Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,4,Mod(17,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.s (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.1513609911\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.20 | ||
Character | \(\chi\) | \(=\) | 189.17 |
Dual form | 189.4.s.a.89.20 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.26829 | + | 2.46430i | 1.50907 | + | 0.871261i | 0.999944 | + | 0.0105673i | \(0.00336375\pi\) |
0.509124 | + | 0.860693i | \(0.329970\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 8.14552 | + | 14.1085i | 1.01819 | + | 1.76356i | ||||
\(5\) | 9.24869 | 0.827228 | 0.413614 | − | 0.910452i | \(-0.364266\pi\) | ||||
0.413614 | + | 0.910452i | \(0.364266\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17.8986 | − | 4.75801i | 0.966436 | − | 0.256908i | ||||
\(8\) | 40.8632i | 1.80592i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 39.4761 | + | 22.7915i | 1.24834 | + | 0.720731i | ||||
\(11\) | 15.2595i | 0.418265i | 0.977887 | + | 0.209132i | \(0.0670639\pi\) | ||||
−0.977887 | + | 0.209132i | \(0.932936\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −61.0927 | − | 35.2719i | −1.30339 | − | 0.752512i | −0.322405 | − | 0.946602i | \(-0.604491\pi\) |
−0.980984 | + | 0.194090i | \(0.937825\pi\) | |||||||
\(14\) | 88.1217 | + | 23.7990i | 1.68225 | + | 0.454326i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −35.5349 | + | 61.5483i | −0.555233 | + | 0.961692i | ||||
\(17\) | −17.8844 | + | 30.9767i | −0.255154 | + | 0.441939i | −0.964937 | − | 0.262481i | \(-0.915459\pi\) |
0.709784 | + | 0.704420i | \(0.248793\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 91.6472 | − | 52.9125i | 1.10660 | − | 0.638893i | 0.168650 | − | 0.985676i | \(-0.446059\pi\) |
0.937945 | + | 0.346783i | \(0.112726\pi\) | |||||||
\(20\) | 75.3354 | + | 130.485i | 0.842275 | + | 1.45886i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −37.6039 | + | 65.1319i | −0.364418 | + | 0.631190i | ||||
\(23\) | 92.4427i | 0.838071i | 0.907970 | + | 0.419035i | \(0.137632\pi\) | ||||
−0.907970 | + | 0.419035i | \(0.862368\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −39.4618 | −0.315695 | ||||||||
\(26\) | −173.841 | − | 301.101i | −1.31127 | − | 2.27118i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 212.922 | + | 213.766i | 1.43709 | + | 1.44278i | ||||
\(29\) | −222.341 | + | 128.369i | −1.42372 | + | 0.821983i | −0.996614 | − | 0.0822202i | \(-0.973799\pi\) |
−0.427102 | + | 0.904203i | \(0.640466\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −123.551 | + | 71.3321i | −0.715819 | + | 0.413278i | −0.813212 | − | 0.581968i | \(-0.802283\pi\) |
0.0973929 | + | 0.995246i | \(0.468950\pi\) | |||||||
\(32\) | −20.2380 | + | 11.6844i | −0.111800 | + | 0.0645478i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −152.672 | + | 88.1451i | −0.770088 | + | 0.444611i | ||||
\(35\) | 165.539 | − | 44.0053i | 0.799462 | − | 0.212522i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −100.112 | − | 173.399i | −0.444818 | − | 0.770447i | 0.553222 | − | 0.833034i | \(-0.313398\pi\) |
−0.998040 | + | 0.0625870i | \(0.980065\pi\) | |||||||
\(38\) | 521.569 | 2.22657 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 377.931i | 1.49390i | ||||||||
\(41\) | 162.085 | − | 280.739i | 0.617401 | − | 1.06937i | −0.372558 | − | 0.928009i | \(-0.621519\pi\) |
0.989958 | − | 0.141360i | \(-0.0451476\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −92.5782 | − | 160.350i | −0.328327 | − | 0.568679i | 0.653853 | − | 0.756621i | \(-0.273151\pi\) |
−0.982180 | + | 0.187943i | \(0.939818\pi\) | |||||||
\(44\) | −215.288 | + | 124.297i | −0.737634 | + | 0.425873i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −227.806 | + | 394.572i | −0.730178 | + | 1.26471i | ||||
\(47\) | 235.747 | − | 408.326i | 0.731643 | − | 1.26724i | −0.224538 | − | 0.974465i | \(-0.572087\pi\) |
0.956181 | − | 0.292778i | \(-0.0945795\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 297.723 | − | 170.324i | 0.867996 | − | 0.496571i | ||||
\(50\) | −168.434 | − | 97.2457i | −0.476404 | − | 0.275052i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 1149.23i | − | 3.06480i | ||||||
\(53\) | 247.615 | + | 142.960i | 0.641745 | + | 0.370512i | 0.785286 | − | 0.619133i | \(-0.212516\pi\) |
−0.143541 | + | 0.989644i | \(0.545849\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 141.130i | 0.346000i | ||||||||
\(56\) | 194.427 | + | 731.396i | 0.463955 | + | 1.74530i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1265.36 | −2.86465 | ||||||||
\(59\) | −85.0742 | − | 147.353i | −0.187724 | − | 0.325147i | 0.756767 | − | 0.653685i | \(-0.226778\pi\) |
−0.944491 | + | 0.328537i | \(0.893444\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 222.571 | + | 128.501i | 0.467169 | + | 0.269720i | 0.715054 | − | 0.699069i | \(-0.246402\pi\) |
−0.247885 | + | 0.968789i | \(0.579736\pi\) | |||||||
\(62\) | −703.134 | −1.44029 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 453.383 | 0.885515 | ||||||||
\(65\) | −565.027 | − | 326.218i | −1.07820 | − | 0.622499i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −501.367 | − | 868.394i | −0.914205 | − | 1.58345i | −0.808061 | − | 0.589099i | \(-0.799483\pi\) |
−0.106145 | − | 0.994351i | \(-0.533851\pi\) | |||||||
\(68\) | −582.712 | −1.03918 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 815.010 | + | 220.110i | 1.39160 | + | 0.375831i | ||||
\(71\) | 445.602i | 0.744835i | 0.928065 | + | 0.372417i | \(0.121471\pi\) | ||||
−0.928065 | + | 0.372417i | \(0.878529\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −81.3323 | − | 46.9572i | −0.130400 | − | 0.0752867i | 0.433381 | − | 0.901211i | \(-0.357321\pi\) |
−0.563781 | + | 0.825924i | \(0.690654\pi\) | |||||||
\(74\) | − | 986.820i | − | 1.55021i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1493.03 | + | 862.001i | 2.25345 | + | 1.30103i | ||||
\(77\) | 72.6048 | + | 273.124i | 0.107456 | + | 0.404226i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −231.624 | + | 401.185i | −0.329871 | + | 0.571353i | −0.982486 | − | 0.186337i | \(-0.940338\pi\) |
0.652615 | + | 0.757689i | \(0.273672\pi\) | |||||||
\(80\) | −328.651 | + | 569.241i | −0.459304 | + | 0.795538i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1383.65 | − | 798.851i | 1.86340 | − | 1.07583i | ||||
\(83\) | 348.156 | + | 603.023i | 0.460422 | + | 0.797475i | 0.998982 | − | 0.0451126i | \(-0.0143647\pi\) |
−0.538560 | + | 0.842587i | \(0.681031\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −165.407 | + | 286.494i | −0.211070 | + | 0.365584i | ||||
\(86\) | − | 912.561i | − | 1.14423i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −623.552 | −0.755351 | ||||||||
\(89\) | 338.803 | + | 586.824i | 0.403518 | + | 0.698913i | 0.994148 | − | 0.108029i | \(-0.0344541\pi\) |
−0.590630 | + | 0.806942i | \(0.701121\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1261.30 | − | 340.639i | −1.45297 | − | 0.392403i | ||||
\(92\) | −1304.22 | + | 752.994i | −1.47799 | + | 0.853316i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2012.47 | − | 1161.90i | 2.20820 | − | 1.27490i | ||||
\(95\) | 847.616 | − | 489.371i | 0.915406 | − | 0.528510i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 402.332 | − | 232.287i | 0.421141 | − | 0.243146i | −0.274424 | − | 0.961609i | \(-0.588487\pi\) |
0.695565 | + | 0.718463i | \(0.255154\pi\) | |||||||
\(98\) | 1690.49 | + | 6.68653i | 1.74251 | + | 0.00689226i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −321.437 | − | 556.745i | −0.321437 | − | 0.556745i | ||||
\(101\) | 508.150 | 0.500622 | 0.250311 | − | 0.968165i | \(-0.419467\pi\) | ||||
0.250311 | + | 0.968165i | \(0.419467\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 657.703i | 0.629179i | 0.949228 | + | 0.314589i | \(0.101867\pi\) | ||||
−0.949228 | + | 0.314589i | \(0.898133\pi\) | |||||||
\(104\) | 1441.32 | − | 2496.44i | 1.35897 | − | 2.35381i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 704.594 | + | 1220.39i | 0.645625 | + | 1.11825i | ||||
\(107\) | −810.389 | + | 467.878i | −0.732180 | + | 0.422724i | −0.819219 | − | 0.573481i | \(-0.805593\pi\) |
0.0870393 | + | 0.996205i | \(0.472259\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −272.351 | + | 471.726i | −0.239326 | + | 0.414524i | −0.960521 | − | 0.278207i | \(-0.910260\pi\) |
0.721195 | + | 0.692732i | \(0.243593\pi\) | |||||||
