Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(251,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 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("360.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.b (of order \(2\), degree \(1\), 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: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.2580992.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + x^{4} + 2x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.1 | ||
Root | \(1.38078 - 0.305697i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 360.251 |
Dual form | 360.2.b.c.251.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.38078 | − | 0.305697i | −0.976358 | − | 0.216160i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.81310 | + | 0.844199i | 0.906550 | + | 0.422099i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.41421i | − | 0.534522i | −0.963624 | − | 0.267261i | \(-0.913881\pi\) | ||
0.963624 | − | 0.267261i | \(-0.0861187\pi\) | |||||||
\(8\) | −2.24542 | − | 1.71991i | −0.793876 | − | 0.608080i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.38078 | + | 0.305697i | 0.436641 | + | 0.0966698i | ||||
\(11\) | 0.191427i | 0.0577173i | 0.999584 | + | 0.0288587i | \(0.00918727\pi\) | ||||
−0.999584 | + | 0.0288587i | \(0.990813\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.63700i | − | 0.731372i | −0.930738 | − | 0.365686i | \(-0.880834\pi\) | ||
0.930738 | − | 0.365686i | \(-0.119166\pi\) | |||||||
\(14\) | −0.432320 | + | 1.95272i | −0.115542 | + | 0.521885i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.57466 | + | 3.06123i | 0.643664 | + | 0.765308i | ||||
\(17\) | − | 6.20522i | − | 1.50499i | −0.658599 | − | 0.752494i | \(-0.728851\pi\) | ||
0.658599 | − | 0.752494i | \(-0.271149\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.52311 | −0.349426 | −0.174713 | − | 0.984619i | \(-0.555900\pi\) | ||||
−0.174713 | + | 0.984619i | \(0.555900\pi\) | |||||||
\(20\) | −1.81310 | − | 0.844199i | −0.405421 | − | 0.188769i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.0585185 | − | 0.264318i | 0.0124762 | − | 0.0563528i | ||||
\(23\) | 5.25240 | 1.09520 | 0.547600 | − | 0.836740i | \(-0.315542\pi\) | ||||
0.547600 | + | 0.836740i | \(0.315542\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.806122 | + | 3.64111i | −0.158094 | + | 0.714081i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.19388 | − | 2.56411i | 0.225622 | − | 0.484571i | ||||
\(29\) | 0.270718 | 0.0502711 | 0.0251356 | − | 0.999684i | \(-0.491998\pi\) | ||||
0.0251356 | + | 0.999684i | \(0.491998\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.20522i | − | 1.11449i | −0.830348 | − | 0.557245i | \(-0.811858\pi\) | ||
0.830348 | − | 0.557245i | \(-0.188142\pi\) | |||||||
\(32\) | −2.61922 | − | 5.01395i | −0.463017 | − | 0.886349i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.89692 | + | 8.56804i | −0.325318 | + | 1.46941i | ||||
\(35\) | 1.41421i | 0.239046i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.61944i | − | 1.25263i | −0.779571 | − | 0.626314i | \(-0.784563\pi\) | ||
0.779571 | − | 0.626314i | \(-0.215437\pi\) | |||||||
\(38\) | 2.10308 | + | 0.465611i | 0.341165 | + | 0.0755321i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.24542 | + | 1.71991i | 0.355032 | + | 0.271942i | ||||
\(41\) | − | 9.22508i | − | 1.44071i | −0.693603 | − | 0.720357i | \(-0.743978\pi\) | ||
0.693603 | − | 0.720357i | \(-0.256022\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.7755 | −1.94825 | −0.974124 | − | 0.226016i | \(-0.927430\pi\) | ||||
−0.974124 | + | 0.226016i | \(0.927430\pi\) | |||||||
\(44\) | −0.161602 | + | 0.347076i | −0.0243625 | + | 0.0523236i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.25240 | − | 1.60564i | −1.06931 | − | 0.236739i | ||||
\(47\) | −3.79383 | −0.553387 | −0.276694 | − | 0.960958i | \(-0.589239\pi\) | ||||
−0.276694 | + | 0.960958i | \(0.589239\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | −1.38078 | − | 0.305697i | −0.195272 | − | 0.0432320i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.22615 | − | 4.78114i | 0.308712 | − | 0.663025i | ||||
\(53\) | 8.77551 | 1.20541 | 0.602705 | − | 0.797964i | \(-0.294090\pi\) | ||||
0.602705 | + | 0.797964i | \(0.294090\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.191427i | − | 0.0258120i | ||||||
\(56\) | −2.43232 | + | 3.17550i | −0.325032 | + | 0.424344i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.373802 | − | 0.0827577i | −0.0490826 | − | 0.0108666i | ||||
\(59\) | 10.4479i | 1.36020i | 0.733121 | + | 0.680098i | \(0.238063\pi\) | ||||
−0.733121 | + | 0.680098i | \(0.761937\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.382853i | 0.0490194i | 0.999700 | + | 0.0245097i | \(0.00780245\pi\) | ||||
−0.999700 | + | 0.0245097i | \(0.992198\pi\) | |||||||
\(62\) | −1.89692 | + | 8.56804i | −0.240909 | + | 1.08814i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.08382 | + | 7.72384i | 0.260477 | + | 0.965480i | ||||
\(65\) | 2.63700i | 0.327080i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.72928 | 0.211265 | 0.105633 | − | 0.994405i | \(-0.466313\pi\) | ||||
0.105633 | + | 0.994405i | \(0.466313\pi\) | |||||||
\(68\) | 5.23844 | − | 11.2507i | 0.635255 | − | 1.36435i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.432320 | − | 1.95272i | 0.0516722 | − | 0.233394i | ||||
\(71\) | 9.72928 | 1.15465 | 0.577327 | − | 0.816513i | \(-0.304096\pi\) | ||||
0.577327 | + | 0.816513i | \(0.304096\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.45856 | −0.638877 | −0.319438 | − | 0.947607i | \(-0.603494\pi\) | ||||
−0.319438 | + | 0.947607i | \(0.603494\pi\) | |||||||
\(74\) | −2.32924 | + | 10.5208i | −0.270768 | + | 1.22301i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.76156 | − | 1.28581i | −0.316772 | − | 0.147493i | ||||
\(77\) | 0.270718 | 0.0308512 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.3077i | 1.60974i | 0.593454 | + | 0.804868i | \(0.297764\pi\) | ||||
−0.593454 | + | 0.804868i | \(0.702236\pi\) | |||||||
\(80\) | −2.57466 | − | 3.06123i | −0.287855 | − | 0.342256i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.82008 | + | 12.7378i | −0.311425 | + | 1.40665i | ||||
\(83\) | 15.2389i | 1.67268i | 0.548208 | + | 0.836342i | \(0.315310\pi\) | ||||
−0.548208 | + | 0.836342i | \(0.684690\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.20522i | 0.673051i | ||||||||
\(86\) | 17.6402 | + | 3.90543i | 1.90219 | + | 0.421134i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.329237 | − | 0.429833i | 0.0350968 | − | 0.0458204i | ||||
\(89\) | − | 3.56822i | − | 0.378231i | −0.981955 | − | 0.189115i | \(-0.939438\pi\) | ||
0.981955 | − | 0.189115i | \(-0.0605620\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.72928 | −0.390935 | ||||||||
\(92\) | 9.52311 | + | 4.43407i | 0.992853 | + | 0.462283i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.23844 | + | 1.15976i | 0.540304 | + | 0.119620i | ||||
\(95\) | 1.52311 | 0.156268 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.31695 | 0.742923 | 0.371462 | − | 0.928448i | \(-0.378857\pi\) | ||||
0.371462 | + | 0.928448i | \(0.378857\pi\) | |||||||
\(98\) | −6.90389 | − | 1.52848i | −0.697399 | − | 0.154400i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.81310 | + | 0.844199i | 0.181310 | + | 0.0844199i | ||||
\(101\) | −15.5510 | −1.54738 | −0.773692 | − | 0.633562i | \(-0.781592\pi\) | ||||
−0.773692 | + | 0.633562i | \(0.781592\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.08863i | − | 0.205799i | −0.994692 | − | 0.102899i | \(-0.967188\pi\) | ||
0.994692 | − | 0.102899i | \(-0.0328120\pi\) | |||||||
\(104\) | −4.53540 | + | 5.92117i | −0.444733 | + | 0.580619i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.1170 | − | 2.68264i | −1.17691 | − | 0.260561i | ||||
\(107\) | 2.82843i | 0.273434i | 0.990610 | + | 0.136717i | \(0.0436552\pi\) | ||||
