Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(289,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.t (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.7 | ||
Character | \(\chi\) | \(=\) | 1512.289 |
Dual form | 1512.2.t.c.361.7 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.468169 | 0.209372 | 0.104686 | − | 0.994505i | \(-0.466616\pi\) | ||||
0.104686 | + | 0.994505i | \(0.466616\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.39007 | + | 1.13471i | −0.903361 | + | 0.428881i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.34859 | 0.406614 | 0.203307 | − | 0.979115i | \(-0.434831\pi\) | ||||
0.203307 | + | 0.979115i | \(0.434831\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.16486 | − | 5.48171i | −0.877775 | − | 1.52035i | −0.853777 | − | 0.520640i | \(-0.825694\pi\) |
−0.0239988 | − | 0.999712i | \(-0.507640\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.47120 | + | 4.28024i | 0.599353 | + | 1.03811i | 0.992917 | + | 0.118813i | \(0.0379089\pi\) |
−0.393563 | + | 0.919298i | \(0.628758\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.38910 | − | 4.13804i | 0.548097 | − | 0.949332i | −0.450308 | − | 0.892873i | \(-0.648686\pi\) |
0.998405 | − | 0.0564585i | \(-0.0179809\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.62799 | −1.59055 | −0.795273 | − | 0.606252i | \(-0.792672\pi\) | ||||
−0.795273 | + | 0.606252i | \(0.792672\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.78082 | −0.956164 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.80565 | − | 3.12747i | 0.335300 | − | 0.580757i | −0.648242 | − | 0.761434i | \(-0.724496\pi\) |
0.983542 | + | 0.180677i | \(0.0578290\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.24939 | + | 5.62810i | −0.583607 | + | 1.01084i | 0.411440 | + | 0.911437i | \(0.365026\pi\) |
−0.995047 | + | 0.0994007i | \(0.968307\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.11896 | + | 0.531237i | −0.189138 | + | 0.0897954i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.24214 | − | 9.07966i | 0.861803 | − | 1.49269i | −0.00838383 | − | 0.999965i | \(-0.502669\pi\) |
0.870187 | − | 0.492722i | \(-0.163998\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.0251630 | + | 0.0435837i | 0.00392981 | + | 0.00680662i | 0.867984 | − | 0.496593i | \(-0.165416\pi\) |
−0.864054 | + | 0.503399i | \(0.832082\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.431869 | + | 0.748019i | −0.0658594 | + | 0.114072i | −0.897075 | − | 0.441879i | \(-0.854312\pi\) |
0.831215 | + | 0.555950i | \(0.187646\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.49417 | − | 9.51619i | −0.801408 | − | 1.38808i | −0.918690 | − | 0.394980i | \(-0.870751\pi\) |
0.117282 | − | 0.993099i | \(-0.462582\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.42486 | − | 5.42408i | 0.632123 | − | 0.774868i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.84976 | − | 10.1321i | −0.803526 | − | 1.39175i | −0.917282 | − | 0.398239i | \(-0.869622\pi\) |
0.113756 | − | 0.993509i | \(-0.463712\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.631366 | 0.0851334 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.93892 | + | 3.35831i | −0.252426 | + | 0.437215i | −0.964193 | − | 0.265201i | \(-0.914562\pi\) |
0.711767 | + | 0.702416i | \(0.247895\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.87231 | − | 3.24294i | −0.239725 | − | 0.415216i | 0.720910 | − | 0.693028i | \(-0.243724\pi\) |
−0.960635 | + | 0.277813i | \(0.910391\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.48169 | − | 2.56637i | −0.183781 | − | 0.318318i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.32436 | − | 2.29385i | 0.161796 | − | 0.280239i | −0.773717 | − | 0.633532i | \(-0.781605\pi\) |
0.935513 | + | 0.353293i | \(0.114938\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.04562 | 0.836161 | 0.418081 | − | 0.908410i | \(-0.362703\pi\) | ||||
0.418081 | + | 0.908410i | \(0.362703\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.30117 | − | 5.71779i | −0.386373 | − | 0.669217i | 0.605586 | − | 0.795780i | \(-0.292939\pi\) |
−0.991959 | + | 0.126563i | \(0.959605\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.22321 | + | 1.53026i | −0.367319 | + | 0.174389i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.58951 | − | 2.75311i | −0.178834 | − | 0.309749i | 0.762648 | − | 0.646814i | \(-0.223899\pi\) |
−0.941481 | + | 0.337065i | \(0.890566\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.90272 | + | 8.49176i | −0.538143 | + | 0.932092i | 0.460861 | + | 0.887472i | \(0.347541\pi\) |
−0.999004 | + | 0.0446192i | \(0.985793\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.15694 | + | 2.00388i | 0.125488 | + | 0.217351i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.30709 | + | 9.19214i | −0.562550 | + | 0.974365i | 0.434723 | + | 0.900564i | \(0.356846\pi\) |
−0.997273 | + | 0.0738011i | \(0.976487\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.7844 | + | 9.51045i | 1.44500 | + | 0.996966i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.11850 | − | 1.93730i | 0.114756 | − | 0.198763i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.97792 | − | 12.0861i | 0.708500 | − | 1.22716i | −0.256913 | − | 0.966434i | \(-0.582706\pi\) |
0.965413 | − | 0.260724i | \(-0.0839611\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.24945 | −0.422836 | −0.211418 | − | 0.977396i | \(-0.567808\pi\) | ||||
−0.211418 | + | 0.977396i | \(0.567808\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.95640 | −0.882501 | −0.441250 | − | 0.897384i | \(-0.645465\pi\) | ||||
−0.441250 | + | 0.897384i | \(0.645465\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.810731 | − | 1.40423i | 0.0783763 | − | 0.135752i | −0.824173 | − | 0.566338i | \(-0.808360\pi\) |
0.902550 | + | 0.430586i | \(0.141693\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.97644 | + | 5.15534i | 0.285091 | + | 0.493792i | 0.972631 | − | 0.232354i | \(-0.0746428\pi\) |