\(110\) | −347.787 | + | 602.385i | −0.301456 | + | 0.522138i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −343.180 | + | 1270.71i | −0.289531 | + | 1.07206i | ||||
\(113\) | −63.9011 | − | 36.8933i | −0.0531974 | − | 0.0307135i | 0.473165 | − | 0.880974i | \(-0.343111\pi\) |
−0.526363 | + | 0.850260i | \(0.676445\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 854.973i | 0.693275i | ||||||||
\(116\) | −3622.18 | − | 2091.26i | −2.89923 | − | 1.67387i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 838.592i | − | 0.654226i | ||||||
\(119\) | −172.719 | + | 639.536i | −0.133052 | + | 0.492657i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1098.15 | 0.825055 | ||||||||
\(122\) | 633.331 | + | 1096.96i | 0.469993 | + | 0.814051i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2012.77 | − | 1162.07i | −1.45768 | − | 0.841592i | ||||
\(125\) | −1521.06 | −1.08838 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2142.49 | −1.49697 | −0.748484 | − | 0.663153i | \(-0.769218\pi\) | ||||
−0.748484 | + | 0.663153i | \(0.769218\pi\) | |||||||
\(128\) | 2097.08 | + | 1210.75i | 1.44810 | + | 0.836062i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1607.80 | − | 2784.79i | −1.08472 | − | 1.87879i | ||||
\(131\) | −2060.85 | −1.37448 | −0.687242 | − | 0.726429i | \(-0.741179\pi\) | ||||
−0.687242 | + | 0.726429i | \(0.741179\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1388.60 | − | 1383.12i | 0.905316 | − | 0.901742i | ||||
\(134\) | − | 4942.07i | − | 3.18604i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1265.81 | − | 730.815i | −0.798105 | − | 0.460786i | ||||
\(137\) | 47.4441i | 0.0295870i | 0.999891 | + | 0.0147935i | \(0.00470909\pi\) | ||||
−0.999891 | + | 0.0147935i | \(0.995291\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −713.061 | − | 411.686i | −0.435115 | − | 0.251214i | 0.266408 | − | 0.963860i | \(-0.414163\pi\) |
−0.701523 | + | 0.712646i | \(0.747496\pi\) | |||||||
\(140\) | 1969.25 | + | 1977.05i | 1.18880 | + | 1.19351i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1098.10 | + | 1901.96i | −0.648945 | + | 1.12401i | ||||
\(143\) | 538.231 | − | 932.243i | 0.314749 | − | 0.545162i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2056.37 | + | 1187.24i | −1.17774 | + | 0.679967i | ||||
\(146\) | −231.433 | − | 400.854i | −0.131189 | − | 0.227225i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1630.92 | − | 2824.84i | 0.905819 | − | 1.56892i | ||||
\(149\) | 1150.98i | 0.632830i | 0.948621 | + | 0.316415i | \(0.102479\pi\) | ||||
−0.948621 | + | 0.316415i | \(0.897521\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −593.799 | −0.320018 | −0.160009 | − | 0.987116i | \(-0.551152\pi\) | ||||
−0.160009 | + | 0.987116i | \(0.551152\pi\) | |||||||
\(152\) | 2162.18 | + | 3745.00i | 1.15379 | + | 1.99842i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −363.161 | + | 1344.69i | −0.190028 | + | 0.703626i | ||||
\(155\) | −1142.68 | + | 659.728i | −0.592145 | + | 0.341875i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −29.3249 | + | 16.9307i | −0.0149069 | + | 0.00860649i | −0.507435 | − | 0.861690i | \(-0.669406\pi\) |
0.492528 | + | 0.870297i | \(0.336073\pi\) | |||||||
\(158\) | −1977.28 | + | 1141.58i | −0.995594 | + | 0.574807i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −187.175 | + | 108.065i | −0.0924842 | + | 0.0533958i | ||||
\(161\) | 439.843 | + | 1654.60i | 0.215307 | + | 0.809942i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2034.98 | + | 3524.68i | 0.977863 | + | 1.69371i | 0.670142 | + | 0.742232i | \(0.266233\pi\) |
0.307721 | + | 0.951477i | \(0.400434\pi\) | |||||||
\(164\) | 5281.07 | 2.51453 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3431.84i | 1.60459i | ||||||||
\(167\) | 729.362 | − | 1263.29i | 0.337962 | − | 0.585368i | −0.646087 | − | 0.763264i | \(-0.723596\pi\) |
0.984049 | + | 0.177896i | \(0.0569290\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1389.71 | + | 2407.05i | 0.632548 | + | 1.09561i | ||||
\(170\) | −1412.01 | + | 815.226i | −0.637038 | + | 0.367794i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1508.20 | − | 2612.27i | 0.668598 | − | 1.15805i | ||||
\(173\) | 245.553 | − | 425.311i | 0.107914 | − | 0.186912i | −0.807011 | − | 0.590536i | \(-0.798916\pi\) |
0.914925 | + | 0.403624i | \(0.132250\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −706.313 | + | 187.760i | −0.305098 | + | 0.0811045i | ||||
\(176\) | −939.196 | − | 542.245i | −0.402242 | − | 0.232234i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3339.65i | 1.40628i | ||||||||
\(179\) | 710.152 | + | 410.006i | 0.296532 | + | 0.171203i | 0.640884 | − | 0.767638i | \(-0.278568\pi\) |
−0.344352 | + | 0.938841i | \(0.611901\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 618.639i | 0.254050i | 0.991900 | + | 0.127025i | \(0.0405429\pi\) | ||||
−0.991900 | + | 0.127025i | \(0.959457\pi\) | |||||||
\(182\) | −4544.15 | − | 4562.16i | −1.85074 | − | 1.85808i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3777.50 | −1.51349 | ||||||||
\(185\) | −925.901 | − | 1603.71i | −0.367966 | − | 0.637335i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −472.689 | − | 272.907i | −0.184847 | − | 0.106722i | ||||
\(188\) | 7681.13 | 2.97981 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4823.83 | 1.84188 | ||||||||
\(191\) | 1335.44 | + | 771.019i | 0.505913 | + | 0.292089i | 0.731152 | − | 0.682215i | \(-0.238983\pi\) |
−0.225239 | + | 0.974303i | \(0.572316\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1405.23 | + | 2433.93i | 0.524097 | + | 0.907763i | 0.999606 | + | 0.0280523i | \(0.00893050\pi\) |
−0.475509 | + | 0.879711i | \(0.657736\pi\) | |||||||
\(194\) | 2289.69 | 0.847373 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4828.11 | + | 2813.03i | 1.75952 | + | 1.02516i | ||||
\(197\) | 1603.61i | 0.579963i | 0.957032 | + | 0.289982i | \(0.0936492\pi\) | ||||
−0.957032 | + | 0.289982i | \(0.906351\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −597.100 | − | 344.736i | −0.212700 | − | 0.122802i | 0.389866 | − | 0.920872i | \(-0.372521\pi\) |
−0.602566 | + | 0.798069i | \(0.705855\pi\) | |||||||
\(200\) | − | 1612.54i | − | 0.570118i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2168.93 | + | 1252.23i | 0.755473 | + | 0.436172i | ||||
\(203\) | −3368.83 | + | 3355.53i | −1.16476 | + | 1.16016i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1499.07 | − | 2596.47i | 0.510731 | − | 0.884612i | ||||
\(206\) | −1620.78 | + | 2807.27i | −0.548179 | + | 0.949474i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4341.85 | − | 2506.77i | 1.44737 | − | 0.835639i | ||||
\(209\) | 807.419 | + | 1398.49i | 0.267226 | + | 0.462850i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2341.89 | − | 4056.27i | 0.764087 | − | 1.32344i | −0.176641 | − | 0.984275i | \(-0.556523\pi\) |
0.940728 | − | 0.339162i | \(-0.110143\pi\) | |||||||
\(212\) | 4657.95i | 1.50901i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4611.96 | −1.47321 | ||||||||
\(215\) | −856.227 | − | 1483.03i | −0.271601 | − | 0.470427i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1871.99 | + | 1864.60i | −0.585618 | + | 0.583307i | ||||
\(218\) | −2324.95 | + | 1342.31i | −0.722318 | + | 0.417030i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1991.13 | + | 1149.58i | −0.610191 | + | 0.352294i | ||||
\(221\) | 2185.21 | − | 1261.63i | 0.665129 | − | 0.384012i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 680.507 | − | 392.891i | 0.204350 | − | 0.117982i | −0.394333 | − | 0.918968i | \(-0.629024\pi\) |
0.598683 | + | 0.800986i | \(0.295691\pi\) | |||||||
\(224\) | −306.638 | + | 305.428i | −0.0914648 | + | 0.0911037i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −181.832 | − | 314.942i | −0.0535190 | − | 0.0926976i | ||||
\(227\) | −1808.61 | −0.528819 | −0.264409 | − | 0.964411i | \(-0.585177\pi\) | ||||
−0.264409 | + | 0.964411i | \(0.585177\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2867.45i | − | 0.827453i | −0.910401 | − | 0.413726i | \(-0.864227\pi\) | ||
0.910401 | − | 0.413726i | \(-0.135773\pi\) | |||||||
\(230\) | −2106.91 | + | 3649.27i | −0.604024 | + | 1.04620i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5245.57 | − | 9085.59i | −1.48443 | − | 2.57111i | ||||
\(233\) | −2302.74 | + | 1329.49i | −0.647456 | + | 0.373809i | −0.787481 | − | 0.616339i | \(-0.788615\pi\) |
0.140025 | + | 0.990148i | \(0.455282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2180.35 | − | 3776.48i | 0.605235 | − | 1.04830i | ||||
