Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(209,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.i (of order \(2\), degree \(1\), 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: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.3317760000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 8x^{6} + 13x^{4} + 12x^{2} + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.7 | ||
Root | \(-0.578737 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.209 |
Dual form | 672.2.i.d.209.6 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.58114 | + | 0.707107i | 0.912871 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.41421i | 0.632456i | 0.948683 | + | 0.316228i | \(0.102416\pi\) | ||||
−0.948683 | + | 0.316228i | \(0.897584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | − | 2.44949i | −0.377964 | − | 0.925820i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.00000 | + | 2.23607i | 0.666667 | + | 0.745356i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46410 | 1.04447 | 0.522233 | − | 0.852803i | \(-0.325099\pi\) | ||||
0.522233 | + | 0.852803i | \(0.325099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.16228 | 0.877058 | 0.438529 | − | 0.898717i | \(-0.355500\pi\) | ||||
0.438529 | + | 0.898717i | \(0.355500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | + | 2.23607i | −0.258199 | + | 0.577350i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.16228 | −0.725476 | −0.362738 | − | 0.931891i | \(-0.618158\pi\) | ||||
−0.362738 | + | 0.931891i | \(0.618158\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.150912 | − | 4.58009i | 0.0329317 | − | 0.999458i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.47214i | 0.932505i | 0.884652 | + | 0.466252i | \(0.154396\pi\) | ||||
−0.884652 | + | 0.466252i | \(0.845604\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.58114 | + | 4.94975i | 0.304290 | + | 0.952579i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.92820 | 1.28654 | 0.643268 | − | 0.765641i | \(-0.277578\pi\) | ||||
0.643268 | + | 0.765641i | \(0.277578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.89898i | 0.879883i | 0.898027 | + | 0.439941i | \(0.145001\pi\) | ||||
−0.898027 | + | 0.439941i | \(0.854999\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.47723 | + | 2.44949i | 0.953463 | + | 0.426401i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.46410 | − | 1.41421i | 0.585540 | − | 0.239046i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.00000 | + | 2.23607i | 0.800641 | + | 0.358057i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.9545 | −1.71080 | −0.855399 | − | 0.517970i | \(-0.826688\pi\) | ||||
−0.855399 | + | 0.517970i | \(0.826688\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.74597i | − | 1.18125i | −0.806947 | − | 0.590624i | \(-0.798881\pi\) | ||
0.806947 | − | 0.590624i | \(-0.201119\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.16228 | + | 2.82843i | −0.471405 | + | 0.421637i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.9545 | −1.59787 | −0.798935 | − | 0.601417i | \(-0.794603\pi\) | ||||
−0.798935 | + | 0.601417i | \(0.794603\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | + | 4.89898i | −0.714286 | + | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.89898i | 0.660578i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.00000 | − | 2.23607i | −0.662266 | − | 0.296174i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 9.89949i | − | 1.28880i | −0.764687 | − | 0.644402i | \(-0.777106\pi\) | ||
0.764687 | − | 0.644402i | \(-0.222894\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.16228 | 0.404888 | 0.202444 | − | 0.979294i | \(-0.435112\pi\) | ||||
0.202444 | + | 0.979294i | \(0.435112\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.47723 | − | 7.13505i | 0.438089 | − | 0.898931i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.47214i | 0.554700i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.74597i | 0.946320i | 0.880976 | + | 0.473160i | \(0.156887\pi\) | ||||
−0.880976 | + | 0.473160i | \(0.843113\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.16228 | + | 7.07107i | −0.380693 | + | 0.851257i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.94427i | − | 1.06149i | −0.847532 | − | 0.530745i | \(-0.821912\pi\) | ||
0.847532 | − | 0.530745i | \(-0.178088\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 14.6969i | − | 1.72015i | −0.510171 | − | 0.860073i | \(-0.670418\pi\) | ||
0.510171 | − | 0.860073i | \(-0.329582\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.74342 | + | 2.12132i | 0.547723 | + | 0.244949i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.46410 | − | 8.48528i | −0.394771 | − | 0.966988i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.0000 | 1.12509 | 0.562544 | − | 0.826767i | \(-0.309823\pi\) | ||||
0.562544 | + | 0.826767i | \(0.309823\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | + | 8.94427i | −0.111111 | + | 0.993808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.07107i | 0.776151i | 0.921628 | + | 0.388075i | \(0.126860\pi\) | ||||
−0.921628 | + | 0.388075i | \(0.873140\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.9545 | + | 4.89898i | 1.17444 | + | 0.525226i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.16228 | − | 7.74597i | −0.331497 | − | 0.811998i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.46410 | + | 7.74597i | −0.359211 | + | 0.803219i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 4.47214i | − | 0.458831i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.89898i | 0.497416i | 0.968579 | + | 0.248708i | \(0.0800060\pi\) | ||||
−0.968579 | + | 0.248708i | \(0.919994\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.92820 | + | 7.74597i | 0.696311 | + | 0.778499i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 15.5563i | − | 1.54791i | −0.633238 | − | 0.773957i | \(-0.718274\pi\) | ||
0.633238 | − | 0.773957i | \(-0.281726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.79796i | − | 0.965422i | −0.875780 | − | 0.482711i | \(-0.839652\pi\) | ||
0.875780 | − | 0.482711i | \(-0.160348\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.47723 | + | 0.213422i | 0.632112 | + | 0.0208278i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.3923 | −1.00466 | −0.502331 | − | 0.864675i | \(-0.667524\pi\) | ||||
−0.502331 | + | 0.864675i | \(0.667524\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4.47214i | − | 0.420703i | −0.977626 | − | 0.210352i | \(-0.932539\pi\) | ||
