Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(289,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.l (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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{7} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.6 | ||
Root | \(-0.473632 - 1.66604i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.289 |
Dual form | 756.2.l.b.361.6 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(5\) | 1.90301 | 0.851051 | 0.425525 | − | 0.904947i | \(-0.360089\pi\) | ||||
0.425525 | + | 0.904947i | \(0.360089\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.43415 | − | 1.03677i | −0.920024 | − | 0.391863i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.06586 | 0.924393 | 0.462196 | − | 0.886778i | \(-0.347062\pi\) | ||||
0.462196 | + | 0.886778i | \(0.347062\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.13161 | + | 1.96000i | 0.313851 | + | 0.543607i | 0.979193 | − | 0.202933i | \(-0.0650473\pi\) |
−0.665341 | + | 0.746539i | \(0.731714\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.713726 | + | 1.23621i | 0.173104 | + | 0.299825i | 0.939503 | − | 0.342539i | \(-0.111287\pi\) |
−0.766400 | + | 0.642364i | \(0.777954\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.98444 | − | 5.16919i | 0.684677 | − | 1.18589i | −0.288862 | − | 0.957371i | \(-0.593277\pi\) |
0.973538 | − | 0.228524i | \(-0.0733898\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.15543 | 1.49201 | 0.746005 | − | 0.665940i | \(-0.231969\pi\) | ||||
0.746005 | + | 0.665940i | \(0.231969\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.37856 | −0.275713 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.468164 | + | 0.810884i | −0.0869359 | + | 0.150577i | −0.906214 | − | 0.422818i | \(-0.861041\pi\) |
0.819279 | + | 0.573396i | \(0.194374\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.11065 | − | 7.11985i | 0.738294 | − | 1.27876i | −0.214969 | − | 0.976621i | \(-0.568965\pi\) |
0.953263 | − | 0.302142i | \(-0.0977016\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.63221 | − | 1.97298i | −0.782987 | − | 0.333495i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.41550 | + | 2.45171i | −0.232706 | + | 0.403059i | −0.958604 | − | 0.284744i | \(-0.908091\pi\) |
0.725897 | + | 0.687803i | \(0.241425\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.31672 | + | 9.20883i | 0.830332 | + | 1.43818i | 0.897775 | + | 0.440454i | \(0.145183\pi\) |
−0.0674429 | + | 0.997723i | \(0.521484\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.98444 | − | 5.16919i | 0.455122 | − | 0.788295i | −0.543573 | − | 0.839362i | \(-0.682929\pi\) |
0.998695 | + | 0.0510671i | \(0.0162622\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.483340 | − | 0.837169i | −0.0705023 | − | 0.122114i | 0.828619 | − | 0.559813i | \(-0.189127\pi\) |
−0.899122 | + | 0.437699i | \(0.855794\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.85021 | + | 5.04732i | 0.692887 | + | 0.721046i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.45142 | − | 9.44213i | −0.748810 | − | 1.29698i | −0.948393 | − | 0.317096i | \(-0.897292\pi\) |
0.199583 | − | 0.979881i | \(-0.436041\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.83436 | 0.786705 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.68180 | + | 9.84117i | −0.739708 | + | 1.28121i | 0.212919 | + | 0.977070i | \(0.431703\pi\) |
−0.952627 | + | 0.304142i | \(0.901630\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.449718 | − | 0.778935i | −0.0575805 | − | 0.0997324i | 0.835798 | − | 0.549037i | \(-0.185005\pi\) |
−0.893379 | + | 0.449304i | \(0.851672\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.15346 | + | 3.72990i | 0.267104 | + | 0.462637i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.813810 | + | 1.40956i | −0.0994227 | + | 0.172205i | −0.911446 | − | 0.411420i | \(-0.865033\pi\) |
0.812023 | + | 0.583625i | \(0.198366\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.36378 | 0.280529 | 0.140264 | − | 0.990114i | \(-0.455205\pi\) | ||||
0.140264 | + | 0.990114i | \(0.455205\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.996286 | − | 1.72562i | −0.116606 | − | 0.201968i | 0.801814 | − | 0.597573i | \(-0.203868\pi\) |
−0.918421 | + | 0.395605i | \(0.870535\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.46279 | − | 3.17860i | −0.850463 | − | 0.362235i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.16945 | + | 7.22169i | 0.469099 | + | 0.812504i | 0.999376 | − | 0.0353209i | \(-0.0112453\pi\) |
−0.530277 | + | 0.847825i | \(0.677912\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.98203 | − | 13.8253i | 0.876141 | − | 1.51752i | 0.0205995 | − | 0.999788i | \(-0.493443\pi\) |
0.855542 | − | 0.517734i | \(-0.173224\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.35822 | + | 2.35251i | 0.147320 | + | 0.255166i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.58992 | − | 4.48587i | 0.274531 | − | 0.475501i | −0.695486 | − | 0.718540i | \(-0.744811\pi\) |
0.970017 | + | 0.243039i | \(0.0781442\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.722433 | − | 5.94416i | −0.0757316 | − | 0.623118i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.67940 | − | 9.83701i | 0.582694 | − | 1.00926i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.922890 | − | 1.59849i | 0.0937053 | − | 0.162302i | −0.815362 | − | 0.578951i | \(-0.803462\pi\) |
0.909068 | + | 0.416649i | \(0.136796\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.06350 | 0.802349 | 0.401174 | − | 0.916002i | \(-0.368602\pi\) | ||||
0.401174 | + | 0.916002i | \(0.368602\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.7986 | −1.75375 | −0.876875 | − | 0.480718i | \(-0.840376\pi\) | ||||
