Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,3,Mod(401,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.401");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.l (of order \(2\), degree \(1\), 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: | \(32.6976317232\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-5}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 401.2 | ||
Root | \(2.23607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.401 |
Dual form | 1200.3.l.h.401.1 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.00000 | + | 2.23607i | −0.666667 | + | 0.745356i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.00000 | 1.14286 | 0.571429 | − | 0.820652i | \(-0.306389\pi\) | ||||
0.571429 | + | 0.820652i | \(0.306389\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | − | 8.94427i | −0.111111 | − | 0.993808i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.94427i | 0.813116i | 0.913625 | + | 0.406558i | \(0.133271\pi\) | ||||
−0.913625 | + | 0.406558i | \(0.866729\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.0000 | −0.923077 | −0.461538 | − | 0.887120i | \(-0.652702\pi\) | ||||
−0.461538 | + | 0.887120i | \(0.652702\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 31.3050i | − | 1.84147i | −0.390191 | − | 0.920734i | \(-0.627591\pi\) | ||
0.390191 | − | 0.920734i | \(-0.372409\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.00000 | −0.315789 | −0.157895 | − | 0.987456i | \(-0.550471\pi\) | ||||
−0.157895 | + | 0.987456i | \(0.550471\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −16.0000 | + | 17.8885i | −0.761905 | + | 0.851835i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.47214i | 0.194441i | 0.995263 | + | 0.0972203i | \(0.0309952\pi\) | ||||
−0.995263 | + | 0.0972203i | \(0.969005\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 22.0000 | + | 15.6525i | 0.814815 | + | 0.579721i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 26.8328i | 0.925270i | 0.886549 | + | 0.462635i | \(0.153096\pi\) | ||||
−0.886549 | + | 0.462635i | \(0.846904\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −34.0000 | −1.09677 | −0.548387 | − | 0.836225i | \(-0.684758\pi\) | ||||
−0.548387 | + | 0.836225i | \(0.684758\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −20.0000 | − | 17.8885i | −0.606061 | − | 0.542077i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −44.0000 | −1.18919 | −0.594595 | − | 0.804026i | \(-0.702687\pi\) | ||||
−0.594595 | + | 0.804026i | \(0.702687\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 24.0000 | − | 26.8328i | 0.615385 | − | 0.688021i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 17.8885i | 0.436306i | 0.975915 | + | 0.218153i | \(0.0700032\pi\) | ||||
−0.975915 | + | 0.218153i | \(0.929997\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −28.0000 | −0.651163 | −0.325581 | − | 0.945514i | \(-0.605560\pi\) | ||||
−0.325581 | + | 0.945514i | \(0.605560\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.47214i | − | 0.0951518i | −0.998868 | − | 0.0475759i | \(-0.984850\pi\) | ||
0.998868 | − | 0.0475759i | \(-0.0151496\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.0000 | 0.306122 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 70.0000 | + | 62.6099i | 1.37255 | + | 1.22765i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 40.2492i | − | 0.759419i | −0.925106 | − | 0.379710i | \(-0.876024\pi\) | ||
0.925106 | − | 0.379710i | \(-0.123976\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.0000 | − | 13.4164i | 0.210526 | − | 0.235376i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 98.3870i | 1.66758i | 0.552085 | + | 0.833788i | \(0.313833\pi\) | ||||
−0.552085 | + | 0.833788i | \(0.686167\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 74.0000 | 1.21311 | 0.606557 | − | 0.795040i | \(-0.292550\pi\) | ||||
0.606557 | + | 0.795040i | \(0.292550\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.00000 | − | 71.5542i | −0.126984 | − | 1.13578i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −92.0000 | −1.37313 | −0.686567 | − | 0.727066i | \(-0.740883\pi\) | ||||
−0.686567 | + | 0.727066i | \(0.740883\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.0000 | − | 8.94427i | −0.144928 | − | 0.129627i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 53.6656i | − | 0.755854i | −0.925835 | − | 0.377927i | \(-0.876637\pi\) | ||
0.925835 | − | 0.377927i | \(-0.123363\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −56.0000 | −0.767123 | −0.383562 | − | 0.923515i | \(-0.625303\pi\) | ||||
−0.383562 | + | 0.923515i | \(0.625303\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 71.5542i | 0.929275i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −78.0000 | −0.987342 | −0.493671 | − | 0.869649i | \(-0.664345\pi\) | ||||
−0.493671 | + | 0.869649i | \(0.664345\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −79.0000 | + | 17.8885i | −0.975309 | + | 0.220846i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 102.859i | − | 1.23927i | −0.784891 | − | 0.619633i | \(-0.787281\pi\) | ||
0.784891 | − | 0.619633i | \(-0.212719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −60.0000 | − | 53.6656i | −0.689655 | − | 0.616846i | ||||
\(88\) | 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 | ||||||||
\(93\) | 68.0000 | − | 76.0263i | 0.731183 | − | 0.817487i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 32.0000 | 0.329897 | 0.164948 | − | 0.986302i | \(-0.447254\pi\) | ||||
0.164948 | + | 0.986302i | \(0.447254\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 80.0000 | − | 8.94427i | 0.808081 | − | 0.0903462i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 152.053i | − | 1.50547i | −0.658323 | − | 0.752736i | \(-0.728734\pi\) | ||
0.658323 | − | 0.752736i | \(-0.271266\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −104.000 | −1.00971 | −0.504854 | − | 0.863205i | \(-0.668454\pi\) | ||||
−0.504854 | + | 0.863205i | \(0.668454\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 147.580i | − | 1.37926i | −0.724163 | − | 0.689628i | \(-0.757774\pi\) | ||
