Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [275,2,Mod(1,275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(275, 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("275.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 275 = 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 275.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: | \(2.19588605559\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.792287\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 275.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.792287 | −0.560232 | −0.280116 | − | 0.959966i | \(-0.590373\pi\) | ||||
−0.280116 | + | 0.959966i | \(0.590373\pi\) | |||||||
\(3\) | −2.52434 | −1.45743 | −0.728714 | − | 0.684819i | \(-0.759881\pi\) | ||||
−0.728714 | + | 0.684819i | \(0.759881\pi\) | |||||||
\(4\) | −1.37228 | −0.686141 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.00000 | 0.816497 | ||||||||
\(7\) | −3.46410 | −1.30931 | −0.654654 | − | 0.755929i | \(-0.727186\pi\) | ||||
−0.654654 | + | 0.755929i | \(0.727186\pi\) | |||||||
\(8\) | 2.67181 | 0.944629 | ||||||||
\(9\) | 3.37228 | 1.12409 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 3.46410 | 1.00000 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 2.74456 | 0.733515 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.627719 | 0.156930 | ||||||||
\(17\) | 5.04868 | 1.22448 | 0.612242 | − | 0.790671i | \(-0.290268\pi\) | ||||
0.612242 | + | 0.790671i | \(0.290268\pi\) | |||||||
\(18\) | −2.67181 | −0.629753 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.74456 | 1.90822 | ||||||||
\(22\) | 0.792287 | 0.168916 | ||||||||
\(23\) | 2.52434 | 0.526361 | 0.263180 | − | 0.964747i | \(-0.415229\pi\) | ||||
0.263180 | + | 0.964747i | \(0.415229\pi\) | |||||||
\(24\) | −6.74456 | −1.37673 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.939764 | −0.180858 | ||||||||
\(28\) | 4.75372 | 0.898369 | ||||||||
\(29\) | −2.74456 | −0.509652 | −0.254826 | − | 0.966987i | \(-0.582018\pi\) | ||||
−0.254826 | + | 0.966987i | \(0.582018\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.37228 | −0.426074 | −0.213037 | − | 0.977044i | \(-0.568336\pi\) | ||||
−0.213037 | + | 0.977044i | \(0.568336\pi\) | |||||||
\(32\) | −5.84096 | −1.03255 | ||||||||
\(33\) | 2.52434 | 0.439431 | ||||||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.62772 | −0.771286 | ||||||||
\(37\) | 11.0371 | 1.81449 | 0.907245 | − | 0.420602i | \(-0.138181\pi\) | ||||
0.907245 | + | 0.420602i | \(0.138181\pi\) | |||||||
\(38\) | −3.16915 | −0.514104 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.74456 | −0.428629 | −0.214314 | − | 0.976765i | \(-0.568752\pi\) | ||||
−0.214314 | + | 0.976765i | \(0.568752\pi\) | |||||||
\(42\) | −6.92820 | −1.06904 | ||||||||
\(43\) | −3.46410 | −0.528271 | −0.264135 | − | 0.964486i | \(-0.585087\pi\) | ||||
−0.264135 | + | 0.964486i | \(0.585087\pi\) | |||||||
\(44\) | 1.37228 | 0.206879 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.00000 | −0.294884 | ||||||||
\(47\) | −6.63325 | −0.967559 | −0.483779 | − | 0.875190i | \(-0.660736\pi\) | ||||
−0.483779 | + | 0.875190i | \(0.660736\pi\) | |||||||
\(48\) | −1.58457 | −0.228714 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.7446 | −1.78460 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.16915 | 0.435316 | 0.217658 | − | 0.976025i | \(-0.430158\pi\) | ||||
0.217658 | + | 0.976025i | \(0.430158\pi\) | |||||||
\(54\) | 0.744563 | 0.101322 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −9.25544 | −1.23681 | ||||||||
\(57\) | −10.0974 | −1.33743 | ||||||||
\(58\) | 2.17448 | 0.285523 | ||||||||
\(59\) | −1.62772 | −0.211911 | −0.105955 | − | 0.994371i | \(-0.533790\pi\) | ||||
−0.105955 | + | 0.994371i | \(0.533790\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.7446 | 1.37570 | 0.687850 | − | 0.725853i | \(-0.258555\pi\) | ||||
0.687850 | + | 0.725853i | \(0.258555\pi\) | |||||||
\(62\) | 1.87953 | 0.238700 | ||||||||
\(63\) | −11.6819 | −1.47178 | ||||||||
\(64\) | 3.37228 | 0.421535 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.00000 | −0.246183 | ||||||||
\(67\) | 0.644810 | 0.0787761 | 0.0393880 | − | 0.999224i | \(-0.487459\pi\) | ||||
0.0393880 | + | 0.999224i | \(0.487459\pi\) | |||||||
\(68\) | −6.92820 | −0.840168 | ||||||||
\(69\) | −6.37228 | −0.767133 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.11684 | 0.844614 | 0.422307 | − | 0.906453i | \(-0.361220\pi\) | ||||
0.422307 | + | 0.906453i | \(0.361220\pi\) | |||||||
\(72\) | 9.01011 | 1.06185 | ||||||||
\(73\) | 6.92820 | 0.810885 | 0.405442 | − | 0.914121i | \(-0.367117\pi\) | ||||
0.405442 | + | 0.914121i | \(0.367117\pi\) | |||||||
\(74\) | −8.74456 | −1.01653 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.48913 | −0.629646 | ||||||||
\(77\) | 3.46410 | 0.394771 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.7446 | 1.43388 | 0.716938 | − | 0.697137i | \(-0.245543\pi\) | ||||
0.716938 | + | 0.697137i | \(0.245543\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.74456 | −0.860507 | ||||||||
\(82\) | 2.17448 | 0.240131 | ||||||||
\(83\) | 6.63325 | 0.728094 | 0.364047 | − | 0.931381i | \(-0.381395\pi\) | ||||
0.364047 | + | 0.931381i | \(0.381395\pi\) | |||||||
\(84\) | −12.0000 | −1.30931 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.74456 | 0.295954 | ||||||||
\(87\) | 6.92820 | 0.742781 | ||||||||
\(88\) | −2.67181 | −0.284816 | ||||||||
\(89\) | −4.37228 | −0.463461 | −0.231730 | − | 0.972780i | \(-0.574439\pi\) | ||||
−0.231730 | + | 0.972780i | \(0.574439\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.46410 | −0.361158 | ||||||||
\(93\) | 5.98844 | 0.620972 | ||||||||
\(94\) | 5.25544 | 0.542057 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 14.7446 | 1.50486 | ||||||||
\(97\) | 4.10891 | 0.417197 | 0.208598 | − | 0.978001i | \(-0.433110\pi\) | ||||
0.208598 | + | 0.978001i | \(0.433110\pi\) | |||||||
\(98\) | −3.96143 | −0.400165 | ||||||||
\(99\) | −3.37228 | −0.338927 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 10.0974 | 0.999787 | ||||||||
\(103\) | 10.3923 | 1.02398 | 0.511992 | − | 0.858990i | \(-0.328908\pi\) | ||||
0.511992 | + | 0.858990i | \(0.328908\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.51087 | −0.243878 | ||||||||
\(107\) | −6.63325 | −0.641260 | −0.320630 | − | 0.947204i | \(-0.603895\pi\) | ||||
−0.320630 | + | 0.947204i | \(0.603895\pi\) | |||||||
\(108\) | 1.28962 | 0.124094 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −27.8614 | −2.64449 | ||||||||
\(112\) | −2.17448 | −0.205469 | ||||||||
