Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(316,507)]
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, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.316");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.j (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.4 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.361 |
Dual form | 507.2.j.f.316.4 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.09077 | − | 1.20711i | 1.47840 | − | 0.853553i | 0.478696 | − | 0.877981i | \(-0.341110\pi\) |
0.999702 | + | 0.0244272i | \(0.00777619\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 1.91421 | − | 3.31552i | 0.957107 | − | 1.65776i | ||||
\(5\) | − | 2.82843i | − | 1.26491i | −0.774597 | − | 0.632456i | \(-0.782047\pi\) | ||
0.774597 | − | 0.632456i | \(-0.217953\pi\) | |||||||
\(6\) | −2.09077 | − | 1.20711i | −0.853553 | − | 0.492799i | ||||
\(7\) | 2.44949 | + | 1.41421i | 0.925820 | + | 0.534522i | 0.885487 | − | 0.464664i | \(-0.153825\pi\) |
0.0403329 | + | 0.999186i | \(0.487158\pi\) | |||||||
\(8\) | − | 4.41421i | − | 1.56066i | ||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −3.41421 | − | 5.91359i | −1.07967 | − | 1.87004i | ||||
\(11\) | −1.73205 | + | 1.00000i | −0.522233 | + | 0.301511i | −0.737848 | − | 0.674967i | \(-0.764158\pi\) |
0.215615 | + | 0.976478i | \(0.430824\pi\) | |||||||
\(12\) | −3.82843 | −1.10517 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 6.82843 | 1.82497 | ||||||||
\(15\) | −2.44949 | + | 1.41421i | −0.632456 | + | 0.365148i | ||||
\(16\) | −1.50000 | − | 2.59808i | −0.375000 | − | 0.649519i | ||||
\(17\) | −1.82843 | + | 3.16693i | −0.443459 | + | 0.768093i | −0.997943 | − | 0.0641009i | \(-0.979582\pi\) |
0.554485 | + | 0.832194i | \(0.312915\pi\) | |||||||
\(18\) | 2.41421i | 0.569036i | ||||||||
\(19\) | 2.44949 | + | 1.41421i | 0.561951 | + | 0.324443i | 0.753928 | − | 0.656957i | \(-0.228157\pi\) |
−0.191977 | + | 0.981399i | \(0.561490\pi\) | |||||||
\(20\) | −9.37769 | − | 5.41421i | −2.09692 | − | 1.21065i | ||||
\(21\) | − | 2.82843i | − | 0.617213i | ||||||
\(22\) | −2.41421 | + | 4.18154i | −0.514712 | + | 0.891507i | ||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | −3.82282 | + | 2.20711i | −0.780330 | + | 0.450524i | ||||
\(25\) | −3.00000 | −0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 9.37769 | − | 5.41421i | 1.77222 | − | 1.02319i | ||||
\(29\) | −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 | ||||
\(31\) | 6.82843i | 1.22642i | 0.789919 | + | 0.613211i | \(0.210122\pi\) | ||||
−0.789919 | + | 0.613211i | \(0.789878\pi\) | |||||||
\(32\) | 1.37333 | + | 0.792893i | 0.242773 | + | 0.140165i | ||||
\(33\) | 1.73205 | + | 1.00000i | 0.301511 | + | 0.174078i | ||||
\(34\) | 8.82843i | 1.51406i | ||||||||
\(35\) | 4.00000 | − | 6.92820i | 0.676123 | − | 1.17108i | ||||
\(36\) | 1.91421 | + | 3.31552i | 0.319036 | + | 0.552586i | ||||
\(37\) | 3.16693 | − | 1.82843i | 0.520640 | − | 0.300592i | −0.216557 | − | 0.976270i | \(-0.569483\pi\) |
0.737196 | + | 0.675679i | \(0.236149\pi\) | |||||||
\(38\) | 6.82843 | 1.10772 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −12.4853 | −1.97410 | ||||||||
\(41\) | −9.37769 | + | 5.41421i | −1.46455 | + | 0.845558i | −0.999217 | − | 0.0395775i | \(-0.987399\pi\) |
−0.465333 | + | 0.885136i | \(0.654065\pi\) | |||||||
\(42\) | −3.41421 | − | 5.91359i | −0.526825 | − | 0.912487i | ||||
\(43\) | 4.82843 | − | 8.36308i | 0.736328 | − | 1.27536i | −0.217810 | − | 0.975991i | \(-0.569891\pi\) |
0.954138 | − | 0.299367i | \(-0.0967754\pi\) | |||||||
\(44\) | 7.65685i | 1.15431i | ||||||||
\(45\) | 2.44949 | + | 1.41421i | 0.365148 | + | 0.210819i | ||||
\(46\) | −8.36308 | − | 4.82843i | −1.23307 | − | 0.711913i | ||||
\(47\) | − | 0.343146i | − | 0.0500530i | −0.999687 | − | 0.0250265i | \(-0.992033\pi\) | ||
0.999687 | − | 0.0250265i | \(-0.00796701\pi\) | |||||||
\(48\) | −1.50000 | + | 2.59808i | −0.216506 | + | 0.375000i | ||||
\(49\) | 0.500000 | + | 0.866025i | 0.0714286 | + | 0.123718i | ||||
\(50\) | −6.27231 | + | 3.62132i | −0.887039 | + | 0.512132i | ||||
\(51\) | 3.65685 | 0.512062 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 2.09077 | − | 1.20711i | 0.284518 | − | 0.164266i | ||||
\(55\) | 2.82843 | + | 4.89898i | 0.381385 | + | 0.660578i | ||||
\(56\) | 6.24264 | − | 10.8126i | 0.834208 | − | 1.44489i | ||||
\(57\) | − | 2.82843i | − | 0.374634i | ||||||
\(58\) | −4.18154 | − | 2.41421i | −0.549063 | − | 0.317002i | ||||
\(59\) | 3.16693 | + | 1.82843i | 0.412299 | + | 0.238041i | 0.691777 | − | 0.722111i | \(-0.256828\pi\) |
−0.279478 | + | 0.960152i | \(0.590161\pi\) | |||||||
\(60\) | 10.8284i | 1.39794i | ||||||||
\(61\) | 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 | ||||
\(63\) | −2.44949 | + | 1.41421i | −0.308607 | + | 0.178174i | ||||
\(64\) | 9.82843 | 1.22855 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.82843 | 0.594338 | ||||||||
\(67\) | −1.01461 | + | 0.585786i | −0.123955 | + | 0.0715652i | −0.560695 | − | 0.828022i | \(-0.689466\pi\) |
0.436741 | + | 0.899587i | \(0.356133\pi\) | |||||||
\(68\) | 7.00000 | + | 12.1244i | 0.848875 | + | 1.47029i | ||||
\(69\) | −2.00000 | + | 3.46410i | −0.240772 | + | 0.417029i | ||||
\(70\) | − | 19.3137i | − | 2.30843i | ||||||
\(71\) | 1.73205 | + | 1.00000i | 0.205557 | + | 0.118678i | 0.599245 | − | 0.800566i | \(-0.295468\pi\) |
−0.393688 | + | 0.919244i | \(0.628801\pi\) | |||||||
\(72\) | 3.82282 | + | 2.20711i | 0.450524 | + | 0.260110i | ||||
\(73\) | 11.6569i | 1.36433i | 0.731198 | + | 0.682166i | \(0.238962\pi\) | ||||
−0.731198 | + | 0.682166i | \(0.761038\pi\) | |||||||
\(74\) | 4.41421 | − | 7.64564i | 0.513142 | − | 0.888788i | ||||
\(75\) | 1.50000 | + | 2.59808i | 0.173205 | + | 0.300000i | ||||
\(76\) | 9.37769 | − | 5.41421i | 1.07570 | − | 0.621053i | ||||
\(77\) | −5.65685 | −0.644658 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3137 | 1.27289 | 0.636446 | − | 0.771321i | \(-0.280404\pi\) | ||||
0.636446 | + | 0.771321i | \(0.280404\pi\) | |||||||
\(80\) | −7.34847 | + | 4.24264i | −0.821584 | + | 0.474342i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −13.0711 | + | 22.6398i | −1.44346 | + | 2.50014i | ||||
\(83\) | 7.65685i | 0.840449i | 0.907420 | + | 0.420224i | \(0.138049\pi\) | ||||
−0.907420 | + | 0.420224i | \(0.861951\pi\) | |||||||
\(84\) | −9.37769 | − | 5.41421i | −1.02319 | − | 0.590739i | ||||
\(85\) | 8.95743 | + | 5.17157i | 0.971569 | + | 0.560936i | ||||
\(86\) | − | 23.3137i | − | 2.51398i | ||||||
\(87\) | −1.00000 | + | 1.73205i | −0.107211 | + | 0.185695i | ||||
\(88\) | 4.41421 | + | 7.64564i | 0.470557 | + | 0.815028i | ||||
\(89\) | 7.94282 | − | 4.58579i | 0.841937 | − | 0.486092i | −0.0159854 | − | 0.999872i | \(-0.505089\pi\) |
0.857922 | + | 0.513780i | \(0.171755\pi\) | |||||||
\(90\) | 6.82843 | 0.719779 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −15.3137 | −1.59656 | ||||||||
\(93\) | 5.91359 | − | 3.41421i | 0.613211 | − | 0.354037i | ||||
\(94\) | −0.414214 | − | 0.717439i | −0.0427229 | − | 0.0739982i | ||||
\(95\) | 4.00000 | − | 6.92820i | 0.410391 | − | 0.710819i | ||||
\(96\) | − | 1.58579i | − | 0.161849i | ||||||
\(97\) | −6.63103 | − | 3.82843i | −0.673279 | − | 0.388718i | 0.124039 | − | 0.992277i | \(-0.460415\pi\) |
−0.797318 | + | 0.603559i | \(0.793749\pi\) | |||||||
\(98\) | 2.09077 | + | 1.20711i | 0.211200 | + | 0.121936i | ||||
\(99\) | − | 2.00000i | − | 0.201008i | ||||||
\(100\) | −5.74264 | + | 9.94655i | −0.574264 | + | 0.994655i | ||||
\(101\) | −1.82843 | − | 3.16693i | −0.181935 | − | 0.315121i | 0.760604 | − | 0.649216i | \(-0.224903\pi\) |
−0.942540 | + | 0.334095i | \(0.891569\pi\) | |||||||
\(102\) | 7.64564 | − | 4.41421i | 0.757031 | − | 0.437072i | ||||
\(103\) | −13.6569 | −1.34565 | −0.672825 | − | 0.739802i | \(-0.734919\pi\) | ||||
−0.672825 | + | 0.739802i | \(0.734919\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.00000 | −0.780720 | ||||||||
\(106\) | −4.18154 | + | 2.41421i | −0.406147 | + | 0.234489i | ||||
\(107\) | −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 | ||||
\(109\) | 17.3137i | 1.65835i | 0.558987 | + | 0.829176i | \(0.311190\pi\) | ||||
−0.558987 | + | 0.829176i | \(0.688810\pi\) | |||||||
\(110\) | 11.8272 | + | 6.82843i | 1.12768 | + | 0.651065i | ||||
\(111\) | −3.16693 | − | 1.82843i | −0.300592 | − | 0.173547i | ||||
\(112\) | − | 8.48528i | − | 0.801784i | ||||||
\(113\) | −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 | ||||
\(115\) | −9.79796 | + | 5.65685i | −0.913664 | + | 0.527504i | ||||
