Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1890,2,Mod(361,1890)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1890, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1890.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1890.l (of order \(3\), 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: | \(15.0917259820\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + 2 x^{14} - 4 x^{13} + 5 x^{12} + 2 x^{11} - 35 x^{10} + 81 x^{9} - 66 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{5} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.8 | ||
Root | \(-1.03843 + 1.38624i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1890.361 |
Dual form | 1890.2.l.i.1801.8 |
$q$-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 \(\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(1081\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.63512 | − | 0.236999i | 0.995980 | − | 0.0895771i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | −1.64324 | −0.495456 | −0.247728 | − | 0.968830i | \(-0.579684\pi\) | ||||
−0.247728 | + | 0.968830i | \(0.579684\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.49250 | + | 4.31714i | −0.691296 | + | 1.19736i | 0.280117 | + | 0.959966i | \(0.409627\pi\) |
−0.971413 | + | 0.237395i | \(0.923707\pi\) | |||||||
\(14\) | −1.11231 | + | 2.40058i | −0.297278 | + | 0.641581i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.52620 | + | 6.10755i | −0.855229 | + | 1.48130i | 0.0212039 | + | 0.999775i | \(0.493250\pi\) |
−0.876433 | + | 0.481524i | \(0.840083\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.51153 | − | 6.08215i | −0.805601 | − | 1.39534i | −0.915885 | − | 0.401441i | \(-0.868509\pi\) |
0.110284 | − | 0.993900i | \(-0.464824\pi\) | |||||||
\(20\) | −0.500000 | − | 0.866025i | −0.111803 | − | 0.193649i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.821620 | − | 1.42309i | 0.175170 | − | 0.303403i | ||||
\(23\) | −7.45235 | −1.55392 | −0.776961 | − | 0.629549i | \(-0.783240\pi\) | ||||
−0.776961 | + | 0.629549i | \(0.783240\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.49250 | − | 4.31714i | −0.488820 | − | 0.846662i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.52280 | − | 2.16358i | −0.287783 | − | 0.408878i | ||||
\(29\) | 2.86866 | + | 4.96867i | 0.532697 | + | 0.922658i | 0.999271 | + | 0.0381762i | \(0.0121548\pi\) |
−0.466574 | + | 0.884482i | \(0.654512\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.82162 | − | 3.15514i | −0.327173 | − | 0.566680i | 0.654777 | − | 0.755822i | \(-0.272763\pi\) |
−0.981950 | + | 0.189142i | \(0.939429\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.52620 | − | 6.10755i | −0.604738 | − | 1.04744i | ||||
\(35\) | 2.63512 | − | 0.236999i | 0.445416 | − | 0.0400601i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.87466 | − | 4.97906i | −0.472592 | − | 0.818553i | 0.526916 | − | 0.849917i | \(-0.323348\pi\) |
−0.999508 | + | 0.0313643i | \(0.990015\pi\) | |||||||
\(38\) | 7.02306 | 1.13929 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −4.30588 | + | 7.45800i | −0.672465 | + | 1.16474i | 0.304738 | + | 0.952436i | \(0.401431\pi\) |
−0.977203 | + | 0.212307i | \(0.931902\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.96195 | + | 5.13024i | 0.451692 | + | 0.782354i | 0.998491 | − | 0.0549098i | \(-0.0174871\pi\) |
−0.546799 | + | 0.837264i | \(0.684154\pi\) | |||||||
\(44\) | 0.821620 | + | 1.42309i | 0.123864 | + | 0.214539i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.72617 | − | 6.45392i | 0.549394 | − | 0.951579i | ||||
\(47\) | 0.820581 | − | 1.42129i | 0.119694 | − | 0.207316i | −0.799952 | − | 0.600064i | \(-0.795142\pi\) |
0.919646 | + | 0.392747i | \(0.128475\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.88766 | − | 1.24904i | 0.983952 | − | 0.178434i | ||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.98501 | 0.691296 | ||||||||
\(53\) | −6.46391 | + | 11.1958i | −0.887886 | + | 1.53786i | −0.0455161 | + | 0.998964i | \(0.514493\pi\) |
−0.842370 | + | 0.538900i | \(0.818840\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.64324 | −0.221575 | ||||||||
\(56\) | 2.63512 | − | 0.236999i | 0.352132 | − | 0.0316703i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.73732 | −0.753347 | ||||||||
\(59\) | 0.391083 | + | 0.677376i | 0.0509147 | + | 0.0881869i | 0.890360 | − | 0.455258i | \(-0.150453\pi\) |
−0.839445 | + | 0.543445i | \(0.817120\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.38034 | + | 4.12287i | −0.304772 | + | 0.527880i | −0.977210 | − | 0.212273i | \(-0.931913\pi\) |
0.672439 | + | 0.740153i | \(0.265247\pi\) | |||||||
\(62\) | 3.64324 | 0.462692 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.49250 | + | 4.31714i | −0.309157 | + | 0.535476i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.97772 | + | 8.62167i | 0.608126 | + | 1.05330i | 0.991549 | + | 0.129732i | \(0.0414117\pi\) |
−0.383423 | + | 0.923573i | \(0.625255\pi\) | |||||||
\(68\) | 7.05240 | 0.855229 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.11231 | + | 2.40058i | −0.132947 | + | 0.286924i | ||||
\(71\) | 7.26549 | 0.862255 | 0.431127 | − | 0.902291i | \(-0.358116\pi\) | ||||
0.431127 | + | 0.902291i | \(0.358116\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.392899 | + | 0.680521i | −0.0459854 | + | 0.0796490i | −0.888102 | − | 0.459647i | \(-0.847976\pi\) |
0.842117 | + | 0.539296i | \(0.181309\pi\) | |||||||
\(74\) | 5.74933 | 0.668346 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.51153 | + | 6.08215i | −0.402800 | + | 0.697671i | ||||
\(77\) | −4.33013 | + | 0.389446i | −0.493464 | + | 0.0443815i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.93134 | + | 5.07722i | −0.329801 | + | 0.571232i | −0.982472 | − | 0.186409i | \(-0.940315\pi\) |
0.652671 | + | 0.757641i | \(0.273648\pi\) | |||||||
\(80\) | −0.500000 | + | 0.866025i | −0.0559017 | + | 0.0968246i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.30588 | − | 7.45800i | −0.475504 | − | 0.823598i | ||||
\(83\) | −3.28544 | − | 5.69055i | −0.360624 | − | 0.624619i | 0.627440 | − | 0.778665i | \(-0.284103\pi\) |
−0.988064 | + | 0.154046i | \(0.950770\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.52620 | + | 6.10755i | −0.382470 | + | 0.662457i | ||||
\(86\) | −5.92389 | −0.638790 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.64324 | −0.175170 | ||||||||
\(89\) | −4.63848 | − | 8.03409i | −0.491678 | − | 0.851612i | 0.508276 | − | 0.861194i | \(-0.330283\pi\) |
−0.999954 | + | 0.00958252i | \(0.996950\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.54488 | + | 11.9669i | −0.581261 | + | 1.25447i | ||||
\(92\) | 3.72617 | + | 6.45392i | 0.388481 | + | 0.672868i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.820581 | + | 1.42129i | 0.0846365 | + | 0.146595i | ||||
\(95\) | −3.51153 | − | 6.08215i | −0.360276 | − | 0.624016i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.99028 | + | 5.17932i | 0.303617 | + | 0.525880i | 0.976953 | − | 0.213457i | \(-0.0684723\pi\) |
−0.673335 | + | 0.739337i | \(0.735139\pi\) | |||||||
\(98\) | −2.36213 | + | 6.58941i | −0.238611 | + | 0.665631i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 4.67998 | 0.465676 | 0.232838 | − | 0.972516i | \(-0.425199\pi\) | ||||
0.232838 | + | 0.972516i | \(0.425199\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.59496 | 0.551287 | 0.275644 | − | 0.961260i | \(-0.411109\pi\) | ||||
0.275644 | + | 0.961260i | \(0.411109\pi\) | |||||||
\(104\) | −2.49250 | + | 4.31714i | −0.244410 | + | 0.423331i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.46391 | − | 11.1958i | −0.627830 | − | 1.08743i | ||||
\(107\) | −3.83855 | − | 6.64856i | −0.371086 | − | 0.642740i | 0.618647 | − | 0.785669i | \(-0.287681\pi\) |
−0.989733 | + | 0.142929i | \(0.954348\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.68250 | − | 16.7706i | 0.927415 | − | 1.60633i | 0.139786 | − | 0.990182i | \(-0.455359\pi\) |
0.787630 | − | 0.616149i | \(-0.211308\pi\) | |||||||
\(110\) | 0.821620 | − | 1.42309i | 0.0783384 | − | 0.135686i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.11231 | + | 2.40058i | −0.105103 | + | 0.226833i | ||||
\(113\) | 0.830795 | − | 1.43898i | 0.0781546 | − | 0.135368i | −0.824299 | − | 0.566154i | \(-0.808431\pi\) |