−0.687540 | + | 0.726146i | \(0.741309\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.14346 | − | 7.17669i | −0.389784 | − | 0.675126i | 0.602636 | − | 0.798016i | \(-0.294117\pi\) |
−0.992420 | + | 0.122890i | \(0.960784\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.57119 | −0.333015 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.7632 | − | 7.42597i | −0.986658 | − | 0.680738i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.18132 | −0.834665 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.57908 | −0.409565 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.12368 | 0.720860 | 0.360430 | − | 0.932786i | \(-0.382630\pi\) | ||||
0.360430 | + | 0.932786i | \(0.382630\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.4965 | −1.70341 | −0.851707 | − | 0.524018i | \(-0.824432\pi\) | ||||
−0.851707 | + | 0.524018i | \(0.824432\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.01463 | + | 12.6011i | −0.0879795 | + | 1.09266i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.1035 | 1.29038 | 0.645189 | − | 0.764023i | \(-0.276779\pi\) | ||||
0.645189 | + | 0.764023i | \(0.276779\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.18826 | − | 3.79017i | −0.185605 | − | 0.321478i | 0.758175 | − | 0.652051i | \(-0.226091\pi\) |
−0.943780 | + | 0.330573i | \(0.892758\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.26809 | − | 7.39255i | −0.356916 | − | 0.618196i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.845348 | − | 1.46419i | 0.0702023 | − | 0.121594i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.7564 | 0.963121 | 0.481561 | − | 0.876413i | \(-0.340070\pi\) | ||||
0.481561 | + | 0.876413i | \(0.340070\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.14305 | −0.418536 | −0.209268 | − | 0.977858i | \(-0.567108\pi\) | ||||
−0.209268 | + | 0.977858i | \(0.567108\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.52126 | + | 2.63490i | −0.122191 | + | 0.211641i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.04447 | − | 10.4693i | 0.482401 | − | 0.835544i | −0.517395 | − | 0.855747i | \(-0.673098\pi\) |
0.999796 | + | 0.0202033i | \(0.00643136\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.2314 | − | 8.65557i | 1.43684 | − | 0.682154i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.74663 | + | 4.75730i | −0.215133 | + | 0.372621i | −0.953314 | − | 0.301982i | \(-0.902352\pi\) |
0.738181 | + | 0.674603i | \(0.235685\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.59378 | + | 6.22461i | 0.278095 | + | 0.481675i | 0.970911 | − | 0.239440i | \(-0.0769637\pi\) |
−0.692816 | + | 0.721114i | \(0.743630\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.5327 | + | 23.4394i | −1.04098 | + | 1.80303i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.97951 | − | 6.89271i | −0.302557 | − | 0.524043i | 0.674158 | − | 0.738587i | \(-0.264507\pi\) |
−0.976714 | + | 0.214544i | \(0.931173\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.4265 | − | 5.42485i | 0.863761 | − | 0.410080i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.168821 | − | 0.292406i | −0.0126182 | − | 0.0218554i | 0.859647 | − | 0.510888i | \(-0.170683\pi\) |
−0.872266 | + | 0.489032i | \(0.837350\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.05801 | 0.524618 | 0.262309 | − | 0.964984i | \(-0.415516\pi\) | ||||
0.262309 | + | 0.964984i | \(0.415516\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.45421 | − | 4.25082i | 0.180437 | − | 0.312526i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.33262 | + | 5.77227i | 0.243705 | + | 0.422110i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.85934 | + | 15.3448i | 0.641039 | + | 1.11031i | 0.985201 | + | 0.171402i | \(0.0548298\pi\) |
−0.344162 | + | 0.938910i | \(0.611837\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.40121 | − | 14.5513i | 0.604732 | − | 1.04743i | −0.387362 | − | 0.921928i | \(-0.626614\pi\) |
0.992094 | − | 0.125499i | \(-0.0400531\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.97545 | −0.425733 | −0.212867 | − | 0.977081i | \(-0.568280\pi\) | ||||
−0.212867 | + | 0.977081i | \(0.568280\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.26093 | + | 10.8443i | 0.443826 | + | 0.768729i | 0.997970 | − | 0.0636923i | \(-0.0202876\pi\) |
−0.554144 | + | 0.832421i | \(0.686954\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.766842 | + | 9.52376i | −0.0538217 | + | 0.668437i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0117806 | + | 0.0204045i | 0.000822790 | + | 0.00142511i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.22190 | − | 5.58050i | 0.222864 | − | 0.386011i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.17688 | + | 2.03842i | 0.0810198 | + | 0.140330i | 0.903688 | − | 0.428191i | \(-0.140849\pi\) |
−0.822668 | + | 0.568521i | \(0.807516\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.202188 | + | 0.350199i | −0.0137891 | + | 0.0238834i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.37999 | − | 17.1387i | 0.0936795 | − | 1.16345i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.6420 | − | 27.0928i | 1.05220 | − | 1.82246i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.30709 | − | 9.19215i | 0.355389 | − | 0.615552i | −0.631795 | − | 0.775135i | \(-0.717682\pi\) |
0.987184 | + | 0.159583i | \(0.0510150\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.27550 | −0.0846578 | −0.0423289 | − | 0.999104i | \(-0.513478\pi\) | ||||
−0.0423289 | + | 0.999104i | \(0.513478\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.4663 | −0.889876 | −0.444938 | − | 0.895561i | \(-0.646774\pi\) | ||||
−0.444938 | + | 0.895561i | \(0.646774\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.98509 | + | 17.2947i | −0.654145 | + | 1.13301i | 0.327963 | + | 0.944691i | \(0.393638\pi\) |
−0.982107 | + | 0.188321i | \(0.939695\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.57220 | − | 4.45519i | −0.167792 | − | 0.290624i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.1092 | + | 24.4379i | 0.912650 | + | 1.58076i | 0.810305 | + | 0.586008i | \(0.199301\pi\) |
