Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,2,Mod(767,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 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("1280.767");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.n (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: | \(10.2208514587\) |
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: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1023.4 | ||
Root | \(-0.951057 - 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.1023 |
Dual form | 1280.2.n.q.767.4 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.61803 | − | 1.61803i | 0.934172 | − | 0.934172i | −0.0637909 | − | 0.997963i | \(-0.520319\pi\) |
0.997963 | + | 0.0637909i | \(0.0203191\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.17557 | + | 1.90211i | 0.525731 | + | 0.850651i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.17557 | + | 1.17557i | 0.444324 | + | 0.444324i | 0.893462 | − | 0.449138i | \(-0.148269\pi\) |
−0.449138 | + | 0.893462i | \(0.648269\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.23607i | − | 0.745356i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.23607i | − | 0.372689i | −0.982485 | − | 0.186344i | \(-0.940336\pi\) | ||
0.982485 | − | 0.186344i | \(-0.0596640\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.07768 | + | 3.07768i | 0.853596 | + | 0.853596i | 0.990574 | − | 0.136978i | \(-0.0437390\pi\) |
−0.136978 | + | 0.990574i | \(0.543739\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.97980 | + | 1.17557i | 1.28578 | + | 0.303531i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | + | 1.00000i | −0.242536 | + | 0.242536i | −0.817898 | − | 0.575363i | \(-0.804861\pi\) |
0.575363 | + | 0.817898i | \(0.304861\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.80423 | 0.830150 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.62866 | − | 2.62866i | 0.548113 | − | 0.548113i | −0.377782 | − | 0.925895i | \(-0.623313\pi\) |
0.925895 | + | 0.377782i | \(0.123313\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.23607 | + | 4.47214i | −0.447214 | + | 0.894427i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.23607 | + | 1.23607i | 0.237881 | + | 0.237881i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.45309i | 0.269831i | 0.990857 | + | 0.134916i | \(0.0430763\pi\) | ||||
−0.990857 | + | 0.134916i | \(0.956924\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | −0.854102 | + | 3.61803i | −0.144370 | + | 0.611559i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.07768 | + | 3.07768i | −0.505968 | + | 0.505968i | −0.913286 | − | 0.407318i | \(-0.866464\pi\) |
0.407318 | + | 0.913286i | \(0.366464\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.95959 | 1.59481 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.70820 | 1.20382 | 0.601910 | − | 0.798564i | \(-0.294407\pi\) | ||||
0.601910 | + | 0.798564i | \(0.294407\pi\) | |||||||
\(42\) | 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 | ||||||||
\(45\) | 4.25325 | − | 2.62866i | 0.634038 | − | 0.391857i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.33094 | + | 7.33094i | 1.06933 | + | 1.06933i | 0.997411 | + | 0.0719165i | \(0.0229115\pi\) |
0.0719165 | + | 0.997411i | \(0.477088\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 4.23607i | − | 0.605153i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.23607i | 0.453140i | ||||||||
\(52\) | 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 | ||||||||
\(55\) | 2.35114 | − | 1.45309i | 0.317028 | − | 0.195934i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.23607 | + | 3.23607i | −0.428628 | + | 0.428628i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.47214 | −1.10298 | −0.551489 | − | 0.834182i | \(-0.685940\pi\) | ||||
−0.551489 | + | 0.834182i | \(0.685940\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.95959 | −1.27520 | −0.637598 | − | 0.770370i | \(-0.720072\pi\) | ||||
−0.637598 | + | 0.770370i | \(0.720072\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.62866 | − | 2.62866i | 0.331179 | − | 0.331179i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.23607 | + | 9.47214i | −0.277350 | + | 1.17487i | ||||
\(66\) | 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 | ||||||||
\(69\) | − | 8.50651i | − | 1.02406i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.05342i | 0.837087i | 0.908197 | + | 0.418544i | \(0.137459\pi\) | ||||
−0.908197 | + | 0.418544i | \(0.862541\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.70820 | − | 8.70820i | −1.01922 | − | 1.01922i | −0.999812 | − | 0.0194065i | \(-0.993822\pi\) |
−0.0194065 | − | 0.999812i | \(-0.506178\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.61803 | + | 10.8541i | 0.417775 | + | 1.25332i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.45309 | − | 1.45309i | 0.165594 | − | 0.165594i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.3107 | 1.38507 | 0.692533 | − | 0.721386i | \(-0.256495\pi\) | ||||
0.692533 | + | 0.721386i | \(0.256495\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.7082 | 1.18980 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.38197 | − | 4.38197i | 0.480983 | − | 0.480983i | −0.424462 | − | 0.905446i | \(-0.639537\pi\) |
0.905446 | + | 0.424462i | \(0.139537\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.07768 | − | 0.726543i | −0.333822 | − | 0.0788046i | ||||
\(86\) | 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 | ||||||||
\(91\) | 7.23607i | 0.758546i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.50651 | − | 8.50651i | −0.882084 | − | 0.882084i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.35114 | − | 3.80423i | −0.241222 | − | 0.390305i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.236068 | + | 0.236068i | −0.0239691 | + | 0.0239691i | −0.718990 | − | 0.695021i | \(-0.755395\pi\) |
0.695021 | + | 0.718990i | \(0.255395\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.76393 | −0.277786 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.3107 | −1.22496 | −0.612482 | − | 0.790485i | \(-0.709829\pi\) | ||||
