Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(1,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 11x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.182370\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.1 |
$q$-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 | ||||||||
\(5\) | −2.89219 | −1.29342 | −0.646712 | − | 0.762734i | \(-0.723857\pi\) | ||||
−0.646712 | + | 0.762734i | \(0.723857\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.89219 | −0.914589 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.364739 | −0.101160 | −0.0505802 | − | 0.998720i | \(-0.516107\pi\) | ||||
−0.0505802 | + | 0.998720i | \(0.516107\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.89219 | −0.701458 | −0.350729 | − | 0.936477i | \(-0.614066\pi\) | ||||
−0.350729 | + | 0.936477i | \(0.614066\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.25693 | 1.66485 | 0.832426 | − | 0.554136i | \(-0.186951\pi\) | ||||
0.832426 | + | 0.554136i | \(0.186951\pi\) | |||||||
\(20\) | −2.89219 | −0.646712 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 8.14911 | 1.69921 | 0.849604 | − | 0.527422i | \(-0.176841\pi\) | ||||
0.849604 | + | 0.527422i | \(0.176841\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.36474 | 0.672948 | ||||||||
\(26\) | −0.364739 | −0.0715312 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −2.36474 | −0.439121 | −0.219561 | − | 0.975599i | \(-0.570462\pi\) | ||||
−0.219561 | + | 0.975599i | \(0.570462\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.6766 | 1.91757 | 0.958783 | − | 0.284139i | \(-0.0917076\pi\) | ||||
0.958783 | + | 0.284139i | \(0.0917076\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.89219 | −0.496006 | ||||||||
\(35\) | −2.89219 | −0.488869 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.78437 | −0.622147 | −0.311073 | − | 0.950386i | \(-0.600689\pi\) | ||||
−0.311073 | + | 0.950386i | \(0.600689\pi\) | |||||||
\(38\) | 7.25693 | 1.17723 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.89219 | −0.457295 | ||||||||
\(41\) | 2.89219 | 0.451684 | 0.225842 | − | 0.974164i | \(-0.427487\pi\) | ||||
0.225842 | + | 0.974164i | \(0.427487\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.4196 | 1.74148 | 0.870739 | − | 0.491746i | \(-0.163641\pi\) | ||||
0.870739 | + | 0.491746i | \(0.163641\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.14911 | 1.20152 | ||||||||
\(47\) | −6.52745 | −0.952126 | −0.476063 | − | 0.879411i | \(-0.657937\pi\) | ||||
−0.476063 | + | 0.879411i | \(0.657937\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.36474 | 0.475846 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.364739 | −0.0505802 | ||||||||
\(53\) | 11.7844 | 1.61871 | 0.809354 | − | 0.587321i | \(-0.199817\pi\) | ||||
0.809354 | + | 0.587321i | \(0.199817\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.89219 | −0.389982 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.36474 | −0.310505 | ||||||||
\(59\) | −10.5139 | −1.36879 | −0.684393 | − | 0.729113i | \(-0.739933\pi\) | ||||
−0.684393 | + | 0.729113i | \(0.739933\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.9335 | −1.52793 | −0.763963 | − | 0.645260i | \(-0.776749\pi\) | ||||
−0.763963 | + | 0.645260i | \(0.776749\pi\) | |||||||
\(62\) | 10.6766 | 1.35592 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.05489 | 0.130843 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.14911 | −0.751233 | −0.375617 | − | 0.926775i | \(-0.622569\pi\) | ||||
−0.375617 | + | 0.926775i | \(0.622569\pi\) | |||||||
\(68\) | −2.89219 | −0.350729 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.89219 | −0.345682 | ||||||||
\(71\) | 13.9335 | 1.65360 | 0.826800 | − | 0.562496i | \(-0.190159\pi\) | ||||
0.826800 | + | 0.562496i | \(0.190159\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.10781 | −0.129660 | −0.0648299 | − | 0.997896i | \(-0.520650\pi\) | ||||
−0.0648299 | + | 0.997896i | \(0.520650\pi\) | |||||||
\(74\) | −3.78437 | −0.439924 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.25693 | 0.832426 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.1491 | 1.14186 | 0.570932 | − | 0.820997i | \(-0.306582\pi\) | ||||
0.570932 | + | 0.820997i | \(0.306582\pi\) | |||||||
\(80\) | −2.89219 | −0.323356 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.89219 | 0.319389 | ||||||||
\(83\) | −3.10781 | −0.341127 | −0.170563 | − | 0.985347i | \(-0.554559\pi\) | ||||
−0.170563 | + | 0.985347i | \(0.554559\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.36474 | 0.907283 | ||||||||
\(86\) | 11.4196 | 1.23141 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 2.14911 | 0.227805 | 0.113903 | − | 0.993492i | \(-0.463665\pi\) | ||||
0.113903 | + | 0.993492i | \(0.463665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.364739 | −0.0382351 | ||||||||
\(92\) | 8.14911 | 0.849604 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.52745 | −0.673255 | ||||||||
\(95\) | −20.9884 | −2.15336 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.72948 | 0.683275 | 0.341638 | − | 0.939832i | \(-0.389018\pi\) | ||||
0.341638 | + | 0.939832i | \(0.389018\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.36474 | 0.336474 | ||||||||
\(101\) | −1.27052 | −0.126422 | −0.0632108 | − | 0.998000i | \(-0.520134\pi\) | ||||
−0.0632108 | + | 0.998000i | \(0.520134\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.892186 | −0.0879097 | −0.0439548 | − | 0.999034i | \(-0.513996\pi\) | ||||
−0.0439548 | + | 0.999034i | \(0.513996\pi\) | |||||||
\(104\) | −0.364739 | −0.0357656 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.7844 | 1.14460 | ||||||||
\(107\) | 5.78437 | 0.559196 | 0.279598 | − | 0.960117i | \(-0.409799\pi\) | ||||
0.279598 | + | 0.960117i | \(0.409799\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00000 | 0.766261 | 0.383131 | − | 0.923694i | \(-0.374846\pi\) | ||||
0.383131 | + | 0.923694i | \(0.374846\pi\) | |||||||
\(110\) | −2.89219 | −0.275759 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −19.9335 | −1.87518 | −0.937592 | − | 0.347737i | \(-0.886950\pi\) | ||||
−0.937592 | + | 0.347737i | \(0.886950\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −23.5687 | −2.19780 | ||||||||
\(116\) | −2.36474 | −0.219561 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.5139 | −0.967878 | ||||||||
\(119\) | −2.89219 | −0.265126 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −11.9335 | −1.08041 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.6766 | 0.958783 | ||||||||
