Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [495,2,Mod(1,495)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(495, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("495.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 495 = 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 495.a (trivial) |
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: | yes |
Analytic conductor: | \(3.95259490005\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.48704.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 6x^{2} + 4x + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.852061\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 495.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.85206 | 1.30961 | 0.654803 | − | 0.755800i | \(-0.272752\pi\) | ||||
0.654803 | + | 0.755800i | \(0.272752\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.43013 | 0.715065 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.90749 | 1.85486 | 0.927429 | − | 0.373999i | \(-0.122014\pi\) | ||||
0.927429 | + | 0.373999i | \(0.122014\pi\) | |||||||
\(8\) | −1.05543 | −0.373152 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.85206 | 0.585673 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.61162 | −1.27903 | −0.639516 | − | 0.768778i | \(-0.720865\pi\) | ||||
−0.639516 | + | 0.768778i | \(0.720865\pi\) | |||||||
\(14\) | 9.08898 | 2.42913 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.81499 | −1.20375 | ||||||||
\(17\) | 3.76776 | 0.913815 | 0.456907 | − | 0.889514i | \(-0.348957\pi\) | ||||
0.456907 | + | 0.889514i | \(0.348957\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.84386 | 1.11126 | 0.555629 | − | 0.831430i | \(-0.312478\pi\) | ||||
0.555629 | + | 0.831430i | \(0.312478\pi\) | |||||||
\(20\) | 1.43013 | 0.319787 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.85206 | −0.394861 | ||||||||
\(23\) | −0.860262 | −0.179377 | −0.0896885 | − | 0.995970i | \(-0.528587\pi\) | ||||
−0.0896885 | + | 0.995970i | \(0.528587\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −8.54100 | −1.67503 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.01836 | 1.32635 | ||||||||
\(29\) | −10.3794 | −1.92740 | −0.963700 | − | 0.266986i | \(-0.913972\pi\) | ||||
−0.963700 | + | 0.266986i | \(0.913972\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.81499 | 1.40361 | 0.701807 | − | 0.712368i | \(-0.252377\pi\) | ||||
0.701807 | + | 0.712368i | \(0.252377\pi\) | |||||||
\(32\) | −6.80679 | −1.20328 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.97811 | 1.19674 | ||||||||
\(35\) | 4.90749 | 0.829518 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.67525 | −0.768606 | −0.384303 | − | 0.923207i | \(-0.625558\pi\) | ||||
−0.384303 | + | 0.923207i | \(0.625558\pi\) | |||||||
\(38\) | 8.97113 | 1.45531 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.05543 | −0.166879 | ||||||||
\(41\) | 2.97113 | 0.464012 | 0.232006 | − | 0.972714i | \(-0.425471\pi\) | ||||
0.232006 | + | 0.972714i | \(0.425471\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.907494 | −0.138391 | −0.0691957 | − | 0.997603i | \(-0.522043\pi\) | ||||
−0.0691957 | + | 0.997603i | \(0.522043\pi\) | |||||||
\(44\) | −1.43013 | −0.215600 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.59326 | −0.234913 | ||||||||
\(47\) | −13.2232 | −1.92881 | −0.964403 | − | 0.264436i | \(-0.914814\pi\) | ||||
−0.964403 | + | 0.264436i | \(0.914814\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.0835 | 2.44050 | ||||||||
\(50\) | 1.85206 | 0.261921 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.59522 | −0.914592 | ||||||||
\(53\) | 5.13974 | 0.705997 | 0.352999 | − | 0.935624i | \(-0.385162\pi\) | ||||
0.352999 | + | 0.935624i | \(0.385162\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −5.17953 | −0.692144 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −19.2232 | −2.52413 | ||||||||
\(59\) | −12.5480 | −1.63361 | −0.816804 | − | 0.576915i | \(-0.804256\pi\) | ||||
−0.816804 | + | 0.576915i | \(0.804256\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.2232 | −1.43699 | −0.718494 | − | 0.695533i | \(-0.755168\pi\) | ||||
−0.718494 | + | 0.695533i | \(0.755168\pi\) | |||||||
\(62\) | 14.4738 | 1.83818 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.97661 | −0.372076 | ||||||||
\(65\) | −4.61162 | −0.572001 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.26851 | 0.521481 | 0.260741 | − | 0.965409i | \(-0.416033\pi\) | ||||
0.260741 | + | 0.965409i | \(0.416033\pi\) | |||||||
\(68\) | 5.38838 | 0.653438 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 9.08898 | 1.08634 | ||||||||
\(71\) | −5.13974 | −0.609975 | −0.304987 | − | 0.952356i | \(-0.598652\pi\) | ||||
−0.304987 | + | 0.952356i | \(0.598652\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.61162 | −0.539749 | −0.269874 | − | 0.962896i | \(-0.586982\pi\) | ||||
−0.269874 | + | 0.962896i | \(0.586982\pi\) | |||||||
\(74\) | −8.65885 | −1.00657 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.92735 | 0.794622 | ||||||||
\(77\) | −4.90749 | −0.559261 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.843861 | −0.0949417 | −0.0474709 | − | 0.998873i | \(-0.515116\pi\) | ||||
−0.0474709 | + | 0.998873i | \(0.515116\pi\) | |||||||
\(80\) | −4.81499 | −0.538332 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.50271 | 0.607673 | ||||||||
\(83\) | −5.75135 | −0.631293 | −0.315647 | − | 0.948877i | \(-0.602221\pi\) | ||||
−0.315647 | + | 0.948877i | \(0.602221\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.76776 | 0.408670 | ||||||||
\(86\) | −1.68073 | −0.181238 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.05543 | 0.112509 | ||||||||
\(89\) | 1.40825 | 0.149274 | 0.0746368 | − | 0.997211i | \(-0.476220\pi\) | ||||
0.0746368 | + | 0.997211i | \(0.476220\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −22.6315 | −2.37242 | ||||||||
\(92\) | −1.23029 | −0.128266 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −24.4902 | −2.52598 | ||||||||
\(95\) | 4.84386 | 0.496970 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.54798 | 0.867916 | 0.433958 | − | 0.900933i | \(-0.357117\pi\) | ||||
0.433958 | + | 0.900933i | \(0.357117\pi\) | |||||||
\(98\) | 31.6397 | 3.19609 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.43013 | 0.143013 | ||||||||
\(101\) | −4.56438 | −0.454173 | −0.227087 | − | 0.973875i | \(-0.572920\pi\) | ||||
−0.227087 | + | 0.973875i | \(0.572920\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.73300 | −0.466356 | −0.233178 | − | 0.972434i | \(-0.574912\pi\) | ||||
−0.233178 | + | 0.972434i | \(0.574912\pi\) | |||||||
\(104\) | 4.86725 | 0.477273 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.51911 | 0.924578 | ||||||||
\(107\) | 7.34461 | 0.710030 | 0.355015 | − | 0.934861i | \(-0.384476\pi\) | ||||