−0.612482 | + | 0.790485i | \(0.709829\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.33094 | − | 7.33094i | 0.722339 | − | 0.722339i | −0.246742 | − | 0.969081i | \(-0.579360\pi\) |
0.969081 | + | 0.246742i | \(0.0793601\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.47214 | + | 7.23607i | 0.436436 | + | 0.706168i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0902 | − | 12.0902i | −1.16880 | − | 1.16880i | −0.982491 | − | 0.186310i | \(-0.940347\pi\) |
−0.186310 | − | 0.982491i | \(-0.559653\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.71040i | − | 0.642739i | −0.946954 | − | 0.321370i | \(-0.895857\pi\) | ||
0.946954 | − | 0.321370i | \(-0.104143\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.95959i | 0.945323i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.70820 | − | 4.70820i | −0.442911 | − | 0.442911i | 0.450078 | − | 0.892989i | \(-0.351396\pi\) |
−0.892989 | + | 0.450078i | \(0.851396\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.09017 | + | 1.90983i | 0.754412 | + | 0.178093i | ||||
\(116\) | 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 | ||||||||
\(125\) | −11.1352 | + | 1.00406i | −0.995959 | + | 0.0898056i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.78402 | − | 8.78402i | −0.779456 | − | 0.779456i | 0.200282 | − | 0.979738i | \(-0.435814\pi\) |
−0.979738 | + | 0.200282i | \(0.935814\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 7.70820i | − | 0.678670i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.291796i | 0.0254943i | 0.999919 | + | 0.0127472i | \(0.00405766\pi\) | ||||
−0.999919 | + | 0.0127472i | \(0.995942\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.35114 | − | 2.35114i | −0.203870 | − | 0.203870i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.898056 | + | 3.80423i | −0.0772924 | + | 0.327416i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.47214 | + | 3.47214i | −0.296645 | + | 0.296645i | −0.839698 | − | 0.543054i | \(-0.817268\pi\) |
0.543054 | + | 0.839698i | \(0.317268\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.41641 | 0.459414 | 0.229707 | − | 0.973260i | \(-0.426223\pi\) | ||||
0.229707 | + | 0.973260i | \(0.426223\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 23.7234 | 1.99787 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.80423 | − | 3.80423i | 0.318125 | − | 0.318125i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.76393 | + | 1.70820i | −0.229532 | + | 0.141859i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.85410 | − | 6.85410i | −0.565317 | − | 0.565317i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.2088i | 1.08211i | 0.840988 | + | 0.541053i | \(0.181974\pi\) | ||||
−0.840988 | + | 0.541053i | \(0.818026\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 14.6619i | − | 1.19317i | −0.802551 | − | 0.596583i | \(-0.796525\pi\) | ||
0.802551 | − | 0.596583i | \(-0.203475\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.23607 | + | 2.23607i | 0.180775 | + | 0.180775i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.0000 | − | 6.18034i | 0.803219 | − | 0.496417i | ||||
\(156\) | 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 | −0.369515 | − | 0.929225i | \(-0.620476\pi\) |
0.929225 | + | 0.369515i | \(0.120476\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.45309 | − | 6.15537i | 0.113123 | − | 0.479195i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.277515 | + | 0.277515i | 0.0214747 | + | 0.0214747i | 0.717763 | − | 0.696288i | \(-0.245166\pi\) |
−0.696288 | + | 0.717763i | \(0.745166\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.94427i | 0.457252i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.47214i | 0.341993i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.32688 | + | 6.32688i | 0.481024 | + | 0.481024i | 0.905459 | − | 0.424435i | \(-0.139527\pi\) |
−0.424435 | + | 0.905459i | \(0.639527\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.88597 | + | 2.62866i | −0.596123 | + | 0.198708i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.7082 | + | 13.7082i | −1.03037 | + | 1.03037i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.4721 | −1.23119 | −0.615593 | − | 0.788065i | \(-0.711083\pi\) | ||||
−0.615593 | + | 0.788065i | \(0.711083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.40456 | 0.699036 | 0.349518 | − | 0.936930i | \(-0.386345\pi\) | ||||
0.349518 | + | 0.936930i | \(0.386345\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.1150 | + | 16.1150i | −1.19125 | + | 1.19125i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.47214 | − | 2.23607i | −0.696405 | − | 0.164399i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.23607 | + | 1.23607i | 0.0903902 | + | 0.0903902i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.90617i | 0.211393i | ||||||||
\(190\) | 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 | \(-0.374187\pi\) |
−0.922899 | + | 0.385043i | \(0.874187\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.7082 | + | 18.9443i | 0.838442 | + | 1.35663i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.17963 | + | 2.17963i | −0.155292 | + | 0.155292i | −0.780477 | − | 0.625185i | \(-0.785024\pi\) |
0.625185 | + | 0.780477i | \(0.285024\pi\) | |||||||
\(198\) | 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 | ||||||||
\(205\) | 9.06154 | + | 14.6619i | 0.632885 | + | 1.02403i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.87785 | − | 5.87785i | −0.408539 | − | 0.408539i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.47214i | 0.171001i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.7082i | 1.08140i | 0.841216 | + | 0.540699i | \(0.181840\pi\) | ||||
−0.841216 | + | 0.540699i | \(0.818160\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.4127 | + | 11.4127i | 0.781984 | + | 0.781984i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.33094 | + | 1.73060i | 0.499966 | + | 0.118026i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.18034 | − | 6.18034i | 0.419549 | − | 0.419549i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −28.1803 | −1.90425 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.15537 | −0.414055 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.73060 | + | 1.73060i | −0.115890 | + | 0.115890i | −0.762673 | − | 0.646784i | \(-0.776114\pi\) |
