.36339 | − | 3.09655i | 0.228281 | − | 0.131798i | ||||
\(553\) | −28.3646 | + | 16.3763i | −1.20618 | + | 0.696391i | ||||
\(554\) | 18.9182 | − | 18.9182i | 0.803759 | − | 0.803759i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −26.1364 | − | 15.0899i | −1.10843 | − | 0.639953i | ||||
\(557\) | 11.5174 | − | 19.9488i | 0.488009 | − | 0.845256i | −0.511896 | − | 0.859047i | \(-0.671057\pi\) |
0.999905 | + | 0.0137912i | \(0.00439001\pi\) | |||||||
\(558\) | −5.09711 | + | 5.09711i | −0.215778 | + | 0.215778i | ||||
\(559\) | −3.22674 | − | 3.38371i | −0.136477 | − | 0.143116i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.3960 | + | 38.7985i | 0.438920 | + | 1.63807i | ||||
\(562\) | 7.94172 | + | 29.6389i | 0.335001 | + | 1.25024i | ||||
\(563\) | −5.85629 | − | 1.56919i | −0.246813 | − | 0.0661334i | 0.133291 | − | 0.991077i | \(-0.457445\pi\) |
−0.380105 | + | 0.924943i | \(0.624112\pi\) | |||||||
\(564\) | −35.4331 | − | 35.4331i | −1.49200 | − | 1.49200i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.38167 | − | 8.88851i | 0.100109 | − | 0.373612i | ||||
\(567\) | 32.9345 | 1.38312 | ||||||||
\(568\) | −6.97447 | + | 26.0291i | −0.292642 | + | 1.09216i | ||||
\(569\) | −11.2211 | + | 19.4355i | −0.470413 | + | 0.814779i | −0.999427 | − | 0.0338340i | \(-0.989228\pi\) |
0.529015 | + | 0.848613i | \(0.322562\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.7374i | 1.74665i | 0.487135 | + | 0.873327i | \(0.338042\pi\) | ||||
−0.487135 | + | 0.873327i | \(0.661958\pi\) | |||||||
\(572\) | 9.91140 | + | 40.8449i | 0.414417 | + | 1.70781i | ||||
\(573\) | −29.1339 | − | 29.1339i | −1.21708 | − | 1.21708i | ||||
\(574\) | −45.4904 | + | 12.1891i | −1.89873 | + | 0.508764i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.55178 | − | 3.20532i | 0.231324 | − | 0.133555i | ||||
\(577\) | − | 10.4937i | − | 0.436859i | −0.975853 | − | 0.218429i | \(-0.929907\pi\) | ||
0.975853 | − | 0.218429i | \(-0.0700933\pi\) | |||||||
\(578\) | 21.8653 | + | 37.8717i | 0.909475 | + | 1.57526i | ||||
\(579\) | −30.0650 | − | 8.05590i | −1.24946 | − | 0.334792i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.4994 | − | 25.1138i | −0.601538 | − | 1.04189i | ||||
\(582\) | −56.3689 | + | 15.1040i | −2.33657 | + | 0.626081i | ||||
\(583\) | −13.2240 | − | 7.63488i | −0.547682 | − | 0.316205i | ||||
\(584\) | 22.9284 | 0.948784 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 56.5874 | 2.33760 | ||||||||
\(587\) | 40.6217 | + | 23.4529i | 1.67664 | + | 0.968006i | 0.963782 | + | 0.266693i | \(0.0859308\pi\) |
0.712853 | + | 0.701313i | \(0.247402\pi\) | |||||||
\(588\) | −19.6471 | + | 5.26441i | −0.810231 | + | 0.217101i | ||||
\(589\) | −24.8977 | − | 43.1241i | −1.02589 | − | 1.77690i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.07921 | − | 1.36097i | −0.208931 | − | 0.0559828i | ||||
\(592\) | −0.0388150 | − | 0.0672296i | −0.00159529 | − | 0.00276312i | ||||
\(593\) | − | 24.0105i | − | 0.985994i | −0.870031 | − | 0.492997i | \(-0.835901\pi\) | ||
0.870031 | − | 0.492997i | \(-0.164099\pi\) | |||||||
\(594\) | −33.2511 | + | 19.1975i | −1.36431 | + | 0.787683i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 46.8653 | − | 12.5575i | 1.91968 | − | 0.514377i | ||||
\(597\) | −24.5396 | − | 24.5396i | −1.00434 | − | 1.00434i | ||||
\(598\) | −6.86273 | + | 6.54437i | −0.280638 | + | 0.267619i | ||||
\(599\) | − | 2.24349i | − | 0.0916664i | −0.998949 | − | 0.0458332i | \(-0.985406\pi\) | ||
0.998949 | − | 0.0458332i | \(-0.0145943\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.5199 | + | 33.8095i | −0.796234 | + | 1.37912i | 0.125818 | + | 0.992053i | \(0.459845\pi\) |
−0.922052 | + | 0.387065i | \(0.873489\pi\) | |||||||
\(602\) | −2.47474 | + | 9.23587i | −0.100863 | + | 0.376426i | ||||
\(603\) | 4.14899 | 0.168960 | ||||||||
\(604\) | −12.3331 | + | 46.0276i | −0.501825 | + | 1.87284i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −27.2696 | − | 27.2696i | −1.10775 | − | 1.10775i | ||||
\(607\) | −21.7504 | − | 5.82801i | −0.882823 | − | 0.236552i | −0.211198 | − | 0.977443i | \(-0.567737\pi\) |
−0.671625 | + | 0.740892i | \(0.734403\pi\) | |||||||
