Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,4,Mod(1,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.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: | \(63.7220628062\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{241}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 60 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-7.26209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.26209 | 0.284126 | 0.142063 | − | 0.989858i | \(-0.454626\pi\) | ||||
0.142063 | + | 0.989858i | \(0.454626\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.2621 | 0.281285 | 0.140643 | − | 0.990060i | \(-0.455083\pi\) | ||||
0.140643 | + | 0.990060i | \(0.455083\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −58.5725 | −1.24962 | −0.624811 | − | 0.780776i | \(-0.714824\pi\) | ||||
−0.624811 | + | 0.780776i | \(0.714824\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −33.8346 | −0.482712 | −0.241356 | − | 0.970437i | \(-0.577592\pi\) | ||||
−0.241356 | + | 0.970437i | \(0.577592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 119.883 | 1.44753 | 0.723764 | − | 0.690047i | \(-0.242410\pi\) | ||||
0.723764 | + | 0.690047i | \(0.242410\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 182.455 | 1.65411 | 0.827056 | − | 0.562119i | \(-0.190014\pi\) | ||||
0.827056 | + | 0.562119i | \(0.190014\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −49.4071 | −0.316368 | −0.158184 | − | 0.987410i | \(-0.550564\pi\) | ||||
−0.158184 | + | 0.987410i | \(0.550564\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −200.980 | −1.16442 | −0.582210 | − | 0.813039i | \(-0.697812\pi\) | ||||
−0.582210 | + | 0.813039i | \(0.697812\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −26.3104 | −0.127065 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −89.6896 | −0.398510 | −0.199255 | − | 0.979948i | \(-0.563852\pi\) | ||||
−0.199255 | + | 0.979948i | \(0.563852\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −136.621 | −0.520405 | −0.260202 | − | 0.965554i | \(-0.583789\pi\) | ||||
−0.260202 | + | 0.965554i | \(0.583789\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −254.552 | −0.902764 | −0.451382 | − | 0.892331i | \(-0.649069\pi\) | ||||
−0.451382 | + | 0.892331i | \(0.649069\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −61.8346 | −0.191904 | −0.0959522 | − | 0.995386i | \(-0.530590\pi\) | ||||
−0.0959522 | + | 0.995386i | \(0.530590\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −315.310 | −0.919272 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 671.104 | 1.73931 | 0.869654 | − | 0.493663i | \(-0.164342\pi\) | ||||
0.869654 | + | 0.493663i | \(0.164342\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −51.3104 | −0.125795 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −450.290 | −0.993606 | −0.496803 | − | 0.867863i | \(-0.665493\pi\) | ||||
−0.496803 | + | 0.867863i | \(0.665493\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −126.310 | −0.265121 | −0.132561 | − | 0.991175i | \(-0.542320\pi\) | ||||
−0.132561 | + | 0.991175i | \(0.542320\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 292.863 | 0.558848 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 466.132 | 0.849957 | 0.424979 | − | 0.905203i | \(-0.360282\pi\) | ||||
0.424979 | + | 0.905203i | \(0.360282\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 370.056 | 0.618557 | 0.309279 | − | 0.950971i | \(-0.399912\pi\) | ||||
0.309279 | + | 0.950971i | \(0.399912\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 151.705 | 0.243229 | 0.121614 | − | 0.992577i | \(-0.461193\pi\) | ||||
0.121614 | + | 0.992577i | \(0.461193\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 54.0000 | 0.0799204 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 44.8626 | 0.0638916 | 0.0319458 | − | 0.999490i | \(-0.489830\pi\) | ||||
0.0319458 | + | 0.999490i | \(0.489830\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −855.435 | −1.13128 | −0.565640 | − | 0.824652i | \(-0.691371\pi\) | ||||
−0.565640 | + | 0.824652i | \(0.691371\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 169.173 | 0.215875 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1098.60 | −1.30844 | −0.654219 | − | 0.756306i | \(-0.727002\pi\) | ||||
−0.654219 | + | 0.756306i | \(0.727002\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −308.214 | −0.355050 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −599.415 | −0.647354 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1207.08 | −1.26351 | −0.631757 | − | 0.775167i | \(-0.717666\pi\) | ||||
−0.631757 | + | 0.775167i | \(0.717666\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 523.463 | 0.515708 | 0.257854 | − | 0.966184i | \(-0.416985\pi\) | ||||
0.257854 | + | 0.966184i | \(0.416985\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −969.883 | −0.927819 | −0.463910 | − | 0.885882i | \(-0.653554\pi\) | ||||
−0.463910 | + | 0.885882i | \(0.653554\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 374.000 | 0.337906 | 0.168953 | − | 0.985624i | \(-0.445961\pi\) | ||||
