Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(218,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 15, 12]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.218");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.ct (of order \(20\), degree \(8\), 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(256\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{20})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 368.2 | ||
Character | \(\chi\) | \(=\) | 825.368 |
Dual form | 825.2.ct.c.482.2 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.15673 | + | 2.27022i | −0.817934 | + | 1.60529i | −0.0221122 | + | 0.999755i | \(0.507039\pi\) |
−0.795822 | + | 0.605531i | \(0.792961\pi\) | |||||||
\(3\) | 1.70213 | + | 0.320526i | 0.982728 | + | 0.185056i | ||||
\(4\) | −2.64028 | − | 3.63404i | −1.32014 | − | 1.81702i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.69658 | + | 3.49345i | −1.10087 | + | 1.42620i | ||||
\(7\) | 0.237778 | − | 1.50127i | 0.0898718 | − | 0.567428i | −0.901127 | − | 0.433556i | \(-0.857259\pi\) |
0.990999 | − | 0.133873i | \(-0.0427413\pi\) | |||||||
\(8\) | 6.27105 | − | 0.993237i | 2.21715 | − | 0.351162i | ||||
\(9\) | 2.79453 | + | 1.09116i | 0.931509 | + | 0.363720i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.991249 | + | 3.16503i | −0.298873 | + | 0.954293i | ||||
\(12\) | −3.32931 | − | 7.03191i | −0.961090 | − | 2.02994i | ||||
\(13\) | 1.69413 | − | 3.32493i | 0.469868 | − | 0.922168i | −0.527492 | − | 0.849560i | \(-0.676868\pi\) |
0.997361 | − | 0.0726086i | \(-0.0231324\pi\) | |||||||
\(14\) | 3.13317 | + | 2.27638i | 0.837375 | + | 0.608389i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.22292 | + | 6.84143i | −0.555729 | + | 1.71036i | ||||
\(17\) | 4.74982 | − | 2.42015i | 1.15200 | − | 0.586973i | 0.229629 | − | 0.973278i | \(-0.426249\pi\) |
0.922371 | + | 0.386305i | \(0.126249\pi\) | |||||||
\(18\) | −5.70969 | + | 5.08200i | −1.34579 | + | 1.19784i | ||||
\(19\) | −0.443752 | + | 0.610772i | −0.101804 | + | 0.140121i | −0.856880 | − | 0.515517i | \(-0.827600\pi\) |
0.755076 | + | 0.655637i | \(0.227600\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.885929 | − | 2.47916i | 0.193326 | − | 0.540996i | ||||
\(22\) | −6.03870 | − | 5.91145i | −1.28746 | − | 1.26033i | ||||
\(23\) | 4.86491 | − | 4.86491i | 1.01440 | − | 1.01440i | 0.0145098 | − | 0.999895i | \(-0.495381\pi\) |
0.999895 | − | 0.0145098i | \(-0.00461879\pi\) | |||||||
\(24\) | 10.9925 | + | 0.319415i | 2.24384 | + | 0.0652003i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.58864 | + | 7.69211i | 1.09602 | + | 1.50855i | ||||
\(27\) | 4.40691 | + | 2.75302i | 0.848111 | + | 0.529819i | ||||
\(28\) | −6.08349 | + | 3.09969i | −1.14967 | + | 0.585787i | ||||
\(29\) | 3.88618 | − | 2.82348i | 0.721646 | − | 0.524306i | −0.165264 | − | 0.986249i | \(-0.552848\pi\) |
0.886910 | + | 0.461943i | \(0.152848\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.607937 | − | 1.87104i | −0.109189 | − | 0.336048i | 0.881502 | − | 0.472180i | \(-0.156533\pi\) |
−0.990691 | + | 0.136132i | \(0.956533\pi\) | |||||||
\(32\) | −3.98105 | − | 3.98105i | −0.703757 | − | 0.703757i | ||||
\(33\) | −2.70172 | + | 5.06959i | −0.470308 | + | 0.882502i | ||||
\(34\) | 13.5826i | 2.32939i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.41303 | − | 13.0364i | −0.568838 | − | 2.17273i | ||||
\(37\) | −1.53731 | + | 9.70619i | −0.252732 | + | 1.59569i | 0.455848 | + | 0.890057i | \(0.349336\pi\) |
−0.708580 | + | 0.705630i | \(0.750664\pi\) | |||||||
\(38\) | −0.873283 | − | 1.71391i | −0.141665 | − | 0.278034i | ||||
\(39\) | 3.94937 | − | 5.11646i | 0.632406 | − | 0.819289i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.14117 | + | 5.69984i | −0.646743 | + | 0.890165i | −0.998953 | − | 0.0457560i | \(-0.985430\pi\) |
0.352210 | + | 0.935921i | \(0.385430\pi\) | |||||||
\(42\) | 4.60344 | + | 4.87897i | 0.710326 | + | 0.752842i | ||||
\(43\) | −7.47601 | − | 7.47601i | −1.14008 | − | 1.14008i | −0.988435 | − | 0.151646i | \(-0.951543\pi\) |
−0.151646 | − | 0.988435i | \(-0.548457\pi\) | |||||||
\(44\) | 14.1190 | − | 4.75435i | 2.12852 | − | 0.716745i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.41700 | + | 16.6718i | 0.798693 | + | 2.45813i | ||||
\(47\) | 1.66286 | + | 10.4989i | 0.242553 | + | 1.53142i | 0.745148 | + | 0.666900i | \(0.232379\pi\) |
−0.502594 | + | 0.864522i | \(0.667621\pi\) | |||||||
\(48\) | −5.97656 | + | 10.9325i | −0.862642 | + | 1.57798i | ||||
\(49\) | 4.46011 | + | 1.44918i | 0.637159 | + | 0.207025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.86055 | − | 2.59698i | 1.24073 | − | 0.363650i | ||||
\(52\) | −16.5559 | + | 2.62220i | −2.29589 | + | 0.363633i | ||||
\(53\) | 7.14378 | + | 3.63994i | 0.981274 | + | 0.499984i | 0.869598 | − | 0.493761i | \(-0.164378\pi\) |
0.111676 | + | 0.993745i | \(0.464378\pi\) | |||||||
\(54\) | −11.3476 | + | 6.82014i | −1.54421 | + | 0.928104i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 9.65074i | − | 1.28963i | ||||||
\(57\) | −0.951094 | + | 0.897382i | −0.125975 | + | 0.118861i | ||||
\(58\) | 1.91463 | + | 12.0885i | 0.251403 | + | 1.58730i | ||||
\(59\) | −8.99601 | + | 6.53598i | −1.17118 | + | 0.850912i | −0.991150 | − | 0.132749i | \(-0.957620\pi\) |
−0.180030 | + | 0.983661i | \(0.557620\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.364812 | + | 1.12278i | −0.0467094 | + | 0.143757i | −0.971691 | − | 0.236255i | \(-0.924080\pi\) |
0.924982 | + | 0.380012i | \(0.124080\pi\) | |||||||
\(62\) | 4.95088 | + | 0.784143i | 0.628763 | + | 0.0995863i | ||||
\(63\) | 2.30261 | − | 3.93589i | 0.290101 | − | 0.495876i | ||||
\(64\) | −0.0399837 | + | 0.0129915i | −0.00499796 | + | 0.00162394i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.38391 | − | 11.9976i | −1.03199 | − | 1.47681i | ||||
\(67\) | 11.0297 | − | 11.0297i | 1.34749 | − | 1.34749i | 0.459113 | − | 0.888378i | \(-0.348167\pi\) |
0.888378 | − | 0.459113i | \(-0.151833\pi\) | |||||||
\(68\) | −21.3358 | − | 10.8711i | −2.58734 | − | 1.31832i | ||||
\(69\) | 9.84007 | − | 6.72140i | 1.18461 | − | 0.809162i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.382309 | − | 0.124220i | −0.0453717 | − | 0.0147422i | 0.286243 | − | 0.958157i | \(-0.407593\pi\) |
−0.331615 | + | 0.943415i | \(0.607593\pi\) | |||||||
\(72\) | 18.6084 | + | 4.06709i | 2.19302 | + | 0.479311i | ||||
\(73\) | 2.52125 | + | 0.399326i | 0.295089 | + | 0.0467376i | 0.302224 | − | 0.953237i | \(-0.402271\pi\) |
−0.00713442 | + | 0.999975i | \(0.502271\pi\) | |||||||
\(74\) | −20.2569 | − | 14.7175i | −2.35482 | − | 1.71087i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.39120 | 0.388997 | ||||||||
\(77\) | 4.51588 | + | 2.24071i | 0.514633 | + | 0.255353i | ||||
\(78\) | 7.04710 | + | 14.8843i | 0.797927 | + | 1.68532i | ||||
\(79\) | 2.47554 | − | 0.804351i | 0.278520 | − | 0.0904966i | −0.166426 | − | 0.986054i | \(-0.553223\pi\) |
0.444946 | + | 0.895557i | \(0.353223\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.61875 | + | 6.09854i | 0.735416 | + | 0.677616i | ||||
\(82\) | −8.14963 | − | 15.9946i | −0.899977 | − | 1.76630i | ||||
\(83\) | −2.72789 | − | 5.35379i | −0.299425 | − | 0.587655i | 0.691452 | − | 0.722422i | \(-0.256971\pi\) |
−0.990877 | + | 0.134767i | \(0.956971\pi\) | |||||||
\(84\) | −11.3485 | + | 3.32618i | −1.23822 | + | 0.362916i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 25.6199 | − | 8.32442i | 2.76267 | − | 0.897645i | ||||
\(87\) | 7.51980 | − | 3.56031i | 0.806208 | − | 0.381706i | ||||
\(88\) | −3.07255 | + | 20.8326i | −0.327534 | + | 2.22077i | ||||
\(89\) | −1.88195 | −0.199486 | −0.0997432 | − | 0.995013i | \(-0.531802\pi\) | ||||
−0.0997432 | + | 0.995013i | \(0.531802\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.58880 | − | 3.33396i | −0.481036 | − | 0.349493i | ||||
\(92\) | −30.5240 | − | 4.83453i | −3.18235 | − | 0.504035i | ||||
\(93\) | −0.435074 | − | 3.37962i | −0.0451150 | − | 0.350450i | ||||
\(94\) | −25.7583 | − | 8.36937i | −2.65676 | − | 0.863235i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.50026 | − | 8.05232i | −0.561368 | − | 0.821837i | ||||
\(97\) | −1.33177 | − | 0.678570i | −0.135221 | − | 0.0688983i | 0.385071 | − | 0.922887i | \(-0.374177\pi\) |
−0.520292 | + | 0.853988i | \(0.674177\pi\) | |||||||
\(98\) | −8.44911 | + | 8.44911i | −0.853489 | + | 0.853489i | ||||
\(99\) | −6.22362 | + | 7.76315i | −0.625497 | + | 0.780226i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.393972 | + | 0.128009i | −0.0392017 | + | 0.0127374i | −0.328552 | − | 0.944486i | \(-0.606561\pi\) |
0.289351 | + | 0.957223i | \(0.406561\pi\) | |||||||
\(102\) | −4.35358 | + | 23.1194i | −0.431068 | + | 2.28916i | ||||
\(103\) | 1.12655 | + | 0.178428i | 0.111002 | + | 0.0175810i | 0.211688 | − | 0.977337i | \(-0.432104\pi\) |
−0.100686 | + | 0.994918i | \(0.532104\pi\) | |||||||
\(104\) | 7.32157 | − | 22.5335i | 0.717939 | − | 2.20959i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.5269 | + | 12.0075i | −1.60523 | + | 1.16627i | ||||
\(107\) | −1.79112 | − | 11.3087i | −0.173155 | − | 1.09325i | −0.909211 | − | 0.416335i | \(-0.863314\pi\) |
0.736057 | − | 0.676920i | \(-0.236686\pi\) | |||||||
\(108\) | −1.63093 | − | 23.2837i | −0.156936 | − | 2.24047i | ||||
\(109\) | 2.63188i | 0.252088i | 0.992025 | + | 0.126044i | \(0.0402281\pi\) | ||||
−0.992025 | + | 0.126044i | \(0.959772\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.72780 | + | 16.0285i | −0.543659 | + | 1.52136i | ||||
\(112\) | 9.74230 | + | 4.96395i | 0.920561 | + | 0.469049i | ||||
\(113\) | −6.74974 | + | 1.06905i | −0.634962 | + | 0.100568i | −0.465614 | − | 0.884988i | \(-0.654166\pi\) |
