Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(193,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.q (of order \(3\), degree \(2\), 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: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.193 |
Dual form | 672.2.q.d.289.1 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | + | 0.866025i | 0.944911 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | + | 1.73205i | −0.301511 | + | 0.522233i | −0.976478 | − | 0.215615i | \(-0.930824\pi\) |
0.674967 | + | 0.737848i | \(0.264158\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | − | 1.73205i | 0.242536 | − | 0.420084i | −0.718900 | − | 0.695113i | \(-0.755354\pi\) |
0.961436 | + | 0.275029i | \(0.0886875\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.50000 | + | 4.33013i | 0.573539 | + | 0.993399i | 0.996199 | + | 0.0871106i | \(0.0277634\pi\) |
−0.422659 | + | 0.906289i | \(0.638903\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | + | 1.73205i | −0.436436 | + | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | + | 5.19615i | 0.625543 | + | 1.08347i | 0.988436 | + | 0.151642i | \(0.0484560\pi\) |
−0.362892 | + | 0.931831i | \(0.618211\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.00000 | −1.48556 | −0.742781 | − | 0.669534i | \(-0.766494\pi\) | ||||
−0.742781 | + | 0.669534i | \(0.766494\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | + | 2.59808i | −0.269408 | + | 0.466628i | −0.968709 | − | 0.248199i | \(-0.920161\pi\) |
0.699301 | + | 0.714827i | \(0.253495\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | − | 1.73205i | −0.174078 | − | 0.301511i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.50000 | + | 7.79423i | 0.739795 | + | 1.28136i | 0.952587 | + | 0.304266i | \(0.0984111\pi\) |
−0.212792 | + | 0.977098i | \(0.568256\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.500000 | + | 0.866025i | −0.0800641 | + | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.00000 | + | 6.92820i | 0.583460 | + | 1.01058i | 0.995066 | + | 0.0992202i | \(0.0316348\pi\) |
−0.411606 | + | 0.911362i | \(0.635032\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.00000 | + | 1.73205i | 0.140028 | + | 0.242536i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.00000 | + | 5.19615i | −0.412082 | + | 0.713746i | −0.995117 | − | 0.0987002i | \(-0.968532\pi\) |
0.583036 | + | 0.812447i | \(0.301865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.00000 | −0.662266 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.00000 | − | 5.19615i | 0.390567 | − | 0.676481i | −0.601958 | − | 0.798528i | \(-0.705612\pi\) |
0.992524 | + | 0.122047i | \(0.0389457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | + | 1.73205i | 0.128037 | + | 0.221766i | 0.922916 | − | 0.385002i | \(-0.125799\pi\) |
−0.794879 | + | 0.606768i | \(0.792466\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.500000 | − | 2.59808i | −0.0629941 | − | 0.327327i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.50000 | + | 4.33013i | −0.305424 | + | 0.529009i | −0.977356 | − | 0.211604i | \(-0.932131\pi\) |
0.671932 | + | 0.740613i | \(0.265465\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.00000 | −0.474713 | −0.237356 | − | 0.971423i | \(-0.576281\pi\) | ||||
−0.237356 | + | 0.971423i | \(0.576281\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.50000 | − | 9.52628i | 0.643726 | − | 1.11497i | −0.340868 | − | 0.940111i | \(-0.610721\pi\) |
0.984594 | − | 0.174855i | \(-0.0559458\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.50000 | + | 4.33013i | 0.288675 | + | 0.500000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.00000 | + | 3.46410i | −0.455842 | + | 0.394771i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.50000 | − | 4.33013i | −0.281272 | − | 0.487177i | 0.690426 | − | 0.723403i | \(-0.257423\pi\) |
−0.971698 | + | 0.236225i | \(0.924090\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.00000 | − | 6.92820i | 0.428845 | − | 0.742781i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | − | 10.3923i | −0.635999 | − | 1.10158i | −0.986303 | − | 0.164946i | \(-0.947255\pi\) |
0.350304 | − | 0.936636i | \(-0.386078\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.50000 | + | 0.866025i | 0.262071 | + | 0.0907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.50000 | − | 2.59808i | −0.155543 | − | 0.269408i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.0000 | 1.82762 | 0.913812 | − | 0.406138i | \(-0.133125\pi\) | ||||
0.913812 | + | 0.406138i | \(0.133125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.00000 | − | 5.19615i | 0.298511 | − | 0.517036i | −0.677284 | − | 0.735721i | \(-0.736843\pi\) |
0.975796 | + | 0.218685i | \(0.0701767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.50000 | − | 9.52628i | −0.541931 | − | 0.938652i | −0.998793 | − | 0.0491146i | \(-0.984360\pi\) |
0.456862 | − | 0.889538i | \(-0.348973\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.00000 | − | 15.5885i | −0.870063 | − | 1.50699i | −0.861931 | − | 0.507026i | \(-0.830745\pi\) |
−0.00813215 | − | 0.999967i | \(-0.502589\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.50000 | − | 2.59808i | 0.143674 | − | 0.248851i | −0.785203 | − | 0.619238i | \(-0.787442\pi\) |
0.928877 | + | 0.370387i | \(0.120775\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.00000 | −0.854242 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.0000 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.500000 | − | 0.866025i | −0.0462250 | − | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.00000 | − | 3.46410i | 0.366679 | − | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.00000 | + | 1.73205i | −0.0901670 | + | 0.156174i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.00000 | −0.798621 | −0.399310 | − | 0.916816i | \(-0.630750\pi\) | ||||
−0.399310 | + | 0.916816i | \(0.630750\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.500000 | − | 0.866025i | 0.0440225 | − | 0.0762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.00000 | − | 8.66025i | −0.436852 | − | 0.756650i | 0.560593 | − | 0.828092i | \(-0.310573\pi\) |
−0.997445 | + | 0.0714417i | \(0.977240\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.50000 | + | 12.9904i | 0.216777 | + | 1.12641i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | − | 10.3923i | 0.512615 | − | 0.887875i | −0.487278 | − | 0.873247i | \(-0.662010\pi\) |