−0.990610 | + | 0.136717i | \(0.956345\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.27400i | 0.505158i | 0.967576 | + | 0.252579i | \(0.0812787\pi\) | ||||
−0.967576 | + | 0.252579i | \(0.918721\pi\) | |||||||
\(110\) | −0.0585185 | + | 0.264318i | −0.00557952 | + | 0.0252017i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.32924 | − | 3.64111i | 0.409074 | − | 0.344053i | ||||
\(113\) | 5.82237i | 0.547722i | 0.961769 | + | 0.273861i | \(0.0883009\pi\) | ||||
−0.961769 | + | 0.273861i | \(0.911699\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.25240 | −0.489788 | ||||||||
\(116\) | 0.490839 | + | 0.228540i | 0.0455733 | + | 0.0212194i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.19388 | − | 14.4262i | 0.294020 | − | 1.32804i | ||||
\(119\) | −8.77551 | −0.804450 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9634 | 0.996669 | ||||||||
\(122\) | 0.117037 | − | 0.528636i | 0.0105960 | − | 0.0478604i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.23844 | − | 11.2507i | 0.470426 | − | 1.01034i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.5388i | 1.82252i | 0.411829 | + | 0.911261i | \(0.364890\pi\) | ||||
−0.411829 | + | 0.911261i | \(0.635110\pi\) | |||||||
\(128\) | −0.516138 | − | 11.3019i | −0.0456206 | − | 0.998959i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.806122 | − | 3.64111i | 0.0707016 | − | 0.319347i | ||||
\(131\) | − | 13.5679i | − | 1.18543i | −0.805413 | − | 0.592715i | \(-0.798056\pi\) | ||
0.805413 | − | 0.592715i | \(-0.201944\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.15401i | 0.186776i | ||||||||
\(134\) | −2.38776 | − | 0.528636i | −0.206271 | − | 0.0456672i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.6724 | + | 13.9333i | −0.915153 | + | 1.19477i | ||||
\(137\) | − | 4.72563i | − | 0.403738i | −0.979413 | − | 0.201869i | \(-0.935298\pi\) | ||
0.979413 | − | 0.201869i | \(-0.0647015\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.7572 | 1.33651 | 0.668254 | − | 0.743934i | \(-0.267042\pi\) | ||||
0.668254 | + | 0.743934i | \(0.267042\pi\) | |||||||
\(140\) | −1.19388 | + | 2.56411i | −0.100901 | + | 0.216707i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.4340 | − | 2.97421i | −1.12735 | − | 0.249590i | ||||
\(143\) | 0.504792 | 0.0422129 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.270718 | −0.0224819 | ||||||||
\(146\) | 7.53707 | + | 1.66866i | 0.623772 | + | 0.138100i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.43232 | − | 13.8148i | 0.528733 | − | 1.13557i | ||||
\(149\) | −7.72928 | −0.633207 | −0.316604 | − | 0.948558i | \(-0.602543\pi\) | ||||
−0.316604 | + | 0.948558i | \(0.602543\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 22.2098i | − | 1.80741i | −0.428158 | − | 0.903704i | \(-0.640837\pi\) | ||
0.428158 | − | 0.903704i | \(-0.359163\pi\) | |||||||
\(152\) | 3.42003 | + | 2.61962i | 0.277401 | + | 0.212479i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.373802 | − | 0.0827577i | −0.0301218 | − | 0.00666880i | ||||
\(155\) | 6.20522i | 0.498416i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.00229i | − | 0.638652i | −0.947645 | − | 0.319326i | \(-0.896543\pi\) | ||
0.947645 | − | 0.319326i | \(-0.103457\pi\) | |||||||
\(158\) | 4.37380 | − | 19.7557i | 0.347961 | − | 1.57168i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.61922 | + | 5.01395i | 0.207068 | + | 0.396387i | ||||
\(161\) | − | 7.42801i | − | 0.585409i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.953771 | −0.0747051 | −0.0373526 | − | 0.999302i | \(-0.511892\pi\) | ||||
−0.0373526 | + | 0.999302i | \(0.511892\pi\) | |||||||
\(164\) | 7.78780 | − | 16.7260i | 0.608125 | − | 1.30608i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.65847 | − | 21.0415i | 0.361568 | − | 1.63314i | ||||
\(167\) | −11.7572 | −0.909799 | −0.454899 | − | 0.890543i | \(-0.650325\pi\) | ||||
−0.454899 | + | 0.890543i | \(0.650325\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.04623 | 0.465095 | ||||||||
\(170\) | 1.89692 | − | 8.56804i | 0.145487 | − | 0.657139i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −23.1633 | − | 10.7851i | −1.76618 | − | 0.822354i | ||||
\(173\) | −3.22449 | −0.245153 | −0.122577 | − | 0.992459i | \(-0.539116\pi\) | ||||
−0.122577 | + | 0.992459i | \(0.539116\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.41421i | − | 0.106904i | ||||||
\(176\) | −0.586002 | + | 0.492858i | −0.0441715 | + | 0.0371506i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.09079 | + | 4.92693i | −0.0817585 | + | 0.369289i | ||||
\(179\) | − | 12.6019i | − | 0.941908i | −0.882158 | − | 0.470954i | \(-0.843910\pi\) | ||
0.882158 | − | 0.470954i | \(-0.156090\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.1070i | 1.79186i | 0.444195 | + | 0.895930i | \(0.353490\pi\) | ||||
−0.444195 | + | 0.895930i | \(0.646510\pi\) | |||||||
\(182\) | 5.14931 | + | 1.14003i | 0.381692 | + | 0.0845046i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −11.7938 | − | 9.03365i | −0.869453 | − | 0.665970i | ||||
\(185\) | 7.61944i | 0.560192i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.18785 | 0.0868639 | ||||||||
\(188\) | −6.87859 | − | 3.20275i | −0.501673 | − | 0.233585i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.10308 | − | 0.465611i | −0.152574 | − | 0.0337790i | ||||
\(191\) | −10.9171 | −0.789936 | −0.394968 | − | 0.918695i | \(-0.629244\pi\) | ||||
−0.394968 | + | 0.918695i | \(0.629244\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.3169 | −1.10254 | −0.551269 | − | 0.834328i | \(-0.685856\pi\) | ||||
−0.551269 | + | 0.834328i | \(0.685856\pi\) | |||||||
\(194\) | −10.1031 | − | 2.23677i | −0.725359 | − | 0.160590i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.06550 | + | 4.22099i | 0.647535 | + | 0.301500i | ||||
\(197\) | 17.0462 | 1.21449 | 0.607247 | − | 0.794513i | \(-0.292274\pi\) | ||||
0.607247 | + | 0.794513i | \(0.292274\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4.72563i | − | 0.334991i | −0.985873 | − | 0.167496i | \(-0.946432\pi\) | ||
0.985873 | − | 0.167496i | \(-0.0535680\pi\) | |||||||
\(200\) | −2.24542 | − | 1.71991i | −0.158775 | − | 0.121616i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 21.4725 | + | 4.75390i | 1.51080 | + | 0.334483i | ||||
\(203\) | − | 0.382853i | − | 0.0268710i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.22508i | 0.644307i | ||||||||
\(206\) | −0.638488 | + | 2.88394i | −0.0444856 | + | 0.200933i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 8.07247 | − | 6.78937i | 0.559725 | − | 0.470758i | ||||
\(209\) | − | 0.291565i | − | 0.0201680i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.8401 | 1.15932 | 0.579659 | − | 0.814859i | \(-0.303186\pi\) | ||||
0.579659 | + | 0.814859i | \(0.303186\pi\) | |||||||
\(212\) | 15.9109 | + | 7.40828i | 1.09276 | + | 0.508803i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.864641 | − | 3.90543i | 0.0591056 | − | 0.266970i | ||||
\(215\) | 12.7755 | 0.871283 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.77551 | −0.595720 | ||||||||
\(218\) | 1.61224 | − | 7.28223i | 0.109195 | − | 0.493215i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.161602 | − | 0.347076i | 0.0108952 | − | 0.0233998i | ||||
\(221\) | −16.3632 | −1.10071 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.3099i | 1.49398i | 0.664833 | + | 0.746992i | \(0.268503\pi\) | ||||
−0.664833 | + | 0.746992i | \(0.731497\pi\) | |||||||
\(224\) | −7.09079 | + | 3.70414i | −0.473774 | + | 0.247493i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.77988 | − | 8.03940i | 0.118396 | − | 0.534773i | ||||
\(227\) | − | 8.86813i | − | 0.588599i | −0.955713 | − | 0.294299i | \(-0.904914\pi\) | ||
0.955713 | − | 0.294299i | \(-0.0950863\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 21.2786i | − | 1.40613i | −0.711126 | − | 0.703064i | \(-0.751815\pi\) | ||
0.711126 | − | 0.703064i | \(-0.248185\pi\) | |||||||
