Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1872,2,Mod(289,1872)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1872, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1872.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1872.t (of order \(3\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(14.9479952584\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1153.2 | ||
Root | \(1.28078 - 2.21837i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1872.1153 |
Dual form | 1872.2.t.r.289.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1872\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(209\) | \(469\) | \(703\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.56155 | 1.59277 | 0.796387 | − | 0.604787i | \(-0.206742\pi\) | ||||
0.796387 | + | 0.604787i | \(0.206742\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.280776 | + | 0.486319i | 0.106124 | + | 0.183811i | 0.914197 | − | 0.405271i | \(-0.132823\pi\) |
−0.808073 | + | 0.589082i | \(0.799489\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | − | 1.73205i | 0.301511 | − | 0.522233i | −0.674967 | − | 0.737848i | \(-0.735842\pi\) |
0.976478 | + | 0.215615i | \(0.0691756\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | + | 3.57071i | 0.138675 | + | 0.990338i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.780776 | − | 1.35234i | −0.189366 | − | 0.327992i | 0.755673 | − | 0.654949i | \(-0.227310\pi\) |
−0.945039 | + | 0.326957i | \(0.893977\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.56155 | + | 6.16879i | 0.817076 | + | 1.41522i | 0.907827 | + | 0.419344i | \(0.137740\pi\) |
−0.0907512 | + | 0.995874i | \(0.528927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | + | 1.73205i | −0.208514 | + | 0.361158i | −0.951247 | − | 0.308431i | \(-0.900196\pi\) |
0.742732 | + | 0.669588i | \(0.233529\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.68466 | 1.53693 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.34233 | − | 5.78908i | 0.620655 | − | 1.07501i | −0.368709 | − | 0.929545i | \(-0.620200\pi\) |
0.989364 | − | 0.145461i | \(-0.0464665\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.56155 | −0.460068 | −0.230034 | − | 0.973183i | \(-0.573884\pi\) | ||||
−0.230034 | + | 0.973183i | \(0.573884\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | + | 1.73205i | 0.169031 | + | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.78078 | + | 6.54850i | −0.621556 | + | 1.07657i | 0.367640 | + | 0.929968i | \(0.380166\pi\) |
−0.989196 | + | 0.146598i | \(0.953168\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.780776 | + | 1.35234i | −0.121937 | + | 0.211201i | −0.920531 | − | 0.390669i | \(-0.872244\pi\) |
0.798595 | + | 0.601869i | \(0.205577\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.28078 | + | 3.95042i | 0.347815 | + | 0.602433i | 0.985861 | − | 0.167565i | \(-0.0535903\pi\) |
−0.638046 | + | 0.769998i | \(0.720257\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.24621 | 1.20283 | 0.601417 | − | 0.798935i | \(-0.294603\pi\) | ||||
0.601417 | + | 0.798935i | \(0.294603\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.34233 | − | 5.78908i | 0.477476 | − | 0.827012i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.684658 | 0.0940451 | 0.0470225 | − | 0.998894i | \(-0.485027\pi\) | ||||
0.0470225 | + | 0.998894i | \(0.485027\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.56155 | − | 6.16879i | 0.480240 | − | 0.831800i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.43845 | + | 2.49146i | 0.187270 | + | 0.324361i | 0.944339 | − | 0.328974i | \(-0.106703\pi\) |
−0.757069 | + | 0.653335i | \(0.773369\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.93845 | − | 3.35749i | −0.248193 | − | 0.429882i | 0.714832 | − | 0.699297i | \(-0.246503\pi\) |
−0.963024 | + | 0.269414i | \(0.913170\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.78078 | + | 12.7173i | 0.220878 | + | 1.57739i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.28078 | − | 3.95042i | 0.278641 | − | 0.482621i | −0.692406 | − | 0.721508i | \(-0.743449\pi\) |
0.971047 | + | 0.238887i | \(0.0767826\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.00000 | − | 12.1244i | −0.830747 | − | 1.43890i | −0.897447 | − | 0.441123i | \(-0.854580\pi\) |
0.0666994 | − | 0.997773i | \(-0.478753\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.1231 | −1.18482 | −0.592410 | − | 0.805637i | \(-0.701823\pi\) | ||||
−0.592410 | + | 0.805637i | \(0.701823\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.12311 | 0.127990 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.43845 | −0.611873 | −0.305937 | − | 0.952052i | \(-0.598970\pi\) | ||||
−0.305937 | + | 0.952052i | \(0.598970\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.876894 | −0.0962517 | −0.0481258 | − | 0.998841i | \(-0.515325\pi\) | ||||
−0.0481258 | + | 0.998841i | \(0.515325\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.78078 | − | 4.81645i | −0.301618 | − | 0.522417i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.43845 | − | 4.22351i | 0.258475 | − | 0.447692i | −0.707359 | − | 0.706855i | \(-0.750113\pi\) |
0.965834 | + | 0.259163i | \(0.0834467\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.59612 | + | 1.24573i | −0.167319 | + | 0.130588i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.6847 | + | 21.9705i | 1.30142 | + | 2.25412i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.28078 | + | 7.41452i | 0.434647 | + | 0.752831i | 0.997267 | − | 0.0738851i | \(-0.0235398\pi\) |
−0.562620 | + | 0.826716i | \(0.690206\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.78078 | + | 6.54850i | −0.376201 | + | 0.651600i | −0.990506 | − | 0.137469i | \(-0.956103\pi\) |
