Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(1,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, 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("1134.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.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: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.37228 | 0.613703 | 0.306851 | − | 0.951757i | \(-0.400725\pi\) | ||||
0.306851 | + | 0.951757i | \(0.400725\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.37228 | 0.433953 | ||||||||
\(11\) | −4.37228 | −1.31829 | −0.659146 | − | 0.752015i | \(-0.729082\pi\) | ||||
−0.659146 | + | 0.752015i | \(0.729082\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.37228 | 1.06043 | 0.530217 | − | 0.847862i | \(-0.322110\pi\) | ||||
0.530217 | + | 0.847862i | \(0.322110\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.00000 | 1.14708 | 0.573539 | − | 0.819178i | \(-0.305570\pi\) | ||||
0.573539 | + | 0.819178i | \(0.305570\pi\) | |||||||
\(20\) | 1.37228 | 0.306851 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.37228 | −0.932174 | ||||||||
\(23\) | 7.37228 | 1.53723 | 0.768613 | − | 0.639713i | \(-0.220947\pi\) | ||||
0.768613 | + | 0.639713i | \(0.220947\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.11684 | −0.623369 | ||||||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −2.74456 | −0.509652 | −0.254826 | − | 0.966987i | \(-0.582018\pi\) | ||||
−0.254826 | + | 0.966987i | \(0.582018\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.37228 | 0.749840 | ||||||||
\(35\) | 1.37228 | 0.231958 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 5.00000 | 0.811107 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.37228 | 0.216977 | ||||||||
\(41\) | −10.3723 | −1.61988 | −0.809939 | − | 0.586514i | \(-0.800500\pi\) | ||||
−0.809939 | + | 0.586514i | \(0.800500\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.11684 | 1.39031 | 0.695153 | − | 0.718862i | \(-0.255337\pi\) | ||||
0.695153 | + | 0.718862i | \(0.255337\pi\) | |||||||
\(44\) | −4.37228 | −0.659146 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.37228 | 1.08698 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.11684 | −0.440788 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | −2.74456 | −0.376995 | −0.188497 | − | 0.982074i | \(-0.560362\pi\) | ||||
−0.188497 | + | 0.982074i | \(0.560362\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.00000 | −0.809040 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.74456 | −0.360379 | ||||||||
\(59\) | −7.11684 | −0.926534 | −0.463267 | − | 0.886219i | \(-0.653323\pi\) | ||||
−0.463267 | + | 0.886219i | \(0.653323\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.1168 | −1.80748 | −0.903738 | − | 0.428085i | \(-0.859188\pi\) | ||||
−0.903738 | + | 0.428085i | \(0.859188\pi\) | |||||||
\(62\) | 2.00000 | 0.254000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.74456 | 0.340421 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.1168 | 1.84682 | 0.923408 | − | 0.383819i | \(-0.125391\pi\) | ||||
0.923408 | + | 0.383819i | \(0.125391\pi\) | |||||||
\(68\) | 4.37228 | 0.530217 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.37228 | 0.164019 | ||||||||
\(71\) | −10.1168 | −1.20065 | −0.600324 | − | 0.799757i | \(-0.704962\pi\) | ||||
−0.600324 | + | 0.799757i | \(0.704962\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.11684 | −0.598881 | −0.299441 | − | 0.954115i | \(-0.596800\pi\) | ||||
−0.299441 | + | 0.954115i | \(0.596800\pi\) | |||||||
\(74\) | 2.00000 | 0.232495 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.00000 | 0.573539 | ||||||||
\(77\) | −4.37228 | −0.498268 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.1168 | 1.36325 | 0.681626 | − | 0.731701i | \(-0.261273\pi\) | ||||
0.681626 | + | 0.731701i | \(0.261273\pi\) | |||||||
\(80\) | 1.37228 | 0.153426 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.3723 | −1.14543 | ||||||||
\(83\) | 5.48913 | 0.602510 | 0.301255 | − | 0.953544i | \(-0.402594\pi\) | ||||
0.301255 | + | 0.953544i | \(0.402594\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.00000 | 0.650791 | ||||||||
\(86\) | 9.11684 | 0.983095 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.37228 | −0.466087 | ||||||||
\(89\) | −3.25544 | −0.345076 | −0.172538 | − | 0.985003i | \(-0.555197\pi\) | ||||
−0.172538 | + | 0.985003i | \(0.555197\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | 7.37228 | 0.768613 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.86141 | 0.703965 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.11684 | 0.925675 | 0.462838 | − | 0.886443i | \(-0.346831\pi\) | ||||
0.462838 | + | 0.886443i | \(0.346831\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.11684 | −0.311684 | ||||||||
\(101\) | −7.37228 | −0.733569 | −0.366785 | − | 0.930306i | \(-0.619541\pi\) | ||||
−0.366785 | + | 0.930306i | \(0.619541\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.0000 | −0.985329 | −0.492665 | − | 0.870219i | \(-0.663977\pi\) | ||||
−0.492665 | + | 0.870219i | \(0.663977\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.74456 | −0.266575 | ||||||||
\(107\) | 1.62772 | 0.157358 | 0.0786788 | − | 0.996900i | \(-0.474930\pi\) | ||||
0.0786788 | + | 0.996900i | \(0.474930\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | −6.00000 | −0.572078 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −1.37228 | −0.129093 | −0.0645467 | − | 0.997915i | \(-0.520560\pi\) | ||||
−0.0645467 | + | 0.997915i | \(0.520560\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.1168 | 0.943401 | ||||||||
\(116\) | −2.74456 | −0.254826 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.11684 | −0.655159 | ||||||||
\(119\) | 4.37228 | 0.400806 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.11684 | 0.737895 | ||||||||
\(122\) | −14.1168 | −1.27808 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.00000 | 0.179605 | ||||||||
\(125\) | −11.1386 | −0.996266 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.1168 | −1.25267 | −0.626334 | − | 0.779555i | \(-0.715445\pi\) | ||||
−0.626334 | + | 0.779555i | \(0.715445\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.74456 | 0.240714 | ||||||||
