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 | 688.2 | ||
Root | \(-0.923880 + 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 867.688 |
Dual form | 867.2.h.d.712.2 |
$q$-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 \(\left(\mathbb{Z}/867\mathbb{Z}\right)^\times\).
\(n\) | \(290\) | \(292\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | −0.411438 | − | 0.911438i | \(-0.634973\pi\) |
0.911438 | + | 0.411438i | \(0.134973\pi\) | |||||||
\(3\) | 0.382683 | − | 0.923880i | 0.220942 | − | 0.533402i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(6\) | −0.382683 | − | 0.923880i | −0.156230 | − | 0.377172i | ||||
\(7\) | 3.69552 | − | 1.53073i | 1.39677 | − | 0.578563i | 0.447862 | − | 0.894103i | \(-0.352186\pi\) |
0.948912 | + | 0.315540i | \(0.102186\pi\) | |||||||
\(8\) | 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 | 0.967768 | + | 0.251845i | \(0.0810372\pi\) |
−0.506234 | + | 0.862396i | \(0.668963\pi\) | |||||||
\(12\) | 0.923880 | + | 0.382683i | 0.266701 | + | 0.110471i | ||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | 1.53073 | − | 3.69552i | 0.409106 | − | 0.987669i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.82843 | + | 2.82843i | −0.648886 | + | 0.648886i | −0.952724 | − | 0.303838i | \(-0.901732\pi\) |
0.303838 | + | 0.952724i | \(0.401732\pi\) | |||||||
\(20\) | 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 | 0.999298 | + | 0.0374660i | \(0.0119286\pi\) |
−0.680118 | + | 0.733103i | \(0.738071\pi\) | |||||||
\(24\) | 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 | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.53073 | − | 3.69552i | 0.274928 | − | 0.663735i | −0.724753 | − | 0.689009i | \(-0.758046\pi\) |
0.999681 | + | 0.0252745i | \(0.00804598\pi\) | |||||||
\(32\) | −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 | −0.444373 | − | 0.895842i | \(-0.646573\pi\) |
0.947675 | − | 0.319237i | \(-0.103427\pi\) | |||||||
\(38\) | 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 | 0.278317 | − | 0.960489i | \(-0.410223\pi\) |
0.875969 | + | 0.482368i | \(0.160223\pi\) | |||||||
\(42\) | −2.82843 | − | 2.82843i | −0.436436 | − | 0.436436i | ||||
\(43\) | −2.82843 | − | 2.82843i | −0.431331 | − | 0.431331i | 0.457750 | − | 0.889081i | \(-0.348656\pi\) |
−0.889081 | + | 0.457750i | \(0.848656\pi\) | |||||||
\(44\) | −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 | \(-0.801699\pi\) | ||
0.812142 | − | 0.583460i | \(-0.198301\pi\) | |||||||
\(48\) | 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 | −0.352892 | − | 0.935664i | \(-0.614802\pi\) |
0.935664 | + | 0.352892i | \(0.114802\pi\) | |||||||
\(54\) | −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 | 0.993837 | + | 0.110853i | \(0.0353582\pi\) |
0.110853 | + | 0.993837i | \(0.464642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.39104 | + | 3.06147i | −0.946325 | + | 0.391981i | −0.801848 | − | 0.597527i | \(-0.796150\pi\) |
−0.144477 | + | 0.989508i | \(0.546150\pi\) | |||||||
\(62\) | −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 | −0.376168 | − | 0.926552i | \(-0.622758\pi\) |
0.921162 | − | 0.389180i | \(-0.127242\pi\) | |||||||
\(72\) | − | 3.00000i | − | 0.353553i | ||||||
\(73\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(74\) | −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 | 0.814076 | − | 0.580759i | \(-0.197244\pi\) |
−0.986297 | + | 0.164980i | \(0.947244\pi\) | |||||||
\(80\) | 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 | −0.997792 | − | 0.0664117i | \(-0.978845\pi\) |
0.0664117 | + | 0.997792i | \(0.478845\pi\) | |||||||
\(84\) | 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 | \(0.177808\pi\) | ||||
