Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5054,2,Mod(1,5054)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5054.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5054 = 2 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5054.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: | \(40.3563931816\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.36538000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 13x^{4} - 4x^{3} + 41x^{2} + 16x - 16 \) |
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 | 1.6 | ||
Root | \(3.11392\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5054.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 3.11392 | 1.79782 | 0.898911 | − | 0.438132i | \(-0.144360\pi\) | ||||
0.898911 | + | 0.438132i | \(0.144360\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.959972 | −0.429312 | −0.214656 | − | 0.976690i | \(-0.568863\pi\) | ||||
−0.214656 | + | 0.976690i | \(0.568863\pi\) | |||||||
\(6\) | −3.11392 | −1.27125 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 6.69649 | 2.23216 | ||||||||
\(10\) | 0.959972 | 0.303570 | ||||||||
\(11\) | −2.70721 | −0.816256 | −0.408128 | − | 0.912925i | \(-0.633818\pi\) | ||||
−0.408128 | + | 0.912925i | \(0.633818\pi\) | |||||||
\(12\) | 3.11392 | 0.898911 | ||||||||
\(13\) | −3.55327 | −0.985499 | −0.492750 | − | 0.870171i | \(-0.664008\pi\) | ||||
−0.492750 | + | 0.870171i | \(0.664008\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −2.98927 | −0.771827 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.67457 | −1.61882 | −0.809410 | − | 0.587243i | \(-0.800213\pi\) | ||||
−0.809410 | + | 0.587243i | \(0.800213\pi\) | |||||||
\(18\) | −6.69649 | −1.57838 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −0.959972 | −0.214656 | ||||||||
\(21\) | 3.11392 | 0.679513 | ||||||||
\(22\) | 2.70721 | 0.577180 | ||||||||
\(23\) | 3.52062 | 0.734101 | 0.367050 | − | 0.930201i | \(-0.380368\pi\) | ||||
0.367050 | + | 0.930201i | \(0.380368\pi\) | |||||||
\(24\) | −3.11392 | −0.635626 | ||||||||
\(25\) | −4.07845 | −0.815691 | ||||||||
\(26\) | 3.55327 | 0.696853 | ||||||||
\(27\) | 11.5106 | 2.21521 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −7.12793 | −1.32362 | −0.661812 | − | 0.749670i | \(-0.730212\pi\) | ||||
−0.661812 | + | 0.749670i | \(0.730212\pi\) | |||||||
\(30\) | 2.98927 | 0.545764 | ||||||||
\(31\) | −2.50554 | −0.450007 | −0.225004 | − | 0.974358i | \(-0.572239\pi\) | ||||
−0.225004 | + | 0.974358i | \(0.572239\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −8.43004 | −1.46748 | ||||||||
\(34\) | 6.67457 | 1.14468 | ||||||||
\(35\) | −0.959972 | −0.162265 | ||||||||
\(36\) | 6.69649 | 1.11608 | ||||||||
\(37\) | −7.59908 | −1.24928 | −0.624640 | − | 0.780913i | \(-0.714754\pi\) | ||||
−0.624640 | + | 0.780913i | \(0.714754\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.0646 | −1.77175 | ||||||||
\(40\) | 0.959972 | 0.151785 | ||||||||
\(41\) | 7.24185 | 1.13099 | 0.565493 | − | 0.824753i | \(-0.308686\pi\) | ||||
0.565493 | + | 0.824753i | \(0.308686\pi\) | |||||||
\(42\) | −3.11392 | −0.480488 | ||||||||
\(43\) | −0.282061 | −0.0430138 | −0.0215069 | − | 0.999769i | \(-0.506846\pi\) | ||||
−0.0215069 | + | 0.999769i | \(0.506846\pi\) | |||||||
\(44\) | −2.70721 | −0.408128 | ||||||||
\(45\) | −6.42844 | −0.958295 | ||||||||
\(46\) | −3.52062 | −0.519088 | ||||||||
\(47\) | 6.90889 | 1.00777 | 0.503883 | − | 0.863772i | \(-0.331904\pi\) | ||||
0.503883 | + | 0.863772i | \(0.331904\pi\) | |||||||
\(48\) | 3.11392 | 0.449455 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.07845 | 0.576780 | ||||||||
\(51\) | −20.7841 | −2.91035 | ||||||||
\(52\) | −3.55327 | −0.492750 | ||||||||
\(53\) | 9.51902 | 1.30754 | 0.653769 | − | 0.756694i | \(-0.273187\pi\) | ||||
0.653769 | + | 0.756694i | \(0.273187\pi\) | |||||||
\(54\) | −11.5106 | −1.56639 | ||||||||
\(55\) | 2.59885 | 0.350429 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.12793 | 0.935943 | ||||||||
\(59\) | −10.2036 | −1.32839 | −0.664195 | − | 0.747559i | \(-0.731226\pi\) | ||||
−0.664195 | + | 0.747559i | \(0.731226\pi\) | |||||||
\(60\) | −2.98927 | −0.385914 | ||||||||
\(61\) | −13.3882 | −1.71419 | −0.857093 | − | 0.515162i | \(-0.827732\pi\) | ||||
−0.857093 | + | 0.515162i | \(0.827732\pi\) | |||||||
\(62\) | 2.50554 | 0.318203 | ||||||||
\(63\) | 6.69649 | 0.843678 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.41104 | 0.423087 | ||||||||
\(66\) | 8.43004 | 1.03767 | ||||||||
\(67\) | 4.15441 | 0.507542 | 0.253771 | − | 0.967264i | \(-0.418329\pi\) | ||||
0.253771 | + | 0.967264i | \(0.418329\pi\) | |||||||
\(68\) | −6.67457 | −0.809410 | ||||||||
\(69\) | 10.9629 | 1.31978 | ||||||||
\(70\) | 0.959972 | 0.114739 | ||||||||
\(71\) | 2.22784 | 0.264396 | 0.132198 | − | 0.991223i | \(-0.457797\pi\) | ||||
0.132198 | + | 0.991223i | \(0.457797\pi\) | |||||||
\(72\) | −6.69649 | −0.789189 | ||||||||
\(73\) | −8.57661 | −1.00382 | −0.501908 | − | 0.864921i | \(-0.667368\pi\) | ||||
−0.501908 | + | 0.864921i | \(0.667368\pi\) | |||||||
\(74\) | 7.59908 | 0.883375 | ||||||||
\(75\) | −12.7000 | −1.46647 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.70721 | −0.308516 | ||||||||
\(78\) | 11.0646 | 1.25282 | ||||||||
\(79\) | −15.0035 | −1.68802 | −0.844012 | − | 0.536324i | \(-0.819812\pi\) | ||||
−0.844012 | + | 0.536324i | \(0.819812\pi\) | |||||||
\(80\) | −0.959972 | −0.107328 | ||||||||
\(81\) | 15.7535 | 1.75039 | ||||||||
\(82\) | −7.24185 | −0.799729 | ||||||||
\(83\) | −17.4698 | −1.91756 | −0.958781 | − | 0.284145i | \(-0.908290\pi\) | ||||
−0.958781 | + | 0.284145i | \(0.908290\pi\) | |||||||
\(84\) | 3.11392 | 0.339756 | ||||||||
\(85\) | 6.40740 | 0.694980 | ||||||||
\(86\) | 0.282061 | 0.0304154 | ||||||||
\(87\) | −22.1958 | −2.37964 | ||||||||
\(88\) | 2.70721 | 0.288590 | ||||||||
\(89\) | 8.35574 | 0.885706 | 0.442853 | − | 0.896594i | \(-0.353966\pi\) | ||||
0.442853 | + | 0.896594i | \(0.353966\pi\) | |||||||
\(90\) | 6.42844 | 0.677617 | ||||||||
\(91\) | −3.55327 | −0.372484 | ||||||||
\(92\) | 3.52062 | 0.367050 | ||||||||
\(93\) | −7.80203 | −0.809033 | ||||||||
\(94\) | −6.90889 | −0.712598 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.11392 | −0.317813 | ||||||||
\(97\) | −13.2383 | −1.34414 | −0.672072 | − | 0.740486i | \(-0.734595\pi\) | ||||
−0.672072 | + | 0.740486i | \(0.734595\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −18.1288 | −1.82202 | ||||||||
\(100\) | −4.07845 | −0.407845 | ||||||||
\(101\) | 12.4091 | 1.23476 | 0.617378 | − | 0.786667i | \(-0.288195\pi\) | ||||
0.617378 | + | 0.786667i | \(0.288195\pi\) | |||||||
\(102\) | 20.7841 | 2.05793 | ||||||||
\(103\) | 3.60252 | 0.354967 | 0.177483 | − | 0.984124i | \(-0.443204\pi\) | ||||
0.177483 | + | 0.984124i | \(0.443204\pi\) | |||||||
\(104\) | 3.55327 | 0.348427 | ||||||||
\(105\) | −2.98927 | −0.291723 | ||||||||
\(106\) | −9.51902 | −0.924569 | ||||||||
\(107\) | −9.93200 | −0.960163 | −0.480082 | − | 0.877224i | \(-0.659393\pi\) | ||||
−0.480082 | + | 0.877224i | \(0.659393\pi\) | |||||||
