Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,2,Mod(274,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("975.274");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.78541419707\) |
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: | \( 2 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.2 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 975.274 |
Dual form | 975.2.c.h.274.3 |
$q$-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 \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(326\) | \(352\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 0.414214i | − 0.292893i | −0.989219 | − | 0.146447i | \(-0.953216\pi\) | ||||
0.989219 | − | 0.146447i | \(-0.0467837\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.82843 | 0.914214 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.414214 | 0.169102 | ||||||||
\(7\) | − 2.82843i | − 1.06904i | −0.845154 | − | 0.534522i | \(-0.820491\pi\) | ||||
0.845154 | − | 0.534522i | \(-0.179509\pi\) | |||||||
\(8\) | − 1.58579i | − 0.560660i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 1.82843i | 0.527821i | ||||||||
\(13\) | − 1.00000i | − 0.277350i | ||||||||
\(14\) | −1.17157 | −0.313116 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | − 7.65685i | − 1.85706i | −0.371257 | − | 0.928530i | \(-0.621073\pi\) | ||||
0.371257 | − | 0.928530i | \(-0.378927\pi\) | |||||||
\(18\) | 0.414214i | 0.0976311i | ||||||||
\(19\) | 2.82843 | 0.648886 | 0.324443 | − | 0.945905i | \(-0.394823\pi\) | ||||
0.324443 | + | 0.945905i | \(0.394823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.82843 | 0.617213 | ||||||||
\(22\) | 0.828427i | 0.176621i | ||||||||
\(23\) | − 4.00000i | − 0.834058i | −0.908893 | − | 0.417029i | \(-0.863071\pi\) | ||||
0.908893 | − | 0.417029i | \(-0.136929\pi\) | |||||||
\(24\) | 1.58579 | 0.323697 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.414214 | −0.0812340 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | − 5.17157i | − 0.977335i | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.17157 | −0.210421 | −0.105210 | − | 0.994450i | \(-0.533552\pi\) | ||||
−0.105210 | + | 0.994450i | \(0.533552\pi\) | |||||||
\(32\) | − 4.41421i | − 0.780330i | ||||||||
\(33\) | − 2.00000i | − 0.348155i | ||||||||
\(34\) | −3.17157 | −0.543920 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.82843 | −0.304738 | ||||||||
\(37\) | 7.65685i | 1.25878i | 0.777090 | + | 0.629390i | \(0.216695\pi\) | ||||
−0.777090 | + | 0.629390i | \(0.783305\pi\) | |||||||
\(38\) | − 1.17157i | − 0.190054i | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.17157 | 0.807664 | 0.403832 | − | 0.914833i | \(-0.367678\pi\) | ||||
0.403832 | + | 0.914833i | \(0.367678\pi\) | |||||||
\(42\) | − 1.17157i | − 0.180778i | ||||||||
\(43\) | − 1.65685i | − 0.252668i | −0.991988 | − | 0.126334i | \(-0.959679\pi\) | ||||
0.991988 | − | 0.126334i | \(-0.0403211\pi\) | |||||||
\(44\) | −3.65685 | −0.551292 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.65685 | −0.244290 | ||||||||
\(47\) | 11.6569i | 1.70033i | 0.526519 | + | 0.850163i | \(0.323497\pi\) | ||||
−0.526519 | + | 0.850163i | \(0.676503\pi\) | |||||||
\(48\) | 3.00000i | 0.433013i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.65685 | 1.07217 | ||||||||
\(52\) | − 1.82843i | − 0.253557i | ||||||||
\(53\) | − 2.00000i | − 0.274721i | −0.990521 | − | 0.137361i | \(-0.956138\pi\) | ||||
0.990521 | − | 0.137361i | \(-0.0438619\pi\) | |||||||
\(54\) | −0.414214 | −0.0563673 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.48528 | −0.599371 | ||||||||
\(57\) | 2.82843i | 0.374634i | ||||||||
\(58\) | 0.828427i | 0.108778i | ||||||||
\(59\) | −7.65685 | −0.996838 | −0.498419 | − | 0.866936i | \(-0.666086\pi\) | ||||
−0.498419 | + | 0.866936i | \(0.666086\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.3137 | 1.70465 | 0.852323 | − | 0.523016i | \(-0.175193\pi\) | ||||
0.852323 | + | 0.523016i | \(0.175193\pi\) | |||||||
\(62\) | 0.485281i | 0.0616308i | ||||||||
\(63\) | 2.82843i | 0.356348i | ||||||||
\(64\) | 4.17157 | 0.521447 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.828427 | −0.101972 | ||||||||
\(67\) | − 6.82843i | − 0.834225i | −0.908855 | − | 0.417113i | \(-0.863042\pi\) | ||||
0.908855 | − | 0.417113i | \(-0.136958\pi\) | |||||||
\(68\) | − 14.0000i | − 1.69775i | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 1.58579i | 0.186887i | ||||||||
\(73\) | 0.343146i | 0.0401622i | 0.999798 | + | 0.0200811i | \(0.00639244\pi\) | ||||
−0.999798 | + | 0.0200811i | \(0.993608\pi\) | |||||||
\(74\) | 3.17157 | 0.368688 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.17157 | 0.593220 | ||||||||
\(77\) | 5.65685i | 0.644658i | ||||||||
\(78\) | − 0.414214i | − 0.0469005i | ||||||||
\(79\) | 11.3137 | 1.27289 | 0.636446 | − | 0.771321i | \(-0.280404\pi\) | ||||
0.636446 | + | 0.771321i | \(0.280404\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 2.14214i | − 0.236559i | ||||||||
\(83\) | 3.65685i | 0.401392i | 0.979654 | + | 0.200696i | \(0.0643203\pi\) | ||||
−0.979654 | + | 0.200696i | \(0.935680\pi\) | |||||||
\(84\) | 5.17157 | 0.564265 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.686292 | −0.0740047 | ||||||||
\(87\) | − 2.00000i | − 0.214423i | ||||||||
\(88\) | 3.17157i | 0.338091i | ||||||||
\(89\) | −14.8284 | −1.57181 | −0.785905 | − | 0.618347i | \(-0.787803\pi\) | ||||
−0.785905 | + | 0.618347i | \(0.787803\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.82843 | −0.296500 | ||||||||
\(92\) | − 7.31371i | − 0.762507i | ||||||||
\(93\) | − 1.17157i | − 0.121486i | ||||||||
\(94\) | 4.82843 | 0.498014 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 4.41421 | 0.450524 | ||||||||
\(97\) | − 3.65685i | − 0.371297i | −0.982616 | − | 0.185649i | \(-0.940561\pi\) | ||||
0.982616 | − | 0.185649i | \(-0.0594386\pi\) | |||||||
\(98\) | 0.414214i | 0.0418419i | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.65685 | 0.761885 | 0.380943 | − | 0.924599i | \(-0.375599\pi\) | ||||
0.380943 | + | 0.924599i | \(0.375599\pi\) | |||||||
\(102\) | − 3.17157i | − 0.314033i | ||||||||
\(103\) | 2.34315i | 0.230877i | 0.993315 | + | 0.115439i | \(0.0368273\pi\) | ||||
−0.993315 | + | 0.115439i | \(0.963173\pi\) | |||||||
\(104\) | −1.58579 | −0.155499 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.828427 | −0.0804640 | ||||||||
\(107\) | 11.3137i | 1.09374i | 0.837218 | + | 0.546869i | \(0.184180\pi\) | ||||
−0.837218 | + | 0.546869i | \(0.815820\pi\) | |||||||
\(108\) | − 1.82843i | − 0.175940i | ||||||||
\(109\) | −5.31371 | −0.508961 | −0.254480 | − | 0.967078i | \(-0.581904\pi\) | ||||
−0.254480 | + | 0.967078i | \(0.581904\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.65685 | −0.726756 | ||||||||
\(112\) | − 8.48528i | − 0.801784i | ||||||||
\(113\) | − 5.31371i | − 0.499872i | −0.968262 | − | 0.249936i | \(-0.919590\pi\) | ||||
