Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(22,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.22");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 484.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.484 |
Dual form | 507.2.e.h.22.2 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.20711 | + | 2.09077i | 0.853553 | + | 1.47840i | 0.877981 | + | 0.478696i | \(0.158890\pi\) |
−0.0244272 | + | 0.999702i | \(0.507776\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −1.91421 | + | 3.31552i | −0.957107 | + | 1.65776i | ||||
\(5\) | 2.82843 | 1.26491 | 0.632456 | − | 0.774597i | \(-0.282047\pi\) | ||||
0.632456 | + | 0.774597i | \(0.282047\pi\) | |||||||
\(6\) | 1.20711 | − | 2.09077i | 0.492799 | − | 0.853553i | ||||
\(7\) | 1.41421 | − | 2.44949i | 0.534522 | − | 0.925820i | −0.464664 | − | 0.885487i | \(-0.653825\pi\) |
0.999186 | − | 0.0403329i | \(-0.0128419\pi\) | |||||||
\(8\) | −4.41421 | −1.56066 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 3.41421 | + | 5.91359i | 1.07967 | + | 1.87004i | ||||
\(11\) | 1.00000 | + | 1.73205i | 0.301511 | + | 0.522233i | 0.976478 | − | 0.215615i | \(-0.0691756\pi\) |
−0.674967 | + | 0.737848i | \(0.735842\pi\) | |||||||
\(12\) | 3.82843 | 1.10517 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 6.82843 | 1.82497 | ||||||||
\(15\) | −1.41421 | − | 2.44949i | −0.365148 | − | 0.632456i | ||||
\(16\) | −1.50000 | − | 2.59808i | −0.375000 | − | 0.649519i | ||||
\(17\) | 1.82843 | − | 3.16693i | 0.443459 | − | 0.768093i | −0.554485 | − | 0.832194i | \(-0.687085\pi\) |
0.997943 | + | 0.0641009i | \(0.0204179\pi\) | |||||||
\(18\) | −2.41421 | −0.569036 | ||||||||
\(19\) | −1.41421 | + | 2.44949i | −0.324443 | + | 0.561951i | −0.981399 | − | 0.191977i | \(-0.938510\pi\) |
0.656957 | + | 0.753928i | \(0.271843\pi\) | |||||||
\(20\) | −5.41421 | + | 9.37769i | −1.21065 | + | 2.09692i | ||||
\(21\) | −2.82843 | −0.617213 | ||||||||
\(22\) | −2.41421 | + | 4.18154i | −0.514712 | + | 0.891507i | ||||
\(23\) | 2.00000 | + | 3.46410i | 0.417029 | + | 0.722315i | 0.995639 | − | 0.0932891i | \(-0.0297381\pi\) |
−0.578610 | + | 0.815604i | \(0.696405\pi\) | |||||||
\(24\) | 2.20711 | + | 3.82282i | 0.450524 | + | 0.780330i | ||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 5.41421 | + | 9.37769i | 1.02319 | + | 1.77222i | ||||
\(29\) | −1.00000 | − | 1.73205i | −0.185695 | − | 0.321634i | 0.758115 | − | 0.652121i | \(-0.226120\pi\) |
−0.943811 | + | 0.330487i | \(0.892787\pi\) | |||||||
\(30\) | 3.41421 | − | 5.91359i | 0.623347 | − | 1.07967i | ||||
\(31\) | −6.82843 | −1.22642 | −0.613211 | − | 0.789919i | \(-0.710122\pi\) | ||||
−0.613211 | + | 0.789919i | \(0.710122\pi\) | |||||||
\(32\) | −0.792893 | + | 1.37333i | −0.140165 | + | 0.242773i | ||||
\(33\) | 1.00000 | − | 1.73205i | 0.174078 | − | 0.301511i | ||||
\(34\) | 8.82843 | 1.51406 | ||||||||
\(35\) | 4.00000 | − | 6.92820i | 0.676123 | − | 1.17108i | ||||
\(36\) | −1.91421 | − | 3.31552i | −0.319036 | − | 0.552586i | ||||
\(37\) | −1.82843 | − | 3.16693i | −0.300592 | − | 0.520640i | 0.675679 | − | 0.737196i | \(-0.263851\pi\) |
−0.976270 | + | 0.216557i | \(0.930517\pi\) | |||||||
\(38\) | −6.82843 | −1.10772 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −12.4853 | −1.97410 | ||||||||
\(41\) | −5.41421 | − | 9.37769i | −0.845558 | − | 1.46455i | −0.885136 | − | 0.465333i | \(-0.845935\pi\) |
0.0395775 | − | 0.999217i | \(-0.487399\pi\) | |||||||
\(42\) | −3.41421 | − | 5.91359i | −0.526825 | − | 0.912487i | ||||
\(43\) | −4.82843 | + | 8.36308i | −0.736328 | + | 1.27536i | 0.217810 | + | 0.975991i | \(0.430109\pi\) |
−0.954138 | + | 0.299367i | \(0.903225\pi\) | |||||||
\(44\) | −7.65685 | −1.15431 | ||||||||
\(45\) | −1.41421 | + | 2.44949i | −0.210819 | + | 0.365148i | ||||
\(46\) | −4.82843 | + | 8.36308i | −0.711913 | + | 1.23307i | ||||
\(47\) | −0.343146 | −0.0500530 | −0.0250265 | − | 0.999687i | \(-0.507967\pi\) | ||||
−0.0250265 | + | 0.999687i | \(0.507967\pi\) | |||||||
\(48\) | −1.50000 | + | 2.59808i | −0.216506 | + | 0.375000i | ||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 3.62132 | + | 6.27231i | 0.512132 | + | 0.887039i | ||||
\(51\) | −3.65685 | −0.512062 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 1.20711 | + | 2.09077i | 0.164266 | + | 0.284518i | ||||
\(55\) | 2.82843 | + | 4.89898i | 0.381385 | + | 0.660578i | ||||
\(56\) | −6.24264 | + | 10.8126i | −0.834208 | + | 1.44489i | ||||
\(57\) | 2.82843 | 0.374634 | ||||||||
\(58\) | 2.41421 | − | 4.18154i | 0.317002 | − | 0.549063i | ||||
\(59\) | 1.82843 | − | 3.16693i | 0.238041 | − | 0.412299i | −0.722111 | − | 0.691777i | \(-0.756828\pi\) |
0.960152 | + | 0.279478i | \(0.0901614\pi\) | |||||||
\(60\) | 10.8284 | 1.39794 | ||||||||
\(61\) | 4.65685 | − | 8.06591i | 0.596249 | − | 1.03273i | −0.397120 | − | 0.917767i | \(-0.629990\pi\) |
0.993369 | − | 0.114967i | \(-0.0366763\pi\) | |||||||
\(62\) | −8.24264 | − | 14.2767i | −1.04682 | − | 1.81314i | ||||
\(63\) | 1.41421 | + | 2.44949i | 0.178174 | + | 0.308607i | ||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.82843 | 0.594338 | ||||||||
\(67\) | −0.585786 | − | 1.01461i | −0.0715652 | − | 0.123955i | 0.828022 | − | 0.560695i | \(-0.189466\pi\) |
−0.899587 | + | 0.436741i | \(0.856133\pi\) | |||||||
\(68\) | 7.00000 | + | 12.1244i | 0.848875 | + | 1.47029i | ||||
\(69\) | 2.00000 | − | 3.46410i | 0.240772 | − | 0.417029i | ||||
\(70\) | 19.3137 | 2.30843 | ||||||||
\(71\) | −1.00000 | + | 1.73205i | −0.118678 | + | 0.205557i | −0.919244 | − | 0.393688i | \(-0.871199\pi\) |
0.800566 | + | 0.599245i | \(0.204532\pi\) | |||||||
\(72\) | 2.20711 | − | 3.82282i | 0.260110 | − | 0.450524i | ||||
\(73\) | 11.6569 | 1.36433 | 0.682166 | − | 0.731198i | \(-0.261038\pi\) | ||||
0.682166 | + | 0.731198i | \(0.261038\pi\) | |||||||
\(74\) | 4.41421 | − | 7.64564i | 0.513142 | − | 0.888788i | ||||
\(75\) | −1.50000 | − | 2.59808i | −0.173205 | − | 0.300000i | ||||
\(76\) | −5.41421 | − | 9.37769i | −0.621053 | − | 1.07570i | ||||
\(77\) | 5.65685 | 0.644658 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3137 | 1.27289 | 0.636446 | − | 0.771321i | \(-0.280404\pi\) | ||||
0.636446 | + | 0.771321i | \(0.280404\pi\) | |||||||
\(80\) | −4.24264 | − | 7.34847i | −0.474342 | − | 0.821584i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 13.0711 | − | 22.6398i | 1.44346 | − | 2.50014i | ||||
\(83\) | −7.65685 | −0.840449 | −0.420224 | − | 0.907420i | \(-0.638049\pi\) | ||||
−0.420224 | + | 0.907420i | \(0.638049\pi\) | |||||||
\(84\) | 5.41421 | − | 9.37769i | 0.590739 | − | 1.02319i | ||||
\(85\) | 5.17157 | − | 8.95743i | 0.560936 | − | 0.971569i | ||||
\(86\) | −23.3137 | −2.51398 | ||||||||
\(87\) | −1.00000 | + | 1.73205i | −0.107211 | + | 0.185695i | ||||
\(88\) | −4.41421 | − | 7.64564i | −0.470557 | − | 0.815028i | ||||
\(89\) | −4.58579 | − | 7.94282i | −0.486092 | − | 0.841937i | 0.513780 | − | 0.857922i | \(-0.328245\pi\) |
−0.999872 | + | 0.0159854i | \(0.994911\pi\) | |||||||
\(90\) | −6.82843 | −0.719779 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −15.3137 | −1.59656 | ||||||||
\(93\) | 3.41421 | + | 5.91359i | 0.354037 | + | 0.613211i | ||||
\(94\) | −0.414214 | − | 0.717439i | −0.0427229 | − | 0.0739982i | ||||
\(95\) | −4.00000 | + | 6.92820i | −0.410391 | + | 0.710819i | ||||
\(96\) | 1.58579 | 0.161849 | ||||||||
\(97\) | 3.82843 | − | 6.63103i | 0.388718 | − | 0.673279i | −0.603559 | − | 0.797318i | \(-0.706251\pi\) |
0.992277 | + | 0.124039i | \(0.0395847\pi\) | |||||||
\(98\) | 1.20711 | − | 2.09077i | 0.121936 | − | 0.211200i | ||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | −5.74264 | + | 9.94655i | −0.574264 | + | 0.994655i | ||||
\(101\) | 1.82843 | + | 3.16693i | 0.181935 | + | 0.315121i | 0.942540 | − | 0.334095i | \(-0.108431\pi\) |
−0.760604 | + | 0.649216i | \(0.775097\pi\) | |||||||
\(102\) | −4.41421 | − | 7.64564i | −0.437072 | − | 0.757031i | ||||
\(103\) | 13.6569 | 1.34565 | 0.672825 | − | 0.739802i | \(-0.265081\pi\) | ||||
0.672825 | + | 0.739802i | \(0.265081\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.00000 | −0.780720 | ||||||||
\(106\) | −2.41421 | − | 4.18154i | −0.234489 | − | 0.406147i | ||||
\(107\) | −5.65685 | − | 9.79796i | −0.546869 | − | 0.947204i | −0.998487 | − | 0.0549930i | \(-0.982486\pi\) |
0.451618 | − | 0.892211i | \(-0.350847\pi\) | |||||||
\(108\) | −1.91421 | + | 3.31552i | −0.184195 | + | 0.319036i | ||||
\(109\) | −17.3137 | −1.65835 | −0.829176 | − | 0.558987i | \(-0.811190\pi\) | ||||
−0.829176 | + | 0.558987i | \(0.811190\pi\) | |||||||
\(110\) | −6.82843 | + | 11.8272i | −0.651065 | + | 1.12768i | ||||
\(111\) | −1.82843 | + | 3.16693i | −0.173547 | + | 0.300592i | ||||
\(112\) | −8.48528 | −0.801784 | ||||||||
\(113\) | −8.65685 | + | 14.9941i | −0.814368 | + | 1.41053i | 0.0954122 | + | 0.995438i | \(0.469583\pi\) |
−0.909781 | + | 0.415090i | \(0.863750\pi\) | |||||||
\(114\) | 3.41421 | + | 5.91359i | 0.319770 | + | 0.553859i | ||||