0.355015 | + | 0.934861i | \(0.384476\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.40825 | 0.901146 | 0.450573 | − | 0.892739i | \(-0.351220\pi\) | ||||
0.450573 | + | 0.892739i | \(0.351220\pi\) | |||||||
\(110\) | −1.85206 | −0.176587 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −23.6295 | −2.23278 | ||||||||
\(113\) | 10.9547 | 1.03053 | 0.515267 | − | 0.857030i | \(-0.327693\pi\) | ||||
0.515267 | + | 0.857030i | \(0.327693\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.860262 | −0.0802198 | ||||||||
\(116\) | −14.8439 | −1.37822 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −23.2396 | −2.13938 | ||||||||
\(119\) | 18.4902 | 1.69500 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −20.7861 | −1.88189 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 11.1765 | 1.00368 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.62802 | 0.588141 | 0.294071 | − | 0.955784i | \(-0.404990\pi\) | ||||
0.294071 | + | 0.955784i | \(0.404990\pi\) | |||||||
\(128\) | 8.10071 | 0.716008 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.54100 | −0.749095 | ||||||||
\(131\) | 13.2232 | 1.15532 | 0.577660 | − | 0.816278i | \(-0.303966\pi\) | ||||
0.577660 | + | 0.816278i | \(0.303966\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23.7712 | 2.06123 | ||||||||
\(134\) | 7.90554 | 0.682934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.97661 | −0.340992 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.9711 | −1.10020 | −0.550098 | − | 0.835100i | \(-0.685410\pi\) | ||||
−0.550098 | + | 0.835100i | \(0.685410\pi\) | |||||||
\(140\) | 7.01836 | 0.593160 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.51911 | −0.798826 | ||||||||
\(143\) | 4.61162 | 0.385643 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.3794 | −0.861960 | ||||||||
\(146\) | −8.54100 | −0.706858 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.68622 | −0.549604 | ||||||||
\(149\) | −0.0273705 | −0.00224228 | −0.00112114 | − | 0.999999i | \(-0.500357\pi\) | ||||
−0.00112114 | + | 0.999999i | \(0.500357\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.84386 | 0.394188 | 0.197094 | − | 0.980385i | \(-0.436850\pi\) | ||||
0.197094 | + | 0.980385i | \(0.436850\pi\) | |||||||
\(152\) | −5.11237 | −0.414668 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.08898 | −0.732411 | ||||||||
\(155\) | 7.81499 | 0.627715 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.12727 | 0.169774 | 0.0848872 | − | 0.996391i | \(-0.472947\pi\) | ||||
0.0848872 | + | 0.996391i | \(0.472947\pi\) | |||||||
\(158\) | −1.56288 | −0.124336 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.80679 | −0.538124 | ||||||||
\(161\) | −4.22173 | −0.332719 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0835 | 0.789800 | 0.394900 | − | 0.918724i | \(-0.370779\pi\) | ||||
0.394900 | + | 0.918724i | \(0.370779\pi\) | |||||||
\(164\) | 4.24910 | 0.331799 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.6519 | −0.826745 | ||||||||
\(167\) | 17.7514 | 1.37364 | 0.686821 | − | 0.726827i | \(-0.259006\pi\) | ||||
0.686821 | + | 0.726827i | \(0.259006\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.26700 | 0.635923 | ||||||||
\(170\) | 6.97811 | 0.535197 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.29783 | −0.0989590 | ||||||||
\(173\) | 15.7678 | 1.19880 | 0.599400 | − | 0.800450i | \(-0.295406\pi\) | ||||
0.599400 | + | 0.800450i | \(0.295406\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.90749 | 0.370972 | ||||||||
\(176\) | 4.81499 | 0.362943 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.60816 | 0.195490 | ||||||||
\(179\) | 7.40825 | 0.553718 | 0.276859 | − | 0.960911i | \(-0.410706\pi\) | ||||
0.276859 | + | 0.960911i | \(0.410706\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.26700 | 0.540152 | 0.270076 | − | 0.962839i | \(-0.412951\pi\) | ||||
0.270076 | + | 0.962839i | \(0.412951\pi\) | |||||||
\(182\) | −41.9149 | −3.10694 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.907948 | 0.0669348 | ||||||||
\(185\) | −4.67525 | −0.343731 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.76776 | −0.275526 | ||||||||
\(188\) | −18.9110 | −1.37922 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.97113 | 0.650834 | ||||||||
\(191\) | −2.87123 | −0.207755 | −0.103877 | − | 0.994590i | \(-0.533125\pi\) | ||||
−0.103877 | + | 0.994590i | \(0.533125\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.8911 | 1.35981 | 0.679905 | − | 0.733300i | \(-0.262021\pi\) | ||||
0.679905 | + | 0.733300i | \(0.262021\pi\) | |||||||
\(194\) | 15.8314 | 1.13663 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 24.4316 | 1.74512 | ||||||||
\(197\) | 14.0472 | 1.00082 | 0.500412 | − | 0.865787i | \(-0.333182\pi\) | ||||
0.500412 | + | 0.865787i | \(0.333182\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.40825 | 0.241604 | 0.120802 | − | 0.992677i | \(-0.461453\pi\) | ||||
0.120802 | + | 0.992677i | \(0.461453\pi\) | |||||||
\(200\) | −1.05543 | −0.0746303 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.45352 | −0.594788 | ||||||||
\(203\) | −50.9367 | −3.57506 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.97113 | 0.207512 | ||||||||
\(206\) | −8.76580 | −0.610742 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 22.2049 | 1.53963 | ||||||||
\(209\) | −4.84386 | −0.335057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.4738 | −1.68485 | −0.842424 | − | 0.538815i | \(-0.818872\pi\) | ||||
−0.842424 | + | 0.538815i | \(0.818872\pi\) | |||||||
\(212\) | 7.35050 | 0.504834 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.6027 | 0.929859 | ||||||||
\(215\) | −0.907494 | −0.0618906 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 38.3520 | 2.60350 | ||||||||
\(218\) | 17.4246 | 1.18015 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.43013 | −0.0964194 | ||||||||
\(221\) | −17.3754 | −1.16880 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.5355 | −0.772475 | −0.386237 | − | 0.922399i | \(-0.626225\pi\) | ||||
−0.386237 | + | 0.922399i | \(0.626225\pi\) | |||||||
\(224\) | −33.4043 | −2.23192 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.2888 | 1.34959 | ||||||||
\(227\) | −1.15960 | −0.0769653 | −0.0384827 | − | 0.999259i | \(-0.512252\pi\) | ||||
−0.0384827 | + | 0.999259i | \(0.512252\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.4465 | −1.61547 | −0.807734 | − | 0.589547i | \(-0.799306\pi\) | ||||
−0.807734 | + | 0.589547i | \(0.799306\pi\) | |||||||
\(230\) | −1.59326 | −0.105056 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.9547 | 0.719213 | ||||||||
\(233\) | 9.45548 | 0.619449 | 0.309724 | − | 0.950826i | \(-0.399763\pi\) | ||||
0.309724 | + | 0.950826i | \(0.399763\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.2232 | −0.862589 | ||||||||
