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: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) 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 | ||||||||
\(5\) | −1.73205 | −0.774597 | −0.387298 | − | 0.921954i | \(-0.626592\pi\) | ||||
−0.387298 | + | 0.921954i | \(0.626592\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.73205 | 0.547723 | ||||||||
\(11\) | −1.26795 | −0.382301 | −0.191151 | − | 0.981561i | \(-0.561222\pi\) | ||||
−0.191151 | + | 0.981561i | \(0.561222\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.464102 | 0.112561 | 0.0562806 | − | 0.998415i | \(-0.482076\pi\) | ||||
0.0562806 | + | 0.998415i | \(0.482076\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.19615 | 0.962663 | 0.481332 | − | 0.876539i | \(-0.340153\pi\) | ||||
0.481332 | + | 0.876539i | \(0.340153\pi\) | |||||||
\(20\) | −1.73205 | −0.387298 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.26795 | 0.270328 | ||||||||
\(23\) | −4.73205 | −0.986701 | −0.493350 | − | 0.869831i | \(-0.664228\pi\) | ||||
−0.493350 | + | 0.869831i | \(0.664228\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | −0.400000 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 0.464102 | 0.0861815 | 0.0430908 | − | 0.999071i | \(-0.486280\pi\) | ||||
0.0430908 | + | 0.999071i | \(0.486280\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.19615 | −1.11286 | −0.556431 | − | 0.830894i | \(-0.687830\pi\) | ||||
−0.556431 | + | 0.830894i | \(0.687830\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.464102 | −0.0795928 | ||||||||
\(35\) | −1.73205 | −0.292770 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.19615 | 1.18304 | 0.591520 | − | 0.806290i | \(-0.298528\pi\) | ||||
0.591520 | + | 0.806290i | \(0.298528\pi\) | |||||||
\(38\) | −4.19615 | −0.680706 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.73205 | 0.273861 | ||||||||
\(41\) | −9.46410 | −1.47804 | −0.739022 | − | 0.673681i | \(-0.764712\pi\) | ||||
−0.739022 | + | 0.673681i | \(0.764712\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.39230 | −1.27981 | −0.639907 | − | 0.768452i | \(-0.721027\pi\) | ||||
−0.639907 | + | 0.768452i | \(0.721027\pi\) | |||||||
\(44\) | −1.26795 | −0.191151 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.73205 | 0.697703 | ||||||||
\(47\) | 8.19615 | 1.19553 | 0.597766 | − | 0.801671i | \(-0.296055\pi\) | ||||
0.597766 | + | 0.801671i | \(0.296055\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.00000 | 0.282843 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −2.53590 | −0.348332 | −0.174166 | − | 0.984716i | \(-0.555723\pi\) | ||||
−0.174166 | + | 0.984716i | \(0.555723\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.19615 | 0.296129 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.464102 | −0.0609395 | ||||||||
\(59\) | −2.19615 | −0.285915 | −0.142957 | − | 0.989729i | \(-0.545661\pi\) | ||||
−0.142957 | + | 0.989729i | \(0.545661\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.3923 | −1.45864 | −0.729318 | − | 0.684175i | \(-0.760162\pi\) | ||||
−0.729318 | + | 0.684175i | \(0.760162\pi\) | |||||||
\(62\) | 6.19615 | 0.786912 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.73205 | 0.214834 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.19615 | −0.756980 | −0.378490 | − | 0.925605i | \(-0.623557\pi\) | ||||
−0.378490 | + | 0.925605i | \(0.623557\pi\) | |||||||
\(68\) | 0.464102 | 0.0562806 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.73205 | 0.207020 | ||||||||
\(71\) | −16.3923 | −1.94541 | −0.972704 | − | 0.232048i | \(-0.925457\pi\) | ||||
−0.972704 | + | 0.232048i | \(0.925457\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.19615 | 0.139999 | 0.0699995 | − | 0.997547i | \(-0.477700\pi\) | ||||
0.0699995 | + | 0.997547i | \(0.477700\pi\) | |||||||
\(74\) | −7.19615 | −0.836536 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.19615 | 0.481332 | ||||||||
\(77\) | −1.26795 | −0.144496 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.19615 | 0.472104 | 0.236052 | − | 0.971740i | \(-0.424146\pi\) | ||||
0.236052 | + | 0.971740i | \(0.424146\pi\) | |||||||
\(80\) | −1.73205 | −0.193649 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.46410 | 1.04514 | ||||||||
\(83\) | −4.73205 | −0.519410 | −0.259705 | − | 0.965688i | \(-0.583625\pi\) | ||||
−0.259705 | + | 0.965688i | \(0.583625\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.803848 | −0.0871895 | ||||||||
\(86\) | 8.39230 | 0.904966 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.26795 | 0.135164 | ||||||||
\(89\) | 5.53590 | 0.586804 | 0.293402 | − | 0.955989i | \(-0.405213\pi\) | ||||
0.293402 | + | 0.955989i | \(0.405213\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | −4.73205 | −0.493350 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.19615 | −0.845369 | ||||||||
\(95\) | −7.26795 | −0.745676 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.0000 | −1.62455 | −0.812277 | − | 0.583272i | \(-0.801772\pi\) | ||||
−0.812277 | + | 0.583272i | \(0.801772\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | 0.928203 | 0.0923597 | 0.0461798 | − | 0.998933i | \(-0.485295\pi\) | ||||
0.0461798 | + | 0.998933i | \(0.485295\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.3923 | 1.22105 | 0.610525 | − | 0.791997i | \(-0.290958\pi\) | ||||
0.610525 | + | 0.791997i | \(0.290958\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.53590 | 0.246308 | ||||||||
\(107\) | −13.8564 | −1.33955 | −0.669775 | − | 0.742564i | \(-0.733609\pi\) | ||||
−0.669775 | + | 0.742564i | \(0.733609\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.1962 | −1.45553 | −0.727764 | − | 0.685828i | \(-0.759440\pi\) | ||||
−0.727764 | + | 0.685828i | \(0.759440\pi\) | |||||||
\(110\) | −2.19615 | −0.209395 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 13.7321 | 1.29180 | 0.645901 | − | 0.763421i | \(-0.276482\pi\) | ||||
0.645901 | + | 0.763421i | \(0.276482\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.19615 | 0.764295 | ||||||||
\(116\) | 0.464102 | 0.0430908 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.19615 | 0.202172 | ||||||||
\(119\) | 0.464102 | 0.0425441 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.39230 | −0.853846 | ||||||||
\(122\) | 11.3923 | 1.03141 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.19615 | −0.556431 | ||||||||
\(125\) | 12.1244 | 1.08444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.73205 | −0.151911 | ||||||||