\(115\) | 5.65685 | + | 9.79796i | 0.527504 | + | 0.913664i | ||||
\(116\) | 7.65685 | 0.710921 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.82843 | 0.812723 | ||||||||
\(119\) | −5.17157 | − | 8.95743i | −0.474077 | − | 0.821126i | ||||
\(120\) | 6.24264 | + | 10.8126i | 0.569873 | + | 0.987048i | ||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 22.4853 | 2.03572 | ||||||||
\(123\) | −5.41421 | + | 9.37769i | −0.488183 | + | 0.845558i | ||||
\(124\) | 13.0711 | − | 22.6398i | 1.17382 | − | 2.03311i | ||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | −3.41421 | + | 5.91359i | −0.304162 | + | 0.526825i | ||||
\(127\) | 2.82843 | + | 4.89898i | 0.250982 | + | 0.434714i | 0.963797 | − | 0.266639i | \(-0.0859131\pi\) |
−0.712814 | + | 0.701353i | \(0.752580\pi\) | |||||||
\(128\) | −10.2782 | − | 17.8023i | −0.908471 | − | 1.57352i | ||||
\(129\) | 9.65685 | 0.850239 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.00000 | −0.698963 | −0.349482 | − | 0.936943i | \(-0.613642\pi\) | ||||
−0.349482 | + | 0.936943i | \(0.613642\pi\) | |||||||
\(132\) | 3.82843 | + | 6.63103i | 0.333222 | + | 0.577157i | ||||
\(133\) | 4.00000 | + | 6.92820i | 0.346844 | + | 0.600751i | ||||
\(134\) | 1.41421 | − | 2.44949i | 0.122169 | − | 0.211604i | ||||
\(135\) | 2.82843 | 0.243432 | ||||||||
\(136\) | −8.07107 | + | 13.9795i | −0.692088 | + | 1.19873i | ||||
\(137\) | 2.58579 | − | 4.47871i | 0.220919 | − | 0.382642i | −0.734169 | − | 0.678967i | \(-0.762428\pi\) |
0.955087 | + | 0.296325i | \(0.0957611\pi\) | |||||||
\(138\) | 9.65685 | 0.822046 | ||||||||
\(139\) | −7.65685 | + | 13.2621i | −0.649446 | + | 1.12487i | 0.333810 | + | 0.942641i | \(0.391666\pi\) |
−0.983255 | + | 0.182233i | \(0.941668\pi\) | |||||||
\(140\) | 15.3137 | + | 26.5241i | 1.29424 | + | 2.24170i | ||||
\(141\) | 0.171573 | + | 0.297173i | 0.0144490 | + | 0.0250265i | ||||
\(142\) | −4.82843 | −0.405193 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | −2.82843 | − | 4.89898i | −0.234888 | − | 0.406838i | ||||
\(146\) | 14.0711 | + | 24.3718i | 1.16453 | + | 2.01702i | ||||
\(147\) | −0.500000 | + | 0.866025i | −0.0412393 | + | 0.0714286i | ||||
\(148\) | 14.0000 | 1.15079 | ||||||||
\(149\) | 7.41421 | − | 12.8418i | 0.607396 | − | 1.05204i | −0.384272 | − | 0.923220i | \(-0.625547\pi\) |
0.991668 | − | 0.128821i | \(-0.0411192\pi\) | |||||||
\(150\) | 3.62132 | − | 6.27231i | 0.295680 | − | 0.512132i | ||||
\(151\) | −20.4853 | −1.66707 | −0.833534 | − | 0.552468i | \(-0.813686\pi\) | ||||
−0.833534 | + | 0.552468i | \(0.813686\pi\) | |||||||
\(152\) | 6.24264 | − | 10.8126i | 0.506345 | − | 0.877015i | ||||
\(153\) | 1.82843 | + | 3.16693i | 0.147820 | + | 0.256031i | ||||
\(154\) | 6.82843 | + | 11.8272i | 0.550250 | + | 0.953062i | ||||
\(155\) | −19.3137 | −1.55131 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | 13.6569 | + | 23.6544i | 1.08648 | + | 1.88184i | ||||
\(159\) | 1.00000 | + | 1.73205i | 0.0793052 | + | 0.137361i | ||||
\(160\) | −2.24264 | + | 3.88437i | −0.177296 | + | 0.307086i | ||||
\(161\) | 11.3137 | 0.891645 | ||||||||
\(162\) | 1.20711 | − | 2.09077i | 0.0948393 | − | 0.164266i | ||||
\(163\) | −6.58579 | + | 11.4069i | −0.515839 | + | 0.893459i | 0.483992 | + | 0.875072i | \(0.339186\pi\) |
−0.999831 | + | 0.0183864i | \(0.994147\pi\) | |||||||
\(164\) | 41.4558 | 3.23716 | ||||||||
\(165\) | 2.82843 | − | 4.89898i | 0.220193 | − | 0.381385i | ||||
\(166\) | −9.24264 | − | 16.0087i | −0.717368 | − | 1.24252i | ||||
\(167\) | −3.82843 | − | 6.63103i | −0.296253 | − | 0.513125i | 0.679023 | − | 0.734117i | \(-0.262404\pi\) |
−0.975275 | + | 0.220993i | \(0.929070\pi\) | |||||||
\(168\) | 12.4853 | 0.963260 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 24.9706 | 1.91515 | ||||||||
\(171\) | −1.41421 | − | 2.44949i | −0.108148 | − | 0.187317i | ||||
\(172\) | −18.4853 | − | 32.0174i | −1.40949 | − | 2.44131i | ||||
\(173\) | 0.171573 | − | 0.297173i | 0.0130444 | − | 0.0225936i | −0.859429 | − | 0.511254i | \(-0.829181\pi\) |
0.872474 | + | 0.488661i | \(0.162514\pi\) | |||||||
\(174\) | −4.82843 | −0.366042 | ||||||||
\(175\) | 4.24264 | − | 7.34847i | 0.320713 | − | 0.555492i | ||||
\(176\) | 3.00000 | − | 5.19615i | 0.226134 | − | 0.391675i | ||||
\(177\) | −3.65685 | −0.274866 | ||||||||
\(178\) | 11.0711 | − | 19.1757i | 0.829812 | − | 1.43728i | ||||
\(179\) | 0.343146 | + | 0.594346i | 0.0256479 | + | 0.0444235i | 0.878564 | − | 0.477624i | \(-0.158502\pi\) |
−0.852917 | + | 0.522047i | \(0.825168\pi\) | |||||||
\(180\) | −5.41421 | − | 9.37769i | −0.403552 | − | 0.698972i | ||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.31371 | −0.688489 | ||||||||
\(184\) | −8.82843 | − | 15.2913i | −0.650840 | − | 1.12729i | ||||
\(185\) | −5.17157 | − | 8.95743i | −0.380222 | − | 0.658563i | ||||
\(186\) | −8.24264 | + | 14.2767i | −0.604380 | + | 1.04682i | ||||
\(187\) | 7.31371 | 0.534831 | ||||||||
\(188\) | 0.656854 | − | 1.13770i | 0.0479060 | − | 0.0829757i | ||||
\(189\) | 1.41421 | − | 2.44949i | 0.102869 | − | 0.178174i | ||||
\(190\) | −19.3137 | −1.40116 | ||||||||
\(191\) | 9.65685 | − | 16.7262i | 0.698745 | − | 1.21026i | −0.270156 | − | 0.962817i | \(-0.587075\pi\) |
0.968902 | − | 0.247446i | \(-0.0795913\pi\) | |||||||
\(192\) | 4.91421 | + | 8.51167i | 0.354653 | + | 0.614277i | ||||
\(193\) | 8.65685 | + | 14.9941i | 0.623134 | + | 1.07930i | 0.988899 | + | 0.148592i | \(0.0474742\pi\) |
−0.365765 | + | 0.930707i | \(0.619192\pi\) | |||||||
\(194\) | 18.4853 | 1.32717 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.82843 | 0.273459 | ||||||||
\(197\) | 8.24264 | + | 14.2767i | 0.587264 | + | 1.01717i | 0.994589 | + | 0.103888i | \(0.0331282\pi\) |
−0.407325 | + | 0.913283i | \(0.633538\pi\) | |||||||
\(198\) | −2.41421 | − | 4.18154i | −0.171571 | − | 0.297169i | ||||
\(199\) | −5.17157 | + | 8.95743i | −0.366603 | + | 0.634975i | −0.989032 | − | 0.147701i | \(-0.952813\pi\) |
0.622429 | + | 0.782676i | \(0.286146\pi\) | |||||||
\(200\) | −13.2426 | −0.936396 | ||||||||
\(201\) | −0.585786 | + | 1.01461i | −0.0413182 | + | 0.0715652i | ||||
\(202\) | −4.41421 | + | 7.64564i | −0.310583 | + | 0.537946i | ||||
\(203\) | −5.65685 | −0.397033 | ||||||||
\(204\) | 7.00000 | − | 12.1244i | 0.490098 | − | 0.848875i | ||||
\(205\) | −15.3137 | − | 26.5241i | −1.06956 | − | 1.85252i | ||||
\(206\) | 16.4853 | + | 28.5533i | 1.14858 | + | 1.98941i | ||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.65685 | −0.391293 | ||||||||
\(210\) | −9.65685 | − | 16.7262i | −0.666386 | − | 1.15421i | ||||
\(211\) | 6.00000 | + | 10.3923i | 0.413057 | + | 0.715436i | 0.995222 | − | 0.0976347i | \(-0.0311277\pi\) |
−0.582165 | + | 0.813070i | \(0.697794\pi\) | |||||||
\(212\) | 3.82843 | − | 6.63103i | 0.262937 | − | 0.455421i | ||||
\(213\) | 2.00000 | 0.137038 | ||||||||
\(214\) | 13.6569 | − | 23.6544i | 0.933563 | − | 1.61698i | ||||
\(215\) | −13.6569 | + | 23.6544i | −0.931390 | + | 1.61321i | ||||
\(216\) | −4.41421 | −0.300349 | ||||||||
\(217\) | −9.65685 | + | 16.7262i | −0.655550 | + | 1.13545i | ||||
\(218\) | −20.8995 | − | 36.1990i | −1.41549 | − | 2.45170i | ||||
\(219\) | −5.82843 | − | 10.0951i | −0.393849 | − | 0.682166i | ||||
\(220\) | −21.6569 | −1.46010 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −8.82843 | −0.592525 | ||||||||
\(223\) | −2.24264 | − | 3.88437i | −0.150178 | − | 0.260116i | 0.781115 | − | 0.624388i | \(-0.214651\pi\) |
−0.931293 | + | 0.364271i | \(0.881318\pi\) | |||||||
\(224\) | 2.24264 | + | 3.88437i | 0.149843 | + | 0.259535i | ||||
\(225\) | −1.50000 | + | 2.59808i | −0.100000 | + | 0.173205i | ||||
\(226\) | −41.7990 | −2.78043 | ||||||||
\(227\) | −2.65685 | + | 4.60181i | −0.176342 | + | 0.305433i | −0.940625 | − | 0.339448i | \(-0.889760\pi\) |
0.764283 | + | 0.644881i | \(0.223093\pi\) | |||||||
\(228\) | −5.41421 | + | 9.37769i | −0.358565 | + | 0.621053i | ||||
\(229\) | 21.3137 | 1.40845 | 0.704225 | − | 0.709977i | \(-0.251295\pi\) | ||||
0.704225 | + | 0.709977i | \(0.251295\pi\) | |||||||
\(230\) | −13.6569 | + | 23.6544i | −0.900506 | + | 1.55972i | ||||
\(231\) | −2.82843 | − | 4.89898i | −0.186097 | − | 0.322329i | ||||
\(232\) | 4.41421 | + | 7.64564i | 0.289807 | + | 0.501961i | ||||
\(233\) | −26.9706 | −1.76690 | −0.883450 | − | 0.468525i | \(-0.844786\pi\) | ||||
−0.883450 | + | 0.468525i | \(0.844786\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.970563 | −0.0633125 | ||||||||
\(236\) | 7.00000 | + | 12.1244i | 0.455661 | + | 0.789228i | ||||
\(237\) | −5.65685 | − | 9.79796i | −0.367452 | − | 0.636446i | ||||
\(238\) | 12.4853 | − | 21.6251i | 0.809301 | − | 1.40175i | ||||
\(239\) | 2.00000 | 0.129369 | 0.0646846 | − | 0.997906i | \(-0.479396\pi\) | ||||
0.0646846 | + | 0.997906i | \(0.479396\pi\) | |||||||
\(240\) | −4.24264 | + | 7.34847i | −0.273861 | + | 0.474342i | ||||
\(241\) | −5.82843 | + | 10.0951i | −0.375442 | + | 0.650285i | −0.990393 | − | 0.138281i | \(-0.955842\pi\) |
