Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [832,2,Mod(129,832)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(832, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("832.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 832 = 2^{6} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 832.f (of order \(2\), degree \(1\), 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: | \(6.64355344817\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 104) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.2 | ||
Root | \(-2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 832.129 |
Dual form | 832.2.f.f.129.1 |
$q$-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 \(\left(\mathbb{Z}/832\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(703\) | \(769\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −2.56155 | −1.47891 | −0.739457 | − | 0.673204i | \(-0.764917\pi\) | ||||
−0.739457 | + | 0.673204i | \(0.764917\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.56155i | 1.14556i | 0.819709 | + | 0.572781i | \(0.194135\pi\) | ||||
−0.819709 | + | 0.572781i | \(0.805865\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.56155i | 1.72410i | 0.506819 | + | 0.862052i | \(0.330821\pi\) | ||||
−0.506819 | + | 0.862052i | \(0.669179\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.56155 | 1.18718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.12311i | 0.941652i | 0.882226 | + | 0.470826i | \(0.156044\pi\) | ||||
−0.882226 | + | 0.470826i | \(0.843956\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.56155 | + | 0.561553i | 0.987797 | + | 0.155747i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 6.56155i | − | 1.69419i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.561553 | 0.136197 | 0.0680983 | − | 0.997679i | \(-0.478307\pi\) | ||||
0.0680983 | + | 0.997679i | \(0.478307\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.00000i | − | 0.458831i | −0.973329 | − | 0.229416i | \(-0.926318\pi\) | ||
0.973329 | − | 0.229416i | \(-0.0736815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 11.6847i | − | 2.54980i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.12311 | −1.06824 | −0.534121 | − | 0.845408i | \(-0.679357\pi\) | ||||
−0.534121 | + | 0.845408i | \(0.679357\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.56155 | −0.312311 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.43845 | −0.276829 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.12311 | −0.579946 | −0.289973 | − | 0.957035i | \(-0.593646\pi\) | ||||
−0.289973 | + | 0.957035i | \(0.593646\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.12311i | 0.560926i | 0.959865 | + | 0.280463i | \(0.0904881\pi\) | ||||
−0.959865 | + | 0.280463i | \(0.909512\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 8.00000i | − | 1.39262i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −11.6847 | −1.97507 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.43845i | 0.894075i | 0.894515 | + | 0.447038i | \(0.147521\pi\) | ||||
−0.894515 | + | 0.447038i | \(0.852479\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.12311 | − | 1.43845i | −1.46087 | − | 0.230336i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.00000i | 1.24939i | 0.780869 | + | 0.624695i | \(0.214777\pi\) | ||||
−0.780869 | + | 0.624695i | \(0.785223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.43845 | 0.829355 | 0.414678 | − | 0.909968i | \(-0.363894\pi\) | ||||
0.414678 | + | 0.909968i | \(0.363894\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.12311i | 1.35999i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.43845i | − | 0.501549i | −0.968046 | − | 0.250775i | \(-0.919315\pi\) | ||
0.968046 | − | 0.250775i | \(-0.0806853\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13.8078 | −1.97254 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.43845 | −0.201423 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.24621 | 0.583262 | 0.291631 | − | 0.956531i | \(-0.405802\pi\) | ||||
0.291631 | + | 0.956531i | \(0.405802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.00000 | −1.07872 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.12311i | 0.678572i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 10.0000i | − | 1.30189i | −0.759125 | − | 0.650945i | \(-0.774373\pi\) | ||
0.759125 | − | 0.650945i | \(-0.225627\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.1231 | −1.42417 | −0.712084 | − | 0.702094i | \(-0.752248\pi\) | ||||
−0.712084 | + | 0.702094i | \(0.752248\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 16.2462i | 2.04683i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.43845 | + | 9.12311i | −0.178417 | + | 1.13158i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.876894i | 0.107130i | 0.998564 | + | 0.0535648i | \(0.0170584\pi\) | ||||
−0.998564 | + | 0.0535648i | \(0.982942\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.1231 | 1.57984 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.68466i | − | 0.674645i | −0.941389 | − | 0.337322i | \(-0.890479\pi\) | ||
0.941389 | − | 0.337322i | \(-0.109521\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 15.3693i | − | 1.79884i | −0.437083 | − | 0.899421i | \(-0.643988\pi\) | ||
0.437083 | − | 0.899421i | \(-0.356012\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.00000 | 0.461880 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.2462 | −1.62351 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.87689 | 0.323676 | 0.161838 | − | 0.986817i | \(-0.448258\pi\) | ||||
0.161838 | + | 0.986817i | \(0.448258\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.24621i | 0.905139i | 0.891729 | + | 0.452570i | \(0.149493\pi\) | ||||
−0.891729 | + | 0.452570i | \(0.850507\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.43845i | 0.156022i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.00000 | 0.857690 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5.12311i | − | 0.543048i | −0.962432 | − | 0.271524i | \(-0.912472\pi\) | ||
0.962432 | − | 0.271524i | \(-0.0875277\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.56155 | + | 16.2462i | −0.268524 | + | 1.70307i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 8.00000i | − | 0.829561i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.12311 | 0.525620 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.2462i | 1.04035i | 0.854061 | + | 0.520173i | \(0.174132\pi\) | ||||
−0.854061 | + | 0.520173i | \(0.825868\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.1231i | 1.11791i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.3693 | −1.33030 | −0.665148 | − | 0.746711i | \(-0.731632\pi\) | ||||
