Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,3,Mod(269,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.269");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.t (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: | \(44.1418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.12960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.3 | ||
Root | \(-0.535233 + 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.269 |
Dual form | 1620.3.t.b.1349.3 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(5\) | 2.75495 | − | 4.17256i | 0.550990 | − | 0.834512i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.92820 | + | 4.00000i | 0.989743 | + | 0.571429i | 0.905198 | − | 0.424991i | \(-0.139723\pi\) |
0.0845458 | + | 0.996420i | \(0.473056\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.74597 | − | 4.47214i | −0.704179 | − | 0.406558i | 0.104723 | − | 0.994501i | \(-0.466604\pi\) |
−0.808902 | + | 0.587944i | \(0.799938\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.3923 | − | 6.00000i | 0.799408 | − | 0.461538i | −0.0438561 | − | 0.999038i | \(-0.513964\pi\) |
0.843264 | + | 0.537499i | \(0.180631\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −31.3050 | −1.84147 | −0.920734 | − | 0.390191i | \(-0.872409\pi\) | ||||
−0.920734 | + | 0.390191i | \(0.872409\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.00000 | −0.315789 | −0.157895 | − | 0.987456i | \(-0.550471\pi\) | ||||
−0.157895 | + | 0.987456i | \(0.550471\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.23607 | − | 3.87298i | −0.0972203 | − | 0.168391i | 0.813313 | − | 0.581827i | \(-0.197662\pi\) |
−0.910533 | + | 0.413436i | \(0.864328\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.82051 | − | 22.9904i | −0.392820 | − | 0.919615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −23.2379 | − | 13.4164i | −0.801307 | − | 0.462635i | 0.0426210 | − | 0.999091i | \(-0.486429\pi\) |
−0.843928 | + | 0.536457i | \(0.819763\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −17.0000 | − | 29.4449i | −0.548387 | − | 0.949834i | −0.998385 | − | 0.0568049i | \(-0.981909\pi\) |
0.449998 | − | 0.893029i | \(-0.351425\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 35.7771 | − | 17.8885i | 1.02220 | − | 0.511101i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 44.0000i | − | 1.18919i | −0.804026 | − | 0.594595i | \(-0.797313\pi\) | ||
0.804026 | − | 0.594595i | \(-0.202687\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −15.4919 | + | 8.94427i | −0.377852 | + | 0.218153i | −0.676883 | − | 0.736090i | \(-0.736670\pi\) |
0.299031 | + | 0.954243i | \(0.403337\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 24.2487 | + | 14.0000i | 0.563924 | + | 0.325581i | 0.754719 | − | 0.656048i | \(-0.227773\pi\) |
−0.190795 | + | 0.981630i | \(0.561107\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.23607 | + | 3.87298i | −0.0475759 | + | 0.0824039i | −0.888833 | − | 0.458232i | \(-0.848483\pi\) |
0.841257 | + | 0.540636i | \(0.181816\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.50000 | + | 12.9904i | 0.153061 | + | 0.265110i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 40.2492 | 0.759419 | 0.379710 | − | 0.925106i | \(-0.376024\pi\) | ||||
0.379710 | + | 0.925106i | \(0.376024\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −40.0000 | + | 20.0000i | −0.727273 | + | 0.363636i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −85.2056 | + | 49.1935i | −1.44416 | + | 0.833788i | −0.998124 | − | 0.0612253i | \(-0.980499\pi\) |
−0.446039 | + | 0.895013i | \(0.647166\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −37.0000 | + | 64.0859i | −0.606557 | + | 1.05059i | 0.385246 | + | 0.922814i | \(0.374117\pi\) |
−0.991803 | + | 0.127774i | \(0.959217\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.59492 | − | 59.8922i | 0.0553064 | − | 0.921419i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 79.6743 | − | 46.0000i | 1.18917 | − | 0.686567i | 0.231051 | − | 0.972942i | \(-0.425783\pi\) |
0.958118 | + | 0.286374i | \(0.0924501\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 53.6656i | − | 0.755854i | −0.925835 | − | 0.377927i | \(-0.876637\pi\) | ||
0.925835 | − | 0.377927i | \(-0.123363\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 56.0000i | 0.767123i | 0.923515 | + | 0.383562i | \(0.125303\pi\) | ||||
−0.923515 | + | 0.383562i | \(0.874697\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −35.7771 | − | 61.9677i | −0.464638 | − | 0.804776i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 39.0000 | − | 67.5500i | 0.493671 | − | 0.855063i | −0.506303 | − | 0.862356i | \(-0.668988\pi\) |
0.999973 | + | 0.00729288i | \(0.00232142\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 51.4296 | − | 89.0786i | 0.619633 | − | 1.07324i | −0.369919 | − | 0.929064i | \(-0.620615\pi\) |
0.989553 | − | 0.144172i | \(-0.0460520\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −86.2436 | + | 130.622i | −1.01463 | + | 1.53673i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.8885i | 0.200995i | 0.994937 | + | 0.100497i | \(0.0320434\pi\) | ||||
−0.994937 | + | 0.100497i | \(0.967957\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 96.0000 | 1.05495 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.5297 | + | 25.0354i | −0.173997 | + | 0.263530i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −27.7128 | − | 16.0000i | −0.285699 | − | 0.164948i | 0.350302 | − | 0.936637i | \(-0.386079\pi\) |
−0.636001 | + | 0.771689i | \(0.719412\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −131.681 | − | 76.0263i | −1.30378 | − | 0.752736i | −0.322727 | − | 0.946492i | \(-0.604600\pi\) |
−0.981050 | + | 0.193756i | \(0.937933\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −90.0666 | + | 52.0000i | −0.874433 | + | 0.504854i | −0.868819 | − | 0.495130i | \(-0.835120\pi\) |
