Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [867,2,Mod(688,867)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(867, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("867.688");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 867 = 3 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 867.h (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: | \(6.92302985525\) |
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: | \( 1 \) |
Twist minimal: | no (minimal twist has level 51) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 757.1 | ||
Root | \(-0.382683 - 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 867.757 |
Dual form | 867.2.h.d.733.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/867\mathbb{Z}\right)^\times\).
\(n\) | \(290\) | \(292\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{8}\right)\) |
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 | −0.911438 | − | 0.411438i | \(-0.865027\pi\) |
0.411438 | + | 0.911438i | \(0.365027\pi\) | |||||||
\(3\) | −0.923880 | − | 0.382683i | −0.533402 | − | 0.220942i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(6\) | 0.923880 | − | 0.382683i | 0.377172 | − | 0.156230i | ||||
\(7\) | 1.53073 | + | 3.69552i | 0.578563 | + | 1.39677i | 0.894103 | + | 0.447862i | \(0.147814\pi\) |
−0.315540 | + | 0.948912i | \(0.602186\pi\) | |||||||
\(8\) | −2.12132 | − | 2.12132i | −0.750000 | − | 0.750000i | ||||
\(9\) | 0.707107 | + | 0.707107i | 0.235702 | + | 0.235702i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.69552 | + | 1.53073i | −1.11424 | + | 0.461534i | −0.862396 | − | 0.506234i | \(-0.831037\pi\) |
−0.251845 | + | 0.967768i | \(0.581037\pi\) | |||||||
\(12\) | 0.382683 | − | 0.923880i | 0.110471 | − | 0.266701i | ||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | −3.69552 | − | 1.53073i | −0.987669 | − | 0.409106i | ||||
\(15\) | 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 | ||||||||
\(21\) | − | 4.00000i | − | 0.872872i | ||||||
\(22\) | 1.53073 | − | 3.69552i | 0.326354 | − | 0.787887i | ||||
\(23\) | −3.69552 | + | 1.53073i | −0.770569 | + | 0.319180i | −0.733103 | − | 0.680118i | \(-0.761929\pi\) |
−0.0374660 | + | 0.999298i | \(0.511929\pi\) | |||||||
\(24\) | 1.14805 | + | 2.77164i | 0.234345 | + | 0.565758i | ||||
\(25\) | 3.53553 | + | 3.53553i | 0.707107 | + | 0.707107i | ||||
\(26\) | −1.41421 | − | 1.41421i | −0.277350 | − | 0.277350i | ||||
\(27\) | −0.382683 | − | 0.923880i | −0.0736475 | − | 0.177801i | ||||
\(28\) | −3.69552 | + | 1.53073i | −0.698387 | + | 0.289281i | ||||
\(29\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.69552 | − | 1.53073i | −0.663735 | − | 0.274928i | 0.0252745 | − | 0.999681i | \(-0.491954\pi\) |
−0.689009 | + | 0.724753i | \(0.741954\pi\) | |||||||
\(32\) | 3.53553 | − | 3.53553i | 0.625000 | − | 0.625000i | ||||
\(33\) | 4.00000 | 0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.707107 | + | 0.707107i | −0.117851 | + | 0.117851i | ||||
\(37\) | −7.39104 | − | 3.06147i | −1.21508 | − | 0.503302i | −0.319237 | − | 0.947675i | \(-0.603427\pi\) |
−0.895842 | + | 0.444373i | \(0.853427\pi\) | |||||||
\(38\) | 4.00000i | 0.648886i | ||||||||
\(39\) | 0.765367 | − | 1.84776i | 0.122557 | − | 0.295878i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.06147 | + | 7.39104i | 0.478121 | + | 1.15429i | 0.960489 | + | 0.278317i | \(0.0897767\pi\) |
−0.482368 | + | 0.875969i | \(0.660223\pi\) | |||||||
\(42\) | 2.82843 | + | 2.82843i | 0.436436 | + | 0.436436i | ||||
\(43\) | 2.82843 | + | 2.82843i | 0.431331 | + | 0.431331i | 0.889081 | − | 0.457750i | \(-0.151344\pi\) |
−0.457750 | + | 0.889081i | \(0.651344\pi\) | |||||||
\(44\) | −1.53073 | − | 3.69552i | −0.230767 | − | 0.557120i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.53073 | − | 3.69552i | 0.225694 | − | 0.544874i | ||||
\(47\) | − | 8.00000i | − | 1.16692i | −0.812142 | − | 0.583460i | \(-0.801699\pi\) | ||
0.812142 | − | 0.583460i | \(-0.198301\pi\) | |||||||
\(48\) | −0.923880 | − | 0.382683i | −0.133351 | − | 0.0552356i | ||||
\(49\) | −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 | −0.935664 | − | 0.352892i | \(-0.885198\pi\) |
0.352892 | + | 0.935664i | \(0.385198\pi\) | |||||||
\(54\) | 0.923880 | + | 0.382683i | 0.125724 | + | 0.0520766i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.59220 | − | 11.0866i | 0.613659 | − | 1.48150i | ||||
\(57\) | −3.69552 | + | 1.53073i | −0.489483 | + | 0.202751i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.48528 | − | 8.48528i | −1.10469 | − | 1.10469i | −0.993837 | − | 0.110853i | \(-0.964642\pi\) |
−0.110853 | − | 0.993837i | \(-0.535358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.06147 | − | 7.39104i | −0.391981 | − | 0.946325i | −0.989508 | − | 0.144477i | \(-0.953850\pi\) |
0.597527 | − | 0.801848i | \(-0.296150\pi\) | |||||||
\(62\) | 3.69552 | − | 1.53073i | 0.469331 | − | 0.194403i | ||||
\(63\) | −1.53073 | + | 3.69552i | −0.192854 | + | 0.465592i | ||||
\(64\) | 7.00000i | 0.875000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.82843 | + | 2.82843i | −0.348155 | + | 0.348155i | ||||
\(67\) | −12.0000 | −1.46603 | −0.733017 | − | 0.680211i | \(-0.761888\pi\) | ||||
−0.733017 | + | 0.680211i | \(0.761888\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.0866 | − | 4.59220i | −1.31573 | − | 0.544994i | −0.389180 | − | 0.921162i | \(-0.627242\pi\) |
−0.926552 | + | 0.376168i | \(0.877242\pi\) | |||||||
\(72\) | − | 3.00000i | − | 0.353553i | ||||||
\(73\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(74\) | 7.39104 | − | 3.06147i | 0.859191 | − | 0.355888i | ||||
\(75\) | −1.91342 | − | 4.61940i | −0.220942 | − | 0.533402i | ||||
\(76\) | 2.82843 | + | 2.82843i | 0.324443 | + | 0.324443i | ||||
\(77\) | −11.3137 | − | 11.3137i | −1.28932 | − | 1.28932i | ||||
\(78\) | 0.765367 | + | 1.84776i | 0.0866607 | + | 0.209218i | ||||
\(79\) | 3.69552 | − | 1.53073i | 0.415778 | − | 0.172221i | −0.164980 | − | 0.986297i | \(-0.552756\pi\) |
0.580759 | + | 0.814076i | \(0.302756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000i | 0.111111i | ||||||||
\(82\) | −7.39104 | − | 3.06147i | −0.816203 | − | 0.338083i | ||||
\(83\) | 8.48528 | − | 8.48528i | 0.931381 | − | 0.931381i | −0.0664117 | − | 0.997792i | \(-0.521155\pi\) |
0.997792 | + | 0.0664117i | \(0.0211551\pi\) | |||||||
\(84\) | 4.00000 | 0.436436 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.00000 | −0.431331 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 11.0866 | + | 4.59220i | 1.18183 | + | 0.489530i | ||||
\(89\) | 10.0000i | 1.06000i | 0.847998 | + | 0.529999i | \(0.177808\pi\) | ||||
−0.847998 | + | 0.529999i | \(0.822192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.39104 | + | 3.06147i | −0.774791 | + | 0.320929i | ||||
\(92\) | −1.53073 | − | 3.69552i | −0.159590 | − | 0.385284i | ||||
\(93\) | 2.82843 | + | 2.82843i | 0.293294 | + | 0.293294i | ||||
\(94\) | 5.65685 | + | 5.65685i | 0.583460 | + | 0.583460i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.61940 | + | 1.91342i | −0.471465 | + | 0.195287i | ||||
\(97\) | −6.12293 | + | 14.7821i | −0.621690 | + | 1.50089i | 0.228028 | + | 0.973655i | \(0.426772\pi\) |
−0.849718 | + | 0.527238i | \(0.823228\pi\) | |||||||
\(98\) | − | 9.00000i | − | 0.909137i | ||||||
\(99\) | −3.69552 | − | 1.53073i | −0.371414 | − | 0.153845i | ||||
\(100\) | −3.53553 | + | 3.53553i | −0.353553 | + | 0.353553i | ||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 4.24264 | − | 4.24264i | 0.416025 | − | 0.416025i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 6.00000i | − | 0.582772i | ||||||
\(107\) | −4.59220 | + | 11.0866i | −0.443945 | + | 1.07178i | 0.530608 | + | 0.847618i | \(0.321964\pi\) |
−0.974552 | + | 0.224160i | \(0.928036\pi\) | |||||||
\(108\) | 0.923880 | − | 0.382683i | 0.0889003 | − | 0.0368237i | ||||
\(109\) | −3.06147 | − | 7.39104i | −0.293235 | − | 0.707933i | −1.00000 | 0.000483966i | \(-0.999846\pi\) | |
0.706764 | − | 0.707449i | \(-0.250154\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.65685 | + | 5.65685i | 0.536925 | + | 0.536925i | ||||
\(112\) | 1.53073 | + | 3.69552i | 0.144641 | + | 0.349194i | ||||
\(113\) | 7.39104 | − | 3.06147i | 0.695290 | − | 0.287999i | −0.00691210 | − | 0.999976i | \(-0.502200\pi\) |
