Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 557.5 | ||
Character | \(\chi\) | \(=\) | 784.557 |
Dual form | 784.2.x.m.373.5 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.13468 | − | 0.844095i | 0.802342 | − | 0.596865i | ||||
\(3\) | −2.80718 | + | 0.752181i | −1.62072 | + | 0.434272i | −0.951214 | − | 0.308531i | \(-0.900163\pi\) |
−0.669510 | + | 0.742803i | \(0.733496\pi\) | |||||||
\(4\) | 0.575008 | − | 1.91556i | 0.287504 | − | 0.957779i | ||||
\(5\) | 3.72606 | + | 0.998394i | 1.66634 | + | 0.446495i | 0.964121 | − | 0.265462i | \(-0.0855245\pi\) |
0.702222 | + | 0.711958i | \(0.252191\pi\) | |||||||
\(6\) | −2.55034 | + | 3.22301i | −1.04117 | + | 1.31579i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.964462 | − | 2.65891i | −0.340989 | − | 0.940067i | ||||
\(9\) | 4.71639 | − | 2.72301i | 1.57213 | − | 0.907670i | ||||
\(10\) | 5.07063 | − | 2.01229i | 1.60347 | − | 0.636341i | ||||
\(11\) | 0.336603 | + | 1.25622i | 0.101490 | + | 0.378764i | 0.997923 | − | 0.0644137i | \(-0.0205177\pi\) |
−0.896434 | + | 0.443178i | \(0.853851\pi\) | |||||||
\(12\) | −0.173303 | + | 5.80982i | −0.0500282 | + | 1.67715i | ||||
\(13\) | 1.12607 | + | 1.12607i | 0.312316 | + | 0.312316i | 0.845806 | − | 0.533490i | \(-0.179120\pi\) |
−0.533490 | + | 0.845806i | \(0.679120\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −11.2107 | −2.89458 | ||||||||
\(16\) | −3.33873 | − | 2.20292i | −0.834683 | − | 0.550731i | ||||
\(17\) | −0.754426 | + | 1.30670i | −0.182975 | + | 0.316922i | −0.942892 | − | 0.333098i | \(-0.891906\pi\) |
0.759917 | + | 0.650020i | \(0.225239\pi\) | |||||||
\(18\) | 3.05313 | − | 7.07083i | 0.719629 | − | 1.66661i | ||||
\(19\) | −0.535390 | + | 1.99810i | −0.122827 | + | 0.458396i | −0.999753 | − | 0.0222291i | \(-0.992924\pi\) |
0.876926 | + | 0.480625i | \(0.159590\pi\) | |||||||
\(20\) | 4.05500 | − | 6.56340i | 0.906725 | − | 1.46762i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.44230 | + | 1.14128i | 0.307500 | + | 0.243323i | ||||
\(23\) | 4.13121 | − | 2.38515i | 0.861416 | − | 0.497339i | −0.00307023 | − | 0.999995i | \(-0.500977\pi\) |
0.864486 | + | 0.502657i | \(0.167644\pi\) | |||||||
\(24\) | 4.70740 | + | 6.73859i | 0.960893 | + | 1.37551i | ||||
\(25\) | 8.55659 | + | 4.94015i | 1.71132 | + | 0.988030i | ||||
\(26\) | 2.22825 | + | 0.327223i | 0.436995 | + | 0.0641737i | ||||
\(27\) | −5.02656 | + | 5.02656i | −0.967362 | + | 0.967362i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.10069 | + | 4.10069i | 0.761478 | + | 0.761478i | 0.976590 | − | 0.215111i | \(-0.0690115\pi\) |
−0.215111 | + | 0.976590i | \(0.569011\pi\) | |||||||
\(30\) | −12.7206 | + | 9.46287i | −2.32245 | + | 1.72768i | ||||
\(31\) | 2.05500 | − | 3.55936i | 0.369088 | − | 0.639280i | −0.620335 | − | 0.784337i | \(-0.713003\pi\) |
0.989423 | + | 0.145057i | \(0.0463367\pi\) | |||||||
\(32\) | −5.64788 | + | 0.318587i | −0.998413 | + | 0.0563187i | ||||
\(33\) | −1.88981 | − | 3.27324i | −0.328973 | − | 0.569798i | ||||
\(34\) | 0.246948 | + | 2.11950i | 0.0423513 | + | 0.363491i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.50412 | − | 10.6003i | −0.417354 | − | 1.76671i | ||||
\(37\) | 2.26031 | + | 0.605650i | 0.371593 | + | 0.0995682i | 0.439783 | − | 0.898104i | \(-0.355055\pi\) |
−0.0681892 | + | 0.997672i | \(0.521722\pi\) | |||||||
\(38\) | 1.07909 | + | 2.71913i | 0.175052 | + | 0.441102i | ||||
\(39\) | −4.00810 | − | 2.31408i | −0.641809 | − | 0.370549i | ||||
\(40\) | −0.938997 | − | 10.8702i | −0.148469 | − | 1.71873i | ||||
\(41\) | − | 7.45533i | − | 1.16433i | −0.813072 | − | 0.582163i | \(-0.802206\pi\) | ||
0.813072 | − | 0.582163i | \(-0.197794\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.68992 | − | 5.68992i | 0.867705 | − | 0.867705i | −0.124513 | − | 0.992218i | \(-0.539737\pi\) |
0.992218 | + | 0.124513i | \(0.0397369\pi\) | |||||||
\(44\) | 2.59991 | + | 0.0775535i | 0.391951 | + | 0.0116916i | ||||
\(45\) | 20.2922 | − | 5.43727i | 3.02498 | − | 0.810541i | ||||
\(46\) | 2.67431 | − | 6.19352i | 0.394306 | − | 0.913185i | ||||
\(47\) | 1.79874 | + | 3.11551i | 0.262373 | + | 0.454444i | 0.966872 | − | 0.255261i | \(-0.0821615\pi\) |
−0.704499 | + | 0.709705i | \(0.748828\pi\) | |||||||
\(48\) | 11.0294 | + | 3.67267i | 1.59196 | + | 0.530104i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 13.8790 | − | 1.61707i | 1.96278 | − | 0.228689i | ||||
\(51\) | 1.13493 | − | 4.23561i | 0.158922 | − | 0.593105i | ||||
\(52\) | 2.80456 | − | 1.50956i | 0.388923 | − | 0.209338i | ||||
\(53\) | −0.247329 | − | 0.923043i | −0.0339732 | − | 0.126790i | 0.946857 | − | 0.321656i | \(-0.104239\pi\) |
−0.980830 | + | 0.194866i | \(0.937573\pi\) | |||||||
\(54\) | −1.46066 | + | 9.94644i | −0.198770 | + | 1.35354i | ||||
\(55\) | 5.01680i | 0.676466i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 6.01174i | − | 0.796275i | ||||||
\(58\) | 8.11434 | + | 1.19161i | 1.06547 | + | 0.156466i | ||||
\(59\) | −0.416693 | − | 1.55512i | −0.0542489 | − | 0.202459i | 0.933482 | − | 0.358624i | \(-0.116754\pi\) |
−0.987731 | + | 0.156164i | \(0.950087\pi\) | |||||||
\(60\) | −6.44623 | + | 21.4747i | −0.832205 | + | 2.77237i | ||||
\(61\) | 1.17817 | − | 4.39698i | 0.150849 | − | 0.562975i | −0.848576 | − | 0.529073i | \(-0.822540\pi\) |
0.999425 | − | 0.0339025i | \(-0.0107936\pi\) | |||||||
\(62\) | −0.672667 | − | 5.77335i | −0.0854288 | − | 0.733216i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.13963 | + | 5.12884i | −0.767453 | + | 0.641105i | ||||
\(65\) | 3.07155 | + | 5.32008i | 0.380979 | + | 0.659875i | ||||
\(66\) | −4.90726 | − | 2.11891i | −0.604041 | − | 0.260820i | ||||
\(67\) | 2.08511 | − | 0.558703i | 0.254736 | − | 0.0682564i | −0.129191 | − | 0.991620i | \(-0.541238\pi\) |
0.383927 | + | 0.923363i | \(0.374571\pi\) | |||||||
\(68\) | 2.06927 | + | 2.19651i | 0.250936 | + | 0.266366i | ||||
\(69\) | −9.80296 | + | 9.80296i | −1.18014 | + | 1.18014i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.8202i | 1.64016i | 0.572251 | + | 0.820079i | \(0.306070\pi\) | ||||
−0.572251 | + | 0.820079i | \(0.693930\pi\) | |||||||
\(72\) | −11.7890 | − | 9.91423i | −1.38935 | − | 1.16840i | ||||
\(73\) | −12.5356 | − | 7.23744i | −1.46718 | − | 0.847078i | −0.467857 | − | 0.883804i | \(-0.654974\pi\) |
−0.999325 | + | 0.0367258i | \(0.988307\pi\) | |||||||
\(74\) | 3.07596 | − | 1.22070i | 0.357574 | − | 0.141903i | ||||
\(75\) | −27.7357 | − | 7.43177i | −3.20265 | − | 0.858147i | ||||
\(76\) | 3.51963 | + | 2.17450i | 0.403729 | + | 0.249432i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.50122 | + | 0.757473i | −0.736118 | + | 0.0857669i | ||||
\(79\) | 0.889807 | + | 1.54119i | 0.100111 | + | 0.173397i | 0.911730 | − | 0.410789i | \(-0.134747\pi\) |
−0.811619 | + | 0.584187i | \(0.801414\pi\) | |||||||
\(80\) | −10.2409 | − | 11.5416i | −1.14497 | − | 1.29039i | ||||
\(81\) | 2.16054 | − | 3.74216i | 0.240060 | − | 0.415795i | ||||
\(82\) | −6.29300 | − | 8.45943i | −0.694946 | − | 0.934188i | ||||
\(83\) | 7.16133 | + | 7.16133i | 0.786058 | + | 0.786058i | 0.980845 | − | 0.194787i | \(-0.0624017\pi\) |
−0.194787 | + | 0.980845i | \(0.562402\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.11564 | + | 4.11564i | −0.446404 | + | 0.446404i | ||||
\(86\) | 1.65342 | − | 11.2591i | 0.178293 | − | 1.21410i | ||||
\(87\) | −14.5958 | − | 8.42689i | −1.56483 | − | 0.903458i | ||||
\(88\) | 3.01553 | − | 2.10657i | 0.321457 | − | 0.224561i | ||||
\(89\) | 7.32570 | − | 4.22949i | 0.776522 | − | 0.448325i | −0.0586740 | − | 0.998277i | \(-0.518687\pi\) |
0.835196 | + | 0.549952i | \(0.185354\pi\) | |||||||
\(90\) | 18.4356 | − | 23.2981i | 1.94328 | − | 2.45584i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.19342 | − | 9.28505i | −0.228680 | − | 0.968033i | ||||
\(93\) | −3.09146 | + | 11.5375i | −0.320569 | + | 1.19638i | ||||
\(94\) | 4.67078 | + | 2.01681i | 0.481755 | + | 0.208018i | ||||
\(95\) | −3.98979 | + | 6.91052i | −0.409344 | + | 0.709004i | ||||
\(96\) | 15.6150 | − | 5.14255i | 1.59369 | − | 0.524860i | ||||
\(97\) | −16.2227 | −1.64717 | −0.823585 | − | 0.567194i | \(-0.808029\pi\) | ||||
−0.823585 | + | 0.567194i | \(0.808029\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.00824 | + | 5.00824i | 0.503348 | + | 0.503348i | ||||
\(100\) | 14.3833 | − | 13.5500i | 1.43833 | − | 1.35500i | ||||
\(101\) | 4.23361 | + | 15.8001i | 0.421260 | + | 1.57216i | 0.771957 | + | 0.635675i | \(0.219278\pi\) |
−0.350696 | + | 0.936489i | \(0.614055\pi\) | |||||||
\(102\) | −2.28748 | − | 5.76407i | −0.226494 | − | 0.570727i | ||||
\(103\) | −14.8848 | + | 8.59375i | −1.46664 | + | 0.846768i | −0.999304 | − | 0.0373093i | \(-0.988121\pi\) |
−0.467341 | + | 0.884077i | \(0.654788\pi\) | |||||||
\(104\) | 1.90808 | − | 4.08018i | 0.187102 | − | 0.400095i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.05977 | − | 0.838591i | −0.102934 | − | 0.0814512i | ||||
\(107\) | −5.60266 | − | 1.50123i | −0.541630 | − | 0.145129i | −0.0223764 | − | 0.999750i | \(-0.507123\pi\) |
−0.519253 | + | 0.854620i | \(0.673790\pi\) | |||||||
\(108\) | 6.73836 | + | 12.5190i | 0.648399 | + | 1.20464i | ||||
\(109\) | 4.47170 | − | 1.19819i | 0.428311 | − | 0.114766i | −0.0382223 | − | 0.999269i | \(-0.512169\pi\) |
0.466533 | + | 0.884504i | \(0.345503\pi\) | |||||||
\(110\) | 4.23466 | + | 5.69248i | 0.403759 | + | 0.542757i | ||||
\(111\) | −6.80066 | −0.645490 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.17193 | −0.862822 | −0.431411 | − | 0.902155i | \(-0.641984\pi\) | ||||
−0.431411 | + | 0.902155i | \(0.641984\pi\) | |||||||
\(114\) | −5.07448 | − | 6.82142i | −0.475269 | − | 0.638884i | ||||
\(115\) | 17.7744 | − | 4.76265i | 1.65747 | − | 0.444119i | ||||
\(116\) | 10.2130 | − | 5.49718i | 0.948256 | − | 0.510400i | ||||
\(117\) | 8.37731 | + | 2.24469i | 0.774483 | + | 0.207522i | ||||