−0.665148 | + | 0.746711i | \(0.731632\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.12311 | 0.504795 | 0.252397 | − | 0.967624i | \(-0.418781\pi\) | ||||
0.252397 | + | 0.967624i | \(0.418781\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 29.9309 | 2.92095 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 15.6847i | − | 1.50232i | −0.660121 | − | 0.751159i | \(-0.729495\pi\) | ||
0.660121 | − | 0.751159i | \(-0.270505\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 13.9309i | − | 1.32226i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0000 | 0.940721 | 0.470360 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 13.1231i | − | 1.22374i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.6847 | + | 2.00000i | 1.17270 | + | 0.184900i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.56155i | 0.234817i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.24621 | 0.113292 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 20.4924i | − | 1.84774i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.80776i | 0.787790i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.1231 | 1.16449 | 0.582244 | − | 0.813014i | \(-0.302175\pi\) | ||||
0.582244 | + | 0.813014i | \(0.302175\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.9309 | −1.22654 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.6847 | −1.37037 | −0.685187 | − | 0.728367i | \(-0.740280\pi\) | ||||
−0.685187 | + | 0.728367i | \(0.740280\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.12311 | 0.791074 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 3.68466i | − | 0.317125i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 5.12311i | − | 0.437696i | −0.975759 | − | 0.218848i | \(-0.929770\pi\) | ||
0.975759 | − | 0.218848i | \(-0.0702300\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.8078 | 1.08634 | 0.543170 | − | 0.839623i | \(-0.317224\pi\) | ||||
0.543170 | + | 0.839623i | \(0.317224\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.80776i | 0.741748i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.75379 | + | 11.1231i | −0.146659 | + | 0.930161i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 8.00000i | − | 0.664364i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 35.3693 | 2.91721 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1.12311i | − | 0.0920084i | −0.998941 | − | 0.0460042i | \(-0.985351\pi\) | ||
0.998941 | − | 0.0460042i | \(-0.0146488\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.43845i | 0.605332i | 0.953097 | + | 0.302666i | \(0.0978767\pi\) | ||||
−0.953097 | + | 0.302666i | \(0.902123\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | −0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.24621 | 0.338885 | 0.169442 | − | 0.985540i | \(-0.445803\pi\) | ||||
0.169442 | + | 0.985540i | \(0.445803\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.8769 | −0.862594 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 23.3693i | − | 1.84176i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.75379i | 0.294019i | 0.989135 | + | 0.147010i | \(0.0469649\pi\) | ||||
−0.989135 | + | 0.147010i | \(0.953035\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 20.4924 | 1.59533 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 15.1231i | − | 1.17026i | −0.810939 | − | 0.585131i | \(-0.801043\pi\) | ||
0.810939 | − | 0.585131i | \(-0.198957\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.3693 | + | 4.00000i | 0.951486 | + | 0.307692i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 7.12311i | − | 0.544718i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.2462 | 0.931062 | 0.465531 | − | 0.885032i | \(-0.345863\pi\) | ||||
0.465531 | + | 0.885032i | \(0.345863\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 7.12311i | − | 0.538456i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 25.6155i | 1.92538i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.4384 | 1.00444 | 0.502218 | − | 0.864741i | \(-0.332517\pi\) | ||||
0.502218 | + | 0.864741i | \(0.332517\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.24621 | −0.612936 | −0.306468 | − | 0.951881i | \(-0.599147\pi\) | ||||
−0.306468 | + | 0.951881i | \(0.599147\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28.4924 | 2.10622 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.9309 | −1.02422 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.75379i | 0.128250i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 6.56155i | − | 0.477283i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.75379 | 0.416330 | 0.208165 | − | 0.978094i | \(-0.433251\pi\) | ||||
0.208165 | + | 0.978094i | \(0.433251\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.6155i | 1.26799i | 0.773336 | + | 0.633997i | \(0.218587\pi\) | ||||
−0.773336 | + | 0.633997i | \(0.781413\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.68466 | − | 23.3693i | 0.263864 | − | 1.67351i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.43845i | 0.387473i | 0.981054 | + | 0.193737i | \(0.0620607\pi\) | ||||
−0.981054 | + | 0.193737i | \(0.937939\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.24621 | −0.159230 | −0.0796148 | − | 0.996826i | \(-0.525369\pi\) | ||||
−0.0796148 | + | 0.996826i | \(0.525369\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 2.24621i | − | 0.158436i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 14.2462i | − | 0.999888i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.4924 | −1.43125 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.2462 | −1.26820 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.24621 | 0.432059 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.0540 | 1.03636 | 0.518179 | − | 0.855272i | \(-0.326610\pi\) | ||||
0.518179 | + | 0.855272i | \(0.326610\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.5616i | 0.997741i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.9309i | 0.950077i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.2462 | −0.967096 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 39.3693i | 2.66033i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.00000 | + | 0.315342i | 0.134535 | + | 0.0212122i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 18.1771i | − | 1.21723i | −0.793467 | − | 0.608614i | \(-0.791726\pi\) | ||
0.793467 | − | 0.608614i | \(-0.208274\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.56155 | −0.370770 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.3693i | 1.41833i | 0.705042 | + | 0.709166i | \(0.250928\pi\) | ||||
−0.705042 | + | 0.709166i | \(0.749072\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.31534i | 0.549493i | 0.961517 | + | 0.274747i | \(0.0885940\pi\) | ||||
