Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,2,Mod(575,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 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("1728.575");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.s (of order \(6\), 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: | \(13.7981494693\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.170772624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 575.3 | ||
Root | \(0.774115 - 1.18353i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.575 |
Dual form | 1728.2.s.f.1151.3 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.686141 | − | 0.396143i | 0.306851 | − | 0.177161i | −0.338665 | − | 0.940907i | \(-0.609975\pi\) |
0.645517 | + | 0.763746i | \(0.276642\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.35143 | − | 1.35760i | −0.888756 | − | 0.513124i | −0.0152206 | − | 0.999884i | \(-0.504845\pi\) |
−0.873535 | + | 0.486761i | \(0.838178\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.71352 | − | 2.96790i | 0.516645 | − | 0.894855i | −0.483168 | − | 0.875527i | \(-0.660514\pi\) |
0.999813 | − | 0.0193276i | \(-0.00615256\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.68614 | + | 2.92048i | 0.467651 | + | 0.809996i | 0.999317 | − | 0.0369586i | \(-0.0117670\pi\) |
−0.531666 | + | 0.846954i | \(0.678434\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.52434i | − | 0.612242i | −0.951993 | − | 0.306121i | \(-0.900969\pi\) | ||
0.951993 | − | 0.306121i | \(-0.0990312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.20979i | − | 0.506960i | −0.967341 | − | 0.253480i | \(-0.918425\pi\) | ||
0.967341 | − | 0.253480i | \(-0.0815752\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.07561 | − | 1.86301i | −0.224279 | − | 0.388463i | 0.731824 | − | 0.681494i | \(-0.238670\pi\) |
−0.956103 | + | 0.293031i | \(0.905336\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.18614 | + | 3.78651i | −0.437228 | + | 0.757301i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.686141 | − | 0.396143i | −0.127413 | − | 0.0735620i | 0.434939 | − | 0.900460i | \(-0.356770\pi\) |
−0.562352 | + | 0.826898i | \(0.690103\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.47603 | − | 0.852189i | 0.265104 | − | 0.153058i | −0.361557 | − | 0.932350i | \(-0.617755\pi\) |
0.626660 | + | 0.779292i | \(0.284421\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.15121 | −0.363621 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.74456 | −0.780001 | −0.390001 | − | 0.920815i | \(-0.627525\pi\) | ||||
−0.390001 | + | 0.920815i | \(0.627525\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.127719 | + | 0.0737384i | −0.0199463 | + | 0.0115160i | −0.509940 | − | 0.860210i | \(-0.670332\pi\) |
0.489994 | + | 0.871726i | \(0.336999\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.01594 | − | 3.47331i | −0.917423 | − | 0.529674i | −0.0346108 | − | 0.999401i | \(-0.511019\pi\) |
−0.882812 | + | 0.469727i | \(0.844353\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.77846 | − | 10.0086i | 0.842875 | − | 1.45990i | −0.0445785 | − | 0.999006i | \(-0.514194\pi\) |
0.887454 | − | 0.460897i | \(-0.152472\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.186141 | + | 0.322405i | 0.0265915 | + | 0.0460579i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 8.51278i | − | 1.16932i | −0.811278 | − | 0.584660i | \(-0.801228\pi\) | ||
0.811278 | − | 0.584660i | \(-0.198772\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.71519i | − | 0.366117i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.58891 | − | 4.48412i | −0.337047 | − | 0.583783i | 0.646829 | − | 0.762635i | \(-0.276095\pi\) |
−0.983876 | + | 0.178852i | \(0.942762\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.68614 | − | 2.92048i | 0.215888 | − | 0.373929i | −0.737659 | − | 0.675174i | \(-0.764069\pi\) |
0.953547 | + | 0.301244i | \(0.0974020\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.31386 | + | 1.33591i | 0.286999 | + | 0.165699i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.01594 | + | 3.47331i | −0.734964 | + | 0.424332i | −0.820236 | − | 0.572026i | \(-0.806158\pi\) |
0.0852711 | + | 0.996358i | \(0.472824\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.75079 | −0.207780 | −0.103890 | − | 0.994589i | \(-0.533129\pi\) | ||||
−0.103890 | + | 0.994589i | \(0.533129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.37228 | −0.277655 | −0.138827 | − | 0.990317i | \(-0.544333\pi\) | ||||
−0.138827 | + | 0.990317i | \(0.544333\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.05842 | + | 4.65253i | −0.918342 | + | 0.530205i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.80507 | − | 5.08361i | −0.990647 | − | 0.571951i | −0.0851797 | − | 0.996366i | \(-0.527146\pi\) |
−0.905468 | + | 0.424415i | \(0.860480\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.62725 | − | 6.28258i | 0.398142 | − | 0.689603i | −0.595355 | − | 0.803463i | \(-0.702988\pi\) |
0.993497 | + | 0.113861i | \(0.0363217\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.00000 | − | 1.73205i | −0.108465 | − | 0.187867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5.34363i | − | 0.566424i | −0.959057 | − | 0.283212i | \(-0.908600\pi\) | ||
0.959057 | − | 0.283212i | \(-0.0913999\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 9.15640i | − | 0.959852i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.875393 | − | 1.51622i | −0.0898134 | − | 0.155561i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.24456 | − | 10.8159i | 0.634039 | − | 1.09819i | −0.352679 | − | 0.935745i | \(-0.614729\pi\) |
0.986718 | − | 0.162444i | \(-0.0519376\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.4307 | + | 8.90892i | 1.53541 | + | 0.886471i | 0.999099 | + | 0.0424521i | \(0.0135170\pi\) |