0.702202 | + | 0.711977i | \(0.252200\pi\) | |||||||
\(114\) | 1.53073 | − | 3.69552i | 0.143366 | − | 0.346117i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.41421 | + | 1.41421i | −0.130744 | + | 0.130744i | ||||
\(118\) | 12.0000 | 1.10469 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.53553 | − | 3.53553i | 0.321412 | − | 0.321412i | ||||
\(122\) | 7.39104 | + | 3.06147i | 0.669153 | + | 0.277172i | ||||
\(123\) | − | 8.00000i | − | 0.721336i | ||||||
\(124\) | 1.53073 | − | 3.69552i | 0.137464 | − | 0.331867i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.53073 | − | 3.69552i | −0.136369 | − | 0.329223i | ||||
\(127\) | 5.65685 | + | 5.65685i | 0.501965 | + | 0.501965i | 0.912048 | − | 0.410083i | \(-0.134500\pi\) |
−0.410083 | + | 0.912048i | \(0.634500\pi\) | |||||||
\(128\) | 2.12132 | + | 2.12132i | 0.187500 | + | 0.187500i | ||||
\(129\) | −1.53073 | − | 3.69552i | −0.134774 | − | 0.325372i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.53073 | + | 3.69552i | −0.133741 | + | 0.322879i | −0.976536 | − | 0.215356i | \(-0.930909\pi\) |
0.842795 | + | 0.538235i | \(0.180909\pi\) | |||||||
\(132\) | 4.00000i | 0.348155i | ||||||||
\(133\) | 14.7821 | + | 6.12293i | 1.28177 | + | 0.530926i | ||||
\(134\) | 8.48528 | − | 8.48528i | 0.733017 | − | 0.733017i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.0000 | −0.854358 | −0.427179 | − | 0.904167i | \(-0.640493\pi\) | ||||
−0.427179 | + | 0.904167i | \(0.640493\pi\) | |||||||
\(138\) | −2.82843 | + | 2.82843i | −0.240772 | + | 0.240772i | ||||
\(139\) | −3.69552 | − | 1.53073i | −0.313450 | − | 0.129835i | 0.220412 | − | 0.975407i | \(-0.429260\pi\) |
−0.533862 | + | 0.845572i | \(0.679260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.06147 | + | 7.39104i | −0.257822 | + | 0.622438i | ||||
\(142\) | 11.0866 | − | 4.59220i | 0.930363 | − | 0.385369i | ||||
\(143\) | −3.06147 | − | 7.39104i | −0.256013 | − | 0.618070i | ||||
\(144\) | 0.707107 | + | 0.707107i | 0.0589256 | + | 0.0589256i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.31492 | − | 3.44415i | 0.685803 | − | 0.284069i | ||||
\(148\) | 3.06147 | − | 7.39104i | 0.251651 | − | 0.607539i | ||||
\(149\) | 6.00000i | 0.491539i | 0.969328 | + | 0.245770i | \(0.0790407\pi\) | ||||
−0.969328 | + | 0.245770i | \(0.920959\pi\) | |||||||
\(150\) | 4.61940 | + | 1.91342i | 0.377172 | + | 0.156230i | ||||
\(151\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(152\) | −12.0000 | −0.973329 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 16.0000 | 1.28932 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.84776 | + | 0.765367i | 0.147939 | + | 0.0612784i | ||||
\(157\) | 2.00000i | 0.159617i | 0.996810 | + | 0.0798087i | \(0.0254309\pi\) | ||||
−0.996810 | + | 0.0798087i | \(0.974569\pi\) | |||||||
\(158\) | −1.53073 | + | 3.69552i | −0.121779 | + | 0.294000i | ||||
\(159\) | 5.54328 | − | 2.29610i | 0.439610 | − | 0.182093i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.3137 | − | 11.3137i | −0.891645 | − | 0.891645i | ||||
\(162\) | −0.707107 | − | 0.707107i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | 7.65367 | + | 18.4776i | 0.599482 | + | 1.44728i | 0.874111 | + | 0.485726i | \(0.161445\pi\) |
−0.274629 | + | 0.961550i | \(0.588555\pi\) | |||||||
\(164\) | −7.39104 | + | 3.06147i | −0.577143 | + | 0.239060i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.0000i | 0.931381i | ||||||||
\(167\) | 11.0866 | + | 4.59220i | 0.857903 | + | 0.355355i | 0.767887 | − | 0.640585i | \(-0.221308\pi\) |
0.0900162 | + | 0.995940i | \(0.471308\pi\) | |||||||
\(168\) | −8.48528 | + | 8.48528i | −0.654654 | + | 0.654654i | ||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000 | 0.305888 | ||||||||
\(172\) | −2.82843 | + | 2.82843i | −0.215666 | + | 0.215666i | ||||
\(173\) | 14.7821 | + | 6.12293i | 1.12386 | + | 0.465518i | 0.865690 | − | 0.500581i | \(-0.166880\pi\) |
0.258171 | + | 0.966099i | \(0.416880\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.65367 | + | 18.4776i | −0.578563 | + | 1.39677i | ||||
\(176\) | −3.69552 | + | 1.53073i | −0.278560 | + | 0.115383i | ||||
\(177\) | 4.59220 | + | 11.0866i | 0.345171 | + | 0.833316i | ||||
\(178\) | −7.07107 | − | 7.07107i | −0.529999 | − | 0.529999i | ||||
\(179\) | −2.82843 | − | 2.82843i | −0.211407 | − | 0.211407i | 0.593458 | − | 0.804865i | \(-0.297762\pi\) |
−0.804865 | + | 0.593458i | \(0.797762\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.39104 | − | 3.06147i | 0.549371 | − | 0.227557i | −0.0906923 | − | 0.995879i | \(-0.528908\pi\) |
0.640064 | + | 0.768322i | \(0.278908\pi\) | |||||||
\(182\) | 3.06147 | − | 7.39104i | 0.226931 | − | 0.547860i | ||||
\(183\) | 8.00000i | 0.591377i | ||||||||
\(184\) | 11.0866 | + | 4.59220i | 0.817312 | + | 0.338542i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.00000 | −0.293294 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 8.00000 | 0.583460 | ||||||||
\(189\) | 2.82843 | − | 2.82843i | 0.205738 | − | 0.205738i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00000i | 0.578860i | 0.957199 | + | 0.289430i | \(0.0934657\pi\) | ||||
−0.957199 | + | 0.289430i | \(0.906534\pi\) | |||||||
\(192\) | 2.67878 | − | 6.46716i | 0.193325 | − | 0.466727i | ||||
\(193\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(194\) | −6.12293 | − | 14.7821i | −0.439601 | − | 1.06129i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.36396 | − | 6.36396i | −0.454569 | − | 0.454569i | ||||
\(197\) | 6.12293 | + | 14.7821i | 0.436241 | + | 1.05318i | 0.977236 | + | 0.212153i | \(0.0680477\pi\) |
−0.540995 | + | 0.841026i | \(0.681952\pi\) | |||||||
\(198\) | 3.69552 | − | 1.53073i | 0.262629 | − | 0.108785i | ||||
\(199\) | 7.65367 | − | 18.4776i | 0.542554 | − | 1.30984i | −0.380361 | − | 0.924838i | \(-0.624200\pi\) |
0.922915 | − | 0.385004i | \(-0.125800\pi\) | |||||||
\(200\) | − | 15.0000i | − | 1.06066i | ||||||
\(201\) | 11.0866 | + | 4.59220i | 0.781985 | + | 0.323909i | ||||
\(202\) | −4.24264 | + | 4.24264i | −0.298511 | + | 0.298511i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.69552 | − | 1.53073i | −0.256856 | − | 0.106393i | ||||
\(208\) | 2.00000i | 0.138675i | ||||||||
\(209\) | −6.12293 | + | 14.7821i | −0.423532 | + | 1.02250i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.53073 | − | 3.69552i | −0.105380 | − | 0.254410i | 0.862390 | − | 0.506244i | \(-0.168966\pi\) |
−0.967771 | + | 0.251834i | \(0.918966\pi\) | |||||||
\(212\) | −4.24264 | − | 4.24264i | −0.291386 | − | 0.291386i | ||||
\(213\) | 8.48528 | + | 8.48528i | 0.581402 | + | 0.581402i | ||||
\(214\) | −4.59220 | − | 11.0866i | −0.313916 | − | 0.757861i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.14805 | + | 2.77164i | −0.0781149 | + | 0.188586i | ||||
\(217\) | − | 16.0000i | − | 1.08615i | ||||||
\(218\) | 7.39104 | + | 3.06147i | 0.500584 | + | 0.207349i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −8.00000 | −0.536925 | ||||||||
\(223\) | −11.3137 | + | 11.3137i | −0.757622 | + | 0.757622i | −0.975889 | − | 0.218267i | \(-0.929960\pi\) |
0.218267 | + | 0.975889i | \(0.429960\pi\) | |||||||
\(224\) | 18.4776 | + | 7.65367i | 1.23459 | + | 0.511382i | ||||
\(225\) | 5.00000i | 0.333333i | ||||||||
\(226\) | −3.06147 | + | 7.39104i | −0.203646 | + | 0.491644i | ||||
\(227\) | −11.0866 | + | 4.59220i | −0.735840 | + | 0.304795i | −0.718950 | − | 0.695062i | \(-0.755377\pi\) |
−0.0168909 | + | 0.999857i | \(0.505377\pi\) | |||||||
\(228\) | −1.53073 | − | 3.69552i | −0.101375 | − | 0.244742i | ||||
\(229\) | 7.07107 | + | 7.07107i | 0.467269 | + | 0.467269i | 0.901029 | − | 0.433759i | \(-0.142813\pi\) |
−0.433759 | + | 0.901029i | \(0.642813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.12293 | + | 14.7821i | 0.402860 | + | 0.972589i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.06147 | + | 7.39104i | −0.200563 | + | 0.484203i | −0.991876 | − | 0.127209i | \(-0.959398\pi\) |
0.791313 | + | 0.611412i | \(0.209398\pi\) | |||||||
\(234\) | − | 2.00000i | − | 0.130744i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.48528 | − | 8.48528i | 0.552345 | − | 0.552345i | ||||
\(237\) | −4.00000 | −0.259828 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.7821 | + | 6.12293i | 0.952197 | + | 0.394413i | 0.804056 | − | 0.594553i | \(-0.202671\pi\) |