\(131\) | 9.46410 | 0.826882 | 0.413441 | − | 0.910531i | \(-0.364327\pi\) | ||||
0.413441 | + | 0.910531i | \(0.364327\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.19615 | 0.363853 | ||||||||
\(134\) | 6.19615 | 0.535266 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.464102 | −0.0397964 | ||||||||
\(137\) | −14.6603 | −1.25251 | −0.626255 | − | 0.779618i | \(-0.715413\pi\) | ||||
−0.626255 | + | 0.779618i | \(0.715413\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.80385 | −0.661914 | −0.330957 | − | 0.943646i | \(-0.607371\pi\) | ||||
−0.330957 | + | 0.943646i | \(0.607371\pi\) | |||||||
\(140\) | −1.73205 | −0.146385 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 16.3923 | 1.37561 | ||||||||
\(143\) | 1.26795 | 0.106031 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.803848 | −0.0667559 | ||||||||
\(146\) | −1.19615 | −0.0989943 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.19615 | 0.591520 | ||||||||
\(149\) | −9.92820 | −0.813350 | −0.406675 | − | 0.913573i | \(-0.633312\pi\) | ||||
−0.406675 | + | 0.913573i | \(0.633312\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.58846 | 0.698919 | 0.349459 | − | 0.936952i | \(-0.386365\pi\) | ||||
0.349459 | + | 0.936952i | \(0.386365\pi\) | |||||||
\(152\) | −4.19615 | −0.340353 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.26795 | 0.102174 | ||||||||
\(155\) | 10.7321 | 0.862019 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.39230 | −0.430353 | −0.215176 | − | 0.976575i | \(-0.569033\pi\) | ||||
−0.215176 | + | 0.976575i | \(0.569033\pi\) | |||||||
\(158\) | −4.19615 | −0.333828 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.73205 | 0.136931 | ||||||||
\(161\) | −4.73205 | −0.372938 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.60770 | 0.282576 | 0.141288 | − | 0.989969i | \(-0.454876\pi\) | ||||
0.141288 | + | 0.989969i | \(0.454876\pi\) | |||||||
\(164\) | −9.46410 | −0.739022 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.73205 | 0.367278 | ||||||||
\(167\) | 10.7321 | 0.830471 | 0.415236 | − | 0.909714i | \(-0.363699\pi\) | ||||
0.415236 | + | 0.909714i | \(0.363699\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0.803848 | 0.0616523 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.39230 | −0.639907 | ||||||||
\(173\) | 23.1962 | 1.76357 | 0.881785 | − | 0.471651i | \(-0.156342\pi\) | ||||
0.881785 | + | 0.471651i | \(0.156342\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | −0.151186 | ||||||||
\(176\) | −1.26795 | −0.0955753 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.53590 | −0.414933 | ||||||||
\(179\) | −10.7321 | −0.802151 | −0.401076 | − | 0.916045i | \(-0.631364\pi\) | ||||
−0.401076 | + | 0.916045i | \(0.631364\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.3923 | −1.51575 | −0.757874 | − | 0.652401i | \(-0.773762\pi\) | ||||
−0.757874 | + | 0.652401i | \(0.773762\pi\) | |||||||
\(182\) | 1.00000 | 0.0741249 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.73205 | 0.348851 | ||||||||
\(185\) | −12.4641 | −0.916379 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.588457 | −0.0430323 | ||||||||
\(188\) | 8.19615 | 0.597766 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.26795 | 0.527272 | ||||||||
\(191\) | 6.58846 | 0.476724 | 0.238362 | − | 0.971176i | \(-0.423390\pi\) | ||||
0.238362 | + | 0.971176i | \(0.423390\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.0000 | −1.36765 | −0.683825 | − | 0.729646i | \(-0.739685\pi\) | ||||
−0.683825 | + | 0.729646i | \(0.739685\pi\) | |||||||
\(194\) | 16.0000 | 1.14873 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 15.0000 | 1.06871 | 0.534353 | − | 0.845262i | \(-0.320555\pi\) | ||||
0.534353 | + | 0.845262i | \(0.320555\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.5885 | −0.750596 | −0.375298 | − | 0.926904i | \(-0.622460\pi\) | ||||
−0.375298 | + | 0.926904i | \(0.622460\pi\) | |||||||
\(200\) | 2.00000 | 0.141421 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.928203 | −0.0653082 | ||||||||
\(203\) | 0.464102 | 0.0325735 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.3923 | 1.14489 | ||||||||
\(206\) | −12.3923 | −0.863413 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −5.32051 | −0.368027 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.1962 | 1.52805 | 0.764023 | − | 0.645189i | \(-0.223221\pi\) | ||||
0.764023 | + | 0.645189i | \(0.223221\pi\) | |||||||
\(212\) | −2.53590 | −0.174166 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.8564 | 0.947204 | ||||||||
\(215\) | 14.5359 | 0.991340 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.19615 | −0.420622 | ||||||||
\(218\) | 15.1962 | 1.02921 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.19615 | 0.148065 | ||||||||
\(221\) | −0.464102 | −0.0312189 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.39230 | −0.561990 | −0.280995 | − | 0.959709i | \(-0.590664\pi\) | ||||
−0.280995 | + | 0.959709i | \(0.590664\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.7321 | −0.913442 | ||||||||
\(227\) | 18.9282 | 1.25631 | 0.628154 | − | 0.778089i | \(-0.283811\pi\) | ||||
0.628154 | + | 0.778089i | \(0.283811\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.7846 | 1.30740 | 0.653702 | − | 0.756752i | \(-0.273215\pi\) | ||||
0.653702 | + | 0.756752i | \(0.273215\pi\) | |||||||
\(230\) | −8.19615 | −0.540438 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.464102 | −0.0304698 | ||||||||
\(233\) | −10.2679 | −0.672676 | −0.336338 | − | 0.941741i | \(-0.609188\pi\) | ||||
−0.336338 | + | 0.941741i | \(0.609188\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.1962 | −0.926055 | ||||||||
\(236\) | −2.19615 | −0.142957 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.464102 | −0.0300832 | ||||||||
\(239\) | 9.12436 | 0.590206 | 0.295103 | − | 0.955466i | \(-0.404646\pi\) | ||||
0.295103 | + | 0.955466i | \(0.404646\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.5885 | 1.13297 | 0.566486 | − | 0.824071i | \(-0.308302\pi\) | ||||
0.566486 | + | 0.824071i | \(0.308302\pi\) | |||||||
\(242\) | 9.39230 | 0.603760 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.3923 | −0.729318 | ||||||||
\(245\) | −1.73205 | −0.110657 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.19615 | −0.266995 | ||||||||
\(248\) | 6.19615 | 0.393456 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.1244 | −0.766812 | ||||||||
\(251\) | 14.1962 | 0.896053 | 0.448027 | − | 0.894020i | \(-0.352127\pi\) | ||||