0.614305 | + | 0.789069i | \(0.289437\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.43845 | 0.338800 | 0.169400 | − | 0.985547i | \(-0.445817\pi\) | ||||
0.169400 | + | 0.985547i | \(0.445817\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.12311 | − | 7.14143i | 0.398596 | − | 0.690388i | −0.594957 | − | 0.803757i | \(-0.702831\pi\) |
0.993553 | + | 0.113369i | \(0.0361644\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.80776 | −0.268935 | −0.134468 | − | 0.990918i | \(-0.542932\pi\) | ||||
−0.134468 | + | 0.990918i | \(0.542932\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.90388 | + | 5.02967i | 0.273174 | + | 0.473152i | 0.969673 | − | 0.244406i | \(-0.0785931\pi\) |
−0.696499 | + | 0.717558i | \(0.745260\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.56155 | + | 6.16879i | −0.332117 | + | 0.575243i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.438447 | − | 0.759413i | 0.0401924 | − | 0.0696153i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.56155 | 0.855211 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.71922 | − | 4.70983i | 0.241292 | − | 0.417930i | −0.719791 | − | 0.694191i | \(-0.755762\pi\) |
0.961083 | + | 0.276261i | \(0.0890955\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.36932 | 0.643860 | 0.321930 | − | 0.946763i | \(-0.395668\pi\) | ||||
0.321930 | + | 0.946763i | \(0.395668\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00000 | + | 3.46410i | −0.173422 | + | 0.300376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.78078 | − | 4.81645i | −0.237578 | − | 0.411497i | 0.722441 | − | 0.691433i | \(-0.243020\pi\) |
−0.960019 | + | 0.279936i | \(0.909687\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.96543 | − | 15.5286i | −0.760438 | − | 1.31712i | −0.942625 | − | 0.333854i | \(-0.891651\pi\) |
0.182187 | − | 0.983264i | \(-0.441682\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.68466 | + | 2.70469i | 0.558999 | + | 0.226177i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.9039 | − | 20.6181i | 0.988564 | − | 1.71224i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.21922 | − | 2.11176i | −0.0998827 | − | 0.173002i | 0.811753 | − | 0.584001i | \(-0.198513\pi\) |
−0.911636 | + | 0.410999i | \(0.865180\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.36932 | 0.762464 | 0.381232 | − | 0.924479i | \(-0.375500\pi\) | ||||
0.381232 | + | 0.924479i | \(0.375500\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.12311 | −0.732785 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.3693 | 1.62565 | 0.812824 | − | 0.582509i | \(-0.197929\pi\) | ||||
0.812824 | + | 0.582509i | \(0.197929\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.12311 | −0.0885131 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.40388 | − | 4.16365i | −0.188287 | − | 0.326122i | 0.756393 | − | 0.654118i | \(-0.226960\pi\) |
−0.944679 | + | 0.327996i | \(0.893627\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.12311 | + | 8.87348i | −0.396438 | + | 0.686650i | −0.993284 | − | 0.115706i | \(-0.963087\pi\) |
0.596846 | + | 0.802356i | \(0.296420\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5000 | + | 3.57071i | −0.961538 | + | 0.274670i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.1231 | + | 17.5337i | 0.769645 | + | 1.33307i | 0.937755 | + | 0.347297i | \(0.112900\pi\) |
−0.168110 | + | 0.985768i | \(0.553766\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.15767 | + | 3.73720i | 0.163105 | + | 0.282505i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.43845 | − | 4.22351i | 0.182258 | − | 0.315680i | −0.760391 | − | 0.649466i | \(-0.774993\pi\) |
0.942649 | + | 0.333785i | \(0.108326\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.68466 | −0.199549 | −0.0997745 | − | 0.995010i | \(-0.531812\pi\) | ||||
−0.0997745 | + | 0.995010i | \(0.531812\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.4654 | + | 23.3228i | −0.989998 | + | 1.71473i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.12311 | −0.228384 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.56155 | + | 7.90084i | 0.330062 | + | 0.571685i | 0.982524 | − | 0.186137i | \(-0.0595969\pi\) |
−0.652461 | + | 0.757822i | \(0.726264\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.74621 | − | 11.6848i | 0.485603 | − | 0.841089i | −0.514260 | − | 0.857634i | \(-0.671933\pi\) |
0.999863 | + | 0.0165453i | \(0.00526677\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.68466 | − | 11.5782i | 0.476262 | − | 0.824910i | −0.523368 | − | 0.852107i | \(-0.675325\pi\) |
0.999630 | + | 0.0271965i | \(0.00865798\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.0885 | + | 19.2059i | 0.786046 | + | 1.36147i | 0.928372 | + | 0.371651i | \(0.121208\pi\) |
−0.142327 | + | 0.989820i | \(0.545458\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.75379 | 0.263464 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.78078 | + | 4.81645i | −0.194218 | + | 0.336395i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.2462 | 0.985431 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.84233 | − | 17.0474i | 0.677574 | − | 1.17359i | −0.298136 | − | 0.954524i | \(-0.596365\pi\) |
0.975709 | − | 0.219069i | \(-0.0703019\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.12311 | + | 14.0696i | 0.553991 | + | 0.959541i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.719224 | − | 1.24573i | −0.0488241 | − | 0.0845658i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.43845 | − | 3.46410i | 0.298562 | − | 0.233021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.00000 | − | 6.92820i | 0.267860 | − | 0.463947i | −0.700449 | − | 0.713702i | \(-0.747017\pi\) |
0.968309 | + | 0.249756i | \(0.0803503\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.56155 | − | 6.16879i | −0.236389 | − | 0.409437i | 0.723287 | − | 0.690548i | \(-0.242630\pi\) |