0.977626 | − | 0.210352i | \(-0.0674609\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.32456 | −0.589768 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.32456 | + | 7.07107i | 0.584705 | + | 0.653720i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.3205 | − | 7.74597i | −1.56174 | − | 0.698430i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3137i | 1.01193i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.47723 | − | 12.2474i | 0.482243 | − | 1.07833i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1.41421i | − | 0.123560i | −0.998090 | − | 0.0617802i | \(-0.980322\pi\) | ||
0.998090 | − | 0.0617802i | \(-0.0196778\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.16228 | + | 7.74597i | 0.274204 | + | 0.671660i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.00000 | + | 2.23607i | −0.602464 | + | 0.192450i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 17.8885i | − | 1.52832i | −0.645026 | − | 0.764161i | \(-0.723153\pi\) | ||
0.645026 | − | 0.764161i | \(-0.276847\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.8114 | 1.34110 | 0.670552 | − | 0.741862i | \(-0.266057\pi\) | ||||
0.670552 | + | 0.741862i | \(0.266057\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.3205 | − | 7.74597i | −1.45865 | − | 0.652328i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.9545 | 0.916057 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.79796i | 0.813676i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.3698 | + | 4.21043i | −0.937765 | + | 0.347271i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.92820 | −0.567581 | −0.283790 | − | 0.958886i | \(-0.591592\pi\) | ||||
−0.283790 | + | 0.958886i | \(0.591592\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.92820 | −0.556487 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.8114 | −1.26189 | −0.630943 | − | 0.775829i | \(-0.717332\pi\) | ||||
−0.630943 | + | 0.775829i | \(0.717332\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.9545 | − | 4.47214i | 0.863332 | − | 0.352454i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.2379i | 1.82013i | 0.414462 | + | 0.910066i | \(0.363970\pi\) | ||||
−0.414462 | + | 0.910066i | \(0.636030\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.46410 | + | 7.74597i | −0.269680 | + | 0.603023i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.9089 | −1.69536 | −0.847681 | − | 0.530506i | \(-0.822002\pi\) | ||||
−0.847681 | + | 0.530506i | \(0.822002\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.32456 | − | 7.07107i | −0.483651 | − | 0.540738i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 7.07107i | − | 0.537603i | −0.963196 | − | 0.268802i | \(-0.913372\pi\) | ||
0.963196 | − | 0.268802i | \(-0.0866276\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.00000 | − | 7.34847i | −0.226779 | − | 0.555492i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.00000 | − | 15.6525i | 0.526152 | − | 1.17651i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.3923 | 0.776757 | 0.388379 | − | 0.921500i | \(-0.373035\pi\) | ||||
0.388379 | + | 0.921500i | \(0.373035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.16228 | 0.235050 | 0.117525 | − | 0.993070i | \(-0.462504\pi\) | ||||
0.117525 | + | 0.993070i | \(0.462504\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.00000 | + | 2.23607i | 0.369611 | + | 0.165295i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.5432 | − | 8.82273i | 0.766906 | − | 0.641759i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 8.94427i | − | 0.647185i | −0.946197 | − | 0.323592i | \(-0.895109\pi\) | ||
0.946197 | − | 0.323592i | \(-0.104891\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.00000 | −0.287926 | −0.143963 | − | 0.989583i | \(-0.545985\pi\) | ||||
−0.143963 | + | 0.989583i | \(0.545985\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.16228 | + | 7.07107i | −0.226455 | + | 0.506370i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.47723 | + | 12.2474i | −0.386334 | + | 0.863868i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.92820 | − | 16.9706i | −0.486265 | − | 1.19110i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 15.4919i | − | 1.08200i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.0000 | + | 8.94427i | −0.695048 | + | 0.621670i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.9545 | −0.757735 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.74597i | 0.533254i | 0.963800 | + | 0.266627i | \(0.0859092\pi\) | ||||
−0.963800 | + | 0.266627i | \(0.914091\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.32456 | − | 14.1421i | 0.433351 | − | 0.969003i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.9545 | 0.747087 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0000 | − | 4.89898i | 0.814613 | − | 0.332564i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.3923 | − | 23.2379i | 0.702247 | − | 1.57027i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.79796i | 0.656120i | 0.944657 | + | 0.328060i | \(0.106395\pi\) | ||||
−0.944657 | + | 0.328060i | \(0.893605\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.00000 | + | 6.70820i | 0.400000 | + | 0.447214i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 9.89949i | − | 0.657053i | −0.944495 | − | 0.328526i | \(-0.893448\pi\) | ||
0.944495 | − | 0.328526i | \(-0.106552\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.8114 | −1.04485 | −0.522423 | − | 0.852686i | \(-0.674972\pi\) | ||||
−0.522423 | + | 0.852686i | \(0.674972\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.522774 | − | 15.8659i | 0.0343960 | − | 1.04390i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.94427i | 0.585959i | 0.956119 | + | 0.292979i | \(0.0946467\pi\) | ||||
−0.956119 | + | 0.292979i | \(0.905353\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 15.4919i | − | 1.01058i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.8114 | + | 7.07107i | 1.02706 | + | 0.459315i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.47214i | 0.289278i | 0.989484 | + | 0.144639i | \(0.0462022\pi\) | ||||
−0.989484 | + | 0.144639i | \(0.953798\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.89898i | 0.315571i | 0.987473 | + | 0.157786i | \(0.0504355\pi\) | ||||
−0.987473 | + | 0.157786i | \(0.949565\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.90569 | + | 13.4350i | −0.507151 | + | 0.861858i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.92820 | − | 7.07107i | −0.442627 | − | 0.451754i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.0000 | −0.636285 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.00000 | + | 11.1803i | −0.316862 | + | 0.708525i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.5563i | 0.981908i | 0.871185 | + | 0.490954i | \(0.163352\pi\) | ||||