−0.876875 | + | 0.480718i | \(0.840376\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.76005 | + | 15.1729i | −0.846866 | + | 1.46682i | 0.0371245 | + | 0.999311i | \(0.488180\pi\) |
−0.883991 | + | 0.467505i | \(0.845153\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.11441 | + | 1.93021i | 0.106741 | + | 0.184881i | 0.914448 | − | 0.404703i | \(-0.132625\pi\) |
−0.807707 | + | 0.589584i | \(0.799292\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.59999 | + | 13.1636i | 0.714947 | + | 1.23832i | 0.962980 | + | 0.269573i | \(0.0868824\pi\) |
−0.248033 | + | 0.968751i | \(0.579784\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.6168 | 1.26978 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.455652 | − | 3.74909i | −0.0417695 | − | 0.343679i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.60048 | −0.145498 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1385 | −1.08570 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.9303 | −1.50232 | −0.751161 | − | 0.660119i | \(-0.770506\pi\) | ||||
−0.751161 | + | 0.660119i | \(0.770506\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.38354 | −0.208251 | −0.104125 | − | 0.994564i | \(-0.533204\pi\) | ||||
−0.104125 | + | 0.994564i | \(0.533204\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.6238 | + | 9.48844i | −1.09463 | + | 0.822752i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.9820 | −0.938254 | −0.469127 | − | 0.883131i | \(-0.655431\pi\) | ||||
−0.469127 | + | 0.883131i | \(0.655431\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.70422 | − | 6.41590i | −0.314188 | − | 0.544190i | 0.665076 | − | 0.746775i | \(-0.268399\pi\) |
−0.979265 | + | 0.202585i | \(0.935066\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.46936 | + | 6.00910i | 0.290122 | + | 0.502506i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.890919 | + | 1.54312i | −0.0739868 | + | 0.128149i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.6239 | −1.44381 | −0.721904 | − | 0.691993i | \(-0.756733\pi\) | ||||
−0.721904 | + | 0.691993i | \(0.756733\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.3664 | −1.65739 | −0.828697 | − | 0.559697i | \(-0.810917\pi\) | ||||
−0.828697 | + | 0.559697i | \(0.810917\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.82259 | − | 13.5491i | 0.628326 | − | 1.08829i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.64118 | + | 8.03875i | −0.370406 | + | 0.641562i | −0.989628 | − | 0.143654i | \(-0.954115\pi\) |
0.619222 | + | 0.785216i | \(0.287448\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17.4174 | − | 7.41854i | −1.37268 | − | 0.584663i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.9069 | + | 20.6234i | −0.932623 | + | 1.61535i | −0.153803 | + | 0.988101i | \(0.549152\pi\) |
−0.778819 | + | 0.627248i | \(0.784181\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.883505 | + | 1.53028i | 0.0683676 | + | 0.118416i | 0.898183 | − | 0.439622i | \(-0.144888\pi\) |
−0.829815 | + | 0.558038i | \(0.811554\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.93893 | − | 6.82242i | 0.302994 | − | 0.524802i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.180049 | + | 0.311855i | 0.0136889 | + | 0.0237099i | 0.872789 | − | 0.488098i | \(-0.162309\pi\) |
−0.859100 | + | 0.511808i | \(0.828976\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.35564 | + | 1.42926i | 0.253662 | + | 0.108042i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.57701 | + | 6.19556i | 0.267358 | + | 0.463078i | 0.968179 | − | 0.250260i | \(-0.0805160\pi\) |
−0.700821 | + | 0.713337i | \(0.747183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.0542 | 0.821650 | 0.410825 | − | 0.911714i | \(-0.365241\pi\) | ||||
0.410825 | + | 0.911714i | \(0.365241\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.69370 | + | 4.66563i | −0.198045 | + | 0.343024i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.18819 | + | 3.79005i | 0.160016 | + | 0.277156i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.35083 | − | 7.53586i | −0.314815 | − | 0.545276i | 0.664583 | − | 0.747214i | \(-0.268609\pi\) |
−0.979398 | + | 0.201939i | \(0.935276\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.709644 | − | 1.22914i | 0.0510813 | − | 0.0884754i | −0.839354 | − | 0.543585i | \(-0.817067\pi\) |
0.890435 | + | 0.455110i | \(0.150400\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.69424 | −0.405698 | −0.202849 | − | 0.979210i | \(-0.565020\pi\) | ||||
−0.202849 | + | 0.979210i | \(0.565020\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.61327 | + | 4.52631i | 0.185250 | + | 0.320862i | 0.943661 | − | 0.330915i | \(-0.107357\pi\) |
−0.758411 | + | 0.651777i | \(0.774024\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.98028 | − | 1.48844i | 0.138989 | − | 0.104468i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.1178 | + | 17.5245i | 0.706655 | + | 1.22396i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.14987 | − | 15.8480i | 0.632910 | − | 1.09623i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.93079 | − | 10.2724i | −0.408293 | − | 0.707183i | 0.586406 | − | 0.810017i | \(-0.300542\pi\) |
−0.994699 | + | 0.102834i | \(0.967209\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.67940 | − | 9.83701i | 0.387332 | − | 0.670879i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.3876 | + | 13.0690i | −1.18035 | + | 0.887182i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.61531 | + | 2.79781i | −0.108658 | + | 0.188201i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.2950 | − | 21.2955i | 0.823333 | − | 1.42605i | −0.0798535 | − | 0.996807i | \(-0.525445\pi\) |
0.903187 | − | 0.429248i | \(-0.141221\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.3180 | −1.01669 | −0.508344 | − | 0.861154i | \(-0.669742\pi\) | ||||
