Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3864,2,Mod(1609,3864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3864.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3864.u (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: | \(30.8541953410\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.2992527616.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 13x^{6} + 52x^{4} + 61x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.5 | ||
Root | \(-0.128950i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3864.1609 |
Dual form | 3864.2.u.e.1609.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3864\mathbb{Z}\right)^\times\).
\(n\) | \(967\) | \(1289\) | \(1933\) | \(2761\) | \(2857\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.98337 | −1.33420 | −0.667102 | − | 0.744966i | \(-0.732466\pi\) | ||||
−0.667102 | + | 0.744966i | \(0.732466\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.64261 | − | 0.128950i | −0.998812 | − | 0.0487386i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.65924i | 0.500278i | 0.968210 | + | 0.250139i | \(0.0804764\pi\) | ||||
−0.968210 | + | 0.250139i | \(0.919524\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.64261i | 0.732927i | 0.930432 | + | 0.366464i | \(0.119432\pi\) | ||||
−0.930432 | + | 0.366464i | \(0.880568\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.98337i | − | 0.770303i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.34076 | −1.05279 | −0.526395 | − | 0.850240i | \(-0.676457\pi\) | ||||
−0.526395 | + | 0.850240i | \(0.676457\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.94445 | −1.13433 | −0.567167 | − | 0.823603i | \(-0.691961\pi\) | ||||
−0.567167 | + | 0.823603i | \(0.691961\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.128950 | − | 2.64261i | 0.0281393 | − | 0.576664i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.98337 | + | 3.75493i | −0.622076 | + | 0.782957i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.90051 | 0.780102 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.686549 | −0.127489 | −0.0637444 | − | 0.997966i | \(-0.520304\pi\) | ||||
−0.0637444 | + | 0.997966i | \(0.520304\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.62598i | 1.01046i | 0.862986 | + | 0.505228i | \(0.168592\pi\) | ||||
−0.862986 | + | 0.505228i | \(0.831408\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.65924 | −0.288836 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.88388 | + | 0.384707i | 1.33262 | + | 0.0650273i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.59867i | 1.08481i | 0.840116 | + | 0.542407i | \(0.182487\pi\) | ||||
−0.840116 | + | 0.542407i | \(0.817513\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.64261 | −0.423156 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.91714i | 0.299406i | 0.988731 | + | 0.149703i | \(0.0478318\pi\) | ||||
−0.988731 | + | 0.149703i | \(0.952168\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.83994i | − | 0.890582i | −0.895386 | − | 0.445291i | \(-0.853100\pi\) | ||
0.895386 | − | 0.445291i | \(-0.146900\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.98337 | 0.444735 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 5.74210i | − | 0.837571i | −0.908085 | − | 0.418786i | \(-0.862456\pi\) | ||
0.908085 | − | 0.418786i | \(-0.137544\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.96674 | + | 0.681530i | 0.995249 | + | 0.0973614i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 4.34076i | − | 0.607829i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.46757i | − | 0.888389i | −0.895930 | − | 0.444195i | \(-0.853490\pi\) | ||
0.895930 | − | 0.444195i | \(-0.146510\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.95012i | − | 0.667473i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 4.94445i | − | 0.654908i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 3.66490i | − | 0.477130i | −0.971127 | − | 0.238565i | \(-0.923323\pi\) | ||
0.971127 | − | 0.238565i | \(-0.0766769\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.35145 | −0.813220 | −0.406610 | − | 0.913602i | \(-0.633289\pi\) | ||||
−0.406610 | + | 0.913602i | \(0.633289\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.64261 | + | 0.128950i | 0.332937 | + | 0.0162462i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 7.88388i | − | 0.977875i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.27453i | − | 0.155708i | −0.996965 | − | 0.0778542i | \(-0.975193\pi\) | ||
0.996965 | − | 0.0778542i | \(-0.0248069\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.75493 | − | 2.98337i | −0.452040 | − | 0.359156i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.66992 | −0.198183 | −0.0990916 | − | 0.995078i | \(-0.531594\pi\) | ||||
−0.0990916 | + | 0.995078i | \(0.531594\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.39968i | 0.514944i | 0.966286 | + | 0.257472i | \(0.0828895\pi\) | ||||
−0.966286 | + | 0.257472i | \(0.917111\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.90051i | 0.450392i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.213959 | − | 4.38471i | 0.0243829 | − | 0.499684i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.34076i | 0.713392i | 0.934221 | + | 0.356696i | \(0.116097\pi\) | ||||
−0.934221 | + | 0.356696i | \(0.883903\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.02229 | −0.112211 | −0.0561057 | − | 0.998425i | \(-0.517868\pi\) | ||||
−0.0561057 | + | 0.998425i | \(0.517868\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.9501 | 1.40464 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 0.686549i | − | 0.0736057i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.12515 | −0.543265 | −0.271632 | − | 0.962401i | \(-0.587564\pi\) | ||||
−0.271632 | + | 0.962401i | \(0.587564\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.340765 | − | 6.98337i | 0.0357219 | − | 0.732056i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.62598 | −0.583387 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.7511 | 1.51343 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.1418 | 1.43588 | 0.717940 | − | 0.696105i | \(-0.245085\pi\) | ||||
0.717940 | + | 0.696105i | \(0.245085\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.65924i | − | 0.166759i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.52649i | 0.251395i | 0.992069 | + | 0.125697i | \(0.0401168\pi\) | ||||
−0.992069 | + | 0.125697i | \(0.959883\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.769413 | 0.0758125 | 0.0379063 | − | 0.999281i | \(-0.487931\pi\) | ||||
0.0379063 | + | 0.999281i | \(0.487931\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.384707 | + | 7.88388i | −0.0375435 | + | 0.769388i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.3241i | 1.28809i | 0.764986 | + | 0.644046i | \(0.222746\pi\) | ||||
−0.764986 | + | 0.644046i | \(0.777254\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.53243i | − | 0.146780i | −0.997303 | − | 0.0733900i | \(-0.976618\pi\) | ||
