Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2592,2,Mod(431,2592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2592, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2592.431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2592 = 2^{5} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2592.p (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: | \(20.6972242039\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 431.1 | ||
Root | \(1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2592.431 |
Dual form | 2592.2.p.c.2159.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.22474 | − | 2.12132i | −0.547723 | − | 0.948683i | −0.998430 | − | 0.0560116i | \(-0.982162\pi\) |
0.450708 | − | 0.892672i | \(-0.351172\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00000 | + | 1.73205i | 1.13389 | + | 0.654654i | 0.944911 | − | 0.327327i | \(-0.106148\pi\) |
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.44949 | − | 1.41421i | −0.738549 | − | 0.426401i | 0.0829925 | − | 0.996550i | \(-0.473552\pi\) |
−0.821541 | + | 0.570149i | \(0.806886\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | + | 1.73205i | −0.832050 | + | 0.480384i | −0.854554 | − | 0.519362i | \(-0.826170\pi\) |
0.0225039 | + | 0.999747i | \(0.492836\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.41421i | 0.342997i | 0.985184 | + | 0.171499i | \(0.0548609\pi\) | ||||
−0.985184 | + | 0.171499i | \(0.945139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.44949 | − | 4.24264i | −0.510754 | − | 0.884652i | −0.999922 | − | 0.0124624i | \(-0.996033\pi\) |
0.489168 | − | 0.872189i | \(-0.337300\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.22474 | − | 2.12132i | 0.227429 | − | 0.393919i | −0.729616 | − | 0.683857i | \(-0.760301\pi\) |
0.957046 | + | 0.289938i | \(0.0936346\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | − | 1.73205i | 0.538816 | − | 0.311086i | −0.205783 | − | 0.978598i | \(-0.565974\pi\) |
0.744599 | + | 0.667512i | \(0.232641\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 8.48528i | − | 1.43427i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.22474 | − | 0.707107i | 0.191273 | − | 0.110432i | −0.401305 | − | 0.915944i | \(-0.631443\pi\) |
0.592578 | + | 0.805513i | \(0.298110\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | − | 6.92820i | 0.609994 | − | 1.05654i | −0.381246 | − | 0.924473i | \(-0.624505\pi\) |
0.991241 | − | 0.132068i | \(-0.0421616\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.44949 | − | 4.24264i | 0.357295 | − | 0.618853i | −0.630213 | − | 0.776422i | \(-0.717032\pi\) |
0.987508 | + | 0.157569i | \(0.0503658\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.50000 | + | 4.33013i | 0.357143 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.34847 | −1.00939 | −0.504695 | − | 0.863298i | \(-0.668395\pi\) | ||||
−0.504695 | + | 0.863298i | \(0.668395\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.92820i | 0.934199i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.79796 | − | 5.65685i | 1.27559 | − | 0.736460i | 0.299552 | − | 0.954080i | \(-0.403163\pi\) |
0.976034 | + | 0.217620i | \(0.0698294\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0000 | − | 6.92820i | −1.53644 | − | 0.887066i | −0.999043 | − | 0.0437377i | \(-0.986073\pi\) |
−0.537400 | − | 0.843328i | \(-0.680593\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.34847 | + | 4.24264i | 0.911465 | + | 0.526235i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.00000 | − | 3.46410i | −0.244339 | − | 0.423207i | 0.717607 | − | 0.696449i | \(-0.245238\pi\) |
−0.961946 | + | 0.273241i | \(0.911904\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.6969 | −1.74421 | −0.872103 | − | 0.489323i | \(-0.837244\pi\) | ||||
−0.872103 | + | 0.489323i | \(0.837244\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.89898 | − | 8.48528i | −0.558291 | − | 0.966988i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.00000 | + | 1.73205i | 0.337526 | + | 0.194871i | 0.659178 | − | 0.751987i | \(-0.270905\pi\) |
−0.321651 | + | 0.946858i | \(0.604238\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.2474 | + | 7.07107i | 1.34433 | + | 0.776151i | 0.987440 | − | 0.157995i | \(-0.0505030\pi\) |
0.356892 | + | 0.934146i | \(0.383836\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.00000 | − | 1.73205i | 0.325396 | − | 0.187867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 7.07107i | − | 0.749532i | −0.927119 | − | 0.374766i | \(-0.877723\pi\) | ||
0.927119 | − | 0.374766i | \(-0.122277\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.0000 | −1.25794 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.89898 | − | 8.48528i | −0.502625 | − | 0.870572i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.00000 | + | 6.92820i | −0.406138 | + | 0.703452i | −0.994453 | − | 0.105180i | \(-0.966458\pi\) |
0.588315 | + | 0.808632i | \(0.299792\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.22474 | − | 2.12132i | 0.121867 | − | 0.211079i | −0.798637 | − | 0.601813i | \(-0.794445\pi\) |
0.920504 | + | 0.390734i | \(0.127779\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.00000 | − | 1.73205i | 0.295599 | − | 0.170664i | −0.344865 | − | 0.938652i | \(-0.612075\pi\) |
0.640464 | + | 0.767988i | \(0.278742\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3137i | 1.09374i | 0.837218 | + | 0.546869i | \(0.184180\pi\) | ||||