0.968262 | − | 0.249936i | \(-0.0804095\pi\) | |||||||
\(114\) | 1.17157 | 0.109728 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.65685 | −0.339530 | ||||||||
\(117\) | 1.00000i | 0.0924500i | ||||||||
\(118\) | 3.17157i | 0.291967i | ||||||||
\(119\) | −21.6569 | −1.98528 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | − 5.51472i | − 0.499279i | ||||||||
\(123\) | 5.17157i | 0.466305i | ||||||||
\(124\) | −2.14214 | −0.192369 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.17157 | 0.104372 | ||||||||
\(127\) | − 5.65685i | − 0.501965i | −0.967992 | − | 0.250982i | \(-0.919246\pi\) | ||||
0.967992 | − | 0.250982i | \(-0.0807536\pi\) | |||||||
\(128\) | − 10.5563i | − 0.933058i | ||||||||
\(129\) | 1.65685 | 0.145878 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.00000 | −0.698963 | −0.349482 | − | 0.936943i | \(-0.613642\pi\) | ||||
−0.349482 | + | 0.936943i | \(0.613642\pi\) | |||||||
\(132\) | − 3.65685i | − 0.318288i | ||||||||
\(133\) | − 8.00000i | − 0.693688i | ||||||||
\(134\) | −2.82843 | −0.244339 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.1421 | −1.04118 | ||||||||
\(137\) | 10.8284i | 0.925135i | 0.886584 | + | 0.462567i | \(0.153072\pi\) | ||||
−0.886584 | + | 0.462567i | \(0.846928\pi\) | |||||||
\(138\) | − 1.65685i | − 0.141041i | ||||||||
\(139\) | 7.31371 | 0.620341 | 0.310170 | − | 0.950681i | \(-0.399614\pi\) | ||||
0.310170 | + | 0.950681i | \(0.399614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.6569 | −0.981684 | ||||||||
\(142\) | − 0.828427i | − 0.0695201i | ||||||||
\(143\) | 2.00000i | 0.167248i | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.142136 | 0.0117632 | ||||||||
\(147\) | − 1.00000i | − 0.0824786i | ||||||||
\(148\) | 14.0000i | 1.15079i | ||||||||
\(149\) | 9.17157 | 0.751365 | 0.375682 | − | 0.926749i | \(-0.377408\pi\) | ||||
0.375682 | + | 0.926749i | \(0.377408\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.51472 | −0.286024 | −0.143012 | − | 0.989721i | \(-0.545679\pi\) | ||||
−0.143012 | + | 0.989721i | \(0.545679\pi\) | |||||||
\(152\) | − 4.48528i | − 0.363804i | ||||||||
\(153\) | 7.65685i | 0.619020i | ||||||||
\(154\) | 2.34315 | 0.188816 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.82843 | 0.146391 | ||||||||
\(157\) | 10.0000i | 0.798087i | 0.916932 | + | 0.399043i | \(0.130658\pi\) | ||||
−0.916932 | + | 0.399043i | \(0.869342\pi\) | |||||||
\(158\) | − 4.68629i | − 0.372821i | ||||||||
\(159\) | 2.00000 | 0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.3137 | −0.891645 | ||||||||
\(162\) | − 0.414214i | − 0.0325437i | ||||||||
\(163\) | 18.8284i | 1.47476i | 0.675480 | + | 0.737378i | \(0.263936\pi\) | ||||
−0.675480 | + | 0.737378i | \(0.736064\pi\) | |||||||
\(164\) | 9.45584 | 0.738377 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.51472 | 0.117565 | ||||||||
\(167\) | 3.65685i | 0.282976i | 0.989940 | + | 0.141488i | \(0.0451886\pi\) | ||||
−0.989940 | + | 0.141488i | \(0.954811\pi\) | |||||||
\(168\) | − 4.48528i | − 0.346047i | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.82843 | −0.216295 | ||||||||
\(172\) | − 3.02944i | − 0.230992i | ||||||||
\(173\) | − 11.6569i | − 0.886254i | −0.896459 | − | 0.443127i | \(-0.853869\pi\) | ||||
0.896459 | − | 0.443127i | \(-0.146131\pi\) | |||||||
\(174\) | −0.828427 | −0.0628029 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.00000 | −0.452267 | ||||||||
\(177\) | − 7.65685i | − 0.575524i | ||||||||
\(178\) | 6.14214i | 0.460373i | ||||||||
\(179\) | 23.3137 | 1.74255 | 0.871274 | − | 0.490797i | \(-0.163294\pi\) | ||||
0.871274 | + | 0.490797i | \(0.163294\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 1.17157i | 0.0868428i | ||||||||
\(183\) | 13.3137i | 0.984178i | ||||||||
\(184\) | −6.34315 | −0.467623 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.485281 | −0.0355826 | ||||||||
\(187\) | 15.3137i | 1.11985i | ||||||||
\(188\) | 21.3137i | 1.55446i | ||||||||
\(189\) | −2.82843 | −0.205738 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.31371 | 0.239772 | 0.119886 | − | 0.992788i | \(-0.461747\pi\) | ||||
0.119886 | + | 0.992788i | \(0.461747\pi\) | |||||||
\(192\) | 4.17157i | 0.301057i | ||||||||
\(193\) | 5.31371i | 0.382489i | 0.981542 | + | 0.191245i | \(0.0612524\pi\) | ||||
−0.981542 | + | 0.191245i | \(0.938748\pi\) | |||||||
\(194\) | −1.51472 | −0.108750 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.82843 | −0.130602 | ||||||||
\(197\) | − 0.485281i | − 0.0345749i | −0.999851 | − | 0.0172874i | \(-0.994497\pi\) | ||||
0.999851 | − | 0.0172874i | \(-0.00550304\pi\) | |||||||
\(198\) | − 0.828427i | − 0.0588738i | ||||||||
\(199\) | −21.6569 | −1.53521 | −0.767607 | − | 0.640921i | \(-0.778553\pi\) | ||||
−0.767607 | + | 0.640921i | \(0.778553\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.82843 | 0.481640 | ||||||||
\(202\) | − 3.17157i | − 0.223151i | ||||||||
\(203\) | 5.65685i | 0.397033i | ||||||||
\(204\) | 14.0000 | 0.980196 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.970563 | 0.0676223 | ||||||||
\(207\) | 4.00000i | 0.278019i | ||||||||
\(208\) | − 3.00000i | − 0.208013i | ||||||||
\(209\) | −5.65685 | −0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | − 3.65685i | − 0.251154i | ||||||||
\(213\) | 2.00000i | 0.137038i | ||||||||
\(214\) | 4.68629 | 0.320348 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.58579 | −0.107899 | ||||||||
\(217\) | 3.31371i | 0.224949i | ||||||||
\(218\) | 2.20101i | 0.149071i | ||||||||
\(219\) | −0.343146 | −0.0231876 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.65685 | −0.515056 | ||||||||
\(222\) | 3.17157i | 0.212862i | ||||||||
\(223\) | − 12.4853i | − 0.836076i | −0.908429 | − | 0.418038i | \(-0.862718\pi\) | ||||
0.908429 | − | 0.418038i | \(-0.137282\pi\) | |||||||
\(224\) | −12.4853 | −0.834208 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.20101 | −0.146409 | ||||||||
\(227\) | 17.3137i | 1.14915i | 0.818452 | + | 0.574576i | \(0.194833\pi\) | ||||
−0.818452 | + | 0.574576i | \(0.805167\pi\) | |||||||
\(228\) | 5.17157i | 0.342496i | ||||||||
\(229\) | 1.31371 | 0.0868123 | 0.0434062 | − | 0.999058i | \(-0.486179\pi\) | ||||
0.0434062 | + | 0.999058i | \(0.486179\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.65685 | −0.372194 | ||||||||
\(232\) | 3.17157i | 0.208224i | ||||||||
\(233\) | 6.97056i | 0.456657i | 0.973584 | + | 0.228328i | \(0.0733260\pi\) | ||||
−0.973584 | + | 0.228328i | \(0.926674\pi\) | |||||||
\(234\) | 0.414214 | 0.0270780 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −14.0000 | −0.911322 | ||||||||
\(237\) | 11.3137i | 0.734904i | ||||||||
\(238\) | 8.97056i | 0.581475i | ||||||||
\(239\) | −2.00000 | −0.129369 | −0.0646846 | − | 0.997906i | \(-0.520604\pi\) | ||||