0.999893 | − | 0.0146279i | \(-0.00465636\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.0000 | 1.27228 | 0.636142 | − | 0.771572i | \(-0.280529\pi\) | ||||
0.636142 | + | 0.771572i | \(0.280529\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.00000 | −0.673722 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | + | 1.73205i | −0.0836242 | + | 0.144841i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.50000 | + | 2.59808i | −0.536111 | + | 0.214286i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.0000 | + | 17.3205i | 0.819232 | + | 1.41895i | 0.906249 | + | 0.422744i | \(0.138933\pi\) |
−0.0870170 | + | 0.996207i | \(0.527733\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | − | 13.8564i | 0.651031 | − | 1.12762i | −0.331842 | − | 0.943335i | \(-0.607670\pi\) |
0.982873 | − | 0.184284i | \(-0.0589965\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0000 | − | 19.0526i | 0.877896 | − | 1.52056i | 0.0242497 | − | 0.999706i | \(-0.492280\pi\) |
0.853646 | − | 0.520854i | \(-0.174386\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.00000 | − | 5.19615i | −0.237915 | − | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.00000 | + | 15.5885i | 0.236433 | + | 1.22854i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0000 | − | 17.3205i | −0.783260 | − | 1.35665i | −0.930033 | − | 0.367477i | \(-0.880222\pi\) |
0.146772 | − | 0.989170i | \(-0.453112\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.50000 | − | 4.33013i | 0.191180 | − | 0.331133i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.00000 | − | 15.5885i | −0.684257 | − | 1.18517i | −0.973670 | − | 0.227964i | \(-0.926793\pi\) |
0.289412 | − | 0.957205i | \(-0.406540\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.0000 | − | 8.66025i | 0.755929 | − | 0.654654i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.00000 | + | 5.19615i | 0.225494 | + | 0.390567i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.00000 | − | 3.46410i | 0.149487 | − | 0.258919i | −0.781551 | − | 0.623841i | \(-0.785571\pi\) |
0.931038 | + | 0.364922i | \(0.118904\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.00000 | 0.371647 | 0.185824 | − | 0.982583i | \(-0.440505\pi\) | ||||
0.185824 | + | 0.982583i | \(0.440505\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.00000 | + | 3.46410i | 0.146254 | + | 0.253320i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.50000 | + | 0.866025i | 0.181848 | + | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.0000 | + | 17.3205i | 0.723575 | + | 1.25327i | 0.959558 | + | 0.281511i | \(0.0908356\pi\) |
−0.235983 | + | 0.971757i | \(0.575831\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.50000 | + | 6.06218i | −0.251936 | + | 0.436365i | −0.964059 | − | 0.265689i | \(-0.914400\pi\) |
0.712123 | + | 0.702055i | \(0.247734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.0000 | −0.712470 | −0.356235 | − | 0.934396i | \(-0.615940\pi\) | ||||
−0.356235 | + | 0.934396i | \(0.615940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.00000 | + | 10.3923i | −0.425329 | + | 0.736691i | −0.996451 | − | 0.0841740i | \(-0.973175\pi\) |
0.571122 | + | 0.820865i | \(0.306508\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.50000 | − | 4.33013i | −0.176336 | − | 0.305424i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.0000 | − | 6.92820i | −1.40372 | − | 0.486265i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.00000 | − | 5.19615i | 0.208514 | − | 0.361158i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.0000 | −0.691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.00000 | − | 3.46410i | 0.137038 | − | 0.237356i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | + | 5.19615i | −0.407307 | + | 0.352738i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.50000 | + | 9.52628i | 0.371656 | + | 0.643726i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.00000 | − | 1.73205i | 0.0672673 | − | 0.116510i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.00000 | −0.535720 | −0.267860 | − | 0.963458i | \(-0.586316\pi\) | ||||
−0.267860 | + | 0.963458i | \(0.586316\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.00000 | −0.333333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.0000 | − | 19.0526i | 0.730096 | − | 1.26456i | −0.226746 | − | 0.973954i | \(-0.572809\pi\) |
0.956842 | − | 0.290609i | \(-0.0938578\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.500000 | − | 0.866025i | −0.0330409 | − | 0.0572286i | 0.849032 | − | 0.528341i | \(-0.177186\pi\) |
−0.882073 | + | 0.471113i | \(0.843853\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.00000 | − | 5.19615i | −0.0657952 | − | 0.341882i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.00000 | − | 3.46410i | −0.131024 | − | 0.226941i | 0.793047 | − | 0.609160i | \(-0.208493\pi\) |
−0.924072 | + | 0.382219i | \(0.875160\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.00000 | 0.324785 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.0000 | 1.42306 | 0.711531 | − | 0.702655i | \(-0.248002\pi\) | ||||
0.711531 | + | 0.702655i | \(0.248002\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.50000 | + | 4.33013i | 0.159071 | + | 0.275519i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.00000 | −0.378717 | −0.189358 | − | 0.981908i | \(-0.560641\pi\) | ||||
−0.189358 | + | 0.981908i | \(0.560641\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.0000 | + | 27.7128i | 0.998053 | + | 1.72868i | 0.553047 | + | 0.833150i | \(0.313465\pi\) |
0.445005 | + | 0.895528i | \(0.353202\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.50000 | + | 23.3827i | 0.279616 | + | 1.45293i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.00000 | + | 6.92820i | 0.247594 | + | 0.428845i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.00000 | + | 6.92820i | −0.246651 | + | 0.427211i | −0.962594 | − | 0.270947i | \(-0.912663\pi\) |
0.715944 | + | 0.698158i | \(0.245997\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.0000 | 0.734388 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.0000 | − | 22.5167i | 0.792624 | − | 1.37287i | −0.131713 | − | 0.991288i | \(-0.542048\pi\) |
