Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.246832.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 7x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 209) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.71457\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-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 | ||||||||
\(3\) | −0.121872 | −0.0703629 | −0.0351814 | − | 0.999381i | \(-0.511201\pi\) | ||||
−0.0351814 | + | 0.999381i | \(0.511201\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.06025 | −0.474159 | −0.237080 | − | 0.971490i | \(-0.576190\pi\) | ||||
−0.237080 | + | 0.971490i | \(0.576190\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.36889 | 1.27332 | 0.636660 | − | 0.771145i | \(-0.280316\pi\) | ||||
0.636660 | + | 0.771145i | \(0.280316\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.98515 | −0.995049 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.15993 | −0.599056 | −0.299528 | − | 0.954087i | \(-0.596829\pi\) | ||||
−0.299528 | + | 0.954087i | \(0.596829\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.129215 | 0.0333632 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.67288 | 0.890805 | 0.445402 | − | 0.895330i | \(-0.353061\pi\) | ||||
0.445402 | + | 0.895330i | \(0.353061\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.410573 | −0.0895944 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.15468 | −0.657797 | −0.328898 | − | 0.944365i | \(-0.606677\pi\) | ||||
−0.328898 | + | 0.944365i | \(0.606677\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.87587 | −0.775173 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.729422 | 0.140377 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.17849 | 1.33301 | 0.666506 | − | 0.745499i | \(-0.267789\pi\) | ||||
0.666506 | + | 0.745499i | \(0.267789\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.65295 | −0.835694 | −0.417847 | − | 0.908517i | \(-0.637215\pi\) | ||||
−0.417847 | + | 0.908517i | \(0.637215\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.121872 | 0.0212152 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.57187 | −0.603756 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.27446 | 0.373918 | 0.186959 | − | 0.982368i | \(-0.440137\pi\) | ||||
0.186959 | + | 0.982368i | \(0.440137\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.263235 | 0.0421513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.3852 | −1.77807 | −0.889034 | − | 0.457841i | \(-0.848623\pi\) | ||||
−0.889034 | + | 0.457841i | \(0.848623\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.38838 | −1.43171 | −0.715857 | − | 0.698247i | \(-0.753964\pi\) | ||||
−0.715857 | + | 0.698247i | \(0.753964\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.16501 | 0.471812 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.77094 | 0.841778 | 0.420889 | − | 0.907112i | \(-0.361718\pi\) | ||||
0.420889 | + | 0.907112i | \(0.361718\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.34940 | 0.621342 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.447622 | −0.0626796 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.65820 | −0.777213 | −0.388607 | − | 0.921404i | \(-0.627043\pi\) | ||||
−0.388607 | + | 0.921404i | \(0.627043\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.06025 | 0.142964 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.121872 | −0.0161423 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.7944 | 1.79588 | 0.897939 | − | 0.440121i | \(-0.145064\pi\) | ||||
0.897939 | + | 0.440121i | \(0.145064\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.98152 | 0.893892 | 0.446946 | − | 0.894561i | \(-0.352512\pi\) | ||||
0.446946 | + | 0.894561i | \(0.352512\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.0566 | −1.26702 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.29007 | 0.284048 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.81332 | 0.588041 | 0.294020 | − | 0.955799i | \(-0.405007\pi\) | ||||
0.294020 | + | 0.955799i | \(0.405007\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.384467 | 0.0462844 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.2629 | −1.81137 | −0.905685 | − | 0.423951i | \(-0.860643\pi\) | ||||
−0.905685 | + | 0.423951i | \(0.860643\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.08806 | −0.946636 | −0.473318 | − | 0.880892i | \(-0.656944\pi\) | ||||
−0.473318 | + | 0.880892i | \(0.656944\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.472360 | 0.0545434 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.36889 | −0.383920 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.4291 | −1.51090 | −0.755448 | − | 0.655209i | \(-0.772581\pi\) | ||||
−0.755448 | + | 0.655209i | \(0.772581\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.86655 | 0.985172 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.96666 | −1.09398 | −0.546992 | − | 0.837138i | \(-0.684227\pi\) | ||||
−0.546992 | + | 0.837138i | \(0.684227\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.89418 | −0.422383 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.874858 | −0.0937946 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.61626 | −0.489323 | −0.244661 | − | 0.969609i | \(-0.578677\pi\) | ||||
−0.244661 | + | 0.969609i | \(0.578677\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.27655 | −0.762790 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.567064 | 0.0588018 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.06025 | −0.108780 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.09907 | −0.416197 | −0.208099 | − | 0.978108i | \(-0.566727\pi\) | ||||
−0.208099 | + | 0.978108i | \(0.566727\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.98515 | 0.300019 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.8730 | −1.08190 | −0.540950 | − | 0.841055i | \(-0.681935\pi\) | ||||
−0.540950 | + | 0.841055i | \(0.681935\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.85864 | −0.872867 | −0.436434 | − | 0.899736i | \(-0.643759\pi\) | ||||
−0.436434 | + | 0.899736i | \(0.643759\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.435311 | 0.0424820 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.1669 | 1.75626 | 0.878131 | − | 0.478421i | \(-0.158791\pi\) | ||||
0.878131 | + | 0.478421i | \(0.158791\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.211303 | −0.0202392 | −0.0101196 | − | 0.999949i | \(-0.503221\pi\) | ||||