−0.961517 | + | 0.274747i | \(0.911406\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 36.4924 | 2.40103 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.561553 | 0.0367885 | 0.0183943 | − | 0.999831i | \(-0.494145\pi\) | ||||
0.0183943 | + | 0.999831i | \(0.494145\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.80776 | 0.574555 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.36932 | −0.478689 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.9309i | 1.28922i | 0.764511 | + | 0.644610i | \(0.222980\pi\) | ||||
−0.764511 | + | 0.644610i | \(0.777020\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.8769i | 1.21597i | 0.793949 | + | 0.607984i | \(0.208021\pi\) | ||||
−0.793949 | + | 0.607984i | \(0.791979\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.2462 | 1.42710 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 35.3693i | − | 2.25966i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.12311 | − | 7.12311i | 0.0714615 | − | 0.453232i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 21.1231i | − | 1.33862i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.49242 | −0.536037 | −0.268018 | − | 0.963414i | \(-0.586369\pi\) | ||||
−0.268018 | + | 0.963414i | \(0.586369\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 16.0000i | − | 1.00591i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 3.68466i | − | 0.230742i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.9309 | −1.74228 | −0.871140 | − | 0.491035i | \(-0.836619\pi\) | ||||
−0.871140 | + | 0.491035i | \(0.836619\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.8078 | −1.54148 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.1231 | −0.688503 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −28.4924 | −1.75692 | −0.878459 | − | 0.477818i | \(-0.841428\pi\) | ||||
−0.878459 | + | 0.477818i | \(0.841428\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.8769i | 0.668162i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.1231i | 0.803121i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.1231 | −1.16596 | −0.582978 | − | 0.812488i | \(-0.698113\pi\) | ||||
−0.582978 | + | 0.812488i | \(0.698113\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.31534i | 0.140647i | 0.997524 | + | 0.0703235i | \(0.0224032\pi\) | ||||
−0.997524 | + | 0.0703235i | \(0.977597\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.56155 | − | 41.6155i | 0.397123 | − | 2.51869i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 4.87689i | − | 0.294088i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.3693 | 1.04362 | 0.521811 | − | 0.853061i | \(-0.325257\pi\) | ||||
0.521811 | + | 0.853061i | \(0.325257\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.1231i | 0.665923i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.3693i | 0.916857i | 0.888731 | + | 0.458428i | \(0.151587\pi\) | ||||
−0.888731 | + | 0.458428i | \(0.848413\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.0000 | 0.713326 | 0.356663 | − | 0.934233i | \(-0.383914\pi\) | ||||
0.356663 | + | 0.934233i | \(0.383914\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −13.1231 | −0.777346 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −36.4924 | −2.15408 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6847 | −0.981450 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 26.2462i | − | 1.53858i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 0.315342i | − | 0.0184225i | −0.999958 | − | 0.00921123i | \(-0.997068\pi\) | ||
0.999958 | − | 0.00921123i | \(-0.00293207\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 25.6155 | 1.49139 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 4.49242i | − | 0.260677i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.2462 | − | 2.87689i | −1.05521 | − | 0.166375i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.8078i | 1.42990i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 34.2462 | 1.96739 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 28.4924i | − | 1.63147i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 18.0000i | − | 1.02731i | −0.857996 | − | 0.513657i | \(-0.828290\pi\) | ||
0.857996 | − | 0.513657i | \(-0.171710\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.1231 | −0.746547 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.8769 | −0.616772 | −0.308386 | − | 0.951261i | \(-0.599789\pi\) | ||||
−0.308386 | + | 0.951261i | \(0.599789\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.56155 | 0.483928 | 0.241964 | − | 0.970285i | \(-0.422208\pi\) | ||||
0.241964 | + | 0.970285i | \(0.422208\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −41.6155 | −2.34477 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.87689i | 0.386245i | 0.981175 | + | 0.193122i | \(0.0618615\pi\) | ||||
−0.981175 | + | 0.193122i | \(0.938139\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 9.75379i | − | 0.546107i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.2462 | 0.571888 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.12311i | − | 0.0624913i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.56155 | − | 0.876894i | −0.308499 | − | 0.0486413i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 40.1771i | 2.22180i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.6847 | 0.864723 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.2462i | 0.892973i | 0.894790 | + | 0.446486i | \(0.147325\pi\) | ||||
−0.894790 | + | 0.446486i | \(0.852675\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 19.3693i | 1.06143i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.24621 | −0.122724 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.6847 | 0.745451 | 0.372725 | − | 0.927942i | \(-0.378423\pi\) | ||||
0.372725 | + | 0.927942i | \(0.378423\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −25.6155 | −1.39124 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.75379 | −0.528197 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 31.0540i | − | 1.67676i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 33.6155i | 1.80980i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.56155 | 0.137511 | 0.0687557 | − | 0.997634i | \(-0.478097\pi\) | ||||
0.0687557 | + | 0.997634i | \(0.478097\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.9309i | 0.959817i | 0.877318 | + | 0.479909i | \(0.159330\pi\) | ||||
−0.877318 | + | 0.479909i | \(0.840670\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.12311 | − | 0.807764i | −0.273451 | − | 0.0431153i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.6155i | 1.78917i | 0.446894 | + | 0.894587i | \(0.352530\pi\) | ||||