0.902454 | + | 0.430787i | \(0.141764\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.45235 | −0.694935 | ||||||||
\(116\) | 2.86866 | − | 4.96867i | 0.266349 | − | 0.461329i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.782167 | −0.0720043 | ||||||||
\(119\) | −7.84446 | + | 16.9298i | −0.719100 | + | 1.55195i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.29976 | −0.754524 | ||||||||
\(122\) | −2.38034 | − | 4.12287i | −0.215506 | − | 0.373268i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.82162 | + | 3.15514i | −0.163586 | + | 0.283340i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.4680 | −1.46130 | −0.730649 | − | 0.682754i | \(-0.760782\pi\) | ||||
−0.730649 | + | 0.682754i | \(0.760782\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.49250 | − | 4.31714i | −0.218607 | − | 0.378639i | ||||
\(131\) | −13.6762 | −1.19489 | −0.597445 | − | 0.801910i | \(-0.703818\pi\) | ||||
−0.597445 | + | 0.801910i | \(0.703818\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.6948 | − | 15.1949i | −0.927353 | − | 1.31757i | ||||
\(134\) | −9.95545 | −0.860020 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.52620 | + | 6.10755i | −0.302369 | + | 0.523719i | ||||
\(137\) | −0.843533 | −0.0720679 | −0.0360340 | − | 0.999351i | \(-0.511472\pi\) | ||||
−0.0360340 | + | 0.999351i | \(0.511472\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.92189 | − | 5.06087i | 0.247832 | − | 0.429257i | −0.715092 | − | 0.699030i | \(-0.753615\pi\) |
0.962924 | + | 0.269773i | \(0.0869486\pi\) | |||||||
\(140\) | −1.52280 | − | 2.16358i | −0.128700 | − | 0.182856i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.63274 | + | 6.29210i | −0.304853 | + | 0.528021i | ||||
\(143\) | 4.09579 | − | 7.09411i | 0.342507 | − | 0.593239i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.86866 | + | 4.96867i | 0.238229 | + | 0.412625i | ||||
\(146\) | −0.392899 | − | 0.680521i | −0.0325166 | − | 0.0563203i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.87466 | + | 4.97906i | −0.236296 | + | 0.409276i | ||||
\(149\) | 13.6621 | 1.11924 | 0.559622 | − | 0.828748i | \(-0.310947\pi\) | ||||
0.559622 | + | 0.828748i | \(0.310947\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.578439 | −0.0470727 | −0.0235363 | − | 0.999723i | \(-0.507493\pi\) | ||||
−0.0235363 | + | 0.999723i | \(0.507493\pi\) | |||||||
\(152\) | −3.51153 | − | 6.08215i | −0.284823 | − | 0.493328i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.82779 | − | 3.94472i | 0.147288 | − | 0.317875i | ||||
\(155\) | −1.82162 | − | 3.15514i | −0.146316 | − | 0.253427i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.64913 | + | 2.85638i | 0.131615 | + | 0.227964i | 0.924299 | − | 0.381669i | \(-0.124650\pi\) |
−0.792684 | + | 0.609632i | \(0.791317\pi\) | |||||||
\(158\) | −2.93134 | − | 5.07722i | −0.233205 | − | 0.403922i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | −19.6378 | + | 1.76620i | −1.54768 | + | 0.139196i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.5863 | + | 20.0681i | 0.907510 | + | 1.57185i | 0.817512 | + | 0.575912i | \(0.195353\pi\) |
0.0899989 | + | 0.995942i | \(0.471314\pi\) | |||||||
\(164\) | 8.61175 | 0.672465 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.57089 | 0.510000 | ||||||||
\(167\) | 6.21246 | − | 10.7603i | 0.480734 | − | 0.832656i | −0.519021 | − | 0.854761i | \(-0.673704\pi\) |
0.999756 | + | 0.0221051i | \(0.00703684\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.92516 | − | 10.2627i | −0.455782 | − | 0.789437i | ||||
\(170\) | −3.52620 | − | 6.10755i | −0.270447 | − | 0.468428i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.96195 | − | 5.13024i | 0.225846 | − | 0.391177i | ||||
\(173\) | −6.32646 | + | 10.9577i | −0.480992 | + | 0.833102i | −0.999762 | − | 0.0218117i | \(-0.993057\pi\) |
0.518771 | + | 0.854914i | \(0.326390\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.63512 | − | 0.236999i | 0.199196 | − | 0.0179154i | ||||
\(176\) | 0.821620 | − | 1.42309i | 0.0619320 | − | 0.107269i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.27697 | 0.695338 | ||||||||
\(179\) | −4.33144 | + | 7.50227i | −0.323747 | + | 0.560746i | −0.981258 | − | 0.192699i | \(-0.938276\pi\) |
0.657511 | + | 0.753445i | \(0.271609\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.4358 | −0.775688 | −0.387844 | − | 0.921725i | \(-0.626780\pi\) | ||||
−0.387844 | + | 0.921725i | \(0.626780\pi\) | |||||||
\(182\) | −7.59119 | − | 10.7855i | −0.562697 | − | 0.799471i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.45235 | −0.549394 | ||||||||
\(185\) | −2.87466 | − | 4.97906i | −0.211349 | − | 0.366068i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.79439 | − | 10.0362i | 0.423728 | − | 0.733918i | ||||
\(188\) | −1.64116 | −0.119694 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.02306 | 0.509507 | ||||||||
\(191\) | −8.96784 | + | 15.5328i | −0.648890 | + | 1.12391i | 0.334498 | + | 0.942396i | \(0.391433\pi\) |
−0.983388 | + | 0.181515i | \(0.941900\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.08058 | − | 3.60367i | −0.149763 | − | 0.259398i | 0.781377 | − | 0.624060i | \(-0.214518\pi\) |
−0.931140 | + | 0.364662i | \(0.881185\pi\) | |||||||
\(194\) | −5.98057 | −0.429380 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.52553 | − | 5.34037i | −0.323252 | − | 0.381455i | ||||
\(197\) | 7.80338 | 0.555967 | 0.277984 | − | 0.960586i | \(-0.410334\pi\) | ||||
0.277984 | + | 0.960586i | \(0.410334\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.2477 | + | 21.2136i | −0.868214 | + | 1.50379i | −0.00439303 | + | 0.999990i | \(0.501398\pi\) |
−0.863821 | + | 0.503800i | \(0.831935\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.33999 | + | 4.05298i | −0.164641 | + | 0.285167i | ||||
\(203\) | 8.73682 | + | 12.4131i | 0.613205 | + | 0.871232i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.30588 | + | 7.45800i | −0.300735 | + | 0.520889i | ||||
\(206\) | −2.79748 | + | 4.84537i | −0.194910 | + | 0.337593i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.49250 | − | 4.31714i | −0.172824 | − | 0.299340i | ||||
\(209\) | 5.77029 | + | 9.99444i | 0.399139 | + | 0.691330i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.31753 | − | 9.21023i | 0.366074 | − | 0.634059i | −0.622874 | − | 0.782322i | \(-0.714035\pi\) |
0.988948 | + | 0.148264i | \(0.0473684\pi\) | |||||||
\(212\) | 12.9278 | 0.887886 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.67709 | 0.524795 | ||||||||
\(215\) | 2.96195 | + | 5.13024i | 0.202003 | + | 0.349879i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.54794 | − | 7.88243i | −0.376619 | − | 0.535094i | ||||
\(218\) | 9.68250 | + | 16.7706i | 0.655782 | + | 1.13585i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.821620 | + | 1.42309i | 0.0553936 | + | 0.0959446i | ||||
\(221\) | −17.5781 | − | 30.4462i | −1.18243 | − | 2.04803i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.8215 | + | 22.2074i | 0.858589 | + | 1.48712i | 0.873275 | + | 0.487228i | \(0.161992\pi\) |
−0.0146860 | + | 0.999892i | \(0.504675\pi\) | |||||||
\(224\) | −1.52280 | − | 2.16358i | −0.101747 | − | 0.144560i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.830795 | + | 1.43898i | 0.0552636 | + | 0.0957194i | ||||
\(227\) | 18.9946 | 1.26072 | 0.630358 | − | 0.776305i | \(-0.282908\pi\) | ||||
0.630358 | + | 0.776305i | \(0.282908\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.48895 | 0.296638 | 0.148319 | − | 0.988940i | \(-0.452614\pi\) | ||||
0.148319 | + | 0.988940i | \(0.452614\pi\) | |||||||
\(230\) | 3.72617 | − | 6.45392i | 0.245697 | − | 0.425559i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.86866 | + | 4.96867i | 0.188337 | + | 0.326209i | ||||
\(233\) | −2.86866 | − | 4.96867i | −0.187932 | − | 0.325508i | 0.756628 | − | 0.653845i | \(-0.226845\pi\) |
−0.944561 | + | 0.328337i | \(0.893512\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.820581 | − | 1.42129i | 0.0535288 | − | 0.0927147i | ||||
\(236\) | 0.391083 | − | 0.677376i | 0.0254574 | − | 0.0440934i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.7394 | − | 15.2584i | −0.696133 | − | 0.989056i | ||||
\(239\) | 13.7619 | − | 23.8363i | 0.890183 | − | 1.54184i | 0.0505270 | − | 0.998723i | \(-0.483910\pi\) |
0.839656 | − | 0.543119i | \(-0.182757\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.1967 | −1.30098 | −0.650492 | − | 0.759513i | \(-0.725437\pi\) | ||||
