Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [578,2,Mod(155,578)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(578, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("578.155");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 578 = 2 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 578.d (of order \(8\), degree \(4\), 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: | \(4.61535323683\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 34) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 399.2 | ||
Root | \(-0.923880 - 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 578.399 |
Dual form | 578.2.d.e.423.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/578\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{5}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | 0.765367 | − | 1.84776i | 0.441885 | − | 1.06680i | −0.533402 | − | 0.845862i | \(-0.679087\pi\) |
0.975287 | − | 0.220942i | \(-0.0709133\pi\) | |||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(6\) | 0.765367 | + | 1.84776i | 0.312460 | + | 0.754344i | ||||
\(7\) | 3.69552 | − | 1.53073i | 1.39677 | − | 0.578563i | 0.447862 | − | 0.894103i | \(-0.352186\pi\) |
0.948912 | + | 0.315540i | \(0.102186\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | −0.707107 | − | 0.707107i | −0.235702 | − | 0.235702i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.29610 | + | 5.54328i | 0.692300 | + | 1.67136i | 0.740094 | + | 0.672504i | \(0.234781\pi\) |
−0.0477934 | + | 0.998857i | \(0.515219\pi\) | |||||||
\(12\) | −1.84776 | − | 0.765367i | −0.533402 | − | 0.220942i | ||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | −1.53073 | + | 3.69552i | −0.409106 | + | 0.987669i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 2.82843 | − | 2.82843i | 0.648886 | − | 0.648886i | −0.303838 | − | 0.952724i | \(-0.598268\pi\) |
0.952724 | + | 0.303838i | \(0.0982682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 8.00000i | − | 1.74574i | ||||||
\(22\) | −5.54328 | − | 2.29610i | −1.18183 | − | 0.489530i | ||||
\(23\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(24\) | 1.84776 | − | 0.765367i | 0.377172 | − | 0.156230i | ||||
\(25\) | −3.53553 | − | 3.53553i | −0.707107 | − | 0.707107i | ||||
\(26\) | −1.41421 | − | 1.41421i | −0.277350 | − | 0.277350i | ||||
\(27\) | 3.69552 | − | 1.53073i | 0.711203 | − | 0.294590i | ||||
\(28\) | −1.53073 | − | 3.69552i | −0.289281 | − | 0.698387i | ||||
\(29\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.53073 | + | 3.69552i | −0.274928 | + | 0.663735i | −0.999681 | − | 0.0252745i | \(-0.991954\pi\) |
0.724753 | + | 0.689009i | \(0.241954\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 12.0000 | 2.08893 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.707107 | + | 0.707107i | −0.117851 | + | 0.117851i | ||||
\(37\) | 1.53073 | − | 3.69552i | 0.251651 | − | 0.607539i | −0.746687 | − | 0.665176i | \(-0.768356\pi\) |
0.998338 | + | 0.0576366i | \(0.0183565\pi\) | |||||||
\(38\) | 4.00000i | 0.648886i | ||||||||
\(39\) | 3.69552 | + | 1.53073i | 0.591756 | + | 0.245114i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.54328 | + | 2.29610i | −0.865714 | + | 0.358591i | −0.770940 | − | 0.636908i | \(-0.780213\pi\) |
−0.0947747 | + | 0.995499i | \(0.530213\pi\) | |||||||
\(42\) | 5.65685 | + | 5.65685i | 0.872872 | + | 0.872872i | ||||
\(43\) | −5.65685 | − | 5.65685i | −0.862662 | − | 0.862662i | 0.128984 | − | 0.991647i | \(-0.458828\pi\) |
−0.991647 | + | 0.128984i | \(0.958828\pi\) | |||||||
\(44\) | 5.54328 | − | 2.29610i | 0.835680 | − | 0.346150i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | −0.765367 | + | 1.84776i | −0.110471 | + | 0.266701i | ||||
\(49\) | 6.36396 | − | 6.36396i | 0.909137 | − | 0.909137i | ||||
\(50\) | 5.00000 | 0.707107 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | 4.24264 | − | 4.24264i | 0.582772 | − | 0.582772i | −0.352892 | − | 0.935664i | \(-0.614802\pi\) |
0.935664 | + | 0.352892i | \(0.114802\pi\) | |||||||
\(54\) | −1.53073 | + | 3.69552i | −0.208306 | + | 0.502896i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.69552 | + | 1.53073i | 0.493834 | + | 0.204553i | ||||
\(57\) | −3.06147 | − | 7.39104i | −0.405501 | − | 0.978967i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.69552 | + | 1.53073i | −0.473163 | + | 0.195990i | −0.606505 | − | 0.795080i | \(-0.707429\pi\) |
0.133342 | + | 0.991070i | \(0.457429\pi\) | |||||||
\(62\) | −1.53073 | − | 3.69552i | −0.194403 | − | 0.469331i | ||||
\(63\) | −3.69552 | − | 1.53073i | −0.465592 | − | 0.192854i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.48528 | + | 8.48528i | −1.04447 | + | 1.04447i | ||||
\(67\) | −8.00000 | −0.977356 | −0.488678 | − | 0.872464i | \(-0.662521\pi\) | ||||
−0.488678 | + | 0.872464i | \(0.662521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | −1.84776 | − | 0.765367i | −0.216264 | − | 0.0895794i | 0.271921 | − | 0.962319i | \(-0.412341\pi\) |
−0.488185 | + | 0.872740i | \(0.662341\pi\) | |||||||
\(74\) | 1.53073 | + | 3.69552i | 0.177944 | + | 0.429595i | ||||
\(75\) | −9.23880 | + | 3.82683i | −1.06680 | + | 0.441885i | ||||
\(76\) | −2.82843 | − | 2.82843i | −0.324443 | − | 0.324443i | ||||
\(77\) | 16.9706 | + | 16.9706i | 1.93398 | + | 1.93398i | ||||
\(78\) | −3.69552 | + | 1.53073i | −0.418435 | + | 0.173321i | ||||
\(79\) | 3.06147 | + | 7.39104i | 0.344442 | + | 0.831557i | 0.997255 | + | 0.0740378i | \(0.0235886\pi\) |
−0.652813 | + | 0.757519i | \(0.726411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 11.0000i | − | 1.22222i | ||||||
\(82\) | 2.29610 | − | 5.54328i | 0.253562 | − | 0.612153i | ||||
\(83\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(84\) | −8.00000 | −0.872872 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.29610 | + | 5.54328i | −0.244765 | + | 0.590915i | ||||
\(89\) | 6.00000i | 0.635999i | 0.948091 | + | 0.317999i | \(0.103011\pi\) | ||||
−0.948091 | + | 0.317999i | \(0.896989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.06147 | + | 7.39104i | 0.320929 | + | 0.774791i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.65685 | + | 5.65685i | 0.586588 | + | 0.586588i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.765367 | − | 1.84776i | −0.0781149 | − | 0.188586i | ||||
\(97\) | 12.9343 | + | 5.35757i | 1.31328 | + | 0.543979i | 0.925840 | − | 0.377916i | \(-0.123359\pi\) |
0.387441 | + | 0.921895i | \(0.373359\pi\) | |||||||
\(98\) | 9.00000i | 0.909137i | ||||||||
\(99\) | 2.29610 | − | 5.54328i | 0.230767 | − | 0.557120i | ||||
\(100\) | −3.53553 | + | 3.53553i | −0.353553 | + | 0.353553i | ||||
\(101\) | −18.0000 | −1.79107 | −0.895533 | − | 0.444994i | \(-0.853206\pi\) | ||||
−0.895533 | + | 0.444994i | \(0.853206\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.0000 | −1.57653 | −0.788263 | − | 0.615338i | \(-0.789020\pi\) | ||||
−0.788263 | + | 0.615338i | \(0.789020\pi\) | |||||||
\(104\) | −1.41421 | + | 1.41421i | −0.138675 | + | 0.138675i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000i | 0.582772i | ||||||||
\(107\) | 5.54328 | + | 2.29610i | 0.535889 | + | 0.221972i | 0.634180 | − | 0.773185i | \(-0.281338\pi\) |
−0.0982914 | + | 0.995158i | \(0.531338\pi\) | |||||||
\(108\) | −1.53073 | − | 3.69552i | −0.147295 | − | 0.355601i | ||||
\(109\) | 14.7821 | − | 6.12293i | 1.41587 | − | 0.586471i | 0.462048 | − | 0.886855i | \(-0.347115\pi\) |
0.953818 | + | 0.300384i | \(0.0971149\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.65685 | − | 5.65685i | −0.536925 | − | 0.536925i | ||||
\(112\) | −3.69552 | + | 1.53073i | −0.349194 | + | 0.144641i | ||||
\(113\) | −2.29610 | − | 5.54328i | −0.215999 | − | 0.521468i | 0.778325 | − | 0.627861i | \(-0.216070\pi\) |
−0.994324 | + | 0.106394i | \(0.966070\pi\) | |||||||
\(114\) | 7.39104 | + | 3.06147i | 0.692234 | + | 0.286733i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.41421 | − | 1.41421i | 0.130744 | − | 0.130744i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.6777 | + | 17.6777i | −1.60706 | + | 1.60706i | ||||