−0.00561444 | + | 0.999984i | \(0.501787\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 147.580 | 1.37926 | 0.689628 | − | 0.724163i | \(-0.257774\pi\) | ||||
0.689628 | + | 0.724163i | \(0.257774\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 74.0000 | 0.678899 | 0.339450 | − | 0.940624i | \(-0.389759\pi\) | ||||
0.339450 | + | 0.940624i | \(0.389759\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.1246 | − | 34.8569i | −0.178094 | − | 0.308468i | 0.763134 | − | 0.646241i | \(-0.223660\pi\) |
−0.941228 | + | 0.337773i | \(0.890326\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −22.3205 | − | 1.33975i | −0.194091 | − | 0.0116500i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −216.887 | − | 125.220i | −1.82258 | − | 1.05227i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −20.5000 | − | 35.5070i | −0.169421 | − | 0.293447i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −122.984 | − | 22.3607i | −0.983870 | − | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0000i | 0.125984i | 0.998014 | + | 0.0629921i | \(0.0200643\pi\) | ||||
−0.998014 | + | 0.0629921i | \(0.979936\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −69.7137 | + | 40.2492i | −0.532166 | + | 0.307246i | −0.741898 | − | 0.670513i | \(-0.766074\pi\) |
0.209732 | + | 0.977759i | \(0.432741\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −41.5692 | − | 24.0000i | −0.312551 | − | 0.180451i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 87.2067 | − | 151.046i | 0.636545 | − | 1.10253i | −0.349641 | − | 0.936884i | \(-0.613696\pi\) |
0.986186 | − | 0.165644i | \(-0.0529703\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 59.0000 | + | 102.191i | 0.424460 | + | 0.735187i | 0.996370 | − | 0.0851297i | \(-0.0271305\pi\) |
−0.571909 | + | 0.820317i | \(0.693797\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −107.331 | −0.750568 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −120.000 | + | 60.0000i | −0.827586 | + | 0.413793i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −85.2056 | + | 49.1935i | −0.571850 | + | 0.330158i | −0.757888 | − | 0.652385i | \(-0.773769\pi\) |
0.186038 | + | 0.982543i | \(0.440435\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.0000 | + | 29.4449i | −0.112583 | + | 0.194999i | −0.916811 | − | 0.399322i | \(-0.869246\pi\) |
0.804228 | + | 0.594321i | \(0.202579\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −169.695 | − | 10.1856i | −1.09480 | − | 0.0657135i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 79.6743 | − | 46.0000i | 0.507480 | − | 0.292994i | −0.224317 | − | 0.974516i | \(-0.572015\pi\) |
0.731797 | + | 0.681523i | \(0.238682\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 35.7771i | − | 0.222218i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 68.0000i | − | 0.417178i | −0.978003 | − | 0.208589i | \(-0.933113\pi\) | ||
0.978003 | − | 0.208589i | \(-0.0668871\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 33.5410 | + | 58.0948i | 0.200844 | + | 0.347873i | 0.948801 | − | 0.315875i | \(-0.102298\pi\) |
−0.747956 | + | 0.663748i | \(0.768965\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5000 | + | 21.6506i | −0.0739645 | + | 0.128110i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −38.0132 | + | 65.8407i | −0.219729 | + | 0.380582i | −0.954725 | − | 0.297489i | \(-0.903851\pi\) |
0.734996 | + | 0.678072i | \(0.237184\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 23.9230 | − | 198.564i | 0.136703 | − | 1.13465i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 259.384i | − | 1.44907i | −0.689237 | − | 0.724536i | \(-0.742054\pi\) | ||
0.689237 | − | 0.724536i | \(-0.257946\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −166.000 | −0.917127 | −0.458564 | − | 0.888662i | \(-0.651636\pi\) | ||||
−0.458564 | + | 0.888662i | \(0.651636\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −183.593 | − | 121.218i | −0.992393 | − | 0.655231i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 242.487 | + | 140.000i | 1.29672 | + | 0.748663i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −185.903 | − | 107.331i | −0.973315 | − | 0.561944i | −0.0730699 | − | 0.997327i | \(-0.523280\pi\) |
−0.900245 | + | 0.435383i | \(0.856613\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 27.7128 | − | 16.0000i | 0.143590 | − | 0.0829016i | −0.426484 | − | 0.904495i | \(-0.640248\pi\) |
0.570074 | + | 0.821594i | \(0.306915\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.47214 | 0.0227012 | 0.0113506 | − | 0.999936i | \(-0.496387\pi\) | ||||
0.0113506 | + | 0.999936i | \(0.496387\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 114.000 | 0.572864 | 0.286432 | − | 0.958101i | \(-0.407531\pi\) | ||||
0.286432 | + | 0.958101i | \(0.407531\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −107.331 | − | 185.903i | −0.528725 | − | 0.915779i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.35898 | + | 89.2820i | −0.0261414 | + | 0.435522i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 46.4758 | + | 26.8328i | 0.222372 | + | 0.128387i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.00000 | + | 5.19615i | 0.0142180 | + | 0.0246263i | 0.873047 | − | 0.487636i | \(-0.162141\pi\) |
−0.858829 | + | 0.512263i | \(0.828807\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 125.220 | − | 62.6099i | 0.582418 | − | 0.291209i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 272.000i | − | 1.25346i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −325.331 | + | 187.830i | −1.47208 | + | 0.849908i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −235.559 | − | 136.000i | −1.05632 | − | 0.609865i | −0.131907 | − | 0.991262i | \(-0.542110\pi\) |
−0.924411 | + | 0.381397i | \(0.875443\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 122.984 | − | 213.014i | 0.541779 | − | 0.938388i | −0.457023 | − | 0.889455i | \(-0.651084\pi\) |
