Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,3,Mod(685,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.685");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.c (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: | \(24.0327593166\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.2048.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 685.4 | ||
Root | \(0.765367i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.685 |
Dual form | 882.3.c.d.685.3 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 4.46088i | 0.892177i | 0.894989 | + | 0.446088i | \(0.147183\pi\) | ||||
−0.894989 | + | 0.446088i | \(0.852817\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.30864i | 0.630864i | ||||||||
\(11\) | 2.82843 | 0.257130 | 0.128565 | − | 0.991701i | \(-0.458963\pi\) | ||||
0.128565 | + | 0.991701i | \(0.458963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.6089i | 1.43145i | 0.698380 | + | 0.715727i | \(0.253905\pi\) | ||||
−0.698380 | + | 0.715727i | \(0.746095\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 12.0376i | 0.708096i | 0.935227 | + | 0.354048i | \(0.115195\pi\) | ||||
−0.935227 | + | 0.354048i | \(0.884805\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 13.8854i | − 0.730810i | −0.930849 | − | 0.365405i | \(-0.880931\pi\) | ||||
0.930849 | − | 0.365405i | \(-0.119069\pi\) | |||||||
\(20\) | 8.92177i | 0.446088i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.00000 | 0.181818 | ||||||||
\(23\) | −36.4853 | −1.58632 | −0.793158 | − | 0.609016i | \(-0.791565\pi\) | ||||
−0.793158 | + | 0.609016i | \(0.791565\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.10051 | 0.204020 | ||||||||
\(26\) | 26.3170i | 1.01219i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −12.4437 | −0.429091 | −0.214546 | − | 0.976714i | \(-0.568827\pi\) | ||||
−0.214546 | + | 0.976714i | \(0.568827\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 15.1535i | 0.488822i | 0.969672 | + | 0.244411i | \(0.0785946\pi\) | ||||
−0.969672 | + | 0.244411i | \(0.921405\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 17.0238i | 0.500699i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 45.6985 | 1.23509 | 0.617547 | − | 0.786534i | \(-0.288126\pi\) | ||||
0.617547 | + | 0.786534i | \(0.288126\pi\) | |||||||
\(38\) | − 19.6369i | − 0.516761i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 12.6173i | 0.315432i | ||||||||
\(41\) | 52.6565i | 1.28430i | 0.766577 | + | 0.642152i | \(0.221958\pi\) | ||||
−0.766577 | + | 0.642152i | \(0.778042\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −71.5980 | −1.66507 | −0.832535 | − | 0.553973i | \(-0.813111\pi\) | ||||
−0.832535 | + | 0.553973i | \(0.813111\pi\) | |||||||
\(44\) | 5.65685 | 0.128565 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −51.5980 | −1.12170 | ||||||||
\(47\) | 84.7343i | 1.80286i | 0.432928 | + | 0.901429i | \(0.357480\pi\) | ||||
−0.432928 | + | 0.901429i | \(0.642520\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 7.21320 | 0.144264 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 37.2178i | 0.715727i | ||||||||
\(53\) | 104.225 | 1.96652 | 0.983258 | − | 0.182216i | \(-0.0583271\pi\) | ||||
0.983258 | + | 0.182216i | \(0.0583271\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.6173i | 0.229405i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −17.5980 | −0.303413 | ||||||||
\(59\) | − 24.1203i | − 0.408819i | −0.978885 | − | 0.204410i | \(-0.934473\pi\) | ||||
0.978885 | − | 0.204410i | \(-0.0655274\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.5365i | 0.221910i | 0.993825 | + | 0.110955i | \(0.0353909\pi\) | ||||
−0.993825 | + | 0.110955i | \(0.964609\pi\) | |||||||
\(62\) | 21.4303i | 0.345650i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −83.0122 | −1.27711 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.0597015 | 0.0298507 | − | 0.999554i | \(-0.490497\pi\) | ||||
0.0298507 | + | 0.999554i | \(0.490497\pi\) | |||||||
\(68\) | 24.0753i | 0.354048i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −92.2010 | −1.29861 | −0.649303 | − | 0.760530i | \(-0.724939\pi\) | ||||
−0.649303 | + | 0.760530i | \(0.724939\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 85.4678i | − 1.17079i | −0.810748 | − | 0.585396i | \(-0.800939\pi\) | ||||
0.810748 | − | 0.585396i | \(-0.199061\pi\) | |||||||
\(74\) | 64.6274 | 0.873343 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 27.7708i | − 0.365405i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.59798 | 0.0455440 | 0.0227720 | − | 0.999741i | \(-0.492751\pi\) | ||||
0.0227720 | + | 0.999741i | \(0.492751\pi\) | |||||||
\(80\) | 17.8435i | 0.223044i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 74.4675i | 0.908140i | ||||||||
\(83\) | 80.3410i | 0.967964i | 0.875078 | + | 0.483982i | \(0.160810\pi\) | ||||
−0.875078 | + | 0.483982i | \(0.839190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −53.6985 | −0.631747 | ||||||||
\(86\) | −101.255 | −1.17738 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.00000 | 0.0909091 | ||||||||
\(89\) | 111.925i | 1.25759i | 0.777572 | + | 0.628794i | \(0.216451\pi\) | ||||
−0.777572 | + | 0.628794i | \(0.783549\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −72.9706 | −0.793158 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 119.832i | 1.27481i | ||||||||
\(95\) | 61.9411 | 0.652012 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 23.0791i | 0.237929i | 0.992899 | + | 0.118965i | \(0.0379575\pi\) | ||||
−0.992899 | + | 0.118965i | \(0.962043\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 10.2010 | 0.102010 | ||||||||
\(101\) | − 82.5602i | − 0.817427i | −0.912663 | − | 0.408714i | \(-0.865977\pi\) | ||||
0.912663 | − | 0.408714i | \(-0.134023\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 162.757i | − 1.58016i | −0.613003 | − | 0.790081i | \(-0.710039\pi\) | ||||
0.613003 | − | 0.790081i | \(-0.289961\pi\) | |||||||
\(104\) | 52.6339i | 0.506096i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 147.397 | 1.39054 | ||||||||
\(107\) | −13.8579 | −0.129513 | −0.0647564 | − | 0.997901i | \(-0.520627\pi\) | ||||
−0.0647564 | + | 0.997901i | \(0.520627\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 136.693 | 1.25407 | 0.627034 | − | 0.778992i | \(-0.284269\pi\) | ||||
0.627034 | + | 0.778992i | \(0.284269\pi\) | |||||||
