Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 16x^{8} + 26x^{7} + 93x^{6} - 113x^{5} - 230x^{4} + 197x^{3} + 201x^{2} - 115x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.76763\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | 1.76763 | 1.02054 | 0.510272 | − | 0.860013i | \(-0.329545\pi\) | ||||
0.510272 | + | 0.860013i | \(0.329545\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.187208 | 0.0837220 | 0.0418610 | − | 0.999123i | \(-0.486671\pi\) | ||||
0.0418610 | + | 0.999123i | \(0.486671\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.124526 | 0.0415088 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.330915 | 0.0854420 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.32648 | 1.04933 | 0.524663 | − | 0.851310i | \(-0.324191\pi\) | ||||
0.524663 | + | 0.851310i | \(0.324191\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.79897 | −1.33037 | −0.665187 | − | 0.746677i | \(-0.731648\pi\) | ||||
−0.665187 | + | 0.746677i | \(0.731648\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.76763 | −0.385729 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.19778 | 1.08381 | 0.541906 | − | 0.840439i | \(-0.317703\pi\) | ||||
0.541906 | + | 0.840439i | \(0.317703\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96495 | −0.992991 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.08278 | −0.978182 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.25596 | 0.233226 | 0.116613 | − | 0.993177i | \(-0.462796\pi\) | ||||
0.116613 | + | 0.993177i | \(0.462796\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.52310 | 1.17158 | 0.585792 | − | 0.810462i | \(-0.300784\pi\) | ||||
0.585792 | + | 0.810462i | \(0.300784\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.76763 | −0.307705 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.187208 | −0.0316440 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.96866 | −0.981241 | −0.490621 | − | 0.871373i | \(-0.663230\pi\) | ||||
−0.490621 | + | 0.871373i | \(0.663230\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.76763 | −0.283048 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.23412 | 0.817432 | 0.408716 | − | 0.912662i | \(-0.365977\pi\) | ||||
0.408716 | + | 0.912662i | \(0.365977\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.99762 | −0.609631 | −0.304815 | − | 0.952411i | \(-0.598595\pi\) | ||||
−0.304815 | + | 0.952411i | \(0.598595\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0233124 | 0.00347520 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.21957 | −0.761352 | −0.380676 | − | 0.924708i | \(-0.624309\pi\) | ||||
−0.380676 | + | 0.924708i | \(0.624309\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.64763 | 1.07088 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.33361 | −0.183186 | −0.0915930 | − | 0.995797i | \(-0.529196\pi\) | ||||
−0.0915930 | + | 0.995797i | \(0.529196\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.187208 | −0.0252431 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.2504 | −1.35770 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.28024 | 0.947806 | 0.473903 | − | 0.880577i | \(-0.342845\pi\) | ||||
0.473903 | + | 0.880577i | \(0.342845\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.40345 | −0.435767 | −0.217884 | − | 0.975975i | \(-0.569915\pi\) | ||||
−0.217884 | + | 0.975975i | \(0.569915\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.124526 | −0.0156889 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.187208 | −0.0232203 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.43127 | −0.297027 | −0.148514 | − | 0.988910i | \(-0.547449\pi\) | ||||
−0.148514 | + | 0.988910i | \(0.547449\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.18776 | 1.10608 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.65660 | −0.315281 | −0.157640 | − | 0.987497i | \(-0.550389\pi\) | ||||
−0.157640 | + | 0.987497i | \(0.550389\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.4341 | −1.45530 | −0.727649 | − | 0.685950i | \(-0.759387\pi\) | ||||
−0.727649 | + | 0.685950i | \(0.759387\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.77621 | −1.01339 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.58710 | 0.403580 | 0.201790 | − | 0.979429i | \(-0.435324\pi\) | ||||
0.201790 | + | 0.979429i | \(0.435324\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.35807 | −1.03979 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.04444 | −0.992756 | −0.496378 | − | 0.868107i | \(-0.665337\pi\) | ||||
−0.496378 | + | 0.868107i | \(0.665337\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.809952 | 0.0878516 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.22008 | 0.238018 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.7021 | −1.34642 | −0.673210 | − | 0.739451i | \(-0.735085\pi\) | ||||
−0.673210 | + | 0.739451i | \(0.735085\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.5304 | 1.19565 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.08561 | −0.111382 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.31505 | −0.438127 | −0.219064 | − | 0.975711i | \(-0.570300\pi\) | ||||
−0.219064 | + | 0.975711i | \(0.570300\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.124526 | −0.0125154 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.48362 | 0.247129 | 0.123564 | − | 0.992337i | \(-0.460567\pi\) | ||||
0.123564 | + | 0.992337i | \(0.460567\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.0267 | −1.38209 | −0.691047 | − | 0.722810i | \(-0.742850\pi\) | ||||
−0.691047 | + | 0.722810i | \(0.742850\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.330915 | −0.0322940 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.9847 | 1.25528 | 0.627638 | − | 0.778505i | \(-0.284022\pi\) | ||||
0.627638 | + | 0.778505i | \(0.284022\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.60242 | 0.345049 | 0.172524 | − | 0.985005i | \(-0.444808\pi\) | ||||
0.172524 | + | 0.985005i | \(0.444808\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.5504 | −1.00140 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.7312 | −1.57394 | −0.786970 | − | 0.616991i | \(-0.788351\pi\) | ||||
