Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [480,2,Mod(49,480)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(480, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("480.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 480 = 2^{5} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 480.d (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: | \(3.83281929702\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.839056.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 6x^{4} + 8x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.3 | ||
Root | \(-1.32132i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 480.49 |
Dual form | 480.2.d.b.49.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/480\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(161\) | \(421\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.254102 | − | 2.22158i | 0.113638 | − | 0.993522i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.64265i | − | 0.998827i | −0.866364 | − | 0.499414i | \(-0.833549\pi\) | ||
0.866364 | − | 0.499414i | \(-0.166451\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.51363i | − | 0.456377i | −0.973617 | − | 0.228189i | \(-0.926720\pi\) | ||
0.973617 | − | 0.228189i | \(-0.0732803\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.87086 | −1.07358 | −0.536792 | − | 0.843714i | \(-0.680364\pi\) | ||||
−0.536792 | + | 0.843714i | \(0.680364\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.254102 | − | 2.22158i | 0.0656088 | − | 0.573610i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.31415i | 0.803800i | 0.915684 | + | 0.401900i | \(0.131650\pi\) | ||||
−0.915684 | + | 0.401900i | \(0.868350\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.08582i | − | 1.62560i | −0.582545 | − | 0.812799i | \(-0.697943\pi\) | ||
0.582545 | − | 0.812799i | \(-0.302057\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.64265i | − | 0.576673i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.82778i | 1.00666i | 0.864094 | + | 0.503331i | \(0.167892\pi\) | ||||
−0.864094 | + | 0.503331i | \(0.832108\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.87086 | − | 1.12902i | −0.974173 | − | 0.225803i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.18513i | − | 0.405769i | −0.979203 | − | 0.202885i | \(-0.934968\pi\) | ||
0.979203 | − | 0.202885i | \(-0.0650316\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.36266 | 1.32237 | 0.661187 | − | 0.750222i | \(-0.270053\pi\) | ||||
0.661187 | + | 0.750222i | \(0.270053\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.51363i | − | 0.263490i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.87086 | − | 0.671502i | −0.992357 | − | 0.113504i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.87086 | 1.29396 | 0.646981 | − | 0.762506i | \(-0.276031\pi\) | ||||
0.646981 | + | 0.762506i | \(0.276031\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.87086 | −0.619834 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.72532 | 1.36267 | 0.681333 | − | 0.731973i | \(-0.261400\pi\) | ||||
0.681333 | + | 0.731973i | \(0.261400\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.01641 | 0.155001 | 0.0775003 | − | 0.996992i | \(-0.475306\pi\) | ||||
0.0775003 | + | 0.996992i | \(0.475306\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.254102 | − | 2.22158i | 0.0378792 | − | 0.331174i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.08582i | 1.03357i | 0.856114 | + | 0.516786i | \(0.172872\pi\) | ||||
−0.856114 | + | 0.516786i | \(0.827128\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.0164068 | 0.00234382 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.31415i | 0.464074i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.50820 | −0.619249 | −0.309625 | − | 0.950859i | \(-0.600203\pi\) | ||||
−0.309625 | + | 0.950859i | \(0.600203\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.36266 | − | 0.384617i | −0.453421 | − | 0.0518617i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.08582i | − | 0.938539i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.79893i | 0.885145i | 0.896733 | + | 0.442573i | \(0.145934\pi\) | ||||
−0.896733 | + | 0.442573i | \(0.854066\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.60104i | 0.461065i | 0.973065 | + | 0.230533i | \(0.0740469\pi\) | ||||
−0.973065 | + | 0.230533i | \(0.925953\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2.64265i | − | 0.332942i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.983593 | + | 8.59945i | −0.122000 | + | 1.06663i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.01641 | −0.124174 | −0.0620869 | − | 0.998071i | \(-0.519776\pi\) | ||||
−0.0620869 | + | 0.998071i | \(0.519776\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.82778i | 0.581197i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.72532 | 0.798149 | 0.399074 | − | 0.916919i | \(-0.369331\pi\) | ||||
0.399074 | + | 0.916919i | \(0.369331\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 15.5146i | − | 1.81585i | −0.419132 | − | 0.907925i | \(-0.637666\pi\) | ||
0.419132 | − | 0.907925i | \(-0.362334\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.87086 | − | 1.12902i | −0.562439 | − | 0.130368i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.00000 | −0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.36266 | −0.828364 | −0.414182 | − | 0.910194i | \(-0.635932\pi\) | ||||
−0.414182 | + | 0.910194i | \(0.635932\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.74173 | 0.849765 | 0.424883 | − | 0.905248i | \(-0.360315\pi\) | ||||
0.424883 | + | 0.905248i | \(0.360315\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.36266 | + | 0.842131i | 0.798593 | + | 0.0913420i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 2.18513i | − | 0.234271i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.7581 | −1.56436 | −0.782180 | − | 0.623053i | \(-0.785892\pi\) | ||||
−0.782180 | + | 0.623053i | \(0.785892\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.2293i | 1.07233i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.36266 | 0.763472 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.7417 | − | 1.80052i | −1.61507 | − | 0.184729i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.1444i | 1.13154i | 0.824563 | + | 0.565769i | \(0.191421\pi\) | ||||
−0.824563 | + | 0.565769i | \(0.808579\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.51363i | − | 0.152126i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.3295i | 1.32633i | 0.748471 | + | 0.663167i | \(0.230788\pi\) | ||||
−0.748471 | + | 0.663167i | \(0.769212\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.958386i | − | 0.0944326i | −0.998885 | − | 0.0472163i | \(-0.984965\pi\) | ||
0.998885 | − | 0.0472163i | \(-0.0150350\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.87086 | − | 0.671502i | −0.572938 | − | 0.0655318i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.769233i | 0.0736792i | 0.999321 | + | 0.0368396i | \(0.0117291\pi\) | ||||