0.614951 | + | 0.788565i | \(0.289176\pi\) | |||||||
\(242\) | 16.8995 | 1.08634 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 17.8284 | + | 30.8797i | 1.14135 | + | 1.97687i | ||||
\(245\) | −1.41421 | − | 2.44949i | −0.0903508 | − | 0.156492i | ||||
\(246\) | −26.1421 | −1.66676 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 30.1421 | 1.91403 | ||||||||
\(249\) | 3.82843 | + | 6.63103i | 0.242617 | + | 0.420224i | ||||
\(250\) | −6.82843 | − | 11.8272i | −0.431868 | − | 0.748017i | ||||
\(251\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(252\) | −10.8284 | −0.682127 | ||||||||
\(253\) | −4.00000 | + | 6.92820i | −0.251478 | + | 0.435572i | ||||
\(254\) | −6.82843 | + | 11.8272i | −0.428454 | + | 0.742103i | ||||
\(255\) | −10.3431 | −0.647713 | ||||||||
\(256\) | 14.9853 | − | 25.9553i | 0.936580 | − | 1.62220i | ||||
\(257\) | 7.82843 | + | 13.5592i | 0.488324 | + | 0.845802i | 0.999910 | − | 0.0134304i | \(-0.00427515\pi\) |
−0.511586 | + | 0.859232i | \(0.670942\pi\) | |||||||
\(258\) | 11.6569 | + | 20.1903i | 0.725724 | + | 1.25699i | ||||
\(259\) | −10.3431 | −0.642692 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | −9.65685 | − | 16.7262i | −0.596602 | − | 1.03335i | ||||
\(263\) | −6.00000 | − | 10.3923i | −0.369976 | − | 0.640817i | 0.619586 | − | 0.784929i | \(-0.287301\pi\) |
−0.989561 | + | 0.144112i | \(0.953967\pi\) | |||||||
\(264\) | −4.41421 | + | 7.64564i | −0.271676 | + | 0.470557i | ||||
\(265\) | −5.65685 | −0.347498 | ||||||||
\(266\) | −9.65685 | + | 16.7262i | −0.592100 | + | 1.02555i | ||||
\(267\) | −4.58579 | + | 7.94282i | −0.280646 | + | 0.486092i | ||||
\(268\) | 4.48528 | 0.273982 | ||||||||
\(269\) | −9.00000 | + | 15.5885i | −0.548740 | + | 0.950445i | 0.449622 | + | 0.893219i | \(0.351559\pi\) |
−0.998361 | + | 0.0572259i | \(0.981774\pi\) | |||||||
\(270\) | 3.41421 | + | 5.91359i | 0.207782 | + | 0.359890i | ||||
\(271\) | −5.89949 | − | 10.2182i | −0.358369 | − | 0.620713i | 0.629320 | − | 0.777147i | \(-0.283334\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(272\) | −10.9706 | −0.665188 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.4853 | 0.754263 | ||||||||
\(275\) | 3.00000 | + | 5.19615i | 0.180907 | + | 0.313340i | ||||
\(276\) | 7.65685 | + | 13.2621i | 0.460888 | + | 0.798282i | ||||
\(277\) | 1.00000 | − | 1.73205i | 0.0600842 | − | 0.104069i | −0.834419 | − | 0.551131i | \(-0.814196\pi\) |
0.894503 | + | 0.447062i | \(0.147530\pi\) | |||||||
\(278\) | −36.9706 | −2.21735 | ||||||||
\(279\) | 3.41421 | − | 5.91359i | 0.204404 | − | 0.354037i | ||||
\(280\) | −17.6569 | + | 30.5826i | −1.05520 | + | 1.82766i | ||||
\(281\) | 26.8284 | 1.60045 | 0.800225 | − | 0.599700i | \(-0.204713\pi\) | ||||
0.800225 | + | 0.599700i | \(0.204713\pi\) | |||||||
\(282\) | −0.414214 | + | 0.717439i | −0.0246661 | + | 0.0427229i | ||||
\(283\) | 2.48528 | + | 4.30463i | 0.147735 | + | 0.255884i | 0.930390 | − | 0.366572i | \(-0.119469\pi\) |
−0.782655 | + | 0.622455i | \(0.786135\pi\) | |||||||
\(284\) | −3.82843 | − | 6.63103i | −0.227175 | − | 0.393479i | ||||
\(285\) | 8.00000 | 0.473879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.6274 | −1.80788 | ||||||||
\(288\) | −0.792893 | − | 1.37333i | −0.0467217 | − | 0.0809243i | ||||
\(289\) | 1.81371 | + | 3.14144i | 0.106689 | + | 0.184790i | ||||
\(290\) | 6.82843 | − | 11.8272i | 0.400979 | − | 0.694516i | ||||
\(291\) | −7.65685 | −0.448853 | ||||||||
\(292\) | −22.3137 | + | 38.6485i | −1.30581 | + | 2.26173i | ||||
\(293\) | 13.0711 | − | 22.6398i | 0.763620 | − | 1.32263i | −0.177353 | − | 0.984147i | \(-0.556753\pi\) |
0.940973 | − | 0.338481i | \(-0.109913\pi\) | |||||||
\(294\) | −2.41421 | −0.140800 | ||||||||
\(295\) | 5.17157 | − | 8.95743i | 0.301101 | − | 0.521522i | ||||
\(296\) | 8.07107 | + | 13.9795i | 0.469121 | + | 0.812542i | ||||
\(297\) | 1.00000 | + | 1.73205i | 0.0580259 | + | 0.100504i | ||||
\(298\) | 35.7990 | 2.07378 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 11.4853 | 0.663103 | ||||||||
\(301\) | 13.6569 | + | 23.6544i | 0.787168 | + | 1.36341i | ||||
\(302\) | −24.7279 | − | 42.8300i | −1.42293 | − | 2.46459i | ||||
\(303\) | 1.82843 | − | 3.16693i | 0.105040 | − | 0.181935i | ||||
\(304\) | 8.48528 | 0.486664 | ||||||||
\(305\) | 13.1716 | − | 22.8138i | 0.754202 | − | 1.30632i | ||||
\(306\) | −4.41421 | + | 7.64564i | −0.252344 | + | 0.437072i | ||||
\(307\) | −17.1716 | −0.980033 | −0.490017 | − | 0.871713i | \(-0.663009\pi\) | ||||
−0.490017 | + | 0.871713i | \(0.663009\pi\) | |||||||
\(308\) | −10.8284 | + | 18.7554i | −0.617007 | + | 1.06869i | ||||
\(309\) | −6.82843 | − | 11.8272i | −0.388456 | − | 0.672825i | ||||
\(310\) | −23.3137 | − | 40.3805i | −1.32413 | − | 2.29346i | ||||
\(311\) | 34.6274 | 1.96354 | 0.981770 | − | 0.190071i | \(-0.0608718\pi\) | ||||
0.981770 | + | 0.190071i | \(0.0608718\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.00000 | 0.339140 | 0.169570 | − | 0.985518i | \(-0.445762\pi\) | ||||
0.169570 | + | 0.985518i | \(0.445762\pi\) | |||||||
\(314\) | −12.0711 | − | 20.9077i | −0.681210 | − | 1.17989i | ||||
\(315\) | 4.00000 | + | 6.92820i | 0.225374 | + | 0.390360i | ||||
\(316\) | −21.6569 | + | 37.5108i | −1.21829 | + | 2.11015i | ||||
\(317\) | −8.48528 | −0.476581 | −0.238290 | − | 0.971194i | \(-0.576587\pi\) | ||||
−0.238290 | + | 0.971194i | \(0.576587\pi\) | |||||||
\(318\) | −2.41421 | + | 4.18154i | −0.135382 | + | 0.234489i | ||||
\(319\) | 2.00000 | − | 3.46410i | 0.111979 | − | 0.193952i | ||||
\(320\) | −27.7990 | −1.55401 | ||||||||
\(321\) | −5.65685 | + | 9.79796i | −0.315735 | + | 0.546869i | ||||
\(322\) | 13.6569 | + | 23.6544i | 0.761067 | + | 1.31821i | ||||
\(323\) | 5.17157 | + | 8.95743i | 0.287754 | + | 0.498405i | ||||
\(324\) | 3.82843 | 0.212690 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −31.7990 | −1.76118 | ||||||||
\(327\) | 8.65685 | + | 14.9941i | 0.478725 | + | 0.829176i | ||||
\(328\) | 23.8995 | + | 41.3951i | 1.31963 | + | 2.28566i | ||||
\(329\) | −0.485281 | + | 0.840532i | −0.0267544 | + | 0.0463400i | ||||
\(330\) | 13.6569 | 0.751785 | ||||||||
\(331\) | 1.07107 | − | 1.85514i | 0.0588712 | − | 0.101968i | −0.835088 | − | 0.550117i | \(-0.814583\pi\) |
0.893959 | + | 0.448149i | \(0.147917\pi\) | |||||||
\(332\) | 14.6569 | − | 25.3864i | 0.804399 | − | 1.39326i | ||||
\(333\) | 3.65685 | 0.200394 | ||||||||
\(334\) | 9.24264 | − | 16.0087i | 0.505735 | − | 0.875958i | ||||
\(335\) | −1.65685 | − | 2.86976i | −0.0905236 | − | 0.156792i | ||||
\(336\) | 4.24264 | + | 7.34847i | 0.231455 | + | 0.400892i | ||||
\(337\) | −13.3137 | −0.725244 | −0.362622 | − | 0.931936i | \(-0.618118\pi\) | ||||
−0.362622 | + | 0.931936i | \(0.618118\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.3137 | 0.940352 | ||||||||
\(340\) | 19.7990 | + | 34.2929i | 1.07375 | + | 1.85979i | ||||
\(341\) | −6.82843 | − | 11.8272i | −0.369780 | − | 0.640478i | ||||
\(342\) | 3.41421 | − | 5.91359i | 0.184620 | − | 0.319770i | ||||
\(343\) | 16.9706 | 0.916324 | ||||||||
\(344\) | 21.3137 | − | 36.9164i | 1.14916 | − | 1.99040i | ||||
\(345\) | 5.65685 | − | 9.79796i | 0.304555 | − | 0.527504i | ||||
\(346\) | 0.828427 | 0.0445365 | ||||||||
\(347\) | 15.6569 | − | 27.1185i | 0.840504 | − | 1.45580i | −0.0489652 | − | 0.998800i | \(-0.515592\pi\) |
0.889469 | − | 0.456995i | \(-0.151074\pi\) | |||||||
\(348\) | −3.82843 | − | 6.63103i | −0.205225 | − | 0.355461i | ||||
\(349\) | 3.82843 | + | 6.63103i | 0.204931 | + | 0.354951i | 0.950111 | − | 0.311913i | \(-0.100970\pi\) |
−0.745180 | + | 0.666864i | \(0.767636\pi\) | |||||||
\(350\) | 20.4853 | 1.09498 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.17157 | −0.169045 | ||||||||
\(353\) | −8.72792 | − | 15.1172i | −0.464540 | − | 0.804608i | 0.534640 | − | 0.845080i | \(-0.320447\pi\) |
−0.999181 | + | 0.0404722i | \(0.987114\pi\) | |||||||
\(354\) | −4.41421 | − | 7.64564i | −0.234613 | − | 0.406361i | ||||
\(355\) | −2.82843 | + | 4.89898i | −0.150117 | + | 0.260011i | ||||
\(356\) | 35.1127 | 1.86097 | ||||||||
\(357\) | −5.17157 | + | 8.95743i | −0.273709 | + | 0.474077i | ||||
\(358\) | −0.828427 | + | 1.43488i | −0.0437837 | + | 0.0758357i | ||||
\(359\) | 1.02944 | 0.0543316 | 0.0271658 | − | 0.999631i | \(-0.491352\pi\) | ||||
0.0271658 | + | 0.999631i | \(0.491352\pi\) | |||||||
\(360\) | 6.24264 | − | 10.8126i | 0.329016 | − | 0.569873i | ||||
\(361\) | 5.50000 | + | 9.52628i | 0.289474 | + | 0.501383i | ||||
\(362\) | 16.8995 | + | 29.2708i | 0.888218 | + | 1.53844i | ||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.9706 | 1.72576 | ||||||||
\(366\) | −11.2426 | − | 19.4728i | −0.587662 | − | 1.01786i | ||||
\(367\) | 12.0000 | + | 20.7846i | 0.626395 | + | 1.08495i | 0.988269 | + | 0.152721i | \(0.0488036\pi\) |
−0.361874 | + | 0.932227i | \(0.617863\pi\) | |||||||
\(368\) | 6.00000 | − | 10.3923i | 0.312772 | − | 0.541736i | ||||