−0.786970 | + | 0.616991i | \(0.788351\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.973066 | 0.0907389 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.124526 | −0.0115125 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.32648 | −0.396608 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.25200 | 0.834224 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.86552 | −0.166857 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.1367 | −1.16570 | −0.582848 | − | 0.812582i | \(-0.698062\pi\) | ||||
−0.582848 | + | 0.812582i | \(0.698062\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.06632 | −0.622155 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.10959 | 0.533798 | 0.266899 | − | 0.963725i | \(-0.414001\pi\) | ||||
0.266899 | + | 0.963725i | \(0.414001\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.79897 | 0.502834 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.951538 | −0.0818954 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.6249 | 1.16405 | 0.582025 | − | 0.813171i | \(-0.302260\pi\) | ||||
0.582025 | + | 0.813171i | \(0.302260\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.19652 | 0.101488 | 0.0507439 | − | 0.998712i | \(-0.483841\pi\) | ||||
0.0507439 | + | 0.998712i | \(0.483841\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.22628 | −0.776993 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.235126 | 0.0195262 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.76763 | 0.145792 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.15546 | −0.668121 | −0.334061 | − | 0.942552i | \(-0.608419\pi\) | ||||
−0.334061 | + | 0.942552i | \(0.608419\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.2259 | −0.994934 | −0.497467 | − | 0.867483i | \(-0.665736\pi\) | ||||
−0.497467 | + | 0.867483i | \(0.665736\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.538761 | 0.0435562 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.22118 | 0.0980873 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.2040 | −1.61246 | −0.806228 | − | 0.591605i | \(-0.798494\pi\) | ||||
−0.806228 | + | 0.591605i | \(0.798494\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.35734 | −0.186949 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.19778 | −0.409642 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.7786 | −1.31420 | −0.657099 | − | 0.753804i | \(-0.728217\pi\) | ||||
−0.657099 | + | 0.753804i | \(0.728217\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.330915 | −0.0257617 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.21006 | 0.0936376 | 0.0468188 | − | 0.998903i | \(-0.485092\pi\) | ||||
0.0468188 | + | 0.998903i | \(0.485092\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.722124 | −0.0552222 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.2712 | 1.00899 | 0.504494 | − | 0.863415i | \(-0.331679\pi\) | ||||
0.504494 | + | 0.863415i | \(0.331679\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.96495 | 0.375315 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.8688 | 0.967277 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.5205 | 1.38429 | 0.692144 | − | 0.721759i | \(-0.256666\pi\) | ||||
0.692144 | + | 0.721759i | \(0.256666\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.9939 | 1.11449 | 0.557244 | − | 0.830348i | \(-0.311859\pi\) | ||||
0.557244 | + | 0.830348i | \(0.311859\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.01605 | −0.444719 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.11738 | −0.0821515 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.32648 | −0.316383 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.08278 | 0.369718 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.49034 | −0.614339 | −0.307170 | − | 0.951655i | \(-0.599382\pi\) | ||||
−0.307170 | + | 0.951655i | \(0.599382\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.9141 | −0.785611 | −0.392805 | − | 0.919622i | \(-0.628495\pi\) | ||||
−0.392805 | + | 0.919622i | \(0.628495\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.330915 | −0.0236973 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.8771 | −1.41619 | −0.708094 | − | 0.706119i | \(-0.750445\pi\) | ||||
−0.708094 | + | 0.706119i | \(0.750445\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.7949 | −1.89944 | −0.949720 | − | 0.313100i | \(-0.898633\pi\) | ||||
−0.949720 | + | 0.313100i | \(0.898633\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.29760 | −0.303129 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.25596 | −0.0881513 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.979869 | 0.0684370 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.647260 | 0.0449877 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.79897 | 0.401123 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.3739 | 0.783015 | 0.391507 | − | 0.920175i | \(-0.371954\pi\) | ||||
0.391507 | + | 0.920175i | \(0.371954\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.69590 | −0.321758 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.748387 | −0.0510395 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.52310 | −0.442817 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −21.9789 | −1.48519 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.32648 | −0.291030 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.3245 | −1.56193 | −0.780963 | − | 0.624578i | \(-0.785271\pi\) | ||||
−0.780963 | + | 0.624578i | \(0.785271\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.618268 | −0.0412178 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.19009 | 0.543596 | 0.271798 | − | 0.962354i | \(-0.412382\pi\) | ||||
0.271798 | + | 0.962354i | \(0.412382\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.2055 | −1.07089 | −0.535446 | − | 0.844569i | \(-0.679857\pi\) | ||||
−0.535446 | + | 0.844569i | \(0.679857\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.76763 | 0.116302 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0871 | −1.18492 | −0.592462 | − | 0.805598i | \(-0.701844\pi\) | ||||
−0.592462 | + | 0.805598i | \(0.701844\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.977146 | −0.0637419 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.34068 | 0.411871 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.8444 | 0.766152 | 0.383076 | − | 0.923717i | \(-0.374865\pi\) | ||||
0.383076 | + | 0.923717i | \(0.374865\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.7427 | 1.33615 | 0.668077 | − | 0.744092i | \(-0.267118\pi\) | ||||