0.168953 | + | 0.985624i | \(0.445961\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1962.36 | −1.72440 | −0.862202 | − | 0.506564i | \(-0.830915\pi\) | ||||
−0.862202 | + | 0.506564i | \(0.830915\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −386.649 | −0.321884 | −0.160942 | − | 0.986964i | \(-0.551453\pi\) | ||||
−0.160942 | + | 0.986964i | \(0.551453\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −912.277 | −0.739742 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −178.041 | −0.137151 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1225.69 | −0.920879 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1348.83 | −0.942435 | −0.471218 | − | 0.882017i | \(-0.656185\pi\) | ||||
−0.471218 | + | 0.882017i | \(0.656185\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 353.148 | 0.235532 | 0.117766 | − | 0.993041i | \(-0.462427\pi\) | ||||
0.117766 | + | 0.993041i | \(0.462427\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 630.835 | 0.411280 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1196.48 | 0.746150 | 0.373075 | − | 0.927801i | \(-0.378303\pi\) | ||||
0.373075 | + | 0.927801i | \(0.378303\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2768.71 | −1.68949 | −0.844745 | − | 0.535169i | \(-0.820248\pi\) | ||||
−0.844745 | + | 0.535169i | \(0.820248\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −601.076 | −0.351500 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 247.036 | 0.141484 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3310.89 | 1.82039 | 0.910196 | − | 0.414177i | \(-0.135930\pi\) | ||||
0.910196 | + | 0.414177i | \(0.135930\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 974.715 | 0.525306 | 0.262653 | − | 0.964890i | \(-0.415403\pi\) | ||||
0.262653 | + | 0.964890i | \(0.415403\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1004.90 | 0.520744 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −930.013 | −0.472759 | −0.236379 | − | 0.971661i | \(-0.575961\pi\) | ||||
−0.236379 | + | 0.971661i | \(0.575961\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 960.097 | 0.469977 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1461.81 | −0.702443 | −0.351221 | − | 0.936292i | \(-0.614234\pi\) | ||||
−0.351221 | + | 0.936292i | \(0.614234\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3507.59 | −1.62530 | −0.812652 | − | 0.582750i | \(-0.801977\pi\) | ||||
−0.812652 | + | 0.582750i | \(0.801977\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1233.74 | 0.561557 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2407.46 | −1.05801 | −0.529004 | − | 0.848619i | \(-0.677434\pi\) | ||||
−0.529004 | + | 0.848619i | \(0.677434\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 131.552 | 0.0568252 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −709.089 | −0.296088 | −0.148044 | − | 0.988981i | \(-0.547298\pi\) | ||||
−0.148044 | + | 0.988981i | \(0.547298\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1245.94 | −0.511657 | −0.255828 | − | 0.966722i | \(-0.582348\pi\) | ||||
−0.255828 | + | 0.966722i | \(0.582348\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 448.448 | 0.178219 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −347.214 | −0.135780 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2809.14 | −1.06420 | −0.532099 | − | 0.846682i | \(-0.678597\pi\) | ||||
−0.532099 | + | 0.846682i | \(0.678597\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4285.72 | −1.59841 | −0.799204 | − | 0.601059i | \(-0.794746\pi\) | ||||
−0.799204 | + | 0.601059i | \(0.794746\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2741.44 | 0.991468 | 0.495734 | − | 0.868474i | \(-0.334899\pi\) | ||||
0.495734 | + | 0.868474i | \(0.334899\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2922.07 | 1.04090 | 0.520452 | − | 0.853891i | \(-0.325763\pi\) | ||||
0.520452 | + | 0.853891i | \(0.325763\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −259.985 | −0.0898884 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 683.104 | 0.232732 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1230.25 | 0.407168 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3525.37 | −1.15022 | −0.575111 | − | 0.818076i | \(-0.695041\pi\) | ||||
−0.575111 | + | 0.818076i | \(0.695041\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1272.76 | 0.403728 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1057.57 | −0.330842 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1981.78 | 0.603207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3631.29 | −1.09044 | −0.545222 | − | 0.838292i | \(-0.683555\pi\) | ||||
−0.545222 | + | 0.838292i | \(0.683555\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3795.86 | 1.10987 | 0.554934 | − | 0.831895i | \(-0.312744\pi\) | ||||
0.554934 | + | 0.831895i | \(0.312744\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −257.913 | −0.0744253 | −0.0372126 | − | 0.999307i | \(-0.511848\pi\) | ||||