\(608\) | 11.2767 | + | 42.0852i | 0.457331 | + | 1.70678i | ||||
\(609\) | −1.57658 | − | 5.88389i | −0.0638864 | − | 0.238427i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.3141 | + | 15.4277i | 1.02410 | + | 0.624137i | ||||
\(612\) | 6.87517 | − | 6.87517i | 0.277912 | − | 0.277912i | ||||
\(613\) | 1.61960 | − | 2.80523i | 0.0654151 | − | 0.113302i | −0.831463 | − | 0.555580i | \(-0.812496\pi\) |
0.896878 | + | 0.442278i | \(0.145830\pi\) | |||||||
\(614\) | −14.7226 | − | 8.50008i | −0.594154 | − | 0.343035i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 23.4819 | − | 23.4819i | 0.946113 | − | 0.946113i | ||||
\(617\) | −30.1380 | + | 17.4002i | −1.21331 | + | 0.700504i | −0.963478 | − | 0.267786i | \(-0.913708\pi\) |
−0.249830 | + | 0.968290i | \(0.580375\pi\) | |||||||
\(618\) | 9.12674 | − | 5.26933i | 0.367131 | − | 0.211963i | ||||
\(619\) | 5.38094 | − | 5.38094i | 0.216278 | − | 0.216278i | −0.590650 | − | 0.806928i | \(-0.701129\pi\) |
0.806928 | + | 0.590650i | \(0.201129\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.64921 | − | 2.68422i | −0.186566 | − | 0.107714i | ||||
\(622\) | 1.91618 | − | 3.31893i | 0.0768319 | − | 0.133077i | ||||
\(623\) | 1.54728 | − | 1.54728i | 0.0619906 | − | 0.0619906i | ||||
\(624\) | 0.508176 | − | 0.484602i | 0.0203433 | − | 0.0193996i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −13.3080 | − | 49.6661i | −0.531894 | − | 1.98506i | ||||
\(627\) | 13.6217 | + | 50.8368i | 0.543997 | + | 2.03022i | ||||
\(628\) | −70.8859 | − | 18.9938i | −2.82866 | − | 0.757936i | ||||
\(629\) | 3.16537 | + | 3.16537i | 0.126211 | + | 0.126211i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.4197 | + | 38.8868i | −0.414801 | + | 1.54806i | 0.370433 | + | 0.928859i | \(0.379209\pi\) |
−0.785234 | + | 0.619199i | \(0.787457\pi\) | |||||||
\(632\) | −29.4177 | −1.17017 | ||||||||
\(633\) | 9.78453 | − | 36.5164i | 0.388900 | − | 1.45140i | ||||
\(634\) | 1.72584 | − | 2.98925i | 0.0685420 | − | 0.118718i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 26.0198i | 1.03175i | ||||||||
\(637\) | 10.5609 | − | 5.76749i | 0.418438 | − | 0.228516i | ||||
\(638\) | 5.87632 | + | 5.87632i | 0.232646 | + | 0.232646i | ||||
\(639\) | −4.47721 | + | 1.19966i | −0.177116 | + | 0.0474580i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.1015 | + | 17.9565i | −1.22844 | + | 0.709239i | −0.966703 | − | 0.255901i | \(-0.917628\pi\) |
−0.261734 | + | 0.965140i | \(0.584294\pi\) | |||||||
\(642\) | 42.1925i | 1.66521i | ||||||||
\(643\) | 3.02845 | + | 5.24544i | 0.119431 | + | 0.206860i | 0.919542 | − | 0.392991i | \(-0.128560\pi\) |
−0.800112 | + | 0.599851i | \(0.795226\pi\) | |||||||
\(644\) | 11.6084 | + | 3.11047i | 0.457437 | + | 0.122570i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 54.1909 | + | 93.8613i | 2.13211 | + | 3.69292i | ||||
\(647\) | −19.0229 | + | 5.09717i | −0.747867 | + | 0.200390i | −0.612572 | − | 0.790415i | \(-0.709865\pi\) |
−0.135295 | + | 0.990805i | \(0.543198\pi\) | |||||||
\(648\) | 25.6180 | + | 14.7906i | 1.00637 | + | 0.581028i | ||||
\(649\) | −23.8951 | −0.937964 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −38.0449 | −1.49110 | ||||||||
\(652\) | 24.5488 | + | 14.1733i | 0.961406 | + | 0.555068i | ||||
\(653\) | 12.9452 | − | 3.46867i | 0.506587 | − | 0.135739i | 0.00353138 | − | 0.999994i | \(-0.498876\pi\) |
0.503055 | + | 0.864254i | \(0.332209\pi\) | |||||||
\(654\) | 18.7007 | + | 32.3905i | 0.731254 | + | 1.26657i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.642554 | − | 0.172172i | −0.0250875 | − | 0.00672218i | ||||
\(657\) | 1.97193 | + | 3.41549i | 0.0769324 | + | 0.133251i | ||||
\(658\) | − | 60.6239i | − | 2.36337i | ||||||
\(659\) | 12.2454 | − | 7.06989i | 0.477013 | − | 0.275404i | −0.242158 | − | 0.970237i | \(-0.577855\pi\) |
0.719171 | + | 0.694833i | \(0.244522\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.7807 | − | 11.7310i | 1.70287 | − | 0.456283i | 0.729213 | − | 0.684287i | \(-0.239886\pi\) |
0.973660 | + | 0.228004i | \(0.0732198\pi\) | |||||||
\(662\) | −3.85504 | − | 3.85504i | −0.149830 | − | 0.149830i | ||||