−0.0101196 | + | 0.999949i | \(0.503221\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.277193 | −0.0263100 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.198345 | −0.0186587 | −0.00932935 | − | 0.999956i | \(-0.502970\pi\) | ||||
−0.00932935 | + | 0.999956i | \(0.502970\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.34476 | 0.311900 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.44770 | 0.596090 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.3735 | 1.13428 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.38754 | 0.125110 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.41066 | 0.841715 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.60331 | 0.319742 | 0.159871 | − | 0.987138i | \(-0.448892\pi\) | ||||
0.159871 | + | 0.987138i | \(0.448892\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.14418 | 0.100739 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.8741 | −1.47430 | −0.737150 | − | 0.675729i | \(-0.763829\pi\) | ||||
−0.737150 | + | 0.675729i | \(0.763829\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.36889 | 0.292119 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.773371 | −0.0665612 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.10839 | −0.521875 | −0.260937 | − | 0.965356i | \(-0.584032\pi\) | ||||
−0.260937 | + | 0.965356i | \(0.584032\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.3347 | −0.961398 | −0.480699 | − | 0.876886i | \(-0.659617\pi\) | ||||
−0.480699 | + | 0.876886i | \(0.659617\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.703316 | −0.0592299 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.15993 | 0.180622 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.61101 | −0.632060 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.530070 | −0.0437194 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.75698 | 0.553554 | 0.276777 | − | 0.960934i | \(-0.410734\pi\) | ||||
0.276777 | + | 0.960934i | \(0.410734\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.46231 | −0.525895 | −0.262948 | − | 0.964810i | \(-0.584695\pi\) | ||||
−0.262948 | + | 0.964810i | \(0.584695\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.9641 | −0.886395 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.93330 | 0.396252 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.248382 | 0.0198230 | 0.00991152 | − | 0.999951i | \(-0.496845\pi\) | ||||
0.00991152 | + | 0.999951i | \(0.496845\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.689576 | 0.0546869 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.6278 | −0.837585 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.9710 | 1.32927 | 0.664637 | − | 0.747167i | \(-0.268586\pi\) | ||||
0.664637 | + | 0.747167i | \(0.268586\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.129215 | −0.0100594 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.865538 | 0.0669773 | 0.0334887 | − | 0.999439i | \(-0.489338\pi\) | ||||
0.0334887 | + | 0.999439i | \(0.489338\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.33471 | −0.641132 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.98515 | −0.228280 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.14483 | −0.315125 | −0.157563 | − | 0.987509i | \(-0.550364\pi\) | ||||
−0.157563 | + | 0.987509i | \(0.550364\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.0574 | −0.987043 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.68115 | −0.126363 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.04584 | −0.152913 | −0.0764567 | − | 0.997073i | \(-0.524361\pi\) | ||||
−0.0764567 | + | 0.997073i | \(0.524361\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.27519 | 0.392101 | 0.196051 | − | 0.980594i | \(-0.437188\pi\) | ||||
0.196051 | + | 0.980594i | \(0.437188\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.850852 | −0.0628968 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.41150 | −0.177297 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.67288 | −0.268588 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.45734 | 0.178745 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.1899 | 1.17146 | 0.585729 | − | 0.810507i | \(-0.300808\pi\) | ||||
0.585729 | + | 0.810507i | \(0.300808\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.0620 | −1.44409 | −0.722045 | − | 0.691846i | \(-0.756798\pi\) | ||||
−0.722045 | + | 0.691846i | \(0.756798\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.279095 | −0.0199864 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.8398 | −1.69851 | −0.849257 | − | 0.527979i | \(-0.822950\pi\) | ||||
−0.849257 | + | 0.527979i | \(0.822950\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.90194 | 0.134825 | 0.0674125 | − | 0.997725i | \(-0.478526\pi\) | ||||
0.0674125 | + | 0.997725i | \(0.478526\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.586609 | −0.0413762 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24.1835 | 1.69735 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.0712 | 0.843087 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.41719 | 0.654540 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.3048 | −0.847100 | −0.423550 | − | 0.905873i | \(-0.639216\pi\) | ||||
−0.423550 | + | 0.905873i | \(0.639216\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.86012 | 0.127453 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.95405 | 0.678860 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.6753 | −1.06411 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.985709 | 0.0666080 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.93316 | −0.533642 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.8473 | −1.52997 | −0.764985 | − | 0.644048i | \(-0.777254\pi\) | ||||
−0.764985 | + | 0.644048i | \(0.777254\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.5700 | 0.771335 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.00654 | −0.265923 | −0.132962 | − | 0.991121i | \(-0.542449\pi\) | ||||
−0.132962 | + | 0.991121i | \(0.542449\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.6024 | −1.62577 | −0.812887 | − | 0.582422i | \(-0.802105\pi\) | ||||
−0.812887 | + | 0.582422i | \(0.802105\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.410573 | 0.0270137 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.2994 | 1.06781 | 0.533903 | − | 0.845545i | \(-0.320725\pi\) | ||||
