Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [196,2,Mod(19,196)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(196, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("196.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 196 = 2^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 196.f (of order \(6\), degree \(2\), 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: | \(1.56506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 196.31 |
Dual form | 196.2.f.a.19.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).
\(n\) | \(99\) | \(101\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36603 | − | 0.366025i | −0.965926 | − | 0.258819i | ||||
\(3\) | −0.866025 | + | 1.50000i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(4\) | 1.73205 | + | 1.00000i | 0.866025 | + | 0.500000i | ||||
\(5\) | 1.50000 | − | 0.866025i | 0.670820 | − | 0.387298i | −0.125567 | − | 0.992085i | \(-0.540075\pi\) |
0.796387 | + | 0.604787i | \(0.206742\pi\) | |||||||
\(6\) | 1.73205 | − | 1.73205i | 0.707107 | − | 0.707107i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.00000 | − | 2.00000i | −0.707107 | − | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.36603 | + | 0.633975i | −0.748203 | + | 0.200480i | ||||
\(11\) | 0.866025 | + | 0.500000i | 0.261116 | + | 0.150756i | 0.624844 | − | 0.780750i | \(-0.285163\pi\) |
−0.363727 | + | 0.931505i | \(0.618496\pi\) | |||||||
\(12\) | −3.00000 | + | 1.73205i | −0.866025 | + | 0.500000i | ||||
\(13\) | 3.46410i | 0.960769i | 0.877058 | + | 0.480384i | \(0.159503\pi\) | ||||
−0.877058 | + | 0.480384i | \(0.840497\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.00000i | 0.774597i | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | 1.50000 | + | 0.866025i | 0.363803 | + | 0.210042i | 0.670748 | − | 0.741685i | \(-0.265973\pi\) |
−0.306944 | + | 0.951727i | \(0.599307\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.59808 | + | 4.50000i | 0.596040 | + | 1.03237i | 0.993399 | + | 0.114708i | \(0.0365932\pi\) |
−0.397360 | + | 0.917663i | \(0.630073\pi\) | |||||||
\(20\) | 3.46410 | 0.774597 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | − | 1.00000i | −0.213201 | − | 0.213201i | ||||
\(23\) | 0.866025 | − | 0.500000i | 0.180579 | − | 0.104257i | −0.406986 | − | 0.913434i | \(-0.633420\pi\) |
0.587565 | + | 0.809177i | \(0.300087\pi\) | |||||||
\(24\) | 4.73205 | − | 1.26795i | 0.965926 | − | 0.258819i | ||||
\(25\) | −1.00000 | + | 1.73205i | −0.200000 | + | 0.346410i | ||||
\(26\) | 1.26795 | − | 4.73205i | 0.248665 | − | 0.928032i | ||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00000 | 0.742781 | 0.371391 | − | 0.928477i | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 1.09808 | − | 4.09808i | 0.200480 | − | 0.748203i | ||||
\(31\) | 0.866025 | − | 1.50000i | 0.155543 | − | 0.269408i | −0.777714 | − | 0.628619i | \(-0.783621\pi\) |
0.933257 | + | 0.359211i | \(0.116954\pi\) | |||||||
\(32\) | −1.46410 | − | 5.46410i | −0.258819 | − | 0.965926i | ||||
\(33\) | −1.50000 | + | 0.866025i | −0.261116 | + | 0.150756i | ||||
\(34\) | −1.73205 | − | 1.73205i | −0.297044 | − | 0.297044i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.50000 | − | 2.59808i | −0.246598 | − | 0.427121i | 0.715981 | − | 0.698119i | \(-0.245980\pi\) |
−0.962580 | + | 0.270998i | \(0.912646\pi\) | |||||||
\(38\) | −1.90192 | − | 7.09808i | −0.308533 | − | 1.15146i | ||||
\(39\) | −5.19615 | − | 3.00000i | −0.832050 | − | 0.480384i | ||||
\(40\) | −4.73205 | − | 1.26795i | −0.748203 | − | 0.200480i | ||||
\(41\) | − | 3.46410i | − | 0.541002i | −0.962720 | − | 0.270501i | \(-0.912811\pi\) | ||
0.962720 | − | 0.270501i | \(-0.0871893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000i | 0.304997i | 0.988304 | + | 0.152499i | \(0.0487319\pi\) | ||||
−0.988304 | + | 0.152499i | \(0.951268\pi\) | |||||||
\(44\) | 1.00000 | + | 1.73205i | 0.150756 | + | 0.261116i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.36603 | + | 0.366025i | −0.201409 | + | 0.0539675i | ||||
\(47\) | −4.33013 | − | 7.50000i | −0.631614 | − | 1.09399i | −0.987222 | − | 0.159352i | \(-0.949059\pi\) |
0.355608 | − | 0.934635i | \(-0.384274\pi\) | |||||||
\(48\) | −6.92820 | −1.00000 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.00000 | − | 2.00000i | 0.282843 | − | 0.282843i | ||||
\(51\) | −2.59808 | + | 1.50000i | −0.363803 | + | 0.210042i | ||||
\(52\) | −3.46410 | + | 6.00000i | −0.480384 | + | 0.832050i | ||||
\(53\) | 0.500000 | − | 0.866025i | 0.0686803 | − | 0.118958i | −0.829640 | − | 0.558298i | \(-0.811454\pi\) |
0.898321 | + | 0.439340i | \(0.144788\pi\) | |||||||
\(54\) | 7.09808 | + | 1.90192i | 0.965926 | + | 0.258819i | ||||
\(55\) | 1.73205 | 0.233550 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.00000 | −1.19208 | ||||||||
\(58\) | −5.46410 | − | 1.46410i | −0.717472 | − | 0.192246i | ||||
\(59\) | 2.59808 | − | 4.50000i | 0.338241 | − | 0.585850i | −0.645861 | − | 0.763455i | \(-0.723502\pi\) |
0.984102 | + | 0.177605i | \(0.0568349\pi\) | |||||||
\(60\) | −3.00000 | + | 5.19615i | −0.387298 | + | 0.670820i | ||||
\(61\) | 4.50000 | − | 2.59808i | 0.576166 | − | 0.332650i | −0.183442 | − | 0.983030i | \(-0.558724\pi\) |
0.759608 | + | 0.650381i | \(0.225391\pi\) | |||||||
\(62\) | −1.73205 | + | 1.73205i | −0.219971 | + | 0.219971i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | 3.00000 | + | 5.19615i | 0.372104 | + | 0.644503i | ||||
\(66\) | 2.36603 | − | 0.633975i | 0.291238 | − | 0.0780369i | ||||
\(67\) | 2.59808 | + | 1.50000i | 0.317406 | + | 0.183254i | 0.650236 | − | 0.759733i | \(-0.274670\pi\) |
−0.332830 | + | 0.942987i | \(0.608004\pi\) | |||||||
\(68\) | 1.73205 | + | 3.00000i | 0.210042 | + | 0.363803i | ||||
\(69\) | 1.73205i | 0.208514i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.0000i | − | 1.66149i | −0.556650 | − | 0.830747i | \(-0.687914\pi\) | ||
0.556650 | − | 0.830747i | \(-0.312086\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.50000 | − | 4.33013i | −0.877809 | − | 0.506803i | −0.00787336 | − | 0.999969i | \(-0.502506\pi\) |
−0.869935 | + | 0.493166i | \(0.835840\pi\) | |||||||
\(74\) | 1.09808 | + | 4.09808i | 0.127649 | + | 0.476392i | ||||
\(75\) | −1.73205 | − | 3.00000i | −0.200000 | − | 0.346410i | ||||
\(76\) | 10.3923i | 1.19208i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.00000 | + | 6.00000i | 0.679366 | + | 0.679366i | ||||
\(79\) | 7.79423 | − | 4.50000i | 0.876919 | − | 0.506290i | 0.00727784 | − | 0.999974i | \(-0.497683\pi\) |
0.869641 | + | 0.493684i | \(0.164350\pi\) | |||||||
\(80\) | 6.00000 | + | 3.46410i | 0.670820 | + | 0.387298i | ||||
\(81\) | 4.50000 | − | 7.79423i | 0.500000 | − | 0.866025i | ||||
\(82\) | −1.26795 | + | 4.73205i | −0.140022 | + | 0.522568i | ||||
\(83\) | 13.8564 | 1.52094 | 0.760469 | − | 0.649374i | \(-0.224969\pi\) | ||||
0.760469 | + | 0.649374i | \(0.224969\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.00000 | 0.325396 | ||||||||
\(86\) | 0.732051 | − | 2.73205i | 0.0789391 | − | 0.294605i | ||||
\(87\) | −3.46410 | + | 6.00000i | −0.371391 | + | 0.643268i | ||||
\(88\) | −0.732051 | − | 2.73205i | −0.0780369 | − | 0.291238i | ||||
\(89\) | −13.5000 | + | 7.79423i | −1.43100 | + | 0.826187i | −0.997197 | − | 0.0748225i | \(-0.976161\pi\) |
−0.433800 | + | 0.901009i | \(0.642828\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.00000 | 0.208514 | ||||||||
\(93\) | 1.50000 | + | 2.59808i | 0.155543 | + | 0.269408i | ||||
\(94\) | 3.16987 | + | 11.8301i | 0.326947 | + | 1.22018i | ||||
\(95\) | 7.79423 | + | 4.50000i | 0.799671 | + | 0.461690i | ||||
\(96\) | 9.46410 | + | 2.53590i | 0.965926 | + | 0.258819i | ||||
\(97\) | − | 17.3205i | − | 1.75863i | −0.476240 | − | 0.879316i | \(-0.658000\pi\) | ||
0.476240 | − | 0.879316i | \(-0.342000\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.46410 | + | 2.00000i | −0.346410 | + | 0.200000i | ||||
\(101\) | 7.50000 | + | 4.33013i | 0.746278 | + | 0.430864i | 0.824347 | − | 0.566084i | \(-0.191542\pi\) |
−0.0780696 | + | 0.996948i | \(0.524876\pi\) | |||||||
\(102\) | 4.09808 | − | 1.09808i | 0.405770 | − | 0.108726i | ||||
\(103\) | 4.33013 | + | 7.50000i | 0.426660 | + | 0.738997i | 0.996574 | − | 0.0827075i | \(-0.0263567\pi\) |
−0.569914 | + | 0.821705i | \(0.693023\pi\) | |||||||
\(104\) | 6.92820 | − | 6.92820i | 0.679366 | − | 0.679366i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.00000 | + | 1.00000i | −0.0971286 | + | 0.0971286i | ||||
\(107\) | −11.2583 | + | 6.50000i | −1.08838 | + | 0.628379i | −0.933146 | − | 0.359498i | \(-0.882948\pi\) |
−0.155238 | + | 0.987877i | \(0.549614\pi\) | |||||||
\(108\) | −9.00000 | − | 5.19615i | −0.866025 | − | 0.500000i | ||||
\(109\) | −4.50000 | + | 7.79423i | −0.431022 | + | 0.746552i | −0.996962 | − | 0.0778949i | \(-0.975180\pi\) |