\(131\) | 7.37228 | 0.644119 | 0.322060 | − | 0.946719i | \(-0.395625\pi\) | ||||
0.322060 | + | 0.946719i | \(0.395625\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.00000 | 0.433555 | ||||||||
\(134\) | 15.1168 | 1.30590 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.37228 | 0.374920 | ||||||||
\(137\) | −16.3723 | −1.39878 | −0.699389 | − | 0.714741i | \(-0.746545\pi\) | ||||
−0.699389 | + | 0.714741i | \(0.746545\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.2337 | −1.80102 | −0.900509 | − | 0.434837i | \(-0.856806\pi\) | ||||
−0.900509 | + | 0.434837i | \(0.856806\pi\) | |||||||
\(140\) | 1.37228 | 0.115979 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.1168 | −0.848987 | ||||||||
\(143\) | −8.74456 | −0.731257 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.76631 | −0.312775 | ||||||||
\(146\) | −5.11684 | −0.423473 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | −14.7446 | −1.20792 | −0.603961 | − | 0.797014i | \(-0.706412\pi\) | ||||
−0.603961 | + | 0.797014i | \(0.706412\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.11684 | −0.660539 | −0.330270 | − | 0.943887i | \(-0.607140\pi\) | ||||
−0.330270 | + | 0.943887i | \(0.607140\pi\) | |||||||
\(152\) | 5.00000 | 0.405554 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.37228 | −0.352328 | ||||||||
\(155\) | 2.74456 | 0.220449 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.11684 | −0.647795 | −0.323897 | − | 0.946092i | \(-0.604993\pi\) | ||||
−0.323897 | + | 0.946092i | \(0.604993\pi\) | |||||||
\(158\) | 12.1168 | 0.963964 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.37228 | 0.108488 | ||||||||
\(161\) | 7.37228 | 0.581017 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.2337 | 1.27152 | 0.635760 | − | 0.771887i | \(-0.280687\pi\) | ||||
0.635760 | + | 0.771887i | \(0.280687\pi\) | |||||||
\(164\) | −10.3723 | −0.809939 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.48913 | 0.426039 | ||||||||
\(167\) | −17.4891 | −1.35335 | −0.676675 | − | 0.736282i | \(-0.736580\pi\) | ||||
−0.676675 | + | 0.736282i | \(0.736580\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 6.00000 | 0.460179 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.11684 | 0.695153 | ||||||||
\(173\) | 6.00000 | 0.456172 | 0.228086 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228086 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.11684 | −0.235611 | ||||||||
\(176\) | −4.37228 | −0.329573 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.25544 | −0.244005 | ||||||||
\(179\) | −14.7446 | −1.10206 | −0.551030 | − | 0.834485i | \(-0.685765\pi\) | ||||
−0.551030 | + | 0.834485i | \(0.685765\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.1168 | 1.34661 | 0.673307 | − | 0.739363i | \(-0.264873\pi\) | ||||
0.673307 | + | 0.739363i | \(0.264873\pi\) | |||||||
\(182\) | 2.00000 | 0.148250 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.37228 | 0.543492 | ||||||||
\(185\) | 2.74456 | 0.201784 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.1168 | −1.39796 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.86141 | 0.497779 | ||||||||
\(191\) | 1.88316 | 0.136260 | 0.0681302 | − | 0.997676i | \(-0.478297\pi\) | ||||
0.0681302 | + | 0.997676i | \(0.478297\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.00000 | −0.503871 | −0.251936 | − | 0.967744i | \(-0.581067\pi\) | ||||
−0.251936 | + | 0.967744i | \(0.581067\pi\) | |||||||
\(194\) | 9.11684 | 0.654551 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0000 | −0.708881 | −0.354441 | − | 0.935079i | \(-0.615329\pi\) | ||||
−0.354441 | + | 0.935079i | \(0.615329\pi\) | |||||||
\(200\) | −3.11684 | −0.220394 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.37228 | −0.518712 | ||||||||
\(203\) | −2.74456 | −0.192631 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.2337 | −0.994124 | ||||||||
\(206\) | −10.0000 | −0.696733 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | −21.8614 | −1.51219 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | −2.74456 | −0.188497 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.62772 | 0.111269 | ||||||||
\(215\) | 12.5109 | 0.853235 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | 14.0000 | 0.948200 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.00000 | −0.404520 | ||||||||
\(221\) | 8.74456 | 0.588223 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | −0.267860 | −0.133930 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133930 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.37228 | −0.0912828 | ||||||||
\(227\) | 23.7446 | 1.57598 | 0.787991 | − | 0.615687i | \(-0.211121\pi\) | ||||
0.787991 | + | 0.615687i | \(0.211121\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.1168 | −1.32936 | −0.664679 | − | 0.747129i | \(-0.731432\pi\) | ||||
−0.664679 | + | 0.747129i | \(0.731432\pi\) | |||||||
\(230\) | 10.1168 | 0.667085 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.74456 | −0.180189 | ||||||||
\(233\) | 11.7446 | 0.769412 | 0.384706 | − | 0.923039i | \(-0.374303\pi\) | ||||
0.384706 | + | 0.923039i | \(0.374303\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.11684 | −0.463267 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.37228 | 0.283413 | ||||||||
\(239\) | 18.8614 | 1.22004 | 0.610021 | − | 0.792385i | \(-0.291161\pi\) | ||||
0.610021 | + | 0.792385i | \(0.291161\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.883156 | 0.0568891 | 0.0284445 | − | 0.999595i | \(-0.490945\pi\) | ||||
0.0284445 | + | 0.999595i | \(0.490945\pi\) | |||||||
\(242\) | 8.11684 | 0.521770 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.1168 | −0.903738 | ||||||||
\(245\) | 1.37228 | 0.0876718 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.0000 | 0.636285 | ||||||||
\(248\) | 2.00000 | 0.127000 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.1386 | −0.704467 | ||||||||
\(251\) | 9.00000 | 0.568075 | 0.284037 | − | 0.958813i | \(-0.408326\pi\) | ||||
0.284037 | + | 0.958813i | \(0.408326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.2337 | −2.02651 | ||||||||