\(116\) | −7.65685 | −0.710921 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.82843 | 0.812723 | ||||||||
\(119\) | −8.95743 | + | 5.17157i | −0.821126 | + | 0.474077i | ||||
\(120\) | 6.24264 | + | 10.8126i | 0.569873 | + | 0.987048i | ||||
\(121\) | −3.50000 | + | 6.06218i | −0.318182 | + | 0.551107i | ||||
\(122\) | − | 22.4853i | − | 2.03572i | ||||||
\(123\) | 9.37769 | + | 5.41421i | 0.845558 | + | 0.488183i | ||||
\(124\) | 22.6398 | + | 13.0711i | 2.03311 | + | 1.17382i | ||||
\(125\) | − | 5.65685i | − | 0.505964i | ||||||
\(126\) | −3.41421 | + | 5.91359i | −0.304162 | + | 0.526825i | ||||
\(127\) | −2.82843 | − | 4.89898i | −0.250982 | − | 0.434714i | 0.712814 | − | 0.701353i | \(-0.247420\pi\) |
−0.963797 | + | 0.266639i | \(0.914087\pi\) | |||||||
\(128\) | 17.8023 | − | 10.2782i | 1.57352 | − | 0.908471i | ||||
\(129\) | −9.65685 | −0.850239 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.00000 | −0.698963 | −0.349482 | − | 0.936943i | \(-0.613642\pi\) | ||||
−0.349482 | + | 0.936943i | \(0.613642\pi\) | |||||||
\(132\) | 6.63103 | − | 3.82843i | 0.577157 | − | 0.333222i | ||||
\(133\) | 4.00000 | + | 6.92820i | 0.346844 | + | 0.600751i | ||||
\(134\) | −1.41421 | + | 2.44949i | −0.122169 | + | 0.211604i | ||||
\(135\) | − | 2.82843i | − | 0.243432i | ||||||
\(136\) | 13.9795 | + | 8.07107i | 1.19873 | + | 0.692088i | ||||
\(137\) | 4.47871 | + | 2.58579i | 0.382642 | + | 0.220919i | 0.678967 | − | 0.734169i | \(-0.262428\pi\) |
−0.296325 | + | 0.955087i | \(0.595761\pi\) | |||||||
\(138\) | 9.65685i | 0.822046i | ||||||||
\(139\) | −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 | ||||
\(141\) | −0.297173 | + | 0.171573i | −0.0250265 | + | 0.0144490i | ||||
\(142\) | 4.82843 | 0.405193 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | −4.89898 | + | 2.82843i | −0.406838 | + | 0.234888i | ||||
\(146\) | 14.0711 | + | 24.3718i | 1.16453 | + | 2.01702i | ||||
\(147\) | 0.500000 | − | 0.866025i | 0.0412393 | − | 0.0714286i | ||||
\(148\) | − | 14.0000i | − | 1.15079i | ||||||
\(149\) | −12.8418 | − | 7.41421i | −1.05204 | − | 0.607396i | −0.128821 | − | 0.991668i | \(-0.541119\pi\) |
−0.923220 | + | 0.384272i | \(0.874453\pi\) | |||||||
\(150\) | 6.27231 | + | 3.62132i | 0.512132 | + | 0.295680i | ||||
\(151\) | − | 20.4853i | − | 1.66707i | −0.552468 | − | 0.833534i | \(-0.686314\pi\) | ||
0.552468 | − | 0.833534i | \(-0.313686\pi\) | |||||||
\(152\) | 6.24264 | − | 10.8126i | 0.506345 | − | 0.877015i | ||||
\(153\) | −1.82843 | − | 3.16693i | −0.147820 | − | 0.256031i | ||||
\(154\) | −11.8272 | + | 6.82843i | −0.953062 | + | 0.550250i | ||||
\(155\) | 19.3137 | 1.55131 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | 23.6544 | − | 13.6569i | 1.88184 | − | 1.08648i | ||||
\(159\) | 1.00000 | + | 1.73205i | 0.0793052 | + | 0.137361i | ||||
\(160\) | 2.24264 | − | 3.88437i | 0.177296 | − | 0.307086i | ||||
\(161\) | − | 11.3137i | − | 0.891645i | ||||||
\(162\) | −2.09077 | − | 1.20711i | −0.164266 | − | 0.0948393i | ||||
\(163\) | −11.4069 | − | 6.58579i | −0.893459 | − | 0.515839i | −0.0183864 | − | 0.999831i | \(-0.505853\pi\) |
−0.875072 | + | 0.483992i | \(0.839186\pi\) | |||||||
\(164\) | 41.4558i | 3.23716i | ||||||||
\(165\) | 2.82843 | − | 4.89898i | 0.220193 | − | 0.381385i | ||||
\(166\) | 9.24264 | + | 16.0087i | 0.717368 | + | 1.24252i | ||||
\(167\) | 6.63103 | − | 3.82843i | 0.513125 | − | 0.296253i | −0.220993 | − | 0.975275i | \(-0.570930\pi\) |
0.734117 | + | 0.679023i | \(0.237596\pi\) | |||||||
\(168\) | −12.4853 | −0.963260 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 24.9706 | 1.91515 | ||||||||
\(171\) | −2.44949 | + | 1.41421i | −0.187317 | + | 0.108148i | ||||
\(172\) | −18.4853 | − | 32.0174i | −1.40949 | − | 2.44131i | ||||
\(173\) | −0.171573 | + | 0.297173i | −0.0130444 | + | 0.0225936i | −0.872474 | − | 0.488661i | \(-0.837486\pi\) |
0.859429 | + | 0.511254i | \(0.170819\pi\) | |||||||
\(174\) | 4.82843i | 0.366042i | ||||||||
\(175\) | −7.34847 | − | 4.24264i | −0.555492 | − | 0.320713i | ||||
\(176\) | 5.19615 | + | 3.00000i | 0.391675 | + | 0.226134i | ||||
\(177\) | − | 3.65685i | − | 0.274866i | ||||||
\(178\) | 11.0711 | − | 19.1757i | 0.829812 | − | 1.43728i | ||||
\(179\) | −0.343146 | − | 0.594346i | −0.0256479 | − | 0.0444235i | 0.852917 | − | 0.522047i | \(-0.174832\pi\) |
−0.878564 | + | 0.477624i | \(0.841498\pi\) | |||||||
\(180\) | 9.37769 | − | 5.41421i | 0.698972 | − | 0.403552i | ||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.31371 | −0.688489 | ||||||||
\(184\) | −15.2913 | + | 8.82843i | −1.12729 | + | 0.650840i | ||||
\(185\) | −5.17157 | − | 8.95743i | −0.380222 | − | 0.658563i | ||||
\(186\) | 8.24264 | − | 14.2767i | 0.604380 | − | 1.04682i | ||||
\(187\) | − | 7.31371i | − | 0.534831i | ||||||
\(188\) | −1.13770 | − | 0.656854i | −0.0829757 | − | 0.0479060i | ||||
\(189\) | 2.44949 | + | 1.41421i | 0.178174 | + | 0.102869i | ||||
\(190\) | − | 19.3137i | − | 1.40116i | ||||||
\(191\) | 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 | ||||
\(193\) | −14.9941 | + | 8.65685i | −1.07930 | + | 0.623134i | −0.930707 | − | 0.365765i | \(-0.880808\pi\) |
−0.148592 | + | 0.988899i | \(0.547474\pi\) | |||||||
\(194\) | −18.4853 | −1.32717 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.82843 | 0.273459 | ||||||||
\(197\) | 14.2767 | − | 8.24264i | 1.01717 | − | 0.587264i | 0.103888 | − | 0.994589i | \(-0.466872\pi\) |
0.913283 | + | 0.407325i | \(0.133538\pi\) | |||||||
\(198\) | −2.41421 | − | 4.18154i | −0.171571 | − | 0.297169i | ||||
\(199\) | 5.17157 | − | 8.95743i | 0.366603 | − | 0.634975i | −0.622429 | − | 0.782676i | \(-0.713854\pi\) |
0.989032 | + | 0.147701i | \(0.0471874\pi\) | |||||||
\(200\) | 13.2426i | 0.936396i | ||||||||
\(201\) | 1.01461 | + | 0.585786i | 0.0715652 | + | 0.0413182i | ||||
\(202\) | −7.64564 | − | 4.41421i | −0.537946 | − | 0.310583i | ||||
\(203\) | − | 5.65685i | − | 0.397033i | ||||||
\(204\) | 7.00000 | − | 12.1244i | 0.490098 | − | 0.848875i | ||||
\(205\) | 15.3137 | + | 26.5241i | 1.06956 | + | 1.85252i | ||||
\(206\) | −28.5533 | + | 16.4853i | −1.98941 | + | 1.14858i | ||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.65685 | −0.391293 | ||||||||
\(210\) | −16.7262 | + | 9.65685i | −1.15421 | + | 0.666386i | ||||
\(211\) | 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 | ||||
\(213\) | − | 2.00000i | − | 0.137038i | ||||||
\(214\) | −23.6544 | − | 13.6569i | −1.61698 | − | 0.933563i | ||||
\(215\) | −23.6544 | − | 13.6569i | −1.61321 | − | 0.931390i | ||||
\(216\) | − | 4.41421i | − | 0.300349i | ||||||
\(217\) | −9.65685 | + | 16.7262i | −0.655550 | + | 1.13545i | ||||
\(218\) | 20.8995 | + | 36.1990i | 1.41549 | + | 2.45170i | ||||
\(219\) | 10.0951 | − | 5.82843i | 0.682166 | − | 0.393849i | ||||
\(220\) | 21.6569 | 1.46010 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −8.82843 | −0.592525 | ||||||||
\(223\) | −3.88437 | + | 2.24264i | −0.260116 | + | 0.150178i | −0.624388 | − | 0.781115i | \(-0.714651\pi\) |
0.364271 | + | 0.931293i | \(0.381318\pi\) | |||||||
\(224\) | 2.24264 | + | 3.88437i | 0.149843 | + | 0.259535i | ||||
\(225\) | 1.50000 | − | 2.59808i | 0.100000 | − | 0.173205i | ||||
\(226\) | 41.7990i | 2.78043i | ||||||||
\(227\) | 4.60181 | + | 2.65685i | 0.305433 | + | 0.176342i | 0.644881 | − | 0.764283i | \(-0.276907\pi\) |
−0.339448 | + | 0.940625i | \(0.610240\pi\) | |||||||
\(228\) | −9.37769 | − | 5.41421i | −0.621053 | − | 0.358565i | ||||
\(229\) | 21.3137i | 1.40845i | 0.709977 | + | 0.704225i | \(0.248705\pi\) | ||||
−0.709977 | + | 0.704225i | \(0.751295\pi\) | |||||||
\(230\) | −13.6569 | + | 23.6544i | −0.900506 | + | 1.55972i | ||||
\(231\) | 2.82843 | + | 4.89898i | 0.186097 | + | 0.322329i | ||||
\(232\) | −7.64564 | + | 4.41421i | −0.501961 | + | 0.289807i | ||||
\(233\) | 26.9706 | 1.76690 | 0.883450 | − | 0.468525i | \(-0.155214\pi\) | ||||
0.883450 | + | 0.468525i | \(0.155214\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.970563 | −0.0633125 | ||||||||
\(236\) | 12.1244 | − | 7.00000i | 0.789228 | − | 0.455661i | ||||
\(237\) | −5.65685 | − | 9.79796i | −0.367452 | − | 0.636446i | ||||
\(238\) | −12.4853 | + | 21.6251i | −0.809301 | + | 1.40175i | ||||
\(239\) | − | 2.00000i | − | 0.129369i | −0.997906 | − | 0.0646846i | \(-0.979396\pi\) | ||
0.997906 | − | 0.0646846i | \(-0.0206041\pi\) | |||||||
\(240\) | 7.34847 | + | 4.24264i | 0.474342 | + | 0.273861i | ||||
\(241\) | −10.0951 | − | 5.82843i | −0.650285 | − | 0.375442i | 0.138281 | − | 0.990393i | \(-0.455842\pi\) |