0.533903 | + | 0.845545i | \(0.320725\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.11865 | −0.399137 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.63664 | 0.106311 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.4182 | 0.997324 | 0.498662 | − | 0.866797i | \(-0.333825\pi\) | ||||
0.498662 | + | 0.866797i | \(0.333825\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.1441 | 1.55526 | 0.777629 | − | 0.628723i | \(-0.216422\pi\) | ||||
0.777629 | + | 0.628723i | \(0.216422\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.26885 | −0.209697 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.61146 | −0.294615 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.15993 | −0.137433 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.21466 | 0.0769758 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.9099 | 1.25670 | 0.628350 | − | 0.777931i | \(-0.283731\pi\) | ||||
0.628350 | + | 0.777931i | \(0.283731\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.15468 | 0.198333 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.474592 | 0.0297201 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.3126 | −1.39182 | −0.695911 | − | 0.718128i | \(-0.744999\pi\) | ||||
−0.695911 | + | 0.718128i | \(0.744999\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.66239 | 0.476118 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.4289 | −1.32641 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.7963 | −0.850716 | −0.425358 | − | 0.905025i | \(-0.639852\pi\) | ||||
−0.425358 | + | 0.905025i | \(0.639852\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.99912 | 0.368523 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.562593 | 0.0344301 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.2028 | −0.683048 | −0.341524 | − | 0.939873i | \(-0.610943\pi\) | ||||
−0.341524 | + | 0.939873i | \(0.610943\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.1234 | −1.04017 | −0.520085 | − | 0.854115i | \(-0.674100\pi\) | ||||
−0.520085 | + | 0.854115i | \(0.674100\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.886808 | 0.0536721 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.87587 | 0.233723 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.7127 | −0.823919 | −0.411960 | − | 0.911202i | \(-0.635156\pi\) | ||||
−0.411960 | + | 0.911202i | \(0.635156\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.8897 | 0.831557 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.8599 | 1.54267 | 0.771337 | − | 0.636427i | \(-0.219588\pi\) | ||||
0.771337 | + | 0.636427i | \(0.219588\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.8711 | −1.71621 | −0.858103 | − | 0.513477i | \(-0.828357\pi\) | ||||
−0.858103 | + | 0.513477i | \(0.828357\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.129215 | 0.00765404 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −38.3554 | −2.26405 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.50993 | −0.206467 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.499562 | 0.0292848 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.37971 | 0.372707 | 0.186353 | − | 0.982483i | \(-0.440333\pi\) | ||||
0.186353 | + | 0.982483i | \(0.440333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.6255 | −0.851532 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.729422 | −0.0423254 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.81389 | 0.394057 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −31.6284 | −1.82303 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.32511 | 0.0761256 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.40217 | −0.423847 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.4299 | −0.595264 | −0.297632 | − | 0.954681i | \(-0.596197\pi\) | ||||
−0.297632 | + | 0.954681i | \(0.596197\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.07962 | 0.0614174 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.26224 | 0.468508 | 0.234254 | − | 0.972175i | \(-0.424735\pi\) | ||||
0.234254 | + | 0.972175i | \(0.424735\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.1167 | −1.36315 | −0.681577 | − | 0.731746i | \(-0.738706\pi\) | ||||
−0.681577 | + | 0.731746i | \(0.738706\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.6626 | 0.600767 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.7330 | −0.658989 | −0.329495 | − | 0.944157i | \(-0.606878\pi\) | ||||
−0.329495 | + | 0.944157i | \(0.606878\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.17849 | −0.401918 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.21404 | −0.123576 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.67288 | 0.204365 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.37159 | 0.464372 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.0257519 | 0.00142409 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.4416 | 1.07185 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.95223 | 0.382129 | 0.191065 | − | 0.981577i | \(-0.438806\pi\) | ||||
0.191065 | + | 0.981577i | \(0.438806\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.78959 | −0.372067 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.10333 | −0.278825 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.4416 | 1.60379 | 0.801893 | − | 0.597468i | \(-0.203826\pi\) | ||||
0.801893 | + | 0.597468i | \(0.203826\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.0241727 | 0.00131288 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.65295 | 0.251971 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.92959 | −0.482152 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.407632 | −0.0219462 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.2180 | 0.924311 | 0.462155 | − | 0.886799i | \(-0.347076\pi\) | ||||
0.462155 | + | 0.886799i | \(0.347076\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.32405 | 0.231461 | 0.115731 | − | 0.993281i | \(-0.463079\pi\) | ||||
0.115731 | + | 0.993281i | \(0.463079\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.57550 | −0.0840939 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.4421 | 1.24770 | 0.623848 | − | 0.781545i | \(-0.285568\pi\) | ||||
0.623848 | + | 0.781545i | \(0.285568\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.1825 | 0.858878 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.50799 | −0.0798111 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.20544 | −0.433066 | −0.216533 | − | 0.976275i | \(-0.569475\pi\) | ||||