−0.169349 | + | 0.985556i | \(0.554166\pi\) | |||||||
\(114\) | −0.937090 | − | 3.19722i | −0.0877665 | − | 0.299447i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −20.5212 | − | 6.66776i | −1.90535 | − | 0.619086i | ||||
\(117\) | 8.36232 | − | 7.44302i | 0.773097 | − | 0.688107i | ||||
\(118\) | −4.43212 | − | 27.9833i | −0.408009 | − | 2.57607i | ||||
\(119\) | −2.50391 | − | 7.70623i | −0.229533 | − | 0.706429i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.03485 | − | 6.27467i | −0.821350 | − | 0.570424i | ||||
\(122\) | −2.12695 | − | 2.12695i | −0.192565 | − | 0.192565i | ||||
\(123\) | −8.87578 | + | 8.37453i | −0.800303 | + | 0.755106i | ||||
\(124\) | −5.19430 | + | 7.14934i | −0.466462 | + | 0.642030i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.27183 | + | 9.78020i | 0.558739 | + | 0.871289i | ||||
\(127\) | −1.39126 | − | 2.73050i | −0.123454 | − | 0.242293i | 0.821005 | − | 0.570921i | \(-0.193414\pi\) |
−0.944459 | + | 0.328628i | \(0.893414\pi\) | |||||||
\(128\) | 1.77823 | − | 11.2273i | 0.157175 | − | 0.992361i | ||||
\(129\) | −10.3289 | − | 15.1214i | −0.909411 | − | 1.33137i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.30648i | 0.463629i | 0.972760 | + | 0.231814i | \(0.0744662\pi\) | ||||
−0.972760 | + | 0.231814i | \(0.925534\pi\) | |||||||
\(132\) | 25.5564 | − | 3.56702i | 2.22440 | − | 0.310469i | ||||
\(133\) | 0.811421 | + | 0.811421i | 0.0703592 | + | 0.0703592i | ||||
\(134\) | 12.2814 | + | 37.7982i | 1.06095 | + | 3.26527i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 27.3826 | − | 19.8946i | 2.34804 | − | 1.70595i | ||||
\(137\) | −9.72594 | + | 4.95561i | −0.830943 | + | 0.423387i | −0.817085 | − | 0.576517i | \(-0.804411\pi\) |
−0.0138581 | + | 0.999904i | \(0.504411\pi\) | |||||||
\(138\) | 3.87671 | + | 30.1140i | 0.330007 | + | 2.56347i | ||||
\(139\) | −6.65265 | − | 9.15659i | −0.564271 | − | 0.776652i | 0.427591 | − | 0.903972i | \(-0.359362\pi\) |
−0.991862 | + | 0.127320i | \(0.959362\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.534760 | + | 18.4035i | −0.0450349 | + | 1.54986i | ||||
\(142\) | 0.724235 | − | 0.724235i | 0.0607765 | − | 0.0607765i | ||||
\(143\) | 8.84419 | + | 8.65782i | 0.739588 | + | 0.724003i | ||||
\(144\) | −13.6771 | + | 16.6930i | −1.13976 | + | 1.39108i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.82297 | + | 5.26186i | −0.316391 | + | 0.435475i | ||||
\(147\) | 7.12721 | + | 3.89628i | 0.587842 | + | 0.321360i | ||||
\(148\) | 39.3316 | − | 20.0405i | 3.23304 | − | 1.64732i | ||||
\(149\) | 2.19997 | − | 6.77082i | 0.180229 | − | 0.554687i | −0.819605 | − | 0.572929i | \(-0.805807\pi\) |
0.999834 | + | 0.0182422i | \(0.00580701\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.370455 | + | 0.269151i | 0.0301472 | + | 0.0219032i | 0.602757 | − | 0.797925i | \(-0.294069\pi\) |
−0.572610 | + | 0.819828i | \(0.694069\pi\) | |||||||
\(152\) | −2.17615 | + | 4.27094i | −0.176509 | + | 0.346419i | ||||
\(153\) | 15.9143 | − | 1.58037i | 1.28659 | − | 0.127766i | ||||
\(154\) | −10.3106 | + | 7.66013i | −0.830850 | + | 0.617271i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −29.0209 | − | 0.843272i | −2.32353 | − | 0.0675158i | ||||
\(157\) | 20.7447 | − | 3.28564i | 1.65561 | − | 0.262223i | 0.742472 | − | 0.669877i | \(-0.233653\pi\) |
0.913136 | + | 0.407655i | \(0.133653\pi\) | |||||||
\(158\) | −1.03749 | + | 6.55043i | −0.0825380 | + | 0.521124i | ||||
\(159\) | 10.9930 | + | 8.48544i | 0.871800 | + | 0.672939i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.14680 | − | 8.46034i | −0.484435 | − | 0.666768i | ||||
\(162\) | −21.5011 | + | 7.97161i | −1.68929 | + | 0.626309i | ||||
\(163\) | 1.63257 | − | 3.20411i | 0.127873 | − | 0.250965i | −0.818190 | − | 0.574948i | \(-0.805022\pi\) |
0.946063 | + | 0.323983i | \(0.105022\pi\) | |||||||
\(164\) | 31.6473 | 2.47124 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.3097 | 1.18826 | ||||||||
\(167\) | −5.62090 | + | 11.0316i | −0.434959 | + | 0.853654i | 0.564640 | + | 0.825337i | \(0.309015\pi\) |
−0.999599 | + | 0.0283173i | \(0.990985\pi\) | |||||||
\(168\) | 3.09332 | − | 16.4269i | 0.238655 | − | 1.26736i | ||||
\(169\) | −0.543831 | − | 0.748519i | −0.0418331 | − | 0.0575784i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.90652 | + | 1.22261i | −0.145796 | + | 0.0934957i | ||||
\(172\) | −7.42933 | + | 46.9069i | −0.566481 | + | 3.57662i | ||||
\(173\) | −4.05036 | + | 0.641513i | −0.307943 | + | 0.0487734i | −0.308493 | − | 0.951226i | \(-0.599825\pi\) |
0.000550497 | 1.00000i | \(0.499825\pi\) | ||||||||
\(174\) | −0.615725 | + | 21.1899i | −0.0466780 | + | 1.60640i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −19.4499 | − | 13.8172i | −1.46609 | − | 1.04151i | ||||
\(177\) | −17.4074 | + | 8.24166i | −1.30842 | + | 0.619481i | ||||
\(178\) | 2.17691 | − | 4.27244i | 0.163167 | − | 0.320233i | ||||
\(179\) | 3.70351 | + | 2.69076i | 0.276814 | + | 0.201117i | 0.717526 | − | 0.696531i | \(-0.245274\pi\) |
−0.440713 | + | 0.897648i | \(0.645274\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.60201 | − | 17.2412i | 0.416394 | − | 1.28153i | −0.494603 | − | 0.869119i | \(-0.664687\pi\) |
0.910998 | − | 0.412411i | \(-0.135313\pi\) | |||||||
\(182\) | 12.8768 | − | 6.56107i | 0.954493 | − | 0.486339i | ||||
\(183\) | −0.980838 | + | 1.79418i | −0.0725056 | + | 0.132630i | ||||
\(184\) | 25.6761 | − | 35.3402i | 1.89287 | − | 2.60531i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 8.17573 | + | 2.92161i | 0.599474 | + | 0.214223i | ||||
\(187\) | 2.95161 | + | 17.4323i | 0.215843 | + | 1.27478i | ||||
\(188\) | 33.7630 | − | 33.7630i | 2.46242 | − | 2.46242i | ||||
\(189\) | 5.18090 | − | 5.96138i | 0.376855 | − | 0.433626i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.11298 | + | 1.53189i | 0.0805325 | + | 0.110843i | 0.847383 | − | 0.530983i | \(-0.178177\pi\) |
−0.766850 | + | 0.641826i | \(0.778177\pi\) | |||||||
\(192\) | −0.0722218 | + | 0.00929744i | −0.00521216 | + | 0.000670985i | ||||
\(193\) | −15.0733 | + | 7.68023i | −1.08500 | + | 0.552835i | −0.902640 | − | 0.430397i | \(-0.858374\pi\) |
−0.182360 | + | 0.983232i | \(0.558374\pi\) | |||||||
\(194\) | 3.08100 | − | 2.23848i | 0.221203 | − | 0.160713i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50959 | − | 20.0345i | −0.464971 | − | 1.43103i | ||||
\(197\) | −11.9790 | − | 11.9790i | −0.853469 | − | 0.853469i | 0.137089 | − | 0.990559i | \(-0.456225\pi\) |
−0.990559 | + | 0.137089i | \(0.956225\pi\) | |||||||
\(198\) | −10.4250 | − | 23.1089i | −0.740871 | − | 1.64228i | ||||
\(199\) | 17.4666i | 1.23817i | 0.785323 | + | 0.619087i | \(0.212497\pi\) | ||||
−0.785323 | + | 0.619087i | \(0.787503\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.3093 | − | 15.2387i | 1.57358 | − | 1.07486i | ||||
\(202\) | 0.165112 | − | 1.04247i | 0.0116172 | − | 0.0733483i | ||||
\(203\) | −3.31476 | − | 6.50559i | −0.232651 | − | 0.456603i | ||||
\(204\) | −32.8319 | − | 25.3428i | −2.29869 | − | 1.77435i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.70819 | + | 2.35112i | −0.119015 | + | 0.163810i | ||||
\(207\) | 18.9035 | − | 8.28673i | 1.31389 | − | 0.575968i | ||||
\(208\) | 18.9813 | + | 18.9813i | 1.31612 | + | 1.31612i | ||||
\(209\) | −1.49324 | − | 2.00992i | −0.103290 | − | 0.139029i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.31392 | − | 22.5099i | −0.503511 | − | 1.54965i | −0.803259 | − | 0.595630i | \(-0.796903\pi\) |
0.299748 | − | 0.954018i | \(-0.403097\pi\) | |||||||
\(212\) | −5.63393 | − | 35.5713i | −0.386940 | − | 2.44304i | ||||
\(213\) | −0.610926 | − | 0.333979i | −0.0418599 | − | 0.0228839i | ||||
\(214\) | 27.7451 | + | 9.01493i | 1.89662 | + | 0.616248i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 30.3704 | + | 12.8872i | 2.06644 | + | 0.876864i | ||||
\(217\) | −2.95349 | + | 0.467788i | −0.200496 | + | 0.0317555i | ||||
\(218\) | −5.97493 | − | 3.04438i | −0.404673 | − | 0.206191i | ||||
\(219\) | 4.16351 | + | 1.48783i | 0.281344 | + | 0.100538i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 19.8928i | − | 1.33814i | ||||||
\(222\) | −29.7626 | − | 31.5440i | −1.99754 | − | 2.11710i | ||||
\(223\) | −3.30324 | − | 20.8559i | −0.221202 | − | 1.39661i | −0.809097 | − | 0.587675i | \(-0.800043\pi\) |
0.587895 | − | 0.808937i | \(-0.299957\pi\) | |||||||
\(224\) | −6.92326 | + | 5.03004i | −0.462580 | + | 0.336084i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.38067 | − | 16.5600i | 0.357917 | − | 1.10155i | ||||
\(227\) | 20.1363 | + | 3.18928i | 1.33649 | + | 0.211680i | 0.783441 | − | 0.621467i | \(-0.213463\pi\) |
0.553053 | + | 0.833146i | \(0.313463\pi\) | |||||||
\(228\) | 5.77228 | + | 1.08697i | 0.382279 | + | 0.0719863i | ||||
\(229\) | 7.43142 | − | 2.41461i | 0.491082 | − | 0.159562i | −0.0529996 | − | 0.998595i | \(-0.516878\pi\) |
0.544082 | + | 0.839032i | \(0.316878\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.96843 | + | 5.26145i | 0.458489 | + | 0.346178i | ||||
\(232\) | 21.5661 | − | 21.5661i | 1.41588 | − | 1.41588i | ||||
\(233\) | 11.8179 | + | 6.02151i | 0.774215 | + | 0.394482i | 0.796013 | − | 0.605280i | \(-0.206939\pi\) |
−0.0217973 | + | 0.999762i | \(0.506939\pi\) | |||||||
\(234\) | 7.22430 | + | 27.5939i | 0.472267 | + | 1.80387i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 47.5040 | + | 15.4350i | 3.09225 | + | 1.00473i | ||||
\(237\) | 4.47151 | − | 0.575638i | 0.290456 | − | 0.0373917i | ||||
\(238\) | 20.3912 | + | 3.22965i | 1.32176 | + | 0.209347i | ||||
\(239\) | 5.47156 | + | 3.97532i | 0.353926 | + | 0.257142i | 0.750514 | − | 0.660854i | \(-0.229806\pi\) |
−0.396588 | + | 0.917997i | \(0.629806\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.14988 | −0.267317 | −0.133659 | − | 0.991027i | \(-0.542673\pi\) | ||||
