Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(107,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.l (of order \(4\), degree \(2\), 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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 107.7 | ||
Character | \(\chi\) | \(=\) | 432.107 |
Dual form | 432.2.l.a.323.7 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.604480 | − | 1.27852i | −0.427432 | − | 0.904047i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.26921 | + | 1.54568i | −0.634604 | + | 0.772838i | ||||
\(5\) | 0.217410 | − | 0.217410i | 0.0972289 | − | 0.0972289i | −0.656819 | − | 0.754048i | \(-0.728099\pi\) |
0.754048 | + | 0.656819i | \(0.228099\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.81401 | −1.44156 | −0.720779 | − | 0.693165i | \(-0.756216\pi\) | ||||
−0.720779 | + | 0.693165i | \(0.756216\pi\) | |||||||
\(8\) | 2.74338 | + | 0.688372i | 0.969932 | + | 0.243376i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.409383 | − | 0.146542i | −0.129458 | − | 0.0463408i | ||||
\(11\) | 3.83163 | + | 3.83163i | 1.15528 | + | 1.15528i | 0.985478 | + | 0.169803i | \(0.0543130\pi\) |
0.169803 | + | 0.985478i | \(0.445687\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.88926 | + | 2.88926i | −0.801337 | + | 0.801337i | −0.983305 | − | 0.181967i | \(-0.941754\pi\) |
0.181967 | + | 0.983305i | \(0.441754\pi\) | |||||||
\(14\) | 2.30549 | + | 4.87627i | 0.616168 | + | 1.30324i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.778226 | − | 3.92357i | −0.194556 | − | 0.980891i | ||||
\(17\) | − | 4.71852i | − | 1.14441i | −0.820111 | − | 0.572205i | \(-0.806088\pi\) | ||
0.820111 | − | 0.572205i | \(-0.193912\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.77663 | + | 4.77663i | 1.09583 | + | 1.09583i | 0.994892 | + | 0.100943i | \(0.0321859\pi\) |
0.100943 | + | 0.994892i | \(0.467814\pi\) | |||||||
\(20\) | 0.0601071 | + | 0.611985i | 0.0134404 | + | 0.136844i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.58266 | − | 7.21495i | 0.550625 | − | 1.53823i | ||||
\(23\) | 6.18488i | 1.28964i | 0.764336 | + | 0.644818i | \(0.223067\pi\) | ||||
−0.764336 | + | 0.644818i | \(0.776933\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.90547i | 0.981093i | ||||||||
\(26\) | 5.44047 | + | 1.94747i | 1.06696 | + | 0.381930i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.84076 | − | 5.89522i | 0.914818 | − | 1.11409i | ||||
\(29\) | 0.322843 | + | 0.322843i | 0.0599505 | + | 0.0599505i | 0.736446 | − | 0.676496i | \(-0.236502\pi\) |
−0.676496 | + | 0.736446i | \(0.736502\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.20520i | 0.934881i | 0.884024 | + | 0.467441i | \(0.154824\pi\) | ||||
−0.884024 | + | 0.467441i | \(0.845176\pi\) | |||||||
\(32\) | −4.54592 | + | 3.36669i | −0.803613 | + | 0.595153i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.03271 | + | 2.85225i | −1.03460 | + | 0.489158i | ||||
\(35\) | −0.829205 | + | 0.829205i | −0.140161 | + | 0.140161i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.92710 | − | 2.92710i | −0.481212 | − | 0.481212i | 0.424307 | − | 0.905519i | \(-0.360518\pi\) |
−0.905519 | + | 0.424307i | \(0.860518\pi\) | |||||||
\(38\) | 3.21962 | − | 8.99438i | 0.522292 | − | 1.45908i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.746099 | − | 0.446781i | 0.117969 | − | 0.0706422i | ||||
\(41\) | 1.31513 | 0.205389 | 0.102694 | − | 0.994713i | \(-0.467254\pi\) | ||||
0.102694 | + | 0.994713i | \(0.467254\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.505290 | − | 0.505290i | 0.0770560 | − | 0.0770560i | −0.667528 | − | 0.744584i | \(-0.732648\pi\) |
0.744584 | + | 0.667528i | \(0.232648\pi\) | |||||||
\(44\) | −10.7856 | + | 1.05932i | −1.62599 | + | 0.159699i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.90747 | − | 3.73864i | 1.16589 | − | 0.551232i | ||||
\(47\) | 5.41806 | 0.790306 | 0.395153 | − | 0.918615i | \(-0.370692\pi\) | ||||
0.395153 | + | 0.918615i | \(0.370692\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.54664 | 1.07809 | ||||||||
\(50\) | 6.27172 | − | 2.96526i | 0.886955 | − | 0.419351i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.798789 | − | 8.13294i | −0.110772 | − | 1.12784i | ||||
\(53\) | 1.85772 | − | 1.85772i | 0.255178 | − | 0.255178i | −0.567912 | − | 0.823090i | \(-0.692248\pi\) |
0.823090 | + | 0.567912i | \(0.192248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.66607 | 0.224653 | ||||||||
\(56\) | −10.4633 | − | 2.62545i | −1.39821 | − | 0.350841i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.217608 | − | 0.607913i | 0.0285733 | − | 0.0798229i | ||||
\(59\) | −4.77662 | − | 4.77662i | −0.621863 | − | 0.621863i | 0.324145 | − | 0.946007i | \(-0.394923\pi\) |
−0.946007 | + | 0.324145i | \(0.894923\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.832278 | + | 0.832278i | −0.106562 | + | 0.106562i | −0.758378 | − | 0.651815i | \(-0.774008\pi\) |
0.651815 | + | 0.758378i | \(0.274008\pi\) | |||||||
\(62\) | 6.65493 | − | 3.14644i | 0.845177 | − | 0.399598i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.05229 | + | 3.77693i | 0.881536 | + | 0.472117i | ||||
\(65\) | 1.25631i | 0.155826i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.48244 | − | 6.48244i | −0.791956 | − | 0.791956i | 0.189856 | − | 0.981812i | \(-0.439198\pi\) |
−0.981812 | + | 0.189856i | \(0.939198\pi\) | |||||||
\(68\) | 7.29331 | + | 5.98879i | 0.884444 | + | 0.726247i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.56139 | + | 0.558914i | 0.186622 | + | 0.0668030i | ||||
\(71\) | − | 2.47601i | − | 0.293849i | −0.989148 | − | 0.146924i | \(-0.953063\pi\) | ||
0.989148 | − | 0.146924i | \(-0.0469374\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.68986i | 0.782989i | 0.920180 | + | 0.391494i | \(0.128042\pi\) | ||||
−0.920180 | + | 0.391494i | \(0.871958\pi\) | |||||||
\(74\) | −1.97297 | + | 5.51171i | −0.229353 | + | 0.640724i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −13.4457 | + | 1.32059i | −1.54232 | + | 0.151482i | ||||
\(77\) | −14.6139 | − | 14.6139i | −1.66541 | − | 1.66541i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.28617i | 1.04478i | 0.852708 | + | 0.522388i | \(0.174959\pi\) | ||||
−0.852708 | + | 0.522388i | \(0.825041\pi\) | |||||||
\(80\) | −1.02222 | − | 0.683830i | −0.114288 | − | 0.0764545i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.794971 | − | 1.68142i | −0.0877898 | − | 0.185681i | ||||
\(83\) | −8.24616 | + | 8.24616i | −0.905134 | + | 0.905134i | −0.995875 | − | 0.0907409i | \(-0.971076\pi\) |
0.0907409 | + | 0.995875i | \(0.471076\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.02586 | − | 1.02586i | −0.111270 | − | 0.111270i | ||||
\(86\) | −0.951459 | − | 0.340583i | −0.102598 | − | 0.0367261i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.87404 | + | 13.1492i | 0.839376 | + | 1.40171i | ||||
\(89\) | −12.3741 | −1.31165 | −0.655825 | − | 0.754913i | \(-0.727679\pi\) | ||||
−0.655825 | + | 0.754913i | \(0.727679\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.0197 | − | 11.0197i | 1.15517 | − | 1.15517i | ||||
\(92\) | −9.55982 | − | 7.84989i | −0.996680 | − | 0.818408i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.27511 | − | 6.92708i | −0.337802 | − | 0.714474i | ||||
\(95\) | 2.07698 | 0.213094 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.81552 | −0.285873 | −0.142937 | − | 0.989732i | \(-0.545654\pi\) | ||||
−0.142937 | + | 0.989732i | \(0.545654\pi\) | |||||||
\(98\) | −4.56179 | − | 9.64850i | −0.460811 | − | 0.974646i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.58226 | − | 6.22605i | −0.758226 | − | 0.622605i | ||||
\(101\) | 6.38111 | − | 6.38111i | 0.634944 | − | 0.634944i | −0.314360 | − | 0.949304i | \(-0.601790\pi\) |
0.949304 | + | 0.314360i | \(0.101790\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.5734 | −1.83009 | −0.915046 | − | 0.403350i | \(-0.867846\pi\) | ||||
−0.915046 | + | 0.403350i | \(0.867846\pi\) | |||||||
\(104\) | −9.91524 | + | 5.93747i | −0.972269 | + | 0.582216i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.49809 | − | 1.25217i | −0.339764 | − | 0.121622i | ||||
\(107\) | 12.4921 | + | 12.4921i | 1.20766 | + | 1.20766i | 0.971783 | + | 0.235876i | \(0.0757958\pi\) |
0.235876 | + | 0.971783i | \(0.424204\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.93373 | − | 4.93373i | 0.472565 | − | 0.472565i | −0.430179 | − | 0.902744i | \(-0.641549\pi\) |
0.902744 | + | 0.430179i | \(0.141549\pi\) | |||||||
\(110\) | −1.00711 | − | 2.13010i | −0.0960241 | − | 0.203097i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.96816 | + | 14.9645i | 0.280464 | + | 1.41401i | ||||