−0.0372126 | + | 0.999307i | \(0.511848\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1579.73 | 0.444170 | 0.222085 | − | 0.975027i | \(-0.428714\pi\) | ||||
0.222085 | + | 0.975027i | \(0.428714\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 309.173 | 0.0858222 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2892.29 | −0.782790 | −0.391395 | − | 0.920223i | \(-0.628007\pi\) | ||||
−0.391395 | + | 0.920223i | \(0.628007\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2028.30 | −0.542135 | −0.271067 | − | 0.962560i | \(-0.587377\pi\) | ||||
−0.271067 | + | 0.962560i | \(0.587377\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1576.55 | 0.411111 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7021.85 | −1.80886 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6509.83 | −1.63704 | −0.818520 | − | 0.574479i | \(-0.805205\pi\) | ||||
−0.818520 | + | 0.574479i | \(0.805205\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1872.37 | 0.465277 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1966.13 | 0.477214 | 0.238607 | − | 0.971116i | \(-0.423309\pi\) | ||||
0.238607 | + | 0.971116i | \(0.423309\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −471.954 | −0.113227 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −38.8089 | −0.00909909 | −0.00454955 | − | 0.999990i | \(-0.501448\pi\) | ||||
−0.00454955 | + | 0.999990i | \(0.501448\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3355.52 | −0.777842 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2109.23 | −0.478074 | −0.239037 | − | 0.971010i | \(-0.576832\pi\) | ||||
−0.239037 | + | 0.971010i | \(0.576832\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 607.852 | 0.136252 | 0.0681262 | − | 0.997677i | \(-0.478298\pi\) | ||||
0.0681262 | + | 0.997677i | \(0.478298\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 256.552 | 0.0562570 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8360.69 | 1.81352 | 0.906760 | − | 0.421647i | \(-0.138548\pi\) | ||||
0.906760 | + | 0.421647i | \(0.138548\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 443.944 | 0.0942473 | 0.0471236 | − | 0.998889i | \(-0.484995\pi\) | ||||
0.0471236 | + | 0.998889i | \(0.484995\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6190.56 | 1.30032 | 0.650160 | − | 0.759798i | \(-0.274702\pi\) | ||||
0.650160 | + | 0.759798i | \(0.274702\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −718.911 | −0.147861 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3768.22 | −0.766989 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3187.87 | 0.635623 | 0.317811 | − | 0.948154i | \(-0.397052\pi\) | ||||
0.317811 | + | 0.948154i | \(0.397052\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2251.45 | 0.444354 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10686.9 | −2.06702 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1339.48 | −0.256499 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 631.552 | 0.118566 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.2874 | 0.00525879 | 0.00262940 | − | 0.999997i | \(-0.499163\pi\) | ||||
0.00262940 | + | 0.999997i | \(0.499163\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −229.923 | −0.0419220 | −0.0209610 | − | 0.999780i | \(-0.506673\pi\) | ||||
−0.0209610 | + | 0.999780i | \(0.506673\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7115.56 | 1.28497 | 0.642484 | − | 0.766299i | \(-0.277904\pi\) | ||||
0.642484 | + | 0.766299i | \(0.277904\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4346.34 | 0.770078 | 0.385039 | − | 0.922900i | \(-0.374188\pi\) | ||||
0.385039 | + | 0.922900i | \(0.374188\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −507.020 | −0.0889896 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4056.19 | −0.698739 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1464.31 | −0.249925 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −325.379 | −0.0545250 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5567.01 | 0.924443 | 0.462222 | − | 0.886764i | \(-0.347052\pi\) | ||||
0.462222 | + | 0.886764i | \(0.347052\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2330.66 | −0.380112 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2803.11 | −0.453101 | −0.226551 | − | 0.973999i | \(-0.572745\pi\) | ||||
−0.226551 | + | 0.973999i | \(0.572745\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2062.47 | −0.327534 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3464.09 | −0.545315 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5508.55 | 0.852203 | 0.426102 | − | 0.904675i | \(-0.359887\pi\) | ||||
0.426102 | + | 0.904675i | \(0.359887\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3195.98 | −0.490192 | −0.245096 | − | 0.969499i | \(-0.578819\pi\) | ||||
−0.245096 | + | 0.969499i | \(0.578819\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7565.44 | 1.14070 | 0.570351 | − | 0.821401i | \(-0.306807\pi\) | ||||
