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 | 712.2 | ||
Root | \(-0.923880 - 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 867.712 |
Dual form | 867.2.h.d.688.2 |
$q$-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 \(\left(\mathbb{Z}/867\mathbb{Z}\right)^\times\).
\(n\) | \(290\) | \(292\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{8}\right)\) |
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 | \(-0.134973\pi\) |
−0.411438 | + | 0.911438i | \(0.634973\pi\) | |||||||
\(3\) | 0.382683 | + | 0.923880i | 0.220942 | + | 0.533402i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(6\) | −0.382683 | + | 0.923880i | −0.156230 | + | 0.377172i | ||||
\(7\) | 3.69552 | + | 1.53073i | 1.39677 | + | 0.578563i | 0.948912 | − | 0.315540i | \(-0.102186\pi\) |
0.447862 | + | 0.894103i | \(0.352186\pi\) | |||||||
\(8\) | 2.12132 | − | 2.12132i | 0.750000 | − | 0.750000i | ||||
\(9\) | −0.707107 | + | 0.707107i | −0.235702 | + | 0.235702i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.53073 | − | 3.69552i | 0.461534 | − | 1.11424i | −0.506234 | − | 0.862396i | \(-0.668963\pi\) |
0.967768 | − | 0.251845i | \(-0.0810372\pi\) | |||||||
\(12\) | 0.923880 | − | 0.382683i | 0.266701 | − | 0.110471i | ||||
\(13\) | − | 2.00000i | − | 0.554700i | −0.960769 | − | 0.277350i | \(-0.910544\pi\) | ||
0.960769 | − | 0.277350i | \(-0.0894562\pi\) | |||||||
\(14\) | 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 | \(-0.401732\pi\) |
−0.952724 | + | 0.303838i | \(0.901732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00000i | 0.872872i | ||||||||
\(22\) | 3.69552 | − | 1.53073i | 0.787887 | − | 0.326354i | ||||
\(23\) | 1.53073 | − | 3.69552i | 0.319180 | − | 0.770569i | −0.680118 | − | 0.733103i | \(-0.738071\pi\) |
0.999298 | − | 0.0374660i | \(-0.0119286\pi\) | |||||||
\(24\) | 2.77164 | + | 1.14805i | 0.565758 | + | 0.234345i | ||||
\(25\) | −3.53553 | + | 3.53553i | −0.707107 | + | 0.707107i | ||||
\(26\) | 1.41421 | − | 1.41421i | 0.277350 | − | 0.277350i | ||||
\(27\) | −0.923880 | − | 0.382683i | −0.177801 | − | 0.0736475i | ||||
\(28\) | 1.53073 | − | 3.69552i | 0.289281 | − | 0.698387i | ||||
\(29\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.53073 | + | 3.69552i | 0.274928 | + | 0.663735i | 0.999681 | − | 0.0252745i | \(-0.00804598\pi\) |
−0.724753 | + | 0.689009i | \(0.758046\pi\) | |||||||
\(32\) | −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 | ||||
\(37\) | 3.06147 | + | 7.39104i | 0.503302 | + | 1.21508i | 0.947675 | + | 0.319237i | \(0.103427\pi\) |
−0.444373 | + | 0.895842i | \(0.646573\pi\) | |||||||
\(38\) | − | 4.00000i | − | 0.648886i | ||||||
\(39\) | 1.84776 | − | 0.765367i | 0.295878 | − | 0.122557i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.39104 | + | 3.06147i | 1.15429 | + | 0.478121i | 0.875969 | − | 0.482368i | \(-0.160223\pi\) |
0.278317 | + | 0.960489i | \(0.410223\pi\) | |||||||
\(42\) | −2.82843 | + | 2.82843i | −0.436436 | + | 0.436436i | ||||
\(43\) | −2.82843 | + | 2.82843i | −0.431331 | + | 0.431331i | −0.889081 | − | 0.457750i | \(-0.848656\pi\) |
0.457750 | + | 0.889081i | \(0.348656\pi\) | |||||||
\(44\) | −3.69552 | − | 1.53073i | −0.557120 | − | 0.230767i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.69552 | − | 1.53073i | 0.544874 | − | 0.225694i | ||||
\(47\) | 8.00000i | 1.16692i | 0.812142 | + | 0.583460i | \(0.198301\pi\) | ||||
−0.812142 | + | 0.583460i | \(0.801699\pi\) | |||||||
\(48\) | 0.382683 | + | 0.923880i | 0.0552356 | + | 0.133351i | ||||
\(49\) | 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 | \(-0.114802\pi\) |
−0.352892 | + | 0.935664i | \(0.614802\pi\) | |||||||
\(54\) | −0.382683 | − | 0.923880i | −0.0520766 | − | 0.125724i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 11.0866 | − | 4.59220i | 1.48150 | − | 0.613659i | ||||
\(57\) | 1.53073 | − | 3.69552i | 0.202751 | − | 0.489483i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.48528 | − | 8.48528i | 1.10469 | − | 1.10469i | 0.110853 | − | 0.993837i | \(-0.464642\pi\) |
0.993837 | − | 0.110853i | \(-0.0353582\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.39104 | − | 3.06147i | −0.946325 | − | 0.391981i | −0.144477 | − | 0.989508i | \(-0.546150\pi\) |
−0.801848 | + | 0.597527i | \(0.796150\pi\) | |||||||
\(62\) | −1.53073 | + | 3.69552i | −0.194403 | + | 0.469331i | ||||
\(63\) | −3.69552 | + | 1.53073i | −0.465592 | + | 0.192854i | ||||
\(64\) | − | 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 | ||||||||
\(71\) | 4.59220 | + | 11.0866i | 0.544994 | + | 1.31573i | 0.921162 | + | 0.389180i | \(0.127242\pi\) |
−0.376168 | + | 0.926552i | \(0.622758\pi\) | |||||||
\(72\) | 3.00000i | 0.353553i | ||||||||
\(73\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(74\) | −3.06147 | + | 7.39104i | −0.355888 | + | 0.859191i | ||||
\(75\) | −4.61940 | − | 1.91342i | −0.533402 | − | 0.220942i | ||||
\(76\) | −2.82843 | + | 2.82843i | −0.324443 | + | 0.324443i | ||||
\(77\) | 11.3137 | − | 11.3137i | 1.28932 | − | 1.28932i | ||||
\(78\) | 1.84776 | + | 0.765367i | 0.209218 | + | 0.0866607i | ||||
\(79\) | −1.53073 | + | 3.69552i | −0.172221 | + | 0.415778i | −0.986297 | − | 0.164980i | \(-0.947244\pi\) |
0.814076 | + | 0.580759i | \(0.197244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 1.00000i | − | 0.111111i | ||||||
\(82\) | 3.06147 | + | 7.39104i | 0.338083 | + | 0.816203i | ||||
\(83\) | −8.48528 | − | 8.48528i | −0.931381 | − | 0.931381i | 0.0664117 | − | 0.997792i | \(-0.478845\pi\) |
−0.997792 | + | 0.0664117i | \(0.978845\pi\) | |||||||
\(84\) | 4.00000 | 0.436436 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.00000 | −0.431331 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.59220 | − | 11.0866i | −0.489530 | − | 1.18183i | ||||
\(89\) | − | 10.0000i | − | 1.06000i | −0.847998 | − | 0.529999i | \(-0.822192\pi\) | ||
0.847998 | − | 0.529999i | \(-0.177808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.06147 | − | 7.39104i | 0.320929 | − | 0.774791i | ||||
\(92\) | −3.69552 | − | 1.53073i | −0.385284 | − | 0.159590i | ||||
\(93\) | −2.82843 | + | 2.82843i | −0.293294 | + | 0.293294i | ||||
\(94\) | −5.65685 | + | 5.65685i | −0.583460 | + | 0.583460i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.91342 | − | 4.61940i | 0.195287 | − | 0.471465i | ||||
\(97\) | −14.7821 | + | 6.12293i | −1.50089 | + | 0.621690i | −0.973655 | − | 0.228028i | \(-0.926772\pi\) |
−0.527238 | + | 0.849718i | \(0.676772\pi\) | |||||||
\(98\) | 9.00000i | 0.909137i | ||||||||
\(99\) | 1.53073 | + | 3.69552i | 0.153845 | + | 0.371414i | ||||
\(100\) | 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 | ||||||||
\(107\) | −11.0866 | + | 4.59220i | −1.07178 | + | 0.443945i | −0.847618 | − | 0.530608i | \(-0.821964\pi\) |
−0.224160 | + | 0.974552i | \(0.571964\pi\) | |||||||
\(108\) | −0.382683 | + | 0.923880i | −0.0368237 | + | 0.0889003i | ||||
\(109\) | −7.39104 | − | 3.06147i | −0.707933 | − | 0.293235i | −0.000483966 | − | 1.00000i | \(-0.500154\pi\) |
−0.707449 | + | 0.706764i | \(0.750154\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.65685 | + | 5.65685i | −0.536925 | + | 0.536925i | ||||
\(112\) | 3.69552 | + | 1.53073i | 0.349194 | + | 0.144641i | ||||