−0.0646846 | + | 0.997906i | \(0.520604\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.343146 | 0.0221040 | 0.0110520 | − | 0.999939i | \(-0.496482\pi\) | ||||
0.0110520 | + | 0.999939i | \(0.496482\pi\) | |||||||
\(242\) | 2.89949i | 0.186387i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 24.3431 | 1.55841 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.14214 | 0.136578 | ||||||||
\(247\) | − 2.82843i | − 0.179969i | ||||||||
\(248\) | 1.85786i | 0.117975i | ||||||||
\(249\) | −3.65685 | −0.231744 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 5.17157i | 0.325778i | ||||||||
\(253\) | 8.00000i | 0.502956i | ||||||||
\(254\) | −2.34315 | −0.147022 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | 4.34315i | 0.270918i | 0.990783 | + | 0.135459i | \(0.0432509\pi\) | ||||
−0.990783 | + | 0.135459i | \(0.956749\pi\) | |||||||
\(258\) | − 0.686292i | − 0.0427266i | ||||||||
\(259\) | 21.6569 | 1.34569 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | 3.31371i | 0.204722i | ||||||||
\(263\) | 12.0000i | 0.739952i | 0.929041 | + | 0.369976i | \(0.120634\pi\) | ||||
−0.929041 | + | 0.369976i | \(0.879366\pi\) | |||||||
\(264\) | −3.17157 | −0.195197 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.31371 | −0.203177 | ||||||||
\(267\) | − 14.8284i | − 0.907485i | ||||||||
\(268\) | − 12.4853i | − 0.762660i | ||||||||
\(269\) | −18.0000 | −1.09748 | −0.548740 | − | 0.835993i | \(-0.684892\pi\) | ||||
−0.548740 | + | 0.835993i | \(0.684892\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.7990 | −1.68867 | −0.844334 | − | 0.535817i | \(-0.820004\pi\) | ||||
−0.844334 | + | 0.535817i | \(0.820004\pi\) | |||||||
\(272\) | − 22.9706i | − 1.39279i | ||||||||
\(273\) | − 2.82843i | − 0.171184i | ||||||||
\(274\) | 4.48528 | 0.270966 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 7.31371 | 0.440234 | ||||||||
\(277\) | 2.00000i | 0.120168i | 0.998193 | + | 0.0600842i | \(0.0191369\pi\) | ||||
−0.998193 | + | 0.0600842i | \(0.980863\pi\) | |||||||
\(278\) | − 3.02944i | − 0.181694i | ||||||||
\(279\) | 1.17157 | 0.0701402 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.1716 | 1.26299 | 0.631495 | − | 0.775380i | \(-0.282442\pi\) | ||||
0.631495 | + | 0.775380i | \(0.282442\pi\) | |||||||
\(282\) | 4.82843i | 0.287529i | ||||||||
\(283\) | 28.9706i | 1.72212i | 0.508502 | + | 0.861061i | \(0.330199\pi\) | ||||
−0.508502 | + | 0.861061i | \(0.669801\pi\) | |||||||
\(284\) | 3.65685 | 0.216994 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.828427 | 0.0489859 | ||||||||
\(287\) | − 14.6274i | − 0.863429i | ||||||||
\(288\) | 4.41421i | 0.260110i | ||||||||
\(289\) | −41.6274 | −2.44867 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.65685 | 0.214369 | ||||||||
\(292\) | 0.627417i | 0.0367168i | ||||||||
\(293\) | 2.14214i | 0.125145i | 0.998040 | + | 0.0625724i | \(0.0199304\pi\) | ||||
−0.998040 | + | 0.0625724i | \(0.980070\pi\) | |||||||
\(294\) | −0.414214 | −0.0241574 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 12.1421 | 0.705747 | ||||||||
\(297\) | 2.00000i | 0.116052i | ||||||||
\(298\) | − 3.79899i | − 0.220070i | ||||||||
\(299\) | −4.00000 | −0.231326 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.68629 | −0.270113 | ||||||||
\(302\) | 1.45584i | 0.0837744i | ||||||||
\(303\) | 7.65685i | 0.439875i | ||||||||
\(304\) | 8.48528 | 0.486664 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.17157 | 0.181307 | ||||||||
\(307\) | 22.8284i | 1.30289i | 0.758697 | + | 0.651444i | \(0.225836\pi\) | ||||
−0.758697 | + | 0.651444i | \(0.774164\pi\) | |||||||
\(308\) | 10.3431i | 0.589355i | ||||||||
\(309\) | −2.34315 | −0.133297 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.6274 | −0.602626 | −0.301313 | − | 0.953525i | \(-0.597425\pi\) | ||||
−0.301313 | + | 0.953525i | \(0.597425\pi\) | |||||||
\(312\) | − 1.58579i | − 0.0897775i | ||||||||
\(313\) | 6.00000i | 0.339140i | 0.985518 | + | 0.169570i | \(0.0542379\pi\) | ||||
−0.985518 | + | 0.169570i | \(0.945762\pi\) | |||||||
\(314\) | 4.14214 | 0.233754 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 20.6863 | 1.16369 | ||||||||
\(317\) | − 8.48528i | − 0.476581i | −0.971194 | − | 0.238290i | \(-0.923413\pi\) | ||||
0.971194 | − | 0.238290i | \(-0.0765870\pi\) | |||||||
\(318\) | − 0.828427i | − 0.0464559i | ||||||||
\(319\) | 4.00000 | 0.223957 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.3137 | −0.631470 | ||||||||
\(322\) | 4.68629i | 0.261157i | ||||||||
\(323\) | − 21.6569i | − 1.20502i | ||||||||
\(324\) | 1.82843 | 0.101579 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.79899 | 0.431946 | ||||||||
\(327\) | − 5.31371i | − 0.293849i | ||||||||
\(328\) | − 8.20101i | − 0.452825i | ||||||||
\(329\) | 32.9706 | 1.81773 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.1421 | 1.43690 | 0.718451 | − | 0.695578i | \(-0.244852\pi\) | ||||
0.718451 | + | 0.695578i | \(0.244852\pi\) | |||||||
\(332\) | 6.68629i | 0.366958i | ||||||||
\(333\) | − 7.65685i | − 0.419593i | ||||||||
\(334\) | 1.51472 | 0.0828817 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 8.48528 | 0.462910 | ||||||||
\(337\) | − 9.31371i | − 0.507350i | −0.967290 | − | 0.253675i | \(-0.918361\pi\) | ||||
0.967290 | − | 0.253675i | \(-0.0816394\pi\) | |||||||
\(338\) | 0.414214i | 0.0225302i | ||||||||
\(339\) | 5.31371 | 0.288601 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.34315 | 0.126888 | ||||||||
\(342\) | 1.17157i | 0.0633514i | ||||||||
\(343\) | − 16.9706i | − 0.916324i | ||||||||
\(344\) | −2.62742 | −0.141661 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.82843 | −0.259578 | ||||||||
\(347\) | 8.68629i | 0.466305i | 0.972440 | + | 0.233152i | \(0.0749041\pi\) | ||||
−0.972440 | + | 0.233152i | \(0.925096\pi\) | |||||||
\(348\) | − 3.65685i | − 0.196028i | ||||||||
\(349\) | −3.65685 | −0.195747 | −0.0978735 | − | 0.995199i | \(-0.531204\pi\) | ||||
−0.0978735 | + | 0.995199i | \(0.531204\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 8.82843i | 0.470557i | ||||||||
\(353\) | − 33.4558i | − 1.78067i | −0.455301 | − | 0.890337i | \(-0.650468\pi\) | ||||
0.455301 | − | 0.890337i | \(-0.349532\pi\) | |||||||
\(354\) | −3.17157 | −0.168567 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −27.1127 | −1.43697 | ||||||||
\(357\) | − 21.6569i | − 1.14620i | ||||||||
\(358\) | − 9.65685i | − 0.510381i | ||||||||
\(359\) | −34.9706 | −1.84568 | −0.922838 | − | 0.385189i | \(-0.874136\pi\) | ||||
−0.922838 | + | 0.385189i | \(0.874136\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | − 5.79899i | − 0.304788i | ||||||||
\(363\) | − 7.00000i | − 0.367405i | ||||||||
\(364\) | −5.17157 | −0.271064 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.51472 | 0.288259 | ||||||||
\(367\) | 24.0000i | 1.25279i | 0.779506 | + | 0.626395i | \(0.215470\pi\) | ||||
−0.779506 | + | 0.626395i | \(0.784530\pi\) | |||||||