\(110\) | 17.8435i | 0.162214i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 132.794 | 1.17517 | 0.587584 | − | 0.809163i | \(-0.300079\pi\) | ||||
0.587584 | + | 0.809163i | \(0.300079\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 162.757i | − 1.41528i | ||||||||
\(116\) | −24.8873 | −0.214546 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 34.1113i | − 0.289079i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −113.000 | −0.933884 | ||||||||
\(122\) | 19.1435i | 0.156914i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 30.3070i | 0.244411i | ||||||||
\(125\) | 134.275i | 1.07420i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 150.392 | 1.18419 | 0.592094 | − | 0.805869i | \(-0.298301\pi\) | ||||
0.592094 | + | 0.805869i | \(0.298301\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −117.397 | −0.903054 | ||||||||
\(131\) | 217.709i | 1.66190i | 0.556345 | + | 0.830951i | \(0.312203\pi\) | ||||
−0.556345 | + | 0.830951i | \(0.687797\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.65685 | 0.0422153 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 34.0476i | 0.250350i | ||||||||
\(137\) | 52.0416 | 0.379866 | 0.189933 | − | 0.981797i | \(-0.439173\pi\) | ||||
0.189933 | + | 0.981797i | \(0.439173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 143.799i | − 1.03452i | −0.855827 | − | 0.517262i | \(-0.826951\pi\) | ||||
0.855827 | − | 0.517262i | \(-0.173049\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −130.392 | −0.918253 | ||||||||
\(143\) | 52.6339i | 0.368069i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 55.5097i | − 0.382825i | ||||||||
\(146\) | − 120.870i | − 0.827875i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 91.3970 | 0.617547 | ||||||||
\(149\) | −19.0883 | −0.128109 | −0.0640547 | − | 0.997946i | \(-0.520403\pi\) | ||||
−0.0640547 | + | 0.997946i | \(0.520403\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 154.392 | 1.02246 | 0.511232 | − | 0.859443i | \(-0.329189\pi\) | ||||
0.511232 | + | 0.859443i | \(0.329189\pi\) | |||||||
\(152\) | − 39.2738i | − 0.258380i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −67.5980 | −0.436116 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 117.677i | − 0.749535i | −0.927119 | − | 0.374767i | \(-0.877723\pi\) | ||||
0.927119 | − | 0.374767i | \(-0.122277\pi\) | |||||||
\(158\) | 5.08831 | 0.0322045 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 25.2346i | 0.157716i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 185.990 | 1.14104 | 0.570521 | − | 0.821283i | \(-0.306741\pi\) | ||||
0.570521 | + | 0.821283i | \(0.306741\pi\) | |||||||
\(164\) | 105.313i | 0.642152i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 113.619i | 0.684454i | ||||||||
\(167\) | − 206.142i | − 1.23439i | −0.786812 | − | 0.617193i | \(-0.788270\pi\) | ||||
0.786812 | − | 0.617193i | \(-0.211730\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −177.291 | −1.04906 | ||||||||
\(170\) | −75.9411 | −0.446713 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −143.196 | −0.832535 | ||||||||
\(173\) | − 206.075i | − 1.19118i | −0.803287 | − | 0.595592i | \(-0.796917\pi\) | ||||
0.803287 | − | 0.595592i | \(-0.203083\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.3137 | 0.0642824 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 158.286i | 0.889250i | ||||||||
\(179\) | −160.083 | −0.894320 | −0.447160 | − | 0.894454i | \(-0.647565\pi\) | ||||
−0.447160 | + | 0.894454i | \(0.647565\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 99.9235i | − 0.552064i | −0.961149 | − | 0.276032i | \(-0.910980\pi\) | ||||
0.961149 | − | 0.276032i | \(-0.0890195\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −103.196 | −0.560848 | ||||||||
\(185\) | 203.856i | 1.10192i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 34.0476i | 0.182073i | ||||||||
\(188\) | 169.469i | 0.901429i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 87.5980 | 0.461042 | ||||||||
\(191\) | 69.5736 | 0.364260 | 0.182130 | − | 0.983274i | \(-0.441701\pi\) | ||||
0.182130 | + | 0.983274i | \(0.441701\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 135.196 | 0.700497 | 0.350249 | − | 0.936657i | \(-0.386097\pi\) | ||||
0.350249 | + | 0.936657i | \(0.386097\pi\) | |||||||
\(194\) | 32.6388i | 0.168241i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.4903 | 0.109088 | 0.0545440 | − | 0.998511i | \(-0.482629\pi\) | ||||
0.0545440 | + | 0.998511i | \(0.482629\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 259.827i | − 1.30566i | −0.757503 | − | 0.652831i | \(-0.773581\pi\) | ||||
0.757503 | − | 0.652831i | \(-0.226419\pi\) | |||||||
\(200\) | 14.4264 | 0.0721320 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 116.758i | − 0.578008i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −234.894 | −1.14583 | ||||||||
\(206\) | − 230.173i | − 1.11734i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 74.4356i | 0.357864i | ||||||||
\(209\) | − 39.2738i | − 0.187913i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −251.598 | −1.19241 | −0.596204 | − | 0.802833i | \(-0.703325\pi\) | ||||
−0.596204 | + | 0.802833i | \(0.703325\pi\) | |||||||
\(212\) | 208.451 | 0.983258 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −19.5980 | −0.0915793 | ||||||||
\(215\) | − 319.390i | − 1.48554i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 193.314 | 0.886760 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 25.2346i | 0.114703i | ||||||||
\(221\) | −224.007 | −1.01361 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 29.0389i | 0.130219i | 0.997878 | + | 0.0651096i | \(0.0207397\pi\) | ||||
−0.997878 | + | 0.0651096i | \(0.979260\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 187.799 | 0.830969 | ||||||||
\(227\) | − 275.543i | − 1.21385i | −0.794761 | − | 0.606923i | \(-0.792404\pi\) | ||||
0.794761 | − | 0.606923i | \(-0.207596\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 41.8457i | 0.182733i | 0.995817 | + | 0.0913663i | \(0.0291234\pi\) | ||||
−0.995817 | + | 0.0913663i | \(0.970877\pi\) | |||||||
\(230\) | − 230.173i | − 1.00075i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −35.1960 | −0.151707 | ||||||||
\(233\) | 217.213 | 0.932246 | 0.466123 | − | 0.884720i | \(-0.345651\pi\) | ||||
0.466123 | + | 0.884720i | \(0.345651\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −377.990 | −1.60847 | ||||||||
\(236\) | − 48.2406i | − 0.204410i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 68.7208 | 0.287535 | 0.143767 | − | 0.989612i | \(-0.454078\pi\) | ||||