−0.999321 | + | 0.0368396i | \(0.988271\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.87086 | 0.747069 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.4585i | 1.36014i | 0.733146 | + | 0.680071i | \(0.238051\pi\) | ||||
−0.733146 | + | 0.680071i | \(0.761949\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.7253 | + | 1.22675i | 1.00014 | + | 0.114395i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.87086 | −0.357862 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.75814 | 0.802857 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.70892 | 0.791720 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.72532 | 0.786736 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.74590 | + | 10.5341i | −0.335043 | + | 0.942203i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.5290i | − | 1.02303i | −0.859274 | − | 0.511516i | \(-0.829084\pi\) | ||
0.859274 | − | 0.511516i | \(-0.170916\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.01641 | 0.0894896 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.37270i | 0.644156i | 0.946713 | + | 0.322078i | \(0.104381\pi\) | ||||
−0.946713 | + | 0.322078i | \(0.895619\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.7253 | −1.62369 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.254102 | − | 2.22158i | 0.0218696 | − | 0.191203i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3.88792i | − | 0.332167i | −0.986112 | − | 0.166084i | \(-0.946888\pi\) | ||
0.986112 | − | 0.166084i | \(-0.0531122\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.6291i | 1.24083i | 0.784275 | + | 0.620414i | \(0.213035\pi\) | ||||
−0.784275 | + | 0.620414i | \(0.786965\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.08582i | 0.596733i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.85907i | 0.489960i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.85446 | − | 0.555246i | −0.403141 | − | 0.0461107i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.0164068 | 0.00135321 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 11.0715i | − | 0.907010i | −0.891254 | − | 0.453505i | \(-0.850173\pi\) | ||
0.891254 | − | 0.453505i | \(-0.149827\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.637339 | −0.0518659 | −0.0259329 | − | 0.999664i | \(-0.508256\pi\) | ||||
−0.0259329 | + | 0.999664i | \(0.508256\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.31415i | 0.267933i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.87086 | − | 16.3568i | 0.150271 | − | 1.31381i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.129135 | −0.0103061 | −0.00515306 | − | 0.999987i | \(-0.501640\pi\) | ||||
−0.00515306 | + | 0.999987i | \(0.501640\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.50820 | −0.357524 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.7581 | 1.00548 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.4835 | −1.52606 | −0.763031 | − | 0.646362i | \(-0.776290\pi\) | ||||
−0.763031 | + | 0.646362i | \(0.776290\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.36266 | − | 0.384617i | −0.261783 | − | 0.0299424i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.80052i | − | 0.139328i | −0.997571 | − | 0.0696641i | \(-0.977807\pi\) | ||
0.997571 | − | 0.0696641i | \(-0.0221928\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.98359 | 0.152584 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 7.08582i | − | 0.541866i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.2335 | 1.76641 | 0.883206 | − | 0.468985i | \(-0.155380\pi\) | ||||
0.883206 | + | 0.468985i | \(0.155380\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.98359 | + | 12.8720i | −0.225538 | + | 0.973031i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.79893i | 0.511039i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.85664i | 0.213515i | 0.994285 | + | 0.106757i | \(0.0340468\pi\) | ||||
−0.994285 | + | 0.106757i | \(0.965953\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.28530i | − | 0.392853i | −0.980519 | − | 0.196427i | \(-0.937066\pi\) | ||
0.980519 | − | 0.196427i | \(-0.0629337\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.60104i | 0.266196i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.00000 | − | 17.4858i | 0.147043 | − | 1.28558i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.01641 | 0.366836 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 2.64265i | − | 0.192224i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.96719 | 0.431770 | 0.215885 | − | 0.976419i | \(-0.430736\pi\) | ||||
0.215885 | + | 0.976419i | \(0.430736\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.9409i | 1.07547i | 0.843115 | + | 0.537733i | \(0.180719\pi\) | ||||
−0.843115 | + | 0.537733i | \(0.819281\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.983593 | + | 8.59945i | −0.0704366 | + | 0.615819i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.23353 | −0.230379 | −0.115190 | − | 0.993344i | \(-0.536748\pi\) | ||||
−0.115190 | + | 0.993344i | \(0.536748\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.12080 | −0.575668 | −0.287834 | − | 0.957680i | \(-0.592935\pi\) | ||||
−0.287834 | + | 0.957680i | \(0.592935\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.01641 | −0.0716918 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.77454 | −0.405293 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.21712 | − | 19.3840i | 0.154850 | − | 1.35384i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.82778i | 0.335554i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.7253 | −0.741886 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 13.7141i | − | 0.944119i | −0.881567 | − | 0.472059i | \(-0.843511\pi\) | ||
0.881567 | − | 0.472059i | \(-0.156489\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.72532 | 0.460812 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.258271 | − | 2.25803i | 0.0176139 | − | 0.153997i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 19.4569i | − | 1.32082i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 15.5146i | − | 1.04838i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 12.8286i | − | 0.862947i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 9.84472i | − | 0.659251i | −0.944112 | − | 0.329626i | \(-0.893077\pi\) | ||
0.944112 | − | 0.329626i | \(-0.106923\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.87086 | − | 1.12902i | −0.324724 | − | 0.0752677i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.70892 | −0.378914 | −0.189457 | − | 0.981889i | \(-0.560673\pi\) | ||||
−0.189457 | + | 0.981889i | \(0.560673\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 0.769233i | − | 0.0508324i | −0.999677 | − | 0.0254162i | \(-0.991909\pi\) | ||