\(368\) | − 12.0000i | − 0.625543i | ||||||||
\(369\) | −5.17157 | −0.269221 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.65685 | −0.293689 | ||||||||
\(372\) | − 2.14214i | − 0.111065i | ||||||||
\(373\) | 10.0000i | 0.517780i | 0.965907 | + | 0.258890i | \(0.0833568\pi\) | ||||
−0.965907 | + | 0.258890i | \(0.916643\pi\) | |||||||
\(374\) | 6.34315 | 0.327996 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.4853 | 0.953306 | ||||||||
\(377\) | 2.00000i | 0.103005i | ||||||||
\(378\) | 1.17157i | 0.0602592i | ||||||||
\(379\) | −0.485281 | −0.0249272 | −0.0124636 | − | 0.999922i | \(-0.503967\pi\) | ||||
−0.0124636 | + | 0.999922i | \(0.503967\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.65685 | 0.289809 | ||||||||
\(382\) | − 1.37258i | − 0.0702275i | ||||||||
\(383\) | 30.9706i | 1.58252i | 0.611479 | + | 0.791261i | \(0.290575\pi\) | ||||
−0.611479 | + | 0.791261i | \(0.709425\pi\) | |||||||
\(384\) | 10.5563 | 0.538701 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.20101 | 0.112028 | ||||||||
\(387\) | 1.65685i | 0.0842226i | ||||||||
\(388\) | − 6.68629i | − 0.339445i | ||||||||
\(389\) | 26.9706 | 1.36746 | 0.683731 | − | 0.729734i | \(-0.260356\pi\) | ||||
0.683731 | + | 0.729734i | \(0.260356\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.6274 | −1.54890 | ||||||||
\(392\) | 1.58579i | 0.0800943i | ||||||||
\(393\) | − 8.00000i | − 0.403547i | ||||||||
\(394\) | −0.201010 | −0.0101267 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.65685 | 0.183764 | ||||||||
\(397\) | − 30.9706i | − 1.55437i | −0.629273 | − | 0.777184i | \(-0.716647\pi\) | ||||
0.629273 | − | 0.777184i | \(-0.283353\pi\) | |||||||
\(398\) | 8.97056i | 0.449654i | ||||||||
\(399\) | 8.00000 | 0.400501 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.1421 | 1.30548 | 0.652738 | − | 0.757584i | \(-0.273620\pi\) | ||||
0.652738 | + | 0.757584i | \(0.273620\pi\) | |||||||
\(402\) | − 2.82843i | − 0.141069i | ||||||||
\(403\) | 1.17157i | 0.0583602i | ||||||||
\(404\) | 14.0000 | 0.696526 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.34315 | 0.116288 | ||||||||
\(407\) | − 15.3137i | − 0.759072i | ||||||||
\(408\) | − 12.1421i | − 0.601125i | ||||||||
\(409\) | 34.9706 | 1.72918 | 0.864592 | − | 0.502475i | \(-0.167577\pi\) | ||||
0.864592 | + | 0.502475i | \(0.167577\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.8284 | −0.534127 | ||||||||
\(412\) | 4.28427i | 0.211071i | ||||||||
\(413\) | 21.6569i | 1.06566i | ||||||||
\(414\) | 1.65685 | 0.0814299 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.41421 | −0.216425 | ||||||||
\(417\) | 7.31371i | 0.358154i | ||||||||
\(418\) | 2.34315i | 0.114607i | ||||||||
\(419\) | −14.6274 | −0.714596 | −0.357298 | − | 0.933990i | \(-0.616302\pi\) | ||||
−0.357298 | + | 0.933990i | \(0.616302\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.3137 | 1.81856 | 0.909279 | − | 0.416186i | \(-0.136634\pi\) | ||||
0.909279 | + | 0.416186i | \(0.136634\pi\) | |||||||
\(422\) | 4.97056i | 0.241963i | ||||||||
\(423\) | − 11.6569i | − 0.566776i | ||||||||
\(424\) | −3.17157 | −0.154025 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.828427 | 0.0401374 | ||||||||
\(427\) | − 37.6569i | − 1.82234i | ||||||||
\(428\) | 20.6863i | 0.999910i | ||||||||
\(429\) | −2.00000 | −0.0965609 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.34315 | 0.401875 | 0.200938 | − | 0.979604i | \(-0.435601\pi\) | ||||
0.200938 | + | 0.979604i | \(0.435601\pi\) | |||||||
\(432\) | − 3.00000i | − 0.144338i | ||||||||
\(433\) | − 21.3137i | − 1.02427i | −0.858905 | − | 0.512136i | \(-0.828854\pi\) | ||||
0.858905 | − | 0.512136i | \(-0.171146\pi\) | |||||||
\(434\) | 1.37258 | 0.0658861 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.71573 | −0.465299 | ||||||||
\(437\) | − 11.3137i | − 0.541208i | ||||||||
\(438\) | 0.142136i | 0.00679150i | ||||||||
\(439\) | −16.9706 | −0.809961 | −0.404980 | − | 0.914325i | \(-0.632722\pi\) | ||||
−0.404980 | + | 0.914325i | \(0.632722\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 3.17157i | 0.150856i | ||||||||
\(443\) | − 25.9411i | − 1.23250i | −0.787551 | − | 0.616250i | \(-0.788651\pi\) | ||||
0.787551 | − | 0.616250i | \(-0.211349\pi\) | |||||||
\(444\) | −14.0000 | −0.664411 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.17157 | −0.244881 | ||||||||
\(447\) | 9.17157i | 0.433801i | ||||||||
\(448\) | − 11.7990i | − 0.557450i | ||||||||
\(449\) | 31.7990 | 1.50069 | 0.750344 | − | 0.661048i | \(-0.229888\pi\) | ||||
0.750344 | + | 0.661048i | \(0.229888\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.3431 | −0.487040 | ||||||||
\(452\) | − 9.71573i | − 0.456989i | ||||||||
\(453\) | − 3.51472i | − 0.165136i | ||||||||
\(454\) | 7.17157 | 0.336579 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.48528 | 0.210043 | ||||||||
\(457\) | 7.65685i | 0.358173i | 0.983833 | + | 0.179086i | \(0.0573141\pi\) | ||||
−0.983833 | + | 0.179086i | \(0.942686\pi\) | |||||||
\(458\) | − 0.544156i | − 0.0254267i | ||||||||
\(459\) | −7.65685 | −0.357391 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.17157 | 0.240864 | 0.120432 | − | 0.992722i | \(-0.461572\pi\) | ||||
0.120432 | + | 0.992722i | \(0.461572\pi\) | |||||||
\(462\) | 2.34315i | 0.109013i | ||||||||
\(463\) | − 24.4853i | − 1.13793i | −0.822363 | − | 0.568964i | \(-0.807344\pi\) | ||||
0.822363 | − | 0.568964i | \(-0.192656\pi\) | |||||||
\(464\) | −6.00000 | −0.278543 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.88730 | 0.133752 | ||||||||
\(467\) | 8.00000i | 0.370196i | 0.982720 | + | 0.185098i | \(0.0592602\pi\) | ||||
−0.982720 | + | 0.185098i | \(0.940740\pi\) | |||||||
\(468\) | 1.82843i | 0.0845191i | ||||||||
\(469\) | −19.3137 | −0.891824 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.0000 | −0.460776 | ||||||||
\(472\) | 12.1421i | 0.558887i | ||||||||
\(473\) | 3.31371i | 0.152364i | ||||||||
\(474\) | 4.68629 | 0.215248 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −39.5980 | −1.81497 | ||||||||
\(477\) | 2.00000i | 0.0915737i | ||||||||
\(478\) | 0.828427i | 0.0378914i | ||||||||
\(479\) | −25.3137 | −1.15661 | −0.578306 | − | 0.815820i | \(-0.696286\pi\) | ||||
−0.578306 | + | 0.815820i | \(0.696286\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.65685 | 0.349123 | ||||||||
\(482\) | − 0.142136i | − 0.00647410i | ||||||||
\(483\) | − 11.3137i | − 0.514792i | ||||||||
\(484\) | −12.7990 | −0.581772 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.414214 | 0.0187891 | ||||||||
\(487\) | 7.79899i | 0.353406i | 0.984264 | + | 0.176703i | \(0.0565432\pi\) | ||||
−0.984264 | + | 0.176703i | \(0.943457\pi\) | |||||||
\(488\) | − 21.1127i | − 0.955727i | ||||||||
\(489\) | −18.8284 | −0.851451 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.6274 | 1.38220 | 0.691098 | − | 0.722761i | \(-0.257127\pi\) | ||||