−0.871185 | + | 0.490954i | \(0.836648\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.4919i | 0.973970i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.9545 | −0.683320 | −0.341660 | − | 0.939824i | \(-0.610989\pi\) | ||||
−0.341660 | + | 0.939824i | \(0.610989\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.8564 | + | 15.4919i | 0.857690 | + | 0.958927i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 8.94427i | − | 0.551527i | −0.961225 | − | 0.275764i | \(-0.911069\pi\) | ||
0.961225 | − | 0.275764i | \(-0.0889307\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.89949i | 0.603583i | 0.953374 | + | 0.301791i | \(0.0975846\pi\) | ||||
−0.953374 | + | 0.301791i | \(0.902415\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.477226 | − | 14.4835i | 0.0288830 | − | 0.876582i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.3923 | 0.626680 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 15.4919i | − | 0.930820i | −0.885095 | − | 0.465410i | \(-0.845907\pi\) | ||
0.885095 | − | 0.465410i | \(-0.154093\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.9545 | + | 9.79796i | −0.655826 | + | 0.586588i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.94427i | 0.533571i | 0.963756 | + | 0.266785i | \(0.0859614\pi\) | ||||
−0.963756 | + | 0.266785i | \(0.914039\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.8114 | 0.939889 | 0.469945 | − | 0.882696i | \(-0.344274\pi\) | ||||
0.469945 | + | 0.882696i | \(0.344274\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.16228 | − | 7.07107i | 0.187317 | − | 0.418854i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.9545 | + | 26.8328i | 0.646621 | + | 1.58389i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.46410 | + | 7.74597i | −0.203069 | + | 0.454077i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.8701i | 1.56977i | 0.619644 | + | 0.784883i | \(0.287277\pi\) | ||||
−0.619644 | + | 0.784883i | \(0.712723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.0000 | 0.815112 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.47723 | + | 17.1464i | 0.317821 | + | 0.994937i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.1421i | 0.817861i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.9737 | + | 7.74597i | −1.09362 | + | 0.446470i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.0000 | − | 24.5967i | 0.631933 | − | 1.41305i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.47214i | 0.256074i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.16228 | −0.180481 | −0.0902404 | − | 0.995920i | \(-0.528764\pi\) | ||||
−0.0902404 | + | 0.995920i | \(0.528764\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.92820 | − | 15.4919i | 0.394132 | − | 0.881305i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.9545 | 0.621170 | 0.310585 | − | 0.950546i | \(-0.399475\pi\) | ||||
0.310585 | + | 0.950546i | \(0.399475\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 9.79796i | − | 0.553813i | −0.960897 | − | 0.276907i | \(-0.910691\pi\) | ||
0.960897 | − | 0.276907i | \(-0.0893093\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.0905 | + | 4.91754i | 0.568534 | + | 0.277072i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.92820 | 0.389127 | 0.194563 | − | 0.980890i | \(-0.437671\pi\) | ||||
0.194563 | + | 0.980890i | \(0.437671\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.0000 | 1.34374 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.4317 | − | 7.34847i | −0.917127 | − | 0.410152i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.48683 | 0.526235 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.9545 | + | 26.8328i | 0.603938 | + | 1.47934i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 7.74597i | − | 0.425757i | −0.977079 | − | 0.212878i | \(-0.931716\pi\) | ||
0.977079 | − | 0.212878i | \(-0.0682838\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.9545 | −0.598506 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.00000 | 0.435788 | 0.217894 | − | 0.975972i | \(-0.430081\pi\) | ||||
0.217894 | + | 0.975972i | \(0.430081\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.16228 | − | 7.07107i | 0.171751 | − | 0.384048i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.9706i | 0.919007i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0000 | + | 7.34847i | 0.917914 | + | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.0000 | − | 4.47214i | −0.538382 | − | 0.240772i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.3205 | 0.929814 | 0.464907 | − | 0.885360i | \(-0.346088\pi\) | ||||
0.464907 | + | 0.885360i | \(0.346088\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.1359 | 1.18491 | 0.592455 | − | 0.805604i | \(-0.298159\pi\) | ||||
0.592455 | + | 0.805604i | \(0.298159\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.00000 | + | 15.6525i | 0.266880 | + | 0.835467i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.9545 | 0.583047 | 0.291523 | − | 0.956564i | \(-0.405838\pi\) | ||||
0.291523 | + | 0.956564i | \(0.405838\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.6491 | 0.671345 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.3050i | 1.65221i | 0.563515 | + | 0.826106i | \(0.309449\pi\) | ||||
−0.563515 | + | 0.826106i | \(0.690551\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.00000 | −0.473684 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.58114 | + | 0.707107i | 0.0829883 | + | 0.0371135i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.7846 | 1.08792 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 19.5959i | − | 1.02290i | −0.859313 | − | 0.511449i | \(-0.829109\pi\) | ||
0.859313 | − | 0.511449i | \(-0.170891\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −21.9089 | − | 24.4949i | −1.14053 | − | 1.27515i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 30.9839i | − | 1.60428i | −0.597133 | − | 0.802142i | \(-0.703694\pi\) | ||
0.597133 | − | 0.802142i | \(-0.296306\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.00000 | + | 17.8885i | −0.413118 | + | 0.923760i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.9089 | 1.12837 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 23.2379i | − | 1.19365i | −0.802371 | − | 0.596825i | \(-0.796429\pi\) | ||