0.565940 | + | 0.824447i | \(0.308513\pi\) | |||||||
\(110\) | −2.36603 | − | 0.633975i | −0.225592 | − | 0.0604471i | ||||
\(111\) | 5.19615 | 0.493197 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.0000 | −1.50515 | −0.752577 | − | 0.658505i | \(-0.771189\pi\) | ||||
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 12.2942 | + | 3.29423i | 1.15146 | + | 0.308533i | ||||
\(115\) | 0.866025 | − | 1.50000i | 0.0807573 | − | 0.139876i | ||||
\(116\) | 6.92820 | + | 4.00000i | 0.643268 | + | 0.371391i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.19615 | + | 5.19615i | −0.478345 | + | 0.478345i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 6.00000 | − | 6.00000i | 0.547723 | − | 0.547723i | ||||
\(121\) | −5.00000 | − | 8.66025i | −0.454545 | − | 0.787296i | ||||
\(122\) | −7.09808 | + | 1.90192i | −0.642630 | + | 0.172192i | ||||
\(123\) | 5.19615 | + | 3.00000i | 0.468521 | + | 0.270501i | ||||
\(124\) | 3.00000 | − | 1.73205i | 0.269408 | − | 0.155543i | ||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.00000i | 0.532414i | 0.963916 | + | 0.266207i | \(0.0857705\pi\) | ||||
−0.963916 | + | 0.266207i | \(0.914230\pi\) | |||||||
\(128\) | 2.92820 | − | 10.9282i | 0.258819 | − | 0.965926i | ||||
\(129\) | −3.00000 | − | 1.73205i | −0.264135 | − | 0.152499i | ||||
\(130\) | −2.19615 | − | 8.19615i | −0.192615 | − | 0.718850i | ||||
\(131\) | −2.59808 | − | 4.50000i | −0.226995 | − | 0.393167i | 0.729921 | − | 0.683531i | \(-0.239557\pi\) |
−0.956916 | + | 0.290365i | \(0.906223\pi\) | |||||||
\(132\) | −3.46410 | −0.301511 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.00000 | − | 3.00000i | −0.259161 | − | 0.259161i | ||||
\(135\) | −7.79423 | + | 4.50000i | −0.670820 | + | 0.387298i | ||||
\(136\) | −1.26795 | − | 4.73205i | −0.108726 | − | 0.405770i | ||||
\(137\) | −0.500000 | + | 0.866025i | −0.0427179 | + | 0.0739895i | −0.886594 | − | 0.462549i | \(-0.846935\pi\) |
0.843876 | + | 0.536538i | \(0.180268\pi\) | |||||||
\(138\) | 0.633975 | − | 2.36603i | 0.0539675 | − | 0.201409i | ||||
\(139\) | −6.92820 | −0.587643 | −0.293821 | − | 0.955860i | \(-0.594927\pi\) | ||||
−0.293821 | + | 0.955860i | \(0.594927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.0000 | 1.26323 | ||||||||
\(142\) | −5.12436 | + | 19.1244i | −0.430026 | + | 1.60488i | ||||
\(143\) | −1.73205 | + | 3.00000i | −0.144841 | + | 0.250873i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.00000 | − | 3.46410i | 0.498273 | − | 0.287678i | ||||
\(146\) | 8.66025 | + | 8.66025i | 0.716728 | + | 0.716728i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 6.00000i | − | 0.493197i | ||||||
\(149\) | −0.500000 | − | 0.866025i | −0.0409616 | − | 0.0709476i | 0.844818 | − | 0.535054i | \(-0.179709\pi\) |
−0.885779 | + | 0.464107i | \(0.846375\pi\) | |||||||
\(150\) | 1.26795 | + | 4.73205i | 0.103528 | + | 0.386370i | ||||
\(151\) | −6.06218 | − | 3.50000i | −0.493333 | − | 0.284826i | 0.232623 | − | 0.972567i | \(-0.425269\pi\) |
−0.725956 | + | 0.687741i | \(0.758602\pi\) | |||||||
\(152\) | 3.80385 | − | 14.1962i | 0.308533 | − | 1.15146i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 3.00000i | − | 0.240966i | ||||||
\(156\) | −6.00000 | − | 10.3923i | −0.480384 | − | 0.832050i | ||||
\(157\) | −1.50000 | − | 0.866025i | −0.119713 | − | 0.0691164i | 0.438948 | − | 0.898513i | \(-0.355351\pi\) |
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | −12.2942 | + | 3.29423i | −0.978076 | + | 0.262075i | ||||
\(159\) | 0.866025 | + | 1.50000i | 0.0686803 | + | 0.118958i | ||||
\(160\) | −6.92820 | − | 6.92820i | −0.547723 | − | 0.547723i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −9.00000 | + | 9.00000i | −0.707107 | + | 0.707107i | ||||
\(163\) | 18.1865 | − | 10.5000i | 1.42448 | − | 0.822423i | 0.427802 | − | 0.903873i | \(-0.359288\pi\) |
0.996678 | + | 0.0814491i | \(0.0259548\pi\) | |||||||
\(164\) | 3.46410 | − | 6.00000i | 0.270501 | − | 0.468521i | ||||
\(165\) | −1.50000 | + | 2.59808i | −0.116775 | + | 0.202260i | ||||
\(166\) | −18.9282 | − | 5.07180i | −1.46911 | − | 0.393648i | ||||
\(167\) | −17.3205 | −1.34030 | −0.670151 | − | 0.742225i | \(-0.733770\pi\) | ||||
−0.670151 | + | 0.742225i | \(0.733770\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −4.09808 | − | 1.09808i | −0.314308 | − | 0.0842186i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.00000 | + | 3.46410i | −0.152499 | + | 0.264135i | ||||
\(173\) | 10.5000 | − | 6.06218i | 0.798300 | − | 0.460899i | −0.0445762 | − | 0.999006i | \(-0.514194\pi\) |
0.842876 | + | 0.538107i | \(0.180860\pi\) | |||||||
\(174\) | 6.92820 | − | 6.92820i | 0.525226 | − | 0.525226i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.00000i | 0.301511i | ||||||||
\(177\) | 4.50000 | + | 7.79423i | 0.338241 | + | 0.585850i | ||||
\(178\) | 21.2942 | − | 5.70577i | 1.59607 | − | 0.427666i | ||||
\(179\) | −16.4545 | − | 9.50000i | −1.22987 | − | 0.710063i | −0.262864 | − | 0.964833i | \(-0.584667\pi\) |
−0.967002 | + | 0.254770i | \(0.918000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.92820i | 0.514969i | 0.966282 | + | 0.257485i | \(0.0828937\pi\) | ||||
−0.966282 | + | 0.257485i | \(0.917106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.00000i | 0.665299i | ||||||||
\(184\) | −2.73205 | − | 0.732051i | −0.201409 | − | 0.0539675i | ||||
\(185\) | −4.50000 | − | 2.59808i | −0.330847 | − | 0.191014i | ||||
\(186\) | −1.09808 | − | 4.09808i | −0.0805149 | − | 0.300486i | ||||
\(187\) | 0.866025 | + | 1.50000i | 0.0633300 | + | 0.109691i | ||||
\(188\) | − | 17.3205i | − | 1.26323i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.00000 | − | 9.00000i | −0.652929 | − | 0.652929i | ||||
\(191\) | −0.866025 | + | 0.500000i | −0.0626634 | + | 0.0361787i | −0.531004 | − | 0.847369i | \(-0.678185\pi\) |
0.468341 | + | 0.883548i | \(0.344852\pi\) | |||||||
\(192\) | −12.0000 | − | 6.92820i | −0.866025 | − | 0.500000i | ||||
\(193\) | 7.50000 | − | 12.9904i | 0.539862 | − | 0.935068i | −0.459049 | − | 0.888411i | \(-0.651810\pi\) |
0.998911 | − | 0.0466572i | \(-0.0148568\pi\) | |||||||
\(194\) | −6.33975 | + | 23.6603i | −0.455167 | + | 1.69871i | ||||
\(195\) | −10.3923 | −0.744208 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.0000 | 1.13995 | 0.569976 | − | 0.821661i | \(-0.306952\pi\) | ||||
0.569976 | + | 0.821661i | \(0.306952\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.2583 | − | 19.5000i | 0.798082 | − | 1.38232i | −0.122782 | − | 0.992434i | \(-0.539182\pi\) |
0.920864 | − | 0.389885i | \(-0.127485\pi\) | |||||||
\(200\) | 5.46410 | − | 1.46410i | 0.386370 | − | 0.103528i | ||||
\(201\) | −4.50000 | + | 2.59808i | −0.317406 | + | 0.183254i | ||||
\(202\) | −8.66025 | − | 8.66025i | −0.609333 | − | 0.609333i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.00000 | −0.420084 | ||||||||
\(205\) | −3.00000 | − | 5.19615i | −0.209529 | − | 0.362915i | ||||
\(206\) | −3.16987 | − | 11.8301i | −0.220856 | − | 0.824244i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.0000 | + | 6.92820i | −0.832050 | + | 0.480384i | ||||
\(209\) | 5.19615i | 0.359425i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000i | 0.688428i | 0.938891 | + | 0.344214i | \(0.111855\pi\) | ||||
−0.938891 | + | 0.344214i | \(0.888145\pi\) | |||||||
\(212\) | 1.73205 | − | 1.00000i | 0.118958 | − | 0.0686803i | ||||
\(213\) | 21.0000 | + | 12.1244i | 1.43890 | + | 0.830747i | ||||
\(214\) | 17.7583 | − | 4.75833i | 1.21393 | − | 0.325273i | ||||
\(215\) | 1.73205 | + | 3.00000i | 0.118125 | + | 0.204598i | ||||
\(216\) | 10.3923 | + | 10.3923i | 0.707107 | + | 0.707107i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 9.00000 | − | 9.00000i | 0.609557 | − | 0.609557i | ||||
\(219\) | 12.9904 | − | 7.50000i | 0.877809 | − | 0.506803i | ||||
\(220\) | 3.00000 | + | 1.73205i | 0.202260 | + | 0.116775i | ||||
\(221\) | −3.00000 | + | 5.19615i | −0.201802 | + | 0.349531i | ||||
\(222\) | −7.09808 | − | 1.90192i | −0.476392 | − | 0.127649i | ||||
\(223\) | 6.92820 | 0.463947 | 0.231973 | − | 0.972722i | \(-0.425482\pi\) | ||||
0.231973 | + | 0.972722i | \(0.425482\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 21.8564 | + | 5.85641i | 1.45387 | + | 0.389562i | ||||
\(227\) | −9.52628 | + | 16.5000i | −0.632281 | + | 1.09514i | 0.354803 | + | 0.934941i | \(0.384548\pi\) |
−0.987084 | + | 0.160202i | \(0.948785\pi\) | |||||||
\(228\) | −15.5885 | − | 9.00000i | −1.03237 | − | 0.596040i | ||||
\(229\) | 13.5000 | − | 7.79423i | 0.892105 | − | 0.515057i | 0.0174746 | − | 0.999847i | \(-0.494437\pi\) |
0.874630 | + | 0.484790i | \(0.161104\pi\) | |||||||
\(230\) | −1.73205 | + | 1.73205i | −0.114208 | + | 0.114208i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.00000 | − | 8.00000i | −0.525226 | − | 0.525226i | ||||