−0.959675 | + | 0.281111i | \(0.909297\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.2462 | −1.07358 | −0.536790 | − | 0.843716i | \(-0.680363\pi\) | ||||
−0.536790 | + | 0.843716i | \(0.680363\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.0000 | −1.70332 | −0.851658 | − | 0.524097i | \(-0.824403\pi\) | ||||
−0.851658 | + | 0.524097i | \(0.824403\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.3693 | 1.91584 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.3693 | −1.64100 | −0.820502 | − | 0.571643i | \(-0.806306\pi\) | ||||
−0.820502 | + | 0.571643i | \(0.806306\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.90388 | + | 15.4220i | 0.573549 | + | 0.993417i | 0.996198 | + | 0.0871229i | \(0.0277673\pi\) |
−0.422648 | + | 0.906294i | \(0.638899\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.9039 | − | 20.6181i | 0.760511 | − | 1.31724i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.2462 | + | 15.8017i | −1.28824 | + | 1.00544i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.36932 | − | 16.2281i | −0.591386 | − | 1.02431i | −0.994046 | − | 0.108961i | \(-0.965248\pi\) |
0.402660 | − | 0.915350i | \(-0.368086\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.00000 | + | 3.46410i | 0.125739 | + | 0.217786i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.5885 | − | 25.2681i | 0.910008 | − | 1.57618i | 0.0959583 | − | 0.995385i | \(-0.469408\pi\) |
0.814050 | − | 0.580795i | \(-0.197258\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.24621 | −0.263847 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.68466 | + | 8.11407i | −0.288868 | + | 0.500335i | −0.973540 | − | 0.228517i | \(-0.926612\pi\) |
0.684672 | + | 0.728852i | \(0.259946\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.43845 | 0.149793 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.6847 | − | 18.5064i | −0.651455 | − | 1.12835i | −0.982770 | − | 0.184833i | \(-0.940826\pi\) |
0.331315 | − | 0.943520i | \(-0.392508\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.9654 | + | 25.9209i | −0.909085 | + | 1.57458i | −0.0937481 | + | 0.995596i | \(0.529885\pi\) |
−0.815337 | + | 0.578986i | \(0.803449\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.68466 | − | 13.3102i | 0.463402 | − | 0.802636i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.65767 | − | 4.60322i | −0.159684 | − | 0.276581i | 0.775071 | − | 0.631874i | \(-0.217714\pi\) |
−0.934755 | + | 0.355294i | \(0.884381\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.8078 | −1.06232 | −0.531161 | − | 0.847271i | \(-0.678244\pi\) | ||||
−0.531161 | + | 0.847271i | \(0.678244\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.84233 | + | 11.8513i | −0.406734 | + | 0.704484i | −0.994522 | − | 0.104531i | \(-0.966666\pi\) |
0.587787 | + | 0.809015i | \(0.299999\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.876894 | −0.0517614 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.28078 | − | 12.6107i | 0.428281 | − | 0.741804i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.2192 | + | 17.7002i | 0.597013 | + | 1.03406i | 0.993259 | + | 0.115913i | \(0.0369794\pi\) |
−0.396246 | + | 0.918144i | \(0.629687\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.12311 | + | 8.87348i | 0.298279 | + | 0.516634i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.68466 | − | 2.70469i | −0.386584 | − | 0.156416i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.28078 | + | 2.21837i | −0.0738227 | + | 0.127865i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.90388 | − | 11.9579i | −0.395315 | − | 0.684706i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.8078 | −1.75829 | −0.879146 | − | 0.476553i | \(-0.841886\pi\) | ||||
−0.879146 | + | 0.476553i | \(0.841886\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.1231 | −1.08437 | −0.542186 | − | 0.840259i | \(-0.682403\pi\) | ||||
−0.542186 | + | 0.840259i | \(0.682403\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.6847 | −0.773503 | −0.386751 | − | 0.922184i | \(-0.626403\pi\) | ||||
−0.386751 | + | 0.922184i | \(0.626403\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.0540 | −0.789350 | −0.394675 | − | 0.918821i | \(-0.629143\pi\) | ||||
−0.394675 | + | 0.918821i | \(0.629143\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.68466 | − | 11.5782i | −0.374269 | − | 0.648253i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.56155 | − | 9.63289i | 0.309453 | − | 0.535988i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.84233 | + | 27.4397i | 0.213134 | + | 1.52208i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.31534 | + | 4.01029i | 0.127649 | + | 0.221094i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.59612 | − | 2.76456i | −0.0877306 | − | 0.151954i | 0.818821 | − | 0.574049i | \(-0.194628\pi\) |
−0.906552 | + | 0.422095i | \(0.861295\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.12311 | − | 14.0696i | 0.443813 | − | 0.768706i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.12311 | −0.333547 | −0.166773 | − | 0.985995i | \(-0.553335\pi\) | ||||
−0.166773 | + | 0.985995i | \(0.553335\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.56155 | + | 4.43674i | −0.138716 | + | 0.240263i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.68466 | 0.414933 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.8078 | − | 23.9157i | −0.741240 | − | 1.28386i | −0.951931 | − | 0.306312i | \(-0.900905\pi\) |
0.210692 | − | 0.977553i | \(-0.432428\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.40388 | + | 5.89570i | −0.182206 | + | 0.315589i | −0.942631 | − | 0.333836i | \(-0.891657\pi\) |