0.802371 | − | 0.596825i | \(-0.203571\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.6491 | − | 5.65685i | −0.648034 | − | 0.289809i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.9545 | 0.559746 | 0.279873 | − | 0.960037i | \(-0.409708\pi\) | ||||
0.279873 | + | 0.960037i | \(0.409708\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.0000 | − | 4.89898i | 0.611577 | − | 0.249675i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.3205 | − | 15.4919i | 0.880451 | − | 0.787499i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.7128 | 1.40510 | 0.702548 | − | 0.711637i | \(-0.252046\pi\) | ||||
0.702548 | + | 0.711637i | \(0.252046\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.00000 | − | 2.23607i | 0.0504433 | − | 0.112795i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.1421i | 0.711568i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.1359 | 1.11097 | 0.555486 | − | 0.831526i | \(-0.312532\pi\) | ||||
0.555486 | + | 0.831526i | \(0.312532\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.477226 | + | 14.4835i | −0.0238912 | + | 0.725083i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 4.47214i | − | 0.223328i | −0.993746 | − | 0.111664i | \(-0.964382\pi\) | ||
0.993746 | − | 0.111664i | \(-0.0356180\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.4919i | 0.771708i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.6491 | − | 1.41421i | −0.628539 | − | 0.0702728i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.79796i | 0.484478i | 0.970217 | + | 0.242239i | \(0.0778818\pi\) | ||||
−0.970217 | + | 0.242239i | \(0.922118\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.6491 | − | 28.2843i | 0.623935 | − | 1.39516i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.2487 | + | 9.89949i | −1.19320 | + | 0.487122i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.0000 | −0.490881 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25.0000 | + | 11.1803i | 1.22426 | + | 0.547504i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.0416i | 1.17451i | 0.809402 | + | 0.587255i | \(0.199792\pi\) | ||||
−0.809402 | + | 0.587255i | \(0.800208\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.9839i | 1.51006i | 0.655690 | + | 0.755031i | \(0.272378\pi\) | ||||
−0.655690 | + | 0.755031i | \(0.727622\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21.9089 | − | 24.4949i | −1.06525 | − | 1.19098i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.16228 | − | 7.74597i | −0.153033 | − | 0.374854i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17.3205 | + | 7.74597i | 0.836242 | + | 0.373979i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 22.3607i | − | 1.07708i | −0.842601 | − | 0.538538i | \(-0.818977\pi\) | ||
0.842601 | − | 0.538538i | \(-0.181023\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.6969i | 0.706290i | 0.935569 | + | 0.353145i | \(0.114888\pi\) | ||||
−0.935569 | + | 0.353145i | \(0.885112\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.92820 | + | 15.4919i | −0.332182 | + | 0.742781i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 14.1421i | − | 0.676510i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.4949i | 1.16908i | 0.811366 | + | 0.584539i | \(0.198725\pi\) | ||||
−0.811366 | + | 0.584539i | \(0.801275\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.9545 | − | 1.38238i | −0.997831 | − | 0.0658277i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.3205 | −0.822922 | −0.411461 | − | 0.911427i | \(-0.634981\pi\) | ||||
−0.411461 | + | 0.911427i | \(0.634981\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.9545 | − | 4.89898i | −0.518128 | − | 0.231714i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.94427i | 0.422106i | 0.977475 | + | 0.211053i | \(0.0676893\pi\) | ||||
−0.977475 | + | 0.211053i | \(0.932311\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −37.9473 | −1.78687 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.6491 | − | 5.65685i | −0.594307 | − | 0.265782i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.9545 | − | 4.47214i | 0.513553 | − | 0.209657i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.00000 | 0.374224 | 0.187112 | − | 0.982339i | \(-0.440087\pi\) | ||||
0.187112 | + | 0.982339i | \(0.440087\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 15.5563i | − | 0.724531i | −0.932075 | − | 0.362266i | \(-0.882003\pi\) | ||
0.932075 | − | 0.362266i | \(-0.117997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.0000 | −0.650635 | −0.325318 | − | 0.945605i | \(-0.605471\pi\) | ||||
−0.325318 | + | 0.945605i | \(0.605471\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.9545 | − | 4.89898i | −0.508001 | − | 0.227185i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.07107i | 0.327210i | 0.986526 | + | 0.163605i | \(0.0523123\pi\) | ||||
−0.986526 | + | 0.163605i | \(0.947688\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.9737 | − | 7.74597i | 0.876122 | − | 0.357676i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.0000 | − | 11.1803i | −1.15194 | − | 0.515163i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 26.8328i | − | 1.23377i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.48683 | −0.435286 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.9545 | −0.500522 | −0.250261 | − | 0.968178i | \(-0.580516\pi\) | ||||
−0.250261 | + | 0.968178i | \(0.580516\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 20.4828 | + | 0.674899i | 0.931999 | + | 0.0307090i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.92820 | −0.314594 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.00000 | −0.362515 | −0.181257 | − | 0.983436i | \(-0.558017\pi\) | ||||
−0.181257 | + | 0.983436i | \(0.558017\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.4317 | + | 36.7423i | −0.743066 | + | 1.66155i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.46410 | −0.156333 | −0.0781664 | − | 0.996940i | \(-0.524907\pi\) | ||||
−0.0781664 | + | 0.996940i | \(0.524907\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.9545 | + | 9.79796i | −0.492366 | + | 0.440386i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −21.9089 | + | 8.94427i | −0.982749 | + | 0.401205i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.74597i | 0.346757i | 0.984855 | + | 0.173379i | \(0.0554684\pi\) | ||||
−0.984855 | + | 0.173379i | \(0.944532\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −34.6410 | − | 15.4919i | −1.54765 | − | 0.692129i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.8634 | 1.46530 | 0.732652 | − | 0.680603i | \(-0.238282\pi\) | ||||