−0.446894 | + | 0.894587i | \(0.647470\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.5616 | 0.772847 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 6.56155i | − | 0.347274i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 4.87689i | − | 0.257393i | −0.991684 | − | 0.128696i | \(-0.958921\pi\) | ||
0.991684 | − | 0.128696i | \(-0.0410792\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.19224 | −0.167549 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 39.3693 | 2.06068 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.49242 | 0.234503 | 0.117251 | − | 0.993102i | \(-0.462592\pi\) | ||||
0.117251 | + | 0.993102i | \(0.462592\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 28.4924i | 1.48326i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.3693i | 1.00560i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.6307 | 0.550436 | 0.275218 | − | 0.961382i | \(-0.411250\pi\) | ||||
0.275218 | + | 0.961382i | \(0.411250\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 22.5616i | − | 1.16507i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.1231 | − | 1.75379i | −0.572869 | − | 0.0903247i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 26.0000i | − | 1.33553i | −0.744372 | − | 0.667765i | \(-0.767251\pi\) | ||
0.744372 | − | 0.667765i | \(-0.232749\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −33.6155 | −1.72218 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 9.19224i | − | 0.469701i | −0.972031 | − | 0.234851i | \(-0.924540\pi\) | ||
0.972031 | − | 0.234851i | \(-0.0754601\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 36.4924i | − | 1.85983i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 19.3693 | 0.984598 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.2462 | 1.43214 | 0.716070 | − | 0.698029i | \(-0.245939\pi\) | ||||
0.716070 | + | 0.698029i | \(0.245939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.87689 | −0.145491 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 40.1771 | 2.02667 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.36932i | 0.370791i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 9.12311i | − | 0.457876i | −0.973441 | − | 0.228938i | \(-0.926475\pi\) | ||
0.973441 | − | 0.228938i | \(-0.0735252\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −23.3693 | −1.16993 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 7.36932i | − | 0.368006i | −0.982926 | − | 0.184003i | \(-0.941094\pi\) | ||
0.982926 | − | 0.184003i | \(-0.0589056\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.75379 | + | 11.1231i | −0.0873624 | + | 0.554081i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 17.9309i | − | 0.890992i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.9848 | −0.841908 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 0.630683i | − | 0.0311853i | −0.999878 | − | 0.0155926i | \(-0.995037\pi\) | ||
0.999878 | − | 0.0155926i | \(-0.00496349\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.1231i | 0.647315i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 45.6155 | 2.24459 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.1231 | −1.03689 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −32.8078 | −1.60660 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.5616 | −1.68844 | −0.844221 | − | 0.535995i | \(-0.819937\pi\) | ||||
−0.844221 | + | 0.535995i | \(0.819937\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 3.19224i | − | 0.155580i | −0.996970 | − | 0.0777900i | \(-0.975214\pi\) | ||
0.996970 | − | 0.0777900i | \(-0.0247864\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 12.2462i | − | 0.595431i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.876894 | −0.0425356 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 50.7386i | − | 2.45541i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.49242 | − | 28.4924i | 0.216896 | − | 1.37563i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.4233i | 1.17643i | 0.808705 | + | 0.588214i | \(0.200169\pi\) | ||||
−0.808705 | + | 0.588214i | \(0.799831\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.6847 | 1.04210 | 0.521049 | − | 0.853527i | \(-0.325541\pi\) | ||||
0.521049 | + | 0.853527i | \(0.325541\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 20.4924i | 0.982536i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.2462i | 0.490143i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.8617 | −0.947949 | −0.473975 | − | 0.880539i | \(-0.657181\pi\) | ||||
−0.473975 | + | 0.880539i | \(0.657181\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −49.1771 | −2.34177 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.1771 | 1.71882 | 0.859412 | − | 0.511283i | \(-0.170830\pi\) | ||||
0.859412 | + | 0.511283i | \(0.170830\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.1231 | 0.622095 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.87689i | 0.136072i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 16.0000i | − | 0.755087i | −0.925992 | − | 0.377543i | \(-0.876769\pi\) | ||
0.925992 | − | 0.377543i | \(-0.123231\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.9848 | −1.17649 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 19.0540i | − | 0.895234i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −41.6155 | − | 6.56155i | −1.95097 | − | 0.307610i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 25.6155i | − | 1.19824i | −0.800658 | − | 0.599122i | \(-0.795516\pi\) | ||
0.800658 | − | 0.599122i | \(-0.204484\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.807764 | −0.0377032 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 36.1771i | − | 1.68493i | −0.538747 | − | 0.842467i | \(-0.681102\pi\) | ||
0.538747 | − | 0.842467i | \(-0.318898\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.6155i | 1.84109i | 0.390637 | + | 0.920545i | \(0.372255\pi\) | ||||
−0.390637 | + | 0.920545i | \(0.627745\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 20.4924 | 0.950313 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.4924 | −0.763178 | −0.381589 | − | 0.924332i | \(-0.624623\pi\) | ||||
−0.381589 | + | 0.924332i | \(0.624623\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.00000 | −0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.8769 | −0.501181 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.9848i | 0.780964i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.12311i | 0.143298i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.1231 | 0.692439 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 9.19224i | − | 0.420004i | −0.977701 | − | 0.210002i | \(-0.932653\pi\) | ||
