Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,3,Mod(257,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.257");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.e (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: | \(20.9264843029\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 8x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 24) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 257.2 | ||
Root | \(-2.57794i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.257 |
Dual form | 768.3.e.l.257.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −2.64575 | + | 1.41421i | −0.881917 | + | 0.471405i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 5.65685i | − | 1.13137i | −0.824621 | − | 0.565685i | \(-0.808612\pi\) | ||
0.824621 | − | 0.565685i | \(-0.191388\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.00000 | 0.571429 | 0.285714 | − | 0.958315i | \(-0.407769\pi\) | ||||
0.285714 | + | 0.958315i | \(0.407769\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.00000 | − | 7.48331i | 0.555556 | − | 0.831479i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 8.48528i | − | 0.771389i | −0.922627 | − | 0.385695i | \(-0.873962\pi\) | ||
0.922627 | − | 0.385695i | \(-0.126038\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10.5830 | −0.814077 | −0.407039 | − | 0.913411i | \(-0.633439\pi\) | ||||
−0.407039 | + | 0.913411i | \(0.633439\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.00000 | + | 14.9666i | 0.533333 | + | 0.997775i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 14.9666i | − | 0.880390i | −0.897902 | − | 0.440195i | \(-0.854909\pi\) | ||
0.897902 | − | 0.440195i | \(-0.145091\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.29150 | 0.278500 | 0.139250 | − | 0.990257i | \(-0.455531\pi\) | ||||
0.139250 | + | 0.990257i | \(0.455531\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.5830 | + | 5.65685i | −0.503953 | + | 0.269374i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 29.9333i | 1.30145i | 0.759315 | + | 0.650723i | \(0.225534\pi\) | ||||
−0.759315 | + | 0.650723i | \(0.774466\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.00000 | −0.280000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.64575 | + | 26.8701i | −0.0979908 | + | 0.995187i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 16.9706i | − | 0.585192i | −0.956236 | − | 0.292596i | \(-0.905481\pi\) | ||
0.956236 | − | 0.292596i | \(-0.0945191\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.129032 | 0.0645161 | − | 0.997917i | \(-0.479450\pi\) | ||||
0.0645161 | + | 0.997917i | \(0.479450\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.0000 | + | 22.4499i | 0.363636 | + | 0.680301i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 22.6274i | − | 0.646498i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −52.9150 | −1.43014 | −0.715068 | − | 0.699055i | \(-0.753604\pi\) | ||||
−0.715068 | + | 0.699055i | \(0.753604\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 28.0000 | − | 14.9666i | 0.717949 | − | 0.383760i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 29.9333i | 0.730079i | 0.930992 | + | 0.365040i | \(0.118945\pi\) | ||||
−0.930992 | + | 0.365040i | \(0.881055\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.29150 | 0.123058 | 0.0615291 | − | 0.998105i | \(-0.480402\pi\) | ||||
0.0615291 | + | 0.998105i | \(0.480402\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −42.3320 | − | 28.2843i | −0.940712 | − | 0.628539i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −33.0000 | −0.673469 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 21.1660 | + | 39.5980i | 0.415020 | + | 0.776431i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 50.9117i | − | 0.960598i | −0.877105 | − | 0.480299i | \(-0.840528\pi\) | ||
0.877105 | − | 0.480299i | \(-0.159472\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −48.0000 | −0.872727 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14.0000 | + | 7.48331i | −0.245614 | + | 0.131286i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 48.0833i | − | 0.814971i | −0.913212 | − | 0.407485i | \(-0.866406\pi\) | ||
0.913212 | − | 0.407485i | \(-0.133594\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −95.2470 | −1.56143 | −0.780714 | − | 0.624889i | \(-0.785144\pi\) | ||||
−0.780714 | + | 0.624889i | \(0.785144\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 20.0000 | − | 29.9333i | 0.317460 | − | 0.475131i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 59.8665i | 0.921023i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −47.6235 | −0.710799 | −0.355399 | − | 0.934715i | \(-0.615655\pi\) | ||||
−0.355399 | + | 0.934715i | \(0.615655\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −42.3320 | − | 79.1960i | −0.613508 | − | 1.14777i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 89.7998i | − | 1.26479i | −0.774648 | − | 0.632393i | \(-0.782073\pi\) | ||
0.774648 | − | 0.632393i | \(-0.217927\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | 0.0821918 | 0.0410959 | − | 0.999155i | \(-0.486915\pi\) | ||||
0.0410959 | + | 0.999155i | \(0.486915\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 18.5203 | − | 9.89949i | 0.246937 | − | 0.131993i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 33.9411i | − | 0.440794i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −124.000 | −1.56962 | −0.784810 | − | 0.619736i | \(-0.787240\pi\) | ||||
−0.784810 | + | 0.619736i | \(0.787240\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −31.0000 | − | 74.8331i | −0.382716 | − | 0.923866i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.82843i | − | 0.0340774i | −0.999855 | − | 0.0170387i | \(-0.994576\pi\) | ||
0.999855 | − | 0.0170387i | \(-0.00542385\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −84.6640 | −0.996048 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 24.0000 | + | 44.8999i | 0.275862 | + | 0.516091i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 104.766i | − | 1.17715i | −0.808442 | − | 0.588575i | \(-0.799689\pi\) | ||
0.808442 | − | 0.588575i | \(-0.200311\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −42.3320 | −0.465187 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.5830 | + | 5.65685i | −0.113796 | + | 0.0608264i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 29.9333i | − | 0.315087i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 118.000 | 1.21649 | 0.608247 | − | 0.793747i | \(-0.291873\pi\) | ||||
0.608247 | + | 0.793747i | \(0.291873\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −63.4980 | − | 42.4264i | −0.641394 | − | 0.428550i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 62.2254i | 0.616093i | 0.951371 | + | 0.308047i | \(0.0996752\pi\) | ||||
−0.951371 | + | 0.308047i | \(0.900325\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −108.000 | −1.04854 | −0.524272 | − | 0.851551i | \(-0.675662\pi\) | ||||
−0.524272 | + | 0.851551i | \(0.675662\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 32.0000 | + | 59.8665i | 0.304762 | + | 0.570157i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 144.250i | 1.34813i | 0.738673 | + | 0.674064i | \(0.235453\pi\) | ||||