0.536314 | + | 0.844019i | \(0.319816\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.6325 | + | 7.29339i | −1.24472 | + | 0.718640i | −0.970051 | − | 0.242899i | \(-0.921901\pi\) |
−0.274669 | + | 0.961539i | \(0.588568\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.2332 | 1.27930 | 0.639650 | − | 0.768667i | \(-0.279080\pi\) | ||||
0.639650 | + | 0.768667i | \(0.279080\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.48913 | 0.908893 | 0.454447 | − | 0.890774i | \(-0.349837\pi\) | ||||
0.454447 | + | 0.890774i | \(0.349837\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.8030 | + | 7.96916i | −1.29848 | + | 0.749675i | −0.980141 | − | 0.198303i | \(-0.936457\pi\) |
−0.318335 | + | 0.947978i | \(0.603124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.47603 | − | 0.852189i | −0.137641 | − | 0.0794670i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.42703 | + | 5.93580i | −0.314156 | + | 0.544134i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.372281 | − | 0.644810i | −0.0338438 | − | 0.0586191i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.42554i | 0.664160i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16.2912i | − | 1.44561i | −0.691053 | − | 0.722804i | \(-0.742853\pi\) | ||
0.691053 | − | 0.722804i | \(-0.257147\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.62725 | − | 6.28258i | −0.316914 | − | 0.548911i | 0.662928 | − | 0.748683i | \(-0.269313\pi\) |
−0.979843 | + | 0.199771i | \(0.935980\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.00000 | + | 5.19615i | −0.260133 | + | 0.450564i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.2446 | + | 9.37880i | 1.38787 | + | 0.801285i | 0.993075 | − | 0.117485i | \(-0.0374833\pi\) |
0.394792 | + | 0.918771i | \(0.370817\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.09262 | − | 4.67228i | 0.686407 | − | 0.396297i | −0.115858 | − | 0.993266i | \(-0.536962\pi\) |
0.802265 | + | 0.596968i | \(0.203628\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.5569 | 0.966438 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.627719 | −0.0521292 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.31386 | + | 4.80001i | −0.681098 | + | 0.393232i | −0.800269 | − | 0.599642i | \(-0.795310\pi\) |
0.119171 | + | 0.992874i | \(0.461976\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.92967 | + | 4.57820i | 0.645308 | + | 0.372569i | 0.786656 | − | 0.617391i | \(-0.211810\pi\) |
−0.141348 | + | 0.989960i | \(0.545144\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.675178 | − | 1.16944i | 0.0542316 | − | 0.0939319i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.43070 | − | 14.6024i | −0.672843 | − | 1.16540i | −0.977094 | − | 0.212807i | \(-0.931739\pi\) |
0.304251 | − | 0.952592i | \(-0.401594\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.84096i | 0.460332i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.8716i | 0.929855i | 0.885349 | + | 0.464928i | \(0.153920\pi\) | ||||
−0.885349 | + | 0.464928i | \(0.846080\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.60592 | − | 16.6379i | −0.743329 | − | 1.28748i | −0.950972 | − | 0.309278i | \(-0.899913\pi\) |
0.207643 | − | 0.978205i | \(-0.433421\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.813859 | − | 1.40965i | 0.0626046 | − | 0.108434i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.80298 | − | 2.77300i | −0.365164 | − | 0.210828i | 0.306180 | − | 0.951974i | \(-0.400949\pi\) |
−0.671344 | + | 0.741146i | \(0.734283\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.2811 | − | 5.93580i | 0.777178 | − | 0.448704i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.8114 | −1.40603 | −0.703016 | − | 0.711174i | \(-0.748164\pi\) | ||||
−0.703016 | + | 0.711174i | \(0.748164\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.00000 | 0.297318 | 0.148659 | − | 0.988889i | \(-0.452504\pi\) | ||||
0.148659 | + | 0.988889i | \(0.452504\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.25544 | + | 1.87953i | −0.239345 | + | 0.138186i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.49198 | − | 4.32550i | −0.547868 | − | 0.316312i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.95100 | − | 3.37923i | 0.141169 | − | 0.244512i | −0.786768 | − | 0.617249i | \(-0.788247\pi\) |
0.927937 | + | 0.372736i | \(0.121580\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.87228 | + | 3.24289i | 0.134770 | + | 0.233428i | 0.925509 | − | 0.378724i | \(-0.123637\pi\) |
−0.790740 | + | 0.612153i | \(0.790304\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 10.6873i | − | 0.761436i | −0.924691 | − | 0.380718i | \(-0.875677\pi\) | ||
0.924691 | − | 0.380718i | \(-0.124323\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.3236i | 1.36981i | 0.728630 | + | 0.684907i | \(0.240157\pi\) | ||||
−0.728630 | + | 0.684907i | \(0.759843\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.07561 | + | 1.86301i | 0.0754928 | + | 0.130757i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0584220 | + | 0.101190i | −0.00408037 | + | 0.00706741i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.55842 | − | 3.78651i | −0.453656 | − | 0.261918i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.30350 | + | 3.06198i | −0.365108 | + | 0.210795i | −0.671319 | − | 0.741169i | \(-0.734272\pi\) |
0.306211 | + | 0.951964i | \(0.400939\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.50371 | −0.375350 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.62772 | −0.314150 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.37228 | − | 4.25639i | 0.495913 | − | 0.286316i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.47603 | + | 0.852189i | 0.0988426 | + | 0.0570668i | 0.548606 | − | 0.836081i | \(-0.315159\pi\) |
