Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1519,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3344.1519");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1519.6 | ||
Character | \(\chi\) | \(=\) | 3344.1519 |
Dual form | 3344.2.o.b.1519.5 |
$q$-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 \(\left(\mathbb{Z}/3344\mathbb{Z}\right)^\times\).
\(n\) | \(705\) | \(837\) | \(2433\) | \(2927\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −2.58608 | −1.49307 | −0.746537 | − | 0.665344i | \(-0.768285\pi\) | ||||
−0.746537 | + | 0.665344i | \(0.768285\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.42833 | 1.53319 | 0.766597 | − | 0.642128i | \(-0.221948\pi\) | ||||
0.766597 | + | 0.642128i | \(0.221948\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.59904i | 1.73827i | 0.494573 | + | 0.869136i | \(0.335324\pi\) | ||||
−0.494573 | + | 0.869136i | \(0.664676\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.68782 | 1.22927 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.60992i | 1.55591i | 0.628319 | + | 0.777956i | \(0.283743\pi\) | ||||
−0.628319 | + | 0.777956i | \(0.716257\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.86593 | −2.28917 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.86607 | 1.66527 | 0.832633 | − | 0.553825i | \(-0.186832\pi\) | ||||
0.832633 | + | 0.553825i | \(0.186832\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.01679 | − | 3.14626i | −0.692100 | − | 0.721802i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 11.8935i | − | 2.59537i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.41922i | 0.921472i | 0.887537 | + | 0.460736i | \(0.152414\pi\) | ||||
−0.887537 | + | 0.460736i | \(0.847586\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.75343 | 1.35069 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.77875 | −0.342320 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.50430i | 1.57921i | 0.613617 | + | 0.789604i | \(0.289714\pi\) | ||||
−0.613617 | + | 0.789604i | \(0.710286\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.23088 | 1.65791 | 0.828957 | − | 0.559312i | \(-0.188935\pi\) | ||||
0.828957 | + | 0.559312i | \(0.188935\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.58608i | 0.450179i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 15.7670i | 2.66511i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.06747i | − | 0.175491i | −0.996143 | − | 0.0877457i | \(-0.972034\pi\) | ||
0.996143 | − | 0.0877457i | \(-0.0279663\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 14.5077i | − | 2.32309i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.23290i | 0.348721i | 0.984682 | + | 0.174360i | \(0.0557858\pi\) | ||||
−0.984682 | + | 0.174360i | \(0.944214\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.51453i | 0.840957i | 0.907302 | + | 0.420479i | \(0.138138\pi\) | ||||
−0.907302 | + | 0.420479i | \(0.861862\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12.6430 | 1.88471 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 7.03024i | − | 1.02547i | −0.858548 | − | 0.512733i | \(-0.828633\pi\) | ||
0.858548 | − | 0.512733i | \(-0.171367\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14.1511 | −2.02159 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −17.7562 | −2.48637 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 8.19169i | − | 1.12522i | −0.826724 | − | 0.562608i | \(-0.809798\pi\) | ||
0.826724 | − | 0.562608i | \(-0.190202\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.42833i | − | 0.462276i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.80167 | + | 8.13649i | 1.03336 | + | 1.07770i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.18092 | 0.674498 | 0.337249 | − | 0.941415i | \(-0.390504\pi\) | ||||
0.337249 | + | 0.941415i | \(0.390504\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8947 | −1.39493 | −0.697465 | − | 0.716619i | \(-0.745689\pi\) | ||||
−0.697465 | + | 0.716619i | \(0.745689\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 16.9604i | 2.13681i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 19.2326i | 2.38552i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.76156 | 1.07039 | 0.535197 | − | 0.844727i | \(-0.320237\pi\) | ||||
0.535197 | + | 0.844727i | \(0.320237\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 11.4285i | − | 1.37583i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.34801 | −0.872048 | −0.436024 | − | 0.899935i | \(-0.643614\pi\) | ||||
−0.436024 | + | 0.899935i | \(0.643614\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.44436 | 1.10538 | 0.552690 | − | 0.833387i | \(-0.313602\pi\) | ||||
0.552690 | + | 0.833387i | \(0.313602\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −17.4649 | −2.01668 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.59904 | 0.524109 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.3209 | 1.16119 | 0.580595 | − | 0.814193i | \(-0.302820\pi\) | ||||
0.580595 | + | 0.814193i | \(0.302820\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.46347 | −0.718163 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.87340i | 0.315396i | 0.987487 | + | 0.157698i | \(0.0504073\pi\) | ||||
−0.987487 | + | 0.157698i | \(0.949593\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 23.5391 | 2.55318 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 21.9928i | − | 2.35788i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 10.3594i | − | 1.09809i | −0.835793 | − | 0.549045i | \(-0.814991\pi\) | ||
0.835793 | − | 0.549045i | \(-0.185009\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25.8002 | −2.70460 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −23.8718 | −2.47539 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.3426 | − | 10.7864i | −1.06112 | − | 1.10666i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 5.06525i | − | 0.514298i | −0.966372 | − | 0.257149i | \(-0.917217\pi\) | ||
0.966372 | − | 0.257149i | \(-0.0827832\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.68782i | − | 0.370639i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.31548 | −0.727918 | −0.363959 | − | 0.931415i | \(-0.618575\pi\) | ||||
−0.363959 | + | 0.931415i | \(0.618575\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.92887 | 0.781255 | 0.390628 | − | 0.920549i | \(-0.372258\pi\) | ||||
0.390628 | + | 0.920549i | \(0.372258\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 40.7747i | − | 3.97921i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.3368 | −1.77268 | −0.886342 | − | 0.463032i | \(-0.846762\pi\) | ||||
−0.886342 | + | 0.463032i | \(0.846762\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 9.43599i | − | 0.903804i | −0.892068 | − | 0.451902i | \(-0.850746\pi\) | ||