0.724163 | − | 0.689628i | \(-0.242226\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −74.0000 | −0.678899 | −0.339450 | − | 0.940624i | \(-0.610241\pi\) | ||||
−0.339450 | + | 0.940624i | \(0.610241\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 88.0000 | − | 98.3870i | 0.792793 | − | 0.886369i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 40.2492i | − | 0.356188i | −0.984013 | − | 0.178094i | \(-0.943007\pi\) | ||
0.984013 | − | 0.178094i | \(-0.0569931\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.0000 | + | 107.331i | 0.102564 | + | 0.917361i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 250.440i | − | 2.10453i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 41.0000 | 0.338843 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −40.0000 | − | 35.7771i | −0.325203 | − | 0.290871i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.0000 | −0.125984 | −0.0629921 | − | 0.998014i | \(-0.520064\pi\) | ||||
−0.0629921 | + | 0.998014i | \(0.520064\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 56.0000 | − | 62.6099i | 0.434109 | − | 0.485348i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 80.4984i | − | 0.614492i | −0.951630 | − | 0.307246i | \(-0.900593\pi\) | ||
0.951630 | − | 0.307246i | \(-0.0994074\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −48.0000 | −0.360902 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 174.413i | − | 1.27309i | −0.771240 | − | 0.636545i | \(-0.780363\pi\) | ||
0.771240 | − | 0.636545i | \(-0.219637\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −118.000 | −0.848921 | −0.424460 | − | 0.905446i | \(-0.639536\pi\) | ||||
−0.424460 | + | 0.905446i | \(0.639536\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.0000 | + | 8.94427i | 0.0709220 | + | 0.0634346i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 107.331i | − | 0.750568i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −30.0000 | + | 33.5410i | −0.204082 | + | 0.228170i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 98.3870i | − | 0.660315i | −0.943926 | − | 0.330158i | \(-0.892898\pi\) | ||
0.943926 | − | 0.330158i | \(-0.107102\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −34.0000 | −0.225166 | −0.112583 | − | 0.993642i | \(-0.535912\pi\) | ||||
−0.112583 | + | 0.993642i | \(0.535912\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −280.000 | + | 31.3050i | −1.83007 | + | 0.204608i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 92.0000 | 0.585987 | 0.292994 | − | 0.956114i | \(-0.405349\pi\) | ||||
0.292994 | + | 0.956114i | \(0.405349\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 90.0000 | + | 80.4984i | 0.566038 | + | 0.506280i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 35.7771i | 0.222218i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −68.0000 | −0.417178 | −0.208589 | − | 0.978003i | \(-0.566887\pi\) | ||||
−0.208589 | + | 0.978003i | \(0.566887\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 67.0820i | 0.401689i | 0.979623 | + | 0.200844i | \(0.0643686\pi\) | ||||
−0.979623 | + | 0.200844i | \(0.935631\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −25.0000 | −0.147929 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.00000 | + | 53.6656i | 0.0350877 | + | 0.313834i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 76.0263i | − | 0.439458i | −0.975561 | − | 0.219729i | \(-0.929483\pi\) | ||
0.975561 | − | 0.219729i | \(-0.0705174\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −220.000 | − | 196.774i | −1.24294 | − | 1.11172i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 259.384i | 1.44907i | 0.689237 | + | 0.724536i | \(0.257946\pi\) | ||||
−0.689237 | + | 0.724536i | \(0.742054\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −166.000 | −0.917127 | −0.458564 | − | 0.888662i | \(-0.651636\pi\) | ||||
−0.458564 | + | 0.888662i | \(0.651636\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −148.000 | + | 165.469i | −0.808743 | + | 0.904202i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 280.000 | 1.49733 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 176.000 | + | 125.220i | 0.931217 | + | 0.662539i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 214.663i | 1.12389i | 0.827175 | + | 0.561944i | \(0.189946\pi\) | ||||
−0.827175 | + | 0.561944i | \(0.810054\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −32.0000 | −0.165803 | −0.0829016 | − | 0.996558i | \(-0.526419\pi\) | ||||
−0.0829016 | + | 0.996558i | \(0.526419\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.47214i | 0.0227012i | 0.999936 | + | 0.0113506i | \(0.00361309\pi\) | ||||
−0.999936 | + | 0.0113506i | \(0.996387\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 114.000 | 0.572864 | 0.286432 | − | 0.958101i | \(-0.407531\pi\) | ||||
0.286432 | + | 0.958101i | \(0.407531\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 184.000 | − | 205.718i | 0.915423 | − | 1.02347i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 214.663i | 1.05745i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 40.0000 | − | 4.47214i | 0.193237 | − | 0.0216045i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 53.6656i | − | 0.256773i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.00000 | 0.0284360 | 0.0142180 | − | 0.999899i | \(-0.495474\pi\) | ||||
0.0142180 | + | 0.999899i | \(0.495474\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 120.000 | + | 107.331i | 0.563380 | + | 0.503903i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −272.000 | −1.25346 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 112.000 | − | 125.220i | 0.511416 | − | 0.571780i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 375.659i | 1.69982i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 272.000 | 1.21973 | 0.609865 | − | 0.792505i | \(-0.291223\pi\) | ||||
0.609865 | + | 0.792505i | \(0.291223\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 245.967i | 1.08356i | 0.840521 | + | 0.541779i | \(0.182249\pi\) | ||||