−0.449764 | + | 0.893147i | \(0.648492\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.44298 | + | 16.3557i | −0.626752 | + | 1.08557i | 0.361447 | + | 0.932393i | \(0.382283\pi\) |
−0.988199 | + | 0.153174i | \(0.951050\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.68614 | + | 8.11663i | 0.309669 | + | 0.536362i | 0.978290 | − | 0.207241i | \(-0.0664485\pi\) |
−0.668621 | + | 0.743603i | \(0.733115\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 28.0627i | − | 1.83845i | −0.393737 | − | 0.919223i | \(-0.628818\pi\) | ||
0.393737 | − | 0.919223i | \(-0.371182\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 9.15640i | − | 0.597298i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.33010 | + | 14.4282i | 0.538830 | + | 0.933280i | 0.998967 | + | 0.0454327i | \(0.0144667\pi\) |
−0.460138 | + | 0.887847i | \(0.652200\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.24456 | + | 14.2800i | −0.531079 | + | 0.919856i | 0.468263 | + | 0.883589i | \(0.344880\pi\) |
−0.999342 | + | 0.0362667i | \(0.988453\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.255437 | + | 0.147477i | 0.0163193 | + | 0.00942195i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.45364 | − | 3.72601i | 0.410635 | − | 0.237080i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.7347 | 1.05629 | 0.528144 | − | 0.849155i | \(-0.322888\pi\) | ||||
0.528144 | + | 0.849155i | \(0.322888\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.37228 | −0.463491 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.98913 | − | 5.76722i | 0.623105 | − | 0.359750i | −0.154972 | − | 0.987919i | \(-0.549529\pi\) |
0.778077 | + | 0.628169i | \(0.216195\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.1565 | + | 6.44121i | 0.693231 | + | 0.400237i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.25343 | + | 10.8313i | −0.385603 | + | 0.667884i | −0.991853 | − | 0.127391i | \(-0.959340\pi\) |
0.606250 | + | 0.795274i | \(0.292673\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.37228 | − | 5.84096i | −0.207158 | − | 0.358807i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 24.9484i | − | 1.52113i | −0.649260 | − | 0.760566i | \(-0.724921\pi\) | ||
0.649260 | − | 0.760566i | \(-0.275079\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.38712i | 0.0842618i | 0.999112 | + | 0.0421309i | \(0.0134147\pi\) | ||||
−0.999112 | + | 0.0421309i | \(0.986585\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.49198 | + | 12.9765i | 0.451783 | + | 0.782512i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.313859 | − | 0.543620i | 0.0188580 | − | 0.0326630i | −0.856442 | − | 0.516243i | \(-0.827330\pi\) |
0.875300 | + | 0.483580i | \(0.160664\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.56930 | + | 3.21543i | 0.332236 | + | 0.191817i | 0.656834 | − | 0.754036i | \(-0.271895\pi\) |
−0.324597 | + | 0.945852i | \(0.605229\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.80507 | − | 5.08361i | 0.523407 | − | 0.302189i | −0.214921 | − | 0.976632i | \(-0.568949\pi\) |
0.738327 | + | 0.674442i | \(0.235616\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.400428 | 0.0236365 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.6277 | 0.625160 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.3139 | + | 9.99616i | −1.01149 | + | 0.583982i | −0.911627 | − | 0.411020i | \(-0.865173\pi\) |
−0.0998599 | + | 0.995002i | \(0.531839\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.55271 | − | 2.05116i | −0.206847 | − | 0.119423i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.62725 | − | 6.28258i | 0.209769 | − | 0.363331i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.43070 | + | 16.3345i | 0.543577 | + | 0.941502i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 2.67181i | − | 0.152988i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.9530i | 1.48121i | 0.671938 | + | 0.740607i | \(0.265462\pi\) | ||||
−0.671938 | + | 0.740607i | \(0.734538\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.6591 | + | 27.1224i | 0.887948 | + | 1.53797i | 0.842297 | + | 0.539014i | \(0.181203\pi\) |
0.0456512 | + | 0.998957i | \(0.485464\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.24456 | + | 3.88770i | −0.126870 | + | 0.219746i | −0.922462 | − | 0.386087i | \(-0.873826\pi\) |
0.795592 | + | 0.605832i | \(0.207160\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.6644 | + | 11.9306i | 1.16063 | + | 0.670089i | 0.951454 | − | 0.307790i | \(-0.0995893\pi\) |
0.209173 | + | 0.977879i | \(0.432923\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.35143 | + | 1.35760i | −0.131655 | + | 0.0760109i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.57825 | −0.310382 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.7446 | −0.817881 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.1753 | + | 15.6896i | −1.49822 | + | 0.864998i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.1149 | + | 13.9228i | 1.32548 | + | 0.765264i | 0.984596 | − | 0.174843i | \(-0.0559419\pi\) |
0.340879 | + | 0.940107i | \(0.389275\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.75186 | + | 4.76635i | −0.150350 | + | 0.260414i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.12772 | + | 3.68532i | 0.115904 | + | 0.200752i | 0.918141 | − | 0.396254i | \(-0.129690\pi\) |
−0.802237 | + | 0.597006i | \(0.796357\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 5.84096i | − | 0.316306i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.9955i | 0.971668i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.86473 | + | 6.69391i | 0.207470 | + | 0.359348i | 0.950917 | − | 0.309447i | \(-0.100144\pi\) |
−0.743447 | + | 0.668795i | \(0.766811\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.68614 | + | 9.84868i | −0.304372 | + | 0.527188i | −0.977121 | − | 0.212683i | \(-0.931780\pi\) |