−0.847998 | + | 0.529999i | \(0.822192\pi\) | |||||||
\(90\) | 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 | −0.527238 | − | 0.849718i | \(-0.676772\pi\) |
−0.973655 | + | 0.228028i | \(0.926772\pi\) | |||||||
\(98\) | − | 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 | −0.224160 | − | 0.974552i | \(-0.571964\pi\) |
−0.847618 | + | 0.530608i | \(0.821964\pi\) | |||||||
\(108\) | −0.382683 | − | 0.923880i | −0.0368237 | − | 0.0889003i | ||||
\(109\) | −7.39104 | + | 3.06147i | −0.707933 | + | 0.293235i | −0.707449 | − | 0.706764i | \(-0.750154\pi\) |
−0.000483966 | 1.00000i | \(0.500154\pi\) | ||||||||
\(110\) | 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 | 0.711977 | − | 0.702202i | \(-0.247800\pi\) |
−0.999976 | + | 0.00691210i | \(0.997800\pi\) | |||||||
\(114\) | 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 | 0.410083 | − | 0.912048i | \(-0.365500\pi\) |
−0.912048 | + | 0.410083i | \(0.865500\pi\) | |||||||
\(128\) | −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 | 0.215356 | − | 0.976536i | \(-0.430909\pi\) |
−0.538235 | + | 0.842795i | \(0.680909\pi\) | |||||||
\(132\) | 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 | −0.845572 | − | 0.533862i | \(-0.820740\pi\) |
0.975407 | + | 0.220412i | \(0.0707402\pi\) | |||||||
\(140\) | 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 | \(0.0790407\pi\) | ||||
−0.969328 | + | 0.245770i | \(0.920959\pi\) | |||||||
\(150\) | −1.91342 | + | 4.61940i | −0.156230 | + | 0.377172i | ||||
\(151\) | 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 | ||||||||
\(156\) | −0.765367 | + | 1.84776i | −0.0612784 | + | 0.147939i | ||||
\(157\) | 2.00000i | 0.159617i | 0.996810 | + | 0.0798087i | \(0.0254309\pi\) | ||||
−0.996810 | + | 0.0798087i | \(0.974569\pi\) | |||||||
\(158\) | −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 | 0.485726 | − | 0.874111i | \(-0.338555\pi\) |
0.961550 | + | 0.274629i | \(0.0885551\pi\) | |||||||
\(164\) | 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 | 0.640585 | + | 0.767887i | \(0.278692\pi\) |
−0.995940 | + | 0.0900162i | \(0.971308\pi\) | |||||||
\(168\) | 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 | 0.500581 | + | 0.865690i | \(0.333120\pi\) |
−0.966099 | + | 0.258171i | \(0.916880\pi\) | |||||||
\(174\) | 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 | 0.804865 | − | 0.593458i | \(-0.202238\pi\) |
−0.593458 | + | 0.804865i | \(0.702238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.06147 | − | 7.39104i | −0.227557 | − | 0.549371i | 0.768322 | − | 0.640064i | \(-0.221092\pi\) |
−0.995879 | + | 0.0906923i | \(0.971092\pi\) | |||||||
\(182\) | 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 | \(0.0934657\pi\) | ||||
−0.957199 | + | 0.289430i | \(0.906534\pi\) | |||||||
\(192\) | 6.46716 | + | 2.67878i | 0.466727 | + | 0.193325i | ||||
\(193\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(194\) | −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 | 0.212153 | − | 0.977236i | \(-0.431952\pi\) |
0.841026 | + | 0.540995i | \(0.181952\pi\) | |||||||
\(198\) | −1.53073 | − | 3.69552i | −0.108785 | − | 0.262629i | ||||
\(199\) | 18.4776 | + | 7.65367i | 1.30984 | + | 0.542554i | 0.924838 | − | 0.380361i | \(-0.124200\pi\) |
0.385004 | + | 0.922915i | \(0.374200\pi\) | |||||||
\(200\) | − | 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 | −0.506244 | − | 0.862390i | \(-0.668966\pi\) |
0.251834 | + | 0.967771i | \(0.418966\pi\) | |||||||
\(212\) | 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 | −0.218267 | − | 0.975889i | \(-0.570040\pi\) |
0.975889 | + | 0.218267i | \(0.0700404\pi\) | |||||||
\(224\) | −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 | 0.999857 | + | 0.0168909i | \(0.00537679\pi\) |