\(113\) | −3.06147 | + | 7.39104i | −0.287999 | + | 0.695290i | −0.999976 | − | 0.00691210i | \(-0.997800\pi\) |
0.711977 | + | 0.702202i | \(0.247800\pi\) | |||||||
\(114\) | 3.69552 | − | 1.53073i | 0.346117 | − | 0.143366i | ||||
\(115\) | 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 | ||||
\(122\) | −3.06147 | − | 7.39104i | −0.277172 | − | 0.669153i | ||||
\(123\) | 8.00000i | 0.721336i | ||||||||
\(124\) | 3.69552 | − | 1.53073i | 0.331867 | − | 0.137464i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.69552 | − | 1.53073i | −0.329223 | − | 0.136369i | ||||
\(127\) | −5.65685 | + | 5.65685i | −0.501965 | + | 0.501965i | −0.912048 | − | 0.410083i | \(-0.865500\pi\) |
0.410083 | + | 0.912048i | \(0.365500\pi\) | |||||||
\(128\) | −2.12132 | + | 2.12132i | −0.187500 | + | 0.187500i | ||||
\(129\) | −3.69552 | − | 1.53073i | −0.325372 | − | 0.134774i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.69552 | + | 1.53073i | −0.322879 | + | 0.133741i | −0.538235 | − | 0.842795i | \(-0.680909\pi\) |
0.215356 | + | 0.976536i | \(0.430909\pi\) | |||||||
\(132\) | − | 4.00000i | − | 0.348155i | ||||||
\(133\) | −6.12293 | − | 14.7821i | −0.530926 | − | 1.28177i | ||||
\(134\) | −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 | ||||
\(139\) | 1.53073 | + | 3.69552i | 0.129835 | + | 0.313450i | 0.975407 | − | 0.220412i | \(-0.0707402\pi\) |
−0.845572 | + | 0.533862i | \(0.820740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.39104 | + | 3.06147i | −0.622438 | + | 0.257822i | ||||
\(142\) | −4.59220 | + | 11.0866i | −0.385369 | + | 0.930363i | ||||
\(143\) | −7.39104 | − | 3.06147i | −0.618070 | − | 0.256013i | ||||
\(144\) | −0.707107 | + | 0.707107i | −0.0589256 | + | 0.0589256i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.44415 | + | 8.31492i | −0.284069 | + | 0.685803i | ||||
\(148\) | 7.39104 | − | 3.06147i | 0.607539 | − | 0.251651i | ||||
\(149\) | − | 6.00000i | − | 0.491539i | −0.969328 | − | 0.245770i | \(-0.920959\pi\) | ||
0.969328 | − | 0.245770i | \(-0.0790407\pi\) | |||||||
\(150\) | −1.91342 | − | 4.61940i | −0.156230 | − | 0.377172i | ||||
\(151\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(152\) | −12.0000 | −0.973329 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 16.0000 | 1.28932 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.765367 | − | 1.84776i | −0.0612784 | − | 0.147939i | ||||
\(157\) | − | 2.00000i | − | 0.159617i | −0.996810 | − | 0.0798087i | \(-0.974569\pi\) | ||
0.996810 | − | 0.0798087i | \(-0.0254309\pi\) | |||||||
\(158\) | −3.69552 | + | 1.53073i | −0.294000 | + | 0.121779i | ||||
\(159\) | −2.29610 | + | 5.54328i | −0.182093 | + | 0.439610i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.3137 | − | 11.3137i | 0.891645 | − | 0.891645i | ||||
\(162\) | 0.707107 | − | 0.707107i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | 18.4776 | + | 7.65367i | 1.44728 | + | 0.599482i | 0.961550 | − | 0.274629i | \(-0.0885551\pi\) |
0.485726 | + | 0.874111i | \(0.338555\pi\) | |||||||
\(164\) | 3.06147 | − | 7.39104i | 0.239060 | − | 0.577143i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 12.0000i | − | 0.931381i | ||||||
\(167\) | −4.59220 | − | 11.0866i | −0.355355 | − | 0.857903i | −0.995940 | − | 0.0900162i | \(-0.971308\pi\) |
0.640585 | − | 0.767887i | \(-0.278692\pi\) | |||||||
\(168\) | 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 | ||||
\(173\) | −6.12293 | − | 14.7821i | −0.465518 | − | 1.12386i | −0.966099 | − | 0.258171i | \(-0.916880\pi\) |
0.500581 | − | 0.865690i | \(-0.333120\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.4776 | + | 7.65367i | −1.39677 | + | 0.578563i | ||||
\(176\) | 1.53073 | − | 3.69552i | 0.115383 | − | 0.278560i | ||||
\(177\) | 11.0866 | + | 4.59220i | 0.833316 | + | 0.345171i | ||||
\(178\) | 7.07107 | − | 7.07107i | 0.529999 | − | 0.529999i | ||||
\(179\) | 2.82843 | − | 2.82843i | 0.211407 | − | 0.211407i | −0.593458 | − | 0.804865i | \(-0.702238\pi\) |
0.804865 | + | 0.593458i | \(0.202238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.06147 | + | 7.39104i | −0.227557 | + | 0.549371i | −0.995879 | − | 0.0906923i | \(-0.971092\pi\) |
0.768322 | + | 0.640064i | \(0.221092\pi\) | |||||||
\(182\) | 7.39104 | − | 3.06147i | 0.547860 | − | 0.226931i | ||||
\(183\) | − | 8.00000i | − | 0.591377i | ||||||
\(184\) | −4.59220 | − | 11.0866i | −0.338542 | − | 0.817312i | ||||
\(185\) | 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 | \(-0.906534\pi\) | ||
0.957199 | − | 0.289430i | \(-0.0934657\pi\) | |||||||
\(192\) | 6.46716 | − | 2.67878i | 0.466727 | − | 0.193325i | ||||
\(193\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(194\) | −14.7821 | − | 6.12293i | −1.06129 | − | 0.439601i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.36396 | − | 6.36396i | 0.454569 | − | 0.454569i | ||||
\(197\) | 14.7821 | + | 6.12293i | 1.05318 | + | 0.436241i | 0.841026 | − | 0.540995i | \(-0.181952\pi\) |
0.212153 | + | 0.977236i | \(0.431952\pi\) | |||||||
\(198\) | −1.53073 | + | 3.69552i | −0.108785 | + | 0.262629i | ||||
\(199\) | 18.4776 | − | 7.65367i | 1.30984 | − | 0.542554i | 0.385004 | − | 0.922915i | \(-0.374200\pi\) |
0.924838 | + | 0.380361i | \(0.124200\pi\) | |||||||
\(200\) | 15.0000i | 1.06066i | ||||||||
\(201\) | −4.59220 | − | 11.0866i | −0.323909 | − | 0.781985i | ||||
\(202\) | 4.24264 | + | 4.24264i | 0.298511 | + | 0.298511i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.53073 | + | 3.69552i | 0.106393 | + | 0.256856i | ||||
\(208\) | − | 2.00000i | − | 0.138675i | ||||||
\(209\) | −14.7821 | + | 6.12293i | −1.02250 | + | 0.423532i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.69552 | − | 1.53073i | −0.254410 | − | 0.105380i | 0.251834 | − | 0.967771i | \(-0.418966\pi\) |
−0.506244 | + | 0.862390i | \(0.668966\pi\) | |||||||
\(212\) | 4.24264 | − | 4.24264i | 0.291386 | − | 0.291386i | ||||
\(213\) | −8.48528 | + | 8.48528i | −0.581402 | + | 0.581402i | ||||
\(214\) | −11.0866 | − | 4.59220i | −0.757861 | − | 0.313916i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.77164 | + | 1.14805i | −0.188586 | + | 0.0781149i | ||||
\(217\) | 16.0000i | 1.08615i | ||||||||
\(218\) | −3.06147 | − | 7.39104i | −0.207349 | − | 0.500584i | ||||
\(219\) | 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 | \(-0.0700404\pi\) |
−0.218267 | + | 0.975889i | \(0.570040\pi\) | |||||||
\(224\) | −7.65367 | − | 18.4776i | −0.511382 | − | 1.23459i | ||||
\(225\) | − | 5.00000i | − | 0.333333i | ||||||
\(226\) | −7.39104 | + | 3.06147i | −0.491644 | + | 0.203646i | ||||
\(227\) | 4.59220 | − | 11.0866i | 0.304795 | − | 0.735840i | −0.695062 | − | 0.718950i | \(-0.744623\pi\) |
0.999857 | − | 0.0168909i | \(-0.00537679\pi\) | |||||||
\(228\) | −3.69552 | − | 1.53073i | −0.244742 | − | 0.101375i | ||||
\(229\) | −7.07107 | + | 7.07107i | −0.467269 | + | 0.467269i | −0.901029 | − | 0.433759i | \(-0.857187\pi\) |
0.433759 | + | 0.901029i | \(0.357187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.7821 | + | 6.12293i | 0.972589 | + | 0.402860i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.39104 | + | 3.06147i | −0.484203 | + | 0.200563i | −0.611412 | − | 0.791313i | \(-0.709398\pi\) |