0.924337 | − | 0.381577i | \(-0.124619\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | − | 6.92820i | −0.242983 | − | 0.420858i | 0.718580 | − | 0.695444i | \(-0.244792\pi\) |
−0.961563 | + | 0.274586i | \(0.911459\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.00000 | + | 1.73205i | −0.121046 | + | 0.104828i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.00000 | + | 8.66025i | 0.301511 | + | 0.522233i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.50000 | − | 9.52628i | 0.330463 | − | 0.572379i | −0.652140 | − | 0.758099i | \(-0.726128\pi\) |
0.982603 | + | 0.185720i | \(0.0594618\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.00000 | 0.179605 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.0000 | −0.835170 | −0.417585 | − | 0.908638i | \(-0.637123\pi\) | ||||
−0.417585 | + | 0.908638i | \(0.637123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.5000 | + | 26.8468i | −0.921379 | + | 1.59588i | −0.124096 | + | 0.992270i | \(0.539603\pi\) |
−0.797283 | + | 0.603606i | \(0.793730\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.00000 | + | 1.73205i | 0.295141 | + | 0.102240i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.00000 | + | 15.5885i | −0.527589 | + | 0.913812i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.0000 | 1.63578 | 0.817889 | − | 0.575376i | \(-0.195144\pi\) | ||||
0.817889 | + | 0.575376i | \(0.195144\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | + | 1.73205i | −0.0580259 | + | 0.100504i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.00000 | + | 5.19615i | 0.173494 | + | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.50000 | − | 0.866025i | −0.144098 | − | 0.0499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.00000 | + | 5.19615i | 0.172345 | + | 0.298511i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.0000 | 1.42683 | 0.713413 | − | 0.700744i | \(-0.247149\pi\) | ||||
0.713413 | + | 0.700744i | \(0.247149\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.0000 | 0.625768 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.00000 | + | 8.66025i | −0.283524 | + | 0.491078i | −0.972250 | − | 0.233944i | \(-0.924837\pi\) |
0.688726 | + | 0.725022i | \(0.258170\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.5000 | − | 26.8468i | −0.876112 | − | 1.51747i | −0.855574 | − | 0.517681i | \(-0.826795\pi\) |
−0.0205381 | − | 0.999789i | \(-0.506538\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.00000 | − | 3.46410i | −0.112331 | − | 0.194563i | 0.804379 | − | 0.594117i | \(-0.202498\pi\) |
−0.916710 | + | 0.399554i | \(0.869165\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.00000 | − | 13.8564i | 0.447914 | − | 0.775810i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.0000 | 1.00466 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.0000 | 0.556415 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.50000 | − | 4.33013i | 0.138675 | − | 0.240192i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.50000 | + | 2.59808i | 0.0829502 | + | 0.143674i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.00000 | + | 20.7846i | 0.220527 | + | 1.14589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.50000 | − | 14.7224i | −0.467202 | − | 0.809218i | 0.532096 | − | 0.846684i | \(-0.321405\pi\) |
−0.999298 | + | 0.0374662i | \(0.988071\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.50000 | − | 7.79423i | 0.246598 | − | 0.427121i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.0000 | −1.68868 | −0.844339 | − | 0.535810i | \(-0.820006\pi\) | ||||
−0.844339 | + | 0.535810i | \(0.820006\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000 | − | 10.3923i | 0.325875 | − | 0.564433i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.00000 | − | 5.19615i | −0.162459 | − | 0.281387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.00000 | + | 15.5885i | −0.483145 | + | 0.836832i | −0.999813 | − | 0.0193540i | \(-0.993839\pi\) |
0.516667 | + | 0.856186i | \(0.327172\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0000 | −0.749403 | −0.374701 | − | 0.927146i | \(-0.622255\pi\) | ||||
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0000 | − | 20.7846i | 0.638696 | − | 1.10625i | −0.347024 | − | 0.937856i | \(-0.612808\pi\) |
0.985719 | − | 0.168397i | \(-0.0538590\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.00000 | + | 5.19615i | 0.0529256 | + | 0.275010i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.0000 | + | 27.7128i | 0.844448 | + | 1.46263i | 0.886100 | + | 0.463494i | \(0.153404\pi\) |
−0.0416523 | + | 0.999132i | \(0.513262\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | + | 5.19615i | −0.157895 | + | 0.273482i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.5000 | + | 32.0429i | −0.965692 | + | 1.67263i | −0.257948 | + | 0.966159i | \(0.583046\pi\) |
−0.707744 | + | 0.706469i | \(0.750287\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.00000 | − | 1.73205i | −0.0520579 | − | 0.0901670i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0000 | + | 10.3923i | −0.623009 | + | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.500000 | + | 0.866025i | 0.0258890 | + | 0.0448411i | 0.878680 | − | 0.477412i | \(-0.158425\pi\) |
−0.852791 | + | 0.522253i | \(0.825092\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.00000 | −0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.0000 | 1.28416 | 0.642082 | − | 0.766636i | \(-0.278071\pi\) | ||||
0.642082 | + | 0.766636i | \(0.278071\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.50000 | − | 7.79423i | 0.230542 | − | 0.399310i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.00000 | − | 1.73205i | −0.0510976 | − | 0.0885037i | 0.839345 | − | 0.543599i | \(-0.182939\pi\) |
−0.890443 | + | 0.455095i | \(0.849605\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.500000 | + | 0.866025i | 0.0254164 | + | 0.0440225i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.00000 | − | 6.92820i | 0.202808 | − | 0.351274i | −0.746624 | − | 0.665246i | \(-0.768327\pi\) |
0.949432 | + | 0.313972i | \(0.101660\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.0000 | 0.504433 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.50000 | − | 12.9904i | −0.376414 | − | 0.651969i | 0.614123 | − | 0.789210i | \(-0.289510\pi\) |