0.448027 | + | 0.894020i | \(0.352127\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | 0.377217 | ||||||||
\(254\) | 4.00000 | 0.250982 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.0718 | 0.877775 | 0.438887 | − | 0.898542i | \(-0.355373\pi\) | ||||
0.438887 | + | 0.898542i | \(0.355373\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.19615 | 0.447147 | ||||||||
\(260\) | 1.73205 | 0.107417 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.46410 | −0.584694 | ||||||||
\(263\) | 9.12436 | 0.562632 | 0.281316 | − | 0.959615i | \(-0.409229\pi\) | ||||
0.281316 | + | 0.959615i | \(0.409229\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.39230 | 0.269817 | ||||||||
\(266\) | −4.19615 | −0.257283 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.19615 | −0.378490 | ||||||||
\(269\) | 29.4449 | 1.79529 | 0.897643 | − | 0.440724i | \(-0.145278\pi\) | ||||
0.897643 | + | 0.440724i | \(0.145278\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.8038 | 1.08151 | 0.540753 | − | 0.841181i | \(-0.318139\pi\) | ||||
0.540753 | + | 0.841181i | \(0.318139\pi\) | |||||||
\(272\) | 0.464102 | 0.0281403 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.6603 | 0.885658 | ||||||||
\(275\) | 2.53590 | 0.152920 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.7846 | 1.36899 | 0.684497 | − | 0.729015i | \(-0.260022\pi\) | ||||
0.684497 | + | 0.729015i | \(0.260022\pi\) | |||||||
\(278\) | 7.80385 | 0.468044 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.73205 | 0.103510 | ||||||||
\(281\) | 10.2679 | 0.612534 | 0.306267 | − | 0.951946i | \(-0.400920\pi\) | ||||
0.306267 | + | 0.951946i | \(0.400920\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.3923 | 1.44997 | 0.724986 | − | 0.688764i | \(-0.241846\pi\) | ||||
0.724986 | + | 0.688764i | \(0.241846\pi\) | |||||||
\(284\) | −16.3923 | −0.972704 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.26795 | −0.0749754 | ||||||||
\(287\) | −9.46410 | −0.558648 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7846 | −0.987330 | ||||||||
\(290\) | 0.803848 | 0.0472036 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.19615 | 0.0699995 | ||||||||
\(293\) | 9.33975 | 0.545634 | 0.272817 | − | 0.962066i | \(-0.412045\pi\) | ||||
0.272817 | + | 0.962066i | \(0.412045\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.80385 | 0.221469 | ||||||||
\(296\) | −7.19615 | −0.418268 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.92820 | 0.575125 | ||||||||
\(299\) | 4.73205 | 0.273662 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.39230 | −0.483724 | ||||||||
\(302\) | −8.58846 | −0.494210 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.19615 | 0.240666 | ||||||||
\(305\) | 19.7321 | 1.12985 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.00000 | 0.456584 | 0.228292 | − | 0.973593i | \(-0.426686\pi\) | ||||
0.228292 | + | 0.973593i | \(0.426686\pi\) | |||||||
\(308\) | −1.26795 | −0.0722481 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10.7321 | −0.609540 | ||||||||
\(311\) | −28.9808 | −1.64335 | −0.821674 | − | 0.569958i | \(-0.806960\pi\) | ||||
−0.821674 | + | 0.569958i | \(0.806960\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.9808 | −1.69461 | −0.847306 | − | 0.531104i | \(-0.821777\pi\) | ||||
−0.847306 | + | 0.531104i | \(0.821777\pi\) | |||||||
\(314\) | 5.39230 | 0.304305 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.19615 | 0.236052 | ||||||||
\(317\) | −19.3923 | −1.08918 | −0.544590 | − | 0.838702i | \(-0.683315\pi\) | ||||
−0.544590 | + | 0.838702i | \(0.683315\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.588457 | −0.0329473 | ||||||||
\(320\) | −1.73205 | −0.0968246 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.73205 | 0.263707 | ||||||||
\(323\) | 1.94744 | 0.108359 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.00000 | 0.110940 | ||||||||
\(326\) | −3.60770 | −0.199812 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.46410 | 0.522568 | ||||||||
\(329\) | 8.19615 | 0.451869 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.1769 | 1.82357 | 0.911784 | − | 0.410670i | \(-0.134705\pi\) | ||||
0.911784 | + | 0.410670i | \(0.134705\pi\) | |||||||
\(332\) | −4.73205 | −0.259705 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.7321 | −0.587232 | ||||||||
\(335\) | 10.7321 | 0.586355 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.6077 | −0.632311 | −0.316156 | − | 0.948707i | \(-0.602392\pi\) | ||||
−0.316156 | + | 0.948707i | \(0.602392\pi\) | |||||||
\(338\) | 12.0000 | 0.652714 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.803848 | −0.0435948 | ||||||||
\(341\) | 7.85641 | 0.425448 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 8.39230 | 0.452483 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −23.1962 | −1.24703 | ||||||||
\(347\) | 4.39230 | 0.235791 | 0.117896 | − | 0.993026i | \(-0.462385\pi\) | ||||
0.117896 | + | 0.993026i | \(0.462385\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.39230 | −0.449230 | −0.224615 | − | 0.974448i | \(-0.572112\pi\) | ||||
−0.224615 | + | 0.974448i | \(0.572112\pi\) | |||||||
\(350\) | 2.00000 | 0.106904 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.26795 | 0.0675819 | ||||||||
\(353\) | −31.8564 | −1.69555 | −0.847773 | − | 0.530360i | \(-0.822057\pi\) | ||||
−0.847773 | + | 0.530360i | \(0.822057\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 28.3923 | 1.50691 | ||||||||
\(356\) | 5.53590 | 0.293402 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.7321 | 0.567207 | ||||||||
\(359\) | −5.07180 | −0.267679 | −0.133840 | − | 0.991003i | \(-0.542731\pi\) | ||||
−0.133840 | + | 0.991003i | \(0.542731\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.39230 | −0.0732792 | ||||||||
\(362\) | 20.3923 | 1.07180 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.00000 | −0.0524142 | ||||||||
\(365\) | −2.07180 | −0.108443 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.5885 | 1.38791 | 0.693953 | − | 0.720020i | \(-0.255867\pi\) | ||||
0.693953 | + | 0.720020i | \(0.255867\pi\) | |||||||
\(368\) | −4.73205 | −0.246675 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.4641 | 0.647978 | ||||||||
\(371\) | −2.53590 | −0.131657 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.0000 | 1.03556 | 0.517780 | − | 0.855514i | \(-0.326758\pi\) | ||||
0.517780 | + | 0.855514i | \(0.326758\pi\) | |||||||
\(374\) | 0.588457 | 0.0304284 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.19615 | −0.422684 | ||||||||