\(254\) | −14.1168 | −0.885770 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.8614 | −1.36368 | −0.681839 | − | 0.731503i | \(-0.738819\pi\) | ||||
−0.681839 | + | 0.731503i | \(0.738819\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.00000 | 0.124274 | ||||||||
\(260\) | 2.74456 | 0.170211 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.37228 | 0.455461 | ||||||||
\(263\) | −13.3723 | −0.824570 | −0.412285 | − | 0.911055i | \(-0.635269\pi\) | ||||
−0.412285 | + | 0.911055i | \(0.635269\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.76631 | −0.231363 | ||||||||
\(266\) | 5.00000 | 0.306570 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.1168 | 0.923408 | ||||||||
\(269\) | 7.37228 | 0.449496 | 0.224748 | − | 0.974417i | \(-0.427844\pi\) | ||||
0.224748 | + | 0.974417i | \(0.427844\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.2337 | −1.10762 | −0.553809 | − | 0.832644i | \(-0.686826\pi\) | ||||
−0.553809 | + | 0.832644i | \(0.686826\pi\) | |||||||
\(272\) | 4.37228 | 0.265108 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.3723 | −0.989086 | ||||||||
\(275\) | 13.6277 | 0.821782 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.2337 | 1.33589 | 0.667946 | − | 0.744209i | \(-0.267174\pi\) | ||||
0.667946 | + | 0.744209i | \(0.267174\pi\) | |||||||
\(278\) | −21.2337 | −1.27351 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.37228 | 0.0820095 | ||||||||
\(281\) | −10.6277 | −0.633997 | −0.316998 | − | 0.948426i | \(-0.602675\pi\) | ||||
−0.316998 | + | 0.948426i | \(0.602675\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.88316 | 0.587493 | 0.293746 | − | 0.955883i | \(-0.405098\pi\) | ||||
0.293746 | + | 0.955883i | \(0.405098\pi\) | |||||||
\(284\) | −10.1168 | −0.600324 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.74456 | −0.517077 | ||||||||
\(287\) | −10.3723 | −0.612256 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.11684 | 0.124520 | ||||||||
\(290\) | −3.76631 | −0.221165 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.11684 | −0.299441 | ||||||||
\(293\) | 4.62772 | 0.270354 | 0.135177 | − | 0.990821i | \(-0.456840\pi\) | ||||
0.135177 | + | 0.990821i | \(0.456840\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.76631 | −0.568617 | ||||||||
\(296\) | 2.00000 | 0.116248 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.7446 | −0.854130 | ||||||||
\(299\) | 14.7446 | 0.852700 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.11684 | 0.525486 | ||||||||
\(302\) | −8.11684 | −0.467072 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.00000 | 0.286770 | ||||||||
\(305\) | −19.3723 | −1.10925 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.0000 | −0.741949 | −0.370975 | − | 0.928643i | \(-0.620976\pi\) | ||||
−0.370975 | + | 0.928643i | \(0.620976\pi\) | |||||||
\(308\) | −4.37228 | −0.249134 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.74456 | 0.155881 | ||||||||
\(311\) | 26.2337 | 1.48758 | 0.743788 | − | 0.668416i | \(-0.233027\pi\) | ||||
0.743788 | + | 0.668416i | \(0.233027\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.88316 | −0.162966 | −0.0814828 | − | 0.996675i | \(-0.525966\pi\) | ||||
−0.0814828 | + | 0.996675i | \(0.525966\pi\) | |||||||
\(314\) | −8.11684 | −0.458060 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.1168 | 0.681626 | ||||||||
\(317\) | 6.00000 | 0.336994 | 0.168497 | − | 0.985702i | \(-0.446109\pi\) | ||||
0.168497 | + | 0.985702i | \(0.446109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0000 | 0.671871 | ||||||||
\(320\) | 1.37228 | 0.0767129 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.37228 | 0.410841 | ||||||||
\(323\) | 21.8614 | 1.21640 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.23369 | −0.345783 | ||||||||
\(326\) | 16.2337 | 0.899101 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.3723 | −0.572713 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.2337 | −0.672424 | −0.336212 | − | 0.941786i | \(-0.609146\pi\) | ||||
−0.336212 | + | 0.941786i | \(0.609146\pi\) | |||||||
\(332\) | 5.48913 | 0.301255 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −17.4891 | −0.956962 | ||||||||
\(335\) | 20.7446 | 1.13340 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.11684 | 0.496626 | 0.248313 | − | 0.968680i | \(-0.420124\pi\) | ||||
0.248313 | + | 0.968680i | \(0.420124\pi\) | |||||||
\(338\) | −9.00000 | −0.489535 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.00000 | 0.325396 | ||||||||
\(341\) | −8.74456 | −0.473545 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 9.11684 | 0.491547 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.00000 | 0.322562 | ||||||||
\(347\) | −7.11684 | −0.382052 | −0.191026 | − | 0.981585i | \(-0.561182\pi\) | ||||
−0.191026 | + | 0.981585i | \(0.561182\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.0000 | −1.17763 | −0.588817 | − | 0.808267i | \(-0.700406\pi\) | ||||
−0.588817 | + | 0.808267i | \(0.700406\pi\) | |||||||
\(350\) | −3.11684 | −0.166602 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.37228 | −0.233043 | ||||||||
\(353\) | 7.62772 | 0.405983 | 0.202991 | − | 0.979181i | \(-0.434934\pi\) | ||||
0.202991 | + | 0.979181i | \(0.434934\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.8832 | −0.736841 | ||||||||
\(356\) | −3.25544 | −0.172538 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.7446 | −0.779274 | ||||||||
\(359\) | 6.86141 | 0.362131 | 0.181066 | − | 0.983471i | \(-0.442045\pi\) | ||||
0.181066 | + | 0.983471i | \(0.442045\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | 18.1168 | 0.952200 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | −7.02175 | −0.367535 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.2337 | 1.16059 | 0.580295 | − | 0.814407i | \(-0.302937\pi\) | ||||
0.580295 | + | 0.814407i | \(0.302937\pi\) | |||||||
\(368\) | 7.37228 | 0.384307 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.74456 | 0.142683 | ||||||||
\(371\) | −2.74456 | −0.142491 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | −19.1168 | −0.988508 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.48913 | −0.282704 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.11684 | 0.468301 | 0.234150 | − | 0.972200i | \(-0.424769\pi\) | ||||