0.892068 | − | 0.451902i | \(-0.149254\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.76057i | 0.262022i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.08600i | − | 0.478450i | −0.970964 | − | 0.239225i | \(-0.923107\pi\) | ||
0.970964 | − | 0.239225i | \(-0.0768934\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.1505i | 1.41280i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 20.6883i | 1.91264i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 31.5773i | 2.89468i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 5.77447i | − | 0.520666i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.01135 | 0.537671 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.84691 | −0.163887 | −0.0819435 | − | 0.996637i | \(-0.526113\pi\) | ||||
−0.0819435 | + | 0.996637i | \(0.526113\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 14.2610i | − | 1.25561i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.87682i | 0.251349i | 0.992072 | + | 0.125675i | \(0.0401095\pi\) | ||||
−0.992072 | + | 0.125675i | \(0.959890\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.4698 | − | 13.8743i | 1.25469 | − | 1.20306i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.09812 | −0.524843 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.85476 | −0.585642 | −0.292821 | − | 0.956167i | \(-0.594594\pi\) | ||||
−0.292821 | + | 0.956167i | \(0.594594\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 0.344300i | − | 0.0292031i | −0.999893 | − | 0.0146016i | \(-0.995352\pi\) | ||
0.999893 | − | 0.0146016i | \(-0.00464799\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.1808i | 1.53110i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.60992 | 0.469125 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 29.1555i | 2.42123i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 36.5960 | 3.01838 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.8752 | −0.890934 | −0.445467 | − | 0.895298i | \(-0.646962\pi\) | ||||
−0.445467 | + | 0.895298i | \(0.646962\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.4126 | 1.90529 | 0.952644 | − | 0.304087i | \(-0.0983515\pi\) | ||||
0.952644 | + | 0.304087i | \(0.0983515\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 25.3208 | 2.04706 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 31.6465 | 2.54191 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.4364 | 0.992529 | 0.496264 | − | 0.868171i | \(-0.334705\pi\) | ||||
0.496264 | + | 0.868171i | \(0.334705\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 21.1844i | 1.68003i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.3242 | −1.60177 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.81988i | 0.377522i | 0.982023 | + | 0.188761i | \(0.0604472\pi\) | ||||
−0.982023 | + | 0.188761i | \(0.939553\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.86593i | 0.690212i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.8383 | −0.993461 | −0.496730 | − | 0.867905i | \(-0.665466\pi\) | ||||
−0.496730 | + | 0.867905i | \(0.665466\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.4712 | −1.42086 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.1254 | − | 11.6028i | −0.850778 | − | 0.887291i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.39987i | 0.410544i | 0.978705 | + | 0.205272i | \(0.0658080\pi\) | ||||
−0.978705 | + | 0.205272i | \(0.934192\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 31.0593i | 2.34786i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.3983 | −1.00708 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.55865 | −0.639704 | −0.319852 | − | 0.947468i | \(-0.603633\pi\) | ||||
−0.319852 | + | 0.947468i | \(0.603633\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.845010i | 0.0628091i | 0.999507 | + | 0.0314045i | \(0.00999802\pi\) | ||||
−0.999507 | + | 0.0314045i | \(0.990002\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28.1747 | 2.08273 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3.65964i | − | 0.269062i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6.86607i | − | 0.502097i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 8.18051i | − | 0.595045i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.2355i | 1.31947i | 0.751496 | + | 0.659737i | \(0.229332\pi\) | ||||
−0.751496 | + | 0.659737i | \(0.770668\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.2601i | 1.09845i | 0.835675 | + | 0.549224i | \(0.185077\pi\) | ||||
−0.835675 | + | 0.549224i | \(0.814923\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 49.7372i | − | 3.56175i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.4384 | 1.24243 | 0.621217 | − | 0.783638i | \(-0.286638\pi\) | ||||
0.621217 | + | 0.783638i | \(0.286638\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.23774i | 0.442182i | 0.975253 | + | 0.221091i | \(0.0709617\pi\) | ||||
−0.975253 | + | 0.221091i | \(0.929038\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −22.6581 | −1.59818 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −39.1116 | −2.74509 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.65512i | 0.534657i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.2973i | 1.13274i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.14626 | + | 3.01679i | −0.217631 | + | 0.208676i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.568833 | −0.0391601 | −0.0195800 | − | 0.999808i | \(-0.506233\pi\) | ||||
−0.0195800 | + | 0.999808i | \(0.506233\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 19.0026 | 1.30203 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.9056i | 1.28935i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 42.4531i | 2.88191i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −24.4239 | −1.65041 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 38.5181i | 2.59101i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.276933 | 0.0185448 | 0.00927241 | − | 0.999957i | \(-0.497048\pi\) | ||||
0.00927241 | + | 0.999957i | \(0.497048\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 24.9054 | 1.66036 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.93585 | −0.393976 | −0.196988 | − | 0.980406i | \(-0.563116\pi\) | ||||
−0.196988 | + | 0.980406i | \(0.563116\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.45100 | 0.426294 | 0.213147 | − | 0.977020i | \(-0.431629\pi\) | ||||
0.213147 | + | 0.977020i | \(0.431629\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.8935 | −0.782533 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.1654 | −0.993522 | −0.496761 | − | 0.867887i | \(-0.665477\pi\) | ||||