0.691098 | + | 0.722761i | \(0.257127\pi\) | |||||||
\(492\) | 9.45584i | 0.426302i | ||||||||
\(493\) | 15.3137i | 0.689695i | ||||||||
\(494\) | −1.17157 | −0.0527116 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.51472 | −0.157816 | ||||||||
\(497\) | − 5.65685i | − 0.253745i | ||||||||
\(498\) | 1.51472i | 0.0678762i | ||||||||
\(499\) | −26.1421 | −1.17028 | −0.585141 | − | 0.810931i | \(-0.698961\pi\) | ||||
−0.585141 | + | 0.810931i | \(0.698961\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.65685 | −0.163376 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 7.31371i | − 0.326102i | −0.986618 | − | 0.163051i | \(-0.947866\pi\) | ||||
0.986618 | − | 0.163051i | \(-0.0521335\pi\) | |||||||
\(504\) | 4.48528 | 0.199790 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.31371 | 0.147312 | ||||||||
\(507\) | − 1.00000i | − 0.0444116i | ||||||||
\(508\) | − 10.3431i | − 0.458903i | ||||||||
\(509\) | −11.7990 | −0.522981 | −0.261491 | − | 0.965206i | \(-0.584214\pi\) | ||||
−0.261491 | + | 0.965206i | \(0.584214\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.970563 | 0.0429352 | ||||||||
\(512\) | − 22.7574i | − 1.00574i | ||||||||
\(513\) | − 2.82843i | − 0.124878i | ||||||||
\(514\) | 1.79899 | 0.0793500 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.02944 | 0.133364 | ||||||||
\(517\) | − 23.3137i | − 1.02534i | ||||||||
\(518\) | − 8.97056i | − 0.394144i | ||||||||
\(519\) | 11.6569 | 0.511679 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.3137 | 1.10901 | 0.554507 | − | 0.832179i | \(-0.312907\pi\) | ||||
0.554507 | + | 0.832179i | \(0.312907\pi\) | |||||||
\(522\) | − 0.828427i | − 0.0362593i | ||||||||
\(523\) | − 15.3137i | − 0.669622i | −0.942285 | − | 0.334811i | \(-0.891328\pi\) | ||||
0.942285 | − | 0.334811i | \(-0.108672\pi\) | |||||||
\(524\) | −14.6274 | −0.639002 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.97056 | 0.216727 | ||||||||
\(527\) | 8.97056i | 0.390764i | ||||||||
\(528\) | − 6.00000i | − 0.261116i | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.65685 | 0.332279 | ||||||||
\(532\) | − 14.6274i | − 0.634179i | ||||||||
\(533\) | − 5.17157i | − 0.224006i | ||||||||
\(534\) | −6.14214 | −0.265796 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −10.8284 | −0.467717 | ||||||||
\(537\) | 23.3137i | 1.00606i | ||||||||
\(538\) | 7.45584i | 0.321444i | ||||||||
\(539\) | 2.00000 | 0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.0000 | 0.429934 | 0.214967 | − | 0.976621i | \(-0.431036\pi\) | ||||
0.214967 | + | 0.976621i | \(0.431036\pi\) | |||||||
\(542\) | 11.5147i | 0.494600i | ||||||||
\(543\) | 14.0000i | 0.600798i | ||||||||
\(544\) | −33.7990 | −1.44912 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.17157 | −0.0501387 | ||||||||
\(547\) | − 23.3137i | − 0.996822i | −0.866941 | − | 0.498411i | \(-0.833917\pi\) | ||||
0.866941 | − | 0.498411i | \(-0.166083\pi\) | |||||||
\(548\) | 19.7990i | 0.845771i | ||||||||
\(549\) | −13.3137 | −0.568215 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.65685 | −0.240990 | ||||||||
\(552\) | − 6.34315i | − 0.269982i | ||||||||
\(553\) | − 32.0000i | − 1.36078i | ||||||||
\(554\) | 0.828427 | 0.0351965 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.3726 | 0.567124 | ||||||||
\(557\) | 7.79899i | 0.330454i | 0.986256 | + | 0.165227i | \(0.0528356\pi\) | ||||
−0.986256 | + | 0.165227i | \(0.947164\pi\) | |||||||
\(558\) | − 0.485281i | − 0.0205436i | ||||||||
\(559\) | −1.65685 | −0.0700775 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.3137 | −0.646545 | ||||||||
\(562\) | − 8.76955i | − 0.369921i | ||||||||
\(563\) | 4.00000i | 0.168580i | 0.996441 | + | 0.0842900i | \(0.0268622\pi\) | ||||
−0.996441 | + | 0.0842900i | \(0.973138\pi\) | |||||||
\(564\) | −21.3137 | −0.897469 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 12.0000 | 0.504398 | ||||||||
\(567\) | − 2.82843i | − 0.118783i | ||||||||
\(568\) | − 3.17157i | − 0.133076i | ||||||||
\(569\) | 42.9706 | 1.80142 | 0.900710 | − | 0.434421i | \(-0.143047\pi\) | ||||
0.900710 | + | 0.434421i | \(0.143047\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.9706 | −0.542801 | −0.271401 | − | 0.962466i | \(-0.587487\pi\) | ||||
−0.271401 | + | 0.962466i | \(0.587487\pi\) | |||||||
\(572\) | 3.65685i | 0.152901i | ||||||||
\(573\) | 3.31371i | 0.138432i | ||||||||
\(574\) | −6.05887 | −0.252893 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.17157 | −0.173816 | ||||||||
\(577\) | 31.9411i | 1.32973i | 0.746965 | + | 0.664863i | \(0.231510\pi\) | ||||
−0.746965 | + | 0.664863i | \(0.768490\pi\) | |||||||
\(578\) | 17.2426i | 0.717199i | ||||||||
\(579\) | −5.31371 | −0.220830 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.3431 | 0.429106 | ||||||||
\(582\) | − 1.51472i | − 0.0627871i | ||||||||
\(583\) | 4.00000i | 0.165663i | ||||||||
\(584\) | 0.544156 | 0.0225173 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.887302 | 0.0366541 | ||||||||
\(587\) | 10.9706i | 0.452804i | 0.974034 | + | 0.226402i | \(0.0726962\pi\) | ||||
−0.974034 | + | 0.226402i | \(0.927304\pi\) | |||||||
\(588\) | − 1.82843i | − 0.0754031i | ||||||||
\(589\) | −3.31371 | −0.136539 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.485281 | 0.0199618 | ||||||||
\(592\) | 22.9706i | 0.944084i | ||||||||
\(593\) | − 20.4853i | − 0.841230i | −0.907239 | − | 0.420615i | \(-0.861814\pi\) | ||||
0.907239 | − | 0.420615i | \(-0.138186\pi\) | |||||||
\(594\) | 0.828427 | 0.0339908 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.7696 | 0.686908 | ||||||||
\(597\) | − 21.6569i | − 0.886356i | ||||||||
\(598\) | 1.65685i | 0.0677538i | ||||||||
\(599\) | 23.3137 | 0.952572 | 0.476286 | − | 0.879290i | \(-0.341983\pi\) | ||||
0.476286 | + | 0.879290i | \(0.341983\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.627417 | −0.0255929 | −0.0127964 | − | 0.999918i | \(-0.504073\pi\) | ||||
−0.0127964 | + | 0.999918i | \(0.504073\pi\) | |||||||
\(602\) | 1.94113i | 0.0791144i | ||||||||
\(603\) | 6.82843i | 0.278075i | ||||||||
\(604\) | −6.42641 | −0.261487 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.17157 | 0.128836 | ||||||||
\(607\) | − 41.9411i | − 1.70234i | −0.524892 | − | 0.851169i | \(-0.675894\pi\) | ||||
0.524892 | − | 0.851169i | \(-0.324106\pi\) | |||||||
\(608\) | − 12.4853i | − 0.506345i | ||||||||
\(609\) | −5.65685 | −0.229227 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.6569 | 0.471586 | ||||||||
\(612\) | 14.0000i | 0.565916i | ||||||||
\(613\) | − 47.6569i | − 1.92484i | −0.271561 | − | 0.962421i | \(-0.587540\pi\) | ||||
0.271561 | − | 0.962421i | \(-0.412460\pi\) | |||||||
\(614\) | 9.45584 | 0.381607 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.97056 | 0.361434 | ||||||||
\(617\) | 34.8284i | 1.40214i | 0.713093 | + | 0.701070i | \(0.247294\pi\) | ||||