0.760426 | + | 0.649425i | \(0.224990\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.65767 | − | 4.60322i | 0.141454 | − | 0.245005i | −0.786591 | − | 0.617475i | \(-0.788156\pi\) |
0.928044 | + | 0.372470i | \(0.121489\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24.9309 | − | 43.1815i | −1.32319 | − | 2.29184i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.36932 | −0.494494 | −0.247247 | − | 0.968953i | \(-0.579526\pi\) | ||||
−0.247247 | + | 0.968953i | \(0.579526\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.8693 | + | 27.4865i | −0.835227 | + | 1.44666i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −36.0540 | −1.88715 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.52699 | + | 14.7692i | −0.445105 | + | 0.770945i | −0.998060 | − | 0.0622668i | \(-0.980167\pi\) |
0.552954 | + | 0.833212i | \(0.313500\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.192236 | + | 0.332962i | 0.00998039 | + | 0.0172865i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.1847 | − | 24.5685i | −0.734454 | − | 1.27211i | −0.954963 | − | 0.296726i | \(-0.904105\pi\) |
0.220509 | − | 0.975385i | \(-0.429228\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.3423 | + | 9.03996i | 1.15069 | + | 0.465582i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.8423 | − | 20.5115i | 0.608300 | − | 1.05361i | −0.383221 | − | 0.923657i | \(-0.625185\pi\) |
0.991521 | − | 0.129949i | \(-0.0414814\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.3693 | + | 19.6922i | 0.580945 | + | 1.00623i | 0.995368 | + | 0.0961417i | \(0.0306502\pi\) |
−0.414423 | + | 0.910085i | \(0.636016\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | 0.203859 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −34.0540 | −1.72661 | −0.863303 | − | 0.504687i | \(-0.831608\pi\) | ||||
−0.863303 | + | 0.504687i | \(0.831608\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.12311 | 0.157942 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19.3693 | −0.974576 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.5270 | − | 21.6974i | −0.628711 | − | 1.08896i | −0.987811 | − | 0.155661i | \(-0.950249\pi\) |
0.359099 | − | 0.933299i | \(-0.383084\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.21922 | − | 12.5041i | 0.360511 | − | 0.624423i | −0.627534 | − | 0.778589i | \(-0.715936\pi\) |
0.988045 | + | 0.154166i | \(0.0492691\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.28078 | − | 9.14657i | −0.0638000 | − | 0.455623i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.56155 | + | 13.0970i | 0.374812 | + | 0.649194i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.18466 | − | 5.51599i | −0.157471 | − | 0.272748i | 0.776485 | − | 0.630136i | \(-0.217001\pi\) |
−0.933956 | + | 0.357388i | \(0.883667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.807764 | + | 1.39909i | −0.0397475 | + | 0.0688446i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.12311 | −0.153307 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.1231 | − | 29.6581i | 0.836518 | − | 1.44889i | −0.0562697 | − | 0.998416i | \(-0.517921\pi\) |
0.892788 | − | 0.450477i | \(-0.148746\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.2462 | 1.52285 | 0.761424 | − | 0.648255i | \(-0.224501\pi\) | ||||
0.761424 | + | 0.648255i | \(0.224501\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.00000 | − | 10.3923i | −0.291043 | − | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.08854 | − | 1.88541i | 0.0526782 | − | 0.0912413i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.56155 | − | 9.63289i | 0.267891 | − | 0.464000i | −0.700426 | − | 0.713725i | \(-0.747007\pi\) |
0.968317 | + | 0.249725i | \(0.0803401\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.37689 | − | 7.58100i | −0.210340 | − | 0.364320i | 0.741481 | − | 0.670974i | \(-0.234124\pi\) |
−0.951821 | + | 0.306654i | \(0.900790\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.2462 | −0.681489 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.84233 | + | 11.8513i | −0.326567 | + | 0.565630i | −0.981828 | − | 0.189772i | \(-0.939225\pi\) |
0.655262 | + | 0.755402i | \(0.272558\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.7386 | −1.65048 | −0.825241 | − | 0.564781i | \(-0.808961\pi\) | ||||
−0.825241 | + | 0.564781i | \(0.808961\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.68466 | − | 15.0423i | 0.411692 | − | 0.713072i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.12311 | − | 7.14143i | −0.194581 | − | 0.337025i | 0.752182 | − | 0.658956i | \(-0.229002\pi\) |
−0.946763 | + | 0.321931i | \(0.895668\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.56155 | + | 2.70469i | 0.0735307 | + | 0.127359i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.68466 | + | 4.43674i | −0.266501 | + | 0.207998i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.30776 | + | 10.9254i | −0.295065 | + | 0.511067i | −0.975000 | − | 0.222205i | \(-0.928675\pi\) |
0.679935 | + | 0.733272i | \(0.262008\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.09612 | − | 14.0229i | −0.377074 | − | 0.653111i | 0.613561 | − | 0.789647i | \(-0.289736\pi\) |
−0.990635 | + | 0.136536i | \(0.956403\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.3153 | 0.665290 | 0.332645 | − | 0.943052i | \(-0.392059\pi\) | ||||
0.332645 | + | 0.943052i | \(0.392059\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.0000 | −1.20314 | −0.601568 | − | 0.798821i | \(-0.705457\pi\) | ||||
−0.601568 | + | 0.798821i | \(0.705457\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.56155 | 0.118282 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.12311 | 0.419481 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 27.3693 | + | 47.4050i | 1.25579 | + | 2.17509i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.12311 | + | 8.87348i | −0.234081 | + | 0.405440i | −0.959005 | − | 0.283389i | \(-0.908541\pi\) |