\(118\) | −1.78548 | − | 1.41284i | −0.164367 | − | 0.130062i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 10.8123 | + | 29.8082i | 0.987021 | + | 2.72110i | ||||
\(121\) | 8.06150 | − | 4.65431i | 0.732863 | − | 0.423119i | ||||
\(122\) | −2.37462 | − | 5.98366i | −0.214988 | − | 0.541735i | ||||
\(123\) | 5.60775 | + | 20.9284i | 0.505634 | + | 1.88705i | ||||
\(124\) | −5.63652 | − | 5.98313i | −0.506174 | − | 0.537301i | ||||
\(125\) | 13.3118 | + | 13.3118i | 1.19064 | + | 1.19064i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.9787 | −1.15167 | −0.575835 | − | 0.817566i | \(-0.695323\pi\) | ||||
−0.575835 | + | 0.817566i | \(0.695323\pi\) | |||||||
\(128\) | −2.63730 | + | 11.0020i | −0.233107 | + | 0.972451i | ||||
\(129\) | −11.6928 | + | 20.2525i | −1.02949 | + | 1.78313i | ||||
\(130\) | 7.97588 | + | 3.44392i | 0.699531 | + | 0.302052i | ||||
\(131\) | 2.49617 | − | 9.31582i | 0.218091 | − | 0.813927i | −0.766964 | − | 0.641690i | \(-0.778234\pi\) |
0.985055 | − | 0.172237i | \(-0.0550996\pi\) | |||||||
\(132\) | −7.35674 | + | 1.73790i | −0.640322 | + | 0.151264i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.89434 | − | 2.39398i | 0.163646 | − | 0.206808i | ||||
\(135\) | −23.7477 | + | 13.7108i | −2.04388 | + | 1.18004i | ||||
\(136\) | 4.20203 | + | 0.745686i | 0.360321 | + | 0.0639421i | ||||
\(137\) | −19.6192 | − | 11.3271i | −1.67618 | − | 0.967742i | −0.964061 | − | 0.265682i | \(-0.914403\pi\) |
−0.712118 | − | 0.702060i | \(-0.752264\pi\) | |||||||
\(138\) | −2.84862 | + | 19.3979i | −0.242491 | + | 1.65126i | ||||
\(139\) | 6.64728 | − | 6.64728i | 0.563815 | − | 0.563815i | −0.366574 | − | 0.930389i | \(-0.619469\pi\) |
0.930389 | + | 0.366574i | \(0.119469\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.39281 | − | 7.39281i | −0.622587 | − | 0.622587i | ||||
\(142\) | 11.6656 | + | 15.6816i | 0.978953 | + | 1.31597i | ||||
\(143\) | −1.03555 | + | 1.79363i | −0.0865974 | + | 0.149991i | ||||
\(144\) | −21.7453 | − | 1.29845i | −1.81211 | − | 0.108204i | ||||
\(145\) | 11.1853 | + | 19.3735i | 0.928888 | + | 1.60888i | ||||
\(146\) | −20.3330 | + | 2.36905i | −1.68277 | + | 0.196064i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.45986 | − | 3.98151i | 0.202199 | − | 0.327278i | ||||
\(149\) | −10.6144 | − | 2.84413i | −0.869568 | − | 0.233000i | −0.203667 | − | 0.979040i | \(-0.565286\pi\) |
−0.665901 | + | 0.746040i | \(0.731953\pi\) | |||||||
\(150\) | −37.7444 | + | 14.9789i | −3.08182 | + | 1.22302i | ||||
\(151\) | 4.73568 | + | 2.73415i | 0.385384 | + | 0.222502i | 0.680158 | − | 0.733065i | \(-0.261911\pi\) |
−0.294774 | + | 0.955567i | \(0.595244\pi\) | |||||||
\(152\) | 5.82915 | − | 0.503539i | 0.472806 | − | 0.0408424i | ||||
\(153\) | 8.21724i | 0.664324i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.2107 | − | 11.2107i | 0.900463 | − | 0.900463i | ||||
\(156\) | −6.73744 | + | 6.34713i | −0.539427 | + | 0.508177i | ||||
\(157\) | −7.67327 | + | 2.05605i | −0.612393 | + | 0.164090i | −0.551667 | − | 0.834064i | \(-0.686008\pi\) |
−0.0607259 | + | 0.998154i | \(0.519342\pi\) | |||||||
\(158\) | 2.31056 | + | 0.997680i | 0.183818 | + | 0.0793712i | ||||
\(159\) | 1.38859 | + | 2.40511i | 0.110122 | + | 0.190737i | ||||
\(160\) | −21.3624 | − | 4.45173i | −1.68885 | − | 0.351940i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.707214 | − | 6.06986i | −0.0555640 | − | 0.476893i | ||||
\(163\) | −2.31239 | + | 8.62997i | −0.181121 | + | 0.675951i | 0.814307 | + | 0.580434i | \(0.197117\pi\) |
−0.995428 | + | 0.0955171i | \(0.969550\pi\) | |||||||
\(164\) | −14.2811 | − | 4.28687i | −1.11517 | − | 0.334749i | ||||
\(165\) | −3.77354 | − | 14.0831i | −0.293770 | − | 1.09636i | ||||
\(166\) | 14.1707 | + | 2.08099i | 1.09986 | + | 0.161516i | ||||
\(167\) | − | 11.8175i | − | 0.914463i | −0.889348 | − | 0.457231i | \(-0.848841\pi\) | ||
0.889348 | − | 0.457231i | \(-0.151159\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 10.4639i | − | 0.804917i | ||||||
\(170\) | −1.19595 | + | 8.14394i | −0.0917255 | + | 0.624611i | ||||
\(171\) | 2.91575 | + | 10.8817i | 0.222973 | + | 0.832145i | ||||
\(172\) | −7.62763 | − | 14.1711i | −0.581601 | − | 1.08054i | ||||
\(173\) | −2.06387 | + | 7.70245i | −0.156913 | + | 0.585606i | 0.842021 | + | 0.539444i | \(0.181366\pi\) |
−0.998934 | + | 0.0461620i | \(0.985301\pi\) | |||||||
\(174\) | −23.6747 | + | 2.75840i | −1.79477 | + | 0.209114i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.64353 | − | 4.93569i | 0.123886 | − | 0.372041i | ||||
\(177\) | 2.33946 | + | 4.05207i | 0.175845 | + | 0.304572i | ||||
\(178\) | 4.74225 | − | 10.9827i | 0.355446 | − | 0.823189i | ||||
\(179\) | −16.0204 | + | 4.29266i | −1.19742 | + | 0.320849i | −0.801816 | − | 0.597571i | \(-0.796133\pi\) |
−0.395608 | + | 0.918420i | \(0.629466\pi\) | |||||||
\(180\) | 1.25275 | − | 41.9974i | 0.0933746 | − | 3.13030i | ||||
\(181\) | 4.18574 | − | 4.18574i | 0.311124 | − | 0.311124i | −0.534221 | − | 0.845345i | \(-0.679395\pi\) |
0.845345 | + | 0.534221i | \(0.179395\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.2293i | 0.977937i | ||||||||
\(184\) | −10.3263 | − | 8.68413i | −0.761265 | − | 0.640202i | ||||
\(185\) | 7.81739 | + | 4.51337i | 0.574746 | + | 0.331830i | ||||
\(186\) | 6.23090 | + | 15.7009i | 0.456872 | + | 1.15124i | ||||
\(187\) | −1.89545 | − | 0.507884i | −0.138609 | − | 0.0371401i | ||||
\(188\) | 7.00223 | − | 1.65415i | 0.510690 | − | 0.120641i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.30599 | + | 11.2090i | 0.0947464 | + | 0.813187i | ||||
\(191\) | −6.18382 | − | 10.7107i | −0.447445 | − | 0.774998i | 0.550774 | − | 0.834655i | \(-0.314333\pi\) |
−0.998219 | + | 0.0596566i | \(0.980999\pi\) | |||||||
\(192\) | 13.3772 | − | 19.0157i | 0.965417 | − | 1.37234i | ||||
\(193\) | −11.8419 | + | 20.5107i | −0.852395 | + | 1.47639i | 0.0266452 | + | 0.999645i | \(0.491518\pi\) |
−0.879041 | + | 0.476747i | \(0.841816\pi\) | |||||||
\(194\) | −18.4076 | + | 13.6935i | −1.32159 | + | 0.983138i | ||||
\(195\) | −12.6240 | − | 12.6240i | −0.904026 | − | 0.904026i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.4195 | + | 11.4195i | −0.813606 | + | 0.813606i | −0.985173 | − | 0.171566i | \(-0.945117\pi\) |
0.171566 | + | 0.985173i | \(0.445117\pi\) | |||||||
\(198\) | 9.91020 | + | 1.45533i | 0.704287 | + | 0.103426i | ||||
\(199\) | −4.76039 | − | 2.74841i | −0.337455 | − | 0.194830i | 0.321691 | − | 0.946845i | \(-0.395749\pi\) |
−0.659146 | + | 0.752015i | \(0.729082\pi\) | |||||||
\(200\) | 4.88292 | − | 27.5158i | 0.345275 | − | 1.94566i | ||||
\(201\) | −5.43302 | + | 3.13675i | −0.383216 | + | 0.221250i | ||||
\(202\) | 18.1406 | + | 14.3545i | 1.27636 | + | 1.00998i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7.46098 | − | 4.60954i | −0.522373 | − | 0.322732i | ||||
\(205\) | 7.44336 | − | 27.7790i | 0.519867 | − | 1.94017i | ||||
\(206\) | −9.63560 | + | 22.3154i | −0.671344 | + | 1.55479i | ||||
\(207\) | 12.9896 | − | 22.4986i | 0.902839 | − | 1.56376i | ||||
\(208\) | −1.27900 | − | 6.24031i | −0.0886829 | − | 0.432688i | ||||
\(209\) | −2.69027 | −0.186090 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.907874 | + | 0.907874i | 0.0625007 | + | 0.0625007i | 0.737666 | − | 0.675166i | \(-0.235928\pi\) |
−0.675166 | + | 0.737666i | \(0.735928\pi\) | |||||||
\(212\) | −1.91036 | − | 0.0569846i | −0.131204 | − | 0.00391372i | ||||
\(213\) | −10.3953 | − | 38.7958i | −0.712274 | − | 2.65824i | ||||
\(214\) | −7.62442 | + | 3.02576i | −0.521195 | + | 0.206837i | ||||
\(215\) | 26.8818 | − | 15.5202i | 1.83332 | − | 1.05847i | ||||
\(216\) | 18.2131 | + | 8.51726i | 1.23925 | + | 0.579526i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.06257 | − | 5.13410i | 0.275152 | − | 0.347725i | ||||
\(219\) | 40.6336 | + | 10.8877i | 2.74576 | + | 0.735724i | ||||
\(220\) | 9.60998 | + | 2.88470i | 0.647905 | + | 0.194487i | ||||
\(221\) | −2.32098 | + | 0.621906i | −0.156126 | + | 0.0418339i | ||||
\(222\) | −7.71659 | + | 5.74040i | −0.517904 | + | 0.385271i | ||||
\(223\) | 3.20318 | 0.214501 | 0.107250 | − | 0.994232i | \(-0.465795\pi\) | ||||
0.107250 | + | 0.994232i | \(0.465795\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 53.8083 | 3.58722 | ||||||||
\(226\) | −10.4072 | + | 7.74197i | −0.692278 | + | 0.514988i | ||||
\(227\) | −18.8417 | + | 5.04862i | −1.25057 | + | 0.335089i | −0.822556 | − | 0.568684i | \(-0.807453\pi\) |
−0.428012 | + | 0.903773i | \(0.640786\pi\) | |||||||
\(228\) | −11.5158 | − | 3.45680i | −0.762655 | − | 0.228932i | ||||
\(229\) | 9.59192 | + | 2.57015i | 0.633852 | + | 0.169840i | 0.561417 | − | 0.827533i | \(-0.310256\pi\) |
0.0724349 | + | 0.997373i | \(0.476923\pi\) | |||||||
\(230\) | 16.1482 | − | 20.4074i | 1.06478 | − | 1.34562i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.94841 | − | 14.8583i | 0.456185 | − | 0.975496i | ||||
\(233\) | −2.54488 | + | 1.46929i | −0.166720 | + | 0.0962561i | −0.581039 | − | 0.813876i | \(-0.697353\pi\) |
0.414318 | + | 0.910132i | \(0.364020\pi\) | |||||||
\(234\) | 11.4003 | − | 4.52423i | 0.745262 | − | 0.295758i | ||||
\(235\) | 3.59170 | + | 13.4044i | 0.234297 | + | 0.874408i | ||||
\(236\) | −3.21853 | − | 0.0960064i | −0.209508 | − | 0.00624948i | ||||
\(237\) | −3.65710 | − | 3.65710i | −0.237554 | − | 0.237554i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.2109 | 1.04859 | 0.524297 | − | 0.851536i | \(-0.324328\pi\) | ||||
0.524297 | + | 0.851536i | \(0.324328\pi\) | |||||||
\(240\) | 37.4294 | + | 24.6963i | 2.41606 | + | 1.59414i | ||||
\(241\) | −7.05829 | + | 12.2253i | −0.454665 | + | 0.787502i | −0.998669 | − | 0.0515803i | \(-0.983574\pi\) |
0.544004 | + | 0.839082i | \(0.316908\pi\) | |||||||
\(242\) | 5.21856 | − | 12.0858i | 0.335462 | − | 0.776906i | ||||
\(243\) | 2.26932 | − | 8.46922i | 0.145577 | − | 0.543301i | ||||