−0.216533 | + | 0.976275i | \(0.569475\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.121872 | −0.00639662 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.57539 | 0.448856 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.1494 | −1.73039 | −0.865193 | − | 0.501439i | \(-0.832804\pi\) | ||||
−0.865193 | + | 0.501439i | \(0.832804\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 33.9865 | 1.76926 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.0618 | −0.989640 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.5840 | −0.858685 | −0.429343 | − | 0.903142i | \(-0.641255\pi\) | ||||
−0.429343 | + | 0.903142i | \(0.641255\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.14690 | −0.0592254 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.5050 | −0.798550 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.79467 | −0.297652 | −0.148826 | − | 0.988863i | \(-0.547549\pi\) | ||||
−0.148826 | + | 0.988863i | \(0.547549\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.439143 | −0.0224980 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.89016 | −0.300973 | −0.150487 | − | 0.988612i | \(-0.548084\pi\) | ||||
−0.150487 | + | 0.988612i | \(0.548084\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.57187 | 0.182039 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 28.0257 | 1.42463 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.8055 | 0.699964 | 0.349982 | − | 0.936756i | \(-0.386188\pi\) | ||||
0.349982 | + | 0.936756i | \(0.386188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.5868 | −0.585968 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.05649 | 0.103736 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.2383 | 0.716405 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.48471 | 0.325458 | 0.162729 | − | 0.986671i | \(-0.447970\pi\) | ||||
0.162729 | + | 0.986671i | \(0.447970\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.410573 | −0.0205544 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.70806 | 0.185172 | 0.0925858 | − | 0.995705i | \(-0.470487\pi\) | ||||
0.0925858 | + | 0.995705i | \(0.470487\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.0500 | 0.500628 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.40077 | −0.467128 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.27446 | −0.112741 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.0569 | 1.53567 | 0.767833 | − | 0.640650i | \(-0.221335\pi\) | ||||
0.767833 | + | 0.640650i | \(0.221335\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.744442 | 0.0367206 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 46.4717 | 2.28673 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.5672 | 0.518722 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.38138 | 0.0676467 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.2871 | 0.551410 | 0.275705 | − | 0.961242i | \(-0.411089\pi\) | ||||
0.275705 | + | 0.961242i | \(0.411089\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.5194 | 1.68237 | 0.841186 | − | 0.540746i | \(-0.181858\pi\) | ||||
0.841186 | + | 0.540746i | \(0.181858\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −17.2271 | −0.837611 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.2356 | −0.690528 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.5199 | 1.13821 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.263235 | −0.0127091 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.1654 | −0.874996 | −0.437498 | − | 0.899219i | \(-0.644135\pi\) | ||||
−0.437498 | + | 0.899219i | \(0.644135\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.7804 | 0.518075 | 0.259037 | − | 0.965867i | \(-0.416595\pi\) | ||||
0.259037 | + | 0.965867i | \(0.416595\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.927570 | 0.0444736 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.15468 | −0.150909 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.38742 | 0.0662180 | 0.0331090 | − | 0.999452i | \(-0.489459\pi\) | ||||
0.0331090 | + | 0.999452i | \(0.489459\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.9836 | −0.618266 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.26792 | 0.345310 | 0.172655 | − | 0.984982i | \(-0.444766\pi\) | ||||
0.172655 | + | 0.984982i | \(0.444766\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.89440 | 0.232017 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.823487 | −0.0389496 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.4298 | 1.01134 | 0.505668 | − | 0.862728i | \(-0.331246\pi\) | ||||
0.505668 | + | 0.862728i | \(0.331246\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.3852 | 0.536108 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.787575 | 0.0370035 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.71498 | 0.361684 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.6312 | −0.824754 | −0.412377 | − | 0.911013i | \(-0.635301\pi\) | ||||
−0.412377 | + | 0.911013i | \(0.635301\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.67908 | 0.125049 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.2073 | 1.59320 | 0.796598 | − | 0.604510i | \(-0.206631\pi\) | ||||
0.796598 | + | 0.604510i | \(0.206631\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.0009 | 0.511253 | 0.255626 | − | 0.966776i | \(-0.417718\pi\) | ||||
0.255626 | + | 0.966776i | \(0.417718\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.601231 | −0.0278814 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.38453 | −0.202892 | −0.101446 | − | 0.994841i | \(-0.532347\pi\) | ||||
−0.101446 | + | 0.994841i | \(0.532347\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.2155 | 0.748764 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.0302708 | −0.00139481 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.38838 | 0.431678 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.87587 | −0.177837 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.8905 | 0.773365 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.3683 | 0.656505 | 0.328253 | − | 0.944590i | \(-0.393540\pi\) | ||||
0.328253 | + | 0.944590i | \(0.393540\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.91266 | −0.223998 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.29523 | 0.0589349 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.34604 | 0.197344 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.01712 | −0.0460899 | −0.0230449 | − | 0.999734i | \(-0.507336\pi\) | ||||
−0.0230449 | + | 0.999734i | \(0.507336\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.06829 | −0.0935314 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.41045 | 0.108782 | 0.0543910 | − | 0.998520i | \(-0.482678\pi\) | ||||
