Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,2,Mod(53,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 10, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.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: | \(12.9357651274\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 593.1 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.593 |
Dual form | 1620.2.x.a.377.1 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.48356 | + | 1.67303i | −0.663470 | + | 0.748203i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.732051 | + | 2.73205i | 0.276689 | + | 1.03262i | 0.954701 | + | 0.297567i | \(0.0961752\pi\) |
−0.678012 | + | 0.735051i | \(0.737158\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.44949 | + | 1.41421i | 0.738549 | + | 0.426401i | 0.821541 | − | 0.570149i | \(-0.193114\pi\) |
−0.0829925 | + | 0.996550i | \(0.526448\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.09808 | − | 4.09808i | 0.304552 | − | 1.13660i | −0.628779 | − | 0.777584i | \(-0.716445\pi\) |
0.933331 | − | 0.359018i | \(-0.116888\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.41421 | + | 1.41421i | 0.342997 | + | 0.342997i | 0.857493 | − | 0.514496i | \(-0.172021\pi\) |
−0.514496 | + | 0.857493i | \(0.672021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.00000i | − | 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.72741 | + | 2.07055i | 1.61128 | + | 0.431740i | 0.948422 | − | 0.317009i | \(-0.102679\pi\) |
0.662853 | + | 0.748749i | \(0.269345\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.598076 | − | 4.96410i | −0.119615 | − | 0.992820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.94975 | + | 8.57321i | −0.919145 | + | 1.59201i | −0.118428 | + | 0.992963i | \(0.537786\pi\) |
−0.800717 | + | 0.599043i | \(0.795548\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | + | 6.92820i | 0.718421 | + | 1.24434i | 0.961625 | + | 0.274367i | \(0.0884683\pi\) |
−0.243204 | + | 0.969975i | \(0.578198\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.65685 | − | 2.82843i | −0.956183 | − | 0.478091i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | + | 3.00000i | −0.493197 | + | 0.493197i | −0.909312 | − | 0.416115i | \(-0.863391\pi\) |
0.416115 | + | 0.909312i | \(0.363391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.22474 | − | 0.707107i | 0.191273 | − | 0.110432i | −0.401305 | − | 0.915944i | \(-0.631443\pi\) |
0.592578 | + | 0.805513i | \(0.298110\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.5911 | + | 3.10583i | −1.69074 | + | 0.453032i | −0.970580 | − | 0.240779i | \(-0.922597\pi\) |
−0.720157 | + | 0.693811i | \(0.755930\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.866025 | + | 0.500000i | −0.123718 | + | 0.0714286i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.07107 | + | 7.07107i | −0.971286 | + | 0.971286i | −0.999599 | − | 0.0283132i | \(-0.990986\pi\) |
0.0283132 | + | 0.999599i | \(0.490986\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.00000 | + | 2.00000i | −0.809040 | + | 0.269680i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.41421 | + | 2.44949i | 0.184115 | + | 0.318896i | 0.943278 | − | 0.332004i | \(-0.107725\pi\) |
−0.759163 | + | 0.650901i | \(0.774391\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.22715 | + | 7.91688i | 0.648348 | + | 0.981968i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.9282 | − | 2.92820i | −1.33509 | − | 0.357737i | −0.480481 | − | 0.877005i | \(-0.659538\pi\) |
−0.854611 | + | 0.519268i | \(0.826205\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.65685i | − | 0.671345i | −0.941979 | − | 0.335673i | \(-0.891036\pi\) | ||
0.941979 | − | 0.335673i | \(-0.108964\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.00000 | + | 7.00000i | 0.819288 | + | 0.819288i | 0.986005 | − | 0.166717i | \(-0.0533166\pi\) |
−0.166717 | + | 0.986005i | \(0.553317\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.07055 | + | 7.72741i | −0.235961 | + | 0.880620i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.10583 | + | 11.5911i | 0.340909 | + | 1.27229i | 0.897319 | + | 0.441382i | \(0.145512\pi\) |
−0.556410 | + | 0.830908i | \(0.687822\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.46410 | + | 0.267949i | −0.484200 | + | 0.0290632i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.41421 | −0.149906 | −0.0749532 | − | 0.997187i | \(-0.523881\pi\) | ||||
−0.0749532 | + | 0.997187i | \(0.523881\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0000 | 1.25794 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.69213 | + | 5.93426i | 0.686598 | + | 0.608842i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.09808 | + | 4.09808i | 0.111493 | + | 0.416097i | 0.999001 | − | 0.0446959i | \(-0.0142319\pi\) |
−0.887508 | + | 0.460793i | \(0.847565\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.22474 | + | 0.707107i | 0.121867 | + | 0.0703598i | 0.559694 | − | 0.828699i | \(-0.310919\pi\) |
−0.437828 | + | 0.899059i | \(0.644252\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.732051 | + | 2.73205i | −0.0721311 | + | 0.269197i | −0.992567 | − | 0.121695i | \(-0.961167\pi\) |
0.920436 | + | 0.390892i | \(0.127834\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.82843 | − | 2.82843i | −0.273434 | − | 0.273434i | 0.557047 | − | 0.830481i | \(-0.311934\pi\) |
−0.830481 | + | 0.557047i | \(0.811934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8.00000i | − | 0.766261i | −0.923694 | − | 0.383131i | \(-0.874846\pi\) | ||