\(122\) | 1.53073 | − | 3.69552i | 0.138586 | − | 0.334576i | ||||
\(123\) | 12.0000i | 1.08200i | ||||||||
\(124\) | 3.69552 | + | 1.53073i | 0.331867 | + | 0.137464i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.69552 | − | 1.53073i | 0.329223 | − | 0.136369i | ||||
\(127\) | −11.3137 | − | 11.3137i | −1.00393 | − | 1.00393i | −0.999992 | − | 0.00393704i | \(-0.998747\pi\) |
−0.00393704 | − | 0.999992i | \(-0.501253\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | −14.7821 | + | 6.12293i | −1.30149 | + | 0.539094i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.54328 | − | 2.29610i | −0.484318 | − | 0.200611i | 0.127145 | − | 0.991884i | \(-0.459419\pi\) |
−0.611463 | + | 0.791273i | \(0.709419\pi\) | |||||||
\(132\) | − | 12.0000i | − | 1.04447i | ||||||
\(133\) | 6.12293 | − | 14.7821i | 0.530926 | − | 1.28177i | ||||
\(134\) | 5.65685 | − | 5.65685i | 0.488678 | − | 0.488678i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | 0.512615 | 0.256307 | − | 0.966595i | \(-0.417494\pi\) | ||||
0.256307 | + | 0.966595i | \(0.417494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.765367 | + | 1.84776i | −0.0649176 | + | 0.156725i | −0.953009 | − | 0.302942i | \(-0.902031\pi\) |
0.888091 | + | 0.459667i | \(0.152031\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.0866 | + | 4.59220i | −0.927104 | + | 0.384019i | ||||
\(144\) | 0.707107 | + | 0.707107i | 0.0589256 | + | 0.0589256i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.84776 | − | 0.765367i | 0.152922 | − | 0.0633422i | ||||
\(147\) | −6.88830 | − | 16.6298i | −0.568138 | − | 1.37161i | ||||
\(148\) | −3.69552 | − | 1.53073i | −0.303770 | − | 0.125826i | ||||
\(149\) | 6.00000i | 0.491539i | 0.969328 | + | 0.245770i | \(0.0790407\pi\) | ||||
−0.969328 | + | 0.245770i | \(0.920959\pi\) | |||||||
\(150\) | 3.82683 | − | 9.23880i | 0.312460 | − | 0.754344i | ||||
\(151\) | −11.3137 | + | 11.3137i | −0.920697 | + | 0.920697i | −0.997079 | − | 0.0763821i | \(-0.975663\pi\) |
0.0763821 | + | 0.997079i | \(0.475663\pi\) | |||||||
\(152\) | 4.00000 | 0.324443 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −24.0000 | −1.93398 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.53073 | − | 3.69552i | 0.122557 | − | 0.295878i | ||||
\(157\) | − | 14.0000i | − | 1.11732i | −0.829396 | − | 0.558661i | \(-0.811315\pi\) | ||
0.829396 | − | 0.558661i | \(-0.188685\pi\) | |||||||
\(158\) | −7.39104 | − | 3.06147i | −0.587999 | − | 0.243557i | ||||
\(159\) | −4.59220 | − | 11.0866i | −0.364185 | − | 0.879221i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.77817 | + | 7.77817i | 0.611111 | + | 0.611111i | ||||
\(163\) | 1.84776 | − | 0.765367i | 0.144728 | − | 0.0599482i | −0.309144 | − | 0.951015i | \(-0.600042\pi\) |
0.453872 | + | 0.891067i | \(0.350042\pi\) | |||||||
\(164\) | 2.29610 | + | 5.54328i | 0.179295 | + | 0.432857i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.59220 | − | 11.0866i | 0.355355 | − | 0.857903i | −0.640585 | − | 0.767887i | \(-0.721308\pi\) |
0.995940 | − | 0.0900162i | \(-0.0286919\pi\) | |||||||
\(168\) | 5.65685 | − | 5.65685i | 0.436436 | − | 0.436436i | ||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | −0.305888 | ||||||||
\(172\) | −5.65685 | + | 5.65685i | −0.431331 | + | 0.431331i | ||||
\(173\) | −9.18440 | + | 22.1731i | −0.698277 | + | 1.68579i | 0.0291222 | + | 0.999576i | \(0.490729\pi\) |
−0.727399 | + | 0.686214i | \(0.759271\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.4776 | − | 7.65367i | −1.39677 | − | 0.578563i | ||||
\(176\) | −2.29610 | − | 5.54328i | −0.173075 | − | 0.417840i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.24264 | − | 4.24264i | −0.317999 | − | 0.317999i | ||||
\(179\) | −8.48528 | − | 8.48528i | −0.634220 | − | 0.634220i | 0.314904 | − | 0.949124i | \(-0.398028\pi\) |
−0.949124 | + | 0.314904i | \(0.898028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.53073 | − | 3.69552i | −0.113779 | − | 0.274686i | 0.856725 | − | 0.515774i | \(-0.172496\pi\) |
−0.970503 | + | 0.241088i | \(0.922496\pi\) | |||||||
\(182\) | −7.39104 | − | 3.06147i | −0.547860 | − | 0.226931i | ||||
\(183\) | 8.00000i | 0.591377i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −8.00000 | −0.586588 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.3137 | − | 11.3137i | 0.822951 | − | 0.822951i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.0000i | 1.73658i | 0.496058 | + | 0.868290i | \(0.334780\pi\) | ||||
−0.496058 | + | 0.868290i | \(0.665220\pi\) | |||||||
\(192\) | 1.84776 | + | 0.765367i | 0.133351 | + | 0.0552356i | ||||
\(193\) | 3.82683 | + | 9.23880i | 0.275462 | + | 0.665023i | 0.999699 | − | 0.0245275i | \(-0.00780812\pi\) |
−0.724238 | + | 0.689551i | \(0.757808\pi\) | |||||||
\(194\) | −12.9343 | + | 5.35757i | −0.928630 | + | 0.384651i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.36396 | − | 6.36396i | −0.454569 | − | 0.454569i | ||||
\(197\) | −11.0866 | + | 4.59220i | −0.789884 | + | 0.327181i | −0.740897 | − | 0.671619i | \(-0.765599\pi\) |
−0.0489872 | + | 0.998799i | \(0.515599\pi\) | |||||||
\(198\) | 2.29610 | + | 5.54328i | 0.163177 | + | 0.393944i | ||||
\(199\) | −14.7821 | − | 6.12293i | −1.04787 | − | 0.434043i | −0.208741 | − | 0.977971i | \(-0.566937\pi\) |
−0.839132 | + | 0.543928i | \(0.816937\pi\) | |||||||
\(200\) | − | 5.00000i | − | 0.353553i | ||||||
\(201\) | −6.12293 | + | 14.7821i | −0.431879 | + | 1.04265i | ||||
\(202\) | 12.7279 | − | 12.7279i | 0.895533 | − | 0.895533i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 11.3137 | − | 11.3137i | 0.788263 | − | 0.788263i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 2.00000i | − | 0.138675i | ||||||
\(209\) | 22.1731 | + | 9.18440i | 1.53375 | + | 0.635298i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.23880 | − | 3.82683i | 0.636025 | − | 0.263450i | −0.0412856 | − | 0.999147i | \(-0.513145\pi\) |
0.677311 | + | 0.735697i | \(0.263145\pi\) | |||||||
\(212\) | −4.24264 | − | 4.24264i | −0.291386 | − | 0.291386i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.54328 | + | 2.29610i | −0.378931 | + | 0.156958i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.69552 | + | 1.53073i | 0.251448 | + | 0.104153i | ||||
\(217\) | 16.0000i | 1.08615i | ||||||||
\(218\) | −6.12293 | + | 14.7821i | −0.414697 | + | 1.00117i | ||||
\(219\) | −2.82843 | + | 2.82843i | −0.191127 | + | 0.191127i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 8.00000 | 0.536925 | ||||||||
\(223\) | −5.65685 | + | 5.65685i | −0.378811 | + | 0.378811i | −0.870673 | − | 0.491862i | \(-0.836316\pi\) |
0.491862 | + | 0.870673i | \(0.336316\pi\) | |||||||
\(224\) | 1.53073 | − | 3.69552i | 0.102276 | − | 0.246917i | ||||
\(225\) | 5.00000i | 0.333333i | ||||||||
\(226\) | 5.54328 | + | 2.29610i | 0.368733 | + | 0.152734i | ||||
\(227\) | 2.29610 | + | 5.54328i | 0.152398 | + | 0.367920i | 0.981578 | − | 0.191060i | \(-0.0611926\pi\) |
−0.829181 | + | 0.558981i | \(0.811193\pi\) | |||||||
\(228\) | −7.39104 | + | 3.06147i | −0.489483 | + | 0.202751i | ||||
\(229\) | 9.89949 | + | 9.89949i | 0.654177 | + | 0.654177i | 0.953996 | − | 0.299819i | \(-0.0969263\pi\) |
−0.299819 | + | 0.953996i | \(0.596926\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 44.3462 | − | 18.3688i | 2.91777 | − | 1.20858i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.6298 | + | 6.88830i | 1.08946 | + | 0.451268i | 0.853817 | − | 0.520573i | \(-0.174282\pi\) |
0.235639 | + | 0.971841i | \(0.424282\pi\) | |||||||
\(234\) | 2.00000i | 0.130744i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.0000 | 1.03931 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.82683 | − | 9.23880i | 0.246508 | − | 0.595123i | −0.751395 | − | 0.659853i | \(-0.770619\pi\) |
0.997903 | + | 0.0647298i | \(0.0206186\pi\) | |||||||
\(242\) | − | 25.0000i | − | 1.60706i | ||||||