−0.990538 | + | 0.137241i | \(0.956176\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.5000 | − | 4.33013i | −0.625783 | − | 0.216777i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.0000 | + | 19.0526i | 0.549314 | + | 0.951439i | 0.998322 | + | 0.0579116i | \(0.0184442\pi\) |
−0.449008 | + | 0.893528i | \(0.648223\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.50000 | + | 2.59808i | −0.0747203 | + | 0.129419i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.0000 | −0.892227 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.50000 | + | 4.33013i | −0.123617 | + | 0.214111i | −0.921192 | − | 0.389109i | \(-0.872783\pi\) |
0.797574 | + | 0.603220i | \(0.206116\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | + | 10.3923i | 0.295958 | + | 0.512615i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.0000 | − | 10.3923i | 0.590481 | − | 0.511372i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.50000 | + | 12.9904i | −0.367277 | + | 0.636142i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.0000 | 1.66101 | 0.830504 | − | 0.557012i | \(-0.188052\pi\) | ||||
0.830504 | + | 0.557012i | \(0.188052\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.0000 | −0.536107 | −0.268054 | − | 0.963404i | \(-0.586380\pi\) | ||||
−0.268054 | + | 0.963404i | \(0.586380\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.00000 | − | 6.92820i | 0.194487 | − | 0.336861i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.00000 | − | 8.66025i | −0.242536 | − | 0.420084i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.00000 | + | 5.19615i | 0.0483934 | + | 0.251459i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.00000 | − | 1.73205i | −0.0482805 | − | 0.0836242i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.00000 | − | 10.3923i | 0.289010 | − | 0.500580i | −0.684564 | − | 0.728953i | \(-0.740007\pi\) |
0.973574 | + | 0.228373i | \(0.0733406\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.0000 | −1.20142 | −0.600712 | − | 0.799466i | \(-0.705116\pi\) | ||||
−0.600712 | + | 0.799466i | \(0.705116\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.0000 | + | 25.9808i | −0.717547 | + | 1.24283i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | − | 6.92820i | 0.0476190 | − | 0.329914i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.0000 | − | 19.0526i | −0.522626 | − | 0.905214i | −0.999653 | − | 0.0263261i | \(-0.991619\pi\) |
0.477028 | − | 0.878888i | \(-0.341714\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.0000 | −0.945968 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.0000 | 1.13263 | 0.566315 | − | 0.824189i | \(-0.308369\pi\) | ||||
0.566315 | + | 0.824189i | \(0.308369\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.00000 | + | 3.46410i | −0.0941763 | + | 0.163118i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.00000 | + | 13.8564i | 0.375873 | + | 0.651031i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.500000 | − | 0.866025i | −0.0233890 | − | 0.0405110i | 0.854094 | − | 0.520119i | \(-0.174112\pi\) |
−0.877483 | + | 0.479608i | \(0.840779\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.00000 | − | 1.73205i | 0.0466760 | − | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0000 | 0.558896 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.0000 | −0.511213 | −0.255607 | − | 0.966781i | \(-0.582275\pi\) | ||||
−0.255607 | + | 0.966781i | \(0.582275\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.0000 | + | 17.3205i | 0.462745 | + | 0.801498i | 0.999097 | − | 0.0424970i | \(-0.0135313\pi\) |
−0.536352 | + | 0.843995i | \(0.680198\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.0000 | + | 8.66025i | −0.461757 | + | 0.399893i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.0000 | + | 19.0526i | 0.506853 | + | 0.877896i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.00000 | − | 1.73205i | 0.0459800 | − | 0.0796398i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.0000 | 1.14708 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.00000 | 0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.00000 | − | 5.19615i | 0.137073 | − | 0.237418i | −0.789314 | − | 0.613990i | \(-0.789564\pi\) |
0.926388 | + | 0.376571i | \(0.122897\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.50000 | + | 7.79423i | 0.205182 | + | 0.355386i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.0000 | − | 5.19615i | −0.682524 | − | 0.236433i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.50000 | − | 6.06218i | 0.158600 | − | 0.274703i | −0.775764 | − | 0.631023i | \(-0.782635\pi\) |
0.934364 | + | 0.356320i | \(0.115969\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.0000 | 0.904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.00000 | + | 13.8564i | −0.360302 | + | 0.624061i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.0000 | − | 3.46410i | −0.448561 | − | 0.155386i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.5000 | − | 19.9186i | −0.514811 | − | 0.891678i | −0.999852 | − | 0.0171872i | \(-0.994529\pi\) |
0.485042 | − | 0.874491i | \(-0.338804\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.00000 | − | 10.3923i | 0.268060 | − | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −42.0000 | −1.87269 | −0.936344 | − | 0.351085i | \(-0.885813\pi\) | ||||
−0.936344 | + | 0.351085i | \(0.885813\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.00000 | − | 10.3923i | 0.266469 | − | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.0000 | + | 17.3205i | 0.443242 | + | 0.767718i | 0.997928 | − | 0.0643419i | \(-0.0204948\pi\) |
−0.554686 | + | 0.832060i | \(0.687161\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.0000 | − | 19.0526i | 0.973223 | − | 0.842836i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.50000 | + | 4.33013i | 0.110378 | + | 0.191180i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.0000 | −0.703679 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.0000 | 0.790112 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.50000 | − | 11.2583i | −0.284225 | − | 0.492292i | 0.688196 | − | 0.725525i | \(-0.258403\pi\) |