\(113\) | − | 11.7427i | − | 1.10466i | −0.833626 | − | 0.552329i | \(-0.813739\pi\) | ||
0.833626 | − | 0.552329i | \(-0.186261\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.34466 | + | 1.34466i | 0.125390 | + | 0.125390i | ||||
\(116\) | −0.908766 | + | 0.0892559i | −0.0843768 | + | 0.00828721i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.21961 | + | 8.99435i | −0.296389 | + | 0.827997i | ||||
\(119\) | 17.9965i | 1.64973i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.3628i | 1.66935i | ||||||||
\(122\) | 1.56718 | + | 0.560985i | 0.141885 | + | 0.0507892i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.04555 | − | 6.60648i | −0.722512 | − | 0.593279i | ||||
\(125\) | 2.15355 | + | 2.15355i | 0.192620 | + | 0.192620i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.2988i | 1.35755i | 0.734347 | + | 0.678774i | \(0.237489\pi\) | ||||
−0.734347 | + | 0.678774i | \(0.762511\pi\) | |||||||
\(128\) | 0.565902 | − | 11.2995i | 0.0500192 | − | 0.998748i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.60622 | − | 0.759416i | 0.140874 | − | 0.0666052i | ||||
\(131\) | 3.55187 | − | 3.55187i | 0.310329 | − | 0.310329i | −0.534708 | − | 0.845037i | \(-0.679578\pi\) |
0.845037 | + | 0.534708i | \(0.179578\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.2181 | − | 18.2181i | −1.57971 | − | 1.57971i | ||||
\(134\) | −4.36939 | + | 12.2064i | −0.377458 | + | 1.05447i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.24810 | − | 12.9447i | 0.278522 | − | 1.11000i | ||||
\(137\) | 4.11222 | 0.351331 | 0.175665 | − | 0.984450i | \(-0.443792\pi\) | ||||
0.175665 | + | 0.984450i | \(0.443792\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.64500 | − | 6.64500i | 0.563621 | − | 0.563621i | −0.366713 | − | 0.930334i | \(-0.619517\pi\) |
0.930334 | + | 0.366713i | \(0.119517\pi\) | |||||||
\(140\) | −0.229249 | − | 2.33411i | −0.0193751 | − | 0.197269i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.16562 | + | 1.49670i | −0.265653 | + | 0.125600i | ||||
\(143\) | −22.1412 | −1.85154 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.140379 | 0.0116578 | ||||||||
\(146\) | 8.55310 | − | 4.04389i | 0.707859 | − | 0.334675i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.23944 | − | 0.809249i | 0.677278 | − | 0.0665199i | ||||
\(149\) | −0.723047 | + | 0.723047i | −0.0592343 | + | 0.0592343i | −0.736103 | − | 0.676869i | \(-0.763336\pi\) |
0.676869 | + | 0.736103i | \(0.263336\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.94167 | 0.483526 | 0.241763 | − | 0.970335i | \(-0.422274\pi\) | ||||
0.241763 | + | 0.970335i | \(0.422274\pi\) | |||||||
\(152\) | 9.81603 | + | 16.3922i | 0.796185 | + | 1.32959i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.85027 | + | 27.5179i | −0.793758 | + | 2.21745i | ||||
\(155\) | 1.13166 | + | 1.13166i | 0.0908975 | + | 0.0908975i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0754 | − | 14.0754i | 1.12334 | − | 1.12334i | 0.132104 | − | 0.991236i | \(-0.457827\pi\) |
0.991236 | − | 0.132104i | \(-0.0421732\pi\) | |||||||
\(158\) | 11.8725 | − | 5.61331i | 0.944527 | − | 0.446571i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.256377 | + | 1.72028i | −0.0202683 | + | 0.136000i | ||||
\(161\) | − | 23.5892i | − | 1.85909i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.39073 | − | 3.39073i | −0.265583 | − | 0.265583i | 0.561735 | − | 0.827317i | \(-0.310134\pi\) |
−0.827317 | + | 0.561735i | \(0.810134\pi\) | |||||||
\(164\) | −1.66917 | + | 2.03277i | −0.130341 | + | 0.158732i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.5275 | + | 5.55821i | 1.20517 | + | 0.431401i | ||||
\(167\) | − | 9.15420i | − | 0.708373i | −0.935175 | − | 0.354187i | \(-0.884758\pi\) | ||
0.935175 | − | 0.354187i | \(-0.115242\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 3.69568i | − | 0.284283i | ||||||
\(170\) | −0.691464 | + | 1.93168i | −0.0530329 | + | 0.148153i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.139697 | + | 1.42233i | 0.0106518 | + | 0.108452i | ||||
\(173\) | 2.30022 | + | 2.30022i | 0.174883 | + | 0.174883i | 0.789121 | − | 0.614238i | \(-0.210537\pi\) |
−0.614238 | + | 0.789121i | \(0.710537\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 18.7095i | − | 1.41430i | ||||||
\(176\) | 12.0518 | − | 18.0155i | 0.908438 | − | 1.35797i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.47989 | + | 15.8205i | 0.560641 | + | 1.18579i | ||||
\(179\) | 7.17306 | − | 7.17306i | 0.536140 | − | 0.536140i | −0.386253 | − | 0.922393i | \(-0.626231\pi\) |
0.922393 | + | 0.386253i | \(0.126231\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.0999 | − | 17.0999i | −1.27103 | − | 1.27103i | −0.945550 | − | 0.325476i | \(-0.894476\pi\) |
−0.325476 | − | 0.945550i | \(-0.605524\pi\) | |||||||
\(182\) | −20.7500 | − | 7.42765i | −1.53809 | − | 0.550574i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.25750 | + | 16.9675i | −0.313867 | + | 1.25086i | ||||
\(185\) | −1.27276 | −0.0935754 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.0797 | − | 18.0797i | 1.32212 | − | 1.32212i | ||||
\(188\) | −6.87664 | + | 8.37457i | −0.501531 | + | 0.610778i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.25549 | − | 2.65545i | −0.0910831 | − | 0.192647i | ||||
\(191\) | 23.6865 | 1.71390 | 0.856949 | − | 0.515401i | \(-0.172357\pi\) | ||||
0.856949 | + | 0.515401i | \(0.172357\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.5740 | 1.91284 | 0.956420 | − | 0.291995i | \(-0.0943191\pi\) | ||||
0.956420 | + | 0.291995i | \(0.0943191\pi\) | |||||||
\(194\) | 1.70193 | + | 3.59969i | 0.122191 | + | 0.258443i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.57825 | + | 11.6647i | −0.684161 | + | 0.833190i | ||||
\(197\) | −14.5507 | + | 14.5507i | −1.03670 | + | 1.03670i | −0.0373962 | + | 0.999301i | \(0.511906\pi\) |
−0.999301 | + | 0.0373962i | \(0.988094\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.329215 | −0.0233375 | −0.0116687 | − | 0.999932i | \(-0.503714\pi\) | ||||
−0.0116687 | + | 0.999932i | \(0.503714\pi\) | |||||||
\(200\) | −3.37678 | + | 13.4576i | −0.238775 | + | 0.951594i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.0156 | − | 4.30110i | −0.845415 | − | 0.302624i | ||||
\(203\) | −1.23133 | − | 1.23133i | −0.0864222 | − | 0.0864222i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.285923 | − | 0.285923i | 0.0199697 | − | 0.0199697i | ||||
\(206\) | 11.2273 | + | 23.7464i | 0.782240 | + | 1.65449i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 13.5847 | + | 9.08771i | 0.941930 | + | 0.630120i | ||||
\(209\) | 36.6046i | 2.53199i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.20144 | − | 5.20144i | −0.358082 | − | 0.358082i | 0.505024 | − | 0.863105i | \(-0.331484\pi\) |
−0.863105 | + | 0.505024i | \(0.831484\pi\) | |||||||
\(212\) | 0.513601 | + | 5.22927i | 0.0352743 | + | 0.359148i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.42014 | − | 23.5226i | 0.575589 | − | 1.60797i | ||||
\(215\) | − | 0.219711i | − | 0.0149841i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 19.8527i | − | 1.34769i | ||||||
\(218\) | −9.29019 | − | 3.32551i | −0.629211 | − | 0.225232i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.11459 | + | 2.57521i | −0.142566 | + | 0.173621i | ||||
\(221\) | 13.6331 | + | 13.6331i | 0.917059 | + | 0.917059i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 0.790802i | − | 0.0529560i | −0.999649 | − | 0.0264780i | \(-0.991571\pi\) | ||
0.999649 | − | 0.0264780i | \(-0.00842919\pi\) | |||||||
\(224\) | 17.3382 | − | 12.8406i | 1.15845 | − | 0.857947i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.0132 | + | 7.09822i | −0.998664 | + | 0.472167i | ||||
\(227\) | 4.35838 | − | 4.35838i | 0.289276 | − | 0.289276i | −0.547518 | − | 0.836794i | \(-0.684427\pi\) |
0.836794 | + | 0.547518i | \(0.184427\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.9442 | + | 11.9442i | 0.789298 | + | 0.789298i | 0.981379 | − | 0.192081i | \(-0.0615237\pi\) |
−0.192081 | + | 0.981379i | \(0.561524\pi\) | |||||||
\(230\) | 0.906348 | − | 2.53199i | 0.0597628 | − | 0.166954i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.663446 | + | 1.10792i | 0.0435574 | + | 0.0727385i | ||||
\(233\) | 26.4938 | 1.73567 | 0.867833 | − | 0.496855i | \(-0.165512\pi\) | ||||
0.867833 | + | 0.496855i | \(0.165512\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.17794 | − | 1.17794i | 0.0768406 | − | 0.0768406i | ||||
\(236\) | 13.4456 | − | 1.32058i | 0.875235 | − | 0.0859626i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 23.0088 | − | 10.8785i | 1.49144 | − | 0.705149i | ||||
