Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 765.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.765 |
Dual form | 784.2.x.e.165.1 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(4\) | 1.73205 | − | 1.00000i | 0.866025 | − | 0.500000i | ||||
\(5\) | −0.732051 | − | 2.73205i | −0.327383 | − | 1.22181i | −0.911894 | − | 0.410425i | \(-0.865380\pi\) |
0.584511 | − | 0.811386i | \(-0.301286\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.00000 | − | 2.00000i | 0.707107 | − | 0.707107i | ||||
\(9\) | 2.59808 | + | 1.50000i | 0.866025 | + | 0.500000i | ||||
\(10\) | −2.00000 | − | 3.46410i | −0.632456 | − | 1.09545i | ||||
\(11\) | −1.36603 | − | 0.366025i | −0.411872 | − | 0.110361i | 0.0469323 | − | 0.998898i | \(-0.485055\pi\) |
−0.458804 | + | 0.888537i | \(0.651722\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | −1.00000 | − | 1.73205i | −0.242536 | − | 0.420084i | 0.718900 | − | 0.695113i | \(-0.244646\pi\) |
−0.961436 | + | 0.275029i | \(0.911312\pi\) | |||||||
\(18\) | 4.09808 | + | 1.09808i | 0.965926 | + | 0.258819i | ||||
\(19\) | 2.73205 | − | 0.732051i | 0.626775 | − | 0.167944i | 0.0685694 | − | 0.997646i | \(-0.478157\pi\) |
0.558206 | + | 0.829702i | \(0.311490\pi\) | |||||||
\(20\) | −4.00000 | − | 4.00000i | −0.894427 | − | 0.894427i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | −5.19615 | − | 3.00000i | −1.08347 | − | 0.625543i | −0.151642 | − | 0.988436i | \(-0.548456\pi\) |
−0.931831 | + | 0.362892i | \(0.881789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.59808 | + | 1.50000i | −0.519615 | + | 0.300000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.00000 | + | 7.00000i | 1.29987 | + | 1.29987i | 0.928477 | + | 0.371391i | \(0.121119\pi\) |
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | − | 6.92820i | −0.718421 | − | 1.24434i | −0.961625 | − | 0.274367i | \(-0.911532\pi\) |
0.243204 | − | 0.969975i | \(-0.421802\pi\) | |||||||
\(32\) | 1.46410 | − | 5.46410i | 0.258819 | − | 0.965926i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | − | 2.00000i | −0.342997 | − | 0.342997i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | −1.83013 | − | 6.83013i | −0.300871 | − | 1.12287i | −0.936442 | − | 0.350823i | \(-0.885902\pi\) |
0.635571 | − | 0.772043i | \(-0.280765\pi\) | |||||||
\(38\) | 3.46410 | − | 2.00000i | 0.561951 | − | 0.324443i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.92820 | − | 4.00000i | −1.09545 | − | 0.632456i | ||||
\(41\) | 10.0000i | 1.56174i | 0.624695 | + | 0.780869i | \(0.285223\pi\) | ||||
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | + | 1.00000i | −0.152499 | + | 0.152499i | −0.779233 | − | 0.626734i | \(-0.784391\pi\) |
0.626734 | + | 0.779233i | \(0.284391\pi\) | |||||||
\(44\) | −2.73205 | + | 0.732051i | −0.411872 | + | 0.110361i | ||||
\(45\) | 2.19615 | − | 8.19615i | 0.327383 | − | 1.22181i | ||||
\(46\) | −8.19615 | − | 2.19615i | −1.20846 | − | 0.323805i | ||||
\(47\) | −6.00000 | + | 10.3923i | −0.875190 | + | 1.51587i | −0.0186297 | + | 0.999826i | \(0.505930\pi\) |
−0.856560 | + | 0.516047i | \(0.827403\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.00000 | + | 3.00000i | −0.424264 | + | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.36603 | + | 0.366025i | 0.187638 | + | 0.0502775i | 0.351414 | − | 0.936220i | \(-0.385701\pi\) |
−0.163776 | + | 0.986498i | \(0.552368\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000i | 0.539360i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12.1244 | + | 7.00000i | 1.59201 | + | 0.919145i | ||||
\(59\) | 10.9282 | + | 2.92820i | 1.42273 | + | 0.381220i | 0.886452 | − | 0.462821i | \(-0.153163\pi\) |
0.536279 | + | 0.844041i | \(0.319829\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.19615 | − | 2.19615i | 1.04941 | − | 0.281189i | 0.307402 | − | 0.951580i | \(-0.400540\pi\) |
0.742008 | + | 0.670391i | \(0.233874\pi\) | |||||||
\(62\) | −8.00000 | − | 8.00000i | −1.01600 | − | 1.01600i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.09808 | − | 4.09808i | 0.134151 | − | 0.500660i | −0.865849 | − | 0.500306i | \(-0.833221\pi\) |
1.00000 | 0.000353546i | \(-0.000112537\pi\) | ||||||||
\(68\) | −3.46410 | − | 2.00000i | −0.420084 | − | 0.242536i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 8.19615 | − | 2.19615i | 0.965926 | − | 0.258819i | ||||
\(73\) | −5.19615 | + | 3.00000i | −0.608164 | + | 0.351123i | −0.772246 | − | 0.635323i | \(-0.780867\pi\) |
0.164083 | + | 0.986447i | \(0.447534\pi\) | |||||||
\(74\) | −5.00000 | − | 8.66025i | −0.581238 | − | 1.00673i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.00000 | − | 4.00000i | 0.458831 | − | 0.458831i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.00000 | + | 8.66025i | −0.562544 | + | 0.974355i | 0.434730 | + | 0.900561i | \(0.356844\pi\) |
−0.997274 | + | 0.0737937i | \(0.976489\pi\) | |||||||
\(80\) | −10.9282 | − | 2.92820i | −1.22181 | − | 0.327383i | ||||
\(81\) | 4.50000 | + | 7.79423i | 0.500000 | + | 0.866025i | ||||
\(82\) | 3.66025 | + | 13.6603i | 0.404207 | + | 1.50852i | ||||
\(83\) | 10.0000 | + | 10.0000i | 1.09764 | + | 1.09764i | 0.994686 | + | 0.102957i | \(0.0328303\pi\) |
0.102957 | + | 0.994686i | \(0.467170\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | + | 4.00000i | −0.433861 | + | 0.433861i | ||||
\(86\) | −1.00000 | + | 1.73205i | −0.107833 | + | 0.186772i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.46410 | + | 2.00000i | −0.369274 | + | 0.213201i | ||||
\(89\) | 12.1244 | + | 7.00000i | 1.28518 | + | 0.741999i | 0.977790 | − | 0.209585i | \(-0.0672115\pi\) |
0.307389 | + | 0.951584i | \(0.400545\pi\) | |||||||
\(90\) | − | 12.0000i | − | 1.26491i | ||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −12.0000 | −1.25109 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.39230 | + | 16.3923i | −0.453032 | + | 1.69074i | ||||
\(95\) | −4.00000 | − | 6.92820i | −0.410391 | − | 0.710819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.00000 | − | 3.00000i | −0.301511 | − | 0.301511i | ||||
\(100\) | −3.00000 | + | 5.19615i | −0.300000 | + | 0.519615i | ||||
\(101\) | 8.19615 | + | 2.19615i | 0.815548 | + | 0.218525i | 0.642399 | − | 0.766370i | \(-0.277939\pi\) |
0.173149 | + | 0.984896i | \(0.444606\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.46410 | − | 2.00000i | −0.341328 | − | 0.197066i | 0.319531 | − | 0.947576i | \(-0.396475\pi\) |
−0.660859 | + | 0.750510i | \(0.729808\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.00000 | 0.194257 | ||||||||
\(107\) | 1.83013 | + | 6.83013i | 0.176925 | + | 0.660293i | 0.996216 | + | 0.0869149i | \(0.0277008\pi\) |
−0.819291 | + | 0.573378i | \(0.805633\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.09808 | + | 4.09808i | −0.105177 | + | 0.392525i | −0.998365 | − | 0.0571579i | \(-0.981796\pi\) |
0.893189 | + | 0.449682i | \(0.148463\pi\) | |||||||
\(110\) | 1.46410 | + | 5.46410i | 0.139597 | + | 0.520982i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00000 | 0.376288 | 0.188144 | − | 0.982141i | \(-0.439753\pi\) | ||||
0.188144 | + | 0.982141i | \(0.439753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.39230 | + | 16.3923i | −0.409585 | + | 1.52859i | ||||
\(116\) | 19.1244 | + | 5.12436i | 1.77565 | + | 0.475784i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 16.0000 | 1.47292 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.79423 | − | 4.50000i | −0.708566 | − | 0.409091i | ||||
\(122\) | 10.3923 | − | 6.00000i | 0.940875 | − | 0.543214i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −13.8564 | − | 8.00000i | −1.24434 | − | 0.718421i | ||||