0.672749 | + | 0.739871i | \(0.265113\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.24456 | + | 2.45060i | 0.225915 | + | 0.130432i | 0.608686 | − | 0.793411i | \(-0.291697\pi\) |
−0.382771 | + | 0.923843i | \(0.625030\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.20128 | + | 0.693562i | −0.0637576 | + | 0.0368105i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.9679 | −1.58165 | −0.790823 | − | 0.612045i | \(-0.790347\pi\) | ||||
−0.790823 | + | 0.612045i | \(0.790347\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.1168 | 0.742992 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.62772 | + | 0.939764i | −0.0851987 | + | 0.0491895i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.7571 | + | 6.78799i | 0.613718 | + | 0.354330i | 0.774419 | − | 0.632673i | \(-0.218042\pi\) |
−0.160701 | + | 0.987003i | \(0.551376\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.5569 | + | 20.0172i | −0.600006 | + | 1.03924i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.43070 | + | 7.67420i | 0.229413 | + | 0.397355i | 0.957634 | − | 0.287987i | \(-0.0929860\pi\) |
−0.728221 | + | 0.685342i | \(0.759653\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.67181i | − | 0.137605i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.66181i | − | 0.496294i | −0.968722 | − | 0.248147i | \(-0.920178\pi\) | ||
0.968722 | − | 0.248147i | \(-0.0798216\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.200214 | − | 0.346781i | −0.0102305 | − | 0.0177197i | 0.860865 | − | 0.508834i | \(-0.169923\pi\) |
−0.871095 | + | 0.491114i | \(0.836590\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.68614 | + | 6.38458i | −0.187863 | + | 0.325388i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.19702 | + | 4.15520i | 0.364903 | + | 0.210677i | 0.671229 | − | 0.741250i | \(-0.265767\pi\) |
−0.306326 | + | 0.951927i | \(0.599100\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.70285 | + | 2.71519i | −0.237834 | + | 0.137313i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.05535 | −0.405309 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.25544 | 0.364140 | 0.182070 | − | 0.983286i | \(-0.441720\pi\) | ||||
0.182070 | + | 0.983286i | \(0.441720\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.9891 | − | 10.9634i | 0.948272 | − | 0.547485i | 0.0557281 | − | 0.998446i | \(-0.482252\pi\) |
0.892544 | + | 0.450961i | \(0.148919\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.97760 | + | 2.87382i | 0.247952 | + | 0.143155i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.12989 | + | 14.0814i | −0.402984 | + | 0.697988i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.12772 | − | 1.95327i | −0.0557621 | − | 0.0965828i | 0.836797 | − | 0.547513i | \(-0.184426\pi\) |
−0.892559 | + | 0.450931i | \(0.851092\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.0588i | 0.691788i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 5.74764i | − | 0.282141i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.82639 | + | 4.89545i | 0.138078 | + | 0.239159i | 0.926769 | − | 0.375631i | \(-0.122574\pi\) |
−0.788691 | + | 0.614790i | \(0.789241\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.8030 | − | 25.6395i | 0.721453 | − | 1.24959i | −0.238964 | − | 0.971028i | \(-0.576808\pi\) |
0.960417 | − | 0.278565i | \(-0.0898589\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.55842 | + | 5.51856i | 0.463652 | + | 0.267689i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.92967 | + | 4.57820i | −0.383744 | + | 0.221555i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.6581 | 0.706054 | 0.353027 | − | 0.935613i | \(-0.385152\pi\) | ||||
0.353027 | + | 0.935613i | \(0.385152\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.3723 | −0.690688 | −0.345344 | − | 0.938476i | \(-0.612238\pi\) | ||||
−0.345344 | + | 0.938476i | \(0.612238\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.11684 | + | 2.37686i | −0.196935 | + | 0.113701i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.4919 | + | 16.4498i | 1.35984 | + | 0.785106i | 0.989602 | − | 0.143830i | \(-0.0459418\pi\) |
0.370241 | + | 0.928936i | \(0.379275\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.58891 | − | 4.48412i | 0.123003 | − | 0.213047i | −0.797948 | − | 0.602727i | \(-0.794081\pi\) |
0.920950 | + | 0.389680i | \(0.127414\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.11684 | − | 3.66648i | −0.100348 | − | 0.173808i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3.81396i | − | 0.179992i | −0.995942 | − | 0.0899959i | \(-0.971315\pi\) | ||
0.995942 | − | 0.0899959i | \(-0.0286854\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.505408i | 0.0237987i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.62725 | − | 6.28258i | −0.170048 | − | 0.294532i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.98913 | − | 5.17732i | 0.139825 | − | 0.242185i | −0.787605 | − | 0.616180i | \(-0.788679\pi\) |
0.927430 | + | 0.373996i | \(0.122013\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.8030 | − | 11.4333i | −0.922317 | − | 0.532500i | −0.0379435 | − | 0.999280i | \(-0.512081\pi\) |
−0.884373 | + | 0.466780i | \(0.845414\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.2108 | − | 10.5140i | 0.846327 | − | 0.488627i | −0.0130831 | − | 0.999914i | \(-0.504165\pi\) |
0.859410 | + | 0.511288i | \(0.170831\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.3897 | −1.12862 | −0.564310 | − | 0.825563i | \(-0.690858\pi\) | ||||