0.724924 | + | 0.688828i | \(0.241875\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.2732 | − | 10.2258i | −1.15236 | − | 0.466257i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.2462 | + | 26.4072i | 0.692295 | + | 1.19909i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.56155 | + | 6.16879i | 0.161389 | + | 0.279535i | 0.935367 | − | 0.353678i | \(-0.115069\pi\) |
−0.773978 | + | 0.633213i | \(0.781736\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.1231 | − | 31.3901i | 0.817884 | − | 1.41662i | −0.0893539 | − | 0.996000i | \(-0.528480\pi\) |
0.907238 | − | 0.420617i | \(-0.138186\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.4384 | −0.470124 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.93087 | − | 6.80847i | 0.176324 | − | 0.305401i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.49242 | −0.201108 | −0.100554 | − | 0.994932i | \(-0.532062\pi\) | ||||
−0.100554 | + | 0.994932i | \(0.532062\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.1231 | + | 24.4619i | 0.629718 | + | 1.09070i | 0.987608 | + | 0.156940i | \(0.0501630\pi\) |
−0.357890 | + | 0.933764i | \(0.616504\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.4654 | + | 23.3228i | −0.599204 | + | 1.03785i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.90388 | + | 11.9579i | −0.306009 | + | 0.530023i | −0.977486 | − | 0.211003i | \(-0.932327\pi\) |
0.671476 | + | 0.741026i | \(0.265660\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.84233 | − | 4.92306i | −0.125737 | − | 0.217783i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.2462 | 0.539633 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.24621 | − | 14.2829i | 0.362668 | − | 0.628159i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.06913 | 0.397326 | 0.198663 | − | 0.980068i | \(-0.436340\pi\) | ||||
0.198663 | + | 0.980068i | \(0.436340\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.9309 | − | 29.3251i | 0.740335 | − | 1.28230i | −0.212007 | − | 0.977268i | \(-0.568000\pi\) |
0.952343 | − | 0.305030i | \(-0.0986666\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.00000 | + | 3.46410i | 0.0871214 | + | 0.150899i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.50000 | + | 16.4545i | 0.413043 | + | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.21922 | − | 2.11176i | −0.226070 | − | 0.0914704i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.6847 | − | 25.4346i | 0.634873 | − | 1.09963i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.68466 | − | 11.5782i | −0.287929 | − | 0.498707i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.7386 | 0.848630 | 0.424315 | − | 0.905515i | \(-0.360515\pi\) | ||||
0.424315 | + | 0.905515i | \(0.360515\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.0000 | −0.428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.93087 | −0.168072 | −0.0840359 | − | 0.996463i | \(-0.526781\pi\) | ||||
−0.0840359 | + | 0.996463i | \(0.526781\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 47.6155 | 2.02849 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.52699 | − | 2.64482i | −0.0649341 | − | 0.112469i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.4654 | + | 37.1792i | −0.909520 | + | 1.57533i | −0.0947869 | + | 0.995498i | \(0.530217\pi\) |
−0.814733 | + | 0.579837i | \(0.803116\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.9654 | + | 10.1192i | −0.548379 | + | 0.427997i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.6847 | + | 20.2384i | 0.492450 | + | 0.852948i | 0.999962 | − | 0.00869657i | \(-0.00276824\pi\) |
−0.507513 | + | 0.861644i | \(0.669435\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.3423 | + | 17.9134i | 0.435105 | + | 0.753624i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.36932 | + | 7.56788i | −0.183171 | + | 0.317262i | −0.942959 | − | 0.332910i | \(-0.891970\pi\) |
0.759787 | + | 0.650171i | \(0.225303\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.36932 | 0.224699 | 0.112349 | − | 0.993669i | \(-0.464162\pi\) | ||||
0.112349 | + | 0.993669i | \(0.464162\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.68466 | + | 13.3102i | −0.320472 | + | 0.555074i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.3153 | −0.720847 | −0.360424 | − | 0.932789i | \(-0.617368\pi\) | ||||
−0.360424 | + | 0.932789i | \(0.617368\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.246211 | − | 0.426450i | −0.0102146 | − | 0.0176921i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.684658 | − | 1.18586i | 0.0283557 | − | 0.0491134i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.6847 | + | 34.0948i | −0.812473 | + | 1.40724i | 0.0986556 | + | 0.995122i | \(0.468546\pi\) |
−0.911128 | + | 0.412123i | \(0.864788\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.12311 | − | 15.8017i | −0.375911 | − | 0.651097i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.4233 | 0.715489 | 0.357744 | − | 0.933820i | \(-0.383546\pi\) | ||||
0.357744 | + | 0.933820i | \(0.383546\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.56155 | − | 2.70469i | 0.0640174 | − | 0.110881i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −41.6155 | −1.70036 | −0.850182 | − | 0.526489i | \(-0.823508\pi\) | ||||
−0.850182 | + | 0.526489i | \(0.823508\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.53457 | − | 6.12205i | 0.144178 | − | 0.249723i | −0.784888 | − | 0.619638i | \(-0.787280\pi\) |
0.929066 | + | 0.369914i | \(0.120613\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.4654 | + | 21.5908i | 0.506792 | + | 0.877789i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.00000 | − | 13.8564i | −0.324710 | − | 0.562414i | 0.656744 | − | 0.754114i | \(-0.271933\pi\) |
