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: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1519.9 | ||
Character | \(\chi\) | \(=\) | 3344.1519 |
Dual form | 3344.2.o.a.1519.10 |
$q$-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 | ||||||||
\(3\) | −1.71785 | −0.991803 | −0.495902 | − | 0.868379i | \(-0.665162\pi\) | ||||
−0.495902 | + | 0.868379i | \(0.665162\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.66778 | −1.64028 | −0.820141 | − | 0.572162i | \(-0.806105\pi\) | ||||
−0.820141 | + | 0.572162i | \(0.806105\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.65082i | 1.00192i | 0.865471 | + | 0.500958i | \(0.167019\pi\) | ||||
−0.865471 | + | 0.500958i | \(0.832981\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.0489799 | −0.0163266 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00362i | 1.11040i | 0.831715 | + | 0.555202i | \(0.187359\pi\) | ||||
−0.831715 | + | 0.555202i | \(0.812641\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.30071 | 1.62684 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.00587 | 1.21410 | 0.607051 | − | 0.794663i | \(-0.292352\pi\) | ||||
0.607051 | + | 0.794663i | \(0.292352\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.66960 | + | 4.02647i | −0.383033 | + | 0.923735i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 4.55372i | − | 0.993704i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.204072i | 0.0425519i | 0.999774 | + | 0.0212759i | \(0.00677285\pi\) | ||||
−0.999774 | + | 0.0212759i | \(0.993227\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.45262 | 1.69052 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.23770 | 1.00800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.62744i | − | 1.23069i | −0.788260 | − | 0.615343i | \(-0.789018\pi\) | ||
0.788260 | − | 0.615343i | \(-0.210982\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.91321 | 1.60086 | 0.800430 | − | 0.599426i | \(-0.204605\pi\) | ||||
0.800430 | + | 0.599426i | \(0.204605\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.71785i | − | 0.299040i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 9.72263i | − | 1.64343i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.2007i | 1.84139i | 0.390286 | + | 0.920694i | \(0.372376\pi\) | ||||
−0.390286 | + | 0.920694i | \(0.627624\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 6.87764i | − | 1.10130i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.16260i | 0.181568i | 0.995871 | + | 0.0907840i | \(0.0289373\pi\) | ||||
−0.995871 | + | 0.0907840i | \(0.971063\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.59761i | 1.31112i | 0.755142 | + | 0.655562i | \(0.227568\pi\) | ||||
−0.755142 | + | 0.655562i | \(0.772432\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.179648 | 0.0267803 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 7.02526i | − | 1.02474i | −0.858765 | − | 0.512370i | \(-0.828768\pi\) | ||
0.858765 | − | 0.512370i | \(-0.171232\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.0268544 | −0.00383635 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.59936 | −1.20415 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.64742i | 0.775733i | 0.921715 | + | 0.387867i | \(0.126788\pi\) | ||||
−0.921715 | + | 0.387867i | \(0.873212\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.66778i | − | 0.494564i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.86813 | − | 6.91688i | 0.379893 | − | 0.916163i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.7855 | 1.40416 | 0.702078 | − | 0.712100i | \(-0.252256\pi\) | ||||
0.702078 | + | 0.712100i | \(0.252256\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.0588 | −1.92808 | −0.964041 | − | 0.265753i | \(-0.914380\pi\) | ||||
−0.964041 | + | 0.265753i | \(0.914380\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 0.129837i | − | 0.0163579i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 14.6844i | − | 1.82138i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.02412 | 1.10247 | 0.551236 | − | 0.834349i | \(-0.314156\pi\) | ||||
0.551236 | + | 0.834349i | \(0.314156\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 0.350565i | − | 0.0422031i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.63267 | −0.431118 | −0.215559 | − | 0.976491i | \(-0.569157\pi\) | ||||
−0.215559 | + | 0.976491i | \(0.569157\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.45373 | −0.872393 | −0.436197 | − | 0.899851i | \(-0.643675\pi\) | ||||
−0.436197 | + | 0.899851i | \(0.643675\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.5204 | −1.67667 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.65082 | −0.302089 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.2460 | 1.26527 | 0.632636 | − | 0.774449i | \(-0.281973\pi\) | ||||
0.632636 | + | 0.774449i | \(0.281973\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.85066 | −0.983407 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.09050i | 0.339226i | 0.985511 | + | 0.169613i | \(0.0542518\pi\) | ||||
−0.985511 | + | 0.169613i | \(0.945748\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18.3604 | −1.99147 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.3850i | 1.22060i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1.40070i | − | 0.148474i | −0.997241 | − | 0.0742370i | \(-0.976348\pi\) | ||
0.997241 | − | 0.0742370i | \(-0.0236521\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.6129 | −1.11253 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −15.3116 | −1.58774 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.12373 | − | 14.7682i | 0.628282 | − | 1.51519i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.0507i | 1.62970i | 0.579669 | + | 0.814852i | \(0.303182\pi\) | ||||
−0.579669 | + | 0.814852i | \(0.696818\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 0.0489799i | − | 0.00492267i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.68888 | 0.566065 | 0.283032 | − | 0.959110i | \(-0.408660\pi\) | ||||
0.283032 | + | 0.959110i | \(0.408660\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.86903 | −0.184161 | −0.0920807 | − | 0.995752i | \(-0.529352\pi\) | ||||
−0.0920807 | + | 0.995752i | \(0.529352\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 16.7021i | 1.62995i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.8824 | 1.53541 | 0.767703 | − | 0.640806i | \(-0.221400\pi\) | ||||
0.767703 | + | 0.640806i | \(0.221400\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.05519i | 0.484200i | 0.970251 | + | 0.242100i | \(0.0778361\pi\) | ||||