−0.650492 | + | 0.759513i | \(0.725437\pi\) | |||||||
\(242\) | 4.14988 | − | 7.18780i | 0.266764 | − | 0.462049i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.76069 | 0.304772 | ||||||||
\(245\) | 6.88766 | − | 1.24904i | 0.440037 | − | 0.0797981i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 35.0100 | 2.22764 | ||||||||
\(248\) | −1.82162 | − | 3.15514i | −0.115673 | − | 0.200352i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.500000 | + | 0.866025i | −0.0316228 | + | 0.0547723i | ||||
\(251\) | −24.3941 | −1.53974 | −0.769871 | − | 0.638200i | \(-0.779679\pi\) | ||||
−0.769871 | + | 0.638200i | \(0.779679\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.2460 | 0.769900 | ||||||||
\(254\) | 8.23399 | − | 14.2617i | 0.516647 | − | 0.894858i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 7.71485 | 0.481239 | 0.240620 | − | 0.970620i | \(-0.422649\pi\) | ||||
0.240620 | + | 0.970620i | \(0.422649\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.75510 | − | 12.4391i | −0.544015 | − | 0.772929i | ||||
\(260\) | 4.98501 | 0.309157 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.83808 | − | 11.8439i | 0.422458 | − | 0.731718i | ||||
\(263\) | 12.9732 | 0.799959 | 0.399979 | − | 0.916524i | \(-0.369017\pi\) | ||||
0.399979 | + | 0.916524i | \(0.369017\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.46391 | + | 11.1958i | −0.397075 | + | 0.687753i | ||||
\(266\) | 18.5066 | − | 1.66446i | 1.13471 | − | 0.102054i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.97772 | − | 8.62167i | 0.304063 | − | 0.526652i | ||||
\(269\) | −10.5195 | + | 18.2203i | −0.641384 | + | 1.11091i | 0.343741 | + | 0.939065i | \(0.388306\pi\) |
−0.985124 | + | 0.171844i | \(0.945027\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.04460 | − | 12.2016i | −0.427929 | − | 0.741195i | 0.568760 | − | 0.822503i | \(-0.307423\pi\) |
−0.996689 | + | 0.0813089i | \(0.974090\pi\) | |||||||
\(272\) | −3.52620 | − | 6.10755i | −0.213807 | − | 0.370325i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.421767 | − | 0.730521i | 0.0254799 | − | 0.0441324i | ||||
\(275\) | −1.64324 | −0.0990911 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.78303 | 0.407553 | 0.203776 | − | 0.979017i | \(-0.434678\pi\) | ||||
0.203776 | + | 0.979017i | \(0.434678\pi\) | |||||||
\(278\) | 2.92189 | + | 5.06087i | 0.175244 | + | 0.303531i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.63512 | − | 0.236999i | 0.157478 | − | 0.0141634i | ||||
\(281\) | −5.76128 | − | 9.97883i | −0.343689 | − | 0.595287i | 0.641426 | − | 0.767185i | \(-0.278343\pi\) |
−0.985115 | + | 0.171898i | \(0.945010\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.46998 | − | 4.27813i | −0.146825 | − | 0.254308i | 0.783227 | − | 0.621735i | \(-0.213572\pi\) |
−0.930052 | + | 0.367427i | \(0.880239\pi\) | |||||||
\(284\) | −3.63274 | − | 6.29210i | −0.215564 | − | 0.373367i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.09579 | + | 7.09411i | 0.242189 | + | 0.419483i | ||||
\(287\) | −9.57894 | + | 20.6732i | −0.565427 | + | 1.22030i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3682 | − | 28.3505i | −0.962832 | − | 1.66767i | ||||
\(290\) | −5.73732 | −0.336907 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.785798 | 0.0459854 | ||||||||
\(293\) | −1.17274 | + | 2.03124i | −0.0685121 | + | 0.118667i | −0.898247 | − | 0.439492i | \(-0.855159\pi\) |
0.829734 | + | 0.558158i | \(0.188492\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.391083 | + | 0.677376i | 0.0227698 | + | 0.0394384i | ||||
\(296\) | −2.87466 | − | 4.97906i | −0.167086 | − | 0.289402i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.83105 | + | 11.8317i | −0.395712 | + | 0.685394i | ||||
\(299\) | 18.5750 | − | 32.1729i | 1.07422 | − | 1.86061i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.02093 | + | 12.8168i | 0.519958 | + | 0.738748i | ||||
\(302\) | 0.289219 | − | 0.500943i | 0.0166427 | − | 0.0288260i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.02306 | 0.402800 | ||||||||
\(305\) | −2.38034 | + | 4.12287i | −0.136298 | + | 0.236075i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00934 | 0.228825 | 0.114412 | − | 0.993433i | \(-0.463501\pi\) | ||||
0.114412 | + | 0.993433i | \(0.463501\pi\) | |||||||
\(308\) | 2.50233 | + | 3.55528i | 0.142584 | + | 0.202581i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.64324 | 0.206922 | ||||||||
\(311\) | −8.97252 | − | 15.5409i | −0.508785 | − | 0.881242i | −0.999948 | − | 0.0101740i | \(-0.996761\pi\) |
0.491163 | − | 0.871068i | \(-0.336572\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.17015 | − | 5.49087i | 0.179188 | − | 0.310362i | −0.762415 | − | 0.647089i | \(-0.775986\pi\) |
0.941603 | + | 0.336726i | \(0.109320\pi\) | |||||||
\(314\) | −3.29826 | −0.186132 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.86267 | 0.329801 | ||||||||
\(317\) | 5.45724 | − | 9.45221i | 0.306509 | − | 0.530889i | −0.671087 | − | 0.741378i | \(-0.734172\pi\) |
0.977596 | + | 0.210489i | \(0.0675057\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.71390 | − | 8.16472i | −0.263928 | − | 0.457136i | ||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.28933 | − | 17.8899i | 0.461946 | − | 0.996967i | ||||
\(323\) | 49.5294 | 2.75589 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.49250 | + | 4.31714i | −0.138259 | + | 0.239472i | ||||
\(326\) | −23.1726 | −1.28341 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.30588 | + | 7.45800i | −0.237752 | + | 0.411799i | ||||
\(329\) | 1.82548 | − | 3.93974i | 0.100642 | − | 0.217205i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.1462 | + | 22.7699i | −0.722580 | + | 1.25154i | 0.237383 | + | 0.971416i | \(0.423710\pi\) |
−0.959962 | + | 0.280129i | \(0.909623\pi\) | |||||||
\(332\) | −3.28544 | + | 5.69055i | −0.180312 | + | 0.312310i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.21246 | + | 10.7603i | 0.339930 | + | 0.588777i | ||||
\(335\) | 4.97772 | + | 8.62167i | 0.271962 | + | 0.471052i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.15482 | + | 14.1246i | −0.444221 | + | 0.769414i | −0.997998 | − | 0.0632518i | \(-0.979853\pi\) |
0.553776 | + | 0.832665i | \(0.313186\pi\) | |||||||
\(338\) | 11.8503 | 0.644572 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.05240 | 0.382470 | ||||||||
\(341\) | 2.99336 | + | 5.18465i | 0.162100 | + | 0.280765i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8538 | − | 4.92373i | 0.964013 | − | 0.265856i | ||||
\(344\) | 2.96195 | + | 5.13024i | 0.159697 | + | 0.276604i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.32646 | − | 10.9577i | −0.340112 | − | 0.589092i | ||||
\(347\) | 3.85402 | + | 6.67535i | 0.206894 | + | 0.358352i | 0.950735 | − | 0.310006i | \(-0.100331\pi\) |
−0.743840 | + | 0.668357i | \(0.766998\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.9427 | + | 29.3456i | 0.906923 | + | 1.57084i | 0.818315 | + | 0.574770i | \(0.194908\pi\) |
0.0886077 | + | 0.996067i | \(0.471758\pi\) | |||||||
\(350\) | −1.11231 | + | 2.40058i | −0.0594555 | + | 0.128316i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.821620 | + | 1.42309i | 0.0437925 | + | 0.0758509i | ||||
\(353\) | −11.9883 | −0.638075 | −0.319038 | − | 0.947742i | \(-0.603360\pi\) | ||||
−0.319038 | + | 0.947742i | \(0.603360\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.26549 | 0.385612 | ||||||||
\(356\) | −4.63848 | + | 8.03409i | −0.245839 | + | 0.425806i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.33144 | − | 7.50227i | −0.228924 | − | 0.396507i | ||||
\(359\) | 6.92259 | + | 11.9903i | 0.365360 | + | 0.632823i | 0.988834 | − | 0.149022i | \(-0.0476125\pi\) |
−0.623474 | + | 0.781844i | \(0.714279\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.1617 | + | 26.2608i | −0.797985 | + | 1.38215i | ||||
\(362\) | 5.21791 | − | 9.03768i | 0.274247 | − | 0.475010i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13.1361 | − | 1.18144i | 0.688517 | − | 0.0619243i | ||||
\(365\) | −0.392899 | + | 0.680521i | −0.0205653 | + | 0.0356201i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.2848 | −0.902258 | −0.451129 | − | 0.892459i | \(-0.648979\pi\) | ||||
−0.451129 | + | 0.892459i | \(0.648979\pi\) | |||||||