−0.133659 | + | 0.991027i | \(0.542673\pi\) | |||||||
\(242\) | 24.6958 | − | 13.2530i | 1.58750 | − | 0.851933i | ||||
\(243\) | 9.31125 | + | 12.5020i | 0.597317 | + | 0.802005i | ||||
\(244\) | 5.04342 | − | 1.63871i | 0.322872 | − | 0.104907i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.74510 | − | 29.8371i | −0.557567 | − | 1.90234i | ||||
\(247\) | 1.27900 | + | 2.51017i | 0.0813806 | + | 0.159718i | ||||
\(248\) | −5.67079 | − | 11.1296i | −0.360096 | − | 0.706727i | ||||
\(249\) | −2.92721 | − | 9.98724i | −0.185504 | − | 0.632915i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.7703 | + | 5.44901i | −1.05853 | + | 0.343938i | −0.786012 | − | 0.618211i | \(-0.787858\pi\) |
−0.272521 | + | 0.962150i | \(0.587858\pi\) | |||||||
\(252\) | −20.3827 | + | 2.02412i | −1.28399 | + | 0.127508i | ||||
\(253\) | 10.5753 | + | 20.2199i | 0.664861 | + | 1.27122i | ||||
\(254\) | 7.80815 | 0.489927 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 23.3634 | + | 16.9745i | 1.46021 | + | 1.06091i | ||||
\(257\) | −13.1691 | − | 2.08578i | −0.821465 | − | 0.130107i | −0.268466 | − | 0.963289i | \(-0.586517\pi\) |
−0.552999 | + | 0.833182i | \(0.686517\pi\) | |||||||
\(258\) | 46.2768 | − | 5.95742i | 2.88107 | − | 0.370893i | ||||
\(259\) | 14.2061 | + | 4.61584i | 0.882725 | + | 0.286815i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.9409 | − | 3.64984i | 0.862920 | − | 0.225919i | ||||
\(262\) | −12.0469 | − | 6.13818i | −0.744257 | − | 0.379218i | ||||
\(263\) | −13.9748 | + | 13.9748i | −0.861722 | + | 0.861722i | −0.991538 | − | 0.129816i | \(-0.958561\pi\) |
0.129816 | + | 0.991538i | \(0.458561\pi\) | |||||||
\(264\) | −11.9073 | + | 34.4751i | −0.732843 | + | 2.12180i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.78070 | + | 0.903505i | −0.170496 | + | 0.0553974i | ||||
\(267\) | −3.20333 | − | 0.603215i | −0.196041 | − | 0.0369161i | ||||
\(268\) | −69.2038 | − | 10.9608i | −4.22730 | − | 0.669538i | ||||
\(269\) | −3.33489 | + | 10.2637i | −0.203332 | + | 0.625792i | 0.796446 | + | 0.604710i | \(0.206711\pi\) |
−0.999778 | + | 0.0210817i | \(0.993289\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.6761 | + | 12.1159i | −1.01300 | + | 0.735990i | −0.964837 | − | 0.262849i | \(-0.915338\pi\) |
−0.0481667 | + | 0.998839i | \(0.515338\pi\) | |||||||
\(272\) | 5.99886 | + | 37.8753i | 0.363734 | + | 2.29653i | ||||
\(273\) | −6.74213 | − | 7.14567i | −0.408052 | − | 0.432476i | ||||
\(274\) | − | 27.8123i | − | 1.68020i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −50.4064 | − | 18.0128i | −3.03411 | − | 1.08424i | ||||
\(277\) | −8.56011 | − | 4.36159i | −0.514327 | − | 0.262063i | 0.177507 | − | 0.984120i | \(-0.443197\pi\) |
−0.691834 | + | 0.722057i | \(0.743197\pi\) | |||||||
\(278\) | 28.4828 | − | 4.51123i | 1.70828 | − | 0.270566i | ||||
\(279\) | 0.342703 | − | 5.89202i | 0.0205171 | − | 0.352746i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.56570 | − | 1.15857i | −0.212712 | − | 0.0691143i | 0.200723 | − | 0.979648i | \(-0.435671\pi\) |
−0.413435 | + | 0.910534i | \(0.635671\pi\) | |||||||
\(282\) | −41.1614 | − | 22.5020i | −2.45113 | − | 1.33997i | ||||
\(283\) | −3.21136 | − | 20.2757i | −0.190895 | − | 1.20527i | −0.877983 | − | 0.478692i | \(-0.841111\pi\) |
0.687088 | − | 0.726574i | \(-0.258889\pi\) | |||||||
\(284\) | 0.557985 | + | 1.71730i | 0.0331103 | + | 0.101903i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −29.8855 | + | 10.0634i | −1.76717 | + | 0.595064i | ||||
\(287\) | 7.57233 | + | 7.57233i | 0.446981 | + | 0.446981i | ||||
\(288\) | −6.78120 | − | 15.4691i | −0.399586 | − | 0.911526i | ||||
\(289\) | 6.71126 | − | 9.23726i | 0.394780 | − | 0.543368i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.04935 | − | 1.58188i | −0.120135 | − | 0.0927317i | ||||
\(292\) | −5.20564 | − | 10.2166i | −0.304637 | − | 0.597884i | ||||
\(293\) | −2.67282 | + | 16.8755i | −0.156148 | + | 0.985879i | 0.777811 | + | 0.628498i | \(0.216330\pi\) |
−0.933959 | + | 0.357381i | \(0.883670\pi\) | |||||||
\(294\) | −17.0897 | + | 11.6734i | −0.996691 | + | 0.680804i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 62.3950i | 3.62663i | ||||||||
\(297\) | −13.0817 | + | 11.2191i | −0.759079 | + | 0.650998i | ||||
\(298\) | 12.8264 | + | 12.8264i | 0.743016 | + | 0.743016i | ||||
\(299\) | −7.93366 | − | 24.4173i | −0.458815 | − | 1.41209i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.0012 | + | 9.44591i | −0.749375 | + | 0.544453i | ||||
\(302\) | −1.03955 | + | 0.529677i | −0.0598193 | + | 0.0304795i | ||||
\(303\) | −0.711624 | + | 0.0916106i | −0.0408817 | + | 0.00526289i | ||||
\(304\) | −3.19213 | − | 4.39359i | −0.183081 | − | 0.251990i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −14.8208 | + | 37.9569i | −0.847246 | + | 2.16985i | ||||
\(307\) | 19.7867 | − | 19.7867i | 1.12928 | − | 1.12928i | 0.138990 | − | 0.990294i | \(-0.455614\pi\) |
0.990294 | − | 0.138990i | \(-0.0443857\pi\) | |||||||
\(308\) | −3.78038 | − | 22.3270i | −0.215407 | − | 1.27220i | ||||
\(309\) | 1.86035 | + | 0.664797i | 0.105831 | + | 0.0378190i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.75146 | + | 2.41067i | −0.0993160 | + | 0.136697i | −0.855783 | − | 0.517336i | \(-0.826924\pi\) |
0.756467 | + | 0.654032i | \(0.226924\pi\) | |||||||
\(312\) | 19.6849 | − | 36.0082i | 1.11444 | − | 2.03857i | ||||
\(313\) | −13.4239 | + | 6.83984i | −0.758766 | + | 0.386611i | −0.790163 | − | 0.612896i | \(-0.790004\pi\) |
0.0313971 | + | 0.999507i | \(0.490004\pi\) | |||||||
\(314\) | −16.5370 | + | 50.8956i | −0.933236 | + | 2.87221i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.45917 | − | 6.87249i | −0.532120 | − | 0.386608i | ||||
\(317\) | 2.94350 | − | 5.77694i | 0.165323 | − | 0.324466i | −0.793451 | − | 0.608634i | \(-0.791718\pi\) |
0.958774 | + | 0.284169i | \(0.0917176\pi\) | |||||||
\(318\) | −31.9797 | + | 15.1411i | −1.79333 | + | 0.849069i | ||||
\(319\) | 5.08422 | + | 15.0987i | 0.284662 | + | 0.845362i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.576007 | − | 19.8231i | 0.0321496 | − | 1.10642i | ||||
\(322\) | 26.3170 | − | 4.16821i | 1.46659 | − | 0.232285i | ||||
\(323\) | −0.629578 | + | 3.97500i | −0.0350307 | + | 0.221175i | ||||
\(324\) | 4.68697 | − | 40.1547i | 0.260387 | − | 2.23081i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.38556 | + | 7.41259i | 0.298279 | + | 0.410546i | ||||
\(327\) | −0.843586 | + | 4.47981i | −0.0466504 | + | 0.247734i | ||||
\(328\) | −20.3082 | + | 39.8572i | −1.12133 | + | 2.20074i | ||||
\(329\) | 16.1571 | 0.890771 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.1458 | −1.10732 | −0.553658 | − | 0.832744i | \(-0.686768\pi\) | ||||
−0.553658 | + | 0.832744i | \(0.686768\pi\) | |||||||
\(332\) | −12.2535 | + | 24.0488i | −0.672497 | + | 1.31985i | ||||
\(333\) | −14.8870 | + | 25.4467i | −0.815805 | + | 1.39447i | ||||
\(334\) | −18.5423 | − | 25.5213i | −1.01459 | − | 1.39647i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 14.9916 | + | 11.5720i | 0.817860 | + | 0.631303i | ||||
\(337\) | −4.97858 | + | 31.4335i | −0.271201 | + | 1.71229i | 0.356884 | + | 0.934149i | \(0.383839\pi\) |
−0.628084 | + | 0.778145i | \(0.716161\pi\) | |||||||
\(338\) | 2.32837 | − | 0.368777i | 0.126647 | − | 0.0200588i | ||||
\(339\) | −11.8316 | − | 0.343797i | −0.642606 | − | 0.0186725i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.52451 | − | 0.0694766i | 0.353322 | − | 0.00376237i | ||||
\(342\) | −0.570259 | − | 5.74247i | −0.0308361 | − | 0.310517i | ||||
\(343\) | 8.06655 | − | 15.8315i | 0.435553 | − | 0.854820i | ||||
\(344\) | −54.3079 | − | 39.4570i | −2.92809 | − | 2.12738i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.22881 | − | 9.93725i | 0.173582 | − | 0.534230i | ||||
\(347\) | −21.3809 | + | 10.8941i | −1.14779 | + | 0.584827i | −0.921171 | − | 0.389157i | \(-0.872766\pi\) |
−0.226616 | + | 0.973984i | \(0.572766\pi\) | |||||||
\(348\) | −32.7927 | − | 17.9270i | −1.75788 | − | 0.960990i | ||||
\(349\) | −7.88353 | + | 10.8507i | −0.421995 | + | 0.580827i | −0.966093 | − | 0.258195i | \(-0.916872\pi\) |
0.544097 | + | 0.839022i | \(0.316872\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.6195 | − | 9.98868i | 0.887082 | − | 0.533156i | ||||
\(352\) | 16.5464 | − | 8.65395i | 0.881925 | − | 0.461257i | ||||
\(353\) | −1.90374 | + | 1.90374i | −0.101326 | + | 0.101326i | −0.755953 | − | 0.654626i | \(-0.772826\pi\) |
0.654626 | + | 0.755953i | \(0.272826\pi\) | |||||||
\(354\) | 1.42532 | − | 49.0519i | 0.0757551 | − | 2.60708i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.96888 | + | 6.83908i | 0.263350 | + | 0.362471i | ||||
\(357\) | −1.79194 | − | 13.9196i | −0.0948393 | − | 0.736704i | ||||
\(358\) | −10.3926 | + | 5.29529i | −0.549265 | + | 0.279865i | ||||
\(359\) | 16.6144 | − | 12.0710i | 0.876872 | − | 0.637085i | −0.0555499 | − | 0.998456i | \(-0.517691\pi\) |
0.932422 | + | 0.361371i | \(0.117691\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.69520 | + | 17.5280i | 0.299747 | + | 0.922527i | ||||
\(362\) | 32.6613 | + | 32.6613i | 1.71664 | + | 1.71664i | ||||
\(363\) | −13.3673 | − | 13.5762i | −0.701603 | − | 0.712568i | ||||
\(364\) | 25.4785i | 1.33543i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.93862 | − | 4.30211i | −0.153604 | − | 0.224875i | ||||
\(367\) | −3.78926 | + | 23.9244i | −0.197798 | + | 1.24885i | 0.666362 | + | 0.745628i | \(0.267850\pi\) |
−0.864160 | + | 0.503217i | \(0.832150\pi\) | |||||||
\(368\) | 22.4687 | + | 44.0973i | 1.17126 | + | 2.29873i | ||||
\(369\) | −17.7920 | + | 11.4097i | −0.926217 | + | 0.593963i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.16318 | − | 9.85927i | 0.371894 | − | 0.511868i | ||||