\(113\) | −16.0858 | −1.51322 | −0.756612 | − | 0.653864i | \(-0.773147\pi\) | ||||
−0.756612 | + | 0.653864i | \(0.773147\pi\) | |||||||
\(114\) | 8.00000 | 0.749269 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.76631 | 0.349693 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.28962 | 0.118719 | ||||||||
\(119\) | −17.4891 | −1.60323 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −8.51278 | −0.770711 | ||||||||
\(123\) | 6.92820 | 0.624695 | ||||||||
\(124\) | 3.25544 | 0.292347 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 9.25544 | 0.824540 | ||||||||
\(127\) | −11.6819 | −1.03660 | −0.518302 | − | 0.855198i | \(-0.673436\pi\) | ||||
−0.518302 | + | 0.855198i | \(0.673436\pi\) | |||||||
\(128\) | 9.01011 | 0.796389 | ||||||||
\(129\) | 8.74456 | 0.769916 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.74456 | 0.764016 | 0.382008 | − | 0.924159i | \(-0.375233\pi\) | ||||
0.382008 | + | 0.924159i | \(0.375233\pi\) | |||||||
\(132\) | −3.46410 | −0.301511 | ||||||||
\(133\) | −13.8564 | −1.20150 | ||||||||
\(134\) | −0.510875 | −0.0441329 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.4891 | 1.15668 | ||||||||
\(137\) | 2.22938 | 0.190469 | 0.0952346 | − | 0.995455i | \(-0.469640\pi\) | ||||
0.0952346 | + | 0.995455i | \(0.469640\pi\) | |||||||
\(138\) | 5.04868 | 0.429772 | ||||||||
\(139\) | 18.2337 | 1.54656 | 0.773281 | − | 0.634064i | \(-0.218614\pi\) | ||||
0.773281 | + | 0.634064i | \(0.218614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.7446 | 1.41015 | ||||||||
\(142\) | −5.63858 | −0.473179 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.11684 | 0.176404 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.48913 | −0.454283 | ||||||||
\(147\) | −12.6217 | −1.04102 | ||||||||
\(148\) | −15.1460 | −1.24500 | ||||||||
\(149\) | 11.4891 | 0.941226 | 0.470613 | − | 0.882340i | \(-0.344033\pi\) | ||||
0.470613 | + | 0.882340i | \(0.344033\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.2337 | 1.80935 | 0.904676 | − | 0.426100i | \(-0.140113\pi\) | ||||
0.904676 | + | 0.426100i | \(0.140113\pi\) | |||||||
\(152\) | 10.6873 | 0.866851 | ||||||||
\(153\) | 17.0256 | 1.37643 | ||||||||
\(154\) | −2.74456 | −0.221163 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.39853 | −0.430850 | −0.215425 | − | 0.976520i | \(-0.569114\pi\) | ||||
−0.215425 | + | 0.976520i | \(0.569114\pi\) | |||||||
\(158\) | −10.0974 | −0.803302 | ||||||||
\(159\) | −8.00000 | −0.634441 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.74456 | −0.689168 | ||||||||
\(162\) | 6.13592 | 0.482083 | ||||||||
\(163\) | 3.46410 | 0.271329 | 0.135665 | − | 0.990755i | \(-0.456683\pi\) | ||||
0.135665 | + | 0.990755i | \(0.456683\pi\) | |||||||
\(164\) | 3.76631 | 0.294100 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.25544 | −0.407901 | ||||||||
\(167\) | 22.3692 | 1.73098 | 0.865490 | − | 0.500927i | \(-0.167007\pi\) | ||||
0.865490 | + | 0.500927i | \(0.167007\pi\) | |||||||
\(168\) | 23.3639 | 1.80256 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.4891 | 1.03154 | ||||||||
\(172\) | 4.75372 | 0.362468 | ||||||||
\(173\) | 1.87953 | 0.142898 | 0.0714489 | − | 0.997444i | \(-0.477238\pi\) | ||||
0.0714489 | + | 0.997444i | \(0.477238\pi\) | |||||||
\(174\) | −5.48913 | −0.416130 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.627719 | −0.0473161 | ||||||||
\(177\) | 4.10891 | 0.308845 | ||||||||
\(178\) | 3.46410 | 0.259645 | ||||||||
\(179\) | −15.8614 | −1.18554 | −0.592769 | − | 0.805373i | \(-0.701965\pi\) | ||||
−0.592769 | + | 0.805373i | \(0.701965\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.88316 | 0.511621 | 0.255810 | − | 0.966727i | \(-0.417658\pi\) | ||||
0.255810 | + | 0.966727i | \(0.417658\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −27.1229 | −2.00498 | ||||||||
\(184\) | 6.74456 | 0.497216 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.74456 | −0.347888 | ||||||||
\(187\) | −5.04868 | −0.369196 | ||||||||
\(188\) | 9.10268 | 0.663881 | ||||||||
\(189\) | 3.25544 | 0.236798 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.6277 | −0.986067 | −0.493034 | − | 0.870010i | \(-0.664112\pi\) | ||||
−0.493034 | + | 0.870010i | \(0.664112\pi\) | |||||||
\(192\) | −8.51278 | −0.614357 | ||||||||
\(193\) | −23.3639 | −1.68177 | −0.840883 | − | 0.541216i | \(-0.817964\pi\) | ||||
−0.840883 | + | 0.541216i | \(0.817964\pi\) | |||||||
\(194\) | −3.25544 | −0.233727 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.86141 | −0.490100 | ||||||||
\(197\) | −1.87953 | −0.133911 | −0.0669554 | − | 0.997756i | \(-0.521329\pi\) | ||||
−0.0669554 | + | 0.997756i | \(0.521329\pi\) | |||||||
\(198\) | 2.67181 | 0.189878 | ||||||||
\(199\) | −8.00000 | −0.567105 | −0.283552 | − | 0.958957i | \(-0.591513\pi\) | ||||
−0.283552 | + | 0.958957i | \(0.591513\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.62772 | −0.114810 | ||||||||
\(202\) | −4.75372 | −0.334471 | ||||||||
\(203\) | 9.50744 | 0.667292 | ||||||||
\(204\) | 17.4891 | 1.22448 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.23369 | −0.573668 | ||||||||
\(207\) | 8.51278 | 0.591679 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.4891 | −1.47937 | −0.739686 | − | 0.672952i | \(-0.765026\pi\) | ||||
−0.739686 | + | 0.672952i | \(0.765026\pi\) | |||||||
\(212\) | −4.34896 | −0.298688 | ||||||||
\(213\) | −17.9653 | −1.23096 | ||||||||
\(214\) | 5.25544 | 0.359254 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.51087 | −0.170843 | ||||||||
\(217\) | 8.21782 | 0.557862 | ||||||||
\(218\) | −7.92287 | −0.536604 | ||||||||
\(219\) | −17.4891 | −1.18181 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 22.0742 | 1.48153 | ||||||||
\(223\) | −7.57301 | −0.507126 | −0.253563 | − | 0.967319i | \(-0.581603\pi\) | ||||
−0.253563 | + | 0.967319i | \(0.581603\pi\) | |||||||
\(224\) | 20.2337 | 1.35192 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.7446 | 0.847756 | ||||||||
\(227\) | 9.80240 | 0.650608 | 0.325304 | − | 0.945609i | \(-0.394533\pi\) | ||||
0.325304 | + | 0.945609i | \(0.394533\pi\) | |||||||
\(228\) | 13.8564 | 0.917663 | ||||||||
\(229\) | 20.3723 | 1.34624 | 0.673119 | − | 0.739534i | \(-0.264954\pi\) | ||||
0.673119 | + | 0.739534i | \(0.264954\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.74456 | −0.575350 | ||||||||
\(232\) | −7.33296 | −0.481433 | ||||||||
\(233\) | 17.0256 | 1.11538 | 0.557691 | − | 0.830049i | \(-0.311688\pi\) | ||||
0.557691 | + | 0.830049i | \(0.311688\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.23369 | 0.145401 | ||||||||
\(237\) | −32.1716 | −2.08977 | ||||||||