\(236\) | 1385.95 | − | 2400.53i | 0.382277 | − | 0.662124i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2313.22 | + | 2304.09i | −0.630017 | + | 0.627530i | ||||
\(239\) | 1674.76 | + | 966.920i | 0.453267 | + | 0.261694i | 0.709209 | − | 0.704998i | \(-0.249052\pi\) |
−0.255942 | + | 0.966692i | \(0.582386\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4139.22i | 1.10635i | 0.833065 | + | 0.553175i | \(0.186584\pi\) | ||||
−0.833065 | + | 0.553175i | \(0.813416\pi\) | |||||||
\(242\) | 4687.21 | + | 2706.16i | 1.24506 | + | 0.718838i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4186.84i | 1.09851i | ||||||||
\(245\) | 2753.54 | − | 1575.27i | 0.718030 | − | 0.410777i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7465.29 | −1.92310 | ||||||||
\(248\) | −2914.86 | − | 5048.68i | −0.746346 | − | 1.29271i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6492.30 | − | 3748.33i | −1.64244 | − | 0.948262i | ||||
\(251\) | −370.848 | −0.0932577 | −0.0466289 | − | 0.998912i | \(-0.514848\pi\) | ||||
−0.0466289 | + | 0.998912i | \(0.514848\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1410.63 | −0.350535 | ||||||||
\(254\) | −9144.75 | − | 5279.72i | −2.25903 | − | 1.30425i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4153.75 | + | 7194.50i | 1.01410 | + | 1.75647i | ||||
\(257\) | −6849.66 | −1.66253 | −0.831265 | − | 0.555877i | \(-0.812383\pi\) | ||||
−0.831265 | + | 0.555877i | \(0.812383\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2616.89 | − | 2627.27i | −0.627822 | − | 0.630310i | ||||
\(260\) | − | 10628.9i | − | 2.53529i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −8796.30 | − | 5078.55i | −2.07419 | − | 1.19753i | ||||
\(263\) | 5271.14i | 1.23587i | 0.786231 | + | 0.617933i | \(0.212030\pi\) | ||||
−0.786231 | + | 0.617933i | \(0.787970\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2290.11 | + | 1322.20i | 0.530869 | + | 0.306498i | ||||
\(266\) | 9335.37 | − | 2481.63i | 2.15184 | − | 0.572024i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8167.80 | − | 14147.0i | 1.86167 | − | 3.22451i | ||||
\(269\) | −553.460 | + | 958.621i | −0.125446 | + | 0.217279i | −0.921907 | − | 0.387410i | \(-0.873370\pi\) |
0.796461 | + | 0.604690i | \(0.206703\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4357.92 | − | 2516.05i | 0.976844 | − | 0.563981i | 0.0755283 | − | 0.997144i | \(-0.475936\pi\) |
0.901316 | + | 0.433162i | \(0.142602\pi\) | |||||||
\(272\) | −1271.04 | − | 2201.51i | −0.283340 | − | 0.490758i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −116.916 | + | 202.505i | −0.0257780 | + | 0.0446488i | ||||
\(275\) | − | 602.167i | − | 0.132044i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8751.34 | 1.89826 | 0.949128 | − | 0.314890i | \(-0.101968\pi\) | ||||
0.949128 | + | 0.314890i | \(0.101968\pi\) | |||||||
\(278\) | −2029.03 | − | 3514.39i | −0.437746 | − | 0.758197i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1798.20 | + | 6764.45i | 0.383796 | + | 1.44376i | ||||
\(281\) | 5849.25 | − | 3377.07i | 1.24177 | − | 0.716936i | 0.272315 | − | 0.962208i | \(-0.412211\pi\) |
0.969454 | + | 0.245273i | \(0.0788775\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 654.152 | − | 377.675i | 0.137404 | − | 0.0793302i | −0.429722 | − | 0.902961i | \(-0.641389\pi\) |
0.567126 | + | 0.823631i | \(0.308055\pi\) | |||||||
\(284\) | −6286.76 | + | 3629.67i | −1.31356 | + | 0.758384i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4594.65 | − | 2652.72i | 0.949956 | − | 0.548457i | ||||
\(287\) | 1565.34 | − | 5796.06i | 0.321948 | − | 1.19209i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1816.79 | + | 3146.78i | 0.369793 | + | 0.640501i | ||||
\(290\) | −11702.9 | −2.36971 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 1529.96i | − | 0.306625i | ||||||
\(293\) | 3949.45 | − | 6840.64i | 0.787472 | − | 1.36394i | −0.140040 | − | 0.990146i | \(-0.544723\pi\) |
0.927511 | − | 0.373795i | \(-0.121944\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −786.824 | − | 1362.82i | −0.155290 | − | 0.268971i | ||||
\(296\) | 7085.62 | − | 4090.89i | 1.39136 | − | 0.803304i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2836.35 | + | 4912.70i | −0.551360 | + | 0.954983i | ||||
\(299\) | 3260.63 | − | 5647.57i | 0.630658 | − | 1.09233i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2419.97 | − | 2429.56i | −0.463405 | − | 0.465241i | ||||
\(302\) | −2534.50 | − | 1463.30i | −0.482928 | − | 0.278819i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7520.97i | 1.41894i | ||||||||
\(305\) | 2058.49 | + | 1188.47i | 0.386455 | + | 0.223120i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1715.02i | − | 0.318832i | −0.987212 | − | 0.159416i | \(-0.949039\pi\) | ||
0.987212 | − | 0.159416i | \(-0.0509610\pi\) | |||||||
\(308\) | −3261.96 | + | 3249.08i | −0.603466 | + | 0.601083i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6503.07 | −1.19145 | ||||||||
\(311\) | 1576.29 | + | 2730.21i | 0.287405 | + | 0.497800i | 0.973190 | − | 0.230004i | \(-0.0738740\pi\) |
−0.685784 | + | 0.727805i | \(0.740541\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4698.26 | − | 2712.54i | −0.848440 | − | 0.489847i | 0.0116844 | − | 0.999932i | \(-0.496281\pi\) |
−0.860124 | + | 0.510085i | \(0.829614\pi\) | |||||||
\(314\) | −166.889 | −0.0299940 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7546.81 | −1.34348 | ||||||||
\(317\) | −1209.31 | − | 698.194i | −0.214263 | − | 0.123705i | 0.389028 | − | 0.921226i | \(-0.372811\pi\) |
−0.603291 | + | 0.797521i | \(0.706144\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1958.85 | − | 3392.82i | −0.343807 | − | 0.595490i | ||||
\(320\) | 4193.20 | 0.732522 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2200.05 | + | 8146.21i | −0.380757 | + | 1.40985i | ||||
\(323\) | 3785.24i | 0.652063i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2410.83 | + | 1391.89i | 0.411473 | + | 0.237564i | ||||
\(326\) | 20059.2i | 3.40790i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11471.9 | + | 6623.31i | 1.93119 | + | 1.11497i | ||||
\(329\) | 2276.73 | − | 8430.16i | 0.381521 | − | 1.41267i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −844.559 | + | 1462.82i | −0.140245 | + | 0.242912i | −0.927589 | − | 0.373603i | \(-0.878122\pi\) |
0.787344 | + | 0.616514i | \(0.211456\pi\) | |||||||
\(332\) | −5671.82 | + | 9823.88i | −0.937595 | + | 1.62396i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6226.25 | − | 3594.73i | 1.02002 | − | 0.588907i | ||||
\(335\) | −4636.99 | − | 8031.50i | −0.756256 | − | 1.30987i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 823.056 | − | 1425.57i | 0.133041 | − | 0.230433i | −0.791807 | − | 0.610772i | \(-0.790859\pi\) |
0.924847 | + | 0.380339i | \(0.124193\pi\) | |||||||
\(338\) | 13698.6i | 2.20446i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5389.32 | −0.859638 | ||||||||
\(341\) | −1088.49 | − | 1885.32i | −0.172860 | − | 0.299402i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4518.43 | − | 4465.13i | 0.711290 | − | 0.702899i | ||||
\(344\) | 6552.43 | − | 3783.04i | 1.02699 | − | 0.592930i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2096.18 | − | 1210.23i | 0.325698 | − | 0.188042i | ||||
\(347\) | 829.925 | − | 479.157i | 0.128394 | − | 0.0741283i | −0.434427 | − | 0.900707i | \(-0.643049\pi\) |
0.562821 | + | 0.826579i | \(0.309716\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4992.01 | + | 2882.14i | −0.765662 | + | 0.442055i | −0.831325 | − | 0.555787i | \(-0.812417\pi\) |
0.0656629 | + | 0.997842i | \(0.479084\pi\) | |||||||
\(350\) | −3477.44 | − | 939.153i | −0.531078 | − | 0.143428i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −178.298 | − | 308.822i | −0.0269981 | − | 0.0467621i | ||||
\(353\) | 2092.13 | 0.315447 | 0.157724 | − | 0.987483i | \(-0.449584\pi\) | ||||
0.157724 | + | 0.987483i | \(0.449584\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4121.24i | 0.616148i | ||||||||
\(356\) | −5519.46 | + | 9559.99i | −0.821716 | + | 1.42325i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2020.76 | + | 3500.05i | 0.298325 | + | 0.516713i | ||||
\(359\) | −7692.73 | + | 4441.40i | −1.13094 | + | 0.652948i | −0.944171 | − | 0.329456i | \(-0.893135\pi\) |
−0.186768 | + | 0.982404i | \(0.559801\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2169.97 | − | 3758.50i | 0.316368 | − | 0.547966i | ||||
\(362\) | −1524.51 | + | 2640.53i | −0.221344 | + | 0.383379i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5468.05 | − | 20569.7i | −0.787373 | − | 2.96193i | ||||