\(239\) | −1.09196 | −0.0706333 | −0.0353167 | − | 0.999376i | \(-0.511244\pi\) | ||||
−0.0353167 | + | 0.999376i | \(0.511244\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.3414 | 0.923814 | 0.461907 | − | 0.886928i | \(-0.347165\pi\) | ||||
0.461907 | + | 0.886928i | \(0.347165\pi\) | |||||||
\(242\) | 23.4772 | − | 11.1000i | 1.50917 | − | 0.713533i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.230098 | − | 2.34276i | −0.0147305 | − | 0.149980i | ||||
\(245\) | 1.64072 | − | 1.64072i | 0.104822 | − | 0.104822i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −27.6019 | −1.75627 | ||||||||
\(248\) | −3.58311 | + | 14.2798i | −0.227528 | + | 0.906771i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.45157 | − | 4.05513i | 0.0918054 | − | 0.256469i | ||||
\(251\) | −5.97677 | − | 5.97677i | −0.377250 | − | 0.377250i | 0.492859 | − | 0.870109i | \(-0.335952\pi\) |
−0.870109 | + | 0.492859i | \(0.835952\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −23.6982 | + | 23.6982i | −1.48989 | + | 1.48989i | ||||
\(254\) | 19.5598 | − | 9.24782i | 1.22729 | − | 0.580260i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.7887 | + | 6.10684i | −0.924296 | + | 0.381677i | ||||
\(257\) | 23.4079i | 1.46015i | 0.683369 | + | 0.730073i | \(0.260514\pi\) | ||||
−0.683369 | + | 0.730073i | \(0.739486\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.1640 | + | 11.1640i | 0.693695 | + | 0.693695i | ||||
\(260\) | −1.94185 | − | 1.59452i | −0.120428 | − | 0.0988880i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.68816 | − | 2.39409i | −0.413196 | − | 0.147907i | ||||
\(263\) | − | 13.3165i | − | 0.821128i | −0.911832 | − | 0.410564i | \(-0.865332\pi\) | ||
0.911832 | − | 0.410564i | \(-0.134668\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.807777i | − | 0.0496213i | ||||||
\(266\) | −12.2797 | + | 34.3046i | −0.752914 | + | 2.10335i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 18.2473 | − | 1.79219i | 1.11463 | − | 0.109475i | ||||
\(269\) | 8.78530 | + | 8.78530i | 0.535649 | + | 0.535649i | 0.922248 | − | 0.386599i | \(-0.126350\pi\) |
−0.386599 | + | 0.922248i | \(0.626350\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.46274i | − | 0.0888554i | −0.999013 | − | 0.0444277i | \(-0.985854\pi\) | ||
0.999013 | − | 0.0444277i | \(-0.0141464\pi\) | |||||||
\(272\) | −18.5134 | + | 3.67208i | −1.12254 | + | 0.222652i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.48575 | − | 5.25754i | −0.150170 | − | 0.317619i | ||||
\(275\) | −18.7959 | + | 18.7959i | −1.13344 | + | 1.13344i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.83891 | + | 2.83891i | 0.170573 | + | 0.170573i | 0.787231 | − | 0.616658i | \(-0.211514\pi\) |
−0.616658 | + | 0.787231i | \(0.711514\pi\) | |||||||
\(278\) | −12.5125 | − | 4.47897i | −0.750450 | − | 0.268631i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.84563 | + | 1.70402i | −0.170059 | + | 0.101835i | ||||
\(281\) | −6.53163 | −0.389644 | −0.194822 | − | 0.980839i | \(-0.562413\pi\) | ||||
−0.194822 | + | 0.980839i | \(0.562413\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.82128 | + | 1.82128i | −0.108264 | + | 0.108264i | −0.759164 | − | 0.650900i | \(-0.774392\pi\) |
0.650900 | + | 0.759164i | \(0.274392\pi\) | |||||||
\(284\) | 3.82711 | + | 3.14257i | 0.227097 | + | 0.186477i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.3839 | + | 28.3079i | 0.791407 | + | 1.67388i | ||||
\(287\) | −5.01592 | −0.296080 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.26448 | −0.309675 | ||||||||
\(290\) | −0.0848564 | − | 0.179477i | −0.00498294 | − | 0.0105392i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.3404 | − | 8.49082i | −0.605123 | − | 0.496888i | ||||
\(293\) | 22.9270 | − | 22.9270i | 1.33941 | − | 1.33941i | 0.442778 | − | 0.896631i | \(-0.353993\pi\) |
0.896631 | − | 0.442778i | \(-0.146007\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.07697 | −0.120926 | ||||||||
\(296\) | −6.01522 | − | 10.0451i | −0.349627 | − | 0.583858i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.36149 | + | 0.487360i | 0.0788693 | + | 0.0282320i | ||||
\(299\) | −17.8697 | − | 17.8697i | −1.03343 | − | 1.03343i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.92718 | + | 1.92718i | −0.111081 | + | 0.111081i | ||||
\(302\) | −3.59162 | − | 7.59652i | −0.206674 | − | 0.437130i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 15.0241 | − | 22.4587i | 0.861693 | − | 1.28810i | ||||
\(305\) | 0.361892i | 0.0207219i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.8441 | + | 10.8441i | 0.618904 | + | 0.618904i | 0.945250 | − | 0.326346i | \(-0.105817\pi\) |
−0.326346 | + | 0.945250i | \(0.605817\pi\) | |||||||
\(308\) | 41.1363 | − | 4.04027i | 2.34396 | − | 0.230216i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.762783 | − | 2.13092i | 0.0433231 | − | 0.121028i | ||||
\(311\) | − | 16.4393i | − | 0.932189i | −0.884735 | − | 0.466095i | \(-0.845661\pi\) | ||
0.884735 | − | 0.466095i | \(-0.154339\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 0.171508i | − | 0.00969419i | −0.999988 | − | 0.00484710i | \(-0.998457\pi\) | ||
0.999988 | − | 0.00484710i | \(-0.00154288\pi\) | |||||||
\(314\) | −26.5039 | − | 9.48733i | −1.49570 | − | 0.535401i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.3534 | − | 11.7861i | −0.807442 | − | 0.663019i | ||||
\(317\) | −11.9635 | − | 11.9635i | −0.671937 | − | 0.671937i | 0.286226 | − | 0.958162i | \(-0.407599\pi\) |
−0.958162 | + | 0.286226i | \(0.907599\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.47403i | 0.138519i | ||||||||
\(320\) | 2.35439 | − | 0.712096i | 0.131614 | − | 0.0398074i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −30.1591 | + | 14.2592i | −1.68070 | + | 0.794633i | ||||
\(323\) | 22.5387 | − | 22.5387i | 1.25408 | − | 1.25408i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.1732 | − | 14.1732i | −0.786187 | − | 0.786187i | ||||
\(326\) | −2.28547 | + | 6.38473i | −0.126581 | + | 0.353618i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.60791 | + | 0.905299i | 0.199213 | + | 0.0499868i | ||||
\(329\) | −20.6645 | −1.13927 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.32460 | + | 2.32460i | −0.127772 | + | 0.127772i | −0.768101 | − | 0.640329i | \(-0.778798\pi\) |
0.640329 | + | 0.768101i | \(0.278798\pi\) | |||||||
\(332\) | −2.27980 | − | 23.2120i | −0.125120 | − | 1.27392i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.7038 | + | 5.53353i | −0.640403 | + | 0.302781i | ||||
\(335\) | −2.81870 | −0.154002 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.9566 | −0.596842 | −0.298421 | − | 0.954434i | \(-0.596460\pi\) | ||||
−0.298421 | + | 0.954434i | \(0.596460\pi\) | |||||||
\(338\) | −4.72499 | + | 2.23397i | −0.257006 | + | 0.121512i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.88767 | − | 0.283617i | 0.156606 | − | 0.0153813i | ||||
\(341\) | −19.9444 | + | 19.9444i | −1.08005 | + | 1.08005i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.08489 | −0.112573 | ||||||||
\(344\) | 1.73403 | − | 1.03838i | 0.0934926 | − | 0.0559854i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.55043 | − | 4.33131i | 0.0833517 | − | 0.232853i | ||||
\(347\) | 1.35986 | + | 1.35986i | 0.0730012 | + | 0.0730012i | 0.742665 | − | 0.669663i | \(-0.233562\pi\) |
−0.669663 | + | 0.742665i | \(0.733562\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.55298 | − | 2.55298i | 0.136658 | − | 0.136658i | −0.635469 | − | 0.772127i | \(-0.719193\pi\) |
0.772127 | + | 0.635469i | \(0.219193\pi\) | |||||||
\(350\) | −23.9204 | + | 11.3095i | −1.27860 | + | 0.604519i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −30.3182 | − | 4.51837i | −1.61597 | − | 0.240830i | ||||
\(353\) | − | 12.5253i | − | 0.666656i | −0.942811 | − | 0.333328i | \(-0.891828\pi\) | ||
0.942811 | − | 0.333328i | \(-0.108172\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.538311 | − | 0.538311i | −0.0285706 | − | 0.0285706i | ||||
\(356\) | 15.7053 | − | 19.1263i | 0.832378 | − | 1.01369i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.5068 | − | 4.83490i | −0.713859 | − | 0.255532i | ||||
\(359\) | 11.1836i | 0.590248i | 0.955459 | + | 0.295124i | \(0.0953610\pi\) | ||||
−0.955459 | + | 0.295124i | \(0.904639\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.6325i | 1.40171i | ||||||||
\(362\) | −11.5260 | + | 32.1991i | −0.605791 | + | 1.69235i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.04659 | + | 31.0191i | 0.159685 | + | 1.62584i | ||||
