Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,2,Mod(110,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.110");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.d (of order \(8\), degree \(4\), 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: | \(2.30767661842\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 17) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 134.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.134 |
Dual form | 289.2.d.a.110.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.70711 | − | 1.70711i | −1.20711 | − | 1.20711i | −0.971960 | − | 0.235147i | \(-0.924443\pi\) |
−0.235147 | − | 0.971960i | \(-0.575557\pi\) | |||||||
\(3\) | −0.414214 | − | 1.00000i | −0.239146 | − | 0.577350i | 0.758049 | − | 0.652198i | \(-0.226153\pi\) |
−0.997195 | + | 0.0748477i | \(0.976153\pi\) | |||||||
\(4\) | 3.82843i | 1.91421i | ||||||||
\(5\) | 0.707107 | − | 0.292893i | 0.316228 | − | 0.130986i | −0.218924 | − | 0.975742i | \(-0.570255\pi\) |
0.535151 | + | 0.844756i | \(0.320255\pi\) | |||||||
\(6\) | −1.00000 | + | 2.41421i | −0.408248 | + | 0.985599i | ||||
\(7\) | 2.41421 | + | 1.00000i | 0.912487 | + | 0.377964i | 0.789008 | − | 0.614383i | \(-0.210595\pi\) |
0.123479 | + | 0.992347i | \(0.460595\pi\) | |||||||
\(8\) | 3.12132 | − | 3.12132i | 1.10355 | − | 1.10355i | ||||
\(9\) | 1.29289 | − | 1.29289i | 0.430964 | − | 0.430964i | ||||
\(10\) | −1.70711 | − | 0.707107i | −0.539835 | − | 0.223607i | ||||
\(11\) | 1.00000 | − | 2.41421i | 0.301511 | − | 0.727913i | −0.698414 | − | 0.715694i | \(-0.746111\pi\) |
0.999925 | − | 0.0122188i | \(-0.00388946\pi\) | |||||||
\(12\) | 3.82843 | − | 1.58579i | 1.10517 | − | 0.457777i | ||||
\(13\) | − | 1.41421i | − | 0.392232i | −0.980581 | − | 0.196116i | \(-0.937167\pi\) | ||
0.980581 | − | 0.196116i | \(-0.0628330\pi\) | |||||||
\(14\) | −2.41421 | − | 5.82843i | −0.645226 | − | 1.55771i | ||||
\(15\) | −0.585786 | − | 0.585786i | −0.151249 | − | 0.151249i | ||||
\(16\) | −3.00000 | −0.750000 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −4.41421 | −1.04044 | ||||||||
\(19\) | 0.585786 | + | 0.585786i | 0.134389 | + | 0.134389i | 0.771101 | − | 0.636713i | \(-0.219706\pi\) |
−0.636713 | + | 0.771101i | \(0.719706\pi\) | |||||||
\(20\) | 1.12132 | + | 2.70711i | 0.250735 | + | 0.605327i | ||||
\(21\) | − | 2.82843i | − | 0.617213i | ||||||
\(22\) | −5.82843 | + | 2.41421i | −1.24262 | + | 0.514712i | ||||
\(23\) | 1.82843 | − | 4.41421i | 0.381253 | − | 0.920427i | −0.610471 | − | 0.792039i | \(-0.709020\pi\) |
0.991724 | − | 0.128388i | \(-0.0409804\pi\) | |||||||
\(24\) | −4.41421 | − | 1.82843i | −0.901048 | − | 0.373226i | ||||
\(25\) | −3.12132 | + | 3.12132i | −0.624264 | + | 0.624264i | ||||
\(26\) | −2.41421 | + | 2.41421i | −0.473466 | + | 0.473466i | ||||
\(27\) | −4.82843 | − | 2.00000i | −0.929231 | − | 0.384900i | ||||
\(28\) | −3.82843 | + | 9.24264i | −0.723505 | + | 1.74669i | ||||
\(29\) | 0.292893 | − | 0.121320i | 0.0543889 | − | 0.0225286i | −0.355323 | − | 0.934744i | \(-0.615629\pi\) |
0.409712 | + | 0.912215i | \(0.365629\pi\) | |||||||
\(30\) | 2.00000i | 0.365148i | ||||||||
\(31\) | 3.00000 | + | 7.24264i | 0.538816 | + | 1.30082i | 0.925550 | + | 0.378625i | \(0.123603\pi\) |
−0.386734 | + | 0.922191i | \(0.626397\pi\) | |||||||
\(32\) | −1.12132 | − | 1.12132i | −0.198223 | − | 0.198223i | ||||
\(33\) | −2.82843 | −0.492366 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000 | 0.338062 | ||||||||
\(36\) | 4.94975 | + | 4.94975i | 0.824958 | + | 0.824958i | ||||
\(37\) | −3.53553 | − | 8.53553i | −0.581238 | − | 1.40323i | −0.891691 | − | 0.452644i | \(-0.850481\pi\) |
0.310453 | − | 0.950589i | \(-0.399519\pi\) | |||||||
\(38\) | − | 2.00000i | − | 0.324443i | ||||||
\(39\) | −1.41421 | + | 0.585786i | −0.226455 | + | 0.0938009i | ||||
\(40\) | 1.29289 | − | 3.12132i | 0.204424 | − | 0.493524i | ||||
\(41\) | −1.12132 | − | 0.464466i | −0.175121 | − | 0.0725374i | 0.293400 | − | 0.955990i | \(-0.405213\pi\) |
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | −4.82843 | + | 4.82843i | −0.745042 | + | 0.745042i | ||||
\(43\) | −0.585786 | + | 0.585786i | −0.0893316 | + | 0.0893316i | −0.750360 | − | 0.661029i | \(-0.770120\pi\) |
0.661029 | + | 0.750360i | \(0.270120\pi\) | |||||||
\(44\) | 9.24264 | + | 3.82843i | 1.39338 | + | 0.577157i | ||||
\(45\) | 0.535534 | − | 1.29289i | 0.0798327 | − | 0.192733i | ||||
\(46\) | −10.6569 | + | 4.41421i | −1.57127 | + | 0.650840i | ||||
\(47\) | − | 5.17157i | − | 0.754351i | −0.926142 | − | 0.377176i | \(-0.876895\pi\) | ||
0.926142 | − | 0.377176i | \(-0.123105\pi\) | |||||||
\(48\) | 1.24264 | + | 3.00000i | 0.179360 | + | 0.433013i | ||||
\(49\) | −0.121320 | − | 0.121320i | −0.0173315 | − | 0.0173315i | ||||
\(50\) | 10.6569 | 1.50711 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.41421 | 0.750816 | ||||||||
\(53\) | −1.00000 | − | 1.00000i | −0.137361 | − | 0.137361i | 0.635083 | − | 0.772444i | \(-0.280966\pi\) |
−0.772444 | + | 0.635083i | \(0.780966\pi\) | |||||||
\(54\) | 4.82843 | + | 11.6569i | 0.657066 | + | 1.58630i | ||||
\(55\) | − | 2.00000i | − | 0.269680i | ||||||
\(56\) | 10.6569 | − | 4.41421i | 1.42408 | − | 0.589874i | ||||
\(57\) | 0.343146 | − | 0.828427i | 0.0454508 | − | 0.109728i | ||||
\(58\) | −0.707107 | − | 0.292893i | −0.0928477 | − | 0.0384588i | ||||
\(59\) | 4.24264 | − | 4.24264i | 0.552345 | − | 0.552345i | −0.374772 | − | 0.927117i | \(-0.622279\pi\) |
0.927117 | + | 0.374772i | \(0.122279\pi\) | |||||||
\(60\) | 2.24264 | − | 2.24264i | 0.289524 | − | 0.289524i | ||||
\(61\) | 3.53553 | + | 1.46447i | 0.452679 | + | 0.187506i | 0.597361 | − | 0.801973i | \(-0.296216\pi\) |
−0.144682 | + | 0.989478i | \(0.546216\pi\) | |||||||
\(62\) | 7.24264 | − | 17.4853i | 0.919816 | − | 2.22063i | ||||
\(63\) | 4.41421 | − | 1.82843i | 0.556139 | − | 0.230360i | ||||
\(64\) | 9.82843i | 1.22855i | ||||||||
\(65\) | −0.414214 | − | 1.00000i | −0.0513769 | − | 0.124035i | ||||
\(66\) | 4.82843 | + | 4.82843i | 0.594338 | + | 0.594338i | ||||
\(67\) | 1.17157 | 0.143130 | 0.0715652 | − | 0.997436i | \(-0.477201\pi\) | ||||
0.0715652 | + | 0.997436i | \(0.477201\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.17157 | −0.622584 | ||||||||
\(70\) | −3.41421 | − | 3.41421i | −0.408077 | − | 0.408077i | ||||
\(71\) | 2.07107 | + | 5.00000i | 0.245791 | + | 0.593391i | 0.997838 | − | 0.0657178i | \(-0.0209337\pi\) |
−0.752048 | + | 0.659109i | \(0.770934\pi\) | |||||||
\(72\) | − | 8.07107i | − | 0.951184i | ||||||
\(73\) | 11.9497 | − | 4.94975i | 1.39861 | − | 0.579324i | 0.449221 | − | 0.893421i | \(-0.351702\pi\) |
0.949391 | + | 0.314097i | \(0.101702\pi\) | |||||||
\(74\) | −8.53553 | + | 20.6066i | −0.992236 | + | 2.39547i | ||||
\(75\) | 4.41421 | + | 1.82843i | 0.509709 | + | 0.211129i | ||||
\(76\) | −2.24264 | + | 2.24264i | −0.257249 | + | 0.257249i | ||||
\(77\) | 4.82843 | − | 4.82843i | 0.550250 | − | 0.550250i | ||||
\(78\) | 3.41421 | + | 1.41421i | 0.386584 | + | 0.160128i | ||||
\(79\) | −1.82843 | + | 4.41421i | −0.205714 | + | 0.496638i | −0.992740 | − | 0.120283i | \(-0.961620\pi\) |
0.787026 | + | 0.616920i | \(0.211620\pi\) | |||||||
\(80\) | −2.12132 | + | 0.878680i | −0.237171 | + | 0.0982394i | ||||
\(81\) | 0.171573i | 0.0190637i | ||||||||
\(82\) | 1.12132 | + | 2.70711i | 0.123829 | + | 0.298950i | ||||
\(83\) | 8.24264 | + | 8.24264i | 0.904747 | + | 0.904747i | 0.995842 | − | 0.0910949i | \(-0.0290366\pi\) |
−0.0910949 | + | 0.995842i | \(0.529037\pi\) | |||||||
\(84\) | 10.8284 | 1.18148 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.00000 | 0.215666 | ||||||||
\(87\) | −0.242641 | − | 0.242641i | −0.0260138 | − | 0.0260138i | ||||
\(88\) | −4.41421 | − | 10.6569i | −0.470557 | − | 1.13602i | ||||
\(89\) | 6.58579i | 0.698092i | 0.937106 | + | 0.349046i | \(0.113494\pi\) | ||||
−0.937106 | + | 0.349046i | \(0.886506\pi\) | |||||||
\(90\) | −3.12132 | + | 1.29289i | −0.329016 | + | 0.136283i | ||||
\(91\) | 1.41421 | − | 3.41421i | 0.148250 | − | 0.357907i | ||||
\(92\) | 16.8995 | + | 7.00000i | 1.76189 | + | 0.729800i | ||||
\(93\) | 6.00000 | − | 6.00000i | 0.622171 | − | 0.622171i | ||||
\(94\) | −8.82843 | + | 8.82843i | −0.910583 | + | 0.910583i | ||||
\(95\) | 0.585786 | + | 0.242641i | 0.0601004 | + | 0.0248944i | ||||
\(96\) | −0.656854 | + | 1.58579i | −0.0670399 | + | 0.161849i | ||||
\(97\) | −9.53553 | + | 3.94975i | −0.968187 | + | 0.401036i | −0.810037 | − | 0.586379i | \(-0.800553\pi\) |
−0.158150 | + | 0.987415i | \(0.550553\pi\) | |||||||
\(98\) | 0.414214i | 0.0418419i | ||||||||
\(99\) | −1.82843 | − | 4.41421i | −0.183764 | − | 0.443645i | ||||
\(100\) | −11.9497 | − | 11.9497i | −1.19497 | − | 1.19497i | ||||
\(101\) | −10.5858 | −1.05333 | −0.526663 | − | 0.850074i | \(-0.676557\pi\) | ||||
−0.526663 | + | 0.850074i | \(0.676557\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.4853 | 1.23021 | 0.615106 | − | 0.788445i | \(-0.289113\pi\) | ||||
0.615106 | + | 0.788445i | \(0.289113\pi\) | |||||||
\(104\) | −4.41421 | − | 4.41421i | −0.432849 | − | 0.432849i | ||||
\(105\) | −0.828427 | − | 2.00000i | −0.0808462 | − | 0.195180i | ||||
\(106\) | 3.41421i | 0.331618i | ||||||||
\(107\) | −0.414214 | + | 0.171573i | −0.0400435 | + | 0.0165866i | −0.402615 | − | 0.915369i | \(-0.631899\pi\) |
0.362572 | + | 0.931956i | \(0.381899\pi\) | |||||||
\(108\) | 7.65685 | − | 18.4853i | 0.736781 | − | 1.77875i | ||||
\(109\) | −14.3640 | − | 5.94975i | −1.37582 | − | 0.569882i | −0.432458 | − | 0.901654i | \(-0.642354\pi\) |