0.127209 | + | 0.991876i | \(0.459398\pi\) | |||||||
\(234\) | 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 | ||||||||
\(241\) | −6.12293 | − | 14.7821i | −0.394413 | − | 0.952197i | −0.988966 | − | 0.148141i | \(-0.952671\pi\) |
0.594553 | − | 0.804056i | \(-0.297329\pi\) | |||||||
\(242\) | − | 5.00000i | − | 0.321412i | ||||||
\(243\) | 0.923880 | − | 0.382683i | 0.0592669 | − | 0.0245492i | ||||
\(244\) | −3.06147 | + | 7.39104i | −0.195990 | + | 0.473163i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.65685 | + | 5.65685i | −0.360668 | + | 0.360668i | ||||
\(247\) | −5.65685 | + | 5.65685i | −0.359937 | + | 0.359937i | ||||
\(248\) | 11.0866 | + | 4.59220i | 0.703997 | + | 0.291605i | ||||
\(249\) | 4.59220 | − | 11.0866i | 0.291019 | − | 0.702582i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 12.0000i | − | 0.757433i | −0.925513 | − | 0.378717i | \(-0.876365\pi\) | ||
0.925513 | − | 0.378717i | \(-0.123635\pi\) | |||||||
\(252\) | 1.53073 | + | 3.69552i | 0.0964272 | + | 0.232796i | ||||
\(253\) | −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 | \(-0.269869\pi\) |
−0.749838 | + | 0.661622i | \(0.769869\pi\) | |||||||
\(258\) | −1.53073 | − | 3.69552i | −0.0952993 | − | 0.230073i | ||||
\(259\) | 32.0000i | 1.98838i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.69552 | − | 1.53073i | −0.228310 | − | 0.0945690i | ||||
\(263\) | −16.9706 | + | 16.9706i | −1.04645 | + | 1.04645i | −0.0475824 | + | 0.998867i | \(0.515152\pi\) |
−0.998867 | + | 0.0475824i | \(0.984848\pi\) | |||||||
\(264\) | 8.48528 | − | 8.48528i | 0.522233 | − | 0.522233i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.12293 | − | 14.7821i | 0.375421 | − | 0.906347i | ||||
\(267\) | 9.23880 | − | 3.82683i | 0.565405 | − | 0.234198i | ||||
\(268\) | 12.0000i | 0.733017i | ||||||||
\(269\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(270\) | 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 | ||||
\(275\) | 7.65367 | + | 18.4776i | 0.461534 | + | 1.11424i | ||||
\(276\) | − | 4.00000i | − | 0.240772i | ||||||
\(277\) | −7.39104 | + | 3.06147i | −0.444084 | + | 0.183946i | −0.593509 | − | 0.804827i | \(-0.702258\pi\) |
0.149425 | + | 0.988773i | \(0.452258\pi\) | |||||||
\(278\) | −1.53073 | + | 3.69552i | −0.0918073 | + | 0.221642i | ||||
\(279\) | −3.69552 | − | 1.53073i | −0.221245 | − | 0.0916426i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.07107 | − | 7.07107i | 0.421825 | − | 0.421825i | −0.464007 | − | 0.885832i | \(-0.653589\pi\) |
0.885832 | + | 0.464007i | \(0.153589\pi\) | |||||||
\(282\) | −7.39104 | − | 3.06147i | −0.440130 | − | 0.182308i | ||||
\(283\) | 1.53073 | − | 3.69552i | 0.0909927 | − | 0.219676i | −0.871831 | − | 0.489807i | \(-0.837067\pi\) |
0.962823 | + | 0.270131i | \(0.0870672\pi\) | |||||||
\(284\) | 11.0866 | − | 4.59220i | 0.657866 | − | 0.272497i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.06147 | − | 7.39104i | −0.181028 | − | 0.437041i | ||||
\(287\) | 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 | \(-0.905645\pi\) | ||
0.956387 | − | 0.292103i | \(-0.0943550\pi\) | |||||||
\(294\) | −8.31492 | + | 3.44415i | −0.484936 | + | 0.200867i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 22.1731 | + | 9.18440i | 1.28879 | + | 0.533833i | ||||
\(297\) | −2.82843 | + | 2.82843i | −0.164122 | + | 0.164122i | ||||
\(298\) | 4.24264 | − | 4.24264i | 0.245770 | − | 0.245770i | ||||
\(299\) | −7.39104 | − | 3.06147i | −0.427435 | − | 0.177049i | ||||
\(300\) | −1.91342 | + | 4.61940i | −0.110471 | + | 0.266701i | ||||
\(301\) | −14.7821 | + | 6.12293i | −0.852024 | + | 0.352920i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.29610 | + | 5.54328i | 0.131908 | + | 0.318453i | ||||
\(304\) | −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 | ||||||||
\(311\) | 11.0866 | − | 4.59220i | 0.628661 | − | 0.260400i | −0.0455232 | − | 0.998963i | \(-0.514495\pi\) |
0.674184 | + | 0.738563i | \(0.264495\pi\) | |||||||
\(312\) | 2.29610 | − | 5.54328i | 0.129991 | − | 0.313826i | ||||
\(313\) | 14.7821 | + | 6.12293i | 0.835532 | + | 0.346089i | 0.759090 | − | 0.650985i | \(-0.225644\pi\) |
0.0764418 | + | 0.997074i | \(0.475644\pi\) | |||||||
\(314\) | 1.41421 | − | 1.41421i | 0.0798087 | − | 0.0798087i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.69552 | + | 1.53073i | 0.207889 | + | 0.0861105i | ||||
\(317\) | −12.2459 | + | 29.5641i | −0.687797 | + | 1.66049i | 0.0613775 | + | 0.998115i | \(0.480451\pi\) |
−0.749174 | + | 0.662373i | \(0.769549\pi\) | |||||||
\(318\) | −5.54328 | + | 2.29610i | −0.310852 | + | 0.128759i | ||||
\(319\) | 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 | ||||
\(326\) | 7.65367 | + | 18.4776i | 0.423898 | + | 1.02338i | ||||
\(327\) | − | 8.00000i | − | 0.442401i | ||||||
\(328\) | 22.1731 | − | 9.18440i | 1.22431 | − | 0.507124i | ||||
\(329\) | −12.2459 | + | 29.5641i | −0.675137 | + | 1.62992i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.1421 | − | 14.1421i | 0.777322 | − | 0.777322i | −0.202053 | − | 0.979375i | \(-0.564761\pi\) |
0.979375 | + | 0.202053i | \(0.0647612\pi\) | |||||||
\(332\) | −8.48528 | + | 8.48528i | −0.465690 | + | 0.465690i | ||||
\(333\) | −7.39104 | − | 3.06147i | −0.405026 | − | 0.167767i | ||||
\(334\) | 4.59220 | − | 11.0866i | 0.251274 | − | 0.606629i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.00000i | 0.218218i | ||||||||
\(337\) | 6.12293 | + | 14.7821i | 0.333538 | + | 0.805231i | 0.998306 | + | 0.0581814i | \(0.0185302\pi\) |
−0.664769 | + | 0.747049i | \(0.731470\pi\) | |||||||
\(338\) | 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 | ||||
\(343\) | 3.06147 | + | 7.39104i | 0.165304 | + | 0.399078i | ||||
\(344\) | 12.0000i | 0.646997i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.12293 | − | 14.7821i | 0.329171 | − | 0.794689i | ||||
\(347\) | −3.69552 | − | 1.53073i | −0.198386 | − | 0.0821741i | 0.281278 | − | 0.959626i | \(-0.409242\pi\) |
−0.479664 | + | 0.877452i | \(0.659242\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.41421 | + | 1.41421i | −0.0757011 | + | 0.0757011i | −0.743944 | − | 0.668242i | \(-0.767047\pi\) |
0.668242 | + | 0.743944i | \(0.267047\pi\) | |||||||
\(350\) | −18.4776 | − | 7.65367i | −0.987669 | − | 0.409106i | ||||
\(351\) | −0.765367 | + | 1.84776i | −0.0408523 | + | 0.0986261i | ||||
\(352\) | −18.4776 | + | 7.65367i | −0.984859 | + | 0.407942i | ||||
\(353\) | − | 18.0000i | − | 0.958043i | −0.877803 | − | 0.479022i | \(-0.840992\pi\) | ||
0.877803 | − | 0.479022i | \(-0.159008\pi\) | |||||||
\(354\) | 4.59220 | + | 11.0866i | 0.244073 | + | 0.589244i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −10.0000 | −0.529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.00000 | 0.211407 | ||||||||
\(359\) | 22.6274 | + | 22.6274i | 1.19423 | + | 1.19423i | 0.975868 | + | 0.218361i | \(0.0700712\pi\) |
0.218361 | + | 0.975868i | \(0.429929\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 3.00000i | − | 0.157895i | ||||||
\(362\) | −7.39104 | + | 3.06147i | −0.388464 | + | 0.160907i | ||||
\(363\) | 1.91342 | − | 4.61940i | 0.100428 | − | 0.242455i | ||||