\(372\) | −11.1329 | + | 10.5042i | −0.577216 | + | 0.544619i | ||||
\(373\) | 17.4780 | + | 17.4780i | 0.904976 | + | 0.904976i | 0.995861 | − | 0.0908853i | \(-0.0289697\pi\) |
−0.0908853 | + | 0.995861i | \(0.528970\pi\) | |||||||
\(374\) | −42.9893 | − | 13.4637i | −2.22292 | − | 0.696192i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.8558 | + | 64.1876i | 1.07556 | + | 3.31022i | ||||
\(377\) | −2.80414 | − | 17.7046i | −0.144420 | − | 0.911834i | ||||
\(378\) | 7.54070 | + | 18.6575i | 0.387852 | + | 0.959638i | ||||
\(379\) | −12.8286 | − | 4.16826i | −0.658960 | − | 0.214109i | −0.0395991 | − | 0.999216i | \(-0.512608\pi\) |
−0.619361 | + | 0.785107i | \(0.712608\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.49291 | − | 5.09361i | −0.0764843 | − | 0.260954i | ||||
\(382\) | −4.76514 | + | 0.754724i | −0.243806 | + | 0.0386150i | ||||
\(383\) | −23.5502 | − | 11.9994i | −1.20336 | − | 0.613142i | −0.266834 | − | 0.963743i | \(-0.585977\pi\) |
−0.936525 | + | 0.350601i | \(0.885977\pi\) | |||||||
\(384\) | 6.62543 | − | 18.5404i | 0.338102 | − | 0.946135i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 43.1036i | − | 2.19392i | ||||||
\(387\) | −12.7344 | − | 29.0494i | −0.647326 | − | 1.47667i | ||||
\(388\) | 1.05030 | + | 6.63132i | 0.0533208 | + | 0.336654i | ||||
\(389\) | −21.0424 | + | 15.2882i | −1.06689 | + | 0.775144i | −0.975351 | − | 0.220658i | \(-0.929180\pi\) |
−0.0915423 | + | 0.995801i | \(0.529180\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.3336 | − | 34.8813i | 0.573165 | − | 1.76402i | ||||
\(392\) | 29.4090 | + | 4.65792i | 1.48538 | + | 0.235261i | ||||
\(393\) | −1.70087 | + | 9.03234i | −0.0857973 | + | 0.455621i | ||||
\(394\) | 41.0515 | − | 13.3384i | 2.06814 | − | 0.671981i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 44.6437 | + | 2.11995i | 2.24343 | + | 0.106532i | ||||
\(397\) | 8.26181 | − | 8.26181i | 0.414648 | − | 0.414648i | −0.468706 | − | 0.883354i | \(-0.655280\pi\) |
0.883354 | + | 0.468706i | \(0.155280\pi\) | |||||||
\(398\) | −39.6529 | − | 20.2042i | −1.98762 | − | 1.01274i | ||||
\(399\) | 1.12107 | + | 1.64123i | 0.0561235 | + | 0.0821643i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.81862 | − | 2.86534i | −0.440381 | − | 0.143088i | 0.0804306 | − | 0.996760i | \(-0.474370\pi\) |
−0.520811 | + | 0.853672i | \(0.674370\pi\) | |||||||
\(402\) | 8.78924 | + | 68.2741i | 0.438367 | + | 3.40520i | ||||
\(403\) | −7.25099 | − | 1.14844i | −0.361197 | − | 0.0572081i | ||||
\(404\) | 1.50539 | + | 1.09373i | 0.0748959 | + | 0.0544151i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.6034 | 0.923271 | ||||||||
\(407\) | −29.1965 | − | 14.4869i | −1.44722 | − | 0.718088i | ||||
\(408\) | 52.9856 | − | 25.0865i | 2.62318 | − | 1.24196i | ||||
\(409\) | 2.94643 | − | 0.957353i | 0.145692 | − | 0.0473380i | −0.235263 | − | 0.971932i | \(-0.575595\pi\) |
0.380955 | + | 0.924594i | \(0.375595\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.1433 | + | 5.31770i | −0.894941 | + | 0.262303i | ||||
\(412\) | −2.32600 | − | 4.56502i | −0.114594 | − | 0.224903i | ||||
\(413\) | 7.67324 | + | 15.0596i | 0.377576 | + | 0.741034i | ||||
\(414\) | −3.05365 | + | 52.5006i | −0.150079 | + | 2.58027i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −19.9811 | + | 6.49227i | −0.979656 | + | 0.318310i | ||||
\(417\) | −8.38878 | − | 17.7181i | −0.410800 | − | 0.867659i | ||||
\(418\) | 6.29023 | − | 1.06505i | 0.307665 | − | 0.0520934i | ||||
\(419\) | 9.02879 | 0.441085 | 0.220543 | − | 0.975377i | \(-0.429217\pi\) | ||||
0.220543 | + | 0.975377i | \(0.429217\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.22658 | − | 3.79733i | −0.254728 | − | 0.185071i | 0.453092 | − | 0.891464i | \(-0.350321\pi\) |
−0.707820 | + | 0.706393i | \(0.750321\pi\) | |||||||
\(422\) | 59.5627 | + | 9.43381i | 2.89947 | + | 0.459231i | ||||
\(423\) | −6.80905 | + | 31.1539i | −0.331067 | + | 1.51475i | ||||
\(424\) | 48.4144 | + | 15.7308i | 2.35121 | + | 0.763954i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.46488 | − | 1.00061i | 0.0709738 | − | 0.0484797i | ||||
\(427\) | 1.59885 | + | 0.814654i | 0.0773737 | + | 0.0394239i | ||||
\(428\) | −36.3672 | + | 36.3672i | −1.75788 | + | 1.75788i | ||||
\(429\) | 12.2789 | + | 17.5716i | 0.592833 | + | 0.848363i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.6607 | + | 4.43862i | −0.658012 | + | 0.213801i | −0.618943 | − | 0.785436i | \(-0.712439\pi\) |
−0.0390683 | + | 0.999237i | \(0.512439\pi\) | |||||||
\(432\) | −28.6308 | + | 24.0299i | −1.37750 | + | 1.15614i | ||||
\(433\) | 10.7522 | + | 1.70299i | 0.516719 | + | 0.0818403i | 0.409347 | − | 0.912379i | \(-0.365756\pi\) |
0.107372 | + | 0.994219i | \(0.465756\pi\) | |||||||
\(434\) | 2.35443 | − | 7.24618i | 0.113016 | − | 0.347828i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.56434 | − | 6.94890i | 0.458049 | − | 0.332792i | ||||
\(437\) | 0.812539 | + | 5.13017i | 0.0388690 | + | 0.245409i | ||||
\(438\) | −8.19377 | + | 7.73104i | −0.391513 | + | 0.369403i | ||||
\(439\) | 13.8909i | 0.662975i | 0.943460 | + | 0.331488i | \(0.107551\pi\) | ||||
−0.943460 | + | 0.331488i | \(0.892449\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.8826 | + | 8.91645i | 0.518220 | + | 0.424593i | ||||
\(442\) | 45.1611 | + | 23.0107i | 2.14809 | + | 1.09451i | ||||
\(443\) | 4.52898 | − | 0.717321i | 0.215179 | − | 0.0340809i | −0.0479143 | − | 0.998851i | \(-0.515257\pi\) |
0.263093 | + | 0.964771i | \(0.415257\pi\) | |||||||
\(444\) | 73.3712 | − | 21.5047i | 3.48204 | − | 1.02057i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 51.1683 | + | 16.6256i | 2.42289 | + | 0.787245i | ||||
\(447\) | 5.91487 | − | 10.8197i | 0.279764 | − | 0.511754i | ||||
\(448\) | 0.00999653 | + | 0.0631156i | 0.000472292 | + | 0.00298193i | ||||
\(449\) | −9.12613 | − | 28.0873i | −0.430689 | − | 1.32552i | −0.897440 | − | 0.441136i | \(-0.854576\pi\) |
0.466752 | − | 0.884388i | \(-0.345424\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.9352 | − | 18.7569i | −0.656184 | − | 0.883228i | ||||
\(452\) | 21.7062 | + | 21.7062i | 1.02097 | + | 1.02097i | ||||
\(453\) | 0.544294 | + | 0.576872i | 0.0255732 | + | 0.0271038i | ||||
\(454\) | −30.5327 | + | 42.0246i | −1.43297 | + | 1.97231i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.07305 | + | 6.57219i | −0.237567 | + | 0.307771i | ||||
\(457\) | −7.48292 | − | 14.6861i | −0.350036 | − | 0.686985i | 0.647117 | − | 0.762391i | \(-0.275975\pi\) |
−0.997153 | + | 0.0754062i | \(0.975975\pi\) | |||||||
\(458\) | −3.11447 | + | 19.6640i | −0.145530 | + | 0.918839i | ||||
\(459\) | 27.5948 | + | 2.41093i | 1.28801 | + | 0.112532i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 28.5289i | − | 1.32872i | −0.747412 | − | 0.664361i | \(-0.768704\pi\) | ||
0.747412 | − | 0.664361i | \(-0.231296\pi\) | |||||||
\(462\) | −20.0053 | + | 9.73376i | −0.930729 | + | 0.452855i | ||||
\(463\) | −11.3562 | − | 11.3562i | −0.527765 | − | 0.527765i | 0.392140 | − | 0.919905i | \(-0.371735\pi\) |
−0.919905 | + | 0.392140i | \(0.871735\pi\) | |||||||
\(464\) | 10.6780 | + | 32.8634i | 0.495712 | + | 1.52564i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.3403 | + | 19.8639i | −1.26651 | + | 0.920177i | ||||
\(467\) | −25.7711 | + | 13.1310i | −1.19255 | + | 0.607632i | −0.933620 | − | 0.358265i | \(-0.883368\pi\) |
−0.258926 | + | 0.965897i | \(0.583368\pi\) | |||||||
\(468\) | −49.1271 | − | 10.7373i | −2.27090 | − | 0.496333i | ||||
\(469\) | −13.9360 | − | 19.1812i | −0.643503 | − | 0.885706i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 36.3634 | + | 1.05663i | 1.67554 | + | 0.0486869i | ||||
\(472\) | −49.9227 | + | 49.9227i | −2.29788 | + | 2.29788i | ||||
\(473\) | 31.0724 | − | 16.2512i | 1.42871 | − | 0.747232i | ||||
\(474\) | −3.86553 | + | 10.8172i | −0.177550 | + | 0.496849i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −21.3937 | + | 29.4459i | −0.980580 | + | 1.34965i | ||||
\(477\) | 15.9917 | + | 17.9669i | 0.732211 | + | 0.822648i | ||||
\(478\) | −15.3540 | + | 7.82325i | −0.702275 | + | 0.357827i | ||||
\(479\) | −2.41099 | + | 7.42025i | −0.110161 | + | 0.339040i | −0.990907 | − | 0.134548i | \(-0.957042\pi\) |
0.880746 | + | 0.473589i | \(0.157042\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.6679 | + | 21.5550i | 1.35274 | + | 0.982825i | ||||
\(482\) | 4.80030 | − | 9.42112i | 0.218648 | − | 0.429120i | ||||
\(483\) | −7.75091 | − | 16.3708i | −0.352679 | − | 0.744899i | ||||
\(484\) | 1.05220 | + | 49.3999i | 0.0478271 | + | 2.24545i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −39.1529 | + | 6.67706i | −1.77601 | + | 0.302878i | ||||
\(487\) | −24.8900 | + | 3.94219i | −1.12787 | + | 0.178638i | −0.692365 | − | 0.721547i | \(-0.743431\pi\) |
−0.435508 | + | 0.900185i | \(0.643431\pi\) | |||||||
\(488\) | −1.17257 | + | 7.40333i | −0.0530798 | + | 0.335133i | ||||
\(489\) | 3.80586 | − | 4.93054i | 0.172107 | − | 0.222967i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.3332 | − | 16.9752i | −0.556590 | − | 0.766080i | 0.434298 | − | 0.900769i | \(-0.356996\pi\) |
−0.990888 | + | 0.134689i | \(0.956996\pi\) | |||||||
\(492\) | 53.8680 | + | 10.1438i | 2.42856 | + | 0.457318i | ||||
\(493\) | 11.6254 | − | 22.8161i | 0.523582 | − | 1.02759i | ||||
\(494\) | −7.17809 | −0.322958 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.1520 | 0.635442 | ||||||||
\(497\) | −0.277393 | + | 0.544414i | −0.0124428 | + | 0.0244203i | ||||
\(498\) | 26.0592 | + | 4.90717i | 1.16774 | + | 0.219896i | ||||
\(499\) | −5.26071 | − | 7.24075i | −0.235502 | − | 0.324140i | 0.674866 | − | 0.737940i | \(-0.264201\pi\) |
