Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,2,Mod(143,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.o (of order \(4\), 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: | \(6.38803216170\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 207.1 | ||
Root | \(-0.951057 + 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 800.207 |
Dual form | 800.2.o.g.143.1 |
$q$-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 \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | −1.61803 | + | 1.61803i | −0.934172 | + | 0.934172i | −0.997963 | − | 0.0637909i | \(-0.979681\pi\) |
0.0637909 | + | 0.997963i | \(0.479681\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.17557 | + | 1.17557i | −0.444324 | + | 0.444324i | −0.893462 | − | 0.449138i | \(-0.851731\pi\) |
0.449138 | + | 0.893462i | \(0.351731\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.23607i | − | 0.745356i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.23607 | −0.372689 | −0.186344 | − | 0.982485i | \(-0.559664\pi\) | ||||
−0.186344 | + | 0.982485i | \(0.559664\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.07768 | − | 3.07768i | −0.853596 | − | 0.853596i | 0.136978 | − | 0.990574i | \(-0.456261\pi\) |
−0.990574 | + | 0.136978i | \(0.956261\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | + | 1.00000i | 0.242536 | + | 0.242536i | 0.817898 | − | 0.575363i | \(-0.195139\pi\) |
−0.575363 | + | 0.817898i | \(0.695139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000i | 0.458831i | 0.973329 | + | 0.229416i | \(0.0736815\pi\) | ||||
−0.973329 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 3.80423i | − | 0.830150i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.62866 | − | 2.62866i | −0.548113 | − | 0.548113i | 0.377782 | − | 0.925895i | \(-0.376687\pi\) |
−0.925895 | + | 0.377782i | \(0.876687\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.23607 | − | 1.23607i | −0.237881 | − | 0.237881i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.45309 | 0.269831 | 0.134916 | − | 0.990857i | \(-0.456924\pi\) | ||||
0.134916 | + | 0.990857i | \(0.456924\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.25731i | − | 0.944241i | −0.881534 | − | 0.472120i | \(-0.843489\pi\) | ||
0.881534 | − | 0.472120i | \(-0.156511\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000 | − | 2.00000i | 0.348155 | − | 0.348155i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.07768 | − | 3.07768i | 0.505968 | − | 0.505968i | −0.407318 | − | 0.913286i | \(-0.633536\pi\) |
0.913286 | + | 0.407318i | \(0.133536\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.95959 | 1.59481 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.70820 | −1.20382 | −0.601910 | − | 0.798564i | \(-0.705593\pi\) | ||||
−0.601910 | + | 0.798564i | \(0.705593\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.38197 | − | 2.38197i | 0.363246 | − | 0.363246i | −0.501760 | − | 0.865007i | \(-0.667314\pi\) |
0.865007 | + | 0.501760i | \(0.167314\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.33094 | − | 7.33094i | 1.06933 | − | 1.06933i | 0.0719165 | − | 0.997411i | \(-0.477088\pi\) |
0.997411 | − | 0.0719165i | \(-0.0229115\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.23607i | 0.605153i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.23607 | −0.453140 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.726543 | − | 0.726543i | −0.0997983 | − | 0.0997983i | 0.655445 | − | 0.755243i | \(-0.272481\pi\) |
−0.755243 | + | 0.655445i | \(0.772481\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.23607 | − | 3.23607i | −0.428628 | − | 0.428628i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 8.47214i | − | 1.10298i | −0.834182 | − | 0.551489i | \(-0.814060\pi\) | ||
0.834182 | − | 0.551489i | \(-0.185940\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 9.95959i | − | 1.27520i | −0.770370 | − | 0.637598i | \(-0.779928\pi\) | ||
0.770370 | − | 0.637598i | \(-0.220072\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.62866 | + | 2.62866i | 0.331179 | + | 0.331179i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.38197 | − | 2.38197i | −0.291003 | − | 0.291003i | 0.546473 | − | 0.837477i | \(-0.315970\pi\) |
−0.837477 | + | 0.546473i | \(0.815970\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.50651 | 1.02406 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.05342i | − | 0.837087i | −0.908197 | − | 0.418544i | \(-0.862541\pi\) | ||
0.908197 | − | 0.418544i | \(-0.137459\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.70820 | + | 8.70820i | −1.01922 | + | 1.01922i | −0.0194065 | + | 0.999812i | \(0.506178\pi\) |
−0.999812 | + | 0.0194065i | \(0.993822\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.45309 | − | 1.45309i | 0.165594 | − | 0.165594i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.3107 | −1.38507 | −0.692533 | − | 0.721386i | \(-0.743505\pi\) | ||||
−0.692533 | + | 0.721386i | \(0.743505\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.7082 | 1.18980 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.38197 | + | 4.38197i | −0.480983 | + | 0.480983i | −0.905446 | − | 0.424462i | \(-0.860463\pi\) |
0.424462 | + | 0.905446i | \(0.360463\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.35114 | + | 2.35114i | −0.252069 | + | 0.252069i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.47214i | − | 0.686045i | −0.939327 | − | 0.343023i | \(-0.888549\pi\) | ||
0.939327 | − | 0.343023i | \(-0.111451\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.23607 | 0.758546 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.50651 | + | 8.50651i | 0.882084 | + | 0.882084i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.236068 | + | 0.236068i | 0.0239691 | + | 0.0239691i | 0.718990 | − | 0.695021i | \(-0.244605\pi\) |
−0.695021 | + | 0.718990i | \(0.744605\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.76393i | 0.277786i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.3107i | 1.22496i | 0.790485 | + | 0.612482i | \(0.209829\pi\) | ||||
−0.790485 | + | 0.612482i | \(0.790171\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.33094 | − | 7.33094i | −0.722339 | − | 0.722339i | 0.246742 | − | 0.969081i | \(-0.420640\pi\) |