−0.695062 | + | 0.718950i | \(0.744623\pi\) | |||||||
\(228\) | −3.69552 | + | 1.53073i | −0.244742 | + | 0.101375i | ||||
\(229\) | −7.07107 | − | 7.07107i | −0.467269 | − | 0.467269i | 0.433759 | − | 0.901029i | \(-0.357187\pi\) |
−0.901029 | + | 0.433759i | \(0.857187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.7821 | − | 6.12293i | 0.972589 | − | 0.402860i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.39104 | − | 3.06147i | −0.484203 | − | 0.200563i | 0.127209 | − | 0.991876i | \(-0.459398\pi\) |
−0.611412 | + | 0.791313i | \(0.709398\pi\) | |||||||
\(234\) | − | 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 | 0.594553 | + | 0.804056i | \(0.297329\pi\) |
−0.988966 | + | 0.148141i | \(0.952671\pi\) | |||||||
\(242\) | 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 | \(0.123635\pi\) | ||||
−0.925513 | + | 0.378717i | \(0.876365\pi\) | |||||||
\(252\) | 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 | −0.749838 | − | 0.661622i | \(-0.769869\pi\) |
0.661622 | + | 0.749838i | \(0.269869\pi\) | |||||||
\(258\) | −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 | −0.998867 | − | 0.0475824i | \(-0.984848\pi\) |
−0.0475824 | − | 0.998867i | \(-0.515152\pi\) | |||||||
\(264\) | 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 | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(270\) | 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 | 0.149425 | − | 0.988773i | \(-0.452258\pi\) |
−0.593509 | + | 0.804827i | \(0.702258\pi\) | |||||||
\(278\) | −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 | 0.885832 | − | 0.464007i | \(-0.153589\pi\) |
−0.464007 | + | 0.885832i | \(0.653589\pi\) | |||||||
\(282\) | −7.39104 | + | 3.06147i | −0.440130 | + | 0.182308i | ||||
\(283\) | 1.53073 | + | 3.69552i | 0.0909927 | + | 0.219676i | 0.962823 | − | 0.270131i | \(-0.0870672\pi\) |
−0.871831 | + | 0.489807i | \(0.837067\pi\) | |||||||
\(284\) | 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 | \(0.0943550\pi\) | ||||
−0.956387 | + | 0.292103i | \(0.905645\pi\) | |||||||
\(294\) | −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 | 0.674184 | − | 0.738563i | \(-0.264495\pi\) |
−0.0455232 | + | 0.998963i | \(0.514495\pi\) | |||||||
\(312\) | 2.29610 | + | 5.54328i | 0.129991 | + | 0.313826i | ||||
\(313\) | 14.7821 | − | 6.12293i | 0.835532 | − | 0.346089i | 0.0764418 | − | 0.997074i | \(-0.475644\pi\) |
0.759090 | + | 0.650985i | \(0.225644\pi\) | |||||||
\(314\) | 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 | −0.749174 | − | 0.662373i | \(-0.769549\pi\) |
0.0613775 | − | 0.998115i | \(-0.480451\pi\) | |||||||
\(318\) | −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 | 0.979375 | − | 0.202053i | \(-0.0647612\pi\) |
−0.202053 | + | 0.979375i | \(0.564761\pi\) | |||||||
\(332\) | −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 | −0.664769 | − | 0.747049i | \(-0.731470\pi\) |
0.998306 | − | 0.0581814i | \(-0.0185302\pi\) | |||||||
\(338\) | 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 | −0.479664 | − | 0.877452i | \(-0.659242\pi\) |
0.281278 | + | 0.959626i | \(0.409242\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.41421 | − | 1.41421i | −0.0757011 | − | 0.0757011i | 0.668242 | − | 0.743944i | \(-0.267047\pi\) |
−0.743944 | + | 0.668242i | \(0.767047\pi\) | |||||||
\(350\) | −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 | \(0.159008\pi\) | ||||
−0.877803 | + | 0.479022i | \(0.840992\pi\) | |||||||
\(354\) | 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 | 0.218361 | − | 0.975868i | \(-0.429929\pi\) |
0.975868 | − | 0.218361i | \(-0.0700712\pi\) | |||||||
\(360\) | 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 | −0.0740732 | − | 0.997253i | \(-0.523600\pi\) |