0.102345 | + | 0.994749i | \(0.467365\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.3524 | −1.11777 | −0.558884 | − | 0.829246i | \(-0.688770\pi\) | ||||
−0.558884 | + | 0.829246i | \(0.688770\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.07158 | − | 2.53939i | 0.132349 | − | 0.162235i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.2447 | −1.92442 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.29051 | −0.397054 | −0.198527 | − | 0.980095i | \(-0.563616\pi\) | ||||
−0.198527 | + | 0.980095i | \(0.563616\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.2870 | −0.646738 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.13637 | 0.382777 | 0.191388 | − | 0.981514i | \(-0.438701\pi\) | ||||
0.191388 | + | 0.981514i | \(0.438701\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.22629 | + | 27.6493i | −0.138335 | + | 1.71805i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.87914 | −0.362523 | −0.181262 | − | 0.983435i | \(-0.558018\pi\) | ||||
−0.181262 | + | 0.983435i | \(0.558018\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.73868 | − | 4.74352i | −0.168235 | − | 0.291392i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.4633 | + | 26.7832i | 0.942812 | + | 1.63300i | 0.760074 | + | 0.649837i | \(0.225163\pi\) |
0.182738 | + | 0.983162i | \(0.441504\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.44528 | − | 9.43150i | 0.330777 | − | 0.572923i | −0.651887 | − | 0.758316i | \(-0.726022\pi\) |
0.982664 | + | 0.185393i | \(0.0593558\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.44734 | −0.388789 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.5900 | 1.17705 | 0.588524 | − | 0.808480i | \(-0.299709\pi\) | ||||
0.588524 | + | 0.808480i | \(0.299709\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.142477 | − | 0.246777i | 0.00849944 | − | 0.0147215i | −0.861744 | − | 0.507343i | \(-0.830628\pi\) |
0.870244 | + | 0.492621i | \(0.163961\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.42135 | + | 2.46185i | −0.0844903 | + | 0.146342i | −0.905174 | − | 0.425041i | \(-0.860260\pi\) |
0.820684 | + | 0.571383i | \(0.193593\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.109596 | − | 0.0756152i | −0.00646926 | − | 0.00446342i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.71364 | + | 6.43221i | −0.218449 | + | 0.378365i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.45979 | + | 2.52842i | 0.0852816 | + | 0.147712i | 0.905511 | − | 0.424322i | \(-0.139488\pi\) |
−0.820230 | + | 0.572034i | \(0.806154\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.907743 | + | 1.57226i | −0.0528509 | + | 0.0915404i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 24.1415 | + | 41.8144i | 1.39614 | + | 2.41819i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.183411 | − | 2.27786i | 0.0105716 | − | 0.131294i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.876558 | − | 1.51824i | −0.0501916 | − | 0.0869344i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.12553 | −0.235457 | −0.117728 | − | 0.993046i | \(-0.537561\pi\) | ||||
−0.117728 | + | 0.993046i | \(0.537561\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.69583 | − | 13.3296i | 0.436390 | − | 0.755850i | −0.561018 | − | 0.827804i | \(-0.689590\pi\) |
0.997408 | + | 0.0719535i | \(0.0229233\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.3620 | + | 17.9475i | 0.585694 | + | 1.01445i | 0.994789 | + | 0.101959i | \(0.0325112\pi\) |
−0.409095 | + | 0.912492i | \(0.634156\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.244146 | − | 0.422873i | −0.0137126 | − | 0.0237509i | 0.859088 | − | 0.511828i | \(-0.171032\pi\) |
−0.872800 | + | 0.488078i | \(0.837698\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.43507 | − | 4.21766i | 0.136338 | − | 0.236144i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.6157 | 1.31402 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.1306 | + | 26.2070i | 0.839297 | + | 1.45370i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 23.9296 | + | 16.5100i | 1.31928 | + | 0.910228i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.47864 | + | 16.4175i | 0.520993 | + | 0.902387i | 0.999702 | + | 0.0244131i | \(0.00777169\pi\) |
−0.478709 | + | 0.877974i | \(0.658895\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.620023 | − | 1.07391i | 0.0338755 | − | 0.0586740i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.6202 | + | 20.1268i | 0.632993 | + | 1.09638i | 0.986937 | + | 0.161109i | \(0.0515071\pi\) |
−0.353944 | + | 0.935267i | \(0.615160\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.38208 | + | 7.58998i | −0.237303 | + | 0.411020i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.42096 | + | 17.9849i | −0.238709 | + | 0.971091i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.09439 | − | 15.7519i | 0.488212 | − | 0.845609i | −0.511696 | − | 0.859167i | \(-0.670982\pi\) |
0.999908 | + | 0.0135582i | \(0.00431583\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.40155 | + | 16.2840i | −0.503253 | + | 0.871661i | 0.496740 | + | 0.867900i | \(0.334530\pi\) |
−0.999993 | + | 0.00376081i | \(0.998803\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.9199 | 0.634435 | 0.317217 | − | 0.948353i | \(-0.397252\pi\) | ||||
0.317217 | + | 0.948353i | \(0.397252\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.29854 | 0.175068 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.3849 | − | 30.1115i | 0.917540 | − | 1.58923i | 0.114400 | − | 0.993435i | \(-0.463505\pi\) |
0.803140 | − | 0.595791i | \(-0.203161\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.91559 | − | 3.31790i | −0.100821 | − | 0.174626i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.54551 | − | 2.67689i | −0.0808954 | − | 0.140115i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.8861 | −1.50784 | −0.753922 | − | 0.656964i | \(-0.771840\pi\) | ||||
