Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,2,Mod(719,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("720.719");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.o (of order \(2\), degree \(1\), 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: | \(5.74922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 719.7 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.719 |
Dual form | 720.2.o.b.719.5 |
$q$-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 \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.73205 | + | 1.41421i | 0.774597 | + | 0.632456i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.24264 | −1.60357 | −0.801784 | − | 0.597614i | \(-0.796115\pi\) | ||||
−0.801784 | + | 0.597614i | \(0.796115\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.44949 | −0.738549 | −0.369274 | − | 0.929320i | \(-0.620394\pi\) | ||||
−0.369274 | + | 0.929320i | \(0.620394\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44949i | 0.679366i | 0.940540 | + | 0.339683i | \(0.110320\pi\) | ||||
−0.940540 | + | 0.339683i | \(0.889680\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.92820 | −1.68034 | −0.840168 | − | 0.542326i | \(-0.817544\pi\) | ||||
−0.840168 | + | 0.542326i | \(0.817544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.92820i | 1.58944i | 0.606977 | + | 0.794719i | \(0.292382\pi\) | ||||
−0.606977 | + | 0.794719i | \(0.707618\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.00000i | − | 1.25109i | −0.780189 | − | 0.625543i | \(-0.784877\pi\) | ||
0.780189 | − | 0.625543i | \(-0.215123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | + | 4.89898i | 0.200000 | + | 0.979796i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.82843i | − | 0.525226i | −0.964901 | − | 0.262613i | \(-0.915416\pi\) | ||
0.964901 | − | 0.262613i | \(-0.0845842\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.46410i | 0.622171i | 0.950382 | + | 0.311086i | \(0.100693\pi\) | ||||
−0.950382 | + | 0.311086i | \(0.899307\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.34847 | − | 6.00000i | −1.24212 | − | 1.01419i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.44949i | − | 0.402694i | −0.979520 | − | 0.201347i | \(-0.935468\pi\) | ||
0.979520 | − | 0.201347i | \(-0.0645318\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.07107i | 1.10432i | 0.833740 | + | 0.552158i | \(0.186195\pi\) | ||||
−0.833740 | + | 0.552158i | \(0.813805\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.48528 | −1.29399 | −0.646997 | − | 0.762493i | \(-0.723975\pi\) | ||||
−0.646997 | + | 0.762493i | \(0.723975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.0000 | 1.57143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.24264 | − | 3.46410i | −0.572078 | − | 0.467099i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.2474 | 1.59448 | 0.797241 | − | 0.603661i | \(-0.206292\pi\) | ||||
0.797241 | + | 0.603661i | \(0.206292\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.46410 | + | 4.24264i | −0.429669 | + | 0.526235i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.79796 | −1.16280 | −0.581402 | − | 0.813617i | \(-0.697496\pi\) | ||||
−0.581402 | + | 0.813617i | \(0.697496\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.89898i | 0.573382i | 0.958023 | + | 0.286691i | \(0.0925553\pi\) | ||||
−0.958023 | + | 0.286691i | \(0.907445\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.3923 | 1.18431 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.3923i | 1.16923i | 0.811312 | + | 0.584613i | \(0.198754\pi\) | ||||
−0.811312 | + | 0.584613i | \(0.801246\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000i | 1.31717i | 0.752506 | + | 0.658586i | \(0.228845\pi\) | ||||
−0.752506 | + | 0.658586i | \(0.771155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.0000 | − | 9.79796i | −1.30158 | − | 1.06274i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 7.07107i | − | 0.749532i | −0.927119 | − | 0.374766i | \(-0.877723\pi\) | ||
0.927119 | − | 0.374766i | \(-0.122277\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 10.3923i | − | 1.08941i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.79796 | + | 12.0000i | −1.00525 | + | 1.23117i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.6969i | 1.49225i | 0.665807 | + | 0.746124i | \(0.268087\pi\) | ||||
−0.665807 | + | 0.746124i | \(0.731913\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 11.3137i | − | 1.12576i | −0.826540 | − | 0.562878i | \(-0.809694\pi\) | ||
0.826540 | − | 0.562878i | \(-0.190306\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.7279 | 1.25412 | 0.627060 | − | 0.778971i | \(-0.284258\pi\) | ||||
0.627060 | + | 0.778971i | \(0.284258\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 12.0000i | − | 1.16008i | −0.814587 | − | 0.580042i | \(-0.803036\pi\) | ||
0.814587 | − | 0.580042i | \(-0.196964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.92820 | −0.651751 | −0.325875 | − | 0.945413i | \(-0.605659\pi\) | ||||