0.646784 | + | 0.762673i | \(0.276114\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.0000 | + | 5.00000i | 0.666667 | + | 0.333333i | ||||
\(226\) | 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 | ||||||||
\(229\) | 21.3723i | 1.41232i | 0.708053 | + | 0.706160i | \(0.249574\pi\) | ||||
−0.708053 | + | 0.706160i | \(0.750426\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 4.70228i | − | 0.309387i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.47214 | + | 3.47214i | 0.227467 | + | 0.227467i | 0.811634 | − | 0.584167i | \(-0.198579\pi\) |
−0.584167 | + | 0.811634i | \(0.698579\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.32624 | + | 22.5623i | −0.347445 | + | 1.47180i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.9192 | − | 19.9192i | 1.29389 | − | 1.29389i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −29.3238 | −1.89680 | −0.948398 | − | 0.317083i | \(-0.897297\pi\) | ||||
−0.948398 | + | 0.317083i | \(0.897297\pi\) | |||||||
\(240\) | 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 | ||||||||
\(245\) | 8.05748 | − | 4.97980i | 0.514774 | − | 0.318148i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.15537 | − | 6.15537i | −0.391657 | − | 0.391657i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 14.1803i | − | 0.898643i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.1803i | 1.40001i | 0.714138 | + | 0.700005i | \(0.246819\pi\) | ||||
−0.714138 | + | 0.700005i | \(0.753181\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.24920 | − | 3.24920i | −0.204275 | − | 0.204275i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.15537 | + | 3.80423i | −0.385464 | + | 0.238230i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.7082 | − | 18.7082i | 1.16699 | − | 1.16699i | 0.184073 | − | 0.982913i | \(-0.441072\pi\) |
0.982913 | − | 0.184073i | \(-0.0589283\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.23607 | −0.449627 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.24920 | 0.201120 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.3925 | + | 16.3925i | −1.01080 | + | 1.01080i | −0.0108623 | + | 0.999941i | \(0.503458\pi\) |
−0.999941 | + | 0.0108623i | \(0.996542\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.527864 | − | 2.23607i | 0.0324264 | − | 0.137361i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.4721 | − | 10.4721i | −0.640884 | − | 0.640884i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.9111i | 1.09206i | 0.837766 | + | 0.546029i | \(0.183861\pi\) | ||||
−0.837766 | + | 0.546029i | \(0.816139\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | 5.52786 | + | 2.76393i | 0.333343 | + | 0.166671i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.17963 | − | 2.17963i | 0.130961 | − | 0.130961i | −0.638588 | − | 0.769549i | \(-0.720481\pi\) |
0.769549 | + | 0.638588i | \(0.220481\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.7557 | −0.703796 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.70820 | −0.221213 | −0.110606 | − | 0.993864i | \(-0.535279\pi\) | ||||
−0.110606 | + | 0.993864i | \(0.535279\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | −9.95959 | − | 2.35114i | −0.589955 | − | 0.139270i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.06154 | + | 9.06154i | 0.534886 | + | 0.534886i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.0000i | 0.882353i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.763932i | 0.0447825i | ||||||||
\(292\) | 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 | ||||||||
\(295\) | −9.95959 | − | 16.1150i | −0.579870 | − | 0.938249i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.52786 | − | 1.52786i | 0.0886557 | − | 0.0886557i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.1803 | 0.935733 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.60034 | 0.322798 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −19.9192 | + | 19.9192i | −1.14433 | + | 1.14433i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.7082 | − | 18.9443i | −0.670410 | − | 1.08475i | ||||
\(306\) | 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 | ||||||||
\(309\) | − | 23.7234i | − | 1.34958i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.16348i | 0.462909i | 0.972846 | + | 0.231454i | \(0.0743484\pi\) | ||||
−0.972846 | + | 0.231454i | \(0.925652\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.23607 | + | 6.23607i | 0.352483 | + | 0.352483i | 0.861033 | − | 0.508549i | \(-0.169818\pi\) |
−0.508549 | + | 0.861033i | \(0.669818\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.09017 | + | 1.90983i | 0.455829 | + | 0.107607i | ||||
\(316\) | 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 | ||||||||
\(325\) | −20.6457 | + | 6.88191i | −1.14522 | + | 0.381740i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.8576 | − | 10.8576i | −0.600429 | − | 0.600429i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.2361i | 0.950255i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 28.0689i | − | 1.54281i | −0.636347 | − | 0.771403i | \(-0.719555\pi\) | ||
0.636347 | − | 0.771403i | \(-0.280445\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.88191 | + | 6.88191i | 0.377126 | + | 0.377126i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.73060 | − | 7.33094i | 0.0945528 | − | 0.400532i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.05573 | + | 2.05573i | −0.111983 | + | 0.111983i | −0.760878 | − | 0.648895i | \(-0.775231\pi\) |
0.648895 | + | 0.760878i | \(0.275231\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.2361 | −0.827510 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.49839 | −0.351908 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.2088 | − | 13.2088i | 0.713208 | − | 0.713208i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16.1803 | − | 10.0000i | 0.871120 | − | 0.538382i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.03444 | + | 3.03444i | 0.162897 | + | 0.162897i | 0.783849 | − | 0.620952i | \(-0.213254\pi\) |