−0.508344 | + | 0.861154i | \(0.669742\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.0459 | 1.12643 | 0.563214 | − | 0.826311i | \(-0.309565\pi\) | ||||
0.563214 | + | 0.826311i | \(0.309565\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.88255 | + | 17.1171i | −0.647427 | + | 1.12138i | 0.336308 | + | 0.941752i | \(0.390822\pi\) |
−0.983735 | + | 0.179625i | \(0.942512\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.919799 | − | 1.59314i | −0.0600011 | − | 0.103925i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.35041 | − | 14.4633i | −0.540143 | − | 0.935555i | −0.998895 | − | 0.0469909i | \(-0.985037\pi\) |
0.458752 | − | 0.888564i | \(-0.348297\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.39995 | 0.412257 | 0.206129 | − | 0.978525i | \(-0.433914\pi\) | ||||
0.206129 | + | 0.978525i | \(0.433914\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.22999 | + | 9.60509i | 0.589682 | + | 0.613647i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.5088 | 0.859547 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.8346 | 1.69378 | 0.846891 | − | 0.531766i | \(-0.178471\pi\) | ||||
0.846891 | + | 0.531766i | \(0.178471\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.9376 | 1.37920 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.17597 | −0.447625 | −0.223812 | − | 0.974632i | \(-0.571850\pi\) | ||||
−0.223812 | + | 0.974632i | \(0.571850\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.98741 | − | 4.50030i | 0.372039 | − | 0.279635i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.4137 | −1.25876 | −0.629382 | − | 0.777096i | \(-0.716692\pi\) | ||||
−0.629382 | + | 0.777096i | \(0.716692\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.3741 | − | 17.9685i | −0.637275 | − | 1.10379i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.37251 | + | 5.84136i | 0.205626 | + | 0.356154i | 0.950332 | − | 0.311238i | \(-0.100744\pi\) |
−0.744706 | + | 0.667392i | \(0.767410\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.04632 | + | 1.81228i | −0.0635596 | + | 0.110088i | −0.896054 | − | 0.443945i | \(-0.853579\pi\) |
0.832495 | + | 0.554033i | \(0.186912\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.22649 | −0.254867 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.5410 | −1.41444 | −0.707221 | − | 0.706992i | \(-0.750052\pi\) | ||||
−0.707221 | + | 0.706992i | \(0.750052\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.66048 | + | 16.7324i | −0.576296 | + | 0.998173i | 0.419604 | + | 0.907707i | \(0.362169\pi\) |
−0.995900 | + | 0.0904661i | \(0.971164\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.22658 | − | 3.85655i | 0.132356 | − | 0.229248i | −0.792228 | − | 0.610225i | \(-0.791079\pi\) |
0.924584 | + | 0.380977i | \(0.124412\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.39426 | − | 27.9279i | −0.200357 | − | 1.64853i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.48119 | − | 12.9578i | 0.440070 | − | 0.762224i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.7314 | + | 20.3193i | 0.685354 | + | 1.18707i | 0.973325 | + | 0.229429i | \(0.0736858\pi\) |
−0.287972 | + | 0.957639i | \(0.592981\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.8125 | + | 18.7278i | −0.629529 | + | 1.09038i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.09714 | + | 14.0247i | 0.468270 | + | 0.811067i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.6238 | + | 9.48844i | −0.727627 | + | 0.546904i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.855817 | − | 1.48232i | −0.0490039 | − | 0.0848773i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.79955 | 0.445144 | 0.222572 | − | 0.974916i | \(-0.428555\pi\) | ||||
0.222572 | + | 0.974916i | \(0.428555\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.49449 | − | 12.9808i | 0.424974 | − | 0.736076i | −0.571444 | − | 0.820641i | \(-0.693617\pi\) |
0.996418 | + | 0.0845650i | \(0.0269501\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.46332 | − | 5.99864i | −0.195758 | − | 0.339063i | 0.751391 | − | 0.659858i | \(-0.229383\pi\) |
−0.947149 | + | 0.320794i | \(0.896050\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.42872 | + | 9.40282i | 0.304907 | + | 0.528115i | 0.977241 | − | 0.212133i | \(-0.0680412\pi\) |
−0.672333 | + | 0.740249i | \(0.734708\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.43533 | + | 2.48606i | −0.0803629 | + | 0.139193i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.52027 | 0.474081 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.55999 | − | 2.70199i | −0.0865328 | − | 0.149879i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.308570 | + | 2.53891i | 0.0170120 | + | 0.139975i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.02584 | + | 6.97297i | 0.221280 | + | 0.383269i | 0.955197 | − | 0.295971i | \(-0.0956431\pi\) |
−0.733917 | + | 0.679240i | \(0.762310\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.54869 | + | 2.68240i | −0.0846138 | + | 0.146555i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.4293 | + | 19.7961i | 0.622594 | + | 1.07836i | 0.989001 | + | 0.147909i | \(0.0472543\pi\) |
−0.366407 | + | 0.930455i | \(0.619412\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.6027 | − | 21.8285i | 0.682474 | − | 1.18208i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.57324 | − | 17.3145i | −0.354922 | − | 0.934896i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.8892 | − | 22.3247i | 0.691928 | − | 1.19845i | −0.279278 | − | 0.960210i | \(-0.590095\pi\) |
0.971205 | − | 0.238244i | \(-0.0765716\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.90108 | − | 11.9530i | 0.369406 | − | 0.639830i | −0.620067 | − | 0.784549i | \(-0.712894\pi\) |
0.989473 | + | 0.144719i | \(0.0462277\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.9028 | 1.32544 | 0.662721 | − | 0.748866i | \(-0.269402\pi\) | ||||