\(365\) | −752.217 | − | 434.293i | −0.107871 | − | 0.0622792i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7198.29i | 1.02384i | 0.859034 | + | 0.511918i | \(0.171065\pi\) | ||||
−0.859034 | + | 0.511918i | \(0.828935\pi\) | |||||||
\(368\) | −5689.69 | − | 3284.94i | −0.805966 | − | 0.465325i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 9126.79i | − | 1.28238i | ||||||
\(371\) | 5112.17 | + | 1380.64i | 0.715393 | + | 0.193206i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5497.21 | 0.763096 | 0.381548 | − | 0.924349i | \(-0.375391\pi\) | ||||
0.381548 | + | 0.924349i | \(0.375391\pi\) | |||||||
\(374\) | −1345.05 | − | 2329.69i | −0.185965 | − | 0.322101i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 16685.5 | + | 9633.38i | 2.28853 | + | 1.32129i | ||||
\(377\) | 18111.2 | 2.47421 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2873.36 | −0.389432 | −0.194716 | − | 0.980860i | \(-0.562379\pi\) | ||||
−0.194716 | + | 0.980860i | \(0.562379\pi\) | |||||||
\(380\) | 13808.6 | + | 7972.37i | 1.86412 | + | 1.07625i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3800.04 | + | 6581.86i | 0.508971 | + | 0.881564i | ||||
\(383\) | −1477.45 | −0.197112 | −0.0985561 | − | 0.995131i | \(-0.531422\pi\) | ||||
−0.0985561 | + | 0.995131i | \(0.531422\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 671.499 | + | 2526.04i | 0.0888903 | + | 0.334387i | ||||
\(386\) | 13851.6i | 1.82650i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6554.41 | + | 3784.19i | 0.857603 | + | 0.495137i | ||||
\(389\) | − | 10500.0i | − | 1.36857i | −0.729215 | − | 0.684284i | \(-0.760115\pi\) | ||
0.729215 | − | 0.684284i | \(-0.239885\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2863.57 | − | 1653.28i | −0.370376 | − | 0.213837i | ||||
\(392\) | 6959.98 | + | 12165.9i | 0.896765 | + | 1.56753i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3951.78 | + | 6844.69i | −0.505299 | + | 0.875204i | ||||
\(395\) | −2142.22 | + | 3710.44i | −0.272878 | + | 0.472639i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3627.85 | + | 2094.54i | −0.458631 | + | 0.264791i | −0.711468 | − | 0.702718i | \(-0.751970\pi\) |
0.252838 | + | 0.967509i | \(0.418636\pi\) | |||||||
\(398\) | −1699.06 | − | 2942.86i | −0.213986 | − | 0.370634i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1402.27 | − | 2428.81i | 0.175284 | − | 0.303601i | ||||
\(401\) | − | 6712.82i | − | 0.835966i | −0.908455 | − | 0.417983i | \(-0.862737\pi\) | ||
0.908455 | − | 0.417983i | \(-0.137263\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10064.1 | 1.24399 | ||||||||
\(404\) | 4139.15 | + | 7169.22i | 0.509729 | + | 0.882876i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −22648.2 | + | 6020.58i | −2.76850 | + | 0.735951i | ||||
\(407\) | 2645.97 | − | 1527.65i | 0.322251 | − | 0.186052i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1922.39 | − | 1109.89i | 0.232411 | − | 0.134183i | −0.379273 | − | 0.925285i | \(-0.623826\pi\) |
0.611684 | + | 0.791102i | \(0.290492\pi\) | |||||||
\(410\) | 12797.0 | − | 7388.32i | 1.54145 | − | 0.889959i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9279.18 | + | 5357.34i | −1.10959 | + | 0.640624i | ||||
\(413\) | −2223.82 | − | 2232.63i | −0.264956 | − | 0.266006i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3219.98 | + | 5577.17i | 0.380874 | + | 0.659693i | ||||
\(416\) | 1648.52 | 0.194292 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7958.88i | 0.931295i | ||||||||
\(419\) | −3763.65 | + | 6518.82i | −0.438821 | + | 0.760061i | −0.997599 | − | 0.0692569i | \(-0.977937\pi\) |
0.558778 | + | 0.829318i | \(0.311271\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 297.422 | + | 515.151i | 0.0344311 | + | 0.0596363i | 0.882727 | − | 0.469885i | \(-0.155705\pi\) |
−0.848296 | + | 0.529522i | \(0.822371\pi\) | |||||||
\(422\) | 19991.7 | − | 11542.2i | 2.30612 | − | 1.33144i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5841.82 | + | 10118.3i | −0.669113 | + | 1.15894i | ||||
\(425\) | 705.752 | − | 1222.40i | 0.0805506 | − | 0.139518i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4595.13 | + | 1241.01i | 0.520782 | + | 0.140648i | ||||
\(428\) | −13202.1 | − | 7622.23i | −1.49100 | − | 0.860828i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 8439.99i | − | 0.946541i | ||||||
\(431\) | −9080.39 | − | 5242.57i | −1.01482 | − | 0.585906i | −0.102220 | − | 0.994762i | \(-0.532595\pi\) |
−0.912599 | + | 0.408856i | \(0.865928\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 7417.04i | − | 0.823188i | −0.911367 | − | 0.411594i | \(-0.864972\pi\) | ||
0.911367 | − | 0.411594i | \(-0.135028\pi\) | |||||||
\(434\) | −12585.1 | + | 3345.52i | −1.39195 | + | 0.370023i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8873.77 | −0.974717 | ||||||||
\(437\) | 4891.38 | + | 8472.11i | 0.535438 | + | 0.927405i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14857.3 | − | 8577.85i | −1.61526 | − | 0.932570i | −0.988124 | − | 0.153660i | \(-0.950894\pi\) |
−0.627136 | − | 0.778910i | \(-0.715773\pi\) | |||||||
\(440\) | −5767.04 | −0.624847 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12436.2 | 1.33830 | ||||||||
\(443\) | 1474.37 | + | 851.230i | 0.158126 | + | 0.0912938i | 0.576975 | − | 0.816762i | \(-0.304233\pi\) |
−0.418849 | + | 0.908056i | \(0.637566\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3133.48 | + | 5427.35i | 0.333801 | + | 0.578160i | ||||
\(446\) | 3872.80 | 0.411172 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8114.95 | − | 2157.20i | 0.855793 | − | 0.227496i | ||||
\(449\) | 10147.0i | 1.06651i | 0.845953 | + | 0.533257i | \(0.179032\pi\) | ||||
−0.845953 | + | 0.533257i | \(0.820968\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4283.94 | + | 2473.34i | 0.447279 | + | 0.258237i | ||||
\(452\) | − | 1202.06i | − | 0.125089i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7719.68 | − | 4456.96i | −0.798023 | − | 0.460739i | ||||
\(455\) | −11665.4 | − | 3150.46i | −1.20194 | − | 0.324607i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3479.42 | + | 6026.53i | −0.356150 | + | 0.616869i | −0.987314 | − | 0.158780i | \(-0.949244\pi\) |
0.631164 | + | 0.775649i | \(0.282577\pi\) | |||||||
\(458\) | 7066.26 | − | 12239.1i | 0.720927 | − | 1.24868i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12062.4 | + | 6964.20i | −1.22263 | + | 0.705886i | ||||
\(461\) | 7791.99 | + | 13496.1i | 0.787222 | + | 1.36351i | 0.927663 | + | 0.373419i | \(0.121815\pi\) |
−0.140441 | + | 0.990089i | \(0.544852\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6042.09 | − | 10465.2i | 0.606479 | − | 1.05045i | −0.385337 | − | 0.922776i | \(-0.625915\pi\) |
0.991816 | − | 0.127677i | \(-0.0407520\pi\) | |||||||
\(464\) | − | 18246.3i | − | 1.82557i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13105.0 | −1.30274 | ||||||||
\(467\) | −8837.65 | − | 15307.3i | −0.875712 | − | 1.51678i | −0.856002 | − | 0.516972i | \(-0.827059\pi\) |
−0.0197099 | − | 0.999806i | \(-0.506274\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13105.6 | − | 13157.6i | −1.29032 | − | 1.29544i | ||||
\(470\) | 18612.7 | − | 10746.1i | 1.82668 | − | 1.05464i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6021.31 | − | 3476.40i | 0.587189 | − | 0.339014i | ||||
\(473\) | 2446.86 | − | 1412.70i | 0.237858 | − | 0.137327i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3616.56 | + | 2088.02i | −0.349346 | + | 0.201695i | ||||
\(476\) | −10429.8 | + | 2772.55i | −1.00430 | + | 0.266974i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4765.56 | + | 8254.19i | 0.456007 | + | 0.789828i | ||||
\(479\) | 11188.3 | 1.06724 | 0.533618 | − | 0.845726i | \(-0.320832\pi\) | ||||
0.533618 | + | 0.845726i | \(0.320832\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14124.5i | 1.33892i | ||||||||
\(482\) | −10200.3 | + | 17667.4i | −0.963920 | + | 1.66956i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8944.99 | + | 15493.2i | 0.840063 | + | 1.45503i | ||||
\(485\) | 3721.04 | − | 2148.35i | 0.348379 | − | 0.201137i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8832.68 | − | 15298.7i | 0.821862 | − | 1.42351i | −0.0824315 | − | 0.996597i | \(-0.526269\pi\) |
0.904294 | − | 0.426911i | \(-0.140398\pi\) | |||||||
\(488\) | −5250.98 | + | 9094.96i | −0.487092 | + | 0.843667i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 15634.9 | + | 61.8416i | 1.44145 | + | 0.00570147i | ||||