0.732652 | + | 0.680603i | \(0.238282\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.0000 | 0.978987 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.74342 | − | 2.12132i | −0.210663 | − | 0.0942111i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.89949i | 0.438787i | 0.975636 | + | 0.219394i | \(0.0704079\pi\) | ||||
−0.975636 | + | 0.219394i | \(0.929592\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36.0000 | + | 14.6969i | −1.59255 | + | 0.650154i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.00000 | − | 15.6525i | −0.220755 | − | 0.691074i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.8564 | 0.610586 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −37.9473 | −1.66892 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.00000 | − | 11.1803i | 0.219476 | − | 0.490762i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.8634 | 1.43977 | 0.719885 | − | 0.694094i | \(-0.244195\pi\) | ||||
0.719885 | + | 0.694094i | \(0.244195\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.16228 | −0.138277 | −0.0691384 | − | 0.997607i | \(-0.522025\pi\) | ||||
−0.0691384 | + | 0.997607i | \(0.522025\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.452736 | − | 13.7403i | 0.0197590 | − | 0.599675i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.00000 | 0.130435 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.1359 | − | 19.7990i | 0.960618 | − | 0.859203i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −34.6410 | −1.50047 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 14.6969i | − | 0.635404i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.4317 | + | 7.34847i | 0.709079 | + | 0.317110i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17.3205 | + | 16.9706i | −0.746047 | + | 0.730974i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.00000 | + | 2.23607i | 0.214571 | + | 0.0959589i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 7.74597i | − | 0.331194i | −0.986194 | − | 0.165597i | \(-0.947045\pi\) | ||
0.986194 | − | 0.165597i | \(-0.0529550\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.32456 | + | 7.07107i | 0.269925 | + | 0.301786i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.9089 | −0.933351 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.0000 | − | 24.4949i | −0.425243 | − | 1.04163i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 24.4949i | − | 1.03602i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1.41421i | − | 0.0596020i | −0.999556 | − | 0.0298010i | \(-0.990513\pi\) | ||
0.999556 | − | 0.0298010i | \(-0.00948736\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.32456 | 0.266076 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.9089 | − | 6.49478i | 0.962083 | − | 0.272755i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.3607i | 0.937408i | 0.883355 | + | 0.468704i | \(0.155279\pi\) | ||||
−0.883355 | + | 0.468704i | \(0.844721\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.74597i | 0.324159i | 0.986778 | + | 0.162079i | \(0.0518200\pi\) | ||||
−0.986778 | + | 0.162079i | \(0.948180\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.32456 | − | 14.1421i | 0.264212 | − | 0.590796i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.4164i | 0.559503i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.3939i | 1.22368i | 0.790980 | + | 0.611842i | \(0.209571\pi\) | ||||
−0.790980 | + | 0.611842i | \(0.790429\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.32456 | − | 2.82843i | −0.262840 | − | 0.117545i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.3205 | − | 7.07107i | 0.718576 | − | 0.293357i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.0000 | + | 8.94427i | −0.413449 | + | 0.369800i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 35.3553i | − | 1.45927i | −0.683836 | − | 0.729636i | \(-0.739690\pi\) | ||
0.683836 | − | 0.729636i | \(-0.260310\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 15.4919i | − | 0.638334i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.8634 | 1.34954 | 0.674768 | − | 0.738030i | \(-0.264244\pi\) | ||||
0.674768 | + | 0.738030i | \(0.264244\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 8.94427i | − | 0.365453i | −0.983164 | − | 0.182727i | \(-0.941508\pi\) | ||
0.983164 | − | 0.182727i | \(-0.0584923\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 24.4949i | − | 0.999168i | −0.866266 | − | 0.499584i | \(-0.833486\pi\) | ||
0.866266 | − | 0.499584i | \(-0.166514\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.3205 | + | 15.4919i | −0.705346 | + | 0.630880i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.41421i | 0.0574960i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.5959i | 0.795374i | 0.917521 | + | 0.397687i | \(0.130187\pi\) | ||||
−0.917521 | + | 0.397687i | \(0.869813\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.04555 | − | 31.7318i | 0.0423678 | − | 1.28584i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −34.6410 | −1.40143 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.4758i | 1.87714i | 0.345089 | + | 0.938570i | \(0.387849\pi\) | ||||
−0.345089 | + | 0.938570i | \(0.612151\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.9545 | − | 24.4949i | 0.441726 | − | 0.987730i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 31.3050i | − | 1.26029i | −0.776478 | − | 0.630145i | \(-0.782995\pi\) | ||
0.776478 | − | 0.630145i | \(-0.217005\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.16228 | −0.127103 | −0.0635513 | − | 0.997979i | \(-0.520243\pi\) | ||||
−0.0635513 | + | 0.997979i | \(0.520243\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22.1359 | + | 7.07107i | −0.888285 | + | 0.283752i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −17.3205 | − | 7.74597i | −0.691714 | − | 0.309344i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.0000 | 0.398094 | 0.199047 | − | 0.979990i | \(-0.436215\pi\) | ||||
0.199047 | + | 0.979990i | \(0.436215\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.47723 | + | 12.2474i | −0.217700 | + | 0.486792i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 11.3137i | − | 0.448971i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.8114 | + | 15.4919i | −0.626470 | + | 0.613813i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 20.0000 | − | 17.8885i | 0.791188 | − | 0.707660i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 31.3050i | − | 1.23647i | −0.785993 | − | 0.618236i | \(-0.787848\pi\) | ||
