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 | 218.1 | ||
Character | \(\chi\) | \(=\) | 825.218 |
Dual form | 825.2.ct.c.632.1 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.27022 | + | 1.15673i | −1.60529 | + | 0.817934i | −0.605531 | + | 0.795822i | \(0.707039\pi\) |
−0.999755 | + | 0.0221122i | \(0.992961\pi\) | |||||||
\(3\) | −0.830827 | + | 1.51978i | −0.479678 | + | 0.877444i | ||||
\(4\) | 2.64028 | − | 3.63404i | 1.32014 | − | 1.81702i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.128180 | − | 4.41127i | 0.0523294 | − | 1.80089i | ||||
\(7\) | −1.50127 | + | 0.237778i | −0.567428 | + | 0.0898718i | −0.433556 | − | 0.901127i | \(-0.642741\pi\) |
−0.133873 | + | 0.990999i | \(0.542741\pi\) | |||||||
\(8\) | −0.993237 | + | 6.27105i | −0.351162 | + | 2.21715i | ||||
\(9\) | −1.61945 | − | 2.52535i | −0.539817 | − | 0.841782i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.991249 | + | 3.16503i | 0.298873 | + | 0.954293i | ||||
\(12\) | 3.32931 | + | 7.03191i | 0.961090 | + | 2.02994i | ||||
\(13\) | 3.32493 | − | 1.69413i | 0.922168 | − | 0.469868i | 0.0726086 | − | 0.997361i | \(-0.476868\pi\) |
0.849560 | + | 0.527492i | \(0.176868\pi\) | |||||||
\(14\) | 3.13317 | − | 2.27638i | 0.837375 | − | 0.608389i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.22292 | − | 6.84143i | −0.555729 | − | 1.71036i | ||||
\(17\) | 2.42015 | − | 4.74982i | 0.586973 | − | 1.15200i | −0.386305 | − | 0.922371i | \(-0.626249\pi\) |
0.973278 | − | 0.229629i | \(-0.0737511\pi\) | |||||||
\(18\) | 6.59766 | + | 3.85981i | 1.55508 | + | 0.909766i | ||||
\(19\) | 0.443752 | + | 0.610772i | 0.101804 | + | 0.140121i | 0.856880 | − | 0.515517i | \(-0.172400\pi\) |
−0.755076 | + | 0.655637i | \(0.772400\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.885929 | − | 2.47916i | 0.193326 | − | 0.540996i | ||||
\(22\) | −5.91145 | − | 6.03870i | −1.26033 | − | 1.28746i | ||||
\(23\) | −4.86491 | + | 4.86491i | −1.01440 | + | 1.01440i | −0.0145098 | + | 0.999895i | \(0.504619\pi\) |
−0.999895 | + | 0.0145098i | \(0.995381\pi\) | |||||||
\(24\) | −8.70540 | − | 6.71966i | −1.77698 | − | 1.37165i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.58864 | + | 7.69211i | −1.09602 | + | 1.50855i | ||||
\(27\) | 5.18345 | − | 0.363080i | 0.997556 | − | 0.0698748i | ||||
\(28\) | −3.09969 | + | 6.08349i | −0.585787 | + | 1.14967i | ||||
\(29\) | 3.88618 | + | 2.82348i | 0.721646 | + | 0.524306i | 0.886910 | − | 0.461943i | \(-0.152848\pi\) |
−0.165264 | + | 0.986249i | \(0.552848\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.607937 | + | 1.87104i | −0.109189 | + | 0.336048i | −0.990691 | − | 0.136132i | \(-0.956533\pi\) |
0.881502 | + | 0.472180i | \(0.156533\pi\) | |||||||
\(32\) | 3.98105 | + | 3.98105i | 0.703757 | + | 0.703757i | ||||
\(33\) | −5.63370 | − | 1.12312i | −0.980702 | − | 0.195510i | ||||
\(34\) | 13.5826i | 2.32939i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −13.4530 | − | 0.782481i | −2.24217 | − | 0.130414i | ||||
\(37\) | 9.70619 | − | 1.53731i | 1.59569 | − | 0.252732i | 0.705630 | − | 0.708580i | \(-0.250664\pi\) |
0.890057 | + | 0.455848i | \(0.150664\pi\) | |||||||
\(38\) | −1.71391 | − | 0.873283i | −0.278034 | − | 0.141665i | ||||
\(39\) | −0.187731 | + | 6.46068i | −0.0300610 | + | 1.03454i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.14117 | + | 5.69984i | 0.646743 | + | 0.890165i | 0.998953 | − | 0.0457560i | \(-0.0145697\pi\) |
−0.352210 | + | 0.935921i | \(0.614570\pi\) | |||||||
\(42\) | 0.856472 | + | 6.65301i | 0.132156 | + | 1.02658i | ||||
\(43\) | 7.47601 | + | 7.47601i | 1.14008 | + | 1.14008i | 0.988435 | + | 0.151646i | \(0.0484575\pi\) |
0.151646 | + | 0.988435i | \(0.451543\pi\) | |||||||
\(44\) | 14.1190 | + | 4.75435i | 2.12852 | + | 0.716745i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.41700 | − | 16.6718i | 0.798693 | − | 2.45813i | ||||
\(47\) | −10.4989 | − | 1.66286i | −1.53142 | − | 0.242553i | −0.666900 | − | 0.745148i | \(-0.732379\pi\) |
−0.864522 | + | 0.502594i | \(0.832379\pi\) | |||||||
\(48\) | 12.2443 | + | 2.30571i | 1.76731 | + | 0.332800i | ||||
\(49\) | −4.46011 | + | 1.44918i | −0.637159 | + | 0.207025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.20794 | + | 7.62437i | 0.729257 | + | 1.06763i | ||||
\(52\) | 2.62220 | − | 16.5559i | 0.363633 | − | 2.29589i | ||||
\(53\) | 3.63994 | + | 7.14378i | 0.499984 | + | 0.981274i | 0.993745 | + | 0.111676i | \(0.0356219\pi\) |
−0.493761 | + | 0.869598i | \(0.664378\pi\) | |||||||
\(54\) | −11.3476 | + | 6.82014i | −1.54421 | + | 0.928104i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 9.65074i | − | 1.28963i | ||||||
\(57\) | −1.29692 | + | 0.166958i | −0.171781 | + | 0.0221142i | ||||
\(58\) | −12.0885 | − | 1.91463i | −1.58730 | − | 0.251403i | ||||
\(59\) | −8.99601 | − | 6.53598i | −1.17118 | − | 0.850912i | −0.180030 | − | 0.983661i | \(-0.557620\pi\) |
−0.991150 | + | 0.132749i | \(0.957620\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.364812 | − | 1.12278i | −0.0467094 | − | 0.143757i | 0.924982 | − | 0.380012i | \(-0.124080\pi\) |
−0.971691 | + | 0.236255i | \(0.924080\pi\) | |||||||
\(62\) | −0.784143 | − | 4.95088i | −0.0995863 | − | 0.628763i | ||||
\(63\) | 3.03171 | + | 3.40617i | 0.381960 | + | 0.429137i | ||||
\(64\) | 0.0399837 | + | 0.0129915i | 0.00499796 | + | 0.00162394i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 14.0889 | − | 3.96697i | 1.73422 | − | 0.488301i | ||||
\(67\) | −11.0297 | + | 11.0297i | −1.34749 | + | 1.34749i | −0.459113 | + | 0.888378i | \(0.651833\pi\) |
−0.888378 | + | 0.459113i | \(0.848167\pi\) | |||||||
\(68\) | −10.8711 | − | 21.3358i | −1.31832 | − | 2.58734i | ||||
\(69\) | −3.35169 | − | 11.4355i | −0.403496 | − | 1.37667i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.382309 | − | 0.124220i | 0.0453717 | − | 0.0147422i | −0.286243 | − | 0.958157i | \(-0.592407\pi\) |
0.331615 | + | 0.943415i | \(0.392407\pi\) | |||||||
\(72\) | 17.4451 | − | 7.64740i | 2.05592 | − | 0.901255i | ||||
\(73\) | −0.399326 | − | 2.52125i | −0.0467376 | − | 0.295089i | 0.953237 | − | 0.302224i | \(-0.0977290\pi\) |
−0.999975 | + | 0.00713442i | \(0.997729\pi\) | |||||||
\(74\) | −20.2569 | + | 14.7175i | −2.35482 | + | 1.71087i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.39120 | 0.388997 | ||||||||
\(77\) | −2.24071 | − | 4.51588i | −0.255353 | − | 0.514633i | ||||
\(78\) | −7.04710 | − | 14.8843i | −0.797927 | − | 1.68532i | ||||
\(79\) | −2.47554 | − | 0.804351i | −0.278520 | − | 0.0904966i | 0.166426 | − | 0.986054i | \(-0.446777\pi\) |
−0.444946 | + | 0.895557i | \(0.646777\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.75475 | + | 8.17935i | −0.417195 | + | 0.908817i | ||||
\(82\) | −15.9946 | − | 8.14963i | −1.76630 | − | 0.899977i | ||||
\(83\) | −5.35379 | − | 2.72789i | −0.587655 | − | 0.299425i | 0.134767 | − | 0.990877i | \(-0.456971\pi\) |
−0.722422 | + | 0.691452i | \(0.756971\pi\) | |||||||
\(84\) | −6.67025 | − | 9.76518i | −0.727784 | − | 1.06547i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −25.6199 | − | 8.32442i | −2.76267 | − | 0.897645i | ||||
\(87\) | −7.51980 | + | 3.56031i | −0.806208 | + | 0.381706i | ||||
\(88\) | −20.8326 | + | 3.07255i | −2.22077 | + | 0.327534i | ||||
\(89\) | −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 | ||||
\(92\) | 4.83453 | + | 30.5240i | 0.504035 | + | 3.18235i | ||||
\(93\) | −2.33847 | − | 2.47844i | −0.242488 | − | 0.257002i | ||||
\(94\) | 25.7583 | − | 8.36937i | 2.65676 | − | 0.863235i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9.35789 | + | 2.74275i | −0.955085 | + | 0.279931i | ||||
\(97\) | −0.678570 | − | 1.33177i | −0.0688983 | − | 0.135221i | 0.853988 | − | 0.520292i | \(-0.174177\pi\) |
−0.922887 | + | 0.385071i | \(0.874177\pi\) | |||||||
\(98\) | 8.44911 | − | 8.44911i | 0.853489 | − | 0.853489i | ||||
\(99\) | 6.38752 | − | 7.62886i | 0.641970 | − | 0.766730i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.393972 | + | 0.128009i | 0.0392017 | + | 0.0127374i | 0.328552 | − | 0.944486i | \(-0.393439\pi\) |
−0.289351 | + | 0.957223i | \(0.593439\pi\) | |||||||
\(102\) | −20.6425 | − | 11.2848i | −2.04391 | − | 1.11736i | ||||
\(103\) | −0.178428 | − | 1.12655i | −0.0175810 | − | 0.111002i | 0.977337 | − | 0.211688i | \(-0.0678962\pi\) |
−0.994918 | + | 0.100686i | \(0.967896\pi\) | |||||||
\(104\) | 7.32157 | + | 22.5335i | 0.717939 | + | 2.20959i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.5269 | − | 12.0075i | −1.60523 | − | 1.16627i | ||||
\(107\) | 11.3087 | + | 1.79112i | 1.09325 | + | 0.173155i | 0.676920 | − | 0.736057i | \(-0.263314\pi\) |
0.416335 | + | 0.909211i | \(0.363314\pi\) | |||||||
\(108\) | 12.3663 | − | 19.7955i | 1.18995 | − | 1.90482i | ||||
\(109\) | 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 | ||||
\(112\) | 4.96395 | + | 9.74230i | 0.469049 | + | 0.920561i | ||||
\(113\) | 1.06905 | − | 6.74974i | 0.100568 | − | 0.634962i | −0.884988 | − | 0.465614i | \(-0.845834\pi\) |
0.985556 | − | 0.169349i | \(-0.0541664\pi\) | |||||||
\(114\) | 2.75116 | − | 1.87922i | 0.257670 | − | 0.176005i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 20.5212 | − | 6.66776i | 1.90535 | − | 0.619086i | ||||