−0.970251 | + | 0.242100i | \(0.922164\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 19.2412i | − | 1.82629i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.9592i | 1.97168i | 0.167693 | + | 0.985839i | \(0.446368\pi\) | ||||
−0.167693 | + | 0.985839i | \(0.553632\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 0.748490i | − | 0.0697971i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 0.196097i | − | 0.0181292i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.2697i | 1.21643i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 1.99718i | − | 0.180080i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.6635 | −1.13265 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.61496 | −0.232040 | −0.116020 | − | 0.993247i | \(-0.537014\pi\) | ||||
−0.116020 | + | 0.993247i | \(0.537014\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 14.7694i | − | 1.30038i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.6760i | 1.10751i | 0.832680 | + | 0.553755i | \(0.186805\pi\) | ||||
−0.832680 | + | 0.553755i | \(0.813195\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.6734 | − | 4.42581i | −0.925505 | − | 0.383767i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −19.2107 | −1.65340 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.63104 | 0.310221 | 0.155110 | − | 0.987897i | \(-0.450427\pi\) | ||||
0.155110 | + | 0.987897i | \(0.450427\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 5.78076i | − | 0.490318i | −0.969483 | − | 0.245159i | \(-0.921160\pi\) | ||
0.969483 | − | 0.245159i | \(-0.0788402\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0684i | 1.01634i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.00362 | −0.334800 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.3080i | 2.01867i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.0461320 | 0.00380490 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.59920 | −0.212935 | −0.106467 | − | 0.994316i | \(-0.533954\pi\) | ||||
−0.106467 | + | 0.994316i | \(0.533954\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.20707 | 0.260987 | 0.130494 | − | 0.991449i | \(-0.458344\pi\) | ||||
0.130494 | + | 0.991449i | \(0.458344\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.245187 | −0.0198222 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −32.6917 | −2.62586 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.4857 | −1.63494 | −0.817468 | − | 0.575974i | \(-0.804623\pi\) | ||||
−0.817468 | + | 0.575974i | \(0.804623\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 9.70145i | − | 0.769375i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.540957 | −0.0426334 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 19.1956i | − | 1.50351i | −0.659440 | − | 0.751757i | \(-0.729206\pi\) | ||
0.659440 | − | 0.751757i | \(-0.270794\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.30071i | 0.490510i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.4044 | −1.88847 | −0.944233 | − | 0.329278i | \(-0.893195\pi\) | ||||
−0.944233 | + | 0.329278i | \(0.893195\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.02899 | −0.232999 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0817769 | − | 0.197216i | 0.00625364 | − | 0.0150815i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.7675i | 1.73098i | 0.500929 | + | 0.865489i | \(0.332992\pi\) | ||||
−0.500929 | + | 0.865489i | \(0.667008\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.4064i | 1.69376i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −18.5280 | −1.39265 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.38421 | 0.178204 | 0.0891022 | − | 0.996022i | \(-0.471600\pi\) | ||||
0.0891022 | + | 0.996022i | \(0.471600\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 23.3640i | − | 1.73663i | −0.496014 | − | 0.868315i | \(-0.665203\pi\) | ||
0.496014 | − | 0.868315i | \(-0.334797\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 25.8688 | 1.91228 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 41.0818i | − | 3.02039i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.00587i | 0.366066i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.8842i | 1.00993i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.3871i | 1.83695i | 0.395483 | + | 0.918473i | \(0.370577\pi\) | ||||
−0.395483 | + | 0.918473i | \(0.629423\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 7.82933i | − | 0.563568i | −0.959478 | − | 0.281784i | \(-0.909074\pi\) | ||
0.959478 | − | 0.281784i | \(-0.0909261\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 25.2257i | 1.80645i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.25592 | −0.516963 | −0.258482 | − | 0.966016i | \(-0.583222\pi\) | ||||
−0.258482 | + | 0.966016i | \(0.583222\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 11.4278i | − | 0.810093i | −0.914296 | − | 0.405047i | \(-0.867255\pi\) | ||
0.914296 | − | 0.405047i | \(-0.132745\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.5021 | −1.09344 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.5682 | 1.23304 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 4.26417i | − | 0.297823i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 0.00999541i | − | 0.000694729i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.02647 | − | 1.66960i | −0.278517 | − | 0.115489i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.37087 | −0.232060 | −0.116030 | − | 0.993246i | \(-0.537017\pi\) | ||||
−0.116030 | + | 0.993246i | \(0.537017\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.24039 | 0.427584 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 31.5342i | − | 2.15061i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.6273i | 1.60393i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.8044 | 0.865242 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.0416i | 1.34815i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.5024 | 0.770259 | 0.385130 | − | 0.922862i | \(-0.374157\pi\) | ||||
0.385130 | + | 0.922862i | \(0.374157\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.414009 | −0.0276006 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.63696 | −0.506883 | −0.253441 | − | 0.967351i | \(-0.581562\pi\) | ||||
−0.253441 | + | 0.967351i | \(0.581562\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.4568 | −1.28574 | −0.642871 | − | 0.765974i | \(-0.722257\pi\) | ||||
−0.642871 | + | 0.765974i | \(0.722257\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.55372 | 0.299613 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.6632 | 1.09164 | 0.545821 | − | 0.837902i | \(-0.316218\pi\) | ||||
0.545821 | + | 0.837902i | \(0.316218\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.7671i | 1.68086i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −19.3189 | −1.25490 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.8632i | 0.961420i | 0.876880 | + | 0.480710i | \(0.159621\pi\) | ||||