0.148141 | + | 0.988966i | \(0.452671\pi\) | |||||||
\(242\) | 5.00000i | 0.321412i | ||||||||
\(243\) | 0.382683 | − | 0.923880i | 0.0245492 | − | 0.0592669i | ||||
\(244\) | 7.39104 | − | 3.06147i | 0.473163 | − | 0.195990i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.65685 | + | 5.65685i | 0.360668 | + | 0.360668i | ||||
\(247\) | 5.65685 | + | 5.65685i | 0.359937 | + | 0.359937i | ||||
\(248\) | 4.59220 | + | 11.0866i | 0.291605 | + | 0.703997i | ||||
\(249\) | −11.0866 | + | 4.59220i | −0.702582 | + | 0.291019i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000i | 0.757433i | 0.925513 | + | 0.378717i | \(0.123635\pi\) | ||||
−0.925513 | + | 0.378717i | \(0.876365\pi\) | |||||||
\(252\) | −3.69552 | − | 1.53073i | −0.232796 | − | 0.0964272i | ||||
\(253\) | 11.3137 | − | 11.3137i | 0.711287 | − | 0.711287i | ||||
\(254\) | −8.00000 | −0.501965 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | 1.41421 | − | 1.41421i | 0.0882162 | − | 0.0882162i | −0.661622 | − | 0.749838i | \(-0.730131\pi\) |
0.749838 | + | 0.661622i | \(0.230131\pi\) | |||||||
\(258\) | 3.69552 | + | 1.53073i | 0.230073 | + | 0.0952993i | ||||
\(259\) | − | 32.0000i | − | 1.98838i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.53073 | − | 3.69552i | −0.0945690 | − | 0.228310i | ||||
\(263\) | 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 | ||||||||
\(266\) | −14.7821 | + | 6.12293i | −0.906347 | + | 0.375421i | ||||
\(267\) | 3.82683 | − | 9.23880i | 0.234198 | − | 0.565405i | ||||
\(268\) | − | 12.0000i | − | 0.733017i | ||||||
\(269\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.00000 | 0.484182 | ||||||||
\(274\) | 7.07107 | − | 7.07107i | 0.427179 | − | 0.427179i | ||||
\(275\) | −18.4776 | − | 7.65367i | −1.11424 | − | 0.461534i | ||||
\(276\) | 4.00000i | 0.240772i | ||||||||
\(277\) | −3.06147 | + | 7.39104i | −0.183946 | + | 0.444084i | −0.988773 | − | 0.149425i | \(-0.952258\pi\) |
0.804827 | + | 0.593509i | \(0.202258\pi\) | |||||||
\(278\) | 3.69552 | − | 1.53073i | 0.221642 | − | 0.0918073i | ||||
\(279\) | −1.53073 | − | 3.69552i | −0.0916426 | − | 0.221245i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.07107 | − | 7.07107i | −0.421825 | − | 0.421825i | 0.464007 | − | 0.885832i | \(-0.346411\pi\) |
−0.885832 | + | 0.464007i | \(0.846411\pi\) | |||||||
\(282\) | −3.06147 | − | 7.39104i | −0.182308 | − | 0.440130i | ||||
\(283\) | −3.69552 | + | 1.53073i | −0.219676 | + | 0.0909927i | −0.489807 | − | 0.871831i | \(-0.662933\pi\) |
0.270131 | + | 0.962823i | \(0.412933\pi\) | |||||||
\(284\) | 4.59220 | − | 11.0866i | 0.272497 | − | 0.657866i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.39104 | + | 3.06147i | 0.437041 | + | 0.181028i | ||||
\(287\) | −22.6274 | + | 22.6274i | −1.33565 | + | 1.33565i | ||||
\(288\) | 5.00000 | 0.294628 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.3137 | − | 11.3137i | 0.663221 | − | 0.663221i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.0000i | 0.584206i | 0.956387 | + | 0.292103i | \(0.0943550\pi\) | ||||
−0.956387 | + | 0.292103i | \(0.905645\pi\) | |||||||
\(294\) | −3.44415 | + | 8.31492i | −0.200867 | + | 0.484936i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.18440 | + | 22.1731i | 0.533833 | + | 1.28879i | ||||
\(297\) | 2.82843 | + | 2.82843i | 0.164122 | + | 0.164122i | ||||
\(298\) | −4.24264 | − | 4.24264i | −0.245770 | − | 0.245770i | ||||
\(299\) | −3.06147 | − | 7.39104i | −0.177049 | − | 0.427435i | ||||
\(300\) | 4.61940 | − | 1.91342i | 0.266701 | − | 0.110471i | ||||
\(301\) | −6.12293 | + | 14.7821i | −0.352920 | + | 0.852024i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.54328 | − | 2.29610i | −0.318453 | − | 0.131908i | ||||
\(304\) | 2.82843 | − | 2.82843i | 0.162221 | − | 0.162221i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.0000 | −0.684876 | −0.342438 | − | 0.939540i | \(-0.611253\pi\) | ||||
−0.342438 | + | 0.939540i | \(0.611253\pi\) | |||||||
\(308\) | 11.3137 | − | 11.3137i | 0.644658 | − | 0.644658i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.59220 | − | 11.0866i | 0.260400 | − | 0.628661i | −0.738563 | − | 0.674184i | \(-0.764495\pi\) |
0.998963 | + | 0.0455232i | \(0.0144955\pi\) | |||||||
\(312\) | −5.54328 | + | 2.29610i | −0.313826 | + | 0.129991i | ||||
\(313\) | 6.12293 | + | 14.7821i | 0.346089 | + | 0.835532i | 0.997074 | + | 0.0764418i | \(0.0243559\pi\) |
−0.650985 | + | 0.759090i | \(0.725644\pi\) | |||||||
\(314\) | −1.41421 | − | 1.41421i | −0.0798087 | − | 0.0798087i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.53073 | + | 3.69552i | 0.0861105 | + | 0.207889i | ||||
\(317\) | 29.5641 | − | 12.2459i | 1.66049 | − | 0.687797i | 0.662373 | − | 0.749174i | \(-0.269549\pi\) |
0.998115 | + | 0.0613775i | \(0.0195493\pi\) | |||||||
\(318\) | −2.29610 | + | 5.54328i | −0.128759 | + | 0.310852i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.48528 | − | 8.48528i | 0.473602 | − | 0.473602i | ||||
\(322\) | 16.0000 | 0.891645 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −7.07107 | + | 7.07107i | −0.392232 | + | 0.392232i | ||||
\(326\) | −18.4776 | − | 7.65367i | −1.02338 | − | 0.423898i | ||||
\(327\) | 8.00000i | 0.442401i | ||||||||
\(328\) | 9.18440 | − | 22.1731i | 0.507124 | − | 1.22431i | ||||
\(329\) | 29.5641 | − | 12.2459i | 1.62992 | − | 0.675137i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.1421 | − | 14.1421i | −0.777322 | − | 0.777322i | 0.202053 | − | 0.979375i | \(-0.435239\pi\) |
−0.979375 | + | 0.202053i | \(0.935239\pi\) | |||||||
\(332\) | 8.48528 | + | 8.48528i | 0.465690 | + | 0.465690i | ||||
\(333\) | −3.06147 | − | 7.39104i | −0.167767 | − | 0.405026i | ||||
\(334\) | −11.0866 | + | 4.59220i | −0.606629 | + | 0.251274i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 4.00000i | − | 0.218218i | ||||||
\(337\) | −14.7821 | − | 6.12293i | −0.805231 | − | 0.333538i | −0.0581814 | − | 0.998306i | \(-0.518530\pi\) |
−0.747049 | + | 0.664769i | \(0.768530\pi\) | |||||||
\(338\) | −6.36396 | + | 6.36396i | −0.346154 | + | 0.346154i | ||||
\(339\) | −8.00000 | −0.434500 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0000 | 0.866449 | ||||||||
\(342\) | −2.82843 | + | 2.82843i | −0.152944 | + | 0.152944i | ||||
\(343\) | −7.39104 | − | 3.06147i | −0.399078 | − | 0.165304i | ||||
\(344\) | − | 12.0000i | − | 0.646997i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.7821 | + | 6.12293i | −0.794689 | + | 0.329171i | ||||
\(347\) | −1.53073 | − | 3.69552i | −0.0821741 | − | 0.198386i | 0.877452 | − | 0.479664i | \(-0.159242\pi\) |
−0.959626 | + | 0.281278i | \(0.909242\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.41421 | + | 1.41421i | 0.0757011 | + | 0.0757011i | 0.743944 | − | 0.668242i | \(-0.232953\pi\) |
−0.668242 | + | 0.743944i | \(0.732953\pi\) | |||||||
\(350\) | −7.65367 | − | 18.4776i | −0.409106 | − | 0.987669i | ||||
\(351\) | 1.84776 | − | 0.765367i | 0.0986261 | − | 0.0408523i | ||||
\(352\) | −7.65367 | + | 18.4776i | −0.407942 | + | 0.984859i | ||||
\(353\) | 18.0000i | 0.958043i | 0.877803 | + | 0.479022i | \(0.159008\pi\) | ||||
−0.877803 | + | 0.479022i | \(0.840992\pi\) | |||||||
\(354\) | −11.0866 | − | 4.59220i | −0.589244 | − | 0.244073i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −10.0000 | −0.529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.00000 | 0.211407 | ||||||||
\(359\) | −22.6274 | + | 22.6274i | −1.19423 | + | 1.19423i | −0.218361 | + | 0.975868i | \(0.570071\pi\) |
−0.975868 | + | 0.218361i | \(0.929929\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000i | 0.157895i | ||||||||
\(362\) | −3.06147 | + | 7.39104i | −0.160907 | + | 0.388464i | ||||
\(363\) | −4.61940 | + | 1.91342i | −0.242455 | + | 0.100428i | ||||
\(364\) | −3.06147 | − | 7.39104i | −0.160464 | − | 0.387396i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.65685 | − | 5.65685i | −0.295689 | − | 0.295689i | ||||
\(367\) | 4.59220 | + | 11.0866i | 0.239711 | + | 0.578713i | 0.997253 | − | 0.0740732i | \(-0.0235998\pi\) |
−0.757542 | + | 0.652787i | \(0.773600\pi\) | |||||||
\(368\) | −3.69552 | + | 1.53073i | −0.192642 | + | 0.0797950i | ||||
\(369\) | −3.06147 | + | 7.39104i | −0.159374 | + | 0.384762i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.1731 | − | 9.18440i | −1.15117 | − | 0.476830i | ||||