−0.788565 | + | 0.614951i | \(0.789176\pi\) | |||||||
\(242\) | 16.8995i | 1.08634i | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −17.8284 | − | 30.8797i | −1.14135 | − | 1.97687i | ||||
\(245\) | 2.44949 | − | 1.41421i | 0.156492 | − | 0.0903508i | ||||
\(246\) | 26.1421 | 1.66676 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 30.1421 | 1.91403 | ||||||||
\(249\) | 6.63103 | − | 3.82843i | 0.420224 | − | 0.242617i | ||||
\(250\) | −6.82843 | − | 11.8272i | −0.431868 | − | 0.748017i | ||||
\(251\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(252\) | 10.8284i | 0.682127i | ||||||||
\(253\) | 6.92820 | + | 4.00000i | 0.435572 | + | 0.251478i | ||||
\(254\) | −11.8272 | − | 6.82843i | −0.742103 | − | 0.428454i | ||||
\(255\) | − | 10.3431i | − | 0.647713i | ||||||
\(256\) | 14.9853 | − | 25.9553i | 0.936580 | − | 1.62220i | ||||
\(257\) | −7.82843 | − | 13.5592i | −0.488324 | − | 0.845802i | 0.511586 | − | 0.859232i | \(-0.329058\pi\) |
−0.999910 | + | 0.0134304i | \(0.995725\pi\) | |||||||
\(258\) | −20.1903 | + | 11.6569i | −1.25699 | + | 0.725724i | ||||
\(259\) | 10.3431 | 0.642692 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | −16.7262 | + | 9.65685i | −1.03335 | + | 0.596602i | ||||
\(263\) | −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 | ||||
\(265\) | 5.65685i | 0.347498i | ||||||||
\(266\) | 16.7262 | + | 9.65685i | 1.02555 | + | 0.592100i | ||||
\(267\) | −7.94282 | − | 4.58579i | −0.486092 | − | 0.280646i | ||||
\(268\) | 4.48528i | 0.273982i | ||||||||
\(269\) | −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 | ||||
\(271\) | 10.2182 | − | 5.89949i | 0.620713 | − | 0.358369i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
0.777147 | + | 0.629320i | \(0.216666\pi\) | |||||||
\(272\) | 10.9706 | 0.665188 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.4853 | 0.754263 | ||||||||
\(275\) | 5.19615 | − | 3.00000i | 0.313340 | − | 0.180907i | ||||
\(276\) | 7.65685 | + | 13.2621i | 0.460888 | + | 0.798282i | ||||
\(277\) | −1.00000 | + | 1.73205i | −0.0600842 | + | 0.104069i | −0.894503 | − | 0.447062i | \(-0.852470\pi\) |
0.834419 | + | 0.551131i | \(0.185804\pi\) | |||||||
\(278\) | 36.9706i | 2.21735i | ||||||||
\(279\) | −5.91359 | − | 3.41421i | −0.354037 | − | 0.204404i | ||||
\(280\) | −30.5826 | − | 17.6569i | −1.82766 | − | 1.05520i | ||||
\(281\) | 26.8284i | 1.60045i | 0.599700 | + | 0.800225i | \(0.295287\pi\) | ||||
−0.599700 | + | 0.800225i | \(0.704713\pi\) | |||||||
\(282\) | −0.414214 | + | 0.717439i | −0.0246661 | + | 0.0427229i | ||||
\(283\) | −2.48528 | − | 4.30463i | −0.147735 | − | 0.255884i | 0.782655 | − | 0.622455i | \(-0.213865\pi\) |
−0.930390 | + | 0.366572i | \(0.880531\pi\) | |||||||
\(284\) | 6.63103 | − | 3.82843i | 0.393479 | − | 0.227175i | ||||
\(285\) | −8.00000 | −0.473879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.6274 | −1.80788 | ||||||||
\(288\) | −1.37333 | + | 0.792893i | −0.0809243 | + | 0.0467217i | ||||
\(289\) | 1.81371 | + | 3.14144i | 0.106689 | + | 0.184790i | ||||
\(290\) | −6.82843 | + | 11.8272i | −0.400979 | + | 0.694516i | ||||
\(291\) | 7.65685i | 0.448853i | ||||||||
\(292\) | 38.6485 | + | 22.3137i | 2.26173 | + | 1.30581i | ||||
\(293\) | 22.6398 | + | 13.0711i | 1.32263 | + | 0.763620i | 0.984147 | − | 0.177353i | \(-0.0567535\pi\) |
0.338481 | + | 0.940973i | \(0.390087\pi\) | |||||||
\(294\) | − | 2.41421i | − | 0.140800i | ||||||
\(295\) | 5.17157 | − | 8.95743i | 0.301101 | − | 0.521522i | ||||
\(296\) | −8.07107 | − | 13.9795i | −0.469121 | − | 0.812542i | ||||
\(297\) | −1.73205 | + | 1.00000i | −0.100504 | + | 0.0580259i | ||||
\(298\) | −35.7990 | −2.07378 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 11.4853 | 0.663103 | ||||||||
\(301\) | 23.6544 | − | 13.6569i | 1.36341 | − | 0.787168i | ||||
\(302\) | −24.7279 | − | 42.8300i | −1.42293 | − | 2.46459i | ||||
\(303\) | −1.82843 | + | 3.16693i | −0.105040 | + | 0.181935i | ||||
\(304\) | − | 8.48528i | − | 0.486664i | ||||||
\(305\) | −22.8138 | − | 13.1716i | −1.30632 | − | 0.754202i | ||||
\(306\) | −7.64564 | − | 4.41421i | −0.437072 | − | 0.252344i | ||||
\(307\) | − | 17.1716i | − | 0.980033i | −0.871713 | − | 0.490017i | \(-0.836991\pi\) | ||
0.871713 | − | 0.490017i | \(-0.163009\pi\) | |||||||
\(308\) | −10.8284 | + | 18.7554i | −0.617007 | + | 1.06869i | ||||
\(309\) | 6.82843 | + | 11.8272i | 0.388456 | + | 0.672825i | ||||
\(310\) | 40.3805 | − | 23.3137i | 2.29346 | − | 1.32413i | ||||
\(311\) | −34.6274 | −1.96354 | −0.981770 | − | 0.190071i | \(-0.939128\pi\) | ||||
−0.981770 | + | 0.190071i | \(0.939128\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.00000 | 0.339140 | 0.169570 | − | 0.985518i | \(-0.445762\pi\) | ||||
0.169570 | + | 0.985518i | \(0.445762\pi\) | |||||||
\(314\) | −20.9077 | + | 12.0711i | −1.17989 | + | 0.681210i | ||||
\(315\) | 4.00000 | + | 6.92820i | 0.225374 | + | 0.390360i | ||||
\(316\) | 21.6569 | − | 37.5108i | 1.21829 | − | 2.11015i | ||||
\(317\) | 8.48528i | 0.476581i | 0.971194 | + | 0.238290i | \(0.0765870\pi\) | ||||
−0.971194 | + | 0.238290i | \(0.923413\pi\) | |||||||
\(318\) | 4.18154 | + | 2.41421i | 0.234489 | + | 0.135382i | ||||
\(319\) | 3.46410 | + | 2.00000i | 0.193952 | + | 0.111979i | ||||
\(320\) | − | 27.7990i | − | 1.55401i | ||||||
\(321\) | −5.65685 | + | 9.79796i | −0.315735 | + | 0.546869i | ||||
\(322\) | −13.6569 | − | 23.6544i | −0.761067 | − | 1.31821i | ||||
\(323\) | −8.95743 | + | 5.17157i | −0.498405 | + | 0.287754i | ||||
\(324\) | −3.82843 | −0.212690 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −31.7990 | −1.76118 | ||||||||
\(327\) | 14.9941 | − | 8.65685i | 0.829176 | − | 0.478725i | ||||
\(328\) | 23.8995 | + | 41.3951i | 1.31963 | + | 2.28566i | ||||
\(329\) | 0.485281 | − | 0.840532i | 0.0267544 | − | 0.0463400i | ||||
\(330\) | − | 13.6569i | − | 0.751785i | ||||||
\(331\) | −1.85514 | − | 1.07107i | −0.101968 | − | 0.0588712i | 0.448149 | − | 0.893959i | \(-0.352083\pi\) |
−0.550117 | + | 0.835088i | \(0.685417\pi\) | |||||||
\(332\) | 25.3864 | + | 14.6569i | 1.39326 | + | 0.804399i | ||||
\(333\) | 3.65685i | 0.200394i | ||||||||
\(334\) | 9.24264 | − | 16.0087i | 0.505735 | − | 0.875958i | ||||
\(335\) | 1.65685 | + | 2.86976i | 0.0905236 | + | 0.156792i | ||||
\(336\) | −7.34847 | + | 4.24264i | −0.400892 | + | 0.231455i | ||||
\(337\) | 13.3137 | 0.725244 | 0.362622 | − | 0.931936i | \(-0.381882\pi\) | ||||
0.362622 | + | 0.931936i | \(0.381882\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.3137 | 0.940352 | ||||||||
\(340\) | 34.2929 | − | 19.7990i | 1.85979 | − | 1.07375i | ||||
\(341\) | −6.82843 | − | 11.8272i | −0.369780 | − | 0.640478i | ||||
\(342\) | −3.41421 | + | 5.91359i | −0.184620 | + | 0.319770i | ||||
\(343\) | − | 16.9706i | − | 0.916324i | ||||||
\(344\) | −36.9164 | − | 21.3137i | −1.99040 | − | 1.14916i | ||||
\(345\) | 9.79796 | + | 5.65685i | 0.527504 | + | 0.304555i | ||||
\(346\) | 0.828427i | 0.0445365i | ||||||||
\(347\) | 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 | ||||
\(349\) | −6.63103 | + | 3.82843i | −0.354951 | + | 0.204931i | −0.666864 | − | 0.745180i | \(-0.732364\pi\) |
0.311913 | + | 0.950111i | \(0.399030\pi\) | |||||||
\(350\) | −20.4853 | −1.09498 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.17157 | −0.169045 | ||||||||
\(353\) | −15.1172 | + | 8.72792i | −0.804608 | + | 0.464540i | −0.845080 | − | 0.534640i | \(-0.820447\pi\) |
0.0404722 | + | 0.999181i | \(0.487114\pi\) | |||||||
\(354\) | −4.41421 | − | 7.64564i | −0.234613 | − | 0.406361i | ||||
\(355\) | 2.82843 | − | 4.89898i | 0.150117 | − | 0.260011i | ||||
\(356\) | − | 35.1127i | − | 1.86097i | ||||||
\(357\) | 8.95743 | + | 5.17157i | 0.474077 | + | 0.273709i | ||||
\(358\) | −1.43488 | − | 0.828427i | −0.0758357 | − | 0.0437837i | ||||
\(359\) | 1.02944i | 0.0543316i | 0.999631 | + | 0.0271658i | \(0.00864821\pi\) | ||||
−0.999631 | + | 0.0271658i | \(0.991352\pi\) | |||||||
\(360\) | 6.24264 | − | 10.8126i | 0.329016 | − | 0.569873i | ||||
\(361\) | −5.50000 | − | 9.52628i | −0.289474 | − | 0.501383i | ||||
\(362\) | −29.2708 | + | 16.8995i | −1.53844 | + | 0.888218i | ||||
\(363\) | 7.00000 | 0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.9706 | 1.72576 | ||||||||
\(366\) | −19.4728 | + | 11.2426i | −1.01786 | + | 0.587662i | ||||
\(367\) | 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 | ||||
\(369\) | − | 10.8284i | − | 0.563705i | ||||||
\(370\) | −21.6251 | − | 12.4853i | −1.12424 | − | 0.649079i | ||||