−0.753922 | + | 0.656964i | \(0.771840\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.4783 | + | 17.5786i | 1.32277 | + | 0.912634i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.3094 | 0.740915 | 0.370457 | − | 0.928849i | \(-0.379201\pi\) | ||||
0.370457 | + | 0.928849i | \(0.379201\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −22.8585 | −1.17727 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.15511 | 0.0593340 | 0.0296670 | − | 0.999560i | \(-0.490555\pi\) | ||||
0.0296670 | + | 0.999560i | \(0.490555\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −33.8262 | −1.72844 | −0.864219 | − | 0.503115i | \(-0.832187\pi\) | ||||
−0.864219 | + | 0.503115i | \(0.832187\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.50901 | + | 0.716418i | −0.0769062 | + | 0.0365121i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.3216 | −0.979644 | −0.489822 | − | 0.871822i | \(-0.662938\pi\) | ||||
−0.489822 | + | 0.871822i | \(0.662938\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.8503 | − | 32.6496i | −0.953299 | − | 1.65116i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.744159 | − | 1.28892i | −0.0374427 | − | 0.0648526i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.18190 | + | 10.7074i | −0.310261 | + | 0.537387i | −0.978419 | − | 0.206632i | \(-0.933750\pi\) |
0.668158 | + | 0.744019i | \(0.267083\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.5136 | 1.52378 | 0.761889 | − | 0.647708i | \(-0.224272\pi\) | ||||
0.761889 | + | 0.647708i | \(0.224272\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 41.1355 | 2.04910 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.06948 | − | 12.2447i | 0.350421 | − | 0.606947i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.62723 | − | 4.55050i | 0.129908 | − | 0.225008i | −0.793733 | − | 0.608267i | \(-0.791865\pi\) |
0.923641 | + | 0.383259i | \(0.125198\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.823443 | − | 10.2267i | 0.0405190 | − | 0.503224i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.29530 | + | 3.97558i | −0.112672 | + | 0.195154i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.2824 | − | 26.4699i | −0.746594 | − | 1.29314i | −0.949446 | − | 0.313930i | \(-0.898354\pi\) |
0.202852 | − | 0.979209i | \(-0.434979\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.11608 | − | 5.39721i | 0.151869 | − | 0.263044i | −0.780046 | − | 0.625722i | \(-0.784804\pi\) |
0.931914 | + | 0.362678i | \(0.118138\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.8143 | − | 20.4630i | −0.573080 | − | 0.992604i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.15475 | + | 5.62631i | 0.394636 | + | 0.272276i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.8142 | − | 25.6590i | −0.713576 | − | 1.23595i | −0.963506 | − | 0.267686i | \(-0.913741\pi\) |
0.249930 | − | 0.968264i | \(-0.419592\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.36815 | 0.354091 | 0.177045 | − | 0.984203i | \(-0.443346\pi\) | ||||
0.177045 | + | 0.984203i | \(0.443346\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18.2240 | + | 31.5649i | −0.871773 | + | 1.50996i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.22135 | − | 9.04364i | −0.249201 | − | 0.431629i | 0.714103 | − | 0.700041i | \(-0.246835\pi\) |
−0.963304 | + | 0.268411i | \(0.913501\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.83332 | + | 4.90745i | 0.134615 | + | 0.233160i | 0.925450 | − | 0.378869i | \(-0.123687\pi\) |
−0.790835 | + | 0.612029i | \(0.790354\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.48461 | + | 4.30348i | −0.117782 | + | 0.204004i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.4794 | −0.541748 | −0.270874 | − | 0.962615i | \(-0.587313\pi\) | ||||
−0.270874 | + | 0.962615i | \(0.587313\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0339345 | + | 0.0587763i | 0.00159791 | + | 0.00276767i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.45343 | + | 4.45250i | 0.302541 | + | 0.208736i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.79361 | − | 16.9630i | −0.458126 | − | 0.793497i | 0.540736 | − | 0.841192i | \(-0.318146\pi\) |
−0.998862 | + | 0.0476953i | \(0.984812\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.3028 | + | 29.9693i | −0.805871 | + | 1.39581i | 0.109830 | + | 0.993950i | \(0.464969\pi\) |
−0.915701 | + | 0.401859i | \(0.868364\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.91882 | + | 11.9837i | 0.321545 | + | 0.556932i | 0.980807 | − | 0.194981i | \(-0.0624646\pi\) |
−0.659262 | + | 0.751913i | \(0.729131\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.71088 | + | 6.42743i | −0.171719 | + | 0.297426i | −0.939021 | − | 0.343860i | \(-0.888265\pi\) |
0.767302 | + | 0.641286i | \(0.221599\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.562442 | + | 6.98523i | −0.0259712 | + | 0.322548i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.582412 | + | 1.00877i | −0.0267793 | + | 0.0463832i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.4218 | + | 19.7832i | −0.524070 | + | 0.907716i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.79154 | 0.356005 | 0.178002 | − | 0.984030i | \(-0.443037\pi\) | ||||
0.178002 | + | 0.984030i | \(0.443037\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −66.3627 | −3.02588 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.26684 | − | 5.65834i | 0.148340 | − | 0.256932i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.04434 | − | 1.80886i | −0.0473238 | − | 0.0819672i | 0.841393 | − | 0.540423i | \(-0.181736\pi\) |
−0.888717 | + | 0.458456i | \(0.848403\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.8767 | + | 29.2312i | 0.761633 | + | 1.31919i | 0.942008 | + | 0.335590i | \(0.108936\pi\) |
−0.180375 | + | 0.983598i | \(0.557731\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.8484 | 0.803853 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.8395 | + | 7.99475i | −0.755356 | + | 0.358613i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 41.8196 | 1.87210 | 0.936052 | − | 0.351862i | \(-0.114451\pi\) | ||||