\(125\) | 4.72948 | 0.423017 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.1491 | 0.900588 | 0.450294 | − | 0.892880i | \(-0.351319\pi\) | ||||
0.450294 | + | 0.892880i | \(0.351319\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.05489 | 0.0925203 | ||||||||
\(131\) | −20.8922 | −1.82536 | −0.912679 | − | 0.408676i | \(-0.865990\pi\) | ||||
−0.912679 | + | 0.408676i | \(0.865990\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.25693 | 0.629255 | ||||||||
\(134\) | −6.14911 | −0.531202 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.89219 | −0.248003 | ||||||||
\(137\) | −7.93348 | −0.677803 | −0.338902 | − | 0.940822i | \(-0.610055\pi\) | ||||
−0.338902 | + | 0.940822i | \(0.610055\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.8257 | 1.59677 | 0.798386 | − | 0.602146i | \(-0.205687\pi\) | ||||
0.798386 | + | 0.602146i | \(0.205687\pi\) | |||||||
\(140\) | −2.89219 | −0.244434 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13.9335 | 1.16927 | ||||||||
\(143\) | −0.364739 | −0.0305010 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.83927 | 0.567970 | ||||||||
\(146\) | −1.10781 | −0.0916833 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.78437 | −0.311073 | ||||||||
\(149\) | −1.27052 | −0.104085 | −0.0520426 | − | 0.998645i | \(-0.516573\pi\) | ||||
−0.0520426 | + | 0.998645i | \(0.516573\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.29822 | −0.675300 | −0.337650 | − | 0.941272i | \(-0.609632\pi\) | ||||
−0.337650 | + | 0.941272i | \(0.609632\pi\) | |||||||
\(152\) | 7.25693 | 0.588614 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | −30.8786 | −2.48023 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.8922 | −1.50776 | −0.753880 | − | 0.657012i | \(-0.771820\pi\) | ||||
−0.753880 | + | 0.657012i | \(0.771820\pi\) | |||||||
\(158\) | 10.1491 | 0.807420 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.89219 | −0.228647 | ||||||||
\(161\) | 8.14911 | 0.642240 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.2982 | −1.58988 | −0.794940 | − | 0.606688i | \(-0.792498\pi\) | ||||
−0.794940 | + | 0.606688i | \(0.792498\pi\) | |||||||
\(164\) | 2.89219 | 0.225842 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.10781 | −0.241213 | ||||||||
\(167\) | 1.05489 | 0.0816301 | 0.0408151 | − | 0.999167i | \(-0.487005\pi\) | ||||
0.0408151 | + | 0.999167i | \(0.487005\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8670 | −0.989767 | ||||||||
\(170\) | 8.36474 | 0.641546 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.4196 | 0.870739 | ||||||||
\(173\) | −16.5139 | −1.25552 | −0.627762 | − | 0.778405i | \(-0.716029\pi\) | ||||
−0.627762 | + | 0.778405i | \(0.716029\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.36474 | 0.254350 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.14911 | 0.161083 | ||||||||
\(179\) | 20.9884 | 1.56874 | 0.784372 | − | 0.620290i | \(-0.212985\pi\) | ||||
0.784372 | + | 0.620290i | \(0.212985\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.10781 | −0.0823432 | −0.0411716 | − | 0.999152i | \(-0.513109\pi\) | ||||
−0.0411716 | + | 0.999152i | \(0.513109\pi\) | |||||||
\(182\) | −0.364739 | −0.0270363 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.14911 | 0.600760 | ||||||||
\(185\) | 10.9451 | 0.804700 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.89219 | −0.211498 | ||||||||
\(188\) | −6.52745 | −0.476063 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −20.9884 | −1.52266 | ||||||||
\(191\) | −10.6902 | −0.773512 | −0.386756 | − | 0.922182i | \(-0.626405\pi\) | ||||
−0.386756 | + | 0.922182i | \(0.626405\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.5687 | −1.55255 | −0.776276 | − | 0.630393i | \(-0.782894\pi\) | ||||
−0.776276 | + | 0.630393i | \(0.782894\pi\) | |||||||
\(194\) | 6.72948 | 0.483148 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −4.90578 | −0.349523 | −0.174761 | − | 0.984611i | \(-0.555915\pi\) | ||||
−0.174761 | + | 0.984611i | \(0.555915\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.10781 | −0.503860 | −0.251930 | − | 0.967746i | \(-0.581065\pi\) | ||||
−0.251930 | + | 0.967746i | \(0.581065\pi\) | |||||||
\(200\) | 3.36474 | 0.237923 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.27052 | −0.0893936 | ||||||||
\(203\) | −2.36474 | −0.165972 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.36474 | −0.584219 | ||||||||
\(206\) | −0.892186 | −0.0621615 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.364739 | −0.0252901 | ||||||||
\(209\) | 7.25693 | 0.501972 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.87859 | 0.611227 | 0.305614 | − | 0.952156i | \(-0.401138\pi\) | ||||
0.305614 | + | 0.952156i | \(0.401138\pi\) | |||||||
\(212\) | 11.7844 | 0.809354 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.78437 | 0.395412 | ||||||||
\(215\) | −33.0277 | −2.25247 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.6766 | 0.724772 | ||||||||
\(218\) | 8.00000 | 0.541828 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.89219 | −0.194991 | ||||||||
\(221\) | 1.05489 | 0.0709598 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.2453 | 1.48966 | 0.744828 | − | 0.667257i | \(-0.232532\pi\) | ||||
0.744828 | + | 0.667257i | \(0.232532\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.9335 | −1.32596 | ||||||||
\(227\) | 8.46093 | 0.561572 | 0.280786 | − | 0.959770i | \(-0.409405\pi\) | ||||
0.280786 | + | 0.959770i | \(0.409405\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.16271 | −0.142916 | −0.0714579 | − | 0.997444i | \(-0.522765\pi\) | ||||
−0.0714579 | + | 0.997444i | \(0.522765\pi\) | |||||||
\(230\) | −23.5687 | −1.55408 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.36474 | −0.155253 | ||||||||
\(233\) | −3.45896 | −0.226604 | −0.113302 | − | 0.993561i | \(-0.536143\pi\) | ||||
−0.113302 | + | 0.993561i | \(0.536143\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.8786 | 1.23150 | ||||||||
\(236\) | −10.5139 | −0.684393 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.89219 | −0.187473 | ||||||||
\(239\) | 16.2982 | 1.05424 | 0.527122 | − | 0.849790i | \(-0.323271\pi\) | ||||
0.527122 | + | 0.849790i | \(0.323271\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.67656 | 0.301244 | 0.150622 | − | 0.988591i | \(-0.451872\pi\) | ||||
0.150622 | + | 0.988591i | \(0.451872\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.9335 | −0.763963 | ||||||||