\(372\) | −2.82843 | + | 2.82843i | −0.146647 | + | 0.146647i | ||||
\(373\) | −26.0000 | −1.34623 | −0.673114 | − | 0.739538i | \(-0.735044\pi\) | ||||
−0.673114 | + | 0.739538i | \(0.735044\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −16.9706 | + | 16.9706i | −0.875190 | + | 0.875190i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 4.00000i | 0.205738i | ||||||||
\(379\) | 7.65367 | − | 18.4776i | 0.393143 | − | 0.949130i | −0.596109 | − | 0.802904i | \(-0.703287\pi\) |
0.989251 | − | 0.146226i | \(-0.0467128\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.06147 | − | 7.39104i | −0.156844 | − | 0.378654i | ||||
\(382\) | −5.65685 | − | 5.65685i | −0.289430 | − | 0.289430i | ||||
\(383\) | 11.3137 | + | 11.3137i | 0.578103 | + | 0.578103i | 0.934380 | − | 0.356277i | \(-0.115954\pi\) |
−0.356277 | + | 0.934380i | \(0.615954\pi\) | |||||||
\(384\) | −1.14805 | − | 2.77164i | −0.0585862 | − | 0.141440i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.00000i | 0.203331i | ||||||||
\(388\) | −14.7821 | − | 6.12293i | −0.750446 | − | 0.310845i | ||||
\(389\) | −4.24264 | + | 4.24264i | −0.215110 | + | 0.215110i | −0.806434 | − | 0.591324i | \(-0.798606\pi\) |
0.591324 | + | 0.806434i | \(0.298606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 27.0000 | 1.36371 | ||||||||
\(393\) | 2.82843 | − | 2.82843i | 0.142675 | − | 0.142675i | ||||
\(394\) | −14.7821 | − | 6.12293i | −0.744710 | − | 0.308469i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.53073 | − | 3.69552i | 0.0769223 | − | 0.185707i | ||||
\(397\) | −7.39104 | + | 3.06147i | −0.370945 | + | 0.153651i | −0.560365 | − | 0.828246i | \(-0.689339\pi\) |
0.189420 | + | 0.981896i | \(0.439339\pi\) | |||||||
\(398\) | 7.65367 | + | 18.4776i | 0.383644 | + | 0.926198i | ||||
\(399\) | −11.3137 | − | 11.3137i | −0.566394 | − | 0.566394i | ||||
\(400\) | 3.53553 | + | 3.53553i | 0.176777 | + | 0.176777i | ||||
\(401\) | −9.18440 | − | 22.1731i | −0.458647 | − | 1.10727i | −0.968945 | − | 0.247275i | \(-0.920465\pi\) |
0.510298 | − | 0.859997i | \(-0.329535\pi\) | |||||||
\(402\) | −11.0866 | + | 4.59220i | −0.552947 | + | 0.229038i | ||||
\(403\) | 3.06147 | − | 7.39104i | 0.152503 | − | 0.368174i | ||||
\(404\) | 6.00000i | 0.298511i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 32.0000 | 1.58618 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0000 | 0.494468 | 0.247234 | − | 0.968956i | \(-0.420478\pi\) | ||||
0.247234 | + | 0.968956i | \(0.420478\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.23880 | + | 3.82683i | 0.455716 | + | 0.188764i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.3688 | − | 44.3462i | 0.903870 | − | 2.18213i | ||||
\(414\) | 3.69552 | − | 1.53073i | 0.181625 | − | 0.0752315i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7.07107 | + | 7.07107i | 0.346688 | + | 0.346688i | ||||
\(417\) | 2.82843 | + | 2.82843i | 0.138509 | + | 0.138509i | ||||
\(418\) | −6.12293 | − | 14.7821i | −0.299483 | − | 0.723015i | ||||
\(419\) | −3.69552 | + | 1.53073i | −0.180538 | + | 0.0747812i | −0.471121 | − | 0.882068i | \(-0.656151\pi\) |
0.290583 | + | 0.956850i | \(0.406151\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 22.0000i | − | 1.07221i | −0.844150 | − | 0.536107i | \(-0.819894\pi\) | ||
0.844150 | − | 0.536107i | \(-0.180106\pi\) | |||||||
\(422\) | 3.69552 | + | 1.53073i | 0.179895 | + | 0.0745150i | ||||
\(423\) | 5.65685 | − | 5.65685i | 0.275046 | − | 0.275046i | ||||
\(424\) | 18.0000 | 0.874157 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −12.0000 | −0.581402 | ||||||||
\(427\) | 22.6274 | − | 22.6274i | 1.09502 | − | 1.09502i | ||||
\(428\) | −11.0866 | − | 4.59220i | −0.535889 | − | 0.221972i | ||||
\(429\) | 8.00000i | 0.386244i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.4776 | + | 7.65367i | −0.890034 | + | 0.368664i | −0.780380 | − | 0.625306i | \(-0.784974\pi\) |
−0.109654 | + | 0.993970i | \(0.534974\pi\) | |||||||
\(432\) | −0.382683 | − | 0.923880i | −0.0184119 | − | 0.0444502i | ||||
\(433\) | −1.41421 | − | 1.41421i | −0.0679628 | − | 0.0679628i | 0.672308 | − | 0.740271i | \(-0.265303\pi\) |
−0.740271 | + | 0.672308i | \(0.765303\pi\) | |||||||
\(434\) | 11.3137 | + | 11.3137i | 0.543075 | + | 0.543075i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.39104 | − | 3.06147i | 0.353966 | − | 0.146618i | ||||
\(437\) | −6.12293 | + | 14.7821i | −0.292900 | + | 0.707122i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.2597 | − | 13.7766i | −1.58740 | − | 0.657521i | −0.597834 | − | 0.801620i | \(-0.703972\pi\) |
−0.989563 | + | 0.144099i | \(0.953972\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.00000 | −0.428571 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.0000 | −0.950229 | −0.475114 | − | 0.879924i | \(-0.657593\pi\) | ||||
−0.475114 | + | 0.879924i | \(0.657593\pi\) | |||||||
\(444\) | −5.65685 | + | 5.65685i | −0.268462 | + | 0.268462i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 16.0000i | − | 0.757622i | ||||||
\(447\) | 2.29610 | − | 5.54328i | 0.108602 | − | 0.262188i | ||||
\(448\) | −25.8686 | + | 10.7151i | −1.22218 | + | 0.506243i | ||||
\(449\) | −3.06147 | − | 7.39104i | −0.144480 | − | 0.348805i | 0.835029 | − | 0.550205i | \(-0.185451\pi\) |
−0.979509 | + | 0.201401i | \(0.935451\pi\) | |||||||
\(450\) | −3.53553 | − | 3.53553i | −0.166667 | − | 0.166667i | ||||
\(451\) | −22.6274 | − | 22.6274i | −1.06548 | − | 1.06548i | ||||
\(452\) | 3.06147 | + | 7.39104i | 0.143999 | + | 0.347645i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.59220 | − | 11.0866i | 0.215523 | − | 0.520318i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 11.0866 | + | 4.59220i | 0.519175 | + | 0.215050i | ||||
\(457\) | 26.8701 | − | 26.8701i | 1.25693 | − | 1.25693i | 0.304376 | − | 0.952552i | \(-0.401552\pi\) |
0.952552 | − | 0.304376i | \(-0.0984481\pi\) | |||||||
\(458\) | −10.0000 | −0.467269 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.0416 | − | 24.0416i | 1.11973 | − | 1.11973i | 0.127950 | − | 0.991781i | \(-0.459160\pi\) |
0.991781 | − | 0.127950i | \(-0.0408396\pi\) | |||||||
\(462\) | −14.7821 | − | 6.12293i | −0.687724 | − | 0.284865i | ||||
\(463\) | 40.0000i | 1.85896i | 0.368875 | + | 0.929479i | \(0.379743\pi\) | ||||
−0.368875 | + | 0.929479i | \(0.620257\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.06147 | − | 7.39104i | −0.141820 | − | 0.342383i | ||||
\(467\) | 2.82843 | + | 2.82843i | 0.130884 | + | 0.130884i | 0.769514 | − | 0.638630i | \(-0.220499\pi\) |
−0.638630 | + | 0.769514i | \(0.720499\pi\) | |||||||
\(468\) | −1.41421 | − | 1.41421i | −0.0653720 | − | 0.0653720i | ||||
\(469\) | −18.3688 | − | 44.3462i | −0.848193 | − | 2.04772i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.765367 | − | 1.84776i | 0.0352662 | − | 0.0851402i | ||||
\(472\) | 36.0000i | 1.65703i | ||||||||
\(473\) | −14.7821 | − | 6.12293i | −0.679680 | − | 0.281533i | ||||
\(474\) | 2.82843 | − | 2.82843i | 0.129914 | − | 0.129914i | ||||
\(475\) | 20.0000 | 0.917663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 5.65685 | − | 5.65685i | 0.258738 | − | 0.258738i | ||||
\(479\) | −11.0866 | − | 4.59220i | −0.506558 | − | 0.209823i | 0.114743 | − | 0.993395i | \(-0.463395\pi\) |
−0.621301 | + | 0.783572i | \(0.713395\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.12293 | − | 14.7821i | 0.279182 | − | 0.674004i | ||||
\(482\) | −14.7821 | + | 6.12293i | −0.673305 | + | 0.278892i | ||||
\(483\) | 6.12293 | + | 14.7821i | 0.278603 | + | 0.672608i | ||||
\(484\) | 3.53553 | + | 3.53553i | 0.160706 | + | 0.160706i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.382683 | + | 0.923880i | 0.0173589 | + | 0.0419080i | ||||
\(487\) | 3.69552 | − | 1.53073i | 0.167460 | − | 0.0693642i | −0.297379 | − | 0.954760i | \(-0.596112\pi\) |
0.464839 | + | 0.885395i | \(0.346112\pi\) | |||||||
\(488\) | −9.18440 | + | 22.1731i | −0.415758 | + | 1.00373i | ||||
\(489\) | − | 20.0000i | − | 0.904431i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.1421 | + | 14.1421i | −0.638226 | + | 0.638226i | −0.950118 | − | 0.311892i | \(-0.899037\pi\) |
0.311892 | + | 0.950118i | \(0.399037\pi\) | |||||||