\(230\) | 7.25240 | + | 1.60564i | 0.478209 | + | 0.105873i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.607876 | − | 0.465611i | −0.0399090 | − | 0.0305689i | ||||
\(233\) | 15.0734i | 0.987488i | 0.869607 | + | 0.493744i | \(0.164372\pi\) | ||||
−0.869607 | + | 0.493744i | \(0.835628\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.79383 | 0.247482 | ||||||||
\(236\) | −8.82008 | + | 18.9430i | −0.574138 | + | 1.23309i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 12.1170 | + | 2.68264i | 0.785431 | + | 0.173890i | ||||
\(239\) | −19.0462 | −1.23200 | −0.615999 | − | 0.787747i | \(-0.711247\pi\) | ||||
−0.615999 | + | 0.787747i | \(0.711247\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.5048 | 1.19200 | 0.595999 | − | 0.802985i | \(-0.296756\pi\) | ||||
0.595999 | + | 0.802985i | \(0.296756\pi\) | |||||||
\(242\) | −15.1380 | − | 3.35146i | −0.973105 | − | 0.215440i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.323204 | + | 0.694151i | −0.0206910 | + | 0.0444385i | ||||
\(245\) | −5.00000 | −0.319438 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.01645i | 0.255561i | ||||||||
\(248\) | −10.6724 | + | 13.9333i | −0.677700 | + | 0.884767i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.38078 | + | 0.305697i | 0.0873281 | + | 0.0193340i | ||||
\(251\) | − | 16.8186i | − | 1.06158i | −0.847503 | − | 0.530790i | \(-0.821895\pi\) | ||
0.847503 | − | 0.530790i | \(-0.178105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.00545i | 0.0632120i | ||||||||
\(254\) | 6.27864 | − | 28.3595i | 0.393957 | − | 1.77943i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.74229 | + | 15.7632i | −0.171393 | + | 0.985203i | ||||
\(257\) | 9.79936i | 0.611267i | 0.952149 | + | 0.305634i | \(0.0988682\pi\) | ||||
−0.952149 | + | 0.305634i | \(0.901132\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.7755 | −0.669558 | ||||||||
\(260\) | −2.22615 | + | 4.78114i | −0.138060 | + | 0.296514i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.14765 | + | 18.7342i | −0.256243 | + | 1.15740i | ||||
\(263\) | 5.79383 | 0.357263 | 0.178632 | − | 0.983916i | \(-0.442833\pi\) | ||||
0.178632 | + | 0.983916i | \(0.442833\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.77551 | −0.539075 | ||||||||
\(266\) | 0.658473 | − | 2.97421i | 0.0403736 | − | 0.182360i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.13536 | + | 1.45986i | 0.191523 | + | 0.0891750i | ||||
\(269\) | 15.1878 | 0.926019 | 0.463010 | − | 0.886353i | \(-0.346770\pi\) | ||||
0.463010 | + | 0.886353i | \(0.346770\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 10.1304i | − | 0.615377i | −0.951487 | − | 0.307689i | \(-0.900444\pi\) | ||
0.951487 | − | 0.307689i | \(-0.0995555\pi\) | |||||||
\(272\) | 18.9956 | − | 15.9763i | 1.15178 | − | 0.968706i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.44461 | + | 6.52505i | −0.0872721 | + | 0.394193i | ||||
\(275\) | 0.191427i | 0.0115435i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 14.7559i | − | 0.886595i | −0.896375 | − | 0.443298i | \(-0.853809\pi\) | ||
0.896375 | − | 0.443298i | \(-0.146191\pi\) | |||||||
\(278\) | −21.7572 | − | 4.81692i | −1.30491 | − | 0.288900i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.43232 | − | 3.17550i | 0.145359 | − | 0.189773i | ||||
\(281\) | 21.5442i | 1.28522i | 0.766193 | + | 0.642611i | \(0.222149\pi\) | ||||
−0.766193 | + | 0.642611i | \(0.777851\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.2707 | 1.08608 | 0.543041 | − | 0.839706i | \(-0.317273\pi\) | ||||
0.543041 | + | 0.839706i | \(0.317273\pi\) | |||||||
\(284\) | 17.6402 | + | 8.21345i | 1.04675 | + | 0.487379i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.697006 | − | 0.154313i | −0.0412149 | − | 0.00912474i | ||||
\(287\) | −13.0462 | −0.770095 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −21.5048 | −1.26499 | ||||||||
\(290\) | 0.373802 | + | 0.0827577i | 0.0219504 | + | 0.00485970i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.89692 | − | 4.60811i | −0.579173 | − | 0.269669i | ||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 10.4479i | − | 0.608298i | ||||||
\(296\) | −13.1047 | + | 17.1088i | −0.761698 | + | 0.994431i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.6724 | + | 2.36282i | 0.618237 | + | 0.136874i | ||||
\(299\) | − | 13.8506i | − | 0.800999i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.0673i | 1.04138i | ||||||||
\(302\) | −6.78946 | + | 30.6668i | −0.390690 | + | 1.76468i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.92150 | − | 4.66261i | −0.224913 | − | 0.267419i | ||||
\(305\) | − | 0.382853i | − | 0.0219221i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.5048 | 1.28442 | 0.642208 | − | 0.766530i | \(-0.278018\pi\) | ||||
0.642208 | + | 0.766530i | \(0.278018\pi\) | |||||||
\(308\) | 0.490839 | + | 0.228540i | 0.0279681 | + | 0.0130223i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.89692 | − | 8.56804i | 0.107738 | − | 0.486632i | ||||
\(311\) | 31.0462 | 1.76047 | 0.880235 | − | 0.474538i | \(-0.157385\pi\) | ||||
0.880235 | + | 0.474538i | \(0.157385\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.23407 | −0.126277 | −0.0631387 | − | 0.998005i | \(-0.520111\pi\) | ||||
−0.0631387 | + | 0.998005i | \(0.520111\pi\) | |||||||
\(314\) | −2.44627 | + | 11.0494i | −0.138051 | + | 0.623553i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.0785 | + | 25.9412i | −0.679469 | + | 1.45931i | ||||
\(317\) | 16.5048 | 0.927001 | 0.463501 | − | 0.886097i | \(-0.346593\pi\) | ||||
0.463501 | + | 0.886097i | \(0.346593\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0518227i | 0.00290151i | ||||||||
\(320\) | −2.08382 | − | 7.72384i | −0.116489 | − | 0.431776i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.27072 | + | 10.2564i | −0.126542 | + | 0.571569i | ||||
\(323\) | 9.45126i | 0.525882i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.63700i | − | 0.146274i | ||||||
\(326\) | 1.31695 | + | 0.291565i | 0.0729389 | + | 0.0161483i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −15.8663 | + | 20.7142i | −0.876070 | + | 1.14375i | ||||
\(329\) | 5.36529i | 0.295798i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.9817 | −0.713538 | −0.356769 | − | 0.934193i | \(-0.616122\pi\) | ||||
−0.356769 | + | 0.934193i | \(0.616122\pi\) | |||||||
\(332\) | −12.8646 | + | 27.6296i | −0.706039 | + | 1.51637i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.2341 | + | 3.59413i | 0.888289 | + | 0.196662i | ||||
\(335\) | −1.72928 | −0.0944808 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.0096 | −1.47131 | −0.735653 | − | 0.677359i | \(-0.763125\pi\) | ||||
−0.735653 | + | 0.677359i | \(0.763125\pi\) | |||||||
\(338\) | −8.34850 | − | 1.84831i | −0.454099 | − | 0.100535i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.23844 | + | 11.2507i | −0.284094 | + | 0.610154i | ||||
\(341\) | 1.18785 | 0.0643254 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.9706i | − | 0.916324i | ||||||
\(344\) | 28.6864 | + | 21.9727i | 1.54667 | + | 1.18469i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.45231 | + | 0.985716i | 0.239357 | + | 0.0529924i | ||||
\(347\) | − | 5.07372i | − | 0.272372i | −0.990683 | − | 0.136186i | \(-0.956516\pi\) | ||
0.990683 | − | 0.136186i | \(-0.0434844\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 20.1300i | − | 1.07754i | −0.842454 | − | 0.538768i | \(-0.818890\pi\) | ||
0.842454 | − | 0.538768i | \(-0.181110\pi\) | |||||||
\(350\) | −0.432320 | + | 1.95272i | −0.0231085 | + | 0.104377i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.959804 | − | 0.501389i | 0.0511577 | − | 0.0267241i | ||||
\(353\) | 14.3077i | 0.761519i | 0.924674 | + | 0.380760i | \(0.124337\pi\) | ||||
−0.924674 | + | 0.380760i | \(0.875663\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.72928 | −0.516377 | ||||||||
\(356\) | 3.01229 | − | 6.46954i | 0.159651 | − | 0.342885i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.85235 | + | 17.4004i | −0.203603 | + | 0.919640i | ||||