−0.876880 | + | 0.480710i | \(0.840379\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 15.6223i | − | 1.00632i | −0.864194 | − | 0.503159i | \(-0.832171\pi\) | ||
0.864194 | − | 0.503159i | \(-0.167829\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.508963 | −0.0326500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.0984962 | 0.00629269 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.1205 | − | 6.68445i | −1.02572 | − | 0.425321i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 5.30902i | − | 0.336445i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.32092i | 0.588331i | 0.955754 | + | 0.294166i | \(0.0950417\pi\) | ||||
−0.955754 | + | 0.294166i | \(0.904958\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.204072 | −0.0128299 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 31.5406 | 1.97515 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.94776i | 0.183876i | 0.995765 | + | 0.0919382i | \(0.0293062\pi\) | ||||
−0.995765 | + | 0.0919382i | \(0.970694\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29.6911 | −1.84492 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.324612i | 0.0200930i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 16.3181i | − | 1.00622i | −0.864223 | − | 0.503109i | \(-0.832189\pi\) | ||
0.864223 | − | 0.503109i | \(-0.167811\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 20.7135i | − | 1.27242i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.40620i | 0.147257i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.63414i | 0.160606i | 0.996770 | + | 0.0803032i | \(0.0255889\pi\) | ||||
−0.996770 | + | 0.0803032i | \(0.974411\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.7783i | 0.654738i | 0.944897 | + | 0.327369i | \(0.106162\pi\) | ||||
−0.944897 | + | 0.327369i | \(0.893838\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 18.2314 | 1.10341 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.45262i | 0.509712i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.6339 | 1.78053 | 0.890265 | − | 0.455443i | \(-0.150519\pi\) | ||||
0.890265 | + | 0.455443i | \(0.150519\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.436568 | −0.0261367 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 19.6765i | − | 1.17380i | −0.809659 | − | 0.586901i | \(-0.800348\pi\) | ||
0.809659 | − | 0.586901i | \(-0.199652\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.89175i | 0.290784i | 0.989374 | + | 0.145392i | \(0.0464444\pi\) | ||||
−0.989374 | + | 0.145392i | \(0.953556\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.5197 | + | 25.3696i | −0.623132 | + | 1.50277i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.08185 | −0.181916 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.05876 | 0.474045 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 27.5728i | − | 1.61634i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 24.3037i | − | 1.41984i | −0.704283 | − | 0.709919i | \(-0.748731\pi\) | ||
0.704283 | − | 0.709919i | \(-0.251269\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −39.5590 | −2.30321 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.23770i | 0.303922i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.817025 | −0.0472498 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.7907 | −1.31364 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.77266 | −0.561425 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 55.2324 | 3.16260 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.2075 | 0.810867 | 0.405433 | − | 0.914125i | \(-0.367121\pi\) | ||||
0.405433 | + | 0.914125i | \(0.367121\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.21073 | 0.182652 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.9799i | 1.70001i | 0.526778 | + | 0.850003i | \(0.323400\pi\) | ||||
−0.526778 | + | 0.850003i | \(0.676600\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.33727 | −0.188634 | −0.0943169 | − | 0.995542i | \(-0.530067\pi\) | ||||
−0.0943169 | + | 0.995542i | \(0.530067\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.476214i | 0.0268316i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 4.21066i | − | 0.236494i | −0.992984 | − | 0.118247i | \(-0.962272\pi\) | ||
0.992984 | − | 0.118247i | \(-0.0377275\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.62744 | 0.371066 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −27.2836 | −1.52282 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.35781 | + | 20.1560i | −0.465041 | + | 1.12151i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 33.8411i | 1.87717i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 8.68408i | − | 0.480231i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.6227 | 1.02670 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.5725 | −0.910906 | −0.455453 | − | 0.890260i | \(-0.650523\pi\) | ||||
−0.455453 | + | 0.890260i | \(0.650523\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 0.548610i | − | 0.0300637i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −33.0985 | −1.80836 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.18321i | 0.282347i | 0.989985 | + | 0.141174i | \(0.0450876\pi\) | ||||
−0.989985 | + | 0.141174i | \(0.954912\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 36.0049i | − | 1.95552i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.91321i | 0.482677i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4846i | 0.998073i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.28580i | 0.0692249i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 18.0317i | − | 0.967992i | −0.875070 | − | 0.483996i | \(-0.839185\pi\) | ||
0.875070 | − | 0.483996i | \(-0.160815\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.10853 | −0.434040 | −0.217020 | − | 0.976167i | \(-0.569634\pi\) | ||||
−0.217020 | + | 0.976167i | \(0.569634\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.9698i | 1.11928i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.417540 | −0.0222234 | −0.0111117 | − | 0.999938i | \(-0.503537\pi\) | ||||
−0.0111117 | + | 0.999938i | \(0.503537\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.3238 | 0.707155 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 22.7954i | − | 1.20646i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 18.3062i | − | 0.966163i | −0.875575 | − | 0.483082i | \(-0.839517\pi\) | ||