0.923694 | − | 0.383131i | \(-0.125154\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.86370 | + | 1.03528i | 0.363467 | + | 0.0973906i | 0.435930 | − | 0.899980i | \(-0.356419\pi\) |
−0.0724636 | + | 0.997371i | \(0.523086\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.9282 | + | 9.85641i | −1.39206 | + | 0.919115i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.82843 | + | 4.89898i | −0.259281 | + | 0.449089i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.50000 | − | 2.59808i | −0.136364 | − | 0.236189i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.19239 | + | 6.36396i | 0.822192 | + | 0.569210i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0000 | + | 10.0000i | −0.887357 | + | 0.887357i | −0.994268 | − | 0.106912i | \(-0.965904\pi\) |
0.106912 | + | 0.994268i | \(0.465904\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.44949 | + | 1.41421i | −0.214013 | + | 0.123560i | −0.603175 | − | 0.797609i | \(-0.706098\pi\) |
0.389162 | + | 0.921169i | \(0.372765\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.9282 | − | 2.92820i | 0.947595 | − | 0.253907i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.5911 | − | 3.10583i | 0.990295 | − | 0.265349i | 0.272921 | − | 0.962037i | \(-0.412010\pi\) |
0.717375 | + | 0.696688i | \(0.245344\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.8564 | − | 8.00000i | 1.17529 | − | 0.678551i | 0.220366 | − | 0.975417i | \(-0.429275\pi\) |
0.954919 | + | 0.296866i | \(0.0959415\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.48528 | − | 8.48528i | 0.709575 | − | 0.709575i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.00000 | − | 21.0000i | −0.581318 | − | 1.74396i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.36396 | + | 11.0227i | 0.521356 | + | 0.903015i | 0.999691 | + | 0.0248379i | \(0.00790696\pi\) |
−0.478335 | + | 0.878177i | \(0.658760\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000 | − | 17.3205i | 0.813788 | − | 1.40952i | −0.0964061 | − | 0.995342i | \(-0.530735\pi\) |
0.910195 | − | 0.414181i | \(-0.135932\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.5254 | − | 3.58630i | −1.40767 | − | 0.288059i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.2942 | + | 3.29423i | 0.981186 | + | 0.262908i | 0.713544 | − | 0.700610i | \(-0.247089\pi\) |
0.267642 | + | 0.963518i | \(0.413756\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 22.6274i | 1.78329i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | − | 4.00000i | −0.313304 | − | 0.313304i | 0.532884 | − | 0.846188i | \(-0.321108\pi\) |
−0.846188 | + | 0.532884i | \(0.821108\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.14110 | − | 15.4548i | 0.320448 | − | 1.19593i | −0.598361 | − | 0.801227i | \(-0.704181\pi\) |
0.918809 | − | 0.394702i | \(-0.129152\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.33013 | − | 2.50000i | −0.333087 | − | 0.192308i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.03528 | + | 3.86370i | 0.0787106 | + | 0.293752i | 0.994049 | − | 0.108933i | \(-0.0347435\pi\) |
−0.915338 | + | 0.402685i | \(0.868077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.1244 | − | 5.26795i | 0.992108 | − | 0.398220i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.1421 | −1.05703 | −0.528516 | − | 0.848923i | \(-0.677252\pi\) | ||||
−0.528516 | + | 0.848923i | \(0.677252\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.00000 | 0.594635 | 0.297318 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297318 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.568406 | − | 9.46979i | −0.0417900 | − | 0.696233i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.46410 | + | 5.46410i | 0.107066 | + | 0.399575i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.79796 | − | 5.65685i | −0.708955 | − | 0.409316i | 0.101719 | − | 0.994813i | \(-0.467566\pi\) |
−0.810674 | + | 0.585498i | \(0.800899\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.49038 | + | 20.4904i | −0.395206 | + | 1.47493i | 0.426222 | + | 0.904618i | \(0.359844\pi\) |
−0.821429 | + | 0.570311i | \(0.806823\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.48528 | − | 8.48528i | −0.604551 | − | 0.604551i | 0.336966 | − | 0.941517i | \(-0.390599\pi\) |
−0.941517 | + | 0.336966i | \(0.890599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.0000i | 0.850657i | 0.905039 | + | 0.425329i | \(0.139842\pi\) | ||||
−0.905039 | + | 0.425329i | \(0.860158\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −27.0459 | − | 7.24693i | −1.89825 | − | 0.508635i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.633975 | + | 3.09808i | −0.0442787 | + | 0.216379i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.65685 | − | 9.79796i | 0.391293 | − | 0.677739i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | − | 6.92820i | −0.275371 | − | 0.476957i | 0.694857 | − | 0.719148i | \(-0.255467\pi\) |
−0.970229 | + | 0.242190i | \(0.922134\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.0000 | + | 16.0000i | −1.08615 | + | 1.08615i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.34847 | − | 4.24264i | 0.494312 | − | 0.285391i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.19615 | − | 2.19615i | 0.548855 | − | 0.147065i | 0.0262738 | − | 0.999655i | \(-0.491636\pi\) |
0.522581 | + | 0.852590i | \(0.324969\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.72741 | − | 2.07055i | 0.512886 | − | 0.137427i | 0.00691198 | − | 0.999976i | \(-0.497800\pi\) |
0.505974 | + | 0.862549i | \(0.331133\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.19615 | + | 3.00000i | −0.343371 | + | 0.198246i | −0.661762 | − | 0.749714i | \(-0.730191\pi\) |