0.570351 | + | 0.821401i | \(0.306807\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1850.28 | −0.276627 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3410.73 | 0.501424 | 0.250712 | − | 0.968062i | \(-0.419335\pi\) | ||||
0.250712 | + | 0.968062i | \(0.419335\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7512.92 | 1.09534 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −758.525 | −0.108775 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7358.20 | 1.04658 | 0.523290 | − | 0.852155i | \(-0.324704\pi\) | ||||
0.523290 | + | 0.852155i | \(0.324704\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3531.41 | 0.494182 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10392.0 | −1.44256 | −0.721282 | − | 0.692641i | \(-0.756447\pi\) | ||||
−0.721282 | + | 0.692641i | \(0.756447\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2893.90 | 0.395341 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3672.63 | 0.497758 | 0.248879 | − | 0.968535i | \(-0.419938\pi\) | ||||
0.248879 | + | 0.968535i | \(0.419938\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10622.3 | −1.41716 | −0.708580 | − | 0.705631i | \(-0.750664\pi\) | ||||
−0.708580 | + | 0.705631i | \(0.750664\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −270.000 | −0.0357415 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5493.15 | −0.715974 | −0.357987 | − | 0.933727i | \(-0.616537\pi\) | ||||
−0.357987 | + | 0.933727i | \(0.616537\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6173.31 | −0.798460 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −224.313 | −0.0285732 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6081.41 | 0.768809 | 0.384405 | − | 0.923165i | \(-0.374407\pi\) | ||||
0.384405 | + | 0.923165i | \(0.374407\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1655.04 | 0.206107 | 0.103053 | − | 0.994676i | \(-0.467139\pi\) | ||||
0.103053 | + | 0.994676i | \(0.467139\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11771.9 | 1.45509 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −920.402 | −0.112095 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1065.37 | 0.128800 | 0.0644001 | − | 0.997924i | \(-0.479487\pi\) | ||||
0.0644001 | + | 0.997924i | \(0.479487\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2369.47 | −0.282309 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4277.18 | 0.505924 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10677.2 | −1.24491 | −0.622453 | − | 0.782657i | \(-0.713864\pi\) | ||||
−0.622453 | + | 0.782657i | \(0.713864\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10200.3 | 1.18083 | 0.590417 | − | 0.807099i | \(-0.298963\pi\) | ||||
0.590417 | + | 0.807099i | \(0.298963\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −845.865 | −0.0965423 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −664.657 | −0.0753278 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4424.46 | 0.494475 | 0.247237 | − | 0.968955i | \(-0.420477\pi\) | ||||
0.247237 | + | 0.968955i | \(0.420477\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7655.90 | 0.849698 | 0.424849 | − | 0.905264i | \(-0.360327\pi\) | ||||
0.424849 | + | 0.905264i | \(0.360327\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21873.3 | 2.39438 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13343.5 | 1.45068 | 0.725340 | − | 0.688391i | \(-0.241683\pi\) | ||||
0.725340 | + | 0.688391i | \(0.241683\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9738.80 | −1.04448 | −0.522240 | − | 0.852799i | \(-0.674903\pi\) | ||||
−0.522240 | + | 0.852799i | \(0.674903\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5492.98 | 0.585151 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6559.09 | −0.689404 | −0.344702 | − | 0.938712i | \(-0.612020\pi\) | ||||
−0.344702 | + | 0.938712i | \(0.612020\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1402.02 | −0.146382 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1541.07 | 0.158783 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3490.55 | −0.357288 | −0.178644 | − | 0.983914i | \(-0.557171\pi\) | ||||
−0.178644 | + | 0.983914i | \(0.557171\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19441.9 | 1.96420 | 0.982102 | − | 0.188350i | \(-0.0603138\pi\) | ||||
0.982102 | + | 0.188350i | \(0.0603138\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3239.12 | −0.325129 | −0.162565 | − | 0.986698i | \(-0.551977\pi\) | ||||
−0.162565 | + | 0.986698i | \(0.551977\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13057.4 | 1.29384 | 0.646920 | − | 0.762558i | \(-0.276057\pi\) | ||||
0.646920 | + | 0.762558i | \(0.276057\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2452.83 | 0.241495 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2612.24 | −0.253934 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2997.07 | 0.289506 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7892.32 | −0.752837 | −0.376419 | − | 0.926450i | \(-0.622845\pi\) | ||||