0.0543910 | + | 0.998520i | \(0.482678\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.3658 | 1.18745 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.16501 | −0.142257 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −51.4189 | −2.30645 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.07426 | −0.182389 | −0.0911945 | − | 0.995833i | \(-0.529069\pi\) | ||||
−0.0911945 | + | 0.995833i | \(0.529069\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.105485 | −0.00471272 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.9553 | 0.889762 | 0.444881 | − | 0.895590i | \(-0.353246\pi\) | ||||
0.444881 | + | 0.895590i | \(0.353246\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.5281 | 0.512993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.01577 | 0.0451118 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.79239 | −0.389716 | −0.194858 | − | 0.980831i | \(-0.562425\pi\) | ||||
−0.194858 | + | 0.980831i | \(0.562425\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.2478 | −1.20537 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.729422 | 0.0322048 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.39239 | 0.413878 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.77094 | −0.253806 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.505138 | 0.0221731 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.3483 | 1.19815 | 0.599075 | − | 0.800693i | \(-0.295535\pi\) | ||||
0.599075 | + | 0.800693i | \(0.295535\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.7043 | 1.82360 | 0.911800 | − | 0.410634i | \(-0.134693\pi\) | ||||
0.911800 | + | 0.410634i | \(0.134693\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.59133 | 0.0694512 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.0897 | −0.744441 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0480 | −0.567304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −41.1783 | −1.78699 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.5912 | 1.06516 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.2615 | −0.832748 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.249331 | 0.0107594 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.34940 | −0.187342 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.7584 | −0.892472 | −0.446236 | − | 0.894915i | \(-0.647236\pi\) | ||||
−0.446236 | + | 0.894915i | \(0.647236\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.642898 | −0.0275894 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.224035 | 0.00959659 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.39396 | −0.230629 | −0.115315 | − | 0.993329i | \(-0.536788\pi\) | ||||
−0.115315 | + | 0.993329i | \(0.536788\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −20.8409 | −0.889466 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.17849 | 0.305814 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −45.2412 | −1.92385 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.293894 | 0.0124751 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.0076 | −1.61043 | −0.805217 | − | 0.592981i | \(-0.797951\pi\) | ||||
−0.805217 | + | 0.592981i | \(0.797951\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.2782 | 0.857677 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.447622 | 0.0188986 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.4313 | 1.11395 | 0.556973 | − | 0.830530i | \(-0.311963\pi\) | ||||
0.556973 | + | 0.830530i | \(0.311963\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.210295 | 0.00884719 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 29.8704 | 1.25444 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 40.6105 | 1.70248 | 0.851239 | − | 0.524778i | \(-0.175852\pi\) | ||||
0.851239 | + | 0.524778i | \(0.175852\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.44299 | −0.353328 | −0.176664 | − | 0.984271i | \(-0.556531\pi\) | ||||
−0.176664 | + | 0.984271i | \(0.556531\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.97309 | −0.0824271 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.2271 | 0.509906 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.9771 | 0.873288 | 0.436644 | − | 0.899634i | \(-0.356167\pi\) | ||||
0.436644 | + | 0.899634i | \(0.356167\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.44499 | 0.101610 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33.5766 | −1.39299 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.65820 | 0.234339 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.83619 | −0.282642 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.1452 | 0.872756 | 0.436378 | − | 0.899764i | \(-0.356261\pi\) | ||||
0.436378 | + | 0.899764i | \(0.356261\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.65295 | −0.191721 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.90540 | 0.119512 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.7731 | 1.14051 | 0.570253 | − | 0.821469i | \(-0.306845\pi\) | ||||
0.570253 | + | 0.821469i | \(0.306845\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.1191 | −0.537829 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.231793 | −0.00948667 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.0129 | −0.940281 | −0.470140 | − | 0.882592i | \(-0.655797\pi\) | ||||
−0.470140 | + | 0.882592i | \(0.655797\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.3322 | 0.951738 | 0.475869 | − | 0.879516i | \(-0.342134\pi\) | ||||
0.475869 | + | 0.879516i | \(0.342134\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.3685 | −0.585129 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.06025 | −0.0431054 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.22857 | 0.131044 | 0.0655218 | − | 0.997851i | \(-0.479129\pi\) | ||||
0.0655218 | + | 0.997851i | \(0.479129\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.94730 | −0.119430 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.4648 | −0.504273 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.2202 | −0.695519 | −0.347759 | − | 0.937584i | \(-0.613057\pi\) | ||||
−0.347759 | + | 0.937584i | \(0.613057\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.47114 | −0.0593220 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.4776 | −1.10621 | −0.553103 | − | 0.833113i | \(-0.686557\pi\) | ||||