\(365\) | 1.45445 | + | 1.45445i | 0.0761292 | + | 0.0761292i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.0743i | 0.682473i | 0.939977 | + | 0.341237i | \(0.110846\pi\) | ||||
−0.939977 | + | 0.341237i | \(0.889154\pi\) | |||||||
\(368\) | 24.2668 | − | 4.81323i | 1.26499 | − | 0.250907i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.769360 | + | 1.62725i | 0.0399971 | + | 0.0845966i | ||||
\(371\) | −7.08537 | + | 7.08537i | −0.367854 | + | 0.367854i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.64329 | − | 5.64329i | −0.292198 | − | 0.292198i | 0.545750 | − | 0.837948i | \(-0.316245\pi\) |
−0.837948 | + | 0.545750i | \(0.816245\pi\) | |||||||
\(374\) | −34.0439 | − | 12.1863i | −1.76037 | − | 0.630141i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 14.8638 | + | 3.72964i | 0.766543 | + | 0.192342i | ||||
\(377\) | −1.86556 | −0.0960812 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.86282 | + | 9.86282i | −0.506619 | + | 0.506619i | −0.913487 | − | 0.406868i | \(-0.866621\pi\) |
0.406868 | + | 0.913487i | \(0.366621\pi\) | |||||||
\(380\) | −2.63612 | + | 3.21034i | −0.135230 | + | 0.164687i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14.3180 | − | 30.2836i | −0.732575 | − | 1.54945i | ||||
\(383\) | 14.8365 | 0.758111 | 0.379055 | − | 0.925374i | \(-0.376249\pi\) | ||||
0.379055 | + | 0.925374i | \(0.376249\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.35442 | −0.323851 | ||||||||
\(386\) | −16.0635 | − | 33.9753i | −0.817609 | − | 1.72930i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.57348 | − | 4.35189i | 0.181416 | − | 0.220934i | ||||
\(389\) | 3.64954 | − | 3.64954i | 0.185039 | − | 0.185039i | −0.608508 | − | 0.793548i | \(-0.708232\pi\) |
0.793548 | + | 0.608508i | \(0.208232\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 29.1835 | 1.47587 | ||||||||
\(392\) | 20.7033 | + | 5.19489i | 1.04568 | + | 0.262382i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 27.3990 | + | 9.80772i | 1.38034 | + | 0.494106i | ||||
\(395\) | 2.01891 | + | 2.01891i | 0.101582 | + | 0.101582i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.3913 | − | 13.3913i | 0.672088 | − | 0.672088i | −0.286109 | − | 0.958197i | \(-0.592362\pi\) |
0.958197 | + | 0.286109i | \(0.0923619\pi\) | |||||||
\(398\) | 0.199004 | + | 0.420907i | 0.00997518 | + | 0.0210982i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.2469 | − | 3.81756i | 0.962346 | − | 0.190878i | ||||
\(401\) | 27.5346i | 1.37501i | 0.726179 | + | 0.687505i | \(0.241294\pi\) | ||||
−0.726179 | + | 0.687505i | \(0.758706\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.0392 | − | 15.0392i | −0.749155 | − | 0.749155i | ||||
\(404\) | 1.76417 | + | 17.9621i | 0.0877709 | + | 0.893646i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.829958 | + | 2.31858i | −0.0411901 | + | 0.115069i | ||||
\(407\) | − | 22.4311i | − | 1.11187i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.2349i | 0.802762i | 0.915911 | + | 0.401381i | \(0.131470\pi\) | ||||
−0.915911 | + | 0.401381i | \(0.868530\pi\) | |||||||
\(410\) | −0.538392 | − | 0.192723i | −0.0265893 | − | 0.00951789i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 23.5735 | − | 28.7084i | 1.16138 | − | 1.41436i | ||||
\(413\) | 18.2180 | + | 18.2180i | 0.896451 | + | 0.896451i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.58560i | 0.176010i | ||||||||
\(416\) | 3.40710 | − | 22.8616i | 0.167047 | − | 1.12088i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 46.7996 | − | 22.1268i | 2.28904 | − | 1.08226i | ||||
\(419\) | −2.15752 | + | 2.15752i | −0.105402 | + | 0.105402i | −0.757841 | − | 0.652439i | \(-0.773746\pi\) |
0.652439 | + | 0.757841i | \(0.273746\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.2411 | + | 17.2411i | 0.840281 | + | 0.840281i | 0.988895 | − | 0.148615i | \(-0.0474814\pi\) |
−0.148615 | + | 0.988895i | \(0.547481\pi\) | |||||||
\(422\) | −3.50596 | + | 9.79429i | −0.170667 | + | 0.476778i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.37525 | − | 3.81764i | 0.309609 | − | 0.185401i | ||||
\(425\) | 23.1466 | 1.12277 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.17431 | − | 3.17431i | 0.153616 | − | 0.153616i | ||||
\(428\) | −35.1639 | + | 3.45367i | −1.69971 | + | 0.166940i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.280903 | + | 0.132811i | −0.0135464 | + | 0.00640470i | ||||
\(431\) | −33.3451 | −1.60618 | −0.803089 | − | 0.595860i | \(-0.796811\pi\) | ||||
−0.803089 | + | 0.595860i | \(0.796811\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.2248 | −1.06805 | −0.534027 | − | 0.845467i | \(-0.679322\pi\) | ||||
−0.534027 | + | 0.845467i | \(0.679322\pi\) | |||||||
\(434\) | −25.3819 | + | 12.0005i | −1.21837 | + | 0.576044i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.36402 | + | 13.8879i | 0.0653246 | + | 0.665108i | ||||
\(437\) | −29.5429 | + | 29.5429i | −1.41323 | + | 1.41323i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.240504 | −0.0114786 | −0.00573932 | − | 0.999984i | \(-0.501827\pi\) | ||||
−0.00573932 | + | 0.999984i | \(0.501827\pi\) | |||||||
\(440\) | 4.57068 | + | 1.14688i | 0.217899 | + | 0.0546753i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.18917 | − | 25.6710i | 0.437084 | − | 1.22105i | ||||
\(443\) | −26.5432 | − | 26.5432i | −1.26110 | − | 1.26110i | −0.950559 | − | 0.310546i | \(-0.899488\pi\) |
−0.310546 | − | 0.950559i | \(-0.600512\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.69025 | + | 2.69025i | −0.127530 | + | 0.127530i | ||||
\(446\) | −1.01105 | + | 0.478024i | −0.0478747 | + | 0.0226351i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −26.8975 | − | 14.4052i | −1.27079 | − | 0.680584i | ||||
\(449\) | − | 31.9534i | − | 1.50797i | −0.656890 | − | 0.753987i | \(-0.728128\pi\) | ||
0.656890 | − | 0.753987i | \(-0.271872\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.03910 | + | 5.03910i | 0.237282 | + | 0.237282i | ||||
\(452\) | 18.1504 | + | 14.9039i | 0.853722 | + | 0.701020i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.20681 | − | 2.93770i | −0.385165 | − | 0.137873i | ||||
\(455\) | − | 4.79158i | − | 0.224633i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.0060i | 0.608395i | 0.952609 | + | 0.304198i | \(0.0983883\pi\) | ||||
−0.952609 | + | 0.304198i | \(0.901612\pi\) | |||||||
\(458\) | 8.05085 | − | 22.4910i | 0.376191 | − | 1.05093i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.78505 | + | 0.371755i | −0.176479 | + | 0.0173332i | ||||
\(461\) | −14.0979 | − | 14.0979i | −0.656603 | − | 0.656603i | 0.297972 | − | 0.954575i | \(-0.403690\pi\) |
−0.954575 | + | 0.297972i | \(0.903690\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.7903i | 1.66331i | 0.555289 | + | 0.831657i | \(0.312607\pi\) | ||||
−0.555289 | + | 0.831657i | \(0.687393\pi\) | |||||||
\(464\) | 1.01545 | − | 1.51794i | 0.0471412 | − | 0.0704687i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.0150 | − | 33.8728i | −0.741880 | − | 1.56912i | ||||
\(467\) | 15.2548 | − | 15.2548i | 0.705909 | − | 0.705909i | −0.259763 | − | 0.965672i | \(-0.583645\pi\) |
0.965672 | + | 0.259763i | \(0.0836446\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.7240 | + | 24.7240i | 1.14165 | + | 1.14165i | ||||
\(470\) | −2.21806 | − | 0.793976i | −0.102312 | − | 0.0366234i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.81600 | − | 16.3922i | −0.451818 | − | 0.754511i | ||||
\(473\) | 3.87217 | 0.178043 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.4316 | + | 23.4316i | −1.07512 | + | 1.07512i | ||||
\(476\) | −27.8167 | − | 22.8413i | −1.27498 | − | 1.04693i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.660071 | + | 1.39609i | 0.0301909 | + | 0.0638559i | ||||
\(479\) | −23.2925 | −1.06426 | −0.532131 | − | 0.846662i | \(-0.678609\pi\) | ||||
−0.532131 | + | 0.846662i | \(0.678609\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.9143 | 0.771226 | ||||||||
\(482\) | −8.66912 | − | 18.3358i | −0.394868 | − | 0.835172i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −28.3830 | − | 23.3062i | −1.29013 | − | 1.05937i | ||||
\(485\) | −0.612124 | + | 0.612124i | −0.0277951 | + | 0.0277951i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.49302 | 0.294227 | 0.147113 | − | 0.989120i | \(-0.453002\pi\) | ||||
0.147113 | + | 0.989120i | \(0.453002\pi\) | |||||||
\(488\) | −2.85617 | + | 1.71034i | −0.129293 | + | 0.0774234i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.08947 | − | 1.10590i | −0.139568 | − | 0.0499596i | ||||
\(491\) | −9.99765 | − | 9.99765i | −0.451188 | − | 0.451188i | 0.444561 | − | 0.895749i | \(-0.353360\pi\) |