\(108\) | 11.5106 | 1.10760 | ||||||||
\(109\) | 8.02328 | 0.768491 | 0.384245 | − | 0.923231i | \(-0.374462\pi\) | ||||
0.384245 | + | 0.923231i | \(0.374462\pi\) | |||||||
\(110\) | −2.59885 | −0.247791 | ||||||||
\(111\) | −23.6629 | −2.24598 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 7.08000 | 0.666030 | 0.333015 | − | 0.942922i | \(-0.391934\pi\) | ||||
0.333015 | + | 0.942922i | \(0.391934\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.37970 | −0.315159 | ||||||||
\(116\) | −7.12793 | −0.661812 | ||||||||
\(117\) | −23.7944 | −2.19979 | ||||||||
\(118\) | 10.2036 | 0.939314 | ||||||||
\(119\) | −6.67457 | −0.611857 | ||||||||
\(120\) | 2.98927 | 0.272882 | ||||||||
\(121\) | −3.67099 | −0.333727 | ||||||||
\(122\) | 13.3882 | 1.21211 | ||||||||
\(123\) | 22.5505 | 2.03331 | ||||||||
\(124\) | −2.50554 | −0.225004 | ||||||||
\(125\) | 8.71506 | 0.779499 | ||||||||
\(126\) | −6.69649 | −0.596571 | ||||||||
\(127\) | −19.6653 | −1.74501 | −0.872505 | − | 0.488606i | \(-0.837506\pi\) | ||||
−0.872505 | + | 0.488606i | \(0.837506\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.878313 | −0.0773312 | ||||||||
\(130\) | −3.41104 | −0.299168 | ||||||||
\(131\) | 7.89393 | 0.689696 | 0.344848 | − | 0.938659i | \(-0.387931\pi\) | ||||
0.344848 | + | 0.938659i | \(0.387931\pi\) | |||||||
\(132\) | −8.43004 | −0.733741 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.15441 | −0.358887 | ||||||||
\(135\) | −11.0498 | −0.951017 | ||||||||
\(136\) | 6.67457 | 0.572340 | ||||||||
\(137\) | 7.42167 | 0.634076 | 0.317038 | − | 0.948413i | \(-0.397312\pi\) | ||||
0.317038 | + | 0.948413i | \(0.397312\pi\) | |||||||
\(138\) | −10.9629 | −0.933227 | ||||||||
\(139\) | 16.4405 | 1.39447 | 0.697234 | − | 0.716844i | \(-0.254414\pi\) | ||||
0.697234 | + | 0.716844i | \(0.254414\pi\) | |||||||
\(140\) | −0.959972 | −0.0811324 | ||||||||
\(141\) | 21.5137 | 1.81178 | ||||||||
\(142\) | −2.22784 | −0.186956 | ||||||||
\(143\) | 9.61945 | 0.804419 | ||||||||
\(144\) | 6.69649 | 0.558041 | ||||||||
\(145\) | 6.84261 | 0.568248 | ||||||||
\(146\) | 8.57661 | 0.709805 | ||||||||
\(147\) | 3.11392 | 0.256832 | ||||||||
\(148\) | −7.59908 | −0.624640 | ||||||||
\(149\) | 5.05395 | 0.414036 | 0.207018 | − | 0.978337i | \(-0.433624\pi\) | ||||
0.207018 | + | 0.978337i | \(0.433624\pi\) | |||||||
\(150\) | 12.7000 | 1.03695 | ||||||||
\(151\) | 7.51527 | 0.611584 | 0.305792 | − | 0.952098i | \(-0.401079\pi\) | ||||
0.305792 | + | 0.952098i | \(0.401079\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −44.6962 | −3.61347 | ||||||||
\(154\) | 2.70721 | 0.218153 | ||||||||
\(155\) | 2.40524 | 0.193194 | ||||||||
\(156\) | −11.0646 | −0.885876 | ||||||||
\(157\) | 2.10544 | 0.168032 | 0.0840162 | − | 0.996464i | \(-0.473225\pi\) | ||||
0.0840162 | + | 0.996464i | \(0.473225\pi\) | |||||||
\(158\) | 15.0035 | 1.19361 | ||||||||
\(159\) | 29.6415 | 2.35072 | ||||||||
\(160\) | 0.959972 | 0.0758924 | ||||||||
\(161\) | 3.52062 | 0.277464 | ||||||||
\(162\) | −15.7535 | −1.23771 | ||||||||
\(163\) | 7.58995 | 0.594491 | 0.297245 | − | 0.954801i | \(-0.403932\pi\) | ||||
0.297245 | + | 0.954801i | \(0.403932\pi\) | |||||||
\(164\) | 7.24185 | 0.565493 | ||||||||
\(165\) | 8.09260 | 0.630008 | ||||||||
\(166\) | 17.4698 | 1.35592 | ||||||||
\(167\) | 8.82254 | 0.682708 | 0.341354 | − | 0.939935i | \(-0.389114\pi\) | ||||
0.341354 | + | 0.939935i | \(0.389114\pi\) | |||||||
\(168\) | −3.11392 | −0.240244 | ||||||||
\(169\) | −0.374292 | −0.0287917 | ||||||||
\(170\) | −6.40740 | −0.491425 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.282061 | −0.0215069 | ||||||||
\(173\) | −3.13833 | −0.238603 | −0.119301 | − | 0.992858i | \(-0.538065\pi\) | ||||
−0.119301 | + | 0.992858i | \(0.538065\pi\) | |||||||
\(174\) | 22.1958 | 1.68266 | ||||||||
\(175\) | −4.07845 | −0.308302 | ||||||||
\(176\) | −2.70721 | −0.204064 | ||||||||
\(177\) | −31.7731 | −2.38821 | ||||||||
\(178\) | −8.35574 | −0.626289 | ||||||||
\(179\) | −23.5378 | −1.75930 | −0.879648 | − | 0.475626i | \(-0.842222\pi\) | ||||
−0.879648 | + | 0.475626i | \(0.842222\pi\) | |||||||
\(180\) | −6.42844 | −0.479148 | ||||||||
\(181\) | −11.0476 | −0.821158 | −0.410579 | − | 0.911825i | \(-0.634673\pi\) | ||||
−0.410579 | + | 0.911825i | \(0.634673\pi\) | |||||||
\(182\) | 3.55327 | 0.263386 | ||||||||
\(183\) | −41.6898 | −3.08180 | ||||||||
\(184\) | −3.52062 | −0.259544 | ||||||||
\(185\) | 7.29490 | 0.536332 | ||||||||
\(186\) | 7.80203 | 0.572073 | ||||||||
\(187\) | 18.0695 | 1.32137 | ||||||||
\(188\) | 6.90889 | 0.503883 | ||||||||
\(189\) | 11.5106 | 0.837270 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.32300 | 0.529874 | 0.264937 | − | 0.964266i | \(-0.414649\pi\) | ||||
0.264937 | + | 0.964266i | \(0.414649\pi\) | |||||||
\(192\) | 3.11392 | 0.224728 | ||||||||
\(193\) | −21.2936 | −1.53275 | −0.766374 | − | 0.642395i | \(-0.777941\pi\) | ||||
−0.766374 | + | 0.642395i | \(0.777941\pi\) | |||||||
\(194\) | 13.2383 | 0.950453 | ||||||||
\(195\) | 10.6217 | 0.760635 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 26.9859 | 1.92266 | 0.961331 | − | 0.275394i | \(-0.0888083\pi\) | ||||
0.961331 | + | 0.275394i | \(0.0888083\pi\) | |||||||
\(198\) | 18.1288 | 1.28836 | ||||||||
\(199\) | 2.84678 | 0.201803 | 0.100901 | − | 0.994896i | \(-0.467827\pi\) | ||||
0.100901 | + | 0.994896i | \(0.467827\pi\) | |||||||
\(200\) | 4.07845 | 0.288390 | ||||||||
\(201\) | 12.9365 | 0.912471 | ||||||||
\(202\) | −12.4091 | −0.873104 | ||||||||
\(203\) | −7.12793 | −0.500283 | ||||||||
\(204\) | −20.7841 | −1.45518 | ||||||||
\(205\) | −6.95197 | −0.485547 | ||||||||
\(206\) | −3.60252 | −0.250999 | ||||||||
\(207\) | 23.5758 | 1.63863 | ||||||||
\(208\) | −3.55327 | −0.246375 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.98927 | 0.206280 | ||||||||
\(211\) | −14.4955 | −0.997910 | −0.498955 | − | 0.866628i | \(-0.666283\pi\) | ||||
−0.498955 | + | 0.866628i | \(0.666283\pi\) | |||||||
\(212\) | 9.51902 | 0.653769 | ||||||||
\(213\) | 6.93730 | 0.475336 | ||||||||
\(214\) | 9.93200 | 0.678938 | ||||||||
\(215\) | 0.270770 | 0.0184664 | ||||||||
\(216\) | −11.5106 | −0.783195 | ||||||||
\(217\) | −2.50554 | −0.170087 | ||||||||
\(218\) | −8.02328 | −0.543405 | ||||||||
\(219\) | −26.7068 | −1.80468 | ||||||||
\(220\) | 2.59885 | 0.175214 | ||||||||
\(221\) | 23.7165 | 1.59535 | ||||||||
\(222\) | 23.6629 | 1.58815 | ||||||||
\(223\) | −17.6629 | −1.18280 | −0.591399 | − | 0.806379i | \(-0.701424\pi\) | ||||
−0.591399 | + | 0.806379i | \(0.701424\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −27.3113 | −1.82075 | ||||||||
\(226\) | −7.08000 | −0.470954 | ||||||||
\(227\) | −0.588393 | −0.0390530 | −0.0195265 | − | 0.999809i | \(-0.506216\pi\) | ||||
−0.0195265 | + | 0.999809i | \(0.506216\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.10188 | 0.601469 | 0.300735 | − | 0.953708i | \(-0.402768\pi\) | ||||
0.300735 | + | 0.953708i | \(0.402768\pi\) | |||||||
\(230\) | 3.37970 | 0.222851 | ||||||||
\(231\) | −8.43004 | −0.554656 | ||||||||
\(232\) | 7.12793 | 0.467972 | ||||||||