−0.553103 | + | 0.833113i | \(0.686557\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.53870 | 0.383393 | 0.191696 | − | 0.981454i | \(-0.438601\pi\) | ||||
0.191696 | + | 0.981454i | \(0.438601\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.30109 | −0.0923397 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.5517 | −0.623064 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.40166 | 0.376066 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.121872 | 0.00486710 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.35381 | 0.333088 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.16647 | −0.0464363 | −0.0232182 | − | 0.999730i | \(-0.507391\pi\) | ||||
−0.0232182 | + | 0.999730i | \(0.507391\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.49962 | 0.0596044 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.82042 | −0.151609 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.39438 | −0.372219 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 45.5619 | 1.80240 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.0249 | 0.395960 | 0.197980 | − | 0.980206i | \(-0.436562\pi\) | ||||
0.197980 | + | 0.980206i | \(0.436562\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.7197 | 1.60583 | 0.802915 | − | 0.596094i | \(-0.203281\pi\) | ||||
0.802915 | + | 0.596094i | \(0.203281\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.21312 | −0.0477666 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.6460 | 0.654423 | 0.327211 | − | 0.944951i | \(-0.393891\pi\) | ||||
0.327211 | + | 0.944951i | \(0.393891\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.7944 | −0.541477 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.91038 | 0.0748735 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −34.7416 | −1.35954 | −0.679771 | − | 0.733424i | \(-0.737921\pi\) | ||||
−0.679771 | + | 0.733424i | \(0.737921\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.8908 | 0.699053 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 24.1441 | 0.941949 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.9537 | 0.894148 | 0.447074 | − | 0.894497i | \(-0.352466\pi\) | ||||
0.447074 | + | 0.894497i | \(0.352466\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.7141 | −0.883476 | −0.441738 | − | 0.897144i | \(-0.645638\pi\) | ||||
−0.441738 | + | 0.897144i | \(0.645638\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.966831 | 0.0375486 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.57187 | −0.138511 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.6459 | −0.876851 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.78445 | 0.107653 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.98152 | −0.269518 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.9448 | 0.807364 | 0.403682 | − | 0.914899i | \(-0.367730\pi\) | ||||
0.403682 | + | 0.914899i | \(0.367730\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.82714 | −0.108817 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.4153 | 0.438726 | 0.219363 | − | 0.975643i | \(-0.429602\pi\) | ||||
0.219363 | + | 0.975643i | \(0.429602\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.8093 | −0.529952 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.488285 | 0.0187111 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.9550 | 1.33752 | 0.668759 | − | 0.743479i | \(-0.266826\pi\) | ||||
0.668759 | + | 0.743479i | \(0.266826\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.47643 | 0.247452 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.99835 | 0.114394 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.2213 | 0.465594 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.8717 | 0.603789 | 0.301894 | − | 0.953341i | \(-0.402381\pi\) | ||||
0.301894 | + | 0.953341i | \(0.402381\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.0566 | 0.382019 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.0177 | 0.455855 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −41.8165 | −1.58391 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.98644 | −0.0751339 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.5830 | −0.701869 | −0.350935 | − | 0.936400i | \(-0.614136\pi\) | ||||
−0.350935 | + | 0.936400i | \(0.614136\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.27446 | 0.0857828 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.745693 | 0.0280844 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −36.6298 | −1.37760 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.8063 | 0.894064 | 0.447032 | − | 0.894518i | \(-0.352481\pi\) | ||||
0.447032 | + | 0.894518i | \(0.352481\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 40.0880 | 1.50342 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.6786 | 0.549717 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.29007 | −0.0856437 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.87905 | −0.0701745 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −37.0144 | −1.38040 | −0.690202 | − | 0.723616i | \(-0.742478\pi\) | ||||
−0.690202 | + | 0.723616i | \(0.742478\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.8437 | −1.11144 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.94249 | −0.109432 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −27.8229 | −1.03332 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.0744 | 0.818694 | 0.409347 | − | 0.912379i | \(-0.365757\pi\) | ||||
0.409347 | + | 0.912379i | \(0.365757\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.2013 | −0.970417 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34.4824 | −1.27538 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.7090 | −0.691031 | −0.345515 | − | 0.938413i | \(-0.612296\pi\) | ||||
−0.345515 | + | 0.938413i | \(0.612296\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.562008 | 0.0207300 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.81332 | −0.177301 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.91630 | 0.217635 | 0.108817 | − | 0.994062i | \(-0.465294\pi\) | ||||
0.108817 | + | 0.994062i | \(0.465294\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.263235 | 0.00967017 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.0422 | −0.515159 | −0.257579 | − | 0.966257i | \(-0.582925\pi\) | ||||
−0.257579 | + | 0.966257i | \(0.582925\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.16411 | −0.262473 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 29.7520 | 1.08857 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 61.2023 | 2.23628 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.91166 | −0.179229 | −0.0896145 | − | 0.995977i | \(-0.528563\pi\) | ||||