−0.738673 | + | 0.674064i | \(0.764547\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −52.9150 | −0.485459 | −0.242729 | − | 0.970094i | \(-0.578043\pi\) | ||||
−0.242729 | + | 0.970094i | \(0.578043\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 140.000 | − | 74.8331i | 1.26126 | − | 0.674173i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 89.7998i | − | 0.794688i | −0.917670 | − | 0.397344i | \(-0.869932\pi\) | ||
0.917670 | − | 0.397344i | \(-0.130068\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 169.328 | 1.47242 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −52.9150 | + | 79.1960i | −0.452265 | + | 0.676889i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 59.8665i | − | 0.503080i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 49.0000 | 0.404959 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −42.3320 | − | 79.1960i | −0.344163 | − | 0.643870i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 101.823i | − | 0.814587i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −76.0000 | −0.598425 | −0.299213 | − | 0.954186i | \(-0.596724\pi\) | ||||
−0.299213 | + | 0.954186i | \(0.596724\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.0000 | + | 7.48331i | −0.108527 | + | 0.0580102i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.1421i | 0.107955i | 0.998542 | + | 0.0539776i | \(0.0171900\pi\) | ||||
−0.998542 | + | 0.0539776i | \(0.982810\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.1660 | 0.159143 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 152.000 | + | 14.9666i | 1.12593 | + | 0.110864i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 121.705 | 0.875572 | 0.437786 | − | 0.899079i | \(-0.355763\pi\) | ||||
0.437786 | + | 0.899079i | \(0.355763\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 89.7998i | 0.627970i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −96.0000 | −0.662069 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 87.3098 | − | 46.6690i | 0.593944 | − | 0.317477i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 186.676i | − | 1.25286i | −0.779478 | − | 0.626430i | \(-0.784515\pi\) | ||
0.779478 | − | 0.626430i | \(-0.215485\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −60.0000 | −0.397351 | −0.198675 | − | 0.980065i | \(-0.563664\pi\) | ||||
−0.198675 | + | 0.980065i | \(0.563664\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −112.000 | − | 74.8331i | −0.732026 | − | 0.489106i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 22.6274i | − | 0.145983i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 116.413 | 0.741484 | 0.370742 | − | 0.928736i | \(-0.379103\pi\) | ||||
0.370742 | + | 0.928736i | \(0.379103\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 72.0000 | + | 134.700i | 0.452830 | + | 0.847168i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 119.733i | 0.743683i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −291.033 | −1.78548 | −0.892738 | − | 0.450576i | \(-0.851219\pi\) | ||||
−0.892738 | + | 0.450576i | \(0.851219\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 126.996 | − | 67.8823i | 0.769673 | − | 0.411408i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 329.266i | 1.97165i | 0.167772 | + | 0.985826i | \(0.446343\pi\) | ||||
−0.167772 | + | 0.985826i | \(0.553657\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −57.0000 | −0.337278 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 26.4575 | − | 39.5980i | 0.154722 | − | 0.231567i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 186.676i | 1.07905i | 0.841969 | + | 0.539527i | \(0.181397\pi\) | ||||
−0.841969 | + | 0.539527i | \(0.818603\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −28.0000 | −0.160000 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 68.0000 | + | 127.216i | 0.384181 | + | 0.718736i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 319.612i | 1.78554i | 0.450509 | + | 0.892772i | \(0.351242\pi\) | ||||
−0.450509 | + | 0.892772i | \(0.648758\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 116.413 | 0.643166 | 0.321583 | − | 0.946881i | \(-0.395785\pi\) | ||||
0.321583 | + | 0.946881i | \(0.395785\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 252.000 | − | 134.700i | 1.37705 | − | 0.736064i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 299.333i | 1.61801i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −126.996 | −0.679123 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.5830 | + | 107.480i | −0.0559947 | + | 0.568678i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 59.8665i | 0.313437i | 0.987643 | + | 0.156719i | \(0.0500916\pi\) | ||||
−0.987643 | + | 0.156719i | \(0.949908\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −102.000 | −0.528497 | −0.264249 | − | 0.964455i | \(-0.585124\pi\) | ||||
−0.264249 | + | 0.964455i | \(0.585124\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −84.6640 | − | 158.392i | −0.434175 | − | 0.812266i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 243.245i | 1.23474i | 0.786671 | + | 0.617372i | \(0.211803\pi\) | ||||
−0.786671 | + | 0.617372i | \(0.788197\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −188.000 | −0.944724 | −0.472362 | − | 0.881405i | \(-0.656598\pi\) | ||||
−0.472362 | + | 0.881405i | \(0.656598\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 126.000 | − | 67.3498i | 0.626866 | − | 0.335074i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 67.8823i | − | 0.334395i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 169.328 | 0.825991 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 224.000 | + | 149.666i | 1.08213 | + | 0.723026i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 44.8999i | − | 0.214832i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 248.701 | 1.17868 | 0.589338 | − | 0.807887i | \(-0.299389\pi\) | ||||
0.589338 | + | 0.807887i | \(0.299389\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 126.996 | + | 237.588i | 0.596226 | + | 1.11544i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 29.9333i | − | 0.139224i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.0000 | 0.0737327 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.8745 | + | 8.48528i | −0.0724863 | + | 0.0387456i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 158.392i | 0.716706i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −188.000 | −0.843049 | −0.421525 | − | 0.906817i | \(-0.638505\pi\) | ||||
−0.421525 | + | 0.906817i | \(0.638505\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −35.0000 | + | 52.3832i | −0.155556 | + | 0.232814i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 387.495i | − | 1.70702i | −0.521073 | − | 0.853512i | \(-0.674468\pi\) | ||
0.521073 | − | 0.853512i | \(-0.325532\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 243.409 | 1.06292 | 0.531461 | − | 0.847083i | \(-0.321643\pi\) | ||||
0.531461 | + | 0.847083i | \(0.321643\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 48.0000 | + | 89.7998i | 0.207792 | + | 0.388744i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 104.766i | − | 0.449641i | −0.974400 | − | 0.224821i | \(-0.927820\pi\) | ||
0.974400 | − | 0.224821i | \(-0.0721796\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 328.073 | − | 175.362i | 1.38427 | − | 0.739926i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 359.199i | − | 1.50293i | −0.659776 | − | 0.751463i | \(-0.729349\pi\) | ||