−0.840521 | + | 0.541779i | \(0.817751\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −154.000 | −0.672489 | −0.336245 | − | 0.941775i | \(-0.609157\pi\) | ||||
−0.336245 | + | 0.941775i | \(0.609157\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −160.000 | − | 143.108i | −0.692641 | − | 0.619517i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 183.358i | − | 0.786942i | −0.919337 | − | 0.393471i | \(-0.871274\pi\) | ||
0.919337 | − | 0.393471i | \(-0.128726\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 156.000 | − | 174.413i | 0.658228 | − | 0.735921i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 178.885i | − | 0.748475i | −0.927333 | − | 0.374237i | \(-0.877905\pi\) | ||
0.927333 | − | 0.374237i | \(-0.122095\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −206.000 | −0.854772 | −0.427386 | − | 0.904069i | \(-0.640565\pi\) | ||||
−0.427386 | + | 0.904069i | \(0.640565\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 118.000 | − | 212.426i | 0.485597 | − | 0.874183i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 72.0000 | 0.291498 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 230.000 | + | 205.718i | 0.923695 | + | 0.826178i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 26.8328i | − | 0.106904i | −0.998570 | − | 0.0534518i | \(-0.982978\pi\) | ||
0.998570 | − | 0.0534518i | \(-0.0170224\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −40.0000 | −0.158103 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 40.2492i | 0.156612i | 0.996929 | + | 0.0783059i | \(0.0249511\pi\) | ||||
−0.996929 | + | 0.0783059i | \(0.975049\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −352.000 | −1.35907 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 240.000 | − | 26.8328i | 0.919540 | − | 0.102808i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 210.190i | − | 0.799203i | −0.916689 | − | 0.399602i | \(-0.869149\pi\) | ||
0.916689 | − | 0.399602i | \(-0.130851\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −40.0000 | − | 35.7771i | −0.149813 | − | 0.133997i | ||||
\(268\) | 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 | \(-0.237502\pi\) | ||||
0.734317 | + | 0.678806i | \(0.237502\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 192.000 | − | 214.663i | 0.703297 | − | 0.786310i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 292.000 | 1.05415 | 0.527076 | − | 0.849818i | \(-0.323288\pi\) | ||||
0.527076 | + | 0.849818i | \(0.323288\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 34.0000 | + | 304.105i | 0.121864 | + | 1.08998i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 53.6656i | 0.190981i | 0.995430 | + | 0.0954904i | \(0.0304419\pi\) | ||||
−0.995430 | + | 0.0954904i | \(0.969558\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 52.0000 | 0.183746 | 0.0918728 | − | 0.995771i | \(-0.470715\pi\) | ||||
0.0918728 | + | 0.995771i | \(0.470715\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 143.108i | 0.498635i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −691.000 | −2.39100 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −64.0000 | + | 71.5542i | −0.219931 | + | 0.245891i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 389.076i | 1.32790i | 0.747775 | + | 0.663952i | \(0.231122\pi\) | ||||
−0.747775 | + | 0.663952i | \(0.768878\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −140.000 | + | 196.774i | −0.471380 | + | 0.662539i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 53.6656i | − | 0.179484i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −224.000 | −0.744186 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 340.000 | + | 304.105i | 1.12211 | + | 1.00365i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −492.000 | −1.60261 | −0.801303 | − | 0.598259i | \(-0.795859\pi\) | ||||
−0.801303 | + | 0.598259i | \(0.795859\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 208.000 | − | 232.551i | 0.673139 | − | 0.752592i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 482.991i | 1.55302i | 0.630102 | + | 0.776512i | \(0.283013\pi\) | ||||
−0.630102 | + | 0.776512i | \(0.716987\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 568.000 | 1.81470 | 0.907348 | − | 0.420380i | \(-0.138103\pi\) | ||||
0.907348 | + | 0.420380i | \(0.138103\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 612.683i | 1.93275i | 0.257132 | + | 0.966376i | \(0.417223\pi\) | ||||
−0.257132 | + | 0.966376i | \(0.582777\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −240.000 | −0.752351 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 330.000 | + | 295.161i | 1.02804 | + | 0.919505i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 187.830i | 0.581516i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 148.000 | − | 165.469i | 0.452599 | − | 0.506021i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 35.7771i | − | 0.108745i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −202.000 | −0.610272 | −0.305136 | − | 0.952309i | \(-0.598702\pi\) | ||||
−0.305136 | + | 0.952309i | \(0.598702\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 44.0000 | + | 393.548i | 0.132132 | + | 1.18183i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −368.000 | −1.09199 | −0.545994 | − | 0.837789i | \(-0.683848\pi\) | ||||
−0.545994 | + | 0.837789i | \(0.683848\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 90.0000 | + | 80.4984i | 0.265487 | + | 0.237459i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 304.105i | − | 0.891804i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −272.000 | −0.793003 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 254.912i | − | 0.734616i | −0.930099 | − | 0.367308i | \(-0.880280\pi\) | ||
0.930099 | − | 0.367308i | \(-0.119720\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 118.000 | 0.338109 | 0.169054 | − | 0.985607i | \(-0.445929\pi\) | ||||
0.169054 | + | 0.985607i | \(0.445929\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −264.000 | − | 187.830i | −0.752137 | − | 0.535127i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.3050i | 0.0886826i | 0.999016 | + | 0.0443413i | \(0.0141189\pi\) | ||||