−0.969081 | + | 0.246742i | \(0.920640\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0902 | + | 12.0902i | 1.16880 | + | 1.16880i | 0.982491 | + | 0.186310i | \(0.0596528\pi\) |
0.186310 | + | 0.982491i | \(0.440347\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.71040 | −0.642739 | −0.321370 | − | 0.946954i | \(-0.604143\pi\) | ||||
−0.321370 | + | 0.946954i | \(0.604143\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.95959i | 0.945323i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.70820 | − | 4.70820i | 0.442911 | − | 0.442911i | −0.450078 | − | 0.892989i | \(-0.648604\pi\) |
0.892989 | + | 0.450078i | \(0.148604\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.88191 | + | 6.88191i | −0.636233 | + | 0.636233i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.35114 | −0.215529 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.47214 | −0.861103 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.4721 | − | 12.4721i | 1.12457 | − | 1.12457i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.78402 | + | 8.78402i | −0.779456 | + | 0.779456i | −0.979738 | − | 0.200282i | \(-0.935814\pi\) |
0.200282 | + | 0.979738i | \(0.435814\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.70820i | 0.678670i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.291796 | −0.0254943 | −0.0127472 | − | 0.999919i | \(-0.504058\pi\) | ||||
−0.0127472 | + | 0.999919i | \(0.504058\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.35114 | − | 2.35114i | −0.203870 | − | 0.203870i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.47214 | − | 3.47214i | −0.296645 | − | 0.296645i | 0.543054 | − | 0.839698i | \(-0.317268\pi\) |
−0.839698 | + | 0.543054i | \(0.817268\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.41641i | 0.459414i | 0.973260 | + | 0.229707i | \(0.0737767\pi\) | ||||
−0.973260 | + | 0.229707i | \(0.926223\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 23.7234i | 1.99787i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.80423 | + | 3.80423i | 0.318125 | + | 0.318125i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.85410 | − | 6.85410i | −0.565317 | − | 0.565317i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.2088 | −1.08211 | −0.541053 | − | 0.840988i | \(-0.681974\pi\) | ||||
−0.541053 | + | 0.840988i | \(0.681974\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.6619i | 1.19317i | 0.802551 | + | 0.596583i | \(0.203475\pi\) | ||||
−0.802551 | + | 0.596583i | \(0.796525\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.23607 | − | 2.23607i | 0.180775 | − | 0.180775i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.78808 | + | 9.78808i | −0.781174 | + | 0.781174i | −0.980029 | − | 0.198855i | \(-0.936278\pi\) |
0.198855 | + | 0.980029i | \(0.436278\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.35114 | 0.186458 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.18034 | 0.487079 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.14590 | + | 7.14590i | −0.559710 | + | 0.559710i | −0.929225 | − | 0.369515i | \(-0.879524\pi\) |
0.369515 | + | 0.929225i | \(0.379524\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.277515 | + | 0.277515i | −0.0214747 | + | 0.0214747i | −0.717763 | − | 0.696288i | \(-0.754834\pi\) |
0.696288 | + | 0.717763i | \(0.254834\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.94427i | 0.457252i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.47214 | 0.341993 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.32688 | − | 6.32688i | −0.481024 | − | 0.481024i | 0.424435 | − | 0.905459i | \(-0.360473\pi\) |
−0.905459 | + | 0.424435i | \(0.860473\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.7082 | + | 13.7082i | 1.03037 | + | 1.03037i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.4721i | 1.23119i | 0.788065 | + | 0.615593i | \(0.211083\pi\) | ||||
−0.788065 | + | 0.615593i | \(0.788917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.40456i | − | 0.699036i | −0.936930 | − | 0.349518i | \(-0.886345\pi\) | ||
0.936930 | − | 0.349518i | \(-0.113655\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.1150 | + | 16.1150i | 1.19125 | + | 1.19125i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.23607 | − | 1.23607i | −0.0903902 | − | 0.0903902i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.90617 | 0.211393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.8658i | 0.930934i | 0.885065 | + | 0.465467i | \(0.154114\pi\) | ||||
−0.885065 | + | 0.465467i | \(0.845886\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.47214 | − | 7.47214i | 0.537856 | − | 0.537856i | −0.385043 | − | 0.922899i | \(-0.625813\pi\) |
0.922899 | + | 0.385043i | \(0.125813\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.17963 | − | 2.17963i | 0.155292 | − | 0.155292i | −0.625185 | − | 0.780477i | \(-0.714976\pi\) |
0.780477 | + | 0.625185i | \(0.214976\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.1231 | −1.28471 | −0.642355 | − | 0.766407i | \(-0.722043\pi\) | ||||
−0.642355 | + | 0.766407i | \(0.722043\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.70820 | 0.543695 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.70820 | + | 1.70820i | −0.119892 | + | 0.119892i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.87785 | + | 5.87785i | −0.408539 | + | 0.408539i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2.47214i | − | 0.171001i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.7082 | −1.08140 | −0.540699 | − | 0.841216i | \(-0.681840\pi\) | ||||
−0.540699 | + | 0.841216i | \(0.681840\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.4127 | + | 11.4127i | 0.781984 | + | 0.781984i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.18034 | + | 6.18034i | 0.419549 | + | 0.419549i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 28.1803i | − | 1.90425i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 6.15537i | − | 0.414055i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.73060 | − | 1.73060i | −0.115890 | − | 0.115890i | 0.646784 | − | 0.762673i | \(-0.276114\pi\) |
−0.762673 | + | 0.646784i | \(0.776114\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.6180 | − | 11.6180i | −0.771116 | − | 0.771116i | 0.207186 | − | 0.978302i | \(-0.433570\pi\) |