0.668077 | + | 0.744092i | \(0.267118\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.29329 | −0.0829647 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.187208 | 0.0119603 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.79897 | 0.368979 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.9872 | −1.01315 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.39562 | 0.593046 | 0.296523 | − | 0.955026i | \(-0.404173\pi\) | ||||
0.296523 | + | 0.955026i | \(0.404173\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.19778 | −0.326781 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.43170 | 0.0896564 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.86272 | −0.490463 | −0.245232 | − | 0.969465i | \(-0.578864\pi\) | ||||
−0.245232 | + | 0.969465i | \(0.578864\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.96866 | 0.370874 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.156400 | 0.00968094 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.230621 | −0.0142207 | −0.00711036 | − | 0.999975i | \(-0.502263\pi\) | ||||
−0.00711036 | + | 0.999975i | \(0.502263\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.249663 | −0.0153367 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −22.4526 | −1.37408 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.4203 | 1.06214 | 0.531069 | − | 0.847329i | \(-0.321791\pi\) | ||||
0.531069 | + | 0.847329i | \(0.321791\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.7770 | −1.01913 | −0.509564 | − | 0.860433i | \(-0.670193\pi\) | ||||
−0.509564 | + | 0.860433i | \(0.670193\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.76763 | 0.106982 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.96495 | 0.299398 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.16058 | 0.189901 | 0.0949504 | − | 0.995482i | \(-0.469731\pi\) | ||||
0.0949504 | + | 0.995482i | \(0.469731\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.812298 | 0.0486310 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.2627 | 0.671877 | 0.335938 | − | 0.941884i | \(-0.390947\pi\) | ||||
0.335938 | + | 0.941884i | \(0.390947\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.4640 | 0.978682 | 0.489341 | − | 0.872092i | \(-0.337237\pi\) | ||||
0.489341 | + | 0.872092i | \(0.337237\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.91897 | −0.113670 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.23412 | −0.308960 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.71842 | 0.101083 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.62743 | −0.447128 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.3742 | −0.606068 | −0.303034 | − | 0.952980i | \(-0.598000\pi\) | ||||
−0.303034 | + | 0.952980i | \(0.598000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.36292 | 0.0793523 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.08278 | 0.294933 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.19778 | −0.300595 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.99762 | 0.230419 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.39012 | 0.252206 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.637154 | −0.0364833 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.28375 | 0.472778 | 0.236389 | − | 0.971658i | \(-0.424036\pi\) | ||||
0.236389 | + | 0.971658i | \(0.424036\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −24.7941 | −1.41049 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.90180 | −0.334660 | −0.167330 | − | 0.985901i | \(-0.553515\pi\) | ||||
−0.167330 | + | 0.985901i | \(0.553515\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.92094 | −0.560765 | −0.280382 | − | 0.959888i | \(-0.590461\pi\) | ||||
−0.280382 | + | 0.959888i | \(0.590461\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0233124 | −0.00131350 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.69036 | −0.375768 | −0.187884 | − | 0.982191i | \(-0.560163\pi\) | ||||
−0.187884 | + | 0.982191i | \(0.560163\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.25596 | −0.0703204 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 22.9521 | 1.28106 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.0891 | −1.39599 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.96495 | 0.275406 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.36775 | 0.352137 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.21957 | 0.287764 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.8852 | 1.03803 | 0.519013 | − | 0.854766i | \(-0.326299\pi\) | ||||
0.519013 | + | 0.854766i | \(0.326299\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.743256 | −0.0407302 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.455154 | −0.0248677 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.3932 | −0.620627 | −0.310313 | − | 0.950634i | \(-0.600434\pi\) | ||||
−0.310313 | + | 0.950634i | \(0.600434\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −29.5746 | −1.60627 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.52310 | −0.353246 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.72002 | 0.0926030 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.6924 | −0.842411 | −0.421205 | − | 0.906965i | \(-0.638393\pi\) | ||||
−0.421205 | + | 0.906965i | \(0.638393\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.1132 | −0.755465 | −0.377732 | − | 0.925915i | \(-0.623296\pi\) | ||||
−0.377732 | + | 0.925915i | \(0.623296\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.08278 | 0.271299 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.8716 | 1.00443 | 0.502217 | − | 0.864741i | \(-0.332518\pi\) | ||||
0.502217 | + | 0.864741i | \(0.332518\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.497338 | −0.0263959 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.64763 | −0.404755 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.09500 | 0.216126 | 0.108063 | − | 0.994144i | \(-0.465535\pi\) | ||||
0.108063 | + | 0.994144i | \(0.465535\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.6280 | 0.769895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.76763 | 0.0927767 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.32776 | −0.121840 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.8091 | 0.564230 | 0.282115 | − | 0.959381i | \(-0.408964\pi\) | ||||