0.652787 | + | 0.757542i | \(0.273600\pi\) | |||||||
\(368\) | 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 | 0.802904 | − | 0.596109i | \(-0.203287\pi\) |
0.146226 | + | 0.989251i | \(0.453287\pi\) | |||||||
\(380\) | 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 | 0.356277 | − | 0.934380i | \(-0.384046\pi\) |
−0.934380 | + | 0.356277i | \(0.884046\pi\) | |||||||
\(384\) | −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 | −0.591324 | − | 0.806434i | \(-0.701394\pi\) |
0.806434 | + | 0.591324i | \(0.201394\pi\) | |||||||
\(390\) | 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 | 0.981896 | − | 0.189420i | \(-0.0606607\pi\) |
−0.828246 | + | 0.560365i | \(0.810661\pi\) | |||||||
\(398\) | 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 | −0.859997 | − | 0.510298i | \(-0.829535\pi\) |
−0.247275 | + | 0.968945i | \(0.579535\pi\) | |||||||
\(402\) | 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 | 0.956850 | − | 0.290583i | \(-0.0938494\pi\) |
−0.882068 | + | 0.471121i | \(0.843849\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 22.0000i | − | 1.07221i | −0.844150 | − | 0.536107i | \(-0.819894\pi\) | ||
0.844150 | − | 0.536107i | \(-0.180106\pi\) | |||||||
\(422\) | −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 | 0.993970 | + | 0.109654i | \(0.0349743\pi\) |
−0.625306 | + | 0.780380i | \(0.715026\pi\) | |||||||
\(432\) | −0.923880 | + | 0.382683i | −0.0444502 | + | 0.0184119i | ||||
\(433\) | 1.41421 | + | 1.41421i | 0.0679628 | + | 0.0679628i | 0.740271 | − | 0.672308i | \(-0.234697\pi\) |
−0.672308 | + | 0.740271i | \(0.734697\pi\) | |||||||
\(434\) | −11.3137 | − | 11.3137i | −0.543075 | − | 0.543075i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −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 | −0.144099 | − | 0.989563i | \(-0.546028\pi\) |
0.801620 | − | 0.597834i | \(-0.203972\pi\) | |||||||
\(440\) | 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 | −0.550205 | − | 0.835029i | \(-0.685451\pi\) |
0.201401 | + | 0.979509i | \(0.435451\pi\) | |||||||
\(450\) | 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 | −0.304376 | + | 0.952552i | \(0.598448\pi\) |
−0.952552 | + | 0.304376i | \(0.901552\pi\) | |||||||
\(458\) | −10.0000 | −0.467269 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.0416 | + | 24.0416i | −1.11973 | + | 1.11973i | −0.127950 | + | 0.991781i | \(0.540840\pi\) |
−0.991781 | + | 0.127950i | \(0.959160\pi\) | |||||||
\(462\) | 6.12293 | − | 14.7821i | 0.284865 | − | 0.687724i | ||||
\(463\) | 40.0000i | 1.85896i | 0.368875 | + | 0.929479i | \(0.379743\pi\) | ||||
−0.368875 | + | 0.929479i | \(0.620257\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.39104 | + | 3.06147i | −0.342383 | + | 0.141820i | ||||
\(467\) | −2.82843 | − | 2.82843i | −0.130884 | − | 0.130884i | 0.638630 | − | 0.769514i | \(-0.279501\pi\) |
−0.769514 | + | 0.638630i | \(0.779501\pi\) | |||||||
\(468\) | 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 | −0.783572 | − | 0.621301i | \(-0.786605\pi\) |
0.993395 | + | 0.114743i | \(0.0366045\pi\) | |||||||
\(480\) | 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 | 0.885395 | − | 0.464839i | \(-0.153888\pi\) |
−0.954760 | + | 0.297379i | \(0.903888\pi\) | |||||||
\(488\) | −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 | −0.311892 | − | 0.950118i | \(-0.600963\pi\) |
0.950118 | + | 0.311892i | \(0.100963\pi\) | |||||||
\(492\) | 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 | −0.855485 | − | 0.517828i | \(-0.826741\pi\) |
0.238759 | − | 0.971079i | \(-0.423259\pi\) | |||||||
\(500\) | 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 | −0.121572 | − | 0.992583i | \(-0.538794\pi\) |