\(236\) | −17.9453 | −1.16814 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 34.2451 | 2.21978 | ||||||||
\(239\) | −14.9438 | −0.966631 | −0.483316 | − | 0.875446i | \(-0.660568\pi\) | ||||
−0.483316 | + | 0.875446i | \(0.660568\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.81499 | 0.503408 | 0.251704 | − | 0.967804i | \(-0.419009\pi\) | ||||
0.251704 | + | 0.967804i | \(0.419009\pi\) | |||||||
\(242\) | 1.85206 | 0.119055 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −16.0507 | −1.02754 | ||||||||
\(245\) | 17.0835 | 1.09142 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.3380 | −1.42133 | ||||||||
\(248\) | −8.24819 | −0.523761 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.85206 | 0.117135 | ||||||||
\(251\) | 3.41921 | 0.215819 | 0.107909 | − | 0.994161i | \(-0.465584\pi\) | ||||
0.107909 | + | 0.994161i | \(0.465584\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.860262 | 0.0540842 | ||||||||
\(254\) | 12.2755 | 0.770233 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.9562 | 1.30976 | ||||||||
\(257\) | 1.53551 | 0.0957826 | 0.0478913 | − | 0.998853i | \(-0.484750\pi\) | ||||
0.0478913 | + | 0.998853i | \(0.484750\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.9438 | −1.42566 | ||||||||
\(260\) | −6.59522 | −0.409018 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 24.4902 | 1.51301 | ||||||||
\(263\) | −0.190899 | −0.0117713 | −0.00588567 | − | 0.999983i | \(-0.501873\pi\) | ||||
−0.00588567 | + | 0.999983i | \(0.501873\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.13974 | 0.315732 | ||||||||
\(266\) | 44.0257 | 2.69939 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.10452 | 0.372893 | ||||||||
\(269\) | 14.4465 | 0.880817 | 0.440408 | − | 0.897798i | \(-0.354834\pi\) | ||||
0.440408 | + | 0.897798i | \(0.354834\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.97263 | −0.605794 | −0.302897 | − | 0.953023i | \(-0.597954\pi\) | ||||
−0.302897 | + | 0.953023i | \(0.597954\pi\) | |||||||
\(272\) | −18.1417 | −1.10000 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.1124 | −0.671323 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.5788 | 0.755788 | 0.377894 | − | 0.925849i | \(-0.376648\pi\) | ||||
0.377894 | + | 0.925849i | \(0.376648\pi\) | |||||||
\(278\) | −24.0233 | −1.44082 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.17953 | −0.309536 | ||||||||
\(281\) | −16.6917 | −0.995740 | −0.497870 | − | 0.867252i | \(-0.665884\pi\) | ||||
−0.497870 | + | 0.867252i | \(0.665884\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.5937 | −1.28361 | −0.641806 | − | 0.766867i | \(-0.721815\pi\) | ||||
−0.641806 | + | 0.766867i | \(0.721815\pi\) | |||||||
\(284\) | −7.35050 | −0.436172 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.54100 | 0.505040 | ||||||||
\(287\) | 14.5808 | 0.860677 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.80402 | −0.164942 | ||||||||
\(290\) | −19.2232 | −1.12883 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.59522 | −0.385956 | ||||||||
\(293\) | 33.0855 | 1.93287 | 0.966436 | − | 0.256906i | \(-0.0827031\pi\) | ||||
0.966436 | + | 0.256906i | \(0.0827031\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.5480 | −0.730572 | ||||||||
\(296\) | 4.93441 | 0.286807 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.0506919 | −0.00293650 | ||||||||
\(299\) | 3.96720 | 0.229429 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.45352 | −0.256697 | ||||||||
\(302\) | 8.97113 | 0.516230 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −23.3231 | −1.33767 | ||||||||
\(305\) | −11.2232 | −0.642640 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.72398 | 0.440831 | 0.220416 | − | 0.975406i | \(-0.429259\pi\) | ||||
0.220416 | + | 0.975406i | \(0.429259\pi\) | |||||||
\(308\) | −7.01836 | −0.399908 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14.4738 | 0.822059 | ||||||||
\(311\) | −12.1780 | −0.690549 | −0.345274 | − | 0.938502i | \(-0.612214\pi\) | ||||
−0.345274 | + | 0.938502i | \(0.612214\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.95473 | −0.167011 | −0.0835055 | − | 0.996507i | \(-0.526612\pi\) | ||||
−0.0835055 | + | 0.996507i | \(0.526612\pi\) | |||||||
\(314\) | 3.93983 | 0.222337 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.20683 | −0.0678896 | ||||||||
\(317\) | 27.4917 | 1.54409 | 0.772045 | − | 0.635568i | \(-0.219234\pi\) | ||||
0.772045 | + | 0.635568i | \(0.219234\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.3794 | 0.581133 | ||||||||
\(320\) | −2.97661 | −0.166398 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.81890 | −0.435730 | ||||||||
\(323\) | 18.2505 | 1.01548 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.61162 | −0.255806 | ||||||||
\(326\) | 18.6752 | 1.03433 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.13582 | −0.173147 | ||||||||
\(329\) | −64.8929 | −3.57766 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.5737 | 0.910975 | 0.455487 | − | 0.890242i | \(-0.349465\pi\) | ||||
0.455487 | + | 0.890242i | \(0.349465\pi\) | |||||||
\(332\) | −8.22519 | −0.451416 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 32.8766 | 1.79893 | ||||||||
\(335\) | 4.26851 | 0.233213 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.64442 | 0.252998 | 0.126499 | − | 0.991967i | \(-0.459626\pi\) | ||||
0.126499 | + | 0.991967i | \(0.459626\pi\) | |||||||
\(338\) | 15.3110 | 0.832809 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.38838 | 0.292226 | ||||||||
\(341\) | −7.81499 | −0.423205 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 49.4847 | 2.67192 | ||||||||
\(344\) | 0.957798 | 0.0516410 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 29.2028 | 1.56995 | ||||||||
\(347\) | 23.6936 | 1.27194 | 0.635970 | − | 0.771714i | \(-0.280600\pi\) | ||||
0.635970 | + | 0.771714i | \(0.280600\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.7572 | −1.16464 | −0.582319 | − | 0.812960i | \(-0.697855\pi\) | ||||
−0.582319 | + | 0.812960i | \(0.697855\pi\) | |||||||
\(350\) | 9.08898 | 0.485826 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.80679 | 0.362803 | ||||||||
\(353\) | 6.49024 | 0.345440 | 0.172720 | − | 0.984971i | \(-0.444744\pi\) | ||||
0.172720 | + | 0.984971i | \(0.444744\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.13974 | −0.272789 | ||||||||
\(356\) | 2.01397 | 0.106740 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.7205 | 0.725152 | ||||||||
\(359\) | 19.1655 | 1.01152 | 0.505758 | − | 0.862676i | \(-0.331213\pi\) | ||||
0.505758 | + | 0.862676i | \(0.331213\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.46299 | 0.234894 | ||||||||
\(362\) | 13.4589 | 0.707386 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −32.3660 | −1.69644 | ||||||||