−0.496761 | + | 0.867887i | \(0.665477\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 24.1020i | − | 1.57224i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −26.6906 | −1.73374 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.73085i | 0.241329i | 0.992693 | + | 0.120664i | \(0.0385024\pi\) | ||||
−0.992693 | + | 0.120664i | \(0.961498\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.6667i | 1.71775i | 0.512183 | + | 0.858877i | \(0.328837\pi\) | ||||
−0.512183 | + | 0.858877i | \(0.671163\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.0513 | 1.41459 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −48.5147 | −3.09949 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.6503 | − | 16.9240i | 1.12306 | − | 1.07685i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 7.43084i | − | 0.470910i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 0.0265278i | − | 0.00167442i | −1.00000 | 0.000837210i | \(-0.999734\pi\) | |||
1.00000 | 0.000837210i | \(-0.000266492\pi\) | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.41922 | 0.277834 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −60.8741 | −3.81208 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.6893i | 0.916294i | 0.888877 | + | 0.458147i | \(0.151487\pi\) | ||||
−0.888877 | + | 0.458147i | \(0.848513\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.90934 | 0.305052 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 31.3623i | 1.94128i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.9602i | 0.799159i | 0.916698 | + | 0.399580i | \(0.130844\pi\) | ||||
−0.916698 | + | 0.399580i | \(0.869156\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 28.0838i | − | 1.72517i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.7902i | 1.63953i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 15.1407i | − | 0.923144i | −0.887103 | − | 0.461572i | \(-0.847286\pi\) | ||
0.887103 | − | 0.461572i | \(-0.152714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 27.7238i | − | 1.68410i | −0.539399 | − | 0.842050i | \(-0.681349\pi\) | ||
0.539399 | − | 0.842050i | \(-0.318651\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 66.7214 | 4.03817 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 6.75343i | − | 0.407247i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.5680 | −1.17573 | −0.587863 | − | 0.808961i | \(-0.700031\pi\) | ||||
−0.587863 | + | 0.808961i | \(0.700031\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 34.0418 | 2.03803 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.7616i | 1.35784i | 0.734211 | + | 0.678922i | \(0.237552\pi\) | ||||
−0.734211 | + | 0.678922i | \(0.762448\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.39636i | 0.261336i | 0.991426 | + | 0.130668i | \(0.0417123\pi\) | ||||
−0.991426 | + | 0.130668i | \(0.958288\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 26.7467 | + | 27.8946i | 1.58434 | + | 1.65233i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.2692 | −0.606171 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.1429 | 1.77311 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.0992i | 0.767886i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 14.2402i | − | 0.831920i | −0.909383 | − | 0.415960i | \(-0.863446\pi\) | ||
0.909383 | − | 0.415960i | \(-0.136554\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.7619 | 1.03414 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.77875i | 0.103213i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.7915 | −1.43373 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.3615 | −1.46181 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.9184 | 1.08684 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −37.3508 | −2.13870 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.7282 | 0.612291 | 0.306145 | − | 0.951985i | \(-0.400961\pi\) | ||||
0.306145 | + | 0.951985i | \(0.400961\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20.5047 | −1.16647 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 7.49622i | − | 0.425072i | −0.977153 | − | 0.212536i | \(-0.931828\pi\) | ||
0.977153 | − | 0.212536i | \(-0.0681723\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.45589 | −0.195339 | −0.0976694 | − | 0.995219i | \(-0.531139\pi\) | ||||
−0.0976694 | + | 0.995219i | \(0.531139\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 58.1458i | 3.27614i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 17.6599i | − | 0.991879i | −0.868357 | − | 0.495940i | \(-0.834824\pi\) | ||
0.868357 | − | 0.495940i | \(-0.165176\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.50430 | 0.476149 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 47.4204 | 2.64675 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.7135 | − | 21.6024i | −1.15253 | − | 1.20199i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 37.8862i | 2.10155i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 24.4022i | 1.34945i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 32.3323 | 1.78254 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.7578 | −1.63564 | −0.817819 | − | 0.575476i | \(-0.804817\pi\) | ||||
−0.817819 | + | 0.575476i | \(0.804817\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 3.93664i | − | 0.215727i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 30.0375 | 1.64112 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 14.7960i | − | 0.805989i | −0.915202 | − | 0.402995i | \(-0.867969\pi\) | ||
0.915202 | − | 0.402995i | \(-0.132031\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.1528i | 0.714362i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 9.23088i | − | 0.499880i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 32.8883i | − | 1.77580i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 39.1805i | − | 2.10941i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.101260i | 0.00543590i | 0.999996 | + | 0.00271795i | \(0.000865151\pi\) | ||||
−0.999996 | + | 0.00271795i | \(0.999135\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.1533 | −1.07878 | −0.539390 | − | 0.842056i | \(-0.681345\pi\) | ||||
−0.539390 | + | 0.842056i | \(0.681345\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 9.97862i | − | 0.532619i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.0446 | 1.33299 | 0.666494 | − | 0.745510i | \(-0.267794\pi\) | ||||
0.666494 | + | 0.745510i | \(0.267794\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.1914 | −1.33702 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 81.6614i | − | 4.32198i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.7124i | 1.04038i | 0.854050 | + | 0.520191i | \(0.174139\pi\) | ||||