\(377\) | −0.464102 | −0.0239024 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.5885 | 0.749359 | 0.374679 | − | 0.927154i | \(-0.377753\pi\) | ||||
0.374679 | + | 0.927154i | \(0.377753\pi\) | |||||||
\(380\) | −7.26795 | −0.372838 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.58846 | −0.337095 | ||||||||
\(383\) | 37.8564 | 1.93437 | 0.967186 | − | 0.254069i | \(-0.0817691\pi\) | ||||
0.967186 | + | 0.254069i | \(0.0817691\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.19615 | 0.111926 | ||||||||
\(386\) | 19.0000 | 0.967075 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.0000 | −0.812277 | ||||||||
\(389\) | −18.2487 | −0.925246 | −0.462623 | − | 0.886555i | \(-0.653092\pi\) | ||||
−0.462623 | + | 0.886555i | \(0.653092\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.19615 | −0.111064 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15.0000 | −0.755689 | ||||||||
\(395\) | −7.26795 | −0.365690 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.60770 | −0.432008 | −0.216004 | − | 0.976392i | \(-0.569302\pi\) | ||||
−0.216004 | + | 0.976392i | \(0.569302\pi\) | |||||||
\(398\) | 10.5885 | 0.530751 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | −0.100000 | ||||||||
\(401\) | −25.7321 | −1.28500 | −0.642499 | − | 0.766287i | \(-0.722102\pi\) | ||||
−0.642499 | + | 0.766287i | \(0.722102\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.19615 | 0.308652 | ||||||||
\(404\) | 0.928203 | 0.0461798 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.464102 | −0.0230330 | ||||||||
\(407\) | −9.12436 | −0.452278 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.8038 | −0.534216 | −0.267108 | − | 0.963667i | \(-0.586068\pi\) | ||||
−0.267108 | + | 0.963667i | \(0.586068\pi\) | |||||||
\(410\) | −16.3923 | −0.809558 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.3923 | 0.610525 | ||||||||
\(413\) | −2.19615 | −0.108066 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.19615 | 0.402333 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.32051 | 0.260235 | ||||||||
\(419\) | 11.3205 | 0.553043 | 0.276522 | − | 0.961008i | \(-0.410818\pi\) | ||||
0.276522 | + | 0.961008i | \(0.410818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.80385 | 0.136651 | 0.0683256 | − | 0.997663i | \(-0.478234\pi\) | ||||
0.0683256 | + | 0.997663i | \(0.478234\pi\) | |||||||
\(422\) | −22.1962 | −1.08049 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.53590 | 0.123154 | ||||||||
\(425\) | −0.928203 | −0.0450245 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.3923 | −0.551312 | ||||||||
\(428\) | −13.8564 | −0.669775 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14.5359 | −0.700983 | ||||||||
\(431\) | −35.3205 | −1.70133 | −0.850665 | − | 0.525709i | \(-0.823800\pi\) | ||||
−0.850665 | + | 0.525709i | \(0.823800\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.411543 | −0.0197775 | −0.00988874 | − | 0.999951i | \(-0.503148\pi\) | ||||
−0.00988874 | + | 0.999951i | \(0.503148\pi\) | |||||||
\(434\) | 6.19615 | 0.297425 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.1962 | −0.727764 | ||||||||
\(437\) | −19.8564 | −0.949861 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −41.1769 | −1.96527 | −0.982633 | − | 0.185557i | \(-0.940591\pi\) | ||||
−0.982633 | + | 0.185557i | \(0.940591\pi\) | |||||||
\(440\) | −2.19615 | −0.104697 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.464102 | 0.0220751 | ||||||||
\(443\) | 8.19615 | 0.389411 | 0.194705 | − | 0.980862i | \(-0.437625\pi\) | ||||
0.194705 | + | 0.980862i | \(0.437625\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.58846 | −0.454536 | ||||||||
\(446\) | 8.39230 | 0.397387 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | 0.565058 | ||||||||
\(452\) | 13.7321 | 0.645901 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −18.9282 | −0.888345 | ||||||||
\(455\) | 1.73205 | 0.0811998 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | −0.0467780 | −0.0233890 | − | 0.999726i | \(-0.507446\pi\) | ||||
−0.0233890 | + | 0.999726i | \(0.507446\pi\) | |||||||
\(458\) | −19.7846 | −0.924474 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.19615 | 0.382148 | ||||||||
\(461\) | −24.9282 | −1.16102 | −0.580511 | − | 0.814252i | \(-0.697147\pi\) | ||||
−0.580511 | + | 0.814252i | \(0.697147\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.1962 | 0.752699 | 0.376350 | − | 0.926478i | \(-0.377179\pi\) | ||||
0.376350 | + | 0.926478i | \(0.377179\pi\) | |||||||
\(464\) | 0.464102 | 0.0215454 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.2679 | 0.475654 | ||||||||
\(467\) | 4.73205 | 0.218973 | 0.109487 | − | 0.993988i | \(-0.465079\pi\) | ||||
0.109487 | + | 0.993988i | \(0.465079\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.19615 | −0.286112 | ||||||||
\(470\) | 14.1962 | 0.654820 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.19615 | 0.101086 | ||||||||
\(473\) | 10.6410 | 0.489274 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.39230 | −0.385065 | ||||||||
\(476\) | 0.464102 | 0.0212721 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.12436 | −0.417338 | ||||||||
\(479\) | −13.2679 | −0.606228 | −0.303114 | − | 0.952954i | \(-0.598026\pi\) | ||||
−0.303114 | + | 0.952954i | \(0.598026\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.19615 | −0.328116 | ||||||||
\(482\) | −17.5885 | −0.801132 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.39230 | −0.426923 | ||||||||
\(485\) | 27.7128 | 1.25837 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.19615 | 0.190146 | 0.0950729 | − | 0.995470i | \(-0.469692\pi\) | ||||
0.0950729 | + | 0.995470i | \(0.469692\pi\) | |||||||
\(488\) | 11.3923 | 0.515705 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.73205 | 0.0782461 | ||||||||
\(491\) | 23.3205 | 1.05244 | 0.526220 | − | 0.850349i | \(-0.323609\pi\) | ||||
0.526220 | + | 0.850349i | \(0.323609\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.215390 | 0.00970069 | ||||||||
\(494\) | 4.19615 | 0.188794 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.19615 | −0.278215 | ||||||||
\(497\) | −16.3923 | −0.735295 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.5885 | −0.474004 | −0.237002 | − | 0.971509i | \(-0.576165\pi\) | ||||
−0.237002 | + | 0.971509i | \(0.576165\pi\) | |||||||
\(500\) | 12.1244 | 0.542218 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −14.1962 | −0.633605 | ||||||||
\(503\) | −28.9808 | −1.29219 | −0.646094 | − | 0.763258i | \(-0.723599\pi\) | ||||