−0.713093 | + | 0.701070i | \(0.752706\pi\) | |||||||
\(618\) | 0.970563i | 0.0390418i | ||||||||
\(619\) | −23.7990 | −0.956562 | −0.478281 | − | 0.878207i | \(-0.658740\pi\) | ||||
−0.478281 | + | 0.878207i | \(0.658740\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | 4.40202i | 0.176505i | ||||||||
\(623\) | 41.9411i | 1.68034i | ||||||||
\(624\) | 3.00000 | 0.120096 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.48528 | 0.0993318 | ||||||||
\(627\) | − 5.65685i | − 0.225913i | ||||||||
\(628\) | 18.2843i | 0.729622i | ||||||||
\(629\) | 58.6274 | 2.33763 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.1127 | 1.71629 | 0.858145 | − | 0.513408i | \(-0.171617\pi\) | ||||
0.858145 | + | 0.513408i | \(0.171617\pi\) | |||||||
\(632\) | − 17.9411i | − 0.713660i | ||||||||
\(633\) | − 12.0000i | − 0.476957i | ||||||||
\(634\) | −3.51472 | −0.139587 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.65685 | 0.145004 | ||||||||
\(637\) | 1.00000i | 0.0396214i | ||||||||
\(638\) | − 1.65685i | − 0.0655955i | ||||||||
\(639\) | −2.00000 | −0.0791188 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.2843 | 1.19616 | 0.598078 | − | 0.801438i | \(-0.295931\pi\) | ||||
0.598078 | + | 0.801438i | \(0.295931\pi\) | |||||||
\(642\) | 4.68629i | 0.184953i | ||||||||
\(643\) | 22.8284i | 0.900265i | 0.892962 | + | 0.450133i | \(0.148623\pi\) | ||||
−0.892962 | + | 0.450133i | \(0.851377\pi\) | |||||||
\(644\) | −20.6863 | −0.815154 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.97056 | −0.352942 | ||||||||
\(647\) | − 11.3137i | − 0.444788i | −0.974957 | − | 0.222394i | \(-0.928613\pi\) | ||||
0.974957 | − | 0.222394i | \(-0.0713871\pi\) | |||||||
\(648\) | − 1.58579i | − 0.0622956i | ||||||||
\(649\) | 15.3137 | 0.601116 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.31371 | −0.129874 | ||||||||
\(652\) | 34.4264i | 1.34824i | ||||||||
\(653\) | − 25.3137i | − 0.990602i | −0.868721 | − | 0.495301i | \(-0.835058\pi\) | ||||
0.868721 | − | 0.495301i | \(-0.164942\pi\) | |||||||
\(654\) | −2.20101 | −0.0860663 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 15.5147 | 0.605748 | ||||||||
\(657\) | − 0.343146i | − 0.0133874i | ||||||||
\(658\) | − 13.6569i | − 0.532400i | ||||||||
\(659\) | 47.3137 | 1.84308 | 0.921540 | − | 0.388283i | \(-0.126932\pi\) | ||||
0.921540 | + | 0.388283i | \(0.126932\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.9706 | −1.36020 | −0.680099 | − | 0.733121i | \(-0.738063\pi\) | ||||
−0.680099 | + | 0.733121i | \(0.738063\pi\) | |||||||
\(662\) | − 10.8284i | − 0.420859i | ||||||||
\(663\) | − 7.65685i | − 0.297368i | ||||||||
\(664\) | 5.79899 | 0.225044 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.17157 | −0.122896 | ||||||||
\(667\) | 8.00000i | 0.309761i | ||||||||
\(668\) | 6.68629i | 0.258700i | ||||||||
\(669\) | 12.4853 | 0.482709 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.6274 | −1.02794 | ||||||||
\(672\) | − 12.4853i | − 0.481630i | ||||||||
\(673\) | 16.6274i | 0.640940i | 0.947259 | + | 0.320470i | \(0.103841\pi\) | ||||
−0.947259 | + | 0.320470i | \(0.896159\pi\) | |||||||
\(674\) | −3.85786 | −0.148599 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.82843 | −0.0703241 | ||||||||
\(677\) | − 26.6863i | − 1.02564i | −0.858497 | − | 0.512819i | \(-0.828601\pi\) | ||||
0.858497 | − | 0.512819i | \(-0.171399\pi\) | |||||||
\(678\) | − 2.20101i | − 0.0845293i | ||||||||
\(679\) | −10.3431 | −0.396934 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.3137 | −0.663463 | ||||||||
\(682\) | − 0.970563i | − 0.0371648i | ||||||||
\(683\) | 47.9411i | 1.83442i | 0.398408 | + | 0.917208i | \(0.369563\pi\) | ||||
−0.398408 | + | 0.917208i | \(0.630437\pi\) | |||||||
\(684\) | −5.17157 | −0.197740 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −7.02944 | −0.268385 | ||||||||
\(687\) | 1.31371i | 0.0501211i | ||||||||
\(688\) | − 4.97056i | − 0.189501i | ||||||||
\(689\) | −2.00000 | −0.0761939 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.85786 | −0.222844 | −0.111422 | − | 0.993773i | \(-0.535540\pi\) | ||||
−0.111422 | + | 0.993773i | \(0.535540\pi\) | |||||||
\(692\) | − 21.3137i | − 0.810226i | ||||||||
\(693\) | − 5.65685i | − 0.214886i | ||||||||
\(694\) | 3.59798 | 0.136577 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.17157 | −0.120218 | ||||||||
\(697\) | − 39.5980i | − 1.49988i | ||||||||
\(698\) | 1.51472i | 0.0573329i | ||||||||
\(699\) | −6.97056 | −0.263651 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.02944 | 0.189959 | 0.0949796 | − | 0.995479i | \(-0.469721\pi\) | ||||
0.0949796 | + | 0.995479i | \(0.469721\pi\) | |||||||
\(702\) | 0.414214i | 0.0156335i | ||||||||
\(703\) | 21.6569i | 0.816804i | ||||||||
\(704\) | −8.34315 | −0.314444 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.8579 | −0.521548 | ||||||||
\(707\) | − 21.6569i | − 0.814490i | ||||||||
\(708\) | − 14.0000i | − 0.526152i | ||||||||
\(709\) | 4.62742 | 0.173786 | 0.0868931 | − | 0.996218i | \(-0.472306\pi\) | ||||
0.0868931 | + | 0.996218i | \(0.472306\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.3137 | −0.424297 | ||||||||
\(712\) | 23.5147i | 0.881251i | ||||||||
\(713\) | 4.68629i | 0.175503i | ||||||||
\(714\) | −8.97056 | −0.335715 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 42.6274 | 1.59306 | ||||||||
\(717\) | − 2.00000i | − 0.0746914i | ||||||||
\(718\) | 14.4853i | 0.540586i | ||||||||
\(719\) | 29.9411 | 1.11662 | 0.558308 | − | 0.829634i | \(-0.311451\pi\) | ||||
0.558308 | + | 0.829634i | \(0.311451\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.62742 | 0.246818 | ||||||||
\(722\) | 4.55635i | 0.169570i | ||||||||
\(723\) | 0.343146i | 0.0127617i | ||||||||
\(724\) | 25.5980 | 0.951341 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.89949 | −0.107610 | ||||||||
\(727\) | 10.3431i | 0.383606i | 0.981433 | + | 0.191803i | \(0.0614335\pi\) | ||||
−0.981433 | + | 0.191803i | \(0.938567\pi\) | |||||||
\(728\) | 4.48528i | 0.166236i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.6863 | −0.469219 | ||||||||
\(732\) | 24.3431i | 0.899749i | ||||||||
\(733\) | − 36.6274i | − 1.35286i | −0.736505 | − | 0.676432i | \(-0.763525\pi\) | ||||
0.736505 | − | 0.676432i | \(-0.236475\pi\) | |||||||
\(734\) | 9.94113 | 0.366934 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.6569 | −0.650840 | ||||||||
\(737\) | 13.6569i | 0.503057i | ||||||||
\(738\) | 2.14214i | 0.0788531i | ||||||||
\(739\) | 18.1421 | 0.667369 | 0.333685 | − | 0.942685i | \(-0.391708\pi\) | ||||
0.333685 | + | 0.942685i | \(0.391708\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.82843 | 0.103905 | ||||||||
\(742\) | 2.34315i | 0.0860196i | ||||||||
\(743\) | 2.00000i | 0.0733729i | 0.999327 | + | 0.0366864i | \(0.0116803\pi\) | ||||
−0.999327 | + | 0.0366864i | \(0.988320\pi\) | |||||||