\(244\) | −7.74522 | − | 4.78515i | −0.495837 | − | 0.306338i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 24.0286 | + | 19.0136i | 1.53201 | + | 1.21227i | ||||
\(247\) | −2.85290 | + | 1.64712i | −0.181526 | + | 0.104804i | ||||
\(248\) | −11.4460 | − | 2.03119i | −0.726821 | − | 0.128981i | ||||
\(249\) | −25.4897 | − | 14.7165i | −1.61535 | − | 0.932621i | ||||
\(250\) | 26.3411 | + | 3.86825i | 1.66596 | + | 0.244649i | ||||
\(251\) | 14.1967 | − | 14.1967i | 0.896091 | − | 0.896091i | −0.0989969 | − | 0.995088i | \(-0.531563\pi\) |
0.995088 | + | 0.0989969i | \(0.0315634\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.38685 | + | 4.38685i | 0.275799 | + | 0.275799i | ||||
\(254\) | −14.7267 | + | 10.9552i | −0.924033 | + | 0.687392i | ||||
\(255\) | 8.45763 | − | 14.6490i | 0.529637 | − | 0.917358i | ||||
\(256\) | 6.29425 | + | 14.7099i | 0.393391 | + | 0.919371i | ||||
\(257\) | −1.61839 | − | 2.80314i | −0.100953 | − | 0.174855i | 0.811125 | − | 0.584873i | \(-0.198856\pi\) |
−0.912077 | + | 0.410018i | \(0.865522\pi\) | |||||||
\(258\) | 3.82742 | + | 32.8499i | 0.238285 | + | 2.04515i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 11.9571 | − | 2.82464i | 0.741547 | − | 0.175177i | ||||
\(261\) | 30.5066 | + | 8.17423i | 1.88831 | + | 0.505972i | ||||
\(262\) | −5.03108 | − | 12.6775i | −0.310821 | − | 0.783218i | ||||
\(263\) | 20.7985 | + | 12.0080i | 1.28249 | + | 0.740448i | 0.977304 | − | 0.211844i | \(-0.0679468\pi\) |
0.305190 | + | 0.952292i | \(0.401280\pi\) | |||||||
\(264\) | −6.88061 | + | 8.18175i | −0.423473 | + | 0.503552i | ||||
\(265\) | − | 3.68624i | − | 0.226444i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.3832 | + | 17.3832i | −1.06383 | + | 1.06383i | ||||
\(268\) | 0.128725 | − | 4.31540i | 0.00786316 | − | 0.263605i | ||||
\(269\) | −0.119533 | + | 0.0320287i | −0.00728804 | + | 0.00195282i | −0.262461 | − | 0.964943i | \(-0.584534\pi\) |
0.255173 | + | 0.966895i | \(0.417868\pi\) | |||||||
\(270\) | −15.3730 | + | 35.6027i | −0.935569 | + | 2.16671i | ||||
\(271\) | −5.05692 | − | 8.75884i | −0.307186 | − | 0.532062i | 0.670560 | − | 0.741856i | \(-0.266054\pi\) |
−0.977746 | + | 0.209794i | \(0.932721\pi\) | |||||||
\(272\) | 5.39739 | − | 2.70079i | 0.327265 | − | 0.163760i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −31.8227 | + | 3.70774i | −1.92248 | + | 0.223993i | ||||
\(275\) | −3.32573 | + | 12.4118i | −0.200549 | + | 0.748460i | ||||
\(276\) | 13.1414 | + | 24.4149i | 0.791017 | + | 1.46961i | ||||
\(277\) | −4.02921 | − | 15.0372i | −0.242092 | − | 0.903498i | −0.974823 | − | 0.222980i | \(-0.928422\pi\) |
0.732732 | − | 0.680518i | \(-0.238245\pi\) | |||||||
\(278\) | 1.93162 | − | 13.1535i | 0.115851 | − | 0.788894i | ||||
\(279\) | − | 22.3831i | − | 1.34004i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.21999i | 0.251743i | 0.992047 | + | 0.125872i | \(0.0401727\pi\) | ||||
−0.992047 | + | 0.125872i | \(0.959827\pi\) | |||||||
\(282\) | −14.6287 | − | 2.14826i | −0.871128 | − | 0.127927i | ||||
\(283\) | 6.06995 | + | 22.6533i | 0.360821 | + | 1.34660i | 0.872999 | + | 0.487722i | \(0.162172\pi\) |
−0.512178 | + | 0.858879i | \(0.671161\pi\) | |||||||
\(284\) | 26.4734 | + | 7.94674i | 1.57091 | + | 0.471552i | ||||
\(285\) | 6.00209 | − | 22.4001i | 0.355533 | − | 1.32687i | ||||
\(286\) | 0.338971 | + | 2.90931i | 0.0200438 | + | 0.172031i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −25.7701 | + | 16.8818i | −1.51852 | + | 0.994770i | ||||
\(289\) | 7.36168 | + | 12.7508i | 0.433040 | + | 0.750048i | ||||
\(290\) | 29.0448 | + | 12.5413i | 1.70557 | + | 0.736451i | ||||
\(291\) | 45.5401 | − | 12.2024i | 2.66961 | − | 0.715319i | ||||
\(292\) | −21.0718 | + | 19.8511i | −1.23314 | + | 1.16170i | ||||
\(293\) | 13.5242 | − | 13.5242i | 0.790093 | − | 0.790093i | −0.191416 | − | 0.981509i | \(-0.561308\pi\) |
0.981509 | + | 0.191416i | \(0.0613079\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 6.21049i | − | 0.361589i | ||||||
\(296\) | −0.569618 | − | 6.59410i | −0.0331084 | − | 0.383275i | ||||
\(297\) | −8.00641 | − | 4.62250i | −0.464579 | − | 0.268225i | ||||
\(298\) | −14.4447 | + | 5.73241i | −0.836761 | + | 0.332069i | ||||
\(299\) | 7.33790 | + | 1.96618i | 0.424361 | + | 0.113707i | ||||
\(300\) | −30.1843 | + | 48.8561i | −1.74269 | + | 2.82071i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.68137 | − | 0.894976i | 0.442013 | − | 0.0515001i | ||||
\(303\) | −23.7690 | − | 41.1691i | −1.36549 | − | 2.36510i | ||||
\(304\) | 6.18919 | − | 5.49171i | 0.354975 | − | 0.314971i | ||||
\(305\) | 8.77984 | − | 15.2071i | 0.502732 | − | 0.870757i | ||||
\(306\) | 6.93613 | + | 9.32395i | 0.396512 | + | 0.533015i | ||||
\(307\) | 8.93389 | + | 8.93389i | 0.509884 | + | 0.509884i | 0.914491 | − | 0.404607i | \(-0.132592\pi\) |
−0.404607 | + | 0.914491i | \(0.632592\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 35.3203 | − | 35.3203i | 2.00930 | − | 2.00930i | ||||
\(310\) | 3.25768 | − | 22.1834i | 0.185024 | − | 1.25993i | ||||
\(311\) | −17.1245 | − | 9.88684i | −0.971042 | − | 0.560631i | −0.0714882 | − | 0.997441i | \(-0.522775\pi\) |
−0.899554 | + | 0.436810i | \(0.856108\pi\) | |||||||
\(312\) | −2.28727 | + | 12.8890i | −0.129491 | + | 0.729697i | ||||
\(313\) | 7.55817 | − | 4.36371i | 0.427213 | − | 0.246652i | −0.270945 | − | 0.962595i | \(-0.587336\pi\) |
0.698159 | + | 0.715943i | \(0.254003\pi\) | |||||||
\(314\) | −6.97122 | + | 8.80992i | −0.393409 | + | 0.497173i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.46389 | − | 0.818280i | 0.194859 | − | 0.0460319i | ||||
\(317\) | 6.96171 | − | 25.9814i | 0.391008 | − | 1.45926i | −0.437465 | − | 0.899235i | \(-0.644124\pi\) |
0.828474 | − | 0.560028i | \(-0.189210\pi\) | |||||||
\(318\) | 3.60575 | + | 1.55693i | 0.202200 | + | 0.0873084i | ||||
\(319\) | −3.77105 | + | 6.53166i | −0.211138 | + | 0.365703i | ||||
\(320\) | −27.9972 | + | 12.9806i | −1.56509 | + | 0.725636i | ||||
\(321\) | 16.8569 | 0.940858 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.20702 | − | 2.20702i | −0.122802 | − | 0.122802i | ||||
\(324\) | −5.92600 | − | 6.29040i | −0.329222 | − | 0.349467i | ||||
\(325\) | 4.07238 | + | 15.1983i | 0.225895 | + | 0.843051i | ||||
\(326\) | 4.66068 | + | 11.7442i | 0.258131 | + | 0.650448i | ||||
\(327\) | −11.6516 | + | 6.72705i | −0.644335 | + | 0.372007i | ||||
\(328\) | −19.8231 | + | 7.19038i | −1.09455 | + | 0.397022i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −16.1692 | − | 12.7946i | −0.890086 | − | 0.704318i | ||||
\(331\) | −30.5071 | − | 8.17436i | −1.67682 | − | 0.449303i | −0.709885 | − | 0.704317i | \(-0.751253\pi\) |
−0.966937 | + | 0.255014i | \(0.917920\pi\) | |||||||
\(332\) | 17.8358 | − | 9.60012i | 0.978865 | − | 0.526875i | ||||
\(333\) | 12.3097 | − | 3.29838i | 0.674568 | − | 0.180750i | ||||
\(334\) | −9.97506 | − | 13.4091i | −0.545811 | − | 0.733712i | ||||
\(335\) | 8.32703 | 0.454954 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.4825 | −1.27918 | −0.639588 | − | 0.768718i | \(-0.720895\pi\) | ||||
−0.639588 | + | 0.768718i | \(0.720895\pi\) | |||||||
\(338\) | −8.83254 | − | 11.8732i | −0.480427 | − | 0.645818i | ||||
\(339\) | 25.7472 | − | 6.89895i | 1.39840 | − | 0.374699i | ||||
\(340\) | 5.51722 | + | 10.2503i | 0.299214 | + | 0.555899i | ||||
\(341\) | 5.16305 | + | 1.38343i | 0.279595 | + | 0.0749172i | ||||
\(342\) | 12.4936 | + | 9.88612i | 0.675579 | + | 0.534580i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −20.6167 | − | 9.64129i | −1.11158 | − | 0.519824i | ||||
\(345\) | −46.3136 | + | 26.7392i | −2.49344 | + | 1.43959i | ||||
\(346\) | 4.15977 | + | 10.4819i | 0.223630 | + | 0.563512i | ||||
\(347\) | −2.30492 | − | 8.60207i | −0.123735 | − | 0.461784i | 0.876057 | − | 0.482208i | \(-0.160165\pi\) |
−0.999791 | + | 0.0204242i | \(0.993498\pi\) | |||||||
\(348\) | −24.5349 | + | 23.1136i | −1.31521 | + | 1.23902i | ||||
\(349\) | −6.94033 | − | 6.94033i | −0.371507 | − | 0.371507i | 0.496519 | − | 0.868026i | \(-0.334611\pi\) |
−0.868026 | + | 0.496519i | \(0.834611\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.3206 | −0.604246 | ||||||||
\(352\) | −2.30130 | − | 6.98773i | −0.122660 | − | 0.372447i | ||||
\(353\) | 15.0467 | − | 26.0617i | 0.800856 | − | 1.38712i | −0.118198 | − | 0.992990i | \(-0.537712\pi\) |
0.919054 | − | 0.394133i | \(-0.128955\pi\) | |||||||
\(354\) | 6.07488 | + | 2.62308i | 0.322876 | + | 0.139415i | ||||
\(355\) | −13.7980 | + | 51.4949i | −0.732323 | + | 2.73307i | ||||
\(356\) | −3.88951 | − | 16.4648i | −0.206144 | − | 0.872633i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.5547 | + | 18.3936i | −0.769239 | + | 0.972131i | ||||
\(359\) | −8.98209 | + | 5.18581i | −0.474057 | + | 0.273697i | −0.717936 | − | 0.696109i | \(-0.754913\pi\) |
0.243880 | + | 0.969806i | \(0.421580\pi\) | |||||||
\(360\) | −34.0283 | − | 48.7111i | −1.79345 | − | 2.56730i | ||||
\(361\) | 12.7487 | + | 7.36047i | 0.670985 | + | 0.387393i | ||||
\(362\) | 1.21632 | − | 8.28265i | 0.0639286 | − | 0.435326i | ||||
\(363\) | −19.1292 | + | 19.1292i | −1.00402 | + | 1.00402i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −39.4826 | − | 39.4826i | −2.06661 | − | 2.06661i | ||||
\(366\) | 11.1668 | + | 15.0110i | 0.583697 | + | 0.784640i | ||||
\(367\) | −4.06486 | + | 7.04055i | −0.212184 | + | 0.367514i | −0.952398 | − | 0.304858i | \(-0.901391\pi\) |
0.740214 | + | 0.672372i | \(0.234724\pi\) | |||||||
\(368\) | −19.0473 | − | 1.13735i | −0.992909 | − | 0.0592883i | ||||
\(369\) | −20.3009 | − | 35.1622i | −1.05682 | − | 1.83047i | ||||
\(370\) | 12.6800 | − | 1.47737i | 0.659200 | − | 0.0768050i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 20.3231 | + | 12.5560i | 1.05370 | + | 0.650999i | ||||
\(373\) | 4.35336 | + | 1.16648i | 0.225408 | + | 0.0603980i | 0.369755 | − | 0.929129i | \(-0.379441\pi\) |