−0.943360 | + | 0.331772i | \(0.892354\pi\) | |||||||
\(110\) | −3.41421 | + | 3.41421i | −0.325532 | + | 0.325532i | ||||
\(111\) | −7.07107 | + | 7.07107i | −0.671156 | + | 0.671156i | ||||
\(112\) | −7.24264 | − | 3.00000i | −0.684365 | − | 0.283473i | ||||
\(113\) | −5.05025 | + | 12.1924i | −0.475088 | + | 1.14696i | 0.486799 | + | 0.873514i | \(0.338165\pi\) |
−0.961886 | + | 0.273449i | \(0.911835\pi\) | |||||||
\(114\) | −2.00000 | + | 0.828427i | −0.187317 | + | 0.0775893i | ||||
\(115\) | − | 3.65685i | − | 0.341003i | ||||||
\(116\) | 0.464466 | + | 1.12132i | 0.0431246 | + | 0.104112i | ||||
\(117\) | −1.82843 | − | 1.82843i | −0.169038 | − | 0.169038i | ||||
\(118\) | −14.4853 | −1.33348 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.65685 | −0.333824 | ||||||||
\(121\) | 2.94975 | + | 2.94975i | 0.268159 | + | 0.268159i | ||||
\(122\) | −3.53553 | − | 8.53553i | −0.320092 | − | 0.772771i | ||||
\(123\) | 1.31371i | 0.118453i | ||||||||
\(124\) | −27.7279 | + | 11.4853i | −2.49004 | + | 1.03141i | ||||
\(125\) | −2.75736 | + | 6.65685i | −0.246626 | + | 0.595407i | ||||
\(126\) | −10.6569 | − | 4.41421i | −0.949388 | − | 0.393249i | ||||
\(127\) | −3.75736 | + | 3.75736i | −0.333412 | + | 0.333412i | −0.853881 | − | 0.520469i | \(-0.825757\pi\) |
0.520469 | + | 0.853881i | \(0.325757\pi\) | |||||||
\(128\) | 14.5355 | − | 14.5355i | 1.28477 | − | 1.28477i | ||||
\(129\) | 0.828427 | + | 0.343146i | 0.0729389 | + | 0.0302123i | ||||
\(130\) | −1.00000 | + | 2.41421i | −0.0877058 | + | 0.211741i | ||||
\(131\) | 14.0711 | − | 5.82843i | 1.22939 | − | 0.509232i | 0.329010 | − | 0.944326i | \(-0.393285\pi\) |
0.900385 | + | 0.435094i | \(0.143285\pi\) | |||||||
\(132\) | − | 10.8284i | − | 0.942494i | ||||||
\(133\) | 0.828427 | + | 2.00000i | 0.0718337 | + | 0.173422i | ||||
\(134\) | −2.00000 | − | 2.00000i | −0.172774 | − | 0.172774i | ||||
\(135\) | −4.00000 | −0.344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.7279 | −1.42916 | −0.714581 | − | 0.699552i | \(-0.753383\pi\) | ||||
−0.714581 | + | 0.699552i | \(0.753383\pi\) | |||||||
\(138\) | 8.82843 | + | 8.82843i | 0.751526 | + | 0.751526i | ||||
\(139\) | 8.17157 | + | 19.7279i | 0.693104 | + | 1.67330i | 0.738432 | + | 0.674328i | \(0.235567\pi\) |
−0.0453279 | + | 0.998972i | \(0.514433\pi\) | |||||||
\(140\) | 7.65685i | 0.647122i | ||||||||
\(141\) | −5.17157 | + | 2.14214i | −0.435525 | + | 0.180400i | ||||
\(142\) | 5.00000 | − | 12.0711i | 0.419591 | − | 1.01298i | ||||
\(143\) | −3.41421 | − | 1.41421i | −0.285511 | − | 0.118262i | ||||
\(144\) | −3.87868 | + | 3.87868i | −0.323223 | + | 0.323223i | ||||
\(145\) | 0.171573 | − | 0.171573i | 0.0142484 | − | 0.0142484i | ||||
\(146\) | −28.8492 | − | 11.9497i | −2.38758 | − | 0.988968i | ||||
\(147\) | −0.0710678 | + | 0.171573i | −0.00586157 | + | 0.0141511i | ||||
\(148\) | 32.6777 | − | 13.5355i | 2.68609 | − | 1.11261i | ||||
\(149\) | 16.9706i | 1.39028i | 0.718873 | + | 0.695141i | \(0.244658\pi\) | ||||
−0.718873 | + | 0.695141i | \(0.755342\pi\) | |||||||
\(150\) | −4.41421 | − | 10.6569i | −0.360419 | − | 0.870129i | ||||
\(151\) | 5.07107 | + | 5.07107i | 0.412678 | + | 0.412678i | 0.882670 | − | 0.469993i | \(-0.155743\pi\) |
−0.469993 | + | 0.882670i | \(0.655743\pi\) | |||||||
\(152\) | 3.65685 | 0.296610 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −16.4853 | −1.32842 | ||||||||
\(155\) | 4.24264 | + | 4.24264i | 0.340777 | + | 0.340777i | ||||
\(156\) | −2.24264 | − | 5.41421i | −0.179555 | − | 0.433484i | ||||
\(157\) | − | 9.65685i | − | 0.770701i | −0.922770 | − | 0.385350i | \(-0.874081\pi\) | ||
0.922770 | − | 0.385350i | \(-0.125919\pi\) | |||||||
\(158\) | 10.6569 | − | 4.41421i | 0.847814 | − | 0.351176i | ||||
\(159\) | −0.585786 | + | 1.41421i | −0.0464559 | + | 0.112154i | ||||
\(160\) | −1.12132 | − | 0.464466i | −0.0886482 | − | 0.0367193i | ||||
\(161\) | 8.82843 | − | 8.82843i | 0.695778 | − | 0.695778i | ||||
\(162\) | 0.292893 | − | 0.292893i | 0.0230119 | − | 0.0230119i | ||||
\(163\) | 7.82843 | + | 3.24264i | 0.613170 | + | 0.253983i | 0.667583 | − | 0.744535i | \(-0.267329\pi\) |
−0.0544134 | + | 0.998518i | \(0.517329\pi\) | |||||||
\(164\) | 1.77817 | − | 4.29289i | 0.138852 | − | 0.335219i | ||||
\(165\) | −2.00000 | + | 0.828427i | −0.155700 | + | 0.0644930i | ||||
\(166\) | − | 28.1421i | − | 2.18425i | ||||||
\(167\) | −0.757359 | − | 1.82843i | −0.0586062 | − | 0.141488i | 0.891864 | − | 0.452304i | \(-0.149398\pi\) |
−0.950470 | + | 0.310816i | \(0.899398\pi\) | |||||||
\(168\) | −8.82843 | − | 8.82843i | −0.681128 | − | 0.681128i | ||||
\(169\) | 11.0000 | 0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.51472 | 0.115833 | ||||||||
\(172\) | −2.24264 | − | 2.24264i | −0.171000 | − | 0.171000i | ||||
\(173\) | −1.12132 | − | 2.70711i | −0.0852524 | − | 0.205818i | 0.875504 | − | 0.483211i | \(-0.160530\pi\) |
−0.960756 | + | 0.277393i | \(0.910530\pi\) | |||||||
\(174\) | 0.828427i | 0.0628029i | ||||||||
\(175\) | −10.6569 | + | 4.41421i | −0.805582 | + | 0.333683i | ||||
\(176\) | −3.00000 | + | 7.24264i | −0.226134 | + | 0.545935i | ||||
\(177\) | −6.00000 | − | 2.48528i | −0.450988 | − | 0.186805i | ||||
\(178\) | 11.2426 | − | 11.2426i | 0.842672 | − | 0.842672i | ||||
\(179\) | −4.24264 | + | 4.24264i | −0.317110 | + | 0.317110i | −0.847656 | − | 0.530546i | \(-0.821987\pi\) |
0.530546 | + | 0.847656i | \(0.321987\pi\) | |||||||
\(180\) | 4.94975 | + | 2.05025i | 0.368932 | + | 0.152817i | ||||
\(181\) | 4.46447 | − | 10.7782i | 0.331841 | − | 0.801135i | −0.666605 | − | 0.745411i | \(-0.732253\pi\) |
0.998446 | − | 0.0557243i | \(-0.0177468\pi\) | |||||||
\(182\) | −8.24264 | + | 3.41421i | −0.610985 | + | 0.253078i | ||||
\(183\) | − | 4.14214i | − | 0.306195i | ||||||
\(184\) | −8.07107 | − | 19.4853i | −0.595007 | − | 1.43647i | ||||
\(185\) | −5.00000 | − | 5.00000i | −0.367607 | − | 0.367607i | ||||
\(186\) | −20.4853 | −1.50205 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 19.7990 | 1.44399 | ||||||||
\(189\) | −9.65685 | − | 9.65685i | −0.702433 | − | 0.702433i | ||||
\(190\) | −0.585786 | − | 1.41421i | −0.0424974 | − | 0.102598i | ||||
\(191\) | 20.0000i | 1.44715i | 0.690246 | + | 0.723575i | \(0.257502\pi\) | ||||
−0.690246 | + | 0.723575i | \(0.742498\pi\) | |||||||
\(192\) | 9.82843 | − | 4.07107i | 0.709306 | − | 0.293804i | ||||
\(193\) | −0.878680 | + | 2.12132i | −0.0632487 | + | 0.152696i | −0.952344 | − | 0.305027i | \(-0.901335\pi\) |
0.889095 | + | 0.457722i | \(0.151335\pi\) | |||||||
\(194\) | 23.0208 | + | 9.53553i | 1.65280 | + | 0.684611i | ||||
\(195\) | −0.828427 | + | 0.828427i | −0.0593249 | + | 0.0593249i | ||||
\(196\) | 0.464466 | − | 0.464466i | 0.0331761 | − | 0.0331761i | ||||
\(197\) | 4.29289 | + | 1.77817i | 0.305856 | + | 0.126690i | 0.530332 | − | 0.847790i | \(-0.322067\pi\) |
−0.224476 | + | 0.974480i | \(0.572067\pi\) | |||||||
\(198\) | −4.41421 | + | 10.6569i | −0.313704 | + | 0.757350i | ||||
\(199\) | −10.6569 | + | 4.41421i | −0.755444 | + | 0.312915i | −0.726961 | − | 0.686679i | \(-0.759068\pi\) |
−0.0284836 | + | 0.999594i | \(0.509068\pi\) | |||||||
\(200\) | 19.4853i | 1.37782i | ||||||||
\(201\) | −0.485281 | − | 1.17157i | −0.0342291 | − | 0.0826364i | ||||
\(202\) | 18.0711 | + | 18.0711i | 1.27148 | + | 1.27148i | ||||
\(203\) | 0.828427 | 0.0581442 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.928932 | −0.0648794 | ||||||||
\(206\) | −21.3137 | − | 21.3137i | −1.48500 | − | 1.48500i | ||||
\(207\) | −3.34315 | − | 8.07107i | −0.232365 | − | 0.560978i | ||||
\(208\) | 4.24264i | 0.294174i | ||||||||
\(209\) | 2.00000 | − | 0.828427i | 0.138343 | − | 0.0573035i | ||||
\(210\) | −2.00000 | + | 4.82843i | −0.138013 | + | 0.333193i | ||||
\(211\) | 19.7279 | + | 8.17157i | 1.35813 | + | 0.562554i | 0.938543 | − | 0.345163i | \(-0.112176\pi\) |
0.419583 | + | 0.907717i | \(0.362176\pi\) | |||||||
\(212\) | 3.82843 | − | 3.82843i | 0.262937 | − | 0.262937i | ||||
\(213\) | 4.14214 | − | 4.14214i | 0.283814 | − | 0.283814i | ||||
\(214\) | 1.00000 | + | 0.414214i | 0.0683586 | + | 0.0283151i | ||||
\(215\) | −0.242641 | + | 0.585786i | −0.0165480 | + | 0.0399503i | ||||
\(216\) | −21.3137 | + | 8.82843i | −1.45021 | + | 0.600698i | ||||
\(217\) | 20.4853i | 1.39063i | ||||||||
\(218\) | 14.3640 | + | 34.6777i | 0.972850 | + | 2.34867i | ||||
\(219\) | −9.89949 | − | 9.89949i | −0.668946 | − | 0.668946i | ||||
\(220\) | 7.65685 | 0.516225 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 24.1421 | 1.62031 | ||||||||
\(223\) | 3.41421 | + | 3.41421i | 0.228633 | + | 0.228633i | 0.812121 | − | 0.583489i | \(-0.198313\pi\) |
−0.583489 | + | 0.812121i | \(0.698313\pi\) | |||||||
\(224\) | −1.58579 | − | 3.82843i | −0.105955 | − | 0.255798i | ||||
\(225\) | 8.07107i | 0.538071i | ||||||||
\(226\) | 29.4350 | − | 12.1924i | 1.95799 | − | 0.811026i | ||||
\(227\) | −6.65685 | + | 16.0711i | −0.441831 | + | 1.06667i | 0.533475 | + | 0.845816i | \(0.320886\pi\) |
−0.975306 | + | 0.220858i | \(0.929114\pi\) | |||||||
\(228\) | 3.17157 | + | 1.31371i | 0.210043 | + | 0.0870025i | ||||
\(229\) | −12.1421 | + | 12.1421i | −0.802375 | + | 0.802375i | −0.983466 | − | 0.181091i | \(-0.942037\pi\) |
0.181091 | + | 0.983466i | \(0.442037\pi\) | |||||||
\(230\) | −6.24264 | + | 6.24264i | −0.411628 | + | 0.411628i | ||||
\(231\) | −6.82843 | − | 2.82843i | −0.449278 | − | 0.186097i | ||||
\(232\) | 0.535534 | − | 1.29289i | 0.0351595 | − | 0.0848826i | ||||
\(233\) | −8.12132 | + | 3.36396i | −0.532045 | + | 0.220380i | −0.632499 | − | 0.774561i | \(-0.717971\pi\) |