−0.837218 | + | 0.546869i | \(0.815820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.3923i | − | 0.995402i | −0.867349 | − | 0.497701i | \(-0.834178\pi\) | ||
0.867349 | − | 0.497701i | \(-0.165822\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.9217 | − | 9.19239i | 1.49779 | − | 0.864747i | 0.497789 | − | 0.867298i | \(-0.334145\pi\) |
0.999997 | + | 0.00255090i | \(0.000811977\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.00000 | + | 10.3923i | −0.559503 | + | 0.969087i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.44949 | + | 4.24264i | −0.224544 | + | 0.388922i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.50000 | − | 2.59808i | −0.136364 | − | 0.236189i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.79796 | −0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.3923i | − | 0.922168i | −0.887357 | − | 0.461084i | \(-0.847461\pi\) | ||
0.887357 | − | 0.461084i | \(-0.152539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.89898 | + | 2.82843i | −0.428026 | + | 0.247121i | −0.698505 | − | 0.715605i | \(-0.746151\pi\) |
0.270479 | + | 0.962726i | \(0.412818\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.0000 | + | 6.92820i | 1.04053 | + | 0.600751i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.57321 | − | 4.94975i | −0.732459 | − | 0.422885i | 0.0868620 | − | 0.996220i | \(-0.472316\pi\) |
−0.819321 | + | 0.573335i | \(0.805649\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.00000 | − | 3.46410i | −0.169638 | − | 0.293821i | 0.768655 | − | 0.639664i | \(-0.220926\pi\) |
−0.938293 | + | 0.345843i | \(0.887593\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.79796 | 0.819346 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | −0.498273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.57321 | − | 14.8492i | −0.702345 | − | 1.21650i | −0.967641 | − | 0.252330i | \(-0.918803\pi\) |
0.265296 | − | 0.964167i | \(-0.414530\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.00000 | + | 1.73205i | 0.244137 | + | 0.140952i | 0.617076 | − | 0.786903i | \(-0.288317\pi\) |
−0.372940 | + | 0.927855i | \(0.621650\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.34847 | − | 4.24264i | −0.590243 | − | 0.340777i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.0000 | + | 6.92820i | −0.957704 | + | 0.552931i | −0.895466 | − | 0.445130i | \(-0.853157\pi\) |
−0.0622385 | + | 0.998061i | \(0.519824\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 16.9706i | − | 1.33747i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.0000 | 1.25322 | 0.626608 | − | 0.779334i | \(-0.284443\pi\) | ||||
0.626608 | + | 0.779334i | \(0.284443\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.79796 | − | 16.9706i | −0.758189 | − | 1.31322i | −0.943773 | − | 0.330593i | \(-0.892751\pi\) |
0.185584 | − | 0.982628i | \(-0.440582\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | + | 0.866025i | −0.0384615 | + | 0.0666173i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.22474 | − | 2.12132i | 0.0931156 | − | 0.161281i | −0.815705 | − | 0.578468i | \(-0.803651\pi\) |
0.908821 | + | 0.417187i | \(0.136984\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.00000 | + | 1.73205i | −0.226779 | + | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 5.65685i | − | 0.422813i | −0.977398 | − | 0.211407i | \(-0.932196\pi\) | ||
0.977398 | − | 0.211407i | \(-0.0678044\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.3923i | 0.772454i | 0.922404 | + | 0.386227i | \(0.126222\pi\) | ||||
−0.922404 | + | 0.386227i | \(0.873778\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.00000 | − | 3.46410i | 0.146254 | − | 0.253320i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.79796 | − | 16.9706i | 0.708955 | − | 1.22795i | −0.256290 | − | 0.966600i | \(-0.582500\pi\) |
0.965245 | − | 0.261347i | \(-0.0841666\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.00000 | − | 12.1244i | −0.503871 | − | 0.872730i | −0.999990 | − | 0.00447566i | \(-0.998575\pi\) |
0.496119 | − | 0.868255i | \(-0.334758\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.34847 | 0.523557 | 0.261778 | − | 0.965128i | \(-0.415691\pi\) | ||||
0.261778 | + | 0.965128i | \(0.415691\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 10.3923i | − | 0.736691i | −0.929689 | − | 0.368345i | \(-0.879924\pi\) | ||
0.929689 | − | 0.368345i | \(-0.120076\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.34847 | − | 4.24264i | 0.515761 | − | 0.297775i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.00000 | − | 1.73205i | −0.209529 | − | 0.120972i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.79796 | − | 5.65685i | −0.677739 | − | 0.391293i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000 | + | 17.3205i | 0.688428 | + | 1.19239i | 0.972346 | + | 0.233544i | \(0.0750324\pi\) |
−0.283918 | + | 0.958849i | \(0.591634\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.5959 | −1.33643 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0000 | 0.814613 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.44949 | − | 4.24264i | −0.164771 | − | 0.285391i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.0000 | − | 8.66025i | −1.00447 | − | 0.579934i | −0.0949052 | − | 0.995486i | \(-0.530255\pi\) |
−0.909569 | + | 0.415553i | \(0.863588\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.44949 | − | 1.41421i | −0.162578 | − | 0.0938647i | 0.416503 | − | 0.909134i | \(-0.363255\pi\) |