\(245\) | −2.89219 | −0.184775 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.64688 | −0.168417 | ||||||||
\(248\) | 10.6766 | 0.677962 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.72948 | 0.299118 | ||||||||
\(251\) | −10.0826 | −0.636408 | −0.318204 | − | 0.948022i | \(-0.603080\pi\) | ||||
−0.318204 | + | 0.948022i | \(0.603080\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.14911 | 0.512330 | ||||||||
\(254\) | 10.1491 | 0.636812 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.41963 | 0.587581 | 0.293790 | − | 0.955870i | \(-0.405083\pi\) | ||||
0.293790 | + | 0.955870i | \(0.405083\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.78437 | −0.235149 | ||||||||
\(260\) | 1.05489 | 0.0654217 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −20.8922 | −1.29072 | ||||||||
\(263\) | 6.87859 | 0.424152 | 0.212076 | − | 0.977253i | \(-0.431978\pi\) | ||||
0.212076 | + | 0.977253i | \(0.431978\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −34.0826 | −2.09368 | ||||||||
\(266\) | 7.25693 | 0.444951 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.14911 | −0.375617 | ||||||||
\(269\) | 26.8922 | 1.63965 | 0.819823 | − | 0.572617i | \(-0.194072\pi\) | ||||
0.819823 | + | 0.572617i | \(0.194072\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.7844 | −1.32331 | −0.661653 | − | 0.749810i | \(-0.730145\pi\) | ||||
−0.661653 | + | 0.749810i | \(0.730145\pi\) | |||||||
\(272\) | −2.89219 | −0.175365 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.93348 | −0.479279 | ||||||||
\(275\) | 3.36474 | 0.202901 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.27052 | 0.196507 | 0.0982533 | − | 0.995161i | \(-0.468674\pi\) | ||||
0.0982533 | + | 0.995161i | \(0.468674\pi\) | |||||||
\(278\) | 18.8257 | 1.12909 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.89219 | −0.172841 | ||||||||
\(281\) | 10.2982 | 0.614340 | 0.307170 | − | 0.951655i | \(-0.400618\pi\) | ||||
0.307170 | + | 0.951655i | \(0.400618\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.3118 | −1.68296 | −0.841481 | − | 0.540286i | \(-0.818316\pi\) | ||||
−0.841481 | + | 0.540286i | \(0.818316\pi\) | |||||||
\(284\) | 13.9335 | 0.826800 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.364739 | −0.0215675 | ||||||||
\(287\) | 2.89219 | 0.170720 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.63526 | −0.507957 | ||||||||
\(290\) | 6.83927 | 0.401615 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.10781 | −0.0648299 | ||||||||
\(293\) | 11.7844 | 0.688450 | 0.344225 | − | 0.938887i | \(-0.388142\pi\) | ||||
0.344225 | + | 0.938887i | \(0.388142\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 30.4080 | 1.77042 | ||||||||
\(296\) | −3.78437 | −0.219962 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.27052 | −0.0735993 | ||||||||
\(299\) | −2.97230 | −0.171893 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.4196 | 0.658217 | ||||||||
\(302\) | −8.29822 | −0.477509 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.25693 | 0.416213 | ||||||||
\(305\) | 34.5139 | 1.97626 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.01360 | 0.229068 | 0.114534 | − | 0.993419i | \(-0.463463\pi\) | ||||
0.114534 | + | 0.993419i | \(0.463463\pi\) | |||||||
\(308\) | 1.00000 | 0.0569803 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −30.8786 | −1.75379 | ||||||||
\(311\) | −6.52745 | −0.370138 | −0.185069 | − | 0.982726i | \(-0.559251\pi\) | ||||
−0.185069 | + | 0.982726i | \(0.559251\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.513850 | 0.0290445 | 0.0145223 | − | 0.999895i | \(-0.495377\pi\) | ||||
0.0145223 | + | 0.999895i | \(0.495377\pi\) | |||||||
\(314\) | −18.8922 | −1.06615 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.1491 | 0.570932 | ||||||||
\(317\) | 7.48615 | 0.420464 | 0.210232 | − | 0.977652i | \(-0.432578\pi\) | ||||
0.210232 | + | 0.977652i | \(0.432578\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.36474 | −0.132400 | ||||||||
\(320\) | −2.89219 | −0.161678 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.14911 | 0.454132 | ||||||||
\(323\) | −20.9884 | −1.16782 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.22725 | −0.0680757 | ||||||||
\(326\) | −20.2982 | −1.12421 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.89219 | 0.159694 | ||||||||
\(329\) | −6.52745 | −0.359870 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.4196 | −0.737610 | −0.368805 | − | 0.929507i | \(-0.620233\pi\) | ||||
−0.368805 | + | 0.929507i | \(0.620233\pi\) | |||||||
\(332\) | −3.10781 | −0.170563 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.05489 | 0.0577212 | ||||||||
\(335\) | 17.7844 | 0.971664 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.94511 | −0.487271 | −0.243636 | − | 0.969867i | \(-0.578340\pi\) | ||||
−0.243636 | + | 0.969867i | \(0.578340\pi\) | |||||||
\(338\) | −12.8670 | −0.699871 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.36474 | 0.453642 | ||||||||
\(341\) | 10.6766 | 0.578168 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 11.4196 | 0.615705 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.5139 | −0.887790 | ||||||||
\(347\) | 5.78437 | 0.310521 | 0.155261 | − | 0.987874i | \(-0.450378\pi\) | ||||
0.155261 | + | 0.987874i | \(0.450378\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.1491 | 1.18561 | 0.592807 | − | 0.805344i | \(-0.298020\pi\) | ||||
0.592807 | + | 0.805344i | \(0.298020\pi\) | |||||||
\(350\) | 3.36474 | 0.179853 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 9.41963 | 0.501356 | 0.250678 | − | 0.968070i | \(-0.419346\pi\) | ||||
0.250678 | + | 0.968070i | \(0.419346\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −40.2982 | −2.13881 | ||||||||
\(356\) | 2.14911 | 0.113903 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.9884 | 1.10927 | ||||||||
\(359\) | −18.4473 | −0.973613 | −0.486806 | − | 0.873510i | \(-0.661838\pi\) | ||||
−0.486806 | + | 0.873510i | \(0.661838\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 33.6630 | 1.77173 | ||||||||
\(362\) | −1.10781 | −0.0582254 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.364739 | −0.0191175 | ||||||||
\(365\) | 3.20400 | 0.167705 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.6766 | −0.974908 | −0.487454 | − | 0.873149i | \(-0.662074\pi\) | ||||
−0.487454 | + | 0.873149i | \(0.662074\pi\) | |||||||
\(368\) | 8.14911 | 0.424802 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.9451 | 0.569009 | ||||||||