\(243\) | −9.23880 | − | 3.82683i | −0.592669 | − | 0.245492i | ||||
\(244\) | 1.53073 | + | 3.69552i | 0.0979952 | + | 0.236581i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.48528 | − | 8.48528i | −0.541002 | − | 0.541002i | ||||
\(247\) | 5.65685 | + | 5.65685i | 0.359937 | + | 0.359937i | ||||
\(248\) | −3.69552 | + | 1.53073i | −0.234666 | + | 0.0972017i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 24.0000i | − | 1.51487i | −0.652913 | − | 0.757433i | \(-0.726453\pi\) | ||
0.652913 | − | 0.757433i | \(-0.273547\pi\) | |||||||
\(252\) | −1.53073 | + | 3.69552i | −0.0964272 | + | 0.232796i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 16.0000 | 1.00393 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.24264 | + | 4.24264i | −0.264649 | + | 0.264649i | −0.826940 | − | 0.562291i | \(-0.809920\pi\) |
0.562291 | + | 0.826940i | \(0.309920\pi\) | |||||||
\(258\) | 6.12293 | − | 14.7821i | 0.381197 | − | 0.920292i | ||||
\(259\) | − | 16.0000i | − | 0.994192i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.54328 | − | 2.29610i | 0.342465 | − | 0.141854i | ||||
\(263\) | 16.9706 | + | 16.9706i | 1.04645 | + | 1.04645i | 0.998867 | + | 0.0475824i | \(0.0151517\pi\) |
0.0475824 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(264\) | 8.48528 | + | 8.48528i | 0.522233 | + | 0.522233i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.12293 | + | 14.7821i | 0.375421 | + | 0.906347i | ||||
\(267\) | 11.0866 | + | 4.59220i | 0.678486 | + | 0.281038i | ||||
\(268\) | 8.00000i | 0.488678i | ||||||||
\(269\) | −9.18440 | + | 22.1731i | −0.559983 | + | 1.35192i | 0.349796 | + | 0.936826i | \(0.386251\pi\) |
−0.909779 | + | 0.415093i | \(0.863749\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.0000 | 0.968364 | ||||||||
\(274\) | −4.24264 | + | 4.24264i | −0.256307 | + | 0.256307i | ||||
\(275\) | 11.4805 | − | 27.7164i | 0.692300 | − | 1.67136i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.39104 | − | 3.06147i | −0.444084 | − | 0.183946i | 0.149425 | − | 0.988773i | \(-0.452258\pi\) |
−0.593509 | + | 0.804827i | \(0.702258\pi\) | |||||||
\(278\) | −0.765367 | − | 1.84776i | −0.0459037 | − | 0.110821i | ||||
\(279\) | 3.69552 | − | 1.53073i | 0.221245 | − | 0.0916426i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.24264 | − | 4.24264i | −0.253095 | − | 0.253095i | 0.569143 | − | 0.822238i | \(-0.307275\pi\) |
−0.822238 | + | 0.569143i | \(0.807275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.35757 | + | 12.9343i | 0.318474 | + | 0.768865i | 0.999335 | + | 0.0364525i | \(0.0116058\pi\) |
−0.680861 | + | 0.732413i | \(0.738394\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.59220 | − | 11.0866i | 0.271543 | − | 0.655562i | ||||
\(287\) | −16.9706 | + | 16.9706i | −1.00174 | + | 1.00174i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.7990 | − | 19.7990i | 1.16064 | − | 1.16064i | ||||
\(292\) | −0.765367 | + | 1.84776i | −0.0447897 | + | 0.108132i | ||||
\(293\) | − | 6.00000i | − | 0.350524i | −0.984522 | − | 0.175262i | \(-0.943923\pi\) | ||
0.984522 | − | 0.175262i | \(-0.0560772\pi\) | |||||||
\(294\) | 16.6298 | + | 6.88830i | 0.969871 | + | 0.401734i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.69552 | − | 1.53073i | 0.214798 | − | 0.0889721i | ||||
\(297\) | 16.9706 | + | 16.9706i | 0.984732 | + | 0.984732i | ||||
\(298\) | −4.24264 | − | 4.24264i | −0.245770 | − | 0.245770i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 3.82683 | + | 9.23880i | 0.220942 | + | 0.533402i | ||||
\(301\) | −29.5641 | − | 12.2459i | −1.70405 | − | 0.705840i | ||||
\(302\) | − | 16.0000i | − | 0.920697i | ||||||
\(303\) | −13.7766 | + | 33.2597i | −0.791445 | + | 1.91072i | ||||
\(304\) | −2.82843 | + | 2.82843i | −0.162221 | + | 0.162221i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | 16.9706 | − | 16.9706i | 0.966988 | − | 0.966988i | ||||
\(309\) | −12.2459 | + | 29.5641i | −0.696643 | + | 1.68185i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.0866 | − | 4.59220i | −0.628661 | − | 0.260400i | 0.0455232 | − | 0.998963i | \(-0.485505\pi\) |
−0.674184 | + | 0.738563i | \(0.735505\pi\) | |||||||
\(312\) | 1.53073 | + | 3.69552i | 0.0866607 | + | 0.209218i | ||||
\(313\) | 31.4119 | − | 13.0112i | 1.77551 | − | 0.735439i | 0.781785 | − | 0.623548i | \(-0.214309\pi\) |
0.993721 | − | 0.111891i | \(-0.0356907\pi\) | |||||||
\(314\) | 9.89949 | + | 9.89949i | 0.558661 | + | 0.558661i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.39104 | − | 3.06147i | 0.415778 | − | 0.172221i | ||||
\(317\) | −4.59220 | − | 11.0866i | −0.257924 | − | 0.622683i | 0.740877 | − | 0.671641i | \(-0.234410\pi\) |
−0.998801 | + | 0.0489576i | \(0.984410\pi\) | |||||||
\(318\) | 11.0866 | + | 4.59220i | 0.621703 | + | 0.257518i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.48528 | − | 8.48528i | 0.473602 | − | 0.473602i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −11.0000 | −0.611111 | ||||||||
\(325\) | 7.07107 | − | 7.07107i | 0.392232 | − | 0.392232i | ||||
\(326\) | −0.765367 | + | 1.84776i | −0.0423898 | + | 0.102338i | ||||
\(327\) | − | 32.0000i | − | 1.76960i | ||||||
\(328\) | −5.54328 | − | 2.29610i | −0.306076 | − | 0.126781i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.3137 | − | 11.3137i | −0.621858 | − | 0.621858i | 0.324149 | − | 0.946006i | \(-0.394922\pi\) |
−0.946006 | + | 0.324149i | \(0.894922\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.69552 | + | 1.53073i | −0.202513 | + | 0.0838837i | ||||
\(334\) | 4.59220 | + | 11.0866i | 0.251274 | + | 0.606629i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 8.00000i | 0.436436i | ||||||||
\(337\) | −8.41904 | + | 20.3253i | −0.458614 | + | 1.10719i | 0.510345 | + | 0.859970i | \(0.329518\pi\) |
−0.968959 | + | 0.247222i | \(0.920482\pi\) | |||||||
\(338\) | −6.36396 | + | 6.36396i | −0.346154 | + | 0.346154i | ||||
\(339\) | −12.0000 | −0.651751 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.0000 | −1.29967 | ||||||||
\(342\) | 2.82843 | − | 2.82843i | 0.152944 | − | 0.152944i | ||||
\(343\) | 3.06147 | − | 7.39104i | 0.165304 | − | 0.399078i | ||||
\(344\) | − | 8.00000i | − | 0.431331i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.18440 | − | 22.1731i | −0.493757 | − | 1.19203i | ||||
\(347\) | −16.6298 | + | 6.88830i | −0.892736 | + | 0.369783i | −0.781423 | − | 0.624002i | \(-0.785506\pi\) |
−0.111313 | + | 0.993785i | \(0.535506\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.3848 | − | 18.3848i | −0.984115 | − | 0.984115i | 0.0157613 | − | 0.999876i | \(-0.494983\pi\) |
−0.999876 | + | 0.0157613i | \(0.994983\pi\) | |||||||
\(350\) | 18.4776 | − | 7.65367i | 0.987669 | − | 0.409106i | ||||
\(351\) | 3.06147 | + | 7.39104i | 0.163409 | + | 0.394504i | ||||
\(352\) | 5.54328 | + | 2.29610i | 0.295458 | + | 0.122383i | ||||
\(353\) | 6.00000i | 0.319348i | 0.987170 | + | 0.159674i | \(0.0510443\pi\) | ||||
−0.987170 | + | 0.159674i | \(0.948956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0000 | 0.634220 | ||||||||
\(359\) | −16.9706 | + | 16.9706i | −0.895672 | + | 0.895672i | −0.995050 | − | 0.0993777i | \(-0.968315\pi\) |
0.0993777 | + | 0.995050i | \(0.468315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000i | 0.157895i | ||||||||
\(362\) | 3.69552 | + | 1.53073i | 0.194232 | + | 0.0804536i | ||||
\(363\) | 19.1342 | + | 46.1940i | 1.00428 | + | 2.42455i | ||||
\(364\) | 7.39104 | − | 3.06147i | 0.387396 | − | 0.160464i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.65685 | − | 5.65685i | −0.295689 | − | 0.295689i | ||||
\(367\) | −14.7821 | + | 6.12293i | −0.771618 | + | 0.319615i | −0.733528 | − | 0.679660i | \(-0.762127\pi\) |
−0.0380903 | + | 0.999274i | \(0.512127\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.54328 | + | 2.29610i | 0.288571 | + | 0.119530i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.18440 | − | 22.1731i | 0.476830 | − | 1.15117i | ||||
\(372\) | 5.65685 | − | 5.65685i | 0.293294 | − | 0.293294i | ||||