0.997303 | − | 0.0733900i | \(-0.0233818\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.59867 | −0.626318 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.81764i | − | 0.265062i | −0.991179 | − | 0.132531i | \(-0.957690\pi\) | ||
0.991179 | − | 0.132531i | \(-0.0423103\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.90051 | − | 11.2023i | 0.829977 | − | 1.04462i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 2.64261i | − | 0.244309i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.4709 | + | 0.559743i | 1.05154 | + | 0.0513115i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.24694 | 0.749722 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.91714 | −0.172862 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.28019 | 0.293390 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.93376 | −0.260329 | −0.130165 | − | 0.991492i | \(-0.541551\pi\) | ||||
−0.130165 | + | 0.991492i | \(0.541551\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.83994 | 0.514178 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 11.2023i | − | 0.978754i | −0.872072 | − | 0.489377i | \(-0.837224\pi\) | ||
0.872072 | − | 0.489377i | \(-0.162776\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.0662 | + | 0.637588i | 1.13299 | + | 0.0552859i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.98337i | 0.256768i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 13.0812i | − | 1.11760i | −0.829301 | − | 0.558802i | \(-0.811261\pi\) | ||
0.829301 | − | 0.558802i | \(-0.188739\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 12.3464i | − | 1.04721i | −0.851961 | − | 0.523605i | \(-0.824587\pi\) | ||
0.851961 | − | 0.523605i | \(-0.175413\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.74210 | 0.483572 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.38471 | −0.366668 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.04823 | 0.170096 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.681530 | + | 6.96674i | −0.0562116 | + | 0.574607i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 12.4493i | − | 1.01989i | −0.860208 | − | 0.509943i | \(-0.829667\pi\) | ||
0.860208 | − | 0.509943i | \(-0.170333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.80102 | −0.146565 | −0.0732823 | − | 0.997311i | \(-0.523347\pi\) | ||||
−0.0732823 | + | 0.997311i | \(0.523347\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.34076 | 0.350930 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 16.7844i | − | 1.34815i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.51746 | −0.121106 | −0.0605531 | − | 0.998165i | \(-0.519286\pi\) | ||||
−0.0605531 | + | 0.998165i | \(0.519286\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.46757 | 0.512912 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.36808 | − | 9.53810i | 0.659497 | − | 0.751707i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.5871 | −1.22087 | −0.610436 | − | 0.792065i | \(-0.709006\pi\) | ||||
−0.610436 | + | 0.792065i | \(0.709006\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.95012 | 0.385366 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 23.9642i | − | 1.85440i | −0.374563 | − | 0.927201i | \(-0.622207\pi\) | ||
0.374563 | − | 0.927201i | \(-0.377793\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.01663 | 0.462818 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.94445 | 0.378111 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.7455i | 1.42519i | 0.701575 | + | 0.712596i | \(0.252481\pi\) | ||||
−0.701575 | + | 0.712596i | \(0.747519\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.3075 | − | 0.502971i | −0.779174 | − | 0.0380211i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.66490 | 0.275471 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.1907 | −1.50913 | −0.754563 | − | 0.656227i | \(-0.772151\pi\) | ||||
−0.754563 | + | 0.656227i | \(0.772151\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.85228 | −0.212008 | −0.106004 | − | 0.994366i | \(-0.533806\pi\) | ||||
−0.106004 | + | 0.994366i | \(0.533806\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 6.35145i | − | 0.469513i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 19.6863i | − | 1.44736i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 7.20235i | − | 0.526688i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.128950 | + | 2.64261i | −0.00937975 | + | 0.192221i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.34578i | 0.314450i | 0.987563 | + | 0.157225i | \(0.0502548\pi\) | ||||
−0.987563 | + | 0.157225i | \(0.949745\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.7362 | 1.20469 | 0.602347 | − | 0.798234i | \(-0.294232\pi\) | ||||
0.602347 | + | 0.798234i | \(0.294232\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.88388 | 0.564576 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.8656 | 1.41537 | 0.707683 | − | 0.706531i | \(-0.249741\pi\) | ||||
0.707683 | + | 0.706531i | \(0.249741\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.8290 | 1.90186 | 0.950928 | − | 0.309413i | \(-0.100132\pi\) | ||||
0.950928 | + | 0.309413i | \(0.100132\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.27453 | 0.0898983 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.81428 | + | 0.0885306i | 0.127337 | + | 0.00621363i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 5.71953i | − | 0.399469i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.98337 | − | 3.75493i | 0.207359 | − | 0.260986i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 8.20400i | − | 0.567483i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.35509 | 0.437503 | 0.218751 | − | 0.975781i | \(-0.429802\pi\) | ||||
0.218751 | + | 0.975781i | \(0.429802\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 1.66992i | − | 0.114421i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.4227i | 1.18822i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.725471 | − | 14.8673i | 0.0492482 | − | 1.00925i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.39968 | −0.297303 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 11.4709i | − | 0.771619i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.6127i | 1.44729i | 0.690170 | + | 0.723647i | \(0.257536\pi\) | ||||
−0.690170 | + | 0.723647i | \(0.742464\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.90051 | −0.260034 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.209670 | 0.0139163 | 0.00695816 | − | 0.999976i | \(-0.497785\pi\) | ||||
0.00695816 | + | 0.999976i | \(0.497785\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.0166 | 0.860163 | 0.430082 | − | 0.902790i | \(-0.358485\pi\) | ||||
0.430082 | + | 0.902790i | \(0.358485\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.38471 | + | 0.213959i | 0.288493 | + | 0.0140775i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.74275 | 0.114171 | 0.0570856 | − | 0.998369i | \(-0.481819\pi\) | ||||