−0.854050 | + | 0.520191i | \(0.825861\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.797928 | + | 18.9832i | −0.0419962 | + | 0.999118i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.58608 | 0.135734 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.3784 | 1.69476 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 13.0344i | − | 0.680391i | −0.940355 | − | 0.340196i | \(-0.889507\pi\) | ||
0.940355 | − | 0.340196i | \(-0.110493\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.23453i | 0.428673i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 37.6739 | 1.95593 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 3.37555i | − | 0.174779i | −0.996174 | − | 0.0873896i | \(-0.972147\pi\) | ||
0.996174 | − | 0.0873896i | \(-0.0278525\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −15.5458 | −0.802783 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −47.7084 | −2.45711 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.3941 | 0.739378 | 0.369689 | − | 0.929156i | \(-0.379464\pi\) | ||||
0.369689 | + | 0.929156i | \(0.379464\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.77626 | 0.244695 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.8626 | 1.21932 | 0.609662 | − | 0.792661i | \(-0.291305\pi\) | ||||
0.609662 | + | 0.792661i | \(0.291305\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.7670 | 0.803561 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.3365i | 1.03376i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.3711 | −0.880751 | −0.440375 | − | 0.897814i | \(-0.645155\pi\) | ||||
−0.440375 | + | 0.897814i | \(0.645155\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.3427i | 1.53450i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 7.43969i | − | 0.375283i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 35.3834 | 1.78033 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.37708 | 0.119302 | 0.0596511 | − | 0.998219i | \(-0.481001\pi\) | ||||
0.0596511 | + | 0.998219i | \(0.481001\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −37.4200 | + | 35.8802i | −1.87334 | + | 1.79625i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.0128i | 1.14921i | 0.818432 | + | 0.574603i | \(0.194844\pi\) | ||||
−0.818432 | + | 0.574603i | \(0.805156\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 51.7845i | 2.57957i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −22.1589 | −1.10108 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.06747 | −0.0529126 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.44119i | 0.219603i | 0.993954 | + | 0.109801i | \(0.0350215\pi\) | ||||
−0.993954 | + | 0.109801i | \(0.964979\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.7270 | 0.874407 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 23.8272i | 1.17246i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.85095i | 0.483564i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.890387i | 0.0436024i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.7150i | 0.767730i | 0.923389 | + | 0.383865i | \(0.125407\pi\) | ||||
−0.923389 | + | 0.383865i | \(0.874593\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 28.0775i | − | 1.36842i | −0.729287 | − | 0.684208i | \(-0.760148\pi\) | ||
0.729287 | − | 0.684208i | \(-0.239852\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 25.9262i | − | 1.26058i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 46.3695 | 2.24925 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 50.1053i | − | 2.42477i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.5077 | −0.700439 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.9226 | −0.766964 | −0.383482 | − | 0.923548i | \(-0.625275\pi\) | ||||
−0.383482 | + | 0.923548i | \(0.625275\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.3119i | 0.831954i | 0.909375 | + | 0.415977i | \(0.136560\pi\) | ||||
−0.909375 | + | 0.415977i | \(0.863440\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 75.3985i | − | 3.61508i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.9040 | − | 13.3319i | 0.665120 | − | 0.637750i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.4325 | −0.784282 | −0.392141 | − | 0.919905i | \(-0.628266\pi\) | ||||
−0.392141 | + | 0.919905i | \(0.628266\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −52.1867 | −2.48508 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 31.1867i | − | 1.48172i | −0.671658 | − | 0.740862i | \(-0.734417\pi\) | ||
0.671658 | − | 0.740862i | \(-0.265583\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 35.5153i | − | 1.68359i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 28.1242 | 1.33023 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 18.7193i | − | 0.883416i | −0.897159 | − | 0.441708i | \(-0.854373\pi\) | ||
0.897159 | − | 0.441708i | \(-0.145627\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.23290 | 0.105143 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −60.5468 | −2.84474 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −88.4516 | −4.14668 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.3648 | 1.18652 | 0.593258 | − | 0.805013i | \(-0.297842\pi\) | ||||
0.593258 | + | 0.805013i | \(0.297842\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.2130 | −0.570053 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.4580 | 1.37200 | 0.685998 | − | 0.727603i | \(-0.259366\pi\) | ||||
0.685998 | + | 0.727603i | \(0.259366\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.6991i | 0.822549i | 0.911512 | + | 0.411274i | \(0.134916\pi\) | ||||
−0.911512 | + | 0.411274i | \(0.865084\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −81.8403 | −3.79525 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.42834i | 0.204919i | 0.994737 | + | 0.102460i | \(0.0326713\pi\) | ||||
−0.994737 | + | 0.102460i | \(0.967329\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 40.2947i | 1.86064i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −32.1614 | −1.48192 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.51453 | 0.253558 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.3737 | − | 21.2481i | −0.934810 | − | 0.974928i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 30.2094i | − | 1.38320i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 37.1502i | − | 1.69743i | −0.528847 | − | 0.848717i | \(-0.677376\pi\) | ||
0.528847 | − | 0.848717i | \(-0.322624\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.98843 | 0.273049 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 52.5599 | 2.39156 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 17.3653i | − | 0.788520i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.07559 | −0.320626 | −0.160313 | − | 0.987066i | \(-0.551250\pi\) | ||||
