Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(1549,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.1549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2125.3 | ||
Root | \(0.500000 - 2.05195i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.2125 |
Dual form | 2646.2.e.o.1549.3 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.230252 | − | 0.398809i | 0.102972 | − | 0.178353i | −0.809936 | − | 0.586519i | \(-0.800498\pi\) |
0.912908 | + | 0.408166i | \(0.133831\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.230252 | + | 0.398809i | −0.0728122 | + | 0.126114i | ||||
\(11\) | −1.82383 | − | 3.15897i | −0.549906 | − | 0.952465i | −0.998280 | − | 0.0586193i | \(-0.981330\pi\) |
0.448374 | − | 0.893846i | \(-0.352003\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.730252 | − | 1.26483i | −0.202536 | − | 0.350802i | 0.746809 | − | 0.665038i | \(-0.231585\pi\) |
−0.949345 | + | 0.314236i | \(0.898252\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.86693 | + | 3.23361i | −0.452796 | + | 0.784266i | −0.998558 | − | 0.0536743i | \(-0.982907\pi\) |
0.545763 | + | 0.837940i | \(0.316240\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.02704 | + | 3.51094i | 0.465035 | + | 0.805465i | 0.999203 | − | 0.0399136i | \(-0.0127083\pi\) |
−0.534168 | + | 0.845378i | \(0.679375\pi\) | |||||||
\(20\) | 0.230252 | − | 0.398809i | 0.0514860 | − | 0.0891764i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.82383 | + | 3.15897i | 0.388842 | + | 0.673495i | ||||
\(23\) | 0.566537 | − | 0.981271i | 0.118131 | − | 0.204609i | −0.800896 | − | 0.598804i | \(-0.795643\pi\) |
0.919027 | + | 0.394194i | \(0.128976\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.39397 | + | 4.14647i | 0.478794 | + | 0.829295i | ||||
\(26\) | 0.730252 | + | 1.26483i | 0.143214 | + | 0.248054i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.48755 | − | 7.77266i | 0.833317 | − | 1.44335i | −0.0620772 | − | 0.998071i | \(-0.519772\pi\) |
0.895394 | − | 0.445275i | \(-0.146894\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.514589 | 0.0924229 | 0.0462115 | − | 0.998932i | \(-0.485285\pi\) | ||||
0.0462115 | + | 0.998932i | \(0.485285\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.86693 | − | 3.23361i | 0.320175 | − | 0.554560i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.55408 | − | 7.88791i | −0.748687 | − | 1.29676i | −0.948452 | − | 0.316920i | \(-0.897351\pi\) |
0.199765 | − | 0.979844i | \(-0.435982\pi\) | |||||||
\(38\) | −2.02704 | − | 3.51094i | −0.328830 | − | 0.569550i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.230252 | + | 0.398809i | −0.0364061 | + | 0.0630572i | ||||
\(41\) | −0.472958 | − | 0.819187i | −0.0738636 | − | 0.127936i | 0.826728 | − | 0.562602i | \(-0.190200\pi\) |
−0.900592 | + | 0.434666i | \(0.856866\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.66372 | − | 8.07779i | 0.711210 | − | 1.23185i | −0.253193 | − | 0.967416i | \(-0.581481\pi\) |
0.964403 | − | 0.264436i | \(-0.0851858\pi\) | |||||||
\(44\) | −1.82383 | − | 3.15897i | −0.274953 | − | 0.476233i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.566537 | + | 0.981271i | −0.0835314 | + | 0.144681i | ||||
\(47\) | 2.32743 | 0.339491 | 0.169745 | − | 0.985488i | \(-0.445705\pi\) | ||||
0.169745 | + | 0.985488i | \(0.445705\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.39397 | − | 4.14647i | −0.338558 | − | 0.586400i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.730252 | − | 1.26483i | −0.101268 | − | 0.175401i | ||||
\(53\) | −6.21780 | + | 10.7695i | −0.854080 | + | 1.47931i | 0.0234151 | + | 0.999726i | \(0.492546\pi\) |
−0.877495 | + | 0.479585i | \(0.840787\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.67977 | −0.226500 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.48755 | + | 7.77266i | −0.589244 | + | 1.02060i | ||||
\(59\) | −12.8961 | −1.67893 | −0.839465 | − | 0.543414i | \(-0.817131\pi\) | ||||
−0.839465 | + | 0.543414i | \(0.817131\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0833 | −1.54710 | −0.773552 | − | 0.633733i | \(-0.781522\pi\) | ||||
−0.773552 | + | 0.633733i | \(0.781522\pi\) | |||||||
\(62\) | −0.514589 | −0.0653529 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.672570 | −0.0834220 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.32023 | −0.283462 | −0.141731 | − | 0.989905i | \(-0.545267\pi\) | ||||
−0.141731 | + | 0.989905i | \(0.545267\pi\) | |||||||
\(68\) | −1.86693 | + | 3.23361i | −0.226398 | + | 0.392133i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.67977 | −0.199352 | −0.0996758 | − | 0.995020i | \(-0.531781\pi\) | ||||
−0.0996758 | + | 0.995020i | \(0.531781\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.62062 | − | 11.4673i | 0.774885 | − | 1.34214i | −0.159974 | − | 0.987121i | \(-0.551141\pi\) |
0.934859 | − | 0.355019i | \(-0.115526\pi\) | |||||||
\(74\) | 4.55408 | + | 7.88791i | 0.529402 | + | 0.916950i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.02704 | + | 3.51094i | 0.232518 | + | 0.402732i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.00720 | −0.563354 | −0.281677 | − | 0.959509i | \(-0.590891\pi\) | ||||
−0.281677 | + | 0.959509i | \(0.590891\pi\) | |||||||
\(80\) | 0.230252 | − | 0.398809i | 0.0257430 | − | 0.0445882i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.472958 | + | 0.819187i | 0.0522295 | + | 0.0904641i | ||||
\(83\) | 3.32383 | − | 5.75705i | 0.364838 | − | 0.631918i | −0.623912 | − | 0.781494i | \(-0.714458\pi\) |
0.988750 | + | 0.149577i | \(0.0477911\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.859728 | + | 1.48909i | 0.0932506 | + | 0.161515i | ||||
\(86\) | −4.66372 | + | 8.07779i | −0.502901 | + | 0.871051i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.82383 | + | 3.15897i | 0.194421 | + | 0.336747i | ||||
\(89\) | −1.36333 | − | 2.36135i | −0.144512 | − | 0.250303i | 0.784679 | − | 0.619903i | \(-0.212828\pi\) |
−0.929191 | + | 0.369600i | \(0.879495\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.566537 | − | 0.981271i | 0.0590656 | − | 0.102305i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.32743 | −0.240056 | ||||||||
\(95\) | 1.86693 | 0.191543 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.59358 | − | 9.68836i | 0.567942 | − | 0.983704i | −0.428827 | − | 0.903386i | \(-0.641073\pi\) |
0.996769 | − | 0.0803178i | \(-0.0255935\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.39397 | + | 4.14647i | 0.239397 | + | 0.414647i | ||||
\(101\) | −6.87792 | − | 11.9129i | −0.684378 | − | 1.18538i | −0.973632 | − | 0.228125i | \(-0.926740\pi\) |
0.289254 | − | 0.957253i | \(-0.406593\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.58113 | − | 9.66679i | 0.549925 | − | 0.952498i | −0.448354 | − | 0.893856i | \(-0.647990\pi\) |
0.998279 | − | 0.0586417i | \(-0.0186769\pi\) | |||||||
\(104\) | 0.730252 | + | 1.26483i | 0.0716071 | + | 0.124027i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.21780 | − | 10.7695i | 0.603926 | − | 1.04603i | ||||
\(107\) | 3.89037 | + | 6.73832i | 0.376096 | + | 0.651418i | 0.990490 | − | 0.137581i | \(-0.0439329\pi\) |
−0.614394 | + | 0.788999i | \(0.710600\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.75729 | + | 6.50783i | −0.359884 | + | 0.623337i | −0.987941 | − | 0.154830i | \(-0.950517\pi\) |
0.628058 | + | 0.778167i | \(0.283850\pi\) | |||||||
\(110\) | 1.67977 | 0.160159 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.03064 | − | 5.24922i | −0.285099 | − | 0.493805i | 0.687534 | − | 0.726152i | \(-0.258693\pi\) |