0.662721 | + | 0.748866i | \(0.269402\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.49829 | 0.238744 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.6980 | + | 18.5295i | −0.564620 | + | 0.977951i | 0.432465 | + | 0.901651i | \(0.357644\pi\) |
−0.997085 | + | 0.0763002i | \(0.975689\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.31371 | − | 14.3998i | −0.437564 | − | 0.757883i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.89594 | − | 3.28386i | −0.0992380 | − | 0.171885i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.5158 | −0.601121 | −0.300560 | − | 0.953763i | \(-0.597174\pi\) | ||||
−0.300560 | + | 0.953763i | \(0.597174\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.48026 | + | 28.6355i | 0.180686 | + | 1.48668i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.69398 | −0.0877109 | −0.0438555 | − | 0.999038i | \(-0.513964\pi\) | ||||
−0.0438555 | + | 0.999038i | \(0.513964\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.11911 | −0.109140 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.50319 | 0.436780 | 0.218390 | − | 0.975862i | \(-0.429920\pi\) | ||||
0.218390 | + | 0.975862i | \(0.429920\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.7819 | 0.653124 | 0.326562 | − | 0.945176i | \(-0.394110\pi\) | ||||
0.326562 | + | 0.945176i | \(0.394110\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.2017 | − | 6.04890i | −0.723787 | − | 0.308280i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.55959 | −0.180479 | −0.0902393 | − | 0.995920i | \(-0.528763\pi\) | ||||
−0.0902393 | + | 0.995920i | \(0.528763\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.10701 | + | 8.84560i | 0.258273 | + | 0.447341i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.93448 | + | 13.7429i | 0.399227 | + | 0.691482i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.0411 | − | 19.1238i | 0.554138 | − | 0.959795i | −0.443832 | − | 0.896110i | \(-0.646381\pi\) |
0.997970 | − | 0.0636848i | \(-0.0202852\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.59853 | −0.129765 | −0.0648823 | − | 0.997893i | \(-0.520667\pi\) | ||||
−0.0648823 | + | 0.997893i | \(0.520667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.6066 | 0.926859 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.33973 | + | 7.51662i | −0.215112 | + | 0.372585i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.51604 | + | 2.62585i | −0.0749632 | + | 0.129840i | −0.901070 | − | 0.433673i | \(-0.857217\pi\) |
0.826107 | + | 0.563513i | \(0.190551\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.0334 | − | 18.0642i | 1.18261 | − | 0.888881i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.1899 | − | 26.3096i | 0.745641 | − | 1.29149i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.4979 | + | 30.3073i | 0.854829 | + | 1.48061i | 0.876804 | + | 0.480848i | \(0.159671\pi\) |
−0.0219749 | + | 0.999759i | \(0.506995\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.3264 | − | 23.0820i | 0.649488 | − | 1.12495i | −0.333757 | − | 0.942659i | \(-0.608316\pi\) |
0.983245 | − | 0.182288i | \(-0.0583502\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.983916 | − | 1.70419i | −0.0477269 | − | 0.0826655i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.287106 | + | 2.36230i | 0.0138940 | + | 0.114320i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.77241 | + | 15.1943i | 0.422552 | + | 0.731882i | 0.996188 | − | 0.0872286i | \(-0.0278010\pi\) |
−0.573636 | + | 0.819110i | \(0.694468\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.0202 | −0.865997 | −0.432998 | − | 0.901395i | \(-0.642544\pi\) | ||||
−0.432998 | + | 0.901395i | \(0.642544\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.3549 | − | 36.9878i | 1.02154 | − | 1.76937i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.7159 | − | 32.4169i | −0.893263 | − | 1.54718i | −0.835940 | − | 0.548820i | \(-0.815077\pi\) |
−0.0573222 | − | 0.998356i | \(-0.518256\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.67162 | + | 6.35944i | 0.174444 | + | 0.302146i | 0.939969 | − | 0.341261i | \(-0.110854\pi\) |
−0.765525 | + | 0.643407i | \(0.777521\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.92863 | − | 8.53664i | 0.233639 | − | 0.404675i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 40.3618 | 1.90479 | 0.952395 | − | 0.304866i | \(-0.0986115\pi\) | ||||
0.952395 | + | 0.304866i | \(0.0986115\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.3003 | + | 28.2330i | 0.767553 | + | 1.32944i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.37480 | − | 11.3118i | −0.0644514 | − | 0.530305i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.7360 | + | 23.7914i | 0.642543 | + | 1.11292i | 0.984863 | + | 0.173333i | \(0.0554538\pi\) |
−0.342321 | + | 0.939583i | \(0.611213\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.36325 | − | 5.82532i | 0.156642 | − | 0.271312i | −0.777014 | − | 0.629484i | \(-0.783266\pi\) |
0.933656 | + | 0.358172i | \(0.116600\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.89569 | + | 3.28344i | 0.0881004 | + | 0.152594i | 0.906708 | − | 0.421759i | \(-0.138587\pi\) |
−0.818608 | + | 0.574353i | \(0.805254\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.2166 | + | 17.6957i | −0.472769 | + | 0.818860i | −0.999514 | − | 0.0311635i | \(-0.990079\pi\) |
0.526746 | + | 0.850023i | \(0.323412\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.44233 | − | 2.58735i | 0.158952 | − | 0.119473i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.14987 | − | 15.8480i | 0.420712 | − | 0.728694i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.11423 | + | 7.12606i | −0.188774 | + | 0.326966i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.9079 | −1.27514 | −0.637572 | − | 0.770391i | \(-0.720061\pi\) | ||||