0.998802 | − | 0.0489334i | \(-0.0155822\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −77.0000 | − | 133.368i | −0.336245 | − | 0.582393i | 0.647479 | − | 0.762084i | \(-0.275824\pi\) |
−0.983723 | + | 0.179691i | \(0.942490\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 183.358 | 0.786942 | 0.393471 | − | 0.919337i | \(-0.371274\pi\) | ||||
0.393471 | + | 0.919337i | \(0.371274\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.0000 | + | 20.0000i | 0.0425532 | + | 0.0851064i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 154.919 | − | 89.4427i | 0.648198 | − | 0.374237i | −0.139567 | − | 0.990213i | \(-0.544571\pi\) |
0.787766 | + | 0.615975i | \(0.211238\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 103.000 | − | 178.401i | 0.427386 | − | 0.740254i | −0.569254 | − | 0.822162i | \(-0.692768\pi\) |
0.996640 | + | 0.0819076i | \(0.0261012\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 74.8653 | + | 4.49364i | 0.305572 | + | 0.0183414i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −62.3538 | + | 36.0000i | −0.252445 | + | 0.145749i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 26.8328i | − | 0.106904i | −0.998570 | − | 0.0534518i | \(-0.982978\pi\) | ||
0.998570 | − | 0.0534518i | \(-0.0170224\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 40.0000i | 0.158103i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.1246 | − | 34.8569i | −0.0783059 | − | 0.135630i | 0.824213 | − | 0.566280i | \(-0.191618\pi\) |
−0.902519 | + | 0.430650i | \(0.858284\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 176.000 | − | 304.841i | 0.679537 | − | 1.17699i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 105.095 | − | 182.030i | 0.399602 | − | 0.692130i | −0.594075 | − | 0.804410i | \(-0.702482\pi\) |
0.993677 | + | 0.112279i | \(0.0358152\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 110.885 | − | 167.942i | 0.418432 | − | 0.633744i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 134.164i | 0.498751i | 0.968407 | + | 0.249376i | \(0.0802254\pi\) | ||||
−0.968407 | + | 0.249376i | \(0.919775\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −398.000 | −1.46863 | −0.734317 | − | 0.678806i | \(-0.762498\pi\) | ||||
−0.734317 | + | 0.678806i | \(0.762498\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −26.7468 | + | 222.001i | −0.0972610 | + | 0.807278i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −252.879 | − | 146.000i | −0.912922 | − | 0.527076i | −0.0315519 | − | 0.999502i | \(-0.510045\pi\) |
−0.881370 | + | 0.472426i | \(0.843378\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 46.4758 | + | 26.8328i | 0.165394 | + | 0.0954904i | 0.580412 | − | 0.814323i | \(-0.302891\pi\) |
−0.415018 | + | 0.909813i | \(0.636225\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 45.0333 | − | 26.0000i | 0.159128 | − | 0.0918728i | −0.418321 | − | 0.908299i | \(-0.637381\pi\) |
0.577450 | + | 0.816426i | \(0.304048\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −143.108 | −0.498635 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 691.000 | 2.39100 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 194.538 | + | 336.950i | 0.663952 | + | 1.15000i | 0.979568 | + | 0.201112i | \(0.0644554\pi\) |
−0.315616 | + | 0.948887i | \(0.602211\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −29.4744 | + | 491.051i | −0.0999133 | + | 1.66458i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −46.4758 | − | 26.8328i | −0.155437 | − | 0.0897419i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 112.000 | + | 193.990i | 0.372093 | + | 0.644484i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 165.469 | + | 330.938i | 0.542521 | + | 1.08504i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 492.000i | 1.60261i | 0.598259 | + | 0.801303i | \(0.295859\pi\) | ||||
−0.598259 | + | 0.801303i | \(0.704141\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 418.282 | − | 241.495i | 1.34496 | − | 0.776512i | 0.357428 | − | 0.933941i | \(-0.383654\pi\) |
0.987530 | + | 0.157428i | \(0.0503203\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 491.902 | + | 284.000i | 1.57157 | + | 0.907348i | 0.995977 | + | 0.0896145i | \(0.0285635\pi\) |
0.575597 | + | 0.817734i | \(0.304770\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −306.341 | + | 530.599i | −0.966376 | + | 1.67381i | −0.260506 | + | 0.965472i | \(0.583889\pi\) |
−0.705871 | + | 0.708341i | \(0.749444\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 120.000 | + | 207.846i | 0.376176 | + | 0.651555i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 187.830 | 0.581516 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −240.000 | − | 180.000i | −0.738462 | − | 0.553846i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −30.9839 | + | 17.8885i | −0.0941759 | + | 0.0543725i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −101.000 | + | 174.937i | −0.305136 | + | 0.528511i | −0.977292 | − | 0.211899i | \(-0.932035\pi\) |
0.672156 | + | 0.740410i | \(0.265369\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 27.5610 | − | 459.174i | 0.0822717 | − | 1.37067i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −318.697 | + | 184.000i | −0.945689 | + | 0.545994i | −0.891739 | − | 0.452550i | \(-0.850515\pi\) |
−0.0539502 | + | 0.998544i | \(0.517181\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 304.105i | 0.891804i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 272.000i | − | 0.793003i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −127.456 | − | 220.760i | −0.367308 | − | 0.636196i | 0.621836 | − | 0.783148i | \(-0.286387\pi\) |
−0.989144 | + | 0.146952i | \(0.953054\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 59.0000 | − | 102.191i | 0.169054 | − | 0.292811i | −0.769033 | − | 0.639209i | \(-0.779262\pi\) |
0.938088 | + | 0.346398i | \(0.112595\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.6525 | − | 27.1109i | 0.0443413 | − | 0.0768014i | −0.843003 | − | 0.537909i | \(-0.819214\pi\) |