\(238\) | 13.8564 | 0.898177 | ||||||||
\(239\) | −3.25544 | −0.210577 | −0.105288 | − | 0.994442i | \(-0.533577\pi\) | ||||
−0.105288 | + | 0.994442i | \(0.533577\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.25544 | 0.338532 | 0.169266 | − | 0.985570i | \(-0.445860\pi\) | ||||
0.169266 | + | 0.985570i | \(0.445860\pi\) | |||||||
\(242\) | −0.792287 | −0.0509301 | ||||||||
\(243\) | 22.3692 | 1.43498 | ||||||||
\(244\) | −14.7446 | −0.943924 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.48913 | −0.349974 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.33830 | −0.402482 | ||||||||
\(249\) | −16.7446 | −1.06114 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.88316 | −0.308222 | −0.154111 | − | 0.988054i | \(-0.549251\pi\) | ||||
−0.154111 | + | 0.988054i | \(0.549251\pi\) | |||||||
\(252\) | 16.0309 | 1.00985 | ||||||||
\(253\) | −2.52434 | −0.158704 | ||||||||
\(254\) | 9.25544 | 0.580738 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.8832 | −0.867697 | ||||||||
\(257\) | −23.9538 | −1.49419 | −0.747097 | − | 0.664715i | \(-0.768553\pi\) | ||||
−0.747097 | + | 0.664715i | \(0.768553\pi\) | |||||||
\(258\) | −6.92820 | −0.431331 | ||||||||
\(259\) | −38.2337 | −2.37573 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.25544 | −0.572897 | ||||||||
\(262\) | −6.92820 | −0.428026 | ||||||||
\(263\) | −14.1514 | −0.872610 | −0.436305 | − | 0.899799i | \(-0.643713\pi\) | ||||
−0.436305 | + | 0.899799i | \(0.643713\pi\) | |||||||
\(264\) | 6.74456 | 0.415099 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 10.9783 | 0.673120 | ||||||||
\(267\) | 11.0371 | 0.675460 | ||||||||
\(268\) | −0.884861 | −0.0540515 | ||||||||
\(269\) | 11.4891 | 0.700504 | 0.350252 | − | 0.936655i | \(-0.386096\pi\) | ||||
0.350252 | + | 0.936655i | \(0.386096\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.48913 | −0.576423 | −0.288212 | − | 0.957567i | \(-0.593061\pi\) | ||||
−0.288212 | + | 0.957567i | \(0.593061\pi\) | |||||||
\(272\) | 3.16915 | 0.192158 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.76631 | −0.106707 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.74456 | 0.526361 | ||||||||
\(277\) | −8.21782 | −0.493761 | −0.246881 | − | 0.969046i | \(-0.579406\pi\) | ||||
−0.246881 | + | 0.969046i | \(0.579406\pi\) | |||||||
\(278\) | −14.4463 | −0.866432 | ||||||||
\(279\) | −8.00000 | −0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.4891 | −1.40124 | −0.700622 | − | 0.713533i | \(-0.747094\pi\) | ||||
−0.700622 | + | 0.713533i | \(0.747094\pi\) | |||||||
\(282\) | −13.2665 | −0.790009 | ||||||||
\(283\) | 4.75372 | 0.282579 | 0.141290 | − | 0.989968i | \(-0.454875\pi\) | ||||
0.141290 | + | 0.989968i | \(0.454875\pi\) | |||||||
\(284\) | −9.76631 | −0.579524 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.50744 | 0.561207 | ||||||||
\(288\) | −19.6974 | −1.16068 | ||||||||
\(289\) | 8.48913 | 0.499360 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.3723 | −0.608034 | ||||||||
\(292\) | −9.50744 | −0.556381 | ||||||||
\(293\) | 10.0974 | 0.589894 | 0.294947 | − | 0.955514i | \(-0.404698\pi\) | ||||
0.294947 | + | 0.955514i | \(0.404698\pi\) | |||||||
\(294\) | 10.0000 | 0.583212 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 29.4891 | 1.71402 | ||||||||
\(297\) | 0.939764 | 0.0545306 | ||||||||
\(298\) | −9.10268 | −0.527304 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0000 | 0.691669 | ||||||||
\(302\) | −17.6155 | −1.01366 | ||||||||
\(303\) | −15.1460 | −0.870117 | ||||||||
\(304\) | 2.51087 | 0.144009 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −13.4891 | −0.771122 | ||||||||
\(307\) | 28.1176 | 1.60475 | 0.802377 | − | 0.596817i | \(-0.203568\pi\) | ||||
0.802377 | + | 0.596817i | \(0.203568\pi\) | |||||||
\(308\) | −4.75372 | −0.270868 | ||||||||
\(309\) | −26.2337 | −1.49238 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.4891 | −0.991717 | −0.495859 | − | 0.868403i | \(-0.665147\pi\) | ||||
−0.495859 | + | 0.868403i | \(0.665147\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.8217 | 1.79867 | 0.899335 | − | 0.437260i | \(-0.144051\pi\) | ||||
0.899335 | + | 0.437260i | \(0.144051\pi\) | |||||||
\(314\) | 4.27719 | 0.241376 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.4891 | −0.983840 | ||||||||
\(317\) | 3.51900 | 0.197647 | 0.0988235 | − | 0.995105i | \(-0.468492\pi\) | ||||
0.0988235 | + | 0.995105i | \(0.468492\pi\) | |||||||
\(318\) | 6.33830 | 0.355434 | ||||||||
\(319\) | 2.74456 | 0.153666 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.7446 | 0.934590 | ||||||||
\(322\) | 6.92820 | 0.386094 | ||||||||
\(323\) | 20.1947 | 1.12366 | ||||||||
\(324\) | 10.6277 | 0.590429 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.74456 | −0.152007 | ||||||||
\(327\) | −25.2434 | −1.39596 | ||||||||
\(328\) | −7.33296 | −0.404895 | ||||||||
\(329\) | 22.9783 | 1.26683 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.11684 | 0.171317 | 0.0856586 | − | 0.996325i | \(-0.472701\pi\) | ||||
0.0856586 | + | 0.996325i | \(0.472701\pi\) | |||||||
\(332\) | −9.10268 | −0.499575 | ||||||||
\(333\) | 37.2203 | 2.03966 | ||||||||
\(334\) | −17.7228 | −0.969749 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.48913 | 0.299456 | ||||||||
\(337\) | 12.5668 | 0.684556 | 0.342278 | − | 0.939599i | \(-0.388801\pi\) | ||||
0.342278 | + | 0.939599i | \(0.388801\pi\) | |||||||
\(338\) | 10.2997 | 0.560232 | ||||||||
\(339\) | 40.6060 | 2.20541 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.37228 | 0.128466 | ||||||||
\(342\) | −10.6873 | −0.577901 | ||||||||
\(343\) | 6.92820 | 0.374088 | ||||||||
\(344\) | −9.25544 | −0.499020 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.48913 | −0.0800559 | ||||||||
\(347\) | 29.2974 | 1.57277 | 0.786383 | − | 0.617739i | \(-0.211951\pi\) | ||||
0.786383 | + | 0.617739i | \(0.211951\pi\) | |||||||
\(348\) | −9.50744 | −0.509652 | ||||||||
\(349\) | −7.48913 | −0.400884 | −0.200442 | − | 0.979706i | \(-0.564238\pi\) | ||||
−0.200442 | + | 0.979706i | \(0.564238\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.84096 | 0.311324 | ||||||||
\(353\) | −21.7244 | −1.15627 | −0.578136 | − | 0.815941i | \(-0.696220\pi\) | ||||
−0.578136 | + | 0.815941i | \(0.696220\pi\) | |||||||
\(354\) | −3.25544 | −0.173025 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 44.1485 | 2.33658 | ||||||||
\(358\) | 12.5668 | 0.664175 | ||||||||
\(359\) | 6.51087 | 0.343631 | 0.171815 | − | 0.985129i | \(-0.445037\pi\) | ||||
0.171815 | + | 0.985129i | \(0.445037\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | −5.45343 | −0.286626 | ||||||||