\(365\) | −4.61162 | −0.241383 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.1850 | −0.531653 | −0.265827 | − | 0.964021i | \(-0.585645\pi\) | ||||
−0.265827 | + | 0.964021i | \(0.585645\pi\) | |||||||
\(368\) | 4.14215 | 0.215924 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.65885 | −0.450152 | ||||||||
\(371\) | 25.2232 | 1.30952 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.0184 | 0.984733 | 0.492367 | − | 0.870388i | \(-0.336132\pi\) | ||||
0.492367 | + | 0.870388i | \(0.336132\pi\) | |||||||
\(374\) | −6.97811 | −0.360830 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.9562 | 0.719738 | ||||||||
\(377\) | 47.8657 | 2.46521 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.0710 | 0.568680 | 0.284340 | − | 0.958723i | \(-0.408226\pi\) | ||||
0.284340 | + | 0.958723i | \(0.408226\pi\) | |||||||
\(380\) | 6.92735 | 0.355366 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.31770 | −0.272077 | ||||||||
\(383\) | −12.7330 | −0.650626 | −0.325313 | − | 0.945606i | \(-0.605470\pi\) | ||||
−0.325313 | + | 0.945606i | \(0.605470\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.90749 | −0.250109 | ||||||||
\(386\) | 34.9875 | 1.78081 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 12.2247 | 0.620617 | ||||||||
\(389\) | −32.7587 | −1.66093 | −0.830467 | − | 0.557068i | \(-0.811926\pi\) | ||||
−0.830467 | + | 0.557068i | \(0.811926\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.24126 | −0.163917 | ||||||||
\(392\) | −18.0305 | −0.910676 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 26.0163 | 1.31068 | ||||||||
\(395\) | −0.843861 | −0.0424592 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.0820 | −0.756943 | −0.378472 | − | 0.925613i | \(-0.623550\pi\) | ||||
−0.378472 | + | 0.925613i | \(0.623550\pi\) | |||||||
\(398\) | 6.31228 | 0.316406 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.81499 | −0.240749 | ||||||||
\(401\) | 18.7259 | 0.935129 | 0.467564 | − | 0.883959i | \(-0.345132\pi\) | ||||
0.467564 | + | 0.883959i | \(0.345132\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −36.0397 | −1.79527 | ||||||||
\(404\) | −6.52767 | −0.324764 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −94.3379 | −4.68191 | ||||||||
\(407\) | 4.67525 | 0.231744 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.4793 | 1.21042 | 0.605211 | − | 0.796065i | \(-0.293089\pi\) | ||||
0.605211 | + | 0.796065i | \(0.293089\pi\) | |||||||
\(410\) | 5.50271 | 0.271759 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.76880 | −0.333475 | ||||||||
\(413\) | −61.5791 | −3.03011 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.75135 | −0.282323 | ||||||||
\(416\) | 31.3903 | 1.53904 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.97113 | −0.438792 | ||||||||
\(419\) | 9.12877 | 0.445970 | 0.222985 | − | 0.974822i | \(-0.428420\pi\) | ||||
0.222985 | + | 0.974822i | \(0.428420\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.5465 | −0.660215 | −0.330108 | − | 0.943943i | \(-0.607085\pi\) | ||||
−0.330108 | + | 0.943943i | \(0.607085\pi\) | |||||||
\(422\) | −45.3270 | −2.20649 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.42465 | −0.263444 | ||||||||
\(425\) | 3.76776 | 0.182763 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −55.0779 | −2.66541 | ||||||||
\(428\) | 10.5038 | 0.507718 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.68073 | −0.0810522 | ||||||||
\(431\) | −26.4465 | −1.27388 | −0.636941 | − | 0.770913i | \(-0.719800\pi\) | ||||
−0.636941 | + | 0.770913i | \(0.719800\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.1780 | −0.777463 | −0.388732 | − | 0.921351i | \(-0.627087\pi\) | ||||
−0.388732 | + | 0.921351i | \(0.627087\pi\) | |||||||
\(434\) | 71.0303 | 3.40956 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.4550 | 0.644379 | ||||||||
\(437\) | −4.16699 | −0.199334 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.02887 | −0.335470 | −0.167735 | − | 0.985832i | \(-0.553645\pi\) | ||||
−0.167735 | + | 0.985832i | \(0.553645\pi\) | |||||||
\(440\) | 1.05543 | 0.0503158 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −32.1804 | −1.53066 | ||||||||
\(443\) | −24.3630 | −1.15752 | −0.578760 | − | 0.815498i | \(-0.696463\pi\) | ||||
−0.578760 | + | 0.815498i | \(0.696463\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.40825 | 0.0667572 | ||||||||
\(446\) | −21.3645 | −1.01164 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −14.6077 | −0.690149 | ||||||||
\(449\) | −38.3887 | −1.81168 | −0.905838 | − | 0.423625i | \(-0.860758\pi\) | ||||
−0.905838 | + | 0.423625i | \(0.860758\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.97113 | −0.139905 | ||||||||
\(452\) | 15.6667 | 0.736899 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.14765 | −0.100794 | ||||||||
\(455\) | −22.6315 | −1.06098 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.9621 | 1.02734 | 0.513672 | − | 0.857987i | \(-0.328285\pi\) | ||||
0.513672 | + | 0.857987i | \(0.328285\pi\) | |||||||
\(458\) | −45.2764 | −2.11562 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.23029 | −0.0573624 | ||||||||
\(461\) | 27.5698 | 1.28405 | 0.642027 | − | 0.766682i | \(-0.278094\pi\) | ||||
0.642027 | + | 0.766682i | \(0.278094\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.8860 | −1.15655 | −0.578275 | − | 0.815842i | \(-0.696274\pi\) | ||||
−0.578275 | + | 0.815842i | \(0.696274\pi\) | |||||||
\(464\) | 49.9765 | 2.32010 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.5121 | 0.811233 | ||||||||
\(467\) | −29.0273 | −1.34322 | −0.671610 | − | 0.740904i | \(-0.734397\pi\) | ||||
−0.671610 | + | 0.740904i | \(0.734397\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.9477 | 0.967274 | ||||||||
\(470\) | −24.4902 | −1.12965 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.2435 | 0.609584 | ||||||||
\(473\) | 0.907494 | 0.0417266 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.84386 | 0.222252 | ||||||||
\(476\) | 26.4435 | 1.21203 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −27.6768 | −1.26591 | ||||||||
\(479\) | 29.4450 | 1.34537 | 0.672687 | − | 0.739927i | \(-0.265140\pi\) | ||||
0.672687 | + | 0.739927i | \(0.265140\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.5605 | 0.983072 | ||||||||
\(482\) | 14.4738 | 0.659265 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.43013 | 0.0650060 | ||||||||
\(485\) | 8.54798 | 0.388144 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.5285 | 1.24743 | 0.623717 | − | 0.781650i | \(-0.285622\pi\) | ||||
0.623717 | + | 0.781650i | \(0.285622\pi\) | |||||||
\(488\) | 11.8454 | 0.536214 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 31.6397 | 1.42933 | ||||||||
\(491\) | 22.2795 | 1.00546 | 0.502729 | − | 0.864444i | \(-0.332329\pi\) | ||||