−0.637572 | + | 0.770391i | \(0.720061\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.40715 | −0.292141 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.75627 | − | 3.04194i | 0.0797480 | − | 0.138128i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.89480 | − | 10.2101i | −0.267119 | − | 0.462663i | 0.700998 | − | 0.713163i | \(-0.252738\pi\) |
−0.968117 | + | 0.250500i | \(0.919405\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.2596 | − | 22.9662i | −0.598396 | − | 1.03645i | −0.993058 | − | 0.117626i | \(-0.962472\pi\) |
0.394662 | − | 0.918826i | \(-0.370862\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.33656 | −0.0601957 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.75380 | − | 2.45070i | −0.258093 | − | 0.109929i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 42.3329 | 1.89508 | 0.947540 | − | 0.319637i | \(-0.103561\pi\) | ||||
0.947540 | + | 0.319637i | \(0.103561\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.0768 | −0.493890 | −0.246945 | − | 0.969029i | \(-0.579427\pi\) | ||||
−0.246945 | + | 0.969029i | \(0.579427\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.3449 | 0.682839 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.7262 | −1.09597 | −0.547984 | − | 0.836489i | \(-0.684605\pi\) | ||||
−0.547984 | + | 0.836489i | \(0.684605\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.636042 | + | 5.23334i | 0.0281368 | + | 0.231509i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −33.8709 | −1.49253 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.48185 | − | 2.56665i | −0.0651719 | − | 0.112881i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.42298 | − | 11.1249i | −0.281396 | − | 0.487392i | 0.690333 | − | 0.723492i | \(-0.257464\pi\) |
−0.971729 | + | 0.236100i | \(0.924131\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.70453 | + | 2.95234i | −0.0745340 | + | 0.129097i | −0.900884 | − | 0.434061i | \(-0.857080\pi\) |
0.826350 | + | 0.563158i | \(0.190414\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.7355 | 0.511206 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28.2002 | 1.22609 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.0329 | + | 20.8416i | −0.521202 | + | 0.902748i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.6704 | + | 28.8741i | −0.720726 | + | 1.24833i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.8701 | + | 15.4744i | 0.640500 | + | 0.666530i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.9553 | + | 39.7598i | −0.986926 | + | 1.70941i | −0.353884 | + | 0.935289i | \(0.615139\pi\) |
−0.633043 | + | 0.774117i | \(0.718194\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.12073 | + | 3.67321i | 0.0908421 | + | 0.157343i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.5502 | + | 21.7376i | −0.536608 | + | 0.929432i | 0.462476 | + | 0.886632i | \(0.346961\pi\) |
−0.999084 | + | 0.0428004i | \(0.986372\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.79441 | + | 4.84006i | 0.119046 | + | 0.206194i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.66183 | − | 21.9015i | −0.113192 | − | 0.931345i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.836144 | − | 1.44824i | −0.0354285 | − | 0.0613640i | 0.847767 | − | 0.530368i | \(-0.177946\pi\) |
−0.883196 | + | 0.469004i | \(0.844613\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.5088 | 0.571363 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.3764 | + | 19.7046i | −0.479460 | + | 0.830449i | −0.999722 | − | 0.0235574i | \(-0.992501\pi\) |
0.520263 | + | 0.854006i | \(0.325834\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.4628 | + | 25.0504i | 0.608456 | + | 1.05388i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.0292 | − | 22.5673i | −0.546214 | − | 0.946071i | −0.998529 | − | 0.0542125i | \(-0.982735\pi\) |
0.452315 | − | 0.891858i | \(-0.350598\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.24174 | + | 10.8110i | −0.261209 | + | 0.452427i | −0.966563 | − | 0.256428i | \(-0.917454\pi\) |
0.705355 | + | 0.708855i | \(0.250788\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.86421 | −0.411366 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.3756 | − | 17.9710i | −0.431941 | − | 0.748143i | 0.565100 | − | 0.825023i | \(-0.308838\pi\) |
−0.997040 | + | 0.0768793i | \(0.975504\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33.7631 | + | 25.3773i | −1.40073 | + | 1.05283i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.7133 | − | 28.9483i | −0.692195 | − | 1.19892i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.67294 | + | 15.0220i | −0.357971 | + | 0.620023i | −0.987622 | − | 0.156855i | \(-0.949865\pi\) |
0.629651 | + | 0.776878i | \(0.283198\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.5359 | − | 42.4975i | −1.01099 | − | 1.75108i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.0203 | − | 24.2839i | 0.575745 | − | 0.997220i | −0.420215 | − | 0.907425i | \(-0.638045\pi\) |
0.995960 | − | 0.0897956i | \(-0.0286214\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.867109 | − | 7.13455i | −0.0355480 | − | 0.292488i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.6047 | − | 20.0999i | 0.474155 | − | 0.821260i | −0.525407 | − | 0.850851i | \(-0.676087\pi\) |
0.999562 | + | 0.0295906i | \(0.00942035\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.348014 | + | 0.602779i | −0.0141958 | + | 0.0245878i | −0.873036 | − | 0.487656i | \(-0.837852\pi\) |
0.858840 | + | 0.512244i | \(0.171185\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.04572 | −0.123826 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.71065 | −0.0694333 | −0.0347166 | − | 0.999397i | \(-0.511053\pi\) | ||||