−0.564310 | + | 0.825563i | \(0.690858\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.8614 | 0.870939 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.6168 | + | 11.9031i | −0.947963 | + | 0.547307i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.36737 | + | 4.83090i | 0.383921 | + | 0.221657i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.90307 | − | 8.49236i | 0.224027 | − | 0.388026i | −0.732000 | − | 0.681304i | \(-0.761413\pi\) |
0.956027 | + | 0.293278i | \(0.0947463\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | − | 13.8564i | −0.364769 | − | 0.631798i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 9.89497i | − | 0.449308i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.9365i | 0.812780i | 0.913700 | + | 0.406390i | \(0.133213\pi\) | ||||
−0.913700 | + | 0.406390i | \(0.866787\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.3950 | + | 21.4689i | 0.559381 | + | 0.968876i | 0.997548 | + | 0.0699824i | \(0.0222943\pi\) |
−0.438168 | + | 0.898893i | \(0.644372\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.00000 | + | 1.73205i | −0.0450377 | + | 0.0780076i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.11684 | + | 2.37686i | 0.184666 | + | 0.106617i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.437696 | − | 0.252704i | 0.0195940 | − | 0.0113126i | −0.490171 | − | 0.871626i | \(-0.663066\pi\) |
0.509765 | + | 0.860314i | \(0.329732\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.9073 | 0.575507 | 0.287754 | − | 0.957704i | \(-0.407092\pi\) | ||||
0.287754 | + | 0.957704i | \(0.407092\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.1168 | 0.628191 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.6861 | − | 9.05640i | 0.695276 | − | 0.401418i | −0.110310 | − | 0.993897i | \(-0.535184\pi\) |
0.805586 | + | 0.592480i | \(0.201851\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.57825 | + | 3.22060i | 0.246767 | + | 0.142471i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.77846 | + | 10.0086i | −0.254629 | + | 0.441031i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.8030 | − | 34.2998i | −0.870934 | − | 1.50850i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.4472i | 0.457700i | 0.973462 | + | 0.228850i | \(0.0734966\pi\) | ||||
−0.973462 | + | 0.228850i | \(0.926503\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.41957i | 0.193254i | 0.995321 | + | 0.0966272i | \(0.0308055\pi\) | ||||
−0.995321 | + | 0.0966272i | \(0.969195\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.15121 | − | 3.72601i | −0.0937083 | − | 0.162308i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.18614 | − | 15.9109i | 0.399397 | − | 0.691777i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.430703 | − | 0.248667i | −0.0186558 | − | 0.0107709i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.07982 | − | 5.24224i | 0.392555 | − | 0.226642i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.27582 | 0.0549535 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.9783 | −1.58982 | −0.794910 | − | 0.606728i | \(-0.792482\pi\) | ||||
−0.794910 | + | 0.606728i | \(0.792482\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.51087 | − | 3.75906i | 0.278895 | − | 0.161020i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.21723 | − | 4.16687i | −0.308586 | − | 0.178162i | 0.337707 | − | 0.941251i | \(-0.390349\pi\) |
−0.646294 | + | 0.763089i | \(0.723682\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.875393 | + | 1.51622i | −0.0372930 | + | 0.0645933i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.8030 | + | 23.9075i | 0.586963 | + | 1.01665i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.4897i | 0.868175i | 0.900871 | + | 0.434087i | \(0.142929\pi\) | ||||
−0.900871 | + | 0.434087i | \(0.857071\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 23.4259i | − | 0.990811i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.54098 | − | 9.59726i | −0.233524 | − | 0.404476i | 0.725318 | − | 0.688414i | \(-0.241693\pi\) |
−0.958843 | + | 0.283937i | \(0.908359\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.31386 | + | 10.9359i | −0.265626 | + | 0.460078i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.989125 | − | 0.571072i | −0.0414663 | − | 0.0239406i | 0.479124 | − | 0.877747i | \(-0.340955\pi\) |
−0.520590 | + | 0.853807i | \(0.674288\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.5463 | − | 8.39829i | 0.608742 | − | 0.351457i | −0.163731 | − | 0.986505i | \(-0.552353\pi\) |
0.772473 | + | 0.635048i | \(0.219020\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.40571 | 0.392245 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −42.8397 | −1.78344 | −0.891719 | − | 0.452589i | \(-0.850500\pi\) | ||||
−0.891719 | + | 0.452589i | \(0.850500\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.0584 | + | 9.84868i | −0.707703 | + | 0.408592i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.2651 | − | 14.5868i | −1.04637 | − | 0.604123i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.41637 | − | 11.1135i | 0.264832 | − | 0.458702i | −0.702688 | − | 0.711499i | \(-0.748017\pi\) |
0.967520 | + | 0.252796i | \(0.0813502\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.88316 | − | 3.26172i | −0.0775941 | − | 0.134397i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.4410i | 0.634085i | 0.948411 | + | 0.317043i | \(0.102690\pi\) | ||||
−0.948411 | + | 0.317043i | \(0.897310\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.43039i | 0.222624i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.20550 | + | 15.9444i | 0.376126 | + | 0.651470i | 0.990495 | − | 0.137549i | \(-0.0439225\pi\) |
−0.614369 | + | 0.789019i | \(0.710589\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.9891 | − | 25.9619i | 0.611419 | − | 1.05901i | −0.379582 | − | 0.925158i | \(-0.623932\pi\) |