\(663\) | −21.0727 | + | 34.5765i | −0.818396 | + | 1.34284i | ||||
\(664\) | − | 26.0462i | − | 1.01079i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.424543 | − | 0.735330i | 0.0164507 | − | 0.0284935i | ||||
\(667\) | −0.300739 | + | 1.12237i | −0.0116447 | + | 0.0434585i | ||||
\(668\) | −10.8939 | −0.421498 | ||||||||
\(669\) | 9.86183 | − | 36.8049i | 0.381280 | − | 1.42296i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.69645 | − | 4.69645i | −0.181304 | − | 0.181304i | ||||
\(672\) | 32.1541 | + | 8.61568i | 1.24037 | + | 0.332357i | ||||
\(673\) | 5.90434 | + | 22.0353i | 0.227596 | + | 0.849399i | 0.981348 | + | 0.192240i | \(0.0615752\pi\) |
−0.753752 | + | 0.657159i | \(0.771758\pi\) | |||||||
\(674\) | −2.53524 | − | 9.46165i | −0.0976539 | − | 0.364449i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.9028 | + | 35.6467i | −0.880877 | + | 1.37103i | ||||
\(677\) | 21.3802 | − | 21.3802i | 0.821709 | − | 0.821709i | −0.164644 | − | 0.986353i | \(-0.552647\pi\) |
0.986353 | + | 0.164644i | \(0.0526474\pi\) | |||||||
\(678\) | −32.5345 | + | 56.3514i | −1.24948 | + | 2.16416i | ||||
\(679\) | −37.8913 | − | 21.8766i | −1.45414 | − | 0.839545i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.99290 | − | 8.99290i | 0.344609 | − | 0.344609i | ||||
\(682\) | 44.9497 | − | 25.9517i | 1.72121 | − | 0.993742i | ||||
\(683\) | 34.0351 | − | 19.6502i | 1.30232 | − | 0.751894i | 0.321517 | − | 0.946904i | \(-0.395807\pi\) |
0.980801 | + | 0.195010i | \(0.0624740\pi\) | |||||||
\(684\) | 9.00838 | − | 9.00838i | 0.344444 | − | 0.344444i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 23.3877 | + | 13.5029i | 0.892948 | + | 0.515543i | ||||
\(687\) | 8.92101 | − | 15.4516i | 0.340358 | − | 0.589517i | ||||
\(688\) | −0.0955012 | + | 0.0955012i | −0.00364095 | + | 0.00364095i | ||||
\(689\) | −3.62997 | − | 14.9591i | −0.138291 | − | 0.569897i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.4916 | − | 39.1552i | −0.399119 | − | 1.48953i | −0.814650 | − | 0.579953i | \(-0.803071\pi\) |
0.415531 | − | 0.909579i | \(-0.363596\pi\) | |||||||
\(692\) | −4.07073 | − | 15.1922i | −0.154746 | − | 0.577520i | ||||
\(693\) | 5.51748 | + | 1.47840i | 0.209592 | + | 0.0561599i | ||||
\(694\) | 5.97093 | + | 5.97093i | 0.226653 | + | 0.226653i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.41606 | − | 5.28479i | 0.0536755 | − | 0.200320i | ||||
\(697\) | 38.3597 | 1.45298 | ||||||||
\(698\) | 5.98375 | − | 22.3316i | 0.226488 | − | 0.845265i | ||||
\(699\) | 19.8804 | − | 34.4339i | 0.751946 | − | 1.30241i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 34.8480i | − | 1.31619i | −0.752935 | − | 0.658094i | \(-0.771363\pi\) | ||
0.752935 | − | 0.658094i | \(-0.228637\pi\) | |||||||
\(702\) | −37.1383 | − | 10.9024i | −1.40169 | − | 0.411485i | ||||
\(703\) | 4.14751 | + | 4.14751i | 0.156426 | + | 0.156426i | ||||
\(704\) | −44.5865 | + | 11.9469i | −1.68042 | + | 0.450266i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 53.8520 | − | 31.0915i | 2.02675 | − | 1.17014i | ||||
\(707\) | − | 28.9140i | − | 1.08742i | ||||||
\(708\) | 20.3587 | + | 35.2624i | 0.765128 | + | 1.32524i | ||||
\(709\) | 36.3341 | + | 9.73570i | 1.36456 | + | 0.365632i | 0.865488 | − | 0.500930i | \(-0.167009\pi\) |
0.499069 | + | 0.866562i | \(0.333675\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.53004 | − | 4.38216i | −0.0948839 | − | 0.164344i | ||||
\(712\) | 1.89842 | − | 0.508680i | 0.0711463 | − | 0.0190636i | ||||
\(713\) | 6.28492 | + | 3.62860i | 0.235372 | + | 0.135892i | ||||
\(714\) | 82.8063 | 3.09895 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.2931 | 0.384673 | ||||||||
\(717\) | 18.7519 | + | 10.8264i | 0.700303 | + | 0.404320i | ||||
\(718\) | 2.80137 | − | 0.750624i | 0.104546 | − | 0.0280130i | ||||
\(719\) | −17.9827 | − | 31.1470i | −0.670642 | − | 1.16159i | −0.977722 | − | 0.209902i | \(-0.932685\pi\) |
0.307080 | − | 0.951684i | \(-0.400648\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.63207 | + | 2.04501i | 0.284233 | + | 0.0761600i | ||||
\(722\) | 49.2187 | + | 85.2493i | 1.83173 | + | 3.17265i | ||||