\(369\) | 10.8284 | 0.563705 | ||||||||
\(370\) | 12.4853 | − | 21.6251i | 0.649079 | − | 1.12424i | ||||
\(371\) | −2.82843 | + | 4.89898i | −0.146845 | + | 0.254342i | ||||
\(372\) | −26.1421 | −1.35541 | ||||||||
\(373\) | −5.00000 | + | 8.66025i | −0.258890 | + | 0.448411i | −0.965945 | − | 0.258748i | \(-0.916690\pi\) |
0.707055 | + | 0.707159i | \(0.250023\pi\) | |||||||
\(374\) | 8.82843 | + | 15.2913i | 0.456507 | + | 0.790693i | ||||
\(375\) | 2.82843 | + | 4.89898i | 0.146059 | + | 0.252982i | ||||
\(376\) | 1.51472 | 0.0781156 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 6.82843 | 0.351216 | ||||||||
\(379\) | 8.24264 | + | 14.2767i | 0.423396 | + | 0.733343i | 0.996269 | − | 0.0863007i | \(-0.0275046\pi\) |
−0.572873 | + | 0.819644i | \(0.694171\pi\) | |||||||
\(380\) | −15.3137 | − | 26.5241i | −0.785577 | − | 1.36066i | ||||
\(381\) | 2.82843 | − | 4.89898i | 0.144905 | − | 0.250982i | ||||
\(382\) | 46.6274 | 2.38567 | ||||||||
\(383\) | 1.48528 | − | 2.57258i | 0.0758943 | − | 0.131453i | −0.825581 | − | 0.564284i | \(-0.809152\pi\) |
0.901475 | + | 0.432832i | \(0.142485\pi\) | |||||||
\(384\) | −10.2782 | + | 17.8023i | −0.524506 | + | 0.908471i | ||||
\(385\) | 16.0000 | 0.815436 | ||||||||
\(386\) | −20.8995 | + | 36.1990i | −1.06376 | + | 1.84248i | ||||
\(387\) | −4.82843 | − | 8.36308i | −0.245443 | − | 0.425119i | ||||
\(388\) | 14.6569 | + | 25.3864i | 0.744089 | + | 1.28880i | ||||
\(389\) | 6.97056 | 0.353422 | 0.176711 | − | 0.984263i | \(-0.443454\pi\) | ||||
0.176711 | + | 0.984263i | \(0.443454\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.6274 | 0.739740 | ||||||||
\(392\) | 2.20711 | + | 3.82282i | 0.111476 | + | 0.193082i | ||||
\(393\) | 4.00000 | + | 6.92820i | 0.201773 | + | 0.349482i | ||||
\(394\) | −19.8995 | + | 34.4669i | −1.00252 | + | 1.73642i | ||||
\(395\) | 32.0000 | 1.61009 | ||||||||
\(396\) | 3.82843 | − | 6.63103i | 0.192386 | − | 0.333222i | ||||
\(397\) | 1.48528 | − | 2.57258i | 0.0745441 | − | 0.129114i | −0.826344 | − | 0.563166i | \(-0.809583\pi\) |
0.900888 | + | 0.434052i | \(0.142917\pi\) | |||||||
\(398\) | −24.9706 | −1.25166 | ||||||||
\(399\) | 4.00000 | − | 6.92820i | 0.200250 | − | 0.346844i | ||||
\(400\) | −4.50000 | − | 7.79423i | −0.225000 | − | 0.389711i | ||||
\(401\) | 1.07107 | + | 1.85514i | 0.0534866 | + | 0.0926415i | 0.891529 | − | 0.452964i | \(-0.149633\pi\) |
−0.838042 | + | 0.545605i | \(0.816300\pi\) | |||||||
\(402\) | −2.82843 | −0.141069 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.0000 | −0.696526 | ||||||||
\(405\) | −1.41421 | − | 2.44949i | −0.0702728 | − | 0.121716i | ||||
\(406\) | −6.82843 | − | 11.8272i | −0.338889 | − | 0.586973i | ||||
\(407\) | 3.65685 | − | 6.33386i | 0.181264 | − | 0.313958i | ||||
\(408\) | 16.1421 | 0.799155 | ||||||||
\(409\) | 0.514719 | − | 0.891519i | 0.0254512 | − | 0.0440828i | −0.853019 | − | 0.521879i | \(-0.825231\pi\) |
0.878470 | + | 0.477797i | \(0.158564\pi\) | |||||||
\(410\) | 36.9706 | − | 64.0349i | 1.82585 | − | 3.16246i | ||||
\(411\) | −5.17157 | −0.255095 | ||||||||
\(412\) | −26.1421 | + | 45.2795i | −1.28793 | + | 2.23076i | ||||
\(413\) | −5.17157 | − | 8.95743i | −0.254476 | − | 0.440766i | ||||
\(414\) | −4.82843 | − | 8.36308i | −0.237304 | − | 0.411023i | ||||
\(415\) | −21.6569 | −1.06309 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.3137 | 0.749916 | ||||||||
\(418\) | −6.82843 | − | 11.8272i | −0.333989 | − | 0.578486i | ||||
\(419\) | 15.3137 | + | 26.5241i | 0.748124 | + | 1.29579i | 0.948721 | + | 0.316114i | \(0.102378\pi\) |
−0.200597 | + | 0.979674i | \(0.564288\pi\) | |||||||
\(420\) | 15.3137 | − | 26.5241i | 0.747232 | − | 1.29424i | ||||
\(421\) | 14.6863 | 0.715766 | 0.357883 | − | 0.933766i | \(-0.383499\pi\) | ||||
0.357883 | + | 0.933766i | \(0.383499\pi\) | |||||||
\(422\) | −14.4853 | + | 25.0892i | −0.705132 | + | 1.22133i | ||||
\(423\) | 0.171573 | − | 0.297173i | 0.00834216 | − | 0.0144490i | ||||
\(424\) | 8.82843 | 0.428746 | ||||||||
\(425\) | 5.48528 | − | 9.50079i | 0.266075 | − | 0.460856i | ||||
\(426\) | 2.41421 | + | 4.18154i | 0.116969 | + | 0.202596i | ||||
\(427\) | −13.1716 | − | 22.8138i | −0.637417 | − | 1.10404i | ||||
\(428\) | 43.3137 | 2.09365 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −65.9411 | −3.17996 | ||||||||
\(431\) | −9.82843 | − | 17.0233i | −0.473419 | − | 0.819985i | 0.526118 | − | 0.850411i | \(-0.323647\pi\) |
−0.999537 | + | 0.0304262i | \(0.990314\pi\) | |||||||
\(432\) | −1.50000 | − | 2.59808i | −0.0721688 | − | 0.125000i | ||||
\(433\) | −0.656854 | + | 1.13770i | −0.0315664 | + | 0.0546746i | −0.881377 | − | 0.472414i | \(-0.843383\pi\) |
0.849811 | + | 0.527088i | \(0.176716\pi\) | |||||||
\(434\) | −46.6274 | −2.23819 | ||||||||
\(435\) | −2.82843 | + | 4.89898i | −0.135613 | + | 0.234888i | ||||
\(436\) | 33.1421 | − | 57.4039i | 1.58722 | − | 2.74915i | ||||
\(437\) | −11.3137 | −0.541208 | ||||||||
\(438\) | 14.0711 | − | 24.3718i | 0.672342 | − | 1.16453i | ||||
\(439\) | 8.48528 | + | 14.6969i | 0.404980 | + | 0.701447i | 0.994319 | − | 0.106439i | \(-0.0339450\pi\) |
−0.589339 | + | 0.807886i | \(0.700612\pi\) | |||||||
\(440\) | −12.4853 | − | 21.6251i | −0.595212 | − | 1.03094i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 41.9411 | 1.99268 | 0.996342 | − | 0.0854611i | \(-0.0272364\pi\) | ||||
0.996342 | + | 0.0854611i | \(0.0272364\pi\) | |||||||
\(444\) | −7.00000 | − | 12.1244i | −0.332205 | − | 0.575396i | ||||
\(445\) | −12.9706 | − | 22.4657i | −0.614864 | − | 1.06498i | ||||
\(446\) | 5.41421 | − | 9.37769i | 0.256370 | − | 0.444047i | ||||
\(447\) | −14.8284 | −0.701361 | ||||||||
\(448\) | −13.8995 | + | 24.0746i | −0.656689 | + | 1.13742i | ||||
\(449\) | −3.89949 | + | 6.75412i | −0.184029 | + | 0.318747i | −0.943249 | − | 0.332087i | \(-0.892247\pi\) |
0.759220 | + | 0.650834i | \(0.225581\pi\) | |||||||
\(450\) | −7.24264 | −0.341421 | ||||||||
\(451\) | 10.8284 | − | 18.7554i | 0.509891 | − | 0.883157i | ||||
\(452\) | −33.1421 | − | 57.4039i | −1.55887 | − | 2.70005i | ||||
\(453\) | 10.2426 | + | 17.7408i | 0.481241 | + | 0.833534i | ||||
\(454\) | −12.8284 | −0.602068 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.4853 | −0.584677 | ||||||||
\(457\) | −1.82843 | − | 3.16693i | −0.0855302 | − | 0.148143i | 0.820087 | − | 0.572239i | \(-0.193925\pi\) |
−0.905617 | + | 0.424096i | \(0.860592\pi\) | |||||||
\(458\) | 25.7279 | + | 44.5621i | 1.20219 | + | 2.08225i | ||||
\(459\) | 1.82843 | − | 3.16693i | 0.0853437 | − | 0.147820i | ||||
\(460\) | −43.3137 | −2.01951 | ||||||||
\(461\) | −5.41421 | + | 9.37769i | −0.252165 | + | 0.436763i | −0.964122 | − | 0.265461i | \(-0.914476\pi\) |
0.711957 | + | 0.702223i | \(0.247809\pi\) | |||||||
\(462\) | 6.82843 | − | 11.8272i | 0.317687 | − | 0.550250i | ||||
\(463\) | −7.51472 | −0.349239 | −0.174619 | − | 0.984636i | \(-0.555869\pi\) | ||||
−0.174619 | + | 0.984636i | \(0.555869\pi\) | |||||||
\(464\) | −3.00000 | + | 5.19615i | −0.139272 | + | 0.241225i | ||||
\(465\) | 9.65685 | + | 16.7262i | 0.447826 | + | 0.775657i | ||||
\(466\) | −32.5563 | − | 56.3893i | −1.50814 | − | 2.61218i | ||||
\(467\) | −8.00000 | −0.370196 | −0.185098 | − | 0.982720i | \(-0.559260\pi\) | ||||
−0.185098 | + | 0.982720i | \(0.559260\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.31371 | −0.153013 | ||||||||
\(470\) | −1.17157 | − | 2.02922i | −0.0540406 | − | 0.0936011i | ||||
\(471\) | 5.00000 | + | 8.66025i | 0.230388 | + | 0.399043i | ||||
\(472\) | −8.07107 | + | 13.9795i | −0.371501 | + | 0.643459i | ||||
\(473\) | −19.3137 | −0.888045 | ||||||||
\(474\) | 13.6569 | − | 23.6544i | 0.627280 | − | 1.08648i | ||||
\(475\) | −4.24264 | + | 7.34847i | −0.194666 | + | 0.337171i | ||||
\(476\) | 39.5980 | 1.81497 | ||||||||
\(477\) | 1.00000 | − | 1.73205i | 0.0457869 | − | 0.0793052i | ||||
\(478\) | 2.41421 | + | 4.18154i | 0.110424 | + | 0.191259i | ||||
\(479\) | −1.34315 | − | 2.32640i | −0.0613699 | − | 0.106296i | 0.833708 | − | 0.552205i | \(-0.186214\pi\) |
−0.895078 | + | 0.445910i | \(0.852880\pi\) | |||||||
\(480\) | 4.48528 | 0.204724 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −28.1421 | −1.28184 | ||||||||
\(483\) | −5.65685 | − | 9.79796i | −0.257396 | − | 0.445823i | ||||
\(484\) | 13.3995 | + | 23.2086i | 0.609068 | + | 1.05494i | ||||
\(485\) | 10.8284 | − | 18.7554i | 0.491694 | − | 0.851638i | ||||
\(486\) | −2.41421 | −0.109511 | ||||||||
\(487\) | −15.8995 | + | 27.5387i | −0.720475 | + | 1.24790i | 0.240335 | + | 0.970690i | \(0.422743\pi\) |
−0.960810 | + | 0.277209i | \(0.910591\pi\) | |||||||
\(488\) | −20.5563 | + | 35.6046i | −0.930542 | + | 1.61175i | ||||
\(489\) | 13.1716 | 0.595639 | ||||||||
\(490\) | 3.41421 | − | 5.91359i | 0.154238 | − | 0.267149i | ||||
\(491\) | 7.31371 | + | 12.6677i | 0.330063 | + | 0.571686i | 0.982524 | − | 0.186136i | \(-0.0595967\pi\) |
−0.652461 | + | 0.757822i | \(0.726263\pi\) | |||||||