0.659776 | − | 0.751463i | \(-0.270651\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 122.000 | 0.506224 | 0.253112 | − | 0.967437i | \(-0.418546\pi\) | ||||
0.253112 | + | 0.967437i | \(0.418546\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 187.848 | + | 154.149i | 0.773038 | + | 0.634359i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 186.676i | 0.761944i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −56.0000 | −0.226721 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.00000 | + | 7.48331i | 0.0160643 | + | 0.0300535i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 161.220i | 0.642312i | 0.947026 | + | 0.321156i | \(0.104071\pi\) | ||||
−0.947026 | + | 0.321156i | \(0.895929\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 253.992 | 1.00392 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 224.000 | − | 119.733i | 0.878431 | − | 0.469541i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 448.999i | − | 1.74708i | −0.486755 | − | 0.873539i | \(-0.661819\pi\) | ||
0.486755 | − | 0.873539i | \(-0.338181\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −211.660 | −0.817220 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −126.996 | − | 84.8528i | −0.486575 | − | 0.325107i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 209.533i | − | 0.796703i | −0.917233 | − | 0.398351i | \(-0.869582\pi\) | ||
0.917233 | − | 0.398351i | \(-0.130418\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −288.000 | −1.08679 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 148.162 | + | 277.186i | 0.554914 | + | 1.03815i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 50.9117i | 0.189263i | 0.995512 | + | 0.0946314i | \(0.0301672\pi\) | ||||
−0.995512 | + | 0.0946314i | \(0.969833\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −348.000 | −1.28413 | −0.642066 | − | 0.766649i | \(-0.721923\pi\) | ||||
−0.642066 | + | 0.766649i | \(0.721923\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 112.000 | − | 59.8665i | 0.410256 | − | 0.219291i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 59.3970i | 0.215989i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 243.409 | 0.878733 | 0.439367 | − | 0.898308i | \(-0.355203\pi\) | ||||
0.439367 | + | 0.898308i | \(0.355203\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.0000 | − | 29.9333i | 0.0716846 | − | 0.107288i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 314.299i | − | 1.11850i | −0.828998 | − | 0.559251i | \(-0.811089\pi\) | ||
0.828998 | − | 0.559251i | \(-0.188911\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −89.9555 | −0.317864 | −0.158932 | − | 0.987290i | \(-0.550805\pi\) | ||||
−0.158932 | + | 0.987290i | \(0.550805\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 42.3320 | + | 79.1960i | 0.148533 | + | 0.277881i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 119.733i | 0.417188i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 65.0000 | 0.224913 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −312.199 | + | 166.877i | −1.07285 | + | 0.573461i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.9706i | 0.0579200i | 0.999581 | + | 0.0289600i | \(0.00921954\pi\) | ||||
−0.999581 | + | 0.0289600i | \(0.990780\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −272.000 | −0.922034 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 228.000 | + | 22.4499i | 0.767677 | + | 0.0755890i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 316.784i | − | 1.05948i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.1660 | 0.0703190 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −88.0000 | − | 164.633i | −0.290429 | − | 0.543343i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 538.799i | 1.76655i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 460.361 | 1.49955 | 0.749773 | − | 0.661695i | \(-0.230163\pi\) | ||||
0.749773 | + | 0.661695i | \(0.230163\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 285.741 | − | 152.735i | 0.924729 | − | 0.494288i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 149.666i | − | 0.481242i | −0.970619 | − | 0.240621i | \(-0.922649\pi\) | ||
0.970619 | − | 0.240621i | \(-0.0773511\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 562.000 | 1.79553 | 0.897764 | − | 0.440478i | \(-0.145191\pi\) | ||||
0.897764 | + | 0.440478i | \(0.145191\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −169.328 | − | 113.137i | −0.537549 | − | 0.359165i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.65685i | 0.0178450i | 0.999960 | + | 0.00892248i | \(0.00284015\pi\) | ||||
−0.999960 | + | 0.00892248i | \(0.997160\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −144.000 | −0.451411 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −204.000 | − | 381.649i | −0.635514 | − | 1.18894i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 79.1960i | − | 0.245189i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 74.0810 | 0.227942 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 140.000 | − | 74.8331i | 0.428135 | − | 0.228848i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 418.029 | 1.26293 | 0.631463 | − | 0.775406i | \(-0.282455\pi\) | ||||
0.631463 | + | 0.775406i | \(0.282455\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −264.575 | + | 395.980i | −0.794520 | + | 1.18913i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 269.399i | 0.804177i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −50.0000 | −0.148368 | −0.0741840 | − | 0.997245i | \(-0.523635\pi\) | ||||
−0.0741840 | + | 0.997245i | \(0.523635\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 126.996 | + | 237.588i | 0.374620 | + | 0.700849i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 33.9411i | − | 0.0995341i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −328.000 | −0.956268 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −448.000 | + | 239.466i | −1.29855 | + | 0.694105i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 359.210i | − | 1.03519i | −0.855626 | − | 0.517594i | \(-0.826828\pi\) | ||
0.855626 | − | 0.517594i | \(-0.173172\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 116.413 | 0.333562 | 0.166781 | − | 0.985994i | \(-0.446663\pi\) | ||||
0.166781 | + | 0.985994i | \(0.446663\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 28.0000 | − | 284.366i | 0.0797721 | − | 0.810159i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 179.600i | 0.508781i | 0.967102 | + | 0.254390i | \(0.0818748\pi\) | ||||
−0.967102 | + | 0.254390i | \(0.918125\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −507.984 | −1.43094 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 84.6640 | + | 158.392i | 0.237154 | + | 0.443675i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 329.266i | − | 0.917175i | −0.888649 | − | 0.458588i | \(-0.848356\pi\) | ||
0.888649 | − | 0.458588i | \(-0.151644\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −333.000 | −0.922438 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −129.642 | + | 69.2965i | −0.357140 | + | 0.190899i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 33.9411i | − | 0.0929894i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 228.000 | 0.621253 | 0.310627 | − | 0.950532i | \(-0.399461\pi\) | ||||