0.282115 | + | 0.959381i | \(0.408964\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.651786 | 0.0339306 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.33361 | 0.0692378 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.5928 | 1.06625 | 0.533127 | − | 0.846035i | \(-0.321017\pi\) | ||||
0.533127 | + | 0.846035i | \(0.321017\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.29756 | −0.170285 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.25596 | −0.0646853 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.8324 | −1.63512 | −0.817560 | − | 0.575843i | \(-0.804674\pi\) | ||||
−0.817560 | + | 0.575843i | \(0.804674\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −23.2209 | −1.18964 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.47019 | 0.0751232 | 0.0375616 | − | 0.999294i | \(-0.488041\pi\) | ||||
0.0375616 | + | 0.999294i | \(0.488041\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.187208 | 0.00954101 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.497809 | −0.0253050 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.97538 | −0.100156 | −0.0500780 | − | 0.998745i | \(-0.515947\pi\) | ||||
−0.0500780 | + | 0.998745i | \(0.515947\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.4881 | 1.13727 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.7995 | 0.544764 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.671535 | 0.0337886 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.8123 | 1.39586 | 0.697929 | − | 0.716166i | \(-0.254105\pi\) | ||||
0.697929 | + | 0.716166i | \(0.254105\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.2504 | 0.513164 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.71223 | 0.385130 | 0.192565 | − | 0.981284i | \(-0.438319\pi\) | ||||
0.192565 | + | 0.981284i | \(0.438319\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.52310 | −0.324939 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.75191 | −0.0870530 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.96866 | 0.295855 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.7736 | −1.52166 | −0.760828 | − | 0.648953i | \(-0.775207\pi\) | ||||
−0.760828 | + | 0.648953i | \(0.775207\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.0838 | 1.18796 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.28024 | −0.358237 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.69319 | −0.0831155 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.11501 | 0.103573 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.0196 | −1.07573 | −0.537865 | − | 0.843031i | \(-0.680769\pi\) | ||||
−0.537865 | + | 0.843031i | \(0.680769\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.39136 | −0.408970 | −0.204485 | − | 0.978870i | \(-0.565552\pi\) | ||||
−0.204485 | + | 0.978870i | \(0.565552\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.649974 | −0.0316028 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.4808 | −1.04197 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.40345 | 0.164704 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.76763 | 0.0853421 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.60175 | 0.125322 | 0.0626610 | − | 0.998035i | \(-0.480041\pi\) | ||||
0.0626610 | + | 0.998035i | \(0.480041\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.06670 | 0.291547 | 0.145773 | − | 0.989318i | \(-0.453433\pi\) | ||||
0.145773 | + | 0.989318i | \(0.453433\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.415617 | 0.0199273 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −30.1417 | −1.44187 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.5583 | 1.50619 | 0.753097 | − | 0.657910i | \(-0.228559\pi\) | ||||
0.753097 | + | 0.657910i | \(0.228559\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.124526 | 0.00592983 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.90800 | −0.375720 | −0.187860 | − | 0.982196i | \(-0.560155\pi\) | ||||
−0.187860 | + | 0.982196i | \(0.560155\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.37794 | −0.112725 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.4159 | −0.681847 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.2243 | 1.66234 | 0.831170 | − | 0.556019i | \(-0.187672\pi\) | ||||
0.831170 | + | 0.556019i | \(0.187672\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.23412 | −0.246465 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −21.6110 | −1.01537 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.187208 | 0.00877645 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.2350 | −0.712662 | −0.356331 | − | 0.934360i | \(-0.615972\pi\) | ||||
−0.356331 | + | 0.934360i | \(0.615972\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −21.9905 | −1.02643 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.0347 | −0.467362 | −0.233681 | − | 0.972313i | \(-0.575077\pi\) | ||||
−0.233681 | + | 0.972313i | \(0.575077\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.1534 | 0.564819 | 0.282409 | − | 0.959294i | \(-0.408866\pi\) | ||||
0.282409 | + | 0.959294i | \(0.408866\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.15859 | 0.100102 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.4572 | 0.669001 | 0.334501 | − | 0.942396i | \(-0.391432\pi\) | ||||
0.334501 | + | 0.942396i | \(0.391432\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.43127 | 0.112266 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −35.7133 | −1.64558 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.99762 | 0.183811 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.7916 | 1.32105 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.166070 | −0.00760383 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.5569 | 0.528049 | 0.264024 | − | 0.964516i | \(-0.414950\pi\) | ||||
0.264024 | + | 0.964516i | \(0.414950\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.96866 | 0.272147 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.18776 | −0.418058 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.807813 | −0.0366809 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.0710 | 0.682932 | 0.341466 | − | 0.939894i | \(-0.389077\pi\) | ||||