0.785993 | − | 0.618236i | \(-0.212152\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.16228 | −0.124708 | −0.0623540 | − | 0.998054i | \(-0.519861\pi\) | ||||
−0.0623540 | + | 0.998054i | \(0.519861\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.3205 | + | 7.74597i | 0.681994 | + | 0.304997i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 34.2929i | − | 1.34611i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.4378 | + | 0.739315i | 0.879405 | + | 0.0289760i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −48.4974 | −1.89785 | −0.948925 | − | 0.315501i | \(-0.897828\pi\) | ||||
−0.948925 | + | 0.315501i | \(0.897828\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.00000 | 0.0781465 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 32.8634 | − | 29.3939i | 1.28212 | − | 1.14676i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.2487 | 0.944596 | 0.472298 | − | 0.881439i | \(-0.343425\pi\) | ||||
0.472298 | + | 0.881439i | \(0.343425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.1096 | 1.59898 | 0.799489 | − | 0.600680i | \(-0.205104\pi\) | ||||
0.799489 | + | 0.600680i | \(0.205104\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.9545 | + | 4.47214i | −0.424795 | + | 0.173422i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.9839i | 1.19970i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.92820 | + | 15.4919i | −0.267860 | + | 0.598953i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.9545 | 0.422892 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −46.0000 | −1.77317 | −0.886585 | − | 0.462566i | \(-0.846929\pi\) | ||||
−0.886585 | + | 0.462566i | \(0.846929\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.74342 | + | 14.8492i | 0.182574 | + | 0.571548i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 7.07107i | − | 0.271763i | −0.990725 | − | 0.135882i | \(-0.956613\pi\) | ||
0.990725 | − | 0.135882i | \(-0.0433867\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0000 | − | 4.89898i | 0.460518 | − | 0.188006i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.00000 | − | 15.6525i | 0.268241 | − | 0.599804i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.1769 | −1.19295 | −0.596476 | − | 0.802631i | \(-0.703433\pi\) | ||||
−0.596476 | + | 0.802631i | \(0.703433\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.2982 | 0.966595 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.0000 | − | 11.1803i | −0.953809 | − | 0.426557i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.16228 | −0.120299 | −0.0601494 | − | 0.998189i | \(-0.519158\pi\) | ||||
−0.0601494 | + | 0.998189i | \(0.519158\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.0455 | − | 24.7165i | 0.457569 | − | 0.938903i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.3607i | 0.848189i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.32456 | + | 14.1421i | −0.239217 | + | 0.534905i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.7846 | −0.785024 | −0.392512 | − | 0.919747i | \(-0.628394\pi\) | ||||
−0.392512 | + | 0.919747i | \(0.628394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.9545 | − | 24.4949i | 0.412568 | − | 0.922531i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −38.1051 | + | 15.5563i | −1.43309 | + | 0.585057i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.9839i | 1.16362i | 0.813323 | + | 0.581812i | \(0.197656\pi\) | ||||
−0.813323 | + | 0.581812i | \(0.802344\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.0000 | + | 22.3607i | 0.750059 | + | 0.838591i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.9089 | −0.820495 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.4919i | 0.579365i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.16228 | + | 7.07107i | −0.118097 | + | 0.264074i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.8634 | 1.22560 | 0.612798 | − | 0.790239i | \(-0.290044\pi\) | ||||
0.612798 | + | 0.790239i | \(0.290044\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0000 | + | 9.79796i | −0.893807 | + | 0.364895i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.46410 | + | 7.74597i | −0.128831 | + | 0.288076i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20.7846 | 0.771921 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 19.5959i | − | 0.726772i | −0.931639 | − | 0.363386i | \(-0.881621\pi\) | ||
0.931639 | − | 0.363386i | \(-0.118379\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.0000 | + | 15.6525i | −0.814815 | + | 0.579721i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.8114 | −0.584007 | −0.292003 | − | 0.956417i | \(-0.594322\pi\) | ||||
−0.292003 | + | 0.956417i | \(0.594322\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.95445 | − | 16.0793i | −0.219633 | − | 0.593095i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.8328i | 0.988399i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 23.2379i | − | 0.854820i | −0.904058 | − | 0.427410i | \(-0.859426\pi\) | ||
0.904058 | − | 0.427410i | \(-0.140574\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.8114 | − | 7.07107i | −0.580846 | − | 0.259762i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 49.1935i | − | 1.80473i | −0.430968 | − | 0.902367i | \(-0.641828\pi\) | ||
0.430968 | − | 0.902367i | \(-0.358172\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 9.79796i | − | 0.358969i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.8114 | + | 14.1421i | −0.578508 | + | 0.517434i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.3923 | + | 25.4558i | 0.379727 | + | 0.930136i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.0000 | 1.45962 | 0.729810 | − | 0.683650i | \(-0.239608\pi\) | ||||
0.729810 | + | 0.683650i | \(0.239608\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.0000 | + | 24.5967i | −0.400862 | + | 0.896355i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 11.3137i | − | 0.411748i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 46.4758i | − | 1.68919i | −0.535404 | − | 0.844596i | \(-0.679841\pi\) | ||
0.535404 | − | 0.844596i | \(-0.320159\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.9545 | + | 24.4949i | −0.397621 | + | 0.889108i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.9545 | −0.397099 | −0.198549 | − | 0.980091i | \(-0.563623\pi\) | ||||
−0.198549 | + | 0.980091i | \(0.563623\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 31.3050i | − | 1.13036i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.4949i | 0.883309i | 0.897185 | + | 0.441654i | \(0.145608\pi\) | ||||