\(492\) | 8.00000 | 0.360668 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −8.00000 | −0.359937 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.69552 | − | 1.53073i | −0.165934 | − | 0.0687320i | ||||
\(497\) | − | 48.0000i | − | 2.15309i | ||||||
\(498\) | 4.59220 | − | 11.0866i | 0.205781 | − | 0.496800i | ||||
\(499\) | 33.2597 | − | 13.7766i | 1.48891 | − | 0.616725i | 0.517828 | − | 0.855485i | \(-0.326741\pi\) |
0.971079 | + | 0.238759i | \(0.0767406\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.48528 | − | 8.48528i | −0.379094 | − | 0.379094i | ||||
\(502\) | −8.48528 | − | 8.48528i | −0.378717 | − | 0.378717i | ||||
\(503\) | 4.59220 | + | 11.0866i | 0.204756 | + | 0.494325i | 0.992583 | − | 0.121572i | \(-0.0387936\pi\) |
−0.787826 | + | 0.615897i | \(0.788794\pi\) | |||||||
\(504\) | 11.0866 | − | 4.59220i | 0.493834 | − | 0.204553i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 16.0000i | 0.711287i | ||||||||
\(507\) | −8.31492 | − | 3.44415i | −0.369278 | − | 0.152960i | ||||
\(508\) | −5.65685 | + | 5.65685i | −0.250982 | + | 0.250982i | ||||
\(509\) | 18.0000 | 0.797836 | 0.398918 | − | 0.916987i | \(-0.369386\pi\) | ||||
0.398918 | + | 0.916987i | \(0.369386\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 7.77817 | − | 7.77817i | 0.343750 | − | 0.343750i | ||||
\(513\) | −3.69552 | − | 1.53073i | −0.163161 | − | 0.0675835i | ||||
\(514\) | 2.00000i | 0.0882162i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.69552 | − | 1.53073i | 0.162686 | − | 0.0673868i | ||||
\(517\) | 12.2459 | + | 29.5641i | 0.538573 | + | 1.30023i | ||||
\(518\) | 22.6274 | + | 22.6274i | 0.994192 | + | 0.994192i | ||||
\(519\) | −11.3137 | − | 11.3137i | −0.496617 | − | 0.496617i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.1731 | + | 9.18440i | −0.971422 | + | 0.402376i | −0.811241 | − | 0.584712i | \(-0.801208\pi\) |
−0.160180 | + | 0.987088i | \(0.551208\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 12.0000i | − | 0.524723i | −0.964970 | − | 0.262362i | \(-0.915499\pi\) | ||
0.964970 | − | 0.262362i | \(-0.0845013\pi\) | |||||||
\(524\) | −3.69552 | − | 1.53073i | −0.161439 | − | 0.0668704i | ||||
\(525\) | 14.1421 | − | 14.1421i | 0.617213 | − | 0.617213i | ||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 4.00000 | 0.174078 | ||||||||
\(529\) | −4.94975 | + | 4.94975i | −0.215206 | + | 0.215206i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 12.0000i | − | 0.520756i | ||||||
\(532\) | −6.12293 | + | 14.7821i | −0.265463 | + | 0.640884i | ||||
\(533\) | −14.7821 | + | 6.12293i | −0.640283 | + | 0.265214i | ||||
\(534\) | 3.82683 | + | 9.23880i | 0.165603 | + | 0.399802i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 25.4558 | + | 25.4558i | 1.09952 | + | 1.09952i | ||||
\(537\) | 1.53073 | + | 3.69552i | 0.0660560 | + | 0.159473i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.7766 | − | 33.2597i | 0.593400 | − | 1.43260i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.9552 | + | 15.3073i | 1.58883 | + | 0.658114i | 0.989780 | − | 0.142600i | \(-0.0455463\pi\) |
0.599047 | + | 0.800714i | \(0.295546\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.00000 | −0.343313 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.65685 | + | 5.65685i | −0.242091 | + | 0.242091i | ||||
\(547\) | −33.2597 | − | 13.7766i | −1.42208 | − | 0.589045i | −0.466698 | − | 0.884417i | \(-0.654557\pi\) |
−0.955382 | + | 0.295372i | \(0.904557\pi\) | |||||||
\(548\) | − | 10.0000i | − | 0.427179i | ||||||
\(549\) | 3.06147 | − | 7.39104i | 0.130660 | − | 0.315442i | ||||
\(550\) | 18.4776 | − | 7.65367i | 0.787887 | − | 0.326354i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −8.48528 | − | 8.48528i | −0.361158 | − | 0.361158i | ||||
\(553\) | 11.3137 | + | 11.3137i | 0.481108 | + | 0.481108i | ||||
\(554\) | −3.06147 | − | 7.39104i | −0.130069 | − | 0.314015i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.53073 | − | 3.69552i | 0.0649176 | − | 0.156725i | ||||
\(557\) | 18.0000i | 0.762684i | 0.924434 | + | 0.381342i | \(0.124538\pi\) | ||||
−0.924434 | + | 0.381342i | \(0.875462\pi\) | |||||||
\(558\) | 3.69552 | + | 1.53073i | 0.156444 | + | 0.0648011i | ||||
\(559\) | −5.65685 | + | 5.65685i | −0.239259 | + | 0.239259i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.0000 | 0.421825 | ||||||||
\(563\) | −31.1127 | + | 31.1127i | −1.31124 | + | 1.31124i | −0.390745 | + | 0.920499i | \(0.627783\pi\) |
−0.920499 | + | 0.390745i | \(0.872217\pi\) | |||||||
\(564\) | −7.39104 | − | 3.06147i | −0.311219 | − | 0.128911i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.53073 | − | 3.69552i | 0.0643415 | − | 0.155334i | ||||
\(567\) | −3.69552 | + | 1.53073i | −0.155197 | + | 0.0642848i | ||||
\(568\) | 13.7766 | + | 33.2597i | 0.578053 | + | 1.39554i | ||||
\(569\) | 18.3848 | + | 18.3848i | 0.770730 | + | 0.770730i | 0.978234 | − | 0.207504i | \(-0.0665341\pi\) |
−0.207504 | + | 0.978234i | \(0.566534\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.65367 | + | 18.4776i | 0.320296 | + | 0.773263i | 0.999236 | + | 0.0390697i | \(0.0124394\pi\) |
−0.678940 | + | 0.734193i | \(0.737561\pi\) | |||||||
\(572\) | 7.39104 | − | 3.06147i | 0.309035 | − | 0.128006i | ||||
\(573\) | 3.06147 | − | 7.39104i | 0.127895 | − | 0.308765i | ||||
\(574\) | − | 32.0000i | − | 1.33565i | ||||||
\(575\) | −18.4776 | − | 7.65367i | −0.770569 | − | 0.319180i | ||||
\(576\) | −4.94975 | + | 4.94975i | −0.206239 | + | 0.206239i | ||||
\(577\) | −30.0000 | −1.24892 | −0.624458 | − | 0.781058i | \(-0.714680\pi\) | ||||
−0.624458 | + | 0.781058i | \(0.714680\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 44.3462 | + | 18.3688i | 1.83979 | + | 0.762066i | ||||
\(582\) | 16.0000i | 0.663221i | ||||||||
\(583\) | 9.18440 | − | 22.1731i | 0.380379 | − | 0.918316i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.07107 | − | 7.07107i | −0.292103 | − | 0.292103i | ||||
\(587\) | −8.48528 | − | 8.48528i | −0.350225 | − | 0.350225i | 0.509968 | − | 0.860193i | \(-0.329657\pi\) |
−0.860193 | + | 0.509968i | \(0.829657\pi\) | |||||||
\(588\) | 3.44415 | + | 8.31492i | 0.142034 | + | 0.342901i | ||||
\(589\) | −14.7821 | + | 6.12293i | −0.609085 | + | 0.252291i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 16.0000i | − | 0.658152i | ||||||
\(592\) | −7.39104 | − | 3.06147i | −0.303770 | − | 0.125826i | ||||
\(593\) | −32.5269 | + | 32.5269i | −1.33572 | + | 1.33572i | −0.435561 | + | 0.900159i | \(0.643450\pi\) |
−0.900159 | + | 0.435561i | \(0.856550\pi\) | |||||||
\(594\) | −4.00000 | −0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | −14.1421 | + | 14.1421i | −0.578799 | + | 0.578799i | ||||
\(598\) | 7.39104 | + | 3.06147i | 0.302242 | + | 0.125193i | ||||
\(599\) | 8.00000i | 0.326871i | 0.986554 | + | 0.163436i | \(0.0522576\pi\) | ||||
−0.986554 | + | 0.163436i | \(0.947742\pi\) | |||||||
\(600\) | −5.74025 | + | 13.8582i | −0.234345 | + | 0.565758i | ||||
\(601\) | 14.7821 | − | 6.12293i | 0.602973 | − | 0.249760i | −0.0602475 | − | 0.998183i | \(-0.519189\pi\) |
0.663221 | + | 0.748424i | \(0.269189\pi\) | |||||||
\(602\) | −6.12293 | − | 14.7821i | −0.249552 | − | 0.602472i | ||||
\(603\) | −8.48528 | − | 8.48528i | −0.345547 | − | 0.345547i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.54328 | − | 2.29610i | 0.225180 | − | 0.0932727i | ||||
\(607\) | 1.53073 | − | 3.69552i | 0.0621306 | − | 0.149996i | −0.889765 | − | 0.456419i | \(-0.849132\pi\) |
0.951896 | + | 0.306422i | \(0.0991319\pi\) | |||||||
\(608\) | − | 20.0000i | − | 0.811107i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.0000 | 0.647291 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.00000 | 0.242338 | 0.121169 | − | 0.992632i | \(-0.461336\pi\) | ||||
0.121169 | + | 0.992632i | \(0.461336\pi\) | |||||||
\(614\) | 8.48528 | − | 8.48528i | 0.342438 | − | 0.342438i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 48.0000i | 1.93398i | ||||||||
\(617\) | −9.18440 | + | 22.1731i | −0.369750 | + | 0.892656i | 0.624041 | + | 0.781392i | \(0.285490\pi\) |
−0.993791 | + | 0.111264i | \(0.964510\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.7766 | − | 33.2597i | −0.553728 | − | 1.33682i | −0.914659 | − | 0.404226i | \(-0.867541\pi\) |