0.341466 | + | 0.939894i | \(0.389077\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −29.6583 | −1.34120 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.9728 | 1.93933 | 0.969667 | − | 0.244430i | \(-0.0786009\pi\) | ||||
0.969667 | + | 0.244430i | \(0.0786009\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.43389 | 0.244730 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.0233124 | −0.00104781 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.65660 | 0.119165 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.91705 | 0.264884 | 0.132442 | − | 0.991191i | \(-0.457718\pi\) | ||||
0.132442 | + | 0.991191i | \(0.457718\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.13895 | 0.0955612 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −43.6034 | −1.94418 | −0.972090 | − | 0.234607i | \(-0.924620\pi\) | ||||
−0.972090 | + | 0.234607i | \(0.924620\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.464953 | 0.0206901 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.76763 | 0.0785033 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.5945 | −0.558242 | −0.279121 | − | 0.960256i | \(-0.590043\pi\) | ||||
−0.279121 | + | 0.960256i | \(0.590043\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.4341 | 0.550051 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 29.4749 | 1.30135 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.62592 | −0.115712 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.21957 | 0.229556 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.4585 | 1.02972 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.89362 | 0.214393 | 0.107197 | − | 0.994238i | \(-0.465813\pi\) | ||||
0.107197 | + | 0.994238i | \(0.465813\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.0064 | 0.437551 | 0.218775 | − | 0.975775i | \(-0.429794\pi\) | ||||
0.218775 | + | 0.975775i | \(0.429794\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.77621 | 0.383025 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.2221 | 1.22937 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.01688 | 0.174647 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.906582 | 0.0393423 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.23412 | −0.226715 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.43084 | 0.105094 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 32.7375 | 1.41273 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.34680 | −0.229877 | −0.114938 | − | 0.993373i | \(-0.536667\pi\) | ||||
−0.114938 | + | 0.993373i | \(0.536667\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 26.5037 | 1.13738 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.674402 | 0.0288882 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.1478 | 1.28903 | 0.644513 | − | 0.764593i | \(-0.277060\pi\) | ||||
0.644513 | + | 0.764593i | \(0.277060\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.423819 | −0.0180882 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.28328 | −0.310278 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.58710 | −0.152539 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.97512 | −0.0838392 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.8352 | 0.501474 | 0.250737 | − | 0.968055i | \(-0.419327\pi\) | ||||
0.250737 | + | 0.968055i | \(0.419327\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.99762 | 0.169081 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.64763 | −0.322883 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.17425 | −0.260214 | −0.130107 | − | 0.991500i | \(-0.541532\pi\) | ||||
−0.130107 | + | 0.991500i | \(0.541532\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.13222 | −0.131773 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.35807 | 0.393002 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.9554 | 0.752730 | 0.376365 | − | 0.926472i | \(-0.377174\pi\) | ||||
0.376365 | + | 0.926472i | \(0.377174\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.5500 | 1.06923 | 0.534617 | − | 0.845094i | \(-0.320456\pi\) | ||||
0.534617 | + | 0.845094i | \(0.320456\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.0078 | −0.626960 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −25.8067 | −1.07621 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.6591 | −1.52614 | −0.763069 | − | 0.646317i | \(-0.776308\pi\) | ||||
−0.763069 | + | 0.646317i | \(0.776308\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.2920 | −0.801750 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.04444 | 0.375226 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.33361 | 0.0552326 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0233124 | −0.000963847 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 42.7022 | 1.76251 | 0.881254 | − | 0.472643i | \(-0.156700\pi\) | ||||
0.881254 | + | 0.472643i | \(0.156700\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −37.8272 | −1.55864 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −35.1355 | −1.44528 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.02047 | −0.165101 | −0.0825504 | − | 0.996587i | \(-0.526307\pi\) | ||||
−0.0825504 | + | 0.996587i | \(0.526307\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.809952 | −0.0332048 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −47.3636 | −1.93846 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.16880 | −0.333768 | −0.166884 | − | 0.985977i | \(-0.553371\pi\) | ||||
−0.166884 | + | 0.985977i | \(0.553371\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.7887 | −0.562452 | −0.281226 | − | 0.959642i | \(-0.590741\pi\) | ||||
−0.281226 | + | 0.959642i | \(0.590741\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.302757 | −0.0123292 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.187208 | 0.00761109 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.7177 | 1.57150 | 0.785752 | − | 0.618541i | \(-0.212276\pi\) | ||||
0.785752 | + | 0.618541i | \(0.212276\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.22008 | −0.0899622 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.21957 | 0.211161 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.7798 | 1.20280 | 0.601398 | − | 0.798949i | \(-0.294610\pi\) | ||||
0.601398 | + | 0.798949i | \(0.294610\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.73205 | 0.0698430 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.1833 | −1.29565 | −0.647826 | − | 0.761788i | \(-0.724322\pi\) | ||||