0.999677 | − | 0.0254162i | \(-0.00809109\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.00000 | −0.263181 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 18.4008i | − | 1.20548i | −0.797939 | − | 0.602739i | \(-0.794076\pi\) | ||
0.797939 | − | 0.602739i | \(-0.205924\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.7417 | + | 1.80052i | 1.02688 | + | 0.117453i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.36266 | −0.478256 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.0328 | 0.648969 | 0.324484 | − | 0.945891i | \(-0.394809\pi\) | ||||
0.324484 | + | 0.945891i | \(0.394809\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.7581 | 0.692992 | 0.346496 | − | 0.938051i | \(-0.387371\pi\) | ||||
0.346496 | + | 0.938051i | \(0.387371\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.00416898 | − | 0.0364490i | 0.000266347 | − | 0.00232864i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.4282i | 1.74522i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.74173 | 0.490612 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 12.6580i | − | 0.798966i | −0.916741 | − | 0.399483i | \(-0.869190\pi\) | ||
0.916741 | − | 0.399483i | \(-0.130810\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.30749 | 0.459418 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.36266 | + | 0.842131i | 0.461068 | + | 0.0527363i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 13.3110i | − | 0.830316i | −0.909749 | − | 0.415158i | \(-0.863726\pi\) | ||
0.909749 | − | 0.415158i | \(-0.136274\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 20.7999i | − | 1.29244i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 2.18513i | − | 0.135256i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 18.4256i | − | 1.13617i | −0.822969 | − | 0.568087i | \(-0.807684\pi\) | ||
0.822969 | − | 0.568087i | \(-0.192316\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.14554 | + | 10.0153i | −0.0703701 | + | 0.615238i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.7581 | −0.903183 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 3.86940i | − | 0.235921i | −0.993018 | − | 0.117961i | \(-0.962364\pi\) | ||
0.993018 | − | 0.117961i | \(-0.0376357\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.3955 | 1.05670 | 0.528350 | − | 0.849027i | \(-0.322811\pi\) | ||||
0.528350 | + | 0.849027i | \(0.322811\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.2293i | 0.619108i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.70892 | + | 7.37270i | −0.103052 | + | 0.444591i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.887271 | −0.0533110 | −0.0266555 | − | 0.999645i | \(-0.508486\pi\) | ||||
−0.0266555 | + | 0.999645i | \(0.508486\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.36266 | 0.440791 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.4835 | −0.804356 | −0.402178 | − | 0.915562i | \(-0.631747\pi\) | ||||
−0.402178 | + | 0.915562i | \(0.631747\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.4342 | −1.69024 | −0.845120 | − | 0.534577i | \(-0.820471\pi\) | ||||
−0.845120 | + | 0.534577i | \(0.820471\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −15.7417 | − | 1.80052i | −0.932460 | − | 0.106653i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 23.0580i | − | 1.36107i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.01641 | 0.353906 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.1444i | 0.653294i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.99166 | 0.466878 | 0.233439 | − | 0.972371i | \(-0.425002\pi\) | ||||
0.233439 | + | 0.972371i | \(0.425002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.1044 | + | 1.72762i | 0.879412 | + | 0.100586i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.51363i | − | 0.0878299i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 18.6877i | − | 1.08074i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 2.68601i | − | 0.154819i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.3295i | 0.765760i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.00000 | + | 0.915029i | 0.458079 | + | 0.0523944i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.4506 | 0.995961 | 0.497980 | − | 0.867188i | \(-0.334075\pi\) | ||||
0.497980 | + | 0.867188i | \(0.334075\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 0.958386i | − | 0.0545207i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.4506 | −1.21635 | −0.608177 | − | 0.793801i | \(-0.708099\pi\) | ||||
−0.608177 | + | 0.793801i | \(0.708099\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.73879i | 0.437422i | 0.975790 | + | 0.218711i | \(0.0701853\pi\) | ||||
−0.975790 | + | 0.218711i | \(0.929815\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.87086 | − | 0.671502i | −0.330786 | − | 0.0378348i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.2335 | −0.630938 | −0.315469 | − | 0.948936i | \(-0.602162\pi\) | ||||
−0.315469 | + | 0.948936i | \(0.602162\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.30749 | −0.185184 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.4835 | 1.30665 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.8545 | + | 4.37027i | 1.04586 | + | 0.242419i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.769233i | 0.0425387i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.7253 | 1.03236 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00084i | 0.439766i | 0.975526 | + | 0.219883i | \(0.0705676\pi\) | ||||
−0.975526 | + | 0.219883i | \(0.929432\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.87086 | 0.431321 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.258271 | + | 2.25803i | −0.0141108 | + | 0.123369i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.5692i | 1.17495i | 0.809243 | + | 0.587474i | \(0.199877\pi\) | ||||
−0.809243 | + | 0.587474i | \(0.800123\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.4585i | 0.785279i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 11.1444i | − | 0.603501i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.5419i | − | 1.00117i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.7253 | + | 1.22675i | 0.577432 | + | 0.0660459i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.7089 | 1.16540 | 0.582698 | − | 0.812689i | \(-0.301997\pi\) | ||||
0.582698 | + | 0.812689i | \(0.301997\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.7422i | 1.32442i | 0.749318 | + | 0.662211i | \(0.230382\pi\) | ||||
−0.749318 | + | 0.662211i | \(0.769618\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.87086 | −0.206611 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.31415i | 0.176394i | 0.996103 | + | 0.0881972i | \(0.0281106\pi\) | ||||
−0.996103 | + | 0.0881972i | \(0.971889\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.70892 | − | 14.9409i | 0.0906998 | − | 0.792979i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.75814 | 0.463530 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.7581 | −0.884461 | −0.442230 | − | 0.896902i | \(-0.645813\pi\) | ||||