0.143767 | + | 0.989612i | \(0.454078\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 18.0386i | − 0.0748489i | −0.999299 | − | 0.0374244i | \(-0.988085\pi\) | ||||
0.999299 | − | 0.0374244i | \(-0.0119154\pi\) | |||||||
\(242\) | −159.806 | −0.660356 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 27.0730i | 0.110955i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 258.392 | 1.04612 | ||||||||
\(248\) | 42.8605i | 0.172825i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 189.893i | 0.759573i | ||||||||
\(251\) | − 166.869i | − 0.664815i | −0.943136 | − | 0.332408i | \(-0.892139\pi\) | ||||
0.943136 | − | 0.332408i | \(-0.107861\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −103.196 | −0.407889 | ||||||||
\(254\) | 212.686 | 0.837348 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − 305.873i | − 1.19017i | −0.803664 | − | 0.595083i | \(-0.797119\pi\) | ||||
0.803664 | − | 0.595083i | \(-0.202881\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −166.024 | −0.638555 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 307.887i | 1.17514i | ||||||||
\(263\) | −9.62237 | −0.0365869 | −0.0182935 | − | 0.999833i | \(-0.505823\pi\) | ||||
−0.0182935 | + | 0.999833i | \(0.505823\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 464.938i | 1.75448i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.00000 | 0.0298507 | ||||||||
\(269\) | 99.6422i | 0.370417i | 0.982699 | + | 0.185209i | \(0.0592961\pi\) | ||||
−0.982699 | + | 0.185209i | \(0.940704\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 504.628i | − 1.86210i | −0.364898 | − | 0.931048i | \(-0.618896\pi\) | ||||
0.364898 | − | 0.931048i | \(-0.381104\pi\) | |||||||
\(272\) | 48.1505i | 0.177024i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 73.5980 | 0.268606 | ||||||||
\(275\) | 14.4264 | 0.0524597 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 314.000 | 1.13357 | 0.566787 | − | 0.823864i | \(-0.308186\pi\) | ||||
0.566787 | + | 0.823864i | \(0.308186\pi\) | |||||||
\(278\) | − 203.362i | − 0.731519i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −155.002 | −0.551609 | −0.275804 | − | 0.961214i | \(-0.588944\pi\) | ||||
−0.275804 | + | 0.961214i | \(0.588944\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 276.503i | 0.977044i | 0.872552 | + | 0.488522i | \(0.162464\pi\) | ||||
−0.872552 | + | 0.488522i | \(0.837536\pi\) | |||||||
\(284\) | −184.402 | −0.649303 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 74.4356i | 0.260264i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 144.095 | 0.498600 | ||||||||
\(290\) | − 78.5026i | − 0.270698i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 170.936i | − 0.585396i | ||||||||
\(293\) | − 485.027i | − 1.65538i | −0.561185 | − | 0.827690i | \(-0.689654\pi\) | ||||
0.561185 | − | 0.827690i | \(-0.310346\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 107.598 | 0.364739 | ||||||||
\(296\) | 129.255 | 0.436672 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −26.9949 | −0.0905871 | ||||||||
\(299\) | − 678.951i | − 2.27074i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 218.343 | 0.722991 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 55.5416i | − 0.182702i | ||||||||
\(305\) | −60.3848 | −0.197983 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 126.364i | − 0.411609i | −0.978593 | − | 0.205805i | \(-0.934019\pi\) | ||||
0.978593 | − | 0.205805i | \(-0.0659811\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −95.5980 | −0.308381 | ||||||||
\(311\) | 421.968i | 1.35681i | 0.734688 | + | 0.678405i | \(0.237329\pi\) | ||||
−0.734688 | + | 0.678405i | \(0.762671\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 431.650i | 1.37907i | 0.724251 | + | 0.689536i | \(0.242186\pi\) | ||||
−0.724251 | + | 0.689536i | \(0.757814\pi\) | |||||||
\(314\) | − 166.420i | − 0.530001i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.19596 | 0.0227720 | ||||||||
\(317\) | 256.804 | 0.810107 | 0.405054 | − | 0.914293i | \(-0.367253\pi\) | ||||
0.405054 | + | 0.914293i | \(0.367253\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −35.1960 | −0.110332 | ||||||||
\(320\) | 35.6871i | 0.111522i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 167.147 | 0.517484 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 94.9148i | 0.292046i | ||||||||
\(326\) | 263.029 | 0.806839 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 148.935i | 0.454070i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 155.598 | 0.470085 | 0.235042 | − | 0.971985i | \(-0.424477\pi\) | ||||
0.235042 | + | 0.971985i | \(0.424477\pi\) | |||||||
\(332\) | 160.682i | 0.483982i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 291.529i | − 0.872843i | ||||||||
\(335\) | 17.8435i | 0.0532643i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 39.7086 | 0.117830 | 0.0589148 | − | 0.998263i | \(-0.481236\pi\) | ||||
0.0589148 | + | 0.998263i | \(0.481236\pi\) | |||||||
\(338\) | −250.728 | −0.741799 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −107.397 | −0.315873 | ||||||||
\(341\) | 42.8605i | 0.125691i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −202.510 | −0.588691 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 291.434i | − 0.842294i | ||||||||
\(347\) | −649.671 | −1.87225 | −0.936126 | − | 0.351666i | \(-0.885615\pi\) | ||||
−0.936126 | + | 0.351666i | \(0.885615\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 616.789i | 1.76730i | 0.468143 | + | 0.883652i | \(0.344923\pi\) | ||||
−0.468143 | + | 0.883652i | \(0.655077\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.0000 | 0.0454545 | ||||||||
\(353\) | − 530.755i | − 1.50356i | −0.659416 | − | 0.751778i | \(-0.729197\pi\) | ||||
0.659416 | − | 0.751778i | \(-0.270803\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 411.298i | − 1.15859i | ||||||||
\(356\) | 223.851i | 0.628794i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −226.392 | −0.632380 | ||||||||
\(359\) | 532.014 | 1.48193 | 0.740967 | − | 0.671541i | \(-0.234367\pi\) | ||||
0.740967 | + | 0.671541i | \(0.234367\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 168.196 | 0.465917 | ||||||||
\(362\) | − 141.313i | − 0.390368i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 381.262 | 1.04455 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 391.072i | 1.06559i | 0.846244 | + | 0.532796i | \(0.178859\pi\) | ||||