−0.579082 | + | 0.815270i | \(0.696589\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.0000 | − | 8.66025i | 0.991228 | − | 0.572286i | 0.0855868 | − | 0.996331i | \(-0.472724\pi\) |
0.905641 | + | 0.424045i | \(0.139390\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.41421i | 0.0926482i | 0.998926 | + | 0.0463241i | \(0.0147507\pi\) | ||||
−0.998926 | + | 0.0463241i | \(0.985249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.0000 | −0.782794 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.89898 | + | 8.48528i | 0.316889 | + | 0.548867i | 0.979837 | − | 0.199798i | \(-0.0640285\pi\) |
−0.662949 | + | 0.748665i | \(0.730695\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | − | 24.2487i | 0.901819 | − | 1.56200i | 0.0766885 | − | 0.997055i | \(-0.475565\pi\) |
0.825131 | − | 0.564942i | \(-0.191101\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.12372 | − | 10.6066i | 0.391230 | − | 0.677631i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.0000 | + | 6.92820i | −0.763542 | + | 0.440831i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 14.1421i | − | 0.892644i | −0.894873 | − | 0.446322i | \(-0.852734\pi\) | ||
0.894873 | − | 0.446322i | \(-0.147266\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.8564i | 0.871145i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.8207 | + | 12.0208i | −1.29876 | + | 0.749838i | −0.980189 | − | 0.198062i | \(-0.936535\pi\) |
−0.318568 | + | 0.947900i | \(0.603202\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.89898 | + | 8.48528i | −0.302084 | + | 0.523225i | −0.976608 | − | 0.215028i | \(-0.931016\pi\) |
0.674524 | + | 0.738253i | \(0.264349\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.00000 | + | 15.5885i | 0.552866 | + | 0.957591i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.34847 | −0.448044 | −0.224022 | − | 0.974584i | \(-0.571919\pi\) | ||||
−0.224022 | + | 0.974584i | \(0.571919\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.1769i | 1.89386i | 0.321436 | + | 0.946931i | \(0.395835\pi\) | ||||
−0.321436 | + | 0.946931i | \(0.604165\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.44949 | − | 1.41421i | 0.147710 | − | 0.0852803i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.0000 | + | 8.66025i | 0.901263 | + | 0.520344i | 0.877610 | − | 0.479376i | \(-0.159137\pi\) |
0.0236530 | + | 0.999720i | \(0.492470\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.8207 | + | 12.0208i | 1.24206 | + | 0.717102i | 0.969513 | − | 0.245042i | \(-0.0788016\pi\) |
0.272544 | + | 0.962143i | \(0.412135\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.00000 | − | 13.8564i | −0.475551 | − | 0.823678i | 0.524057 | − | 0.851683i | \(-0.324418\pi\) |
−0.999608 | + | 0.0280052i | \(0.991084\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.89898 | 0.289178 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.0000 | 0.882353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.4722 | + | 23.3345i | 0.787054 | + | 1.36322i | 0.927764 | + | 0.373167i | \(0.121728\pi\) |
−0.140710 | + | 0.990051i | \(0.544939\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.0000 | − | 13.8564i | −1.39733 | − | 0.806751i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.6969 | + | 8.48528i | 0.849946 | + | 0.490716i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.0000 | − | 13.8564i | 1.38334 | − | 0.798670i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 33.9411i | 1.94346i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00000 | 0.228292 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.89898 | + | 8.48528i | 0.277796 | + | 0.481156i | 0.970837 | − | 0.239742i | \(-0.0770629\pi\) |
−0.693041 | + | 0.720898i | \(0.743730\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.00000 | − | 8.66025i | 0.282617 | − | 0.489506i | −0.689412 | − | 0.724370i | \(-0.742131\pi\) |
0.972028 | + | 0.234863i | \(0.0754642\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.12372 | + | 10.6066i | −0.343943 | + | 0.595726i | −0.985161 | − | 0.171632i | \(-0.945096\pi\) |
0.641218 | + | 0.767358i | \(0.278429\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.00000 | + | 3.46410i | −0.335936 | + | 0.193952i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.65685i | 0.314756i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 3.46410i | − | 0.192154i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.6969 | − | 8.48528i | 0.810268 | − | 0.467809i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.00000 | + | 3.46410i | −0.109930 | + | 0.190404i | −0.915742 | − | 0.401768i | \(-0.868396\pi\) |
0.805812 | + | 0.592172i | \(0.201729\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.89898 | + | 8.48528i | −0.267660 | + | 0.463600i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000 | + | 3.46410i | 0.108947 | + | 0.188702i | 0.915344 | − | 0.402673i | \(-0.131919\pi\) |
−0.806397 | + | 0.591375i | \(0.798585\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.79796 | −0.530589 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6.92820i | − | 0.374088i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.2474 | + | 7.07107i | −0.657477 | + | 0.379595i | −0.791315 | − | 0.611408i | \(-0.790603\pi\) |
0.133838 | + | 0.991003i | \(0.457270\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.0000 | + | 13.8564i | 1.28469 | + | 0.741716i | 0.977702 | − | 0.209997i | \(-0.0673454\pi\) |