−0.442230 | + | 0.896902i | \(0.645813\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −31.2088 | −1.64257 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.70892 | 0.457100 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −34.4671 | − | 3.94229i | −1.80409 | − | 0.206349i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.5324i | 1.48938i | 0.667411 | + | 0.744690i | \(0.267403\pi\) | ||||
−0.667411 | + | 0.744690i | \(0.732597\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.72532 | 0.454222 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.9136i | 0.618523i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −37.5798 | −1.94581 | −0.972904 | − | 0.231211i | \(-0.925731\pi\) | ||||
−0.972904 | + | 0.231211i | \(0.925731\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.74590 | + | 10.5341i | −0.193437 | + | 0.543981i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.45836i | 0.435628i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.74456i | 0.346445i | 0.984883 | + | 0.173222i | \(0.0554179\pi\) | ||||
−0.984883 | + | 0.173222i | \(0.944582\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 11.5290i | − | 0.590648i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 21.8312i | − | 1.11552i | −0.830001 | − | 0.557762i | \(-0.811660\pi\) | ||
0.830001 | − | 0.557762i | \(-0.188340\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.01641 | + | 8.88633i | −0.0518009 | + | 0.452889i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.01641 | 0.0516669 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.81344i | 0.446859i | 0.974720 | + | 0.223429i | \(0.0717252\pi\) | ||||
−0.974720 | + | 0.223429i | \(0.928275\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.37270i | 0.371904i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.87086 | + | 16.3568i | −0.0941334 | + | 0.822998i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.821644 | 0.0412372 | 0.0206186 | − | 0.999787i | \(-0.493436\pi\) | ||||
0.0206186 | + | 0.999787i | \(0.493436\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18.7253 | −0.937439 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.7253 | −0.635472 | −0.317736 | − | 0.948179i | \(-0.602923\pi\) | ||||
−0.317736 | + | 0.948179i | \(0.602923\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.4999 | −1.41968 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.254102 | − | 2.22158i | 0.0126264 | − | 0.110391i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 11.9136i | − | 0.590535i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.25827 | −0.111664 | −0.0558321 | − | 0.998440i | \(-0.517781\pi\) | ||||
−0.0558321 | + | 0.998440i | \(0.517781\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 3.88792i | − | 0.191777i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.9672 | 0.884107 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.96719 | − | 17.1989i | 0.0965654 | − | 0.844261i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.6291i | 0.716392i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.4579i | 1.63453i | 0.576264 | + | 0.817263i | \(0.304510\pi\) | ||||
−0.576264 | + | 0.817263i | \(0.695490\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.3398i | 0.552669i | 0.961061 | + | 0.276335i | \(0.0891198\pi\) | ||||
−0.961061 | + | 0.276335i | \(0.910880\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.08582i | 0.344524i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.74173 | − | 16.1428i | 0.181501 | − | 0.783040i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.51627 | 0.460525 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.85907i | 0.282878i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.6597 | −0.513459 | −0.256730 | − | 0.966483i | \(-0.582645\pi\) | ||||
−0.256730 | + | 0.966483i | \(0.582645\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 26.5132i | − | 1.27414i | −0.770805 | − | 0.637072i | \(-0.780146\pi\) | ||
0.770805 | − | 0.637072i | \(-0.219854\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.85446 | − | 0.555246i | −0.232753 | − | 0.0266220i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 34.2088 | 1.63643 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.8789 | 1.56923 | 0.784613 | − | 0.619986i | \(-0.212862\pi\) | ||||
0.784613 | + | 0.619986i | \(0.212862\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.0164068 | 0.000781274 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.70892 | 0.271239 | 0.135619 | − | 0.990761i | \(-0.456698\pi\) | ||||
0.135619 | + | 0.990761i | \(0.456698\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.75007 | + | 32.7864i | −0.177770 | + | 1.55423i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 11.0715i | − | 0.523662i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.00000 | 0.0943858 | 0.0471929 | − | 0.998886i | \(-0.484972\pi\) | ||||
0.0471929 | + | 0.998886i | \(0.484972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 13.2069i | − | 0.621890i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.637339 | −0.0299448 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 22.7253 | + | 2.59929i | 1.06538 | + | 0.121857i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 3.94229i | − | 0.184413i | −0.995740 | − | 0.0922064i | \(-0.970608\pi\) | ||
0.995740 | − | 0.0922064i | \(-0.0293920\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.31415i | 0.154691i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.8969i | 1.57874i | 0.613920 | + | 0.789369i | \(0.289592\pi\) | ||||
−0.613920 | + | 0.789369i | \(0.710408\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.8688i | 1.06280i | 0.847120 | + | 0.531402i | \(0.178335\pi\) | ||||
−0.847120 | + | 0.531402i | \(0.821665\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.87086 | − | 16.3568i | 0.0867593 | − | 0.758527i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.7417 | −0.728440 | −0.364220 | − | 0.931313i | \(-0.618664\pi\) | ||||
−0.364220 | + | 0.931313i | \(0.618664\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.68601i | 0.124028i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.129135 | −0.00595024 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.53847i | − | 0.0707388i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.00000 | + | 34.5140i | −0.367065 | + | 1.58361i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.50820 | −0.206416 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.6925 | 0.945465 | 0.472732 | − | 0.881206i | \(-0.343268\pi\) | ||||
0.472732 | + | 0.881206i | \(0.343268\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.4671 | −1.38918 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.7581 | 0.580515 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 24.7581 | + | 2.83180i | 1.12421 | + | 0.128586i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 30.8401i | − | 1.39750i | −0.715366 | − | 0.698750i | \(-0.753740\pi\) | ||