0.234150 | + | 0.972200i | \(0.424769\pi\) | |||||||
\(380\) | 6.86141 | 0.351983 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.88316 | 0.0963506 | ||||||||
\(383\) | 21.2554 | 1.08610 | 0.543051 | − | 0.839700i | \(-0.317269\pi\) | ||||
0.543051 | + | 0.839700i | \(0.317269\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00000 | −0.305788 | ||||||||
\(386\) | −7.00000 | −0.356291 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.11684 | 0.462838 | ||||||||
\(389\) | 34.9783 | 1.77347 | 0.886734 | − | 0.462280i | \(-0.152969\pi\) | ||||
0.886734 | + | 0.462280i | \(0.152969\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.2337 | 1.63013 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.00000 | 0.302276 | ||||||||
\(395\) | 16.6277 | 0.836631 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.0000 | −1.10415 | −0.552074 | − | 0.833795i | \(-0.686163\pi\) | ||||
−0.552074 | + | 0.833795i | \(0.686163\pi\) | |||||||
\(398\) | −10.0000 | −0.501255 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.11684 | −0.155842 | ||||||||
\(401\) | 0.255437 | 0.0127559 | 0.00637797 | − | 0.999980i | \(-0.497970\pi\) | ||||
0.00637797 | + | 0.999980i | \(0.497970\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000 | 0.199254 | ||||||||
\(404\) | −7.37228 | −0.366785 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.74456 | −0.136210 | ||||||||
\(407\) | −8.74456 | −0.433452 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.3505 | 1.45129 | 0.725645 | − | 0.688069i | \(-0.241541\pi\) | ||||
0.725645 | + | 0.688069i | \(0.241541\pi\) | |||||||
\(410\) | −14.2337 | −0.702952 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.0000 | −0.492665 | ||||||||
\(413\) | −7.11684 | −0.350197 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.53262 | 0.369762 | ||||||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −21.8614 | −1.06928 | ||||||||
\(419\) | −27.6060 | −1.34864 | −0.674320 | − | 0.738439i | \(-0.735563\pi\) | ||||
−0.674320 | + | 0.738439i | \(0.735563\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.233688 | −0.0113893 | −0.00569463 | − | 0.999984i | \(-0.501813\pi\) | ||||
−0.00569463 | + | 0.999984i | \(0.501813\pi\) | |||||||
\(422\) | −16.0000 | −0.778868 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.74456 | −0.133288 | ||||||||
\(425\) | −13.6277 | −0.661041 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.1168 | −0.683162 | ||||||||
\(428\) | 1.62772 | 0.0786788 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.5109 | 0.603328 | ||||||||
\(431\) | 29.4891 | 1.42044 | 0.710221 | − | 0.703979i | \(-0.248595\pi\) | ||||
0.710221 | + | 0.703979i | \(0.248595\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.88316 | −0.138556 | −0.0692778 | − | 0.997597i | \(-0.522069\pi\) | ||||
−0.0692778 | + | 0.997597i | \(0.522069\pi\) | |||||||
\(434\) | 2.00000 | 0.0960031 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.0000 | 0.670478 | ||||||||
\(437\) | 36.8614 | 1.76332 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | −6.00000 | −0.286039 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.74456 | 0.415936 | ||||||||
\(443\) | 22.8832 | 1.08721 | 0.543606 | − | 0.839341i | \(-0.317059\pi\) | ||||
0.543606 | + | 0.839341i | \(0.317059\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.46738 | −0.211774 | ||||||||
\(446\) | −4.00000 | −0.189405 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −33.0000 | −1.55737 | −0.778683 | − | 0.627417i | \(-0.784112\pi\) | ||||
−0.778683 | + | 0.627417i | \(0.784112\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 45.3505 | 2.13547 | ||||||||
\(452\) | −1.37228 | −0.0645467 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 23.7446 | 1.11439 | ||||||||
\(455\) | 2.74456 | 0.128667 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.4674 | 1.56554 | 0.782769 | − | 0.622312i | \(-0.213807\pi\) | ||||
0.782769 | + | 0.622312i | \(0.213807\pi\) | |||||||
\(458\) | −20.1168 | −0.939998 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10.1168 | 0.471700 | ||||||||
\(461\) | −30.8614 | −1.43736 | −0.718680 | − | 0.695341i | \(-0.755253\pi\) | ||||
−0.718680 | + | 0.695341i | \(0.755253\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.88316 | −0.273413 | −0.136707 | − | 0.990612i | \(-0.543652\pi\) | ||||
−0.136707 | + | 0.990612i | \(0.543652\pi\) | |||||||
\(464\) | −2.74456 | −0.127413 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.7446 | 0.544056 | ||||||||
\(467\) | 30.0951 | 1.39263 | 0.696317 | − | 0.717734i | \(-0.254821\pi\) | ||||
0.696317 | + | 0.717734i | \(0.254821\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.1168 | 0.698031 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.11684 | −0.327579 | ||||||||
\(473\) | −39.8614 | −1.83283 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.5842 | −0.715053 | ||||||||
\(476\) | 4.37228 | 0.200403 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.8614 | 0.862701 | ||||||||
\(479\) | −21.2554 | −0.971186 | −0.485593 | − | 0.874185i | \(-0.661396\pi\) | ||||
−0.485593 | + | 0.874185i | \(0.661396\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | 0.182384 | ||||||||
\(482\) | 0.883156 | 0.0402267 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.11684 | 0.368947 | ||||||||
\(485\) | 12.5109 | 0.568090 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.3505 | −0.740913 | −0.370457 | − | 0.928850i | \(-0.620799\pi\) | ||||
−0.370457 | + | 0.928850i | \(0.620799\pi\) | |||||||
\(488\) | −14.1168 | −0.639040 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.37228 | 0.0619934 | ||||||||
\(491\) | 19.6277 | 0.885787 | 0.442893 | − | 0.896574i | \(-0.353952\pi\) | ||||
0.442893 | + | 0.896574i | \(0.353952\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.0000 | −0.540453 | ||||||||
\(494\) | 10.0000 | 0.449921 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −10.1168 | −0.453802 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.883156 | 0.0395355 | 0.0197677 | − | 0.999805i | \(-0.493707\pi\) | ||||
0.0197677 | + | 0.999805i | \(0.493707\pi\) | |||||||
\(500\) | −11.1386 | −0.498133 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.00000 | 0.401690 | ||||||||