\(371\) | −4.89898 | − | 2.82843i | −0.254342 | − | 0.146845i | ||||
\(372\) | − | 26.1421i | − | 1.35541i | ||||||
\(373\) | −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 | ||||
\(375\) | −4.89898 | + | 2.82843i | −0.252982 | + | 0.146059i | ||||
\(376\) | −1.51472 | −0.0781156 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 6.82843 | 0.351216 | ||||||||
\(379\) | 14.2767 | − | 8.24264i | 0.733343 | − | 0.423396i | −0.0863007 | − | 0.996269i | \(-0.527505\pi\) |
0.819644 | + | 0.572873i | \(0.194171\pi\) | |||||||
\(380\) | −15.3137 | − | 26.5241i | −0.785577 | − | 1.36066i | ||||
\(381\) | −2.82843 | + | 4.89898i | −0.144905 | + | 0.250982i | ||||
\(382\) | − | 46.6274i | − | 2.38567i | ||||||
\(383\) | −2.57258 | − | 1.48528i | −0.131453 | − | 0.0758943i | 0.432832 | − | 0.901475i | \(-0.357515\pi\) |
−0.564284 | + | 0.825581i | \(0.690848\pi\) | |||||||
\(384\) | −17.8023 | − | 10.2782i | −0.908471 | − | 0.524506i | ||||
\(385\) | 16.0000i | 0.815436i | ||||||||
\(386\) | −20.8995 | + | 36.1990i | −1.06376 | + | 1.84248i | ||||
\(387\) | 4.82843 | + | 8.36308i | 0.245443 | + | 0.425119i | ||||
\(388\) | −25.3864 | + | 14.6569i | −1.28880 | + | 0.744089i | ||||
\(389\) | −6.97056 | −0.353422 | −0.176711 | − | 0.984263i | \(-0.556546\pi\) | ||||
−0.176711 | + | 0.984263i | \(0.556546\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.6274 | 0.739740 | ||||||||
\(392\) | 3.82282 | − | 2.20711i | 0.193082 | − | 0.111476i | ||||
\(393\) | 4.00000 | + | 6.92820i | 0.201773 | + | 0.349482i | ||||
\(394\) | 19.8995 | − | 34.4669i | 1.00252 | − | 1.73642i | ||||
\(395\) | − | 32.0000i | − | 1.61009i | ||||||
\(396\) | −6.63103 | − | 3.82843i | −0.333222 | − | 0.192386i | ||||
\(397\) | 2.57258 | + | 1.48528i | 0.129114 | + | 0.0745441i | 0.563166 | − | 0.826344i | \(-0.309583\pi\) |
−0.434052 | + | 0.900888i | \(0.642917\pi\) | |||||||
\(398\) | − | 24.9706i | − | 1.25166i | ||||||
\(399\) | 4.00000 | − | 6.92820i | 0.200250 | − | 0.346844i | ||||
\(400\) | 4.50000 | + | 7.79423i | 0.225000 | + | 0.389711i | ||||
\(401\) | −1.85514 | + | 1.07107i | −0.0926415 | + | 0.0534866i | −0.545605 | − | 0.838042i | \(-0.683700\pi\) |
0.452964 | + | 0.891529i | \(0.350367\pi\) | |||||||
\(402\) | 2.82843 | 0.141069 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.0000 | −0.696526 | ||||||||
\(405\) | −2.44949 | + | 1.41421i | −0.121716 | + | 0.0702728i | ||||
\(406\) | −6.82843 | − | 11.8272i | −0.338889 | − | 0.586973i | ||||
\(407\) | −3.65685 | + | 6.33386i | −0.181264 | + | 0.313958i | ||||
\(408\) | − | 16.1421i | − | 0.799155i | ||||||
\(409\) | −0.891519 | − | 0.514719i | −0.0440828 | − | 0.0254512i | 0.477797 | − | 0.878470i | \(-0.341436\pi\) |
−0.521879 | + | 0.853019i | \(0.674769\pi\) | |||||||
\(410\) | 64.0349 | + | 36.9706i | 3.16246 | + | 1.82585i | ||||
\(411\) | − | 5.17157i | − | 0.255095i | ||||||
\(412\) | −26.1421 | + | 45.2795i | −1.28793 | + | 2.23076i | ||||
\(413\) | 5.17157 | + | 8.95743i | 0.254476 | + | 0.440766i | ||||
\(414\) | 8.36308 | − | 4.82843i | 0.411023 | − | 0.237304i | ||||
\(415\) | 21.6569 | 1.06309 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.3137 | 0.749916 | ||||||||
\(418\) | −11.8272 | + | 6.82843i | −0.578486 | + | 0.333989i | ||||
\(419\) | 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 | ||||
\(421\) | − | 14.6863i | − | 0.715766i | −0.933766 | − | 0.357883i | \(-0.883499\pi\) | ||
0.933766 | − | 0.357883i | \(-0.116501\pi\) | |||||||
\(422\) | 25.0892 | + | 14.4853i | 1.22133 | + | 0.705132i | ||||
\(423\) | 0.297173 | + | 0.171573i | 0.0144490 | + | 0.00834216i | ||||
\(424\) | 8.82843i | 0.428746i | ||||||||
\(425\) | 5.48528 | − | 9.50079i | 0.266075 | − | 0.460856i | ||||
\(426\) | −2.41421 | − | 4.18154i | −0.116969 | − | 0.202596i | ||||
\(427\) | 22.8138 | − | 13.1716i | 1.10404 | − | 0.637417i | ||||
\(428\) | −43.3137 | −2.09365 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −65.9411 | −3.17996 | ||||||||
\(431\) | −17.0233 | + | 9.82843i | −0.819985 | + | 0.473419i | −0.850411 | − | 0.526118i | \(-0.823647\pi\) |
0.0304262 | + | 0.999537i | \(0.490314\pi\) | |||||||
\(432\) | −1.50000 | − | 2.59808i | −0.0721688 | − | 0.125000i | ||||
\(433\) | 0.656854 | − | 1.13770i | 0.0315664 | − | 0.0546746i | −0.849811 | − | 0.527088i | \(-0.823284\pi\) |
0.881377 | + | 0.472414i | \(0.156617\pi\) | |||||||
\(434\) | 46.6274i | 2.23819i | ||||||||
\(435\) | 4.89898 | + | 2.82843i | 0.234888 | + | 0.135613i | ||||
\(436\) | 57.4039 | + | 33.1421i | 2.74915 | + | 1.58722i | ||||
\(437\) | − | 11.3137i | − | 0.541208i | ||||||
\(438\) | 14.0711 | − | 24.3718i | 0.672342 | − | 1.16453i | ||||
\(439\) | −8.48528 | − | 14.6969i | −0.404980 | − | 0.701447i | 0.589339 | − | 0.807886i | \(-0.299388\pi\) |
−0.994319 | + | 0.106439i | \(0.966055\pi\) | |||||||
\(440\) | 21.6251 | − | 12.4853i | 1.03094 | − | 0.595212i | ||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 41.9411 | 1.99268 | 0.996342 | − | 0.0854611i | \(-0.0272364\pi\) | ||||
0.996342 | + | 0.0854611i | \(0.0272364\pi\) | |||||||
\(444\) | −12.1244 | + | 7.00000i | −0.575396 | + | 0.332205i | ||||
\(445\) | −12.9706 | − | 22.4657i | −0.614864 | − | 1.06498i | ||||
\(446\) | −5.41421 | + | 9.37769i | −0.256370 | + | 0.444047i | ||||
\(447\) | 14.8284i | 0.701361i | ||||||||
\(448\) | 24.0746 | + | 13.8995i | 1.13742 | + | 0.656689i | ||||
\(449\) | −6.75412 | − | 3.89949i | −0.318747 | − | 0.184029i | 0.332087 | − | 0.943249i | \(-0.392247\pi\) |
−0.650834 | + | 0.759220i | \(0.725581\pi\) | |||||||
\(450\) | − | 7.24264i | − | 0.341421i | ||||||
\(451\) | 10.8284 | − | 18.7554i | 0.509891 | − | 0.883157i | ||||
\(452\) | 33.1421 | + | 57.4039i | 1.55887 | + | 2.70005i | ||||
\(453\) | −17.7408 | + | 10.2426i | −0.833534 | + | 0.481241i | ||||
\(454\) | 12.8284 | 0.602068 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.4853 | −0.584677 | ||||||||
\(457\) | −3.16693 | + | 1.82843i | −0.148143 | + | 0.0855302i | −0.572239 | − | 0.820087i | \(-0.693925\pi\) |
0.424096 | + | 0.905617i | \(0.360592\pi\) | |||||||
\(458\) | 25.7279 | + | 44.5621i | 1.20219 | + | 2.08225i | ||||
\(459\) | −1.82843 | + | 3.16693i | −0.0853437 | + | 0.147820i | ||||
\(460\) | 43.3137i | 2.01951i | ||||||||
\(461\) | 9.37769 | + | 5.41421i | 0.436763 | + | 0.252165i | 0.702223 | − | 0.711957i | \(-0.252191\pi\) |
−0.265461 | + | 0.964122i | \(0.585524\pi\) | |||||||
\(462\) | 11.8272 | + | 6.82843i | 0.550250 | + | 0.317687i | ||||
\(463\) | − | 7.51472i | − | 0.349239i | −0.984636 | − | 0.174619i | \(-0.944131\pi\) | ||
0.984636 | − | 0.174619i | \(-0.0558695\pi\) | |||||||
\(464\) | −3.00000 | + | 5.19615i | −0.139272 | + | 0.241225i | ||||
\(465\) | −9.65685 | − | 16.7262i | −0.447826 | − | 0.775657i | ||||
\(466\) | 56.3893 | − | 32.5563i | 2.61218 | − | 1.50814i | ||||
\(467\) | 8.00000 | 0.370196 | 0.185098 | − | 0.982720i | \(-0.440740\pi\) | ||||
0.185098 | + | 0.982720i | \(0.440740\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.31371 | −0.153013 | ||||||||
\(470\) | −2.02922 | + | 1.17157i | −0.0936011 | + | 0.0540406i | ||||
\(471\) | 5.00000 | + | 8.66025i | 0.230388 | + | 0.399043i | ||||
\(472\) | 8.07107 | − | 13.9795i | 0.371501 | − | 0.643459i | ||||
\(473\) | 19.3137i | 0.888045i | ||||||||
\(474\) | −23.6544 | − | 13.6569i | −1.08648 | − | 0.627280i | ||||
\(475\) | −7.34847 | − | 4.24264i | −0.337171 | − | 0.194666i | ||||
\(476\) | 39.5980i | 1.81497i | ||||||||
\(477\) | 1.00000 | − | 1.73205i | 0.0457869 | − | 0.0793052i | ||||
\(478\) | −2.41421 | − | 4.18154i | −0.110424 | − | 0.191259i | ||||
\(479\) | 2.32640 | − | 1.34315i | 0.106296 | − | 0.0613699i | −0.445910 | − | 0.895078i | \(-0.647120\pi\) |
0.552205 | + | 0.833708i | \(0.313786\pi\) | |||||||
\(480\) | −4.48528 | −0.204724 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −28.1421 | −1.28184 | ||||||||
\(483\) | −9.79796 | + | 5.65685i | −0.445823 | + | 0.257396i | ||||
\(484\) | 13.3995 | + | 23.2086i | 0.609068 | + | 1.05494i | ||||
\(485\) | −10.8284 | + | 18.7554i | −0.491694 | + | 0.851638i | ||||
\(486\) | 2.41421i | 0.109511i | ||||||||
\(487\) | 27.5387 | + | 15.8995i | 1.24790 | + | 0.720475i | 0.970690 | − | 0.240335i | \(-0.0772572\pi\) |
0.277209 | + | 0.960810i | \(0.410591\pi\) | |||||||
\(488\) | −35.6046 | − | 20.5563i | −1.61175 | − | 0.930542i | ||||
\(489\) | 13.1716i | 0.595639i | ||||||||
\(490\) | 3.41421 | − | 5.91359i | 0.154238 | − | 0.267149i | ||||
\(491\) | −7.31371 | − | 12.6677i | −0.330063 | − | 0.571686i | 0.652461 | − | 0.757822i | \(-0.273737\pi\) |