0.991001 | − | 0.133851i | \(-0.0427344\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.510875 | − | 0.294954i | −0.0207700 | − | 0.0119916i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.1947 | + | 19.1650i | −1.34733 | + | 0.777883i | −0.987871 | − | 0.155277i | \(-0.950373\pi\) |
−0.359462 | + | 0.933160i | \(0.617040\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 38.9732 | 1.57669 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.2337 | 1.22113 | 0.610564 | − | 0.791967i | \(-0.290943\pi\) | ||||
0.610564 | + | 0.791967i | \(0.290943\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.24456 | + | 4.18265i | −0.291655 | + | 0.168387i | −0.638688 | − | 0.769466i | \(-0.720523\pi\) |
0.347033 | + | 0.937853i | \(0.387189\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.9520 | − | 13.8287i | −0.962711 | − | 0.555821i | −0.0657046 | − | 0.997839i | \(-0.520930\pi\) |
−0.897006 | + | 0.442018i | \(0.854263\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.25450 | + | 12.5652i | −0.290645 | + | 0.503412i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.98913 | − | 13.8376i | −0.319565 | − | 0.553503i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.9769i | 0.477549i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 17.9365i | − | 0.714040i | −0.934097 | − | 0.357020i | \(-0.883793\pi\) | ||
0.934097 | − | 0.357020i | \(-0.116207\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.45364 | − | 11.1780i | −0.256105 | − | 0.443587i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.627719 | + | 1.08724i | −0.0248711 | + | 0.0430780i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.8723 | − | 13.7827i | −0.942898 | − | 0.544383i | −0.0520307 | − | 0.998645i | \(-0.516569\pi\) |
−0.890868 | + | 0.454263i | \(0.849903\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.46644 | − | 3.15605i | 0.215575 | − | 0.124463i | −0.388324 | − | 0.921523i | \(-0.626946\pi\) |
0.603900 | + | 0.797060i | \(0.293613\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −36.9711 | −1.45348 | −0.726741 | − | 0.686912i | \(-0.758966\pi\) | ||||
−0.726741 | + | 0.686912i | \(0.758966\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.7446 | −0.696535 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.68614 | − | 3.86025i | 0.261649 | − | 0.151063i | −0.363438 | − | 0.931619i | \(-0.618397\pi\) |
0.625087 | + | 0.780555i | \(0.285064\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.97760 | − | 2.87382i | −0.194491 | − | 0.112290i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.33010 | − | 14.4282i | 0.324495 | − | 0.562041i | −0.656915 | − | 0.753964i | \(-0.728139\pi\) |
0.981410 | + | 0.191923i | \(0.0614724\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.6861 | + | 18.5089i | 0.415643 | + | 0.719914i | 0.995496 | − | 0.0948069i | \(-0.0302234\pi\) |
−0.579853 | + | 0.814721i | \(0.696890\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.75372i | 0.184341i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.70438i | 0.0659938i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.77846 | − | 10.0086i | −0.223075 | − | 0.386377i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.569297 | + | 0.986051i | −0.0219448 | + | 0.0380095i | −0.876789 | − | 0.480875i | \(-0.840319\pi\) |
0.854844 | + | 0.518884i | \(0.173652\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.5475 | + | 16.4819i | 1.09717 | + | 0.633452i | 0.935477 | − | 0.353389i | \(-0.114971\pi\) |
0.161695 | + | 0.986841i | \(0.448304\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.3673 | + | 16.9552i | −1.12701 | + | 0.650681i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.07668 | 0.0794618 | 0.0397309 | − | 0.999210i | \(-0.487350\pi\) | ||||
0.0397309 | + | 0.999210i | \(0.487350\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.8614 | 0.567825 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.8614 | − | 14.3537i | 0.947144 | − | 0.546834i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.0064 | + | 5.77717i | 0.380660 | + | 0.219774i | 0.678105 | − | 0.734965i | \(-0.262801\pi\) |
−0.297446 | + | 0.954739i | \(0.596135\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.70178 | − | 6.41168i | 0.140417 | − | 0.243209i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.186141 | + | 0.322405i | 0.00705058 | + | 0.0122120i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.1282i | 0.986850i | 0.869788 | + | 0.493425i | \(0.164255\pi\) | ||||
−0.869788 | + | 0.493425i | \(0.835745\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.4845i | 0.395429i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.1895 | − | 41.8974i | −0.909738 | − | 1.57571i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.43070 | + | 4.21010i | −0.0912870 | + | 0.158114i | −0.908053 | − | 0.418855i | \(-0.862431\pi\) |
0.816766 | + | 0.576969i | \(0.195765\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.17527 | − | 1.83324i | −0.118915 | − | 0.0686554i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.92967 | − | 4.57820i | 0.296553 | − | 0.171215i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.65492 | 0.285481 | 0.142740 | − | 0.989760i | \(-0.454409\pi\) | ||||
0.142740 | + | 0.989760i | \(0.454409\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 39.6060 | 1.47500 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.00000 | − | 1.73205i | 0.111417 | − | 0.0643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.67732 | + | 1.54575i | 0.0992963 | + | 0.0573287i | 0.548826 | − | 0.835937i | \(-0.315075\pi\) |
−0.449530 | + | 0.893265i | \(0.648408\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.76780 | + | 15.1863i | −0.324289 | + | 0.561685i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.68614 | − | 4.65253i | −0.0992149 | − | 0.171845i | 0.812145 | − | 0.583456i | \(-0.198300\pi\) |