−0.144347 | + | 0.989527i | \(0.546108\pi\) | |||||||
\(374\) | −2.57943 | + | 1.02365i | −0.133379 | + | 0.0529317i | ||||
\(375\) | −47.3815 | − | 27.3557i | −2.44677 | − | 1.41264i | ||||
\(376\) | 6.54905 | − | 7.78748i | 0.337742 | − | 0.401609i | ||||
\(377\) | 9.23534i | 0.475644i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.839080 | + | 0.839080i | −0.0431006 | + | 0.0431006i | −0.728329 | − | 0.685228i | \(-0.759703\pi\) |
0.685228 | + | 0.728329i | \(0.259703\pi\) | |||||||
\(380\) | 10.9433 | + | 11.6163i | 0.561382 | + | 0.595903i | ||||
\(381\) | 36.4334 | − | 9.76231i | 1.86654 | − | 0.500138i | ||||
\(382\) | −16.0575 | − | 6.93350i | −0.821573 | − | 0.354749i | ||||
\(383\) | −17.1874 | − | 29.7695i | −0.878237 | − | 1.52115i | −0.853274 | − | 0.521463i | \(-0.825386\pi\) |
−0.0249634 | − | 0.999688i | \(-0.507947\pi\) | |||||||
\(384\) | −0.872140 | − | 32.8684i | −0.0445062 | − | 1.67731i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.87623 | + | 33.2688i | 0.197295 | + | 1.69334i | ||||
\(387\) | 11.3422 | − | 42.3296i | 0.576556 | − | 2.15173i | ||||
\(388\) | −9.32820 | + | 31.0756i | −0.473568 | + | 1.57762i | ||||
\(389\) | 4.01283 | + | 14.9761i | 0.203459 | + | 0.759319i | 0.989914 | + | 0.141671i | \(0.0452475\pi\) |
−0.786455 | + | 0.617648i | \(0.788086\pi\) | |||||||
\(390\) | −24.9802 | − | 3.66839i | −1.26492 | − | 0.185756i | ||||
\(391\) | 7.19768i | 0.364003i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 28.0287i | 1.41386i | ||||||||
\(394\) | −3.31837 | + | 22.5967i | −0.167177 | + | 1.13840i | ||||
\(395\) | 1.77676 | + | 6.63094i | 0.0893983 | + | 0.333639i | ||||
\(396\) | 12.4734 | − | 6.71381i | 0.626810 | − | 0.337381i | ||||
\(397\) | −9.67679 | + | 36.1143i | −0.485664 | + | 1.81252i | 0.0913869 | + | 0.995815i | \(0.470870\pi\) |
−0.577051 | + | 0.816708i | \(0.695797\pi\) | |||||||
\(398\) | −7.72146 | + | 0.899646i | −0.387042 | + | 0.0450952i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −17.6854 | − | 35.3433i | −0.884269 | − | 1.76717i | ||||
\(401\) | −2.48812 | − | 4.30956i | −0.124251 | − | 0.215209i | 0.797189 | − | 0.603730i | \(-0.206319\pi\) |
−0.921440 | + | 0.388521i | \(0.872986\pi\) | |||||||
\(402\) | −3.51703 | + | 8.14520i | −0.175414 | + | 0.406246i | ||||
\(403\) | 6.32217 | − | 1.69402i | 0.314930 | − | 0.0843852i | ||||
\(404\) | 32.7003 | + | 0.975427i | 1.62690 | + | 0.0485293i | ||||
\(405\) | 11.7864 | − | 11.7864i | 0.585672 | − | 0.585672i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.04331i | 0.150851i | ||||||||
\(408\) | −12.3567 | + | 1.06741i | −0.611749 | + | 0.0528447i | ||||
\(409\) | −3.51917 | − | 2.03180i | −0.174012 | − | 0.100466i | 0.410464 | − | 0.911877i | \(-0.365367\pi\) |
−0.584476 | + | 0.811411i | \(0.698700\pi\) | |||||||
\(410\) | −15.0022 | − | 37.8032i | −0.740908 | − | 1.86697i | ||||
\(411\) | 63.5945 | + | 17.0401i | 3.13689 | + | 0.840526i | ||||
\(412\) | 7.90295 | + | 33.4542i | 0.389350 | + | 1.64817i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.25192 | − | 36.4932i | −0.208970 | − | 1.79354i | ||||
\(415\) | 19.5337 | + | 33.8334i | 0.958871 | + | 1.66081i | ||||
\(416\) | −6.71867 | − | 6.00117i | −0.329410 | − | 0.294232i | ||||
\(417\) | −13.6601 | + | 23.6600i | −0.668940 | + | 1.15864i | ||||
\(418\) | −3.05260 | + | 2.27084i | −0.149308 | + | 0.111070i | ||||
\(419\) | −0.552238 | − | 0.552238i | −0.0269786 | − | 0.0269786i | 0.693489 | − | 0.720467i | \(-0.256073\pi\) |
−0.720467 | + | 0.693489i | \(0.756073\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.77763 | + | 3.77763i | −0.184110 | + | 0.184110i | −0.793144 | − | 0.609034i | \(-0.791557\pi\) |
0.609034 | + | 0.793144i | \(0.291557\pi\) | |||||||
\(422\) | 1.79648 | + | 0.263817i | 0.0874513 | + | 0.0128424i | ||||
\(423\) | 16.9671 | + | 9.79598i | 0.824970 | + | 0.476297i | ||||
\(424\) | −2.21575 | + | 1.54786i | −0.107606 | + | 0.0751709i | ||||
\(425\) | −12.9106 | + | 7.45395i | −0.626257 | + | 0.361570i | ||||
\(426\) | −44.5427 | − | 35.2463i | −2.15810 | − | 1.70769i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.09727 | + | 9.86901i | −0.294723 | + | 0.477037i | ||||
\(429\) | 1.55785 | − | 5.81397i | 0.0752136 | − | 0.280701i | ||||
\(430\) | 17.4017 | − | 40.3012i | 0.839187 | − | 1.94350i | ||||
\(431\) | −0.590931 | + | 1.02352i | −0.0284641 | + | 0.0493013i | −0.879907 | − | 0.475147i | \(-0.842395\pi\) |
0.851442 | + | 0.524448i | \(0.175728\pi\) | |||||||
\(432\) | 27.8555 | − | 5.70921i | 1.34020 | − | 0.274684i | ||||
\(433\) | 15.2584 | 0.733273 | 0.366637 | − | 0.930364i | \(-0.380509\pi\) | ||||
0.366637 | + | 0.930364i | \(0.380509\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −45.9715 | − | 45.9715i | −2.20416 | − | 2.20416i | ||||
\(436\) | 0.276063 | − | 9.25477i | 0.0132210 | − | 0.443223i | ||||
\(437\) | 2.55398 | + | 9.53156i | 0.122173 | + | 0.455957i | ||||
\(438\) | 55.2964 | − | 21.9445i | 2.64217 | − | 1.04855i | ||||
\(439\) | 3.76290 | − | 2.17251i | 0.179593 | − | 0.103688i | −0.407508 | − | 0.913202i | \(-0.633602\pi\) |
0.587102 | + | 0.809513i | \(0.300269\pi\) | |||||||
\(440\) | 13.3392 | − | 4.83851i | 0.635923 | − | 0.230667i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.10863 | + | 2.66479i | −0.100297 | + | 0.126751i | ||||
\(443\) | 5.89293 | + | 1.57901i | 0.279981 | + | 0.0750208i | 0.396077 | − | 0.918217i | \(-0.370371\pi\) |
−0.116096 | + | 0.993238i | \(0.537038\pi\) | |||||||
\(444\) | −3.91044 | + | 13.0271i | −0.185581 | + | 0.618237i | ||||
\(445\) | 31.5187 | − | 8.44540i | 1.49413 | − | 0.400351i | ||||
\(446\) | 3.63459 | − | 2.70379i | 0.172103 | − | 0.128028i | ||||
\(447\) | 31.9359 | 1.51052 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.72499 | 0.175793 | 0.0878967 | − | 0.996130i | \(-0.471985\pi\) | ||||
0.0878967 | + | 0.996130i | \(0.471985\pi\) | |||||||
\(450\) | 61.0553 | − | 45.4193i | 2.87818 | − | 2.14109i | ||||
\(451\) | 9.36552 | − | 2.50948i | 0.441005 | − | 0.118167i | ||||
\(452\) | −5.27393 | + | 17.5694i | −0.248065 | + | 0.826393i | ||||
\(453\) | −15.3505 | − | 4.11315i | −0.721228 | − | 0.193252i | ||||
\(454\) | −17.1178 | + | 21.6328i | −0.803380 | + | 1.01528i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15.9847 | + | 5.79809i | −0.748552 | + | 0.271521i | ||||
\(457\) | −9.30556 | + | 5.37257i | −0.435296 | + | 0.251318i | −0.701600 | − | 0.712571i | \(-0.747531\pi\) |
0.266304 | + | 0.963889i | \(0.414197\pi\) | |||||||
\(458\) | 13.0532 | − | 5.18019i | 0.609937 | − | 0.242054i | ||||
\(459\) | −2.77606 | − | 10.3604i | −0.129575 | − | 0.483582i | ||||
\(460\) | 1.09732 | − | 36.7865i | 0.0511626 | − | 1.71518i | ||||
\(461\) | −7.88785 | − | 7.88785i | −0.367374 | − | 0.367374i | 0.499145 | − | 0.866519i | \(-0.333648\pi\) |
−0.866519 | + | 0.499145i | \(0.833648\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.3485 | 1.27099 | 0.635496 | − | 0.772104i | \(-0.280796\pi\) | ||||
0.635496 | + | 0.772104i | \(0.280796\pi\) | |||||||
\(464\) | −4.65759 | − | 22.7246i | −0.216223 | − | 1.05496i | ||||
\(465\) | −23.0379 | + | 39.9028i | −1.06836 | + | 1.85045i | ||||
\(466\) | −1.64741 | + | 3.81529i | −0.0763148 | + | 0.176740i | ||||
\(467\) | −4.16957 | + | 15.5610i | −0.192945 | + | 0.720079i | 0.799845 | + | 0.600207i | \(0.204915\pi\) |
−0.992789 | + | 0.119872i | \(0.961752\pi\) | |||||||
\(468\) | 9.11686 | − | 14.7565i | 0.421427 | − | 0.682120i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 15.3900 | + | 12.1780i | 0.709890 | + | 0.561730i | ||||
\(471\) | 19.9937 | − | 11.5434i | 0.921261 | − | 0.531890i | ||||
\(472\) | −3.73304 | + | 2.60781i | −0.171827 | + | 0.120034i | ||||
\(473\) | 9.06303 | + | 5.23254i | 0.416718 | + | 0.240592i | ||||
\(474\) | −7.23658 | − | 1.06271i | −0.332387 | − | 0.0488118i | ||||
\(475\) | −14.4520 | + | 14.4520i | −0.663105 | + | 0.663105i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.67995 | − | 3.67995i | −0.168493 | − | 0.168493i | ||||
\(478\) | 18.3942 | − | 13.6835i | 0.841330 | − | 0.625869i | ||||
\(479\) | 5.69399 | − | 9.86229i | 0.260165 | − | 0.450619i | −0.706120 | − | 0.708092i | \(-0.749556\pi\) |
0.966286 | + | 0.257472i | \(0.0828896\pi\) | |||||||
\(480\) | 63.3165 | − | 3.57158i | 2.88999 | − | 0.163019i | ||||
\(481\) | 1.86327 | + | 3.22729i | 0.0849580 | + | 0.147152i | ||||
\(482\) | 2.31041 | + | 19.8297i | 0.105236 | + | 0.903219i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.28017 | − | 18.1185i | −0.194553 | − | 0.823570i | ||||
\(485\) | −60.4468 | − | 16.1967i | −2.74475 | − | 0.735453i | ||||
\(486\) | −4.57387 | − | 11.5254i | −0.207475 | − | 0.522802i | ||||
\(487\) | −27.1526 | − | 15.6766i | −1.23040 | − | 0.710373i | −0.263288 | − | 0.964717i | \(-0.584807\pi\) |
−0.967114 | + | 0.254344i | \(0.918140\pi\) | |||||||
\(488\) | −12.8275 | + | 1.10807i | −0.580673 | + | 0.0501602i | ||||
\(489\) | − | 25.9652i | − | 1.17419i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.2775 | − | 20.2775i | 0.915112 | − | 0.915112i | −0.0815572 | − | 0.996669i | \(-0.525989\pi\) |
0.996669 | + | 0.0815572i | \(0.0259893\pi\) | |||||||
\(492\) | 43.3141 | + | 1.29203i | 1.95275 | + | 0.0582492i | ||||
\(493\) | −8.45204 | + | 2.26472i | −0.380661 | + | 0.101998i | ||||
\(494\) | −1.84681 | + | 4.27708i | −0.0830918 | + | 0.192435i | ||||
\(495\) | 13.6608 | + | 23.6612i | 0.614008 | + | 1.06349i | ||||
\(496\) | −14.7021 | + | 7.35674i | −0.660143 | + | 0.330327i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −41.3449 | + | 4.81719i | −1.85271 | + | 0.215864i | ||||
\(499\) | −6.77758 | + | 25.2943i | −0.303406 | + | 1.13233i | 0.630902 | + | 0.775862i | \(0.282685\pi\) |
−0.934309 | + | 0.356465i | \(0.883982\pi\) | |||||||
\(500\) | 33.1540 | − | 17.8452i | 1.48269 | − | 0.798060i | ||||
\(501\) | 8.88887 | + | 33.1737i | 0.397126 | + | 1.48209i | ||||