−0.647826 | + | 0.761788i | \(0.724322\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.9357 | 1.36399 | 0.681996 | − | 0.731356i | \(-0.261112\pi\) | ||||
0.681996 | + | 0.731356i | \(0.261112\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −26.4192 | −1.06016 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.7021 | 0.508899 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.4755 | 0.979021 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.2504 | 0.409363 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −25.8233 | −1.02964 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.7604 | −1.50322 | −0.751610 | − | 0.659608i | \(-0.770722\pi\) | ||||
−0.751610 | + | 0.659608i | \(0.770722\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.1050 | 0.799101 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.45930 | −0.0975944 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.330817 | −0.0130869 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.9804 | 0.710184 | 0.355092 | − | 0.934831i | \(-0.384450\pi\) | ||||
0.355092 | + | 0.934831i | \(0.384450\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.5417 | −1.04670 | −0.523351 | − | 0.852117i | \(-0.675318\pi\) | ||||
−0.523351 | + | 0.852117i | \(0.675318\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.32287 | −0.0520881 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −43.3705 | −1.70507 | −0.852534 | − | 0.522671i | \(-0.824936\pi\) | ||||
−0.852534 | + | 0.522671i | \(0.824936\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.28024 | −0.285774 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.5304 | −0.451914 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.5353 | −0.568812 | −0.284406 | − | 0.958704i | \(-0.591796\pi\) | ||||
−0.284406 | + | 0.958704i | \(0.591796\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.14377 | 0.0446906 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.54837 | −0.0604076 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.7224 | 1.74214 | 0.871069 | − | 0.491161i | \(-0.163427\pi\) | ||||
0.871069 | + | 0.491161i | \(0.163427\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.4491 | −0.717589 | −0.358794 | − | 0.933417i | \(-0.616812\pi\) | ||||
−0.358794 | + | 0.933417i | \(0.616812\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.64763 | −0.297009 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.08561 | 0.0420983 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.52821 | 0.252773 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −41.2292 | −1.59401 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.40345 | 0.131389 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.8438 | 1.69005 | 0.845026 | − | 0.534725i | \(-0.179585\pi\) | ||||
0.845026 | + | 0.534725i | \(0.179585\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.2358 | 0.971325 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.1603 | −0.851690 | −0.425845 | − | 0.904796i | \(-0.640023\pi\) | ||||
−0.425845 | + | 0.904796i | \(0.640023\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.31505 | 0.165596 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.4771 | 0.554763 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.2063 | 1.23234 | 0.616170 | − | 0.787613i | \(-0.288683\pi\) | ||||
0.616170 | + | 0.787613i | \(0.288683\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.55069 | 0.0974567 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.6455 | −1.09289 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.33361 | 0.0508066 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.70081 | −0.0647020 | −0.0323510 | − | 0.999477i | \(-0.510299\pi\) | ||||
−0.0323510 | + | 0.999477i | \(0.510299\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.124526 | 0.00473037 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.223999 | 0.00849676 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.6453 | 0.857751 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −31.9713 | −1.20927 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.11443 | 0.306478 | 0.153239 | − | 0.988189i | \(-0.451030\pi\) | ||||
0.153239 | + | 0.988189i | \(0.451030\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 34.6120 | 1.30542 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.72723 | −0.0650514 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.48362 | −0.0934060 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.6051 | −1.56251 | −0.781256 | − | 0.624211i | \(-0.785421\pi\) | ||||
−0.781256 | + | 0.624211i | \(0.785421\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.446689 | 0.0167521 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 33.9056 | 1.26978 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.187208 | 0.00700119 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.9366 | 0.781891 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.5432 | 0.691545 | 0.345773 | − | 0.938318i | \(-0.387617\pi\) | ||||
0.345773 | + | 0.938318i | \(0.387617\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.0267 | 0.522383 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 36.6655 | 1.36360 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.23579 | −0.231592 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.6335 | 1.21031 | 0.605155 | − | 0.796107i | \(-0.293111\pi\) | ||||
0.605155 | + | 0.796107i | \(0.293111\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.7882 | 0.955117 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.2956 | −0.639701 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.50958 | 0.166565 | 0.0832826 | − | 0.996526i | \(-0.473460\pi\) | ||||
0.0832826 | + | 0.996526i | \(0.473460\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.330915 | 0.0122060 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.43127 | 0.0895570 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.1237 | 0.666690 | 0.333345 | − | 0.942805i | \(-0.391823\pi\) | ||||
0.333345 | + | 0.942805i | \(0.391823\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.2504 | 0.376559 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.2109 | −1.62194 | −0.810971 | − | 0.585087i | \(-0.801061\pi\) | ||||