0.715366 | − | 0.698750i | \(-0.246260\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.4835 | −0.881072 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 10.9737i | − | 0.495238i | −0.968858 | − | 0.247619i | \(-0.920352\pi\) | ||
0.968858 | − | 0.247619i | \(-0.0796481\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.24186 | 0.326157 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.36266 | − | 0.384617i | −0.151140 | − | 0.0172872i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 17.7727i | − | 0.797213i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3.71729i | − | 0.166409i | −0.996533 | − | 0.0832044i | \(-0.973485\pi\) | ||
0.996533 | − | 0.0832044i | \(-0.0265154\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 1.80052i | − | 0.0804412i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.9451i | 1.78107i | 0.454919 | + | 0.890533i | \(0.349668\pi\) | ||||
−0.454919 | + | 0.890533i | \(0.650332\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.6126 | + | 3.38705i | 1.31774 | + | 0.150722i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.98359 | 0.0880945 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 0.0728979i | − | 0.00323114i | −0.999999 | − | 0.00161557i | \(-0.999486\pi\) | ||
0.999999 | − | 0.00161557i | \(-0.000514253\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −40.9997 | −1.81372 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 7.08582i | − | 0.312846i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.12914 | − | 0.243528i | −0.0938209 | − | 0.0107311i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.7253 | 0.471699 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.2335 | 1.01984 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.9672 | −0.524292 | −0.262146 | − | 0.965028i | \(-0.584430\pi\) | ||||
−0.262146 | + | 0.965028i | \(0.584430\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0656 | 0.702501 | 0.351250 | − | 0.936282i | \(-0.385757\pi\) | ||||
0.351250 | + | 0.936282i | \(0.385757\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.98359 | + | 12.8720i | −0.130215 | + | 0.561779i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.4010i | 1.06292i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.307491 | −0.0133692 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.79893i | 0.295048i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.7745 | −1.46294 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.01641 | + | 8.88633i | −0.0439431 | + | 0.384190i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.85664i | 0.123273i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 0.0248338i | − | 0.00106967i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 15.8559i | − | 0.681698i | −0.940118 | − | 0.340849i | \(-0.889285\pi\) | ||
0.940118 | − | 0.340849i | \(-0.110715\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 5.28530i | − | 0.226814i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.70892 | + | 0.195463i | 0.0732019 | + | 0.00837274i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.95078 | 0.211680 | 0.105840 | − | 0.994383i | \(-0.466247\pi\) | ||||
0.105840 | + | 0.994383i | \(0.466247\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.60104i | 0.153688i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.4835 | −0.659618 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.4569i | 0.827393i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.00000 | − | 17.4858i | 0.0848953 | − | 0.742230i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.26634 | 0.0536565 | 0.0268283 | − | 0.999640i | \(-0.491459\pi\) | ||||
0.0268283 | + | 0.999640i | \(0.491459\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.93437 | −0.166406 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.01641 | 0.211793 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.70892 | −0.240602 | −0.120301 | − | 0.992737i | \(-0.538386\pi\) | ||||
−0.120301 | + | 0.992737i | \(0.538386\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32.1208 | + | 3.67393i | 1.35133 | + | 0.154564i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.64265i | − | 0.110981i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.75814 | 0.115627 | 0.0578135 | − | 0.998327i | \(-0.481587\pi\) | ||||
0.0578135 | + | 0.998327i | \(0.481587\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.7735i | 1.07859i | 0.842118 | + | 0.539294i | \(0.181309\pi\) | ||||
−0.842118 | + | 0.539294i | \(0.818691\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.96719 | 0.249283 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.45065 | − | 23.5155i | 0.227308 | − | 0.980663i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 32.7135i | − | 1.36188i | −0.732338 | − | 0.680941i | \(-0.761571\pi\) | ||
0.732338 | − | 0.680941i | \(-0.238429\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.9409i | 0.620921i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 20.4587i | − | 0.848769i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.82376i | 0.282611i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.983593 | + | 8.59945i | −0.0406666 | + | 0.355543i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −43.4835 | −1.79475 | −0.897377 | − | 0.441264i | \(-0.854530\pi\) | ||||
−0.897377 | + | 0.441264i | \(0.854530\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 52.1705i | − | 2.14965i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.23353 | −0.133009 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 7.83021i | − | 0.321548i | −0.986991 | − | 0.160774i | \(-0.948601\pi\) | ||
0.986991 | − | 0.160774i | \(-0.0513991\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.22546 | − | 19.4569i | 0.0912348 | − | 0.797656i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.12080 | −0.332362 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.7581 | −1.33846 | −0.669231 | − | 0.743055i | \(-0.733376\pi\) | ||||
−0.669231 | + | 0.743055i | \(0.733376\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.8074 | 0.726377 | 0.363189 | − | 0.931716i | \(-0.381688\pi\) | ||||
0.363189 | + | 0.931716i | \(0.381688\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.01641 | −0.0413913 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.21295 | − | 19.3476i | 0.0899692 | − | 0.786591i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.41188i | 0.138484i | 0.997600 | + | 0.0692420i | \(0.0220581\pi\) | ||||
−0.997600 | + | 0.0692420i | \(0.977942\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.77454 | −0.233996 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 27.4282i | − | 1.10963i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.6290 | −1.47943 | −0.739716 | − | 0.672920i | \(-0.765040\pi\) | ||||