0.502729 | + | 0.864444i | \(0.332329\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −39.1069 | −1.76129 | ||||||||
\(494\) | −41.3714 | −1.86139 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −37.6291 | −1.68959 | ||||||||
\(497\) | −25.2232 | −1.13142 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.0382 | −1.56853 | −0.784263 | − | 0.620428i | \(-0.786959\pi\) | ||||
−0.784263 | + | 0.620428i | \(0.786959\pi\) | |||||||
\(500\) | 1.43013 | 0.0639574 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.33259 | 0.282638 | ||||||||
\(503\) | −33.9731 | −1.51478 | −0.757392 | − | 0.652960i | \(-0.773527\pi\) | ||||
−0.757392 | + | 0.652960i | \(0.773527\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.56438 | −0.203112 | ||||||||
\(506\) | 1.59326 | 0.0708289 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.47893 | 0.420560 | ||||||||
\(509\) | 13.3505 | 0.591750 | 0.295875 | − | 0.955227i | \(-0.404389\pi\) | ||||
0.295875 | + | 0.955227i | \(0.404389\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.6315 | −1.00116 | ||||||||
\(512\) | 22.6108 | 0.999266 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.84386 | 0.125437 | ||||||||
\(515\) | −4.73300 | −0.208561 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.2232 | 0.581557 | ||||||||
\(518\) | −42.4932 | −1.86705 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.86725 | 0.213443 | ||||||||
\(521\) | −7.46599 | −0.327091 | −0.163546 | − | 0.986536i | \(-0.552293\pi\) | ||||
−0.163546 | + | 0.986536i | \(0.552293\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.9785 | −0.698692 | −0.349346 | − | 0.936994i | \(-0.613596\pi\) | ||||
−0.349346 | + | 0.936994i | \(0.613596\pi\) | |||||||
\(524\) | 18.9110 | 0.826129 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.353557 | −0.0154158 | ||||||||
\(527\) | 29.4450 | 1.28264 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.2599 | −0.967824 | ||||||||
\(530\) | 9.51911 | 0.413484 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 33.9960 | 1.47391 | ||||||||
\(533\) | −13.7017 | −0.593486 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.34461 | 0.317535 | ||||||||
\(536\) | −4.50512 | −0.194592 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 26.7557 | 1.15352 | ||||||||
\(539\) | −17.0835 | −0.735838 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.46299 | −0.234872 | −0.117436 | − | 0.993080i | \(-0.537468\pi\) | ||||
−0.117436 | + | 0.993080i | \(0.537468\pi\) | |||||||
\(542\) | −18.4699 | −0.793351 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −25.6463 | −1.09958 | ||||||||
\(545\) | 9.40825 | 0.403005 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.8895 | 1.66279 | 0.831397 | − | 0.555679i | \(-0.187542\pi\) | ||||
0.831397 | + | 0.555679i | \(0.187542\pi\) | |||||||
\(548\) | −8.58079 | −0.366553 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.85206 | −0.0789722 | ||||||||
\(551\) | −50.2762 | −2.14184 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.14124 | −0.176103 | ||||||||
\(554\) | 23.2967 | 0.989783 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.5504 | −0.786713 | ||||||||
\(557\) | −6.58425 | −0.278983 | −0.139492 | − | 0.990223i | \(-0.544547\pi\) | ||||
−0.139492 | + | 0.990223i | \(0.544547\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.18501 | 0.177007 | ||||||||
\(560\) | −23.6295 | −0.998529 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −30.9140 | −1.30403 | ||||||||
\(563\) | −25.0323 | −1.05499 | −0.527494 | − | 0.849559i | \(-0.676868\pi\) | ||||
−0.527494 | + | 0.849559i | \(0.676868\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.9547 | 0.460869 | ||||||||
\(566\) | −39.9929 | −1.68103 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.42465 | 0.227613 | ||||||||
\(569\) | 34.5066 | 1.44659 | 0.723297 | − | 0.690537i | \(-0.242626\pi\) | ||||
0.723297 | + | 0.690537i | \(0.242626\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.6588 | −0.780848 | −0.390424 | − | 0.920635i | \(-0.627672\pi\) | ||||
−0.390424 | + | 0.920635i | \(0.627672\pi\) | |||||||
\(572\) | 6.59522 | 0.275760 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 27.0045 | 1.12715 | ||||||||
\(575\) | −0.860262 | −0.0358754 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.6697 | −1.56821 | −0.784105 | − | 0.620628i | \(-0.786878\pi\) | ||||
−0.784105 | + | 0.620628i | \(0.786878\pi\) | |||||||
\(578\) | −5.19321 | −0.216009 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −14.8439 | −0.616358 | ||||||||
\(581\) | −28.2247 | −1.17096 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.13974 | −0.212866 | ||||||||
\(584\) | 4.86725 | 0.201408 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 61.2763 | 2.53130 | ||||||||
\(587\) | −11.0242 | −0.455019 | −0.227510 | − | 0.973776i | \(-0.573058\pi\) | ||||
−0.227510 | + | 0.973776i | \(0.573058\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 37.8547 | 1.55978 | ||||||||
\(590\) | −23.2396 | −0.956761 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 22.5113 | 0.925207 | ||||||||
\(593\) | 39.4703 | 1.62085 | 0.810425 | − | 0.585843i | \(-0.199236\pi\) | ||||
0.810425 | + | 0.585843i | \(0.199236\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.4902 | 0.758026 | ||||||||
\(596\) | −0.0391434 | −0.00160338 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.34749 | 0.300461 | ||||||||
\(599\) | 2.44646 | 0.0999598 | 0.0499799 | − | 0.998750i | \(-0.484084\pi\) | ||||
0.0499799 | + | 0.998750i | \(0.484084\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.6697 | −1.53658 | −0.768290 | − | 0.640103i | \(-0.778892\pi\) | ||||
−0.768290 | + | 0.640103i | \(0.778892\pi\) | |||||||
\(602\) | −8.24819 | −0.336171 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.92735 | 0.281870 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.62802 | 0.269023 | 0.134511 | − | 0.990912i | \(-0.457053\pi\) | ||||
0.134511 | + | 0.990912i | \(0.457053\pi\) | |||||||
\(608\) | −32.9711 | −1.33716 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.7861 | −0.841605 | ||||||||
\(611\) | 60.9805 | 2.46701 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.6498 | 0.632091 | 0.316045 | − | 0.948744i | \(-0.397645\pi\) | ||||
0.316045 | + | 0.948744i | \(0.397645\pi\) | |||||||
\(614\) | 14.3053 | 0.577315 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.17953 | 0.208689 | ||||||||
\(617\) | −27.7463 | −1.11702 | −0.558511 | − | 0.829497i | \(-0.688627\pi\) | ||||
−0.558511 | + | 0.829497i | \(0.688627\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.5737 | 0.666154 | 0.333077 | − | 0.942900i | \(-0.391913\pi\) | ||||
0.333077 | + | 0.942900i | \(0.391913\pi\) | |||||||
\(620\) | 11.1765 | 0.448857 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −22.5543 | −0.904346 | ||||||||