−0.846244 | + | 0.532796i | \(0.821141\pi\) | |||||||
\(368\) | −145.941 | −0.396579 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 288.295i | 0.779177i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 72.8040 | 0.195185 | 0.0975925 | − | 0.995226i | \(-0.468886\pi\) | ||||
0.0975925 | + | 0.995226i | \(0.468886\pi\) | |||||||
\(374\) | 48.1505i | 0.128745i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 239.665i | 0.637406i | ||||||||
\(377\) | − 231.563i | − 0.614225i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.8141 | −0.0813038 | −0.0406519 | − | 0.999173i | \(-0.512943\pi\) | ||||
−0.0406519 | + | 0.999173i | \(0.512943\pi\) | |||||||
\(380\) | 123.882 | 0.326006 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 98.3919 | 0.257570 | ||||||||
\(383\) | 446.269i | 1.16519i | 0.812762 | + | 0.582596i | \(0.197963\pi\) | ||||
−0.812762 | + | 0.582596i | \(0.802037\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 191.196 | 0.495326 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 46.1582i | 0.118965i | ||||||||
\(389\) | −260.208 | −0.668916 | −0.334458 | − | 0.942411i | \(-0.608553\pi\) | ||||
−0.334458 | + | 0.942411i | \(0.608553\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 439.196i | − 1.12326i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 30.3919 | 0.0771369 | ||||||||
\(395\) | 16.0502i | 0.0406334i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 609.847i | 1.53614i | 0.640367 | + | 0.768069i | \(0.278782\pi\) | ||||
−0.640367 | + | 0.768069i | \(0.721218\pi\) | |||||||
\(398\) | − 367.451i | − 0.923243i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 20.4020 | 0.0510051 | ||||||||
\(401\) | −147.057 | −0.366725 | −0.183363 | − | 0.983045i | \(-0.558698\pi\) | ||||
−0.183363 | + | 0.983045i | \(0.558698\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −281.990 | −0.699727 | ||||||||
\(404\) | − 165.120i | − 0.408714i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 129.255 | 0.317579 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 158.763i | − 0.388173i | −0.980984 | − | 0.194087i | \(-0.937826\pi\) | ||||
0.980984 | − | 0.194087i | \(-0.0621743\pi\) | |||||||
\(410\) | −332.191 | −0.810222 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 325.513i | − 0.790081i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −358.392 | −0.863595 | ||||||||
\(416\) | 105.268i | 0.253048i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 55.5416i | − 0.132875i | ||||||||
\(419\) | 577.000i | 1.37709i | 0.725195 | + | 0.688544i | \(0.241750\pi\) | ||||
−0.725195 | + | 0.688544i | \(0.758250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.9798 | −0.0902133 | −0.0451066 | − | 0.998982i | \(-0.514363\pi\) | ||||
−0.0451066 | + | 0.998982i | \(0.514363\pi\) | |||||||
\(422\) | −355.813 | −0.843159 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 294.794 | 0.695269 | ||||||||
\(425\) | 61.3980i | 0.144466i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −27.7157 | −0.0647564 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − 451.686i | − 1.05043i | ||||||||
\(431\) | 785.151 | 1.82170 | 0.910848 | − | 0.412741i | \(-0.135429\pi\) | ||||
0.910848 | + | 0.412741i | \(0.135429\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 582.519i | − 1.34531i | −0.739957 | − | 0.672655i | \(-0.765154\pi\) | ||||
0.739957 | − | 0.672655i | \(-0.234846\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 273.387 | 0.627034 | ||||||||
\(437\) | 506.612i | 1.15930i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.46796i | 0.0147334i | 0.999973 | + | 0.00736669i | \(0.00234491\pi\) | ||||
−0.999973 | + | 0.00736669i | \(0.997655\pi\) | |||||||
\(440\) | 35.6871i | 0.0811070i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −316.794 | −0.716728 | ||||||||
\(443\) | −291.897 | −0.658909 | −0.329454 | − | 0.944172i | \(-0.606865\pi\) | ||||
−0.329454 | + | 0.944172i | \(0.606865\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −499.286 | −1.12199 | ||||||||
\(446\) | 41.0672i | 0.0920789i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −457.480 | −1.01889 | −0.509443 | − | 0.860504i | \(-0.670149\pi\) | ||||
−0.509443 | + | 0.860504i | \(0.670149\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 148.935i | 0.330233i | ||||||||
\(452\) | 265.588 | 0.587584 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 389.677i | − 0.858319i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −680.764 | −1.48964 | −0.744818 | − | 0.667268i | \(-0.767464\pi\) | ||||
−0.744818 | + | 0.667268i | \(0.767464\pi\) | |||||||
\(458\) | 59.1788i | 0.129211i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 325.513i | − 0.707638i | ||||||||
\(461\) | 156.401i | 0.339265i | 0.985507 | + | 0.169633i | \(0.0542581\pi\) | ||||
−0.985507 | + | 0.169633i | \(0.945742\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 370.774 | 0.800807 | 0.400404 | − | 0.916339i | \(-0.368870\pi\) | ||||
0.400404 | + | 0.916339i | \(0.368870\pi\) | |||||||
\(464\) | −49.7746 | −0.107273 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 307.186 | 0.659197 | ||||||||
\(467\) | − 40.1705i | − 0.0860182i | −0.999075 | − | 0.0430091i | \(-0.986306\pi\) | ||||
0.999075 | − | 0.0430091i | \(-0.0136944\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −534.558 | −1.13736 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 68.2226i | − 0.144539i | ||||||||
\(473\) | −202.510 | −0.428139 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 70.8225i | − 0.149100i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 97.1859 | 0.203318 | ||||||||
\(479\) | − 213.136i | − 0.444960i | −0.974937 | − | 0.222480i | \(-0.928585\pi\) | ||||
0.974937 | − | 0.222480i | \(-0.0714152\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 850.399i | 1.76798i | ||||||||
\(482\) | − 25.5104i | − 0.0529262i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −226.000 | −0.466942 | ||||||||
\(485\) | −102.953 | −0.212275 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −843.598 | −1.73223 | −0.866117 | − | 0.499841i | \(-0.833392\pi\) | ||||
−0.866117 | + | 0.499841i | \(0.833392\pi\) | |||||||
\(488\) | 38.2870i | 0.0784570i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 614.621 | 1.25177 | 0.625887 | − | 0.779913i | \(-0.284737\pi\) | ||||
0.625887 | + | 0.779913i | \(0.284737\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 149.792i | − 0.303838i | ||||||||