−0.620952 | + | 0.783849i | \(0.713254\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 15.5599i | − | 0.832904i | −0.909158 | − | 0.416452i | \(-0.863273\pi\) | ||
0.909158 | − | 0.416452i | \(-0.136727\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.60845i | 0.406109i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.41641 | + | 4.41641i | 0.235062 | + | 0.235062i | 0.814802 | − | 0.579740i | \(-0.196846\pi\) |
−0.579740 | + | 0.814802i | \(0.696846\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.4164 | + | 8.29180i | −0.712069 | + | 0.440083i | ||||
\(356\) | 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 | ||||||||
\(365\) | 6.32688 | − | 26.8011i | 0.331164 | − | 1.40283i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.0009 | − | 24.0009i | −1.25284 | − | 1.25284i | −0.954442 | − | 0.298396i | \(-0.903548\pi\) |
−0.298396 | − | 0.954442i | \(-0.596452\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 17.2361i | − | 0.897274i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.70820i | − | 0.0886855i | ||||||
\(372\) | 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 | ||||||||
\(375\) | −16.3925 | + | 19.6417i | −0.846504 | + | 1.01429i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.47214 | + | 4.47214i | −0.230327 | + | 0.230327i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.8885 | −1.84347 | −0.921735 | − | 0.387820i | \(-0.873228\pi\) | ||||
−0.921735 | + | 0.387820i | \(0.873228\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −28.4257 | −1.45629 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.1352 | + | 11.1352i | −0.568980 | + | 0.568980i | −0.931843 | − | 0.362862i | \(-0.881799\pi\) |
0.362862 | + | 0.931843i | \(0.381799\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.47214 | + | 1.05573i | 0.227921 | + | 0.0538049i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.32624 | − | 5.32624i | −0.270748 | − | 0.270748i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 23.7234i | − | 1.20282i | −0.798939 | − | 0.601412i | \(-0.794605\pi\) | ||
0.798939 | − | 0.601412i | \(-0.205395\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.25731i | 0.265874i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.472136 | + | 0.472136i | 0.0238161 | + | 0.0238161i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.4721 | + | 23.4164i | 0.728172 | + | 1.17821i | ||||
\(396\) | 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 | ||||||||
\(405\) | 12.5882 | + | 20.3682i | 0.625515 | + | 1.01210i | ||||
\(406\) | 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 | ||||||||
\(411\) | 11.2361i | 0.554234i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.95959 | − | 9.95959i | −0.490080 | − | 0.490080i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.4863 | + | 3.18368i | 0.662017 | + | 0.156281i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.76393 | − | 8.76393i | 0.429172 | − | 0.429172i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.8328 | 1.21316 | 0.606581 | − | 0.795022i | \(-0.292540\pi\) | ||||
0.606581 | + | 0.795022i | \(0.292540\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.46120 | 0.168689 | 0.0843443 | − | 0.996437i | \(-0.473120\pi\) | ||||
0.0843443 | + | 0.996437i | \(0.473120\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 16.3925 | − | 16.3925i | 0.797029 | − | 0.797029i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.23607 | − | 6.70820i | −0.108465 | − | 0.325396i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.7082 | − | 11.7082i | −0.566600 | − | 0.566600i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 12.3107i | − | 0.594368i | ||||||
\(430\) | 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 | 0.992608 | + | 0.121369i | \(0.0387283\pi\) |
0.121369 | + | 0.992608i | \(0.461272\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.70820 | + | 7.23607i | −0.0819021 | + | 0.346943i | ||||
\(436\) | 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 | ||||||||
\(445\) | 12.3107 | − | 7.60845i | 0.583585 | − | 0.360675i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.3723 | + | 21.3723i | 1.01087 | + | 1.01087i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.5967i | 1.49114i | 0.666426 | + | 0.745571i | \(0.267823\pi\) | ||||
−0.666426 | + | 0.745571i | \(0.732177\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 9.52786i | − | 0.448650i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −23.7234 | − | 23.7234i | −1.11462 | − | 1.11462i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.7638 | + | 8.50651i | −0.645258 | + | 0.398791i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.6525 | − | 21.6525i | 1.01286 | − | 1.01286i | 0.0129439 | − | 0.999916i | \(-0.495880\pi\) |
0.999916 | − | 0.0129439i | \(-0.00412028\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.47214 | −0.115389 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.49839 | −0.302660 | −0.151330 | − | 0.988483i | \(-0.548356\pi\) | ||||
−0.151330 | + | 0.988483i | \(0.548356\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.2905 | − | 17.2905i | 0.803559 | − | 0.803559i | −0.180091 | − | 0.983650i | \(-0.557639\pi\) |
0.983650 | + | 0.180091i | \(0.0576392\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.18034 | − | 26.1803i | 0.286606 | − | 1.21408i | ||||
\(466\) | 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 | ||||||||
\(469\) | − | 5.60034i | − | 0.258600i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 31.6749i | 1.45950i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.94427 | − | 2.94427i | −0.135378 | − | 0.135378i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.47214 | − | 8.94427i | 0.205196 | − | 0.410391i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.62460 | + | 1.62460i | −0.0743853 | + | 0.0743853i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.60845 | 0.347639 | 0.173820 | − | 0.984778i | \(-0.444389\pi\) | ||||