\(233\) | 3.50000 | + | 6.06218i | 0.229293 | + | 0.397146i | 0.957599 | − | 0.288106i | \(-0.0930254\pi\) |
−0.728306 | + | 0.685252i | \(0.759692\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.9904 | − | 7.50000i | −0.847399 | − | 0.489246i | ||||
\(236\) | 9.00000 | − | 5.19615i | 0.585850 | − | 0.338241i | ||||
\(237\) | 15.5885i | 1.01258i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.0000i | 1.29369i | 0.762620 | + | 0.646846i | \(0.223912\pi\) | ||||
−0.762620 | + | 0.646846i | \(0.776088\pi\) | |||||||
\(240\) | −10.3923 | + | 6.00000i | −0.670820 | + | 0.387298i | ||||
\(241\) | 4.50000 | + | 2.59808i | 0.289870 | + | 0.167357i | 0.637883 | − | 0.770133i | \(-0.279810\pi\) |
−0.348013 | + | 0.937490i | \(0.613143\pi\) | |||||||
\(242\) | 3.66025 | + | 13.6603i | 0.235290 | + | 0.878114i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.3923 | 0.665299 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | − | 6.00000i | −0.382546 | − | 0.382546i | ||||
\(247\) | −15.5885 | + | 9.00000i | −0.991870 | + | 0.572656i | ||||
\(248\) | −4.73205 | + | 1.26795i | −0.300486 | + | 0.0805149i | ||||
\(249\) | −12.0000 | + | 20.7846i | −0.760469 | + | 1.31717i | ||||
\(250\) | 4.43782 | − | 16.5622i | 0.280673 | − | 1.04748i | ||||
\(251\) | −3.46410 | −0.218652 | −0.109326 | − | 0.994006i | \(-0.534869\pi\) | ||||
−0.109326 | + | 0.994006i | \(0.534869\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.00000 | 0.0628695 | ||||||||
\(254\) | 2.19615 | − | 8.19615i | 0.137799 | − | 0.514272i | ||||
\(255\) | −2.59808 | + | 4.50000i | −0.162698 | + | 0.281801i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −4.50000 | + | 2.59808i | −0.280702 | + | 0.162064i | −0.633741 | − | 0.773545i | \(-0.718482\pi\) |
0.353039 | + | 0.935609i | \(0.385148\pi\) | |||||||
\(258\) | 3.46410 | + | 3.46410i | 0.215666 | + | 0.215666i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 12.0000i | 0.744208i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.90192 | + | 7.09808i | 0.117501 | + | 0.438521i | ||||
\(263\) | 19.9186 | + | 11.5000i | 1.22823 | + | 0.709120i | 0.966660 | − | 0.256063i | \(-0.0824256\pi\) |
0.261573 | + | 0.965184i | \(0.415759\pi\) | |||||||
\(264\) | 4.73205 | + | 1.26795i | 0.291238 | + | 0.0780369i | ||||
\(265\) | − | 1.73205i | − | 0.106399i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 27.0000i | − | 1.65237i | ||||||
\(268\) | 3.00000 | + | 5.19615i | 0.183254 | + | 0.317406i | ||||
\(269\) | −19.5000 | − | 11.2583i | −1.18894 | − | 0.686433i | −0.230871 | − | 0.972984i | \(-0.574158\pi\) |
−0.958065 | + | 0.286552i | \(0.907491\pi\) | |||||||
\(270\) | 12.2942 | − | 3.29423i | 0.748203 | − | 0.200480i | ||||
\(271\) | 7.79423 | + | 13.5000i | 0.473466 | + | 0.820067i | 0.999539 | − | 0.0303728i | \(-0.00966946\pi\) |
−0.526073 | + | 0.850439i | \(0.676336\pi\) | |||||||
\(272\) | 6.92820i | 0.420084i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.00000 | − | 1.00000i | 0.0604122 | − | 0.0604122i | ||||
\(275\) | −1.73205 | + | 1.00000i | −0.104447 | + | 0.0603023i | ||||
\(276\) | −1.73205 | + | 3.00000i | −0.104257 | + | 0.180579i | ||||
\(277\) | 6.50000 | − | 11.2583i | 0.390547 | − | 0.676448i | −0.601975 | − | 0.798515i | \(-0.705619\pi\) |
0.992522 | + | 0.122068i | \(0.0389525\pi\) | |||||||
\(278\) | 9.46410 | + | 2.53590i | 0.567619 | + | 0.152093i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.00000 | −0.238620 | −0.119310 | − | 0.992857i | \(-0.538068\pi\) | ||||
−0.119310 | + | 0.992857i | \(0.538068\pi\) | |||||||
\(282\) | −20.4904 | − | 5.49038i | −1.22018 | − | 0.326947i | ||||
\(283\) | −6.06218 | + | 10.5000i | −0.360359 | + | 0.624160i | −0.988020 | − | 0.154327i | \(-0.950679\pi\) |
0.627661 | + | 0.778487i | \(0.284012\pi\) | |||||||
\(284\) | 14.0000 | − | 24.2487i | 0.830747 | − | 1.43890i | ||||
\(285\) | −13.5000 | + | 7.79423i | −0.799671 | + | 0.461690i | ||||
\(286\) | 3.46410 | − | 3.46410i | 0.204837 | − | 0.204837i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | − | 12.1244i | −0.411765 | − | 0.713197i | ||||
\(290\) | −9.46410 | + | 2.53590i | −0.555751 | + | 0.148913i | ||||
\(291\) | 25.9808 | + | 15.0000i | 1.52302 | + | 0.879316i | ||||
\(292\) | −8.66025 | − | 15.0000i | −0.506803 | − | 0.877809i | ||||
\(293\) | − | 20.7846i | − | 1.21425i | −0.794606 | − | 0.607125i | \(-0.792323\pi\) | ||
0.794606 | − | 0.607125i | \(-0.207677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 9.00000i | − | 0.524000i | ||||||
\(296\) | −2.19615 | + | 8.19615i | −0.127649 | + | 0.476392i | ||||
\(297\) | −4.50000 | − | 2.59808i | −0.261116 | − | 0.150756i | ||||
\(298\) | 0.366025 | + | 1.36603i | 0.0212033 | + | 0.0791317i | ||||
\(299\) | 1.73205 | + | 3.00000i | 0.100167 | + | 0.173494i | ||||
\(300\) | − | 6.92820i | − | 0.400000i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.00000 | + | 7.00000i | 0.402805 | + | 0.402805i | ||||
\(303\) | −12.9904 | + | 7.50000i | −0.746278 | + | 0.430864i | ||||
\(304\) | −10.3923 | + | 18.0000i | −0.596040 | + | 1.03237i | ||||
\(305\) | 4.50000 | − | 7.79423i | 0.257669 | − | 0.446296i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.7846 | 1.18624 | 0.593120 | − | 0.805114i | \(-0.297896\pi\) | ||||
0.593120 | + | 0.805114i | \(0.297896\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.0000 | −0.853320 | ||||||||
\(310\) | −1.09808 | + | 4.09808i | −0.0623665 | + | 0.232755i | ||||
\(311\) | −4.33013 | + | 7.50000i | −0.245539 | + | 0.425286i | −0.962283 | − | 0.272050i | \(-0.912298\pi\) |
0.716744 | + | 0.697336i | \(0.245632\pi\) | |||||||
\(312\) | 4.39230 | + | 16.3923i | 0.248665 | + | 0.928032i | ||||
\(313\) | −1.50000 | + | 0.866025i | −0.0847850 | + | 0.0489506i | −0.541793 | − | 0.840512i | \(-0.682254\pi\) |
0.457008 | + | 0.889463i | \(0.348921\pi\) | |||||||
\(314\) | 1.73205 | + | 1.73205i | 0.0977453 | + | 0.0977453i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 18.0000 | 1.01258 | ||||||||
\(317\) | −5.50000 | − | 9.52628i | −0.308911 | − | 0.535049i | 0.669214 | − | 0.743070i | \(-0.266631\pi\) |
−0.978124 | + | 0.208021i | \(0.933298\pi\) | |||||||
\(318\) | −0.633975 | − | 2.36603i | −0.0355515 | − | 0.132680i | ||||
\(319\) | 3.46410 | + | 2.00000i | 0.193952 | + | 0.111979i | ||||
\(320\) | 6.92820 | + | 12.0000i | 0.387298 | + | 0.670820i | ||||
\(321\) | − | 22.5167i | − | 1.25676i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.00000i | 0.500773i | ||||||||
\(324\) | 15.5885 | − | 9.00000i | 0.866025 | − | 0.500000i | ||||
\(325\) | −6.00000 | − | 3.46410i | −0.332820 | − | 0.192154i | ||||
\(326\) | −28.6865 | + | 7.68653i | −1.58880 | + | 0.425718i | ||||
\(327\) | −7.79423 | − | 13.5000i | −0.431022 | − | 0.746552i | ||||
\(328\) | −6.92820 | + | 6.92820i | −0.382546 | + | 0.382546i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.00000 | − | 3.00000i | 0.165145 | − | 0.165145i | ||||
\(331\) | −6.06218 | + | 3.50000i | −0.333207 | + | 0.192377i | −0.657264 | − | 0.753660i | \(-0.728286\pi\) |
0.324057 | + | 0.946038i | \(0.394953\pi\) | |||||||
\(332\) | 24.0000 | + | 13.8564i | 1.31717 | + | 0.760469i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 23.6603 | + | 6.33975i | 1.29463 | + | 0.346895i | ||||
\(335\) | 5.19615 | 0.283896 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | −1.36603 | − | 0.366025i | −0.0743020 | − | 0.0199092i | ||||
\(339\) | 13.8564 | − | 24.0000i | 0.752577 | − | 1.30350i | ||||
\(340\) | 5.19615 | + | 3.00000i | 0.281801 | + | 0.162698i | ||||
\(341\) | 1.50000 | − | 0.866025i | 0.0812296 | − | 0.0468979i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.00000 | − | 4.00000i | 0.215666 | − | 0.215666i | ||||
\(345\) | 1.50000 | + | 2.59808i | 0.0807573 | + | 0.139876i | ||||
\(346\) | −16.5622 | + | 4.43782i | −0.890388 | + | 0.238579i | ||||
\(347\) | −11.2583 | − | 6.50000i | −0.604379 | − | 0.348938i | 0.166383 | − | 0.986061i | \(-0.446791\pi\) |
−0.770762 | + | 0.637123i | \(0.780124\pi\) | |||||||
\(348\) | −12.0000 | + | 6.92820i | −0.643268 | + | 0.371391i | ||||
\(349\) | 10.3923i | 0.556287i | 0.960539 | + | 0.278144i | \(0.0897191\pi\) | ||||
−0.960539 | + | 0.278144i | \(0.910281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 18.0000i | − | 0.960769i | ||||||
\(352\) | 1.46410 | − | 5.46410i | 0.0780369 | − | 0.291238i | ||||
\(353\) | 25.5000 | + | 14.7224i | 1.35723 | + | 0.783596i | 0.989249 | − | 0.146238i | \(-0.0467166\pi\) |
0.367979 | + | 0.929834i | \(0.380050\pi\) | |||||||
\(354\) | −3.29423 | − | 12.2942i | −0.175086 | − | 0.653431i | ||||
\(355\) | −12.1244 | − | 21.0000i | −0.643494 | − | 1.11456i | ||||
\(356\) | −31.1769 | −1.65237 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.0000 | + | 19.0000i | 1.00418 | + | 1.00418i | ||||
\(359\) | 19.9186 | − | 11.5000i | 1.05126 | − | 0.606947i | 0.128260 | − | 0.991741i | \(-0.459061\pi\) |