\(364\) | −7.39104 | − | 3.06147i | −0.387396 | − | 0.160464i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.65685 | − | 5.65685i | 0.295689 | − | 0.295689i | ||||
\(367\) | 11.0866 | + | 4.59220i | 0.578713 | + | 0.239711i | 0.652787 | − | 0.757542i | \(-0.273600\pi\) |
−0.0740732 | + | 0.997253i | \(0.523600\pi\) | |||||||
\(368\) | 1.53073 | − | 3.69552i | 0.0797950 | − | 0.192642i | ||||
\(369\) | −7.39104 | + | 3.06147i | −0.384762 | + | 0.159374i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.18440 | + | 22.1731i | 0.476830 | + | 1.15117i | ||||
\(372\) | 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 | ||||||
\(379\) | 18.4776 | − | 7.65367i | 0.949130 | − | 0.393143i | 0.146226 | − | 0.989251i | \(-0.453287\pi\) |
0.802904 | + | 0.596109i | \(0.203287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.39104 | − | 3.06147i | −0.378654 | − | 0.156844i | ||||
\(382\) | 5.65685 | − | 5.65685i | 0.289430 | − | 0.289430i | ||||
\(383\) | −11.3137 | + | 11.3137i | −0.578103 | + | 0.578103i | −0.934380 | − | 0.356277i | \(-0.884046\pi\) |
0.356277 | + | 0.934380i | \(0.384046\pi\) | |||||||
\(384\) | −2.77164 | − | 1.14805i | −0.141440 | − | 0.0585862i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 4.00000i | − | 0.203331i | ||||||
\(388\) | 6.12293 | + | 14.7821i | 0.310845 | + | 0.750446i | ||||
\(389\) | 4.24264 | + | 4.24264i | 0.215110 | + | 0.215110i | 0.806434 | − | 0.591324i | \(-0.201394\pi\) |
−0.591324 | + | 0.806434i | \(0.701394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 27.0000 | 1.36371 | ||||||||
\(393\) | −2.82843 | − | 2.82843i | −0.142675 | − | 0.142675i | ||||
\(394\) | 6.12293 | + | 14.7821i | 0.308469 | + | 0.744710i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.69552 | − | 1.53073i | 0.185707 | − | 0.0769223i | ||||
\(397\) | 3.06147 | − | 7.39104i | 0.153651 | − | 0.370945i | −0.828246 | − | 0.560365i | \(-0.810661\pi\) |
0.981896 | + | 0.189420i | \(0.0606607\pi\) | |||||||
\(398\) | 18.4776 | + | 7.65367i | 0.926198 | + | 0.383644i | ||||
\(399\) | 11.3137 | − | 11.3137i | 0.566394 | − | 0.566394i | ||||
\(400\) | −3.53553 | + | 3.53553i | −0.176777 | + | 0.176777i | ||||
\(401\) | −22.1731 | − | 9.18440i | −1.10727 | − | 0.458647i | −0.247275 | − | 0.968945i | \(-0.579535\pi\) |
−0.859997 | + | 0.510298i | \(0.829535\pi\) | |||||||
\(402\) | 4.59220 | − | 11.0866i | 0.229038 | − | 0.552947i | ||||
\(403\) | 7.39104 | − | 3.06147i | 0.368174 | − | 0.152503i | ||||
\(404\) | − | 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 | ||||||||
\(411\) | −3.82683 | − | 9.23880i | −0.188764 | − | 0.455716i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 44.3462 | − | 18.3688i | 2.18213 | − | 0.903870i | ||||
\(414\) | −1.53073 | + | 3.69552i | −0.0752315 | + | 0.181625i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.07107 | + | 7.07107i | −0.346688 | + | 0.346688i | ||||
\(417\) | −2.82843 | + | 2.82843i | −0.138509 | + | 0.138509i | ||||
\(418\) | −14.7821 | − | 6.12293i | −0.723015 | − | 0.299483i | ||||
\(419\) | 1.53073 | − | 3.69552i | 0.0747812 | − | 0.180538i | −0.882068 | − | 0.471121i | \(-0.843849\pi\) |
0.956850 | + | 0.290583i | \(0.0938494\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0000i | 1.07221i | 0.844150 | + | 0.536107i | \(0.180106\pi\) | ||||
−0.844150 | + | 0.536107i | \(0.819894\pi\) | |||||||
\(422\) | −1.53073 | − | 3.69552i | −0.0745150 | − | 0.179895i | ||||
\(423\) | −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 | ||||
\(428\) | 4.59220 | + | 11.0866i | 0.221972 | + | 0.535889i | ||||
\(429\) | − | 8.00000i | − | 0.386244i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.65367 | − | 18.4776i | 0.368664 | − | 0.890034i | −0.625306 | − | 0.780380i | \(-0.715026\pi\) |
0.993970 | − | 0.109654i | \(-0.0349743\pi\) | |||||||
\(432\) | −0.923880 | − | 0.382683i | −0.0444502 | − | 0.0184119i | ||||
\(433\) | 1.41421 | − | 1.41421i | 0.0679628 | − | 0.0679628i | −0.672308 | − | 0.740271i | \(-0.734697\pi\) |
0.740271 | + | 0.672308i | \(0.234697\pi\) | |||||||
\(434\) | −11.3137 | + | 11.3137i | −0.543075 | + | 0.543075i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.06147 | + | 7.39104i | −0.146618 | + | 0.353966i | ||||
\(437\) | −14.7821 | + | 6.12293i | −0.707122 | + | 0.292900i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.7766 | + | 33.2597i | 0.657521 | + | 1.58740i | 0.801620 | + | 0.597834i | \(0.203972\pi\) |
−0.144099 | + | 0.989563i | \(0.546028\pi\) | |||||||
\(440\) | 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 | ||||||||
\(447\) | 5.54328 | − | 2.29610i | 0.262188 | − | 0.108602i | ||||
\(448\) | 10.7151 | − | 25.8686i | 0.506243 | − | 1.22218i | ||||
\(449\) | −7.39104 | − | 3.06147i | −0.348805 | − | 0.144480i | 0.201401 | − | 0.979509i | \(-0.435451\pi\) |
−0.550205 | + | 0.835029i | \(0.685451\pi\) | |||||||
\(450\) | 3.53553 | − | 3.53553i | 0.166667 | − | 0.166667i | ||||
\(451\) | 22.6274 | − | 22.6274i | 1.06548 | − | 1.06548i | ||||
\(452\) | 7.39104 | + | 3.06147i | 0.347645 | + | 0.143999i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.0866 | − | 4.59220i | 0.520318 | − | 0.215523i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.59220 | − | 11.0866i | −0.215050 | − | 0.519175i | ||||
\(457\) | −26.8701 | − | 26.8701i | −1.25693 | − | 1.25693i | −0.952552 | − | 0.304376i | \(-0.901552\pi\) |
−0.304376 | − | 0.952552i | \(-0.598448\pi\) | |||||||
\(458\) | −10.0000 | −0.467269 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.0416 | − | 24.0416i | −1.11973 | − | 1.11973i | −0.991781 | − | 0.127950i | \(-0.959160\pi\) |
−0.127950 | − | 0.991781i | \(-0.540840\pi\) | |||||||
\(462\) | 6.12293 | + | 14.7821i | 0.284865 | + | 0.687724i | ||||
\(463\) | − | 40.0000i | − | 1.85896i | −0.368875 | − | 0.929479i | \(-0.620257\pi\) | ||
0.368875 | − | 0.929479i | \(-0.379743\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.39104 | − | 3.06147i | −0.342383 | − | 0.141820i | ||||
\(467\) | −2.82843 | + | 2.82843i | −0.130884 | + | 0.130884i | −0.769514 | − | 0.638630i | \(-0.779501\pi\) |
0.638630 | + | 0.769514i | \(0.279501\pi\) | |||||||
\(468\) | 1.41421 | − | 1.41421i | 0.0653720 | − | 0.0653720i | ||||
\(469\) | −44.3462 | − | 18.3688i | −2.04772 | − | 0.848193i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.84776 | − | 0.765367i | 0.0851402 | − | 0.0352662i | ||||
\(472\) | − | 36.0000i | − | 1.65703i | ||||||
\(473\) | 6.12293 | + | 14.7821i | 0.281533 | + | 0.679680i | ||||
\(474\) | −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 | ||||
\(479\) | 4.59220 | + | 11.0866i | 0.209823 | + | 0.506558i | 0.993395 | − | 0.114743i | \(-0.0366045\pi\) |
−0.783572 | + | 0.621301i | \(0.786605\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.7821 | − | 6.12293i | 0.674004 | − | 0.279182i | ||||
\(482\) | 6.12293 | − | 14.7821i | 0.278892 | − | 0.673305i | ||||
\(483\) | 14.7821 | + | 6.12293i | 0.672608 | + | 0.278603i | ||||
\(484\) | −3.53553 | + | 3.53553i | −0.160706 | + | 0.160706i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.923880 | + | 0.382683i | 0.0419080 | + | 0.0173589i | ||||
\(487\) | −1.53073 | + | 3.69552i | −0.0693642 | + | 0.167460i | −0.954760 | − | 0.297379i | \(-0.903888\pi\) |