0.977701 | − | 0.210002i | \(-0.0673470\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.05398 | + | 19.3693i | −0.139249 | + | 0.883165i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 59.8617i | 2.72380i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.2462 | −1.19178 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.8617i | 1.89694i | 0.316872 | + | 0.948468i | \(0.397367\pi\) | ||||
−0.316872 | + | 0.948468i | \(0.602633\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 9.61553i | − | 0.434829i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.1922 | 0.505099 | 0.252549 | − | 0.967584i | \(-0.418731\pi\) | ||||
0.252549 | + | 0.967584i | \(0.418731\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.75379 | −0.0789867 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −28.4924 | −1.28064 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.9309 | 1.16316 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.8769i | 0.755514i | 0.925905 | + | 0.377757i | \(0.123304\pi\) | ||||
−0.925905 | + | 0.377757i | \(0.876696\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 38.7386i | 1.73071i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.3693 | 0.685284 | 0.342642 | − | 0.939466i | \(-0.388678\pi\) | ||||
0.342642 | + | 0.939466i | \(0.388678\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 34.2462i | − | 1.52394i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −31.6847 | − | 10.2462i | −1.40717 | − | 0.455050i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.3693i | 1.21312i | 0.795036 | + | 0.606562i | \(0.207452\pi\) | ||||
−0.795036 | + | 0.606562i | \(0.792548\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 70.1080 | 3.10139 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.87689i | 0.127018i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.1231i | 0.578273i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.7386 | 0.472285 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −31.3693 | −1.37696 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.9309 | −1.22367 | −0.611837 | − | 0.790984i | \(-0.709569\pi\) | ||||
−0.611837 | + | 0.790984i | \(0.709569\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.2462 | −1.32257 | −0.661287 | − | 0.750133i | \(-0.729990\pi\) | ||||
−0.661287 | + | 0.750133i | \(0.729990\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 18.2462i | 0.796330i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.75379i | 0.0763962i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.24621 | 0.141140 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 35.6155i | − | 1.54558i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.49242 | + | 28.4924i | −0.194588 | + | 1.23414i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 10.2462i | − | 0.442982i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −34.4233 | −1.48547 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 43.1231i | − | 1.85744i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 20.1771i | − | 0.867480i | −0.901038 | − | 0.433740i | \(-0.857194\pi\) | ||
0.901038 | − | 0.433740i | \(-0.142806\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.1231 | 0.906479 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 40.1771 | 1.72100 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.19224 | 0.136490 | 0.0682451 | − | 0.997669i | \(-0.478260\pi\) | ||||
0.0682451 | + | 0.997669i | \(0.478260\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −39.6155 | −1.69075 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.24621i | 0.266098i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.1231i | 0.558051i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 35.6847 | 1.51473 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 9.93087i | − | 0.420784i | −0.977617 | − | 0.210392i | \(-0.932526\pi\) | ||
0.977617 | − | 0.210392i | \(-0.0674741\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.3693 | + | 3.05398i | 0.819235 | + | 0.129169i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 4.49242i | − | 0.189670i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.93087 | 0.0813765 | 0.0406882 | − | 0.999172i | \(-0.487045\pi\) | ||||
0.0406882 | + | 0.999172i | \(0.487045\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25.6155i | 1.07765i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 31.9309i | − | 1.34097i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.8078 | −0.956151 | −0.478076 | − | 0.878319i | \(-0.658666\pi\) | ||||
−0.478076 | + | 0.878319i | \(0.658666\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.0540 | 0.964779 | 0.482389 | − | 0.875957i | \(-0.339769\pi\) | ||||
0.482389 | + | 0.875957i | \(0.339769\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.7386 | −0.615715 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.00000 | 0.333623 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 27.8617i | − | 1.15990i | −0.814652 | − | 0.579950i | \(-0.803072\pi\) | ||
0.814652 | − | 0.579950i | \(-0.196928\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 45.1231i | − | 1.87525i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −37.6155 | −1.56056 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.2614i | 0.549230i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.12311 | + | 32.4924i | −0.211814 | + | 1.34340i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 42.4924i | 1.75385i | 0.480627 | + | 0.876925i | \(0.340409\pi\) | ||||
−0.480627 | + | 0.876925i | \(0.659591\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.24621 | 0.257371 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 13.9309i | − | 0.573039i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.2462i | 1.73484i | 0.497573 | + | 0.867422i | \(0.334225\pi\) | ||||
−0.497573 | + | 0.867422i | \(0.665775\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.56155 | −0.268997 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.75379 | 0.235487 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.6307 | −0.679511 | −0.339756 | − | 0.940514i | \(-0.610344\pi\) | ||||
−0.339756 | + | 0.940514i | \(0.610344\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.19224 | 0.0486323 | 0.0243162 | − | 0.999704i | \(-0.492259\pi\) | ||||
0.0243162 | + | 0.999704i | \(0.492259\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.12311i | 0.127183i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.19224i | 0.129783i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.6155 | −1.36441 | −0.682206 | − | 0.731160i | \(-0.738979\pi\) | ||||