−0.999016 | + | 0.0443413i | \(0.985881\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 560.000 | + | 500.879i | 1.56863 | + | 1.40302i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 53.6656i | 0.149486i | 0.997203 | + | 0.0747432i | \(0.0238137\pi\) | ||||
−0.997203 | + | 0.0747432i | \(0.976186\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −325.000 | −0.900277 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −82.0000 | + | 91.6788i | −0.225895 | + | 0.252559i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −352.000 | −0.959128 | −0.479564 | − | 0.877507i | \(-0.659205\pi\) | ||||
−0.479564 | + | 0.877507i | \(0.659205\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 160.000 | − | 17.8885i | 0.433604 | − | 0.0484784i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 321.994i | − | 0.867908i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −132.000 | −0.353887 | −0.176944 | − | 0.984221i | \(-0.556621\pi\) | ||||
−0.176944 | + | 0.984221i | \(0.556621\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 321.994i | − | 0.854095i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 394.000 | 1.03958 | 0.519789 | − | 0.854295i | \(-0.326011\pi\) | ||||
0.519789 | + | 0.854295i | \(0.326011\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 32.0000 | − | 35.7771i | 0.0839895 | − | 0.0939031i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 76.0263i | 0.198502i | 0.995062 | + | 0.0992511i | \(0.0316447\pi\) | ||||
−0.995062 | + | 0.0992511i | \(0.968355\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 28.0000 | + | 250.440i | 0.0723514 | + | 0.647131i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 277.272i | − | 0.712783i | −0.934337 | − | 0.356391i | \(-0.884007\pi\) | ||
0.934337 | − | 0.356391i | \(-0.115993\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 140.000 | 0.358056 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 180.000 | + | 160.997i | 0.458015 | + | 0.409661i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 652.000 | 1.64232 | 0.821159 | − | 0.570700i | \(-0.193328\pi\) | ||||
0.821159 | + | 0.570700i | \(0.193328\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 96.0000 | − | 107.331i | 0.240602 | − | 0.269001i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 178.885i | − | 0.446098i | −0.974807 | − | 0.223049i | \(-0.928399\pi\) | ||
0.974807 | − | 0.223049i | \(-0.0716011\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 408.000 | 1.01241 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 393.548i | − | 0.966948i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 206.000 | 0.503667 | 0.251834 | − | 0.967771i | \(-0.418966\pi\) | ||||
0.251834 | + | 0.967771i | \(0.418966\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 390.000 | + | 348.827i | 0.948905 | + | 0.848727i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 787.096i | 1.90580i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 236.000 | − | 263.856i | 0.565947 | − | 0.632748i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 205.718i | − | 0.490974i | −0.969400 | − | 0.245487i | \(-0.921052\pi\) | ||
0.969400 | − | 0.245487i | \(-0.0789479\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.0000 | −0.0902613 | −0.0451306 | − | 0.998981i | \(-0.514370\pi\) | ||||
−0.0451306 | + | 0.998981i | \(0.514370\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −40.0000 | + | 4.47214i | −0.0945626 | + | 0.0105724i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 592.000 | 1.38642 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 240.000 | + | 214.663i | 0.559441 | + | 0.500379i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 608.210i | − | 1.41116i | −0.708630 | − | 0.705581i | \(-0.750686\pi\) | ||
0.708630 | − | 0.705581i | \(-0.249314\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −272.000 | −0.628176 | −0.314088 | − | 0.949394i | \(-0.601699\pi\) | ||||
−0.314088 | + | 0.949394i | \(0.601699\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 26.8328i | − | 0.0614023i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −366.000 | −0.833713 | −0.416856 | − | 0.908972i | \(-0.636868\pi\) | ||||
−0.416856 | + | 0.908972i | \(0.636868\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.0000 | − | 134.164i | −0.0340136 | − | 0.304227i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 576.906i | 1.30227i | 0.758962 | + | 0.651135i | \(0.225707\pi\) | ||||
−0.758962 | + | 0.651135i | \(0.774293\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 220.000 | + | 196.774i | 0.492170 | + | 0.440210i | ||||
\(448\) | 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 | ||||||||
\(453\) | 68.0000 | − | 76.0263i | 0.150110 | − | 0.167829i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −104.000 | −0.227571 | −0.113786 | − | 0.993505i | \(-0.536298\pi\) | ||||
−0.113786 | + | 0.993505i | \(0.536298\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 490.000 | − | 688.709i | 1.06754 | − | 1.50046i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 509.823i | 1.10591i | 0.833212 | + | 0.552954i | \(0.186499\pi\) | ||||
−0.833212 | + | 0.552954i | \(0.813501\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 96.0000 | 0.207343 | 0.103672 | − | 0.994612i | \(-0.466941\pi\) | ||||
0.103672 | + | 0.994612i | \(0.466941\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 147.580i | − | 0.316018i | −0.987438 | − | 0.158009i | \(-0.949492\pi\) | ||
0.987438 | − | 0.158009i | \(-0.0505075\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −736.000 | −1.56930 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −184.000 | + | 205.718i | −0.390658 | + | 0.436769i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 250.440i | − | 0.529471i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −360.000 | + | 40.2492i | −0.754717 | + | 0.0843799i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 572.433i | 1.19506i | 0.801847 | + | 0.597530i | \(0.203851\pi\) | ||||