\(491\) | −7981.84 | − | 4608.32i | −0.733636 | − | 0.423565i | 0.0861147 | − | 0.996285i | \(-0.472555\pi\) |
−0.819751 | + | 0.572720i | \(0.805888\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 9183.22i | − | 0.838928i | ||||||
\(494\) | −31864.0 | − | 18396.7i | −2.90209 | − | 1.67552i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 10139.1i | − | 0.917863i | ||||||
\(497\) | 2120.18 | + | 7975.68i | 0.191354 | + | 0.719835i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −461.057 | −0.0413622 | −0.0206811 | − | 0.999786i | \(-0.506583\pi\) | ||||
−0.0206811 | + | 0.999786i | \(0.506583\pi\) | |||||||
\(500\) | −12389.8 | − | 21459.8i | −1.10818 | − | 1.91942i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1582.88 | − | 913.879i | −0.140732 | − | 0.0812518i | ||||
\(503\) | −12711.5 | −1.12679 | −0.563397 | − | 0.826186i | \(-0.690506\pi\) | ||||
−0.563397 | + | 0.826186i | \(0.690506\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4699.72 | 0.414129 | ||||||||
\(506\) | −6020.97 | − | 3476.21i | −0.528982 | − | 0.305408i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −17451.7 | − | 30227.2i | −1.52420 | − | 2.63999i | ||||
\(509\) | 5598.28 | 0.487504 | 0.243752 | − | 0.969838i | \(-0.421622\pi\) | ||||
0.243752 | + | 0.969838i | \(0.421622\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1679.16 | − | 453.491i | −0.145365 | − | 0.0392588i | ||||
\(512\) | 21572.3i | 1.86205i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −29236.3 | − | 16879.6i | −2.50887 | − | 1.44850i | ||||
\(515\) | 6082.89i | 0.520474i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6230.84 | + | 3597.38i | 0.530043 | + | 0.306020i | ||||
\(518\) | −4695.30 | − | 17662.7i | −0.398262 | − | 1.49818i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 13330.3 | − | 23088.8i | 1.12418 | − | 1.94714i | ||||
\(521\) | −1390.74 | + | 2408.83i | −0.116947 | + | 0.202558i | −0.918556 | − | 0.395290i | \(-0.870644\pi\) |
0.801609 | + | 0.597848i | \(0.203977\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7662.01 | + | 4423.66i | −0.640605 | + | 0.369853i | −0.784848 | − | 0.619689i | \(-0.787259\pi\) |
0.144243 | + | 0.989542i | \(0.453925\pi\) | |||||||
\(524\) | −16786.7 | − | 29075.4i | −1.39949 | − | 2.42398i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12989.7 | + | 22498.8i | −1.07676 | + | 1.86500i | ||||
\(527\) | − | 5102.94i | − | 0.421798i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3621.35 | 0.297637 | ||||||||
\(530\) | 6516.57 | + | 11287.0i | 0.534079 | + | 0.925051i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 30824.6 | + | 8324.80i | 2.51206 | + | 0.678432i | ||||
\(533\) | −19804.4 | + | 11434.1i | −1.60943 | + | 0.929203i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7495.03 | + | 4327.26i | −0.605679 | + | 0.349689i | ||||
\(536\) | 35485.4 | − | 20487.5i | 2.85958 | − | 1.65098i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4724.66 | + | 2727.78i | −0.378614 | + | 0.218593i | ||||
\(539\) | 2599.05 | + | 4543.10i | 0.207698 | + | 0.363052i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5968.54 | + | 10337.8i | 0.474321 | + | 0.821548i | 0.999568 | − | 0.0294020i | \(-0.00936029\pi\) |
−0.525247 | + | 0.850950i | \(0.676027\pi\) | |||||||
\(542\) | 24801.1 | 1.96550 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 835.876i | − | 0.0658785i | ||||||
\(545\) | −2518.89 | + | 4362.85i | −0.197977 | + | 0.342906i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3335.96 | − | 5778.05i | −0.260759 | − | 0.451648i | 0.705685 | − | 0.708526i | \(-0.250640\pi\) |
−0.966444 | + | 0.256878i | \(0.917306\pi\) | |||||||
\(548\) | −669.363 | + | 386.457i | −0.0521784 | + | 0.0301252i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1483.92 | − | 2570.22i | 0.115045 | − | 0.199263i | ||||
\(551\) | −13584.6 | + | 23529.3i | −1.05032 | + | 1.81920i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2236.92 | + | 8282.74i | −0.172014 | + | 0.636922i | ||||
\(554\) | 37353.2 | + | 21565.9i | 2.86460 | + | 1.65388i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 13413.6i | − | 1.02313i | ||||||
\(557\) | 18890.9 | + | 10906.6i | 1.43704 | + | 0.829675i | 0.997643 | − | 0.0686176i | \(-0.0218588\pi\) |
0.439397 | + | 0.898293i | \(0.355192\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13061.6i | 0.988279i | ||||||||
\(560\) | −3173.96 | + | 11752.4i | −0.239508 | + | 0.886836i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 33288.4 | 2.49855 | ||||||||
\(563\) | 3934.60 | + | 6814.92i | 0.294536 | + | 0.510151i | 0.974877 | − | 0.222745i | \(-0.0715017\pi\) |
−0.680341 | + | 0.732896i | \(0.738168\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −591.001 | − | 341.214i | −0.0440064 | − | 0.0254071i | ||||
\(566\) | 3722.81 | 0.276469 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −18208.7 | −1.34511 | ||||||||
\(569\) | −8743.96 | − | 5048.33i | −0.644228 | − | 0.371945i | 0.142013 | − | 0.989865i | \(-0.454642\pi\) |
−0.786241 | + | 0.617919i | \(0.787976\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4725.12 | + | 8184.15i | 0.346305 | + | 0.599818i | 0.985590 | − | 0.169152i | \(-0.0541029\pi\) |
−0.639285 | + | 0.768970i | \(0.720770\pi\) | |||||||
\(572\) | 17536.7 | 1.28190 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 20964.5 | − | 20881.8i | 1.52446 | − | 1.51845i | ||||
\(575\) | − | 3647.96i | − | 0.264574i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22282.2 | + | 12864.6i | 1.60766 | + | 0.928184i | 0.989892 | + | 0.141825i | \(0.0452970\pi\) |
0.617770 | + | 0.786359i | \(0.288036\pi\) | |||||||
\(578\) | 17908.5i | 1.28875i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −33500.4 | − | 19341.4i | −2.39832 | − | 1.38467i | ||||
\(581\) | 9100.70 | + | 9136.77i | 0.649846 | + | 0.652422i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2181.50 | + | 3778.48i | −0.154972 | + | 0.268419i | ||||
\(584\) | 1918.82 | − | 3323.50i | 0.135961 | − | 0.235492i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 33714.8 | − | 19465.2i | 2.37670 | − | 1.37219i | ||||
\(587\) | −7519.63 | − | 13024.4i | −0.528736 | − | 0.915798i | −0.999439 | − | 0.0335059i | \(-0.989333\pi\) |
0.470702 | − | 0.882292i | \(-0.344001\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7548.72 | + | 13074.8i | −0.528081 | + | 0.914663i | ||||
\(590\) | − | 7755.87i | − | 0.541194i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 14229.8 | 0.987911 | ||||||||
\(593\) | 1728.25 | + | 2993.41i | 0.119681 | + | 0.207293i | 0.919641 | − | 0.392760i | \(-0.128480\pi\) |
−0.799960 | + | 0.600053i | \(0.795146\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1597.43 | + | 5914.87i | −0.110064 | + | 0.407539i | ||||
\(596\) | −16238.5 | + | 9375.31i | −1.11603 | + | 0.644341i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 27834.6 | − | 16070.3i | 1.90341 | − | 1.09894i | ||||
\(599\) | 3692.69 | − | 2131.97i | 0.251885 | − | 0.145426i | −0.368742 | − | 0.929532i | \(-0.620211\pi\) |
0.620627 | + | 0.784106i | \(0.286878\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18500.7 | − | 10681.4i | 1.25567 | − | 0.724963i | 0.283442 | − | 0.958989i | \(-0.408524\pi\) |
0.972230 | + | 0.234026i | \(0.0751902\pi\) | |||||||
\(602\) | −4341.97 | − | 16333.6i | −0.293963 | − | 1.10583i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4836.80 | − | 8377.59i | −0.325839 | − | 0.564369i | ||||
\(605\) | 10156.4 | 0.682508 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12892.4i | 0.862087i | 0.902331 | + | 0.431043i | \(0.141854\pi\) | ||||
−0.902331 | + | 0.431043i | \(0.858146\pi\) | |||||||
\(608\) | −1236.50 | + | 2141.69i | −0.0824783 | + | 0.142857i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5857.48 | + | 10145.5i | 0.388791 | + | 0.673406i | ||||
\(611\) | −28804.8 | + | 16630.5i | −1.90723 | + | 1.10114i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2804.94 | + | 4858.29i | −0.184813 | + | 0.320105i | −0.943513 | − | 0.331334i | \(-0.892501\pi\) |
0.758701 | + | 0.651439i | \(0.225835\pi\) | |||||||
\(614\) | 4226.32 | − | 7320.19i | 0.277785 | − | 0.481138i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11160.7 | + | 2966.87i | −0.729998 | + | 0.194056i | ||||
\(617\) | −18116.5 | − | 10459.6i | −1.18208 | − | 0.682473i | −0.225583 | − | 0.974224i | \(-0.572429\pi\) |
−0.956494 | + | 0.291751i | \(0.905762\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 12344.6i | − | 0.801568i | −0.916173 | − | 0.400784i | \(-0.868738\pi\) | ||