0.875575 | − | 0.483082i | \(-0.160483\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.4249 | − | 13.4452i | −0.706572 | − | 0.707641i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.71785 | 0.0901639 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 27.3387 | 1.43097 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.0040i | 0.626605i | 0.949653 | + | 0.313303i | \(0.101435\pi\) | ||||
−0.949653 | + | 0.313303i | \(0.898565\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 0.0569442i | − | 0.00296440i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.9703 | −0.777220 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 22.5730i | − | 1.16878i | −0.811471 | − | 0.584392i | \(-0.801333\pi\) | ||
0.811471 | − | 0.584392i | \(-0.198667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 21.7540 | 1.12337 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.5338 | 1.36656 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.87561 | −0.507276 | −0.253638 | − | 0.967299i | \(-0.581627\pi\) | ||||
−0.253638 | + | 0.967299i | \(0.581627\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.49211 | 0.230138 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.5253 | 1.25319 | 0.626593 | − | 0.779347i | \(-0.284449\pi\) | ||||
0.626593 | + | 0.779347i | \(0.284449\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.72263 | 0.495511 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 0.421110i | − | 0.0214062i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.2454 | 0.519462 | 0.259731 | − | 0.965681i | \(-0.416366\pi\) | ||||
0.259731 | + | 0.965681i | \(0.416366\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.02156i | 0.0516623i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 21.7755i | − | 1.09843i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −41.2478 | −2.07540 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.8533 | −1.39791 | −0.698957 | − | 0.715163i | \(-0.746352\pi\) | ||||
−0.698957 | + | 0.715163i | \(0.746352\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18.3354 | + | 7.60290i | 0.917919 | + | 0.380621i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 0.250244i | − | 0.0124966i | −0.999980 | − | 0.00624830i | \(-0.998011\pi\) | ||
0.999980 | − | 0.00624830i | \(-0.00198891\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.6851i | 1.77760i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 32.4623 | 1.61306 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.2007 | −0.555199 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.25022i | 0.210160i | 0.994464 | + | 0.105080i | \(0.0335098\pi\) | ||||
−0.994464 | + | 0.105080i | \(0.966490\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.23760 | −0.307678 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.5905i | 1.40685i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 11.3353i | − | 0.556426i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.93050i | 0.486299i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.73744i | 0.231439i | 0.993282 | + | 0.115719i | \(0.0369174\pi\) | ||||
−0.993282 | + | 0.115719i | \(0.963083\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.6268i | 0.615390i | 0.951485 | + | 0.307695i | \(0.0995577\pi\) | ||||
−0.951485 | + | 0.307695i | \(0.900442\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.344097i | 0.0167306i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 42.3128 | 2.05247 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 39.9182i | − | 1.93178i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.87764 | 0.332055 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.4612 | −0.792909 | −0.396455 | − | 0.918054i | \(-0.629760\pi\) | ||||
−0.396455 | + | 0.918054i | \(0.629760\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.8234i | 1.52933i | 0.644425 | + | 0.764667i | \(0.277097\pi\) | ||||
−0.644425 | + | 0.764667i | \(0.722903\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 41.7576i | − | 2.00212i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.821687 | − | 0.340718i | −0.0393066 | − | 0.0162988i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.2196 | 1.68094 | 0.840470 | − | 0.541858i | \(-0.182279\pi\) | ||||
0.840470 | + | 0.541858i | \(0.182279\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.00131533 | 6.26346e−5 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 23.8869i | − | 1.13490i | −0.823407 | − | 0.567451i | \(-0.807930\pi\) | ||
0.823407 | − | 0.567451i | \(-0.192070\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.13746i | 0.243539i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.46505 | 0.211189 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 36.2880i | − | 1.71254i | −0.516530 | − | 0.856269i | \(-0.672776\pi\) | ||
0.516530 | − | 0.856269i | \(-0.327224\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.16260 | −0.0547448 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.50927 | −0.258848 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 38.9258 | 1.82487 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.71654 | −0.173852 | −0.0869262 | − | 0.996215i | \(-0.527704\pi\) | ||||
−0.0869262 | + | 0.996215i | \(0.527704\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 26.2193 | 1.22381 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.36558 | −0.110176 | −0.0550880 | − | 0.998482i | \(-0.517544\pi\) | ||||
−0.0550880 | + | 0.998482i | \(0.517544\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.6355i | − | 0.773118i | −0.922265 | − | 0.386559i | \(-0.873663\pi\) | ||
0.922265 | − | 0.386559i | \(-0.126337\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 56.1596 | 2.60434 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 26.8430i | − | 1.24215i | −0.783752 | − | 0.621074i | \(-0.786697\pi\) | ||
0.783752 | − | 0.621074i | \(-0.213303\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.9213i | 1.10458i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 35.1914 | 1.62153 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.59761 | −0.395319 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.1125 | + | 34.0342i | −0.647526 | + | 1.56160i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 0.276610i | − | 0.0126651i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 32.2789i | − | 1.47486i | −0.675422 | − | 0.737431i | \(-0.736039\pi\) | ||
0.675422 | − | 0.737431i | \(-0.263961\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −44.8435 | −2.04469 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.929285 | 0.0422839 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 58.8705i | − | 2.67317i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.3882 | 1.33171 | 0.665854 | − | 0.746082i | \(-0.268067\pi\) | ||||