0.318390 | + | 0.947960i | \(0.396858\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.24264 | − | 4.24264i | 0.277945 | − | 0.277945i | −0.554343 | − | 0.832288i | \(-0.687031\pi\) |
0.832288 | + | 0.554343i | \(0.187031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.0000 | − | 24.0000i | 0.782794 | − | 1.56559i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.00000 | + | 8.66025i | −0.322078 | + | 0.557856i | −0.980917 | − | 0.194429i | \(-0.937715\pi\) |
0.658838 | + | 0.752285i | \(0.271048\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.448288 | − | 2.19067i | 0.0286401 | − | 0.139957i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.3923 | − | 4.39230i | −1.04302 | − | 0.279476i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 25.4558i | − | 1.60676i | −0.595468 | − | 0.803379i | \(-0.703033\pi\) | ||
0.595468 | − | 0.803379i | \(-0.296967\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0000 | + | 16.0000i | 1.00591 | + | 1.00591i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.17638 | + | 19.3185i | −0.322894 | + | 1.20506i | 0.593519 | + | 0.804820i | \(0.297738\pi\) |
−0.916412 | + | 0.400236i | \(0.868928\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.3923 | − | 6.00000i | −0.645746 | − | 0.372822i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.14110 | − | 15.4548i | −0.255351 | − | 0.952985i | −0.967895 | − | 0.251356i | \(-0.919123\pi\) |
0.712543 | − | 0.701628i | \(-0.247543\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.33975 | − | 22.3205i | −0.0822999 | − | 1.37114i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.3848 | 1.12094 | 0.560470 | − | 0.828175i | \(-0.310621\pi\) | ||||
0.560470 | + | 0.828175i | \(0.310621\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | 0.728948 | 0.364474 | − | 0.931214i | \(-0.381249\pi\) | ||||
0.364474 | + | 0.931214i | \(0.381249\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.55532 | − | 13.0053i | 0.334998 | − | 0.784251i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.49038 | + | 20.4904i | 0.329885 | + | 1.23115i | 0.909309 | + | 0.416121i | \(0.136611\pi\) |
−0.579424 | + | 0.815026i | \(0.696722\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.0227 | + | 6.36396i | 0.657559 | + | 0.379642i | 0.791346 | − | 0.611368i | \(-0.209380\pi\) |
−0.133787 | + | 0.991010i | \(0.542714\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.46410 | + | 5.46410i | −0.0870318 | + | 0.324807i | −0.995691 | − | 0.0927310i | \(-0.970440\pi\) |
0.908659 | + | 0.417538i | \(0.137107\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.82843 | + | 2.82843i | 0.166957 | + | 0.166957i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 13.0000i | − | 0.764706i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.5911 | − | 3.10583i | −0.677160 | − | 0.181444i | −0.0961820 | − | 0.995364i | \(-0.530663\pi\) |
−0.580978 | + | 0.813919i | \(0.697330\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.19615 | − | 1.26795i | −0.360754 | − | 0.0738229i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.9706 | − | 29.3939i | 0.981433 | − | 1.69989i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.0000 | + | 12.0000i | −0.684876 | + | 0.684876i | −0.961095 | − | 0.276219i | \(-0.910919\pi\) |
0.276219 | + | 0.961095i | \(0.410919\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.89898 | + | 2.82843i | −0.277796 | + | 0.160385i | −0.632425 | − | 0.774622i | \(-0.717940\pi\) |
0.354629 | + | 0.935007i | \(0.384607\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.09808 | + | 1.09808i | −0.231637 | + | 0.0620669i | −0.372770 | − | 0.927924i | \(-0.621592\pi\) |
0.141133 | + | 0.989991i | \(0.454925\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.79555 | − | 1.55291i | 0.325511 | − | 0.0872204i | −0.0923631 | − | 0.995725i | \(-0.529442\pi\) |
0.417874 | + | 0.908505i | \(0.362775\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.2487 | + | 14.0000i | −1.35767 | + | 0.783850i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.65685 | − | 5.65685i | 0.314756 | − | 0.314756i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.0000 | − | 3.00000i | −1.16487 | − | 0.166410i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.9706 | − | 29.3939i | −0.935617 | − | 1.62054i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000 | − | 17.3205i | 0.549650 | − | 0.952021i | −0.448649 | − | 0.893708i | \(-0.648095\pi\) |
0.998298 | − | 0.0583130i | \(-0.0185721\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.1117 | − | 13.9391i | 1.15345 | − | 0.761572i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.09808 | + | 1.09808i | 0.223236 | + | 0.0598160i | 0.368703 | − | 0.929547i | \(-0.379802\pi\) |
−0.145467 | + | 0.989363i | \(0.546468\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.6274i | 1.22534i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0000 | + | 12.0000i | 0.647939 | + | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.07055 | − | 7.72741i | 0.111153 | − | 0.414829i | −0.887817 | − | 0.460196i | \(-0.847779\pi\) |
0.998970 | + | 0.0453672i | \(0.0144458\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.7128 | − | 16.0000i | −1.48343 | − | 0.856460i | −0.483610 | − | 0.875284i | \(-0.660675\pi\) |
−0.999823 | + | 0.0188232i | \(0.994008\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.65874 | − | 17.3867i | −0.247960 | − | 0.925399i | −0.971873 | − | 0.235507i | \(-0.924325\pi\) |