\(125\) | −4.00000 | − | 4.00000i | −0.357771 | − | 0.357771i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | −2.92820 | − | 10.9282i | −0.258819 | − | 0.965926i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.1244 | + | 5.12436i | −1.67090 | + | 0.447717i | −0.965354 | − | 0.260944i | \(-0.915966\pi\) |
−0.705549 | + | 0.708661i | \(0.749299\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 6.00000i | − | 0.518321i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.46410 | − | 1.46410i | −0.468543 | − | 0.125546i | ||||
\(137\) | −10.3923 | + | 6.00000i | −0.887875 | + | 0.512615i | −0.873247 | − | 0.487278i | \(-0.837990\pi\) |
−0.0146279 | + | 0.999893i | \(0.504656\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00000 | − | 2.00000i | 0.169638 | − | 0.169638i | −0.617182 | − | 0.786820i | \(-0.711726\pi\) |
0.786820 | + | 0.617182i | \(0.211726\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 10.3923 | − | 6.00000i | 0.866025 | − | 0.500000i | ||||
\(145\) | 14.0000 | − | 24.2487i | 1.16264 | − | 2.01375i | ||||
\(146\) | −6.00000 | + | 6.00000i | −0.496564 | + | 0.496564i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.0000 | − | 10.0000i | −0.821995 | − | 0.821995i | ||||
\(149\) | 1.09808 | + | 4.09808i | 0.0899579 | + | 0.335727i | 0.996207 | − | 0.0870170i | \(-0.0277334\pi\) |
−0.906249 | + | 0.422744i | \(0.861067\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.66025 | + | 5.00000i | −0.704761 | + | 0.406894i | −0.809118 | − | 0.587646i | \(-0.800055\pi\) |
0.104357 | + | 0.994540i | \(0.466722\pi\) | |||||||
\(152\) | 4.00000 | − | 6.92820i | 0.324443 | − | 0.561951i | ||||
\(153\) | − | 6.00000i | − | 0.485071i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.0000 | + | 16.0000i | −1.28515 | + | 1.28515i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.39230 | − | 16.3923i | 0.350544 | − | 1.30825i | −0.535456 | − | 0.844563i | \(-0.679860\pi\) |
0.886000 | − | 0.463685i | \(-0.153473\pi\) | |||||||
\(158\) | −3.66025 | + | 13.6603i | −0.291194 | + | 1.08675i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −16.0000 | −1.26491 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.00000 | + | 9.00000i | 0.707107 | + | 0.707107i | ||||
\(163\) | −20.4904 | + | 5.49038i | −1.60493 | + | 0.430040i | −0.946527 | − | 0.322625i | \(-0.895435\pi\) |
−0.658404 | + | 0.752665i | \(0.728768\pi\) | |||||||
\(164\) | 10.0000 | + | 17.3205i | 0.780869 | + | 1.35250i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.3205 | + | 10.0000i | 1.34433 | + | 0.776151i | ||||
\(167\) | 12.0000i | 0.928588i | 0.885681 | + | 0.464294i | \(0.153692\pi\) | ||||
−0.885681 | + | 0.464294i | \(0.846308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 13.0000i | − | 1.00000i | ||||||
\(170\) | −4.00000 | + | 6.92820i | −0.306786 | + | 0.531369i | ||||
\(171\) | 8.19615 | + | 2.19615i | 0.626775 | + | 0.167944i | ||||
\(172\) | −0.732051 | + | 2.73205i | −0.0558184 | + | 0.208317i | ||||
\(173\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.00000 | + | 4.00000i | −0.301511 | + | 0.301511i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 19.1244 | + | 5.12436i | 1.43343 | + | 0.384087i | ||||
\(179\) | −1.09808 | + | 4.09808i | −0.0820741 | + | 0.306305i | −0.994744 | − | 0.102393i | \(-0.967350\pi\) |
0.912670 | + | 0.408697i | \(0.134017\pi\) | |||||||
\(180\) | −4.39230 | − | 16.3923i | −0.327383 | − | 1.22181i | ||||
\(181\) | 4.00000 | − | 4.00000i | 0.297318 | − | 0.297318i | −0.542645 | − | 0.839962i | \(-0.682577\pi\) |
0.839962 | + | 0.542645i | \(0.182577\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.3923 | + | 4.39230i | −1.20846 | + | 0.323805i | ||||
\(185\) | −17.3205 | + | 10.0000i | −1.27343 | + | 0.735215i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.732051 | + | 2.73205i | 0.0535329 | + | 0.199787i | ||||
\(188\) | 24.0000i | 1.75038i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.00000 | − | 8.00000i | −0.580381 | − | 0.580381i | ||||
\(191\) | 9.00000 | − | 15.5885i | 0.651217 | − | 1.12794i | −0.331611 | − | 0.943416i | \(-0.607592\pi\) |
0.982828 | − | 0.184525i | \(-0.0590746\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.00000 | + | 13.8564i | 0.575853 | + | 0.997406i | 0.995948 | + | 0.0899262i | \(0.0286631\pi\) |
−0.420096 | + | 0.907480i | \(0.638004\pi\) | |||||||
\(194\) | 2.73205 | − | 0.732051i | 0.196150 | − | 0.0525582i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.00000 | − | 5.00000i | 0.356235 | − | 0.356235i | −0.506188 | − | 0.862423i | \(-0.668946\pi\) |
0.862423 | + | 0.506188i | \(0.168946\pi\) | |||||||
\(198\) | −5.19615 | − | 3.00000i | −0.369274 | − | 0.213201i | ||||
\(199\) | −20.7846 | + | 12.0000i | −1.47338 | + | 0.850657i | −0.999551 | − | 0.0299585i | \(-0.990462\pi\) |
−0.473831 | + | 0.880616i | \(0.657129\pi\) | |||||||
\(200\) | −2.19615 | + | 8.19615i | −0.155291 | + | 0.579555i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.0000 | 0.844317 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 27.3205 | − | 7.32051i | 1.90815 | − | 0.511286i | ||||
\(206\) | −5.46410 | − | 1.46410i | −0.380702 | − | 0.102009i | ||||
\(207\) | −9.00000 | − | 15.5885i | −0.625543 | − | 1.08347i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.00000 | − | 9.00000i | −0.619586 | − | 0.619586i | 0.325840 | − | 0.945425i | \(-0.394353\pi\) |
−0.945425 | + | 0.325840i | \(0.894353\pi\) | |||||||
\(212\) | 2.73205 | − | 0.732051i | 0.187638 | − | 0.0502775i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.00000 | + | 8.66025i | 0.341793 | + | 0.592003i | ||||
\(215\) | 3.46410 | + | 2.00000i | 0.236250 | + | 0.136399i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.00000i | 0.406371i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.00000 | + | 6.92820i | 0.269680 | + | 0.467099i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | −0.267860 | −0.133930 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133930 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.00000 | −0.600000 | ||||||||
\(226\) | 5.46410 | − | 1.46410i | 0.363467 | − | 0.0973906i | ||||
\(227\) | 0.732051 | − | 2.73205i | 0.0485879 | − | 0.181333i | −0.937367 | − | 0.348343i | \(-0.886745\pi\) |
0.985955 | + | 0.167010i | \(0.0534112\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.92820 | − | 10.9282i | −0.193501 | − | 0.722156i | −0.992650 | − | 0.121023i | \(-0.961383\pi\) |
0.799149 | − | 0.601133i | \(-0.205284\pi\) | |||||||
\(230\) | 24.0000i | 1.58251i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 28.0000 | 1.83829 | ||||||||
\(233\) | −13.8564 | − | 8.00000i | −0.907763 | − | 0.524097i | −0.0280525 | − | 0.999606i | \(-0.508931\pi\) |
−0.879711 | + | 0.475509i | \(0.842264\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.7846 | + | 8.78461i | 2.13863 | + | 0.573045i | ||||
\(236\) | 21.8564 | − | 5.85641i | 1.42273 | − | 0.381220i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0000 | + | 19.0526i | 0.708572 | + | 1.22728i | 0.965387 | + | 0.260822i | \(0.0839937\pi\) |
−0.256814 | + | 0.966461i | \(0.582673\pi\) | |||||||
\(242\) | −12.2942 | − | 3.29423i | −0.790303 | − | 0.211761i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.0000 | − | 12.0000i | 0.768221 | − | 0.768221i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −21.8564 | − | 5.85641i | −1.38788 | − | 0.371882i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.92820 | − | 4.00000i | −0.438178 | − | 0.252982i | ||||
\(251\) | 14.0000 | − | 14.0000i | 0.883672 | − | 0.883672i | −0.110234 | − | 0.993906i | \(-0.535160\pi\) |
0.993906 | + | 0.110234i | \(0.0351599\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | + | 6.00000i | 0.377217 | + | 0.377217i | ||||
\(254\) | 10.9282 | − | 2.92820i | 0.685696 | − | 0.183732i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | −1.00000 | + | 1.73205i | −0.0623783 | + | 0.108042i | −0.895528 | − | 0.445005i | \(-0.853202\pi\) |