\(373\) | 22.0000 | 1.13912 | 0.569558 | − | 0.821951i | \(-0.307114\pi\) | ||||
0.569558 | + | 0.821951i | \(0.307114\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 16.0000i | 0.822951i | ||||||||
\(379\) | −12.9343 | − | 5.35757i | −0.664391 | − | 0.275200i | 0.0248939 | − | 0.999690i | \(-0.492075\pi\) |
−0.689285 | + | 0.724490i | \(0.742075\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −29.5641 | + | 12.2459i | −1.51462 | + | 0.627375i | ||||
\(382\) | −16.9706 | − | 16.9706i | −0.868290 | − | 0.868290i | ||||
\(383\) | 16.9706 | + | 16.9706i | 0.867155 | + | 0.867155i | 0.992157 | − | 0.125001i | \(-0.0398935\pi\) |
−0.125001 | + | 0.992157i | \(0.539894\pi\) | |||||||
\(384\) | −1.84776 | + | 0.765367i | −0.0942931 | + | 0.0390575i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.23880 | − | 3.82683i | −0.470242 | − | 0.194781i | ||||
\(387\) | 8.00000i | 0.406663i | ||||||||
\(388\) | 5.35757 | − | 12.9343i | 0.271989 | − | 0.656640i | ||||
\(389\) | 21.2132 | − | 21.2132i | 1.07555 | − | 1.07555i | 0.0786498 | − | 0.996902i | \(-0.474939\pi\) |
0.996902 | − | 0.0786498i | \(-0.0250609\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 9.00000 | 0.454569 | ||||||||
\(393\) | −8.48528 | + | 8.48528i | −0.428026 | + | 0.428026i | ||||
\(394\) | 4.59220 | − | 11.0866i | 0.231352 | − | 0.558533i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.54328 | − | 2.29610i | −0.278560 | − | 0.115383i | ||||
\(397\) | −7.65367 | − | 18.4776i | −0.384127 | − | 0.927364i | −0.991158 | − | 0.132686i | \(-0.957640\pi\) |
0.607032 | − | 0.794678i | \(-0.292360\pi\) | |||||||
\(398\) | 14.7821 | − | 6.12293i | 0.740958 | − | 0.306915i | ||||
\(399\) | −22.6274 | − | 22.6274i | −1.13279 | − | 1.13279i | ||||
\(400\) | 3.53553 | + | 3.53553i | 0.176777 | + | 0.176777i | ||||
\(401\) | 27.7164 | − | 11.4805i | 1.38409 | − | 0.573309i | 0.438518 | − | 0.898722i | \(-0.355503\pi\) |
0.945572 | + | 0.325413i | \(0.105503\pi\) | |||||||
\(402\) | −6.12293 | − | 14.7821i | −0.305384 | − | 0.737263i | ||||
\(403\) | −7.39104 | − | 3.06147i | −0.368174 | − | 0.152503i | ||||
\(404\) | 18.0000i | 0.895533i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.0000 | 1.18964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0000 | −0.494468 | −0.247234 | − | 0.968956i | \(-0.579522\pi\) | ||||
−0.247234 | + | 0.968956i | \(0.579522\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.59220 | − | 11.0866i | 0.226517 | − | 0.546859i | ||||
\(412\) | 16.0000i | 0.788263i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.41421 | + | 1.41421i | 0.0693375 | + | 0.0693375i | ||||
\(417\) | 2.82843 | + | 2.82843i | 0.138509 | + | 0.138509i | ||||
\(418\) | −22.1731 | + | 9.18440i | −1.08452 | + | 0.449224i | ||||
\(419\) | −11.4805 | − | 27.7164i | −0.560859 | − | 1.35403i | −0.909080 | − | 0.416622i | \(-0.863214\pi\) |
0.348221 | − | 0.937413i | \(-0.386786\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00000i | 0.0974740i | 0.998812 | + | 0.0487370i | \(0.0155196\pi\) | ||||
−0.998812 | + | 0.0487370i | \(0.984480\pi\) | |||||||
\(422\) | −3.82683 | + | 9.23880i | −0.186287 | + | 0.449738i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.3137 | + | 11.3137i | −0.547509 | + | 0.547509i | ||||
\(428\) | 2.29610 | − | 5.54328i | 0.110986 | − | 0.267944i | ||||
\(429\) | 24.0000i | 1.15873i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.18440 | − | 22.1731i | −0.442397 | − | 1.06804i | −0.975105 | − | 0.221742i | \(-0.928826\pi\) |
0.532708 | − | 0.846299i | \(-0.321174\pi\) | |||||||
\(432\) | −3.69552 | + | 1.53073i | −0.177801 | + | 0.0736475i | ||||
\(433\) | 1.41421 | + | 1.41421i | 0.0679628 | + | 0.0679628i | 0.740271 | − | 0.672308i | \(-0.234697\pi\) |
−0.672308 | + | 0.740271i | \(0.734697\pi\) | |||||||
\(434\) | −11.3137 | − | 11.3137i | −0.543075 | − | 0.543075i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.12293 | − | 14.7821i | −0.293235 | − | 0.707933i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | − | 4.00000i | − | 0.191127i | ||||||
\(439\) | 3.06147 | − | 7.39104i | 0.146116 | − | 0.352755i | −0.833829 | − | 0.552022i | \(-0.813856\pi\) |
0.979945 | + | 0.199268i | \(0.0638563\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.00000 | −0.428571 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.0000 | −1.14027 | −0.570137 | − | 0.821549i | \(-0.693110\pi\) | ||||
−0.570137 | + | 0.821549i | \(0.693110\pi\) | |||||||
\(444\) | −5.65685 | + | 5.65685i | −0.268462 | + | 0.268462i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 8.00000i | − | 0.378811i | ||||||
\(447\) | 11.0866 | + | 4.59220i | 0.524376 | + | 0.217204i | ||||
\(448\) | 1.53073 | + | 3.69552i | 0.0723204 | + | 0.174597i | ||||
\(449\) | 16.6298 | − | 6.88830i | 0.784810 | − | 0.325079i | 0.0459553 | − | 0.998943i | \(-0.485367\pi\) |
0.738855 | + | 0.673864i | \(0.235367\pi\) | |||||||
\(450\) | −3.53553 | − | 3.53553i | −0.166667 | − | 0.166667i | ||||
\(451\) | −25.4558 | − | 25.4558i | −1.19867 | − | 1.19867i | ||||
\(452\) | −5.54328 | + | 2.29610i | −0.260734 | + | 0.107999i | ||||
\(453\) | 12.2459 | + | 29.5641i | 0.575361 | + | 1.38904i | ||||
\(454\) | −5.54328 | − | 2.29610i | −0.260159 | − | 0.107761i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.06147 | − | 7.39104i | 0.143366 | − | 0.346117i | ||||
\(457\) | 18.3848 | − | 18.3848i | 0.860004 | − | 0.860004i | −0.131335 | − | 0.991338i | \(-0.541926\pi\) |
0.991338 | + | 0.131335i | \(0.0419262\pi\) | |||||||
\(458\) | −14.0000 | −0.654177 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.24264 | − | 4.24264i | 0.197599 | − | 0.197599i | −0.601371 | − | 0.798970i | \(-0.705378\pi\) |
0.798970 | + | 0.601371i | \(0.205378\pi\) | |||||||
\(462\) | −18.3688 | + | 44.3462i | −0.854594 | + | 2.06317i | ||||
\(463\) | 16.0000i | 0.743583i | 0.928316 | + | 0.371792i | \(0.121256\pi\) | ||||
−0.928316 | + | 0.371792i | \(0.878744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.6298 | + | 6.88830i | −0.770362 | + | 0.319094i | ||||
\(467\) | 8.48528 | + | 8.48528i | 0.392652 | + | 0.392652i | 0.875632 | − | 0.482980i | \(-0.160445\pi\) |
−0.482980 | + | 0.875632i | \(0.660445\pi\) | |||||||
\(468\) | −1.41421 | − | 1.41421i | −0.0653720 | − | 0.0653720i | ||||
\(469\) | −29.5641 | + | 12.2459i | −1.36515 | + | 0.565462i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.8686 | − | 10.7151i | −1.19196 | − | 0.493727i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.3688 | − | 44.3462i | 0.844599 | − | 2.03904i | ||||
\(474\) | −11.3137 | + | 11.3137i | −0.519656 | + | 0.519656i | ||||
\(475\) | −20.0000 | −0.917663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | −16.9706 | + | 16.9706i | −0.776215 | + | 0.776215i | ||||
\(479\) | −9.18440 | + | 22.1731i | −0.419646 | + | 1.01312i | 0.562804 | + | 0.826590i | \(0.309723\pi\) |
−0.982450 | + | 0.186525i | \(0.940277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.39104 | + | 3.06147i | 0.337002 | + | 0.139591i | ||||
\(482\) | 3.82683 | + | 9.23880i | 0.174308 | + | 0.420816i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 17.6777 | + | 17.6777i | 0.803530 | + | 0.803530i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 9.23880 | − | 3.82683i | 0.419080 | − | 0.173589i | ||||
\(487\) | 3.06147 | + | 7.39104i | 0.138728 | + | 0.334920i | 0.977940 | − | 0.208885i | \(-0.0669833\pi\) |
−0.839212 | + | 0.543804i | \(0.816983\pi\) | |||||||
\(488\) | −3.69552 | − | 1.53073i | −0.167288 | − | 0.0692931i | ||||
\(489\) | − | 4.00000i | − | 0.180886i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.48528 | + | 8.48528i | −0.382935 | + | 0.382935i | −0.872159 | − | 0.489223i | \(-0.837280\pi\) |
0.489223 | + | 0.872159i | \(0.337280\pi\) | |||||||