\(359\) | 31.8217 | 1.67949 | 0.839744 | − | 0.542983i | \(-0.182705\pi\) | ||||
0.839744 | + | 0.542983i | \(0.182705\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.6801 | −0.877901 | ||||||||
\(362\) | 7.36943 | − | 33.2864i | 0.387329 | − | 1.74950i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.76156 | − | 3.14826i | −0.354402 | − | 0.165013i | ||||
\(365\) | 5.45856 | 0.285714 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.9844i | 1.19977i | 0.800085 | + | 0.599887i | \(0.204788\pi\) | ||||
−0.800085 | + | 0.599887i | \(0.795212\pi\) | |||||||
\(368\) | 13.5231 | + | 16.0788i | 0.704941 | + | 0.838166i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.32924 | − | 10.5208i | 0.121091 | − | 0.546948i | ||||
\(371\) | − | 12.4104i | − | 0.644318i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.2423i | 0.737437i | 0.929541 | + | 0.368718i | \(0.120203\pi\) | ||||
−0.929541 | + | 0.368718i | \(0.879797\pi\) | |||||||
\(374\) | −1.64015 | − | 0.363120i | −0.0848102 | − | 0.0187765i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.51875 | + | 6.52505i | 0.439321 | + | 0.336504i | ||||
\(377\) | − | 0.713884i | − | 0.0367669i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.71096 | −0.447452 | −0.223726 | − | 0.974652i | \(-0.571822\pi\) | ||||
−0.223726 | + | 0.974652i | \(0.571822\pi\) | |||||||
\(380\) | 2.76156 | + | 1.28581i | 0.141665 | + | 0.0659607i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.0741 | + | 3.33733i | 0.771260 | + | 0.170753i | ||||
\(383\) | −18.7110 | −0.956085 | −0.478043 | − | 0.878337i | \(-0.658654\pi\) | ||||
−0.478043 | + | 0.878337i | \(0.658654\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.270718 | −0.0137971 | ||||||||
\(386\) | 21.1493 | + | 4.68234i | 1.07647 | + | 0.238325i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.2663 | + | 6.17696i | 0.673497 | + | 0.313588i | ||||
\(389\) | 27.0096 | 1.36944 | 0.684720 | − | 0.728806i | \(-0.259924\pi\) | ||||
0.684720 | + | 0.728806i | \(0.259924\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 32.5923i | − | 1.64826i | ||||||
\(392\) | −11.2271 | − | 8.59955i | −0.567054 | − | 0.434343i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −23.5371 | − | 5.21098i | −1.18578 | − | 0.262525i | ||||
\(395\) | − | 14.3077i | − | 0.719896i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 25.3952i | − | 1.27455i | −0.770638 | − | 0.637274i | \(-0.780062\pi\) | ||
0.770638 | − | 0.637274i | \(-0.219938\pi\) | |||||||
\(398\) | −1.44461 | + | 6.52505i | −0.0724118 | + | 0.327071i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.57466 | + | 3.06123i | 0.128733 | + | 0.153062i | ||||
\(401\) | 6.01380i | 0.300315i | 0.988662 | + | 0.150157i | \(0.0479780\pi\) | ||||
−0.988662 | + | 0.150157i | \(0.952022\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.3632 | −0.815108 | ||||||||
\(404\) | −28.1955 | − | 13.1282i | −1.40278 | − | 0.653150i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.117037 | + | 0.528636i | −0.00580845 | + | 0.0262358i | ||||
\(407\) | 1.45856 | 0.0722983 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.5510 | −0.966736 | −0.483368 | − | 0.875417i | \(-0.660587\pi\) | ||||
−0.483368 | + | 0.875417i | \(0.660587\pi\) | |||||||
\(410\) | 2.82008 | − | 12.7378i | 0.139274 | − | 0.629075i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.76322 | − | 3.78690i | 0.0868676 | − | 0.186567i | ||||
\(413\) | 14.7755 | 0.727055 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 15.2389i | − | 0.748047i | ||||||
\(416\) | −13.2218 | + | 6.90689i | −0.648251 | + | 0.338638i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.0891304 | + | 0.402586i | −0.00435951 | + | 0.0196911i | ||||
\(419\) | 1.96258i | 0.0958784i | 0.998850 | + | 0.0479392i | \(0.0152654\pi\) | ||||
−0.998850 | + | 0.0479392i | \(0.984735\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.30802i | 0.209960i | 0.994474 | + | 0.104980i | \(0.0334778\pi\) | ||||
−0.994474 | + | 0.104980i | \(0.966522\pi\) | |||||||
\(422\) | −23.2524 | − | 5.14795i | −1.13191 | − | 0.250598i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −19.7047 | − | 15.0931i | −0.956945 | − | 0.732985i | ||||
\(425\) | − | 6.20522i | − | 0.300998i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.541436 | 0.0262019 | ||||||||
\(428\) | −2.38776 | + | 5.12822i | −0.115417 | + | 0.247882i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.6402 | − | 3.90543i | −0.850684 | − | 0.188337i | ||||
\(431\) | 11.8217 | 0.569433 | 0.284717 | − | 0.958612i | \(-0.408101\pi\) | ||||
0.284717 | + | 0.958612i | \(0.408101\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.45856 | 0.454550 | 0.227275 | − | 0.973831i | \(-0.427018\pi\) | ||||
0.227275 | + | 0.973831i | \(0.427018\pi\) | |||||||
\(434\) | 12.1170 | + | 2.68264i | 0.581636 | + | 0.128771i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.45231 | + | 9.56229i | −0.213227 | + | 0.457950i | ||||
\(437\) | −8.00000 | −0.382692 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 16.0393i | − | 0.765516i | −0.923849 | − | 0.382758i | \(-0.874974\pi\) | ||
0.923849 | − | 0.382758i | \(-0.125026\pi\) | |||||||
\(440\) | −0.329237 | + | 0.429833i | −0.0156957 | + | 0.0204915i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 22.5939 | + | 5.00217i | 1.07468 | + | 0.237929i | ||||
\(443\) | − | 25.0730i | − | 1.19125i | −0.803261 | − | 0.595627i | \(-0.796904\pi\) | ||
0.803261 | − | 0.595627i | \(-0.203096\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.56822i | 0.169150i | ||||||||
\(446\) | 6.82008 | − | 30.8051i | 0.322940 | − | 1.45866i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.9232 | − | 2.94696i | 0.516071 | − | 0.139231i | ||||
\(449\) | 4.24264i | 0.200223i | 0.994976 | + | 0.100111i | \(0.0319199\pi\) | ||||
−0.994976 | + | 0.100111i | \(0.968080\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.76593 | 0.0831542 | ||||||||
\(452\) | −4.91524 | + | 10.5565i | −0.231193 | + | 0.496538i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.71096 | + | 12.2449i | −0.127232 | + | 0.574683i | ||||
\(455\) | 3.72928 | 0.174831 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.8680 | 1.35039 | 0.675193 | − | 0.737641i | \(-0.264060\pi\) | ||||
0.675193 | + | 0.737641i | \(0.264060\pi\) | |||||||
\(458\) | −6.50479 | + | 29.3810i | −0.303949 | + | 1.37288i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.52311 | − | 4.43407i | −0.444017 | − | 0.206739i | ||||
\(461\) | −36.7389 | −1.71110 | −0.855550 | − | 0.517721i | \(-0.826781\pi\) | ||||
−0.855550 | + | 0.517721i | \(0.826781\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.6136i | 0.772100i | 0.922478 | + | 0.386050i | \(0.126161\pi\) | ||||
−0.922478 | + | 0.386050i | \(0.873839\pi\) | |||||||
\(464\) | 0.697006 | + | 0.828731i | 0.0323577 | + | 0.0384729i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.60788 | − | 20.8130i | 0.213456 | − | 0.964142i | ||||
\(467\) | − | 1.47959i | − | 0.0684673i | −0.999414 | − | 0.0342336i | \(-0.989101\pi\) | ||
0.999414 | − | 0.0342336i | \(-0.0108990\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 2.44557i | − | 0.112926i | ||||||
\(470\) | −5.23844 | − | 1.15976i | −0.241631 | − | 0.0534958i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 17.9694 | − | 23.4598i | 0.827108 | − | 1.07983i | ||||
\(473\) | − | 2.44557i | − | 0.112448i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.52311 | −0.0698853 | ||||||||
\(476\) | −15.9109 | − | 7.40828i | −0.729274 | − | 0.339558i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 26.2986 | + | 5.82237i | 1.20287 | + | 0.266309i | ||||
\(479\) | −2.81215 | −0.128491 | −0.0642453 | − | 0.997934i | \(-0.520464\pi\) | ||||
−0.0642453 | + | 0.997934i | \(0.520464\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0925 | −0.916137 | ||||||||
\(482\) | −25.5510 | − | 5.65685i | −1.16382 | − | 0.257663i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.8776 | + | 9.25525i | 0.903530 | + | 0.420693i | ||||