\(233\) | −25.0109 | −1.63852 | −0.819261 | − | 0.573421i | \(-0.805616\pi\) | ||||
−0.819261 | + | 0.573421i | \(0.805616\pi\) | |||||||
\(234\) | 23.7944 | 1.55549 | ||||||||
\(235\) | −6.63234 | −0.432646 | ||||||||
\(236\) | −10.2036 | −0.664195 | ||||||||
\(237\) | −46.7196 | −3.03477 | ||||||||
\(238\) | 6.67457 | 0.432648 | ||||||||
\(239\) | 11.5301 | 0.745820 | 0.372910 | − | 0.927868i | \(-0.378360\pi\) | ||||
0.372910 | + | 0.927868i | \(0.378360\pi\) | |||||||
\(240\) | −2.98927 | −0.192957 | ||||||||
\(241\) | −3.81708 | −0.245880 | −0.122940 | − | 0.992414i | \(-0.539232\pi\) | ||||
−0.122940 | + | 0.992414i | \(0.539232\pi\) | |||||||
\(242\) | 3.67099 | 0.235980 | ||||||||
\(243\) | 14.5234 | 0.931676 | ||||||||
\(244\) | −13.3882 | −0.857093 | ||||||||
\(245\) | −0.959972 | −0.0613304 | ||||||||
\(246\) | −22.5505 | −1.43777 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.50554 | 0.159102 | ||||||||
\(249\) | −54.3996 | −3.44744 | ||||||||
\(250\) | −8.71506 | −0.551189 | ||||||||
\(251\) | 22.0339 | 1.39077 | 0.695385 | − | 0.718637i | \(-0.255234\pi\) | ||||
0.695385 | + | 0.718637i | \(0.255234\pi\) | |||||||
\(252\) | 6.69649 | 0.421839 | ||||||||
\(253\) | −9.53108 | −0.599214 | ||||||||
\(254\) | 19.6653 | 1.23391 | ||||||||
\(255\) | 19.9521 | 1.24945 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.4193 | 0.774697 | 0.387349 | − | 0.921933i | \(-0.373391\pi\) | ||||
0.387349 | + | 0.921933i | \(0.373391\pi\) | |||||||
\(258\) | 0.878313 | 0.0546814 | ||||||||
\(259\) | −7.59908 | −0.472184 | ||||||||
\(260\) | 3.41104 | 0.211544 | ||||||||
\(261\) | −47.7321 | −2.95454 | ||||||||
\(262\) | −7.89393 | −0.487689 | ||||||||
\(263\) | −6.52472 | −0.402332 | −0.201166 | − | 0.979557i | \(-0.564473\pi\) | ||||
−0.201166 | + | 0.979557i | \(0.564473\pi\) | |||||||
\(264\) | 8.43004 | 0.518833 | ||||||||
\(265\) | −9.13799 | −0.561342 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.0191 | 1.59234 | ||||||||
\(268\) | 4.15441 | 0.253771 | ||||||||
\(269\) | −19.0246 | −1.15995 | −0.579974 | − | 0.814635i | \(-0.696937\pi\) | ||||
−0.579974 | + | 0.814635i | \(0.696937\pi\) | |||||||
\(270\) | 11.0498 | 0.672470 | ||||||||
\(271\) | −11.1907 | −0.679789 | −0.339895 | − | 0.940464i | \(-0.610391\pi\) | ||||
−0.339895 | + | 0.940464i | \(0.610391\pi\) | |||||||
\(272\) | −6.67457 | −0.404705 | ||||||||
\(273\) | −11.0646 | −0.669659 | ||||||||
\(274\) | −7.42167 | −0.448360 | ||||||||
\(275\) | 11.0412 | 0.665812 | ||||||||
\(276\) | 10.9629 | 0.659891 | ||||||||
\(277\) | 18.7528 | 1.12675 | 0.563374 | − | 0.826202i | \(-0.309503\pi\) | ||||
0.563374 | + | 0.826202i | \(0.309503\pi\) | |||||||
\(278\) | −16.4405 | −0.986037 | ||||||||
\(279\) | −16.7783 | −1.00449 | ||||||||
\(280\) | 0.959972 | 0.0573693 | ||||||||
\(281\) | −6.48900 | −0.387101 | −0.193551 | − | 0.981090i | \(-0.562000\pi\) | ||||
−0.193551 | + | 0.981090i | \(0.562000\pi\) | |||||||
\(282\) | −21.5137 | −1.28112 | ||||||||
\(283\) | 23.6428 | 1.40542 | 0.702709 | − | 0.711478i | \(-0.251974\pi\) | ||||
0.702709 | + | 0.711478i | \(0.251974\pi\) | |||||||
\(284\) | 2.22784 | 0.132198 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.61945 | −0.568810 | ||||||||
\(287\) | 7.24185 | 0.427473 | ||||||||
\(288\) | −6.69649 | −0.394594 | ||||||||
\(289\) | 27.5499 | 1.62058 | ||||||||
\(290\) | −6.84261 | −0.401812 | ||||||||
\(291\) | −41.2229 | −2.41653 | ||||||||
\(292\) | −8.57661 | −0.501908 | ||||||||
\(293\) | 23.2099 | 1.35594 | 0.677969 | − | 0.735090i | \(-0.262860\pi\) | ||||
0.677969 | + | 0.735090i | \(0.262860\pi\) | |||||||
\(294\) | −3.11392 | −0.181607 | ||||||||
\(295\) | 9.79514 | 0.570295 | ||||||||
\(296\) | 7.59908 | 0.441687 | ||||||||
\(297\) | −31.1616 | −1.80818 | ||||||||
\(298\) | −5.05395 | −0.292767 | ||||||||
\(299\) | −12.5097 | −0.723455 | ||||||||
\(300\) | −12.7000 | −0.733233 | ||||||||
\(301\) | −0.282061 | −0.0162577 | ||||||||
\(302\) | −7.51527 | −0.432455 | ||||||||
\(303\) | 38.6410 | 2.21987 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.8523 | 0.735921 | ||||||||
\(306\) | 44.6962 | 2.55511 | ||||||||
\(307\) | 25.0604 | 1.43027 | 0.715137 | − | 0.698984i | \(-0.246364\pi\) | ||||
0.715137 | + | 0.698984i | \(0.246364\pi\) | |||||||
\(308\) | −2.70721 | −0.154258 | ||||||||
\(309\) | 11.2179 | 0.638166 | ||||||||
\(310\) | −2.40524 | −0.136609 | ||||||||
\(311\) | −21.0148 | −1.19164 | −0.595820 | − | 0.803118i | \(-0.703173\pi\) | ||||
−0.595820 | + | 0.803118i | \(0.703173\pi\) | |||||||
\(312\) | 11.0646 | 0.626409 | ||||||||
\(313\) | 18.2477 | 1.03142 | 0.515711 | − | 0.856762i | \(-0.327528\pi\) | ||||
0.515711 | + | 0.856762i | \(0.327528\pi\) | |||||||
\(314\) | −2.10544 | −0.118817 | ||||||||
\(315\) | −6.42844 | −0.362202 | ||||||||
\(316\) | −15.0035 | −0.844012 | ||||||||
\(317\) | 10.7596 | 0.604321 | 0.302160 | − | 0.953257i | \(-0.402292\pi\) | ||||
0.302160 | + | 0.953257i | \(0.402292\pi\) | |||||||
\(318\) | −29.6415 | −1.66221 | ||||||||
\(319\) | 19.2968 | 1.08042 | ||||||||
\(320\) | −0.959972 | −0.0536641 | ||||||||
\(321\) | −30.9275 | −1.72620 | ||||||||
\(322\) | −3.52062 | −0.196197 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 15.7535 | 0.875194 | ||||||||
\(325\) | 14.4918 | 0.803862 | ||||||||
\(326\) | −7.58995 | −0.420368 | ||||||||
\(327\) | 24.9838 | 1.38161 | ||||||||
\(328\) | −7.24185 | −0.399864 | ||||||||
\(329\) | 6.90889 | 0.380900 | ||||||||
\(330\) | −8.09260 | −0.445483 | ||||||||
\(331\) | −36.1010 | −1.98429 | −0.992146 | − | 0.125087i | \(-0.960079\pi\) | ||||
−0.992146 | + | 0.125087i | \(0.960079\pi\) | |||||||
\(332\) | −17.4698 | −0.958781 | ||||||||
\(333\) | −50.8871 | −2.78860 | ||||||||
\(334\) | −8.82254 | −0.482748 | ||||||||
\(335\) | −3.98812 | −0.217894 | ||||||||
\(336\) | 3.11392 | 0.169878 | ||||||||
\(337\) | −18.8352 | −1.02602 | −0.513009 | − | 0.858383i | \(-0.671469\pi\) | ||||
−0.513009 | + | 0.858383i | \(0.671469\pi\) | |||||||
\(338\) | 0.374292 | 0.0203588 | ||||||||
\(339\) | 22.0465 | 1.19740 | ||||||||
\(340\) | 6.40740 | 0.347490 | ||||||||
\(341\) | 6.78302 | 0.367321 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0.282061 | 0.0152077 | ||||||||
\(345\) | −10.5241 | −0.566599 | ||||||||
\(346\) | 3.13833 | 0.168718 | ||||||||
\(347\) | −12.6195 | −0.677451 | −0.338726 | − | 0.940885i | \(-0.609996\pi\) | ||||
−0.338726 | + | 0.940885i | \(0.609996\pi\) | |||||||
\(348\) | −22.1958 | −1.18982 | ||||||||
\(349\) | 0.227609 | 0.0121836 | 0.00609181 | − | 0.999981i | \(-0.498061\pi\) | ||||
0.00609181 | + | 0.999981i | \(0.498061\pi\) | |||||||
\(350\) | 4.07845 | 0.218003 | ||||||||
\(351\) | −40.9001 | −2.18309 | ||||||||
\(352\) | 2.70721 | 0.144295 | ||||||||
\(353\) | −11.9425 | −0.635637 | −0.317818 | − | 0.948152i | \(-0.602950\pi\) | ||||
−0.317818 | + | 0.948152i | \(0.602950\pi\) | |||||||
\(354\) | 31.7731 | 1.68872 | ||||||||
\(355\) | −2.13866 | −0.113508 | ||||||||
\(356\) | 8.35574 | 0.442853 | ||||||||
\(357\) | −20.7841 | −1.10001 | ||||||||
\(358\) | 23.5378 | 1.24401 | ||||||||