0.833150 | + | 0.553047i | \(0.186535\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.68653 | + | 28.6865i | 0.475784 | + | 1.77565i | ||||
\(262\) | −24.2487 | + | 14.0000i | −1.49809 | + | 0.864923i | ||||
\(263\) | 13.8564 | − | 8.00000i | 0.854423 | − | 0.493301i | −0.00771799 | − | 0.999970i | \(-0.502457\pi\) |
0.862141 | + | 0.506669i | \(0.169123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.00000i | − | 0.245718i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.19615 | − | 8.19615i | −0.134151 | − | 0.500660i | ||||
\(269\) | 2.92820 | − | 10.9282i | 0.178536 | − | 0.666304i | −0.817387 | − | 0.576089i | \(-0.804578\pi\) |
0.995922 | − | 0.0902148i | \(-0.0287554\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | + | 6.92820i | −0.242983 | + | 0.420858i | −0.961563 | − | 0.274586i | \(-0.911459\pi\) |
0.718580 | + | 0.695444i | \(0.244792\pi\) | |||||||
\(272\) | −8.00000 | −0.485071 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.0000 | + | 12.0000i | −0.724947 | + | 0.724947i | ||||
\(275\) | 4.09808 | − | 1.09808i | 0.247123 | − | 0.0662165i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.4904 | + | 5.49038i | 1.23115 | + | 0.329885i | 0.815026 | − | 0.579424i | \(-0.196722\pi\) |
0.416121 | + | 0.909309i | \(0.363389\pi\) | |||||||
\(278\) | 2.00000 | − | 3.46410i | 0.119952 | − | 0.207763i | ||||
\(279\) | − | 24.0000i | − | 1.43684i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.46410 | + | 1.46410i | 0.324807 | + | 0.0870318i | 0.417538 | − | 0.908659i | \(-0.362893\pi\) |
−0.0927310 | + | 0.995691i | \(0.529560\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 12.0000 | − | 12.0000i | 0.707107 | − | 0.707107i | ||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 10.2487 | − | 38.2487i | 0.601825 | − | 2.24604i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.00000 | + | 10.3923i | −0.351123 | + | 0.608164i | ||||
\(293\) | −14.0000 | + | 14.0000i | −0.817889 | + | 0.817889i | −0.985802 | − | 0.167913i | \(-0.946297\pi\) |
0.167913 | + | 0.985802i | \(0.446297\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 32.0000i | − | 1.86311i | ||||||
\(296\) | −17.3205 | − | 10.0000i | −1.00673 | − | 0.581238i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00000 | + | 5.19615i | 0.173785 | + | 0.301005i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −10.0000 | + | 10.0000i | −0.575435 | + | 0.575435i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.92820 | − | 10.9282i | 0.167944 | − | 0.626775i | ||||
\(305\) | −12.0000 | − | 20.7846i | −0.687118 | − | 1.19012i | ||||
\(306\) | −2.19615 | − | 8.19615i | −0.125546 | − | 0.468543i | ||||
\(307\) | −18.0000 | − | 18.0000i | −1.02731 | − | 1.02731i | −0.999616 | − | 0.0276979i | \(-0.991182\pi\) |
−0.0276979 | − | 0.999616i | \(-0.508818\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −16.0000 | + | 27.7128i | −0.908739 | + | 1.57398i | ||||
\(311\) | 17.3205 | − | 10.0000i | 0.982156 | − | 0.567048i | 0.0792356 | − | 0.996856i | \(-0.474752\pi\) |
0.902920 | + | 0.429808i | \(0.141419\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.1244 | − | 7.00000i | −0.685309 | − | 0.395663i | 0.116543 | − | 0.993186i | \(-0.462819\pi\) |
−0.801852 | + | 0.597522i | \(0.796152\pi\) | |||||||
\(314\) | − | 24.0000i | − | 1.35440i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 20.0000i | 1.12509i | ||||||||
\(317\) | 9.56218 | − | 2.56218i | 0.537065 | − | 0.143906i | 0.0199164 | − | 0.999802i | \(-0.493660\pi\) |
0.517149 | + | 0.855895i | \(0.326993\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.00000 | − | 12.1244i | −0.391925 | − | 0.678834i | ||||
\(320\) | −21.8564 | + | 5.85641i | −1.22181 | + | 0.327383i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.00000 | − | 4.00000i | −0.222566 | − | 0.222566i | ||||
\(324\) | 15.5885 | + | 9.00000i | 0.866025 | + | 0.500000i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −25.9808 | + | 15.0000i | −1.43894 | + | 0.830773i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 20.0000 | + | 20.0000i | 1.10432 | + | 1.10432i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.68653 | + | 28.6865i | 0.422490 | + | 1.57675i | 0.769344 | + | 0.638835i | \(0.220583\pi\) |
−0.346854 | + | 0.937919i | \(0.612750\pi\) | |||||||
\(332\) | 27.3205 | + | 7.32051i | 1.49941 | + | 0.401765i | ||||
\(333\) | 5.49038 | − | 20.4904i | 0.300871 | − | 1.12287i | ||||
\(334\) | 4.39230 | + | 16.3923i | 0.240336 | + | 0.896947i | ||||
\(335\) | −12.0000 | −0.655630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.00000 | 0.435788 | 0.217894 | − | 0.975972i | \(-0.430081\pi\) | ||||
0.217894 | + | 0.975972i | \(0.430081\pi\) | |||||||
\(338\) | −4.75833 | − | 17.7583i | −0.258819 | − | 0.965926i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.92820 | + | 10.9282i | −0.158804 | + | 0.592665i | ||||
\(341\) | 2.92820 | + | 10.9282i | 0.158571 | + | 0.591795i | ||||
\(342\) | 12.0000 | 0.648886 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.00000i | 0.215666i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.4904 | − | 5.49038i | −1.09998 | − | 0.294739i | −0.337224 | − | 0.941424i | \(-0.609488\pi\) |
−0.762757 | + | 0.646685i | \(0.776155\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.0000 | − | 12.0000i | −0.642345 | − | 0.642345i | 0.308786 | − | 0.951131i | \(-0.400077\pi\) |
−0.951131 | + | 0.308786i | \(0.900077\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.00000 | + | 6.92820i | −0.213201 | + | 0.369274i | ||||
\(353\) | −3.00000 | − | 5.19615i | −0.159674 | − | 0.276563i | 0.775077 | − | 0.631867i | \(-0.217711\pi\) |
−0.934751 | + | 0.355303i | \(0.884378\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 28.0000 | 1.48400 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.00000i | 0.317110i | ||||||||
\(359\) | 5.19615 | + | 3.00000i | 0.274242 | + | 0.158334i | 0.630814 | − | 0.775934i | \(-0.282721\pi\) |
−0.356572 | + | 0.934268i | \(0.616054\pi\) | |||||||
\(360\) | −12.0000 | − | 20.7846i | −0.632456 | − | 1.09545i | ||||
\(361\) | −9.52628 | + | 5.50000i | −0.501383 | + | 0.289474i | ||||
\(362\) | 4.00000 | − | 6.92820i | 0.210235 | − | 0.364138i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.0000 | + | 12.0000i | 0.628109 | + | 0.628109i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.0000 | − | 27.7128i | −0.835193 | − | 1.44660i | −0.893873 | − | 0.448320i | \(-0.852022\pi\) |
0.0586798 | − | 0.998277i | \(-0.481311\pi\) | |||||||
\(368\) | −20.7846 | + | 12.0000i | −1.08347 | + | 0.625543i | ||||
\(369\) | −15.0000 | + | 25.9808i | −0.780869 | + | 1.35250i | ||||
\(370\) | −20.0000 | + | 20.0000i | −1.03975 | + | 1.03975i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.02628 | − | 15.0263i | −0.208473 | − | 0.778031i | −0.988363 | − | 0.152115i | \(-0.951392\pi\) |
0.779890 | − | 0.625917i | \(-0.215275\pi\) | |||||||
\(374\) | 2.00000 | + | 3.46410i | 0.103418 | + | 0.179124i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.78461 | + | 32.7846i | 0.453032 | + | 1.69074i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.0000 | − | 13.0000i | 0.667765 | − | 0.667765i | −0.289433 | − | 0.957198i | \(-0.593467\pi\) |
0.957198 | + | 0.289433i | \(0.0934668\pi\) | |||||||
\(380\) | −13.8564 | − | 8.00000i | −0.710819 | − | 0.410391i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.58846 | − | 24.5885i | 0.337095 | − | 1.25805i | ||||
\(383\) | 2.00000 | − | 3.46410i | 0.102195 | − | 0.177007i | −0.810394 | − | 0.585886i | \(-0.800747\pi\) |
0.912589 | + | 0.408879i | \(0.134080\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.0000 | + | 16.0000i | 0.814379 | + | 0.814379i | ||||
\(387\) | −4.09808 | + | 1.09808i | −0.208317 | + | 0.0558184i | ||||