0.887344 | + | 0.461108i | \(0.152548\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −223.923 | − | 147.846i | −0.630769 | − | 0.416468i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 53.6656i | − | 0.149486i | −0.997203 | − | 0.0747432i | \(-0.976186\pi\) | ||
0.997203 | − | 0.0747432i | \(-0.0238137\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −325.000 | −0.900277 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 233.663 | + | 154.277i | 0.640174 | + | 0.422677i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −304.841 | − | 176.000i | −0.830629 | − | 0.479564i | 0.0234388 | − | 0.999725i | \(-0.492539\pi\) |
−0.854068 | + | 0.520161i | \(0.825872\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 278.855 | + | 160.997i | 0.751630 | + | 0.433954i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 114.315 | − | 66.0000i | 0.306475 | − | 0.176944i | −0.338873 | − | 0.940832i | \(-0.610046\pi\) |
0.645348 | + | 0.763889i | \(0.276712\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −321.994 | −0.854095 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 394.000 | 1.03958 | 0.519789 | − | 0.854295i | \(-0.326011\pi\) | ||||
0.519789 | + | 0.854295i | \(0.326011\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −38.0132 | − | 65.8407i | −0.0992511 | − | 0.171908i | 0.812124 | − | 0.583485i | \(-0.198311\pi\) |
−0.911375 | + | 0.411577i | \(0.864978\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −357.128 | − | 21.4359i | −0.927606 | − | 0.0556778i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 240.125 | + | 138.636i | 0.617288 | + | 0.356391i | 0.775812 | − | 0.630964i | \(-0.217340\pi\) |
−0.158524 | + | 0.987355i | \(0.550674\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 70.0000 | + | 121.244i | 0.179028 | + | 0.310086i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −174.413 | − | 348.827i | −0.441553 | − | 0.883105i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 652.000i | 1.64232i | 0.570700 | + | 0.821159i | \(0.306672\pi\) | ||||
−0.570700 | + | 0.821159i | \(0.693328\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 154.919 | − | 89.4427i | 0.386333 | − | 0.223049i | −0.294237 | − | 0.955732i | \(-0.595066\pi\) |
0.680570 | + | 0.732683i | \(0.261732\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −353.338 | − | 204.000i | −0.876770 | − | 0.506203i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −196.774 | + | 340.823i | −0.483474 | + | 0.837402i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 103.000 | + | 178.401i | 0.251834 | + | 0.436189i | 0.964031 | − | 0.265791i | \(-0.0856331\pi\) |
−0.712197 | + | 0.701980i | \(0.752300\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −787.096 | −1.90580 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −230.000 | − | 460.000i | −0.554217 | − | 1.10843i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 178.157 | − | 102.859i | 0.425196 | − | 0.245487i | −0.272102 | − | 0.962268i | \(-0.587719\pi\) |
0.697298 | + | 0.716781i | \(0.254385\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.0000 | − | 32.9090i | 0.0451306 | − | 0.0781686i | −0.842578 | − | 0.538575i | \(-0.818963\pi\) |
0.887708 | + | 0.460406i | \(0.152296\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 307.431 | + | 719.713i | 0.723366 | + | 1.69344i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −512.687 | + | 296.000i | −1.20067 | + | 0.693208i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 608.210i | − | 1.41116i | −0.708630 | − | 0.705581i | \(-0.750686\pi\) | ||
0.708630 | − | 0.705581i | \(-0.249314\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 272.000i | 0.628176i | 0.949394 | + | 0.314088i | \(0.101699\pi\) | ||||
−0.949394 | + | 0.314088i | \(0.898301\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.4164 | + | 23.2379i | 0.0307012 | + | 0.0531760i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 183.000 | − | 316.965i | 0.416856 | − | 0.722017i | −0.578765 | − | 0.815494i | \(-0.696465\pi\) |
0.995621 | + | 0.0934778i | \(0.0297984\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −288.453 | + | 499.615i | −0.651135 | + | 1.12780i | 0.331713 | + | 0.943380i | \(0.392373\pi\) |
−0.982848 | + | 0.184418i | \(0.940960\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 74.6410 | + | 49.2820i | 0.167733 | + | 0.110746i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 429.325i | 0.956181i | 0.878311 | + | 0.478090i | \(0.158671\pi\) | ||||
−0.878311 | + | 0.478090i | \(0.841329\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 160.000 | 0.354767 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 264.475 | − | 400.566i | 0.581264 | − | 0.880364i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 90.0666 | + | 52.0000i | 0.197082 | + | 0.113786i | 0.595294 | − | 0.803508i | \(-0.297036\pi\) |
−0.398211 | + | 0.917294i | \(0.630369\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 441.520 | + | 254.912i | 0.957744 | + | 0.552954i | 0.895478 | − | 0.445106i | \(-0.146834\pi\) |
0.0622662 | + | 0.998060i | \(0.480167\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 83.1384 | − | 48.0000i | 0.179565 | − | 0.103672i | −0.407523 | − | 0.913195i | \(-0.633608\pi\) |
0.587088 | + | 0.809523i | \(0.300274\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 147.580 | 0.316018 | 0.158009 | − | 0.987438i | \(-0.449492\pi\) | ||||
0.158009 | + | 0.987438i | \(0.449492\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 736.000 | 1.56930 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −125.220 | − | 216.887i | −0.264735 | − | 0.458535i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 58.9230 | + | 137.942i | 0.124049 | + | 0.290405i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 495.742 | + | 286.217i | 1.03495 | + | 0.597530i | 0.918399 | − | 0.395655i | \(-0.129482\pi\) |