\(359\) | −22.9370 | −1.21057 | −0.605285 | − | 0.796009i | \(-0.706941\pi\) | ||||
−0.605285 | + | 0.796009i | \(0.706941\pi\) | |||||||
\(360\) | 6.42844 | 0.338809 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 11.0476 | 0.580646 | ||||||||
\(363\) | −11.4312 | −0.599981 | ||||||||
\(364\) | −3.55327 | −0.186242 | ||||||||
\(365\) | 8.23330 | 0.430951 | ||||||||
\(366\) | 41.6898 | 2.17916 | ||||||||
\(367\) | 14.2300 | 0.742802 | 0.371401 | − | 0.928473i | \(-0.378878\pi\) | ||||
0.371401 | + | 0.928473i | \(0.378878\pi\) | |||||||
\(368\) | 3.52062 | 0.183525 | ||||||||
\(369\) | 48.4950 | 2.52455 | ||||||||
\(370\) | −7.29490 | −0.379244 | ||||||||
\(371\) | 9.51902 | 0.494203 | ||||||||
\(372\) | −7.80203 | −0.404517 | ||||||||
\(373\) | 5.07840 | 0.262949 | 0.131475 | − | 0.991320i | \(-0.458029\pi\) | ||||
0.131475 | + | 0.991320i | \(0.458029\pi\) | |||||||
\(374\) | −18.0695 | −0.934351 | ||||||||
\(375\) | 27.1380 | 1.40140 | ||||||||
\(376\) | −6.90889 | −0.356299 | ||||||||
\(377\) | 25.3274 | 1.30443 | ||||||||
\(378\) | −11.5106 | −0.592039 | ||||||||
\(379\) | 4.95870 | 0.254711 | 0.127356 | − | 0.991857i | \(-0.459351\pi\) | ||||
0.127356 | + | 0.991857i | \(0.459351\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −61.2360 | −3.13722 | ||||||||
\(382\) | −7.32300 | −0.374677 | ||||||||
\(383\) | 3.11820 | 0.159333 | 0.0796663 | − | 0.996822i | \(-0.474615\pi\) | ||||
0.0796663 | + | 0.996822i | \(0.474615\pi\) | |||||||
\(384\) | −3.11392 | −0.158906 | ||||||||
\(385\) | 2.59885 | 0.132450 | ||||||||
\(386\) | 21.2936 | 1.08382 | ||||||||
\(387\) | −1.88881 | −0.0960139 | ||||||||
\(388\) | −13.2383 | −0.672072 | ||||||||
\(389\) | 12.7019 | 0.644010 | 0.322005 | − | 0.946738i | \(-0.395643\pi\) | ||||
0.322005 | + | 0.946738i | \(0.395643\pi\) | |||||||
\(390\) | −10.6217 | −0.537850 | ||||||||
\(391\) | −23.4986 | −1.18838 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 24.5810 | 1.23995 | ||||||||
\(394\) | −26.9859 | −1.35953 | ||||||||
\(395\) | 14.4029 | 0.724690 | ||||||||
\(396\) | −18.1288 | −0.911008 | ||||||||
\(397\) | 33.5926 | 1.68597 | 0.842983 | − | 0.537940i | \(-0.180797\pi\) | ||||
0.842983 | + | 0.537940i | \(0.180797\pi\) | |||||||
\(398\) | −2.84678 | −0.142696 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.07845 | −0.203923 | ||||||||
\(401\) | 26.6682 | 1.33174 | 0.665872 | − | 0.746066i | \(-0.268060\pi\) | ||||
0.665872 | + | 0.746066i | \(0.268060\pi\) | |||||||
\(402\) | −12.9365 | −0.645214 | ||||||||
\(403\) | 8.90284 | 0.443482 | ||||||||
\(404\) | 12.4091 | 0.617378 | ||||||||
\(405\) | −15.1229 | −0.751463 | ||||||||
\(406\) | 7.12793 | 0.353753 | ||||||||
\(407\) | 20.5723 | 1.01973 | ||||||||
\(408\) | 20.7841 | 1.02896 | ||||||||
\(409\) | 4.35206 | 0.215196 | 0.107598 | − | 0.994195i | \(-0.465684\pi\) | ||||
0.107598 | + | 0.994195i | \(0.465684\pi\) | |||||||
\(410\) | 6.95197 | 0.343333 | ||||||||
\(411\) | 23.1105 | 1.13996 | ||||||||
\(412\) | 3.60252 | 0.177483 | ||||||||
\(413\) | −10.2036 | −0.502085 | ||||||||
\(414\) | −23.5758 | −1.15869 | ||||||||
\(415\) | 16.7705 | 0.823234 | ||||||||
\(416\) | 3.55327 | 0.174213 | ||||||||
\(417\) | 51.1945 | 2.50700 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.26629 | 0.452688 | 0.226344 | − | 0.974047i | \(-0.427323\pi\) | ||||
0.226344 | + | 0.974047i | \(0.427323\pi\) | |||||||
\(420\) | −2.98927 | −0.145862 | ||||||||
\(421\) | 17.3214 | 0.844193 | 0.422097 | − | 0.906551i | \(-0.361294\pi\) | ||||
0.422097 | + | 0.906551i | \(0.361294\pi\) | |||||||
\(422\) | 14.4955 | 0.705629 | ||||||||
\(423\) | 46.2653 | 2.24950 | ||||||||
\(424\) | −9.51902 | −0.462285 | ||||||||
\(425\) | 27.2219 | 1.32046 | ||||||||
\(426\) | −6.93730 | −0.336113 | ||||||||
\(427\) | −13.3882 | −0.647901 | ||||||||
\(428\) | −9.93200 | −0.480082 | ||||||||
\(429\) | 29.9542 | 1.44620 | ||||||||
\(430\) | −0.270770 | −0.0130577 | ||||||||
\(431\) | 21.3963 | 1.03062 | 0.515311 | − | 0.857003i | \(-0.327676\pi\) | ||||
0.515311 | + | 0.857003i | \(0.327676\pi\) | |||||||
\(432\) | 11.5106 | 0.553802 | ||||||||
\(433\) | −19.2137 | −0.923353 | −0.461676 | − | 0.887048i | \(-0.652752\pi\) | ||||
−0.461676 | + | 0.887048i | \(0.652752\pi\) | |||||||
\(434\) | 2.50554 | 0.120270 | ||||||||
\(435\) | 21.3073 | 1.02161 | ||||||||
\(436\) | 8.02328 | 0.384245 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 26.7068 | 1.27610 | ||||||||
\(439\) | −22.5139 | −1.07453 | −0.537265 | − | 0.843414i | \(-0.680542\pi\) | ||||
−0.537265 | + | 0.843414i | \(0.680542\pi\) | |||||||
\(440\) | −2.59885 | −0.123895 | ||||||||
\(441\) | 6.69649 | 0.318880 | ||||||||
\(442\) | −23.7165 | −1.12808 | ||||||||
\(443\) | 0.978663 | 0.0464977 | 0.0232489 | − | 0.999730i | \(-0.492599\pi\) | ||||
0.0232489 | + | 0.999730i | \(0.492599\pi\) | |||||||
\(444\) | −23.6629 | −1.12299 | ||||||||
\(445\) | −8.02127 | −0.380245 | ||||||||
\(446\) | 17.6629 | 0.836364 | ||||||||
\(447\) | 15.7376 | 0.744362 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −32.9060 | −1.55293 | −0.776466 | − | 0.630159i | \(-0.782990\pi\) | ||||
−0.776466 | + | 0.630159i | \(0.782990\pi\) | |||||||
\(450\) | 27.3113 | 1.28747 | ||||||||
\(451\) | −19.6052 | −0.923174 | ||||||||
\(452\) | 7.08000 | 0.333015 | ||||||||
\(453\) | 23.4019 | 1.09952 | ||||||||
\(454\) | 0.588393 | 0.0276147 | ||||||||
\(455\) | 3.41104 | 0.159912 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.9971 | 0.888649 | 0.444324 | − | 0.895866i | \(-0.353444\pi\) | ||||
0.444324 | + | 0.895866i | \(0.353444\pi\) | |||||||
\(458\) | −9.10188 | −0.425303 | ||||||||
\(459\) | −76.8280 | −3.58603 | ||||||||
\(460\) | −3.37970 | −0.157579 | ||||||||
\(461\) | −37.7120 | −1.75642 | −0.878211 | − | 0.478274i | \(-0.841263\pi\) | ||||
−0.878211 | + | 0.478274i | \(0.841263\pi\) | |||||||
\(462\) | 8.43004 | 0.392201 | ||||||||
\(463\) | −25.5830 | −1.18894 | −0.594470 | − | 0.804117i | \(-0.702638\pi\) | ||||
−0.594470 | + | 0.804117i | \(0.702638\pi\) | |||||||
\(464\) | −7.12793 | −0.330906 | ||||||||
\(465\) | 7.48973 | 0.347328 | ||||||||
\(466\) | 25.0109 | 1.15861 | ||||||||
\(467\) | −4.52094 | −0.209204 | −0.104602 | − | 0.994514i | \(-0.533357\pi\) | ||||
−0.104602 | + | 0.994514i | \(0.533357\pi\) | |||||||
\(468\) | −23.7944 | −1.09990 | ||||||||
\(469\) | 4.15441 | 0.191833 | ||||||||
\(470\) | 6.63234 | 0.305927 | ||||||||
\(471\) | 6.55617 | 0.302092 | ||||||||
\(472\) | 10.2036 | 0.469657 | ||||||||
\(473\) | 0.763598 | 0.0351103 | ||||||||
\(474\) | 46.7196 | 2.14590 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.67457 | −0.305928 | ||||||||
\(477\) | 63.7440 | 2.91864 | ||||||||
\(478\) | −11.5301 | −0.527374 | ||||||||
\(479\) | −7.34593 | −0.335644 | −0.167822 | − | 0.985817i | \(-0.553673\pi\) | ||||
−0.167822 | + | 0.985817i | \(0.553673\pi\) | |||||||
\(480\) | 2.98927 | 0.136441 | ||||||||
\(481\) | 27.0016 | 1.23116 | ||||||||
\(482\) | 3.81708 | 0.173863 | ||||||||
\(483\) | 10.9629 | 0.498831 | ||||||||
\(484\) | −3.67099 | −0.166863 | ||||||||
\(485\) | 12.7084 | 0.577058 | ||||||||