−0.895749 | + | 0.444561i | \(0.853360\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.52334 | − | 1.52334i | 0.0686080 | − | 0.0686080i | ||||
\(494\) | 16.6848 | + | 35.2895i | 0.750685 | + | 1.58775i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.4229 | − | 4.05082i | 0.917017 | − | 0.181887i | ||||
\(497\) | 9.44353i | 0.423600i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.6215 | − | 16.6215i | −0.744080 | − | 0.744080i | 0.229281 | − | 0.973360i | \(-0.426363\pi\) |
−0.973360 | + | 0.229281i | \(0.926363\pi\) | |||||||
\(500\) | −6.06200 | + | 0.595389i | −0.271101 | + | 0.0266266i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.02856 | + | 11.2542i | −0.179803 | + | 0.502301i | ||||
\(503\) | − | 22.3009i | − | 0.994348i | −0.867651 | − | 0.497174i | \(-0.834371\pi\) | ||
0.867651 | − | 0.497174i | \(-0.165629\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 2.77464i | − | 0.123470i | ||||||
\(506\) | 44.6236 | + | 15.9734i | 1.98376 | + | 0.710106i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −23.6470 | − | 19.4173i | −1.04916 | − | 0.861505i | ||||
\(509\) | 19.1255 | + | 19.1255i | 0.847721 | + | 0.847721i | 0.989848 | − | 0.142128i | \(-0.0453943\pi\) |
−0.142128 | + | 0.989848i | \(0.545394\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 25.5152i | − | 1.12872i | ||||||
\(512\) | 16.7472 | + | 15.2162i | 0.740128 | + | 0.672466i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 29.9274 | − | 14.1496i | 1.32004 | − | 0.624114i | ||||
\(515\) | −4.03805 | + | 4.03805i | −0.177938 | + | 0.177938i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.7600 | + | 20.7600i | 0.913025 | + | 0.913025i | ||||
\(518\) | 7.52492 | − | 21.0217i | 0.330626 | − | 0.923641i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.864810 | + | 3.44654i | −0.0379244 | + | 0.151141i | ||||
\(521\) | −5.15019 | −0.225634 | −0.112817 | − | 0.993616i | \(-0.535987\pi\) | ||||
−0.112817 | + | 0.993616i | \(0.535987\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.348495 | + | 0.348495i | −0.0152386 | + | 0.0152386i | −0.714685 | − | 0.699446i | \(-0.753430\pi\) |
0.699446 | + | 0.714685i | \(0.253430\pi\) | |||||||
\(524\) | 0.981980 | + | 9.99810i | 0.0428980 | + | 0.436769i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.0253 | + | 8.04953i | −0.742338 | + | 0.350976i | ||||
\(527\) | 24.5609 | 1.06989 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.2527 | −0.663163 | ||||||||
\(530\) | −1.03276 | + | 0.488285i | −0.0448600 | + | 0.0212098i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 51.2818 | − | 5.03673i | 2.22335 | − | 0.218370i | ||||
\(533\) | −3.79976 | + | 3.79976i | −0.164586 | + | 0.164586i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.43184 | 0.234839 | ||||||||
\(536\) | −13.3215 | − | 22.2461i | −0.575400 | − | 0.960886i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.92161 | − | 16.5427i | 0.255299 | − | 0.713206i | ||||
\(539\) | 28.9160 | + | 28.9160i | 1.24550 | + | 1.24550i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.2936 | − | 13.2936i | 0.571536 | − | 0.571536i | −0.361021 | − | 0.932558i | \(-0.617572\pi\) |
0.932558 | + | 0.361021i | \(0.117572\pi\) | |||||||
\(542\) | −1.87014 | + | 0.884200i | −0.0803295 | + | 0.0379797i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15.8858 | + | 21.4500i | 0.681099 | + | 0.919663i | ||||
\(545\) | − | 2.14529i | − | 0.0918940i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.0584 | + | 17.0584i | 0.729366 | + | 0.729366i | 0.970494 | − | 0.241127i | \(-0.0775171\pi\) |
−0.241127 | + | 0.970494i | \(0.577517\pi\) | |||||||
\(548\) | −5.21926 | + | 6.35615i | −0.222956 | + | 0.271521i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 35.3927 | + | 12.6691i | 1.50915 | + | 0.540214i | ||||
\(551\) | 3.08421i | 0.131392i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 35.4175i | − | 1.50611i | ||||||
\(554\) | 1.91352 | − | 5.34565i | 0.0812979 | − | 0.227115i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.83713 | + | 18.7049i | 0.0779117 | + | 0.793264i | ||||
\(557\) | 14.5673 | + | 14.5673i | 0.617236 | + | 0.617236i | 0.944822 | − | 0.327586i | \(-0.106235\pi\) |
−0.327586 | + | 0.944822i | \(0.606235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.91983i | 0.123496i | ||||||||
\(560\) | 3.89875 | + | 2.60813i | 0.164752 | + | 0.110214i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.94824 | + | 8.35079i | 0.166546 | + | 0.352257i | ||||
\(563\) | 21.3310 | − | 21.3310i | 0.898994 | − | 0.898994i | −0.0963535 | − | 0.995347i | \(-0.530718\pi\) |
0.995347 | + | 0.0963535i | \(0.0307179\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.55298 | − | 2.55298i | −0.107405 | − | 0.107405i | ||||
\(566\) | 3.42946 | + | 1.22761i | 0.144151 | + | 0.0516001i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.70442 | − | 6.79265i | 0.0715158 | − | 0.285013i | ||||
\(569\) | −21.5582 | −0.903765 | −0.451882 | − | 0.892077i | \(-0.649247\pi\) | ||||
−0.451882 | + | 0.892077i | \(0.649247\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.5802 | + | 31.5802i | −1.32159 | + | 1.32159i | −0.409100 | + | 0.912490i | \(0.634157\pi\) |
−0.912490 | + | 0.409100i | \(0.865843\pi\) | |||||||
\(572\) | 28.1018 | − | 34.2231i | 1.17499 | − | 1.43094i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.03202 | + | 6.41293i | 0.126554 | + | 0.267671i | ||||
\(575\) | −30.3397 | −1.26525 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.0498 | −1.08447 | −0.542235 | − | 0.840227i | \(-0.682422\pi\) | ||||
−0.542235 | + | 0.840227i | \(0.682422\pi\) | |||||||
\(578\) | 3.18227 | + | 6.73072i | 0.132365 | + | 0.279961i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.178170 | + | 0.216981i | −0.00739811 | + | 0.00900963i | ||||
\(581\) | 31.4509 | − | 31.4509i | 1.30480 | − | 1.30480i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.2362 | 0.589604 | ||||||||
\(584\) | −4.60511 | + | 18.3528i | −0.190561 | + | 0.759446i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −43.1714 | − | 15.4536i | −1.78340 | − | 0.638383i | ||||
\(587\) | −0.757628 | − | 0.757628i | −0.0312707 | − | 0.0312707i | 0.691299 | − | 0.722569i | \(-0.257039\pi\) |
−0.722569 | + | 0.691299i | \(0.757039\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.8633 | + | 24.8633i | −1.02448 | + | 1.02448i | ||||
\(590\) | 1.25549 | + | 2.65544i | 0.0516877 | + | 0.109323i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.20672 | + | 13.7626i | −0.378394 | + | 0.565639i | ||||
\(593\) | 32.5463i | 1.33652i | 0.743929 | + | 0.668259i | \(0.232960\pi\) | ||||
−0.743929 | + | 0.668259i | \(0.767040\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.91262 | + | 3.91262i | 0.160402 | + | 0.160402i | ||||
\(596\) | −0.199899 | − | 2.03529i | −0.00818820 | − | 0.0833688i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.0449 | + | 33.6487i | −0.492551 | + | 1.37600i | ||||
\(599\) | 30.0578i | 1.22813i | 0.789256 | + | 0.614065i | \(0.210467\pi\) | ||||
−0.789256 | + | 0.614065i | \(0.789533\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 23.7148i | − | 0.967348i | −0.875248 | − | 0.483674i | \(-0.839302\pi\) | ||
0.875248 | − | 0.483674i | \(-0.160698\pi\) | |||||||
\(602\) | 3.62887 | + | 1.29899i | 0.147902 | + | 0.0529428i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.54121 | + | 9.18389i | −0.306847 | + | 0.373687i | ||||
\(605\) | 3.99227 | + | 3.99227i | 0.162309 | + | 0.162309i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 36.9838i | − | 1.50113i | −0.660799 | − | 0.750563i | \(-0.729782\pi\) | ||
0.660799 | − | 0.750563i | \(-0.270218\pi\) | |||||||
\(608\) | −37.7956 | − | 5.63274i | −1.53282 | − | 0.228438i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.462685 | − | 0.218756i | 0.0187336 | − | 0.00885719i | ||||
\(611\) | −15.6542 | + | 15.6542i | −0.633302 | + | 0.633302i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.51791 | + | 9.51791i | 0.384425 | + | 0.384425i | 0.872693 | − | 0.488269i | \(-0.162371\pi\) |
−0.488269 | + | 0.872693i | \(0.662371\pi\) | |||||||
\(614\) | 7.30930 | − | 20.4194i | 0.294979 | − | 0.824058i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −30.0316 | − | 50.1512i | −1.21001 | − | 2.02065i | ||||
\(617\) | 37.4296 | 1.50686 | 0.753430 | − | 0.657528i | \(-0.228398\pi\) | ||||
0.753430 | + | 0.657528i | \(0.228398\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.0391337 | + | 0.0391337i | −0.00157291 | + | 0.00157291i | −0.707893 | − | 0.706320i | \(-0.750354\pi\) |
0.706320 | + | 0.707893i | \(0.250354\pi\) | |||||||