−0.739716 | + | 0.672920i | \(0.765040\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.21712 | − | 19.3840i | 0.0894029 | − | 0.781640i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.3979i | 1.62636i | 0.582012 | + | 0.813180i | \(0.302266\pi\) | ||||
−0.582012 | + | 0.813180i | \(0.697734\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.5172i | 0.985430i | 0.870191 | + | 0.492715i | \(0.163996\pi\) | ||||
−0.870191 | + | 0.492715i | \(0.836004\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.82778i | 0.193732i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 39.0006i | 1.56252i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.4506 | + | 10.9986i | 0.898026 | + | 0.439943i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.7253 | −0.428328 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26.0852i | 1.04009i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.7805 | −0.747640 | −0.373820 | − | 0.927501i | \(-0.621952\pi\) | ||||
−0.373820 | + | 0.927501i | \(0.621952\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 13.7141i | − | 0.545087i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −25.6126 | − | 2.92953i | −1.01640 | − | 0.116255i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.0635083 | −0.00251629 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.72532 | 0.266050 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.5163 | −0.612856 | −0.306428 | − | 0.951894i | \(-0.599134\pi\) | ||||
−0.306428 | + | 0.951894i | \(0.599134\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.4506 | 0.688186 | 0.344093 | − | 0.938936i | \(-0.388186\pi\) | ||||
0.344093 | + | 0.938936i | \(0.388186\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.258271 | − | 2.25803i | 0.0101694 | − | 0.0889099i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.1403i | 0.516600i | 0.966065 | + | 0.258300i | \(0.0831624\pi\) | ||||
−0.966065 | + | 0.258300i | \(0.916838\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.2911 | 0.403960 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 19.4569i | − | 0.762577i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.7993 | 0.579141 | 0.289570 | − | 0.957157i | \(-0.406488\pi\) | ||||
0.289570 | + | 0.957157i | \(0.406488\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.3791 | + | 1.87342i | 0.639983 | + | 0.0732004i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 15.5146i | − | 0.605284i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 7.99614i | − | 0.311485i | −0.987798 | − | 0.155743i | \(-0.950223\pi\) | ||
0.987798 | − | 0.155743i | \(-0.0497771\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.915029i | 0.0355905i | 0.999842 | + | 0.0177953i | \(0.00566470\pi\) | ||||
−0.999842 | + | 0.0177953i | \(0.994335\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 12.8286i | − | 0.498223i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.75814 | + | 41.5999i | −0.184513 | + | 1.61317i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.5494 | 0.408473 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 9.84472i | − | 0.380619i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.45065 | 0.210420 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 34.3978i | − | 1.32594i | −0.748647 | − | 0.662969i | \(-0.769296\pi\) | ||
0.748647 | − | 0.662969i | \(-0.230704\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.87086 | − | 1.12902i | −0.187480 | − | 0.0434559i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −40.1676 | −1.54377 | −0.771884 | − | 0.635764i | \(-0.780685\pi\) | ||||
−0.771884 | + | 0.635764i | \(0.780685\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.4506 | 1.13021 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.70892 | −0.218766 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.2580 | 1.27258 | 0.636291 | − | 0.771449i | \(-0.280468\pi\) | ||||
0.636291 | + | 0.771449i | \(0.280468\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.63734 | − | 0.987927i | −0.330016 | − | 0.0377468i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 0.769233i | − | 0.0293481i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17.4506 | 0.664817 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 50.2241i | − | 1.91062i | −0.295611 | − | 0.955308i | \(-0.595523\pi\) | ||
0.295611 | − | 0.955308i | \(-0.404477\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.00000 | −0.151947 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 32.4999 | + | 3.71729i | 1.23279 | + | 0.141005i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28.9170i | 1.09531i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 18.4008i | − | 0.695983i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 23.7543i | − | 0.897188i | −0.893736 | − | 0.448594i | \(-0.851925\pi\) | ||
0.893736 | − | 0.448594i | \(-0.148075\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 55.7715i | − | 2.10346i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.7417 | + | 1.80052i | 0.592868 | + | 0.0678114i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 35.2252 | 1.32478 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 36.3146i | − | 1.36382i | −0.731435 | − | 0.681911i | \(-0.761149\pi\) | ||
0.731435 | − | 0.681911i | \(-0.238851\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.36266 | −0.276121 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 35.5453i | 1.33118i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.0164 | + | 1.48880i | 0.486786 | + | 0.0556779i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.0328 | 0.374682 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.7253 | 1.14586 | 0.572931 | − | 0.819604i | \(-0.305806\pi\) | ||||
0.572931 | + | 0.819604i | \(0.305806\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.53268 | −0.0943219 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.7581 | 0.400099 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.46705 | + | 10.6435i | −0.0916240 | + | 0.395289i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 5.47445i | − | 0.203036i | −0.994834 | − | 0.101518i | \(-0.967630\pi\) | ||
0.994834 | − | 0.101518i | \(-0.0323700\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.36852i | 0.124589i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.1455 | 0.633285 | 0.316643 | − | 0.948545i | \(-0.397444\pi\) | ||||
0.316643 | + | 0.948545i | \(0.397444\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.00416898 | − | 0.0364490i | 0.000153775 | − | 0.00134444i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.53847i | 0.0566701i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 11.6019i | − | 0.426782i | −0.976967 | − | 0.213391i | \(-0.931549\pi\) | ||