−0.910368 | + | 0.413800i | \(0.864201\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.1035 | + | 16.9757i | −0.585420 | + | 0.758418i | ||||
\(502\) | 7.02836 | − | 44.3753i | 0.313691 | − | 1.98057i | ||||
\(503\) | −21.9496 | + | 3.47647i | −0.978684 | + | 0.155008i | −0.625227 | − | 0.780443i | \(-0.714994\pi\) |
−0.353456 | + | 0.935451i | \(0.614994\pi\) | |||||||
\(504\) | 10.5305 | − | 26.9692i | 0.469065 | − | 1.20131i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −58.1364 | + | 0.619069i | −2.58448 | + | 0.0275210i | ||||
\(507\) | −0.685753 | − | 1.44839i | −0.0304554 | − | 0.0643253i | ||||
\(508\) | −6.24943 | + | 12.2652i | −0.277273 | + | 0.544180i | ||||
\(509\) | −15.1837 | − | 11.0316i | −0.673004 | − | 0.488966i | 0.198026 | − | 0.980197i | \(-0.436547\pi\) |
−0.871029 | + | 0.491231i | \(0.836547\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.19900 | − | 3.69013i | 0.0530404 | − | 0.163242i | ||||
\(512\) | −45.3046 | + | 23.0838i | −2.00220 | + | 1.02017i | ||||
\(513\) | −3.63704 | + | 1.46996i | −0.160579 | + | 0.0649004i | ||||
\(514\) | 19.9683 | − | 27.4840i | 0.880764 | − | 1.21227i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −27.6806 | + | 77.4606i | −1.21857 | + | 3.41001i | ||||
\(517\) | −34.8777 | − | 5.14401i | −1.53392 | − | 0.226233i | ||||
\(518\) | −26.9117 | + | 26.9117i | −1.18243 | + | 1.18243i | ||||
\(519\) | −7.09987 | − | 0.206304i | −0.311650 | − | 0.00905575i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.74842 | + | 2.40650i | 0.0765998 | + | 0.105431i | 0.845598 | − | 0.533821i | \(-0.179244\pi\) |
−0.768998 | + | 0.639251i | \(0.779244\pi\) | |||||||
\(522\) | −7.83998 | + | 35.8708i | −0.343147 | + | 1.57002i | ||||
\(523\) | 20.7752 | − | 10.5855i | 0.908435 | − | 0.462871i | 0.0636475 | − | 0.997972i | \(-0.479727\pi\) |
0.844788 | + | 0.535102i | \(0.179727\pi\) | |||||||
\(524\) | 19.2839 | − | 14.0106i | 0.842423 | − | 0.612056i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.5607 | − | 47.8909i | −0.678478 | − | 2.08814i | ||||
\(527\) | −7.41578 | − | 7.41578i | −0.323037 | − | 0.323037i | ||||
\(528\) | −28.6776 | − | 29.7529i | −1.24803 | − | 1.29483i | ||||
\(529\) | − | 24.3348i | − | 1.05803i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −32.2714 | + | 8.44890i | −1.40046 | + | 0.366651i | ||||
\(532\) | 0.806354 | − | 5.09112i | 0.0349599 | − | 0.220728i | ||||
\(533\) | 11.9358 | + | 23.4254i | 0.516998 | + | 1.01467i | ||||
\(534\) | 5.07483 | − | 6.57450i | 0.219609 | − | 0.284507i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 58.2127 | − | 80.1229i | 2.51440 | − | 3.46078i | ||||
\(537\) | 5.44142 | + | 5.76711i | 0.234815 | + | 0.248869i | ||||
\(538\) | −19.4434 | − | 19.4434i | −0.838263 | − | 0.838263i | ||||
\(539\) | −9.00777 | + | 12.6799i | −0.387992 | + | 0.546162i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0736 | + | 34.0809i | 0.476089 | + | 1.46525i | 0.844483 | + | 0.535582i | \(0.179908\pi\) |
−0.368394 | + | 0.929670i | \(0.620092\pi\) | |||||||
\(542\) | −8.21594 | − | 51.8734i | −0.352905 | − | 2.22815i | ||||
\(543\) | 15.0617 | − | 27.5513i | 0.646357 | − | 1.18234i | ||||
\(544\) | −28.5440 | − | 9.27452i | −1.22381 | − | 0.397642i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 24.0211 | − | 7.04046i | 1.02801 | − | 0.301304i | ||||
\(547\) | 30.5049 | − | 4.83151i | 1.30430 | − | 0.206580i | 0.534663 | − | 0.845065i | \(-0.320439\pi\) |
0.769634 | + | 0.638485i | \(0.220439\pi\) | |||||||
\(548\) | 43.6881 | + | 22.2602i | 1.86626 | + | 0.950909i | ||||
\(549\) | −2.24460 | + | 2.73956i | −0.0957973 | + | 0.116921i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.62649i | 0.154494i | ||||||||
\(552\) | 55.0317 | − | 51.9238i | 2.34230 | − | 2.21002i | ||||
\(553\) | −0.618922 | − | 3.90772i | −0.0263192 | − | 0.166173i | ||||
\(554\) | 19.8035 | − | 14.3881i | 0.841372 | − | 0.611292i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.7105 | + | 48.3520i | −0.666274 | + | 2.05058i | ||||
\(557\) | −0.985507 | − | 0.156089i | −0.0417573 | − | 0.00661370i | 0.135521 | − | 0.990774i | \(-0.456729\pi\) |
−0.177278 | + | 0.984161i | \(0.556729\pi\) | |||||||
\(558\) | 12.9797 | + | 7.59351i | 0.549476 | + | 0.321459i | ||||
\(559\) | −37.5226 | + | 12.1918i | −1.58703 | + | 0.515659i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.563472 | + | 30.6182i | −0.0237898 | + | 1.29270i | ||||
\(562\) | 6.75477 | − | 6.75477i | 0.284933 | − | 0.284933i | ||||
\(563\) | 0.324370 | + | 0.165275i | 0.0136706 | + | 0.00696550i | 0.460812 | − | 0.887498i | \(-0.347558\pi\) |
−0.447142 | + | 0.894463i | \(0.647558\pi\) | |||||||
\(564\) | 68.2911 | − | 46.6472i | 2.87557 | − | 1.96420i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 49.7450 | + | 16.1631i | 2.09094 | + | 0.679387i | ||||
\(567\) | 10.7294 | − | 8.48645i | 0.450591 | − | 0.356397i | ||||
\(568\) | −2.52086 | − | 0.399265i | −0.105773 | − | 0.0167528i | ||||
\(569\) | 36.2145 | + | 26.3114i | 1.51819 | + | 1.10303i | 0.962374 | + | 0.271728i | \(0.0875951\pi\) |
0.555819 | + | 0.831304i | \(0.312405\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.86298 | 0.412753 | 0.206376 | − | 0.978473i | \(-0.433833\pi\) | ||||
0.206376 | + | 0.978473i | \(0.433833\pi\) | |||||||
\(572\) | 8.11168 | − | 54.9992i | 0.339166 | − | 2.29963i | ||||
\(573\) | 1.40343 | + | 2.96422i | 0.0586293 | + | 0.123832i | ||||
\(574\) | −25.9500 | + | 8.43167i | −1.08313 | + | 0.351931i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.125911 | − | 0.00732350i | −0.00524630 | − | 0.000305146i | ||||
\(577\) | −12.0447 | − | 23.6391i | −0.501427 | − | 0.984107i | −0.993530 | − | 0.113570i | \(-0.963772\pi\) |
0.492103 | − | 0.870537i | \(-0.336228\pi\) | |||||||
\(578\) | 13.2074 | + | 25.9211i | 0.549357 | + | 1.07817i | ||||
\(579\) | −28.1185 | + | 8.24139i | −1.16857 | + | 0.342501i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.68614 | + | 2.82230i | −0.360362 | + | 0.117089i | ||||
\(582\) | 5.96177 | − | 2.82265i | 0.247123 | − | 0.117003i | ||||
\(583\) | −18.6018 | + | 19.0022i | −0.770407 | + | 0.786991i | ||||
\(584\) | 16.2075 | 0.670671 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −35.2194 | − | 25.5884i | −1.45490 | − | 1.05705i | ||||
\(587\) | −5.59840 | − | 0.886699i | −0.231071 | − | 0.0365980i | 0.0398252 | − | 0.999207i | \(-0.487320\pi\) |
−0.270896 | + | 0.962609i | \(0.587320\pi\) | |||||||
\(588\) | −4.65863 | − | 36.1878i | −0.192118 | − | 1.49236i | ||||
\(589\) | 1.41255 | + | 0.458966i | 0.0582031 | + | 0.0189113i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.5503 | − | 24.2295i | −0.680789 | − | 0.996668i | ||||
\(592\) | −62.9869 | − | 32.0934i | −2.58875 | − | 1.31903i | ||||
\(593\) | 29.9393 | − | 29.9393i | 1.22946 | − | 1.22946i | 0.265293 | − | 0.964168i | \(-0.414531\pi\) |
0.964168 | − | 0.265293i | \(-0.0854688\pi\) | |||||||
\(594\) | −10.3377 | − | 42.6759i | −0.424161 | − | 1.75101i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −30.4140 | + | 9.88210i | −1.24580 | + | 0.404786i | ||||
\(597\) | −5.59850 | + | 29.7305i | −0.229131 | + | 1.21679i | ||||
\(598\) | 64.6097 | + | 10.2332i | 2.64209 | + | 0.418465i | ||||
\(599\) | −6.05826 | + | 18.6454i | −0.247534 | + | 0.761830i | 0.747676 | + | 0.664064i | \(0.231170\pi\) |
−0.995209 | + | 0.0977664i | \(0.968830\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.66141 | + | 5.56634i | −0.312515 | + | 0.227056i | −0.732975 | − | 0.680256i | \(-0.761869\pi\) |
0.420460 | + | 0.907311i | \(0.361869\pi\) | |||||||
\(602\) | −6.40537 | − | 40.4419i | −0.261063 | − | 1.64829i | ||||
\(603\) | 42.8579 | − | 18.7876i | 1.74531 | − | 0.765091i | ||||
\(604\) | − | 2.05688i | − | 0.0836934i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.615183 | − | 1.72151i | 0.0249901 | − | 0.0699316i | ||||
\(607\) | −32.2074 | − | 16.4105i | −1.30726 | − | 0.666081i | −0.345098 | − | 0.938567i | \(-0.612154\pi\) |
−0.962160 | + | 0.272486i | \(0.912154\pi\) | |||||||
\(608\) | 4.19812 | − | 0.664916i | 0.170256 | − | 0.0269659i | ||||
\(609\) | −3.55696 | − | 12.1359i | −0.144135 | − | 0.491770i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 37.7252 | + | 12.2577i | 1.52620 | + | 0.495891i | ||||
\(612\) | −47.7613 | − | 53.6604i | −1.93064 | − | 2.16909i | ||||
\(613\) | −0.527373 | − | 3.32971i | −0.0213004 | − | 0.134486i | 0.974746 | − | 0.223314i | \(-0.0716876\pi\) |
−0.996047 | + | 0.0888287i | \(0.971688\pi\) | |||||||
\(614\) | 22.0321 | + | 67.8079i | 0.889144 | + | 2.73650i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 30.5449 | + | 9.56628i | 1.23069 | + | 0.385437i | ||||
\(617\) | −1.43952 | − | 1.43952i | −0.0579528 | − | 0.0579528i | 0.677536 | − | 0.735489i | \(-0.263048\pi\) |
−0.735489 | + | 0.677536i | \(0.763048\pi\) | |||||||
\(618\) | −3.66116 | + | 3.45440i | −0.147273 | + | 0.138956i | ||||
\(619\) | −1.47379 | + | 2.02850i | −0.0592367 | + | 0.0815323i | −0.837608 | − | 0.546272i | \(-0.816046\pi\) |
0.778371 | + | 0.627805i | \(0.216046\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 34.8325 | − | 8.04606i | 1.39778 | − | 0.322877i | ||||
\(622\) | −3.44678 | − | 6.76469i | −0.138203 | − | 0.271239i | ||||
\(623\) | −0.447487 | + | 2.82532i | −0.0179282 | + | 0.113194i | ||||
\(624\) | 26.2248 | + | 38.3928i | 1.04983 | + | 1.53694i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 38.3872i | − | 1.53426i | ||||||
\(627\) | −1.89747 | − | 3.89977i | −0.0757777 | − | 0.155742i | ||||
\(628\) | −66.7121 | − | 66.7121i | −2.66210 | − | 2.66210i | ||||
\(629\) | 16.1885 | + | 49.8231i | 0.645478 | + | 1.98658i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.5361 | + | 25.0919i | −1.37486 | + | 0.998894i | −0.377520 | + | 0.926002i | \(0.623223\pi\) |