−0.0896145 | + | 0.995977i | \(0.528563\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.42646 | −0.0884250 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.85168 | 0.249358 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.2829 | 1.79122 | 0.895609 | − | 0.444843i | \(-0.146741\pi\) | ||||
0.895609 | + | 0.444843i | \(0.146741\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.384467 | −0.0139553 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.25922 | −0.263146 | −0.131573 | − | 0.991306i | \(-0.542003\pi\) | ||||
−0.131573 | + | 0.991306i | \(0.542003\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.711856 | −0.0257709 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.6247 | 0.420292 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −29.7949 | −1.07583 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.5123 | −0.775755 | −0.387877 | − | 0.921711i | \(-0.626792\pi\) | ||||
−0.387877 | + | 0.921711i | \(0.626792\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.71928 | 0.0979325 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.54038 | 0.163306 | 0.0816530 | − | 0.996661i | \(-0.473980\pi\) | ||||
0.0816530 | + | 0.996661i | \(0.473980\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.0342 | 0.647808 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.933831 | −0.0335010 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.3852 | −0.407917 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.2629 | 0.546149 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.23615 | 0.187125 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.263348 | −0.00939928 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.25028 | 0.258444 | 0.129222 | − | 0.991616i | \(-0.458752\pi\) | ||||
0.129222 | + | 0.991616i | \(0.458752\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.68138 | 0.0598588 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.668201 | −0.0237585 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.0796 | −0.535491 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.731124 | −0.0259303 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.8674 | 0.668319 | 0.334159 | − | 0.942517i | \(-0.391548\pi\) | ||||
0.334159 | + | 0.942517i | \(0.391548\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.1960 | 0.749860 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.7802 | 0.486900 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.08806 | 0.285422 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.2681 | 0.397149 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.36531 | 0.0480612 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.4948 | −0.685399 | −0.342700 | − | 0.939445i | \(-0.611341\pi\) | ||||
−0.342700 | + | 0.939445i | \(0.611341\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.28635 | −0.150514 | −0.0752570 | − | 0.997164i | \(-0.523978\pi\) | ||||
−0.0752570 | + | 0.997164i | \(0.523978\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.08686 | 0.0731893 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.9936 | −0.630287 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.38838 | −0.328458 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21.7216 | 0.759014 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.37419 | 0.187561 | 0.0937803 | − | 0.995593i | \(-0.470105\pi\) | ||||
0.0937803 | + | 0.995593i | \(0.470105\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.3196 | −0.917445 | −0.458723 | − | 0.888580i | \(-0.651693\pi\) | ||||
−0.458723 | + | 0.888580i | \(0.651693\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.472360 | −0.0164455 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.11186 | 0.282077 | 0.141039 | − | 0.990004i | \(-0.454956\pi\) | ||||
0.141039 | + | 0.990004i | \(0.454956\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.5948 | −0.750017 | −0.375009 | − | 0.927021i | \(-0.622360\pi\) | ||||
−0.375009 | + | 0.927021i | \(0.622360\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.67120 | 0.0579733 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.9748 | 0.553495 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.917688 | −0.0317579 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.39396 | −0.117313 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.35109 | 0.150216 | 0.0751082 | − | 0.997175i | \(-0.476070\pi\) | ||||
0.0751082 | + | 0.997175i | \(0.476070\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.5308 | 0.776923 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.15160 | −0.108547 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.83689 | 0.303998 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.36889 | 0.115756 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.51858 | 0.120757 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.17519 | −0.245962 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.5022 | 0.667744 | 0.333872 | − | 0.942618i | \(-0.391645\pi\) | ||||
0.333872 | + | 0.942618i | \(0.391645\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.16501 | 0.108241 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.3462 | 0.455898 | 0.227949 | − | 0.973673i | \(-0.426798\pi\) | ||||
0.227949 | + | 0.973673i | \(0.426798\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.6016 | −0.737036 | −0.368518 | − | 0.929621i | \(-0.620135\pi\) | ||||
−0.368518 | + | 0.929621i | \(0.620135\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.67445 | 0.159305 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.72425 | 0.0927345 | 0.0463673 | − | 0.998924i | \(-0.485236\pi\) | ||||
0.0463673 | + | 0.998924i | \(0.485236\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.39456 | 0.149420 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.427763 | 0.0145276 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.4291 | 0.455552 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.3964 | −0.352269 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.2363 | 0.414137 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.7034 | 1.07177 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.29130 | 0.0436041 | 0.0218021 | − | 0.999762i | \(-0.493060\pi\) | ||||
0.0218021 | + | 0.999762i | \(0.493060\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.777508 | −0.0262247 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.9873 | 0.841844 | 0.420922 | − | 0.907097i | \(-0.361707\pi\) | ||||