0.173820 | + | 0.984778i | \(0.444389\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.9443 | −0.863784 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.0000 | − | 10.0000i | 0.455016 | − | 0.455016i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.726543 | − | 0.171513i | −0.0329906 | − | 0.00778802i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.33905 | − | 9.33905i | −0.423193 | − | 0.423193i | 0.463109 | − | 0.886302i | \(-0.346734\pi\) |
−0.886302 | + | 0.463109i | \(0.846734\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 23.1246i | − | 1.04573i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.7639i | 0.485769i | 0.970055 | + | 0.242885i | \(0.0780937\pi\) | ||||
−0.970055 | + | 0.242885i | \(0.921906\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.45309 | − | 1.45309i | −0.0654437 | − | 0.0654437i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.24920 | − | 5.25731i | −0.146041 | − | 0.236299i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.29180 | + | 8.29180i | −0.371938 | + | 0.371938i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.8885 | −1.06940 | −0.534699 | − | 0.845043i | \(-0.679575\pi\) | ||||
−0.534699 | + | 0.845043i | \(0.679575\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.898056 | 0.0401222 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.53483 | − | 5.53483i | 0.246786 | − | 0.246786i | −0.572864 | − | 0.819650i | \(-0.694168\pi\) |
0.819650 | + | 0.572864i | \(0.194168\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.4721 | − | 23.4164i | −0.644002 | − | 1.04202i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.61803 | + | 9.61803i | 0.427152 | + | 0.427152i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.06154i | 0.401646i | 0.979628 | + | 0.200823i | \(0.0643615\pi\) | ||||
−0.979628 | + | 0.200823i | \(0.935638\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 20.4742i | − | 0.905726i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.47214 | − | 2.47214i | −0.109147 | − | 0.109147i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.5623 | + | 5.32624i | 0.994214 | + | 0.234702i | ||||
\(516\) | 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 | \(-0.559418\pi\) | ||||
−0.185586 | + | 0.982628i | \(0.559418\pi\) | |||||||
\(522\) | 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 | ||||||||
\(525\) | −8.50651 | + | 17.0130i | −0.371254 | + | 0.742509i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.25731 | + | 5.25731i | 0.229012 | + | 0.229012i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.18034i | 0.399145i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.9443i | 0.822111i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.7234 | + | 23.7234i | 1.02758 | + | 1.02758i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.78402 | − | 37.2097i | 0.379766 | − | 1.60872i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26.6525 | + | 26.6525i | −1.15014 | + | 1.15014i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.23607 | −0.225533 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.90617 | −0.124946 | −0.0624730 | − | 0.998047i | \(-0.519899\pi\) | ||||
−0.0624730 | + | 0.998047i | \(0.519899\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.2169 | − | 15.2169i | 0.653020 | − | 0.653020i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.7639 | − | 7.88854i | 0.546747 | − | 0.337908i | ||||
\(546\) | 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 | ||||||||
\(549\) | 22.2703i | 0.950474i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.90617i | − | 0.123807i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.4721 | + | 14.4721i | 0.615418 | + | 0.615418i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −18.9443 | + | 11.7082i | −0.804140 | + | 0.496986i | ||||
\(556\) | 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 | −0.904281 | − | 0.426937i | \(-0.859593\pi\) |
0.426937 | + | 0.904281i | \(0.359593\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.42071 | − | 14.4904i | 0.143910 | − | 0.609614i | ||||
\(566\) | 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 | ||||||||
\(571\) | 8.65248i | 0.362095i | 0.983474 | + | 0.181047i | \(0.0579488\pi\) | ||||
−0.983474 | + | 0.181047i | \(0.942051\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.8172 | + | 20.8172i | 0.869653 | + | 0.869653i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.87785 | + | 17.6336i | 0.245123 | + | 0.735370i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.7639 | − | 21.7639i | 0.906044 | − | 0.906044i | −0.0899059 | − | 0.995950i | \(-0.528657\pi\) |
0.995950 | + | 0.0899059i | \(0.0286566\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.1803 | −1.00490 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.3026 | 0.427425 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.898056 | + | 0.898056i | −0.0371937 | + | 0.0371937i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 21.1803 | + | 5.00000i | 0.875699 | + | 0.206725i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.90983 | − | 5.90983i | −0.243925 | − | 0.243925i | 0.574547 | − | 0.818472i | \(-0.305178\pi\) |
−0.818472 | + | 0.574547i | \(0.805178\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.5146i | 0.433247i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.05342i | 0.290139i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.41641 | − | 6.41641i | −0.263490 | − | 0.263490i | 0.562980 | − | 0.826470i | \(-0.309655\pi\) |
−0.826470 | + | 0.562980i | \(0.809655\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.76393 | − | 4.47214i | −0.113310 | − | 0.183340i | ||||
\(596\) | 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 | \(-0.472102\pi\) | ||||
0.0875330 | + | 0.996162i | \(0.472102\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.32624 | + | 5.32624i | −0.216901 | + | 0.216901i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.1352 | + | 18.0171i | 0.452709 | + | 0.732498i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.08985 | − | 6.08985i | −0.247180 | − | 0.247180i | 0.572633 | − | 0.819812i | \(-0.305922\pi\) |
−0.819812 | + | 0.572633i | \(0.805922\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.52786i | 0.224000i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 45.1246i | 1.82555i | ||||||||
\(612\) | 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 | ||||||||