−0.376419 | + | 0.926450i | \(0.622845\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5253.34 | 0.497987 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6035.42 | 0.565060 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15479.0 | 1.44029 | 0.720143 | − | 0.693826i | \(-0.244076\pi\) | ||||
0.720143 | + | 0.693826i | \(0.244076\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14417.7 | −1.32518 | −0.662590 | − | 0.748983i | \(-0.730543\pi\) | ||||
−0.662590 | + | 0.748983i | \(0.730543\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1671.67 | 0.152715 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1947.27 | 0.175748 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3611.04 | −0.323953 | −0.161976 | − | 0.986795i | \(-0.551787\pi\) | ||||
−0.161976 | + | 0.986795i | \(0.551787\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6050.08 | 0.536302 | 0.268151 | − | 0.963377i | \(-0.413587\pi\) | ||||
0.268151 | + | 0.963377i | \(0.413587\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2617.32 | −0.230632 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −708.919 | −0.0617334 | −0.0308667 | − | 0.999524i | \(-0.509827\pi\) | ||||
−0.0308667 | + | 0.999524i | \(0.509827\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 798.284 | 0.0691077 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4849.41 | 0.414933 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −634.552 | −0.0539798 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19852.8 | −1.66942 | −0.834709 | − | 0.550691i | \(-0.814364\pi\) | ||||
−0.834709 | + | 0.550691i | \(0.814364\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1684.83 | 0.140865 | 0.0704325 | − | 0.997517i | \(-0.477562\pi\) | ||||
0.0704325 | + | 0.997517i | \(0.477562\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6800.07 | 0.562079 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21123.0 | 1.73609 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8002.23 | 0.650310 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1870.00 | −0.151116 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3235.74 | −0.258578 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15054.7 | 1.19640 | 0.598200 | − | 0.801347i | \(-0.295883\pi\) | ||||
0.598200 | + | 0.801347i | \(0.295883\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9811.81 | 0.771177 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2796.32 | 0.218578 | 0.109289 | − | 0.994010i | \(-0.465143\pi\) | ||||
0.109289 | + | 0.994010i | \(0.465143\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5923.07 | −0.457952 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 236.071 | 0.0181533 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10530.4 | 0.801057 | 0.400529 | − | 0.916284i | \(-0.368827\pi\) | ||||
0.400529 | + | 0.916284i | \(0.368827\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14909.8 | 1.12811 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11472.7 | −0.858819 | −0.429410 | − | 0.903110i | \(-0.641278\pi\) | ||||
−0.429410 | + | 0.903110i | \(0.641278\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1933.24 | 0.143951 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5727.73 | −0.422002 | −0.211001 | − | 0.977486i | \(-0.567672\pi\) | ||||
−0.211001 | + | 0.977486i | \(0.567672\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2466.83 | −0.180794 | −0.0903972 | − | 0.995906i | \(-0.528814\pi\) | ||||
−0.0903972 | + | 0.995906i | \(0.528814\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4561.39 | 0.330823 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4094.13 | −0.295392 | −0.147696 | − | 0.989033i | \(-0.547186\pi\) | ||||
−0.147696 | + | 0.989033i | \(0.547186\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4501.37 | −0.321426 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6886.93 | 0.489241 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9253.56 | −0.650657 | −0.325328 | − | 0.945601i | \(-0.605475\pi\) | ||||
−0.325328 | + | 0.945601i | \(0.605475\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24094.0 | −1.68553 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23367.6 | −1.61820 | −0.809100 | − | 0.587671i | \(-0.800045\pi\) | ||||
−0.809100 | + | 0.587671i | \(0.800045\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 890.203 | 0.0613358 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9990.04 | −0.681439 | −0.340720 | − | 0.940165i | \(-0.610671\pi\) | ||||
−0.340720 | + | 0.940165i | \(0.610671\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2726.36 | 0.185042 | 0.0925212 | − | 0.995711i | \(-0.470507\pi\) | ||||
0.0925212 | + | 0.995711i | \(0.470507\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6128.45 | 0.411829 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3765.23 | −0.251773 | −0.125886 | − | 0.992045i | \(-0.540177\pi\) | ||||
−0.125886 | + | 0.992045i | \(0.540177\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3621.81 | 0.239808 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13014.2 | 0.857484 | 0.428742 | − | 0.903427i | \(-0.358957\pi\) | ||||