0.310627 | + | 0.950532i | \(0.399461\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 224.000 | + | 149.666i | 0.607046 | + | 0.405600i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 203.647i | − | 0.548913i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −137.579 | −0.368845 | −0.184422 | − | 0.982847i | \(-0.559041\pi\) | ||||
−0.184422 | + | 0.982847i | \(0.559041\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 144.000 | + | 269.399i | 0.384000 | + | 0.718398i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 179.600i | 0.476391i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −164.037 | −0.432814 | −0.216407 | − | 0.976303i | \(-0.569434\pi\) | ||||
−0.216407 | + | 0.976303i | \(0.569434\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 201.077 | − | 107.480i | 0.527761 | − | 0.282100i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 179.600i | − | 0.468928i | −0.972125 | − | 0.234464i | \(-0.924666\pi\) | ||
0.972125 | − | 0.234464i | \(-0.0753336\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −192.000 | −0.498701 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 26.4575 | − | 39.5980i | 0.0683657 | − | 0.102320i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 96.1665i | − | 0.247215i | −0.992331 | − | 0.123607i | \(-0.960554\pi\) | ||
0.992331 | − | 0.123607i | \(-0.0394463\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 448.000 | 1.14578 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.0000 | − | 37.4166i | −0.0508906 | − | 0.0952076i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 701.450i | 1.77582i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −52.9150 | −0.133287 | −0.0666436 | − | 0.997777i | \(-0.521229\pi\) | ||||
−0.0666436 | + | 0.997777i | \(0.521229\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −56.0000 | + | 29.9333i | −0.140351 | + | 0.0750207i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 134.700i | 0.335909i | 0.985795 | + | 0.167955i | \(0.0537162\pi\) | ||||
−0.985795 | + | 0.167955i | \(0.946284\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −42.3320 | −0.105042 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −423.320 | + | 175.362i | −1.04524 | + | 0.432994i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 448.999i | 1.10319i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 158.000 | 0.386308 | 0.193154 | − | 0.981168i | \(-0.438128\pi\) | ||||
0.193154 | + | 0.981168i | \(0.438128\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 192.333i | − | 0.465697i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.0000 | −0.0385542 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −322.000 | + | 172.116i | −0.772182 | + | 0.412749i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 330.926i | − | 0.789799i | −0.918724 | − | 0.394900i | \(-0.870779\pi\) | ||
0.918724 | − | 0.394900i | \(-0.129221\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −518.567 | −1.23175 | −0.615876 | − | 0.787843i | \(-0.711198\pi\) | ||||
−0.615876 | + | 0.787843i | \(0.711198\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 104.766i | 0.246509i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −380.988 | −0.892244 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −126.996 | − | 237.588i | −0.296028 | − | 0.553818i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 359.199i | 0.833409i | 0.909042 | + | 0.416704i | \(0.136815\pi\) | ||||
−0.909042 | + | 0.416704i | \(0.863185\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 86.0000 | 0.198614 | 0.0993072 | − | 0.995057i | \(-0.468337\pi\) | ||||
0.0993072 | + | 0.995057i | \(0.468337\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 253.992 | − | 135.765i | 0.583890 | − | 0.312102i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 158.392i | 0.362453i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −156.000 | −0.355353 | −0.177677 | − | 0.984089i | \(-0.556858\pi\) | ||||
−0.177677 | + | 0.984089i | \(0.556858\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −165.000 | + | 246.949i | −0.374150 | + | 0.559976i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 212.132i | − | 0.478853i | −0.970914 | − | 0.239427i | \(-0.923041\pi\) | ||
0.970914 | − | 0.239427i | \(-0.0769595\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −592.648 | −1.33179 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 264.000 | + | 493.899i | 0.590604 | + | 1.10492i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 493.899i | − | 1.10000i | −0.835166 | − | 0.549999i | \(-0.814628\pi\) | ||
0.835166 | − | 0.549999i | \(-0.185372\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 253.992 | 0.563175 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 158.745 | − | 84.8528i | 0.350431 | − | 0.187313i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 239.466i | 0.526299i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −194.000 | −0.424508 | −0.212254 | − | 0.977215i | \(-0.568080\pi\) | ||||
−0.212254 | + | 0.977215i | \(0.568080\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 402.154 | + | 39.5980i | 0.876153 | + | 0.0862701i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 560.029i | − | 1.21481i | −0.794391 | − | 0.607406i | \(-0.792210\pi\) | ||
0.794391 | − | 0.607406i | \(-0.207790\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 404.000 | 0.872570 | 0.436285 | − | 0.899808i | \(-0.356294\pi\) | ||||
0.436285 | + | 0.899808i | \(0.356294\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 32.0000 | + | 59.8665i | 0.0688172 | + | 0.128745i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 664.680i | 1.42330i | 0.702535 | + | 0.711649i | \(0.252051\pi\) | ||||
−0.702535 | + | 0.711649i | \(0.747949\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −190.494 | −0.406171 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −308.000 | + | 164.633i | −0.653928 | + | 0.349539i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 44.8999i | − | 0.0949258i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −37.0405 | −0.0779800 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −380.988 | − | 254.558i | −0.798717 | − | 0.533665i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 239.466i | − | 0.499929i | −0.968255 | − | 0.249965i | \(-0.919581\pi\) | ||
0.968255 | − | 0.249965i | \(-0.0804190\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 560.000 | 1.16424 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −169.328 | − | 316.784i | −0.350576 | − | 0.655867i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 667.509i | − | 1.37631i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 500.000 | 1.02669 | 0.513347 | − | 0.858181i | \(-0.328405\pi\) | ||||
0.513347 | + | 0.858181i | \(0.328405\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 770.000 | − | 411.582i | 1.57464 | − | 0.841682i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 115.966i | − | 0.236182i | −0.993003 | − | 0.118091i | \(-0.962322\pi\) | ||