−0.160313 | + | 0.987066i | \(0.551250\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 12.4646i | − | 0.563669i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14.7919i | − | 0.667549i | −0.942653 | − | 0.333775i | \(-0.891678\pi\) | ||
0.942653 | − | 0.333775i | \(-0.108322\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 58.3911i | 2.62980i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 12.6430i | − | 0.568262i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 33.7938i | − | 1.51586i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 26.5174i | − | 1.18708i | −0.804804 | − | 0.593540i | \(-0.797730\pi\) | ||
0.804804 | − | 0.593540i | \(-0.202270\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 33.2010 | 1.48331 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 10.4684i | − | 0.466765i | −0.972385 | − | 0.233382i | \(-0.925021\pi\) | ||
0.972385 | − | 0.233382i | \(-0.0749793\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.0799 | −1.11604 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 47.7680 | 2.12145 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 4.61765i | − | 0.204674i | −0.994750 | − | 0.102337i | \(-0.967368\pi\) | ||
0.994750 | − | 0.102337i | \(-0.0326320\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 43.4350i | 1.92145i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.36611 | + | 5.59640i | 0.236919 | + | 0.247087i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 27.1828 | 1.19782 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.03024 | −0.309190 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 13.9645i | − | 0.612973i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.8648i | 0.782673i | 0.920248 | + | 0.391336i | \(0.127987\pi\) | ||||
−0.920248 | + | 0.391336i | \(0.872013\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.7321 | −1.47500 | −0.737501 | − | 0.675346i | \(-0.763994\pi\) | ||||
−0.737501 | + | 0.675346i | \(0.763994\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 80.3218i | − | 3.50553i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 63.3798 | 2.76087 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.47047 | 0.150890 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.1063 | 0.829142 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.5264 | −0.542579 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −62.8645 | −2.71787 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22.1334 | 0.955126 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.1511i | 0.609532i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.34978 | 0.230005 | 0.115002 | − | 0.993365i | \(-0.463312\pi\) | ||||
0.115002 | + | 0.993365i | \(0.463312\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 2.18526i | − | 0.0937786i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 32.3497i | − | 1.38571i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.97366 | −0.169901 | −0.0849507 | − | 0.996385i | \(-0.527073\pi\) | ||||
−0.0849507 | + | 0.996385i | \(0.527073\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −40.1778 | −1.71475 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26.7567 | − | 25.6557i | 1.13988 | − | 1.09297i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 47.4661i | 2.01846i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.46414i | 0.401730i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.1337 | 1.02258 | 0.511289 | − | 0.859409i | \(-0.329168\pi\) | ||||
0.511289 | + | 0.859409i | \(0.329168\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −30.9360 | −1.30846 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.7562i | 0.749668i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.0225 | −0.885994 | −0.442997 | − | 0.896523i | \(-0.646085\pi\) | ||||
−0.442997 | + | 0.896523i | \(0.646085\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 17.4365i | − | 0.733558i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 29.7257i | − | 1.24836i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.0052i | 0.796740i | 0.917225 | + | 0.398370i | \(0.130424\pi\) | ||||
−0.917225 | + | 0.398370i | \(0.869576\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.9025i | 0.581803i | 0.956753 | + | 0.290902i | \(0.0939553\pi\) | ||||
−0.956753 | + | 0.290902i | \(0.906045\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 47.1585i | − | 1.97007i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 29.8449i | 1.24462i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.33191 | 0.221970 | 0.110985 | − | 0.993822i | \(-0.464599\pi\) | ||||
0.110985 | + | 0.993822i | \(0.464599\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 39.4639i | − | 1.64006i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.2149 | −0.548245 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.19169 | −0.339265 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 70.9264i | 2.93245i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.78000i | 0.114743i | 0.998353 | + | 0.0573715i | \(0.0182720\pi\) | ||||
−0.998353 | + | 0.0573715i | \(0.981728\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.8476 | − | 29.0428i | −1.14744 | − | 1.19669i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −45.0971 | −1.85505 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −37.5686 | −1.54276 | −0.771380 | − | 0.636375i | \(-0.780433\pi\) | ||||
−0.771380 | + | 0.636375i | \(0.780433\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 108.257i | 4.43812i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 16.1313i | − | 0.660210i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.9866 | 1.63381 | 0.816904 | − | 0.576773i | \(-0.195688\pi\) | ||||
0.816904 | + | 0.576773i | \(0.195688\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 24.2948i | − | 0.991004i | −0.868607 | − | 0.495502i | \(-0.834984\pi\) | ||
0.868607 | − | 0.495502i | \(-0.165016\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.3110 | 1.31581 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.42833 | −0.139381 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.4901 | −0.628723 | −0.314362 | − | 0.949303i | \(-0.601790\pi\) | ||||
−0.314362 | + | 0.949303i | \(0.601790\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 101.146 | 4.09863 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 39.4391 | 1.59553 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.7184 | 1.80616 | 0.903081 | − | 0.429471i | \(-0.141300\pi\) | ||||
0.903081 | + | 0.429471i | \(0.141300\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 19.7968i | − | 0.798283i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.5964 | 0.949956 | 0.474978 | − | 0.879998i | \(-0.342456\pi\) | ||||