0.100453 | + | 0.994942i | \(0.467971\pi\) | |||||||
\(234\) | 6.24264i | 0.408094i | ||||||||
\(235\) | −1.51472 | − | 3.65685i | −0.0988093 | − | 0.238547i | ||||
\(236\) | 16.2426 | + | 16.2426i | 1.05731 | + | 1.05731i | ||||
\(237\) | 5.17157 | 0.335930 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.8284 | 0.959171 | 0.479586 | − | 0.877495i | \(-0.340787\pi\) | ||||
0.479586 | + | 0.877495i | \(0.340787\pi\) | |||||||
\(240\) | 1.75736 | + | 1.75736i | 0.113437 | + | 0.113437i | ||||
\(241\) | 1.36396 | + | 3.29289i | 0.0878605 | + | 0.212114i | 0.961702 | − | 0.274097i | \(-0.0883788\pi\) |
−0.873842 | + | 0.486211i | \(0.838379\pi\) | |||||||
\(242\) | − | 10.0711i | − | 0.647393i | ||||||
\(243\) | −14.3137 | + | 5.92893i | −0.918225 | + | 0.380341i | ||||
\(244\) | −5.60660 | + | 13.5355i | −0.358926 | + | 0.866524i | ||||
\(245\) | −0.121320 | − | 0.0502525i | −0.00775087 | − | 0.00321052i | ||||
\(246\) | 2.24264 | − | 2.24264i | 0.142986 | − | 0.142986i | ||||
\(247\) | 0.828427 | − | 0.828427i | 0.0527116 | − | 0.0527116i | ||||
\(248\) | 31.9706 | + | 13.2426i | 2.03013 | + | 0.840909i | ||||
\(249\) | 4.82843 | − | 11.6569i | 0.305989 | − | 0.738723i | ||||
\(250\) | 16.0711 | − | 6.65685i | 1.01642 | − | 0.421016i | ||||
\(251\) | − | 20.4853i | − | 1.29302i | −0.762906 | − | 0.646510i | \(-0.776228\pi\) | ||
0.762906 | − | 0.646510i | \(-0.223772\pi\) | |||||||
\(252\) | 7.00000 | + | 16.8995i | 0.440959 | + | 1.06457i | ||||
\(253\) | −8.82843 | − | 8.82843i | −0.555038 | − | 0.555038i | ||||
\(254\) | 12.8284 | 0.804927 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | −4.34315 | − | 4.34315i | −0.270918 | − | 0.270918i | 0.558552 | − | 0.829470i | \(-0.311357\pi\) |
−0.829470 | + | 0.558552i | \(0.811357\pi\) | |||||||
\(258\) | −0.828427 | − | 2.00000i | −0.0515756 | − | 0.124515i | ||||
\(259\) | − | 24.1421i | − | 1.50012i | ||||||
\(260\) | 3.82843 | − | 1.58579i | 0.237429 | − | 0.0983463i | ||||
\(261\) | 0.221825 | − | 0.535534i | 0.0137306 | − | 0.0331487i | ||||
\(262\) | −33.9706 | − | 14.0711i | −2.09871 | − | 0.869313i | ||||
\(263\) | −7.41421 | + | 7.41421i | −0.457180 | + | 0.457180i | −0.897729 | − | 0.440549i | \(-0.854784\pi\) |
0.440549 | + | 0.897729i | \(0.354784\pi\) | |||||||
\(264\) | −8.82843 | + | 8.82843i | −0.543352 | + | 0.543352i | ||||
\(265\) | −1.00000 | − | 0.414214i | −0.0614295 | − | 0.0254449i | ||||
\(266\) | 2.00000 | − | 4.82843i | 0.122628 | − | 0.296050i | ||||
\(267\) | 6.58579 | − | 2.72792i | 0.403044 | − | 0.166946i | ||||
\(268\) | 4.48528i | 0.273982i | ||||||||
\(269\) | −10.1213 | − | 24.4350i | −0.617108 | − | 1.48983i | −0.855047 | − | 0.518550i | \(-0.826472\pi\) |
0.237939 | − | 0.971280i | \(-0.423528\pi\) | |||||||
\(270\) | 6.82843 | + | 6.82843i | 0.415565 | + | 0.415565i | ||||
\(271\) | 22.1421 | 1.34504 | 0.672519 | − | 0.740079i | \(-0.265212\pi\) | ||||
0.672519 | + | 0.740079i | \(0.265212\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.00000 | −0.242091 | ||||||||
\(274\) | 28.5563 | + | 28.5563i | 1.72515 | + | 1.72515i | ||||
\(275\) | 4.41421 | + | 10.6569i | 0.266187 | + | 0.642632i | ||||
\(276\) | − | 19.7990i | − | 1.19176i | ||||||
\(277\) | 18.4350 | − | 7.63604i | 1.10765 | − | 0.458805i | 0.247525 | − | 0.968882i | \(-0.420383\pi\) |
0.860129 | + | 0.510077i | \(0.170383\pi\) | |||||||
\(278\) | 19.7279 | − | 47.6274i | 1.18320 | − | 2.85650i | ||||
\(279\) | 13.2426 | + | 5.48528i | 0.792816 | + | 0.328395i | ||||
\(280\) | 6.24264 | − | 6.24264i | 0.373069 | − | 0.373069i | ||||
\(281\) | −1.34315 | + | 1.34315i | −0.0801254 | + | 0.0801254i | −0.746034 | − | 0.665908i | \(-0.768044\pi\) |
0.665908 | + | 0.746034i | \(0.268044\pi\) | |||||||
\(282\) | 12.4853 | + | 5.17157i | 0.743488 | + | 0.307963i | ||||
\(283\) | 7.14214 | − | 17.2426i | 0.424556 | − | 1.02497i | −0.556431 | − | 0.830894i | \(-0.687830\pi\) |
0.980987 | − | 0.194075i | \(-0.0621704\pi\) | |||||||
\(284\) | −19.1421 | + | 7.92893i | −1.13588 | + | 0.470496i | ||||
\(285\) | − | 0.686292i | − | 0.0406524i | ||||||
\(286\) | 3.41421 | + | 8.24264i | 0.201887 | + | 0.487398i | ||||
\(287\) | −2.24264 | − | 2.24264i | −0.132379 | − | 0.132379i | ||||
\(288\) | −2.89949 | −0.170854 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −0.585786 | −0.0343986 | ||||||||
\(291\) | 7.89949 | + | 7.89949i | 0.463077 | + | 0.463077i | ||||
\(292\) | 18.9497 | + | 45.7487i | 1.10895 | + | 2.67724i | ||||
\(293\) | − | 12.3431i | − | 0.721094i | −0.932741 | − | 0.360547i | \(-0.882590\pi\) | ||
0.932741 | − | 0.360547i | \(-0.117410\pi\) | |||||||
\(294\) | 0.414214 | − | 0.171573i | 0.0241574 | − | 0.0100063i | ||||
\(295\) | 1.75736 | − | 4.24264i | 0.102317 | − | 0.247016i | ||||
\(296\) | −37.6777 | − | 15.6066i | −2.18997 | − | 0.907115i | ||||
\(297\) | −9.65685 | + | 9.65685i | −0.560348 | + | 0.560348i | ||||
\(298\) | 28.9706 | − | 28.9706i | 1.67822 | − | 1.67822i | ||||
\(299\) | −6.24264 | − | 2.58579i | −0.361021 | − | 0.149540i | ||||
\(300\) | −7.00000 | + | 16.8995i | −0.404145 | + | 0.975693i | ||||
\(301\) | −2.00000 | + | 0.828427i | −0.115278 | + | 0.0477497i | ||||
\(302\) | − | 17.3137i | − | 0.996292i | ||||||
\(303\) | 4.38478 | + | 10.5858i | 0.251899 | + | 0.608138i | ||||
\(304\) | −1.75736 | − | 1.75736i | −0.100791 | − | 0.100791i | ||||
\(305\) | 2.92893 | 0.167710 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.1421 | −1.49201 | −0.746005 | − | 0.665940i | \(-0.768031\pi\) | ||||
−0.746005 | + | 0.665940i | \(0.768031\pi\) | |||||||
\(308\) | 18.4853 | + | 18.4853i | 1.05330 | + | 1.05330i | ||||
\(309\) | −5.17157 | − | 12.4853i | −0.294201 | − | 0.710263i | ||||
\(310\) | − | 14.4853i | − | 0.822709i | ||||||
\(311\) | −23.7279 | + | 9.82843i | −1.34549 | + | 0.557319i | −0.935032 | − | 0.354562i | \(-0.884630\pi\) |
−0.410455 | + | 0.911881i | \(0.634630\pi\) | |||||||
\(312\) | −2.58579 | + | 6.24264i | −0.146391 | + | 0.353420i | ||||
\(313\) | 9.12132 | + | 3.77817i | 0.515568 | + | 0.213555i | 0.625269 | − | 0.780410i | \(-0.284989\pi\) |
−0.109701 | + | 0.993965i | \(0.534989\pi\) | |||||||
\(314\) | −16.4853 | + | 16.4853i | −0.930318 | + | 0.930318i | ||||
\(315\) | 2.58579 | − | 2.58579i | 0.145693 | − | 0.145693i | ||||
\(316\) | −16.8995 | − | 7.00000i | −0.950671 | − | 0.393781i | ||||
\(317\) | −7.36396 | + | 17.7782i | −0.413601 | + | 0.998522i | 0.570562 | + | 0.821255i | \(0.306726\pi\) |
−0.984163 | + | 0.177267i | \(0.943274\pi\) | |||||||
\(318\) | 3.41421 | − | 1.41421i | 0.191460 | − | 0.0793052i | ||||
\(319\) | − | 0.828427i | − | 0.0463830i | ||||||
\(320\) | 2.87868 | + | 6.94975i | 0.160923 | + | 0.388503i | ||||
\(321\) | 0.343146 | + | 0.343146i | 0.0191525 | + | 0.0191525i | ||||
\(322\) | −30.1421 | −1.67976 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.656854 | −0.0364919 | ||||||||
\(325\) | 4.41421 | + | 4.41421i | 0.244857 | + | 0.244857i | ||||
\(326\) | −7.82843 | − | 18.8995i | −0.433576 | − | 1.04675i | ||||
\(327\) | 16.8284i | 0.930614i | ||||||||
\(328\) | −4.94975 | + | 2.05025i | −0.273304 | + | 0.113206i | ||||
\(329\) | 5.17157 | − | 12.4853i | 0.285118 | − | 0.688336i | ||||
\(330\) | 4.82843 | + | 2.00000i | 0.265796 | + | 0.110096i | ||||
\(331\) | −15.4142 | + | 15.4142i | −0.847242 | + | 0.847242i | −0.989788 | − | 0.142546i | \(-0.954471\pi\) |
0.142546 | + | 0.989788i | \(0.454471\pi\) | |||||||
\(332\) | −31.5563 | + | 31.5563i | −1.73188 | + | 1.73188i | ||||
\(333\) | −15.6066 | − | 6.46447i | −0.855237 | − | 0.354251i | ||||
\(334\) | −1.82843 | + | 4.41421i | −0.100047 | + | 0.241535i | ||||
\(335\) | 0.828427 | − | 0.343146i | 0.0452618 | − | 0.0187481i | ||||
\(336\) | 8.48528i | 0.462910i | ||||||||
\(337\) | 2.15076 | + | 5.19239i | 0.117159 | + | 0.282847i | 0.971571 | − | 0.236750i | \(-0.0760821\pi\) |
−0.854411 | + | 0.519597i | \(0.826082\pi\) | |||||||
\(338\) | −18.7782 | − | 18.7782i | −1.02140 | − | 1.02140i | ||||
\(339\) | 14.2843 | 0.775815 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.4853 | 1.10934 | ||||||||
\(342\) | −2.58579 | − | 2.58579i | −0.139823 | − | 0.139823i | ||||
\(343\) | −7.17157 | − | 17.3137i | −0.387229 | − | 0.934852i | ||||
\(344\) | 3.65685i | 0.197164i | ||||||||
\(345\) | −3.65685 | + | 1.51472i | −0.196878 | + | 0.0815497i | ||||
\(346\) | −2.70711 | + | 6.53553i | −0.145535 | + | 0.351352i | ||||
\(347\) | −15.4853 | − | 6.41421i | −0.831293 | − | 0.344333i | −0.0738788 | − | 0.997267i | \(-0.523538\pi\) |
−0.757415 | + | 0.652934i | \(0.773538\pi\) | |||||||
\(348\) | 0.928932 | − | 0.928932i | 0.0497960 | − | 0.0497960i | ||||
\(349\) | 3.00000 | − | 3.00000i | 0.160586 | − | 0.160586i | −0.622240 | − | 0.782826i | \(-0.713777\pi\) |
0.782826 | + | 0.622240i | \(0.213777\pi\) | |||||||
\(350\) | 25.7279 | + | 10.6569i | 1.37522 | + | 0.569633i | ||||
\(351\) | −2.82843 | + | 6.82843i | −0.150970 | + | 0.364474i | ||||
\(352\) | −3.82843 | + | 1.58579i | −0.204056 | + | 0.0845227i | ||||
\(353\) | 14.0000i | 0.745145i | 0.928003 | + | 0.372572i | \(0.121524\pi\) | ||||
−0.928003 | + | 0.372572i | \(0.878476\pi\) | |||||||
\(354\) | 6.00000 | + | 14.4853i | 0.318896 | + | 0.769884i | ||||
\(355\) | 2.92893 | + | 2.92893i | 0.155452 | + | 0.155452i | ||||
\(356\) | −25.2132 | −1.33630 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.4853 | 0.765571 | ||||||||
\(359\) | −20.3848 | − | 20.3848i | −1.07587 | − | 1.07587i | −0.996875 | − | 0.0789921i | \(-0.974830\pi\) |