−0.972421 | + | 0.233233i | \(0.925070\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.50000 | + | 12.9904i | 0.109109 | + | 0.566947i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.00000 | + | 5.19615i | 0.130682 | + | 0.226348i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.00000 | 0.0866296 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.00000 | + | 3.46410i | 0.0863064 | + | 0.149487i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.0000 | + | 5.19615i | −0.559950 | + | 0.223814i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.5000 | − | 21.6506i | −0.537417 | − | 0.930834i | −0.999042 | − | 0.0437584i | \(-0.986067\pi\) |
0.461625 | − | 0.887075i | \(-0.347267\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.50000 | + | 4.33013i | −0.107285 | + | 0.185824i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.00000 | − | 1.73205i | 0.0426790 | − | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.0000 | − | 34.6410i | −0.852029 | − | 1.47576i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.50000 | − | 12.9904i | −0.106311 | − | 0.552407i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.0000 | + | 22.5167i | −0.550828 | + | 0.954062i | 0.447387 | + | 0.894340i | \(0.352355\pi\) |
−0.998215 | + | 0.0597213i | \(0.980979\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.00000 | −0.0422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.00000 | −0.168880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.0000 | − | 17.3205i | 0.421450 | − | 0.729972i | −0.574632 | − | 0.818412i | \(-0.694855\pi\) |
0.996082 | + | 0.0884397i | \(0.0281881\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.00000 | + | 1.73205i | −0.0839921 | + | 0.0727393i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.0000 | − | 22.5167i | −0.544988 | − | 0.943948i | −0.998608 | − | 0.0527519i | \(-0.983201\pi\) |
0.453619 | − | 0.891196i | \(-0.350133\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.50000 | + | 6.06218i | −0.146470 | + | 0.253694i | −0.929921 | − | 0.367760i | \(-0.880125\pi\) |
0.783450 | + | 0.621455i | \(0.213458\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.0000 | −0.835512 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.0000 | 1.25109 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.50000 | − | 14.7224i | 0.353860 | − | 0.612903i | −0.633062 | − | 0.774101i | \(-0.718202\pi\) |
0.986922 | + | 0.161198i | \(0.0515357\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.50000 | − | 6.06218i | −0.145455 | − | 0.251936i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.00000 | − | 10.3923i | −0.248495 | − | 0.430405i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.0000 | −0.990586 | −0.495293 | − | 0.868726i | \(-0.664939\pi\) | ||||
−0.495293 | + | 0.868726i | \(0.664939\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.0000 | −0.618064 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.00000 | − | 8.66025i | 0.205673 | − | 0.356235i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.00000 | − | 12.1244i | −0.287456 | − | 0.497888i | 0.685746 | − | 0.727841i | \(-0.259476\pi\) |
−0.973202 | + | 0.229953i | \(0.926143\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.00000 | − | 10.3923i | −0.245564 | − | 0.425329i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.0000 | − | 17.3205i | 0.408589 | − | 0.707697i | −0.586143 | − | 0.810208i | \(-0.699354\pi\) |
0.994732 | + | 0.102511i | \(0.0326876\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.00000 | 0.122373 | 0.0611863 | − | 0.998126i | \(-0.480512\pi\) | ||||
0.0611863 | + | 0.998126i | \(0.480512\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.00000 | 0.203616 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.50000 | − | 11.2583i | −0.263827 | − | 0.456962i | 0.703429 | − | 0.710766i | \(-0.251651\pi\) |
−0.967256 | + | 0.253804i | \(0.918318\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.0000 | − | 13.8564i | 0.648353 | − | 0.561490i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.00000 | + | 6.92820i | 0.161823 | + | 0.280285i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.00000 | + | 8.66025i | −0.201948 | + | 0.349784i | −0.949156 | − | 0.314806i | \(-0.898061\pi\) |
0.747208 | + | 0.664590i | \(0.231394\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.0000 | 1.36879 | 0.684394 | − | 0.729112i | \(-0.260067\pi\) | ||||
0.684394 | + | 0.729112i | \(0.260067\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.50000 | + | 4.33013i | −0.100483 | + | 0.174042i | −0.911884 | − | 0.410448i | \(-0.865372\pi\) |
0.811400 | + | 0.584491i | \(0.198706\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.00000 | + | 5.19615i | 0.120386 | + | 0.208514i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.00000 | − | 31.1769i | −0.240385 | − | 1.24908i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.00000 | − | 8.66025i | 0.199681 | − | 0.345857i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.0000 | 0.717707 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.0000 | −1.75161 | −0.875806 | − | 0.482663i | \(-0.839670\pi\) | ||||
−0.875806 | + | 0.482663i | \(0.839670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.00000 | − | 10.3923i | 0.238479 | − | 0.413057i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.50000 | + | 4.33013i | 0.217918 | + | 0.171566i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.00000 | + | 3.46410i | 0.0791188 | + | 0.137038i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.0000 | − | 32.9090i | 0.750455 | − | 1.29983i | −0.197148 | − | 0.980374i | \(-0.563168\pi\) |
0.947602 | − | 0.319452i | \(-0.103499\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.0000 | −0.512670 | −0.256335 | − | 0.966588i | \(-0.582515\pi\) | ||||
−0.256335 | + | 0.966588i | \(0.582515\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.0000 | − | 36.3731i | 0.825595 | − | 1.42997i | −0.0758684 | − | 0.997118i | \(-0.524173\pi\) |
0.901464 | − | 0.432855i | \(-0.142494\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.00000 | + | 10.3923i | 0.235521 | + | 0.407934i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.50000 | − | 7.79423i | −0.0587896 | − | 0.305480i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.0000 | + | 32.9090i | 0.743527 | + | 1.28783i | 0.950880 | + | 0.309561i | \(0.100182\pi\) |
−0.207352 | + | 0.978266i | \(0.566485\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.0000 | −0.429151 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.00000 | 0.233727 | 0.116863 | − | 0.993148i | \(-0.462716\pi\) | ||||