−0.982524 | + | 0.186136i | \(0.940403\pi\) | |||||||
\(492\) | 35.9018 | − | 20.7279i | 1.61858 | − | 0.934487i | ||||
\(493\) | 7.31371 | 0.329393 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.65685 | −0.254257 | ||||||||
\(496\) | 17.7408 | − | 10.2426i | 0.796584 | − | 0.459908i | ||||
\(497\) | 2.82843 | + | 4.89898i | 0.126872 | + | 0.219749i | ||||
\(498\) | 9.24264 | − | 16.0087i | 0.414173 | − | 0.717368i | ||||
\(499\) | 2.14214i | 0.0958952i | 0.998850 | + | 0.0479476i | \(0.0152680\pi\) | ||||
−0.998850 | + | 0.0479476i | \(0.984732\pi\) | |||||||
\(500\) | −18.7554 | − | 10.8284i | −0.838766 | − | 0.484262i | ||||
\(501\) | −6.63103 | − | 3.82843i | −0.296253 | − | 0.171042i | ||||
\(502\) | 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 | ||||
\(505\) | −8.95743 | + | 5.17157i | −0.398600 | + | 0.230132i | ||||
\(506\) | 19.3137 | 0.858599 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −21.6569 | −0.960868 | ||||||||
\(509\) | 24.0746 | − | 13.8995i | 1.06709 | − | 0.616084i | 0.139705 | − | 0.990193i | \(-0.455385\pi\) |
0.927385 | + | 0.374109i | \(0.122051\pi\) | |||||||
\(510\) | −12.4853 | − | 21.6251i | −0.552858 | − | 0.957577i | ||||
\(511\) | −16.4853 | + | 28.5533i | −0.729266 | + | 1.26313i | ||||
\(512\) | − | 31.2426i | − | 1.38074i | ||||||
\(513\) | 2.44949 | + | 1.41421i | 0.108148 | + | 0.0624391i | ||||
\(514\) | −32.7349 | − | 18.8995i | −1.44387 | − | 0.833621i | ||||
\(515\) | 38.6274i | 1.70213i | ||||||||
\(516\) | −18.4853 | + | 32.0174i | −0.813769 | + | 1.40949i | ||||
\(517\) | 0.343146 | + | 0.594346i | 0.0150915 | + | 0.0261393i | ||||
\(518\) | 21.6251 | − | 12.4853i | 0.950154 | − | 0.548572i | ||||
\(519\) | 0.343146 | 0.0150624 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.68629 | 0.117689 | 0.0588443 | − | 0.998267i | \(-0.481258\pi\) | ||||
0.0588443 | + | 0.998267i | \(0.481258\pi\) | |||||||
\(522\) | 4.18154 | − | 2.41421i | 0.183021 | − | 0.105667i | ||||
\(523\) | −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 | ||||
\(525\) | 8.48528i | 0.370328i | ||||||||
\(526\) | −25.0892 | − | 14.4853i | −1.09394 | − | 0.631588i | ||||
\(527\) | −21.6251 | − | 12.4853i | −0.942006 | − | 0.543867i | ||||
\(528\) | − | 6.00000i | − | 0.261116i | ||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 6.82843 | + | 11.8272i | 0.296608 | + | 0.513740i | ||||
\(531\) | −3.16693 | + | 1.82843i | −0.137433 | + | 0.0793470i | ||||
\(532\) | 30.6274 | 1.32787 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −22.1421 | −0.958184 | ||||||||
\(535\) | −27.7128 | + | 16.0000i | −1.19813 | + | 0.691740i | ||||
\(536\) | 2.58579 | + | 4.47871i | 0.111689 | + | 0.193451i | ||||
\(537\) | −0.343146 | + | 0.594346i | −0.0148078 | + | 0.0256479i | ||||
\(538\) | 43.4558i | 1.87351i | ||||||||
\(539\) | −1.73205 | − | 1.00000i | −0.0746047 | − | 0.0430730i | ||||
\(540\) | −9.37769 | − | 5.41421i | −0.403552 | − | 0.232991i | ||||
\(541\) | 10.0000i | 0.429934i | 0.976621 | + | 0.214967i | \(0.0689643\pi\) | ||||
−0.976621 | + | 0.214967i | \(0.931036\pi\) | |||||||
\(542\) | 14.2426 | − | 24.6690i | 0.611774 | − | 1.05962i | ||||
\(543\) | 7.00000 | + | 12.1244i | 0.300399 | + | 0.520306i | ||||
\(544\) | −5.02207 | + | 2.89949i | −0.215320 | + | 0.124315i | ||||
\(545\) | 48.9706 | 2.09767 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.686292 | 0.0293437 | 0.0146719 | − | 0.999892i | \(-0.495330\pi\) | ||||
0.0146719 | + | 0.999892i | \(0.495330\pi\) | |||||||
\(548\) | 17.1464 | − | 9.89949i | 0.732459 | − | 0.422885i | ||||
\(549\) | 4.65685 | + | 8.06591i | 0.198750 | + | 0.344245i | ||||
\(550\) | 7.24264 | − | 12.5446i | 0.308827 | − | 0.534904i | ||||
\(551\) | − | 5.65685i | − | 0.240990i | ||||||
\(552\) | 15.2913 | + | 8.82843i | 0.650840 | + | 0.375763i | ||||
\(553\) | 27.7128 | + | 16.0000i | 1.17847 | + | 0.680389i | ||||
\(554\) | 4.82843i | 0.205140i | ||||||||
\(555\) | −5.17157 | + | 8.95743i | −0.219521 | + | 0.380222i | ||||
\(556\) | 29.3137 | + | 50.7728i | 1.24318 | + | 2.15325i | ||||
\(557\) | 27.5387 | − | 15.8995i | 1.16685 | − | 0.673683i | 0.213917 | − | 0.976852i | \(-0.431378\pi\) |
0.952937 | + | 0.303169i | \(0.0980446\pi\) | |||||||
\(558\) | −16.4853 | −0.697878 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −24.0000 | −1.01419 | ||||||||
\(561\) | −6.33386 | + | 3.65685i | −0.267416 | + | 0.154393i | ||||
\(562\) | 32.3848 | + | 56.0921i | 1.36607 | + | 2.36610i | ||||
\(563\) | 2.00000 | − | 3.46410i | 0.0842900 | − | 0.145994i | −0.820798 | − | 0.571218i | \(-0.806471\pi\) |
0.905088 | + | 0.425223i | \(0.139804\pi\) | |||||||
\(564\) | 1.31371i | 0.0553171i | ||||||||
\(565\) | 42.4098 | + | 24.4853i | 1.78419 | + | 1.03010i | ||||
\(566\) | −10.3923 | − | 6.00000i | −0.436821 | − | 0.252199i | ||||
\(567\) | − | 2.82843i | − | 0.118783i | ||||||
\(568\) | 4.41421 | − | 7.64564i | 0.185216 | − | 0.320804i | ||||
\(569\) | −4.51472 | − | 7.81972i | −0.189267 | − | 0.327820i | 0.755739 | − | 0.654873i | \(-0.227278\pi\) |
−0.945006 | + | 0.327053i | \(0.893944\pi\) | |||||||
\(570\) | −16.7262 | + | 9.65685i | −0.700582 | + | 0.404481i | ||||
\(571\) | −20.9706 | −0.877591 | −0.438795 | − | 0.898587i | \(-0.644595\pi\) | ||||
−0.438795 | + | 0.898587i | \(0.644595\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.3137 | −0.806842 | ||||||||
\(574\) | −64.0349 | + | 36.9706i | −2.67276 | + | 1.54312i | ||||
\(575\) | 6.00000 | + | 10.3923i | 0.250217 | + | 0.433389i | ||||
\(576\) | −4.91421 | + | 8.51167i | −0.204759 | + | 0.354653i | ||||
\(577\) | − | 35.9411i | − | 1.49625i | −0.663559 | − | 0.748124i | \(-0.730955\pi\) | ||
0.663559 | − | 0.748124i | \(-0.269045\pi\) | |||||||
\(578\) | 7.58410 | + | 4.37868i | 0.315457 | + | 0.182129i | ||||
\(579\) | 14.9941 | + | 8.65685i | 0.623134 | + | 0.359767i | ||||
\(580\) | 21.6569i | 0.899252i | ||||||||
\(581\) | −10.8284 | + | 18.7554i | −0.449239 | + | 0.778105i | ||||
\(582\) | 9.24264 | + | 16.0087i | 0.383120 | + | 0.663583i | ||||
\(583\) | 3.46410 | − | 2.00000i | 0.143468 | − | 0.0828315i | ||||
\(584\) | 51.4558 | 2.12926 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 63.1127 | 2.60716 | ||||||||
\(587\) | −19.8931 | + | 11.4853i | −0.821076 | + | 0.474048i | −0.850787 | − | 0.525510i | \(-0.823874\pi\) |
0.0297116 | + | 0.999559i | \(0.490541\pi\) | |||||||
\(588\) | −1.91421 | − | 3.31552i | −0.0789408 | − | 0.136730i | ||||
\(589\) | −9.65685 | + | 16.7262i | −0.397904 | + | 0.689190i | ||||
\(590\) | − | 24.9706i | − | 1.02802i | ||||||
\(591\) | −14.2767 | − | 8.24264i | −0.587264 | − | 0.339057i | ||||
\(592\) | −9.50079 | − | 5.48528i | −0.390480 | − | 0.225444i | ||||
\(593\) | − | 3.51472i | − | 0.144332i | −0.997393 | − | 0.0721661i | \(-0.977009\pi\) | ||
0.997393 | − | 0.0721661i | \(-0.0229912\pi\) | |||||||
\(594\) | −2.41421 | + | 4.18154i | −0.0990564 | + | 0.171571i | ||||
\(595\) | 14.6274 | + | 25.3354i | 0.599666 | + | 1.03865i | ||||
\(596\) | −49.1639 | + | 28.3848i | −2.01383 | + | 1.16269i | ||||
\(597\) | −10.3431 | −0.423317 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.686292 | −0.0280411 | −0.0140206 | − | 0.999902i | \(-0.504463\pi\) | ||||
−0.0140206 | + | 0.999902i | \(0.504463\pi\) | |||||||
\(600\) | 11.4685 | − | 6.62132i | 0.468198 | − | 0.270314i | ||||
\(601\) | −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 | ||||
\(603\) | − | 1.17157i | − | 0.0477101i | ||||||
\(604\) | −67.9193 | − | 39.2132i | −2.76360 | − | 1.59556i | ||||
\(605\) | 17.1464 | + | 9.89949i | 0.697101 | + | 0.402472i | ||||
\(606\) | 8.82843i | 0.358630i | ||||||||
\(607\) | 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 | ||||
\(609\) | −4.89898 | + | 2.82843i | −0.198517 | + | 0.114614i | ||||
\(610\) | −63.5980 | −2.57501 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −14.0000 | −0.565916 | ||||||||
\(613\) | 31.4741 | − | 18.1716i | 1.27123 | − | 0.733943i | 0.296008 | − | 0.955186i | \(-0.404345\pi\) |
0.975219 | + | 0.221243i | \(0.0710113\pi\) | |||||||
\(614\) | −20.7279 | − | 35.9018i | −0.836511 | − | 1.44888i | ||||
\(615\) | 15.3137 | − | 26.5241i | 0.617508 | − | 1.06956i | ||||
\(616\) | 24.9706i | 1.00609i | ||||||||
\(617\) | −25.2633 | − | 14.5858i | −1.01706 | − | 0.587202i | −0.103811 | − | 0.994597i | \(-0.533104\pi\) |
−0.913252 | + | 0.407395i | \(0.866437\pi\) | |||||||
\(618\) | 28.5533 | + | 16.4853i | 1.14858 | + | 0.663135i | ||||