0.993003 | − | 0.118091i | \(-0.0376775\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −253.992 | −0.515197 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −240.000 | + | 359.199i | −0.484848 | + | 0.725655i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 359.199i | − | 0.722735i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 333.365 | 0.668065 | 0.334033 | − | 0.942561i | \(-0.391590\pi\) | ||||
0.334033 | + | 0.942561i | \(0.391590\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −465.652 | − | 871.156i | −0.929446 | − | 1.73883i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 448.999i | 0.892642i | 0.894873 | + | 0.446321i | \(0.147266\pi\) | ||||
−0.894873 | + | 0.446321i | \(0.852734\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 352.000 | 0.697030 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 150.808 | − | 80.6102i | 0.297451 | − | 0.158994i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 322.441i | 0.633479i | 0.948513 | + | 0.316739i | \(0.102588\pi\) | ||||
−0.948513 | + | 0.316739i | \(0.897412\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.0000 | 0.0469667 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.0000 | + | 142.183i | −0.0272904 | + | 0.277160i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 610.940i | 1.18629i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −264.000 | − | 493.899i | −0.508671 | − | 0.951635i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 179.600i | − | 0.344721i | −0.985034 | − | 0.172360i | \(-0.944861\pi\) | ||
0.985034 | − | 0.172360i | \(-0.0551394\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 555.608 | 1.06235 | 0.531174 | − | 0.847263i | \(-0.321751\pi\) | ||||
0.531174 | + | 0.847263i | \(0.321751\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 74.0810 | − | 39.5980i | 0.141107 | − | 0.0754247i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 59.8665i | − | 0.113599i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −367.000 | −0.693762 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −359.822 | − | 240.416i | −0.677631 | − | 0.452761i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 316.784i | − | 0.594341i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 816.000 | 1.52523 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −452.000 | − | 845.615i | −0.841713 | − | 1.57470i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 280.014i | 0.519507i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −772.559 | −1.42802 | −0.714011 | − | 0.700135i | \(-0.753123\pi\) | ||||
−0.714011 | + | 0.700135i | \(0.753123\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −308.000 | + | 164.633i | −0.567219 | + | 0.303191i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 299.333i | 0.549234i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −502.693 | −0.919000 | −0.459500 | − | 0.888178i | \(-0.651971\pi\) | ||||
−0.459500 | + | 0.888178i | \(0.651971\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −476.235 | + | 712.764i | −0.867459 | + | 1.29829i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 89.7998i | − | 0.162976i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −496.000 | −0.896926 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −423.320 | − | 791.960i | −0.762739 | − | 1.42695i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 526.087i | 0.944502i | 0.881464 | + | 0.472251i | \(0.156558\pi\) | ||||
−0.881464 | + | 0.472251i | \(0.843442\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −56.0000 | −0.100179 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 336.000 | − | 179.600i | 0.598930 | − | 0.320142i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.48528i | 0.0150715i | 0.999972 | + | 0.00753577i | \(0.00239873\pi\) | ||||
−0.999972 | + | 0.00753577i | \(0.997601\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −507.984 | −0.899087 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −124.000 | − | 299.333i | −0.218695 | − | 0.527923i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 359.199i | 0.631281i | 0.948879 | + | 0.315641i | \(0.102219\pi\) | ||||
−0.948879 | + | 0.315641i | \(0.897781\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.29150 | −0.00926708 | −0.00463354 | − | 0.999989i | \(-0.501475\pi\) | ||||
−0.00463354 | + | 0.999989i | \(0.501475\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −84.6640 | − | 158.392i | −0.147756 | − | 0.276426i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 209.533i | − | 0.364405i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.0000 | −0.0311958 | −0.0155979 | − | 0.999878i | \(-0.504965\pi\) | ||||
−0.0155979 | + | 0.999878i | \(0.504965\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 269.867 | − | 144.250i | 0.466091 | − | 0.249136i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 11.3137i | − | 0.0194728i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −432.000 | −0.740995 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 448.000 | + | 299.333i | 0.765812 | + | 0.511680i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 121.622i | 0.207193i | 0.994619 | + | 0.103597i | \(0.0330351\pi\) | ||||
−0.994619 | + | 0.103597i | \(0.966965\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.1660 | 0.0359355 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −344.000 | − | 643.565i | −0.582064 | − | 1.08894i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 718.398i | − | 1.21146i | −0.795669 | − | 0.605732i | \(-0.792880\pi\) | ||
0.795669 | − | 0.605732i | \(-0.207120\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −338.656 | −0.569170 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 497.401 | − | 265.872i | 0.833168 | − | 0.445347i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 688.465i | − | 1.14936i | −0.818379 | − | 0.574679i | \(-0.805127\pi\) | ||
0.818379 | − | 0.574679i | \(-0.194873\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 358.000 | 0.595674 | 0.297837 | − | 0.954617i | \(-0.403735\pi\) | ||||
0.297837 | + | 0.954617i | \(0.403735\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −238.118 | + | 356.382i | −0.394888 | + | 0.591015i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 277.186i | − | 0.458158i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 884.000 | 1.45634 | 0.728171 | − | 0.685395i | \(-0.240371\pi\) | ||||
0.728171 | + | 0.685395i | \(0.240371\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 96.0000 | + | 179.600i | 0.157635 | + | 0.294909i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −391.571 | −0.638778 | −0.319389 | − | 0.947624i | \(-0.603478\pi\) | ||||
−0.319389 | + | 0.947624i | \(0.603478\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −448.000 | + | 239.466i | −0.728455 | + | 0.389376i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 104.766i | 0.169800i | 0.996389 | + | 0.0848998i | \(0.0270570\pi\) | ||||
−0.996389 | + | 0.0848998i | \(0.972943\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −682.604 | −1.10275 | −0.551376 | − | 0.834257i | \(-0.685897\pi\) | ||||