−0.646094 | + | 0.763258i | \(0.723599\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.60770 | −0.0715415 | ||||||||
\(506\) | −6.00000 | −0.266733 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.00000 | −0.177471 | ||||||||
\(509\) | −33.7128 | −1.49429 | −0.747147 | − | 0.664659i | \(-0.768577\pi\) | ||||
−0.747147 | + | 0.664659i | \(0.768577\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.19615 | 0.0529147 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.0718 | −0.620680 | ||||||||
\(515\) | −21.4641 | −0.945821 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.3923 | −0.457053 | ||||||||
\(518\) | −7.19615 | −0.316181 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.73205 | −0.0759555 | ||||||||
\(521\) | −16.1436 | −0.707264 | −0.353632 | − | 0.935385i | \(-0.615053\pi\) | ||||
−0.353632 | + | 0.935385i | \(0.615053\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.3923 | 1.59132 | 0.795662 | − | 0.605741i | \(-0.207123\pi\) | ||||
0.795662 | + | 0.605741i | \(0.207123\pi\) | |||||||
\(524\) | 9.46410 | 0.413441 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.12436 | −0.397841 | ||||||||
\(527\) | −2.87564 | −0.125265 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.607695 | −0.0264215 | ||||||||
\(530\) | −4.39230 | −0.190790 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.19615 | 0.181926 | ||||||||
\(533\) | 9.46410 | 0.409936 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.0000 | 1.03761 | ||||||||
\(536\) | 6.19615 | 0.267633 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −29.4449 | −1.26946 | ||||||||
\(539\) | −1.26795 | −0.0546144 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.411543 | −0.0176936 | −0.00884680 | − | 0.999961i | \(-0.502816\pi\) | ||||
−0.00884680 | + | 0.999961i | \(0.502816\pi\) | |||||||
\(542\) | −17.8038 | −0.764741 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.464102 | −0.0198982 | ||||||||
\(545\) | 26.3205 | 1.12745 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.1962 | −1.29109 | −0.645547 | − | 0.763720i | \(-0.723371\pi\) | ||||
−0.645547 | + | 0.763720i | \(0.723371\pi\) | |||||||
\(548\) | −14.6603 | −0.626255 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.53590 | −0.108131 | ||||||||
\(551\) | 1.94744 | 0.0829638 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.19615 | 0.178439 | ||||||||
\(554\) | −22.7846 | −0.968025 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.80385 | −0.330957 | ||||||||
\(557\) | −13.1436 | −0.556912 | −0.278456 | − | 0.960449i | \(-0.589823\pi\) | ||||
−0.278456 | + | 0.960449i | \(0.589823\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.39230 | 0.354957 | ||||||||
\(560\) | −1.73205 | −0.0731925 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.2679 | −0.433127 | ||||||||
\(563\) | −24.0000 | −1.01148 | −0.505740 | − | 0.862686i | \(-0.668780\pi\) | ||||
−0.505740 | + | 0.862686i | \(0.668780\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23.7846 | −1.00063 | ||||||||
\(566\) | −24.3923 | −1.02529 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.3923 | 0.687806 | ||||||||
\(569\) | −43.9808 | −1.84377 | −0.921885 | − | 0.387464i | \(-0.873351\pi\) | ||||
−0.921885 | + | 0.387464i | \(0.873351\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.1962 | −1.26367 | −0.631835 | − | 0.775103i | \(-0.717698\pi\) | ||||
−0.631835 | + | 0.775103i | \(0.717698\pi\) | |||||||
\(572\) | 1.26795 | 0.0530156 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.46410 | 0.395024 | ||||||||
\(575\) | 9.46410 | 0.394680 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.8038 | 0.866076 | 0.433038 | − | 0.901376i | \(-0.357442\pi\) | ||||
0.433038 | + | 0.901376i | \(0.357442\pi\) | |||||||
\(578\) | 16.7846 | 0.698148 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.803848 | −0.0333780 | ||||||||
\(581\) | −4.73205 | −0.196319 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.21539 | 0.133168 | ||||||||
\(584\) | −1.19615 | −0.0494971 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.33975 | −0.385821 | ||||||||
\(587\) | 7.26795 | 0.299980 | 0.149990 | − | 0.988687i | \(-0.452076\pi\) | ||||
0.149990 | + | 0.988687i | \(0.452076\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.0000 | −1.07131 | ||||||||
\(590\) | −3.80385 | −0.156602 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.19615 | 0.295760 | ||||||||
\(593\) | 13.1436 | 0.539743 | 0.269871 | − | 0.962896i | \(-0.413019\pi\) | ||||
0.269871 | + | 0.962896i | \(0.413019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.803848 | −0.0329545 | ||||||||
\(596\) | −9.92820 | −0.406675 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.73205 | −0.193508 | ||||||||
\(599\) | 14.1962 | 0.580039 | 0.290020 | − | 0.957021i | \(-0.406338\pi\) | ||||
0.290020 | + | 0.957021i | \(0.406338\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.19615 | 0.0487921 | 0.0243960 | − | 0.999702i | \(-0.492234\pi\) | ||||
0.0243960 | + | 0.999702i | \(0.492234\pi\) | |||||||
\(602\) | 8.39230 | 0.342045 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.58846 | 0.349459 | ||||||||
\(605\) | 16.2679 | 0.661386 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.58846 | 0.105062 | 0.0525311 | − | 0.998619i | \(-0.483271\pi\) | ||||
0.0525311 | + | 0.998619i | \(0.483271\pi\) | |||||||
\(608\) | −4.19615 | −0.170176 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.7321 | −0.798927 | ||||||||
\(611\) | −8.19615 | −0.331581 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.7846 | 1.40494 | 0.702469 | − | 0.711715i | \(-0.252081\pi\) | ||||
0.702469 | + | 0.711715i | \(0.252081\pi\) | |||||||
\(614\) | −8.00000 | −0.322854 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.26795 | 0.0510871 | ||||||||
\(617\) | 28.5167 | 1.14804 | 0.574019 | − | 0.818842i | \(-0.305384\pi\) | ||||
0.574019 | + | 0.818842i | \(0.305384\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | 10.7321 | 0.431010 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 28.9808 | 1.16202 | ||||||||
\(623\) | 5.53590 | 0.221791 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 29.9808 | 1.19827 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.39230 | −0.215176 | ||||||||
\(629\) | 3.33975 | 0.133164 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.58846 | 0.341901 | 0.170951 | − | 0.985280i | \(-0.445316\pi\) | ||||
0.170951 | + | 0.985280i | \(0.445316\pi\) | |||||||