0.936052 | + | 0.351862i | \(0.114451\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.54978 | −0.292040 | −0.146020 | − | 0.989282i | \(-0.546646\pi\) | ||||
−0.146020 | + | 0.989282i | \(0.546646\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.98946 | −0.0885299 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.6131 | 0.559064 | 0.279532 | − | 0.960136i | \(-0.409821\pi\) | ||||
0.279532 | + | 0.960136i | \(0.409821\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.3781 | + | 9.92004i | 0.636048 | + | 0.438837i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.19311 | −0.184771 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.40936 | − | 12.8334i | −0.325863 | − | 0.564412i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.2688 | − | 17.7861i | −0.449883 | − | 0.779221i | 0.548495 | − | 0.836154i | \(-0.315201\pi\) |
−0.998378 | + | 0.0569331i | \(0.981868\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.4579 | − | 25.0419i | 0.632202 | − | 1.09501i | −0.354899 | − | 0.934905i | \(-0.615485\pi\) |
0.987101 | − | 0.160101i | \(-0.0511820\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −32.1195 | −1.39915 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35.1862 | 1.52983 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.159275 | − | 0.275873i | 0.00689897 | − | 0.0119494i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.379559 | − | 0.657416i | 0.0164098 | − | 0.0284226i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.96730 | − | 7.31483i | 0.257030 | − | 0.315072i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.29262 | − | 5.70299i | 0.141561 | − | 0.245191i | −0.786524 | − | 0.617560i | \(-0.788121\pi\) |
0.928085 | + | 0.372369i | \(0.121455\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.39348 | + | 2.41357i | 0.0596900 | + | 0.103386i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.46777 | − | 7.73840i | 0.191028 | − | 0.330870i | −0.754563 | − | 0.656227i | \(-0.772151\pi\) |
0.945591 | + | 0.325357i | \(0.105485\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.62774 | − | 14.9437i | −0.367554 | − | 0.636622i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.92302 | + | 4.77649i | 0.294397 | + | 0.203117i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.93523 | + | 5.08396i | 0.124370 | + | 0.215414i | 0.921486 | − | 0.388411i | \(-0.126976\pi\) |
−0.797117 | + | 0.603825i | \(0.793642\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.46723 | 0.231239 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.7986 | − | 23.8998i | 0.581541 | − | 1.00726i | −0.413756 | − | 0.910388i | \(-0.635783\pi\) |
0.995297 | − | 0.0968707i | \(-0.0308833\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.93984 | − | 3.35991i | −0.0816098 | − | 0.141352i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.9601 | − | 24.1796i | −0.585238 | − | 1.01366i | −0.994846 | − | 0.101400i | \(-0.967668\pi\) |
0.409608 | − | 0.912262i | \(-0.365665\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.8987 | − | 27.5373i | 0.665339 | − | 1.15240i | −0.313854 | − | 0.949471i | \(-0.601620\pi\) |
0.979193 | − | 0.202930i | \(-0.0650463\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.4680 | 1.52082 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.7476 | + | 23.8115i | 0.572320 | + | 0.991287i | 0.996327 | + | 0.0856281i | \(0.0272897\pi\) |
−0.424007 | + | 0.905659i | \(0.639377\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.08214 | − | 25.8591i | 0.0863817 | − | 1.07281i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.88889 | − | 13.6640i | −0.326725 | − | 0.565904i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.12422 | − | 12.3395i | 0.294048 | − | 0.509306i | −0.680715 | − | 0.732548i | \(-0.738331\pi\) |
0.974763 | + | 0.223242i | \(0.0716641\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.5262 | + | 26.8922i | 0.639747 | + | 1.10807i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.4636 | + | 26.7838i | −0.635015 | + | 1.09988i | 0.351498 | + | 0.936189i | \(0.385673\pi\) |
−0.986512 | + | 0.163689i | \(0.947661\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.03898 | − | 3.47661i | −0.206578 | − | 0.142527i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.2657 | − | 31.6372i | 0.746318 | − | 1.29266i | −0.203258 | − | 0.979125i | \(-0.565153\pi\) |
0.949576 | − | 0.313536i | \(-0.101514\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.11575 | − | 12.3248i | 0.290257 | − | 0.502741i | −0.683613 | − | 0.729845i | \(-0.739592\pi\) |
0.973871 | + | 0.227104i | \(0.0729257\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.29841 | −0.174755 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.3457 | −1.19111 | −0.595553 | − | 0.803316i | \(-0.703067\pi\) | ||||
−0.595553 | + | 0.803316i | \(0.703067\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −34.7766 | + | 60.2349i | −1.40691 | + | 2.43684i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.79264 | − | 6.56905i | −0.153183 | − | 0.265321i | 0.779213 | − | 0.626760i | \(-0.215619\pi\) |
−0.932396 | + | 0.361438i | \(0.882286\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.4367 | + | 18.0769i | 0.420165 | + | 0.727748i | 0.995955 | − | 0.0898500i | \(-0.0286388\pi\) |
−0.575790 | + | 0.817598i | \(0.695305\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.2600 | −1.01528 | −0.507642 | − | 0.861568i | \(-0.669483\pi\) | ||||
−0.507642 | + | 0.861568i | \(0.669483\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.25387 | − | 27.9919i | 0.0902995 | − | 1.12147i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.7603 | 0.870412 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 51.8175 | 2.06610 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.0114 | −1.35397 | −0.676986 | − | 0.735996i | \(-0.736714\pi\) | ||||