\(492\) | −20.7279 | − | 35.9018i | −0.934487 | − | 1.61858i | ||||
\(493\) | −7.31371 | −0.329393 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.65685 | −0.254257 | ||||||||
\(496\) | 10.2426 | + | 17.7408i | 0.459908 | + | 0.796584i | ||||
\(497\) | 2.82843 | + | 4.89898i | 0.126872 | + | 0.219749i | ||||
\(498\) | −9.24264 | + | 16.0087i | −0.414173 | + | 0.717368i | ||||
\(499\) | −2.14214 | −0.0958952 | −0.0479476 | − | 0.998850i | \(-0.515268\pi\) | ||||
−0.0479476 | + | 0.998850i | \(0.515268\pi\) | |||||||
\(500\) | 10.8284 | − | 18.7554i | 0.484262 | − | 0.838766i | ||||
\(501\) | −3.82843 | + | 6.63103i | −0.171042 | + | 0.296253i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.65685 | + | 13.2621i | −0.341402 | + | 0.591326i | −0.984693 | − | 0.174296i | \(-0.944235\pi\) |
0.643291 | + | 0.765622i | \(0.277569\pi\) | |||||||
\(504\) | −6.24264 | − | 10.8126i | −0.278069 | − | 0.481630i | ||||
\(505\) | 5.17157 | + | 8.95743i | 0.230132 | + | 0.398600i | ||||
\(506\) | −19.3137 | −0.858599 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −21.6569 | −0.960868 | ||||||||
\(509\) | 13.8995 | + | 24.0746i | 0.616084 | + | 1.06709i | 0.990193 | + | 0.139705i | \(0.0446153\pi\) |
−0.374109 | + | 0.927385i | \(0.622051\pi\) | |||||||
\(510\) | −12.4853 | − | 21.6251i | −0.552858 | − | 0.957577i | ||||
\(511\) | 16.4853 | − | 28.5533i | 0.729266 | − | 1.26313i | ||||
\(512\) | 31.2426 | 1.38074 | ||||||||
\(513\) | −1.41421 | + | 2.44949i | −0.0624391 | + | 0.108148i | ||||
\(514\) | −18.8995 | + | 32.7349i | −0.833621 | + | 1.44387i | ||||
\(515\) | 38.6274 | 1.70213 | ||||||||
\(516\) | −18.4853 | + | 32.0174i | −0.813769 | + | 1.40949i | ||||
\(517\) | −0.343146 | − | 0.594346i | −0.0150915 | − | 0.0261393i | ||||
\(518\) | −12.4853 | − | 21.6251i | −0.548572 | − | 0.950154i | ||||
\(519\) | −0.343146 | −0.0150624 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.68629 | 0.117689 | 0.0588443 | − | 0.998267i | \(-0.481258\pi\) | ||||
0.0588443 | + | 0.998267i | \(0.481258\pi\) | |||||||
\(522\) | 2.41421 | + | 4.18154i | 0.105667 | + | 0.183021i | ||||
\(523\) | −3.65685 | − | 6.33386i | −0.159903 | − | 0.276960i | 0.774930 | − | 0.632046i | \(-0.217785\pi\) |
−0.934834 | + | 0.355086i | \(0.884452\pi\) | |||||||
\(524\) | 15.3137 | − | 26.5241i | 0.668982 | − | 1.15871i | ||||
\(525\) | −8.48528 | −0.370328 | ||||||||
\(526\) | 14.4853 | − | 25.0892i | 0.631588 | − | 1.09394i | ||||
\(527\) | −12.4853 | + | 21.6251i | −0.543867 | + | 0.942006i | ||||
\(528\) | −6.00000 | −0.261116 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | −6.82843 | − | 11.8272i | −0.296608 | − | 0.513740i | ||||
\(531\) | 1.82843 | + | 3.16693i | 0.0793470 | + | 0.137433i | ||||
\(532\) | −30.6274 | −1.32787 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −22.1421 | −0.958184 | ||||||||
\(535\) | −16.0000 | − | 27.7128i | −0.691740 | − | 1.19813i | ||||
\(536\) | 2.58579 | + | 4.47871i | 0.111689 | + | 0.193451i | ||||
\(537\) | 0.343146 | − | 0.594346i | 0.0148078 | − | 0.0256479i | ||||
\(538\) | −43.4558 | −1.87351 | ||||||||
\(539\) | 1.00000 | − | 1.73205i | 0.0430730 | − | 0.0746047i | ||||
\(540\) | −5.41421 | + | 9.37769i | −0.232991 | + | 0.403552i | ||||
\(541\) | 10.0000 | 0.429934 | 0.214967 | − | 0.976621i | \(-0.431036\pi\) | ||||
0.214967 | + | 0.976621i | \(0.431036\pi\) | |||||||
\(542\) | 14.2426 | − | 24.6690i | 0.611774 | − | 1.05962i | ||||
\(543\) | −7.00000 | − | 12.1244i | −0.300399 | − | 0.520306i | ||||
\(544\) | 2.89949 | + | 5.02207i | 0.124315 | + | 0.215320i | ||||
\(545\) | −48.9706 | −2.09767 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.686292 | 0.0293437 | 0.0146719 | − | 0.999892i | \(-0.495330\pi\) | ||||
0.0146719 | + | 0.999892i | \(0.495330\pi\) | |||||||
\(548\) | 9.89949 | + | 17.1464i | 0.422885 | + | 0.732459i | ||||
\(549\) | 4.65685 | + | 8.06591i | 0.198750 | + | 0.344245i | ||||
\(550\) | −7.24264 | + | 12.5446i | −0.308827 | + | 0.534904i | ||||
\(551\) | 5.65685 | 0.240990 | ||||||||
\(552\) | −8.82843 | + | 15.2913i | −0.375763 | + | 0.650840i | ||||
\(553\) | 16.0000 | − | 27.7128i | 0.680389 | − | 1.17847i | ||||
\(554\) | 4.82843 | 0.205140 | ||||||||
\(555\) | −5.17157 | + | 8.95743i | −0.219521 | + | 0.380222i | ||||
\(556\) | −29.3137 | − | 50.7728i | −1.24318 | − | 2.15325i | ||||
\(557\) | −15.8995 | − | 27.5387i | −0.673683 | − | 1.16685i | −0.976852 | − | 0.213917i | \(-0.931378\pi\) |
0.303169 | − | 0.952937i | \(-0.401955\pi\) | |||||||
\(558\) | 16.4853 | 0.697878 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −24.0000 | −1.01419 | ||||||||
\(561\) | −3.65685 | − | 6.33386i | −0.154393 | − | 0.267416i | ||||
\(562\) | 32.3848 | + | 56.0921i | 1.36607 | + | 2.36610i | ||||
\(563\) | −2.00000 | + | 3.46410i | −0.0842900 | + | 0.145994i | −0.905088 | − | 0.425223i | \(-0.860196\pi\) |
0.820798 | + | 0.571218i | \(0.193529\pi\) | |||||||
\(564\) | −1.31371 | −0.0553171 | ||||||||
\(565\) | −24.4853 | + | 42.4098i | −1.03010 | + | 1.78419i | ||||
\(566\) | −6.00000 | + | 10.3923i | −0.252199 | + | 0.436821i | ||||
\(567\) | −2.82843 | −0.118783 | ||||||||
\(568\) | 4.41421 | − | 7.64564i | 0.185216 | − | 0.320804i | ||||
\(569\) | 4.51472 | + | 7.81972i | 0.189267 | + | 0.327820i | 0.945006 | − | 0.327053i | \(-0.106056\pi\) |
−0.755739 | + | 0.654873i | \(0.772722\pi\) | |||||||
\(570\) | 9.65685 | + | 16.7262i | 0.404481 | + | 0.700582i | ||||
\(571\) | 20.9706 | 0.877591 | 0.438795 | − | 0.898587i | \(-0.355405\pi\) | ||||
0.438795 | + | 0.898587i | \(0.355405\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.3137 | −0.806842 | ||||||||
\(574\) | −36.9706 | − | 64.0349i | −1.54312 | − | 2.67276i | ||||
\(575\) | 6.00000 | + | 10.3923i | 0.250217 | + | 0.433389i | ||||
\(576\) | 4.91421 | − | 8.51167i | 0.204759 | − | 0.354653i | ||||
\(577\) | 35.9411 | 1.49625 | 0.748124 | − | 0.663559i | \(-0.230955\pi\) | ||||
0.748124 | + | 0.663559i | \(0.230955\pi\) | |||||||
\(578\) | −4.37868 | + | 7.58410i | −0.182129 | + | 0.315457i | ||||
\(579\) | 8.65685 | − | 14.9941i | 0.359767 | − | 0.623134i | ||||
\(580\) | 21.6569 | 0.899252 | ||||||||
\(581\) | −10.8284 | + | 18.7554i | −0.449239 | + | 0.778105i | ||||
\(582\) | −9.24264 | − | 16.0087i | −0.383120 | − | 0.663583i | ||||
\(583\) | −2.00000 | − | 3.46410i | −0.0828315 | − | 0.143468i | ||||
\(584\) | −51.4558 | −2.12926 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 63.1127 | 2.60716 | ||||||||
\(587\) | −11.4853 | − | 19.8931i | −0.474048 | − | 0.821076i | 0.525510 | − | 0.850787i | \(-0.323874\pi\) |
−0.999559 | + | 0.0297116i | \(0.990541\pi\) | |||||||
\(588\) | −1.91421 | − | 3.31552i | −0.0789408 | − | 0.136730i | ||||
\(589\) | 9.65685 | − | 16.7262i | 0.397904 | − | 0.689190i | ||||
\(590\) | 24.9706 | 1.02802 | ||||||||
\(591\) | 8.24264 | − | 14.2767i | 0.339057 | − | 0.587264i | ||||
\(592\) | −5.48528 | + | 9.50079i | −0.225444 | + | 0.390480i | ||||
\(593\) | −3.51472 | −0.144332 | −0.0721661 | − | 0.997393i | \(-0.522991\pi\) | ||||
−0.0721661 | + | 0.997393i | \(0.522991\pi\) | |||||||
\(594\) | −2.41421 | + | 4.18154i | −0.0990564 | + | 0.171571i | ||||
\(595\) | −14.6274 | − | 25.3354i | −0.599666 | − | 1.03865i | ||||
\(596\) | 28.3848 | + | 49.1639i | 1.16269 | + | 2.01383i | ||||
\(597\) | 10.3431 | 0.423317 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.686292 | −0.0280411 | −0.0140206 | − | 0.999902i | \(-0.504463\pi\) | ||||
−0.0140206 | + | 0.999902i | \(0.504463\pi\) | |||||||
\(600\) | 6.62132 | + | 11.4685i | 0.270314 | + | 0.468198i | ||||
\(601\) | −22.3137 | − | 38.6485i | −0.910195 | − | 1.57650i | −0.813788 | − | 0.581162i | \(-0.802598\pi\) |
−0.0964075 | − | 0.995342i | \(-0.530735\pi\) | |||||||
\(602\) | −32.9706 | + | 57.1067i | −1.34378 | + | 2.32749i | ||||
\(603\) | 1.17157 | 0.0477101 | ||||||||
\(604\) | 39.2132 | − | 67.9193i | 1.59556 | − | 2.76360i | ||||
\(605\) | 9.89949 | − | 17.1464i | 0.402472 | − | 0.697101i | ||||
\(606\) | 8.82843 | 0.358630 | ||||||||
\(607\) | 12.9706 | − | 22.4657i | 0.526459 | − | 0.911854i | −0.473066 | − | 0.881027i | \(-0.656853\pi\) |
0.999525 | − | 0.0308265i | \(-0.00981393\pi\) | |||||||
\(608\) | −2.24264 | − | 3.88437i | −0.0909511 | − | 0.157532i | ||||
\(609\) | 2.82843 | + | 4.89898i | 0.114614 | + | 0.198517i | ||||
\(610\) | 63.5980 | 2.57501 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −14.0000 | −0.565916 | ||||||||
\(613\) | 18.1716 | + | 31.4741i | 0.733943 | + | 1.27123i | 0.955186 | + | 0.296008i | \(0.0956554\pi\) |
−0.221243 | + | 0.975219i | \(0.571011\pi\) | |||||||
\(614\) | −20.7279 | − | 35.9018i | −0.836511 | − | 1.44888i | ||||
\(615\) | −15.3137 | + | 26.5241i | −0.617508 | + | 1.06956i | ||||
\(616\) | −24.9706 | −1.00609 | ||||||||
\(617\) | 14.5858 | − | 25.2633i | 0.587202 | − | 1.01706i | −0.407395 | − | 0.913252i | \(-0.633563\pi\) |
0.994597 | − | 0.103811i | \(-0.0331038\pi\) | |||||||