−0.897185 | + | 0.441654i | \(0.854392\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.3205 | − | 7.74597i | −0.623783 | − | 0.278964i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.3553i | 1.27164i | 0.771836 | + | 0.635822i | \(0.219339\pi\) | ||||
−0.771836 | + | 0.635822i | \(0.780661\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.6969i | 0.527930i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34.6410 | 1.24114 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 30.9839i | − | 1.10869i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.9545 | + | 34.2929i | 0.391480 | + | 1.22553i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 22.3607i | − | 0.798087i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 53.7587 | 1.91629 | 0.958146 | − | 0.286281i | \(-0.0924191\pi\) | ||||
0.958146 | + | 0.286281i | \(0.0924191\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.32456 | − | 14.1421i | 0.225160 | − | 0.503473i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.9545 | + | 4.47214i | −0.389495 | + | 0.159011i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.0000 | 0.355110 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 49.4975i | − | 1.75329i | −0.481137 | − | 0.876645i | \(-0.659776\pi\) | ||
0.481137 | − | 0.876645i | \(-0.340224\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 50.9117i | − | 1.79663i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.32456 | + | 15.4919i | 0.222911 | + | 0.546019i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.00000 | + | 15.6525i | −0.246412 | + | 0.550993i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.3607i | 0.786160i | 0.919504 | + | 0.393080i | \(0.128590\pi\) | ||||
−0.919504 | + | 0.393080i | \(0.871410\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.1359 | −0.777298 | −0.388649 | − | 0.921386i | \(-0.627058\pi\) | ||||
−0.388649 | + | 0.921386i | \(0.627058\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −32.8634 | −1.15115 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.4949i | 0.856968i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.9960 | − | 22.5630i | 0.384230 | − | 0.788415i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.8564 | −0.483592 | −0.241796 | − | 0.970327i | \(-0.577736\pi\) | ||||
−0.241796 | + | 0.970327i | \(0.577736\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.0000 | −0.906303 | −0.453152 | − | 0.891434i | \(-0.649700\pi\) | ||||
−0.453152 | + | 0.891434i | \(0.649700\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 16.4317 | + | 7.34847i | 0.572078 | + | 0.255841i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 51.9615 | 1.80688 | 0.903440 | − | 0.428715i | \(-0.141034\pi\) | ||||
0.903440 | + | 0.428715i | \(0.141034\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.7851 | −1.20813 | −0.604067 | − | 0.796933i | \(-0.706454\pi\) | ||||
−0.604067 | + | 0.796933i | \(0.706454\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.9545 | − | 24.4949i | 0.380006 | − | 0.849719i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 30.9839i | − | 1.07224i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −24.2487 | + | 7.74597i | −0.838158 | + | 0.267740i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.9089 | 0.756379 | 0.378190 | − | 0.925728i | \(-0.376547\pi\) | ||||
0.378190 | + | 0.925728i | \(0.376547\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.0000 | 0.655172 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.32456 | + | 14.1421i | −0.217829 | + | 0.487081i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 4.24264i | − | 0.145951i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | − | 2.44949i | −0.0343604 | − | 0.0841655i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.0000 | + | 11.1803i | 0.857998 | + | 0.383708i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −53.7587 | −1.84066 | −0.920332 | − | 0.391139i | \(-0.872081\pi\) | ||||
−0.920332 | + | 0.391139i | \(0.872081\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.0000 | − | 8.94427i | 0.341993 | − | 0.305888i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −54.7723 | −1.87098 | −0.935492 | − | 0.353347i | \(-0.885043\pi\) | ||||
−0.935492 | + | 0.353347i | \(0.885043\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.16228 | −0.107896 | −0.0539478 | − | 0.998544i | \(-0.517180\pi\) | ||||
−0.0539478 | + | 0.998544i | \(0.517180\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.65316 | + | 50.1724i | −0.0563395 | + | 1.70987i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 8.94427i | − | 0.304467i | −0.988345 | − | 0.152233i | \(-0.951353\pi\) | ||
0.988345 | − | 0.152233i | \(-0.0486465\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.0000 | 0.340010 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26.8794 | − | 12.0208i | −0.912871 | − | 0.408248i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34.6410 | 1.17512 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.4949i | 0.829978i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.9545 | + | 9.79796i | −0.370752 | + | 0.331611i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 27.7128 | − | 11.3137i | 0.936864 | − | 0.382473i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.4919i | 0.523125i | 0.965186 | + | 0.261563i | \(0.0842378\pi\) | ||||
−0.965186 | + | 0.261563i | \(0.915762\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.0000 | + | 42.4853i | −0.640854 | + | 1.43299i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.8634 | 1.10719 | 0.553597 | − | 0.832785i | \(-0.313255\pi\) | ||||
0.553597 | + | 0.832785i | \(0.313255\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 23.2379i | − | 0.782018i | −0.920387 | − | 0.391009i | \(-0.872126\pi\) | ||
0.920387 | − | 0.391009i | \(-0.127874\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22.1359 | + | 9.89949i | 0.744092 | + | 0.332768i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.9089 | −0.735629 | −0.367814 | − | 0.929899i | \(-0.619894\pi\) | ||||
−0.367814 | + | 0.929899i | \(0.619894\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.00000 | + | 19.5959i | 0.268311 | + | 0.657226i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.46410 | + | 30.9839i | −0.116052 | + | 1.03800i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34.6410 | 1.15922 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.6969i | 0.491264i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.0000 | + | 22.3607i | −0.333890 | + | 0.746601i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33.9411i | 1.13200i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −35.4772 | − | 1.16896i | −1.18061 | − | 0.0389005i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.47214i | 0.148659i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.7298i | 1.28600i | 0.765865 | + | 0.643002i | \(0.222311\pi\) | ||||