\(486\) | −14.5234 | −0.658794 | ||||||||
\(487\) | 6.74975 | 0.305860 | 0.152930 | − | 0.988237i | \(-0.451129\pi\) | ||||
0.152930 | + | 0.988237i | \(0.451129\pi\) | |||||||
\(488\) | 13.3882 | 0.606056 | ||||||||
\(489\) | 23.6345 | 1.06879 | ||||||||
\(490\) | 0.959972 | 0.0433671 | ||||||||
\(491\) | −14.7330 | −0.664890 | −0.332445 | − | 0.943123i | \(-0.607874\pi\) | ||||
−0.332445 | + | 0.943123i | \(0.607874\pi\) | |||||||
\(492\) | 22.5505 | 1.01666 | ||||||||
\(493\) | 47.5759 | 2.14271 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.4032 | 0.782214 | ||||||||
\(496\) | −2.50554 | −0.112502 | ||||||||
\(497\) | 2.22784 | 0.0999321 | ||||||||
\(498\) | 54.3996 | 2.43771 | ||||||||
\(499\) | 11.6484 | 0.521454 | 0.260727 | − | 0.965413i | \(-0.416038\pi\) | ||||
0.260727 | + | 0.965413i | \(0.416038\pi\) | |||||||
\(500\) | 8.71506 | 0.389749 | ||||||||
\(501\) | 27.4727 | 1.22739 | ||||||||
\(502\) | −22.0339 | −0.983423 | ||||||||
\(503\) | 27.5583 | 1.22876 | 0.614382 | − | 0.789009i | \(-0.289405\pi\) | ||||
0.614382 | + | 0.789009i | \(0.289405\pi\) | |||||||
\(504\) | −6.69649 | −0.298285 | ||||||||
\(505\) | −11.9124 | −0.530096 | ||||||||
\(506\) | 9.53108 | 0.423708 | ||||||||
\(507\) | −1.16552 | −0.0517624 | ||||||||
\(508\) | −19.6653 | −0.872505 | ||||||||
\(509\) | 9.56347 | 0.423893 | 0.211947 | − | 0.977281i | \(-0.432020\pi\) | ||||
0.211947 | + | 0.977281i | \(0.432020\pi\) | |||||||
\(510\) | −19.9521 | −0.883495 | ||||||||
\(511\) | −8.57661 | −0.379407 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.4193 | −0.547794 | ||||||||
\(515\) | −3.45831 | −0.152392 | ||||||||
\(516\) | −0.878313 | −0.0386656 | ||||||||
\(517\) | −18.7038 | −0.822594 | ||||||||
\(518\) | 7.59908 | 0.333884 | ||||||||
\(519\) | −9.77251 | −0.428965 | ||||||||
\(520\) | −3.41104 | −0.149584 | ||||||||
\(521\) | 8.24050 | 0.361023 | 0.180511 | − | 0.983573i | \(-0.442225\pi\) | ||||
0.180511 | + | 0.983573i | \(0.442225\pi\) | |||||||
\(522\) | 47.7321 | 2.08918 | ||||||||
\(523\) | 5.11939 | 0.223855 | 0.111928 | − | 0.993716i | \(-0.464298\pi\) | ||||
0.111928 | + | 0.993716i | \(0.464298\pi\) | |||||||
\(524\) | 7.89393 | 0.344848 | ||||||||
\(525\) | −12.7000 | −0.554272 | ||||||||
\(526\) | 6.52472 | 0.284491 | ||||||||
\(527\) | 16.7234 | 0.728481 | ||||||||
\(528\) | −8.43004 | −0.366871 | ||||||||
\(529\) | −10.6052 | −0.461096 | ||||||||
\(530\) | 9.13799 | 0.396929 | ||||||||
\(531\) | −68.3280 | −2.96518 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −25.7322 | −1.11459 | ||||||||
\(534\) | −26.0191 | −1.12596 | ||||||||
\(535\) | 9.53445 | 0.412210 | ||||||||
\(536\) | −4.15441 | −0.179443 | ||||||||
\(537\) | −73.2947 | −3.16290 | ||||||||
\(538\) | 19.0246 | 0.820207 | ||||||||
\(539\) | −2.70721 | −0.116608 | ||||||||
\(540\) | −11.0498 | −0.475508 | ||||||||
\(541\) | −1.79356 | −0.0771112 | −0.0385556 | − | 0.999256i | \(-0.512276\pi\) | ||||
−0.0385556 | + | 0.999256i | \(0.512276\pi\) | |||||||
\(542\) | 11.1907 | 0.480683 | ||||||||
\(543\) | −34.4012 | −1.47630 | ||||||||
\(544\) | 6.67457 | 0.286170 | ||||||||
\(545\) | −7.70212 | −0.329923 | ||||||||
\(546\) | 11.0646 | 0.473520 | ||||||||
\(547\) | 35.6163 | 1.52284 | 0.761421 | − | 0.648257i | \(-0.224502\pi\) | ||||
0.761421 | + | 0.648257i | \(0.224502\pi\) | |||||||
\(548\) | 7.42167 | 0.317038 | ||||||||
\(549\) | −89.6540 | −3.82634 | ||||||||
\(550\) | −11.0412 | −0.470800 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −10.9629 | −0.466613 | ||||||||
\(553\) | −15.0035 | −0.638013 | ||||||||
\(554\) | −18.7528 | −0.796732 | ||||||||
\(555\) | 22.7157 | 0.964229 | ||||||||
\(556\) | 16.4405 | 0.697234 | ||||||||
\(557\) | −6.83610 | −0.289655 | −0.144827 | − | 0.989457i | \(-0.546263\pi\) | ||||
−0.144827 | + | 0.989457i | \(0.546263\pi\) | |||||||
\(558\) | 16.7783 | 0.710281 | ||||||||
\(559\) | 1.00224 | 0.0423901 | ||||||||
\(560\) | −0.959972 | −0.0405662 | ||||||||
\(561\) | 56.2669 | 2.37559 | ||||||||
\(562\) | 6.48900 | 0.273722 | ||||||||
\(563\) | −40.7543 | −1.71759 | −0.858795 | − | 0.512320i | \(-0.828786\pi\) | ||||
−0.858795 | + | 0.512320i | \(0.828786\pi\) | |||||||
\(564\) | 21.5137 | 0.905891 | ||||||||
\(565\) | −6.79660 | −0.285935 | ||||||||
\(566\) | −23.6428 | −0.993780 | ||||||||
\(567\) | 15.7535 | 0.661584 | ||||||||
\(568\) | −2.22784 | −0.0934780 | ||||||||
\(569\) | −2.27766 | −0.0954843 | −0.0477422 | − | 0.998860i | \(-0.515203\pi\) | ||||
−0.0477422 | + | 0.998860i | \(0.515203\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.3291 | 1.43663 | 0.718315 | − | 0.695718i | \(-0.244914\pi\) | ||||
0.718315 | + | 0.695718i | \(0.244914\pi\) | |||||||
\(572\) | 9.61945 | 0.402210 | ||||||||
\(573\) | 22.8032 | 0.952618 | ||||||||
\(574\) | −7.24185 | −0.302269 | ||||||||
\(575\) | −14.3587 | −0.598799 | ||||||||
\(576\) | 6.69649 | 0.279020 | ||||||||
\(577\) | 5.62687 | 0.234249 | 0.117125 | − | 0.993117i | \(-0.462632\pi\) | ||||
0.117125 | + | 0.993117i | \(0.462632\pi\) | |||||||
\(578\) | −27.5499 | −1.14592 | ||||||||
\(579\) | −66.3066 | −2.75561 | ||||||||
\(580\) | 6.84261 | 0.284124 | ||||||||
\(581\) | −17.4698 | −0.724771 | ||||||||
\(582\) | 41.2229 | 1.70874 | ||||||||
\(583\) | −25.7700 | −1.06729 | ||||||||
\(584\) | 8.57661 | 0.354902 | ||||||||
\(585\) | 22.8420 | 0.944399 | ||||||||
\(586\) | −23.2099 | −0.958793 | ||||||||
\(587\) | 12.0832 | 0.498725 | 0.249363 | − | 0.968410i | \(-0.419779\pi\) | ||||
0.249363 | + | 0.968410i | \(0.419779\pi\) | |||||||
\(588\) | 3.11392 | 0.128416 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −9.79514 | −0.403259 | ||||||||
\(591\) | 84.0318 | 3.45661 | ||||||||
\(592\) | −7.59908 | −0.312320 | ||||||||
\(593\) | −12.7656 | −0.524219 | −0.262109 | − | 0.965038i | \(-0.584418\pi\) | ||||
−0.262109 | + | 0.965038i | \(0.584418\pi\) | |||||||
\(594\) | 31.1616 | 1.27857 | ||||||||
\(595\) | 6.40740 | 0.262678 | ||||||||
\(596\) | 5.05395 | 0.207018 | ||||||||
\(597\) | 8.86464 | 0.362805 | ||||||||
\(598\) | 12.5097 | 0.511560 | ||||||||
\(599\) | −15.9830 | −0.653047 | −0.326524 | − | 0.945189i | \(-0.605877\pi\) | ||||
−0.326524 | + | 0.945189i | \(0.605877\pi\) | |||||||
\(600\) | 12.7000 | 0.518474 | ||||||||
\(601\) | −31.3548 | −1.27899 | −0.639494 | − | 0.768796i | \(-0.720856\pi\) | ||||
−0.639494 | + | 0.768796i | \(0.720856\pi\) | |||||||
\(602\) | 0.282061 | 0.0114959 | ||||||||
\(603\) | 27.8200 | 1.13292 | ||||||||
\(604\) | 7.51527 | 0.305792 | ||||||||
\(605\) | 3.52405 | 0.143273 | ||||||||
\(606\) | −38.6410 | −1.56969 | ||||||||
\(607\) | −20.3460 | −0.825818 | −0.412909 | − | 0.910772i | \(-0.635487\pi\) | ||||
−0.412909 | + | 0.910772i | \(0.635487\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −22.1958 | −0.899419 | ||||||||
\(610\) | −12.8523 | −0.520375 | ||||||||
\(611\) | −24.5491 | −0.993152 | ||||||||
\(612\) | −44.6962 | −1.80674 | ||||||||
\(613\) | −35.8659 | −1.44861 | −0.724306 | − | 0.689479i | \(-0.757840\pi\) | ||||
−0.724306 | + | 0.689479i | \(0.757840\pi\) | |||||||
\(614\) | −25.0604 | −1.01136 | ||||||||