\(117\) | −9.66283 | − | 5.65302i | −0.893329 | − | 0.522622i | ||||
\(118\) | 27.9833 | + | 4.43212i | 2.57607 | + | 0.408009i | ||||
\(119\) | −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 | ||||
\(123\) | −12.1031 | + | 1.55809i | −1.09130 | + | 0.140488i | ||||
\(124\) | 5.19430 | + | 7.14934i | 0.466462 | + | 0.642030i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −10.8227 | − | 4.22585i | −0.964161 | − | 0.376469i | ||||
\(127\) | −2.73050 | − | 1.39126i | −0.242293 | − | 0.123454i | 0.328628 | − | 0.944459i | \(-0.393414\pi\) |
−0.570921 | + | 0.821005i | \(0.693414\pi\) | |||||||
\(128\) | −11.2273 | + | 1.77823i | −0.992361 | + | 0.157175i | ||||
\(129\) | −17.5732 | + | 5.15060i | −1.54723 | + | 0.453485i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.30648i | 0.463629i | 0.972760 | + | 0.231814i | \(0.0744662\pi\) | ||||
−0.972760 | + | 0.231814i | \(0.925534\pi\) | |||||||
\(132\) | −18.9560 | + | 17.5078i | −1.64991 | + | 1.52385i | ||||
\(133\) | −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 | ||||
\(137\) | −4.95561 | + | 9.72594i | −0.423387 | + | 0.830943i | 0.576517 | + | 0.817085i | \(0.304411\pi\) |
−0.999904 | + | 0.0138581i | \(0.995589\pi\) | |||||||
\(138\) | 20.8369 | + | 22.0840i | 1.77375 | + | 1.87992i | ||||
\(139\) | 6.65265 | − | 9.15659i | 0.564271 | − | 0.776652i | −0.427591 | − | 0.903972i | \(-0.640638\pi\) |
0.991862 | + | 0.127320i | \(0.0406376\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.2500 | − | 14.5744i | 0.947417 | − | 1.22739i | ||||
\(142\) | −0.724235 | + | 0.724235i | −0.0607765 | + | 0.0607765i | ||||
\(143\) | 8.65782 | + | 8.84419i | 0.724003 | + | 0.739588i | ||||
\(144\) | −13.6771 | + | 16.6930i | −1.13976 | + | 1.39108i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.82297 | + | 5.26186i | 0.316391 | + | 0.435475i | ||||
\(147\) | 1.50315 | − | 7.98240i | 0.123978 | − | 0.658377i | ||||
\(148\) | 20.0405 | − | 39.3316i | 1.64732 | − | 3.23304i | ||||
\(149\) | 2.19997 | + | 6.77082i | 0.180229 | + | 0.554687i | 0.999834 | − | 0.0182422i | \(-0.00580701\pi\) |
−0.819605 | + | 0.572929i | \(0.805807\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.370455 | − | 0.269151i | 0.0301472 | − | 0.0219032i | −0.572610 | − | 0.819828i | \(-0.694069\pi\) |
0.602757 | + | 0.797925i | \(0.294069\pi\) | |||||||
\(152\) | −4.27094 | + | 2.17615i | −0.346419 | + | 0.176509i | ||||
\(153\) | −15.9143 | + | 1.58037i | −1.28659 | + | 0.127766i | ||||
\(154\) | 10.3106 | + | 7.66013i | 0.830850 | + | 0.617271i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 22.9827 | + | 17.7403i | 1.84009 | + | 1.42036i | ||||
\(157\) | −3.28564 | + | 20.7447i | −0.262223 | + | 1.65561i | 0.407655 | + | 0.913136i | \(0.366347\pi\) |
−0.669877 | + | 0.742472i | \(0.733653\pi\) | |||||||
\(158\) | 6.55043 | − | 1.03749i | 0.521124 | − | 0.0825380i | ||||
\(159\) | −13.8811 | − | 0.403350i | −1.10084 | − | 0.0319877i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.14680 | − | 8.46034i | 0.484435 | − | 0.666768i | ||||
\(162\) | −0.937230 | − | 22.9122i | −0.0736358 | − | 1.80015i | ||||
\(163\) | 3.20411 | − | 1.63257i | 0.250965 | − | 0.127873i | −0.323983 | − | 0.946063i | \(-0.605022\pi\) |
0.574948 | + | 0.818190i | \(0.305022\pi\) | |||||||
\(164\) | 31.6473 | 2.47124 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.3097 | 1.18826 | ||||||||
\(167\) | −11.0316 | + | 5.62090i | −0.853654 | + | 0.434959i | −0.825337 | − | 0.564640i | \(-0.809015\pi\) |
−0.0283173 | + | 0.999599i | \(0.509015\pi\) | |||||||
\(168\) | 14.6670 | + | 8.01810i | 1.13158 | + | 0.618610i | ||||
\(169\) | 0.543831 | − | 0.748519i | 0.0418331 | − | 0.0575784i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.823776 | − | 2.10974i | 0.0629958 | − | 0.161336i | ||||
\(172\) | 46.9069 | − | 7.42933i | 3.57662 | − | 0.566481i | ||||
\(173\) | 0.641513 | − | 4.05036i | 0.0487734 | − | 0.307943i | −0.951226 | − | 0.308493i | \(-0.900175\pi\) |
1.00000 | 0.000550497i | \(0.000175228\pi\) | ||||||||
\(174\) | 12.9533 | − | 16.7811i | 0.981984 | − | 1.27217i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 19.4499 | − | 13.8172i | 1.46609 | − | 1.04151i | ||||
\(177\) | 17.4074 | − | 8.24166i | 1.30842 | − | 0.619481i | ||||
\(178\) | 4.27244 | − | 2.17691i | 0.320233 | − | 0.163167i | ||||
\(179\) | 3.70351 | − | 2.69076i | 0.276814 | − | 0.201117i | −0.440713 | − | 0.897648i | \(-0.645274\pi\) |
0.717526 | + | 0.696531i | \(0.245274\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.60201 | + | 17.2412i | 0.416394 | + | 1.28153i | 0.910998 | + | 0.412411i | \(0.135313\pi\) |
−0.494603 | + | 0.869119i | \(0.664687\pi\) | |||||||
\(182\) | 6.56107 | − | 12.8768i | 0.486339 | − | 0.954493i | ||||
\(183\) | 2.00946 | + | 0.378399i | 0.148544 | + | 0.0279721i | ||||
\(184\) | −25.6761 | − | 35.3402i | −1.89287 | − | 2.60531i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 8.17573 | + | 2.92161i | 0.599474 | + | 0.214223i | ||||
\(187\) | 17.4323 | + | 2.95161i | 1.27478 | + | 0.215843i | ||||
\(188\) | −33.7630 | + | 33.7630i | −2.46242 | + | 2.46242i | ||||
\(189\) | −7.69545 | + | 1.77760i | −0.559762 | + | 0.129301i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.11298 | + | 1.53189i | −0.0805325 | + | 0.110843i | −0.847383 | − | 0.530983i | \(-0.821823\pi\) |
0.766850 | + | 0.641826i | \(0.221823\pi\) | |||||||
\(192\) | −0.0529638 | + | 0.0499727i | −0.00382233 | + | 0.00360647i | ||||
\(193\) | −7.68023 | + | 15.0733i | −0.552835 | + | 1.08500i | 0.430397 | + | 0.902640i | \(0.358374\pi\) |
−0.983232 | + | 0.182360i | \(0.941626\pi\) | |||||||
\(194\) | 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 | 0.990559 | − | 0.137089i | \(-0.0437747\pi\) |
−0.137089 | + | 0.990559i | \(0.543775\pi\) | |||||||
\(198\) | −5.67651 | + | 24.7078i | −0.403412 | + | 1.75591i | ||||
\(199\) | 17.4666i | 1.23817i | 0.785323 | + | 0.619087i | \(0.212497\pi\) | ||||
−0.785323 | + | 0.619087i | \(0.787503\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.59891 | − | 25.9264i | −0.535986 | − | 1.82871i | ||||
\(202\) | −1.04247 | + | 0.165112i | −0.0733483 | + | 0.0116172i | ||||
\(203\) | −6.50559 | − | 3.31476i | −0.456603 | − | 0.232651i | ||||
\(204\) | 41.4577 | + | 1.20465i | 2.90262 | + | 0.0843427i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.70819 | + | 2.35112i | 0.119015 | + | 0.163810i | ||||
\(207\) | 20.1641 | + | 4.40710i | 1.40150 | + | 0.306315i | ||||
\(208\) | −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 | 0.299748 | + | 0.954018i | \(0.403097\pi\) |
−0.803259 | + | 0.595630i | \(0.796903\pi\) | |||||||
\(212\) | 35.5713 | + | 5.63393i | 2.44304 | + | 0.386940i | ||||
\(213\) | −0.128846 | + | 0.684230i | −0.00882841 | + | 0.0468827i | ||||
\(214\) | −27.7451 | + | 9.01493i | −1.89662 | + | 0.616248i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.87150 | + | 32.8663i | −0.195381 | + | 2.23627i | ||||
\(217\) | 0.467788 | − | 2.95349i | 0.0317555 | − | 0.200496i | ||||
\(218\) | −3.04438 | − | 5.97493i | −0.206191 | − | 0.404673i | ||||
\(219\) | 4.16351 | + | 1.48783i | 0.281344 | + | 0.100538i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 19.8928i | − | 1.33814i | ||||||
\(222\) | −5.53735 | − | 43.0137i | −0.371643 | − | 2.88689i | ||||
\(223\) | 20.8559 | + | 3.30324i | 1.39661 | + | 0.221202i | 0.808937 | − | 0.587895i | \(-0.200043\pi\) |
0.587675 | + | 0.809097i | \(0.300043\pi\) | |||||||
\(224\) | −6.92326 | − | 5.03004i | −0.462580 | − | 0.336084i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.38067 | + | 16.5600i | 0.357917 | + | 1.10155i | ||||
\(227\) | −3.18928 | − | 20.1363i | −0.211680 | − | 1.33649i | −0.833146 | − | 0.553053i | \(-0.813463\pi\) |
0.621467 | − | 0.783441i | \(-0.286537\pi\) | |||||||
\(228\) | −2.81750 | + | 5.15387i | −0.186594 | + | 0.341324i | ||||
\(229\) | −7.43142 | − | 2.41461i | −0.491082 | − | 0.159562i | 0.0529996 | − | 0.998595i | \(-0.483122\pi\) |
−0.544082 | + | 0.839032i | \(0.683122\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.72478 | + | 0.346534i | 0.574049 | + | 0.0228002i | ||||
\(232\) | −21.5661 | + | 21.5661i | −1.41588 | + | 1.41588i | ||||
\(233\) | 6.02151 | + | 11.8179i | 0.394482 | + | 0.774215i | 0.999762 | − | 0.0217973i | \(-0.00693884\pi\) |
−0.605280 | + | 0.796013i | \(0.706939\pi\) | |||||||
\(234\) | 28.4758 | + | 1.65626i | 1.86152 | + | 0.108273i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −47.5040 | + | 15.4350i | −3.09225 | + | 1.00473i | ||||
\(237\) | 3.27918 | − | 3.09399i | 0.213006 | − | 0.200976i | ||||
\(238\) | −3.22965 | − | 20.3912i | −0.209347 | − | 1.32176i | ||||
\(239\) | 5.47156 | − | 3.97532i | 0.353926 | − | 0.257142i | −0.396588 | − | 0.917997i | \(-0.629806\pi\) |
0.750514 | + | 0.660854i | \(0.229806\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.14988 | −0.267317 | −0.133659 | − | 0.991027i | \(-0.542673\pi\) | ||||
−0.133659 | + | 0.991027i | \(0.542673\pi\) | |||||||
\(242\) | 13.2530 | − | 24.6958i | 0.851933 | − | 1.58750i | ||||
\(243\) | −9.31125 | − | 12.5020i | −0.597317 | − | 0.802005i | ||||