0.116552 | + | 0.993185i | \(0.462816\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −264.000 | − | 457.261i | −0.548857 | − | 0.950647i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −143.108 | + | 71.5542i | −0.295069 | + | 0.147534i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 648.000i | − | 1.33060i | −0.746578 | − | 0.665298i | \(-0.768305\pi\) | ||
0.746578 | − | 0.665298i | \(-0.231695\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −116.190 | + | 67.0820i | −0.236638 | + | 0.136623i | −0.613631 | − | 0.789593i | \(-0.710292\pi\) |
0.376992 | + | 0.926216i | \(0.376958\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 727.461 | + | 420.000i | 1.47558 | + | 0.851927i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 214.663 | − | 371.806i | 0.431917 | − | 0.748101i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 243.000 | + | 420.888i | 0.486974 | + | 0.843464i | 0.999888 | − | 0.0149764i | \(-0.00476733\pi\) |
−0.512914 | + | 0.858440i | \(0.671434\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 791.568 | 1.57369 | 0.786847 | − | 0.617148i | \(-0.211712\pi\) | ||||
0.786847 | + | 0.617148i | \(0.211712\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −680.000 | + | 340.000i | −1.34653 | + | 0.673267i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.2379 | − | 13.4164i | 0.0456540 | − | 0.0263584i | −0.476999 | − | 0.878904i | \(-0.658276\pi\) |
0.522653 | + | 0.852545i | \(0.324942\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −224.000 | + | 387.979i | −0.438356 | + | 0.759255i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −31.1559 | + | 519.066i | −0.0604970 | + | 1.00789i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.6410 | − | 20.0000i | 0.0670039 | − | 0.0386847i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 983.870i | 1.88843i | 0.329336 | + | 0.944213i | \(0.393175\pi\) | ||||
−0.329336 | + | 0.944213i | \(0.606825\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 292.000i | 0.558317i | 0.960245 | + | 0.279159i | \(0.0900556\pi\) | ||||
−0.960245 | + | 0.279159i | \(0.909944\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 532.184 | + | 921.770i | 1.00984 | + | 1.74909i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 254.500 | − | 440.807i | 0.481096 | − | 0.833283i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −107.331 | + | 185.903i | −0.201372 | + | 0.348786i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 406.577 | − | 615.788i | 0.759957 | − | 1.15101i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 134.164i | − | 0.248913i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −86.0000 | −0.158965 | −0.0794824 | − | 0.996836i | \(-0.525327\pi\) | ||||
−0.0794824 | + | 0.996836i | \(0.525327\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 203.866 | − | 308.769i | 0.374067 | − | 0.566549i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 142.028 | + | 82.0000i | 0.259649 | + | 0.149909i | 0.624175 | − | 0.781285i | \(-0.285435\pi\) |
−0.364525 | + | 0.931193i | \(0.618769\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 139.427 | + | 80.4984i | 0.253044 | + | 0.146095i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 540.400 | − | 312.000i | 0.977215 | − | 0.564195i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 362.243 | 0.650347 | 0.325173 | − | 0.945654i | \(-0.394577\pi\) | ||||
0.325173 | + | 0.945654i | \(0.394577\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 336.000 | 0.601073 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 498.643 | + | 863.675i | 0.885689 | + | 1.53406i | 0.844921 | + | 0.534890i | \(0.179647\pi\) |
0.0407680 | + | 0.999169i | \(0.487020\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −200.885 | − | 12.0577i | −0.355548 | − | 0.0213411i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 542.218 | + | 313.050i | 0.952931 | + | 0.550175i | 0.893990 | − | 0.448087i | \(-0.147894\pi\) |
0.0589407 | + | 0.998261i | \(0.481228\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −197.000 | − | 341.214i | −0.345009 | − | 0.597573i | 0.640347 | − | 0.768086i | \(-0.278791\pi\) |
−0.985355 | + | 0.170513i | \(0.945457\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −67.0820 | + | 89.4427i | −0.116664 | + | 0.155553i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 608.000i | − | 1.05373i | −0.849950 | − | 0.526863i | \(-0.823368\pi\) | ||
0.849950 | − | 0.526863i | \(-0.176632\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 712.629 | − | 411.437i | 1.22656 | − | 0.708152i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −311.769 | − | 180.000i | −0.534767 | − | 0.308748i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 355.535 | − | 615.804i | 0.605681 | − | 1.04907i | −0.386262 | − | 0.922389i | \(-0.626234\pi\) |
0.991943 | − | 0.126681i | \(-0.0404326\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 102.000 | + | 176.669i | 0.173175 | + | 0.299948i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −603.738 | −1.01811 | −0.509054 | − | 0.860734i | \(-0.670005\pi\) | ||||
−0.509054 | + | 0.860734i | \(0.670005\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1120.00 | + | 560.000i | −1.88235 | + | 0.941176i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 46.4758 | − | 26.8328i | 0.0775890 | − | 0.0447960i | −0.460704 | − | 0.887554i | \(-0.652403\pi\) |
0.538293 | + | 0.842758i | \(0.319070\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −217.000 | + | 375.855i | −0.361065 | + | 0.625383i | −0.988136 | − | 0.153579i | \(-0.950920\pi\) |
0.627071 | + | 0.778962i | \(0.284253\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −204.632 | − | 12.2826i | −0.338234 | − | 0.0203019i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 568.113 | − | 328.000i | 0.935935 | − | 0.540362i | 0.0472514 | − | 0.998883i | \(-0.484954\pi\) |