0.0570856 | + | 0.998369i | \(0.481819\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.1308i | 1.11749i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.34076 | −0.411877 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.14745 | −0.138907 | −0.0694534 | − | 0.997585i | \(-0.522126\pi\) | ||||
−0.0694534 | + | 0.997585i | \(0.522126\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.0420 | 1.54868 | 0.774341 | − | 0.632768i | \(-0.218082\pi\) | ||||
0.774341 | + | 0.632768i | \(0.218082\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −20.7844 | − | 2.03326i | −1.32787 | − | 0.129900i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 13.0662i | − | 0.831385i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 1.02229i | − | 0.0647853i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.136761 | 0.00863226 | 0.00431613 | − | 0.999991i | \(-0.498626\pi\) | ||||
0.00431613 | + | 0.999991i | \(0.498626\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.23031 | − | 4.95012i | −0.391696 | − | 0.311211i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.9501i | 0.810968i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 2.45260i | − | 0.152989i | −0.997070 | − | 0.0764944i | \(-0.975627\pi\) | ||
0.997070 | − | 0.0764944i | \(-0.0243727\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.850900 | − | 17.4377i | 0.0528723 | − | 1.08352i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.686549 | 0.0424963 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.1186i | 1.11724i | 0.829424 | + | 0.558619i | \(0.188669\pi\) | ||||
−0.829424 | + | 0.558619i | \(0.811331\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.2952i | 1.18529i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 5.12515i | − | 0.313654i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 10.4104i | − | 0.634731i | −0.948303 | − | 0.317366i | \(-0.897202\pi\) | ||
0.948303 | − | 0.317366i | \(-0.102798\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.9874i | 1.82160i | 0.412844 | + | 0.910802i | \(0.364536\pi\) | ||||
−0.412844 | + | 0.910802i | \(0.635464\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.98337 | + | 0.340765i | 0.422653 | + | 0.0206240i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.47186i | 0.390268i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.63666 | −0.338674 | −0.169337 | − | 0.985558i | \(-0.554163\pi\) | ||||
−0.169337 | + | 0.985558i | \(0.554163\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 5.62598i | − | 0.336819i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 24.3614i | − | 1.45328i | −0.687019 | − | 0.726640i | \(-0.741081\pi\) | ||
0.687019 | − | 0.726640i | \(-0.258919\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.9228 | −1.06540 | −0.532700 | − | 0.846304i | \(-0.678823\pi\) | ||||
−0.532700 | + | 0.846304i | \(0.678823\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.7511i | 0.873782i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.247215 | − | 5.06624i | 0.0145926 | − | 0.299050i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.84224 | 0.108367 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.1418i | 0.829006i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.2836 | −1.41866 | −0.709330 | − | 0.704876i | \(-0.751003\pi\) | ||||
−0.709330 | + | 0.704876i | \(0.751003\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.9338i | 0.636588i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.65924 | 0.0962786 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.92280 | − | 7.88388i | −0.573850 | − | 0.455937i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.753061 | + | 15.4327i | −0.0434057 | + | 0.889524i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.52649 | −0.145143 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.9487 | 1.08500 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.3449i | 0.989923i | 0.868915 | + | 0.494962i | \(0.164818\pi\) | ||||
−0.868915 | + | 0.494962i | \(0.835182\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.769413i | 0.0437704i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.4650i | 1.16046i | 0.814452 | + | 0.580232i | \(0.197038\pi\) | ||||
−0.814452 | + | 0.580232i | \(0.802962\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.57472 | −0.258578 | −0.129289 | − | 0.991607i | \(-0.541270\pi\) | ||||
−0.129289 | + | 0.991607i | \(0.541270\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.88388 | − | 0.384707i | −0.444206 | − | 0.0216758i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.78604 | −0.437308 | −0.218654 | − | 0.975802i | \(-0.570167\pi\) | ||||
−0.218654 | + | 0.975802i | \(0.570167\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.13915i | − | 0.0637799i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.3241 | −0.743681 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.4627 | 1.19422 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.3075i | 0.571758i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.53243 | 0.0847435 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.740445 | + | 15.1741i | −0.0408221 | + | 0.836576i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.8337 | 1.41995 | 0.709975 | − | 0.704227i | \(-0.248706\pi\) | ||||
0.709975 | + | 0.704227i | \(0.248706\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 6.59867i | − | 0.361605i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.80239i | 0.207747i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 14.8673i | − | 0.809871i | −0.914345 | − | 0.404935i | \(-0.867294\pi\) | ||
0.914345 | − | 0.404935i | \(-0.132706\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.81764 | 0.153033 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.33482 | −0.505509 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.3225 | − | 2.69938i | −0.989321 | − | 0.145753i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.2023 | + | 8.90051i | 0.603114 | + | 0.479187i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.32349 | −0.285780 | −0.142890 | − | 0.989739i | \(-0.545639\pi\) | ||||
−0.142890 | + | 0.989739i | \(0.545639\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.2064i | 1.40279i | 0.712771 | + | 0.701397i | \(0.247440\pi\) | ||||
−0.712771 | + | 0.701397i | \(0.752560\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.64261 | 0.141052 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 23.7509i | − | 1.26413i | −0.774915 | − | 0.632065i | \(-0.782207\pi\) | ||
0.774915 | − | 0.632065i | \(-0.217793\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.98199 | 0.264417 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.559743 | + | 11.4709i | −0.0296247 | + | 0.607106i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 9.79033i | − | 0.516714i | −0.966050 | − | 0.258357i | \(-0.916819\pi\) | ||