−0.765865 | + | 0.643002i | \(0.777689\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 34.7851 | − | 31.1127i | 1.15375 | − | 1.03194i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.3050i | 1.03718i | 0.855023 | + | 0.518590i | \(0.173543\pi\) | ||||
−0.855023 | + | 0.518590i | \(0.826457\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.4949i | 0.810663i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.16228 | + | 7.07107i | −0.104542 | + | 0.233762i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.46410 | + | 1.41421i | −0.114395 | + | 0.0467014i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.0000 | 0.329870 | 0.164935 | − | 0.986304i | \(-0.447259\pi\) | ||||
0.164935 | + | 0.986304i | \(0.447259\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.00000 | − | 2.23607i | −0.164756 | − | 0.0736809i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 28.2843i | − | 0.930988i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 21.9089 | − | 19.5959i | 0.719583 | − | 0.643614i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.9089 | −0.718808 | −0.359404 | − | 0.933182i | \(-0.617020\pi\) | ||||
−0.359404 | + | 0.933182i | \(0.617020\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.8114 | − | 15.4919i | 0.518197 | − | 0.507728i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.3205 | + | 7.74597i | 0.567048 | + | 0.253592i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 44.0908i | − | 1.44038i | −0.693775 | − | 0.720192i | \(-0.744054\pi\) | ||
0.693775 | − | 0.720192i | \(-0.255946\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.92820 | − | 15.4919i | 0.226093 | − | 0.505560i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.41421i | 0.0461020i | 0.999734 | + | 0.0230510i | \(0.00733802\pi\) | ||||
−0.999734 | + | 0.0230510i | \(0.992662\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 48.9898i | − | 1.59533i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12.4772 | + | 14.9104i | 0.405884 | + | 0.485034i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.3205 | −0.562841 | −0.281420 | − | 0.959585i | \(-0.590806\pi\) | ||||
−0.281420 | + | 0.959585i | \(0.590806\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 46.4758i | − | 1.50867i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.9545 | + | 4.89898i | 0.355222 | + | 0.158860i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 17.8885i | − | 0.579467i | −0.957107 | − | 0.289733i | \(-0.906433\pi\) | ||
0.957107 | − | 0.289733i | \(-0.0935666\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.6491 | 0.409316 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 37.9473 | + | 16.9706i | 1.22666 | + | 0.548580i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −43.8178 | + | 17.8885i | −1.41495 | + | 0.577651i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.00000 | 0.225806 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.7846 | − | 23.2379i | −0.669775 | − | 0.748831i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 5.65685i | − | 0.182101i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.0000 | −1.02905 | −0.514525 | − | 0.857475i | \(-0.672032\pi\) | ||||
−0.514525 | + | 0.857475i | \(0.672032\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.0122i | 1.31614i | 0.752955 | + | 0.658072i | \(0.228628\pi\) | ||||
−0.752955 | + | 0.658072i | \(0.771372\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.8114 | − | 38.7298i | −0.506890 | − | 1.24162i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15.0000 | + | 6.70820i | 0.480384 | + | 0.214834i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.94427i | 0.286153i | 0.989712 | + | 0.143076i | \(0.0456994\pi\) | ||||
−0.989712 | + | 0.143076i | \(0.954301\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −43.8178 | −1.39757 | −0.698785 | − | 0.715331i | \(-0.746276\pi\) | ||||
−0.698785 | + | 0.715331i | \(0.746276\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.65316 | + | 50.1724i | −0.0526206 | + | 1.59700i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.6410 | 1.10152 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.00000 | −0.0635321 | −0.0317660 | − | 0.999495i | \(-0.510113\pi\) | ||||
−0.0317660 | + | 0.999495i | \(0.510113\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.47723 | − | 12.2474i | 0.173814 | − | 0.388661i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.16228 | 0.100150 | 0.0500752 | − | 0.998745i | \(-0.484054\pi\) | ||||
0.0500752 | + | 0.998745i | \(0.484054\pi\) | |||||||
\(998\) | 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 \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 672.2.i.d.209.7 | 8 | ||
3.2 | odd | 2 | inner | 672.2.i.d.209.5 | 8 | ||
4.3 | odd | 2 | 168.2.i.e.125.7 | yes | 8 | ||
7.6 | odd | 2 | inner | 672.2.i.d.209.2 | 8 | ||
8.3 | odd | 2 | 168.2.i.e.125.4 | yes | 8 | ||
8.5 | even | 2 | inner | 672.2.i.d.209.1 | 8 | ||
12.11 | even | 2 | 168.2.i.e.125.1 | ✓ | 8 | ||
21.20 | even | 2 | inner | 672.2.i.d.209.4 | 8 | ||
24.5 | odd | 2 | inner | 672.2.i.d.209.3 | 8 | ||
24.11 | even | 2 | 168.2.i.e.125.6 | yes | 8 | ||
28.27 | even | 2 | 168.2.i.e.125.8 | yes | 8 | ||
56.13 | odd | 2 | inner | 672.2.i.d.209.8 | 8 | ||
56.27 | even | 2 | 168.2.i.e.125.3 | yes | 8 | ||
84.83 | odd | 2 | 168.2.i.e.125.2 | yes | 8 | ||
168.83 | odd | 2 | 168.2.i.e.125.5 | yes | 8 | ||
168.125 | even | 2 | inner | 672.2.i.d.209.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.i.e.125.1 | ✓ | 8 | 12.11 | even | 2 | ||
168.2.i.e.125.2 | yes | 8 | 84.83 | odd | 2 | ||
168.2.i.e.125.3 | yes | 8 | 56.27 | even | 2 | ||
168.2.i.e.125.4 | yes | 8 | 8.3 | odd | 2 | ||
168.2.i.e.125.5 | yes | 8 | 168.83 | odd | 2 | ||
168.2.i.e.125.6 | yes | 8 | 24.11 | even | 2 | ||
168.2.i.e.125.7 | yes | 8 | 4.3 | odd | 2 | ||
168.2.i.e.125.8 | yes | 8 | 28.27 | even | 2 | ||
672.2.i.d.209.1 | 8 | 8.5 | even | 2 | inner | ||
672.2.i.d.209.2 | 8 | 7.6 | odd | 2 | inner | ||
672.2.i.d.209.3 | 8 | 24.5 | odd | 2 | inner | ||
672.2.i.d.209.4 | 8 | 21.20 | even | 2 | inner | ||
672.2.i.d.209.5 | 8 | 3.2 | odd | 2 | inner | ||
672.2.i.d.209.6 | 8 | 168.125 | even | 2 | inner | ||
672.2.i.d.209.7 | 8 | 1.1 | even | 1 | trivial | ||
672.2.i.d.209.8 | 8 | 56.13 | odd | 2 | inner |