\(494\) | 365.421 | 0.739719 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 60.6140i | 0.122206i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 659.980 | 1.32260 | 0.661302 | − | 0.750119i | \(-0.270004\pi\) | ||||
0.661302 | + | 0.750119i | \(0.270004\pi\) | |||||||
\(500\) | 268.550i | 0.537100i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 235.988i | − 0.470095i | ||||||||
\(503\) | − 301.276i | − 0.598959i | −0.954103 | − | 0.299480i | \(-0.903187\pi\) | ||||
0.954103 | − | 0.299480i | \(-0.0968130\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 368.291 | 0.729290 | ||||||||
\(506\) | −145.941 | −0.288421 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 300.784 | 0.592094 | ||||||||
\(509\) | 866.644i | 1.70264i | 0.524646 | + | 0.851320i | \(0.324198\pi\) | ||||
−0.524646 | + | 0.851320i | \(0.675802\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 432.569i | − 0.841574i | ||||||||
\(515\) | 726.039 | 1.40978 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 239.665i | 0.463568i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −234.794 | −0.451527 | ||||||||
\(521\) | − 623.830i | − 1.19737i | −0.800984 | − | 0.598685i | \(-0.795690\pi\) | ||||
0.800984 | − | 0.598685i | \(-0.204310\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 770.604i | − 1.47343i | −0.676203 | − | 0.736715i | \(-0.736376\pi\) | ||||
0.676203 | − | 0.736715i | \(-0.263624\pi\) | |||||||
\(524\) | 435.418i | 0.830951i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.6081 | −0.0258709 | ||||||||
\(527\) | −182.412 | −0.346133 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 802.176 | 1.51640 | ||||||||
\(530\) | 657.521i | 1.24061i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −979.879 | −1.83842 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 61.8183i | − 0.115548i | ||||||||
\(536\) | 11.3137 | 0.0211077 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 140.915i | 0.261924i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1033.57 | −1.91048 | −0.955238 | − | 0.295838i | \(-0.904401\pi\) | ||||
−0.955238 | + | 0.295838i | \(0.904401\pi\) | |||||||
\(542\) | − 713.651i | − 1.31670i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 68.0951i | 0.125175i | ||||||||
\(545\) | 609.774i | 1.11885i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 923.176 | 1.68771 | 0.843854 | − | 0.536574i | \(-0.180282\pi\) | ||||
0.843854 | + | 0.536574i | \(0.180282\pi\) | |||||||
\(548\) | 104.083 | 0.189933 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 20.4020 | 0.0370946 | ||||||||
\(551\) | 172.785i | 0.313584i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 444.063 | 0.801558 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 287.598i | − 0.517262i | ||||||||
\(557\) | 381.255 | 0.684479 | 0.342240 | − | 0.939613i | \(-0.388815\pi\) | ||||
0.342240 | + | 0.939613i | \(0.388815\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 1332.36i | − 2.38347i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −219.206 | −0.390046 | ||||||||
\(563\) | 214.659i | 0.381277i | 0.981660 | + | 0.190638i | \(0.0610557\pi\) | ||||
−0.981660 | + | 0.190638i | \(0.938944\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 592.378i | 1.04846i | ||||||||
\(566\) | 391.035i | 0.690874i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −260.784 | −0.459126 | ||||||||
\(569\) | −131.252 | −0.230671 | −0.115336 | − | 0.993327i | \(-0.536794\pi\) | ||||
−0.115336 | + | 0.993327i | \(0.536794\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −101.186 | −0.177208 | −0.0886041 | − | 0.996067i | \(-0.528241\pi\) | ||||
−0.0886041 | + | 0.996067i | \(0.528241\pi\) | |||||||
\(572\) | 105.268i | 0.184035i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −186.093 | −0.323641 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 920.331i | 1.59503i | 0.603301 | + | 0.797514i | \(0.293852\pi\) | ||||
−0.603301 | + | 0.797514i | \(0.706148\pi\) | |||||||
\(578\) | 203.782 | 0.352564 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 111.019i | − 0.191413i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 294.794 | 0.505650 | ||||||||
\(584\) | − 241.739i | − 0.413937i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 685.931i | − 1.17053i | ||||||||
\(587\) | 595.384i | 1.01428i | 0.861863 | + | 0.507141i | \(0.169298\pi\) | ||||
−0.861863 | + | 0.507141i | \(0.830702\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 210.412 | 0.357236 | ||||||||
\(590\) | 152.167 | 0.257909 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 182.794 | 0.308774 | ||||||||
\(593\) | 441.134i | 0.743903i | 0.928252 | + | 0.371951i | \(0.121311\pi\) | ||||
−0.928252 | + | 0.371951i | \(0.878689\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −38.1766 | −0.0640547 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 960.182i | − 1.60566i | ||||||||
\(599\) | 250.053 | 0.417451 | 0.208725 | − | 0.977974i | \(-0.433069\pi\) | ||||
0.208725 | + | 0.977974i | \(0.433069\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 593.457i | 0.987449i | 0.869618 | + | 0.493725i | \(0.164365\pi\) | ||||
−0.869618 | + | 0.493725i | \(0.835635\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 308.784 | 0.511232 | ||||||||
\(605\) | − 504.080i | − 0.833190i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 338.449i | 0.557577i | 0.960353 | + | 0.278788i | \(0.0899328\pi\) | ||||
−0.960353 | + | 0.278788i | \(0.910067\pi\) | |||||||
\(608\) | − 78.5476i | − 0.129190i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −85.3970 | −0.139995 | ||||||||
\(611\) | −1576.81 | −2.58071 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 805.477 | 1.31399 | 0.656996 | − | 0.753894i | \(-0.271827\pi\) | ||||
0.656996 | + | 0.753894i | \(0.271827\pi\) | |||||||
\(614\) | − 178.706i | − 0.291052i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.1148 | 0.0293595 | 0.0146797 | − | 0.999892i | \(-0.495327\pi\) | ||||
0.0146797 | + | 0.999892i | \(0.495327\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 448.137i | 0.723969i | 0.932184 | + | 0.361984i | \(0.117901\pi\) | ||||
−0.932184 | + | 0.361984i | \(0.882099\pi\) | |||||||
\(620\) | −135.196 | −0.218058 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 596.753i | 0.959410i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −471.472 | −0.754356 | ||||||||