−0.325875 | + | 0.945413i | \(0.605659\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.48528 | − | 10.3923i | 0.791257 | − | 0.969087i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 29.3939 | 2.69453 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.19615 | + | 9.89949i | −0.464758 | + | 0.885438i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.7279 | 1.12942 | 0.564710 | − | 0.825289i | \(-0.308988\pi\) | ||||
0.564710 | + | 0.825289i | \(0.308988\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.44949 | 0.214013 | 0.107006 | − | 0.994258i | \(-0.465873\pi\) | ||||
0.107006 | + | 0.994258i | \(0.465873\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 29.3939i | − | 2.54877i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.8564 | 1.18383 | 0.591916 | − | 0.805999i | \(-0.298372\pi\) | ||||
0.591916 | + | 0.805999i | \(0.298372\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.46410i | 0.293821i | 0.989150 | + | 0.146911i | \(0.0469330\pi\) | ||||
−0.989150 | + | 0.146911i | \(0.953067\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 6.00000i | − | 0.501745i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.00000 | − | 4.89898i | 0.332182 | − | 0.406838i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 22.6274i | − | 1.85371i | −0.375419 | − | 0.926855i | \(-0.622501\pi\) | ||
0.375419 | − | 0.926855i | \(-0.377499\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 17.3205i | − | 1.40952i | −0.709444 | − | 0.704761i | \(-0.751054\pi\) | ||
0.709444 | − | 0.704761i | \(-0.248946\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.89898 | + | 6.00000i | −0.393496 | + | 0.481932i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 12.2474i | − | 0.977453i | −0.872437 | − | 0.488726i | \(-0.837462\pi\) | ||
0.872437 | − | 0.488726i | \(-0.162538\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 25.4558i | 2.00620i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.48528 | 0.664619 | 0.332309 | − | 0.943170i | \(-0.392172\pi\) | ||||
0.332309 | + | 0.943170i | \(0.392172\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.0000i | 1.39288i | 0.717614 | + | 0.696441i | \(0.245234\pi\) | ||||
−0.717614 | + | 0.696441i | \(0.754766\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.8564 | 1.05348 | 0.526742 | − | 0.850026i | \(-0.323414\pi\) | ||||
0.526742 | + | 0.850026i | \(0.323414\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.24264 | − | 20.7846i | −0.320713 | − | 1.57117i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.2474 | 0.915417 | 0.457709 | − | 0.889102i | \(-0.348670\pi\) | ||||
0.457709 | + | 0.889102i | \(0.348670\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.46410 | − | 4.24264i | 0.254686 | − | 0.311925i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.9706 | 1.24101 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.89898 | 0.354478 | 0.177239 | − | 0.984168i | \(-0.443283\pi\) | ||||
0.177239 | + | 0.984168i | \(0.443283\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.5959i | 1.41055i | 0.708936 | + | 0.705273i | \(0.249175\pi\) | ||||
−0.708936 | + | 0.705273i | \(0.750825\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.46410 | −0.246807 | −0.123404 | − | 0.992357i | \(-0.539381\pi\) | ||||
−0.123404 | + | 0.992357i | \(0.539381\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.3923i | 0.736691i | 0.929689 | + | 0.368345i | \(0.120076\pi\) | ||||
−0.929689 | + | 0.368345i | \(0.879924\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.0000i | 0.842235i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.0000 | + | 12.2474i | −0.698430 | + | 0.855399i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 16.9706i | − | 1.17388i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.46410i | 0.238479i | 0.992866 | + | 0.119239i | \(0.0380456\pi\) | ||||
−0.992866 | + | 0.119239i | \(0.961954\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.6969 | − | 12.0000i | −1.00232 | − | 0.818393i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 14.6969i | − | 0.997693i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 16.9706i | − | 1.14156i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.24264 | −0.284108 | −0.142054 | − | 0.989859i | \(-0.545371\pi\) | ||||
−0.142054 | + | 0.989859i | \(0.545371\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.0000i | 1.59294i | 0.604681 | + | 0.796468i | \(0.293301\pi\) | ||||
−0.604681 | + | 0.796468i | \(0.706699\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.92820 | −0.453882 | −0.226941 | − | 0.973909i | \(-0.572872\pi\) | ||||
−0.226941 | + | 0.973909i | \(0.572872\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.6969 | 0.950666 | 0.475333 | − | 0.879806i | \(-0.342328\pi\) | ||||
0.475333 | + | 0.879806i | \(0.342328\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.00000 | −0.515325 | −0.257663 | − | 0.966235i | \(-0.582952\pi\) | ||||
−0.257663 | + | 0.966235i | \(0.582952\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 19.0526 | + | 15.5563i | 1.21722 | + | 0.993859i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.9706 | −1.07981 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.0454 | −1.39149 | −0.695747 | − | 0.718287i | \(-0.744926\pi\) | ||||