0.966050 | − | 0.258357i | \(-0.0831811\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.44758 | 0.286715 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.24694i | 0.432852i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 13.1259i | − | 0.687040i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.6153 | −1.02391 | −0.511955 | − | 0.859012i | \(-0.671079\pi\) | ||||
−0.511955 | + | 0.859012i | \(0.671079\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1.91714i | − | 0.0998021i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.833995 | + | 17.0912i | −0.0432989 | + | 0.887333i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.9718i | 1.44832i | 0.689630 | + | 0.724161i | \(0.257773\pi\) | ||||
−0.689630 | + | 0.724161i | \(0.742227\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.28019i | 0.169389i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.81428i | − | 0.0934401i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 15.4320i | − | 0.792689i | −0.918102 | − | 0.396345i | \(-0.870279\pi\) | ||
0.918102 | − | 0.396345i | \(-0.129721\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 2.93376i | − | 0.150301i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −35.8174 | −1.83018 | −0.915091 | − | 0.403247i | \(-0.867881\pi\) | ||||
−0.915091 | + | 0.403247i | \(0.867881\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.638319 | + | 13.0812i | −0.0325317 | + | 0.666680i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.83994i | 0.296861i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.49890i | 0.430911i | 0.976514 | + | 0.215456i | \(0.0691236\pi\) | ||||
−0.976514 | + | 0.215456i | \(0.930876\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.9501 | − | 16.2993i | 0.654915 | − | 0.824289i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.2023 | 0.565084 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 18.9169i | − | 0.951810i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 5.76347i | − | 0.289260i | −0.989486 | − | 0.144630i | \(-0.953801\pi\) | ||
0.989486 | − | 0.144630i | \(-0.0461992\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.637588 | + | 13.0662i | −0.0319193 | + | 0.654130i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 11.4859i | − | 0.573579i | −0.957994 | − | 0.286789i | \(-0.907412\pi\) | ||
0.957994 | − | 0.286789i | \(-0.0925880\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.8673 | −0.740591 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.98337 | −0.148245 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.9487 | −0.542709 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 18.1042i | − | 0.895197i | −0.894235 | − | 0.447598i | \(-0.852279\pi\) | ||
0.894235 | − | 0.447598i | \(-0.147721\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.0812 | 0.645249 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.472590 | + | 9.68489i | −0.0232546 | + | 0.476562i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.04988 | 0.149713 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.3464 | 0.604607 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.2626 | 0.647923 | 0.323961 | − | 0.946070i | \(-0.394985\pi\) | ||||
0.323961 | + | 0.946070i | \(0.394985\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 4.98839i | − | 0.243119i | −0.992584 | − | 0.121560i | \(-0.961210\pi\) | ||
0.992584 | − | 0.121560i | \(-0.0387896\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.74210i | 0.279190i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.9312 | −0.821283 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.7844 | + | 0.819021i | 0.812253 | + | 0.0396352i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 4.38471i | − | 0.211696i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.0057i | 1.25265i | 0.779563 | + | 0.626324i | \(0.215441\pi\) | ||||
−0.779563 | + | 0.626324i | \(0.784559\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.4766 | 1.51267 | 0.756334 | − | 0.654185i | \(-0.226988\pi\) | ||||
0.756334 | + | 0.654185i | \(0.226988\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.04823i | 0.0982051i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.7511 | − | 18.5661i | 0.705642 | − | 0.888135i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.18802i | 0.247611i | 0.992307 | + | 0.123805i | \(0.0395099\pi\) | ||||
−0.992307 | + | 0.123805i | \(0.960490\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.96674 | − | 0.681530i | −0.331750 | − | 0.0324538i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.8354 | −1.65508 | −0.827539 | − | 0.561408i | \(-0.810260\pi\) | ||||
−0.827539 | + | 0.561408i | \(0.810260\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.2902 | 0.724827 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.4493 | 0.588831 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.4524 | 1.53152 | 0.765761 | − | 0.643125i | \(-0.222362\pi\) | ||||
0.765761 | + | 0.643125i | \(0.222362\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.18098 | −0.149786 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 1.80102i | − | 0.0846191i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.01663 | + | 20.8340i | −0.0476603 | + | 0.976713i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 26.9169i | − | 1.25912i | −0.776953 | − | 0.629559i | \(-0.783236\pi\) | ||
0.776953 | − | 0.629559i | \(-0.216764\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.34076i | 0.202610i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 32.1731i | − | 1.49845i | −0.662315 | − | 0.749225i | \(-0.730426\pi\) | ||
0.662315 | − | 0.749225i | \(-0.269574\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.1572 | −1.81979 | −0.909895 | − | 0.414839i | \(-0.863838\pi\) | ||||
−0.909895 | + | 0.414839i | \(0.863838\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.7844 | 0.778357 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.4833 | −0.670206 | −0.335103 | − | 0.942181i | \(-0.608771\pi\) | ||||
−0.335103 | + | 0.942181i | \(0.608771\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.164351 | + | 3.36808i | −0.00758901 | + | 0.155523i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 1.51746i | − | 0.0699207i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.68983 | 0.445539 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.2859 | −0.884896 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.46757i | 0.296130i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.447578 | −0.0204504 | −0.0102252 | − | 0.999948i | \(-0.503255\pi\) | ||||
−0.0102252 | + | 0.999948i | \(0.503255\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.4377 | −0.795090 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.53810 | + | 8.36808i | 0.433998 | + | 0.380761i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −42.1902 | −1.91576 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.2137 | −1.05191 | −0.525956 | − | 0.850512i | \(-0.676292\pi\) | ||||