\(371\) | 11.7844 | 0.611814 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.2040 | −0.994346 | −0.497173 | − | 0.867652i | \(-0.665629\pi\) | ||||
−0.497173 | + | 0.867652i | \(0.665629\pi\) | |||||||
\(374\) | −2.89219 | −0.149551 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.52745 | −0.336627 | ||||||||
\(377\) | 0.862513 | 0.0444217 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.8670 | −1.63690 | −0.818448 | − | 0.574581i | \(-0.805165\pi\) | ||||
−0.818448 | + | 0.574581i | \(0.805165\pi\) | |||||||
\(380\) | −20.9884 | −1.07668 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.6902 | −0.546956 | ||||||||
\(383\) | 29.0413 | 1.48394 | 0.741970 | − | 0.670433i | \(-0.233891\pi\) | ||||
0.741970 | + | 0.670433i | \(0.233891\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.89219 | −0.147399 | ||||||||
\(386\) | −21.5687 | −1.09782 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.72948 | 0.341638 | ||||||||
\(389\) | −26.5964 | −1.34849 | −0.674247 | − | 0.738506i | \(-0.735532\pi\) | ||||
−0.674247 | + | 0.738506i | \(0.735532\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.5687 | −1.19192 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.90578 | −0.247150 | ||||||||
\(395\) | −29.3531 | −1.47692 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.37834 | −0.420497 | −0.210248 | − | 0.977648i | \(-0.567427\pi\) | ||||
−0.210248 | + | 0.977648i | \(0.567427\pi\) | |||||||
\(398\) | −7.10781 | −0.356283 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.36474 | 0.168237 | ||||||||
\(401\) | −7.93348 | −0.396179 | −0.198090 | − | 0.980184i | \(-0.563474\pi\) | ||||
−0.198090 | + | 0.980184i | \(0.563474\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.89416 | −0.193982 | ||||||||
\(404\) | −1.27052 | −0.0632108 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.36474 | −0.117360 | ||||||||
\(407\) | −3.78437 | −0.187584 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.6766 | −1.22018 | −0.610089 | − | 0.792333i | \(-0.708866\pi\) | ||||
−0.610089 | + | 0.792333i | \(0.708866\pi\) | |||||||
\(410\) | −8.36474 | −0.413105 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.892186 | −0.0439548 | ||||||||
\(413\) | −10.5139 | −0.517353 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.98838 | 0.441222 | ||||||||
\(416\) | −0.364739 | −0.0178828 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.25693 | 0.354948 | ||||||||
\(419\) | −2.54104 | −0.124138 | −0.0620690 | − | 0.998072i | \(-0.519770\pi\) | ||||
−0.0620690 | + | 0.998072i | \(0.519770\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.43126 | 0.118492 | 0.0592461 | − | 0.998243i | \(-0.481130\pi\) | ||||
0.0592461 | + | 0.998243i | \(0.481130\pi\) | |||||||
\(422\) | 8.87859 | 0.432203 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.7844 | 0.572300 | ||||||||
\(425\) | −9.73145 | −0.472045 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.9335 | −0.577502 | ||||||||
\(428\) | 5.78437 | 0.279598 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −33.0277 | −1.59274 | ||||||||
\(431\) | 2.58037 | 0.124292 | 0.0621460 | − | 0.998067i | \(-0.480206\pi\) | ||||
0.0621460 | + | 0.998067i | \(0.480206\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.1375 | 1.78471 | 0.892357 | − | 0.451331i | \(-0.149050\pi\) | ||||
0.892357 | + | 0.451331i | \(0.149050\pi\) | |||||||
\(434\) | 10.6766 | 0.512491 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.00000 | 0.383131 | ||||||||
\(437\) | 59.1375 | 2.82893 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.5139 | 0.883618 | 0.441809 | − | 0.897109i | \(-0.354337\pi\) | ||||
0.441809 | + | 0.897109i | \(0.354337\pi\) | |||||||
\(440\) | −2.89219 | −0.137880 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.05489 | 0.0501762 | ||||||||
\(443\) | −21.4196 | −1.01768 | −0.508839 | − | 0.860862i | \(-0.669925\pi\) | ||||
−0.508839 | + | 0.860862i | \(0.669925\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.21563 | −0.294649 | ||||||||
\(446\) | 22.2453 | 1.05335 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 4.06652 | 0.191911 | 0.0959554 | − | 0.995386i | \(-0.469409\pi\) | ||||
0.0959554 | + | 0.995386i | \(0.469409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.89219 | 0.136188 | ||||||||
\(452\) | −19.9335 | −0.937592 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.46093 | 0.397091 | ||||||||
\(455\) | 1.05489 | 0.0494542 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.8393 | −0.787708 | −0.393854 | − | 0.919173i | \(-0.628858\pi\) | ||||
−0.393854 | + | 0.919173i | \(0.628858\pi\) | |||||||
\(458\) | −2.16271 | −0.101057 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −23.5687 | −1.09890 | ||||||||
\(461\) | −15.4590 | −0.719995 | −0.359998 | − | 0.932953i | \(-0.617223\pi\) | ||||
−0.359998 | + | 0.932953i | \(0.617223\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.5687 | 0.909437 | 0.454718 | − | 0.890635i | \(-0.349740\pi\) | ||||
0.454718 | + | 0.890635i | \(0.349740\pi\) | |||||||
\(464\) | −2.36474 | −0.109780 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.45896 | −0.160233 | ||||||||
\(467\) | 16.2982 | 0.754192 | 0.377096 | − | 0.926174i | \(-0.376923\pi\) | ||||
0.377096 | + | 0.926174i | \(0.376923\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.14911 | −0.283940 | ||||||||
\(470\) | 18.8786 | 0.870804 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10.5139 | −0.483939 | ||||||||
\(473\) | 11.4196 | 0.525075 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.4177 | 1.12036 | ||||||||
\(476\) | −2.89219 | −0.132563 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 16.2982 | 0.745463 | ||||||||
\(479\) | −0.431256 | −0.0197046 | −0.00985231 | − | 0.999951i | \(-0.503136\pi\) | ||||
−0.00985231 | + | 0.999951i | \(0.503136\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.38031 | 0.0629367 | ||||||||
\(482\) | 4.67656 | 0.213011 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −19.4629 | −0.883765 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.0826 | −0.638143 | −0.319072 | − | 0.947731i | \(-0.603371\pi\) | ||||
−0.319072 | + | 0.947731i | \(0.603371\pi\) | |||||||
\(488\) | −11.9335 | −0.540203 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.89219 | −0.130656 | ||||||||
\(491\) | −23.5687 | −1.06364 | −0.531821 | − | 0.846857i | \(-0.678492\pi\) | ||||
−0.531821 | + | 0.846857i | \(0.678492\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.83927 | 0.308025 | ||||||||
\(494\) | −2.64688 | −0.119089 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.6766 | 0.479392 | ||||||||