0.615897 | + | 0.787826i | \(0.288794\pi\) | |||||||
\(504\) | −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 | 0.987088 | + | 0.160180i | \(0.0512076\pi\) |
−0.584712 | + | 0.811241i | \(0.698792\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 12.0000i | − | 0.524723i | −0.964970 | − | 0.262362i | \(-0.915499\pi\) | ||
0.964970 | − | 0.262362i | \(-0.0845013\pi\) | |||||||
\(524\) | 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 | 0.142600 | + | 0.989780i | \(0.454454\pi\) |
−0.800714 | + | 0.599047i | \(0.795546\pi\) | |||||||
\(542\) | 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 | −0.295372 | − | 0.955382i | \(-0.595443\pi\) |
0.884417 | − | 0.466698i | \(-0.154557\pi\) | |||||||
\(548\) | − | 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 | \(0.124538\pi\) | ||||
−0.924434 | + | 0.381342i | \(0.875462\pi\) | |||||||
\(558\) | −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 | 0.390745 | − | 0.920499i | \(-0.372217\pi\) |
0.920499 | − | 0.390745i | \(-0.127783\pi\) | |||||||
\(564\) | 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 | 0.207504 | − | 0.978234i | \(-0.433466\pi\) |
−0.978234 | + | 0.207504i | \(0.933466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.4776 | − | 7.65367i | 0.773263 | − | 0.320296i | 0.0390697 | − | 0.999236i | \(-0.487561\pi\) |
0.734193 | + | 0.678940i | \(0.237561\pi\) | |||||||
\(572\) | −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 | 0.860193 | − | 0.509968i | \(-0.170343\pi\) |
−0.509968 | + | 0.860193i | \(0.670343\pi\) | |||||||
\(588\) | 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 | 0.435561 | − | 0.900159i | \(-0.356550\pi\) |
0.900159 | − | 0.435561i | \(-0.143450\pi\) | |||||||
\(594\) | −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 | \(0.0522576\pi\) | ||||
−0.986554 | + | 0.163436i | \(0.947742\pi\) | |||||||
\(600\) | −13.8582 | − | 5.74025i | −0.565758 | − | 0.234345i | ||||
\(601\) | −6.12293 | − | 14.7821i | −0.249760 | − | 0.602973i | 0.748424 | − | 0.663221i | \(-0.230811\pi\) |
−0.998183 | + | 0.0602475i | \(0.980811\pi\) | |||||||
\(602\) | −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 | 0.456419 | − | 0.889765i | \(-0.349132\pi\) |
−0.306422 | + | 0.951896i | \(0.599132\pi\) | |||||||
\(608\) | − | 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 | −0.111264 | − | 0.993791i | \(-0.535490\pi\) |
−0.781392 | + | 0.624041i | \(0.785490\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.2597 | + | 13.7766i | −1.33682 | + | 0.553728i | −0.932593 | − | 0.360931i | \(-0.882459\pi\) |
−0.404226 | + | 0.914659i | \(0.632459\pi\) | |||||||
\(620\) | 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 | −0.810682 | − | 0.585486i | \(-0.800904\pi\) |
0.585486 | + | 0.810682i | \(0.300904\pi\) | |||||||
\(632\) | 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 | 0.231913 | − | 0.972737i | \(-0.425502\pi\) |
−0.523841 | + | 0.851816i | \(0.675502\pi\) | |||||||
\(642\) | 12.0000i | 0.473602i | ||||||||
\(643\) | −1.53073 | + | 3.69552i | −0.0603662 | + | 0.145737i | −0.951185 | − | 0.308623i | \(-0.900132\pi\) |
0.890818 | + | 0.454360i | \(0.150132\pi\) | |||||||
\(644\) | −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 | 0.280081 | − | 0.959976i | \(-0.409639\pi\) |
0.876853 | + | 0.480758i | \(0.159639\pi\) | |||||||
\(654\) | 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 | \(-0.975176\pi\) | ||
0.996960 | − | 0.0779089i | \(-0.0248243\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.6985 | − | 29.6985i | 1.15514 | − | 1.15514i | 0.169629 | − | 0.985508i | \(-0.445743\pi\) |
0.985508 | − | 0.169629i | \(-0.0542570\pi\) | |||||||