0.916173 | − | 0.400784i | \(-0.131262\pi\) | |||||||
\(620\) | −18615.5 | − | 10747.7i | −1.20583 | − | 0.696188i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15537.8i | 1.00162i | ||||||||
\(623\) | 8856.23 | + | 8891.33i | 0.569530 | + | 0.571788i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9135.04 | −0.584642 | ||||||||
\(626\) | −13369.0 | − | 23155.8i | −0.853569 | − | 1.47842i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −477.733 | − | 275.819i | −0.0303561 | − | 0.0175261i | ||||
\(629\) | 7161.76 | 0.453987 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5767.92 | −0.363894 | −0.181947 | − | 0.983308i | \(-0.558240\pi\) | ||||
−0.181947 | + | 0.983308i | \(0.558240\pi\) | |||||||
\(632\) | −16393.7 | − | 9464.92i | −1.03182 | − | 0.595719i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3441.11 | − | 5960.18i | −0.215558 | − | 0.373358i | ||||
\(635\) | −19815.2 | −1.23833 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24196.3 | − | 95.7053i | −1.50501 | − | 0.00595288i | ||||
\(638\) | − | 19308.7i | − | 1.19818i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 19395.2 | + | 11197.8i | 1.19791 | + | 0.691613i | ||||
\(641\) | − | 27080.3i | − | 1.66866i | −0.551268 | − | 0.834328i | \(-0.685856\pi\) | ||
0.551268 | − | 0.834328i | \(-0.314144\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14289.4 | − | 8250.01i | −0.876392 | − | 0.505985i | −0.00692488 | − | 0.999976i | \(-0.502204\pi\) |
−0.869467 | + | 0.493991i | \(0.835538\pi\) | |||||||
\(644\) | −19761.1 | + | 19683.1i | −1.20915 | + | 1.20438i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9327.96 | + | 16156.5i | −0.568117 | + | 0.984008i | ||||
\(647\) | 1814.64 | − | 3143.04i | 0.110264 | − | 0.190983i | −0.805613 | − | 0.592442i | \(-0.798164\pi\) |
0.915877 | + | 0.401460i | \(0.131497\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2248.53 | − | 1298.19i | 0.135998 | − | 0.0785183i | ||||
\(650\) | 6860.07 | + | 11882.0i | 0.413960 | + | 0.717000i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −33151.9 | + | 57420.8i | −1.99130 | + | 3.44904i | ||||
\(653\) | 23075.3i | 1.38286i | 0.722444 | + | 0.691430i | \(0.243019\pi\) | ||||
−0.722444 | + | 0.691430i | \(0.756981\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19060.2 | −1.13701 | ||||||||
\(656\) | 11519.4 | + | 19952.1i | 0.685603 | + | 1.18750i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 30492.2 | − | 30371.8i | 1.80655 | − | 1.79942i | ||||
\(659\) | −4090.21 | + | 2361.48i | −0.241778 | + | 0.139591i | −0.615994 | − | 0.787751i | \(-0.711245\pi\) |
0.374215 | + | 0.927342i | \(0.377912\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2370.90 | + | 1368.84i | −0.139512 | + | 0.0805471i | −0.568131 | − | 0.822938i | \(-0.692333\pi\) |
0.428620 | + | 0.903485i | \(0.359000\pi\) | |||||||
\(662\) | −7209.64 | + | 4162.49i | −0.423279 | + | 0.244380i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −24641.5 | + | 14226.8i | −1.44017 | + | 0.831484i | ||||
\(665\) | 12842.7 | − | 12792.0i | 0.748903 | − | 0.745946i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11866.8 | − | 20553.8i | −0.688880 | − | 1.19318i | ||||
\(668\) | 23764.1 | 1.37644 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 45707.7i | − | 2.63558i | ||||||
\(671\) | −1960.87 | + | 3396.32i | −0.112814 | + | 0.195400i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9072.16 | + | 15713.4i | 0.519623 | + | 0.900013i | 0.999740 | + | 0.0228084i | \(0.00726078\pi\) |
−0.480117 | + | 0.877204i | \(0.659406\pi\) | |||||||
\(674\) | 7026.08 | − | 4056.51i | 0.401535 | − | 0.231826i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22639.8 | + | 39213.3i | −1.28811 | + | 2.23107i | ||||
\(677\) | 12329.9 | − | 21355.9i | 0.699963 | − | 1.21237i | −0.268515 | − | 0.963275i | \(-0.586533\pi\) |
0.968479 | − | 0.249097i | \(-0.0801337\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6095.98 | − | 6071.92i | 0.344539 | − | 0.343179i | ||||
\(680\) | −11707.1 | − | 6759.08i | −0.660214 | − | 0.381175i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 10729.5i | − | 0.602423i | ||||||
\(683\) | 13961.0 | + | 8060.40i | 0.782143 | + | 0.451570i | 0.837189 | − | 0.546913i | \(-0.184197\pi\) |
−0.0550463 | + | 0.998484i | \(0.517531\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 438.795i | 0.0244752i | ||||||||
\(686\) | 30289.4 | − | 7923.71i | 1.68579 | − | 0.441004i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 13159.0 | 0.729192 | ||||||||
\(689\) | −10085.0 | − | 17467.7i | −0.557629 | − | 0.965842i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9861.10 | − | 5693.31i | −0.542886 | − | 0.313435i | 0.203362 | − | 0.979104i | \(-0.434813\pi\) |
−0.746248 | + | 0.665668i | \(0.768147\pi\) | |||||||
\(692\) | 8000.64 | 0.439507 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4723.14 | 0.258340 | ||||||||
\(695\) | −6594.87 | − | 3807.55i | −0.359939 | − | 0.207811i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5797.60 | + | 10041.7i | 0.315064 | + | 0.545707i | ||||
\(698\) | −28409.8 | −1.54058 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8402.29 | − | 8435.59i | −0.453681 | − | 0.455479i | ||||
\(701\) | 19448.3i | 1.04786i | 0.851761 | + | 0.523930i | \(0.175535\pi\) | ||||
−0.851761 | + | 0.523930i | \(0.824465\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18349.9 | − | 10594.3i | −0.984466 | − | 0.568382i | ||||
\(704\) | 6918.40i | 0.370379i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8929.82 | + | 5155.63i | 0.476031 | + | 0.274837i | ||||
\(707\) | 9095.20 | − | 2417.78i | 0.483819 | − | 0.128614i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12475.9 | − | 21608.8i | 0.660847 | − | 1.14462i | −0.319546 | − | 0.947571i | \(-0.603530\pi\) |
0.980393 | − | 0.197050i | \(-0.0631363\pi\) | |||||||
\(710\) | −10156.0 | + | 17590.6i | −0.536826 | + | 0.929809i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −23979.5 | + | 13844.6i | −1.26218 | + | 0.728719i | ||||
\(713\) | −6594.13 | − | 11421.4i | −0.346356 | − | 0.599907i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4977.93 | − | 8622.02i | 0.260369 | − | 0.450973i | ||||
\(716\) | 13358.9i | 0.697268i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −43779.7 | −2.27555 | ||||||||
\(719\) | 3243.11 | + | 5617.23i | 0.168216 | + | 0.291359i | 0.937793 | − | 0.347195i | \(-0.112866\pi\) |
−0.769576 | + | 0.638555i | \(0.779533\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3129.36 | + | 11772.0i | 0.161641 | + | 0.608061i | ||||
\(722\) | 18524.1 | − | 10694.9i | 0.954843 | − | 0.551279i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8728.05 | + | 5039.14i | −0.448032 | + | 0.258671i | ||||
\(725\) | 8774.00 | − | 5065.67i | 0.449459 | − | 0.259496i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12957.4 | − | 7480.97i | 0.661023 | − | 0.381642i | −0.131643 | − | 0.991297i | \(-0.542025\pi\) |
0.792667 | + | 0.609655i | \(0.208692\pi\) | |||||||
\(728\) | 13919.6 | − | 51540.7i | 0.708647 | − | 2.62394i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2140.45 | − | 3707.37i | −0.108523 | − | 0.187967i | ||||
\(731\) | 6622.84 | 0.335095 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 12098.0i | − | 0.609617i | −0.952414 | − | 0.304808i | \(-0.901408\pi\) | ||
0.952414 | − | 0.304808i | \(-0.0985925\pi\) | |||||||
\(734\) | −17738.7 | + | 30724.4i | −0.892028 | + | 1.54504i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1080.14 | − | 1870.85i | −0.0540957 | − | 0.0936964i | ||||
\(737\) | 13251.2 | − | 7650.61i | 0.662301 | − | 0.382380i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1933.82 | − | 3349.47i | 0.0962606 | − | 0.166728i | −0.813873 | − | 0.581042i | \(-0.802645\pi\) |
0.910134 | + | 0.414314i | \(0.135978\pi\) | |||||||
\(740\) | 15083.9 | − | 26126.1i | 0.749318 | − | 1.29786i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18417.9 | + | 18490.9i | 0.911244 | + | 0.914855i | ||||
\(743\) | 25571.4 | + | 14763.7i | 1.26262 | + | 0.728972i | 0.973580 | − | 0.228346i | \(-0.0733317\pi\) |
0.289037 | + | 0.957318i | \(0.406665\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10645.0i | 0.523494i | ||||||||
\(746\) | 23463.7 | + | 13546.8i | 1.15156 | + | 0.664855i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 8891.90i | − | 0.434652i | ||||||