\(497\) | 13.9335 | 0.625002 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.9884 | 1.29770 | 0.648849 | − | 0.760917i | \(-0.275251\pi\) | ||||
0.648849 | + | 0.760917i | \(0.275251\pi\) | |||||||
\(500\) | 4.72948 | 0.211509 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.0826 | −0.450008 | ||||||||
\(503\) | 25.0549 | 1.11714 | 0.558571 | − | 0.829457i | \(-0.311350\pi\) | ||||
0.558571 | + | 0.829457i | \(0.311350\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.67458 | 0.163517 | ||||||||
\(506\) | 8.14911 | 0.362272 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.1491 | 0.450294 | ||||||||
\(509\) | 29.0020 | 1.28549 | 0.642745 | − | 0.766080i | \(-0.277796\pi\) | ||||
0.642745 | + | 0.766080i | \(0.277796\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.10781 | −0.0490068 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.41963 | 0.415482 | ||||||||
\(515\) | 2.58037 | 0.113705 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.52745 | −0.287077 | ||||||||
\(518\) | −3.78437 | −0.166276 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.05489 | 0.0462601 | ||||||||
\(521\) | 20.9884 | 0.919517 | 0.459759 | − | 0.888044i | \(-0.347936\pi\) | ||||
0.459759 | + | 0.888044i | \(0.347936\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.8806 | −0.694408 | −0.347204 | − | 0.937790i | \(-0.612869\pi\) | ||||
−0.347204 | + | 0.937790i | \(0.612869\pi\) | |||||||
\(524\) | −20.8922 | −0.912679 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.87859 | 0.299921 | ||||||||
\(527\) | −30.8786 | −1.34509 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 43.4080 | 1.88730 | ||||||||
\(530\) | −34.0826 | −1.48045 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.25693 | 0.314628 | ||||||||
\(533\) | −1.05489 | −0.0456925 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.7295 | −0.723278 | ||||||||
\(536\) | −6.14911 | −0.265601 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 26.8922 | 1.15940 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.4745 | −0.622308 | −0.311154 | − | 0.950359i | \(-0.600716\pi\) | ||||
−0.311154 | + | 0.950359i | \(0.600716\pi\) | |||||||
\(542\) | −21.7844 | −0.935719 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.89219 | −0.124001 | ||||||||
\(545\) | −23.1375 | −0.991101 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.0710 | −1.24298 | −0.621492 | − | 0.783420i | \(-0.713473\pi\) | ||||
−0.621492 | + | 0.783420i | \(0.713473\pi\) | |||||||
\(548\) | −7.93348 | −0.338902 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.36474 | 0.143473 | ||||||||
\(551\) | −17.1607 | −0.731072 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.1491 | 0.431584 | ||||||||
\(554\) | 3.27052 | 0.138951 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.8257 | 0.798386 | ||||||||
\(557\) | 37.5022 | 1.58902 | 0.794510 | − | 0.607251i | \(-0.207728\pi\) | ||||
0.794510 | + | 0.607251i | \(0.207728\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.16519 | −0.176169 | ||||||||
\(560\) | −2.89219 | −0.122217 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.2982 | 0.434404 | ||||||||
\(563\) | −27.1078 | −1.14246 | −0.571229 | − | 0.820791i | \(-0.693533\pi\) | ||||
−0.571229 | + | 0.820791i | \(0.693533\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 57.6513 | 2.42541 | ||||||||
\(566\) | −28.3118 | −1.19003 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.9335 | 0.584636 | ||||||||
\(569\) | 46.2982 | 1.94092 | 0.970461 | − | 0.241257i | \(-0.0775597\pi\) | ||||
0.970461 | + | 0.241257i | \(0.0775597\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.63526 | 0.235828 | 0.117914 | − | 0.993024i | \(-0.462379\pi\) | ||||
0.117914 | + | 0.993024i | \(0.462379\pi\) | |||||||
\(572\) | −0.364739 | −0.0152505 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.89219 | 0.120718 | ||||||||
\(575\) | 27.4196 | 1.14348 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.513850 | 0.0213919 | 0.0106959 | − | 0.999943i | \(-0.496595\pi\) | ||||
0.0106959 | + | 0.999943i | \(0.496595\pi\) | |||||||
\(578\) | −8.63526 | −0.359179 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.83927 | 0.283985 | ||||||||
\(581\) | −3.10781 | −0.128934 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.7844 | 0.488059 | ||||||||
\(584\) | −1.10781 | −0.0458417 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.7844 | 0.486808 | ||||||||
\(587\) | 17.7844 | 0.734040 | 0.367020 | − | 0.930213i | \(-0.380378\pi\) | ||||
0.367020 | + | 0.930213i | \(0.380378\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 77.4790 | 3.19247 | ||||||||
\(590\) | 30.4080 | 1.25188 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.78437 | −0.155537 | ||||||||
\(593\) | 26.0297 | 1.06891 | 0.534455 | − | 0.845197i | \(-0.320517\pi\) | ||||
0.534455 | + | 0.845197i | \(0.320517\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.36474 | 0.342921 | ||||||||
\(596\) | −1.27052 | −0.0520426 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.97230 | −0.121546 | ||||||||
\(599\) | 25.9335 | 1.05961 | 0.529807 | − | 0.848118i | \(-0.322264\pi\) | ||||
0.529807 | + | 0.848118i | \(0.322264\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.2730 | −1.35723 | −0.678617 | − | 0.734492i | \(-0.737420\pi\) | ||||
−0.678617 | + | 0.734492i | \(0.737420\pi\) | |||||||
\(602\) | 11.4196 | 0.465429 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.29822 | −0.337650 | ||||||||
\(605\) | −2.89219 | −0.117584 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.4080 | −1.39658 | −0.698289 | − | 0.715816i | \(-0.746055\pi\) | ||||
−0.698289 | + | 0.715816i | \(0.746055\pi\) | |||||||
\(608\) | 7.25693 | 0.294307 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 34.5139 | 1.39742 | ||||||||
\(611\) | 2.38082 | 0.0963175 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.33704 | 0.296340 | 0.148170 | − | 0.988962i | \(-0.452662\pi\) | ||||
0.148170 | + | 0.988962i | \(0.452662\pi\) | |||||||
\(614\) | 4.01360 | 0.161976 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | −7.70178 | −0.310062 | −0.155031 | − | 0.987910i | \(-0.549548\pi\) | ||||
−0.155031 | + | 0.987910i | \(0.549548\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.2982 | −0.815854 | −0.407927 | − | 0.913014i | \(-0.633748\pi\) | ||||
−0.407927 | + | 0.913014i | \(0.633748\pi\) | |||||||
\(620\) | −30.8786 | −1.24011 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.52745 | −0.261727 | ||||||||