−0.997340 | + | 0.0728922i | \(0.976777\pi\) | |||||||
\(632\) | 14.7253 | − | 7.50293i | 0.585742 | − | 0.298450i | ||||
\(633\) | −5.23425 | − | 40.6593i | −0.208043 | − | 1.61606i | ||||
\(634\) | 9.71007 | + | 13.3648i | 0.385636 | + | 0.530783i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.81182 | − | 62.3529i | 0.0718432 | − | 2.47245i | ||||
\(637\) | 12.3744 | − | 12.3744i | 0.490293 | − | 0.490293i | ||||
\(638\) | −40.1583 | − | 5.92284i | −1.58988 | − | 0.234487i | ||||
\(639\) | −0.932829 | − | 0.764295i | −0.0369021 | − | 0.0302350i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.237865 | + | 0.327394i | −0.00939512 | + | 0.0129313i | −0.813689 | − | 0.581301i | \(-0.802544\pi\) |
0.804294 | + | 0.594232i | \(0.202544\pi\) | |||||||
\(642\) | 44.3364 | + | 24.2377i | 1.74982 | + | 0.956584i | ||||
\(643\) | 4.95472 | − | 2.52455i | 0.195395 | − | 0.0995587i | −0.353556 | − | 0.935413i | \(-0.615028\pi\) |
0.548951 | + | 0.835855i | \(0.315028\pi\) | |||||||
\(644\) | −14.5159 | + | 44.6754i | −0.572007 | + | 1.76046i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.29586 | − | 6.02730i | −0.326396 | − | 0.237141i | ||||
\(647\) | 12.7057 | − | 24.9364i | 0.499514 | − | 0.980352i | −0.494299 | − | 0.869292i | \(-0.664575\pi\) |
0.993814 | − | 0.111060i | \(-0.0354246\pi\) | |||||||
\(648\) | 47.5638 | + | 31.6703i | 1.86848 | + | 1.24413i | ||||
\(649\) | −11.7693 | − | 34.9514i | −0.461986 | − | 1.37196i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.17718 | − | 0.150436i | −0.202910 | − | 0.00589604i | ||||
\(652\) | −15.9543 | + | 2.52691i | −0.624819 | + | 0.0989616i | ||||
\(653\) | −0.412229 | + | 2.60271i | −0.0161318 | + | 0.101852i | −0.994440 | − | 0.105300i | \(-0.966420\pi\) |
0.978309 | + | 0.207152i | \(0.0664196\pi\) | |||||||
\(654\) | −9.19434 | − | 7.09707i | −0.359527 | − | 0.277517i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −29.7896 | − | 41.0018i | −1.16309 | − | 1.60085i | ||||
\(657\) | 6.60996 | + | 3.86701i | 0.257879 | + | 0.150866i | ||||
\(658\) | −18.6895 | + | 36.6802i | −0.728592 | + | 1.42994i | ||||
\(659\) | −0.616435 | −0.0240129 | −0.0120064 | − | 0.999928i | \(-0.503822\pi\) | ||||
−0.0120064 | + | 0.999928i | \(0.503822\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 50.0465 | 1.94658 | 0.973292 | − | 0.229570i | \(-0.0737321\pi\) | ||||
0.973292 | + | 0.229570i | \(0.0737321\pi\) | |||||||
\(662\) | 23.3034 | − | 45.7355i | 0.905711 | − | 1.77756i | ||||
\(663\) | 6.37618 | − | 33.8603i | 0.247630 | − | 1.31503i | ||||
\(664\) | −22.4244 | − | 30.8645i | −0.870234 | − | 1.19777i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −40.5493 | − | 63.2319i | −1.57125 | − | 2.45019i | ||||
\(667\) | 5.16997 | − | 32.6419i | 0.200182 | − | 1.26390i | ||||
\(668\) | 54.9302 | − | 8.70009i | 2.12531 | − | 0.336617i | ||||
\(669\) | 1.06229 | − | 36.5583i | 0.0410705 | − | 1.41342i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.19200 | − | 2.26759i | −0.123226 | − | 0.0875393i | ||||
\(672\) | −13.3966 | + | 6.34272i | −0.516784 | + | 0.244676i | ||||
\(673\) | −22.5469 | + | 44.2508i | −0.869119 | + | 1.70574i | −0.176677 | + | 0.984269i | \(0.556535\pi\) |
−0.692442 | + | 0.721474i | \(0.743465\pi\) | |||||||
\(674\) | −65.6021 | − | 47.6627i | −2.52690 | − | 1.83590i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.28428 | + | 3.95260i | −0.0493954 | + | 0.152023i | ||||
\(677\) | −24.3494 | + | 12.4067i | −0.935825 | + | 0.476827i | −0.854263 | − | 0.519841i | \(-0.825991\pi\) |
−0.0815625 | + | 0.996668i | \(0.525991\pi\) | |||||||
\(678\) | 14.4665 | − | 26.4627i | 0.555584 | − | 1.01629i | ||||
\(679\) | −1.33538 | + | 1.83800i | −0.0512474 | + | 0.0705360i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 33.2525 | + | 11.8828i | 1.27424 | + | 0.455350i | ||||
\(682\) | −7.38939 | + | 14.8924i | −0.282954 | + | 0.570260i | ||||
\(683\) | −3.88464 | + | 3.88464i | −0.148642 | + | 0.148642i | −0.777511 | − | 0.628869i | \(-0.783518\pi\) |
0.628869 | + | 0.777511i | \(0.283518\pi\) | |||||||
\(684\) | 9.47680 | + | 3.70034i | 0.362354 | + | 0.141486i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.6101 | + | 36.6256i | 1.01598 | + | 1.39837i | ||||
\(687\) | 13.4232 | − | 1.72803i | 0.512128 | − | 0.0659286i | ||||
\(688\) | 67.7652 | − | 34.5281i | 2.58352 | − | 1.31637i | ||||
\(689\) | 24.2050 | − | 17.5860i | 0.922139 | − | 0.669973i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.3367 | + | 37.9684i | 0.469309 | + | 1.44439i | 0.853481 | + | 0.521124i | \(0.174487\pi\) |
−0.384172 | + | 0.923262i | \(0.625513\pi\) | |||||||
\(692\) | 13.0254 | + | 13.0254i | 0.495151 | + | 0.495151i | ||||
\(693\) | 10.1748 | + | 11.1893i | 0.386508 | + | 0.425045i | ||||
\(694\) | − | 61.1409i | − | 2.32088i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 43.6209 | − | 29.7959i | 1.65344 | − | 1.12941i | ||||
\(697\) | −5.87534 | + | 37.0954i | −0.222544 | + | 1.40509i | ||||
\(698\) | −15.5144 | − | 30.4487i | −0.587229 | − | 1.15250i | ||||
\(699\) | 18.1856 | + | 14.0374i | 0.687842 | + | 0.530942i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.01734 | + | 11.0349i | −0.302811 | + | 0.416783i | −0.933122 | − | 0.359559i | \(-0.882927\pi\) |
0.630312 | + | 0.776342i | \(0.282927\pi\) | |||||||
\(702\) | 3.45216 | + | 49.2841i | 0.130293 | + | 1.86011i | ||||
\(703\) | −5.24608 | − | 5.24608i | −0.197860 | − | 0.197860i | ||||
\(704\) | −0.00148470 | − | 0.139428i | −5.59568e−5 | − | 0.00525487i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.11979 | − | 6.52404i | −0.0797793 | − | 0.245535i | ||||
\(707\) | 0.0984989 | + | 0.621898i | 0.00370443 | + | 0.0233889i | ||||
\(708\) | 75.9109 | + | 41.4987i | 2.85291 | + | 1.55962i | ||||
\(709\) | 6.78298 | + | 2.20392i | 0.254740 | + | 0.0827701i | 0.433603 | − | 0.901104i | \(-0.357242\pi\) |
−0.178863 | + | 0.983874i | \(0.557242\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.79563 | + | 0.453425i | 0.292359 | + | 0.0170048i | ||||
\(712\) | −11.8018 | + | 1.86922i | −0.442292 | + | 0.0700521i | ||||
\(713\) | −12.0600 | − | 6.14488i | −0.451650 | − | 0.230127i | ||||
\(714\) | 33.6734 | + | 12.0332i | 1.26019 | + | 0.450331i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 20.5631i | − | 0.768479i | ||||||
\(717\) | 8.03914 | + | 8.52032i | 0.300227 | + | 0.318197i | ||||
\(718\) | 8.18549 | + | 51.6812i | 0.305480 | + | 1.92872i | ||||
\(719\) | 25.1579 | − | 18.2783i | 0.938231 | − | 0.681665i | −0.00976304 | − | 0.999952i | \(-0.503108\pi\) |
0.947994 | + | 0.318287i | \(0.103108\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.535738 | − | 1.64883i | 0.0199519 | − | 0.0614057i | ||||
\(722\) | −46.3802 | − | 7.34591i | −1.72609 | − | 0.273386i | ||||
\(723\) | −7.06365 | − | 1.33015i | −0.262700 | − | 0.0494686i | ||||
\(724\) | −77.4462 | + | 25.1638i | −2.87827 | + | 0.935205i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 46.2835 | − | 14.6427i | 1.71774 | − | 0.543441i | ||||
\(727\) | −24.0226 | + | 24.0226i | −0.890948 | + | 0.890948i | −0.994612 | − | 0.103664i | \(-0.966943\pi\) |
0.103664 | + | 0.994612i | \(0.466943\pi\) | |||||||
\(728\) | −32.0880 | − | 16.3497i | −1.18926 | − | 0.605958i | ||||
\(729\) | 11.8418 | + | 24.2646i | 0.438584 | + | 0.898690i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −53.6028 | − | 17.4166i | −1.98257 | − | 0.644176i | ||||
\(732\) | 9.10982 | − | 1.17275i | 0.336709 | − | 0.0433460i | ||||
\(733\) | −2.17268 | − | 0.344119i | −0.0802498 | − | 0.0127103i | 0.116180 | − | 0.993228i | \(-0.462935\pi\) |
−0.196430 | + | 0.980518i | \(0.562935\pi\) | |||||||
\(734\) | −49.9305 | − | 36.2766i | −1.84297 | − | 1.33899i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −38.7350 | −1.42779 | ||||||||
\(737\) | 23.9762 | + | 45.8425i | 0.883173 | + | 1.68863i | ||||
\(738\) | −5.32176 | − | 53.5897i | −0.195897 | − | 1.97267i | ||||
\(739\) | −27.7836 | + | 9.02744i | −1.02204 | + | 0.332080i | −0.771637 | − | 0.636063i | \(-0.780562\pi\) |
−0.250399 | + | 0.968143i | \(0.580562\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.37245 | + | 4.68260i | 0.0504181 | + | 0.172020i | ||||
\(742\) | 14.0968 | + | 27.6665i | 0.517510 | + | 1.01567i | ||||
\(743\) | 3.10012 | + | 6.08432i | 0.113732 | + | 0.223212i | 0.940855 | − | 0.338809i | \(-0.110024\pi\) |
−0.827123 | + | 0.562021i | \(0.810024\pi\) | |||||||
\(744\) | −6.08513 | − | 20.7616i | −0.223092 | − | 0.761159i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −59.8962 | + | 19.4615i | −2.19296 | + | 0.712535i | ||||
\(747\) | −1.78133 | − | 17.9379i | −0.0651755 | − | 0.656312i | ||||
\(748\) | 55.5565 | − | 56.7525i | 2.03135 | − | 2.07508i | ||||
\(749\) | −17.4034 | −0.635905 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.0310 | + | 13.8268i | 0.694451 | + | 0.504548i | 0.878120 | − | 0.478440i | \(-0.158798\pi\) |
−0.183669 | + | 0.982988i | \(0.558798\pi\) | |||||||
\(752\) | −75.5239 | − | 11.9618i | −2.75407 | − | 0.436202i | ||||
\(753\) | −30.2919 | + | 3.89961i | −1.10390 | + | 0.142110i | ||||
\(754\) | 43.4370 | + | 14.1135i | 1.58188 | + | 0.513984i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −35.3429 | − | 3.08788i | −1.28541 | − | 0.112305i | ||||
\(757\) | −2.70814 | − | 1.37987i | −0.0984291 | − | 0.0501522i | 0.404083 | − | 0.914722i | \(-0.367591\pi\) |
−0.502512 | + | 0.864570i | \(0.667591\pi\) | |||||||
\(758\) | 24.3021 | − | 24.3021i | 0.882692 | − | 0.882692i | ||||
\(759\) | 11.5195 | + | 37.8067i | 0.418131 | + | 1.37230i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.08911 | + | 2.30339i | −0.256980 | + | 0.0834979i | −0.434674 | − | 0.900588i | \(-0.643136\pi\) |