\(615\) | −21.6479 | −0.872927 | ||||||||
\(616\) | 2.70721 | 0.109077 | ||||||||
\(617\) | −42.3015 | −1.70300 | −0.851498 | − | 0.524358i | \(-0.824305\pi\) | ||||
−0.851498 | + | 0.524358i | \(0.824305\pi\) | |||||||
\(618\) | −11.2179 | −0.451252 | ||||||||
\(619\) | −11.2595 | −0.452557 | −0.226279 | − | 0.974063i | \(-0.572656\pi\) | ||||
−0.226279 | + | 0.974063i | \(0.572656\pi\) | |||||||
\(620\) | 2.40524 | 0.0965969 | ||||||||
\(621\) | 40.5244 | 1.62619 | ||||||||
\(622\) | 21.0148 | 0.842617 | ||||||||
\(623\) | 8.35574 | 0.334766 | ||||||||
\(624\) | −11.0646 | −0.442938 | ||||||||
\(625\) | 12.0261 | 0.481042 | ||||||||
\(626\) | −18.2477 | −0.729326 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.10544 | 0.0840162 | ||||||||
\(629\) | 50.7206 | 2.02236 | ||||||||
\(630\) | 6.42844 | 0.256115 | ||||||||
\(631\) | −10.4446 | −0.415792 | −0.207896 | − | 0.978151i | \(-0.566661\pi\) | ||||
−0.207896 | + | 0.978151i | \(0.566661\pi\) | |||||||
\(632\) | 15.0035 | 0.596807 | ||||||||
\(633\) | −45.1377 | −1.79406 | ||||||||
\(634\) | −10.7596 | −0.427319 | ||||||||
\(635\) | 18.8781 | 0.749154 | ||||||||
\(636\) | 29.6415 | 1.17536 | ||||||||
\(637\) | −3.55327 | −0.140786 | ||||||||
\(638\) | −19.2968 | −0.763969 | ||||||||
\(639\) | 14.9187 | 0.590174 | ||||||||
\(640\) | 0.959972 | 0.0379462 | ||||||||
\(641\) | 10.5196 | 0.415500 | 0.207750 | − | 0.978182i | \(-0.433386\pi\) | ||||
0.207750 | + | 0.978182i | \(0.433386\pi\) | |||||||
\(642\) | 30.9275 | 1.22061 | ||||||||
\(643\) | −32.5808 | −1.28486 | −0.642430 | − | 0.766344i | \(-0.722074\pi\) | ||||
−0.642430 | + | 0.766344i | \(0.722074\pi\) | |||||||
\(644\) | 3.52062 | 0.138732 | ||||||||
\(645\) | 0.843156 | 0.0331992 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.8195 | −0.503985 | −0.251993 | − | 0.967729i | \(-0.581086\pi\) | ||||
−0.251993 | + | 0.967729i | \(0.581086\pi\) | |||||||
\(648\) | −15.7535 | −0.618855 | ||||||||
\(649\) | 27.6232 | 1.08431 | ||||||||
\(650\) | −14.4918 | −0.568417 | ||||||||
\(651\) | −7.80203 | −0.305786 | ||||||||
\(652\) | 7.58995 | 0.297245 | ||||||||
\(653\) | −7.65425 | −0.299534 | −0.149767 | − | 0.988721i | \(-0.547852\pi\) | ||||
−0.149767 | + | 0.988721i | \(0.547852\pi\) | |||||||
\(654\) | −24.9838 | −0.976945 | ||||||||
\(655\) | −7.57795 | −0.296095 | ||||||||
\(656\) | 7.24185 | 0.282747 | ||||||||
\(657\) | −57.4331 | −2.24068 | ||||||||
\(658\) | −6.90889 | −0.269337 | ||||||||
\(659\) | −40.6414 | −1.58317 | −0.791583 | − | 0.611062i | \(-0.790743\pi\) | ||||
−0.791583 | + | 0.611062i | \(0.790743\pi\) | |||||||
\(660\) | 8.09260 | 0.315004 | ||||||||
\(661\) | 16.5058 | 0.642000 | 0.321000 | − | 0.947079i | \(-0.395981\pi\) | ||||
0.321000 | + | 0.947079i | \(0.395981\pi\) | |||||||
\(662\) | 36.1010 | 1.40311 | ||||||||
\(663\) | 73.8513 | 2.86815 | ||||||||
\(664\) | 17.4698 | 0.677961 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 50.8871 | 1.97184 | ||||||||
\(667\) | −25.0948 | −0.971673 | ||||||||
\(668\) | 8.82254 | 0.341354 | ||||||||
\(669\) | −55.0009 | −2.12646 | ||||||||
\(670\) | 3.98812 | 0.154075 | ||||||||
\(671\) | 36.2448 | 1.39921 | ||||||||
\(672\) | −3.11392 | −0.120122 | ||||||||
\(673\) | −23.2797 | −0.897366 | −0.448683 | − | 0.893691i | \(-0.648107\pi\) | ||||
−0.448683 | + | 0.893691i | \(0.648107\pi\) | |||||||
\(674\) | 18.8352 | 0.725504 | ||||||||
\(675\) | −46.9453 | −1.80693 | ||||||||
\(676\) | −0.374292 | −0.0143959 | ||||||||
\(677\) | 26.6199 | 1.02309 | 0.511544 | − | 0.859257i | \(-0.329074\pi\) | ||||
0.511544 | + | 0.859257i | \(0.329074\pi\) | |||||||
\(678\) | −22.0465 | −0.846692 | ||||||||
\(679\) | −13.2383 | −0.508038 | ||||||||
\(680\) | −6.40740 | −0.245713 | ||||||||
\(681\) | −1.83221 | −0.0702104 | ||||||||
\(682\) | −6.78302 | −0.259735 | ||||||||
\(683\) | −7.15388 | −0.273736 | −0.136868 | − | 0.990589i | \(-0.543704\pi\) | ||||
−0.136868 | + | 0.990589i | \(0.543704\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.12460 | −0.272217 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 28.3425 | 1.08133 | ||||||||
\(688\) | −0.282061 | −0.0107535 | ||||||||
\(689\) | −33.8236 | −1.28858 | ||||||||
\(690\) | 10.5241 | 0.400646 | ||||||||
\(691\) | 11.3824 | 0.433005 | 0.216503 | − | 0.976282i | \(-0.430535\pi\) | ||||
0.216503 | + | 0.976282i | \(0.430535\pi\) | |||||||
\(692\) | −3.13833 | −0.119301 | ||||||||
\(693\) | −18.1288 | −0.688657 | ||||||||
\(694\) | 12.6195 | 0.479030 | ||||||||
\(695\) | −15.7824 | −0.598662 | ||||||||
\(696\) | 22.1958 | 0.841330 | ||||||||
\(697\) | −48.3362 | −1.83087 | ||||||||
\(698\) | −0.227609 | −0.00861512 | ||||||||
\(699\) | −77.8820 | −2.94577 | ||||||||
\(700\) | −4.07845 | −0.154151 | ||||||||
\(701\) | 20.2961 | 0.766573 | 0.383286 | − | 0.923630i | \(-0.374792\pi\) | ||||
0.383286 | + | 0.923630i | \(0.374792\pi\) | |||||||
\(702\) | 40.9001 | 1.54367 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −2.70721 | −0.102032 | ||||||||
\(705\) | −20.6526 | −0.777821 | ||||||||
\(706\) | 11.9425 | 0.449463 | ||||||||
\(707\) | 12.4091 | 0.466694 | ||||||||
\(708\) | −31.7731 | −1.19411 | ||||||||
\(709\) | 26.3844 | 0.990887 | 0.495444 | − | 0.868640i | \(-0.335006\pi\) | ||||
0.495444 | + | 0.868640i | \(0.335006\pi\) | |||||||
\(710\) | 2.13866 | 0.0802625 | ||||||||
\(711\) | −100.471 | −3.76794 | ||||||||
\(712\) | −8.35574 | −0.313145 | ||||||||
\(713\) | −8.82105 | −0.330351 | ||||||||
\(714\) | 20.7841 | 0.777824 | ||||||||
\(715\) | −9.23441 | −0.345347 | ||||||||
\(716\) | −23.5378 | −0.879648 | ||||||||
\(717\) | 35.9038 | 1.34085 | ||||||||
\(718\) | 22.9370 | 0.856002 | ||||||||
\(719\) | 33.7903 | 1.26016 | 0.630082 | − | 0.776529i | \(-0.283021\pi\) | ||||
0.630082 | + | 0.776529i | \(0.283021\pi\) | |||||||
\(720\) | −6.42844 | −0.239574 | ||||||||
\(721\) | 3.60252 | 0.134165 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.8861 | −0.442048 | ||||||||
\(724\) | −11.0476 | −0.410579 | ||||||||
\(725\) | 29.0709 | 1.07967 | ||||||||
\(726\) | 11.4312 | 0.424251 | ||||||||
\(727\) | −12.9012 | −0.478479 | −0.239239 | − | 0.970961i | \(-0.576898\pi\) | ||||
−0.239239 | + | 0.970961i | \(0.576898\pi\) | |||||||
\(728\) | 3.55327 | 0.131693 | ||||||||
\(729\) | −2.03582 | −0.0754007 | ||||||||
\(730\) | −8.23330 | −0.304728 | ||||||||
\(731\) | 1.88263 | 0.0696317 | ||||||||
\(732\) | −41.6898 | −1.54090 | ||||||||
\(733\) | 19.4232 | 0.717413 | 0.358706 | − | 0.933450i | \(-0.383218\pi\) | ||||
0.358706 | + | 0.933450i | \(0.383218\pi\) | |||||||
\(734\) | −14.2300 | −0.525240 | ||||||||
\(735\) | −2.98927 | −0.110261 | ||||||||
\(736\) | −3.52062 | −0.129772 | ||||||||
\(737\) | −11.2469 | −0.414284 | ||||||||
\(738\) | −48.4950 | −1.78512 | ||||||||
\(739\) | 1.37651 | 0.0506359 | 0.0253179 | − | 0.999679i | \(-0.491940\pi\) | ||||
0.0253179 | + | 0.999679i | \(0.491940\pi\) | |||||||
\(740\) | 7.29490 | 0.268166 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.51902 | −0.349454 | ||||||||
\(743\) | −4.83509 | −0.177382 | −0.0886912 | − | 0.996059i | \(-0.528268\pi\) | ||||