\(503\) | −2.23369 | −0.0995952 | −0.0497976 | − | 0.998759i | \(-0.515858\pi\) | ||||
−0.0497976 | + | 0.998759i | \(0.515858\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.1168 | −0.450194 | ||||||||
\(506\) | −32.2337 | −1.43296 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.1168 | −0.626334 | ||||||||
\(509\) | −16.9783 | −0.752548 | −0.376274 | − | 0.926508i | \(-0.622795\pi\) | ||||
−0.376274 | + | 0.926508i | \(0.622795\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.11684 | −0.226356 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −21.8614 | −0.964265 | ||||||||
\(515\) | −13.7228 | −0.604699 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 2.00000 | 0.0878750 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.74456 | 0.120357 | ||||||||
\(521\) | −3.86141 | −0.169171 | −0.0845856 | − | 0.996416i | \(-0.526957\pi\) | ||||
−0.0845856 | + | 0.996416i | \(0.526957\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.8832 | −0.781976 | −0.390988 | − | 0.920396i | \(-0.627867\pi\) | ||||
−0.390988 | + | 0.920396i | \(0.627867\pi\) | |||||||
\(524\) | 7.37228 | 0.322060 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.3723 | −0.583059 | ||||||||
\(527\) | 8.74456 | 0.380919 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 31.3505 | 1.36307 | ||||||||
\(530\) | −3.76631 | −0.163598 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.00000 | 0.216777 | ||||||||
\(533\) | −20.7446 | −0.898547 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.23369 | 0.0965708 | ||||||||
\(536\) | 15.1168 | 0.652948 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.37228 | 0.317842 | ||||||||
\(539\) | −4.37228 | −0.188327 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.2337 | 1.21386 | 0.606931 | − | 0.794755i | \(-0.292401\pi\) | ||||
0.606931 | + | 0.794755i | \(0.292401\pi\) | |||||||
\(542\) | −18.2337 | −0.783204 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.37228 | 0.187460 | ||||||||
\(545\) | 19.2119 | 0.822949 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.883156 | 0.0377610 | 0.0188805 | − | 0.999822i | \(-0.493990\pi\) | ||||
0.0188805 | + | 0.999822i | \(0.493990\pi\) | |||||||
\(548\) | −16.3723 | −0.699389 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 13.6277 | 0.581088 | ||||||||
\(551\) | −13.7228 | −0.584611 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.1168 | 0.515261 | ||||||||
\(554\) | 22.2337 | 0.944619 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.2337 | −0.900509 | ||||||||
\(557\) | −6.51087 | −0.275875 | −0.137937 | − | 0.990441i | \(-0.544047\pi\) | ||||
−0.137937 | + | 0.990441i | \(0.544047\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.2337 | 0.771203 | ||||||||
\(560\) | 1.37228 | 0.0579895 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.6277 | −0.448303 | ||||||||
\(563\) | −3.00000 | −0.126435 | −0.0632175 | − | 0.998000i | \(-0.520136\pi\) | ||||
−0.0632175 | + | 0.998000i | \(0.520136\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.88316 | −0.0792250 | ||||||||
\(566\) | 9.88316 | 0.415420 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.1168 | −0.424493 | ||||||||
\(569\) | 1.11684 | 0.0468205 | 0.0234103 | − | 0.999726i | \(-0.492548\pi\) | ||||
0.0234103 | + | 0.999726i | \(0.492548\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.3505 | 1.22828 | 0.614141 | − | 0.789197i | \(-0.289503\pi\) | ||||
0.614141 | + | 0.789197i | \(0.289503\pi\) | |||||||
\(572\) | −8.74456 | −0.365629 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.3723 | −0.432931 | ||||||||
\(575\) | −22.9783 | −0.958259 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.1168 | 1.12889 | 0.564444 | − | 0.825471i | \(-0.309090\pi\) | ||||
0.564444 | + | 0.825471i | \(0.309090\pi\) | |||||||
\(578\) | 2.11684 | 0.0880491 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.76631 | −0.156388 | ||||||||
\(581\) | 5.48913 | 0.227727 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0000 | 0.496989 | ||||||||
\(584\) | −5.11684 | −0.211737 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.62772 | 0.191169 | ||||||||
\(587\) | 8.48913 | 0.350384 | 0.175192 | − | 0.984534i | \(-0.443945\pi\) | ||||
0.175192 | + | 0.984534i | \(0.443945\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.0000 | 0.412043 | ||||||||
\(590\) | −9.76631 | −0.402073 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.00000 | 0.0821995 | ||||||||
\(593\) | −3.25544 | −0.133685 | −0.0668424 | − | 0.997764i | \(-0.521292\pi\) | ||||
−0.0668424 | + | 0.997764i | \(0.521292\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.00000 | 0.245976 | ||||||||
\(596\) | −14.7446 | −0.603961 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 14.7446 | 0.602950 | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.88316 | 0.280770 | 0.140385 | − | 0.990097i | \(-0.455166\pi\) | ||||
0.140385 | + | 0.990097i | \(0.455166\pi\) | |||||||
\(602\) | 9.11684 | 0.371575 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.11684 | −0.330270 | ||||||||
\(605\) | 11.1386 | 0.452848 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.2337 | −0.496550 | −0.248275 | − | 0.968690i | \(-0.579864\pi\) | ||||
−0.248275 | + | 0.968690i | \(0.579864\pi\) | |||||||
\(608\) | 5.00000 | 0.202777 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.3723 | −0.784361 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.76631 | −0.0713407 | −0.0356703 | − | 0.999364i | \(-0.511357\pi\) | ||||
−0.0356703 | + | 0.999364i | \(0.511357\pi\) | |||||||
\(614\) | −13.0000 | −0.524637 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.37228 | −0.176164 | ||||||||
\(617\) | 9.86141 | 0.397005 | 0.198503 | − | 0.980100i | \(-0.436392\pi\) | ||||
0.198503 | + | 0.980100i | \(0.436392\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.4674 | −0.943233 | −0.471617 | − | 0.881804i | \(-0.656329\pi\) | ||||
−0.471617 | + | 0.881804i | \(0.656329\pi\) | |||||||
\(620\) | 2.74456 | 0.110224 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26.2337 | 1.05188 | ||||||||
\(623\) | −3.25544 | −0.130426 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.298936 | 0.0119574 | ||||||||