−0.978302 | + | 0.207186i | \(0.933570\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.3723 | −1.41232 | −0.706160 | − | 0.708053i | \(-0.749574\pi\) | ||||
−0.706160 | + | 0.708053i | \(0.749574\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.70228i | 0.309387i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.47214 | − | 3.47214i | 0.227467 | − | 0.227467i | −0.584167 | − | 0.811634i | \(-0.698579\pi\) |
0.811634 | + | 0.584167i | \(0.198579\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.9192 | − | 19.9192i | 1.29389 | − | 1.29389i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.3238 | 1.89680 | 0.948398 | − | 0.317083i | \(-0.102703\pi\) | ||||
0.948398 | + | 0.317083i | \(0.102703\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.76393 | 0.435703 | 0.217852 | − | 0.975982i | \(-0.430095\pi\) | ||||
0.217852 | + | 0.975982i | \(0.430095\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.6180 | + | 13.6180i | −0.873597 | + | 0.873597i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.15537 | − | 6.15537i | 0.391657 | − | 0.391657i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 14.1803i | − | 0.898643i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.1803 | 1.40001 | 0.700005 | − | 0.714138i | \(-0.253181\pi\) | ||||
0.700005 | + | 0.714138i | \(0.253181\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.24920 | + | 3.24920i | 0.204275 | + | 0.204275i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.7082 | − | 18.7082i | −1.16699 | − | 1.16699i | −0.982913 | − | 0.184073i | \(-0.941072\pi\) |
−0.184073 | − | 0.982913i | \(-0.558928\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.23607i | 0.449627i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 3.24920i | − | 0.201120i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.3925 | + | 16.3925i | 1.01080 | + | 1.01080i | 0.999941 | + | 0.0108623i | \(0.00345764\pi\) |
0.0108623 | + | 0.999941i | \(0.496542\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.4721 | + | 10.4721i | 0.640884 | + | 0.640884i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.9111 | 1.09206 | 0.546029 | − | 0.837766i | \(-0.316139\pi\) | ||||
0.546029 | + | 0.837766i | \(0.316139\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 31.6749i | − | 1.92411i | −0.272851 | − | 0.962056i | \(-0.587967\pi\) | ||
0.272851 | − | 0.962056i | \(-0.412033\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.7082 | + | 11.7082i | −0.708613 | + | 0.708613i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.17963 | + | 2.17963i | −0.130961 | + | 0.130961i | −0.769549 | − | 0.638588i | \(-0.779519\pi\) |
0.638588 | + | 0.769549i | \(0.279519\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.7557 | −0.703796 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.70820 | 0.221213 | 0.110606 | − | 0.993864i | \(-0.464721\pi\) | ||||
0.110606 | + | 0.993864i | \(0.464721\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.6180 | − | 15.6180i | 0.928396 | − | 0.928396i | −0.0692066 | − | 0.997602i | \(-0.522047\pi\) |
0.997602 | + | 0.0692066i | \(0.0220468\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.06154 | − | 9.06154i | 0.534886 | − | 0.534886i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 15.0000i | − | 0.882353i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.763932 | −0.0447825 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.726543 | + | 0.726543i | 0.0424451 | + | 0.0424451i | 0.728011 | − | 0.685566i | \(-0.240445\pi\) |
−0.685566 | + | 0.728011i | \(0.740445\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.52786 | + | 1.52786i | 0.0886557 | + | 0.0886557i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.1803i | 0.935733i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.60034i | 0.322798i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −19.9192 | − | 19.9192i | −1.14433 | − | 1.14433i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.56231 | + | 6.56231i | 0.374531 | + | 0.374531i | 0.869124 | − | 0.494594i | \(-0.164683\pi\) |
−0.494594 | + | 0.869124i | \(0.664683\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.7234 | 1.34958 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8.16348i | − | 0.462909i | −0.972846 | − | 0.231454i | \(-0.925652\pi\) | ||
0.972846 | − | 0.231454i | \(-0.0743484\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.23607 | − | 6.23607i | 0.352483 | − | 0.352483i | −0.508549 | − | 0.861033i | \(-0.669818\pi\) |
0.861033 | + | 0.508549i | \(0.169818\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.6861 | + | 10.6861i | −0.600193 | + | 0.600193i | −0.940364 | − | 0.340171i | \(-0.889515\pi\) |
0.340171 | + | 0.940364i | \(0.389515\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.79611 | −0.100563 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −39.1246 | −2.18372 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.00000 | + | 2.00000i | −0.111283 | + | 0.111283i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.8576 | − | 10.8576i | 0.600429 | − | 0.600429i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.2361i | 0.950255i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.0689 | −1.54281 | −0.771403 | − | 0.636347i | \(-0.780445\pi\) | ||||
−0.771403 | + | 0.636347i | \(0.780445\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.88191 | − | 6.88191i | −0.377126 | − | 0.377126i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.05573 | + | 2.05573i | 0.111983 | + | 0.111983i | 0.760878 | − | 0.648895i | \(-0.224769\pi\) |
−0.648895 | + | 0.760878i | \(0.724769\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.2361i | 0.827510i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.49839i | 0.351908i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.2088 | − | 13.2088i | −0.713208 | − | 0.713208i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.03444 | − | 3.03444i | −0.162897 | − | 0.162897i | 0.620952 | − | 0.783849i | \(-0.286746\pi\) |
−0.783849 | + | 0.620952i | \(0.786746\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.5599 | −0.832904 | −0.416452 | − | 0.909158i | \(-0.636727\pi\) | ||||
−0.416452 | + | 0.909158i | \(0.636727\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.60845i | 0.406109i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.41641 | + | 4.41641i | −0.235062 | + | 0.235062i | −0.814802 | − | 0.579740i | \(-0.803154\pi\) |