−0.911360 | + | 0.411610i | \(0.864966\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.8063i | 0.876916i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.66181i | 0.355415i | 0.984083 | + | 0.177708i | \(0.0568681\pi\) | ||||
−0.984083 | + | 0.177708i | \(0.943132\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.5132 | − | 38.9940i | −0.825929 | − | 1.43055i | −0.901207 | − | 0.433389i | \(-0.857318\pi\) |
0.0752776 | − | 0.997163i | \(-0.476016\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.80298 | + | 6.58696i | −0.139331 | + | 0.241328i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −31.1168 | − | 17.9653i | −1.13698 | − | 0.656438i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.9743 | − | 23.0792i | 1.45868 | − | 0.842170i | 0.459735 | − | 0.888056i | \(-0.347944\pi\) |
0.998947 | + | 0.0458859i | \(0.0146111\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.25450 | 0.264018 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.0000 | −0.508839 | −0.254419 | − | 0.967094i | \(-0.581884\pi\) | ||||
−0.254419 | + | 0.967094i | \(0.581884\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.5475 | − | 9.55373i | 0.599848 | − | 0.346322i | −0.169134 | − | 0.985593i | \(-0.554097\pi\) |
0.768982 | + | 0.639271i | \(0.220764\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.3130 | − | 12.8824i | −0.807784 | − | 0.466375i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.73053 | − | 15.1217i | 0.315241 | − | 0.546014i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.5475 | + | 47.7138i | 0.993390 | + | 1.72060i | 0.596105 | + | 0.802907i | \(0.296714\pi\) |
0.397285 | + | 0.917695i | \(0.369952\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 45.7330i | − | 1.64490i | −0.568835 | − | 0.822451i | \(-0.692606\pi\) | ||
0.568835 | − | 0.822451i | \(-0.307394\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.45202i | 0.267685i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.162946 | + | 0.282231i | 0.00583815 | + | 0.0101120i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.00000 | + | 5.19615i | −0.107348 | + | 0.185933i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.5693 | − | 6.67954i | −0.412926 | − | 0.238403i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.0095 | + | 9.82043i | −0.606323 | + | 0.350061i | −0.771525 | − | 0.636199i | \(-0.780506\pi\) |
0.165202 | + | 0.986260i | \(0.447172\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 43.2756 | 1.53870 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.3723 | 0.403842 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.8030 | − | 23.5576i | 1.44532 | − | 0.834454i | 0.447119 | − | 0.894475i | \(-0.352450\pi\) |
0.998197 | + | 0.0600211i | \(0.0191168\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.2651 | − | 14.5868i | −0.893814 | − | 0.516043i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.06494 | + | 7.04069i | −0.143449 | + | 0.248461i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.31386 | + | 4.00772i | 0.0815528 | + | 0.141254i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 27.1778i | − | 0.955521i | −0.878490 | − | 0.477760i | \(-0.841449\pi\) | ||
0.878490 | − | 0.477760i | \(-0.158551\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 25.9530i | − | 0.911332i | −0.890151 | − | 0.455666i | \(-0.849401\pi\) | ||
0.890151 | − | 0.455666i | \(-0.150599\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.70285 | + | 8.14558i | 0.164734 | + | 0.285327i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.67527 | + | 13.2940i | −0.268524 | + | 0.465096i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.6861 | − | 10.7884i | −0.652151 | − | 0.376519i | 0.137129 | − | 0.990553i | \(-0.456213\pi\) |
−0.789280 | + | 0.614034i | \(0.789546\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.8657 | − | 14.9336i | 0.901622 | − | 0.520552i | 0.0238957 | − | 0.999714i | \(-0.492393\pi\) |
0.877726 | + | 0.479163i | \(0.159060\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.00314 | −0.243523 | −0.121762 | − | 0.992559i | \(-0.538854\pi\) | ||||
−0.121762 | + | 0.992559i | \(0.538854\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.7663 | 0.478124 | 0.239062 | − | 0.971004i | \(-0.423160\pi\) | ||||
0.239062 | + | 0.971004i | \(0.423160\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.813859 | − | 0.469882i | 0.0281986 | − | 0.0162804i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.1820 | − | 7.61065i | −0.456183 | − | 0.263377i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.8391 | − | 39.5585i | 0.788493 | − | 1.36571i | −0.138397 | − | 0.990377i | \(-0.544195\pi\) |
0.926890 | − | 0.375333i | \(-0.122472\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.1861 | − | 24.5711i | −0.489177 | − | 0.847280i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 1.28962i | − | 0.0443643i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.02163i | 0.0694641i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.10328 | + | 8.83915i | 0.174938 | + | 0.303002i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.19702 | − | 3.80534i | 0.0752244 | − | 0.130292i | −0.825959 | − | 0.563730i | \(-0.809366\pi\) |
0.901184 | + | 0.433437i | \(0.142699\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.0367 | + | 12.7229i | 0.752758 | + | 0.434605i | 0.826690 | − | 0.562658i | \(-0.190221\pi\) |
−0.0739313 | + | 0.997263i | \(0.523555\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.4056 | + | 17.5547i | −1.03743 | + | 0.598958i | −0.919103 | − | 0.394017i | \(-0.871085\pi\) |
−0.118323 | + | 0.992975i | \(0.537752\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.15335 | 0.141382 | 0.0706909 | − | 0.997498i | \(-0.477480\pi\) | ||||