\(363\) | −2.52434 | −0.132493 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 21.4891 | 1.12325 | ||||||||
\(367\) | 24.0087 | 1.25324 | 0.626621 | − | 0.779324i | \(-0.284437\pi\) | ||||
0.626621 | + | 0.779324i | \(0.284437\pi\) | |||||||
\(368\) | 1.58457 | 0.0826016 | ||||||||
\(369\) | −9.25544 | −0.481819 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.9783 | −0.569962 | ||||||||
\(372\) | −8.21782 | −0.426074 | ||||||||
\(373\) | −8.21782 | −0.425503 | −0.212751 | − | 0.977106i | \(-0.568242\pi\) | ||||
−0.212751 | + | 0.977106i | \(0.568242\pi\) | |||||||
\(374\) | 4.00000 | 0.206835 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.7228 | −0.913984 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.57924 | −0.132662 | ||||||||
\(379\) | −6.37228 | −0.327322 | −0.163661 | − | 0.986517i | \(-0.552330\pi\) | ||||
−0.163661 | + | 0.986517i | \(0.552330\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 29.4891 | 1.51077 | ||||||||
\(382\) | 10.7971 | 0.552426 | ||||||||
\(383\) | −5.69349 | −0.290924 | −0.145462 | − | 0.989364i | \(-0.546467\pi\) | ||||
−0.145462 | + | 0.989364i | \(0.546467\pi\) | |||||||
\(384\) | −22.7446 | −1.16068 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.5109 | 0.942179 | ||||||||
\(387\) | −11.6819 | −0.593826 | ||||||||
\(388\) | −5.63858 | −0.286256 | ||||||||
\(389\) | −9.86141 | −0.499993 | −0.249997 | − | 0.968247i | \(-0.580429\pi\) | ||||
−0.249997 | + | 0.968247i | \(0.580429\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.7446 | 0.644520 | ||||||||
\(392\) | 13.3591 | 0.674735 | ||||||||
\(393\) | −22.0742 | −1.11350 | ||||||||
\(394\) | 1.48913 | 0.0750210 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.62772 | 0.232552 | ||||||||
\(397\) | −23.3639 | −1.17260 | −0.586299 | − | 0.810095i | \(-0.699416\pi\) | ||||
−0.586299 | + | 0.810095i | \(0.699416\pi\) | |||||||
\(398\) | 6.33830 | 0.317710 | ||||||||
\(399\) | 34.9783 | 1.75110 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.4891 | 0.573740 | 0.286870 | − | 0.957970i | \(-0.407385\pi\) | ||||
0.286870 | + | 0.957970i | \(0.407385\pi\) | |||||||
\(402\) | 1.28962 | 0.0643204 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −8.23369 | −0.409641 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.53262 | −0.373838 | ||||||||
\(407\) | −11.0371 | −0.547089 | ||||||||
\(408\) | −34.0511 | −1.68578 | ||||||||
\(409\) | 4.51087 | 0.223048 | 0.111524 | − | 0.993762i | \(-0.464427\pi\) | ||||
0.111524 | + | 0.993762i | \(0.464427\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.62772 | −0.277595 | ||||||||
\(412\) | −14.2612 | −0.702597 | ||||||||
\(413\) | 5.63858 | 0.277457 | ||||||||
\(414\) | −6.74456 | −0.331477 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −46.0280 | −2.25400 | ||||||||
\(418\) | 3.16915 | 0.155008 | ||||||||
\(419\) | 22.9783 | 1.12256 | 0.561280 | − | 0.827626i | \(-0.310309\pi\) | ||||
0.561280 | + | 0.827626i | \(0.310309\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.4891 | 1.53469 | 0.767343 | − | 0.641237i | \(-0.221578\pi\) | ||||
0.767343 | + | 0.641237i | \(0.221578\pi\) | |||||||
\(422\) | 17.0256 | 0.828791 | ||||||||
\(423\) | −22.3692 | −1.08763 | ||||||||
\(424\) | 8.46738 | 0.411212 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 14.2337 | 0.689624 | ||||||||
\(427\) | −37.2203 | −1.80121 | ||||||||
\(428\) | 9.10268 | 0.439995 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.7228 | 1.52803 | 0.764017 | − | 0.645196i | \(-0.223224\pi\) | ||||
0.764017 | + | 0.645196i | \(0.223224\pi\) | |||||||
\(432\) | −0.589907 | −0.0283819 | ||||||||
\(433\) | 20.5446 | 0.987308 | 0.493654 | − | 0.869658i | \(-0.335661\pi\) | ||||
0.493654 | + | 0.869658i | \(0.335661\pi\) | |||||||
\(434\) | −6.51087 | −0.312532 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.7228 | −0.657204 | ||||||||
\(437\) | 10.0974 | 0.483022 | ||||||||
\(438\) | 13.8564 | 0.662085 | ||||||||
\(439\) | −1.48913 | −0.0710721 | −0.0355360 | − | 0.999368i | \(-0.511314\pi\) | ||||
−0.0355360 | + | 0.999368i | \(0.511314\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.8614 | 0.802924 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.0911 | 0.717001 | 0.358500 | − | 0.933530i | \(-0.383288\pi\) | ||||
0.358500 | + | 0.933530i | \(0.383288\pi\) | |||||||
\(444\) | 38.2337 | 1.81449 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.00000 | 0.284108 | ||||||||
\(447\) | −29.0024 | −1.37177 | ||||||||
\(448\) | −11.6819 | −0.551919 | ||||||||
\(449\) | −21.8614 | −1.03170 | −0.515852 | − | 0.856678i | \(-0.672524\pi\) | ||||
−0.515852 | + | 0.856678i | \(0.672524\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.74456 | 0.129236 | ||||||||
\(452\) | 22.0742 | 1.03828 | ||||||||
\(453\) | −56.1253 | −2.63700 | ||||||||
\(454\) | −7.76631 | −0.364491 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −26.9783 | −1.26337 | ||||||||
\(457\) | 20.7846 | 0.972263 | 0.486132 | − | 0.873886i | \(-0.338408\pi\) | ||||
0.486132 | + | 0.873886i | \(0.338408\pi\) | |||||||
\(458\) | −16.1407 | −0.754205 | ||||||||
\(459\) | −4.74456 | −0.221457 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.2337 | −1.50127 | −0.750636 | − | 0.660716i | \(-0.770253\pi\) | ||||
−0.750636 | + | 0.660716i | \(0.770253\pi\) | |||||||
\(462\) | 6.92820 | 0.322329 | ||||||||
\(463\) | 20.1398 | 0.935976 | 0.467988 | − | 0.883735i | \(-0.344979\pi\) | ||||
0.467988 | + | 0.883735i | \(0.344979\pi\) | |||||||
\(464\) | −1.72281 | −0.0799796 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.4891 | −0.624872 | ||||||||
\(467\) | 4.40387 | 0.203787 | 0.101893 | − | 0.994795i | \(-0.467510\pi\) | ||||
0.101893 | + | 0.994795i | \(0.467510\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.23369 | −0.103142 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.6277 | 0.627932 | ||||||||
\(472\) | −4.34896 | −0.200177 | ||||||||
\(473\) | 3.46410 | 0.159280 | ||||||||
\(474\) | 25.4891 | 1.17075 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 24.0000 | 1.10004 | ||||||||
\(477\) | 10.6873 | 0.489336 | ||||||||
\(478\) | 2.57924 | 0.117972 | ||||||||
\(479\) | 17.4891 | 0.799099 | 0.399549 | − | 0.916712i | \(-0.369167\pi\) | ||||
0.399549 | + | 0.916712i | \(0.369167\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −4.16381 | −0.189657 | ||||||||
\(483\) | 22.0742 | 1.00441 | ||||||||
\(484\) | −1.37228 | −0.0623764 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −17.7228 | −0.803923 | ||||||||