0.306988 | + | 0.951713i | \(0.400679\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.4722 | + | 7.77817i | 0.717053 | + | 0.413990i | 0.813667 | − | 0.581331i | \(-0.197468\pi\) |
−0.0966144 | + | 0.995322i | \(0.530801\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.0000 | + | 31.1769i | 0.955341 | + | 1.65470i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.6969 | 0.775675 | 0.387837 | − | 0.921728i | \(-0.373222\pi\) | ||||
0.387837 | + | 0.921728i | \(0.373222\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.89898 | + | 8.48528i | 0.256424 | + | 0.444140i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.0000 | + | 12.1244i | 1.09619 | + | 0.632886i | 0.935218 | − | 0.354073i | \(-0.115203\pi\) |
0.160973 | + | 0.986959i | \(0.448537\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.0454 | − | 12.7279i | −1.14454 | − | 0.660801i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.0000 | + | 6.92820i | −0.621336 | + | 0.358729i | −0.777389 | − | 0.629020i | \(-0.783456\pi\) |
0.156053 | + | 0.987749i | \(0.450123\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.48528i | 0.437014i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.00000 | 0.205466 | 0.102733 | − | 0.994709i | \(-0.467241\pi\) | ||||
0.102733 | + | 0.994709i | \(0.467241\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.89898 | + | 8.48528i | 0.250326 | + | 0.433578i | 0.963616 | − | 0.267292i | \(-0.0861288\pi\) |
−0.713289 | + | 0.700870i | \(0.752795\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.0000 | + | 20.7846i | −0.611577 | + | 1.05928i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.4722 | + | 23.3345i | −0.683067 | + | 1.18311i | 0.290973 | + | 0.956731i | \(0.406021\pi\) |
−0.974040 | + | 0.226376i | \(0.927312\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.00000 | − | 3.46410i | 0.303433 | − | 0.175187i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 8.48528i | − | 0.426941i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.22474 | − | 0.707107i | 0.0611608 | − | 0.0353112i | −0.469108 | − | 0.883141i | \(-0.655424\pi\) |
0.530269 | + | 0.847830i | \(0.322091\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.00000 | + | 10.3923i | −0.298881 | + | 0.517678i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.0000 | − | 27.7128i | −0.791149 | − | 1.37031i | −0.925256 | − | 0.379344i | \(-0.876150\pi\) |
0.134107 | − | 0.990967i | \(-0.457183\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 39.1918 | 1.92850 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 34.6410i | − | 1.70046i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.1464 | − | 9.89949i | 0.837658 | − | 0.483622i | −0.0188096 | − | 0.999823i | \(-0.505988\pi\) |
0.856467 | + | 0.516201i | \(0.172654\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.0000 | − | 12.1244i | −1.02348 | − | 0.590905i | −0.108368 | − | 0.994111i | \(-0.534563\pi\) |
−0.915109 | + | 0.403206i | \(0.867896\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.22474 | − | 0.707107i | −0.0594089 | − | 0.0342997i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.0000 | − | 41.5692i | −1.16144 | − | 2.01168i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.6969 | 0.707927 | 0.353963 | − | 0.935259i | \(-0.384834\pi\) | ||||
0.353963 | + | 0.935259i | \(0.384834\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.0000 | −1.05725 | −0.528626 | − | 0.848855i | \(-0.677293\pi\) | ||||
−0.528626 | + | 0.848855i | \(0.677293\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.79796 | − | 16.9706i | −0.468700 | − | 0.811812i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.00000 | + | 1.73205i | 0.143182 | + | 0.0826663i | 0.569880 | − | 0.821728i | \(-0.306990\pi\) |
−0.426698 | + | 0.904394i | \(0.640323\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.44949 | − | 1.41421i | −0.116379 | − | 0.0671913i | 0.440681 | − | 0.897664i | \(-0.354737\pi\) |
−0.557059 | + | 0.830473i | \(0.688070\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.0000 | + | 8.66025i | −0.711068 | + | 0.410535i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 24.0416i | − | 1.13459i | −0.823513 | − | 0.567297i | \(-0.807989\pi\) | ||
0.823513 | − | 0.567297i | \(-0.192011\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.00000 | −0.188353 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.6969 | + | 25.4558i | 0.689003 | + | 1.19339i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.00000 | + | 6.92820i | −0.187112 | + | 0.324088i | −0.944286 | − | 0.329125i | \(-0.893246\pi\) |
0.757174 | + | 0.653213i | \(0.226579\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.57321 | − | 14.8492i | 0.399294 | − | 0.691598i | −0.594345 | − | 0.804210i | \(-0.702588\pi\) |
0.993639 | + | 0.112612i | \(0.0359218\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.0000 | + | 8.66025i | −0.697109 | + | 0.402476i | −0.806270 | − | 0.591548i | \(-0.798517\pi\) |
0.109161 | + | 0.994024i | \(0.465184\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.7696i | 1.70149i | 0.525577 | + | 0.850746i | \(0.323849\pi\) | ||||
−0.525577 | + | 0.850746i | \(0.676151\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 13.8564i | − | 0.639829i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.5959 | + | 11.3137i | −0.901021 | + | 0.520205i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.00000 | + | 3.46410i | −0.0917663 | + | 0.158944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.2474 | + | 21.2132i | −0.559600 | + | 0.969256i | 0.437929 | + | 0.899009i | \(0.355712\pi\) |