0.579740 | + | 0.814802i | \(0.303154\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.80423 | − | 3.80423i | 0.201341 | − | 0.201341i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.79611 | −0.0947952 | −0.0473976 | − | 0.998876i | \(-0.515093\pi\) | ||||
−0.0473976 | + | 0.998876i | \(0.515093\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.3262 | − | 15.3262i | 0.804419 | − | 0.804419i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.0009 | + | 24.0009i | −1.25284 | + | 1.25284i | −0.298396 | + | 0.954442i | \(0.596452\pi\) |
−0.954442 | + | 0.298396i | \(0.903548\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17.2361i | 0.897274i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.70820 | 0.0886855 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.0454 | − | 15.0454i | −0.779021 | − | 0.779021i | 0.200644 | − | 0.979664i | \(-0.435697\pi\) |
−0.979664 | + | 0.200644i | \(0.935697\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.47214 | − | 4.47214i | −0.230327 | − | 0.230327i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 35.8885i | − | 1.84347i | −0.387820 | − | 0.921735i | \(-0.626772\pi\) | ||
0.387820 | − | 0.921735i | \(-0.373228\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 28.4257i | − | 1.45629i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.1352 | − | 11.1352i | −0.568980 | − | 0.568980i | 0.362862 | − | 0.931843i | \(-0.381799\pi\) |
−0.931843 | + | 0.362862i | \(0.881799\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.32624 | − | 5.32624i | −0.270748 | − | 0.270748i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.7234 | 1.20282 | 0.601412 | − | 0.798939i | \(-0.294605\pi\) | ||||
0.601412 | + | 0.798939i | \(0.294605\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 5.25731i | − | 0.265874i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.472136 | − | 0.472136i | 0.0238161 | − | 0.0238161i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.22494 | + | 7.22494i | −0.362609 | + | 0.362609i | −0.864773 | − | 0.502164i | \(-0.832538\pi\) |
0.502164 | + | 0.864773i | \(0.332538\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.60845 | 0.380899 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.88854 | −0.194185 | −0.0970923 | − | 0.995275i | \(-0.530954\pi\) | ||||
−0.0970923 | + | 0.995275i | \(0.530954\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.1803 | + | 16.1803i | −0.806000 | + | 0.806000i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.80423 | + | 3.80423i | −0.188568 | + | 0.188568i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.5967i | 1.36457i | 0.731086 | + | 0.682286i | \(0.239014\pi\) | ||||
−0.731086 | + | 0.682286i | \(0.760986\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.2361 | 0.554234 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.95959 | + | 9.95959i | 0.490080 | + | 0.490080i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.76393 | − | 8.76393i | −0.429172 | − | 0.429172i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 24.8328i | − | 1.21316i | −0.795022 | − | 0.606581i | \(-0.792540\pi\) | ||
0.795022 | − | 0.606581i | \(-0.207460\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 3.46120i | − | 0.168689i | −0.996437 | − | 0.0843443i | \(-0.973120\pi\) | ||
0.996437 | − | 0.0843443i | \(-0.0268795\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −16.3925 | − | 16.3925i | −0.797029 | − | 0.797029i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.7082 | + | 11.7082i | 0.566600 | + | 0.566600i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.3107 | −0.594368 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.7557i | 0.566252i | 0.959083 | + | 0.283126i | \(0.0913715\pi\) | ||||
−0.959083 | + | 0.283126i | \(0.908628\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.1803 | + | 23.1803i | −1.11398 | + | 1.11398i | −0.121369 | + | 0.992608i | \(0.538728\pi\) |
−0.992608 | + | 0.121369i | \(0.961272\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.25731 | − | 5.25731i | 0.251491 | − | 0.251491i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.2007 | 0.534579 | 0.267290 | − | 0.963616i | \(-0.413872\pi\) | ||||
0.267290 | + | 0.963616i | \(0.413872\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.47214 | 0.451054 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.0902 | − | 10.0902i | 0.479398 | − | 0.479398i | −0.425541 | − | 0.904939i | \(-0.639916\pi\) |
0.904939 | + | 0.425541i | \(0.139916\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.3723 | − | 21.3723i | 1.01087 | − | 1.01087i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 31.5967i | − | 1.49114i | −0.666426 | − | 0.745571i | \(-0.732177\pi\) | ||
0.666426 | − | 0.745571i | \(-0.267823\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.52786 | 0.448650 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −23.7234 | − | 23.7234i | −1.11462 | − | 1.11462i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.6525 | + | 21.6525i | 1.01286 | + | 1.01286i | 0.999916 | + | 0.0129439i | \(0.00412028\pi\) |
0.0129439 | + | 0.999916i | \(0.495880\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 2.47214i | − | 0.115389i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 6.49839i | − | 0.302660i | −0.988483 | − | 0.151330i | \(-0.951644\pi\) | ||
0.988483 | − | 0.151330i | \(-0.0483557\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.2905 | + | 17.2905i | 0.803559 | + | 0.803559i | 0.983650 | − | 0.180091i | \(-0.0576392\pi\) |
−0.180091 | + | 0.983650i | \(0.557639\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.67376 | − | 2.67376i | −0.123727 | − | 0.123727i | 0.642532 | − | 0.766259i | \(-0.277884\pi\) |
−0.766259 | + | 0.642532i | \(0.777884\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.60034 | 0.258600 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 31.6749i | − | 1.45950i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.94427 | + | 2.94427i | −0.135378 | + | 0.135378i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.62460 | + | 1.62460i | −0.0743853 | + | 0.0743853i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.60845 | −0.347639 | −0.173820 | − | 0.984778i | \(-0.555611\pi\) | ||||