\(244\) | −5.04342 | − | 1.63871i | −0.322872 | − | 0.104907i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 25.6744 | − | 17.5372i | 1.63694 | − | 1.11813i | ||||
\(247\) | 2.51017 | + | 1.27900i | 0.159718 | + | 0.0813806i | ||||
\(248\) | −11.1296 | − | 5.67079i | −0.706727 | − | 0.360096i | ||||
\(249\) | 8.59387 | − | 5.87017i | 0.544614 | − | 0.372007i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.7703 | + | 5.44901i | 1.05853 | + | 0.343938i | 0.786012 | − | 0.618211i | \(-0.212142\pi\) |
0.272521 | + | 0.962150i | \(0.412142\pi\) | |||||||
\(252\) | 20.3827 | − | 2.02412i | 1.28399 | − | 0.127508i | ||||
\(253\) | −20.2199 | − | 10.5753i | −1.27122 | − | 0.664861i | ||||
\(254\) | 7.80815 | 0.489927 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 23.3634 | − | 16.9745i | 1.46021 | − | 1.06091i | ||||
\(257\) | 2.08578 | + | 13.1691i | 0.130107 | + | 0.821465i | 0.963289 | + | 0.268466i | \(0.0865167\pi\) |
−0.833182 | + | 0.552999i | \(0.813483\pi\) | |||||||
\(258\) | 33.9370 | − | 32.0205i | 2.11283 | − | 1.99351i | ||||
\(259\) | −14.2061 | + | 4.61584i | −0.882725 | + | 0.286815i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.836773 | − | 14.3864i | 0.0517949 | − | 0.890498i | ||||
\(262\) | −6.13818 | − | 12.0469i | −0.379218 | − | 0.744257i | ||||
\(263\) | 13.9748 | − | 13.9748i | 0.861722 | − | 0.861722i | −0.129816 | − | 0.991538i | \(-0.541439\pi\) |
0.991538 | + | 0.129816i | \(0.0414388\pi\) | |||||||
\(264\) | 12.6387 | − | 34.2137i | 0.777860 | − | 2.10571i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.78070 | + | 0.903505i | 0.170496 | + | 0.0553974i | ||||
\(267\) | 1.56358 | − | 2.86015i | 0.0956893 | − | 0.175038i | ||||
\(268\) | 10.9608 | + | 69.2038i | 0.669538 | + | 4.22730i | ||||
\(269\) | −3.33489 | − | 10.2637i | −0.203332 | − | 0.625792i | −0.999778 | − | 0.0210817i | \(-0.993289\pi\) |
0.796446 | − | 0.604710i | \(-0.206711\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.6761 | − | 12.1159i | −1.01300 | − | 0.735990i | −0.0481667 | − | 0.998839i | \(-0.515338\pi\) |
−0.964837 | + | 0.262849i | \(0.915338\pi\) | |||||||
\(272\) | −37.8753 | − | 5.99886i | −2.29653 | − | 0.363734i | ||||
\(273\) | −1.25438 | − | 9.74389i | −0.0759183 | − | 0.589727i | ||||
\(274\) | − | 27.8123i | − | 1.68020i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −50.4064 | − | 18.0128i | −3.03411 | − | 1.08424i | ||||
\(277\) | −4.36159 | − | 8.56011i | −0.262063 | − | 0.514327i | 0.722057 | − | 0.691834i | \(-0.243197\pi\) |
−0.984120 | + | 0.177507i | \(0.943197\pi\) | |||||||
\(278\) | −4.51123 | + | 28.4828i | −0.270566 | + | 1.70828i | ||||
\(279\) | 5.70954 | − | 1.49480i | 0.341821 | − | 0.0894916i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.56570 | − | 1.15857i | 0.212712 | − | 0.0691143i | −0.200723 | − | 0.979648i | \(-0.564329\pi\) |
0.413435 | + | 0.910534i | \(0.364329\pi\) | |||||||
\(282\) | −8.68109 | + | 46.1004i | −0.516952 | + | 2.74524i | ||||
\(283\) | 20.2757 | + | 3.21136i | 1.20527 | + | 0.190895i | 0.726574 | − | 0.687088i | \(-0.241111\pi\) |
0.478692 | + | 0.877983i | \(0.341111\pi\) | |||||||
\(284\) | 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 | ||||
\(288\) | 3.60642 | − | 16.5007i | 0.212510 | − | 0.972311i | ||||
\(289\) | −6.71126 | − | 9.23726i | −0.394780 | − | 0.543368i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.58777 | + | 0.0751939i | 0.151698 | + | 0.00440794i | ||||
\(292\) | −10.2166 | − | 5.20564i | −0.597884 | − | 0.304637i | ||||
\(293\) | 16.8755 | − | 2.67282i | 0.985879 | − | 0.156148i | 0.357381 | − | 0.933959i | \(-0.383670\pi\) |
0.628498 | + | 0.777811i | \(0.283670\pi\) | |||||||
\(294\) | 5.82102 | + | 19.8605i | 0.339489 | + | 1.15829i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 62.3950i | 3.62663i | ||||||||
\(297\) | 6.28725 | + | 16.0459i | 0.364823 | + | 0.931077i | ||||
\(298\) | −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 | ||||
\(302\) | −0.529677 | + | 1.03955i | −0.0304795 | + | 0.0598193i | ||||
\(303\) | −0.521868 | + | 0.492397i | −0.0299806 | + | 0.0282874i | ||||
\(304\) | 3.19213 | − | 4.39359i | 0.183081 | − | 0.251990i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 34.3007 | − | 21.9963i | 1.96084 | − | 1.25745i | ||||
\(307\) | −19.7867 | + | 19.7867i | −1.12928 | + | 1.12928i | −0.138990 | + | 0.990294i | \(0.544386\pi\) |
−0.990294 | + | 0.138990i | \(0.955614\pi\) | |||||||
\(308\) | −22.3270 | − | 3.78038i | −1.27220 | − | 0.215407i | ||||
\(309\) | 1.86035 | + | 0.664797i | 0.105831 | + | 0.0378190i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.75146 | + | 2.41067i | 0.0993160 | + | 0.136697i | 0.855783 | − | 0.517336i | \(-0.173076\pi\) |
−0.756467 | + | 0.654032i | \(0.773076\pi\) | |||||||
\(312\) | −40.3288 | − | 7.59426i | −2.28317 | − | 0.429940i | ||||
\(313\) | −6.83984 | + | 13.4239i | −0.386611 | + | 0.758766i | −0.999507 | − | 0.0313971i | \(-0.990004\pi\) |
0.612896 | + | 0.790163i | \(0.290004\pi\) | |||||||
\(314\) | −16.5370 | − | 50.8956i | −0.933236 | − | 2.87221i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.45917 | + | 6.87249i | −0.532120 | + | 0.386608i | ||||
\(317\) | 5.77694 | − | 2.94350i | 0.324466 | − | 0.165323i | −0.284169 | − | 0.958774i | \(-0.591718\pi\) |
0.608634 | + | 0.793451i | \(0.291718\pi\) | |||||||
\(318\) | 31.9797 | − | 15.1411i | 1.79333 | − | 0.849069i | ||||
\(319\) | −5.08422 | + | 15.0987i | −0.284662 | + | 0.845362i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.1177 | + | 15.6986i | −0.676344 | + | 0.876212i | ||||
\(322\) | −4.16821 | + | 26.3170i | −0.232285 | + | 1.46659i | ||||
\(323\) | 3.97500 | − | 0.629578i | 0.221175 | − | 0.0350307i | ||||
\(324\) | 19.8105 | + | 35.2407i | 1.10058 | + | 1.95782i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.38556 | + | 7.41259i | −0.298279 | + | 0.410546i | ||||
\(327\) | −3.99987 | − | 2.18664i | −0.221193 | − | 0.120921i | ||||
\(328\) | −39.8572 | + | 20.3082i | −2.20074 | + | 1.12133i | ||||
\(329\) | 16.1571 | 0.890771 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.1458 | −1.10732 | −0.553658 | − | 0.832744i | \(-0.686768\pi\) | ||||
−0.553658 | + | 0.832744i | \(0.686768\pi\) | |||||||
\(332\) | −24.0488 | + | 12.2535i | −1.31985 | + | 0.672497i | ||||
\(333\) | −19.6009 | − | 22.0219i | −1.07413 | − | 1.20679i | ||||
\(334\) | 18.5423 | − | 25.5213i | 1.01459 | − | 1.39647i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −18.9303 | − | 0.550067i | −1.03273 | − | 0.0300086i | ||||
\(337\) | 31.4335 | − | 4.97858i | 1.71229 | − | 0.271201i | 0.778145 | − | 0.628084i | \(-0.216161\pi\) |
0.934149 | + | 0.356884i | \(0.116161\pi\) | |||||||
\(338\) | −0.368777 | + | 2.32837i | −0.0200588 | + | 0.126647i | ||||
\(339\) | 9.36991 | + | 7.23259i | 0.508904 | + | 0.392821i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.52451 | − | 0.0694766i | −0.353322 | − | 0.00376237i | ||||
\(342\) | 0.570259 | + | 5.74247i | 0.0308361 | + | 0.310517i | ||||
\(343\) | 15.8315 | − | 8.06655i | 0.854820 | − | 0.435553i | ||||
\(344\) | −54.3079 | + | 39.4570i | −2.92809 | + | 2.12738i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.22881 | + | 9.93725i | 0.173582 | + | 0.534230i | ||||
\(347\) | −10.8941 | + | 21.3809i | −0.584827 | + | 1.14779i | 0.389157 | + | 0.921171i | \(0.372766\pi\) |
−0.973984 | + | 0.226616i | \(0.927234\pi\) | |||||||
\(348\) | −6.91610 | + | 36.7275i | −0.370742 | + | 1.96880i | ||||
\(349\) | 7.88353 | + | 10.8507i | 0.421995 | + | 0.580827i | 0.966093 | − | 0.258195i | \(-0.0831278\pi\) |
−0.544097 | + | 0.839022i | \(0.683128\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.6195 | − | 9.98868i | 0.887082 | − | 0.533156i | ||||
\(352\) | −8.65395 | + | 16.5464i | −0.461257 | + | 0.881925i | ||||
\(353\) | 1.90374 | − | 1.90374i | 0.101326 | − | 0.101326i | −0.654626 | − | 0.755953i | \(-0.727174\pi\) |
0.755953 | + | 0.654626i | \(0.227174\pi\) | |||||||
\(354\) | −29.9851 | + | 38.8461i | −1.59369 | + | 2.06464i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.96888 | + | 6.83908i | −0.263350 | + | 0.362471i | ||||
\(357\) | −9.63145 | − | 10.2079i | −0.509751 | − | 0.540261i | ||||
\(358\) | −5.29529 | + | 10.3926i | −0.279865 | + | 0.549265i | ||||
\(359\) | 16.6144 | + | 12.0710i | 0.876872 | + | 0.637085i | 0.932422 | − | 0.361371i | \(-0.117691\pi\) |
−0.0555499 | + | 0.998456i | \(0.517691\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.69520 | − | 17.5280i | 0.299747 | − | 0.922527i | ||||
\(362\) | −32.6613 | − | 32.6613i | −1.71664 | − | 1.71664i | ||||
\(363\) | −2.02970 | − | 18.9441i | −0.106532 | − | 0.994309i | ||||
\(364\) | 25.4785i | 1.33543i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.99963 | + | 1.46537i | −0.261335 | + | 0.0765959i | ||||
\(367\) | 23.9244 | − | 3.78926i | 1.24885 | − | 0.197798i | 0.503217 | − | 0.864160i | \(-0.332150\pi\) |
0.745628 | + | 0.666362i | \(0.232150\pi\) | |||||||
\(368\) | 44.0973 | + | 22.4687i | 2.29873 | + | 1.17126i | ||||
\(369\) | 7.68763 | − | 19.6885i | 0.400202 | − | 1.02494i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.16318 | − | 9.85927i | −0.371894 | − | 0.511868i | ||||