−0.801847 | + | 0.597530i | \(0.796149\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 528.000 | 1.09771 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −80.0000 | − | 71.5542i | −0.165631 | − | 0.148145i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 648.000 | 1.33060 | 0.665298 | − | 0.746578i | \(-0.268305\pi\) | ||||
0.665298 | + | 0.746578i | \(0.268305\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 136.000 | − | 152.053i | 0.278119 | − | 0.310946i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 134.164i | − | 0.273247i | −0.990623 | − | 0.136623i | \(-0.956375\pi\) | ||
0.990623 | − | 0.136623i | \(-0.0436250\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 840.000 | 1.70385 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 429.325i | − | 0.863833i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −486.000 | −0.973948 | −0.486974 | − | 0.873416i | \(-0.661899\pi\) | ||||
−0.486974 | + | 0.873416i | \(0.661899\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −150.000 | − | 134.164i | −0.299401 | − | 0.267793i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 791.568i | 1.57369i | 0.617148 | + | 0.786847i | \(0.288288\pi\) | ||||
−0.617148 | + | 0.786847i | \(0.711712\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 50.0000 | − | 55.9017i | 0.0986193 | − | 0.110260i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.8328i | 0.0527167i | 0.999653 | + | 0.0263584i | \(0.00839110\pi\) | ||||
−0.999653 | + | 0.0263584i | \(0.991609\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −448.000 | −0.876712 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −132.000 | − | 93.9149i | −0.257310 | − | 0.183070i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 40.0000 | 0.0773694 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 170.000 | + | 152.053i | 0.327553 | + | 0.292972i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 983.870i | − | 1.88843i | −0.329336 | − | 0.944213i | \(-0.606825\pi\) | ||
0.329336 | − | 0.944213i | \(-0.393175\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 292.000 | 0.558317 | 0.279159 | − | 0.960245i | \(-0.409944\pi\) | ||||
0.279159 | + | 0.960245i | \(0.409944\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1064.37i | 2.01967i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 509.000 | 0.962193 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 880.000 | − | 98.3870i | 1.65725 | − | 0.185286i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 214.663i | − | 0.402744i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −580.000 | − | 518.768i | −1.08007 | − | 0.966048i | ||||
\(538\) | 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 | ||||||||
\(543\) | 332.000 | − | 371.187i | 0.611418 | − | 0.683586i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 164.000 | 0.299817 | 0.149909 | − | 0.988700i | \(-0.452102\pi\) | ||||
0.149909 | + | 0.988700i | \(0.452102\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −74.0000 | − | 661.876i | −0.134791 | − | 1.20560i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 160.997i | − | 0.292190i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −624.000 | −1.12839 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 362.243i | 0.650347i | 0.945654 | + | 0.325173i | \(0.105423\pi\) | ||||
−0.945654 | + | 0.325173i | \(0.894577\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 336.000 | 0.601073 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −560.000 | + | 626.099i | −0.998217 | + | 1.11604i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 997.286i | − | 1.77138i | −0.464278 | − | 0.885689i | \(-0.653686\pi\) | ||
0.464278 | − | 0.885689i | \(-0.346314\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −632.000 | + | 143.108i | −1.11464 | + | 0.252396i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 626.099i | − | 1.10035i | −0.835049 | − | 0.550175i | \(-0.814561\pi\) | ||
0.835049 | − | 0.550175i | \(-0.185439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −394.000 | −0.690018 | −0.345009 | − | 0.938599i | \(-0.612124\pi\) | ||||
−0.345009 | + | 0.938599i | \(0.612124\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −480.000 | − | 429.325i | −0.837696 | − | 0.749258i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −608.000 | −1.05373 | −0.526863 | − | 0.849950i | \(-0.676632\pi\) | ||||
−0.526863 | + | 0.849950i | \(0.676632\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 64.0000 | − | 71.5542i | 0.110535 | − | 0.123582i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 822.873i | − | 1.41630i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 360.000 | 0.617496 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 711.070i | 1.21136i | 0.795707 | + | 0.605681i | \(0.207099\pi\) | ||||
−0.795707 | + | 0.605681i | \(0.792901\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 204.000 | 0.346350 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.0000 | − | 8.94427i | −0.0169205 | − | 0.0151341i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 603.738i | 1.01811i | 0.860734 | + | 0.509054i | \(0.170005\pi\) | ||||
−0.860734 | + | 0.509054i | \(0.829995\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −228.000 | + | 254.912i | −0.381910 | + | 0.426988i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 53.6656i | − | 0.0895920i | −0.998996 | − | 0.0447960i | \(-0.985736\pi\) | ||
0.998996 | − | 0.0447960i | \(-0.0142638\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 434.000 | 0.722130 | 0.361065 | − | 0.932541i | \(-0.382413\pi\) | ||||
0.361065 | + | 0.932541i | \(0.382413\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 92.0000 | + | 822.873i | 0.152570 | + | 1.36463i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −656.000 | −1.08072 | −0.540362 | − | 0.841432i | \(-0.681713\pi\) | ||||
−0.540362 | + | 0.841432i | \(0.681713\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −480.000 | − | 429.325i | −0.788177 | − | 0.704967i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 53.6656i | 0.0878325i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 844.000 | 1.37684 | 0.688418 | − | 0.725315i | \(-0.258306\pi\) | ||||