0.474978 | + | 0.879998i | \(0.342456\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 30.5416i | − | 1.22757i | −0.789473 | − | 0.613785i | \(-0.789646\pi\) | ||
0.789473 | − | 0.613785i | \(-0.210354\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 7.86067i | − | 0.315438i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 47.6431 | 1.90878 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.1583 | −0.526332 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.13649 | − | 7.80167i | 0.324940 | − | 0.311569i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 7.32933i | − | 0.292240i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.67775i | − | 0.106600i | −0.998579 | − | 0.0532998i | \(-0.983026\pi\) | ||
0.998579 | − | 0.0532998i | \(-0.0169739\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.47105 | 0.0584689 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.33182 | −0.251271 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 79.3867i | − | 3.14541i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27.0981 | −1.07198 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 11.3550i | − | 0.448496i | −0.974532 | − | 0.224248i | \(-0.928007\pi\) | ||
0.974532 | − | 0.224248i | \(-0.0719926\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.8287i | 1.09746i | 0.836001 | + | 0.548728i | \(0.184888\pi\) | ||||
−0.836001 | + | 0.548728i | \(0.815112\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 48.8914i | − | 1.92510i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 44.3945i | − | 1.74533i | −0.488320 | − | 0.872664i | \(-0.662390\pi\) | ||
0.488320 | − | 0.872664i | \(-0.337610\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 5.18092i | − | 0.203369i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 109.787i | − | 4.30290i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.45552 | −0.291757 | −0.145879 | − | 0.989302i | \(-0.546601\pi\) | ||||
−0.145879 | + | 0.989302i | \(0.546601\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.86269i | 0.385367i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 34.8291 | 1.35881 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.65692 | 0.0645443 | 0.0322721 | − | 0.999479i | \(-0.489726\pi\) | ||||
0.0322721 | + | 0.999479i | \(0.489726\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 39.6930i | − | 1.54388i | −0.635695 | − | 0.771940i | \(-0.719287\pi\) | ||
0.635695 | − | 0.771940i | \(-0.280713\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 99.6109i | − | 3.86857i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 49.6071 | − | 47.5658i | 1.92368 | − | 1.84452i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −37.5824 | −1.45520 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.716171 | −0.0276888 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.8947i | 0.420587i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.7846i | 0.762641i | 0.924443 | + | 0.381321i | \(0.124531\pi\) | ||||
−0.924443 | + | 0.381321i | \(0.875469\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.0126 | −0.462367 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.7145i | 0.527092i | 0.964647 | + | 0.263546i | \(0.0848921\pi\) | ||||
−0.964647 | + | 0.263546i | \(0.915108\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.2953 | 0.893990 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.3506 | 0.588236 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.8828 | −0.875586 | −0.437793 | − | 0.899076i | \(-0.644240\pi\) | ||||
−0.437793 | + | 0.899076i | \(0.644240\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23.5004 | −0.897903 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.6828 | −0.636489 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 45.9547 | 1.75074 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.562354i | 0.0213930i | 0.999943 | + | 0.0106965i | \(0.00340486\pi\) | ||||
−0.999943 | + | 0.0106965i | \(0.996595\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.9604 | 0.644272 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 1.18037i | − | 0.0447741i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.3313i | 0.580713i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 39.2191 | 1.48340 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.3892 | 0.430164 | 0.215082 | − | 0.976596i | \(-0.430998\pi\) | ||||
0.215082 | + | 0.976596i | \(0.430998\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.35855 | + | 3.22034i | −0.126670 | + | 0.121457i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 62.3296i | 2.34747i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 33.6442i | − | 1.26532i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.1622 | −1.09521 | −0.547605 | − | 0.836737i | \(-0.684460\pi\) | ||||
−0.547605 | + | 0.836737i | \(0.684460\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 38.0615 | 1.42742 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40.7933i | 1.52772i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.2326 | 0.719260 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 9.64828i | − | 0.360321i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 44.4806i | − | 1.65885i | −0.558621 | − | 0.829423i | \(-0.688669\pi\) | ||
0.558621 | − | 0.829423i | \(-0.311331\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36.4652i | 1.35803i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 68.9623i | − | 2.56473i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 57.4332i | 2.13302i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 45.8238i | − | 1.69951i | −0.527178 | − | 0.849755i | \(-0.676750\pi\) | ||
0.527178 | − | 0.849755i | \(-0.323250\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −37.6360 | −1.39393 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.8631i | 1.40042i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.9409 | −1.17976 | −0.589882 | − | 0.807490i | \(-0.700826\pi\) | ||||
−0.589882 | + | 0.807490i | \(0.700826\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 125.463 | 4.62777 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 8.76156i | − | 0.322736i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 13.2689i | − | 0.488104i | −0.969762 | − | 0.244052i | \(-0.921523\pi\) | ||
0.969762 | − | 0.244052i | \(-0.0784767\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −45.6450 | + | 43.7667i | −1.67681 | + | 1.60781i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.3480 | −0.416317 | −0.208158 | − | 0.978095i | \(-0.566747\pi\) | ||||