−0.682206 | + | 0.731160i | \(0.738979\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 36.4924i | 1.47875i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.93087 | − | 12.2462i | 0.0781146 | − | 0.495429i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 43.3693i | − | 1.75167i | −0.482610 | − | 0.875835i | \(-0.660311\pi\) | ||
0.482610 | − | 0.875835i | \(-0.339689\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 52.4924 | 2.11670 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.2462i | 0.734565i | 0.930109 | + | 0.367282i | \(0.119712\pi\) | ||||
−0.930109 | + | 0.367282i | \(0.880288\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.6155i | 0.949188i | 0.880205 | + | 0.474594i | \(0.157405\pi\) | ||||
−0.880205 | + | 0.474594i | \(0.842595\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.36932 | 0.295720 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.3693 | 0.936272 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.3693 | −1.21477 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.0000 | −0.638978 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.05398i | 0.121770i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.43845i | 0.296120i | 0.988978 | + | 0.148060i | \(0.0473029\pi\) | ||||
−0.988978 | + | 0.148060i | \(0.952697\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −38.5616 | −1.53268 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 33.6155i | 1.33399i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −49.1771 | − | 7.75379i | −1.94847 | − | 0.307216i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 20.2462i | − | 0.800928i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.2462 | 0.799677 | 0.399839 | − | 0.916586i | \(-0.369066\pi\) | ||||
0.399839 | + | 0.916586i | \(0.369066\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.8769i | 0.665560i | 0.943005 | + | 0.332780i | \(0.107987\pi\) | ||||
−0.943005 | + | 0.332780i | \(0.892013\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 35.6847i | − | 1.40508i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.12311 | 0.201410 | 0.100705 | − | 0.994916i | \(-0.467890\pi\) | ||||
0.100705 | + | 0.994916i | \(0.467890\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.2311 | 1.22593 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 36.4924 | 1.43025 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.6155 | 1.08068 | 0.540340 | − | 0.841447i | \(-0.318296\pi\) | ||||
0.540340 | + | 0.841447i | \(0.318296\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 40.1771i | − | 1.56985i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 54.7386i | − | 2.13556i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.7386 | −1.66486 | −0.832430 | − | 0.554130i | \(-0.813051\pi\) | ||||
−0.832430 | + | 0.554130i | \(0.813051\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.1231i | 1.59950i | 0.600331 | + | 0.799752i | \(0.295036\pi\) | ||||
−0.600331 | + | 0.799752i | \(0.704964\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.12311 | − | 0.807764i | −0.198965 | − | 0.0313710i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 23.3693i | 0.906223i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.0000 | 0.619522 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 46.5616i | 1.80017i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 34.7386i | − | 1.34107i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.3002 | 1.20653 | 0.603267 | − | 0.797539i | \(-0.293865\pi\) | ||||
0.603267 | + | 0.797539i | \(0.293865\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.24621 | 0.0864567 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.7386 | −0.797050 | −0.398525 | − | 0.917157i | \(-0.630478\pi\) | ||||
−0.398525 | + | 0.917157i | \(0.630478\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −46.7386 | −1.79366 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 54.7386i | − | 2.09759i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 4.24621i | − | 0.162477i | −0.996695 | − | 0.0812384i | \(-0.974112\pi\) | ||
0.996695 | − | 0.0812384i | \(-0.0258875\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.1231 | 0.501408 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 21.3002i | − | 0.812653i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.1231 | + | 2.38447i | 0.576144 | + | 0.0908411i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 29.8617i | − | 1.13599i | −0.823031 | − | 0.567997i | \(-0.807718\pi\) | ||
0.823031 | − | 0.567997i | \(-0.192282\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −50.7386 | −1.92740 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 32.8078i | 1.24447i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.49242i | 0.170163i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.43845 | −0.0544071 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.2311 | 1.70835 | 0.854177 | − | 0.519983i | \(-0.174062\pi\) | ||||
0.854177 | + | 0.519983i | \(0.174062\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.8769 | 0.410230 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −22.5616 | −0.849717 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 60.9848i | − | 2.29357i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.12311i | − | 0.0421791i | −0.999778 | − | 0.0210896i | \(-0.993286\pi\) | ||
0.999778 | − | 0.0210896i | \(-0.00671351\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.2462 | 0.384263 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 16.0000i | − | 0.599205i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28.4924 | − | 4.49242i | −1.06556 | − | 0.168007i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 51.0540i | − | 1.90665i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.0000 | 0.596699 | 0.298350 | − | 0.954457i | \(-0.403564\pi\) | ||||
0.298350 | + | 0.954457i | \(0.403564\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.3693i | 0.870319i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 48.3542i | − | 1.79831i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.87689 | 0.181123 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 43.2311 | 1.60335 | 0.801676 | − | 0.597759i | \(-0.203942\pi\) | ||||
0.801676 | + | 0.597759i | \(0.203942\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −35.9848 | −1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.05398 | 0.112955 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 49.3002i | − | 1.82094i | −0.413571 | − | 0.910472i | \(-0.635719\pi\) | ||
0.413571 | − | 0.910472i | \(-0.364281\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 90.6004i | 3.34185i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.73863 | −0.100879 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.8617i | 1.53991i | 0.638099 | + | 0.769954i | \(0.279721\pi\) | ||||