\(723\) | 34.2899i | 1.27526i | ||||||||
\(724\) | −5.09931 | + | 2.94409i | −0.189514 | + | 0.109416i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.42414 | + | 1.98929i | −0.275536 | + | 0.0738296i | ||||
\(727\) | −2.50307 | − | 2.50307i | −0.0928336 | − | 0.0928336i | 0.659165 | − | 0.751998i | \(-0.270910\pi\) |
−0.751998 | + | 0.659165i | \(0.770910\pi\) | |||||||
\(728\) | 33.4675 | + | 0.794707i | 1.24039 | + | 0.0294538i | ||||
\(729\) | − | 21.1716i | − | 0.784134i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.89406 | − | 6.74472i | 0.144027 | − | 0.249462i | ||||
\(732\) | −2.92923 | + | 10.9320i | −0.108267 | + | 0.404059i | ||||
\(733\) | 1.25540 | 0.0463694 | 0.0231847 | − | 0.999731i | \(-0.492619\pi\) | ||||
0.0231847 | + | 0.999731i | \(0.492619\pi\) | |||||||
\(734\) | −7.72750 | + | 28.8394i | −0.285227 | + | 1.06448i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.49005 | − | 4.49005i | −0.165505 | − | 0.165505i | ||||
\(737\) | −28.8565 | − | 7.73206i | −1.06294 | − | 0.284814i | ||||
\(738\) | −1.88314 | − | 7.02799i | −0.0693195 | − | 0.258704i | ||||
\(739\) | 5.60031 | + | 20.9006i | 0.206011 | + | 0.768842i | 0.989139 | + | 0.146982i | \(0.0469560\pi\) |
−0.783129 | + | 0.621860i | \(0.786377\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −27.6111 | + | 45.3048i | −1.01432 | + | 1.66431i | ||||
\(742\) | −22.2592 | + | 22.2592i | −0.817162 | + | 0.817162i | ||||
\(743\) | −5.48351 | + | 9.49772i | −0.201171 | + | 0.348438i | −0.948906 | − | 0.315559i | \(-0.897808\pi\) |
0.747735 | + | 0.663997i | \(0.231141\pi\) | |||||||
\(744\) | −29.5931 | − | 17.0856i | −1.08494 | − | 0.626388i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 17.0206 | − | 17.0206i | 0.623168 | − | 0.623168i | ||||
\(747\) | 3.87992 | − | 2.24007i | 0.141959 | − | 0.0819601i | ||||
\(748\) | −60.6299 | + | 35.0047i | −2.21685 | + | 1.27990i | ||||
\(749\) | −22.3683 | + | 22.3683i | −0.817321 | + | 0.817321i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.9580 | + | 16.1416i | 1.02020 | + | 0.589015i | 0.914163 | − | 0.405347i | \(-0.132849\pi\) |
0.106041 | + | 0.994362i | \(0.466183\pi\) | |||||||
\(752\) | 0.428158 | − | 0.741591i | 0.0156133 | − | 0.0270430i | ||||
\(753\) | 34.5935 | − | 34.5935i | 1.26066 | − | 1.26066i | ||||
\(754\) | −0.198875 | + | 8.37520i | −0.00724259 | + | 0.305007i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 12.6957 | + | 47.3810i | 0.461738 | + | 1.72323i | ||||
\(757\) | −8.31633 | − | 31.0370i | −0.302262 | − | 1.12806i | −0.935277 | − | 0.353918i | \(-0.884849\pi\) |
0.633014 | − | 0.774140i | \(-0.281817\pi\) | |||||||
\(758\) | −22.3504 | − | 5.98876i | −0.811802 | − | 0.217522i | ||||
\(759\) | −5.42374 | − | 5.42374i | −0.196869 | − | 0.196869i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.3043 | − | 38.4564i | 0.373532 | − | 1.39404i | −0.481945 | − | 0.876201i | \(-0.660069\pi\) |
0.855477 | − | 0.517840i | \(-0.173264\pi\) | |||||||
\(762\) | −51.9372 | −1.88149 | ||||||||
\(763\) | −7.25766 | + | 27.0860i | −0.262745 | + | 0.980578i | ||||
\(764\) | 35.9061 | − | 62.1912i | 1.29904 | − | 2.25000i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 24.6634i | − | 0.891123i | ||||||
\(767\) | −16.6238 | − | 17.4325i | −0.600252 | − | 0.629452i | ||||
\(768\) | 22.0394 | + | 22.0394i | 0.795280 | + | 0.795280i | ||||
\(769\) | 18.0132 | − | 4.82663i | 0.649573 | − | 0.174053i | 0.0810373 | − | 0.996711i | \(-0.474177\pi\) |
0.568536 | + | 0.822658i | \(0.307510\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.3940 | + | 7.73304i | −0.482374 | + | 0.278499i | ||||
\(772\) | − | 54.2504i | − | 1.95251i | ||||||
\(773\) | −5.10195 | − | 8.83684i | −0.183504 | − | 0.317839i | 0.759567 | − | 0.650429i | \(-0.225411\pi\) |
−0.943072 | + | 0.332590i | \(0.892077\pi\) | |||||||
\(774\) | −1.42689 | − | 0.382333i | −0.0512884 | − | 0.0137427i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −19.6491 | − | 34.0332i | −0.705361 | − | 1.22172i | ||||
\(777\) | 4.32866 | − | 1.15986i | 0.155290 | − | 0.0416098i | ||||
\(778\) | 69.4297 | + | 40.0852i | 2.48917 | + | 1.43713i | ||||