−0.981454 | + | 0.191700i | \(0.938600\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.12311 | + | 29.4449i | 0.166803 | + | 1.19121i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.4309 | − | 30.1912i | 0.704026 | − | 1.21941i | −0.263016 | − | 0.964792i | \(-0.584717\pi\) |
0.967042 | − | 0.254618i | \(-0.0819496\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.90388 | + | 8.49377i | 0.197423 | + | 0.341946i | 0.947692 | − | 0.319186i | \(-0.103409\pi\) |
−0.750269 | + | 0.661132i | \(0.770076\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.3002 | −1.17767 | −0.588837 | − | 0.808252i | \(-0.700414\pi\) | ||||
−0.588837 | + | 0.808252i | \(0.700414\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.73863 | 0.109721 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.36932 | −0.174773 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.8078 | 0.470806 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.28078 | − | 16.0748i | −0.369462 | − | 0.639927i | 0.620020 | − | 0.784586i | \(-0.287125\pi\) |
−0.989481 | + | 0.144660i | \(0.953791\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.68466 | − | 16.7743i | 0.384324 | − | 0.665669i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.3423 | + | 9.03996i | 0.885235 | + | 0.358176i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.58854 | − | 16.6078i | −0.378725 | − | 0.655970i | 0.612152 | − | 0.790740i | \(-0.290304\pi\) |
−0.990877 | + | 0.134770i | \(0.956971\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.7732 | − | 27.3200i | −0.622034 | − | 1.07739i | −0.989106 | − | 0.147202i | \(-0.952973\pi\) |
0.367072 | − | 0.930192i | \(-0.380360\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.19224 | − | 5.52911i | 0.125500 | − | 0.217372i | −0.796428 | − | 0.604733i | \(-0.793280\pi\) |
0.921928 | + | 0.387361i | \(0.126613\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.75379 | 0.225856 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.5616 | − | 20.0252i | 0.452439 | − | 0.783647i | −0.546098 | − | 0.837721i | \(-0.683888\pi\) |
0.998537 | + | 0.0540745i | \(0.0172209\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.2462 | 1.02552 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.12311 | + | 1.94528i | 0.0437500 | + | 0.0757772i | 0.887071 | − | 0.461633i | \(-0.152736\pi\) |
−0.843321 | + | 0.537410i | \(0.819403\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.81534 | + | 4.87631i | −0.109504 | + | 0.189667i | −0.915569 | − | 0.402160i | \(-0.868260\pi\) |
0.806065 | + | 0.591827i | \(0.201593\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.12311 | + | 12.3376i | −0.276222 | + | 0.478431i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.68466 | + | 11.5782i | 0.258831 | + | 0.448308i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.75379 | −0.299332 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.6231 | − | 20.1318i | 0.448038 | − | 0.776024i | −0.550220 | − | 0.835019i | \(-0.685456\pi\) |
0.998258 | + | 0.0589952i | \(0.0187897\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.6155 | 0.600153 | 0.300077 | − | 0.953915i | \(-0.402988\pi\) | ||||
0.300077 | + | 0.953915i | \(0.402988\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.40388 | + | 4.16365i | −0.0922525 | + | 0.159786i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.0540 | + | 33.0025i | 0.729080 | + | 1.26280i | 0.957272 | + | 0.289188i | \(0.0933852\pi\) |
−0.228192 | + | 0.973616i | \(0.573281\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.90388 | − | 17.1540i | −0.378408 | − | 0.655422i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.342329 | + | 2.44472i | 0.0130417 | + | 0.0931364i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.6501 | + | 44.4273i | −0.975776 | + | 1.69009i | −0.298424 | + | 0.954433i | \(0.596461\pi\) |
−0.677352 | + | 0.735659i | \(0.736872\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31.9309 | − | 55.3059i | −1.21121 | − | 2.09787i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.43845 | 0.0923628 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.36932 | 0.202796 | 0.101398 | − | 0.994846i | \(-0.467668\pi\) | ||||
0.101398 | + | 0.994846i | \(0.467668\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −53.8617 | −2.03143 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.24621 | −0.159695 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.74621 | + | 6.48863i | 0.140692 | + | 0.243686i | 0.927757 | − | 0.373184i | \(-0.121734\pi\) |
−0.787065 | + | 0.616869i | \(0.788401\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.56155 | − | 4.43674i | 0.0959309 | − | 0.166157i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.8078 | + | 9.63289i | 0.890360 | + | 0.360250i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.6847 | + | 20.2384i | 0.435764 | + | 0.754766i | 0.997358 | − | 0.0726475i | \(-0.0231448\pi\) |
−0.561593 | + | 0.827413i | \(0.689811\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.965435 | + | 1.67218i | 0.0359547 | + | 0.0622753i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.6847 | − | 44.4871i | 0.953904 | − | 1.65221i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.6695 | 1.43417 | 0.717086 | − | 0.696984i | \(-0.245475\pi\) | ||||
0.717086 | + | 0.696984i | \(0.245475\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.56155 | − | 6.16879i | 0.131729 | − | 0.228161i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.5076 | 0.757465 | 0.378732 | − | 0.925506i | \(-0.376360\pi\) | ||||