\(487\) | −22.7190 | −1.02950 | −0.514749 | − | 0.857341i | \(-0.672115\pi\) | ||||
−0.514749 | + | 0.857341i | \(0.672115\pi\) | |||||||
\(488\) | 28.7075 | 1.29953 | ||||||||
\(489\) | −8.74456 | −0.395443 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.4891 | 1.33083 | 0.665413 | − | 0.746476i | \(-0.268256\pi\) | ||||
0.665413 | + | 0.746476i | \(0.268256\pi\) | |||||||
\(492\) | −9.50744 | −0.428629 | ||||||||
\(493\) | −13.8564 | −0.624061 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.48913 | −0.0668637 | ||||||||
\(497\) | −24.6535 | −1.10586 | ||||||||
\(498\) | 13.2665 | 0.594486 | ||||||||
\(499\) | −20.0000 | −0.895323 | −0.447661 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447661 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −56.4674 | −2.52278 | ||||||||
\(502\) | 3.86886 | 0.172676 | ||||||||
\(503\) | −0.294954 | −0.0131513 | −0.00657567 | − | 0.999978i | \(-0.502093\pi\) | ||||
−0.00657567 | + | 0.999978i | \(0.502093\pi\) | |||||||
\(504\) | −31.2119 | −1.39029 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.00000 | 0.0889108 | ||||||||
\(507\) | 32.8164 | 1.45743 | ||||||||
\(508\) | 16.0309 | 0.711256 | ||||||||
\(509\) | 28.3723 | 1.25758 | 0.628790 | − | 0.777575i | \(-0.283551\pi\) | ||||
0.628790 | + | 0.777575i | \(0.283551\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.0000 | −1.06170 | ||||||||
\(512\) | −7.02078 | −0.310277 | ||||||||
\(513\) | −3.75906 | −0.165966 | ||||||||
\(514\) | 18.9783 | 0.837095 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −12.0000 | −0.528271 | ||||||||
\(517\) | 6.63325 | 0.291730 | ||||||||
\(518\) | 30.2921 | 1.33096 | ||||||||
\(519\) | −4.74456 | −0.208263 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.6060 | 0.815142 | 0.407571 | − | 0.913173i | \(-0.366376\pi\) | ||||
0.407571 | + | 0.913173i | \(0.366376\pi\) | |||||||
\(522\) | 7.33296 | 0.320955 | ||||||||
\(523\) | −9.10268 | −0.398033 | −0.199016 | − | 0.979996i | \(-0.563775\pi\) | ||||
−0.199016 | + | 0.979996i | \(0.563775\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.2119 | 0.488864 | ||||||||
\(527\) | −11.9769 | −0.521721 | ||||||||
\(528\) | 1.58457 | 0.0689597 | ||||||||
\(529\) | −16.6277 | −0.722944 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.48913 | −0.238208 | ||||||||
\(532\) | 19.0149 | 0.824400 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −8.74456 | −0.378414 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.72281 | 0.0744142 | ||||||||
\(537\) | 40.0395 | 1.72783 | ||||||||
\(538\) | −9.10268 | −0.392445 | ||||||||
\(539\) | −5.00000 | −0.215365 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.233688 | −0.0100470 | −0.00502351 | − | 0.999987i | \(-0.501599\pi\) | ||||
−0.00502351 | + | 0.999987i | \(0.501599\pi\) | |||||||
\(542\) | 7.51811 | 0.322930 | ||||||||
\(543\) | −17.3754 | −0.745650 | ||||||||
\(544\) | −29.4891 | −1.26434 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.10268 | 0.389203 | 0.194601 | − | 0.980882i | \(-0.437659\pi\) | ||||
0.194601 | + | 0.980882i | \(0.437659\pi\) | |||||||
\(548\) | −3.05934 | −0.130689 | ||||||||
\(549\) | 36.2337 | 1.54642 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.9783 | −0.467689 | ||||||||
\(552\) | −17.0256 | −0.724656 | ||||||||
\(553\) | −44.1485 | −1.87738 | ||||||||
\(554\) | 6.51087 | 0.276621 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −25.0217 | −1.06116 | ||||||||
\(557\) | −32.1716 | −1.36315 | −0.681577 | − | 0.731747i | \(-0.738705\pi\) | ||||
−0.681577 | + | 0.731747i | \(0.738705\pi\) | |||||||
\(558\) | 6.33830 | 0.268321 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.7446 | 0.538076 | ||||||||
\(562\) | 18.6101 | 0.785021 | ||||||||
\(563\) | 12.2718 | 0.517196 | 0.258598 | − | 0.965985i | \(-0.416739\pi\) | ||||
0.258598 | + | 0.965985i | \(0.416739\pi\) | |||||||
\(564\) | −22.9783 | −0.967559 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.76631 | −0.158310 | ||||||||
\(567\) | 26.8280 | 1.12667 | ||||||||
\(568\) | 19.0149 | 0.797847 | ||||||||
\(569\) | −38.7446 | −1.62426 | −0.812128 | − | 0.583479i | \(-0.801691\pi\) | ||||
−0.812128 | + | 0.583479i | \(0.801691\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.4891 | −0.899292 | −0.449646 | − | 0.893207i | \(-0.648450\pi\) | ||||
−0.449646 | + | 0.893207i | \(0.648450\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 34.4010 | 1.43712 | ||||||||
\(574\) | −7.53262 | −0.314406 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 11.3723 | 0.473845 | ||||||||
\(577\) | −31.8217 | −1.32476 | −0.662378 | − | 0.749170i | \(-0.730453\pi\) | ||||
−0.662378 | + | 0.749170i | \(0.730453\pi\) | |||||||
\(578\) | −6.72582 | −0.279757 | ||||||||
\(579\) | 58.9783 | 2.45105 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.9783 | −0.953298 | ||||||||
\(582\) | 8.21782 | 0.340640 | ||||||||
\(583\) | −3.16915 | −0.131253 | ||||||||
\(584\) | 18.5109 | 0.765985 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.00000 | −0.330477 | ||||||||
\(587\) | 28.0078 | 1.15600 | 0.578002 | − | 0.816035i | \(-0.303833\pi\) | ||||
0.578002 | + | 0.816035i | \(0.303833\pi\) | |||||||
\(588\) | 17.3205 | 0.714286 | ||||||||
\(589\) | −9.48913 | −0.390993 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.74456 | 0.195165 | ||||||||
\(592\) | 6.92820 | 0.284747 | ||||||||
\(593\) | −43.5586 | −1.78874 | −0.894368 | − | 0.447333i | \(-0.852374\pi\) | ||||
−0.894368 | + | 0.447333i | \(0.852374\pi\) | |||||||
\(594\) | −0.744563 | −0.0305498 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.7663 | −0.645813 | ||||||||
\(597\) | 20.1947 | 0.826514 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.9783 | −1.42917 | −0.714586 | − | 0.699547i | \(-0.753385\pi\) | ||||
−0.714586 | + | 0.699547i | \(0.753385\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.4674 | 1.24279 | 0.621395 | − | 0.783497i | \(-0.286566\pi\) | ||||
0.621395 | + | 0.783497i | \(0.286566\pi\) | |||||||
\(602\) | −9.50744 | −0.387494 | ||||||||
\(603\) | 2.17448 | 0.0885517 | ||||||||
\(604\) | −30.5109 | −1.24147 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 12.0000 | 0.487467 | ||||||||
\(607\) | −3.46410 | −0.140604 | −0.0703018 | − | 0.997526i | \(-0.522396\pi\) | ||||
−0.0703018 | + | 0.997526i | \(0.522396\pi\) | |||||||
\(608\) | −23.3639 | −0.947529 | ||||||||
\(609\) | −24.0000 | −0.972529 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −23.3639 | −0.944428 | ||||||||
\(613\) | 44.1485 | 1.78314 | 0.891570 | − | 0.452883i | \(-0.149605\pi\) | ||||
0.891570 | + | 0.452883i | \(0.149605\pi\) | |||||||