0.420922 | + | 0.907097i | \(0.361707\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.5046 | −0.521772 | −0.260886 | − | 0.965370i | \(-0.584015\pi\) | ||||
−0.260886 | + | 0.965370i | \(0.584015\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.78244 | 0.0599162 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.98029 | 0.335105 | 0.167553 | − | 0.985863i | \(-0.446414\pi\) | ||||
0.167553 | + | 0.985863i | \(0.446414\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.1391 | 0.407134 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.86655 | −0.297040 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.77094 | 0.193117 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.16911 | 0.0725053 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.830422 | −0.0277270 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −33.4012 | −1.11399 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.7819 | −0.692345 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.85461 | 0.128274 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.59303 | −0.185919 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.8887 | −0.394758 | −0.197379 | − | 0.980327i | \(-0.563243\pi\) | ||||
−0.197379 | + | 0.980327i | \(0.563243\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 32.4574 | 1.07654 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.7166 | 0.785767 | 0.392883 | − | 0.919588i | \(-0.371478\pi\) | ||||
0.392883 | + | 0.919588i | \(0.371478\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.96666 | 0.329848 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.902117 | 0.0298231 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −56.8471 | −1.87726 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.1426 | −0.598470 | −0.299235 | − | 0.954179i | \(-0.596731\pi\) | ||||
−0.299235 | + | 0.954179i | \(0.596731\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.27111 | 0.0418845 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.9667 | 1.08511 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.81549 | −0.289852 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.4443 | 0.868546 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50.5019 | −1.65691 | −0.828457 | − | 0.560053i | \(-0.810781\pi\) | ||||
−0.828457 | + | 0.560053i | \(0.810781\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.34940 | 0.142546 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.00694 | −0.0329656 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.89418 | 0.127353 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.6587 | −1.29559 | −0.647797 | − | 0.761813i | \(-0.724309\pi\) | ||||
−0.647797 | + | 0.761813i | \(0.724309\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.93915 | 0.0959154 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.8809 | −1.13709 | −0.568543 | − | 0.822653i | \(-0.692493\pi\) | ||||
−0.568543 | + | 0.822653i | \(0.692493\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.9166 | 1.16961 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.60540 | −0.0847537 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.3067 | 0.984835 | 0.492417 | − | 0.870359i | \(-0.336113\pi\) | ||||
0.492417 | + | 0.870359i | \(0.336113\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.4696 | 0.567088 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.42992 | 0.0463684 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.65804 | −0.215675 | −0.107838 | − | 0.994169i | \(-0.534393\pi\) | ||||
−0.107838 | + | 0.994169i | \(0.534393\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.1653 | −0.555457 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.874858 | 0.0282801 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.5785 | −0.664513 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.35006 | −0.301615 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −54.2309 | −1.74757 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.2707 | 0.684729 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.0020 | 0.643221 | 0.321611 | − | 0.946872i | \(-0.395776\pi\) | ||||
0.321611 | + | 0.946872i | \(0.395776\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.447622 | −0.0143797 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.491941 | 0.0157871 | 0.00789357 | − | 0.999969i | \(-0.497487\pi\) | ||||
0.00789357 | + | 0.999969i | \(0.497487\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −38.1853 | −1.22417 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.02026 | −0.0326746 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.6515 | 0.756679 | 0.378339 | − | 0.925667i | \(-0.376495\pi\) | ||||
0.378339 | + | 0.925667i | \(0.376495\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.61626 | 0.147536 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.630771 | 0.0201390 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.5609 | −1.26180 | −0.630899 | − | 0.775865i | \(-0.717314\pi\) | ||||
−0.630899 | + | 0.775865i | \(0.717314\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.2762 | 0.805366 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.36939 | −0.0754186 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.6173 | 0.941777 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.6096 | 0.432322 | 0.216161 | − | 0.976358i | \(-0.430646\pi\) | ||||
0.216161 | + | 0.976358i | \(0.430646\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.847283 | −0.0268877 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.01654 | −0.0639285 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.1821 | 1.30425 | 0.652125 | − | 0.758111i | \(-0.273878\pi\) | ||||
0.652125 | + | 0.758111i | \(0.273878\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.65904 | 0.0524897 |
(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 | 3344.2.a.t.1.3 | 5 | ||
4.3 | odd | 2 | 209.2.a.c.1.5 | ✓ | 5 | ||
12.11 | even | 2 | 1881.2.a.k.1.1 | 5 | |||
20.19 | odd | 2 | 5225.2.a.h.1.1 | 5 | |||
44.43 | even | 2 | 2299.2.a.n.1.1 | 5 | |||
76.75 | even | 2 | 3971.2.a.h.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
209.2.a.c.1.5 | ✓ | 5 | 4.3 | odd | 2 | ||
1881.2.a.k.1.1 | 5 | 12.11 | even | 2 | |||
2299.2.a.n.1.1 | 5 | 44.43 | even | 2 | |||
3344.2.a.t.1.3 | 5 | 1.1 | even | 1 | trivial | ||
3971.2.a.h.1.1 | 5 | 76.75 | even | 2 | |||
5225.2.a.h.1.1 | 5 | 20.19 | odd | 2 |