−0.972633 | + | 0.232346i | \(0.925360\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.260893 | − | 0.451880i | −0.0243284 | − | 0.0421380i | ||||
\(116\) | 4.48755 | − | 7.77266i | 0.416658 | − | 0.721673i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.8961 | 1.18718 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.15272 | + | 1.99658i | −0.104793 | + | 0.181507i | ||||
\(122\) | 12.0833 | 1.09397 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.514589 | 0.0462115 | ||||||||
\(125\) | 4.50739 | 0.403153 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.80992 | 0.781754 | 0.390877 | − | 0.920443i | \(-0.372172\pi\) | ||||
0.390877 | + | 0.920443i | \(0.372172\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.672570 | 0.0589883 | ||||||||
\(131\) | −10.5687 | + | 18.3055i | −0.923389 | + | 1.59936i | −0.129258 | + | 0.991611i | \(0.541260\pi\) |
−0.794131 | + | 0.607746i | \(0.792074\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.32023 | 0.200438 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.86693 | − | 3.23361i | 0.160088 | − | 0.277280i | ||||
\(137\) | −2.20321 | − | 3.81607i | −0.188233 | − | 0.326029i | 0.756428 | − | 0.654077i | \(-0.226943\pi\) |
−0.944661 | + | 0.328048i | \(0.893609\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.01245 | + | 1.75362i | 0.0858751 | + | 0.148740i | 0.905764 | − | 0.423783i | \(-0.139298\pi\) |
−0.819889 | + | 0.572523i | \(0.805965\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.67977 | 0.140963 | ||||||||
\(143\) | −2.66372 | + | 4.61369i | −0.222751 | + | 0.385816i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.06654 | − | 3.57935i | −0.171617 | − | 0.297249i | ||||
\(146\) | −6.62062 | + | 11.4673i | −0.547927 | + | 0.949037i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.55408 | − | 7.88791i | −0.374343 | − | 0.648382i | ||||
\(149\) | −4.58113 | + | 7.93474i | −0.375300 | + | 0.650040i | −0.990372 | − | 0.138432i | \(-0.955794\pi\) |
0.615071 | + | 0.788471i | \(0.289127\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.0519482 | + | 0.0899768i | 0.00422748 | + | 0.00732221i | 0.868131 | − | 0.496334i | \(-0.165321\pi\) |
−0.863904 | + | 0.503657i | \(0.831988\pi\) | |||||||
\(152\) | −2.02704 | − | 3.51094i | −0.164415 | − | 0.284775i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.118485 | − | 0.205223i | 0.00951698 | − | 0.0164839i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.9823 | −1.67457 | −0.837285 | − | 0.546767i | \(-0.815858\pi\) | ||||
−0.837285 | + | 0.546767i | \(0.815858\pi\) | |||||||
\(158\) | 5.00720 | 0.398351 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.230252 | + | 0.398809i | −0.0182031 | + | 0.0315286i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.5182 | − | 19.9501i | −0.902174 | − | 1.56261i | −0.824666 | − | 0.565620i | \(-0.808637\pi\) |
−0.0775078 | − | 0.996992i | \(-0.524696\pi\) | |||||||
\(164\) | −0.472958 | − | 0.819187i | −0.0369318 | − | 0.0639678i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.32383 | + | 5.75705i | −0.257979 | + | 0.446833i | ||||
\(167\) | −5.31498 | − | 9.20581i | −0.411285 | − | 0.712367i | 0.583745 | − | 0.811937i | \(-0.301587\pi\) |
−0.995031 | + | 0.0995698i | \(0.968253\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.43346 | − | 9.41103i | 0.417959 | − | 0.723926i | ||||
\(170\) | −0.859728 | − | 1.48909i | −0.0659382 | − | 0.114208i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.66372 | − | 8.07779i | 0.355605 | − | 0.615926i | ||||
\(173\) | 2.93872 | 0.223427 | 0.111713 | − | 0.993740i | \(-0.464366\pi\) | ||||
0.111713 | + | 0.993740i | \(0.464366\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.82383 | − | 3.15897i | −0.137476 | − | 0.238116i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.36333 | + | 2.36135i | 0.102186 | + | 0.176991i | ||||
\(179\) | 4.58113 | − | 7.93474i | 0.342409 | − | 0.593071i | −0.642470 | − | 0.766311i | \(-0.722090\pi\) |
0.984880 | + | 0.173240i | \(0.0554237\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.4284 | −1.66709 | −0.833545 | − | 0.552452i | \(-0.813692\pi\) | ||||
−0.833545 | + | 0.552452i | \(0.813692\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.566537 | + | 0.981271i | −0.0417657 | + | 0.0723403i | ||||
\(185\) | −4.19436 | −0.308375 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.6198 | 0.995981 | ||||||||
\(188\) | 2.32743 | 0.169745 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.86693 | −0.135441 | ||||||||
\(191\) | −2.48968 | −0.180147 | −0.0900736 | − | 0.995935i | \(-0.528710\pi\) | ||||
−0.0900736 | + | 0.995935i | \(0.528710\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.48968 | 0.323174 | 0.161587 | − | 0.986858i | \(-0.448339\pi\) | ||||
0.161587 | + | 0.986858i | \(0.448339\pi\) | |||||||
\(194\) | −5.59358 | + | 9.68836i | −0.401596 | + | 0.695584i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.7339 | −0.907249 | −0.453625 | − | 0.891193i | \(-0.649869\pi\) | ||||
−0.453625 | + | 0.891193i | \(0.649869\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.47296 | − | 2.55124i | 0.104415 | − | 0.180852i | −0.809084 | − | 0.587693i | \(-0.800036\pi\) |
0.913499 | + | 0.406841i | \(0.133370\pi\) | |||||||
\(200\) | −2.39397 | − | 4.14647i | −0.169279 | − | 0.293200i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.87792 | + | 11.9129i | 0.483928 | + | 0.838189i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.435599 | −0.0304235 | ||||||||
\(206\) | −5.58113 | + | 9.66679i | −0.388855 | + | 0.673517i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.730252 | − | 1.26483i | −0.0506339 | − | 0.0877005i | ||||
\(209\) | 7.39397 | − | 12.8067i | 0.511451 | − | 0.885860i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.608168 | − | 1.05338i | −0.0418680 | − | 0.0725176i | 0.844332 | − | 0.535820i | \(-0.179998\pi\) |
−0.886200 | + | 0.463303i | \(0.846664\pi\) | |||||||
\(212\) | −6.21780 | + | 10.7695i | −0.427040 | + | 0.739655i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.89037 | − | 6.73832i | −0.265940 | − | 0.460622i | ||||
\(215\) | −2.14766 | − | 3.71986i | −0.146469 | − | 0.253693i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.75729 | − | 6.50783i | 0.254476 | − | 0.440766i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.67977 | −0.113250 | ||||||||
\(221\) | 5.45331 | 0.366829 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.445916 | − | 0.772349i | 0.0298607 | − | 0.0517203i | −0.850709 | − | 0.525637i | \(-0.823827\pi\) |
0.880570 | + | 0.473917i | \(0.157160\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.03064 | + | 5.24922i | 0.201595 | + | 0.349173i | ||||
\(227\) | 7.32597 | + | 12.6889i | 0.486242 | + | 0.842195i | 0.999875 | − | 0.0158147i | \(-0.00503418\pi\) |
−0.513633 | + | 0.858010i | \(0.671701\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.78794 | + | 8.29295i | −0.316396 | + | 0.548013i | −0.979733 | − | 0.200307i | \(-0.935806\pi\) |
0.663338 | + | 0.748320i | \(0.269139\pi\) | |||||||
\(230\) | 0.260893 | + | 0.451880i | 0.0172028 | + | 0.0297961i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.48755 | + | 7.77266i | −0.294622 | + | 0.510300i | ||||
\(233\) | −7.21420 | − | 12.4954i | −0.472618 | − | 0.818598i | 0.526891 | − | 0.849933i | \(-0.323358\pi\) |
−0.999509 | + | 0.0313345i | \(0.990024\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.535897 | − | 0.928200i | 0.0349580 | − | 0.0605491i | ||||