\(388\) | 3.46410 | − | 2.00000i | 0.175863 | − | 0.101535i | ||||
\(389\) | −4.09808 | − | 1.09808i | −0.207781 | − | 0.0556747i | 0.153427 | − | 0.988160i | \(-0.450969\pi\) |
−0.361208 | + | 0.932485i | \(0.617636\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000i | 0.606866i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.00000 | − | 8.66025i | 0.251896 | − | 0.436297i | ||||
\(395\) | 27.3205 | + | 7.32051i | 1.37464 | + | 0.368335i | ||||
\(396\) | −8.19615 | − | 2.19615i | −0.411872 | − | 0.110361i | ||||
\(397\) | −16.3923 | + | 4.39230i | −0.822706 | + | 0.220443i | −0.645529 | − | 0.763736i | \(-0.723363\pi\) |
−0.177177 | + | 0.984179i | \(0.556696\pi\) | |||||||
\(398\) | −24.0000 | + | 24.0000i | −1.20301 | + | 1.20301i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.0000i | 0.600000i | ||||||||
\(401\) | −6.00000 | + | 10.3923i | −0.299626 | + | 0.518967i | −0.976050 | − | 0.217545i | \(-0.930195\pi\) |
0.676425 | + | 0.736512i | \(0.263528\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 16.3923 | − | 4.39230i | 0.815548 | − | 0.218525i | ||||
\(405\) | 18.0000 | − | 18.0000i | 0.894427 | − | 0.894427i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.0000i | 0.495682i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.1244 | + | 7.00000i | −0.599511 | + | 0.346128i | −0.768849 | − | 0.639430i | \(-0.779170\pi\) |
0.169338 | + | 0.985558i | \(0.445837\pi\) | |||||||
\(410\) | 34.6410 | − | 20.0000i | 1.71080 | − | 0.987730i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.00000 | −0.394132 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −18.0000 | − | 18.0000i | −0.884652 | − | 0.884652i | ||||
\(415\) | 20.0000 | − | 34.6410i | 0.981761 | − | 1.70046i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.46410 | + | 1.46410i | −0.267258 | + | 0.0716116i | ||||
\(419\) | −12.0000 | − | 12.0000i | −0.586238 | − | 0.586238i | 0.350372 | − | 0.936611i | \(-0.386055\pi\) |
−0.936611 | + | 0.350372i | \(0.886055\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.00000 | + | 9.00000i | −0.438633 | + | 0.438633i | −0.891552 | − | 0.452919i | \(-0.850383\pi\) |
0.452919 | + | 0.891552i | \(0.350383\pi\) | |||||||
\(422\) | −15.5885 | − | 9.00000i | −0.758834 | − | 0.438113i | ||||
\(423\) | −31.1769 | + | 18.0000i | −1.51587 | + | 0.875190i | ||||
\(424\) | 3.46410 | − | 2.00000i | 0.168232 | − | 0.0971286i | ||||
\(425\) | 5.19615 | + | 3.00000i | 0.252050 | + | 0.145521i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10.0000 | + | 10.0000i | 0.483368 | + | 0.483368i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.46410 | + | 1.46410i | 0.263502 | + | 0.0706052i | ||||
\(431\) | 4.00000 | + | 6.92820i | 0.192673 | + | 0.333720i | 0.946135 | − | 0.323772i | \(-0.104951\pi\) |
−0.753462 | + | 0.657491i | \(0.771618\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.00000 | 0.288342 | 0.144171 | − | 0.989553i | \(-0.453949\pi\) | ||||
0.144171 | + | 0.989553i | \(0.453949\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.19615 | + | 8.19615i | 0.105177 | + | 0.392525i | ||||
\(437\) | −16.3923 | − | 4.39230i | −0.784150 | − | 0.210112i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.8564 | − | 8.00000i | −0.661330 | − | 0.381819i | 0.131453 | − | 0.991322i | \(-0.458036\pi\) |
−0.792784 | + | 0.609503i | \(0.791369\pi\) | |||||||
\(440\) | 8.00000 | + | 8.00000i | 0.381385 | + | 0.381385i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.366025 | − | 1.36603i | −0.0173904 | − | 0.0649018i | 0.956685 | − | 0.291124i | \(-0.0940292\pi\) |
−0.974076 | + | 0.226222i | \(0.927363\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.2487 | − | 38.2487i | 0.485836 | − | 1.81316i | ||||
\(446\) | −5.46410 | + | 1.46410i | −0.258733 | + | 0.0693272i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | −12.2942 | + | 3.29423i | −0.579555 | + | 0.155291i | ||||
\(451\) | 3.66025 | − | 13.6603i | 0.172355 | − | 0.643236i | ||||
\(452\) | 6.92820 | − | 4.00000i | 0.325875 | − | 0.188144i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 4.00000i | − | 0.187729i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.0526 | + | 11.0000i | 0.891241 | + | 0.514558i | 0.874348 | − | 0.485299i | \(-0.161289\pi\) |
0.0168929 | + | 0.999857i | \(0.494623\pi\) | |||||||
\(458\) | −8.00000 | − | 13.8564i | −0.373815 | − | 0.647467i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.78461 | + | 32.7846i | 0.409585 | + | 1.52859i | ||||
\(461\) | −16.0000 | − | 16.0000i | −0.745194 | − | 0.745194i | 0.228378 | − | 0.973572i | \(-0.426658\pi\) |
−0.973572 | + | 0.228378i | \(0.926658\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0000 | 0.650635 | 0.325318 | − | 0.945605i | \(-0.394529\pi\) | ||||
0.325318 | + | 0.945605i | \(0.394529\pi\) | |||||||
\(464\) | 38.2487 | − | 10.2487i | 1.77565 | − | 0.475784i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.8564 | − | 5.85641i | −1.01248 | − | 0.271293i | ||||
\(467\) | 24.5885 | − | 6.58846i | 1.13782 | − | 0.304877i | 0.359745 | − | 0.933051i | \(-0.382864\pi\) |
0.778073 | + | 0.628173i | \(0.216197\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 48.0000 | 2.21407 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 27.7128 | − | 16.0000i | 1.27559 | − | 0.736460i | ||||
\(473\) | 1.73205 | − | 1.00000i | 0.0796398 | − | 0.0459800i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.00000 | + | 6.00000i | −0.275299 | + | 0.275299i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.00000 | + | 3.00000i | 0.137361 | + | 0.137361i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.0000 | − | 17.3205i | −0.456912 | − | 0.791394i | 0.541884 | − | 0.840453i | \(-0.317711\pi\) |
−0.998796 | + | 0.0490589i | \(0.984378\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 22.0000 | + | 22.0000i | 1.00207 | + | 1.00207i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18.0000 | −0.818182 | ||||||||
\(485\) | −1.46410 | − | 5.46410i | −0.0664814 | − | 0.248112i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.0526 | + | 11.0000i | −0.863354 | + | 0.498458i | −0.865134 | − | 0.501541i | \(-0.832767\pi\) |
0.00178012 | + | 0.999998i | \(0.499433\pi\) | |||||||
\(488\) | 12.0000 | − | 20.7846i | 0.543214 | − | 0.940875i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.0000 | + | 19.0000i | −0.857458 | + | 0.857458i | −0.991038 | − | 0.133580i | \(-0.957353\pi\) |
0.133580 | + | 0.991038i | \(0.457353\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.12436 | − | 19.1244i | 0.230789 | − | 0.861318i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.00000 | + | 10.3923i | −0.269680 | + | 0.467099i | ||||
\(496\) | −32.0000 | −1.43684 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.4186 | − | 8.41858i | 1.40649 | − | 0.376868i | 0.525818 | − | 0.850597i | \(-0.323759\pi\) |
0.880671 | + | 0.473729i | \(0.157092\pi\) | |||||||
\(500\) | −10.9282 | − | 2.92820i | −0.488724 | − | 0.130953i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.0000 | − | 24.2487i | 0.624851 | − | 1.08227i | ||||
\(503\) | − | 16.0000i | − | 0.713405i | −0.934218 | − | 0.356702i | \(-0.883901\pi\) | ||
0.934218 | − | 0.356702i | \(-0.116099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 24.0000i | − | 1.06799i | ||||||
\(506\) | 10.3923 | + | 6.00000i | 0.461994 | + | 0.266733i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.8564 | − | 8.00000i | 0.614779 | − | 0.354943i | ||||
\(509\) | −10.9282 | + | 2.92820i | −0.484384 | + | 0.129790i | −0.492743 | − | 0.870175i | \(-0.664006\pi\) |
0.00835918 | + | 0.999965i | \(0.497339\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.707107 | − | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.732051 | + | 2.73205i | −0.0322894 | + | 0.120506i | ||||