\(779\) | 50.2618 | 1.80082 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.3750 | 1.19425 | ||||||||
\(782\) | −13.6794 | − | 7.89780i | −0.489174 | − | 0.282425i | ||||
\(783\) | −4.58108 | + | 1.22750i | −0.163714 | + | 0.0438671i | ||||
\(784\) | −0.173794 | − | 0.301019i | −0.00620692 | − | 0.0107507i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.288352 | − | 0.0772636i | −0.0102852 | − | 0.00275590i | ||||
\(787\) | −10.5661 | − | 18.3010i | −0.376640 | − | 0.652360i | 0.613931 | − | 0.789360i | \(-0.289587\pi\) |
−0.990571 | + | 0.137000i | \(0.956254\pi\) | |||||||
\(788\) | − | 9.16510i | − | 0.326493i | ||||||
\(789\) | 21.4076 | − | 12.3597i | 0.762132 | − | 0.440017i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −47.1228 | + | 12.6265i | −1.67549 | + | 0.448947i | ||||
\(792\) | 3.62781 | + | 3.62781i | 0.128909 | + | 0.128909i | ||||
\(793\) | 0.158944 | − | 6.69360i | 0.00564426 | − | 0.237697i | ||||
\(794\) | − | 14.0038i | − | 0.496976i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 30.2439 | − | 52.3840i | 1.07197 | − | 1.85670i | ||||
\(797\) | −6.55155 | + | 24.4507i | −0.232068 | + | 0.866089i | 0.747381 | + | 0.664396i | \(0.231311\pi\) |
−0.979449 | + | 0.201693i | \(0.935356\pi\) | |||||||
\(798\) | 108.499 | 3.84083 | ||||||||
\(799\) | −12.7802 | + | 47.6965i | −0.452133 | + | 1.68738i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.239046 | + | 0.239046i | 0.00844628 | + | 0.00844628i | ||||
\(802\) | −0.613954 | − | 0.164508i | −0.0216795 | − | 0.00580900i | ||||
\(803\) | −7.34980 | − | 27.4298i | −0.259369 | − | 0.967978i | ||||
\(804\) | 13.1755 | + | 49.1717i | 0.464665 | + | 1.73415i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 50.2045 | + | 14.7382i | 1.76838 | + | 0.519130i | ||||
\(807\) | −7.45357 | + | 7.45357i | −0.262378 | + | 0.262378i | ||||
\(808\) | 12.9850 | − | 22.4906i | 0.456810 | − | 0.791217i | ||||
\(809\) | 3.76608 | + | 2.17435i | 0.132408 | + | 0.0764459i | 0.564741 | − | 0.825268i | \(-0.308976\pi\) |
−0.432333 | + | 0.901714i | \(0.642309\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.7750 | + | 21.7750i | −0.764623 | + | 0.764623i | −0.977154 | − | 0.212531i | \(-0.931829\pi\) |
0.212531 | + | 0.977154i | \(0.431829\pi\) | |||||||
\(812\) | 9.19468 | − | 5.30855i | 0.322670 | − | 0.186294i | ||||
\(813\) | −12.2797 | + | 7.08967i | −0.430667 | + | 0.248646i | ||||
\(814\) | −4.32309 | + | 4.32309i | −0.151524 | + | 0.151524i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.01294 | + | 0.584822i | 0.0354600 | + | 0.0204729i | ||||
\(817\) | 5.10230 | − | 8.83745i | 0.178507 | − | 0.309183i | ||||
\(818\) | 24.4675 | − | 24.4675i | 0.855488 | − | 0.855488i | ||||
\(819\) | 2.75996 | + | 5.05377i | 0.0964406 | + | 0.176593i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.18315 | + | 8.14764i | 0.0761926 | + | 0.284355i | 0.993501 | − | 0.113823i | \(-0.0363096\pi\) |
−0.917309 | + | 0.398177i | \(0.869643\pi\) | |||||||
\(822\) | −11.7152 | − | 43.7218i | −0.408615 | − | 1.52497i | ||||
\(823\) | 18.8493 | + | 5.05067i | 0.657047 | + | 0.176055i | 0.571913 | − | 0.820314i | \(-0.306202\pi\) |
0.0851339 | + | 0.996370i | \(0.472868\pi\) | |||||||
\(824\) | 5.01819 | + | 5.01819i | 0.174817 | + | 0.174817i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.7496 | + | 47.5822i | −0.443616 | + | 1.65560i | ||||
\(827\) | −6.08198 | −0.211491 | −0.105745 | − | 0.994393i | \(-0.533723\pi\) | ||||
−0.105745 | + | 0.994393i | \(0.533723\pi\) | |||||||
\(828\) | −0.480549 | + | 1.79343i | −0.0167002 | + | 0.0623262i | ||||
\(829\) | −24.8232 | + | 42.9950i | −0.862145 | + | 1.49328i | 0.00771009 | + | 0.999970i | \(0.497546\pi\) |
−0.869855 | + | 0.493308i | \(0.835788\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.8155i | 0.756772i | ||||||||
\(832\) | −39.7347 | − | 24.2163i | −1.37755 | − | 0.839551i | ||||
\(833\) | 14.1729 | + | 14.1729i | 0.491061 | + | 0.491061i | ||||
\(834\) | 38.3562 | − | 10.2775i | 1.32817 | − | 0.355881i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −79.4419 | + | 45.8658i | −2.74756 | + | 1.58630i | ||||
\(837\) | 29.6210i | 1.02385i | ||||||||