−0.695747 | + | 0.718287i | \(0.744926\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.6969i | 0.923989i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.7128 | −1.72868 | −0.864339 | − | 0.502910i | \(-0.832263\pi\) | ||||
−0.864339 | + | 0.502910i | \(0.832263\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.3923i | 0.645746i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.00000i | 0.369976i | 0.982741 | + | 0.184988i | \(0.0592246\pi\) | ||||
−0.982741 | + | 0.184988i | \(0.940775\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.7990i | 1.20717i | 0.797300 | + | 0.603583i | \(0.206261\pi\) | ||||
−0.797300 | + | 0.603583i | \(0.793739\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 10.3923i | − | 0.631288i | −0.948878 | − | 0.315644i | \(-0.897780\pi\) | ||
0.948878 | − | 0.315644i | \(-0.102220\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.44949 | − | 12.0000i | −0.147710 | − | 0.723627i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 7.34847i | − | 0.441527i | −0.975327 | − | 0.220763i | \(-0.929145\pi\) | ||
0.975327 | − | 0.220763i | \(-0.0708548\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.07107i | 0.421825i | 0.977505 | + | 0.210912i | \(0.0676434\pi\) | ||||
−0.977505 | + | 0.210912i | \(0.932357\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 30.0000i | − | 1.77084i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.0000 | 1.82353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.3205 | 1.01187 | 0.505937 | − | 0.862570i | \(-0.331147\pi\) | ||||
0.505937 | + | 0.862570i | \(0.331147\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.2132 | + | 17.3205i | 1.23508 | + | 1.00844i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.6969 | 0.849946 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 36.0000 | 2.07501 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.46410 | − | 2.82843i | −0.198354 | − | 0.161955i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −33.9411 | −1.93712 | −0.968561 | − | 0.248776i | \(-0.919972\pi\) | ||||
−0.968561 | + | 0.248776i | \(0.919972\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.89898 | −0.277796 | −0.138898 | − | 0.990307i | \(-0.544356\pi\) | ||||
−0.138898 | + | 0.990307i | \(0.544356\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 19.5959i | − | 1.10763i | −0.832641 | − | 0.553813i | \(-0.813172\pi\) | ||
0.832641 | − | 0.553813i | \(-0.186828\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.2487 | −1.36194 | −0.680972 | − | 0.732310i | \(-0.738442\pi\) | ||||
−0.680972 | + | 0.732310i | \(0.738442\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.92820i | 0.387905i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 48.0000i | − | 2.67079i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.0000 | + | 2.44949i | −0.665640 | + | 0.135873i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.8564i | 0.761617i | 0.924654 | + | 0.380808i | \(0.124354\pi\) | ||||
−0.924654 | + | 0.380808i | \(0.875646\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.6969i | 0.800593i | 0.916386 | + | 0.400297i | \(0.131093\pi\) | ||||
−0.916386 | + | 0.400297i | \(0.868907\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 8.48528i | − | 0.459504i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 12.0000i | − | 0.644194i | −0.946707 | − | 0.322097i | \(-0.895612\pi\) | ||
0.946707 | − | 0.322097i | \(-0.104388\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0000 | 0.749403 | 0.374701 | − | 0.927146i | \(-0.377745\pi\) | ||||
0.374701 | + | 0.927146i | \(0.377745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.9706 | − | 13.8564i | −0.900704 | − | 0.735422i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.2929 | −1.80991 | −0.904954 | − | 0.425510i | \(-0.860095\pi\) | ||||
−0.904954 | + | 0.425510i | \(0.860095\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −29.0000 | −1.52632 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.92820 | + | 8.48528i | −0.362639 | + | 0.444140i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.24264 | −0.221464 | −0.110732 | − | 0.993850i | \(-0.535320\pi\) | ||||
−0.110732 | + | 0.993850i | \(0.535320\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.0454i | 1.14147i | 0.821135 | + | 0.570734i | \(0.193341\pi\) | ||||
−0.821135 | + | 0.570734i | \(0.806659\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.92820 | 0.356821 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.3923i | 0.533817i | 0.963722 | + | 0.266908i | \(0.0860021\pi\) | ||||
−0.963722 | + | 0.266908i | \(0.913998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.0000i | 1.22634i | 0.789950 | + | 0.613171i | \(0.210106\pi\) | ||||
−0.789950 | + | 0.613171i | \(0.789894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.0000 | + | 14.6969i | 0.917365 | + | 0.749025i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.82843i | 0.143407i | 0.997426 | + | 0.0717035i | \(0.0228435\pi\) | ||||