0.177694 | + | 0.984086i | \(0.443136\pi\) | |||||||
\(762\) | 13.2905 | + | 2.50272i | 0.481465 | + | 0.0906639i | ||||
\(763\) | 3.95117 | + | 0.625803i | 0.143042 | + | 0.0226556i | ||||
\(764\) | 2.62835 | − | 8.08923i | 0.0950904 | − | 0.292658i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 54.4826 | − | 39.5839i | 1.96854 | − | 1.43023i | ||||
\(767\) | 6.49121 | + | 40.9839i | 0.234384 | + | 1.47984i | ||||
\(768\) | 34.3269 | + | 36.3815i | 1.23867 | + | 1.31281i | ||||
\(769\) | 41.9788i | 1.51379i | 0.653534 | + | 0.756897i | \(0.273286\pi\) | ||||
−0.653534 | + | 0.756897i | \(0.726714\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.7470 | − | 7.77132i | −0.783200 | − | 0.279877i | ||||
\(772\) | 67.7081 | + | 34.4990i | 2.43687 | + | 1.24165i | ||||
\(773\) | −1.26205 | + | 0.199890i | −0.0453929 | + | 0.00718953i | −0.179090 | − | 0.983833i | \(-0.557315\pi\) |
0.133697 | + | 0.991022i | \(0.457315\pi\) | |||||||
\(774\) | 80.6788 | + | 4.69260i | 2.89994 | + | 0.168672i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −9.02557 | − | 2.93259i | −0.323999 | − | 0.105274i | ||||
\(777\) | 22.7012 | + | 12.4102i | 0.814401 | + | 0.445214i | ||||
\(778\) | −10.3671 | − | 65.4553i | −0.371679 | − | 2.34669i | ||||
\(779\) | −1.64365 | − | 5.05863i | −0.0588898 | − | 0.181244i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.772123 | − | 1.08689i | 0.0276287 | − | 0.0388919i | ||||
\(782\) | 66.0781 | + | 66.0781i | 2.36295 | + | 2.36295i | ||||
\(783\) | 24.8992 | − | 1.74409i | 0.889823 | − | 0.0623286i | ||||
\(784\) | −19.8289 | + | 27.2921i | −0.708175 | + | 0.974719i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −18.5379 | − | 14.3093i | −0.661226 | − | 0.510397i | ||||
\(787\) | 1.32944 | + | 2.60917i | 0.0473894 | + | 0.0930069i | 0.913487 | − | 0.406868i | \(-0.133379\pi\) |
−0.866097 | + | 0.499875i | \(0.833379\pi\) | |||||||
\(788\) | −11.9042 | + | 75.1602i | −0.424070 | + | 2.67747i | ||||
\(789\) | −28.2662 | + | 19.3077i | −1.00630 | + | 0.687371i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.3874i | 0.369334i | ||||||||
\(792\) | −31.3180 | + | 54.8647i | −1.11284 | + | 1.94953i | ||||
\(793\) | 3.11510 | + | 3.11510i | 0.110621 | + | 0.110621i | ||||
\(794\) | 9.19939 | + | 28.3128i | 0.326474 | + | 1.00478i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 63.4743 | − | 46.1167i | 2.24979 | − | 1.63456i | ||||
\(797\) | 49.1462 | − | 25.0412i | 1.74085 | − | 0.887006i | 0.773406 | − | 0.633911i | \(-0.218551\pi\) |
0.967441 | − | 0.253096i | \(-0.0814487\pi\) | |||||||
\(798\) | −5.02273 | + | 0.646598i | −0.177803 | + | 0.0228893i | ||||
\(799\) | 33.3072 | + | 45.8435i | 1.17832 | + | 1.62183i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.25916 | − | 2.05351i | −0.185823 | − | 0.0725571i | ||||
\(802\) | 16.7057 | − | 16.7057i | 0.589900 | − | 0.589900i | ||||
\(803\) | −3.76306 | + | 7.58399i | −0.132796 | + | 0.267633i | ||||
\(804\) | −114.281 | − | 40.8384i | −4.03038 | − | 1.44026i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.9947 | − | 15.1329i | 0.387271 | − | 0.533033i | ||||
\(807\) | −8.96624 | + | 16.4014i | −0.315627 | + | 0.577355i | ||||
\(808\) | −2.34348 | + | 1.19406i | −0.0824432 | + | 0.0420069i | ||||
\(809\) | 6.83297 | − | 21.0297i | 0.240234 | − | 0.739366i | −0.756149 | − | 0.654399i | \(-0.772922\pi\) |
0.996384 | − | 0.0849665i | \(-0.0270783\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.37165 | + | 0.996565i | 0.0481653 | + | 0.0349941i | 0.611607 | − | 0.791161i | \(-0.290523\pi\) |
−0.563442 | + | 0.826156i | \(0.690523\pi\) | |||||||
\(812\) | −14.8896 | + | 29.2226i | −0.522524 | + | 1.02551i | ||||
\(813\) | −32.2685 | + | 15.2778i | −1.13171 | + | 0.535816i | ||||
\(814\) | 66.6610 | − | 49.5250i | 2.33647 | − | 1.73585i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.92917 | + | 66.3917i | −0.0675346 | + | 2.32417i | ||||
\(817\) | 7.88363 | − | 1.24864i | 0.275813 | − | 0.0436846i | ||||
\(818\) | −1.23483 | + | 7.79644i | −0.0431750 | + | 0.272596i | ||||
\(819\) | −9.18563 | − | 14.3239i | −0.320972 | − | 0.500518i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.3901 | + | 28.0645i | 0.711618 | + | 0.979458i | 0.999761 | + | 0.0218708i | \(0.00696224\pi\) |
−0.288143 | + | 0.957587i | \(0.593038\pi\) | |||||||
\(822\) | 8.91458 | − | 47.3403i | 0.310932 | − | 1.65118i | ||||
\(823\) | 6.44187 | − | 12.6429i | 0.224550 | − | 0.440703i | −0.751055 | − | 0.660240i | \(-0.770455\pi\) |
0.975604 | + | 0.219537i | \(0.0704546\pi\) | |||||||
\(824\) | 7.24187 | 0.252283 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −43.0644 | −1.49840 | ||||||||
\(827\) | −20.5163 | + | 40.2655i | −0.713421 | + | 1.40017i | 0.194447 | + | 0.980913i | \(0.437709\pi\) |
−0.907868 | + | 0.419255i | \(0.862291\pi\) | |||||||
\(828\) | −80.0250 | − | 46.8168i | −2.78106 | − | 1.62700i | ||||
\(829\) | 12.9853 | + | 17.8727i | 0.450997 | + | 0.620745i | 0.972611 | − | 0.232437i | \(-0.0746699\pi\) |
−0.521614 | + | 0.853182i | \(0.674670\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.1725 | − | 10.1678i | −0.456947 | − | 0.352716i | ||||
\(832\) | −0.0245420 | + | 0.154952i | −0.000850841 | + | 0.00537200i | ||||
\(833\) | 24.6919 | − | 3.91082i | 0.855525 | − | 0.135502i | ||||
\(834\) | 49.9275 | + | 1.45077i | 1.72885 | + | 0.0502359i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.36152 | + | 10.7333i | −0.116261 | + | 0.371217i | ||||
\(837\) | 2.47188 | − | 9.91916i | 0.0854405 | − | 0.342856i | ||||
\(838\) | −10.4439 | + | 20.4973i | −0.360779 | + | 0.708068i | ||||
\(839\) | −26.4386 | − | 19.2088i | −0.912763 | − | 0.663161i | 0.0289492 | − | 0.999581i | \(-0.490784\pi\) |
−0.941712 | + | 0.336420i | \(0.890784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.83110 | + | 5.63555i | −0.0631415 | + | 0.194329i | ||||
\(842\) | 14.6665 | − | 7.47297i | 0.505442 | − | 0.257536i | ||||
\(843\) | −5.69795 | − | 3.11494i | −0.196248 | − | 0.107284i | ||||
\(844\) | −62.4912 | + | 86.0117i | −2.15103 | + | 2.96065i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −62.8498 | − | 51.4948i | −2.16082 | − | 1.77043i | ||||
\(847\) | −11.5683 | + | 12.0718i | −0.397491 | + | 0.414792i | ||||
\(848\) | −40.7824 | + | 40.7824i | −1.40047 | + | 1.40047i | ||||
\(849\) | 1.03274 | − | 35.5413i | 0.0354435 | − | 1.21977i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39.7409 | + | 54.6986i | 1.36230 | + | 1.87505i | ||||
\(852\) | 0.399325 | + | 3.10193i | 0.0136807 | + | 0.106270i | ||||
\(853\) | 6.44353 | − | 3.28314i | 0.220622 | − | 0.112413i | −0.340187 | − | 0.940358i | \(-0.610490\pi\) |
0.560809 | + | 0.827945i | \(0.310490\pi\) | |||||||
\(854\) | −3.69888 | + | 2.68740i | −0.126573 | + | 0.0919608i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −22.4645 | − | 69.1386i | −0.767820 | − | 2.36311i | ||||
\(857\) | 18.6061 | + | 18.6061i | 0.635574 | + | 0.635574i | 0.949460 | − | 0.313887i | \(-0.101631\pi\) |
−0.313887 | + | 0.949460i | \(0.601631\pi\) | |||||||
\(858\) | −54.0947 | + | 7.55024i | −1.84676 | + | 0.257761i | ||||
\(859\) | − | 20.5206i | − | 0.700154i | −0.936721 | − | 0.350077i | \(-0.886155\pi\) | ||
0.936721 | − | 0.350077i | \(-0.113845\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.4620 | + | 15.3163i | 0.356544 | + | 0.521977i | ||||
\(862\) | 5.72512 | − | 36.1470i | 0.194999 | − | 1.23117i | ||||
\(863\) | −11.6170 | − | 22.7997i | −0.395448 | − | 0.776110i | 0.604340 | − | 0.796727i | \(-0.293437\pi\) |
−0.999787 | + | 0.0206166i | \(0.993437\pi\) | |||||||
\(864\) | −6.58425 | − | 28.5041i | −0.224001 | − | 0.969728i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16.3036 | + | 22.4400i | −0.554020 | + | 0.762543i | ||||
\(867\) | 14.3843 | − | 13.5719i | 0.488515 | − | 0.460927i | ||||
\(868\) | 9.49802 | + | 9.49802i | 0.322384 | + | 0.322384i | ||||
\(869\) | 0.0919233 | + | 8.63247i | 0.00311829 | + | 0.292836i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.9871 | − | 55.3587i | −0.609470 | − | 1.87576i | ||||
\(872\) | 2.61408 | + | 16.5046i | 0.0885239 | + | 0.558918i | ||||
\(873\) | −2.98123 | − | 3.34945i | −0.100899 | − | 0.113362i | ||||
\(874\) | −12.5865 | − | 4.08960i | −0.425744 | − | 0.138333i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.58599 | − | 19.0586i | −0.188733 | − | 0.643932i | ||||
\(877\) | 25.3503 | − | 4.01510i | 0.856020 | − | 0.135580i | 0.287027 | − | 0.957922i | \(-0.407333\pi\) |
0.568993 | + | 0.822342i | \(0.307333\pi\) | |||||||
\(878\) | −31.5353 | − | 16.0680i | −1.06426 | − | 0.542270i | ||||
\(879\) | −9.95855 | + | 27.8677i | −0.335894 | + | 0.939955i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.0994i | 0.441330i | 0.975350 | + | 0.220665i | \(0.0708228\pi\) | ||||
−0.975350 | + | 0.220665i | \(0.929177\pi\) | |||||||
\(882\) | −32.8306 | + | 14.3919i | −1.10546 | + | 0.484602i | ||||
\(883\) | −1.83055 | − | 11.5576i | −0.0616029 | − | 0.388945i | −0.999155 | − | 0.0411006i | \(-0.986914\pi\) |
0.937552 | − | 0.347845i | \(-0.113086\pi\) | |||||||
\(884\) | −72.2914 | + | 52.5228i | −2.43142 | + | 1.76653i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.61035 | + | 11.1115i | −0.121292 | + | 0.373299i | ||||
\(887\) | 27.6213 | + | 4.37479i | 0.927434 | + | 0.146891i | 0.601838 | − | 0.798618i | \(-0.294435\pi\) |
0.325596 | + | 0.945509i | \(0.394435\pi\) | |||||||
\(888\) | −19.9992 | + | 106.205i | −0.671130 | + | 3.56399i | ||||
\(889\) | −4.43004 | + | 1.43941i | −0.148579 | + | 0.0482762i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −25.8629 | + | 14.9034i | −0.866440 | + | 0.499282i | ||||
\(892\) | −67.0695 | + | 67.0695i | −2.24565 | + | 2.24565i | ||||