0.360931 | − | 0.932593i | \(-0.382459\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.82843 | + | 2.82843i | 0.113501 | + | 0.113501i | ||||
\(622\) | 4.59220 | + | 11.0866i | 0.184130 | + | 0.444530i | ||||
\(623\) | −36.9552 | + | 15.3073i | −1.48058 | + | 0.613276i | ||||
\(624\) | 0.765367 | − | 1.84776i | 0.0306392 | − | 0.0739696i | ||||
\(625\) | 25.0000i | 1.00000i | ||||||||
\(626\) | −14.7821 | − | 6.12293i | −0.590810 | − | 0.244722i | ||||
\(627\) | 11.3137 | − | 11.3137i | 0.451826 | − | 0.451826i | ||||
\(628\) | −2.00000 | −0.0798087 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.65685 | − | 5.65685i | 0.225196 | − | 0.225196i | −0.585486 | − | 0.810682i | \(-0.699096\pi\) |
0.810682 | + | 0.585486i | \(0.199096\pi\) | |||||||
\(632\) | −11.0866 | − | 4.59220i | −0.440999 | − | 0.182668i | ||||
\(633\) | 4.00000i | 0.158986i | ||||||||
\(634\) | −12.2459 | + | 29.5641i | −0.486346 | + | 1.17414i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.29610 | + | 5.54328i | 0.0910463 | + | 0.219805i | ||||
\(637\) | −12.7279 | − | 12.7279i | −0.504299 | − | 0.504299i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.59220 | − | 11.0866i | −0.181665 | − | 0.438577i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.06147 | + | 7.39104i | −0.120921 | + | 0.291928i | −0.972737 | − | 0.231913i | \(-0.925502\pi\) |
0.851816 | + | 0.523841i | \(0.175502\pi\) | |||||||
\(642\) | 12.0000i | 0.473602i | ||||||||
\(643\) | 3.69552 | + | 1.53073i | 0.145737 | + | 0.0603662i | 0.454360 | − | 0.890818i | \(-0.349868\pi\) |
−0.308623 | + | 0.951185i | \(0.599868\pi\) | |||||||
\(644\) | 11.3137 | − | 11.3137i | 0.445823 | − | 0.445823i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.0000 | 1.25805 | 0.629025 | − | 0.777385i | \(-0.283454\pi\) | ||||
0.629025 | + | 0.777385i | \(0.283454\pi\) | |||||||
\(648\) | 2.12132 | − | 2.12132i | 0.0833333 | − | 0.0833333i | ||||
\(649\) | 44.3462 | + | 18.3688i | 1.74074 | + | 0.721039i | ||||
\(650\) | − | 10.0000i | − | 0.392232i | ||||||
\(651\) | −6.12293 | + | 14.7821i | −0.239977 | + | 0.579355i | ||||
\(652\) | −18.4776 | + | 7.65367i | −0.723638 | + | 0.299741i | ||||
\(653\) | 12.2459 | + | 29.5641i | 0.479218 | + | 1.15693i | 0.959976 | + | 0.280081i | \(0.0903614\pi\) |
−0.480758 | + | 0.876853i | \(0.659639\pi\) | |||||||
\(654\) | −5.65685 | − | 5.65685i | −0.221201 | − | 0.221201i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.06147 | + | 7.39104i | 0.119530 | + | 0.288571i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.2459 | + | 29.5641i | −0.477394 | + | 1.15253i | ||||
\(659\) | − | 4.00000i | − | 0.155818i | −0.996960 | − | 0.0779089i | \(-0.975176\pi\) | ||
0.996960 | − | 0.0779089i | \(-0.0248243\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.6985 | + | 29.6985i | −1.15514 | + | 1.15514i | −0.169629 | + | 0.985508i | \(0.554257\pi\) |
−0.985508 | + | 0.169629i | \(0.945743\pi\) | |||||||
\(662\) | 20.0000 | 0.777322 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −36.0000 | −1.39707 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.39104 | + | 3.06147i | 0.286397 | + | 0.118629i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −4.59220 | + | 11.0866i | −0.177678 | + | 0.428952i | ||||
\(669\) | 14.7821 | − | 6.12293i | 0.571508 | − | 0.236726i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.6274 | + | 22.6274i | 0.873522 | + | 0.873522i | ||||
\(672\) | −14.1421 | − | 14.1421i | −0.545545 | − | 0.545545i | ||||
\(673\) | 12.2459 | + | 29.5641i | 0.472044 | + | 1.13961i | 0.963259 | + | 0.268576i | \(0.0865529\pi\) |
−0.491215 | + | 0.871038i | \(0.663447\pi\) | |||||||
\(674\) | 14.7821 | − | 6.12293i | 0.569384 | − | 0.235847i | ||||
\(675\) | 1.91342 | − | 4.61940i | 0.0736475 | − | 0.177801i | ||||
\(676\) | 9.00000i | 0.346154i | ||||||||
\(677\) | 44.3462 | + | 18.3688i | 1.70436 | + | 0.705971i | 0.999993 | − | 0.00386145i | \(-0.00122914\pi\) |
0.704371 | + | 0.709832i | \(0.251229\pi\) | |||||||
\(678\) | 5.65685 | − | 5.65685i | 0.217250 | − | 0.217250i | ||||
\(679\) | −64.0000 | −2.45609 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.0000 | 0.459841 | ||||||||
\(682\) | −11.3137 | + | 11.3137i | −0.433224 | + | 0.433224i | ||||
\(683\) | 11.0866 | + | 4.59220i | 0.424215 | + | 0.175716i | 0.584569 | − | 0.811344i | \(-0.301264\pi\) |
−0.160354 | + | 0.987060i | \(0.551264\pi\) | |||||||
\(684\) | 4.00000i | 0.152944i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.39104 | − | 3.06147i | 0.282191 | − | 0.116887i | ||||
\(687\) | −3.82683 | − | 9.23880i | −0.146003 | − | 0.352482i | ||||
\(688\) | 2.82843 | + | 2.82843i | 0.107833 | + | 0.107833i | ||||
\(689\) | −8.48528 | − | 8.48528i | −0.323263 | − | 0.323263i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.4776 | + | 7.65367i | −0.702921 | + | 0.291159i | −0.705372 | − | 0.708838i | \(-0.749220\pi\) |
0.00245092 | + | 0.999997i | \(0.499220\pi\) | |||||||
\(692\) | −6.12293 | + | 14.7821i | −0.232759 | + | 0.561930i | ||||
\(693\) | − | 16.0000i | − | 0.607790i | ||||||
\(694\) | 3.69552 | + | 1.53073i | 0.140280 | + | 0.0581059i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −2.00000 | −0.0757011 | ||||||||
\(699\) | 5.65685 | − | 5.65685i | 0.213962 | − | 0.213962i | ||||
\(700\) | −18.4776 | − | 7.65367i | −0.698387 | − | 0.289281i | ||||
\(701\) | − | 34.0000i | − | 1.28416i | −0.766637 | − | 0.642081i | \(-0.778071\pi\) | ||
0.766637 | − | 0.642081i | \(-0.221929\pi\) | |||||||
\(702\) | −0.765367 | + | 1.84776i | −0.0288869 | + | 0.0697392i | ||||
\(703\) | −29.5641 | + | 12.2459i | −1.11503 | + | 0.461862i | ||||
\(704\) | −10.7151 | − | 25.8686i | −0.403842 | − | 0.974961i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.7279 | − | 12.7279i | −0.479022 | − | 0.479022i | ||||
\(707\) | 9.18440 | + | 22.1731i | 0.345415 | + | 0.833906i | ||||
\(708\) | −11.0866 | + | 4.59220i | −0.416658 | + | 0.172585i | ||||
\(709\) | 15.3073 | − | 36.9552i | 0.574879 | − | 1.38788i | −0.322478 | − | 0.946577i | \(-0.604516\pi\) |
0.897358 | − | 0.441304i | \(-0.145484\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.69552 | + | 1.53073i | 0.138593 | + | 0.0574070i | ||||
\(712\) | 21.2132 | − | 21.2132i | 0.794998 | − | 0.794998i | ||||
\(713\) | 16.0000 | 0.599205 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.82843 | − | 2.82843i | 0.105703 | − | 0.105703i | ||||
\(717\) | 7.39104 | + | 3.06147i | 0.276023 | + | 0.114333i | ||||
\(718\) | − | 32.0000i | − | 1.19423i | ||||||
\(719\) | −13.7766 | + | 33.2597i | −0.513781 | + | 1.24038i | 0.427887 | + | 0.903832i | \(0.359258\pi\) |
−0.941668 | + | 0.336544i | \(0.890742\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.12132 | − | 2.12132i | −0.0789474 | − | 0.0789474i | ||||
\(723\) | −11.3137 | − | 11.3137i | −0.420761 | − | 0.420761i | ||||
\(724\) | 3.06147 | + | 7.39104i | 0.113779 | + | 0.274686i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.91342 | − | 4.61940i | 0.0710136 | − | 0.171442i | ||||
\(727\) | 8.00000i | 0.296704i | 0.988935 | + | 0.148352i | \(0.0473968\pi\) | ||||
−0.988935 | + | 0.148352i | \(0.952603\pi\) | |||||||
\(728\) | 22.1731 | + | 9.18440i | 0.821790 | + | 0.340397i | ||||
\(729\) | −0.707107 | + | 0.707107i | −0.0261891 | + | 0.0261891i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −8.00000 | −0.295689 | ||||||||
\(733\) | 24.0416 | − | 24.0416i | 0.887998 | − | 0.887998i | −0.106333 | − | 0.994331i | \(-0.533911\pi\) |
0.994331 | + | 0.106333i | \(0.0339109\pi\) | |||||||
\(734\) | −11.0866 | − | 4.59220i | −0.409212 | − | 0.169501i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.65367 | + | 18.4776i | −0.282118 | + | 0.681093i | ||||
\(737\) | 44.3462 | − | 18.3688i | 1.63351 | − | 0.676624i | ||||
\(738\) | −3.06147 | − | 7.39104i | −0.112694 | − | 0.272068i | ||||
\(739\) | −2.82843 | − | 2.82843i | −0.104045 | − | 0.104045i | 0.653168 | − | 0.757213i | \(-0.273440\pi\) |
−0.757213 | + | 0.653168i | \(0.773440\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.06147 | − | 7.39104i | −0.112466 | − | 0.271517i | ||||
\(742\) | 22.1731 | − | 9.18440i | 0.814000 | − | 0.337170i | ||||
\(743\) | 13.7766 | − | 33.2597i | 0.505415 | − | 1.22018i | −0.441083 | − | 0.897467i | \(-0.645405\pi\) |
0.946497 | − | 0.322712i | \(-0.104595\pi\) | |||||||