−0.997530 | + | 0.0702467i | \(0.977621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.5959 | 0.889805 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 10.3923i | − | 0.470920i | −0.971884 | − | 0.235460i | \(-0.924340\pi\) | ||
0.971884 | − | 0.235460i | \(-0.0756597\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.2929 | + | 19.7990i | −1.54761 | + | 0.893516i | −0.549292 | + | 0.835631i | \(0.685102\pi\) |
−0.998323 | + | 0.0578852i | \(0.981564\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.00000 | + | 1.73205i | 0.135113 | + | 0.0780076i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −44.0908 | − | 25.4558i | −1.97774 | − | 1.14185i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.0000 | + | 27.7128i | 0.716258 | + | 1.24060i | 0.962472 | + | 0.271380i | \(0.0874801\pi\) |
−0.246214 | + | 0.969216i | \(0.579187\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.6969 | 0.655304 | 0.327652 | − | 0.944798i | \(-0.393743\pi\) | ||||
0.327652 | + | 0.944798i | \(0.393743\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.00000 | −0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.8207 | + | 36.0624i | 0.922860 | + | 1.59844i | 0.794968 | + | 0.606652i | \(0.207488\pi\) |
0.127892 | + | 0.991788i | \(0.459179\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0000 | − | 6.92820i | −0.530849 | − | 0.306486i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.34847 | − | 4.24264i | −0.323812 | − | 0.186953i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0000 | + | 6.92820i | −0.527759 | + | 0.304702i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.8701i | 1.17720i | 0.808425 | + | 0.588599i | \(0.200320\pi\) | ||||
−0.808425 | + | 0.588599i | \(0.799680\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.0000 | −0.874539 | −0.437269 | − | 0.899331i | \(-0.644054\pi\) | ||||
−0.437269 | + | 0.899331i | \(0.644054\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.44949 | + | 4.24264i | 0.106701 | + | 0.184812i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.44949 | + | 4.24264i | −0.106099 | + | 0.183769i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.0000 | − | 13.8564i | 1.03761 | − | 0.599065i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 14.1421i | − | 0.609145i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 10.3923i | − | 0.446800i | −0.974727 | − | 0.223400i | \(-0.928284\pi\) | ||
0.974727 | − | 0.223400i | \(-0.0717156\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −22.0454 | + | 12.7279i | −0.944322 | + | 0.545204i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.00000 | − | 6.92820i | 0.171028 | − | 0.296229i | −0.767752 | − | 0.640747i | \(-0.778625\pi\) |
0.938779 | + | 0.344519i | \(0.111958\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.89898 | − | 8.48528i | 0.208704 | − | 0.361485i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.00000 | + | 10.3923i | 0.255146 | + | 0.441926i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.34847 | −0.311365 | −0.155682 | − | 0.987807i | \(-0.549758\pi\) | ||||
−0.155682 | + | 0.987807i | \(0.549758\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.7128i | 1.17213i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.2474 | + | 7.07107i | −0.516168 | + | 0.298010i | −0.735366 | − | 0.677671i | \(-0.762990\pi\) |
0.219197 | + | 0.975681i | \(0.429656\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −39.0000 | − | 22.5167i | −1.64074 | − | 0.947283i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.57321 | − | 4.94975i | −0.359408 | − | 0.207504i | 0.309413 | − | 0.950928i | \(-0.399867\pi\) |
−0.668821 | + | 0.743423i | \(0.733201\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0000 | − | 34.6410i | −0.836974 | − | 1.44968i | −0.892413 | − | 0.451219i | \(-0.850989\pi\) |
0.0554391 | − | 0.998462i | \(-0.482344\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.89898 | 0.204302 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0000 | 0.582828 | 0.291414 | − | 0.956597i | \(-0.405874\pi\) | ||||
0.291414 | + | 0.956597i | \(0.405874\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.4949 | + | 42.4264i | 1.01622 | + | 1.76014i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.0000 | + | 10.3923i | 0.745484 | + | 0.430405i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.5959 | + | 11.3137i | 0.808810 | + | 0.466967i | 0.846542 | − | 0.532321i | \(-0.178680\pi\) |
−0.0377324 | + | 0.999288i | \(0.512013\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.0000 | − | 6.92820i | 0.494451 | − | 0.285472i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 7.07107i | − | 0.290374i | −0.989404 | − | 0.145187i | \(-0.953622\pi\) | ||
0.989404 | − | 0.145187i | \(-0.0463784\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.0000 | 0.491952 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.44949 | − | 4.24264i | −0.100083 | − | 0.173350i | 0.811635 | − | 0.584164i | \(-0.198578\pi\) |
−0.911719 | + | 0.410815i | \(0.865244\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.00000 | − | 8.66025i | 0.203954 | − | 0.353259i | −0.745845 | − | 0.666120i | \(-0.767954\pi\) |
0.949799 | + | 0.312861i | \(0.101287\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.67423 | + | 6.36396i | −0.149379 | + | 0.258732i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.0000 | − | 22.5167i | 1.58296 | − | 0.913923i | 0.588537 | − | 0.808470i | \(-0.299704\pi\) |