−0.208158 | + | 0.978095i | \(0.566747\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −37.2839 | −1.36598 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.5966i | 0.387708i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 84.3315i | − | 3.08141i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.9390 | 1.09249 | 0.546245 | − | 0.837626i | \(-0.316057\pi\) | ||||
0.546245 | + | 0.837626i | \(0.316057\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.0686030i | 0.00250003i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 80.2660 | 2.92118 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.6514 | 1.58654 | 0.793268 | − | 0.608873i | \(-0.208378\pi\) | ||||
0.793268 | + | 0.608873i | \(0.208378\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.4285 | −0.414827 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.2174 | −0.479130 | −0.239565 | − | 0.970880i | \(-0.577005\pi\) | ||||
−0.239565 | + | 0.970880i | \(0.577005\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.3965 | 1.57106 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 86.8080 | 3.13855 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 29.0645i | 1.04946i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.7572 | 0.928829 | 0.464415 | − | 0.885618i | \(-0.346265\pi\) | ||||
0.464415 | + | 0.885618i | \(0.346265\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 37.9877i | − | 1.36809i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.1357i | 0.724230i | 0.932133 | + | 0.362115i | \(0.117945\pi\) | ||||
−0.932133 | + | 0.362115i | \(0.882055\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 62.3401 | 2.23932 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.6960 | −0.455465 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.02530 | − | 6.73620i | 0.251707 | − | 0.241349i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.34801i | 0.262932i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 15.1270i | − | 0.540594i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 42.6359 | 1.52174 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.3712 | −0.904387 | −0.452194 | − | 0.891920i | \(-0.649358\pi\) | ||||
−0.452194 | + | 0.891920i | \(0.649358\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 33.5161i | − | 1.19320i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.3907 | 0.831677 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 61.1186i | − | 2.17039i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 72.6270i | 2.57581i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.2342i | 1.49601i | 0.663693 | + | 0.748005i | \(0.268988\pi\) | ||||
−0.663693 | + | 0.748005i | \(0.731012\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 48.2701i | − | 1.70767i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 38.2034i | − | 1.34985i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 9.44436i | − | 0.333284i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −69.6779 | −2.45582 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 39.1551i | 1.37832i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −49.5585 | −1.74238 | −0.871192 | − | 0.490943i | \(-0.836652\pi\) | ||||
−0.871192 | + | 0.490943i | \(0.836652\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.1154 | 0.495659 | 0.247829 | − | 0.968804i | \(-0.420283\pi\) | ||||
0.247829 | + | 0.968804i | \(0.420283\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 71.6960i | 2.51449i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.5241i | 0.578815i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.3501 | − | 16.6362i | 0.607005 | − | 0.582026i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −95.1464 | −3.32469 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.80868 | 0.342325 | 0.171163 | − | 0.985243i | \(-0.445248\pi\) | ||||
0.171163 | + | 0.985243i | \(0.445248\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 10.2365i | − | 0.356822i | −0.983956 | − | 0.178411i | \(-0.942904\pi\) | ||
0.983956 | − | 0.178411i | \(-0.0570956\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17.4649i | 0.608051i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.20782 | 0.0767733 | 0.0383867 | − | 0.999263i | \(-0.487778\pi\) | ||||
0.0383867 | + | 0.999263i | \(0.487778\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.7742i | 0.374202i | 0.982341 | + | 0.187101i | \(0.0599092\pi\) | ||||
−0.982341 | + | 0.187101i | \(0.940091\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 50.6044 | 1.75545 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −97.1626 | −3.36648 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −44.0141 | −1.52317 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.4194 | −0.567537 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.2319 | −0.733005 | −0.366503 | − | 0.930417i | \(-0.619445\pi\) | ||||
−0.366503 | + | 0.930417i | \(0.619445\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −43.3231 | −1.49390 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 58.8634i | − | 2.02736i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −63.3253 | −2.17846 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4.59904i | − | 0.158025i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 11.3693i | − | 0.390195i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.71740 | 0.161710 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.55636 | −0.224485 | −0.112243 | − | 0.993681i | \(-0.535803\pi\) | ||||
−0.112243 | + | 0.993681i | \(0.535803\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −38.1414 | − | 39.7783i | −1.30441 | − | 1.36039i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 0.108265i | − | 0.00369827i | −0.999998 | − | 0.00184913i | \(-0.999411\pi\) | ||
0.999998 | − | 0.00184913i | \(-0.000588598\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.7505i | 1.25391i | 0.779055 | + | 0.626956i | \(0.215699\pi\) | ||||
−0.779055 | + | 0.626956i | \(0.784301\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26.5570 | 0.905059 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.40999 | 0.150118 | 0.0750589 | − | 0.997179i | \(-0.476086\pi\) | ||||
0.0750589 | + | 0.997179i | \(0.476086\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.5125i | 0.629445i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −77.9519 | −2.64739 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 10.3209i | − | 0.350112i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49.1516i | 1.66544i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 18.6797i | − | 0.632212i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 27.6464i | 0.934618i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 39.5801i | − | 1.33652i | −0.743926 | − | 0.668262i | \(-0.767038\pi\) | ||