\(614\) | −22.2772 | −0.899034 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.25544 | 0.372912 | ||||||||
\(617\) | 3.75906 | 0.151334 | 0.0756669 | − | 0.997133i | \(-0.475891\pi\) | ||||
0.0756669 | + | 0.997133i | \(0.475891\pi\) | |||||||
\(618\) | 20.7846 | 0.836080 | ||||||||
\(619\) | −3.11684 | −0.125277 | −0.0626383 | − | 0.998036i | \(-0.519951\pi\) | ||||
−0.0626383 | + | 0.998036i | \(0.519951\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.37228 | −0.0951964 | ||||||||
\(622\) | 13.8564 | 0.555591 | ||||||||
\(623\) | 15.1460 | 0.606813 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −25.2119 | −1.00767 | ||||||||
\(627\) | 10.0974 | 0.403249 | ||||||||
\(628\) | 7.40830 | 0.295624 | ||||||||
\(629\) | 55.7228 | 2.22181 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.6060 | −0.661073 | −0.330537 | − | 0.943793i | \(-0.607230\pi\) | ||||
−0.330537 | + | 0.943793i | \(0.607230\pi\) | |||||||
\(632\) | 34.0511 | 1.35448 | ||||||||
\(633\) | 54.2458 | 2.15608 | ||||||||
\(634\) | −2.78806 | −0.110728 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 10.9783 | 0.435316 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.17448 | −0.0860885 | ||||||||
\(639\) | 24.0000 | 0.949425 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.6277 | −0.775248 | −0.387624 | − | 0.921818i | \(-0.626704\pi\) | ||||
−0.387624 | + | 0.921818i | \(0.626704\pi\) | |||||||
\(642\) | −13.2665 | −0.523587 | ||||||||
\(643\) | −39.1547 | −1.54411 | −0.772055 | − | 0.635556i | \(-0.780771\pi\) | ||||
−0.772055 | + | 0.635556i | \(0.780771\pi\) | |||||||
\(644\) | 12.0000 | 0.472866 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.0000 | −0.629512 | ||||||||
\(647\) | −41.0342 | −1.61322 | −0.806611 | − | 0.591083i | \(-0.798701\pi\) | ||||
−0.806611 | + | 0.591083i | \(0.798701\pi\) | |||||||
\(648\) | −20.6920 | −0.812860 | ||||||||
\(649\) | 1.62772 | 0.0638935 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.7446 | −0.813044 | ||||||||
\(652\) | −4.75372 | −0.186170 | ||||||||
\(653\) | −25.5932 | −1.00154 | −0.500770 | − | 0.865580i | \(-0.666950\pi\) | ||||
−0.500770 | + | 0.865580i | \(0.666950\pi\) | |||||||
\(654\) | 20.0000 | 0.782062 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.72281 | −0.0672646 | ||||||||
\(657\) | 23.3639 | 0.911511 | ||||||||
\(658\) | −18.2054 | −0.709719 | ||||||||
\(659\) | 32.7446 | 1.27555 | 0.637774 | − | 0.770224i | \(-0.279856\pi\) | ||||
0.637774 | + | 0.770224i | \(0.279856\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.3505 | 1.37498 | 0.687488 | − | 0.726196i | \(-0.258713\pi\) | ||||
0.687488 | + | 0.726196i | \(0.258713\pi\) | |||||||
\(662\) | −2.46943 | −0.0959773 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.7228 | 0.687779 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −29.4891 | −1.14268 | ||||||||
\(667\) | −6.92820 | −0.268261 | ||||||||
\(668\) | −30.6968 | −1.18770 | ||||||||
\(669\) | 19.1168 | 0.739100 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.7446 | −0.414789 | ||||||||
\(672\) | −51.0767 | −1.97033 | ||||||||
\(673\) | 1.28962 | 0.0497112 | 0.0248556 | − | 0.999691i | \(-0.492087\pi\) | ||||
0.0248556 | + | 0.999691i | \(0.492087\pi\) | |||||||
\(674\) | −9.95650 | −0.383510 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.8397 | 0.686141 | ||||||||
\(677\) | −43.4487 | −1.66987 | −0.834935 | − | 0.550348i | \(-0.814495\pi\) | ||||
−0.834935 | + | 0.550348i | \(0.814495\pi\) | |||||||
\(678\) | −32.1716 | −1.23554 | ||||||||
\(679\) | −14.2337 | −0.546239 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.7446 | −0.948214 | ||||||||
\(682\) | −1.87953 | −0.0719708 | ||||||||
\(683\) | −44.4434 | −1.70058 | −0.850290 | − | 0.526314i | \(-0.823573\pi\) | ||||
−0.850290 | + | 0.526314i | \(0.823573\pi\) | |||||||
\(684\) | −18.5109 | −0.707781 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.48913 | −0.209576 | ||||||||
\(687\) | −51.4265 | −1.96204 | ||||||||
\(688\) | −2.17448 | −0.0829013 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.1386 | 0.613941 | 0.306971 | − | 0.951719i | \(-0.400685\pi\) | ||||
0.306971 | + | 0.951719i | \(0.400685\pi\) | |||||||
\(692\) | −2.57924 | −0.0980480 | ||||||||
\(693\) | 11.6819 | 0.443760 | ||||||||
\(694\) | −23.2119 | −0.881113 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 18.5109 | 0.701653 | ||||||||
\(697\) | −13.8564 | −0.524849 | ||||||||
\(698\) | 5.93354 | 0.224588 | ||||||||
\(699\) | −42.9783 | −1.62559 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.4891 | −1.34041 | −0.670203 | − | 0.742178i | \(-0.733793\pi\) | ||||
−0.670203 | + | 0.742178i | \(0.733793\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 44.1485 | 1.66509 | ||||||||
\(704\) | −3.37228 | −0.127098 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.2119 | 0.647780 | ||||||||
\(707\) | −20.7846 | −0.781686 | ||||||||
\(708\) | −5.63858 | −0.211911 | ||||||||
\(709\) | 41.1168 | 1.54418 | 0.772088 | − | 0.635516i | \(-0.219213\pi\) | ||||
0.772088 | + | 0.635516i | \(0.219213\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 42.9783 | 1.61181 | ||||||||
\(712\) | −11.6819 | −0.437799 | ||||||||
\(713\) | −5.98844 | −0.224269 | ||||||||
\(714\) | −34.9783 | −1.30903 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 21.7663 | 0.813445 | ||||||||
\(717\) | 8.21782 | 0.306900 | ||||||||
\(718\) | −5.15848 | −0.192513 | ||||||||
\(719\) | 21.3505 | 0.796240 | 0.398120 | − | 0.917333i | \(-0.369663\pi\) | ||||
0.398120 | + | 0.917333i | \(0.369663\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −36.0000 | −1.34071 | ||||||||
\(722\) | 2.37686 | 0.0884576 | ||||||||
\(723\) | −13.2665 | −0.493386 | ||||||||
\(724\) | −9.44563 | −0.351044 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.00000 | 0.0742270 | ||||||||
\(727\) | 15.7908 | 0.585650 | 0.292825 | − | 0.956166i | \(-0.405405\pi\) | ||||
0.292825 | + | 0.956166i | \(0.405405\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −33.2337 | −1.23088 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.4891 | −0.646859 | ||||||||
\(732\) | 37.2203 | 1.37570 | ||||||||
\(733\) | −30.2921 | −1.11886 | −0.559431 | − | 0.828877i | \(-0.688980\pi\) | ||||
−0.559431 | + | 0.828877i | \(0.688980\pi\) | |||||||
\(734\) | −19.0217 | −0.702106 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.7446 | −0.543492 | ||||||||
\(737\) | −0.644810 | −0.0237519 | ||||||||
\(738\) | 7.33296 | 0.269930 | ||||||||
\(739\) | 0.744563 | 0.0273892 | 0.0136946 | − | 0.999906i | \(-0.495641\pi\) | ||||