−0.525956 | + | 0.850512i | \(0.676292\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 15.5871i | − | 0.704871i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.6034 | −0.794431 | −0.397215 | − | 0.917725i | \(-0.630023\pi\) | ||||
−0.397215 | + | 0.917725i | \(0.630023\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.98015 | 0.134219 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.95012i | 0.222491i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.41294 | + | 0.215337i | 0.197948 | + | 0.00965917i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.95177 | −0.445502 | −0.222751 | − | 0.974875i | \(-0.571504\pi\) | ||||
−0.222751 | + | 0.974875i | \(0.571504\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.9642 | 1.07064 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.02796 | 0.0458345 | 0.0229173 | − | 0.999737i | \(-0.492705\pi\) | ||||
0.0229173 | + | 0.999737i | \(0.492705\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 7.53745i | − | 0.335412i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.01663i | 0.267208i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.76512i | 0.299859i | 0.988697 | + | 0.149929i | \(0.0479047\pi\) | ||||
−0.988697 | + | 0.149929i | \(0.952095\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.567340 | − | 11.6266i | 0.0250976 | − | 0.514332i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.94445i | 0.218303i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.29545 | −0.101149 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.52749 | 0.419019 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.7455 | −0.822835 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.7388 | 0.689529 | 0.344764 | − | 0.938689i | \(-0.387959\pi\) | ||||
0.344764 | + | 0.938689i | \(0.387959\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.2809 | 0.668188 | 0.334094 | − | 0.942540i | \(-0.391570\pi\) | ||||
0.334094 | + | 0.942540i | \(0.391570\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.502971 | − | 10.3075i | 0.0219515 | − | 0.449857i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 24.4211i | − | 1.06380i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.19898 | − | 22.4047i | −0.226043 | − | 0.974117i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.66490i | 0.159043i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.06624 | −0.219443 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 39.7509i | − | 1.71858i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 20.1907i | − | 0.871295i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.13082 | + | 11.5595i | −0.0487078 | + | 0.497901i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.3598 | −1.26227 | −0.631137 | − | 0.775671i | \(-0.717411\pi\) | ||||
−0.631137 | + | 0.775671i | \(0.717411\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 2.85228i | − | 0.122403i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.57181i | 0.195835i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.98172 | −0.426787 | −0.213394 | − | 0.976966i | \(-0.568452\pi\) | ||||
−0.213394 | + | 0.976966i | \(0.568452\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.35145 | 0.271073 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.39461 | 0.144615 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.817643 | − | 16.7561i | 0.0347697 | − | 0.712544i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19.6863 | 0.835636 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.5818i | 0.956820i | 0.878137 | + | 0.478410i | \(0.158787\pi\) | ||||
−0.878137 | + | 0.478410i | \(0.841213\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.4327 | 0.652732 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.20235 | 0.304083 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.8715 | −0.542471 | −0.271235 | − | 0.962513i | \(-0.587432\pi\) | ||||
−0.271235 | + | 0.962513i | \(0.587432\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.40608i | 0.353646i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.64261 | − | 0.128950i | −0.110979 | − | 0.00541540i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.90023i | − | 0.0796618i | −0.999206 | − | 0.0398309i | \(-0.987318\pi\) | ||
0.999206 | − | 0.0398309i | \(-0.0126819\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.6890i | 1.20060i | 0.799776 | + | 0.600298i | \(0.204952\pi\) | ||||
−0.799776 | + | 0.600298i | \(0.795048\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.34578 | −0.181548 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.6367 | + | 14.6461i | −0.485282 | + | 0.610786i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 31.1854i | − | 1.29827i | −0.760674 | − | 0.649134i | \(-0.775132\pi\) | ||
0.760674 | − | 0.649134i | \(-0.224868\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.7362i | 0.695531i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.70152 | + | 0.131825i | 0.112078 | + | 0.00546903i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.7312 | 0.444442 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.88388i | 0.325958i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 27.1722i | − | 1.12152i | −0.827980 | − | 0.560758i | \(-0.810510\pi\) | ||
0.827980 | − | 0.560758i | \(-0.189490\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 27.8174i | − | 1.14619i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.8656i | 0.817161i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 9.94537i | − | 0.408408i | −0.978928 | − | 0.204204i | \(-0.934539\pi\) | ||
0.978928 | − | 0.204204i | \(-0.0654605\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −34.2221 | − | 1.66992i | −1.40297 | − | 0.0684601i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 26.8290i | 1.09804i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.8905 | −0.853561 | −0.426781 | − | 0.904355i | \(-0.640352\pi\) | ||||
−0.426781 | + | 0.904355i | \(0.640352\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.2236i | 1.51838i | 0.650867 | + | 0.759192i | \(0.274406\pi\) | ||||
−0.650867 | + | 0.759192i | \(0.725594\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.27453i | 0.0519028i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.6037 | −1.00028 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.1335i | 1.14190i | 0.820983 | + | 0.570952i | \(0.193426\pi\) | ||||
−0.820983 | + | 0.570952i | \(0.806574\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.0885306 | + | 1.81428i | −0.00358744 | + | 0.0735183i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.1741 | 0.613879 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.5738i | 0.629020i | 0.949254 | + | 0.314510i | \(0.101840\pi\) | ||||
−0.949254 | + | 0.314510i | \(0.898160\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.71953 | 0.230634 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.0414i | 0.887352i | 0.896187 | + | 0.443676i | \(0.146326\pi\) | ||||