\(623\) | 6.91095 | 0.276882 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −5.47233 | −0.218718 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.04227 | 0.121400 | ||||||||
\(629\) | −17.6152 | −0.702364 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.8547 | −1.50697 | −0.753486 | − | 0.657464i | \(-0.771629\pi\) | ||||
−0.753486 | + | 0.657464i | \(0.771629\pi\) | |||||||
\(632\) | 0.890638 | 0.0354277 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 50.9164 | 2.02215 | ||||||||
\(635\) | 6.62802 | 0.263025 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −78.7825 | −3.12148 | ||||||||
\(638\) | 19.2232 | 0.761055 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.10071 | 0.320209 | ||||||||
\(641\) | 11.9423 | 0.471691 | 0.235845 | − | 0.971791i | \(-0.424214\pi\) | ||||
0.235845 | + | 0.971791i | \(0.424214\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.3380 | 0.407692 | 0.203846 | − | 0.979003i | \(-0.434656\pi\) | ||||
0.203846 | + | 0.979003i | \(0.434656\pi\) | |||||||
\(644\) | −6.03763 | −0.237916 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 33.8010 | 1.32988 | ||||||||
\(647\) | 11.0125 | 0.432945 | 0.216472 | − | 0.976289i | \(-0.430545\pi\) | ||||
0.216472 | + | 0.976289i | \(0.430545\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.5480 | 0.492551 | ||||||||
\(650\) | −8.54100 | −0.335005 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.4207 | 0.564759 | ||||||||
\(653\) | 13.2810 | 0.519725 | 0.259862 | − | 0.965646i | \(-0.416323\pi\) | ||||
0.259862 | + | 0.965646i | \(0.416323\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.2232 | 0.516674 | ||||||||
\(656\) | −14.3059 | −0.558553 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −120.186 | −4.68533 | ||||||||
\(659\) | −10.2247 | −0.398299 | −0.199150 | − | 0.979969i | \(-0.563818\pi\) | ||||
−0.199150 | + | 0.979969i | \(0.563818\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.0710 | 0.663986 | 0.331993 | − | 0.943282i | \(-0.392279\pi\) | ||||
0.331993 | + | 0.943282i | \(0.392279\pi\) | |||||||
\(662\) | 30.6956 | 1.19302 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.07017 | 0.235568 | ||||||||
\(665\) | 23.7712 | 0.921808 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.92898 | 0.345731 | ||||||||
\(668\) | 25.3868 | 0.982243 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.90554 | 0.305418 | ||||||||
\(671\) | 11.2232 | 0.433268 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.8926 | 1.07518 | 0.537590 | − | 0.843206i | \(-0.319335\pi\) | ||||
0.537590 | + | 0.843206i | \(0.319335\pi\) | |||||||
\(674\) | 8.60175 | 0.331327 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.8229 | 0.454727 | ||||||||
\(677\) | −19.4922 | −0.749146 | −0.374573 | − | 0.927197i | \(-0.622211\pi\) | ||||
−0.374573 | + | 0.927197i | \(0.622211\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.9492 | 1.60986 | ||||||||
\(680\) | −3.97661 | −0.152496 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14.4738 | −0.554232 | ||||||||
\(683\) | −26.9438 | −1.03097 | −0.515487 | − | 0.856897i | \(-0.672389\pi\) | ||||
−0.515487 | + | 0.856897i | \(0.672389\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.00000 | −0.229248 | ||||||||
\(686\) | 91.6487 | 3.49916 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.36957 | 0.166588 | ||||||||
\(689\) | −23.7025 | −0.902993 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.2849 | 1.57055 | 0.785276 | − | 0.619146i | \(-0.212521\pi\) | ||||
0.785276 | + | 0.619146i | \(0.212521\pi\) | |||||||
\(692\) | 22.5500 | 0.857221 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 43.8820 | 1.66574 | ||||||||
\(695\) | −12.9711 | −0.492023 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.1945 | 0.424021 | ||||||||
\(698\) | −40.2957 | −1.52522 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.01836 | 0.265269 | ||||||||
\(701\) | 41.1631 | 1.55471 | 0.777354 | − | 0.629064i | \(-0.216562\pi\) | ||||
0.777354 | + | 0.629064i | \(0.216562\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.6463 | −0.854120 | ||||||||
\(704\) | 2.97661 | 0.112185 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.0203 | 0.452391 | ||||||||
\(707\) | −22.3997 | −0.842427 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.8040 | −0.743756 | −0.371878 | − | 0.928282i | \(-0.621286\pi\) | ||||
−0.371878 | + | 0.928282i | \(0.621286\pi\) | |||||||
\(710\) | −9.51911 | −0.357246 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.48631 | −0.0557017 | ||||||||
\(713\) | −6.72294 | −0.251776 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.61162 | 0.172465 | ||||||||
\(716\) | 10.5948 | 0.395945 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 35.4957 | 1.32469 | ||||||||
\(719\) | −42.6682 | −1.59126 | −0.795628 | − | 0.605786i | \(-0.792859\pi\) | ||||
−0.795628 | + | 0.605786i | \(0.792859\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.2271 | −0.865024 | ||||||||
\(722\) | 8.26572 | 0.307618 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.3928 | 0.386244 | ||||||||
\(725\) | −10.3794 | −0.385480 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.0054 | −1.44663 | −0.723315 | − | 0.690518i | \(-0.757383\pi\) | ||||
−0.723315 | + | 0.690518i | \(0.757383\pi\) | |||||||
\(728\) | 23.8860 | 0.885274 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.54100 | −0.316116 | ||||||||
\(731\) | −3.41921 | −0.126464 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.2744 | −0.453365 | −0.226683 | − | 0.973969i | \(-0.572788\pi\) | ||||
−0.226683 | + | 0.973969i | \(0.572788\pi\) | |||||||
\(734\) | −18.8633 | −0.696256 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.85562 | 0.215841 | ||||||||
\(737\) | −4.26851 | −0.157232 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.0343 | 1.25197 | 0.625986 | − | 0.779834i | \(-0.284697\pi\) | ||||
0.625986 | + | 0.779834i | \(0.284697\pi\) | |||||||
\(740\) | −6.68622 | −0.245790 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 46.7150 | 1.71496 | ||||||||
\(743\) | 16.2854 | 0.597452 | 0.298726 | − | 0.954339i | \(-0.403438\pi\) | ||||
0.298726 | + | 0.954339i | \(0.403438\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.0273705 | −0.00100278 | ||||||||
\(746\) | 35.2232 | 1.28961 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.38838 | −0.197019 | ||||||||
\(749\) | 36.0436 | 1.31701 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.0577 | 0.512974 | 0.256487 | − | 0.966548i | \(-0.417435\pi\) | ||||
0.256487 | + | 0.966548i | \(0.417435\pi\) | |||||||
\(752\) | 63.6697 | 2.32179 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 88.6502 | 3.22845 | ||||||||