0.888684 | + | 0.458521i | \(0.151620\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 53.6656i | 0.0878325i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 844.000i | − | 1.37684i | −0.725315 | − | 0.688418i | \(-0.758306\pi\) | ||
0.725315 | − | 0.688418i | \(-0.241694\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 230.315 | + | 398.917i | 0.373282 | + | 0.646543i | 0.990068 | − | 0.140587i | \(-0.0448991\pi\) |
−0.616786 | + | 0.787131i | \(0.711566\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 523.000 | − | 905.863i | 0.844911 | − | 1.46343i | −0.0407872 | − | 0.999168i | \(-0.512987\pi\) |
0.885698 | − | 0.464261i | \(-0.153680\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −71.5542 | + | 123.935i | −0.114854 | + | 0.198933i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −432.115 | + | 451.554i | −0.691384 | + | 0.722487i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1377.42i | 2.18985i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.0000 | −0.0729002 | −0.0364501 | − | 0.999335i | \(-0.511605\pi\) | ||||
−0.0364501 | + | 0.999335i | \(0.511605\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 66.7610 | + | 44.0792i | 0.105135 | + | 0.0694160i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 155.885 | + | 90.0000i | 0.244717 | + | 0.141287i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 991.484 | + | 572.433i | 1.54678 | + | 0.893032i | 0.998385 | + | 0.0568101i | \(0.0180930\pi\) |
0.548391 | + | 0.836222i | \(0.315240\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −696.284 | + | 402.000i | −1.08287 | + | 0.625194i | −0.931669 | − | 0.363309i | \(-0.881647\pi\) |
−0.151200 | + | 0.988503i | \(0.548314\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 576.906 | 0.891662 | 0.445831 | − | 0.895117i | \(-0.352908\pi\) | ||||
0.445831 | + | 0.895117i | \(0.352908\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 880.000 | 1.35593 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −538.892 | − | 933.389i | −0.825256 | − | 1.42939i | −0.901723 | − | 0.432314i | \(-0.857697\pi\) |
0.0764669 | − | 0.997072i | \(-0.475636\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.1154 | + | 401.769i | −0.0368174 | + | 0.613388i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −704.883 | − | 406.964i | −1.06963 | − | 0.617548i | −0.141546 | − | 0.989932i | \(-0.545207\pi\) |
−0.928079 | + | 0.372383i | \(0.878541\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −541.000 | − | 937.039i | −0.818457 | − | 1.41761i | −0.906819 | − | 0.421520i | \(-0.861497\pi\) |
0.0883620 | − | 0.996088i | \(-0.471837\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −214.663 | + | 107.331i | −0.322801 | + | 0.161400i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 120.000i | 0.179910i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 573.202 | − | 330.938i | 0.854250 | − | 0.493201i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −914.523 | − | 528.000i | −1.35887 | − | 0.784547i | −0.369403 | − | 0.929269i | \(-0.620438\pi\) |
−0.989472 | + | 0.144723i | \(0.953771\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −306.341 | + | 530.599i | −0.452498 | + | 0.783750i | −0.998541 | − | 0.0540077i | \(-0.982800\pi\) |
0.546042 | + | 0.837758i | \(0.316134\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −128.000 | − | 221.703i | −0.188513 | − | 0.326513i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −317.522 | −0.464893 | −0.232446 | − | 0.972609i | \(-0.574673\pi\) | ||||
−0.232446 | + | 0.972609i | \(0.574673\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −390.000 | − | 780.000i | −0.569343 | − | 1.13869i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 418.282 | − | 241.495i | 0.607086 | − | 0.350501i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −461.000 | + | 798.475i | −0.667149 | + | 1.15554i | 0.311549 | + | 0.950230i | \(0.399152\pi\) |
−0.978698 | + | 0.205306i | \(0.934181\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 588.940 | + | 35.3500i | 0.847396 | + | 0.0508633i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 484.974 | − | 280.000i | 0.695802 | − | 0.401722i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 474.046i | − | 0.676243i | −0.941102 | − | 0.338122i | \(-0.890209\pi\) | ||
0.941102 | − | 0.338122i | \(-0.109791\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 264.000i | 0.375533i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −608.210 | − | 1053.45i | −0.860269 | − | 1.49003i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 483.000 | − | 836.581i | 0.681241 | − | 1.17994i | −0.293361 | − | 0.956002i | \(-0.594774\pi\) |
0.974602 | − | 0.223943i | \(-0.0718928\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −76.0263 | + | 131.681i | −0.106629 | + | 0.184686i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −295.692 | + | 447.846i | −0.413556 | + | 0.626358i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1109.09i | − | 1.54254i | −0.636505 | − | 0.771272i | \(-0.719621\pi\) | ||
0.636505 | − | 0.771272i | \(-0.280379\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −832.000 | −1.15395 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −80.2403 | + | 666.004i | −0.110676 | + | 0.918626i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 353.338 | + | 204.000i | 0.486023 | + | 0.280605i | 0.722923 | − | 0.690929i | \(-0.242798\pi\) |
−0.236900 | + | 0.971534i | \(0.576132\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −759.105 | − | 438.269i | −1.03845 | − | 0.599548i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −142.028 | + | 82.0000i | −0.193763 | + | 0.111869i | −0.593743 | − | 0.804655i | \(-0.702350\pi\) |
0.399980 | + | 0.916524i | \(0.369017\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −822.873 | −1.11652 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1082.00 | 1.46414 | 0.732070 | − | 0.681229i | \(-0.238554\pi\) | ||||