0.116863 | + | 0.993148i | \(0.462716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.50000 | + | 12.9904i | −0.291716 | + | 0.505267i | −0.974216 | − | 0.225619i | \(-0.927560\pi\) |
0.682499 | + | 0.730886i | \(0.260893\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.00000 | + | 1.73205i | 0.0388368 | + | 0.0672673i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.0000 | − | 41.5692i | −0.929284 | − | 1.60957i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.00000 | − | 6.92820i | 0.154649 | − | 0.267860i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.00000 | −0.154418 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.0000 | 1.34915 | 0.674575 | − | 0.738206i | \(-0.264327\pi\) | ||||
0.674575 | + | 0.738206i | \(0.264327\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.50000 | − | 4.33013i | 0.0962250 | − | 0.166667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.0000 | − | 31.1769i | −0.691796 | − | 1.19823i | −0.971249 | − | 0.238067i | \(-0.923486\pi\) |
0.279453 | − | 0.960159i | \(-0.409847\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 45.0000 | + | 15.5885i | 1.72694 | + | 0.598230i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.0000 | + | 19.0526i | 0.421521 | + | 0.730096i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.00000 | + | 15.5885i | −0.344375 | + | 0.596476i | −0.985240 | − | 0.171178i | \(-0.945243\pi\) |
0.640865 | + | 0.767654i | \(0.278576\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.00000 | 0.0381524 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.00000 | + | 5.19615i | −0.114291 | + | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.5000 | − | 25.1147i | −0.551606 | − | 0.955410i | −0.998159 | − | 0.0606524i | \(-0.980682\pi\) |
0.446553 | − | 0.894757i | \(-0.352651\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.00000 | + | 1.73205i | 0.189934 | + | 0.0657952i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.00000 | − | 3.46410i | 0.0757554 | − | 0.131212i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.00000 | 0.151294 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.0000 | −0.528773 | −0.264386 | − | 0.964417i | \(-0.585169\pi\) | ||||
−0.264386 | + | 0.964417i | \(0.585169\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.5000 | + | 38.9711i | −0.848604 | + | 1.46982i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.0000 | − | 10.3923i | 0.451306 | − | 0.390843i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.00000 | − | 8.66025i | −0.187779 | − | 0.325243i | 0.756730 | − | 0.653727i | \(-0.226796\pi\) |
−0.944509 | + | 0.328484i | \(0.893462\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.50000 | + | 4.33013i | −0.0937573 | + | 0.162392i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.0000 | −0.674105 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.0000 | + | 19.0526i | −0.410803 | + | 0.711531i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.0000 | + | 25.9808i | 0.559406 | + | 0.968919i | 0.997546 | + | 0.0700124i | \(0.0223039\pi\) |
−0.438141 | + | 0.898906i | \(0.644363\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.50000 | − | 28.5788i | −0.204831 | − | 1.06433i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.00000 | − | 8.66025i | −0.185952 | − | 0.322078i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.0000 | + | 34.6410i | −0.742781 | + | 1.28654i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.0000 | 0.630495 | 0.315248 | − | 0.949009i | \(-0.397912\pi\) | ||||
0.315248 | + | 0.949009i | \(0.397912\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.00000 | + | 1.73205i | −0.0369863 | + | 0.0640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.5000 | + | 33.7750i | 0.720249 | + | 1.24751i | 0.960900 | + | 0.276896i | \(0.0893058\pi\) |
−0.240651 | + | 0.970612i | \(0.577361\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.00000 | − | 8.66025i | −0.184177 | − | 0.319005i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.5000 | − | 28.5788i | 0.606962 | − | 1.05129i | −0.384776 | − | 0.923010i | \(-0.625721\pi\) |
0.991738 | − | 0.128279i | \(-0.0409454\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.00000 | −0.183680 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −54.0000 | −1.98107 | −0.990534 | − | 0.137268i | \(-0.956168\pi\) | ||||
−0.990534 | + | 0.137268i | \(0.956168\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.00000 | − | 46.7654i | −0.328853 | − | 1.70877i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.5000 | − | 26.8468i | −0.565603 | − | 0.979653i | −0.996993 | − | 0.0774878i | \(-0.975310\pi\) |
0.431390 | − | 0.902165i | \(-0.358023\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.00000 | − | 5.19615i | 0.109326 | − | 0.189358i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.0000 | 1.38113 | 0.690567 | − | 0.723269i | \(-0.257361\pi\) | ||||
0.690567 | + | 0.723269i | \(0.257361\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.00000 | − | 10.3923i | 0.217786 | − | 0.377217i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.0000 | + | 43.3013i | 0.906249 | + | 1.56967i | 0.819231 | + | 0.573463i | \(0.194400\pi\) |
0.0870179 | + | 0.996207i | \(0.472266\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.00000 | − | 5.19615i | 0.217215 | − | 0.188113i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.00000 | − | 5.19615i | 0.108324 | − | 0.187622i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.0000 | 0.829401 | 0.414701 | − | 0.909958i | \(-0.363886\pi\) | ||||
0.414701 | + | 0.909958i | \(0.363886\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −32.0000 | −1.15245 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.0000 | + | 36.3731i | −0.755318 | + | 1.30825i | 0.189899 | + | 0.981804i | \(0.439184\pi\) |
−0.945216 | + | 0.326445i | \(0.894149\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.50000 | + | 12.9904i | 0.269408 | + | 0.466628i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −22.5000 | − | 7.79423i | −0.807183 | − | 0.279616i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.00000 | + | 8.66025i | 0.179144 | + | 0.310286i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.00000 | − | 6.92820i | 0.143131 | − | 0.247911i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.00000 | −0.285897 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.00000 | + | 6.92820i | −0.142585 | + | 0.246964i | −0.928469 | − | 0.371409i | \(-0.878875\pi\) |