\(515\) | −2.92820 | + | 10.9282i | −0.129032 | + | 0.481554i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.0000 | − | 12.0000i | 0.527759 | − | 0.527759i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.66025 | + | 5.00000i | −0.379413 | + | 0.219054i | −0.677563 | − | 0.735465i | \(-0.736964\pi\) |
0.298150 | + | 0.954519i | \(0.403630\pi\) | |||||||
\(522\) | 21.0000 | + | 36.3731i | 0.919145 | + | 1.59201i | ||||
\(523\) | −8.78461 | − | 32.7846i | −0.384124 | − | 1.43357i | −0.839543 | − | 0.543293i | \(-0.817177\pi\) |
0.455419 | − | 0.890277i | \(-0.349490\pi\) | |||||||
\(524\) | −28.0000 | + | 28.0000i | −1.22319 | + | 1.22319i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.0000 | − | 16.0000i | 0.697633 | − | 0.697633i | ||||
\(527\) | −8.00000 | + | 13.8564i | −0.348485 | + | 0.603595i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.50000 | + | 11.2583i | 0.282609 | + | 0.489493i | ||||
\(530\) | −1.46410 | − | 5.46410i | −0.0635965 | − | 0.237345i | ||||
\(531\) | 24.0000 | + | 24.0000i | 1.04151 | + | 1.04151i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.3205 | − | 10.0000i | 0.748831 | − | 0.432338i | ||||
\(536\) | −6.00000 | − | 10.3923i | −0.259161 | − | 0.448879i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 16.0000i | − | 0.689809i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.0263 | + | 4.02628i | −0.646030 | + | 0.173103i | −0.566933 | − | 0.823764i | \(-0.691870\pi\) |
−0.0790969 | + | 0.996867i | \(0.525204\pi\) | |||||||
\(542\) | −2.92820 | + | 10.9282i | −0.125777 | + | 0.469407i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10.9282 | + | 2.92820i | −0.468543 | + | 0.125546i | ||||
\(545\) | 12.0000 | 0.514024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.0000 | + | 23.0000i | 0.983409 | + | 0.983409i | 0.999865 | − | 0.0164556i | \(-0.00523822\pi\) |
−0.0164556 | + | 0.999865i | \(0.505238\pi\) | |||||||
\(548\) | −12.0000 | + | 20.7846i | −0.512615 | + | 0.887875i | ||||
\(549\) | 24.5885 | + | 6.58846i | 1.04941 | + | 0.281189i | ||||
\(550\) | 5.19615 | − | 3.00000i | 0.221565 | − | 0.127920i | ||||
\(551\) | 24.2487 | + | 14.0000i | 1.03303 | + | 0.596420i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 30.0000 | 1.27458 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.46410 | − | 5.46410i | 0.0620917 | − | 0.231730i | ||||
\(557\) | −6.22243 | + | 23.2224i | −0.263653 | + | 0.983966i | 0.699417 | + | 0.714714i | \(0.253443\pi\) |
−0.963070 | + | 0.269252i | \(0.913224\pi\) | |||||||
\(558\) | −8.78461 | − | 32.7846i | −0.371882 | − | 1.38788i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.32051 | + | 27.3205i | −0.308523 | + | 1.15142i | 0.621348 | + | 0.783535i | \(0.286585\pi\) |
−0.929870 | + | 0.367887i | \(0.880081\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.92820 | − | 10.9282i | −0.123190 | − | 0.459753i | ||||
\(566\) | 8.00000 | 0.336265 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.1244 | − | 7.00000i | −0.508279 | − | 0.293455i | 0.223847 | − | 0.974624i | \(-0.428139\pi\) |
−0.732126 | + | 0.681169i | \(0.761472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.2942 | + | 3.29423i | 0.514497 | + | 0.137859i | 0.506720 | − | 0.862111i | \(-0.330858\pi\) |
0.00777727 | + | 0.999970i | \(0.497524\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.0000 | 0.750652 | ||||||||
\(576\) | 12.0000 | − | 20.7846i | 0.500000 | − | 0.866025i | ||||
\(577\) | −1.00000 | − | 1.73205i | −0.0416305 | − | 0.0721062i | 0.844459 | − | 0.535620i | \(-0.179922\pi\) |
−0.886090 | + | 0.463513i | \(0.846589\pi\) | |||||||
\(578\) | 4.75833 | − | 17.7583i | 0.197920 | − | 0.738649i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 56.0000i | − | 2.32527i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.73205 | − | 1.00000i | −0.0717342 | − | 0.0414158i | ||||
\(584\) | −4.39230 | + | 16.3923i | −0.181755 | + | 0.678318i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.0000 | + | 24.2487i | −0.578335 | + | 1.00171i | ||||
\(587\) | −10.0000 | + | 10.0000i | −0.412744 | + | 0.412744i | −0.882693 | − | 0.469949i | \(-0.844272\pi\) |
0.469949 | + | 0.882693i | \(0.344272\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0000 | − | 16.0000i | −0.659269 | − | 0.659269i | ||||
\(590\) | −11.7128 | − | 43.7128i | −0.482209 | − | 1.79963i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −27.3205 | − | 7.32051i | −1.12287 | − | 0.300871i | ||||
\(593\) | −3.00000 | + | 5.19615i | −0.123195 | + | 0.213380i | −0.921026 | − | 0.389501i | \(-0.872647\pi\) |
0.797831 | + | 0.602881i | \(0.205981\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.00000 | + | 6.00000i | 0.245770 | + | 0.245770i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.7846 | − | 12.0000i | 0.849236 | − | 0.490307i | −0.0111569 | − | 0.999938i | \(-0.503551\pi\) |
0.860393 | + | 0.509631i | \(0.170218\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.0000i | 0.407909i | 0.978980 | + | 0.203954i | \(0.0653794\pi\) | ||||
−0.978980 | + | 0.203954i | \(0.934621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.00000 | − | 9.00000i | 0.366508 | − | 0.366508i | ||||
\(604\) | −10.0000 | + | 17.3205i | −0.406894 | + | 0.704761i | ||||
\(605\) | −6.58846 | + | 24.5885i | −0.267859 | + | 0.999663i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.0000 | − | 24.2487i | 0.568242 | − | 0.984225i | −0.428497 | − | 0.903543i | \(-0.640957\pi\) |
0.996740 | − | 0.0806818i | \(-0.0257098\pi\) | |||||||
\(608\) | − | 16.0000i | − | 0.648886i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −24.0000 | − | 24.0000i | −0.971732 | − | 0.971732i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −6.00000 | − | 10.3923i | −0.242536 | − | 0.420084i | ||||
\(613\) | −12.2942 | − | 3.29423i | −0.496559 | − | 0.133053i | 0.00184345 | − | 0.999998i | \(-0.499413\pi\) |
−0.498403 | + | 0.866946i | \(0.666080\pi\) | |||||||
\(614\) | −31.1769 | − | 18.0000i | −1.25820 | − | 0.726421i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 42.0000i | − | 1.69086i | −0.534089 | − | 0.845428i | \(-0.679345\pi\) | ||
0.534089 | − | 0.845428i | \(-0.320655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.3923 | − | 4.39230i | −0.658862 | − | 0.176542i | −0.0861298 | − | 0.996284i | \(-0.527450\pi\) |
−0.572733 | + | 0.819742i | \(0.694117\pi\) | |||||||
\(620\) | −11.7128 | + | 43.7128i | −0.470398 | + | 1.75555i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.0000 | − | 20.0000i | 0.801927 | − | 0.801927i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.5000 | + | 26.8468i | −0.620000 | + | 1.07387i | ||||
\(626\) | −19.1244 | − | 5.12436i | −0.764363 | − | 0.204810i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.78461 | − | 32.7846i | −0.350544 | − | 1.30825i | ||||
\(629\) | −10.0000 | + | 10.0000i | −0.398726 | + | 0.398726i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.0000i | 1.59237i | 0.605050 | + | 0.796187i | \(0.293153\pi\) | ||||
−0.605050 | + | 0.796187i | \(0.706847\pi\) | |||||||
\(632\) | 7.32051 | + | 27.3205i | 0.291194 | + | 1.08675i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.1244 | − | 7.00000i | 0.481520 | − | 0.278006i | ||||
\(635\) | −5.85641 | − | 21.8564i | −0.232404 | − | 0.867345i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.0000 | − | 14.0000i | −0.554265 | − | 0.554265i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −27.7128 | + | 16.0000i | −1.09545 | + | 0.632456i | ||||
\(641\) | −6.00000 | − | 10.3923i | −0.236986 | − | 0.410471i | 0.722862 | − | 0.690992i | \(-0.242826\pi\) |
−0.959848 | + | 0.280521i | \(0.909493\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.92820 | − | 4.00000i | −0.272587 | − | 0.157378i | ||||