\(755\) | 4.84386 | 0.176286 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.2286 | 1.38944 | 0.694722 | − | 0.719278i | \(-0.255527\pi\) | ||||
0.694722 | + | 0.719278i | \(0.255527\pi\) | |||||||
\(758\) | 20.5042 | 0.744746 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.11237 | −0.185445 | ||||||||
\(761\) | −9.52616 | −0.345323 | −0.172662 | − | 0.984981i | \(-0.555237\pi\) | ||||
−0.172662 | + | 0.984981i | \(0.555237\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 46.1709 | 1.67150 | ||||||||
\(764\) | −4.10624 | −0.148558 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23.5823 | −0.852063 | ||||||||
\(767\) | 57.8665 | 2.08944 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.24276 | 0.0808760 | 0.0404380 | − | 0.999182i | \(-0.487125\pi\) | ||||
0.0404380 | + | 0.999182i | \(0.487125\pi\) | |||||||
\(770\) | −9.08898 | −0.327544 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 27.0167 | 0.972354 | ||||||||
\(773\) | −17.7025 | −0.636715 | −0.318357 | − | 0.947971i | \(-0.603131\pi\) | ||||
−0.318357 | + | 0.947971i | \(0.603131\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.81499 | 0.280723 | ||||||||
\(776\) | −9.02182 | −0.323864 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −60.6712 | −2.17517 | ||||||||
\(779\) | 14.3917 | 0.515637 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.13974 | 0.183914 | ||||||||
\(782\) | −6.00301 | −0.214667 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −82.2568 | −2.93774 | ||||||||
\(785\) | 2.12727 | 0.0759254 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.4445 | −0.621830 | −0.310915 | − | 0.950438i | \(-0.600635\pi\) | ||||
−0.310915 | + | 0.950438i | \(0.600635\pi\) | |||||||
\(788\) | 20.0894 | 0.715655 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.56288 | −0.0556048 | ||||||||
\(791\) | 53.7602 | 1.91149 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 51.7572 | 1.83795 | ||||||||
\(794\) | −27.9328 | −0.991297 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.87424 | 0.172763 | ||||||||
\(797\) | 11.2093 | 0.397052 | 0.198526 | − | 0.980096i | \(-0.436385\pi\) | ||||
0.198526 | + | 0.980096i | \(0.436385\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −49.8219 | −1.76257 | ||||||||
\(800\) | −6.80679 | −0.240656 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 34.6816 | 1.22465 | ||||||||
\(803\) | 4.61162 | 0.162740 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.22173 | −0.148796 | ||||||||
\(806\) | −66.7478 | −2.35109 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.81740 | 0.169476 | ||||||||
\(809\) | 43.1381 | 1.51666 | 0.758328 | − | 0.651874i | \(-0.226017\pi\) | ||||
0.758328 | + | 0.651874i | \(0.226017\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.0289 | 0.387276 | 0.193638 | − | 0.981073i | \(-0.437971\pi\) | ||||
0.193638 | + | 0.981073i | \(0.437971\pi\) | |||||||
\(812\) | −72.8462 | −2.55640 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.65885 | 0.303492 | ||||||||
\(815\) | 10.0835 | 0.353209 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.39577 | −0.153789 | ||||||||
\(818\) | 45.3371 | 1.58517 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.24910 | 0.148385 | ||||||||
\(821\) | 14.9164 | 0.520585 | 0.260293 | − | 0.965530i | \(-0.416181\pi\) | ||||
0.260293 | + | 0.965530i | \(0.416181\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.4589 | −1.44517 | −0.722584 | − | 0.691283i | \(-0.757046\pi\) | ||||
−0.722584 | + | 0.691283i | \(0.757046\pi\) | |||||||
\(824\) | 4.99536 | 0.174022 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −114.048 | −3.96825 | ||||||||
\(827\) | 19.4171 | 0.675200 | 0.337600 | − | 0.941290i | \(-0.390385\pi\) | ||||
0.337600 | + | 0.941290i | \(0.390385\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.8290 | −0.619225 | −0.309613 | − | 0.950863i | \(-0.600199\pi\) | ||||
−0.309613 | + | 0.950863i | \(0.600199\pi\) | |||||||
\(830\) | −10.6519 | −0.369731 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13.7270 | 0.475898 | ||||||||
\(833\) | 64.3664 | 2.23016 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.7514 | 0.614311 | ||||||||
\(836\) | −6.92735 | −0.239588 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.9070 | 0.584044 | ||||||||
\(839\) | 12.2935 | 0.424417 | 0.212209 | − | 0.977224i | \(-0.431934\pi\) | ||||
0.212209 | + | 0.977224i | \(0.431934\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 78.7314 | 2.71487 | ||||||||
\(842\) | −25.0889 | −0.864621 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −35.0008 | −1.20478 | ||||||||
\(845\) | 8.26700 | 0.284394 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.90749 | 0.168623 | ||||||||
\(848\) | −24.7478 | −0.849842 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.97811 | 0.239347 | ||||||||
\(851\) | 4.02194 | 0.137870 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.0776 | −0.618966 | −0.309483 | − | 0.950905i | \(-0.600156\pi\) | ||||
−0.309483 | + | 0.950905i | \(0.600156\pi\) | |||||||
\(854\) | −102.008 | −3.49063 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.75174 | −0.264949 | ||||||||
\(857\) | −55.3649 | −1.89123 | −0.945615 | − | 0.325288i | \(-0.894539\pi\) | ||||
−0.945615 | + | 0.325288i | \(0.894539\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.943756 | −0.0322005 | −0.0161003 | − | 0.999870i | \(-0.505125\pi\) | ||||
−0.0161003 | + | 0.999870i | \(0.505125\pi\) | |||||||
\(860\) | −1.29783 | −0.0442558 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −48.9805 | −1.66828 | ||||||||
\(863\) | −23.6370 | −0.804614 | −0.402307 | − | 0.915505i | \(-0.631792\pi\) | ||||
−0.402307 | + | 0.915505i | \(0.631792\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.7678 | 0.536120 | ||||||||
\(866\) | −29.9626 | −1.01817 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 54.8484 | 1.86168 | ||||||||
\(869\) | 0.843861 | 0.0286260 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.6847 | −0.666991 | ||||||||
\(872\) | −9.92977 | −0.336264 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.71752 | −0.261049 | ||||||||
\(875\) | 4.90749 | 0.165904 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.6841 | −0.563383 | −0.281692 | − | 0.959505i | \(-0.590896\pi\) | ||||
−0.281692 | + | 0.959505i | \(0.590896\pi\) | |||||||
\(878\) | −13.0179 | −0.439333 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.81499 | 0.162313 | ||||||||
\(881\) | −16.2217 | −0.546524 | −0.273262 | − | 0.961940i | \(-0.588103\pi\) | ||||
−0.273262 | + | 0.961940i | \(0.588103\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.0710 | 1.18023 | 0.590117 | − | 0.807318i | \(-0.299082\pi\) | ||||
0.590117 | + | 0.807318i | \(0.299082\pi\) | |||||||
\(884\) | −24.8492 | −0.835768 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −45.1217 | −1.51589 | ||||||||