\(744\) | − | 12.0000i | − | 0.439941i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 18.3848 | − | 18.3848i | 0.673114 | − | 0.673114i | ||||
\(747\) | 12.0000 | 0.439057 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −48.0000 | −1.75388 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.4776 | + | 7.65367i | 0.674257 | + | 0.279286i | 0.693424 | − | 0.720530i | \(-0.256101\pi\) |
−0.0191669 | + | 0.999816i | \(0.506101\pi\) | |||||||
\(752\) | − | 8.00000i | − | 0.291730i | ||||||
\(753\) | 4.59220 | − | 11.0866i | 0.167349 | − | 0.404017i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.82843 | + | 2.82843i | 0.102869 | + | 0.102869i | ||||
\(757\) | 26.8701 | + | 26.8701i | 0.976609 | + | 0.976609i | 0.999733 | − | 0.0231238i | \(-0.00736118\pi\) |
−0.0231238 | + | 0.999733i | \(0.507361\pi\) | |||||||
\(758\) | 7.65367 | + | 18.4776i | 0.277994 | + | 0.671136i | ||||
\(759\) | −14.7821 | + | 6.12293i | −0.536555 | + | 0.222248i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.00000i | 0.217500i | 0.994069 | + | 0.108750i | \(0.0346848\pi\) | ||||
−0.994069 | + | 0.108750i | \(0.965315\pi\) | |||||||
\(762\) | 7.39104 | + | 3.06147i | 0.267749 | + | 0.110905i | ||||
\(763\) | 22.6274 | − | 22.6274i | 0.819167 | − | 0.819167i | ||||
\(764\) | −8.00000 | −0.289430 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.0000 | −0.578103 | ||||||||
\(767\) | 16.9706 | − | 16.9706i | 0.612772 | − | 0.612772i | ||||
\(768\) | 15.7060 | + | 6.50562i | 0.566740 | + | 0.234751i | ||||
\(769\) | 34.0000i | 1.22607i | 0.790055 | + | 0.613036i | \(0.210052\pi\) | ||||
−0.790055 | + | 0.613036i | \(0.789948\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.84776 | + | 0.765367i | −0.0665454 | + | 0.0275640i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.24264 | − | 4.24264i | −0.152597 | − | 0.152597i | 0.626680 | − | 0.779277i | \(-0.284413\pi\) |
−0.779277 | + | 0.626680i | \(0.784413\pi\) | |||||||
\(774\) | −2.82843 | − | 2.82843i | −0.101666 | − | 0.101666i | ||||
\(775\) | −7.65367 | − | 18.4776i | −0.274928 | − | 0.663735i | ||||
\(776\) | 44.3462 | − | 18.3688i | 1.59194 | − | 0.659402i | ||||
\(777\) | −12.2459 | + | 29.5641i | −0.439318 | + | 1.06061i | ||||
\(778\) | − | 6.00000i | − | 0.215110i | ||||||
\(779\) | 29.5641 | + | 12.2459i | 1.05925 | + | 0.438754i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 48.0000 | 1.71758 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.36396 | + | 6.36396i | −0.227284 | + | 0.227284i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.00000i | 0.142675i | ||||||||
\(787\) | −4.59220 | + | 11.0866i | −0.163694 | + | 0.395193i | −0.984349 | − | 0.176232i | \(-0.943609\pi\) |
0.820654 | + | 0.571425i | \(0.193609\pi\) | |||||||
\(788\) | −14.7821 | + | 6.12293i | −0.526590 | + | 0.218121i | ||||
\(789\) | −9.18440 | − | 22.1731i | −0.326973 | − | 0.789384i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.6274 | + | 22.6274i | 0.804538 | + | 0.804538i | ||||
\(792\) | 4.59220 | + | 11.0866i | 0.163177 | + | 0.393944i | ||||
\(793\) | 14.7821 | − | 6.12293i | 0.524927 | − | 0.217432i | ||||
\(794\) | 3.06147 | − | 7.39104i | 0.108647 | − | 0.262298i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.4776 | + | 7.65367i | 0.654921 | + | 0.271277i | ||||
\(797\) | −12.7279 | + | 12.7279i | −0.450846 | + | 0.450846i | −0.895635 | − | 0.444789i | \(-0.853279\pi\) |
0.444789 | + | 0.895635i | \(0.353279\pi\) | |||||||
\(798\) | 16.0000 | 0.566394 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 25.0000 | 0.883883 | ||||||||
\(801\) | −7.07107 | + | 7.07107i | −0.249844 | + | 0.249844i | ||||
\(802\) | 22.1731 | + | 9.18440i | 0.782960 | + | 0.324313i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −4.59220 | + | 11.0866i | −0.161954 | + | 0.390993i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.06147 | + | 7.39104i | 0.107836 | + | 0.260338i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.7279 | − | 12.7279i | −0.447767 | − | 0.447767i | ||||
\(809\) | −15.3073 | − | 36.9552i | −0.538177 | − | 1.29927i | −0.925994 | − | 0.377538i | \(-0.876771\pi\) |
0.387817 | − | 0.921737i | \(-0.373229\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.53073 | + | 3.69552i | −0.0537513 | + | 0.129767i | −0.948474 | − | 0.316855i | \(-0.897373\pi\) |
0.894723 | + | 0.446622i | \(0.147373\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −22.6274 | + | 22.6274i | −0.793091 | + | 0.793091i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.0000 | 0.559769 | ||||||||
\(818\) | −7.07107 | + | 7.07107i | −0.247234 | + | 0.247234i | ||||
\(819\) | −7.39104 | − | 3.06147i | −0.258264 | − | 0.106976i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.2459 | − | 29.5641i | 0.427384 | − | 1.03180i | −0.552730 | − | 0.833360i | \(-0.686414\pi\) |
0.980114 | − | 0.198435i | \(-0.0635860\pi\) | |||||||
\(822\) | −9.23880 | + | 3.82683i | −0.322240 | + | 0.133476i | ||||
\(823\) | −16.8381 | − | 40.6507i | −0.586938 | − | 1.41699i | −0.886415 | − | 0.462891i | \(-0.846812\pi\) |
0.299477 | − | 0.954104i | \(-0.403188\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14.1421 | + | 14.1421i | 0.492366 | + | 0.492366i | ||||
\(826\) | 18.3688 | + | 44.3462i | 0.639132 | + | 1.54300i | ||||
\(827\) | 11.0866 | − | 4.59220i | 0.385517 | − | 0.159686i | −0.181503 | − | 0.983390i | \(-0.558096\pi\) |
0.567020 | + | 0.823704i | \(0.308096\pi\) | |||||||
\(828\) | 1.53073 | − | 3.69552i | 0.0531967 | − | 0.128428i | ||||
\(829\) | − | 2.00000i | − | 0.0694629i | −0.999397 | − | 0.0347314i | \(-0.988942\pi\) | ||
0.999397 | − | 0.0347314i | \(-0.0110576\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.65685 | − | 5.65685i | 0.196234 | − | 0.196234i | ||||
\(832\) | −14.0000 | −0.485363 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.00000 | −0.138509 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −14.7821 | − | 6.12293i | −0.511249 | − | 0.211766i | ||||
\(837\) | 4.00000i | 0.138260i | ||||||||
\(838\) | 1.53073 | − | 3.69552i | 0.0528783 | − | 0.127660i | ||||
\(839\) | 40.6507 | − | 16.8381i | 1.40342 | − | 0.581315i | 0.452782 | − | 0.891622i | \(-0.350432\pi\) |
0.950636 | + | 0.310307i | \(0.100432\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.5061 | + | 20.5061i | 0.707107 | + | 0.707107i | ||||
\(842\) | 15.5563 | + | 15.5563i | 0.536107 | + | 0.536107i | ||||
\(843\) | 3.82683 | + | 9.23880i | 0.131803 | + | 0.318201i | ||||
\(844\) | 3.69552 | − | 1.53073i | 0.127205 | − | 0.0526900i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.00000i | 0.275046i | ||||||||
\(847\) | 18.4776 | + | 7.65367i | 0.634898 | + | 0.262983i | ||||
\(848\) | −4.24264 | + | 4.24264i | −0.145693 | + | 0.145693i | ||||
\(849\) | 4.00000 | 0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32.0000 | 1.09695 | ||||||||
\(852\) | −8.48528 | + | 8.48528i | −0.290701 | + | 0.290701i | ||||
\(853\) | 22.1731 | + | 9.18440i | 0.759193 | + | 0.314468i | 0.728486 | − | 0.685060i | \(-0.240224\pi\) |
0.0307066 | + | 0.999528i | \(0.490224\pi\) | |||||||
\(854\) | 32.0000i | 1.09502i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 33.2597 | − | 13.7766i | 1.13679 | − | 0.470875i | ||||
\(857\) | −3.06147 | − | 7.39104i | −0.104578 | − | 0.252473i | 0.862926 | − | 0.505331i | \(-0.168630\pi\) |
−0.967503 | + | 0.252858i | \(0.918630\pi\) | |||||||
\(858\) | −5.65685 | − | 5.65685i | −0.193122 | − | 0.193122i | ||||
\(859\) | 2.82843 | + | 2.82843i | 0.0965047 | + | 0.0965047i | 0.753711 | − | 0.657206i | \(-0.228262\pi\) |
−0.657206 | + | 0.753711i | \(0.728262\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 29.5641 | − | 12.2459i | 1.00754 | − | 0.417338i | ||||
\(862\) | 7.65367 | − | 18.4776i | 0.260685 | − | 0.629349i | ||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | −4.61940 | − | 1.91342i | −0.157155 | − | 0.0650958i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.00000 | 0.0679628 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.0000 | 0.543075 | ||||||||
\(869\) | −11.3137 | + | 11.3137i | −0.383791 | + | 0.383791i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 24.0000i | − | 0.813209i | ||||||
\(872\) | −9.18440 | + | 22.1731i | −0.311023 | + | 0.750876i | ||||
\(873\) | −14.7821 | + | 6.12293i | −0.500297 | + | 0.207230i | ||||