\(632\) | −4.19615 | −0.166914 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 19.3923 | 0.770167 | ||||||||
\(635\) | 6.92820 | 0.274937 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0.588457 | 0.0232972 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.73205 | 0.0684653 | ||||||||
\(641\) | −26.6603 | −1.05302 | −0.526508 | − | 0.850170i | \(-0.676499\pi\) | ||||
−0.526508 | + | 0.850170i | \(0.676499\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.1962 | 1.11195 | 0.555974 | − | 0.831200i | \(-0.312345\pi\) | ||||
0.555974 | + | 0.831200i | \(0.312345\pi\) | |||||||
\(644\) | −4.73205 | −0.186469 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.94744 | −0.0766210 | ||||||||
\(647\) | −11.3205 | −0.445055 | −0.222528 | − | 0.974926i | \(-0.571431\pi\) | ||||
−0.222528 | + | 0.974926i | \(0.571431\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.78461 | 0.109305 | ||||||||
\(650\) | −2.00000 | −0.0784465 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.60770 | 0.141288 | ||||||||
\(653\) | 0.679492 | 0.0265906 | 0.0132953 | − | 0.999912i | \(-0.495768\pi\) | ||||
0.0132953 | + | 0.999912i | \(0.495768\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.3923 | −0.640500 | ||||||||
\(656\) | −9.46410 | −0.369511 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.19615 | −0.319519 | ||||||||
\(659\) | −35.3205 | −1.37589 | −0.687946 | − | 0.725762i | \(-0.741487\pi\) | ||||
−0.687946 | + | 0.725762i | \(0.741487\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.6077 | 0.490383 | 0.245191 | − | 0.969475i | \(-0.421149\pi\) | ||||
0.245191 | + | 0.969475i | \(0.421149\pi\) | |||||||
\(662\) | −33.1769 | −1.28946 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.73205 | 0.183639 | ||||||||
\(665\) | −7.26795 | −0.281839 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.19615 | −0.0850354 | ||||||||
\(668\) | 10.7321 | 0.415236 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.7321 | −0.414615 | ||||||||
\(671\) | 14.4449 | 0.557638 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.1769 | −1.70289 | −0.851447 | − | 0.524440i | \(-0.824275\pi\) | ||||
−0.851447 | + | 0.524440i | \(0.824275\pi\) | |||||||
\(674\) | 11.6077 | 0.447112 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | −3.21539 | −0.123577 | −0.0617887 | − | 0.998089i | \(-0.519681\pi\) | ||||
−0.0617887 | + | 0.998089i | \(0.519681\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.0000 | −0.614024 | ||||||||
\(680\) | 0.803848 | 0.0308261 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.85641 | −0.300837 | ||||||||
\(683\) | −15.7128 | −0.601234 | −0.300617 | − | 0.953745i | \(-0.597193\pi\) | ||||
−0.300617 | + | 0.953745i | \(0.597193\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.3923 | 0.970190 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.39230 | −0.319954 | ||||||||
\(689\) | 2.53590 | 0.0966100 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.0000 | 1.67384 | 0.836919 | − | 0.547326i | \(-0.184354\pi\) | ||||
0.836919 | + | 0.547326i | \(0.184354\pi\) | |||||||
\(692\) | 23.1962 | 0.881785 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.39230 | −0.166730 | ||||||||
\(695\) | 13.5167 | 0.512716 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.39230 | −0.166370 | ||||||||
\(698\) | 8.39230 | 0.317653 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.00000 | −0.0755929 | ||||||||
\(701\) | 16.1769 | 0.610994 | 0.305497 | − | 0.952193i | \(-0.401177\pi\) | ||||
0.305497 | + | 0.952193i | \(0.401177\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.1962 | 1.13887 | ||||||||
\(704\) | −1.26795 | −0.0477876 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 31.8564 | 1.19893 | ||||||||
\(707\) | 0.928203 | 0.0349087 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.5885 | 0.885883 | 0.442942 | − | 0.896550i | \(-0.353935\pi\) | ||||
0.442942 | + | 0.896550i | \(0.353935\pi\) | |||||||
\(710\) | −28.3923 | −1.06554 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.53590 | −0.207467 | ||||||||
\(713\) | 29.3205 | 1.09806 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.19615 | −0.0821314 | ||||||||
\(716\) | −10.7321 | −0.401076 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.07180 | 0.189278 | ||||||||
\(719\) | 11.3205 | 0.422184 | 0.211092 | − | 0.977466i | \(-0.432298\pi\) | ||||
0.211092 | + | 0.977466i | \(0.432298\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.3923 | 0.461514 | ||||||||
\(722\) | 1.39230 | 0.0518162 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −20.3923 | −0.757874 | ||||||||
\(725\) | −0.928203 | −0.0344726 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.3923 | 1.34972 | 0.674858 | − | 0.737948i | \(-0.264205\pi\) | ||||
0.674858 | + | 0.737948i | \(0.264205\pi\) | |||||||
\(728\) | 1.00000 | 0.0370625 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.07180 | 0.0766806 | ||||||||
\(731\) | −3.89488 | −0.144057 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.1769 | 1.22542 | 0.612709 | − | 0.790309i | \(-0.290080\pi\) | ||||
0.612709 | + | 0.790309i | \(0.290080\pi\) | |||||||
\(734\) | −26.5885 | −0.981398 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.73205 | 0.174426 | ||||||||
\(737\) | 7.85641 | 0.289394 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.8038 | −0.507783 | −0.253891 | − | 0.967233i | \(-0.581711\pi\) | ||||
−0.253891 | + | 0.967233i | \(0.581711\pi\) | |||||||
\(740\) | −12.4641 | −0.458189 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.53590 | 0.0930958 | ||||||||
\(743\) | 14.5359 | 0.533270 | 0.266635 | − | 0.963798i | \(-0.414088\pi\) | ||||
0.266635 | + | 0.963798i | \(0.414088\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.1962 | 0.630018 | ||||||||
\(746\) | −20.0000 | −0.732252 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.588457 | −0.0215161 | ||||||||
\(749\) | −13.8564 | −0.506302 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.00000 | −0.145962 | −0.0729810 | − | 0.997333i | \(-0.523251\pi\) | ||||
−0.0729810 | + | 0.997333i | \(0.523251\pi\) | |||||||
\(752\) | 8.19615 | 0.298883 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.464102 | 0.0169016 | ||||||||
\(755\) | −14.8756 | −0.541380 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.7846 | −1.33696 | −0.668480 | − | 0.743730i | \(-0.733055\pi\) | ||||
−0.668480 | + | 0.743730i | \(0.733055\pi\) | |||||||
\(758\) | −14.5885 | −0.529877 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.26795 | 0.263636 | ||||||||