0.885395 | + | 0.464839i | \(0.153888\pi\) | |||||||
\(488\) | −22.1731 | + | 9.18440i | −1.00373 | + | 0.415758i | ||||
\(489\) | 20.0000i | 0.904431i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.1421 | + | 14.1421i | 0.638226 | + | 0.638226i | 0.950118 | − | 0.311892i | \(-0.100963\pi\) |
−0.311892 | + | 0.950118i | \(0.600963\pi\) | |||||||
\(492\) | 8.00000 | 0.360668 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −8.00000 | −0.359937 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.53073 | + | 3.69552i | 0.0687320 | + | 0.165934i | ||||
\(497\) | 48.0000i | 2.15309i | ||||||||
\(498\) | 11.0866 | − | 4.59220i | 0.496800 | − | 0.205781i | ||||
\(499\) | −13.7766 | + | 33.2597i | −0.616725 | + | 1.48891i | 0.238759 | + | 0.971079i | \(0.423259\pi\) |
−0.855485 | + | 0.517828i | \(0.826741\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.48528 | − | 8.48528i | 0.379094 | − | 0.379094i | ||||
\(502\) | 8.48528 | − | 8.48528i | 0.378717 | − | 0.378717i | ||||
\(503\) | 11.0866 | + | 4.59220i | 0.494325 | + | 0.204756i | 0.615897 | − | 0.787826i | \(-0.288794\pi\) |
−0.121572 | + | 0.992583i | \(0.538794\pi\) | |||||||
\(504\) | −4.59220 | + | 11.0866i | −0.204553 | + | 0.493834i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 16.0000i | − | 0.711287i | ||||||
\(507\) | 3.44415 | + | 8.31492i | 0.152960 | + | 0.369278i | ||||
\(508\) | 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 | ||||
\(513\) | 1.53073 | + | 3.69552i | 0.0675835 | + | 0.163161i | ||||
\(514\) | − | 2.00000i | − | 0.0882162i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.53073 | + | 3.69552i | −0.0673868 | + | 0.162686i | ||||
\(517\) | 29.5641 | + | 12.2459i | 1.30023 | + | 0.538573i | ||||
\(518\) | −22.6274 | + | 22.6274i | −0.994192 | + | 0.994192i | ||||
\(519\) | 11.3137 | − | 11.3137i | 0.496617 | − | 0.496617i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.18440 | − | 22.1731i | 0.402376 | − | 0.971422i | −0.584712 | − | 0.811241i | \(-0.698792\pi\) |
0.987088 | − | 0.160180i | \(-0.0512076\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.0000i | 0.524723i | 0.964970 | + | 0.262362i | \(0.0845013\pi\) | ||||
−0.964970 | + | 0.262362i | \(0.915499\pi\) | |||||||
\(524\) | 1.53073 | + | 3.69552i | 0.0668704 | + | 0.161439i | ||||
\(525\) | −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 | ||||||||
\(532\) | −14.7821 | + | 6.12293i | −0.640884 | + | 0.265463i | ||||
\(533\) | 6.12293 | − | 14.7821i | 0.265214 | − | 0.640283i | ||||
\(534\) | 9.23880 | + | 3.82683i | 0.399802 | + | 0.165603i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −25.4558 | + | 25.4558i | −1.09952 | + | 1.09952i | ||||
\(537\) | 3.69552 | + | 1.53073i | 0.159473 | + | 0.0660560i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 33.2597 | − | 13.7766i | 1.43260 | − | 0.593400i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.3073 | − | 36.9552i | −0.658114 | − | 1.58883i | −0.800714 | − | 0.599047i | \(-0.795546\pi\) |
0.142600 | − | 0.989780i | \(-0.454454\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.00000 | −0.343313 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.65685 | + | 5.65685i | 0.242091 | + | 0.242091i | ||||
\(547\) | 13.7766 | + | 33.2597i | 0.589045 | + | 1.42208i | 0.884417 | + | 0.466698i | \(0.154557\pi\) |
−0.295372 | + | 0.955382i | \(0.595443\pi\) | |||||||
\(548\) | 10.0000i | 0.427179i | ||||||||
\(549\) | 7.39104 | − | 3.06147i | 0.315442 | − | 0.130660i | ||||
\(550\) | −7.65367 | + | 18.4776i | −0.326354 | + | 0.787887i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 8.48528 | − | 8.48528i | 0.361158 | − | 0.361158i | ||||
\(553\) | −11.3137 | + | 11.3137i | −0.481108 | + | 0.481108i | ||||
\(554\) | −7.39104 | − | 3.06147i | −0.314015 | − | 0.130069i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.69552 | − | 1.53073i | 0.156725 | − | 0.0649176i | ||||
\(557\) | − | 18.0000i | − | 0.762684i | −0.924434 | − | 0.381342i | \(-0.875462\pi\) | ||
0.924434 | − | 0.381342i | \(-0.124538\pi\) | |||||||
\(558\) | −1.53073 | − | 3.69552i | −0.0648011 | − | 0.156444i | ||||
\(559\) | 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 | 0.920499 | + | 0.390745i | \(0.127783\pi\) |
0.390745 | + | 0.920499i | \(0.372217\pi\) | |||||||
\(564\) | 3.06147 | + | 7.39104i | 0.128911 | + | 0.311219i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.69552 | − | 1.53073i | 0.155334 | − | 0.0643415i | ||||
\(567\) | 1.53073 | − | 3.69552i | 0.0642848 | − | 0.155197i | ||||
\(568\) | 33.2597 | + | 13.7766i | 1.39554 | + | 0.578053i | ||||
\(569\) | −18.3848 | + | 18.3848i | −0.770730 | + | 0.770730i | −0.978234 | − | 0.207504i | \(-0.933466\pi\) |
0.207504 | + | 0.978234i | \(0.433466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.4776 | + | 7.65367i | 0.773263 | + | 0.320296i | 0.734193 | − | 0.678940i | \(-0.237561\pi\) |
0.0390697 | + | 0.999236i | \(0.487561\pi\) | |||||||
\(572\) | −3.06147 | + | 7.39104i | −0.128006 | + | 0.309035i | ||||
\(573\) | 7.39104 | − | 3.06147i | 0.308765 | − | 0.127895i | ||||
\(574\) | 32.0000i | 1.33565i | ||||||||
\(575\) | 7.65367 | + | 18.4776i | 0.319180 | + | 0.770569i | ||||
\(576\) | 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 | ||||||||
\(581\) | −18.3688 | − | 44.3462i | −0.762066 | − | 1.83979i | ||||
\(582\) | − | 16.0000i | − | 0.663221i | ||||||
\(583\) | 22.1731 | − | 9.18440i | 0.918316 | − | 0.380379i | ||||
\(584\) | 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 | \(-0.670343\pi\) |
0.860193 | + | 0.509968i | \(0.170343\pi\) | |||||||
\(588\) | 8.31492 | + | 3.44415i | 0.342901 | + | 0.142034i | ||||
\(589\) | 6.12293 | − | 14.7821i | 0.252291 | − | 0.609085i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.0000i | 0.658152i | ||||||||
\(592\) | 3.06147 | + | 7.39104i | 0.125826 | + | 0.303770i | ||||
\(593\) | 32.5269 | + | 32.5269i | 1.33572 | + | 1.33572i | 0.900159 | + | 0.435561i | \(0.143450\pi\) |
0.435561 | + | 0.900159i | \(0.356550\pi\) | |||||||
\(594\) | −4.00000 | −0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | 14.1421 | + | 14.1421i | 0.578799 | + | 0.578799i | ||||
\(598\) | −3.06147 | − | 7.39104i | −0.125193 | − | 0.302242i | ||||
\(599\) | − | 8.00000i | − | 0.326871i | −0.986554 | − | 0.163436i | \(-0.947742\pi\) | ||
0.986554 | − | 0.163436i | \(-0.0522576\pi\) | |||||||
\(600\) | −13.8582 | + | 5.74025i | −0.565758 | + | 0.234345i | ||||
\(601\) | −6.12293 | + | 14.7821i | −0.249760 | + | 0.602973i | −0.998183 | − | 0.0602475i | \(-0.980811\pi\) |
0.748424 | + | 0.663221i | \(0.230811\pi\) | |||||||
\(602\) | −14.7821 | − | 6.12293i | −0.602472 | − | 0.249552i | ||||
\(603\) | 8.48528 | − | 8.48528i | 0.345547 | − | 0.345547i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.29610 | + | 5.54328i | −0.0932727 | + | 0.225180i | ||||
\(607\) | 3.69552 | − | 1.53073i | 0.149996 | − | 0.0621306i | −0.306422 | − | 0.951896i | \(-0.599132\pi\) |
0.456419 | + | 0.889765i | \(0.349132\pi\) | |||||||
\(608\) | 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 | ||||||
\(617\) | −22.1731 | + | 9.18440i | −0.892656 | + | 0.369750i | −0.781392 | − | 0.624041i | \(-0.785490\pi\) |