−0.173820 | + | 0.984778i | \(0.555611\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.9443 | −0.863784 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.0000 | + | 10.0000i | −0.455016 | + | 0.455016i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.33905 | − | 9.33905i | 0.423193 | − | 0.423193i | −0.463109 | − | 0.886302i | \(-0.653266\pi\) |
0.886302 | + | 0.463109i | \(0.153266\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 23.1246i | − | 1.04573i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.7639 | 0.485769 | 0.242885 | − | 0.970055i | \(-0.421906\pi\) | ||||
0.242885 | + | 0.970055i | \(0.421906\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.45309 | + | 1.45309i | 0.0654437 | + | 0.0654437i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.29180 | + | 8.29180i | 0.371938 | + | 0.371938i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.8885i | 1.06940i | 0.845043 | + | 0.534699i | \(0.179575\pi\) | ||||
−0.845043 | + | 0.534699i | \(0.820425\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 0.898056i | − | 0.0401222i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.53483 | − | 5.53483i | −0.246786 | − | 0.246786i | 0.572864 | − | 0.819650i | \(-0.305832\pi\) |
−0.819650 | + | 0.572864i | \(0.805832\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.61803 | − | 9.61803i | −0.427152 | − | 0.427152i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.06154 | 0.401646 | 0.200823 | − | 0.979628i | \(-0.435638\pi\) | ||||
0.200823 | + | 0.979628i | \(0.435638\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 20.4742i | − | 0.905726i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.47214 | − | 2.47214i | 0.109147 | − | 0.109147i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.06154 | + | 9.06154i | −0.398526 | + | 0.398526i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.4742 | 0.898718 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.47214 | 0.371171 | 0.185586 | − | 0.982628i | \(-0.440582\pi\) | ||||
0.185586 | + | 0.982628i | \(0.440582\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.7426 | + | 16.7426i | −0.732105 | + | 0.732105i | −0.971036 | − | 0.238932i | \(-0.923203\pi\) |
0.238932 | + | 0.971036i | \(0.423203\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.25731 | − | 5.25731i | 0.229012 | − | 0.229012i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 9.18034i | − | 0.399145i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.9443 | −0.822111 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.7234 | + | 23.7234i | 1.02758 | + | 1.02758i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26.6525 | − | 26.6525i | −1.15014 | − | 1.15014i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 5.23607i | − | 0.225533i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 2.90617i | − | 0.124946i | −0.998047 | − | 0.0624730i | \(-0.980101\pi\) | ||
0.998047 | − | 0.0624730i | \(-0.0198987\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.2169 | + | 15.2169i | 0.653020 | + | 0.653020i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.56231 | − | 8.56231i | −0.366098 | − | 0.366098i | 0.499954 | − | 0.866052i | \(-0.333350\pi\) |
−0.866052 | + | 0.499954i | \(0.833350\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −22.2703 | −0.950474 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.90617i | 0.123807i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.4721 | − | 14.4721i | 0.615418 | − | 0.615418i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.1845 | − | 17.1845i | 0.728132 | − | 0.728132i | −0.242116 | − | 0.970247i | \(-0.577841\pi\) |
0.970247 | + | 0.242116i | \(0.0778413\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.6619 | −0.620131 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.00000 | 0.168880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.3262 | − | 11.3262i | 0.477344 | − | 0.477344i | −0.426937 | − | 0.904281i | \(-0.640407\pi\) |
0.904281 | + | 0.426937i | \(0.140407\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.5882 | + | 12.5882i | −0.528657 | + | 0.528657i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.1246i | 0.550212i | 0.961414 | + | 0.275106i | \(0.0887130\pi\) | ||||
−0.961414 | + | 0.275106i | \(0.911287\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.65248 | 0.362095 | 0.181047 | − | 0.983474i | \(-0.442051\pi\) | ||||
0.181047 | + | 0.983474i | \(0.442051\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.8172 | − | 20.8172i | −0.869653 | − | 0.869653i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.7639 | − | 21.7639i | −0.906044 | − | 0.906044i | 0.0899059 | − | 0.995950i | \(-0.471343\pi\) |
−0.995950 | + | 0.0899059i | \(0.971343\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.1803i | 1.00490i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 10.3026i | − | 0.427425i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.898056 | + | 0.898056i | 0.0371937 | + | 0.0371937i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.90983 | + | 5.90983i | 0.243925 | + | 0.243925i | 0.818472 | − | 0.574547i | \(-0.194822\pi\) |
−0.574547 | + | 0.818472i | \(0.694822\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.5146 | 0.433247 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.05342i | 0.290139i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.41641 | − | 6.41641i | 0.263490 | − | 0.263490i | −0.562980 | − | 0.826470i | \(-0.690345\pi\) |
0.826470 | + | 0.562980i | \(0.190345\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.3238 | − | 29.3238i | 1.20014 | − | 1.20014i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.5276 | 1.12475 | 0.562374 | − | 0.826883i | \(-0.309888\pi\) | ||||
0.562374 | + | 0.826883i | \(0.309888\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.29180 | −0.175066 | −0.0875330 | − | 0.996162i | \(-0.527898\pi\) | ||||
−0.0875330 | + | 0.996162i | \(0.527898\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.32624 | + | 5.32624i | −0.216901 | + | 0.216901i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.08985 | + | 6.08985i | −0.247180 | + | 0.247180i | −0.819812 | − | 0.572633i | \(-0.805922\pi\) |