0.976967 | − | 0.213391i | \(-0.0684508\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 27.4282i | 1.00760i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 23.6613i | − | 0.868048i | −0.900901 | − | 0.434024i | \(-0.857093\pi\) | ||
0.900901 | − | 0.434024i | \(-0.142907\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.5962 | − | 2.81328i | −0.901135 | − | 0.103071i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.74173 | 0.283255 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.5706i | 0.386241i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.4283 | 0.417024 | 0.208512 | − | 0.978020i | \(-0.433138\pi\) | ||||
0.208512 | + | 0.978020i | \(0.433138\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 12.6580i | − | 0.461283i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.161949 | + | 1.41590i | −0.00589392 | + | 0.0515299i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.1784 | 0.697049 | 0.348525 | − | 0.937300i | \(-0.386683\pi\) | ||||
0.348525 | + | 0.937300i | \(0.386683\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.30749 | 0.265245 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.03281 | 0.146189 | 0.0730947 | − | 0.997325i | \(-0.476712\pi\) | ||||
0.0730947 | + | 0.997325i | \(0.476712\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.03281 | 0.0735928 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.36266 | + | 0.842131i | 0.266198 | + | 0.0304473i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 26.3177i | − | 0.950279i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.95078 | 0.106408 | 0.0532039 | − | 0.998584i | \(-0.483057\pi\) | ||||
0.0532039 | + | 0.998584i | \(0.483057\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 13.3110i | − | 0.479383i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −45.2663 | −1.62812 | −0.814059 | − | 0.580783i | \(-0.802747\pi\) | ||||
−0.814059 | + | 0.580783i | \(0.802747\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −35.8625 | − | 8.31256i | −1.28822 | − | 0.298596i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 20.7999i | − | 0.746193i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 61.8260i | − | 2.21515i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 10.1797i | − | 0.364257i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 2.18513i | − | 0.0780903i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.0328135 | + | 0.286885i | −0.00117116 | + | 0.0102394i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −52.9997 | −1.88924 | −0.944618 | − | 0.328171i | \(-0.893568\pi\) | ||||
−0.944618 | + | 0.328171i | \(0.893568\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 18.4256i | − | 0.655970i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.2088 | 1.35855 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 13.9391i | − | 0.494993i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.14554 | + | 10.0153i | −0.0406282 | + | 0.355208i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.5738 | −0.587075 | −0.293538 | − | 0.955948i | \(-0.594833\pi\) | ||||
−0.293538 | + | 0.955948i | \(0.594833\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.4835 | −0.830785 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.7581 | −0.521453 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.4835 | −0.828713 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.24186 | − | 28.3433i | 0.114261 | − | 0.998969i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 3.86940i | − | 0.136209i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37.5491 | 1.32016 | 0.660078 | − | 0.751197i | \(-0.270523\pi\) | ||||
0.660078 | + | 0.751197i | \(0.270523\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.1102i | 1.12754i | 0.825931 | + | 0.563771i | \(0.190650\pi\) | ||||
−0.825931 | + | 0.563771i | \(0.809350\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.3955 | 0.610086 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.95078 | + | 43.2841i | −0.173418 | + | 1.51618i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 7.20207i | − | 0.251969i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.2293i | 0.357442i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 29.3809i | − | 1.02540i | −0.858568 | − | 0.512699i | \(-0.828646\pi\) | ||
0.858568 | − | 0.512699i | \(-0.171354\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.3866i | 0.989495i | 0.869037 | + | 0.494748i | \(0.164740\pi\) | ||||
−0.869037 | + | 0.494748i | \(0.835260\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.70892 | + | 7.37270i | −0.0594968 | + | 0.256684i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.45065 | −0.0504439 | −0.0252219 | − | 0.999682i | \(-0.508029\pi\) | ||||
−0.0252219 | + | 0.999682i | \(0.508029\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.4621i | 1.30111i | 0.759458 | + | 0.650556i | \(0.225464\pi\) | ||||
−0.759458 | + | 0.650556i | \(0.774536\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.887271 | −0.0307791 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.0543744i | 0.00188396i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.00000 | − | 0.457515i | −0.138426 | − | 0.0158329i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.36266 | 0.254491 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −48.7581 | −1.68332 | −0.841659 | − | 0.540010i | \(-0.818421\pi\) | ||||
−0.841659 | + | 0.540010i | \(0.818421\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.2252 | 0.835351 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.4835 | −0.464395 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.504034 | − | 4.40672i | 0.0173393 | − | 0.151596i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 23.0146i | − | 0.790791i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.4342 | −0.975861 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 37.9988i | 1.30258i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.37073 | 0.149651 | 0.0748255 | − | 0.997197i | \(-0.476160\pi\) | ||||
0.0748255 | + | 0.997197i | \(0.476160\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.7417 | − | 1.80052i | −0.538356 | − | 0.0615764i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.5130i | 0.700712i | 0.936617 | + | 0.350356i | \(0.113939\pi\) | ||||
−0.936617 | + | 0.350356i | \(0.886061\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.1131i | 0.345054i | 0.985005 | + | 0.172527i | \(0.0551932\pi\) | ||||
−0.985005 | + | 0.172527i | \(0.944807\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 23.0580i | − | 0.785813i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.2861i | 0.452266i | 0.974096 | + | 0.226133i | \(0.0726083\pi\) | ||||