0.688418 | + | 0.725315i | \(0.258306\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 460.630i | − | 0.746564i | −0.927718 | − | 0.373282i | \(-0.878232\pi\) | ||
0.927718 | − | 0.373282i | \(-0.121768\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1046.00 | −1.68982 | −0.844911 | − | 0.534907i | \(-0.820347\pi\) | ||||
−0.844911 | + | 0.534907i | \(0.820347\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −70.0000 | + | 98.3870i | −0.112721 | + | 0.158433i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 143.108i | 0.229708i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 120.000 | + | 107.331i | 0.191388 | + | 0.171182i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1377.42i | 2.18985i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.0000 | 0.0729002 | 0.0364501 | − | 0.999335i | \(-0.488395\pi\) | ||||
0.0364501 | + | 0.999335i | \(0.488395\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.0000 | + | 13.4164i | −0.0189573 | + | 0.0211950i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −180.000 | −0.282575 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −480.000 | + | 53.6656i | −0.751174 | + | 0.0839838i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1144.87i | 1.78606i | 0.449994 | + | 0.893032i | \(0.351426\pi\) | ||||
−0.449994 | + | 0.893032i | \(0.648574\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −804.000 | −1.25039 | −0.625194 | − | 0.780469i | \(-0.714980\pi\) | ||||
−0.625194 | + | 0.780469i | \(0.714980\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 576.906i | − | 0.891662i | −0.895117 | − | 0.445831i | \(-0.852908\pi\) | ||
0.895117 | − | 0.445831i | \(-0.147092\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −880.000 | −1.35593 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 544.000 | − | 608.210i | 0.835637 | − | 0.934271i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1077.78i | − | 1.65051i | −0.564758 | − | 0.825256i | \(-0.691031\pi\) | ||
0.564758 | − | 0.825256i | \(-0.308969\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 56.0000 | + | 500.879i | 0.0852359 | + | 0.762373i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 813.929i | − | 1.23510i | −0.786533 | − | 0.617548i | \(-0.788126\pi\) | ||
0.786533 | − | 0.617548i | \(-0.211874\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1082.00 | 1.63691 | 0.818457 | − | 0.574568i | \(-0.194830\pi\) | ||||
0.818457 | + | 0.574568i | \(0.194830\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −840.000 | − | 751.319i | −1.26697 | − | 1.13321i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −120.000 | −0.179910 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −544.000 | + | 608.210i | −0.813154 | + | 0.909134i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 661.876i | 0.986403i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1056.00 | −1.56909 | −0.784547 | − | 0.620070i | \(-0.787104\pi\) | ||||
−0.784547 | + | 0.620070i | \(0.787104\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 612.683i | 0.904996i | 0.891765 | + | 0.452498i | \(0.149467\pi\) | ||||
−0.891765 | + | 0.452498i | \(0.850533\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 256.000 | 0.377025 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −550.000 | − | 491.935i | −0.807636 | − | 0.722371i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 317.522i | − | 0.464893i | −0.972609 | − | 0.232446i | \(-0.925327\pi\) | ||
0.972609 | − | 0.232446i | \(-0.0746730\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 308.000 | − | 344.354i | 0.448326 | − | 0.501244i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 482.991i | 0.701002i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −922.000 | −1.33430 | −0.667149 | − | 0.744924i | \(-0.732486\pi\) | ||||
−0.667149 | + | 0.744924i | \(0.732486\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 640.000 | − | 71.5542i | 0.923521 | − | 0.103253i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 560.000 | 0.803443 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 410.000 | + | 366.715i | 0.586552 | + | 0.524628i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 474.046i | 0.676243i | 0.941102 | + | 0.338122i | \(0.109791\pi\) | ||||
−0.941102 | + | 0.338122i | \(0.890209\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 264.000 | 0.375533 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 1216.42i | − | 1.72054i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 966.000 | 1.36248 | 0.681241 | − | 0.732059i | \(-0.261441\pi\) | ||||
0.681241 | + | 0.732059i | \(0.261441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 78.0000 | + | 697.653i | 0.109705 | + | 0.981228i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 152.053i | − | 0.213258i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 400.000 | + | 357.771i | 0.557880 | + | 0.498983i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1109.09i | 1.54254i | 0.636505 | + | 0.771272i | \(0.280379\pi\) | ||||
−0.636505 | + | 0.771272i | \(0.719621\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −832.000 | −1.15395 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 412.000 | − | 460.630i | 0.569848 | − | 0.637109i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 408.000 | 0.561210 | 0.280605 | − | 0.959823i | \(-0.409465\pi\) | ||||
0.280605 | + | 0.959823i | \(0.409465\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 239.000 | + | 688.709i | 0.327846 | + | 0.944731i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 876.539i | 1.19910i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 164.000 | 0.223738 | 0.111869 | − | 0.993723i | \(-0.464316\pi\) | ||||
0.111869 | + | 0.993723i | \(0.464316\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 822.873i | − | 1.11652i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1082.00 | 1.46414 | 0.732070 | − | 0.681229i | \(-0.238554\pi\) | ||||