\(368\) | 3.72617 | − | 6.45392i | 0.194240 | − | 0.336434i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.74933 | 0.298893 | ||||||||
\(371\) | −14.3797 | + | 31.0342i | −0.746559 | + | 1.61122i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.5426 | −0.804765 | −0.402383 | − | 0.915472i | \(-0.631818\pi\) | ||||
−0.402383 | + | 0.915472i | \(0.631818\pi\) | |||||||
\(374\) | 5.79439 | + | 10.0362i | 0.299621 | + | 0.518959i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.820581 | − | 1.42129i | 0.0423183 | − | 0.0732974i | ||||
\(377\) | −28.6006 | −1.47301 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.7020 | 1.11476 | 0.557379 | − | 0.830259i | \(-0.311807\pi\) | ||||
0.557379 | + | 0.830259i | \(0.311807\pi\) | |||||||
\(380\) | −3.51153 | + | 6.08215i | −0.180138 | + | 0.312008i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.96784 | − | 15.5328i | −0.458835 | − | 0.794725i | ||||
\(383\) | 25.4155 | 1.29867 | 0.649334 | − | 0.760503i | \(-0.275048\pi\) | ||||
0.649334 | + | 0.760503i | \(0.275048\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.33013 | + | 0.389446i | −0.220684 | + | 0.0198480i | ||||
\(386\) | 4.16116 | 0.211797 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.99028 | − | 5.17932i | 0.151809 | − | 0.262940i | ||||
\(389\) | 10.3954 | 0.527068 | 0.263534 | − | 0.964650i | \(-0.415112\pi\) | ||||
0.263534 | + | 0.964650i | \(0.415112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.2785 | − | 45.5156i | 1.32896 | − | 2.30182i | ||||
\(392\) | 6.88766 | − | 1.24904i | 0.347880 | − | 0.0630859i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.90169 | + | 6.75792i | −0.196564 | + | 0.340459i | ||||
\(395\) | −2.93134 | + | 5.07722i | −0.147492 | + | 0.255463i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.36768 | + | 2.36890i | 0.0686421 | + | 0.118892i | 0.898304 | − | 0.439375i | \(-0.144800\pi\) |
−0.829662 | + | 0.558266i | \(0.811467\pi\) | |||||||
\(398\) | −12.2477 | − | 21.2136i | −0.613920 | − | 1.06334i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | 0.0354191 | 0.00176874 | 0.000884372 | − | 1.00000i | \(-0.499718\pi\) | ||||
0.000884372 | 1.00000i | \(0.499718\pi\) | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.1616 | 0.904693 | ||||||||
\(404\) | −2.33999 | − | 4.05298i | −0.116419 | − | 0.201644i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.1185 | + | 1.35974i | −0.750319 | + | 0.0674827i | ||||
\(407\) | 4.72376 | + | 8.18180i | 0.234148 | + | 0.405557i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.17292 | − | 14.1559i | −0.404125 | − | 0.699965i | 0.590094 | − | 0.807334i | \(-0.299091\pi\) |
−0.994219 | + | 0.107369i | \(0.965757\pi\) | |||||||
\(410\) | −4.30588 | − | 7.45800i | −0.212652 | − | 0.368324i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.79748 | − | 4.84537i | −0.137822 | − | 0.238714i | ||||
\(413\) | 1.19109 | + | 1.69228i | 0.0586096 | + | 0.0832716i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.28544 | − | 5.69055i | −0.161276 | − | 0.279338i | ||||
\(416\) | 4.98501 | 0.244410 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.5406 | −0.564468 | ||||||||
\(419\) | 4.00800 | − | 6.94206i | 0.195804 | − | 0.339142i | −0.751360 | − | 0.659892i | \(-0.770602\pi\) |
0.947164 | + | 0.320751i | \(0.103935\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.7469 | + | 29.0066i | 0.816196 | + | 1.41369i | 0.908466 | + | 0.417959i | \(0.137255\pi\) |
−0.0922696 | + | 0.995734i | \(0.529412\pi\) | |||||||
\(422\) | 5.31753 | + | 9.21023i | 0.258853 | + | 0.448347i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.46391 | + | 11.1958i | −0.313915 | + | 0.543717i | ||||
\(425\) | −3.52620 | + | 6.10755i | −0.171046 | + | 0.296260i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.29536 | + | 11.4284i | −0.256260 | + | 0.553058i | ||||
\(428\) | −3.83855 | + | 6.64856i | −0.185543 | + | 0.321370i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.92389 | −0.285675 | ||||||||
\(431\) | 12.2779 | − | 21.2660i | 0.591406 | − | 1.02434i | −0.402638 | − | 0.915360i | \(-0.631906\pi\) |
0.994043 | − | 0.108985i | \(-0.0347602\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.8917 | 1.24428 | 0.622138 | − | 0.782907i | \(-0.286264\pi\) | ||||
0.622138 | + | 0.782907i | \(0.286264\pi\) | |||||||
\(434\) | 9.60036 | − | 0.863443i | 0.460832 | − | 0.0414466i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −19.3650 | −0.927415 | ||||||||
\(437\) | 26.1692 | + | 45.3263i | 1.25184 | + | 2.16825i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.01813 | − | 10.4237i | 0.287230 | − | 0.497497i | −0.685918 | − | 0.727679i | \(-0.740599\pi\) |
0.973147 | + | 0.230182i | \(0.0739323\pi\) | |||||||
\(440\) | −1.64324 | −0.0783384 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 35.1563 | 1.67221 | ||||||||
\(443\) | 1.00770 | − | 1.74539i | 0.0478773 | − | 0.0829259i | −0.841094 | − | 0.540890i | \(-0.818088\pi\) |
0.888971 | + | 0.457964i | \(0.151421\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.63848 | − | 8.03409i | −0.219885 | − | 0.380852i | ||||
\(446\) | −25.6429 | −1.21423 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.63512 | − | 0.236999i | 0.124497 | − | 0.0111971i | ||||
\(449\) | 0.742369 | 0.0350346 | 0.0175173 | − | 0.999847i | \(-0.494424\pi\) | ||||
0.0175173 | + | 0.999847i | \(0.494424\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.07559 | − | 12.2553i | 0.333177 | − | 0.577079i | ||||
\(452\) | −1.66159 | −0.0781546 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.49730 | + | 16.4498i | −0.445730 | + | 0.772027i | ||||
\(455\) | −5.54488 | + | 11.9669i | −0.259948 | + | 0.561017i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.61374 | − | 9.72328i | 0.262600 | − | 0.454836i | −0.704332 | − | 0.709870i | \(-0.748754\pi\) |
0.966932 | + | 0.255035i | \(0.0820869\pi\) | |||||||
\(458\) | −2.24447 | + | 3.88754i | −0.104877 | + | 0.181653i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.72617 | + | 6.45392i | 0.173734 | + | 0.300916i | ||||
\(461\) | −9.12633 | − | 15.8073i | −0.425056 | − | 0.736218i | 0.571370 | − | 0.820693i | \(-0.306412\pi\) |
−0.996426 | + | 0.0844747i | \(0.973079\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.5347 | − | 25.1748i | 0.675484 | − | 1.16997i | −0.300843 | − | 0.953674i | \(-0.597268\pi\) |
0.976327 | − | 0.216299i | \(-0.0693985\pi\) | |||||||
\(464\) | −5.73732 | −0.266349 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.73732 | 0.265776 | ||||||||
\(467\) | 3.65873 | + | 6.33711i | 0.169306 | + | 0.293246i | 0.938176 | − | 0.346159i | \(-0.112514\pi\) |
−0.768870 | + | 0.639405i | \(0.779181\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.1602 | + | 21.5394i | 0.700033 | + | 0.994596i | ||||
\(470\) | 0.820581 | + | 1.42129i | 0.0378506 | + | 0.0655592i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.391083 | + | 0.677376i | 0.0180011 | + | 0.0311788i | ||||
\(473\) | −4.86719 | − | 8.43022i | −0.223794 | − | 0.387622i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.51153 | − | 6.08215i | −0.161120 | − | 0.279068i | ||||
\(476\) | 18.5839 | − | 1.67141i | 0.851791 | − | 0.0766089i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13.7619 | + | 23.8363i | 0.629454 | + | 1.09025i | ||||
\(479\) | −6.17671 | −0.282221 | −0.141110 | − | 0.989994i | \(-0.545067\pi\) | ||||
−0.141110 | + | 0.989994i | \(0.545067\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.6604 | 1.30680 | ||||||||
\(482\) | 10.0984 | − | 17.4909i | 0.459967 | − | 0.796687i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.14988 | + | 7.18780i | 0.188631 | + | 0.326718i | ||||
\(485\) | 2.99028 | + | 5.17932i | 0.135782 | + | 0.235181i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.11014 | − | 5.38693i | 0.140934 | − | 0.244105i | −0.786915 | − | 0.617062i | \(-0.788323\pi\) |
0.927849 | + | 0.372957i | \(0.121656\pi\) | |||||||
\(488\) | −2.38034 | + | 4.12287i | −0.107753 | + | 0.186634i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.36213 | + | 6.58941i | −0.106710 | + | 0.297679i | ||||
\(491\) | 3.94447 | − | 6.83202i | 0.178011 | − | 0.308325i | −0.763188 | − | 0.646177i | \(-0.776367\pi\) |
0.941199 | + | 0.337852i | \(0.109700\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −40.4619 | −1.82231 | ||||||||