\(236\) | −12.8961 | −0.839465 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.15486 | + | 15.8567i | 0.592179 | + | 1.02568i | 0.993938 | + | 0.109938i | \(0.0350654\pi\) |
−0.401760 | + | 0.915745i | \(0.631601\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.0466924 | + | 0.0808735i | 0.00300772 | + | 0.00520952i | 0.867525 | − | 0.497393i | \(-0.165709\pi\) |
−0.864518 | + | 0.502602i | \(0.832376\pi\) | |||||||
\(242\) | 1.15272 | − | 1.99658i | 0.0741000 | − | 0.128345i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.0833 | −0.773552 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.96050 | − | 5.12774i | 0.188372 | − | 0.326271i | ||||
\(248\) | −0.514589 | −0.0326764 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.50739 | −0.285072 | ||||||||
\(251\) | −18.2733 | −1.15340 | −0.576702 | − | 0.816955i | \(-0.695661\pi\) | ||||
−0.576702 | + | 0.816955i | \(0.695661\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.13307 | −0.259844 | ||||||||
\(254\) | −8.80992 | −0.552783 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.5256 | − | 18.2308i | 0.656568 | − | 1.13721i | −0.324931 | − | 0.945738i | \(-0.605341\pi\) |
0.981498 | − | 0.191471i | \(-0.0613257\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.672570 | −0.0417110 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.5687 | − | 18.3055i | 0.652935 | − | 1.13092i | ||||
\(263\) | −2.58259 | − | 4.47318i | −0.159249 | − | 0.275828i | 0.775349 | − | 0.631533i | \(-0.217574\pi\) |
−0.934598 | + | 0.355705i | \(0.884241\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.86333 | + | 4.95943i | 0.175893 | + | 0.304655i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.32023 | −0.141731 | ||||||||
\(269\) | 8.42840 | − | 14.5984i | 0.513889 | − | 0.890081i | −0.485981 | − | 0.873969i | \(-0.661538\pi\) |
0.999870 | − | 0.0161123i | \(-0.00512891\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.5562 | − | 21.7480i | −0.762736 | − | 1.32110i | −0.941435 | − | 0.337194i | \(-0.890522\pi\) |
0.178699 | − | 0.983904i | \(-0.442811\pi\) | |||||||
\(272\) | −1.86693 | + | 3.23361i | −0.113199 | + | 0.196066i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.20321 | + | 3.81607i | 0.133101 | + | 0.230537i | ||||
\(275\) | 8.73239 | − | 15.1249i | 0.526583 | − | 0.912068i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.69076 | − | 2.92848i | −0.101588 | − | 0.175955i | 0.810751 | − | 0.585391i | \(-0.199059\pi\) |
−0.912339 | + | 0.409436i | \(0.865726\pi\) | |||||||
\(278\) | −1.01245 | − | 1.75362i | −0.0607229 | − | 0.105175i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.1388 | − | 17.5609i | 0.604831 | − | 1.04760i | −0.387248 | − | 0.921976i | \(-0.626574\pi\) |
0.992078 | − | 0.125622i | \(-0.0400925\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.3494 | −1.03132 | −0.515658 | − | 0.856795i | \(-0.672452\pi\) | ||||
−0.515658 | + | 0.856795i | \(0.672452\pi\) | |||||||
\(284\) | −1.67977 | −0.0996758 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.66372 | − | 4.61369i | 0.157509 | − | 0.272813i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.52918 | + | 2.64861i | 0.0899517 | + | 0.155801i | ||||
\(290\) | 2.06654 | + | 3.57935i | 0.121351 | + | 0.210187i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.62062 | − | 11.4673i | 0.387443 | − | 0.671070i | ||||
\(293\) | −4.93560 | − | 8.54871i | −0.288341 | − | 0.499421i | 0.685073 | − | 0.728474i | \(-0.259770\pi\) |
−0.973414 | + | 0.229054i | \(0.926437\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.96936 | + | 5.14308i | −0.172883 | + | 0.299442i | ||||
\(296\) | 4.55408 | + | 7.88791i | 0.264701 | + | 0.458475i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.58113 | − | 7.93474i | 0.265378 | − | 0.459647i | ||||
\(299\) | −1.65486 | −0.0957031 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.0519482 | − | 0.0899768i | −0.00298928 | − | 0.00517759i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.02704 | + | 3.51094i | 0.116259 | + | 0.201366i | ||||
\(305\) | −2.78220 | + | 4.81891i | −0.159308 | + | 0.275930i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.78794 | −0.444481 | −0.222240 | − | 0.974992i | \(-0.571337\pi\) | ||||
−0.222240 | + | 0.974992i | \(0.571337\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.118485 | + | 0.205223i | −0.00672952 | + | 0.0116559i | ||||
\(311\) | 15.4107 | 0.873860 | 0.436930 | − | 0.899495i | \(-0.356066\pi\) | ||||
0.436930 | + | 0.899495i | \(0.356066\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.49688 | −0.480272 | −0.240136 | − | 0.970739i | \(-0.577192\pi\) | ||||
−0.240136 | + | 0.970739i | \(0.577192\pi\) | |||||||
\(314\) | 20.9823 | 1.18410 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.00720 | −0.281677 | ||||||||
\(317\) | 14.1052 | 0.792229 | 0.396115 | − | 0.918201i | \(-0.370358\pi\) | ||||
0.396115 | + | 0.918201i | \(0.370358\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −32.7381 | −1.83298 | ||||||||
\(320\) | 0.230252 | − | 0.398809i | 0.0128715 | − | 0.0222941i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.1373 | −0.842264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.49640 | − | 6.05594i | 0.193945 | − | 0.335923i | ||||
\(326\) | 11.5182 | + | 19.9501i | 0.637933 | + | 1.10493i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.472958 | + | 0.819187i | 0.0261147 | + | 0.0452320i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.5438 | 1.51394 | 0.756971 | − | 0.653448i | \(-0.226678\pi\) | ||||
0.756971 | + | 0.653448i | \(0.226678\pi\) | |||||||
\(332\) | 3.32383 | − | 5.75705i | 0.182419 | − | 0.315959i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.31498 | + | 9.20581i | 0.290823 | + | 0.503720i | ||||
\(335\) | −0.534239 | + | 0.925330i | −0.0291886 | + | 0.0505562i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.748440 | + | 1.29634i | 0.0407701 | + | 0.0706159i | 0.885690 | − | 0.464276i | \(-0.153686\pi\) |
−0.844920 | + | 0.534892i | \(0.820352\pi\) | |||||||
\(338\) | −5.43346 | + | 9.41103i | −0.295541 | + | 0.511893i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.859728 | + | 1.48909i | 0.0466253 | + | 0.0807574i | ||||
\(341\) | −0.938524 | − | 1.62557i | −0.0508239 | − | 0.0880296i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.66372 | + | 8.07779i | −0.251451 | + | 0.435525i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.93872 | −0.157986 | ||||||||
\(347\) | 18.2881 | 0.981758 | 0.490879 | − | 0.871228i | \(-0.336676\pi\) | ||||
0.490879 | + | 0.871228i | \(0.336676\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.90136 | − | 6.75735i | 0.208835 | − | 0.361713i | −0.742513 | − | 0.669832i | \(-0.766366\pi\) |
0.951348 | + | 0.308119i | \(0.0996995\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.82383 | + | 3.15897i | 0.0972106 | + | 0.168374i | ||||
\(353\) | −13.4626 | − | 23.3180i | −0.716544 | − | 1.24109i | −0.962361 | − | 0.271774i | \(-0.912390\pi\) |
0.245817 | − | 0.969316i | \(-0.420944\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.386770 | + | 0.669906i | −0.0205276 | + | 0.0355549i | ||||
\(356\) | −1.36333 | − | 2.36135i | −0.0722562 | − | 0.125151i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.58113 | + | 7.93474i | −0.242120 | + | 0.419364i | ||||
\(359\) | 3.13161 | + | 5.42411i | 0.165280 | + | 0.286274i | 0.936755 | − | 0.349987i | \(-0.113814\pi\) |
−0.771475 | + | 0.636260i | \(0.780481\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.28220 | − | 2.22084i | 0.0674842 | − | 0.116886i | ||||