0.378732 | + | 0.925506i | \(0.376360\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.56155 | − | 7.90084i | −0.168027 | − | 0.291031i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.12311 | − | 8.87348i | 0.188456 | − | 0.326416i | −0.756279 | − | 0.654249i | \(-0.772985\pi\) |
0.944736 | + | 0.327833i | \(0.106318\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.31534 | − | 10.9385i | 0.231687 | − | 0.401294i | −0.726617 | − | 0.687042i | \(-0.758909\pi\) |
0.958305 | + | 0.285748i | \(0.0922420\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.34233 | − | 7.52113i | −0.159091 | − | 0.275553i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.63068 | 0.169201 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.0540 | − | 38.1986i | 0.804761 | − | 1.39389i | −0.111691 | − | 0.993743i | \(-0.535627\pi\) |
0.916452 | − | 0.400144i | \(-0.131040\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33.3693 | 1.21443 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0000 | + | 25.9808i | −0.545184 | + | 0.944287i | 0.453411 | + | 0.891302i | \(0.350207\pi\) |
−0.998595 | + | 0.0529853i | \(0.983126\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.68466 | + | 8.11407i | 0.169819 | + | 0.294135i | 0.938356 | − | 0.345670i | \(-0.112348\pi\) |
−0.768537 | + | 0.639805i | \(0.779015\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.788354 | − | 1.36547i | −0.0285403 | − | 0.0494333i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.17708 | + | 6.38202i | −0.295257 | + | 0.230441i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.00000 | − | 15.5885i | 0.324548 | − | 0.562134i | −0.656873 | − | 0.754002i | \(-0.728121\pi\) |
0.981421 | + | 0.191867i | \(0.0614544\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.1231 | − | 20.9978i | −0.436038 | − | 0.755240i | 0.561342 | − | 0.827584i | \(-0.310285\pi\) |
−0.997380 | + | 0.0723444i | \(0.976952\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.6847 | −0.707094 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.1231 | −0.398527 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.0000 | −1.00192 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 72.5464 | 2.58929 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.0885 | + | 38.2585i | 0.787371 | + | 1.36377i | 0.927572 | + | 0.373644i | \(0.121892\pi\) |
−0.140201 | + | 0.990123i | \(0.544775\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.63068 | + | 2.82443i | −0.0579804 | + | 0.100425i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.0194 | − | 8.60039i | 0.391311 | − | 0.305409i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.192236 | − | 0.332962i | −0.00680935 | − | 0.0117941i | 0.862601 | − | 0.505885i | \(-0.168834\pi\) |
−0.869410 | + | 0.494091i | \(0.835501\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.43845 | − | 11.1517i | −0.227776 | − | 0.394519i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.1231 | + | 17.5337i | −0.357237 | + | 0.618752i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.00000 | −0.140981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.15009 | + | 14.1164i | −0.286542 | + | 0.496305i | −0.972982 | − | 0.230881i | \(-0.925839\pi\) |
0.686440 | + | 0.727187i | \(0.259172\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.56155 | −0.0899483 | −0.0449741 | − | 0.998988i | \(-0.514321\pi\) | ||||
−0.0449741 | + | 0.998988i | \(0.514321\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.56155 | − | 14.8290i | −0.299898 | − | 0.519439i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.2462 | + | 28.1393i | −0.568383 | + | 0.984468i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.24621 | − | 5.62260i | 0.113294 | − | 0.196230i | −0.803803 | − | 0.594896i | \(-0.797193\pi\) |
0.917096 | + | 0.398666i | \(0.130527\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.00000 | + | 6.92820i | 0.139431 | + | 0.241502i | 0.927281 | − | 0.374365i | \(-0.122139\pi\) |
−0.787850 | + | 0.615867i | \(0.788806\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.7386 | −0.512513 | −0.256256 | − | 0.966609i | \(-0.582489\pi\) | ||||
−0.256256 | + | 0.966609i | \(0.582489\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.74621 | + | 11.6848i | −0.234306 | + | 0.405829i | −0.959071 | − | 0.283167i | \(-0.908615\pi\) |
0.724765 | + | 0.688996i | \(0.241948\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.4384 | −0.361671 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.2462 | + | 31.6034i | −0.631436 | + | 1.09368i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.8078 | − | 18.7196i | −0.373125 | − | 0.646272i | 0.616919 | − | 0.787027i | \(-0.288381\pi\) |
−0.990045 | + | 0.140754i | \(0.955047\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.84233 | − | 13.5833i | −0.270425 | − | 0.468390i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −44.5194 | + | 12.7173i | −1.53151 | + | 0.437488i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.96543 | + | 3.40423i | −0.0675331 | + | 0.116971i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.56155 | − | 13.0970i | −0.259207 | − | 0.448959i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.12311 | 0.0726938 | 0.0363469 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363469 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.5616 | −1.21476 | −0.607380 | − | 0.794412i | \(-0.707779\pi\) | ||||
−0.607380 | + | 0.794412i | \(0.707779\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.5616 | −0.838029 | −0.419015 | − | 0.907979i | \(-0.637624\pi\) | ||||
−0.419015 | + | 0.907979i | \(0.637624\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.4924 | 1.03797 | 0.518987 | − | 0.854782i | \(-0.326309\pi\) | ||||