\(502\) | 4.12540 | − | 28.0922i | 0.184126 | − | 1.25382i | ||||
\(503\) | − | 31.9854i | − | 1.42616i | −0.701082 | − | 0.713080i | \(-0.747299\pi\) | ||
0.701082 | − | 0.713080i | \(-0.252701\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 63.0987i | 2.80786i | ||||||||
\(506\) | 8.68059 | + | 1.27476i | 0.385899 | + | 0.0566702i | ||||
\(507\) | 7.87076 | + | 29.3741i | 0.349553 | + | 1.30455i | ||||
\(508\) | −7.46284 | + | 24.8614i | −0.331110 | + | 1.10305i | ||||
\(509\) | −4.45247 | + | 16.6168i | −0.197352 | + | 0.736529i | 0.794293 | + | 0.607535i | \(0.207841\pi\) |
−0.991645 | + | 0.128994i | \(0.958825\pi\) | |||||||
\(510\) | −2.76846 | − | 23.7610i | −0.122589 | − | 1.05216i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 19.5586 | + | 11.3782i | 0.864375 | + | 0.502849i | ||||
\(513\) | −7.35242 | − | 12.7348i | −0.324617 | − | 0.562254i | ||||
\(514\) | −4.20248 | − | 1.81460i | −0.185363 | − | 0.0800384i | ||||
\(515\) | −64.0417 | + | 17.1599i | −2.82201 | + | 0.756156i | ||||
\(516\) | 32.0714 | + | 34.0435i | 1.41186 | + | 1.49868i | ||||
\(517\) | −3.30830 | + | 3.30830i | −0.145499 | + | 0.145499i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 23.1745i | − | 1.01725i | ||||||
\(520\) | 11.1832 | − | 13.2980i | 0.490417 | − | 0.583155i | ||||
\(521\) | 29.8192 | + | 17.2161i | 1.30640 | + | 0.754251i | 0.981494 | − | 0.191495i | \(-0.0613336\pi\) |
0.324907 | + | 0.945746i | \(0.394667\pi\) | |||||||
\(522\) | 41.5152 | − | 16.4753i | 1.81707 | − | 0.721106i | ||||
\(523\) | −21.0410 | − | 5.63792i | −0.920060 | − | 0.246529i | −0.232449 | − | 0.972609i | \(-0.574674\pi\) |
−0.687611 | + | 0.726079i | \(0.741340\pi\) | |||||||
\(524\) | −16.4097 | − | 10.1382i | −0.716861 | − | 0.442890i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 33.7357 | − | 3.93062i | 1.47094 | − | 0.171383i | ||||
\(527\) | 3.10069 | + | 5.37054i | 0.135068 | + | 0.233945i | ||||
\(528\) | −0.901144 | + | 15.0916i | −0.0392173 | + | 0.656776i | ||||
\(529\) | −0.122092 | + | 0.211469i | −0.00530834 | + | 0.00919432i | ||||
\(530\) | −3.11154 | − | 4.18271i | −0.135157 | − | 0.181685i | ||||
\(531\) | −6.19990 | − | 6.19990i | −0.269053 | − | 0.269053i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.39524 | − | 8.39524i | 0.363638 | − | 0.363638i | ||||
\(534\) | −5.05134 | + | 34.3975i | −0.218593 | + | 1.48852i | ||||
\(535\) | −19.3770 | − | 11.1873i | −0.837742 | − | 0.483670i | ||||
\(536\) | −3.49655 | − | 5.00527i | −0.151028 | − | 0.216195i | ||||
\(537\) | 41.7433 | − | 24.1005i | 1.80136 | − | 1.04001i | ||||
\(538\) | −0.108596 | + | 0.137239i | −0.00468192 | + | 0.00591681i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 12.6086 | + | 53.3740i | 0.542589 | + | 2.29685i | ||||
\(541\) | −8.68080 | + | 32.3972i | −0.373217 | + | 1.39286i | 0.482716 | + | 0.875777i | \(0.339650\pi\) |
−0.855933 | + | 0.517087i | \(0.827016\pi\) | |||||||
\(542\) | −13.1313 | − | 5.66998i | −0.564037 | − | 0.243547i | ||||
\(543\) | −8.60168 | + | 14.8985i | −0.369133 | + | 0.639358i | ||||
\(544\) | 3.84461 | − | 7.62045i | 0.164836 | − | 0.326724i | ||||
\(545\) | 17.8581 | 0.764956 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.8819 | + | 27.8819i | 1.19214 | + | 1.19214i | 0.976464 | + | 0.215680i | \(0.0691967\pi\) |
0.215680 | + | 0.976464i | \(0.430803\pi\) | |||||||
\(548\) | −32.9790 | + | 31.0685i | −1.40879 | + | 1.32718i | ||||
\(549\) | −6.41632 | − | 23.9460i | −0.273842 | − | 1.02199i | ||||
\(550\) | 6.70309 | + | 16.8907i | 0.285821 | + | 0.720222i | ||||
\(551\) | −10.3891 | + | 5.99813i | −0.442589 | + | 0.255529i | ||||
\(552\) | 35.5198 | + | 16.6106i | 1.51182 | + | 0.706995i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −17.2647 | − | 13.6614i | −0.733506 | − | 0.580418i | ||||
\(555\) | −25.3397 | − | 6.78974i | −1.07561 | − | 0.288208i | ||||
\(556\) | −8.91102 | − | 16.5555i | −0.377911 | − | 0.702109i | ||||
\(557\) | −0.376946 | + | 0.101002i | −0.0159717 | + | 0.00427960i | −0.266796 | − | 0.963753i | \(-0.585965\pi\) |
0.250824 | + | 0.968033i | \(0.419298\pi\) | |||||||
\(558\) | −18.8935 | − | 25.3977i | −0.799824 | − | 1.07517i | ||||
\(559\) | 12.8145 | 0.541997 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.70288 | 0.240776 | ||||||||
\(562\) | 3.56207 | + | 4.78834i | 0.150257 | + | 0.201984i | ||||
\(563\) | −18.9755 | + | 5.08448i | −0.799724 | + | 0.214285i | −0.635463 | − | 0.772132i | \(-0.719191\pi\) |
−0.164261 | + | 0.986417i | \(0.552524\pi\) | |||||||
\(564\) | −18.4123 | + | 9.91044i | −0.775297 | + | 0.417305i | ||||
\(565\) | −34.1751 | − | 9.15720i | −1.43776 | − | 0.385246i | ||||
\(566\) | 26.0090 | + | 20.5807i | 1.09324 | + | 0.865073i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 36.7467 | − | 13.3291i | 1.54186 | − | 0.559275i | ||||
\(569\) | 6.99814 | − | 4.04038i | 0.293377 | − | 0.169381i | −0.346087 | − | 0.938203i | \(-0.612490\pi\) |
0.639464 | + | 0.768821i | \(0.279156\pi\) | |||||||
\(570\) | −12.0973 | − | 30.4833i | −0.506702 | − | 1.27681i | ||||
\(571\) | −2.76648 | − | 10.3246i | −0.115774 | − | 0.432073i | 0.883570 | − | 0.468299i | \(-0.155133\pi\) |
−0.999344 | + | 0.0362262i | \(0.988466\pi\) | |||||||
\(572\) | 2.84036 | + | 3.01502i | 0.118761 | + | 0.126064i | ||||
\(573\) | 25.4154 | + | 25.4154i | 1.06175 | + | 1.06175i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 47.1320 | 1.96554 | ||||||||
\(576\) | −14.9910 | + | 40.9079i | −0.624626 | + | 1.70449i | ||||
\(577\) | 0.979847 | − | 1.69714i | 0.0407915 | − | 0.0706530i | −0.844909 | − | 0.534910i | \(-0.820345\pi\) |
0.885700 | + | 0.464257i | \(0.153679\pi\) | |||||||
\(578\) | 19.1161 | + | 8.25416i | 0.795123 | + | 0.343328i | ||||
\(579\) | 17.8144 | − | 66.4844i | 0.740343 | − | 2.76300i | ||||
\(580\) | 43.5427 | − | 10.2862i | 1.80801 | − | 0.427110i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 41.3735 | − | 52.2860i | 1.71499 | − | 2.16733i | ||||
\(583\) | 1.07629 | − | 0.621397i | 0.0445754 | − | 0.0257356i | ||||
\(584\) | −7.15360 | + | 40.3113i | −0.296018 | + | 1.66809i | ||||
\(585\) | 28.9733 | + | 16.7277i | 1.19790 | + | 0.691606i | ||||
\(586\) | 3.92997 | − | 26.7614i | 0.162346 | − | 1.10550i | ||||
\(587\) | −24.6131 | + | 24.6131i | −1.01589 | + | 1.01589i | −0.0160192 | + | 0.999872i | \(0.505099\pi\) |
−0.999872 | + | 0.0160192i | \(0.994901\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.01174 | + | 6.01174i | 0.247709 | + | 0.247709i | ||||
\(590\) | −5.24225 | − | 7.04694i | −0.215820 | − | 0.290118i | ||||
\(591\) | 23.4670 | − | 40.6461i | 0.965305 | − | 1.67196i | ||||
\(592\) | −6.21238 | − | 7.00140i | −0.255327 | − | 0.287756i | ||||
\(593\) | 8.27415 | + | 14.3313i | 0.339779 | + | 0.588514i | 0.984391 | − | 0.175996i | \(-0.0563144\pi\) |
−0.644612 | + | 0.764510i | \(0.722981\pi\) | |||||||
\(594\) | −12.9866 | + | 1.51310i | −0.532845 | + | 0.0620831i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.5515 | + | 18.6972i | −0.473167 | + | 0.765866i | ||||
\(597\) | 15.4306 | + | 4.13461i | 0.631531 | + | 0.169218i | ||||
\(598\) | 9.98583 | − | 3.96289i | 0.408351 | − | 0.162054i | ||||
\(599\) | 8.88965 | + | 5.13244i | 0.363221 | + | 0.209706i | 0.670493 | − | 0.741916i | \(-0.266083\pi\) |
−0.307272 | + | 0.951622i | \(0.599416\pi\) | |||||||
\(600\) | 6.98964 | + | 80.9146i | 0.285351 | + | 3.30332i | ||||
\(601\) | 35.6586i | 1.45455i | 0.686348 | + | 0.727273i | \(0.259213\pi\) | ||||
−0.686348 | + | 0.727273i | \(0.740787\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.31283 | − | 8.31283i | 0.338524 | − | 0.338524i | ||||
\(604\) | 7.96048 | − | 7.49932i | 0.323907 | − | 0.305143i | ||||
\(605\) | 34.6844 | − | 9.29367i | 1.41012 | − | 0.377841i | ||||
\(606\) | −61.7209 | − | 26.6506i | −2.50724 | − | 1.08261i | ||||
\(607\) | 11.5556 | + | 20.0148i | 0.469026 | + | 0.812377i | 0.999373 | − | 0.0354040i | \(-0.0112718\pi\) |
−0.530347 | + | 0.847780i | \(0.677938\pi\) | |||||||
\(608\) | 2.38725 | − | 11.4556i | 0.0968157 | − | 0.464586i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.87393 | − | 24.6663i | −0.116362 | − | 0.998708i | ||||
\(611\) | −1.48278 | + | 5.53381i | −0.0599868 | + | 0.223874i | ||||
\(612\) | 15.7406 | + | 4.72498i | 0.636276 | + | 0.190996i | ||||
\(613\) | −9.85340 | − | 36.7734i | −0.397975 | − | 1.48526i | −0.816653 | − | 0.577129i | \(-0.804173\pi\) |
0.418678 | − | 0.908135i | \(-0.362493\pi\) | |||||||
\(614\) | 17.6782 | + | 2.59608i | 0.713433 | + | 0.104769i | ||||
\(615\) | 83.5793i | 3.37024i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 47.9337i | − | 1.92974i | −0.262732 | − | 0.964869i | \(-0.584623\pi\) | ||
0.262732 | − | 0.964869i | \(-0.415377\pi\) | |||||||
\(618\) | 10.2636 | − | 69.8909i | 0.412864 | − | 2.81143i | ||||
\(619\) | −1.48260 | − | 5.53313i | −0.0595906 | − | 0.222395i | 0.929709 | − | 0.368296i | \(-0.120059\pi\) |
−0.989299 | + | 0.145901i | \(0.953392\pi\) | |||||||
\(620\) | −15.0285 | − | 27.9209i | −0.603558 | − | 1.12133i | ||||
\(621\) | −8.77664 | + | 32.7549i | −0.352195 | + | 1.31441i | ||||
\(622\) | −27.7763 | + | 3.23629i | −1.11373 | + | 0.129763i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8.28423 | + | 16.5556i | 0.331634 | + | 0.662755i | ||||
\(625\) | 11.6094 | + | 20.1081i | 0.464376 | + | 0.804323i | ||||
\(626\) | 4.89274 | − | 11.3312i | 0.195553 | − | 0.452888i | ||||
\(627\) | 7.55206 | − | 2.02357i | 0.301600 | − | 0.0808135i | ||||
\(628\) | −0.473714 | + | 15.8808i | −0.0189033 | + | 0.633714i | ||||
\(629\) | −2.49664 | + | 2.49664i | −0.0995477 | + | 0.0995477i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.35784i | − | 0.0938640i | −0.998898 | − | 0.0469320i | \(-0.985056\pi\) | ||
0.998898 | − | 0.0469320i | \(-0.0149444\pi\) | |||||||
\(632\) | 3.23971 | − | 3.85234i | 0.128869 | − | 0.153238i | ||||