\(494\) | −17.5050 | + | 30.3196i | −0.787588 | + | 1.36414i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.64324 | 0.163586 | ||||||||
\(497\) | 19.1454 | − | 1.72191i | 0.858789 | − | 0.0772383i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.68946 | 0.388994 | 0.194497 | − | 0.980903i | \(-0.437693\pi\) | ||||
0.194497 | + | 0.980903i | \(0.437693\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.1970 | − | 21.1259i | 0.544381 | − | 0.942895i | ||||
\(503\) | −23.0236 | −1.02657 | −0.513285 | − | 0.858218i | \(-0.671572\pi\) | ||||
−0.513285 | + | 0.858218i | \(0.671572\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.67998 | 0.208257 | ||||||||
\(506\) | −6.12300 | + | 10.6054i | −0.272201 | + | 0.471465i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.23399 | + | 14.2617i | 0.365324 | + | 0.632760i | ||||
\(509\) | −16.5940 | −0.735514 | −0.367757 | − | 0.929922i | \(-0.619874\pi\) | ||||
−0.367757 | + | 0.929922i | \(0.619874\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.874052 | + | 1.88637i | −0.0386658 | + | 0.0834480i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.85742 | + | 6.68125i | −0.170144 | + | 0.294698i | ||||
\(515\) | 5.59496 | 0.246543 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.34841 | + | 2.33552i | −0.0593031 | + | 0.102716i | ||||
\(518\) | 15.1501 | − | 1.36258i | 0.665659 | − | 0.0598685i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.49250 | + | 4.31714i | −0.109304 | + | 0.189319i | ||||
\(521\) | 0.696803 | − | 1.20690i | 0.0305275 | − | 0.0528751i | −0.850358 | − | 0.526205i | \(-0.823615\pi\) |
0.880886 | + | 0.473329i | \(0.156948\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.36346 | − | 12.7539i | −0.321982 | − | 0.557689i | 0.658915 | − | 0.752217i | \(-0.271016\pi\) |
−0.980897 | + | 0.194529i | \(0.937682\pi\) | |||||||
\(524\) | 6.83808 | + | 11.8439i | 0.298723 | + | 0.517403i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.48658 | + | 11.2351i | −0.282828 | + | 0.489873i | ||||
\(527\) | 25.6936 | 1.11923 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32.5375 | 1.41467 | ||||||||
\(530\) | −6.46391 | − | 11.1958i | −0.280774 | − | 0.486315i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.81183 | + | 16.8594i | −0.338686 | + | 0.730948i | ||||
\(533\) | −21.4648 | − | 37.1782i | −0.929745 | − | 1.61037i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.83855 | − | 6.64856i | −0.165955 | − | 0.287442i | ||||
\(536\) | 4.97772 | + | 8.62167i | 0.215005 | + | 0.372399i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.5195 | − | 18.2203i | −0.453527 | − | 0.785531i | ||||
\(539\) | −11.3181 | + | 2.05247i | −0.487505 | + | 0.0884061i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5237 | + | 21.6917i | 0.538437 | + | 0.932601i | 0.998988 | + | 0.0449675i | \(0.0143184\pi\) |
−0.460551 | + | 0.887633i | \(0.652348\pi\) | |||||||
\(542\) | 14.0892 | 0.605183 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.05240 | 0.302369 | ||||||||
\(545\) | 9.68250 | − | 16.7706i | 0.414753 | − | 0.718373i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.32171 | + | 9.21747i | 0.227540 | + | 0.394110i | 0.957078 | − | 0.289829i | \(-0.0935985\pi\) |
−0.729539 | + | 0.683940i | \(0.760265\pi\) | |||||||
\(548\) | 0.421767 | + | 0.730521i | 0.0180170 | + | 0.0312063i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.821620 | − | 1.42309i | 0.0350340 | − | 0.0606807i | ||||
\(551\) | 20.1468 | − | 34.8953i | 0.858282 | − | 1.48659i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.52111 | + | 14.0738i | −0.277306 | + | 0.598478i | ||||
\(554\) | −3.39152 | + | 5.87428i | −0.144092 | + | 0.249574i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.84379 | −0.247832 | ||||||||
\(557\) | 21.3732 | − | 37.0195i | 0.905613 | − | 1.56857i | 0.0855219 | − | 0.996336i | \(-0.472744\pi\) |
0.820092 | − | 0.572232i | \(-0.193922\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.5306 | −1.24901 | ||||||||
\(560\) | −1.11231 | + | 2.40058i | −0.0470037 | + | 0.101443i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.5226 | 0.486050 | ||||||||
\(563\) | −6.57437 | − | 11.3872i | −0.277077 | − | 0.479911i | 0.693580 | − | 0.720379i | \(-0.256032\pi\) |
−0.970657 | + | 0.240468i | \(0.922699\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.830795 | − | 1.43898i | 0.0349518 | − | 0.0605383i | ||||
\(566\) | 4.93996 | 0.207642 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.26549 | 0.304853 | ||||||||
\(569\) | −1.17495 | + | 2.03507i | −0.0492563 | + | 0.0853144i | −0.889602 | − | 0.456736i | \(-0.849018\pi\) |
0.840346 | + | 0.542050i | \(0.182352\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.30646 | + | 12.6552i | 0.305766 | + | 0.529602i | 0.977432 | − | 0.211252i | \(-0.0677541\pi\) |
−0.671666 | + | 0.740854i | \(0.734421\pi\) | |||||||
\(572\) | −8.19157 | −0.342507 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −13.1140 | − | 18.6322i | −0.547368 | − | 0.777693i | ||||
\(575\) | −7.45235 | −0.310784 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.53371 | − | 7.85261i | 0.188741 | − | 0.326909i | −0.756090 | − | 0.654468i | \(-0.772893\pi\) |
0.944831 | + | 0.327559i | \(0.106226\pi\) | |||||||
\(578\) | 32.7363 | 1.36165 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.86866 | − | 4.96867i | 0.119115 | − | 0.206313i | ||||
\(581\) | −10.0062 | − | 14.2166i | −0.415126 | − | 0.589805i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.6218 | − | 18.3974i | 0.439908 | − | 0.761943i | ||||
\(584\) | −0.392899 | + | 0.680521i | −0.0162583 | + | 0.0281602i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.17274 | − | 2.03124i | −0.0484454 | − | 0.0839099i | ||||
\(587\) | 19.8453 | + | 34.3730i | 0.819103 | + | 1.41873i | 0.906344 | + | 0.422540i | \(0.138861\pi\) |
−0.0872417 | + | 0.996187i | \(0.527805\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.7934 | + | 22.1587i | −0.527141 | + | 0.913035i | ||||
\(590\) | −0.782167 | −0.0322013 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.74933 | 0.236296 | ||||||||
\(593\) | −17.8017 | − | 30.8334i | −0.731028 | − | 1.26618i | −0.956444 | − | 0.291915i | \(-0.905708\pi\) |
0.225416 | − | 0.974263i | \(-0.427626\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.84446 | + | 16.9298i | −0.321591 | + | 0.694055i | ||||
\(596\) | −6.83105 | − | 11.8317i | −0.279811 | − | 0.484646i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 18.5750 | + | 32.1729i | 0.759589 | + | 1.31565i | ||||
\(599\) | 1.11211 | + | 1.92624i | 0.0454398 | + | 0.0787040i | 0.887851 | − | 0.460132i | \(-0.152198\pi\) |
−0.842411 | + | 0.538836i | \(0.818864\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.28720 | + | 3.96154i | 0.0932967 | + | 0.161595i | 0.908896 | − | 0.417022i | \(-0.136926\pi\) |
−0.815600 | + | 0.578616i | \(0.803593\pi\) | |||||||
\(602\) | −15.6101 | + | 1.40395i | −0.636222 | + | 0.0572209i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.289219 | + | 0.500943i | 0.0117682 | + | 0.0203831i | ||||
\(605\) | −8.29976 | −0.337433 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.2757 | 1.22885 | 0.614427 | − | 0.788974i | \(-0.289387\pi\) | ||||
0.614427 | + | 0.788974i | \(0.289387\pi\) | |||||||
\(608\) | −3.51153 | + | 6.08215i | −0.142411 | + | 0.246664i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.38034 | − | 4.12287i | −0.0963773 | − | 0.166930i | ||||
\(611\) | 4.09061 | + | 7.08514i | 0.165488 | + | 0.286634i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.43790 | + | 4.22257i | −0.0984660 | + | 0.170548i | −0.911050 | − | 0.412296i | \(-0.864727\pi\) |
0.812584 | + | 0.582844i | \(0.198060\pi\) | |||||||
\(614\) | −2.00467 | + | 3.47219i | −0.0809018 | + | 0.140126i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.33013 | + | 0.389446i | −0.174466 | + | 0.0156912i | ||||
\(617\) | −12.4725 | + | 21.6030i | −0.502125 | + | 0.869705i | 0.497872 | + | 0.867250i | \(0.334115\pi\) |
−0.999997 | + | 0.00245498i | \(0.999219\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.0943 | 1.49094 | 0.745472 | − | 0.666537i | \(-0.232224\pi\) | ||||
0.745472 | + | 0.666537i | \(0.232224\pi\) | |||||||
\(620\) | −1.82162 | + | 3.15514i | −0.0731580 | + | 0.126713i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.9450 | 0.719531 | ||||||||