\(362\) | 22.4284 | 1.17881 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.04883 | − | 5.28073i | −0.159583 | − | 0.276406i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.6367 | + | 25.3515i | 0.764028 | + | 1.32334i | 0.940759 | + | 0.339076i | \(0.110114\pi\) |
−0.176731 | + | 0.984259i | \(0.556552\pi\) | |||||||
\(368\) | 0.566537 | − | 0.981271i | 0.0295328 | − | 0.0511523i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.19436 | 0.218054 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.92986 | + | 15.4670i | −0.462371 | + | 0.800850i | −0.999079 | − | 0.0429184i | \(-0.986334\pi\) |
0.536708 | + | 0.843768i | \(0.319668\pi\) | |||||||
\(374\) | −13.6198 | −0.704265 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.32743 | −0.120028 | ||||||||
\(377\) | −13.1082 | −0.675105 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.4255 | −1.15192 | −0.575960 | − | 0.817478i | \(-0.695371\pi\) | ||||
−0.575960 | + | 0.817478i | \(0.695371\pi\) | |||||||
\(380\) | 1.86693 | 0.0957713 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.48968 | 0.127383 | ||||||||
\(383\) | 7.07014 | − | 12.2458i | 0.361267 | − | 0.625733i | −0.626903 | − | 0.779098i | \(-0.715678\pi\) |
0.988170 | + | 0.153365i | \(0.0490109\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.48968 | −0.228519 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.59358 | − | 9.68836i | 0.283971 | − | 0.491852i | ||||
\(389\) | −11.5651 | − | 20.0313i | −0.586373 | − | 1.01563i | −0.994703 | − | 0.102793i | \(-0.967222\pi\) |
0.408330 | − | 0.912834i | \(-0.366111\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.11537 | + | 3.66392i | 0.106979 | + | 0.185292i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.7339 | 0.641522 | ||||||||
\(395\) | −1.15292 | + | 1.99691i | −0.0580097 | + | 0.100476i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.13307 | + | 8.89075i | 0.257622 | + | 0.446214i | 0.965604 | − | 0.260016i | \(-0.0837279\pi\) |
−0.707983 | + | 0.706230i | \(0.750395\pi\) | |||||||
\(398\) | −1.47296 | + | 2.55124i | −0.0738327 | + | 0.127882i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.39397 | + | 4.14647i | 0.119698 | + | 0.207324i | ||||
\(401\) | 17.0167 | − | 29.4738i | 0.849775 | − | 1.47185i | −0.0316345 | − | 0.999500i | \(-0.510071\pi\) |
0.881409 | − | 0.472353i | \(-0.156595\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.375780 | − | 0.650870i | −0.0187189 | − | 0.0324221i | ||||
\(404\) | −6.87792 | − | 11.9129i | −0.342189 | − | 0.592689i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.6118 | + | 28.7724i | −0.823415 | + | 1.42620i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.48968 | 0.172554 | 0.0862769 | − | 0.996271i | \(-0.472503\pi\) | ||||
0.0862769 | + | 0.996271i | \(0.472503\pi\) | |||||||
\(410\) | 0.435599 | 0.0215127 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.58113 | − | 9.66679i | 0.274962 | − | 0.476249i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.53064 | − | 2.65115i | −0.0751362 | − | 0.130140i | ||||
\(416\) | 0.730252 | + | 1.26483i | 0.0358036 | + | 0.0620136i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.39397 | + | 12.8067i | −0.361651 | + | 0.626398i | ||||
\(419\) | 14.4897 | + | 25.0969i | 0.707867 | + | 1.22606i | 0.965647 | + | 0.259858i | \(0.0836759\pi\) |
−0.257779 | + | 0.966204i | \(0.582991\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.06128 | + | 1.83819i | −0.0517237 | + | 0.0895881i | −0.890728 | − | 0.454537i | \(-0.849805\pi\) |
0.839004 | + | 0.544125i | \(0.183138\pi\) | |||||||
\(422\) | 0.608168 | + | 1.05338i | 0.0296052 | + | 0.0512777i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.21780 | − | 10.7695i | 0.301963 | − | 0.523015i | ||||
\(425\) | −17.8774 | −0.867183 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.89037 | + | 6.73832i | 0.188048 | + | 0.325709i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.14766 | + | 3.71986i | 0.103570 | + | 0.179388i | ||||
\(431\) | −10.9356 | + | 18.9410i | −0.526749 | + | 0.912356i | 0.472765 | + | 0.881189i | \(0.343256\pi\) |
−0.999514 | + | 0.0311679i | \(0.990077\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.0512 | 0.627199 | 0.313599 | − | 0.949555i | \(-0.398465\pi\) | ||||
0.313599 | + | 0.949555i | \(0.398465\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.75729 | + | 6.50783i | −0.179942 | + | 0.311668i | ||||
\(437\) | 4.59358 | 0.219741 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.86400 | −0.232146 | −0.116073 | − | 0.993241i | \(-0.537031\pi\) | ||||
−0.116073 | + | 0.993241i | \(0.537031\pi\) | |||||||
\(440\) | 1.67977 | 0.0800797 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.45331 | −0.259387 | ||||||||
\(443\) | 11.5395 | 0.548258 | 0.274129 | − | 0.961693i | \(-0.411610\pi\) | ||||
0.274129 | + | 0.961693i | \(0.411610\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.25564 | −0.0595229 | ||||||||
\(446\) | −0.445916 | + | 0.772349i | −0.0211147 | + | 0.0365718i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.4251 | 1.24708 | 0.623538 | − | 0.781793i | \(-0.285694\pi\) | ||||
0.623538 | + | 0.781793i | \(0.285694\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.72519 | + | 2.98812i | −0.0812361 | + | 0.140705i | ||||
\(452\) | −3.03064 | − | 5.24922i | −0.142549 | − | 0.246903i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.32597 | − | 12.6889i | −0.343825 | − | 0.595522i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.73812 | −0.174862 | −0.0874310 | − | 0.996171i | \(-0.527866\pi\) | ||||
−0.0874310 | + | 0.996171i | \(0.527866\pi\) | |||||||
\(458\) | 4.78794 | − | 8.29295i | 0.223726 | − | 0.387504i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.260893 | − | 0.451880i | −0.0121642 | − | 0.0210690i | ||||
\(461\) | −7.90496 | + | 13.6918i | −0.368171 | + | 0.637690i | −0.989280 | − | 0.146034i | \(-0.953349\pi\) |
0.621109 | + | 0.783724i | \(0.286682\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.1965 | + | 33.2493i | 0.892137 | + | 1.54523i | 0.837309 | + | 0.546730i | \(0.184128\pi\) |
0.0548278 | + | 0.998496i | \(0.482539\pi\) | |||||||
\(464\) | 4.48755 | − | 7.77266i | 0.208329 | − | 0.360837i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.21420 | + | 12.4954i | 0.334191 | + | 0.578836i | ||||
\(467\) | 3.15652 | + | 5.46725i | 0.146066 | + | 0.252994i | 0.929770 | − | 0.368140i | \(-0.120005\pi\) |
−0.783704 | + | 0.621134i | \(0.786672\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.535897 | + | 0.928200i | −0.0247191 | + | 0.0428147i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.8961 | 0.593591 | ||||||||
\(473\) | −34.0233 | −1.56439 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.70535 | + | 16.8102i | −0.445312 | + | 0.771303i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.15486 | − | 15.8567i | −0.418734 | − | 0.725268i | ||||
\(479\) | 10.2068 | + | 17.6787i | 0.466361 | + | 0.807761i | 0.999262 | − | 0.0384168i | \(-0.0122314\pi\) |
−0.532901 | + | 0.846178i | \(0.678898\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.65126 | + | 11.5203i | −0.303271 | + | 0.525282i | ||||
\(482\) | −0.0466924 | − | 0.0808735i | −0.00212678 | − | 0.00368369i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.15272 | + | 1.99658i | −0.0523966 | + | 0.0907535i | ||||