\(615\) | 38.3853 | + | 9.06154i | 1.54784 | + | 0.365396i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.8885 | − | 30.8885i | 1.24353 | − | 1.24353i | 0.284998 | − | 0.958528i | \(-0.408007\pi\) |
0.958528 | − | 0.284998i | \(-0.0919929\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.3050 | 1.09748 | 0.548739 | − | 0.835994i | \(-0.315108\pi\) | ||||
0.548739 | + | 0.835994i | \(0.315108\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.49839 | 0.260772 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.60845 | − | 7.60845i | 0.304826 | − | 0.304826i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.0000 | − | 20.0000i | −0.600000 | − | 0.800000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.00000 | + | 4.00000i | 0.159745 | + | 0.159745i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 6.15537i | − | 0.245431i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 28.0827i | − | 1.11795i | −0.829183 | − | 0.558977i | \(-0.811194\pi\) | ||
0.829183 | − | 0.558977i | \(-0.188806\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.4164 | + | 25.4164i | 1.01021 | + | 1.01021i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.38197 | − | 27.0344i | 0.253261 | − | 1.07283i | ||||
\(636\) | 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 | −0.855488 | − | 0.517823i | \(-0.826742\pi\) |
0.517823 | + | 0.855488i | \(0.326742\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.6619 | − | 9.06154i | 0.577311 | − | 0.356798i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.8909 | + | 22.8909i | 0.899933 | + | 0.899933i | 0.995430 | − | 0.0954968i | \(-0.0304440\pi\) |
−0.0954968 | + | 0.995430i | \(0.530444\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.4721i | 0.411067i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 20.0000i | − | 0.783862i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.2412 | + | 11.2412i | 0.439901 | + | 0.439901i | 0.891979 | − | 0.452078i | \(-0.149317\pi\) |
−0.452078 | + | 0.891979i | \(0.649317\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.555029 | + | 0.343027i | −0.0216868 | + | 0.0134032i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −19.4721 | + | 19.4721i | −0.759680 | + | 0.759680i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.0000 | 0.701180 | 0.350590 | − | 0.936529i | \(-0.385981\pi\) | ||||
0.350590 | + | 0.936529i | \(0.385981\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.35114 | 0.0914488 | 0.0457244 | − | 0.998954i | \(-0.485440\pi\) | ||||
0.0457244 | + | 0.998954i | \(0.485440\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.95959 | + | 9.95959i | −0.386799 | + | 0.386799i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.70820 | − | 7.23607i | 0.0662413 | − | 0.280603i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.81966 | + | 3.81966i | 0.147898 | + | 0.147898i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.60034i | 0.216522i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.3107i | 0.475251i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.7082 | − | 30.7082i | −1.18371 | − | 1.18371i | −0.978775 | − | 0.204940i | \(-0.934300\pi\) |
−0.204940 | − | 0.978775i | \(-0.565700\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.29180 | + | 2.76393i | −0.319151 | + | 0.106384i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.33499 | − | 8.33499i | 0.320340 | − | 0.320340i | −0.528558 | − | 0.848897i | \(-0.677267\pi\) |
0.848897 | + | 0.528558i | \(0.177267\pi\) | |||||||
\(678\) | 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 | ||||||||
\(685\) | −10.6861 | − | 2.52265i | −0.408296 | − | 0.0963857i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 34.5811 | + | 34.5811i | 1.31935 | + | 1.31935i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 4.47214i | − | 0.170375i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 31.1246i | − | 1.18404i | −0.805925 | − | 0.592018i | \(-0.798331\pi\) | ||
0.805925 | − | 0.592018i | \(-0.201669\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.24920 | − | 3.24920i | −0.123427 | − | 0.123427i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.36737 | + | 10.3026i | 0.241528 | + | 0.390801i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.70820 | + | 7.70820i | −0.291969 | + | 0.291969i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.2361 | 0.424987 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.3934 | 1.52564 | 0.762819 | − | 0.646612i | \(-0.223815\pi\) | ||||
0.762819 | + | 0.646612i | \(0.223815\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.15537 | − | 6.15537i | 0.232154 | − | 0.232154i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 27.8885 | + | 45.1246i | 1.05034 | + | 1.69949i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.4721 | − | 14.4721i | −0.544281 | − | 0.544281i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.7638i | 0.516911i | 0.966023 | + | 0.258456i | \(0.0832136\pi\) | ||||
−0.966023 | + | 0.258456i | \(0.916786\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 27.5276i | − | 1.03237i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.8197 | − | 13.8197i | −0.517550 | − | 0.517550i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.7082 | + | 2.76393i | 0.437862 | + | 0.103365i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −47.4468 | + | 47.4468i | −1.77193 | + | 1.77193i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.5407 | 1.66109 | 0.830543 | − | 0.556954i | \(-0.188030\pi\) | ||||
0.830543 | + | 0.556954i | \(0.188030\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.2361 | 0.641905 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.9443 | − | 10.9443i | 0.407022 | − | 0.407022i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.49839 | − | 3.24920i | −0.241344 | − | 0.120672i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.87785 | + | 5.87785i | 0.217997 | + | 0.217997i | 0.807654 | − | 0.589657i | \(-0.200737\pi\) |