−0.810971 | + | 0.585087i | \(0.801061\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.52677 | −0.0559365 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.12627 | −0.0412081 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.9847 | −0.474450 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.1389 | −0.771369 | −0.385684 | − | 0.922631i | \(-0.626035\pi\) | ||||
−0.385684 | + | 0.922631i | \(0.626035\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.6080 | 0.605229 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.28880 | −0.0832979 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.2934 | 0.919305 | 0.459653 | − | 0.888099i | \(-0.347974\pi\) | ||||
0.459653 | + | 0.888099i | \(0.347974\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.18776 | −0.333495 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.7837 | −0.680910 | −0.340455 | − | 0.940261i | \(-0.610581\pi\) | ||||
−0.340455 | + | 0.940261i | \(0.610581\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.60242 | −0.130416 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.100860 | 0.00364662 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.28024 | −0.262874 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.0937 | −1.59006 | −0.795030 | − | 0.606570i | \(-0.792545\pi\) | ||||
−0.795030 | + | 0.606570i | \(0.792545\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.8984 | −0.500539 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.7377 | −1.03362 | −0.516811 | − | 0.856100i | \(-0.672881\pi\) | ||||
−0.516811 | + | 0.856100i | \(0.672881\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.3869 | −1.16337 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.5504 | 0.378493 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30.3525 | −1.08749 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.65660 | 0.0950607 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.38378 | −0.228138 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.78236 | −0.134998 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.0356 | 0.714193 | 0.357097 | − | 0.934067i | \(-0.383767\pi\) | ||||
0.357097 | + | 0.934067i | \(0.383767\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.407654 | −0.0145129 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.7312 | 0.594893 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.40345 | 0.120860 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.441313 | −0.0156518 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.4961 | 0.442633 | 0.221317 | − | 0.975202i | \(-0.428965\pi\) | ||||
0.221317 | + | 0.975202i | \(0.428965\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.5823 | −0.798906 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.58175 | −0.0558883 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.4341 | 0.438789 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.973066 | −0.0342961 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.7928 | 1.08396 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.5390 | −0.511162 | −0.255581 | − | 0.966788i | \(-0.582267\pi\) | ||||
−0.255581 | + | 0.966788i | \(0.582267\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.8243 | 1.18773 | 0.593866 | − | 0.804564i | \(-0.297601\pi\) | ||||
0.593866 | + | 0.804564i | \(0.297601\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.6555 | −1.04006 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.14108 | −0.110027 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.1820 | 0.811037 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.124526 | 0.00435130 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.6665 | −0.476966 | −0.238483 | − | 0.971147i | \(-0.576650\pi\) | ||||
−0.238483 | + | 0.971147i | \(0.576650\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.95988 | −0.138033 | −0.0690163 | − | 0.997616i | \(-0.521986\pi\) | ||||
−0.0690163 | + | 0.997616i | \(0.521986\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.77621 | 0.305549 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45.6515 | −1.58746 | −0.793728 | − | 0.608272i | \(-0.791863\pi\) | ||||
−0.793728 | + | 0.608272i | \(0.791863\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.4499 | −1.50908 | −0.754538 | − | 0.656257i | \(-0.772139\pi\) | ||||
−0.754538 | + | 0.656257i | \(0.772139\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.58674 | 0.193802 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.32648 | 0.149904 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.226534 | 0.00783953 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −33.1555 | −1.14602 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.2572 | 0.595785 | 0.297893 | − | 0.954599i | \(-0.403716\pi\) | ||||
0.297893 | + | 0.954599i | \(0.403716\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.4226 | −0.945605 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.9083 | 0.685680 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.187208 | 0.00644016 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.1023 | 0.998788 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −31.0238 | −1.06348 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.52750 | 0.0865401 | 0.0432700 | − | 0.999063i | \(-0.486222\pi\) | ||||
0.0432700 | + | 0.999063i | \(0.486222\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.135188 | −0.00462332 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.7291 | 1.32296 | 0.661480 | − | 0.749963i | \(-0.269929\pi\) | ||||
0.661480 | + | 0.749963i | \(0.269929\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.04338 | −0.172078 | −0.0860390 | − | 0.996292i | \(-0.527421\pi\) | ||||
−0.0860390 | + | 0.996292i | \(0.527421\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.25200 | −0.315307 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.5510 | −0.937846 | −0.468923 | − | 0.883239i | \(-0.655358\pi\) | ||||
−0.468923 | + | 0.883239i | \(0.655358\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.48447 | 0.0844745 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.03753 | 0.103160 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.58710 | −0.121684 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.43127 | 0.0823805 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.537338 | −0.0181861 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.86552 | 0.0630661 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.3947 | 0.823751 | 0.411876 | − | 0.911240i | \(-0.364874\pi\) | ||||