\(626\) | 610.445i | 0.975152i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 235.354i | − 0.374767i | ||||||||
\(629\) | 550.101i | 0.874565i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 696.764 | 1.10422 | 0.552111 | − | 0.833771i | \(-0.313823\pi\) | ||||
0.552111 | + | 0.833771i | \(0.313823\pi\) | |||||||
\(632\) | 10.1766 | 0.0161023 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 363.176 | 0.572832 | ||||||||
\(635\) | 670.881i | 1.05651i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −49.7746 | −0.0780166 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 50.4692i | 0.0788581i | ||||||||
\(641\) | 985.394 | 1.53728 | 0.768638 | − | 0.639684i | \(-0.220935\pi\) | ||||
0.768638 | + | 0.639684i | \(0.220935\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 675.943i | 1.05123i | 0.850722 | + | 0.525616i | \(0.176165\pi\) | ||||
−0.850722 | + | 0.525616i | \(0.823835\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 236.382 | 0.365916 | ||||||||
\(647\) | 116.745i | 0.180440i | 0.995922 | + | 0.0902199i | \(0.0287570\pi\) | ||||
−0.995922 | + | 0.0902199i | \(0.971243\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 68.2226i | − 0.105120i | ||||||||
\(650\) | 134.230i | 0.206507i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 371.980 | 0.570521 | ||||||||
\(653\) | −941.248 | −1.44142 | −0.720710 | − | 0.693236i | \(-0.756184\pi\) | ||||
−0.720710 | + | 0.693236i | \(0.756184\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −971.176 | −1.48271 | ||||||||
\(656\) | 210.626i | 0.321076i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1159.61 | −1.75965 | −0.879827 | − | 0.475294i | \(-0.842342\pi\) | ||||
−0.879827 | + | 0.475294i | \(0.842342\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 740.805i | 1.12073i | 0.828244 | + | 0.560367i | \(0.189340\pi\) | ||||
−0.828244 | + | 0.560367i | \(0.810660\pi\) | |||||||
\(662\) | 220.049 | 0.332400 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 227.239i | 0.342227i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 454.010 | 0.680675 | ||||||||
\(668\) | − 412.285i | − 0.617193i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 25.2346i | 0.0376635i | ||||||||
\(671\) | 38.2870i | 0.0570596i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −573.075 | −0.851523 | −0.425762 | − | 0.904835i | \(-0.639994\pi\) | ||||
−0.425762 | + | 0.904835i | \(0.639994\pi\) | |||||||
\(674\) | 56.1564 | 0.0833181 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −354.583 | −0.524531 | ||||||||
\(677\) | − 136.629i | − 0.201816i | −0.994896 | − | 0.100908i | \(-0.967825\pi\) | ||||
0.994896 | − | 0.100908i | \(-0.0321747\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −151.882 | −0.223356 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 60.6140i | 0.0888768i | ||||||||
\(683\) | −266.455 | −0.390124 | −0.195062 | − | 0.980791i | \(-0.562491\pi\) | ||||
−0.195062 | + | 0.980791i | \(0.562491\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 232.152i | 0.338908i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −286.392 | −0.416267 | ||||||||
\(689\) | 1939.52i | 2.81498i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 127.568i | − 0.184614i | −0.995731 | − | 0.0923071i | \(-0.970576\pi\) | ||||
0.995731 | − | 0.0923071i | \(-0.0294242\pi\) | |||||||
\(692\) | − 412.150i | − 0.595592i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −918.774 | −1.32388 | ||||||||
\(695\) | 641.470 | 0.922979 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −633.859 | −0.909410 | ||||||||
\(698\) | 872.272i | 1.24967i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 545.325 | 0.777924 | 0.388962 | − | 0.921254i | \(-0.372834\pi\) | ||||
0.388962 | + | 0.921254i | \(0.372834\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 634.541i | − 0.902619i | ||||||||
\(704\) | 22.6274 | 0.0321412 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 750.601i | − 1.06317i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −171.106 | −0.241334 | −0.120667 | − | 0.992693i | \(-0.538503\pi\) | ||||
−0.120667 | + | 0.992693i | \(0.538503\pi\) | |||||||
\(710\) | − 581.663i | − 0.819244i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 316.573i | 0.444625i | ||||||||
\(713\) | − 552.879i | − 0.775427i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −234.794 | −0.328383 | ||||||||
\(716\) | −320.167 | −0.447160 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 752.382 | 1.04789 | ||||||||
\(719\) | 233.579i | 0.324867i | 0.986720 | + | 0.162433i | \(0.0519342\pi\) | ||||
−0.986720 | + | 0.162433i | \(0.948066\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 237.865 | 0.329453 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 199.847i | − 0.276032i | ||||||||
\(725\) | −63.4689 | −0.0875433 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 912.568i | − 1.25525i | −0.778515 | − | 0.627626i | \(-0.784027\pi\) | ||||
0.778515 | − | 0.627626i | \(-0.215973\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 539.186 | 0.738611 | ||||||||
\(731\) | − 861.870i | − 1.17903i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 333.754i | 0.455327i | 0.973740 | + | 0.227663i | \(0.0731085\pi\) | ||||
−0.973740 | + | 0.227663i | \(0.926891\pi\) | |||||||
\(734\) | 553.060i | 0.753487i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −206.392 | −0.280424 | ||||||||
\(737\) | 11.3137 | 0.0153510 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −640.382 | −0.866552 | −0.433276 | − | 0.901261i | \(-0.642642\pi\) | ||||
−0.433276 | + | 0.901261i | \(0.642642\pi\) | |||||||
\(740\) | 407.711i | 0.550961i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 750.642 | 1.01028 | 0.505142 | − | 0.863036i | \(-0.331440\pi\) | ||||
0.505142 | + | 0.863036i | \(0.331440\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 85.1508i | − 0.114296i | ||||||||
\(746\) | 102.960 | 0.138017 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 68.0951i | 0.0910363i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 795.980 | 1.05989 | 0.529947 | − | 0.848031i | \(-0.322212\pi\) | ||||
0.529947 | + | 0.848031i | \(0.322212\pi\) | |||||||
\(752\) | 338.937i | 0.450714i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 327.479i | − 0.434323i | ||||||||
\(755\) | 688.725i | 0.912218i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −145.678 | −0.192442 | −0.0962208 | − | 0.995360i | \(-0.530675\pi\) | ||||