\(647\) | 10.3923 | − | 6.00000i | 0.408564 | − | 0.235884i | −0.281609 | − | 0.959529i | \(-0.590868\pi\) |
0.690172 | + | 0.723645i | \(0.257535\pi\) | |||||||
\(648\) | 24.5885 | + | 6.58846i | 0.965926 | + | 0.258819i | ||||
\(649\) | −13.8564 | − | 8.00000i | −0.543912 | − | 0.314027i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −30.0000 | + | 30.0000i | −1.17489 | + | 1.17489i | ||||
\(653\) | −34.1506 | + | 9.15064i | −1.33642 | + | 0.358092i | −0.855104 | − | 0.518456i | \(-0.826507\pi\) |
−0.481314 | + | 0.876548i | \(0.659840\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.0000 | + | 48.4974i | 1.09405 | + | 1.89495i | ||||
\(656\) | 34.6410 | + | 20.0000i | 1.35250 | + | 0.780869i | ||||
\(657\) | −18.0000 | −0.702247 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.00000 | − | 3.00000i | −0.116863 | − | 0.116863i | 0.646257 | − | 0.763120i | \(-0.276334\pi\) |
−0.763120 | + | 0.646257i | \(0.776334\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.5167 | + | 9.51666i | 1.38144 | + | 0.370155i | 0.871643 | − | 0.490141i | \(-0.163055\pi\) |
0.509795 | + | 0.860296i | \(0.329721\pi\) | |||||||
\(662\) | 21.0000 | + | 36.3731i | 0.816188 | + | 1.41368i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 40.0000 | 1.55230 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 30.0000i | − | 1.16248i | ||||||
\(667\) | −15.3731 | − | 57.3731i | −0.595248 | − | 2.22149i | ||||
\(668\) | 12.0000 | + | 20.7846i | 0.464294 | + | 0.804181i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −16.3923 | + | 4.39230i | −0.633290 | + | 0.169690i | ||||
\(671\) | −12.0000 | −0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.0000 | 1.31060 | 0.655302 | − | 0.755367i | \(-0.272541\pi\) | ||||
0.655302 | + | 0.755367i | \(0.272541\pi\) | |||||||
\(674\) | 10.9282 | − | 2.92820i | 0.420939 | − | 0.112790i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.0000 | − | 22.5167i | −0.500000 | − | 0.866025i | ||||
\(677\) | 7.32051 | + | 27.3205i | 0.281350 | + | 1.05001i | 0.951465 | + | 0.307756i | \(0.0995779\pi\) |
−0.670115 | + | 0.742257i | \(0.733755\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 16.0000i | 0.613572i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.00000 | + | 13.8564i | 0.306336 | + | 0.530589i | ||||
\(683\) | 15.0263 | + | 4.02628i | 0.574965 | + | 0.154061i | 0.534573 | − | 0.845123i | \(-0.320473\pi\) |
0.0403921 | + | 0.999184i | \(0.487139\pi\) | |||||||
\(684\) | 16.3923 | − | 4.39230i | 0.626775 | − | 0.167944i | ||||
\(685\) | 24.0000 | + | 24.0000i | 0.916993 | + | 0.916993i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.46410 | + | 5.46410i | 0.0558184 | + | 0.208317i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.5167 | − | 9.51666i | 1.35112 | − | 0.362031i | 0.490570 | − | 0.871402i | \(-0.336788\pi\) |
0.860547 | + | 0.509371i | \(0.170122\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −30.0000 | −1.13878 | ||||||||
\(695\) | −6.92820 | − | 4.00000i | −0.262802 | − | 0.151729i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.3205 | − | 10.0000i | 0.656061 | − | 0.378777i | ||||
\(698\) | −20.7846 | − | 12.0000i | −0.786709 | − | 0.454207i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.0000 | − | 19.0000i | −0.717620 | − | 0.717620i | 0.250497 | − | 0.968117i | \(-0.419406\pi\) |
−0.968117 | + | 0.250497i | \(0.919406\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.0000 | − | 17.3205i | −0.377157 | − | 0.653255i | ||||
\(704\) | −2.92820 | + | 10.9282i | −0.110361 | + | 0.411872i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.00000 | − | 6.00000i | −0.225813 | − | 0.225813i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.56218 | − | 9.56218i | −0.0962246 | − | 0.359115i | 0.900978 | − | 0.433865i | \(-0.142851\pi\) |
−0.997202 | + | 0.0747503i | \(0.976184\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −25.9808 | + | 15.0000i | −0.974355 | + | 0.562544i | ||||
\(712\) | 38.2487 | − | 10.2487i | 1.43343 | − | 0.384087i | ||||
\(713\) | 48.0000i | 1.79761i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.19615 | + | 8.19615i | 0.0820741 | + | 0.306305i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.19615 | + | 2.19615i | 0.305878 | + | 0.0819597i | ||||
\(719\) | 10.0000 | − | 17.3205i | 0.372937 | − | 0.645946i | −0.617079 | − | 0.786901i | \(-0.711684\pi\) |
0.990016 | + | 0.140955i | \(0.0450174\pi\) | |||||||
\(720\) | −24.0000 | − | 24.0000i | −0.894427 | − | 0.894427i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −11.0000 | + | 11.0000i | −0.409378 | + | 0.409378i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.92820 | − | 10.9282i | 0.108826 | − | 0.406143i | ||||
\(725\) | −28.6865 | − | 7.68653i | −1.06539 | − | 0.285471i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0000i | 1.18681i | 0.804902 | + | 0.593407i | \(0.202218\pi\) | ||||
−0.804902 | + | 0.593407i | \(0.797782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | 20.7846 | + | 12.0000i | 0.769273 | + | 0.444140i | ||||
\(731\) | 2.73205 | + | 0.732051i | 0.101049 | + | 0.0270759i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.6603 | + | 3.66025i | −0.504553 | + | 0.135195i | −0.502112 | − | 0.864802i | \(-0.667444\pi\) |
−0.00244074 | + | 0.999997i | \(0.500777\pi\) | |||||||
\(734\) | −32.0000 | − | 32.0000i | −1.18114 | − | 1.18114i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24.0000 | + | 24.0000i | −0.884652 | + | 0.884652i | ||||
\(737\) | −3.00000 | + | 5.19615i | −0.110506 | + | 0.191403i | ||||
\(738\) | −10.9808 | + | 40.9808i | −0.404207 | + | 1.50852i | ||||
\(739\) | 2.56218 | − | 9.56218i | 0.0942512 | − | 0.351750i | −0.902654 | − | 0.430368i | \(-0.858384\pi\) |
0.996905 | + | 0.0786174i | \(0.0250505\pi\) | |||||||
\(740\) | −20.0000 | + | 34.6410i | −0.735215 | + | 1.27343i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.00000i | 0.220119i | 0.993925 | + | 0.110059i | \(0.0351041\pi\) | ||||
−0.993925 | + | 0.110059i | \(0.964896\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.3923 | − | 6.00000i | 0.380745 | − | 0.219823i | ||||
\(746\) | −11.0000 | − | 19.0526i | −0.402739 | − | 0.697564i | ||||
\(747\) | 10.9808 | + | 40.9808i | 0.401765 | + | 1.49941i | ||||
\(748\) | 4.00000 | + | 4.00000i | 0.146254 | + | 0.146254i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.0000 | + | 27.7128i | −0.583848 | + | 1.01125i | 0.411170 | + | 0.911559i | \(0.365120\pi\) |
−0.995018 | + | 0.0996961i | \(0.968213\pi\) | |||||||
\(752\) | 24.0000 | + | 41.5692i | 0.875190 | + | 1.51587i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.0000 | + | 20.0000i | 0.727875 | + | 0.727875i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0000 | + | 15.0000i | −0.545184 | + | 0.545184i | −0.925044 | − | 0.379860i | \(-0.875972\pi\) |
0.379860 | + | 0.925044i | \(0.375972\pi\) | |||||||
\(758\) | 13.0000 | − | 22.5167i | 0.472181 | − | 0.817842i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −21.8564 | − | 5.85641i | −0.792815 | − | 0.212434i | ||||
\(761\) | 25.9808 | + | 15.0000i | 0.941802 | + | 0.543750i | 0.890525 | − | 0.454935i | \(-0.150337\pi\) |
0.0512772 | + | 0.998684i | \(0.483671\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 36.0000i | − | 1.30243i | ||||||
\(765\) | −16.3923 | + | 4.39230i | −0.592665 | + | 0.158804i | ||||
\(766\) | 1.46410 | − | 5.46410i | 0.0529001 | − | 0.197426i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.0000 | 0.360609 | 0.180305 | − | 0.983611i | \(-0.442292\pi\) | ||||
0.180305 | + | 0.983611i | \(0.442292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 27.7128 | + | 16.0000i | 0.997406 | + | 0.575853i | ||||
\(773\) | −8.19615 | − | 2.19615i | −0.294795 | − | 0.0789901i | 0.108390 | − | 0.994108i | \(-0.465430\pi\) |