0.785885 | + | 0.618373i | \(0.212208\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.00000 | − | 6.92820i | −0.142404 | − | 0.246651i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.0000 | − | 10.3923i | −1.06668 | − | 0.369508i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00000 | + | 1.73205i | 0.0355110 | + | 0.0615069i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.00000 | 0.212531 | 0.106265 | − | 0.994338i | \(-0.466111\pi\) | ||||
0.106265 | + | 0.994338i | \(0.466111\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.0000 | 0.566039 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.00000 | + | 10.3923i | −0.212000 | + | 0.367194i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.0000 | + | 19.0526i | 0.388182 | + | 0.672350i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.0000 | + | 22.5167i | 0.457622 | + | 0.792624i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.0000 | − | 24.2487i | 0.492214 | − | 0.852539i | −0.507746 | − | 0.861507i | \(-0.669521\pi\) |
0.999960 | + | 0.00896753i | \(0.00285449\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.0000 | 0.983213 | 0.491606 | − | 0.870817i | \(-0.336410\pi\) | ||||
0.491606 | + | 0.870817i | \(0.336410\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.00000 | 0.280572 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.50000 | − | 4.33013i | −0.0874639 | − | 0.151492i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.500000 | − | 2.59808i | −0.0174714 | − | 0.0907841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.0000 | − | 41.5692i | −0.837606 | − | 1.45078i | −0.891891 | − | 0.452250i | \(-0.850621\pi\) |
0.0542853 | − | 0.998525i | \(-0.482712\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.0000 | − | 27.7128i | 0.557725 | − | 0.966008i | −0.439961 | − | 0.898017i | \(-0.645008\pi\) |
0.997686 | − | 0.0679910i | \(-0.0216589\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.0000 | −0.348155 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.0000 | 0.834562 | 0.417281 | − | 0.908778i | \(-0.362983\pi\) | ||||
0.417281 | + | 0.908778i | \(0.362983\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.5000 | + | 42.4352i | −0.850920 | + | 1.47384i | 0.0294587 | + | 0.999566i | \(0.490622\pi\) |
−0.880379 | + | 0.474271i | \(0.842712\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.50000 | + | 9.52628i | 0.190793 | + | 0.330463i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.0000 | − | 5.19615i | 0.450423 | − | 0.180036i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.50000 | + | 2.59808i | −0.0518476 | + | 0.0898027i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.00000 | 0.138095 | 0.0690477 | − | 0.997613i | \(-0.478004\pi\) | ||||
0.0690477 | + | 0.997613i | \(0.478004\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.00000 | − | 12.1244i | 0.241093 | − | 0.417585i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.50000 | + | 18.1865i | 0.120261 | + | 0.624897i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.5000 | − | 26.8468i | −0.531959 | − | 0.921379i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.0000 | + | 46.7654i | −0.925548 | + | 1.60310i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.0000 | −0.719026 | −0.359513 | − | 0.933140i | \(-0.617057\pi\) | ||||
−0.359513 | + | 0.933140i | \(0.617057\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.00000 | + | 6.92820i | −0.136637 | + | 0.236663i | −0.926222 | − | 0.376979i | \(-0.876963\pi\) |
0.789584 | + | 0.613642i | \(0.210296\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.0000 | + | 38.1051i | 0.750630 | + | 1.30013i | 0.947518 | + | 0.319704i | \(0.103583\pi\) |
−0.196887 | + | 0.980426i | \(0.563083\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.00000 | + | 3.46410i | −0.136320 | + | 0.118056i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.00000 | − | 15.5885i | −0.306364 | − | 0.530637i | 0.671200 | − | 0.741276i | \(-0.265779\pi\) |
−0.977564 | + | 0.210639i | \(0.932446\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.0000 | −0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.0000 | 0.339227 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.50000 | + | 4.33013i | −0.0847093 | + | 0.146721i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.00000 | − | 15.5885i | −0.304604 | − | 0.527589i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.00000 | − | 8.66025i | −0.168838 | − | 0.292436i | 0.769174 | − | 0.639040i | \(-0.220668\pi\) |
−0.938012 | + | 0.346604i | \(0.887335\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.0000 | + | 24.2487i | −0.472208 | + | 0.817889i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.0000 | −1.81931 | −0.909653 | − | 0.415369i | \(-0.863653\pi\) | ||||
−0.909653 | + | 0.415369i | \(0.863653\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.0000 | −0.639401 | −0.319700 | − | 0.947519i | \(-0.603582\pi\) | ||||
−0.319700 | + | 0.947519i | \(0.603582\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.00000 | − | 5.19615i | −0.100730 | − | 0.174470i | 0.811256 | − | 0.584692i | \(-0.198785\pi\) |
−0.911986 | + | 0.410222i | \(0.865451\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.5000 | − | 7.79423i | −0.754626 | − | 0.261410i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | − | 1.73205i | −0.0335013 | − | 0.0580259i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.0000 | + | 34.6410i | −0.669274 | + | 1.15922i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.00000 | −0.200334 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.0000 | − | 20.7846i | 0.400222 | − | 0.693206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.00000 | + | 10.3923i | 0.199889 | + | 0.346218i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.00000 | − | 1.73205i | 0.0665558 | − | 0.0576390i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.500000 | + | 0.866025i | −0.0166022 | + | 0.0287559i | −0.874207 | − | 0.485553i | \(-0.838618\pi\) |
0.857605 | + | 0.514309i | \(0.171952\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.0000 | 0.728893 | 0.364446 | − | 0.931224i | \(-0.381258\pi\) | ||||