0.428742 | + | 0.903427i | \(0.358957\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11152.4 | 0.727678 | 0.363839 | − | 0.931462i | \(-0.381466\pi\) | ||||
0.363839 | + | 0.931462i | \(0.381466\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8128.37 | 0.527797 | 0.263899 | − | 0.964550i | \(-0.414992\pi\) | ||||
0.263899 | + | 0.964550i | \(0.414992\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5780.91 | −0.371761 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3034.61 | 0.192365 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11271.8 | −0.711129 | −0.355565 | − | 0.934652i | \(-0.615711\pi\) | ||||
−0.355565 | + | 0.934652i | \(0.615711\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6744.15 | 0.421470 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18468.5 | 1.14874 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19862.2 | −1.22388 | −0.611942 | − | 0.790903i | \(-0.709611\pi\) | ||||
−0.611942 | + | 0.790903i | \(0.709611\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28296.6 | −1.73547 | −0.867735 | − | 0.497026i | \(-0.834425\pi\) | ||||
−0.867735 | + | 0.497026i | \(0.834425\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20338.9 | 1.23586 | 0.617932 | − | 0.786232i | \(-0.287971\pi\) | ||||
0.617932 | + | 0.786232i | \(0.287971\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4620.92 | −0.279487 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2905.09 | −0.174096 | −0.0870482 | − | 0.996204i | \(-0.527743\pi\) | ||||
−0.0870482 | + | 0.996204i | \(0.527743\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1765.74 | −0.105333 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22802.3 | 1.34788 | 0.673940 | − | 0.738786i | \(-0.264601\pi\) | ||||
0.673940 | + | 0.738786i | \(0.264601\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21658.0 | −1.27443 | −0.637216 | − | 0.770685i | \(-0.719914\pi\) | ||||
−0.637216 | + | 0.770685i | \(0.719914\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3154.17 | −0.183930 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9014.60 | −0.523309 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1296.21 | −0.0745746 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26706.4 | 1.52965 | 0.764826 | − | 0.644237i | \(-0.222825\pi\) | ||||
0.764826 | + | 0.644237i | \(0.222825\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7679.87 | −0.435984 | −0.217992 | − | 0.975951i | \(-0.569951\pi\) | ||||
−0.217992 | + | 0.975951i | \(0.569951\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6351.78 | −0.358997 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27373.5 | 1.53355 | 0.766777 | − | 0.641914i | \(-0.221859\pi\) | ||||
0.766777 | + | 0.641914i | \(0.221859\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5982.42 | −0.333688 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −39308.3 | −2.17348 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21036.1 | 1.15810 | 0.579052 | − | 0.815290i | \(-0.303423\pi\) | ||||
0.579052 | + | 0.815290i | \(0.303423\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13843.6 | 0.755563 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4622.51 | 0.251205 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8762.99 | 0.472145 | 0.236072 | − | 0.971735i | \(-0.424140\pi\) | ||||
0.236072 | + | 0.971735i | \(0.424140\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10752.3 | −0.576855 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2754.51 | 0.146526 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12012.0 | −0.636278 | −0.318139 | − | 0.948044i | \(-0.603058\pi\) | ||||
−0.318139 | + | 0.948044i | \(0.603058\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −36669.8 | −1.92608 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3005.38 | 0.157196 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23304.8 | −1.20879 | −0.604395 | − | 0.796685i | \(-0.706585\pi\) | ||||
−0.604395 | + | 0.796685i | \(0.706585\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5103.61 | −0.263618 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1235.18 | −0.0632736 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4348.04 | 0.221816 | 0.110908 | − | 0.993831i | \(-0.464624\pi\) | ||||
0.110908 | + | 0.993831i | \(0.464624\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8612.67 | 0.435775 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37182.4 | 1.87362 | 0.936809 | − | 0.349840i | \(-0.113764\pi\) | ||||
0.936809 | + | 0.349840i | \(0.113764\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4783.49 | 0.239080 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5384.48 | 0.268026 | 0.134013 | − | 0.990980i | \(-0.457214\pi\) | ||||
0.134013 | + | 0.990980i | \(0.457214\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5771.71 | −0.284984 | −0.142492 | − | 0.989796i | \(-0.545512\pi\) | ||||