\(874\) | −6.12293 | − | 14.7821i | −0.207111 | − | 0.500011i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.3073 | − | 36.9552i | −0.516892 | − | 1.24789i | −0.939803 | − | 0.341717i | \(-0.888992\pi\) |
0.422911 | − | 0.906171i | \(-0.361008\pi\) | |||||||
\(878\) | 33.2597 | − | 13.7766i | 1.12246 | − | 0.464938i | ||||
\(879\) | 3.82683 | − | 9.23880i | 0.129076 | − | 0.311617i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.1731 | + | 9.18440i | 0.747031 | + | 0.309430i | 0.723530 | − | 0.690293i | \(-0.242519\pi\) |
0.0235015 | + | 0.999724i | \(0.492519\pi\) | |||||||
\(882\) | 6.36396 | − | 6.36396i | 0.214286 | − | 0.214286i | ||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.1421 | − | 14.1421i | 0.475114 | − | 0.475114i | ||||
\(887\) | 3.69552 | + | 1.53073i | 0.124083 | + | 0.0513970i | 0.443861 | − | 0.896096i | \(-0.353608\pi\) |
−0.319778 | + | 0.947493i | \(0.603608\pi\) | |||||||
\(888\) | − | 24.0000i | − | 0.805387i | ||||||
\(889\) | −12.2459 | + | 29.5641i | −0.410713 | + | 0.991550i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.53073 | − | 3.69552i | −0.0512815 | − | 0.123805i | ||||
\(892\) | −11.3137 | − | 11.3137i | −0.378811 | − | 0.378811i | ||||
\(893\) | −22.6274 | − | 22.6274i | −0.757198 | − | 0.757198i | ||||
\(894\) | 2.29610 | + | 5.54328i | 0.0767931 | + | 0.185395i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.59220 | + | 11.0866i | −0.153415 | + | 0.370376i | ||||
\(897\) | 8.00000i | 0.267112i | ||||||||
\(898\) | 7.39104 | + | 3.06147i | 0.246642 | + | 0.102162i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −5.00000 | −0.166667 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 32.0000 | 1.06548 | ||||||||
\(903\) | 11.3137 | − | 11.3137i | 0.376497 | − | 0.376497i | ||||
\(904\) | −22.1731 | − | 9.18440i | −0.737467 | − | 0.305469i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.8686 | + | 10.7151i | −0.858954 | + | 0.355790i | −0.768298 | − | 0.640092i | \(-0.778896\pi\) |
−0.0906554 | + | 0.995882i | \(0.528896\pi\) | |||||||
\(908\) | −4.59220 | − | 11.0866i | −0.152398 | − | 0.367920i | ||||
\(909\) | 4.24264 | + | 4.24264i | 0.140720 | + | 0.140720i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.7151 | + | 25.8686i | 0.355008 | + | 0.857066i | 0.995986 | + | 0.0895065i | \(0.0285290\pi\) |
−0.640978 | + | 0.767559i | \(0.721471\pi\) | |||||||
\(912\) | −3.69552 | + | 1.53073i | −0.122371 | + | 0.0506877i | ||||
\(913\) | −18.3688 | + | 44.3462i | −0.607919 | + | 1.46765i | ||||
\(914\) | 38.0000i | 1.25693i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.07107 | + | 7.07107i | −0.233635 | + | 0.233635i | ||||
\(917\) | −16.0000 | −0.528367 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.0000 | 0.791687 | 0.395843 | − | 0.918318i | \(-0.370452\pi\) | ||||
0.395843 | + | 0.918318i | \(0.370452\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.0866 | + | 4.59220i | 0.365314 | + | 0.151318i | ||||
\(922\) | 34.0000i | 1.11973i | ||||||||
\(923\) | 9.18440 | − | 22.1731i | 0.302308 | − | 0.729837i | ||||
\(924\) | −14.7821 | + | 6.12293i | −0.486294 | + | 0.201430i | ||||
\(925\) | −15.3073 | − | 36.9552i | −0.503302 | − | 1.21508i | ||||
\(926\) | −28.2843 | − | 28.2843i | −0.929479 | − | 0.929479i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.1731 | + | 9.18440i | −0.727476 | + | 0.301330i | −0.715514 | − | 0.698598i | \(-0.753808\pi\) |
−0.0119617 | + | 0.999928i | \(0.503808\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.0000i | 1.17985i | ||||||||
\(932\) | −7.39104 | − | 3.06147i | −0.242101 | − | 0.100282i | ||||
\(933\) | −8.48528 | + | 8.48528i | −0.277796 | + | 0.277796i | ||||
\(934\) | −4.00000 | −0.130884 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.00000 | 0.196116 | ||||||||
\(937\) | −18.3848 | + | 18.3848i | −0.600604 | + | 0.600604i | −0.940473 | − | 0.339869i | \(-0.889617\pi\) |
0.339869 | + | 0.940473i | \(0.389617\pi\) | |||||||
\(938\) | 44.3462 | + | 18.3688i | 1.44796 | + | 0.599763i | ||||
\(939\) | − | 16.0000i | − | 0.522140i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.3462 | + | 18.3688i | −1.44565 | + | 0.598806i | −0.961160 | − | 0.275993i | \(-0.910993\pi\) |
−0.484486 | + | 0.874799i | \(0.660993\pi\) | |||||||
\(942\) | 0.765367 | + | 1.84776i | 0.0249370 | + | 0.0602032i | ||||
\(943\) | −22.6274 | − | 22.6274i | −0.736850 | − | 0.736850i | ||||
\(944\) | −8.48528 | − | 8.48528i | −0.276172 | − | 0.276172i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.7821 | − | 6.12293i | 0.480607 | − | 0.199074i | ||||
\(947\) | 4.59220 | − | 11.0866i | 0.149226 | − | 0.360265i | −0.831536 | − | 0.555471i | \(-0.812538\pi\) |
0.980762 | + | 0.195207i | \(0.0625378\pi\) | |||||||
\(948\) | − | 4.00000i | − | 0.129914i | ||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −14.1421 | + | 14.1421i | −0.458831 | + | 0.458831i | ||||
\(951\) | −32.0000 | −1.03767 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.0000 | −1.36051 | −0.680257 | − | 0.732974i | \(-0.738132\pi\) | ||||
−0.680257 | + | 0.732974i | \(0.738132\pi\) | |||||||
\(954\) | 4.24264 | − | 4.24264i | 0.137361 | − | 0.137361i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 8.00000i | − | 0.258738i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.0866 | − | 4.59220i | 0.358190 | − | 0.148367i | ||||
\(959\) | −15.3073 | − | 36.9552i | −0.494300 | − | 1.19335i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.6066 | − | 10.6066i | −0.342148 | − | 0.342148i | ||||
\(962\) | 6.12293 | + | 14.7821i | 0.197411 | + | 0.476593i | ||||
\(963\) | −11.0866 | + | 4.59220i | −0.357259 | + | 0.147982i | ||||
\(964\) | −6.12293 | + | 14.7821i | −0.197206 | + | 0.476098i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −14.7821 | − | 6.12293i | −0.475605 | − | 0.197002i | ||||
\(967\) | 16.9706 | − | 16.9706i | 0.545737 | − | 0.545737i | −0.379468 | − | 0.925205i | \(-0.623893\pi\) |
0.925205 | + | 0.379468i | \(0.123893\pi\) | |||||||
\(968\) | −15.0000 | −0.482118 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.4558 | + | 25.4558i | −0.816917 | + | 0.816917i | −0.985660 | − | 0.168743i | \(-0.946029\pi\) |
0.168743 | + | 0.985660i | \(0.446029\pi\) | |||||||
\(972\) | 0.923880 | + | 0.382683i | 0.0296334 | + | 0.0122746i | ||||
\(973\) | − | 16.0000i | − | 0.512936i | ||||||
\(974\) | −1.53073 | + | 3.69552i | −0.0490479 | + | 0.118412i | ||||
\(975\) | 9.23880 | − | 3.82683i | 0.295878 | − | 0.122557i | ||||
\(976\) | −3.06147 | − | 7.39104i | −0.0979952 | − | 0.236581i | ||||
\(977\) | −32.5269 | − | 32.5269i | −1.04063 | − | 1.04063i | −0.999139 | − | 0.0414892i | \(-0.986790\pi\) |
−0.0414892 | − | 0.999139i | \(-0.513210\pi\) | |||||||
\(978\) | 14.1421 | + | 14.1421i | 0.452216 | + | 0.452216i | ||||
\(979\) | −15.3073 | − | 36.9552i | −0.489225 | − | 1.18109i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.06147 | − | 7.39104i | 0.0977451 | − | 0.235978i | ||||
\(982\) | − | 20.0000i | − | 0.638226i | ||||||
\(983\) | −18.4776 | − | 7.65367i | −0.589344 | − | 0.244114i | 0.0680246 | − | 0.997684i | \(-0.478330\pi\) |
−0.657368 | + | 0.753570i | \(0.728330\pi\) | |||||||
\(984\) | −16.9706 | + | 16.9706i | −0.541002 | + | 0.541002i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −32.0000 | −1.01857 | ||||||||
\(988\) | −5.65685 | + | 5.65685i | −0.179969 | + | 0.179969i | ||||
\(989\) | −14.7821 | − | 6.12293i | −0.470043 | − | 0.194698i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.59220 | − | 11.0866i | 0.145876 | − | 0.352176i | −0.834005 | − | 0.551756i | \(-0.813958\pi\) |
0.979881 | + | 0.199580i | \(0.0639579\pi\) | |||||||
\(992\) | −18.4776 | + | 7.65367i | −0.586664 | + | 0.243004i | ||||
\(993\) | 7.65367 | + | 18.4776i | 0.242882 | + | 0.586369i | ||||
\(994\) | 33.9411 | + | 33.9411i | 1.07655 | + | 1.07655i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.59220 | − | 11.0866i | −0.145509 | − | 0.351291i | ||||
\(997\) | −7.39104 | + | 3.06147i | −0.234076 | + | 0.0969576i | −0.496639 | − | 0.867957i | \(-0.665433\pi\) |
0.262562 | + | 0.964915i | \(0.415433\pi\) | |||||||
\(998\) | −13.7766 | + | 33.2597i | −0.436091 | + | 1.05282i | ||||
\(999\) | 8.00000i | 0.253109i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))