0.411876 | + | 0.911240i | \(0.364874\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.3378 | −0.618518 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.5933 | 0.660117 | 0.330058 | − | 0.943961i | \(-0.392932\pi\) | ||||
0.330058 | + | 0.943961i | \(0.392932\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −52.4809 | −1.76612 | −0.883061 | − | 0.469258i | \(-0.844521\pi\) | ||||
−0.883061 | + | 0.469258i | \(0.844521\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.40914 | 0.0809824 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.77851 | −0.261177 | −0.130588 | − | 0.991437i | \(-0.541687\pi\) | ||||
−0.130588 | + | 0.991437i | \(0.541687\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.1367 | 0.440591 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.35807 | 0.313507 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30.2681 | 1.01288 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.46719 | 0.115895 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.18776 | −0.306770 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.19277 | 0.273244 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.76985 | −0.192222 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.06632 | 0.235152 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.80698 | 0.0933073 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.8514 | 0.825178 | 0.412589 | − | 0.910917i | \(-0.364625\pi\) | ||||
0.412589 | + | 0.910917i | \(0.364625\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.309276 | 0.0102580 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.1481 | 0.468748 | 0.234374 | − | 0.972147i | \(-0.424696\pi\) | ||||
0.234374 | + | 0.972147i | \(0.424696\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.04444 | 0.299327 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.12625 | −0.0372328 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.10959 | −0.201756 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.8296 | 1.14892 | 0.574462 | − | 0.818532i | \(-0.305211\pi\) | ||||
0.574462 | + | 0.818532i | \(0.305211\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.6426 | 0.482491 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.65660 | 0.0874431 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.6341 | 0.974364 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.74670 | −0.0573691 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −39.7577 | −1.30441 | −0.652204 | − | 0.758043i | \(-0.726156\pi\) | ||||
−0.652204 | + | 0.758043i | \(0.726156\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.79897 | −0.190053 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.4322 | −0.341535 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.809952 | −0.0264883 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.61195 | 0.248672 | 0.124336 | − | 0.992240i | \(-0.460320\pi\) | ||||
0.124336 | + | 0.992240i | \(0.460320\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.5366 | −0.572285 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.6401 | −0.672849 | −0.336424 | − | 0.941710i | \(-0.609218\pi\) | ||||
−0.336424 | + | 0.941710i | \(0.609218\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.2058 | 0.885942 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.951538 | 0.0309535 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.8689 | 1.36056 | 0.680278 | − | 0.732954i | \(-0.261859\pi\) | ||||
0.680278 | + | 0.732954i | \(0.261859\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.4341 | 0.403627 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.8261 | −0.383488 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.13721 | 0.263590 | 0.131795 | − | 0.991277i | \(-0.457926\pi\) | ||||
0.131795 | + | 0.991277i | \(0.457926\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.58946 | −0.0514337 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.22008 | −0.0717650 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.6249 | −0.439970 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.5508 | 0.372607 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.61693 | 0.0521050 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.04320 | −0.0657729 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.5726 | 1.56199 | 0.780995 | − | 0.624538i | \(-0.214713\pi\) | ||||
0.780995 | + | 0.624538i | \(0.214713\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −44.3483 | −1.42467 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.5249 | 0.947500 | 0.473750 | − | 0.880659i | \(-0.342900\pi\) | ||||
0.473750 | + | 0.880659i | \(0.342900\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.19652 | −0.0383588 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.77621 | 0.281064 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.68546 | −0.277873 | −0.138936 | − | 0.990301i | \(-0.544368\pi\) | ||||
−0.138936 | + | 0.990301i | \(0.544368\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.7021 | 0.405961 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.448596 | 0.0143226 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.3899 | −0.522756 | −0.261378 | − | 0.965237i | \(-0.584177\pi\) | ||||
−0.261378 | + | 0.965237i | \(0.584177\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.72116 | −0.118566 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.22628 | 0.293676 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20.7787 | −0.660725 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.3457 | −1.18633 | −0.593163 | − | 0.805083i | \(-0.702121\pi\) | ||||
−0.593163 | + | 0.805083i | \(0.702121\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.3822 | 1.05935 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.01622 | −0.159025 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.5699 | 0.398092 | 0.199046 | − | 0.979990i | \(-0.436216\pi\) | ||||
0.199046 | + | 0.979990i | \(0.436216\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 30.3374 | 0.959833 |
(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 | 8008.2.a.u.1.8 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.u.1.8 | ✓ | 10 | 1.1 | even | 1 | trivial |