0.0706909 | + | 0.997498i | \(0.477480\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.39403 | −0.149402 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30.1753 | + | 17.4217i | −1.02363 | + | 0.590991i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.2875 | − | 11.7130i | −0.687414 | − | 0.396879i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.0809 | − | 17.4606i | 0.340796 | − | 0.590276i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.6861 | + | 23.7051i | 0.462148 | + | 0.800464i | 0.999068 | − | 0.0431693i | \(-0.0137455\pi\) |
−0.536920 | + | 0.843633i | \(0.680412\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.7899i | 0.666740i | 0.942796 | + | 0.333370i | \(0.108186\pi\) | ||||
−0.942796 | + | 0.333370i | \(0.891814\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 34.7921i | − | 1.17085i | −0.810727 | − | 0.585424i | \(-0.800928\pi\) | ||
0.810727 | − | 0.585424i | \(-0.199072\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.75186 | + | 4.76635i | 0.0923983 | + | 0.160039i | 0.908520 | − | 0.417842i | \(-0.137213\pi\) |
−0.816122 | + | 0.577880i | \(0.803880\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.1168 | + | 38.3075i | −0.741775 | + | 1.28479i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.1168 | − | 12.7692i | −0.740112 | − | 0.427304i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.9073 | + | 7.45202i | −0.431443 | + | 0.249094i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.35036 | −0.0450369 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.4891 | −0.715907 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.74456 | − | 1.58457i | 0.0912323 | − | 0.0526730i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.3258 | − | 12.3125i | −0.708111 | − | 0.408828i | 0.102250 | − | 0.994759i | \(-0.467396\pi\) |
−0.810361 | + | 0.585930i | \(0.800729\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.57932 | + | 11.3957i | −0.217983 | + | 0.377557i | −0.954191 | − | 0.299198i | \(-0.903281\pi\) |
0.736209 | + | 0.676755i | \(0.236614\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.4307 | − | 21.5306i | −0.411396 | − | 0.712559i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.6974i | 0.650464i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 46.0993i | − | 1.52067i | −0.649529 | − | 0.760337i | \(-0.725034\pi\) | ||
0.649529 | − | 0.760337i | \(-0.274966\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.95207 | − | 5.11313i | −0.0971686 | − | 0.168301i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.3723 | − | 17.9653i | 0.341039 | − | 0.590696i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.4307 | − | 17.5692i | −0.998399 | − | 0.576426i | −0.0906248 | − | 0.995885i | \(-0.528886\pi\) |
−0.907774 | + | 0.419459i | \(0.862220\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.712446 | − | 0.411331i | 0.0233495 | − | 0.0134808i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.85407 | −0.224152 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.7228 | −0.382968 | −0.191484 | − | 0.981496i | \(-0.561330\pi\) | ||||
−0.191484 | + | 0.981496i | \(0.561330\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.8030 | − | 18.3615i | 1.03675 | − | 0.598567i | 0.117837 | − | 0.993033i | \(-0.462404\pi\) |
0.918910 | + | 0.394466i | \(0.129071\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.274750 | + | 0.158627i | 0.00894709 | + | 0.00516561i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.2757 | − | 38.5827i | 0.723864 | − | 1.25377i | −0.235576 | − | 0.971856i | \(-0.575698\pi\) |
0.959440 | − | 0.281913i | \(-0.0909689\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.00000 | − | 6.92820i | −0.129845 | − | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 32.8164i | − | 1.06303i | −0.847050 | − | 0.531514i | \(-0.821623\pi\) | ||
0.847050 | − | 0.531514i | \(-0.178377\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 3.09150i | − | 0.100039i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25.4653 | − | 44.1071i | −0.822317 | − | 1.42429i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0475 | + | 24.3311i | −0.453147 | + | 0.784873i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.56930 | + | 1.48338i | 0.0827086 | + | 0.0477518i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.7282 | + | 28.1332i | −1.56699 | + | 0.904704i | −0.570476 | + | 0.821314i | \(0.693241\pi\) |
−0.996517 | + | 0.0833895i | \(0.973425\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.7156 | −0.793160 | −0.396580 | − | 0.918000i | \(-0.629803\pi\) | ||||
−0.396580 | + | 0.918000i | \(0.629803\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.3723 | −0.813398 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.6386 | − | 10.7610i | 0.596301 | − | 0.344275i | −0.171284 | − | 0.985222i | \(-0.554791\pi\) |
0.767585 | + | 0.640947i | \(0.221458\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.8593 | − | 9.15640i | −0.506867 | − | 0.292640i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.40464 | − | 14.5573i | 0.268066 | − | 0.464305i | −0.700296 | − | 0.713852i | \(-0.746949\pi\) |
0.968362 | + | 0.249548i | \(0.0802820\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.23369 | − | 7.33296i | −0.134897 | − | 0.233648i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.9436i | 0.475180i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.2912i | 0.517506i | 0.965944 | + | 0.258753i | \(0.0833116\pi\) | ||||
−0.965944 | + | 0.258753i | \(0.916688\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.65492 | + | 13.2587i | 0.242677 | + | 0.420330i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.4307 | + | 45.7793i | −0.837069 | + | 1.44985i | 0.0552661 | + | 0.998472i | \(0.482399\pi\) |
−0.892335 | + | 0.451374i | \(0.850934\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))