\(620\) | −3.18550 | + | 0.312869i | −0.127933 | + | 0.0125651i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21.0180 | + | 9.93725i | −0.842743 | + | 0.398448i | ||||
\(623\) | 47.1948 | 1.89082 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.5909 | −0.943637 | ||||||||
\(626\) | −0.219275 | + | 0.103673i | −0.00876401 | + | 0.00414361i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.89140 | + | 39.6206i | 0.155284 | + | 1.58103i | ||||
\(629\) | −13.8116 | + | 13.8116i | −0.550704 | + | 0.550704i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.6535 | 1.45915 | 0.729576 | − | 0.683900i | \(-0.239717\pi\) | ||||
0.729576 | + | 0.683900i | \(0.239717\pi\) | |||||||
\(632\) | −6.39234 | + | 25.4755i | −0.254274 | + | 1.01336i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.06382 | + | 22.5272i | −0.320255 | + | 0.894670i | ||||
\(635\) | 3.32612 | + | 3.32612i | 0.131993 | + | 0.131993i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.8042 | + | 21.8042i | −0.863915 | + | 0.863915i | ||||
\(638\) | 3.16309 | − | 1.49551i | 0.125228 | − | 0.0592076i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.33361 | − | 2.57967i | −0.0922439 | − | 0.101971i | ||||
\(641\) | 12.4650i | 0.492339i | 0.969227 | + | 0.246169i | \(0.0791719\pi\) | ||||
−0.969227 | + | 0.246169i | \(0.920828\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.95415 | − | 5.95415i | −0.234809 | − | 0.234809i | 0.579888 | − | 0.814696i | \(-0.303096\pi\) |
−0.814696 | + | 0.579888i | \(0.803096\pi\) | |||||||
\(644\) | 36.4612 | + | 29.9395i | 1.43677 | + | 1.17978i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −42.4402 | − | 15.1919i | −1.66979 | − | 0.597716i | ||||
\(647\) | − | 8.17712i | − | 0.321476i | −0.986997 | − | 0.160738i | \(-0.948613\pi\) | ||
0.986997 | − | 0.160738i | \(-0.0513874\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 36.6045i | − | 1.43685i | ||||||
\(650\) | −9.55323 | + | 26.6880i | −0.374709 | + | 1.04679i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.54451 | − | 0.937429i | 0.373792 | − | 0.0367126i | ||||
\(653\) | −26.9263 | − | 26.9263i | −1.05371 | − | 1.05371i | −0.998473 | − | 0.0552346i | \(-0.982409\pi\) |
−0.0552346 | − | 0.998473i | \(-0.517591\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 1.54443i | − | 0.0603458i | ||||||
\(656\) | −1.02347 | − | 5.16000i | −0.0399597 | − | 0.201464i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.4913 | + | 26.4199i | 0.486961 | + | 1.02996i | ||||
\(659\) | −1.76198 | + | 1.76198i | −0.0686372 | + | 0.0686372i | −0.740592 | − | 0.671955i | \(-0.765455\pi\) |
0.671955 | + | 0.740592i | \(0.265455\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.153923 | − | 0.153923i | −0.00598692 | − | 0.00598692i | 0.704107 | − | 0.710094i | \(-0.251348\pi\) |
−0.710094 | + | 0.704107i | \(0.751348\pi\) | |||||||
\(662\) | 4.37721 | + | 1.56686i | 0.170125 | + | 0.0608979i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −28.2988 | + | 16.9459i | −1.09821 | + | 0.657630i | ||||
\(665\) | −7.92162 | −0.307187 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.99675 | + | 1.99675i | −0.0773144 | + | 0.0773144i | ||||
\(668\) | 14.1494 | + | 11.6186i | 0.547458 | + | 0.449536i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.70385 | + | 3.60375i | 0.0658254 | + | 0.139225i | ||||
\(671\) | −6.37797 | −0.246219 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.0014 | −0.886639 | −0.443320 | − | 0.896364i | \(-0.646199\pi\) | ||||
−0.443320 | + | 0.896364i | \(0.646199\pi\) | |||||||
\(674\) | 6.62302 | + | 14.0081i | 0.255109 | + | 0.539573i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.71233 | + | 4.69059i | 0.219705 | + | 0.180407i | ||||
\(677\) | 25.8728 | − | 25.8728i | 0.994374 | − | 0.994374i | −0.00561069 | − | 0.999984i | \(-0.501786\pi\) |
0.999984 | + | 0.00561069i | \(0.00178595\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.7384 | 0.412103 | ||||||||
\(680\) | −2.10815 | − | 3.52049i | −0.0808437 | − | 0.135005i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 37.5553 | + | 13.4432i | 1.43806 | + | 0.514769i | ||||
\(683\) | 16.4249 | + | 16.4249i | 0.628480 | + | 0.628480i | 0.947686 | − | 0.319205i | \(-0.103416\pi\) |
−0.319205 | + | 0.947686i | \(0.603416\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.894039 | − | 0.894039i | 0.0341595 | − | 0.0341595i | ||||
\(686\) | 1.26027 | + | 2.66556i | 0.0481175 | + | 0.101772i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.37577 | − | 1.58931i | −0.0905752 | − | 0.0605918i | ||||
\(689\) | 10.7349i | 0.408967i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.0989768 | + | 0.0989768i | 0.00376526 | + | 0.00376526i | 0.708987 | − | 0.705222i | \(-0.249153\pi\) |
−0.705222 | + | 0.708987i | \(0.749153\pi\) | |||||||
\(692\) | −6.47485 | + | 0.635938i | −0.246137 | + | 0.0241747i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.916595 | − | 2.56061i | 0.0347935 | − | 0.0971996i | ||||
\(695\) | − | 2.88938i | − | 0.109601i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 6.20548i | − | 0.235049i | ||||||
\(698\) | −4.80726 | − | 1.72080i | −0.181957 | − | 0.0651333i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 28.9188 | + | 23.7462i | 1.09303 | + | 0.897522i | ||||
\(701\) | 9.89571 | + | 9.89571i | 0.373756 | + | 0.373756i | 0.868843 | − | 0.495087i | \(-0.164864\pi\) |
−0.495087 | + | 0.868843i | \(0.664864\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 27.9633i | − | 1.05466i | ||||||
\(704\) | 12.5500 | + | 41.4936i | 0.472994 | + | 1.56385i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.0138 | + | 7.57131i | −0.602688 | + | 0.284950i | ||||
\(707\) | −24.3376 | + | 24.3376i | −0.915309 | + | 0.915309i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.60454 | − | 8.60454i | −0.323150 | − | 0.323150i | 0.526824 | − | 0.849974i | \(-0.323383\pi\) |
−0.849974 | + | 0.526824i | \(0.823383\pi\) | |||||||
\(710\) | −0.362841 | + | 1.01364i | −0.0136172 | + | 0.0380412i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −33.9468 | − | 8.51797i | −1.27221 | − | 0.319224i | ||||
\(713\) | −32.1935 | −1.20566 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.81373 | + | 4.81373i | −0.180023 | + | 0.180023i | ||||
\(716\) | 1.98312 | + | 20.1913i | 0.0741128 | + | 0.754585i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.2984 | − | 6.76027i | 0.533612 | − | 0.252291i | ||||
\(719\) | 39.6092 | 1.47717 | 0.738586 | − | 0.674159i | \(-0.235494\pi\) | ||||
0.738586 | + | 0.674159i | \(0.235494\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 70.8390 | 2.63818 | ||||||||
\(722\) | 34.0500 | − | 16.0988i | 1.26721 | − | 0.599135i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 48.1342 | − | 4.72758i | 1.78889 | − | 0.175699i | ||||
\(725\) | −1.58370 | + | 1.58370i | −0.0588170 | + | 0.0588170i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.9378 | −0.665278 | −0.332639 | − | 0.943054i | \(-0.607939\pi\) | ||||
−0.332639 | + | 0.943054i | \(0.607939\pi\) | |||||||
\(728\) | 37.8168 | − | 22.6455i | 1.40158 | − | 0.839299i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.980349 | − | 2.73872i | 0.0362843 | − | 0.101364i | ||||
\(731\) | −2.38422 | − | 2.38422i | −0.0881836 | − | 0.0881836i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.8729 | − | 17.8729i | 0.660152 | − | 0.660152i | −0.295264 | − | 0.955416i | \(-0.595408\pi\) |
0.955416 | + | 0.295264i | \(0.0954075\pi\) | |||||||
\(734\) | 16.7157 | − | 7.90316i | 0.616988 | − | 0.291711i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20.8226 | − | 28.1160i | −0.767531 | − | 1.03637i | ||||
\(737\) | − | 49.6766i | − | 1.82986i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.9555 | − | 17.9555i | −0.660504 | − | 0.660504i | 0.294995 | − | 0.955499i | \(-0.404682\pi\) |
−0.955499 | + | 0.294995i | \(0.904682\pi\) | |||||||
\(740\) | 1.61540 | − | 1.96728i | 0.0593833 | − | 0.0723186i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.3417 | + | 4.77579i | 0.489790 | + | 0.175325i | ||||
\(743\) | 48.9933i | 1.79739i | 0.438576 | + | 0.898694i | \(0.355483\pi\) | ||||
−0.438576 | + | 0.898694i | \(0.644517\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.314396i | 0.0115186i | ||||||||
\(746\) | −3.80378 | + | 10.6263i | −0.139266 | + | 0.389056i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.99845 | + | 50.8921i | 0.182761 | + | 1.86080i | ||||
\(749\) | −47.6450 | − | 47.6450i | −1.74091 | − | 1.74091i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 28.5197i | − | 1.04070i | −0.853954 | − | 0.520349i | \(-0.825802\pi\) | ||