\(662\) | 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 | 0.268576 | − | 0.963259i | \(-0.413447\pi\) |
0.871038 | + | 0.491215i | \(0.163447\pi\) | |||||||
\(674\) | −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 | 0.00386145 | + | 0.999993i | \(0.498771\pi\) |
−0.709832 | + | 0.704371i | \(0.751229\pi\) | |||||||
\(678\) | −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 | −0.987060 | − | 0.160354i | \(-0.948736\pi\) |
0.811344 | + | 0.584569i | \(0.198736\pi\) | |||||||
\(684\) | 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 | 0.999997 | − | 0.00245092i | \(-0.000780153\pi\) |
−0.708838 | + | 0.705372i | \(0.750780\pi\) | |||||||
\(692\) | −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 | \(-0.778071\pi\) | ||
0.766637 | − | 0.642081i | \(-0.221929\pi\) | |||||||
\(702\) | −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 | 0.946577 | − | 0.322478i | \(-0.104516\pi\) |
0.441304 | + | 0.897358i | \(0.354516\pi\) | |||||||
\(710\) | 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 | −0.336544 | − | 0.941668i | \(-0.609258\pi\) |
−0.903832 | + | 0.427887i | \(0.859258\pi\) | |||||||
\(720\) | 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 | \(0.0473968\pi\) | ||||
−0.988935 | + | 0.148352i | \(0.952603\pi\) | |||||||
\(728\) | −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 | −0.994331 | − | 0.106333i | \(-0.966089\pi\) |
0.106333 | + | 0.994331i | \(0.466089\pi\) | |||||||
\(734\) | 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 | 0.757213 | − | 0.653168i | \(-0.226560\pi\) |
−0.653168 | + | 0.757213i | \(0.726560\pi\) | |||||||
\(740\) | 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 | 0.897467 | − | 0.441083i | \(-0.145405\pi\) |
0.322712 | + | 0.946497i | \(0.395405\pi\) | |||||||
\(744\) | − | 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 | −0.999816 | − | 0.0191669i | \(-0.993899\pi\) |
0.720530 | + | 0.693424i | \(0.243899\pi\) | |||||||
\(752\) | − | 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 | 0.0231238 | − | 0.999733i | \(-0.492639\pi\) |
−0.999733 | + | 0.0231238i | \(0.992639\pi\) | |||||||
\(758\) | 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 | \(0.0346848\pi\) | ||||
−0.994069 | + | 0.108750i | \(0.965315\pi\) | |||||||
\(762\) | −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 | \(0.210052\pi\) | ||||
−0.790055 | + | 0.613036i | \(0.789948\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.765367 | + | 1.84776i | 0.0275640 | + | 0.0665454i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.24264 | + | 4.24264i | 0.152597 | + | 0.152597i | 0.779277 | − | 0.626680i | \(-0.215587\pi\) |
−0.626680 | + | 0.779277i | \(0.715587\pi\) | |||||||
\(774\) | 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 | 0.176232 | − | 0.984349i | \(-0.443609\pi\) |
−0.571425 | + | 0.820654i | \(0.693609\pi\) | |||||||
\(788\) | 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 | −0.444789 | − | 0.895635i | \(-0.646721\pi\) |
0.895635 | + | 0.444789i | \(0.146721\pi\) | |||||||
\(798\) | 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 | −0.921737 | − | 0.387817i | \(-0.873229\pi\) |
−0.377538 | + | 0.925994i | \(0.623229\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.69552 | − | 1.53073i | −0.129767 | − | 0.0537513i | 0.316855 | − | 0.948474i | \(-0.397373\pi\) |
−0.446622 | + | 0.894723i | \(0.647373\pi\) | |||||||
\(812\) | 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 | 0.833360 | − | 0.552730i | \(-0.186414\pi\) |
0.198435 | + | 0.980114i | \(0.436414\pi\) | |||||||
\(822\) | 3.82683 | + | 9.23880i | 0.133476 | + | 0.322240i | ||||
\(823\) | −40.6507 | + | 16.8381i | −1.41699 | + | 0.586938i | −0.954104 | − | 0.299477i | \(-0.903188\pi\) |
−0.462891 | + | 0.886415i | \(0.653188\pi\) | |||||||