\(618\) | 16.4853 | − | 28.5533i | 0.663135 | − | 1.14858i | ||||
\(619\) | −15.7990 | −0.635015 | −0.317508 | − | 0.948256i | \(-0.602846\pi\) | ||||
−0.317508 | + | 0.948256i | \(0.602846\pi\) | |||||||
\(620\) | 36.9706 | − | 64.0349i | 1.48477 | − | 2.57170i | ||||
\(621\) | 2.00000 | + | 3.46410i | 0.0802572 | + | 0.139010i | ||||
\(622\) | 41.7990 | + | 72.3980i | 1.67599 | + | 2.90289i | ||||
\(623\) | −25.9411 | −1.03931 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 7.24264 | + | 12.5446i | 0.289474 | + | 0.501384i | ||||
\(627\) | 2.82843 | + | 4.89898i | 0.112956 | + | 0.195646i | ||||
\(628\) | 19.1421 | − | 33.1552i | 0.763854 | − | 1.32303i | ||||
\(629\) | −13.3726 | −0.533200 | ||||||||
\(630\) | −9.65685 | + | 16.7262i | −0.384738 | + | 0.666386i | ||||
\(631\) | 9.55635 | − | 16.5521i | 0.380432 | − | 0.658928i | −0.610692 | − | 0.791868i | \(-0.709109\pi\) |
0.991124 | + | 0.132940i | \(0.0424419\pi\) | |||||||
\(632\) | −49.9411 | −1.98655 | ||||||||
\(633\) | 6.00000 | − | 10.3923i | 0.238479 | − | 0.413057i | ||||
\(634\) | −10.2426 | − | 17.7408i | −0.406787 | − | 0.704576i | ||||
\(635\) | 8.00000 | + | 13.8564i | 0.317470 | + | 0.549875i | ||||
\(636\) | −7.65685 | −0.303614 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.65685 | 0.382319 | ||||||||
\(639\) | −1.00000 | − | 1.73205i | −0.0395594 | − | 0.0685189i | ||||
\(640\) | −29.0711 | − | 50.3526i | −1.14913 | − | 1.99036i | ||||
\(641\) | 13.1421 | − | 22.7628i | 0.519083 | − | 0.899078i | −0.480671 | − | 0.876901i | \(-0.659607\pi\) |
0.999754 | − | 0.0221773i | \(-0.00705984\pi\) | |||||||
\(642\) | −27.3137 | −1.07799 | ||||||||
\(643\) | −8.58579 | + | 14.8710i | −0.338590 | + | 0.586456i | −0.984168 | − | 0.177239i | \(-0.943283\pi\) |
0.645577 | + | 0.763695i | \(0.276617\pi\) | |||||||
\(644\) | −21.6569 | + | 37.5108i | −0.853400 | + | 1.47813i | ||||
\(645\) | 27.3137 | 1.07548 | ||||||||
\(646\) | −12.4853 | + | 21.6251i | −0.491227 | + | 0.850830i | ||||
\(647\) | 5.65685 | + | 9.79796i | 0.222394 | + | 0.385198i | 0.955534 | − | 0.294880i | \(-0.0952796\pi\) |
−0.733140 | + | 0.680077i | \(0.761946\pi\) | |||||||
\(648\) | 2.20711 | + | 3.82282i | 0.0867033 | + | 0.150175i | ||||
\(649\) | 7.31371 | 0.287088 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.3137 | 0.756964 | ||||||||
\(652\) | −25.2132 | − | 43.6705i | −0.987425 | − | 1.71027i | ||||
\(653\) | 1.34315 | + | 2.32640i | 0.0525614 | + | 0.0910389i | 0.891109 | − | 0.453789i | \(-0.149928\pi\) |
−0.838548 | + | 0.544828i | \(0.816595\pi\) | |||||||
\(654\) | −20.8995 | + | 36.1990i | −0.817235 | + | 1.41549i | ||||
\(655\) | −22.6274 | −0.884126 | ||||||||
\(656\) | −16.2426 | + | 28.1331i | −0.634169 | + | 1.09841i | ||||
\(657\) | −5.82843 | + | 10.0951i | −0.227389 | + | 0.393849i | ||||
\(658\) | −2.34315 | −0.0913453 | ||||||||
\(659\) | 12.3431 | − | 21.3790i | 0.480821 | − | 0.832806i | −0.518937 | − | 0.854812i | \(-0.673672\pi\) |
0.999758 | + | 0.0220065i | \(0.00700546\pi\) | |||||||
\(660\) | 10.8284 | + | 18.7554i | 0.421496 | + | 0.730052i | ||||
\(661\) | 0.514719 | + | 0.891519i | 0.0200202 | + | 0.0346761i | 0.875862 | − | 0.482562i | \(-0.160294\pi\) |
−0.855842 | + | 0.517238i | \(0.826960\pi\) | |||||||
\(662\) | 5.17157 | 0.200999 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 33.7990 | 1.31166 | ||||||||
\(665\) | 11.3137 | + | 19.5959i | 0.438727 | + | 0.759897i | ||||
\(666\) | 4.41421 | + | 7.64564i | 0.171047 | + | 0.296263i | ||||
\(667\) | 4.00000 | − | 6.92820i | 0.154881 | − | 0.268261i | ||||
\(668\) | 29.3137 | 1.13418 | ||||||||
\(669\) | −2.24264 | + | 3.88437i | −0.0867055 | + | 0.150178i | ||||
\(670\) | 4.00000 | − | 6.92820i | 0.154533 | − | 0.267660i | ||||
\(671\) | 18.6274 | 0.719103 | ||||||||
\(672\) | 2.24264 | − | 3.88437i | 0.0865117 | − | 0.149843i | ||||
\(673\) | 14.3137 | + | 24.7921i | 0.551753 | + | 0.955664i | 0.998148 | + | 0.0608282i | \(0.0193742\pi\) |
−0.446395 | + | 0.894836i | \(0.647292\pi\) | |||||||
\(674\) | −16.0711 | − | 27.8359i | −0.619034 | − | 1.07220i | ||||
\(675\) | 3.00000 | 0.115470 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 49.3137 | 1.89528 | 0.947640 | − | 0.319341i | \(-0.103462\pi\) | ||||
0.947640 | + | 0.319341i | \(0.103462\pi\) | |||||||
\(678\) | 20.8995 | + | 36.1990i | 0.802640 | + | 1.39021i | ||||
\(679\) | −10.8284 | − | 18.7554i | −0.415557 | − | 0.719766i | ||||
\(680\) | −22.8284 | + | 39.5400i | −0.875430 | + | 1.51629i | ||||
\(681\) | 5.31371 | 0.203622 | ||||||||
\(682\) | 16.4853 | − | 28.5533i | 0.631254 | − | 1.09336i | ||||
\(683\) | 9.97056 | − | 17.2695i | 0.381513 | − | 0.660800i | −0.609766 | − | 0.792582i | \(-0.708736\pi\) |
0.991279 | + | 0.131782i | \(0.0420698\pi\) | |||||||
\(684\) | 10.8284 | 0.414035 | ||||||||
\(685\) | 7.31371 | − | 12.6677i | 0.279442 | − | 0.484008i | ||||
\(686\) | 20.4853 | + | 35.4815i | 0.782132 | + | 1.35469i | ||||
\(687\) | −10.6569 | − | 18.4582i | −0.406584 | − | 0.704225i | ||||
\(688\) | 28.9706 | 1.10449 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 27.3137 | 1.03982 | ||||||||
\(691\) | 17.0711 | + | 29.5680i | 0.649414 | + | 1.12482i | 0.983263 | + | 0.182192i | \(0.0583191\pi\) |
−0.333849 | + | 0.942627i | \(0.608348\pi\) | |||||||
\(692\) | 0.656854 | + | 1.13770i | 0.0249699 | + | 0.0432491i | ||||
\(693\) | −2.82843 | + | 4.89898i | −0.107443 | + | 0.186097i | ||||
\(694\) | 75.5980 | 2.86966 | ||||||||
\(695\) | −21.6569 | + | 37.5108i | −0.821491 | + | 1.42286i | ||||
\(696\) | 4.41421 | − | 7.64564i | 0.167320 | − | 0.289807i | ||||
\(697\) | −39.5980 | −1.49988 | ||||||||
\(698\) | −9.24264 | + | 16.0087i | −0.349839 | + | 0.605939i | ||||
\(699\) | 13.4853 | + | 23.3572i | 0.510060 | + | 0.883450i | ||||
\(700\) | 16.2426 | + | 28.1331i | 0.613914 | + | 1.06333i | ||||
\(701\) | 38.9706 | 1.47190 | 0.735949 | − | 0.677037i | \(-0.236736\pi\) | ||||
0.735949 | + | 0.677037i | \(0.236736\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.3431 | 0.390099 | ||||||||
\(704\) | −9.82843 | − | 17.0233i | −0.370423 | − | 0.641591i | ||||
\(705\) | 0.485281 | + | 0.840532i | 0.0182768 | + | 0.0316563i | ||||
\(706\) | 21.0711 | − | 36.4962i | 0.793020 | − | 1.37355i | ||||
\(707\) | 10.3431 | 0.388994 | ||||||||
\(708\) | 7.00000 | − | 12.1244i | 0.263076 | − | 0.455661i | ||||
\(709\) | −20.3137 | + | 35.1844i | −0.762897 | + | 1.32138i | 0.178454 | + | 0.983948i | \(0.442891\pi\) |
−0.941351 | + | 0.337429i | \(0.890443\pi\) | |||||||
\(710\) | −13.6569 | −0.512533 | ||||||||
\(711\) | −5.65685 | + | 9.79796i | −0.212149 | + | 0.367452i | ||||
\(712\) | 20.2426 | + | 35.0613i | 0.758625 | + | 1.31398i | ||||
\(713\) | −13.6569 | − | 23.6544i | −0.511453 | − | 0.885863i | ||||
\(714\) | −24.9706 | −0.934500 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.62742 | −0.0981912 | ||||||||
\(717\) | −1.00000 | − | 1.73205i | −0.0373457 | − | 0.0646846i | ||||
\(718\) | 1.24264 | + | 2.15232i | 0.0463749 | + | 0.0803237i | ||||
\(719\) | −18.9706 | + | 32.8580i | −0.707483 | + | 1.22540i | 0.258305 | + | 0.966063i | \(0.416836\pi\) |
−0.965788 | + | 0.259333i | \(0.916497\pi\) | |||||||
\(720\) | 8.48528 | 0.316228 | ||||||||
\(721\) | 19.3137 | − | 33.4523i | 0.719280 | − | 1.24583i | ||||
\(722\) | −13.2782 | + | 22.9985i | −0.494162 | + | 0.855915i | ||||
\(723\) | 11.6569 | 0.433523 | ||||||||
\(724\) | −26.7990 | + | 46.4172i | −0.995977 | + | 1.72508i | ||||
\(725\) | −3.00000 | − | 5.19615i | −0.111417 | − | 0.192980i | ||||
\(726\) | −8.44975 | − | 14.6354i | −0.313600 | − | 0.543170i | ||||
\(727\) | −21.6569 | −0.803208 | −0.401604 | − | 0.915813i | \(-0.631547\pi\) | ||||
−0.401604 | + | 0.915813i | \(0.631547\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 39.7990 | + | 68.9339i | 1.47303 | + | 2.55136i | ||||
\(731\) | 17.6569 | + | 30.5826i | 0.653062 | + | 1.13114i | ||||
\(732\) | 17.8284 | − | 30.8797i | 0.658958 | − | 1.14135i | ||||
\(733\) | 8.62742 | 0.318661 | 0.159330 | − | 0.987225i | \(-0.449066\pi\) | ||||
0.159330 | + | 0.987225i | \(0.449066\pi\) | |||||||
\(734\) | −28.9706 | + | 50.1785i | −1.06932 | + | 1.85212i | ||||
\(735\) | −1.41421 | + | 2.44949i | −0.0521641 | + | 0.0903508i | ||||
\(736\) | −6.34315 | −0.233811 | ||||||||
\(737\) | 1.17157 | − | 2.02922i | 0.0431554 | − | 0.0747474i | ||||
\(738\) | 13.0711 | + | 22.6398i | 0.481153 | + | 0.833381i | ||||
\(739\) | −5.07107 | − | 8.78335i | −0.186542 | − | 0.323101i | 0.757553 | − | 0.652774i | \(-0.226395\pi\) |
−0.944095 | + | 0.329673i | \(0.893061\pi\) | |||||||
\(740\) | 39.5980 | 1.45565 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −13.6569 | −0.501359 | ||||||||
\(743\) | −1.00000 | − | 1.73205i | −0.0366864 | − | 0.0635428i | 0.847099 | − | 0.531435i | \(-0.178347\pi\) |
−0.883786 | + | 0.467892i | \(0.845014\pi\) | |||||||
\(744\) | −15.0711 | − | 26.1039i | −0.552532 | − | 0.957014i | ||||
\(745\) | 20.9706 | − | 36.3221i | 0.768302 | − | 1.33074i | ||||