\(372\) | −15.1810 | + | 1.95432i | −0.787097 | + | 0.101327i | ||||
\(373\) | −17.4780 | − | 17.4780i | −0.904976 | − | 0.904976i | 0.0908853 | − | 0.995861i | \(-0.471030\pi\) |
−0.995861 | + | 0.0908853i | \(0.971030\pi\) | |||||||
\(374\) | −42.9893 | + | 13.4637i | −2.22292 | + | 0.696192i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.8558 | − | 64.1876i | 1.07556 | − | 3.31022i | ||||
\(377\) | 17.7046 | + | 2.80414i | 0.911834 | + | 0.144420i | ||||
\(378\) | 15.4141 | − | 12.9371i | 0.792818 | − | 0.665413i | ||||
\(379\) | 12.8286 | − | 4.16826i | 0.658960 | − | 0.214109i | 0.0395991 | − | 0.999216i | \(-0.487392\pi\) |
0.619361 | + | 0.785107i | \(0.287392\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.38298 | − | 2.99386i | 0.224547 | − | 0.153380i | ||||
\(382\) | 0.754724 | − | 4.76514i | 0.0386150 | − | 0.243806i | ||||
\(383\) | −11.9994 | − | 23.5502i | −0.613142 | − | 1.20336i | −0.963743 | − | 0.266834i | \(-0.914023\pi\) |
0.350601 | − | 0.936525i | \(-0.385977\pi\) | |||||||
\(384\) | 6.62543 | − | 18.5404i | 0.338102 | − | 0.946135i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 43.1036i | − | 2.19392i | ||||||
\(387\) | 6.77248 | − | 30.9866i | 0.344265 | − | 1.57514i | ||||
\(388\) | −6.63132 | − | 1.05030i | −0.336654 | − | 0.0533208i | ||||
\(389\) | −21.0424 | − | 15.2882i | −1.06689 | − | 0.775144i | −0.0915423 | − | 0.995801i | \(-0.529180\pi\) |
−0.975351 | + | 0.220658i | \(0.929180\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.3336 | + | 34.8813i | 0.573165 | + | 1.76402i | ||||
\(392\) | −4.65792 | − | 29.4090i | −0.235261 | − | 1.48538i | ||||
\(393\) | −8.06467 | − | 4.40876i | −0.406809 | − | 0.222393i | ||||
\(394\) | −41.0515 | − | 13.3384i | −2.06814 | − | 0.671981i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −10.8587 | − | 43.3549i | −0.545671 | − | 2.17866i | ||||
\(397\) | −8.26181 | + | 8.26181i | −0.414648 | + | 0.414648i | −0.883354 | − | 0.468706i | \(-0.844720\pi\) |
0.468706 | + | 0.883354i | \(0.344720\pi\) | |||||||
\(398\) | −20.2042 | − | 39.6529i | −1.01274 | − | 1.98762i | ||||
\(399\) | 1.90733 | − | 0.559030i | 0.0954860 | − | 0.0279865i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.81862 | − | 2.86534i | 0.440381 | − | 0.143088i | −0.0804306 | − | 0.996760i | \(-0.525630\pi\) |
0.520811 | + | 0.853672i | \(0.325630\pi\) | |||||||
\(402\) | 47.2412 | + | 50.0688i | 2.35618 | + | 2.49720i | ||||
\(403\) | 1.14844 | + | 7.25099i | 0.0572081 | + | 0.361197i | ||||
\(404\) | 1.50539 | − | 1.09373i | 0.0748959 | − | 0.0544151i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.6034 | 0.923271 | ||||||||
\(407\) | 14.4869 | + | 29.1965i | 0.718088 | + | 1.44722i | ||||
\(408\) | −52.9856 | + | 25.0865i | −2.62318 | + | 1.24196i | ||||
\(409\) | −2.94643 | − | 0.957353i | −0.145692 | − | 0.0473380i | 0.235263 | − | 0.971932i | \(-0.424405\pi\) |
−0.380955 | + | 0.924594i | \(0.624405\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.6640 | − | 15.6120i | −0.526017 | − | 0.770084i | ||||
\(412\) | −4.56502 | − | 2.32600i | −0.224903 | − | 0.114594i | ||||
\(413\) | 15.0596 | + | 7.67324i | 0.741034 | + | 0.377576i | ||||
\(414\) | −50.8747 | + | 13.3194i | −2.50036 | + | 0.654613i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 19.9811 | + | 6.49227i | 0.979656 | + | 0.318310i | ||||
\(417\) | 8.38878 | + | 17.7181i | 0.410800 | + | 0.867659i | ||||
\(418\) | 1.06505 | − | 6.29023i | 0.0520934 | − | 0.307665i | ||||
\(419\) | 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 | −0.707820 | − | 0.706393i | \(-0.750321\pi\) |
0.453092 | + | 0.891464i | \(0.350321\pi\) | |||||||
\(422\) | −9.43381 | − | 59.5627i | −0.459231 | − | 2.89947i | ||||
\(423\) | 12.8032 | + | 29.2063i | 0.622511 | + | 1.42006i | ||||
\(424\) | −48.4144 | + | 15.7308i | −2.35121 | + | 0.763954i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.498963 | − | 1.70239i | −0.0241748 | − | 0.0824812i | ||||
\(427\) | 0.814654 | + | 1.59885i | 0.0394239 | + | 0.0773737i | ||||
\(428\) | 36.3672 | − | 36.3672i | 1.75788 | − | 1.75788i | ||||
\(429\) | −20.6344 | + | 5.80997i | −0.996236 | + | 0.280508i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.6607 | + | 4.43862i | 0.658012 | + | 0.213801i | 0.618943 | − | 0.785436i | \(-0.287561\pi\) |
0.0390683 | + | 0.999237i | \(0.487561\pi\) | |||||||
\(432\) | −14.0064 | − | 34.6551i | −0.673881 | − | 1.66735i | ||||
\(433\) | −1.70299 | − | 10.7522i | −0.0818403 | − | 0.516719i | −0.994219 | − | 0.107372i | \(-0.965756\pi\) |
0.912379 | − | 0.409347i | \(-0.134244\pi\) | |||||||
\(434\) | 2.35443 | + | 7.24618i | 0.113016 | + | 0.347828i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.56434 | + | 6.94890i | 0.458049 | + | 0.332792i | ||||
\(437\) | −5.13017 | − | 0.812539i | −0.245409 | − | 0.0388690i | ||||
\(438\) | −11.1731 | + | 1.43836i | −0.533871 | + | 0.0687276i | ||||
\(439\) | 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 | ||||
\(442\) | 23.0107 | + | 45.1611i | 1.09451 | + | 2.14809i | ||||
\(443\) | −0.717321 | + | 4.52898i | −0.0340809 | + | 0.215179i | −0.998851 | − | 0.0479143i | \(-0.984743\pi\) |
0.964771 | + | 0.263093i | \(0.0847426\pi\) | |||||||
\(444\) | 43.1252 | + | 63.1348i | 2.04663 | + | 2.99625i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −51.1683 | + | 16.6256i | −2.42289 | + | 0.787245i | ||||
\(447\) | −12.1179 | − | 2.28191i | −0.573159 | − | 0.107931i | ||||
\(448\) | −0.0631156 | − | 0.00999653i | −0.00298193 | − | 0.000472292i | ||||
\(449\) | −9.12613 | + | 28.0873i | −0.430689 | + | 1.32552i | 0.466752 | + | 0.884388i | \(0.345424\pi\) |
−0.897440 | + | 0.441136i | \(0.854576\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.9352 | + | 18.7569i | −0.656184 | + | 0.883228i | ||||
\(452\) | −21.7062 | − | 21.7062i | −1.02097 | − | 1.02097i | ||||
\(453\) | 0.101266 | + | 0.786627i | 0.00475790 | + | 0.0369590i | ||||
\(454\) | 30.5327 | + | 42.0246i | 1.43297 | + | 1.97231i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.241144 | − | 8.29888i | 0.0112926 | − | 0.388631i | ||||
\(457\) | −14.6861 | − | 7.48292i | −0.686985 | − | 0.350036i | 0.0754062 | − | 0.997153i | \(-0.475975\pi\) |
−0.762391 | + | 0.647117i | \(0.775975\pi\) | |||||||
\(458\) | 19.6640 | − | 3.11447i | 0.918839 | − | 0.145530i | ||||
\(459\) | 10.8202 | − | 25.4992i | 0.505043 | − | 1.19020i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 28.5289i | − | 1.32872i | −0.747412 | − | 0.664361i | \(-0.768704\pi\) | ||
0.747412 | − | 0.664361i | \(-0.231296\pi\) | |||||||
\(462\) | −20.2080 | + | 9.30554i | −0.940161 | + | 0.432933i | ||||
\(463\) | 11.3562 | + | 11.3562i | 0.527765 | + | 0.527765i | 0.919905 | − | 0.392140i | \(-0.128265\pi\) |
−0.392140 | + | 0.919905i | \(0.628265\pi\) | |||||||
\(464\) | 10.6780 | − | 32.8634i | 0.495712 | − | 1.52564i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.3403 | − | 19.8639i | −1.26651 | − | 0.920177i | ||||
\(467\) | −13.1310 | + | 25.7711i | −0.607632 | + | 1.19255i | 0.358265 | + | 0.933620i | \(0.383368\pi\) |
−0.965897 | + | 0.258926i | \(0.916632\pi\) | |||||||
\(468\) | −46.0559 | + | 20.1895i | −2.12894 | + | 0.933261i | ||||
\(469\) | 13.9360 | − | 19.1812i | 0.643503 | − | 0.885706i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −28.7976 | − | 22.2287i | −1.32692 | − | 1.02425i | ||||
\(472\) | 49.9227 | − | 49.9227i | 2.29788 | − | 2.29788i | ||||
\(473\) | −16.2512 | + | 31.0724i | −0.747232 | + | 1.42871i | ||||
\(474\) | −3.86553 | + | 10.8172i | −0.177550 | + | 0.496849i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 21.3937 | + | 29.4459i | 0.980580 | + | 1.34965i | ||||
\(477\) | 12.1458 | − | 20.7611i | 0.556119 | − | 0.950586i | ||||
\(478\) | −7.82325 | + | 15.3540i | −0.357827 | + | 0.702275i | ||||
\(479\) | −2.41099 | − | 7.42025i | −0.110161 | − | 0.339040i | 0.880746 | − | 0.473589i | \(-0.157042\pi\) |
−0.990907 | + | 0.134548i | \(0.957042\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.6679 | − | 21.5550i | 1.35274 | − | 0.982825i | ||||
\(482\) | 9.42112 | − | 4.80030i | 0.429120 | − | 0.218648i | ||||
\(483\) | 7.75091 | + | 16.3708i | 0.352679 | + | 0.744899i | ||||
\(484\) | −1.05220 | + | 49.3999i | −0.0478271 | + | 2.24545i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 35.6001 | + | 17.6117i | 1.61485 | + | 0.798882i | ||||
\(487\) | 3.94219 | − | 24.8900i | 0.178638 | − | 1.12787i | −0.721547 | − | 0.692365i | \(-0.756569\pi\) |
0.900185 | − | 0.435508i | \(-0.143431\pi\) | |||||||
\(488\) | 7.40333 | − | 1.17257i | 0.335133 | − | 0.0530798i | ||||
\(489\) | −0.180909 | + | 6.22592i | −0.00818100 | + | 0.281546i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.3332 | − | 16.9752i | 0.556590 | − | 0.766080i | −0.434298 | − | 0.900769i | \(-0.643004\pi\) |
0.990888 | + | 0.134689i | \(0.0430036\pi\) | |||||||
\(492\) | −26.2935 | + | 48.0969i | −1.18540 | + | 2.16838i | ||||
\(493\) | 22.8161 | − | 11.6254i | 1.02759 | − | 0.523582i | ||||
\(494\) | −7.17809 | −0.322958 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.1520 | 0.635442 | ||||||||
\(497\) | −0.544414 | + | 0.277393i | −0.0244203 | + | 0.0124428i | ||||