\(838\) | −10.1401 | − | 17.5632i | −0.350284 | − | 0.606710i | ||||
\(839\) | 2.83726 | + | 0.760241i | 0.0979530 | + | 0.0262464i | 0.307463 | − | 0.951560i | \(-0.400520\pi\) |
−0.209510 | + | 0.977807i | \(0.567187\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.9867 | − | 24.2257i | −0.482301 | − | 0.835370i | ||||
\(842\) | −20.6184 | + | 5.52468i | −0.710557 | + | 0.190393i | ||||
\(843\) | −21.6680 | − | 12.5100i | −0.746285 | − | 0.430868i | ||||
\(844\) | 65.8914 | 2.26808 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.36603 | 0.322011 | ||||||||
\(847\) | −4.99053 | − | 2.88128i | −0.171477 | − | 0.0990020i | ||||
\(848\) | −0.429496 | + | 0.115083i | −0.0147489 | + | 0.00395197i | ||||
\(849\) | 3.75167 | + | 6.49808i | 0.128757 | + | 0.223014i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.825707 | − | 0.221248i | −0.0283049 | − | 0.00758427i | ||||
\(852\) | −28.4356 | − | 49.2520i | −0.974189 | − | 1.68734i | ||||
\(853\) | − | 52.5348i | − | 1.79876i | −0.437171 | − | 0.899378i | \(-0.644020\pi\) | ||
0.437171 | − | 0.899378i | \(-0.355980\pi\) | |||||||
\(854\) | −11.8579 | + | 6.84616i | −0.405769 | + | 0.234271i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −27.4445 | + | 7.35374i | −0.938034 | + | 0.251346i | ||||
\(857\) | 21.4029 | + | 21.4029i | 0.731110 | + | 0.731110i | 0.970840 | − | 0.239730i | \(-0.0770588\pi\) |
−0.239730 | + | 0.970840i | \(0.577059\pi\) | |||||||
\(858\) | −47.2227 | − | 28.7800i | −1.61216 | − | 0.982531i | ||||
\(859\) | 44.8260i | 1.52944i | 0.644360 | + | 0.764722i | \(0.277124\pi\) | ||||
−0.644360 | + | 0.764722i | \(0.722876\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.2006 | − | 33.2565i | 0.654356 | − | 1.13338i | ||||
\(862\) | 4.32311 | − | 16.1341i | 0.147246 | − | 0.549528i | ||||
\(863\) | −17.5619 | −0.597815 | −0.298907 | − | 0.954282i | \(-0.596622\pi\) | ||||
−0.298907 | + | 0.954282i | \(0.596622\pi\) | |||||||
\(864\) | 6.70799 | − | 25.0345i | 0.228210 | − | 0.851693i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17.7931 | − | 17.7931i | −0.604635 | − | 0.604635i | ||||
\(867\) | −34.4427 | − | 9.22891i | −1.16974 | − | 0.313430i | ||||
\(868\) | −17.1624 | − | 64.0509i | −0.582530 | − | 2.17403i | ||||
\(869\) | 9.42998 | + | 35.1932i | 0.319890 | + | 1.19385i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.4346 | − | 26.4313i | −0.489098 | − | 0.895590i | ||||
\(872\) | −17.8094 | + | 17.8094i | −0.603102 | + | 0.603102i | ||||
\(873\) | 3.37980 | − | 5.85398i | 0.114389 | − | 0.198127i | ||||
\(874\) | −17.9238 | − | 10.3483i | −0.606281 | − | 0.350037i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −34.2166 | + | 34.2166i | −1.15607 | + | 1.15607i | ||||
\(877\) | 7.40312 | − | 4.27420i | 0.249986 | − | 0.144329i | −0.369772 | − | 0.929123i | \(-0.620564\pi\) |
0.619758 | + | 0.784793i | \(0.287231\pi\) | |||||||
\(878\) | −23.2785 | + | 13.4398i | −0.785611 | + | 0.453573i | ||||
\(879\) | −32.6268 | + | 32.6268i | −1.10047 | + | 1.10047i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.8333 | + | 21.8430i | 1.27464 | + | 0.735911i | 0.975857 | − | 0.218411i | \(-0.0700875\pi\) |
0.298779 | + | 0.954322i | \(0.403421\pi\) | |||||||
\(882\) | 1.90088 | − | 3.29243i | 0.0640061 | − | 0.110862i | ||||
\(883\) | −26.5027 | + | 26.5027i | −0.891887 | + | 0.891887i | −0.994701 | − | 0.102814i | \(-0.967215\pi\) |
0.102814 | + | 0.994701i | \(0.467215\pi\) | |||||||
\(884\) | −67.7178 | − | 19.8794i | −2.27760 | − | 0.668617i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.2238 | − | 60.5481i | −0.545050 | − | 2.03415i | ||||
\(887\) | 4.76472 | + | 17.7822i | 0.159984 | + | 0.597067i | 0.998627 | + | 0.0523860i | \(0.0166826\pi\) |
−0.838643 | + | 0.544681i | \(0.816651\pi\) | |||||||
\(888\) | 3.88791 | + | 1.04176i | 0.130470 | + | 0.0349593i | ||||
\(889\) | −27.5345 | − | 27.5345i | −0.923478 | − | 0.923478i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.48236 | − | 35.3886i | 0.317671 | − | 1.18556i | ||||
\(892\) | 66.4120 | 2.22364 | ||||||||
\(893\) | −16.7457 | + | 62.4957i | −0.560372 | + | 2.09134i | ||||