0.0136946 | + | 0.999906i | \(0.495641\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.69793 | 0.319311 | ||||||||
\(743\) | 21.7793 | 0.799004 | 0.399502 | − | 0.916732i | \(-0.369183\pi\) | ||||
0.399502 | + | 0.916732i | \(0.369183\pi\) | |||||||
\(744\) | 16.0000 | 0.586588 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.51087 | 0.238380 | ||||||||
\(747\) | 22.3692 | 0.818446 | ||||||||
\(748\) | 6.92820 | 0.253320 | ||||||||
\(749\) | 22.9783 | 0.839607 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.6277 | 0.789207 | 0.394603 | − | 0.918852i | \(-0.370882\pi\) | ||||
0.394603 | + | 0.918852i | \(0.370882\pi\) | |||||||
\(752\) | −4.16381 | −0.151839 | ||||||||
\(753\) | 12.3267 | 0.449211 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.46738 | −0.162477 | ||||||||
\(757\) | 39.7995 | 1.44654 | 0.723269 | − | 0.690567i | \(-0.242639\pi\) | ||||
0.723269 | + | 0.690567i | \(0.242639\pi\) | |||||||
\(758\) | 5.04868 | 0.183376 | ||||||||
\(759\) | 6.37228 | 0.231299 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.2554 | 0.770509 | 0.385255 | − | 0.922810i | \(-0.374114\pi\) | ||||
0.385255 | + | 0.922810i | \(0.374114\pi\) | |||||||
\(762\) | −23.3639 | −0.846383 | ||||||||
\(763\) | −34.6410 | −1.25409 | ||||||||
\(764\) | 18.7011 | 0.676581 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.51087 | 0.162985 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 35.0458 | 1.26461 | ||||||||
\(769\) | −51.2119 | −1.84675 | −0.923375 | − | 0.383900i | \(-0.874581\pi\) | ||||
−0.923375 | + | 0.383900i | \(0.874581\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 60.4674 | 2.17768 | ||||||||
\(772\) | 32.0618 | 1.15393 | ||||||||
\(773\) | 30.8820 | 1.11075 | 0.555373 | − | 0.831601i | \(-0.312575\pi\) | ||||
0.555373 | + | 0.831601i | \(0.312575\pi\) | |||||||
\(774\) | 9.25544 | 0.332680 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.9783 | 0.394096 | ||||||||
\(777\) | 96.5147 | 3.46245 | ||||||||
\(778\) | 7.81306 | 0.280112 | ||||||||
\(779\) | −10.9783 | −0.393337 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.11684 | −0.254661 | ||||||||
\(782\) | −10.0974 | −0.361081 | ||||||||
\(783\) | 2.57924 | 0.0921745 | ||||||||
\(784\) | 3.13859 | 0.112093 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 17.4891 | 0.623816 | ||||||||
\(787\) | −4.75372 | −0.169452 | −0.0847259 | − | 0.996404i | \(-0.527001\pi\) | ||||
−0.0847259 | + | 0.996404i | \(0.527001\pi\) | |||||||
\(788\) | 2.57924 | 0.0918816 | ||||||||
\(789\) | 35.7228 | 1.27177 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 55.7228 | 1.98128 | ||||||||
\(792\) | −9.01011 | −0.320160 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 18.5109 | 0.656926 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.9783 | 0.389114 | ||||||||
\(797\) | 31.2318 | 1.10629 | 0.553144 | − | 0.833086i | \(-0.313428\pi\) | ||||
0.553144 | + | 0.833086i | \(0.313428\pi\) | |||||||
\(798\) | −27.7128 | −0.981023 | ||||||||
\(799\) | −33.4891 | −1.18476 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.7446 | −0.520974 | ||||||||
\(802\) | −9.10268 | −0.321427 | ||||||||
\(803\) | −6.92820 | −0.244491 | ||||||||
\(804\) | 2.23369 | 0.0787761 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29.0024 | −1.02093 | ||||||||
\(808\) | 16.0309 | 0.563965 | ||||||||
\(809\) | −21.2554 | −0.747301 | −0.373651 | − | 0.927569i | \(-0.621894\pi\) | ||||
−0.373651 | + | 0.927569i | \(0.621894\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.2337 | 1.20211 | 0.601054 | − | 0.799209i | \(-0.294748\pi\) | ||||
0.601054 | + | 0.799209i | \(0.294748\pi\) | |||||||
\(812\) | −13.0469 | −0.457856 | ||||||||
\(813\) | 23.9538 | 0.840095 | ||||||||
\(814\) | 8.74456 | 0.306497 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.00000 | −0.280056 | ||||||||
\(817\) | −13.8564 | −0.484774 | ||||||||
\(818\) | −3.57391 | −0.124959 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.0000 | −0.628204 | −0.314102 | − | 0.949389i | \(-0.601703\pi\) | ||||
−0.314102 | + | 0.949389i | \(0.601703\pi\) | |||||||
\(822\) | 4.45877 | 0.155517 | ||||||||
\(823\) | 33.5161 | 1.16830 | 0.584149 | − | 0.811646i | \(-0.301428\pi\) | ||||
0.584149 | + | 0.811646i | \(0.301428\pi\) | |||||||
\(824\) | 27.7663 | 0.967285 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.46738 | −0.155440 | ||||||||
\(827\) | 18.0202 | 0.626624 | 0.313312 | − | 0.949650i | \(-0.398561\pi\) | ||||
0.313312 | + | 0.949650i | \(0.398561\pi\) | |||||||
\(828\) | −11.6819 | −0.405975 | ||||||||
\(829\) | 31.3505 | 1.08885 | 0.544424 | − | 0.838810i | \(-0.316748\pi\) | ||||
0.544424 | + | 0.838810i | \(0.316748\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.7446 | 0.719621 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 25.2434 | 0.874631 | ||||||||
\(834\) | 36.4674 | 1.26276 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.48913 | 0.189845 | ||||||||
\(837\) | 2.22938 | 0.0770588 | ||||||||
\(838\) | −18.2054 | −0.628894 | ||||||||
\(839\) | 7.11684 | 0.245701 | 0.122850 | − | 0.992425i | \(-0.460796\pi\) | ||||
0.122850 | + | 0.992425i | \(0.460796\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.4674 | −0.740254 | ||||||||
\(842\) | −24.9484 | −0.859779 | ||||||||
\(843\) | 59.2945 | 2.04221 | ||||||||
\(844\) | 29.4891 | 1.01506 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 17.7228 | 0.609323 | ||||||||
\(847\) | −3.46410 | −0.119028 | ||||||||
\(848\) | 1.98933 | 0.0683140 | ||||||||
\(849\) | −12.0000 | −0.411839 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.8614 | 0.955077 | ||||||||
\(852\) | 24.6535 | 0.844614 | ||||||||
\(853\) | 24.6535 | 0.844119 | 0.422059 | − | 0.906568i | \(-0.361307\pi\) | ||||
0.422059 | + | 0.906568i | \(0.361307\pi\) | |||||||
\(854\) | 29.4891 | 1.00910 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.7228 | −0.605753 | ||||||||
\(857\) | 10.6873 | 0.365070 | 0.182535 | − | 0.983199i | \(-0.441570\pi\) | ||||
0.182535 | + | 0.983199i | \(0.441570\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.1168 | 0.379302 | 0.189651 | − | 0.981852i | \(-0.439264\pi\) | ||||
0.189651 | + | 0.981852i | \(0.439264\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −24.0000 | −0.817918 | ||||||||
\(862\) | −25.1336 | −0.856053 | ||||||||
\(863\) | −23.6588 | −0.805355 | −0.402678 | − | 0.915342i | \(-0.631920\pi\) | ||||
−0.402678 | + | 0.915342i | \(0.631920\pi\) | |||||||
\(864\) | 5.48913 | 0.186744 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16.2772 | −0.553121 | ||||||||
\(867\) | −21.4294 | −0.727781 | ||||||||
\(868\) | −11.2772 | −0.382772 | ||||||||