\(498\) | −12.7197 | + | 23.2674i | −0.569985 | + | 1.04264i | ||||
\(499\) | 5.26071 | − | 7.24075i | 0.235502 | − | 0.324140i | −0.674866 | − | 0.737940i | \(-0.735799\pi\) |
0.910368 | + | 0.413800i | \(0.135799\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.622865 | − | 21.4357i | 0.0278276 | − | 0.957674i | ||||
\(502\) | −44.3753 | + | 7.02836i | −1.98057 | + | 0.313691i | ||||
\(503\) | 3.47647 | − | 21.9496i | 0.155008 | − | 0.978684i | −0.780443 | − | 0.625227i | \(-0.785006\pi\) |
0.935451 | − | 0.353456i | \(-0.114994\pi\) | |||||||
\(504\) | −24.3715 | + | 15.6289i | −1.08559 | + | 0.696167i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 58.1364 | + | 0.619069i | 2.58448 | + | 0.0275210i | ||||
\(507\) | 0.685753 | + | 1.44839i | 0.0304554 | + | 0.0643253i | ||||
\(508\) | −12.2652 | + | 6.24943i | −0.544180 | + | 0.277273i | ||||
\(509\) | −15.1837 | + | 11.0316i | −0.673004 | + | 0.488966i | −0.871029 | − | 0.491231i | \(-0.836547\pi\) |
0.198026 | + | 0.980197i | \(0.436547\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.19900 | + | 3.69013i | 0.0530404 | + | 0.163242i | ||||
\(512\) | −23.0838 | + | 45.3046i | −1.02017 | + | 2.00220i | ||||
\(513\) | 2.52193 | + | 3.00479i | 0.111346 | + | 0.132665i | ||||
\(514\) | −19.9683 | − | 27.4840i | −0.880764 | − | 1.21227i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −27.6806 | + | 77.4606i | −1.21857 | + | 3.41001i | ||||
\(517\) | −5.14401 | − | 34.8777i | −0.226233 | − | 1.53392i | ||||
\(518\) | 26.9117 | − | 26.9117i | 1.18243 | − | 1.18243i | ||||
\(519\) | 5.62266 | + | 4.34011i | 0.246807 | + | 0.190509i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.74842 | + | 2.40650i | −0.0765998 | + | 0.105431i | −0.845598 | − | 0.533821i | \(-0.820756\pi\) |
0.768998 | + | 0.639251i | \(0.220756\pi\) | |||||||
\(522\) | 14.7416 | + | 33.6283i | 0.645223 | + | 1.47187i | ||||
\(523\) | 10.5855 | − | 20.7752i | 0.462871 | − | 0.908435i | −0.535102 | − | 0.844788i | \(-0.679727\pi\) |
0.997972 | − | 0.0636475i | \(-0.0202733\pi\) | |||||||
\(524\) | 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 | ||||
\(528\) | 4.83952 | + | 41.0392i | 0.210613 | + | 1.78600i | ||||
\(529\) | − | 24.3348i | − | 1.05803i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.93702 | + | 33.3027i | −0.0840595 | + | 1.44522i | ||||
\(532\) | −5.09112 | + | 0.806354i | −0.220728 | + | 0.0349599i | ||||
\(533\) | 23.4254 | + | 11.9358i | 1.01467 | + | 0.516998i | ||||
\(534\) | −0.241229 | + | 8.30180i | −0.0104390 | + | 0.359254i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −58.2127 | − | 80.1229i | −2.51440 | − | 3.46078i | ||||
\(537\) | 1.01238 | + | 7.86408i | 0.0436873 | + | 0.339360i | ||||
\(538\) | 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 | −0.368394 | − | 0.929670i | \(-0.620092\pi\) |
0.844483 | − | 0.535582i | \(-0.179908\pi\) | |||||||
\(542\) | 51.8734 | + | 8.21594i | 2.22815 | + | 0.352905i | ||||
\(543\) | −30.8571 | − | 5.81066i | −1.32421 | − | 0.249359i | ||||
\(544\) | 28.5440 | − | 9.27452i | 1.22381 | − | 0.397642i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 14.1188 | + | 20.6698i | 0.604229 | + | 0.884585i | ||||
\(547\) | −4.83151 | + | 30.5049i | −0.206580 | + | 1.30430i | 0.638485 | + | 0.769634i | \(0.279561\pi\) |
−0.845065 | + | 0.534663i | \(0.820439\pi\) | |||||||
\(548\) | 22.2602 | + | 43.6881i | 0.950909 | + | 1.86626i | ||||
\(549\) | −2.24460 | + | 2.73956i | −0.0957973 | + | 0.116921i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.62649i | 0.154494i | ||||||||
\(552\) | 75.0416 | − | 9.66045i | 3.19398 | − | 0.411176i | ||||
\(553\) | 3.90772 | + | 0.618922i | 0.166173 | + | 0.0263192i | ||||
\(554\) | 19.8035 | + | 14.3881i | 0.841372 | + | 0.611292i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.7105 | − | 48.3520i | −0.666274 | − | 2.05058i | ||||
\(557\) | 0.156089 | + | 0.985507i | 0.00661370 | + | 0.0417573i | 0.990774 | − | 0.135521i | \(-0.0432708\pi\) |
−0.984161 | + | 0.177278i | \(0.943271\pi\) | |||||||
\(558\) | −11.2328 | + | 9.99795i | −0.475523 | + | 0.423247i | ||||
\(559\) | 37.5226 | + | 12.1918i | 1.58703 | + | 0.515659i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.9690 | + | 24.0409i | −0.800873 | + | 1.01501i | ||||
\(562\) | −6.75477 | + | 6.75477i | −0.284933 | + | 0.284933i | ||||
\(563\) | 0.165275 | + | 0.324370i | 0.00696550 | + | 0.0136706i | 0.894463 | − | 0.447142i | \(-0.147558\pi\) |
−0.887498 | + | 0.460812i | \(0.847558\pi\) | |||||||
\(564\) | −23.2610 | − | 79.3635i | −0.979466 | − | 3.34180i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −49.7450 | + | 16.1631i | −2.09094 | + | 0.679387i | ||||
\(567\) | 3.69204 | − | 13.1723i | 0.155051 | − | 0.553183i | ||||
\(568\) | 0.399265 | + | 2.52086i | 0.0167528 | + | 0.105773i | ||||
\(569\) | 36.2145 | − | 26.3114i | 1.51819 | − | 1.10303i | 0.555819 | − | 0.831304i | \(-0.312405\pi\) |
0.962374 | − | 0.271728i | \(-0.0875951\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.86298 | 0.412753 | 0.206376 | − | 0.978473i | \(-0.433833\pi\) | ||||
0.206376 | + | 0.978473i | \(0.433833\pi\) | |||||||
\(572\) | 54.9992 | − | 8.11168i | 2.29963 | − | 0.339166i | ||||
\(573\) | −1.40343 | − | 2.96422i | −0.0586293 | − | 0.123832i | ||||
\(574\) | 25.9500 | + | 8.43167i | 1.08313 | + | 0.351931i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.0319437 | − | 0.122012i | −0.00133099 | − | 0.00508383i | ||||
\(577\) | −23.6391 | − | 12.0447i | −0.984107 | − | 0.501427i | −0.113570 | − | 0.993530i | \(-0.536228\pi\) |
−0.870537 | + | 0.492103i | \(0.836228\pi\) | |||||||
\(578\) | 25.9211 | + | 13.2074i | 1.07817 | + | 0.549357i | ||||
\(579\) | −16.5271 | − | 24.1956i | −0.686844 | − | 1.00553i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.68614 | + | 2.82230i | 0.360362 | + | 0.117089i | ||||
\(582\) | −5.96177 | + | 2.82265i | −0.247123 | + | 0.117003i | ||||
\(583\) | −19.0022 | + | 18.6018i | −0.786991 | + | 0.770407i | ||||
\(584\) | 16.2075 | 0.670671 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −35.2194 | + | 25.5884i | −1.45490 | + | 1.05705i | ||||
\(587\) | 0.886699 | + | 5.59840i | 0.0365980 | + | 0.231071i | 0.999207 | − | 0.0398252i | \(-0.0126801\pi\) |
−0.962609 | + | 0.270896i | \(0.912680\pi\) | |||||||
\(588\) | −25.0396 | − | 26.5383i | −1.03262 | − | 1.09442i | ||||
\(589\) | −1.41255 | + | 0.458966i | −0.0582031 | + | 0.0189113i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −28.1579 | + | 8.25295i | −1.15826 | + | 0.339481i | ||||
\(592\) | −32.0934 | − | 62.9869i | −1.31903 | − | 2.58875i | ||||
\(593\) | −29.9393 | + | 29.9393i | −1.22946 | + | 1.22946i | −0.265293 | + | 0.964168i | \(0.585469\pi\) |
−0.964168 | + | 0.265293i | \(0.914531\pi\) | |||||||
\(594\) | −32.8342 | − | 29.1550i | −1.34721 | − | 1.19624i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 30.4140 | + | 9.88210i | 1.24580 | + | 0.404786i | ||||
\(597\) | −26.5453 | − | 14.5117i | −1.08643 | − | 0.593925i | ||||
\(598\) | −10.2332 | − | 64.6097i | −0.418465 | − | 2.64209i | ||||
\(599\) | −6.05826 | − | 18.6454i | −0.247534 | − | 0.761830i | −0.995209 | − | 0.0977664i | \(-0.968830\pi\) |
0.747676 | − | 0.664064i | \(-0.231170\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.66141 | − | 5.56634i | −0.312515 | − | 0.227056i | 0.420460 | − | 0.907311i | \(-0.361869\pi\) |
−0.732975 | + | 0.680256i | \(0.761869\pi\) | |||||||
\(602\) | 40.4419 | + | 6.40537i | 1.64829 | + | 0.261063i | ||||
\(603\) | 45.7158 | + | 9.99174i | 1.86169 | + | 0.406895i | ||||
\(604\) | − | 2.05688i | − | 0.0836934i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.615183 | − | 1.72151i | 0.0249901 | − | 0.0699316i | ||||
\(607\) | −16.4105 | − | 32.2074i | −0.666081 | − | 1.30726i | −0.938567 | − | 0.345098i | \(-0.887846\pi\) |
0.272486 | − | 0.962160i | \(-0.412154\pi\) | |||||||
\(608\) | −0.664916 | + | 4.19812i | −0.0269659 | + | 0.170256i | ||||
\(609\) | 10.4427 | − | 7.13305i | 0.423160 | − | 0.289046i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −37.7252 | + | 12.2577i | −1.52620 | + | 0.495891i | ||||
\(612\) | −36.2750 | + | 62.0057i | −1.46633 | + | 2.50643i | ||||
\(613\) | 3.32971 | + | 0.527373i | 0.134486 | + | 0.0213004i | 0.223314 | − | 0.974746i | \(-0.428312\pi\) |
−0.0888287 | + | 0.996047i | \(0.528312\pi\) | |||||||
\(614\) | 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 | 0.735489 | − | 0.677536i | \(-0.236952\pi\) |
−0.677536 | + | 0.735489i | \(0.736952\pi\) | |||||||
\(618\) | −4.99239 | + | 0.642692i | −0.200823 | + | 0.0258529i | ||||
\(619\) | 1.47379 | + | 2.02850i | 0.0592367 | + | 0.0815323i | 0.837608 | − | 0.546272i | \(-0.183954\pi\) |
−0.778371 | + | 0.627805i | \(0.783954\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −23.4507 | + | 26.9834i | −0.941044 | + | 1.08281i | ||||
\(622\) | −6.76469 | − | 3.44678i | −0.271239 | − | 0.138203i | ||||
\(623\) | 2.82532 | − | 0.447487i | 0.113194 | − | 0.0179282i | ||||
\(624\) | 44.6176 | − | 13.0772i | 1.78613 | − | 0.523507i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 38.3872i | − | 1.53426i | ||||||
\(627\) | −1.81400 | − | 3.93929i | −0.0724441 | − | 0.157320i | ||||