0.572633 | + | 0.819812i | \(0.305922\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 5.52786i | − | 0.224000i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −45.1246 | −1.82555 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.3561 | + | 27.3561i | 1.10490 | + | 1.10490i | 0.993810 | + | 0.111094i | \(0.0354353\pi\) |
0.111094 | + | 0.993810i | \(0.464565\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.8885 | + | 30.8885i | 1.24353 | + | 1.24353i | 0.958528 | + | 0.284998i | \(0.0919929\pi\) |
0.284998 | + | 0.958528i | \(0.408007\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.3050i | 1.09748i | 0.835994 | + | 0.548739i | \(0.184892\pi\) | ||||
−0.835994 | + | 0.548739i | \(0.815108\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.49839i | 0.260772i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.60845 | + | 7.60845i | 0.304826 | + | 0.304826i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.00000 | + | 4.00000i | 0.159745 | + | 0.159745i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.15537 | 0.245431 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.0827i | 1.11795i | 0.829183 | + | 0.558977i | \(0.188806\pi\) | ||||
−0.829183 | + | 0.558977i | \(0.811194\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.4164 | − | 25.4164i | 1.01021 | − | 1.01021i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.0373 | − | 13.0373i | 0.516556 | − | 0.516556i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.7719 | −0.623928 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.34752 | −0.290210 | −0.145105 | − | 0.989416i | \(-0.546352\pi\) | ||||
−0.145105 | + | 0.989416i | \(0.546352\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.56231 | − | 8.56231i | 0.337664 | − | 0.337664i | −0.517823 | − | 0.855488i | \(-0.673258\pi\) |
0.855488 | + | 0.517823i | \(0.173258\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.8909 | + | 22.8909i | −0.899933 | + | 0.899933i | −0.995430 | − | 0.0954968i | \(-0.969556\pi\) |
0.0954968 | + | 0.995430i | \(0.469556\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.4721i | 0.411067i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.0000 | −0.783862 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.2412 | − | 11.2412i | −0.439901 | − | 0.439901i | 0.452078 | − | 0.891979i | \(-0.350683\pi\) |
−0.891979 | + | 0.452078i | \(0.850683\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19.4721 | + | 19.4721i | 0.759680 | + | 0.759680i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 18.0000i | − | 0.701180i | −0.936529 | − | 0.350590i | \(-0.885981\pi\) | ||
0.936529 | − | 0.350590i | \(-0.114019\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 2.35114i | − | 0.0914488i | −0.998954 | − | 0.0457244i | \(-0.985440\pi\) | ||
0.998954 | − | 0.0457244i | \(-0.0145596\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.95959 | + | 9.95959i | 0.386799 | + | 0.386799i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.81966 | − | 3.81966i | −0.147898 | − | 0.147898i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.60034 | 0.216522 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.3107i | 0.475251i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.7082 | − | 30.7082i | 1.18371 | − | 1.18371i | 0.204940 | − | 0.978775i | \(-0.434300\pi\) |
0.978775 | − | 0.204940i | \(-0.0656998\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.33499 | + | 8.33499i | −0.320340 | + | 0.320340i | −0.848897 | − | 0.528558i | \(-0.822733\pi\) |
0.528558 | + | 0.848897i | \(0.322733\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.555029 | −0.0213001 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 37.5967 | 1.44071 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.79837 | − | 1.79837i | 0.0688129 | − | 0.0688129i | −0.671863 | − | 0.740676i | \(-0.734506\pi\) |
0.740676 | + | 0.671863i | \(0.234506\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 34.5811 | − | 34.5811i | 1.31935 | − | 1.31935i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.47214i | 0.170375i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.1246 | 1.18404 | 0.592018 | − | 0.805925i | \(-0.298331\pi\) | ||||
0.592018 | + | 0.805925i | \(0.298331\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.24920 | − | 3.24920i | −0.123427 | − | 0.123427i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.70820 | − | 7.70820i | −0.291969 | − | 0.291969i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.2361i | 0.424987i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.3934i | 1.52564i | 0.646612 | + | 0.762819i | \(0.276185\pi\) | ||||
−0.646612 | + | 0.762819i | \(0.723815\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.15537 | + | 6.15537i | 0.232154 | + | 0.232154i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.4721 | − | 14.4721i | −0.544281 | − | 0.544281i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.7638 | −0.516911 | −0.258456 | − | 0.966023i | \(-0.583214\pi\) | ||||
−0.258456 | + | 0.966023i | \(0.583214\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.5276i | 1.03237i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.8197 | + | 13.8197i | −0.517550 | + | 0.517550i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −47.4468 | + | 47.4468i | −1.77193 | + | 1.77193i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −44.5407 | −1.66109 | −0.830543 | − | 0.556954i | \(-0.811970\pi\) | ||||
−0.830543 | + | 0.556954i | \(0.811970\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.2361 | 0.641905 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.9443 | + | 10.9443i | −0.407022 | + | 0.407022i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.87785 | + | 5.87785i | −0.217997 | + | 0.217997i | −0.807654 | − | 0.589657i | \(-0.799263\pi\) |
0.589657 | + | 0.807654i | \(0.299263\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 11.9443i | − | 0.442380i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.76393 | 0.176200 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.28157 | + | 1.28157i | 0.0473359 | + | 0.0473359i | 0.730379 | − | 0.683043i | \(-0.239344\pi\) |
−0.683043 | + | 0.730379i | \(0.739344\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.94427 | + | 2.94427i | 0.108454 | + | 0.108454i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 17.4164i | − | 0.640673i | −0.947304 | − | 0.320336i | \(-0.896204\pi\) | ||