\(761\) | −26.3205 | −0.954118 | −0.477059 | − | 0.878871i | \(-0.658297\pi\) | ||||
−0.477059 | + | 0.878871i | \(0.658297\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.1962 | −0.550138 | ||||||||
\(764\) | 6.58846 | 0.238362 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −37.8564 | −1.36781 | ||||||||
\(767\) | 2.19615 | 0.0792985 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.19615 | −0.115256 | −0.0576281 | − | 0.998338i | \(-0.518354\pi\) | ||||
−0.0576281 | + | 0.998338i | \(0.518354\pi\) | |||||||
\(770\) | −2.19615 | −0.0791438 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −19.0000 | −0.683825 | ||||||||
\(773\) | 38.6603 | 1.39051 | 0.695256 | − | 0.718762i | \(-0.255291\pi\) | ||||
0.695256 | + | 0.718762i | \(0.255291\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.3923 | 0.445145 | ||||||||
\(776\) | 16.0000 | 0.574367 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.2487 | 0.654248 | ||||||||
\(779\) | −39.7128 | −1.42286 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.7846 | 0.743732 | ||||||||
\(782\) | 2.19615 | 0.0785343 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 9.33975 | 0.333350 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.1769 | −0.612291 | −0.306145 | − | 0.951985i | \(-0.599039\pi\) | ||||
−0.306145 | + | 0.951985i | \(0.599039\pi\) | |||||||
\(788\) | 15.0000 | 0.534353 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.26795 | 0.258582 | ||||||||
\(791\) | 13.7321 | 0.488256 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.3923 | 0.404553 | ||||||||
\(794\) | 8.60770 | 0.305476 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.5885 | −0.375298 | ||||||||
\(797\) | −38.6603 | −1.36942 | −0.684708 | − | 0.728817i | \(-0.740070\pi\) | ||||
−0.684708 | + | 0.728817i | \(0.740070\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.80385 | 0.134570 | ||||||||
\(800\) | 2.00000 | 0.0707107 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 25.7321 | 0.908630 | ||||||||
\(803\) | −1.51666 | −0.0535218 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.19615 | 0.288876 | ||||||||
\(806\) | −6.19615 | −0.218250 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.928203 | −0.0326541 | ||||||||
\(809\) | −24.1244 | −0.848167 | −0.424084 | − | 0.905623i | \(-0.639404\pi\) | ||||
−0.424084 | + | 0.905623i | \(0.639404\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.01924 | 0.106020 | 0.0530099 | − | 0.998594i | \(-0.483119\pi\) | ||||
0.0530099 | + | 0.998594i | \(0.483119\pi\) | |||||||
\(812\) | 0.464102 | 0.0162868 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.12436 | 0.319809 | ||||||||
\(815\) | −6.24871 | −0.218883 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −35.2154 | −1.23203 | ||||||||
\(818\) | 10.8038 | 0.377748 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16.3923 | 0.572444 | ||||||||
\(821\) | 15.0000 | 0.523504 | 0.261752 | − | 0.965135i | \(-0.415700\pi\) | ||||
0.261752 | + | 0.965135i | \(0.415700\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.7846 | 0.585075 | 0.292537 | − | 0.956254i | \(-0.405500\pi\) | ||||
0.292537 | + | 0.956254i | \(0.405500\pi\) | |||||||
\(824\) | −12.3923 | −0.431706 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.19615 | 0.0764139 | ||||||||
\(827\) | −40.3923 | −1.40458 | −0.702289 | − | 0.711892i | \(-0.747839\pi\) | ||||
−0.702289 | + | 0.711892i | \(0.747839\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.0000 | 0.903017 | 0.451509 | − | 0.892267i | \(-0.350886\pi\) | ||||
0.451509 | + | 0.892267i | \(0.350886\pi\) | |||||||
\(830\) | −8.19615 | −0.284493 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 0.464102 | 0.0160802 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.5885 | −0.643280 | ||||||||
\(836\) | −5.32051 | −0.184014 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.3205 | −0.391060 | ||||||||
\(839\) | 6.24871 | 0.215729 | 0.107865 | − | 0.994166i | \(-0.465599\pi\) | ||||
0.107865 | + | 0.994166i | \(0.465599\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7846 | −0.992573 | ||||||||
\(842\) | −2.80385 | −0.0966270 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 22.1962 | 0.764023 | ||||||||
\(845\) | 20.7846 | 0.715012 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.39230 | −0.322723 | ||||||||
\(848\) | −2.53590 | −0.0870831 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.928203 | 0.0318371 | ||||||||
\(851\) | −34.0526 | −1.16731 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.00000 | 0.0684787 | 0.0342393 | − | 0.999414i | \(-0.489099\pi\) | ||||
0.0342393 | + | 0.999414i | \(0.489099\pi\) | |||||||
\(854\) | 11.3923 | 0.389837 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.8564 | 0.473602 | ||||||||
\(857\) | 11.5359 | 0.394059 | 0.197029 | − | 0.980398i | \(-0.436871\pi\) | ||||
0.197029 | + | 0.980398i | \(0.436871\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.3923 | −0.695776 | −0.347888 | − | 0.937536i | \(-0.613101\pi\) | ||||
−0.347888 | + | 0.937536i | \(0.613101\pi\) | |||||||
\(860\) | 14.5359 | 0.495670 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 35.3205 | 1.20302 | ||||||||
\(863\) | 41.9090 | 1.42660 | 0.713299 | − | 0.700860i | \(-0.247200\pi\) | ||||
0.713299 | + | 0.700860i | \(0.247200\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40.1769 | −1.36606 | ||||||||
\(866\) | 0.411543 | 0.0139848 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.19615 | −0.210311 | ||||||||
\(869\) | −5.32051 | −0.180486 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.19615 | 0.209949 | ||||||||
\(872\) | 15.1962 | 0.514607 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19.8564 | 0.671653 | ||||||||
\(875\) | 12.1244 | 0.409878 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.8038 | 0.702496 | 0.351248 | − | 0.936282i | \(-0.385757\pi\) | ||||
0.351248 | + | 0.936282i | \(0.385757\pi\) | |||||||
\(878\) | 41.1769 | 1.38965 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.19615 | 0.0740323 | ||||||||
\(881\) | −37.1769 | −1.25252 | −0.626261 | − | 0.779613i | \(-0.715416\pi\) | ||||
−0.626261 | + | 0.779613i | \(0.715416\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.9808 | −1.31181 | −0.655904 | − | 0.754845i | \(-0.727712\pi\) | ||||
−0.655904 | + | 0.754845i | \(0.727712\pi\) | |||||||
\(884\) | −0.464102 | −0.0156094 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.19615 | −0.275355 | ||||||||
\(887\) | −18.3397 | −0.615788 | −0.307894 | − | 0.951421i | \(-0.599624\pi\) | ||||