0.732070 | + | 0.681229i | \(0.238554\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −144.000 | + | 160.997i | −0.194332 | + | 0.217270i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1140.39i | − | 1.53485i | −0.641138 | − | 0.767426i | \(-0.721537\pi\) | ||
0.641138 | − | 0.767426i | \(-0.278463\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −920.000 | + | 102.859i | −1.23159 | + | 0.137696i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1180.64i | − | 1.57629i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 958.000 | 1.27563 | 0.637816 | − | 0.770189i | \(-0.279838\pi\) | ||||
0.637816 | + | 0.770189i | \(0.279838\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 60.0000 | + | 53.6656i | 0.0796813 | + | 0.0712691i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 772.000 | 1.01982 | 0.509908 | − | 0.860229i | \(-0.329680\pi\) | ||||
0.509908 | + | 0.860229i | \(0.329680\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 80.0000 | − | 89.4427i | 0.105402 | − | 0.117843i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1126.98i | 1.48092i | 0.672102 | + | 0.740459i | \(0.265392\pi\) | ||||
−0.672102 | + | 0.740459i | \(0.734608\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −592.000 | −0.775885 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1180.64i | − | 1.53930i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1326.00 | 1.72432 | 0.862159 | − | 0.506638i | \(-0.169112\pi\) | ||||
0.862159 | + | 0.506638i | \(0.169112\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −90.0000 | − | 80.4984i | −0.116732 | − | 0.104408i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 147.580i | − | 0.190919i | −0.995433 | − | 0.0954596i | \(-0.969568\pi\) | ||
0.995433 | − | 0.0954596i | \(-0.0304321\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 704.000 | − | 787.096i | 0.906049 | − | 1.01299i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 107.331i | − | 0.137781i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 480.000 | 0.614597 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −420.000 | + | 590.322i | −0.536398 | + | 0.753923i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1132.00 | −1.43837 | −0.719187 | − | 0.694817i | \(-0.755485\pi\) | ||||
−0.719187 | + | 0.694817i | \(0.755485\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 470.000 | + | 420.381i | 0.595691 | + | 0.532802i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 321.994i | − | 0.407072i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −888.000 | −1.11980 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 612.683i | 0.768736i | 0.923180 | + | 0.384368i | \(0.125581\pi\) | ||||
−0.923180 | + | 0.384368i | \(0.874419\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −140.000 | −0.175219 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 160.000 | − | 17.8885i | 0.199750 | − | 0.0223328i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 500.879i | − | 0.623760i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −300.000 | − | 268.328i | −0.371747 | − | 0.332501i | ||||
\(808\) | 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 | \(-0.681138\pi\) | ||||
−0.538841 | + | 0.842408i | \(0.681138\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −796.000 | + | 889.955i | −0.979090 | + | 1.09466i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 168.000 | 0.205630 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 96.0000 | + | 858.650i | 0.117216 | + | 1.04841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 259.384i | − | 0.315937i | −0.987444 | − | 0.157968i | \(-0.949506\pi\) | ||
0.987444 | − | 0.157968i | \(-0.0504944\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1368.00 | −1.66221 | −0.831106 | − | 0.556114i | \(-0.812292\pi\) | ||||
−0.831106 | + | 0.556114i | \(0.812292\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 460.630i | 0.556989i | 0.960438 | + | 0.278495i | \(0.0898354\pi\) | ||||
−0.960438 | + | 0.278495i | \(0.910165\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1002.00 | −1.20869 | −0.604343 | − | 0.796725i | \(-0.706564\pi\) | ||||
−0.604343 | + | 0.796725i | \(0.706564\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −584.000 | + | 652.932i | −0.702768 | + | 0.785718i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 469.574i | − | 0.563715i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −748.000 | − | 532.184i | −0.893668 | − | 0.635823i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 304.105i | − | 0.362462i | −0.983441 | − | 0.181231i | \(-0.941992\pi\) | ||
0.983441 | − | 0.181231i | \(-0.0580081\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 121.000 | 0.143876 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −120.000 | − | 107.331i | −0.142349 | − | 0.127321i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 328.000 | 0.387249 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −104.000 | + | 116.276i | −0.122497 | + | 0.136956i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 196.774i | − | 0.231227i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −772.000 | −0.905041 | −0.452521 | − | 0.891754i | \(-0.649475\pi\) | ||||
−0.452521 | + | 0.891754i | \(0.649475\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 898.899i | 1.04889i | 0.851444 | + | 0.524445i | \(0.175727\pi\) | ||||
−0.851444 | + | 0.524445i | \(0.824273\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −278.000 | −0.323632 | −0.161816 | − | 0.986821i | \(-0.551735\pi\) | ||||
−0.161816 | + | 0.986821i | \(0.551735\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −320.000 | − | 286.217i | −0.371661 | − | 0.332424i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 576.906i | 0.668488i | 0.942486 | + | 0.334244i | \(0.108481\pi\) | ||||
−0.942486 | + | 0.334244i | \(0.891519\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1382.00 | − | 1545.12i | 1.59400 | − | 1.78215i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 697.653i | − | 0.802823i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1104.00 | 1.26751 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −32.0000 | − | 286.217i | −0.0366552 | − | 0.327854i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −628.000 | −0.716078 | −0.358039 | − | 0.933707i | \(-0.616554\pi\) | ||||