0.665854 | + | 0.746082i | \(0.268067\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.9752i | 1.49119i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 21.9234i | − | 0.989388i | −0.869067 | − | 0.494694i | \(-0.835280\pi\) | ||
0.869067 | − | 0.494694i | \(-0.164720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 33.1761i | − | 1.49418i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.179648i | 0.00807456i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 9.62955i | − | 0.431944i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3.41686i | − | 0.152959i | −0.997071 | − | 0.0764797i | \(-0.975632\pi\) | ||
0.997071 | − | 0.0764797i | \(-0.0243680\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 41.9231 | 1.87299 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.3118i | 1.70824i | 0.520078 | + | 0.854118i | \(0.325903\pi\) | ||||
−0.520078 | + | 0.854118i | \(0.674097\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.8656 | −0.928506 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.20336 | 0.231089 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 7.07903i | − | 0.313772i | −0.987617 | − | 0.156886i | \(-0.949854\pi\) | ||
0.987617 | − | 0.156886i | \(-0.0501456\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 19.7585i | − | 0.874065i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.74487 | + | 21.0894i | −0.386095 | + | 0.931121i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.85521 | 0.302077 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.02526 | 0.308971 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 39.1111i | − | 1.71679i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.25070i | 0.273848i | 0.990582 | + | 0.136924i | \(0.0437216\pi\) | ||||
−0.990582 | + | 0.136924i | \(0.956278\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.45340 | −0.0635529 | −0.0317764 | − | 0.999495i | \(-0.510116\pi\) | ||||
−0.0317764 | + | 0.999495i | \(0.510116\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 38.4909i | − | 1.67988i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 44.6184 | 1.94361 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.9584 | 0.998189 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.528275 | −0.0229252 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.65462 | −0.201614 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −58.2530 | −2.51850 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.09573 | −0.176744 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 0.0268544i | − | 0.00115670i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.8041 | −1.23839 | −0.619193 | − | 0.785239i | \(-0.712540\pi\) | ||||
−0.619193 | + | 0.785239i | \(0.712540\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 40.1359i | 1.72239i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 18.5413i | − | 0.794224i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.3286 | 1.25400 | 0.627001 | − | 0.779019i | \(-0.284282\pi\) | ||||
0.627001 | + | 0.779019i | \(0.284282\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.737579 | 0.0314791 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26.6852 | + | 11.0652i | 1.13683 | + | 0.471393i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 29.8111i | 1.26770i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 70.5725i | 2.99564i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.45427 | 0.315847 | 0.157924 | − | 0.987451i | \(-0.449520\pi\) | ||||
0.157924 | + | 0.987451i | \(0.449520\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −34.4216 | −1.45588 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 8.59936i | − | 0.363065i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.27872 | −0.138181 | −0.0690907 | − | 0.997610i | \(-0.522010\pi\) | ||||
−0.0690907 | + | 0.997610i | \(0.522010\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 76.8739i | − | 3.23411i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 23.4615i | − | 0.985291i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 6.12088i | − | 0.256601i | −0.991735 | − | 0.128300i | \(-0.959048\pi\) | ||
0.991735 | − | 0.128300i | \(-0.0409522\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.6973i | 1.82867i | 0.404953 | + | 0.914337i | \(0.367288\pi\) | ||||
−0.404953 | + | 0.914337i | \(0.632712\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 43.6113i | − | 1.82189i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.72494i | 0.0719350i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.0802 | −1.12737 | −0.563683 | − | 0.825991i | \(-0.690616\pi\) | ||||
−0.563683 | + | 0.825991i | \(0.690616\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.4496i | 0.558948i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.19235 | −0.339876 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.64742 | −0.233892 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.719241i | 0.0297370i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 19.8786i | − | 0.820478i | −0.911978 | − | 0.410239i | \(-0.865445\pi\) | ||
0.911978 | − | 0.410239i | \(-0.134555\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.8815 | + | 35.8887i | −0.613182 | + | 1.47877i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.4646 | 0.512726 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.6987 | 0.891061 | 0.445530 | − | 0.895267i | \(-0.353015\pi\) | ||||
0.445530 | + | 0.895267i | \(0.353015\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 48.6703i | − | 1.99529i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.6312i | 0.803453i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.7503 | −1.74673 | −0.873366 | − | 0.487065i | \(-0.838068\pi\) | ||||
−0.873366 | + | 0.487065i | \(0.838068\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.3839i | 0.423568i | 0.977316 | + | 0.211784i | \(0.0679274\pi\) | ||||
−0.977316 | + | 0.211784i | \(0.932073\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.442001 | −0.0179997 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.66778 | 0.149117 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.1604 | −0.493575 | −0.246787 | − | 0.969070i | \(-0.579375\pi\) | ||||
−0.246787 | + | 0.969070i | \(0.579375\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −30.1795 | −1.22294 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28.1265 | 1.13788 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.8015 | 0.476656 | 0.238328 | − | 0.971185i | \(-0.423401\pi\) | ||||
0.238328 | + | 0.971185i | \(0.423401\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.32522i | 0.295382i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.1184 | −0.930714 | −0.465357 | − | 0.885123i | \(-0.654074\pi\) | ||||