−0.997426 | + | 0.0717035i | \(0.977156\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.5692i | 2.10225i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.6969 | + | 18.0000i | −0.739483 | + | 0.905678i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.8434i | 1.59817i | 0.601216 | + | 0.799086i | \(0.294683\pi\) | ||||
−0.601216 | + | 0.799086i | \(0.705317\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.3553i | 1.76556i | 0.469785 | + | 0.882781i | \(0.344331\pi\) | ||||
−0.469785 | + | 0.882781i | \(0.655669\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.48528 | −0.422682 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.00000i | 0.297409i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.0000 | −1.28562 | −0.642809 | − | 0.766027i | \(-0.722231\pi\) | ||||
−0.642809 | + | 0.766027i | \(0.722231\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −51.9615 | −2.55686 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.9706 | + | 20.7846i | −0.833052 | + | 1.02028i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.34847 | −0.358996 | −0.179498 | − | 0.983758i | \(-0.557447\pi\) | ||||
−0.179498 | + | 0.983758i | \(0.557447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.92820 | − | 33.9411i | −0.336067 | − | 1.64639i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.48528 | 0.410632 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.89898 | −0.235976 | −0.117988 | − | 0.993015i | \(-0.537644\pi\) | ||||
−0.117988 | + | 0.993015i | \(0.537644\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4.89898i | − | 0.235430i | −0.993047 | − | 0.117715i | \(-0.962443\pi\) | ||
0.993047 | − | 0.117715i | \(-0.0375569\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 41.5692 | 1.98853 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 3.46410i | − | 0.165333i | −0.996577 | − | 0.0826663i | \(-0.973656\pi\) | ||
0.996577 | − | 0.0826663i | \(-0.0263436\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 12.0000i | − | 0.570137i | −0.958507 | − | 0.285069i | \(-0.907984\pi\) | ||
0.958507 | − | 0.285069i | \(-0.0920164\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.0000 | − | 12.2474i | 0.474045 | − | 0.580585i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 9.89949i | − | 0.467186i | −0.972334 | − | 0.233593i | \(-0.924952\pi\) | ||
0.972334 | − | 0.233593i | \(-0.0750483\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 17.3205i | − | 0.815591i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.6969 | − | 18.0000i | 0.689003 | − | 0.843853i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 4.89898i | − | 0.229165i | −0.993414 | − | 0.114582i | \(-0.963447\pi\) | ||
0.993414 | − | 0.114582i | \(-0.0365530\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 11.3137i | − | 0.526932i | −0.964669 | − | 0.263466i | \(-0.915134\pi\) | ||
0.964669 | − | 0.263466i | \(-0.0848657\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.2132 | −0.985861 | −0.492931 | − | 0.870069i | \(-0.664074\pi\) | ||||
−0.492931 | + | 0.870069i | \(0.664074\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.7846 | 0.955677 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −33.9411 | + | 6.92820i | −1.55733 | + | 0.317888i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.5959 | −0.895360 | −0.447680 | − | 0.894194i | \(-0.647750\pi\) | ||||
−0.447680 | + | 0.894194i | \(0.647750\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.00000 | 0.273576 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.7846 | + | 25.4558i | −0.943781 | + | 1.15589i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.2132 | 0.961262 | 0.480631 | − | 0.876923i | \(-0.340408\pi\) | ||||
0.480631 | + | 0.876923i | \(0.340408\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.1464 | 0.773807 | 0.386904 | − | 0.922120i | \(-0.373545\pi\) | ||||
0.386904 | + | 0.922120i | \(0.373545\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.5959i | 0.882556i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 41.5692 | 1.86463 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 13.8564i | − | 0.620298i | −0.950688 | − | 0.310149i | \(-0.899621\pi\) | ||
0.950688 | − | 0.310149i | \(-0.100379\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.0000 | − | 19.5959i | 0.711991 | − | 0.872007i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 39.5980i | 1.75515i | 0.479440 | + | 0.877575i | \(0.340840\pi\) | ||||
−0.479440 | + | 0.877575i | \(0.659160\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 20.7846i | − | 0.919457i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.0454 | + | 18.0000i | 0.971437 | + | 0.793175i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7.07107i | − | 0.309789i | −0.987931 | − | 0.154895i | \(-0.950496\pi\) | ||
0.987931 | − | 0.154895i | \(-0.0495038\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.4558 | 1.11311 | 0.556553 | − | 0.830812i | \(-0.312124\pi\) | ||||