−0.0789921 | − | 0.996875i | \(-0.525170\pi\) | |||||||
\(360\) | −2.36396 | − | 5.70711i | −0.124592 | − | 0.300791i | ||||
\(361\) | − | 18.3137i | − | 0.963879i | ||||||
\(362\) | −26.0208 | + | 10.7782i | −1.36762 | + | 0.566488i | ||||
\(363\) | 1.72792 | − | 4.17157i | 0.0906924 | − | 0.218951i | ||||
\(364\) | 13.0711 | + | 5.41421i | 0.685110 | + | 0.283782i | ||||
\(365\) | 7.00000 | − | 7.00000i | 0.366397 | − | 0.366397i | ||||
\(366\) | −7.07107 | + | 7.07107i | −0.369611 | + | 0.369611i | ||||
\(367\) | 4.07107 | + | 1.68629i | 0.212508 | + | 0.0880237i | 0.486398 | − | 0.873737i | \(-0.338310\pi\) |
−0.273890 | + | 0.961761i | \(0.588310\pi\) | |||||||
\(368\) | −5.48528 | + | 13.2426i | −0.285940 | + | 0.690320i | ||||
\(369\) | −2.05025 | + | 0.849242i | −0.106732 | + | 0.0442098i | ||||
\(370\) | 17.0711i | 0.887483i | ||||||||
\(371\) | −1.41421 | − | 3.41421i | −0.0734223 | − | 0.177257i | ||||
\(372\) | 22.9706 | + | 22.9706i | 1.19097 | + | 1.19097i | ||||
\(373\) | 11.5563 | 0.598365 | 0.299183 | − | 0.954196i | \(-0.403286\pi\) | ||||
0.299183 | + | 0.954196i | \(0.403286\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.79899 | 0.402738 | ||||||||
\(376\) | −16.1421 | − | 16.1421i | −0.832467 | − | 0.832467i | ||||
\(377\) | −0.171573 | − | 0.414214i | −0.00883645 | − | 0.0213331i | ||||
\(378\) | 32.9706i | 1.69582i | ||||||||
\(379\) | 2.41421 | − | 1.00000i | 0.124010 | − | 0.0513665i | −0.319816 | − | 0.947480i | \(-0.603621\pi\) |
0.443826 | + | 0.896113i | \(0.353621\pi\) | |||||||
\(380\) | −0.928932 | + | 2.24264i | −0.0476532 | + | 0.115045i | ||||
\(381\) | 5.31371 | + | 2.20101i | 0.272230 | + | 0.112761i | ||||
\(382\) | 34.1421 | − | 34.1421i | 1.74686 | − | 1.74686i | ||||
\(383\) | −15.8995 | + | 15.8995i | −0.812426 | + | 0.812426i | −0.984997 | − | 0.172571i | \(-0.944793\pi\) |
0.172571 | + | 0.984997i | \(0.444793\pi\) | |||||||
\(384\) | −20.5563 | − | 8.51472i | −1.04901 | − | 0.434515i | ||||
\(385\) | 2.00000 | − | 4.82843i | 0.101929 | − | 0.246079i | ||||
\(386\) | 5.12132 | − | 2.12132i | 0.260668 | − | 0.107972i | ||||
\(387\) | 1.51472i | 0.0769975i | ||||||||
\(388\) | −15.1213 | − | 36.5061i | −0.767669 | − | 1.85332i | ||||
\(389\) | −8.58579 | − | 8.58579i | −0.435317 | − | 0.435317i | 0.455116 | − | 0.890432i | \(-0.349598\pi\) |
−0.890432 | + | 0.455116i | \(0.849598\pi\) | |||||||
\(390\) | 2.82843 | 0.143223 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.757359 | −0.0382524 | ||||||||
\(393\) | −11.6569 | − | 11.6569i | −0.588011 | − | 0.588011i | ||||
\(394\) | −4.29289 | − | 10.3640i | −0.216273 | − | 0.522129i | ||||
\(395\) | 3.65685i | 0.183996i | ||||||||
\(396\) | 16.8995 | − | 7.00000i | 0.849232 | − | 0.351763i | ||||
\(397\) | −6.80761 | + | 16.4350i | −0.341664 | + | 0.824850i | 0.655884 | + | 0.754862i | \(0.272296\pi\) |
−0.997548 | + | 0.0699884i | \(0.977704\pi\) | |||||||
\(398\) | 25.7279 | + | 10.6569i | 1.28962 | + | 0.534180i | ||||
\(399\) | 1.65685 | − | 1.65685i | 0.0829465 | − | 0.0829465i | ||||
\(400\) | 9.36396 | − | 9.36396i | 0.468198 | − | 0.468198i | ||||
\(401\) | 0.535534 | + | 0.221825i | 0.0267433 | + | 0.0110774i | 0.396015 | − | 0.918244i | \(-0.370393\pi\) |
−0.369272 | + | 0.929321i | \(0.620393\pi\) | |||||||
\(402\) | −1.17157 | + | 2.82843i | −0.0584327 | + | 0.141069i | ||||
\(403\) | 10.2426 | − | 4.24264i | 0.510222 | − | 0.211341i | ||||
\(404\) | − | 40.5269i | − | 2.01629i | ||||||
\(405\) | 0.0502525 | + | 0.121320i | 0.00249707 | + | 0.00602846i | ||||
\(406\) | −1.41421 | − | 1.41421i | −0.0701862 | − | 0.0701862i | ||||
\(407\) | −24.1421 | −1.19668 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.31371 | −0.163852 | −0.0819262 | − | 0.996638i | \(-0.526107\pi\) | ||||
−0.0819262 | + | 0.996638i | \(0.526107\pi\) | |||||||
\(410\) | 1.58579 | + | 1.58579i | 0.0783164 | + | 0.0783164i | ||||
\(411\) | 6.92893 | + | 16.7279i | 0.341779 | + | 0.825128i | ||||
\(412\) | 47.7990i | 2.35489i | ||||||||
\(413\) | 14.4853 | − | 6.00000i | 0.712774 | − | 0.295241i | ||||
\(414\) | −8.07107 | + | 19.4853i | −0.396671 | + | 0.957649i | ||||
\(415\) | 8.24264 | + | 3.41421i | 0.404615 | + | 0.167597i | ||||
\(416\) | −1.58579 | + | 1.58579i | −0.0777496 | + | 0.0777496i | ||||
\(417\) | 16.3431 | − | 16.3431i | 0.800327 | − | 0.800327i | ||||
\(418\) | −4.82843 | − | 2.00000i | −0.236166 | − | 0.0978232i | ||||
\(419\) | 5.10051 | − | 12.3137i | 0.249176 | − | 0.601564i | −0.748959 | − | 0.662617i | \(-0.769446\pi\) |
0.998135 | + | 0.0610528i | \(0.0194458\pi\) | |||||||
\(420\) | 7.65685 | − | 3.17157i | 0.373616 | − | 0.154757i | ||||
\(421\) | − | 14.5858i | − | 0.710868i | −0.934701 | − | 0.355434i | \(-0.884333\pi\) | ||
0.934701 | − | 0.355434i | \(-0.115667\pi\) | |||||||
\(422\) | −19.7279 | − | 47.6274i | −0.960340 | − | 2.31847i | ||||
\(423\) | −6.68629 | − | 6.68629i | −0.325099 | − | 0.325099i | ||||
\(424\) | −6.24264 | −0.303169 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −14.1421 | −0.685189 | ||||||||
\(427\) | 7.07107 | + | 7.07107i | 0.342193 | + | 0.342193i | ||||
\(428\) | −0.656854 | − | 1.58579i | −0.0317502 | − | 0.0766519i | ||||
\(429\) | 4.00000i | 0.193122i | ||||||||
\(430\) | 1.41421 | − | 0.585786i | 0.0681994 | − | 0.0282491i | ||||
\(431\) | −2.79899 | + | 6.75736i | −0.134823 | + | 0.325491i | −0.976844 | − | 0.213954i | \(-0.931366\pi\) |
0.842021 | + | 0.539445i | \(0.181366\pi\) | |||||||
\(432\) | 14.4853 | + | 6.00000i | 0.696923 | + | 0.288675i | ||||
\(433\) | 14.7279 | − | 14.7279i | 0.707779 | − | 0.707779i | −0.258289 | − | 0.966068i | \(-0.583159\pi\) |
0.966068 | + | 0.258289i | \(0.0831587\pi\) | |||||||
\(434\) | 34.9706 | − | 34.9706i | 1.67864 | − | 1.67864i | ||||
\(435\) | −0.242641 | − | 0.100505i | −0.0116337 | − | 0.00481885i | ||||
\(436\) | 22.7782 | − | 54.9914i | 1.09088 | − | 2.63361i | ||||
\(437\) | 3.65685 | − | 1.51472i | 0.174931 | − | 0.0724588i | ||||
\(438\) | 33.7990i | 1.61498i | ||||||||
\(439\) | 4.07107 | + | 9.82843i | 0.194301 | + | 0.469085i | 0.990763 | − | 0.135604i | \(-0.0432974\pi\) |
−0.796462 | + | 0.604689i | \(0.793297\pi\) | |||||||
\(440\) | −6.24264 | − | 6.24264i | −0.297606 | − | 0.297606i | ||||
\(441\) | −0.313708 | −0.0149385 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.7990 | −1.13072 | −0.565362 | − | 0.824843i | \(-0.691264\pi\) | ||||
−0.565362 | + | 0.824843i | \(0.691264\pi\) | |||||||
\(444\) | −27.0711 | − | 27.0711i | −1.28474 | − | 1.28474i | ||||
\(445\) | 1.92893 | + | 4.65685i | 0.0914402 | + | 0.220756i | ||||
\(446\) | − | 11.6569i | − | 0.551968i | ||||||
\(447\) | 16.9706 | − | 7.02944i | 0.802680 | − | 0.332481i | ||||
\(448\) | −9.82843 | + | 23.7279i | −0.464350 | + | 1.12104i | ||||
\(449\) | −11.1924 | − | 4.63604i | −0.528201 | − | 0.218788i | 0.102614 | − | 0.994721i | \(-0.467279\pi\) |
−0.630815 | + | 0.775933i | \(0.717279\pi\) | |||||||
\(450\) | 13.7782 | − | 13.7782i | 0.649509 | − | 0.649509i | ||||
\(451\) | −2.24264 | + | 2.24264i | −0.105602 | + | 0.105602i | ||||
\(452\) | −46.6777 | − | 19.3345i | −2.19553 | − | 0.909419i | ||||
\(453\) | 2.97056 | − | 7.17157i | 0.139569 | − | 0.336950i | ||||
\(454\) | 38.7990 | − | 16.0711i | 1.82093 | − | 0.754253i | ||||
\(455\) | − | 2.82843i | − | 0.132599i | ||||||
\(456\) | −1.51472 | − | 3.65685i | −0.0709332 | − | 0.171248i | ||||
\(457\) | 9.31371 | + | 9.31371i | 0.435677 | + | 0.435677i | 0.890554 | − | 0.454877i | \(-0.150317\pi\) |
−0.454877 | + | 0.890554i | \(0.650317\pi\) | |||||||
\(458\) | 41.4558 | 1.93710 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14.0000 | 0.652753 | ||||||||
\(461\) | 17.0000 | + | 17.0000i | 0.791769 | + | 0.791769i | 0.981782 | − | 0.190013i | \(-0.0608529\pi\) |
−0.190013 | + | 0.981782i | \(0.560853\pi\) | |||||||
\(462\) | 6.82843 | + | 16.4853i | 0.317687 | + | 0.766965i | ||||
\(463\) | 14.6274i | 0.679794i | 0.940463 | + | 0.339897i | \(0.110392\pi\) | ||||
−0.940463 | + | 0.339897i | \(0.889608\pi\) | |||||||
\(464\) | −0.878680 | + | 0.363961i | −0.0407917 | + | 0.0168965i | ||||
\(465\) | 2.48528 | − | 6.00000i | 0.115252 | − | 0.278243i | ||||
\(466\) | 19.6066 | + | 8.12132i | 0.908258 | + | 0.376213i | ||||
\(467\) | 23.0711 | − | 23.0711i | 1.06760 | − | 1.06760i | 0.0700588 | − | 0.997543i | \(-0.477681\pi\) |
0.997543 | − | 0.0700588i | \(-0.0223187\pi\) | |||||||
\(468\) | 7.00000 | − | 7.00000i | 0.323575 | − | 0.323575i | ||||
\(469\) | 2.82843 | + | 1.17157i | 0.130605 | + | 0.0540982i | ||||
\(470\) | −3.65685 | + | 8.82843i | −0.168678 | + | 0.407225i | ||||
\(471\) | −9.65685 | + | 4.00000i | −0.444964 | + | 0.184310i | ||||
\(472\) | − | 26.4853i | − | 1.21908i | ||||||
\(473\) | 0.828427 | + | 2.00000i | 0.0380911 | + | 0.0919601i | ||||
\(474\) | −8.82843 | − | 8.82843i | −0.405503 | − | 0.405503i | ||||
\(475\) | −3.65685 | −0.167788 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.58579 | −0.118395 | ||||||||
\(478\) | −25.3137 | − | 25.3137i | −1.15782 | − | 1.15782i | ||||
\(479\) | −1.97056 | − | 4.75736i | −0.0900373 | − | 0.217369i | 0.872446 | − | 0.488711i | \(-0.162533\pi\) |
−0.962483 | + | 0.271342i | \(0.912533\pi\) | |||||||
\(480\) | 1.31371i | 0.0599623i | ||||||||
\(481\) | −12.0711 | + | 5.00000i | −0.550393 | + | 0.227980i | ||||
\(482\) | 3.29289 | − | 7.94975i | 0.149987 | − | 0.362101i | ||||
\(483\) | −12.4853 | − | 5.17157i | −0.568100 | − | 0.235315i | ||||
\(484\) | −11.2929 | + | 11.2929i | −0.513313 | + | 0.513313i | ||||
\(485\) | −5.58579 | + | 5.58579i | −0.253637 | + | 0.253637i | ||||