\(623\) | 2.14911 | 0.0861023 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.5022 | −1.22009 | ||||||||
\(626\) | 0.513850 | 0.0205376 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −18.8922 | −0.753880 | ||||||||
\(629\) | 10.9451 | 0.436410 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.2433 | 1.40301 | 0.701507 | − | 0.712662i | \(-0.252511\pi\) | ||||
0.701507 | + | 0.712662i | \(0.252511\pi\) | |||||||
\(632\) | 10.1491 | 0.403710 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.48615 | 0.297313 | ||||||||
\(635\) | −29.3531 | −1.16484 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.364739 | −0.0144515 | ||||||||
\(638\) | −2.36474 | −0.0936209 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.89219 | −0.114324 | ||||||||
\(641\) | 25.7572 | 1.01735 | 0.508674 | − | 0.860959i | \(-0.330136\pi\) | ||||
0.508674 | + | 0.860959i | \(0.330136\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.48615 | −0.216353 | −0.108176 | − | 0.994132i | \(-0.534501\pi\) | ||||
−0.108176 | + | 0.994132i | \(0.534501\pi\) | |||||||
\(644\) | 8.14911 | 0.321120 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −20.9884 | −0.825777 | ||||||||
\(647\) | 17.4726 | 0.686917 | 0.343458 | − | 0.939168i | \(-0.388402\pi\) | ||||
0.343458 | + | 0.939168i | \(0.388402\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.5139 | −0.412705 | ||||||||
\(650\) | −1.22725 | −0.0481368 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.2982 | −0.794940 | ||||||||
\(653\) | −8.54104 | −0.334237 | −0.167118 | − | 0.985937i | \(-0.553446\pi\) | ||||
−0.167118 | + | 0.985937i | \(0.553446\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 60.4241 | 2.36096 | ||||||||
\(656\) | 2.89219 | 0.112921 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.52745 | −0.254466 | ||||||||
\(659\) | −43.5416 | −1.69614 | −0.848069 | − | 0.529886i | \(-0.822235\pi\) | ||||
−0.848069 | + | 0.529886i | \(0.822235\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.8650 | 0.733763 | 0.366882 | − | 0.930268i | \(-0.380425\pi\) | ||||
0.366882 | + | 0.930268i | \(0.380425\pi\) | |||||||
\(662\) | −13.4196 | −0.521569 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.10781 | −0.120607 | ||||||||
\(665\) | −20.9884 | −0.813894 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.2705 | −0.746158 | ||||||||
\(668\) | 1.05489 | 0.0408151 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 17.7844 | 0.687070 | ||||||||
\(671\) | −11.9335 | −0.460687 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.08259 | −0.311561 | −0.155781 | − | 0.987792i | \(-0.549789\pi\) | ||||
−0.155781 | + | 0.987792i | \(0.549789\pi\) | |||||||
\(674\) | −8.94511 | −0.344553 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.8670 | −0.494883 | ||||||||
\(677\) | −6.62364 | −0.254567 | −0.127284 | − | 0.991866i | \(-0.540626\pi\) | ||||
−0.127284 | + | 0.991866i | \(0.540626\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.72948 | 0.258254 | ||||||||
\(680\) | 8.36474 | 0.320773 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.6766 | 0.408827 | ||||||||
\(683\) | 13.7179 | 0.524899 | 0.262450 | − | 0.964946i | \(-0.415470\pi\) | ||||
0.262450 | + | 0.964946i | \(0.415470\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.9451 | 0.876687 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.4196 | 0.435369 | ||||||||
\(689\) | −4.29822 | −0.163749 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.3808 | −0.699239 | −0.349620 | − | 0.936892i | \(-0.613689\pi\) | ||||
−0.349620 | + | 0.936892i | \(0.613689\pi\) | |||||||
\(692\) | −16.5139 | −0.627762 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.78437 | 0.219572 | ||||||||
\(695\) | −54.4473 | −2.06531 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.36474 | −0.316837 | ||||||||
\(698\) | 22.1491 | 0.838356 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.36474 | 0.127175 | ||||||||
\(701\) | −31.3259 | −1.18316 | −0.591582 | − | 0.806245i | \(-0.701496\pi\) | ||||
−0.591582 | + | 0.806245i | \(0.701496\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.4629 | −1.03578 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.41963 | 0.354513 | ||||||||
\(707\) | −1.27052 | −0.0477829 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.1103 | −1.54393 | −0.771965 | − | 0.635665i | \(-0.780726\pi\) | ||||
−0.771965 | + | 0.635665i | \(0.780726\pi\) | |||||||
\(710\) | −40.2982 | −1.51237 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.14911 | 0.0805413 | ||||||||
\(713\) | 87.0045 | 3.25834 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.05489 | 0.0394508 | ||||||||
\(716\) | 20.9884 | 0.784372 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18.4473 | −0.688448 | ||||||||
\(719\) | 1.17433 | 0.0437952 | 0.0218976 | − | 0.999760i | \(-0.493029\pi\) | ||||
0.0218976 | + | 0.999760i | \(0.493029\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.892186 | −0.0332267 | ||||||||
\(722\) | 33.6630 | 1.25281 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.10781 | −0.0411716 | ||||||||
\(725\) | −7.95673 | −0.295506 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 43.2730 | 1.60491 | 0.802453 | − | 0.596715i | \(-0.203528\pi\) | ||||
0.802453 | + | 0.596715i | \(0.203528\pi\) | |||||||
\(728\) | −0.364739 | −0.0135181 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.20400 | 0.118586 | ||||||||
\(731\) | −33.0277 | −1.22157 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.9058 | −0.550558 | −0.275279 | − | 0.961364i | \(-0.588770\pi\) | ||||
−0.275279 | + | 0.961364i | \(0.588770\pi\) | |||||||
\(734\) | −18.6766 | −0.689364 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.14911 | 0.300380 | ||||||||
\(737\) | −6.14911 | −0.226505 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.9058 | 0.916174 | 0.458087 | − | 0.888907i | \(-0.348535\pi\) | ||||
0.458087 | + | 0.888907i | \(0.348535\pi\) | |||||||
\(740\) | 10.9451 | 0.402350 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.7844 | 0.432618 | ||||||||
\(743\) | −11.5687 | −0.424416 | −0.212208 | − | 0.977225i | \(-0.568065\pi\) | ||||
−0.212208 | + | 0.977225i | \(0.568065\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.67458 | 0.134626 | ||||||||
\(746\) | −19.2040 | −0.703109 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.89219 | −0.105749 | ||||||||
\(749\) | 5.78437 | 0.211356 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.3808 | 1.25457 | 0.627287 | − | 0.778788i | \(-0.284165\pi\) | ||||