0.556553 | + | 0.830812i | \(0.312124\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 24.0000i | − | 1.04546i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.3205 | −0.750234 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.9706 | − | 20.7846i | 0.733701 | − | 0.898597i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26.9444 | −1.16058 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.0000 | 1.63375 | 0.816874 | − | 0.576816i | \(-0.195705\pi\) | ||||
0.816874 | + | 0.576816i | \(0.195705\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.46410 | − | 2.82843i | −0.148386 | − | 0.121157i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.48528 | 0.362804 | 0.181402 | − | 0.983409i | \(-0.441936\pi\) | ||||
0.181402 | + | 0.983409i | \(0.441936\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.5959 | 0.834814 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 44.0908i | − | 1.87493i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.7128 | −1.17423 | −0.587115 | − | 0.809504i | \(-0.699736\pi\) | ||||
−0.587115 | + | 0.809504i | \(0.699736\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 20.7846i | − | 0.879095i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.0000i | 0.505740i | 0.967500 | + | 0.252870i | \(0.0813744\pi\) | ||||
−0.967500 | + | 0.252870i | \(0.918626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.0000 | − | 9.79796i | −0.504844 | − | 0.412203i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 9.89949i | − | 0.415008i | −0.978234 | − | 0.207504i | \(-0.933466\pi\) | ||
0.978234 | − | 0.207504i | \(-0.0665341\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.7128i | 1.15975i | 0.814707 | + | 0.579873i | \(0.196898\pi\) | ||||
−0.814707 | + | 0.579873i | \(0.803102\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 29.3939 | − | 6.00000i | 1.22581 | − | 0.250217i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 4.89898i | − | 0.203947i | −0.994787 | − | 0.101974i | \(-0.967484\pi\) | ||
0.994787 | − | 0.101974i | \(-0.0325157\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 50.9117i | − | 2.11217i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 12.0000i | − | 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.0000 | −0.988903 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.7128 | 1.13803 | 0.569014 | − | 0.822328i | \(-0.307325\pi\) | ||||
0.569014 | + | 0.822328i | \(0.307325\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 50.9117 | + | 41.5692i | 2.08718 | + | 1.70417i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.89898 | 0.200167 | 0.100083 | − | 0.994979i | \(-0.468089\pi\) | ||||
0.100083 | + | 0.994979i | \(0.468089\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −44.0000 | −1.79480 | −0.897399 | − | 0.441221i | \(-0.854546\pi\) | ||||
−0.897399 | + | 0.441221i | \(0.854546\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.66025 | − | 7.07107i | −0.352089 | − | 0.287480i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.2132 | 0.861017 | 0.430509 | − | 0.902586i | \(-0.358334\pi\) | ||||
0.430509 | + | 0.902586i | \(0.358334\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 22.0454i | − | 0.890406i | −0.895430 | − | 0.445203i | \(-0.853132\pi\) | ||
0.895430 | − | 0.445203i | \(-0.146868\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.8564 | −0.557838 | −0.278919 | − | 0.960315i | \(-0.589976\pi\) | ||||
−0.278919 | + | 0.960315i | \(0.589976\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 31.1769i | − | 1.25311i | −0.779379 | − | 0.626553i | \(-0.784465\pi\) | ||
0.779379 | − | 0.626553i | \(-0.215535\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 30.0000i | 1.20192i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.0000 | + | 9.79796i | −0.920000 | + | 0.391918i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.9706i | 0.676661i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 17.3205i | − | 0.689519i | −0.938691 | − | 0.344759i | \(-0.887961\pi\) | ||
0.938691 | − | 0.344759i | \(-0.112039\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.0454 | + | 18.0000i | 0.874845 | + | 0.714308i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.9444i | 1.06758i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.5563i | 0.614439i | 0.951639 | + | 0.307219i | \(0.0993986\pi\) | ||||
−0.951639 | + | 0.307219i | \(0.900601\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.4558 | 1.00388 | 0.501940 | − | 0.864902i | \(-0.332620\pi\) | ||||
0.501940 | + | 0.864902i | \(0.332620\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.0000i | 0.943537i | 0.881722 | + | 0.471769i | \(0.156384\pi\) | ||||
−0.881722 | + | 0.471769i | \(0.843616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30.0000 | −1.17760 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.3923 | 0.406682 | 0.203341 | − | 0.979108i | \(-0.434820\pi\) | ||||
0.203341 | + | 0.979108i | \(0.434820\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.24264 | + | 3.46410i | 0.165774 | + | 0.135354i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.7423 | −1.43128 | −0.715639 | − | 0.698470i | \(-0.753865\pi\) | ||||