\(749\) | −12278.7 | + | 12230.2i | −0.599003 | + | 0.596639i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6081.58 | 0.295499 | 0.147750 | − | 0.989025i | \(-0.452797\pi\) | ||||
0.147750 | + | 0.989025i | \(0.452797\pi\) | |||||||
\(752\) | 16754.5 | + | 29019.6i | 0.812465 | + | 1.40723i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 77304.0 | + | 44631.5i | 3.73375 | + | 2.15568i | ||||
\(755\) | −5491.86 | −0.264727 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27611.0 | −1.32568 | −0.662840 | − | 0.748761i | \(-0.730649\pi\) | ||||
−0.662840 | + | 0.748761i | \(0.730649\pi\) | |||||||
\(758\) | −12264.3 | − | 7080.82i | −0.587679 | − | 0.339297i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 19997.3 | + | 34636.3i | 0.954445 | + | 1.65315i | ||||
\(761\) | 9596.16 | 0.457110 | 0.228555 | − | 0.973531i | \(-0.426600\pi\) | ||||
0.228555 | + | 0.973531i | \(0.426600\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2630.24 | + | 9739.10i | −0.124798 | + | 0.462096i | ||||
\(764\) | 25121.4i | 1.18961i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6306.17 | − | 3640.87i | −0.297456 | − | 0.171736i | ||||
\(767\) | 12002.9i | 0.565058i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 612.746 | + | 353.769i | 0.0287337 | + | 0.0165894i | 0.514298 | − | 0.857612i | \(-0.328053\pi\) |
−0.485564 | + | 0.874201i | \(0.661386\pi\) | |||||||
\(770\) | −3358.76 | + | 12436.6i | −0.157197 | + | 0.582059i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −22892.7 | + | 39651.3i | −1.06726 | + | 1.84855i | ||||
\(773\) | −2632.55 | + | 4559.71i | −0.122492 | + | 0.212162i | −0.920750 | − | 0.390154i | \(-0.872422\pi\) |
0.798258 | + | 0.602316i | \(0.205755\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4875.54 | − | 2814.89i | 0.225980 | − | 0.130470i | ||||
\(776\) | 9491.98 | + | 16440.6i | 0.439101 | + | 0.760545i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 25875.2 | − | 44817.2i | 1.19238 | − | 2.06526i | ||||
\(779\) | − | 34305.3i | − | 1.57781i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6799.67 | −0.311538 | ||||||||
\(782\) | −8148.37 | − | 14113.4i | −0.372615 | − | 0.645388i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −96.4191 | + | 24376.8i | −0.00439227 | + | 1.11046i | ||||
\(785\) | −271.217 | + | 156.587i | −0.0123314 | + | 0.00711953i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27206.6 | + | 15707.8i | −1.23229 | + | 0.711463i | −0.967507 | − | 0.252845i | \(-0.918634\pi\) |
−0.264783 | + | 0.964308i | \(0.585300\pi\) | |||||||
\(788\) | −22624.5 | + | 13062.3i | −1.02280 | + | 0.590513i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −18287.2 | + | 10558.1i | −0.823583 | + | 0.475496i | ||||
\(791\) | −1319.28 | − | 356.298i | −0.0593024 | − | 0.0160158i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9064.97 | − | 15701.0i | −0.405935 | − | 0.703100i | ||||
\(794\) | −20646.3 | −0.922807 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 11232.2i | − | 0.500145i | ||||||
\(797\) | 1477.45 | − | 2559.02i | 0.0656637 | − | 0.113733i | −0.831325 | − | 0.555787i | \(-0.812417\pi\) |
0.896988 | + | 0.442055i | \(0.145750\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8432.40 | + | 14605.3i | 0.373363 | + | 0.646683i | ||||
\(800\) | 798.628 | − | 461.088i | 0.0352947 | − | 0.0203774i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16542.4 | − | 28652.3i | 0.728344 | − | 1.26153i | ||||
\(803\) | 716.544 | − | 1241.09i | 0.0314898 | − | 0.0545419i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4067.97 | + | 15302.9i | 0.178108 | + | 0.670006i | ||||
\(806\) | 42956.3 | + | 24800.9i | 1.87726 | + | 1.08384i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 20764.7i | 0.904082i | ||||||||
\(809\) | −1592.89 | − | 919.657i | −0.0692251 | − | 0.0399671i | 0.464988 | − | 0.885317i | \(-0.346059\pi\) |
−0.534213 | + | 0.845350i | \(0.679392\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 3301.11i | − | 0.142932i | −0.997443 | − | 0.0714658i | \(-0.977232\pi\) | ||
0.997443 | − | 0.0714658i | \(-0.0227677\pi\) | |||||||
\(812\) | −74782.3 | − | 20196.4i | −3.23195 | − | 0.872853i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15058.4 | 0.648398 | ||||||||
\(815\) | 18820.9 | + | 32598.7i | 0.808916 | + | 1.40108i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16969.1 | − | 9797.10i | −0.726649 | − | 0.419531i | ||||
\(818\) | 10940.4 | 0.467633 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 48842.9 | 2.08008 | ||||||||
\(821\) | 7082.07 | + | 4088.84i | 0.301055 | + | 0.173814i | 0.642917 | − | 0.765936i | \(-0.277724\pi\) |
−0.341862 | + | 0.939750i | \(0.611057\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15950.3 | − | 27626.7i | −0.675567 | − | 1.17012i | −0.976303 | − | 0.216409i | \(-0.930565\pi\) |
0.300735 | − | 0.953708i | \(-0.402768\pi\) | |||||||
\(824\) | −26875.9 | −1.13624 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3990.03 | − | 15009.7i | −0.168076 | − | 0.632267i | ||||
\(827\) | − | 41211.0i | − | 1.73283i | −0.499327 | − | 0.866414i | \(-0.666419\pi\) | ||
0.499327 | − | 0.866414i | \(-0.333581\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9494.26 | + | 5481.52i | 0.397768 | + | 0.229651i | 0.685520 | − | 0.728053i | \(-0.259575\pi\) |
−0.287753 | + | 0.957705i | \(0.592908\pi\) | |||||||
\(830\) | 31740.0i | 1.32736i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −27698.4 | − | 15991.7i | −1.15417 | − | 0.666360i | ||||
\(833\) | −48.5269 | + | 12268.6i | −0.00201844 | + | 0.510303i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6745.64 | − | 11683.8i | 0.279572 | − | 0.484233i | ||||
\(836\) | −13153.7 | + | 22782.9i | −0.544175 | + | 0.942538i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −32128.6 | + | 18549.5i | −1.32442 | + | 0.764655i | ||||
\(839\) | 10865.3 | + | 18819.2i | 0.447093 | + | 0.774388i | 0.998195 | − | 0.0600500i | \(-0.0191260\pi\) |
−0.551102 | + | 0.834438i | \(0.685793\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20762.7 | − | 35962.0i | 0.851312 | − | 1.47452i | ||||
\(842\) | 2931.75i | 0.119994i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 76303.7 | 3.11194 | ||||||||
\(845\) | 12853.0 | + | 22262.0i | 0.523261 | + | 0.906315i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19655.4 | − | 5225.00i | 0.797362 | − | 0.211963i | ||||
\(848\) | −17597.9 | + | 10160.2i | −0.712637 | + | 0.411441i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6024.71 | − | 3478.37i | 0.243113 | − | 0.140361i | ||||
\(851\) | 16029.4 | − | 9254.59i | 0.645689 | − | 0.372789i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33620.5 | − | 19410.8i | 1.34952 | − | 0.779148i | 0.361342 | − | 0.932433i | \(-0.382319\pi\) |
0.988182 | + | 0.153285i | \(0.0489854\pi\) | |||||||
\(854\) | 16555.1 | + | 16620.7i | 0.663354 | + | 0.665983i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −19119.0 | − | 33115.1i | −0.763405 | − | 1.32226i | ||||
\(857\) | −24474.4 | −0.975531 | −0.487765 | − | 0.872975i | \(-0.662188\pi\) | ||||
−0.487765 | + | 0.872975i | \(0.662188\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 33413.7i | − | 1.32720i | −0.748089 | − | 0.663599i | \(-0.769028\pi\) | ||
0.748089 | − | 0.663599i | \(-0.230972\pi\) | |||||||
\(860\) | 13948.8 | − | 24160.1i | 0.553083 | − | 0.957968i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −25838.5 | − | 44753.6i | −1.02095 | − | 1.76834i | ||||
\(863\) | 20331.0 | − | 11738.1i | 0.801942 | − | 0.463001i | −0.0422080 | − | 0.999109i | \(-0.513439\pi\) |
0.844150 | + | 0.536108i | \(0.180106\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2271.04 | − | 3933.56i | 0.0892692 | − | 0.154619i | ||||
\(866\) | 18277.8 | − | 31658.1i | 0.717211 | − | 1.24225i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −41555.1 | − | 11222.8i | −1.62497 | − | 0.438855i | ||||
\(869\) | −6121.89 | − | 3534.47i | −0.238977 | − | 0.137973i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 70736.6i | 2.75180i | ||||||||
\(872\) | −19276.2 | − | 11129.1i | −0.748596 | − | 0.432202i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 48215.2i | 1.86602i | ||||||||
\(875\) | −27224.8 | + | 7237.19i | −1.05185 | + | 0.279613i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9596.84 | 0.369512 | 0.184756 | − | 0.982784i | \(-0.440850\pi\) | ||||
0.184756 | + | 0.982784i | \(0.440850\pi\) | |||||||
\(878\) | −42276.7 | − | 73225.5i | −1.62502 | − | 2.81462i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8686.33 | − | 5015.06i | −0.332746 | − | 0.192111i | ||||