\(628\) | 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 | −0.997340 | − | 0.0728922i | \(-0.976777\pi\) |
−0.377520 | − | 0.926002i | \(-0.623223\pi\) | |||||||
\(632\) | 7.50293 | − | 14.7253i | 0.298450 | − | 0.585742i | ||||
\(633\) | −28.1335 | − | 29.8174i | −1.11821 | − | 1.18514i | ||||
\(634\) | −9.71007 | + | 13.3648i | −0.385636 | + | 0.530783i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −38.1159 | + | 49.3796i | −1.51139 | + | 1.95803i | ||||
\(637\) | −12.3744 | + | 12.3744i | −0.490293 | + | 0.490293i | ||||
\(638\) | −5.92284 | − | 40.1583i | −0.234487 | − | 1.58988i | ||||
\(639\) | −0.932829 | − | 0.764295i | −0.0369021 | − | 0.0302350i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.237865 | + | 0.327394i | 0.00939512 | + | 0.0129313i | 0.813689 | − | 0.581301i | \(-0.197456\pi\) |
−0.804294 | + | 0.594232i | \(0.797456\pi\) | |||||||
\(642\) | 9.35069 | − | 49.6562i | 0.369042 | − | 1.95978i | ||||
\(643\) | 2.52455 | − | 4.95472i | 0.0995587 | − | 0.195395i | −0.835855 | − | 0.548951i | \(-0.815028\pi\) |
0.935413 | + | 0.353556i | \(0.115028\pi\) | |||||||
\(644\) | −14.5159 | − | 44.6754i | −0.572007 | − | 1.76046i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.29586 | + | 6.02730i | −0.326396 | + | 0.237141i | ||||
\(647\) | 24.9364 | − | 12.7057i | 0.980352 | − | 0.499514i | 0.111060 | − | 0.993814i | \(-0.464575\pi\) |
0.869292 | + | 0.494299i | \(0.164575\pi\) | |||||||
\(648\) | −47.5638 | − | 31.6703i | −1.86848 | − | 1.24413i | ||||
\(649\) | 11.7693 | − | 34.9514i | 0.461986 | − | 1.37196i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.10001 | + | 3.16478i | 0.160692 | + | 0.124037i | ||||
\(652\) | 2.52691 | − | 15.9543i | 0.0989616 | − | 0.624819i | ||||
\(653\) | 2.60271 | − | 0.412229i | 0.101852 | − | 0.0161318i | −0.105300 | − | 0.994440i | \(-0.533580\pi\) |
0.207152 | + | 0.978309i | \(0.433580\pi\) | |||||||
\(654\) | 11.6099 | + | 0.337355i | 0.453984 | + | 0.0131916i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 29.7896 | − | 41.0018i | 1.16309 | − | 1.60085i | ||||
\(657\) | −5.72033 | + | 5.09147i | −0.223171 | + | 0.198637i | ||||
\(658\) | −36.6802 | + | 18.6895i | −1.42994 | + | 0.728592i | ||||
\(659\) | −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 | \(0.0737321\pi\) | |||||||
\(662\) | 45.7355 | − | 23.3034i | 1.77756 | − | 0.905711i | ||||
\(663\) | 30.2327 | + | 16.5275i | 1.17414 | + | 0.641876i | ||||
\(664\) | 22.4244 | − | 30.8645i | 0.870234 | − | 1.19777i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 69.9719 | + | 27.3214i | 2.71135 | + | 1.05868i | ||||
\(667\) | −32.6419 | + | 5.16997i | −1.26390 | + | 0.200182i | ||||
\(668\) | −8.70009 | + | 54.9302i | −0.336617 | + | 2.12531i | ||||
\(669\) | −22.3478 | + | 28.9519i | −0.864017 | + | 1.11934i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.19200 | − | 2.26759i | 0.123226 | − | 0.0875393i | ||||
\(672\) | 13.3966 | − | 6.34272i | 0.516784 | − | 0.244676i | ||||
\(673\) | −44.2508 | + | 22.5469i | −1.70574 | + | 0.869119i | −0.721474 | + | 0.692442i | \(0.756535\pi\) |
−0.984269 | + | 0.176677i | \(0.943465\pi\) | |||||||
\(674\) | −65.6021 | + | 47.6627i | −2.52690 | + | 1.83590i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.28428 | − | 3.95260i | −0.0493954 | − | 0.152023i | ||||
\(677\) | −12.4067 | + | 24.3494i | −0.476827 | + | 0.935825i | 0.519841 | + | 0.854263i | \(0.325991\pi\) |
−0.996668 | + | 0.0815625i | \(0.974009\pi\) | |||||||
\(678\) | −29.6379 | − | 5.58107i | −1.13824 | − | 0.214340i | ||||
\(679\) | 1.33538 | + | 1.83800i | 0.0512474 | + | 0.0705360i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 33.2525 | + | 11.8828i | 1.27424 | + | 0.455350i | ||||
\(682\) | 14.8924 | − | 7.38939i | 0.570260 | − | 0.282954i | ||||
\(683\) | 3.88464 | − | 3.88464i | 0.148642 | − | 0.148642i | −0.628869 | − | 0.777511i | \(-0.716482\pi\) |
0.777511 | + | 0.628869i | \(0.216482\pi\) | |||||||
\(684\) | −5.49189 | − | 8.56396i | −0.209988 | − | 0.327451i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −26.6101 | + | 36.6256i | −1.01598 | + | 1.39837i | ||||
\(687\) | 9.84390 | − | 9.28798i | 0.375568 | − | 0.354359i | ||||
\(688\) | 34.5281 | − | 67.7652i | 1.31637 | − | 2.58352i | ||||
\(689\) | 24.2050 | + | 17.5860i | 0.922139 | + | 0.669973i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.3367 | − | 37.9684i | 0.469309 | − | 1.44439i | −0.384172 | − | 0.923262i | \(-0.625513\pi\) |
0.853481 | − | 0.521124i | \(-0.174487\pi\) | |||||||
\(692\) | −13.0254 | − | 13.0254i | −0.495151 | − | 0.495151i | ||||
\(693\) | −7.77544 | + | 12.9718i | −0.295365 | + | 0.492759i | ||||
\(694\) | − | 61.1409i | − | 2.32088i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −14.8580 | − | 50.6933i | −0.563190 | − | 1.92153i | ||||
\(697\) | 37.0954 | − | 5.87534i | 1.40509 | − | 0.222544i | ||||
\(698\) | −30.4487 | − | 15.5144i | −1.15250 | − | 0.587229i | ||||
\(699\) | −22.9634 | − | 0.667258i | −0.868556 | − | 0.0252380i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.01734 | + | 11.0349i | 0.302811 | + | 0.416783i | 0.933122 | − | 0.359559i | \(-0.117073\pi\) |
−0.630312 | + | 0.776342i | \(0.717073\pi\) | |||||||
\(702\) | −26.1756 | + | 41.9008i | −0.987935 | + | 1.58144i | ||||
\(703\) | 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 | ||||
\(707\) | −0.621898 | − | 0.0984989i | −0.0233889 | − | 0.00370443i | ||||
\(708\) | 16.0099 | − | 85.0194i | 0.601688 | − | 3.19522i | ||||
\(709\) | −6.78298 | + | 2.20392i | −0.254740 | + | 0.0827701i | −0.433603 | − | 0.901104i | \(-0.642758\pi\) |
0.178863 | + | 0.983874i | \(0.442758\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.97775 | + | 7.55420i | 0.0741714 | + | 0.283305i | ||||
\(712\) | 1.86922 | − | 11.8018i | 0.0700521 | − | 0.442292i | ||||
\(713\) | −6.14488 | − | 12.0600i | −0.230127 | − | 0.451650i | ||||
\(714\) | 33.6734 | + | 12.0332i | 1.26019 | + | 0.450331i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 20.5631i | − | 0.768479i | ||||||
\(717\) | 1.49569 | + | 11.6184i | 0.0558574 | + | 0.433896i | ||||
\(718\) | −51.6812 | − | 8.18549i | −1.92872 | − | 0.305480i | ||||
\(719\) | 25.1579 | + | 18.2783i | 0.938231 | + | 0.681665i | 0.947994 | − | 0.318287i | \(-0.103108\pi\) |
−0.00976304 | + | 0.999952i | \(0.503108\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.535738 | + | 1.64883i | 0.0199519 | + | 0.0614057i | ||||
\(722\) | 7.34591 | + | 46.3802i | 0.273386 | + | 1.72609i | ||||
\(723\) | 3.44783 | − | 6.30689i | 0.128226 | − | 0.234556i | ||||
\(724\) | 77.4462 | + | 25.1638i | 2.87827 | + | 0.935205i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 26.5212 | + | 40.6595i | 0.984293 | + | 1.50902i | ||||
\(727\) | 24.0226 | − | 24.0226i | 0.890948 | − | 0.890948i | −0.103664 | − | 0.994612i | \(-0.533057\pi\) |
0.994612 | + | 0.103664i | \(0.0330567\pi\) | |||||||
\(728\) | −16.3497 | − | 32.0880i | −0.605958 | − | 1.18926i | ||||
\(729\) | 26.7363 | − | 3.76402i | 0.990235 | − | 0.139408i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 53.6028 | − | 17.4166i | 1.98257 | − | 0.644176i | ||||
\(732\) | 6.68068 | − | 6.30339i | 0.246925 | − | 0.232980i | ||||
\(733\) | 0.344119 | + | 2.17268i | 0.0127103 | + | 0.0802498i | 0.993228 | − | 0.116180i | \(-0.0370651\pi\) |
−0.980518 | + | 0.196430i | \(0.937065\pi\) | |||||||
\(734\) | −49.9305 | + | 36.2766i | −1.84297 | + | 1.33899i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −38.7350 | −1.42779 | ||||||||
\(737\) | −45.8425 | − | 23.9762i | −1.68863 | − | 0.883173i | ||||
\(738\) | 5.32176 | + | 53.5897i | 0.195897 | + | 1.97267i | ||||
\(739\) | 27.7836 | + | 9.02744i | 1.02204 | + | 0.332080i | 0.771637 | − | 0.636063i | \(-0.219438\pi\) |
0.250399 | + | 0.968143i | \(0.419438\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.02931 | + | 2.75228i | −0.148020 | + | 0.101107i | ||||
\(742\) | 27.6665 | + | 14.0968i | 1.01567 | + | 0.517510i | ||||
\(743\) | 6.08432 | + | 3.10012i | 0.223212 | + | 0.113732i | 0.562021 | − | 0.827123i | \(-0.310024\pi\) |
−0.338809 | + | 0.940855i | \(0.610024\pi\) | |||||||
\(744\) | 17.8651 | − | 12.2030i | 0.654966 | − | 0.447384i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 59.8962 | + | 19.4615i | 2.19296 | + | 0.712535i | ||||
\(747\) | 1.78133 | + | 17.9379i | 0.0651755 | + | 0.656312i | ||||
\(748\) | 56.7525 | − | 55.5565i | 2.07508 | − | 2.03135i | ||||
\(749\) | −17.4034 | −0.635905 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.0310 | − | 13.8268i | 0.694451 | − | 0.504548i | −0.183669 | − | 0.982988i | \(-0.558798\pi\) |
0.878120 | + | 0.478440i | \(0.158798\pi\) | |||||||
\(752\) | 11.9618 | + | 75.5239i | 0.436202 | + | 2.75407i | ||||
\(753\) | −22.2145 | + | 20.9600i | −0.809542 | + | 0.763824i | ||||
\(754\) | −43.4370 | + | 14.1135i | −1.58188 | + | 0.513984i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −13.8583 | + | 32.6589i | −0.504022 | + | 1.18779i | ||||
\(757\) | −1.37987 | − | 2.70814i | −0.0501522 | − | 0.0984291i | 0.864570 | − | 0.502512i | \(-0.167591\pi\) |
−0.914722 | + | 0.404083i | \(0.867591\pi\) | |||||||