\(744\) | −1.85786 | −0.0681126 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.14214 | 0.151654 | ||||||||
\(747\) | − 3.65685i | − 0.133797i | ||||||||
\(748\) | 28.0000i | 1.02378i | ||||||||
\(749\) | 32.0000 | 1.16925 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.970563 | −0.0354163 | −0.0177082 | − | 0.999843i | \(-0.505637\pi\) | ||||
−0.0177082 | + | 0.999843i | \(0.505637\pi\) | |||||||
\(752\) | 34.9706i | 1.27525i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.828427 | 0.0301695 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.17157 | −0.188088 | ||||||||
\(757\) | − 51.9411i | − 1.88783i | −0.330185 | − | 0.943916i | \(-0.607111\pi\) | ||||
0.330185 | − | 0.943916i | \(-0.392889\pi\) | |||||||
\(758\) | 0.201010i | 0.00730102i | ||||||||
\(759\) | −8.00000 | −0.290382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.4853 | 1.17759 | 0.588795 | − | 0.808282i | \(-0.299602\pi\) | ||||
0.588795 | + | 0.808282i | \(0.299602\pi\) | |||||||
\(762\) | − 2.34315i | − 0.0848832i | ||||||||
\(763\) | 15.0294i | 0.544102i | ||||||||
\(764\) | 6.05887 | 0.219202 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.8284 | 0.463510 | ||||||||
\(767\) | 7.65685i | 0.276473i | ||||||||
\(768\) | 3.97056i | 0.143275i | ||||||||
\(769\) | −42.0000 | −1.51456 | −0.757279 | − | 0.653091i | \(-0.773472\pi\) | ||||
−0.757279 | + | 0.653091i | \(0.773472\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.34315 | −0.156415 | ||||||||
\(772\) | 9.71573i | 0.349677i | ||||||||
\(773\) | 34.1421i | 1.22801i | 0.789303 | + | 0.614004i | \(0.210442\pi\) | ||||
−0.789303 | + | 0.614004i | \(0.789558\pi\) | |||||||
\(774\) | 0.686292 | 0.0246682 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.79899 | −0.208172 | ||||||||
\(777\) | 21.6569i | 0.776935i | ||||||||
\(778\) | − 11.1716i | − 0.400520i | ||||||||
\(779\) | 14.6274 | 0.524082 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00000 | −0.143131 | ||||||||
\(782\) | 12.6863i | 0.453661i | ||||||||
\(783\) | 2.00000i | 0.0714742i | ||||||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.31371 | −0.118196 | ||||||||
\(787\) | 40.7696i | 1.45328i | 0.687020 | + | 0.726639i | \(0.258919\pi\) | ||||
−0.687020 | + | 0.726639i | \(0.741081\pi\) | |||||||
\(788\) | − 0.887302i | − 0.0316088i | ||||||||
\(789\) | −12.0000 | −0.427211 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.0294 | −0.534385 | ||||||||
\(792\) | − 3.17157i | − 0.112697i | ||||||||
\(793\) | − 13.3137i | − 0.472784i | ||||||||
\(794\) | −12.8284 | −0.455264 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −39.5980 | −1.40351 | ||||||||
\(797\) | − 24.3431i | − 0.862278i | −0.902285 | − | 0.431139i | \(-0.858112\pi\) | ||||
0.902285 | − | 0.431139i | \(-0.141888\pi\) | |||||||
\(798\) | − 3.31371i | − 0.117304i | ||||||||
\(799\) | 89.2548 | 3.15761 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.8284 | 0.523937 | ||||||||
\(802\) | − 10.8284i | − 0.382365i | ||||||||
\(803\) | − 0.686292i | − 0.0242187i | ||||||||
\(804\) | 12.4853 | 0.440322 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.485281 | 0.0170933 | ||||||||
\(807\) | − 18.0000i | − 0.633630i | ||||||||
\(808\) | − 12.1421i | − 0.427159i | ||||||||
\(809\) | −18.6863 | −0.656975 | −0.328488 | − | 0.944508i | \(-0.606539\pi\) | ||||
−0.328488 | + | 0.944508i | \(0.606539\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.1421 | −1.05843 | −0.529217 | − | 0.848487i | \(-0.677514\pi\) | ||||
−0.529217 | + | 0.848487i | \(0.677514\pi\) | |||||||
\(812\) | 10.3431i | 0.362973i | ||||||||
\(813\) | − 27.7990i | − 0.974953i | ||||||||
\(814\) | −6.34315 | −0.222327 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 22.9706 | 0.804131 | ||||||||
\(817\) | − 4.68629i | − 0.163953i | ||||||||
\(818\) | − 14.4853i | − 0.506466i | ||||||||
\(819\) | 2.82843 | 0.0988332 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.7990 | −0.830590 | −0.415295 | − | 0.909687i | \(-0.636322\pi\) | ||||
−0.415295 | + | 0.909687i | \(0.636322\pi\) | |||||||
\(822\) | 4.48528i | 0.156442i | ||||||||
\(823\) | 15.0294i | 0.523893i | 0.965082 | + | 0.261947i | \(0.0843644\pi\) | ||||
−0.965082 | + | 0.261947i | \(0.915636\pi\) | |||||||
\(824\) | 3.71573 | 0.129444 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.97056 | 0.312126 | ||||||||
\(827\) | 26.0000i | 0.904109i | 0.891990 | + | 0.452054i | \(0.149309\pi\) | ||||
−0.891990 | + | 0.452054i | \(0.850691\pi\) | |||||||
\(828\) | 7.31371i | 0.254169i | ||||||||
\(829\) | 17.3137 | 0.601330 | 0.300665 | − | 0.953730i | \(-0.402791\pi\) | ||||
0.300665 | + | 0.953730i | \(0.402791\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.00000 | −0.0693792 | ||||||||
\(832\) | − 4.17157i | − 0.144623i | ||||||||
\(833\) | 7.65685i | 0.265294i | ||||||||
\(834\) | 3.02944 | 0.104901 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10.3431 | −0.357725 | ||||||||
\(837\) | 1.17157i | 0.0404955i | ||||||||
\(838\) | 6.05887i | 0.209300i | ||||||||
\(839\) | −43.2548 | −1.49332 | −0.746661 | − | 0.665204i | \(-0.768344\pi\) | ||||
−0.746661 | + | 0.665204i | \(0.768344\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | − 15.4558i | − 0.532644i | ||||||||
\(843\) | 21.1716i | 0.729188i | ||||||||
\(844\) | −21.9411 | −0.755245 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.82843 | −0.166005 | ||||||||
\(847\) | 19.7990i | 0.680301i | ||||||||
\(848\) | − 6.00000i | − 0.206041i | ||||||||
\(849\) | −28.9706 | −0.994267 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 30.6274 | 1.04989 | ||||||||
\(852\) | 3.65685i | 0.125282i | ||||||||
\(853\) | 3.65685i | 0.125208i | 0.998038 | + | 0.0626042i | \(0.0199406\pi\) | ||||
−0.998038 | + | 0.0626042i | \(0.980059\pi\) | |||||||
\(854\) | −15.5980 | −0.533752 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.9411 | 0.613215 | ||||||||
\(857\) | 49.5980i | 1.69423i | 0.531406 | + | 0.847117i | \(0.321664\pi\) | ||||
−0.531406 | + | 0.847117i | \(0.678336\pi\) | |||||||
\(858\) | 0.828427i | 0.0282820i | ||||||||
\(859\) | 0.686292 | 0.0234160 | 0.0117080 | − | 0.999931i | \(-0.496273\pi\) | ||||
0.0117080 | + | 0.999931i | \(0.496273\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.6274 | 0.498501 | ||||||||
\(862\) | − 3.45584i | − 0.117707i | ||||||||
\(863\) | − 28.3431i | − 0.964812i | −0.875948 | − | 0.482406i | \(-0.839763\pi\) | ||||
0.875948 | − | 0.482406i | \(-0.160237\pi\) | |||||||
\(864\) | −4.41421 | −0.150175 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8.82843 | −0.300002 | ||||||||
\(867\) | − 41.6274i | − 1.41374i | ||||||||
\(868\) | 6.05887i | 0.205652i | ||||||||
\(869\) | −22.6274 | −0.767583 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.82843 | −0.231372 | ||||||||
\(872\) | 8.42641i | 0.285354i | ||||||||