−0.0886912 | + | 0.996059i | \(0.528268\pi\) | |||||||
\(744\) | 7.80203 | 0.286036 | ||||||||
\(745\) | −4.85165 | −0.177751 | ||||||||
\(746\) | −5.07840 | −0.185933 | ||||||||
\(747\) | −116.986 | −4.28031 | ||||||||
\(748\) | 18.0695 | 0.660686 | ||||||||
\(749\) | −9.93200 | −0.362908 | ||||||||
\(750\) | −27.1380 | −0.990939 | ||||||||
\(751\) | −9.88523 | −0.360717 | −0.180359 | − | 0.983601i | \(-0.557726\pi\) | ||||
−0.180359 | + | 0.983601i | \(0.557726\pi\) | |||||||
\(752\) | 6.90889 | 0.251941 | ||||||||
\(753\) | 68.6119 | 2.50036 | ||||||||
\(754\) | −25.3274 | −0.922371 | ||||||||
\(755\) | −7.21445 | −0.262561 | ||||||||
\(756\) | 11.5106 | 0.418635 | ||||||||
\(757\) | 20.3586 | 0.739947 | 0.369973 | − | 0.929042i | \(-0.379367\pi\) | ||||
0.369973 | + | 0.929042i | \(0.379367\pi\) | |||||||
\(758\) | −4.95870 | −0.180108 | ||||||||
\(759\) | −29.6790 | −1.07728 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.1626 | 0.440893 | 0.220446 | − | 0.975399i | \(-0.429249\pi\) | ||||
0.220446 | + | 0.975399i | \(0.429249\pi\) | |||||||
\(762\) | 61.2360 | 2.21835 | ||||||||
\(763\) | 8.02328 | 0.290462 | ||||||||
\(764\) | 7.32300 | 0.264937 | ||||||||
\(765\) | 42.9071 | 1.55131 | ||||||||
\(766\) | −3.11820 | −0.112665 | ||||||||
\(767\) | 36.2560 | 1.30913 | ||||||||
\(768\) | 3.11392 | 0.112364 | ||||||||
\(769\) | 43.6397 | 1.57369 | 0.786844 | − | 0.617151i | \(-0.211713\pi\) | ||||
0.786844 | + | 0.617151i | \(0.211713\pi\) | |||||||
\(770\) | −2.59885 | −0.0936560 | ||||||||
\(771\) | 38.6728 | 1.39277 | ||||||||
\(772\) | −21.2936 | −0.766374 | ||||||||
\(773\) | −24.2346 | −0.871660 | −0.435830 | − | 0.900029i | \(-0.643545\pi\) | ||||
−0.435830 | + | 0.900029i | \(0.643545\pi\) | |||||||
\(774\) | 1.88881 | 0.0678921 | ||||||||
\(775\) | 10.2187 | 0.367067 | ||||||||
\(776\) | 13.2383 | 0.475226 | ||||||||
\(777\) | −23.6629 | −0.848902 | ||||||||
\(778\) | −12.7019 | −0.455384 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 10.6217 | 0.380318 | ||||||||
\(781\) | −6.03123 | −0.215814 | ||||||||
\(782\) | 23.4986 | 0.840310 | ||||||||
\(783\) | −82.0465 | −2.93210 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −2.02116 | −0.0721384 | ||||||||
\(786\) | −24.5810 | −0.876777 | ||||||||
\(787\) | 40.6719 | 1.44980 | 0.724898 | − | 0.688856i | \(-0.241887\pi\) | ||||
0.724898 | + | 0.688856i | \(0.241887\pi\) | |||||||
\(788\) | 26.9859 | 0.961331 | ||||||||
\(789\) | −20.3175 | −0.723321 | ||||||||
\(790\) | −14.4029 | −0.512433 | ||||||||
\(791\) | 7.08000 | 0.251736 | ||||||||
\(792\) | 18.1288 | 0.644180 | ||||||||
\(793\) | 47.5719 | 1.68933 | ||||||||
\(794\) | −33.5926 | −1.19216 | ||||||||
\(795\) | −28.4550 | −1.00919 | ||||||||
\(796\) | 2.84678 | 0.100901 | ||||||||
\(797\) | −27.8150 | −0.985258 | −0.492629 | − | 0.870239i | \(-0.663964\pi\) | ||||
−0.492629 | + | 0.870239i | \(0.663964\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −46.1139 | −1.63139 | ||||||||
\(800\) | 4.07845 | 0.144195 | ||||||||
\(801\) | 55.9541 | 1.97704 | ||||||||
\(802\) | −26.6682 | −0.941686 | ||||||||
\(803\) | 23.2187 | 0.819370 | ||||||||
\(804\) | 12.9365 | 0.456235 | ||||||||
\(805\) | −3.37970 | −0.119119 | ||||||||
\(806\) | −8.90284 | −0.313589 | ||||||||
\(807\) | −59.2409 | −2.08538 | ||||||||
\(808\) | −12.4091 | −0.436552 | ||||||||
\(809\) | 41.6235 | 1.46340 | 0.731702 | − | 0.681625i | \(-0.238726\pi\) | ||||
0.731702 | + | 0.681625i | \(0.238726\pi\) | |||||||
\(810\) | 15.1229 | 0.531365 | ||||||||
\(811\) | −26.2635 | −0.922236 | −0.461118 | − | 0.887339i | \(-0.652551\pi\) | ||||
−0.461118 | + | 0.887339i | \(0.652551\pi\) | |||||||
\(812\) | −7.12793 | −0.250141 | ||||||||
\(813\) | −34.8471 | −1.22214 | ||||||||
\(814\) | −20.5723 | −0.721060 | ||||||||
\(815\) | −7.28614 | −0.255222 | ||||||||
\(816\) | −20.7841 | −0.727588 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −4.35206 | −0.152166 | ||||||||
\(819\) | −23.7944 | −0.831444 | ||||||||
\(820\) | −6.95197 | −0.242773 | ||||||||
\(821\) | 42.7713 | 1.49273 | 0.746365 | − | 0.665537i | \(-0.231798\pi\) | ||||
0.746365 | + | 0.665537i | \(0.231798\pi\) | |||||||
\(822\) | −23.1105 | −0.806070 | ||||||||
\(823\) | −45.8586 | −1.59853 | −0.799265 | − | 0.600978i | \(-0.794778\pi\) | ||||
−0.799265 | + | 0.600978i | \(0.794778\pi\) | |||||||
\(824\) | −3.60252 | −0.125500 | ||||||||
\(825\) | 34.3815 | 1.19701 | ||||||||
\(826\) | 10.2036 | 0.355027 | ||||||||
\(827\) | −32.5669 | −1.13246 | −0.566232 | − | 0.824246i | \(-0.691599\pi\) | ||||
−0.566232 | + | 0.824246i | \(0.691599\pi\) | |||||||
\(828\) | 23.5758 | 0.819316 | ||||||||
\(829\) | −27.5270 | −0.956052 | −0.478026 | − | 0.878346i | \(-0.658647\pi\) | ||||
−0.478026 | + | 0.878346i | \(0.658647\pi\) | |||||||
\(830\) | −16.7705 | −0.582114 | ||||||||
\(831\) | 58.3948 | 2.02569 | ||||||||
\(832\) | −3.55327 | −0.123187 | ||||||||
\(833\) | −6.67457 | −0.231260 | ||||||||
\(834\) | −51.1945 | −1.77272 | ||||||||
\(835\) | −8.46939 | −0.293095 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −28.8401 | −0.996860 | ||||||||
\(838\) | −9.26629 | −0.320099 | ||||||||
\(839\) | −12.2800 | −0.423951 | −0.211976 | − | 0.977275i | \(-0.567990\pi\) | ||||
−0.211976 | + | 0.977275i | \(0.567990\pi\) | |||||||
\(840\) | 2.98927 | 0.103140 | ||||||||
\(841\) | 21.8074 | 0.751979 | ||||||||
\(842\) | −17.3214 | −0.596935 | ||||||||
\(843\) | −20.2062 | −0.695939 | ||||||||
\(844\) | −14.4955 | −0.498955 | ||||||||
\(845\) | 0.359310 | 0.0123606 | ||||||||
\(846\) | −46.2653 | −1.59063 | ||||||||
\(847\) | −3.67099 | −0.126137 | ||||||||
\(848\) | 9.51902 | 0.326885 | ||||||||
\(849\) | 73.6217 | 2.52669 | ||||||||
\(850\) | −27.2219 | −0.933704 | ||||||||
\(851\) | −26.7535 | −0.917098 | ||||||||
\(852\) | 6.93730 | 0.237668 | ||||||||
\(853\) | 4.00634 | 0.137174 | 0.0685872 | − | 0.997645i | \(-0.478151\pi\) | ||||
0.0685872 | + | 0.997645i | \(0.478151\pi\) | |||||||
\(854\) | 13.3882 | 0.458135 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.93200 | 0.339469 | ||||||||
\(857\) | −33.0216 | −1.12800 | −0.563998 | − | 0.825776i | \(-0.690738\pi\) | ||||
−0.563998 | + | 0.825776i | \(0.690738\pi\) | |||||||
\(858\) | −29.9542 | −1.02262 | ||||||||
\(859\) | 36.4962 | 1.24523 | 0.622616 | − | 0.782527i | \(-0.286070\pi\) | ||||
0.622616 | + | 0.782527i | \(0.286070\pi\) | |||||||
\(860\) | 0.270770 | 0.00923319 | ||||||||
\(861\) | 22.5505 | 0.768520 | ||||||||
\(862\) | −21.3963 | −0.728760 | ||||||||
\(863\) | 1.98259 | 0.0674882 | 0.0337441 | − | 0.999431i | \(-0.489257\pi\) | ||||
0.0337441 | + | 0.999431i | \(0.489257\pi\) | |||||||
\(864\) | −11.5106 | −0.391597 | ||||||||
\(865\) | 3.01271 | 0.102435 | ||||||||
\(866\) | 19.2137 | 0.652909 | ||||||||
\(867\) | 85.7881 | 2.91352 | ||||||||
\(868\) | −2.50554 | −0.0850434 | ||||||||
\(869\) | 40.6176 | 1.37786 | ||||||||
\(870\) | −21.3073 | −0.722387 | ||||||||
\(871\) | −14.7617 | −0.500182 | ||||||||
\(872\) | −8.02328 | −0.271702 | ||||||||