\(626\) | −2.88316 | −0.115234 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.11684 | −0.323897 | ||||||||
\(629\) | 8.74456 | 0.348669 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.3505 | 0.571286 | 0.285643 | − | 0.958336i | \(-0.407793\pi\) | ||||
0.285643 | + | 0.958336i | \(0.407793\pi\) | |||||||
\(632\) | 12.1168 | 0.481982 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.00000 | 0.238290 | ||||||||
\(635\) | −19.3723 | −0.768766 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | 0.0792429 | ||||||||
\(638\) | 12.0000 | 0.475085 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.37228 | 0.0542442 | ||||||||
\(641\) | 46.2119 | 1.82526 | 0.912631 | − | 0.408785i | \(-0.134047\pi\) | ||||
0.912631 | + | 0.408785i | \(0.134047\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.3505 | −0.999727 | −0.499864 | − | 0.866104i | \(-0.666617\pi\) | ||||
−0.499864 | + | 0.866104i | \(0.666617\pi\) | |||||||
\(644\) | 7.37228 | 0.290509 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 21.8614 | 0.860126 | ||||||||
\(647\) | 17.4891 | 0.687568 | 0.343784 | − | 0.939049i | \(-0.388291\pi\) | ||||
0.343784 | + | 0.939049i | \(0.388291\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.1168 | 1.22144 | ||||||||
\(650\) | −6.23369 | −0.244505 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.2337 | 0.635760 | ||||||||
\(653\) | 15.2554 | 0.596991 | 0.298496 | − | 0.954411i | \(-0.403515\pi\) | ||||
0.298496 | + | 0.954411i | \(0.403515\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.1168 | 0.395298 | ||||||||
\(656\) | −10.3723 | −0.404970 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.25544 | 0.360541 | 0.180270 | − | 0.983617i | \(-0.442303\pi\) | ||||
0.180270 | + | 0.983617i | \(0.442303\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.88316 | 0.384410 | 0.192205 | − | 0.981355i | \(-0.438436\pi\) | ||||
0.192205 | + | 0.981355i | \(0.438436\pi\) | |||||||
\(662\) | −12.2337 | −0.475476 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.48913 | 0.213019 | ||||||||
\(665\) | 6.86141 | 0.266074 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.2337 | −0.783452 | ||||||||
\(668\) | −17.4891 | −0.676675 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 20.7446 | 0.801432 | ||||||||
\(671\) | 61.7228 | 2.38278 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.1168 | −0.775447 | −0.387724 | − | 0.921776i | \(-0.626739\pi\) | ||||
−0.387724 | + | 0.921776i | \(0.626739\pi\) | |||||||
\(674\) | 9.11684 | 0.351168 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 34.4674 | 1.32469 | 0.662344 | − | 0.749199i | \(-0.269562\pi\) | ||||
0.662344 | + | 0.749199i | \(0.269562\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.11684 | 0.349872 | ||||||||
\(680\) | 6.00000 | 0.230089 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.74456 | −0.334847 | ||||||||
\(683\) | 44.8397 | 1.71574 | 0.857871 | − | 0.513865i | \(-0.171787\pi\) | ||||
0.857871 | + | 0.513865i | \(0.171787\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.4674 | −0.858434 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.11684 | 0.347576 | ||||||||
\(689\) | −5.48913 | −0.209119 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.88316 | −0.223806 | −0.111903 | − | 0.993719i | \(-0.535695\pi\) | ||||
−0.111903 | + | 0.993719i | \(0.535695\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.11684 | −0.270152 | ||||||||
\(695\) | −29.1386 | −1.10529 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −45.3505 | −1.71777 | ||||||||
\(698\) | −22.0000 | −0.832712 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.11684 | −0.117806 | ||||||||
\(701\) | 3.76631 | 0.142252 | 0.0711258 | − | 0.997467i | \(-0.477341\pi\) | ||||
0.0711258 | + | 0.997467i | \(0.477341\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.0000 | 0.377157 | ||||||||
\(704\) | −4.37228 | −0.164787 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.62772 | 0.287073 | ||||||||
\(707\) | −7.37228 | −0.277263 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.0000 | 1.65245 | 0.826227 | − | 0.563337i | \(-0.190483\pi\) | ||||
0.826227 | + | 0.563337i | \(0.190483\pi\) | |||||||
\(710\) | −13.8832 | −0.521026 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.25544 | −0.122003 | ||||||||
\(713\) | 14.7446 | 0.552188 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0000 | −0.448775 | ||||||||
\(716\) | −14.7446 | −0.551030 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.86141 | 0.256065 | ||||||||
\(719\) | 8.74456 | 0.326117 | 0.163059 | − | 0.986616i | \(-0.447864\pi\) | ||||
0.163059 | + | 0.986616i | \(0.447864\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.0000 | −0.372419 | ||||||||
\(722\) | 6.00000 | 0.223297 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.1168 | 0.673307 | ||||||||
\(725\) | 8.55437 | 0.317701 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.76631 | −0.0655089 | −0.0327544 | − | 0.999463i | \(-0.510428\pi\) | ||||
−0.0327544 | + | 0.999463i | \(0.510428\pi\) | |||||||
\(728\) | 2.00000 | 0.0741249 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.02175 | −0.259887 | ||||||||
\(731\) | 39.8614 | 1.47433 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.8832 | −0.882144 | −0.441072 | − | 0.897472i | \(-0.645402\pi\) | ||||
−0.441072 | + | 0.897472i | \(0.645402\pi\) | |||||||
\(734\) | 22.2337 | 0.820660 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.37228 | 0.271746 | ||||||||
\(737\) | −66.0951 | −2.43464 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.11684 | 0.335369 | 0.167684 | − | 0.985841i | \(-0.446371\pi\) | ||||
0.167684 | + | 0.985841i | \(0.446371\pi\) | |||||||
\(740\) | 2.74456 | 0.100892 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.74456 | −0.100756 | ||||||||
\(743\) | −43.7228 | −1.60403 | −0.802017 | − | 0.597301i | \(-0.796240\pi\) | ||||
−0.802017 | + | 0.597301i | \(0.796240\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.2337 | −0.741305 | ||||||||
\(746\) | −10.0000 | −0.366126 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −19.1168 | −0.698981 | ||||||||