\(633\) | −3.23145 | − | 1.86568i | −0.128439 | − | 0.0741541i | ||||
\(634\) | −14.0315 | − | 35.3570i | −0.557261 | − | 1.40421i | ||||
\(635\) | −48.3593 | − | 12.9578i | −1.91908 | − | 0.514216i | ||||
\(636\) | 5.40558 | − | 1.27697i | 0.214345 | − | 0.0506351i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.23439 | + | 10.5945i | 0.0488699 | + | 0.419440i | ||||
\(639\) | 37.6326 | + | 65.1815i | 1.48872 | + | 2.57854i | ||||
\(640\) | −20.8111 | + | 38.3611i | −0.822631 | + | 1.51636i | ||||
\(641\) | 24.9208 | − | 43.1640i | 0.984311 | − | 1.70488i | 0.339354 | − | 0.940659i | \(-0.389791\pi\) |
0.644957 | − | 0.764219i | \(-0.276875\pi\) | |||||||
\(642\) | 19.1272 | − | 14.2288i | 0.754890 | − | 0.561565i | ||||
\(643\) | 6.07975 | + | 6.07975i | 0.239762 | + | 0.239762i | 0.816751 | − | 0.576990i | \(-0.195773\pi\) |
−0.576990 | + | 0.816751i | \(0.695773\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −63.7879 | + | 63.7879i | −2.51165 | + | 2.51165i | ||||
\(646\) | −4.36720 | − | 0.641332i | −0.171825 | − | 0.0252329i | ||||
\(647\) | 0.401199 | + | 0.231632i | 0.0157727 | + | 0.00910640i | 0.507866 | − | 0.861436i | \(-0.330435\pi\) |
−0.492093 | + | 0.870543i | \(0.663768\pi\) | |||||||
\(648\) | −12.0338 | − | 2.13551i | −0.472733 | − | 0.0838907i | ||||
\(649\) | 1.81331 | − | 1.04692i | 0.0711787 | − | 0.0410950i | ||||
\(650\) | 17.4497 | + | 13.8078i | 0.684432 | + | 0.541586i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.2016 | + | 9.39183i | 0.595339 | + | 0.367812i | ||||
\(653\) | 2.42919 | − | 9.06587i | 0.0950617 | − | 0.354775i | −0.901967 | − | 0.431805i | \(-0.857877\pi\) |
0.997029 | + | 0.0770297i | \(0.0245436\pi\) | |||||||
\(654\) | −7.54259 | + | 17.4681i | −0.294939 | + | 0.683057i | ||||
\(655\) | 18.6017 | − | 32.2191i | 0.726829 | − | 1.25891i | ||||
\(656\) | −16.4235 | + | 24.8913i | −0.641231 | + | 0.971843i | ||||
\(657\) | −78.8305 | −3.07547 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.62922 | − | 4.62922i | −0.180329 | − | 0.180329i | 0.611170 | − | 0.791499i | \(-0.290699\pi\) |
−0.791499 | + | 0.611170i | \(0.790699\pi\) | |||||||
\(660\) | −29.1467 | − | 0.869427i | −1.13454 | − | 0.0338424i | ||||
\(661\) | 0.826161 | + | 3.08328i | 0.0321339 | + | 0.119926i | 0.980130 | − | 0.198357i | \(-0.0635606\pi\) |
−0.947996 | + | 0.318283i | \(0.896894\pi\) | |||||||
\(662\) | −41.5158 | + | 16.4756i | −1.61356 | + | 0.640342i | ||||
\(663\) | 6.04763 | − | 3.49160i | 0.234870 | − | 0.135602i | ||||
\(664\) | 12.1345 | − | 25.9482i | 0.470911 | − | 1.00698i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.1835 | − | 14.1332i | 0.433351 | − | 0.547650i | ||||
\(667\) | 26.7215 | + | 7.16001i | 1.03466 | + | 0.277237i | ||||
\(668\) | −22.6371 | − | 6.79514i | −0.875854 | − | 0.262912i | ||||
\(669\) | −8.99190 | + | 2.40937i | −0.347647 | + | 0.0931517i | ||||
\(670\) | 9.44854 | − | 7.02881i | 0.365029 | − | 0.271546i | ||||
\(671\) | 5.92014 | 0.228544 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.82222 | 0.262977 | 0.131489 | − | 0.991318i | \(-0.458024\pi\) | ||||
0.131489 | + | 0.991318i | \(0.458024\pi\) | |||||||
\(674\) | −26.6452 | + | 19.8215i | −1.02634 | + | 0.763495i | ||||
\(675\) | −67.8422 | + | 18.1783i | −2.61125 | + | 0.699682i | ||||
\(676\) | −20.0443 | − | 6.01684i | −0.770933 | − | 0.231417i | ||||
\(677\) | 6.52747 | + | 1.74903i | 0.250871 | + | 0.0672207i | 0.382063 | − | 0.924136i | \(-0.375214\pi\) |
−0.131192 | + | 0.991357i | \(0.541880\pi\) | |||||||
\(678\) | 23.3916 | − | 29.5612i | 0.898347 | − | 1.13529i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 14.9125 | + | 6.97375i | 0.571868 | + | 0.267431i | ||||
\(681\) | 49.0946 | − | 28.3448i | 1.88131 | − | 1.08617i | ||||
\(682\) | 7.02617 | − | 2.78834i | 0.269046 | − | 0.106771i | ||||
\(683\) | −10.7149 | − | 39.9884i | −0.409993 | − | 1.53012i | −0.794657 | − | 0.607059i | \(-0.792349\pi\) |
0.384664 | − | 0.923057i | \(-0.374317\pi\) | |||||||
\(684\) | 22.5211 | + | 0.671790i | 0.861117 | + | 0.0256865i | ||||
\(685\) | −61.7932 | − | 61.7932i | −2.36100 | − | 2.36100i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.8594 | −1.10106 | ||||||||
\(688\) | −31.5316 | + | 6.46266i | −1.20213 | + | 0.246386i | ||||
\(689\) | 0.760903 | − | 1.31792i | 0.0289881 | − | 0.0502089i | ||||
\(690\) | −29.9808 | + | 69.4336i | −1.14135 | + | 2.64329i | ||||
\(691\) | 1.70225 | − | 6.35289i | 0.0647567 | − | 0.241675i | −0.925959 | − | 0.377624i | \(-0.876741\pi\) |
0.990716 | + | 0.135948i | \(0.0434080\pi\) | |||||||
\(692\) | 13.5678 | + | 8.38243i | 0.515769 | + | 0.318652i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.87632 | − | 7.81505i | −0.374900 | − | 0.296655i | ||||
\(695\) | 31.4048 | − | 18.1315i | 1.19125 | − | 0.687769i | ||||
\(696\) | −8.32927 | + | 46.9364i | −0.315720 | + | 1.77912i | ||||
\(697\) | 9.74191 | + | 5.62449i | 0.369001 | + | 0.213043i | ||||
\(698\) | −13.7334 | − | 2.01677i | −0.519816 | − | 0.0763360i | ||||
\(699\) | 6.03875 | − | 6.03875i | 0.228407 | − | 0.228407i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.01206 | − | 4.01206i | −0.151533 | − | 0.151533i | 0.627269 | − | 0.778802i | \(-0.284173\pi\) |
−0.778802 | + | 0.627269i | \(0.784173\pi\) | |||||||
\(702\) | −12.8452 | + | 9.55562i | −0.484812 | + | 0.360654i | ||||
\(703\) | −2.42030 | + | 4.19208i | −0.0912834 | + | 0.158107i | ||||
\(704\) | −8.50955 | − | 5.98633i | −0.320716 | − | 0.225618i | ||||
\(705\) | −20.1651 | − | 34.9270i | −0.759462 | − | 1.31543i | ||||
\(706\) | −4.92528 | − | 42.2726i | −0.185365 | − | 1.59095i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 9.10719 | − | 2.15141i | 0.342269 | − | 0.0808549i | ||||
\(709\) | −49.1929 | − | 13.1812i | −1.84748 | − | 0.495030i | −0.848085 | − | 0.529861i | \(-0.822244\pi\) |
−0.999393 | + | 0.0348304i | \(0.988911\pi\) | |||||||
\(710\) | 27.8102 | + | 70.0772i | 1.04370 | + | 2.62995i | ||||
\(711\) | 8.39335 | + | 4.84590i | 0.314775 | + | 0.181736i | ||||
\(712\) | −18.3112 | − | 15.3992i | −0.686241 | − | 0.577110i | ||||
\(713\) | − | 19.6059i | − | 0.734248i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.64929 | + | 5.64929i | −0.211271 | + | 0.211271i | ||||
\(716\) | −0.989032 | + | 33.1564i | −0.0369619 | + | 1.23911i | ||||
\(717\) | −45.5068 | + | 12.1935i | −1.69948 | + | 0.455375i | ||||
\(718\) | −5.81451 | + | 13.4660i | −0.216995 | + | 0.502546i | ||||
\(719\) | 3.81125 | + | 6.60127i | 0.142135 | + | 0.246186i | 0.928301 | − | 0.371831i | \(-0.121270\pi\) |
−0.786165 | + | 0.618017i | \(0.787936\pi\) | |||||||
\(720\) | −79.7281 | − | 26.5485i | −2.97129 | − | 0.989406i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 20.6787 | − | 2.40932i | 0.769580 | − | 0.0896657i | ||||
\(723\) | 10.6182 | − | 39.6278i | 0.394896 | − | 1.47377i | ||||
\(724\) | −5.61120 | − | 10.4249i | −0.208538 | − | 0.387437i | ||||
\(725\) | 14.8299 | + | 55.3459i | 0.550768 | + | 2.05549i | ||||
\(726\) | −5.55870 | + | 37.8524i | −0.206303 | + | 1.40483i | ||||
\(727\) | − | 25.4856i | − | 0.945207i | −0.881275 | − | 0.472604i | \(-0.843314\pi\) | ||
0.881275 | − | 0.472604i | \(-0.156686\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 38.4448i | 1.42388i | ||||||||
\(730\) | −78.1273 | − | 11.4732i | −2.89162 | − | 0.424641i | ||||
\(731\) | 3.14242 | + | 11.7277i | 0.116227 | + | 0.433763i | ||||
\(732\) | 25.3415 | + | 7.60695i | 0.936648 | + | 0.281161i | ||||
\(733\) | 5.48115 | − | 20.4559i | 0.202451 | − | 0.755557i | −0.787761 | − | 0.615982i | \(-0.788760\pi\) |
0.990211 | − | 0.139575i | \(-0.0445738\pi\) | |||||||
\(734\) | 1.33056 | + | 11.4199i | 0.0491120 | + | 0.421517i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −22.5727 | + | 14.7872i | −0.832039 | + | 0.545063i | ||||
\(737\) | 1.40371 | + | 2.43129i | 0.0517061 | + | 0.0895577i | ||||
\(738\) | −52.7154 | − | 22.7621i | −1.94048 | − | 0.837883i | ||||
\(739\) | 16.8591 | − | 4.51737i | 0.620170 | − | 0.166174i | 0.0649652 | − | 0.997888i | \(-0.479306\pi\) |
0.555205 | + | 0.831713i | \(0.312640\pi\) | |||||||
\(740\) | 13.1407 | − | 12.3794i | 0.483061 | − | 0.455077i | ||||
\(741\) | 6.76966 | − | 6.76966i | 0.248690 | − | 0.248690i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 10.6724i | − | 0.391531i | −0.980651 | − | 0.195766i | \(-0.937281\pi\) | ||
0.980651 | − | 0.195766i | \(-0.0627192\pi\) | |||||||
\(744\) | 33.6587 | − | 2.90754i | 1.23399 | − | 0.106596i | ||||
\(745\) | −36.7104 | − | 21.1948i | −1.34497 | − | 0.776517i | ||||
\(746\) | 5.92430 | − | 2.35106i | 0.216904 | − | 0.0860786i | ||||
\(747\) | 53.2760 | + | 14.2753i | 1.94927 | + | 0.522305i | ||||
\(748\) | −2.06278 | + | 3.33880i | −0.0754226 | + | 0.122079i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −76.8538 | + | 8.95442i | −2.80630 | + | 0.326969i | ||||
\(751\) | 1.41476 | + | 2.45044i | 0.0516254 | + | 0.0894178i | 0.890683 | − | 0.454624i | \(-0.150226\pi\) |
−0.839058 | + | 0.544042i | \(0.816893\pi\) | |||||||
\(752\) | 0.857719 | − | 14.3643i | 0.0312778 | − | 0.523814i | ||||
\(753\) | −29.1743 | + | 50.5313i | −1.06317 | + | 1.84146i | ||||
\(754\) | 7.79550 | + | 10.4792i | 0.283896 | + | 0.381629i | ||||
\(755\) | 14.9157 | + | 14.9157i | 0.542837 | + | 0.542837i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.6590 | − | 15.6590i | 0.569136 | − | 0.569136i | −0.362750 | − | 0.931886i | \(-0.618162\pi\) |
0.931886 | + | 0.362750i | \(0.118162\pi\) | |||||||
\(758\) | −0.243826 | + | 1.66035i | −0.00885617 | + | 0.0603067i | ||||
\(759\) | −15.6144 | − | 9.01496i | −0.566765 | − | 0.327222i | ||||
\(760\) | 22.2225 | + | 3.94357i | 0.806093 | + | 0.143048i | ||||
\(761\) | 4.15144 | − | 2.39683i | 0.150490 | − | 0.0868852i | −0.422864 | − | 0.906193i | \(-0.638975\pi\) |
0.573354 | + | 0.819308i | \(0.305642\pi\) | |||||||