0.723913 | − | 0.689892i | \(-0.242342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.46410 | + | 8.39230i | 0.502302 | + | 0.445417i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.3137 | 0.597115 | 0.298557 | − | 0.954392i | \(-0.403495\pi\) | ||||
0.298557 | + | 0.954392i | \(0.403495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.0962 | + | 1.32628i | −1.15657 | + | 0.0694207i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.12436 | + | 19.1244i | 0.267489 | + | 0.998283i | 0.960709 | + | 0.277557i | \(0.0895248\pi\) |
−0.693220 | + | 0.720726i | \(0.743809\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.4949 | − | 14.1421i | −1.27171 | − | 0.734223i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.83013 | + | 6.83013i | −0.0947604 | + | 0.353651i | −0.996983 | − | 0.0776200i | \(-0.975268\pi\) |
0.902223 | + | 0.431271i | \(0.141935\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 29.6985 | + | 29.6985i | 1.52955 | + | 1.52955i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 16.0000i | − | 0.821865i | −0.911666 | − | 0.410932i | \(-0.865203\pi\) | ||
0.911666 | − | 0.410932i | \(-0.134797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 34.7733 | + | 9.31749i | 1.77683 | + | 0.476101i | 0.990000 | − | 0.141064i | \(-0.0450523\pi\) |
0.786834 | + | 0.617165i | \(0.211719\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.85641 | − | 14.9282i | −0.502329 | − | 0.760812i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.6066 | − | 18.3712i | 0.537776 | − | 0.931455i | −0.461247 | − | 0.887272i | \(-0.652598\pi\) |
0.999023 | − | 0.0441839i | \(-0.0140687\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | + | 13.8564i | 0.404577 | + | 0.700749i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.0000 | + | 17.0000i | −0.853206 | + | 0.853206i | −0.990527 | − | 0.137321i | \(-0.956151\pi\) |
0.137321 | + | 0.990527i | \(0.456151\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.3712 | + | 10.6066i | −0.917413 | + | 0.529668i | −0.882809 | − | 0.469733i | \(-0.844350\pi\) |
−0.0346039 | + | 0.999401i | \(0.511017\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.7846 | − | 8.78461i | 1.63312 | − | 0.437593i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.5911 | + | 3.10583i | −0.574550 | + | 0.153950i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.7846 | − | 12.0000i | 1.02773 | − | 0.593362i | 0.111398 | − | 0.993776i | \(-0.464467\pi\) |
0.916334 | + | 0.400414i | \(0.131134\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.65685 | + | 5.65685i | −0.278356 | + | 0.278356i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.0000 | − | 12.0000i | −1.17811 | − | 0.589057i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.7279 | − | 22.0454i | −0.621800 | − | 1.07699i | −0.989150 | − | 0.146906i | \(-0.953068\pi\) |
0.367351 | − | 0.930082i | \(-0.380265\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0000 | − | 19.0526i | 0.536107 | − | 0.928565i | −0.463002 | − | 0.886357i | \(-0.653228\pi\) |
0.999109 | − | 0.0422075i | \(-0.0134391\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.17449 | − | 7.86611i | 0.299507 | − | 0.381562i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 28.2843i | − | 1.36241i | −0.732095 | − | 0.681203i | \(-0.761457\pi\) | ||
0.732095 | − | 0.681203i | \(-0.238543\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.0000 | + | 23.0000i | 1.10531 | + | 1.10531i | 0.993759 | + | 0.111551i | \(0.0355818\pi\) |
0.111551 | + | 0.993759i | \(0.464418\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.28221 | − | 30.9096i | 0.396192 | − | 1.47861i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.3205 | + | 10.0000i | 0.826663 | + | 0.477274i | 0.852709 | − | 0.522387i | \(-0.174958\pi\) |
−0.0260459 | + | 0.999661i | \(0.508292\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.21166 | − | 23.1822i | −0.295125 | − | 1.10142i | −0.941118 | − | 0.338078i | \(-0.890223\pi\) |
0.645994 | − | 0.763343i | \(-0.276443\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.09808 | − | 2.36603i | 0.0994584 | − | 0.112160i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.41421 | 0.0667409 | 0.0333704 | − | 0.999443i | \(-0.489376\pi\) | ||||
0.0333704 | + | 0.999443i | \(0.489376\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −17.8028 | + | 20.0764i | −0.834607 | + | 0.941196i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.49038 | + | 20.4904i | 0.256829 | + | 0.958500i | 0.967064 | + | 0.254534i | \(0.0819222\pi\) |
−0.710235 | + | 0.703965i | \(0.751411\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.4722 | + | 7.77817i | 0.627463 | + | 0.362266i | 0.779769 | − | 0.626068i | \(-0.215337\pi\) |
−0.152306 | + | 0.988333i | \(0.548670\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.51666 | − | 35.5167i | 0.442277 | − | 1.65060i | −0.280751 | − | 0.959781i | \(-0.590584\pi\) |
0.723028 | − | 0.690819i | \(-0.242750\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.7990 | − | 19.7990i | −0.916188 | − | 0.916188i | 0.0805616 | − | 0.996750i | \(-0.474329\pi\) |
−0.996750 | + | 0.0805616i | \(0.974329\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 32.0000i | − | 1.47762i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.8564 | + | 2.39230i | −0.911074 | + | 0.109766i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.7990 | + | 34.2929i | −0.904639 | + | 1.56688i | −0.0832378 | + | 0.996530i | \(0.526526\pi\) |