\(869\) | −12.7446 | −0.432330 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 26.7181 | 0.904791 | ||||||||
\(873\) | 13.8564 | 0.468968 | ||||||||
\(874\) | −8.00000 | −0.270604 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 24.0000 | 0.810885 | ||||||||
\(877\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(878\) | 1.17981 | 0.0398168 | ||||||||
\(879\) | −25.4891 | −0.859727 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.8614 | 0.736530 | 0.368265 | − | 0.929721i | \(-0.379952\pi\) | ||||
0.368265 | + | 0.929721i | \(0.379952\pi\) | |||||||
\(882\) | −13.3591 | −0.449823 | ||||||||
\(883\) | −24.2487 | −0.816034 | −0.408017 | − | 0.912974i | \(-0.633780\pi\) | ||||
−0.408017 | + | 0.912974i | \(0.633780\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.9565 | −0.401687 | ||||||||
\(887\) | 14.1514 | 0.475156 | 0.237578 | − | 0.971368i | \(-0.423646\pi\) | ||||
0.237578 | + | 0.971368i | \(0.423646\pi\) | |||||||
\(888\) | −74.4405 | −2.49806 | ||||||||
\(889\) | 40.4674 | 1.35723 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.74456 | 0.259453 | ||||||||
\(892\) | 10.3923 | 0.347960 | ||||||||
\(893\) | −26.5330 | −0.887893 | ||||||||
\(894\) | 22.9783 | 0.768508 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −31.2119 | −1.04272 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.3205 | 0.577993 | ||||||||
\(899\) | 6.51087 | 0.217150 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.0000 | 0.533037 | ||||||||
\(902\) | −2.17448 | −0.0724023 | ||||||||
\(903\) | −30.2921 | −1.00806 | ||||||||
\(904\) | −42.9783 | −1.42944 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 44.4674 | 1.47733 | ||||||||
\(907\) | −19.8997 | −0.660760 | −0.330380 | − | 0.943848i | \(-0.607177\pi\) | ||||
−0.330380 | + | 0.943848i | \(0.607177\pi\) | |||||||
\(908\) | −13.4516 | −0.446409 | ||||||||
\(909\) | 20.2337 | 0.671109 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.5109 | −1.01087 | −0.505435 | − | 0.862865i | \(-0.668668\pi\) | ||||
−0.505435 | + | 0.862865i | \(0.668668\pi\) | |||||||
\(912\) | −6.33830 | −0.209882 | ||||||||
\(913\) | −6.63325 | −0.219529 | ||||||||
\(914\) | −16.4674 | −0.544692 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −27.9565 | −0.923709 | ||||||||
\(917\) | −30.2921 | −1.00033 | ||||||||
\(918\) | 3.75906 | 0.124067 | ||||||||
\(919\) | 6.23369 | 0.205630 | 0.102815 | − | 0.994700i | \(-0.467215\pi\) | ||||
0.102815 | + | 0.994700i | \(0.467215\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −70.9783 | −2.33881 | ||||||||
\(922\) | 25.5383 | 0.841060 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 12.0000 | 0.394771 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −15.9565 | −0.524363 | ||||||||
\(927\) | 35.0458 | 1.15105 | ||||||||
\(928\) | 16.0309 | 0.526240 | ||||||||
\(929\) | −52.9783 | −1.73816 | −0.869080 | − | 0.494672i | \(-0.835288\pi\) | ||||
−0.869080 | + | 0.494672i | \(0.835288\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.0000 | 0.655474 | ||||||||
\(932\) | −23.3639 | −0.765308 | ||||||||
\(933\) | 44.1485 | 1.44536 | ||||||||
\(934\) | −3.48913 | −0.114168 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.9431 | 0.847524 | 0.423762 | − | 0.905774i | \(-0.360709\pi\) | ||||
0.423762 | + | 0.905774i | \(0.360709\pi\) | |||||||
\(938\) | 1.76972 | 0.0577835 | ||||||||
\(939\) | −80.3288 | −2.62143 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.4674 | 0.341227 | 0.170613 | − | 0.985338i | \(-0.445425\pi\) | ||||
0.170613 | + | 0.985338i | \(0.445425\pi\) | |||||||
\(942\) | −10.7971 | −0.351787 | ||||||||
\(943\) | −6.92820 | −0.225613 | ||||||||
\(944\) | −1.02175 | −0.0332551 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.74456 | −0.0892334 | ||||||||
\(947\) | −56.1802 | −1.82561 | −0.912806 | − | 0.408393i | \(-0.866089\pi\) | ||||
−0.912806 | + | 0.408393i | \(0.866089\pi\) | |||||||
\(948\) | 44.1485 | 1.43388 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.88316 | −0.288056 | ||||||||
\(952\) | −46.7277 | −1.51445 | ||||||||
\(953\) | 41.6790 | 1.35012 | 0.675058 | − | 0.737765i | \(-0.264119\pi\) | ||||
0.675058 | + | 0.737765i | \(0.264119\pi\) | |||||||
\(954\) | −8.46738 | −0.274141 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.46738 | 0.144485 | ||||||||
\(957\) | −6.92820 | −0.223957 | ||||||||
\(958\) | −13.8564 | −0.447680 | ||||||||
\(959\) | −7.72281 | −0.249383 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.3723 | −0.818461 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.3692 | −0.720837 | ||||||||
\(964\) | −7.21194 | −0.232281 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −17.4891 | −0.562703 | ||||||||
\(967\) | 46.3229 | 1.48965 | 0.744823 | − | 0.667262i | \(-0.232534\pi\) | ||||
0.744823 | + | 0.667262i | \(0.232534\pi\) | |||||||
\(968\) | 2.67181 | 0.0858754 | ||||||||
\(969\) | −50.9783 | −1.63766 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 54.0951 | 1.73599 | 0.867997 | − | 0.496569i | \(-0.165407\pi\) | ||||
0.867997 | + | 0.496569i | \(0.165407\pi\) | |||||||
\(972\) | −30.6968 | −0.984601 | ||||||||
\(973\) | −63.1633 | −2.02492 | ||||||||
\(974\) | 18.0000 | 0.576757 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.74456 | 0.215888 | ||||||||
\(977\) | 27.3630 | 0.875419 | 0.437709 | − | 0.899117i | \(-0.355790\pi\) | ||||
0.437709 | + | 0.899117i | \(0.355790\pi\) | |||||||
\(978\) | 6.92820 | 0.221540 | ||||||||
\(979\) | 4.37228 | 0.139739 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.7228 | 1.07669 | ||||||||
\(982\) | −23.3639 | −0.745570 | ||||||||
\(983\) | 8.16292 | 0.260357 | 0.130178 | − | 0.991491i | \(-0.458445\pi\) | ||||
0.130178 | + | 0.991491i | \(0.458445\pi\) | |||||||
\(984\) | 18.5109 | 0.590105 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 10.9783 | 0.349619 | ||||||||
\(987\) | −58.0049 | −1.84632 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.74456 | −0.278061 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.9783 | −0.856992 | −0.428496 | − | 0.903544i | \(-0.640956\pi\) | ||||
−0.428496 | + | 0.903544i | \(0.640956\pi\) | |||||||
\(992\) | 13.8564 | 0.439941 | ||||||||
\(993\) | −7.86797 | −0.249682 | ||||||||
\(994\) | 19.5326 | 0.619537 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 22.9783 | 0.728094 | ||||||||
\(997\) | −22.0742 | −0.699098 | −0.349549 | − | 0.936918i | \(-0.613665\pi\) | ||||
−0.349549 | + | 0.936918i | \(0.613665\pi\) | |||||||
\(998\) | 15.8457 | 0.501588 | ||||||||
\(999\) | −10.3723 | −0.328164 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))