\(894\) | −31.9194 | + | 55.2860i | −1.06754 | + | 1.84904i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 59.5559i | 1.98962i | ||||||||
\(897\) | 0.183558 | − | 7.73017i | 0.00612882 | − | 0.258103i | ||||
\(898\) | −33.5211 | − | 33.5211i | −1.11861 | − | 1.11861i | ||||
\(899\) | 6.19283 | − | 1.65936i | 0.206542 | − | 0.0553428i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.2052 | − | 12.8202i | 0.739762 | − | 0.427102i | ||||
\(902\) | 52.3896i | 1.74438i | ||||||||
\(903\) | −3.89828 | − | 6.75203i | −0.129727 | − | 0.224693i | ||||
\(904\) | −42.3247 | − | 11.3409i | −1.40770 | − | 0.377192i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −31.3488 | − | 54.2977i | −1.04149 | − | 1.80392i | ||||
\(907\) | −12.5901 | + | 3.37350i | −0.418046 | + | 0.112015i | −0.461710 | − | 0.887031i | \(-0.652764\pi\) |
0.0436633 | + | 0.999046i | \(0.486097\pi\) | |||||||
\(908\) | 19.1969 | + | 11.0833i | 0.637071 | + | 0.367813i | ||||
\(909\) | 4.46703 | 0.148162 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.7946 | −1.28532 | −0.642662 | − | 0.766150i | \(-0.722170\pi\) | ||||
−0.642662 | + | 0.766150i | \(0.722170\pi\) | |||||||
\(912\) | 1.32723 | + | 0.766278i | 0.0439491 | + | 0.0253740i | ||||
\(913\) | −31.1597 | + | 8.34922i | −1.03124 | + | 0.276319i | ||||
\(914\) | 2.93601 | + | 5.08532i | 0.0971146 | + | 0.168207i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 30.0381 | + | 8.04869i | 0.992487 | + | 0.265936i | ||||
\(917\) | −0.111908 | − | 0.193831i | −0.00369553 | − | 0.00640085i | ||||
\(918\) | − | 64.4713i | − | 2.12787i | ||||||
\(919\) | 21.9085 | − | 12.6489i | 0.722695 | − | 0.417248i | −0.0930490 | − | 0.995662i | \(-0.529661\pi\) |
0.815744 | + | 0.578414i | \(0.196328\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.3896 | − | 3.58772i | 0.441201 | − | 0.118219i | ||||
\(922\) | 16.4028 | + | 16.4028i | 0.540196 | + | 0.540196i | ||||
\(923\) | 23.2190 | + | 24.3485i | 0.764263 | + | 0.801442i | ||||
\(924\) | 70.0852i | 2.30563i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −14.0529 | + | 24.3403i | −0.461806 | + | 0.799871i | ||||
\(927\) | −0.315941 | + | 1.17911i | −0.0103769 | + | 0.0387270i | ||||
\(928\) | −5.60973 | −0.184148 | ||||||||
\(929\) | 10.0323 | − | 37.4412i | 0.329150 | − | 1.22841i | −0.580923 | − | 0.813959i | \(-0.697308\pi\) |
0.910073 | − | 0.414448i | \(-0.136025\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.5704 | + | 18.5704i | 0.608620 | + | 0.608620i | ||||
\(932\) | 66.9398 | + | 17.9365i | 2.19268 | + | 0.587528i | ||||
\(933\) | 0.808784 | + | 3.01842i | 0.0264784 | + | 0.0988188i | ||||
\(934\) | −13.6778 | − | 51.0462i | −0.447551 | − | 1.67028i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.122777 | + | 5.17053i | −0.00401311 | + | 0.169004i | ||||
\(937\) | −18.4851 | + | 18.4851i | −0.603883 | + | 0.603883i | −0.941341 | − | 0.337457i | \(-0.890433\pi\) |
0.337457 | + | 0.941341i | \(0.390433\pi\) | |||||||
\(938\) | −30.7937 | + | 53.3362i | −1.00545 | + | 1.74149i | ||||
\(939\) | 36.3091 | + | 20.9631i | 1.18490 | + | 0.684105i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.1581 | − | 13.1581i | 0.428942 | − | 0.428942i | −0.459326 | − | 0.888268i | \(-0.651909\pi\) |
0.888268 | + | 0.459326i | \(0.151909\pi\) | |||||||
\(942\) | 83.6225 | − | 48.2795i | 2.72457 | − | 1.57303i | ||||
\(943\) | −6.34379 | + | 3.66259i | −0.206582 | + | 0.119270i | ||||
\(944\) | −0.492012 | + | 0.492012i | −0.0160136 | + | 0.0160136i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.21157 | + | 5.31830i | 0.299494 | + | 0.172913i | ||||
\(947\) | 12.5632 | − | 21.7601i | 0.408249 | − | 0.707109i | −0.586444 | − | 0.809990i | \(-0.699473\pi\) |
0.994694 | + | 0.102881i | \(0.0328061\pi\) | |||||||
\(948\) | 43.9007 | − | 43.9007i | 1.42583 | − | 1.42583i | ||||
\(949\) | 14.8980 | − | 24.4450i | 0.483610 | − | 0.793518i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.728445 | + | 2.71859i | 0.0236215 | + | 0.0881565i | ||||
\(952\) | 14.4323 | + | 53.8622i | 0.467754 | + | 1.74568i | ||||
\(953\) | 16.2171 | + | 4.34536i | 0.525324 | + | 0.140760i | 0.511728 | − | 0.859147i | \(-0.329006\pi\) |