0.923003 | + | 0.384794i | \(0.125727\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.00000 | + | 6.92820i | −0.210526 | + | 0.364642i | ||||
\(362\) | 2.53590 | − | 9.46410i | 0.133284 | − | 0.497422i | ||||
\(363\) | 17.3205 | 0.909091 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.0000 | −0.785136 | ||||||||
\(366\) | 3.29423 | − | 12.2942i | 0.172192 | − | 0.642630i | ||||
\(367\) | −0.866025 | + | 1.50000i | −0.0452062 | + | 0.0782994i | −0.887743 | − | 0.460339i | \(-0.847728\pi\) |
0.842537 | + | 0.538639i | \(0.181061\pi\) | |||||||
\(368\) | 3.46410 | + | 2.00000i | 0.180579 | + | 0.104257i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.19615 | + | 5.19615i | 0.270135 | + | 0.270135i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 6.00000i | 0.311086i | ||||||||
\(373\) | 14.5000 | + | 25.1147i | 0.750782 | + | 1.30039i | 0.947444 | + | 0.319921i | \(0.103656\pi\) |
−0.196663 | + | 0.980471i | \(0.563010\pi\) | |||||||
\(374\) | −0.633975 | − | 2.36603i | −0.0327820 | − | 0.122344i | ||||
\(375\) | −18.1865 | − | 10.5000i | −0.939149 | − | 0.542218i | ||||
\(376\) | −6.33975 | + | 23.6603i | −0.326947 | + | 1.22018i | ||||
\(377\) | 13.8564i | 0.713641i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 8.00000i | − | 0.410932i | −0.978664 | − | 0.205466i | \(-0.934129\pi\) | ||
0.978664 | − | 0.205466i | \(-0.0658711\pi\) | |||||||
\(380\) | 9.00000 | + | 15.5885i | 0.461690 | + | 0.799671i | ||||
\(381\) | −9.00000 | − | 5.19615i | −0.461084 | − | 0.266207i | ||||
\(382\) | 1.36603 | − | 0.366025i | 0.0698919 | − | 0.0187275i | ||||
\(383\) | 2.59808 | + | 4.50000i | 0.132755 | + | 0.229939i | 0.924738 | − | 0.380605i | \(-0.124284\pi\) |
−0.791982 | + | 0.610544i | \(0.790951\pi\) | |||||||
\(384\) | 13.8564 | + | 13.8564i | 0.707107 | + | 0.707107i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.0000 | + | 15.0000i | −0.763480 | + | 0.763480i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.3205 | − | 30.0000i | 0.879316 | − | 1.52302i | ||||
\(389\) | 9.50000 | − | 16.4545i | 0.481669 | − | 0.834275i | −0.518110 | − | 0.855314i | \(-0.673364\pi\) |
0.999779 | + | 0.0210389i | \(0.00669738\pi\) | |||||||
\(390\) | 14.1962 | + | 3.80385i | 0.718850 | + | 0.192615i | ||||
\(391\) | 1.73205 | 0.0875936 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.00000 | 0.453990 | ||||||||
\(394\) | −21.8564 | − | 5.85641i | −1.10111 | − | 0.295041i | ||||
\(395\) | 7.79423 | − | 13.5000i | 0.392170 | − | 0.679259i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.5000 | + | 9.52628i | −0.828111 | + | 0.478110i | −0.853206 | − | 0.521575i | \(-0.825345\pi\) |
0.0250943 | + | 0.999685i | \(0.492011\pi\) | |||||||
\(398\) | −22.5167 | + | 22.5167i | −1.12866 | + | 1.12866i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.00000 | −0.400000 | ||||||||
\(401\) | 11.5000 | + | 19.9186i | 0.574283 | + | 0.994687i | 0.996119 | + | 0.0880147i | \(0.0280523\pi\) |
−0.421837 | + | 0.906672i | \(0.638614\pi\) | |||||||
\(402\) | 7.09808 | − | 1.90192i | 0.354020 | − | 0.0948593i | ||||
\(403\) | 5.19615 | + | 3.00000i | 0.258839 | + | 0.149441i | ||||
\(404\) | 8.66025 | + | 15.0000i | 0.430864 | + | 0.746278i | ||||
\(405\) | − | 15.5885i | − | 0.774597i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.00000i | − | 0.148704i | ||||||
\(408\) | 8.19615 | + | 2.19615i | 0.405770 | + | 0.108726i | ||||
\(409\) | −22.5000 | − | 12.9904i | −1.11255 | − | 0.642333i | −0.173064 | − | 0.984911i | \(-0.555367\pi\) |
−0.939490 | + | 0.342578i | \(0.888700\pi\) | |||||||
\(410\) | 2.19615 | + | 8.19615i | 0.108460 | + | 0.404779i | ||||
\(411\) | −0.866025 | − | 1.50000i | −0.0427179 | − | 0.0739895i | ||||
\(412\) | 17.3205i | 0.853320i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.7846 | − | 12.0000i | 1.02028 | − | 0.589057i | ||||
\(416\) | 18.9282 | − | 5.07180i | 0.928032 | − | 0.248665i | ||||
\(417\) | 6.00000 | − | 10.3923i | 0.293821 | − | 0.508913i | ||||
\(418\) | 1.90192 | − | 7.09808i | 0.0930261 | − | 0.347178i | ||||
\(419\) | −20.7846 | −1.01539 | −0.507697 | − | 0.861536i | \(-0.669503\pi\) | ||||
−0.507697 | + | 0.861536i | \(0.669503\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0000 | −0.974740 | −0.487370 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487370 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(422\) | 3.66025 | − | 13.6603i | 0.178178 | − | 0.664971i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.73205 | + | 0.732051i | −0.132680 | + | 0.0355515i | ||||
\(425\) | −3.00000 | + | 1.73205i | −0.145521 | + | 0.0840168i | ||||
\(426\) | −24.2487 | − | 24.2487i | −1.17485 | − | 1.17485i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −26.0000 | −1.25676 | ||||||||
\(429\) | −3.00000 | − | 5.19615i | −0.144841 | − | 0.250873i | ||||
\(430\) | −1.26795 | − | 4.73205i | −0.0611459 | − | 0.228200i | ||||
\(431\) | −19.9186 | − | 11.5000i | −0.959444 | − | 0.553936i | −0.0634424 | − | 0.997985i | \(-0.520208\pi\) |
−0.896002 | + | 0.444050i | \(0.853541\pi\) | |||||||
\(432\) | −10.3923 | − | 18.0000i | −0.500000 | − | 0.866025i | ||||
\(433\) | − | 10.3923i | − | 0.499422i | −0.968320 | − | 0.249711i | \(-0.919664\pi\) | ||
0.968320 | − | 0.249711i | \(-0.0803357\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.0000i | 0.575356i | ||||||||
\(436\) | −15.5885 | + | 9.00000i | −0.746552 | + | 0.431022i | ||||
\(437\) | 4.50000 | + | 2.59808i | 0.215264 | + | 0.124283i | ||||
\(438\) | −20.4904 | + | 5.49038i | −0.979068 | + | 0.262341i | ||||
\(439\) | −11.2583 | − | 19.5000i | −0.537331 | − | 0.930684i | −0.999047 | − | 0.0436563i | \(-0.986099\pi\) |
0.461716 | − | 0.887028i | \(-0.347234\pi\) | |||||||
\(440\) | −3.46410 | − | 3.46410i | −0.165145 | − | 0.165145i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.00000 | − | 6.00000i | 0.285391 | − | 0.285391i | ||||
\(443\) | −14.7224 | + | 8.50000i | −0.699484 | + | 0.403847i | −0.807155 | − | 0.590339i | \(-0.798994\pi\) |
0.107671 | + | 0.994187i | \(0.465661\pi\) | |||||||
\(444\) | 9.00000 | + | 5.19615i | 0.427121 | + | 0.246598i | ||||
\(445\) | −13.5000 | + | 23.3827i | −0.639961 | + | 1.10845i | ||||
\(446\) | −9.46410 | − | 2.53590i | −0.448138 | − | 0.120078i | ||||
\(447\) | 1.73205 | 0.0819232 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.00000 | 0.377543 | 0.188772 | − | 0.982021i | \(-0.439549\pi\) | ||||
0.188772 | + | 0.982021i | \(0.439549\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.73205 | − | 3.00000i | 0.0815591 | − | 0.141264i | ||||
\(452\) | −27.7128 | − | 16.0000i | −1.30350 | − | 0.752577i | ||||
\(453\) | 10.5000 | − | 6.06218i | 0.493333 | − | 0.284826i | ||||
\(454\) | 19.0526 | − | 19.0526i | 0.894181 | − | 0.894181i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 18.0000 | + | 18.0000i | 0.842927 | + | 0.842927i | ||||
\(457\) | −7.50000 | − | 12.9904i | −0.350835 | − | 0.607664i | 0.635561 | − | 0.772051i | \(-0.280769\pi\) |
−0.986396 | + | 0.164386i | \(0.947436\pi\) | |||||||
\(458\) | −21.2942 | + | 5.70577i | −0.995014 | + | 0.266613i | ||||
\(459\) | −7.79423 | − | 4.50000i | −0.363803 | − | 0.210042i | ||||
\(460\) | 3.00000 | − | 1.73205i | 0.139876 | − | 0.0807573i | ||||
\(461\) | − | 17.3205i | − | 0.806696i | −0.915047 | − | 0.403348i | \(-0.867846\pi\) | ||
0.915047 | − | 0.403348i | \(-0.132154\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 30.0000i | − | 1.39422i | −0.716965 | − | 0.697109i | \(-0.754469\pi\) | ||
0.716965 | − | 0.697109i | \(-0.245531\pi\) | |||||||
\(464\) | 8.00000 | + | 13.8564i | 0.371391 | + | 0.643268i | ||||
\(465\) | 4.50000 | + | 2.59808i | 0.208683 | + | 0.120483i | ||||
\(466\) | −2.56218 | − | 9.56218i | −0.118691 | − | 0.442959i | ||||
\(467\) | 4.33013 | + | 7.50000i | 0.200374 | + | 0.347059i | 0.948649 | − | 0.316330i | \(-0.102451\pi\) |
−0.748275 | + | 0.663389i | \(0.769117\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 15.0000 | + | 15.0000i | 0.691898 | + | 0.691898i | ||||
\(471\) | 2.59808 | − | 1.50000i | 0.119713 | − | 0.0691164i | ||||
\(472\) | −14.1962 | + | 3.80385i | −0.653431 | + | 0.175086i | ||||
\(473\) | −1.00000 | + | 1.73205i | −0.0459800 | + | 0.0796398i | ||||
\(474\) | 5.70577 | − | 21.2942i | 0.262075 | − | 0.978076i | ||||
\(475\) | −10.3923 | −0.476832 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.32051 | − | 27.3205i | 0.334832 | − | 1.24961i | ||||
\(479\) | 6.06218 | − | 10.5000i | 0.276988 | − | 0.479757i | −0.693647 | − | 0.720315i | \(-0.743997\pi\) |
0.970635 | + | 0.240558i | \(0.0773304\pi\) | |||||||
\(480\) | 16.3923 | − | 4.39230i | 0.748203 | − | 0.200480i | ||||
\(481\) | 9.00000 | − | 5.19615i | 0.410365 | − | 0.236924i | ||||