\(486\) | 34.5563 | + | 14.3137i | 1.56751 | + | 0.649283i | ||||
\(487\) | −10.0711 | + | 24.3137i | −0.456364 | + | 1.10176i | 0.513495 | + | 0.858092i | \(0.328350\pi\) |
−0.969859 | + | 0.243667i | \(0.921650\pi\) | |||||||
\(488\) | 15.6066 | − | 6.46447i | 0.706478 | − | 0.292633i | ||||
\(489\) | − | 9.17157i | − | 0.414753i | ||||||
\(490\) | 0.121320 | + | 0.292893i | 0.00548069 | + | 0.0132316i | ||||
\(491\) | 26.2426 | + | 26.2426i | 1.18431 | + | 1.18431i | 0.978615 | + | 0.205698i | \(0.0659466\pi\) |
0.205698 | + | 0.978615i | \(0.434053\pi\) | |||||||
\(492\) | −5.02944 | −0.226745 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −2.82843 | −0.127257 | ||||||||
\(495\) | −2.58579 | − | 2.58579i | −0.116222 | − | 0.116222i | ||||
\(496\) | −9.00000 | − | 21.7279i | −0.404112 | − | 0.975613i | ||||
\(497\) | 14.1421i | 0.634361i | ||||||||
\(498\) | −28.1421 | + | 11.6569i | −1.26108 | + | 0.522356i | ||||
\(499\) | 8.21320 | − | 19.8284i | 0.367673 | − | 0.887642i | −0.626457 | − | 0.779456i | \(-0.715496\pi\) |
0.994131 | − | 0.108186i | \(-0.0345043\pi\) | |||||||
\(500\) | −25.4853 | − | 10.5563i | −1.13974 | − | 0.472094i | ||||
\(501\) | −1.51472 | + | 1.51472i | −0.0676726 | + | 0.0676726i | ||||
\(502\) | −34.9706 | + | 34.9706i | −1.56081 | + | 1.56081i | ||||
\(503\) | 19.7279 | + | 8.17157i | 0.879625 | + | 0.364352i | 0.776351 | − | 0.630301i | \(-0.217068\pi\) |
0.103273 | + | 0.994653i | \(0.467068\pi\) | |||||||
\(504\) | 8.07107 | − | 19.4853i | 0.359514 | − | 0.867943i | ||||
\(505\) | −7.48528 | + | 3.10051i | −0.333091 | + | 0.137971i | ||||
\(506\) | 30.1421i | 1.33998i | ||||||||
\(507\) | −4.55635 | − | 11.0000i | −0.202355 | − | 0.488527i | ||||
\(508\) | −14.3848 | − | 14.3848i | −0.638221 | − | 0.638221i | ||||
\(509\) | −36.9706 | −1.63869 | −0.819346 | − | 0.573300i | \(-0.805663\pi\) | ||||
−0.819346 | + | 0.573300i | \(0.805663\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 33.7990 | 1.49518 | ||||||||
\(512\) | 22.0919 | + | 22.0919i | 0.976333 | + | 0.976333i | ||||
\(513\) | −1.65685 | − | 4.00000i | −0.0731519 | − | 0.176604i | ||||
\(514\) | 14.8284i | 0.654054i | ||||||||
\(515\) | 8.82843 | − | 3.65685i | 0.389027 | − | 0.161140i | ||||
\(516\) | −1.31371 | + | 3.17157i | −0.0578328 | + | 0.139621i | ||||
\(517\) | −12.4853 | − | 5.17157i | −0.549102 | − | 0.227446i | ||||
\(518\) | −41.2132 | + | 41.2132i | −1.81080 | + | 1.81080i | ||||
\(519\) | −2.24264 | + | 2.24264i | −0.0984410 | + | 0.0984410i | ||||
\(520\) | −4.41421 | − | 1.82843i | −0.193576 | − | 0.0801818i | ||||
\(521\) | −7.12132 | + | 17.1924i | −0.311991 | + | 0.753212i | 0.687640 | + | 0.726051i | \(0.258647\pi\) |
−0.999631 | + | 0.0271607i | \(0.991353\pi\) | |||||||
\(522\) | −1.29289 | + | 0.535534i | −0.0565884 | + | 0.0234397i | ||||
\(523\) | − | 1.17157i | − | 0.0512293i | −0.999672 | − | 0.0256147i | \(-0.991846\pi\) | ||
0.999672 | − | 0.0256147i | \(-0.00815429\pi\) | |||||||
\(524\) | 22.3137 | + | 53.8701i | 0.974779 | + | 2.35332i | ||||
\(525\) | 8.82843 | + | 8.82843i | 0.385304 | + | 0.385304i | ||||
\(526\) | 25.3137 | 1.10373 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 8.48528 | 0.369274 | ||||||||
\(529\) | 0.121320 | + | 0.121320i | 0.00527480 | + | 0.00527480i | ||||
\(530\) | 1.00000 | + | 2.41421i | 0.0434372 | + | 0.104867i | ||||
\(531\) | − | 10.9706i | − | 0.476082i | ||||||
\(532\) | −7.65685 | + | 3.17157i | −0.331967 | + | 0.137505i | ||||
\(533\) | −0.656854 | + | 1.58579i | −0.0284515 | + | 0.0686880i | ||||
\(534\) | −15.8995 | − | 6.58579i | −0.688038 | − | 0.284995i | ||||
\(535\) | −0.242641 | + | 0.242641i | −0.0104903 | + | 0.0104903i | ||||
\(536\) | 3.65685 | − | 3.65685i | 0.157952 | − | 0.157952i | ||||
\(537\) | 6.00000 | + | 2.48528i | 0.258919 | + | 0.107248i | ||||
\(538\) | −24.4350 | + | 58.9914i | −1.05347 | + | 2.54330i | ||||
\(539\) | −0.414214 | + | 0.171573i | −0.0178414 | + | 0.00739017i | ||||
\(540\) | − | 15.3137i | − | 0.658997i | ||||||
\(541\) | 7.05025 | + | 17.0208i | 0.303114 | + | 0.731782i | 0.999895 | + | 0.0144979i | \(0.00461500\pi\) |
−0.696781 | + | 0.717284i | \(0.745385\pi\) | |||||||
\(542\) | −37.7990 | − | 37.7990i | −1.62361 | − | 1.62361i | ||||
\(543\) | −12.6274 | −0.541894 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.8995 | −0.509718 | ||||||||
\(546\) | 6.82843 | + | 6.82843i | 0.292230 | + | 0.292230i | ||||
\(547\) | −3.10051 | − | 7.48528i | −0.132568 | − | 0.320048i | 0.843631 | − | 0.536923i | \(-0.180413\pi\) |
−0.976199 | + | 0.216875i | \(0.930413\pi\) | |||||||
\(548\) | − | 64.0416i | − | 2.73572i | ||||||
\(549\) | 6.46447 | − | 2.67767i | 0.275897 | − | 0.114280i | ||||
\(550\) | 10.6569 | − | 25.7279i | 0.454410 | − | 1.09704i | ||||
\(551\) | 0.242641 | + | 0.100505i | 0.0103368 | + | 0.00428166i | ||||
\(552\) | −16.1421 | + | 16.1421i | −0.687055 | + | 0.687055i | ||||
\(553\) | −8.82843 | + | 8.82843i | −0.375423 | + | 0.375423i | ||||
\(554\) | −44.5061 | − | 18.4350i | −1.89088 | − | 0.783229i | ||||
\(555\) | −2.92893 | + | 7.07107i | −0.124326 | + | 0.300150i | ||||
\(556\) | −75.5269 | + | 31.2843i | −3.20305 | + | 1.32675i | ||||
\(557\) | 19.7574i | 0.837146i | 0.908183 | + | 0.418573i | \(0.137470\pi\) | ||||
−0.908183 | + | 0.418573i | \(0.862530\pi\) | |||||||
\(558\) | −13.2426 | − | 31.9706i | −0.560606 | − | 1.35342i | ||||
\(559\) | 0.828427 | + | 0.828427i | 0.0350387 | + | 0.0350387i | ||||
\(560\) | −6.00000 | −0.253546 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.58579 | 0.193440 | ||||||||
\(563\) | 24.5858 | + | 24.5858i | 1.03617 | + | 1.03617i | 0.999321 | + | 0.0368464i | \(0.0117312\pi\) |
0.0368464 | + | 0.999321i | \(0.488269\pi\) | |||||||
\(564\) | −8.20101 | − | 19.7990i | −0.345325 | − | 0.833688i | ||||
\(565\) | 10.1005i | 0.424931i | ||||||||
\(566\) | −41.6274 | + | 17.2426i | −1.74973 | + | 0.724762i | ||||
\(567\) | −0.171573 | + | 0.414214i | −0.00720538 | + | 0.0173953i | ||||
\(568\) | 22.0711 | + | 9.14214i | 0.926081 | + | 0.383595i | ||||
\(569\) | 8.51472 | − | 8.51472i | 0.356956 | − | 0.356956i | −0.505734 | − | 0.862690i | \(-0.668778\pi\) |
0.862690 | + | 0.505734i | \(0.168778\pi\) | |||||||
\(570\) | −1.17157 | + | 1.17157i | −0.0490718 | + | 0.0490718i | ||||
\(571\) | 3.92893 | + | 1.62742i | 0.164421 | + | 0.0681053i | 0.463376 | − | 0.886162i | \(-0.346638\pi\) |
−0.298955 | + | 0.954267i | \(0.596638\pi\) | |||||||
\(572\) | 5.41421 | − | 13.0711i | 0.226380 | − | 0.546529i | ||||
\(573\) | 20.0000 | − | 8.28427i | 0.835512 | − | 0.346080i | ||||
\(574\) | 7.65685i | 0.319591i | ||||||||
\(575\) | 8.07107 | + | 19.4853i | 0.336587 | + | 0.812592i | ||||
\(576\) | 12.7071 | + | 12.7071i | 0.529463 | + | 0.529463i | ||||
\(577\) | −27.0711 | −1.12698 | −0.563492 | − | 0.826122i | \(-0.690542\pi\) | ||||
−0.563492 | + | 0.826122i | \(0.690542\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.48528 | 0.103285 | ||||||||
\(580\) | 0.656854 | + | 0.656854i | 0.0272744 | + | 0.0272744i | ||||
\(581\) | 11.6569 | + | 28.1421i | 0.483608 | + | 1.16753i | ||||
\(582\) | − | 26.9706i | − | 1.11797i | ||||||
\(583\) | −3.41421 | + | 1.41421i | −0.141402 | + | 0.0585707i | ||||
\(584\) | 21.8492 | − | 52.7487i | 0.904128 | − | 2.18276i | ||||
\(585\) | −1.82843 | − | 0.757359i | −0.0755962 | − | 0.0313130i | ||||
\(586\) | −21.0711 | + | 21.0711i | −0.870438 | + | 0.870438i | ||||
\(587\) | 32.0416 | − | 32.0416i | 1.32250 | − | 1.32250i | 0.410753 | − | 0.911747i | \(-0.365266\pi\) |
0.911747 | − | 0.410753i | \(-0.134734\pi\) | |||||||
\(588\) | −0.656854 | − | 0.272078i | −0.0270882 | − | 0.0112203i | ||||
\(589\) | −2.48528 | + | 6.00000i | −0.102404 | + | 0.247226i | ||||
\(590\) | −10.2426 | + | 4.24264i | −0.421683 | + | 0.174667i | ||||
\(591\) | − | 5.02944i | − | 0.206883i | ||||||
\(592\) | 10.6066 | + | 25.6066i | 0.435929 | + | 1.05242i | ||||
\(593\) | 9.14214 | + | 9.14214i | 0.375423 | + | 0.375423i | 0.869448 | − | 0.494025i | \(-0.164475\pi\) |
−0.494025 | + | 0.869448i | \(0.664475\pi\) | |||||||
\(594\) | 32.9706 | 1.35280 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −64.9706 | −2.66130 | ||||||||
\(597\) | 8.82843 | + | 8.82843i | 0.361323 | + | 0.361323i | ||||
\(598\) | 6.24264 | + | 15.0711i | 0.255281 | + | 0.616302i | ||||
\(599\) | − | 10.6274i | − | 0.434224i | −0.976147 | − | 0.217112i | \(-0.930336\pi\) | ||
0.976147 | − | 0.217112i | \(-0.0696638\pi\) | |||||||
\(600\) | 19.4853 | − | 8.07107i | 0.795483 | − | 0.329500i | ||||
\(601\) | 3.22183 | − | 7.77817i | 0.131421 | − | 0.317278i | −0.844447 | − | 0.535639i | \(-0.820071\pi\) |
0.975868 | + | 0.218360i | \(0.0700709\pi\) | |||||||
\(602\) | 4.82843 | + | 2.00000i | 0.196792 | + | 0.0815139i | ||||
\(603\) | 1.51472 | − | 1.51472i | 0.0616841 | − | 0.0616841i | ||||
\(604\) | −19.4142 | + | 19.4142i | −0.789953 | + | 0.789953i | ||||
\(605\) | 2.94975 | + | 1.22183i | 0.119924 | + | 0.0496743i | ||||
\(606\) | 10.5858 | − | 25.5563i | 0.430018 | − | 1.03816i | ||||
\(607\) | −15.1421 | + | 6.27208i | −0.614600 | + | 0.254576i | −0.668194 | − | 0.743987i | \(-0.732932\pi\) |
0.0535937 | + | 0.998563i | \(0.482932\pi\) | |||||||
\(608\) | − | 1.31371i | − | 0.0532779i | ||||||
\(609\) | −0.343146 | − | 0.828427i | −0.0139050 | − | 0.0335696i | ||||
\(610\) | −5.00000 | − | 5.00000i | −0.202444 | − | 0.202444i | ||||
\(611\) | −7.31371 | −0.295881 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.31371 | 0.214619 | 0.107309 | − | 0.994226i | \(-0.465776\pi\) | ||||