\(881\) | −48210.3 | −1.84364 | −0.921821 | − | 0.387617i | \(-0.873298\pi\) | ||||
−0.921821 | + | 0.387617i | \(0.873298\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21780.5 | −0.830094 | −0.415047 | − | 0.909800i | \(-0.636235\pi\) | ||||
−0.415047 | + | 0.909800i | \(0.636235\pi\) | |||||||
\(884\) | 35599.4 | + | 20553.3i | 1.35446 | + | 0.781995i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4195.37 | + | 7266.59i | 0.159081 | + | 0.275537i | ||||
\(887\) | 32602.2 | 1.23413 | 0.617066 | − | 0.786911i | \(-0.288321\pi\) | ||||
0.617066 | + | 0.786911i | \(0.288321\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −38347.6 | + | 10194.0i | −1.44672 | + | 0.384583i | ||||
\(890\) | 30887.4i | 1.16331i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11086.2 | + | 6400.61i | 0.416135 | + | 0.240256i | ||||
\(893\) | − | 49895.9i | − | 1.86977i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6567.97 | + | 3792.02i | 0.245299 | + | 0.141624i | ||||
\(896\) | 43295.5 | + | 11692.8i | 1.61429 | + | 0.435971i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −25005.1 | + | 43310.2i | −0.929212 | + | 1.60944i | ||||
\(899\) | 18313.7 | − | 31720.2i | 0.679415 | − | 1.17678i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8856.89 | + | 5113.53i | −0.327487 | + | 0.189075i | ||||
\(902\) | 12190.1 | + | 21113.8i | 0.449983 | + | 0.779394i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1507.58 | − | 2611.20i | 0.0554661 | − | 0.0960700i | ||||
\(905\) | 5721.60i | 0.210157i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45098.6 | 1.65102 | 0.825510 | − | 0.564387i | \(-0.190887\pi\) | ||||
0.825510 | + | 0.564387i | \(0.190887\pi\) | |||||||
\(908\) | −14732.1 | − | 25516.7i | −0.538438 | − | 0.932602i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −42027.4 | − | 42194.0i | −1.53098 | − | 1.53705i | ||||
\(911\) | −27846.3 | + | 16077.1i | −1.01272 | + | 0.584695i | −0.911988 | − | 0.410218i | \(-0.865453\pi\) |
−0.100735 | + | 0.994913i | \(0.532119\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9201.83 | + | 5312.68i | −0.333556 | + | 0.192578i | ||||
\(914\) | −29702.3 | + | 17148.7i | −1.07491 | + | 0.620598i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 40455.4 | − | 23356.9i | 1.45926 | − | 0.842505i | ||||
\(917\) | −36886.4 | + | 9805.54i | −1.32835 | + | 0.353116i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8217.77 | + | 14233.6i | 0.294972 | + | 0.510907i | 0.974978 | − | 0.222300i | \(-0.0713563\pi\) |
−0.680006 | + | 0.733206i | \(0.738023\pi\) | |||||||
\(920\) | −34937.0 | −1.25200 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 76807.1i | 2.74350i | ||||||||
\(923\) | 15717.2 | − | 27223.0i | 0.560497 | − | 0.970809i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3950.59 | + | 6842.62i | 0.140427 | + | 0.243226i | ||||
\(926\) | 51578.8 | − | 29779.0i | 1.83044 | − | 1.05680i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2999.83 | − | 5195.86i | 0.106114 | − | 0.183796i | ||||
\(929\) | −11690.1 | + | 20247.9i | −0.412852 | + | 0.715081i | −0.995200 | − | 0.0978584i | \(-0.968801\pi\) |
0.582348 | + | 0.812940i | \(0.302134\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18273.2 | − | 31363.0i | 0.643265 | − | 1.10406i | ||||
\(932\) | −37514.0 | − | 21658.7i | −1.31847 | − | 0.761218i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 87114.4i | − | 3.05189i | ||||||
\(935\) | −4371.76 | − | 2524.03i | −0.152911 | − | 0.0882832i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 24806.5i | − | 0.864880i | −0.901663 | − | 0.432440i | \(-0.857653\pi\) | ||
0.901663 | − | 0.432440i | \(-0.142347\pi\) | |||||||
\(938\) | −23514.4 | − | 88456.4i | −0.818521 | − | 3.07911i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 71040.3 | 2.46498 | ||||||||
\(941\) | −4448.30 | − | 7704.69i | −0.154103 | − | 0.266914i | 0.778629 | − | 0.627484i | \(-0.215915\pi\) |
−0.932732 | + | 0.360571i | \(0.882582\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25952.3 | + | 14983.6i | 0.896207 | + | 0.517425i | ||||
\(944\) | 12092.4 | 0.416922 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13925.2 | 0.478592 | ||||||||
\(947\) | −5275.81 | − | 3045.99i | −0.181036 | − | 0.104521i | 0.406744 | − | 0.913542i | \(-0.366664\pi\) |
−0.587779 | + | 0.809021i | \(0.699998\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3312.54 | + | 5737.48i | 0.113308 | + | 0.196256i | ||||
\(950\) | −20582.1 | −0.702916 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −26133.5 | − | 7057.87i | −0.889697 | − | 0.240280i | ||||
\(953\) | − | 50366.8i | − | 1.71201i | −0.516971 | − | 0.856003i | \(-0.672941\pi\) | ||
0.516971 | − | 0.856003i | \(-0.327059\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12351.1 | + | 7130.91i | 0.418505 | + | 0.241624i | ||||
\(956\) | 31504.3i | 1.06582i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 47754.8 | + | 27571.3i | 1.61053 | + | 0.929840i | ||||
\(959\) | 225.739 | + | 849.184i | 0.00760115 | + | 0.0285939i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4718.96 | + | 8173.48i | −0.158402 | + | 0.274361i | ||||
\(962\) | −34807.0 | + | 60287.4i | −1.16655 | + | 2.02053i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −58398.0 | + | 33716.1i | −1.95111 | + | 1.12648i | ||||
\(965\) | 12996.5 | + | 22510.7i | 0.433548 | + | 0.750927i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3986.98 | + | 6905.65i | −0.132588 | + | 0.229649i | −0.924673 | − | 0.380761i | \(-0.875662\pi\) |
0.792085 | + | 0.610410i | \(0.208995\pi\) | |||||||
\(968\) | 44873.8i | 1.48998i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 21176.7 | 0.700971 | ||||||||
\(971\) | 11779.8 | + | 20403.3i | 0.389323 | + | 0.674327i | 0.992359 | − | 0.123387i | \(-0.0393757\pi\) |
−0.603036 | + | 0.797714i | \(0.706042\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14721.6 | − | 3975.87i | −0.485050 | − | 0.130997i | ||||
\(974\) | 75400.9 | − | 43532.7i | 2.48049 | − | 1.43211i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15818.1 | + | 9132.58i | −0.518775 | + | 0.299515i | ||||
\(977\) | −17441.0 | + | 10069.6i | −0.571124 | + | 0.329739i | −0.757598 | − | 0.652721i | \(-0.773627\pi\) |
0.186474 | + | 0.982460i | \(0.440294\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8954.65 | + | 5169.97i | −0.292331 | + | 0.168777i | ||||
\(980\) | 44653.7 | + | 26016.9i | 1.45552 | + | 0.848039i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −22712.5 | − | 39339.3i | −0.738071 | − | 1.27838i | ||||
\(983\) | 17607.8 | 0.571313 | 0.285656 | − | 0.958332i | \(-0.407788\pi\) | ||||
0.285656 | + | 0.958332i | \(0.407788\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14831.3i | 0.479762i | ||||||||
\(986\) | 22630.2 | − | 39196.6i | 0.730925 | − | 1.26600i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −60808.7 | − | 105324.i | −1.95808 | − | 3.39149i | ||||
\(989\) | 14823.2 | − | 8558.18i | 0.476593 | − | 0.275161i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24487.2 | + | 42413.1i | −0.784927 | + | 1.35953i | 0.144116 | + | 0.989561i | \(0.453966\pi\) |
−0.929043 | + | 0.369972i | \(0.879367\pi\) | |||||||
\(992\) | 1666.95 | − | 2887.24i | 0.0533524 | − | 0.0924091i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10604.9 | + | 39267.2i | −0.338398 | + | 1.25300i | ||||
\(995\) | −5522.39 | − | 3188.35i | −0.175951 | − | 0.101586i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 56049.9i | − | 1.78046i | −0.455511 | − | 0.890230i | \(-0.650544\pi\) | ||
0.455511 | − | 0.890230i | \(-0.349456\pi\) | |||||||
\(998\) | −1967.93 | − | 1136.18i | −0.0624184 | − | 0.0360373i | ||||
\(999\) | 0 | 0 |
(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 | 189.4.s.a.17.20 | 44 | ||
3.2 | odd | 2 | 63.4.s.a.59.3 | yes | 44 | ||
7.5 | odd | 6 | 189.4.i.a.152.3 | 44 | |||
9.2 | odd | 6 | 189.4.i.a.143.20 | 44 | |||
9.7 | even | 3 | 63.4.i.a.38.3 | yes | 44 | ||
21.5 | even | 6 | 63.4.i.a.5.20 | ✓ | 44 | ||
63.47 | even | 6 | inner | 189.4.s.a.89.20 | 44 | ||
63.61 | odd | 6 | 63.4.s.a.47.3 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.i.a.5.20 | ✓ | 44 | 21.5 | even | 6 | ||
63.4.i.a.38.3 | yes | 44 | 9.7 | even | 3 | ||
63.4.s.a.47.3 | yes | 44 | 63.61 | odd | 6 | ||
63.4.s.a.59.3 | yes | 44 | 3.2 | odd | 2 | ||
189.4.i.a.143.20 | 44 | 9.2 | odd | 6 | |||
189.4.i.a.152.3 | 44 | 7.5 | odd | 6 | |||
189.4.s.a.17.20 | 44 | 1.1 | even | 1 | trivial | ||
189.4.s.a.89.20 | 44 | 63.47 | even | 6 | inner |