\(492\) | 12.0000 | 0.541002 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −8.00000 | −0.359937 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.53073 | − | 3.69552i | 0.0687320 | − | 0.165934i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.35757 | − | 12.9343i | −0.239838 | − | 0.579019i | 0.757428 | − | 0.652919i | \(-0.226456\pi\) |
−0.997266 | + | 0.0738993i | \(0.976456\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.9706 | − | 16.9706i | −0.758189 | − | 0.758189i | ||||
\(502\) | 16.9706 | + | 16.9706i | 0.757433 | + | 0.757433i | ||||
\(503\) | −22.1731 | + | 9.18440i | −0.988650 | + | 0.409512i | −0.817623 | − | 0.575754i | \(-0.804709\pi\) |
−0.171027 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(504\) | −1.53073 | − | 3.69552i | −0.0681843 | − | 0.164611i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.88830 | − | 16.6298i | 0.305920 | − | 0.738557i | ||||
\(508\) | −11.3137 | + | 11.3137i | −0.501965 | + | 0.501965i | ||||
\(509\) | −30.0000 | −1.32973 | −0.664863 | − | 0.746965i | \(-0.731510\pi\) | ||||
−0.664863 | + | 0.746965i | \(0.731510\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.00000 | −0.353899 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 6.12293 | − | 14.7821i | 0.270334 | − | 0.652644i | ||||
\(514\) | − | 6.00000i | − | 0.264649i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.12293 | + | 14.7821i | 0.269547 | + | 0.650744i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 11.3137 | + | 11.3137i | 0.497096 | + | 0.497096i | ||||
\(519\) | 33.9411 | + | 33.9411i | 1.48985 | + | 1.48985i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.88830 | − | 16.6298i | −0.301782 | − | 0.728566i | −0.999921 | − | 0.0126035i | \(-0.995988\pi\) |
0.698139 | − | 0.715963i | \(-0.254012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 16.0000i | − | 0.699631i | −0.936819 | − | 0.349816i | \(-0.886244\pi\) | ||
0.936819 | − | 0.349816i | \(-0.113756\pi\) | |||||||
\(524\) | −2.29610 | + | 5.54328i | −0.100306 | + | 0.242159i | ||||
\(525\) | −28.2843 | + | 28.2843i | −1.23443 | + | 1.23443i | ||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −12.0000 | −0.522233 | ||||||||
\(529\) | 16.2635 | − | 16.2635i | 0.707107 | − | 0.707107i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.7821 | − | 6.12293i | −0.640884 | − | 0.265463i | ||||
\(533\) | −4.59220 | − | 11.0866i | −0.198910 | − | 0.480212i | ||||
\(534\) | −11.0866 | + | 4.59220i | −0.479762 | + | 0.198724i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.65685 | − | 5.65685i | −0.244339 | − | 0.244339i | ||||
\(537\) | −22.1731 | + | 9.18440i | −0.956840 | + | 0.396336i | ||||
\(538\) | −9.18440 | − | 22.1731i | −0.395968 | − | 0.955951i | ||||
\(539\) | 49.8895 | + | 20.6649i | 2.14889 | + | 0.890100i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.65367 | − | 18.4776i | 0.329057 | − | 0.794414i | −0.669606 | − | 0.742717i | \(-0.733537\pi\) |
0.998663 | − | 0.0516971i | \(-0.0164630\pi\) | |||||||
\(542\) | 5.65685 | − | 5.65685i | 0.242983 | − | 0.242983i | ||||
\(543\) | −8.00000 | −0.343313 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −11.3137 | + | 11.3137i | −0.484182 | + | 0.484182i | ||||
\(547\) | −0.765367 | + | 1.84776i | −0.0327247 | + | 0.0790045i | −0.939397 | − | 0.342831i | \(-0.888614\pi\) |
0.906672 | + | 0.421836i | \(0.138614\pi\) | |||||||
\(548\) | − | 6.00000i | − | 0.256307i | ||||||
\(549\) | 3.69552 | + | 1.53073i | 0.157721 | + | 0.0653301i | ||||
\(550\) | 11.4805 | + | 27.7164i | 0.489530 | + | 1.18183i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.6274 | + | 22.6274i | 0.962216 | + | 0.962216i | ||||
\(554\) | 7.39104 | − | 3.06147i | 0.314015 | − | 0.130069i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.84776 | + | 0.765367i | 0.0783624 | + | 0.0324588i | ||||
\(557\) | − | 30.0000i | − | 1.27114i | −0.772043 | − | 0.635570i | \(-0.780765\pi\) | ||
0.772043 | − | 0.635570i | \(-0.219235\pi\) | |||||||
\(558\) | −1.53073 | + | 3.69552i | −0.0648011 | + | 0.156444i | ||||
\(559\) | 11.3137 | − | 11.3137i | 0.478519 | − | 0.478519i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.00000 | 0.253095 | ||||||||
\(563\) | 16.9706 | − | 16.9706i | 0.715224 | − | 0.715224i | −0.252399 | − | 0.967623i | \(-0.581220\pi\) |
0.967623 | + | 0.252399i | \(0.0812196\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −12.9343 | − | 5.35757i | −0.543670 | − | 0.225195i | ||||
\(567\) | −16.8381 | − | 40.6507i | −0.707133 | − | 1.70717i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.2132 | − | 21.2132i | −0.889304 | − | 0.889304i | 0.105152 | − | 0.994456i | \(-0.466467\pi\) |
−0.994456 | + | 0.105152i | \(0.966467\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.0209 | − | 9.94977i | 1.00524 | − | 0.416385i | 0.181525 | − | 0.983386i | \(-0.441897\pi\) |
0.823717 | + | 0.567001i | \(0.191897\pi\) | |||||||
\(572\) | 4.59220 | + | 11.0866i | 0.192010 | + | 0.463552i | ||||
\(573\) | 44.3462 | + | 18.3688i | 1.85259 | + | 0.767368i | ||||
\(574\) | − | 24.0000i | − | 1.00174i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.707107 | − | 0.707107i | 0.0294628 | − | 0.0294628i | ||||
\(577\) | −14.0000 | −0.582828 | −0.291414 | − | 0.956597i | \(-0.594126\pi\) | ||||
−0.291414 | + | 0.956597i | \(0.594126\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.0000 | 0.831172 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 28.0000i | 1.16064i | ||||||||
\(583\) | 33.2597 | + | 13.7766i | 1.37747 | + | 0.570569i | ||||
\(584\) | −0.765367 | − | 1.84776i | −0.0316711 | − | 0.0764608i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.24264 | + | 4.24264i | 0.175262 | + | 0.175262i | ||||
\(587\) | −8.48528 | − | 8.48528i | −0.350225 | − | 0.350225i | 0.509968 | − | 0.860193i | \(-0.329657\pi\) |
−0.860193 | + | 0.509968i | \(0.829657\pi\) | |||||||
\(588\) | −16.6298 | + | 6.88830i | −0.685803 | + | 0.284069i | ||||
\(589\) | 6.12293 | + | 14.7821i | 0.252291 | + | 0.609085i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.0000i | 0.987228i | ||||||||
\(592\) | −1.53073 | + | 3.69552i | −0.0629128 | + | 0.151885i | ||||
\(593\) | −21.2132 | + | 21.2132i | −0.871122 | + | 0.871122i | −0.992595 | − | 0.121473i | \(-0.961238\pi\) |
0.121473 | + | 0.992595i | \(0.461238\pi\) | |||||||
\(594\) | −24.0000 | −0.984732 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.00000 | 0.245770 | ||||||||
\(597\) | −22.6274 | + | 22.6274i | −0.926079 | + | 0.926079i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0000i | 0.980613i | 0.871550 | + | 0.490307i | \(0.163115\pi\) | ||||
−0.871550 | + | 0.490307i | \(0.836885\pi\) | |||||||
\(600\) | −9.23880 | − | 3.82683i | −0.377172 | − | 0.156230i | ||||
\(601\) | 17.6034 | + | 42.4985i | 0.718059 | + | 1.73355i | 0.678804 | + | 0.734319i | \(0.262498\pi\) |
0.0392547 | + | 0.999229i | \(0.487502\pi\) | |||||||
\(602\) | 29.5641 | − | 12.2459i | 1.20494 | − | 0.499104i | ||||
\(603\) | 5.65685 | + | 5.65685i | 0.230365 | + | 0.230365i | ||||
\(604\) | 11.3137 | + | 11.3137i | 0.460348 | + | 0.460348i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −13.7766 | − | 33.2597i | −0.559636 | − | 1.35108i | ||||
\(607\) | 18.4776 | + | 7.65367i | 0.749982 | + | 0.310653i | 0.724734 | − | 0.689028i | \(-0.241962\pi\) |
0.0252479 | + | 0.999681i | \(0.491962\pi\) | |||||||
\(608\) | − | 4.00000i | − | 0.162221i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.0000 | 0.565455 | 0.282727 | − | 0.959200i | \(-0.408761\pi\) | ||||
0.282727 | + | 0.959200i | \(0.408761\pi\) | |||||||
\(614\) | −14.1421 | + | 14.1421i | −0.570730 | + | 0.570730i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 24.0000i | 0.966988i | ||||||||
\(617\) | 27.7164 | + | 11.4805i | 1.11582 | + | 0.462188i | 0.862938 | − | 0.505310i | \(-0.168622\pi\) |
0.252882 | + | 0.967497i | \(0.418622\pi\) | |||||||
\(618\) | −12.2459 | − | 29.5641i | −0.492601 | − | 1.18924i | ||||
\(619\) | −24.0209 | + | 9.94977i | −0.965480 | + | 0.399915i | −0.809028 | − | 0.587770i | \(-0.800006\pi\) |