\(623\) | −14.1270 | − | 20.0714i | −0.565987 | − | 0.804145i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 3.17015 | + | 5.49087i | 0.126705 | + | 0.219459i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.64913 | − | 2.85638i | 0.0658075 | − | 0.113982i | ||||
\(629\) | 40.5465 | 1.61670 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.4560 | −0.854152 | −0.427076 | − | 0.904216i | \(-0.640456\pi\) | ||||
−0.427076 | + | 0.904216i | \(0.640456\pi\) | |||||||
\(632\) | −2.93134 | + | 5.07722i | −0.116602 | + | 0.201961i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.45724 | + | 9.45221i | 0.216735 | + | 0.375395i | ||||
\(635\) | −16.4680 | −0.653512 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.7753 | + | 32.8483i | −0.466553 | + | 1.30150i | ||||
\(638\) | 9.42780 | 0.373250 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | 42.7642 | 1.68908 | 0.844542 | − | 0.535490i | \(-0.179873\pi\) | ||||
0.844542 | + | 0.535490i | \(0.179873\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.01808 | + | 15.6198i | −0.355638 | + | 0.615983i | −0.987227 | − | 0.159320i | \(-0.949070\pi\) |
0.631589 | + | 0.775304i | \(0.282403\pi\) | |||||||
\(644\) | 11.3485 | + | 16.1237i | 0.447192 | + | 0.635364i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −24.7647 | + | 42.8937i | −0.974355 | + | 1.68763i | ||||
\(647\) | −13.8584 | + | 24.0035i | −0.544831 | + | 0.943676i | 0.453786 | + | 0.891111i | \(0.350073\pi\) |
−0.998618 | + | 0.0525650i | \(0.983260\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.642644 | − | 1.11309i | −0.0252260 | − | 0.0436927i | ||||
\(650\) | −2.49250 | − | 4.31714i | −0.0977641 | − | 0.169332i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.5863 | − | 20.0681i | 0.453755 | − | 0.785927i | ||||
\(653\) | 11.6085 | 0.454276 | 0.227138 | − | 0.973863i | \(-0.427063\pi\) | ||||
0.227138 | + | 0.973863i | \(0.427063\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.6762 | −0.534371 | ||||||||
\(656\) | −4.30588 | − | 7.45800i | −0.168116 | − | 0.291186i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.49917 | + | 3.55078i | 0.0974278 | + | 0.138424i | ||||
\(659\) | 2.05194 | + | 3.55407i | 0.0799324 | + | 0.138447i | 0.903221 | − | 0.429177i | \(-0.141196\pi\) |
−0.823288 | + | 0.567624i | \(0.807863\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.05561 | − | 13.9527i | −0.313327 | − | 0.542698i | 0.665753 | − | 0.746172i | \(-0.268110\pi\) |
−0.979080 | + | 0.203474i | \(0.934777\pi\) | |||||||
\(662\) | −13.1462 | − | 22.7699i | −0.510941 | − | 0.884976i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.28544 | − | 5.69055i | −0.127500 | − | 0.220836i | ||||
\(665\) | −10.6948 | − | 15.1949i | −0.414725 | − | 0.589234i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.3783 | − | 37.0282i | −0.827770 | − | 1.43374i | ||||
\(668\) | −12.4249 | −0.480734 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −9.95545 | −0.384613 | ||||||||
\(671\) | 3.91148 | − | 6.77488i | 0.151001 | − | 0.261541i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.0611 | + | 31.2827i | 0.696203 | + | 1.20586i | 0.969774 | + | 0.244007i | \(0.0784619\pi\) |
−0.273571 | + | 0.961852i | \(0.588205\pi\) | |||||||
\(674\) | −8.15482 | − | 14.1246i | −0.314112 | − | 0.544058i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.92516 | + | 10.2627i | −0.227891 | + | 0.394718i | ||||
\(677\) | 0.0268412 | − | 0.0464903i | 0.00103159 | − | 0.00178677i | −0.865509 | − | 0.500893i | \(-0.833005\pi\) |
0.866541 | + | 0.499106i | \(0.166338\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.10723 | + | 12.9394i | 0.349503 | + | 0.496569i | ||||
\(680\) | −3.52620 | + | 6.10755i | −0.135224 | + | 0.234214i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.98672 | −0.229243 | ||||||||
\(683\) | 7.74990 | − | 13.4232i | 0.296542 | − | 0.513625i | −0.678801 | − | 0.734323i | \(-0.737500\pi\) |
0.975342 | + | 0.220697i | \(0.0708333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.843533 | −0.0322298 | ||||||||
\(686\) | −4.66281 | + | 17.9237i | −0.178027 | + | 0.684329i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.92389 | −0.225846 | ||||||||
\(689\) | −32.2226 | − | 55.8112i | −1.22758 | − | 2.12624i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.3801 | + | 28.3712i | −0.623129 | + | 1.07929i | 0.365770 | + | 0.930705i | \(0.380806\pi\) |
−0.988899 | + | 0.148586i | \(0.952528\pi\) | |||||||
\(692\) | 12.6529 | 0.480992 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.70803 | −0.292593 | ||||||||
\(695\) | 2.92189 | − | 5.06087i | 0.110834 | − | 0.191970i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.3667 | − | 52.5967i | −1.15022 | − | 1.99224i | ||||
\(698\) | −33.8854 | −1.28258 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.52280 | − | 2.16358i | −0.0575566 | − | 0.0817755i | ||||
\(701\) | 20.2343 | 0.764237 | 0.382119 | − | 0.924113i | \(-0.375195\pi\) | ||||
0.382119 | + | 0.924113i | \(0.375195\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.1889 | + | 34.9683i | −0.761440 | + | 1.31885i | ||||
\(704\) | −1.64324 | −0.0619320 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.99417 | − | 10.3822i | 0.225594 | − | 0.390740i | ||||
\(707\) | 12.3323 | − | 1.10915i | 0.463804 | − | 0.0417139i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.7836 | − | 22.1418i | 0.480097 | − | 0.831553i | −0.519642 | − | 0.854384i | \(-0.673935\pi\) |
0.999739 | + | 0.0228313i | \(0.00726807\pi\) | |||||||
\(710\) | −3.63274 | + | 6.29210i | −0.136334 | + | 0.236138i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.63848 | − | 8.03409i | −0.173835 | − | 0.301090i | ||||
\(713\) | 13.5754 | + | 23.5132i | 0.508401 | + | 0.880576i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.09579 | − | 7.09411i | 0.153174 | − | 0.265305i | ||||
\(716\) | 8.66287 | 0.323747 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −13.8452 | −0.516697 | ||||||||
\(719\) | −10.0236 | − | 17.3614i | −0.373818 | − | 0.647472i | 0.616331 | − | 0.787487i | \(-0.288618\pi\) |
−0.990149 | + | 0.140015i | \(0.955285\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.7434 | − | 1.32600i | 0.549071 | − | 0.0493827i | ||||
\(722\) | −15.1617 | − | 26.2608i | −0.564260 | − | 0.977328i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.21791 | + | 9.03768i | 0.193922 | + | 0.335883i | ||||
\(725\) | 2.86866 | + | 4.96867i | 0.106539 | + | 0.184532i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.67928 | + | 9.83680i | 0.210633 | + | 0.364827i | 0.951913 | − | 0.306369i | \(-0.0991142\pi\) |
−0.741280 | + | 0.671196i | \(0.765781\pi\) | |||||||
\(728\) | −5.54488 | + | 11.9669i | −0.205507 | + | 0.443523i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.392899 | − | 0.680521i | −0.0145418 | − | 0.0251872i | ||||
\(731\) | −41.7776 | −1.54520 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.3366 | −1.23131 | −0.615657 | − | 0.788014i | \(-0.711109\pi\) | ||||
−0.615657 | + | 0.788014i | \(0.711109\pi\) | |||||||
\(734\) | 8.64239 | − | 14.9691i | 0.318997 | − | 0.552518i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.72617 | + | 6.45392i | 0.137349 | + | 0.237895i | ||||
\(737\) | −8.17960 | − | 14.1675i | −0.301299 | − | 0.521866i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.5958 | − | 35.6730i | 0.757630 | − | 1.31225i | −0.186427 | − | 0.982469i | \(-0.559691\pi\) |
0.944056 | − | 0.329784i | \(-0.106976\pi\) | |||||||
\(740\) | −2.87466 | + | 4.97906i | −0.105675 | + | 0.183034i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −19.6865 | − | 27.9703i | −0.722715 | − | 1.02682i | ||||
\(743\) | 12.2773 | − | 21.2649i | 0.450410 | − | 0.780133i | −0.548001 | − | 0.836478i | \(-0.684611\pi\) |
0.998411 | + | 0.0563442i | \(0.0179444\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.6621 | 0.500541 | ||||||||
\(746\) | 7.77130 | − | 13.4603i | 0.284528 | − | 0.492816i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11.5888 | −0.423728 | ||||||||
\(749\) | −11.6907 | − | 16.6100i | −0.427169 | − | 0.606916i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.3239 | −0.449706 | −0.224853 | − | 0.974393i | \(-0.572190\pi\) | ||||
−0.224853 | + | 0.974393i | \(0.572190\pi\) | |||||||
\(752\) | 0.820581 | + | 1.42129i | 0.0299235 | + | 0.0518291i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14.3003 | − | 24.7689i | 0.520786 | − | 0.902028i | ||||