−0.465357 | + | 0.885123i | \(0.654074\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.7739i | 1.19671i | 0.801230 | + | 0.598357i | \(0.204179\pi\) | ||||
−0.801230 | + | 0.598357i | \(0.795821\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.06887i | 0.0428921i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.71301 | 0.148758 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.18372 | 0.167349 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.91688 | + | 2.86813i | 0.276234 | + | 0.114542i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 56.0694i | 2.23563i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.8991i | 1.11065i | 0.831635 | + | 0.555323i | \(0.187405\pi\) | ||||
−0.831635 | + | 0.555323i | \(0.812595\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.79066 | 0.230158 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.59108 | 0.380611 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 0.107515i | − | 0.00425990i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.177928 | 0.00703871 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 3.51931i | − | 0.139005i | −0.997582 | − | 0.0695023i | \(-0.977859\pi\) | ||
0.997582 | − | 0.0695023i | \(-0.0221411\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 14.0262i | − | 0.553139i | −0.960994 | − | 0.276569i | \(-0.910802\pi\) | ||
0.960994 | − | 0.276569i | \(-0.0891976\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 54.1711i | 2.13298i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.8561i | 0.977194i | 0.872510 | + | 0.488597i | \(0.162491\pi\) | ||||
−0.872510 | + | 0.488597i | \(0.837509\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.7855i | 0.423369i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 40.5883i | − | 1.59078i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.0746 | −0.511647 | −0.255824 | − | 0.966723i | \(-0.582347\pi\) | ||||
−0.255824 | + | 0.966723i | \(0.582347\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 46.4929i | − | 1.81663i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.365083 | 0.0142433 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.7481 | 0.808233 | 0.404116 | − | 0.914708i | \(-0.367579\pi\) | ||||
0.404116 | + | 0.914708i | \(0.367579\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.4434i | 0.561784i | 0.959739 | + | 0.280892i | \(0.0906303\pi\) | ||||
−0.959739 | + | 0.280892i | \(0.909370\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 34.4286i | − | 1.33709i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 39.1479 | + | 16.2329i | 1.51809 | + | 0.629486i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.35247 | 0.0523679 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.7595 | −0.763945 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 15.0588i | − | 0.581339i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.3974i | 0.901904i | 0.892548 | + | 0.450952i | \(0.148915\pi\) | ||||
−0.892548 | + | 0.450952i | \(0.851085\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 44.2723 | 1.70404 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 4.15282i | − | 0.159606i | −0.996811 | − | 0.0798029i | \(-0.974571\pi\) | ||
0.996811 | − | 0.0798029i | \(-0.0254291\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −42.5476 | −1.63283 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.1192 | 0.502728 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.280657 | −0.0107390 | −0.00536952 | − | 0.999986i | \(-0.501709\pi\) | ||||
−0.00536952 | + | 0.999986i | \(0.501709\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.3179 | −0.508850 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 33.4239 | 1.27520 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.6102 | −0.861378 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 21.6198i | − | 0.822455i | −0.911533 | − | 0.411228i | \(-0.865100\pi\) | ||
0.911533 | − | 0.411228i | \(-0.134900\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.129837 | 0.00493210 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.2026i | 0.804260i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.81984i | 0.220442i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −28.6249 | −1.08269 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.3334 | 0.654673 | 0.327337 | − | 0.944908i | \(-0.393849\pi\) | ||||
0.327337 | + | 0.944908i | \(0.393849\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −45.0993 | − | 18.7007i | −1.70095 | − | 0.705312i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 44.2642i | − | 1.66708i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.0802i | 0.567150i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.4277 | 1.55585 | 0.777925 | − | 0.628357i | \(-0.216272\pi\) | ||||
0.777925 | + | 0.628357i | \(0.216272\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.550827 | −0.0206576 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.81893i | 0.0681196i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.6844 | 0.549166 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 25.5328i | − | 0.953540i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.29720i | 0.0483775i | 0.999707 | + | 0.0241888i | \(0.00770028\pi\) | ||||
−0.999707 | + | 0.0241888i | \(0.992300\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 4.95448i | − | 0.184514i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26.8367i | 0.998069i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 56.0193i | − | 2.08050i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.4537i | 1.16655i | 0.812274 | + | 0.583276i | \(0.198230\pi\) | ||||
−0.812274 | + | 0.583276i | \(0.801770\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.4263 | 1.01579 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 43.0385i | 1.59184i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.3465 | −0.751516 | −0.375758 | − | 0.926718i | \(-0.622618\pi\) | ||||
−0.375758 | + | 0.926718i | \(0.622618\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.169202 | −0.00624111 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.02412i | 0.332408i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 35.2610i | − | 1.29710i | −0.761173 | − | 0.648549i | \(-0.775376\pi\) | ||
0.761173 | − | 0.648549i | \(-0.224624\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 27.6926 | + | 11.4829i | 1.01731 | + | 0.421835i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.0758 | −1.36018 | −0.680090 | − | 0.733129i | \(-0.738059\pi\) | ||||