\(485\) | −2.57587 | − | 4.46154i | −0.116964 | − | 0.202588i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.18190 | − | 10.7074i | 0.280129 | − | 0.485197i | −0.691287 | − | 0.722580i | \(-0.742956\pi\) |
0.971416 | + | 0.237383i | \(0.0762895\pi\) | |||||||
\(488\) | 12.0833 | 0.546984 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.207004 | − | 0.358541i | −0.00934194 | − | 0.0161807i | 0.861317 | − | 0.508069i | \(-0.169640\pi\) |
−0.870659 | + | 0.491888i | \(0.836307\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.7558 | + | 29.0220i | 0.754645 | + | 1.30708i | ||||
\(494\) | −2.96050 | + | 5.12774i | −0.133199 | + | 0.230708i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.514589 | 0.0231057 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.461967 | − | 0.800151i | 0.0206805 | − | 0.0358197i | −0.855500 | − | 0.517803i | \(-0.826750\pi\) |
0.876180 | + | 0.481983i | \(0.160083\pi\) | |||||||
\(500\) | 4.50739 | 0.201577 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.2733 | 0.815579 | ||||||||
\(503\) | −23.8142 | −1.06182 | −0.530911 | − | 0.847428i | \(-0.678150\pi\) | ||||
−0.530911 | + | 0.847428i | \(0.678150\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.33463 | −0.281887 | ||||||||
\(506\) | 4.13307 | 0.183738 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.80992 | 0.390877 | ||||||||
\(509\) | 15.3171 | − | 26.5300i | 0.678919 | − | 1.17592i | −0.296388 | − | 0.955068i | \(-0.595782\pi\) |
0.975307 | − | 0.220855i | \(-0.0708846\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.5256 | + | 18.2308i | −0.464263 | + | 0.804128i | ||||
\(515\) | −2.57014 | − | 4.45161i | −0.113254 | − | 0.196161i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.24484 | − | 7.35228i | −0.186688 | − | 0.323353i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.672570 | 0.0294941 | ||||||||
\(521\) | −13.4518 | + | 23.2993i | −0.589336 | + | 1.02076i | 0.404984 | + | 0.914324i | \(0.367277\pi\) |
−0.994320 | + | 0.106436i | \(0.966056\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.85301 | + | 13.6018i | 0.343388 | + | 0.594766i | 0.985060 | − | 0.172214i | \(-0.0550920\pi\) |
−0.641671 | + | 0.766980i | \(0.721759\pi\) | |||||||
\(524\) | −10.5687 | + | 18.3055i | −0.461695 | + | 0.799679i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.58259 | + | 4.47318i | 0.112606 | + | 0.195040i | ||||
\(527\) | −0.960699 | + | 1.66398i | −0.0418487 | + | 0.0724841i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.8581 | + | 18.8067i | 0.472090 | + | 0.817684i | ||||
\(530\) | −2.86333 | − | 4.95943i | −0.124375 | − | 0.215424i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.690757 | + | 1.19643i | −0.0299200 | + | 0.0518230i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.58307 | 0.154910 | ||||||||
\(536\) | 2.32023 | 0.100219 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.42840 | + | 14.5984i | −0.363374 | + | 0.629383i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.05934 | − | 3.56688i | −0.0885379 | − | 0.153352i | 0.818355 | − | 0.574713i | \(-0.194886\pi\) |
−0.906893 | + | 0.421360i | \(0.861553\pi\) | |||||||
\(542\) | 12.5562 | + | 21.7480i | 0.539336 | + | 0.934157i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.86693 | − | 3.23361i | 0.0800438 | − | 0.138640i | ||||
\(545\) | 1.73025 | + | 2.99689i | 0.0741159 | + | 0.128372i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.8602 | + | 20.5425i | −0.507106 | + | 0.878333i | 0.492860 | + | 0.870108i | \(0.335951\pi\) |
−0.999966 | + | 0.00822465i | \(0.997382\pi\) | |||||||
\(548\) | −2.20321 | − | 3.81607i | −0.0941165 | − | 0.163015i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.73239 | + | 15.1249i | −0.372350 | + | 0.644930i | ||||
\(551\) | 36.3858 | 1.55009 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.69076 | + | 2.92848i | 0.0718334 | + | 0.124419i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.01245 | + | 1.75362i | 0.0429376 | + | 0.0743701i | ||||
\(557\) | 21.0313 | − | 36.4273i | 0.891125 | − | 1.54347i | 0.0525975 | − | 0.998616i | \(-0.483250\pi\) |
0.838528 | − | 0.544859i | \(-0.183417\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.6228 | −0.576181 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.1388 | + | 17.5609i | −0.427680 | + | 0.740763i | ||||
\(563\) | 11.8243 | 0.498335 | 0.249168 | − | 0.968460i | \(-0.419843\pi\) | ||||
0.249168 | + | 0.968460i | \(0.419843\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.79125 | −0.117429 | ||||||||
\(566\) | 17.3494 | 0.729250 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.67977 | 0.0704815 | ||||||||
\(569\) | −14.2016 | −0.595360 | −0.297680 | − | 0.954666i | \(-0.596213\pi\) | ||||
−0.297680 | + | 0.954666i | \(0.596213\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.9574 | 0.500401 | 0.250200 | − | 0.968194i | \(-0.419503\pi\) | ||||
0.250200 | + | 0.968194i | \(0.419503\pi\) | |||||||
\(572\) | −2.66372 | + | 4.61369i | −0.111376 | + | 0.192908i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.42509 | 0.226242 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.3135 | + | 36.9161i | −0.887293 | + | 1.53684i | −0.0442307 | + | 0.999021i | \(0.514084\pi\) |
−0.843062 | + | 0.537816i | \(0.819250\pi\) | |||||||
\(578\) | −1.52918 | − | 2.64861i | −0.0636054 | − | 0.110168i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.06654 | − | 3.57935i | −0.0858083 | − | 0.148624i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 45.3609 | 1.87866 | ||||||||
\(584\) | −6.62062 | + | 11.4673i | −0.273963 | + | 0.474518i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.93560 | + | 8.54871i | 0.203888 | + | 0.353144i | ||||
\(587\) | 20.5328 | − | 35.5638i | 0.847478 | − | 1.46788i | −0.0359730 | − | 0.999353i | \(-0.511453\pi\) |
0.883451 | − | 0.468523i | \(-0.155214\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.04309 | + | 1.80669i | 0.0429799 | + | 0.0744434i | ||||
\(590\) | 2.96936 | − | 5.14308i | 0.122247 | − | 0.211737i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.55408 | − | 7.88791i | −0.187172 | − | 0.324191i | ||||
\(593\) | 16.1008 | + | 27.8874i | 0.661180 | + | 1.14520i | 0.980306 | + | 0.197485i | \(0.0632772\pi\) |
−0.319126 | + | 0.947712i | \(0.603389\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.58113 | + | 7.93474i | −0.187650 | + | 0.325020i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.65486 | 0.0676723 | ||||||||
\(599\) | −19.0718 | −0.779252 | −0.389626 | − | 0.920973i | \(-0.627396\pi\) | ||||
−0.389626 | + | 0.920973i | \(0.627396\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.27188 | + | 7.39912i | −0.174254 | + | 0.301816i | −0.939903 | − | 0.341442i | \(-0.889085\pi\) |
0.765649 | + | 0.643259i | \(0.222418\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.0519482 | + | 0.0899768i | 0.00211374 | + | 0.00366111i | ||||
\(605\) | 0.530835 | + | 0.919434i | 0.0215815 | + | 0.0373803i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.0057 | − | 32.9189i | 0.771419 | − | 1.33614i | −0.165366 | − | 0.986232i | \(-0.552881\pi\) |
0.936785 | − | 0.349905i | \(-0.113786\pi\) | |||||||
\(608\) | −2.02704 | − | 3.51094i | −0.0822074 | − | 0.142387i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.78220 | − | 4.81891i | 0.112648 | − | 0.195112i | ||||
\(611\) | −1.69961 | − | 2.94381i | −0.0687589 | − | 0.119094i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.3296 | − | 19.6234i | 0.457597 | − | 0.792581i | −0.541237 | − | 0.840870i | \(-0.682044\pi\) |
0.998833 | + | 0.0482894i | \(0.0153770\pi\) | |||||||