0.853954 | − | 0.520349i | \(-0.174198\pi\) | |||||||
\(752\) | −4.21647 | − | 21.2581i | −0.153759 | − | 0.775204i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.12769 | + | 2.38515i | 0.0410682 | + | 0.0868620i | ||||
\(755\) | 1.29178 | − | 1.29178i | 0.0470127 | − | 0.0470127i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.5077 | + | 34.5077i | 1.25420 | + | 1.25420i | 0.953817 | + | 0.300388i | \(0.0971161\pi\) |
0.300388 | + | 0.953817i | \(0.402884\pi\) | |||||||
\(758\) | 18.5717 | + | 6.64790i | 0.674553 | + | 0.241462i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.69795 | + | 1.42973i | 0.206686 | + | 0.0518619i | ||||
\(761\) | 25.2483 | 0.915248 | 0.457624 | − | 0.889146i | \(-0.348701\pi\) | ||||
0.457624 | + | 0.889146i | \(0.348701\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.8173 | + | 18.8173i | −0.681230 | + | 0.681230i | ||||
\(764\) | −30.0631 | + | 36.6117i | −1.08765 | + | 1.32456i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.96838 | − | 18.9687i | −0.324041 | − | 0.685368i | ||||
\(767\) | 27.6018 | 0.996644 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.4742 | −0.702259 | −0.351129 | − | 0.936327i | \(-0.614202\pi\) | ||||
−0.351129 | + | 0.936327i | \(0.614202\pi\) | |||||||
\(770\) | 3.84112 | + | 8.12422i | 0.138424 | + | 0.292777i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −33.7279 | + | 41.0748i | −1.21389 | + | 1.47831i | ||||
\(773\) | 10.2401 | − | 10.2401i | 0.368309 | − | 0.368309i | −0.498551 | − | 0.866860i | \(-0.666134\pi\) |
0.866860 | + | 0.498551i | \(0.166134\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25.5339 | −0.917206 | ||||||||
\(776\) | −7.72406 | − | 1.93813i | −0.277278 | − | 0.0695747i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.87208 | − | 2.45992i | −0.246376 | − | 0.0881925i | ||||
\(779\) | 6.28190 | + | 6.28190i | 0.225072 | + | 0.225072i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.48717 | − | 9.48717i | 0.339478 | − | 0.339478i | ||||
\(782\) | −17.6409 | − | 37.3116i | −0.630836 | − | 1.33426i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.87299 | − | 29.6097i | −0.209750 | − | 1.05749i | ||||
\(785\) | − | 6.12028i | − | 0.218442i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.7690 | + | 32.7690i | 1.16809 | + | 1.16809i | 0.982657 | + | 0.185432i | \(0.0593683\pi\) |
0.185432 | + | 0.982657i | \(0.440632\pi\) | |||||||
\(788\) | −4.02281 | − | 40.9586i | −0.143307 | − | 1.45909i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.36082 | − | 3.80160i | 0.0484158 | − | 0.135255i | ||||
\(791\) | 44.7867i | 1.59243i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 4.80934i | − | 0.170785i | ||||||
\(794\) | −25.2157 | − | 9.02619i | −0.894872 | − | 0.320328i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.417842 | − | 0.508860i | 0.0148100 | − | 0.0180361i | ||||
\(797\) | −18.9380 | − | 18.9380i | −0.670817 | − | 0.670817i | 0.287087 | − | 0.957904i | \(-0.407313\pi\) |
−0.957904 | + | 0.287087i | \(0.907313\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 25.5653i | − | 0.904434i | ||||||
\(800\) | −16.5152 | − | 22.2999i | −0.583900 | − | 0.788419i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 35.2034 | − | 16.6441i | 1.24307 | − | 0.587723i | ||||
\(803\) | −25.6331 | + | 25.6331i | −0.904572 | + | 0.904572i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.12853 | − | 5.12853i | −0.180757 | − | 0.180757i | ||||
\(806\) | −10.1370 | + | 28.3187i | −0.357059 | + | 0.997485i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 21.8984 | − | 13.1132i | 0.770383 | − | 0.461322i | ||||
\(809\) | 29.2888 | 1.02974 | 0.514870 | − | 0.857268i | \(-0.327840\pi\) | ||||
0.514870 | + | 0.857268i | \(0.327840\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.8548 | + | 12.8548i | −0.451393 | + | 0.451393i | −0.895817 | − | 0.444424i | \(-0.853408\pi\) |
0.444424 | + | 0.895817i | \(0.353408\pi\) | |||||||
\(812\) | 3.46604 | − | 0.340423i | 0.121634 | − | 0.0119465i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −28.6786 | + | 13.5592i | −1.00518 | + | 0.475249i | ||||
\(815\) | −1.47436 | −0.0516446 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.82717 | 0.168881 | ||||||||
\(818\) | 20.7565 | − | 9.81365i | 0.725735 | − | 0.343126i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0790487 | + | 0.804840i | 0.00276050 | + | 0.0281062i | ||||
\(821\) | 18.6497 | − | 18.6497i | 0.650880 | − | 0.650880i | −0.302325 | − | 0.953205i | \(-0.597763\pi\) |
0.953205 | + | 0.302325i | \(0.0977627\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.21917 | −0.0773554 | −0.0386777 | − | 0.999252i | \(-0.512315\pi\) | ||||
−0.0386777 | + | 0.999252i | \(0.512315\pi\) | |||||||
\(824\) | −50.9539 | − | 12.7854i | −1.77506 | − | 0.445401i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.2796 | − | 34.3045i | 0.427263 | − | 1.19361i | ||||
\(827\) | 21.7284 | + | 21.7284i | 0.755570 | + | 0.755570i | 0.975513 | − | 0.219943i | \(-0.0705871\pi\) |
−0.219943 | + | 0.975513i | \(0.570587\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.37469 | − | 1.37469i | 0.0477451 | − | 0.0477451i | −0.682831 | − | 0.730576i | \(-0.739252\pi\) |
0.730576 | + | 0.682831i | \(0.239252\pi\) | |||||||
\(830\) | 4.58425 | − | 2.16743i | 0.159122 | − | 0.0752325i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −31.2885 | + | 9.46336i | −1.08473 | + | 0.328083i | ||||
\(833\) | − | 35.6090i | − | 1.23378i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.99022 | − | 1.99022i | −0.0688744 | − | 0.0688744i | ||||
\(836\) | −56.5789 | − | 46.4588i | −1.95682 | − | 1.60681i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.06261 | + | 1.45425i | 0.140340 | + | 0.0502362i | ||||
\(839\) | 2.77829i | 0.0959171i | 0.998849 | + | 0.0479585i | \(0.0152715\pi\) | ||||
−0.998849 | + | 0.0479585i | \(0.984728\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 28.7915i | − | 0.992812i | ||||||
\(842\) | 11.6211 | − | 32.4650i | 0.400491 | − | 1.11882i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.6414 | − | 1.43803i | 0.503979 | − | 0.0494991i | ||||
\(845\) | −0.803481 | − | 0.803481i | −0.0276406 | − | 0.0276406i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 70.0359i | − | 2.40646i | ||||||
\(848\) | −8.73463 | − | 5.84317i | −0.299948 | − | 0.200655i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13.9916 | − | 29.5933i | −0.479909 | − | 1.01504i | ||||
\(851\) | 18.1037 | − | 18.1037i | 0.620588 | − | 0.620588i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.0961 | + | 17.0961i | 0.585360 | + | 0.585360i | 0.936371 | − | 0.351011i | \(-0.114162\pi\) |
−0.351011 | + | 0.936371i | \(0.614162\pi\) | |||||||
\(854\) | −5.97722 | − | 2.13960i | −0.204536 | − | 0.0732156i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 25.6714 | + | 42.8699i | 0.877432 | + | 1.46526i | ||||
\(857\) | −49.4967 | −1.69078 | −0.845388 | − | 0.534153i | \(-0.820631\pi\) | ||||
−0.845388 | + | 0.534153i | \(0.820631\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.5374 | − | 25.5374i | 0.871324 | − | 0.871324i | −0.121293 | − | 0.992617i | \(-0.538704\pi\) |
0.992617 | + | 0.121293i | \(0.0387040\pi\) | |||||||
\(860\) | 0.339601 | + | 0.278858i | 0.0115803 | + | 0.00950899i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.1565 | + | 42.6323i | 0.686532 | + | 1.45206i | ||||
\(863\) | −45.8222 | −1.55981 | −0.779904 | − | 0.625900i | \(-0.784732\pi\) | ||||
−0.779904 | + | 0.625900i | \(0.784732\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.00018 | 0.0340073 | ||||||||
\(866\) | 13.4344 | + | 28.4147i | 0.456520 | + | 0.965571i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 30.6858 | + | 25.1971i | 1.04154 | + | 0.855247i | ||||
\(869\) | −35.5812 | + | 35.5812i | −1.20701 | + | 1.20701i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37.4589 | 1.26925 | ||||||||
\(872\) | 16.9313 | − | 10.1389i | 0.573367 | − | 0.343345i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 55.6292 | + | 19.9130i | 1.88169 | + | 0.673567i | ||||
\(875\) | −8.21366 | − | 8.21366i | −0.277672 | − | 0.277672i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.65581 | − | 9.65581i | 0.326054 | − | 0.326054i | −0.525030 | − | 0.851084i | \(-0.675946\pi\) |
0.851084 | + | 0.525030i | \(0.175946\pi\) | |||||||
\(878\) | 0.145380 | + | 0.307489i | 0.00490634 | + | 0.0103772i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.29658 | − | 6.53695i | −0.0437078 | − | 0.220361i | ||||
\(881\) | − | 54.5487i | − | 1.83779i | −0.394499 | − | 0.918896i | \(-0.629082\pi\) | ||