−0.0347166 | + | 0.999397i | \(0.511053\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.09390 | − | 1.89469i | 0.0442545 | − | 0.0766511i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.77253 | + | 3.07010i | 0.0715916 | + | 0.124000i | 0.899599 | − | 0.436717i | \(-0.143859\pi\) |
−0.828007 | + | 0.560717i | \(0.810525\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.58526 | − | 9.67395i | −0.224854 | − | 0.389458i | 0.731422 | − | 0.681925i | \(-0.238857\pi\) |
−0.956276 | + | 0.292467i | \(0.905524\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.2172 | 0.772403 | 0.386201 | − | 0.922415i | \(-0.373787\pi\) | ||||
0.386201 | + | 0.922415i | \(0.373787\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.9551 | + | 8.23414i | −0.438906 | + | 0.329894i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.2067 | −0.648270 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.04111 | −0.161130 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.1101 | −0.920000 | −0.460000 | − | 0.887919i | \(-0.652151\pi\) | ||||
−0.460000 | + | 0.887919i | \(0.652151\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −32.2185 | −1.27855 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.40423 | + | 15.2180i | −0.174502 | + | 0.602960i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.3938 | 0.805506 | 0.402753 | − | 0.915309i | \(-0.368053\pi\) | ||||
0.402753 | + | 0.915309i | \(0.368053\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.31644 | − | 2.28015i | −0.0519154 | − | 0.0899202i | 0.838900 | − | 0.544286i | \(-0.183199\pi\) |
−0.890815 | + | 0.454366i | \(0.849866\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.63856 | − | 6.30217i | −0.143047 | − | 0.247764i | 0.785596 | − | 0.618740i | \(-0.212357\pi\) |
−0.928642 | + | 0.370976i | \(0.879023\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.4196 | + | 30.1717i | −0.683781 | + | 1.18434i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.8671 | −0.894858 | −0.447429 | − | 0.894319i | \(-0.647660\pi\) | ||||
−0.447429 | + | 0.894319i | \(0.647660\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.53589 | −0.177232 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.59545 | − | 6.22750i | 0.140059 | − | 0.242589i | −0.787460 | − | 0.616366i | \(-0.788604\pi\) |
0.927519 | + | 0.373777i | \(0.121938\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.2064 | − | 29.8023i | 0.669250 | − | 1.15918i | −0.308864 | − | 0.951106i | \(-0.599949\pi\) |
0.978114 | − | 0.208069i | \(-0.0667179\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −24.0233 | + | 18.0566i | −0.931583 | + | 0.700204i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.34991 | + | 5.80222i | −0.129709 | + | 0.224663i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.37877 | − | 2.38811i | −0.0532270 | − | 0.0921919i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.46705 | − | 6.00511i | 0.133645 | − | 0.231480i | −0.791434 | − | 0.611255i | \(-0.790665\pi\) |
0.925079 | + | 0.379775i | \(0.123998\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.3014 | + | 29.9668i | 0.664945 | + | 1.15172i | 0.979300 | + | 0.202413i | \(0.0648784\pi\) |
−0.314355 | + | 0.949306i | \(0.601788\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.90373 | + | 2.93415i | −0.149811 | + | 0.112602i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.1618 | + | 33.1892i | 0.733206 | + | 1.26995i | 0.955506 | + | 0.294971i | \(0.0953101\pi\) |
−0.222300 | + | 0.974978i | \(0.571357\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.8988 | −0.798502 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.3377 | − | 21.3696i | 0.470030 | − | 0.814116i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.94953 | + | 6.84079i | 0.150247 | + | 0.260236i | 0.931318 | − | 0.364206i | \(-0.118660\pi\) |
−0.781071 | + | 0.624442i | \(0.785326\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.04916 | − | 12.2095i | −0.267390 | − | 0.463133i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.58936 | + | 13.1452i | −0.287467 | + | 0.497908i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.9291 | 0.979329 | 0.489664 | − | 0.871911i | \(-0.337119\pi\) | ||||
0.489664 | + | 0.871911i | \(0.337119\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.44893 | + | 14.6340i | 0.318657 | + | 0.551931i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.6278 | − | 8.36001i | −0.738180 | − | 0.314410i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.0523 | − | 24.3394i | −0.527746 | − | 0.914084i | −0.999477 | − | 0.0323408i | \(-0.989704\pi\) |
0.471731 | − | 0.881743i | \(-0.343630\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29.4134 | − | 50.9456i | 1.10154 | − | 1.90793i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.60221 | + | 11.4354i | 0.246909 | + | 0.427658i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.89461 | − | 10.2098i | 0.219832 | − | 0.380760i | −0.734924 | − | 0.678149i | \(-0.762782\pi\) |
0.954756 | + | 0.297389i | \(0.0961158\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 43.3246 | + | 18.4531i | 1.61349 | + | 0.687229i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.645394 | − | 1.11785i | 0.0239693 | − | 0.0415161i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.5207 | + | 42.4711i | −0.909423 | + | 1.57517i | −0.0945549 | + | 0.995520i | \(0.530143\pi\) |
−0.814868 | + | 0.579647i | \(0.803191\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.52027 | 0.315134 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.0927 | 0.557461 | 0.278731 | − | 0.960369i | \(-0.410086\pi\) | ||||
0.278731 | + | 0.960369i | \(0.410086\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.49503 | + | 4.32152i | −0.0919056 | + | 0.159185i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.9556 | + | 27.6359i | 0.586937 | + | 1.01660i | 0.994631 | + | 0.103486i | \(0.0329996\pi\) |