\(824\) | 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 | 0.823704 | − | 0.567020i | \(-0.191904\pi\) |
−0.983390 | + | 0.181503i | \(0.941904\pi\) | |||||||
\(828\) | 3.69552 | + | 1.53073i | 0.128428 | + | 0.0531967i | ||||
\(829\) | − | 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 | ||||||||
\(836\) | 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 | −0.891622 | − | 0.452782i | \(-0.850432\pi\) |
0.310307 | − | 0.950636i | \(-0.399568\pi\) | |||||||
\(840\) | 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 | 0.685060 | + | 0.728486i | \(0.259776\pi\) |
−0.999528 | + | 0.0307066i | \(0.990224\pi\) | |||||||
\(854\) | 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 | −0.505331 | − | 0.862926i | \(-0.668630\pi\) |
0.252858 | + | 0.967503i | \(0.418630\pi\) | |||||||
\(858\) | 5.65685 | + | 5.65685i | 0.193122 | + | 0.193122i | ||||
\(859\) | −2.82843 | − | 2.82843i | −0.0965047 | − | 0.0965047i | 0.657206 | − | 0.753711i | \(-0.271738\pi\) |
−0.753711 | + | 0.657206i | \(0.771738\pi\) | |||||||
\(860\) | 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 | −0.906171 | − | 0.422911i | \(-0.861008\pi\) |
−0.341717 | + | 0.939803i | \(0.611008\pi\) | |||||||
\(878\) | −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 | 0.690293 | + | 0.723530i | \(0.257481\pi\) |
−0.999724 | + | 0.0235015i | \(0.992519\pi\) | |||||||
\(882\) | −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 | −0.947493 | − | 0.319778i | \(-0.896392\pi\) |
0.896096 | + | 0.443861i | \(0.146392\pi\) | |||||||
\(888\) | − | 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 | 0.995882 | + | 0.0906554i | \(0.0288962\pi\) |
−0.640092 | + | 0.768298i | \(0.721104\pi\) | |||||||
\(908\) | −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 | 0.0895065 | − | 0.995986i | \(-0.471471\pi\) |
0.767559 | + | 0.640978i | \(0.221471\pi\) | |||||||
\(912\) | 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 | 0.999928 | + | 0.0119617i | \(0.00380762\pi\) |
−0.698598 | + | 0.715514i | \(0.746192\pi\) | |||||||
\(930\) | 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 | −0.339869 | − | 0.940473i | \(-0.610383\pi\) |
0.940473 | + | 0.339869i | \(0.110383\pi\) | |||||||
\(938\) | −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 | 0.874799 | + | 0.484486i | \(0.160993\pi\) |
−0.275993 | + | 0.961160i | \(0.589007\pi\) | |||||||
\(942\) | 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 | 0.555471 | − | 0.831536i | \(-0.312538\pi\) |
−0.195207 | + | 0.980762i | \(0.562538\pi\) | |||||||
\(948\) | − | 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 | −0.925205 | − | 0.379468i | \(-0.876107\pi\) |
0.379468 | + | 0.925205i | \(0.376107\pi\) | |||||||
\(968\) | −15.0000 | −0.482118 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.4558 | − | 25.4558i | 0.816917 | − | 0.816917i | −0.168743 | − | 0.985660i | \(-0.553971\pi\) |
0.985660 | + | 0.168743i | \(0.0539708\pi\) | |||||||
\(972\) | −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 | 0.999139 | + | 0.0414892i | \(0.0132102\pi\) |
0.0414892 | + | 0.999139i | \(0.486790\pi\) | |||||||
\(978\) | −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 | −0.753570 | − | 0.657368i | \(-0.771670\pi\) |
0.997684 | + | 0.0680246i | \(0.0216696\pi\) | |||||||
\(984\) | 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 | 0.551756 | − | 0.834005i | \(-0.313958\pi\) |
−0.199580 | + | 0.979881i | \(0.563958\pi\) | |||||||
\(992\) | 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 | 0.964915 | − | 0.262562i | \(-0.0845675\pi\) |
−0.867957 | + | 0.496639i | \(0.834567\pi\) | |||||||
\(998\) | −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 \(a_p\))