0.107309 | + | 0.994226i | \(0.465776\pi\) | |||||||
\(614\) | 44.6274 | + | 44.6274i | 1.80102 | + | 1.80102i | ||||
\(615\) | 0.384776 | + | 0.928932i | 0.0155157 | + | 0.0374582i | ||||
\(616\) | − | 30.1421i | − | 1.21446i | ||||||
\(617\) | 2.70711 | − | 1.12132i | 0.108984 | − | 0.0451427i | −0.327525 | − | 0.944842i | \(-0.606215\pi\) |
0.436509 | + | 0.899700i | \(0.356215\pi\) | |||||||
\(618\) | −12.4853 | + | 30.1421i | −0.502232 | + | 1.21249i | ||||
\(619\) | −26.3137 | − | 10.8995i | −1.05764 | − | 0.438088i | −0.215025 | − | 0.976609i | \(-0.568983\pi\) |
−0.842612 | + | 0.538521i | \(0.818983\pi\) | |||||||
\(620\) | −16.2426 | + | 16.2426i | −0.652320 | + | 0.652320i | ||||
\(621\) | −17.6569 | + | 17.6569i | −0.708545 | + | 0.708545i | ||||
\(622\) | 57.2843 | + | 23.7279i | 2.29689 | + | 0.951403i | ||||
\(623\) | −6.58579 | + | 15.8995i | −0.263854 | + | 0.637000i | ||||
\(624\) | 4.24264 | − | 1.75736i | 0.169842 | − | 0.0703507i | ||||
\(625\) | − | 16.5563i | − | 0.662254i | ||||||
\(626\) | −9.12132 | − | 22.0208i | −0.364561 | − | 0.880129i | ||||
\(627\) | −1.65685 | − | 1.65685i | −0.0661684 | − | 0.0661684i | ||||
\(628\) | 36.9706 | 1.47529 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −8.82843 | −0.351733 | ||||||||
\(631\) | −20.7279 | − | 20.7279i | −0.825166 | − | 0.825166i | 0.161678 | − | 0.986844i | \(-0.448309\pi\) |
−0.986844 | + | 0.161678i | \(0.948309\pi\) | |||||||
\(632\) | 8.07107 | + | 19.4853i | 0.321050 | + | 0.775083i | ||||
\(633\) | − | 23.1127i | − | 0.918647i | ||||||
\(634\) | 42.9203 | − | 17.7782i | 1.70458 | − | 0.706062i | ||||
\(635\) | −1.55635 | + | 3.75736i | −0.0617618 | + | 0.149106i | ||||
\(636\) | −5.41421 | − | 2.24264i | −0.214688 | − | 0.0889265i | ||||
\(637\) | −0.171573 | + | 0.171573i | −0.00679796 | + | 0.00679796i | ||||
\(638\) | −1.41421 | + | 1.41421i | −0.0559893 | + | 0.0559893i | ||||
\(639\) | 9.14214 | + | 3.78680i | 0.361657 | + | 0.149803i | ||||
\(640\) | 6.02082 | − | 14.5355i | 0.237994 | − | 0.574567i | ||||
\(641\) | 38.2635 | − | 15.8492i | 1.51132 | − | 0.626007i | 0.535487 | − | 0.844544i | \(-0.320128\pi\) |
0.975829 | + | 0.218536i | \(0.0701282\pi\) | |||||||
\(642\) | − | 1.17157i | − | 0.0462383i | ||||||
\(643\) | −11.0416 | − | 26.6569i | −0.435439 | − | 1.05124i | −0.977506 | − | 0.210908i | \(-0.932358\pi\) |
0.542066 | − | 0.840336i | \(-0.317642\pi\) | |||||||
\(644\) | 33.7990 | + | 33.7990i | 1.33187 | + | 1.33187i | ||||
\(645\) | 0.686292 | 0.0270227 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.82843 | −0.111197 | −0.0555985 | − | 0.998453i | \(-0.517707\pi\) | ||||
−0.0555985 | + | 0.998453i | \(0.517707\pi\) | |||||||
\(648\) | 0.535534 | + | 0.535534i | 0.0210378 | + | 0.0210378i | ||||
\(649\) | −6.00000 | − | 14.4853i | −0.235521 | − | 0.568597i | ||||
\(650\) | − | 15.0711i | − | 0.591136i | ||||||
\(651\) | 20.4853 | − | 8.48528i | 0.802881 | − | 0.332564i | ||||
\(652\) | −12.4142 | + | 29.9706i | −0.486178 | + | 1.17374i | ||||
\(653\) | −8.77817 | − | 3.63604i | −0.343517 | − | 0.142289i | 0.204254 | − | 0.978918i | \(-0.434523\pi\) |
−0.547770 | + | 0.836629i | \(0.684523\pi\) | |||||||
\(654\) | 28.7279 | − | 28.7279i | 1.12335 | − | 1.12335i | ||||
\(655\) | 8.24264 | − | 8.24264i | 0.322067 | − | 0.322067i | ||||
\(656\) | 3.36396 | + | 1.39340i | 0.131341 | + | 0.0544031i | ||||
\(657\) | 9.05025 | − | 21.8492i | 0.353084 | − | 0.852420i | ||||
\(658\) | −30.1421 | + | 12.4853i | −1.17506 | + | 0.486727i | ||||
\(659\) | 8.48528i | 0.330540i | 0.986248 | + | 0.165270i | \(0.0528495\pi\) | ||||
−0.986248 | + | 0.165270i | \(0.947151\pi\) | |||||||
\(660\) | −3.17157 | − | 7.65685i | −0.123453 | − | 0.298043i | ||||
\(661\) | 0.857864 | + | 0.857864i | 0.0333671 | + | 0.0333671i | 0.723593 | − | 0.690226i | \(-0.242489\pi\) |
−0.690226 | + | 0.723593i | \(0.742489\pi\) | |||||||
\(662\) | 52.6274 | 2.04542 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 51.4558 | 1.99687 | ||||||||
\(665\) | 1.17157 | + | 1.17157i | 0.0454316 | + | 0.0454316i | ||||
\(666\) | 15.6066 | + | 37.6777i | 0.604744 | + | 1.45998i | ||||
\(667\) | − | 1.51472i | − | 0.0586501i | ||||||
\(668\) | 7.00000 | − | 2.89949i | 0.270838 | − | 0.112185i | ||||
\(669\) | 2.00000 | − | 4.82843i | 0.0773245 | − | 0.186678i | ||||
\(670\) | −2.00000 | − | 0.828427i | −0.0772667 | − | 0.0320049i | ||||
\(671\) | 7.07107 | − | 7.07107i | 0.272976 | − | 0.272976i | ||||
\(672\) | −3.17157 | + | 3.17157i | −0.122346 | + | 0.122346i | ||||
\(673\) | −4.12132 | − | 1.70711i | −0.158865 | − | 0.0658041i | 0.301834 | − | 0.953361i | \(-0.402401\pi\) |
−0.460699 | + | 0.887556i | \(0.652401\pi\) | |||||||
\(674\) | 5.19239 | − | 12.5355i | 0.200003 | − | 0.482851i | ||||
\(675\) | 21.3137 | − | 8.82843i | 0.820365 | − | 0.339806i | ||||
\(676\) | 42.1127i | 1.61972i | ||||||||
\(677\) | 14.5772 | + | 35.1924i | 0.560246 | + | 1.35255i | 0.909570 | + | 0.415551i | \(0.136411\pi\) |
−0.349324 | + | 0.937002i | \(0.613589\pi\) | |||||||
\(678\) | −24.3848 | − | 24.3848i | −0.936492 | − | 0.936492i | ||||
\(679\) | −26.9706 | −1.03504 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.8284 | 0.721507 | ||||||||
\(682\) | −34.9706 | − | 34.9706i | −1.33909 | − | 1.33909i | ||||
\(683\) | 9.10051 | + | 21.9706i | 0.348221 | + | 0.840680i | 0.996830 | + | 0.0795585i | \(0.0253510\pi\) |
−0.648609 | + | 0.761122i | \(0.724649\pi\) | |||||||
\(684\) | 5.79899i | 0.221730i | ||||||||
\(685\) | −11.8284 | + | 4.89949i | −0.451941 | + | 0.187200i | ||||
\(686\) | −17.3137 | + | 41.7990i | −0.661040 | + | 1.59589i | ||||
\(687\) | 17.1716 | + | 7.11270i | 0.655136 | + | 0.271366i | ||||
\(688\) | 1.75736 | − | 1.75736i | 0.0669987 | − | 0.0669987i | ||||
\(689\) | −1.41421 | + | 1.41421i | −0.0538772 | + | 0.0538772i | ||||
\(690\) | 8.82843 | + | 3.65685i | 0.336092 | + | 0.139214i | ||||
\(691\) | 7.62742 | − | 18.4142i | 0.290161 | − | 0.700510i | −0.709832 | − | 0.704371i | \(-0.751229\pi\) |
0.999993 | + | 0.00386139i | \(0.00122912\pi\) | |||||||
\(692\) | 10.3640 | − | 4.29289i | 0.393979 | − | 0.163191i | ||||
\(693\) | − | 12.4853i | − | 0.474277i | ||||||
\(694\) | 15.4853 | + | 37.3848i | 0.587813 | + | 1.41911i | ||||
\(695\) | 11.5563 | + | 11.5563i | 0.438357 | + | 0.438357i | ||||
\(696\) | −1.51472 | −0.0574153 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −10.2426 | −0.387690 | ||||||||
\(699\) | 6.72792 | + | 6.72792i | 0.254473 | + | 0.254473i | ||||
\(700\) | −16.8995 | − | 40.7990i | −0.638741 | − | 1.54206i | ||||
\(701\) | 37.6985i | 1.42385i | 0.702254 | + | 0.711926i | \(0.252177\pi\) | ||||
−0.702254 | + | 0.711926i | \(0.747823\pi\) | |||||||
\(702\) | 16.4853 | − | 6.82843i | 0.622197 | − | 0.257722i | ||||
\(703\) | 2.92893 | − | 7.07107i | 0.110467 | − | 0.266690i | ||||
\(704\) | 23.7279 | + | 9.82843i | 0.894280 | + | 0.370423i | ||||
\(705\) | −3.02944 | + | 3.02944i | −0.114095 | + | 0.114095i | ||||
\(706\) | 23.8995 | − | 23.8995i | 0.899469 | − | 0.899469i | ||||
\(707\) | −25.5563 | − | 10.5858i | −0.961145 | − | 0.398119i | ||||
\(708\) | 9.51472 | − | 22.9706i | 0.357585 | − | 0.863287i | ||||
\(709\) | −22.4350 | + | 9.29289i | −0.842565 | + | 0.349002i | −0.761864 | − | 0.647736i | \(-0.775716\pi\) |
−0.0807007 | + | 0.996738i | \(0.525716\pi\) | |||||||
\(710\) | − | 10.0000i | − | 0.375293i | ||||||
\(711\) | 3.34315 | + | 8.07107i | 0.125378 | + | 0.302689i | ||||
\(712\) | 20.5563 | + | 20.5563i | 0.770382 | + | 0.770382i | ||||
\(713\) | 37.4558 | 1.40273 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.82843 | −0.105777 | ||||||||
\(716\) | −16.2426 | − | 16.2426i | −0.607016 | − | 0.607016i | ||||
\(717\) | −6.14214 | − | 14.8284i | −0.229382 | − | 0.553778i | ||||
\(718\) | 69.5980i | 2.59737i | ||||||||
\(719\) | 31.3848 | − | 13.0000i | 1.17045 | − | 0.484818i | 0.289112 | − | 0.957295i | \(-0.406640\pi\) |
0.881343 | + | 0.472477i | \(0.156640\pi\) | |||||||
\(720\) | −1.60660 | + | 3.87868i | −0.0598745 | + | 0.144550i | ||||
\(721\) | 30.1421 | + | 12.4853i | 1.12255 | + | 0.464976i | ||||
\(722\) | −31.2635 | + | 31.2635i | −1.16351 | + | 1.16351i | ||||
\(723\) | 2.72792 | − | 2.72792i | 0.101453 | − | 0.101453i | ||||
\(724\) | 41.2635 | + | 17.0919i | 1.53354 | + | 0.635215i | ||||
\(725\) | −0.535534 | + | 1.29289i | −0.0198892 | + | 0.0480168i | ||||
\(726\) | −10.0711 | + | 4.17157i | −0.373772 | + | 0.154822i | ||||
\(727\) | 43.1127i | 1.59896i | 0.600692 | + | 0.799481i | \(0.294892\pi\) | ||||
−0.600692 | + | 0.799481i | \(0.705108\pi\) | |||||||
\(728\) | −6.24264 | − | 15.0711i | −0.231368 | − | 0.558571i | ||||
\(729\) | 12.2218 | + | 12.2218i | 0.452660 | + | 0.452660i | ||||
\(730\) | −23.8995 | −0.884560 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 15.8579 | 0.586124 | ||||||||
\(733\) | −25.4853 | − | 25.4853i | −0.941320 | − | 0.941320i | 0.0570509 | − | 0.998371i | \(-0.481830\pi\) |
−0.998371 | + | 0.0570509i | \(0.981830\pi\) | |||||||
\(734\) | −4.07107 | − | 9.82843i | −0.150266 | − | 0.362774i | ||||
\(735\) | 0.142136i | 0.00524275i | ||||||||
\(736\) | −7.00000 | + | 2.89949i | −0.258023 | + | 0.106877i | ||||
\(737\) | 1.17157 | − | 2.82843i | 0.0431554 | − | 0.104186i | ||||
\(738\) | 4.94975 | + | 2.05025i | 0.182203 | + | 0.0754708i | ||||
\(739\) | 15.7574 | − | 15.7574i | 0.579644 | − | 0.579644i | −0.355161 | − | 0.934805i | \(-0.615574\pi\) |
0.934805 | + | 0.355161i | \(0.115574\pi\) | |||||||
\(740\) | 19.1421 | − | 19.1421i | 0.703679 | − | 0.703679i | ||||
\(741\) | −1.17157 | − | 0.485281i | −0.0430388 | − | 0.0178273i | ||||