\(619\) | − | 15.7990i | − | 0.635015i | −0.948256 | − | 0.317508i | \(-0.897154\pi\) | ||
0.948256 | − | 0.317508i | \(-0.102846\pi\) | |||||||
\(620\) | 36.9706 | − | 64.0349i | 1.48477 | − | 2.57170i | ||||
\(621\) | −2.00000 | − | 3.46410i | −0.0802572 | − | 0.139010i | ||||
\(622\) | −72.3980 | + | 41.7990i | −2.90289 | + | 1.67599i | ||||
\(623\) | 25.9411 | 1.03931 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 12.5446 | − | 7.24264i | 0.501384 | − | 0.289474i | ||||
\(627\) | 2.82843 | + | 4.89898i | 0.112956 | + | 0.195646i | ||||
\(628\) | −19.1421 | + | 33.1552i | −0.763854 | + | 1.32303i | ||||
\(629\) | 13.3726i | 0.533200i | ||||||||
\(630\) | 16.7262 | + | 9.65685i | 0.666386 | + | 0.384738i | ||||
\(631\) | 16.5521 | + | 9.55635i | 0.658928 | + | 0.380432i | 0.791868 | − | 0.610692i | \(-0.209109\pi\) |
−0.132940 | + | 0.991124i | \(0.542442\pi\) | |||||||
\(632\) | − | 49.9411i | − | 1.98655i | ||||||
\(633\) | 6.00000 | − | 10.3923i | 0.238479 | − | 0.413057i | ||||
\(634\) | 10.2426 | + | 17.7408i | 0.406787 | + | 0.704576i | ||||
\(635\) | −13.8564 | + | 8.00000i | −0.549875 | + | 0.317470i | ||||
\(636\) | 7.65685 | 0.303614 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.65685 | 0.382319 | ||||||||
\(639\) | −1.73205 | + | 1.00000i | −0.0685189 | + | 0.0395594i | ||||
\(640\) | −29.0711 | − | 50.3526i | −1.14913 | − | 1.99036i | ||||
\(641\) | −13.1421 | + | 22.7628i | −0.519083 | + | 0.899078i | 0.480671 | + | 0.876901i | \(0.340393\pi\) |
−0.999754 | + | 0.0221773i | \(0.992940\pi\) | |||||||
\(642\) | 27.3137i | 1.07799i | ||||||||
\(643\) | 14.8710 | + | 8.58579i | 0.586456 | + | 0.338590i | 0.763695 | − | 0.645577i | \(-0.223383\pi\) |
−0.177239 | + | 0.984168i | \(0.556717\pi\) | |||||||
\(644\) | −37.5108 | − | 21.6569i | −1.47813 | − | 0.853400i | ||||
\(645\) | 27.3137i | 1.07548i | ||||||||
\(646\) | −12.4853 | + | 21.6251i | −0.491227 | + | 0.850830i | ||||
\(647\) | −5.65685 | − | 9.79796i | −0.222394 | − | 0.385198i | 0.733140 | − | 0.680077i | \(-0.238054\pi\) |
−0.955534 | + | 0.294880i | \(0.904720\pi\) | |||||||
\(648\) | −3.82282 | + | 2.20711i | −0.150175 | + | 0.0867033i | ||||
\(649\) | −7.31371 | −0.287088 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.3137 | 0.756964 | ||||||||
\(652\) | −43.6705 | + | 25.2132i | −1.71027 | + | 0.987425i | ||||
\(653\) | 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 | ||||
\(655\) | 22.6274i | 0.884126i | ||||||||
\(656\) | 28.1331 | + | 16.2426i | 1.09841 | + | 0.634169i | ||||
\(657\) | −10.0951 | − | 5.82843i | −0.393849 | − | 0.227389i | ||||
\(658\) | − | 2.34315i | − | 0.0913453i | ||||||
\(659\) | 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 | ||||
\(661\) | −0.891519 | + | 0.514719i | −0.0346761 | + | 0.0200202i | −0.517238 | − | 0.855842i | \(-0.673040\pi\) |
0.482562 | + | 0.875862i | \(0.339706\pi\) | |||||||
\(662\) | −5.17157 | −0.200999 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 33.7990 | 1.31166 | ||||||||
\(665\) | 19.5959 | − | 11.3137i | 0.759897 | − | 0.438727i | ||||
\(666\) | 4.41421 | + | 7.64564i | 0.171047 | + | 0.296263i | ||||
\(667\) | −4.00000 | + | 6.92820i | −0.154881 | + | 0.268261i | ||||
\(668\) | − | 29.3137i | − | 1.13418i | ||||||
\(669\) | 3.88437 | + | 2.24264i | 0.150178 | + | 0.0867055i | ||||
\(670\) | 6.92820 | + | 4.00000i | 0.267660 | + | 0.154533i | ||||
\(671\) | 18.6274i | 0.719103i | ||||||||
\(672\) | 2.24264 | − | 3.88437i | 0.0865117 | − | 0.149843i | ||||
\(673\) | −14.3137 | − | 24.7921i | −0.551753 | − | 0.955664i | −0.998148 | − | 0.0608282i | \(-0.980626\pi\) |
0.446395 | − | 0.894836i | \(-0.352708\pi\) | |||||||
\(674\) | 27.8359 | − | 16.0711i | 1.07220 | − | 0.619034i | ||||
\(675\) | −3.00000 | −0.115470 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 49.3137 | 1.89528 | 0.947640 | − | 0.319341i | \(-0.103462\pi\) | ||||
0.947640 | + | 0.319341i | \(0.103462\pi\) | |||||||
\(678\) | 36.1990 | − | 20.8995i | 1.39021 | − | 0.802640i | ||||
\(679\) | −10.8284 | − | 18.7554i | −0.415557 | − | 0.719766i | ||||
\(680\) | 22.8284 | − | 39.5400i | 0.875430 | − | 1.51629i | ||||
\(681\) | − | 5.31371i | − | 0.203622i | ||||||
\(682\) | −28.5533 | − | 16.4853i | −1.09336 | − | 0.631254i | ||||
\(683\) | 17.2695 | + | 9.97056i | 0.660800 | + | 0.381513i | 0.792582 | − | 0.609766i | \(-0.208736\pi\) |
−0.131782 | + | 0.991279i | \(0.542070\pi\) | |||||||
\(684\) | 10.8284i | 0.414035i | ||||||||
\(685\) | 7.31371 | − | 12.6677i | 0.279442 | − | 0.484008i | ||||
\(686\) | −20.4853 | − | 35.4815i | −0.782132 | − | 1.35469i | ||||
\(687\) | 18.4582 | − | 10.6569i | 0.704225 | − | 0.406584i | ||||
\(688\) | −28.9706 | −1.10449 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 27.3137 | 1.03982 | ||||||||
\(691\) | 29.5680 | − | 17.0711i | 1.12482 | − | 0.649414i | 0.182192 | − | 0.983263i | \(-0.441681\pi\) |
0.942627 | + | 0.333849i | \(0.108348\pi\) | |||||||
\(692\) | 0.656854 | + | 1.13770i | 0.0249699 | + | 0.0432491i | ||||
\(693\) | 2.82843 | − | 4.89898i | 0.107443 | − | 0.186097i | ||||
\(694\) | − | 75.5980i | − | 2.86966i | ||||||
\(695\) | 37.5108 | + | 21.6569i | 1.42286 | + | 0.821491i | ||||
\(696\) | 7.64564 | + | 4.41421i | 0.289807 | + | 0.167320i | ||||
\(697\) | − | 39.5980i | − | 1.49988i | ||||||
\(698\) | −9.24264 | + | 16.0087i | −0.349839 | + | 0.605939i | ||||
\(699\) | −13.4853 | − | 23.3572i | −0.510060 | − | 0.883450i | ||||
\(700\) | −28.1331 | + | 16.2426i | −1.06333 | + | 0.613914i | ||||
\(701\) | −38.9706 | −1.47190 | −0.735949 | − | 0.677037i | \(-0.763264\pi\) | ||||
−0.735949 | + | 0.677037i | \(0.763264\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.3431 | 0.390099 | ||||||||
\(704\) | −17.0233 | + | 9.82843i | −0.641591 | + | 0.370423i | ||||
\(705\) | 0.485281 | + | 0.840532i | 0.0182768 | + | 0.0316563i | ||||
\(706\) | −21.0711 | + | 36.4962i | −0.793020 | + | 1.37355i | ||||
\(707\) | − | 10.3431i | − | 0.388994i | ||||||
\(708\) | −12.1244 | − | 7.00000i | −0.455661 | − | 0.263076i | ||||
\(709\) | −35.1844 | − | 20.3137i | −1.32138 | − | 0.762897i | −0.337429 | − | 0.941351i | \(-0.609557\pi\) |
−0.983948 | + | 0.178454i | \(0.942891\pi\) | |||||||
\(710\) | − | 13.6569i | − | 0.512533i | ||||||
\(711\) | −5.65685 | + | 9.79796i | −0.212149 | + | 0.367452i | ||||
\(712\) | −20.2426 | − | 35.0613i | −0.758625 | − | 1.31398i | ||||
\(713\) | 23.6544 | − | 13.6569i | 0.885863 | − | 0.511453i | ||||
\(714\) | 24.9706 | 0.934500 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.62742 | −0.0981912 | ||||||||
\(717\) | −1.73205 | + | 1.00000i | −0.0646846 | + | 0.0373457i | ||||
\(718\) | 1.24264 | + | 2.15232i | 0.0463749 | + | 0.0803237i | ||||
\(719\) | 18.9706 | − | 32.8580i | 0.707483 | − | 1.22540i | −0.258305 | − | 0.966063i | \(-0.583164\pi\) |
0.965788 | − | 0.259333i | \(-0.0835026\pi\) | |||||||
\(720\) | − | 8.48528i | − | 0.316228i | ||||||
\(721\) | −33.4523 | − | 19.3137i | −1.24583 | − | 0.719280i | ||||
\(722\) | −22.9985 | − | 13.2782i | −0.855915 | − | 0.494162i | ||||
\(723\) | 11.6569i | 0.433523i | ||||||||
\(724\) | −26.7990 | + | 46.4172i | −0.995977 | + | 1.72508i | ||||
\(725\) | 3.00000 | + | 5.19615i | 0.111417 | + | 0.192980i | ||||
\(726\) | 14.6354 | − | 8.44975i | 0.543170 | − | 0.313600i | ||||
\(727\) | 21.6569 | 0.803208 | 0.401604 | − | 0.915813i | \(-0.368453\pi\) | ||||
0.401604 | + | 0.915813i | \(0.368453\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 68.9339 | − | 39.7990i | 2.55136 | − | 1.47303i | ||||
\(731\) | 17.6569 | + | 30.5826i | 0.653062 | + | 1.13114i | ||||
\(732\) | −17.8284 | + | 30.8797i | −0.658958 | + | 1.14135i | ||||
\(733\) | − | 8.62742i | − | 0.318661i | −0.987225 | − | 0.159330i | \(-0.949066\pi\) | ||
0.987225 | − | 0.159330i | \(-0.0509335\pi\) | |||||||
\(734\) | 50.1785 | + | 28.9706i | 1.85212 | + | 1.06932i | ||||
\(735\) | −2.44949 | − | 1.41421i | −0.0903508 | − | 0.0521641i | ||||
\(736\) | − | 6.34315i | − | 0.233811i | ||||||
\(737\) | 1.17157 | − | 2.02922i | 0.0431554 | − | 0.0747474i | ||||
\(738\) | −13.0711 | − | 22.6398i | −0.481153 | − | 0.833381i | ||||
\(739\) | 8.78335 | − | 5.07107i | 0.323101 | − | 0.186542i | −0.329673 | − | 0.944095i | \(-0.606939\pi\) |
0.652774 | + | 0.757553i | \(0.273605\pi\) | |||||||
\(740\) | −39.5980 | −1.45565 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −13.6569 | −0.501359 | ||||||||
\(743\) | −1.73205 | + | 1.00000i | −0.0635428 | + | 0.0366864i | −0.531435 | − | 0.847099i | \(-0.678347\pi\) |
0.467892 | + | 0.883786i | \(0.345014\pi\) | |||||||