−0.715639 | + | 0.698470i | \(0.753865\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000 | 0.855701 | 0.427850 | − | 0.903850i | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 41.5692 | − | 50.9117i | 1.61199 | − | 1.97427i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.9706 | −0.657103 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.89898 | 0.189123 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.2929i | 1.32189i | 0.750433 | + | 0.660946i | \(0.229845\pi\) | ||||
−0.750433 | + | 0.660946i | \(0.770155\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.3923 | −0.399409 | −0.199704 | − | 0.979856i | \(-0.563998\pi\) | ||||
−0.199704 | + | 0.979856i | \(0.563998\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 62.3538i | − | 2.39292i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.0000i | 0.918334i | 0.888350 | + | 0.459167i | \(0.151852\pi\) | ||||
−0.888350 | + | 0.459167i | \(0.848148\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.0000 | + | 19.5959i | 0.916993 | + | 0.748722i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 20.7846i | − | 0.790684i | −0.918534 | − | 0.395342i | \(-0.870626\pi\) | ||
0.918534 | − | 0.395342i | \(-0.129374\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.89898 | + | 6.00000i | −0.185829 | + | 0.227593i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 48.9898i | − | 1.85562i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 5.65685i | − | 0.213656i | −0.994277 | − | 0.106828i | \(-0.965931\pi\) | ||
0.994277 | − | 0.106828i | \(-0.0340695\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.9706 | 0.640057 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 48.0000i | 1.80523i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.00000 | 0.0751116 | 0.0375558 | − | 0.999295i | \(-0.488043\pi\) | ||||
0.0375558 | + | 0.999295i | \(0.488043\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.7846 | 0.778390 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.48528 | − | 10.3923i | 0.317332 | − | 0.388650i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.89898 | 0.182701 | 0.0913506 | − | 0.995819i | \(-0.470882\pi\) | ||||
0.0913506 | + | 0.995819i | \(0.470882\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −54.0000 | −2.01107 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.8564 | − | 2.82843i | 0.514614 | − | 0.105045i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.2132 | −0.786754 | −0.393377 | − | 0.919377i | \(-0.628693\pi\) | ||||
−0.393377 | + | 0.919377i | \(0.628693\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 58.7878 | 2.17434 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 7.34847i | − | 0.271422i | −0.990748 | − | 0.135711i | \(-0.956668\pi\) | ||
0.990748 | − | 0.135711i | \(-0.0433318\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 27.7128i | − | 1.01943i | −0.860343 | − | 0.509716i | \(-0.829750\pi\) | ||
0.860343 | − | 0.509716i | \(-0.170250\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 24.0000i | − | 0.880475i | −0.897881 | − | 0.440237i | \(-0.854894\pi\) | ||
0.897881 | − | 0.440237i | \(-0.145106\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32.0000 | − | 39.1918i | 1.17239 | − | 1.43588i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 50.9117i | 1.86027i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 51.9615i | 1.89610i | 0.318117 | + | 0.948051i | \(0.396950\pi\) | ||||
−0.318117 | + | 0.948051i | \(0.603050\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.4949 | − | 30.0000i | 0.891461 | − | 1.09181i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 36.7423i | − | 1.33542i | −0.744420 | − | 0.667712i | \(-0.767274\pi\) | ||
0.744420 | − | 0.667712i | \(-0.232726\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.41421i | 0.0512652i | 0.999671 | + | 0.0256326i | \(0.00816000\pi\) | ||||
−0.999671 | + | 0.0256326i | \(0.991840\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.48528 | 0.307188 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 30.0000i | 1.08324i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.0000 | 1.15395 | 0.576975 | − | 0.816762i | \(-0.304233\pi\) | ||||
0.576975 | + | 0.816762i | \(0.304233\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.1051 | 1.37055 | 0.685273 | − | 0.728286i | \(-0.259683\pi\) | ||||
0.685273 | + | 0.728286i | \(0.259683\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.9706 | + | 3.46410i | −0.609601 | + | 0.124434i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −48.9898 | −1.75524 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000 | 0.858788 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.3205 | − | 21.2132i | 0.618195 | − | 0.757132i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.4558 | 0.907403 | 0.453701 | − | 0.891154i | \(-0.350103\pi\) | ||||