\(873\) | 3.65685i | 0.123766i | ||||||||
\(874\) | −4.68629 | −0.158516 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.627417 | −0.0211985 | ||||||||
\(877\) | − 42.2843i | − 1.42784i | −0.700228 | − | 0.713919i | \(-0.746918\pi\) | ||||
0.700228 | − | 0.713919i | \(-0.253082\pi\) | |||||||
\(878\) | 7.02944i | 0.237232i | ||||||||
\(879\) | −2.14214 | −0.0722524 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.5980 | −0.862418 | −0.431209 | − | 0.902252i | \(-0.641913\pi\) | ||||
−0.431209 | + | 0.902252i | \(0.641913\pi\) | |||||||
\(882\) | − 0.414214i | − 0.0139473i | ||||||||
\(883\) | 27.5980i | 0.928746i | 0.885640 | + | 0.464373i | \(0.153720\pi\) | ||||
−0.885640 | + | 0.464373i | \(0.846280\pi\) | |||||||
\(884\) | −14.0000 | −0.470871 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.7452 | −0.360991 | ||||||||
\(887\) | 8.00000i | 0.268614i | 0.990940 | + | 0.134307i | \(0.0428808\pi\) | ||||
−0.990940 | + | 0.134307i | \(0.957119\pi\) | |||||||
\(888\) | 12.1421i | 0.407463i | ||||||||
\(889\) | −16.0000 | −0.536623 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.00000 | −0.0670025 | ||||||||
\(892\) | − 22.8284i | − 0.764352i | ||||||||
\(893\) | 32.9706i | 1.10332i | ||||||||
\(894\) | 3.79899 | 0.127057 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −29.8579 | −0.997481 | ||||||||
\(897\) | − 4.00000i | − 0.133556i | ||||||||
\(898\) | − 13.1716i | − 0.439541i | ||||||||
\(899\) | 2.34315 | 0.0781483 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.3137 | −0.510174 | ||||||||
\(902\) | 4.28427i | 0.142651i | ||||||||
\(903\) | − 4.68629i | − 0.155950i | ||||||||
\(904\) | −8.42641 | −0.280258 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.45584 | −0.0483672 | ||||||||
\(907\) | 12.9706i | 0.430680i | 0.976539 | + | 0.215340i | \(0.0690860\pi\) | ||||
−0.976539 | + | 0.215340i | \(0.930914\pi\) | |||||||
\(908\) | 31.6569i | 1.05057i | ||||||||
\(909\) | −7.65685 | −0.253962 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.0000 | −1.32526 | −0.662630 | − | 0.748947i | \(-0.730560\pi\) | ||||
−0.662630 | + | 0.748947i | \(0.730560\pi\) | |||||||
\(912\) | 8.48528i | 0.280976i | ||||||||
\(913\) | − 7.31371i | − 0.242048i | ||||||||
\(914\) | 3.17157 | 0.104906 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.40202 | 0.0793650 | ||||||||
\(917\) | 22.6274i | 0.747223i | ||||||||
\(918\) | 3.17157i | 0.104678i | ||||||||
\(919\) | −3.31371 | −0.109309 | −0.0546546 | − | 0.998505i | \(-0.517406\pi\) | ||||
−0.0546546 | + | 0.998505i | \(0.517406\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.8284 | −0.752222 | ||||||||
\(922\) | − 2.14214i | − 0.0705475i | ||||||||
\(923\) | − 2.00000i | − 0.0658308i | ||||||||
\(924\) | −10.3431 | −0.340265 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −10.1421 | −0.333291 | ||||||||
\(927\) | − 2.34315i | − 0.0769590i | ||||||||
\(928\) | 8.82843i | 0.289807i | ||||||||
\(929\) | −11.7990 | −0.387112 | −0.193556 | − | 0.981089i | \(-0.562002\pi\) | ||||
−0.193556 | + | 0.981089i | \(0.562002\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.82843 | −0.0926980 | ||||||||
\(932\) | 12.7452i | 0.417482i | ||||||||
\(933\) | − 10.6274i | − 0.347926i | ||||||||
\(934\) | 3.31371 | 0.108428 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.58579 | 0.0518331 | ||||||||
\(937\) | 21.3137i | 0.696289i | 0.937441 | + | 0.348144i | \(0.113188\pi\) | ||||
−0.937441 | + | 0.348144i | \(0.886812\pi\) | |||||||
\(938\) | 8.00000i | 0.261209i | ||||||||
\(939\) | −6.00000 | −0.195803 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.1421 | 1.11300 | 0.556501 | − | 0.830847i | \(-0.312144\pi\) | ||||
0.556501 | + | 0.830847i | \(0.312144\pi\) | |||||||
\(942\) | 4.14214i | 0.134958i | ||||||||
\(943\) | − 20.6863i | − 0.673638i | ||||||||
\(944\) | −22.9706 | −0.747628 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.37258 | 0.0446265 | ||||||||
\(947\) | 21.0294i | 0.683365i | 0.939815 | + | 0.341682i | \(0.110997\pi\) | ||||
−0.939815 | + | 0.341682i | \(0.889003\pi\) | |||||||
\(948\) | 20.6863i | 0.671860i | ||||||||
\(949\) | 0.343146 | 0.0111390 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.48528 | 0.275154 | ||||||||
\(952\) | 34.3431i | 1.11307i | ||||||||
\(953\) | 40.3431i | 1.30684i | 0.756994 | + | 0.653421i | \(0.226667\pi\) | ||||
−0.756994 | + | 0.653421i | \(0.773333\pi\) | |||||||
\(954\) | 0.828427 | 0.0268213 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.65685 | −0.118271 | ||||||||
\(957\) | 4.00000i | 0.129302i | ||||||||
\(958\) | 10.4853i | 0.338764i | ||||||||
\(959\) | 30.6274 | 0.989011 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6274 | −0.955723 | ||||||||
\(962\) | − 3.17157i | − 0.102256i | ||||||||
\(963\) | − 11.3137i | − 0.364579i | ||||||||
\(964\) | 0.627417 | 0.0202077 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.68629 | −0.150779 | ||||||||
\(967\) | − 18.1421i | − 0.583412i | −0.956508 | − | 0.291706i | \(-0.905777\pi\) | ||||
0.956508 | − | 0.291706i | \(-0.0942228\pi\) | |||||||
\(968\) | 11.1005i | 0.356784i | ||||||||
\(969\) | 21.6569 | 0.695718 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.3137 | −0.491440 | −0.245720 | − | 0.969341i | \(-0.579024\pi\) | ||||
−0.245720 | + | 0.969341i | \(0.579024\pi\) | |||||||
\(972\) | 1.82843i | 0.0586468i | ||||||||
\(973\) | − 20.6863i | − 0.663172i | ||||||||
\(974\) | 3.23045 | 0.103510 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 39.9411 | 1.27848 | ||||||||
\(977\) | − 42.1421i | − 1.34825i | −0.738619 | − | 0.674123i | \(-0.764522\pi\) | ||||
0.738619 | − | 0.674123i | \(-0.235478\pi\) | |||||||
\(978\) | 7.79899i | 0.249384i | ||||||||
\(979\) | 29.6569 | 0.947837 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.31371 | 0.169654 | ||||||||
\(982\) | − 12.6863i | − 0.404836i | ||||||||
\(983\) | 25.3137i | 0.807382i | 0.914895 | + | 0.403691i | \(0.132273\pi\) | ||||
−0.914895 | + | 0.403691i | \(0.867727\pi\) | |||||||
\(984\) | 8.20101 | 0.261439 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.34315 | 0.202007 | ||||||||
\(987\) | 32.9706i | 1.04946i | ||||||||
\(988\) | − 5.17157i | − 0.164530i | ||||||||
\(989\) | −6.62742 | −0.210740 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.68629 | 0.148865 | 0.0744325 | − | 0.997226i | \(-0.476285\pi\) | ||||
0.0744325 | + | 0.997226i | \(0.476285\pi\) | |||||||
\(992\) | 5.17157i | 0.164198i | ||||||||
\(993\) | 26.1421i | 0.829596i | ||||||||
\(994\) | −2.34315 | −0.0743201 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.68629 | −0.211863 | ||||||||
\(997\) | 39.2548i | 1.24321i | 0.783330 | + | 0.621607i | \(0.213520\pi\) | ||||
−0.783330 | + | 0.621607i | \(0.786480\pi\) | |||||||
\(998\) | 10.8284i | 0.342768i | ||||||||
\(999\) | 7.65685 | 0.242252 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))