0.947304 | − | 0.320336i | \(-0.103796\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19.9192i | 0.731750i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.4863 | + | 13.4863i | 0.494765 | + | 0.494765i | 0.909804 | − | 0.415039i | \(-0.136232\pi\) |
−0.415039 | + | 0.909804i | \(0.636232\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.79837 | + | 9.79837i | 0.358504 | + | 0.358504i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −28.4257 | −1.03865 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.05342i | 0.257383i | 0.991685 | + | 0.128692i | \(0.0410777\pi\) | ||||
−0.991685 | + | 0.128692i | \(0.958922\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −35.8885 | + | 35.8885i | −1.30785 | + | 1.30785i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.0018 | + | 38.0018i | −1.38120 | + | 1.38120i | −0.538701 | + | 0.842497i | \(0.681085\pi\) |
−0.842497 | + | 0.538701i | \(0.818915\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.5146 | −0.381657 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.9443 | −0.541729 | −0.270865 | − | 0.962617i | \(-0.587310\pi\) | ||||
−0.270865 | + | 0.962617i | \(0.587310\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.88854 | − | 7.88854i | 0.285584 | − | 0.285584i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.0746 | + | 26.0746i | −0.941498 | + | 0.941498i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.47214i | 0.0891475i | 0.999006 | + | 0.0445738i | \(0.0141930\pi\) | ||||
−0.999006 | + | 0.0445738i | \(0.985807\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 60.5410 | 2.18033 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.18774 | − | 4.18774i | −0.150623 | − | 0.150623i | 0.627773 | − | 0.778396i | \(-0.283966\pi\) |
−0.778396 | + | 0.627773i | \(0.783966\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.7082 | − | 11.7082i | −0.420029 | − | 0.420029i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 15.4164i | − | 0.552350i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.71851i | 0.311973i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.79611 | − | 1.79611i | −0.0641878 | − | 0.0641878i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.1459 | + | 11.1459i | 0.397308 | + | 0.397308i | 0.877283 | − | 0.479974i | \(-0.159354\pi\) |
−0.479974 | + | 0.877283i | \(0.659354\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −53.0472 | −1.88853 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.0697i | 0.393591i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.6525 | + | 30.6525i | −1.08850 | + | 1.08850i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.7477 | − | 19.7477i | 0.699498 | − | 0.699498i | −0.264804 | − | 0.964302i | \(-0.585307\pi\) |
0.964302 | + | 0.264804i | \(0.0853072\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.6619 | 0.518700 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.4721 | −0.511348 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.7639 | − | 10.7639i | 0.379851 | − | 0.379851i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28.9807 | + | 28.9807i | −1.02017 | + | 1.02017i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.9443i | 0.455096i | 0.973767 | + | 0.227548i | \(0.0730709\pi\) | ||||
−0.973767 | + | 0.227548i | \(0.926929\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.0689 | 1.12609 | 0.563045 | − | 0.826426i | \(-0.309630\pi\) | ||||
0.563045 | + | 0.826426i | \(0.309630\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 51.2511 | + | 51.2511i | 1.79745 | + | 1.79745i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.76393 | + | 4.76393i | 0.166669 | + | 0.166669i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 16.1803i | − | 0.565387i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.4742i | 0.714555i | 0.933998 | + | 0.357278i | \(0.116295\pi\) | ||||
−0.933998 | + | 0.357278i | \(0.883705\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.3440 | − | 24.3440i | −0.848577 | − | 0.848577i | 0.141379 | − | 0.989956i | \(-0.454846\pi\) |
−0.989956 | + | 0.141379i | \(0.954846\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.8541 | + | 14.8541i | 0.516528 | + | 0.516528i | 0.916519 | − | 0.399991i | \(-0.130987\pi\) |
−0.399991 | + | 0.916519i | \(0.630987\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.11817 | −0.108299 | −0.0541493 | − | 0.998533i | \(-0.517245\pi\) | ||||
−0.0541493 | + | 0.998533i | \(0.517245\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 7.05342i | − | 0.244681i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.23607 | + | 4.23607i | −0.146771 | + | 0.146771i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.49839 | + | 6.49839i | −0.224617 | + | 0.224617i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.40456 | −0.324682 | −0.162341 | − | 0.986735i | \(-0.551904\pi\) | ||||
−0.162341 | + | 0.986735i | \(0.551904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.8885 | −0.927191 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.00000 | + | 6.00000i | −0.206651 | + | 0.206651i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.1352 | − | 11.1352i | 0.382609 | − | 0.382609i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 50.5410i | 1.73456i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.1803 | −0.554655 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.7930 | − | 24.7930i | −0.848896 | − | 0.848896i | 0.141100 | − | 0.989995i | \(-0.454936\pi\) |
−0.989995 | + | 0.141100i | \(0.954936\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.8328 | + | 17.8328i | 0.609157 | + | 0.609157i | 0.942726 | − | 0.333568i | \(-0.108253\pi\) |
−0.333568 | + | 0.942726i | \(0.608253\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.52786i | 0.256847i | 0.991719 | + | 0.128424i | \(0.0409917\pi\) | ||||
−0.991719 | + | 0.128424i | \(0.959008\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 29.3238i | 0.999351i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.22088 | − | 6.22088i | −0.211761 | − | 0.211761i | 0.593254 | − | 0.805015i | \(-0.297843\pi\) |