\(482\) | −5.19615 | − | 5.19615i | −0.236678 | − | 0.236678i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 20.0000i | − | 0.909091i | ||||||
\(485\) | −15.0000 | − | 25.9808i | −0.681115 | − | 1.17973i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.8468 | + | 15.5000i | 1.21654 | + | 0.702372i | 0.964177 | − | 0.265260i | \(-0.0854576\pi\) |
0.252367 | + | 0.967632i | \(0.418791\pi\) | |||||||
\(488\) | −14.1962 | − | 3.80385i | −0.642630 | − | 0.172192i | ||||
\(489\) | 36.3731i | 1.64485i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.0000i | 1.44414i | 0.691820 | + | 0.722070i | \(0.256809\pi\) | ||||
−0.691820 | + | 0.722070i | \(0.743191\pi\) | |||||||
\(492\) | 6.00000 | + | 10.3923i | 0.270501 | + | 0.468521i | ||||
\(493\) | 6.00000 | + | 3.46410i | 0.270226 | + | 0.156015i | ||||
\(494\) | 24.5885 | − | 6.58846i | 1.10629 | − | 0.296429i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.92820 | 0.311086 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 24.0000 | − | 24.0000i | 1.07547 | − | 1.07547i | ||||
\(499\) | −30.3109 | + | 17.5000i | −1.35690 | + | 0.783408i | −0.989205 | − | 0.146538i | \(-0.953187\pi\) |
−0.367697 | + | 0.929946i | \(0.619854\pi\) | |||||||
\(500\) | −12.1244 | + | 21.0000i | −0.542218 | + | 0.939149i | ||||
\(501\) | 15.0000 | − | 25.9808i | 0.670151 | − | 1.16073i | ||||
\(502\) | 4.73205 | + | 1.26795i | 0.211202 | + | 0.0565913i | ||||
\(503\) | −6.92820 | −0.308913 | −0.154457 | − | 0.988000i | \(-0.549363\pi\) | ||||
−0.154457 | + | 0.988000i | \(0.549363\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.0000 | 0.667491 | ||||||||
\(506\) | −1.36603 | − | 0.366025i | −0.0607272 | − | 0.0162718i | ||||
\(507\) | −0.866025 | + | 1.50000i | −0.0384615 | + | 0.0666173i | ||||
\(508\) | −6.00000 | + | 10.3923i | −0.266207 | + | 0.461084i | ||||
\(509\) | −10.5000 | + | 6.06218i | −0.465404 | + | 0.268701i | −0.714314 | − | 0.699825i | \(-0.753261\pi\) |
0.248910 | + | 0.968527i | \(0.419928\pi\) | |||||||
\(510\) | 5.19615 | − | 5.19615i | 0.230089 | − | 0.230089i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.707107 | − | 0.707107i | ||||
\(513\) | −13.5000 | − | 23.3827i | −0.596040 | − | 1.03237i | ||||
\(514\) | 7.09808 | − | 1.90192i | 0.313083 | − | 0.0838903i | ||||
\(515\) | 12.9904 | + | 7.50000i | 0.572425 | + | 0.330489i | ||||
\(516\) | −3.46410 | − | 6.00000i | −0.152499 | − | 0.264135i | ||||
\(517\) | − | 8.66025i | − | 0.380878i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.0000i | 0.921798i | ||||||||
\(520\) | 4.39230 | − | 16.3923i | 0.192615 | − | 0.718850i | ||||
\(521\) | −1.50000 | − | 0.866025i | −0.0657162 | − | 0.0379413i | 0.466782 | − | 0.884372i | \(-0.345413\pi\) |
−0.532498 | + | 0.846431i | \(0.678747\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.9904 | + | 22.5000i | 0.568030 | + | 0.983856i | 0.996761 | + | 0.0804241i | \(0.0256275\pi\) |
−0.428731 | + | 0.903432i | \(0.641039\pi\) | |||||||
\(524\) | − | 10.3923i | − | 0.453990i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −23.0000 | − | 23.0000i | −1.00285 | − | 1.00285i | ||||
\(527\) | 2.59808 | − | 1.50000i | 0.113174 | − | 0.0653410i | ||||
\(528\) | −6.00000 | − | 3.46410i | −0.261116 | − | 0.150756i | ||||
\(529\) | −11.0000 | + | 19.0526i | −0.478261 | + | 0.828372i | ||||
\(530\) | −0.633975 | + | 2.36603i | −0.0275381 | + | 0.102774i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000 | 0.519778 | ||||||||
\(534\) | −9.88269 | + | 36.8827i | −0.427666 | + | 1.59607i | ||||
\(535\) | −11.2583 | + | 19.5000i | −0.486740 | + | 0.843059i | ||||
\(536\) | −2.19615 | − | 8.19615i | −0.0948593 | − | 0.354020i | ||||
\(537\) | 28.5000 | − | 16.4545i | 1.22987 | − | 0.710063i | ||||
\(538\) | 22.5167 | + | 22.5167i | 0.970762 | + | 0.970762i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −18.0000 | −0.774597 | ||||||||
\(541\) | 9.50000 | + | 16.4545i | 0.408437 | + | 0.707433i | 0.994715 | − | 0.102677i | \(-0.0327407\pi\) |
−0.586278 | + | 0.810110i | \(0.699407\pi\) | |||||||
\(542\) | −5.70577 | − | 21.2942i | −0.245084 | − | 0.914665i | ||||
\(543\) | −10.3923 | − | 6.00000i | −0.445976 | − | 0.257485i | ||||
\(544\) | 2.53590 | − | 9.46410i | 0.108726 | − | 0.405770i | ||||
\(545\) | 15.5885i | 0.667736i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | −1.73205 | + | 1.00000i | −0.0739895 | + | 0.0427179i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.73205 | − | 0.732051i | 0.116495 | − | 0.0312148i | ||||
\(551\) | 10.3923 | + | 18.0000i | 0.442727 | + | 0.766826i | ||||
\(552\) | 3.46410 | − | 3.46410i | 0.147442 | − | 0.147442i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −13.0000 | + | 13.0000i | −0.552317 | + | 0.552317i | ||||
\(555\) | 7.79423 | − | 4.50000i | 0.330847 | − | 0.191014i | ||||
\(556\) | −12.0000 | − | 6.92820i | −0.508913 | − | 0.293821i | ||||
\(557\) | −18.5000 | + | 32.0429i | −0.783870 | + | 1.35770i | 0.145802 | + | 0.989314i | \(0.453424\pi\) |
−0.929672 | + | 0.368389i | \(0.879909\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.92820 | −0.293032 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.00000 | −0.126660 | ||||||||
\(562\) | 5.46410 | + | 1.46410i | 0.230489 | + | 0.0617594i | ||||
\(563\) | −11.2583 | + | 19.5000i | −0.474482 | + | 0.821827i | −0.999573 | − | 0.0292191i | \(-0.990698\pi\) |
0.525091 | + | 0.851046i | \(0.324031\pi\) | |||||||
\(564\) | 25.9808 | + | 15.0000i | 1.09399 | + | 0.631614i | ||||
\(565\) | −24.0000 | + | 13.8564i | −1.00969 | + | 0.582943i | ||||
\(566\) | 12.1244 | − | 12.1244i | 0.509625 | − | 0.509625i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −28.0000 | + | 28.0000i | −1.17485 | + | 1.17485i | ||||
\(569\) | 6.50000 | + | 11.2583i | 0.272494 | + | 0.471974i | 0.969500 | − | 0.245092i | \(-0.0788181\pi\) |
−0.697006 | + | 0.717066i | \(0.745485\pi\) | |||||||
\(570\) | 21.2942 | − | 5.70577i | 0.891917 | − | 0.238988i | ||||
\(571\) | 18.1865 | + | 10.5000i | 0.761083 | + | 0.439411i | 0.829684 | − | 0.558233i | \(-0.188520\pi\) |
−0.0686016 | + | 0.997644i | \(0.521854\pi\) | |||||||
\(572\) | −6.00000 | + | 3.46410i | −0.250873 | + | 0.144841i | ||||
\(573\) | − | 1.73205i | − | 0.0723575i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.00000i | 0.0834058i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.5000 | + | 16.4545i | 1.18647 | + | 0.685009i | 0.957503 | − | 0.288425i | \(-0.0931316\pi\) |
0.228968 | + | 0.973434i | \(0.426465\pi\) | |||||||
\(578\) | 5.12436 | + | 19.1244i | 0.213145 | + | 0.795468i | ||||
\(579\) | 12.9904 | + | 22.5000i | 0.539862 | + | 0.935068i | ||||
\(580\) | 13.8564 | 0.575356 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −30.0000 | − | 30.0000i | −1.24354 | − | 1.24354i | ||||
\(583\) | 0.866025 | − | 0.500000i | 0.0358671 | − | 0.0207079i | ||||
\(584\) | 6.33975 | + | 23.6603i | 0.262341 | + | 0.979068i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.60770 | + | 28.3923i | −0.314271 | + | 1.17288i | ||||
\(587\) | 6.92820 | 0.285958 | 0.142979 | − | 0.989726i | \(-0.454332\pi\) | ||||
0.142979 | + | 0.989726i | \(0.454332\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.00000 | 0.370839 | ||||||||
\(590\) | −3.29423 | + | 12.2942i | −0.135621 | + | 0.506145i | ||||
\(591\) | −13.8564 | + | 24.0000i | −0.569976 | + | 0.987228i | ||||
\(592\) | 6.00000 | − | 10.3923i | 0.246598 | − | 0.427121i | ||||
\(593\) | 13.5000 | − | 7.79423i | 0.554379 | − | 0.320071i | −0.196508 | − | 0.980502i | \(-0.562960\pi\) |
0.750886 | + | 0.660432i | \(0.229627\pi\) | |||||||
\(594\) | 5.19615 | + | 5.19615i | 0.213201 | + | 0.213201i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 2.00000i | − | 0.0819232i | ||||||
\(597\) | 19.5000 | + | 33.7750i | 0.798082 | + | 1.38232i | ||||
\(598\) | −1.26795 | − | 4.73205i | −0.0518503 | − | 0.193508i | ||||
\(599\) | −14.7224 | − | 8.50000i | −0.601542 | − | 0.347301i | 0.168106 | − | 0.985769i | \(-0.446235\pi\) |
−0.769648 | + | 0.638468i | \(0.779568\pi\) | |||||||
\(600\) | −2.53590 | + | 9.46410i | −0.103528 | + | 0.386370i | ||||
\(601\) | 38.1051i | 1.55434i | 0.629291 | + | 0.777170i | \(0.283346\pi\) | ||||
−0.629291 | + | 0.777170i | \(0.716654\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.00000 | − | 12.1244i | −0.284826 | − | 0.493333i | ||||
\(605\) | −15.0000 | − | 8.66025i | −0.609837 | − | 0.352089i | ||||
\(606\) | 20.4904 | − | 5.49038i | 0.832365 | − | 0.223031i | ||||
\(607\) | −7.79423 | − | 13.5000i | −0.316358 | − | 0.547948i | 0.663367 | − | 0.748294i | \(-0.269127\pi\) |
−0.979725 | + | 0.200346i | \(0.935793\pi\) | |||||||
\(608\) | 20.7846 | − | 20.7846i | 0.842927 | − | 0.842927i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.00000 | + | 9.00000i | −0.364399 | + | 0.364399i | ||||