\(749\) | 1.62772 | 0.0594755 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.116844 | 0.00426370 | 0.00213185 | − | 0.999998i | \(-0.499321\pi\) | ||||
0.00213185 | + | 0.999998i | \(0.499321\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.48913 | −0.199902 | ||||||||
\(755\) | −11.1386 | −0.405375 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.7663 | 0.427654 | 0.213827 | − | 0.976872i | \(-0.431407\pi\) | ||||
0.213827 | + | 0.976872i | \(0.431407\pi\) | |||||||
\(758\) | 9.11684 | 0.331139 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.86141 | 0.248889 | ||||||||
\(761\) | −12.5109 | −0.453519 | −0.226759 | − | 0.973951i | \(-0.572813\pi\) | ||||
−0.226759 | + | 0.973951i | \(0.572813\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.0000 | 0.506834 | ||||||||
\(764\) | 1.88316 | 0.0681302 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.2554 | 0.767990 | ||||||||
\(767\) | −14.2337 | −0.513949 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.0000 | −0.360609 | −0.180305 | − | 0.983611i | \(-0.557708\pi\) | ||||
−0.180305 | + | 0.983611i | \(0.557708\pi\) | |||||||
\(770\) | −6.00000 | −0.216225 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.00000 | −0.251936 | ||||||||
\(773\) | 11.1386 | 0.400627 | 0.200314 | − | 0.979732i | \(-0.435804\pi\) | ||||
0.200314 | + | 0.979732i | \(0.435804\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.23369 | −0.223921 | ||||||||
\(776\) | 9.11684 | 0.327276 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 34.9783 | 1.25403 | ||||||||
\(779\) | −51.8614 | −1.85813 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44.2337 | 1.58281 | ||||||||
\(782\) | 32.2337 | 1.15267 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −11.1386 | −0.397553 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.00000 | −0.142585 | −0.0712923 | − | 0.997455i | \(-0.522712\pi\) | ||||
−0.0712923 | + | 0.997455i | \(0.522712\pi\) | |||||||
\(788\) | 6.00000 | 0.213741 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 16.6277 | 0.591588 | ||||||||
\(791\) | −1.37228 | −0.0487927 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28.2337 | −1.00261 | ||||||||
\(794\) | −22.0000 | −0.780751 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.0000 | −0.354441 | ||||||||
\(797\) | 36.8614 | 1.30570 | 0.652849 | − | 0.757488i | \(-0.273574\pi\) | ||||
0.652849 | + | 0.757488i | \(0.273574\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −3.11684 | −0.110197 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.255437 | 0.00901981 | ||||||||
\(803\) | 22.3723 | 0.789501 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.1168 | 0.356572 | ||||||||
\(806\) | 4.00000 | 0.140894 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.37228 | −0.259356 | ||||||||
\(809\) | −21.8614 | −0.768606 | −0.384303 | − | 0.923207i | \(-0.625558\pi\) | ||||
−0.384303 | + | 0.923207i | \(0.625558\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.8832 | 0.873766 | 0.436883 | − | 0.899518i | \(-0.356082\pi\) | ||||
0.436883 | + | 0.899518i | \(0.356082\pi\) | |||||||
\(812\) | −2.74456 | −0.0963153 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.74456 | −0.306497 | ||||||||
\(815\) | 22.2772 | 0.780336 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 45.5842 | 1.59479 | ||||||||
\(818\) | 29.3505 | 1.02622 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14.2337 | −0.497062 | ||||||||
\(821\) | 38.2337 | 1.33436 | 0.667182 | − | 0.744894i | \(-0.267500\pi\) | ||||
0.667182 | + | 0.744894i | \(0.267500\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.2337 | 0.775018 | 0.387509 | − | 0.921866i | \(-0.373336\pi\) | ||||
0.387509 | + | 0.921866i | \(0.373336\pi\) | |||||||
\(824\) | −10.0000 | −0.348367 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.11684 | −0.247627 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −48.2337 | −1.67523 | −0.837613 | − | 0.546265i | \(-0.816049\pi\) | ||||
−0.837613 | + | 0.546265i | \(0.816049\pi\) | |||||||
\(830\) | 7.53262 | 0.261461 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | 4.37228 | 0.151491 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.0000 | −0.830554 | ||||||||
\(836\) | −21.8614 | −0.756093 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −27.6060 | −0.953632 | ||||||||
\(839\) | 17.4891 | 0.603792 | 0.301896 | − | 0.953341i | \(-0.402381\pi\) | ||||
0.301896 | + | 0.953341i | \(0.402381\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.4674 | −0.740254 | ||||||||
\(842\) | −0.233688 | −0.00805342 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.0000 | −0.550743 | ||||||||
\(845\) | −12.3505 | −0.424871 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.11684 | 0.278898 | ||||||||
\(848\) | −2.74456 | −0.0942487 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13.6277 | −0.467427 | ||||||||
\(851\) | 14.7446 | 0.505437 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.8832 | −0.612308 | −0.306154 | − | 0.951982i | \(-0.599042\pi\) | ||||
−0.306154 | + | 0.951982i | \(0.599042\pi\) | |||||||
\(854\) | −14.1168 | −0.483068 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.62772 | 0.0556343 | ||||||||
\(857\) | −51.9565 | −1.77480 | −0.887400 | − | 0.461000i | \(-0.847491\pi\) | ||||
−0.887400 | + | 0.461000i | \(0.847491\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.1168 | 1.74408 | 0.872042 | − | 0.489431i | \(-0.162795\pi\) | ||||
0.872042 | + | 0.489431i | \(0.162795\pi\) | |||||||
\(860\) | 12.5109 | 0.426617 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 29.4891 | 1.00440 | ||||||||
\(863\) | 18.8614 | 0.642050 | 0.321025 | − | 0.947071i | \(-0.395973\pi\) | ||||
0.321025 | + | 0.947071i | \(0.395973\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.23369 | 0.279954 | ||||||||
\(866\) | −2.88316 | −0.0979736 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.00000 | 0.0678844 | ||||||||
\(869\) | −52.9783 | −1.79716 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.2337 | 1.02443 | ||||||||
\(872\) | 14.0000 | 0.474100 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 36.8614 | 1.24686 | ||||||||