\(746\) | −24.1421 | −0.883906 | ||||||||
\(747\) | 3.82843 | − | 6.63103i | 0.140075 | − | 0.242617i | ||||
\(748\) | −14.0000 | + | 24.2487i | −0.511891 | + | 0.886621i | ||||
\(749\) | −32.0000 | −1.16925 | ||||||||
\(750\) | −6.82843 | + | 11.8272i | −0.249339 | + | 0.431868i | ||||
\(751\) | −16.4853 | − | 28.5533i | −0.601556 | − | 1.04193i | −0.992586 | − | 0.121548i | \(-0.961214\pi\) |
0.391029 | − | 0.920378i | \(-0.372119\pi\) | |||||||
\(752\) | 0.514719 | + | 0.891519i | 0.0187699 | + | 0.0325103i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −57.9411 | −2.10869 | ||||||||
\(756\) | 5.41421 | + | 9.37769i | 0.196913 | + | 0.341063i | ||||
\(757\) | 7.97056 | + | 13.8054i | 0.289695 | + | 0.501767i | 0.973737 | − | 0.227676i | \(-0.0731128\pi\) |
−0.684042 | + | 0.729443i | \(0.739779\pi\) | |||||||
\(758\) | −19.8995 | + | 34.4669i | −0.722782 | + | 1.25190i | ||||
\(759\) | 8.00000 | 0.290382 | ||||||||
\(760\) | 17.6569 | − | 30.5826i | 0.640481 | − | 1.10935i | ||||
\(761\) | −7.75736 | + | 13.4361i | −0.281204 | + | 0.487060i | −0.971682 | − | 0.236294i | \(-0.924067\pi\) |
0.690478 | + | 0.723354i | \(0.257400\pi\) | |||||||
\(762\) | 13.6569 | 0.494736 | ||||||||
\(763\) | −24.4853 | + | 42.4098i | −0.886427 | + | 1.53534i | ||||
\(764\) | 36.9706 | + | 64.0349i | 1.33755 | + | 2.31670i | ||||
\(765\) | 5.17157 | + | 8.95743i | 0.186979 | + | 0.323856i | ||||
\(766\) | 7.17157 | 0.259119 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −29.9706 | −1.08147 | ||||||||
\(769\) | −21.0000 | − | 36.3731i | −0.757279 | − | 1.31165i | −0.944233 | − | 0.329278i | \(-0.893195\pi\) |
0.186954 | − | 0.982369i | \(-0.440139\pi\) | |||||||
\(770\) | 19.3137 | + | 33.4523i | 0.696018 | + | 1.20554i | ||||
\(771\) | 7.82843 | − | 13.5592i | 0.281934 | − | 0.488324i | ||||
\(772\) | −66.2843 | −2.38562 | ||||||||
\(773\) | −2.92893 | + | 5.07306i | −0.105346 | + | 0.182465i | −0.913880 | − | 0.405985i | \(-0.866928\pi\) |
0.808533 | + | 0.588450i | \(0.200262\pi\) | |||||||
\(774\) | 11.6569 | − | 20.1903i | 0.418997 | − | 0.725724i | ||||
\(775\) | −20.4853 | −0.735853 | ||||||||
\(776\) | −16.8995 | + | 29.2708i | −0.606657 | + | 1.05076i | ||||
\(777\) | 5.17157 | + | 8.95743i | 0.185529 | + | 0.321346i | ||||
\(778\) | 8.41421 | + | 14.5738i | 0.301664 | + | 0.522498i | ||||
\(779\) | 30.6274 | 1.09734 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00000 | −0.143131 | ||||||||
\(782\) | 17.6569 | + | 30.5826i | 0.631408 | + | 1.09363i | ||||
\(783\) | −1.00000 | − | 1.73205i | −0.0357371 | − | 0.0618984i | ||||
\(784\) | −1.50000 | + | 2.59808i | −0.0535714 | + | 0.0927884i | ||||
\(785\) | −28.2843 | −1.00951 | ||||||||
\(786\) | −9.65685 | + | 16.7262i | −0.344449 | + | 0.596602i | ||||
\(787\) | −16.3848 | + | 28.3793i | −0.584054 | + | 1.01161i | 0.410938 | + | 0.911663i | \(0.365201\pi\) |
−0.994993 | + | 0.0999484i | \(0.968132\pi\) | |||||||
\(788\) | −63.1127 | −2.24830 | ||||||||
\(789\) | −6.00000 | + | 10.3923i | −0.213606 | + | 0.369976i | ||||
\(790\) | 38.6274 | + | 66.9046i | 1.37430 | + | 2.38036i | ||||
\(791\) | 24.4853 | + | 42.4098i | 0.870596 | + | 1.50792i | ||||
\(792\) | 8.82843 | 0.313704 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 7.17157 | 0.254510 | ||||||||
\(795\) | 2.82843 | + | 4.89898i | 0.100314 | + | 0.173749i | ||||
\(796\) | −19.7990 | − | 34.2929i | −0.701757 | − | 1.21548i | ||||
\(797\) | −17.8284 | + | 30.8797i | −0.631515 | + | 1.09382i | 0.355727 | + | 0.934590i | \(0.384233\pi\) |
−0.987242 | + | 0.159227i | \(0.949100\pi\) | |||||||
\(798\) | 19.3137 | 0.683698 | ||||||||
\(799\) | −0.627417 | + | 1.08672i | −0.0221964 | + | 0.0384453i | ||||
\(800\) | −2.37868 | + | 4.11999i | −0.0840990 | + | 0.145664i | ||||
\(801\) | 9.17157 | 0.324062 | ||||||||
\(802\) | −2.58579 | + | 4.47871i | −0.0913073 | + | 0.158149i | ||||
\(803\) | 11.6569 | + | 20.1903i | 0.411361 | + | 0.712499i | ||||
\(804\) | −2.24264 | − | 3.88437i | −0.0790918 | − | 0.136991i | ||||
\(805\) | 32.0000 | 1.12785 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.0000 | 0.633630 | ||||||||
\(808\) | −8.07107 | − | 13.9795i | −0.283939 | − | 0.491797i | ||||
\(809\) | −20.6569 | − | 35.7787i | −0.726256 | − | 1.25791i | −0.958455 | − | 0.285244i | \(-0.907925\pi\) |
0.232198 | − | 0.972668i | \(-0.425408\pi\) | |||||||
\(810\) | 3.41421 | − | 5.91359i | 0.119963 | − | 0.207782i | ||||
\(811\) | −1.85786 | −0.0652384 | −0.0326192 | − | 0.999468i | \(-0.510385\pi\) | ||||
−0.0326192 | + | 0.999468i | \(0.510385\pi\) | |||||||
\(812\) | 10.8284 | − | 18.7554i | 0.380003 | − | 0.658185i | ||||
\(813\) | −5.89949 | + | 10.2182i | −0.206904 | + | 0.358369i | ||||
\(814\) | 17.6569 | 0.618872 | ||||||||
\(815\) | −18.6274 | + | 32.2636i | −0.652490 | + | 1.13015i | ||||
\(816\) | 5.48528 | + | 9.50079i | 0.192023 | + | 0.332594i | ||||
\(817\) | −13.6569 | − | 23.6544i | −0.477793 | − | 0.827561i | ||||
\(818\) | 2.48528 | 0.0868958 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 117.255 | 4.09472 | ||||||||
\(821\) | −7.89949 | − | 13.6823i | −0.275694 | − | 0.477516i | 0.694616 | − | 0.719381i | \(-0.255574\pi\) |
−0.970310 | + | 0.241864i | \(0.922241\pi\) | |||||||
\(822\) | −6.24264 | − | 10.8126i | −0.217737 | − | 0.377132i | ||||
\(823\) | −24.4853 | + | 42.4098i | −0.853503 | + | 1.47831i | 0.0245234 | + | 0.999699i | \(0.492193\pi\) |
−0.878027 | + | 0.478612i | \(0.841140\pi\) | |||||||
\(824\) | −60.2843 | −2.10010 | ||||||||
\(825\) | 3.00000 | − | 5.19615i | 0.104447 | − | 0.180907i | ||||
\(826\) | 12.4853 | − | 21.6251i | 0.434418 | − | 0.752435i | ||||
\(827\) | −26.0000 | −0.904109 | −0.452054 | − | 0.891990i | \(-0.649309\pi\) | ||||
−0.452054 | + | 0.891990i | \(0.649309\pi\) | |||||||
\(828\) | 7.65685 | − | 13.2621i | 0.266094 | − | 0.460888i | ||||
\(829\) | −2.65685 | − | 4.60181i | −0.0922764 | − | 0.159827i | 0.816192 | − | 0.577780i | \(-0.196081\pi\) |
−0.908469 | + | 0.417953i | \(0.862748\pi\) | |||||||
\(830\) | −26.1421 | − | 45.2795i | −0.907407 | − | 1.57167i | ||||
\(831\) | −2.00000 | −0.0693792 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.65685 | −0.126702 | ||||||||
\(834\) | 18.4853 | + | 32.0174i | 0.640093 | + | 1.10867i | ||||
\(835\) | −10.8284 | − | 18.7554i | −0.374733 | − | 0.649057i | ||||
\(836\) | 10.8284 | − | 18.7554i | 0.374509 | − | 0.648669i | ||||
\(837\) | −6.82843 | −0.236025 | ||||||||
\(838\) | −36.9706 | + | 64.0349i | −1.27713 | + | 2.21205i | ||||
\(839\) | 23.6274 | − | 40.9239i | 0.815709 | − | 1.41285i | −0.0931087 | − | 0.995656i | \(-0.529680\pi\) |
0.908818 | − | 0.417194i | \(-0.136986\pi\) | |||||||
\(840\) | 35.3137 | 1.21844 | ||||||||
\(841\) | 12.5000 | − | 21.6506i | 0.431034 | − | 0.746574i | ||||
\(842\) | 17.7279 | + | 30.7057i | 0.610945 | + | 1.05819i | ||||
\(843\) | −13.4142 | − | 23.2341i | −0.462010 | − | 0.800225i | ||||
\(844\) | −45.9411 | −1.58136 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.828427 | 0.0284819 | ||||||||
\(847\) | −9.89949 | − | 17.1464i | −0.340151 | − | 0.589158i | ||||
\(848\) | 3.00000 | + | 5.19615i | 0.103020 | + | 0.178437i | ||||
\(849\) | 2.48528 | − | 4.30463i | 0.0852946 | − | 0.147735i | ||||
\(850\) | 26.4853 | 0.908438 | ||||||||
\(851\) | 7.31371 | − | 12.6677i | 0.250711 | − | 0.434244i | ||||
\(852\) | −3.82843 | + | 6.63103i | −0.131160 | + | 0.227175i | ||||
\(853\) | −7.65685 | −0.262166 | −0.131083 | − | 0.991371i | \(-0.541845\pi\) | ||||
−0.131083 | + | 0.991371i | \(0.541845\pi\) | |||||||
\(854\) | 31.7990 | − | 55.0775i | 1.08814 | − | 1.88471i | ||||
\(855\) | −4.00000 | − | 6.92820i | −0.136797 | − | 0.236940i | ||||
\(856\) | 24.9706 | + | 43.2503i | 0.853476 | + | 1.47826i | ||||
\(857\) | 29.5980 | 1.01105 | 0.505524 | − | 0.862813i | \(-0.331299\pi\) | ||||
0.505524 | + | 0.862813i | \(0.331299\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.3137 | −0.795453 | −0.397727 | − | 0.917504i | \(-0.630201\pi\) | ||||
−0.397727 | + | 0.917504i | \(0.630201\pi\) | |||||||
\(860\) | −52.2843 | − | 90.5590i | −1.78288 | − | 3.08804i | ||||
\(861\) | 15.3137 | + | 26.5241i | 0.521890 | + | 0.903940i | ||||
\(862\) | 23.7279 | − | 41.0980i | 0.808176 | − | 1.39980i | ||||
\(863\) | −39.6569 | −1.34994 | −0.674968 | − | 0.737847i | \(-0.735842\pi\) | ||||
−0.674968 | + | 0.737847i | \(0.735842\pi\) | |||||||
\(864\) | −0.792893 | + | 1.37333i | −0.0269748 | + | 0.0467217i | ||||
\(865\) | 0.485281 | − | 0.840532i | 0.0165001 | − | 0.0285789i | ||||
\(866\) | −3.17157 | −0.107774 | ||||||||
\(867\) | 1.81371 | − | 3.14144i | 0.0615968 | − | 0.106689i | ||||
\(868\) | −36.9706 | − | 64.0349i | −1.25486 | − | 2.17349i | ||||
\(869\) | 11.3137 | + | 19.5959i | 0.383791 | + | 0.664746i | ||||
\(870\) | −13.6569 | −0.463011 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 76.4264 | 2.58812 | ||||||||
\(873\) | 3.82843 | + | 6.63103i | 0.129573 | + | 0.224426i | ||||