−0.589657 | + | 0.807654i | \(0.700737\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 11.9443i | − | 0.442380i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.76393i | 0.176200i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.28157 | − | 1.28157i | −0.0473359 | − | 0.0473359i | 0.683043 | − | 0.730379i | \(-0.260656\pi\) |
−0.730379 | + | 0.683043i | \(0.760656\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.97980 | − | 21.0948i | 0.183683 | − | 0.778092i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.94427 | + | 2.94427i | −0.108454 | + | 0.108454i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.4164 | 0.640673 | 0.320336 | − | 0.947304i | \(-0.396204\pi\) | ||||
0.320336 | + | 0.947304i | \(0.396204\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.9192 | −0.731750 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.4863 | + | 13.4863i | −0.494765 | + | 0.494765i | −0.909804 | − | 0.415039i | \(-0.863768\pi\) |
0.415039 | + | 0.909804i | \(0.363768\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25.1246 | + | 15.5279i | −0.920495 | + | 0.568897i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.79837 | − | 9.79837i | −0.358504 | − | 0.358504i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 28.4257i | − | 1.03865i | ||||||
\(750\) | 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 | ||||||||
\(755\) | 27.8885 | − | 17.2361i | 1.01497 | − | 0.627285i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.0018 | − | 38.0018i | 1.38120 | − | 1.38120i | 0.538701 | − | 0.842497i | \(-0.318915\pi\) |
0.842497 | − | 0.538701i | \(-0.181085\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.5146 | −0.381657 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.9443 | 0.541729 | 0.270865 | − | 0.962617i | \(-0.412690\pi\) | ||||
0.270865 | + | 0.962617i | \(0.412690\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.88854 | − | 7.88854i | 0.285584 | − | 0.285584i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.62460 | + | 6.88191i | −0.0587375 | + | 0.248816i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.0746 | − | 26.0746i | −0.941498 | − | 0.941498i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2.47214i | − | 0.0891475i | −0.999006 | − | 0.0445738i | \(-0.985807\pi\) | ||
0.999006 | − | 0.0445738i | \(-0.0141930\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 60.5410i | − | 2.18033i | ||||||
\(772\) | 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 | ||||||||
\(775\) | 23.5114 | + | 11.7557i | 0.844555 | + | 0.422277i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.7082 | + | 11.7082i | −0.420029 | + | 0.420029i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.4164 | −0.552350 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.71851 | 0.311973 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.79611 | + | 1.79611i | −0.0641878 | + | 0.0641878i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −30.1246 | − | 7.11146i | −1.07519 | − | 0.253819i | ||||
\(786\) | 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 | ||||||||
\(789\) | 53.0472i | 1.88853i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 11.0697i | − | 0.393591i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.6525 | − | 30.6525i | −1.08850 | − | 1.08850i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.76393 | − | 4.47214i | −0.0980266 | − | 0.158610i | ||||
\(796\) | 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 | ||||||||
\(805\) | 7.26543 | + | 11.7557i | 0.256073 | + | 0.414334i | ||||
\(806\) | 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 | ||||||||
\(811\) | 32.0689i | 1.12609i | 0.826426 | + | 0.563045i | \(0.190370\pi\) | ||||
−0.826426 | + | 0.563045i | \(0.809630\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −51.2511 | − | 51.2511i | −1.79745 | − | 1.79745i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.9928 | + | 5.19180i | 0.770375 | + | 0.181861i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.76393 | + | 4.76393i | −0.166669 | + | 0.166669i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.1803 | 0.565387 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.4742 | −0.714555 | −0.357278 | − | 0.933998i | \(-0.616295\pi\) | ||||
−0.357278 | + | 0.933998i | \(0.616295\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.3440 | − | 24.3440i | 0.848577 | − | 0.848577i | −0.141379 | − | 0.989956i | \(-0.545154\pi\) |
0.989956 | + | 0.141379i | \(0.0451535\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.4164 | − | 4.47214i | 0.467099 | − | 0.155700i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.8541 | − | 14.8541i | −0.516528 | − | 0.516528i | 0.399991 | − | 0.916519i | \(-0.369013\pi\) |
−0.916519 | + | 0.399991i | \(0.869013\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 3.11817i | − | 0.108299i | −0.998533 | − | 0.0541493i | \(-0.982755\pi\) | ||
0.998533 | − | 0.0541493i | \(-0.0172447\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 7.05342i | − | 0.244681i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.23607 | + | 4.23607i | 0.146771 | + | 0.146771i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.201626 | + | 0.854102i | −0.00697756 | + | 0.0295574i | ||||
\(836\) | 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 | ||||||||
\(845\) | −11.3067 | + | 6.98791i | −0.388962 | + | 0.240391i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.1352 | + | 11.1352i | 0.382609 | + | 0.382609i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 50.5410i | − | 1.73456i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.1803i | 0.554655i | ||||||||
\(852\) | 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 | ||||||||
\(855\) | −8.50651 | + | 5.25731i | −0.290916 | + | 0.179796i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.8328 | − | 17.8328i | 0.609157 | − | 0.609157i | −0.333568 | − | 0.942726i | \(-0.608253\pi\) |
0.942726 | + | 0.333568i | \(0.108253\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.52786 | 0.256847 | 0.128424 | − | 0.991719i | \(-0.459008\pi\) | ||||
0.128424 | + | 0.991719i | \(0.459008\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 29.3238 | 0.999351 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.22088 | + | 6.22088i | −0.211761 | + | 0.211761i | −0.805015 | − | 0.593254i | \(-0.797843\pi\) |