−0.0962208 | + | 0.995360i | \(0.530675\pi\) | |||||||
\(758\) | −43.5778 | −0.0574905 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 175.196 | 0.230521 | ||||||||
\(761\) | 866.153i | 1.13818i | 0.822276 | + | 0.569089i | \(0.192704\pi\) | ||||
−0.822276 | + | 0.569089i | \(0.807296\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 139.147 | 0.182130 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 631.119i | 0.823916i | ||||||||
\(767\) | 448.853 | 0.585206 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1051.96i | 1.36796i | 0.729502 | + | 0.683978i | \(0.239752\pi\) | ||||
−0.729502 | + | 0.683978i | \(0.760248\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 270.392 | 0.350249 | ||||||||
\(773\) | − 855.796i | − 1.10711i | −0.832813 | − | 0.553555i | \(-0.813271\pi\) | ||||
0.832813 | − | 0.553555i | \(-0.186729\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 77.2905i | 0.0997296i | ||||||||
\(776\) | 65.2776i | 0.0841206i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −367.990 | −0.472995 | ||||||||
\(779\) | 731.156 | 0.938582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −260.784 | −0.333910 | ||||||||
\(782\) | − 621.117i | − 0.794268i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 524.943 | 0.668717 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1405.91i | 1.78642i | 0.449643 | + | 0.893208i | \(0.351551\pi\) | ||||
−0.449643 | + | 0.893208i | \(0.648449\pi\) | |||||||
\(788\) | 42.9807 | 0.0545440 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 22.6984i | 0.0287321i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −251.899 | −0.317654 | ||||||||
\(794\) | 862.454i | 1.08621i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 519.654i | − 0.652831i | ||||||||
\(797\) | − 253.331i | − 0.317856i | −0.987290 | − | 0.158928i | \(-0.949196\pi\) | ||||
0.987290 | − | 0.158928i | \(-0.0508037\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1020.00 | −1.27660 | ||||||||
\(800\) | 28.8528 | 0.0360660 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −207.970 | −0.259314 | ||||||||
\(803\) | − 241.739i | − 0.301045i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −398.794 | −0.494782 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 233.515i | − 0.289004i | ||||||||
\(809\) | −739.882 | −0.914564 | −0.457282 | − | 0.889322i | \(-0.651177\pi\) | ||||
−0.457282 | + | 0.889322i | \(0.651177\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 764.518i | 0.942686i | 0.881950 | + | 0.471343i | \(0.156231\pi\) | ||||
−0.881950 | + | 0.471343i | \(0.843769\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 182.794 | 0.224563 | ||||||||
\(815\) | 829.680i | 1.01801i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 994.166i | 1.21685i | ||||||||
\(818\) | − 224.524i | − 0.274480i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −469.789 | −0.572913 | ||||||||
\(821\) | 119.902 | 0.146044 | 0.0730222 | − | 0.997330i | \(-0.476736\pi\) | ||||
0.0730222 | + | 0.997330i | \(0.476736\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −307.196 | −0.373264 | −0.186632 | − | 0.982430i | \(-0.559757\pi\) | ||||
−0.186632 | + | 0.982430i | \(0.559757\pi\) | |||||||
\(824\) | − 460.345i | − 0.558671i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −514.504 | −0.622133 | −0.311066 | − | 0.950388i | \(-0.600686\pi\) | ||||
−0.311066 | + | 0.950388i | \(0.600686\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 806.651i | − 0.973041i | −0.873669 | − | 0.486520i | \(-0.838266\pi\) | ||||
0.873669 | − | 0.486520i | \(-0.161734\pi\) | |||||||
\(830\) | −506.843 | −0.610654 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 148.871i | 0.178932i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 919.578 | 1.10129 | ||||||||
\(836\) | − 78.5476i | − 0.0939565i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 816.001i | 0.973748i | ||||||||
\(839\) | 100.694i | 0.120017i | 0.998198 | + | 0.0600085i | \(0.0191128\pi\) | ||||
−0.998198 | + | 0.0600085i | \(0.980887\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −686.156 | −0.815881 | ||||||||
\(842\) | −53.7115 | −0.0637904 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −503.196 | −0.596204 | ||||||||
\(845\) | − 790.877i | − 0.935949i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 416.902 | 0.491629 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 86.8299i | 0.102153i | ||||||||
\(851\) | −1667.32 | −1.95925 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 137.712i | − 0.161444i | −0.996737 | − | 0.0807219i | \(-0.974277\pi\) | ||||
0.996737 | − | 0.0807219i | \(-0.0257226\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −39.1960 | −0.0457897 | ||||||||
\(857\) | − 557.744i | − 0.650809i | −0.945575 | − | 0.325405i | \(-0.894499\pi\) | ||||
0.945575 | − | 0.325405i | \(-0.105501\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1578.94i | − 1.83811i | −0.394126 | − | 0.919056i | \(-0.628953\pi\) | ||||
0.394126 | − | 0.919056i | \(-0.371047\pi\) | |||||||
\(860\) | − 638.781i | − 0.742768i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1110.37 | 1.28813 | ||||||||
\(863\) | −525.249 | −0.608631 | −0.304316 | − | 0.952571i | \(-0.598428\pi\) | ||||
−0.304316 | + | 0.952571i | \(0.598428\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 919.276 | 1.06275 | ||||||||
\(866\) | − 823.806i | − 0.951277i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.1766 | 0.0117107 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 74.4356i | 0.0854600i | ||||||||
\(872\) | 386.627 | 0.443380 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 716.458i | 0.819746i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.2611 | −0.0390663 | −0.0195331 | − | 0.999809i | \(-0.506218\pi\) | ||||
−0.0195331 | + | 0.999809i | \(0.506218\pi\) | |||||||
\(878\) | 9.14707i | 0.0104181i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 50.4692i | 0.0573513i | ||||||||
\(881\) | − 366.173i | − 0.415634i | −0.978168 | − | 0.207817i | \(-0.933364\pi\) | ||||
0.978168 | − | 0.207817i | \(-0.0666358\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 493.186 | 0.558534 | 0.279267 | − | 0.960213i | \(-0.409908\pi\) | ||||
0.279267 | + | 0.960213i | \(0.409908\pi\) | |||||||
\(884\) | −448.014 | −0.506803 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −412.804 | −0.465919 | ||||||||
\(887\) | 204.619i | 0.230687i | 0.993326 | + | 0.115344i | \(0.0367969\pi\) | ||||