−0.111264 | + | 0.993791i | \(0.535490\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.2597 | − | 13.7766i | −1.33682 | − | 0.553728i | −0.404226 | − | 0.914659i | \(-0.632459\pi\) |
−0.932593 | + | 0.360931i | \(0.882459\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.82843 | + | 2.82843i | −0.113501 | + | 0.113501i | ||||
\(622\) | 11.0866 | + | 4.59220i | 0.444530 | + | 0.184130i | ||||
\(623\) | 15.3073 | − | 36.9552i | 0.613276 | − | 1.48058i | ||||
\(624\) | 1.84776 | − | 0.765367i | 0.0739696 | − | 0.0306392i | ||||
\(625\) | − | 25.0000i | − | 1.00000i | ||||||
\(626\) | 6.12293 | + | 14.7821i | 0.244722 | + | 0.590810i | ||||
\(627\) | −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 | \(-0.300904\pi\) |
−0.810682 | + | 0.585486i | \(0.800904\pi\) | |||||||
\(632\) | 4.59220 | + | 11.0866i | 0.182668 | + | 0.440999i | ||||
\(633\) | − | 4.00000i | − | 0.158986i | ||||||
\(634\) | −29.5641 | + | 12.2459i | −1.17414 | + | 0.486346i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.54328 | + | 2.29610i | 0.219805 | + | 0.0910463i | ||||
\(637\) | 12.7279 | − | 12.7279i | 0.504299 | − | 0.504299i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.0866 | − | 4.59220i | −0.438577 | − | 0.181665i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.39104 | + | 3.06147i | −0.291928 | + | 0.120921i | −0.523841 | − | 0.851816i | \(-0.675502\pi\) |
0.231913 | + | 0.972737i | \(0.425502\pi\) | |||||||
\(642\) | − | 12.0000i | − | 0.473602i | ||||||
\(643\) | −1.53073 | − | 3.69552i | −0.0603662 | − | 0.145737i | 0.890818 | − | 0.454360i | \(-0.150132\pi\) |
−0.951185 | + | 0.308623i | \(0.900132\pi\) | |||||||
\(644\) | −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 | ||||
\(649\) | −18.3688 | − | 44.3462i | −0.721039 | − | 1.74074i | ||||
\(650\) | 10.0000i | 0.392232i | ||||||||
\(651\) | −14.7821 | + | 6.12293i | −0.579355 | + | 0.239977i | ||||
\(652\) | 7.65367 | − | 18.4776i | 0.299741 | − | 0.723638i | ||||
\(653\) | 29.5641 | + | 12.2459i | 1.15693 | + | 0.479218i | 0.876853 | − | 0.480758i | \(-0.159639\pi\) |
0.280081 | + | 0.959976i | \(0.409639\pi\) | |||||||
\(654\) | 5.65685 | − | 5.65685i | 0.221201 | − | 0.221201i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.39104 | + | 3.06147i | 0.288571 | + | 0.119530i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −29.5641 | + | 12.2459i | −1.15253 | + | 0.477394i | ||||
\(659\) | 4.00000i | 0.155818i | 0.996960 | + | 0.0779089i | \(0.0248243\pi\) | ||||
−0.996960 | + | 0.0779089i | \(0.975176\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.6985 | + | 29.6985i | 1.15514 | + | 1.15514i | 0.985508 | + | 0.169629i | \(0.0542570\pi\) |
0.169629 | + | 0.985508i | \(0.445743\pi\) | |||||||
\(662\) | 20.0000 | 0.777322 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −36.0000 | −1.39707 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.06147 | − | 7.39104i | −0.118629 | − | 0.286397i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −11.0866 | + | 4.59220i | −0.428952 | + | 0.177678i | ||||
\(669\) | −6.12293 | + | 14.7821i | −0.236726 | + | 0.571508i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.6274 | + | 22.6274i | −0.873522 | + | 0.873522i | ||||
\(672\) | 14.1421 | − | 14.1421i | 0.545545 | − | 0.545545i | ||||
\(673\) | 29.5641 | + | 12.2459i | 1.13961 | + | 0.472044i | 0.871038 | − | 0.491215i | \(-0.163447\pi\) |
0.268576 | + | 0.963259i | \(0.413447\pi\) | |||||||
\(674\) | −6.12293 | + | 14.7821i | −0.235847 | + | 0.569384i | ||||
\(675\) | 4.61940 | − | 1.91342i | 0.177801 | − | 0.0736475i | ||||
\(676\) | − | 9.00000i | − | 0.346154i | ||||||
\(677\) | −18.3688 | − | 44.3462i | −0.705971 | − | 1.70436i | −0.709832 | − | 0.704371i | \(-0.751229\pi\) |
0.00386145 | − | 0.999993i | \(-0.498771\pi\) | |||||||
\(678\) | −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 | ||||
\(683\) | −4.59220 | − | 11.0866i | −0.175716 | − | 0.424215i | 0.811344 | − | 0.584569i | \(-0.198736\pi\) |
−0.987060 | + | 0.160354i | \(0.948736\pi\) | |||||||
\(684\) | − | 4.00000i | − | 0.152944i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.06147 | + | 7.39104i | −0.116887 | + | 0.282191i | ||||
\(687\) | −9.23880 | − | 3.82683i | −0.352482 | − | 0.146003i | ||||
\(688\) | −2.82843 | + | 2.82843i | −0.107833 | + | 0.107833i | ||||
\(689\) | 8.48528 | − | 8.48528i | 0.323263 | − | 0.323263i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.65367 | − | 18.4776i | 0.291159 | − | 0.702921i | −0.708838 | − | 0.705372i | \(-0.750780\pi\) |
0.999997 | + | 0.00245092i | \(0.000780153\pi\) | |||||||
\(692\) | −14.7821 | + | 6.12293i | −0.561930 | + | 0.232759i | ||||
\(693\) | 16.0000i | 0.607790i | ||||||||
\(694\) | −1.53073 | − | 3.69552i | −0.0581059 | − | 0.140280i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −2.00000 | −0.0757011 | ||||||||
\(699\) | −5.65685 | − | 5.65685i | −0.213962 | − | 0.213962i | ||||
\(700\) | 7.65367 | + | 18.4776i | 0.289281 | + | 0.698387i | ||||
\(701\) | 34.0000i | 1.28416i | 0.766637 | + | 0.642081i | \(0.221929\pi\) | ||||
−0.766637 | + | 0.642081i | \(0.778071\pi\) | |||||||
\(702\) | −1.84776 | + | 0.765367i | −0.0697392 | + | 0.0288869i | ||||
\(703\) | 12.2459 | − | 29.5641i | 0.461862 | − | 1.11503i | ||||
\(704\) | −25.8686 | − | 10.7151i | −0.974961 | − | 0.403842i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.7279 | − | 12.7279i | 0.479022 | − | 0.479022i | ||||
\(707\) | 22.1731 | + | 9.18440i | 0.833906 | + | 0.345415i | ||||
\(708\) | 4.59220 | − | 11.0866i | 0.172585 | − | 0.416658i | ||||
\(709\) | 36.9552 | − | 15.3073i | 1.38788 | − | 0.574879i | 0.441304 | − | 0.897358i | \(-0.354516\pi\) |
0.946577 | + | 0.322478i | \(0.104516\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.53073 | − | 3.69552i | −0.0574070 | − | 0.138593i | ||||
\(712\) | −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 | ||||
\(717\) | −3.06147 | − | 7.39104i | −0.114333 | − | 0.276023i | ||||
\(718\) | 32.0000i | 1.19423i | ||||||||
\(719\) | −33.2597 | + | 13.7766i | −1.24038 | + | 0.513781i | −0.903832 | − | 0.427887i | \(-0.859258\pi\) |
−0.336544 | + | 0.941668i | \(0.609258\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.12132 | − | 2.12132i | 0.0789474 | − | 0.0789474i | ||||
\(723\) | 11.3137 | − | 11.3137i | 0.420761 | − | 0.420761i | ||||
\(724\) | 7.39104 | + | 3.06147i | 0.274686 | + | 0.113779i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.61940 | − | 1.91342i | 0.171442 | − | 0.0710136i | ||||
\(727\) | − | 8.00000i | − | 0.296704i | −0.988935 | − | 0.148352i | \(-0.952603\pi\) | ||
0.988935 | − | 0.148352i | \(-0.0473968\pi\) | |||||||
\(728\) | −9.18440 | − | 22.1731i | −0.340397 | − | 0.821790i | ||||
\(729\) | 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 | \(-0.466089\pi\) |
−0.994331 | + | 0.106333i | \(0.966089\pi\) | |||||||
\(734\) | 4.59220 | + | 11.0866i | 0.169501 | + | 0.409212i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.4776 | + | 7.65367i | −0.681093 | + | 0.282118i | ||||
\(737\) | −18.3688 | + | 44.3462i | −0.676624 | + | 1.63351i | ||||
\(738\) | −7.39104 | − | 3.06147i | −0.272068 | − | 0.112694i | ||||