\(614\) | 7.78794 | 0.314295 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.1388 | + | 17.5609i | 0.408173 | + | 0.706977i | 0.994685 | − | 0.102964i | \(-0.0328327\pi\) |
−0.586512 | + | 0.809941i | \(0.699499\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.03064 | + | 1.78512i | 0.0414249 | + | 0.0717501i | 0.885994 | − | 0.463696i | \(-0.153477\pi\) |
−0.844570 | + | 0.535446i | \(0.820144\pi\) | |||||||
\(620\) | 0.118485 | − | 0.205223i | 0.00475849 | − | 0.00824194i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.4107 | −0.617912 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.9320 | + | 18.9348i | −0.437280 | + | 0.757391i | ||||
\(626\) | 8.49688 | 0.339604 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −20.9823 | −0.837285 | ||||||||
\(629\) | 34.0085 | 1.35601 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.63715 | 0.0651740 | 0.0325870 | − | 0.999469i | \(-0.489625\pi\) | ||||
0.0325870 | + | 0.999469i | \(0.489625\pi\) | |||||||
\(632\) | 5.00720 | 0.199176 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.1052 | −0.560191 | ||||||||
\(635\) | 2.02850 | − | 3.51347i | 0.0804988 | − | 0.139428i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 32.7381 | 1.29611 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.230252 | + | 0.398809i | −0.00910153 | + | 0.0157643i | ||||
\(641\) | 10.9662 | + | 18.9941i | 0.433140 | + | 0.750221i | 0.997142 | − | 0.0755526i | \(-0.0240721\pi\) |
−0.564001 | + | 0.825774i | \(0.690739\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.1819 | + | 24.5638i | 0.559280 | + | 0.968701i | 0.997557 | + | 0.0698609i | \(0.0222555\pi\) |
−0.438277 | + | 0.898840i | \(0.644411\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.1373 | 0.595571 | ||||||||
\(647\) | 17.3904 | − | 30.1210i | 0.683686 | − | 1.18418i | −0.290162 | − | 0.956978i | \(-0.593709\pi\) |
0.973848 | − | 0.227201i | \(-0.0729575\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23.5203 | + | 40.7384i | 0.923253 | + | 1.59912i | ||||
\(650\) | −3.49640 | + | 6.05594i | −0.137140 | + | 0.237534i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.5182 | − | 19.9501i | −0.451087 | − | 0.781306i | ||||
\(653\) | −1.59931 | + | 2.77009i | −0.0625860 | + | 0.108402i | −0.895621 | − | 0.444819i | \(-0.853268\pi\) |
0.833035 | + | 0.553221i | \(0.186601\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.86693 | + | 8.42976i | 0.190167 | + | 0.329378i | ||||
\(656\) | −0.472958 | − | 0.819187i | −0.0184659 | − | 0.0319839i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.30418 | + | 9.18711i | −0.206622 | + | 0.357879i | −0.950648 | − | 0.310271i | \(-0.899580\pi\) |
0.744027 | + | 0.668150i | \(0.232914\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.1301 | −0.394017 | −0.197009 | − | 0.980402i | \(-0.563123\pi\) | ||||
−0.197009 | + | 0.980402i | \(0.563123\pi\) | |||||||
\(662\) | −27.5438 | −1.07052 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.32383 | + | 5.75705i | −0.128990 | + | 0.223417i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.08472 | − | 8.80700i | −0.196881 | − | 0.341008i | ||||
\(668\) | −5.31498 | − | 9.20581i | −0.205643 | − | 0.356184i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.534239 | − | 0.925330i | 0.0206395 | − | 0.0357486i | ||||
\(671\) | 22.0378 | + | 38.1707i | 0.850761 | + | 1.47356i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.60817 | − | 2.78543i | 0.0619903 | − | 0.107370i | −0.833365 | − | 0.552724i | \(-0.813589\pi\) |
0.895355 | + | 0.445353i | \(0.146922\pi\) | |||||||
\(674\) | −0.748440 | − | 1.29634i | −0.0288288 | − | 0.0499330i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.43346 | − | 9.41103i | 0.208979 | − | 0.361963i | ||||
\(677\) | −29.3638 | −1.12854 | −0.564271 | − | 0.825589i | \(-0.690843\pi\) | ||||
−0.564271 | + | 0.825589i | \(0.690843\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.859728 | − | 1.48909i | −0.0329691 | − | 0.0571041i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.938524 | + | 1.62557i | 0.0359379 | + | 0.0622463i | ||||
\(683\) | −12.6278 | + | 21.8720i | −0.483190 | + | 0.836910i | −0.999814 | − | 0.0193029i | \(-0.993855\pi\) |
0.516624 | + | 0.856213i | \(0.327189\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.02918 | −0.0775309 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.66372 | − | 8.07779i | 0.177802 | − | 0.307963i | ||||
\(689\) | 18.1623 | 0.691927 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.3638 | 0.584467 | 0.292233 | − | 0.956347i | \(-0.405602\pi\) | ||||
0.292233 | + | 0.956347i | \(0.405602\pi\) | |||||||
\(692\) | 2.93872 | 0.111713 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.2881 | −0.694208 | ||||||||
\(695\) | 0.932479 | 0.0353709 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.53191 | 0.133781 | ||||||||
\(698\) | −3.90136 | + | 6.75735i | −0.147669 | + | 0.255770i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.3700 | 0.504980 | 0.252490 | − | 0.967600i | \(-0.418751\pi\) | ||||
0.252490 | + | 0.967600i | \(0.418751\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.4626 | − | 31.9782i | 0.696332 | − | 1.20608i | ||||
\(704\) | −1.82383 | − | 3.15897i | −0.0687382 | − | 0.119058i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.4626 | + | 23.3180i | 0.506673 | + | 0.877584i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.12588 | −0.0422832 | −0.0211416 | − | 0.999776i | \(-0.506730\pi\) | ||||
−0.0211416 | + | 0.999776i | \(0.506730\pi\) | |||||||
\(710\) | 0.386770 | − | 0.669906i | 0.0145152 | − | 0.0251411i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.36333 | + | 2.36135i | 0.0510928 | + | 0.0884954i | ||||
\(713\) | 0.291534 | − | 0.504951i | 0.0109180 | − | 0.0189106i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.22665 | + | 2.12463i | 0.0458743 | + | 0.0794565i | ||||
\(716\) | 4.58113 | − | 7.93474i | 0.171205 | − | 0.296535i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.13161 | − | 5.42411i | −0.116871 | − | 0.202426i | ||||
\(719\) | 9.13667 | + | 15.8252i | 0.340740 | + | 0.590180i | 0.984570 | − | 0.174989i | \(-0.0559889\pi\) |
−0.643830 | + | 0.765169i | \(0.722656\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.28220 | + | 2.22084i | −0.0477186 | + | 0.0826510i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −22.4284 | −0.833545 | ||||||||
\(725\) | 42.9722 | 1.59595 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.8478 | − | 25.7171i | 0.550673 | − | 0.953793i | −0.447553 | − | 0.894257i | \(-0.647705\pi\) |
0.998226 | − | 0.0595359i | \(-0.0189621\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.04883 | + | 5.28073i | 0.112842 | + | 0.195448i | ||||
\(731\) | 17.4136 | + | 30.1613i | 0.644066 | + | 1.11555i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.61390 | − | 16.6518i | 0.355098 | − | 0.615047i | −0.632037 | − | 0.774938i | \(-0.717781\pi\) |
0.987135 | + | 0.159891i | \(0.0511143\pi\) | |||||||
\(734\) | −14.6367 | − | 25.3515i | −0.540249 | − | 0.935740i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.566537 | + | 0.981271i | −0.0208828 | + | 0.0361701i | ||||
\(737\) | 4.23171 | + | 7.32955i | 0.155877 | + | 0.269987i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.1336 | + | 26.2121i | −0.556697 | + | 0.964227i | 0.441073 | + | 0.897471i | \(0.354598\pi\) |
−0.997769 | + | 0.0667556i | \(0.978735\pi\) | |||||||
\(740\) | −4.19436 | −0.154188 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.8815 | + | 20.5794i | 0.435890 | + | 0.754984i | 0.997368 | − | 0.0725076i | \(-0.0231002\pi\) |