−0.821401 | + | 0.570351i | \(0.806807\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.00000 | + | 15.5885i | 0.410365 | + | 0.710772i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.48528 | − | 4.24264i | −0.385297 | − | 0.192648i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.00000 | − | 6.00000i | 0.271886 | − | 0.271886i | −0.557973 | − | 0.829859i | \(-0.688421\pi\) |
0.829859 | + | 0.557973i | \(0.188421\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.8434 | − | 18.3848i | 1.43707 | − | 0.829693i | 0.439426 | − | 0.898279i | \(-0.355182\pi\) |
0.997645 | + | 0.0685856i | \(0.0218486\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.1244 | + | 5.12436i | −0.861318 | + | 0.230789i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.4548 | − | 4.14110i | 0.693243 | − | 0.185754i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.46410 | − | 2.00000i | 0.155074 | − | 0.0895323i | −0.420455 | − | 0.907314i | \(-0.638129\pi\) |
0.575529 | + | 0.817781i | \(0.304796\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.48528 | + | 8.48528i | −0.378340 | + | 0.378340i | −0.870503 | − | 0.492163i | \(-0.836206\pi\) |
0.492163 | + | 0.870503i | \(0.336206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.00000 | + | 1.00000i | −0.133498 | + | 0.0444994i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.707107 | − | 1.22474i | −0.0313420 | − | 0.0542859i | 0.849929 | − | 0.526897i | \(-0.176645\pi\) |
−0.881271 | + | 0.472611i | \(0.843311\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.0000 | + | 24.2487i | −0.619324 | + | 1.07270i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.48477 | − | 5.27792i | −0.153557 | − | 0.232573i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −32.7846 | − | 8.78461i | −1.44187 | − | 0.386347i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 29.6985i | − | 1.30111i | −0.759457 | − | 0.650557i | \(-0.774535\pi\) | ||
0.759457 | − | 0.650557i | \(-0.225465\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.14110 | + | 15.4548i | −0.180389 | + | 0.673222i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35.5070 | + | 20.5000i | 1.54378 | + | 0.891304i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.55291 | − | 5.79555i | −0.0672642 | − | 0.251033i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.92820 | − | 0.535898i | 0.386000 | − | 0.0231689i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.82843 | −0.121829 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.0000 | 1.71973 | 0.859867 | − | 0.510518i | \(-0.170546\pi\) | ||||
0.859867 | + | 0.510518i | \(0.170546\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.3843 | + | 11.8685i | 0.573319 | + | 0.508391i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.39230 | − | 16.3923i | −0.187801 | − | 0.700884i | −0.994013 | − | 0.109258i | \(-0.965153\pi\) |
0.806212 | − | 0.591627i | \(-0.201514\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.2929 | + | 19.7990i | 1.46092 | + | 0.843465i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.7279 | + | 12.7279i | 0.539299 | + | 0.539299i | 0.923323 | − | 0.384024i | \(-0.125462\pi\) |
−0.384024 | + | 0.923323i | \(0.625462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.1822 | − | 6.21166i | −0.977014 | − | 0.261790i | −0.265227 | − | 0.964186i | \(-0.585447\pi\) |
−0.711787 | + | 0.702396i | \(0.752114\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.46410 | + | 4.92820i | −0.314017 | + | 0.207331i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.77817 | + | 13.4722i | −0.326078 | + | 0.564784i | −0.981730 | − | 0.190280i | \(-0.939061\pi\) |
0.655652 | + | 0.755063i | \(0.272394\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | + | 3.46410i | 0.0836974 | + | 0.144968i | 0.904835 | − | 0.425762i | \(-0.139994\pi\) |
−0.821138 | + | 0.570730i | \(0.806660\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.65685 | − | 39.5980i | 0.235907 | − | 1.65135i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.00000 | − | 7.00000i | 0.291414 | − | 0.291414i | −0.546225 | − | 0.837639i | \(-0.683936\pi\) |
0.837639 | + | 0.546225i | \(0.183936\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29.3939 | + | 16.9706i | −1.21946 | + | 0.704058i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.3205 | + | 7.32051i | −1.13150 | + | 0.303184i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.5911 | + | 3.10583i | −0.478416 | + | 0.128191i | −0.489965 | − | 0.871742i | \(-0.662990\pi\) |
0.0115488 | + | 0.999933i | \(0.496324\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.7128 | − | 16.0000i | 1.14189 | − | 0.659269i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.1421 | + | 14.1421i | −0.580748 | + | 0.580748i | −0.935109 | − | 0.354361i | \(-0.884698\pi\) |
0.354361 | + | 0.935109i | \(0.384698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.00000 | − | 12.0000i | −0.163984 | − | 0.491952i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.1421 | + | 24.4949i | 0.577832 | + | 1.00083i | 0.995728 | + | 0.0923393i | \(0.0294344\pi\) |
−0.417896 | + | 0.908495i | \(0.637232\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.0000 | − | 34.6410i | 0.815817 | − | 1.41304i | −0.0929227 | − | 0.995673i | \(-0.529621\pi\) |
0.908740 | − | 0.417363i | \(-0.137046\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.57201 | + | 1.34486i | 0.267190 | + | 0.0546765i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.5885 | − | 6.58846i | −0.998015 | − | 0.267417i | −0.277401 | − | 0.960754i | \(-0.589473\pi\) |