−0.156452 | + | 0.987685i | \(0.550006\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.0866 | − | 4.59220i | 0.444530 | − | 0.184130i | ||||
\(623\) | 9.18440 | + | 22.1731i | 0.367965 | + | 0.888347i | ||||
\(624\) | −3.69552 | − | 1.53073i | −0.147939 | − | 0.0612784i | ||||
\(625\) | 25.0000i | 1.00000i | ||||||||
\(626\) | −13.0112 | + | 31.4119i | −0.520034 | + | 1.25547i | ||||
\(627\) | 33.9411 | − | 33.9411i | 1.35548 | − | 1.35548i | ||||
\(628\) | −14.0000 | −0.558661 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.65685 | + | 5.65685i | −0.225196 | + | 0.225196i | −0.810682 | − | 0.585486i | \(-0.800904\pi\) |
0.585486 | + | 0.810682i | \(0.300904\pi\) | |||||||
\(632\) | −3.06147 | + | 7.39104i | −0.121779 | + | 0.294000i | ||||
\(633\) | − | 20.0000i | − | 0.794929i | ||||||
\(634\) | 11.0866 | + | 4.59220i | 0.440303 | + | 0.182380i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −11.0866 | + | 4.59220i | −0.439610 | + | 0.182093i | ||||
\(637\) | 12.7279 | + | 12.7279i | 0.504299 | + | 0.504299i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.6298 | − | 6.88830i | −0.656839 | − | 0.272072i | 0.0292688 | − | 0.999572i | \(-0.490682\pi\) |
−0.686108 | + | 0.727500i | \(0.740682\pi\) | |||||||
\(642\) | 12.0000i | 0.473602i | ||||||||
\(643\) | 5.35757 | − | 12.9343i | 0.211282 | − | 0.510080i | −0.782339 | − | 0.622853i | \(-0.785973\pi\) |
0.993621 | + | 0.112774i | \(0.0359734\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −48.0000 | −1.88707 | −0.943537 | − | 0.331266i | \(-0.892524\pi\) | ||||
−0.943537 | + | 0.331266i | \(0.892524\pi\) | |||||||
\(648\) | 7.77817 | − | 7.77817i | 0.305556 | − | 0.305556i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 10.0000i | 0.392232i | ||||||||
\(651\) | 29.5641 | + | 12.2459i | 1.15871 | + | 0.479953i | ||||
\(652\) | −0.765367 | − | 1.84776i | −0.0299741 | − | 0.0723638i | ||||
\(653\) | −22.1731 | + | 9.18440i | −0.867701 | + | 0.359413i | −0.771714 | − | 0.635969i | \(-0.780601\pi\) |
−0.0959864 | + | 0.995383i | \(0.530601\pi\) | |||||||
\(654\) | 22.6274 | + | 22.6274i | 0.884802 | + | 0.884802i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.54328 | − | 2.29610i | 0.216429 | − | 0.0896477i | ||||
\(657\) | 0.765367 | + | 1.84776i | 0.0298598 | + | 0.0720879i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 12.0000i | − | 0.467454i | −0.972302 | − | 0.233727i | \(-0.924908\pi\) | ||
0.972302 | − | 0.233727i | \(-0.0750921\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.5269 | + | 32.5269i | −1.26515 | + | 1.26515i | −0.316587 | + | 0.948564i | \(0.602537\pi\) |
−0.948564 | + | 0.316587i | \(0.897463\pi\) | |||||||
\(662\) | 16.0000 | 0.621858 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.53073 | − | 3.69552i | 0.0593147 | − | 0.143198i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −11.0866 | − | 4.59220i | −0.428952 | − | 0.177678i | ||||
\(669\) | 6.12293 | + | 14.7821i | 0.236726 | + | 0.571508i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.9706 | − | 16.9706i | −0.655141 | − | 0.655141i | ||||
\(672\) | −5.65685 | − | 5.65685i | −0.218218 | − | 0.218218i | ||||
\(673\) | 35.1074 | − | 14.5420i | 1.35329 | − | 0.560552i | 0.416085 | − | 0.909326i | \(-0.363402\pi\) |
0.937207 | + | 0.348774i | \(0.113402\pi\) | |||||||
\(674\) | −8.41904 | − | 20.3253i | −0.324289 | − | 0.782903i | ||||
\(675\) | −18.4776 | − | 7.65367i | −0.711203 | − | 0.294590i | ||||
\(676\) | − | 9.00000i | − | 0.346154i | ||||||
\(677\) | −4.59220 | + | 11.0866i | −0.176493 | + | 0.426091i | −0.987226 | − | 0.159324i | \(-0.949068\pi\) |
0.810734 | + | 0.585415i | \(0.199068\pi\) | |||||||
\(678\) | 8.48528 | − | 8.48528i | 0.325875 | − | 0.325875i | ||||
\(679\) | 56.0000 | 2.14908 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.0000 | 0.459841 | ||||||||
\(682\) | 16.9706 | − | 16.9706i | 0.649836 | − | 0.649836i | ||||
\(683\) | −11.4805 | + | 27.7164i | −0.439289 | + | 1.06054i | 0.536906 | + | 0.843642i | \(0.319593\pi\) |
−0.976195 | + | 0.216896i | \(0.930407\pi\) | |||||||
\(684\) | 4.00000i | 0.152944i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.06147 | + | 7.39104i | 0.116887 | + | 0.282191i | ||||
\(687\) | 25.8686 | − | 10.7151i | 0.986950 | − | 0.408808i | ||||
\(688\) | 5.65685 | + | 5.65685i | 0.215666 | + | 0.215666i | ||||
\(689\) | 8.48528 | + | 8.48528i | 0.323263 | + | 0.323263i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.82683 | − | 9.23880i | −0.145580 | − | 0.351460i | 0.834223 | − | 0.551427i | \(-0.185917\pi\) |
−0.979803 | + | 0.199967i | \(0.935917\pi\) | |||||||
\(692\) | 22.1731 | + | 9.18440i | 0.842895 | + | 0.349139i | ||||
\(693\) | − | 24.0000i | − | 0.911685i | ||||||
\(694\) | 6.88830 | − | 16.6298i | 0.261476 | − | 0.631260i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 26.0000 | 0.984115 | ||||||||
\(699\) | 25.4558 | − | 25.4558i | 0.962828 | − | 0.962828i | ||||
\(700\) | −7.65367 | + | 18.4776i | −0.289281 | + | 0.698387i | ||||
\(701\) | − | 18.0000i | − | 0.679851i | −0.940452 | − | 0.339925i | \(-0.889598\pi\) | ||
0.940452 | − | 0.339925i | \(-0.110402\pi\) | |||||||
\(702\) | −7.39104 | − | 3.06147i | −0.278957 | − | 0.115548i | ||||
\(703\) | −6.12293 | − | 14.7821i | −0.230931 | − | 0.557516i | ||||
\(704\) | −5.54328 | + | 2.29610i | −0.208920 | + | 0.0865375i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.24264 | − | 4.24264i | −0.159674 | − | 0.159674i | ||||
\(707\) | −66.5193 | + | 27.5532i | −2.50172 | + | 1.03625i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.7821 | − | 6.12293i | −0.555152 | − | 0.229952i | 0.0874268 | − | 0.996171i | \(-0.472136\pi\) |
−0.642579 | + | 0.766219i | \(0.722136\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.06147 | − | 7.39104i | 0.114814 | − | 0.277186i | ||||
\(712\) | −4.24264 | + | 4.24264i | −0.159000 | + | 0.159000i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.48528 | + | 8.48528i | −0.317110 | + | 0.317110i | ||||
\(717\) | 18.3688 | − | 44.3462i | 0.685996 | − | 1.65614i | ||||
\(718\) | − | 24.0000i | − | 0.895672i | ||||||
\(719\) | −44.3462 | − | 18.3688i | −1.65383 | − | 0.685041i | −0.656253 | − | 0.754541i | \(-0.727860\pi\) |
−0.997582 | + | 0.0695002i | \(0.977860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −59.1283 | + | 24.4917i | −2.20205 | + | 0.912120i | ||||
\(722\) | −2.12132 | − | 2.12132i | −0.0789474 | − | 0.0789474i | ||||
\(723\) | −14.1421 | − | 14.1421i | −0.525952 | − | 0.525952i | ||||
\(724\) | −3.69552 | + | 1.53073i | −0.137343 | + | 0.0568893i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −46.1940 | − | 19.1342i | −1.71442 | − | 0.710136i | ||||
\(727\) | 8.00000i | 0.296704i | 0.988935 | + | 0.148352i | \(0.0473968\pi\) | ||||
−0.988935 | + | 0.148352i | \(0.952603\pi\) | |||||||
\(728\) | −3.06147 | + | 7.39104i | −0.113466 | + | 0.273930i | ||||
\(729\) | 9.19239 | − | 9.19239i | 0.340459 | − | 0.340459i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 8.00000 | 0.295689 | ||||||||
\(733\) | 15.5563 | − | 15.5563i | 0.574587 | − | 0.574587i | −0.358820 | − | 0.933407i | \(-0.616821\pi\) |
0.933407 | + | 0.358820i | \(0.116821\pi\) | |||||||
\(734\) | 6.12293 | − | 14.7821i | 0.226002 | − | 0.545616i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.3688 | − | 44.3462i | −0.676624 | − | 1.63351i | ||||
\(738\) | −5.54328 | + | 2.29610i | −0.204051 | + | 0.0845206i | ||||
\(739\) | 14.1421 | + | 14.1421i | 0.520227 | + | 0.520227i | 0.917640 | − | 0.397413i | \(-0.130092\pi\) |
−0.397413 | + | 0.917640i | \(0.630092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.7821 | − | 6.12293i | 0.543033 | − | 0.224932i | ||||
\(742\) | 9.18440 | + | 22.1731i | 0.337170 | + | 0.814000i | ||||
\(743\) | −33.2597 | − | 13.7766i | −1.22018 | − | 0.505415i | −0.322712 | − | 0.946497i | \(-0.604595\pi\) |
−0.897467 | + | 0.441083i | \(0.854595\pi\) | |||||||