\(485\) | −7.31695 | −0.332245 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 16.9447i | − | 0.767835i | −0.923367 | − | 0.383918i | \(-0.874575\pi\) | ||
0.923367 | − | 0.383918i | \(-0.125425\pi\) | |||||||
\(488\) | 0.658473 | − | 0.859666i | 0.0298077 | − | 0.0389153i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.90389 | + | 1.52848i | 0.311886 | + | 0.0690498i | ||||
\(491\) | 26.0696i | 1.17650i | 0.808678 | + | 0.588252i | \(0.200184\pi\) | ||||
−0.808678 | + | 0.588252i | \(0.799816\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.67987i | − | 0.0756574i | ||||||
\(494\) | 1.22782 | − | 5.54583i | 0.0552421 | − | 0.249519i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.9956 | − | 15.9763i | 0.852929 | − | 0.717358i | ||||
\(497\) | − | 13.7593i | − | 0.617188i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.5327 | 1.00870 | 0.504351 | − | 0.863499i | \(-0.331732\pi\) | ||||
0.504351 | + | 0.863499i | \(0.331732\pi\) | |||||||
\(500\) | −1.81310 | − | 0.844199i | −0.0810843 | − | 0.0377537i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.14139 | + | 23.2228i | −0.229472 | + | 1.03648i | ||||
\(503\) | −8.80342 | −0.392525 | −0.196262 | − | 0.980551i | \(-0.562880\pi\) | ||||
−0.196262 | + | 0.980551i | \(0.562880\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.5510 | 0.692011 | ||||||||
\(506\) | 0.307362 | − | 1.38830i | 0.0136639 | − | 0.0617176i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −17.3388 | + | 37.2389i | −0.769286 | + | 1.65221i | ||||
\(509\) | 20.6339 | 0.914581 | 0.457291 | − | 0.889317i | \(-0.348820\pi\) | ||||
0.457291 | + | 0.889317i | \(0.348820\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.71957i | 0.341494i | ||||||||
\(512\) | 8.60527 | − | 20.9272i | 0.380303 | − | 0.924862i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.99563 | − | 13.5307i | 0.132132 | − | 0.596815i | ||||
\(515\) | 2.08863i | 0.0920361i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 0.726241i | − | 0.0319400i | ||||||
\(518\) | 14.8786 | + | 3.29404i | 0.653728 | + | 0.144732i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.53540 | − | 5.92117i | 0.198891 | − | 0.259661i | ||||
\(521\) | − | 8.55066i | − | 0.374611i | −0.982302 | − | 0.187306i | \(-0.940025\pi\) | ||
0.982302 | − | 0.187306i | \(-0.0599755\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.0096 | 1.44341 | 0.721704 | − | 0.692202i | \(-0.243359\pi\) | ||||
0.721704 | + | 0.692202i | \(0.243359\pi\) | |||||||
\(524\) | 11.4540 | − | 24.5999i | 0.500369 | − | 1.07465i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.00000 | − | 1.77116i | −0.348817 | − | 0.0772261i | ||||
\(527\) | −38.5048 | −1.67730 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.58767 | 0.199464 | ||||||||
\(530\) | 12.1170 | + | 2.68264i | 0.526330 | + | 0.116527i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.81841 | + | 3.90543i | −0.0788382 | + | 0.169322i | ||||
\(533\) | −24.3265 | −1.05370 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2.82843i | − | 0.122284i | ||||||
\(536\) | −3.88296 | − | 2.97421i | −0.167718 | − | 0.128466i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.9711 | − | 4.64287i | −0.904126 | − | 0.200169i | ||||
\(539\) | 0.957133i | 0.0412267i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.6493i | 1.18874i | 0.804193 | + | 0.594369i | \(0.202598\pi\) | ||||
−0.804193 | + | 0.594369i | \(0.797402\pi\) | |||||||
\(542\) | −3.09683 | + | 13.9878i | −0.133020 | + | 0.600828i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −31.1127 | + | 16.2529i | −1.33394 | + | 0.696835i | ||||
\(545\) | − | 5.27400i | − | 0.225913i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.85838 | −0.421514 | −0.210757 | − | 0.977538i | \(-0.567593\pi\) | ||||
−0.210757 | + | 0.977538i | \(0.567593\pi\) | |||||||
\(548\) | 3.98937 | − | 8.56804i | 0.170418 | − | 0.366008i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.0585185 | − | 0.264318i | 0.00249524 | − | 0.0112706i | ||||
\(551\) | −0.412335 | −0.0175661 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.2341 | 0.860440 | ||||||||
\(554\) | −4.51082 | + | 20.3746i | −0.191647 | + | 0.865634i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 28.5693 | + | 13.3022i | 1.21161 | + | 0.564139i | ||||
\(557\) | −2.68305 | −0.113685 | −0.0568423 | − | 0.998383i | \(-0.518103\pi\) | ||||
−0.0568423 | + | 0.998383i | \(0.518103\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.6890i | 1.42489i | ||||||||
\(560\) | −4.32924 | + | 3.64111i | −0.182944 | + | 0.153865i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.58600 | − | 29.7478i | 0.277814 | − | 1.25484i | ||||
\(563\) | 12.0794i | 0.509087i | 0.967061 | + | 0.254543i | \(0.0819251\pi\) | ||||
−0.967061 | + | 0.254543i | \(0.918075\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 5.82237i | − | 0.244949i | ||||||
\(566\) | −25.2278 | − | 5.58530i | −1.06040 | − | 0.234768i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21.8463 | − | 16.7335i | −0.916651 | − | 0.702122i | ||||
\(569\) | − | 15.8479i | − | 0.664379i | −0.943213 | − | 0.332190i | \(-0.892213\pi\) | ||
0.943213 | − | 0.332190i | \(-0.107787\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.11078 | 0.0464847 | 0.0232423 | − | 0.999730i | \(-0.492601\pi\) | ||||
0.0232423 | + | 0.999730i | \(0.492601\pi\) | |||||||
\(572\) | 0.915238 | + | 0.426145i | 0.0382680 | + | 0.0178180i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 18.0140 | + | 3.98819i | 0.751888 | + | 0.166464i | ||||
\(575\) | 5.25240 | 0.219040 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.7755 | 0.615113 | 0.307556 | − | 0.951530i | \(-0.400489\pi\) | ||||
0.307556 | + | 0.951530i | \(0.400489\pi\) | |||||||
\(578\) | 29.6934 | + | 6.57394i | 1.23508 | + | 0.273440i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.490839 | − | 0.228540i | −0.0203810 | − | 0.00948961i | ||||
\(581\) | 21.5510 | 0.894087 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.67987i | 0.0695730i | ||||||||
\(584\) | 12.2568 | + | 9.38824i | 0.507189 | + | 0.388488i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.28467 | − | 1.83418i | −0.342237 | − | 0.0757693i | ||||
\(587\) | 13.5590i | 0.559640i | 0.960052 | + | 0.279820i | \(0.0902748\pi\) | ||||
−0.960052 | + | 0.279820i | \(0.909725\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.45126i | 0.389433i | ||||||||
\(590\) | −3.19388 | + | 14.4262i | −0.131490 | + | 0.593917i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 23.3249 | − | 19.6174i | 0.958646 | − | 0.806271i | ||||
\(593\) | − | 31.9921i | − | 1.31376i | −0.753996 | − | 0.656879i | \(-0.771876\pi\) | ||
0.753996 | − | 0.656879i | \(-0.228124\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.77551 | 0.359761 | ||||||||
\(596\) | −14.0140 | − | 6.52505i | −0.574034 | − | 0.267277i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.23407 | + | 19.1246i | −0.173144 | + | 0.782062i | ||||
\(599\) | −3.82174 | −0.156152 | −0.0780760 | − | 0.996947i | \(-0.524878\pi\) | ||||
−0.0780760 | + | 0.996947i | \(0.524878\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.6435 | 1.29076 | 0.645382 | − | 0.763860i | \(-0.276698\pi\) | ||||
0.645382 | + | 0.763860i | \(0.276698\pi\) | |||||||
\(602\) | 5.52311 | − | 24.9469i | 0.225105 | − | 1.01676i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 18.7495 | − | 40.2686i | 0.762906 | − | 1.63850i | ||||
\(605\) | −10.9634 | −0.445724 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.7204i | 1.40926i | 0.709576 | + | 0.704629i | \(0.248886\pi\) | ||||
−0.709576 | + | 0.704629i | \(0.751114\pi\) | |||||||
\(608\) | 3.98937 | + | 7.63682i | 0.161790 | + | 0.309714i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.117037 | + | 0.528636i | −0.00473869 | + | 0.0214038i | ||||