0.994424 | − | 0.105453i | \(-0.0336291\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.9706i | 0.686555i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.8207 | + | 12.0208i | −0.838208 | + | 0.483940i | −0.856655 | − | 0.515890i | \(-0.827461\pi\) |
0.0184465 | + | 0.999830i | \(0.494128\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.00000 | − | 6.92820i | 0.160774 | − | 0.278468i | −0.774373 | − | 0.632730i | \(-0.781934\pi\) |
0.935146 | + | 0.354262i | \(0.115268\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.2474 | − | 21.2132i | 0.490684 | − | 0.849889i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.1769i | 1.24113i | 0.784154 | + | 0.620567i | \(0.213097\pi\) | ||||
−0.784154 | + | 0.620567i | \(0.786903\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.0454 | + | 12.7279i | −0.874845 | + | 0.505092i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.0000 | − | 8.66025i | −0.594322 | − | 0.343132i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.4722 | + | 7.77817i | 0.532120 | + | 0.307219i | 0.741879 | − | 0.670534i | \(-0.233935\pi\) |
−0.209760 | + | 0.977753i | \(0.567268\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.0000 | + | 27.7128i | 0.630978 | + | 1.09289i | 0.987352 | + | 0.158543i | \(0.0506797\pi\) |
−0.356374 | + | 0.934344i | \(0.615987\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.6969 | 0.577796 | 0.288898 | − | 0.957360i | \(-0.406711\pi\) | ||||
0.288898 | + | 0.957360i | \(0.406711\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.0000 | −1.25611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.57321 | − | 14.8492i | −0.335496 | − | 0.581096i | 0.648084 | − | 0.761569i | \(-0.275570\pi\) |
−0.983580 | + | 0.180473i | \(0.942237\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.0000 | + | 6.92820i | 0.468879 | + | 0.270707i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.79796 | − | 5.65685i | −0.381674 | − | 0.220360i | 0.296872 | − | 0.954917i | \(-0.404056\pi\) |
−0.678546 | + | 0.734557i | \(0.737390\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.0000 | + | 6.92820i | −0.466746 | + | 0.269476i | −0.714877 | − | 0.699251i | \(-0.753517\pi\) |
0.248131 | + | 0.968727i | \(0.420184\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 33.9411i | − | 1.31618i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.0000 | −0.464642 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.5959 | + | 33.9411i | 0.756492 | + | 1.31028i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.00000 | + | 12.1244i | −0.269830 | + | 0.467360i | −0.968818 | − | 0.247774i | \(-0.920301\pi\) |
0.698988 | + | 0.715134i | \(0.253634\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.57321 | − | 14.8492i | 0.329495 | − | 0.570703i | −0.652916 | − | 0.757430i | \(-0.726455\pi\) |
0.982412 | + | 0.186727i | \(0.0597881\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.0000 | + | 13.8564i | −0.921035 | + | 0.531760i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.7696i | 1.40695i | 0.710721 | + | 0.703474i | \(0.248369\pi\) | ||||
−0.710721 | + | 0.703474i | \(0.751631\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.2487i | 0.926496i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.0454 | − | 12.7279i | 0.839863 | − | 0.484895i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.0000 | − | 27.7128i | 0.608669 | − | 1.05425i | −0.382791 | − | 0.923835i | \(-0.625037\pi\) |
0.991460 | − | 0.130410i | \(-0.0416295\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.89898 | + | 8.48528i | −0.185829 | + | 0.321865i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.00000 | + | 1.73205i | 0.0378777 | + | 0.0656061i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.34847 | 0.277548 | 0.138774 | − | 0.990324i | \(-0.455684\pi\) | ||||
0.138774 | + | 0.990324i | \(0.455684\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.34847 | − | 4.24264i | 0.276368 | − | 0.159561i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.00000 | − | 1.73205i | −0.112667 | − | 0.0650485i | 0.442607 | − | 0.896716i | \(-0.354054\pi\) |
−0.555275 | + | 0.831667i | \(0.687387\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.6969 | − | 8.48528i | −0.550405 | − | 0.317776i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0000 | − | 20.7846i | −0.448775 | − | 0.777300i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −44.0908 | −1.64431 | −0.822155 | − | 0.569264i | \(-0.807228\pi\) | ||||
−0.822155 | + | 0.569264i | \(0.807228\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000 | 0.446903 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.22474 | + | 2.12132i | 0.0454859 | + | 0.0787839i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.0000 | + | 12.1244i | 0.778847 | + | 0.449667i | 0.836021 | − | 0.548697i | \(-0.184876\pi\) |
−0.0571746 | + | 0.998364i | \(0.518209\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.79796 | + | 5.65685i | 0.362391 | + | 0.209226i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.0000 | − | 19.0526i | 1.21888 | − | 0.703722i | 0.254204 | − | 0.967151i | \(-0.418187\pi\) |
0.964679 | + | 0.263428i | \(0.0848533\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.3137i | 0.416746i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.0000 | 1.47142 | 0.735712 | − | 0.677295i | \(-0.236848\pi\) | ||||