\(744\) | 8.00000i | 0.293294i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.5563 | + | 15.5563i | −0.569558 | + | 0.569558i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.0000 | 0.876941 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.06147 | + | 7.39104i | −0.111715 | + | 0.269703i | −0.969842 | − | 0.243734i | \(-0.921628\pi\) |
0.858128 | + | 0.513436i | \(0.171628\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −44.3462 | − | 18.3688i | −1.61607 | − | 0.669396i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −11.3137 | − | 11.3137i | −0.411476 | − | 0.411476i | ||||
\(757\) | 7.07107 | + | 7.07107i | 0.257002 | + | 0.257002i | 0.823834 | − | 0.566831i | \(-0.191831\pi\) |
−0.566831 | + | 0.823834i | \(0.691831\pi\) | |||||||
\(758\) | 12.9343 | − | 5.35757i | 0.469795 | − | 0.194596i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.00000i | 0.217500i | 0.994069 | + | 0.108750i | \(0.0346848\pi\) | ||||
−0.994069 | + | 0.108750i | \(0.965315\pi\) | |||||||
\(762\) | 12.2459 | − | 29.5641i | 0.443621 | − | 1.07100i | ||||
\(763\) | 45.2548 | − | 45.2548i | 1.63833 | − | 1.63833i | ||||
\(764\) | 24.0000 | 0.868290 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24.0000 | −0.867155 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.765367 | − | 1.84776i | 0.0276178 | − | 0.0666753i | ||||
\(769\) | − | 14.0000i | − | 0.504853i | −0.967616 | − | 0.252426i | \(-0.918771\pi\) | ||
0.967616 | − | 0.252426i | \(-0.0812286\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.59220 | + | 11.0866i | 0.165384 | + | 0.399273i | ||||
\(772\) | 9.23880 | − | 3.82683i | 0.332512 | − | 0.137731i | ||||
\(773\) | −29.6985 | − | 29.6985i | −1.06818 | − | 1.06818i | −0.997499 | − | 0.0706813i | \(-0.977483\pi\) |
−0.0706813 | − | 0.997499i | \(-0.522517\pi\) | |||||||
\(774\) | −5.65685 | − | 5.65685i | −0.203331 | − | 0.203331i | ||||
\(775\) | 18.4776 | − | 7.65367i | 0.663735 | − | 0.274928i | ||||
\(776\) | 5.35757 | + | 12.9343i | 0.192325 | + | 0.464315i | ||||
\(777\) | −29.5641 | − | 12.2459i | −1.06061 | − | 0.439318i | ||||
\(778\) | 30.0000i | 1.07555i | ||||||||
\(779\) | −9.18440 | + | 22.1731i | −0.329065 | + | 0.794434i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.36396 | + | 6.36396i | −0.227284 | + | 0.227284i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | − | 12.0000i | − | 0.428026i | ||||||
\(787\) | 42.4985 | + | 17.6034i | 1.51491 | + | 0.627495i | 0.976563 | − | 0.215231i | \(-0.0690504\pi\) |
0.538343 | + | 0.842726i | \(0.319050\pi\) | |||||||
\(788\) | 4.59220 | + | 11.0866i | 0.163590 | + | 0.394942i | ||||
\(789\) | 44.3462 | − | 18.3688i | 1.57877 | − | 0.653947i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.9706 | − | 16.9706i | −0.603404 | − | 0.603404i | ||||
\(792\) | 5.54328 | − | 2.29610i | 0.196972 | − | 0.0815884i | ||||
\(793\) | −3.06147 | − | 7.39104i | −0.108716 | − | 0.262463i | ||||
\(794\) | 18.4776 | + | 7.65367i | 0.655745 | + | 0.271619i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.12293 | + | 14.7821i | −0.217022 | + | 0.523937i | ||||
\(797\) | 29.6985 | − | 29.6985i | 1.05197 | − | 1.05197i | 0.0534012 | − | 0.998573i | \(-0.482994\pi\) |
0.998573 | − | 0.0534012i | \(-0.0170062\pi\) | |||||||
\(798\) | 32.0000 | 1.13279 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −5.00000 | −0.176777 | ||||||||
\(801\) | 4.24264 | − | 4.24264i | 0.149906 | − | 0.149906i | ||||
\(802\) | −11.4805 | + | 27.7164i | −0.405391 | + | 0.978700i | ||||
\(803\) | − | 12.0000i | − | 0.423471i | ||||||
\(804\) | 14.7821 | + | 6.12293i | 0.521324 | + | 0.215939i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.39104 | − | 3.06147i | 0.260338 | − | 0.107836i | ||||
\(807\) | 33.9411 | + | 33.9411i | 1.19478 | + | 1.19478i | ||||
\(808\) | −12.7279 | − | 12.7279i | −0.447767 | − | 0.447767i | ||||
\(809\) | 27.7164 | − | 11.4805i | 0.974456 | − | 0.403633i | 0.162087 | − | 0.986776i | \(-0.448177\pi\) |
0.812369 | + | 0.583143i | \(0.198177\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.1074 | + | 14.5420i | 1.23279 | + | 0.510638i | 0.901454 | − | 0.432876i | \(-0.142501\pi\) |
0.331335 | + | 0.943513i | \(0.392501\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.12293 | + | 14.7821i | −0.214741 | + | 0.518430i | ||||
\(814\) | −16.9706 | + | 16.9706i | −0.594818 | + | 0.594818i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.0000 | −1.11954 | ||||||||
\(818\) | 7.07107 | − | 7.07107i | 0.247234 | − | 0.247234i | ||||
\(819\) | 3.06147 | − | 7.39104i | 0.106976 | − | 0.258264i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.2597 | − | 13.7766i | −1.16077 | − | 0.480807i | −0.282639 | − | 0.959226i | \(-0.591210\pi\) |
−0.878131 | + | 0.478420i | \(0.841210\pi\) | |||||||
\(822\) | 4.59220 | + | 11.0866i | 0.160171 | + | 0.386688i | ||||
\(823\) | 14.7821 | − | 6.12293i | 0.515271 | − | 0.213432i | −0.109867 | − | 0.993946i | \(-0.535043\pi\) |
0.625138 | + | 0.780514i | \(0.285043\pi\) | |||||||
\(824\) | −11.3137 | − | 11.3137i | −0.394132 | − | 0.394132i | ||||
\(825\) | −42.4264 | − | 42.4264i | −1.47710 | − | 1.47710i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.29610 | + | 5.54328i | 0.0798432 | + | 0.192759i | 0.958760 | − | 0.284216i | \(-0.0917333\pi\) |
−0.878917 | + | 0.476975i | \(0.841733\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 10.0000i | − | 0.347314i | −0.984806 | − | 0.173657i | \(-0.944442\pi\) | ||
0.984806 | − | 0.173657i | \(-0.0555585\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.3137 | + | 11.3137i | −0.392468 | + | 0.392468i | ||||
\(832\) | −2.00000 | −0.0693375 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.00000 | −0.138509 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 9.18440 | − | 22.1731i | 0.317649 | − | 0.766873i | ||||
\(837\) | 16.0000i | 0.553041i | ||||||||
\(838\) | 27.7164 | + | 11.4805i | 0.957447 | + | 0.396587i | ||||
\(839\) | 13.7766 | + | 33.2597i | 0.475621 | + | 1.14825i | 0.961643 | + | 0.274304i | \(0.0884476\pi\) |
−0.486022 | + | 0.873947i | \(0.661552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.5061 | − | 20.5061i | −0.707107 | − | 0.707107i | ||||
\(842\) | −1.41421 | − | 1.41421i | −0.0487370 | − | 0.0487370i | ||||
\(843\) | −11.0866 | + | 4.59220i | −0.381841 | + | 0.158164i | ||||
\(844\) | −3.82683 | − | 9.23880i | −0.131725 | − | 0.318012i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −38.2683 | + | 92.3880i | −1.31492 | + | 3.17449i | ||||
\(848\) | −4.24264 | + | 4.24264i | −0.145693 | + | 0.145693i | ||||
\(849\) | 28.0000 | 0.960958 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.3073 | − | 36.9552i | 0.524113 | − | 1.26532i | −0.411214 | − | 0.911539i | \(-0.634895\pi\) |
0.935328 | − | 0.353783i | \(-0.115105\pi\) | |||||||
\(854\) | − | 16.0000i | − | 0.547509i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.29610 | + | 5.54328i | 0.0784791 | + | 0.189465i | ||||
\(857\) | 16.6298 | − | 6.88830i | 0.568064 | − | 0.235300i | −0.0801177 | − | 0.996785i | \(-0.525530\pi\) |
0.648182 | + | 0.761486i | \(0.275530\pi\) | |||||||
\(858\) | −16.9706 | − | 16.9706i | −0.579365 | − | 0.579365i | ||||
\(859\) | 11.3137 | + | 11.3137i | 0.386019 | + | 0.386019i | 0.873265 | − | 0.487246i | \(-0.161998\pi\) |
−0.487246 | + | 0.873265i | \(0.661998\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.3688 | + | 44.3462i | 0.626007 | + | 1.51132i | ||||
\(862\) | 22.1731 | + | 9.18440i | 0.755219 | + | 0.312822i | ||||
\(863\) | 48.0000i | 1.63394i | 0.576681 | + | 0.816970i | \(0.304348\pi\) | ||||
−0.576681 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(864\) | 1.53073 | − | 3.69552i | 0.0520766 | − | 0.125724i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.00000 | −0.0679628 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.0000 | 0.543075 | ||||||||
\(869\) | −33.9411 | + | 33.9411i | −1.15137 | + | 1.15137i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 16.0000i | − | 0.542139i | ||||||
\(872\) | 14.7821 | + | 6.12293i | 0.500584 | + | 0.207349i | ||||