\(755\) | −0.578439 | −0.0210515 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.4874 | −0.599245 | −0.299622 | − | 0.954058i | \(-0.596861\pi\) | ||||
−0.299622 | + | 0.954058i | \(0.596861\pi\) | |||||||
\(758\) | −10.8510 | + | 18.7945i | −0.394126 | + | 0.682646i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.51153 | − | 6.08215i | −0.127377 | − | 0.220623i | ||||
\(761\) | −40.0477 | −1.45173 | −0.725864 | − | 0.687838i | \(-0.758560\pi\) | ||||
−0.725864 | + | 0.687838i | \(0.758560\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.5399 | − | 46.4872i | 0.779797 | − | 1.68295i | ||||
\(764\) | 17.9357 | 0.648890 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.7077 | + | 22.0104i | −0.459149 | + | 0.795269i | ||||
\(767\) | −3.89911 | −0.140789 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.91652 | + | 6.78361i | −0.141233 | + | 0.244623i | −0.927961 | − | 0.372677i | \(-0.878440\pi\) |
0.786728 | + | 0.617300i | \(0.211773\pi\) | |||||||
\(770\) | 1.82779 | − | 3.94472i | 0.0658691 | − | 0.142158i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.08058 | + | 3.60367i | −0.0748817 | + | 0.129699i | ||||
\(773\) | −16.2391 | + | 28.1269i | −0.584079 | + | 1.01165i | 0.410911 | + | 0.911676i | \(0.365211\pi\) |
−0.994990 | + | 0.0999786i | \(0.968123\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.82162 | − | 3.15514i | −0.0654345 | − | 0.113336i | ||||
\(776\) | 2.99028 | + | 5.17932i | 0.107345 | + | 0.185927i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.19770 | + | 9.00269i | −0.186347 | + | 0.322762i | ||||
\(779\) | 60.4809 | 2.16695 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.9389 | −0.427209 | ||||||||
\(782\) | 26.2785 | + | 45.5156i | 0.939716 | + | 1.62764i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.36213 | + | 6.58941i | −0.0843619 | + | 0.235336i | ||||
\(785\) | 1.64913 | + | 2.85638i | 0.0588600 | + | 0.101949i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.78696 | − | 15.2195i | −0.313221 | − | 0.542515i | 0.665837 | − | 0.746098i | \(-0.268075\pi\) |
−0.979058 | + | 0.203583i | \(0.934741\pi\) | |||||||
\(788\) | −3.90169 | − | 6.75792i | −0.138992 | − | 0.240741i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.93134 | − | 5.07722i | −0.104292 | − | 0.180640i | ||||
\(791\) | 1.84820 | − | 3.98877i | 0.0657145 | − | 0.141824i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.8660 | − | 20.5526i | −0.421375 | − | 0.729843i | ||||
\(794\) | −2.73537 | −0.0970745 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.4953 | 0.868214 | ||||||||
\(797\) | −27.9349 | + | 48.3847i | −0.989506 | + | 1.71388i | −0.369623 | + | 0.929182i | \(0.620513\pi\) |
−0.619884 | + | 0.784694i | \(0.712820\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.78707 | + | 10.0235i | 0.204732 | + | 0.354606i | ||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.0177095 | + | 0.0306738i | −0.000625345 | + | 0.00108313i | ||||
\(803\) | 0.645628 | − | 1.11826i | 0.0227837 | − | 0.0394625i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.6378 | + | 1.76620i | −0.692141 | + | 0.0622503i | ||||
\(806\) | −9.08079 | + | 15.7284i | −0.319857 | + | 0.554009i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.67998 | 0.164641 | ||||||||
\(809\) | −17.3337 | + | 30.0228i | −0.609420 | + | 1.05555i | 0.381917 | + | 0.924197i | \(0.375264\pi\) |
−0.991336 | + | 0.131349i | \(0.958069\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.8549 | 1.15369 | 0.576845 | − | 0.816854i | \(-0.304284\pi\) | ||||
0.576845 | + | 0.816854i | \(0.304284\pi\) | |||||||
\(812\) | 6.38169 | − | 13.7729i | 0.223953 | − | 0.483333i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.44753 | −0.331136 | ||||||||
\(815\) | 11.5863 | + | 20.0681i | 0.405851 | + | 0.702955i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.8019 | − | 36.0300i | 0.727767 | − | 1.26053i | ||||
\(818\) | 16.3458 | 0.571519 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.61175 | 0.300735 | ||||||||
\(821\) | −6.81852 | + | 11.8100i | −0.237968 | + | 0.412173i | −0.960131 | − | 0.279550i | \(-0.909815\pi\) |
0.722163 | + | 0.691723i | \(0.243148\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.04275 | + | 1.80609i | 0.0363478 | + | 0.0629563i | 0.883627 | − | 0.468191i | \(-0.155094\pi\) |
−0.847279 | + | 0.531148i | \(0.821761\pi\) | |||||||
\(824\) | 5.59496 | 0.194910 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.06110 | + | 0.185373i | −0.0717148 | + | 0.00644993i | ||||
\(827\) | 4.20031 | 0.146059 | 0.0730295 | − | 0.997330i | \(-0.476733\pi\) | ||||
0.0730295 | + | 0.997330i | \(0.476733\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.2645 | − | 22.9747i | 0.460694 | − | 0.797945i | −0.538302 | − | 0.842752i | \(-0.680934\pi\) |
0.998996 | + | 0.0448071i | \(0.0142673\pi\) | |||||||
\(830\) | 6.57089 | 0.228079 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.49250 | + | 4.31714i | −0.0864121 | + | 0.149670i | ||||
\(833\) | −16.6587 | + | 46.4711i | −0.577190 | + | 1.61013i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.21246 | − | 10.7603i | 0.214991 | − | 0.372375i | ||||
\(836\) | 5.77029 | − | 9.99444i | 0.199570 | − | 0.345665i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.00800 | + | 6.94206i | 0.138454 | + | 0.239810i | ||||
\(839\) | −2.18181 | − | 3.77901i | −0.0753244 | − | 0.130466i | 0.825903 | − | 0.563812i | \(-0.190666\pi\) |
−0.901227 | + | 0.433347i | \(0.857333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.95844 | + | 3.39211i | −0.0675323 | + | 0.116969i | ||||
\(842\) | −33.4939 | −1.15428 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.6351 | −0.366074 | ||||||||
\(845\) | −5.92516 | − | 10.2627i | −0.203832 | − | 0.353047i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.8708 | + | 1.96703i | −0.751490 | + | 0.0675880i | ||||
\(848\) | −6.46391 | − | 11.1958i | −0.221971 | − | 0.384466i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.52620 | − | 6.10755i | −0.120948 | − | 0.209487i | ||||
\(851\) | 21.4230 | + | 37.1057i | 0.734371 | + | 1.27197i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.9693 | − | 24.1956i | −0.478300 | − | 0.828440i | 0.521390 | − | 0.853318i | \(-0.325414\pi\) |
−0.999690 | + | 0.0248783i | \(0.992080\pi\) | |||||||
\(854\) | −7.24959 | − | 10.3001i | −0.248076 | − | 0.352463i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.83855 | − | 6.64856i | −0.131199 | − | 0.227243i | ||||
\(857\) | 4.53888 | 0.155045 | 0.0775225 | − | 0.996991i | \(-0.475299\pi\) | ||||
0.0775225 | + | 0.996991i | \(0.475299\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.6827 | −0.500968 | −0.250484 | − | 0.968121i | \(-0.580590\pi\) | ||||
−0.250484 | + | 0.968121i | \(0.580590\pi\) | |||||||
\(860\) | 2.96195 | − | 5.13024i | 0.101001 | − | 0.174940i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.2779 | + | 21.2660i | 0.418187 | + | 0.724321i | ||||
\(863\) | −14.6627 | − | 25.3966i | −0.499125 | − | 0.864510i | 0.500874 | − | 0.865520i | \(-0.333012\pi\) |
−0.999999 | + | 0.00100981i | \(0.999679\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.32646 | + | 10.9577i | −0.215106 | + | 0.372574i | ||||
\(866\) | −12.9459 | + | 22.4229i | −0.439918 | + | 0.761961i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.05242 | + | 8.74588i | −0.137548 | + | 0.296854i | ||||
\(869\) | 4.81689 | − | 8.34310i | 0.163402 | − | 0.283020i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −49.6280 | −1.68158 | ||||||||
\(872\) | 9.68250 | − | 16.7706i | 0.327891 | − | 0.567924i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −52.3383 | −1.77037 | ||||||||
\(875\) | 2.63512 | − | 0.236999i | 0.0890831 | − | 0.00801202i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.5683 | 1.20106 | 0.600529 | − | 0.799603i | \(-0.294957\pi\) | ||||
0.600529 | + | 0.799603i | \(0.294957\pi\) | |||||||
\(878\) | 6.01813 | + | 10.4237i | 0.203102 | + | 0.351783i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.821620 | − | 1.42309i | 0.0276968 | − | 0.0479723i | ||||
\(881\) | −5.92938 | −0.199766 | −0.0998829 | − | 0.994999i | \(-0.531847\pi\) | ||||
−0.0998829 | + | 0.994999i | \(0.531847\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.3953 | 0.383483 | 0.191742 | − | 0.981445i | \(-0.438586\pi\) | ||||