−0.407694 | + | 0.913119i | \(0.633667\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.1582 | − | 21.0586i | −0.446041 | − | 0.772565i | 0.552083 | − | 0.833789i | \(-0.313833\pi\) |
−0.998124 | + | 0.0612238i | \(0.980500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33.5385 | −1.22875 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 37.0541 | − | 27.8509i | 1.35393 | − | 1.01765i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.4463 | −1.22047 | −0.610237 | − | 0.792219i | \(-0.708926\pi\) | ||||
−0.610237 | + | 0.792219i | \(0.708926\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −38.7574 | −1.41053 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.1248 | −1.16759 | −0.583797 | − | 0.811899i | \(-0.698434\pi\) | ||||
−0.583797 | + | 0.811899i | \(0.698434\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.7957 | −1.22509 | −0.612547 | − | 0.790435i | \(-0.709855\pi\) | ||||
−0.612547 | + | 0.790435i | \(0.709855\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.711454 | − | 5.85382i | −0.0257563 | − | 0.211923i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25.7183 | −0.928634 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.8957 | + | 29.2643i | 0.609276 | + | 1.05530i | 0.991360 | + | 0.131170i | \(0.0418733\pi\) |
−0.382084 | + | 0.924128i | \(0.624793\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.0231 | + | 20.8247i | 0.432443 | + | 0.749012i | 0.997083 | − | 0.0763245i | \(-0.0243185\pi\) |
−0.564640 | + | 0.825337i | \(0.690985\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.66679 | + | 9.81516i | −0.203557 | + | 0.352571i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 63.4696 | 2.27404 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.24703 | 0.259319 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.83219 | + | 15.2978i | −0.315234 | + | 0.546002i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.22897 | − | 5.59274i | 0.115100 | − | 0.199360i | −0.802719 | − | 0.596357i | \(-0.796614\pi\) |
0.917820 | + | 0.396997i | \(0.129948\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.85193 | − | 39.9216i | −0.172515 | − | 1.41945i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.01781 | − | 1.76290i | 0.0361435 | − | 0.0626023i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.6987 | − | 32.3871i | −0.662341 | − | 1.14721i | −0.979999 | − | 0.199003i | \(-0.936230\pi\) |
0.317658 | − | 0.948205i | \(-0.397104\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.689944 | − | 1.19502i | 0.0244085 | − | 0.0422767i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.05448 | − | 5.29051i | −0.107790 | − | 0.186698i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −33.1455 | − | 14.1175i | −1.16822 | − | 0.497578i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.0048 | + | 34.6493i | 0.703331 | + | 1.21821i | 0.967290 | + | 0.253672i | \(0.0816383\pi\) |
−0.263959 | + | 0.964534i | \(0.585028\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.6946 | −0.972489 | −0.486245 | − | 0.873823i | \(-0.661634\pi\) | ||||
−0.486245 | + | 0.873823i | \(0.661634\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.6590 | + | 39.2465i | −0.793709 | + | 1.37474i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.8137 | − | 30.8543i | −0.623223 | − | 1.07945i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.188732 | − | 0.326893i | −0.00658679 | − | 0.0114087i | 0.862713 | − | 0.505693i | \(-0.168763\pi\) |
−0.869300 | + | 0.494285i | \(0.835430\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.50313 | + | 9.53170i | −0.191827 | + | 0.332254i | −0.945856 | − | 0.324587i | \(-0.894775\pi\) |
0.754029 | + | 0.656841i | \(0.228108\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.2473 | −0.982254 | −0.491127 | − | 0.871088i | \(-0.663415\pi\) | ||||
−0.491127 | + | 0.871088i | \(0.663415\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.7833 | − | 25.6054i | −0.513445 | − | 0.889313i | −0.999878 | − | 0.0155953i | \(-0.995036\pi\) |
0.486433 | − | 0.873718i | \(-0.338298\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.77783 | + | 9.59828i | −0.0962460 | + | 0.332561i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.68132 | + | 2.91212i | 0.0581843 | + | 0.100778i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.91508 | + | 11.9773i | −0.238735 | + | 0.413501i | −0.960352 | − | 0.278792i | \(-0.910066\pi\) |
0.721617 | + | 0.692293i | \(0.243399\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0616 | + | 24.3555i | 0.484884 | + | 0.839844i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.49581 | − | 12.9831i | 0.257864 | − | 0.446633i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.89581 | + | 1.65933i | 0.133861 | + | 0.0570152i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.1285 | + | 17.5431i | −0.347200 | + | 0.601369i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.59367 | − | 7.95647i | 0.157284 | − | 0.272424i | −0.776604 | − | 0.629989i | \(-0.783059\pi\) |
0.933888 | + | 0.357565i | \(0.116393\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40.4460 | −1.38161 | −0.690805 | − | 0.723041i | \(-0.742744\pi\) | ||||
−0.690805 | + | 0.723041i | \(0.742744\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.5128 | −0.426933 | −0.213466 | − | 0.976950i | \(-0.568475\pi\) | ||||
−0.213466 | + | 0.976950i | \(0.568475\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.8005 | − | 20.4391i | 0.401694 | − | 0.695755i | −0.592236 | − | 0.805764i | \(-0.701755\pi\) |