−0.561477 | + | 0.827492i | \(0.689767\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.10963 | + | 3.65399i | 0.0772909 | + | 0.133872i | ||||
\(746\) | 8.92986 | − | 15.4670i | 0.326946 | − | 0.566286i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 13.6198 | 0.497990 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.33415 | + | 10.9711i | −0.231136 | + | 0.400340i | −0.958143 | − | 0.286291i | \(-0.907578\pi\) |
0.727006 | + | 0.686631i | \(0.240911\pi\) | |||||||
\(752\) | 2.32743 | 0.0848727 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13.1082 | 0.477371 | ||||||||
\(755\) | 0.0478448 | 0.00174125 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.0799 | −1.05693 | −0.528464 | − | 0.848955i | \(-0.677232\pi\) | ||||
−0.528464 | + | 0.848955i | \(0.677232\pi\) | |||||||
\(758\) | 22.4255 | 0.814530 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.86693 | −0.0677205 | ||||||||
\(761\) | −14.6015 | + | 25.2905i | −0.529302 | + | 0.916778i | 0.470114 | + | 0.882606i | \(0.344213\pi\) |
−0.999416 | + | 0.0341724i | \(0.989120\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.48968 | −0.0900736 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.07014 | + | 12.2458i | −0.255454 | + | 0.442460i | ||||
\(767\) | 9.41741 | + | 16.3114i | 0.340043 | + | 0.588972i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.5869 | − | 21.8011i | −0.453894 | − | 0.786167i | 0.544730 | − | 0.838611i | \(-0.316632\pi\) |
−0.998624 | + | 0.0524443i | \(0.983299\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.48968 | 0.161587 | ||||||||
\(773\) | −0.752039 | + | 1.30257i | −0.0270490 | + | 0.0468502i | −0.879233 | − | 0.476392i | \(-0.841944\pi\) |
0.852184 | + | 0.523242i | \(0.175278\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.23191 | + | 2.13373i | 0.0442515 | + | 0.0766458i | ||||
\(776\) | −5.59358 | + | 9.68836i | −0.200798 | + | 0.347792i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.5651 | + | 20.0313i | 0.414628 | + | 0.718157i | ||||
\(779\) | 1.91741 | − | 3.32105i | 0.0686984 | − | 0.118989i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.06361 | + | 5.30633i | 0.109625 | + | 0.189875i | ||||
\(782\) | −2.11537 | − | 3.66392i | −0.0756453 | − | 0.131022i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.83122 | + | 8.36792i | −0.172434 | + | 0.298664i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.9531 | 0.533021 | 0.266510 | − | 0.963832i | \(-0.414129\pi\) | ||||
0.266510 | + | 0.963832i | \(0.414129\pi\) | |||||||
\(788\) | −12.7339 | −0.453625 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.15292 | − | 1.99691i | 0.0410190 | − | 0.0710470i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.82383 | + | 15.2833i | 0.313343 | + | 0.542727i | ||||
\(794\) | −5.13307 | − | 8.89075i | −0.182166 | − | 0.315521i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.47296 | − | 2.55124i | 0.0522076 | − | 0.0904262i | ||||
\(797\) | −4.56294 | − | 7.90324i | −0.161628 | − | 0.279947i | 0.773825 | − | 0.633400i | \(-0.218341\pi\) |
−0.935453 | + | 0.353452i | \(0.885008\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.34514 | + | 7.52600i | −0.153720 | + | 0.266251i | ||||
\(800\) | −2.39397 | − | 4.14647i | −0.0846395 | − | 0.146600i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17.0167 | + | 29.4738i | −0.600881 | + | 1.04076i | ||||
\(803\) | −48.2996 | −1.70446 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.375780 | + | 0.650870i | 0.0132363 | + | 0.0229259i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.87792 | + | 11.9129i | 0.241964 | + | 0.419094i | ||||
\(809\) | −17.7755 | + | 30.7880i | −0.624953 | + | 1.08245i | 0.363597 | + | 0.931556i | \(0.381548\pi\) |
−0.988550 | + | 0.150894i | \(0.951785\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.5070 | 0.474295 | 0.237148 | − | 0.971474i | \(-0.423788\pi\) | ||||
0.237148 | + | 0.971474i | \(0.423788\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 16.6118 | − | 28.7724i | 0.582242 | − | 1.00847i | ||||
\(815\) | −10.6084 | −0.371595 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 37.8142 | 1.32295 | ||||||||
\(818\) | −3.48968 | −0.122014 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.435599 | −0.0152118 | ||||||||
\(821\) | −21.6228 | −0.754639 | −0.377320 | − | 0.926083i | \(-0.623154\pi\) | ||||
−0.377320 | + | 0.926083i | \(0.623154\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.50700 | −0.0525308 | −0.0262654 | − | 0.999655i | \(-0.508361\pi\) | ||||
−0.0262654 | + | 0.999655i | \(0.508361\pi\) | |||||||
\(824\) | −5.58113 | + | 9.66679i | −0.194428 | + | 0.336759i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.3786 | −0.812953 | −0.406477 | − | 0.913661i | \(-0.633243\pi\) | ||||
−0.406477 | + | 0.913661i | \(0.633243\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.0095 | − | 19.0691i | 0.382377 | − | 0.662296i | −0.609025 | − | 0.793151i | \(-0.708439\pi\) |
0.991401 | + | 0.130855i | \(0.0417723\pi\) | |||||||
\(830\) | 1.53064 | + | 2.65115i | 0.0531293 | + | 0.0920227i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.730252 | − | 1.26483i | −0.0253169 | − | 0.0438502i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.89515 | −0.169404 | ||||||||
\(836\) | 7.39397 | − | 12.8067i | 0.255726 | − | 0.442930i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14.4897 | − | 25.0969i | −0.500538 | − | 0.866957i | ||||
\(839\) | −1.06507 | + | 1.84476i | −0.0367705 | + | 0.0636883i | −0.883825 | − | 0.467818i | \(-0.845040\pi\) |
0.847055 | + | 0.531506i | \(0.178374\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.7762 | − | 44.6456i | −0.888833 | − | 1.53950i | ||||
\(842\) | 1.06128 | − | 1.83819i | 0.0365742 | − | 0.0633483i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.608168 | − | 1.05338i | −0.0209340 | − | 0.0362588i | ||||
\(845\) | −2.50214 | − | 4.33383i | −0.0860761 | − | 0.149088i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.21780 | + | 10.7695i | −0.213520 | + | 0.369828i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 17.8774 | 0.613191 | ||||||||
\(851\) | −10.3202 | −0.353773 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.50146 | − | 6.06471i | 0.119888 | − | 0.207652i | −0.799835 | − | 0.600220i | \(-0.795080\pi\) |
0.919723 | + | 0.392568i | \(0.128413\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.89037 | − | 6.73832i | −0.132970 | − | 0.230311i | ||||
\(857\) | −5.46410 | − | 9.46410i | −0.186650 | − | 0.323288i | 0.757481 | − | 0.652857i | \(-0.226430\pi\) |
−0.944131 | + | 0.329569i | \(0.893096\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.95379 | + | 12.0443i | −0.237260 | + | 0.410947i | −0.959927 | − | 0.280250i | \(-0.909583\pi\) |
0.722667 | + | 0.691196i | \(0.242916\pi\) | |||||||
\(860\) | −2.14766 | − | 3.71986i | −0.0732347 | − | 0.126846i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.9356 | − | 18.9410i | 0.372468 | − | 0.645133i | ||||
\(863\) | 18.4231 | + | 31.9098i | 0.627131 | + | 1.08622i | 0.988125 | + | 0.153655i | \(0.0491043\pi\) |
−0.360993 | + | 0.932568i | \(0.617562\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.676647 | − | 1.17199i | 0.0230067 | − | 0.0398488i | ||||
\(866\) | −13.0512 | −0.443496 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.13229 | + | 15.8176i | 0.309792 | + | 0.536575i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.69436 | + | 2.93471i | 0.0574111 | + | 0.0994389i | ||||