−0.403185 | + | 0.915118i | \(0.632097\pi\) | |||||||
\(774\) | −5.19615 | + | 3.00000i | −0.186772 | + | 0.107833i | ||||
\(775\) | 20.7846 | + | 12.0000i | 0.746605 | + | 0.431053i | ||||
\(776\) | 4.00000 | − | 4.00000i | 0.143592 | − | 0.143592i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.00000 | −0.215110 | ||||||||
\(779\) | 7.32051 | + | 27.3205i | 0.262284 | + | 0.978859i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 4.39230 | + | 16.3923i | 0.157069 | + | 0.586188i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −48.0000 | −1.71319 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.58846 | + | 24.5885i | −0.234853 | + | 0.876484i | 0.743362 | + | 0.668889i | \(0.233230\pi\) |
−0.978215 | + | 0.207594i | \(0.933437\pi\) | |||||||
\(788\) | 3.66025 | − | 13.6603i | 0.130391 | − | 0.486626i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 40.0000 | 1.42314 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −12.0000 | −0.426401 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −20.7846 | + | 12.0000i | −0.737618 | + | 0.425864i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −24.0000 | + | 41.5692i | −0.850657 | + | 1.47338i | ||||
\(797\) | 32.0000 | + | 32.0000i | 1.13350 | + | 1.13350i | 0.989591 | + | 0.143907i | \(0.0459666\pi\) |
0.143907 | + | 0.989591i | \(0.454033\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 4.39230 | + | 16.3923i | 0.155291 | + | 0.579555i | ||||
\(801\) | 21.0000 | + | 36.3731i | 0.741999 | + | 1.28518i | ||||
\(802\) | −4.39230 | + | 16.3923i | −0.155098 | + | 0.578832i | ||||
\(803\) | 8.19615 | − | 2.19615i | 0.289236 | − | 0.0775005i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 20.7846 | − | 12.0000i | 0.731200 | − | 0.422159i | ||||
\(809\) | −5.19615 | + | 3.00000i | −0.182687 | + | 0.105474i | −0.588555 | − | 0.808458i | \(-0.700303\pi\) |
0.405868 | + | 0.913932i | \(0.366969\pi\) | |||||||
\(810\) | 18.0000 | − | 31.1769i | 0.632456 | − | 1.09545i | ||||
\(811\) | 24.0000 | − | 24.0000i | 0.842754 | − | 0.842754i | −0.146462 | − | 0.989216i | \(-0.546789\pi\) |
0.989216 | + | 0.146462i | \(0.0467887\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.66025 | + | 13.6603i | 0.128292 | + | 0.478792i | ||||
\(815\) | 30.0000 | + | 51.9615i | 1.05085 | + | 1.82013i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.00000 | + | 3.46410i | −0.0699711 | + | 0.121194i | ||||
\(818\) | −14.0000 | + | 14.0000i | −0.489499 | + | 0.489499i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 40.0000 | − | 40.0000i | 1.39686 | − | 1.39686i | ||||
\(821\) | 0.366025 | + | 1.36603i | 0.0127744 | + | 0.0476746i | 0.972019 | − | 0.234903i | \(-0.0754772\pi\) |
−0.959244 | + | 0.282578i | \(0.908811\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.7846 | + | 12.0000i | −0.724506 | + | 0.418294i | −0.816409 | − | 0.577474i | \(-0.804038\pi\) |
0.0919029 | + | 0.995768i | \(0.470705\pi\) | |||||||
\(824\) | −10.9282 | + | 2.92820i | −0.380702 | + | 0.102009i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.00000 | + | 5.00000i | −0.173867 | + | 0.173867i | −0.788676 | − | 0.614809i | \(-0.789233\pi\) |
0.614809 | + | 0.788676i | \(0.289233\pi\) | |||||||
\(828\) | −31.1769 | − | 18.0000i | −1.08347 | − | 0.625543i | ||||
\(829\) | −0.732051 | + | 2.73205i | −0.0254252 | + | 0.0948880i | −0.977473 | − | 0.211063i | \(-0.932308\pi\) |
0.952047 | + | 0.305951i | \(0.0989743\pi\) | |||||||
\(830\) | 14.6410 | − | 54.6410i | 0.508197 | − | 1.89662i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.7846 | − | 8.78461i | 1.13456 | − | 0.304004i | ||||
\(836\) | −6.92820 | + | 4.00000i | −0.239617 | + | 0.138343i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20.7846 | − | 12.0000i | −0.717992 | − | 0.414533i | ||||
\(839\) | − | 4.00000i | − | 0.138095i | −0.997613 | − | 0.0690477i | \(-0.978004\pi\) | ||
0.997613 | − | 0.0690477i | \(-0.0219961\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 69.0000i | 2.37931i | ||||||||
\(842\) | −9.00000 | + | 15.5885i | −0.310160 | + | 0.537214i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −24.5885 | − | 6.58846i | −0.846370 | − | 0.226784i | ||||
\(845\) | −35.5167 | + | 9.51666i | −1.22181 | + | 0.327383i | ||||
\(846\) | −36.0000 | + | 36.0000i | −1.23771 | + | 1.23771i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.00000 | − | 4.00000i | 0.137361 | − | 0.137361i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.19615 | + | 2.19615i | 0.281126 | + | 0.0753274i | ||||
\(851\) | −10.9808 | + | 40.9808i | −0.376416 | + | 1.40480i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.0000 | + | 24.0000i | −0.821744 | + | 0.821744i | −0.986358 | − | 0.164614i | \(-0.947362\pi\) |
0.164614 | + | 0.986358i | \(0.447362\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 24.0000i | − | 0.820783i | ||||||
\(856\) | 17.3205 | + | 10.0000i | 0.592003 | + | 0.341793i | ||||
\(857\) | −15.5885 | + | 9.00000i | −0.532492 | + | 0.307434i | −0.742030 | − | 0.670366i | \(-0.766137\pi\) |
0.209539 | + | 0.977800i | \(0.432804\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.732051 | + | 2.73205i | 0.0249773 | + | 0.0932164i | 0.977289 | − | 0.211909i | \(-0.0679682\pi\) |
−0.952312 | + | 0.305126i | \(0.901302\pi\) | |||||||
\(860\) | 8.00000 | 0.272798 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.00000 | + | 8.00000i | 0.272481 | + | 0.272481i | ||||
\(863\) | −7.00000 | + | 12.1244i | −0.238283 | + | 0.412718i | −0.960222 | − | 0.279239i | \(-0.909918\pi\) |
0.721939 | + | 0.691957i | \(0.243251\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.19615 | − | 2.19615i | 0.278517 | − | 0.0746283i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.0000 | − | 10.0000i | 0.339227 | − | 0.339227i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 6.00000 | + | 10.3923i | 0.203186 | + | 0.351928i | ||||
\(873\) | 5.19615 | + | 3.00000i | 0.175863 | + | 0.101535i | ||||
\(874\) | −24.0000 | −0.811812 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.09808 | + | 1.09808i | −0.138382 | + | 0.0370794i | −0.327345 | − | 0.944905i | \(-0.606154\pi\) |
0.188963 | + | 0.981984i | \(0.439487\pi\) | |||||||
\(878\) | −21.8564 | − | 5.85641i | −0.737618 | − | 0.197644i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 13.8564 | + | 8.00000i | 0.467099 | + | 0.269680i | ||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.0000 | − | 25.0000i | −0.841317 | − | 0.841317i | 0.147713 | − | 0.989030i | \(-0.452809\pi\) |
−0.989030 | + | 0.147713i | \(0.952809\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.00000 | − | 1.73205i | −0.0335957 | − | 0.0581894i | ||||
\(887\) | −10.3923 | − | 6.00000i | −0.348939 | − | 0.201460i | 0.315279 | − | 0.948999i | \(-0.397902\pi\) |
−0.664218 | + | 0.747539i | \(0.731235\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 56.0000i | − | 1.87712i | ||||||
\(891\) | −3.29423 | − | 12.2942i | −0.110361 | − | 0.411872i | ||||
\(892\) | −6.92820 | + | 4.00000i | −0.231973 | + | 0.133930i | ||||
\(893\) | −8.78461 | + | 32.7846i | −0.293966 | + | 1.09710i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.0000 | 0.401116 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −40.9808 | + | 10.9808i | −1.36755 | + | 0.366433i | ||||
\(899\) | 20.4974 | − | 76.4974i | 0.683627 | − | 2.55133i | ||||
\(900\) | −15.5885 | + | 9.00000i | −0.519615 | + | 0.300000i | ||||
\(901\) | −0.732051 | − | 2.73205i | −0.0243881 | − | 0.0910178i | ||||
\(902\) | − | 20.0000i | − | 0.665927i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.00000 | − | 8.00000i | 0.266076 | − | 0.266076i | ||||
\(905\) | −13.8564 | − | 8.00000i | −0.460603 | − | 0.265929i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.4904 | − | 5.49038i | −0.680372 | − | 0.182305i | −0.0979495 | − | 0.995191i | \(-0.531228\pi\) |