−0.805015 | + | 0.593254i | \(0.797843\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24.2705 | + | 24.2705i | 0.824270 | + | 0.824270i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.2169 | 0.516198 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.6619i | 0.496799i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.527864 | − | 0.527864i | 0.0178655 | − | 0.0178655i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.08580 | + | 5.08580i | −0.171735 | + | 0.171735i | −0.787741 | − | 0.616006i | \(-0.788750\pi\) |
0.616006 | + | 0.787741i | \(0.288750\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.35114 | −0.0793020 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.1246 | 1.58767 | 0.793834 | − | 0.608134i | \(-0.208082\pi\) | ||||
0.793834 | + | 0.608134i | \(0.208082\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.7984 | − | 21.7984i | 0.733574 | − | 0.733574i | −0.237752 | − | 0.971326i | \(-0.576411\pi\) |
0.971326 | + | 0.237752i | \(0.0764106\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.1482 | − | 28.1482i | 0.945123 | − | 0.945123i | −0.0534473 | − | 0.998571i | \(-0.517021\pi\) |
0.998571 | + | 0.0534473i | \(0.0170209\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 20.6525i | − | 0.692662i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.2361 | −0.443425 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.6619 | + | 14.6619i | 0.490641 | + | 0.490641i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −26.1803 | − | 26.1803i | −0.874136 | − | 0.874136i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 7.63932i | − | 0.254786i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.45309i | − | 0.0484093i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.06154 | − | 9.06154i | −0.301549 | − | 0.301549i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.3262 | − | 23.3262i | −0.774535 | − | 0.774535i | 0.204361 | − | 0.978896i | \(-0.434488\pi\) |
−0.978896 | + | 0.204361i | \(0.934488\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 27.5276 | 0.913034 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.1765i | 0.834135i | 0.908876 | + | 0.417067i | \(0.136942\pi\) | ||||
−0.908876 | + | 0.417067i | \(0.863058\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.41641 | − | 5.41641i | 0.179257 | − | 0.179257i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.343027 | − | 0.343027i | 0.0113277 | − | 0.0113277i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.7153 | −0.716322 | −0.358161 | − | 0.933660i | \(-0.616596\pi\) | ||||
−0.358161 | + | 0.933660i | \(0.616596\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.2361 | −0.699752 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21.7082 | + | 21.7082i | −0.714534 | + | 0.714534i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.3925 | + | 16.3925i | −0.538400 | + | 0.538400i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 5.34752i | − | 0.175447i | −0.996145 | − | 0.0877233i | \(-0.972041\pi\) | ||
0.996145 | − | 0.0877233i | \(-0.0279591\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.47214 | −0.277663 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.2088 | + | 13.2088i | 0.432436 | + | 0.432436i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.3050 | − | 20.3050i | −0.663334 | − | 0.663334i | 0.292831 | − | 0.956164i | \(-0.405403\pi\) |
−0.956164 | + | 0.292831i | \(0.905403\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.1803i | 0.658561i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 60.8676i | − | 1.98423i | −0.125340 | − | 0.992114i | \(-0.540002\pi\) | ||
0.125340 | − | 0.992114i | \(-0.459998\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.2622 | + | 20.2622i | 0.659828 | + | 0.659828i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.85410 | − | 8.85410i | −0.287720 | − | 0.287720i | 0.548458 | − | 0.836178i | \(-0.315215\pi\) |
−0.836178 | + | 0.548458i | \(0.815215\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 53.6022 | 1.74000 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 34.5811i | − | 1.12137i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.81966 | − | 6.81966i | 0.220910 | − | 0.220910i | −0.587971 | − | 0.808882i | \(-0.700073\pi\) |
0.808882 | + | 0.587971i | \(0.200073\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.90617 | − | 2.90617i | 0.0939431 | − | 0.0939431i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.16348 | 0.263613 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.36068 | 0.108409 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 27.0344 | − | 27.0344i | 0.871173 | − | 0.871173i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.0332 | − | 12.0332i | 0.386962 | − | 0.386962i | −0.486640 | − | 0.873602i | \(-0.661778\pi\) |
0.873602 | + | 0.486640i | \(0.161778\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 6.47214i | − | 0.207915i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.5967 | −1.07817 | −0.539085 | − | 0.842251i | \(-0.681230\pi\) | ||||
−0.539085 | + | 0.842251i | \(0.681230\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.36737 | − | 6.36737i | −0.204128 | − | 0.204128i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.2361 | + | 28.2361i | 0.903352 | + | 0.903352i | 0.995725 | − | 0.0923727i | \(-0.0294451\pi\) |
−0.0923727 | + | 0.995725i | \(0.529445\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.00000i | 0.255681i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.0049i | 0.479070i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.620541 | − | 0.620541i | −0.0197922 | − | 0.0197922i | 0.697141 | − | 0.716934i | \(-0.254455\pi\) |
−0.716934 | + | 0.697141i | \(0.754455\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −27.8885 | − | 27.8885i | −0.887702 | − | 0.887702i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.5227 | −0.398200 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 19.3642i | − | 0.615123i | −0.951528 | − | 0.307561i | \(-0.900487\pi\) | ||
0.951528 | − | 0.307561i | \(-0.0995129\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 45.4164 | − | 45.4164i | 1.44125 | − | 1.44125i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.6506 | − | 35.6506i | 1.12907 | − | 1.12907i | 0.138738 | − | 0.990329i | \(-0.455696\pi\) |
0.990329 | − | 0.138738i | \(-0.0443045\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.60845 | −0.240721 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))