\(887\) | 16.1581 | 0.542536 | 0.271268 | − | 0.962504i | \(-0.412557\pi\) | ||||
0.271268 | + | 0.962504i | \(0.412557\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.5270 | 1.09092 | ||||||||
\(890\) | 2.60816 | 0.0874256 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16.4973 | −0.552370 | ||||||||
\(893\) | −64.0515 | −2.14340 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.40825 | 0.247630 | ||||||||
\(896\) | 39.7542 | 1.32809 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −71.0983 | −2.37258 | ||||||||
\(899\) | −81.1147 | −2.70533 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.3653 | 0.645151 | ||||||||
\(902\) | −5.50271 | −0.183220 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.5620 | −0.384545 | ||||||||
\(905\) | 7.26700 | 0.241563 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.9820 | 1.39399 | 0.696994 | − | 0.717077i | \(-0.254520\pi\) | ||||
0.696994 | + | 0.717077i | \(0.254520\pi\) | |||||||
\(908\) | −1.65838 | −0.0550352 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −41.9149 | −1.38946 | ||||||||
\(911\) | −57.2302 | −1.89612 | −0.948060 | − | 0.318092i | \(-0.896958\pi\) | ||||
−0.948060 | + | 0.318092i | \(0.896958\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.75135 | 0.190342 | ||||||||
\(914\) | 40.6752 | 1.34542 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −34.9616 | −1.15517 | ||||||||
\(917\) | 64.8929 | 2.14295 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.346569 | −0.0114323 | −0.00571613 | − | 0.999984i | \(-0.501820\pi\) | ||||
−0.00571613 | + | 0.999984i | \(0.501820\pi\) | |||||||
\(920\) | 0.907948 | 0.0299342 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 51.0610 | 1.68160 | ||||||||
\(923\) | 23.7025 | 0.780177 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.67525 | −0.153721 | ||||||||
\(926\) | −46.0904 | −1.51462 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 70.6502 | 2.31921 | ||||||||
\(929\) | −7.66278 | −0.251408 | −0.125704 | − | 0.992068i | \(-0.540119\pi\) | ||||
−0.125704 | + | 0.992068i | \(0.540119\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 82.7501 | 2.71202 | ||||||||
\(932\) | 13.5226 | 0.442947 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −53.7602 | −1.75909 | ||||||||
\(935\) | −3.76776 | −0.123219 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.0894 | 1.11365 | 0.556826 | − | 0.830629i | \(-0.312019\pi\) | ||||
0.556826 | + | 0.830629i | \(0.312019\pi\) | |||||||
\(938\) | 38.7964 | 1.26675 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18.9110 | −0.616807 | ||||||||
\(941\) | −28.1944 | −0.919110 | −0.459555 | − | 0.888149i | \(-0.651991\pi\) | ||||
−0.459555 | + | 0.888149i | \(0.651991\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.55595 | −0.0832331 | ||||||||
\(944\) | 60.4184 | 1.96645 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.68073 | 0.0546454 | ||||||||
\(947\) | 29.7602 | 0.967078 | 0.483539 | − | 0.875323i | \(-0.339351\pi\) | ||||
0.483539 | + | 0.875323i | \(0.339351\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.2670 | 0.690356 | ||||||||
\(950\) | 8.97113 | 0.291062 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −19.5152 | −0.632491 | ||||||||
\(953\) | −20.8309 | −0.674780 | −0.337390 | − | 0.941365i | \(-0.609544\pi\) | ||||
−0.337390 | + | 0.941365i | \(0.609544\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.87123 | −0.0929109 | ||||||||
\(956\) | −21.3715 | −0.691205 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 54.5339 | 1.76191 | ||||||||
\(959\) | −29.4450 | −0.950827 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.0740 | 0.970130 | ||||||||
\(962\) | 39.9313 | 1.28744 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.1765 | 0.359969 | ||||||||
\(965\) | 18.8911 | 0.608126 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.7225 | −0.987968 | −0.493984 | − | 0.869471i | \(-0.664460\pi\) | ||||
−0.493984 | + | 0.869471i | \(0.664460\pi\) | |||||||
\(968\) | −1.05543 | −0.0339229 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 15.8314 | 0.508315 | ||||||||
\(971\) | 21.9095 | 0.703108 | 0.351554 | − | 0.936168i | \(-0.385653\pi\) | ||||
0.351554 | + | 0.936168i | \(0.385653\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −63.6557 | −2.04071 | ||||||||
\(974\) | 50.9844 | 1.63365 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 54.0397 | 1.72977 | ||||||||
\(977\) | −14.1889 | −0.453944 | −0.226972 | − | 0.973901i | \(-0.572883\pi\) | ||||
−0.226972 | + | 0.973901i | \(0.572883\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.40825 | −0.0450077 | ||||||||
\(980\) | 24.4316 | 0.780440 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 41.2630 | 1.31675 | ||||||||
\(983\) | −5.52454 | −0.176206 | −0.0881028 | − | 0.996111i | \(-0.528080\pi\) | ||||
−0.0881028 | + | 0.996111i | \(0.528080\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.0472 | 0.447582 | ||||||||
\(986\) | −72.4284 | −2.30659 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −31.9463 | −1.01635 | ||||||||
\(989\) | 0.780682 | 0.0248243 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.93048 | 0.251920 | 0.125960 | − | 0.992035i | \(-0.459799\pi\) | ||||
0.125960 | + | 0.992035i | \(0.459799\pi\) | |||||||
\(992\) | −53.1950 | −1.68894 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −46.7150 | −1.48171 | ||||||||
\(995\) | 3.40825 | 0.108049 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −52.0596 | −1.64874 | −0.824372 | − | 0.566049i | \(-0.808471\pi\) | ||||
−0.824372 | + | 0.566049i | \(0.808471\pi\) | |||||||
\(998\) | −64.8929 | −2.05415 | ||||||||
\(999\) | 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 | 495.2.a.g.1.3 | yes | 4 | |
3.2 | odd | 2 | 495.2.a.f.1.2 | ✓ | 4 | ||
4.3 | odd | 2 | 7920.2.a.cn.1.1 | 4 | |||
5.2 | odd | 4 | 2475.2.c.s.199.6 | 8 | |||
5.3 | odd | 4 | 2475.2.c.s.199.3 | 8 | |||
5.4 | even | 2 | 2475.2.a.bf.1.2 | 4 | |||
11.10 | odd | 2 | 5445.2.a.bh.1.2 | 4 | |||
12.11 | even | 2 | 7920.2.a.cm.1.1 | 4 | |||
15.2 | even | 4 | 2475.2.c.t.199.3 | 8 | |||
15.8 | even | 4 | 2475.2.c.t.199.6 | 8 | |||
15.14 | odd | 2 | 2475.2.a.bj.1.3 | 4 | |||
33.32 | even | 2 | 5445.2.a.bs.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
495.2.a.f.1.2 | ✓ | 4 | 3.2 | odd | 2 | ||
495.2.a.g.1.3 | yes | 4 | 1.1 | even | 1 | trivial | |
2475.2.a.bf.1.2 | 4 | 5.4 | even | 2 | |||
2475.2.a.bj.1.3 | 4 | 15.14 | odd | 2 | |||
2475.2.c.s.199.3 | 8 | 5.3 | odd | 4 | |||
2475.2.c.s.199.6 | 8 | 5.2 | odd | 4 | |||
2475.2.c.t.199.3 | 8 | 15.2 | even | 4 | |||
2475.2.c.t.199.6 | 8 | 15.8 | even | 4 | |||
5445.2.a.bh.1.2 | 4 | 11.10 | odd | 2 | |||
5445.2.a.bs.1.3 | 4 | 33.32 | even | 2 | |||
7920.2.a.cm.1.1 | 4 | 12.11 | even | 2 | |||
7920.2.a.cn.1.1 | 4 | 4.3 | odd | 2 |