−0.551376 | + | 0.834257i | \(0.685897\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −804.308 | − | 79.1960i | −1.29518 | − | 0.127530i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 419.066i | − | 0.672658i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −751.000 | −1.20160 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 63.4980 | + | 118.794i | 0.101273 | + | 0.189464i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 791.960i | 1.25908i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −428.000 | −0.678288 | −0.339144 | − | 0.940734i | \(-0.610137\pi\) | ||||
−0.339144 | + | 0.940734i | \(0.610137\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −658.000 | + | 351.716i | −1.03949 | + | 0.555633i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 429.921i | 0.677041i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 349.239 | 0.548256 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −672.000 | − | 448.999i | −1.05164 | − | 0.702659i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 793.231i | 1.23749i | 0.785592 | + | 0.618745i | \(0.212359\pi\) | ||||
−0.785592 | + | 0.618745i | \(0.787641\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 851.932 | 1.32493 | 0.662467 | − | 0.749092i | \(-0.269510\pi\) | ||||
0.662467 | + | 0.749092i | \(0.269510\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 42.3320 | + | 79.1960i | 0.0656310 | + | 0.122784i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 448.999i | 0.693970i | 0.937871 | + | 0.346985i | \(0.112795\pi\) | ||||
−0.937871 | + | 0.346985i | \(0.887205\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −408.000 | −0.628659 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −42.3320 | + | 22.6274i | −0.0650261 | + | 0.0347579i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1103.09i | − | 1.68926i | −0.535351 | − | 0.844630i | \(-0.679821\pi\) | ||
0.535351 | − | 0.844630i | \(-0.320179\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 80.0000 | 0.122137 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 30.0000 | − | 44.8999i | 0.0456621 | − | 0.0683408i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 924.896i | − | 1.40348i | −0.712431 | − | 0.701742i | \(-0.752406\pi\) | ||
0.712431 | − | 0.701742i | \(-0.247594\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −433.903 | −0.656435 | −0.328217 | − | 0.944602i | \(-0.606448\pi\) | ||||
−0.328217 | + | 0.944602i | \(0.606448\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −224.000 | − | 419.066i | −0.337858 | − | 0.632075i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 119.733i | − | 0.180050i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 507.984 | 0.761596 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 497.401 | − | 265.872i | 0.743500 | − | 0.397417i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 808.198i | 1.20447i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 566.000 | 0.841010 | 0.420505 | − | 0.907290i | \(-0.361853\pi\) | ||||
0.420505 | + | 0.907290i | \(0.361853\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.5203 | − | 188.090i | 0.0274374 | − | 0.278652i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 797.616i | − | 1.17816i | −0.808074 | − | 0.589082i | \(-0.799490\pi\) | ||
0.808074 | − | 0.589082i | \(-0.200510\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 472.000 | 0.695140 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 548.000 | + | 1025.21i | 0.804699 | + | 1.50545i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 404.465i | − | 0.592189i | −0.955159 | − | 0.296094i | \(-0.904316\pi\) | ||
0.955159 | − | 0.296094i | \(-0.0956843\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −644.000 | + | 344.232i | −0.937409 | + | 0.501066i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 538.799i | 0.782001i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −121.705 | −0.176128 | −0.0880641 | − | 0.996115i | \(-0.528068\pi\) | ||||
−0.0880641 | + | 0.996115i | \(0.528068\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −253.992 | − | 169.706i | −0.366511 | − | 0.244885i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 688.465i | − | 0.990597i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 448.000 | 0.642755 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 148.162 | + | 277.186i | 0.211963 | + | 0.396546i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 333.754i | − | 0.476112i | −0.971251 | − | 0.238056i | \(-0.923490\pi\) | ||
0.971251 | − | 0.238056i | \(-0.0765102\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −280.000 | −0.398293 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 248.902i | 0.352053i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 370.405 | 0.522433 | 0.261217 | − | 0.965280i | \(-0.415876\pi\) | ||||
0.261217 | + | 0.965280i | \(0.415876\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −620.000 | + | 927.931i | −0.872011 | + | 1.30511i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 119.733i | 0.167929i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 507.984 | 0.710467 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 507.984 | + | 950.352i | 0.708486 | + | 1.32546i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1017.73i | − | 1.41548i | −0.706473 | − | 0.707740i | \(-0.749715\pi\) | ||
0.706473 | − | 0.707740i | \(-0.250285\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −432.000 | −0.599168 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −322.782 | + | 172.534i | −0.446448 | + | 0.238636i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 118.794i | 0.163854i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1140.00 | 1.56809 | 0.784044 | − | 0.620705i | \(-0.213154\pi\) | ||||
0.784044 | + | 0.620705i | \(0.213154\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −715.000 | − | 142.183i | −0.980796 | − | 0.195038i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 79.1960i | − | 0.108339i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 370.405 | 0.505328 | 0.252664 | − | 0.967554i | \(-0.418693\pi\) | ||||
0.252664 | + | 0.967554i | \(0.418693\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −264.000 | − | 493.899i | −0.359184 | − | 0.671971i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 404.099i | 0.548303i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.29150 | −0.00716036 | −0.00358018 | − | 0.999994i | \(-0.501140\pi\) | ||||
−0.00358018 | + | 0.999994i | \(0.501140\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 148.162 | − | 79.1960i | 0.199949 | − | 0.106877i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 748.331i | − | 1.00718i | −0.863944 | − | 0.503588i | \(-0.832013\pi\) | ||
0.863944 | − | 0.503588i | \(-0.167987\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1056.00 | −1.41745 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −21.1660 | − | 14.1421i | −0.0283347 | − | 0.0189319i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 576.999i | 0.770359i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1108.00 | 1.47537 | 0.737683 | − | 0.675147i | \(-0.235920\pi\) | ||||
0.737683 | + | 0.675147i | \(0.235920\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −228.000 | − | 426.549i | −0.302789 | − | 0.566466i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 339.411i | 0.449551i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1047.72 | 1.38404 | 0.692019 | − | 0.721879i | \(-0.256721\pi\) | ||||