−0.680090 | + | 0.733129i | \(0.738059\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.53330 | 0.349273 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 0.151372i | − | 0.00553842i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 42.1013i | 1.53835i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.7816 | 0.575880 | 0.287940 | − | 0.957648i | \(-0.407030\pi\) | ||||
0.287940 | + | 0.957648i | \(0.407030\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 16.0120i | − | 0.583509i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.7628 | −0.428093 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.48836 | −0.126787 | −0.0633933 | − | 0.997989i | \(-0.520192\pi\) | ||||
−0.0633933 | + | 0.997989i | \(0.520192\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.350565 | 0.0127247 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.6483 | 0.821002 | 0.410501 | − | 0.911860i | \(-0.365354\pi\) | ||||
0.410501 | + | 0.911860i | \(0.365354\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.4004 | −0.485127 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.899293 | 0.0325140 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 43.1812i | 1.55918i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.2418 | −0.369328 | −0.184664 | − | 0.982802i | \(-0.559120\pi\) | ||||
−0.184664 | + | 0.982802i | \(0.559120\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 5.06383i | − | 0.182369i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.4205i | 0.482701i | 0.970438 | + | 0.241350i | \(0.0775903\pi\) | ||||
−0.970438 | + | 0.241350i | \(0.922410\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 75.3400 | 2.70629 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 51.0050 | 1.82979 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.68118 | − | 1.94108i | −0.167721 | − | 0.0695465i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 3.63267i | − | 0.129987i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 34.7126i | − | 1.24053i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 75.1371 | 2.68176 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 40.1920 | 1.43269 | 0.716345 | − | 0.697746i | \(-0.245814\pi\) | ||||
0.716345 | + | 0.697746i | \(0.245814\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28.0321i | 0.997970i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −55.5592 | −1.97546 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 60.2898i | − | 2.14095i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 35.5828i | 1.26199i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 32.8581i | − | 1.16389i | −0.813227 | − | 0.581947i | \(-0.802291\pi\) | ||
0.813227 | − | 0.581947i | \(-0.197709\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 35.1676i | − | 1.24414i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.0686062i | 0.00242408i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 7.45373i | − | 0.263037i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.98411 | 0.0699308 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 4.52507i | − | 0.159290i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.82725 | 0.134559 | 0.0672795 | − | 0.997734i | \(-0.478568\pi\) | ||||
0.0672795 | + | 0.997734i | \(0.478568\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.7176 | −0.797723 | −0.398861 | − | 0.917011i | \(-0.630595\pi\) | ||||
−0.398861 | + | 0.917011i | \(0.630595\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 18.5156i | − | 0.649371i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 70.4052i | 2.46619i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −34.6180 | − | 14.3546i | −1.21113 | − | 0.502203i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.519818 | 0.0181639 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.6944 | −0.687339 | −0.343669 | − | 0.939091i | \(-0.611670\pi\) | ||||
−0.343669 | + | 0.939091i | \(0.611670\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 22.6781i | − | 0.790509i | −0.918572 | − | 0.395255i | \(-0.870656\pi\) | ||
0.918572 | − | 0.395255i | \(-0.129344\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 14.5204i | − | 0.505534i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.5689 | 1.23685 | 0.618425 | − | 0.785844i | \(-0.287771\pi\) | ||||
0.618425 | + | 0.785844i | \(0.287771\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 29.0453i | − | 1.00878i | −0.863475 | − | 0.504392i | \(-0.831717\pi\) | ||
0.863475 | − | 0.504392i | \(-0.168283\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −50.9067 | −1.76593 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.134430 | −0.00465772 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 89.5099 | 3.09762 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 46.6847 | 1.61366 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.10711 | 0.210841 | 0.105420 | − | 0.994428i | \(-0.466381\pi\) | ||||
0.105420 | + | 0.994428i | \(0.466381\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.9230 | −0.514586 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 33.8013i | 1.16418i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.1097 | 0.382184 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2.65082i | − | 0.0910833i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 8.40331i | − | 0.288401i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.28575 | −0.0783545 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.3492 | 1.27881 | 0.639406 | − | 0.768870i | \(-0.279180\pi\) | ||||
0.639406 | + | 0.768870i | \(0.279180\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.299940 | + | 0.723345i | −0.0102577 | + | 0.0247379i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.574397i | 0.0196210i | 0.999952 | + | 0.00981052i | \(0.00312284\pi\) | ||||
−0.999952 | + | 0.00981052i | \(0.996877\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.8875i | 0.712672i | 0.934358 | + | 0.356336i | \(0.115974\pi\) | ||||
−0.934358 | + | 0.356336i | \(0.884026\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.29417 | 0.180425 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.0812 | 1.05802 | 0.529009 | − | 0.848616i | \(-0.322564\pi\) | ||||
0.529009 | + | 0.848616i | \(0.322564\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 83.5060i | − | 2.83929i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.8438 | −0.470159 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.2460i | 0.381494i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36.1292i | 1.22419i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 0.786163i | − | 0.0266076i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 33.5686i | − | 1.13483i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.0821i | 0.948264i | 0.880454 | + | 0.474132i | \(0.157238\pi\) | ||||