0.191742 | + | 0.981445i | \(0.438586\pi\) | |||||||
\(884\) | −17.5781 | + | 30.4462i | −0.591217 | + | 1.02402i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.00770 | + | 1.74539i | 0.0338543 | + | 0.0586374i | ||||
\(887\) | −7.84921 | −0.263551 | −0.131775 | − | 0.991280i | \(-0.542068\pi\) | ||||
−0.131775 | + | 0.991280i | \(0.542068\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −43.3950 | + | 3.90289i | −1.45542 | + | 0.130899i | ||||
\(890\) | 9.27697 | 0.310965 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.8215 | − | 22.2074i | 0.429295 | − | 0.743560i | ||||
\(893\) | −11.5260 | −0.385703 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.33144 | + | 7.50227i | −0.144784 | + | 0.250773i | ||||
\(896\) | −1.11231 | + | 2.40058i | −0.0371597 | + | 0.0801976i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.371185 | + | 0.642911i | −0.0123866 | + | 0.0214542i | ||||
\(899\) | 10.4512 | − | 18.1021i | 0.348568 | − | 0.603737i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −45.5860 | − | 78.9573i | −1.51869 | − | 2.63045i | ||||
\(902\) | 7.07559 | + | 12.2553i | 0.235591 | + | 0.408056i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.830795 | − | 1.43898i | 0.0276318 | − | 0.0478597i | ||||
\(905\) | −10.4358 | −0.346898 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.7902 | 0.657121 | 0.328561 | − | 0.944483i | \(-0.393436\pi\) | ||||
0.328561 | + | 0.944483i | \(0.393436\pi\) | |||||||
\(908\) | −9.49730 | − | 16.4498i | −0.315179 | − | 0.545906i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.59119 | − | 10.7855i | −0.251646 | − | 0.357534i | ||||
\(911\) | 0.911882 | + | 1.57943i | 0.0302120 | + | 0.0523287i | 0.880736 | − | 0.473607i | \(-0.157048\pi\) |
−0.850524 | + | 0.525936i | \(0.823715\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.39877 | + | 9.35095i | 0.178673 | + | 0.309471i | ||||
\(914\) | 5.61374 | + | 9.72328i | 0.185686 | + | 0.321617i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.24447 | − | 3.88754i | −0.0741595 | − | 0.128448i | ||||
\(917\) | −36.0382 | + | 3.24123i | −1.19009 | + | 0.107035i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.5671 | + | 28.6951i | 0.546499 | + | 0.946564i | 0.998511 | + | 0.0545518i | \(0.0173730\pi\) |
−0.452012 | + | 0.892012i | \(0.649294\pi\) | |||||||
\(920\) | −7.45235 | −0.245697 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.2527 | 0.601119 | ||||||||
\(923\) | −18.1093 | + | 31.3662i | −0.596074 | + | 1.03243i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.87466 | − | 4.97906i | −0.0945183 | − | 0.163711i | ||||
\(926\) | 14.5347 | + | 25.1748i | 0.477639 | + | 0.827295i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.86866 | − | 4.96867i | 0.0941684 | − | 0.163104i | ||||
\(929\) | −0.739757 | + | 1.28130i | −0.0242706 | + | 0.0420380i | −0.877906 | − | 0.478834i | \(-0.841060\pi\) |
0.853635 | + | 0.520872i | \(0.174393\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31.7831 | − | 37.5058i | −1.04165 | − | 1.22920i | ||||
\(932\) | −2.86866 | + | 4.96867i | −0.0939662 | + | 0.162754i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.31746 | −0.239435 | ||||||||
\(935\) | 5.79439 | − | 10.0362i | 0.189497 | − | 0.328218i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.9616 | −1.04414 | −0.522070 | − | 0.852902i | \(-0.674840\pi\) | ||||
−0.522070 | + | 0.852902i | \(0.674840\pi\) | |||||||
\(938\) | −26.2338 | + | 2.35943i | −0.856562 | + | 0.0770381i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.64116 | −0.0535288 | ||||||||
\(941\) | −9.39061 | − | 16.2650i | −0.306125 | − | 0.530224i | 0.671386 | − | 0.741108i | \(-0.265699\pi\) |
−0.977511 | + | 0.210884i | \(0.932366\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.0889 | − | 55.5796i | 1.04496 | − | 1.80992i | ||||
\(944\) | −0.782167 | −0.0254574 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.73438 | 0.316492 | ||||||||
\(947\) | −6.41697 | + | 11.1145i | −0.208523 | + | 0.361173i | −0.951250 | − | 0.308422i | \(-0.900199\pi\) |
0.742726 | + | 0.669595i | \(0.233532\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.95861 | − | 3.39240i | −0.0635790 | − | 0.110122i | ||||
\(950\) | 7.02306 | 0.227858 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.84446 | + | 16.9298i | −0.254240 | + | 0.548698i | ||||
\(953\) | 34.9964 | 1.13364 | 0.566822 | − | 0.823841i | \(-0.308173\pi\) | ||||
0.566822 | + | 0.823841i | \(0.308173\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.96784 | + | 15.5328i | −0.290193 | + | 0.502628i | ||||
\(956\) | −27.5238 | −0.890183 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.08835 | − | 5.34918i | 0.0997802 | − | 0.172824i | ||||
\(959\) | −2.22281 | + | 0.199916i | −0.0717782 | + | 0.00645563i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.86340 | − | 15.3519i | 0.285916 | − | 0.495221i | ||||
\(962\) | −14.3302 | + | 24.8207i | −0.462025 | + | 0.800251i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.0984 | + | 17.4909i | 0.325246 | + | 0.563343i | ||||
\(965\) | −2.08058 | − | 3.60367i | −0.0669762 | − | 0.116006i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.2132 | + | 22.8860i | −0.424908 | + | 0.735963i | −0.996412 | − | 0.0846367i | \(-0.973027\pi\) |
0.571503 | + | 0.820600i | \(0.306360\pi\) | |||||||
\(968\) | −8.29976 | −0.266764 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.98057 | −0.192024 | ||||||||
\(971\) | 16.2985 | + | 28.2298i | 0.523043 | + | 0.905938i | 0.999640 | + | 0.0268157i | \(0.00853673\pi\) |
−0.476597 | + | 0.879122i | \(0.658130\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.50011 | − | 14.0285i | 0.208384 | − | 0.449732i | ||||
\(974\) | 3.11014 | + | 5.38693i | 0.0996554 | + | 0.172608i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.38034 | − | 4.12287i | −0.0761929 | − | 0.131970i | ||||
\(977\) | 20.4822 | + | 35.4762i | 0.655284 | + | 1.13499i | 0.981823 | + | 0.189801i | \(0.0607844\pi\) |
−0.326538 | + | 0.945184i | \(0.605882\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.62215 | + | 13.2019i | 0.243605 | + | 0.421936i | ||||
\(980\) | −4.52553 | − | 5.34037i | −0.144563 | − | 0.170592i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.94447 | + | 6.83202i | 0.125873 | + | 0.218019i | ||||
\(983\) | −15.3520 | −0.489652 | −0.244826 | − | 0.969567i | \(-0.578731\pi\) | ||||
−0.244826 | + | 0.969567i | \(0.578731\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.80338 | 0.248636 | ||||||||
\(986\) | 20.2309 | − | 35.0410i | 0.644284 | − | 1.11593i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17.5050 | − | 30.3196i | −0.556909 | − | 0.964594i | ||||
\(989\) | −22.0734 | − | 38.2323i | −0.701895 | − | 1.21572i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.62129 | + | 8.00431i | −0.146800 | + | 0.254265i | −0.930043 | − | 0.367450i | \(-0.880231\pi\) |
0.783243 | + | 0.621716i | \(0.213564\pi\) | |||||||
\(992\) | −1.82162 | + | 3.15514i | −0.0578365 | + | 0.100176i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.08148 | + | 17.4414i | −0.256329 | + | 0.553206i | ||||
\(995\) | −12.2477 | + | 21.2136i | −0.388277 | + | 0.672515i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.7325 | −0.339902 | −0.169951 | − | 0.985453i | \(-0.554361\pi\) | ||||
−0.169951 | + | 0.985453i | \(0.554361\pi\) | |||||||
\(998\) | −4.34473 | + | 7.52530i | −0.137530 | + | 0.238209i | ||||
\(999\) | 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 | 1890.2.l.i.361.8 | 16 | ||
3.2 | odd | 2 | 630.2.l.i.571.2 | yes | 16 | ||
7.2 | even | 3 | 1890.2.i.i.1171.2 | 16 | |||
9.2 | odd | 6 | 630.2.i.i.151.5 | yes | 16 | ||
9.7 | even | 3 | 1890.2.i.i.991.2 | 16 | |||
21.2 | odd | 6 | 630.2.i.i.121.5 | ✓ | 16 | ||
63.2 | odd | 6 | 630.2.l.i.331.2 | yes | 16 | ||
63.16 | even | 3 | inner | 1890.2.l.i.1801.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.i.i.121.5 | ✓ | 16 | 21.2 | odd | 6 | ||
630.2.i.i.151.5 | yes | 16 | 9.2 | odd | 6 | ||
630.2.l.i.331.2 | yes | 16 | 63.2 | odd | 6 | ||
630.2.l.i.571.2 | yes | 16 | 3.2 | odd | 2 | ||
1890.2.i.i.991.2 | 16 | 9.7 | even | 3 | |||
1890.2.i.i.1171.2 | 16 | 7.2 | even | 3 | |||
1890.2.l.i.361.8 | 16 | 1.1 | even | 1 | trivial | ||
1890.2.l.i.1801.8 | 16 | 63.16 | even | 3 | inner |