\(744\) | −15.0711 | − | 26.1039i | −0.552532 | − | 0.957014i | ||||
\(745\) | −20.9706 | + | 36.3221i | −0.768302 | + | 1.33074i | ||||
\(746\) | 24.1421i | 0.883906i | ||||||||
\(747\) | −6.63103 | − | 3.82843i | −0.242617 | − | 0.140075i | ||||
\(748\) | −24.2487 | − | 14.0000i | −0.886621 | − | 0.511891i | ||||
\(749\) | − | 32.0000i | − | 1.16925i | ||||||
\(750\) | −6.82843 | + | 11.8272i | −0.249339 | + | 0.431868i | ||||
\(751\) | 16.4853 | + | 28.5533i | 0.601556 | + | 1.04193i | 0.992586 | + | 0.121548i | \(0.0387858\pi\) |
−0.391029 | + | 0.920378i | \(0.627881\pi\) | |||||||
\(752\) | −0.891519 | + | 0.514719i | −0.0325103 | + | 0.0187699i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −57.9411 | −2.10869 | ||||||||
\(756\) | 9.37769 | − | 5.41421i | 0.341063 | − | 0.196913i | ||||
\(757\) | 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 | ||||
\(759\) | − | 8.00000i | − | 0.290382i | ||||||
\(760\) | −30.5826 | − | 17.6569i | −1.10935 | − | 0.640481i | ||||
\(761\) | −13.4361 | − | 7.75736i | −0.487060 | − | 0.281204i | 0.236294 | − | 0.971682i | \(-0.424067\pi\) |
−0.723354 | + | 0.690478i | \(0.757400\pi\) | |||||||
\(762\) | 13.6569i | 0.494736i | ||||||||
\(763\) | −24.4853 | + | 42.4098i | −0.886427 | + | 1.53534i | ||||
\(764\) | −36.9706 | − | 64.0349i | −1.33755 | − | 2.31670i | ||||
\(765\) | −8.95743 | + | 5.17157i | −0.323856 | + | 0.186979i | ||||
\(766\) | −7.17157 | −0.259119 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −29.9706 | −1.08147 | ||||||||
\(769\) | −36.3731 | + | 21.0000i | −1.31165 | + | 0.757279i | −0.982369 | − | 0.186954i | \(-0.940139\pi\) |
−0.329278 | + | 0.944233i | \(0.606805\pi\) | |||||||
\(770\) | 19.3137 | + | 33.4523i | 0.696018 | + | 1.20554i | ||||
\(771\) | −7.82843 | + | 13.5592i | −0.281934 | + | 0.488324i | ||||
\(772\) | 66.2843i | 2.38562i | ||||||||
\(773\) | 5.07306 | + | 2.92893i | 0.182465 | + | 0.105346i | 0.588450 | − | 0.808533i | \(-0.299738\pi\) |
−0.405985 | + | 0.913880i | \(0.633072\pi\) | |||||||
\(774\) | 20.1903 | + | 11.6569i | 0.725724 | + | 0.418997i | ||||
\(775\) | − | 20.4853i | − | 0.735853i | ||||||
\(776\) | −16.8995 | + | 29.2708i | −0.606657 | + | 1.05076i | ||||
\(777\) | −5.17157 | − | 8.95743i | −0.185529 | − | 0.321346i | ||||
\(778\) | −14.5738 | + | 8.41421i | −0.522498 | + | 0.301664i | ||||
\(779\) | −30.6274 | −1.09734 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00000 | −0.143131 | ||||||||
\(782\) | 30.5826 | − | 17.6569i | 1.09363 | − | 0.631408i | ||||
\(783\) | −1.00000 | − | 1.73205i | −0.0357371 | − | 0.0618984i | ||||
\(784\) | 1.50000 | − | 2.59808i | 0.0535714 | − | 0.0927884i | ||||
\(785\) | 28.2843i | 1.00951i | ||||||||
\(786\) | 16.7262 | + | 9.65685i | 0.596602 | + | 0.344449i | ||||
\(787\) | −28.3793 | − | 16.3848i | −1.01161 | − | 0.584054i | −0.0999484 | − | 0.994993i | \(-0.531868\pi\) |
−0.911663 | + | 0.410938i | \(0.865201\pi\) | |||||||
\(788\) | − | 63.1127i | − | 2.24830i | ||||||
\(789\) | −6.00000 | + | 10.3923i | −0.213606 | + | 0.369976i | ||||
\(790\) | −38.6274 | − | 66.9046i | −1.37430 | − | 2.38036i | ||||
\(791\) | −42.4098 | + | 24.4853i | −1.50792 | + | 0.870596i | ||||
\(792\) | −8.82843 | −0.313704 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 7.17157 | 0.254510 | ||||||||
\(795\) | 4.89898 | − | 2.82843i | 0.173749 | − | 0.100314i | ||||
\(796\) | −19.7990 | − | 34.2929i | −0.701757 | − | 1.21548i | ||||
\(797\) | 17.8284 | − | 30.8797i | 0.631515 | − | 1.09382i | −0.355727 | − | 0.934590i | \(-0.615767\pi\) |
0.987242 | − | 0.159227i | \(-0.0509000\pi\) | |||||||
\(798\) | − | 19.3137i | − | 0.683698i | ||||||
\(799\) | 1.08672 | + | 0.627417i | 0.0384453 | + | 0.0221964i | ||||
\(800\) | −4.11999 | − | 2.37868i | −0.145664 | − | 0.0840990i | ||||
\(801\) | 9.17157i | 0.324062i | ||||||||
\(802\) | −2.58579 | + | 4.47871i | −0.0913073 | + | 0.158149i | ||||
\(803\) | −11.6569 | − | 20.1903i | −0.411361 | − | 0.712499i | ||||
\(804\) | 3.88437 | − | 2.24264i | 0.136991 | − | 0.0790918i | ||||
\(805\) | −32.0000 | −1.12785 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.0000 | 0.633630 | ||||||||
\(808\) | −13.9795 | + | 8.07107i | −0.491797 | + | 0.283939i | ||||
\(809\) | −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 | ||||
\(811\) | 1.85786i | 0.0652384i | 0.999468 | + | 0.0326192i | \(0.0103849\pi\) | ||||
−0.999468 | + | 0.0326192i | \(0.989615\pi\) | |||||||
\(812\) | −18.7554 | − | 10.8284i | −0.658185 | − | 0.380003i | ||||
\(813\) | −10.2182 | − | 5.89949i | −0.358369 | − | 0.206904i | ||||
\(814\) | 17.6569i | 0.618872i | ||||||||
\(815\) | −18.6274 | + | 32.2636i | −0.652490 | + | 1.13015i | ||||
\(816\) | −5.48528 | − | 9.50079i | −0.192023 | − | 0.332594i | ||||
\(817\) | 23.6544 | − | 13.6569i | 0.827561 | − | 0.477793i | ||||
\(818\) | −2.48528 | −0.0868958 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 117.255 | 4.09472 | ||||||||
\(821\) | −13.6823 | + | 7.89949i | −0.477516 | + | 0.275694i | −0.719381 | − | 0.694616i | \(-0.755574\pi\) |
0.241864 | + | 0.970310i | \(0.422241\pi\) | |||||||
\(822\) | −6.24264 | − | 10.8126i | −0.217737 | − | 0.377132i | ||||
\(823\) | 24.4853 | − | 42.4098i | 0.853503 | − | 1.47831i | −0.0245234 | − | 0.999699i | \(-0.507807\pi\) |
0.878027 | − | 0.478612i | \(-0.158860\pi\) | |||||||
\(824\) | 60.2843i | 2.10010i | ||||||||
\(825\) | −5.19615 | − | 3.00000i | −0.180907 | − | 0.104447i | ||||
\(826\) | 21.6251 | + | 12.4853i | 0.752435 | + | 0.434418i | ||||
\(827\) | − | 26.0000i | − | 0.904109i | −0.891990 | − | 0.452054i | \(-0.850691\pi\) | ||
0.891990 | − | 0.452054i | \(-0.149309\pi\) | |||||||
\(828\) | 7.65685 | − | 13.2621i | 0.266094 | − | 0.460888i | ||||
\(829\) | 2.65685 | + | 4.60181i | 0.0922764 | + | 0.159827i | 0.908469 | − | 0.417953i | \(-0.137252\pi\) |
−0.816192 | + | 0.577780i | \(0.803919\pi\) | |||||||
\(830\) | 45.2795 | − | 26.1421i | 1.57167 | − | 0.907407i | ||||
\(831\) | 2.00000 | 0.0693792 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.65685 | −0.126702 | ||||||||
\(834\) | 32.0174 | − | 18.4853i | 1.10867 | − | 0.640093i | ||||
\(835\) | −10.8284 | − | 18.7554i | −0.374733 | − | 0.649057i | ||||
\(836\) | −10.8284 | + | 18.7554i | −0.374509 | + | 0.648669i | ||||
\(837\) | 6.82843i | 0.236025i | ||||||||
\(838\) | 64.0349 | + | 36.9706i | 2.21205 | + | 1.27713i | ||||
\(839\) | 40.9239 | + | 23.6274i | 1.41285 | + | 0.815709i | 0.995656 | − | 0.0931087i | \(-0.0296804\pi\) |
0.417194 | + | 0.908818i | \(0.363014\pi\) | |||||||
\(840\) | 35.3137i | 1.21844i | ||||||||
\(841\) | 12.5000 | − | 21.6506i | 0.431034 | − | 0.746574i | ||||
\(842\) | −17.7279 | − | 30.7057i | −0.610945 | − | 1.05819i | ||||
\(843\) | 23.2341 | − | 13.4142i | 0.800225 | − | 0.462010i | ||||
\(844\) | 45.9411 | 1.58136 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.828427 | 0.0284819 | ||||||||
\(847\) | −17.1464 | + | 9.89949i | −0.589158 | + | 0.340151i | ||||
\(848\) | 3.00000 | + | 5.19615i | 0.103020 | + | 0.178437i | ||||
\(849\) | −2.48528 | + | 4.30463i | −0.0852946 | + | 0.147735i | ||||
\(850\) | − | 26.4853i | − | 0.908438i | ||||||
\(851\) | −12.6677 | − | 7.31371i | −0.434244 | − | 0.250711i | ||||
\(852\) | −6.63103 | − | 3.82843i | −0.227175 | − | 0.131160i | ||||
\(853\) | − | 7.65685i | − | 0.262166i | −0.991371 | − | 0.131083i | \(-0.958155\pi\) | ||
0.991371 | − | 0.131083i | \(-0.0418454\pi\) | |||||||
\(854\) | 31.7990 | − | 55.0775i | 1.08814 | − | 1.88471i | ||||
\(855\) | 4.00000 | + | 6.92820i | 0.136797 | + | 0.236940i | ||||
\(856\) | −43.2503 | + | 24.9706i | −1.47826 | + | 0.853476i | ||||
\(857\) | −29.5980 | −1.01105 | −0.505524 | − | 0.862813i | \(-0.668701\pi\) | ||||
−0.505524 | + | 0.862813i | \(0.668701\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.3137 | −0.795453 | −0.397727 | − | 0.917504i | \(-0.630201\pi\) | ||||
−0.397727 | + | 0.917504i | \(0.630201\pi\) | |||||||
\(860\) | −90.5590 | + | 52.2843i | −3.08804 | + | 1.78288i | ||||
\(861\) | 15.3137 | + | 26.5241i | 0.521890 | + | 0.903940i | ||||
\(862\) | −23.7279 | + | 41.0980i | −0.808176 | + | 1.39980i | ||||
\(863\) | 39.6569i | 1.34994i | 0.737847 | + | 0.674968i | \(0.235842\pi\) | ||||
−0.737847 | + | 0.674968i | \(0.764158\pi\) | |||||||
\(864\) | 1.37333 | + | 0.792893i | 0.0467217 | + | 0.0269748i | ||||
\(865\) | 0.840532 | + | 0.485281i | 0.0285789 | + | 0.0165001i | ||||
\(866\) | − | 3.17157i | − | 0.107774i | ||||||
\(867\) | 1.81371 | − | 3.14144i | 0.0615968 | − | 0.106689i | ||||