\(762\) | 33.1001 | − | 41.8304i | 1.19909 | − | 1.51535i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −24.0727 | + | 5.68674i | −0.870920 | + | 0.205739i | ||||
\(765\) | −8.20404 | + | 30.6179i | −0.296618 | + | 1.10699i | ||||
\(766\) | −44.6306 | − | 19.2711i | −1.61257 | − | 0.696294i | ||||
\(767\) | 1.28195 | − | 2.22041i | 0.0462886 | − | 0.0801742i | ||||
\(768\) | −28.7336 | − | 36.5590i | −1.03684 | − | 1.31921i | ||||
\(769\) | −13.5489 | −0.488585 | −0.244293 | − | 0.969702i | \(-0.578556\pi\) | ||||
−0.244293 | + | 0.969702i | \(0.578556\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.65159 | + | 6.65159i | 0.239551 | + | 0.239551i | ||||
\(772\) | 32.4803 | + | 34.4776i | 1.16899 | + | 1.24088i | ||||
\(773\) | −6.87406 | − | 25.6544i | −0.247243 | − | 0.922723i | −0.972243 | − | 0.233974i | \(-0.924827\pi\) |
0.725000 | − | 0.688749i | \(-0.241840\pi\) | |||||||
\(774\) | −22.8604 | − | 57.6045i | −0.821701 | − | 2.07055i | ||||
\(775\) | 35.1675 | − | 20.3040i | 1.26325 | − | 0.729340i | ||||
\(776\) | 15.6462 | + | 43.1348i | 0.561666 | + | 1.54845i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.1945 | + | 13.6059i | 0.616454 | + | 0.487795i | ||||
\(779\) | 14.8965 | + | 3.99151i | 0.533723 | + | 0.143011i | ||||
\(780\) | −31.4410 | + | 16.9232i | −1.12577 | + | 0.605947i | ||||
\(781\) | −17.3612 | + | 4.65192i | −0.621233 | + | 0.166459i | ||||
\(782\) | 6.07553 | + | 8.16709i | 0.217260 | + | 0.292054i | ||||
\(783\) | −41.2247 | −1.47325 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −30.6438 | −1.09372 | ||||||||
\(786\) | 23.6589 | + | 31.8037i | 0.843885 | + | 1.13440i | ||||
\(787\) | 33.4454 | − | 8.96168i | 1.19220 | − | 0.319449i | 0.392446 | − | 0.919775i | \(-0.371629\pi\) |
0.799756 | + | 0.600326i | \(0.204962\pi\) | |||||||
\(788\) | 15.3084 | + | 28.4410i | 0.545340 | + | 1.01317i | ||||
\(789\) | −67.4174 | − | 18.0644i | −2.40012 | − | 0.643111i | ||||
\(790\) | 7.61320 | + | 6.02426i | 0.270865 | + | 0.214334i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 8.48622 | − | 18.1467i | 0.301545 | − | 0.644816i | ||||
\(793\) | 6.27802 | − | 3.62462i | 0.222939 | − | 0.128714i | ||||
\(794\) | 19.5038 | + | 49.1464i | 0.692163 | + | 1.74414i | ||||
\(795\) | 2.77272 | + | 10.3479i | 0.0983383 | + | 0.367003i | ||||
\(796\) | −8.00201 | + | 7.53845i | −0.283624 | + | 0.267193i | ||||
\(797\) | 17.6690 | + | 17.6690i | 0.625870 | + | 0.625870i | 0.947026 | − | 0.321157i | \(-0.104072\pi\) |
−0.321157 | + | 0.947026i | \(0.604072\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.42807 | −0.192031 | ||||||||
\(800\) | −49.9004 | − | 25.1753i | −1.76425 | − | 0.890082i | ||||
\(801\) | 23.0339 | − | 39.8959i | 0.813863 | − | 1.40965i | ||||
\(802\) | −6.46090 | − | 2.78977i | −0.228142 | − | 0.0985100i | ||||
\(803\) | 4.87228 | − | 18.1836i | 0.171939 | − | 0.641686i | ||||
\(804\) | 2.88461 | + | 12.2109i | 0.101732 | + | 0.430646i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.74374 | − | 7.25869i | 0.202315 | − | 0.255676i | ||||
\(807\) | 0.311458 | − | 0.179820i | 0.0109638 | − | 0.00632998i | ||||
\(808\) | 37.9278 | − | 26.4954i | 1.33430 | − | 0.932103i | ||||
\(809\) | −2.59269 | − | 1.49689i | −0.0911540 | − | 0.0526278i | 0.453730 | − | 0.891139i | \(-0.350093\pi\) |
−0.544884 | + | 0.838511i | \(0.683426\pi\) | |||||||
\(810\) | 3.42499 | − | 23.3227i | 0.120342 | − | 0.819477i | ||||
\(811\) | 2.28628 | − | 2.28628i | 0.0802820 | − | 0.0802820i | −0.665825 | − | 0.746108i | \(-0.731920\pi\) |
0.746108 | + | 0.665825i | \(0.231920\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.7839 | + | 20.7839i | 0.728923 | + | 0.728923i | ||||
\(814\) | 2.56884 | + | 3.45319i | 0.0900379 | + | 0.121034i | ||||
\(815\) | −17.2322 | + | 29.8471i | −0.603618 | + | 1.04550i | ||||
\(816\) | −13.1200 | + | 11.6414i | −0.459290 | + | 0.407531i | ||||
\(817\) | 8.32272 | + | 14.4154i | 0.291175 | + | 0.504330i | ||||
\(818\) | −5.70817 | + | 0.665073i | −0.199582 | + | 0.0232537i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −48.9323 | − | 30.2313i | −1.70879 | − | 1.05572i | ||||
\(821\) | 39.1150 | + | 10.4808i | 1.36512 | + | 0.365783i | 0.865695 | − | 0.500572i | \(-0.166877\pi\) |
0.499428 | + | 0.866356i | \(0.333544\pi\) | |||||||
\(822\) | 86.5431 | − | 34.3447i | 3.01854 | − | 1.19791i | ||||
\(823\) | 35.5496 | + | 20.5246i | 1.23918 | + | 0.715442i | 0.968927 | − | 0.247347i | \(-0.0795588\pi\) |
0.270255 | + | 0.962789i | \(0.412892\pi\) | |||||||
\(824\) | 37.2059 | + | 31.2891i | 1.29613 | + | 1.09001i | ||||
\(825\) | − | 37.3437i | − | 1.30014i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.3987 | + | 20.3987i | −0.709331 | + | 0.709331i | −0.966394 | − | 0.257064i | \(-0.917245\pi\) |
0.257064 | + | 0.966394i | \(0.417245\pi\) | |||||||
\(828\) | −35.6283 | − | 37.8192i | −1.23817 | − | 1.31431i | ||||
\(829\) | −25.2567 | + | 6.76750i | −0.877200 | + | 0.235045i | −0.669199 | − | 0.743083i | \(-0.733363\pi\) |
−0.208001 | + | 0.978129i | \(0.566696\pi\) | |||||||
\(830\) | 50.7231 | + | 21.9018i | 1.76062 | + | 0.760223i | ||||
\(831\) | 22.6214 | + | 39.1814i | 0.784727 | + | 1.35919i | ||||
\(832\) | −12.6891 | − | 1.13822i | −0.439916 | − | 0.0394608i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.47141 | + | 38.3771i | 0.154832 | + | 1.32889i | ||||
\(835\) | 11.7985 | − | 44.0326i | 0.408304 | − | 1.52381i | ||||
\(836\) | −1.54693 | + | 5.15337i | −0.0535016 | + | 0.178233i | ||||
\(837\) | 7.56177 | + | 28.2209i | 0.261373 | + | 0.975457i | ||||
\(838\) | −1.09276 | − | 0.160473i | −0.0377486 | − | 0.00554346i | ||||
\(839\) | − | 41.9862i | − | 1.44953i | −0.688999 | − | 0.724763i | \(-0.741949\pi\) | ||
0.688999 | − | 0.724763i | \(-0.258051\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.63123i | 0.159698i | ||||||||
\(842\) | −1.09773 | + | 7.47508i | −0.0378303 | + | 0.257608i | ||||
\(843\) | −3.17419 | − | 11.8462i | −0.109325 | − | 0.408006i | ||||
\(844\) | 2.26112 | − | 1.21705i | 0.0778310 | − | 0.0418926i | ||||
\(845\) | 10.4471 | − | 38.9892i | 0.359392 | − | 1.34127i | ||||
\(846\) | 27.5210 | − | 3.20654i | 0.946193 | − | 0.110243i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.20763 | + | 3.62664i | −0.0414701 | + | 0.124539i | ||||
\(849\) | −34.0788 | − | 59.0263i | −1.16958 | − | 2.02578i | ||||
\(850\) | −8.35762 | + | 19.3557i | −0.286664 | + | 0.663894i | ||||
\(851\) | 10.7824 | − | 2.88913i | 0.369616 | − | 0.0990382i | ||||
\(852\) | −80.2930 | − | 2.39508i | −2.75079 | − | 0.0820542i | ||||
\(853\) | −10.9845 | + | 10.9845i | −0.376104 | + | 0.376104i | −0.869694 | − | 0.493591i | \(-0.835684\pi\) |
0.493591 | + | 0.869694i | \(0.335684\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 43.4570i | 1.48620i | ||||||||
\(856\) | 1.41192 | + | 16.3449i | 0.0482583 | + | 0.558656i | ||||
\(857\) | −40.9817 | − | 23.6608i | −1.39991 | − | 0.808237i | −0.405524 | − | 0.914084i | \(-0.632911\pi\) |
−0.994382 | + | 0.105848i | \(0.966244\pi\) | |||||||
\(858\) | −3.13988 | − | 7.91198i | −0.107194 | − | 0.270111i | ||||
\(859\) | 6.98214 | + | 1.87086i | 0.238228 | + | 0.0638329i | 0.375957 | − | 0.926637i | \(-0.377314\pi\) |
−0.137730 | + | 0.990470i | \(0.543981\pi\) | |||||||
\(860\) | −14.2726 | − | 60.4178i | −0.486692 | − | 2.06023i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.193431 | + | 1.66017i | 0.00658828 | + | 0.0565458i | ||||
\(863\) | −5.05527 | − | 8.75599i | −0.172084 | − | 0.298057i | 0.767065 | − | 0.641570i | \(-0.221717\pi\) |
−0.939148 | + | 0.343512i | \(0.888383\pi\) | |||||||
\(864\) | 26.7880 | − | 29.9908i | 0.911346 | − | 1.02031i | ||||
\(865\) | −15.3802 | + | 26.6392i | −0.522941 | + | 0.905761i | ||||
\(866\) | 17.3135 | − | 12.8796i | 0.588335 | − | 0.437665i | ||||
\(867\) | −30.2565 | − | 30.2565i | −1.02756 | − | 1.02756i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.63656 | + | 1.63656i | −0.0555165 | + | 0.0555165i | ||||
\(870\) | −90.9673 | − | 13.3587i | −3.08408 | − | 0.452904i | ||||
\(871\) | 2.97712 | + | 1.71884i | 0.100876 | + | 0.0582408i | ||||
\(872\) | −7.49866 | − | 10.7342i | −0.253937 | − | 0.363507i | ||||
\(873\) | −76.5128 | + | 44.1747i | −2.58956 | + | 1.49509i | ||||
\(874\) | 10.9435 | + | 8.65950i | 0.370169 | + | 0.292912i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 44.2207 | − | 71.5754i | 1.49408 | − | 2.41831i | ||||
\(877\) | −13.9324 | + | 51.9964i | −0.470463 | + | 1.75579i | 0.167646 | + | 0.985847i | \(0.446384\pi\) |
−0.638109 | + | 0.769946i | \(0.720283\pi\) | |||||||
\(878\) | 2.43589 | − | 5.64135i | 0.0822073 | − | 0.190386i | ||||
\(879\) | −27.7922 | + | 48.1375i | −0.937408 | + | 1.62364i | ||||
\(880\) | 11.0516 | − | 16.7498i | 0.372551 | − | 0.564634i | ||||
\(881\) | 21.5769 | 0.726946 | 0.363473 | − | 0.931605i | \(-0.381591\pi\) | ||||
0.363473 | + | 0.931605i | \(0.381591\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.5700 | + | 21.5700i | 0.725888 | + | 0.725888i | 0.969798 | − | 0.243910i | \(-0.0784300\pi\) |
−0.243910 | + | 0.969798i | \(0.578430\pi\) | |||||||
\(884\) | −0.143287 | + | 4.80358i | −0.00481928 | + | 0.161562i | ||||
\(885\) | 4.67141 | + | 17.4340i | 0.157028 | + | 0.586036i | ||||
\(886\) | 8.01943 | − | 3.18252i | 0.269418 | − | 0.106919i | ||||
\(887\) | 29.1946 | − | 16.8555i | 0.980260 | − | 0.565953i | 0.0779110 | − | 0.996960i | \(-0.475175\pi\) |
0.902348 | + | 0.431007i | \(0.141842\pi\) | |||||||
\(888\) | 6.55898 | + | 18.0824i | 0.220105 | + | 0.606804i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 28.6350 | − | 36.1876i | 0.959846 | − | 1.21301i | ||||
\(891\) | 5.42821 | + | 1.45448i | 0.181852 | + | 0.0487271i | ||||
\(892\) | 1.84186 | − | 6.13588i | 0.0616699 | − | 0.205445i | ||||
\(893\) | −7.18814 | + | 1.92606i | −0.240542 | + | 0.0644530i | ||||
\(894\) | 36.2371 | − | 26.9569i | 1.21195 | − | 0.901574i | ||||