0.692019 | + | 0.721879i | \(0.256721\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −672.000 | + | 359.199i | −0.885375 | + | 0.473253i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1287.13i | − | 1.69137i | −0.533685 | − | 0.845683i | \(-0.679193\pi\) | ||
0.533685 | − | 0.845683i | \(-0.320807\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −211.660 | −0.277405 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −423.320 | + | 633.568i | −0.553360 | + | 0.828193i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 508.865i | 0.663449i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 538.000 | 0.699610 | 0.349805 | − | 0.936823i | \(-0.386248\pi\) | ||||
0.349805 | + | 0.936823i | \(0.386248\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 634.980 | + | 1187.94i | 0.823580 | + | 1.54078i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 62.2254i | 0.0804986i | 0.999190 | + | 0.0402493i | \(0.0128152\pi\) | ||||
−0.999190 | + | 0.0402493i | \(0.987185\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.0000 | −0.0361290 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 560.000 | − | 299.333i | 0.720721 | − | 0.385241i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 158.392i | 0.203327i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −761.976 | −0.975642 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 456.000 | + | 44.8999i | 0.582375 | + | 0.0573434i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 658.532i | − | 0.838894i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1476.33 | −1.87589 | −0.937947 | − | 0.346778i | \(-0.887276\pi\) | ||||
−0.937947 | + | 0.346778i | \(0.887276\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 296.324 | + | 554.372i | 0.375569 | + | 0.702626i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 359.199i | − | 0.454108i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1008.00 | 1.27112 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 761.976 | − | 407.294i | 0.958461 | − | 0.512319i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1250.16i | 1.56859i | 0.620389 | + | 0.784294i | \(0.286975\pi\) | ||||
−0.620389 | + | 0.784294i | \(0.713025\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −784.000 | − | 523.832i | −0.978777 | − | 0.653973i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 50.9117i | − | 0.0634019i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 677.312 | 0.841382 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −72.0000 | − | 134.700i | −0.0892193 | − | 0.166914i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 448.999i | 0.555005i | 0.960725 | + | 0.277502i | \(0.0895066\pi\) | ||||
−0.960725 | + | 0.277502i | \(0.910493\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1391.67 | −1.71599 | −0.857993 | − | 0.513661i | \(-0.828289\pi\) | ||||
−0.857993 | + | 0.513661i | \(0.828289\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 920.721 | − | 492.146i | 1.13250 | − | 0.605346i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1646.33i | 2.02004i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.0000 | 0.0342717 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −211.660 | + | 316.784i | −0.258437 | + | 0.386793i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 469.519i | 0.571887i | 0.958247 | + | 0.285943i | \(0.0923069\pi\) | ||||
−0.958247 | + | 0.285943i | \(0.907693\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1268.00 | 1.54070 | 0.770352 | − | 0.637618i | \(-0.220080\pi\) | ||||
0.770352 | + | 0.637618i | \(0.220080\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −84.0000 | − | 157.150i | −0.101818 | − | 0.190484i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1145.51i | − | 1.38514i | −0.721349 | − | 0.692571i | \(-0.756478\pi\) | ||
0.721349 | − | 0.692571i | \(-0.243522\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1217.05 | 1.46809 | 0.734044 | − | 0.679101i | \(-0.237630\pi\) | ||||
0.734044 | + | 0.679101i | \(0.237630\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −644.000 | + | 344.232i | −0.774970 | + | 0.414239i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 493.899i | 0.592916i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1862.61 | 2.23067 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.5830 | + | 107.480i | −0.0126440 | + | 0.128411i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1227.26i | 1.46277i | 0.681965 | + | 0.731385i | \(0.261126\pi\) | ||||
−0.681965 | + | 0.731385i | \(0.738874\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 553.000 | 0.657551 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 444.486 | + | 831.558i | 0.527267 | + | 0.986427i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 322.441i | 0.381587i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 196.000 | 0.231405 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 238.000 | − | 127.216i | 0.280330 | − | 0.149843i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1583.92i | − | 1.86124i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1047.72 | 1.22827 | 0.614137 | − | 0.789200i | \(-0.289504\pi\) | ||||
0.614137 | + | 0.789200i | \(0.289504\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −224.000 | − | 149.666i | −0.261988 | − | 0.175048i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 359.199i | 0.419135i | 0.977794 | + | 0.209568i | \(0.0672057\pi\) | ||||
−0.977794 | + | 0.209568i | \(0.932794\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 513.276 | 0.597527 | 0.298764 | − | 0.954327i | \(-0.403426\pi\) | ||||
0.298764 | + | 0.954327i | \(0.403426\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −169.328 | − | 316.784i | −0.196664 | − | 0.367925i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 538.799i | − | 0.624332i | −0.950028 | − | 0.312166i | \(-0.898945\pi\) | ||
0.950028 | − | 0.312166i | \(-0.101055\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1056.00 | 1.22081 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −171.974 | + | 91.9239i | −0.198355 | + | 0.106025i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1052.17i | 1.21079i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 504.000 | 0.578645 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 590.000 | − | 883.031i | 0.675830 | − | 1.01149i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 407.294i | − | 0.465478i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1344.04 | 1.53254 | 0.766272 | − | 0.642516i | \(-0.222109\pi\) | ||||
0.766272 | + | 0.642516i | \(0.222109\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.0000 | − | 44.8999i | −0.0273038 | − | 0.0510806i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 748.331i | − | 0.849411i | −0.905331 | − | 0.424706i | \(-0.860378\pi\) | ||
0.905331 | − | 0.424706i | \(-0.139622\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −418.029 | −0.473419 | −0.236709 | − | 0.971581i | \(-0.576069\pi\) | ||||
−0.236709 | + | 0.971581i | \(0.576069\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 719.644 | − | 384.666i | 0.813157 | − | 0.434651i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1167.40i | 1.31612i | 0.752966 | + | 0.658059i | \(0.228622\pi\) | ||||