\(742\) | −3.41421 | + | 8.24264i | −0.125340 | + | 0.302597i | ||||
\(743\) | −47.1421 | + | 19.5269i | −1.72948 | + | 0.716373i | −0.730020 | + | 0.683426i | \(0.760489\pi\) |
−0.999457 | + | 0.0329473i | \(0.989511\pi\) | |||||||
\(744\) | − | 37.4558i | − | 1.37320i | ||||||
\(745\) | 4.97056 | + | 12.0000i | 0.182107 | + | 0.439646i | ||||
\(746\) | −19.7279 | − | 19.7279i | −0.722291 | − | 0.722291i | ||||
\(747\) | 21.3137 | 0.779828 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.17157 | −0.0428083 | ||||||||
\(750\) | −13.3137 | − | 13.3137i | −0.486148 | − | 0.486148i | ||||
\(751\) | −18.2132 | − | 43.9706i | −0.664609 | − | 1.60451i | −0.790498 | − | 0.612464i | \(-0.790178\pi\) |
0.125889 | − | 0.992044i | \(-0.459822\pi\) | |||||||
\(752\) | 15.5147i | 0.565764i | ||||||||
\(753\) | −20.4853 | + | 8.48528i | −0.746525 | + | 0.309221i | ||||
\(754\) | −0.414214 | + | 1.00000i | −0.0150848 | + | 0.0364179i | ||||
\(755\) | 5.07107 | + | 2.10051i | 0.184555 | + | 0.0764452i | ||||
\(756\) | 36.9706 | − | 36.9706i | 1.34461 | − | 1.34461i | ||||
\(757\) | −1.79899 | + | 1.79899i | −0.0653854 | + | 0.0653854i | −0.739043 | − | 0.673658i | \(-0.764722\pi\) |
0.673658 | + | 0.739043i | \(0.264722\pi\) | |||||||
\(758\) | −5.82843 | − | 2.41421i | −0.211698 | − | 0.0876882i | ||||
\(759\) | −5.17157 | + | 12.4853i | −0.187716 | + | 0.453187i | ||||
\(760\) | 2.58579 | − | 1.07107i | 0.0937963 | − | 0.0388517i | ||||
\(761\) | − | 37.6985i | − | 1.36657i | −0.730152 | − | 0.683285i | \(-0.760551\pi\) | ||
0.730152 | − | 0.683285i | \(-0.239449\pi\) | |||||||
\(762\) | −5.31371 | − | 12.8284i | −0.192495 | − | 0.464725i | ||||
\(763\) | −28.7279 | − | 28.7279i | −1.04002 | − | 1.04002i | ||||
\(764\) | −76.5685 | −2.77015 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 54.2843 | 1.96137 | ||||||||
\(767\) | −6.00000 | − | 6.00000i | −0.216647 | − | 0.216647i | ||||
\(768\) | 12.4142 | + | 29.9706i | 0.447959 | + | 1.08147i | ||||
\(769\) | 12.7279i | 0.458981i | 0.973311 | + | 0.229490i | \(0.0737059\pi\) | ||||
−0.973311 | + | 0.229490i | \(0.926294\pi\) | |||||||
\(770\) | −11.6569 | + | 4.82843i | −0.420084 | + | 0.174004i | ||||
\(771\) | −2.54416 | + | 6.14214i | −0.0916255 | + | 0.221204i | ||||
\(772\) | −8.12132 | − | 3.36396i | −0.292293 | − | 0.121072i | ||||
\(773\) | −0.585786 | + | 0.585786i | −0.0210693 | + | 0.0210693i | −0.717563 | − | 0.696494i | \(-0.754742\pi\) |
0.696494 | + | 0.717563i | \(0.254742\pi\) | |||||||
\(774\) | 2.58579 | − | 2.58579i | 0.0929442 | − | 0.0929442i | ||||
\(775\) | −31.9706 | − | 13.2426i | −1.14842 | − | 0.475690i | ||||
\(776\) | −17.4350 | + | 42.0919i | −0.625881 | + | 1.51101i | ||||
\(777\) | −24.1421 | + | 10.0000i | −0.866094 | + | 0.358748i | ||||
\(778\) | 29.3137i | 1.05095i | ||||||||
\(779\) | −0.384776 | − | 0.928932i | −0.0137860 | − | 0.0332824i | ||||
\(780\) | −3.17157 | − | 3.17157i | −0.113561 | − | 0.113561i | ||||
\(781\) | 14.1421 | 0.506045 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.65685 | −0.0592111 | ||||||||
\(784\) | 0.363961 | + | 0.363961i | 0.0129986 | + | 0.0129986i | ||||
\(785\) | −2.82843 | − | 6.82843i | −0.100951 | − | 0.243717i | ||||
\(786\) | 39.7990i | 1.41958i | ||||||||
\(787\) | 19.0000 | − | 7.87006i | 0.677277 | − | 0.280537i | −0.0174112 | − | 0.999848i | \(-0.505542\pi\) |
0.694688 | + | 0.719311i | \(0.255542\pi\) | |||||||
\(788\) | −6.80761 | + | 16.4350i | −0.242511 | + | 0.585474i | ||||
\(789\) | 10.4853 | + | 4.34315i | 0.373286 | + | 0.154620i | ||||
\(790\) | 6.24264 | − | 6.24264i | 0.222103 | − | 0.222103i | ||||
\(791\) | −24.3848 | + | 24.3848i | −0.867023 | + | 0.867023i | ||||
\(792\) | −19.4853 | − | 8.07107i | −0.692379 | − | 0.286793i | ||||
\(793\) | 2.07107 | − | 5.00000i | 0.0735458 | − | 0.177555i | ||||
\(794\) | 39.6777 | − | 16.4350i | 1.40811 | − | 0.583257i | ||||
\(795\) | 1.17157i | 0.0415514i | ||||||||
\(796\) | −16.8995 | − | 40.7990i | −0.598987 | − | 1.44608i | ||||
\(797\) | −17.8284 | − | 17.8284i | −0.631515 | − | 0.631515i | 0.316933 | − | 0.948448i | \(-0.397347\pi\) |
−0.948448 | + | 0.316933i | \(0.897347\pi\) | |||||||
\(798\) | −5.65685 | −0.200250 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 7.00000 | 0.247487 | ||||||||
\(801\) | 8.51472 | + | 8.51472i | 0.300853 | + | 0.300853i | ||||
\(802\) | −0.535534 | − | 1.29289i | −0.0189104 | − | 0.0456536i | ||||
\(803\) | − | 33.7990i | − | 1.19274i | ||||||
\(804\) | 4.48528 | − | 1.85786i | 0.158184 | − | 0.0655218i | ||||
\(805\) | 3.65685 | − | 8.82843i | 0.128887 | − | 0.311161i | ||||
\(806\) | −24.7279 | − | 10.2426i | −0.871004 | − | 0.360782i | ||||
\(807\) | −20.2426 | + | 20.2426i | −0.712575 | + | 0.712575i | ||||
\(808\) | −33.0416 | + | 33.0416i | −1.16240 | + | 1.16240i | ||||
\(809\) | 32.6066 | + | 13.5061i | 1.14639 | + | 0.474849i | 0.873321 | − | 0.487146i | \(-0.161962\pi\) |
0.273067 | + | 0.961995i | \(0.411962\pi\) | |||||||
\(810\) | 0.121320 | − | 0.292893i | 0.00426276 | − | 0.0102912i | ||||
\(811\) | 50.9411 | − | 21.1005i | 1.78878 | − | 0.740939i | 0.798481 | − | 0.602020i | \(-0.205637\pi\) |
0.990304 | − | 0.138919i | \(-0.0443628\pi\) | |||||||
\(812\) | 3.17157i | 0.111300i | ||||||||
\(813\) | −9.17157 | − | 22.1421i | −0.321661 | − | 0.776559i | ||||
\(814\) | 41.2132 | + | 41.2132i | 1.44452 | + | 1.44452i | ||||
\(815\) | 6.48528 | 0.227169 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.686292 | −0.0240103 | ||||||||
\(818\) | 5.65685 | + | 5.65685i | 0.197787 | + | 0.197787i | ||||
\(819\) | −2.58579 | − | 6.24264i | −0.0903547 | − | 0.218136i | ||||
\(820\) | − | 3.55635i | − | 0.124193i | ||||||
\(821\) | −35.5061 | + | 14.7071i | −1.23917 | + | 0.513282i | −0.903456 | − | 0.428682i | \(-0.858978\pi\) |
−0.335716 | + | 0.941963i | \(0.608978\pi\) | |||||||
\(822\) | 16.7279 | − | 40.3848i | 0.583453 | − | 1.40858i | ||||
\(823\) | −9.00000 | − | 3.72792i | −0.313720 | − | 0.129947i | 0.220267 | − | 0.975440i | \(-0.429307\pi\) |
−0.533987 | + | 0.845492i | \(0.679307\pi\) | |||||||
\(824\) | 38.9706 | − | 38.9706i | 1.35760 | − | 1.35760i | ||||
\(825\) | 8.82843 | − | 8.82843i | 0.307366 | − | 0.307366i | ||||
\(826\) | −34.9706 | − | 14.4853i | −1.21678 | − | 0.504007i | ||||
\(827\) | 17.9289 | − | 43.2843i | 0.623450 | − | 1.50514i | −0.224177 | − | 0.974549i | \(-0.571969\pi\) |
0.847627 | − | 0.530593i | \(-0.178031\pi\) | |||||||
\(828\) | 30.8995 | − | 12.7990i | 1.07383 | − | 0.444796i | ||||
\(829\) | − | 53.9411i | − | 1.87345i | −0.350062 | − | 0.936726i | \(-0.613840\pi\) | ||
0.350062 | − | 0.936726i | \(-0.386160\pi\) | |||||||
\(830\) | −8.24264 | − | 19.8995i | −0.286106 | − | 0.690722i | ||||
\(831\) | −15.2721 | − | 15.2721i | −0.529783 | − | 0.529783i | ||||
\(832\) | 13.8995 | 0.481878 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −55.7990 | −1.93216 | ||||||||
\(835\) | −1.07107 | − | 1.07107i | −0.0370658 | − | 0.0370658i | ||||
\(836\) | 3.17157 | + | 7.65685i | 0.109691 | + | 0.264818i | ||||
\(837\) | − | 40.9706i | − | 1.41615i | ||||||
\(838\) | −29.7279 | + | 12.3137i | −1.02693 | + | 0.425370i | ||||
\(839\) | 6.41421 | − | 15.4853i | 0.221443 | − | 0.534611i | −0.773643 | − | 0.633622i | \(-0.781568\pi\) |
0.995086 | + | 0.0990102i | \(0.0315677\pi\) | |||||||
\(840\) | −8.82843 | − | 3.65685i | −0.304610 | − | 0.126173i | ||||
\(841\) | −20.4350 | + | 20.4350i | −0.704656 | + | 0.704656i | ||||
\(842\) | −24.8995 | + | 24.8995i | −0.858093 | + | 0.858093i | ||||
\(843\) | 1.89949 | + | 0.786797i | 0.0654221 | + | 0.0270987i | ||||
\(844\) | −31.2843 | + | 75.5269i | −1.07685 | + | 2.59974i | ||||
\(845\) | 7.77817 | − | 3.22183i | 0.267577 | − | 0.110834i | ||||
\(846\) | 22.8284i | 0.784857i | ||||||||
\(847\) | 4.17157 | + | 10.0711i | 0.143337 | + | 0.346046i | ||||
\(848\) | 3.00000 | + | 3.00000i | 0.103020 | + | 0.103020i | ||||
\(849\) | −20.2010 | −0.693297 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −44.1421 | −1.51317 | ||||||||
\(852\) | 15.8579 | + | 15.8579i | 0.543281 | + | 0.543281i | ||||
\(853\) | 7.33452 | + | 17.7071i | 0.251129 | + | 0.606280i | 0.998296 | − | 0.0583572i | \(-0.0185862\pi\) |
−0.747166 | + | 0.664637i | \(0.768586\pi\) | |||||||
\(854\) | − | 24.1421i | − | 0.826127i | ||||||
\(855\) | 1.07107 | − | 0.443651i | 0.0366297 | − | 0.0151725i | ||||
\(856\) | −0.757359 | + | 1.82843i | −0.0258860 | + | 0.0624944i | ||||
\(857\) | 8.53553 | + | 3.53553i | 0.291568 | + | 0.120772i | 0.523673 | − | 0.851919i | \(-0.324561\pi\) |
−0.232105 | + | 0.972691i | \(0.574561\pi\) | |||||||
\(858\) | 6.82843 | − | 6.82843i | 0.233119 | − | 0.233119i | ||||
\(859\) | 24.7279 | − | 24.7279i | 0.843706 | − | 0.843706i | −0.145633 | − | 0.989339i | \(-0.546522\pi\) |
0.989339 | + | 0.145633i | \(0.0465218\pi\) | |||||||
\(860\) | −2.24264 | − | 0.928932i | −0.0764734 | − | 0.0316763i | ||||
\(861\) | −1.31371 | + | 3.17157i | −0.0447711 | + | 0.108087i | ||||
\(862\) | 16.3137 | − | 6.75736i | 0.555647 | − | 0.230157i | ||||
\(863\) | 10.6274i | 0.361761i | 0.983505 | + | 0.180881i | \(0.0578948\pi\) | ||||
−0.983505 | + | 0.180881i | \(0.942105\pi\) | |||||||
\(864\) | 3.17157 | + | 7.65685i | 0.107899 | + | 0.260491i | ||||
\(865\) | −1.58579 | − | 1.58579i | −0.0539184 | − | 0.0539184i | ||||
\(866\) | −50.2843 | −1.70873 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −78.4264 | −2.66197 | ||||||||
\(869\) | 8.82843 | + | 8.82843i | 0.299484 | + | 0.299484i | ||||
\(870\) | 0.242641 | + | 0.585786i | 0.00822629 | + | 0.0198600i | ||||