−0.896187 | + | 0.443676i | \(0.853674\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.0490 | 0.564675 | 0.282338 | − | 0.959315i | \(-0.408890\pi\) | ||||
0.282338 | + | 0.959315i | \(0.408890\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.75493 | + | 2.98337i | 0.150680 | + | 0.119719i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.5438 | + | 0.660890i | 0.542619 | + | 0.0264780i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.2886 | −1.17154 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.20400 | 0.327636 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 28.6433i | − | 1.14208i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 14.9558i | − | 0.595380i | −0.954663 | − | 0.297690i | \(-0.903784\pi\) | ||
0.954663 | − | 0.297690i | \(-0.0962162\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.35509i | 0.252592i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.75251 | 0.347333 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.80102 | + | 18.4104i | −0.0713588 | + | 0.729445i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.66992 | 0.0660610 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 17.6999i | − | 0.699103i | −0.936917 | − | 0.349551i | \(-0.886334\pi\) | ||
0.936917 | − | 0.349551i | \(-0.113666\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.344406 | −0.0135820 | −0.00679102 | − | 0.999977i | \(-0.502162\pi\) | ||||
−0.00679102 | + | 0.999977i | \(0.502162\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.4227 | −0.686018 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 43.1715i | − | 1.69724i | −0.528999 | − | 0.848622i | \(-0.677432\pi\) | ||
0.528999 | − | 0.848622i | \(-0.322568\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.08093 | 0.238698 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.8673 | + | 0.725471i | 0.582694 | + | 0.0284335i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.5105 | −0.841771 | −0.420886 | − | 0.907114i | \(-0.638281\pi\) | ||||
−0.420886 | + | 0.907114i | \(0.638281\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33.4208i | 1.30586i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 4.39968i | − | 0.171648i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.3159i | 0.596622i | 0.954469 | + | 0.298311i | \(0.0964233\pi\) | ||||
−0.954469 | + | 0.298311i | \(0.903577\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.0361 | 0.973790 | 0.486895 | − | 0.873460i | \(-0.338129\pi\) | ||||
0.486895 | + | 0.873460i | \(0.338129\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.4709 | 0.445494 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −38.9814 | − | 1.90216i | −1.51164 | − | 0.0737627i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.04823 | − | 2.57794i | 0.0793078 | − | 0.0998183i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.6127 | −0.835596 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 10.5385i | − | 0.406836i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.345053 | −0.0133008 | −0.00665041 | − | 0.999978i | \(-0.502117\pi\) | ||||
−0.00665041 | + | 0.999978i | \(0.502117\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 3.90051i | − | 0.150131i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.8786 | −0.418098 | −0.209049 | − | 0.977905i | \(-0.567037\pi\) | ||||
−0.209049 | + | 0.977905i | \(0.567037\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −37.3712 | − | 1.82359i | −1.43417 | − | 0.0699828i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.209670i | 0.00803459i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.643254 | −0.0246134 | −0.0123067 | − | 0.999924i | \(-0.503917\pi\) | ||||
−0.0123067 | + | 0.999924i | \(0.503917\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39.0261i | 1.49111i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.0166i | 0.496615i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17.0912 | 0.651125 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.0763i | 0.497445i | 0.968575 | + | 0.248722i | \(0.0800107\pi\) | ||||
−0.968575 | + | 0.248722i | \(0.919989\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.213959 | + | 4.38471i | −0.00812762 | + | 0.166561i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 36.8340i | 1.39719i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 8.32184i | − | 0.315212i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.74275i | 0.0659167i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.7742i | 1.50225i | 0.660161 | + | 0.751125i | \(0.270488\pi\) | ||||
−0.660161 | + | 0.751125i | \(0.729512\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 32.6268i | − | 1.23054i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.1308 | −0.645184 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.325791 | − | 6.67651i | 0.0122526 | − | 0.251096i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.4806i | 0.844277i | 0.906531 | + | 0.422139i | \(0.138720\pi\) | ||||
−0.906531 | + | 0.422139i | \(0.861280\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 6.34076i | − | 0.237797i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.1252 | − | 16.7844i | −0.791143 | − | 0.628580i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.0812 | 0.489210 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 2.14745i | − | 0.0801978i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 45.7438i | − | 1.70596i | −0.521947 | − | 0.852978i | \(-0.674794\pi\) | ||
0.521947 | − | 0.852978i | \(-0.325206\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.03326 | − | 0.0992160i | −0.0757224 | − | 0.00369500i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24.0420i | 0.894132i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.67789 | −0.0994543 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.9785 | 1.55690 | 0.778448 | − | 0.627709i | \(-0.216007\pi\) | ||||
0.778448 | + | 0.627709i | \(0.216007\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.3498i | 0.937596i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.14943 | −0.190199 | −0.0950993 | − | 0.995468i | \(-0.530317\pi\) | ||||
−0.0950993 | + | 0.995468i | \(0.530317\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.03326 | − | 20.7844i | 0.0749978 | − | 0.766644i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.11474 | 0.0778976 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.9847 | −1.06622 | −0.533111 | − | 0.846046i | \(-0.678977\pi\) | ||||
−0.533111 | + | 0.846046i | \(0.678977\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.0662 | 0.480000 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.7119i | 1.31014i | 0.755567 | + | 0.655072i | \(0.227362\pi\) | ||||