0.518987 | + | 0.854782i | \(0.326309\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.0540 | + | 62.4473i | 1.22587 | + | 2.12327i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.43845 | + | 9.41967i | −0.184487 | + | 0.319540i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.2462 | + | 6.16879i | 0.516598 | + | 0.209021i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.68466 | + | 4.64996i | 0.0907580 | + | 0.157198i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.7808 | − | 20.4049i | −0.397809 | − | 0.689025i | 0.595647 | − | 0.803247i | \(-0.296896\pi\) |
−0.993455 | + | 0.114222i | \(0.963563\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.53457 | + | 7.85410i | −0.152773 | + | 0.264611i | −0.932246 | − | 0.361825i | \(-0.882154\pi\) |
0.779473 | + | 0.626436i | \(0.215487\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.80776 | −0.296405 | −0.148202 | − | 0.988957i | \(-0.547349\pi\) | ||||
−0.148202 | + | 0.988957i | \(0.547349\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.3153 | + | 21.3308i | −0.413509 | + | 0.716218i | −0.995271 | − | 0.0971410i | \(-0.969030\pi\) |
0.581762 | + | 0.813359i | \(0.302364\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.05398 | 0.102427 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 29.3693 | + | 50.8691i | 0.982807 | + | 1.70227i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.68466 | − | 15.0423i | 0.290296 | − | 0.502808i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.56155 | + | 14.8290i | −0.285544 | + | 0.494576i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.534565 | − | 0.925894i | −0.0178089 | − | 0.0308460i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.56155 | −0.317837 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.0000 | − | 24.2487i | 0.464862 | − | 0.805165i | −0.534333 | − | 0.845274i | \(-0.679437\pi\) |
0.999195 | + | 0.0401089i | \(0.0127705\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.7386 | 1.28347 | 0.641734 | − | 0.766927i | \(-0.278215\pi\) | ||||
0.641734 | + | 0.766927i | \(0.278215\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.876894 | + | 1.51883i | −0.0290210 | + | 0.0502658i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.06913 | + | 3.58384i | 0.0683287 | + | 0.118349i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.75379 | + | 9.96585i | 0.189800 | + | 0.328743i | 0.945183 | − | 0.326540i | \(-0.105883\pi\) |
−0.755383 | + | 0.655283i | \(0.772549\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 39.7926 | − | 31.0572i | 1.30979 | − | 1.02226i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29.0540 | + | 50.3230i | −0.955289 | + | 1.65461i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.90388 | − | 6.76172i | −0.128082 | − | 0.221845i | 0.794851 | − | 0.606804i | \(-0.207549\pi\) |
−0.922934 | + | 0.384959i | \(0.874215\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 47.6155 | 1.56054 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.1231 | −0.363764 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.56155 | −0.247025 | −0.123513 | − | 0.992343i | \(-0.539416\pi\) | ||||
−0.123513 | + | 0.992343i | \(0.539416\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.4924 | −0.994025 | −0.497012 | − | 0.867744i | \(-0.665570\pi\) | ||||
−0.497012 | + | 0.867744i | \(0.665570\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.56155 | − | 2.70469i | −0.0508512 | − | 0.0880768i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.3693 | − | 33.5486i | 0.629418 | − | 1.09018i | −0.358250 | − | 0.933626i | \(-0.616627\pi\) |
0.987669 | − | 0.156559i | \(-0.0500401\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.06155 | − | 36.1467i | −0.164305 | − | 1.17337i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.4924 | + | 26.8337i | 0.501849 | + | 0.869228i | 0.999998 | + | 0.00213612i | \(0.000679948\pi\) |
−0.498149 | + | 0.867091i | \(0.665987\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.2462 | + | 28.1393i | 0.525715 | + | 0.910565i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.56155 | − | 2.70469i | 0.0504252 | − | 0.0873390i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.4384 | −0.788337 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.0270 | − | 41.6160i | 0.773456 | − | 1.33967i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.876894 | 0.0281990 | 0.0140995 | − | 0.999901i | \(-0.495512\pi\) | ||||
0.0140995 | + | 0.999901i | \(0.495512\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.49242 | + | 11.2452i | 0.208352 | + | 0.360876i | 0.951195 | − | 0.308589i | \(-0.0998568\pi\) |
−0.742844 | + | 0.669465i | \(0.766523\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.03457 | − | 8.72012i | 0.161401 | − | 0.279554i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.5885 | − | 52.9809i | 0.978614 | − | 1.69501i | 0.311162 | − | 0.950357i | \(-0.399282\pi\) |
0.667453 | − | 0.744652i | \(-0.267385\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.87689 | − | 8.44703i | −0.155866 | − | 0.269968i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.6155 | 0.434268 | 0.217134 | − | 0.976142i | \(-0.430329\pi\) | ||||
0.217134 | + | 0.976142i | \(0.430329\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.8078 | − | 41.2363i | 0.758578 | − | 1.31390i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.12311 | −0.290098 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.1771 | + | 43.6080i | −0.799776 | + | 1.38525i | 0.119985 | + | 0.992776i | \(0.461715\pi\) |
−0.919762 | + | 0.392478i | \(0.871618\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39.4924 | + | 68.4029i | 1.25199 | + | 2.16852i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.3078 | + | 17.8536i | 0.326450 | + | 0.565428i | 0.981805 | − | 0.189893i | \(-0.0608141\pi\) |
−0.655355 | + | 0.755321i | \(0.727481\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))