0.394499 | − | 0.918896i | \(-0.370918\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.7878 | − | 12.7878i | −0.430344 | − | 0.430344i | 0.458401 | − | 0.888745i | \(-0.348422\pi\) |
−0.888745 | + | 0.458401i | \(0.848422\pi\) | |||||||
\(884\) | −38.3755 | + | 3.76911i | −1.29071 | + | 0.126769i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.8911 | + | 49.9807i | −0.601062 | + | 1.67913i | ||||
\(887\) | − | 29.3515i | − | 0.985527i | −0.870163 | − | 0.492763i | \(-0.835987\pi\) | ||
0.870163 | − | 0.492763i | \(-0.164013\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 58.3497i | − | 1.95699i | ||||||
\(890\) | 5.06574 | + | 1.81333i | 0.169804 | + | 0.0607829i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.22232 | + | 1.00369i | 0.0409264 | + | 0.0336061i | ||||
\(893\) | 25.8801 | + | 25.8801i | 0.866045 | + | 0.866045i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3.11900i | − | 0.104257i | ||||||
\(896\) | −2.15835 | + | 43.0965i | −0.0721055 | + | 1.43975i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −40.8529 | + | 19.3152i | −1.36328 | + | 0.644556i | ||||
\(899\) | −1.68046 | + | 1.68046i | −0.0560466 | + | 0.0560466i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.76571 | − | 8.76571i | −0.292028 | − | 0.292028i | ||||
\(902\) | 3.39653 | − | 9.48861i | 0.113092 | − | 0.315936i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.08333 | − | 32.2147i | 0.268848 | − | 1.07144i | ||||
\(905\) | −7.43540 | −0.247161 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.0905 | − | 22.0905i | 0.733505 | − | 0.733505i | −0.237808 | − | 0.971312i | \(-0.576429\pi\) |
0.971312 | + | 0.237808i | \(0.0764288\pi\) | |||||||
\(908\) | 1.20495 | + | 12.2683i | 0.0399878 | + | 0.407139i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.12612 | + | 2.89642i | −0.203079 | + | 0.0960153i | ||||
\(911\) | −48.9197 | −1.62078 | −0.810391 | − | 0.585889i | \(-0.800745\pi\) | ||||
−0.810391 | + | 0.585889i | \(0.800745\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −63.1925 | −2.09137 | ||||||||
\(914\) | 16.6284 | − | 7.86187i | 0.550018 | − | 0.260048i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −33.6216 | + | 3.30220i | −1.11089 | + | 0.109108i | ||||
\(917\) | −13.5469 | + | 13.5469i | −0.447357 | + | 0.447357i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.4269 | 0.706810 | 0.353405 | − | 0.935470i | \(-0.385024\pi\) | ||||
0.353405 | + | 0.935470i | \(0.385024\pi\) | |||||||
\(920\) | 2.76328 | + | 4.61453i | 0.0911028 | + | 0.152137i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9.50247 | + | 26.5462i | −0.312947 | + | 0.874254i | ||||
\(923\) | 7.15385 | + | 7.15385i | 0.235472 | + | 0.235472i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.3588 | − | 14.3588i | 0.472114 | − | 0.472114i | ||||
\(926\) | 45.7584 | − | 21.6345i | 1.50372 | − | 0.710954i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.55453 | − | 0.380706i | −0.0838567 | − | 0.0124973i | ||||
\(929\) | − | 15.5610i | − | 0.510539i | −0.966870 | − | 0.255269i | \(-0.917836\pi\) | ||
0.966870 | − | 0.255269i | \(-0.0821642\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.0475 | + | 36.0475i | 1.18141 | + | 1.18141i | ||||
\(932\) | −33.6261 | + | 40.9508i | −1.10146 | + | 1.34139i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −28.7248 | − | 10.2823i | −0.939903 | − | 0.336447i | ||||
\(935\) | − | 7.86141i | − | 0.257096i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19.4793i | − | 0.636360i | −0.948030 | − | 0.318180i | \(-0.896928\pi\) | ||
0.948030 | − | 0.318180i | \(-0.103072\pi\) | |||||||
\(938\) | 16.6649 | − | 46.5553i | 0.544128 | − | 1.52008i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.325664 | + | 3.31577i | 0.0106220 | + | 0.108149i | ||||
\(941\) | −5.26841 | − | 5.26841i | −0.171745 | − | 0.171745i | 0.616001 | − | 0.787746i | \(-0.288752\pi\) |
−0.787746 | + | 0.616001i | \(0.788752\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.13393i | 0.264877i | ||||||||
\(944\) | −15.0241 | + | 22.4587i | −0.488992 | + | 0.730967i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.34065 | − | 4.95063i | −0.0761011 | − | 0.160959i | ||||
\(947\) | 23.4075 | − | 23.4075i | 0.760641 | − | 0.760641i | −0.215797 | − | 0.976438i | \(-0.569235\pi\) |
0.976438 | + | 0.215797i | \(0.0692350\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.3288 | − | 19.3288i | −0.627438 | − | 0.627438i | ||||
\(950\) | 44.1216 | + | 15.7937i | 1.43150 | + | 0.512417i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −12.3883 | + | 49.3712i | −0.401506 | + | 1.60013i | ||||
\(953\) | −61.1868 | −1.98204 | −0.991018 | − | 0.133731i | \(-0.957304\pi\) | ||||
−0.991018 | + | 0.133731i | \(0.957304\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.14970 | − | 5.14970i | 0.166640 | − | 0.166640i | ||||
\(956\) | 1.38593 | − | 1.68782i | 0.0448242 | − | 0.0545881i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.0799 | + | 29.7799i | 0.454900 | + | 0.962144i | ||||
\(959\) | −15.6840 | −0.506464 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.90591 | 0.125997 | ||||||||
\(962\) | −10.2244 | − | 21.6252i | −0.329647 | − | 0.697225i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18.2023 | + | 22.1672i | −0.586256 | + | 0.713958i | ||||
\(965\) | 5.77747 | − | 5.77747i | 0.185983 | − | 0.185983i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.4866 | 1.10902 | 0.554508 | − | 0.832178i | \(-0.312907\pi\) | ||||
0.554508 | + | 0.832178i | \(0.312907\pi\) | |||||||
\(968\) | −12.6404 | + | 50.3762i | −0.406279 | + | 1.61915i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.15263 | + | 0.412594i | 0.0370087 | + | 0.0132476i | ||||
\(971\) | −17.8898 | − | 17.8898i | −0.574110 | − | 0.574110i | 0.359165 | − | 0.933274i | \(-0.383062\pi\) |
−0.933274 | + | 0.359165i | \(0.883062\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.3441 | + | 25.3441i | −0.812493 | + | 0.812493i | ||||
\(974\) | −3.92490 | − | 8.30143i | −0.125762 | − | 0.265995i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.91320 | + | 2.61780i | 0.125258 | + | 0.0837936i | ||||
\(977\) | 33.3136i | 1.06580i | 0.846180 | + | 0.532898i | \(0.178897\pi\) | ||||
−0.846180 | + | 0.532898i | \(0.821103\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −47.4129 | − | 47.4129i | −1.51532 | − | 1.51532i | ||||
\(980\) | 0.453606 | + | 4.61843i | 0.0144899 | + | 0.147530i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.73878 | + | 18.8255i | −0.215043 | + | 0.600747i | ||||
\(983\) | 2.60454i | 0.0830720i | 0.999137 | + | 0.0415360i | \(0.0132251\pi\) | ||||
−0.999137 | + | 0.0415360i | \(0.986775\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.32696i | 0.201594i | ||||||||
\(986\) | −2.86845 | − | 1.02679i | −0.0913501 | − | 0.0326996i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 35.0325 | − | 42.6636i | 1.11453 | − | 1.35731i | ||||
\(989\) | 3.12516 | + | 3.12516i | 0.0993742 | + | 0.0993742i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.4871i | 1.69907i | 0.527530 | + | 0.849537i | \(0.323118\pi\) | ||||
−0.527530 | + | 0.849537i | \(0.676882\pi\) | |||||||
\(992\) | −17.5243 | − | 23.6624i | −0.556397 | − | 0.751282i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12.0737 | − | 5.70843i | 0.382955 | − | 0.181060i | ||||
\(995\) | −0.0715749 | + | 0.0715749i | −0.00226908 | + | 0.00226908i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.9323 | + | 33.9323i | 1.07465 | + | 1.07465i | 0.996979 | + | 0.0776671i | \(0.0247471\pi\) |
0.0776671 | + | 0.996979i | \(0.475253\pi\) | |||||||
\(998\) | −11.2035 | + | 31.2982i | −0.354640 | + | 0.990727i | ||||
\(999\) | 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 | 432.2.l.a.107.7 | ✓ | 32 | |
3.2 | odd | 2 | inner | 432.2.l.a.107.10 | yes | 32 | |
4.3 | odd | 2 | 1728.2.l.a.1295.9 | 32 | |||
12.11 | even | 2 | 1728.2.l.a.1295.8 | 32 | |||
16.3 | odd | 4 | inner | 432.2.l.a.323.10 | yes | 32 | |
16.13 | even | 4 | 1728.2.l.a.431.8 | 32 | |||
48.29 | odd | 4 | 1728.2.l.a.431.9 | 32 | |||
48.35 | even | 4 | inner | 432.2.l.a.323.7 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.l.a.107.7 | ✓ | 32 | 1.1 | even | 1 | trivial | |
432.2.l.a.107.10 | yes | 32 | 3.2 | odd | 2 | inner | |
432.2.l.a.323.7 | yes | 32 | 48.35 | even | 4 | inner | |
432.2.l.a.323.10 | yes | 32 | 16.3 | odd | 4 | inner | |
1728.2.l.a.431.8 | 32 | 16.13 | even | 4 | |||
1728.2.l.a.431.9 | 32 | 48.29 | odd | 4 | |||
1728.2.l.a.1295.8 | 32 | 12.11 | even | 2 | |||
1728.2.l.a.1295.9 | 32 | 4.3 | odd | 2 |