−0.142492 | + | 0.989796i | \(0.545512\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16554.4 | −0.814104 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1968.02 | 0.0960079 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24358.9 | 1.18358 | 0.591790 | − | 0.806092i | \(-0.298421\pi\) | ||||
0.591790 | + | 0.806092i | \(0.298421\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4873.58 | −0.234924 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9401.29 | −0.451381 | −0.225691 | − | 0.974199i | \(-0.572464\pi\) | ||||
−0.225691 | + | 0.974199i | \(0.572464\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38564.4 | 1.83700 | 0.918502 | − | 0.395417i | \(-0.129400\pi\) | ||||
0.918502 | + | 0.395417i | \(0.129400\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10326.1 | −0.489948 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 26374.6 | 1.24163 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14048.8 | −0.658792 | −0.329396 | − | 0.944192i | \(-0.606845\pi\) | ||||
−0.329396 | + | 0.944192i | \(0.606845\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6271.17 | −0.291796 | −0.145898 | − | 0.989300i | \(-0.546607\pi\) | ||||
−0.145898 | + | 0.989300i | \(0.546607\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5024.49 | −0.232884 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16378.5 | −0.753301 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3797.55 | 0.173991 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4650.06 | 0.211424 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5228.24 | 0.236807 | 0.118403 | − | 0.992966i | \(-0.462222\pi\) | ||||
0.118403 | + | 0.992966i | \(0.462222\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2034.58 | −0.0914556 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7398.32 | 0.331301 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40880.5 | 1.81689 | 0.908445 | − | 0.418004i | \(-0.137270\pi\) | ||||
0.908445 | + | 0.418004i | \(0.137270\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2092.15 | 0.0926345 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1556.81 | 0.0684167 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4800.48 | −0.210180 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36230.2 | −1.57452 | −0.787260 | − | 0.616621i | \(-0.788501\pi\) | ||||
−0.787260 | + | 0.616621i | \(0.788501\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12939.3 | −0.560248 | −0.280124 | − | 0.959964i | \(-0.590376\pi\) | ||||
−0.280124 | + | 0.959964i | \(0.590376\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7309.07 | 0.314142 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30516.5 | −1.30678 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13429.0 | 0.570860 | 0.285430 | − | 0.958400i | \(-0.407864\pi\) | ||||
0.285430 | + | 0.958400i | \(0.407864\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37367.4 | −1.58268 | −0.791340 | − | 0.611376i | \(-0.790616\pi\) | ||||
−0.791340 | + | 0.611376i | \(0.790616\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37017.4 | 1.55650 | 0.778248 | − | 0.627958i | \(-0.216109\pi\) | ||||
0.778248 | + | 0.627958i | \(0.216109\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13971.2 | −0.585332 | −0.292666 | − | 0.956215i | \(-0.594542\pi\) | ||||
−0.292666 | + | 0.956215i | \(0.594542\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10668.4 | 0.443744 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17538.0 | 0.726858 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −47630.9 | −1.95995 | −0.979976 | − | 0.199115i | \(-0.936193\pi\) | ||||
−0.979976 | + | 0.199115i | \(0.936193\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21947.9 | −0.899911 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6168.70 | −0.251136 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6449.69 | −0.261646 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16364.4 | −0.659181 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37418.2 | −1.50196 | −0.750982 | − | 0.660323i | \(-0.770420\pi\) | ||||
−0.750982 | + | 0.660323i | \(0.770420\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21465.2 | 0.855587 | 0.427794 | − | 0.903876i | \(-0.359291\pi\) | ||||
0.427794 | + | 0.903876i | \(0.359291\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32638.7 | 1.29641 | 0.648206 | − | 0.761465i | \(-0.275520\pi\) | ||||
0.648206 | + | 0.761465i | \(0.275520\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3305.92 | −0.130400 | −0.0651998 | − | 0.997872i | \(-0.520768\pi\) | ||||
−0.0651998 | + | 0.997872i | \(0.520768\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12037.3 | 0.473156 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 460.384 | 0.0179718 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27302.5 | −1.06213 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −657.761 | −0.0254130 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34721.4 | −1.33690 | −0.668449 | − | 0.743758i | \(-0.733041\pi\) | ||||