−0.720614 | + | 0.693337i | \(0.756140\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 50.9117i | 2.05967i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.0000 | − | 27.0000i | −1.09052 | − | 1.09052i | −0.995473 | − | 0.0950469i | \(-0.969700\pi\) |
−0.0950469 | − | 0.995473i | \(-0.530300\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.55291 | − | 5.79555i | 0.0625180 | − | 0.233320i | −0.927596 | − | 0.373585i | \(-0.878129\pi\) |
0.990114 | + | 0.140264i | \(0.0447952\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.7846 | − | 12.0000i | −0.835404 | − | 0.482321i | 0.0202954 | − | 0.999794i | \(-0.493539\pi\) |
−0.855699 | + | 0.517473i | \(0.826873\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.03528 | − | 3.86370i | −0.0414775 | − | 0.154796i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.2846 | + | 5.93782i | −0.971384 | + | 0.237513i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.48528 | −0.338330 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.89469 | − | 31.5660i | −0.0751884 | − | 1.25266i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.09808 | + | 4.09808i | 0.0435074 | + | 0.162372i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.5176 | − | 20.5061i | −1.40286 | − | 0.809942i | −0.408176 | − | 0.912903i | \(-0.633835\pi\) |
−0.994685 | + | 0.102961i | \(0.967168\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.82843 | + | 2.82843i | 0.111197 | + | 0.111197i | 0.760516 | − | 0.649319i | \(-0.224946\pi\) |
−0.649319 | + | 0.760516i | \(0.724946\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.00000i | 0.314027i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.79555 | + | 1.55291i | 0.226798 | + | 0.0607702i | 0.370428 | − | 0.928861i | \(-0.379211\pi\) |
−0.143630 | + | 0.989631i | \(0.545878\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.26795 | − | 6.19615i | 0.0495429 | − | 0.242104i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.41421 | + | 2.44949i | −0.0550899 | + | 0.0954186i | −0.892255 | − | 0.451531i | \(-0.850878\pi\) |
0.837165 | + | 0.546950i | \(0.184211\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.00000 | + | 13.8564i | 0.311164 | + | 0.538952i | 0.978615 | − | 0.205702i | \(-0.0659478\pi\) |
−0.667451 | + | 0.744654i | \(0.732615\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.3137 | + | 22.6274i | −0.438727 | + | 0.877454i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −56.0000 | + | 56.0000i | −2.16833 | + | 2.16833i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.4186 | − | 8.41858i | 1.21110 | − | 0.324513i | 0.403905 | − | 0.914801i | \(-0.367653\pi\) |
0.807192 | + | 0.590288i | \(0.200986\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.5230 | + | 3.62347i | −0.519730 | + | 0.139261i | −0.509142 | − | 0.860683i | \(-0.670037\pi\) |
−0.0105881 | + | 0.999944i | \(0.503370\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.3923 | + | 6.00000i | −0.398820 | + | 0.230259i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.48528 | − | 8.48528i | 0.324680 | − | 0.324680i | −0.525879 | − | 0.850559i | \(-0.676264\pi\) |
0.850559 | + | 0.525879i | \(0.176264\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | + | 24.0000i | −0.458496 | + | 0.916993i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.2132 | + | 36.7423i | 0.808159 | + | 1.39977i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.00000 | + | 10.3923i | −0.228251 | + | 0.395342i | −0.957290 | − | 0.289130i | \(-0.906634\pi\) |
0.729039 | + | 0.684472i | \(0.239967\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.17260 | + | 35.0507i | −0.272072 | + | 1.32955i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.73205 | + | 0.732051i | 0.103484 | + | 0.0277284i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.89949i | 0.373899i | 0.982370 | + | 0.186949i | \(0.0598600\pi\) | ||||
−0.982370 | + | 0.186949i | \(0.940140\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0000 | + | 12.0000i | 0.452589 | + | 0.452589i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.03528 | + | 3.86370i | −0.0389356 | + | 0.145310i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.66025 | + | 5.00000i | 0.325243 | + | 0.187779i | 0.653727 | − | 0.756730i | \(-0.273204\pi\) |
−0.328484 | + | 0.944509i | \(0.606538\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.5644 | + | 61.8193i | 0.620342 | + | 2.31515i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.60770 | + | 26.7846i | 0.0601244 | + | 1.00169i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 39.5980 | 1.47676 | 0.738378 | − | 0.674387i | \(-0.235592\pi\) | ||||
0.738378 | + | 0.674387i | \(0.235592\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 45.5186 | + | 19.4436i | 1.69052 | + | 0.722118i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.19615 | − | 8.19615i | −0.0814508 | − | 0.303978i | 0.913168 | − | 0.407584i | \(-0.133629\pi\) |
−0.994618 | + | 0.103606i | \(0.966962\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.6147 | + | 39.6147i | −0.392064 | + | 1.46320i | 0.434659 | + | 0.900595i | \(0.356869\pi\) |
−0.826723 | + | 0.562609i | \(0.809798\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.6274 | − | 22.6274i | −0.833492 | − | 0.833492i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.0000i | 1.03000i | 0.857191 | + | 0.514998i | \(0.172207\pi\) | ||||
−0.857191 | + | 0.514998i | \(0.827793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.0459 | + | 7.24693i | 0.992219 | + | 0.265864i | 0.718182 | − | 0.695855i | \(-0.244974\pi\) |