−0.993326 | + | 0.115344i | \(0.963203\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −706.098 | −0.793368 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 58.0778i | 0.0651096i | ||||||||
\(893\) | 1176.57 | 1.31755 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 714.113i | − 0.797892i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −646.975 | −0.720462 | ||||||||
\(899\) | − 188.565i | − 0.209749i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1254.63i | 1.39248i | ||||||||
\(902\) | 210.626i | 0.233510i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 375.598 | 0.415484 | ||||||||
\(905\) | 445.747 | 0.492538 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −136.764 | −0.150787 | −0.0753934 | − | 0.997154i | \(-0.524021\pi\) | ||||
−0.0753934 | + | 0.997154i | \(0.524021\pi\) | |||||||
\(908\) | − 551.086i | − 0.606923i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −676.563 | −0.742659 | −0.371330 | − | 0.928501i | \(-0.621098\pi\) | ||||
−0.371330 | + | 0.928501i | \(0.621098\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 227.239i | 0.248892i | ||||||||
\(914\) | −962.745 | −1.05333 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 83.6915i | 0.0913663i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1022.41 | −1.11253 | −0.556263 | − | 0.831006i | \(-0.687765\pi\) | ||||
−0.556263 | + | 0.831006i | \(0.687765\pi\) | |||||||
\(920\) | − 460.345i | − 0.500375i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 221.185i | 0.239897i | ||||||||
\(923\) | − 1715.76i | − 1.85889i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 233.085 | 0.251984 | ||||||||
\(926\) | 524.353 | 0.566256 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −70.3919 | −0.0758534 | ||||||||
\(929\) | − 1797.60i | − 1.93499i | −0.252894 | − | 0.967494i | \(-0.581382\pi\) | ||||
0.252894 | − | 0.967494i | \(-0.418618\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 434.426 | 0.466123 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 56.8097i | − 0.0608240i | ||||||||
\(935\) | −151.882 | −0.162441 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 494.548i | 0.527800i | 0.964550 | + | 0.263900i | \(0.0850088\pi\) | ||||
−0.964550 | + | 0.263900i | \(0.914991\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −755.980 | −0.804234 | ||||||||
\(941\) | 39.6996i | 0.0421888i | 0.999777 | + | 0.0210944i | \(0.00671505\pi\) | ||||
−0.999777 | + | 0.0210944i | \(0.993285\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1921.19i | − 2.03731i | ||||||||
\(944\) | − 96.4813i | − 0.102205i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −286.392 | −0.302740 | ||||||||
\(947\) | 1517.96 | 1.60291 | 0.801455 | − | 0.598055i | \(-0.204060\pi\) | ||||
0.801455 | + | 0.598055i | \(0.204060\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1590.46 | 1.67593 | ||||||||
\(950\) | − 100.158i | − 0.105430i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1512.57 | 1.58717 | 0.793583 | − | 0.608462i | \(-0.208213\pi\) | ||||
0.793583 | + | 0.608462i | \(0.208213\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 310.360i | 0.324984i | ||||||||
\(956\) | 137.442 | 0.143767 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 301.419i | − 0.314634i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 731.372 | 0.761053 | ||||||||
\(962\) | 1202.65i | 1.25015i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 36.0772i | − 0.0374244i | ||||||||
\(965\) | 603.094i | 0.624967i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 308.382 | 0.318906 | 0.159453 | − | 0.987206i | \(-0.449027\pi\) | ||||
0.159453 | + | 0.987206i | \(0.449027\pi\) | |||||||
\(968\) | −319.612 | −0.330178 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −145.598 | −0.150101 | ||||||||
\(971\) | − 683.164i | − 0.703568i | −0.936081 | − | 0.351784i | \(-0.885575\pi\) | ||||
0.936081 | − | 0.351784i | \(-0.114425\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1193.03 | −1.22487 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 54.1460i | 0.0554775i | ||||||||
\(977\) | −1339.53 | −1.37106 | −0.685532 | − | 0.728042i | \(-0.740430\pi\) | ||||
−0.685532 | + | 0.728042i | \(0.740430\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 316.573i | 0.323363i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 869.206 | 0.885139 | ||||||||
\(983\) | − 952.611i | − 0.969085i | −0.874768 | − | 0.484543i | \(-0.838986\pi\) | ||||
0.874768 | − | 0.484543i | \(-0.161014\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 95.8659i | 0.0973258i | ||||||||
\(986\) | − 211.838i | − 0.214846i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 516.784 | 0.523061 | ||||||||
\(989\) | 2612.27 | 2.64133 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1307.92 | 1.31980 | 0.659899 | − | 0.751355i | \(-0.270599\pi\) | ||||
0.659899 | + | 0.751355i | \(0.270599\pi\) | |||||||
\(992\) | 85.7211i | 0.0864124i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1159.06 | 1.16488 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 248.288i | − 0.249035i | −0.992217 | − | 0.124518i | \(-0.960262\pi\) | ||||
0.992217 | − | 0.124518i | \(-0.0397383\pi\) | |||||||
\(998\) | 933.352 | 0.935223 | ||||||||
\(999\) | 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 | 882.3.c.d.685.4 | yes | 4 | |
3.2 | odd | 2 | 882.3.c.e.685.1 | yes | 4 | ||
7.2 | even | 3 | 882.3.n.h.325.2 | 8 | |||
7.3 | odd | 6 | 882.3.n.h.19.2 | 8 | |||
7.4 | even | 3 | 882.3.n.h.19.1 | 8 | |||
7.5 | odd | 6 | 882.3.n.h.325.1 | 8 | |||
7.6 | odd | 2 | inner | 882.3.c.d.685.3 | ✓ | 4 | |
21.2 | odd | 6 | 882.3.n.g.325.3 | 8 | |||
21.5 | even | 6 | 882.3.n.g.325.4 | 8 | |||
21.11 | odd | 6 | 882.3.n.g.19.4 | 8 | |||
21.17 | even | 6 | 882.3.n.g.19.3 | 8 | |||
21.20 | even | 2 | 882.3.c.e.685.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.3.c.d.685.3 | ✓ | 4 | 7.6 | odd | 2 | inner | |
882.3.c.d.685.4 | yes | 4 | 1.1 | even | 1 | trivial | |
882.3.c.e.685.1 | yes | 4 | 3.2 | odd | 2 | ||
882.3.c.e.685.2 | yes | 4 | 21.20 | even | 2 | ||
882.3.n.g.19.3 | 8 | 21.17 | even | 6 | |||
882.3.n.g.19.4 | 8 | 21.11 | odd | 6 | |||
882.3.n.g.325.3 | 8 | 21.2 | odd | 6 | |||
882.3.n.g.325.4 | 8 | 21.5 | even | 6 | |||
882.3.n.h.19.1 | 8 | 7.4 | even | 3 | |||
882.3.n.h.19.2 | 8 | 7.3 | odd | 6 | |||
882.3.n.h.325.1 | 8 | 7.5 | odd | 6 | |||
882.3.n.h.325.2 | 8 | 7.2 | even | 3 |