−0.676986 | + | 0.735996i | \(0.736714\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.80326 | 0.150928 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −43.7373 | − | 7.08931i | −1.73293 | − | 0.280889i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.29894 | −0.209296 | −0.104648 | − | 0.994509i | \(-0.533372\pi\) | ||||
−0.104648 | + | 0.994509i | \(0.533372\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.4304 | + | 33.6544i | 0.766260 | + | 1.32720i | 0.939578 | + | 0.342335i | \(0.111218\pi\) |
−0.173318 | + | 0.984866i | \(0.555449\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.11420 | − | 7.12601i | −0.161746 | − | 0.280152i | 0.773749 | − | 0.633492i | \(-0.218379\pi\) |
−0.935495 | + | 0.353340i | \(0.885046\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.61480 | + | 4.52897i | −0.102640 | + | 0.177778i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −42.0328 | −1.64487 | −0.822436 | − | 0.568858i | \(-0.807385\pi\) | ||||
−0.822436 | + | 0.568858i | \(0.807385\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.12764 | −0.356647 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.33484 | + | 12.7043i | −0.285725 | + | 0.494890i | −0.972785 | − | 0.231711i | \(-0.925568\pi\) |
0.687060 | + | 0.726601i | \(0.258901\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.93303 | + | 5.08015i | −0.114081 | + | 0.197595i | −0.917412 | − | 0.397938i | \(-0.869726\pi\) |
0.803331 | + | 0.595533i | \(0.203059\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.475018 | + | 5.89947i | −0.0184204 | + | 0.228771i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.7734 | + | 23.8563i | −0.533310 | + | 0.923720i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.52497 | − | 4.37338i | −0.0974754 | − | 0.168832i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.42591 | − | 16.3261i | 0.363342 | − | 0.629327i | −0.625167 | − | 0.780491i | \(-0.714969\pi\) |
0.988509 | + | 0.151165i | \(0.0483023\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.9572 | + | 25.9067i | 0.574852 | + | 0.995674i | 0.996058 | + | 0.0887082i | \(0.0282739\pi\) |
−0.421205 | + | 0.906965i | \(0.638393\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.96346 | + | 36.8045i | −0.113727 | + | 1.41243i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.8525 | − | 22.2612i | −0.491788 | − | 0.851802i | 0.508167 | − | 0.861258i | \(-0.330323\pi\) |
−0.999955 | + | 0.00945677i | \(0.996990\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.07099 | 0.270169 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −37.0274 | + | 64.1333i | −1.41063 | + | 2.44328i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.2010 | − | 33.2571i | −0.730440 | − | 1.26516i | −0.956695 | − | 0.291092i | \(-0.905982\pi\) |
0.226255 | − | 0.974068i | \(-0.427352\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.02447 | − | 1.77444i | −0.0388605 | − | 0.0673084i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.124366 | + | 0.215408i | −0.00471069 | + | 0.00815915i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.5694 | −0.436972 | −0.218486 | − | 0.975840i | \(-0.570112\pi\) | ||||
−0.218486 | + | 0.975840i | \(0.570112\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.0480 | − | 43.3844i | −0.944703 | − | 1.63627i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.1565 | − | 4.82190i | 0.381974 | − | 0.181346i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.0275 | − | 45.0810i | −0.977483 | − | 1.69305i | −0.671484 | − | 0.741019i | \(-0.734343\pi\) |
−0.305999 | − | 0.952032i | \(-0.598990\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.7863 | − | 42.9311i | 0.928254 | − | 1.60778i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.99819 | − | 3.46096i | −0.0747280 | − | 0.129433i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.416175 | + | 0.720836i | −0.0155207 | + | 0.0268827i | −0.873681 | − | 0.486498i | \(-0.838274\pi\) |
0.858161 | + | 0.513381i | \(0.171607\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.4064 | − | 10.1629i | 0.797217 | − | 0.378488i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.63247 | + | 14.9519i | −0.320602 | + | 0.555299i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.7029 | − | 18.5379i | 0.396948 | − | 0.687534i | −0.596400 | − | 0.802687i | \(-0.703403\pi\) |
0.993348 | + | 0.115154i | \(0.0367361\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.26894 | −0.157892 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.45240 | −0.275261 | −0.137630 | − | 0.990484i | \(-0.543949\pi\) | ||||
−0.137630 | + | 0.990484i | \(0.543949\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.78601 | − | 3.09346i | 0.0657885 | − | 0.113949i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.9473 | − | 31.0857i | −0.660203 | − | 1.14351i | −0.980562 | − | 0.196210i | \(-0.937137\pi\) |
0.320358 | − | 0.947296i | \(-0.396197\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.8379 | − | 29.1641i | −0.617723 | − | 1.06993i | −0.989900 | − | 0.141766i | \(-0.954722\pi\) |
0.372177 | − | 0.928162i | \(-0.378611\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.50398 | 0.201650 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.344310 | + | 4.27615i | −0.0125808 | + | 0.156247i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.0338 | 0.548590 | 0.274295 | − | 0.961646i | \(-0.411555\pi\) | ||||
0.274295 | + | 0.961646i | \(0.411555\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.40782 | −0.0876295 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.2548 | −1.24501 | −0.622507 | − | 0.782615i | \(-0.713886\pi\) | ||||
−0.622507 | + | 0.782615i | \(0.713886\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.2086 | −1.53006 | −0.765031 | − | 0.643993i | \(-0.777276\pi\) | ||||