−0.358039 | + | 0.933707i | \(0.616554\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −870.000 | − | 778.152i | −0.989761 | − | 0.885269i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 536.656i | − | 0.609145i | −0.952489 | − | 0.304572i | \(-0.901486\pi\) | ||
0.952489 | − | 0.304572i | \(-0.0985135\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −948.000 | −1.07361 | −0.536806 | − | 0.843705i | \(-0.680369\pi\) | ||||
−0.536806 | + | 0.843705i | \(0.680369\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 281.745i | 0.317638i | 0.987308 | + | 0.158819i | \(0.0507686\pi\) | ||||
−0.987308 | + | 0.158819i | \(0.949231\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −128.000 | −0.143982 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −160.000 | − | 706.597i | −0.179574 | − | 0.793039i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.8328i | 0.0300479i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 120.000 | + | 107.331i | 0.133779 | + | 0.119656i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 912.316i | − | 1.01481i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1260.00 | −1.39845 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 448.000 | − | 500.879i | 0.496124 | − | 0.554684i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −516.000 | −0.568908 | −0.284454 | − | 0.958690i | \(-0.591812\pi\) | ||||
−0.284454 | + | 0.958690i | \(0.591812\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1360.00 | + | 152.053i | −1.49615 | + | 0.167275i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 321.994i | 0.353451i | 0.984260 | + | 0.176725i | \(0.0565505\pi\) | ||||
−0.984260 | + | 0.176725i | \(0.943450\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 920.000 | 1.00767 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 643.988i | − | 0.702277i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1314.00 | 1.42982 | 0.714908 | − | 0.699219i | \(-0.246469\pi\) | ||||
0.714908 | + | 0.699219i | \(0.246469\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 984.000 | − | 1100.15i | 1.06840 | − | 1.19451i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 643.988i | 0.697711i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 104.000 | + | 930.204i | 0.112190 | + | 1.00346i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1502.64i | 1.61748i | 0.588167 | + | 0.808739i | \(0.299850\pi\) | ||||
−0.588167 | + | 0.808739i | \(0.700150\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −90.0000 | −0.0966702 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1080.00 | − | 965.981i | −1.15756 | − | 1.03535i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1288.00 | −1.37460 | −0.687300 | − | 0.726374i | \(-0.741204\pi\) | ||||
−0.687300 | + | 0.726374i | \(0.741204\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1136.00 | + | 1270.09i | −1.20980 | + | 1.35259i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 366.715i | 0.389708i | 0.980832 | + | 0.194854i | \(0.0624233\pi\) | ||||
−0.980832 | + | 0.194854i | \(0.937577\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −80.0000 | −0.0848356 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1677.05i | 1.77091i | 0.464726 | + | 0.885455i | \(0.346153\pi\) | ||||
−0.464726 | + | 0.885455i | \(0.653847\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 672.000 | 0.708114 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1370.00 | − | 1225.37i | −1.44059 | − | 1.28850i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 827.345i | − | 0.868148i | −0.900877 | − | 0.434074i | \(-0.857076\pi\) | ||
0.900877 | − | 0.434074i | \(-0.142924\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 480.000 | − | 536.656i | 0.501567 | − | 0.560769i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1395.31i | − | 1.45496i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 195.000 | 0.202914 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1320.00 | + | 147.580i | −1.37072 | + | 0.153251i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −536.000 | −0.554292 | −0.277146 | − | 0.960828i | \(-0.589389\pi\) | ||||
−0.277146 | + | 0.960828i | \(0.589389\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −420.000 | − | 375.659i | −0.433437 | − | 0.387677i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 134.164i | − | 0.138171i | −0.997611 | − | 0.0690855i | \(-0.977992\pi\) | ||
0.997611 | − | 0.0690855i | \(-0.0220081\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −944.000 | −0.970195 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 174.413i | − | 0.178519i | −0.996008 | − | 0.0892596i | \(-0.971550\pi\) | ||
0.996008 | − | 0.0892596i | \(-0.0284501\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −160.000 | −0.163432 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 74.0000 | + | 661.876i | 0.0754332 | + | 0.674695i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1855.94i | − | 1.88803i | −0.329898 | − | 0.944016i | \(-0.607014\pi\) | ||
0.329898 | − | 0.944016i | \(-0.392986\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 80.0000 | + | 71.5542i | 0.0810537 | + | 0.0724966i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 125.220i | − | 0.126613i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1646.00 | 1.66095 | 0.830474 | − | 0.557057i | \(-0.188070\pi\) | ||||
0.830474 | + | 0.557057i | \(0.188070\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 404.000 | − | 451.686i | 0.406848 | − | 0.454870i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1164.00 | −1.16750 | −0.583751 | − | 0.811933i | \(-0.698416\pi\) | ||||
−0.583751 | + | 0.811933i | \(0.698416\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −968.000 | − | 688.709i | −0.968969 | − | 0.689398i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))