−0.668449 | + | 0.743758i | \(0.733041\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −51524.8 | −1.97039 | −0.985195 | − | 0.171435i | \(-0.945160\pi\) | ||||
−0.985195 | + | 0.171435i | \(0.945160\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24558.5 | −0.935969 | −0.467985 | − | 0.883737i | \(-0.655020\pi\) | ||||
−0.467985 | + | 0.883737i | \(0.655020\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33009.1 | 1.24953 | 0.624767 | − | 0.780811i | \(-0.285194\pi\) | ||||
0.624767 | + | 0.780811i | \(0.285194\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7097.66 | −0.267770 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7412.92 | −0.277787 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3545.45 | 0.132415 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9929.83 | 0.368385 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22706.6 | −0.839584 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6229.69 | 0.228820 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26038.7 | −0.953253 | −0.476626 | − | 0.879106i | \(-0.658141\pi\) | ||||
−0.476626 | + | 0.879106i | \(0.658141\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48904.8 | 1.77858 | 0.889291 | − | 0.457341i | \(-0.151198\pi\) | ||||
0.889291 | + | 0.457341i | \(0.151198\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8778.55 | −0.318212 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1858.29 | 0.0669207 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8429.18 | −0.302560 | −0.151280 | − | 0.988491i | \(-0.548340\pi\) | ||||
−0.151280 | + | 0.988491i | \(0.548340\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21675.1 | −0.772963 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2242.24 | −0.0797020 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30915.9 | −1.09184 | −0.545919 | − | 0.837838i | \(-0.683819\pi\) | ||||
−0.545919 | + | 0.837838i | \(0.683819\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −37800.3 | −1.33067 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1736.07 | 0.0607225 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36984.2 | 1.28946 | 0.644729 | − | 0.764411i | \(-0.276970\pi\) | ||||
0.644729 | + | 0.764411i | \(0.276970\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24141.7 | −0.836341 | −0.418170 | − | 0.908369i | \(-0.637329\pi\) | ||||
−0.418170 | + | 0.908369i | \(0.637329\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24927.2 | −0.860808 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19388.6 | 0.665306 | 0.332653 | − | 0.943049i | \(-0.392056\pi\) | ||||
0.332653 | + | 0.943049i | \(0.392056\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8885.74 | −0.303944 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37220.6 | −1.26515 | −0.632577 | − | 0.774497i | \(-0.718003\pi\) | ||||
−0.632577 | + | 0.774497i | \(0.718003\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14045.7 | 0.475924 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6296.00 | 0.212000 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10601.8 | 0.355873 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21428.6 | 0.714830 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38860.3 | −1.29231 | −0.646155 | − | 0.763206i | \(-0.723624\pi\) | ||||
−0.646155 | + | 0.763206i | \(0.723624\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45501.5 | 1.50382 | 0.751912 | − | 0.659263i | \(-0.229132\pi\) | ||||
0.751912 | + | 0.659263i | \(0.229132\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14569.2 | −0.480028 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −55908.4 | −1.83078 | −0.915388 | − | 0.402573i | \(-0.868116\pi\) | ||||
−0.915388 | + | 0.402573i | \(0.868116\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11273.9 | −0.368044 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7730.62 | −0.250833 | −0.125416 | − | 0.992104i | \(-0.540027\pi\) | ||||
−0.125416 | + | 0.992104i | \(0.540027\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13707.2 | −0.443398 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −46444.4 | −1.49327 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28247.8 | 0.905471 | 0.452735 | − | 0.891645i | \(-0.350448\pi\) | ||||
0.452735 | + | 0.891645i | \(0.350448\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14610.3 | −0.465507 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27881.1 | 0.885661 | 0.442831 | − | 0.896605i | \(-0.353974\pi\) | ||||
0.442831 | + | 0.896605i | \(0.353974\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1080.4.a.a.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 1080.4.a.b.1.2 | yes | 2 | ||
4.3 | odd | 2 | 2160.4.a.y.1.1 | 2 | |||
12.11 | even | 2 | 2160.4.a.bd.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.4.a.a.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1080.4.a.b.1.2 | yes | 2 | 3.2 | odd | 2 | ||
2160.4.a.y.1.1 | 2 | 4.3 | odd | 2 | |||
2160.4.a.bd.1.1 | 2 | 12.11 | even | 2 |