\(758\) | −24.3021 | + | 24.3021i | −0.882692 | + | 0.882692i | ||||
\(759\) | 32.8713 | − | 21.9436i | 1.19315 | − | 0.796503i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.08911 | + | 2.30339i | 0.256980 | + | 0.0834979i | 0.434674 | − | 0.900588i | \(-0.356864\pi\) |
−0.177694 | + | 0.984086i | \(0.556864\pi\) | |||||||
\(762\) | −6.48722 | + | 11.8666i | −0.235007 | + | 0.429883i | ||||
\(763\) | −0.625803 | − | 3.95117i | −0.0226556 | − | 0.143042i | ||||
\(764\) | 2.62835 | + | 8.08923i | 0.0950904 | + | 0.292658i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 54.4826 | + | 39.5839i | 1.96854 | + | 1.43023i | ||||
\(767\) | −40.9839 | − | 6.49121i | −1.47984 | − | 0.234384i | ||||
\(768\) | 6.38654 | + | 49.6101i | 0.230454 | + | 1.79015i | ||||
\(769\) | 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 | ||||
\(772\) | 34.4990 | + | 67.7081i | 1.24165 | + | 2.43687i | ||||
\(773\) | 0.199890 | − | 1.26205i | 0.00718953 | − | 0.0453929i | −0.983833 | − | 0.179090i | \(-0.942685\pi\) |
0.991022 | + | 0.133697i | \(0.0426848\pi\) | |||||||
\(774\) | 20.4682 | + | 78.1802i | 0.735714 | + | 2.81013i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.02557 | − | 2.93259i | 0.323999 | − | 0.105274i | ||||
\(777\) | 4.78776 | − | 25.4251i | 0.171760 | − | 0.912121i | ||||
\(778\) | 65.4553 | + | 10.3671i | 2.34669 | + | 0.371679i | ||||
\(779\) | −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 | ||||
\(783\) | 21.1690 | + | 13.2244i | 0.756518 | + | 0.472600i | ||||
\(784\) | 19.8289 | + | 27.2921i | 0.708175 | + | 0.974719i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 23.4083 | + | 0.680186i | 0.834947 | + | 0.0242614i | ||||
\(787\) | 2.60917 | + | 1.32944i | 0.0930069 | + | 0.0473894i | 0.499875 | − | 0.866097i | \(-0.333379\pi\) |
−0.406868 | + | 0.913487i | \(0.633379\pi\) | |||||||
\(788\) | 75.1602 | − | 11.9042i | 2.67747 | − | 0.424070i | ||||
\(789\) | 9.62793 | + | 32.8492i | 0.342764 | + | 1.16946i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.3874i | 0.369334i | ||||||||
\(792\) | 41.4967 | + | 47.6338i | 1.47452 | + | 1.69259i | ||||
\(793\) | −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 | ||||
\(797\) | 25.0412 | − | 49.1462i | 0.887006 | − | 1.74085i | 0.253096 | − | 0.967441i | \(-0.418551\pi\) |
0.633911 | − | 0.773406i | \(-0.281449\pi\) | |||||||
\(798\) | −3.68341 | + | 3.47539i | −0.130391 | + | 0.123028i | ||||
\(799\) | −33.3072 | + | 45.8435i | −1.17832 | + | 1.62183i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.04773 | + | 4.75258i | 0.107686 | + | 0.167924i | ||||
\(802\) | −16.7057 | + | 16.7057i | −0.589900 | + | 0.589900i | ||||
\(803\) | 7.58399 | − | 3.76306i | 0.267633 | − | 0.132796i | ||||
\(804\) | −114.281 | − | 40.8384i | −4.03038 | − | 1.44026i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.9947 | − | 15.1329i | −0.387271 | − | 0.533033i | ||||
\(807\) | 18.3693 | + | 3.45910i | 0.646631 | + | 0.121766i | ||||
\(808\) | −1.19406 | + | 2.34348i | −0.0420069 | + | 0.0824432i | ||||
\(809\) | 6.83297 | + | 21.0297i | 0.240234 | + | 0.739366i | 0.996384 | + | 0.0849665i | \(0.0270783\pi\) |
−0.756149 | + | 0.654399i | \(0.772922\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.37165 | − | 0.996565i | 0.0481653 | − | 0.0349941i | −0.563442 | − | 0.826156i | \(-0.690523\pi\) |
0.611607 | + | 0.791161i | \(0.290523\pi\) | |||||||
\(812\) | −29.2226 | + | 14.8896i | −1.02551 | + | 0.522524i | ||||
\(813\) | 32.2685 | − | 15.2778i | 1.13171 | − | 0.535816i | ||||
\(814\) | −66.6610 | − | 49.5250i | −2.33647 | − | 1.73585i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 40.5848 | − | 52.5781i | 1.42075 | − | 1.84060i | ||||
\(817\) | −1.24864 | + | 7.88363i | −0.0436846 | + | 0.275813i | ||||
\(818\) | 7.79644 | − | 1.23483i | 0.272596 | − | 0.0431750i | ||||
\(819\) | 15.8507 | + | 6.18912i | 0.553869 | + | 0.216265i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.3901 | + | 28.0645i | −0.711618 | + | 0.979458i | 0.288143 | + | 0.957587i | \(0.406962\pi\) |
−0.999761 | + | 0.0218708i | \(0.993038\pi\) | |||||||
\(822\) | 42.2686 | + | 23.1072i | 1.47429 | + | 0.805957i | ||||
\(823\) | 12.6429 | − | 6.44187i | 0.440703 | − | 0.224550i | −0.219537 | − | 0.975604i | \(-0.570455\pi\) |
0.660240 | + | 0.751055i | \(0.270455\pi\) | |||||||
\(824\) | 7.24187 | 0.252283 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −43.0644 | −1.49840 | ||||||||
\(827\) | −40.2655 | + | 20.5163i | −1.40017 | + | 0.713421i | −0.980913 | − | 0.194447i | \(-0.937709\pi\) |
−0.419255 | + | 0.907868i | \(0.637709\pi\) | |||||||
\(828\) | 69.2545 | − | 61.6411i | 2.40676 | − | 2.14218i | ||||
\(829\) | −12.9853 | + | 17.8727i | −0.450997 | + | 0.620745i | −0.972611 | − | 0.232437i | \(-0.925330\pi\) |
0.521614 | + | 0.853182i | \(0.325330\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.6332 | + | 0.483318i | 0.576999 | + | 0.0167661i | ||||
\(832\) | 0.154952 | − | 0.0245420i | 0.00537200 | − | 0.000850841i | ||||
\(833\) | −3.91082 | + | 24.6919i | −0.135502 | + | 0.855525i | ||||
\(834\) | −39.5395 | − | 30.5204i | −1.36914 | − | 1.05683i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.36152 | + | 10.7333i | 0.116261 | + | 0.371217i | ||||
\(837\) | −2.47188 | + | 9.91916i | −0.0854405 | + | 0.342856i | ||||
\(838\) | −20.4973 | + | 10.4439i | −0.708068 | + | 0.360779i | ||||
\(839\) | −26.4386 | + | 19.2088i | −0.912763 | + | 0.663161i | −0.941712 | − | 0.336420i | \(-0.890784\pi\) |
0.0289492 | + | 0.999581i | \(0.490784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.83110 | − | 5.63555i | −0.0631415 | − | 0.194329i | ||||
\(842\) | 7.47297 | − | 14.6665i | 0.257536 | − | 0.505442i | ||||
\(843\) | −1.20172 | + | 6.38165i | −0.0413894 | + | 0.219796i | ||||
\(844\) | 62.4912 | + | 86.0117i | 2.15103 | + | 2.96065i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −62.8498 | − | 51.4948i | −2.16082 | − | 1.77043i | ||||
\(847\) | 12.0718 | − | 11.5683i | 0.414792 | − | 0.397491i | ||||
\(848\) | 40.7824 | − | 40.7824i | 1.40047 | − | 1.40047i | ||||
\(849\) | −21.7262 | + | 28.1465i | −0.745640 | + | 0.965985i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −39.7409 | + | 54.6986i | −1.36230 | + | 1.87505i | ||||
\(852\) | 2.14633 | + | 2.27479i | 0.0735320 | + | 0.0779332i | ||||
\(853\) | 3.28314 | − | 6.44353i | 0.112413 | − | 0.220622i | −0.827945 | − | 0.560809i | \(-0.810490\pi\) |
0.940358 | + | 0.340187i | \(0.110490\pi\) | |||||||
\(854\) | −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 | 0.313887 | − | 0.949460i | \(-0.398369\pi\) |
−0.949460 | + | 0.313887i | \(0.898369\pi\) | |||||||
\(858\) | 40.1239 | − | 37.0583i | 1.36981 | − | 1.26515i | ||||
\(859\) | − | 20.5206i | − | 0.700154i | −0.936721 | − | 0.350077i | \(-0.886155\pi\) | ||
0.936721 | − | 0.350077i | \(-0.113845\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.7996 | − | 5.21697i | 0.606608 | − | 0.177794i | ||||
\(862\) | −36.1470 | + | 5.72512i | −1.23117 | + | 0.194999i | ||||
\(863\) | −22.7997 | − | 11.6170i | −0.776110 | − | 0.395448i | 0.0206166 | − | 0.999787i | \(-0.493437\pi\) |
−0.796727 | + | 0.604340i | \(0.793437\pi\) | |||||||
\(864\) | 22.0810 | + | 19.1902i | 0.751212 | + | 0.652862i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 16.3036 | + | 22.4400i | 0.554020 | + | 0.762543i | ||||
\(867\) | 19.6145 | − | 2.52506i | 0.666143 | − | 0.0857556i | ||||
\(868\) | −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 | ||||
\(872\) | −16.5046 | − | 2.61408i | −0.558918 | − | 0.0885239i | ||||
\(873\) | −2.26427 | + | 3.87036i | −0.0766338 | + | 0.130992i | ||||
\(874\) | 12.5865 | − | 4.08960i | 0.425744 | − | 0.138333i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16.3997 | − | 11.2020i | 0.554094 | − | 0.378482i | ||||
\(877\) | −4.01510 | + | 25.3503i | −0.135580 | + | 0.856020i | 0.822342 | + | 0.568993i | \(0.192667\pi\) |
−0.957922 | + | 0.287027i | \(0.907333\pi\) | |||||||
\(878\) | −16.0680 | − | 31.5353i | −0.542270 | − | 1.06426i | ||||
\(879\) | −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 | \(0.929177\pi\) | |||||||
\(882\) | −35.0199 | − | 7.65400i | −1.17918 | − | 0.257724i | ||||
\(883\) | 11.5576 | + | 1.83055i | 0.388945 | + | 0.0616029i | 0.347845 | − | 0.937552i | \(-0.386914\pi\) |
0.0411006 | + | 0.999155i | \(0.486914\pi\) | |||||||
\(884\) | −72.2914 | − | 52.5228i | −2.43142 | − | 1.76653i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.61035 | − | 11.1115i | −0.121292 | − | 0.373299i | ||||
\(887\) | −4.37479 | − | 27.6213i | −0.146891 | − | 0.927434i | −0.945509 | − | 0.325596i | \(-0.894435\pi\) |
0.798618 | − | 0.601838i | \(-0.205565\pi\) | |||||||
\(888\) | −94.8265 | − | 51.8394i | −3.18217 | − | 1.73962i | ||||
\(889\) | 4.43004 | + | 1.43941i | 0.148579 | + | 0.0482762i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −29.6098 | − | 3.77614i | −0.991966 | − | 0.126505i | ||||
\(892\) | 67.0695 | − | 67.0695i | 2.24565 | − | 2.24565i | ||||
\(893\) | −3.64328 | − | 7.15033i | −0.121918 | − | 0.239277i | ||||
\(894\) | 30.1499 | − | 8.83679i | 1.00836 | − | 0.295546i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 16.4324 | − | 5.33921i | 0.548968 | − | 0.178371i | ||||