−0.765031 | + | 0.643993i | \(0.777276\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.9637 | − | 8.94423i | −0.469318 | − | 0.323803i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.5457 | 0.886294 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.2741 | + | 38.5799i | 0.803226 | + | 1.39123i | 0.917482 | + | 0.397777i | \(0.130218\pi\) |
−0.114256 | + | 0.993451i | \(0.536448\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.61003 | + | 16.6451i | 0.345649 | + | 0.598681i | 0.985471 | − | 0.169841i | \(-0.0543256\pi\) |
−0.639823 | + | 0.768523i | \(0.720992\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.5347 | − | 26.9069i | 0.558024 | − | 0.966526i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.240468 | 0.00861566 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.50162 | 0.339995 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.82984 | − | 4.90142i | 0.101001 | − | 0.174939i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.1751 | − | 34.9443i | 0.719165 | − | 1.24563i | −0.242166 | − | 0.970235i | \(-0.577858\pi\) |
0.961331 | − | 0.275396i | \(-0.0888089\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.0466 | + | 12.4512i | 0.641665 | + | 0.442712i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.8512 | + | 20.5269i | −0.420849 | + | 0.728932i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.4965 | − | 38.9651i | −0.796867 | − | 1.38021i | −0.921647 | − | 0.388029i | \(-0.873156\pi\) |
0.124780 | − | 0.992184i | \(-0.460177\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.1544 | − | 47.0328i | 0.960653 | − | 1.66390i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.45191 | − | 7.71093i | −0.157104 | − | 0.272113i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.53539 | − | 4.05227i | 0.300833 | − | 0.142824i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.8858 | − | 29.2470i | −0.593672 | − | 1.02827i | −0.993733 | − | 0.111782i | \(-0.964344\pi\) |
0.400061 | − | 0.916489i | \(-0.368989\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.7254 | −1.11403 | −0.557014 | − | 0.830503i | \(-0.688053\pi\) | ||||
−0.557014 | + | 0.830503i | \(0.688053\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.28589 | + | 2.22722i | −0.0450427 | + | 0.0780162i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.06356 | + | 3.57418i | 0.0721947 | + | 0.125045i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.87521 | − | 10.1762i | −0.205046 | − | 0.355151i | 0.745101 | − | 0.666951i | \(-0.232401\pi\) |
−0.950147 | + | 0.311801i | \(0.899068\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.25371 | − | 7.36764i | 0.148275 | − | 0.256820i | −0.782315 | − | 0.622883i | \(-0.785961\pi\) |
0.930590 | + | 0.366063i | \(0.119295\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.9662 | 0.485651 | 0.242825 | − | 0.970070i | \(-0.421926\pi\) | ||||
0.242825 | + | 0.970070i | \(0.421926\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.5484 | − | 32.1267i | −0.644212 | − | 1.11581i | −0.984483 | − | 0.175480i | \(-0.943852\pi\) |
0.340271 | − | 0.940327i | \(-0.389481\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.1511 | + | 5.53549i | 1.18326 | + | 0.191793i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.68250 | + | 2.91417i | 0.0582252 | + | 0.100849i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.32105 | − | 2.28813i | 0.0456077 | − | 0.0789949i | −0.842320 | − | 0.538977i | \(-0.818811\pi\) |
0.887928 | + | 0.459982i | \(0.152144\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.97928 | + | 13.8205i | 0.275148 | + | 0.476570i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.33561 | + | 10.9736i | −0.217952 | + | 0.377503i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.9440 | − | 10.4181i | 0.754004 | − | 0.357972i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −39.9870 | + | 69.2595i | −1.37074 | + | 2.37419i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.3405 | − | 30.0346i | 0.593726 | − | 1.02836i | −0.399999 | − | 0.916516i | \(-0.630990\pi\) |
0.993725 | − | 0.111848i | \(-0.0356771\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.7223 | −0.810338 | −0.405169 | − | 0.914242i | \(-0.632787\pi\) | ||||
−0.405169 | + | 0.914242i | \(0.632787\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.8150 | −0.744317 | −0.372158 | − | 0.928169i | \(-0.621382\pi\) | ||||
−0.372158 | + | 0.928169i | \(0.621382\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.6899 | − | 25.4436i | 0.500049 | − | 0.866111i | −0.499951 | − | 0.866054i | \(-0.666649\pi\) |
1.00000 | 5.68129e-5i | \(-1.80841e-5\pi\) | ||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.86308 | − | 3.22696i | −0.0633467 | − | 0.109720i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.14359 | − | 3.71280i | −0.0727162 | − | 0.125948i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.7656 | −0.568082 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.9443 | − | 5.19593i | 0.369985 | − | 0.175655i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.62129 | −0.189817 | −0.0949087 | − | 0.995486i | \(-0.530256\pi\) | ||||
−0.0949087 | + | 0.995486i | \(0.530256\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.75442 | −0.0927987 | −0.0463994 | − | 0.998923i | \(-0.514775\pi\) | ||||
−0.0463994 | + | 0.998923i | \(0.514775\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.8917 | 1.14055 | 0.570274 | − | 0.821455i | \(-0.306837\pi\) | ||||
0.570274 | + | 0.821455i | \(0.306837\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 55.6893 | 1.86986 | 0.934932 | − | 0.354827i | \(-0.115460\pi\) | ||||
0.934932 | + | 0.354827i | \(0.115460\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.4162 | + | 9.21803i | −0.651197 | + | 0.309163i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −52.5045 | −1.75700 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.0790366 | − | 0.136895i | −0.00264190 | − | 0.00457591i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.7345 | + | 20.3247i | 0.391367 | + | 0.677868i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.9118 | − | 50.0767i | 0.963192 | − | 1.66830i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.30434 | 0.109840 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 53.4626 | 1.77519 | 0.887597 | − | 0.460620i | \(-0.152373\pi\) | ||||