0.993931 | + | 0.110010i | \(0.0350881\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.342635 | + | 0.593462i | 0.0116499 | + | 0.0201783i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.7830 | + | 22.1407i | 0.433632 | + | 0.751073i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.68365 | −0.124816 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 29.5469 | + | 12.5848i | 0.998866 | + | 0.425444i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.5467 | −0.930185 | −0.465092 | − | 0.885262i | \(-0.653979\pi\) | ||||
−0.465092 | + | 0.885262i | \(0.653979\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.0894 | −1.41803 | −0.709014 | − | 0.705194i | \(-0.750860\pi\) | ||||
−0.709014 | + | 0.705194i | \(0.750860\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.58158 | 0.288793 | 0.144397 | − | 0.989520i | \(-0.453876\pi\) | ||||
0.144397 | + | 0.989520i | \(0.453876\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.51907 | −0.118159 | −0.0590795 | − | 0.998253i | \(-0.518817\pi\) | ||||
−0.0590795 | + | 0.998253i | \(0.518817\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 41.2110 | + | 17.5529i | 1.38217 | + | 0.588704i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.76998 | −0.193085 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.80707 | + | 11.7902i | 0.227535 | + | 0.394103i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.84891 | + | 6.66651i | 0.128368 | + | 0.222341i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.78163 | − | 13.4782i | 0.259244 | − | 0.449023i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.0362 | 0.699266 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.2826 | 1.23795 | 0.618974 | − | 0.785412i | \(-0.287549\pi\) | ||||
0.618974 | + | 0.785412i | \(0.287549\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.6458 | − | 18.4391i | 0.352711 | − | 0.610914i | −0.634012 | − | 0.773323i | \(-0.718593\pi\) |
0.986723 | + | 0.162409i | \(0.0519265\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.4718 | − | 42.3864i | 0.809899 | − | 1.40279i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.80190 | + | 2.47118i | 0.191595 | + | 0.0816056i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.00453 | − | 10.4001i | 0.198071 | − | 0.343069i | −0.749832 | − | 0.661628i | \(-0.769866\pi\) |
0.947903 | + | 0.318559i | \(0.103199\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.67487 | + | 4.63301i | 0.0880444 | + | 0.152497i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.95135 | − | 3.37984i | 0.0641601 | − | 0.111129i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.2602 | + | 17.7712i | 0.336626 | + | 0.583054i | 0.983796 | − | 0.179292i | \(-0.0573807\pi\) |
−0.647170 | + | 0.762346i | \(0.724047\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40.5657 | − | 10.0083i | 1.32949 | − | 0.328008i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.16413 | + | 7.21249i | 0.136182 | + | 0.235874i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.9040 | −0.356217 | −0.178109 | − | 0.984011i | \(-0.556998\pi\) | ||||
−0.178109 | + | 0.984011i | \(0.556998\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.4807 | + | 26.8134i | −0.504656 | + | 0.874090i | 0.495329 | + | 0.868705i | \(0.335047\pi\) |
−0.999986 | + | 0.00538505i | \(0.998286\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.0434 | + | 65.8931i | 1.23886 | + | 2.14578i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.0909 | − | 27.8702i | −0.522884 | − | 0.905661i | −0.999645 | − | 0.0266283i | \(-0.991523\pi\) |
0.476762 | − | 0.879032i | \(-0.341810\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.25481 | − | 3.90545i | 0.0731942 | − | 0.126776i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.0934 | −1.26636 | −0.633179 | − | 0.774005i | \(-0.718250\pi\) | ||||
−0.633179 | + | 0.774005i | \(0.718250\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.27967 | − | 14.3408i | −0.267924 | − | 0.464057i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 26.7318 | + | 11.3858i | 0.863216 | + | 0.367667i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.2948 | − | 31.6876i | −0.590156 | − | 1.02218i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.35046 | − | 2.33906i | 0.0434728 | − | 0.0752971i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.7235 | − | 22.0377i | −0.409159 | − | 0.708684i | 0.585637 | − | 0.810574i | \(-0.300845\pi\) |
−0.994796 | + | 0.101889i | \(0.967511\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.81455 | + | 15.2673i | −0.282872 | + | 0.489949i | −0.972091 | − | 0.234604i | \(-0.924621\pi\) |
0.689219 | + | 0.724553i | \(0.257954\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.36482 | + | 19.4577i | 0.0758128 | + | 0.623786i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.6269 | − | 23.6025i | 0.435963 | − | 0.755109i | −0.561411 | − | 0.827537i | \(-0.689741\pi\) |
0.997374 | + | 0.0724277i | \(0.0230747\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.94033 | − | 13.7531i | 0.253774 | − | 0.439550i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.6741 | 0.659402 | 0.329701 | − | 0.944085i | \(-0.393052\pi\) | ||||
0.329701 | + | 0.944085i | \(0.393052\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.8362 | −0.345269 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.3549 | − | 36.9878i | 0.679047 | − | 1.17614i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.0081 | − | 45.0474i | −0.826175 | − | 1.43098i | −0.901018 | − | 0.433782i | \(-0.857179\pi\) |
0.0748425 | − | 0.997195i | \(-0.476155\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.97307 | + | 8.61361i | 0.157657 | + | 0.273070i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.28538 | −0.294071 | −0.147035 | − | 0.989131i | \(-0.546973\pi\) | ||||
−0.147035 | + | 0.989131i | \(0.546973\pi\) | |||||||
\(998\) | 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 \(a_p\))