−0.638099 | + | 0.769954i | \(0.720279\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.87689 | + | 18.2462i | −0.105685 | + | 0.670291i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 45.0540i | − | 1.65287i | −0.563032 | − | 0.826435i | \(-0.690365\pi\) | ||
0.563032 | − | 0.826435i | \(-0.309635\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.87689 | 0.105401 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 29.3693i | 1.07457i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 18.2462i | − | 0.666702i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.4924 | 1.33163 | 0.665814 | − | 0.746118i | \(-0.268085\pi\) | ||||
0.665814 | + | 0.746118i | \(0.268085\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21.7538 | 0.792752 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.0540 | −0.693445 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 40.9848i | 1.48766i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 53.1231i | − | 1.92571i | −0.270017 | − | 0.962856i | \(-0.587029\pi\) | ||
0.270017 | − | 0.962856i | \(-0.412971\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 71.5464 | 2.59015 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.12311i | 0.185226i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.61553 | − | 35.6155i | 0.202765 | − | 1.28600i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.49242i | 0.162001i | 0.996714 | + | 0.0810004i | \(0.0258115\pi\) | ||||
−0.996714 | + | 0.0810004i | \(0.974188\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 71.5464 | 2.57668 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.0540i | 0.829194i | 0.910005 | + | 0.414597i | \(0.136077\pi\) | ||||
−0.910005 | + | 0.414597i | \(0.863923\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4.87689i | − | 0.175183i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 63.5464 | 2.27971 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.0000 | 0.573259 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.7538 | 0.635281 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.49242 | 0.160546 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.8769i | 0.388213i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.3693i | 0.761734i | 0.924630 | + | 0.380867i | \(0.124374\pi\) | ||||
−0.924630 | + | 0.380867i | \(0.875626\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 72.9848 | 2.59833 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 45.6155i | 1.62190i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.6155 | − | 6.24621i | −1.40679 | − | 0.221809i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 27.8617i | − | 0.988154i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.24621 | 0.150409 | 0.0752043 | − | 0.997168i | \(-0.476039\pi\) | ||||
0.0752043 | + | 0.997168i | \(0.476039\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.93087i | − | 0.0683093i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 18.2462i | − | 0.644698i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 48.0000 | 1.69388 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 59.8617 | 2.10985 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 48.9848 | 1.72435 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.3153 | 1.06583 | 0.532915 | − | 0.846169i | \(-0.321096\pi\) | ||||
0.532915 | + | 0.846169i | \(0.321096\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.36932i | − | 0.0480832i | −0.999711 | − | 0.0240416i | \(-0.992347\pi\) | ||
0.999711 | − | 0.0240416i | \(-0.00765342\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 5.93087i | − | 0.208005i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.61553 | −0.336817 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 10.8769i | − | 0.380534i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.12311 | + | 57.8617i | −0.318787 | + | 2.02185i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.5464i | 0.961376i | 0.876892 | + | 0.480688i | \(0.159613\pi\) | ||||
−0.876892 | + | 0.480688i | \(0.840387\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.3542 | −1.40666 | −0.703329 | − | 0.710865i | \(-0.748304\pi\) | ||||
−0.703329 | + | 0.710865i | \(0.748304\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.4924i | 0.434930i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.0000i | 0.765015i | 0.923952 | + | 0.382507i | \(0.124939\pi\) | ||||
−0.923952 | + | 0.382507i | \(0.875061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.1231 | 0.525247 | 0.262624 | − | 0.964898i | \(-0.415412\pi\) | ||||
0.262624 | + | 0.964898i | \(0.415412\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −44.4924 | −1.54343 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.75379 | −0.268653 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 38.7386 | 1.34061 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 4.49242i | − | 0.155281i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 13.8617i | − | 0.478560i | −0.970951 | − | 0.239280i | \(-0.923089\pi\) | ||
0.970951 | − | 0.239280i | \(-0.0769114\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.2462 | −0.663662 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 39.3693i | − | 1.35595i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.2462 | + | 31.6847i | −0.352480 | + | 1.08999i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.68466i | 0.195327i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −30.7386 | −1.05495 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 27.8617i | − | 0.955088i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 7.68466i | − | 0.263118i | −0.991308 | − | 0.131559i | \(-0.958002\pi\) | ||
0.991308 | − | 0.131559i | \(-0.0419982\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.2462 | 0.624007 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.5076 | −0.598047 | −0.299024 | − | 0.954246i | \(-0.596661\pi\) | ||||
−0.299024 | + | 0.954246i | \(0.596661\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.24621 | 0.213118 | 0.106559 | − | 0.994306i | \(-0.466017\pi\) | ||||
0.106559 | + | 0.994306i | \(0.466017\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 93.4773 | 3.18570 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.9460i | 0.372607i | 0.982492 | + | 0.186304i | \(0.0596508\pi\) | ||||