0.364446 | + | 0.931224i | \(0.381258\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.00000 | − | 25.9808i | −0.165115 | − | 0.857960i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.5000 | + | 30.3109i | 0.577272 | + | 0.999864i | 0.995791 | + | 0.0916559i | \(0.0292160\pi\) |
−0.418519 | + | 0.908208i | \(0.637451\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.5000 | + | 21.6506i | −0.411889 | + | 0.713413i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.00000 | −0.131662 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 45.0000 | 1.47959 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.50000 | + | 9.52628i | −0.180644 | + | 0.312884i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.00000 | + | 13.8564i | 0.262471 | + | 0.454614i | 0.966898 | − | 0.255163i | \(-0.0821291\pi\) |
−0.704427 | + | 0.709777i | \(0.748796\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.00000 | + | 34.6410i | −0.163868 | + | 1.13531i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.00000 | − | 8.66025i | −0.163693 | − | 0.283524i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.0000 | 1.66610 | 0.833049 | − | 0.553200i | \(-0.186593\pi\) | ||||
0.833049 | + | 0.553200i | \(0.186593\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.0000 | 1.01165 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.0000 | + | 22.5167i | −0.423788 | + | 0.734022i | −0.996306 | − | 0.0858697i | \(-0.972633\pi\) |
0.572518 | + | 0.819892i | \(0.305966\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.00000 | + | 10.3923i | 0.195387 | + | 0.338420i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.0000 | + | 43.3013i | 0.812391 | + | 1.40710i | 0.911186 | + | 0.411994i | \(0.135168\pi\) |
−0.0987955 | + | 0.995108i | \(0.531499\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.50000 | − | 9.52628i | 0.178538 | − | 0.309236i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.00000 | 0.129709 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.0000 | 0.453504 | 0.226752 | − | 0.973952i | \(-0.427189\pi\) | ||||
0.226752 | + | 0.973952i | \(0.427189\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.00000 | + | 13.8564i | 0.258603 | + | 0.447914i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.0000 | − | 20.7846i | 0.775000 | − | 0.671170i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | + | 19.0526i | 0.354839 | + | 0.614599i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.00000 | + | 15.5885i | −0.290021 | + | 0.502331i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.0000 | 0.418052 | 0.209026 | − | 0.977910i | \(-0.432971\pi\) | ||||
0.209026 | + | 0.977910i | \(0.432971\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.00000 | + | 8.66025i | −0.160623 | + | 0.278207i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.0000 | + | 22.5167i | 0.417190 | + | 0.722594i | 0.995656 | − | 0.0931127i | \(-0.0296817\pi\) |
−0.578466 | + | 0.815707i | \(0.696348\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 37.5000 | + | 12.9904i | 1.20219 | + | 0.416452i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.50000 | + | 4.33013i | 0.0800641 | + | 0.138675i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.0000 | + | 25.9808i | −0.479893 | + | 0.831198i | −0.999734 | − | 0.0230645i | \(-0.992658\pi\) |
0.519841 | + | 0.854263i | \(0.325991\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.0000 | 0.767043 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.00000 | −0.0957826 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.00000 | + | 1.73205i | −0.0318950 | + | 0.0552438i | −0.881532 | − | 0.472124i | \(-0.843488\pi\) |
0.849637 | + | 0.527368i | \(0.176821\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −20.0000 | − | 6.92820i | −0.636607 | − | 0.220527i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.00000 | − | 5.19615i | −0.0953945 | − | 0.165228i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.5000 | + | 47.6314i | −0.873566 | + | 1.51306i | −0.0152841 | + | 0.999883i | \(0.504865\pi\) |
−0.858282 | + | 0.513178i | \(0.828468\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.0000 | 0.539479 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.5000 | − | 35.5070i | 0.649242 | − | 1.12452i | −0.334063 | − | 0.942551i | \(-0.608420\pi\) |
0.983304 | − | 0.181968i | \(-0.0582469\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.50000 | + | 7.79423i | 0.142374 | + | 0.246598i |
(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 | 672.2.q.d.193.1 | ✓ | 2 | |
3.2 | odd | 2 | 2016.2.s.h.865.1 | 2 | |||
4.3 | odd | 2 | 672.2.q.h.193.1 | yes | 2 | ||
7.2 | even | 3 | inner | 672.2.q.d.289.1 | yes | 2 | |
7.3 | odd | 6 | 4704.2.a.j.1.1 | 1 | |||
7.4 | even | 3 | 4704.2.a.ba.1.1 | 1 | |||
8.3 | odd | 2 | 1344.2.q.e.193.1 | 2 | |||
8.5 | even | 2 | 1344.2.q.q.193.1 | 2 | |||
12.11 | even | 2 | 2016.2.s.e.865.1 | 2 | |||
21.2 | odd | 6 | 2016.2.s.h.289.1 | 2 | |||
28.3 | even | 6 | 4704.2.a.y.1.1 | 1 | |||
28.11 | odd | 6 | 4704.2.a.g.1.1 | 1 | |||
28.23 | odd | 6 | 672.2.q.h.289.1 | yes | 2 | ||
56.3 | even | 6 | 9408.2.a.x.1.1 | 1 | |||
56.11 | odd | 6 | 9408.2.a.cn.1.1 | 1 | |||
56.37 | even | 6 | 1344.2.q.q.961.1 | 2 | |||
56.45 | odd | 6 | 9408.2.a.ci.1.1 | 1 | |||
56.51 | odd | 6 | 1344.2.q.e.961.1 | 2 | |||
56.53 | even | 6 | 9408.2.a.t.1.1 | 1 | |||
84.23 | even | 6 | 2016.2.s.e.289.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.q.d.193.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
672.2.q.d.289.1 | yes | 2 | 7.2 | even | 3 | inner | |
672.2.q.h.193.1 | yes | 2 | 4.3 | odd | 2 | ||
672.2.q.h.289.1 | yes | 2 | 28.23 | odd | 6 | ||
1344.2.q.e.193.1 | 2 | 8.3 | odd | 2 | |||
1344.2.q.e.961.1 | 2 | 56.51 | odd | 6 | |||
1344.2.q.q.193.1 | 2 | 8.5 | even | 2 | |||
1344.2.q.q.961.1 | 2 | 56.37 | even | 6 | |||
2016.2.s.e.289.1 | 2 | 84.23 | even | 6 | |||
2016.2.s.e.865.1 | 2 | 12.11 | even | 2 | |||
2016.2.s.h.289.1 | 2 | 21.2 | odd | 6 | |||
2016.2.s.h.865.1 | 2 | 3.2 | odd | 2 | |||
4704.2.a.g.1.1 | 1 | 28.11 | odd | 6 | |||
4704.2.a.j.1.1 | 1 | 7.3 | odd | 6 | |||
4704.2.a.y.1.1 | 1 | 28.3 | even | 6 | |||
4704.2.a.ba.1.1 | 1 | 7.4 | even | 3 | |||
9408.2.a.t.1.1 | 1 | 56.53 | even | 6 | |||
9408.2.a.x.1.1 | 1 | 56.3 | even | 6 | |||
9408.2.a.ci.1.1 | 1 | 56.45 | odd | 6 | |||
9408.2.a.cn.1.1 | 1 | 56.11 | odd | 6 |