0.0135958 | + | 0.999908i | \(0.495672\pi\) | |||||||
\(954\) | −3.43891 | − | 3.43891i | −0.111339 | − | 0.111339i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.76778 | + | 36.4539i | −0.315913 | + | 1.17900i | ||||
\(957\) | −6.77626 | −0.219045 | ||||||||
\(958\) | −8.22961 | + | 30.7133i | −0.265887 | + | 0.992303i | ||||
\(959\) | 16.9683 | − | 29.3899i | 0.547934 | − | 0.949049i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 9.04245i | − | 0.291692i | ||||||
\(962\) | −6.16146 | − | 0.146308i | −0.198654 | − | 0.00471716i | ||||
\(963\) | −3.45577 | − | 3.45577i | −0.111361 | − | 0.111361i | ||||
\(964\) | −57.7292 | + | 15.4685i | −1.85933 | + | 0.498207i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −13.6942 | + | 7.90636i | −0.440604 | + | 0.254383i | ||||
\(967\) | − | 58.5376i | − | 1.88244i | −0.337790 | − | 0.941222i | \(-0.609679\pi\) | ||
0.337790 | − | 0.941222i | \(-0.390321\pi\) | |||||||
\(968\) | −2.58791 | − | 4.48239i | −0.0831785 | − | 0.144069i | ||||
\(969\) | −85.3629 | − | 22.8729i | −2.74225 | − | 0.734784i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.3457 | − | 26.5795i | −0.492467 | − | 0.852977i | 0.507496 | − | 0.861654i | \(-0.330571\pi\) |
−0.999962 | + | 0.00867714i | \(0.997238\pi\) | |||||||
\(972\) | −16.0927 | + | 4.31202i | −0.516173 | + | 0.138308i | ||||
\(973\) | 25.7831 | + | 14.8859i | 0.826569 | + | 0.477220i | ||||
\(974\) | 18.9229 | 0.606328 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.193405 | −0.00619074 | ||||||||
\(977\) | −23.2758 | − | 13.4383i | −0.744659 | − | 0.429929i | 0.0791020 | − | 0.996867i | \(-0.474795\pi\) |
−0.823761 | + | 0.566938i | \(0.808128\pi\) | |||||||
\(978\) | −36.0263 | + | 9.65323i | −1.15200 | + | 0.308676i | ||||
\(979\) | −1.21709 | − | 2.10807i | −0.0388985 | − | 0.0673741i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.18462 | − | 1.12126i | −0.133605 | − | 0.0357992i | ||||
\(982\) | 43.0169 | + | 74.5074i | 1.37272 | + | 2.37763i | ||||
\(983\) | 10.4201i | 0.332350i | 0.986096 | + | 0.166175i | \(0.0531417\pi\) | ||||
−0.986096 | + | 0.166175i | \(0.946858\pi\) | |||||||
\(984\) | 29.8703 | − | 17.2456i | 0.952230 | − | 0.549770i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −13.4789 | + | 3.61167i | −0.429257 | + | 0.115019i | ||||
\(987\) | 34.9541 | + | 34.9541i | 1.11260 | + | 1.11260i | ||||
\(988\) | −88.7290 | − | 26.0475i | −2.82285 | − | 0.828682i | ||||
\(989\) | 1.48722i | 0.0472910i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.1088 | − | 33.0974i | 0.607011 | − | 1.05137i | −0.384719 | − | 0.923034i | \(-0.625702\pi\) |
0.991730 | − | 0.128341i | \(-0.0409651\pi\) | |||||||
\(992\) | −9.06804 | + | 33.8424i | −0.287911 | + | 1.07450i | ||||
\(993\) | 4.44543 | 0.141071 | ||||||||
\(994\) | 17.8078 | − | 66.4595i | 0.564828 | − | 2.10797i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 38.8693 | + | 38.8693i | 1.23162 | + | 1.23162i | ||||
\(997\) | 29.2716 | + | 7.84331i | 0.927042 | + | 0.248400i | 0.690593 | − | 0.723244i | \(-0.257350\pi\) |
0.236449 | + | 0.971644i | \(0.424016\pi\) | |||||||
\(998\) | −22.0776 | − | 82.3947i | −0.698854 | − | 2.60816i | ||||
\(999\) | −0.903044 | − | 3.37020i | −0.0285710 | − | 0.106629i |
(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 | 325.2.x.c.318.2 | yes | 40 | |
5.2 | odd | 4 | 325.2.s.c.32.9 | yes | 40 | ||
5.3 | odd | 4 | 325.2.s.c.32.2 | ✓ | 40 | ||
5.4 | even | 2 | inner | 325.2.x.c.318.9 | yes | 40 | |
13.11 | odd | 12 | 325.2.s.c.193.9 | yes | 40 | ||
65.24 | odd | 12 | 325.2.s.c.193.2 | yes | 40 | ||
65.37 | even | 12 | inner | 325.2.x.c.232.2 | yes | 40 | |
65.63 | even | 12 | inner | 325.2.x.c.232.9 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
325.2.s.c.32.2 | ✓ | 40 | 5.3 | odd | 4 | ||
325.2.s.c.32.9 | yes | 40 | 5.2 | odd | 4 | ||
325.2.s.c.193.2 | yes | 40 | 65.24 | odd | 12 | ||
325.2.s.c.193.9 | yes | 40 | 13.11 | odd | 12 | ||
325.2.x.c.232.2 | yes | 40 | 65.37 | even | 12 | inner | |
325.2.x.c.232.9 | yes | 40 | 65.63 | even | 12 | inner | |
325.2.x.c.318.2 | yes | 40 | 1.1 | even | 1 | trivial | |
325.2.x.c.318.9 | yes | 40 | 5.4 | even | 2 | inner |