0.735712 | + | 0.677295i | \(0.236848\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.5959 | + | 33.9411i | 0.718905 | + | 1.24518i | 0.961434 | + | 0.275035i | \(0.0886895\pi\) |
−0.242530 | + | 0.970144i | \(0.577977\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.0000 | + | 36.3731i | −0.769380 | + | 1.33261i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.5959 | + | 33.9411i | −0.716019 | + | 1.24018i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.00000 | − | 1.73205i | 0.109472 | − | 0.0632034i | −0.444265 | − | 0.895896i | \(-0.646535\pi\) |
0.553736 | + | 0.832692i | \(0.313202\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 8.48528i | − | 0.308811i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 10.3923i | − | 0.377715i | −0.982005 | − | 0.188857i | \(-0.939522\pi\) | ||
0.982005 | − | 0.188857i | \(-0.0604784\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.9217 | − | 9.19239i | 0.577161 | − | 0.333224i | −0.182844 | − | 0.983142i | \(-0.558530\pi\) |
0.760004 | + | 0.649918i | \(0.225197\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.0000 | − | 31.1769i | 0.651644 | − | 1.12868i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.5959 | + | 33.9411i | −0.707568 | + | 1.22554i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.00000 | − | 1.73205i | −0.0360609 | − | 0.0624593i | 0.847432 | − | 0.530904i | \(-0.178148\pi\) |
−0.883493 | + | 0.468445i | \(0.844814\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.0454 | 0.792918 | 0.396459 | − | 0.918052i | \(-0.370239\pi\) | ||||
0.396459 | + | 0.918052i | \(0.370239\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.46410i | 0.124434i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.89898 | − | 2.82843i | 0.175524 | − | 0.101339i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0000 | + | 20.7846i | 1.28818 | + | 0.743732i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 29.3939 | + | 16.9706i | 1.04911 | + | 0.605705i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.0000 | + | 17.3205i | 0.356462 | + | 0.617409i | 0.987367 | − | 0.158450i | \(-0.0506498\pi\) |
−0.630905 | + | 0.775860i | \(0.717316\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 63.6867 | 2.26444 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.0000 | 1.70453 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.12372 | + | 10.6066i | 0.216913 | + | 0.375705i | 0.953863 | − | 0.300243i | \(-0.0970677\pi\) |
−0.736949 | + | 0.675948i | \(0.763734\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.00000 | + | 3.46410i | 0.212265 | + | 0.122551i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.79796 | + | 5.65685i | 0.345762 | + | 0.199626i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −36.0000 | + | 20.7846i | −1.26883 | + | 0.732561i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.41421i | 0.0497211i | 0.999691 | + | 0.0248606i | \(0.00791417\pi\) | ||||
−0.999691 | + | 0.0248606i | \(0.992086\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.00000 | 0.140459 | 0.0702295 | − | 0.997531i | \(-0.477627\pi\) | ||||
0.0702295 | + | 0.997531i | \(0.477627\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.5959 | − | 33.9411i | −0.686415 | − | 1.18891i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.0000 | − | 27.7128i | 0.559769 | − | 0.969549i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.22474 | − | 2.12132i | 0.0427439 | − | 0.0740346i | −0.843862 | − | 0.536560i | \(-0.819723\pi\) |
0.886606 | + | 0.462526i | \(0.153057\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.0000 | + | 8.66025i | −0.522867 | + | 0.301877i | −0.738107 | − | 0.674684i | \(-0.764280\pi\) |
0.215240 | + | 0.976561i | \(0.430947\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 5.65685i | − | 0.196708i | −0.995151 | − | 0.0983540i | \(-0.968642\pi\) | ||
0.995151 | − | 0.0983540i | \(-0.0313578\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 10.3923i | − | 0.360940i | −0.983581 | − | 0.180470i | \(-0.942238\pi\) | ||
0.983581 | − | 0.180470i | \(-0.0577618\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.12372 | + | 3.53553i | −0.212174 | + | 0.122499i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.0000 | + | 41.5692i | −0.830554 | + | 1.43856i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.44949 | − | 4.24264i | 0.0845658 | − | 0.146472i | −0.820640 | − | 0.571445i | \(-0.806383\pi\) |
0.905206 | + | 0.424973i | \(0.139716\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.5000 | + | 19.9186i | 0.396552 | + | 0.686848i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.44949 | 0.0842650 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10.3923i | − | 0.357084i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.0000 | − | 6.92820i | −0.410872 | − | 0.237217i | 0.280292 | − | 0.959915i | \(-0.409569\pi\) |
−0.691164 | + | 0.722698i | \(0.742902\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.22474 | − | 0.707107i | −0.0418365 | − | 0.0241543i | 0.478936 | − | 0.877850i | \(-0.341023\pi\) |
−0.520772 | + | 0.853696i | \(0.674356\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.0000 | − | 34.6410i | −0.682391 | − | 1.18194i | −0.974249 | − | 0.225475i | \(-0.927607\pi\) |