\(871\) | − | 1.65685i | − | 0.0561404i | ||||||
\(872\) | −63.4056 | + | 26.2635i | −2.14718 | + | 0.889393i | ||||
\(873\) | −7.22183 | + | 17.4350i | −0.244422 | + | 0.590086i | ||||
\(874\) | −8.82843 | − | 3.65685i | −0.298626 | − | 0.123695i | ||||
\(875\) | −13.3137 | + | 13.3137i | −0.450085 | + | 0.450085i | ||||
\(876\) | 37.8995 | − | 37.8995i | 1.28051 | − | 1.28051i | ||||
\(877\) | −46.4056 | − | 19.2218i | −1.56701 | − | 0.649075i | −0.580717 | − | 0.814105i | \(-0.697228\pi\) |
−0.986288 | + | 0.165031i | \(0.947228\pi\) | |||||||
\(878\) | 9.82843 | − | 23.7279i | 0.331693 | − | 0.800779i | ||||
\(879\) | −12.3431 | + | 5.11270i | −0.416324 | + | 0.172447i | ||||
\(880\) | 6.00000i | 0.202260i | ||||||||
\(881\) | −12.8787 | − | 31.0919i | −0.433894 | − | 1.04751i | −0.978020 | − | 0.208509i | \(-0.933139\pi\) |
0.544127 | − | 0.839003i | \(-0.316861\pi\) | |||||||
\(882\) | 0.535534 | + | 0.535534i | 0.0180324 | + | 0.0180324i | ||||
\(883\) | 8.00000 | 0.269221 | 0.134611 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134611 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.97056 | −0.167084 | ||||||||
\(886\) | 40.6274 | + | 40.6274i | 1.36490 | + | 1.36490i | ||||
\(887\) | −16.8579 | − | 40.6985i | −0.566032 | − | 1.36652i | −0.904875 | − | 0.425678i | \(-0.860035\pi\) |
0.338843 | − | 0.940843i | \(-0.389965\pi\) | |||||||
\(888\) | 44.1421i | 1.48131i | ||||||||
\(889\) | −12.8284 | + | 5.31371i | −0.430252 | + | 0.178216i | ||||
\(890\) | 4.65685 | − | 11.2426i | 0.156098 | − | 0.376854i | ||||
\(891\) | 0.414214 | + | 0.171573i | 0.0138767 | + | 0.00574791i | ||||
\(892\) | −13.0711 | + | 13.0711i | −0.437652 | + | 0.437652i | ||||
\(893\) | 3.02944 | − | 3.02944i | 0.101376 | − | 0.101376i | ||||
\(894\) | −40.9706 | − | 16.9706i | −1.37026 | − | 0.567581i | ||||
\(895\) | −1.75736 | + | 4.24264i | −0.0587420 | + | 0.141816i | ||||
\(896\) | 49.6274 | − | 20.5563i | 1.65794 | − | 0.686739i | ||||
\(897\) | 7.31371i | 0.244198i | ||||||||
\(898\) | 11.1924 | + | 27.0208i | 0.373495 | + | 0.901696i | ||||
\(899\) | 1.75736 | + | 1.75736i | 0.0586112 | + | 0.0586112i | ||||
\(900\) | −30.8995 | −1.02998 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 7.65685 | 0.254945 | ||||||||
\(903\) | 1.65685 | + | 1.65685i | 0.0551367 | + | 0.0551367i | ||||
\(904\) | 22.2929 | + | 53.8198i | 0.741451 | + | 1.79002i | ||||
\(905\) | − | 8.92893i | − | 0.296808i | ||||||
\(906\) | −17.3137 | + | 7.17157i | −0.575209 | + | 0.238260i | ||||
\(907\) | −5.14214 | + | 12.4142i | −0.170742 | + | 0.412207i | −0.985968 | − | 0.166936i | \(-0.946613\pi\) |
0.815226 | + | 0.579143i | \(0.196613\pi\) | |||||||
\(908\) | −61.5269 | − | 25.4853i | −2.04184 | − | 0.845759i | ||||
\(909\) | −13.6863 | + | 13.6863i | −0.453946 | + | 0.453946i | ||||
\(910\) | −4.82843 | + | 4.82843i | −0.160061 | + | 0.160061i | ||||
\(911\) | −5.24264 | − | 2.17157i | −0.173696 | − | 0.0719474i | 0.294141 | − | 0.955762i | \(-0.404967\pi\) |
−0.467837 | + | 0.883815i | \(0.654967\pi\) | |||||||
\(912\) | −1.02944 | + | 2.48528i | −0.0340881 | + | 0.0822959i | ||||
\(913\) | 28.1421 | − | 11.6569i | 0.931369 | − | 0.385786i | ||||
\(914\) | − | 31.7990i | − | 1.05182i | ||||||
\(915\) | −1.21320 | − | 2.92893i | −0.0401073 | − | 0.0968275i | ||||
\(916\) | −46.4853 | − | 46.4853i | −1.53592 | − | 1.53592i | ||||
\(917\) | 39.7990 | 1.31428 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.3137 | 0.637100 | 0.318550 | − | 0.947906i | \(-0.396804\pi\) | ||||
0.318550 | + | 0.947906i | \(0.396804\pi\) | |||||||
\(920\) | −11.4142 | − | 11.4142i | −0.376315 | − | 0.376315i | ||||
\(921\) | 10.8284 | + | 26.1421i | 0.356809 | + | 0.861413i | ||||
\(922\) | − | 58.0416i | − | 1.91150i | ||||||
\(923\) | 7.07107 | − | 2.92893i | 0.232747 | − | 0.0964070i | ||||
\(924\) | 10.8284 | − | 26.1421i | 0.356229 | − | 0.860013i | ||||
\(925\) | 37.6777 | + | 15.6066i | 1.23883 | + | 0.513142i | ||||
\(926\) | 24.9706 | − | 24.9706i | 0.820584 | − | 0.820584i | ||||
\(927\) | 16.1421 | − | 16.1421i | 0.530177 | − | 0.530177i | ||||
\(928\) | −0.464466 | − | 0.192388i | −0.0152468 | − | 0.00631545i | ||||
\(929\) | −6.63604 | + | 16.0208i | −0.217721 | + | 0.525626i | −0.994571 | − | 0.104060i | \(-0.966817\pi\) |
0.776850 | + | 0.629686i | \(0.216817\pi\) | |||||||
\(930\) | −14.4853 | + | 6.00000i | −0.474991 | + | 0.196748i | ||||
\(931\) | − | 0.142136i | − | 0.00465831i | ||||||
\(932\) | −12.8787 | − | 31.0919i | −0.421855 | − | 1.01845i | ||||
\(933\) | 19.6569 | + | 19.6569i | 0.643537 | + | 0.643537i | ||||
\(934\) | −78.7696 | −2.57742 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −11.4142 | −0.373085 | ||||||||
\(937\) | 19.4853 | + | 19.4853i | 0.636556 | + | 0.636556i | 0.949704 | − | 0.313148i | \(-0.101384\pi\) |
−0.313148 | + | 0.949704i | \(0.601384\pi\) | |||||||
\(938\) | −2.82843 | − | 6.82843i | −0.0923514 | − | 0.222956i | ||||
\(939\) | − | 10.6863i | − | 0.348734i | ||||||
\(940\) | 14.0000 | − | 5.79899i | 0.456630 | − | 0.189142i | ||||
\(941\) | 15.2635 | − | 36.8492i | 0.497574 | − | 1.20125i | −0.453212 | − | 0.891403i | \(-0.649722\pi\) |
0.950786 | − | 0.309848i | \(-0.100278\pi\) | |||||||
\(942\) | 23.3137 | + | 9.65685i | 0.759602 | + | 0.314637i | ||||
\(943\) | −4.10051 | + | 4.10051i | −0.133531 | + | 0.133531i | ||||
\(944\) | −12.7279 | + | 12.7279i | −0.414259 | + | 0.414259i | ||||
\(945\) | −9.65685 | − | 4.00000i | −0.314137 | − | 0.130120i | ||||
\(946\) | 2.00000 | − | 4.82843i | 0.0650256 | − | 0.156986i | ||||
\(947\) | −28.3137 | + | 11.7279i | −0.920072 | + | 0.381106i | −0.791904 | − | 0.610646i | \(-0.790910\pi\) |
−0.128168 | + | 0.991752i | \(0.540910\pi\) | |||||||
\(948\) | 19.7990i | 0.643041i | ||||||||
\(949\) | −7.00000 | − | 16.8995i | −0.227230 | − | 0.548581i | ||||
\(950\) | 6.24264 | + | 6.24264i | 0.202538 | + | 0.202538i | ||||
\(951\) | 20.8284 | 0.675408 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 49.6985 | 1.60989 | 0.804946 | − | 0.593348i | \(-0.202194\pi\) | ||||
0.804946 | + | 0.593348i | \(0.202194\pi\) | |||||||
\(954\) | 4.41421 | + | 4.41421i | 0.142915 | + | 0.142915i | ||||
\(955\) | 5.85786 | + | 14.1421i | 0.189556 | + | 0.457629i | ||||
\(956\) | 56.7696i | 1.83606i | ||||||||
\(957\) | −0.828427 | + | 0.343146i | −0.0267792 | + | 0.0110923i | ||||
\(958\) | −4.75736 | + | 11.4853i | −0.153703 | + | 0.371073i | ||||
\(959\) | −40.3848 | − | 16.7279i | −1.30409 | − | 0.540173i | ||||
\(960\) | 5.75736 | − | 5.75736i | 0.185818 | − | 0.185818i | ||||
\(961\) | −21.5355 | + | 21.5355i | −0.694695 | + | 0.694695i | ||||
\(962\) | 29.1421 | + | 12.0711i | 0.939580 | + | 0.389187i | ||||
\(963\) | −0.313708 | + | 0.757359i | −0.0101091 | + | 0.0244056i | ||||
\(964\) | −12.6066 | + | 5.22183i | −0.406031 | + | 0.168184i | ||||
\(965\) | 1.75736i | 0.0565714i | ||||||||
\(966\) | 12.4853 | + | 30.1421i | 0.401707 | + | 0.969807i | ||||
\(967\) | −30.8701 | − | 30.8701i | −0.992714 | − | 0.992714i | 0.00725952 | − | 0.999974i | \(-0.497689\pi\) |
−0.999974 | + | 0.00725952i | \(0.997689\pi\) | |||||||
\(968\) | 18.4142 | 0.591855 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 19.0711 | 0.612335 | ||||||||
\(971\) | −36.5858 | − | 36.5858i | −1.17409 | − | 1.17409i | −0.981224 | − | 0.192869i | \(-0.938221\pi\) |
−0.192869 | − | 0.981224i | \(-0.561779\pi\) | |||||||
\(972\) | −22.6985 | − | 54.7990i | −0.728054 | − | 1.75768i | ||||
\(973\) | 55.7990i | 1.78883i | ||||||||
\(974\) | 58.6985 | − | 24.3137i | 1.88082 | − | 0.779061i | ||||
\(975\) | 2.58579 | − | 6.24264i | 0.0828114 | − | 0.199925i | ||||
\(976\) | −10.6066 | − | 4.39340i | −0.339509 | − | 0.140629i | ||||
\(977\) | −27.1421 | + | 27.1421i | −0.868354 | + | 0.868354i | −0.992290 | − | 0.123936i | \(-0.960448\pi\) |
0.123936 | + | 0.992290i | \(0.460448\pi\) | |||||||
\(978\) | −15.6569 | + | 15.6569i | −0.500651 | + | 0.500651i | ||||
\(979\) | 15.8995 | + | 6.58579i | 0.508150 | + | 0.210483i | ||||
\(980\) | 0.192388 | − | 0.464466i | 0.00614561 | − | 0.0148368i | ||||
\(981\) | −26.2635 | + | 10.8787i | −0.838528 | + | 0.347330i | ||||
\(982\) | − | 89.5980i | − | 2.85919i | ||||||
\(983\) | −3.72792 | − | 9.00000i | −0.118902 | − | 0.287055i | 0.853212 | − | 0.521565i | \(-0.174652\pi\) |
−0.972114 | + | 0.234510i | \(0.924652\pi\) | |||||||
\(984\) | 4.10051 | + | 4.10051i | 0.130719 | + | 0.130719i | ||||
\(985\) | 3.55635 | 0.113315 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.6274 | −0.465596 | ||||||||
\(988\) | 3.17157 | + | 3.17157i | 0.100901 | + | 0.100901i | ||||
\(989\) | 1.51472 | + | 3.65685i | 0.0481653 | + | 0.116281i | ||||
\(990\) | 8.82843i | 0.280586i | ||||||||
\(991\) | −37.7279 | + | 15.6274i | −1.19847 | + | 0.496421i | −0.890503 | − | 0.454977i | \(-0.849648\pi\) |
−0.307964 | + | 0.951398i | \(0.599648\pi\) | |||||||
\(992\) | 4.75736 | − | 11.4853i | 0.151046 | − | 0.364658i | ||||
\(993\) | 21.7990 | + | 9.02944i | 0.691770 | + | 0.286541i | ||||
\(994\) | 24.1421 | − | 24.1421i | 0.765742 | − | 0.765742i | ||||
\(995\) | −6.24264 | + | 6.24264i | −0.197905 | + | 0.197905i | ||||
\(996\) | 44.6274 | + | 18.4853i | 1.41407 | + | 0.585729i | ||||
\(997\) | 2.87868 | − | 6.94975i | 0.0911687 | − | 0.220101i | −0.871717 | − | 0.490009i | \(-0.836993\pi\) |
0.962886 | + | 0.269908i | \(0.0869934\pi\) | |||||||
\(998\) | −47.8701 | + | 19.8284i | −1.51530 | + | 0.627658i | ||||
\(999\) | 48.2843i | 1.52765i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))