0.732070 | + | 0.681229i | \(0.238554\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 570.197 | + | 987.611i | 0.767426 | + | 1.32922i | 0.938955 | + | 0.344041i | \(0.111796\pi\) |
−0.171529 | + | 0.985179i | \(0.554871\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29.4744 | + | 491.051i | −0.0395630 | + | 0.659129i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1022.47 | + | 590.322i | 1.36511 | + | 0.788147i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 479.000 | + | 829.652i | 0.637816 | + | 1.10473i | 0.985911 | + | 0.167271i | \(0.0534954\pi\) |
−0.348095 | + | 0.937459i | \(0.613171\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 76.0263 | + | 152.053i | 0.100697 | + | 0.201394i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 772.000i | 1.01982i | 0.860229 | + | 0.509908i | \(0.170320\pi\) | ||||
−0.860229 | + | 0.509908i | \(0.829680\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −975.992 | + | 563.489i | −1.28251 | + | 0.740459i | −0.977307 | − | 0.211828i | \(-0.932058\pi\) |
−0.305205 | + | 0.952287i | \(0.598725\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 512.687 | + | 296.000i | 0.671936 | + | 0.387942i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −590.322 | + | 1022.47i | −0.769651 | + | 1.33307i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 663.000 | + | 1148.35i | 0.862159 | + | 1.49330i | 0.869841 | + | 0.493332i | \(0.164221\pi\) |
−0.00768240 | + | 0.999970i | \(0.502445\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 147.580 | 0.190919 | 0.0954596 | − | 0.995433i | \(-0.469568\pi\) | ||||
0.0954596 | + | 0.995433i | \(0.469568\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −510.000 | + | 680.000i | −0.658065 | + | 0.877419i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 92.9516 | − | 53.6656i | 0.119322 | − | 0.0688904i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −240.000 | + | 415.692i | −0.307298 | + | 0.532256i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27.5610 | − | 459.174i | 0.0351096 | − | 0.584935i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 980.341 | − | 566.000i | 1.24567 | − | 0.719187i | 0.275426 | − | 0.961322i | \(-0.411181\pi\) |
0.970242 | + | 0.242136i | \(0.0778479\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 321.994i | − | 0.407072i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 888.000i | 1.11980i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −306.341 | − | 530.599i | −0.384368 | − | 0.665745i | 0.607313 | − | 0.794462i | \(-0.292247\pi\) |
−0.991681 | + | 0.128718i | \(0.958914\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 70.0000 | − | 121.244i | 0.0876095 | − | 0.151744i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 250.440 | − | 433.774i | 0.311880 | − | 0.540192i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −149.282 | − | 98.5641i | −0.185444 | − | 0.122440i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1234.31i | − | 1.52572i | −0.646562 | − | 0.762861i | \(-0.723794\pi\) | ||
0.646562 | − | 0.762861i | \(-0.276206\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 874.000 | 1.07768 | 0.538841 | − | 0.842408i | \(-0.318862\pi\) | ||||
0.538841 | + | 0.842408i | \(0.318862\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −283.734 | − | 187.337i | −0.348140 | − | 0.229861i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −145.492 | − | 84.0000i | −0.178081 | − | 0.102815i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −224.633 | − | 129.692i | −0.273609 | − | 0.157968i | 0.356918 | − | 0.934136i | \(-0.383828\pi\) |
−0.630527 | + | 0.776168i | \(0.717161\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1184.72 | + | 684.000i | −1.43952 | + | 0.831106i | −0.997816 | − | 0.0660564i | \(-0.978958\pi\) |
−0.441701 | + | 0.897162i | \(0.645625\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −460.630 | −0.556989 | −0.278495 | − | 0.960438i | \(-0.589835\pi\) | ||||
−0.278495 | + | 0.960438i | \(0.589835\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1002.00 | 1.20869 | 0.604343 | − | 0.796725i | \(-0.293436\pi\) | ||||
0.604343 | + | 0.796725i | \(0.293436\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −234.787 | − | 406.663i | −0.281857 | − | 0.488191i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 334.808 | + | 20.0962i | 0.400967 | + | 0.0240673i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −263.363 | − | 152.053i | −0.313901 | − | 0.181231i | 0.334770 | − | 0.942300i | \(-0.391341\pi\) |
−0.648671 | + | 0.761069i | \(0.724675\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −60.5000 | − | 104.789i | −0.0719382 | − | 0.124601i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 55.9017 | + | 111.803i | 0.0661559 | + | 0.132312i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 328.000i | − | 0.387249i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −170.411 | + | 98.3870i | −0.200248 | + | 0.115613i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −668.572 | − | 386.000i | −0.783789 | − | 0.452521i | 0.0539827 | − | 0.998542i | \(-0.482808\pi\) |
−0.837771 | + | 0.546021i | \(0.816142\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −449.450 | + | 778.470i | −0.524445 | + | 0.908366i | 0.475150 | + | 0.879905i | \(0.342394\pi\) |
−0.999595 | + | 0.0284609i | \(0.990939\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 139.000 | + | 240.755i | 0.161816 | + | 0.280274i | 0.935520 | − | 0.353274i | \(-0.114932\pi\) |
−0.773704 | + | 0.633547i | \(0.781598\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 576.906 | 0.668488 | 0.334244 | − | 0.942486i | \(-0.391519\pi\) | ||||