0.291858 | − | 0.956462i | \(-0.405727\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | −0.204006 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.89898 | − | 8.48528i | −0.166186 | − | 0.287843i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0000 | + | 6.92820i | 0.406604 | + | 0.234753i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −29.3939 | − | 16.9706i | −0.993694 | − | 0.573710i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −48.0000 | + | 27.7128i | −1.62084 | + | 0.935795i | −0.634150 | + | 0.773210i | \(0.718650\pi\) |
−0.986694 | + | 0.162585i | \(0.948017\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.8406i | 1.47703i | 0.674238 | + | 0.738514i | \(0.264472\pi\) | ||||
−0.674238 | + | 0.738514i | \(0.735528\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.0000 | 1.34611 | 0.673054 | − | 0.739594i | \(-0.264982\pi\) | ||||
0.673054 | + | 0.739594i | \(0.264982\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.89898 | + | 8.48528i | 0.164492 | + | 0.284908i | 0.936475 | − | 0.350735i | \(-0.114068\pi\) |
−0.771983 | + | 0.635643i | \(0.780735\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0000 | − | 31.1769i | 0.603701 | − | 1.04564i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.79796 | − | 16.9706i | 0.327876 | − | 0.567898i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0000 | + | 6.92820i | −0.401116 | + | 0.231584i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 8.48528i | − | 0.283000i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 10.3923i | − | 0.346218i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.0454 | − | 12.7279i | 0.732814 | − | 0.423090i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.00000 | − | 6.92820i | 0.132818 | − | 0.230047i | −0.791944 | − | 0.610594i | \(-0.790931\pi\) |
0.924762 | + | 0.380547i | \(0.124264\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.5959 | + | 33.9411i | −0.649242 | + | 1.12452i | 0.334063 | + | 0.942551i | \(0.391580\pi\) |
−0.983304 | + | 0.181969i | \(0.941753\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.0000 | − | 34.6410i | −0.661903 | − | 1.14645i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19.5959 | −0.647114 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.3923i | 0.342811i | 0.985201 | + | 0.171405i | \(0.0548307\pi\) | ||||
−0.985201 | + | 0.171405i | \(0.945169\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 44.0908 | − | 25.4558i | 1.45127 | − | 0.837889i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.22474 | − | 0.707107i | −0.0401826 | − | 0.0231994i | 0.479774 | − | 0.877392i | \(-0.340719\pi\) |
−0.519957 | + | 0.854193i | \(0.674052\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.0000 | + | 17.3205i | 0.327737 | + | 0.567657i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.79796 | −0.320428 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.22474 | − | 2.12132i | −0.0399255 | − | 0.0691531i | 0.845372 | − | 0.534178i | \(-0.179379\pi\) |
−0.885298 | + | 0.465025i | \(0.846045\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.00000 | − | 3.46410i | −0.195387 | − | 0.112807i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.5959 | + | 11.3137i | 0.636782 | + | 0.367646i | 0.783374 | − | 0.621551i | \(-0.213497\pi\) |
−0.146592 | + | 0.989197i | \(0.546830\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.0000 | − | 6.92820i | 0.389536 | − | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.8701i | 0.870407i | 0.900332 | + | 0.435203i | \(0.143323\pi\) | ||||
−0.900332 | + | 0.435203i | \(0.856677\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −48.0000 | −1.55324 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.1464 | − | 29.6985i | −0.553687 | − | 0.959014i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.50000 | + | 16.4545i | −0.306452 | + | 0.530790i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.1464 | + | 29.6985i | −0.551963 | + | 0.956028i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.0000 | − | 22.5167i | 1.25416 | − | 0.724087i | 0.282223 | − | 0.959349i | \(-0.408928\pi\) |
0.971932 | + | 0.235262i | \(0.0755947\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 31.1127i | − | 0.998454i | −0.866471 | − | 0.499227i | \(-0.833617\pi\) | ||
0.866471 | − | 0.499227i | \(-0.166383\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 13.8564i | − | 0.444216i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.8207 | + | 12.0208i | −0.666112 | + | 0.384580i | −0.794602 | − | 0.607131i | \(-0.792320\pi\) |
0.128490 | + | 0.991711i | \(0.458987\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.0000 | + | 17.3205i | −0.319601 | + | 0.553566i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.4949 | − | 42.4264i | 0.781266 | − | 1.35319i | −0.149939 | − | 0.988695i | \(-0.547908\pi\) |
0.931205 | − | 0.364497i | \(-0.118759\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.00000 | − | 15.5885i | −0.286764 | − | 0.496690i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −39.1918 | −1.24623 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 51.9615i | − | 1.65061i | −0.564686 | − | 0.825306i | \(-0.691003\pi\) | ||
0.564686 | − | 0.825306i | \(-0.308997\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.0454 | + | 12.7279i | −0.698886 | + | 0.403502i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.0000 | − | 6.92820i | −0.380044 | − | 0.219418i | 0.297794 | − | 0.954630i | \(-0.403749\pi\) |
−0.677837 | + | 0.735212i | \(0.737083\pi\) | |||||||
\(998\) | 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 \(a_p\))