0.627287 | + | 0.778788i | \(0.284165\pi\) | |||||||
\(752\) | −6.52745 | −0.238031 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.862513 | 0.0314109 | ||||||||
\(755\) | 24.0000 | 0.873449 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.62364 | 0.0953577 | 0.0476789 | − | 0.998863i | \(-0.484818\pi\) | ||||
0.0476789 | + | 0.998863i | \(0.484818\pi\) | |||||||
\(758\) | −31.8670 | −1.15746 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −20.9884 | −0.761328 | ||||||||
\(761\) | −45.7315 | −1.65776 | −0.828882 | − | 0.559424i | \(-0.811023\pi\) | ||||
−0.828882 | + | 0.559424i | \(0.811023\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.00000 | 0.289619 | ||||||||
\(764\) | −10.6902 | −0.386756 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29.0413 | 1.04930 | ||||||||
\(767\) | 3.83481 | 0.138467 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.5668 | 0.525291 | 0.262646 | − | 0.964892i | \(-0.415405\pi\) | ||||
0.262646 | + | 0.964892i | \(0.415405\pi\) | |||||||
\(770\) | −2.89219 | −0.104227 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21.5687 | −0.776276 | ||||||||
\(773\) | −38.0297 | −1.36783 | −0.683916 | − | 0.729561i | \(-0.739725\pi\) | ||||
−0.683916 | + | 0.729561i | \(0.739725\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 35.9238 | 1.29042 | ||||||||
\(776\) | 6.72948 | 0.241574 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.5964 | −0.953529 | ||||||||
\(779\) | 20.9884 | 0.751987 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.9335 | 0.498579 | ||||||||
\(782\) | −23.5687 | −0.842817 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 54.6397 | 1.95017 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.2020 | −0.934002 | −0.467001 | − | 0.884257i | \(-0.654665\pi\) | ||||
−0.467001 | + | 0.884257i | \(0.654665\pi\) | |||||||
\(788\) | −4.90578 | −0.174761 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −29.3531 | −1.04434 | ||||||||
\(791\) | −19.9335 | −0.708753 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.35261 | 0.154566 | ||||||||
\(794\) | −8.37834 | −0.297336 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.10781 | −0.251930 | ||||||||
\(797\) | 13.8373 | 0.490142 | 0.245071 | − | 0.969505i | \(-0.421189\pi\) | ||||
0.245071 | + | 0.969505i | \(0.421189\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.8786 | 0.667876 | ||||||||
\(800\) | 3.36474 | 0.118961 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.93348 | −0.280141 | ||||||||
\(803\) | −1.10781 | −0.0390939 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −23.5687 | −0.830689 | ||||||||
\(806\) | −3.89416 | −0.137166 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.27052 | −0.0446968 | ||||||||
\(809\) | −28.0826 | −0.987331 | −0.493666 | − | 0.869652i | \(-0.664343\pi\) | ||||
−0.493666 | + | 0.869652i | \(0.664343\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 56.1516 | 1.97175 | 0.985875 | − | 0.167486i | \(-0.0535648\pi\) | ||||
0.985875 | + | 0.167486i | \(0.0535648\pi\) | |||||||
\(812\) | −2.36474 | −0.0829861 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.78437 | −0.132642 | ||||||||
\(815\) | 58.7062 | 2.05639 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 82.8714 | 2.89930 | ||||||||
\(818\) | −24.6766 | −0.862796 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.36474 | −0.292109 | ||||||||
\(821\) | −18.0000 | −0.628204 | −0.314102 | − | 0.949389i | \(-0.601703\pi\) | ||||
−0.314102 | + | 0.949389i | \(0.601703\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.2433 | 1.22851 | 0.614253 | − | 0.789109i | \(-0.289458\pi\) | ||||
0.614253 | + | 0.789109i | \(0.289458\pi\) | |||||||
\(824\) | −0.892186 | −0.0310808 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.5139 | −0.365824 | ||||||||
\(827\) | −0.431256 | −0.0149963 | −0.00749813 | − | 0.999972i | \(-0.502387\pi\) | ||||
−0.00749813 | + | 0.999972i | \(0.502387\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.86499 | −0.0995053 | −0.0497527 | − | 0.998762i | \(-0.515843\pi\) | ||||
−0.0497527 | + | 0.998762i | \(0.515843\pi\) | |||||||
\(830\) | 8.98838 | 0.311991 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.364739 | −0.0126451 | ||||||||
\(833\) | −2.89219 | −0.100208 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.05095 | −0.105582 | ||||||||
\(836\) | 7.25693 | 0.250986 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.54104 | −0.0877789 | ||||||||
\(839\) | 1.17433 | 0.0405424 | 0.0202712 | − | 0.999795i | \(-0.493547\pi\) | ||||
0.0202712 | + | 0.999795i | \(0.493547\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.4080 | −0.807173 | ||||||||
\(842\) | 2.43126 | 0.0837866 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.87859 | 0.305614 | ||||||||
\(845\) | 37.2137 | 1.28019 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 11.7844 | 0.404677 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.73145 | −0.333786 | ||||||||
\(851\) | −30.8393 | −1.05716 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −51.8004 | −1.77361 | −0.886807 | − | 0.462140i | \(-0.847082\pi\) | ||||
−0.886807 | + | 0.462140i | \(0.847082\pi\) | |||||||
\(854\) | −11.9335 | −0.408355 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.78437 | 0.197706 | ||||||||
\(857\) | 12.7824 | 0.436638 | 0.218319 | − | 0.975877i | \(-0.429943\pi\) | ||||
0.218319 | + | 0.975877i | \(0.429943\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.7567 | 0.571730 | 0.285865 | − | 0.958270i | \(-0.407719\pi\) | ||||
0.285865 | + | 0.958270i | \(0.407719\pi\) | |||||||
\(860\) | −33.0277 | −1.12624 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.58037 | 0.0878877 | ||||||||
\(863\) | 26.5571 | 0.904015 | 0.452007 | − | 0.892014i | \(-0.350708\pi\) | ||||
0.452007 | + | 0.892014i | \(0.350708\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 47.7611 | 1.62393 | ||||||||
\(866\) | 37.1375 | 1.26198 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10.6766 | 0.362386 | ||||||||
\(869\) | 10.1491 | 0.344285 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.24282 | 0.0759951 | ||||||||
\(872\) | 8.00000 | 0.270914 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 59.1375 | 2.00036 | ||||||||
\(875\) | 4.72948 | 0.159886 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.5687 | −0.525719 | −0.262860 | − | 0.964834i | \(-0.584666\pi\) | ||||
−0.262860 | + | 0.964834i | \(0.584666\pi\) | |||||||