\(611\) | 10.0043i | 0.404732i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 26.3612i | − | 1.06472i | −0.846519 | − | 0.532359i | \(-0.821306\pi\) | ||
0.846519 | − | 0.532359i | \(-0.178694\pi\) | |||||||
\(614\) | −31.0741 | − | 6.87964i | −1.25405 | − | 0.277640i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.607876 | − | 0.465611i | −0.0244920 | − | 0.0187600i | ||||
\(617\) | 7.88509i | 0.317442i | 0.987323 | + | 0.158721i | \(0.0507370\pi\) | ||||
−0.987323 | + | 0.158721i | \(0.949263\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.9325 | −1.56483 | −0.782415 | − | 0.622757i | \(-0.786012\pi\) | ||||
−0.782415 | + | 0.622757i | \(0.786012\pi\) | |||||||
\(620\) | −5.23844 | + | 11.2507i | −0.210381 | + | 0.451838i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −42.8680 | − | 9.49073i | −1.71885 | − | 0.380544i | ||||
\(623\) | −5.04623 | −0.202173 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 3.08476 | + | 0.682949i | 0.123292 | + | 0.0272961i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.75552 | − | 14.5089i | 0.269575 | − | 0.578970i | ||||
\(629\) | −47.2803 | −1.88519 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 0.800468i | − | 0.0318661i | −0.999873 | − | 0.0159331i | \(-0.994928\pi\) | ||
0.999873 | − | 0.0159331i | \(-0.00507186\pi\) | |||||||
\(632\) | 24.6079 | − | 32.1267i | 0.978849 | − | 1.27793i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −22.7895 | − | 5.04546i | −0.905085 | − | 0.200381i | ||||
\(635\) | − | 20.5388i | − | 0.815057i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 13.1850i | − | 0.522409i | ||||||
\(638\) | 0.0158420 | − | 0.0715557i | 0.000627192 | − | 0.00283292i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.516138 | + | 11.3019i | 0.0204021 | + | 0.446748i | ||||
\(641\) | 22.8931i | 0.904222i | 0.891962 | + | 0.452111i | \(0.149329\pi\) | ||||
−0.891962 | + | 0.452111i | \(0.850671\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.9538 | −0.510847 | −0.255423 | − | 0.966829i | \(-0.582215\pi\) | ||||
−0.255423 | + | 0.966829i | \(0.582215\pi\) | |||||||
\(644\) | 6.27072 | − | 13.4677i | 0.247101 | − | 0.530702i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.88922 | − | 13.0501i | 0.113675 | − | 0.513449i | ||||
\(647\) | 15.6647 | 0.615844 | 0.307922 | − | 0.951412i | \(-0.400366\pi\) | ||||
0.307922 | + | 0.951412i | \(0.400366\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.00000 | −0.0785069 | ||||||||
\(650\) | −0.806122 | + | 3.64111i | −0.0316187 | + | 0.142816i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.72928 | − | 0.805173i | −0.0677239 | − | 0.0315330i | ||||
\(653\) | −41.5144 | −1.62458 | −0.812292 | − | 0.583252i | \(-0.801780\pi\) | ||||
−0.812292 | + | 0.583252i | \(0.801780\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.5679i | 0.530140i | ||||||||
\(656\) | 28.2401 | − | 23.7514i | 1.10259 | − | 0.927336i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.64015 | − | 7.40828i | 0.0639398 | − | 0.288805i | ||||
\(659\) | 34.8859i | 1.35896i | 0.733693 | + | 0.679481i | \(0.237795\pi\) | ||||
−0.733693 | + | 0.679481i | \(0.762205\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.7990i | 0.770091i | 0.922897 | + | 0.385046i | \(0.125814\pi\) | ||||
−0.922897 | + | 0.385046i | \(0.874186\pi\) | |||||||
\(662\) | 17.9248 | + | 3.96846i | 0.696668 | + | 0.154238i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 26.2095 | − | 34.2177i | 1.01713 | − | 1.32790i | ||||
\(665\) | − | 2.15401i | − | 0.0835289i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.42192 | 0.0550569 | ||||||||
\(668\) | −21.3169 | − | 9.92541i | −0.824777 | − | 0.384025i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.38776 | + | 0.528636i | 0.0922470 | + | 0.0204230i | ||||
\(671\) | −0.0732884 | −0.00282927 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.1849 | 1.31773 | 0.658866 | − | 0.752260i | \(-0.271036\pi\) | ||||
0.658866 | + | 0.752260i | \(0.271036\pi\) | |||||||
\(674\) | 37.2943 | + | 8.25674i | 1.43652 | + | 0.318038i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.9624 | + | 5.10422i | 0.421631 | + | 0.196316i | ||||
\(677\) | 17.0462 | 0.655140 | 0.327570 | − | 0.944827i | \(-0.393770\pi\) | ||||
0.327570 | + | 0.944827i | \(0.393770\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 10.3477i | − | 0.397109i | ||||||
\(680\) | 10.6724 | − | 13.9333i | 0.409269 | − | 0.534319i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.64015 | − | 0.363120i | −0.0628046 | − | 0.0139046i | ||||
\(683\) | − | 28.6671i | − | 1.09692i | −0.836178 | − | 0.548459i | \(-0.815215\pi\) | ||
0.836178 | − | 0.548459i | \(-0.184785\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.72563i | 0.180557i | ||||||||
\(686\) | −5.18785 | + | 23.4326i | −0.198073 | + | 0.894660i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −32.8925 | − | 39.1088i | −1.25402 | − | 1.49101i | ||||
\(689\) | − | 23.1410i | − | 0.881603i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.0741 | −1.02995 | −0.514974 | − | 0.857206i | \(-0.672199\pi\) | ||||
−0.514974 | + | 0.857206i | \(0.672199\pi\) | |||||||
\(692\) | −5.84632 | − | 2.72211i | −0.222244 | − | 0.103479i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.55102 | + | 7.00569i | −0.0588760 | + | 0.265932i | ||||
\(695\) | −15.7572 | −0.597704 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −57.2437 | −2.16826 | ||||||||
\(698\) | −6.15368 | + | 27.7951i | −0.232920 | + | 1.05206i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.19388 | − | 2.56411i | 0.0451243 | − | 0.0969142i | ||||
\(701\) | 23.5510 | 0.889510 | 0.444755 | − | 0.895652i | \(-0.353291\pi\) | ||||
0.444755 | + | 0.895652i | \(0.353291\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.6053i | 0.437701i | ||||||||
\(704\) | −1.47855 | + | 0.398898i | −0.0557249 | + | 0.0150340i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.37380 | − | 19.7557i | 0.164610 | − | 0.743516i | ||||
\(707\) | 21.9925i | 0.827112i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.85033i | 0.294825i | 0.989075 | + | 0.147413i | \(0.0470945\pi\) | ||||
−0.989075 | + | 0.147413i | \(0.952905\pi\) | |||||||
\(710\) | 13.4340 | + | 2.97421i | 0.504168 | + | 0.111620i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.13702 | + | 8.01216i | −0.229995 | + | 0.300268i | ||||
\(713\) | − | 32.5923i | − | 1.22059i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.504792 | −0.0188782 | ||||||||
\(716\) | 10.6385 | − | 22.8484i | 0.397579 | − | 0.853886i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −43.9388 | − | 9.72780i | −1.63978 | − | 0.363038i | ||||
\(719\) | −10.1416 | −0.378218 | −0.189109 | − | 0.981956i | \(-0.560560\pi\) | ||||
−0.189109 | + | 0.981956i | \(0.560560\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.95377 | −0.110004 | ||||||||
\(722\) | 23.0316 | + | 5.09906i | 0.857146 | + | 0.189767i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −20.3511 | + | 43.7084i | −0.756343 | + | 1.62441i | ||||
\(725\) | 0.270718 | 0.0100542 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.86524i | 0.180442i | 0.995922 | + | 0.0902208i | \(0.0287573\pi\) | ||||
−0.995922 | + | 0.0902208i | \(0.971243\pi\) | |||||||
\(728\) | 8.37380 | + | 6.41403i | 0.310354 | + | 0.237720i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.53707 | − | 1.66866i | −0.278959 | − | 0.0617601i | ||||
\(731\) | 79.2749i | 2.93209i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 9.09903i | − | 0.336080i | −0.985780 | − | 0.168040i | \(-0.946256\pi\) | ||
0.985780 | − | 0.168040i | \(-0.0537438\pi\) | |||||||
\(734\) | 7.02624 | − | 31.7363i | 0.259343 | − | 1.17141i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.7572 | − | 26.3352i | −0.507097 | − | 0.970730i | ||||
\(737\) | 0.331031i | 0.0121937i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.5693 | 0.462371 | 0.231185 | − | 0.972910i | \(-0.425740\pi\) | ||||
0.231185 | + | 0.972910i | \(0.425740\pi\) | |||||||