\(873\) | −5.35757 | − | 12.9343i | −0.181326 | − | 0.437760i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.82843 | + | 2.82843i | 0.0955637 | + | 0.0955637i | ||||
\(877\) | 29.5641 | − | 12.2459i | 0.998310 | − | 0.413514i | 0.177133 | − | 0.984187i | \(-0.443318\pi\) |
0.821177 | + | 0.570673i | \(0.193318\pi\) | |||||||
\(878\) | 3.06147 | + | 7.39104i | 0.103320 | + | 0.249435i | ||||
\(879\) | −11.0866 | − | 4.59220i | −0.373940 | − | 0.154891i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.88830 | − | 16.6298i | 0.232073 | − | 0.560273i | −0.764348 | − | 0.644804i | \(-0.776939\pi\) |
0.996421 | + | 0.0845306i | \(0.0269391\pi\) | |||||||
\(882\) | 6.36396 | − | 6.36396i | 0.214286 | − | 0.214286i | ||||
\(883\) | 16.0000 | 0.538443 | 0.269221 | − | 0.963078i | \(-0.413234\pi\) | ||||
0.269221 | + | 0.963078i | \(0.413234\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.9706 | − | 16.9706i | 0.570137 | − | 0.570137i | ||||
\(887\) | −9.18440 | + | 22.1731i | −0.308382 | + | 0.744500i | 0.691376 | + | 0.722495i | \(0.257005\pi\) |
−0.999758 | + | 0.0220048i | \(0.992995\pi\) | |||||||
\(888\) | − | 8.00000i | − | 0.268462i | ||||||
\(889\) | −59.1283 | − | 24.4917i | −1.98310 | − | 0.821427i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 60.9760 | − | 25.2571i | 2.04277 | − | 0.846145i | ||||
\(892\) | 5.65685 | + | 5.65685i | 0.189405 | + | 0.189405i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −11.0866 | + | 4.59220i | −0.370790 | + | 0.153586i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.69552 | − | 1.53073i | −0.123459 | − | 0.0511382i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.88830 | + | 16.6298i | −0.229866 | + | 0.554945i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 5.00000 | 0.166667 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 36.0000 | 1.19867 | ||||||||
\(903\) | −45.2548 | + | 45.2548i | −1.50599 | + | 1.50599i | ||||
\(904\) | 2.29610 | − | 5.54328i | 0.0763672 | − | 0.184367i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −29.5641 | − | 12.2459i | −0.982203 | − | 0.406842i | ||||
\(907\) | 22.1956 | + | 53.5850i | 0.736994 | + | 1.77926i | 0.617717 | + | 0.786400i | \(0.288058\pi\) |
0.119277 | + | 0.992861i | \(0.461942\pi\) | |||||||
\(908\) | 5.54328 | − | 2.29610i | 0.183960 | − | 0.0761988i | ||||
\(909\) | 12.7279 | + | 12.7279i | 0.422159 | + | 0.422159i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.0866 | − | 4.59220i | 0.367314 | − | 0.152146i | −0.191389 | − | 0.981514i | \(-0.561299\pi\) |
0.558703 | + | 0.829368i | \(0.311299\pi\) | |||||||
\(912\) | 3.06147 | + | 7.39104i | 0.101375 | + | 0.244742i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 26.0000i | 0.860004i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.89949 | − | 9.89949i | 0.327089 | − | 0.327089i | ||||
\(917\) | −24.0000 | −0.792550 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.0000 | 1.84727 | 0.923635 | − | 0.383274i | \(-0.125203\pi\) | ||||
0.923635 | + | 0.383274i | \(0.125203\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.3073 | − | 36.9552i | 0.504394 | − | 1.21771i | ||||
\(922\) | 6.00000i | 0.197599i | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −18.3688 | − | 44.3462i | −0.604289 | − | 1.45888i | ||||
\(925\) | −18.4776 | + | 7.65367i | −0.607539 | + | 0.251651i | ||||
\(926\) | −11.3137 | − | 11.3137i | −0.371792 | − | 0.371792i | ||||
\(927\) | 11.3137 | + | 11.3137i | 0.371591 | + | 0.371591i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.88830 | − | 16.6298i | −0.225998 | − | 0.545607i | 0.769685 | − | 0.638423i | \(-0.220413\pi\) |
−0.995683 | + | 0.0928163i | \(0.970413\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 36.0000i | − | 1.17985i | ||||||
\(932\) | 6.88830 | − | 16.6298i | 0.225634 | − | 0.544728i | ||||
\(933\) | −16.9706 | + | 16.9706i | −0.555591 | + | 0.555591i | ||||
\(934\) | −12.0000 | −0.392652 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.00000 | 0.0653720 | ||||||||
\(937\) | 41.0122 | − | 41.0122i | 1.33981 | − | 1.33981i | 0.443570 | − | 0.896240i | \(-0.353712\pi\) |
0.896240 | − | 0.443570i | \(-0.146288\pi\) | |||||||
\(938\) | 12.2459 | − | 29.5641i | 0.399842 | − | 0.965304i | ||||
\(939\) | − | 68.0000i | − | 2.21910i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.7766 | + | 33.2597i | 0.449104 | + | 1.08423i | 0.972658 | + | 0.232241i | \(0.0746059\pi\) |
−0.523554 | + | 0.851993i | \(0.675394\pi\) | |||||||
\(942\) | 25.8686 | − | 10.7151i | 0.842845 | − | 0.349118i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18.3688 | + | 44.3462i | 0.597221 | + | 1.44182i | ||||
\(947\) | 16.6298 | + | 6.88830i | 0.540397 | + | 0.223840i | 0.636150 | − | 0.771565i | \(-0.280526\pi\) |
−0.0957531 | + | 0.995405i | \(0.530526\pi\) | |||||||
\(948\) | − | 16.0000i | − | 0.519656i | ||||||
\(949\) | 1.53073 | − | 3.69552i | 0.0496897 | − | 0.119962i | ||||
\(950\) | 14.1421 | − | 14.1421i | 0.458831 | − | 0.458831i | ||||
\(951\) | −24.0000 | −0.778253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.0000 | −0.971795 | −0.485898 | − | 0.874016i | \(-0.661507\pi\) | ||||
−0.485898 | + | 0.874016i | \(0.661507\pi\) | |||||||
\(954\) | 4.24264 | − | 4.24264i | 0.137361 | − | 0.137361i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 24.0000i | − | 0.776215i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.18440 | − | 22.1731i | −0.296735 | − | 0.716381i | ||||
\(959\) | 22.1731 | − | 9.18440i | 0.716007 | − | 0.296580i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.6066 | + | 10.6066i | 0.342148 | + | 0.342148i | ||||
\(962\) | −7.39104 | + | 3.06147i | −0.238297 | + | 0.0987057i | ||||
\(963\) | −2.29610 | − | 5.54328i | −0.0739908 | − | 0.178630i | ||||
\(964\) | −9.23880 | − | 3.82683i | −0.297562 | − | 0.123254i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.2843 | + | 28.2843i | −0.909561 | + | 0.909561i | −0.996237 | − | 0.0866757i | \(-0.972376\pi\) |
0.0866757 | + | 0.996237i | \(0.472376\pi\) | |||||||
\(968\) | −25.0000 | −0.803530 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.9706 | − | 16.9706i | 0.544611 | − | 0.544611i | −0.380266 | − | 0.924877i | \(-0.624168\pi\) |
0.924877 | + | 0.380266i | \(0.124168\pi\) | |||||||
\(972\) | −3.82683 | + | 9.23880i | −0.122746 | + | 0.296334i | ||||
\(973\) | 8.00000i | 0.256468i | ||||||||
\(974\) | −7.39104 | − | 3.06147i | −0.236824 | − | 0.0980957i | ||||
\(975\) | −7.65367 | − | 18.4776i | −0.245114 | − | 0.591756i | ||||
\(976\) | 3.69552 | − | 1.53073i | 0.118291 | − | 0.0489976i | ||||
\(977\) | 29.6985 | + | 29.6985i | 0.950139 | + | 0.950139i | 0.998815 | − | 0.0486759i | \(-0.0155002\pi\) |
−0.0486759 | + | 0.998815i | \(0.515500\pi\) | |||||||
\(978\) | 2.82843 | + | 2.82843i | 0.0904431 | + | 0.0904431i | ||||
\(979\) | −33.2597 | + | 13.7766i | −1.06298 | + | 0.440302i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.7821 | − | 6.12293i | −0.471955 | − | 0.195490i | ||||
\(982\) | − | 12.0000i | − | 0.382935i | ||||||
\(983\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(984\) | −8.48528 | + | 8.48528i | −0.270501 | + | 0.270501i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.65685 | − | 5.65685i | 0.179969 | − | 0.179969i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.7821 | + | 6.12293i | 0.469568 | + | 0.194501i | 0.604904 | − | 0.796298i | \(-0.293211\pi\) |
−0.135336 | + | 0.990800i | \(0.543211\pi\) | |||||||
\(992\) | 1.53073 | + | 3.69552i | 0.0486008 | + | 0.117333i | ||||
\(993\) | −29.5641 | + | 12.2459i | −0.938190 | + | 0.388611i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.7151 | − | 25.8686i | −0.339352 | − | 0.819268i | −0.997778 | − | 0.0666226i | \(-0.978778\pi\) |
0.658426 | − | 0.752645i | \(-0.271222\pi\) | |||||||
\(998\) | 12.9343 | + | 5.35757i | 0.409429 | + | 0.169591i | ||||
\(999\) | − | 16.0000i | − | 0.506218i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))