0.453701 | + | 0.891154i | \(0.350103\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.3939 | 1.04513 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 4.89898i | − | 0.173968i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.8564 | −0.490819 | −0.245410 | − | 0.969419i | \(-0.578922\pi\) | ||||
−0.245410 | + | 0.969419i | \(0.578922\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 12.0000i | − | 0.423471i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −36.0000 | + | 44.0908i | −1.26883 | + | 1.55400i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.3848i | 0.646374i | 0.946335 | + | 0.323187i | \(0.104754\pi\) | ||||
−0.946335 | + | 0.323187i | \(0.895246\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 38.1051i | − | 1.33805i | −0.743239 | − | 0.669026i | \(-0.766712\pi\) | ||
0.743239 | − | 0.669026i | \(-0.233288\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.6969 | + | 12.0000i | 0.514811 | + | 0.420342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 58.7878i | − | 2.05672i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.82843i | 0.0987128i | 0.998781 | + | 0.0493564i | \(0.0157170\pi\) | ||||
−0.998781 | + | 0.0493564i | \(0.984283\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.2132 | 0.739446 | 0.369723 | − | 0.929142i | \(-0.379453\pi\) | ||||
0.369723 | + | 0.929142i | \(0.379453\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.0000i | 0.417281i | 0.977992 | + | 0.208640i | \(0.0669038\pi\) | ||||
−0.977992 | + | 0.208640i | \(0.933096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.0000 | −0.903017 | −0.451509 | − | 0.892267i | \(-0.649114\pi\) | ||||
−0.451509 | + | 0.892267i | \(0.649114\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −76.2102 | −2.64053 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.4558 | + | 31.1769i | −0.880936 | + | 1.07892i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.2929 | −1.18392 | −0.591960 | − | 0.805967i | \(-0.701646\pi\) | ||||
−0.591960 | + | 0.805967i | \(0.701646\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.1244 | + | 9.89949i | 0.417091 | + | 0.340553i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.2132 | 0.728894 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.6969 | −0.503805 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.7423i | 1.25803i | 0.777392 | + | 0.629017i | \(0.216542\pi\) | ||||
−0.777392 | + | 0.629017i | \(0.783458\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.8564 | −0.473326 | −0.236663 | − | 0.971592i | \(-0.576054\pi\) | ||||
−0.236663 | + | 0.971592i | \(0.576054\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 45.0333i | − | 1.53652i | −0.640140 | − | 0.768259i | \(-0.721124\pi\) | ||
0.640140 | − | 0.768259i | \(-0.278876\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 18.0000i | − | 0.612727i | −0.951915 | − | 0.306364i | \(-0.900888\pi\) | ||
0.951915 | − | 0.306364i | \(-0.0991123\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.0000 | + | 19.5959i | 0.816024 | + | 0.666281i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 25.4558i | − | 0.863530i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.0454 | − | 42.0000i | 0.745271 | − | 1.41986i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.6413i | 1.40613i | 0.711127 | + | 0.703064i | \(0.248185\pi\) | ||||
−0.711127 | + | 0.703064i | \(0.751815\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 9.89949i | − | 0.333522i | −0.985997 | − | 0.166761i | \(-0.946669\pi\) | ||
0.985997 | − | 0.166761i | \(-0.0533309\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.4264 | −1.42776 | −0.713881 | − | 0.700267i | \(-0.753064\pi\) | ||||
−0.713881 | + | 0.700267i | \(0.753064\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 6.00000i | − | 0.201460i | −0.994914 | − | 0.100730i | \(-0.967882\pi\) | ||
0.994914 | − | 0.100730i | \(-0.0321179\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −54.0000 | −1.81110 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.2132 | + | 17.3205i | 0.709079 | + | 0.578961i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.79796 | 0.326780 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.3205 | − | 14.1421i | −0.575753 | − | 0.470100i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.48528 | 0.281749 | 0.140875 | − | 0.990027i | \(-0.455009\pi\) | ||||
0.140875 | + | 0.990027i | \(0.455009\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.9898 | −1.62310 | −0.811552 | − | 0.584280i | \(-0.801377\pi\) | ||||
−0.811552 | + | 0.584280i | \(0.801377\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 29.3939i | − | 0.972795i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.3923 | −0.343184 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.0333i | 1.48551i | 0.669562 | + | 0.742756i | \(0.266482\pi\) | ||||
−0.669562 | + | 0.742756i | \(0.733518\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 24.0000i | − | 0.789970i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.0000 | − | 2.44949i | 0.394558 | − | 0.0805387i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 9.89949i | − | 0.324792i | −0.986726 | − | 0.162396i | \(-0.948078\pi\) | ||