\(611\) | 25.9808 | − | 15.0000i | 1.05107 | − | 0.606835i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.5000 | − | 26.8468i | 0.626039 | − | 1.08433i | −0.362300 | − | 0.932062i | \(-0.618008\pi\) |
0.988339 | − | 0.152270i | \(-0.0486583\pi\) | |||||||
\(614\) | −28.3923 | − | 7.60770i | −1.14582 | − | 0.307022i | ||||
\(615\) | 10.3923 | 0.419058 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.0000 | 0.805170 | 0.402585 | − | 0.915383i | \(-0.368112\pi\) | ||||
0.402585 | + | 0.915383i | \(0.368112\pi\) | |||||||
\(618\) | 20.4904 | + | 5.49038i | 0.824244 | + | 0.220856i | ||||
\(619\) | −7.79423 | + | 13.5000i | −0.313276 | + | 0.542611i | −0.979070 | − | 0.203526i | \(-0.934760\pi\) |
0.665793 | + | 0.746136i | \(0.268093\pi\) | |||||||
\(620\) | 3.00000 | − | 5.19615i | 0.120483 | − | 0.208683i | ||||
\(621\) | −4.50000 | + | 2.59808i | −0.180579 | + | 0.104257i | ||||
\(622\) | 8.66025 | − | 8.66025i | 0.347245 | − | 0.347245i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 24.0000i | − | 0.960769i | ||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 2.36603 | − | 0.633975i | 0.0945654 | − | 0.0253387i | ||||
\(627\) | −7.79423 | − | 4.50000i | −0.311272 | − | 0.179713i | ||||
\(628\) | −1.73205 | − | 3.00000i | −0.0691164 | − | 0.119713i | ||||
\(629\) | − | 5.19615i | − | 0.207184i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.0000i | 1.19428i | 0.802137 | + | 0.597141i | \(0.203697\pi\) | ||||
−0.802137 | + | 0.597141i | \(0.796303\pi\) | |||||||
\(632\) | −24.5885 | − | 6.58846i | −0.978076 | − | 0.262075i | ||||
\(633\) | −15.0000 | − | 8.66025i | −0.596196 | − | 0.344214i | ||||
\(634\) | 4.02628 | + | 15.0263i | 0.159904 | + | 0.596770i | ||||
\(635\) | 5.19615 | + | 9.00000i | 0.206203 | + | 0.357154i | ||||
\(636\) | 3.46410i | 0.137361i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.00000 | − | 4.00000i | −0.158362 | − | 0.158362i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.07180 | − | 18.9282i | −0.200480 | − | 0.748203i | ||||
\(641\) | 6.50000 | − | 11.2583i | 0.256735 | − | 0.444677i | −0.708631 | − | 0.705580i | \(-0.750687\pi\) |
0.965365 | + | 0.260902i | \(0.0840201\pi\) | |||||||
\(642\) | −8.24167 | + | 30.7583i | −0.325273 | + | 1.21393i | ||||
\(643\) | −13.8564 | −0.546443 | −0.273222 | − | 0.961951i | \(-0.588089\pi\) | ||||
−0.273222 | + | 0.961951i | \(0.588089\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.00000 | −0.236250 | ||||||||
\(646\) | 3.29423 | − | 12.2942i | 0.129610 | − | 0.483710i | ||||
\(647\) | 16.4545 | − | 28.5000i | 0.646892 | − | 1.12045i | −0.336968 | − | 0.941516i | \(-0.609402\pi\) |
0.983861 | − | 0.178935i | \(-0.0572651\pi\) | |||||||
\(648\) | −24.5885 | + | 6.58846i | −0.965926 | + | 0.258819i | ||||
\(649\) | 4.50000 | − | 2.59808i | 0.176640 | − | 0.101983i | ||||
\(650\) | 6.92820 | + | 6.92820i | 0.271746 | + | 0.271746i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 42.0000 | 1.64485 | ||||||||
\(653\) | −15.5000 | − | 26.8468i | −0.606562 | − | 1.05060i | −0.991803 | − | 0.127780i | \(-0.959215\pi\) |
0.385241 | − | 0.922816i | \(-0.374118\pi\) | |||||||
\(654\) | 5.70577 | + | 21.2942i | 0.223113 | + | 0.832670i | ||||
\(655\) | −7.79423 | − | 4.50000i | −0.304546 | − | 0.175830i | ||||
\(656\) | 12.0000 | − | 6.92820i | 0.468521 | − | 0.270501i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 38.0000i | − | 1.48027i | −0.672458 | − | 0.740135i | \(-0.734762\pi\) | ||
0.672458 | − | 0.740135i | \(-0.265238\pi\) | |||||||
\(660\) | −5.19615 | + | 3.00000i | −0.202260 | + | 0.116775i | ||||
\(661\) | 34.5000 | + | 19.9186i | 1.34189 | + | 0.774743i | 0.987085 | − | 0.160196i | \(-0.0512125\pi\) |
0.354809 | + | 0.934939i | \(0.384546\pi\) | |||||||
\(662\) | 9.56218 | − | 2.56218i | 0.371645 | − | 0.0995819i | ||||
\(663\) | −5.19615 | − | 9.00000i | −0.201802 | − | 0.349531i | ||||
\(664\) | −27.7128 | − | 27.7128i | −1.07547 | − | 1.07547i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.46410 | − | 2.00000i | 0.134131 | − | 0.0774403i | ||||
\(668\) | −30.0000 | − | 17.3205i | −1.16073 | − | 0.670151i | ||||
\(669\) | −6.00000 | + | 10.3923i | −0.231973 | + | 0.401790i | ||||
\(670\) | −7.09808 | − | 1.90192i | −0.274223 | − | 0.0734777i | ||||
\(671\) | 5.19615 | 0.200595 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.0000 | 0.925132 | 0.462566 | − | 0.886585i | \(-0.346929\pi\) | ||||
0.462566 | + | 0.886585i | \(0.346929\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.19615 | − | 9.00000i | 0.200000 | − | 0.346410i | ||||
\(676\) | 1.73205 | + | 1.00000i | 0.0666173 | + | 0.0384615i | ||||
\(677\) | 37.5000 | − | 21.6506i | 1.44124 | − | 0.832102i | 0.443309 | − | 0.896369i | \(-0.353804\pi\) |
0.997933 | + | 0.0642672i | \(0.0204710\pi\) | |||||||
\(678\) | −27.7128 | + | 27.7128i | −1.06430 | + | 1.06430i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.00000 | − | 6.00000i | −0.230089 | − | 0.230089i | ||||
\(681\) | −16.5000 | − | 28.5788i | −0.632281 | − | 1.09514i | ||||
\(682\) | −2.36603 | + | 0.633975i | −0.0905998 | + | 0.0242761i | ||||
\(683\) | 21.6506 | + | 12.5000i | 0.828439 | + | 0.478299i | 0.853318 | − | 0.521391i | \(-0.174587\pi\) |
−0.0248792 | + | 0.999690i | \(0.507920\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.73205i | 0.0661783i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.0000i | 1.03011i | ||||||||
\(688\) | −6.92820 | + | 4.00000i | −0.264135 | + | 0.152499i | ||||
\(689\) | 3.00000 | + | 1.73205i | 0.114291 | + | 0.0659859i | ||||
\(690\) | −1.09808 | − | 4.09808i | −0.0418030 | − | 0.156011i | ||||
\(691\) | −6.06218 | − | 10.5000i | −0.230616 | − | 0.399439i | 0.727373 | − | 0.686242i | \(-0.240741\pi\) |
−0.957990 | + | 0.286803i | \(0.907407\pi\) | |||||||
\(692\) | 24.2487 | 0.921798 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.0000 | + | 13.0000i | 0.493473 | + | 0.493473i | ||||
\(695\) | −10.3923 | + | 6.00000i | −0.394203 | + | 0.227593i | ||||
\(696\) | 18.9282 | − | 5.07180i | 0.717472 | − | 0.192246i | ||||
\(697\) | 3.00000 | − | 5.19615i | 0.113633 | − | 0.196818i | ||||
\(698\) | 3.80385 | − | 14.1962i | 0.143978 | − | 0.537332i | ||||
\(699\) | −12.1244 | −0.458585 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.0000 | −0.982006 | −0.491003 | − | 0.871158i | \(-0.663370\pi\) | ||||
−0.491003 | + | 0.871158i | \(0.663370\pi\) | |||||||
\(702\) | −6.58846 | + | 24.5885i | −0.248665 | + | 0.928032i | ||||
\(703\) | 7.79423 | − | 13.5000i | 0.293965 | − | 0.509162i | ||||
\(704\) | −4.00000 | + | 6.92820i | −0.150756 | + | 0.261116i | ||||
\(705\) | 22.5000 | − | 12.9904i | 0.847399 | − | 0.489246i | ||||
\(706\) | −29.4449 | − | 29.4449i | −1.10817 | − | 1.10817i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 18.0000i | 0.676481i | ||||||||
\(709\) | 4.50000 | + | 7.79423i | 0.169001 | + | 0.292718i | 0.938069 | − | 0.346449i | \(-0.112613\pi\) |
−0.769068 | + | 0.639167i | \(0.779279\pi\) | |||||||
\(710\) | 8.87564 | + | 33.1244i | 0.333097 | + | 1.24313i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 42.5885 | + | 11.4115i | 1.59607 | + | 0.427666i | ||||
\(713\) | − | 1.73205i | − | 0.0648658i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000i | 0.224387i | ||||||||
\(716\) | −19.0000 | − | 32.9090i | −0.710063 | − | 1.22987i | ||||
\(717\) | −30.0000 | − | 17.3205i | −1.12037 | − | 0.646846i | ||||
\(718\) | −31.4186 | + | 8.41858i | −1.17253 | + | 0.314179i | ||||
\(719\) | −12.9904 | − | 22.5000i | −0.484459 | − | 0.839108i | 0.515381 | − | 0.856961i | \(-0.327650\pi\) |
−0.999841 | + | 0.0178527i | \(0.994317\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 8.00000 | − | 8.00000i | 0.297729 | − | 0.297729i | ||||
\(723\) | −7.79423 | + | 4.50000i | −0.289870 | + | 0.167357i | ||||
\(724\) | −6.92820 | + | 12.0000i | −0.257485 | + | 0.445976i | ||||
\(725\) | −4.00000 | + | 6.92820i | −0.148556 | + | 0.257307i | ||||
\(726\) | −23.6603 | − | 6.33975i | −0.878114 | − | 0.235290i | ||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 20.4904 | + | 5.49038i | 0.758383 | + | 0.203208i | ||||
\(731\) | −1.73205 | + | 3.00000i | −0.0640622 | + | 0.110959i | ||||
\(732\) | −9.00000 | + | 15.5885i | −0.332650 | + | 0.576166i | ||||
\(733\) | −37.5000 | + | 21.6506i | −1.38509 | + | 0.799684i | −0.992757 | − | 0.120137i | \(-0.961667\pi\) |
−0.392337 | + | 0.919822i | \(0.628333\pi\) | |||||||
\(734\) | 1.73205 | − | 1.73205i | 0.0639312 | − | 0.0639312i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.00000 | − | 4.00000i | −0.147442 | − | 0.147442i | ||||
\(737\) | 1.50000 | + | 2.59808i | 0.0552532 | + | 0.0957014i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.1673 | − | 25.5000i | −1.62472 | − | 0.938033i | −0.985634 | − | 0.168898i | \(-0.945979\pi\) |
−0.639087 | − | 0.769135i | \(-0.720687\pi\) | |||||||
\(740\) | −5.19615 | − | 9.00000i | −0.191014 | − | 0.330847i | ||||