−0.752966 | + | 0.658059i | \(0.771378\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −304.000 | −0.341957 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −634.980 | + | 263.044i | −0.712660 | + | 0.295223i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1808.00 | 2.02011 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 448.000 | + | 838.131i | 0.499443 | + | 0.934372i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 67.8823i | − | 0.0755086i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −761.976 | −0.845701 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −56.0000 | + | 29.9333i | −0.0620155 | + | 0.0331487i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 658.532i | − | 0.727659i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 597.940 | 0.659250 | 0.329625 | − | 0.944112i | \(-0.393078\pi\) | ||||
0.329625 | + | 0.944112i | \(0.393078\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 465.652 | + | 311.127i | 0.512269 | + | 0.342274i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 359.199i | − | 0.394291i | −0.980374 | − | 0.197146i | \(-0.936833\pi\) | ||
0.980374 | − | 0.197146i | \(-0.0631671\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.0000 | −0.0262870 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −761.976 | − | 1425.53i | −0.832761 | − | 1.55795i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 56.5685i | 0.0616887i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −780.000 | −0.848749 | −0.424374 | − | 0.905487i | \(-0.639506\pi\) | ||||
−0.424374 | + | 0.905487i | \(0.639506\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1218.00 | + | 651.048i | −1.32248 | + | 0.706893i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 950.352i | 1.02963i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 370.405 | 0.400438 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −540.000 | + | 808.198i | −0.582524 | + | 0.871842i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1361.96i | − | 1.46605i | −0.680200 | − | 0.733027i | \(-0.738107\pi\) | ||
0.680200 | − | 0.733027i | \(-0.261893\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −174.620 | −0.187561 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 211.660 | + | 395.980i | 0.226860 | + | 0.424416i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 718.398i | 0.768340i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −566.000 | −0.604055 | −0.302028 | − | 0.953299i | \(-0.597664\pi\) | ||||
−0.302028 | + | 0.953299i | \(0.597664\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1486.91 | + | 794.788i | −1.58351 | + | 0.846420i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 424.264i | − | 0.450865i | −0.974259 | − | 0.225433i | \(-0.927620\pi\) | ||
0.974259 | − | 0.225433i | \(-0.0723795\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −896.000 | −0.950159 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 608.000 | + | 59.8665i | 0.643386 | + | 0.0633508i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 466.690i | 0.492809i | 0.969167 | + | 0.246405i | \(0.0792492\pi\) | ||||
−0.969167 | + | 0.246405i | \(0.920751\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −63.4980 | −0.0669105 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.00000 | − | 14.9666i | −0.00841220 | − | 0.0157378i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 897.998i | 0.942285i | 0.882057 | + | 0.471143i | \(0.156158\pi\) | ||||
−0.882057 | + | 0.471143i | \(0.843842\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 338.656 | 0.354614 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 380.988 | − | 203.647i | 0.398107 | − | 0.212797i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −945.000 | −0.983351 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1079.47 | + | 721.249i | 1.12094 | + | 0.748960i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 576.999i | 0.597927i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 692.000 | 0.715615 | 0.357808 | − | 0.933795i | \(-0.383524\pi\) | ||||
0.357808 | + | 0.933795i | \(0.383524\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 112.000 | + | 209.533i | 0.115583 | + | 0.216236i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 449.720i | − | 0.463151i | −0.972817 | − | 0.231576i | \(-0.925612\pi\) | ||
0.972817 | − | 0.231576i | \(-0.0743881\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 486.818 | 0.500327 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −196.000 | + | 104.766i | −0.201026 | + | 0.107453i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 883.031i | 0.903819i | 0.892064 | + | 0.451909i | \(0.149257\pi\) | ||||
−0.892064 | + | 0.451909i | \(0.850743\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −888.972 | −0.908041 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −264.575 | + | 395.980i | −0.269699 | + | 0.403649i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 329.266i | 0.334960i | 0.985875 | + | 0.167480i | \(0.0535630\pi\) | ||||
−0.985875 | + | 0.167480i | \(0.946437\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1376.00 | 1.39695 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 158.392i | 0.160154i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 340.000 | 0.343088 | 0.171544 | − | 0.985176i | \(-0.445124\pi\) | ||||
0.171544 | + | 0.985176i | \(0.445124\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1106.00 | + | 591.182i | −1.11380 | + | 0.595349i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1063.49i | 1.06883i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1555.70 | 1.56038 | 0.780191 | − | 0.625541i | \(-0.215122\pi\) | ||||
0.780191 | + | 0.625541i | \(0.215122\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 140.000 | − | 1421.83i | 0.140140 | − | 1.42325i |
(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 | 768.3.e.l.257.2 | 4 | ||
3.2 | odd | 2 | inner | 768.3.e.l.257.1 | 4 | ||
4.3 | odd | 2 | 768.3.e.i.257.3 | 4 | |||
8.3 | odd | 2 | 768.3.e.i.257.2 | 4 | |||
8.5 | even | 2 | inner | 768.3.e.l.257.3 | 4 | ||
12.11 | even | 2 | 768.3.e.i.257.4 | 4 | |||
16.3 | odd | 4 | 24.3.h.c.5.3 | yes | 4 | ||
16.5 | even | 4 | 96.3.h.c.17.4 | 4 | |||
16.11 | odd | 4 | 24.3.h.c.5.1 | ✓ | 4 | ||
16.13 | even | 4 | 96.3.h.c.17.1 | 4 | |||
24.5 | odd | 2 | inner | 768.3.e.l.257.4 | 4 | ||
24.11 | even | 2 | 768.3.e.i.257.1 | 4 | |||
48.5 | odd | 4 | 96.3.h.c.17.2 | 4 | |||
48.11 | even | 4 | 24.3.h.c.5.4 | yes | 4 | ||
48.29 | odd | 4 | 96.3.h.c.17.3 | 4 | |||
48.35 | even | 4 | 24.3.h.c.5.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.3.h.c.5.1 | ✓ | 4 | 16.11 | odd | 4 | ||
24.3.h.c.5.2 | yes | 4 | 48.35 | even | 4 | ||
24.3.h.c.5.3 | yes | 4 | 16.3 | odd | 4 | ||
24.3.h.c.5.4 | yes | 4 | 48.11 | even | 4 | ||
96.3.h.c.17.1 | 4 | 16.13 | even | 4 | |||
96.3.h.c.17.2 | 4 | 48.5 | odd | 4 | |||
96.3.h.c.17.3 | 4 | 48.29 | odd | 4 | |||
96.3.h.c.17.4 | 4 | 16.5 | even | 4 | |||
768.3.e.i.257.1 | 4 | 24.11 | even | 2 | |||
768.3.e.i.257.2 | 4 | 8.3 | odd | 2 | |||
768.3.e.i.257.3 | 4 | 4.3 | odd | 2 | |||
768.3.e.i.257.4 | 4 | 12.11 | even | 2 | |||
768.3.e.l.257.1 | 4 | 3.2 | odd | 2 | inner | ||
768.3.e.l.257.2 | 4 | 1.1 | even | 1 | trivial | ||
768.3.e.l.257.3 | 4 | 8.5 | even | 2 | inner | ||
768.3.e.l.257.4 | 4 | 24.5 | odd | 2 | inner |