0.986726 | − | 0.162396i | \(-0.0519222\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 76.2102i | 2.49769i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29.3939 | + | 24.0000i | 0.961283 | + | 0.784884i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.9898i | 1.60043i | 0.599715 | + | 0.800213i | \(0.295280\pi\) | ||||
−0.599715 | + | 0.800213i | \(0.704720\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 53.7401i | − | 1.75188i | −0.482422 | − | 0.875939i | \(-0.660243\pi\) | ||
0.482422 | − | 0.875939i | \(-0.339757\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42.4264 | 1.38159 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 60.0000i | − | 1.94974i | −0.222779 | − | 0.974869i | \(-0.571513\pi\) | ||
0.222779 | − | 0.974869i | \(-0.428487\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0000 | −0.389536 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.7128 | 0.897706 | 0.448853 | − | 0.893606i | \(-0.351833\pi\) | ||||
0.448853 | + | 0.893606i | \(0.351833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.48528 | + | 6.92820i | 0.274577 | + | 0.224191i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −58.7878 | −1.89836 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −27.7128 | + | 33.9411i | −0.892107 | + | 1.09260i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.6690 | −1.50078 | −0.750388 | − | 0.660998i | \(-0.770133\pi\) | ||||
−0.750388 | + | 0.660998i | \(0.770133\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.2474 | 0.393039 | 0.196520 | − | 0.980500i | \(-0.437036\pi\) | ||||
0.196520 | + | 0.980500i | \(0.437036\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 14.6969i | − | 0.471162i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.3205i | 0.553566i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 24.0000i | − | 0.765481i | −0.923856 | − | 0.382741i | \(-0.874980\pi\) | ||
0.923856 | − | 0.382741i | \(-0.125020\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.00000 | − | 4.89898i | −0.191176 | − | 0.156094i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 50.9117i | 1.61890i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 17.3205i | − | 0.550204i | −0.961415 | − | 0.275102i | \(-0.911288\pi\) | ||
0.961415 | − | 0.275102i | \(-0.0887116\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.6969 | + | 18.0000i | −0.465924 | + | 0.570638i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 2.44949i | − | 0.0775761i | −0.999247 | − | 0.0387881i | \(-0.987650\pi\) | ||
0.999247 | − | 0.0387881i | \(-0.0123497\pi\) | |||||||
\(998\) | 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 | 720.2.o.b.719.7 | yes | 8 | |
3.2 | odd | 2 | inner | 720.2.o.b.719.1 | ✓ | 8 | |
4.3 | odd | 2 | inner | 720.2.o.b.719.8 | yes | 8 | |
5.2 | odd | 4 | 3600.2.h.f.1151.1 | 4 | |||
5.3 | odd | 4 | 3600.2.h.g.1151.3 | 4 | |||
5.4 | even | 2 | inner | 720.2.o.b.719.4 | yes | 8 | |
8.3 | odd | 2 | 2880.2.o.d.2879.2 | 8 | |||
8.5 | even | 2 | 2880.2.o.d.2879.1 | 8 | |||
12.11 | even | 2 | inner | 720.2.o.b.719.2 | yes | 8 | |
15.2 | even | 4 | 3600.2.h.g.1151.2 | 4 | |||
15.8 | even | 4 | 3600.2.h.f.1151.4 | 4 | |||
15.14 | odd | 2 | inner | 720.2.o.b.719.6 | yes | 8 | |
20.3 | even | 4 | 3600.2.h.f.1151.2 | 4 | |||
20.7 | even | 4 | 3600.2.h.g.1151.4 | 4 | |||
20.19 | odd | 2 | inner | 720.2.o.b.719.3 | yes | 8 | |
24.5 | odd | 2 | 2880.2.o.d.2879.7 | 8 | |||
24.11 | even | 2 | 2880.2.o.d.2879.8 | 8 | |||
40.19 | odd | 2 | 2880.2.o.d.2879.5 | 8 | |||
40.29 | even | 2 | 2880.2.o.d.2879.6 | 8 | |||
60.23 | odd | 4 | 3600.2.h.g.1151.1 | 4 | |||
60.47 | odd | 4 | 3600.2.h.f.1151.3 | 4 | |||
60.59 | even | 2 | inner | 720.2.o.b.719.5 | yes | 8 | |
120.29 | odd | 2 | 2880.2.o.d.2879.4 | 8 | |||
120.59 | even | 2 | 2880.2.o.d.2879.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
720.2.o.b.719.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
720.2.o.b.719.2 | yes | 8 | 12.11 | even | 2 | inner | |
720.2.o.b.719.3 | yes | 8 | 20.19 | odd | 2 | inner | |
720.2.o.b.719.4 | yes | 8 | 5.4 | even | 2 | inner | |
720.2.o.b.719.5 | yes | 8 | 60.59 | even | 2 | inner | |
720.2.o.b.719.6 | yes | 8 | 15.14 | odd | 2 | inner | |
720.2.o.b.719.7 | yes | 8 | 1.1 | even | 1 | trivial | |
720.2.o.b.719.8 | yes | 8 | 4.3 | odd | 2 | inner | |
2880.2.o.d.2879.1 | 8 | 8.5 | even | 2 | |||
2880.2.o.d.2879.2 | 8 | 8.3 | odd | 2 | |||
2880.2.o.d.2879.3 | 8 | 120.59 | even | 2 | |||
2880.2.o.d.2879.4 | 8 | 120.29 | odd | 2 | |||
2880.2.o.d.2879.5 | 8 | 40.19 | odd | 2 | |||
2880.2.o.d.2879.6 | 8 | 40.29 | even | 2 | |||
2880.2.o.d.2879.7 | 8 | 24.5 | odd | 2 | |||
2880.2.o.d.2879.8 | 8 | 24.11 | even | 2 | |||
3600.2.h.f.1151.1 | 4 | 5.2 | odd | 4 | |||
3600.2.h.f.1151.2 | 4 | 20.3 | even | 4 | |||
3600.2.h.f.1151.3 | 4 | 60.47 | odd | 4 | |||
3600.2.h.f.1151.4 | 4 | 15.8 | even | 4 | |||
3600.2.h.g.1151.1 | 4 | 60.23 | odd | 4 | |||
3600.2.h.g.1151.2 | 4 | 15.2 | even | 4 | |||
3600.2.h.g.1151.3 | 4 | 5.3 | odd | 4 | |||
3600.2.h.g.1151.4 | 4 | 20.7 | even | 4 |