\(872\) | 3.75729 | − | 6.50783i | 0.127238 | − | 0.220383i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.59358 | −0.155380 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.17977 | − | 8.97162i | 0.174908 | − | 0.302950i | −0.765221 | − | 0.643767i | \(-0.777370\pi\) |
0.940130 | + | 0.340817i | \(0.110704\pi\) | |||||||
\(878\) | 4.86400 | 0.164152 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.67977 | −0.0566249 | ||||||||
\(881\) | 9.34806 | 0.314944 | 0.157472 | − | 0.987523i | \(-0.449666\pi\) | ||||
0.157472 | + | 0.987523i | \(0.449666\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.29494 | 0.0772308 | 0.0386154 | − | 0.999254i | \(-0.487705\pi\) | ||||
0.0386154 | + | 0.999254i | \(0.487705\pi\) | |||||||
\(884\) | 5.45331 | 0.183415 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.5395 | −0.387677 | ||||||||
\(887\) | 13.8363 | − | 23.9651i | 0.464577 | − | 0.804671i | −0.534605 | − | 0.845102i | \(-0.679540\pi\) |
0.999182 | + | 0.0404309i | \(0.0128731\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.25564 | 0.0420891 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.445916 | − | 0.772349i | 0.0149304 | − | 0.0258602i | ||||
\(893\) | 4.71780 | + | 8.17147i | 0.157875 | + | 0.273448i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.10963 | − | 3.65399i | −0.0705172 | − | 0.122139i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −26.4251 | −0.881817 | ||||||||
\(899\) | 2.30924 | − | 3.99973i | 0.0770176 | − | 0.133398i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.2163 | − | 40.2119i | −0.773448 | − | 1.33965i | ||||
\(902\) | 1.72519 | − | 2.98812i | 0.0574426 | − | 0.0994935i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.03064 | + | 5.24922i | 0.100798 | + | 0.174587i | ||||
\(905\) | −5.16419 | + | 8.94465i | −0.171664 | + | 0.297330i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.46576 | + | 2.53877i | 0.0486698 | + | 0.0842985i | 0.889334 | − | 0.457258i | \(-0.151168\pi\) |
−0.840664 | + | 0.541557i | \(0.817835\pi\) | |||||||
\(908\) | 7.32597 | + | 12.6889i | 0.243121 | + | 0.421098i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.3171 | + | 26.5300i | −0.507479 | + | 0.878979i | 0.492484 | + | 0.870322i | \(0.336089\pi\) |
−0.999963 | + | 0.00865719i | \(0.997244\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.2484 | −0.802506 | ||||||||
\(914\) | 3.73812 | 0.123646 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.78794 | + | 8.29295i | −0.158198 | + | 0.274007i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.1857 | + | 22.8383i | 0.434956 | + | 0.753366i | 0.997292 | − | 0.0735429i | \(-0.0234306\pi\) |
−0.562336 | + | 0.826909i | \(0.690097\pi\) | |||||||
\(920\) | 0.260893 | + | 0.451880i | 0.00860139 | + | 0.0148980i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.90496 | − | 13.6918i | 0.260336 | − | 0.450915i | ||||
\(923\) | 1.22665 | + | 2.12463i | 0.0403758 | + | 0.0699329i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.8047 | − | 37.7668i | 0.716933 | − | 1.24176i | ||||
\(926\) | −19.1965 | − | 33.2493i | −0.630836 | − | 1.09264i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.48755 | + | 7.77266i | −0.147311 | + | 0.255150i | ||||
\(929\) | 17.8741 | 0.586431 | 0.293215 | − | 0.956046i | \(-0.405275\pi\) | ||||
0.293215 | + | 0.956046i | \(0.405275\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7.21420 | − | 12.4954i | −0.236309 | − | 0.409299i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.15652 | − | 5.46725i | −0.103284 | − | 0.178894i | ||||
\(935\) | 3.13600 | − | 5.43171i | 0.102558 | − | 0.177636i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.9134 | −0.519869 | −0.259934 | − | 0.965626i | \(-0.583701\pi\) | ||||
−0.259934 | + | 0.965626i | \(0.583701\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.535897 | − | 0.928200i | 0.0174790 | − | 0.0302745i | ||||
\(941\) | −16.2805 | −0.530731 | −0.265365 | − | 0.964148i | \(-0.585493\pi\) | ||||
−0.265365 | + | 0.964148i | \(0.585493\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.07179 | −0.0349024 | ||||||||
\(944\) | −12.8961 | −0.419732 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 34.0233 | 1.10619 | ||||||||
\(947\) | 28.5903 | 0.929059 | 0.464529 | − | 0.885558i | \(-0.346224\pi\) | ||||
0.464529 | + | 0.885558i | \(0.346224\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.3389 | −0.627767 | ||||||||
\(950\) | 9.70535 | − | 16.8102i | 0.314883 | − | 0.545393i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.3537 | 0.950859 | 0.475430 | − | 0.879754i | \(-0.342293\pi\) | ||||
0.475430 | + | 0.879754i | \(0.342293\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.573256 | + | 0.992908i | −0.0185501 | + | 0.0321297i | ||||
\(956\) | 9.15486 | + | 15.8567i | 0.296089 | + | 0.512842i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10.2068 | − | 17.6787i | −0.329767 | − | 0.571173i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7352 | −0.991458 | ||||||||
\(962\) | 6.65126 | − | 11.5203i | 0.214445 | − | 0.371430i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.0466924 | + | 0.0808735i | 0.00150386 | + | 0.00260476i | ||||
\(965\) | 1.03376 | − | 1.79053i | 0.0332779 | − | 0.0576391i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.69815 | − | 8.13743i | −0.151082 | − | 0.261682i | 0.780543 | − | 0.625102i | \(-0.214943\pi\) |
−0.931626 | + | 0.363419i | \(0.881609\pi\) | |||||||
\(968\) | 1.15272 | − | 1.99658i | 0.0370500 | − | 0.0641724i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.57587 | + | 4.46154i | 0.0827062 | + | 0.143251i | ||||
\(971\) | 7.77335 | + | 13.4638i | 0.249459 | + | 0.432075i | 0.963376 | − | 0.268155i | \(-0.0864140\pi\) |
−0.713917 | + | 0.700230i | \(0.753081\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6.18190 | + | 10.7074i | −0.198081 | + | 0.343086i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.0833 | −0.386776 | ||||||||
\(977\) | 9.59785 | 0.307062 | 0.153531 | − | 0.988144i | \(-0.450935\pi\) | ||||
0.153531 | + | 0.988144i | \(0.450935\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.97296 | + | 8.61342i | −0.158936 | + | 0.275286i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.207004 | + | 0.358541i | 0.00660575 | + | 0.0114415i | ||||
\(983\) | 23.4267 | + | 40.5763i | 0.747197 | + | 1.29418i | 0.949161 | + | 0.314790i | \(0.101934\pi\) |
−0.201964 | + | 0.979393i | \(0.564732\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.93200 | + | 5.07837i | −0.0934213 | + | 0.161810i | ||||
\(986\) | −16.7558 | − | 29.0220i | −0.533614 | − | 0.924247i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.96050 | − | 5.12774i | 0.0941862 | − | 0.163135i | ||||
\(989\) | −5.28434 | − | 9.15274i | −0.168032 | − | 0.291040i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.8260 | − | 18.7511i | 0.343898 | − | 0.595649i | −0.641255 | − | 0.767328i | \(-0.721586\pi\) |
0.985153 | + | 0.171679i | \(0.0549192\pi\) | |||||||
\(992\) | −0.514589 | −0.0163382 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.678304 | − | 1.17486i | −0.0215037 | − | 0.0372455i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.6190 | − | 49.5695i | −0.906372 | − | 1.56988i | −0.819065 | − | 0.573700i | \(-0.805507\pi\) |
−0.0873064 | − | 0.996182i | \(-0.527826\pi\) | |||||||
\(998\) | −0.461967 | + | 0.800151i | −0.0146233 | + | 0.0253283i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))