−0.582422 | + | 0.812886i | \(0.697895\pi\) | |||||||
\(908\) | −1.46410 | − | 5.46410i | −0.0485879 | − | 0.181333i | ||||
\(909\) | 18.0000 | + | 18.0000i | 0.597022 | + | 0.597022i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.0000 | −1.59031 | −0.795155 | − | 0.606406i | \(-0.792611\pi\) | ||||
−0.795155 | + | 0.606406i | \(0.792611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.0000 | − | 17.3205i | −0.330952 | − | 0.573225i | ||||
\(914\) | 30.0526 | + | 8.05256i | 0.994050 | + | 0.266355i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.0000 | − | 16.0000i | −0.528655 | − | 0.528655i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.7846 | − | 12.0000i | −0.685621 | − | 0.395843i | 0.116348 | − | 0.993208i | \(-0.462881\pi\) |
−0.801970 | + | 0.597365i | \(0.796214\pi\) | |||||||
\(920\) | 24.0000 | + | 41.5692i | 0.791257 | + | 1.37050i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −27.7128 | − | 16.0000i | −0.912673 | − | 0.526932i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.0000 | + | 15.0000i | 0.493197 | + | 0.493197i | ||||
\(926\) | 19.1244 | − | 5.12436i | 0.628465 | − | 0.168397i | ||||
\(927\) | −6.00000 | − | 10.3923i | −0.197066 | − | 0.341328i | ||||
\(928\) | 48.4974 | − | 28.0000i | 1.59201 | − | 0.919145i | ||||
\(929\) | −25.0000 | + | 43.3013i | −0.820223 | + | 1.42067i | 0.0852924 | + | 0.996356i | \(0.472818\pi\) |
−0.905516 | + | 0.424313i | \(0.860516\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −32.0000 | −1.04819 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 31.1769 | − | 18.0000i | 1.02014 | − | 0.588978i | ||||
\(935\) | 6.92820 | − | 4.00000i | 0.226576 | − | 0.130814i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 58.0000i | − | 1.89478i | −0.320085 | − | 0.947389i | \(-0.603712\pi\) | ||
0.320085 | − | 0.947389i | \(-0.396288\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 65.5692 | − | 17.5692i | 2.13863 | − | 0.573045i | ||||
\(941\) | −9.51666 | + | 35.5167i | −0.310234 | + | 1.15781i | 0.618111 | + | 0.786091i | \(0.287898\pi\) |
−0.928345 | + | 0.371719i | \(0.878768\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.0000 | − | 51.9615i | 0.976934 | − | 1.69210i | ||||
\(944\) | 32.0000 | − | 32.0000i | 1.04151 | − | 1.04151i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.00000 | − | 2.00000i | 0.0650256 | − | 0.0650256i | ||||
\(947\) | −45.0788 | + | 12.0788i | −1.46487 | + | 0.392510i | −0.901167 | − | 0.433471i | \(-0.857289\pi\) |
−0.563698 | + | 0.825981i | \(0.690622\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −6.00000 | + | 10.3923i | −0.194666 | + | 0.337171i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.0000i | 0.518291i | 0.965838 | + | 0.259145i | \(0.0834409\pi\) | ||||
−0.965838 | + | 0.259145i | \(0.916559\pi\) | |||||||
\(954\) | 5.19615 | + | 3.00000i | 0.168232 | + | 0.0971286i | ||||
\(955\) | −49.1769 | − | 13.1769i | −1.59133 | − | 0.426395i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −20.0000 | − | 20.0000i | −0.646171 | − | 0.646171i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | + | 28.5788i | −0.532258 | + | 0.921898i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.49038 | + | 20.4904i | −0.176925 | + | 0.660293i | ||||
\(964\) | 38.1051 | + | 22.0000i | 1.22728 | + | 0.708572i | ||||
\(965\) | 32.0000 | − | 32.0000i | 1.03012 | − | 1.03012i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2.00000i | − | 0.0643157i | −0.999483 | − | 0.0321578i | \(-0.989762\pi\) | ||
0.999483 | − | 0.0321578i | \(-0.0102379\pi\) | |||||||
\(968\) | −24.5885 | + | 6.58846i | −0.790303 | + | 0.211761i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.00000 | − | 6.92820i | −0.128432 | − | 0.222451i | ||||
\(971\) | 1.46410 | + | 5.46410i | 0.0469853 | + | 0.175351i | 0.985431 | − | 0.170075i | \(-0.0544010\pi\) |
−0.938446 | + | 0.345426i | \(0.887734\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −22.0000 | + | 22.0000i | −0.704925 | + | 0.704925i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.78461 | − | 32.7846i | 0.281189 | − | 1.04941i | ||||
\(977\) | −19.0000 | − | 32.9090i | −0.607864 | − | 1.05285i | −0.991592 | − | 0.129405i | \(-0.958693\pi\) |
0.383728 | − | 0.923446i | \(-0.374640\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.0000 | − | 14.0000i | −0.447442 | − | 0.447442i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.00000 | + | 9.00000i | −0.287348 | + | 0.287348i | ||||
\(982\) | −19.0000 | + | 32.9090i | −0.606314 | + | 1.05017i | ||||
\(983\) | 38.1051 | − | 22.0000i | 1.21536 | − | 0.701691i | 0.251442 | − | 0.967872i | \(-0.419095\pi\) |
0.963923 | + | 0.266181i | \(0.0857620\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.3205 | − | 10.0000i | −0.551877 | − | 0.318626i | ||||
\(986\) | − | 28.0000i | − | 0.891702i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.19615 | − | 2.19615i | 0.260622 | − | 0.0698336i | ||||
\(990\) | −4.39230 | + | 16.3923i | −0.139597 | + | 0.520982i | ||||
\(991\) | −11.0000 | − | 19.0526i | −0.349427 | − | 0.605224i | 0.636721 | − | 0.771094i | \(-0.280290\pi\) |
−0.986148 | + | 0.165870i | \(0.946957\pi\) | |||||||
\(992\) | −43.7128 | + | 11.7128i | −1.38788 | + | 0.371882i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 48.0000 | + | 48.0000i | 1.52170 | + | 1.52170i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.9808 | − | 10.9808i | −1.29787 | − | 0.347764i | −0.457228 | − | 0.889350i | \(-0.651158\pi\) |
−0.840646 | + | 0.541585i | \(0.817824\pi\) | |||||||
\(998\) | 39.8372 | − | 23.0000i | 1.26102 | − | 0.728052i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 784.2.x.e.765.1 | 4 | ||
7.2 | even | 3 | 784.2.m.a.589.1 | 2 | |||
7.3 | odd | 6 | 784.2.x.d.557.1 | 4 | |||
7.4 | even | 3 | inner | 784.2.x.e.557.1 | 4 | ||
7.5 | odd | 6 | 112.2.m.b.29.1 | ✓ | 2 | ||
7.6 | odd | 2 | 784.2.x.d.765.1 | 4 | |||
16.5 | even | 4 | inner | 784.2.x.e.373.1 | 4 | ||
28.19 | even | 6 | 448.2.m.a.337.1 | 2 | |||
56.5 | odd | 6 | 896.2.m.b.673.1 | 2 | |||
56.19 | even | 6 | 896.2.m.c.673.1 | 2 | |||
112.5 | odd | 12 | 112.2.m.b.85.1 | yes | 2 | ||
112.19 | even | 12 | 896.2.m.c.225.1 | 2 | |||
112.37 | even | 12 | 784.2.m.a.197.1 | 2 | |||
112.53 | even | 12 | inner | 784.2.x.e.165.1 | 4 | ||
112.61 | odd | 12 | 896.2.m.b.225.1 | 2 | |||
112.69 | odd | 4 | 784.2.x.d.373.1 | 4 | |||
112.75 | even | 12 | 448.2.m.a.113.1 | 2 | |||
112.101 | odd | 12 | 784.2.x.d.165.1 | 4 | |||
224.5 | odd | 24 | 7168.2.a.b.1.2 | 2 | |||
224.75 | even | 24 | 7168.2.a.k.1.1 | 2 | |||
224.117 | odd | 24 | 7168.2.a.b.1.1 | 2 | |||
224.187 | even | 24 | 7168.2.a.k.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.m.b.29.1 | ✓ | 2 | 7.5 | odd | 6 | ||
112.2.m.b.85.1 | yes | 2 | 112.5 | odd | 12 | ||
448.2.m.a.113.1 | 2 | 112.75 | even | 12 | |||
448.2.m.a.337.1 | 2 | 28.19 | even | 6 | |||
784.2.m.a.197.1 | 2 | 112.37 | even | 12 | |||
784.2.m.a.589.1 | 2 | 7.2 | even | 3 | |||
784.2.x.d.165.1 | 4 | 112.101 | odd | 12 | |||
784.2.x.d.373.1 | 4 | 112.69 | odd | 4 | |||
784.2.x.d.557.1 | 4 | 7.3 | odd | 6 | |||
784.2.x.d.765.1 | 4 | 7.6 | odd | 2 | |||
784.2.x.e.165.1 | 4 | 112.53 | even | 12 | inner | ||
784.2.x.e.373.1 | 4 | 16.5 | even | 4 | inner | ||
784.2.x.e.557.1 | 4 | 7.4 | even | 3 | inner | ||
784.2.x.e.765.1 | 4 | 1.1 | even | 1 | trivial | ||
896.2.m.b.225.1 | 2 | 112.61 | odd | 12 | |||
896.2.m.b.673.1 | 2 | 56.5 | odd | 6 | |||
896.2.m.c.225.1 | 2 | 112.19 | even | 12 | |||
896.2.m.c.673.1 | 2 | 56.19 | even | 6 | |||
7168.2.a.b.1.1 | 2 | 224.117 | odd | 24 | |||
7168.2.a.b.1.2 | 2 | 224.5 | odd | 24 | |||
7168.2.a.k.1.1 | 2 | 224.75 | even | 24 | |||
7168.2.a.k.1.2 | 2 | 224.187 | even | 24 |