−0.755567 | + | 0.655072i | \(0.772638\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 37.1409i | 1.36074i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.02229 | 0.0374038 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.71815 | − | 35.2105i | 0.0627799 | − | 1.28656i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 36.6922i | − | 1.33892i | −0.742849 | − | 0.669459i | \(-0.766526\pi\) | ||
0.742849 | − | 0.669459i | \(-0.233474\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.136761i | 0.00498384i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.37310 | 0.195547 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 9.16909i | − | 0.333256i | −0.986020 | − | 0.166628i | \(-0.946712\pi\) | ||
0.986020 | − | 0.166628i | \(-0.0532880\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.95012 | − | 6.23031i | 0.179678 | − | 0.226146i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 9.01299i | − | 0.326721i | −0.986566 | − | 0.163360i | \(-0.947767\pi\) | ||
0.986566 | − | 0.163360i | \(-0.0522333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.197607 | + | 4.04961i | −0.00715386 | + | 0.146606i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.9501 | −0.468212 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.68489 | 0.349701 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.36735 | 0.121430 | 0.0607148 | − | 0.998155i | \(-0.480662\pi\) | ||||
0.0607148 | + | 0.998155i | \(0.480662\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.45260 | 0.0883281 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 44.3759 | 1.59609 | 0.798045 | − | 0.602598i | \(-0.205868\pi\) | ||||
0.798045 | + | 0.602598i | \(0.205868\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.9442i | 0.788258i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.4377 | + | 0.850900i | 0.625573 | + | 0.0305258i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 9.47918i | − | 0.339627i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 2.77079i | − | 0.0991467i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.686549i | 0.0245352i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.52713 | 0.161580 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.2513 | −0.757527 | −0.378764 | − | 0.925493i | \(-0.623651\pi\) | ||||
−0.378764 | + | 0.925493i | \(0.623651\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.1186 | −0.645038 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.363336 | + | 7.44592i | −0.0129187 | + | 0.264747i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 16.7844i | − | 0.596031i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19.2952 | −0.684329 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.7096 | −0.946104 | −0.473052 | − | 0.881035i | \(-0.656848\pi\) | ||||
−0.473052 | + | 0.881035i | \(0.656848\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.9251i | 0.881787i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.12515 | 0.181088 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.30010 | −0.257615 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.9651 | + | 28.4557i | −0.879904 | + | 1.00293i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.4104 | 0.366462 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.9100 | 1.71958 | 0.859792 | − | 0.510645i | \(-0.170593\pi\) | ||||
0.859792 | + | 0.510645i | \(0.170593\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 27.6330i | − | 0.970327i | −0.874424 | − | 0.485163i | \(-0.838760\pi\) | ||
0.874424 | − | 0.485163i | \(-0.161240\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.9874 | −1.05170 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 46.5020 | 1.62889 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.8753i | 1.01022i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.340765 | + | 6.98337i | −0.0119073 | + | 0.244019i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.7594 | −0.933909 | −0.466954 | − | 0.884281i | \(-0.654649\pi\) | ||||
−0.466954 | + | 0.884281i | \(0.654649\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.4641 | 0.539044 | 0.269522 | − | 0.962994i | \(-0.413134\pi\) | ||||
0.269522 | + | 0.962994i | \(0.413134\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.47186 | −0.225321 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 20.0220i | − | 0.696234i | −0.937451 | − | 0.348117i | \(-0.886821\pi\) | ||
0.937451 | − | 0.348117i | \(-0.113179\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 26.9512i | − | 0.936053i | −0.883714 | − | 0.468027i | \(-0.844965\pi\) | ||
0.883714 | − | 0.468027i | \(-0.155035\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 5.63666i | − | 0.195534i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −30.2410 | − | 2.95836i | −1.04779 | − | 0.102501i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 71.4940i | 2.47415i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.62598 | 0.194462 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.6783 | 0.437704 | 0.218852 | − | 0.975758i | \(-0.429769\pi\) | ||||
0.218852 | + | 0.975758i | \(0.429769\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5287 | −0.983747 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.3614 | 0.839051 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.9498 | −0.617493 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.7934 | − | 1.06344i | −0.748831 | − | 0.0365404i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 17.9228i | − | 0.615109i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.7775 | − | 19.6863i | −0.849362 | − | 0.674837i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 14.3306i | − | 0.490670i | −0.969438 | − | 0.245335i | \(-0.921102\pi\) | ||
0.969438 | − | 0.245335i | \(-0.0788980\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.7511 | −0.504478 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 17.6366i | − | 0.602454i | −0.953552 | − | 0.301227i | \(-0.902604\pi\) | ||
0.953552 | − | 0.301227i | \(-0.0973962\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 44.8107i | − | 1.52892i | −0.644670 | − | 0.764461i | \(-0.723005\pi\) | ||
0.644670 | − | 0.764461i | \(-0.276995\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.06624 | + | 0.247215i | 0.172657 | + | 0.00842507i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.5123 | 1.41310 | 0.706548 | − | 0.707666i | \(-0.250252\pi\) | ||||
0.706548 | + | 0.707666i | \(0.250252\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 55.9247i | − | 1.90150i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.84224i | 0.0625657i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.5208 | −0.356894 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.36808 | 0.114123 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.1418 | −0.478627 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.66827 | − | 0.422982i | −0.293041 | − | 0.0142994i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.9103 | 0.537252 | 0.268626 | − | 0.963245i | \(-0.413430\pi\) | ||||