\(897\) | −30.5174 | − | 32.3440i | −1.01895 | − | 1.07993i | ||||
\(898\) | −11.7713 | − | 74.3209i | −0.392812 | − | 2.48012i | ||||
\(899\) | −7.64538 | + | 5.55470i | −0.254988 | + | 0.185260i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.7408 | 1.42390 | ||||||||
\(902\) | 9.93927 | − | 58.7016i | 0.330942 | − | 1.95455i | ||||
\(903\) | 25.1574 | − | 11.9110i | 0.837186 | − | 0.396373i | ||||
\(904\) | 41.2662 | + | 13.4082i | 1.37249 | + | 0.445950i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.13981 | − | 1.66868i | −0.0378678 | − | 0.0554381i | ||||
\(907\) | −13.0457 | − | 6.64713i | −0.433176 | − | 0.220714i | 0.223785 | − | 0.974638i | \(-0.428159\pi\) |
−0.656961 | + | 0.753924i | \(0.728159\pi\) | |||||||
\(908\) | −81.5967 | − | 41.5756i | −2.70788 | − | 1.37973i | ||||
\(909\) | −0.314751 | − | 1.20222i | −0.0104396 | − | 0.0398751i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.06122 | − | 2.61925i | −0.267080 | − | 0.0867796i | 0.172415 | − | 0.985024i | \(-0.444843\pi\) |
−0.439496 | + | 0.898245i | \(0.644843\pi\) | |||||||
\(912\) | 4.02517 | + | 8.50165i | 0.133287 | + | 0.281518i | ||||
\(913\) | 3.32693 | − | 19.6489i | 0.110105 | − | 0.650285i | ||||
\(914\) | 41.9963 | 1.38911 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −28.3959 | + | 20.6308i | −0.938226 | + | 0.681661i | ||||
\(917\) | −1.26177 | − | 7.96647i | −0.0416672 | − | 0.263076i | ||||
\(918\) | 4.93157 | + | 70.4047i | 0.162766 | + | 2.32370i | ||||
\(919\) | 20.1507 | − | 6.54737i | 0.664711 | − | 0.215978i | 0.0428216 | − | 0.999083i | \(-0.486365\pi\) |
0.621889 | + | 0.783105i | \(0.286365\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.6320 | − | 46.5106i | −0.449191 | − | 1.53258i | ||||
\(922\) | 33.0003 | + | 64.7667i | 1.08681 | + | 2.13298i | ||||
\(923\) | 1.06070 | − | 1.06070i | 0.0349135 | − | 0.0349135i | ||||
\(924\) | 24.2952 | − | 30.7913i | 0.799254 | − | 1.01296i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −38.9170 | − | 12.6449i | −1.27889 | − | 0.415537i | ||||
\(927\) | −2.55597 | + | 2.27498i | −0.0839491 | + | 0.0747203i | ||||
\(928\) | 4.23069 | + | 26.7115i | 0.138879 | + | 0.876848i | ||||
\(929\) | 6.15445 | + | 18.9414i | 0.201921 | + | 0.621449i | 0.999826 | + | 0.0186653i | \(0.00594169\pi\) |
−0.797905 | + | 0.602783i | \(0.794058\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.86430 | − | 2.08104i | −0.0938736 | − | 0.0682032i | ||||
\(932\) | 58.8452 | + | 9.32016i | 1.92754 | + | 0.305292i | ||||
\(933\) | −5.11885 | + | 0.658972i | −0.167583 | + | 0.0215738i | ||||
\(934\) | − | 73.6952i | − | 2.41138i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 45.0479 | − | 54.9814i | 1.47244 | − | 1.79712i | ||||
\(937\) | −17.1027 | − | 33.5660i | −0.558721 | − | 1.09655i | −0.981704 | − | 0.190415i | \(-0.939017\pi\) |
0.422982 | − | 0.906138i | \(-0.360983\pi\) | |||||||
\(938\) | −9.45012 | + | 59.6657i | −0.308557 | + | 1.94815i | ||||
\(939\) | −14.7187 | − | 21.5480i | −0.480326 | − | 0.703193i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.0894 | − | 8.15205i | 0.817892 | − | 0.265749i | 0.129955 | − | 0.991520i | \(-0.458517\pi\) |
0.687937 | + | 0.725770i | \(0.258517\pi\) | |||||||
\(942\) | 91.0894 | + | 17.1529i | 2.96785 | + | 0.558872i | ||||
\(943\) | −47.8757 | − | 7.58276i | −1.55905 | − | 0.246929i | ||||
\(944\) | −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 | 0.636307 | − | 0.771436i | \(-0.280461\pi\) |
−0.771436 | + | 0.636307i | \(0.780461\pi\) | |||||||
\(948\) | −2.58572 | − | 20.0857i | −0.0839803 | − | 0.652353i | ||||
\(949\) | −5.59906 | − | 7.70644i | −0.181753 | − | 0.250162i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.326176 | + | 11.2252i | −0.0105770 | + | 0.364003i | ||||
\(952\) | −45.8392 | − | 23.3563i | −1.48566 | − | 0.756981i | ||||
\(953\) | −20.0765 | + | 3.17981i | −0.650343 | + | 0.103004i | −0.472885 | − | 0.881124i | \(-0.656787\pi\) |
−0.177458 | + | 0.984128i | \(0.556787\pi\) | |||||||
\(954\) | −3.55857 | + | 61.1817i | −0.115213 | + | 1.98083i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 30.3799i | − | 0.982555i | ||||||
\(957\) | −18.7225 | − | 20.2713i | −0.605212 | − | 0.655277i | ||||
\(958\) | 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 | ||||
\(962\) | −42.4193 | + | 83.2525i | −1.36765 | + | 2.68417i | ||||
\(963\) | −13.7907 | − | 31.4591i | −0.444399 | − | 1.01375i | ||||
\(964\) | −10.9569 | + | 15.0808i | −0.352897 | + | 0.485720i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −36.5330 | − | 28.1996i | −1.17543 | − | 0.907309i | ||||
\(967\) | 8.15831 | − | 8.15831i | 0.262354 | − | 0.262354i | −0.563656 | − | 0.826010i | \(-0.690606\pi\) |
0.826010 | + | 0.563656i | \(0.190606\pi\) | |||||||
\(968\) | −30.3750 | − | 62.8903i | −0.976290 | − | 2.02137i | ||||
\(969\) | −2.34572 | + | 6.56419i | −0.0753554 | + | 0.210872i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.72332 | − | 13.3830i | −0.312036 | − | 0.429481i | 0.623979 | − | 0.781441i | \(-0.285515\pi\) |
−0.936015 | + | 0.351960i | \(0.885515\pi\) | |||||||
\(972\) | −70.0172 | + | 0.828573i | −2.24580 | + | 0.0265765i | ||||
\(973\) | −7.81021 | + | 15.3284i | −0.250384 | + | 0.491406i | ||||
\(974\) | 19.8415 | + | 61.0658i | 0.635762 | + | 1.95667i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.87044 | + | 4.99167i | −0.219917 | + | 0.159779i | ||||
\(977\) | −13.6452 | + | 6.95258i | −0.436549 | + | 0.222433i | −0.658432 | − | 0.752641i | \(-0.728780\pi\) |
0.221883 | + | 0.975073i | \(0.428780\pi\) | |||||||
\(978\) | −6.79102 | − | 14.3434i | −0.217153 | − | 0.458653i | ||||
\(979\) | −1.86548 | − | 5.95643i | −0.0596210 | − | 0.190368i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.64640 | − | 4.26220i | 0.212203 | − | 0.136081i | ||||
\(982\) | −8.36327 | + | 52.8036i | −0.266883 | + | 1.68503i | ||||
\(983\) | −6.72404 | + | 1.06498i | −0.214463 | + | 0.0339677i | −0.262741 | − | 0.964866i | \(-0.584627\pi\) |
0.0482781 | + | 0.998834i | \(0.484627\pi\) | |||||||
\(984\) | 2.25040 | − | 77.4467i | 0.0717402 | − | 2.46891i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −38.3501 | + | 52.7844i | −1.22132 | + | 1.68100i | ||||
\(987\) | −13.4238 | + | 24.5552i | −0.427283 | + | 0.781602i | ||||
\(988\) | 11.2755 | − | 5.74515i | 0.358721 | − | 0.182778i | ||||
\(989\) | −72.7403 | −2.31301 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.87509 | −0.250160 | −0.125080 | − | 0.992147i | \(-0.539919\pi\) | ||||
−0.125080 | + | 0.992147i | \(0.539919\pi\) | |||||||
\(992\) | −9.86893 | + | 5.02847i | −0.313339 | + | 0.159654i | ||||
\(993\) | 16.7377 | − | 30.6172i | 0.531155 | − | 0.971608i | ||||
\(994\) | 0.915068 | − | 1.25948i | 0.0290242 | − | 0.0399484i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.35784 | − | 46.7294i | 0.0430247 | − | 1.48068i | ||||
\(997\) | −10.0360 | + | 1.58955i | −0.317843 | + | 0.0503414i | −0.313318 | − | 0.949648i | \(-0.601440\pi\) |
−0.00452544 | + | 0.999990i | \(0.501440\pi\) | |||||||
\(998\) | −3.56734 | + | 22.5233i | −0.112922 | + | 0.712963i | ||||
\(999\) | 49.7534 | − | 11.4927i | 1.57413 | − | 0.363613i |
(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.218.1 | ✓ | 256 | |
3.2 | odd | 2 | inner | 825.2.ct.c.218.31 | yes | 256 | |
5.2 | odd | 4 | inner | 825.2.ct.c.482.1 | yes | 256 | |
5.3 | odd | 4 | inner | 825.2.ct.c.482.32 | yes | 256 | |
5.4 | even | 2 | inner | 825.2.ct.c.218.32 | yes | 256 | |
11.5 | even | 5 | inner | 825.2.ct.c.368.31 | yes | 256 | |
15.2 | even | 4 | inner | 825.2.ct.c.482.31 | yes | 256 | |
15.8 | even | 4 | inner | 825.2.ct.c.482.2 | yes | 256 | |
15.14 | odd | 2 | inner | 825.2.ct.c.218.2 | yes | 256 | |
33.5 | odd | 10 | inner | 825.2.ct.c.368.1 | yes | 256 | |
55.27 | odd | 20 | inner | 825.2.ct.c.632.31 | yes | 256 | |
55.38 | odd | 20 | inner | 825.2.ct.c.632.2 | yes | 256 | |
55.49 | even | 10 | inner | 825.2.ct.c.368.2 | yes | 256 | |
165.38 | even | 20 | inner | 825.2.ct.c.632.32 | yes | 256 | |
165.104 | odd | 10 | inner | 825.2.ct.c.368.32 | yes | 256 | |
165.137 | even | 20 | inner | 825.2.ct.c.632.1 | yes | 256 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.ct.c.218.1 | ✓ | 256 | 1.1 | even | 1 | trivial | |
825.2.ct.c.218.2 | yes | 256 | 15.14 | odd | 2 | inner | |
825.2.ct.c.218.31 | yes | 256 | 3.2 | odd | 2 | inner | |
825.2.ct.c.218.32 | yes | 256 | 5.4 | even | 2 | inner | |
825.2.ct.c.368.1 | yes | 256 | 33.5 | odd | 10 | inner | |
825.2.ct.c.368.2 | yes | 256 | 55.49 | even | 10 | inner | |
825.2.ct.c.368.31 | yes | 256 | 11.5 | even | 5 | inner | |
825.2.ct.c.368.32 | yes | 256 | 165.104 | odd | 10 | inner | |
825.2.ct.c.482.1 | yes | 256 | 5.2 | odd | 4 | inner | |
825.2.ct.c.482.2 | yes | 256 | 15.8 | even | 4 | inner | |
825.2.ct.c.482.31 | yes | 256 | 15.2 | even | 4 | inner | |
825.2.ct.c.482.32 | yes | 256 | 5.3 | odd | 4 | inner | |
825.2.ct.c.632.1 | yes | 256 | 165.137 | even | 20 | inner | |
825.2.ct.c.632.2 | yes | 256 | 55.38 | odd | 20 | inner | |
825.2.ct.c.632.31 | yes | 256 | 55.27 | odd | 20 | inner | |
825.2.ct.c.632.32 | yes | 256 | 165.38 | even | 20 | inner |