\(878\) | 18.5139 | 0.624812 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.89219 | −0.0974956 | ||||||||
\(881\) | −45.6907 | −1.53936 | −0.769679 | − | 0.638431i | \(-0.779584\pi\) | ||||
−0.769679 | + | 0.638431i | \(0.779584\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −55.0045 | −1.85105 | −0.925524 | − | 0.378690i | \(-0.876375\pi\) | ||||
−0.925524 | + | 0.378690i | \(0.876375\pi\) | |||||||
\(884\) | 1.05489 | 0.0354799 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21.4196 | −0.719607 | ||||||||
\(887\) | 30.8393 | 1.03548 | 0.517741 | − | 0.855538i | \(-0.326773\pi\) | ||||
0.517741 | + | 0.855538i | \(0.326773\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.1491 | 0.340390 | ||||||||
\(890\) | −6.21563 | −0.208348 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 22.2453 | 0.744828 | ||||||||
\(893\) | −47.3692 | −1.58515 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −60.7023 | −2.02905 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.06652 | 0.135701 | ||||||||
\(899\) | −25.2473 | −0.842044 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.0826 | −1.13546 | ||||||||
\(902\) | 2.89219 | 0.0962993 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.9335 | −0.662978 | ||||||||
\(905\) | 3.20400 | 0.106505 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.4196 | −0.844045 | −0.422023 | − | 0.906585i | \(-0.638680\pi\) | ||||
−0.422023 | + | 0.906585i | \(0.638680\pi\) | |||||||
\(908\) | 8.46093 | 0.280786 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.05489 | 0.0349694 | ||||||||
\(911\) | 50.5571 | 1.67503 | 0.837516 | − | 0.546413i | \(-0.184007\pi\) | ||||
0.837516 | + | 0.546413i | \(0.184007\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.10781 | −0.102854 | ||||||||
\(914\) | −16.8393 | −0.556993 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.16271 | −0.0714579 | ||||||||
\(917\) | −20.8922 | −0.689921 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.7295 | 0.419907 | 0.209953 | − | 0.977711i | \(-0.432669\pi\) | ||||
0.209953 | + | 0.977711i | \(0.432669\pi\) | |||||||
\(920\) | −23.5687 | −0.777038 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.4590 | −0.509114 | ||||||||
\(923\) | −5.08209 | −0.167279 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.7334 | −0.418672 | ||||||||
\(926\) | 19.5687 | 0.643069 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.36474 | −0.0776264 | ||||||||
\(929\) | −6.44733 | −0.211530 | −0.105765 | − | 0.994391i | \(-0.533729\pi\) | ||||
−0.105765 | + | 0.994391i | \(0.533729\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.25693 | 0.237836 | ||||||||
\(932\) | −3.45896 | −0.113302 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16.2982 | 0.533294 | ||||||||
\(935\) | 8.36474 | 0.273556 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.1904 | 1.28029 | 0.640147 | − | 0.768252i | \(-0.278873\pi\) | ||||
0.640147 | + | 0.768252i | \(0.278873\pi\) | |||||||
\(938\) | −6.14911 | −0.200776 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 18.8786 | 0.615752 | ||||||||
\(941\) | −37.1103 | −1.20976 | −0.604881 | − | 0.796316i | \(-0.706779\pi\) | ||||
−0.604881 | + | 0.796316i | \(0.706779\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.5687 | 0.767504 | ||||||||
\(944\) | −10.5139 | −0.342197 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.4196 | 0.371284 | ||||||||
\(947\) | −49.3259 | −1.60288 | −0.801439 | − | 0.598077i | \(-0.795932\pi\) | ||||
−0.801439 | + | 0.598077i | \(0.795932\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.404063 | 0.0131164 | ||||||||
\(950\) | 24.4177 | 0.792213 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.89219 | −0.0937363 | ||||||||
\(953\) | 24.2156 | 0.784421 | 0.392211 | − | 0.919875i | \(-0.371710\pi\) | ||||
0.392211 | + | 0.919875i | \(0.371710\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.9179 | 1.00048 | ||||||||
\(956\) | 16.2982 | 0.527122 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.431256 | −0.0139333 | ||||||||
\(959\) | −7.93348 | −0.256186 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 82.9889 | 2.67706 | ||||||||
\(962\) | 1.38031 | 0.0445029 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.67656 | 0.150622 | ||||||||
\(965\) | 62.3808 | 2.00811 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.8670 | −1.41067 | −0.705333 | − | 0.708876i | \(-0.749203\pi\) | ||||
−0.705333 | + | 0.708876i | \(0.749203\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −19.4629 | −0.624916 | ||||||||
\(971\) | 28.2982 | 0.908133 | 0.454067 | − | 0.890968i | \(-0.349973\pi\) | ||||
0.454067 | + | 0.890968i | \(0.349973\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.8257 | 0.603523 | ||||||||
\(974\) | −14.0826 | −0.451235 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.9335 | −0.381981 | ||||||||
\(977\) | −28.2982 | −0.905340 | −0.452670 | − | 0.891678i | \(-0.649528\pi\) | ||||
−0.452670 | + | 0.891678i | \(0.649528\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.14911 | 0.0686859 | ||||||||
\(980\) | −2.89219 | −0.0923875 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −23.5687 | −0.752109 | ||||||||
\(983\) | −32.6372 | −1.04097 | −0.520483 | − | 0.853872i | \(-0.674248\pi\) | ||||
−0.520483 | + | 0.853872i | \(0.674248\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.1884 | 0.452081 | ||||||||
\(986\) | 6.83927 | 0.217807 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.64688 | −0.0842086 | ||||||||
\(989\) | 93.0599 | 2.95913 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.8670 | −1.01229 | −0.506144 | − | 0.862449i | \(-0.668929\pi\) | ||||
−0.506144 | + | 0.862449i | \(0.668929\pi\) | |||||||
\(992\) | 10.6766 | 0.338981 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 13.9335 | 0.441943 | ||||||||
\(995\) | 20.5571 | 0.651705 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.4196 | −1.18509 | −0.592546 | − | 0.805537i | \(-0.701877\pi\) | ||||
−0.592546 | + | 0.805537i | \(0.701877\pi\) | |||||||
\(998\) | 28.9884 | 0.917611 | ||||||||
\(999\) | 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 | 1386.2.a.r.1.1 | yes | 3 | |
3.2 | odd | 2 | 1386.2.a.q.1.3 | ✓ | 3 | ||
7.6 | odd | 2 | 9702.2.a.dy.1.3 | 3 | |||
21.20 | even | 2 | 9702.2.a.dx.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.a.q.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
1386.2.a.r.1.1 | yes | 3 | 1.1 | even | 1 | trivial | |
9702.2.a.dx.1.1 | 3 | 21.20 | even | 2 | |||
9702.2.a.dy.1.3 | 3 | 7.6 | odd | 2 |