\(741\) | − | 31.1769i | − | 1.14531i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 34.0000i | − | 1.24734i | −0.781688 | − | 0.623670i | \(-0.785641\pi\) | ||
0.781688 | − | 0.623670i | \(-0.214359\pi\) | |||||||
\(744\) | 2.19615 | − | 8.19615i | 0.0805149 | − | 0.300486i | ||||
\(745\) | −1.50000 | − | 0.866025i | −0.0549557 | − | 0.0317287i | ||||
\(746\) | −10.6147 | − | 39.6147i | −0.388633 | − | 1.45040i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.46410i | 0.126660i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 21.0000 | + | 21.0000i | 0.766812 | + | 0.766812i | ||||
\(751\) | −21.6506 | + | 12.5000i | −0.790043 | + | 0.456131i | −0.839978 | − | 0.542621i | \(-0.817432\pi\) |
0.0499348 | + | 0.998752i | \(0.484099\pi\) | |||||||
\(752\) | 17.3205 | − | 30.0000i | 0.631614 | − | 1.09399i | ||||
\(753\) | 3.00000 | − | 5.19615i | 0.109326 | − | 0.189358i | ||||
\(754\) | 5.07180 | − | 18.9282i | 0.184704 | − | 0.689325i | ||||
\(755\) | −12.1244 | −0.441250 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.0000 | −1.74459 | −0.872295 | − | 0.488980i | \(-0.837369\pi\) | ||||
−0.872295 | + | 0.488980i | \(0.837369\pi\) | |||||||
\(758\) | −2.92820 | + | 10.9282i | −0.106357 | + | 0.396930i | ||||
\(759\) | −0.866025 | + | 1.50000i | −0.0314347 | + | 0.0544466i | ||||
\(760\) | −6.58846 | − | 24.5885i | −0.238988 | − | 0.891917i | ||||
\(761\) | −16.5000 | + | 9.52628i | −0.598125 | + | 0.345327i | −0.768303 | − | 0.640086i | \(-0.778899\pi\) |
0.170179 | + | 0.985413i | \(0.445565\pi\) | |||||||
\(762\) | 10.3923 | + | 10.3923i | 0.376473 | + | 0.376473i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.00000 | −0.0723575 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.90192 | − | 7.09808i | −0.0687193 | − | 0.256464i | ||||
\(767\) | 15.5885 | + | 9.00000i | 0.562867 | + | 0.324971i | ||||
\(768\) | −13.8564 | − | 24.0000i | −0.500000 | − | 0.866025i | ||||
\(769\) | − | 3.46410i | − | 0.124919i | −0.998048 | − | 0.0624593i | \(-0.980106\pi\) | ||
0.998048 | − | 0.0624593i | \(-0.0198944\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 9.00000i | − | 0.324127i | ||||||
\(772\) | 25.9808 | − | 15.0000i | 0.935068 | − | 0.539862i | ||||
\(773\) | −22.5000 | − | 12.9904i | −0.809269 | − | 0.467232i | 0.0374331 | − | 0.999299i | \(-0.488082\pi\) |
−0.846702 | + | 0.532068i | \(0.821415\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.73205 | + | 3.00000i | 0.0622171 | + | 0.107763i | ||||
\(776\) | −34.6410 | + | 34.6410i | −1.24354 | + | 1.24354i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19.0000 | + | 19.0000i | −0.681183 | + | 0.681183i | ||||
\(779\) | 15.5885 | − | 9.00000i | 0.558514 | − | 0.322458i | ||||
\(780\) | −18.0000 | − | 10.3923i | −0.644503 | − | 0.372104i | ||||
\(781\) | 7.00000 | − | 12.1244i | 0.250480 | − | 0.433844i | ||||
\(782\) | −2.36603 | − | 0.633975i | −0.0846089 | − | 0.0226709i | ||||
\(783\) | −20.7846 | −0.742781 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.00000 | −0.107075 | ||||||||
\(786\) | −12.2942 | − | 3.29423i | −0.438521 | − | 0.117501i | ||||
\(787\) | 2.59808 | − | 4.50000i | 0.0926114 | − | 0.160408i | −0.815998 | − | 0.578055i | \(-0.803812\pi\) |
0.908609 | + | 0.417647i | \(0.137145\pi\) | |||||||
\(788\) | 27.7128 | + | 16.0000i | 0.987228 | + | 0.569976i | ||||
\(789\) | −34.5000 | + | 19.9186i | −1.22823 | + | 0.709120i | ||||
\(790\) | −15.5885 | + | 15.5885i | −0.554612 | + | 0.554612i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.00000 | + | 15.5885i | 0.319599 | + | 0.553562i | ||||
\(794\) | 26.0263 | − | 6.97372i | 0.923638 | − | 0.247488i | ||||
\(795\) | 2.59808 | + | 1.50000i | 0.0921443 | + | 0.0531995i | ||||
\(796\) | 39.0000 | − | 22.5167i | 1.38232 | − | 0.798082i | ||||
\(797\) | − | 10.3923i | − | 0.368114i | −0.982916 | − | 0.184057i | \(-0.941077\pi\) | ||
0.982916 | − | 0.184057i | \(-0.0589232\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 15.0000i | − | 0.530662i | ||||||
\(800\) | 10.9282 | + | 2.92820i | 0.386370 | + | 0.103528i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.41858 | − | 31.4186i | −0.297271 | − | 1.10943i | ||||
\(803\) | −4.33013 | − | 7.50000i | −0.152807 | − | 0.264669i | ||||
\(804\) | −10.3923 | −0.366508 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.00000 | − | 6.00000i | −0.211341 | − | 0.211341i | ||||
\(807\) | 33.7750 | − | 19.5000i | 1.18894 | − | 0.686433i | ||||
\(808\) | −6.33975 | − | 23.6603i | −0.223031 | − | 0.832365i | ||||
\(809\) | −21.5000 | + | 37.2391i | −0.755900 | + | 1.30926i | 0.189026 | + | 0.981972i | \(0.439467\pi\) |
−0.944926 | + | 0.327285i | \(0.893866\pi\) | |||||||
\(810\) | −5.70577 | + | 21.2942i | −0.200480 | + | 0.748203i | ||||
\(811\) | 13.8564 | 0.486564 | 0.243282 | − | 0.969956i | \(-0.421776\pi\) | ||||
0.243282 | + | 0.969956i | \(0.421776\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.0000 | −0.946931 | ||||||||
\(814\) | −1.09808 | + | 4.09808i | −0.0384876 | + | 0.143637i | ||||
\(815\) | 18.1865 | − | 31.5000i | 0.637046 | − | 1.10340i | ||||
\(816\) | −10.3923 | − | 6.00000i | −0.363803 | − | 0.210042i | ||||
\(817\) | −9.00000 | + | 5.19615i | −0.314870 | + | 0.181790i | ||||
\(818\) | 25.9808 | + | 25.9808i | 0.908396 | + | 0.908396i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 12.0000i | − | 0.419058i | ||||||
\(821\) | 5.50000 | + | 9.52628i | 0.191951 | + | 0.332469i | 0.945897 | − | 0.324468i | \(-0.105185\pi\) |
−0.753946 | + | 0.656937i | \(0.771852\pi\) | |||||||
\(822\) | 0.633975 | + | 2.36603i | 0.0221124 | + | 0.0825246i | ||||
\(823\) | −7.79423 | − | 4.50000i | −0.271690 | − | 0.156860i | 0.357966 | − | 0.933735i | \(-0.383471\pi\) |
−0.629655 | + | 0.776875i | \(0.716804\pi\) | |||||||
\(824\) | 6.33975 | − | 23.6603i | 0.220856 | − | 0.824244i | ||||
\(825\) | − | 3.46410i | − | 0.120605i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.0000i | 0.765015i | 0.923952 | + | 0.382507i | \(0.124939\pi\) | ||||
−0.923952 | + | 0.382507i | \(0.875061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.50000 | + | 4.33013i | 0.260486 | + | 0.150392i | 0.624556 | − | 0.780980i | \(-0.285280\pi\) |
−0.364070 | + | 0.931371i | \(0.618613\pi\) | |||||||
\(830\) | −32.7846 | + | 8.78461i | −1.13797 | + | 0.304918i | ||||
\(831\) | 11.2583 | + | 19.5000i | 0.390547 | + | 0.676448i | ||||
\(832\) | −27.7128 | −0.960769 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −12.0000 | + | 12.0000i | −0.415526 | + | 0.415526i | ||||
\(835\) | −25.9808 | + | 15.0000i | −0.899101 | + | 0.519096i | ||||
\(836\) | −5.19615 | + | 9.00000i | −0.179713 | + | 0.311272i | ||||
\(837\) | −4.50000 | + | 7.79423i | −0.155543 | + | 0.269408i | ||||
\(838\) | 28.3923 | + | 7.60770i | 0.980796 | + | 0.262803i | ||||
\(839\) | 48.4974 | 1.67432 | 0.837158 | − | 0.546960i | \(-0.184215\pi\) | ||||
0.837158 | + | 0.546960i | \(0.184215\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 27.3205 | + | 7.32051i | 0.941527 | + | 0.252281i | ||||
\(843\) | 3.46410 | − | 6.00000i | 0.119310 | − | 0.206651i | ||||
\(844\) | −10.0000 | + | 17.3205i | −0.344214 | + | 0.596196i | ||||
\(845\) | 1.50000 | − | 0.866025i | 0.0516016 | − | 0.0297922i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.00000 | 0.137361 | ||||||||
\(849\) | −10.5000 | − | 18.1865i | −0.360359 | − | 0.624160i | ||||
\(850\) | 4.73205 | − | 1.26795i | 0.162308 | − | 0.0434903i | ||||
\(851\) | −2.59808 | − | 1.50000i | −0.0890609 | − | 0.0514193i | ||||
\(852\) | 24.2487 | + | 42.0000i | 0.830747 | + | 1.43890i | ||||
\(853\) | − | 24.2487i | − | 0.830260i | −0.909762 | − | 0.415130i | \(-0.863736\pi\) | ||
0.909762 | − | 0.415130i | \(-0.136264\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 35.5167 | + | 9.51666i | 1.21393 | + | 0.325273i | ||||
\(857\) | 22.5000 | + | 12.9904i | 0.768585 | + | 0.443743i | 0.832370 | − | 0.554221i | \(-0.186984\pi\) |
−0.0637844 | + | 0.997964i | \(0.520317\pi\) | |||||||
\(858\) | 2.19615 | + | 8.19615i | 0.0749754 | + | 0.279812i | ||||
\(859\) | −25.1147 | − | 43.5000i | −0.856904 | − | 1.48420i | −0.874868 | − | 0.484362i | \(-0.839052\pi\) |
0.0179638 | − | 0.999839i | \(-0.494282\pi\) | |||||||
\(860\) | 6.92820i | 0.236250i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 23.0000 | + | 23.0000i | 0.783383 | + | 0.783383i | ||||
\(863\) | −30.3109 | + | 17.5000i | −1.03179 | + | 0.595707i | −0.917498 | − | 0.397740i | \(-0.869795\pi\) |
−0.114296 | + | 0.993447i | \(0.536461\pi\) | |||||||
\(864\) | 7.60770 | + | 28.3923i | 0.258819 | + | 0.965926i | ||||
\(865\) | 10.5000 | − | 18.1865i | 0.357011 | − | 0.618361i | ||||
\(866\) | −3.80385 | + | 14.1962i | −0.129260 | + | 0.482405i | ||||
\(867\) | 24.2487 | 0.823529 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.00000 | 0.305304 | ||||||||