−0.880454 | + | 0.474132i | \(0.842762\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 41.7502i | 1.40820i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.38646 | −0.147784 | −0.0738918 | − | 0.997266i | \(-0.523542\pi\) | ||||
−0.0738918 | + | 0.997266i | \(0.523542\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.9628i | 1.00833i | 0.863608 | + | 0.504164i | \(0.168199\pi\) | ||||
−0.863608 | + | 0.504164i | \(0.831801\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 67.9565 | 2.28433 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.2704 | −0.546307 | −0.273154 | − | 0.961970i | \(-0.588067\pi\) | ||||
−0.273154 | + | 0.961970i | \(0.588067\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 6.93178i | − | 0.232484i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 8.85066i | − | 0.296508i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.2870 | + | 11.7294i | 0.946588 | + | 0.392509i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.74477 | −0.292306 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.40353 | 0.0468625 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 59.0718i | − | 1.97015i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.2703i | 0.941820i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 39.1511 | 1.30287 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 85.6939i | 2.84856i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.2924 | 1.13866 | 0.569331 | − | 0.822109i | \(-0.307202\pi\) | ||||
0.569331 | + | 0.822109i | \(0.307202\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.278641 | −0.00924194 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.2972 | −0.705608 | −0.352804 | − | 0.935697i | \(-0.614772\pi\) | ||||
−0.352804 | + | 0.935697i | \(0.614772\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.09050 | −0.102280 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −94.8812 | −3.13668 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −33.6019 | −1.10963 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.3841i | 1.06825i | 0.845404 | + | 0.534127i | \(0.179360\pi\) | ||||
−0.845404 | + | 0.534127i | \(0.820640\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.4065 | −0.804220 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 14.5438i | − | 0.478716i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 94.6755i | 3.11291i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.0915451 | 0.00300674 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.7672 | −1.17348 | −0.586741 | − | 0.809774i | \(-0.699589\pi\) | ||||
−0.586741 | + | 0.809774i | \(0.699589\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0448362 | − | 0.108128i | 0.00146945 | − | 0.00354377i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 51.5011i | − | 1.68607i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 18.3604i | − | 0.600451i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.0421 | 1.01410 | 0.507051 | − | 0.861916i | \(-0.330735\pi\) | ||||
0.507051 | + | 0.861916i | \(0.330735\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.73294 | 0.187088 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 40.4101i | − | 1.31733i | −0.752435 | − | 0.658667i | \(-0.771121\pi\) | ||
0.752435 | − | 0.658667i | \(-0.228879\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.237254 | −0.00772606 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 50.9242i | − | 1.65657i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 34.2044i | − | 1.11149i | −0.831352 | − | 0.555747i | \(-0.812432\pi\) | ||
0.831352 | − | 0.555747i | \(-0.187568\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 29.8419i | − | 0.968710i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.23330i | 0.234556i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 28.6127i | − | 0.926857i | −0.886134 | − | 0.463429i | \(-0.846619\pi\) | ||
0.886134 | − | 0.463429i | \(-0.153381\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 93.1144i | − | 3.01311i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.3850 | −0.368024 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.62524i | 0.310815i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 48.4453 | 1.56275 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.777916 | −0.0250680 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 28.7163i | 0.924410i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 42.8423i | − | 1.37771i | −0.724897 | − | 0.688857i | \(-0.758113\pi\) | ||
0.724897 | − | 0.688857i | \(-0.241887\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.3575 | − | 34.6250i | 0.461229 | − | 1.11232i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.5461 | 0.723537 | 0.361769 | − | 0.932268i | \(-0.382173\pi\) | ||||
0.361769 | + | 0.932268i | \(0.382173\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.3238 | 0.491258 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 58.1341i | − | 1.86178i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.6562i | 1.55665i | 0.627861 | + | 0.778325i | \(0.283931\pi\) | ||||
−0.627861 | + | 0.778325i | \(0.716069\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.40070 | 0.0447666 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 0.247603i | − | 0.00790535i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −44.5854 | −1.42205 | −0.711027 | − | 0.703165i | \(-0.751769\pi\) | ||||
−0.711027 | + | 0.703165i | \(0.751769\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.6131 | 0.847965 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −31.9911 | −1.01829 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.75453 | −0.0557907 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.7244 | −1.61131 | −0.805656 | − | 0.592384i | \(-0.798187\pi\) | ||||
−0.805656 | + | 0.592384i | \(0.798187\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.4691 | 0.903440 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 41.9146i | 1.32878i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.4545 | −0.774481 | −0.387240 | − | 0.921979i | \(-0.626572\pi\) | ||||
−0.387240 | + | 0.921979i | \(0.626572\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 58.6660i | 1.85611i |
(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.a.1519.9 | ✓ | 36 | |
4.3 | odd | 2 | inner | 3344.2.o.a.1519.28 | yes | 36 | |
19.18 | odd | 2 | inner | 3344.2.o.a.1519.27 | yes | 36 | |
76.75 | even | 2 | inner | 3344.2.o.a.1519.10 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3344.2.o.a.1519.9 | ✓ | 36 | 1.1 | even | 1 | trivial | |
3344.2.o.a.1519.10 | yes | 36 | 76.75 | even | 2 | inner | |
3344.2.o.a.1519.27 | yes | 36 | 19.18 | odd | 2 | inner | |
3344.2.o.a.1519.28 | yes | 36 | 4.3 | odd | 2 | inner |