−0.982492 | + | 0.186304i | \(0.940349\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.3693i | 1.06659i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 42.7386 | 1.45148 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.98485i | 0.304790i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.492423 | + | 3.12311i | −0.0166851 | + | 0.105822i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 36.4924i | 1.23508i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −40.1771 | −1.35823 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54.4233i | 1.83774i | 0.394556 | + | 0.918872i | \(0.370898\pi\) | ||||
−0.394556 | + | 0.918872i | \(0.629102\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.807764i | 0.0272452i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.7926 | 1.47541 | 0.737705 | − | 0.675123i | \(-0.235909\pi\) | ||||
0.737705 | + | 0.675123i | \(0.235909\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.1922 | −0.376649 | −0.188324 | − | 0.982107i | \(-0.560306\pi\) | ||||
−0.188324 | + | 0.982107i | \(0.560306\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −65.6155 | −2.20564 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 54.7386 | 1.83794 | 0.918972 | − | 0.394323i | \(-0.129021\pi\) | ||||
0.918972 | + | 0.394323i | \(0.129021\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 59.8617i | 2.00770i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 21.8617i | − | 0.732396i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.87689 | −0.230126 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.4233i | 1.15064i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 46.7386 | + | 7.36932i | 1.56056 | + | 0.246054i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 9.75379i | − | 0.325307i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.38447 | 0.0794383 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 63.5464i | − | 2.11469i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 21.1231i | − | 0.702156i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.5616 | −0.881962 | −0.440981 | − | 0.897516i | \(-0.645369\pi\) | ||||
−0.440981 | + | 0.897516i | \(0.645369\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −47.6155 | −1.57931 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.2462 | −1.39968 | −0.699840 | − | 0.714300i | \(-0.746745\pi\) | ||||
−0.699840 | + | 0.714300i | \(0.746745\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.7538 | −0.852326 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 72.9848i | 2.41280i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 71.5464i | − | 2.36267i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.2462 | −0.601887 | −0.300943 | − | 0.953642i | \(-0.597302\pi\) | ||||
−0.300943 | + | 0.953642i | \(0.597302\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 46.1080i | 1.51931i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.19224 | − | 20.2462i | 0.105074 | − | 0.666412i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 8.49242i | − | 0.279229i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.2462 | 0.599284 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 30.7386i | − | 1.00850i | −0.863557 | − | 0.504251i | \(-0.831769\pi\) | ||
0.863557 | − | 0.504251i | \(-0.168231\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.6155i | 0.905062i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27.8617 | 0.912152 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.49242 | −0.146918 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.2462 | 1.18411 | 0.592056 | − | 0.805897i | \(-0.298316\pi\) | ||||
0.592056 | + | 0.805897i | \(0.298316\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.9309 | −0.715687 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 27.5464i | − | 0.897987i | −0.893535 | − | 0.448993i | \(-0.851783\pi\) | ||
0.893535 | − | 0.448993i | \(-0.148217\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 40.9848i | − | 1.33465i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 16.8078 | 0.546757 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 9.36932i | − | 0.304462i | −0.988345 | − | 0.152231i | \(-0.951354\pi\) | ||
0.988345 | − | 0.152231i | \(-0.0486458\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.63068 | − | 54.7386i | 0.280164 | − | 1.77689i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 17.6155i | − | 0.571223i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.0540 | −0.552432 | −0.276216 | − | 0.961096i | \(-0.589081\pi\) | ||||
−0.276216 | + | 0.961096i | \(0.589081\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.7386i | 0.476931i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24.9848i | 0.807645i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 23.3693 | 0.754635 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.2462 | 0.685362 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.2462 | −0.459078 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −45.1231 | −1.45256 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 11.4384i | − | 0.367836i | −0.982942 | − | 0.183918i | \(-0.941122\pi\) | ||
0.982942 | − | 0.183918i | \(-0.0588780\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.87689i | 0.0924192i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.8229 | −0.379416 | −0.189708 | − | 0.981841i | \(-0.560754\pi\) | ||||
−0.189708 | + | 0.981841i | \(0.560754\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 58.4233i | 1.87296i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.2462 | + | 2.24621i | 0.456244 | + | 0.0719363i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 35.2311i | − | 1.12714i | −0.826068 | − | 0.563571i | \(-0.809427\pi\) | ||
0.826068 | − | 0.563571i | \(-0.190573\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.0000 | 0.511362 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 55.8617i | − | 1.78353i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.8078i | 0.982615i | 0.870986 | + | 0.491308i | \(0.163481\pi\) | ||||
−0.870986 | + | 0.491308i | \(0.836519\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.9309 | −0.443874 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −40.1771 | −1.27885 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.8617 | −0.885952 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.6155 | −1.06783 | −0.533916 | − | 0.845537i | \(-0.679280\pi\) | ||||
−0.533916 | + | 0.845537i | \(0.679280\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 41.6155i | − | 1.32063i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 5.75379i | − | 0.182407i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.6155 | −1.25464 | −0.627318 | − | 0.778763i | \(-0.715847\pi\) | ||||
−0.627318 | + | 0.778763i | \(0.715847\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 7.82292i | − | 0.247506i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))