0.887597 | + | 0.460620i | \(0.152373\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.77060 | + | 16.9232i | −0.323714 | + | 0.560690i | −0.981251 | − | 0.192732i | \(-0.938265\pi\) |
0.657537 | + | 0.753422i | \(0.271598\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.61174 | + | 11.4519i | −0.218817 | + | 0.379001i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 46.5979 | − | 22.1229i | 1.53880 | − | 0.730561i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.0878895 | − | 0.152229i | 0.00289921 | − | 0.00502157i | −0.864572 | − | 0.502509i | \(-0.832410\pi\) |
0.867471 | + | 0.497487i | \(0.165744\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22.2984 | − | 38.6220i | −0.733962 | − | 1.27126i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.0617 | + | 43.4082i | −0.824025 | + | 1.42725i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.3008 | − | 21.3056i | −0.403576 | − | 0.699014i | 0.590579 | − | 0.806980i | \(-0.298900\pi\) |
−0.994155 | + | 0.107966i | \(0.965566\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.8736 | − | 31.2689i | −0.389142 | − | 1.02480i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.56023 | + | 2.70240i | 0.0510250 | + | 0.0883779i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.5655 | −0.933195 | −0.466598 | − | 0.884470i | \(-0.654520\pi\) | ||||
−0.466598 | + | 0.884470i | \(0.654520\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.7802 | − | 32.5283i | 0.612217 | − | 1.06039i | −0.378648 | − | 0.925541i | \(-0.623611\pi\) |
0.990866 | − | 0.134851i | \(-0.0430556\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.191943 | − | 0.332456i | −0.00625053 | − | 0.0108262i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.83381 | + | 8.37241i | 0.157078 | + | 0.272067i | 0.933814 | − | 0.357760i | \(-0.116459\pi\) |
−0.776736 | + | 0.629827i | \(0.783126\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.8955 | + | 36.1921i | −0.678297 | + | 1.17484i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −58.1964 | −1.88517 | −0.942583 | − | 0.333971i | \(-0.891611\pi\) | ||||
−0.942583 | + | 0.333971i | \(0.891611\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.14767 | + | 7.18397i | 0.134215 | + | 0.232468i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −36.0984 | + | 17.1381i | −1.16568 | + | 0.553418i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.61704 | − | 9.72900i | −0.181195 | − | 0.313839i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.93319 | − | 6.81248i | 0.126614 | − | 0.219301i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.97991 | + | 13.8216i | 0.256617 | + | 0.444473i | 0.965333 | − | 0.261020i | \(-0.0840589\pi\) |
−0.708717 | + | 0.705493i | \(0.750726\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.67394 | − | 2.89935i | 0.0537193 | − | 0.0930445i | −0.837915 | − | 0.545800i | \(-0.816226\pi\) |
0.891635 | + | 0.452756i | \(0.149559\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.53083 | + | 6.57573i | 0.305544 | + | 0.210808i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.9402 | − | 20.6810i | 0.382000 | − | 0.661643i | −0.609348 | − | 0.792903i | \(-0.708569\pi\) |
0.991348 | + | 0.131260i | \(0.0419022\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.15706 | + | 12.3964i | −0.228741 | + | 0.396190i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.7573 | −1.20427 | −0.602135 | − | 0.798394i | \(-0.705683\pi\) | ||||
−0.602135 | + | 0.798394i | \(0.705683\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.79752 | −0.0891364 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.29429 | − | 5.70588i | 0.104752 | − | 0.181436i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.08487 | − | 1.87904i | −0.0344619 | − | 0.0596898i | 0.848280 | − | 0.529548i | \(-0.177638\pi\) |
−0.882742 | + | 0.469858i | \(0.844305\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.93117 | + | 5.07694i | 0.0929245 | + | 0.160950i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.69454 | −0.275359 | −0.137679 | − | 0.990477i | \(-0.543964\pi\) | ||||
−0.137679 | + | 0.990477i | \(0.543964\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1512.2.t.c.289.7 | 22 | ||
3.2 | odd | 2 | 504.2.t.c.457.7 | yes | 22 | ||
4.3 | odd | 2 | 3024.2.t.k.289.7 | 22 | |||
7.4 | even | 3 | 1512.2.q.d.1369.5 | 22 | |||
9.4 | even | 3 | 1512.2.q.d.793.5 | 22 | |||
9.5 | odd | 6 | 504.2.q.c.121.1 | yes | 22 | ||
12.11 | even | 2 | 1008.2.t.l.961.5 | 22 | |||
21.11 | odd | 6 | 504.2.q.c.25.1 | ✓ | 22 | ||
28.11 | odd | 6 | 3024.2.q.l.2881.5 | 22 | |||
36.23 | even | 6 | 1008.2.q.l.625.11 | 22 | |||
36.31 | odd | 6 | 3024.2.q.l.2305.5 | 22 | |||
63.4 | even | 3 | inner | 1512.2.t.c.361.7 | 22 | ||
63.32 | odd | 6 | 504.2.t.c.193.7 | yes | 22 | ||
84.11 | even | 6 | 1008.2.q.l.529.11 | 22 | |||
252.67 | odd | 6 | 3024.2.t.k.1873.7 | 22 | |||
252.95 | even | 6 | 1008.2.t.l.193.5 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.1 | ✓ | 22 | 21.11 | odd | 6 | ||
504.2.q.c.121.1 | yes | 22 | 9.5 | odd | 6 | ||
504.2.t.c.193.7 | yes | 22 | 63.32 | odd | 6 | ||
504.2.t.c.457.7 | yes | 22 | 3.2 | odd | 2 | ||
1008.2.q.l.529.11 | 22 | 84.11 | even | 6 | |||
1008.2.q.l.625.11 | 22 | 36.23 | even | 6 | |||
1008.2.t.l.193.5 | 22 | 252.95 | even | 6 | |||
1008.2.t.l.961.5 | 22 | 12.11 | even | 2 | |||
1512.2.q.d.793.5 | 22 | 9.4 | even | 3 | |||
1512.2.q.d.1369.5 | 22 | 7.4 | even | 3 | |||
1512.2.t.c.289.7 | 22 | 1.1 | even | 1 | trivial | ||
1512.2.t.c.361.7 | 22 | 63.4 | even | 3 | inner | ||
3024.2.q.l.2305.5 | 22 | 36.31 | odd | 6 | |||
3024.2.q.l.2881.5 | 22 | 28.11 | odd | 6 | |||
3024.2.t.k.289.7 | 22 | 4.3 | odd | 2 | |||
3024.2.t.k.1873.7 | 22 | 252.67 | odd | 6 |