0.274036 | + | 0.961719i | \(0.411641\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.8827 | − | 5.70577i | −1.02154 | − | 0.209043i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.65685 | − | 9.79796i | 0.206697 | − | 0.358010i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.0000 | + | 20.7846i | 0.437886 | + | 0.758441i | 0.997526 | − | 0.0702946i | \(-0.0223939\pi\) |
−0.559640 | + | 0.828736i | \(0.689061\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.1421 | + | 42.4264i | 0.514685 | + | 1.54406i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.00000 | − | 9.00000i | 0.327111 | − | 0.327111i | −0.524376 | − | 0.851487i | \(-0.675701\pi\) |
0.851487 | + | 0.524376i | \(0.175701\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.2702 | − | 13.4350i | 0.843542 | − | 0.487019i | −0.0149244 | − | 0.999889i | \(-0.504751\pi\) |
0.858467 | + | 0.512869i | \(0.171417\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.8564 | − | 5.85641i | 0.791255 | − | 0.212016i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.5911 | − | 3.10583i | 0.418531 | − | 0.112145i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.92820 | + | 4.00000i | −0.249837 | + | 0.144244i | −0.619690 | − | 0.784847i | \(-0.712742\pi\) |
0.369852 | + | 0.929091i | \(0.379408\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.7279 | − | 12.7279i | 0.457792 | − | 0.457792i | −0.440138 | − | 0.897930i | \(-0.645071\pi\) |
0.897930 | + | 0.440138i | \(0.145071\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.0000 | − | 24.0000i | 1.14947 | − | 0.862105i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.82843 | − | 4.89898i | −0.101339 | − | 0.175524i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | − | 13.8564i | 0.286263 | − | 0.495821i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23.7506 | + | 15.6814i | −0.847696 | + | 0.559695i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.3205 | + | 7.32051i | 0.973871 | + | 0.260948i | 0.710461 | − | 0.703736i | \(-0.248486\pi\) |
0.263410 | + | 0.964684i | \(0.415153\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.3137i | 0.402269i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.10583 | + | 11.5911i | −0.110014 | + | 0.410578i | −0.998866 | − | 0.0476171i | \(-0.984837\pi\) |
0.888852 | + | 0.458195i | \(0.151504\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.7846 | − | 12.0000i | −0.735307 | − | 0.424529i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.24693 | + | 27.0459i | 0.255739 | + | 0.954430i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −37.8564 | − | 33.5692i | −1.33426 | − | 1.18316i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.8406 | −1.54135 | −0.770677 | − | 0.637226i | \(-0.780082\pi\) | ||||
−0.770677 | + | 0.637226i | \(0.780082\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.00000 | 0.280918 | 0.140459 | − | 0.990086i | \(-0.455142\pi\) | ||||
0.140459 | + | 0.990086i | \(0.455142\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.6264 | − | 0.757875i | 0.442283 | − | 0.0265472i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.4722 | + | 7.77817i | 0.470183 | + | 0.271460i | 0.716316 | − | 0.697776i | \(-0.245827\pi\) |
−0.246133 | + | 0.969236i | \(0.579160\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.51666 | − | 35.5167i | 0.331730 | − | 1.23803i | −0.575641 | − | 0.817702i | \(-0.695247\pi\) |
0.907371 | − | 0.420331i | \(-0.138086\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.9411 | − | 33.9411i | −1.18025 | − | 1.18025i | −0.979680 | − | 0.200569i | \(-0.935721\pi\) |
−0.200569 | − | 0.979680i | \(-0.564279\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 8.00000i | − | 0.277851i | −0.990303 | − | 0.138926i | \(-0.955635\pi\) | ||
0.990303 | − | 0.138926i | \(-0.0443649\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.93185 | − | 0.517638i | −0.0669347 | − | 0.0179351i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.7128 | + | 29.8564i | 0.682190 | + | 1.03322i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.65685 | + | 9.79796i | −0.195296 | + | 0.338263i | −0.946998 | − | 0.321241i | \(-0.895900\pi\) |
0.751701 | + | 0.659504i | \(0.229234\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34.5000 | − | 59.7558i | −1.18966 | − | 2.06054i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.6066 | − | 3.53553i | 0.364878 | − | 0.121626i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.00000 | − | 6.00000i | 0.206162 | − | 0.206162i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29.3939 | + | 16.9706i | −1.00761 | + | 0.581743i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.83013 | − | 1.83013i | 0.233859 | − | 0.0626624i | −0.139986 | − | 0.990153i | \(-0.544706\pi\) |
0.373845 | + | 0.927491i | \(0.378039\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40.5689 | + | 10.8704i | −1.38581 | + | 0.371326i | −0.873227 | − | 0.487314i | \(-0.837977\pi\) |
−0.512580 | + | 0.858640i | \(0.671310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.92820 | + | 4.00000i | −0.236387 | + | 0.136478i | −0.613515 | − | 0.789683i | \(-0.710245\pi\) |
0.377128 | + | 0.926161i | \(0.376912\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.65685 | + | 5.65685i | −0.192562 | + | 0.192562i | −0.796802 | − | 0.604240i | \(-0.793477\pi\) |
0.604240 | + | 0.796802i | \(0.293477\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.00000 | − | 4.00000i | −0.272008 | − | 0.136004i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.0000 | + | 41.5692i | −0.813209 | + | 1.40852i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.6574 | + | 29.7728i | −0.360285 | + | 1.00650i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.4904 | + | 5.49038i | 0.691911 | + | 0.185397i | 0.587605 | − | 0.809148i | \(-0.300071\pi\) |