\(895\) | −63.9788 | −2.13858 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.0777 | −0.737153 | ||||||||
\(898\) | 4.22668 | − | 3.14425i | 0.141046 | − | 0.104925i | ||||
\(899\) | 23.0227 | − | 6.16891i | 0.767850 | − | 0.205745i | ||||
\(900\) | 30.9402 | − | 103.073i | 1.03134 | − | 3.43577i | ||||
\(901\) | 1.39273 | + | 0.373182i | 0.0463987 | + | 0.0124325i | ||||
\(902\) | 8.50865 | − | 10.7529i | 0.283307 | − | 0.358031i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.84597 | + | 24.3873i | 0.294213 | + | 0.811111i | ||||
\(905\) | 19.7753 | − | 11.4173i | 0.657354 | − | 0.379524i | ||||
\(906\) | −20.8898 | + | 8.29014i | −0.694017 | + | 0.275421i | ||||
\(907\) | 0.338194 | + | 1.26216i | 0.0112295 | + | 0.0419092i | 0.971313 | − | 0.237804i | \(-0.0764274\pi\) |
−0.960084 | + | 0.279713i | \(0.909761\pi\) | |||||||
\(908\) | −1.16321 | + | 38.9954i | −0.0386023 | + | 1.29411i | ||||
\(909\) | 62.9911 | + | 62.9911i | 2.08928 | + | 2.08928i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.9873 | −0.993522 | −0.496761 | − | 0.867887i | \(-0.665477\pi\) | ||||
−0.496761 | + | 0.867887i | \(0.665477\pi\) | |||||||
\(912\) | −13.2434 | + | 20.0716i | −0.438533 | + | 0.664637i | ||||
\(913\) | −6.58567 | + | 11.4067i | −0.217954 | + | 0.377507i | ||||
\(914\) | −6.02390 | + | 13.9509i | −0.199253 | + | 0.461456i | ||||
\(915\) | −13.2080 | + | 49.2931i | −0.436645 | + | 1.62958i | ||||
\(916\) | 10.4387 | − | 16.8960i | 0.344904 | − | 0.558261i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −11.8951 | − | 9.41250i | −0.392597 | − | 0.310659i | ||||
\(919\) | −11.3211 | + | 6.53623i | −0.373448 | + | 0.215610i | −0.674964 | − | 0.737851i | \(-0.735841\pi\) |
0.301516 | + | 0.953461i | \(0.402507\pi\) | |||||||
\(920\) | −29.8062 | − | 42.6673i | −0.982682 | − | 1.40670i | ||||
\(921\) | −31.7989 | − | 18.3591i | −1.04781 | − | 0.604953i | ||||
\(922\) | −15.6083 | − | 2.29211i | −0.514032 | − | 0.0754866i | ||||
\(923\) | −15.5626 | + | 15.5626i | −0.512248 | + | 0.512248i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.3486 | + | 16.3486i | 0.537538 | + | 0.537538i | ||||
\(926\) | 31.0319 | − | 23.0847i | 1.01977 | − | 0.758611i | ||||
\(927\) | −46.8018 | + | 81.0630i | −1.53717 | + | 2.66246i | ||||
\(928\) | −24.4666 | − | 21.8537i | −0.803155 | − | 0.717384i | ||||
\(929\) | −10.3529 | − | 17.9317i | −0.339667 | − | 0.588320i | 0.644703 | − | 0.764433i | \(-0.276981\pi\) |
−0.984370 | + | 0.176113i | \(0.943648\pi\) | |||||||
\(930\) | 7.54106 | + | 64.7232i | 0.247281 | + | 2.12236i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.35118 | + | 5.71971i | 0.0442593 | + | 0.187355i | ||||
\(933\) | 55.5082 | + | 14.8734i | 1.81726 | + | 0.486933i | ||||
\(934\) | 8.40386 | + | 21.1764i | 0.274983 | + | 0.692911i | ||||
\(935\) | −6.55548 | − | 3.78481i | −0.214387 | − | 0.123776i | ||||
\(936\) | −2.11115 | − | 24.4395i | −0.0690051 | − | 0.798828i | ||||
\(937\) | 5.93799i | 0.193986i | 0.995285 | + | 0.0969929i | \(0.0309224\pi\) | ||||
−0.995285 | + | 0.0969929i | \(0.969078\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.9348 | + | 17.9348i | −0.585281 | + | 0.585281i | ||||
\(940\) | 27.7422 | + | 0.827531i | 0.904851 | + | 0.0269911i | ||||
\(941\) | −19.1182 | + | 5.12272i | −0.623237 | + | 0.166996i | −0.556599 | − | 0.830781i | \(-0.687894\pi\) |
−0.0666382 | + | 0.997777i | \(0.521227\pi\) | |||||||
\(942\) | 12.9428 | − | 29.9746i | 0.421699 | − | 0.976626i | ||||
\(943\) | −17.7821 | − | 30.7995i | −0.579065 | − | 1.00297i | ||||
\(944\) | −2.03459 | + | 6.11007i | −0.0662201 | + | 0.198866i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.7004 | − | 1.71278i | 0.477952 | − | 0.0556873i | ||||
\(947\) | −11.0792 | + | 41.3482i | −0.360027 | + | 1.34364i | 0.514013 | + | 0.857782i | \(0.328158\pi\) |
−0.874039 | + | 0.485855i | \(0.838508\pi\) | |||||||
\(948\) | −9.10825 | + | 4.90253i | −0.295822 | + | 0.159227i | ||||
\(949\) | −5.96613 | − | 22.2659i | −0.193669 | − | 0.722782i | ||||
\(950\) | −4.19958 | + | 28.5974i | −0.136253 | + | 0.927821i | ||||
\(951\) | 78.1710i | 2.53487i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.689500i | 0.0223351i | 0.999938 | + | 0.0111675i | \(0.00355481\pi\) | ||||
−0.999938 | + | 0.0111675i | \(0.996445\pi\) | |||||||
\(954\) | −7.28180 | − | 1.06935i | −0.235757 | − | 0.0346214i | ||||
\(955\) | −12.3478 | − | 46.0825i | −0.399565 | − | 1.49120i | ||||
\(956\) | 9.32138 | − | 31.0529i | 0.301475 | − | 1.00432i | ||||
\(957\) | 5.67303 | − | 21.1720i | 0.183383 | − | 0.684395i | ||||
\(958\) | −1.86383 | − | 15.9968i | −0.0602176 | − | 0.516834i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 68.8294 | − | 57.4977i | 2.22146 | − | 1.85573i | ||||
\(961\) | 7.05398 | + | 12.2179i | 0.227548 | + | 0.394124i | ||||
\(962\) | 4.83836 | + | 2.08916i | 0.155995 | + | 0.0673573i | ||||
\(963\) | −30.5122 | + | 8.17572i | −0.983242 | + | 0.263459i | ||||
\(964\) | 19.3597 | + | 20.5502i | 0.623535 | + | 0.661878i | ||||
\(965\) | −64.6012 | + | 64.6012i | −2.07959 | + | 2.07959i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 14.1022i | − | 0.453497i | −0.973953 | − | 0.226749i | \(-0.927190\pi\) | ||
0.973953 | − | 0.226749i | \(-0.0728096\pi\) | |||||||
\(968\) | −20.1504 | − | 16.9459i | −0.647658 | − | 0.544662i | ||||
\(969\) | 7.85557 | + | 4.53541i | 0.252357 | + | 0.145698i | ||||
\(970\) | −82.2595 | + | 32.6448i | −2.64119 | + | 1.04816i | ||||
\(971\) | −0.348650 | − | 0.0934205i | −0.0111887 | − | 0.00299801i | 0.253220 | − | 0.967409i | \(-0.418510\pi\) |
−0.264409 | + | 0.964411i | \(0.585177\pi\) | |||||||
\(972\) | −14.9184 | − | 9.21689i | −0.478508 | − | 0.295632i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −44.0421 | + | 5.13145i | −1.41120 | + | 0.164422i | ||||
\(975\) | −22.8638 | − | 39.6012i | −0.732226 | − | 1.26825i | ||||
\(976\) | −13.6198 | + | 12.0849i | −0.435959 | + | 0.386829i | ||||
\(977\) | 4.91955 | − | 8.52091i | 0.157390 | − | 0.272608i | −0.776536 | − | 0.630072i | \(-0.783025\pi\) |
0.933927 | + | 0.357464i | \(0.116359\pi\) | |||||||
\(978\) | −21.9171 | − | 29.4622i | −0.700831 | − | 0.942099i | ||||
\(979\) | 7.77902 | + | 7.77902i | 0.248618 | + | 0.248618i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.8276 | − | 17.8276i | 0.569191 | − | 0.569191i | ||||
\(982\) | 5.89239 | − | 40.1247i | 0.188034 | − | 1.28043i | ||||
\(983\) | 23.0786 | + | 13.3244i | 0.736094 | + | 0.424984i | 0.820647 | − | 0.571435i | \(-0.193613\pi\) |
−0.0845537 | + | 0.996419i | \(0.526946\pi\) | |||||||
\(984\) | 50.2384 | − | 35.0952i | 1.60154 | − | 1.11879i | ||||
\(985\) | −53.9509 | + | 31.1486i | −1.71902 | + | 0.992476i | ||||
\(986\) | −7.67875 | + | 9.70406i | −0.244541 | + | 0.309040i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.51472 | + | 6.41201i | 0.0481896 | + | 0.203993i | ||||
\(989\) | 9.93490 | − | 37.0776i | 0.315912 | − | 1.17900i | ||||
\(990\) | 35.4730 | + | 15.3169i | 1.12741 | + | 0.486804i | ||||
\(991\) | −8.41437 | + | 14.5741i | −0.267291 | + | 0.462962i | −0.968161 | − | 0.250327i | \(-0.919462\pi\) |
0.700870 | + | 0.713289i | \(0.252795\pi\) | |||||||
\(992\) | −10.4724 | + | 20.7575i | −0.332499 | + | 0.659052i | ||||
\(993\) | 91.7875 | 2.91279 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.9935 | − | 14.9935i | −0.475326 | − | 0.475326i | ||||
\(996\) | −42.8471 | + | 40.3650i | −1.35766 | + | 1.27901i | ||||
\(997\) | 9.43672 | + | 35.2183i | 0.298864 | + | 1.11538i | 0.938100 | + | 0.346365i | \(0.112584\pi\) |
−0.639236 | + | 0.769011i | \(0.720749\pi\) | |||||||
\(998\) | 13.6604 | + | 34.4219i | 0.432411 | + | 1.08961i | ||||
\(999\) | −14.4059 | + | 8.31728i | −0.455784 | + | 0.263147i |
(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 | 784.2.x.m.557.5 | 24 | ||
7.2 | even | 3 | inner | 784.2.x.m.765.2 | 24 | ||
7.3 | odd | 6 | 112.2.m.d.29.3 | ✓ | 12 | ||
7.4 | even | 3 | 784.2.m.h.589.3 | 12 | |||
7.5 | odd | 6 | 784.2.x.l.765.2 | 24 | |||
7.6 | odd | 2 | 784.2.x.l.557.5 | 24 | |||
16.5 | even | 4 | inner | 784.2.x.m.165.2 | 24 | ||
28.3 | even | 6 | 448.2.m.d.337.6 | 12 | |||
56.3 | even | 6 | 896.2.m.h.673.1 | 12 | |||
56.45 | odd | 6 | 896.2.m.g.673.6 | 12 | |||
112.3 | even | 12 | 896.2.m.h.225.1 | 12 | |||
112.5 | odd | 12 | 784.2.x.l.373.5 | 24 | |||
112.37 | even | 12 | inner | 784.2.x.m.373.5 | 24 | ||
112.45 | odd | 12 | 896.2.m.g.225.6 | 12 | |||
112.53 | even | 12 | 784.2.m.h.197.3 | 12 | |||
112.59 | even | 12 | 448.2.m.d.113.6 | 12 | |||
112.69 | odd | 4 | 784.2.x.l.165.2 | 24 | |||
112.101 | odd | 12 | 112.2.m.d.85.3 | yes | 12 | ||
224.59 | even | 24 | 7168.2.a.bi.1.2 | 12 | |||
224.101 | odd | 24 | 7168.2.a.bj.1.11 | 12 | |||
224.171 | even | 24 | 7168.2.a.bi.1.11 | 12 | |||
224.213 | odd | 24 | 7168.2.a.bj.1.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.m.d.29.3 | ✓ | 12 | 7.3 | odd | 6 | ||
112.2.m.d.85.3 | yes | 12 | 112.101 | odd | 12 | ||
448.2.m.d.113.6 | 12 | 112.59 | even | 12 | |||
448.2.m.d.337.6 | 12 | 28.3 | even | 6 | |||
784.2.m.h.197.3 | 12 | 112.53 | even | 12 | |||
784.2.m.h.589.3 | 12 | 7.4 | even | 3 | |||
784.2.x.l.165.2 | 24 | 112.69 | odd | 4 | |||
784.2.x.l.373.5 | 24 | 112.5 | odd | 12 | |||
784.2.x.l.557.5 | 24 | 7.6 | odd | 2 | |||
784.2.x.l.765.2 | 24 | 7.5 | odd | 6 | |||
784.2.x.m.165.2 | 24 | 16.5 | even | 4 | inner | ||
784.2.x.m.373.5 | 24 | 112.37 | even | 12 | inner | ||
784.2.x.m.557.5 | 24 | 1.1 | even | 1 | trivial | ||
784.2.x.m.765.2 | 24 | 7.2 | even | 3 | inner | ||
896.2.m.g.225.6 | 12 | 112.45 | odd | 12 | |||
896.2.m.g.673.6 | 12 | 56.45 | odd | 6 | |||
896.2.m.h.225.1 | 12 | 112.3 | even | 12 | |||
896.2.m.h.673.1 | 12 | 56.3 | even | 6 | |||
7168.2.a.bi.1.2 | 12 | 224.59 | even | 24 | |||
7168.2.a.bi.1.11 | 12 | 224.171 | even | 24 | |||
7168.2.a.bj.1.2 | 12 | 224.213 | odd | 24 | |||
7168.2.a.bj.1.11 | 12 | 224.101 | odd | 24 |