\(870\) | 4.39230 | − | 16.3923i | 0.148913 | − | 0.555751i | ||||
\(871\) | −5.19615 | + | 9.00000i | −0.176065 | + | 0.304953i | ||||
\(872\) | 24.5885 | − | 6.58846i | 0.832670 | − | 0.223113i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.19615 | − | 5.19615i | −0.175762 | − | 0.175762i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 30.0000 | 1.01361 | ||||||||
\(877\) | −0.500000 | − | 0.866025i | −0.0168838 | − | 0.0292436i | 0.857460 | − | 0.514551i | \(-0.172041\pi\) |
−0.874344 | + | 0.485307i | \(0.838708\pi\) | |||||||
\(878\) | 8.24167 | + | 30.7583i | 0.278143 | + | 1.03804i | ||||
\(879\) | 31.1769 | + | 18.0000i | 1.05157 | + | 0.607125i | ||||
\(880\) | 3.46410 | + | 6.00000i | 0.116775 | + | 0.202260i | ||||
\(881\) | 13.8564i | 0.466834i | 0.972377 | + | 0.233417i | \(0.0749907\pi\) | ||||
−0.972377 | + | 0.233417i | \(0.925009\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 10.0000i | − | 0.336527i | −0.985742 | − | 0.168263i | \(-0.946184\pi\) | ||
0.985742 | − | 0.168263i | \(-0.0538159\pi\) | |||||||
\(884\) | −10.3923 | + | 6.00000i | −0.349531 | + | 0.201802i | ||||
\(885\) | 13.5000 | + | 7.79423i | 0.453798 | + | 0.262000i | ||||
\(886\) | 23.2224 | − | 6.22243i | 0.780173 | − | 0.209047i | ||||
\(887\) | 12.9904 | + | 22.5000i | 0.436174 | + | 0.755476i | 0.997391 | − | 0.0721931i | \(-0.0229998\pi\) |
−0.561216 | + | 0.827669i | \(0.689666\pi\) | |||||||
\(888\) | −10.3923 | − | 10.3923i | −0.348743 | − | 0.348743i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 27.0000 | − | 27.0000i | 0.905042 | − | 0.905042i | ||||
\(891\) | 7.79423 | − | 4.50000i | 0.261116 | − | 0.150756i | ||||
\(892\) | 12.0000 | + | 6.92820i | 0.401790 | + | 0.231973i | ||||
\(893\) | 22.5000 | − | 38.9711i | 0.752934 | − | 1.30412i | ||||
\(894\) | −2.36603 | − | 0.633975i | −0.0791317 | − | 0.0212033i | ||||
\(895\) | −32.9090 | −1.10003 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.00000 | −0.200334 | ||||||||
\(898\) | −10.9282 | − | 2.92820i | −0.364679 | − | 0.0977154i | ||||
\(899\) | 3.46410 | − | 6.00000i | 0.115534 | − | 0.200111i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.50000 | − | 0.866025i | 0.0499722 | − | 0.0288515i | ||||
\(902\) | −3.46410 | + | 3.46410i | −0.115342 | + | 0.115342i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 32.0000 | + | 32.0000i | 1.06430 | + | 1.06430i | ||||
\(905\) | 6.00000 | + | 10.3923i | 0.199447 | + | 0.345452i | ||||
\(906\) | −16.5622 | + | 4.43782i | −0.550242 | + | 0.147437i | ||||
\(907\) | 6.06218 | + | 3.50000i | 0.201291 | + | 0.116216i | 0.597258 | − | 0.802049i | \(-0.296257\pi\) |
−0.395966 | + | 0.918265i | \(0.629590\pi\) | |||||||
\(908\) | −33.0000 | + | 19.0526i | −1.09514 | + | 0.632281i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 26.0000i | − | 0.861418i | −0.902491 | − | 0.430709i | \(-0.858263\pi\) | ||
0.902491 | − | 0.430709i | \(-0.141737\pi\) | |||||||
\(912\) | −18.0000 | − | 31.1769i | −0.596040 | − | 1.03237i | ||||
\(913\) | 12.0000 | + | 6.92820i | 0.397142 | + | 0.229290i | ||||
\(914\) | 5.49038 | + | 20.4904i | 0.181606 | + | 0.677762i | ||||
\(915\) | 7.79423 | + | 13.5000i | 0.257669 | + | 0.446296i | ||||
\(916\) | 31.1769 | 1.03011 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 9.00000 | + | 9.00000i | 0.297044 | + | 0.297044i | ||||
\(919\) | −0.866025 | + | 0.500000i | −0.0285675 | + | 0.0164935i | −0.514216 | − | 0.857661i | \(-0.671917\pi\) |
0.485648 | + | 0.874154i | \(0.338584\pi\) | |||||||
\(920\) | −4.73205 | + | 1.26795i | −0.156011 | + | 0.0418030i | ||||
\(921\) | −18.0000 | + | 31.1769i | −0.593120 | + | 1.02731i | ||||
\(922\) | −6.33975 | + | 23.6603i | −0.208788 | + | 0.779209i | ||||
\(923\) | 48.4974 | 1.59631 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | −10.9808 | + | 40.9808i | −0.360850 | + | 1.34671i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.85641 | − | 21.8564i | −0.192246 | − | 0.717472i | ||||
\(929\) | −7.50000 | + | 4.33013i | −0.246067 | + | 0.142067i | −0.617962 | − | 0.786208i | \(-0.712041\pi\) |
0.371895 | + | 0.928275i | \(0.378708\pi\) | |||||||
\(930\) | −5.19615 | − | 5.19615i | −0.170389 | − | 0.170389i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 14.0000i | 0.458585i | ||||||||
\(933\) | −7.50000 | − | 12.9904i | −0.245539 | − | 0.425286i | ||||
\(934\) | −3.16987 | − | 11.8301i | −0.103721 | − | 0.387094i | ||||
\(935\) | 2.59808 | + | 1.50000i | 0.0849662 | + | 0.0490552i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 3.00000i | − | 0.0979013i | ||||||
\(940\) | −15.0000 | − | 25.9808i | −0.489246 | − | 0.847399i | ||||
\(941\) | −49.5000 | − | 28.5788i | −1.61365 | − | 0.931644i | −0.988514 | − | 0.151131i | \(-0.951708\pi\) |
−0.625140 | − | 0.780513i | \(-0.714958\pi\) | |||||||
\(942\) | −4.09808 | + | 1.09808i | −0.133523 | + | 0.0357773i | ||||
\(943\) | −1.73205 | − | 3.00000i | −0.0564033 | − | 0.0976934i | ||||
\(944\) | 20.7846 | 0.676481 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.00000 | − | 2.00000i | 0.0650256 | − | 0.0650256i | ||||
\(947\) | 25.1147 | − | 14.5000i | 0.816119 | − | 0.471187i | −0.0329571 | − | 0.999457i | \(-0.510492\pi\) |
0.849076 | + | 0.528270i | \(0.177159\pi\) | |||||||
\(948\) | −15.5885 | + | 27.0000i | −0.506290 | + | 0.876919i | ||||
\(949\) | 15.0000 | − | 25.9808i | 0.486921 | − | 0.843371i | ||||
\(950\) | 14.1962 | + | 3.80385i | 0.460584 | + | 0.123413i | ||||
\(951\) | 19.0526 | 0.617822 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.00000 | −0.259145 | −0.129573 | − | 0.991570i | \(-0.541361\pi\) | ||||
−0.129573 | + | 0.991570i | \(0.541361\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.866025 | + | 1.50000i | −0.0280239 | + | 0.0485389i | ||||
\(956\) | −20.0000 | + | 34.6410i | −0.646846 | + | 1.12037i | ||||
\(957\) | −6.00000 | + | 3.46410i | −0.193952 | + | 0.111979i | ||||
\(958\) | −12.1244 | + | 12.1244i | −0.391720 | + | 0.391720i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −24.0000 | −0.774597 | ||||||||
\(961\) | 14.0000 | + | 24.2487i | 0.451613 | + | 0.782216i | ||||
\(962\) | −14.1962 | + | 3.80385i | −0.457702 | + | 0.122641i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.19615 | + | 9.00000i | 0.167357 | + | 0.289870i | ||||
\(965\) | − | 25.9808i | − | 0.836350i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 6.00000i | − | 0.192947i | −0.995336 | − | 0.0964735i | \(-0.969244\pi\) | ||
0.995336 | − | 0.0964735i | \(-0.0307563\pi\) | |||||||
\(968\) | −7.32051 | + | 27.3205i | −0.235290 | + | 0.878114i | ||||
\(969\) | −13.5000 | − | 7.79423i | −0.433682 | − | 0.250387i | ||||
\(970\) | 10.9808 | + | 40.9808i | 0.352571 | + | 1.31581i | ||||
\(971\) | −30.3109 | − | 52.5000i | −0.972723 | − | 1.68481i | −0.687254 | − | 0.726417i | \(-0.741184\pi\) |
−0.285469 | − | 0.958388i | \(-0.592149\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −31.0000 | − | 31.0000i | −0.993304 | − | 0.993304i | ||||
\(975\) | 10.3923 | − | 6.00000i | 0.332820 | − | 0.192154i | ||||
\(976\) | 18.0000 | + | 10.3923i | 0.576166 | + | 0.332650i | ||||
\(977\) | 15.5000 | − | 26.8468i | 0.495889 | − | 0.858905i | −0.504100 | − | 0.863645i | \(-0.668176\pi\) |
0.999989 | + | 0.00474056i | \(0.00150897\pi\) | |||||||
\(978\) | 13.3135 | − | 49.6865i | 0.425718 | − | 1.58880i | ||||
\(979\) | −15.5885 | −0.498209 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.7128 | − | 43.7128i | 0.373771 | − | 1.39493i | ||||
\(983\) | −30.3109 | + | 52.5000i | −0.966767 | + | 1.67449i | −0.261977 | + | 0.965074i | \(0.584374\pi\) |
−0.704790 | + | 0.709416i | \(0.748959\pi\) | |||||||
\(984\) | −4.39230 | − | 16.3923i | −0.140022 | − | 0.522568i | ||||
\(985\) | 24.0000 | − | 13.8564i | 0.764704 | − | 0.441502i | ||||
\(986\) | −6.92820 | − | 6.92820i | −0.220639 | − | 0.220639i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −36.0000 | −1.14531 | ||||||||
\(989\) | 1.00000 | + | 1.73205i | 0.0317982 | + | 0.0550760i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.9186 | + | 11.5000i | 0.632735 | + | 0.365310i | 0.781810 | − | 0.623516i | \(-0.214296\pi\) |
−0.149076 | + | 0.988826i | \(0.547630\pi\) | |||||||
\(992\) | −9.46410 | − | 2.53590i | −0.300486 | − | 0.0805149i | ||||
\(993\) | − | 12.1244i | − | 0.384755i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 39.0000i | − | 1.23638i | ||||||
\(996\) | −41.5692 | + | 24.0000i | −1.31717 | + | 0.760469i | ||||
\(997\) | −19.5000 | − | 11.2583i | −0.617571 | − | 0.356555i | 0.158352 | − | 0.987383i | \(-0.449382\pi\) |
−0.775923 | + | 0.630828i | \(0.782715\pi\) | |||||||
\(998\) | 47.8109 | − | 12.8109i | 1.51343 | − | 0.405522i | ||||
\(999\) | 7.79423 | + | 13.5000i | 0.246598 | + | 0.427121i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))