0.334244 | + | 0.942486i | \(0.391519\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 170.000 | + | 340.000i | 0.196532 | + | 0.393064i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −604.185 | + | 348.827i | −0.695265 | + | 0.401412i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 552.000 | − | 956.092i | 0.633754 | − | 1.09769i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −762.614 | − | 646.854i | −0.871558 | − | 0.739262i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −543.864 | + | 314.000i | −0.620141 | + | 0.358039i | −0.776924 | − | 0.629594i | \(-0.783221\pi\) |
0.156783 | + | 0.987633i | \(0.449888\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 536.656i | 0.609145i | 0.952489 | + | 0.304572i | \(0.0985135\pi\) | ||||
−0.952489 | + | 0.304572i | \(0.901486\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 948.000i | − | 1.07361i | −0.843705 | − | 0.536806i | \(-0.819631\pi\) | ||
0.843705 | − | 0.536806i | \(-0.180369\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 140.872 | + | 243.998i | 0.158819 | + | 0.275082i | 0.934443 | − | 0.356113i | \(-0.115898\pi\) |
−0.775624 | + | 0.631195i | \(0.782565\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −64.0000 | + | 110.851i | −0.0719910 | + | 0.124692i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.4164 | − | 23.2379i | 0.0150240 | − | 0.0260223i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1082.29 | − | 714.589i | −1.20927 | − | 0.798424i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 912.316i | 1.01481i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1260.00 | −1.39845 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −457.322 | + | 692.645i | −0.505328 | + | 0.765353i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −446.869 | − | 258.000i | −0.492689 | − | 0.284454i | 0.233000 | − | 0.972477i | \(-0.425146\pi\) |
−0.725689 | + | 0.688022i | \(0.758479\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −278.855 | − | 160.997i | −0.306097 | − | 0.176725i | 0.339081 | − | 0.940757i | \(-0.389884\pi\) |
−0.645179 | + | 0.764032i | \(0.723217\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −796.743 | + | 460.000i | −0.872665 | + | 0.503834i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −643.988 | −0.702277 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1314.00 | 1.42982 | 0.714908 | − | 0.699219i | \(-0.246469\pi\) | ||||
0.714908 | + | 0.699219i | \(0.246469\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −321.994 | − | 557.710i | −0.348856 | − | 0.604236i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1011.58 | + | 432.102i | −1.09360 | + | 0.467138i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1301.32 | − | 751.319i | −1.40078 | − | 0.808739i | −0.406305 | − | 0.913737i | \(-0.633183\pi\) |
−0.994472 | + | 0.104998i | \(0.966516\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −45.0000 | − | 77.9423i | −0.0483351 | − | 0.0837189i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1252.20 | − | 626.099i | 1.33925 | − | 0.669625i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1288.00i | − | 1.37460i | −0.726374 | − | 0.687300i | \(-0.758796\pi\) | ||
0.726374 | − | 0.687300i | \(-0.241204\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −317.585 | + | 183.358i | −0.337497 | + | 0.194854i | −0.659165 | − | 0.751999i | \(-0.729090\pi\) |
0.321668 | + | 0.946853i | \(0.395757\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 69.2820 | + | 40.0000i | 0.0734698 | + | 0.0424178i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 838.525 | − | 1452.37i | 0.885455 | − | 1.53365i | 0.0402628 | − | 0.999189i | \(-0.487180\pi\) |
0.845192 | − | 0.534463i | \(-0.179486\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 336.000 | + | 581.969i | 0.354057 | + | 0.613245i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 827.345 | 0.868148 | 0.434074 | − | 0.900877i | \(-0.357076\pi\) | ||||
0.434074 | + | 0.900877i | \(0.357076\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −960.000 | + | 480.000i | −1.00524 | + | 0.502618i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1208.37 | − | 697.653i | 1.26003 | − | 0.727480i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −97.5000 | + | 168.875i | −0.101457 | + | 0.175728i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.58644 | − | 159.713i | 0.00993414 | − | 0.165505i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 464.190 | − | 268.000i | 0.480031 | − | 0.277146i | −0.240399 | − | 0.970674i | \(-0.577278\pi\) |
0.720429 | + | 0.693528i | \(0.243945\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 134.164i | − | 0.138171i | −0.997611 | − | 0.0690855i | \(-0.977992\pi\) | ||
0.997611 | − | 0.0690855i | \(-0.0220081\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 944.000i | 0.970195i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 87.2067 | + | 151.046i | 0.0892596 | + | 0.154602i | 0.907198 | − | 0.420703i | \(-0.138217\pi\) |
−0.817939 | + | 0.575305i | \(0.804883\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 80.0000 | − | 138.564i | 0.0817160 | − | 0.141536i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 927.968 | − | 1607.29i | 0.944016 | − | 1.63508i | 0.186308 | − | 0.982491i | \(-0.440348\pi\) |
0.757709 | − | 0.652593i | \(-0.226319\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.3205 | − | 18.6603i | 0.0125081 | − | 0.0189444i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 125.220i | − | 0.126613i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1646.00 | −1.66095 | −0.830474 | − | 0.557057i | \(-0.811930\pi\) | ||||
−0.830474 | + | 0.557057i | \(0.811930\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 314.064 | − | 475.672i | 0.315642 | − | 0.478062i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1008.05 | + | 582.000i | 1.01109 | + | 0.583751i | 0.911510 | − | 0.411279i | \(-0.134918\pi\) |
0.0995771 | + | 0.995030i | \(0.468251\pi\) | |||||||
\(998\) | 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 \(a_p\))