\(739\) | 2.82843 | − | 2.82843i | 0.104045 | − | 0.104045i | −0.653168 | − | 0.757213i | \(-0.726560\pi\) |
0.757213 | + | 0.653168i | \(0.226560\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.39104 | − | 3.06147i | −0.271517 | − | 0.112466i | ||||
\(742\) | −9.18440 | + | 22.1731i | −0.337170 | + | 0.814000i | ||||
\(743\) | 33.2597 | − | 13.7766i | 1.22018 | − | 0.505415i | 0.322712 | − | 0.946497i | \(-0.395405\pi\) |
0.897467 | + | 0.441083i | \(0.145405\pi\) | |||||||
\(744\) | 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 | ||||||||
\(751\) | −7.65367 | − | 18.4776i | −0.279286 | − | 0.674257i | 0.720530 | − | 0.693424i | \(-0.243899\pi\) |
−0.999816 | + | 0.0191669i | \(0.993899\pi\) | |||||||
\(752\) | 8.00000i | 0.291730i | ||||||||
\(753\) | 11.0866 | − | 4.59220i | 0.404017 | − | 0.167349i | ||||
\(754\) | 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 | \(-0.992639\pi\) |
0.0231238 | + | 0.999733i | \(0.492639\pi\) | |||||||
\(758\) | 18.4776 | + | 7.65367i | 0.671136 | + | 0.277994i | ||||
\(759\) | 6.12293 | − | 14.7821i | 0.222248 | − | 0.536555i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 6.00000i | − | 0.217500i | −0.994069 | − | 0.108750i | \(-0.965315\pi\) | ||
0.994069 | − | 0.108750i | \(-0.0346848\pi\) | |||||||
\(762\) | −3.06147 | − | 7.39104i | −0.110905 | − | 0.267749i | ||||
\(763\) | −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 | ||||
\(768\) | −6.50562 | − | 15.7060i | −0.234751 | − | 0.566740i | ||||
\(769\) | − | 34.0000i | − | 1.22607i | −0.790055 | − | 0.613036i | \(-0.789948\pi\) | ||
0.790055 | − | 0.613036i | \(-0.210052\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.765367 | − | 1.84776i | 0.0275640 | − | 0.0665454i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.24264 | − | 4.24264i | 0.152597 | − | 0.152597i | −0.626680 | − | 0.779277i | \(-0.715587\pi\) |
0.779277 | + | 0.626680i | \(0.215587\pi\) | |||||||
\(774\) | 2.82843 | − | 2.82843i | 0.101666 | − | 0.101666i | ||||
\(775\) | −18.4776 | − | 7.65367i | −0.663735 | − | 0.274928i | ||||
\(776\) | −18.3688 | + | 44.3462i | −0.659402 | + | 1.59194i | ||||
\(777\) | −29.5641 | + | 12.2459i | −1.06061 | + | 0.439318i | ||||
\(778\) | 6.00000i | 0.215110i | ||||||||
\(779\) | −12.2459 | − | 29.5641i | −0.438754 | − | 1.05925i | ||||
\(780\) | 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 | ||||||
\(787\) | −11.0866 | + | 4.59220i | −0.395193 | + | 0.163694i | −0.571425 | − | 0.820654i | \(-0.693609\pi\) |
0.176232 | + | 0.984349i | \(0.443609\pi\) | |||||||
\(788\) | 6.12293 | − | 14.7821i | 0.218121 | − | 0.526590i | ||||
\(789\) | −22.1731 | − | 9.18440i | −0.789384 | − | 0.326973i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.6274 | + | 22.6274i | −0.804538 | + | 0.804538i | ||||
\(792\) | 11.0866 | + | 4.59220i | 0.393944 | + | 0.163177i | ||||
\(793\) | −6.12293 | + | 14.7821i | −0.217432 | + | 0.524927i | ||||
\(794\) | 7.39104 | − | 3.06147i | 0.262298 | − | 0.108647i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.65367 | − | 18.4776i | −0.271277 | − | 0.654921i | ||||
\(797\) | 12.7279 | + | 12.7279i | 0.450846 | + | 0.450846i | 0.895635 | − | 0.444789i | \(-0.146721\pi\) |
−0.444789 | + | 0.895635i | \(0.646721\pi\) | |||||||
\(798\) | 16.0000 | 0.566394 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 25.0000 | 0.883883 | ||||||||
\(801\) | 7.07107 | + | 7.07107i | 0.249844 | + | 0.249844i | ||||
\(802\) | −9.18440 | − | 22.1731i | −0.324313 | − | 0.782960i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −11.0866 | + | 4.59220i | −0.390993 | + | 0.161954i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.39104 | + | 3.06147i | 0.260338 | + | 0.107836i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.7279 | − | 12.7279i | 0.447767 | − | 0.447767i | ||||
\(809\) | −36.9552 | − | 15.3073i | −1.29927 | − | 0.538177i | −0.377538 | − | 0.925994i | \(-0.623229\pi\) |
−0.921737 | + | 0.387817i | \(0.873229\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.69552 | + | 1.53073i | −0.129767 | + | 0.0537513i | −0.446622 | − | 0.894723i | \(-0.647373\pi\) |
0.316855 | + | 0.948474i | \(0.397373\pi\) | |||||||
\(812\) | 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 | ||||
\(819\) | 3.06147 | + | 7.39104i | 0.106976 | + | 0.258264i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.5641 | − | 12.2459i | 1.03180 | − | 0.427384i | 0.198435 | − | 0.980114i | \(-0.436414\pi\) |
0.833360 | + | 0.552730i | \(0.186414\pi\) | |||||||
\(822\) | 3.82683 | − | 9.23880i | 0.133476 | − | 0.322240i | ||||
\(823\) | −40.6507 | − | 16.8381i | −1.41699 | − | 0.586938i | −0.462891 | − | 0.886415i | \(-0.653188\pi\) |
−0.954104 | + | 0.299477i | \(0.903188\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14.1421 | + | 14.1421i | −0.492366 | + | 0.492366i | ||||
\(826\) | 44.3462 | + | 18.3688i | 1.54300 | + | 0.639132i | ||||
\(827\) | −4.59220 | + | 11.0866i | −0.159686 | + | 0.385517i | −0.983390 | − | 0.181503i | \(-0.941904\pi\) |
0.823704 | + | 0.567020i | \(0.191904\pi\) | |||||||
\(828\) | 3.69552 | − | 1.53073i | 0.128428 | − | 0.0531967i | ||||
\(829\) | 2.00000i | 0.0694629i | 0.999397 | + | 0.0347314i | \(0.0110576\pi\) | ||||
−0.999397 | + | 0.0347314i | \(0.988942\pi\) | |||||||
\(830\) | 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 | ||||||||
\(836\) | 6.12293 | + | 14.7821i | 0.211766 | + | 0.511249i | ||||
\(837\) | − | 4.00000i | − | 0.138260i | ||||||
\(838\) | 3.69552 | − | 1.53073i | 0.127660 | − | 0.0528783i | ||||
\(839\) | −16.8381 | + | 40.6507i | −0.581315 | + | 1.40342i | 0.310307 | + | 0.950636i | \(0.399568\pi\) |
−0.891622 | + | 0.452782i | \(0.850432\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.5061 | + | 20.5061i | −0.707107 | + | 0.707107i | ||||
\(842\) | −15.5563 | + | 15.5563i | −0.536107 | + | 0.536107i | ||||
\(843\) | 9.23880 | + | 3.82683i | 0.318201 | + | 0.131803i | ||||
\(844\) | −1.53073 | + | 3.69552i | −0.0526900 | + | 0.127205i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 8.00000i | − | 0.275046i | ||||||
\(847\) | −7.65367 | − | 18.4776i | −0.262983 | − | 0.634898i | ||||
\(848\) | 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 | ||||
\(853\) | −9.18440 | − | 22.1731i | −0.314468 | − | 0.759193i | −0.999528 | − | 0.0307066i | \(-0.990224\pi\) |
0.685060 | − | 0.728486i | \(-0.259776\pi\) | |||||||
\(854\) | − | 32.0000i | − | 1.09502i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.7766 | + | 33.2597i | −0.470875 | + | 1.13679i | ||||
\(857\) | −7.39104 | − | 3.06147i | −0.252473 | − | 0.104578i | 0.252858 | − | 0.967503i | \(-0.418630\pi\) |
−0.505331 | + | 0.862926i | \(0.668630\pi\) | |||||||
\(858\) | 5.65685 | − | 5.65685i | 0.193122 | − | 0.193122i | ||||
\(859\) | −2.82843 | + | 2.82843i | −0.0965047 | + | 0.0965047i | −0.753711 | − | 0.657206i | \(-0.771738\pi\) |
0.657206 | + | 0.753711i | \(0.271738\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.2459 | + | 29.5641i | −0.417338 | + | 1.00754i | ||||
\(862\) | 18.4776 | − | 7.65367i | 0.629349 | − | 0.260685i | ||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | 1.91342 | + | 4.61940i | 0.0650958 | + | 0.157155i | ||||
\(865\) | 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 | ||||||||