0.743926 | − | 0.668262i | \(-0.232962\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 36.8262i | 1.24212i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.2196 | −0.917052 | −0.458526 | − | 0.888681i | \(-0.651622\pi\) | ||||
−0.458526 | + | 0.888681i | \(0.651622\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.9728i | 1.31154i | 0.754961 | + | 0.655770i | \(0.227656\pi\) | ||||
−0.754961 | + | 0.655770i | \(0.772344\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −45.9337 | −1.54404 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.1435 | −1.21358 | −0.606791 | − | 0.794862i | \(-0.707543\pi\) | ||||
−0.606791 | + | 0.794862i | \(0.707543\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 8.49401i | − | 0.284880i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.46347i | 0.216534i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.1190 | + | 21.2088i | −0.740183 | + | 0.709724i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −29.3419 | −0.980791 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 64.1128 | 2.14066 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 78.5021i | 2.61819i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 56.2447i | − | 1.87378i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 65.5869 | 2.18259 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.89697i | 0.0962986i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.3775 | 1.20789 | 0.603947 | − | 0.797025i | \(-0.293594\pi\) | ||||
0.603947 | + | 0.797025i | \(0.293594\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −26.9781 | −0.894809 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.77532 | 0.125082 | 0.0625409 | − | 0.998042i | \(-0.480080\pi\) | ||||
0.0625409 | + | 0.998042i | \(0.480080\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.87340 | 0.0950956 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 96.5921 | 3.19324 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.2306 | −0.436913 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 28.6687i | − | 0.945694i | −0.881144 | − | 0.472847i | \(-0.843226\pi\) | ||
0.881144 | − | 0.472847i | \(-0.156774\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.7440 | −0.914196 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 41.2217i | − | 1.35683i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 7.20910i | − | 0.237034i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 29.2402 | 0.960375 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.15858 | −0.300483 | −0.150242 | − | 0.988649i | \(-0.548005\pi\) | ||||
−0.150242 | + | 0.988649i | \(0.548005\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 42.6910 | + | 44.5231i | 1.39914 | + | 1.45919i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19.3858i | 0.634664i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 23.5391i | − | 0.769812i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.47477 | −0.211522 | −0.105761 | − | 0.994392i | \(-0.533728\pi\) | ||||
−0.105761 | + | 0.994392i | \(0.533728\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.93722 | 0.291655 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.8807i | 0.517696i | 0.965918 | + | 0.258848i | \(0.0833429\pi\) | ||||
−0.965918 | + | 0.258848i | \(0.916657\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.86769 | −0.321336 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 28.0455i | − | 0.912320i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 14.0731i | − | 0.457314i | −0.973507 | − | 0.228657i | \(-0.926567\pi\) | ||
0.973507 | − | 0.228657i | \(-0.0734334\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 52.9821i | 1.71987i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 45.6699i | 1.48095i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 50.4548i | − | 1.63439i | −0.576361 | − | 0.817195i | \(-0.695528\pi\) | ||
0.576361 | − | 0.817195i | \(-0.304472\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 62.5173i | 2.02301i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −21.9928 | −0.710926 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 31.5253i | − | 1.01800i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 54.2091 | 1.74868 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −67.6226 | −2.17911 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 52.3167i | 1.68413i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.7979i | 0.443712i | 0.975079 | + | 0.221856i | \(0.0712115\pi\) | ||||
−0.975079 | + | 0.221856i | \(0.928789\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 53.5668 | + | 55.8657i | 1.72081 | + | 1.79466i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.7363 | 0.729642 | 0.364821 | − | 0.931078i | \(-0.381130\pi\) | ||||
0.364821 | + | 0.931078i | \(0.381130\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.58345 | 0.0507630 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 97.9768i | − | 3.13777i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.8532i | 0.763132i | 0.924342 | + | 0.381566i | \(0.124615\pi\) | ||||
−0.924342 | + | 0.381566i | \(0.875385\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.3594 | −0.331087 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 34.7982i | − | 1.11102i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −48.5920 | −1.54984 | −0.774922 | − | 0.632057i | \(-0.782211\pi\) | ||||
−0.774922 | + | 0.632057i | \(0.782211\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 59.7846 | 1.90489 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −83.6140 | −2.66146 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.3699 | −0.774918 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.71808 | 0.0863426 | 0.0431713 | − | 0.999068i | \(-0.486254\pi\) | ||||
0.0431713 | + | 0.999068i | \(0.486254\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 76.9561 | 2.44213 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.3850i | 0.677951i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.2623 | 0.926747 | 0.463373 | − | 0.886163i | \(-0.346639\pi\) | ||||
0.463373 | + | 0.886163i | \(0.346639\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.89876i | 0.0600742i |
(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 | 3344.2.o.b.1519.6 | yes | 64 | |
4.3 | odd | 2 | inner | 3344.2.o.b.1519.59 | yes | 64 | |
19.18 | odd | 2 | inner | 3344.2.o.b.1519.60 | yes | 64 | |
76.75 | even | 2 | inner | 3344.2.o.b.1519.5 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3344.2.o.b.1519.5 | ✓ | 64 | 76.75 | even | 2 | inner | |
3344.2.o.b.1519.6 | yes | 64 | 1.1 | even | 1 | trivial | |
3344.2.o.b.1519.59 | yes | 64 | 4.3 | odd | 2 | inner | |
3344.2.o.b.1519.60 | yes | 64 | 19.18 | odd | 2 | inner |