\(740\) | −6.43232 | + | 13.8148i | −0.236457 | + | 0.507842i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.79383 | + | 17.1361i | −0.139276 | + | 0.629085i | ||||
\(743\) | 23.6647 | 0.868175 | 0.434087 | − | 0.900871i | \(-0.357071\pi\) | ||||
0.434087 | + | 0.900871i | \(0.357071\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.72928 | 0.283179 | ||||||||
\(746\) | 4.35382 | − | 19.6654i | 0.159405 | − | 0.720002i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.15368 | + | 1.00278i | 0.0787464 | + | 0.0366652i | ||||
\(749\) | 4.00000 | 0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.2782i | 1.14136i | 0.821173 | + | 0.570679i | \(0.193320\pi\) | ||||
−0.821173 | + | 0.570679i | \(0.806680\pi\) | |||||||
\(752\) | −9.76781 | − | 11.6138i | −0.356196 | − | 0.423512i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.218232 | + | 0.985716i | −0.00794754 | + | 0.0358977i | ||||
\(755\) | 22.2098i | 0.808297i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.1150i | 1.42166i | 0.703365 | + | 0.710829i | \(0.251680\pi\) | ||||
−0.703365 | + | 0.710829i | \(0.748320\pi\) | |||||||
\(758\) | 12.0279 | + | 2.66291i | 0.436873 | + | 0.0967213i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.42003 | − | 2.61962i | −0.124058 | − | 0.0950236i | ||||
\(761\) | − | 2.76305i | − | 0.100160i | −0.998745 | − | 0.0500802i | \(-0.984052\pi\) | ||
0.998745 | − | 0.0500802i | \(-0.0159477\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.45856 | 0.270018 | ||||||||
\(764\) | −19.7938 | − | 9.21623i | −0.716116 | − | 0.333431i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 25.8357 | + | 5.71988i | 0.933482 | + | 0.206668i | ||||
\(767\) | 27.5510 | 0.994810 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.5606 | 1.67902 | 0.839509 | − | 0.543345i | \(-0.182843\pi\) | ||||
0.839509 | + | 0.543345i | \(0.182843\pi\) | |||||||
\(770\) | 0.373802 | + | 0.0827577i | 0.0134709 | + | 0.00298238i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −27.7711 | − | 12.9306i | −0.999505 | − | 0.465381i | ||||
\(773\) | 29.5877 | 1.06419 | 0.532097 | − | 0.846683i | \(-0.321404\pi\) | ||||
0.532097 | + | 0.846683i | \(0.321404\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 6.20522i | − | 0.222898i | ||||||
\(776\) | −16.4296 | − | 12.5845i | −0.589789 | − | 0.451757i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −37.2943 | − | 8.25674i | −1.33706 | − | 0.296019i | ||||
\(779\) | 14.0508i | 0.503424i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.86244i | 0.0666435i | ||||||||
\(782\) | −9.96336 | + | 45.0027i | −0.356289 | + | 1.60929i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 12.8733 | + | 15.3062i | 0.459760 | + | 0.546649i | ||||
\(785\) | 8.00229i | 0.285614i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.9267 | −1.28065 | −0.640324 | − | 0.768105i | \(-0.721200\pi\) | ||||
−0.640324 | + | 0.768105i | \(0.721200\pi\) | |||||||
\(788\) | 30.9065 | + | 14.3904i | 1.10100 | + | 0.512637i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.37380 | + | 19.7557i | −0.155613 | + | 0.702876i | ||||
\(791\) | 8.23407 | 0.292770 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00958 | 0.0358514 | ||||||||
\(794\) | −7.76322 | + | 35.0651i | −0.275506 | + | 1.24441i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.98937 | − | 8.56804i | 0.141400 | − | 0.303686i | ||||
\(797\) | 9.31695 | 0.330023 | 0.165012 | − | 0.986292i | \(-0.447234\pi\) | ||||
0.165012 | + | 0.986292i | \(0.447234\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.5416i | 0.832841i | ||||||||
\(800\) | −2.61922 | − | 5.01395i | −0.0926035 | − | 0.177270i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.83840 | − | 8.30372i | 0.0649161 | − | 0.293215i | ||||
\(803\) | − | 1.04491i | − | 0.0368742i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.42801i | 0.261803i | ||||||||
\(806\) | 22.5939 | + | 5.00217i | 0.795837 | + | 0.176194i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 34.9186 | + | 26.7464i | 1.22843 | + | 0.940934i | ||||
\(809\) | 34.9207i | 1.22775i | 0.789405 | + | 0.613873i | \(0.210389\pi\) | ||||
−0.789405 | + | 0.613873i | \(0.789611\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.7938 | −0.905744 | −0.452872 | − | 0.891576i | \(-0.649601\pi\) | ||||
−0.452872 | + | 0.891576i | \(0.649601\pi\) | |||||||
\(812\) | 0.323204 | − | 0.694151i | 0.0113423 | − | 0.0243599i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.01395 | − | 0.445878i | −0.0705890 | − | 0.0156280i | ||||
\(815\) | 0.953771 | 0.0334092 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.4586 | 0.680769 | ||||||||
\(818\) | 26.9956 | + | 5.97668i | 0.943880 | + | 0.208970i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.78780 | + | 16.7260i | −0.271962 | + | 0.584096i | ||||
\(821\) | −31.1878 | −1.08846 | −0.544232 | − | 0.838935i | \(-0.683179\pi\) | ||||
−0.544232 | + | 0.838935i | \(0.683179\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 33.5718i | − | 1.17024i | −0.810947 | − | 0.585120i | \(-0.801047\pi\) | ||
0.810947 | − | 0.585120i | \(-0.198953\pi\) | |||||||
\(824\) | −3.59226 | + | 4.68985i | −0.125142 | + | 0.163379i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −20.4017 | − | 4.51683i | −0.709866 | − | 0.157160i | ||||
\(827\) | 53.4362i | 1.85816i | 0.369881 | + | 0.929079i | \(0.379399\pi\) | ||||
−0.369881 | + | 0.929079i | \(0.620601\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 0.634952i | − | 0.0220528i | −0.999939 | − | 0.0110264i | \(-0.996490\pi\) | ||
0.999939 | − | 0.0110264i | \(-0.00350988\pi\) | |||||||
\(830\) | −4.65847 | + | 21.0415i | −0.161698 | + | 0.730361i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 20.3678 | − | 5.49503i | 0.706125 | − | 0.190506i | ||||
\(833\) | − | 31.0261i | − | 1.07499i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.7572 | 0.406874 | ||||||||
\(836\) | 0.246139 | − | 0.528636i | 0.00851288 | − | 0.0182833i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.599955 | − | 2.70989i | 0.0207251 | − | 0.0936117i | ||||
\(839\) | −24.9046 | −0.859803 | −0.429901 | − | 0.902876i | \(-0.641452\pi\) | ||||
−0.429901 | + | 0.902876i | \(0.641452\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9267 | −0.997473 | ||||||||
\(842\) | 1.31695 | − | 5.94842i | 0.0453850 | − | 0.204996i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 30.5327 | + | 14.2164i | 1.05098 | + | 0.489347i | ||||
\(845\) | −6.04623 | −0.207997 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 15.5045i | − | 0.532742i | ||||||
\(848\) | 22.5939 | + | 26.8639i | 0.775878 | + | 0.922509i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.89692 | + | 8.56804i | −0.0650637 | + | 0.293881i | ||||
\(851\) | − | 40.0203i | − | 1.37188i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.5448i | 0.600724i | 0.953825 | + | 0.300362i | \(0.0971075\pi\) | ||||
−0.953825 | + | 0.300362i | \(0.902893\pi\) | |||||||
\(854\) | −0.747604 | − | 0.165515i | −0.0255825 | − | 0.00566382i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.86464 | − | 6.35101i | 0.166270 | − | 0.217073i | ||||
\(857\) | − | 7.30196i | − | 0.249430i | −0.992193 | − | 0.124715i | \(-0.960198\pi\) | ||
0.992193 | − | 0.124715i | \(-0.0398017\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.2890 | 0.521655 | 0.260828 | − | 0.965385i | \(-0.416005\pi\) | ||||
0.260828 | + | 0.965385i | \(0.416005\pi\) | |||||||
\(860\) | 23.1633 | + | 10.7851i | 0.789861 | + | 0.367768i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.3232 | − | 3.61387i | −0.555971 | − | 0.123089i | ||||
\(863\) | −41.9787 | −1.42897 | −0.714487 | − | 0.699649i | \(-0.753340\pi\) | ||||
−0.714487 | + | 0.699649i | \(0.753340\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.22449 | 0.109636 | ||||||||
\(866\) | −13.0602 | − | 2.89145i | −0.443803 | − | 0.0982555i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −15.9109 | − | 7.40828i | −0.540050 | − | 0.251453i | ||||