\(874\) | −13.6569 | − | 23.6544i | −0.461950 | − | 0.800121i | ||||
\(875\) | −8.00000 | + | 13.8564i | −0.270449 | + | 0.468432i | ||||
\(876\) | 44.6274 | 1.50782 | ||||||||
\(877\) | 7.14214 | − | 12.3705i | 0.241173 | − | 0.417724i | −0.719876 | − | 0.694103i | \(-0.755801\pi\) |
0.961049 | + | 0.276379i | \(0.0891346\pi\) | |||||||
\(878\) | −20.4853 | + | 35.4815i | −0.691345 | + | 1.19744i | ||||
\(879\) | −26.1421 | −0.881752 | ||||||||
\(880\) | 8.48528 | − | 14.6969i | 0.286039 | − | 0.495434i | ||||
\(881\) | −26.7990 | − | 46.4172i | −0.902881 | − | 1.56384i | −0.823737 | − | 0.566972i | \(-0.808115\pi\) |
−0.0791441 | − | 0.996863i | \(-0.525219\pi\) | |||||||
\(882\) | 1.20711 | + | 2.09077i | 0.0406454 | + | 0.0703999i | ||||
\(883\) | −51.5980 | −1.73641 | −0.868205 | − | 0.496205i | \(-0.834726\pi\) | ||||
−0.868205 | + | 0.496205i | \(0.834726\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.3431 | −0.347681 | ||||||||
\(886\) | 50.6274 | + | 87.6893i | 1.70086 | + | 2.94598i | ||||
\(887\) | 4.00000 | + | 6.92820i | 0.134307 | + | 0.232626i | 0.925332 | − | 0.379157i | \(-0.123786\pi\) |
−0.791026 | + | 0.611783i | \(0.790453\pi\) | |||||||
\(888\) | 8.07107 | − | 13.9795i | 0.270847 | − | 0.469121i | ||||
\(889\) | 16.0000 | 0.536623 | ||||||||
\(890\) | 31.3137 | − | 54.2369i | 1.04964 | − | 1.81803i | ||||
\(891\) | 1.00000 | − | 1.73205i | 0.0335013 | − | 0.0580259i | ||||
\(892\) | 17.1716 | 0.574947 | ||||||||
\(893\) | 0.485281 | − | 0.840532i | 0.0162393 | − | 0.0281273i | ||||
\(894\) | −17.8995 | − | 31.0028i | −0.598649 | − | 1.03689i | ||||
\(895\) | 0.970563 | + | 1.68106i | 0.0324423 | + | 0.0561918i | ||||
\(896\) | −58.1421 | −1.94239 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.8284 | −0.628313 | ||||||||
\(899\) | 6.82843 | + | 11.8272i | 0.227741 | + | 0.394459i | ||||
\(900\) | −5.74264 | − | 9.94655i | −0.191421 | − | 0.331552i | ||||
\(901\) | −3.65685 | + | 6.33386i | −0.121827 | + | 0.211011i | ||||
\(902\) | 52.2843 | 1.74088 | ||||||||
\(903\) | 13.6569 | − | 23.6544i | 0.454472 | − | 0.787168i | ||||
\(904\) | 38.2132 | − | 66.1872i | 1.27095 | − | 2.20135i | ||||
\(905\) | 39.5980 | 1.31628 | ||||||||
\(906\) | −24.7279 | + | 42.8300i | −0.821530 | + | 1.42293i | ||||
\(907\) | −10.4853 | − | 18.1610i | −0.348158 | − | 0.603027i | 0.637764 | − | 0.770232i | \(-0.279859\pi\) |
−0.985922 | + | 0.167204i | \(0.946526\pi\) | |||||||
\(908\) | −10.1716 | − | 17.6177i | −0.337556 | − | 0.584663i | ||||
\(909\) | −3.65685 | −0.121290 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.0000 | −1.32526 | −0.662630 | − | 0.748947i | \(-0.730560\pi\) | ||||
−0.662630 | + | 0.748947i | \(0.730560\pi\) | |||||||
\(912\) | −4.24264 | − | 7.34847i | −0.140488 | − | 0.243332i | ||||
\(913\) | −7.65685 | − | 13.2621i | −0.253405 | − | 0.438910i | ||||
\(914\) | 4.41421 | − | 7.64564i | 0.146009 | − | 0.252895i | ||||
\(915\) | −26.3431 | −0.870878 | ||||||||
\(916\) | −40.7990 | + | 70.6659i | −1.34804 | + | 2.33487i | ||||
\(917\) | −11.3137 | + | 19.5959i | −0.373612 | + | 0.647114i | ||||
\(918\) | 8.82843 | 0.291382 | ||||||||
\(919\) | 9.65685 | − | 16.7262i | 0.318550 | − | 0.551745i | −0.661636 | − | 0.749826i | \(-0.730137\pi\) |
0.980186 | + | 0.198080i | \(0.0634707\pi\) | |||||||
\(920\) | −24.9706 | − | 43.2503i | −0.823255 | − | 1.42592i | ||||
\(921\) | 8.58579 | + | 14.8710i | 0.282911 | + | 0.490017i | ||||
\(922\) | −26.1421 | −0.860945 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 21.6569 | 0.712458 | ||||||||
\(925\) | −5.48528 | − | 9.50079i | −0.180355 | − | 0.312384i | ||||
\(926\) | −9.07107 | − | 15.7116i | −0.298094 | − | 0.516314i | ||||
\(927\) | −6.82843 | + | 11.8272i | −0.224275 | + | 0.388456i | ||||
\(928\) | 3.17157 | 0.104112 | ||||||||
\(929\) | 13.8995 | − | 24.0746i | 0.456028 | − | 0.789863i | −0.542719 | − | 0.839914i | \(-0.682605\pi\) |
0.998747 | + | 0.0500513i | \(0.0159385\pi\) | |||||||
\(930\) | −23.3137 | + | 40.3805i | −0.764487 | + | 1.32413i | ||||
\(931\) | 2.82843 | 0.0926980 | ||||||||
\(932\) | 51.6274 | − | 89.4213i | 1.69111 | − | 2.92909i | ||||
\(933\) | −17.3137 | − | 29.9882i | −0.566825 | − | 0.981770i | ||||
\(934\) | −9.65685 | − | 16.7262i | −0.315982 | − | 0.547297i | ||||
\(935\) | 20.6863 | 0.676514 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.31371 | 0.0429170 | 0.0214585 | − | 0.999770i | \(-0.493169\pi\) | ||||
0.0214585 | + | 0.999770i | \(0.493169\pi\) | |||||||
\(938\) | −4.00000 | − | 6.92820i | −0.130605 | − | 0.226214i | ||||
\(939\) | −3.00000 | − | 5.19615i | −0.0979013 | − | 0.169570i | ||||
\(940\) | 1.85786 | − | 3.21792i | 0.0605969 | − | 0.104957i | ||||
\(941\) | 5.85786 | 0.190961 | 0.0954805 | − | 0.995431i | \(-0.469561\pi\) | ||||
0.0954805 | + | 0.995431i | \(0.469561\pi\) | |||||||
\(942\) | −12.0711 | + | 20.9077i | −0.393297 | + | 0.681210i | ||||
\(943\) | 21.6569 | − | 37.5108i | 0.705244 | − | 1.22152i | ||||
\(944\) | −10.9706 | −0.357061 | ||||||||
\(945\) | 4.00000 | − | 6.92820i | 0.130120 | − | 0.225374i | ||||
\(946\) | −23.3137 | − | 40.3805i | −0.757994 | − | 1.31288i | ||||
\(947\) | 27.4853 | + | 47.6059i | 0.893152 | + | 1.54698i | 0.836076 | + | 0.548614i | \(0.184844\pi\) |
0.0570760 | + | 0.998370i | \(0.481822\pi\) | |||||||
\(948\) | 43.3137 | 1.40676 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −20.4853 | −0.664630 | ||||||||
\(951\) | 4.24264 | + | 7.34847i | 0.137577 | + | 0.238290i | ||||
\(952\) | 22.8284 | + | 39.5400i | 0.739874 | + | 1.28150i | ||||
\(953\) | −25.8284 | + | 44.7361i | −0.836665 | + | 1.44915i | 0.0560029 | + | 0.998431i | \(0.482164\pi\) |
−0.892668 | + | 0.450715i | \(0.851169\pi\) | |||||||
\(954\) | 4.82843 | 0.156326 | ||||||||
\(955\) | 27.3137 | − | 47.3087i | 0.883851 | − | 1.53087i | ||||
\(956\) | −3.82843 | + | 6.63103i | −0.123820 | + | 0.214463i | ||||
\(957\) | −4.00000 | −0.129302 | ||||||||
\(958\) | 3.24264 | − | 5.61642i | 0.104765 | − | 0.181458i | ||||
\(959\) | −7.31371 | − | 12.6677i | −0.236172 | − | 0.409062i | ||||
\(960\) | 13.8995 | + | 24.0746i | 0.448604 | + | 0.777005i | ||||
\(961\) | 15.6274 | 0.504110 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.3137 | 0.364579 | ||||||||
\(964\) | −22.3137 | − | 38.6485i | −0.718676 | − | 1.24478i | ||||
\(965\) | 24.4853 | + | 42.4098i | 0.788209 | + | 1.36522i | ||||
\(966\) | 13.6569 | − | 23.6544i | 0.439402 | − | 0.761067i | ||||
\(967\) | −10.1421 | −0.326149 | −0.163075 | − | 0.986614i | \(-0.552141\pi\) | ||||
−0.163075 | + | 0.986614i | \(0.552141\pi\) | |||||||
\(968\) | −15.4497 | + | 26.7597i | −0.496574 | + | 0.860091i | ||||
\(969\) | 5.17157 | − | 8.95743i | 0.166135 | − | 0.287754i | ||||
\(970\) | 52.2843 | 1.67875 | ||||||||
\(971\) | −3.65685 | + | 6.33386i | −0.117354 | + | 0.203263i | −0.918718 | − | 0.394913i | \(-0.870775\pi\) |
0.801364 | + | 0.598177i | \(0.204108\pi\) | |||||||
\(972\) | −1.91421 | − | 3.31552i | −0.0613984 | − | 0.106345i | ||||
\(973\) | 21.6569 | + | 37.5108i | 0.694287 | + | 1.20254i | ||||
\(974\) | −76.7696 | −2.45986 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27.9411 | −0.894374 | ||||||||
\(977\) | −6.92893 | − | 12.0013i | −0.221676 | − | 0.383954i | 0.733641 | − | 0.679537i | \(-0.237819\pi\) |
−0.955317 | + | 0.295583i | \(0.904486\pi\) | |||||||
\(978\) | 15.8995 | + | 27.5387i | 0.508410 | + | 0.880592i | ||||
\(979\) | 9.17157 | − | 15.8856i | 0.293125 | − | 0.507707i | ||||
\(980\) | 10.8284 | 0.345901 | ||||||||
\(981\) | 8.65685 | − | 14.9941i | 0.276392 | − | 0.478725i | ||||
\(982\) | −17.6569 | + | 30.5826i | −0.563453 | + | 0.975929i | ||||
\(983\) | 2.68629 | 0.0856794 | 0.0428397 | − | 0.999082i | \(-0.486360\pi\) | ||||
0.0428397 | + | 0.999082i | \(0.486360\pi\) | |||||||
\(984\) | 23.8995 | − | 41.3951i | 0.761888 | − | 1.31963i | ||||
\(985\) | 23.3137 | + | 40.3805i | 0.742837 | + | 1.28663i | ||||
\(986\) | −8.82843 | − | 15.2913i | −0.281154 | − | 0.486974i | ||||
\(987\) | 0.970563 | 0.0308934 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −38.6274 | −1.22828 | ||||||||
\(990\) | −6.82843 | − | 11.8272i | −0.217022 | − | 0.375893i | ||||
\(991\) | −13.6569 | − | 23.6544i | −0.433824 | − | 0.751406i | 0.563375 | − | 0.826202i | \(-0.309503\pi\) |
−0.997199 | + | 0.0747959i | \(0.976169\pi\) | |||||||
\(992\) | 5.41421 | − | 9.37769i | 0.171901 | − | 0.297742i | ||||
\(993\) | −2.14214 | −0.0679786 | ||||||||
\(994\) | −6.82843 | + | 11.8272i | −0.216585 | + | 0.375135i | ||||
\(995\) | −14.6274 | + | 25.3354i | −0.463720 | + | 0.803187i | ||||
\(996\) | −29.3137 | −0.928840 | ||||||||
\(997\) | −25.6274 | + | 44.3880i | −0.811628 | + | 1.40578i | 0.100095 | + | 0.994978i | \(0.468085\pi\) |
−0.911724 | + | 0.410804i | \(0.865248\pi\) | |||||||
\(998\) | −2.58579 | − | 4.47871i | −0.0818516 | − | 0.141771i | ||||
\(999\) | −1.82843 | − | 3.16693i | −0.0578489 | − | 0.100197i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))