\(872\) | −22.1731 | + | 9.18440i | −0.750876 | + | 0.311023i | ||||
\(873\) | 6.12293 | − | 14.7821i | 0.207230 | − | 0.500297i | ||||
\(874\) | −14.7821 | − | 6.12293i | −0.500011 | − | 0.207111i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.9552 | − | 15.3073i | −1.24789 | − | 0.516892i | −0.341717 | − | 0.939803i | \(-0.611008\pi\) |
−0.906171 | + | 0.422911i | \(0.861008\pi\) | |||||||
\(878\) | −13.7766 | + | 33.2597i | −0.464938 | + | 1.12246i | ||||
\(879\) | 9.23880 | − | 3.82683i | 0.311617 | − | 0.129076i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.18440 | − | 22.1731i | −0.309430 | − | 0.747031i | −0.999724 | − | 0.0235015i | \(-0.992519\pi\) |
0.690293 | − | 0.723530i | \(-0.257481\pi\) | |||||||
\(882\) | −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 | ||||
\(887\) | −1.53073 | − | 3.69552i | −0.0513970 | − | 0.124083i | 0.896096 | − | 0.443861i | \(-0.146392\pi\) |
−0.947493 | + | 0.319778i | \(0.896392\pi\) | |||||||
\(888\) | 24.0000i | 0.805387i | ||||||||
\(889\) | −29.5641 | + | 12.2459i | −0.991550 | + | 0.410713i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.69552 | − | 1.53073i | −0.123805 | − | 0.0512815i | ||||
\(892\) | 11.3137 | − | 11.3137i | 0.378811 | − | 0.378811i | ||||
\(893\) | 22.6274 | − | 22.6274i | 0.757198 | − | 0.757198i | ||||
\(894\) | 5.54328 | + | 2.29610i | 0.185395 | + | 0.0767931i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −11.0866 | + | 4.59220i | −0.370376 | + | 0.153415i | ||||
\(897\) | − | 8.00000i | − | 0.267112i | ||||||
\(898\) | −3.06147 | − | 7.39104i | −0.102162 | − | 0.246642i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −5.00000 | −0.166667 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 32.0000 | 1.06548 | ||||||||
\(903\) | −11.3137 | − | 11.3137i | −0.376497 | − | 0.376497i | ||||
\(904\) | 9.18440 | + | 22.1731i | 0.305469 | + | 0.737467i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.7151 | − | 25.8686i | 0.355790 | − | 0.858954i | −0.640092 | − | 0.768298i | \(-0.721104\pi\) |
0.995882 | − | 0.0906554i | \(-0.0288962\pi\) | |||||||
\(908\) | −11.0866 | − | 4.59220i | −0.367920 | − | 0.152398i | ||||
\(909\) | −4.24264 | + | 4.24264i | −0.140720 | + | 0.140720i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.8686 | + | 10.7151i | 0.857066 | + | 0.355008i | 0.767559 | − | 0.640978i | \(-0.221471\pi\) |
0.0895065 | + | 0.995986i | \(0.471471\pi\) | |||||||
\(912\) | 1.53073 | − | 3.69552i | 0.0506877 | − | 0.122371i | ||||
\(913\) | −44.3462 | + | 18.3688i | −1.46765 | + | 0.607919i | ||||
\(914\) | − | 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 | ||||||||
\(921\) | −4.59220 | − | 11.0866i | −0.151318 | − | 0.365314i | ||||
\(922\) | − | 34.0000i | − | 1.11973i | ||||||
\(923\) | 22.1731 | − | 9.18440i | 0.729837 | − | 0.302308i | ||||
\(924\) | 6.12293 | − | 14.7821i | 0.201430 | − | 0.486294i | ||||
\(925\) | −36.9552 | − | 15.3073i | −1.21508 | − | 0.503302i | ||||
\(926\) | 28.2843 | − | 28.2843i | 0.929479 | − | 0.929479i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.18440 | − | 22.1731i | 0.301330 | − | 0.727476i | −0.698598 | − | 0.715514i | \(-0.746192\pi\) |
0.999928 | − | 0.0119617i | \(-0.00380762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 36.0000i | − | 1.17985i | ||||||
\(932\) | 3.06147 | + | 7.39104i | 0.100282 | + | 0.242101i | ||||
\(933\) | 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 | \(-0.110383\pi\) |
−0.339869 | + | 0.940473i | \(0.610383\pi\) | |||||||
\(938\) | −18.3688 | − | 44.3462i | −0.599763 | − | 1.44796i | ||||
\(939\) | 16.0000i | 0.522140i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.3688 | − | 44.3462i | 0.598806 | − | 1.44565i | −0.275993 | − | 0.961160i | \(-0.589007\pi\) |
0.874799 | − | 0.484486i | \(-0.160993\pi\) | |||||||
\(942\) | 1.84776 | + | 0.765367i | 0.0602032 | + | 0.0249370i | ||||
\(943\) | 22.6274 | − | 22.6274i | 0.736850 | − | 0.736850i | ||||
\(944\) | 8.48528 | − | 8.48528i | 0.276172 | − | 0.276172i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.12293 | + | 14.7821i | −0.199074 | + | 0.480607i | ||||
\(947\) | 11.0866 | − | 4.59220i | 0.360265 | − | 0.149226i | −0.195207 | − | 0.980762i | \(-0.562538\pi\) |
0.555471 | + | 0.831536i | \(0.312538\pi\) | |||||||
\(948\) | 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 | ||||||||
\(958\) | −4.59220 | + | 11.0866i | −0.148367 | + | 0.358190i | ||||
\(959\) | −36.9552 | − | 15.3073i | −1.19335 | − | 0.494300i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.6066 | − | 10.6066i | 0.342148 | − | 0.342148i | ||||
\(962\) | 14.7821 | + | 6.12293i | 0.476593 | + | 0.197411i | ||||
\(963\) | 4.59220 | − | 11.0866i | 0.147982 | − | 0.357259i | ||||
\(964\) | −14.7821 | + | 6.12293i | −0.476098 | + | 0.197206i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.12293 | + | 14.7821i | 0.197002 | + | 0.475605i | ||||
\(967\) | −16.9706 | − | 16.9706i | −0.545737 | − | 0.545737i | 0.379468 | − | 0.925205i | \(-0.376107\pi\) |
−0.925205 | + | 0.379468i | \(0.876107\pi\) | |||||||
\(968\) | −15.0000 | −0.482118 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.4558 | + | 25.4558i | 0.816917 | + | 0.816917i | 0.985660 | − | 0.168743i | \(-0.0539708\pi\) |
−0.168743 | + | 0.985660i | \(0.553971\pi\) | |||||||
\(972\) | −0.382683 | − | 0.923880i | −0.0122746 | − | 0.0296334i | ||||
\(973\) | 16.0000i | 0.512936i | ||||||||
\(974\) | −3.69552 | + | 1.53073i | −0.118412 | + | 0.0490479i | ||||
\(975\) | −3.82683 | + | 9.23880i | −0.122557 | + | 0.295878i | ||||
\(976\) | −7.39104 | − | 3.06147i | −0.236581 | − | 0.0979952i | ||||
\(977\) | 32.5269 | − | 32.5269i | 1.04063 | − | 1.04063i | 0.0414892 | − | 0.999139i | \(-0.486790\pi\) |
0.999139 | − | 0.0414892i | \(-0.0132102\pi\) | |||||||
\(978\) | −14.1421 | + | 14.1421i | −0.452216 | + | 0.452216i | ||||
\(979\) | −36.9552 | − | 15.3073i | −1.18109 | − | 0.489225i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.39104 | − | 3.06147i | 0.235978 | − | 0.0977451i | ||||
\(982\) | 20.0000i | 0.638226i | ||||||||
\(983\) | 7.65367 | + | 18.4776i | 0.244114 | + | 0.589344i | 0.997684 | − | 0.0680246i | \(-0.0216696\pi\) |
−0.753570 | + | 0.657368i | \(0.771670\pi\) | |||||||
\(984\) | 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 | ||||
\(989\) | 6.12293 | + | 14.7821i | 0.194698 | + | 0.470043i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.0866 | − | 4.59220i | 0.352176 | − | 0.145876i | −0.199580 | − | 0.979881i | \(-0.563958\pi\) |
0.551756 | + | 0.834005i | \(0.313958\pi\) | |||||||
\(992\) | 7.65367 | − | 18.4776i | 0.243004 | − | 0.586664i | ||||
\(993\) | 18.4776 | + | 7.65367i | 0.586369 | + | 0.242882i | ||||
\(994\) | −33.9411 | + | 33.9411i | −1.07655 | + | 1.07655i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −11.0866 | − | 4.59220i | −0.351291 | − | 0.145509i | ||||
\(997\) | 3.06147 | − | 7.39104i | 0.0969576 | − | 0.234076i | −0.867957 | − | 0.496639i | \(-0.834567\pi\) |
0.964915 | + | 0.262562i | \(0.0845675\pi\) | |||||||
\(998\) | −33.2597 | + | 13.7766i | −1.05282 | + | 0.436091i | ||||
\(999\) | − | 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 \(a_p\))