0.104306 | + | 0.994545i | \(0.466738\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 41.0122i | − | 1.38174i | −0.722981 | − | 0.690868i | \(-0.757229\pi\) | ||
0.722981 | − | 0.690868i | \(-0.242771\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.0000 | − | 20.0000i | −0.673054 | − | 0.673054i | 0.285365 | − | 0.958419i | \(-0.407885\pi\) |
−0.958419 | + | 0.285365i | \(0.907885\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.4233 | + | 46.3644i | −0.417134 | + | 1.55677i | 0.363388 | + | 0.931638i | \(0.381620\pi\) |
−0.780522 | + | 0.625128i | \(0.785047\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34.6410 | − | 20.0000i | −1.16182 | − | 0.670778i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.4233 | + | 46.3644i | 0.415730 | + | 1.55153i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.9808 | − | 23.6603i | 0.701310 | − | 0.790875i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −79.1960 | −2.64133 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.0000 | −0.666297 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.8685 | + | 13.3843i | −0.394523 | + | 0.444908i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.85641 | + | 21.8564i | 0.194459 | + | 0.725730i | 0.992406 | + | 0.123003i | \(0.0392525\pi\) |
−0.797948 | + | 0.602727i | \(0.794081\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.4949 | − | 14.1421i | −0.811552 | − | 0.468550i | 0.0359424 | − | 0.999354i | \(-0.488557\pi\) |
−0.847495 | + | 0.530804i | \(0.821890\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.78461 | + | 32.7846i | −0.290728 | + | 1.08501i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.65685 | − | 5.65685i | −0.186806 | − | 0.186806i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 32.0000i | − | 1.05558i | −0.849374 | − | 0.527791i | \(-0.823020\pi\) | ||
0.849374 | − | 0.527791i | \(-0.176980\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.1822 | − | 6.21166i | −0.763052 | − | 0.204459i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.6865 | + | 13.0981i | 0.548650 | + | 0.430662i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.6777 | + | 30.6186i | −0.579986 | + | 1.00456i | 0.415495 | + | 0.909596i | \(0.363608\pi\) |
−0.995480 | + | 0.0949688i | \(0.969725\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | + | 3.46410i | 0.0655474 | + | 0.113531i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.3137 | − | 5.65685i | −0.369998 | − | 0.184999i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.0000 | − | 37.0000i | 1.20874 | − | 1.20874i | 0.237301 | − | 0.971436i | \(-0.423737\pi\) |
0.971436 | − | 0.237301i | \(-0.0762628\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.0681 | − | 19.0919i | 1.07799 | − | 0.622378i | 0.147636 | − | 0.989042i | \(-0.452834\pi\) |
0.930353 | + | 0.366664i | \(0.119500\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.9282 | − | 2.92820i | 0.355871 | − | 0.0953554i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.9096 | − | 8.28221i | 1.00443 | − | 0.269136i | 0.281128 | − | 0.959670i | \(-0.409291\pi\) |
0.723299 | + | 0.690535i | \(0.242625\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.3731 | − | 21.0000i | 1.18072 | − | 0.681689i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.4558 | − | 25.4558i | 0.824596 | − | 0.824596i | −0.162168 | − | 0.986763i | \(-0.551849\pi\) |
0.986763 | + | 0.162168i | \(0.0518485\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.0000 | − | 8.00000i | 0.776622 | − | 0.258874i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.9706 | + | 29.3939i | 0.548008 | + | 0.949178i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | + | 28.5788i | −0.532258 | + | 0.921898i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −26.1357 | − | 39.5844i | −0.841339 | − | 1.27427i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.73205 | + | 0.732051i | 0.0878568 | + | 0.0235412i | 0.302480 | − | 0.953156i | \(-0.402186\pi\) |
−0.214623 | + | 0.976697i | \(0.568852\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53.7401i | 1.72460i | 0.506396 | + | 0.862301i | \(0.330978\pi\) | ||||
−0.506396 | + | 0.862301i | \(0.669022\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.0000 | + | 32.0000i | 1.02587 | + | 1.02587i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.65874 | − | 17.3867i | 0.149046 | − | 0.556249i | −0.850495 | − | 0.525982i | \(-0.823698\pi\) |
0.999542 | − | 0.0302663i | \(-0.00963555\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.46410 | − | 2.00000i | −0.110713 | − | 0.0639203i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.17638 | + | 19.3185i | 0.165101 | + | 0.616165i | 0.998027 | + | 0.0627812i | \(0.0199970\pi\) |
−0.832926 | + | 0.553384i | \(0.813336\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.7846 | − | 1.60770i | 0.853429 | − | 0.0512254i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.00000 | 0.127064 | 0.0635321 | − | 0.997980i | \(-0.479763\pi\) | ||||
0.0635321 | + | 0.997980i | \(0.479763\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.0764 | − | 17.8028i | −0.636464 | − | 0.564386i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.02628 | − | 15.0263i | −0.127514 | − | 0.475887i | 0.872403 | − | 0.488787i | \(-0.162560\pi\) |
−0.999917 | + | 0.0128998i | \(0.995894\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))