\(873\) | −88.6500 | −3.00035 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.71506 | 0.294623 | ||||||||
\(876\) | −26.7068 | −0.902341 | ||||||||
\(877\) | 51.5828 | 1.74183 | 0.870913 | − | 0.491437i | \(-0.163528\pi\) | ||||
0.870913 | + | 0.491437i | \(0.163528\pi\) | |||||||
\(878\) | 22.5139 | 0.759807 | ||||||||
\(879\) | 72.2738 | 2.43773 | ||||||||
\(880\) | 2.59885 | 0.0876072 | ||||||||
\(881\) | −22.2677 | −0.750217 | −0.375109 | − | 0.926981i | \(-0.622395\pi\) | ||||
−0.375109 | + | 0.926981i | \(0.622395\pi\) | |||||||
\(882\) | −6.69649 | −0.225482 | ||||||||
\(883\) | −35.4865 | −1.19421 | −0.597107 | − | 0.802161i | \(-0.703683\pi\) | ||||
−0.597107 | + | 0.802161i | \(0.703683\pi\) | |||||||
\(884\) | 23.7165 | 0.797673 | ||||||||
\(885\) | 30.5013 | 1.02529 | ||||||||
\(886\) | −0.978663 | −0.0328788 | ||||||||
\(887\) | −0.426198 | −0.0143103 | −0.00715516 | − | 0.999974i | \(-0.502278\pi\) | ||||
−0.00715516 | + | 0.999974i | \(0.502278\pi\) | |||||||
\(888\) | 23.6629 | 0.794075 | ||||||||
\(889\) | −19.6653 | −0.659552 | ||||||||
\(890\) | 8.02127 | 0.268874 | ||||||||
\(891\) | −42.6481 | −1.42876 | ||||||||
\(892\) | −17.6629 | −0.591399 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −15.7376 | −0.526344 | ||||||||
\(895\) | 22.5956 | 0.755287 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −38.9542 | −1.30064 | ||||||||
\(898\) | 32.9060 | 1.09809 | ||||||||
\(899\) | 17.8593 | 0.595640 | ||||||||
\(900\) | −27.3113 | −0.910377 | ||||||||
\(901\) | −63.5354 | −2.11667 | ||||||||
\(902\) | 19.6052 | 0.652783 | ||||||||
\(903\) | −0.878313 | −0.0292284 | ||||||||
\(904\) | −7.08000 | −0.235477 | ||||||||
\(905\) | 10.6053 | 0.352533 | ||||||||
\(906\) | −23.4019 | −0.777477 | ||||||||
\(907\) | −2.37171 | −0.0787515 | −0.0393757 | − | 0.999224i | \(-0.512537\pi\) | ||||
−0.0393757 | + | 0.999224i | \(0.512537\pi\) | |||||||
\(908\) | −0.588393 | −0.0195265 | ||||||||
\(909\) | 83.0976 | 2.75618 | ||||||||
\(910\) | −3.41104 | −0.113075 | ||||||||
\(911\) | −8.99634 | −0.298062 | −0.149031 | − | 0.988833i | \(-0.547615\pi\) | ||||
−0.149031 | + | 0.988833i | \(0.547615\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 47.2946 | 1.56522 | ||||||||
\(914\) | −18.9971 | −0.628369 | ||||||||
\(915\) | 40.0210 | 1.32305 | ||||||||
\(916\) | 9.10188 | 0.300735 | ||||||||
\(917\) | 7.89393 | 0.260680 | ||||||||
\(918\) | 76.8280 | 2.53570 | ||||||||
\(919\) | −38.6656 | −1.27546 | −0.637730 | − | 0.770260i | \(-0.720127\pi\) | ||||
−0.637730 | + | 0.770260i | \(0.720127\pi\) | |||||||
\(920\) | 3.37970 | 0.111425 | ||||||||
\(921\) | 78.0361 | 2.57138 | ||||||||
\(922\) | 37.7120 | 1.24198 | ||||||||
\(923\) | −7.91610 | −0.260562 | ||||||||
\(924\) | −8.43004 | −0.277328 | ||||||||
\(925\) | 30.9925 | 1.01903 | ||||||||
\(926\) | 25.5830 | 0.840708 | ||||||||
\(927\) | 24.1242 | 0.792343 | ||||||||
\(928\) | 7.12793 | 0.233986 | ||||||||
\(929\) | −34.6761 | −1.13768 | −0.568842 | − | 0.822447i | \(-0.692609\pi\) | ||||
−0.568842 | + | 0.822447i | \(0.692609\pi\) | |||||||
\(930\) | −7.48973 | −0.245598 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −25.0109 | −0.819261 | ||||||||
\(933\) | −65.4384 | −2.14236 | ||||||||
\(934\) | 4.52094 | 0.147930 | ||||||||
\(935\) | −17.3462 | −0.567281 | ||||||||
\(936\) | 23.7944 | 0.777745 | ||||||||
\(937\) | −43.0749 | −1.40720 | −0.703598 | − | 0.710598i | \(-0.748424\pi\) | ||||
−0.703598 | + | 0.710598i | \(0.748424\pi\) | |||||||
\(938\) | −4.15441 | −0.135646 | ||||||||
\(939\) | 56.8220 | 1.85431 | ||||||||
\(940\) | −6.63234 | −0.216323 | ||||||||
\(941\) | 14.5064 | 0.472895 | 0.236448 | − | 0.971644i | \(-0.424017\pi\) | ||||
0.236448 | + | 0.971644i | \(0.424017\pi\) | |||||||
\(942\) | −6.55617 | −0.213612 | ||||||||
\(943\) | 25.4958 | 0.830258 | ||||||||
\(944\) | −10.2036 | −0.332098 | ||||||||
\(945\) | −11.0498 | −0.359451 | ||||||||
\(946\) | −0.763598 | −0.0248267 | ||||||||
\(947\) | 1.49014 | 0.0484230 | 0.0242115 | − | 0.999707i | \(-0.492292\pi\) | ||||
0.0242115 | + | 0.999707i | \(0.492292\pi\) | |||||||
\(948\) | −46.7196 | −1.51738 | ||||||||
\(949\) | 30.4750 | 0.989259 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.5046 | 1.08646 | ||||||||
\(952\) | 6.67457 | 0.216324 | ||||||||
\(953\) | 14.8975 | 0.482579 | 0.241289 | − | 0.970453i | \(-0.422430\pi\) | ||||
0.241289 | + | 0.970453i | \(0.422430\pi\) | |||||||
\(954\) | −63.7440 | −2.06379 | ||||||||
\(955\) | −7.02987 | −0.227481 | ||||||||
\(956\) | 11.5301 | 0.372910 | ||||||||
\(957\) | 60.0888 | 1.94239 | ||||||||
\(958\) | 7.34593 | 0.237336 | ||||||||
\(959\) | 7.42167 | 0.239658 | ||||||||
\(960\) | −2.98927 | −0.0964784 | ||||||||
\(961\) | −24.7223 | −0.797493 | ||||||||
\(962\) | −27.0016 | −0.870565 | ||||||||
\(963\) | −66.5095 | −2.14324 | ||||||||
\(964\) | −3.81708 | −0.122940 | ||||||||
\(965\) | 20.4413 | 0.658028 | ||||||||
\(966\) | −10.9629 | −0.352727 | ||||||||
\(967\) | 39.8232 | 1.28063 | 0.640313 | − | 0.768114i | \(-0.278805\pi\) | ||||
0.640313 | + | 0.768114i | \(0.278805\pi\) | |||||||
\(968\) | 3.67099 | 0.117990 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.7084 | −0.408041 | ||||||||
\(971\) | 29.2717 | 0.939373 | 0.469687 | − | 0.882833i | \(-0.344367\pi\) | ||||
0.469687 | + | 0.882833i | \(0.344367\pi\) | |||||||
\(972\) | 14.5234 | 0.465838 | ||||||||
\(973\) | 16.4405 | 0.527059 | ||||||||
\(974\) | −6.74975 | −0.216276 | ||||||||
\(975\) | 45.1264 | 1.44520 | ||||||||
\(976\) | −13.3882 | −0.428546 | ||||||||
\(977\) | 6.77567 | 0.216773 | 0.108386 | − | 0.994109i | \(-0.465432\pi\) | ||||
0.108386 | + | 0.994109i | \(0.465432\pi\) | |||||||
\(978\) | −23.6345 | −0.755747 | ||||||||
\(979\) | −22.6208 | −0.722963 | ||||||||
\(980\) | −0.959972 | −0.0306652 | ||||||||
\(981\) | 53.7278 | 1.71540 | ||||||||
\(982\) | 14.7330 | 0.470148 | ||||||||
\(983\) | 47.7387 | 1.52263 | 0.761313 | − | 0.648384i | \(-0.224555\pi\) | ||||
0.761313 | + | 0.648384i | \(0.224555\pi\) | |||||||
\(984\) | −22.5505 | −0.718885 | ||||||||
\(985\) | −25.9057 | −0.825423 | ||||||||
\(986\) | −47.5759 | −1.51512 | ||||||||
\(987\) | 21.5137 | 0.684789 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.993029 | −0.0315765 | ||||||||
\(990\) | −17.4032 | −0.553109 | ||||||||
\(991\) | −6.87025 | −0.218241 | −0.109120 | − | 0.994029i | \(-0.534803\pi\) | ||||
−0.109120 | + | 0.994029i | \(0.534803\pi\) | |||||||
\(992\) | 2.50554 | 0.0795508 | ||||||||
\(993\) | −112.416 | −3.56740 | ||||||||
\(994\) | −2.22784 | −0.0706627 | ||||||||
\(995\) | −2.73283 | −0.0866364 | ||||||||
\(996\) | −54.3996 | −1.72372 | ||||||||
\(997\) | 19.0339 | 0.602808 | 0.301404 | − | 0.953497i | \(-0.402545\pi\) | ||||
0.301404 | + | 0.953497i | \(0.402545\pi\) | |||||||
\(998\) | −11.6484 | −0.368724 | ||||||||
\(999\) | −87.4696 | −2.76742 |
(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 | 5054.2.a.z.1.6 | ✓ | 6 | |
19.18 | odd | 2 | 5054.2.a.be.1.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5054.2.a.z.1.6 | ✓ | 6 | 1.1 | even | 1 | trivial | |
5054.2.a.be.1.1 | yes | 6 | 19.18 | odd | 2 |