\(868\) | 36.9706 | + | 64.0349i | 1.25486 | + | 2.17349i | ||||
\(869\) | −19.5959 | + | 11.3137i | −0.664746 | + | 0.383791i | ||||
\(870\) | 13.6569 | 0.463011 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 76.4264 | 2.58812 | ||||||||
\(873\) | 6.63103 | − | 3.82843i | 0.224426 | − | 0.129573i | ||||
\(874\) | −13.6569 | − | 23.6544i | −0.461950 | − | 0.800121i | ||||
\(875\) | 8.00000 | − | 13.8564i | 0.270449 | − | 0.468432i | ||||
\(876\) | − | 44.6274i | − | 1.50782i | ||||||
\(877\) | −12.3705 | − | 7.14214i | −0.417724 | − | 0.241173i | 0.276379 | − | 0.961049i | \(-0.410865\pi\) |
−0.694103 | + | 0.719876i | \(0.744199\pi\) | |||||||
\(878\) | −35.4815 | − | 20.4853i | −1.19744 | − | 0.691345i | ||||
\(879\) | − | 26.1421i | − | 0.881752i | ||||||
\(880\) | 8.48528 | − | 14.6969i | 0.286039 | − | 0.495434i | ||||
\(881\) | 26.7990 | + | 46.4172i | 0.902881 | + | 1.56384i | 0.823737 | + | 0.566972i | \(0.191885\pi\) |
0.0791441 | + | 0.996863i | \(0.474781\pi\) | |||||||
\(882\) | −2.09077 | + | 1.20711i | −0.0703999 | + | 0.0406454i | ||||
\(883\) | 51.5980 | 1.73641 | 0.868205 | − | 0.496205i | \(-0.165274\pi\) | ||||
0.868205 | + | 0.496205i | \(0.165274\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.3431 | −0.347681 | ||||||||
\(886\) | 87.6893 | − | 50.6274i | 2.94598 | − | 1.70086i | ||||
\(887\) | 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 | ||||
\(889\) | − | 16.0000i | − | 0.536623i | ||||||
\(890\) | −54.2369 | − | 31.3137i | −1.81803 | − | 1.04964i | ||||
\(891\) | 1.73205 | + | 1.00000i | 0.0580259 | + | 0.0335013i | ||||
\(892\) | 17.1716i | 0.574947i | ||||||||
\(893\) | 0.485281 | − | 0.840532i | 0.0162393 | − | 0.0281273i | ||||
\(894\) | 17.8995 | + | 31.0028i | 0.598649 | + | 1.03689i | ||||
\(895\) | −1.68106 | + | 0.970563i | −0.0561918 | + | 0.0324423i | ||||
\(896\) | 58.1421 | 1.94239 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.8284 | −0.628313 | ||||||||
\(899\) | 11.8272 | − | 6.82843i | 0.394459 | − | 0.227741i | ||||
\(900\) | −5.74264 | − | 9.94655i | −0.191421 | − | 0.331552i | ||||
\(901\) | 3.65685 | − | 6.33386i | 0.121827 | − | 0.211011i | ||||
\(902\) | − | 52.2843i | − | 1.74088i | ||||||
\(903\) | −23.6544 | − | 13.6569i | −0.787168 | − | 0.454472i | ||||
\(904\) | 66.1872 | + | 38.2132i | 2.20135 | + | 1.27095i | ||||
\(905\) | 39.5980i | 1.31628i | ||||||||
\(906\) | −24.7279 | + | 42.8300i | −0.821530 | + | 1.42293i | ||||
\(907\) | 10.4853 | + | 18.1610i | 0.348158 | + | 0.603027i | 0.985922 | − | 0.167204i | \(-0.0534739\pi\) |
−0.637764 | + | 0.770232i | \(0.720141\pi\) | |||||||
\(908\) | 17.6177 | − | 10.1716i | 0.584663 | − | 0.337556i | ||||
\(909\) | 3.65685 | 0.121290 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.0000 | −1.32526 | −0.662630 | − | 0.748947i | \(-0.730560\pi\) | ||||
−0.662630 | + | 0.748947i | \(0.730560\pi\) | |||||||
\(912\) | −7.34847 | + | 4.24264i | −0.243332 | + | 0.140488i | ||||
\(913\) | −7.65685 | − | 13.2621i | −0.253405 | − | 0.438910i | ||||
\(914\) | −4.41421 | + | 7.64564i | −0.146009 | + | 0.252895i | ||||
\(915\) | 26.3431i | 0.870878i | ||||||||
\(916\) | 70.6659 | + | 40.7990i | 2.33487 | + | 1.34804i | ||||
\(917\) | −19.5959 | − | 11.3137i | −0.647114 | − | 0.373612i | ||||
\(918\) | 8.82843i | 0.291382i | ||||||||
\(919\) | 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 | ||||
\(921\) | −14.8710 | + | 8.58579i | −0.490017 | + | 0.282911i | ||||
\(922\) | 26.1421 | 0.860945 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 21.6569 | 0.712458 | ||||||||
\(925\) | −9.50079 | + | 5.48528i | −0.312384 | + | 0.180355i | ||||
\(926\) | −9.07107 | − | 15.7116i | −0.298094 | − | 0.516314i | ||||
\(927\) | 6.82843 | − | 11.8272i | 0.224275 | − | 0.388456i | ||||
\(928\) | − | 3.17157i | − | 0.104112i | ||||||
\(929\) | −24.0746 | − | 13.8995i | −0.789863 | − | 0.456028i | 0.0500513 | − | 0.998747i | \(-0.484062\pi\) |
−0.839914 | + | 0.542719i | \(0.817395\pi\) | |||||||
\(930\) | −40.3805 | − | 23.3137i | −1.32413 | − | 0.764487i | ||||
\(931\) | 2.82843i | 0.0926980i | ||||||||
\(932\) | 51.6274 | − | 89.4213i | 1.69111 | − | 2.92909i | ||||
\(933\) | 17.3137 | + | 29.9882i | 0.566825 | + | 0.981770i | ||||
\(934\) | 16.7262 | − | 9.65685i | 0.547297 | − | 0.315982i | ||||
\(935\) | −20.6863 | −0.676514 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.31371 | 0.0429170 | 0.0214585 | − | 0.999770i | \(-0.493169\pi\) | ||||
0.0214585 | + | 0.999770i | \(0.493169\pi\) | |||||||
\(938\) | −6.92820 | + | 4.00000i | −0.226214 | + | 0.130605i | ||||
\(939\) | −3.00000 | − | 5.19615i | −0.0979013 | − | 0.169570i | ||||
\(940\) | −1.85786 | + | 3.21792i | −0.0605969 | + | 0.104957i | ||||
\(941\) | − | 5.85786i | − | 0.190961i | −0.995431 | − | 0.0954805i | \(-0.969561\pi\) | ||
0.995431 | − | 0.0954805i | \(-0.0304387\pi\) | |||||||
\(942\) | 20.9077 | + | 12.0711i | 0.681210 | + | 0.393297i | ||||
\(943\) | 37.5108 | + | 21.6569i | 1.22152 | + | 0.705244i | ||||
\(944\) | − | 10.9706i | − | 0.357061i | ||||||
\(945\) | 4.00000 | − | 6.92820i | 0.130120 | − | 0.225374i | ||||
\(946\) | 23.3137 | + | 40.3805i | 0.757994 | + | 1.31288i | ||||
\(947\) | −47.6059 | + | 27.4853i | −1.54698 | + | 0.893152i | −0.548614 | + | 0.836076i | \(0.684844\pi\) |
−0.998370 | + | 0.0570760i | \(0.981822\pi\) | |||||||
\(948\) | −43.3137 | −1.40676 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −20.4853 | −0.664630 | ||||||||
\(951\) | 7.34847 | − | 4.24264i | 0.238290 | − | 0.137577i | ||||
\(952\) | 22.8284 | + | 39.5400i | 0.739874 | + | 1.28150i | ||||
\(953\) | 25.8284 | − | 44.7361i | 0.836665 | − | 1.44915i | −0.0560029 | − | 0.998431i | \(-0.517836\pi\) |
0.892668 | − | 0.450715i | \(-0.148831\pi\) | |||||||
\(954\) | − | 4.82843i | − | 0.156326i | ||||||
\(955\) | −47.3087 | − | 27.3137i | −1.53087 | − | 0.883851i | ||||
\(956\) | −6.63103 | − | 3.82843i | −0.214463 | − | 0.123820i | ||||
\(957\) | − | 4.00000i | − | 0.129302i | ||||||
\(958\) | 3.24264 | − | 5.61642i | 0.104765 | − | 0.181458i | ||||
\(959\) | 7.31371 | + | 12.6677i | 0.236172 | + | 0.409062i | ||||
\(960\) | −24.0746 | + | 13.8995i | −0.777005 | + | 0.448604i | ||||
\(961\) | −15.6274 | −0.504110 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.3137 | 0.364579 | ||||||||
\(964\) | −38.6485 | + | 22.3137i | −1.24478 | + | 0.718676i | ||||
\(965\) | 24.4853 | + | 42.4098i | 0.788209 | + | 1.36522i | ||||
\(966\) | −13.6569 | + | 23.6544i | −0.439402 | + | 0.761067i | ||||
\(967\) | 10.1421i | 0.326149i | 0.986614 | + | 0.163075i | \(0.0521411\pi\) | ||||
−0.986614 | + | 0.163075i | \(0.947859\pi\) | |||||||
\(968\) | 26.7597 | + | 15.4497i | 0.860091 | + | 0.496574i | ||||
\(969\) | 8.95743 | + | 5.17157i | 0.287754 | + | 0.166135i | ||||
\(970\) | 52.2843i | 1.67875i | ||||||||
\(971\) | −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 | ||||
\(973\) | −37.5108 | + | 21.6569i | −1.20254 | + | 0.694287i | ||||
\(974\) | 76.7696 | 2.45986 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27.9411 | −0.894374 | ||||||||
\(977\) | −12.0013 | + | 6.92893i | −0.383954 | + | 0.221676i | −0.679537 | − | 0.733641i | \(-0.737819\pi\) |
0.295583 | + | 0.955317i | \(0.404486\pi\) | |||||||
\(978\) | 15.8995 | + | 27.5387i | 0.508410 | + | 0.880592i | ||||
\(979\) | −9.17157 | + | 15.8856i | −0.293125 | + | 0.507707i | ||||
\(980\) | − | 10.8284i | − | 0.345901i | ||||||
\(981\) | −14.9941 | − | 8.65685i | −0.478725 | − | 0.276392i | ||||
\(982\) | −30.5826 | − | 17.6569i | −0.975929 | − | 0.563453i | ||||
\(983\) | 2.68629i | 0.0856794i | 0.999082 | + | 0.0428397i | \(0.0136405\pi\) | ||||
−0.999082 | + | 0.0428397i | \(0.986360\pi\) | |||||||
\(984\) | 23.8995 | − | 41.3951i | 0.761888 | − | 1.31963i | ||||
\(985\) | −23.3137 | − | 40.3805i | −0.742837 | − | 1.28663i | ||||
\(986\) | 15.2913 | − | 8.82843i | 0.486974 | − | 0.281154i | ||||
\(987\) | −0.970563 | −0.0308934 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −38.6274 | −1.22828 | ||||||||
\(990\) | −11.8272 | + | 6.82843i | −0.375893 | + | 0.217022i | ||||
\(991\) | −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 | ||||
\(993\) | 2.14214i | 0.0679786i | ||||||||
\(994\) | 11.8272 | + | 6.82843i | 0.375135 | + | 0.216585i | ||||
\(995\) | −25.3354 | − | 14.6274i | −0.803187 | − | 0.463720i | ||||
\(996\) | − | 29.3137i | − | 0.928840i | ||||||
\(997\) | −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 | ||||
\(999\) | 3.16693 | − | 1.82843i | 0.100197 | − | 0.0578489i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))