0.593254 | + | 0.805015i | \(0.297843\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.59675 | + | 19.4721i | −0.156294 | + | 0.662072i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24.2705 | + | 24.2705i | 0.824270 | + | 0.824270i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 15.2169i | − | 0.516198i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 14.6619i | − | 0.496799i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.527864 | + | 0.527864i | 0.0178655 | + | 0.0178655i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.2705 | − | 11.9098i | −0.482431 | − | 0.402626i | ||||
\(876\) | 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 | −0.971326 | − | 0.237752i | \(-0.923589\pi\) |
0.237752 | + | 0.971326i | \(0.423589\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −42.1895 | − | 9.95959i | −1.41818 | − | 0.334788i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.1482 | − | 28.1482i | −0.945123 | − | 0.945123i | 0.0534473 | − | 0.998571i | \(-0.482979\pi\) |
−0.998571 | + | 0.0534473i | \(0.982979\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 20.6525i | − | 0.692662i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 13.2361i | − | 0.443425i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.6619 | − | 14.6619i | −0.490641 | − | 0.490641i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.3642 | − | 31.3319i | −0.647272 | − | 1.04731i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 26.1803 | − | 26.1803i | 0.874136 | − | 0.874136i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.63932 | 0.254786 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.45309 | 0.0484093 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.06154 | − | 9.06154i | 0.301549 | − | 0.301549i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.0557 | + | 17.8885i | 0.367505 | + | 0.594635i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.3262 | + | 23.3262i | 0.774535 | + | 0.774535i | 0.978896 | − | 0.204361i | \(-0.0655115\pi\) |
−0.204361 | + | 0.978896i | \(0.565512\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 27.5276i | 0.913034i | ||||||||
\(910\) | 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 | ||||||||
\(915\) | −49.5967 | − | 11.7082i | −1.63962 | − | 0.387061i | ||||
\(916\) | 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 | ||||||||
\(925\) | −6.88191 | − | 20.6457i | −0.226276 | − | 0.678827i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.3925 | − | 16.3925i | −0.538400 | − | 0.538400i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.34752i | 0.175447i | 0.996145 | + | 0.0877233i | \(0.0279591\pi\) | ||||
−0.996145 | + | 0.0877233i | \(0.972041\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.47214i | 0.277663i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.2088 | + | 13.2088i | 0.432436 | + | 0.432436i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.898056 | + | 3.80423i | −0.0293696 | + | 0.124411i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.3050 | + | 20.3050i | −0.663334 | + | 0.663334i | −0.956164 | − | 0.292831i | \(-0.905403\pi\) |
0.292831 | + | 0.956164i | \(0.405403\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.1803 | 0.658561 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −60.8676 | −1.98423 | −0.992114 | − | 0.125340i | \(-0.959998\pi\) | ||||
−0.992114 | + | 0.125340i | \(0.959998\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.2622 | − | 20.2622i | 0.659828 | − | 0.659828i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.52786 | + | 3.41641i | −0.179821 | + | 0.111136i | ||||
\(946\) | 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 | ||||||||
\(949\) | − | 53.6022i | − | 1.74000i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 34.5811i | 1.12137i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.81966 | + | 6.81966i | 0.220910 | + | 0.220910i | 0.808882 | − | 0.587971i | \(-0.200073\pi\) |
−0.587971 | + | 0.808882i | \(0.700073\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.4721 | + | 15.1246i | −0.791900 | + | 0.489421i | ||||
\(956\) | 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 | ||||||||
\(965\) | 5.42882 | − | 22.9969i | 0.174760 | − | 0.740295i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.0332 | − | 12.0332i | −0.386962 | − | 0.386962i | 0.486640 | − | 0.873602i | \(-0.338222\pi\) |
−0.873602 | + | 0.486640i | \(0.838222\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 6.47214i | − | 0.207915i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 33.5967i | − | 1.07817i | −0.842251 | − | 0.539085i | \(-0.818770\pi\) | ||
0.842251 | − | 0.539085i | \(-0.181230\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.36737 | + | 6.36737i | 0.204128 | + | 0.204128i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −22.2703 | + | 44.5407i | −0.713221 | + | 1.42644i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.2361 | + | 28.2361i | −0.903352 | + | 0.903352i | −0.995725 | − | 0.0923727i | \(-0.970555\pi\) |
0.0923727 | + | 0.995725i | \(0.470555\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.00000 | −0.255681 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.0049 | −0.479070 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.620541 | − | 0.620541i | 0.0197922 | − | 0.0197922i | −0.697141 | − | 0.716934i | \(-0.745545\pi\) |
0.716934 | + | 0.697141i | \(0.245545\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.70820 | − | 1.58359i | −0.213741 | − | 0.0504574i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 27.8885 | + | 27.8885i | 0.887702 | + | 0.887702i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 12.5227i | − | 0.398200i | ||||||
\(990\) | 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 | ||||||||
\(995\) | −21.3050 | − | 34.4721i | −0.675412 | − | 1.09284i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.6506 | + | 35.6506i | −1.12907 | + | 1.12907i | −0.138738 | + | 0.990329i | \(0.544304\pi\) |
−0.990329 | + | 0.138738i | \(0.955696\pi\) | |||||||
\(998\) | 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 \(a_p\))