\(893\) | −7.15033 | − | 3.64328i | −0.239277 | − | 0.121918i | ||||
\(894\) | 17.7211 | + | 25.9436i | 0.592683 | + | 0.867682i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −16.4324 | − | 5.33921i | −0.548968 | − | 0.178371i | ||||
\(897\) | −5.67777 | − | 44.1045i | −0.189575 | − | 1.47261i | ||||
\(898\) | 74.3209 | + | 11.7713i | 2.48012 | + | 0.392812i | ||||
\(899\) | −7.64538 | − | 5.55470i | −0.254988 | − | 0.185260i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.7408 | 1.42390 | ||||||||
\(902\) | 58.7016 | − | 9.93927i | 1.95455 | − | 0.330942i | ||||
\(903\) | −25.1574 | + | 11.9110i | −0.837186 | + | 0.396373i | ||||
\(904\) | −41.2662 | + | 13.4082i | −1.37249 | + | 0.445950i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.93923 | + | 0.568378i | −0.0644265 | + | 0.0188831i | ||||
\(907\) | −6.64713 | − | 13.0457i | −0.220714 | − | 0.433176i | 0.753924 | − | 0.656961i | \(-0.228159\pi\) |
−0.974638 | + | 0.223785i | \(0.928159\pi\) | |||||||
\(908\) | −41.5756 | − | 81.5967i | −1.37973 | − | 2.70788i | ||||
\(909\) | −1.24064 | − | 0.0721608i | −0.0411495 | − | 0.00239342i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.06122 | − | 2.61925i | 0.267080 | − | 0.0867796i | −0.172415 | − | 0.985024i | \(-0.555157\pi\) |
0.439496 | + | 0.898245i | \(0.355157\pi\) | |||||||
\(912\) | −4.02517 | − | 8.50165i | −0.133287 | − | 0.281518i | ||||
\(913\) | 19.6489 | − | 3.32693i | 0.650285 | − | 0.110105i | ||||
\(914\) | 41.9963 | 1.38911 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −28.3959 | − | 20.6308i | −0.938226 | − | 0.681661i | ||||
\(917\) | 7.96647 | + | 1.26177i | 0.263076 | + | 0.0416672i | ||||
\(918\) | −37.3931 | + | 59.8573i | −1.23416 | + | 1.97558i | ||||
\(919\) | −20.1507 | − | 6.54737i | −0.664711 | − | 0.215978i | −0.0428216 | − | 0.999083i | \(-0.513635\pi\) |
−0.621889 | + | 0.783105i | \(0.713635\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 40.0217 | − | 27.3374i | 1.31876 | − | 0.900798i | ||||
\(922\) | 64.7667 | + | 33.0003i | 2.13298 | + | 1.08681i | ||||
\(923\) | −1.06070 | + | 1.06070i | −0.0349135 | + | 0.0349135i | ||||
\(924\) | 0.721686 | − | 39.2153i | 0.0237417 | − | 1.29009i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 38.9170 | − | 12.6449i | 1.27889 | − | 0.415537i | ||||
\(927\) | 2.95348 | + | 1.72786i | 0.0970049 | + | 0.0567505i | ||||
\(928\) | −26.7115 | − | 4.23069i | −0.876848 | − | 0.138879i | ||||
\(929\) | 6.15445 | − | 18.9414i | 0.201921 | − | 0.621449i | −0.797905 | − | 0.602783i | \(-0.794058\pi\) |
0.999826 | − | 0.0186653i | \(-0.00594169\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.86430 | + | 2.08104i | −0.0938736 | + | 0.0682032i | ||||
\(932\) | −9.32016 | − | 58.8452i | −0.305292 | − | 1.92754i | ||||
\(933\) | −3.75390 | + | 3.54190i | −0.122897 | + | 0.115957i | ||||
\(934\) | − | 73.6952i | − | 2.41138i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 45.0479 | − | 54.9814i | 1.47244 | − | 1.79712i | ||||
\(937\) | −33.5660 | − | 17.1027i | −1.09655 | − | 0.558721i | −0.190415 | − | 0.981704i | \(-0.560983\pi\) |
−0.906138 | + | 0.422982i | \(0.860983\pi\) | |||||||
\(938\) | 59.6657 | − | 9.45012i | 1.94815 | − | 0.308557i | ||||
\(939\) | −25.0417 | + | 7.33960i | −0.817206 | + | 0.239519i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.0894 | − | 8.15205i | −0.817892 | − | 0.265749i | −0.129955 | − | 0.991520i | \(-0.541483\pi\) |
−0.687937 | + | 0.725770i | \(0.741483\pi\) | |||||||
\(942\) | −44.4616 | + | 81.3307i | −1.44864 | + | 2.64990i | ||||
\(943\) | 7.58276 | + | 47.8757i | 0.246929 | + | 1.55905i | ||||
\(944\) | −24.7181 | − | 76.0745i | −0.804505 | − | 2.47601i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.951336 | + | 89.3395i | 0.0309306 | + | 2.90468i | ||||
\(947\) | 4.15839 | + | 4.15839i | 0.135130 | + | 0.135130i | 0.771436 | − | 0.636307i | \(-0.219539\pi\) |
−0.636307 | + | 0.771436i | \(0.719539\pi\) | |||||||
\(948\) | −13.8980 | − | 14.7298i | −0.451385 | − | 0.478402i | ||||
\(949\) | 5.59906 | − | 7.70644i | 0.181753 | − | 0.250162i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.86190 | − | 8.88967i | 0.222512 | − | 0.288267i | ||||
\(952\) | −23.3563 | − | 45.8392i | −0.756981 | − | 1.48566i | ||||
\(953\) | 3.17981 | − | 20.0765i | 0.103004 | − | 0.650343i | −0.881124 | − | 0.472885i | \(-0.843213\pi\) |
0.984128 | − | 0.177458i | \(-0.0567874\pi\) | |||||||
\(954\) | −59.2869 | + | 15.5218i | −1.91949 | + | 0.502536i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 30.3799i | − | 0.982555i | ||||||
\(957\) | 3.81451 | + | 27.3296i | 0.123306 | + | 0.883440i | ||||
\(958\) | −14.0567 | − | 14.0567i | −0.454152 | − | 0.454152i | ||||
\(959\) | 5.12711 | + | 15.7796i | 0.165563 | + | 0.509551i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.9483 | − | 15.9464i | 0.708011 | − | 0.514400i | ||||
\(962\) | −83.2525 | + | 42.4193i | −2.68417 | + | 1.36765i | ||||
\(963\) | 7.33426 | − | 33.5569i | 0.236343 | − | 1.08136i | ||||
\(964\) | 10.9569 | + | 15.0808i | 0.352897 | + | 0.485720i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 46.1311 | + | 1.34045i | 1.48424 | + | 0.0431284i | ||||
\(967\) | −8.15831 | + | 8.15831i | −0.262354 | + | 0.262354i | −0.826010 | − | 0.563656i | \(-0.809394\pi\) |
0.563656 | + | 0.826010i | \(0.309394\pi\) | |||||||
\(968\) | −62.8903 | − | 30.3750i | −2.02137 | − | 0.976290i | ||||
\(969\) | −2.34572 | + | 6.56419i | −0.0753554 | + | 0.210872i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.72332 | − | 13.3830i | 0.312036 | − | 0.429481i | −0.623979 | − | 0.781441i | \(-0.714485\pi\) |
0.936015 | + | 0.351960i | \(0.114485\pi\) | |||||||
\(972\) | 20.8485 | − | 66.8464i | 0.668715 | − | 2.14410i | ||||
\(973\) | −15.3284 | + | 7.81021i | −0.491406 | + | 0.250384i | ||||
\(974\) | 19.8415 | − | 61.0658i | 0.635762 | − | 1.95667i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.87044 | − | 4.99167i | −0.219917 | − | 0.159779i | ||||
\(977\) | −6.95258 | + | 13.6452i | −0.222433 | + | 0.436549i | −0.975073 | − | 0.221883i | \(-0.928780\pi\) |
0.752641 | + | 0.658432i | \(0.228780\pi\) | |||||||
\(978\) | 6.79102 | + | 14.3434i | 0.217153 | + | 0.458653i | ||||
\(979\) | 1.86548 | − | 5.95643i | 0.0596210 | − | 0.190368i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.87179 | + | 7.35485i | −0.0916893 | + | 0.234822i | ||||
\(982\) | 52.8036 | − | 8.36327i | 1.68503 | − | 0.266883i | ||||
\(983\) | 1.06498 | − | 6.72404i | 0.0339677 | − | 0.214463i | −0.964866 | − | 0.262741i | \(-0.915373\pi\) |
0.998834 | + | 0.0482781i | \(0.0153734\pi\) | |||||||
\(984\) | −47.3426 | + | 61.3329i | −1.50923 | + | 1.95522i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 38.3501 | + | 52.7844i | 1.22132 | + | 1.68100i | ||||
\(987\) | 27.5016 | + | 5.17878i | 0.875385 | + | 0.164843i | ||||
\(988\) | 5.74515 | − | 11.2755i | 0.182778 | − | 0.358721i | ||||
\(989\) | −72.7403 | −2.31301 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.87509 | −0.250160 | −0.125080 | − | 0.992147i | \(-0.539919\pi\) | ||||
−0.125080 | + | 0.992147i | \(0.539919\pi\) | |||||||
\(992\) | −5.02847 | + | 9.86893i | −0.159654 | + | 0.313339i | ||||
\(993\) | −34.2909 | − | 6.45728i | −1.08819 | − | 0.204915i | ||||
\(994\) | −0.915068 | − | 1.25948i | −0.0290242 | − | 0.0399484i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −28.5654 | + | 37.0067i | −0.905128 | + | 1.17260i | ||||
\(997\) | 1.58955 | − | 10.0360i | 0.0503414 | − | 0.317843i | −0.949648 | − | 0.313318i | \(-0.898560\pi\) |
0.999990 | − | 0.00452544i | \(-0.00144050\pi\) | |||||||
\(998\) | 22.5233 | − | 3.56734i | 0.712963 | − | 0.112922i | ||||
\(999\) | −33.4961 | + | 38.5421i | −1.05977 | + | 1.21942i |
(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 | 825.2.ct.c.368.2 | yes | 256 | |
3.2 | odd | 2 | inner | 825.2.ct.c.368.32 | yes | 256 | |
5.2 | odd | 4 | inner | 825.2.ct.c.632.2 | yes | 256 | |
5.3 | odd | 4 | inner | 825.2.ct.c.632.31 | yes | 256 | |
5.4 | even | 2 | inner | 825.2.ct.c.368.31 | yes | 256 | |
11.9 | even | 5 | inner | 825.2.ct.c.218.32 | yes | 256 | |
15.2 | even | 4 | inner | 825.2.ct.c.632.32 | yes | 256 | |
15.8 | even | 4 | inner | 825.2.ct.c.632.1 | yes | 256 | |
15.14 | odd | 2 | inner | 825.2.ct.c.368.1 | yes | 256 | |
33.20 | odd | 10 | inner | 825.2.ct.c.218.2 | yes | 256 | |
55.9 | even | 10 | inner | 825.2.ct.c.218.1 | ✓ | 256 | |
55.42 | odd | 20 | inner | 825.2.ct.c.482.32 | yes | 256 | |
55.53 | odd | 20 | inner | 825.2.ct.c.482.1 | yes | 256 | |
165.53 | even | 20 | inner | 825.2.ct.c.482.31 | yes | 256 | |
165.119 | odd | 10 | inner | 825.2.ct.c.218.31 | yes | 256 | |
165.152 | even | 20 | inner | 825.2.ct.c.482.2 | yes | 256 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.ct.c.218.1 | ✓ | 256 | 55.9 | even | 10 | inner | |
825.2.ct.c.218.2 | yes | 256 | 33.20 | odd | 10 | inner | |
825.2.ct.c.218.31 | yes | 256 | 165.119 | odd | 10 | inner | |
825.2.ct.c.218.32 | yes | 256 | 11.9 | even | 5 | inner | |
825.2.ct.c.368.1 | yes | 256 | 15.14 | odd | 2 | inner | |
825.2.ct.c.368.2 | yes | 256 | 1.1 | even | 1 | trivial | |
825.2.ct.c.368.31 | yes | 256 | 5.4 | even | 2 | inner | |
825.2.ct.c.368.32 | yes | 256 | 3.2 | odd | 2 | inner | |
825.2.ct.c.482.1 | yes | 256 | 55.53 | odd | 20 | inner | |
825.2.ct.c.482.2 | yes | 256 | 165.152 | even | 20 | inner | |
825.2.ct.c.482.31 | yes | 256 | 165.53 | even | 20 | inner | |
825.2.ct.c.482.32 | yes | 256 | 55.42 | odd | 20 | inner | |
825.2.ct.c.632.1 | yes | 256 | 15.8 | even | 4 | inner | |
825.2.ct.c.632.2 | yes | 256 | 5.2 | odd | 4 | inner | |
825.2.ct.c.632.31 | yes | 256 | 5.3 | odd | 4 | inner | |
825.2.ct.c.632.32 | yes | 256 | 15.2 | even | 4 | inner |