\(875\) | −11.1386 | −0.376553 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.7011 | 1.50945 | 0.754724 | − | 0.656043i | \(-0.227771\pi\) | ||||
0.754724 | + | 0.656043i | \(0.227771\pi\) | |||||||
\(878\) | 8.00000 | 0.269987 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.00000 | −0.202260 | ||||||||
\(881\) | −14.2337 | −0.479545 | −0.239773 | − | 0.970829i | \(-0.577073\pi\) | ||||
−0.239773 | + | 0.970829i | \(0.577073\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.3505 | 0.381976 | 0.190988 | − | 0.981592i | \(-0.438831\pi\) | ||||
0.190988 | + | 0.981592i | \(0.438831\pi\) | |||||||
\(884\) | 8.74456 | 0.294111 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22.8832 | 0.768775 | ||||||||
\(887\) | 31.7228 | 1.06515 | 0.532574 | − | 0.846383i | \(-0.321225\pi\) | ||||
0.532574 | + | 0.846383i | \(0.321225\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.1168 | −0.473464 | ||||||||
\(890\) | −4.46738 | −0.149747 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.00000 | −0.133930 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.2337 | −0.676338 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.0000 | −1.10122 | ||||||||
\(899\) | −5.48913 | −0.183073 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0000 | −0.399778 | ||||||||
\(902\) | 45.3505 | 1.51001 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.37228 | −0.0456414 | ||||||||
\(905\) | 24.8614 | 0.826421 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.88316 | −0.294960 | −0.147480 | − | 0.989065i | \(-0.547116\pi\) | ||||
−0.147480 | + | 0.989065i | \(0.547116\pi\) | |||||||
\(908\) | 23.7446 | 0.787991 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.74456 | 0.0909814 | ||||||||
\(911\) | 43.3723 | 1.43699 | 0.718494 | − | 0.695533i | \(-0.244832\pi\) | ||||
0.718494 | + | 0.695533i | \(0.244832\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.0000 | −0.794284 | ||||||||
\(914\) | 33.4674 | 1.10700 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −20.1168 | −0.664679 | ||||||||
\(917\) | 7.37228 | 0.243454 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.8832 | −0.985754 | −0.492877 | − | 0.870099i | \(-0.664055\pi\) | ||||
−0.492877 | + | 0.870099i | \(0.664055\pi\) | |||||||
\(920\) | 10.1168 | 0.333542 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −30.8614 | −1.01637 | ||||||||
\(923\) | −20.2337 | −0.666000 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.23369 | −0.204962 | ||||||||
\(926\) | −5.88316 | −0.193333 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.74456 | −0.0900947 | ||||||||
\(929\) | −9.76631 | −0.320422 | −0.160211 | − | 0.987083i | \(-0.551218\pi\) | ||||
−0.160211 | + | 0.987083i | \(0.551218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.00000 | 0.163868 | ||||||||
\(932\) | 11.7446 | 0.384706 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.0951 | 0.984742 | ||||||||
\(935\) | −26.2337 | −0.857933 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.4674 | −1.25667 | −0.628337 | − | 0.777941i | \(-0.716264\pi\) | ||||
−0.628337 | + | 0.777941i | \(0.716264\pi\) | |||||||
\(938\) | 15.1168 | 0.493582 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.88316 | −0.0613891 | −0.0306946 | − | 0.999529i | \(-0.509772\pi\) | ||||
−0.0306946 | + | 0.999529i | \(0.509772\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −76.4674 | −2.49012 | ||||||||
\(944\) | −7.11684 | −0.231634 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −39.8614 | −1.29601 | ||||||||
\(947\) | −16.8832 | −0.548629 | −0.274314 | − | 0.961640i | \(-0.588451\pi\) | ||||
−0.274314 | + | 0.961640i | \(0.588451\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.2337 | −0.332200 | ||||||||
\(950\) | −15.5842 | −0.505619 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.37228 | 0.141706 | ||||||||
\(953\) | −10.8832 | −0.352540 | −0.176270 | − | 0.984342i | \(-0.556403\pi\) | ||||
−0.176270 | + | 0.984342i | \(0.556403\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.58422 | 0.0836234 | ||||||||
\(956\) | 18.8614 | 0.610021 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.2554 | −0.686732 | ||||||||
\(959\) | −16.3723 | −0.528689 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 4.00000 | 0.128965 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.883156 | 0.0284445 | ||||||||
\(965\) | −9.60597 | −0.309227 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.1168 | 1.54733 | 0.773667 | − | 0.633593i | \(-0.218421\pi\) | ||||
0.773667 | + | 0.633593i | \(0.218421\pi\) | |||||||
\(968\) | 8.11684 | 0.260885 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 12.5109 | 0.401700 | ||||||||
\(971\) | −7.37228 | −0.236588 | −0.118294 | − | 0.992979i | \(-0.537742\pi\) | ||||
−0.118294 | + | 0.992979i | \(0.537742\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.2337 | −0.680721 | ||||||||
\(974\) | −16.3505 | −0.523905 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.1168 | −0.451869 | ||||||||
\(977\) | −22.8832 | −0.732097 | −0.366049 | − | 0.930596i | \(-0.619290\pi\) | ||||
−0.366049 | + | 0.930596i | \(0.619290\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.2337 | 0.454911 | ||||||||
\(980\) | 1.37228 | 0.0438359 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 19.6277 | 0.626346 | ||||||||
\(983\) | 50.7446 | 1.61850 | 0.809250 | − | 0.587464i | \(-0.199874\pi\) | ||||
0.809250 | + | 0.587464i | \(0.199874\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.23369 | 0.262347 | ||||||||
\(986\) | −12.0000 | −0.382158 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.0000 | 0.318142 | ||||||||
\(989\) | 67.2119 | 2.13722 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.4674 | −0.650168 | −0.325084 | − | 0.945685i | \(-0.605393\pi\) | ||||
−0.325084 | + | 0.945685i | \(0.605393\pi\) | |||||||
\(992\) | 2.00000 | 0.0635001 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10.1168 | −0.320887 | ||||||||
\(995\) | −13.7228 | −0.435042 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.1168 | 0.383744 | 0.191872 | − | 0.981420i | \(-0.438544\pi\) | ||||
0.191872 | + | 0.981420i | \(0.438544\pi\) | |||||||
\(998\) | 0.883156 | 0.0279558 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))