−0.974096 | + | 0.226133i | \(0.927392\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.90368 | − | 51.6152i | 0.200731 | − | 1.75497i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.01641 | 0.204328 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.1444i | 0.378047i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.93437 | 0.133311 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.1444i | 0.377180i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 27.8381 | + | 9.89909i | 0.941098 | + | 0.334650i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.6454 | −1.13612 | −0.568062 | − | 0.822986i | \(-0.692307\pi\) | ||||
−0.568062 | + | 0.822986i | \(0.692307\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.99166 | 0.269552 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.7909 | −1.10476 | −0.552378 | − | 0.833594i | \(-0.686279\pi\) | ||||
−0.552378 | + | 0.833594i | \(0.686279\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.4506 | 1.12570 | 0.562852 | − | 0.826558i | \(-0.309704\pi\) | ||||
0.562852 | + | 0.826558i | \(0.309704\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.1044 | + | 1.72762i | 0.507729 | + | 0.0580733i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.8924i | 1.17157i | 0.810466 | + | 0.585785i | \(0.199214\pi\) | ||||
−0.810466 | + | 0.585785i | \(0.800786\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.4671 | −1.02183 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1.51363i | − | 0.0507086i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 50.2088 | 1.68017 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.34625 | + | 0.725876i | 0.212132 | + | 0.0242634i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 18.6877i | − | 0.623964i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 16.0884i | − | 0.536578i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 14.9409i | − | 0.497752i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 2.68601i | − | 0.0893847i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.7417 | − | 1.34300i | −0.390308 | − | 0.0446429i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.9836 | −1.02879 | −0.514397 | − | 0.857552i | \(-0.671984\pi\) | ||||
−0.514397 | + | 0.857552i | \(0.671984\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.3295i | 0.442112i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.0000 | −0.530104 | −0.265052 | − | 0.964234i | \(-0.585389\pi\) | ||||
−0.265052 | + | 0.964234i | \(0.585389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 11.7181i | − | 0.387814i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.00000 | + | 0.915029i | 0.264472 | + | 0.0302499i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.4835 | 0.643400 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.6043 | −0.514737 | −0.257368 | − | 0.966313i | \(-0.582855\pi\) | ||||
−0.257368 | + | 0.966313i | \(0.582855\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.4506 | 0.575018 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −26.0328 | −0.856880 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −38.3379 | − | 8.88633i | −1.26054 | − | 0.292181i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 0.958386i | − | 0.0314775i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.9341 | 1.27739 | 0.638693 | − | 0.769461i | \(-0.279475\pi\) | ||||
0.638693 | + | 0.769461i | \(0.279475\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 0.116255i | − | 0.00381011i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.4506 | −0.702263 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.27468 | − | 11.1444i | 0.0416864 | − | 0.364460i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.6027i | 0.640393i | 0.947351 | + | 0.320197i | \(0.103749\pi\) | ||||
−0.947351 | + | 0.320197i | \(0.896251\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.73879i | 0.252546i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.0476i | 0.816530i | 0.912864 | + | 0.408265i | \(0.133866\pi\) | ||||
−0.912864 | + | 0.408265i | \(0.866134\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42.1240i | 1.37175i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.87086 | − | 0.671502i | −0.190979 | − | 0.0218439i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.93437 | −0.257832 | −0.128916 | − | 0.991655i | \(-0.541150\pi\) | ||||
−0.128916 | + | 0.991655i | \(0.541150\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 60.0550i | 1.94947i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.2335 | −0.364272 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.4809i | 0.371903i | 0.982559 | + | 0.185952i | \(0.0595368\pi\) | ||||
−0.982559 | + | 0.185952i | \(0.940463\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.51627 | − | 13.2566i | 0.0490654 | − | 0.428974i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.30749 | −0.106916 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.2744 | −0.331778 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.2088 | 0.748670 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.00000 | −0.128898 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 33.1924 | + | 3.79650i | 1.06850 | + | 0.122214i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 15.8993i | − | 0.511285i | −0.966771 | − | 0.255643i | \(-0.917713\pi\) | ||
0.966771 | − | 0.255643i | \(-0.0822871\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 23.4835 | 0.754397 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.6600i | 1.30484i | 0.757857 | + | 0.652421i | \(0.226246\pi\) | ||||
−0.757857 | + | 0.652421i | \(0.773754\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38.6597 | 1.23937 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.8545 | + | 4.37027i | 0.603826 | + | 0.139961i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 26.5676i | − | 0.849972i | −0.905200 | − | 0.424986i | \(-0.860279\pi\) | ||
0.905200 | − | 0.424986i | \(-0.139721\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.3384i | 0.713938i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.769233i | 0.0245597i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.88057i | 0.315141i | 0.987508 | + | 0.157571i | \(0.0503662\pi\) | ||||
−0.987508 | + | 0.157571i | \(0.949634\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.821644 | + | 7.18355i | −0.0261798 | + | 0.228887i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18.7253 | 0.596034 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.90699i | 0.156033i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.0549 | 1.68534 | 0.842672 | − | 0.538427i | \(-0.180981\pi\) | ||||
0.842672 | + | 0.538427i | \(0.180981\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.00084i | 0.253899i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.06351 | + | 18.0410i | −0.0654176 | + | 0.571939i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.3051 | 1.02311 | 0.511556 | − | 0.859250i | \(-0.329069\pi\) | ||||
0.511556 | + | 0.859250i | \(0.329069\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.87086 | 0.249023 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))