0.268626 | + | 0.963245i | \(0.413430\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 24.2836i | − | 0.819064i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.8497 | −0.432917 | −0.216459 | − | 0.976292i | \(-0.569451\pi\) | ||||
−0.216459 | + | 0.976292i | \(0.569451\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.2287 | −0.647096 | −0.323548 | − | 0.946212i | \(-0.604876\pi\) | ||||
−0.323548 | + | 0.946212i | \(0.604876\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.9338 | −0.367534 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 9.65099i | − | 0.324049i | −0.986787 | − | 0.162024i | \(-0.948198\pi\) | ||
0.986787 | − | 0.162024i | \(-0.0518023\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.75278 | + | 0.378310i | 0.260020 | + | 0.0126881i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.65924i | 0.0555865i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.3915i | 0.950086i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 60.2365 | 2.01348 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.88388 | − | 9.92280i | 0.263235 | − | 0.331313i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 3.86251i | − | 0.128822i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.0742i | 0.935287i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.4327 | − | 0.753061i | −0.513567 | − | 0.0250603i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.50940 | 0.282862 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.9293i | 1.35904i | 0.733659 | + | 0.679518i | \(0.237811\pi\) | ||||
−0.733659 | + | 0.679518i | \(0.762189\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 2.52649i | − | 0.0837983i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.24786i | 0.140738i | 0.997521 | + | 0.0703690i | \(0.0224177\pi\) | ||||
−0.997521 | + | 0.0703690i | \(0.977582\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.69623i | − | 0.0561369i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 18.9487i | 0.626426i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.44455 | + | 29.6034i | −0.0477031 | + | 0.977591i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.00203i | 0.197989i | 0.995088 | + | 0.0989943i | \(0.0315625\pi\) | ||||
−0.995088 | + | 0.0989943i | \(0.968437\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.3449 | −0.571533 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 4.41294i | − | 0.145254i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.7381i | 0.846265i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.769413 | −0.0252708 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47.2883i | 1.55148i | 0.631053 | + | 0.775739i | \(0.282623\pi\) | ||||
−0.631053 | + | 0.775739i | \(0.717377\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34.4467 | − | 3.36979i | −1.12895 | − | 0.110440i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.4650 | −0.669994 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.4873i | 0.702709i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.12022 | −0.0365959 | −0.0182979 | − | 0.999833i | \(-0.505825\pi\) | ||||
−0.0182979 | + | 0.999833i | \(0.505825\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 4.57472i | − | 0.149290i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.6364 | 0.933520 | 0.466760 | − | 0.884384i | \(-0.345421\pi\) | ||||
0.466760 | + | 0.884384i | \(0.345421\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.19871 | − | 5.71953i | −0.234422 | − | 0.186253i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.384707 | − | 7.88388i | 0.0125145 | − | 0.256463i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.835926 | 0.0271639 | 0.0135820 | − | 0.999908i | \(-0.495677\pi\) | ||||
0.0135820 | + | 0.999908i | \(0.495677\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.6266 | −0.377416 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 7.78604i | − | 0.252480i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 50.9500i | 1.65043i | 0.564818 | + | 0.825216i | \(0.308947\pi\) | ||||
−0.564818 | + | 0.825216i | \(0.691053\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 12.9651i | − | 0.419540i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.13915 | 0.0368234 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.68683 | + | 34.5685i | −0.0544704 | + | 1.11627i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.651638 | −0.0210206 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 13.3241i | − | 0.429364i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −49.9302 | −1.60731 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.0827 | −1.41760 | −0.708802 | − | 0.705407i | \(-0.750764\pi\) | ||||
−0.708802 | + | 0.705407i | \(0.750764\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.4627i | 0.689481i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.7288 | −0.954044 | −0.477022 | − | 0.878891i | \(-0.658284\pi\) | ||||
−0.477022 | + | 0.878891i | \(0.658284\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.59208 | + | 32.6268i | −0.0510396 | + | 1.04597i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.3075 | −0.330104 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 11.9354i | − | 0.381848i | −0.981605 | − | 0.190924i | \(-0.938852\pi\) | ||
0.981605 | − | 0.190924i | \(-0.0611484\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 8.50383i | − | 0.271784i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.53243i | 0.0489267i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.5405 | 1.06978 | 0.534888 | − | 0.844923i | \(-0.320354\pi\) | ||||
0.534888 | + | 0.844923i | \(0.320354\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −59.2665 | −1.88839 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.1741 | − | 0.740445i | −0.482997 | − | 0.0235686i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.9286 | + | 17.4227i | 0.697287 | + | 0.554010i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.0229 | 0.477219 | 0.238610 | − | 0.971116i | \(-0.423308\pi\) | ||||
0.238610 | + | 0.971116i | \(0.423308\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.8337i | 0.819808i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −80.0408 | −2.53746 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 51.4584i | − | 1.62970i | −0.579669 | − | 0.814852i | \(-0.696818\pi\) | ||
0.579669 | − | 0.814852i | \(-0.303182\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.59867 | 0.208773 |
(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 | 3864.2.u.e.1609.5 | yes | 8 | |
7.6 | odd | 2 | 3864.2.u.c.1609.4 | ✓ | 8 | ||
23.22 | odd | 2 | 3864.2.u.c.1609.8 | yes | 8 | ||
161.160 | even | 2 | inner | 3864.2.u.e.1609.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.u.c.1609.4 | ✓ | 8 | 7.6 | odd | 2 | ||
3864.2.u.c.1609.8 | yes | 8 | 23.22 | odd | 2 | ||
3864.2.u.e.1609.1 | yes | 8 | 161.160 | even | 2 | inner | |
3864.2.u.e.1609.5 | yes | 8 | 1.1 | even | 1 | trivial |