\(869\) | −2.73887 | −0.0929097 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 4.56012i | − | 0.154514i | ||||||
\(872\) | 9.07081 | − | 11.8423i | 0.307176 | − | 0.401032i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11.0462 | + | 2.44557i | 0.373644 | + | 0.0827228i | ||||
\(875\) | 1.41421i | 0.0478091i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.4800i | 1.29938i | 0.760200 | + | 0.649689i | \(0.225101\pi\) | ||||
−0.760200 | + | 0.649689i | \(0.774899\pi\) | |||||||
\(878\) | −4.90317 | + | 22.1468i | −0.165474 | + | 0.747418i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.586002 | − | 0.492858i | 0.0197541 | − | 0.0166142i | ||||
\(881\) | 7.11053i | 0.239560i | 0.992800 | + | 0.119780i | \(0.0382189\pi\) | ||||
−0.992800 | + | 0.119780i | \(0.961781\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.5048 | −0.891957 | −0.445979 | − | 0.895044i | \(-0.647144\pi\) | ||||
−0.445979 | + | 0.895044i | \(0.647144\pi\) | |||||||
\(884\) | −29.6681 | − | 13.8138i | −0.997845 | − | 0.464608i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.66473 | + | 34.6202i | −0.257502 | + | 1.16309i | ||||
\(887\) | 39.3449 | 1.32107 | 0.660535 | − | 0.750795i | \(-0.270329\pi\) | ||||
0.660535 | + | 0.750795i | \(0.270329\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.0462 | 0.974179 | ||||||||
\(890\) | 1.09079 | − | 4.92693i | 0.0365635 | − | 0.165151i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.8340 | + | 40.4501i | −0.630610 | + | 1.35437i | ||||
\(893\) | 5.77844 | 0.193368 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.6019i | 0.421234i | ||||||||
\(896\) | −15.9833 | + | 0.729929i | −0.533966 | + | 0.0243852i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.29696 | − | 5.85815i | 0.0432802 | − | 0.195489i | ||||
\(899\) | − | 1.67987i | − | 0.0560267i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 54.4540i | − | 1.81413i | ||||||
\(902\) | −2.43835 | − | 0.539838i | −0.0811883 | − | 0.0179746i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.0140 | − | 13.0737i | 0.333059 | − | 0.434824i | ||||
\(905\) | − | 24.1070i | − | 0.801344i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.1974 | −0.737054 | −0.368527 | − | 0.929617i | \(-0.620138\pi\) | ||||
−0.368527 | + | 0.929617i | \(0.620138\pi\) | |||||||
\(908\) | 7.48647 | − | 16.0788i | 0.248447 | − | 0.533594i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.14931 | − | 1.14003i | −0.170698 | − | 0.0377916i | ||||
\(911\) | 20.9538 | 0.694229 | 0.347115 | − | 0.937823i | \(-0.387161\pi\) | ||||
0.347115 | + | 0.937823i | \(0.387161\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.91713 | −0.0965428 | ||||||||
\(914\) | −39.8603 | − | 8.82484i | −1.31846 | − | 0.291900i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.9634 | − | 38.5802i | 0.593526 | − | 1.27472i | ||||
\(917\) | −19.1878 | −0.633638 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.88509i | 0.260105i | 0.991507 | + | 0.130053i | \(0.0415146\pi\) | ||||
−0.991507 | + | 0.130053i | \(0.958485\pi\) | |||||||
\(920\) | 11.7938 | + | 9.03365i | 0.388831 | + | 0.297831i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 50.7282 | + | 11.2310i | 1.67065 | + | 0.369872i | ||||
\(923\) | − | 25.6561i | − | 0.844481i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 7.61944i | − | 0.250526i | ||||||
\(926\) | 5.07873 | − | 22.9397i | 0.166897 | − | 0.753846i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.709071 | − | 1.35737i | −0.0232764 | − | 0.0445578i | ||||
\(929\) | 6.35718i | 0.208572i | 0.994547 | + | 0.104286i | \(0.0332558\pi\) | ||||
−0.994547 | + | 0.104286i | \(0.966744\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.61557 | −0.249590 | ||||||||
\(932\) | −12.7249 | + | 27.3295i | −0.416818 | + | 0.895207i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.452306 | + | 2.04299i | −0.0147999 | + | 0.0668486i | ||||
\(935\) | −1.18785 | −0.0388467 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.0096 | 1.14371 | 0.571857 | − | 0.820354i | \(-0.306223\pi\) | ||||
0.571857 | + | 0.820354i | \(0.306223\pi\) | |||||||
\(938\) | −0.747604 | + | 3.37680i | −0.0244101 | + | 0.110256i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.87859 | + | 3.20275i | 0.224355 | + | 0.104462i | ||||
\(941\) | 28.5606 | 0.931049 | 0.465525 | − | 0.885035i | \(-0.345866\pi\) | ||||
0.465525 | + | 0.885035i | \(0.345866\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 48.4538i | − | 1.57787i | ||||||
\(944\) | −31.9833 | + | 26.8997i | −1.04097 | + | 0.875509i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.747604 | + | 3.37680i | −0.0243067 | + | 0.109789i | ||||
\(947\) | − | 20.7650i | − | 0.674771i | −0.941367 | − | 0.337385i | \(-0.890457\pi\) | ||
0.941367 | − | 0.337385i | \(-0.109543\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.3942i | 0.467257i | ||||||||
\(950\) | 2.10308 | + | 0.465611i | 0.0682330 | + | 0.0151064i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 19.7047 | + | 15.0931i | 0.638633 | + | 0.489170i | ||||
\(953\) | − | 38.4147i | − | 1.24437i | −0.782869 | − | 0.622186i | \(-0.786245\pi\) | ||
0.782869 | − | 0.622186i | \(-0.213755\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.9171 | 0.353270 | ||||||||
\(956\) | −34.5327 | − | 16.0788i | −1.11687 | − | 0.520026i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.88296 | + | 0.859666i | 0.125453 | + | 0.0277746i | ||||
\(959\) | −6.68305 | −0.215807 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.50479 | −0.242090 | ||||||||
\(962\) | 27.7432 | + | 6.14220i | 0.894478 | + | 0.198032i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 33.5510 | + | 15.6217i | 1.08061 | + | 0.503142i | ||||
\(965\) | 15.3169 | 0.493070 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.6013i | 0.533861i | 0.963716 | + | 0.266930i | \(0.0860094\pi\) | ||||
−0.963716 | + | 0.266930i | \(0.913991\pi\) | |||||||
\(968\) | −24.6173 | − | 18.8560i | −0.791231 | − | 0.606054i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.1031 | + | 2.23677i | 0.324390 | + | 0.0718182i | ||||
\(971\) | 10.3171i | 0.331092i | 0.986202 | + | 0.165546i | \(0.0529386\pi\) | ||||
−0.986202 | + | 0.165546i | \(0.947061\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 22.2840i | − | 0.714393i | ||||||
\(974\) | −5.17992 | + | 23.3968i | −0.165975 | + | 0.749682i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.17200 | + | 0.985716i | −0.0375149 | + | 0.0315520i | ||||
\(977\) | 32.0439i | 1.02518i | 0.858635 | + | 0.512588i | \(0.171313\pi\) | ||||
−0.858635 | + | 0.512588i | \(0.828687\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.683053 | 0.0218305 | ||||||||
\(980\) | −9.06550 | − | 4.22099i | −0.289587 | − | 0.134835i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.96939 | − | 35.9963i | 0.254313 | − | 1.14869i | ||||
\(983\) | 24.8034 | 0.791106 | 0.395553 | − | 0.918443i | \(-0.370553\pi\) | ||||
0.395553 | + | 0.918443i | \(0.370553\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.0462 | −0.543138 | ||||||||
\(986\) | −0.513530 | + | 2.31952i | −0.0163541 | + | 0.0738687i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.39069 | + | 7.28223i | −0.107872 | + | 0.231679i | ||||
\(989\) | −67.1020 | −2.13372 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.7872i | 0.501498i | 0.968052 | + | 0.250749i | \(0.0806769\pi\) | ||||
−0.968052 | + | 0.250749i | \(0.919323\pi\) | |||||||
\(992\) | −31.1127 | + | 16.2529i | −0.987828 | + | 0.516029i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.20617 | + | 18.9985i | −0.133412 | + | 0.602597i | ||||
\(995\) | 4.72563i | 0.149813i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 51.3823i | − | 1.62729i | −0.581359 | − | 0.813647i | \(-0.697479\pi\) | ||
0.581359 | − | 0.813647i | \(-0.302521\pi\) | |||||||
\(998\) | −31.1127 | − | 6.88817i | −0.984854 | − | 0.218041i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))