−0.307894 | + | 0.951421i | \(0.599624\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.00000 | −0.134156 | ||||||||
\(890\) | 9.58846 | 0.321406 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.39230 | −0.280995 | ||||||||
\(893\) | 34.3923 | 1.15089 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.5885 | 0.621344 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.00000 | 0.200223 | ||||||||
\(899\) | −2.87564 | −0.0959081 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.17691 | −0.0392087 | ||||||||
\(902\) | −12.0000 | −0.399556 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.7321 | −0.456721 | ||||||||
\(905\) | 35.3205 | 1.17409 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.0000 | 0.664089 | 0.332045 | − | 0.943264i | \(-0.392262\pi\) | ||||
0.332045 | + | 0.943264i | \(0.392262\pi\) | |||||||
\(908\) | 18.9282 | 0.628154 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.73205 | −0.0574169 | ||||||||
\(911\) | −44.1051 | −1.46127 | −0.730634 | − | 0.682769i | \(-0.760775\pi\) | ||||
−0.730634 | + | 0.682769i | \(0.760775\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.00000 | 0.198571 | ||||||||
\(914\) | 1.00000 | 0.0330771 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.7846 | 0.653702 | ||||||||
\(917\) | 9.46410 | 0.312532 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.1962 | −1.58984 | −0.794922 | − | 0.606711i | \(-0.792488\pi\) | ||||
−0.794922 | + | 0.606711i | \(0.792488\pi\) | |||||||
\(920\) | −8.19615 | −0.270219 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 24.9282 | 0.820967 | ||||||||
\(923\) | 16.3923 | 0.539559 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.3923 | −0.473216 | ||||||||
\(926\) | −16.1962 | −0.532239 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.464102 | −0.0152349 | ||||||||
\(929\) | 13.3923 | 0.439387 | 0.219694 | − | 0.975569i | \(-0.429494\pi\) | ||||
0.219694 | + | 0.975569i | \(0.429494\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.19615 | 0.137523 | ||||||||
\(932\) | −10.2679 | −0.336338 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.73205 | −0.154837 | ||||||||
\(935\) | 1.01924 | 0.0333326 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.1962 | −1.08447 | −0.542236 | − | 0.840227i | \(-0.682422\pi\) | ||||
−0.542236 | + | 0.840227i | \(0.682422\pi\) | |||||||
\(938\) | 6.19615 | 0.202312 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −14.1962 | −0.463027 | ||||||||
\(941\) | −46.7654 | −1.52451 | −0.762254 | − | 0.647278i | \(-0.775907\pi\) | ||||
−0.762254 | + | 0.647278i | \(0.775907\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44.7846 | 1.45839 | ||||||||
\(944\) | −2.19615 | −0.0714787 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.6410 | −0.345969 | ||||||||
\(947\) | 28.3923 | 0.922626 | 0.461313 | − | 0.887237i | \(-0.347379\pi\) | ||||
0.461313 | + | 0.887237i | \(0.347379\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.19615 | −0.0388288 | ||||||||
\(950\) | 8.39230 | 0.272282 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.464102 | −0.0150416 | ||||||||
\(953\) | 4.01924 | 0.130196 | 0.0650979 | − | 0.997879i | \(-0.479264\pi\) | ||||
0.0650979 | + | 0.997879i | \(0.479264\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.4115 | −0.369269 | ||||||||
\(956\) | 9.12436 | 0.295103 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.2679 | 0.428668 | ||||||||
\(959\) | −14.6603 | −0.473404 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.39230 | 0.238461 | ||||||||
\(962\) | 7.19615 | 0.232013 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17.5885 | 0.566486 | ||||||||
\(965\) | 32.9090 | 1.05938 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.58846 | 0.276186 | 0.138093 | − | 0.990419i | \(-0.455903\pi\) | ||||
0.138093 | + | 0.990419i | \(0.455903\pi\) | |||||||
\(968\) | 9.39230 | 0.301880 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −27.7128 | −0.889805 | ||||||||
\(971\) | 21.1244 | 0.677913 | 0.338956 | − | 0.940802i | \(-0.389926\pi\) | ||||
0.338956 | + | 0.940802i | \(0.389926\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.80385 | −0.250180 | ||||||||
\(974\) | −4.19615 | −0.134453 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.3923 | −0.364659 | ||||||||
\(977\) | 47.5692 | 1.52187 | 0.760937 | − | 0.648826i | \(-0.224740\pi\) | ||||
0.760937 | + | 0.648826i | \(0.224740\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.01924 | −0.224336 | ||||||||
\(980\) | −1.73205 | −0.0553283 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −23.3205 | −0.744187 | ||||||||
\(983\) | 54.9282 | 1.75194 | 0.875969 | − | 0.482368i | \(-0.160223\pi\) | ||||
0.875969 | + | 0.482368i | \(0.160223\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.9808 | −0.827816 | ||||||||
\(986\) | −0.215390 | −0.00685942 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.19615 | −0.133497 | ||||||||
\(989\) | 39.7128 | 1.26279 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.98076 | −0.285283 | −0.142642 | − | 0.989774i | \(-0.545560\pi\) | ||||
−0.142642 | + | 0.989774i | \(0.545560\pi\) | |||||||
\(992\) | 6.19615 | 0.196728 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 16.3923 | 0.519932 | ||||||||
\(995\) | 18.3397 | 0.581409 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.7846 | 0.626585 | 0.313292 | − | 0.949657i | \(-0.398568\pi\) | ||||
0.313292 | + | 0.949657i | \(0.398568\pi\) | |||||||
\(998\) | 10.5885 | 0.335172 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1134.2.a.j.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1134.2.a.o.1.2 | yes | 2 | ||
4.3 | odd | 2 | 9072.2.a.bi.1.1 | 2 | |||
7.6 | odd | 2 | 7938.2.a.bi.1.2 | 2 | |||
9.2 | odd | 6 | 1134.2.f.q.757.1 | 4 | |||
9.4 | even | 3 | 1134.2.f.t.379.2 | 4 | |||
9.5 | odd | 6 | 1134.2.f.q.379.1 | 4 | |||
9.7 | even | 3 | 1134.2.f.t.757.2 | 4 | |||
12.11 | even | 2 | 9072.2.a.bf.1.2 | 2 | |||
21.20 | even | 2 | 7938.2.a.br.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1134.2.a.j.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1134.2.a.o.1.2 | yes | 2 | 3.2 | odd | 2 | ||
1134.2.f.q.379.1 | 4 | 9.5 | odd | 6 | |||
1134.2.f.q.757.1 | 4 | 9.2 | odd | 6 | |||
1134.2.f.t.379.2 | 4 | 9.4 | even | 3 | |||
1134.2.f.t.757.2 | 4 | 9.7 | even | 3 | |||
7938.2.a.bi.1.2 | 2 | 7.6 | odd | 2 | |||
7938.2.a.br.1.1 | 2 | 21.20 | even | 2 | |||
9072.2.a.bf.1.2 | 2 | 12.11 | even | 2 | |||
9072.2.a.bi.1.1 | 2 | 4.3 | odd | 2 |